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This is PART 25: Centers X(48001) - X(50000)

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)


X(48001) = X(513)X(4507)∩X(514)X(3716)

Barycentrics    (b - c)*(-a^3 + 3*a^2*b + 2*a*b^2 + 3*a^2*c + 7*a*b*c + b^2*c + 2*a*c^2 + b*c^2) : :
X(48001) = 3 X[3716] - 2 X[7662], 3 X[661] - X[46403], X[693] - 3 X[47826], X[2254] - 3 X[47775], 2 X[3837] - 3 X[45315], 3 X[4724] - X[47697], 3 X[47666] + X[47697], 3 X[4893] - 2 X[25380], X[4960] - 3 X[47817], X[7192] - 3 X[47811], 3 X[21146] - 5 X[30795], 6 X[25666] - 5 X[30795], 3 X[30565] - X[47703], X[47672] - 3 X[47821], X[47675] - 3 X[47832]

X(48001) lies on these lines: {513, 4507}, {514, 3716}, {650, 4778}, {659, 28840}, {661, 46403}, {693, 47826}, {2254, 47775}, {3837, 45315}, {4369, 4977}, {4724, 23655}, {4763, 28220}, {4874, 28195}, {4893, 25380}, {4960, 47817}, {4985, 29771}, {7192, 47811}, {9508, 28209}, {21146, 25666}, {24720, 25143}, {28229, 43067}, {30565, 47703}, {47672, 47821}, {47675, 47832}

X(48001) = midpoint of X(4724) and X(47666)
X(48001) = reflection of X(21146) in X(25666)


X(48002) = X(513)X(4507)∩X(514)X(3837)

Barycentrics    (b - c)*(b + c)*(2*a^2 + 3*a*b + 3*a*c + b*c) : :
X(48002) = 3 X[661] - X[4010], 5 X[661] - X[4804], 5 X[4010] - 3 X[4804], 2 X[4010] - 3 X[4806], X[4010] + 3 X[4824], 2 X[4804] - 5 X[4806], X[4804] + 5 X[4824], X[4806] + 2 X[4824], X[659] - 3 X[47775], 2 X[4369] - 3 X[47829], 3 X[4705] - X[4761], X[4784] - 3 X[47825], X[31290] + 3 X[47825], X[4810] - 3 X[47759], X[4960] - 3 X[47837], X[4963] + 3 X[47827], X[7192] - 3 X[47827], X[7662] - 3 X[47777], X[9508] - 3 X[45676], X[21146] - 3 X[47810], 5 X[30795] - 3 X[47780], X[47676] - 3 X[47877], X[47698] + 3 X[47781]

X(48002) lies on these lines: {513, 4507}, {514, 3837}, {523, 661}, {659, 47775}, {693, 28175}, {1491, 2977}, {2254, 28209}, {3835, 4802}, {4369, 47829}, {4444, 28602}, {4705, 4761}, {4776, 28179}, {4784, 31290}, {4810, 47759}, {4948, 47774}, {4960, 47837}, {4963, 7192}, {7662, 47777}, {9508, 28840}, {21146, 28213}, {24720, 28195}, {29078, 45745}, {30795, 47780}, {47676, 47877}, {47698, 47781}

X(48002) = midpoint of X(i) and X(j) for these {i,j}: {661, 4824}, {1491, 47666}, {4122, 4988}, {4784, 31290}, {4948, 47774}, {4963, 7192}
X(48002) = reflection of X(4806) in X(661)
X(48002) = crossdifference of every pair of points on line {58, 2241}
X(48002) = barycentric product X(i)*X(j) for these {i,j}: {523, 29570}, {4064, 31911}
X(48002) = barycentric quotient X(29570)/X(99)
X(48002) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4963, 47827, 7192}, {31290, 47825, 4784}


X(48003) = X(2)X(4978)∩X(241)X(514)

Barycentrics    a*(b - c)*(a^2 - b^2 - 3*b*c - c^2) : :
X(48003) = 3 X[650] - X[905], 5 X[650] - X[3669], 4 X[650] - X[3960], 5 X[905] - 3 X[3669], 4 X[905] - 3 X[3960], 2 X[905] - 3 X[14838], 4 X[3669] - 5 X[3960], 2 X[3669] - 5 X[14838], X[21104] - 3 X[41800], X[693] - 3 X[47794], X[764] - 3 X[47893], X[1019] - 3 X[1635], X[1577] - 3 X[47793], X[17494] + 3 X[47793], X[2530] - 3 X[47827], X[3762] + 5 X[26777], X[4560] - 5 X[26777], X[3777] - 3 X[47888], X[4040] - 3 X[47811], X[4041] + 3 X[47811], X[4170] - 3 X[47821], X[4391] + 3 X[31150], X[4498] + 3 X[4893], 3 X[4893] - X[14349], 2 X[4823] - 3 X[45324], X[4801] - 5 X[31209], X[4801] - 3 X[47795], 5 X[31209] - 3 X[47795], X[4905] - 3 X[47828], 3 X[6546] + X[21124], X[7265] - 3 X[30565], X[8045] - 3 X[10196], X[17166] - 3 X[47818], X[17496] - 3 X[45671], 3 X[21052] - X[47724], X[21146] - 3 X[47837], 7 X[27115] - 3 X[47796], X[46403] - 3 X[47816], X[47694] - 3 X[47817], X[47715] - 3 X[47809], X[47716] - 3 X[47797]

X(48003) lies on these lines: {2, 4978}, {10, 29051}, {37, 31010}, {241, 514}, {523, 21179}, {649, 15309}, {659, 830}, {661, 4063}, {667, 4160}, {693, 47794}, {764, 47893}, {812, 4129}, {918, 21192}, {1019, 1635}, {1577, 17494}, {1734, 4724}, {2530, 2832}, {2814, 39212}, {2826, 44824}, {2977, 29142}, {3716, 4151}, {3743, 6367}, {3762, 4560}, {3777, 47888}, {3835, 29302}, {3887, 4040}, {3900, 4794}, {4147, 29066}, {4170, 47821}, {4391, 31150}, {4401, 8678}, {4468, 23875}, {4498, 4893}, {4522, 29190}, {4762, 4823}, {4791, 20317}, {4801, 31209}, {4905, 47828}, {4913, 8714}, {4960, 16751}, {4977, 8043}, {6003, 46385}, {6129, 28155}, {6372, 9508}, {6546, 21124}, {7265, 30565}, {8045, 10196}, {17072, 29186}, {17166, 47818}, {17496, 45671}, {18004, 29106}, {21051, 29070}, {21052, 47724}, {21146, 47837}, {21201, 35100}, {21260, 29362}, {21385, 24900}, {23789, 25380}, {23883, 25259}, {24948, 47672}, {27115, 47796}, {28175, 31947}, {28473, 38324}, {46403, 47816}, {47660, 47679}, {47661, 47678}, {47694, 47817}, {47715, 47809}, {47716, 47797}

X(48003) = midpoint of X(i) and X(j) for these {i,j}: {659, 4705}, {661, 4063}, {667, 4490}, {1577, 17494}, {1734, 4724}, {3762, 4560}, {4040, 4041}, {4498, 14349}, {47660, 47679}, {47661, 47678}
X(48003) = reflection of X(i) in X(j) for these {i,j}: {3960, 14838}, {4791, 20317}, {14838, 650}, {23789, 25380}
X(48003) = complement of X(4978)
X(48003) = complement of the isotomic conjugate of X(37212)
X(48003) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 46660}, {32, 35076}, {1126, 116}, {1255, 21252}, {1576, 41820}, {4596, 21240}, {4629, 3741}, {6540, 626}, {8701, 141}, {23990, 4988}, {28615, 11}, {33635, 124}, {37212, 2887}
X(48003) = X(101)-isoconjugate of X(5557)
X(48003) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 5557), (4976, 4985)
X(48003) = crosspoint of X(2) and X(37212)
X(48003) = crosssum of X(i) and X(j) for these (i,j): {6, 4979}, {650, 3723}
X(48003) = crossdifference of every pair of points on line {55, 4497}
X(48003) = barycentric product X(i)*X(j) for these {i,j}: {513, 5564}, {514, 27065}, {522, 7269}, {693, 3746}, {4015, 7192}
X(48003) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 5557}, {3746, 100}, {4015, 3952}, {5564, 668}, {7269, 664}, {27065, 190}
X(48003) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4041, 47811, 4040}, {4498, 4893, 14349}, {4801, 31209, 47795}, {17494, 47793, 1577}


X(48004) = X(514)X(3716)∩X(659)X(15309)

Barycentrics    a*(b - c)*(a^2 - 2*a*b - b^2 - 2*a*c - 5*b*c - c^2) : :
X(48004) = X[1019] - 3 X[47811], X[14349] - 3 X[47826], X[4801] - 3 X[47838], 3 X[4893] - X[4905], X[4978] - 3 X[47821], X[7192] - 3 X[47817], 3 X[30565] - X[47715]

X(48004) lies on these lines: {514, 3716}, {659, 15309}, {661, 16546}, {830, 4724}, {1019, 47811}, {2832, 14349}, {3887, 4490}, {3960, 29198}, {4040, 4160}, {4468, 29021}, {4705, 42325}, {4801, 47838}, {4822, 21385}, {4893, 4905}, {4978, 47821}, {6372, 14838}, {7192, 47817}, {20517, 28851}, {23789, 25666}, {30565, 47715}

X(48004) = midpoint of X(4822) and X(21385)
X(48004) = reflection of X(23789) in X(25666)
X(48004) = crossdifference of every pair of points on line {16884, 17469}


X(48005) = X(512)X(661)∩X(514)X(3837)

Barycentrics    a*(b - c)*(b + c)*(a + 2*b + 2*c) : :
X(48005) = 3 X[661] + X[4041], 7 X[661] + X[4729], 5 X[661] + X[4730], 2 X[661] + X[4770], 5 X[661] - X[4822], 3 X[661] - X[4983], X[4041] - 3 X[4705], 7 X[4041] - 3 X[4729], 5 X[4041] - 3 X[4730], 2 X[4041] - 3 X[4770], 5 X[4041] + 3 X[4822], 7 X[4705] - X[4729], 5 X[4705] - X[4730], 5 X[4705] + X[4822], 3 X[4705] + X[4983], 5 X[4729] - 7 X[4730], 2 X[4729] - 7 X[4770], 5 X[4729] + 7 X[4822], 3 X[4729] + 7 X[4983], 2 X[4730] - 5 X[4770], 3 X[4730] + 5 X[4983], 5 X[4770] + 2 X[4822], 3 X[4770] + 2 X[4983], 3 X[4822] - 5 X[4983], X[667] - 3 X[4893], X[1019] - 3 X[47827], 3 X[1491] - X[4905], 5 X[1698] - X[4960], 5 X[1698] + X[4963], 3 X[2530] - X[23738], X[2530] - 3 X[47810], X[23738] - 9 X[47810], X[4162] - 9 X[47777], 3 X[4379] - 5 X[31251], 3 X[4775] - X[4959], X[7192] - 3 X[47837], X[17166] - 3 X[47839], X[21146] - 3 X[47816], X[21301] + 3 X[47775], 2 X[31288] - 3 X[47778], X[31290] + 3 X[47836], X[47666] + 3 X[47814], X[47707] + 3 X[47781]

X(48005) lies on these lines: {512, 661}, {514, 3837}, {523, 4129}, {667, 4893}, {891, 4490}, {1019, 47827}, {1491, 4905}, {1577, 4824}, {1698, 4960}, {1960, 8678}, {2530, 23738}, {3004, 29354}, {3700, 6367}, {3709, 9279}, {3906, 21124}, {4088, 7950}, {4122, 47679}, {4151, 4806}, {4162, 47777}, {4379, 31251}, {4560, 29176}, {4775, 4959}, {4802, 4823}, {4808, 47701}, {4813, 4834}, {4913, 29150}, {4976, 29266}, {7192, 47837}, {8672, 17990}, {9508, 15309}, {17166, 47839}, {18004, 23879}, {21146, 47816}, {21196, 29090}, {21301, 47775}, {29058, 47876}, {31288, 47778}, {31290, 47836}, {47666, 47814}, {47707, 47781}

X(48005) = midpoint of X(i) and X(j) for these {i,j}: {661, 4705}, {1577, 4824}, {4041, 4983}, {4122, 47679}, {4490, 14349}, {4730, 4822}, {4808, 47701}, {4813, 4834}, {4960, 4963}
X(48005) = reflection of X(4770) in X(4705)
X(48005) = X(i)-Ceva conjugate of X(j) for these (i,j): {4802, 4838}, {4813, 4826}
X(48005) = X(i)-isoconjugate of X(j) for these (i,j): {58, 32042}, {81, 37211}, {86, 8652}, {110, 30598}, {662, 25417}, {799, 34819}, {4565, 42030}, {4610, 28625}
X(48005) = X(i)-Dao conjugate of X(j) for these (i, j): (10, 32042), (244, 30598), (1084, 25417), (38996, 34819), (40586, 37211), (40600, 8652)
X(48005) = crosspoint of X(4802) and X(4813)
X(48005) = crosssum of X(i) and X(j) for these (i,j): {81, 4840}, {4467, 5224}, {8652, 37211}
X(48005) = crossdifference of every pair of points on line {81, 16884}
X(48005) = barycentric product X(i)*X(j) for these {i,j}: {1, 4838}, {10, 4813}, {37, 4802}, {42, 4823}, {65, 4820}, {75, 4826}, {321, 4834}, {512, 28605}, {523, 16777}, {594, 4840}, {649, 4066}, {661, 1698}, {756, 4960}, {798, 30596}, {2501, 3927}, {3125, 4756}, {3700, 5221}, {3715, 7178}, {4007, 4017}, {4024, 4658}, {4041, 4654}, {4674, 4958}, {4705, 5333}, {4770, 30589}, {4825, 30587}, {4938, 23894}, {4983, 43260}
X(48005) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 32042}, {42, 37211}, {213, 8652}, {512, 25417}, {661, 30598}, {669, 34819}, {1698, 799}, {3715, 645}, {3927, 4563}, {4007, 7257}, {4041, 42030}, {4066, 1978}, {4654, 4625}, {4658, 4610}, {4756, 4601}, {4770, 30590}, {4802, 274}, {4810, 30940}, {4813, 86}, {4820, 314}, {4823, 310}, {4826, 1}, {4834, 81}, {4838, 75}, {4840, 1509}, {4938, 24039}, {4958, 30939}, {4960, 873}, {5221, 4573}, {5333, 4623}, {16777, 99}, {28605, 670}, {30595, 16741}, {30596, 4602}
X(48005) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 4041, 4983}, {4705, 4983, 4041}


X(48006) = X(1)X(514)∩X(513)X(3004)

Barycentrics    (b - c)*(-a^3 + 3*a^2*b + a*b^2 + b^3 + 3*a^2*c + 4*a*b*c + b^2*c + a*c^2 + b*c^2 + c^3) : :
X(48006) = 2 X[1491] - 3 X[47783], 2 X[3239] - 3 X[47821], X[47690] - 3 X[47821], 2 X[3676] - 3 X[47797], X[4088] - 3 X[47826], 2 X[4369] - 3 X[47800], 4 X[4521] - 3 X[47809], 2 X[4522] - 3 X[47765], 3 X[4776] - X[47687], 2 X[4784] - 3 X[4786], 4 X[4806] - 3 X[47786], 4 X[4874] - 3 X[47789], 2 X[4913] - 3 X[47883], X[7192] - 3 X[47798], 4 X[7658] - 3 X[47824], 2 X[11068] - 3 X[47811], 2 X[21146] - 3 X[21183], 2 X[24720] - 3 X[47757], 4 X[25666] - 3 X[47806], 3 X[30565] - X[47689], X[47703] - 3 X[47832], X[47715] - 3 X[47838], X[47719] - 3 X[47840]

X(48006) lies on these lines: {1, 514}, {513, 3004}, {522, 661}, {523, 4468}, {659, 8646}, {676, 43067}, {1491, 47783}, {2496, 28195}, {3239, 47690}, {3667, 21196}, {3676, 47797}, {3716, 6590}, {4088, 28161}, {4369, 47800}, {4458, 4778}, {4521, 47809}, {4522, 47765}, {4705, 44448}, {4776, 47687}, {4784, 4786}, {4806, 47786}, {4822, 28478}, {4874, 47789}, {4913, 47883}, {4932, 13246}, {6332, 29142}, {7192, 47798}, {7650, 14208}, {7658, 47824}, {7659, 17069}, {11068, 47811}, {21146, 21183}, {24720, 47757}, {25666, 47806}, {28147, 47702}, {28169, 47700}, {30565, 47689}, {47666, 47695}, {47703, 47832}, {47715, 47838}, {47719, 47840}

X(48006) = midpoint of X(i) and X(j) for these {i,j}: {4724, 47701}, {47666, 47695}, {47694, 47699}
X(48006) = reflection of X(i) in X(j) for these {i,j}: {4932, 13246}, {6590, 3716}, {7659, 17069}, {43067, 676}, {44448, 4705}, {47690, 3239}
X(48006) = crossdifference of every pair of points on line {672, 1468}
X(48006) = {X(47690),X(47821)}-harmonic conjugate of X(3239)


X(48007) = X(10)X(514)∩X(513)X(3004)

Barycentrics    (b - c)*(a^3 + a^2*b + 3*a*b^2 + b^3 + a^2*c + 2*a*b*c + b^2*c + 3*a*c^2 + b*c^2 + c^3) : :
X(48007) = X[659] - 3 X[47877], 2 X[4782] - 3 X[47785], 2 X[4874] - 3 X[47757], 2 X[11068] - 3 X[47827], 3 X[31131] - X[47689], 3 X[44429] - X[47660], 3 X[44435] - X[47694], X[47662] - 3 X[47809], X[47663] - 3 X[47825], X[47693] - 3 X[47808], X[47697] - 3 X[47797]

X(48007) lies on these lines: {2, 47696}, {10, 514}, {513, 3004}, {522, 4810}, {523, 2525}, {650, 2523}, {659, 4778}, {812, 4818}, {2977, 28213}, {3837, 6590}, {4522, 28863}, {4782, 47785}, {4874, 47757}, {4913, 28882}, {11068, 28229}, {17494, 47686}, {28195, 47890}, {28209, 47880}, {28220, 47784}, {29208, 44448}, {29362, 45745}, {29832, 47691}, {31131, 47689}, {44429, 47660}, {44435, 47694}, {45746, 46403}, {47653, 47690}, {47662, 47809}, {47663, 47825}, {47693, 47808}, {47697, 47797}

X(48007) = midpoint of X(i) and X(j) for these {i,j}: {17494, 47686}, {45746, 46403}, {47653, 47690}
X(48007) = reflection of X(6590) in X(3837)
X(48007) = complement of X(47696)
X(48007) = crossdifference of every pair of points on line {1914, 3295}


X(48008) = X(239)X(514)∩X(513)X(4507)

Barycentrics    (b - c)*(-2*a^2 + a*b + a*c + b*c) : :
X(48008) = 3 X[649] - X[7192], 5 X[649] - 3 X[47763], X[649] - 3 X[47776], 2 X[3798] - 3 X[45679], 3 X[4063] + X[47683], 3 X[4750] - X[47676], 3 X[4932] - 2 X[7192], X[4932] + 2 X[17494], 5 X[4932] - 6 X[47763], X[4932] - 6 X[47776], X[7192] + 3 X[17494], 5 X[7192] - 9 X[47763], X[7192] - 9 X[47776], 3 X[14435] - X[47755], X[16892] - 3 X[27486], 5 X[17494] + 3 X[47763], X[17494] + 3 X[47776], 3 X[27486] + X[47663], X[47763] - 5 X[47776], 3 X[659] - 2 X[8689], X[4122] - 3 X[47885], 3 X[650] - X[4106], 3 X[650] - 2 X[25666], 5 X[650] - 3 X[47760], 4 X[650] - 3 X[47778], 3 X[3835] - 2 X[4106], 3 X[3835] - 4 X[25666], 5 X[3835] - 6 X[47760], 2 X[3835] - 3 X[47778], 5 X[4106] - 9 X[47760], 4 X[4106] - 9 X[47778], 10 X[25666] - 9 X[47760], 8 X[25666] - 9 X[47778], 4 X[47760] - 5 X[47778], X[661] - 3 X[31150], X[4380] + 3 X[31150], X[693] - 3 X[1635], 3 X[693] - 5 X[24924], 2 X[693] - 3 X[47779], 9 X[1635] - 5 X[24924], 3 X[1635] - 2 X[31286], 5 X[24924] - 6 X[31286], 10 X[24924] - 9 X[47779], 4 X[31286] - 3 X[47779], 4 X[2490] - 3 X[47879], 4 X[2516] - 3 X[4763], 3 X[4763] - 2 X[4885], 2 X[3239] - 3 X[10196], 2 X[3676] - 3 X[45674], X[3700] - 3 X[47884], 2 X[3837] - 3 X[47830], X[4024] - 3 X[47771], 2 X[4369] - 3 X[45313], 4 X[4394] - 3 X[45313], 3 X[4379] - X[26824], 3 X[4379] - 5 X[27013], X[26824] - 5 X[27013], X[4467] + 3 X[47892], 4 X[4521] - 3 X[45661], 3 X[4728] - 5 X[31209], 3 X[4773] - X[4897], X[4804] - 3 X[47804], X[4810] - 3 X[47822], X[4813] - 3 X[47775], X[26853] + 3 X[47775], X[4820] - 3 X[47770], 3 X[4893] - X[20295], 3 X[4893] - 5 X[26777], X[20295] - 5 X[26777], 3 X[4928] - 2 X[23813], 3 X[4928] - 4 X[31287], 2 X[4940] - 3 X[45315], 3 X[6545] - X[47650], 3 X[6546] - X[25259], 4 X[7658] - 3 X[21204], X[17161] + 3 X[47773], 2 X[21212] - 3 X[47785], 3 X[21297] - 7 X[27115], 3 X[21297] - 5 X[30835], 7 X[27115] - 5 X[30835], X[23729] - 3 X[47784], X[23731] - 3 X[47781], X[24719] - 3 X[47827], 5 X[26985] - 7 X[31207], 3 X[30574] - X[47722], 3 X[31148] - X[47675], 5 X[31250] - 6 X[45675], X[46403] - 3 X[47828], X[47652] - 3 X[47886], X[47664] + 3 X[47762], X[47672] - 3 X[47762], X[47671] - 3 X[47791]

X(48008) lies on these lines: {2, 4382}, {10, 29033}, {239, 514}, {513, 4507}, {522, 659}, {523, 4782}, {650, 812}, {661, 4380}, {666, 41405}, {669, 4151}, {693, 1635}, {814, 4147}, {824, 4976}, {890, 8714}, {1015, 24191}, {1577, 30061}, {1960, 23506}, {2490, 47879}, {2516, 4763}, {2786, 4468}, {2977, 4522}, {2978, 29350}, {3004, 28882}, {3227, 32030}, {3239, 4375}, {3667, 4724}, {3676, 45674}, {3700, 47884}, {3776, 6084}, {3837, 47830}, {4024, 47771}, {4041, 28470}, {4129, 29270}, {4369, 4394}, {4379, 26824}, {4467, 30519}, {4521, 45661}, {4728, 31209}, {4773, 4897}, {4778, 4784}, {4790, 28840}, {4804, 47804}, {4810, 47822}, {4813, 26853}, {4818, 4977}, {4820, 47770}, {4841, 28859}, {4893, 20295}, {4928, 23813}, {4940, 45315}, {4979, 47666}, {4984, 28906}, {5075, 21185}, {6009, 47882}, {6545, 47650}, {6546, 25259}, {7658, 8056}, {9508, 24720}, {10566, 47129}, {13246, 47123}, {14838, 28374}, {14936, 44312}, {17072, 23791}, {17161, 47773}, {20954, 29404}, {20979, 29545}, {21051, 29238}, {21212, 24623}, {21225, 23886}, {21297, 27115}, {23729, 47784}, {23731, 47781}, {24719, 47827}, {24769, 42042}, {26277, 47766}, {26854, 47795}, {26985, 31207}, {27293, 47794}, {27648, 30023}, {28161, 47694}, {28372, 45671}, {28984, 46399}, {29226, 43931}, {30574, 47722}, {31148, 47675}, {31250, 45675}, {46403, 47828}, {47652, 47886}, {47662, 47673}, {47664, 47672}, {47671, 47791}

X(48008) = midpoint of X(i) and X(j) for these {i,j}: {649, 17494}, {661, 4380}, {4498, 4560}, {4813, 26853}, {4830, 4913}, {4976, 47890}, {4979, 47666}, {16892, 47663}, {47662, 47673}, {47664, 47672}
X(48008) = reflection of X(i) in X(j) for these {i,j}: {693, 31286}, {3776, 17069}, {3835, 650}, {4106, 25666}, {4369, 4394}, {4522, 2977}, {4885, 2516}, {4932, 649}, {21196, 4765}, {23813, 31287}, {24720, 9508}, {47123, 13246}, {47779, 1635}
X(48008) = complement of X(4382)
X(48008) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {29227, 69}, {36598, 150}, {36614, 149}, {36630, 33650}, {38247, 21293}
X(48008) = X(i)-complementary conjugate of X(j) for these (i,j): {749, 116}, {30651, 11}
X(48008) = X(22215)-cross conjugate of X(4685)
X(48008) = X(i)-isoconjugate of X(j) for these (i,j): {100, 39966}, {101, 39742}
X(48008) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 39742), (8054, 39966)
X(48008) = crosspoint of X(190) and X(330)
X(48008) = crosssum of X(i) and X(j) for these (i,j): {649, 2176}, {4079, 22277}
X(48008) = crossdifference of every pair of points on line {42, 2275}
X(48008) = barycentric product X(i)*X(j) for these {i,j}: {1, 23794}, {513, 17144}, {514, 17349}, {693, 8616}, {799, 22215}, {1019, 22016}, {1978, 23470}, {4685, 7192}, {18197, 27438}
X(48008) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 39742}, {649, 39966}, {4685, 3952}, {8616, 100}, {17144, 668}, {17349, 190}, {22016, 4033}, {22215, 661}, {23470, 649}, {23794, 75}
X(48008) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 4498, 18197}, {650, 3835, 47778}, {650, 4106, 25666}, {693, 1635, 31286}, {693, 31286, 47779}, {2516, 4885, 4763}, {4106, 25666, 3835}, {4369, 4394, 45313}, {4380, 31150, 661}, {17494, 47776, 649}, {20295, 26777, 4893}, {21297, 27115, 30835}, {23813, 31287, 4928}, {26824, 27013, 4379}, {26853, 47775, 4813}, {27486, 47663, 16892}, {47664, 47762, 47672}


X(48009) = X(1)X(514)∩X(513)X(4507)

Barycentrics    (b - c)*(-2*a^3 + 3*a^2*b + a*b^2 + 3*a^2*c + 7*a*b*c + b^2*c + a*c^2 + b*c^2) : :
X(48009) = 3 X[4724] - X[47694], 3 X[661] - X[47685], 2 X[4874] - 3 X[45673], 2 X[21146] - 3 X[47779], 2 X[24720] - 3 X[47778], 2 X[31286] - 3 X[47811], X[46403] - 3 X[47826]

X(48009) lies on these lines: {1, 514}, {513, 4507}, {649, 28225}, {659, 4778}, {661, 47685}, {3667, 17494}, {3776, 4977}, {4147, 29246}, {4782, 28209}, {4824, 4946}, {4874, 45673}, {8689, 28229}, {21146, 47779}, {24720, 47778}, {31286, 47811}, {46403, 47826}

X(48009) = reflection of X(4932) in X(659)


X(48010) = X(10)X(514)∩X(513)X(4507)

Barycentrics    (b - c)*(a^2*b + 3*a*b^2 + a^2*c + 5*a*b*c + b^2*c + 3*a*c^2 + b*c^2) : :
X(48010) = 3 X[1491] - X[21146], 5 X[1491] - 3 X[36848], 3 X[4824] + X[21146], 2 X[4824] + X[24720], 5 X[4824] + 3 X[36848], 2 X[21146] - 3 X[24720], 5 X[21146] - 9 X[36848], 5 X[24720] - 6 X[36848], X[649] - 3 X[47825], X[693] - 3 X[47810], X[4724] - 3 X[47775], 2 X[4369] - 3 X[47830], 3 X[4776] - X[4804], 2 X[4874] - 3 X[47778], 3 X[4893] - X[47694], 3 X[6546] - X[47696], X[7192] - 3 X[47828], 2 X[7662] - 3 X[47831], 4 X[25666] - 3 X[47831], 2 X[8689] - 3 X[47811], X[47697] - 3 X[47811], 3 X[44429] - X[47672], 5 X[30835] - 3 X[47834], 5 X[31209] - 3 X[47813], 2 X[31286] - 3 X[47827], X[47701] - 3 X[47781], 3 X[44435] - X[47704], X[45673] - 4 X[45676], X[47123] - 3 X[47783], X[47667] + 3 X[47808], X[47703] - 3 X[47808], X[47675] - 3 X[47812]

X(48010) lies on these lines: {10, 514}, {513, 4507}, {522, 661}, {523, 3835}, {649, 47825}, {663, 19767}, {693, 4086}, {918, 4818}, {2254, 4778}, {3240, 4724}, {3737, 23655}, {3837, 4802}, {4010, 28161}, {4040, 5312}, {4088, 45746}, {4369, 47830}, {4486, 45344}, {4776, 4804}, {4777, 4806}, {4785, 4948}, {4874, 47778}, {4893, 47694}, {4932, 9508}, {4988, 47690}, {6546, 47696}, {7192, 47828}, {7662, 25666}, {8689, 47697}, {16892, 47698}, {25380, 43067}, {28191, 44429}, {29643, 47691}, {30835, 47834}, {31209, 47813}, {31286, 47827}, {33077, 47701}, {44435, 47704}, {45673, 45676}, {47123, 47783}, {47667, 47703}, {47675, 47812}

X(48010) = midpoint of X(i) and X(j) for these {i,j}: {1491, 4824}, {2254, 47666}, {4088, 45746}, {4988, 47690}, {16892, 47698}, {47667, 47703}
X(48010) = reflection of X(i) in X(j) for these {i,j}: {4147, 4705}, {4932, 9508}, {7662, 25666}, {24720, 1491}, {43067, 25380}, {47697, 8689}
X(48010) = crossdifference of every pair of points on line {1468, 1914}
X(48010) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7662, 25666, 47831}, {47667, 47808, 47703}, {47697, 47811, 8689}


X(48011) = X(239)X(514)∩X(512)X(4401)

Barycentrics    a*(b - c)*(2*a^2 + 2*a*b + 2*a*c - b*c) : :
X(48011) = 3 X[649] - X[1019], 3 X[649] + X[4498], 5 X[649] + X[21385], X[1019] + 3 X[4063], 5 X[1019] + 3 X[21385], 3 X[4063] - X[4498], 5 X[4063] - X[21385], 5 X[4498] - 3 X[21385], 4 X[4782] - X[4794], 3 X[667] - X[4879], 5 X[667] - 3 X[25569], 5 X[4879] - 9 X[25569], 3 X[1635] - X[14349], X[4170] - 3 X[47804], X[4810] - 3 X[47875], X[4978] - 3 X[47762], X[7265] - 3 X[47771], X[20295] - 3 X[47794], X[23729] - 3 X[41800], X[24719] - 3 X[47837], X[26853] + 3 X[47793], 5 X[27013] - 3 X[47795]

X(48011) lies on these lines: {57, 30723}, {239, 514}, {512, 4401}, {659, 4834}, {667, 4879}, {798, 4129}, {812, 4823}, {1577, 4380}, {1635, 14349}, {2533, 29033}, {3667, 6211}, {3803, 3887}, {3960, 8712}, {4010, 4961}, {4142, 29158}, {4170, 47804}, {4369, 29302}, {4391, 29178}, {4394, 14838}, {4790, 15309}, {4791, 29013}, {4807, 28470}, {4810, 47875}, {4830, 29186}, {4978, 47762}, {4992, 31288}, {7265, 47771}, {10015, 29114}, {20295, 47794}, {23729, 41800}, {23875, 47890}, {24719, 47837}, {25511, 31286}, {26853, 47793}, {27013, 47795}

X(48011) = midpoint of X(i) and X(j) for these {i,j}: {649, 4063}, {659, 4834}, {1019, 4498}, {1577, 4380}
X(48011) = reflection of X(i) in X(j) for these {i,j}: {4401, 4782}, {4794, 4401}, {4992, 31288}, {14838, 4394}
X(48011) = X(101)-isoconjugate of X(39711)
X(48011) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 39711), (4790, 4778)
X(48011) = crosspoint of X(i) and X(j) for these (i,j): {81, 4606}, {190, 25417}
X(48011) = crosssum of X(i) and X(j) for these (i,j): {37, 4790}, {649, 16777}
X(48011) = crossdifference of every pair of points on line {42, 16884}
X(48011) = barycentric product X(513)*X(17393)
X(48011) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 39711}, {17393, 668}
X(48011) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 4498, 1019}, {1019, 4063, 4498}


X(48012) = X(10)X(514)∩X(523)X(4823)

Barycentrics    a*(b - c)*(2*b^2 + 3*b*c + 2*c^2) : :
X(48012) = X[764] - 7 X[1491], 3 X[764] - 7 X[2530], 5 X[764] - 7 X[3777], 3 X[764] + 7 X[4490], X[764] + 7 X[4705], 9 X[764] - 7 X[23765], 3 X[1491] - X[2530], 5 X[1491] - X[3777], 3 X[1491] + X[4490], 9 X[1491] - X[23765], 5 X[2530] - 3 X[3777], X[2530] + 3 X[4705], 3 X[2530] - X[23765], 3 X[3777] + 5 X[4490], X[3777] + 5 X[4705], 9 X[3777] - 5 X[23765], X[4490] - 3 X[4705], 3 X[4490] + X[23765], 9 X[4705] + X[23765], X[4040] - 3 X[4893], 3 X[650] - X[3803], 2 X[3803] - 3 X[4401], X[667] - 3 X[47827], X[693] - 3 X[47816], X[1019] - 3 X[47828], X[1577] - 3 X[47814], X[44448] + 3 X[47783], X[4041] + 3 X[47810], X[14349] - 3 X[47810], X[4170] - 3 X[4776], X[4367] - 3 X[47888], X[4378] - 3 X[47893], X[4978] - 3 X[44429], X[17166] - 3 X[47795], X[21301] + 3 X[47825], 3 X[44435] - X[47716], 5 X[31209] - 3 X[47818], 5 X[31251] - 3 X[47833], 2 X[31288] - 3 X[47829], X[47694] - 3 X[47794], X[47697] - 3 X[47817], X[47715] - 3 X[47808]

X(48012) lies on these lines: {10, 514}, {43, 4040}, {386, 663}, {522, 4129}, {523, 4823}, {650, 830}, {661, 1734}, {667, 47827}, {693, 47816}, {784, 4791}, {905, 4160}, {1019, 47828}, {1577, 47814}, {2512, 21261}, {3004, 29047}, {3687, 44448}, {3835, 4151}, {4041, 14349}, {4083, 4770}, {4088, 29358}, {4170, 4776}, {4260, 9029}, {4367, 47888}, {4378, 47893}, {4449, 30116}, {4522, 23879}, {4560, 29344}, {4808, 29260}, {4913, 29013}, {4948, 31149}, {4961, 20295}, {4978, 44429}, {5530, 21185}, {6685, 47778}, {8678, 14838}, {9534, 21302}, {17166, 19858}, {19853, 47796}, {21124, 29318}, {21196, 29062}, {21301, 29033}, {23657, 40627}, {28292, 39212}, {29641, 44435}, {30172, 47691}, {31040, 46915}, {31209, 47818}, {31251, 47833}, {31288, 47829}, {32106, 36238}, {45746, 47711}, {47679, 47690}, {47694, 47794}, {47697, 47817}, {47715, 47808}

X(48012) = midpoint of X(i) and X(j) for these {i,j}: {661, 1734}, {1491, 4705}, {2530, 4490}, {4041, 14349}, {4948, 31149}, {45746, 47711}, {47679, 47690}
X(48012) = reflection of X(i) in X(j) for these {i,j}: {4401, 650}, {4791, 21051}, {4823, 21260}
X(48012) = crossdifference of every pair of points on line {1914, 16884}
X(48012) = barycentric product X(i)*X(j) for these {i,j}: {1, 47665}, {321, 5216}
X(48012) = barycentric quotient X(i)/X(j) for these {i,j}: {5216, 81}, {47665, 75}
X(48012) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1491, 4490, 2530}, {2530, 4705, 4490}, {4041, 47810, 14349}


X(48013) = X(513)X(3004)∩X(514)X(4380)

Barycentrics    (b - c)*(-3*a^2 - 2*a*b + b^2 - 2*a*c + c^2) : :
X(48013) = 10 X[3676] - 9 X[6548], 2 X[3676] - 3 X[47755], 9 X[6548] - 5 X[20295], 3 X[6548] - 5 X[47755], X[20295] - 3 X[47755], 5 X[649] - 3 X[6546], 3 X[649] - 2 X[11068], 5 X[4468] - 6 X[6546], 3 X[4468] - 4 X[11068], 9 X[6546] - 10 X[11068], 2 X[3004] - 3 X[4025], X[3004] - 3 X[4897], 3 X[4467] - X[47657], 3 X[7192] - X[47656], 2 X[650] - 3 X[4786], 2 X[661] - 3 X[47785], 4 X[3798] - 3 X[47785], 3 X[1638] - 2 X[4940], 4 X[2487] - 3 X[47760], 4 X[2527] - 3 X[47770], 2 X[3239] - 3 X[47762], X[44449] - 3 X[47762], 2 X[3700] - 3 X[47789], 2 X[3835] - 3 X[47758], 2 X[4106] - 3 X[21183], 4 X[4369] - 3 X[47787], 4 X[4521] - 5 X[27013], 4 X[4521] - 3 X[47769], 5 X[27013] - 3 X[47769], 3 X[4750] - X[4813], 3 X[4776] - 4 X[7658], 4 X[4885] - 3 X[47786], 4 X[7653] - 3 X[47788], 2 X[14321] - 3 X[47761], 4 X[17069] - 3 X[47783], 2 X[23813] - 3 X[47891], X[25259] - 3 X[47763], 4 X[25666] - 3 X[47764], 3 X[27486] - X[31290], 3 X[30565] - 4 X[43061], 10 X[31286] - 9 X[45684], 4 X[31286] - 3 X[47765], 6 X[45684] - 5 X[47765]

X(48013) lies on these lines: {7, 3676}, {20, 28292}, {27, 3064}, {63, 649}, {513, 3004}, {514, 4380}, {522, 7192}, {650, 4786}, {661, 3798}, {693, 3667}, {900, 43067}, {918, 4790}, {1019, 6332}, {1638, 4940}, {2487, 47760}, {2527, 47770}, {2786, 4932}, {3239, 44449}, {3309, 4131}, {3700, 47789}, {3835, 5249}, {3868, 29350}, {4106, 21183}, {4292, 21184}, {4369, 28867}, {4406, 18155}, {4502, 28372}, {4521, 5273}, {4608, 28169}, {4750, 4813}, {4765, 47666}, {4776, 7658}, {4778, 45746}, {4885, 47786}, {6005, 23829}, {6008, 21104}, {7411, 15599}, {7653, 47788}, {8713, 31291}, {9965, 26853}, {11220, 28589}, {14321, 47761}, {17069, 47783}, {17161, 28147}, {17494, 28878}, {20835, 23865}, {21211, 30094}, {23813, 47891}, {23828, 28591}, {25259, 47763}, {25666, 47764}, {26248, 47806}, {27486, 31290}, {27673, 28287}, {28610, 47663}, {28840, 45745}, {28906, 47768}, {30565, 43061}, {31286, 45684}

X(48013) = midpoint of X(26853) and X(47676)
X(48013) = reflection of X(i) in X(j) for these {i,j}: {661, 3798}, {4025, 4897}, {4468, 649}, {6332, 1019}, {6590, 4932}, {20295, 3676}, {44449, 3239}, {47666, 4765}
X(48013) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 3798, 47785}, {20295, 47755, 3676}, {27013, 47769, 4521}, {44449, 47762, 3239}


X(48014) = X(513)X(3004)∩X(514)X(47692)

Barycentrics    (b - c)*(-3*a^3 + 3*a^2*b - a*b^2 + b^3 + 3*a^2*c + 4*a*b*c + b^2*c - a*c^2 + b*c^2 + c^3) : :
X(48014) = 2 X[4088] - 3 X[4468], X[4088] - 3 X[4724], 3 X[650] - 2 X[4925], 4 X[676] - 3 X[21183], 2 X[2254] - 3 X[47785], 2 X[2526] - 3 X[47783], 2 X[3676] - 3 X[47798], 4 X[3716] - 3 X[47787], 2 X[4369] - 3 X[47801], 4 X[4521] - 3 X[47808], 3 X[4786] - 2 X[7659], 4 X[13246] - 3 X[47758], 2 X[24720] - 3 X[47800]

X(48014) lies on these lines: {513, 3004}, {514, 47692}, {522, 3935}, {523, 2976}, {650, 4925}, {661, 3667}, {676, 21183}, {2254, 47785}, {2526, 47783}, {3239, 47687}, {3676, 47798}, {3716, 47787}, {4040, 6332}, {4369, 47801}, {4521, 47808}, {4778, 47676}, {4786, 7659}, {4811, 14208}, {6006, 27486}, {7661, 23787}, {13246, 47758}, {21185, 29186}, {24720, 47800}

X(48014) = reflection of X(i) in X(j) for these {i,j}: {4468, 4724}, {6332, 4040}, {47687, 3239}
X(48014) = X(7218)-anticomplementary conjugate of X(33650)


X(48015) = X(513)X(3004)∩X(514)X(1734)

Barycentrics    (b - c)*(a^3 - a^2*b + 3*a*b^2 + b^3 - a^2*c + b^2*c + 3*a*c^2 + b*c^2 + c^3) : :
X(48015) = 2 X[659] - 3 X[47785], 2 X[676] - 3 X[47754], 2 X[3239] - 3 X[44429], 2 X[3716] - 3 X[47757], 4 X[3837] - 3 X[47787], 3 X[4453] - X[47697], 4 X[7658] - 3 X[47804], 2 X[7662] - 3 X[21183], 2 X[11068] - 3 X[47828], 4 X[21212] - 3 X[47800], 4 X[25380] - 3 X[47766], X[47696] - 3 X[47824]

X(48015) lies on these lines: {513, 3004}, {514, 1734}, {522, 4382}, {649, 4778}, {659, 47785}, {676, 47754}, {918, 2526}, {1491, 4468}, {2530, 6332}, {3239, 44429}, {3676, 47694}, {3716, 47757}, {3776, 47123}, {3798, 28225}, {3837, 47787}, {4453, 47697}, {4467, 47685}, {4786, 28209}, {4818, 45745}, {6590, 24720}, {7658, 47804}, {7662, 21183}, {11068, 47828}, {21212, 47800}, {23795, 29132}, {25380, 47766}, {29288, 44448}, {47677, 47687}, {47696, 47824}

X(48015) = midpoint of X(i) and X(j) for these {i,j}: {4467, 47685}, {47677, 47687}
X(48015) = reflection of X(i) in X(j) for these {i,j}: {4468, 1491}, {6332, 2530}, {6590, 24720}, {45745, 4818}, {47123, 3776}, {47694, 3676}


X(48016) = X(2)X(649)∩X(513)X(4507)

Barycentrics    (b - c)*(-4*a^2 - a*b - a*c + b*c) : :
X(48016) = 3 X[2] - 5 X[649], 6 X[2] - 5 X[3835], 9 X[2] - 5 X[20295], 33 X[2] - 25 X[26798], 3 X[2] + 5 X[26853], 21 X[2] - 25 X[27013], 39 X[2] - 35 X[27138], 27 X[2] - 25 X[30835], 7 X[2] - 5 X[31147], 33 X[2] - 35 X[31207], 9 X[2] - 10 X[31286], 4 X[2] - 5 X[45313], 11 X[2] - 10 X[45339], 3 X[649] - X[20295], 11 X[649] - 5 X[26798], 7 X[649] - 5 X[27013], 13 X[649] - 7 X[27138], 9 X[649] - 5 X[30835], 7 X[649] - 3 X[31147], 11 X[649] - 7 X[31207], 3 X[649] - 2 X[31286], 4 X[649] - 3 X[45313], 11 X[649] - 6 X[45339], 3 X[3835] - 2 X[20295], 11 X[3835] - 10 X[26798], X[3835] + 2 X[26853], 7 X[3835] - 10 X[27013], 13 X[3835] - 14 X[27138], 9 X[3835] - 10 X[30835], 7 X[3835] - 6 X[31147], 11 X[3835] - 14 X[31207], 3 X[3835] - 4 X[31286], 2 X[3835] - 3 X[45313], 11 X[3835] - 12 X[45339], 11 X[20295] - 15 X[26798], X[20295] + 3 X[26853], 7 X[20295] - 15 X[27013], 13 X[20295] - 21 X[27138], 3 X[20295] - 5 X[30835], 7 X[20295] - 9 X[31147], 11 X[20295] - 21 X[31207], 4 X[20295] - 9 X[45313], 11 X[20295] - 18 X[45339], 5 X[26798] + 11 X[26853], 7 X[26798] - 11 X[27013], 65 X[26798] - 77 X[27138], 9 X[26798] - 11 X[30835], 35 X[26798] - 33 X[31147], 5 X[26798] - 7 X[31207], 15 X[26798] - 22 X[31286], 20 X[26798] - 33 X[45313], 5 X[26798] - 6 X[45339], 7 X[26853] + 5 X[27013], 13 X[26853] + 7 X[27138], 9 X[26853] + 5 X[30835], 7 X[26853] + 3 X[31147], 11 X[26853] + 7 X[31207], 3 X[26853] + 2 X[31286], 4 X[26853] + 3 X[45313], 11 X[26853] + 6 X[45339], 65 X[27013] - 49 X[27138], 9 X[27013] - 7 X[30835], 5 X[27013] - 3 X[31147], 55 X[27013] - 49 X[31207], 15 X[27013] - 14 X[31286], 20 X[27013] - 21 X[45313], 55 X[27013] - 42 X[45339], 63 X[27138] - 65 X[30835], 49 X[27138] - 39 X[31147], 11 X[27138] - 13 X[31207], 21 X[27138] - 26 X[31286], 28 X[27138] - 39 X[45313], 77 X[27138] - 78 X[45339], 35 X[30835] - 27 X[31147], 55 X[30835] - 63 X[31207], 5 X[30835] - 6 X[31286], 20 X[30835] - 27 X[45313], 55 X[30835] - 54 X[45339], 33 X[31147] - 49 X[31207], 9 X[31147] - 14 X[31286], 4 X[31147] - 7 X[45313], 11 X[31147] - 14 X[45339], 21 X[31207] - 22 X[31286], 28 X[31207] - 33 X[45313], 7 X[31207] - 6 X[45339], 8 X[31286] - 9 X[45313], 11 X[31286] - 9 X[45339], 11 X[45313] - 8 X[45339], 5 X[4380] - X[47664], 5 X[4979] + X[47664], 3 X[4790] - X[43067], 3 X[4932] - 2 X[43067], 4 X[2516] - 3 X[45315], 4 X[2527] - 3 X[47879], 2 X[4106] - 3 X[47779], 3 X[4369] - 2 X[23813], X[4382] - 3 X[47763], 4 X[4394] - 3 X[47778], 3 X[4763] - 2 X[4940], 3 X[4786] - 2 X[21212], X[4813] - 3 X[47776], 3 X[4984] - X[45746], X[23731] - 3 X[27486], 4 X[43061] - 3 X[45661]

X(48016) lies on these lines: {2, 649}, {512, 41300}, {513, 4507}, {514, 4380}, {812, 4790}, {2516, 45315}, {2527, 47879}, {3244, 29350}, {3629, 9002}, {3676, 4031}, {4106, 47779}, {4369, 6008}, {4382, 47763}, {4394, 47778}, {4763, 4940}, {4786, 21212}, {4813, 47776}, {4897, 28882}, {4962, 47697}, {4976, 28859}, {4984, 45746}, {6006, 11068}, {6154, 37998}, {23731, 27486}, {28867, 47890}, {43061, 45661}

X(48016) = midpoint of X(i) and X(j) for these {i,j}: {649, 26853}, {4380, 4979}
X(48016) = reflection of X(i) in X(j) for these {i,j}: {3835, 649}, {4932, 4790}, {20295, 31286}
X(48016) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 3835, 45313}, {649, 20295, 31286}, {649, 31147, 27013}, {20295, 31286, 3835}, {26798, 31207, 45339}, {26798, 45339, 3835}


X(48017) = X(513)X(4507)∩X(514)X(1734)

Barycentrics    (b - c)*(-(a^2*b) + 3*a*b^2 - a^2*c + 3*a*b*c + b^2*c + 3*a*c^2 + b*c^2) : :
X(48017) = X[4830] - 3 X[4913], 3 X[1734] - X[4761], 3 X[1491] - X[4010], 3 X[3835] - 2 X[4010], 2 X[676] - 3 X[47882], 3 X[1635] - X[47697], 2 X[3716] - 3 X[47778], X[4024] - 3 X[47808], X[4724] - 3 X[47825], X[4804] - 3 X[44429], 2 X[4874] - 3 X[47830], 2 X[7662] - 3 X[47779], 4 X[25380] - 3 X[47779], 4 X[9508] - 3 X[45313], 2 X[13246] - 3 X[47785], 2 X[31286] - 3 X[47828], X[47694] - 3 X[47828], X[47695] - 3 X[47886]

X(48017) lies on these lines: {513, 4507}, {514, 1734}, {522, 1491}, {523, 3776}, {661, 3667}, {676, 47882}, {693, 17894}, {784, 17072}, {812, 2526}, {1635, 47697}, {3716, 47778}, {3837, 4777}, {4024, 47808}, {4088, 30519}, {4560, 28470}, {4724, 47825}, {4778, 4824}, {4804, 44429}, {4806, 4926}, {4874, 47830}, {4962, 47810}, {7659, 28840}, {7662, 25380}, {9508, 45313}, {13246, 47785}, {21146, 28147}, {21173, 23655}, {21212, 47123}, {25381, 47690}, {28155, 47672}, {28169, 36848}, {28225, 47666}, {31286, 47694}, {47673, 47689}, {47677, 47700}, {47695, 47886}

X(48017) = midpoint of X(i) and X(j) for these {i,j}: {47673, 47689}, {47677, 47700}
X(48017) = reflection of X(i) in X(j) for these {i,j}: {3835, 1491}, {7662, 25380}, {47123, 21212}, {47694, 31286}
X(48017) = crossdifference of every pair of points on line {172, 2280}
X(48017) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7662, 25380, 47779}, {47694, 47828, 31286}


X(48018) = X(1)X(4959)∩X(514)X(1734)

Barycentrics    a*(b - c)*(2*a*b - 2*b^2 + 2*a*c - b*c - 2*c^2) : :
X(48018) = 3 X[1] - X[4959], 3 X[1734] - X[4041], 3 X[1734] + X[4905], 9 X[1734] + X[23738], 3 X[2254] + X[4041], 3 X[2254] - X[4905], 9 X[2254] - X[23738], 3 X[4041] + X[23738], 3 X[4905] - X[23738], 3 X[905] - X[4162], 3 X[1491] - X[4983], X[4040] - 3 X[47828], X[4170] - 3 X[44429], X[4775] - 3 X[47893], 3 X[4800] - 5 X[31251], X[7265] - 3 X[47808]

X(48018) lies on these lines: {1, 4959}, {514, 1734}, {522, 4823}, {525, 4925}, {650, 42325}, {656, 3667}, {900, 21260}, {905, 3887}, {1491, 4983}, {2530, 29350}, {3123, 24196}, {3309, 4794}, {3777, 4730}, {3900, 3960}, {4040, 47828}, {4151, 24720}, {4170, 44429}, {4401, 6004}, {4770, 29198}, {4775, 47893}, {4791, 8714}, {4800, 31251}, {4913, 29186}, {4926, 24168}, {4961, 24719}, {4962, 21189}, {7265, 47808}, {7659, 15309}, {10395, 14837}, {16892, 29260}, {21301, 29178}, {23800, 28161}, {47677, 47710}

X(48018) = midpoint of X(i) and X(j) for these {i,j}: {1734, 2254}, {3777, 4730}, {4041, 4905}, {47677, 47710}
X(48018) = reflection of X(i) in X(j) for these {i,j}: {4401, 9508}, {4791, 17072}, {4794, 14838}, {21201, 14837}
X(48018) = crossdifference of every pair of points on line {2174, 2280}
X(48018) = barycentric product X(i)*X(j) for these {i,j}: {513, 17240}, {514, 4661}
X(48018) = barycentric quotient X(i)/X(j) for these {i,j}: {4661, 190}, {17240, 668}
X(48018) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1734, 4905, 4041}, {2254, 4041, 4905}


X(48019) = X(44)X(513)∩X(514)X(4838)

Barycentrics    a*(b - c)*(2*a + 3*b + 3*c) : :
X(48019) = 5 X[649] - 6 X[650], 2 X[649] - 3 X[661], 8 X[649] - 9 X[1635], 7 X[649] - 8 X[2516], 11 X[649] - 12 X[4394], 7 X[649] - 6 X[4790], X[649] - 3 X[4813], 7 X[649] - 9 X[4893], 4 X[649] - 3 X[4979], 13 X[649] - 18 X[47777], 4 X[650] - 5 X[661], 16 X[650] - 15 X[1635], 21 X[650] - 20 X[2516], 11 X[650] - 10 X[4394], 7 X[650] - 5 X[4790], 2 X[650] - 5 X[4813], 14 X[650] - 15 X[4893], 8 X[650] - 5 X[4979], 13 X[650] - 15 X[47777], 4 X[661] - 3 X[1635], 21 X[661] - 16 X[2516], 11 X[661] - 8 X[4394], 7 X[661] - 4 X[4790], 7 X[661] - 6 X[4893], 13 X[661] - 12 X[47777], 63 X[1635] - 64 X[2516], 33 X[1635] - 32 X[4394], 21 X[1635] - 16 X[4790], 3 X[1635] - 8 X[4813], 7 X[1635] - 8 X[4893], 3 X[1635] - 2 X[4979], 13 X[1635] - 16 X[47777], 22 X[2516] - 21 X[4394], 4 X[2516] - 3 X[4790], 8 X[2516] - 21 X[4813], 8 X[2516] - 9 X[4893], 32 X[2516] - 21 X[4979], 52 X[2516] - 63 X[47777], 14 X[4394] - 11 X[4790], 4 X[4394] - 11 X[4813], 28 X[4394] - 33 X[4893], 16 X[4394] - 11 X[4979], 26 X[4394] - 33 X[47777], 2 X[4784] - 3 X[47810], 2 X[4790] - 7 X[4813], 2 X[4790] - 3 X[4893], 8 X[4790] - 7 X[4979], 13 X[4790] - 21 X[47777], 7 X[4813] - 3 X[4893], 4 X[4813] - X[4979], 13 X[4813] - 6 X[47777], 12 X[4893] - 7 X[4979], 13 X[4893] - 14 X[47777], 13 X[4979] - 24 X[47777], 2 X[1960] - 3 X[4983], 8 X[2527] - 9 X[6544], 4 X[3835] - 3 X[31148], 2 X[4024] - 3 X[4958], 6 X[4369] - 7 X[27138], 2 X[4369] - 3 X[47759], 7 X[27138] - 9 X[47759], 3 X[4379] - 4 X[4940], 3 X[4728] - 2 X[7192], 9 X[4728] - 10 X[26798], 3 X[7192] - 5 X[26798], 2 X[4775] - 3 X[4822], 3 X[4776] - 2 X[4932], 6 X[4776] - 5 X[24924], 4 X[4932] - 5 X[24924], 4 X[4806] - 3 X[47813], 5 X[20295] - 3 X[47869], 5 X[47672] - 6 X[47869], 4 X[25666] - 3 X[47763], X[26853] - 3 X[47774], 5 X[27013] - 6 X[45315], 3 X[31147] - 2 X[43067]

X(48019) lies on these lines: {44, 513}, {514, 4838}, {522, 47669}, {812, 31290}, {900, 4988}, {918, 23731}, {1960, 4983}, {2527, 6544}, {2786, 47673}, {3700, 28209}, {3835, 31148}, {4024, 4958}, {4369, 27138}, {4379, 4940}, {4728, 7192}, {4775, 4822}, {4776, 4932}, {4778, 4931}, {4785, 47666}, {4806, 47813}, {4820, 28195}, {4841, 28217}, {4949, 28220}, {4959, 8678}, {4976, 39386}, {6006, 45745}, {6372, 21836}, {6590, 28225}, {15309, 29738}, {20295, 28840}, {23729, 28902}, {23751, 42664}, {25259, 28859}, {25666, 47763}, {26853, 47774}, {27013, 45315}, {28855, 47652}, {28867, 45746}, {28886, 47676}, {28906, 47677}, {31147, 43067}

X(48019) = reflection of X(i) in X(j) for these {i,j}: {661, 4813}, {4979, 661}, {47672, 20295}
X(48019) = X(i)-Ceva conjugate of X(j) for these (i,j): {1100, 3125}, {1255, 244}
X(48019) = X(2)-isoconjugate of X(28176)
X(48019) = X(32664)-Dao conjugate of X(28176)
X(48019) = crosssum of X(100) and X(35342)
X(48019) = crossdifference of every pair of points on line {1, 4127}
X(48019) = barycentric product X(i)*X(j) for these {i,j}: {1, 28175}, {513, 3634}, {514, 3723}, {649, 4980}, {650, 3982}, {3669, 4060}
X(48019) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 28176}, {3634, 668}, {3723, 190}, {3982, 4554}, {4060, 646}, {4980, 1978}, {28175, 75}
X(48019) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 4893, 2516}, {661, 4979, 1635}, {2516, 4790, 649}, {4776, 4932, 24924}


X(48020) = X(1)X(830)∩X(44)X(513)

Barycentrics    a*(b - c)*(2*a^2 + a*b + 3*b^2 + a*c + 2*b*c + 3*c^2) : :
X(48020) = 2 X[659] - 3 X[47810], 3 X[661] - 2 X[4724], 7 X[661] - 6 X[47826], 4 X[1491] - 3 X[1635], 3 X[1491] - 2 X[4782], 9 X[1635] - 8 X[4782], 3 X[2254] - 2 X[4784], 7 X[4724] - 9 X[47826], 4 X[4784] - 3 X[4979], 8 X[3634] - 9 X[47816], 4 X[3837] - 3 X[47813], 3 X[4728] - 2 X[47694], 2 X[4794] - 3 X[14349], 2 X[4830] - 3 X[47825], 10 X[19862] - 9 X[47818], 4 X[24720] - 3 X[31148], 5 X[24924] - 6 X[44429], 4 X[25666] - 3 X[47805]

X(48020) lies on these lines: {1, 830}, {44, 513}, {514, 47685}, {522, 47673}, {900, 47701}, {2520, 6615}, {3634, 47816}, {3667, 4467}, {3835, 47697}, {3837, 47813}, {4088, 4977}, {4468, 28225}, {4522, 47696}, {4728, 47694}, {4794, 14349}, {4804, 24719}, {4822, 6004}, {4830, 47825}, {8672, 40471}, {19862, 47818}, {21124, 28481}, {24687, 24721}, {24720, 31148}, {24924, 44429}, {25666, 47805}, {28161, 47654}, {32635, 35355}, {46403, 47672}, {47652, 47705}

X(48020) = reflection of X(i) in X(j) for these {i,j}: {649, 2526}, {4804, 24719}, {4979, 2254}, {47672, 46403}, {47696, 4522}, {47697, 3835}, {47705, 47652}
X(48020) = X(i)-Ceva conjugate of X(j) for these (i,j): {1386, 4475}, {1390, 244}
X(48020) = X(830)-line conjugate of X(1)
X(48020) = barycentric product X(513)*X(29604)
X(48020) = barycentric quotient X(29604)/X(668)


X(48021) = X(44)X(513)∩X(514)X(4170)

Barycentrics    a*(b - c)*(3*a*b + b^2 + 3*a*c + 4*b*c + c^2) : :
X(48021) = 2 X[649] - 3 X[47811], 2 X[650] - 3 X[47826], 3 X[661] - 2 X[1491], 4 X[661] - 3 X[47810], 4 X[1491] - 3 X[2254], 8 X[1491] - 9 X[47810], 3 X[1635] - 2 X[4784], 2 X[2254] - 3 X[47810], 2 X[7659] - 3 X[47828], X[764] - 3 X[4983], 4 X[764] - 3 X[23738], 4 X[4983] - X[23738], 4 X[3716] - 3 X[47813], 2 X[7192] - 3 X[47813], 4 X[3835] - 3 X[47812], 2 X[4369] - 3 X[47821], 2 X[4522] - 3 X[47769], 3 X[4728] - 4 X[4806], 3 X[4728] - 2 X[21146], 2 X[4761] - 3 X[14430], 4 X[4775] - 3 X[23057], 3 X[4776] - 2 X[24720], 2 X[4818] - 3 X[47781], 4 X[4874] - 3 X[31148], 2 X[4913] - 3 X[47775], 2 X[4932] - 3 X[47804], 5 X[24924] - 6 X[47822], 4 X[25666] - 3 X[47824], 2 X[43067] - 3 X[47832]

X(48021) lies on these lines: {44, 513}, {514, 4170}, {522, 44449}, {693, 4778}, {764, 4983}, {824, 47699}, {830, 1027}, {900, 4824}, {918, 47701}, {3700, 47703}, {3716, 7192}, {3835, 28225}, {4010, 4977}, {4040, 15309}, {4041, 6005}, {4160, 4895}, {4369, 47821}, {4490, 4729}, {4522, 47769}, {4728, 4806}, {4761, 14430}, {4775, 23057}, {4776, 24720}, {4818, 47781}, {4830, 26853}, {4874, 31148}, {4913, 47775}, {4932, 30765}, {24924, 47822}, {25666, 47824}, {28229, 47675}, {28840, 47694}, {28851, 47691}, {28859, 47696}, {28878, 47123}, {28890, 47688}, {29144, 47700}, {43067, 47832}

X(48021) = reflection of X(i) in X(j) for these {i,j}: {2254, 661}, {4729, 4490}, {4979, 659}, {7192, 3716}, {21146, 4806}, {26853, 4830}, {47672, 4010}, {47703, 3700}
X(48021) = X(i)-Ceva conjugate of X(j) for these (i,j): {30571, 244}, {42302, 2170}
X(48021) = X(101)-isoconjugate of X(42335)
X(48021) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 42335), (31336, 668)
X(48021) = barycentric product X(i)*X(j) for these {i,j}: {513, 24603}, {514, 15569}, {1019, 4733}
X(48021) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 42335}, {4733, 4033}, {15569, 190}, {24603, 668}
X(48021) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 2254, 47810}, {3716, 7192, 47813}, {4806, 21146, 4728}


X(48022) = X(44)X(513)∩X(514)X(4509)

Barycentrics    a*(b - c)*(a^2*b + b^3 + a^2*c + 2*a*b*c + b^2*c + b*c^2 + c^3) : :
X(48022) = 3 X[1635] - 2 X[2483], 2 X[2509] - 3 X[4893]

X(48022) lies on these lines: {44, 513}, {514, 4509}, {918, 21124}, {2489, 8672}, {4391, 47129}, {4435, 38469}, {4581, 47127}, {4822, 9313}, {6590, 7650}, {9013, 21007}, {14349, 23790}, {21834, 29144}, {23874, 45745}, {23885, 47673}

X(48022) = reflection of X(2484) in X(650)
X(48022) = X(4357)-Ceva conjugate of X(3122)
X(48022) = X(2)-isoconjugate of X(29143)
X(48022) = X(32664)-Dao conjugate of X(29143)
X(48022) = crosssum of X(101) and X(3882)
X(48022) = barycentric product X(1)*X(29142)
X(48022) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 29143}, {29142, 75}


X(48023) = X(44)X(513)∩X(514)X(4088)

Barycentrics    a*(b - c)*(a^2 + a*b + 2*b^2 + a*c + 2*b*c + 2*c^2) : :
X(48023) = 3 X[649] - 4 X[9508], 2 X[649] - 3 X[47828], 2 X[650] - 3 X[47810], 2 X[659] - 3 X[4893], 4 X[661] - 3 X[47826], 3 X[1491] - 2 X[9508], 4 X[1491] - 3 X[47828], 3 X[2254] - 2 X[7659], 3 X[2526] - X[7659], 2 X[4724] - 3 X[47826], 2 X[4782] - 3 X[47827], 8 X[9508] - 9 X[47828], 2 X[676] - 3 X[47756], 2 X[3716] - 3 X[4776], 3 X[4776] - X[47697], 4 X[3835] - 3 X[47832], 2 X[47694] - 3 X[47832], 4 X[3837] - 3 X[4379], 2 X[4010] - 3 X[31147], 2 X[4369] - 3 X[44429], 2 X[4458] - 3 X[44435], 3 X[4728] - 2 X[7662], 2 X[4830] - 3 X[31150], 4 X[4874] - 5 X[30835], 4 X[4885] - 3 X[47813], 2 X[4932] - 3 X[47824], 5 X[24924] - 6 X[47802], 4 X[25380] - 3 X[47762], 4 X[25666] - 3 X[47804], 5 X[27013] - 6 X[47830], 7 X[27138] - 6 X[47831], 2 X[43067] - 3 X[47812]

X(48023) lies on these lines: {44, 513}, {514, 4088}, {522, 17161}, {523, 4382}, {663, 830}, {667, 27675}, {676, 47756}, {3005, 8672}, {3250, 23656}, {3309, 4822}, {3667, 21196}, {3716, 4776}, {3835, 47694}, {3837, 4379}, {4010, 31147}, {4106, 4804}, {4367, 28373}, {4369, 30764}, {4380, 4913}, {4449, 8678}, {4458, 44435}, {4467, 4818}, {4468, 4778}, {4498, 4705}, {4522, 47660}, {4581, 30094}, {4728, 7662}, {4777, 4810}, {4802, 47700}, {4814, 29350}, {4824, 29362}, {4830, 31150}, {4874, 30835}, {4885, 47813}, {4905, 15309}, {4932, 47824}, {4963, 28195}, {4983, 6004}, {6006, 27486}, {6371, 20983}, {7192, 24720}, {11934, 42312}, {19949, 23814}, {23838, 44008}, {24721, 28859}, {24924, 47802}, {25380, 47762}, {25666, 47804}, {26824, 28147}, {27013, 47830}, {27138, 47831}, {27468, 43931}, {27469, 43924}, {29033, 47683}, {29190, 47679}, {43067, 47812}, {43927, 44316}, {47666, 47685}

X(48023) = midpoint of X(i) and X(j) for these {i,j}: {47666, 47685}, {47686, 47698}
X(48023) = reflection of X(i) in X(j) for these {i,j}: {649, 1491}, {663, 14349}, {2254, 2526}, {4380, 4913}, {4382, 24719}, {4467, 4818}, {4498, 4705}, {4724, 661}, {4804, 4106}, {7192, 24720}, {43927, 44316}, {47660, 4522}, {47694, 3835}, {47697, 3716}
X(48023) = X(2)-isoconjugate of X(28895)
X(48023) = X(32664)-Dao conjugate of X(28895)
X(48023) = crossdifference of every pair of points on line {1, 5282}
X(48023) = barycentric product X(i)*X(j) for these {i,j}: {1, 28894}, {513, 17308}
X(48023) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 28895}, {17308, 668}, {28894, 75}
X(48023) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 1491, 47828}, {661, 4724, 47826}, {3835, 47694, 47832}, {4776, 47697, 3716}


X(48024) = X(44)X(513)∩X(514)X(4010)

Barycentrics    a*(b - c)*(2*a*b + b^2 + 2*a*c + 3*b*c + c^2) : :
X(48024) = X[649] - 3 X[47826], 3 X[661] - X[2254], 5 X[661] - 3 X[47810], 3 X[1491] - 2 X[2254], 5 X[1491] - 6 X[47810], 5 X[2254] - 9 X[47810], 2 X[4782] - 3 X[47811], 3 X[4893] - 2 X[9508], X[4979] - 3 X[47811], X[7659] - 3 X[47777], 2 X[3837] - 3 X[4776], 3 X[4120] - X[47703], 2 X[4369] - 3 X[47822], 3 X[4800] - 2 X[7662], 2 X[4874] - 3 X[47821], X[7192] - 3 X[47821], 3 X[4951] - 4 X[18004], 3 X[4951] - 2 X[47690], 2 X[18004] - 3 X[47769], X[47690] - 3 X[47769], 2 X[25380] - 3 X[45315], 4 X[25666] - 3 X[47823], 5 X[30795] - 6 X[47760], 2 X[43067] - 3 X[47833], X[46403] - 3 X[47759], X[47693] - 3 X[47772]

X(48024) lies on these lines: {44, 513}, {351, 14315}, {512, 4490}, {514, 4010}, {522, 4824}, {523, 8663}, {667, 15309}, {676, 28902}, {693, 4806}, {3716, 28840}, {3777, 6372}, {3835, 4778}, {3837, 4776}, {4083, 4822}, {4088, 29144}, {4120, 47703}, {4160, 4775}, {4369, 47822}, {4444, 4448}, {4458, 28855}, {4486, 28859}, {4560, 29170}, {4705, 6005}, {4728, 28220}, {4762, 4810}, {4800, 7662}, {4801, 4992}, {4802, 4804}, {4809, 28886}, {4840, 16751}, {4874, 7192}, {4951, 18004}, {17494, 29328}, {20295, 29362}, {21124, 29200}, {21301, 29246}, {23765, 29198}, {24720, 28225}, {25380, 45315}, {25666, 47823}, {28195, 47672}, {28213, 47675}, {29078, 44449}, {29204, 47702}, {30765, 47803}, {30795, 47760}, {31290, 47694}, {36848, 45684}, {43067, 47833}, {46403, 47759}, {47693, 47772}

X(48024) = midpoint of X(i) and X(j) for these {i,j}: {4724, 4813}, {25259, 47699}, {31290, 47694}
X(48024) = reflection of X(i) in X(j) for these {i,j}: {693, 4806}, {1491, 661}, {3777, 14349}, {4784, 650}, {4801, 4992}, {4951, 47769}, {4979, 4782}, {7192, 4874}, {21146, 3835}, {47690, 18004}
X(48024) = crossdifference of every pair of points on line {1, 9346}
X(48024) = barycentric product X(513)*X(29576)
X(48024) = barycentric quotient X(29576)/X(668)
X(48024) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4979, 47811, 4782}, {7192, 47821, 4874}, {18004, 47690, 4951}, {47690, 47769, 18004}


X(48025) = X(44)X(513)∩X(768)X(24287)

Barycentrics    a*(b - c)*(a^2*b + b^3 + a^2*c + a*b*c + b^2*c + b*c^2 + c^3) : :
X(48025) = X[2484] - 3 X[4893]

X(48025) lies on these lines: {44, 513}, {768, 24287}, {832, 21007}, {2485, 8672}, {3063, 9013}, {4036, 47129}, {4079, 29144}, {4983, 9313}, {6590, 30591}, {7653, 28024}, {15413, 47666}, {21192, 28846}, {23885, 45746}

X(48025) = midpoint of X(15413) and X(47666)
X(48025) = reflection of X(2483) in X(650)
X(48025) = X(2)-isoconjugate of X(29022)
X(48025) = X(32664)-Dao conjugate of X(29022)
X(48025) = barycentric product X(i)*X(j) for these {i,j}: {1, 29021}, {513, 29667}
X(48025) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 29022}, {29021, 75}, {29667, 668}


X(48026) = X(44)X(513)∩X(514)X(3700)

Barycentrics    a*(b - c)*(a + 3*b + 3*c) : :
X(48026) = 2 X[649] - 3 X[650], X[649] - 3 X[661], 7 X[649] - 9 X[1635], 3 X[649] - 4 X[2516], 5 X[649] - 6 X[4394], 4 X[649] - 3 X[4790], X[649] + 3 X[4813], 5 X[649] - 9 X[4893], 5 X[649] - 3 X[4979], 4 X[649] - 9 X[47777], 7 X[650] - 6 X[1635], 9 X[650] - 8 X[2516], 5 X[650] - 4 X[4394], X[650] + 2 X[4813], 5 X[650] - 6 X[4893], 5 X[650] - 2 X[4979], 2 X[650] - 3 X[47777], 7 X[661] - 3 X[1635], 9 X[661] - 4 X[2516], 5 X[661] - 2 X[4394], 4 X[661] - X[4790], 5 X[661] - 3 X[4893], 5 X[661] - X[4979], 4 X[661] - 3 X[47777], 27 X[1635] - 28 X[2516], 15 X[1635] - 14 X[4394], 12 X[1635] - 7 X[4790], 3 X[1635] + 7 X[4813], 5 X[1635] - 7 X[4893], 15 X[1635] - 7 X[4979], 4 X[1635] - 7 X[47777], 3 X[2509] - 2 X[2515], 10 X[2516] - 9 X[4394], 16 X[2516] - 9 X[4790], 4 X[2516] + 9 X[4813], 20 X[2516] - 27 X[4893], 20 X[2516] - 9 X[4979], 16 X[2516] - 27 X[47777], 8 X[4394] - 5 X[4790], 2 X[4394] + 5 X[4813], 2 X[4394] - 3 X[4893], 8 X[4394] - 15 X[47777], X[4790] + 4 X[4813], 5 X[4790] - 12 X[4893], 5 X[4790] - 4 X[4979], X[4790] - 3 X[47777], 5 X[4813] + 3 X[4893], 5 X[4813] + X[4979], 4 X[4813] + 3 X[47777], 3 X[4893] - X[4979], 4 X[4893] - 5 X[47777], 4 X[4979] - 15 X[47777], 3 X[693] - 5 X[26798], X[693] - 3 X[47759], 6 X[4940] - 5 X[26798], 2 X[4940] + X[31290], 2 X[4940] - 3 X[47759], 5 X[26798] + 3 X[31290], 5 X[26798] - 9 X[47759], X[31290] + 3 X[47759], 4 X[2490] - 3 X[47768], 4 X[3239] - 3 X[47881], 2 X[3676] - 3 X[47756], 2 X[3798] - 3 X[47784], 4 X[3835] - 3 X[45320], 2 X[43067] - 3 X[45320], 2 X[4025] - 3 X[47880], 3 X[4162] - 4 X[4775], X[4162] - 4 X[4983], X[4775] - 3 X[4983], 4 X[4369] - 5 X[31250], 2 X[4369] - 3 X[47760], 5 X[31250] - 6 X[47760], X[4380] - 3 X[47775], X[4467] - 3 X[47781], 4 X[4521] - 3 X[47767], X[20295] + 3 X[47774], X[47666] - 3 X[47774], 2 X[4765] - 3 X[47876], 3 X[4776] - 2 X[4885], 3 X[4776] - X[7192], 9 X[4776] - 7 X[27138], 6 X[4885] - 7 X[27138], 3 X[7192] - 7 X[27138], 2 X[4949] + X[4988], 2 X[4932] - 3 X[47761], 4 X[25666] - 3 X[47761], 3 X[4944] - 2 X[6590], 3 X[4944] - 4 X[14321], X[6590] - 3 X[47764], 2 X[14321] - 3 X[47764], 3 X[4958] + X[47669], 4 X[7653] - 5 X[24924], 2 X[17069] - 3 X[47783], 3 X[21297] - X[47675], 2 X[23813] - 3 X[31147], 3 X[31147] - X[47672], X[26853] - 3 X[31150], 5 X[27013] - 6 X[44567], 5 X[30835] - 3 X[31148], 5 X[31209] - 3 X[47763], 2 X[31286] - 3 X[45315], 4 X[31287] - 3 X[47762], X[47660] - 3 X[47769], X[47662] - 3 X[47772]

X(48026) lies on these lines: {44, 513}, {514, 3700}, {522, 4841}, {523, 4820}, {693, 4940}, {900, 45745}, {905, 15309}, {1639, 28225}, {2490, 47768}, {2978, 9010}, {3004, 28846}, {3239, 4778}, {3250, 23751}, {3667, 4976}, {3669, 14349}, {3676, 47756}, {3709, 43060}, {3776, 28855}, {3798, 47784}, {3835, 28840}, {3900, 4822}, {4024, 4802}, {4025, 47880}, {4040, 8657}, {4120, 28195}, {4162, 4775}, {4369, 31250}, {4380, 47775}, {4406, 24622}, {4462, 18071}, {4467, 47781}, {4521, 47767}, {4762, 20295}, {4765, 6006}, {4776, 4885}, {4777, 4949}, {4806, 7662}, {4838, 28151}, {4931, 28199}, {4932, 25666}, {4944, 4977}, {4958, 28165}, {6008, 17494}, {7252, 20980}, {7653, 24924}, {14513, 14589}, {17069, 47783}, {20949, 21438}, {20974, 38390}, {21104, 28878}, {21196, 28867}, {21297, 47675}, {21385, 24290}, {23794, 29771}, {23813, 31147}, {25259, 28894}, {26853, 31150}, {27013, 44567}, {28209, 47765}, {28220, 47874}, {28886, 47754}, {28898, 44449}, {28910, 47676}, {30835, 31148}, {31209, 47763}, {31286, 45315}, {31287, 47762}, {38347, 38389}, {39386, 47883}, {47660, 47769}, {47662, 47772}

X(48026) = midpoint of X(i) and X(j) for these {i,j}: {661, 4813}, {693, 31290}, {20295, 47666}, {44449, 45746}
X(48026) = reflection of X(i) in X(j) for these {i,j}: {650, 661}, {693, 4940}, {3669, 14349}, {4790, 650}, {4932, 25666}, {4944, 47764}, {4979, 4394}, {6590, 14321}, {7192, 4885}, {7659, 1491}, {7662, 4806}, {43067, 3835}, {47672, 23813}
X(48026) = X(i)-complementary conjugate of X(j) for these (i,j): {42, 38967}, {39708, 21252}, {39983, 116}, {43356, 3741}
X(48026) = X(45100)-Ceva conjugate of X(11)
X(48026) = X(i)-isoconjugate of X(j) for these (i,j): {2, 28148}, {100, 39948}, {101, 28626}, {109, 30711}
X(48026) = X(i)-Dao conjugate of X(j) for these (i, j): (11, 30711), (1015, 28626), (8054, 39948), (32664, 28148)
X(48026) = crosspoint of X(i) and X(j) for these (i,j): {100, 27789}, {651, 5665}
X(48026) = crosssum of X(i) and X(j) for these (i,j): {513, 16884}, {650, 3601}
X(48026) = crossdifference of every pair of points on line {1, 3683}
X(48026) = barycentric product X(i)*X(j) for these {i,j}: {1, 28147}, {513, 9780}, {514, 3247}, {522, 3339}, {649, 42029}, {661, 25507}, {3737, 3947}, {3951, 7649}
X(48026) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 28148}, {513, 28626}, {649, 39948}, {650, 30711}, {3247, 190}, {3339, 664}, {3951, 4561}, {9780, 668}, {25507, 799}, {28147, 75}, {42029, 1978}
X(48026) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 661, 47777}, {661, 4979, 4893}, {693, 47759, 4940}, {3835, 43067, 45320}, {4369, 47760, 31250}, {4394, 4893, 650}, {4776, 7192, 4885}, {4790, 47777, 650}, {4893, 4979, 4394}, {4932, 25666, 47761}, {6590, 14321, 4944}, {6590, 47764, 14321}, {14300, 46393, 650}, {20295, 47774, 47666}, {21127, 40137, 650}, {31147, 47672, 23813}, {31290, 47759, 693}


X(48027) = X(44)X(513)∩X(514)X(4522)

Barycentrics    a*(b - c)*(a^2 + 2*a*b + 3*b^2 + 2*a*c + 4*b*c + 3*c^2) : :
X(48027) = X[1] - 3 X[14349], X[649] - 3 X[47810], 3 X[650] - 2 X[4782], 3 X[661] - X[4724], 5 X[661] - 3 X[47826], 3 X[1491] - X[4784], 2 X[4394] - 3 X[47827], 5 X[4724] - 9 X[47826], X[4979] - 3 X[47828], 2 X[4369] - 3 X[47802], X[4380] - 3 X[47825], 3 X[4776] - X[47694], X[4804] - 3 X[31147], 2 X[4874] - 3 X[47760], 11 X[5550] - 9 X[47820], X[7192] - 3 X[44429], 7 X[9780] - 9 X[47814], 3 X[21301] - X[47721], 4 X[25666] - 3 X[47803], 3 X[30565] - X[47696], 5 X[30835] - 3 X[47813], X[47697] - 3 X[47821]

X(48027) lies on these lines: {1, 8678}, {44, 513}, {514, 4522}, {523, 4106}, {830, 4794}, {876, 29198}, {2786, 4818}, {3309, 4983}, {3835, 7662}, {3837, 43067}, {4010, 4940}, {4088, 4802}, {4122, 28894}, {4369, 47802}, {4380, 47825}, {4468, 4977}, {4490, 8712}, {4762, 4824}, {4776, 47694}, {4777, 47701}, {4785, 4913}, {4804, 31147}, {4874, 47760}, {4932, 25380}, {5550, 47820}, {7192, 44429}, {9780, 47814}, {21301, 47721}, {24718, 24720}, {25666, 47803}, {28151, 47700}, {28165, 47702}, {30565, 47696}, {30835, 47813}, {46403, 47666}, {47652, 47698}, {47687, 47699}, {47697, 47821}

X(48027) = midpoint of X(i) and X(j) for these {i,j}: {2254, 4813}, {4824, 24719}, {46403, 47666}, {47652, 47698}, {47687, 47699}
X(48027) = reflection of X(i) in X(j) for these {i,j}: {4010, 4940}, {4790, 9508}, {4932, 25380}, {7662, 3835}, {43067, 3837}
X(48027) = X(i)-line conjugate of X(j) for these (i,j): {8678, 1}, {11726, 509}


X(48028) = X(44)X(513)∩X(514)X(4806)

Barycentrics    a*(b - c)*(3*a*b + 2*b^2 + 3*a*c + 5*b*c + 2*c^2) : :
X(48028) = X[659] - 3 X[47826], 3 X[661] - X[1491], 5 X[661] - X[2254], 7 X[661] - 3 X[47810], 5 X[1491] - 3 X[2254], 7 X[1491] - 9 X[47810], 7 X[2254] - 15 X[47810], X[4784] - 3 X[4893], X[4813] + 3 X[47826], X[764] - 3 X[14349], X[4122] - 3 X[47769], X[47699] + 3 X[47769], 3 X[4776] - X[21146], 3 X[4800] + X[4963], 5 X[4874] - 6 X[45337], X[4960] - 3 X[47875], X[7192] - 3 X[47822], X[24719] - 3 X[47759], X[31290] + 3 X[47821], X[47694] + 3 X[47774]

X(48028) lies on these lines: {44, 513}, {514, 4806}, {693, 18158}, {764, 14349}, {3835, 4977}, {3837, 4778}, {4010, 4802}, {4083, 4983}, {4122, 47699}, {4444, 45666}, {4490, 4822}, {4776, 21146}, {4777, 4824}, {4800, 4963}, {4804, 28151}, {4874, 28840}, {4960, 47875}, {7192, 47822}, {7653, 30765}, {8678, 11247}, {23818, 31946}, {24719, 47759}, {24720, 28209}, {29204, 47701}, {31290, 47821}, {47694, 47774}

X(48028) = midpoint of X(i) and X(j) for these {i,j}: {659, 4813}, {4010, 47666}, {4122, 47699}, {4490, 4822}
X(48028) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4813, 47826, 659}, {47699, 47769, 4122}


X(48029) = X(44)X(513)∩X(514)X(3716)

Barycentrics    a*(b - c)*(a^2 - 2*a*b - b^2 - 2*a*c - 4*b*c - c^2) : :
X(48029) = X[649] - 3 X[47811], 3 X[650] - X[7659], 3 X[650] - 2 X[9508], X[661] - 3 X[47826], X[2254] - 3 X[4893], X[2526] - 3 X[47777], X[4724] + 3 X[47826], X[693] - 3 X[47821], 2 X[3676] - 3 X[47799], 2 X[3837] - 3 X[47760], 2 X[4369] - 3 X[47803], 4 X[4521] - 3 X[47807], 3 X[4776] - X[46403], X[4801] - 3 X[47840], 2 X[4885] - 3 X[47822], X[21146] - 3 X[47822], X[4978] - 3 X[47838], X[7192] - 3 X[47804], 2 X[24720] - 3 X[47802], 4 X[25666] - 3 X[47802], 2 X[25380] - 3 X[47778], 3 X[30565] - X[47690], 3 X[30709] - X[47721], 5 X[30835] - 3 X[47812], 5 X[31209] - 3 X[47824], 4 X[31287] - 3 X[47823], X[31290] + 3 X[47805], X[47672] - 3 X[47832], X[47675] - 3 X[47834], X[47676] - 3 X[47797], X[47703] - 3 X[47874]

X(48029) lies on these lines: {44, 513}, {514, 3716}, {523, 4468}, {693, 47821}, {905, 6372}, {1019, 6050}, {2533, 20317}, {3309, 4705}, {3667, 4913}, {3669, 29198}, {3676, 47799}, {3737, 18200}, {3837, 47760}, {3900, 4490}, {4010, 4762}, {4040, 8678}, {4088, 4777}, {4106, 4806}, {4129, 29186}, {4160, 4794}, {4369, 4778}, {4401, 15309}, {4458, 28851}, {4498, 4822}, {4521, 47807}, {4775, 14077}, {4776, 46403}, {4785, 4830}, {4801, 47840}, {4802, 47701}, {4809, 28910}, {4833, 9001}, {4874, 4977}, {4885, 21146}, {4940, 24719}, {4978, 47838}, {7192, 47804}, {7650, 29771}, {8651, 8672}, {13246, 28855}, {14475, 28220}, {21051, 29246}, {21116, 28195}, {24720, 25666}, {25380, 47778}, {26275, 28878}, {27929, 28859}, {28151, 47702}, {28165, 47700}, {28209, 47761}, {28225, 31286}, {28840, 45673}, {30565, 47690}, {30709, 47721}, {30835, 47812}, {31209, 47824}, {31287, 47823}, {31290, 47805}, {47660, 47699}, {47666, 47694}, {47672, 47832}, {47675, 47834}, {47676, 47797}, {47695, 47698}, {47703, 47874}

X(48029) = midpoint of X(i) and X(j) for these {i,j}: {661, 4724}, {4498, 4822}, {47660, 47699}, {47666, 47694}, {47695, 47698}
X(48029) = reflection of X(i) in X(j) for these {i,j}: {1019, 6050}, {2533, 20317}, {4106, 4806}, {4784, 4394}, {4790, 4782}, {7659, 9508}, {7662, 3716}, {21146, 4885}, {24719, 4940}, {24720, 25666}, {43067, 4874}
X(48029) = crossdifference of every pair of points on line {1, 5021}
X(48029) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 7659, 9508}, {4724, 47826, 661}, {21146, 47822, 4885}, {24720, 25666, 47802}


X(48030) = X(44)X(513)∩X(514)X(3837)

Barycentrics    a*(b - c)*(a*b + 2*b^2 + a*c + 3*b*c + 2*c^2) : :
X(48030) = X[649] - 3 X[47827], X[659] - 3 X[4893], 3 X[661] + X[2254], X[661] + 3 X[47810], 3 X[1491] - X[2254], X[1491] - 3 X[47810], X[2254] - 9 X[47810], X[2526] + 3 X[47777], X[4784] - 3 X[47828], X[4813] + 3 X[47828], X[1019] - 3 X[47888], X[2533] - 3 X[47814], X[3716] - 3 X[45315], X[4010] - 3 X[4776], 3 X[4379] - 5 X[30795], 3 X[4448] - X[47697], X[4810] + 3 X[4948], X[4810] - 3 X[31147], X[4932] - 3 X[47830], X[7192] - 3 X[47823], X[7662] - 3 X[47760], X[16892] - 3 X[47877], X[17166] - 3 X[47841], X[20295] + 3 X[47825], X[21146] - 3 X[44429], 3 X[44429] + X[47666], X[23770] - 3 X[47756], 2 X[25380] - 3 X[45323], 7 X[27138] - 3 X[47834], 5 X[30835] - 3 X[47833], 3 X[31149] - X[47724], 2 X[31286] - 3 X[47829], X[31290] + 3 X[47824], X[43067] - 3 X[47802], 3 X[44435] + X[47698], X[46403] + 3 X[47775], X[47690] + 3 X[47781], X[47694] - 3 X[47822], X[47699] + 3 X[47808]

X(48030) lies on these lines: {44, 513}, {514, 3837}, {522, 4806}, {523, 3835}, {693, 4036}, {784, 4129}, {824, 18004}, {1019, 47888}, {1734, 4983}, {2530, 29198}, {2533, 47814}, {2605, 23655}, {3716, 45315}, {3797, 4010}, {4083, 4705}, {4088, 29204}, {4122, 45746}, {4379, 30795}, {4448, 47697}, {4486, 28894}, {4490, 29226}, {4560, 29152}, {4728, 28151}, {4762, 45676}, {4770, 29350}, {4804, 28165}, {4810, 4948}, {4874, 25666}, {4913, 29328}, {4932, 47830}, {4977, 20316}, {7192, 25636}, {7662, 47760}, {14315, 14426}, {16892, 47877}, {17166, 47841}, {17494, 24719}, {20295, 47825}, {21124, 29202}, {21146, 28195}, {21196, 29078}, {21301, 29274}, {23770, 47756}, {23818, 44316}, {24674, 47844}, {25380, 28840}, {25381, 28602}, {27138, 47834}, {27674, 31947}, {28199, 47672}, {28220, 31992}, {30835, 47833}, {31149, 47724}, {31286, 47829}, {31290, 47824}, {43067, 47802}, {44435, 47698}, {46403, 47775}, {47690, 47781}, {47694, 47822}, {47699, 47808}

X(48030) = midpoint of X(i) and X(j) for these {i,j}: {661, 1491}, {693, 4824}, {1734, 4983}, {4122, 45746}, {4705, 14349}, {4784, 4813}, {4948, 31147}, {17494, 24719}, {21146, 47666}
X(48030) = reflection of X(i) in X(j) for these {i,j}: {4782, 650}, {4874, 25666}
X(48030) = crossdifference of every pair of points on line {1, 21793}
X(48030) = barycentric product X(513)*X(29593)
X(48030) = barycentric quotient X(29593)/X(668)
X(48030) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 47810, 1491}, {4813, 47828, 4784}, {44429, 47666, 21146}


X(48031) = X(6)X(832)∩X(44)X(513)

Barycentrics    a*(b - c)*(a^2*b + b^3 + a^2*c - a*b*c + b^2*c + b*c^2 + c^3) : :
X(48031) = 3 X[4776] - X[15413]

X(4) lies on these lines: {6, 832}, {44, 513}, {834, 24290}, {918, 14349}, {2530, 6586}, {4705, 9313}, {4776, 15413}, {6004, 21007}, {6133, 17303}, {9013, 20980}, {21834, 29204}, {23885, 25259}

X(48031) = midpoint of X(2484) and X(4813)
X(48031) = reflection of X(2483) in X(2509)
X(48031) = X(2)-isoconjugate of X(29048)
X(48031) = X(32664)-Dao conjugate of X(29048)
X(48031) = crossdifference of every pair of points on line {1, 9021}
X(48031) = barycentric product X(i)*X(j) for these {i,j}: {1, 29047}, {513, 29679}
X(48031) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 29048}, {29047, 75}, {29679, 668}


X(48032) = X(1)X(2832)∩X(44)X(513)

Barycentrics    a*(b - c)*(2*a^2 - a*b + b^2 - a*c - 2*b*c + c^2) : :
X(48032) = 3 X[649] - 2 X[7659], 4 X[659] - 3 X[1635], 3 X[659] - 2 X[9508], 5 X[661] - 6 X[47826], 2 X[1491] - 3 X[47811], 3 X[1635] - 2 X[2254], 9 X[1635] - 8 X[9508], 3 X[2254] - 4 X[9508], 2 X[2526] - 3 X[4893], 5 X[4724] - 3 X[47826], 4 X[676] - 3 X[6545], 2 X[764] - 3 X[14413], 4 X[1960] - 3 X[14413], 2 X[2505] - 3 X[14425], 2 X[3669] - 3 X[8643], 2 X[3676] - 3 X[47801], 4 X[3716] - 3 X[4728], 3 X[4728] - 2 X[46403], 2 X[3776] - 3 X[47798], 2 X[3837] - 3 X[4448], 2 X[4369] - 3 X[47805], 3 X[4453] - 4 X[13246], 4 X[4458] - 3 X[21115], 2 X[4458] - 3 X[44433], 4 X[4874] - 3 X[47812], 2 X[4925] - 3 X[47884], 8 X[8689] - 5 X[24924], 4 X[8689] - 3 X[47804], 4 X[24720] - 5 X[24924], 2 X[24720] - 3 X[47804], 5 X[24924] - 6 X[47804], 2 X[17072] - 3 X[47815], 2 X[21146] - 3 X[47813], 2 X[21343] - 3 X[23057], 2 X[23789] - 3 X[47818], 5 X[30795] - 6 X[45666]

X(48032) lies on these lines: {1, 2832}, {8, 28521}, {44, 513}, {100, 1293}, {105, 1477}, {244, 1357}, {291, 23834}, {514, 47692}, {522, 47700}, {676, 6545}, {764, 1960}, {812, 17794}, {830, 13259}, {884, 21003}, {891, 4895}, {900, 4088}, {1027, 1438}, {1282, 2820}, {1308, 32665}, {1643, 8658}, {1769, 4491}, {2488, 6363}, {2505, 14425}, {2814, 38329}, {2826, 10609}, {2976, 3021}, {3309, 4498}, {3667, 4380}, {3669, 8643}, {3676, 47801}, {3716, 4728}, {3722, 21320}, {3738, 13256}, {3776, 47798}, {3803, 45695}, {3804, 8672}, {3835, 47685}, {3837, 4448}, {3887, 21385}, {3904, 5592}, {4017, 8642}, {4041, 6004}, {4063, 42325}, {4367, 23738}, {4369, 47805}, {4401, 4905}, {4453, 13246}, {4458, 4778}, {4462, 28470}, {4804, 29362}, {4809, 28209}, {4874, 47812}, {4925, 47884}, {4977, 21125}, {6003, 13258}, {6615, 8641}, {8659, 20662}, {8689, 24720}, {17072, 47815}, {21129, 28294}, {21132, 29240}, {21146, 47813}, {21201, 47680}, {21343, 23057}, {23764, 30725}, {23789, 47818}, {24721, 27929}, {28161, 47664}, {30795, 45666}, {47672, 47694}
X(48032) = reflection of X(i) in X(j) for these {i,j}: {661, 4724}, {764, 1960}, {1769, 4491}, {2254, 659}, {3904, 5592}, {4729, 4498}, {4895, 6161}, {4905, 4401}, {21115, 44433}, {23738, 4367}, {23764, 30725}, {24720, 8689}, {24721, 27929}, {38325, 13266}, {46403, 3716}, {47672, 47694}, {47680, 21201}, {47685, 3835}, {47705, 47695}
X(48032) = X(i)-Ceva conjugate of X(j) for these (i,j): {105, 244}, {518, 27846}, {36041, 31}
X(48032) = X(i)-isoconjugate of X(j) for these (i,j): {2, 6078}, {100, 1280}, {101, 36807}, {518, 39272}, {644, 43760}, {765, 35355}, {1477, 3699}, {1810, 1897}, {3939, 35160}
X(48032) = X(i)-Dao conjugate of X(j) for these (i, j): (513, 35355), (1015, 36807), (8054, 1280), (16593, 668), (32664, 6078), (34467, 1810), (35111, 646), (39048, 190), (40617, 35160)
X(48032) = crosspoint of X(i) and X(j) for these (i,j): {269, 36146}, {513, 1027}
X(48032) = crosssum of X(i) and X(j) for these (i,j): {100, 1026}, {513, 4864}, {649, 2340}, {1280, 35355}, {2348, 4162}, {3912, 4468}
X(48032) = crossdifference of every pair of points on line {1, 644}
X(48032) = X(2832)-line conjugate of X(1)
X(48032) = barycentric product X(i)*X(j) for these {i,j}: {1, 6084}, {75, 8659}, {513, 3008}, {514, 1279}, {1027, 16593}, {1358, 23704}, {2348, 3676}, {2976, 8056}, {3021, 37626}, {3669, 5853}, {5519, 36041}, {8647, 24002}, {17924, 20780}
X(48032) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 6078}, {513, 36807}, {649, 1280}, {1015, 35355}, {1279, 190}, {1357, 37626}, {1438, 39272}, {2348, 3699}, {2976, 18743}, {3008, 668}, {3669, 35160}, {5853, 646}, {6084, 75}, {8647, 644}, {8659, 1}, {20662, 1026}, {20780, 1332}, {22383, 1810}, {23704, 4076}, {43924, 43760}
X(48032) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {659, 2254, 1635}, {764, 1960, 14413}, {3716, 46403, 4728}, {8689, 24720, 47804}, {24720, 47804, 24924}


X(48033) = X(44)X(513)∩X(514)X(15416)

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

X(48033) lies on these lines: {44, 513}, {514, 15416}, {832, 20980}, {918, 4079}, {2530, 3709}, {3063, 6004}, {3762, 21099}, {3777, 21348}, {3835, 15413}, {3837, 21960}, {4041, 9313}, {4171, 17458}, {4885, 28024}, {4978, 22044}, {6371, 24290}, {8672, 47133}, {14349, 23785}, {14430, 21055}

X(48033) = reflection of X(i) in X(j) for these {i,j}: {649, 2509}, {4979, 2483}, {15413, 3835}
X(48033) = X(2)-isoconjugate of X(29289)
X(48033) = X(32664)-Dao conjugate of X(29289)
X(48033) = crossdifference of every pair of points on line {1, 34378}
X(48033) = barycentric product X(1)*X(29288)
X(48033) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 29289}, {29288, 75}
X(48033) = {X(3768),X(8061)}-harmonic conjugate of X(17420)


X(48034) = X(513)X(4468)∩X(514)X(4838)

Barycentrics    (b - c)*(-3*a^2 - 6*a*b + b^2 - 6*a*c + c^2) : :
X(48034) = 5 X[4468] - 4 X[47890], 5 X[44449] - X[47658], 3 X[44449] - X[47665], 3 X[47658] - 5 X[47665], 3 X[31290] - X[47667], 3 X[661] - 2 X[3798], 4 X[661] - 3 X[47785], 8 X[3798] - 9 X[47785], 2 X[3676] - 3 X[47759], 5 X[4025] - 6 X[47880], 2 X[4369] - 3 X[47764], 4 X[4521] - 3 X[47763], 3 X[4813] - X[16892], 2 X[4897] - 3 X[47783], 2 X[4932] - 3 X[47765], 4 X[4940] - 3 X[21183], 2 X[7192] - 3 X[47787], 4 X[14321] - 3 X[47789], 2 X[43067] - 3 X[47786]

X(48034) lies on these lines: {513, 4468}, {514, 4838}, {522, 31290}, {661, 3798}, {3667, 47666}, {3676, 47759}, {4025, 47880}, {4106, 28902}, {4369, 47764}, {4500, 28840}, {4521, 47763}, {4778, 25259}, {4813, 16892}, {4897, 47783}, {4932, 47765}, {4940, 21183}, {4962, 47661}, {6006, 17494}, {6332, 15309}, {7192, 47787}, {14321, 47789}, {20295, 28878}, {23729, 28910}, {28225, 47660}, {28229, 47659}, {28867, 45745}, {43067, 47786}


X(48035) = X(513)X(4468)∩X(514)X(47685)

Barycentrics    (b - c)*(-3*a^3 - a^2*b - 5*a*b^2 + b^3 - a^2*c - 4*a*b*c + b^2*c - 5*a*c^2 + b*c^2 + c^3) : :
X(48035) = 4 X[1491] - 3 X[47785], 4 X[4521] - 3 X[47805], 4 X[25666] - 3 X[47801], 2 X[47694] - 3 X[47787]

X(48035) lies on these lines: {513, 4468}, {514, 47685}, {522, 17161}, {661, 3667}, {830, 6332}, {1491, 47785}, {2526, 4025}, {3239, 47697}, {4088, 4778}, {4521, 47805}, {4724, 6006}, {4790, 4925}, {25666, 47801}, {28147, 47650}, {47694, 47787}

X(48035) = reflection of X(i) in X(j) for these {i,j}: {4025, 2526}, {4790, 4925}, {47697, 3239}


X(48036) = X(513)X(4468)∩X(514)X(4170)

Barycentrics    (b - c)*(a^3 - 5*a^2*b - a*b^2 + b^3 - 5*a^2*c - 8*a*b*c + b^2*c - a*c^2 + b*c^2 + c^3) : :
X(48036) = 2 X[3676] - 3 X[47821], 2 X[3798] - 3 X[47811], 4 X[4521] - 3 X[47824], 2 X[21146] - 3 X[47787], 2 X[24720] - 3 X[47765]

X(48036) lies on these lines: {513, 4468}, {514, 4170}, {522, 47698}, {3676, 47821}, {3798, 47811}, {4106, 4977}, {4120, 4778}, {4521, 47824}, {4724, 28846}, {6332, 6372}, {21146, 47787}, {23731, 28229}, {24720, 47765}, {28851, 47123}, {28878, 47694}


X(48037) = X(513)X(3716)∩X(514)X(4170)

Barycentrics    (b - c)*(-5*a^2*b - a*b^2 - 5*a^2*c - 5*a*b*c + b^2*c - a*c^2 + b*c^2) : :
X(48037) = 5 X[3835] - 4 X[3837], 3 X[3835] - 4 X[4806], 3 X[3835] - 2 X[24720], 3 X[3837] - 5 X[4806], 6 X[3837] - 5 X[24720], 7 X[3624] - 9 X[47838], 2 X[4782] - 3 X[45673], 2 X[4784] - 3 X[45313], 2 X[31286] - 3 X[47821]

X(48037) lies on these lines: {10, 6005}, {513, 3716}, {514, 4170}, {522, 4824}, {661, 3667}, {693, 28225}, {1491, 6006}, {3624, 47838}, {3783, 4724}, {4010, 4778}, {4782, 45673}, {4784, 45313}, {7659, 25666}, {28161, 47666}, {28855, 47123}, {30519, 47701}, {31286, 47821}

X(48037) = reflection of X(i) in X(j) for these {i,j}: {4932, 3716}, {7659, 25666}, {24720, 4806}
X(48037) = {X(4806),X(24720)}-harmonic conjugate of X(3835)


X(48038) = X(513)X(4468)∩X(514)X(4024)

Barycentrics    (b - c)*(-a^2 - 4*a*b + b^2 - 4*a*c + c^2) : :
X(48038) = 3 X[4468] - 2 X[47890], 3 X[4813] - X[23731], 3 X[20295] - X[47650], 3 X[25259] - X[47659], 3 X[31290] + X[47659], 3 X[44449] + X[47661], X[47661] - 3 X[47666], 4 X[650] - 3 X[4786], 4 X[661] - 3 X[47783], 5 X[661] - 3 X[47886], 2 X[4025] - 3 X[47783], 5 X[4025] - 6 X[47886], 5 X[47783] - 4 X[47886], 2 X[693] - 3 X[47786], 2 X[3239] - 3 X[47769], 4 X[3239] - 3 X[47789], X[7192] - 3 X[47769], 2 X[7192] - 3 X[47789], 2 X[3676] - 3 X[4776], 2 X[3798] - 3 X[4893], 4 X[3835] - 3 X[21183], 2 X[3835] - 3 X[47764], 2 X[4369] - 3 X[47765], 4 X[4521] - 3 X[47762], 2 X[4765] - 3 X[47775], 2 X[4897] - 3 X[47785], 2 X[4932] - 3 X[47766], 4 X[7658] - 3 X[47755], 4 X[14321] - 3 X[47787], 2 X[43067] - 3 X[47787], 2 X[17069] - 3 X[47777], 4 X[25666] - 3 X[47758], 4 X[43061] - 3 X[47763], X[45746] - 3 X[47774], X[47676] - 3 X[47759]

X(48038) lies on these lines: {513, 4468}, {514, 4024}, {522, 44449}, {650, 4786}, {661, 4025}, {693, 28878}, {2786, 45745}, {3239, 7192}, {3667, 17494}, {3676, 4776}, {3776, 28871}, {3798, 4893}, {3835, 21183}, {4369, 28886}, {4380, 6006}, {4521, 47762}, {4765, 47775}, {4778, 47660}, {4841, 28898}, {4897, 47785}, {4932, 47766}, {4940, 21104}, {4979, 11068}, {6005, 44448}, {6590, 28840}, {7658, 47755}, {14207, 35518}, {14321, 28902}, {17069, 47777}, {21196, 28906}, {25666, 47758}, {25899, 25924}, {25980, 26545}, {28147, 47665}, {28161, 47667}, {28169, 47668}, {28191, 47658}, {28225, 47772}, {43061, 47763}, {45746, 47774}, {47676, 47759}

X(48038) = midpoint of X(i) and X(j) for these {i,j}: {25259, 31290}, {44449, 47666}
X(48038) = reflection of X(i) in X(j) for these {i,j}: {4025, 661}, {4979, 11068}, {7192, 3239}, {21104, 4940}, {21183, 47764}, {43067, 14321}, {47789, 47769}
X(48038) = X(43533)-anticomplementary conjugate of X(21293)
X(48038) = crosssum of X(649) and X(2271)
X(48038) = crossdifference of every pair of points on line {2308, 16502}
X(48038) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 4025, 47783}, {3239, 7192, 47789}, {7192, 47769, 3239}, {14321, 43067, 47787}


X(48039) = X(513)X(4468)∩X(514)X(4088)

Barycentrics    (b - c)*(-a^3 - a^2*b - 3*a*b^2 + b^3 - a^2*c - 4*a*b*c + b^2*c - 3*a*c^2 + b*c^2 + c^3) : :
X(48039) = 3 X[21301] - X[47722], 2 X[676] - 3 X[47760], 3 X[905] - 2 X[39545], 2 X[3676] - 3 X[44429], 2 X[3716] - 3 X[47765], 2 X[3798] - 3 X[47828], 4 X[3837] - 3 X[21183], 2 X[4010] - 3 X[47786], 2 X[4369] - 3 X[47806], 2 X[4458] - 3 X[47757], 4 X[4521] - 3 X[47804], 2 X[4765] - 3 X[47825], 3 X[4776] - X[47695], 3 X[4786] - 4 X[9508], X[7192] - 3 X[47808], 2 X[7662] - 3 X[47787], 2 X[13246] - 3 X[47778], 3 X[14349] - X[47727], 2 X[14837] - 3 X[47814], 2 X[21188] - 3 X[47816], 4 X[25380] - 3 X[47758], 4 X[25666] - 3 X[47800], 3 X[30565] - X[47697]

X(48039) lies on these lines: {512, 44448}, {513, 4468}, {514, 4088}, {522, 661}, {523, 4106}, {676, 47760}, {905, 39545}, {918, 2526}, {1491, 4025}, {2254, 28846}, {2517, 14208}, {3239, 47694}, {3667, 4724}, {3676, 44429}, {3716, 47765}, {3798, 47828}, {3835, 47123}, {3837, 21183}, {4010, 47786}, {4041, 28478}, {4129, 21185}, {4367, 25901}, {4369, 47806}, {4458, 47757}, {4521, 47804}, {4522, 6590}, {4765, 47825}, {4776, 47695}, {4786, 9508}, {4925, 7659}, {4962, 47826}, {6332, 8678}, {7192, 47808}, {7662, 47787}, {13246, 47778}, {14349, 47727}, {14837, 47814}, {20906, 23684}, {21186, 23806}, {21188, 47816}, {25380, 47758}, {25666, 47800}, {28147, 47670}, {28161, 47701}, {28169, 47702}, {28878, 31131}, {30565, 47697}, {47666, 47687}

X(48039) = midpoint of X(i) and X(j) for these {i,j}: {46403, 47698}, {47666, 47687}
X(48039) = reflection of X(i) in X(j) for these {i,j}: {4025, 1491}, {6590, 4522}, {7659, 4925}, {21185, 4129}, {47123, 3835}, {47694, 3239}
X(48039) = crossdifference of every pair of points on line {1468, 16502}


X(48040) = X(513)X(4468)∩X(514)X(4010)

Barycentrics    (b - c)*(a^3 - 3*a^2*b - a*b^2 + b^3 - 3*a^2*c - 6*a*b*c + b^2*c - a*c^2 + b*c^2 + c^3) : :
X(48040) = 2 X[3676] - 3 X[47822], 2 X[3837] - 3 X[47765], 4 X[4521] - 3 X[47823], 2 X[13246] - 3 X[45673], X[16892] - 3 X[47826], X[46403] - 3 X[47769], X[47676] - 3 X[47821], X[47686] - 3 X[47759], X[47690] - 3 X[47772]

X(48040) lies on these lines: {513, 4468}, {514, 4010}, {659, 28846}, {2977, 7659}, {3239, 21146}, {3676, 47822}, {3716, 28851}, {3837, 47765}, {4521, 47823}, {4784, 11068}, {4830, 28867}, {4944, 4977}, {6332, 29198}, {13246, 45673}, {16892, 47826}, {23813, 28195}, {31290, 47696}, {46403, 47769}, {47676, 47821}, {47686, 47759}, {47690, 47772}

X(48040) = midpoint of X(31290) and X(47696)
X(48040) = reflection of X(i) in X(j) for these {i,j}: {4784, 11068}, {7659, 2977}, {21146, 3239}


X(48041) = X(513)X(3716)∩X(514)X(4024)

Barycentrics    (b - c)*(-2*a^2 - 3*a*b - 3*a*c + b*c) : :
X(48041) = 3 X[3835] - 2 X[4369], 5 X[3835] - 4 X[4885], 7 X[3835] - 6 X[4928], 3 X[3835] - 4 X[4940], 13 X[3835] - 8 X[7653], 4 X[3835] - 3 X[47779], 5 X[4369] - 6 X[4885], 7 X[4369] - 9 X[4928], 4 X[4369] - 3 X[4932], 13 X[4369] - 12 X[7653], 8 X[4369] - 9 X[47779], 14 X[4885] - 15 X[4928], 8 X[4885] - 5 X[4932], 3 X[4885] - 5 X[4940], 13 X[4885] - 10 X[7653], 16 X[4885] - 15 X[47779], 12 X[4928] - 7 X[4932], 9 X[4928] - 14 X[4940], 39 X[4928] - 28 X[7653], 8 X[4928] - 7 X[47779], 3 X[4932] - 8 X[4940], 13 X[4932] - 16 X[7653], 2 X[4932] - 3 X[47779], 13 X[4940] - 6 X[7653], 16 X[4940] - 9 X[47779], 32 X[7653] - 39 X[47779], X[4382] + 3 X[4813], X[4382] - 3 X[20295], 5 X[4382] - 3 X[26824], 5 X[4813] + X[26824], 3 X[4813] - X[31290], 5 X[20295] - X[26824], 3 X[20295] + X[31290], 3 X[26824] + 5 X[31290], 5 X[649] - 7 X[27115], X[649] - 3 X[47759], 2 X[649] - 3 X[47778], 7 X[27115] - 15 X[47759], 14 X[27115] - 15 X[47778], 3 X[661] - X[4380], 5 X[661] - 3 X[31150], 5 X[4380] - 9 X[31150], 3 X[4379] - 5 X[26798], 2 X[4394] - 3 X[45315], 3 X[4776] - X[4979], 3 X[4776] - 2 X[31286], 2 X[4790] - 3 X[45313], 4 X[25666] - 3 X[45313], 3 X[4893] - X[26853], 3 X[4958] - X[47665], X[7192] - 3 X[31147], 5 X[24924] - 6 X[45339], 5 X[30835] - 3 X[47763]

X(48041) lies on these lines: {513, 3716}, {514, 4024}, {649, 27115}, {661, 4380}, {1019, 28398}, {3004, 28867}, {3667, 21196}, {3700, 28859}, {4106, 28840}, {4129, 30094}, {4379, 26798}, {4394, 45315}, {4408, 4842}, {4500, 4977}, {4776, 4979}, {4778, 24719}, {4790, 25666}, {4810, 28147}, {4822, 28470}, {4893, 26853}, {4949, 28894}, {4958, 47665}, {4963, 28191}, {7192, 31147}, {16892, 28906}, {17069, 39386}, {20979, 29807}, {20983, 29350}, {21104, 28886}, {23729, 28851}, {24721, 45661}, {24924, 45339}, {28225, 46403}, {30519, 44449}, {30764, 47805}, {30835, 47763}, {38389, 44312}

X(48041) = midpoint of X(i) and X(j) for these {i,j}: {4382, 31290}, {4813, 20295}, {23731, 25259}
X(48041) = reflection of X(i) in X(j) for these {i,j}: {4369, 4940}, {4790, 25666}, {4932, 3835}, {4979, 31286}, {47778, 47759}
X(48041) = X(i)-complementary conjugate of X(j) for these (i,j): {100, 28651}, {27789, 11}, {28196, 2}, {28650, 116}
X(48041) = crossdifference of every pair of points on line {2176, 2308}
X(48041) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3835, 4932, 47779}, {4369, 4940, 3835}, {4382, 4813, 31290}, {4776, 4979, 31286}, {4790, 25666, 45313}, {20295, 31290, 4382}


X(48042) = X(513)X(3716)∩X(514)X(4088)

Barycentrics    (b - c)*(-2*a^3 - a^2*b - 3*a*b^2 - a^2*c - a*b*c + b^2*c - 3*a*c^2 + b*c^2) : :
X(48042) = 2 X[3716] - 3 X[3835], 4 X[3837] - 3 X[47779], X[4474] - 3 X[21301], X[4810] - 3 X[24719], 2 X[659] - 3 X[47778], 3 X[4728] - X[47697], 2 X[4782] - 3 X[47830], 2 X[8689] - 3 X[47822], 2 X[13246] - 3 X[47757], 4 X[25380] - 3 X[45313], 5 X[30835] - 3 X[47805], 2 X[31286] - 3 X[44429]

X(48042) lies on these lines: {513, 3716}, {514, 4088}, {522, 4810}, {659, 47778}, {661, 47685}, {667, 28399}, {812, 2526}, {2254, 4785}, {3239, 4813}, {3667, 4025}, {4382, 28161}, {4401, 27675}, {4522, 4977}, {4728, 47697}, {4782, 47830}, {4809, 6006}, {8689, 47822}, {13246, 47757}, {17496, 28525}, {25380, 45313}, {26824, 28155}, {28470, 47729}, {30835, 47805}, {31286, 44429}, {47651, 47700}

X(48042) = midpoint of X(i) and X(j) for these {i,j}: {661, 47685}, {4088, 47686}, {47651, 47700}
X(48042) = reflection of X(4932) in X(24720)
X(48042) = crossdifference of every pair of points on line {2176, 7296}


X(48043) = X(512)X(4147)∩X(513)X(3716)

Barycentrics    (b - c)*(-3*a^2*b - a*b^2 - 3*a^2*c - 3*a*b*c + b^2*c - a*c^2 + b*c^2) : :
X(48043) = 3 X[3835] - 2 X[3837], X[3837] - 3 X[4806], 4 X[3837] - 3 X[24720], 2 X[4369] - 3 X[47831], 4 X[4806] - X[24720], X[649] - 3 X[47821], 2 X[659] - 3 X[45673], X[1019] - 3 X[47838], X[2254] - 3 X[4776], X[4088] - 3 X[47769], 3 X[4120] - X[47690], 2 X[4378] - 3 X[45667], X[4380] - 3 X[47811], X[4784] - 3 X[47822], 2 X[31286] - 3 X[47822], X[4979] - 3 X[47804], X[7192] - 3 X[47832], X[7659] - 3 X[47760], 2 X[25380] - 3 X[47760], 2 X[9508] - 3 X[47778], X[17494] - 3 X[47826], 4 X[25666] - 3 X[47830], 5 X[30795] - 6 X[45339], 5 X[30835] - 3 X[47824], 3 X[31147] - X[46403], X[47703] - 3 X[47790]

X(48043) lies on these lines: {512, 4147}, {513, 3716}, {514, 4010}, {522, 661}, {649, 47821}, {659, 4785}, {693, 4778}, {1019, 47838}, {1491, 3667}, {2254, 4776}, {4024, 47699}, {4088, 47769}, {4120, 47690}, {4129, 6005}, {4378, 45667}, {4380, 47811}, {4391, 4822}, {4448, 25381}, {4458, 28846}, {4522, 14321}, {4724, 20295}, {4784, 31286}, {4804, 28147}, {4813, 47694}, {4824, 28161}, {4830, 6008}, {4979, 47804}, {4992, 29198}, {7192, 47832}, {7659, 25380}, {7662, 28840}, {9508, 47778}, {17494, 47826}, {18004, 29144}, {21146, 28225}, {22037, 29318}, {23731, 47696}, {23770, 28851}, {23808, 35353}, {25259, 47701}, {25666, 47830}, {28229, 47672}, {30795, 45339}, {30835, 47824}, {31147, 46403}, {47703, 47790}

X(48043) = midpoint of X(i) and X(j) for these {i,j}: {4024, 47699}, {4391, 4822}, {4724, 20295}, {4804, 47666}, {4813, 47694}, {23731, 47696}, {25259, 47701}
X(48043) = reflection of X(i) in X(j) for these {i,j}: {3835, 4806}, {4522, 14321}, {4784, 31286}, {4932, 4874}, {7659, 25380}, {17072, 4129}, {24720, 3835}
X(48043) = crossdifference of every pair of points on line {1468, 2176}
X(48043) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4784, 47822, 31286}, {7659, 47760, 25380}


X(48044) = X(2)X(2484)∩X(141)X(834)

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

X(48044) lies on these lines: {2, 2484}, {141, 834}, {513, 3716}, {649, 28423}, {661, 15413}, {832, 24285}, {2483, 31286}, {2509, 25666}, {4025, 8061}, {4129, 21188}, {17066, 21260}, {17072, 21262}, {20907, 21099}, {23874, 47842}, {24287, 28623}

X(48044) = midpoint of X(661) and X(15413)
X(48044) = reflection of X(i) in X(j) for these {i,j}: {2483, 31286}, {2509, 25666}
X(48044) = complement of X(2484)
X(48044) = complement of the isogonal conjugate of X(37215)
X(48044) = X(i)-complementary conjugate of X(j) for these (i,j): {2, 5517}, {651, 34261}, {1245, 16592}, {1310, 2}, {1472, 6377}, {2221, 1015}, {2281, 1084}, {2339, 1146}, {14258, 17421}, {30479, 26932}, {32691, 16583}, {36099, 6}, {37215, 10}
X(48044) = barycentric product X(3835)*X(27341)
X(48044) = barycentric quotient X(27341)/X(4598)
X(48044) = {X(3835),X(46399)}-harmonic conjugate of X(42327)


X(48045) = X(513)X(4401)∩X(514)X(4010)

Barycentrics    a*(b - c)*(4*a*b + 2*b^2 + 4*a*c + 5*b*c + 2*c^2) : :
X(48045) = 3 X[661] - X[1734], X[4063] - 3 X[47826], X[4960] - 3 X[47832], X[7192] - 3 X[47838], X[47711] - 3 X[47769]

X(48045) lies on these lines: {513, 4401}, {514, 4010}, {661, 1734}, {4040, 4813}, {4063, 47826}, {4170, 47666}, {4806, 4823}, {4822, 29350}, {4960, 47832}, {4961, 17494}, {7192, 47838}, {7265, 47699}, {23789, 28225}, {23815, 28209}, {28902, 34958}, {29358, 47701}, {47711, 47769}

X(48045) = midpoint of X(i) and X(j) for these {i,j}: {4040, 4813}, {4170, 47666}, {7265, 47699}
X(48045) = reflection of X(4823) in X(4806)
X(48045) = crossdifference of every pair of points on line {3989, 16777}
X(48045) = barycentric product X(1)*X(47668)
X(48045) = barycentric quotient X(47668)/X(75)


X(48046) = X(513)X(4468)∩X(514)X(3700)

Barycentrics    (b - c)*(-3*a*b + b^2 - 3*a*c + c^2) : :
X(48046) = 3 X[3700] - 2 X[4500], 3 X[25259] - X[47665], 3 X[25259] + X[47667], 5 X[25259] + X[47668], X[47665] + 3 X[47666], 5 X[47665] + 3 X[47668], 3 X[47666] - X[47667], 5 X[47666] - X[47668], 5 X[47667] - 3 X[47668], 2 X[649] - 3 X[47884], 3 X[650] - 2 X[3798], 4 X[3798] - 3 X[4897], 3 X[661] - X[16892], 3 X[3004] - 2 X[16892], 2 X[676] - 3 X[47821], X[693] - 3 X[47769], 2 X[14321] - 3 X[47769], 3 X[1638] - 4 X[25666], 3 X[1639] - 2 X[4369], 4 X[2487] - 5 X[31209], 4 X[2487] - 3 X[47755], 5 X[31209] - 3 X[47755], 4 X[2490] - 3 X[47762], 4 X[2516] - 3 X[4786], 4 X[2527] - 3 X[47763], 4 X[3239] - 3 X[47788], 2 X[43067] - 3 X[47788], 2 X[3676] - 3 X[47760], 2 X[3776] - 3 X[47756], 4 X[3835] - 3 X[4927], 3 X[4927] - 2 X[21104], 3 X[4024] - X[47670], 2 X[4025] - 3 X[47784], 3 X[4120] - X[47672], X[4467] - 3 X[47775], 4 X[4521] - 3 X[47761], 3 X[4776] - X[47676], 3 X[4800] - 2 X[47132], 2 X[4885] - 3 X[47765], 4 X[4885] - 3 X[47891], 3 X[4893] - 2 X[17069], 3 X[4931] - X[47671], 2 X[4932] - 3 X[47767], 2 X[4940] - 3 X[47764], X[31290] + 3 X[47772], X[47660] - 3 X[47772], X[4979] - 3 X[6546], X[7192] - 3 X[30565], 6 X[14425] - 5 X[27013], 2 X[21196] - 3 X[47876], 2 X[21212] - 3 X[45315], 2 X[23813] - 3 X[47786], 5 X[24924] - 6 X[45326], 5 X[26798] - 3 X[47871], X[26853] - 3 X[47892], 7 X[27138] - 6 X[45677], 4 X[31287] - 3 X[47758], 2 X[34958] - 3 X[47838], 2 X[43061] - 3 X[45670], X[47652] - 3 X[47759], X[47675] - 3 X[47790], X[47677] - 3 X[47781]

X(48046) lies on these lines: {513, 4468}, {514, 3700}, {523, 8663}, {649, 47884}, {650, 3798}, {661, 918}, {676, 47821}, {693, 14321}, {824, 4841}, {900, 17494}, {1638, 25666}, {1639, 4369}, {2487, 31209}, {2490, 47762}, {2499, 42341}, {2516, 4786}, {2527, 47763}, {2786, 4976}, {2977, 4784}, {2978, 9040}, {3239, 28878}, {3566, 4490}, {3676, 47760}, {3776, 47756}, {3835, 4927}, {4024, 47670}, {4025, 47784}, {4120, 47672}, {4380, 28217}, {4406, 30061}, {4462, 35519}, {4467, 47775}, {4521, 47761}, {4522, 4778}, {4776, 47676}, {4790, 11068}, {4800, 47132}, {4806, 23770}, {4833, 17498}, {4885, 28910}, {4893, 17069}, {4931, 47671}, {4932, 28886}, {4940, 47764}, {4977, 18004}, {4979, 6546}, {4983, 29288}, {4990, 17166}, {6084, 20295}, {7192, 28902}, {10015, 23806}, {14425, 27013}, {21196, 47876}, {21212, 45315}, {23813, 47786}, {24924, 45326}, {25902, 25923}, {25981, 25996}, {26798, 47871}, {26853, 39386}, {27138, 45677}, {28175, 47659}, {28179, 47658}, {28183, 47661}, {28898, 45745}, {31287, 47758}, {34958, 47838}, {43061, 45670}, {47652, 47759}, {47675, 47790}, {47677, 47781}

X(48046) = midpoint of X(i) and X(j) for these {i,j}: {17494, 44449}, {25259, 47666}, {31290, 47660}, {47665, 47667}
X(48046) = reflection of X(i) in X(j) for these {i,j}: {693, 14321}, {3004, 661}, {4784, 2977}, {4790, 11068}, {4897, 650}, {17166, 4990}, {21104, 3835}, {23770, 4806}, {43067, 3239}, {47890, 4468}, {47891, 47765}
X(48046) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 47769, 14321}, {3239, 43067, 47788}, {3835, 21104, 4927}, {25259, 47667, 47665}, {31209, 47755, 2487}, {31290, 47772, 47660}, {47665, 47666, 47667}


X(48047) = X(513)X(4468)∩X(514)X(4522)

Barycentrics    (b - c)*(b + c)*(-a^2 - 2*a*b + b^2 - 2*a*c + c^2) : :
X(48047) = 3 X[661] + X[47700], 3 X[661] - X[47701], 5 X[661] - X[47702], 3 X[4088] - X[47700], 3 X[4088] + X[47701], 5 X[4088] + X[47702], 3 X[4120] - X[4804], 5 X[47700] + 3 X[47702], 5 X[47701] - 3 X[47702], 2 X[676] - 3 X[47822], 3 X[1639] - 2 X[4874], 2 X[3676] - 3 X[47802], 2 X[4369] - 3 X[47807], 2 X[4458] - 3 X[47799], 4 X[25666] - 3 X[47799], X[4467] - 3 X[47825], 4 X[4521] - 3 X[47803], 3 X[4728] - X[47704], 3 X[4776] - X[47691], 2 X[4782] - 3 X[47884], X[7192] - 3 X[47809], 2 X[34958] - 3 X[47839], 3 X[14419] - 2 X[39545], X[16892] - 3 X[47810], 2 X[17069] - 3 X[47827], 3 X[21052] - X[23755], 3 X[30565] - X[47694], 5 X[30835] - 3 X[47887], 3 X[44429] - X[47676], X[47123] - 3 X[47765], 2 X[47132] - 3 X[47832], X[47695] - 3 X[47821]

X(48047) lies on these lines: {12, 7178}, {72, 512}, {355, 28473}, {513, 4468}, {514, 4522}, {523, 661}, {525, 4705}, {649, 2977}, {676, 47822}, {690, 4770}, {693, 47698}, {900, 4724}, {918, 1491}, {958, 4367}, {1019, 41229}, {1499, 4730}, {1639, 4874}, {1867, 16229}, {2786, 4913}, {3239, 7662}, {3566, 4041}, {3667, 4830}, {3676, 47802}, {3800, 4808}, {3835, 23770}, {3837, 21104}, {3910, 4490}, {4036, 14208}, {4129, 21077}, {4369, 47807}, {4458, 25666}, {4467, 47825}, {4500, 28147}, {4521, 47803}, {4728, 47704}, {4776, 47691}, {4782, 47884}, {4784, 5220}, {4802, 23813}, {4818, 30519}, {4879, 12635}, {4897, 9508}, {4976, 29078}, {5791, 47837}, {6084, 24719}, {7192, 47809}, {11374, 34958}, {14349, 29288}, {14419, 39545}, {16892, 47810}, {17069, 47827}, {21052, 23755}, {21677, 44729}, {24720, 28851}, {28183, 47826}, {28840, 45344}, {29370, 47876}, {30565, 47694}, {30835, 47887}, {44429, 47676}, {47123, 47765}, {47132, 47832}, {47666, 47690}, {47689, 47699}, {47695, 47821}

X(48047) = midpoint of X(i) and X(j) for these {i,j}: {661, 4088}, {693, 47698}, {4122, 4824}, {4808, 4983}, {47666, 47690}, {47689, 47699}, {47700, 47701}
X(48047) = reflection of X(i) in X(j) for these {i,j}: {649, 2977}, {3700, 18004}, {4010, 14321}, {4458, 25666}, {4897, 9508}, {7178, 21051}, {7662, 3239}, {21104, 3837}, {23770, 3835}
X(48047) = X(i)-isoconjugate of X(j) for these (i,j): {81, 28847}, {110, 39954}, {163, 39721}, {1576, 40028}
X(48047) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 39721), (244, 39954), (4858, 40028), (40586, 28847)
X(48047) = crossdifference of every pair of points on line {58, 16502}
X(48047) = barycentric product X(i)*X(j) for these {i,j}: {10, 28846}, {514, 4078}, {523, 17316}, {661, 30758}, {1577, 3751}, {4064, 14013}, {7178, 27549}
X(48047) = barycentric quotient X(i)/X(j) for these {i,j}: {42, 28847}, {523, 39721}, {661, 39954}, {1577, 40028}, {3751, 662}, {4078, 190}, {17316, 99}, {27549, 645}, {28846, 86}, {30758, 799}
X(48047) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 47700, 47701}, {4088, 47701, 47700}, {4458, 25666, 47799}


X(48048) = X(513)X(4468)∩X(514)X(4806)

Barycentrics    (b - c)*(a^3 - 2*a^2*b - a*b^2 + b^3 - 2*a^2*c - 5*a*b*c + b^2*c - a*c^2 + b*c^2 + c^3) : :
X(48048) = X[4122] - 3 X[47772], X[4784] - 3 X[6546], 3 X[4800] - X[47704], 3 X[21051] - 2 X[44314], X[21146] - 3 X[30565], X[24719] - 3 X[47769], X[47676] - 3 X[47822]

X(48048) lies on these lines: {513, 4468}, {514, 4806}, {4122, 47772}, {4782, 28846}, {4784, 6546}, {4800, 47704}, {4874, 28851}, {6590, 28195}, {21051, 44314}, {21146, 30565}, {24719, 47769}, {47676, 47822}


X(48049) = X(513)X(3716)∩X(514)X(3700)

Barycentrics    (b - c)*(-a^2 - 2*a*b - 2*a*c + b*c) : :
X(48049) = 3 X[3835] - 2 X[4885], 4 X[3835] - 3 X[4928], 3 X[3835] - X[4932], 9 X[3835] - 4 X[7653], 5 X[3835] - 3 X[47779], 3 X[4369] - 4 X[4885], 2 X[4369] - 3 X[4928], 3 X[4369] - 2 X[4932], X[4369] - 4 X[4940], 9 X[4369] - 8 X[7653], 5 X[4369] - 6 X[47779], 8 X[4885] - 9 X[4928], X[4885] - 3 X[4940], 3 X[4885] - 2 X[7653], 10 X[4885] - 9 X[47779], 9 X[4928] - 4 X[4932], 3 X[4928] - 8 X[4940], 27 X[4928] - 16 X[7653], 5 X[4928] - 4 X[47779], X[4932] - 6 X[4940], 3 X[4932] - 4 X[7653], 5 X[4932] - 9 X[47779], 9 X[4940] - 2 X[7653], 10 X[4940] - 3 X[47779], 20 X[7653] - 27 X[47779], 2 X[649] - 3 X[4763], X[649] - 3 X[4776], 3 X[649] - 5 X[31209], 3 X[4763] - 4 X[25666], 9 X[4763] - 10 X[31209], 3 X[4776] - 2 X[25666], 9 X[4776] - 5 X[31209], 6 X[25666] - 5 X[31209], 2 X[650] - 3 X[45315], 3 X[661] - X[17494], X[661] - 3 X[47759], 5 X[661] - 3 X[47775], X[17494] + 3 X[20295], X[17494] - 9 X[47759], 5 X[17494] - 9 X[47775], X[20295] + 3 X[47759], 5 X[20295] + 3 X[47775], 5 X[47759] - X[47775], X[693] - 3 X[31147], X[4813] + 3 X[31147], 3 X[1635] - X[26853], 2 X[2527] - 3 X[45326], 2 X[3798] - 3 X[47882], 3 X[4024] - X[47658], 3 X[4120] + X[23731], 3 X[4120] - X[47660], X[4380] - 3 X[4893], 2 X[4394] - 3 X[47778], X[4468] - 3 X[47764], 3 X[4728] - X[7192], 3 X[4728] - 5 X[26798], X[7192] - 5 X[26798], X[4790] - 3 X[47760], 2 X[31286] - 3 X[47760], X[4897] - 3 X[47756], 2 X[21212] - 3 X[47756], 3 X[4931] - X[47659], 3 X[4958] + X[47673], X[6590] - 3 X[47786], 3 X[21297] + X[31290], 3 X[21297] - X[47672], 5 X[24924] - 7 X[27138], 5 X[24924] - 6 X[45678], 5 X[24924] - 3 X[47763], 7 X[27138] - 6 X[45678], 7 X[27138] - 3 X[47763], X[26824] + 3 X[47774], 5 X[26985] - 3 X[31148], 5 X[27013] - 6 X[45675], 5 X[30835] - 3 X[47762], 5 X[31250] - 6 X[45339], 4 X[31287] - 3 X[45313]

X(48049) lies on these lines: {2, 4979}, {37, 24083}, {513, 3716}, {514, 3700}, {649, 4763}, {650, 4785}, {661, 812}, {693, 4813}, {740, 8663}, {798, 29807}, {900, 21196}, {1019, 29426}, {1635, 26853}, {2526, 3667}, {2527, 45326}, {2786, 3004}, {3261, 4842}, {3762, 18071}, {3768, 18197}, {3776, 28846}, {3798, 6006}, {4024, 47658}, {4025, 28867}, {4120, 23731}, {4129, 21261}, {4380, 4893}, {4382, 47666}, {4394, 47778}, {4468, 28882}, {4507, 25142}, {4728, 7192}, {4784, 25380}, {4790, 31286}, {4810, 4824}, {4822, 21301}, {4826, 20949}, {4897, 21212}, {4913, 29328}, {4931, 47659}, {4949, 28898}, {4958, 47673}, {4983, 29051}, {6002, 14349}, {6590, 28859}, {16892, 44449}, {17069, 28217}, {21104, 28855}, {21297, 31290}, {23806, 42325}, {24560, 26596}, {24924, 27138}, {25259, 28863}, {26248, 31094}, {26824, 47774}, {26985, 31148}, {27013, 45675}, {28871, 47676}, {28890, 47652}, {30764, 47804}, {30835, 47762}, {31250, 45339}, {31287, 45313}, {38390, 44312}, {39386, 45674}

X(48049) = midpoint of X(i) and X(j) for these {i,j}: {661, 20295}, {693, 4813}, {4382, 47666}, {4810, 4824}, {4822, 21301}, {4826, 20949}, {16892, 44449}, {23731, 47660}, {31290, 47672}
X(48049) = reflection of X(i) in X(j) for these {i,j}: {649, 25666}, {3716, 4806}, {3835, 4940}, {4369, 3835}, {4507, 25142}, {4763, 4776}, {4784, 25380}, {4790, 31286}, {4897, 21212}, {4932, 4885}, {47763, 45678}
X(48049) = complement of X(4979)
X(48049) = complement of the isogonal conjugate of X(37212)
X(48049) = X(i)-complementary conjugate of X(j) for these (i,j): {2, 46660}, {6, 35076}, {110, 41820}, {1126, 1086}, {1171, 244}, {1252, 4988}, {1255, 11}, {1268, 116}, {1796, 2968}, {4102, 124}, {4596, 3739}, {4629, 1125}, {4632, 3741}, {6539, 125}, {6540, 141}, {6578, 17045}, {8701, 2}, {28615, 1015}, {31011, 3259}, {32018, 21252}, {32635, 26932}, {33635, 1146}, {37212, 10}, {40438, 17761}
X(48049) = crossdifference of every pair of points on line {2176, 20985}
X(48049) = barycentric product X(514)*X(17319)
X(48049) = barycentric quotient X(17319)/X(190)
X(48049) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 4776, 25666}, {649, 25666, 4763}, {3835, 4369, 4928}, {3835, 4932, 4885}, {3835, 23803, 42327}, {4120, 23731, 47660}, {4790, 47760, 31286}, {4813, 31147, 693}, {4885, 4932, 4369}, {4897, 47756, 21212}, {7192, 26798, 4728}, {20295, 47759, 661}, {21297, 31290, 47672}, {24924, 27138, 45678}, {27138, 47763, 24924}


X(48050) = X(513)X(3716)∩X(514)X(4522)

Barycentrics    (b - c)*(-a^3 - a^2*b - 2*a*b^2 - a^2*c - a*b*c + b^2*c - 2*a*c^2 + b*c^2) : :
X(48050) = 2 X[4874] - 3 X[4928], X[649] - 3 X[44429], 2 X[25380] - 3 X[44429], X[4913] + 2 X[24719], X[4063] - 3 X[47816], X[4784] - 3 X[36848], X[4380] - 3 X[47828], 2 X[4394] - 3 X[47830], X[4498] - 3 X[47814], X[4724] - 3 X[4776], 3 X[4776] + X[47685], 3 X[4728] - X[47694], 3 X[4763] - 2 X[4782], X[4804] - 3 X[21297], X[4979] - 3 X[47824], X[7192] - 3 X[47812], 2 X[13246] - 3 X[47799], X[17494] - 3 X[47810], 5 X[26985] - 3 X[47813], 7 X[27138] - 3 X[47805], 5 X[30835] - 3 X[47804], 2 X[31286] - 3 X[47802], X[47696] - 3 X[47874], X[47697] - 3 X[47832], X[47704] - 3 X[47871]

X(48050) lies on these lines: {513, 3716}, {514, 4522}, {522, 2526}, {649, 25380}, {650, 4830}, {659, 25666}, {661, 46403}, {812, 1491}, {1019, 25526}, {1638, 6006}, {2254, 20295}, {2530, 6002}, {3239, 4778}, {3454, 4129}, {3667, 21212}, {3907, 21301}, {4063, 47816}, {4086, 18071}, {4088, 47652}, {4122, 28863}, {4142, 28481}, {4147, 8712}, {4375, 4784}, {4380, 47828}, {4394, 47830}, {4486, 21146}, {4498, 47814}, {4724, 4776}, {4728, 47694}, {4763, 4782}, {4775, 28521}, {4785, 45328}, {4804, 21297}, {4979, 47824}, {6371, 30584}, {7192, 47812}, {11263, 42325}, {13246, 47799}, {14349, 29051}, {15309, 23789}, {17494, 47810}, {26798, 31095}, {26985, 47813}, {27138, 47805}, {28209, 45661}, {29512, 31946}, {30835, 47804}, {31286, 47802}, {47687, 47701}, {47688, 47700}, {47696, 47874}, {47697, 47832}, {47704, 47871}

X(48050) = midpoint of X(i) and X(j) for these {i,j}: {661, 46403}, {1491, 24719}, {2254, 20295}, {2526, 4106}, {4088, 47652}, {4724, 47685}, {47687, 47701}, {47688, 47700}
X(48050) = reflection of X(i) in X(j) for these {i,j}: {649, 25380}, {659, 25666}, {3716, 3835}, {4369, 3837}, {4830, 650}, {4913, 1491}
X(48050) = X(1390)-complementary conjugate of X(11)
X(48050) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 44429, 25380}, {4776, 47685, 4724}


X(48051) = X(513)X(4401)∩X(514)X(3700)

Barycentrics    a*(b - c)*(a^2 + 4*a*b + 3*b^2 + 4*a*c + 5*b*c + 3*c^2) : :
X(48051) = 3 X[661] - X[4063], 5 X[4983] - X[6161], X[1577] - 3 X[47759], X[3960] + 2 X[4813], 3 X[4728] - X[4960]

X(48051) lies on these lines: {513, 4401}, {514, 3700}, {661, 4063}, {830, 4983}, {1022, 1255}, {1577, 47759}, {3887, 4822}, {3960, 4813}, {4728, 4960}, {4823, 4940}, {4978, 31290}, {23883, 45746}

X(48051) = midpoint of X(i) and X(j) for these {i,j}: {4813, 14349}, {4978, 31290}
X(48051) = reflection of X(i) in X(j) for these {i,j}: {3960, 14349}, {4823, 4940}


X(48052) = X(513)X(4401)∩X(514)X(4522)

Barycentrics    a*(b - c)*(a^2 + 2*a*b + 3*b^2 + 2*a*c + 3*b*c + 3*c^2) : :
X(48052) = X[663] - 3 X[14349], 3 X[1491] - X[4834], X[4063] - 3 X[47810], X[4960] - 3 X[47812], X[47697] - 3 X[47838]

X(48052) lies on these lines: {513, 4401}, {514, 4522}, {661, 16546}, {663, 830}, {1491, 4834}, {2526, 6005}, {2530, 15309}, {4063, 47810}, {4813, 4905}, {4818, 29216}, {4960, 47812}, {4983, 42325}, {23789, 28840}, {47697, 47838}

X(48052) = midpoint of X(4813) and X(4905)
X(48052) = crossdifference of every pair of points on line {5282, 16777}
X(48052) = barycentric product X(1)*X(47654)
X(48052) = barycentric quotient X(47654)/X(75)


X(48053) = X(513)X(4401)∩X(514)X(4806)

Barycentrics    a*(b - c)*(b + c)*(3*a + 2*b + 2*c) : :
X(48053) = 5 X[661] - X[4041], 3 X[661] - X[4705], 9 X[661] - X[4729], 7 X[661] - X[4730], 4 X[661] - X[4770], 3 X[661] + X[4822], 3 X[4041] - 5 X[4705], 9 X[4041] - 5 X[4729], 7 X[4041] - 5 X[4730], 4 X[4041] - 5 X[4770], 3 X[4041] + 5 X[4822], X[4041] + 5 X[4983], 3 X[4705] - X[4729], 7 X[4705] - 3 X[4730], 4 X[4705] - 3 X[4770], X[4705] + 3 X[4983], 7 X[4729] - 9 X[4730], 4 X[4729] - 9 X[4770], X[4729] + 3 X[4822], X[4729] + 9 X[4983], 4 X[4730] - 7 X[4770], 3 X[4730] + 7 X[4822], X[4730] + 7 X[4983], 3 X[4770] + 4 X[4822], X[4770] + 4 X[4983], X[4822] - 3 X[4983], X[3777] - 3 X[14349], X[4834] - 3 X[4893], X[4960] - 3 X[47833], X[7192] - 3 X[47839], X[17166] + 3 X[47774], X[31290] + 3 X[47840]

X(48053) lies on these lines: {512, 661}, {513, 4401}, {514, 4806}, {667, 4813}, {3004, 29252}, {3709, 14991}, {3777, 6372}, {4170, 4824}, {4502, 23657}, {4778, 23815}, {4834, 4893}, {4841, 6367}, {4932, 31288}, {4960, 47833}, {7180, 42653}, {7192, 47839}, {7950, 47701}, {17166, 47774}, {23789, 28209}, {31290, 47840}

X(48053) = midpoint of X(i) and X(j) for these {i,j}: {661, 4983}, {667, 4813}, {4170, 4824}, {4705, 4822}
X(48053) = reflection of X(4932) in X(31288)
X(48053) = X(28195)-Ceva conjugate of X(47669)
X(48053) = X(i)-isoconjugate of X(j) for these (i,j): {86, 28196}, {110, 28650}, {662, 27789}
X(48053) = X(i)-Dao conjugate of X(j) for these (i, j): (244, 28650), (1084, 27789), (40600, 28196)
X(48053) = crossdifference of every pair of points on line {81, 16777}
X(48053) = barycentric product X(i)*X(j) for these {i,j}: {1, 47669}, {37, 28195}, {523, 16884}, {649, 42031}, {661, 3624}, {4017, 4034}, {4705, 42025}
X(48053) = barycentric quotient X(i)/X(j) for these {i,j}: {213, 28196}, {512, 27789}, {661, 28650}, {3624, 799}, {4034, 7257}, {16884, 99}, {28195, 274}, {42025, 4623}, {42031, 1978}, {47669, 75}
X(48053) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 4822, 4705}, {4705, 4983, 4822}


X(48054) = X(513)X(4401)∩X(514)X(661)

Barycentrics    a*(b - c)*(2*a*b + 2*b^2 + 2*a*c + 3*b*c + 2*c^2) : :
X(48054) = X[1577] - 3 X[4776], X[1734] - 3 X[47810], X[4822] + 3 X[47810], X[4063] - 3 X[4893], 3 X[4379] - X[4960], X[4560] + 3 X[47759], X[4761] - 3 X[47814], X[4784] - 3 X[47888], X[4834] - 3 X[47827], X[4963] + 3 X[47889], X[7192] - 3 X[47795], X[31290] + 3 X[47796], X[47678] - 3 X[47790], X[47679] - 3 X[47781], X[47694] - 3 X[47838]

X(48054) lies on these lines: {513, 4401}, {514, 661}, {784, 4806}, {830, 4794}, {905, 15309}, {1019, 4813}, {1491, 4983}, {1734, 4822}, {2526, 42325}, {3004, 23875}, {4063, 4893}, {4079, 23657}, {4088, 29260}, {4379, 4960}, {4560, 29178}, {4705, 29350}, {4761, 47814}, {4778, 23789}, {4784, 47888}, {4834, 47827}, {4932, 27647}, {4940, 23882}, {4963, 47889}, {4977, 23815}, {6586, 14991}, {7192, 47795}, {7265, 45746}, {20295, 29270}, {20983, 39548}, {21196, 29216}, {29164, 47701}, {31290, 47796}, {47678, 47790}, {47679, 47781}, {47694, 47838}, {47698, 47716}, {47699, 47715}

X(48054) = midpoint of X(i) and X(j) for these {i,j}: {661, 14349}, {1019, 4813}, {1491, 4983}, {1734, 4822}, {4978, 47666}, {7265, 45746}, {20983, 39548}, {47698, 47716}, {47699, 47715}
X(48054) = reflection of X(i) in X(j) for these {i,j}: {4791, 4129}, {4823, 3835}
X(48054) = crossdifference of every pair of points on line {31, 16777}
X(48054) = barycentric product X(i)*X(j) for these {i,j}: {1, 47657}, {693, 5312}
X(48054) = barycentric quotient X(i)/X(j) for these {i,j}: {5312, 100}, {47657, 75}
X(48054) = {X(4822),X(47810)}-harmonic conjugate of X(1734)


X(48055) = X(513)X(4468)∩X(514)X(3716)

Barycentrics    (b - c)*(2*a^3 - a^2*b + b^3 - a^2*c - 4*a*b*c + b^2*c + b*c^2 + c^3) : :
X(48055) = 3 X[1639] - 2 X[3837], 3 X[667] - 2 X[39545], 2 X[676] - 3 X[4448], X[2254] - 3 X[6546], 2 X[2977] - 3 X[6546], 4 X[2490] - 3 X[47823], 2 X[3676] - 3 X[47803], 2 X[3776] - 3 X[47799], 3 X[4040] - X[47727], 3 X[4391] - X[47722], 2 X[4458] - 3 X[26275], 4 X[4521] - 3 X[47802], 3 X[4776] - X[47686], 2 X[9508] - 3 X[47884], 3 X[10196] - 2 X[25380], X[16892] - 3 X[47811], 2 X[24720] - 3 X[47807], 3 X[30565] - X[46403], 5 X[30795] - 6 X[45326], X[47652] - 3 X[47821], X[47676] - 3 X[47804]

X(48055) lies on these lines: {11, 7202}, {513, 4468}, {514, 3716}, {523, 4724}, {659, 918}, {661, 1639}, {667, 39545}, {676, 4448}, {900, 4088}, {2254, 2977}, {2490, 47823}, {2786, 4830}, {2826, 12738}, {3566, 4498}, {3676, 47803}, {3700, 29362}, {3762, 29240}, {3776, 47799}, {4010, 6084}, {4040, 29288}, {4391, 47722}, {4458, 26275}, {4521, 47802}, {4776, 47686}, {4782, 4897}, {4806, 23729}, {4810, 6009}, {4874, 21104}, {4927, 28195}, {4928, 28229}, {9508, 47884}, {10015, 29102}, {10196, 25380}, {14321, 24719}, {16892, 47811}, {21120, 29082}, {24720, 47807}, {28175, 47701}, {28179, 47702}, {28183, 47700}, {28213, 47826}, {29142, 47726}, {30565, 46403}, {30795, 45326}, {47132, 47704}, {47652, 47821}, {47662, 47699}, {47666, 47696}, {47676, 47804}, {47697, 47698}

X(48055) = midpoint of X(i) and X(j) for these {i,j}: {47662, 47699}, {47666, 47696}, {47697, 47698}
X(48055) = reflection of X(i) in X(j) for these {i,j}: {2254, 2977}, {4897, 4782}, {21104, 4874}, {23729, 4806}, {23770, 3716}, {24719, 14321}, {47704, 47132}
X(48055) = crossdifference of every pair of points on line {595, 4253}
X(48055) = {X(2254),X(6546)}-harmonic conjugate of X(2977)


X(48056) = X(513)X(4468)∩X(514)X(3837)

Barycentrics    (b - c)*(a^3 - a*b^2 + b^3 - 3*a*b*c + b^2*c - a*c^2 + b*c^2 + c^3) : :
X(48056) = X[649] - 3 X[47885], X[659] - 3 X[6546], X[4088] + 3 X[6546], 2 X[676] - 3 X[45666], 3 X[1639] - X[23770], X[3801] - 3 X[47793], X[4010] - 3 X[30565], 3 X[4120] - X[4810], 3 X[4448] - X[47695], X[4458] - 3 X[10196], X[4809] - 3 X[31992], 3 X[6545] - 5 X[30795], X[7662] - 3 X[47770], 2 X[13246] - 3 X[45314], 3 X[14431] - X[47680], 3 X[14432] - X[21343], X[16892] - 3 X[47827], X[21104] - 3 X[47807], X[21146] - 3 X[47809], 2 X[21212] - 3 X[47829], 2 X[25380] - 3 X[28602], X[47676] - 3 X[47823], X[47691] - 3 X[47822], X[47693] + 3 X[47775], X[47698] + 3 X[47771], X[47700] + 3 X[47811], X[47704] - 3 X[47833], X[47716] - 3 X[47839], X[47720] - 3 X[47841]

X(48056) lies on these lines: {10, 29102}, {513, 4468}, {514, 3837}, {523, 3716}, {649, 47885}, {659, 4088}, {676, 45666}, {812, 18004}, {900, 4830}, {918, 2977}, {1639, 4802}, {2785, 32212}, {3801, 47793}, {4010, 30565}, {4040, 4808}, {4120, 4810}, {4122, 17494}, {4129, 29098}, {4147, 29082}, {4448, 47695}, {4458, 10196}, {4522, 29362}, {4782, 11068}, {4809, 31992}, {4824, 47660}, {4927, 28199}, {4928, 28175}, {6332, 29226}, {6545, 30795}, {7662, 47770}, {13246, 45314}, {14431, 47680}, {14432, 21343}, {14838, 29354}, {16892, 47827}, {17719, 21112}, {21104, 47807}, {21146, 47809}, {21212, 47829}, {24719, 47663}, {25380, 28602}, {47676, 47823}, {47691, 47822}, {47693, 47775}, {47698, 47771}, {47700, 47811}, {47704, 47833}, {47716, 47839}, {47720, 47841}

X(48056) = midpoint of X(i) and X(j) for these {i,j}: {659, 4088}, {4040, 4808}, {4122, 17494}, {4824, 47660}, {24719, 47663}
X(48056) = reflection of X(i) in X(j) for these {i,j}: {4782, 11068}, {9508, 2977}
X(48056) = crossdifference of every pair of points on line {16502, 21793}
X(48056) = {X(4088),X(6546)}-harmonic conjugate of X(659)


X(48057) = X(512)X(5103)∩X(513)X(3716)

Barycentrics    (b - c)*(-(a^3*b) - a*b^3 - a^3*c + 2*a^2*b*c - a*b^2*c + b^3*c - a*b*c^2 - a*c^3 + b*c^3) : :
X(48057) = X[2484] + 3 X[31147], X[21003] - 3 X[47839]

X(48057) lies on these lines: {141, 6363}, {512, 5103}, {513, 3716}, {2483, 20295}, {2484, 31147}, {2509, 4106}, {3700, 23885}, {9313, 21260}, {14433, 21055}, {21003, 47839}, {21245, 31946}

X(48057) = midpoint of X(i) and X(j) for these {i,j}: {2483, 20295}, {2509, 4106}
X(48057) = X(40398)-complementary conjugate of X(244)


X(48058) = X(513)X(4401)∩X(514)X(3716)

Barycentrics    a*(b - c)*(a^2 - 2*a*b - b^2 - 2*a*c - 3*b*c - c^2) : :
X(48058) = X[663] + 3 X[47826], X[693] - 3 X[47838], X[1577] - 3 X[47821], X[1734] - 3 X[4893], X[4063] - 3 X[47811], X[4822] + 3 X[47811], X[4761] - 3 X[47793], X[4960] - 3 X[47813], X[4978] - 3 X[47840], X[7192] - 3 X[47818], X[21146] - 3 X[47839], 3 X[30565] - X[47711]

X(48058) lies on these lines: {513, 4401}, {514, 3716}, {650, 6005}, {659, 4983}, {661, 830}, {663, 4160}, {667, 15309}, {693, 47838}, {1491, 42325}, {1577, 47821}, {1734, 4893}, {3738, 4833}, {3835, 29186}, {3887, 4705}, {3960, 6372}, {4063, 4822}, {4129, 29051}, {4170, 17494}, {4468, 29047}, {4490, 4775}, {4724, 14349}, {4761, 47793}, {4794, 8678}, {4806, 29070}, {4960, 47813}, {4978, 47840}, {7192, 47818}, {18004, 29086}, {21051, 29188}, {21146, 47839}, {21260, 29246}, {30565, 47711}

X(48058) = midpoint of X(i) and X(j) for these {i,j}: {659, 4983}, {661, 4040}, {4063, 4822}, {4170, 17494}, {4490, 4775}, {4724, 14349}
X(48058) = crossdifference of every pair of points on line {38, 16777}
X(48058) = barycentric product X(1)*X(47661)
X(48058) = barycentric quotient X(47661)/X(75)
X(48058) = {X(4822),X(47811)}-harmonic conjugate of X(4063)


X(48059) = X(513)X(4401)∩X(514)X(3837)

Barycentrics    a*(b - c)*(a*b + 2*b^2 + a*c + 2*b*c + 2*c^2) : :
X(48059) = 3 X[1491] - X[1734], X[1734] + 3 X[14349], 4 X[21051] - 3 X[28603], X[649] - 3 X[47888], X[4705] - 3 X[47810], X[1019] - 3 X[47893], X[2533] - 3 X[47816], X[4063] - 3 X[47827], 2 X[4367] - 3 X[14422], X[4834] - 3 X[47828], 5 X[30835] - 3 X[47875], X[47666] + 3 X[47819], X[47694] - 3 X[47839], X[47719] + 3 X[47781]

X(48059) lies on these lines: {512, 1491}, {513, 4401}, {514, 3837}, {649, 47888}, {661, 665}, {667, 27675}, {784, 3835}, {826, 3004}, {830, 1960}, {891, 4705}, {1019, 47893}, {2254, 4983}, {2526, 6004}, {2533, 47816}, {3250, 23657}, {3906, 47877}, {4063, 47827}, {4083, 4770}, {4151, 4992}, {4367, 14422}, {4481, 6373}, {4560, 29340}, {4806, 8714}, {4824, 4978}, {4834, 47828}, {4977, 23789}, {6371, 47842}, {21124, 29256}, {21196, 29106}, {21301, 29182}, {21714, 28175}, {30835, 47875}, {47666, 47819}, {47694, 47839}, {47719, 47781}

X(48059) = midpoint of X(i) and X(j) for these {i,j}: {661, 2530}, {1491, 14349}, {2254, 4983}, {4824, 4978}
X(48059) = X(17239)-Dao conjugate of X(4427)
X(48059) = crosspoint of X(513) and X(4608)
X(48059) = crosssum of X(100) and X(35327)
X(48059) = crossdifference of every pair of points on line {1621, 16777}
X(48059) = barycentric product X(i)*X(j) for these {i,j}: {1, 47673}, {513, 17239}, {514, 3989}, {661, 17210}
X(48059) = barycentric quotient X(i)/X(j) for these {i,j}: {3989, 190}, {17210, 799}, {17239, 668}, {47673, 75}


X(48060) = X(239)X(514)∩X(513)X(4468)

Barycentrics    (b - c)*(3*a^2 + b^2 + c^2) : :
X(48060) = 3 X[2] - 4 X[43061], 3 X[649] - 2 X[3798], 5 X[649] - 3 X[4750], 4 X[649] - 3 X[4786], 3 X[649] - X[16892], 4 X[3798] - 3 X[4025], 10 X[3798] - 9 X[4750], 8 X[3798] - 9 X[4786], 5 X[4025] - 6 X[4750], 2 X[4025] - 3 X[4786], 3 X[4025] - 2 X[16892], 4 X[4750] - 5 X[4786], 9 X[4750] - 5 X[16892], 2 X[4765] - 3 X[47776], 9 X[4786] - 4 X[16892], 3 X[17494] - X[47667], 3 X[27486] - X[47653], X[45746] - 3 X[47776], X[47676] - 3 X[47763], 3 X[4380] + X[47665], 3 X[47660] - X[47665], 4 X[650] - 3 X[47783], 2 X[693] - 3 X[47789], 2 X[4500] - 3 X[6590], 3 X[1639] - 2 X[4940], X[47666] - 3 X[47892], 4 X[2487] - 3 X[47754], 4 X[2490] - 3 X[47760], 4 X[2516] - 3 X[47784], 4 X[2527] - 3 X[47761], 2 X[3004] - 3 X[47785], 4 X[4394] - 3 X[47785], 2 X[3239] - 3 X[47771], 4 X[3239] - 3 X[47786], X[20295] - 3 X[47771], 2 X[20295] - 3 X[47786], X[25259] - 3 X[47773], X[26853] + 3 X[47773], 2 X[3676] - 3 X[47762], X[47652] - 3 X[47762], 2 X[3776] - 3 X[47758], 2 X[3835] - 3 X[47766], 2 X[4106] - 3 X[47787], 4 X[4369] - 3 X[21183], 2 X[4369] - 3 X[47768], 3 X[4453] - X[47651], 4 X[4521] - 3 X[4776], X[4813] - 3 X[6546], 2 X[4885] - 3 X[47767], X[23729] - 3 X[47767], 3 X[4893] - X[23731], 4 X[7653] - 3 X[47891], 4 X[7658] - 5 X[27013], 4 X[7658] - 3 X[44435], 5 X[27013] - 3 X[44435], 2 X[14321] - 3 X[47770], 2 X[21212] - 3 X[45313], 2 X[23813] - 3 X[47788], 5 X[26777] - 3 X[47781], X[26824] - 3 X[47791], 7 X[27115] - 8 X[31182], 7 X[31207] - 6 X[44432], 4 X[31286] - 3 X[47757], 4 X[31287] - 3 X[47756], X[47650] - 3 X[47780], X[47686] - 3 X[47824]

X(48060) lies on these lines: {2, 43061}, {239, 514}, {513, 4468}, {522, 4380}, {650, 47783}, {659, 8646}, {661, 11068}, {665, 28374}, {693, 47789}, {812, 4500}, {830, 44448}, {918, 4790}, {1639, 4940}, {2254, 4778}, {2487, 47754}, {2490, 47760}, {2516, 47784}, {2527, 47761}, {3004, 4394}, {3239, 20295}, {3667, 25259}, {3676, 47652}, {3700, 6008}, {3732, 35281}, {3766, 30061}, {3776, 47758}, {3793, 3800}, {3835, 47766}, {4106, 47787}, {4369, 21183}, {4401, 8635}, {4453, 47651}, {4467, 47662}, {4521, 4776}, {4813, 6546}, {4885, 23729}, {4893, 23731}, {4897, 30520}, {4976, 28894}, {4979, 28846}, {6006, 44449}, {6084, 43067}, {7649, 10566}, {7653, 47891}, {7658, 27013}, {14321, 47770}, {17894, 20952}, {21185, 29158}, {21212, 45313}, {23813, 47788}, {25009, 30804}, {25900, 25902}, {25981, 26017}, {26777, 47781}, {26824, 47791}, {27115, 31182}, {28147, 47661}, {28161, 47659}, {28169, 47658}, {28191, 47668}, {28225, 31290}, {31207, 44432}, {31286, 47757}, {31287, 47756}, {47650, 47780}, {47686, 47824}

X(48060) = midpoint of X(i) and X(j) for these {i,j}: {4380, 47660}, {4467, 47662}, {7192, 47663}, {25259, 26853}
X(48060) = reflection of X(i) in X(j) for these {i,j}: {661, 11068}, {3004, 4394}, {4025, 649}, {4468, 47890}, {16892, 3798}, {20295, 3239}, {21183, 47768}, {23729, 4885}, {45746, 4765}, {47652, 3676}, {47786, 47771}
X(48060) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1219, 21293}, {2297, 150}, {6574, 69}, {7050, 149}
X(48060) = X(i)-isoconjugate of X(j) for these (i,j): {37, 907}, {100, 39951}, {101, 23051}, {692, 18840}, {906, 8801}, {1783, 34817}
X(48060) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 23051), (1086, 18840), (5190, 8801), (8054, 39951), (39006, 34817), (40589, 907)
X(48060) = crosssum of X(213) and X(8662)
X(48060) = crossdifference of every pair of points on line {42, 16502}
X(48060) = barycentric product X(i)*X(j) for these {i,j}: {75, 3803}, {86, 3800}, {310, 3804}, {513, 39731}, {514, 3618}, {649, 40022}, {3261, 30435}, {3785, 7649}, {3796, 46107}, {4025, 6995}, {8362, 10566}, {16892, 42037}
X(48060) = barycentric quotient X(i)/X(j) for these {i,j}: {58, 907}, {513, 23051}, {514, 18840}, {649, 39951}, {1459, 34817}, {3618, 190}, {3785, 4561}, {3796, 1331}, {3800, 10}, {3803, 1}, {3804, 42}, {3806, 15523}, {6995, 1897}, {7649, 8801}, {8362, 4568}, {30435, 101}, {39731, 668}, {40022, 1978}
X(48060) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 4025, 4786}, {649, 16892, 3798}, {3004, 4394, 47785}, {3239, 20295, 47786}, {3798, 16892, 4025}, {20295, 47771, 3239}, {23729, 47767, 4885}, {26853, 47773, 25259}, {27013, 44435, 7658}, {45746, 47776, 4765}, {47652, 47762, 3676}


X(48061) = X(1)X(514)∩X(513)X(4468)

Barycentrics    (b - c)*(3*a^3 - a^2*b + a*b^2 + b^3 - a^2*c - 4*a*b*c + b^2*c + a*c^2 + b*c^2 + c^3) : :
X(48061) = 3 X[4724] - X[47701], 4 X[4521] - 3 X[44429], 2 X[24720] - 3 X[47766], 2 X[3676] - 3 X[47804], 2 X[3776] - 3 X[47800], 2 X[4458] - 3 X[47801], 4 X[8689] - 3 X[47801], 4 X[4782] - 3 X[4786], 2 X[4818] - 3 X[47883], 4 X[4874] - 3 X[21183], 2 X[14837] - 3 X[47815], 2 X[21146] - 3 X[47789], 2 X[21188] - 3 X[47817], 2 X[24719] - 3 X[47786], 3 X[30565] - X[47685], 4 X[43061] - 3 X[47824], X[47676] - 3 X[47805], X[47686] - 3 X[47821]

X(48061) lies on these lines: {1, 514}, {513, 4468}, {522, 47700}, {523, 2976}, {659, 4025}, {661, 4521}, {2254, 11068}, {3239, 46403}, {3667, 4088}, {3676, 47804}, {3776, 47800}, {3777, 25881}, {4458, 8689}, {4782, 4786}, {4818, 47883}, {4874, 4977}, {6004, 44448}, {14837, 47815}, {21146, 47789}, {21188, 47817}, {24719, 47786}, {28191, 47702}, {30565, 47685}, {43061, 47824}, {47676, 47805}, {47686, 47821}, {47779, 47826}

X(48061) = reflection of X(i) in X(j) for these {i,j}: {2254, 11068}, {4025, 659}, {4458, 8689}, {46403, 3239}
X(48061) = crossdifference of every pair of points on line {672, 3915}
X(48061) = {X(4458),X(8689)}-harmonic conjugate of X(47801)


X(48062) = X(10)X(514)∩X(230)X(231)

Barycentrics    (b - c)*(a^3 + a^2*b - a*b^2 + b^3 + a^2*c - 2*a*b*c + b^2*c - a*c^2 + b*c^2 + c^3) : :
X(48062) = 3 X[17072] - 2 X[44314], 2 X[676] - 3 X[47803], 4 X[2490] - X[47131], 4 X[2490] - 3 X[47803], 2 X[4874] - 3 X[47766], X[47123] - 3 X[47766], X[47131] - 3 X[47803], X[659] - 3 X[47885], 2 X[11068] - 3 X[47885], X[693] - 3 X[47809], 3 X[1635] + X[47700], 5 X[1698] - X[47725], 2 X[3676] - 3 X[47823], X[3801] - 3 X[47835], 2 X[14837] - 3 X[47835], 2 X[3837] - 3 X[47806], 3 X[4379] - X[47704], 4 X[4521] - 3 X[47822], X[4724] - 3 X[6546], X[4804] - 3 X[47874], 2 X[4806] - 3 X[47765], 2 X[4885] - 3 X[47807], X[23770] - 3 X[47807], 3 X[4893] - X[47701], X[16892] - 3 X[47828], X[47716] - 3 X[47795], 2 X[21188] - 3 X[47837], 2 X[21212] - 3 X[47830], 5 X[24924] - X[47705], 5 X[24924] - 3 X[47887], X[47705] - 3 X[47887], X[47694] - 3 X[47771], 3 X[31131] - X[47685], 3 X[31150] + X[47689], 5 X[31209] - X[47692], 5 X[31209] - 3 X[47797], X[47692] - 3 X[47797], 4 X[31287] - 3 X[47799], 3 X[44429] - X[47652], 3 X[44435] - X[47688], X[45746] - 3 X[47825], X[47693] + 3 X[47825], X[46403] - 3 X[47808], X[47663] + 3 X[47808], X[47676] - 3 X[47824], X[47687] + 3 X[47892], X[47695] - 3 X[47804], X[47696] - 3 X[47773], X[47699] - 3 X[47775], X[47708] - 3 X[47793], X[47712] - 3 X[47794], X[47720] - 3 X[47796]

X(48062) lies on these lines: {2, 47691}, {8, 47728}, {10, 514}, {230, 231}, {513, 4468}, {522, 659}, {649, 4088}, {663, 976}, {667, 4808}, {693, 47809}, {812, 4522}, {824, 4913}, {905, 29288}, {1635, 47700}, {1698, 47725}, {2496, 4777}, {2505, 2526}, {3004, 4802}, {3239, 4010}, {3676, 47823}, {3776, 25380}, {3801, 14837}, {3837, 47806}, {3924, 4449}, {4025, 9508}, {4083, 6332}, {4129, 29158}, {4379, 47704}, {4458, 31286}, {4521, 47822}, {4560, 47707}, {4724, 6546}, {4784, 28846}, {4785, 45344}, {4804, 47874}, {4806, 47765}, {4807, 29304}, {4818, 28863}, {4885, 23770}, {4893, 47701}, {7192, 47698}, {14838, 29047}, {16892, 47828}, {17458, 21957}, {17494, 47690}, {18004, 29328}, {19846, 47716}, {19869, 19948}, {21051, 29025}, {21188, 47837}, {21192, 29358}, {21212, 47830}, {21260, 29098}, {23282, 24089}, {24924, 47705}, {26227, 47694}, {28147, 47779}, {28151, 47784}, {28179, 47880}, {28191, 47877}, {28602, 30768}, {29204, 47785}, {31131, 47685}, {31150, 47689}, {31209, 47692}, {31287, 47799}, {44429, 47652}, {44435, 47688}, {45746, 47693}, {46403, 47663}, {47676, 47824}, {47687, 47892}, {47695, 47804}, {47696, 47773}, {47699, 47775}, {47708, 47793}, {47712, 47794}, {47720, 47796}

X(48062) = midpoint of X(i) and X(j) for these {i,j}: {8, 47728}, {649, 4088}, {667, 4808}, {4560, 47707}, {7192, 47698}, {17494, 47690}, {45746, 47693}, {46403, 47663}
X(48062) = reflection of X(i) in X(j) for these {i,j}: {650, 2977}, {659, 11068}, {676, 2490}, {3776, 25380}, {3801, 14837}, {4010, 3239}, {4025, 9508}, {4458, 31286}, {7649, 6133}, {23770, 4885}, {47123, 4874}, {47131, 676}, {47757, 28602}
X(48062) = complement of X(47691)
X(48062) = crosssum of X(i) and X(j) for these (i,j): {6, 9313}, {513, 24476}
X(48062) = crossdifference of every pair of points on line {3, 1914}
X(48062) = barycentric product X(523)*X(16050)
X(48062) = barycentric quotient X(16050)/X(99)
X(48062) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {659, 47885, 11068}, {676, 2490, 47803}, {3801, 47835, 14837}, {23770, 47807, 4885}, {24924, 47705, 47887}, {31209, 47692, 47797}, {47123, 47766, 4874}, {47131, 47803, 676}, {47663, 47808, 46403}, {47693, 47825, 45746}


X(48063) = X(1)X(514)∩X(513)X(3716)

Barycentrics    (b - c)*(2*a^3 - a^2*b + a*b^2 - a^2*c - a*b*c + b^2*c + a*c^2 + b*c^2) : :
X(48063) = 2 X[3837] - 3 X[47831], 4 X[4874] - 3 X[47779], 2 X[24720] - 3 X[47779], X[649] - 3 X[47805], X[1491] - 3 X[4448], 2 X[1491] - 3 X[47778], X[1734] - 3 X[47817], X[2254] - 3 X[47804], 2 X[31286] - 3 X[47804], X[4025] - 3 X[47801], 2 X[13246] - 3 X[47801], X[4041] - 3 X[47815], 3 X[4728] - X[47685], 3 X[4800] - X[24719], X[4905] - 3 X[47818], 3 X[8643] - X[17496], X[16892] - 3 X[47798], 2 X[21212] - 3 X[47800], 2 X[25380] - 3 X[47803], 5 X[45673] - 2 X[45676], X[46403] - 3 X[47832], X[47687] - 3 X[47874]

X(48063) lies on these lines: {1, 514}, {513, 3716}, {522, 659}, {649, 3239}, {661, 47697}, {676, 3776}, {900, 4522}, {1491, 4448}, {1734, 47817}, {2254, 31286}, {2490, 4925}, {2496, 30520}, {2526, 25666}, {3803, 6002}, {3904, 28565}, {4025, 13246}, {4041, 47815}, {4057, 23405}, {4379, 30947}, {4391, 28470}, {4401, 8714}, {4486, 4785}, {4728, 47685}, {4784, 6006}, {4800, 24719}, {4817, 28846}, {4905, 47818}, {6004, 17072}, {6332, 28487}, {6608, 13258}, {7192, 17218}, {7253, 18197}, {8642, 13245}, {8643, 17496}, {16892, 47798}, {17494, 28161}, {21173, 23465}, {21212, 47800}, {24623, 47787}, {25380, 47803}, {25492, 47795}, {26093, 47796}, {28525, 31291}, {30519, 44433}, {45673, 45676}, {46403, 47832}, {47662, 47702}, {47687, 47874}

X(48063) = midpoint of X(i) and X(j) for these {i,j}: {661, 47697}, {4724, 47694}, {21132, 47728}, {47662, 47702}, {47696, 47701}
X(48063) = reflection of X(i) in X(j) for these {i,j}: {659, 8689}, {2254, 31286}, {2526, 25666}, {3776, 676}, {3835, 3716}, {4025, 13246}, {4925, 2490}, {24720, 4874}, {47778, 4448}
X(48063) = X(30555)-complementary conjugate of X(2)
X(48063) = crosspoint of X(190) and X(41527)
X(48063) = crosssum of X(649) and X(21010)
X(48063) = crossdifference of every pair of points on line {672, 1201}
X(48063) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2254, 47804, 31286}, {4025, 47801, 13246}, {4874, 24720, 47779}


X(48064) = X(239)X(514)∩X(513)X(4401)

Barycentrics    a*(b - c)*(2*a^2 + 2*a*b + 2*a*c + b*c) : :
X(48064) = 3 X[649] - X[4063], 5 X[649] - X[4498], 7 X[649] - X[21385], 3 X[1019] + X[4063], 5 X[1019] + X[4498], 7 X[1019] + X[21385], 5 X[4063] - 3 X[4498], 7 X[4063] - 3 X[21385], 7 X[4498] - 5 X[21385], X[4560] + 3 X[47763], 3 X[27486] - X[47679], 2 X[4784] + X[4794], X[1577] - 3 X[47762], X[4170] - 3 X[47820], X[20295] - 3 X[47795], X[26853] + 3 X[47796], 5 X[27013] - 3 X[47794], X[47678] - 3 X[47791]

X(48064) lies on these lines: {239, 514}, {513, 4401}, {650, 15309}, {667, 4784}, {693, 29270}, {905, 4790}, {1577, 29178}, {2483, 28846}, {2533, 29344}, {3733, 8637}, {3801, 29140}, {3803, 7659}, {3960, 8659}, {4129, 31286}, {4142, 29132}, {4170, 47820}, {4367, 4834}, {4369, 4823}, {4380, 4978}, {4458, 29158}, {4782, 6372}, {4785, 21191}, {4791, 6002}, {4806, 31288}, {4874, 29150}, {4897, 23875}, {4979, 14349}, {7178, 29114}, {7254, 21007}, {8045, 29216}, {20295, 47795}, {20517, 29118}, {26853, 47796}, {27013, 47794}, {47678, 47791}

X(48064) = midpoint of X(i) and X(j) for these {i,j}: {649, 1019}, {667, 4784}, {905, 4790}, {3803, 7659}, {4367, 4834}, {4380, 4978}, {4979, 14349}
X(48064) = reflection of X(i) in X(j) for these {i,j}: {4129, 31286}, {4794, 667}, {4806, 31288}, {4823, 4369}, {21192, 3798}
X(48064) = X(i)-isoconjugate of X(j) for these (i,j): {37, 43356}, {100, 39983}, {101, 39708}
X(48064) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 39708), (8054, 39983), (40589, 43356)
X(48064) = crosspoint of X(190) and X(27789)
X(48064) = crosssum of X(649) and X(16884)
X(48064) = crossdifference of every pair of points on line {42, 3711}
X(48064) = barycentric product X(i)*X(j) for these {i,j}: {513, 17394}, {514, 37685}, {4025, 17562}
X(48064) = barycentric quotient X(i)/X(j) for these {i,j}: {58, 43356}, {513, 39708}, {649, 39983}, {17394, 668}, {17562, 1897}, {37685, 190}


X(48065) = X(1)X(514)∩X(513)X(4401)

Barycentrics    a*(b - c)*(2*a^2 - 2*a*b - 2*a*c - 3*b*c) : :
X(48065) = 3 X[1] - 5 X[663], X[1] - 5 X[4040], 7 X[1] - 5 X[4449], X[1] + 5 X[4724], 2 X[1] - 5 X[4794], X[663] - 3 X[4040], 7 X[663] - 3 X[4449], X[663] + 3 X[4724], 2 X[663] - 3 X[4794], 7 X[4040] - X[4449], X[4449] + 7 X[4724], 2 X[4449] - 7 X[4794], 2 X[4724] + X[4794], 3 X[659] - X[4834], X[1734] - 3 X[47811], 6 X[3828] - 5 X[17072], 2 X[3828] - 5 X[45673], X[17072] - 3 X[45673], 5 X[4147] - 4 X[4691], X[4761] - 3 X[47815], 13 X[19877] - 15 X[47794], 8 X[19878] - 5 X[24720], 9 X[19883] - 5 X[23789], X[46403] - 3 X[47838], 11 X[46933] - 15 X[47793]

X(48065) lies on these lines: {1, 514}, {513, 4401}, {650, 42325}, {659, 4834}, {1734, 47811}, {1960, 29198}, {2605, 28229}, {3667, 46385}, {3716, 4823}, {3737, 28225}, {3803, 15309}, {3828, 17072}, {4147, 4691}, {4490, 6161}, {4491, 8637}, {4761, 47815}, {4791, 29051}, {4977, 34958}, {17020, 47783}, {19877, 47794}, {19878, 24720}, {19883, 23789}, {46403, 47838}, {46933, 47793}

X(48065) = midpoint of X(i) and X(j) for these {i,j}: {4040, 4724}, {4490, 6161}
X(48065) = reflection of X(i) in X(j) for these {i,j}: {4794, 4040}, {4823, 3716}
X(48065) = crossdifference of every pair of points on line {672, 16777}
X(48065) = barycentric product X(1)*X(47664)
X(48065) = barycentric quotient X(47664)/X(75)


X(48066) = X(10)X(514)∩X(513)X(4401)

Barycentrics    a*(b - c)*(2*b^2 + b*c + 2*c^2) : :
X(48066) = X[764] + 5 X[1491], X[764] - 5 X[2530], 3 X[764] - 5 X[3777], 3 X[764] + 5 X[4705], 7 X[764] - 5 X[23765], 3 X[1491] + X[3777], 5 X[1491] - X[4490], 3 X[1491] - X[4705], 7 X[1491] + X[23765], 3 X[2530] - X[3777], 5 X[2530] + X[4490], 3 X[2530] + X[4705], 7 X[2530] - X[23765], 5 X[3777] + 3 X[4490], 7 X[3777] - 3 X[23765], 3 X[4490] - 5 X[4705], 7 X[4490] + 5 X[23765], 7 X[4705] + 3 X[23765], 3 X[4401] - 4 X[6050], 2 X[6050] - 3 X[14838], X[659] - 3 X[47888], X[667] - 3 X[47893], X[1577] - 3 X[44429], 3 X[1734] - X[4729], 3 X[2254] + X[4822], X[4822] - 3 X[14349], 3 X[44435] - X[47712], X[3762] - 3 X[47814], X[4063] - 3 X[47828], X[4391] - 3 X[47816], X[4978] - 3 X[47819], X[21185] - 3 X[47757], 5 X[30795] - 3 X[47875], 5 X[31209] - 3 X[47817], 5 X[31251] - 3 X[47872], X[47694] - 3 X[47795], X[47697] - 3 X[47818], X[47711] - 3 X[47808]

X(48066) lies on these lines: {10, 514}, {513, 4401}, {522, 14288}, {523, 23815}, {659, 47888}, {661, 4905}, {663, 995}, {667, 47893}, {784, 3837}, {830, 905}, {978, 4040}, {1577, 44429}, {1734, 4729}, {2254, 4822}, {2512, 3776}, {3004, 29021}, {3669, 4160}, {3705, 44435}, {3762, 47814}, {3800, 4925}, {3835, 8714}, {3960, 8678}, {4063, 47828}, {4391, 47816}, {4560, 29033}, {4724, 17749}, {4770, 29226}, {4778, 47842}, {4791, 21260}, {4794, 6004}, {4818, 23879}, {4844, 21302}, {4893, 16569}, {4913, 29302}, {4978, 47819}, {6686, 47778}, {15654, 44408}, {16892, 29358}, {17069, 28481}, {20517, 21212}, {21123, 23657}, {21185, 24239}, {21196, 29190}, {21301, 29344}, {24719, 29270}, {26038, 47775}, {27452, 45782}, {30795, 47875}, {31209, 47817}, {31251, 47872}, {32094, 36238}, {45746, 47715}, {47679, 47719}, {47694, 47795}, {47697, 47818}, {47711, 47808}

X(48066) = midpoint of X(i) and X(j) for these {i,j}: {661, 4905}, {764, 4490}, {905, 2526}, {1491, 2530}, {2254, 14349}, {3777, 4705}, {45746, 47715}, {47679, 47719}
X(48066) = reflection of X(i) in X(j) for these {i,j}: {4401, 14838}, {4791, 21260}, {4823, 3837}, {20517, 21212}
X(48066) = crossdifference of every pair of points on line {1914, 16777}
X(48066) = barycentric product X(i)*X(j) for these {i,j}: {1, 47677}, {513, 17228}, {514, 7226}
X(48066) = barycentric quotient X(i)/X(j) for these {i,j}: {7226, 190}, {17228, 668}, {47677, 75}
X(48066) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1491, 3777, 4705}, {2530, 4705, 3777}


X(48067) = X(513)X(4468)∩X(514)X(4380)

Barycentrics    (b - c)*(5*a^2 + 2*a*b + b^2 + 2*a*c + c^2) : :
X(48067) = 3 X[4468] - 4 X[47890], 3 X[4380] - X[47661], 5 X[4380] - X[47668], 5 X[47661] - 3 X[47668], 3 X[26853] + X[47659], 3 X[649] - X[23731], 4 X[649] - 3 X[47785], 4 X[23731] - 9 X[47785], 4 X[2527] - 3 X[47760], 4 X[2529] - 3 X[47788], 2 X[3004] - 3 X[4786], 2 X[3676] - 3 X[47763], 2 X[3835] - 3 X[47768], 2 X[4106] - 3 X[47789], 4 X[4394] - 3 X[47783], 4 X[4521] - 3 X[47759], 3 X[4776] - 4 X[43061], 7 X[6590] - 6 X[45343], 3 X[4927] - 4 X[7653], 2 X[4940] - 3 X[47767], 3 X[7192] - X[47650], 2 X[20295] - 3 X[47787], 3 X[21183] - 2 X[23729]

X(48067) lies on these lines: {513, 4468}, {514, 4380}, {522, 26853}, {649, 23731}, {2527, 47760}, {2529, 47788}, {3004, 4786}, {3667, 47660}, {3676, 47763}, {3835, 47768}, {4025, 4790}, {4106, 47789}, {4394, 47783}, {4521, 47759}, {4776, 43061}, {4778, 17494}, {4785, 6590}, {4813, 11068}, {4927, 7653}, {4940, 47767}, {4962, 47665}, {6006, 25259}, {7192, 47650}, {20295, 47787}, {21183, 23729}, {28225, 47666}, {28229, 47667}, {28859, 45745}, {28878, 47663}

X(48067) = reflection of X(i) in X(j) for these {i,j}: {4025, 4790}, {4813, 11068}


X(48068) = X(513)X(4468)∩X(514)X(47692)

Barycentrics    (b - c)*(5*a^3 - a^2*b + 3*a*b^2 + b^3 - a^2*c - 4*a*b*c + b^2*c + 3*a*c^2 + b*c^2 + c^3) : :
X(48068) = 4 X[659] - 3 X[47785], 2 X[3676] - 3 X[47805], 4 X[8689] - 3 X[47800], 2 X[3776] - 3 X[47801], 3 X[3803] - 2 X[39545], 2 X[46403] - 3 X[47787]

X(8068) lies on these lines: {513, 4468}, {514, 47692}, {522, 47663}, {659, 47785}, {661, 28225}, {1443, 1447}, {3239, 47685}, {3776, 47801}, {3803, 39545}, {4088, 6006}, {4962, 47700}, {28209, 47761}, {28229, 47701}, {46403, 47787}

X(48068) = reflection of X(47685) in X(3239)
X(48068) = crossdifference of every pair of points on line {1334, 16502}


X(48069) = X(513)X(4468)∩X(514)X(1734)

Barycentrics    (b - c)*(a^3 + 3*a^2*b - a*b^2 + b^3 + 3*a^2*c + b^2*c - a*c^2 + b*c^2 + c^3) : :
X(48069) = 2 X[676] - 3 X[47761], 2 X[3239] - 3 X[47809], 2 X[3676] - 3 X[47824], X[47691] - 3 X[47824], 2 X[3716] - 3 X[47766], 2 X[3835] - 3 X[47806], 2 X[4010] - 3 X[47787], 3 X[4453] - X[47692], 2 X[4458] - 3 X[47758], 4 X[4521] - 3 X[47821], 4 X[7658] - 3 X[47797], 2 X[7662] - 3 X[47789], 4 X[9508] - 3 X[47785], 2 X[13246] - 3 X[45313], 2 X[14837] - 3 X[47836], X[47708] - 3 X[47836], X[20295] - 3 X[47808], 3 X[21183] - 2 X[23770], 4 X[25380] - 3 X[47757], 5 X[27013] - 3 X[47798], 4 X[31286] - 3 X[47800], 4 X[43061] - 3 X[47804], X[47695] - 3 X[47762], X[47699] - 3 X[47825], X[47701] - 3 X[47828], X[47702] - 3 X[47886]

X(48069) lies on these lines: {10, 29132}, {512, 6332}, {513, 4468}, {514, 1734}, {522, 649}, {523, 4025}, {676, 47761}, {905, 3800}, {918, 7659}, {2526, 4925}, {3239, 47809}, {3676, 47691}, {3716, 47766}, {3798, 28161}, {3835, 47806}, {4010, 47787}, {4088, 28846}, {4369, 47123}, {4380, 47687}, {4453, 47692}, {4458, 47758}, {4467, 47689}, {4521, 47821}, {4724, 11068}, {4750, 28169}, {4777, 4786}, {4913, 45745}, {7658, 47797}, {7662, 47789}, {8678, 44448}, {9508, 29144}, {13246, 45313}, {14837, 47708}, {16892, 28147}, {17072, 29118}, {20295, 47808}, {21183, 23770}, {21188, 47712}, {21192, 29164}, {25380, 47757}, {27013, 47798}, {28292, 47728}, {28878, 47698}, {31286, 47800}, {43061, 47804}, {45882, 47130}, {47695, 47762}, {47699, 47825}, {47701, 47828}, {47702, 47886}

X(48069) = midpoint of X(i) and X(j) for these {i,j}: {4380, 47687}, {4467, 47689}
X(48069) = reflection of X(i) in X(j) for these {i,j}: {2526, 4925}, {4724, 11068}, {45745, 4913}, {47123, 4369}, {47691, 3676}, {47708, 14837}, {47712, 21188}
X(48069) = crossdifference of every pair of points on line {1193, 2271}
X(48069) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47691, 47824, 3676}, {47708, 47836, 14837}


X(48070) = X(513)X(4468)∩X(514)X(15416)

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

X(48070) lies on these lines: {190, 36146}, {513, 4468}, {514, 15416}, {522, 1027}, {525, 2489}, {918, 3669}, {1019, 2484}, {1022, 30701}, {1308, 4568}, {2495, 42341}, {2509, 4025}, {3064, 21438}, {3239, 15413}, {3261, 20927}, {3732, 15742}, {4858, 20907}, {5942, 20293}, {6590, 7199}, {7253, 14954}, {17353, 28590}

X(48070) = reflection of X(i) in X(j) for these {i,j}: {4025, 2509}, {15413, 3239}
X(48070) = isotomic conjugate of X(3732)
X(48070) = isotomic conjugate of the anticomplement of X(1565)
X(48070) = X(42384)-anticomplementary conjugate of X(315)
X(48070) = X(i)-cross conjugate of X(j) for these (i,j): {1565, 2}, {2310, 75}, {38386, 42361}
X(48070) = X(i)-isoconjugate of X(j) for these (i,j): {6, 1633}, {31, 3732}, {99, 21750}, {100, 16502}, {101, 614}, {108, 7124}, {109, 2082}, {110, 16583}, {112, 17441}, {162, 23620}, {163, 3914}, {497, 1415}, {648, 22363}, {651, 7083}, {662, 40934}, {692, 4000}, {906, 1851}, {934, 30706}, {1040, 32674}, {1184, 1310}, {1262, 17115}, {1461, 4319}, {1473, 1783}, {1813, 40987}, {3673, 32739}, {3939, 28017}, {4211, 4574}, {4559, 5324}, {4565, 40965}, {4592, 8020}, {5546, 40961}, {6614, 28070}, {7289, 8750}, {18589, 32676}, {19459, 36099}, {22057, 24019}
X(48070) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 3732), (9, 1633), (11, 2082), (115, 3914), (125, 23620), (244, 16583), (1015, 614), (1084, 40934), (1086, 4000), (1146, 497), (2968, 6554), (5139, 8020), (5190, 1851), (5515, 5286), (8054, 16502), (14714, 30706), (15526, 18589), (26932, 7289), (34591, 17441), (35071, 22057), (35072, 1040), (35508, 4319), (38983, 7124), (38986, 21750), (38991, 7083), (39006, 1473), (40615, 7195), (40617, 28017), (40618, 17170), (40619, 3673), (40626, 27509)
X(48070) = cevapoint of X(i) and X(j) for these (i,j): {513, 2509}, {514, 3239}, {525, 661}, {4391, 21438}
X(48070) = trilinear pole of line {244, 2968}
X(48070) = crossdifference of every pair of points on line {7083, 16502}
X(48070) = barycentric product X(i)*X(j) for these {i,j}: {514, 30701}, {522, 8817}, {525, 40411}, {1037, 35519}, {1041, 35518}, {1577, 40403}, {2484, 40831}, {3239, 30705}, {3261, 7123}, {3942, 42384}, {4391, 7131}, {4572, 14935}, {7084, 40495}, {8269, 24026}
X(48070) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1633}, {2, 3732}, {512, 40934}, {513, 614}, {514, 4000}, {520, 22057}, {521, 1040}, {522, 497}, {523, 3914}, {525, 18589}, {647, 23620}, {649, 16502}, {650, 2082}, {652, 7124}, {656, 17441}, {657, 30706}, {661, 16583}, {663, 7083}, {693, 3673}, {798, 21750}, {810, 22363}, {905, 7289}, {1037, 109}, {1041, 108}, {1459, 1473}, {2310, 17115}, {2484, 1184}, {2489, 8020}, {2509, 15487}, {3239, 6554}, {3669, 28017}, {3676, 7195}, {3729, 28999}, {3737, 5324}, {3900, 4319}, {4017, 40961}, {4025, 17170}, {4041, 40965}, {4064, 21015}, {4079, 21813}, {4130, 28070}, {4163, 4012}, {4466, 21107}, {4468, 41785}, {4580, 18084}, {6332, 27509}, {6590, 5286}, {7084, 692}, {7123, 101}, {7131, 651}, {7199, 16750}, {7649, 1851}, {8269, 7045}, {8817, 664}, {14208, 20235}, {14935, 663}, {18344, 40987}, {22443, 30689}, {23874, 7386}, {25009, 41787}, {25259, 17671}, {30701, 190}, {30705, 658}, {40403, 662}, {40411, 648}


X(48071) = X(513)X(3716)∩X(514)X(4380)

Barycentrics    (b - c)*(4*a^2 + 3*a*b + 3*a*c + b*c) : :
X(48071) = 3 X[3835] - 4 X[4369], 7 X[3835] - 8 X[4885], 11 X[3835] - 12 X[4928], 9 X[3835] - 8 X[4940], 11 X[3835] - 16 X[7653], 5 X[3835] - 6 X[47779], 7 X[4369] - 6 X[4885], 11 X[4369] - 9 X[4928], 2 X[4369] - 3 X[4932], 3 X[4369] - 2 X[4940], 11 X[4369] - 12 X[7653], 10 X[4369] - 9 X[47779], 22 X[4885] - 21 X[4928], 4 X[4885] - 7 X[4932], 9 X[4885] - 7 X[4940], 11 X[4885] - 14 X[7653], 20 X[4885] - 21 X[47779], 6 X[4928] - 11 X[4932], 27 X[4928] - 22 X[4940], 3 X[4928] - 4 X[7653], 10 X[4928] - 11 X[47779], 9 X[4932] - 4 X[4940], 11 X[4932] - 8 X[7653], 5 X[4932] - 3 X[47779], 11 X[4940] - 18 X[7653], 20 X[4940] - 27 X[47779], 40 X[7653] - 33 X[47779], X[4380] - 3 X[4979], 7 X[4380] - 3 X[47664], 7 X[4979] - X[47664], 7 X[649] - 5 X[26777], 3 X[649] - X[31290], 5 X[649] - 3 X[47775], 15 X[26777] - 7 X[31290], 25 X[26777] - 21 X[47775], 5 X[31290] - 9 X[47775], 2 X[661] - 3 X[45313], X[4382] - 3 X[7192], 7 X[4382] - 9 X[47869], 7 X[7192] - 3 X[47869], X[4813] - 3 X[47763], 2 X[31286] - 3 X[47763], 3 X[4984] - X[47667], X[23731] - 3 X[47755]

X(48071) lies on these lines: {513, 3716}, {514, 4380}, {649, 26777}, {661, 45313}, {3798, 28225}, {4382, 4785}, {4500, 28217}, {4778, 21196}, {4790, 28840}, {4813, 31286}, {4897, 28859}, {4984, 47667}, {23731, 47755}, {28886, 47890}, {28906, 47660}

X(48071) = reflection of X(i) in X(j) for these {i,j}: {3835, 4932}, {4813, 31286}
X(48071) = X(28200)-complementary conjugate of X(2)
X(48071) = {X(4813),X(47763)}-harmonic conjugate of X(31286)


X(48072) = X(513)X(3716)∩X(514)X(47692)

Barycentrics    (b - c)*(4*a^3 - a^2*b + 3*a*b^2 - a^2*c - a*b*c + b^2*c + 3*a*c^2 + b*c^2) : :
X(48072) = 4 X[3716] - 3 X[3835], 2 X[2254] - 3 X[45313], 2 X[2526] - 3 X[47778], 2 X[21212] - 3 X[47801], 2 X[31286] - 3 X[47805]

X(48072) lies on these lines: {513, 3716}, {514, 47692}, {1491, 8689}, {2254, 45313}, {2526, 47778}, {3239, 4979}, {4380, 4962}, {4474, 28470}, {4522, 28217}, {21212, 47801}, {28225, 47887}, {28565, 47728}, {31286, 47805}

X(48072) = reflection of X(1491) in X(8689)


X(48073) = X(513)X(3716)∩X(514)X(1734)

Barycentrics    (b - c)*(3*a^2*b - a*b^2 + 3*a^2*c + 3*a*b*c + b^2*c - a*c^2 + b*c^2) : :
X(48073) = 2 X[3716] - 3 X[47779], 3 X[3835] - 4 X[3837], 5 X[3835] - 4 X[4806], 5 X[3837] - 3 X[4806], 2 X[3837] - 3 X[24720], 2 X[4806] - 5 X[24720], 2 X[659] - 3 X[45313], X[4724] - 3 X[47824], 2 X[31286] - 3 X[47824], X[4822] - 3 X[47819], 2 X[13246] - 3 X[47758], 3 X[21115] - X[47692], 4 X[25380] - 3 X[47778], 3 X[31148] - X[47697]

X(48073) lies on these lines: {513, 3716}, {514, 1734}, {522, 21146}, {659, 45313}, {661, 28225}, {693, 3667}, {812, 7659}, {1491, 4778}, {2505, 28902}, {2526, 28840}, {4010, 6006}, {4147, 29198}, {4724, 31286}, {4785, 46403}, {4804, 4962}, {4822, 47819}, {4824, 28229}, {4979, 47685}, {6005, 23789}, {6372, 17072}, {13246, 47758}, {21115, 47692}, {25380, 47778}, {28155, 47675}, {28161, 47672}, {30519, 47690}, {31148, 47697}, {36848, 45684}

X(48073) = midpoint of X(4979) and X(47685)
X(48073) = reflection of X(i) in X(j) for these {i,j}: {3835, 24720}, {4724, 31286}
X(48073) = crossdifference of every pair of points on line {2176, 2280}
X(48073) = {X(4724),X(47824)}-harmonic conjugate of X(31286)


X(48074) = X(513)X(4401)∩X(514)X(4380)

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

X(48074) lies on these lines: {513, 4401}, {514, 4380}, {876, 6005}, {1022, 25417}, {1308, 8652}, {3257, 37211}, {4562, 32042}, {4785, 7199}, {4790, 15309}, {4823, 4932}, {7192, 29270}

X(48074) = reflection of X(4823) in X(4932)
X(48074) = X(i)-Ceva conjugate of X(j) for these (i,j): {30597, 244}, {37211, 25417}
X(48074) = X(i)-cross conjugate of X(j) for these (i,j): {244, 30597}, {14349, 514}
X(48074) = X(i)-isoconjugate of X(j) for these (i,j): {6, 4756}, {8, 36074}, {59, 4820}, {100, 16777}, {101, 1698}, {109, 4007}, {163, 4066}, {644, 5221}, {651, 3715}, {692, 28605}, {765, 4813}, {813, 4716}, {901, 4727}, {1016, 4834}, {1018, 4658}, {1110, 4823}, {1252, 4802}, {1293, 4898}, {1783, 3927}, {3939, 4654}, {4551, 4877}, {4557, 5333}, {4570, 4838}, {4574, 31902}, {4600, 4826}, {4958, 9268}, {15322, 25431}, {30596, 32739}, {35327, 43260}
X(48074) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 4756), (11, 4007), (115, 4066), (513, 4813), (514, 4823), (661, 4802), (1015, 1698), (1086, 28605), (6615, 4820), (8054, 16777), (38979, 4727), (38991, 3715), (39006, 3927), (40617, 4654), (40619, 30596), (40623, 4716)
X(48074) = cevapoint of X(513) and X(4790)
X(48074) = crosspoint of X(25417) and X(37211)
X(48074) = crosssum of X(4813) and X(16777)
X(48074) = trilinear pole of line {244, 7202}
X(48074) = crossdifference of every pair of points on line {3715, 16777}
X(48074) = barycentric product X(i)*X(j) for these {i,j}: {244, 32042}, {513, 30598}, {514, 25417}, {1086, 37211}, {1111, 8652}, {3261, 34819}, {3669, 42030}, {4802, 30597}, {7199, 28625}
X(48074) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4756}, {244, 4802}, {513, 1698}, {514, 28605}, {523, 4066}, {604, 36074}, {649, 16777}, {650, 4007}, {659, 4716}, {663, 3715}, {693, 30596}, {1015, 4813}, {1019, 5333}, {1086, 4823}, {1459, 3927}, {1635, 4727}, {2087, 4958}, {2170, 4820}, {3121, 4826}, {3125, 4838}, {3248, 4834}, {3669, 4654}, {3733, 4658}, {4394, 4898}, {4449, 4942}, {7200, 4842}, {7202, 23883}, {7252, 4877}, {8652, 765}, {14419, 4938}, {16726, 4960}, {25417, 190}, {27846, 4810}, {28625, 1018}, {30597, 32042}, {30598, 668}, {32042, 7035}, {34819, 101}, {37211, 1016}, {42030, 646}, {43924, 5221}


X(48075) = X(513)X(4401)∩X(514)X(1734)

Barycentrics    a*(b - c)*(2*a*b - 2*b^2 + 2*a*c + b*c - 2*c^2) : :
X(48075) = X[1734] - 3 X[2254], 5 X[1734] - 3 X[4041], X[1734] + 3 X[4905], 7 X[1734] + 3 X[23738], 5 X[2254] - X[4041], 7 X[2254] + X[23738], X[4041] + 5 X[4905], 7 X[4041] + 5 X[23738], 7 X[4905] - X[23738], X[1769] - 3 X[23800], X[4170] - 3 X[47819], X[4791] + 2 X[23795]

X(48075) lies on these lines: {513, 4401}, {514, 1734}, {522, 23789}, {656, 28225}, {900, 23815}, {905, 4794}, {1519, 1769}, {2526, 15309}, {2530, 6005}, {3309, 3960}, {3669, 3887}, {3777, 29350}, {3798, 24804}, {4017, 4962}, {4025, 23828}, {4151, 23796}, {4170, 47819}, {4730, 23765}, {4791, 23795}, {4823, 8714}, {6245, 21188}, {16892, 29164}, {21143, 23657}, {24462, 28906}, {29270, 46403}, {47677, 47714}

X(48075) = midpoint of X(i) and X(j) for these {i,j}: {2254, 4905}, {4730, 23765}, {47677, 47714}
X(48075) = reflection of X(i) in X(j) for these {i,j}: {4794, 905}, {4823, 24720}, {21201, 21188}
X(48075) = crossdifference of every pair of points on line {2280, 16777}
X(48075) = barycentric product X(i)*X(j) for these {i,j}: {513, 17241}, {514, 4430}
X(48075) = barycentric quotient X(i)/X(j) for these {i,j}: {4430, 190}, {17241, 668}


X(48076) = X(513)X(4088)∩X(514)X(4838)

Barycentrics    (b - c)*(-a^2 - 3*a*b + b^2 - 3*a*c + c^2) : :
X(48076) = 5 X[649] - 6 X[47884], 3 X[661] - 2 X[4025], 7 X[661] - 6 X[47783], 4 X[661] - 3 X[47886], 7 X[4025] - 9 X[47783], 8 X[4025] - 9 X[47886], 8 X[47783] - 7 X[47886], 4 X[3239] - 3 X[31148], 2 X[3676] - 3 X[47764], 2 X[3776] - 3 X[47759], 3 X[4120] - 2 X[43067], 2 X[4369] - 3 X[47769], 3 X[4379] - 4 X[14321], 2 X[4467] - 3 X[47878], 2 X[4790] - 3 X[6546], 4 X[4806] - 3 X[47887], 3 X[4893] - 2 X[4897], 2 X[4932] - 3 X[30565], 4 X[4940] - 3 X[6545], 2 X[7192] - 3 X[47874], 2 X[21104] - 3 X[31147], 3 X[21116] - 4 X[23813], 5 X[24924] - 6 X[47765], 4 X[25666] - 3 X[47755]

X(48076) lies on these lines: {513, 4088}, {514, 4838}, {649, 47884}, {661, 4025}, {693, 28855}, {824, 31290}, {918, 4813}, {2786, 47666}, {3239, 31148}, {3676, 47764}, {3700, 28902}, {3776, 47759}, {4106, 28910}, {4120, 43067}, {4369, 47769}, {4379, 14321}, {4467, 28906}, {4468, 4979}, {4790, 6546}, {4806, 47887}, {4820, 47671}, {4893, 4897}, {4932, 30565}, {4940, 6545}, {4988, 28898}, {7192, 28886}, {17494, 28867}, {20295, 28851}, {21104, 31147}, {21116, 23813}, {23731, 30520}, {24924, 47765}, {25259, 28840}, {25666, 47755}, {28225, 47687}, {28871, 47676}, {28878, 47672}

X(48076) = reflection of X(i) in X(j) for these {i,j}: {4979, 4468}, {47671, 4820}


X(48077) = X(513)X(4088)∩X(514)X(47685)

Barycentrics    (b - c)*(-a^3 - 2*a*b^2 + b^3 - 2*a*b*c + b^2*c - 2*a*c^2 + b*c^2 + c^3) : :
X(48077) = 4 X[676] - 5 X[30835], 4 X[1491] - 3 X[47886], 4 X[3837] - 3 X[47887], 2 X[4142] - 3 X[47814], 2 X[4369] - 3 X[47808], 2 X[4458] - 3 X[44429], 4 X[4521] - 3 X[47801], 4 X[4522] - 3 X[47874], 2 X[47694] - 3 X[47874], 3 X[4728] - 2 X[47123], 4 X[13246] - 5 X[31209], 2 X[20517] - 3 X[47816], 2 X[24720] - 3 X[31131], 5 X[24924] - 6 X[47806], 4 X[25666] - 3 X[47798]

X(48077) lies on these lines: {8, 28468}, {72, 3309}, {513, 4088}, {514, 47685}, {522, 661}, {523, 4382}, {676, 30835}, {900, 4724}, {1491, 47886}, {2526, 16892}, {3667, 4380}, {3835, 47695}, {3837, 47887}, {4142, 47814}, {4369, 47808}, {4458, 44429}, {4462, 4696}, {4498, 28481}, {4521, 47801}, {4522, 47694}, {4728, 47123}, {4729, 28478}, {4777, 47701}, {4897, 4925}, {13246, 31209}, {20517, 47816}, {20909, 23684}, {21301, 23877}, {24720, 31131}, {24924, 47806}, {25666, 47798}, {28161, 47657}, {28221, 47826}

X(48077) = reflection of X(i) in X(j) for these {i,j}: {4729, 44448}, {4897, 4925}, {16892, 2526}, {47694, 4522}, {47695, 3835}
X(48077) = crossdifference of every pair of points on line {1468, 5299}
X(48077) = {X(4522),X(47694)}-harmonic conjugate of X(47874)


X(48078) = X(513)X(4088)∩X(514)X(4170)

Barycentrics    (b - c)*(a^3 - 2*a^2*b + b^3 - 2*a^2*c - 4*a*b*c + b^2*c + b*c^2 + c^3) : :
X(48078) = 2 X[3004] - 3 X[47826], 4 X[3239] - 3 X[47812], 4 X[3716] - 3 X[47887], 2 X[47676] - 3 X[47887], 2 X[3776] - 3 X[47821], 2 X[4025] - 3 X[47811], 2 X[4522] - 3 X[47772], 2 X[4818] - 3 X[47775], 5 X[8656] - 4 X[39545], 2 X[21104] - 3 X[47832], 2 X[21146] - 3 X[47874], 2 X[24720] - 3 X[30565]

X(48078) lies on these lines: {513, 4088}, {514, 4170}, {522, 47664}, {918, 4724}, {2254, 4468}, {3004, 47826}, {3239, 47812}, {3700, 4813}, {3716, 47676}, {3776, 47821}, {4025, 47811}, {4522, 47772}, {4778, 47660}, {4818, 47775}, {6332, 23738}, {8656, 39545}, {21104, 47832}, {21146, 47874}, {23731, 28195}, {24720, 30565}, {28840, 47696}, {28851, 47694}, {28863, 47699}, {28890, 47691}, {30520, 47701}

X(48078) = reflection of X(i) in X(j) for these {i,j}: {2254, 4468}, {23738, 6332}, {47676, 3716}
X(48078) = {X(3716),X(47676)}-harmonic conjugate of X(47887)


X(48079) = X(2)X(4790)∩X(514)X(4838)

Barycentrics    (b - c)*(-2*a^2 - 2*a*b - 2*a*c + b*c) : :
X(48079) = 3 X[2] - 4 X[4940], 3 X[693] - 4 X[4106], 3 X[693] - 2 X[7192], 5 X[693] - 6 X[21297], 7 X[693] - 8 X[23813], 5 X[693] - 4 X[43067], 7 X[693] - 6 X[47780], 2 X[4106] - 3 X[20295], 10 X[4106] - 9 X[21297], 7 X[4106] - 6 X[23813], 5 X[4106] - 3 X[43067], 14 X[4106] - 9 X[47780], X[7192] - 3 X[20295], 5 X[7192] - 9 X[21297], 7 X[7192] - 12 X[23813], 5 X[7192] - 6 X[43067], 7 X[7192] - 9 X[47780], 5 X[20295] - 3 X[21297], 7 X[20295] - 4 X[23813], 5 X[20295] - 2 X[43067], 7 X[20295] - 3 X[47780], 21 X[21297] - 20 X[23813], 3 X[21297] - 2 X[43067], 7 X[21297] - 5 X[47780], 10 X[23813] - 7 X[43067], 4 X[23813] - 3 X[47780], 14 X[43067] - 15 X[47780], 5 X[649] - 6 X[4763], 2 X[649] - 3 X[4776], 3 X[649] - 4 X[25666], 4 X[649] - 5 X[31209], 4 X[4763] - 5 X[4776], 9 X[4763] - 10 X[25666], 24 X[4763] - 25 X[31209], 9 X[4776] - 8 X[25666], 6 X[4776] - 5 X[31209], 16 X[25666] - 15 X[31209], 2 X[650] - 3 X[47759], X[26853] - 3 X[47759], 4 X[661] - 3 X[31150], 2 X[4380] - 3 X[31150], 4 X[4813] - X[47664], 6 X[3835] - 5 X[24924], 4 X[3835] - 3 X[47762], 3 X[4979] - 5 X[24924], 2 X[4979] - 3 X[47762], 10 X[24924] - 9 X[47762], 2 X[4369] - 3 X[31147], 3 X[4728] - 2 X[4932], 2 X[4784] - 3 X[44429], 4 X[4806] - 3 X[47804], 2 X[4830] - 3 X[47826], 2 X[4834] - 3 X[47814], 4 X[4885] - 5 X[26798], 4 X[4885] - 3 X[47763], 5 X[26798] - 3 X[47763], 2 X[4897] - 3 X[44435], 2 X[4976] - 3 X[47781], 2 X[11068] - 3 X[47764], 4 X[14321] - 3 X[47771], 5 X[26777] - 6 X[47777], 5 X[27013] - 6 X[47760], 7 X[27138] - 6 X[47761], 3 X[47769] - 2 X[47890]

X(48079) lies on these lines: {2, 4790}, {320, 350}, {514, 4838}, {522, 47657}, {649, 4763}, {650, 26853}, {661, 4380}, {812, 4813}, {824, 23731}, {900, 45746}, {918, 47651}, {1019, 29738}, {2642, 27574}, {2786, 47677}, {3004, 28217}, {3667, 4467}, {3766, 6005}, {3835, 4979}, {4024, 28859}, {4025, 6006}, {4369, 31147}, {4382, 28840}, {4608, 28195}, {4728, 4932}, {4762, 31290}, {4784, 26277}, {4801, 15309}, {4806, 47804}, {4820, 47659}, {4830, 47826}, {4834, 47814}, {4885, 26798}, {4897, 39386}, {4926, 17161}, {4976, 47781}, {4977, 47656}, {6008, 17494}, {9400, 20983}, {11068, 47764}, {13401, 27417}, {14321, 47771}, {16874, 26249}, {16892, 28867}, {21124, 28493}, {21189, 23733}, {23725, 23792}, {23729, 47676}, {23836, 30479}, {24191, 38979}, {25259, 47662}, {26777, 47777}, {27013, 47760}, {27138, 47761}, {28846, 47652}, {28898, 47653}, {29013, 47683}, {30804, 42325}, {38389, 40619}, {47769, 47890}

X(48079) = reflection of X(i) in X(j) for these {i,j}: {693, 20295}, {4380, 661}, {4790, 4940}, {4979, 3835}, {7192, 4106}, {26853, 650}, {47659, 4820}, {47662, 25259}, {47664, 47666}, {47666, 4813}, {47675, 4382}, {47676, 23729}
X(48079) = anticomplement of X(4790)
X(48079) = anticomplement of the isogonal conjugate of X(4606)
X(48079) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {100, 41915}, {2334, 4440}, {4606, 8}, {4614, 75}, {4624, 3434}, {4627, 1}, {4633, 17135}, {4866, 37781}, {5545, 3875}, {5936, 150}, {8694, 2}, {14626, 39353}, {25430, 149}, {34074, 192}, {34820, 39351}, {35339, 41821}, {40023, 21293}
X(48079) = X(692)-isoconjugate of X(39711)
X(48079) = X(1086)-Dao conjugate of X(39711)
X(48079) = crosspoint of X(668) and X(30598)
X(48079) = barycentric product X(514)*X(17393)
X(48079) = barycentric quotient X(i)/X(j) for these {i,j}: {514, 39711}, {17393, 190}
X(48079) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 4776, 31209}, {661, 4380, 31150}, {3835, 4979, 47762}, {4106, 7192, 693}, {4790, 4940, 2}, {7192, 20295, 4106}, {21297, 43067, 693}, {23813, 47780, 693}, {26798, 47763, 4885}, {26853, 47759, 650}


X(48080) = X(1)X(29148)∩X(514)X(4170)

Barycentrics    (b - c)*(-2*a^2*b - 2*a^2*c - a*b*c + b^2*c + b*c^2) : :
X(48080) = 3 X[693] - 2 X[21146], 3 X[4010] - X[21146], 2 X[43067] - 3 X[47834], 2 X[649] - 3 X[47804], 4 X[3716] - 3 X[47804], 2 X[650] - 3 X[47821], 2 X[1491] - 3 X[4776], 3 X[4776] - 4 X[4806], 2 X[905] - 3 X[47840], 2 X[1019] - 3 X[47820], 2 X[1734] - 3 X[47814], 4 X[4129] - 3 X[47814], 2 X[2254] - 3 X[44429], 2 X[3798] - 3 X[47800], 4 X[3835] - 3 X[44429], 4 X[3239] - 3 X[47809], 2 X[4025] - 3 X[47797], 2 X[4063] - 3 X[47815], 3 X[4120] - 2 X[4522], 2 X[4369] - 3 X[47832], 3 X[4448] - 2 X[4782], 3 X[4728] - 2 X[24720], X[4784] - 3 X[4800], 2 X[4784] - 3 X[47762], 3 X[4800] - 2 X[4874], 4 X[4874] - 3 X[47762], 4 X[4885] - 3 X[47824], 2 X[7659] - 3 X[47824], 3 X[4893] - 2 X[4913], 3 X[4905] - 4 X[23814], 2 X[4905] - 3 X[47819], 8 X[23814] - 9 X[47819], 2 X[4932] - 3 X[47813], 4 X[9508] - 5 X[31209], 2 X[9508] - 3 X[47822], 5 X[31209] - 6 X[47822], 2 X[14838] - 3 X[47838], 5 X[24924] - 6 X[47831], 4 X[25380] - 5 X[30835], 4 X[25666] - 3 X[47828], X[26853] - 3 X[47805], 5 X[27013] - 6 X[47803], 7 X[27138] - 6 X[47802]

X(48080) lies on these lines: {1, 29148}, {4, 885}, {21, 667}, {320, 350}, {512, 4391}, {514, 4170}, {522, 661}, {523, 8663}, {525, 47708}, {649, 3716}, {650, 47821}, {659, 4380}, {660, 42722}, {663, 6002}, {669, 25902}, {676, 4897}, {784, 4983}, {812, 4724}, {824, 47701}, {826, 47709}, {900, 1491}, {905, 47840}, {918, 47691}, {1019, 47820}, {1499, 10015}, {1577, 6005}, {1734, 4129}, {2254, 3667}, {2476, 21260}, {2496, 10129}, {2526, 4940}, {2787, 4775}, {3239, 47809}, {3485, 3669}, {3486, 4162}, {3700, 47690}, {3762, 29350}, {3777, 4992}, {3800, 47707}, {3801, 29200}, {3837, 28217}, {3869, 4083}, {4025, 47797}, {4040, 29013}, {4063, 12514}, {4120, 4522}, {4122, 29144}, {4147, 4729}, {4367, 29170}, {4369, 47832}, {4444, 28867}, {4448, 4782}, {4486, 4785}, {4500, 47703}, {4728, 6006}, {4761, 4791}, {4777, 4824}, {4778, 47672}, {4784, 4800}, {4794, 29178}, {4801, 6372}, {4810, 29362}, {4879, 29324}, {4885, 7659}, {4893, 4913}, {4905, 12047}, {4932, 47813}, {4962, 47810}, {4977, 47675}, {5698, 6008}, {6161, 11114}, {6872, 31291}, {6875, 39227}, {7265, 29021}, {7927, 47706}, {8641, 16158}, {8714, 14349}, {9508, 31209}, {14009, 30968}, {14838, 47838}, {17577, 31149}, {21132, 28468}, {23655, 42312}, {23729, 47686}, {23745, 28565}, {23770, 47676}, {23836, 34919}, {23875, 47712}, {24457, 35353}, {24924, 47831}, {25009, 25299}, {25380, 30835}, {25537, 25926}, {25666, 47828}, {25834, 25837}, {26546, 44445}, {26853, 47805}, {27013, 47803}, {27138, 47802}, {28846, 47123}, {28851, 47704}, {28939, 41236}, {29029, 47684}, {29126, 47728}, {29132, 47682}, {29168, 47718}, {29188, 47721}, {29212, 47727}, {29358, 47713}, {30520, 47688}, {31131, 47786}, {44449, 47695}

X(48080) = midpoint of X(44449) and X(47695)
X(48080) = reflection of X(i) in X(j) for these {i,j}: {649, 3716}, {693, 4010}, {1491, 4806}, {1734, 4129}, {2254, 3835}, {2526, 4940}, {3777, 4992}, {4380, 659}, {4729, 4147}, {4761, 4791}, {4784, 4874}, {4897, 676}, {7192, 7662}, {7659, 4885}, {31131, 47786}, {46403, 4106}, {47676, 23770}, {47685, 24719}, {47686, 23729}, {47689, 4122}, {47690, 3700}, {47703, 4500}, {47729, 4775}, {47762, 4800}
X(48080) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {28847, 2}, {39721, 150}, {39954, 149}, {40028, 21293}
X(48080) = X(i)-isoconjugate of X(j) for these (i,j): {101, 39981}, {32739, 40030}
X(48080) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 39981), (40619, 40030)
X(48080) = crosspoint of X(668) and X(27475)
X(48080) = crosssum of X(667) and X(2280)
X(48080) = crossdifference of every pair of points on line {213, 1468}
X(48080) = barycentric product X(i)*X(j) for these {i,j}: {513, 30830}, {693, 37657}
X(48080) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 39981}, {693, 40030}, {30830, 668}, {37657, 100}
X(48080) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 3716, 47804}, {1491, 4806, 4776}, {1734, 4129, 47814}, {2254, 3835, 44429}, {3798, 3835, 30765}, {4784, 4800, 4874}, {4784, 4874, 47762}, {4885, 7659, 47824}, {9508, 47822, 31209}


X(48081) = X(36)X(238)∩X(514)X(4170)

Barycentrics    a*(b - c)*(3*a*b + b^2 + 3*a*c + 3*b*c + c^2) : :
X(48081) = 4 X[2530] - 3 X[4905], X[2530] - 3 X[4983], 2 X[2530] - 3 X[14349], 2 X[3803] - 3 X[4040], X[4905] - 4 X[4983], 2 X[4369] - 3 X[47838], 2 X[4932] - 3 X[47818]

X(48081) lies on these lines: {36, 238}, {512, 4490}, {514, 4170}, {661, 1734}, {663, 15309}, {830, 4813}, {2084, 4502}, {2499, 44410}, {4151, 47666}, {4369, 47838}, {4401, 4979}, {4778, 4978}, {4932, 47818}, {4960, 7662}, {4992, 28209}, {6372, 23765}, {8713, 17924}, {19594, 30804}, {20295, 29186}, {23875, 47701}, {23879, 47699}, {28851, 47716}, {29062, 44449}, {29358, 47702}

X(48081) = reflection of X(i) in X(j) for these {i,j}: {1734, 661}, {4905, 14349}, {4960, 7662}, {4979, 4401}, {14349, 4983}, {44410, 2499}
X(48081) = crossdifference of every pair of points on line {37, 32912}
X(48081) = barycentric product X(1)*X(47667)
X(48081) = barycentric quotient X(47667)/X(75)


X(48082) = X(513)X(4088)∩X(514)X(4024)

Barycentrics    (b - c)*(-2*a*b + b^2 - 2*a*c + c^2) : :
X(48082) = 2 X[649] - 3 X[6546], 3 X[649] - 4 X[11068], 4 X[4468] - 3 X[6546], 3 X[4468] - 2 X[11068], 9 X[6546] - 8 X[11068], 3 X[4024] - 2 X[47656], 5 X[4024] - 2 X[47674], 3 X[25259] - X[47656], 4 X[25259] - X[47671], 5 X[25259] - X[47674], 4 X[47656] - 3 X[47671], 5 X[47656] - 3 X[47674], 5 X[47671] - 4 X[47674], 4 X[650] - 3 X[4750], 3 X[661] - 2 X[3004], 4 X[3004] - 3 X[16892], 2 X[693] - 3 X[4120], 4 X[693] - 3 X[21116], 3 X[4988] - 2 X[47657], X[47657] - 3 X[47666], 3 X[1635] - 2 X[4897], 6 X[1639] - 5 X[24924], 4 X[3239] - 3 X[4379], 8 X[3676] - 9 X[14475], 4 X[3676] - 5 X[30835], 2 X[3676] - 3 X[47765], 9 X[14475] - 10 X[30835], 3 X[14475] - 4 X[47765], 5 X[30835] - 6 X[47765], 2 X[3776] - 3 X[4776], 4 X[3835] - 3 X[6545], 2 X[3835] - 3 X[47769], 3 X[6545] - 2 X[47676], X[47676] - 3 X[47769], 2 X[4025] - 3 X[4893], 2 X[4369] - 3 X[30565], 2 X[4378] - 3 X[14432], 3 X[4453] - 4 X[25666], 2 X[4458] - 3 X[47821], 8 X[4521] - 7 X[31207], 4 X[4521] - 3 X[47758], 7 X[31207] - 6 X[47758], 3 X[4728] - 4 X[14321], 3 X[4728] - 2 X[21104], 2 X[4932] - 3 X[47771], 9 X[6544] - 8 X[31286], 3 X[6544] - 2 X[47755], 4 X[31286] - 3 X[47755], X[7192] - 3 X[47772], 6 X[10196] - 5 X[27013], 2 X[21196] - 3 X[47775], 6 X[21204] - 7 X[27138], 5 X[26985] - 6 X[45661], 7 X[27115] - 6 X[45674], 2 X[43067] - 3 X[47874], X[47653] - 3 X[47774]

X(48082) lies on these lines: {63, 649}, {513, 4088}, {514, 4024}, {522, 47698}, {650, 4750}, {661, 918}, {693, 4120}, {812, 44449}, {824, 4988}, {850, 3762}, {1635, 4897}, {1639, 24924}, {2786, 17494}, {3239, 4379}, {3676, 5219}, {3700, 47672}, {3776, 4776}, {3835, 6545}, {4010, 47704}, {4025, 4893}, {4122, 4977}, {4369, 28871}, {4378, 14432}, {4380, 28867}, {4391, 23755}, {4453, 25666}, {4458, 47821}, {4462, 21438}, {4490, 29200}, {4500, 47675}, {4521, 31207}, {4705, 29252}, {4728, 14321}, {4778, 47690}, {4785, 47663}, {4822, 29288}, {4841, 47673}, {4932, 47771}, {4979, 47890}, {4983, 29354}, {4984, 28906}, {5881, 28292}, {6544, 31286}, {6590, 28878}, {7192, 28855}, {10196, 27013}, {14437, 24110}, {18004, 21146}, {21124, 23875}, {21196, 47775}, {21204, 27138}, {21222, 25258}, {21350, 23768}, {26985, 45661}, {27115, 45674}, {28609, 31147}, {28840, 47660}, {28859, 47662}, {28890, 47652}, {28910, 43067}, {30519, 45746}, {47653, 47774}

X(48082) = reflection of X(i) in X(j) for these {i,j}: {649, 4468}, {4024, 25259}, {4979, 47890}, {4988, 47666}, {6545, 47769}, {16892, 661}, {21104, 14321}, {21116, 4120}, {21146, 18004}, {23731, 4813}, {23755, 4391}, {47671, 4024}, {47672, 3700}, {47673, 4841}, {47675, 4500}, {47676, 3835}, {47703, 4122}, {47704, 4010}
X(48082) = crosspoint of X(190) and X(17758)
X(48082) = crosssum of X(649) and X(4251)
X(48082) = crossdifference of every pair of points on line {2308, 5299}
X(48082) = barycentric product X(i)*X(j) for these {i,j}: {514, 17243}, {3676, 4126}
X(48082) = barycentric quotient X(i)/X(j) for these {i,j}: {4126, 3699}, {17243, 190}
X(48082) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 4468, 6546}, {3676, 30835, 14475}, {3676, 47765, 30835}, {3835, 47676, 6545}, {4521, 47758, 31207}, {14321, 21104, 4728}, {47676, 47769, 3835}


X(48083) = X(513)X(4088)∩X(514)X(4010)

Barycentrics    (b - c)*(a^3 - a^2*b + b^3 - a^2*c - 3*a*b*c + b^2*c + b*c^2 + c^3) : :
X(48083) = 6 X[1639] - 5 X[30795], 2 X[3776] - 3 X[47822], 2 X[3837] - 3 X[30565], 3 X[4448] - 2 X[4458], 3 X[4800] - 2 X[23770], 2 X[18004] - 3 X[47772], X[46403] - 3 X[47772], 3 X[6546] - 2 X[9508], 2 X[21104] - 3 X[47833], X[47686] - 3 X[47769]

X(48083) lies on these lines: {513, 4088}, {514, 4010}, {659, 918}, {690, 21385}, {900, 20058}, {1491, 4468}, {1639, 30795}, {3716, 28890}, {3762, 29102}, {3776, 47822}, {3837, 30565}, {3904, 19582}, {4040, 29354}, {4063, 29252}, {4120, 28195}, {4448, 4458}, {4462, 29082}, {4498, 29200}, {4784, 47890}, {4800, 23770}, {4806, 47652}, {4808, 42325}, {4810, 6084}, {4874, 47676}, {4922, 5592}, {4977, 18004}, {6332, 23765}, {6546, 9508}, {21104, 47833}, {21297, 28213}, {25259, 29362}, {29246, 47707}, {29328, 47663}, {47686, 47769}

X(48083) = reflection of X(i) in X(j) for these {i,j}: {1491, 4468}, {4784, 47890}, {4922, 5592}, {23765, 6332}, {24097, 3904}, {46403, 18004}, {47652, 4806}, {47676, 4874}
X(48083) = {X(46403),X(47772)}-harmonic conjugate of X(18004)


X(48084) = X(75)X(18072)∩X(320)X(350)

Barycentrics    b*(b - c)*c*(b^2 + c^2) : :
X(48084) = X[2484] - 3 X[4379]

X(48084) lies on these lines: {75, 18072}, {313, 3261}, {320, 350}, {522, 3663}, {523, 4509}, {816, 4107}, {826, 23285}, {918, 1577}, {2483, 4369}, {2484, 4379}, {2509, 4885}, {2517, 4411}, {2533, 22322}, {3004, 14208}, {3063, 9015}, {3676, 23874}, {3766, 18160}, {4391, 4408}, {4486, 42327}, {4823, 28846}, {8061, 16892}, {18081, 24731}, {20906, 29204}, {21003, 29070}, {21007, 24285}, {22031, 22042}, {23783, 23799}, {23790, 23829}, {35559, 40495}

X(48084) = midpoint of X(693) and X(15413)
X(48084) = reflection of X(i) in X(j) for these {i,j}: {2483, 4369}, {2509, 4885}, {21007, 24285}
X(48084) = isotomic conjugate of the isogonal conjugate of X(2530)
X(48084) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {110, 21378}, {39728, 150}
X(48084) = X(i)-Ceva conjugate of X(j) for these (i,j): {693, 2530}, {4554, 16720}, {6385, 16732}, {40013, 1111}
X(48084) = X(i)-cross conjugate of X(j) for these (i,j): {826, 16892}, {21125, 514}
X(48084) = X(i)-isoconjugate of X(j) for these (i,j): {6, 4628}, {10, 4630}, {37, 34072}, {42, 827}, {82, 692}, {83, 32739}, {100, 46289}, {101, 251}, {163, 18098}, {190, 46288}, {213, 4599}, {1110, 18108}, {1176, 8750}, {1576, 18082}, {1897, 10547}, {1918, 4577}, {2200, 42396}, {2205, 4593}, {2210, 36081}, {4570, 18105}, {10566, 23990}, {32085, 32656}
X(48084) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 4628), (39, 100), (115, 18098), (141, 692), (339, 321), (514, 18108), (1015, 251), (1086, 82), (1111, 18087), (3124, 213), (4858, 18082), (6626, 4599), (6665, 4553), (8054, 46289), (15449, 37), (21208, 32911), (26932, 1176), (34021, 4577), (34467, 10547), (39691, 21802), (40585, 101), (40589, 34072), (40592, 827), (40618, 34055), (40619, 83), (40938, 1783)
X(48084) = cevapoint of X(514) and X(21193)
X(48084) = crosspoint of X(693) and X(40495)
X(48084) = crossdifference of every pair of points on line {213, 14599}
X(48084) = barycentric product X(i)*X(j) for these {i,j}: {38, 3261}, {39, 40495}, {75, 16892}, {76, 2530}, {81, 23285}, {141, 693}, {274, 826}, {286, 2525}, {304, 21108}, {310, 8061}, {427, 15413}, {513, 8024}, {514, 1930}, {523, 16703}, {525, 16747}, {561, 21123}, {850, 16696}, {905, 1235}, {1111, 4568}, {1577, 16887}, {3005, 6385}, {3665, 4391}, {3703, 24002}, {3933, 17924}, {4025, 20883}, {4553, 23989}, {4576, 16732}, {4623, 39691}, {7199, 15523}, {14208, 17171}, {16707, 31067}, {17187, 20948}, {23807, 42551}, {30938, 35366}, {44172, 46387}
X(48084) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4628}, {38, 101}, {39, 692}, {58, 34072}, {81, 827}, {86, 4599}, {141, 100}, {274, 4577}, {286, 42396}, {310, 4593}, {335, 36081}, {427, 1783}, {513, 251}, {514, 82}, {523, 18098}, {649, 46289}, {667, 46288}, {688, 2205}, {693, 83}, {826, 37}, {905, 1176}, {1086, 18108}, {1111, 10566}, {1235, 6335}, {1333, 4630}, {1401, 1415}, {1577, 18082}, {1930, 190}, {1964, 32739}, {2084, 1918}, {2525, 72}, {2528, 3954}, {2530, 6}, {3005, 213}, {3125, 18105}, {3261, 3112}, {3665, 651}, {3703, 644}, {3917, 906}, {3933, 1332}, {3954, 4557}, {4020, 32656}, {4025, 34055}, {4077, 18097}, {4131, 28724}, {4553, 1252}, {4568, 765}, {4576, 4567}, {6385, 689}, {7794, 4553}, {8024, 668}, {8061, 42}, {14424, 21839}, {15413, 1799}, {15523, 1018}, {16696, 110}, {16703, 99}, {16720, 4579}, {16747, 648}, {16887, 662}, {16892, 1}, {17171, 162}, {17187, 163}, {17205, 39179}, {17442, 8750}, {17924, 32085}, {20883, 1897}, {21108, 19}, {21123, 31}, {21125, 16600}, {21126, 17469}, {21207, 18070}, {22383, 10547}, {23285, 321}, {23881, 4463}, {23885, 3920}, {31125, 5380}, {33299, 3939}, {35367, 20332}, {39691, 4705}, {40166, 18101}, {40495, 308}, {41676, 5379}, {46148, 1110}, {46149, 919}, {46150, 32665}, {46152, 7115}, {46153, 2149}, {46158, 36087}, {46387, 2210}
X(48084) = {X(2517),X(24002)}-harmonic conjugate of X(4411)


X(48085) = X(36)X(238)∩X(514)X(4024)

Barycentrics    a*(b - c)*(a^2 + 3*a*b + 2*b^2 + 3*a*c + 3*b*c + 2*c^2) : :
X(48085) = 4 X[905] - 3 X[1019], 2 X[905] - 3 X[14349], 2 X[4129] - 3 X[47759], 2 X[4823] - 3 X[31147], 2 X[4932] - 3 X[47795]

X(48085) lies on these lines: {36, 238}, {514, 4024}, {661, 4063}, {693, 4960}, {830, 4822}, {838, 5216}, {1022, 27789}, {4129, 31040}, {4823, 31147}, {4932, 27293}, {4978, 20954}, {4979, 14838}, {6373, 39548}, {15309, 29738}, {21385, 24290}, {23883, 47673}, {27345, 47794}, {29013, 47683}, {29190, 47699}, {29216, 45746}, {29302, 47666}

X(48085) = reflection of X(i) in X(j) for these {i,j}: {1019, 14349}, {4040, 4983}, {4063, 661}, {4960, 693}, {4979, 14838}
X(48085) = crosssum of X(i) and X(j) for these (i,j): {649, 5153}, {17454, 30600}
X(48085) = crossdifference of every pair of points on line {37, 2308}


X(48086) = X(36)X(238)∩X(514)X(4088)

Barycentrics    a*(b - c)*(a^2 + a*b + 2*b^2 + a*c + b*c + 2*c^2) : :
X(48086) = 5 X[1698] - 6 X[47816], 7 X[3624] - 6 X[47818], 2 X[4782] - 3 X[47888], 2 X[20517] - 3 X[44435], 4 X[25666] - 3 X[47817]

X(48086) lies on these lines: {1, 830}, {36, 238}, {514, 4088}, {661, 16546}, {784, 24719}, {876, 6372}, {1491, 4063}, {1698, 47816}, {1734, 2526}, {3004, 28481}, {3624, 47818}, {4705, 21385}, {4782, 47888}, {4822, 42325}, {4960, 21146}, {7192, 23789}, {8714, 20295}, {20517, 44435}, {23877, 47725}, {25666, 47817}, {29070, 47683}, {29186, 47685}, {29190, 45746}, {29294, 47677}

X(48086) = reflection of X(i) in X(j) for these {i,j}: {1019, 2530}, {1734, 2526}, {4040, 14349}, {4063, 1491}, {4960, 21146}, {7192, 23789}, {21385, 4705}
X(48086) = X(831)-Ceva conjugate of X(1)
X(48086) = crosssum of X(i) and X(j) for these (i,j): {42, 2483}, {513, 29819}
X(48086) = crossdifference of every pair of points on line {37, 17469}
X(48086) = barycentric product X(i)*X(j) for these {i,j}: {1, 47653}, {513, 17307}
X(48086) = barycentric quotient X(i)/X(j) for these {i,j}: {17307, 668}, {47653, 75}


X(48087) = X(513)X(4088)∩X(514)X(3700)

Barycentrics    (b - c)*(a^2 - 3*a*b + 2*b^2 - 3*a*c + 2*c^2) : :
X(48087) = 3 X[650] - 2 X[4025], 5 X[650] - 4 X[17069], 7 X[650] - 6 X[47785], X[4025] - 3 X[4468], 5 X[4025] - 6 X[17069], 7 X[4025] - 9 X[47785], 5 X[4468] - 2 X[17069], 7 X[4468] - 3 X[47785], 14 X[17069] - 15 X[47785], 2 X[693] - 3 X[4944], X[693] - 3 X[47772], 3 X[1638] - 4 X[4521], 3 X[1639] - 2 X[3676], 6 X[1639] - 5 X[31250], 4 X[3676] - 5 X[31250], 4 X[2490] - 3 X[47758], 4 X[2516] - 3 X[4750], 2 X[3004] - 3 X[47777], 4 X[3239] - 3 X[45320], 2 X[21104] - 3 X[45320], 2 X[3776] - 3 X[47760], 2 X[3798] - 3 X[47884], 3 X[4120] - 2 X[23813], 2 X[4369] - 3 X[47770], 2 X[4394] - 3 X[6546], 3 X[4453] - 4 X[31287], 2 X[4885] - 3 X[30565], 3 X[30565] - X[47676], 2 X[4940] - 3 X[47769], X[47652] - 3 X[47769], 2 X[7658] - 3 X[45670], 2 X[16892] - 3 X[47880], 3 X[21115] - 5 X[30835], 4 X[25666] - 3 X[47754], 2 X[43067] - 3 X[47881], X[47651] - 3 X[47759], X[47675] - 3 X[47870], X[47677] - 3 X[47775]

X(48087) lies on these lines: {513, 4088}, {514, 3700}, {650, 918}, {661, 30520}, {693, 4944}, {1638, 4521}, {1639, 3676}, {2490, 47758}, {2516, 4750}, {3004, 47777}, {3239, 21104}, {3762, 4077}, {3776, 47760}, {3798, 47884}, {3835, 28890}, {4120, 23813}, {4369, 47770}, {4394, 6546}, {4453, 31287}, {4462, 20952}, {4762, 4820}, {4790, 28846}, {4802, 4804}, {4885, 30565}, {4897, 11068}, {4932, 28871}, {4940, 47652}, {6008, 44449}, {7192, 28910}, {7658, 45670}, {16892, 47880}, {17494, 28898}, {21115, 30835}, {25666, 47754}, {28851, 43067}, {28894, 47666}, {31290, 47662}, {47651, 47759}, {47675, 47870}, {47677, 47775}

X(48087) = midpoint of X(i) and X(j) for these {i,j}: {31290, 47662}, {44449, 47663}
X(48087) = reflection of X(i) in X(j) for these {i,j}: {650, 4468}, {4790, 47890}, {4820, 25259}, {4897, 11068}, {4944, 47772}, {21104, 3239}, {43052, 3762}, {47652, 4940}, {47676, 4885}
X(48087) = crossdifference of every pair of points on line {5299, 37580}
X(48087) = barycentric product X(693)*X(41711)
X(48087) = barycentric quotient X(41711)/X(100)
X(48087) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1639, 3676, 31250}, {3239, 21104, 45320}, {30565, 47676, 4885}, {47652, 47769, 4940}


X(48088) = X(513)X(4088)∩X(514)X(4522)

Barycentrics    (b - c)*(a^3 - a*b^2 + 2*b^3 - 4*a*b*c + 2*b^2*c - a*c^2 + 2*b*c^2 + 2*c^3) : :
X(48088) = 2 X[3676] - 3 X[47807], 2 X[3776] - 3 X[47802], 2 X[4394] - 3 X[47885], 2 X[4458] - 3 X[47803], 4 X[4521] - 3 X[47799], 3 X[4776] - X[47688], 2 X[4874] - 3 X[47770], 3 X[30565] - X[47691], X[47676] - 3 X[47809], X[47677] - 3 X[47825], X[47692] - 3 X[47821], X[47702] - 3 X[47826], X[47704] - 3 X[47874], X[47705] - 3 X[47832], X[47717] - 3 X[47838]

X(48088) lies on these lines: {513, 4088}, {514, 4522}, {523, 4468}, {661, 4802}, {905, 29354}, {1491, 30520}, {2977, 4025}, {3239, 23770}, {3309, 4808}, {3676, 47807}, {3716, 47131}, {3776, 47802}, {3801, 20317}, {4106, 18004}, {4122, 4762}, {4394, 47885}, {4458, 47803}, {4521, 47799}, {4724, 4777}, {4776, 47688}, {4824, 28894}, {4874, 47770}, {4913, 30519}, {4963, 28195}, {24720, 28890}, {28151, 47701}, {30565, 47691}, {47660, 47698}, {47666, 47693}, {47676, 47809}, {47677, 47825}, {47692, 47821}, {47702, 47826}, {47704, 47874}, {47705, 47832}, {47717, 47838}

X(48088) = midpoint of X(i) and X(j) for these {i,j}: {4724, 47700}, {47660, 47698}, {47666, 47693}
X(48088) = reflection of X(i) in X(j) for these {i,j}: {3801, 20317}, {4025, 2977}, {4106, 18004}, {23770, 3239}, {47131, 3716}
X(48088) = crossdifference of every pair of points on line {5021, 5299}


X(48089) = X(320)X(350)∩X(514)X(4522)

Barycentrics    (b - c)*(-a^3 - a*b^2 + 2*a*b*c + 2*b^2*c - a*c^2 + 2*b*c^2) : :
X(48089) = 3 X[693] + X[47685], 3 X[693] - X[47694], 5 X[693] - X[47697], 5 X[693] - 3 X[47834], X[7662] + 2 X[46403], 3 X[7662] + 2 X[47685], 3 X[7662] - 2 X[47694], 5 X[7662] - 2 X[47697], 5 X[7662] - 6 X[47834], 3 X[46403] - X[47685], 3 X[46403] + X[47694], 5 X[46403] + X[47697], 5 X[46403] + 3 X[47834], 5 X[47685] + 3 X[47697], 5 X[47685] + 9 X[47834], 5 X[47694] - 3 X[47697], 5 X[47694] - 9 X[47834], X[47697] - 3 X[47834], X[649] - 3 X[47812], 2 X[650] - 3 X[47802], 5 X[650] - 6 X[47829], 4 X[3837] - 3 X[47802], 5 X[3837] - 3 X[47829], 5 X[47802] - 4 X[47829], 2 X[659] - 3 X[47803], 4 X[4885] - 3 X[47803], 3 X[905] - 4 X[19947], 2 X[19947] - 3 X[23815], 5 X[1491] - 3 X[4948], 2 X[2977] - 3 X[47806], X[4380] - 3 X[47824], 2 X[4394] - 3 X[47823], X[4560] - 3 X[47819], X[4724] - 3 X[4728], X[4775] - 3 X[30592], X[47687] + 3 X[47871], X[47691] - 3 X[47871], 2 X[4782] - 3 X[47761], 3 X[4789] - X[47696], 2 X[4874] - 3 X[45320], 2 X[6050] - 3 X[47795], 2 X[11068] - 3 X[47807], X[17494] - 3 X[44429], 5 X[26985] - 3 X[47804], 5 X[30795] - 4 X[31287], 5 X[30835] - 3 X[47811], X[47650] + 3 X[47808], X[47663] - 3 X[47809], X[47664] - 3 X[47825]

X(47089) lies on these lines: {320, 350}, {514, 4522}, {522, 3776}, {523, 2525}, {649, 47812}, {650, 3837}, {659, 4885}, {812, 24720}, {814, 3669}, {900, 47123}, {905, 19947}, {1491, 4762}, {2254, 4382}, {2517, 18071}, {2530, 23882}, {2533, 8712}, {2832, 4791}, {2899, 4391}, {2977, 47806}, {3777, 23880}, {3904, 47722}, {3960, 29033}, {4122, 30520}, {4378, 28475}, {4380, 47824}, {4394, 47823}, {4560, 47819}, {4724, 4728}, {4775, 30592}, {4777, 47687}, {4782, 24623}, {4784, 6008}, {4789, 28220}, {4801, 21301}, {4802, 47652}, {4830, 31286}, {4874, 45320}, {4926, 47695}, {4944, 4977}, {4978, 8678}, {4992, 29246}, {6050, 47795}, {6591, 40086}, {7659, 29328}, {11068, 47807}, {15313, 44319}, {17494, 44429}, {20936, 29226}, {23789, 29013}, {26985, 47804}, {28151, 47688}, {28165, 47692}, {28195, 47660}, {28199, 47651}, {28217, 47132}, {30795, 31287}, {30835, 47811}, {47650, 47808}, {47663, 47809}, {47664, 47825}

X(48089) = midpoint of X(i) and X(j) for these {i,j}: {693, 46403}, {2254, 4382}, {3904, 47722}, {4801, 21301}, {21146, 24719}, {47651, 47693}, {47652, 47690}, {47660, 47686}, {47685, 47694}, {47687, 47691}, {47688, 47689}
X(48089) = reflection of X(i) in X(j) for these {i,j}: {650, 3837}, {659, 4885}, {905, 23815}, {4010, 23813}, {4830, 31286}, {7662, 693}, {47131, 23770}
X(48089) = crosspoint of X(668) and X(39721)
X(48089) = crossdifference of every pair of points on line {213, 30435}
X(48089) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 3837, 47802}, {659, 4885, 47803}, {693, 47685, 47694}, {693, 47697, 47834}, {46403, 47694, 47685}, {47687, 47871, 47691}


X(48090) = X(320)X(350)∩X(514)X(4806)

Barycentrics    (b - c)*(-(a^2*b) - a^2*c + a*b*c + 2*b^2*c + 2*b*c^2) : :
X(48090) = 3 X[693] - X[21146], 3 X[4010] + X[21146], X[20295] + 3 X[47834], 3 X[21297] - X[24719], 3 X[21297] + X[47694], X[649] - 3 X[47833], X[4810] + 3 X[47833], X[659] - 3 X[47832], X[4382] + 3 X[47832], X[1491] - 3 X[4728], 3 X[4728] + X[4804], X[4063] - 3 X[47875], 3 X[4120] + X[47704], X[4122] - 3 X[47790], X[47691] + 3 X[47790], 3 X[4379] - X[4784], X[4498] - 3 X[47872], X[4560] - 3 X[47841], X[4724] - 3 X[4800], 3 X[4776] - X[4824], X[4913] - 3 X[4928], 3 X[4951] - X[47700], X[4976] - 3 X[47799], 2 X[23814] - 3 X[23815], X[17494] - 3 X[47822], X[26824] + 3 X[47821], 5 X[26985] - 3 X[47823], 7 X[27138] - 3 X[47825], 5 X[30795] - 3 X[47828], 5 X[30835] - 3 X[47827], X[47688] + 3 X[47870]

X(48090) lies on these lines: {1, 29236}, {320, 350}, {512, 4823}, {514, 4806}, {522, 3837}, {523, 3835}, {649, 4810}, {650, 25686}, {659, 4382}, {661, 4802}, {663, 29274}, {667, 29238}, {812, 4782}, {891, 4791}, {900, 24720}, {905, 16744}, {1491, 4728}, {1577, 4083}, {1960, 29033}, {2254, 4926}, {3700, 23770}, {3716, 29362}, {3801, 29202}, {4024, 24085}, {4036, 25142}, {4063, 47875}, {4120, 47704}, {4122, 29204}, {4151, 21260}, {4367, 29152}, {4369, 29328}, {4379, 4784}, {4391, 19582}, {4444, 28898}, {4458, 29078}, {4474, 21343}, {4486, 4762}, {4498, 47872}, {4560, 47841}, {4724, 4800}, {4775, 47724}, {4776, 4824}, {4885, 9508}, {4913, 4928}, {4951, 47700}, {4976, 47799}, {4978, 29198}, {7178, 29284}, {7265, 29280}, {8043, 27674}, {8045, 29025}, {8714, 23814}, {17494, 47822}, {18080, 28199}, {20517, 29106}, {26824, 47821}, {26985, 47823}, {27138, 47825}, {28195, 47672}, {28205, 44429}, {29122, 47682}, {29146, 47712}, {29232, 34958}, {30795, 47828}, {30835, 47827}, {47688, 47870}

X(48090) = midpoint of X(i) and X(j) for these {i,j}: {649, 4810}, {659, 4382}, {693, 4010}, {1491, 4804}, {3700, 23770}, {4106, 7662}, {4122, 47691}, {4474, 21343}, {4775, 47724}, {24719, 47694}
X(48090) = reflection of X(i) in X(j) for these {i,j}: {4782, 4874}, {9508, 4885}
X(48090) = X(39720)-anticomplementary conjugate of X(150)
X(48090) = X(i)-isoconjugate of X(j) for these (i,j): {101, 39952}, {32739, 40031}
X(48090) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 39952), (40619, 40031)
X(48090) = crosspoint of X(668) and X(27494)
X(48090) = crosssum of X(667) and X(21793)
X(48090) = crossdifference of every pair of points on line {213, 609}
X(48090) = barycentric product X(i)*X(j) for these {i,j}: {513, 31060}, {693, 37673}
X(48090) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 39952}, {693, 40031}, {31060, 668}, {37673, 100}
X(48090) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4382, 47832, 659}, {4728, 4804, 1491}, {4810, 47833, 649}, {21297, 47694, 24719}, {47691, 47790, 4122}


X(48091) = X(36)X(238)∩X(514)X(3700)

Barycentrics    a*(b - c)*(a^2 + 4*a*b + 3*b^2 + 4*a*c + 4*b*c + 3*c^2) : :
X(48091) = 3 X[905] - 2 X[1019], X[1019] - 3 X[14349], 3 X[661] - X[4498], 4 X[4129] - 3 X[45664], X[4391] - 3 X[47759], 2 X[21188] - 3 X[47756], 2 X[21192] - 3 X[47880]

X(48091) lies on these lines: {36, 238}, {514, 3700}, {661, 4498}, {1577, 4940}, {2526, 6005}, {3309, 4822}, {3669, 15309}, {4129, 45664}, {4391, 47759}, {4790, 14838}, {4801, 31290}, {4879, 8678}, {7265, 28894}, {8045, 28859}, {9010, 39548}, {20295, 23882}, {20949, 23685}, {21188, 47756}, {21192, 47880}, {21196, 28493}

X(48091) = midpoint of X(4801) and X(31290)
X(48091) = reflection of X(i) in X(j) for these {i,j}: {905, 14349}, {1577, 4940}, {4790, 14838}


X(48092) = X(36)X(238)∩X(514)X(4522)

Barycentrics    a*(b - c)*(a^2 + 2*a*b + 3*b^2 + 2*a*c + 2*b*c + 3*c^2) : :
X(48092) = X[4040] - 3 X[14349], 2 X[4394] - 3 X[47888], X[4498] - 3 X[47810], X[7192] - 3 X[47819], X[47697] - 3 X[47840]

X(48092) lies on these lines: {36, 238}, {512, 2526}, {514, 4522}, {784, 4106}, {4394, 47888}, {4449, 8678}, {4498, 47810}, {4705, 8712}, {7192, 47819}, {23815, 43067}, {23882, 24719}, {28541, 47877}, {47697, 47840}

X(48092) = reflection of X(43067) in X(23815)


X(48093) = X(36)X(238)∩X(514)X(4806)

Barycentrics    a*(b - c)*(3*a*b + 2*b^2 + 3*a*c + 3*b*c + 2*c^2) : :
X(48093) = 5 X[2530] - 3 X[4905], X[2530] + 3 X[4983], X[2530] - 3 X[14349], X[4905] + 5 X[4983], X[4905] - 5 X[14349], 3 X[661] - X[4490], X[2533] - 3 X[4776], X[7192] - 3 X[47841]

X(48093) lies on these lines: {36, 238}, {514, 4806}, {661, 4083}, {1491, 4822}, {2533, 4776}, {3004, 29200}, {4170, 4777}, {4367, 4813}, {4978, 28195}, {7192, 47841}, {20295, 29238}, {22320, 25142}, {23765, 29198}, {29146, 47701}, {29236, 47759}

X(48093) = midpoint of X(i) and X(j) for these {i,j}: {1491, 4822}, {4367, 4813}, {4983, 14349}
X(48093) = reflection of X(22320) in X(25142)
X(48093) = crossdifference of every pair of points on line {37, 7262}


X(48094) = X(513)X(4088)∩X(514)X(661)

Barycentrics    (b - c)*(a^2 - a*b + b^2 - a*c + c^2) : :
X(48094) = 2 X[693] - 3 X[47874], 4 X[3239] - 3 X[4728], 2 X[3835] - 3 X[30565], 3 X[4776] - X[47651], 3 X[30565] - X[47652], 3 X[649] - 2 X[4897], X[4897] - 3 X[47890], 2 X[650] - 3 X[6546], 4 X[650] - 3 X[47886], 3 X[6546] - X[16892], 2 X[16892] - 3 X[47886], X[17161] - 3 X[17494], 3 X[1635] - 2 X[4025], 3 X[1635] - 4 X[11068], 3 X[1638] - 4 X[2490], 6 X[1638] - 7 X[31207], 8 X[2490] - 7 X[31207], 6 X[1639] - 5 X[30835], 4 X[2977] - 3 X[47828], 2 X[3004] - 3 X[4893], 4 X[3676] - 3 X[21115], 4 X[3676] - 5 X[24924], 2 X[3676] - 3 X[47766], 3 X[21115] - 5 X[24924], 5 X[24924] - 6 X[47766], 2 X[4106] - 3 X[4120], 2 X[4142] - 3 X[47815], 2 X[4369] - 3 X[47771], X[47676] - 3 X[47771], 3 X[4379] - 2 X[21104], 4 X[4394] - 3 X[4750], 3 X[4453] - 4 X[31286], 2 X[4458] - 3 X[47804], X[4467] - 3 X[47892], 2 X[4500] - 3 X[47870], X[26824] - 3 X[47870], 4 X[4521] - 3 X[47757], 2 X[4818] - 3 X[47825], 4 X[4874] - 3 X[47887], 4 X[4885] - 3 X[6545], 2 X[4885] - 3 X[47770], 3 X[4944] - 2 X[23813], 9 X[6544] - 8 X[31287], 3 X[6544] - 2 X[47754], 4 X[31287] - 3 X[47754], X[7192] - 3 X[47773], 4 X[8689] - 3 X[44433], 2 X[9508] - 3 X[47885], 3 X[10196] - 2 X[21212], 6 X[10196] - 5 X[31209], 4 X[21212] - 5 X[31209], 4 X[14321] - 3 X[31147], 2 X[23729] - 3 X[31147], 9 X[14475] - 10 X[31250], 2 X[17069] - 3 X[47884], X[20295] - 3 X[47772], 2 X[20517] - 3 X[47817], 2 X[21196] - 3 X[31150], 3 X[31150] - X[47677], 2 X[23770] - 3 X[47832], 2 X[24720] - 3 X[47809], 4 X[25666] - 3 X[44435], 5 X[26777] - 9 X[44009], 5 X[26777] - 3 X[47894], 3 X[44009] - X[47894], 5 X[26985] - 6 X[47879], 7 X[27115] - 9 X[31992], 7 X[27115] - 6 X[47882], 3 X[31992] - 2 X[47882], 2 X[45746] - 3 X[47878], 4 X[31182] - 3 X[44551], 4 X[43061] - 3 X[47758], X[47650] - 3 X[47790], X[47653] - 3 X[47775], X[47688] - 3 X[47821]

X(48094) lies on these lines: {2, 3776}, {312, 29739}, {513, 4088}, {514, 661}, {522, 47700}, {523, 4724}, {525, 4498}, {649, 918}, {650, 3752}, {663, 29288}, {667, 29354}, {812, 25259}, {824, 17147}, {1635, 4025}, {1638, 2490}, {1639, 30835}, {2786, 4380}, {2977, 47828}, {3004, 4893}, {3175, 4024}, {3676, 21115}, {3700, 4382}, {3716, 47691}, {3810, 19589}, {4040, 29047}, {4063, 23875}, {4106, 4120}, {4122, 29362}, {4142, 47815}, {4369, 28890}, {4379, 21104}, {4394, 4750}, {4453, 31286}, {4458, 47804}, {4467, 30519}, {4474, 29240}, {4500, 26824}, {4521, 47757}, {4522, 46403}, {4718, 4777}, {4785, 44449}, {4794, 47727}, {4802, 47701}, {4808, 6004}, {4818, 47825}, {4834, 29252}, {4874, 47887}, {4885, 6545}, {4944, 23813}, {4979, 28846}, {4988, 28894}, {5592, 47729}, {6544, 31287}, {7035, 33946}, {7192, 28851}, {7265, 29302}, {7662, 47704}, {8689, 44433}, {9508, 47885}, {10015, 24793}, {10196, 21212}, {14321, 23729}, {14475, 31250}, {16612, 30911}, {17069, 47884}, {18004, 24719}, {18071, 21611}, {20295, 28882}, {20517, 47817}, {21107, 21120}, {21116, 47881}, {21125, 29224}, {21196, 31150}, {21385, 23876}, {23770, 47832}, {24720, 47809}, {25666, 44435}, {26777, 44009}, {26853, 28867}, {26985, 47879}, {27115, 31992}, {28147, 47702}, {28175, 47826}, {28859, 31290}, {28863, 45746}, {29051, 47707}, {29094, 33136}, {29186, 47711}, {31182, 44551}, {43061, 47758}, {45745, 47673}, {47123, 47705}, {47650, 47790}, {47653, 47775}, {47664, 47665}, {47688, 47821}, {47696, 47698}

X(48094) = midpoint of X(i) and X(j) for these {i,j}: {25259, 47663}, {47662, 47666}, {47664, 47665}, {47696, 47698}
X(48094) = reflection of X(i) in X(j) for these {i,j}: {649, 47890}, {661, 4468}, {4025, 11068}, {4382, 3700}, {4801, 8045}, {6545, 47770}, {16892, 650}, {21115, 47766}, {21116, 47881}, {23729, 14321}, {24719, 18004}, {26824, 4500}, {46403, 4522}, {47652, 3835}, {47672, 6590}, {47673, 45745}, {47676, 4369}, {47677, 21196}, {47680, 4791}, {47691, 3716}, {47704, 7662}, {47705, 47123}, {47727, 4794}, {47729, 5592}, {47886, 6546}
X(48094) = anticomplement of X(3776)
X(48094) = anticomplement of the isotomic conjugate of X(4621)
X(48094) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {983, 150}, {4621, 6327}, {8684, 20553}, {8685, 7}, {17743, 21293}
X(48094) = X(i)-Ceva conjugate of X(j) for these (i,j): {3673, 2310}, {4621, 2}
X(48094) = X(6)-isoconjugate of X(6012)
X(48094) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 6012), (17279, 3732)
X(48094) = crossdifference of every pair of points on line {31, 4253}
X(48094) = barycentric product X(i)*X(j) for these {i,j}: {75, 6004}, {86, 4808}, {513, 33937}, {514, 17279}, {522, 30617}, {523, 33953}, {561, 8654}, {693, 3938}, {3676, 30615}, {4025, 5101}
X(48094) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 6012}, {3938, 100}, {4808, 10}, {4952, 43290}, {5101, 1897}, {6004, 1}, {8654, 31}, {17279, 190}, {30615, 3699}, {30617, 664}, {33937, 668}, {33953, 99}
X(48094) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 16892, 47886}, {1638, 2490, 31207}, {3676, 47766, 24924}, {4025, 11068, 1635}, {6546, 16892, 650}, {10196, 21212, 31209}, {14321, 23729, 31147}, {21115, 24924, 3676}, {26824, 47870, 4500}, {30565, 47652, 3835}, {31150, 47677, 21196}, {47676, 47771, 4369}


X(48095) = X(241)X(514)∩X(513)X(4088)

Barycentrics    (b - c)*(3*a^2 - a*b + 2*b^2 - a*c + 2*c^2) : :
X(48095) = 3 X[650] - 2 X[3004], 3 X[650] - 4 X[11068], 7 X[650] - 6 X[47784], 4 X[650] - 3 X[47880], 5 X[650] - 6 X[47884], 3 X[1638] - 4 X[43061], 7 X[3004] - 9 X[47784], 8 X[3004] - 9 X[47880], 5 X[3004] - 9 X[47884], X[3004] - 3 X[47890], 2 X[3676] - 3 X[47767], 2 X[3776] - 3 X[47761], 14 X[11068] - 9 X[47784], 16 X[11068] - 9 X[47880], 10 X[11068] - 9 X[47884], 2 X[11068] - 3 X[47890], 4 X[31286] - 3 X[47754], 8 X[47784] - 7 X[47880], 5 X[47784] - 7 X[47884], 3 X[47784] - 7 X[47890], 5 X[47880] - 8 X[47884], 3 X[47880] - 8 X[47890], 3 X[47884] - 5 X[47890], X[693] - 3 X[47773], 2 X[693] - 3 X[47881], 4 X[2490] - 3 X[47757], 4 X[2516] - 3 X[47886], 4 X[2527] - 3 X[47758], 4 X[2529] - 3 X[31148], 2 X[3835] - 3 X[47770], 2 X[4106] - 3 X[4944], 4 X[4521] - 3 X[47756], X[47656] - 3 X[47660], X[47656] + 3 X[47663], 3 X[4789] - X[47650], 2 X[4885] - 3 X[47771], X[47652] - 3 X[47771], 2 X[4940] - 3 X[30565], 3 X[17494] - X[47657], X[47657] + 3 X[47662], 2 X[23813] - 3 X[47874], 3 X[31150] - X[47653], 5 X[31250] - 6 X[47766], 4 X[31287] - 3 X[44435], X[45746] - 3 X[47892], X[47677] - 3 X[47776], X[47686] - 3 X[47809], X[47688] - 3 X[47804], X[47692] - 3 X[47805]

X(48095) lies on these lines: {2, 47651}, {241, 514}, {513, 4088}, {523, 3804}, {649, 30520}, {659, 4802}, {693, 47773}, {812, 4820}, {918, 4790}, {1491, 28195}, {2490, 47757}, {2505, 2526}, {2516, 47886}, {2527, 47758}, {2529, 31148}, {2977, 28213}, {3239, 23729}, {3803, 29047}, {3835, 47770}, {4106, 4944}, {4380, 28898}, {4394, 16892}, {4521, 47756}, {4762, 47656}, {4789, 47650}, {4885, 47652}, {4932, 28890}, {4940, 30565}, {6008, 25259}, {6084, 6590}, {17494, 28894}, {20950, 30061}, {23813, 47874}, {31150, 47653}, {31250, 47766}, {31287, 44435}, {45746, 47892}, {47659, 47664}, {47677, 47776}, {47686, 47809}, {47688, 47804}, {47692, 47805}

X(48095) = midpoint of X(i) and X(j) for these {i,j}: {17494, 47662}, {47659, 47664}, {47660, 47663}
X(48095) = reflection of X(i) in X(j) for these {i,j}: {650, 47890}, {3004, 11068}, {16892, 4394}, {23729, 3239}, {47652, 4885}, {47881, 47773}
X(48095) = complement of X(47651)
X(48095) = crossdifference of every pair of points on line {55, 5299}
X(48095) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3004, 11068, 650}, {3004, 47890, 11068}, {47652, 47771, 4885}


X(48096) = X(513)X(4088)∩X(514)X(3716)

Barycentrics    (b - c)*(3*a^3 + a*b^2 + 2*b^3 - 4*a*b*c + 2*b^2*c + a*c^2 + 2*b*c^2 + 2*c^3) : :
X(48096) = 2 X[3776] - 3 X[47803], 2 X[3837] - 3 X[47770], 3 X[4724] - X[47702], 3 X[30565] - X[47686], X[47651] - 3 X[47821]

X(48096) lies on these lines: {513, 4088}, {514, 3716}, {523, 2976}, {659, 30520}, {661, 28195}, {3776, 47803}, {3803, 29354}, {3837, 47770}, {4468, 4977}, {4724, 4802}, {4830, 30519}, {4926, 47700}, {28199, 47701}, {30565, 47686}, {47651, 47821}


X(48097) = X(513)X(4088)∩X(514)X(3837)

Barycentrics    (b - c)*(2*a^3 + a^2*b + 2*b^3 + a^2*c - 3*a*b*c + 2*b^2*c + 2*b*c^2 + 2*c^3) : :
X(48097) = 3 X[4448] - X[47692], X[16892] - 3 X[47885], X[47688] - 3 X[47822]

X(48097) lies on these lines: {513, 4088}, {514, 3837}, {659, 29204}, {3762, 29122}, {4063, 29280}, {4122, 47663}, {4448, 47692}, {4498, 29202}, {4782, 47890}, {4802, 7662}, {4824, 47662}, {4830, 29370}, {9508, 30520}, {16892, 47885}, {18004, 28882}, {28175, 47831}, {28195, 47808}, {28199, 47881}, {29274, 47707}, {47688, 47822}

X(48097) = midpoint of X(i) and X(j) for these {i,j}: {4122, 47663}, {4824, 47662}
X(48097) = reflection of X(4782) in X(47890)
X(48097) = crossdifference of every pair of points on line {5299, 21793}


X(48098) = X(320)X(350)∩X(514)X(3837)

Barycentrics    (b - c)*(a^2*b + a^2*c + 3*a*b*c + 2*b^2*c + 2*b*c^2) : :
X(48098) = 3 X[693] - X[4010], X[4010] + 3 X[21146], X[46403] + 3 X[47780], X[659] - 3 X[4379], X[663] - 3 X[47889], X[1491] - 3 X[47812], X[47672] + 3 X[47812], X[4761] + 3 X[4978], X[4088] + 3 X[21116], 3 X[4369] - X[4830], 3 X[4782] - 2 X[4830], X[4724] - 3 X[47833], X[4824] - 3 X[44429], 3 X[44429] + X[47675], 3 X[4893] - 5 X[30795], X[4988] - 3 X[47877], 3 X[6545] + X[47703], X[17494] - 3 X[47823], X[26824] + 3 X[47824], 5 X[26985] - 3 X[47822], X[47686] + 3 X[47791]

X(48098) lies on these lines: {320, 350}, {514, 3837}, {523, 3776}, {659, 4379}, {661, 28195}, {663, 47889}, {784, 23789}, {1019, 29238}, {1491, 4802}, {1577, 29198}, {2254, 4777}, {2533, 4801}, {3801, 47719}, {3835, 4977}, {4083, 4761}, {4088, 21116}, {4122, 47676}, {4367, 29274}, {4369, 4782}, {4378, 29236}, {4382, 4784}, {4444, 28894}, {4724, 47833}, {4728, 28220}, {4762, 9508}, {4778, 4806}, {4804, 4926}, {4823, 6372}, {4824, 28199}, {4893, 30795}, {4922, 47721}, {4988, 47877}, {6545, 47703}, {17494, 47823}, {18004, 28851}, {23770, 29144}, {23818, 40086}, {24601, 29809}, {26824, 47824}, {26985, 47822}, {28151, 36848}, {29122, 47680}, {29146, 47715}, {29204, 47690}, {47686, 47791}

X(48098) = midpoint of X(i) and X(j) for these {i,j}: {693, 21146}, {1491, 47672}, {2533, 4801}, {3801, 47719}, {4122, 47676}, {4378, 47724}, {4382, 4784}, {4824, 47675}, {4922, 47721}, {7192, 24719}
X(48098) = reflection of X(4782) in X(4369)
X(48098) = crossdifference of every pair of points on line {213, 7031}
X(48098) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {44429, 47675, 4824}, {47672, 47812, 1491}


X(48099) = X(36)X(238)∩X(514)X(3716)

Barycentrics    a*(b - c)*(a^2 - 2*a*b - b^2 - 2*a*c - 2*b*c - c^2) : :
X(48099) = X[4822] + 2 X[6050], X[693] - 3 X[47840], X[1577] - 3 X[47838], X[2533] - 3 X[47822], X[4041] - 3 X[4893], X[4162] + 3 X[47777], X[4391] - 3 X[47821], X[4449] + 3 X[47826], X[4498] - 3 X[47811], X[4761] - 3 X[47794], 3 X[4776] - X[21301], X[4813] + 3 X[8643], 2 X[4885] - 3 X[47839], X[7192] - 3 X[47820], X[21146] - 3 X[47841], 2 X[21188] - 3 X[47799], 2 X[21260] - 3 X[47760], X[21302] - 3 X[47814], 3 X[30565] - X[47707], 5 X[31209] - 3 X[47836], 4 X[31287] - 3 X[47837], 4 X[31288] - 3 X[47761], X[31291] + 3 X[47759]

X(48099) lies on these lines: {36, 238}, {512, 650}, {514, 3716}, {523, 4990}, {649, 4822}, {661, 663}, {693, 47840}, {814, 4806}, {830, 4794}, {884, 10099}, {1491, 3309}, {1577, 47838}, {2526, 6004}, {2533, 47822}, {3669, 6372}, {3835, 29051}, {3837, 29246}, {3900, 4705}, {4010, 23882}, {4041, 4893}, {4106, 29070}, {4129, 29066}, {4162, 47777}, {4391, 47821}, {4394, 4834}, {4449, 47826}, {4468, 29288}, {4490, 4879}, {4498, 47811}, {4761, 47794}, {4776, 21301}, {4813, 8643}, {4885, 47839}, {4992, 29362}, {6005, 14838}, {6129, 8672}, {6332, 29142}, {7192, 47820}, {14321, 29278}, {15313, 47842}, {17072, 25143}, {17166, 47666}, {18004, 29074}, {21051, 29366}, {21146, 47841}, {21188, 47799}, {21260, 29188}, {21302, 47814}, {22037, 29294}, {28840, 45316}, {30235, 39541}, {30565, 47707}, {31209, 47836}, {31287, 47837}, {31288, 47761}, {31291, 47759}

X(48099) = midpoint of X(i) and X(j) for these {i,j}: {649, 4822}, {661, 663}, {667, 4983}, {4040, 14349}, {4490, 4879}, {4705, 4775}, {17166, 47666}
X(48099) = reflection of X(i) in X(j) for these {i,j}: {649, 6050}, {4834, 4394}, {17072, 25666}
X(48099) = isogonal conjugate of the isotomic conjugate of X(7650)
X(48099) = X(i)-isoconjugate of X(j) for these (i,j): {100, 969}, {190, 967}
X(48099) = X(i)-Dao conjugate of X(j) for these (i, j): (8054, 969), (38960, 75)
X(48099) = crosssum of X(513) and X(5256)
X(48099) = crossdifference of every pair of points on line {37, 63}
X(48099) = barycentric product X(i)*X(j) for these {i,j}: {1, 45745}, {6, 7650}, {513, 966}, {514, 968}, {650, 3485}, {661, 11110}, {693, 2271}, {905, 4207}, {4288, 24006}
X(48099) = barycentric quotient X(i)/X(j) for these {i,j}: {649, 969}, {667, 967}, {966, 668}, {968, 190}, {2271, 100}, {3485, 4554}, {4207, 6335}, {4288, 4592}, {7650, 76}, {11110, 799}, {45745, 75}


X(48100) = X(36)X(238)∩X(514)X(3837)

Barycentrics    a*(b - c)*(a*b + 2*b^2 + a*c + b*c + 2*c^2) : :
X(48100) = 3 X[2530] - X[4905], 3 X[2530] + X[4983], X[4905] + 3 X[14349], X[4983] - 3 X[14349], X[649] - 3 X[47893], 3 X[661] + X[23738], 3 X[3777] - X[23738], 3 X[1491] - X[4041], 3 X[2526] + X[4162], X[2533] - 3 X[44429], X[3801] - 3 X[44435], X[4063] - 3 X[47888], X[4490] - 3 X[47810], X[4498] - 3 X[47827], 3 X[4879] - X[4959], X[21124] - 3 X[47877], X[21146] - 3 X[47819], 5 X[30835] - 3 X[47872], X[47694] - 3 X[47841]

X(48100) lies on these lines: {36, 238}, {514, 3837}, {522, 4992}, {649, 47893}, {659, 28255}, {661, 3777}, {1491, 4041}, {2526, 4162}, {2533, 44429}, {3004, 29017}, {3801, 44435}, {4063, 47888}, {4086, 4802}, {4106, 40106}, {4170, 4926}, {4367, 28373}, {4490, 47810}, {4498, 47827}, {4560, 24719}, {4705, 29226}, {4777, 14288}, {4782, 14838}, {4801, 4824}, {4879, 4959}, {4977, 47843}, {16892, 29280}, {18081, 20906}, {21124, 47877}, {21146, 47819}, {21301, 29236}, {27452, 28372}, {28165, 30592}, {30835, 47872}, {47694, 47841}

X(48100) = midpoint of X(i) and X(j) for these {i,j}: {661, 3777}, {2530, 14349}, {4560, 24719}, {4801, 4824}, {4905, 4983}
X(48100) = reflection of X(4782) in X(14838)
X(48100) = crossdifference of every pair of points on line {37, 8616}
X(48100) = barycentric product X(513)*X(17238)
X(48100) = barycentric quotient X(17238)/X(668)
X(48100) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2530, 4983, 4905}, {4905, 14349, 4983}


X(48101) = X(239)X(514)∩X(513)X(4088)

Barycentrics    (b - c)*(2*a^2 + b^2 + c^2) : :
X(48101) = 5 X[649] - 4 X[3798], 3 X[649] - 2 X[4025], 4 X[649] - 3 X[4750], 7 X[649] - 6 X[4786], 6 X[3798] - 5 X[4025], 16 X[3798] - 15 X[4750], 14 X[3798] - 15 X[4786], 8 X[3798] - 5 X[16892], 8 X[4025] - 9 X[4750], 7 X[4025] - 9 X[4786], 4 X[4025] - 3 X[16892], 7 X[4750] - 8 X[4786], 3 X[4750] - 2 X[16892], 12 X[4786] - 7 X[16892], 3 X[14435] - 2 X[47894], 2 X[21196] - 3 X[47776], X[47653] - 3 X[47776], 2 X[661] - 3 X[6546], 3 X[6546] - X[23731], 3 X[6546] - 4 X[47890], X[23731] - 4 X[47890], 3 X[1635] - 2 X[3004], 3 X[1638] - 4 X[2527], 4 X[2490] - 3 X[47756], 4 X[2516] - 3 X[47880], 4 X[2977] - 3 X[47810], 4 X[3239] - 3 X[31147], 2 X[3676] - 3 X[47768], 2 X[3776] - 3 X[47762], X[47651] - 3 X[47762], 2 X[3835] - 3 X[47771], 2 X[4106] - 3 X[47874], 3 X[4120] - 2 X[20295], X[20295] - 3 X[47773], 4 X[4369] - 3 X[6545], 3 X[6545] - 2 X[47652], 4 X[4394] - 3 X[47886], 2 X[4467] - 3 X[4984], 3 X[4728] - 2 X[23729], 3 X[4893] - 4 X[11068], 2 X[4940] - 3 X[47770], 9 X[6544] - 8 X[25666], 9 X[14475] - 10 X[24924], 3 X[14475] - 4 X[47767], 5 X[24924] - 6 X[47767], 2 X[21104] - 3 X[31148], 3 X[21116] - 4 X[43067], 4 X[21212] - 5 X[27013], 2 X[23770] - 3 X[47813], 2 X[23813] - 3 X[47881], 5 X[26798] - 6 X[45661], 5 X[30835] - 6 X[47766], 7 X[31207] - 8 X[43061], 7 X[31207] - 6 X[47757], 4 X[43061] - 3 X[47757], 4 X[31286] - 3 X[44435], X[47650] - 3 X[47791]

X(48101) lies on these lines: {239, 514}, {513, 4088}, {522, 47693}, {659, 8635}, {661, 1211}, {693, 28882}, {812, 4024}, {824, 4380}, {918, 4979}, {1577, 27610}, {1635, 3004}, {1638, 2527}, {2254, 4824}, {2490, 47756}, {2516, 47880}, {2786, 26853}, {2977, 47810}, {3239, 31147}, {3578, 28840}, {3676, 47768}, {3776, 47651}, {3835, 47771}, {4106, 47874}, {4120, 20295}, {4369, 6545}, {4382, 6590}, {4394, 47886}, {4458, 47688}, {4467, 4984}, {4468, 4813}, {4728, 23729}, {4762, 47671}, {4785, 25259}, {4790, 30520}, {4893, 11068}, {4940, 47770}, {4976, 47673}, {4978, 27575}, {6084, 47672}, {6161, 12073}, {6544, 25666}, {7927, 8664}, {10566, 21205}, {14475, 24924}, {21102, 21122}, {21104, 31148}, {21116, 43067}, {21118, 29025}, {21132, 29029}, {21212, 27013}, {23740, 40471}, {23770, 47813}, {23813, 47881}, {24720, 47686}, {26798, 45661}, {28468, 47684}, {28859, 47666}, {29362, 47703}, {30835, 47766}, {31207, 43061}, {31286, 44435}, {31290, 43990}, {47650, 47791}

X(48101) = midpoint of X(4380) and X(47662)
X(48101) = reflection of X(i) in X(j) for these {i,j}: {661, 47890}, {4024, 47660}, {4120, 47773}, {4382, 6590}, {4813, 4468}, {4988, 17494}, {16892, 649}, {21124, 4063}, {23731, 661}, {47651, 3776}, {47652, 4369}, {47653, 21196}, {47673, 4976}, {47676, 4932}, {47686, 24720}, {47688, 4458}, {47701, 659}
X(48101) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {39722, 21293}, {39977, 150}
X(48101) = X(i)-Ceva conjugate of X(j) for these (i,j): {514, 21126}, {16887, 3122}
X(48101) = crosspoint of X(514) and X(10566)
X(48101) = crosssum of X(i) and X(j) for these (i,j): {101, 46148}, {649, 5280}
X(48101) = crossdifference of every pair of points on line {42, 3108}
X(48101) = X(i)-isoconjugate of X(j) for these (i,j): {37, 7953}, {100, 3108}, {213, 35137}, {692, 10159}, {1783, 41435}
X(48101) = X(i)-Dao conjugate of X(j) for these (i, j): (1086, 10159), (3589, 4568), (4988, 31065), (6292, 190), (6626, 35137), (8054, 3108), (15527, 10), (39006, 41435), (39691, 15523), (40589, 7953)
X(48101) = barycentric product X(i)*X(j) for these {i,j}: {83, 21126}, {86, 7927}, {310, 8664}, {428, 4025}, {514, 3589}, {522, 7198}, {523, 17200}, {649, 39998}, {661, 16707}, {693, 17469}, {1459, 44142}, {3120, 10330}, {3125, 18062}, {3261, 5007}, {3676, 4030}, {6292, 10566}, {7199, 21802}, {7649, 7767}, {18108, 20898}, {22352, 46107}
X(48101) = barycentric quotient X(i)/X(j) for these {i,j}: {58, 7953}, {86, 35137}, {428, 1897}, {514, 10159}, {649, 3108}, {1459, 41435}, {3120, 31065}, {3589, 190}, {4030, 3699}, {4750, 31068}, {5007, 101}, {6292, 4568}, {7198, 664}, {7767, 4561}, {7927, 10}, {8664, 42}, {10330, 4600}, {10566, 40425}, {11205, 46148}, {16707, 799}, {17193, 4576}, {17200, 99}, {17457, 4553}, {17469, 100}, {18062, 4601}, {21126, 141}, {21802, 1018}, {21817, 35309}, {22352, 1331}, {39998, 1978}, {44091, 8750}
X(48101) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 16892, 4750}, {661, 47890, 6546}, {4369, 47652, 6545}, {6546, 23731, 661}, {43061, 47757, 31207}, {47651, 47762, 3776}, {47653, 47776, 21196}


X(48102) = X(1)X(514)∩X(513)X(4088)

Barycentrics    (b - c)*(2*a^3 + a*b^2 + b^3 - 2*a*b*c + b^2*c + a*c^2 + b*c^2 + c^3) : :
X(48102) = 2 X[1491] - 3 X[6546], 2 X[3004] - 3 X[47811], 2 X[3776] - 3 X[47804], 3 X[4120] - 2 X[24719], 2 X[4458] - 3 X[47805], 3 X[4750] - 4 X[4782], 2 X[4818] - 3 X[31150], 4 X[4874] - 3 X[6545], 2 X[4913] - 3 X[47892], 4 X[8689] - 3 X[47798], 4 X[11068] - 3 X[47828], 2 X[21104] - 3 X[47813], 2 X[24720] - 3 X[47771]

X(48102) lies on these lines: {1, 514}, {513, 4088}, {522, 47663}, {659, 16892}, {661, 1639}, {900, 47700}, {1491, 6546}, {2254, 47890}, {2832, 47682}, {3004, 47811}, {3716, 47652}, {3776, 47804}, {3835, 47686}, {4024, 29362}, {4120, 24719}, {4458, 47805}, {4467, 4830}, {4468, 4778}, {4522, 47685}, {4750, 4782}, {4804, 6084}, {4818, 31150}, {4874, 6545}, {4913, 47892}, {8689, 47798}, {11068, 47828}, {21104, 47813}, {21116, 28195}, {24720, 47771}, {28175, 47702}, {28229, 47780}, {47660, 47703}

X(48102) = reflection of X(i) in X(j) for these {i,j}: {2254, 47890}, {4467, 4830}, {16892, 659}, {21105, 47728}, {47652, 3716}, {47685, 4522}, {47686, 3835}, {47701, 4724}, {47703, 47660}, {47704, 47694}, {47725, 21201}
X(48102) = crossdifference of every pair of points on line {595, 672}


X(48103) = X(10)X(514)∩X(513)X(4088)

Barycentrics    (b - c)*(a^3 + a^2*b + b^3 + a^2*c - a*b*c + b^2*c + b*c^2 + c^3) : :
X(48103) = X[47694] - 3 X[47773], 2 X[650] - 3 X[47885], 4 X[2490] - 3 X[47799], 4 X[2977] - 3 X[47827], 2 X[3004] - 3 X[47827], 2 X[3776] - 3 X[47823], 2 X[3837] - 3 X[47809], X[47652] - 3 X[47809], 2 X[4806] - 3 X[30565], 2 X[4874] - 3 X[47771], X[47691] - 3 X[47771], 3 X[6546] - X[47701], 2 X[23770] - 3 X[47833], 5 X[30795] - 6 X[47807], 3 X[44429] - X[47651], X[47653] - 3 X[47825], X[47686] - 3 X[47808], X[47692] - 3 X[47804], X[47702] - 3 X[47811], X[47705] - 3 X[47813], X[47709] - 3 X[47815], X[47713] - 3 X[47817], X[47717] - 3 X[47818]

X(48103) lies on these lines: {2, 47688}, {10, 514}, {23, 385}, {513, 4088}, {650, 4802}, {663, 29208}, {667, 29047}, {812, 4122}, {814, 47707}, {826, 4063}, {830, 4808}, {891, 47682}, {918, 4784}, {1019, 29354}, {1577, 29098}, {1960, 47727}, {2490, 47799}, {2526, 28195}, {2977, 3004}, {3700, 4810}, {3762, 29029}, {3776, 47823}, {3837, 47652}, {4040, 7927}, {4367, 29288}, {4380, 29078}, {4391, 29025}, {4401, 29260}, {4462, 29120}, {4474, 29156}, {4498, 29017}, {4522, 24719}, {4707, 29224}, {4724, 29144}, {4761, 29102}, {4774, 29240}, {4782, 29204}, {4806, 30565}, {4834, 23875}, {4874, 26230}, {4913, 28863}, {4963, 4977}, {6546, 47701}, {9508, 16892}, {11068, 28147}, {18004, 20295}, {21116, 28199}, {21385, 29312}, {23770, 47833}, {25259, 29328}, {28179, 47884}, {28602, 31098}, {29070, 47711}, {29074, 47706}, {29086, 47710}, {29174, 47708}, {29362, 47663}, {30795, 47807}, {44429, 47651}, {47653, 47825}, {47686, 47808}, {47692, 47804}, {47702, 47811}, {47705, 47813}, {47709, 47815}, {47713, 47817}, {47717, 47818}

X(48103) = midpoint of X(i) and X(j) for these {i,j}: {17494, 47693}, {21385, 47726}, {47663, 47690}
X(48103) = reflection of X(i) in X(j) for these {i,j}: {659, 47890}, {3004, 2977}, {4810, 3700}, {16892, 9508}, {20295, 18004}, {24719, 4522}, {47652, 3837}, {47691, 4874}, {47727, 1960}
X(48103) = complement of X(47688)
X(48103) = crossdifference of every pair of points on line {35, 39}
X(48103) = barycentric product X(514)*X(33159)
X(48103) = barycentric quotient X(33159)/X(190)
X(48103) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2977, 3004, 47827}, {47652, 47809, 3837}, {47691, 47771, 4874}


X(48104) = X(513)X(4088)∩X(514)X(4380)

Barycentrics    (b - c)*(3*a^2 + a*b + b^2 + a*c + c^2) : :
X(48104) = 3 X[4380] - X[47657], 3 X[649] - 2 X[3004], 5 X[649] - 4 X[17069], 4 X[649] - 3 X[47886], 5 X[3004] - 6 X[17069], 8 X[3004] - 9 X[47886], 16 X[17069] - 15 X[47886], 3 X[661] - 4 X[11068], 8 X[2527] - 7 X[31207], 4 X[2527] - 3 X[47756], 7 X[31207] - 6 X[47756], 4 X[2529] - 3 X[45320], 2 X[3776] - 3 X[47763], 3 X[4379] - 2 X[23729], 2 X[20295] - 3 X[47874], 5 X[24924] - 6 X[47768], 5 X[26798] - 6 X[47879], 5 X[30835] - 6 X[47767]

X(48104) lies on these lines: {513, 4088}, {514, 4380}, {649, 3004}, {650, 23731}, {661, 11068}, {812, 47656}, {824, 26853}, {2527, 31207}, {2529, 45320}, {2786, 47662}, {3667, 47689}, {3776, 47763}, {4024, 6008}, {4379, 23729}, {4785, 47660}, {4790, 16892}, {4813, 47890}, {4830, 47699}, {4932, 47652}, {7192, 28882}, {17494, 28859}, {20295, 47874}, {24924, 47768}, {26798, 47879}, {28840, 47663}, {30835, 47767}

X(48104) = reflection of X(i) in X(j) for these {i,j}: {4813, 47890}, {16892, 4790}, {23731, 650}, {47652, 4932}, {47699, 4830}
X(48104) = crossdifference of every pair of points on line {5299, 41265}
X(48104) = {X(2527),X(47756)}-harmonic conjugate of X(31207)


X(48105) = X(513)X(4088)∩X(514)X(47692)

Barycentrics    (b - c)*(3*a^3 + 2*a*b^2 + b^3 - 2*a*b*c + b^2*c + 2*a*c^2 + b*c^2 + c^3) : :
X(48105) = 4 X[659] - 3 X[47886], 2 X[2526] - 3 X[6546], 2 X[3776] - 3 X[47805], 2 X[4925] - 3 X[47890], 4 X[8689] - 3 X[47797], 2 X[46403] - 3 X[47874]

X(48105) lies on these lines: {513, 4088}, {514, 47692}, {659, 47886}, {661, 4521}, {676, 1459}, {2526, 6546}, {3667, 47700}, {3716, 47686}, {3776, 47805}, {4468, 28225}, {4925, 47890}, {8689, 47797}, {14475, 28220}, {28195, 47701}, {46403, 47874}

X(48105) = reflection of X(47686) in X(3716)
X(48105) = crossdifference of every pair of points on line {3730, 3915}


X(48106) = X(513)X(4088)∩X(514)X(1734)

Barycentrics    (b - c)*(a^3 + 2*a^2*b + b^3 + 2*a^2*c + b^2*c + b*c^2 + c^3) : :
X(48106) = 2 X[676] - 3 X[47767], 3 X[1635] - X[47702], 4 X[2977] - 3 X[4893], 2 X[3004] - 3 X[47828], 2 X[3716] - 3 X[47771], 2 X[3776] - 3 X[47824], X[47688] - 3 X[47824], 2 X[3835] - 3 X[47809], 2 X[4010] - 3 X[47874], 4 X[4369] - 3 X[47887], 2 X[47691] - 3 X[47887], 3 X[4379] - 2 X[23770], 2 X[4458] - 3 X[47762], X[47692] - 3 X[47762], 4 X[9508] - 3 X[47886], 4 X[11068] - 3 X[47811], 4 X[25380] - 3 X[44435], 5 X[30835] - 6 X[47807], 3 X[31148] - X[47705], 7 X[31207] - 6 X[47799], 4 X[31286] - 3 X[47797], 4 X[43061] - 3 X[47800], 2 X[47123] - 3 X[47813]

X(48106) lies on these lines: {513, 4088}, {514, 1734}, {522, 4380}, {523, 649}, {650, 47701}, {659, 29144}, {663, 3800}, {667, 7927}, {676, 47767}, {812, 47690}, {824, 47693}, {826, 4834}, {1019, 29047}, {1577, 29158}, {1635, 47702}, {2533, 29025}, {2785, 47684}, {2977, 4893}, {3004, 47828}, {3716, 47771}, {3762, 29132}, {3776, 47688}, {3798, 28155}, {3801, 29174}, {3835, 47809}, {4010, 47874}, {4025, 28147}, {4063, 29021}, {4122, 29328}, {4142, 47709}, {4367, 29208}, {4369, 47691}, {4379, 23770}, {4391, 29118}, {4458, 47692}, {4474, 29126}, {4498, 29142}, {4522, 20295}, {4707, 29160}, {4724, 47890}, {4750, 28151}, {4762, 47703}, {4774, 29156}, {4775, 12073}, {4802, 16892}, {4804, 6590}, {4818, 47653}, {4913, 45746}, {4979, 47700}, {6002, 47707}, {7659, 30520}, {9508, 47886}, {11068, 47811}, {14331, 47136}, {20517, 47713}, {23876, 47726}, {24720, 47652}, {25380, 44435}, {28840, 47698}, {28882, 46403}, {29013, 47711}, {29033, 47723}, {29037, 47706}, {29062, 47710}, {29190, 47714}, {29302, 47715}, {29350, 47682}, {30835, 47807}, {31148, 47705}, {31207, 47799}, {31286, 47797}, {43061, 47800}, {43067, 47704}, {47123, 47813}

X(48106) = midpoint of X(i) and X(j) for these {i,j}: {4380, 47689}, {4979, 47700}
X(48106) = reflection of X(i) in X(j) for these {i,j}: {4724, 47890}, {4804, 6590}, {20295, 4522}, {45746, 4913}, {47652, 24720}, {47653, 4818}, {47688, 3776}, {47691, 4369}, {47692, 4458}, {47701, 650}, {47704, 43067}, {47709, 4142}, {47713, 20517}
X(48106) = crossdifference of every pair of points on line {386, 2280}
X(48106) = barycentric product X(514)*X(38047)
X(48106) = barycentric quotient X(38047)/X(190)
X(48106) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4369, 47691, 47887}, {47688, 47824, 3776}, {47692, 47762, 4458}


X(48107) = X(320)X(350)∩X(514)X(4380)

Barycentrics    (b - c)*(2*a^2 + 2*a*b + 2*a*c + b*c) : :
X(48107) = 5 X[693] - 4 X[4106], 3 X[693] - 2 X[20295], 7 X[693] - 6 X[21297], 9 X[693] - 8 X[23813], 3 X[693] - 4 X[43067], 5 X[693] - 6 X[47780], 2 X[4106] - 5 X[7192], 6 X[4106] - 5 X[20295], 14 X[4106] - 15 X[21297], 9 X[4106] - 10 X[23813], 3 X[4106] - 5 X[43067], 2 X[4106] - 3 X[47780], 3 X[7192] - X[20295], 7 X[7192] - 3 X[21297], 9 X[7192] - 4 X[23813], 3 X[7192] - 2 X[43067], 5 X[7192] - 3 X[47780], 7 X[20295] - 9 X[21297], 3 X[20295] - 4 X[23813], 5 X[20295] - 9 X[47780], 27 X[21297] - 28 X[23813], 9 X[21297] - 14 X[43067], 5 X[21297] - 7 X[47780], 2 X[23813] - 3 X[43067], 20 X[23813] - 27 X[47780], 10 X[43067] - 9 X[47780], 4 X[4979] - X[47664], 4 X[649] - 3 X[31150], 3 X[31150] - 2 X[47666], 2 X[650] - 3 X[47763], X[31290] - 3 X[47763], 4 X[661] - 5 X[31209], 3 X[661] - 4 X[31286], 2 X[661] - 3 X[47762], 5 X[661] - 6 X[47778], 8 X[4932] - 5 X[31209], 3 X[4932] - 2 X[31286], 4 X[4932] - 3 X[47762], 5 X[4932] - 3 X[47778], 15 X[31209] - 16 X[31286], 5 X[31209] - 6 X[47762], 25 X[31209] - 24 X[47778], 8 X[31286] - 9 X[47762], 10 X[31286] - 9 X[47778], 5 X[47762] - 4 X[47778], 4 X[2529] - 3 X[47770], 2 X[3004] - 3 X[47755], 2 X[3700] - 3 X[47791], 4 X[3798] - 3 X[47782], 2 X[3835] - 3 X[31148], 4 X[4369] - 3 X[4776], 6 X[4369] - 5 X[30835], 7 X[4369] - 6 X[45678], 3 X[4776] - 2 X[4813], 9 X[4776] - 10 X[30835], 7 X[4776] - 8 X[45678], 3 X[4813] - 5 X[30835], 7 X[4813] - 12 X[45678], 35 X[30835] - 36 X[45678], 4 X[4394] - 3 X[47775], 2 X[4820] - 3 X[47792], 2 X[4841] - 3 X[27486], 4 X[4885] - 3 X[47759], 4 X[4940] - 5 X[26985], 2 X[4983] - 3 X[47820], 4 X[7653] - 3 X[47760], 4 X[17069] - 3 X[47781], 5 X[26798] - 6 X[45320], 5 X[27013] - 3 X[47774], 7 X[27115] - 6 X[47777], 7 X[31207] - 6 X[45315]

X(48107) lies on these lines: {320, 350}, {514, 4380}, {522, 47655}, {649, 28840}, {650, 31290}, {661, 4932}, {812, 47675}, {850, 4406}, {900, 47656}, {918, 47662}, {2529, 47770}, {2786, 47665}, {3004, 28209}, {3700, 47791}, {3768, 27673}, {3776, 23731}, {3798, 47782}, {3835, 31148}, {3937, 40619}, {4024, 28867}, {4025, 4778}, {4369, 4776}, {4391, 15309}, {4394, 47775}, {4453, 13246}, {4608, 4777}, {4762, 26853}, {4785, 47672}, {4790, 17494}, {4802, 17161}, {4820, 47792}, {4841, 27486}, {4885, 47759}, {4897, 4977}, {4940, 26985}, {4960, 29013}, {4976, 47667}, {4983, 47820}, {6008, 26824}, {6372, 23807}, {6590, 44449}, {7653, 47760}, {16892, 28859}, {17069, 47781}, {25511, 26822}, {26248, 44429}, {26798, 45320}, {27013, 47774}, {27115, 47777}, {27417, 46389}, {28220, 47894}, {28846, 47660}, {28898, 47659}, {28902, 47890}, {31207, 45315}, {47651, 47676}

X(48107) = reflection of X(i) in X(j) for these {i,j}: {661, 4932}, {693, 7192}, {4380, 4979}, {4813, 4369}, {17494, 4790}, {20295, 43067}, {23731, 3776}, {31290, 650}, {44449, 6590}, {45746, 4897}, {47651, 47676}, {47657, 4467}, {47664, 4380}, {47666, 649}, {47667, 4976}
X(48107) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {110, 41930}, {28148, 2}, {28626, 150}, {30711, 33650}, {39948, 149}
X(48107) = X(i)-isoconjugate of X(j) for these (i,j): {42, 43356}, {101, 39983}, {692, 39708}
X(48107) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 39983), (1086, 39708), (40592, 43356)
X(48107) = crosspoint of X(668) and X(28650)
X(48107) = crossdifference of every pair of points on line {213, 21820}
X(48107) = barycentric product X(i)*X(j) for these {i,j}: {514, 17394}, {693, 37685}, {15413, 17562}
X(48107) = barycentric quotient X(i)/X(j) for these {i,j}: {81, 43356}, {513, 39983}, {514, 39708}, {17394, 190}, {17562, 1783}, {37685, 100}
X(48107) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 47666, 31150}, {661, 4932, 47762}, {661, 47762, 31209}, {4106, 47780, 693}, {4369, 4813, 4776}, {7192, 20295, 43067}, {20295, 43067, 693}, {31290, 47763, 650}


X(48108) = X(320)X(350)∩X(514)X(1734)

Barycentrics    (b - c)*(2*a^2*b + 2*a^2*c + 3*a*b*c + b^2*c + b*c^2) : :
X(48108) = 3 X[693] - 2 X[4010], X[4010] - 3 X[21146], 2 X[7662] - 3 X[47780], 3 X[649] - 2 X[4830], 2 X[650] - 3 X[47824], 2 X[659] - 3 X[47762], 2 X[661] - 3 X[44429], 4 X[24720] - 3 X[44429], 2 X[676] - 3 X[47891], 4 X[3676] - 3 X[47797], 2 X[3716] - 3 X[4379], 2 X[3835] - 3 X[47812], 4 X[3837] - 3 X[4776], 2 X[4040] - 3 X[47820], 4 X[4369] - 3 X[47804], 2 X[4724] - 3 X[47804], 2 X[4468] - 3 X[47809], 4 X[4885] - 3 X[47821], 3 X[4893] - 4 X[25380], 4 X[9508] - 3 X[31150], 2 X[14349] - 3 X[47819], 4 X[23789] - 3 X[47819], 3 X[21115] - X[47702], 4 X[25666] - 3 X[47826], 5 X[31209] - 6 X[47823], 4 X[31286] - 3 X[47811]

X(48108) lies on these lines: {320, 350}, {512, 4801}, {514, 1734}, {522, 47672}, {523, 47674}, {525, 47719}, {649, 4830}, {650, 47824}, {659, 47762}, {661, 4521}, {676, 47891}, {824, 47703}, {826, 47718}, {918, 47690}, {1019, 29186}, {1491, 2977}, {2533, 4462}, {2787, 47721}, {3004, 47699}, {3309, 17166}, {3667, 4804}, {3676, 47797}, {3716, 4379}, {3776, 47701}, {3800, 47720}, {3810, 23755}, {3835, 28225}, {3837, 4776}, {4040, 47820}, {4088, 28851}, {4367, 29246}, {4369, 4724}, {4378, 29188}, {4380, 4784}, {4391, 6372}, {4444, 28859}, {4468, 47809}, {4762, 7659}, {4818, 4988}, {4824, 28195}, {4885, 47821}, {4893, 25380}, {4978, 6005}, {4983, 23815}, {9508, 31150}, {14349, 23789}, {21104, 47691}, {21115, 47702}, {23793, 47123}, {23875, 47715}, {25666, 47826}, {28220, 31992}, {28878, 31131}, {29102, 47684}, {29126, 47722}, {29132, 47680}, {29144, 47692}, {29148, 47724}, {29168, 47709}, {29212, 47723}, {29354, 47706}, {29358, 47714}, {30520, 47693}, {31209, 47823}, {31286, 47811}

X(48108) = reflection of X(i) in X(j) for these {i,j}: {661, 24720}, {693, 21146}, {4380, 4784}, {4462, 2533}, {4724, 4369}, {4983, 23815}, {4988, 4818}, {14349, 23789}, {47666, 1491}, {47691, 21104}, {47694, 43067}, {47699, 3004}, {47701, 3776}, {47729, 4378}
X(48108) = crossdifference of every pair of points on line {213, 2241}
X(48108) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 24720, 44429}, {4369, 4724, 47804}, {14349, 23789, 47819}


X(48109) = X(320)X(350)∩X(514)X(15416)

Barycentrics    b*(b - c)*c*(3*a^2 + b^2 + c^2) : :
X(48109) = 2 X[21003] - 3 X[47820]

X(48109) lies on these lines: {320, 350}, {514, 15416}, {812, 2484}, {918, 4801}, {2483, 4380}, {2509, 17494}, {2517, 3766}, {3261, 30804}, {3667, 4509}, {4140, 23780}, {4397, 20949}, {4406, 24002}, {4905, 23785}, {4978, 28846}, {20906, 29144}, {21003, 47820}, {21189, 23790}, {23782, 23789}, {23783, 23787}, {23800, 23828}, {23885, 47665}

X(48109) = midpoint of X(4140) and X(23780)
X(48109) = reflection of X(i) in X(j) for these {i,j}: {4380, 2483}, {15413, 693}, {17494, 2509}
X(48109) = isotomic conjugate of the isogonal conjugate of X(3803)
X(48109) = X(i)-isoconjugate of X(j) for these (i,j): {42, 907}, {101, 39951}, {692, 23051}, {8750, 34817}, {8801, 32656}, {18840, 32739}
X(48109) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 39951), (1086, 23051), (26932, 34817), (40592, 907), (40619, 18840)
X(48109) = barycentric product X(i)*X(j) for these {i,j}: {76, 3803}, {274, 3800}, {513, 40022}, {514, 39731}, {693, 3618}, {3785, 17924}, {3804, 6385}, {6995, 15413}, {30435, 40495}
X(48109) = barycentric quotient X(i)/X(j) for these {i,j}: {81, 907}, {513, 39951}, {514, 23051}, {693, 18840}, {905, 34817}, {3618, 100}, {3785, 1332}, {3796, 906}, {3800, 37}, {3803, 6}, {3804, 213}, {3806, 3954}, {6995, 1783}, {8362, 4553}, {17924, 8801}, {30435, 692}, {39731, 190}, {40022, 668}
X(48109) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 23794, 7650}, {693, 23819, 20954}


X(48110) = X(36)X(238)∩X(514)X(4380)

Barycentrics    a*(b - c)*(2*a^2 + 3*a*b + b^2 + 3*a*c + 3*b*c + c^2) : :
X(48110) = 2 X[905] - 3 X[1019], 4 X[905] - 3 X[14349], 2 X[4129] - 3 X[47762], 2 X[4823] - 3 X[31148]

X(48110) lies on these lines: {36, 238}, {514, 4380}, {649, 15309}, {1577, 4932}, {1734, 4784}, {4063, 4790}, {4129, 47762}, {4785, 4978}, {4813, 14838}, {4823, 31148}, {4960, 23882}, {7192, 29013}, {7265, 28867}, {23755, 29114}, {26853, 29302}, {29270, 47672}

X(48110) = reflection of X(i) in X(j) for these {i,j}: {1577, 4932}, {1734, 4784}, {4063, 4790}, {4813, 14838}, {14349, 1019}, {23800, 4840}


X(48111) = X(36)X(238)∩X(514)X(47692)

Barycentrics    a*(b - c)*(2*a^2 - a*b + b^2 - a*c - b*c + c^2) : :
X(48111) = 2 X[10] - 3 X[47815], 4 X[1125] - 3 X[47819], 2 X[3960] - 3 X[8643], 3 X[4448] - 2 X[21260], 4 X[8689] - 3 X[47817], 2 X[17072] - 3 X[47817], 2 X[20517] - 3 X[44433], 2 X[21188] - 3 X[47801], 2 X[23789] - 3 X[47820], 2 X[24720] - 3 X[47818], 5 X[31251] - 6 X[45666], 4 X[31288] - 3 X[36848]

X(48111) lies on these lines: {10, 47815}, {36, 238}, {40, 3309}, {514, 47692}, {649, 42325}, {659, 1734}, {830, 4724}, {1110, 1633}, {1125, 47819}, {1420, 3669}, {1842, 17924}, {1960, 3777}, {2254, 4401}, {2832, 4449}, {2976, 29162}, {3762, 28470}, {3887, 4498}, {3900, 21385}, {3960, 8643}, {4083, 5697}, {4162, 7962}, {4448, 21260}, {4782, 37572}, {5592, 28487}, {6363, 39541}, {8689, 17072}, {20517, 44433}, {21185, 47680}, {21188, 47801}, {23789, 47820}, {24720, 47818}, {29148, 31291}, {29186, 47694}, {31251, 45666}, {31288, 36848}, {41012, 47685}

X(48111) = reflection of X(i) in X(j) for these {i,j}: {1019, 3803}, {1734, 659}, {2254, 4401}, {3777, 1960}, {4905, 667}, {14349, 4040}, {17072, 8689}, {23800, 4057}, {47680, 21185}
X(48111) = crosssum of X(513) and X(3938)
X(48111) = barycentric product X(i)*X(j) for these {i,j}: {1, 47663}, {513, 17352}
X(48111) = barycentric quotient X(i)/X(j) for these {i,j}: {17352, 668}, {47663, 75}
X(48111) = {X(8689),X(17072)}-harmonic conjugate of X(47817)


X(48112) = X(513)X(47700)∩X(514)X(4838)

Barycentrics    (b - c)*(-3*a*b + 2*b^2 - 3*a*c + 2*c^2) : :
X(48112) = 5 X[4838] - 4 X[47655], 3 X[4838] - 4 X[47665], 3 X[4838] - 2 X[47670], 3 X[47655] - 5 X[47665], 6 X[47655] - 5 X[47670], 5 X[661] - 4 X[3004], 3 X[661] - 2 X[16892], 6 X[3004] - 5 X[16892], 4 X[47667] - 3 X[47669], 9 X[1635] - 8 X[3798], 3 X[1635] - 4 X[4468], 2 X[3798] - 3 X[4468], 8 X[2487] - 9 X[6544], 2 X[3776] - 3 X[47769], 4 X[3835] - 3 X[21115], 3 X[4120] - 2 X[21104], 2 X[4369] - 3 X[47772], 2 X[4382] - 3 X[4958], 8 X[4500] - 9 X[4931], 2 X[4500] - 3 X[25259], 4 X[4500] - 3 X[47672], 3 X[4931] - 4 X[25259], 3 X[4931] - 2 X[47672], 3 X[4728] - 2 X[47676], 2 X[4897] - 3 X[6546], 3 X[6545] - 4 X[14321], 4 X[18004] - 3 X[47812], 5 X[24924] - 6 X[30565]

X(48112) lies on these lines: {513, 47700}, {514, 4838}, {661, 918}, {824, 47667}, {1635, 3798}, {2487, 6544}, {3776, 47769}, {3835, 21115}, {4041, 29252}, {4120, 21104}, {4369, 47772}, {4380, 28906}, {4382, 4958}, {4462, 20909}, {4500, 4931}, {4728, 47676}, {4813, 30520}, {4822, 29354}, {4897, 6546}, {4979, 28846}, {6545, 14321}, {7192, 28871}, {18004, 47812}, {20295, 28890}, {24924, 30565}, {28225, 47689}, {28855, 47660}, {28863, 31290}, {28867, 47663}, {30519, 47666}

X(48112) = reflection of X(i) in X(j) for these {i,j}: {47670, 47665}, {47672, 25259}, {47673, 47666}
X(48112) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25259, 47672, 4931}, {47665, 47670, 4838}


X(48113) = X(513)X(47700)∩X(514)X(4170)

Barycentrics    (b - c)*(2*a^3 - a^2*b + a*b^2 + 2*b^3 - a^2*c - 4*a*b*c + 2*b^2*c + a*c^2 + 2*b*c^2 + 2*c^3) : :
X(48113) = 4 X[4468] - 3 X[47810], 4 X[4874] - 3 X[21115], 2 X[16892] - 3 X[47811], 9 X[21052] - 8 X[44314], 2 X[47676] - 3 X[47813]

X(48113) lies on these lines: {513, 47700}, {514, 4170}, {4122, 4977}, {4468, 47810}, {4724, 30520}, {4778, 47662}, {4813, 4931}, {4874, 21115}, {16892, 47811}, {21052, 44314}, {23731, 28213}, {28851, 47696}, {28890, 47694}, {47676, 47813}


X(48114) = X(513)X(4382)∩X(514)X(4838)

Barycentrics    (b - c)*(-2*a^2 - a*b - a*c + 2*b*c) : :
X(48114) = 3 X[4838] - 2 X[47658], 2 X[649] - 3 X[4728], 3 X[649] - 4 X[4885], 4 X[649] - 5 X[24924], 5 X[649] - 6 X[47761], 4 X[4106] - 3 X[4728], 3 X[4106] - 2 X[4885], 8 X[4106] - 5 X[24924], 5 X[4106] - 3 X[47761], 9 X[4728] - 8 X[4885], 6 X[4728] - 5 X[24924], 5 X[4728] - 4 X[47761], 16 X[4885] - 15 X[24924], 10 X[4885] - 9 X[47761], 25 X[24924] - 24 X[47761], 2 X[650] - 3 X[31147], 3 X[661] - 2 X[17494], 5 X[661] - 6 X[47759], 7 X[661] - 6 X[47775], X[17494] - 3 X[20295], 5 X[17494] - 9 X[47759], 7 X[17494] - 9 X[47775], 5 X[20295] - 3 X[47759], 7 X[20295] - 3 X[47775], 7 X[47759] - 5 X[47775], 3 X[693] - 2 X[4932], 4 X[693] - 3 X[31148], 4 X[4932] - 3 X[4979], 8 X[4932] - 9 X[31148], 2 X[4979] - 3 X[31148], 3 X[1635] - 4 X[3835], 3 X[1635] - 2 X[4380], 9 X[1635] - 10 X[31209], 6 X[3835] - 5 X[31209], 3 X[4380] - 5 X[31209], 8 X[2487] - 9 X[14475], 3 X[4120] - 2 X[47890], 2 X[4369] - 3 X[21297], 3 X[21297] - X[26853], 3 X[4379] - 2 X[4790], 9 X[4379] - 8 X[7653], 3 X[4379] - 4 X[23813], 3 X[4790] - 4 X[7653], 2 X[7653] - 3 X[23813], 4 X[4394] - 5 X[30835], 6 X[4763] - 7 X[27138], 2 X[4784] - 3 X[47812], 4 X[4806] - 3 X[47811], 2 X[4830] - 3 X[47821], 3 X[4893] - 4 X[4940], 2 X[4897] - 3 X[6545], 6 X[4928] - 5 X[27013], 3 X[4931] - 2 X[47660], 3 X[4958] - 2 X[25259], 3 X[4984] - 4 X[17069], 3 X[6546] - 4 X[14321], 2 X[11068] - 3 X[47786], 4 X[25666] - 5 X[26798], 4 X[25666] - 3 X[47776], 5 X[26798] - 3 X[47776], 5 X[26777] - 6 X[45315]

X(48114) lies on these lines: {513, 4382}, {514, 4838}, {522, 47673}, {523, 23731}, {649, 4106}, {650, 31147}, {661, 812}, {693, 4785}, {900, 16892}, {1635, 3835}, {1734, 4961}, {2254, 24719}, {2487, 14475}, {2786, 47652}, {3667, 21115}, {4063, 29738}, {4120, 47890}, {4369, 21297}, {4379, 4790}, {4394, 30835}, {4729, 21301}, {4762, 4813}, {4763, 27138}, {4784, 47812}, {4806, 47811}, {4822, 29070}, {4830, 47821}, {4893, 4940}, {4897, 6545}, {4928, 27013}, {4931, 47660}, {4958, 25259}, {4977, 47671}, {4984, 17069}, {6002, 21222}, {6546, 14321}, {11068, 47786}, {14349, 29270}, {21104, 28217}, {21116, 39386}, {23730, 23741}, {23738, 29170}, {25666, 26798}, {26777, 45315}, {26824, 28840}, {28851, 47650}, {28859, 47656}, {28867, 47676}, {30519, 47651}

X(48114) = reflection of X(i) in X(j) for these {i,j}: {649, 4106}, {661, 20295}, {2254, 24719}, {4380, 3835}, {4729, 21301}, {4790, 23813}, {4804, 4810}, {4979, 693}, {16892, 23729}, {26853, 4369}, {47672, 4382}
X(48114) = barycentric product X(514)*X(4852)
X(48114) = barycentric quotient X(4852)/X(190)
X(48114) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 4106, 4728}, {649, 4728, 24924}, {693, 4979, 31148}, {3835, 4380, 1635}, {4790, 23813, 4379}, {21297, 26853, 4369}, {26798, 47776, 25666}


X(48115) = X(513)X(4382)∩X(514)X(47685)

Barycentrics    (b - c)*(-2*a^3 + a^2*b - a*b^2 + a^2*c + 4*a*b*c + 2*b^2*c - a*c^2 + 2*b*c^2) : :
X(48115) = 4 X[659] - 5 X[24924], 2 X[659] - 3 X[47812], 5 X[24924] - 6 X[47812], 3 X[1635] - 4 X[24720], 4 X[3837] - 3 X[47811], 2 X[4724] - 3 X[4728], 2 X[4830] - 3 X[47824], 4 X[21146] - 3 X[31148], 4 X[23814] - 3 X[45671]

X(48115) lies on these lines: {513, 4382}, {514, 47685}, {522, 47705}, {659, 24924}, {661, 46403}, {814, 23738}, {900, 47704}, {1635, 24720}, {2254, 29362}, {2832, 47724}, {3837, 47811}, {4122, 4977}, {4724, 4728}, {4778, 4931}, {4830, 47824}, {21146, 31148}, {23765, 29274}, {23814, 45671}, {47652, 47702}

X(48115) = reflection of X(i) in X(j) for these {i,j}: {661, 46403}, {47700, 47687}, {47702, 47652}
X(48115) = {X(659),X(47812)}-harmonic conjugate of X(24924)


X(48116) = X(513)X(663)∩X(514)X(47685)

Barycentrics    a*(b - c)*(2*a^2 + a*b + 3*b^2 + a*c + 3*c^2) : :
X(48116) = 3 X[2254] - 2 X[4834], 4 X[23789] - 3 X[31148], 4 X[23815] - 3 X[47813]

X(48116) lies on these lines: {513, 663}, {514, 47685}, {661, 16546}, {2254, 4834}, {2526, 4498}, {4905, 4979}, {6332, 28225}, {16892, 28481}, {23789, 31148}, {23815, 47813}, {23877, 47686}, {29190, 47673}

X(48116) = reflection of X(i) in X(j) for these {i,j}: {4498, 2526}, {4979, 4905}
X(48116) = crossdifference of every pair of points on line {9, 17469}


X(48117) = X(513)X(47700)∩X(514)X(4024)

Barycentrics    (b - c)*(a^2 - 2*a*b + 2*b^2 - 2*a*c + 2*c^2) : :
X(48117) = 3 X[4382] - 2 X[47650], 3 X[4608] - 5 X[47659], 3 X[4813] - 2 X[23731], 3 X[25259] - X[47650], 5 X[649] - 4 X[4897], 3 X[649] - 4 X[47890], 3 X[4897] - 5 X[47890], 4 X[3239] - 3 X[6545], 2 X[3776] - 3 X[30565], 4 X[3776] - 5 X[30835], 6 X[30565] - 5 X[30835], 2 X[3835] - 3 X[47772], 2 X[4025] - 3 X[6546], 3 X[4379] - 2 X[47676], 6 X[4453] - 7 X[31207], 4 X[4468] - 3 X[4893], 3 X[4893] - 2 X[16892], 3 X[4750] - 4 X[11068], 4 X[4885] - 3 X[21115], 2 X[4932] - 3 X[47773], 9 X[6544] - 8 X[7658], 2 X[21104] - 3 X[47874], 5 X[24924] - 6 X[47770], 3 X[31147] - 2 X[47652], 2 X[47672] - 3 X[47873]

X(48117) lies on these lines: {513, 47700}, {514, 4024}, {649, 918}, {661, 30520}, {663, 29354}, {693, 28890}, {824, 47661}, {2786, 47663}, {3239, 6545}, {3776, 30565}, {3835, 47772}, {4025, 6546}, {4379, 47676}, {4453, 31207}, {4468, 4893}, {4474, 29102}, {4498, 23875}, {4750, 11068}, {4778, 47693}, {4885, 21115}, {4932, 47773}, {6544, 7658}, {17494, 30519}, {21104, 47874}, {24924, 47770}, {26853, 28906}, {28840, 47662}, {28851, 47660}, {28863, 47666}, {28882, 44449}, {31147, 47652}, {47672, 47873}

X(48117) = reflection of X(i) in X(j) for these {i,j}: {4382, 25259}, {16892, 4468}
X(48117) = barycentric product X(514)*X(17267)
X(48117) = barycentric quotient X(17267)/X(190)
X(48117) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3776, 30565, 30835}, {4468, 16892, 4893}


X(48118) = X(513)X(47700)∩X(514)X(4088)

Barycentrics    (b - c)*(a^3 + a^2*b + 2*b^3 + a^2*c - 2*a*b*c + 2*b^2*c + 2*b*c^2 + 2*c^3) : :
X(48118) = 3 X[47707] - X[47722], 3 X[663] - 2 X[47727], 4 X[2977] - 3 X[47886], 2 X[3776] - 3 X[47809], 2 X[4458] - 3 X[47771], 4 X[4468] - 3 X[47826], 2 X[47701] - 3 X[47826], 2 X[16892] - 3 X[47828], 4 X[18004] - 3 X[31147], 2 X[23770] - 3 X[47874], 2 X[47691] - 3 X[47832]

X(48118) lies on these lines: {513, 47700}, {514, 4088}, {522, 47663}, {523, 4724}, {659, 29204}, {661, 4802}, {663, 29047}, {826, 4498}, {2254, 30520}, {2977, 47886}, {3064, 21119}, {3716, 47692}, {3762, 29160}, {3776, 47809}, {3835, 47688}, {4040, 29260}, {4063, 29358}, {4122, 4382}, {4449, 29288}, {4458, 47771}, {4462, 29116}, {4468, 14779}, {4522, 47652}, {4608, 28191}, {4791, 47725}, {4913, 47677}, {6590, 47704}, {7662, 47705}, {8045, 47720}, {16892, 47828}, {18004, 31147}, {21385, 29318}, {23770, 47874}, {28151, 47702}, {29051, 47706}, {29186, 47710}, {47691, 47832}

X(48118) = reflection of X(i) in X(j) for these {i,j}: {4382, 4122}, {47652, 4522}, {47677, 4913}, {47688, 3835}, {47692, 3716}, {47701, 4468}, {47704, 6590}, {47705, 7662}, {47720, 8045}, {47725, 4791}
X(48118) = crossdifference of every pair of points on line {4253, 21764}
X(48118) = {X(4468),X(47701)}-harmonic conjugate of X(47826)


X(48119) = X(513)X(4382)∩X(514)X(4088)

Barycentrics    (b - c)*(-a^3 + a^2*b + a^2*c + 4*a*b*c + 2*b^2*c + 2*b*c^2) : :
X(48119) = 3 X[4382] - 2 X[4810], 2 X[650] - 3 X[47812], 2 X[659] - 3 X[4379], 3 X[693] - 2 X[3716], 4 X[693] - 3 X[47832], 4 X[3716] - 3 X[4724], 8 X[3716] - 9 X[47832], 2 X[4724] - 3 X[47832], 4 X[3835] - 3 X[47826], 4 X[3837] - 3 X[4893], 3 X[4449] - 2 X[47729], 3 X[4801] - X[47729], 2 X[4830] - 3 X[47762], 4 X[4885] - 3 X[47811], 2 X[17494] - 3 X[47828], 4 X[24720] - 3 X[47828], 4 X[25380] - 3 X[31150], 5 X[26777] - 6 X[47830]

X(48119 lies on these lines: {513, 4382}, {514, 4088}, {522, 26824}, {649, 21146}, {650, 47812}, {659, 4379}, {663, 4978}, {693, 3716}, {2254, 4762}, {3700, 4813}, {3835, 47826}, {3837, 4893}, {4077, 43924}, {4449, 4801}, {4777, 47705}, {4778, 20295}, {4818, 47661}, {4830, 47762}, {4885, 47811}, {4913, 47664}, {17374, 28220}, {17494, 24720}, {23738, 23880}, {25380, 31150}, {26777, 47830}, {28229, 31290}, {47675, 47685}

X(48119) = midpoint of X(47675) and X(47685)
X(48119) = reflection of X(i) in X(j) for these {i,j}: {649, 21146}, {663, 4978}, {4449, 4801}, {4474, 47724}, {4724, 693}, {4813, 24719}, {17494, 24720}, {47661, 4818}, {47664, 4913}
X(48119) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 4724, 47832}, {17494, 24720, 47828}


X(48120) = X(513)X(4382)∩X(514)X(4010)

Barycentrics    (b - c)*(a*b^2 + 3*a*b*c + 2*b^2*c + a*c^2 + 2*b*c^2) : :
X(48120) = 3 X[693] - 2 X[3837], 5 X[693] - 3 X[44429], 3 X[1491] - 4 X[3837], 5 X[1491] - 6 X[44429], 10 X[3837] - 9 X[44429], 2 X[650] - 3 X[47833], 2 X[905] - 3 X[47889], 2 X[2977] - 3 X[47788], 2 X[4088] - 3 X[4951], 3 X[4379] - 2 X[9508], 2 X[4782] - 3 X[47813], 2 X[4874] - 3 X[47834], X[17494] - 3 X[47834], 4 X[4885] - 3 X[47827], 2 X[4913] - 3 X[47823], 3 X[4948] - 5 X[30795], 5 X[30795] - 6 X[45320], 2 X[18004] - 3 X[47790], X[47698] - 3 X[47790], 5 X[26985] - 3 X[47825], X[46403] - 3 X[47869], X[47661] - 3 X[47797], X[47664] - 3 X[47804], X[47693] - 3 X[47792]

X(48120) lies on these lines: {325, 523}, {513, 4382}, {514, 4010}, {522, 21146}, {650, 47833}, {659, 4762}, {661, 4802}, {784, 3777}, {814, 17166}, {905, 47889}, {1577, 4490}, {2254, 4777}, {2977, 47788}, {3835, 4824}, {4024, 47704}, {4088, 4951}, {4122, 4500}, {4367, 23882}, {4379, 9508}, {4705, 4823}, {4728, 28151}, {4774, 14077}, {4776, 28179}, {4782, 47813}, {4784, 43067}, {4801, 23765}, {4806, 28175}, {4874, 17494}, {4885, 47827}, {4913, 47823}, {4948, 30795}, {4977, 47675}, {7192, 29328}, {18004, 47698}, {23755, 29284}, {24720, 28161}, {26824, 29362}, {26985, 47825}, {28165, 47812}, {28169, 36848}, {29144, 47703}, {29204, 47705}, {46403, 47869}, {47650, 47696}, {47659, 47688}, {47661, 47797}, {47664, 47804}, {47671, 47701}, {47674, 47699}, {47678, 47716}, {47681, 47725}, {47693, 47792}

X(48120) = midpoint of X(i) and X(j) for these {i,j}: {4024, 47704}, {4804, 47672}, {26824, 47694}, {47650, 47696}, {47656, 47691}, {47659, 47688}, {47671, 47701}, {47674, 47699}, {47678, 47716}, {47681, 47725}
X(48120) = reflection of X(i) in X(j) for these {i,j}: {659, 7662}, {1491, 693}, {3777, 4978}, {4122, 4500}, {4490, 1577}, {4705, 4823}, {4784, 43067}, {4824, 3835}, {4948, 45320}, {17494, 4874}, {23765, 4801}, {47666, 4806}, {47698, 18004}
X(48120) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {17494, 47834, 4874}, {47698, 47790, 18004}


X(48121) = X(513)X(663)∩X(514)X(4024)

Barycentrics    a*(b - c)*(a^2 + 3*a*b + 2*b^2 + 3*a*c + 2*b*c + 2*c^2) : :
X(48121) = 3 X[649] - 4 X[14838], 3 X[14349] - 2 X[14838], 2 X[1577] - 3 X[31147], 2 X[4063] - 3 X[4893], 2 X[4834] - 3 X[47828], 2 X[4932] - 3 X[47796]

X(48121) lies on these lines: {513, 663}, {514, 4024}, {649, 14349}, {661, 4498}, {905, 4979}, {1577, 31147}, {4063, 4893}, {4467, 28493}, {4560, 4785}, {4724, 4983}, {4801, 23794}, {4826, 28894}, {4834, 47828}, {4932, 47796}, {21124, 28478}, {28093, 28115}, {29270, 47683}

X(48121) = reflection of X(i) in X(j) for these {i,j}: {649, 14349}, {4498, 661}, {4724, 4983}, {4979, 905}
X(48121) = crosssum of X(649) and X(5105)
X(48121) = crossdifference of every pair of points on line {9, 2308}
X(48121) = barycentric product X(514)*X(20182)
X(48121) = barycentric quotient X(20182)/X(190)


X(48122) = X(513)X(663)∩X(514)X(4088)

Barycentrics    a*(b - c)*(a^2 + a*b + 2*b^2 + a*c + 2*c^2) : :
X(48122) = 4 X[3803] - 5 X[8656], 2 X[4063] - 3 X[47828], 2 X[4142] - 3 X[44435], 2 X[4369] - 3 X[47819], 3 X[4379] - 4 X[23815], 2 X[4782] - 3 X[47893], 4 X[25666] - 3 X[47815]

X(48122) lies on these lines: {513, 663}, {514, 4088}, {649, 2473}, {659, 28255}, {784, 4382}, {830, 4449}, {1491, 4498}, {2526, 4041}, {3250, 4813}, {3803, 8656}, {4063, 47828}, {4083, 4814}, {4142, 44435}, {4369, 47819}, {4379, 23815}, {4724, 14349}, {4778, 6332}, {4782, 47893}, {6362, 23729}, {8045, 47696}, {14432, 28225}, {23877, 47652}, {25666, 47815}, {28487, 47708}, {29051, 47685}, {40086, 43927}

X(48122) = reflection of X(i) in X(j) for these {i,j}: {649, 2530}, {4041, 2526}, {4474, 21301}, {4498, 1491}, {4724, 14349}, {43927, 40086}, {47696, 8045}
X(48122) = crosssum of X(522) and X(29667)
X(48122) = crossdifference of every pair of points on line {9, 3920}
X(48122) = barycentric product X(i)*X(j) for these {i,j}: {513, 17306}, {514, 17599}
X(48122) = barycentric quotient X(i)/X(j) for these {i,j}: {17306, 668}, {17599, 190}


X(48123) = X(513)X(663)∩X(514)X(4010)

Barycentrics    a*(b - c)*(2*a*b + b^2 + 2*a*c + b*c + c^2) : :
X(48123) = 3 X[1491] - 2 X[1734], X[1734] - 3 X[14349], X[3777] + 2 X[4822], 2 X[4369] - 3 X[47841], X[4729] - 3 X[47810], X[4774] - 4 X[4940], 3 X[4776] - 2 X[21051], 2 X[4874] - 3 X[47840], 3 X[4951] - 2 X[47711], 4 X[25666] - 3 X[47835], 2 X[43067] - 3 X[47889]

X(48123) lies on these lines: {512, 1491}, {513, 663}, {514, 4010}, {661, 4083}, {693, 4992}, {784, 4170}, {814, 20295}, {830, 4775}, {838, 39548}, {905, 4784}, {1499, 47877}, {2530, 6005}, {2533, 3835}, {3004, 3566}, {3805, 4502}, {3904, 29120}, {4088, 29208}, {4369, 47841}, {4378, 15309}, {4391, 4806}, {4449, 4813}, {4560, 29328}, {4705, 29350}, {4729, 47810}, {4761, 21260}, {4774, 4940}, {4776, 21051}, {4801, 4977}, {4810, 23882}, {4834, 14838}, {4839, 45745}, {4874, 47840}, {4879, 8678}, {4951, 47711}, {6372, 23765}, {8663, 45746}, {16892, 29200}, {17496, 29170}, {18004, 47707}, {21124, 29284}, {21301, 29366}, {24719, 29051}, {25666, 47835}, {29017, 47701}, {29146, 47702}, {29246, 46403}, {43067, 47889}

X(48123) = midpoint of X(4449) and X(4813)
X(48123) = reflection of X(i) in X(j) for these {i,j}: {693, 4992}, {1491, 14349}, {2533, 3835}, {4391, 4806}, {4490, 661}, {4761, 21260}, {4784, 905}, {4834, 14838}, {47707, 18004}
X(48123) = crosssum of X(3900) and X(5302)
X(48123) = crossdifference of every pair of points on line {9, 1961}
X(48123) = barycentric product X(i)*X(j) for these {i,j}: {513, 17248}, {514, 17592}
X(48123) = barycentric quotient X(i)/X(j) for these {i,j}: {17248, 668}, {17592, 190}


X(48124) = X(513)X(47700)∩X(514)X(3700)

Barycentrics    (b - c)*(3*a^2 - 3*a*b + 4*b^2 - 3*a*c + 4*c^2) : :
X(48124) = 5 X[650] - 6 X[6546], 3 X[650] - 2 X[16892], 7 X[650] - 6 X[47886], 9 X[6546] - 5 X[16892], 7 X[6546] - 5 X[47886], 7 X[16892] - 9 X[47886], 4 X[3776] - 5 X[31250], 2 X[3776] - 3 X[47770], 5 X[31250] - 6 X[47770], 2 X[3798] - 3 X[47890], 4 X[4468] - 3 X[47777], 10 X[4885] - 9 X[6548], 2 X[4940] - 3 X[47772], X[47651] - 3 X[47772], 2 X[21104] - 3 X[47881], 6 X[45684] - 5 X[47754]

X(48124) lies on these lines: {513, 47700}, {514, 3700}, {650, 3752}, {918, 4790}, {3776, 31250}, {3798, 47890}, {4162, 29288}, {4468, 47777}, {4762, 42044}, {4820, 6084}, {4885, 6548}, {4940, 47651}, {21104, 47881}, {28195, 47703}, {28890, 43067}, {28894, 47667}, {28898, 47663}, {45684, 47754}

X(48124) = reflection of X(47651) in X(4940)
X(48124) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3776, 47770, 31250}, {47651, 47772, 4940}


X(48125) = X(513)X(4382)∩X(514)X(3700)

Barycentrics    (b - c)*(-a^2 + a*b + a*c + 4*b*c) : :
X(48125) = 6 X[2] - 5 X[650], 3 X[2] - 5 X[693], 9 X[2] - 10 X[4885], 9 X[2] - 5 X[17494], 33 X[2] - 25 X[26777], 3 X[2] + 5 X[26824], 21 X[2] - 25 X[26985], 39 X[2] - 35 X[27115], 7 X[2] - 5 X[31150], 27 X[2] - 25 X[31209], 24 X[2] - 25 X[31250], 21 X[2] - 20 X[31287], 11 X[2] - 10 X[44567], 4 X[2] - 5 X[45320], X[2] - 5 X[47869], 3 X[650] - 4 X[4885], 3 X[650] - 2 X[17494], 11 X[650] - 10 X[26777], X[650] + 2 X[26824], 7 X[650] - 10 X[26985], 13 X[650] - 14 X[27115], 7 X[650] - 6 X[31150], 9 X[650] - 10 X[31209], 4 X[650] - 5 X[31250], 7 X[650] - 8 X[31287], 11 X[650] - 12 X[44567], 2 X[650] - 3 X[45320], 5 X[650] - 2 X[47664], X[650] - 6 X[47869], 3 X[693] - 2 X[4885], 3 X[693] - X[17494], 11 X[693] - 5 X[26777], 7 X[693] - 5 X[26985], 13 X[693] - 7 X[27115], 7 X[693] - 3 X[31150], 9 X[693] - 5 X[31209], 8 X[693] - 5 X[31250], 7 X[693] - 4 X[31287], 11 X[693] - 6 X[44567], 4 X[693] - 3 X[45320], 5 X[693] - X[47664], X[693] - 3 X[47869], 22 X[4885] - 15 X[26777], 2 X[4885] + 3 X[26824], 14 X[4885] - 15 X[26985], 26 X[4885] - 21 X[27115], 14 X[4885] - 9 X[31150], 6 X[4885] - 5 X[31209], 16 X[4885] - 15 X[31250], 7 X[4885] - 6 X[31287], 11 X[4885] - 9 X[44567], 8 X[4885] - 9 X[45320], 10 X[4885] - 3 X[47664], 2 X[4885] - 9 X[47869], 11 X[17494] - 15 X[26777], X[17494] + 3 X[26824], 7 X[17494] - 15 X[26985], 13 X[17494] - 21 X[27115], 7 X[17494] - 9 X[31150], 3 X[17494] - 5 X[31209], 8 X[17494] - 15 X[31250], 7 X[17494] - 12 X[31287], 11 X[17494] - 18 X[44567], 4 X[17494] - 9 X[45320], 5 X[17494] - 3 X[47664], X[17494] - 9 X[47869], 5 X[26777] + 11 X[26824], 7 X[26777] - 11 X[26985], 65 X[26777] - 77 X[27115], 35 X[26777] - 33 X[31150], 9 X[26777] - 11 X[31209], 8 X[26777] - 11 X[31250], 35 X[26777] - 44 X[31287], 5 X[26777] - 6 X[44567], 20 X[26777] - 33 X[45320], 25 X[26777] - 11 X[47664], 5 X[26777] - 33 X[47869], 7 X[26824] + 5 X[26985], 13 X[26824] + 7 X[27115], 7 X[26824] + 3 X[31150], 9 X[26824] + 5 X[31209], 8 X[26824] + 5 X[31250], 7 X[26824] + 4 X[31287], 11 X[26824] + 6 X[44567], 4 X[26824] + 3 X[45320], 5 X[26824] + X[47664], X[26824] + 3 X[47869], 65 X[26985] - 49 X[27115], 5 X[26985] - 3 X[31150], 9 X[26985] - 7 X[31209], 8 X[26985] - 7 X[31250], 5 X[26985] - 4 X[31287], 55 X[26985] - 42 X[44567], 20 X[26985] - 21 X[45320], 25 X[26985] - 7 X[47664], 5 X[26985] - 21 X[47869], 49 X[27115] - 39 X[31150], 63 X[27115] - 65 X[31209], 56 X[27115] - 65 X[31250], 49 X[27115] - 52 X[31287], 77 X[27115] - 78 X[44567], 28 X[27115] - 39 X[45320], 35 X[27115] - 13 X[47664], 7 X[27115] - 39 X[47869], 27 X[31150] - 35 X[31209], 24 X[31150] - 35 X[31250], 3 X[31150] - 4 X[31287], 11 X[31150] - 14 X[44567], 4 X[31150] - 7 X[45320], 15 X[31150] - 7 X[47664], X[31150] - 7 X[47869], 8 X[31209] - 9 X[31250], 35 X[31209] - 36 X[31287], 55 X[31209] - 54 X[44567], 20 X[31209] - 27 X[45320], 25 X[31209] - 9 X[47664], 5 X[31209] - 27 X[47869], 35 X[31250] - 32 X[31287], 55 X[31250] - 48 X[44567], 5 X[31250] - 6 X[45320], 25 X[31250] - 8 X[47664], 5 X[31250] - 24 X[47869], 22 X[31287] - 21 X[44567], 16 X[31287] - 21 X[45320], 20 X[31287] - 7 X[47664], 4 X[31287] - 21 X[47869], 8 X[44567] - 11 X[45320], 30 X[44567] - 11 X[47664], 2 X[44567] - 11 X[47869], 15 X[45320] - 4 X[47664], X[45320] - 4 X[47869], X[47664] - 15 X[47869], 3 X[649] - 4 X[7653], 3 X[4790] - 4 X[4932], 2 X[4932] - 3 X[43067], 3 X[1638] - 2 X[4765], 4 X[2516] - 5 X[24924], X[3632] - 5 X[47724], 2 X[3798] - 3 X[47891], 4 X[3835] - 3 X[47777], 3 X[4379] - 2 X[4394], X[4380] - 3 X[47780], 5 X[4411] - 4 X[4739], 2 X[4468] - 3 X[4944], 3 X[4789] - X[47663], 3 X[4801] - X[21222], 2 X[4940] - 3 X[21297], 3 X[21297] - X[47666], 2 X[11068] - 3 X[47788], 2 X[17069] - 3 X[21183], X[20050] + 5 X[47721], 7 X[20057] - 5 X[47729], 2 X[21196] - 3 X[47754], 3 X[47652] + X[47658], 3 X[47656] - X[47658], 3 X[44435] - X[47661], 2 X[45745] - 3 X[47880], X[45746] - 3 X[47871], 5 X[47174] - 3 X[47312], X[47662] - 3 X[47792], 3 X[47881] - 2 X[47890]

X(48125) lies on these lines: {2, 650}, {382, 8760}, {513, 4382}, {514, 3700}, {522, 21104}, {523, 2525}, {649, 7653}, {661, 23813}, {812, 4790}, {918, 4820}, {1638, 4765}, {2516, 24924}, {3244, 29066}, {3629, 9015}, {3632, 14077}, {3669, 4077}, {3676, 4976}, {3798, 47891}, {3835, 47777}, {3900, 44319}, {4024, 22034}, {4088, 4802}, {4162, 29051}, {4379, 4394}, {4380, 47780}, {4411, 4739}, {4468, 4944}, {4686, 4777}, {4789, 47663}, {4801, 21222}, {4926, 21116}, {4940, 21297}, {6008, 7192}, {6084, 6590}, {6362, 23741}, {7655, 23743}, {7659, 21146}, {7662, 29362}, {9001, 40341}, {11068, 47788}, {17069, 21183}, {20050, 47721}, {20057, 47729}, {20295, 47675}, {21115, 28205}, {21196, 47754}, {23731, 28195}, {28151, 47670}, {28165, 47673}, {28894, 47652}, {28898, 47676}, {28910, 44449}, {44435, 47661}, {45745, 47880}, {45746, 47871}, {47174, 47312}, {47650, 47660}, {47651, 47659}, {47653, 47655}, {47662, 47792}, {47881, 47890}

X(48125) = midpoint of X(i) and X(j) for these {i,j}: {693, 26824}, {4382, 47672}, {20295, 47675}, {47650, 47660}, {47651, 47659}, {47652, 47656}, {47653, 47655}
X(48125) = reflection of X(i) in X(j) for these {i,j}: {650, 693}, {661, 23813}, {3669, 4978}, {4790, 43067}, {4976, 3676}, {7659, 21146}, {17494, 4885}, {47666, 4940}
X(48125) = complement of X(47664)
X(48125) = crossdifference of every pair of points on line {2223, 30435}
X(48125) = barycentric product X(693)*X(4423)
X(48125) = barycentric quotient X(4423)/X(100)
X(48125) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 693, 45320}, {650, 45320, 31250}, {693, 17494, 4885}, {693, 30061, 29808}, {693, 31150, 26985}, {693, 47664, 2}, {4885, 17494, 650}, {21297, 47666, 4940}, {26777, 44567, 650}, {26824, 47869, 693}, {26985, 31150, 31287}, {31150, 31287, 650}


X(48126) = X(513)X(4382)∩X(514)X(4522)

Barycentrics    (b - c)*(-a^3 + 2*a^2*b + a*b^2 + 2*a^2*c + 8*a*b*c + 4*b^2*c + a*c^2 + 4*b*c^2) : :
X(48126) = 5 X[693] - 3 X[47821], X[47664] - 3 X[47824], X[47699] - 3 X[47871]

X(48126) lies on these lines: {513, 4382}, {514, 4522}, {693, 47821}, {2526, 4802}, {4106, 4977}, {4120, 28195}, {4762, 21146}, {4777, 47704}, {28165, 47705}, {29362, 43067}, {46403, 47675}, {47664, 47824}, {47699, 47871}

X(48126) = midpoint of X(46403) and X(47675)


X(48127) = X(513)X(4382)∩X(514)X(4806)

Barycentrics    (b - c)*(a^2*b + 2*a*b^2 + a^2*c + 7*a*b*c + 4*b^2*c + 2*a*c^2 + 4*b*c^2) : :
X(48127) = X[4804] + 3 X[47672], 3 X[693] - X[4824], X[4963] - 3 X[31147], X[24719] - 3 X[47869]

X(48127) lies on these lines: {513, 4382}, {514, 4806}, {523, 3776}, {661, 28199}, {693, 4036}, {1491, 28151}, {2254, 28165}, {3835, 28175}, {3837, 28147}, {4010, 28195}, {4762, 4782}, {4777, 21146}, {4963, 31147}, {17166, 29274}, {24719, 47869}, {29204, 47704}

X(48127) = midpoint of X(4010) and X(47675)


X(48128) = X(513)X(663)∩X(514)X(3700)

Barycentrics    a*(b - c)*(a^2 + 4*a*b + 3*b^2 + 4*a*c + 2*b*c + 3*c^2) : :
X(48128) = 3 X[650] - 2 X[4063], X[4063] - 3 X[14349], X[4462] - 3 X[47759], 3 X[4776] - 2 X[20317], 2 X[14837] - 3 X[47756]

X(48128) lies on these lines: {512, 2526}, {513, 663}, {514, 3700}, {650, 4063}, {661, 8712}, {830, 4162}, {905, 4790}, {1019, 8657}, {2530, 7659}, {3004, 28478}, {4391, 4940}, {4462, 47759}, {4560, 6008}, {4776, 20317}, {4801, 20954}, {4992, 7662}, {14837, 47756}, {20295, 23880}, {23769, 28878}

X(48128) = reflection of X(i) in X(j) for these {i,j}: {650, 14349}, {4391, 4940}, {4790, 905}, {7659, 2530}, {7662, 4992}
X(48128) = crossdifference of every pair of points on line {9, 3745}


X(48129) = X(513)X(663)∩X(514)X(4806)

Barycentrics    a*(b - c)*(3*a*b + 2*b^2 + 3*a*c + b*c + 2*c^2) : :
X(48129) = 3 X[1491] - X[4729], X[4705] - 3 X[14349], 3 X[4782] - 4 X[6050]

X(48129) lies on these lines: {513, 663}, {514, 4806}, {661, 14470}, {1491, 4729}, {3004, 29284}, {4083, 4705}, {4782, 6050}, {4801, 28195}, {4983, 29198}, {20295, 29152}, {23729, 29244}, {24719, 29274}

X(48129) = midpoint of X(3777) and X(4822)


X(48130) = X(513)X(47700)∩X(514)X(661)

Barycentrics    (b - c)*(2*a^2 - a*b + 2*b^2 - a*c + 2*c^2) : :
X(48130) = 3 X[661] - 4 X[4468], 3 X[4728] - 2 X[47652], 3 X[1635] - 2 X[16892], 9 X[1635] - 8 X[17069], 3 X[1635] - 4 X[47890], 3 X[16892] - 4 X[17069], 2 X[17069] - 3 X[47890], 2 X[3004] - 3 X[6546], 4 X[3776] - 5 X[24924], 2 X[3776] - 3 X[47771], 5 X[24924] - 6 X[47771], 3 X[4120] - 2 X[23729], 4 X[4369] - 3 X[21115], 2 X[4369] - 3 X[47773], 2 X[4382] - 3 X[4931], 3 X[4958] - 4 X[25259], 4 X[11068] - 3 X[47886], 2 X[21196] - 3 X[47892], 5 X[30835] - 6 X[47770], 3 X[31148] - 2 X[47676], 7 X[31207] - 6 X[47754]

X(48130) lies on these lines: {513, 47700}, {514, 661}, {649, 30520}, {824, 47663}, {918, 4979}, {1635, 16892}, {2832, 47726}, {3004, 6546}, {3716, 47688}, {3776, 24924}, {4024, 6084}, {4088, 4977}, {4120, 23729}, {4369, 21115}, {4380, 30519}, {4382, 4931}, {4500, 47650}, {4522, 47686}, {4724, 4802}, {4762, 4838}, {4958, 25259}, {4963, 28195}, {4988, 21141}, {7192, 28890}, {11068, 47886}, {17494, 28863}, {21196, 47892}, {28175, 47701}, {28894, 47669}, {30835, 47770}, {31148, 47676}, {31207, 47754}, {47659, 47670}, {47694, 47705}

X(48130) = reflection of X(i) in X(j) for these {i,j}: {16892, 47890}, {21115, 47773}, {47650, 4500}, {47651, 3835}, {47670, 47659}, {47672, 47660}, {47673, 17494}, {47686, 4522}, {47688, 3716}, {47702, 4724}, {47705, 47694}
X(48130) = X(17357)-Dao conjugate of X(33951)
X(48130) = barycentric product X(514)*X(17357)
X(48130) = barycentric quotient X(17357)/X(190)
X(48130) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3776, 47771, 24924}, {16892, 47890, 1635}


X(48131) = X(513)X(663)∩X(514)X(661)

Barycentrics    a*(b - c)*(a*b + b^2 + a*c + c^2) : :
X(48131) = 2 X[10] - 3 X[47816], 2 X[3777] + X[4822], 2 X[4367] - 3 X[14413], 2 X[1577] - 3 X[4728], X[4462] - 3 X[4776], 2 X[4983] + X[23738], 2 X[4705] - 3 X[47810], 4 X[3960] - X[4979], 4 X[1125] - 3 X[47818], 3 X[1635] - 2 X[4063], 3 X[1635] - 4 X[14838], 2 X[3716] - 3 X[47840], 2 X[3803] - 3 X[8643], 2 X[4142] - 3 X[47797], 2 X[4147] - 3 X[47814], 2 X[4369] - 3 X[47796], 2 X[4874] - 3 X[47841], 3 X[6545] - X[23755], 2 X[9508] - 3 X[47893], 3 X[14430] - 4 X[21051], 2 X[14837] - 3 X[47757], 2 X[17072] - 3 X[44429], 2 X[20317] - 3 X[47760], 3 X[21052] - 4 X[21260], X[21120] - 3 X[47756], 4 X[23815] - 3 X[47812], 2 X[24720] - 3 X[47819], 5 X[24924] - 6 X[47795], 4 X[25380] - 3 X[47836], 4 X[25666] - 3 X[47793]

X(48131) lies on these lines: {1, 830}, {10, 47816}, {512, 2254}, {513, 663}, {514, 661}, {523, 14288}, {525, 16892}, {649, 905}, {650, 4498}, {656, 834}, {764, 4983}, {784, 4804}, {786, 20950}, {812, 4481}, {814, 24719}, {824, 21834}, {891, 4705}, {918, 4079}, {951, 23696}, {1019, 3960}, {1022, 1255}, {1125, 47818}, {1491, 4041}, {1635, 4063}, {1734, 4729}, {2170, 45213}, {2292, 42661}, {2526, 3900}, {2533, 3837}, {3004, 3910}, {3309, 38329}, {3676, 7216}, {3716, 47840}, {3803, 8643}, {3810, 47708}, {3907, 21301}, {4010, 4992}, {4025, 28478}, {4088, 29288}, {4106, 23880}, {4142, 47797}, {4147, 47814}, {4170, 8714}, {4369, 26114}, {4382, 23882}, {4449, 8678}, {4490, 29226}, {4502, 28846}, {4522, 47707}, {4775, 6004}, {4785, 44550}, {4839, 4976}, {4874, 47841}, {4879, 4895}, {4905, 6005}, {4977, 14432}, {6002, 17496}, {6292, 39244}, {6371, 17420}, {6545, 23755}, {7178, 28116}, {7192, 26854}, {7254, 21758}, {8042, 41820}, {9508, 47893}, {14430, 21051}, {14837, 47757}, {15309, 29738}, {17072, 44429}, {17458, 28894}, {17494, 27647}, {20317, 47760}, {20909, 23685}, {21052, 21260}, {21120, 46393}, {21385, 24900}, {23729, 29162}, {23765, 29198}, {23815, 47812}, {23877, 47691}, {23879, 47673}, {23887, 47712}, {24720, 47819}, {24924, 47795}, {25380, 47836}, {25666, 27346}, {25900, 25902}, {28468, 44435}, {28470, 47729}, {29021, 47702}, {29047, 47700}, {29051, 46403}, {29142, 47701}, {30023, 30061}, {47705, 47716}

X(48131) = midpoint of X(i) and X(j) for these {i,j}: {764, 4983}, {17496, 20295}
X(48131) = reflection of X(i) in X(j) for these {i,j}: {649, 905}, {661, 14349}, {1019, 3960}, {2254, 2530}, {2292, 42661}, {2533, 3837}, {3762, 4129}, {4010, 4992}, {4041, 1491}, {4063, 14838}, {4391, 3835}, {4498, 650}, {4729, 1734}, {4895, 4879}, {4979, 1019}, {21124, 3004}, {23738, 764}, {47660, 8045}, {47672, 4978}, {47705, 47716}, {47707, 4522}
X(48131) = isogonal conjugate of X(36147)
X(48131) = isogonal conjugate of the isotomic conjugate of X(4509)
X(48131) = X(45989)-anticomplementary conjugate of X(150)
X(48131) = X(i)-Ceva conjugate of X(j) for these (i,j): {86, 244}, {226, 1086}, {514, 21124}, {831, 17108}, {1412, 3942}, {1432, 2170}, {3004, 17420}, {3882, 3666}, {7018, 3123}, {15314, 7004}
X(48131) = X(38364)-cross conjugate of X(6)
X(48131) = X(i)-isoconjugate of X(j) for these (i,j): {1, 36147}, {2, 32736}, {6, 8707}, {8, 8687}, {9, 36098}, {55, 6648}, {82, 35334}, {100, 2298}, {101, 1220}, {110, 14624}, {644, 961}, {692, 30710}, {1018, 2363}, {1169, 3952}, {1240, 32739}, {1252, 4581}, {1783, 1791}, {1897, 2359}, {4557, 14534}
X(48131) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 36147), (9, 8707), (141, 35334), (223, 6648), (244, 14624), (478, 36098), (661, 4581), (960, 1018), (1015, 1220), (1086, 30710), (1211, 190), (2092, 3699), (3125, 10), (3666, 4033), (8054, 2298), (17197, 333), (17419, 8), (32664, 32736), (34467, 2359), (38992, 9), (39006, 1791), (39015, 1), (40615, 31643), (40619, 1240)
X(48131) = crosspoint of X(i) and X(j) for these (i,j): {1, 831}, {514, 1019}, {3666, 3882}, {3676, 7199}
X(48131) = crosssum of X(i) and X(j) for these (i,j): {1, 830}, {100, 4579}, {101, 1018}
X(48131) = crossdifference of every pair of points on line {9, 31}
X(48131) = barycentric product X(i)*X(j) for these {i,j}: {1, 3004}, {6, 4509}, {7, 17420}, {57, 3910}, {75, 6371}, {81, 21124}, {512, 16739}, {513, 4357}, {514, 3666}, {522, 24471}, {649, 20911}, {650, 3674}, {661, 16705}, {693, 1193}, {873, 42661}, {905, 1848}, {960, 3676}, {1019, 1211}, {1086, 3882}, {1577, 40153}, {1829, 4025}, {2092, 7199}, {2269, 24002}, {2292, 7192}, {2300, 3261}, {2354, 15413}, {3669, 3687}, {3704, 7203}, {3733, 18697}, {3737, 41003}, {3835, 27455}, {4077, 4267}, {7178, 17185}, {7252, 45196}, {17096, 21033}, {17108, 47660}, {17217, 45197}, {17924, 22097}, {22345, 46107}, {26721, 41581}
X(48131) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 8707}, {6, 36147}, {31, 32736}, {39, 35334}, {56, 36098}, {57, 6648}, {244, 4581}, {513, 1220}, {514, 30710}, {604, 8687}, {649, 2298}, {661, 14624}, {693, 1240}, {960, 3699}, {1019, 14534}, {1193, 100}, {1211, 4033}, {1459, 1791}, {1829, 1897}, {1848, 6335}, {2092, 1018}, {2269, 644}, {2292, 3952}, {2300, 101}, {2354, 1783}, {3004, 75}, {3666, 190}, {3674, 4554}, {3676, 31643}, {3687, 646}, {3725, 4557}, {3733, 2363}, {3882, 1016}, {3910, 312}, {3942, 15420}, {3965, 6558}, {4267, 643}, {4357, 668}, {4503, 4482}, {4509, 76}, {6371, 1}, {7199, 40827}, {16705, 799}, {16739, 670}, {17185, 645}, {17420, 8}, {18697, 27808}, {20911, 1978}, {20967, 3939}, {21033, 30730}, {21124, 321}, {21810, 4103}, {22074, 4587}, {22097, 1332}, {22345, 1331}, {22383, 2359}, {24471, 664}, {27455, 4598}, {28369, 18047}, {40153, 662}, {40966, 4069}, {42661, 756}, {43924, 961}, {46877, 7256}, {46889, 7259}
X(48131) = {X(4063),X(14838)}-harmonic conjugate of X(1635)


X(48132) = X(241)X(514)∩X(513)X(47700)

Barycentrics    (b - c)*(5*a^2 - a*b + 4*b^2 - a*c + 4*c^2) : :
X(48132) = 5 X[650] - 4 X[3004], 7 X[650] - 8 X[11068], 13 X[650] - 12 X[47784], 7 X[650] - 6 X[47880], 11 X[650] - 12 X[47884], 3 X[650] - 4 X[47890], 7 X[3004] - 10 X[11068], 13 X[3004] - 15 X[47784], 14 X[3004] - 15 X[47880], 11 X[3004] - 15 X[47884], 3 X[3004] - 5 X[47890], 26 X[11068] - 21 X[47784], 4 X[11068] - 3 X[47880], 22 X[11068] - 21 X[47884], 6 X[11068] - 7 X[47890], 14 X[47784] - 13 X[47880], 11 X[47784] - 13 X[47884], 9 X[47784] - 13 X[47890], 11 X[47880] - 14 X[47884], 9 X[47880] - 14 X[47890], 9 X[47884] - 11 X[47890], 3 X[47655] - 5 X[47659], X[47655] - 5 X[47662], X[47659] - 3 X[47662], 2 X[4885] - 3 X[47773], X[47651] - 3 X[47773], 3 X[4944] - 2 X[23729], 4 X[7653] - 3 X[21115], X[47661] - 3 X[47663], 5 X[31250] - 6 X[47771], 3 X[45320] - 2 X[47652], X[47650] - 3 X[47660]

X(48132) lies on these lines: {241, 514}, {513, 47700}, {659, 28199}, {2526, 28195}, {4762, 47655}, {4790, 30520}, {4885, 47651}, {4944, 23729}, {7653, 21115}, {28894, 47661}, {31250, 47771}, {45320, 47652}, {47650, 47660}

X(48132) = reflection of X(47651) in X(4885)
X(48132) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11068, 47880, 650}, {47651, 47773, 4885}


X(48133) = X(241)X(514)∩X(513)X(4382)

Barycentrics    (b - c)*(a^2 + 3*a*b + 3*a*c + 4*b*c) : :
X(48133) = 3 X[650] - 4 X[4369], 11 X[650] - 12 X[4763], 7 X[650] - 8 X[31286], 5 X[650] - 6 X[47761], 4 X[3676] - 3 X[47880], 11 X[4369] - 9 X[4763], 7 X[4369] - 6 X[31286], 2 X[4369] - 3 X[43067], 10 X[4369] - 9 X[47761], 21 X[4763] - 22 X[31286], 6 X[4763] - 11 X[43067], 10 X[4763] - 11 X[47761], 2 X[4841] - 3 X[47880], 4 X[7658] - 3 X[47876], 4 X[31286] - 7 X[43067], 20 X[31286] - 21 X[47761], 5 X[43067] - 3 X[47761], X[4382] - 3 X[47672], 2 X[661] - 3 X[45320], 3 X[693] - 2 X[4940], 7 X[693] - 5 X[26798], 3 X[693] - X[31290], 5 X[693] - 3 X[47759], 14 X[4940] - 15 X[26798], 10 X[4940] - 9 X[47759], 15 X[26798] - 7 X[31290], 25 X[26798] - 21 X[47759], 5 X[31290] - 9 X[47759], 3 X[1635] - 4 X[7653], 4 X[2487] - 3 X[47883], 6 X[4379] - 5 X[31250], 2 X[4380] - 3 X[4790], X[4380] - 3 X[7192], X[4380] + 3 X[47675], X[4790] + 2 X[47675], 2 X[4394] - 3 X[31148], 3 X[4453] - X[47667], 2 X[4468] - 3 X[47881], 4 X[4885] - 3 X[47777], 2 X[4885] - 3 X[47780], 2 X[47666] - 3 X[47777], X[47666] - 3 X[47780], 4 X[31287] - 3 X[47775], X[47661] - 3 X[47755], X[47664] - 3 X[47763], X[47668] - 3 X[47894]

X(48133) lies on these lines: {241, 514}, {513, 4382}, {523, 7659}, {661, 45320}, {693, 4940}, {1635, 7653}, {2487, 47883}, {2526, 21146}, {3700, 28878}, {3716, 28229}, {4106, 28840}, {4162, 17166}, {4379, 31250}, {4380, 4762}, {4394, 31148}, {4453, 47667}, {4462, 18154}, {4467, 47674}, {4468, 47881}, {4500, 28855}, {4608, 47677}, {4777, 47671}, {4778, 23729}, {4801, 18155}, {4802, 16892}, {4813, 23813}, {4820, 28846}, {4874, 28213}, {4885, 47666}, {4913, 28191}, {4977, 7662}, {6008, 26824}, {9508, 21115}, {21116, 28195}, {23731, 28220}, {25259, 28910}, {28151, 47673}, {28165, 47670}, {28894, 47676}, {28898, 47656}, {31287, 47775}, {47661, 47755}, {47664, 47763}, {47668, 47894}

X(48133) = midpoint of X(i) and X(j) for these {i,j}: {4467, 47674}, {4608, 47677}, {7192, 47675}
X(48133) = reflection of X(i) in X(j) for these {i,j}: {650, 43067}, {2526, 21146}, {4162, 17166}, {4790, 7192}, {4813, 23813}, {4841, 3676}, {31290, 4940}, {47666, 4885}, {47777, 47780}
X(48133) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 31290, 4940}, {3676, 4841, 47880}, {4885, 47666, 47777}, {47666, 47780, 4885}


X(48134) = X(513)X(4382)∩X(514)X(3716)

Barycentrics    (b - c)*(a^3 + 2*a^2*b + 3*a*b^2 + 2*a^2*c + 8*a*b*c + 4*b^2*c + 3*a*c^2 + 4*b*c^2) : :
X(48134) = 2 X[3716] - 3 X[7662], X[4988] - 3 X[47887], 2 X[2977] - 3 X[47789], 3 X[4789] - X[47698], 3 X[17166] - X[47729], X[47666] - 3 X[47834], X[47667] - 3 X[47797]

X(48134) lies on these lines: {513, 4382}, {514, 3716}, {523, 4025}, {650, 4802}, {2977, 47789}, {4369, 28147}, {4777, 7659}, {4789, 47698}, {4824, 4885}, {4874, 28175}, {4913, 28155}, {8678, 47724}, {9508, 28151}, {17166, 47729}, {28179, 47761}, {28191, 47803}, {47666, 47834}, {47667, 47797}, {47675, 47694}

X(48134) = midpoint of X(47675) and X(47694)
X(48134) = reflection of X(4824) in X(4885)
X(48134) = crossdifference of every pair of points on line {35, 2271}


X(48135) = X(513)X(4382)∩X(514)X(3837)

Barycentrics    (b - c)*(3*a^2*b + 2*a*b^2 + 3*a^2*c + 9*a*b*c + 4*b^2*c + 2*a*c^2 + 4*b*c^2) : :
X(48135) = X[4804] - 5 X[47672]

X(48135) lies on these lines: {513, 4382}, {514, 3837}, {693, 18158}, {1491, 28199}, {2254, 28151}, {3835, 28213}, {4010, 28220}, {4782, 43067}, {4802, 21146}, {4806, 28229}, {24720, 28175}, {29204, 47703}

X(48135) = midpoint of X(21146) and X(47675)
X(48135) = reflection of X(4782) in X(43067)


X(48136) = X(513)X(663)∩X(514)X(3716)

Barycentrics    a*(b - c)*(a^2 - 2*a*b - b^2 - 2*a*c - c^2) : :
X(48136) = X[8] - 3 X[47814], X[4822] + 3 X[14413], X[2533] - 3 X[47841], 2 X[4885] - 3 X[47841], 5 X[3616] - 3 X[47820], X[3762] - 3 X[47838], X[4391] - 3 X[47840], X[4462] - 3 X[47821], X[4729] - 3 X[47828], X[4730] - 3 X[47888], X[4761] - 3 X[47795], X[4834] - 3 X[14419], X[4922] + 2 X[4940], 2 X[14837] - 3 X[47799], 2 X[17072] - 3 X[47802], 2 X[20317] - 3 X[47822], 2 X[21051] - 3 X[47760], 3 X[21052] - 5 X[30835], X[21302] - 3 X[44429], X[23755] - 3 X[47887], 4 X[31287] - 3 X[47835]

X(48136) lies on these lines: {1, 8678}, {8, 47814}, {512, 905}, {513, 663}, {514, 3716}, {523, 6332}, {650, 3250}, {659, 8712}, {661, 4449}, {667, 22160}, {684, 42661}, {814, 4106}, {1491, 3900}, {1960, 3803}, {2499, 43049}, {2522, 42664}, {2526, 4162}, {2530, 3309}, {2533, 4885}, {2978, 28374}, {3005, 24562}, {3566, 4025}, {3616, 47820}, {3762, 47838}, {3835, 3907}, {3837, 29366}, {3904, 47708}, {3960, 6005}, {4010, 23880}, {4063, 6050}, {4142, 28468}, {4147, 25666}, {4378, 4983}, {4391, 47840}, {4462, 47821}, {4490, 21343}, {4705, 14077}, {4729, 47828}, {4730, 47888}, {4761, 47795}, {4790, 8632}, {4802, 14432}, {4806, 29324}, {4834, 14419}, {4922, 4940}, {14837, 47799}, {14838, 29350}, {17072, 47802}, {20317, 47822}, {21051, 47760}, {21052, 30835}, {21260, 29298}, {21301, 47729}, {21302, 44429}, {23755, 47887}, {23815, 29188}, {23877, 47131}, {28840, 45667}, {31287, 47835}

X(48136) = midpoint of X(i) and X(j) for these {i,j}: {1, 14349}, {661, 4449}, {1491, 4879}, {2526, 4162}, {2530, 4775}, {3904, 47708}, {4378, 4983}, {4490, 21343}, {21301, 47729}
X(48136) = reflection of X(i) in X(j) for these {i,j}: {2533, 4885}, {3803, 1960}, {4063, 6050}, {4106, 4992}, {4147, 25666}
X(48136) = crosspoint of X(i) and X(j) for these (i,j): {1, 1310}, {934, 959}, {4594, 37870}
X(48136) = crosssum of X(i) and X(j) for these (i,j): {1, 8678}, {958, 3900}, {23874, 34822}
X(48136) = crossdifference of every pair of points on line {9, 171}
X(48136) = X(21854)-line conjugate of X(34626)
X(48136) = barycentric product X(i)*X(j) for these {i,j}: {513, 17257}, {514, 17594}, {1019, 4104}
X(48136) = barycentric quotient X(i)/X(j) for these {i,j}: {4104, 4033}, {17257, 668}, {17594, 190}
X(48136) = {X(2533),X(47841)}-harmonic conjugate of X(4885)


X(48137) = X(513)X(663)∩X(514)X(3837)

Barycentrics    a*(b - c)*(a*b + 2*b^2 + a*c - b*c + 2*c^2) : :
X(48137) = 5 X[3777] + X[4822], X[1734] - 3 X[2530], 5 X[1734] - 3 X[4730], 5 X[2530] - X[4730], X[2533] - 3 X[47819], X[4498] - 3 X[47893], X[21385] - 3 X[47888]

X(48137) lies on these lines: {513, 663}, {514, 3837}, {661, 23765}, {764, 14349}, {905, 4782}, {1491, 29226}, {1734, 2530}, {2517, 4801}, {2533, 47819}, {4498, 47893}, {8712, 9508}, {16892, 29202}, {17496, 24719}, {18081, 23807}, {21385, 47888}, {23729, 29124}, {29274, 46403}

X(48137) = midpoint of X(i) and X(j) for these {i,j}: {661, 23765}, {764, 14349}, {17496, 24719}
X(48137) = reflection of X(4782) in X(905)
X(48137) = crossdifference of every pair of points on line {9, 21793}
X(48137) = barycentric product X(i)*X(j) for these {i,j}: {513, 17236}, {514, 17591}
X(48137) = barycentric quotient X(i)/X(j) for these {i,j}: {17236, 668}, {17591, 190}


X(48138) = X(239)X(514)∩X(513)X(47700)

Barycentrics    (b - c)*(3*a^2 + 2*b^2 + 2*c^2) : :
X(48138) = 9 X[649] - 8 X[3798], 5 X[649] - 4 X[4025], 7 X[649] - 6 X[4750], 13 X[649] - 12 X[4786], 3 X[649] - 2 X[16892], 10 X[3798] - 9 X[4025], 28 X[3798] - 27 X[4750], 26 X[3798] - 27 X[4786], 4 X[3798] - 3 X[16892], 14 X[4025] - 15 X[4750], 13 X[4025] - 15 X[4786], 6 X[4025] - 5 X[16892], 13 X[4750] - 14 X[4786], 9 X[4750] - 7 X[16892], 18 X[4786] - 13 X[16892], 3 X[47663] - X[47667], 3 X[47662] - X[47665], 2 X[3835] - 3 X[47773], 3 X[4379] - 2 X[47652], 3 X[4382] - 4 X[4500], 2 X[4382] - 3 X[47873], 2 X[4500] - 3 X[47660], 8 X[4500] - 9 X[47873], 4 X[47660] - 3 X[47873], 3 X[4893] - 4 X[47890], 2 X[23729] - 3 X[47874], 5 X[30835] - 6 X[47771], 7 X[31207] - 6 X[44435]

X(48138) lies on these lines: {239, 514}, {513, 47700}, {812, 47662}, {2254, 28195}, {3835, 47773}, {4369, 47651}, {4379, 47652}, {4380, 28863}, {4382, 4500}, {4468, 23731}, {4762, 47670}, {4778, 47698}, {4893, 47890}, {4979, 30520}, {23729, 47874}, {26853, 30519}, {30835, 47771}, {31207, 44435}

X(48138) = reflection of X(i) in X(j) for these {i,j}: {4382, 47660}, {23731, 4468}, {47651, 4369}
X(48138) = X(39729)-anticomplementary conjugate of X(21293)
X(48138) = barycentric product X(514)*X(47355)
X(48138) = barycentric quotient X(47355)/X(190)
X(48138) = {X(4382),X(47660)}-harmonic conjugate of X(47873)


X(48139) = X(1)X(514)∩X(513)X(47700)

Barycentrics    (b - c)*(3*a^3 + a^2*b + 2*a*b^2 + 2*b^3 + a^2*c - 2*a*b*c + 2*b^2*c + 2*a*c^2 + 2*b*c^2 + 2*c^3) : :
X(48139) = 3 X[4724] - 2 X[47701], 2 X[4818] - 3 X[47892], 2 X[24720] - 3 X[47773], 2 X[47652] - 3 X[47832], 3 X[47828] - 4 X[47890]

X(48139) lies on these lines: {1, 514}, {513, 47700}, {661, 28195}, {3716, 47651}, {4088, 4778}, {4468, 28229}, {4818, 47892}, {4830, 47677}, {24720, 47773}, {28199, 47702}, {28213, 47826}, {47652, 47832}, {47828, 47890}

X(48139) = reflection of X(i) in X(j) for these {i,j}: {47651, 3716}, {47677, 4830}


X(48140) = X(10)X(514)∩X(513)X(47700)

Barycentrics    (b - c)*(2*a^3 + 2*a^2*b + a*b^2 + 2*b^3 + 2*a^2*c - a*b*c + 2*b^2*c + a*c^2 + 2*b*c^2 + 2*c^3) : :
X(48140) = 4 X[2977] - 3 X[47877], 2 X[3004] - 3 X[47885], 2 X[4874] - 3 X[47773], X[47688] - 3 X[47773], 3 X[4951] - 2 X[24719]

X(48140) lies on these lines: {10, 514}, {513, 47700}, {523, 8664}, {650, 28199}, {659, 4802}, {2977, 47877}, {3004, 47885}, {3837, 47651}, {4122, 28882}, {4784, 30520}, {4874, 47688}, {4951, 24719}, {4977, 47698}, {28175, 47667}, {29362, 47693}

X(48140) = reflection of X(i) in X(j) for these {i,j}: {47651, 3837}, {47688, 4874}
X(48140) = crossdifference of every pair of points on line {1914, 7772}
X(48140) = {X(47688),X(47773)}-harmonic conjugate of X(4874)


X(48141) = X(239)X(514)∩X(513)X(4382)

Barycentrics    (b - c)*(a^2 + 2*a*b + 2*a*c + 2*b*c) : :
X(48141) = 3 X[649] - 4 X[4932], 3 X[649] - 2 X[17494], 5 X[649] - 6 X[47763], 7 X[649] - 6 X[47776], 3 X[4750] - 2 X[45745], 2 X[4932] - 3 X[7192], 10 X[4932] - 9 X[47763], 14 X[4932] - 9 X[47776], 3 X[7192] - X[17494], 5 X[7192] - 3 X[47763], 7 X[7192] - 3 X[47776], 5 X[17494] - 9 X[47763], 7 X[17494] - 9 X[47776], 2 X[21196] - 3 X[47755], X[47667] - 3 X[47755], 7 X[47763] - 5 X[47776], 3 X[650] - 4 X[7653], 2 X[650] - 3 X[31148], 8 X[7653] - 9 X[31148], 2 X[661] - 3 X[4379], 3 X[661] - 4 X[4885], 4 X[661] - 5 X[30835], 5 X[661] - 6 X[47760], 9 X[4379] - 8 X[4885], 6 X[4379] - 5 X[30835], 3 X[4379] - 4 X[43067], 5 X[4379] - 4 X[47760], 16 X[4885] - 15 X[30835], 2 X[4885] - 3 X[43067], 10 X[4885] - 9 X[47760], 5 X[30835] - 8 X[43067], 25 X[30835] - 24 X[47760], 5 X[43067] - 3 X[47760], 4 X[693] - 3 X[31147], 2 X[4813] - 3 X[31147], 4 X[2487] - 3 X[47876], 2 X[3835] - 3 X[47780], X[31290] - 3 X[47780], 4 X[4369] - 3 X[4893], 8 X[4369] - 7 X[31207], 6 X[4369] - 5 X[31209], 7 X[4369] - 6 X[45675], 6 X[4893] - 7 X[31207], 9 X[4893] - 10 X[31209], 7 X[4893] - 8 X[45675], 3 X[4893] - 2 X[47666], 21 X[31207] - 20 X[31209], 49 X[31207] - 48 X[45675], 7 X[31207] - 4 X[47666], 35 X[31209] - 36 X[45675], 5 X[31209] - 3 X[47666], 12 X[45675] - 7 X[47666], 3 X[21116] - X[23731], 2 X[4824] - 3 X[47828], 2 X[4841] - 3 X[47886], 4 X[4874] - 3 X[47826], 4 X[17069] - 3 X[47878], 4 X[21212] - 3 X[47781], 2 X[25259] - 3 X[47873], 5 X[26777] - 6 X[45313], 5 X[26985] - 3 X[47774], 4 X[31286] - 3 X[47775]

X(48141) lies on these lines: {239, 514}, {513, 4382}, {522, 47671}, {650, 7653}, {659, 21115}, {661, 4379}, {669, 4378}, {676, 1459}, {693, 4813}, {812, 47675}, {824, 47658}, {2487, 47876}, {2786, 47656}, {2978, 6372}, {3700, 28902}, {3835, 31290}, {3960, 27648}, {4024, 28846}, {4367, 8655}, {4369, 4893}, {4458, 47699}, {4500, 28886}, {4762, 4979}, {4777, 47670}, {4778, 21116}, {4784, 4802}, {4785, 26824}, {4824, 47828}, {4838, 28898}, {4841, 47886}, {4874, 47826}, {6545, 41930}, {6590, 28878}, {17069, 47878}, {21212, 47781}, {23729, 28209}, {23781, 29120}, {24623, 28890}, {25259, 28855}, {26777, 45313}, {26985, 47774}, {27045, 47795}, {27167, 47794}, {28851, 47660}, {28859, 47652}, {30519, 47659}, {31095, 47771}, {31286, 47775}

X(48141) = reflection of X(i) in X(j) for these {i,j}: {649, 7192}, {661, 43067}, {4382, 47672}, {4813, 693}, {4988, 4025}, {17494, 4932}, {31290, 3835}, {44449, 4500}, {47666, 4369}, {47667, 21196}, {47699, 4458}
X(48141) = X(39736)-anticomplementary conjugate of X(21293)
X(48141) = X(i)-isoconjugate of X(j) for these (i,j): {100, 39961}, {101, 39737}
X(48141) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 39737), (8054, 39961)
X(48141) = crossdifference of every pair of points on line {42, 3730}
X(48141) = barycentric product X(i)*X(j) for these {i,j}: {513, 32092}, {514, 15668}, {1889, 4025}, {3676, 4042}
X(48141) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 39737}, {649, 39961}, {1889, 1897}, {4042, 3699}, {15668, 190}, {32092, 668}
X(48141) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 4379, 30835}, {661, 43067, 4379}, {693, 4813, 31147}, {4369, 4893, 31207}, {4369, 47666, 4893}, {4932, 17494, 649}, {7192, 17494, 4932}, {31290, 47780, 3835}, {47667, 47755, 21196}


X(48142) = X(1)X(514)∩X(513)X(4382)

Barycentrics    (b - c)*(a^3 + a^2*b + 2*a*b^2 + a^2*c + 4*a*b*c + 2*b^2*c + 2*a*c^2 + 2*b*c^2) : :
X(48142) = 2 X[650] - 3 X[47813], 2 X[661] - 3 X[47832], 4 X[7662] - 3 X[47832], 2 X[1491] - 3 X[4379], 2 X[2526] - 3 X[47812], 2 X[3004] - 3 X[47887], 4 X[3716] - 3 X[47826], 2 X[47666] - 3 X[47826], 2 X[3835] - 3 X[47834], 2 X[4122] - 3 X[47873], 4 X[4369] - 3 X[47828], 3 X[4453] - 2 X[4818], 2 X[4522] - 3 X[4789], 3 X[4800] - X[4963], 2 X[4824] - 3 X[4893], 4 X[4874] - 3 X[4893], 4 X[4885] - 3 X[47810], 2 X[4913] - 3 X[47762], 2 X[24720] - 3 X[47780], 5 X[30835] - 6 X[47833], 7 X[31207] - 6 X[47827], 4 X[31286] - 3 X[47825], X[47667] - 3 X[47798]

X(48142) lies on these lines: {1, 514}, {513, 4382}, {522, 7192}, {523, 649}, {650, 47813}, {659, 4802}, {661, 7662}, {676, 4841}, {1491, 4379}, {2254, 43067}, {2526, 47812}, {2978, 8672}, {3004, 47887}, {3716, 47666}, {3835, 47834}, {4010, 4813}, {4088, 6590}, {4122, 47873}, {4160, 4474}, {4369, 47828}, {4453, 4818}, {4458, 45746}, {4522, 4789}, {4761, 4814}, {4777, 4784}, {4782, 28151}, {4800, 4963}, {4824, 4874}, {4830, 47664}, {4885, 47810}, {4913, 47762}, {4932, 28161}, {4960, 6005}, {5075, 9131}, {17418, 47844}, {17494, 28147}, {20517, 47679}, {21146, 31136}, {24623, 47689}, {24720, 47780}, {28169, 47763}, {28191, 47805}, {29062, 47678}, {29318, 47681}, {30835, 47833}, {31095, 47808}, {31207, 47827}, {31286, 47825}, {47131, 47702}, {47667, 47798}, {47675, 47697}

X(48142) = midpoint of X(47675) and X(47697)
X(48142) = reflection of X(i) in X(j) for these {i,j}: {661, 7662}, {2254, 43067}, {4088, 6590}, {4449, 17166}, {4724, 47694}, {4813, 4010}, {4814, 4761}, {4824, 4874}, {4841, 676}, {17418, 47844}, {45746, 4458}, {47664, 4830}, {47666, 3716}, {47679, 20517}, {47701, 47123}, {47702, 47131}
X(48142) = crossdifference of every pair of points on line {386, 672}
X(48142) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 7662, 47832}, {3716, 47666, 47826}, {4824, 4874, 4893}


X(48143) = X(10)X(514)∩X(513)X(4382)

Barycentrics    (b - c)*(2*a^2*b + a*b^2 + 2*a^2*c + 5*a*b*c + 2*b^2*c + a*c^2 + 2*b*c^2) : :
X(48143) = 4 X[10] - 3 X[4490], 3 X[1491] - 2 X[4824], 3 X[1491] - 4 X[24720], 5 X[1491] - 6 X[36848], X[4824] - 3 X[21146], 5 X[4824] - 9 X[36848], 3 X[21146] - 2 X[24720], 5 X[21146] - 3 X[36848], 10 X[24720] - 9 X[36848], X[4804] - 3 X[47672], 3 X[693] - 2 X[4806], 2 X[4782] - 3 X[31148], 2 X[4841] - 3 X[47877], 2 X[4874] - 3 X[47780], 3 X[21116] - X[47701]

X(48143) lies on these lines: {10, 514}, {145, 29366}, {513, 4382}, {523, 47674}, {659, 43067}, {661, 28195}, {693, 4806}, {2254, 4802}, {3720, 4724}, {3835, 28229}, {3837, 28213}, {4010, 4778}, {4122, 28851}, {4762, 4784}, {4782, 31148}, {4841, 47877}, {4874, 47780}, {7192, 29362}, {17166, 29246}, {21116, 47701}, {24719, 28840}, {26824, 29328}, {29144, 47704}

X(48143) = reflection of X(i) in X(j) for these {i,j}: {659, 43067}, {1491, 21146}, {4824, 24720}, {47666, 3837}
X(48143) = barycentric product X(514)*X(40328)
X(48143) = barycentric quotient X(40328)/X(190)
X(48143) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4824, 21146, 24720}, {4824, 24720, 1491}


X(48144) = X(239)X(514)∩X(513)X(663)

Barycentrics    a*(b - c)*(a^2 + a*b + a*c + 2*b*c) : :
X(48144) = 3 X[649] - 2 X[4063], 5 X[649] - 2 X[21385], 3 X[1019] - X[4063], 4 X[1019] - X[4498], 5 X[1019] - X[21385], 4 X[4063] - 3 X[4498], 5 X[4063] - 3 X[21385], 5 X[4498] - 4 X[21385], 2 X[4932] + X[21222], 5 X[663] - 6 X[25569], 5 X[4367] - 3 X[25569], X[4822] - 3 X[14413], 4 X[1125] - 3 X[47838], 2 X[1577] - 3 X[4379], 2 X[3716] - 3 X[47820], 2 X[3835] - 3 X[47796], 4 X[3960] - X[4813], 2 X[4040] - 3 X[8643], 4 X[4129] - 5 X[30835], 2 X[4129] - 3 X[47795], 5 X[30835] - 6 X[47795], 2 X[4147] - 3 X[47836], X[4462] - 3 X[47762], 2 X[4705] - 3 X[47828], 2 X[4806] - 3 X[47841], 3 X[4893] - 4 X[14838], 4 X[6050] - 3 X[47811], 2 X[14837] - 3 X[47758], 2 X[17072] - 3 X[47824], 2 X[20317] - 3 X[47761], 2 X[21051] - 3 X[47823], 4 X[25380] - 3 X[47814], 7 X[31207] - 6 X[47794], 4 X[31286] - 3 X[47793]

X(48144) lies on these lines: {1, 6005}, {239, 514}, {512, 4378}, {513, 663}, {522, 17166}, {657, 28878}, {659, 29198}, {661, 905}, {667, 4724}, {693, 6002}, {764, 24286}, {812, 4801}, {814, 21146}, {830, 4905}, {834, 4840}, {885, 7091}, {891, 4834}, {918, 2484}, {1022, 25417}, {1125, 47838}, {1577, 4379}, {1734, 4160}, {2254, 8678}, {2282, 2401}, {2483, 30520}, {2533, 4474}, {3026, 17417}, {3261, 16737}, {3667, 38475}, {3676, 28094}, {3716, 47820}, {3733, 46385}, {3801, 29120}, {3803, 45695}, {3835, 26113}, {3900, 7659}, {3910, 4897}, {3960, 4813}, {4010, 29170}, {4040, 8643}, {4083, 4784}, {4129, 26983}, {4147, 47836}, {4369, 4391}, {4374, 41299}, {4382, 4978}, {4435, 4790}, {4458, 47708}, {4462, 47762}, {4490, 9508}, {4504, 47729}, {4705, 47828}, {4729, 14077}, {4806, 47841}, {4893, 14838}, {4922, 29366}, {6050, 47811}, {6332, 28846}, {7208, 38346}, {8045, 25259}, {8631, 20981}, {8639, 8672}, {14419, 47826}, {14837, 47758}, {16811, 17214}, {17072, 47824}, {17212, 17215}, {20317, 47761}, {20979, 28840}, {21051, 47823}, {21104, 29162}, {21301, 24720}, {23875, 47682}, {23880, 43067}, {23882, 47672}, {25380, 47814}, {25899, 25924}, {27114, 31207}, {27673, 31290}, {28041, 30723}, {28623, 47844}, {29037, 47690}, {29062, 47715}, {29114, 47680}, {29118, 47691}, {29132, 47712}, {29140, 47725}, {29158, 47716}, {29196, 47714}, {29212, 47711}, {29344, 47724}, {29358, 47726}, {31286, 47793}, {39476, 39577}

X(48144) = midpoint of X(7192) and X(17496)
X(48144) = reflection of X(i) in X(j) for these {i,j}: {649, 1019}, {661, 905}, {663, 4367}, {4382, 4978}, {4391, 4369}, {4449, 4378}, {4474, 2533}, {4490, 9508}, {4498, 649}, {4724, 667}, {4813, 14349}, {14349, 3960}, {21124, 4025}, {21301, 24720}, {25259, 8045}, {46385, 3733}, {47708, 4458}, {47729, 4504}, {47826, 14419}
X(48144) = X(43350)-anticomplementary conjugate of X(69)
X(48144) = X(i)-Ceva conjugate of X(j) for these (i,j): {6013, 17110}, {43067, 17418}
X(48144) = X(8672)-cross conjugate of X(43067)
X(48144) = crosspoint of X(i) and X(j) for these (i,j): {1, 6013}, {190, 25430}
X(48144) = crosssum of X(i) and X(j) for these (i,j): {1, 6005}, {522, 31330}, {649, 1449}
X(48144) = crossdifference of every pair of points on line {9, 42}
X(48144) = X(i)-isoconjugate of X(j) for these (i,j): {8, 32693}, {37, 931}, {55, 32038}, {100, 941}, {101, 31359}, {190, 2258}, {644, 959}, {692, 34258}, {1018, 5331}, {1783, 34259}, {3939, 44733}, {4557, 37870}
X(48144) = X(i)-Dao conjugate of X(j) for these (i, j): (223, 32038), (1015, 31359), (1086, 34258), (8054, 941), (17417, 8), (34261, 3699), (39006, 34259), (40589, 931), (40617, 44733)
X(48144) = barycentric product X(i)*X(j) for these {i,j}: {1, 43067}, {7, 17418}, {57, 23880}, {86, 8672}, {310, 8639}, {513, 10436}, {514, 940}, {649, 34284}, {693, 1468}, {905, 5307}, {958, 3676}, {1019, 31993}, {2268, 24002}, {3261, 5019}, {3669, 11679}, {3714, 7203}, {4025, 4185}, {17110, 47666}
X(48144) = barycentric quotient X(i)/X(j) for these {i,j}: {57, 32038}, {58, 931}, {513, 31359}, {514, 34258}, {604, 32693}, {649, 941}, {667, 2258}, {940, 190}, {958, 3699}, {1019, 37870}, {1459, 34259}, {1468, 100}, {2268, 644}, {3261, 40828}, {3669, 44733}, {3713, 6558}, {3733, 5331}, {4185, 1897}, {5019, 101}, {5307, 6335}, {8639, 42}, {8672, 10}, {10436, 668}, {11679, 646}, {17418, 8}, {23880, 312}, {31993, 4033}, {34284, 1978}, {43067, 75}, {43924, 959}, {43927, 34265}
X(48144) = {X(4129),X(47795)}-harmonic conjugate of X(30835)


X(48145) = X(513)X(47700)∩X(514)X(4380)

Barycentrics    (b - c)*(4*a^2 + a*b + 2*b^2 + a*c + 2*c^2) : :
X(48145) = 4 X[47661] - 3 X[47669], 5 X[661] - 6 X[6546], 3 X[661] - 2 X[23731], 3 X[661] - 4 X[47890], 9 X[6546] - 5 X[23731], 9 X[6546] - 10 X[47890], 3 X[4838] - 4 X[47659], 10 X[4369] - 9 X[6548], 3 X[4931] - 4 X[47660], 4 X[4932] - 3 X[21115], 3 X[21115] - 2 X[47651], 2 X[47650] - 3 X[47672], 3 X[31148] - 2 X[47652]

X(48145) lies on these lines: {513, 47700}, {514, 4380}, {661, 1211}, {812, 4838}, {4369, 6548}, {4785, 47662}, {4931, 47660}, {4932, 21115}, {6009, 47671}, {26853, 28863}, {28859, 47663}, {28882, 47650}, {31148, 47652}

X(48145) = reflection of X(i) in X(j) for these {i,j}: {23731, 47890}, {47651, 4932}, {47673, 4380}
X(48145) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4932, 47651, 21115}, {23731, 47890, 661}


X(48146) = X(513)X(47700)∩X(514)X(1734)

Barycentrics    (b - c)*(2*a^3 + 3*a^2*b + a*b^2 + 2*b^3 + 3*a^2*c + 2*b^2*c + a*c^2 + 2*b*c^2 + 2*c^3) : :
X(48146) = 2 X[3716] - 3 X[47773], 2 X[4810] - 3 X[4931], 2 X[47652] - 3 X[47812], 2 X[47691] - 3 X[47813], 2 X[47701] - 3 X[47811], 3 X[47811] - 4 X[47890]

X(48146) lies on these lines: {513, 47700}, {514, 1734}, {522, 47662}, {649, 4802}, {659, 47702}, {812, 47693}, {3716, 47773}, {4025, 28191}, {4369, 47688}, {4804, 47660}, {4810, 4931}, {4913, 47653}, {6084, 47703}, {16892, 28175}, {24720, 47651}, {28147, 47661}, {28859, 47698}, {28882, 47690}, {47652, 47812}, {47691, 47813}, {47701, 47811}

X(48146) = reflection of X(i) in X(j) for these {i,j}: {4804, 47660}, {47651, 24720}, {47653, 4913}, {47688, 4369}, {47701, 47890}, {47702, 659}
X(48146) = crossdifference of every pair of points on line {2280, 5312}
X(48146) = {X(47701),X(47890)}-harmonic conjugate of X(47811)


X(48147) = X(513)X(4382)∩X(514)X(4380)

Barycentrics    (b - c)*(2*a^2 + 3*a*b + 3*a*c + 2*b*c) : :
X(48147) = 6 X[2] - 5 X[661], 9 X[2] - 10 X[4369], 3 X[2] - 5 X[7192], 24 X[2] - 25 X[24924], 21 X[2] - 20 X[25666], 4 X[2] - 5 X[31148], 9 X[2] - 5 X[31290], 11 X[2] - 10 X[45315], 19 X[2] - 20 X[45663], 7 X[2] - 5 X[47774], 3 X[661] - 4 X[4369], 4 X[661] - 5 X[24924], 7 X[661] - 8 X[25666], 2 X[661] - 3 X[31148], 3 X[661] - 2 X[31290], 11 X[661] - 12 X[45315], 19 X[661] - 24 X[45663], 7 X[661] - 6 X[47774], 2 X[4369] - 3 X[7192], 16 X[4369] - 15 X[24924], 7 X[4369] - 6 X[25666], 8 X[4369] - 9 X[31148], 11 X[4369] - 9 X[45315], 19 X[4369] - 18 X[45663], 14 X[4369] - 9 X[47774], 8 X[7192] - 5 X[24924], 7 X[7192] - 4 X[25666], 4 X[7192] - 3 X[31148], 3 X[7192] - X[31290], 11 X[7192] - 6 X[45315], 19 X[7192] - 12 X[45663], 7 X[7192] - 3 X[47774], 35 X[24924] - 32 X[25666], 5 X[24924] - 6 X[31148], 15 X[24924] - 8 X[31290], 55 X[24924] - 48 X[45315], 95 X[24924] - 96 X[45663], 35 X[24924] - 24 X[47774], 16 X[25666] - 21 X[31148], 12 X[25666] - 7 X[31290], 22 X[25666] - 21 X[45315], 19 X[25666] - 21 X[45663], 4 X[25666] - 3 X[47774], 9 X[31148] - 4 X[31290], 11 X[31148] - 8 X[45315], 19 X[31148] - 16 X[45663], 7 X[31148] - 4 X[47774], 11 X[31290] - 18 X[45315], 19 X[31290] - 36 X[45663], 7 X[31290] - 9 X[47774], 19 X[45315] - 22 X[45663], 14 X[45315] - 11 X[47774], 28 X[45663] - 19 X[47774], 2 X[4382] - 3 X[47672], 2 X[4380] - 3 X[4979], 5 X[4380] - 3 X[47664], 5 X[4979] - 2 X[47664], 3 X[1635] - 4 X[4932], 3 X[1635] - 2 X[47666], 4 X[3626] - 5 X[4761], 4 X[3798] - 3 X[47878], 4 X[4500] - 3 X[4958], 3 X[4728] - 2 X[4813], 9 X[4728] - 8 X[4940], 3 X[4728] - 4 X[43067], 3 X[4813] - 4 X[4940], 2 X[4940] - 3 X[43067], 3 X[4750] - 2 X[4841], 3 X[4931] - 2 X[44449], 8 X[7653] - 7 X[31207], 4 X[7653] - 3 X[47777], 7 X[31207] - 6 X[47777], 3 X[21116] - 2 X[23729]

X(48147) lies on these lines: {2, 661}, {513, 4382}, {514, 4380}, {522, 47670}, {900, 47671}, {1635, 4932}, {2786, 4838}, {3626, 4761}, {3632, 4160}, {3798, 47878}, {3982, 4077}, {4458, 4778}, {4500, 4958}, {4728, 4813}, {4750, 4841}, {4785, 47675}, {4897, 4988}, {4931, 44449}, {4960, 15309}, {4963, 9508}, {4977, 16892}, {7653, 31207}, {9013, 40341}, {21104, 23728}, {21116, 23729}, {25259, 28886}, {28225, 47697}, {28855, 47660}, {28859, 47676}, {28867, 47656}, {28906, 47665}

X(48147) = reflection of X(i) in X(j) for these {i,j}: {661, 7192}, {4813, 43067}, {4963, 9508}, {4988, 4897}, {23731, 21104}, {31290, 4369}, {47666, 4932}, {47669, 4467}
fX(48147) = barycentric product X(514)*X(28639)
X(48147) = barycentric quotient X(28639)/X(190)
X(48147) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 7192, 31148}, {661, 8042, 28372}, {661, 31148, 24924}, {4369, 31290, 661}, {4813, 43067, 4728}, {4932, 47666, 1635}, {7192, 31290, 4369}, {7653, 47777, 31207}, {25666, 47774, 661}


X(48148) = X(513)X(4382)∩X(514)X(1734)

Barycentrics    (b - c)*(3*a^2*b + a*b^2 + 3*a^2*c + 6*a*b*c + 2*b^2*c + a*c^2 + 2*b*c^2) : :
X(48148) = 2 X[659] - 3 X[31148], 3 X[661] - 4 X[3837], 2 X[661] - 3 X[47812], 2 X[3837] - 3 X[21146], 8 X[3837] - 9 X[47812], 4 X[21146] - 3 X[47812], 2 X[3716] - 3 X[47780], 4 X[4369] - 3 X[47811], 2 X[4724] - 3 X[47813], 4 X[43067] - 3 X[47813], 2 X[4830] - 3 X[47763], 4 X[4885] - 3 X[47826], 3 X[21116] - 2 X[23770], 4 X[24720] - 3 X[47810], 2 X[47666] - 3 X[47810], 4 X[25380] - 3 X[47775]

X(48148) lies on these lines: {513, 4382}, {514, 1734}, {522, 47675}, {659, 31148}, {661, 1639}, {693, 4778}, {918, 47703}, {1491, 28195}, {3716, 47780}, {3776, 47699}, {4010, 28209}, {4369, 47811}, {4724, 24666}, {4728, 28220}, {4818, 47667}, {4822, 4978}, {4824, 28213}, {4830, 47763}, {4885, 47826}, {4979, 29362}, {21104, 47701}, {21116, 23770}, {24720, 25627}, {25380, 47775}, {28840, 46403}, {28851, 47690}, {28859, 47686}, {28890, 47693}, {29144, 47705}

X(48148) = reflection of X(i) in X(j) for these {i,j}: {661, 21146}, {4724, 43067}, {4804, 47672}, {4822, 4978}, {47666, 24720}, {47667, 4818}, {47699, 3776}, {47701, 21104}
X(48148) = crossdifference of every pair of points on line {595, 2280}
X(48148) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 21146, 47812}, {4724, 43067, 47813}, {24720, 47666, 47810}


X(48149) = X(513)X(663)∩X(514)X(4380)

Barycentrics    a*(b - c)*(2*a^2 + 3*a*b + b^2 + 3*a*c + 4*b*c + c^2) : :
X(48149) = 3 X[661] - 4 X[14838], 3 X[1019] - 2 X[14838], 2 X[1577] - 3 X[31148], 4 X[4129] - 5 X[24924], 4 X[6050] - 3 X[47826]

X(48149) lies on these lines: {513, 663}, {514, 4380}, {656, 4840}, {661, 1019}, {905, 4813}, {1577, 31148}, {4041, 4784}, {4129, 24924}, {4160, 4729}, {4391, 4932}, {4498, 4790}, {4560, 28840}, {4785, 4801}, {4804, 29150}, {4897, 21124}, {6002, 7192}, {6050, 47826}, {8045, 44449}, {23755, 29126}, {23883, 47681}, {28525, 47721}, {29013, 47672}, {29158, 47705}, {29232, 47703}

X(48149) = reflection of X(i) in X(j) for these {i,j}: {656, 4840}, {661, 1019}, {4041, 4784}, {4391, 4932}, {4498, 4790}, {4813, 905}, {4822, 4367}, {21124, 4897}, {44449, 8045}
X(48149) = X(8)-isoconjugate of X(26733)
X(48149) = crosspoint of X(662) and X(39948)
X(48149) = crosssum of X(661) and X(3247)
X(48149) = crossdifference of every pair of points on line {9, 1962}
X(48149) = barycentric product X(i)*X(j) for these {i,j}: {57, 26732}, {514, 37595}, {3676, 5302}
X(48149) = barycentric quotient X(i)/X(j) for these {i,j}: {604, 26733}, {5302, 3699}, {26732, 312}, {37595, 190}


X(48150) = X(513)X(663)∩X(514)X(47692)

Barycentrics    a*(b - c)*(2*a^2 - a*b + b^2 - a*c + c^2) : :
X(48150) = 2 X[10] - 3 X[47817], 2 X[3777] - 3 X[14413], 2 X[905] - 3 X[8643], 3 X[1635] - 2 X[1734], 3 X[1635] - 4 X[4401], 2 X[4142] - 3 X[44433], 2 X[4147] - 3 X[47815], 4 X[8689] - 3 X[47815], 3 X[4448] - 2 X[21051], 2 X[4705] - 3 X[47811], 4 X[6050] - 3 X[47828], 3 X[6545] - 4 X[34958], 2 X[14288] - 3 X[45686], 2 X[14837] - 3 X[47801], 2 X[17072] - 3 X[47804], X[21302] - 3 X[47805], 2 X[24720] - 3 X[47820], 5 X[24924] - 6 X[47818]

X(48150) lies on these lines: {10, 47817}, {21, 1019}, {512, 2292}, {513, 663}, {514, 47692}, {649, 3309}, {656, 4057}, {659, 4041}, {661, 830}, {667, 2254}, {832, 17420}, {905, 8643}, {1281, 40459}, {1633, 9323}, {1635, 1734}, {1960, 2530}, {3250, 4979}, {3667, 6332}, {3716, 21301}, {3810, 47728}, {3887, 4063}, {3888, 9266}, {3900, 4498}, {3904, 28487}, {4083, 4895}, {4129, 5051}, {4142, 44433}, {4147, 8689}, {4162, 8712}, {4171, 21389}, {4378, 23738}, {4391, 28470}, {4448, 21051}, {4491, 9013}, {4504, 21222}, {4705, 47811}, {4724, 8678}, {4794, 14349}, {4804, 29070}, {5216, 35623}, {6002, 31291}, {6050, 47828}, {6545, 34958}, {8045, 47687}, {8062, 44444}, {8645, 22160}, {11031, 44410}, {11068, 44448}, {14288, 45686}, {14432, 28217}, {14837, 47801}, {17072, 47804}, {17115, 28041}, {21118, 29240}, {21302, 28521}, {21303, 26248}, {23696, 28029}, {24720, 47820}, {24924, 47818}, {29051, 47694}, {29186, 47672}, {37311, 39577}, {37998, 44694}

X(48150) = reflection of X(i) in X(j) for these {i,j}: {649, 3803}, {656, 4057}, {661, 4040}, {1734, 4401}, {2254, 667}, {2530, 1960}, {4041, 659}, {4147, 8689}, {4729, 4063}, {14349, 4794}, {21222, 4504}, {21301, 3716}, {23738, 4378}, {44444, 8062}, {44448, 11068}, {47687, 8045}
X(48150) = X(7132)-Ceva conjugate of X(2170)
X(48150) = crosssum of X(100) and X(3888)
X(48150) = crossdifference of every pair of points on line {9, 38}
X(48150) = barycentric product X(i)*X(j) for these {i,j}: {1, 47890}, {513, 17353}, {514, 3744}, {3676, 30618}
X(48150) = barycentric quotient X(i)/X(j) for these {i,j}: {3744, 190}, {17353, 668}, {30618, 3699}, {47890, 75}
X(48150) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1734, 4401, 1635}, {4147, 8689, 47815}


X(48151) = X(513)X(663)∩X(514)X(1734)

Barycentrics    a*(b - c)*(a*b - b^2 + a*c + 2*b*c - c^2) : :
X(48151) = 2 X[663] - 3 X[14413], 2 X[1769] - 3 X[4017], 4 X[1769] - 3 X[6615], 4 X[3669] - 3 X[14413], 4 X[3777] - X[4822], 2 X[1734] - 3 X[2254], 4 X[1734] - 3 X[4041], X[1734] - 3 X[4905], 2 X[1734] + 3 X[23738], X[4041] - 4 X[4905], X[4041] + 2 X[23738], 2 X[4905] + X[23738], 2 X[676] - 3 X[30724], 2 X[1577] - 3 X[47812], 4 X[23789] - 3 X[47812], 2 X[3716] - 3 X[47796], 2 X[3762] - 3 X[21052], X[3762] - 4 X[23796], 3 X[21052] - 8 X[23796], 2 X[3835] - 3 X[47819], 2 X[4142] - 3 X[4453], 2 X[4462] - 3 X[14430], 3 X[14430] - 4 X[17072], 3 X[4728] - 4 X[23815], 2 X[10015] + X[23746], 4 X[14838] - 3 X[47811], 4 X[19947] - 3 X[47839], 2 X[21051] - 3 X[36848], 2 X[21120] - 3 X[30574], 2 X[21185] - 3 X[47887], 4 X[25380] - 3 X[47793], 4 X[31286] - 3 X[47815]

X(48151) lies on these lines: {1, 42325}, {58, 1019}, {512, 764}, {513, 663}, {514, 1734}, {522, 4801}, {651, 9323}, {656, 4977}, {661, 665}, {676, 30724}, {784, 47672}, {824, 47719}, {826, 40471}, {891, 4729}, {905, 4724}, {984, 28871}, {1110, 1308}, {1491, 29198}, {1577, 23789}, {2170, 35505}, {2826, 21118}, {2832, 4063}, {3309, 4449}, {3676, 30804}, {3716, 47796}, {3762, 21052}, {3776, 47708}, {3835, 47819}, {3907, 21222}, {3960, 4040}, {4083, 23765}, {4129, 23814}, {4142, 4453}, {4151, 23795}, {4378, 6004}, {4391, 24720}, {4462, 14430}, {4499, 9266}, {4728, 23815}, {4778, 17420}, {4804, 4978}, {4897, 23740}, {4979, 22383}, {6002, 46403}, {6362, 6608}, {7178, 21132}, {7659, 8712}, {8648, 44408}, {8713, 30719}, {10015, 23746}, {10481, 23599}, {10581, 21127}, {14838, 47811}, {16892, 29142}, {17496, 29051}, {19947, 47839}, {20507, 23780}, {21051, 36848}, {21105, 28473}, {21120, 30574}, {21185, 47887}, {21189, 28225}, {23877, 47676}, {24462, 28855}, {24719, 29170}, {25380, 47793}, {29037, 47687}, {29118, 47652}, {29168, 47702}, {29354, 47700}, {31286, 47815}

X(48151) = midpoint of X(2254) and X(23738)
X(48151) = reflection of X(i) in X(j) for these {i,j}: {661, 2530}, {663, 3669}, {1577, 23789}, {2254, 4905}, {4040, 3960}, {4041, 2254}, {4129, 23814}, {4391, 24720}, {4462, 17072}, {4724, 905}, {4804, 4978}, {4895, 4449}, {6615, 4017}, {17420, 23800}, {21132, 7178}, {47708, 3776}
X(48151) = X(i)-Ceva conjugate of X(j) for these (i,j): {6, 244}, {279, 2170}, {513, 2488}, {21104, 21127}, {35338, 354}
X(48151) = X(2488)-cross conjugate of X(21127)
X(48151) = X(i)-isoconjugate of X(j) for these (i,j): {55, 6606}, {100, 2346}, {101, 32008}, {190, 1174}, {644, 1170}, {651, 6605}, {664, 10482}, {1897, 47487}, {3939, 21453}
X(48151) = X(i)-Dao conjugate of X(j) for these (i, j): (142, 3699), (223, 6606), (1015, 32008), (1111, 76), (1212, 668), (3119, 346), (8054, 2346), (34467, 47487), (38991, 6605), (39025, 10482), (40606, 190), (40615, 31618), (40617, 21453)
X(48151) = crosspoint of X(i) and X(j) for these (i,j): {6, 35326}, {354, 35338}, {513, 3676}
X(48151) = crosssum of X(i) and X(j) for these (i,j): {1, 42325}, {9, 6608}, {100, 3939}, {522, 25006}, {650, 15837}, {6594, 14392}
X(48151) = crossdifference of every pair of points on line {9, 1174}
X(48151) = barycentric product X(i)*X(j) for these {i,j}: {1, 21104}, {7, 21127}, {55, 23599}, {57, 6362}, {85, 2488}, {142, 513}, {279, 6608}, {354, 514}, {512, 16708}, {522, 1418}, {523, 18164}, {649, 20880}, {650, 10481}, {661, 17169}, {667, 1233}, {693, 1475}, {1019, 3925}, {1086, 35338}, {1088, 10581}, {1111, 35326}, {1212, 3676}, {1229, 43924}, {1358, 35341}, {2170, 35312}, {2293, 24002}, {2530, 18087}, {3669, 4847}, {4017, 16713}, {6129, 13156}, {6173, 46003}, {6607, 23062}, {7178, 17194}, {7192, 21808}, {15413, 40983}, {17096, 21039}, {17205, 35310}, {17924, 22053}
X(48151) = barycentric quotient X(i)/X(j) for these {i,j}: {57, 6606}, {142, 668}, {354, 190}, {513, 32008}, {649, 2346}, {663, 6605}, {667, 1174}, {1212, 3699}, {1233, 6386}, {1418, 664}, {1475, 100}, {2293, 644}, {2488, 9}, {3059, 6558}, {3063, 10482}, {3669, 21453}, {3676, 31618}, {3925, 4033}, {4847, 646}, {6362, 312}, {6607, 728}, {6608, 346}, {8012, 4578}, {10481, 4554}, {10581, 200}, {16708, 670}, {16713, 7257}, {17169, 799}, {17194, 645}, {18164, 99}, {20229, 3939}, {20880, 1978}, {21039, 30730}, {21104, 75}, {21127, 8}, {21795, 4069}, {21808, 3952}, {22053, 1332}, {22079, 4587}, {22383, 47487}, {23599, 6063}, {35326, 765}, {35338, 1016}, {35341, 4076}, {40983, 1783}, {43924, 1170}, {43932, 10509}
X(48151) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {663, 3669, 14413}, {1577, 23789, 47812}, {4462, 17072, 14430}, {4905, 23738, 4041}


X(48152) = X(320)X(350)∩X(523)X(18697)

Barycentrics    b*(b - c)*c*(2*a^2 + b^2 + c^2) : :
X(48152) = 3 X[693] - X[15413]

X(48152) lies on these lines: {320, 350}, {523, 18697}, {812, 2483}, {900, 4509}, {918, 4978}, {2484, 4382}, {2509, 4762}, {2517, 4408}, {3261, 29144}, {3287, 40166}, {3766, 4036}, {4024, 23885}, {4140, 23739}, {4375, 8060}, {4801, 30520}, {9015, 20980}, {23783, 23798}, {23785, 23828}, {23789, 23804}

X(48152) = midpoint of X(i) and X(j) for these {i,j}: {2484, 4382}, {4140, 23739}
X(48152) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {39723, 150}, {40044, 21293}
X(48152) = X(16703)-Ceva conjugate of X(3125)
X(48152) = X(i)-isoconjugate of X(j) for these (i,j): {42, 7953}, {101, 3108}, {1918, 35137}, {8750, 41435}, {10159, 32739}
X(48152) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 3108), (3589, 4553), (6292, 100), (15527, 37), (26932, 41435), (34021, 35137), (39691, 3954), (40592, 7953), (40619, 10159)
X(48152) = barycentric product X(i)*X(j) for these {i,j}: {274, 7927}, {428, 15413}, {513, 39998}, {523, 16707}, {693, 3589}, {905, 44142}, {1577, 17200}, {3112, 21126}, {3120, 18062}, {3261, 17469}, {4030, 24002}, {4391, 7198}, {5007, 40495}, {6385, 8664}, {7767, 17924}, {10330, 16732}, {10566, 20898}, {17193, 18070}, {18108, 42554}
X(48152) = barycentric quotient X(i)/X(j) for these {i,j}: {81, 7953}, {274, 35137}, {428, 1783}, {513, 3108}, {693, 10159}, {905, 41435}, {3589, 100}, {4030, 644}, {5007, 692}, {6292, 4553}, {7198, 651}, {7767, 1332}, {7927, 37}, {8664, 213}, {10330, 4567}, {16707, 99}, {16732, 31065}, {17200, 662}, {17457, 46148}, {17469, 101}, {18062, 4600}, {20898, 4568}, {21038, 35309}, {21126, 38}, {21802, 4557}, {22352, 906}, {39998, 668}, {44142, 6335}
X(48152) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 20954, 30591}, {693, 23819, 7650}, {2517, 30804, 4408}


X(48153) = X(513)X(4382)∩X(514)X(47692)

Barycentrics    (b - c)*(2*a^3 + a^2*b + 3*a*b^2 + a^2*c + 4*a*b*c + 2*b^2*c + 3*a*c^2 + 2*b*c^2) : :
X(48153) = 3 X[4804] - 2 X[4810], 3 X[661] - 4 X[3716], 5 X[661] - 6 X[47821], 2 X[3716] - 3 X[47694], 10 X[3716] - 9 X[47821], 5 X[47694] - 3 X[47821], 4 X[1491] - 5 X[24924], 2 X[1491] - 3 X[47813], 5 X[24924] - 6 X[47813], 2 X[2254] - 3 X[31148], 2 X[2526] - 3 X[4379], 3 X[4728] - 4 X[7662], 2 X[4824] - 3 X[47811], 4 X[4874] - 3 X[47810], 4 X[13246] - 3 X[47782]

X(48153) lies on these lines: {513, 4382}, {514, 47692}, {522, 4838}, {661, 3716}, {830, 47724}, {900, 47703}, {1491, 24924}, {2254, 31148}, {2526, 4379}, {4380, 28161}, {4474, 8678}, {4728, 7662}, {4824, 47811}, {4874, 47810}, {4960, 42325}, {4977, 47704}, {13246, 47782}, {28155, 47664}, {47660, 47700}

X(48153) = reflection of X(i) in X(j) for these {i,j}: {661, 47694}, {47700, 47660}, {47702, 47695}
X(48153) = {X(1491),X(47813)}-harmonic conjugate of X(24924)


X(48154) = 72ND HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    6*a^4 - 13*a^2*b^2 + 7*b^4 - 13*a^2*c^2 - 14*b^2*c^2 + 7*c^4 : :
X(48154) = 21 X[2] - X[3], 39 X[2] + X[4], 9 X[2] + X[5], 81 X[2] - X[20], 6 X[2] - X[140], 41 X[2] - X[376], 19 X[2] + X[381], 99 X[2] + X[382], 24 X[2] + X[546], 4 X[2] + X[547], 36 X[2] - X[548], 11 X[2] - X[549], 51 X[2] - X[550], 9 X[2] - X[631], 3 X[2] + X[1656], 141 X[2] - X[1657], 33 X[2] + 7 X[3090], 15 X[2] + X[3091], 159 X[2] + X[3146], 33 X[2] - X[3522], 87 X[2] - 7 X[3523], 43 X[2] - 3 X[3524], 51 X[2] - 11 X[3525], 27 X[2] - 7 X[3526], 207 X[2] - 7 X[3528], 201 X[2] - X[3529], 27 X[2] - 2 X[3530], 57 X[2] - 17 X[3533], 61 X[2] - X[3534], 79 X[2] + X[3543], 183 X[2] + 17 X[3544], 37 X[2] + 3 X[3545], 69 X[2] + X[3627], 3 X[2] + 2 X[3628], 59 X[2] + X[3830], 153 X[2] + 7 X[3832], 77 X[2] + 3 X[3839], 27 X[2] + X[3843], 29 X[2] + X[3845], 33 X[2] + 2 X[3850], 93 X[2] + 7 X[3851], 54 X[2] + X[3853], 303 X[2] + 17 X[3854], 189 X[2] + 11 X[3855], 81 X[2] + 4 X[3856], 123 X[2] + 7 X[3857], 21 X[2] + X[3858], 18 X[2] + X[3859], 43 X[2] + 2 X[3860], 63 X[2] + 2 X[3861], 23 X[2] - 3 X[5054], 17 X[2] + 3 X[5055], 69 X[2] + 11 X[5056], 321 X[2] - X[5059], 14 X[2] + X[5066], 27 X[2] + 13 X[5067], 147 X[2] + 13 X[5068], 9 X[2] + 11 X[5070], 7 X[2] + X[5071], 129 X[2] + 11 X[5072], 219 X[2] + X[5073], 51 X[2] + X[5076], 87 X[2] + 13 X[5079], 63 X[2] + 17 X[7486], 31 X[2] - X[8703], 13 X[2] + 2 X[10109], 7 X[2] - 2 X[10124], 213 X[2] - 13 X[10299], 93 X[2] - 13 X[10303], 83 X[2] - 3 X[10304], 121 X[2] - X[11001], 13 X[2] - 3 X[11539], 19 X[2] - 4 X[11540], 519 X[2] + X[11541], 23 X[2] + 2 X[11737], 17 X[2] - 2 X[11812], 16 X[2] - X[12100], 44 X[2] + X[12101], 93 X[2] + 2 X[12102], 66 X[2] - X[12103], 39 X[2] - 4 X[12108], 51 X[2] + 4 X[12811], 6 X[2] + X[12812], 29 X[2] - X[14093], 97 X[2] + 3 X[14269], 57 X[2] - 7 X[14869], 41 X[2] - 6 X[14890], 37 X[2] - 2 X[14891], 32 X[2] + 3 X[14892], 34 X[2] + X[14893], 141 X[2] + 19 X[15022], 239 X[2] + X[15640], 101 X[2] - X[15681], 119 X[2] + X[15682], 161 X[2] - X[15683], 139 X[2] + X[15684], 181 X[2] - X[15685], 71 X[2] - X[15686], 49 X[2] + X[15687], 103 X[2] - 3 X[15688], 143 X[2] - 3 X[15689], 46 X[2] - X[15690], 56 X[2] - X[15691], 17 X[2] - X[15692], 13 X[2] - X[15693], 5 X[2] - X[15694], 37 X[2] - X[15695], 45 X[2] - X[15696], 49 X[2] - X[15697], 127 X[2] - 7 X[15698], 7 X[2] + 3 X[15699], 107 X[2] - 7 X[15700], 67 X[2] - 7 X[15701], 47 X[2] - 7 X[15702], 13 X[2] + 7 X[15703], 111 X[2] - X[15704], 169 X[2] - 9 X[15705], 149 X[2] - 9 X[15706], 109 X[2] - 9 X[15707], 89 X[2] - 9 X[15708], 49 X[2] - 9 X[15709], 209 X[2] - 9 X[15710], 19 X[2] - X[15711], 15 X[2] - X[15712], 7 X[2] - X[15713], 23 X[2] - X[15714], 211 X[2] - 11 X[15715], 191 X[2] - 11 X[15716], 171 X[2] - 11 X[15717], 151 X[2] - 11 X[15718], 131 X[2] - 11 X[15719], 111 X[2] - 11 X[15720], 91 X[2] - 11 X[15721], 197 X[2] - 17 X[15722], 31 X[2] - 11 X[15723], 47 X[2] - 2 X[15759], 9 X[2] - 4 X[16239], 53 X[2] - 3 X[17504], 57 X[2] - X[17538], 63 X[2] + X[17578], 261 X[2] - X[17800], 25 X[2] - X[19708], 11 X[2] + X[19709], 91 X[2] - X[19710], 97 X[2] - 7 X[19711], 333 X[2] - 13 X[21734], 291 X[2] - 11 X[21735], 67 X[2] + 3 X[23046], 89 X[2] + X[33699], 279 X[2] + X[33703], 57 X[2] - 2 X[33923], 26 X[2] - X[34200], 21 X[2] + 4 X[35018], 47 X[2] - 11 X[35381], 103 X[2] + 13 X[35382], 275 X[2] + X[35384], 379 X[2] + X[35400], 569 X[2] + 11 X[35401], 727 X[2] + 13 X[35402], 43 X[2] + X[35403], 109 X[2] + X[35404], 2769 X[2] + 11 X[35405] (and many more)

See Antreas Hatzipolakis and Peter Moses, euclid 4920.

X(48154) lies on these lines: {2, 3}, {13, 42948}, {14, 42949}, {61, 42778}, {62, 42777}, {141, 15520}, {143, 6688}, {373, 6101}, {395, 42591}, {396, 42590}, {498, 8162}, {517, 31253}, {590, 13993}, {615, 13925}, {952, 19862}, {1132, 9693}, {1216, 32205}, {1483, 5550}, {1698, 5844}, {3055, 5305}, {3070, 43434}, {3071, 43435}, {3316, 13961}, {3317, 13903}, {3411, 16960}, {3412, 16961}, {3589, 5965}, {3614, 4325}, {3624, 37727}, {3634, 5901}, {3655, 30315}, {3763, 34380}, {3815, 5346}, {3819, 10095}, {4301, 11231}, {4309, 10593}, {4317, 10592}, {4330, 7173}, {5237, 43104}, {5238, 43101}, {5318, 43240}, {5319, 31489}, {5321, 43241}, {5326, 15171}, {5349, 42594}, {5350, 42595}, {5446, 15082}, {5447, 13364}, {5462, 10219}, {5650, 10263}, {5690, 9624}, {5735, 38113}, {5843, 20195}, {5881, 34595}, {5882, 38083}, {5886, 19872}, {5892, 14128}, {5943, 14449}, {5972, 20396}, {6409, 42600}, {6410, 42601}, {6468, 9680}, {6469, 42265}, {6470, 8981}, {6471, 13966}, {6667, 20104}, {6668, 20107}, {6723, 10272}, {7294, 18990}, {7583, 32790}, {7584, 32789}, {7746, 9606}, {7747, 11614}, {7751, 9771}, {7759, 15597}, {7796, 37647}, {7814, 37688}, {7988, 31425}, {8167, 32141}, {8227, 28212}, {9588, 22791}, {9607, 31455}, {9705, 13353}, {9780, 10283}, {9955, 28232}, {9956, 19878}, {10170, 12006}, {10171, 40273}, {10172, 18357}, {10194, 13846}, {10195, 13847}, {10247, 46932}, {10577, 31454}, {10627, 13451}, {10645, 42682}, {10646, 42683}, {10993, 38084}, {11017, 46850}, {11230, 11362}, {11271, 21357}, {11465, 23039}, {11488, 42492}, {11489, 42493}, {11542, 43013}, {11543, 43012}, {11591, 11695}, {11592, 13598}, {11694, 36253}, {11793, 12045}, {13339, 43614}, {13392, 23236}, {13881, 31450}, {14531, 15067}, {14926, 43807}, {14981, 34127}, {15048, 31492}, {15056, 45956}, {15063, 34128}, {15069, 38110}, {15079, 15174}, {15081, 22251}, {15172, 31452}, {15325, 37719}, {15644, 18874}, {15808, 38176}, {15888, 37602}, {16003, 40685}, {16644, 42513}, {16645, 42512}, {16772, 16967}, {16773, 16966}, {16836, 45958}, {17704, 32137}, {18583, 34573}, {18907, 31417}, {19116, 31487}, {19117, 32786}, {19876, 38022}, {19877, 38112}, {20582, 25555}, {25339, 38615}, {28174, 31447}, {28224, 37714}, {31235, 31262}, {31239, 32515}, {31260, 31263}, {31423, 38034}, {33416, 42146}, {33417, 42143}, {33606, 42613}, {33607, 42612}, {34126, 37725}, {35255, 42583}, {35256, 42582}, {37484, 44299}, {37687, 45931}, {37832, 42924}, {37835, 42925}, {38318, 43177}, {40111, 43651}, {40693, 42610}, {40694, 42611}, {42103, 43327}, {42106, 43326}, {42107, 42434}, {42110, 42433}, {42111, 43194}, {42114, 43193}, {42117, 42490}, {42118, 42491}, {42121, 42156}, {42122, 42914}, {42123, 42915}, {42124, 42153}, {42125, 43644}, {42128, 43649}, {42157, 42500}, {42158, 42501}, {42496, 43429}, {42497, 43428}, {42498, 42918}, {42499, 42919}, {42580, 42945}, {42581, 42944}, {42596, 42814}, {42597, 42813}, {42598, 42913}, {42599, 42912}, {42684, 42890}, {42685, 42891}, {42779, 43200}, {42780, 43199}, {42817, 42917}, {42818, 42916}, {42910, 43238}, {42911, 43239}, {42962, 43870}, {42963, 43869}, {42978, 43229}, {42979, 43228}, {42984, 43447}, {42985, 43446}, {43000, 43111}, {43001, 43110}

X(48154) = midpoint of X(i) and X(j) for these {i,j}: {3, 3858}, {5, 631}, {140, 12812}, {381, 15711}, {549, 19709}, {550, 5076}, {632, 1656}, {3091, 15712}, {3843, 46853}, {3845, 14093}, {5071, 15713}, {15081, 22251}, {15687, 15697}, {15714, 41099}
X(48154) = reflection of X(i) in X(j) for these {i,j}: {140, 632}, {631, 45760}, {1656, 3628}, {3853, 3843}, {3858, 41989}, {3859, 5}, {5066, 5071}, {12103, 3522}, {12812, 1656}, {15690, 15714}, {15692, 11812}, {15695, 14891}, {15713, 10124}, {17538, 33923}, {17578, 3861}, {34200, 15693}, {35403, 3860}, {41099, 11737}, {41989, 35018}, {45760, 16239}, {46853, 3530}
X(48154) = complement of X(632)
X(48154) = nine-point circle of medial triangle inverse of X(44900)
X(48154) = cevapoint of X(33404) and X(33405)
X(48154) = crosssum of X(6) and X(44111)
X(48155) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5, 16239}, {2, 547, 47598}, {2, 549, 41984}, {2, 1656, 632}, {2, 3090, 46219}, {2, 3628, 140}, {2, 5067, 3526}, {2, 5070, 5}, {2, 14814, 35738}, {2, 15699, 10124}, {2, 15703, 11539}, {2, 46219, 41992}, {2, 46935, 3525}, {2, 46936, 3533}, {2, 47518, 11310}, {2, 47520, 11309}, {2, 47599, 547}, {3, 4, 19710}, {3, 5, 3861}, {3, 1656, 5071}, {3, 5068, 15687}, {3, 5071, 3858}, {3, 7486, 5}, {3, 10124, 140}, {3, 15682, 550}, {3, 15699, = 35018}, {3, 35018, 5066}, {4, 546, 45762}, {4, 11539, 12108}, {4, 12108, 34200}, {4, 15721, 3}, {5, 20, 3856}, {5, 140, 548}, {5, 382, 3850}, {5, 548, 546}, {5, 549, 382}, {5, 550, 3832}, {5, 632, 631}, {5, 3526, 3530}, {5, 3530, 3853}, {5, 3832, 12811}, {5, 3861, 5066}, {5, 5070, 3628}, {5, 7486, 35018}, {5, 11539, 44682}, {5, 15699, 7486}, {5, 16239, 140}, {5, 44682, 4}, {5, 46853, 3843}, {20, 3856, 3853}, {140, 546, 12100}, {140, 547, 546}, {140, 3090, 12101}, {140, 3628, 547}, {140, 3853, 3530}, {140, 5066, 3}, {140, 6677, 34577}, {140, 12103, 549}, {140, 34200, 12108}, {140, 41983, 14869}, {140, 44232, 34004}, {140, 47478, 12103}, {140, 47599, 3628}, {381, 3533, 14869}, {381, 11540, 41983}, {381, 14869, 33923}, {382, 3090, 5}, {546, 547, 44904}, {546, 44904, 14892}, {546, 47598, 140}, {547, 548, 5}, {547, 10124, 15691}, {547, 12100, 14892}, {547, 12101, 47478}, {547, 47598, 12100}, {549, 3090, 3850}, {549, 3850, 12103}, {549, 12101, 41982}, {549, 41982, 12100}, {549, 41992, 46219}, {549, 47478, 12101}, {550, 3525, 11812}, {550, 5055, 12811}, {550, 12811, 14893}, {631, 632, 45760}, {631, 1656, 5}, {631, 3091, 15696}, {631, 3843, 46853}, {631, 3859, 548}, {631, 5071, 17578}, {631, 15696, 15712}, {631, 17538, 15717}, {631, 17578, 3}, {631, 41099, 3528}, {631, 45760, 140}, {631, 46853, 3530}, {632, 3628, 12812}, {632, 3858, 15713}, {632, 15699, 3858}, {632, 15712, 15694}, {1656, 3526, 3843}, {1656, 3858, 35018}, {1656, 5076, 5055}, {1656, 12812, 547}, {1656, 14093, 5079}, {1656, 15694, 3091}, {1656, 15713, 41989}, {1656, 19709, 3090}, {1656, 45760, 3859}, {1656, 46219, 3522}, {1657, 15022, 38071}, {2041, 2042, 15720}, {3090, 3522, 19709}, {3090, 3533, 15710}, {3090, 3850, 47478}, {3090, 41984, 140}, {3090, 46219, 549}, {3091, 15694, 15712}, {3146, 17504, 41981}, {3523, 3845, 44245}, {3523, 5079, 3845}, {3525, 5055, 550}, {3525, 11812, 140}, {3525, 46935, 5055}, {3526, 3530, 140}, {3526, 3843, 631}, {3526, 5067, 5}, {3526, 5070, 5067}, {3528, 15690, 548}, {3530, 3853, 548}, {3530, 3856, 20}, {3530, 16239, 3526}, {3530, 35018, 3855}, {3533, 14869, 11540}, {3533, 33923, 140}, {3533, 46936, 381}, {3545, 15720, 15704}, {3627, 5056, 11737}, {3628, 10124, 35018}, {3628, 16239, 5}, {3628, 35018, 15699}, {3628, 41984, 3850}, {3628, 41992, 12103}, {3628, 46219, 47478}, {3628, 47598, 44904}, {3832, 5055, 5}, {3839, 5071, 19709}, {3843, 3855, 3858}, {3850, 12101, 546}, {3850, 12103, 12101}, {3850, 12108, 15689}, {3850, 46219, 140}, {3851, 8703, 12102}, {3851, 10303, 8703}, {3851, 15723, 10303}, {3853, 3859, 3843}, {3853, 5067, 547}, {3855, 5067, 7486}, {3855, 17578, 3843}, {3858, 5071, 41989}, {3858, 15713, 3}, {3858, 17578, 3861}, {3858, 41989, 5066}, {3859, 12812, 5}, {3861, 35018, 5}, {5020, 13154, 7525}, {5054, 5056, 3627}, {5054, 11737, 15690}, {5054, 41099, 15714}, {5055, 11812, 14893}, {5066, 15699, 547}, {5067, 16239, 3853}, {5068, 15709, 3}, {5071, 15709, 15697}, {5071, 35018, 12812}, {5076, 15692, 550}, {5159, 6639, 16197}, {5943, 32142, 14449}, {6673, 6674, 3589}, {7486, 17578, 5071}, {10109, 11539, 34200}, {10109, 12108, 4}, {10109, 19710, 5066}, {10109, 45762, 14892}, {10124, 15699, 5066}, {10124, 35018, 3}, {10124, 44580, 15709}, {10170, 12006, 31834}, {11311, 11312, 32968}, {11539, 12108, 140}, {11539, 15703, 10109}, {11539, 19710, 15721}, {11540, 14869, 140}, {11540, 33923, 14869}, {11812, 12811, 550}, {12100, 44904, 546}, {12102, 15723, 140}, {12103, 47478, 3850}, {12812, 45760, 548}, {14782, 14783, 21735}, {14869, 33923, 41983}, {15022, 15702, 1657}, {15687, 15709, 44580}, {15694, 15696, 631}, {15697, 15713, 44580}, {15699, 15713, 5071}, {15699, 15721, 10109}, {15702, 38071, 15759}, {15703, 34200, 547}, {15704, 15720, 14891}, {15707, 35404, 46332}, {15710, 17538, 3522}, {15711, 17538, 33923}, {15713, 19710, 15693}, {15759, 45758, 15702}, {15765, 18585, 45759}, {16239, 45760, 632}, {17578, 41989, 3859}, {34551, 34552, 15702}, {34559, 34562, 47599}, {35018, 41989, 5071}, {41991, 45759, 5073}, {41992, 46219, 41984}, {42580, 42945, 43417}, {42581, 42944, 43416}, {42598, 42937, 42913}, {42599, 42936, 42912}, {42610, 43028, 40693}, {42611, 43029, 40694}


X(48155) = X(5)X(11538)∩X(6)X(17)

Barycentrics    a^16-9 a^14 b^2+35 a^12 b^4-77 a^10 b^6+105 a^8 b^8-91 a^6 b^10+49 a^4 b^12-15 a^2 b^14+2 b^16-9 a^14 c^2+48 a^12 b^2 c^2-91 a^10 b^4 c^2+48 a^8 b^6 c^2+73 a^6 b^8 c^2-128 a^4 b^10 c^2+75 a^2 b^12 c^2-16 b^14 c^2+35 a^12 c^4-91 a^10 b^2 c^4+47 a^8 b^4 c^4+15 a^6 b^6 c^4+73 a^4 b^8 c^4-135 a^2 b^10 c^4+56 b^12 c^4-77 a^10 c^6+48 a^8 b^2 c^6+15 a^6 b^4 c^6+12 a^4 b^6 c^6+75 a^2 b^8 c^6-112 b^10 c^6+105 a^8 c^8+73 a^6 b^2 c^8+73 a^4 b^4 c^8+75 a^2 b^6 c^8+140 b^8 c^8-91 a^6 c^10-128 a^4 b^2 c^10-135 a^2 b^4 c^10-112 b^6 c^10+49 a^4 c^12+75 a^2 b^2 c^12+56 b^4 c^12-15 a^2 c^14-16 b^2 c^14+2 c^16 : :
Barycentrics    (12*S^4-R^4*SB*SC+S^2*(-3*R^4-4*R^2*SB-4*R^2*SC+4*SB*SC)) : :

See Kadir Altintas and Ercole Suppa, euclid 4930.

X(48155) lies on these lines: {5,11538}, {6,17}

leftri

Points in a [X(2)X(513), X(2)X(523)] coordinate system: X(48156)-X(48254)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1,L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1: (2bc - ca - ab)α + (2ca - ab - bc)β + (2ab - bc - ca)γ = 0.

L2: (2a^2 - b^2 - c^2)α + (2b^2 - c^2 - a^2)β + (2c^2 - a^2 - b^2)γ = 0.

The origin is given by (0,0) = X(2) = 1 : 1 : 1.

Barycentrics u : v : w for a point U = (x,y) in this system are given by

u : v : w = (b - c) ((a - b)(a - c)(a + b + c) + a x + (b + c) y) : : ,

where, as functions of a,b,c, the coordinate x is symmetric and homogeneous of degree 2, and y is symmetric and homogeneous of degree 1.

The appearance of {x,y}, k in the following table means that (x,y) = X(k):

{-2 (a b+a c+b c), -2 (a b+a c+b c)},47775
{-((2 a b c)/(a+b+c)), -((2 a b c)/(a+b+c))}, 47793
{-2 (a b+a c+b c), 0}, 47821
{-2 (a^2+b^2+c^2), a^2+b^2+c^2}, 31131
{-2 (a b+a c+b c), a^2+b^2+c^2}, 30565
{-2 (a b+a c+b c), a b+a c+b c}, 4800
{-a^2-b^2-c^2,-a^2-b^2-c^2}, 44435
{-a^2-b^2-c^2,-a b-a c-b c}, 1491
{-a b-a c-b c,-a b-a c-b c}, 4893
{-((a b c)/(a+b+c)), -((a b c)/(a+b+c))}, 47794
{-a^2-b^2-c^2,0}, 44429
{-a b-a c-b c,0}, 47822
{-a^2-b^2-c^2,1/2 (a b+a c+b c)}, 3837
{-a b-a c-b c,1/2 (a^2+b^2+c^2)}, 1639
{-a^2-b^2-c^2,a^2+b^2+c^2}, 47808
{-a b-a c-b c,a b+a c+b c}, 47832
{-a^2-b^2-c^2,2 (a b+a c+b c)}, 693
{1/2 (-a^2-b^2-c^2), 1/2 (-a^2-b^2-c^2)}, 47757
{1/2 (-a^2-b^2-c^2), 1/2 (-a b-a c-b c)}, 45323
{1/2 (-a b-a c-b c), 1/2 (-a b-a c-b c)}, 47778
{1/2 (-a^2-b^2-c^2), 0}, 47802
{1/2 (-a^2-b^2-c^2), 1/2 (a^2+b^2+c^2)}, 47806
{1/2 (-a b-a c-b c), 1/2 (a b+a c+b c)}, 47831
{1/2 (-a^2-b^2-c^2), a b+a c+b c}, 45320
{0,-2 (a b+a c+b c)}, 47825
{0,-a^2-b^2-c^2}, 47797
{0,-a b-a c-b c}, 47827
{0,1/2 (-a^2-b^2-c^2)}, 47799
{0,1/2 (-a b-a c-b c)}, 47829
{0,0}, 2
{0,1/2 (a^2+b^2+c^2)}, 47807
{0,a^2+b^2+c^2}, 47809
{0,a b+a c+b c}, 47833
{0,2 (a b+a c+b c)}, 47834
{1/2 (a^2+b^2+c^2), -a b-a c-b c}, 650
{1/2 (a^2+b^2+c^2), 1/2 (-a^2-b^2-c^2)}, 47800
{1/2 (a b+a c+b c), 1/2 (-a b-a c-b c)}, 47830
{1/2 (a^2+b^2+c^2), 0}, 47803
{1/2 (a^2+b^2+c^2), 1/2 (a^2+b^2+c^2)}, 47766
{1/2 (a^2+b^2+c^2), 1/2 (a b+a c+b c)}, 4874
{1/2 (a b+a c+b c), 1/2 (a b+a c+b c)}, 47779
{1/2 (a^2+b^2+c^2), 2 (a b+a c+b c)}, 7662
{a^2+b^2+c^2,-2 (a b+a c+b c)}, 31150
{a^2+b^2+c^2,-a^2-b^2-c^2}, 47798
{a b+a c+b c,-a b-a c-b c}, 47828
{a^2+b^2+c^2,1/2 (-a^2-b^2-c^2)}, 26275
{a^2+b^2+c^2,1/2 (-a b-a c-b c)}, 45314
{a b+a c+b c,1/2 (-a^2-b^2-c^2)}, 1638
{a^2+b^2+c^2,0}, 47804
{a b+a c+b c,0}, 47823
{a^2+b^2+c^2,a^2+b^2+c^2}, 47771
{a b+a c+b c,a b+a c+b c}, 4379
{(a b c)/(a+b+c), (a b c)/(a+b+c)}, 47795
{2 (a^2+b^2+c^2), -a^2-b^2-c^2}, 44433
{2 (a^2+b^2+c^2), -a b-a c-b c}, 659
{2 (a b+a c+b c), -a^2-b^2-c^2}, 4453
{2 (a^2+b^2+c^2), 0}, 47805
{2 (a b+a c+b c), 0}, 47824
{2 (a^2+b^2+c^2), 2 (a^2+b^2+c^2)}, 47773
{2 (a^2+b^2+c^2), 2 (a b+a c+b c)}, 47694
{2 (a b+a c+b c), 2 (a b+a c+b c)}, 47780
{(2 a b c)/(a+b+c), (2 a b c)/(a+b+c)}, 47796
{-2*(a^2 + b^2 + c^2), -2*(a^2 + b^2 + c^2)}, 48156
{-2*(a^2 + b^2 + c^2), -2*(a*b + a*c + b*c)}, 48157
{-2*(a*b + a*c + b*c), -2*(a^2 + b^2 + c^2)}, 48158
{-2*(a^2 + b^2 + c^2), -a^2 - b^2 - c^2}, 48159
{-2*(a^2 + b^2 + c^2), -(a*b) - a*c - b*c}, 48160
{-2*(a*b + a*c + b*c), -a^2 - b^2 - c^2}, 48161
{-2*(a*b + a*c + b*c), -(a*b) - a*c - b*c}, 48162
{-2*(a^2 + b^2 + c^2), (-a^2 - b^2 - c^2)/2}, 48163
{-2*(a^2 + b^2 + c^2), 0}, 48164
{(-2*a*b*c)/(a + b + c), 0}, 48165
{-2*(a*b + a*c + b*c), (a^2 + b^2 + c^2)/2}, 48166
{-2*(a^2 + b^2 + c^2), a*b + a*c + b*c}, 48167
{(-2*a*b*c)/(a + b + c), (a*b*c)/(a + b + c)}, 48168
{-2*(a^2 + b^2 + c^2), 2*(a^2 + b^2 + c^2)}, 48169
{-2*(a^2 + b^2 + c^2), 2*(a*b + a*c + b*c)}, 48170
{-2*(a*b + a*c + b*c), 2*(a^2 + b^2 + c^2)}, 48171
{-2*(a*b + a*c + b*c), 2*(a*b + a*c + b*c)}, 48172
{(-2*a*b*c)/(a + b + c), (2*a*b*c)/(a + b + c)}, 48173
{-a^2 - b^2 - c^2, -2*(a^2 + b^2 + c^2)}, 48174
{-a^2 - b^2 - c^2, -2*(a*b + a*c + b*c)}, 48175
{-(a*b) - a*c - b*c, -2*(a*b + a*c + b*c)}, 48176
{-(a*b) - a*c - b*c, -a^2 - b^2 - c^2}, 48177
{-a^2 - b^2 - c^2, (-a^2 - b^2 - c^2)/2}, 48178
{-(a*b) - a*c - b*c, (-a^2 - b^2 - c^2)/2}, 48179
{-(a*b) - a*c - b*c, (-(a*b) - a*c - b*c)/2}, 48180
{-((a*b*c)/(a + b + c)), 0}, 48181
{-a^2 - b^2 - c^2, (a^2 + b^2 + c^2)/2}, 48182
{-(a*b) - a*c - b*c, (a*b + a*c + b*c)/2}, 48183
{-a^2 - b^2 - c^2, a*b + a*c + b*c}, 48184
{-(a*b) - a*c - b*c, a^2 + b^2 + c^2}, 48185
{-((a*b*c)/(a + b + c)), (a*b*c)/(a + b + c)}, 48186
{-a^2 - b^2 - c^2, 2*(a^2 + b^2 + c^2)}, 48187
{-(a*b) - a*c - b*c, 2*(a^2 + b^2 + c^2)}, 48188
{-(a*b) - a*c - b*c, 2*(a*b + a*c + b*c)}, 48189
{(-a^2 - b^2 - c^2)/2, -2*(a*b + a*c + b*c)}, 48190
{(-(a*b) - a*c - b*c)/2, -2*(a*b + a*c + b*c)}, 48191
{(-a^2 - b^2 - c^2)/2, -a^2 - b^2 - c^2}, 48192
{(-a^2 - b^2 - c^2)/2, -(a*b) - a*c - b*c}, 48193
{(-(a*b) - a*c - b*c)/2, -(a*b) - a*c - b*c}, 48194
{(-(a*b) - a*c - b*c)/2, (-a^2 - b^2 - c^2)/2}, 48195
{-1/2*(a*b*c)/(a + b + c), -1/2*(a*b*c)/(a + b + c)}, 48196
{(-(a*b) - a*c - b*c)/2, 0}, 48197
{(-a^2 - b^2 - c^2)/2, (a*b + a*c + b*c)/2}, 48198
{(-(a*b) - a*c - b*c)/2, (a^2 + b^2 + c^2)/2}, 48199
{(-a^2 - b^2 - c^2)/2, a^2 + b^2 + c^2}, 48200
{(-(a*b) - a*c - b*c)/2, a^2 + b^2 + c^2}, 48201
{(-(a*b) - a*c - b*c)/2, a*b + a*c + b*c}, 48202
{0, -2*(a^2 + b^2 + c^2)}, 48203
{0, (-2*a*b*c)/(a + b + c)}, 48204
{0, -((a*b*c)/(a + b + c))}, 48205
{0, (a*b + a*c + b*c)/2}, 48206
{0, (a*b*c)/(a + b + c)}, 48207
{0, 2*(a^2 + b^2 + c^2)}, 48208
{0, (2*a*b*c)/(a + b + c)}, 48209
{(a^2 + b^2 + c^2)/2, -2*(a*b + a*c + b*c)}, 48210
{(a^2 + b^2 + c^2)/2, -a^2 - b^2 - c^2}, 48211
{(a*b + a*c + b*c)/2, -a^2 - b^2 - c^2}, 48212
{(a*b + a*c + b*c)/2, -(a*b) - a*c - b*c}, 48213
{(a^2 + b^2 + c^2)/2, (-(a*b) - a*c - b*c)/2}, 48214
{(a*b + a*c + b*c)/2, (-a^2 - b^2 - c^2)/2}, 48215
{(a*b + a*c + b*c)/2, 0}, 48216
{(a*b + a*c + b*c)/2, (a^2 + b^2 + c^2)/2}, 48217
{(a*b*c)/(2*(a + b + c)), (a*b*c)/(2*(a + b + c))}, 48218
{(a^2 + b^2 + c^2)/2, a^2 + b^2 + c^2}, 48219
{(a^2 + b^2 + c^2)/2, a*b + a*c + b*c}, 48220
{(a*b + a*c + b*c)/2, a*b + a*c + b*c}, 48221
{(a^2 + b^2 + c^2)/2, 2*(a^2 + b^2 + c^2)}, 48222
{a^2 + b^2 + c^2, -2*(a^2 + b^2 + c^2)}, 48223
{a*b + a*c + b*c, -2*(a^2 + b^2 + c^2)}, 48224
{a*b + a*c + b*c, -2*(a*b + a*c + b*c)}, 48225
{a^2 + b^2 + c^2, -(a*b) - a*c - b*c}, 48226
{a*b + a*c + b*c, -a^2 - b^2 - c^2}, 48227
{(a*b*c)/(a + b + c), -((a*b*c)/(a + b + c))}, 48228
{a*b + a*c + b*c, (-(a*b) - a*c - b*c)/2}, 48229
{(a*b*c)/(a + b + c), 0}, 48230
{a^2 + b^2 + c^2, (a^2 + b^2 + c^2)/2}, 48231
{a*b + a*c + b*c, (a^2 + b^2 + c^2)/2}, 48232
{a*b + a*c + b*c, (a*b + a*c + b*c)/2}, 48233
{a^2 + b^2 + c^2, a*b + a*c + b*c}, 48234
{a*b + a*c + b*c, a^2 + b^2 + c^2}, 48235
{a^2 + b^2 + c^2, 2*(a^2 + b^2 + c^2)}, 48236
{a^2 + b^2 + c^2, 2*(a*b + a*c + b*c)}, 48237
{a*b + a*c + b*c, 2*(a*b + a*c + b*c)}, 48238
{2*(a^2 + b^2 + c^2), -2*(a^2 + b^2 + c^2)}, 48239
{2*(a^2 + b^2 + c^2), -2*(a*b + a*c + b*c)}, 48240
{2*(a*b + a*c + b*c), -2*(a^2 + b^2 + c^2)}, 48241
{2*(a*b + a*c + b*c), -2*(a*b + a*c + b*c)}, 48242
{(2*a*b*c)/(a + b + c), (-2*a*b*c)/(a + b + c)}, 48243
{2*(a*b + a*c + b*c), -(a*b) - a*c - b*c}, 48244
{2*(a*b + a*c + b*c), (-a^2 - b^2 - c^2)/2}, 48245
{(2*a*b*c)/(a + b + c), 0}, 48246
{2*(a^2 + b^2 + c^2), (a^2 + b^2 + c^2)/2}, 48247
{2*(a^2 + b^2 + c^2), (a*b + a*c + b*c)/2}, 48248
{2*(a*b + a*c + b*c), (a^2 + b^2 + c^2)/2}, 48249
{2*(a^2 + b^2 + c^2), a^2 + b^2 + c^2}, 48250
{2*(a^2 + b^2 + c^2), a*b + a*c + b*c}, 48251
{2*(a*b + a*c + b*c), a^2 + b^2 + c^2}, 48252
{2*(a*b + a*c + b*c), a*b + a*c + b*c}, 48253
{2*(a*b + a*c + b*c), 2*(a^2 + b^2 + c^2)}, 48254


X(48156) = X(2)X(514)∩X(523)X(7840)

Barycentrics    (b - c)*(a^2 + a*b + 2*b^2 + a*c - b*c + 2*c^2) : :
X(48156) = 7 X[2] - 8 X[44432], 3 X[2] - 4 X[47757], 5 X[2] - 4 X[47766], 2 X[4379] - 3 X[6548], 3 X[31992] - 4 X[47778], 4 X[44432] - 7 X[44435], 6 X[44432] - 7 X[47757], 10 X[44432] - 7 X[47766], 12 X[44432] - 7 X[47771], 16 X[44432] - 7 X[47773], 3 X[44435] - 2 X[47757], 5 X[44435] - 2 X[47766], 3 X[44435] - X[47771], 4 X[44435] - X[47773], 5 X[47757] - 3 X[47766], 8 X[47757] - 3 X[47773], 6 X[47766] - 5 X[47771], 8 X[47766] - 5 X[47773], 4 X[47771] - 3 X[47773], 2 X[650] + X[47651], 2 X[693] + X[47653], 4 X[693] - X[47659], X[693] + 2 X[47960], 2 X[47653] + X[47659], X[47653] - 4 X[47960], X[47659] + 8 X[47960], X[47792] + 4 X[47960], 2 X[1491] + X[47688], 2 X[2526] + X[47692], 2 X[16892] + X[20295], 4 X[3004] - X[17494], 2 X[3004] + X[47652], X[17494] + 2 X[47652], 2 X[3716] + X[47931], 4 X[3776] - X[7192], 2 X[3776] + X[47958], X[7192] + 2 X[47958], 2 X[3835] + X[47923], 4 X[3837] - X[47693], 4 X[4025] - X[26853], 2 X[4106] + X[47677], 2 X[4369] + X[47916], 2 X[4382] + X[17161], 2 X[4458] + X[47943], X[4467] + 2 X[23729], 2 X[4874] + X[47925], 4 X[4885] - X[47662], 2 X[4885] + X[47919], X[47662] + 2 X[47919], 2 X[4932] + X[47907], 2 X[26275] - 3 X[47797], 4 X[26275] - 3 X[47805], X[14779] + 2 X[47674], 8 X[21212] - 5 X[27013], 4 X[21212] - X[48101], 5 X[27013] - 2 X[48101], 4 X[23813] - X[47665], 2 X[24720] + X[47924], 2 X[25259] - 5 X[26798], 5 X[26798] - 4 X[47786], 4 X[25380] - X[48146], 4 X[25666] - X[48130], 5 X[26777] - 2 X[47663], X[26824] + 2 X[45746], 5 X[26985] - 2 X[47660], 5 X[26985] - 4 X[47788], 7 X[27115] - 4 X[47890], 4 X[30792] - 3 X[47809], X[31290] + 2 X[47676], X[31290] - 4 X[47995], X[47676] + 2 X[47995], X[47694] + 2 X[47968], X[47691] + 2 X[48007], 5 X[31209] - 2 X[48095], 4 X[31286] - X[48138], 4 X[31287] - X[48132], 2 X[45745] + X[47650], X[47657] + 2 X[48125], X[47930] + 2 X[48049], X[47945] - 4 X[47999], 2 X[47950] + X[48107], 2 X[47961] + X[48108]

X(48156) lies on these lines: {2, 514}, {523, 7840}, {614, 47970}, {650, 47651}, {661, 28890}, {663, 17024}, {693, 20950}, {812, 47894}, {824, 21297}, {918, 47759}, {1491, 31079}, {2526, 47692}, {2530, 29128}, {2786, 16892}, {3004, 6084}, {3006, 47725}, {3716, 47931}, {3776, 4817}, {3835, 47923}, {3837, 31096}, {4025, 26853}, {4040, 7191}, {4106, 47677}, {4369, 47916}, {4378, 26249}, {4382, 17161}, {4430, 9029}, {4449, 29815}, {4453, 47763}, {4458, 47943}, {4467, 23729}, {4728, 28863}, {4762, 46915}, {4776, 30520}, {4778, 47798}, {4789, 4927}, {4802, 44429}, {4874, 47925}, {4885, 47662}, {4932, 47907}, {4977, 26275}, {5990, 20045}, {6636, 44408}, {14779, 47674}, {17496, 29126}, {21115, 28840}, {21212, 27013}, {21301, 29110}, {21302, 33090}, {23813, 47665}, {24720, 47924}, {25259, 26798}, {25380, 48146}, {25666, 48130}, {26277, 48141}, {26777, 47663}, {26824, 45746}, {26985, 30815}, {27115, 31194}, {28147, 47808}, {28175, 30792}, {28191, 47806}, {28195, 47804}, {28199, 45676}, {28209, 44433}, {28213, 47799}, {28229, 47800}, {28602, 31098}, {28851, 47774}, {28878, 31290}, {28882, 47776}, {29823, 47694}, {29831, 47728}, {29832, 47691}, {29840, 47712}, {30519, 31147}, {30565, 47756}, {31150, 47880}, {31209, 48095}, {31286, 48138}, {31287, 48132}, {45745, 47650}, {47657, 48125}, {47754, 47762}, {47784, 47892}, {47825, 47877}, {47930, 48049}, {47945, 47999}, {47950, 48107}, {47961, 48108}

X(48156) = midpoint of X(i) and X(j) for these {i,j}: {47652, 47782}, {47653, 47792}
X(48156) = reflection of X(i) in X(j) for these {i,j}: {2, 44435}, {4789, 4927}, {17494, 47782}, {25259, 47786}, {30565, 47756}, {31150, 47880}, {47659, 47792}, {47660, 47788}, {47762, 47754}, {47763, 4453}, {47771, 47757}, {47772, 4776}, {47773, 2}, {47776, 47886}, {47780, 6545}, {47782, 3004}, {47791, 21183}, {47792, 693}, {47805, 47797}, {47825, 47877}, {47869, 47871}, {47870, 4728}, {47892, 47784}, {48103, 28602}
X(48156) = anticomplement of X(47771)
X(48156) = crossdifference of every pair of points on line {902, 5008}
X(48156) = barycentric product X(514)*X(17305)
X(48156) = barycentric quotient X(17305)/X(190)
X(48156) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 47653, 47659}, {693, 47960, 47653}, {3004, 47652, 17494}, {3776, 47958, 7192}, {4885, 47919, 47662}, {21212, 48101, 27013}, {44435, 47771, 47757}, {47676, 47995, 31290}, {47757, 47771, 2}


X(48157) = X(2)X(1491)∩X(523)X(7840)

Barycentrics    (b - c)*(a^3 + 5*a*b^2 + 5*a*b*c + b^2*c + 5*a*c^2 + b*c^2) : :
X(48157) = 5 X[2] - 4 X[4874], 3 X[2] - 4 X[45323], 5 X[1491] - 2 X[4874], 3 X[1491] - 2 X[45323], 4 X[1491] - X[47694], 3 X[4874] - 5 X[45323], 8 X[4874] - 5 X[47694], 8 X[45323] - 3 X[47694], 2 X[31150] - 3 X[47825], 4 X[45676] - 3 X[47775], 2 X[2254] + X[47945], 4 X[2526] - X[46403], 2 X[2526] + X[47975], X[46403] + 2 X[47975], 2 X[48017] + X[48023], 2 X[4818] + X[48077], 3 X[4893] - 2 X[45673], 2 X[4913] + X[48020], X[17166] - 4 X[48066], 4 X[25380] - X[48153], 2 X[31148] - 3 X[47824], 4 X[45328] - 3 X[47824], 3 X[44429] - 2 X[45320], 4 X[45320] - 3 X[47834], 4 X[44561] - 3 X[47820], 4 X[44567] - 3 X[47804], 2 X[45313] - 3 X[47828], 4 X[45314] - 3 X[47805], 2 X[45314] - 3 X[47827], 2 X[45315] - 3 X[47810], 4 X[45315] - 3 X[47821], 2 X[45324] - 3 X[47816], 4 X[45339] - 3 X[47832], 4 X[45340] - 3 X[47833], 4 X[45663] - 3 X[47813], 2 X[45664] - 3 X[47814], 2 X[45685] - 3 X[47806], X[47688] - 4 X[48007], X[47698] + 2 X[48015], X[47909] + 2 X[48073], X[47969] - 4 X[48010]

X(48157) lies on these lines: {2, 1491}, {43, 4724}, {513, 14404}, {514, 3679}, {522, 31147}, {523, 7840}, {784, 31149}, {830, 45671}, {900, 47759}, {1992, 9014}, {2254, 28840}, {2526, 4762}, {4651, 4824}, {4777, 21297}, {4785, 48017}, {4794, 5313}, {4818, 48077}, {4893, 45673}, {4913, 48020}, {4948, 17494}, {4984, 6006}, {8678, 44550}, {17166, 48066}, {24720, 31330}, {25380, 48153}, {28209, 47892}, {31148, 45328}, {36848, 47780}, {44429, 45320}, {44433, 47784}, {44561, 47820}, {44567, 47804}, {45313, 47828}, {45314, 47805}, {45315, 47810}, {45324, 47816}, {45339, 47832}, {45340, 47833}, {45663, 47813}, {45664, 47814}, {45685, 47806}, {47688, 48007}, {47698, 48015}, {47909, 48073}, {47969, 48010}

X(48157) = reflection of X(i) in X(j) for these {i,j}: {2, 1491}, {17494, 4948}, {31148, 45328}, {44433, 47784}, {47694, 2}, {47780, 36848}, {47805, 47827}, {47821, 47810}, {47834, 44429}
X(48157) = crossdifference of every pair of points on line {5008, 8624}
X(48157) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2526, 47975, 46403}, {31148, 45328, 47824}


X(48158) = X(1)X(514)∩X(523)X(4800)

Barycentrics    (b - c)*(-a^3 + 4*a^2*b + a*b^2 + 2*b^3 + 4*a^2*c + 3*a*b*c + b^2*c + a*c^2 + b*c^2 + 2*c^3) : :
X(48158) = 2 X[4724] + X[47688], 2 X[47123] + X[47699], 2 X[47691] + X[47969], X[47691] + 2 X[48006], X[47694] + 2 X[47701], X[47924] + 2 X[48063], X[47969] - 4 X[48006], 2 X[30565] - 3 X[47821], 2 X[1638] - 3 X[47797], 4 X[1638] - 3 X[47824], 4 X[3716] - X[47693], 2 X[3716] + X[47702], X[47693] + 2 X[47702], 4 X[8689] - X[48138], 4 X[45326] - 3 X[47809], X[46403] + 2 X[47972], 2 X[47131] + X[47666], X[47686] + 2 X[48014], X[47692] + 2 X[48029], 2 X[47695] + X[47945], X[47695] + 2 X[47998], X[47945] - 4 X[47998], X[47697] + 2 X[47961], X[47705] + 2 X[48001], X[47709] + 2 X[48099], X[47713] + 2 X[48058], X[47717] + 2 X[48004]

X(48158) lies on these lines: {1, 514}, {2, 29144}, {522, 31147}, {523, 4800}, {900, 3004}, {1638, 47797}, {3716, 47693}, {3797, 4010}, {4024, 28169}, {4448, 47773}, {4581, 30909}, {4809, 47763}, {6006, 48015}, {7927, 47793}, {8689, 48138}, {28151, 47659}, {28165, 45676}, {28209, 47944}, {28871, 48021}, {28898, 48080}, {29021, 47840}, {29164, 47838}, {29168, 47796}, {29192, 30709}, {29204, 47772}, {31131, 47756}, {45326, 47809}, {46403, 47972}, {46919, 48069}, {47131, 47666}, {47686, 48014}, {47690, 47787}, {47692, 48029}, {47695, 47945}, {47697, 47961}, {47705, 48001}, {47709, 48099}, {47713, 48058}, {47717, 48004}

X(48158) = reflection of X(i) in X(j) for these {i,j}: {31131, 47756}, {47690, 47787}, {47763, 4809}, {47773, 4448}, {47824, 47797}, {47870, 4800}, {48069, 46919}
X(48158) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3716, 47702, 47693}, {47691, 48006, 47969}, {47695, 47998, 47945}


X(48159) = X(2)X(4977)∩X(523)X(7840)

Barycentrics    (b - c)*(a^3 + a^2*b + 3*a*b^2 + b^3 + a^2*c + a*b*c + 3*a*c^2 + c^3) : :
X(48159) = X[44433] - 4 X[44435], 3 X[44433] - 4 X[47798], 3 X[44435] - X[47798], 3 X[47797] - 2 X[47798], 3 X[44429] - 2 X[47806], 4 X[47806] - 3 X[47809], 2 X[650] + X[47686], X[693] + 2 X[48007], 2 X[1491] + X[47652], 2 X[2526] + X[47691], 2 X[3004] + X[46403], 2 X[3676] + X[47982], 2 X[3776] + X[48023], 2 X[3835] + X[47973], 4 X[3837] - X[47660], 2 X[3837] + X[47968], X[47660] + 2 X[47968], 2 X[4142] + X[48116], 2 X[4369] + X[47943], X[4382] + 2 X[4818], 2 X[4458] + X[48020], X[4467] + 2 X[24719], 2 X[4522] + X[47923], 4 X[4885] - X[47696], X[7192] + 2 X[47989], X[16892] + 2 X[48050], 2 X[21104] + X[47945], X[21146] + 2 X[47999], 2 X[24720] + X[47958], 5 X[24924] + X[47901], 4 X[25380] - X[48101], 4 X[25666] - X[48102], X[45746] + 2 X[48089], X[47651] + 2 X[48062], X[47667] + 2 X[48126], X[47676] + 2 X[48027], X[47690] + 2 X[47960], X[47938] + 2 X[48073], 2 X[47995] + X[48108], 2 X[48015] + X[48080]

X(48159) lies on these lines: {2, 4977}, {513, 4453}, {514, 14430}, {523, 7840}, {650, 47686}, {659, 31095}, {693, 48007}, {1491, 47652}, {2526, 47691}, {2530, 29029}, {2785, 48131}, {3004, 46403}, {3676, 47982}, {3776, 48023}, {3835, 47973}, {3837, 47660}, {4142, 48116}, {4369, 47943}, {4382, 4818}, {4458, 48020}, {4467, 24719}, {4522, 47923}, {4778, 31148}, {4802, 47808}, {4885, 47696}, {4927, 47834}, {6084, 47825}, {7192, 47989}, {16892, 48050}, {21104, 47945}, {21146, 47999}, {21204, 47813}, {24720, 47958}, {24924, 47901}, {25380, 48101}, {25666, 48102}, {28195, 47771}, {28209, 47799}, {28213, 47773}, {28220, 47803}, {28225, 47800}, {28229, 47766}, {28882, 47828}, {29362, 47782}, {30765, 48148}, {45323, 47885}, {45746, 48089}, {47651, 48062}, {47667, 48126}, {47676, 48027}, {47690, 47960}, {47756, 47821}, {47827, 47892}, {47938, 48073}, {47995, 48108}, {48015, 48080}

X(48159) = reflection of X(i) in X(j) for these {i,j}: {44433, 47797}, {47771, 47802}, {47773, 47807}, {47782, 47877}, {47797, 44435}, {47804, 47757}, {47805, 47799}, {47809, 44429}, {47813, 21204}, {47821, 47756}, {47834, 4927}, {47885, 45323}, {47892, 47827}
X(48159) = {X(3837),X(47968)}-harmonic conjugate of X(47660)


X(48160) = X(44)X(513)∩X(523)X(7840)

Barycentrics    a*(b - c)*(a^2 + 4*b^2 + 3*b*c + 4*c^2) : :
X(48160) = 8 X[650] - 5 X[659], 2 X[650] - 5 X[1491], X[650] + 5 X[2526], 4 X[650] - 5 X[47827], X[659] - 4 X[1491], X[659] + 8 X[2526], X[1491] + 2 X[2526], 5 X[2254] + X[48019], 4 X[2526] + X[47827], X[4784] + 2 X[48023], 2 X[9508] + X[48020], 2 X[14419] - 3 X[47893], X[4367] - 4 X[48066], X[4810] - 4 X[48050], 5 X[4879] - 2 X[4959], X[4879] - 4 X[48100], X[4959] - 10 X[48100], 2 X[4925] + X[47989], X[4963] + 2 X[48108], X[24719] + 2 X[48017], 5 X[30795] - 2 X[47694]

X(48160) lies on these lines: {44, 513}, {522, 47877}, {523, 7840}, {830, 14419}, {2530, 4160}, {2832, 4705}, {3004, 17161}, {3837, 47834}, {4367, 48066}, {4778, 47885}, {4810, 48050}, {4879, 4959}, {4925, 47989}, {4926, 31147}, {4948, 29362}, {4963, 48108}, {24719, 48017}, {28147, 48007}, {28175, 47968}, {28213, 48103}, {28217, 47759}, {28229, 48062}, {30795, 47694}, {44429, 47833}, {45323, 47804}, {47670, 47960}, {47774, 47884}, {47805, 47829}, {47816, 47872}

X(48160) = reflection of X(i) in X(j) for these {i,j}: {659, 47827}, {47804, 45323}, {47805, 47829}, {47826, 48030}, {47827, 1491}, {47833, 44429}, {47834, 3837}, {47872, 47816}
X(48160) = crossdifference of every pair of points on line {1, 5008}


X(48161) = X(513)X(4453)∩X(523)X(4800)

Barycentrics    (b - c)*(-a^3 + 3*a^2*b + a*b^2 + b^3 + 3*a^2*c + 3*a*b*c + a*c^2 + c^3) : :
X(48161) = 2 X[661] + X[47695], 4 X[676] - X[7192], X[693] + 2 X[48006], 4 X[3239] - X[47689], 4 X[3716] - X[47660], 2 X[3716] + X[47701], X[47660] + 2 X[47701], 4 X[3835] - X[47687], 2 X[3835] + X[47972], X[47687] + 2 X[47972], 2 X[4142] + X[4822], 2 X[4458] + X[48021], X[4467] + 2 X[48080], 2 X[4468] + X[47692], 2 X[4724] + X[47652], 2 X[4804] + X[47661], X[4979] - 4 X[13246], 2 X[7662] + X[47699], 2 X[20517] + X[48081], 2 X[23770] + X[47969], 5 X[31209] - 2 X[48069], X[44449] - 4 X[48043], 2 X[47123] + X[47666], 2 X[47131] + X[47698], X[47651] + 2 X[48061], X[47685] + 2 X[48014], X[47688] + 2 X[48055], X[47691] + 2 X[48029], X[47694] + 2 X[47998], X[47696] + 2 X[47961], X[47697] + 2 X[47995], X[47704] + 2 X[48001], X[47708] + 2 X[48099], X[47712] + 2 X[48058], X[47716] + 2 X[48004], X[47720] + 2 X[47966], X[47958] + 2 X[48063], X[47971] + 2 X[48037], 2 X[47979] + X[48107]

X(48161) lies on these lines: {513, 4453}, {522, 4776}, {523, 4800}, {661, 47695}, {676, 7192}, {693, 48006}, {3239, 47689}, {3667, 47886}, {3716, 47660}, {3800, 47793}, {3835, 47687}, {4142, 4822}, {4458, 48021}, {4467, 48080}, {4468, 47692}, {4724, 47652}, {4778, 47887}, {4789, 47832}, {4804, 47661}, {4931, 28161}, {4979, 13246}, {7662, 47699}, {20517, 48081}, {23770, 47969}, {29021, 47838}, {29142, 47840}, {29144, 47809}, {29168, 47839}, {31209, 48069}, {44449, 48043}, {47123, 47666}, {47131, 47698}, {47651, 48061}, {47685, 48014}, {47688, 48055}, {47691, 48029}, {47694, 47998}, {47696, 47961}, {47697, 47995}, {47704, 48001}, {47708, 48099}, {47712, 48058}, {47716, 48004}, {47720, 47966}, {47760, 47808}, {47762, 47800}, {47799, 47824}, {47811, 47892}, {47958, 48063}, {47971, 48037}, {47979, 48107}

X(48161) = reflection of X(i) in X(j) for these {i,j}: {4453, 47797}, {4789, 47832}, {30565, 47821}, {47762, 47800}, {47808, 47760}, {47809, 47822}, {47824, 47799}, {47892, 47811}
X(48161) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3716, 47701, 47660}, {3835, 47972, 47687}


X(48162) = X(44)X(513)∩X(523)X(4800)

Barycentrics    a*(b - c)*(a^2 - 2*a*b - 2*b^2 - 2*a*c - 5*b*c - 2*c^2) : :
X(48162) = X[649] + 2 X[48028], 4 X[650] - X[4784], 2 X[650] + X[48024], X[659] + 2 X[661], X[1491] + 2 X[48029], X[4724] + 2 X[48030], 2 X[4782] + X[4813], X[4784] + 2 X[48024], 3 X[4893] - X[47828], 2 X[9508] + X[48021], 2 X[47826] + X[47827], 3 X[47826] + X[47828], 3 X[47827] - 2 X[47828], 3 X[47822] - 2 X[47831], 4 X[47831] - 3 X[47833], X[4800] + 2 X[47775], X[663] + 2 X[47967], X[667] + 2 X[47997], 2 X[905] + X[47913], X[1019] + 2 X[47994], X[2530] + 2 X[48004], 2 X[3004] + X[48083], 2 X[3716] + X[4824], X[3777] + 2 X[47966], 2 X[3837] + X[47969], X[4705] + 2 X[48058], X[4010] + 2 X[48000], X[4040] + 2 X[48005], X[4063] + 2 X[48053], X[4367] + 2 X[47959], 2 X[4369] + X[47946], X[4449] + 2 X[47922], 2 X[4490] + X[4879], X[4490] + 2 X[48099], X[4879] - 4 X[48099], X[4498] + 2 X[48093], 4 X[4806] - X[4810], 2 X[4806] + X[17494], X[4810] + 2 X[17494], X[4834] + 2 X[48045], 2 X[4874] + X[47666], 2 X[4885] + X[47963], 4 X[4885] - X[48143], 2 X[47963] + X[48143], X[4963] - 4 X[47996], X[4983] + 2 X[48003], 2 X[6050] + X[47955], X[7192] + 2 X[47993], 2 X[7662] + X[47928], 2 X[8689] + X[47985], 2 X[11068] + X[47983], 2 X[14838] + X[47949], X[16892] + 2 X[48048], X[21146] - 4 X[25666], 2 X[21146] - 5 X[30795], X[21146] + 2 X[48001], 8 X[25666] - 5 X[30795], 2 X[25666] + X[48001], 5 X[30795] + 4 X[48001], 5 X[24924] + X[47904], 5 X[30835] + X[47927], 5 X[30835] - 2 X[48098], X[47927] + 2 X[48098], 5 X[31209] + X[47941], 2 X[31286] + X[47986], 2 X[43067] + X[47910], 2 X[45314] + X[47774], X[47694] + 2 X[48002], X[47701] + 2 X[48056], 2 X[47890] + X[47944], X[47924] + 2 X[48097], X[47925] + 2 X[48096], X[47926] + 2 X[48090], X[47929] + 2 X[48100], 2 X[47954] + X[48141], 2 X[47957] + X[48144], 2 X[47961] + X[48140], 2 X[47962] + X[48120], 2 X[47964] + X[48142], 2 X[47965] + X[48123], X[47968] + 2 X[48055], X[47970] + 2 X[48059], 2 X[47990] + X[48101], 2 X[47998] + X[48103], 2 X[47999] + X[48102]

X(48162) lies on these lines: {2, 4977}, {44, 513}, {514, 47822}, {522, 4948}, {523, 4800}, {663, 47967}, {667, 47997}, {900, 47825}, {905, 47913}, {1019, 47994}, {1643, 38348}, {2530, 48004}, {3004, 48083}, {3716, 4824}, {3777, 47966}, {3837, 47969}, {3887, 4705}, {4010, 48000}, {4040, 48005}, {4063, 48053}, {4122, 28161}, {4160, 25569}, {4367, 47959}, {4369, 47946}, {4379, 28195}, {4449, 47922}, {4490, 4879}, {4498, 48093}, {4776, 29362}, {4778, 47778}, {4802, 47832}, {4806, 4810}, {4834, 48045}, {4874, 47666}, {4885, 47963}, {4963, 47996}, {4983, 48003}, {6050, 47955}, {6372, 47893}, {7192, 47993}, {7662, 47928}, {8689, 47985}, {11068, 47983}, {14413, 47918}, {14838, 47949}, {16892, 48048}, {18001, 30571}, {18004, 28183}, {21146, 25666}, {23770, 28175}, {24924, 47904}, {28209, 47824}, {28213, 47780}, {28225, 47830}, {28229, 47779}, {29078, 47769}, {29246, 47814}, {29328, 31150}, {30835, 47927}, {31209, 47941}, {31286, 47986}, {43067, 47910}, {45314, 47774}, {45666, 47813}, {47694, 48002}, {47701, 48056}, {47783, 47877}, {47890, 47944}, {47924, 48097}, {47925, 48096}, {47926, 48090}, {47929, 48100}, {47954, 48141}, {47957, 48144}, {47961, 48140}, {47962, 48120}, {47964, 48142}, {47965, 48123}, {47968, 48055}, {47970, 48059}, {47990, 48101}, {47998, 48103}, {47999, 48102}

X(48162) = midpoint of X(i) and X(j) for these {i,j}: {661, 47811}, {4893, 47826}, {14413, 47918}, {47775, 47821}
X(48162) = reflection of X(i) in X(j) for these {i,j}: {659, 47811}, {4800, 47821}, {47813, 45666}, {47823, 47778}, {47824, 47829}, {47827, 4893}, {47833, 47822}, {47877, 47783}, {47889, 47839}
X(48162) = crosssum of X(i) and X(j) for these (i,j): {4977, 25557}, {17239, 28898}
X(48162) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 48024, 4784}, {4490, 48099, 4879}, {4806, 17494, 4810}, {4885, 47963, 48143}, {21146, 25666, 30795}, {25666, 48001, 21146}, {30835, 47927, 48098}


X(48163) = X(2)X(28209)∩X(523)X(7840)

Barycentrics    (b - c)*(2*a^3 + a^2*b + 6*a*b^2 + b^3 + a^2*c + 2*a*b*c - b^2*c + 6*a*c^2 - b*c^2 + c^3) : :
X(48163) = 2 X[26275] - 3 X[47799], 5 X[26275] - 6 X[47800], 7 X[26275] - 6 X[47801], 4 X[47757] - 3 X[47799], 5 X[47757] - 3 X[47800], 7 X[47757] - 3 X[47801], 5 X[47799] - 4 X[47800], 7 X[47799] - 4 X[47801], 7 X[47800] - 5 X[47801], 2 X[2526] + X[23770], 2 X[2977] + X[47686], 2 X[30792] - 3 X[44429], 4 X[30792] - 3 X[47807], 3 X[44429] - X[47771], 2 X[47771] - 3 X[47807], 2 X[24720] + X[47989]

X(48163) lies on these lines: {2, 28209}, {513, 1638}, {523, 7840}, {900, 44435}, {1491, 6084}, {2526, 23770}, {2530, 29126}, {2786, 48050}, {2977, 47686}, {3837, 47788}, {4778, 45315}, {4977, 30792}, {9013, 37631}, {24720, 28859}, {28175, 47808}, {28195, 47806}, {28213, 47809}, {28217, 47797}, {28220, 47766}, {28225, 47803}, {28602, 31090}, {28878, 48027}, {28890, 48047}, {28894, 48007}, {39386, 47798}, {45323, 47884}, {46403, 47782}, {47786, 48015}

X(48163) = midpoint of X(i) and X(j) for these {i,j}: {46403, 47782}, {47786, 48015}
X(48163) = reflection of X(i) in X(j) for these {i,j}: {26275, 47757}, {47771, 30792}, {47788, 3837}, {47807, 44429}, {47884, 45323}, {47890, 28602}
X(48163) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {26275, 47757, 47799}, {30792, 47771, 47807}, {44429, 47771, 30792}


X(48164) = X(2)X(513)∩X(523)X(7840)

Barycentrics    (b - c)*(-a^3 - 3*a*b^2 - a*b*c + b^2*c - 3*a*c^2 + b*c^2) : :
X(48164) = 3 X[2] - 4 X[47802], 5 X[2] - 4 X[47803], 4 X[36848] - X[47763], 3 X[44429] - 2 X[47802], 5 X[44429] - 2 X[47803], 3 X[44429] - X[47804], 4 X[44429] - X[47805], 5 X[47802] - 3 X[47803], 8 X[47802] - 3 X[47805], 6 X[47803] - 5 X[47804], 8 X[47803] - 5 X[47805], 4 X[47804] - 3 X[47805], X[649] + 2 X[48042], 2 X[650] + X[47685], 4 X[659] - 7 X[27115], 7 X[27115] - 8 X[47829], X[693] + 2 X[2526], 4 X[905] - X[31291], 4 X[1491] - X[17494], 2 X[1491] + X[46403], X[17494] + 2 X[46403], 2 X[2254] + X[20295], X[2254] + 2 X[48050], X[20295] - 4 X[48050], 4 X[2530] - X[17496], 2 X[2530] + X[21301], X[17496] + 2 X[21301], 2 X[3004] + X[47687], 2 X[3676] + X[48035], 4 X[3716] - 7 X[27138], 2 X[3776] + X[48077], 8 X[3837] - 5 X[26985], 4 X[3837] - X[47694], 5 X[26985] - 2 X[47694], 5 X[26985] - 4 X[47833], 2 X[4369] + X[48020], X[4382] + 2 X[48017], 4 X[4521] - X[48068], 2 X[4522] + X[47973], X[4560] - 4 X[48066], X[4813] + 2 X[48073], 4 X[4818] - X[17161], 4 X[4885] - X[47697], 2 X[4925] + X[23729], 3 X[6548] - 2 X[47887], X[7192] - 4 X[24720], X[7192] + 2 X[48023], 2 X[24720] + X[48023], 2 X[7659] + X[48079], 2 X[17072] + X[48122], X[17166] - 4 X[23815], 2 X[21146] + X[47945], X[21302] + 2 X[48131], 2 X[23789] + X[47948], X[25259] + 2 X[48015], 8 X[25380] - 5 X[27013], 4 X[25666] - X[48032], 5 X[26798] - 2 X[48080], X[26824] + 2 X[47975], X[26824] - 4 X[48089], X[47975] + 2 X[48089], 5 X[30835] - 2 X[48063], X[31290] - 4 X[48027], X[31290] + 2 X[48108], 2 X[48027] + X[48108], 2 X[43067] + X[47940], X[47653] + 2 X[47690], X[47653] - 4 X[48007], X[47690] + 2 X[48007], X[47676] + 2 X[48039], X[47686] + 2 X[48062], X[47689] + 2 X[47960], X[47693] + 2 X[47968], X[47969] - 4 X[48030], 2 X[47985] + X[48141], 2 X[47992] + X[48148], 2 X[48000] + X[48115], 2 X[48010] + X[48119]

X(48164) lies on these lines: {2, 513}, {514, 47808}, {522, 21297}, {523, 7840}, {649, 48042}, {650, 47685}, {659, 27115}, {669, 28399}, {693, 2526}, {830, 47796}, {900, 47797}, {905, 31291}, {1491, 17494}, {2254, 20295}, {2530, 2787}, {3004, 47687}, {3263, 20949}, {3667, 4750}, {3676, 48035}, {3716, 27138}, {3776, 48077}, {3837, 26985}, {4369, 48020}, {4382, 48017}, {4521, 48068}, {4522, 47973}, {4560, 29033}, {4778, 45670}, {4813, 48073}, {4818, 17161}, {4885, 47697}, {4925, 23729}, {4932, 30764}, {4977, 47773}, {5996, 8672}, {6004, 47840}, {6006, 47800}, {6548, 47887}, {7192, 24720}, {7378, 44426}, {7409, 16228}, {7659, 48079}, {8678, 47819}, {16830, 23814}, {17072, 48122}, {17166, 23815}, {20906, 31130}, {21007, 33854}, {21146, 47945}, {21302, 48131}, {23789, 47948}, {23796, 39586}, {25259, 48015}, {25380, 27013}, {25666, 48032}, {26275, 39386}, {26798, 48080}, {26824, 47975}, {27675, 28286}, {28209, 47807}, {28217, 44433}, {28225, 47766}, {28475, 44550}, {30709, 31149}, {30765, 48049}, {30835, 48063}, {31096, 31097}, {31290, 48027}, {43067, 47940}, {44432, 47801}, {47653, 47690}, {47676, 48039}, {47686, 48062}, {47689, 47960}, {47693, 47968}, {47775, 47810}, {47776, 47828}, {47780, 47812}, {47793, 47816}, {47969, 48030}, {47985, 48141}, {47992, 48148}, {48000, 48115}, {48010, 48119}

X(48164) = midpoint of X(46403) and X(47825)
X(48164) = reflection of X(i) in X(j) for these {i,j}: {2, 44429}, {659, 47829}, {17494, 47825}, {30709, 31149}, {44433, 47799}, {47694, 47833}, {47763, 47824}, {47771, 47806}, {47773, 47809}, {47775, 47810}, {47776, 47828}, {47780, 47812}, {47793, 47816}, {47798, 47757}, {47801, 44432}, {47804, 47802}, {47805, 2}, {47824, 36848}, {47825, 1491}, {47833, 3837}
X(48164) = anticomplement of X(47804)
X(48164) = crossdifference of every pair of points on line {3230, 5008}
X(48164) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1491, 46403, 17494}, {2254, 48050, 20295}, {2530, 21301, 17496}, {3837, 47694, 26985}, {24720, 48023, 7192}, {31094, 31095, 26985}, {44429, 47804, 47802}, {47690, 48007, 47653}, {47802, 47804, 2}, {47975, 48089, 26824}, {48027, 48108, 31290}


X(48165) = X(2)X(513)∩X(523)X(47793)

Barycentrics    (b - c)*(a^4 + a^3*b - a^2*b^2 - a*b^3 + a^3*c - 3*a^2*b*c - a*b^2*c + b^3*c - a^2*c^2 - a*b*c^2 + 2*b^2*c^2 - a*c^3 + b*c^3) : :
X(48165) = X[26144] + 2 X[47794], 2 X[650] + X[7650], X[656] + 2 X[3716], X[663] + 2 X[20316], 2 X[2605] + X[20293], 2 X[4057] + X[21301], X[4057] + 2 X[31946], X[21301] - 4 X[31946], X[4064] + 2 X[4142], X[4491] + 2 X[44316], 2 X[4521] + X[7661], X[4724] + 2 X[47843], X[4811] + 5 X[31209], X[4815] + 2 X[48003], 4 X[4874] - X[47844], X[4985] + 2 X[14838], X[6129] + 2 X[20317], 4 X[8043] - 7 X[27115], 2 X[8062] + X[17420], X[17494] + 2 X[30591], X[17496] - 4 X[31947], 4 X[21260] - X[44444], X[47694] + 2 X[47842], 4 X[45337] - X[45686]

X(48165) lies on these lines: {2, 513}, {406, 44426}, {522, 14429}, {523, 47793}, {650, 7650}, {656, 3716}, {659, 25686}, {663, 20316}, {834, 47840}, {966, 3063}, {1213, 21007}, {2605, 20293}, {3667, 26078}, {4010, 26049}, {4057, 21301}, {4064, 4142}, {4194, 16228}, {4491, 44316}, {4521, 7661}, {4724, 47843}, {4775, 19853}, {4778, 47795}, {4806, 27345}, {4811, 31209}, {4815, 48003}, {4874, 27527}, {4926, 27545}, {4977, 47796}, {4985, 14838}, {5257, 21390}, {6129, 20317}, {6371, 47839}, {8043, 27115}, {8062, 17420}, {17306, 40474}, {17321, 20906}, {17322, 20949}, {17494, 30591}, {17496, 31947}, {21146, 27193}, {21260, 44444}, {21959, 42312}, {23874, 47800}, {24457, 27529}, {25511, 48029}, {27045, 47694}, {45337, 45686}

X(48165) = {X(4057),X(31946)}-harmonic conjugate of X(21301)


X(48166) = X(513)X(1639)∩X(523)X(4800)

Barycentrics    (b - c)*(2*a^3 - 3*a^2*b - 2*a*b^2 + b^3 - 3*a^2*c - 6*a*b*c + 3*b^2*c - 2*a*c^2 + 3*b*c^2 + c^3) : :
X(48166) = X[659] + 2 X[14321], 4 X[2490] - X[4784], 2 X[2977] + X[48080], 2 X[3239] + X[48029], 2 X[3716] + X[48047], 2 X[3835] + X[48055], 2 X[4468] + X[23770], X[4490] + 2 X[4990], 2 X[4806] + X[47890], 2 X[4874] + X[48046], 2 X[4885] + X[48040], X[21104] + 2 X[48048], 5 X[30835] + X[48078], 2 X[47132] + X[47698]

X(48166) lies on these lines: {513, 1639}, {523, 4800}, {659, 14321}, {918, 47799}, {2490, 4784}, {2977, 48080}, {3239, 48029}, {3566, 47793}, {3716, 48047}, {3835, 48055}, {4120, 47811}, {4468, 23770}, {4490, 4990}, {4776, 4977}, {4778, 47879}, {4806, 47890}, {4874, 48046}, {4885, 48040}, {21104, 48048}, {28217, 28602}, {28846, 47803}, {28851, 47831}, {29252, 41800}, {29288, 47838}, {29328, 47884}, {30835, 48078}, {45326, 47823}, {47132, 47698}, {47769, 47804}, {47772, 47797}, {47826, 47874}

X(48166) = midpoint of X(i) and X(j) for these {i,j}: {4120, 47811}, {30565, 47821}, {47769, 47804}, {47772, 47797}, {47826, 47874}
X(48166) = reflection of X(i) in X(j) for these {i,j}: {47799, 47822}, {47807, 1639}, {47823, 45326}


X(48167) = X(2)X(659)∩X(523)X(7840)

Barycentrics    (b - c)*(-a^3 - 2*a*b^2 + a*b*c + 2*b^2*c - 2*a*c^2 + 2*b*c^2) : :
X(48167) = 4 X[2] - 5 X[30795], 3 X[2] - 4 X[45340], X[659] - 4 X[3837], 2 X[659] - 5 X[30795], 3 X[659] - 4 X[45314], 3 X[659] - 8 X[45340], X[659] + 2 X[46403], 8 X[3837] - 5 X[30795], 3 X[3837] - X[45314], 3 X[3837] - 2 X[45340], 2 X[3837] + X[46403], 15 X[30795] - 8 X[45314], 15 X[30795] - 16 X[45340], 5 X[30795] + 4 X[46403], 2 X[45314] + 3 X[46403], 4 X[45340] + 3 X[46403], 3 X[4728] - 2 X[45342], 3 X[4800] - 4 X[45342], X[31148] - 3 X[47812], 4 X[45320] - 3 X[47833], 4 X[551] - 3 X[25569], 3 X[36848] - 2 X[45328], X[44550] - 3 X[47819], X[1491] + 2 X[48089], X[4948] + 4 X[48089], 3 X[1635] - 4 X[45691], 2 X[1960] - 3 X[25055], 2 X[2254] + X[4810], 2 X[2526] + X[48120], X[4367] - 4 X[23815], 3 X[4448] - 4 X[45337], 3 X[4928] - 2 X[45337], X[21146] + 2 X[48050], X[4784] + 2 X[24719], X[4784] - 4 X[24720], X[24719] + 2 X[24720], 3 X[4809] - 4 X[45668], 3 X[21204] - 2 X[45668], 2 X[4874] + X[47685], X[4963] - 4 X[48027], X[4963] + 2 X[48143], 2 X[48027] + X[48143], 3 X[5054] - 2 X[44805], 3 X[19875] - X[21385], 3 X[26275] - 4 X[45318], 2 X[45318] - 3 X[45677], 2 X[45671] - 3 X[47893], X[31150] - 3 X[44429], 2 X[31150] - 3 X[47827], 3 X[44429] - 2 X[45323], 4 X[45323] - 3 X[47827], 2 X[44567] - 3 X[47802], 2 X[45313] - 3 X[47823], 2 X[45316] - 3 X[47841], 4 X[45324] - 3 X[47872], 4 X[45339] - 3 X[47822], 2 X[45673] - 3 X[47822], 2 X[45676] - 3 X[47810], X[47703] + 2 X[47999], X[47909] + 2 X[48135], X[47928] + 2 X[48126], X[48023] + 2 X[48098], 2 X[48030] + X[48119]

X(48167) lies on these lines: {2, 659}, {381, 2826}, {513, 4379}, {514, 31149}, {519, 21343}, {523, 7840}, {551, 25569}, {812, 36848}, {814, 44550}, {830, 47889}, {876, 7245}, {891, 3679}, {900, 903}, {1491, 4762}, {1635, 45691}, {1960, 25055}, {2254, 4810}, {2526, 48120}, {2821, 31162}, {2832, 14431}, {3766, 43270}, {3887, 30592}, {4367, 23815}, {4448, 4928}, {4486, 21146}, {4778, 45661}, {4784, 4785}, {4809, 21204}, {4874, 47685}, {4945, 23345}, {4951, 30520}, {4963, 48027}, {4977, 30565}, {5054, 44805}, {6084, 10712}, {6550, 31160}, {11236, 24097}, {11237, 30725}, {19875, 21385}, {24712, 24713}, {25574, 31145}, {26275, 45318}, {28209, 47759}, {28220, 47881}, {28470, 45667}, {28602, 47892}, {29070, 45671}, {29240, 45341}, {29362, 31150}, {30792, 47884}, {44567, 47802}, {45313, 47823}, {45316, 47841}, {45324, 47872}, {45339, 45673}, {45676, 47810}, {47703, 47999}, {47806, 47885}, {47909, 48135}, {47928, 48126}, {48023, 48098}, {48030, 48119}

X(48167) = midpoint of X(i) and X(j) for these {i,j}: {2, 46403}, {31131, 47871}
X(48167) = reflection of X(i) in X(j) for these {i,j}: {2, 3837}, {659, 2}, {4448, 4928}, {4800, 4728}, {4809, 21204}, {4948, 1491}, {26275, 45677}, {31150, 45323}, {45314, 45340}, {45673, 45339}, {47827, 44429}, {47884, 30792}, {47885, 47806}, {47892, 28602}
X(48167) = anticomplement of X(45314)
X(48167) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {40735, 39349}, {43077, 30578}
X(48167) = crosspoint of X(4555) and X(14621)
X(48167) = crosssum of X(1960) and X(2276)
X(48167) = crossdifference of every pair of points on line {1017, 5008}
X(48167) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {659, 3837, 30795}, {3837, 45314, 45340}, {3837, 46403, 659}, {24719, 24720, 4784}, {31150, 44429, 45323}, {31150, 45323, 47827}, {45314, 45340, 2}, {45339, 45673, 47822}, {48027, 48143, 4963}


X(48168) = X(2)X(900)∩X(523)X(47793)

Barycentrics    (b - c)*(a^4 + a^3*b - a^2*b^2 - a*b^3 + a^3*c - 3*a^2*b*c + b^3*c - a^2*c^2 + 2*b^2*c^2 - a*c^3 + b*c^3) : :
X(48168) = 3 X[2] + X[27545], 2 X[24959] + X[28396], X[26078] + 3 X[26144], 3 X[26144] - X[27545], 2 X[3837] + X[4491], X[4375] + 2 X[25356], X[4985] + 2 X[31947], X[14304] - 4 X[33528]

X(48168) lies on these lines: {2, 900}, {21, 39478}, {405, 39200}, {406, 39534}, {451, 44428}, {513, 47795}, {523, 47793}, {659, 24542}, {1213, 4435}, {2815, 5886}, {3716, 25493}, {3738, 32557}, {3766, 17322}, {3837, 4491}, {4375, 25356}, {4526, 17303}, {4777, 47794}, {4985, 31947}, {5257, 22108}, {9002, 47841}, {11110, 42741}, {14304, 33528}, {17320, 21433}, {21714, 26115}, {28209, 47796}, {39472, 45700}

X(48168) = midpoint of X(i) and X(j) for these {i,j}: {2, 26144}, {4800, 28284}, {26078, 27545}
X(48168) = complement of X(26078)
X(48168) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 27292, 28779}, {2, 27545, 26078}, {26078, 26144, 27545}


X(48169) = X(2)X(522)∩X(523)X(7840)

Barycentrics    (b - c)*(-a^3 + 2*a^2*b - 3*a*b^2 + 2*b^3 + 2*a^2*c - a*b*c + 3*b^2*c - 3*a*c^2 + 3*b*c^2 + 2*c^3) : :
X(48169) = 5 X[2] - 4 X[47800], 3 X[2] - 4 X[47806], 5 X[47798] - 6 X[47800], X[47798] - 3 X[47808], 3 X[47800] - 5 X[47806], 2 X[47800] - 5 X[47808], 2 X[47806] - 3 X[47808], 4 X[2526] - X[47653], 2 X[2526] + X[47689], X[47653] + 2 X[47689], X[4467] - 4 X[4925], X[7192] + 2 X[48077], X[17161] - 4 X[48017], X[17494] + 2 X[47687], X[26853] - 4 X[48069], 5 X[26985] - 2 X[47695], X[31290] - 4 X[48039], X[47659] - 4 X[47690]

X(48169) lies on these lines: {2, 522}, {513, 47772}, {523, 7840}, {900, 47805}, {1459, 29815}, {1491, 31094}, {2526, 47653}, {2785, 21302}, {3261, 31130}, {3263, 20954}, {3667, 47771}, {3920, 21173}, {4467, 4925}, {4661, 9000}, {4777, 44429}, {4926, 47804}, {4962, 4984}, {7192, 48077}, {15246, 39199}, {17161, 48017}, {17494, 47687}, {20293, 33091}, {21225, 31087}, {21301, 29029}, {26853, 48069}, {26985, 47695}, {28161, 44435}, {28183, 47797}, {28205, 47802}, {28221, 44433}, {31290, 48039}, {47659, 47690}

X(48169) = reflection of X(i) in X(j) for these {i,j}: {2, 47808}, {44433, 47807}, {47798, 47806}, {47805, 47809}
X(48169) = anticomplement of X(47798)
X(48169) = crossdifference of every pair of points on line {1055, 5008}
X(48169) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2526, 47689, 47653}, {47798, 47806, 2}, {47798, 47808, 47806}


X(48170) = X(320)X(350)∩X(523)X(7840)

Barycentrics    (b - c)*(-a^3 - a*b^2 + 3*a*b*c + 3*b^2*c - a*c^2 + 3*b*c^2) : :
X(48170) = 5 X[693] - 2 X[7662], 2 X[693] + X[46403], 5 X[693] + X[47685], 4 X[693] - X[47694], 7 X[693] - X[47697], X[693] + 2 X[48089], 2 X[4106] + X[48108], X[7192] + 2 X[24719], X[7192] - 4 X[48098], 4 X[7662] + 5 X[46403], 2 X[7662] + X[47685], 8 X[7662] - 5 X[47694], 14 X[7662] - 5 X[47697], 4 X[7662] - 5 X[47834], X[7662] + 5 X[48089], X[20295] + 2 X[21146], 4 X[23813] - X[48080], X[24719] + 2 X[48098], 5 X[46403] - 2 X[47685], 2 X[46403] + X[47694], 7 X[46403] + 2 X[47697], X[46403] - 4 X[48089], 4 X[47685] + 5 X[47694], 7 X[47685] + 5 X[47697], 2 X[47685] + 5 X[47834], X[47685] - 10 X[48089], 7 X[47694] - 4 X[47697], X[47694] + 8 X[48089], 2 X[47697] - 7 X[47834], X[47697] + 14 X[48089], X[47834] + 4 X[48089], 2 X[659] - 5 X[26985], 2 X[1491] + X[26824], 2 X[3716] + X[48115], 4 X[3835] - X[47969], 2 X[3835] + X[48119], X[47969] + 2 X[48119], 4 X[3837] - X[17494], 2 X[4978] + X[21301], X[4382] + 2 X[24720], 2 X[4500] + X[47973], X[4560] - 4 X[23815], 2 X[4830] - 5 X[24924], 4 X[4940] - X[47941], 2 X[6590] + X[47686], 2 X[14419] - 3 X[47796], 2 X[23770] + X[47687], 4 X[25380] - X[47932], 5 X[26798] - 2 X[48024], 7 X[27115] - 10 X[30795], X[47688] + 2 X[47690], 2 X[47652] + X[47693], X[31290] + 2 X[48143], X[47650] + 2 X[48062], X[47656] + 2 X[48007], X[47659] + 2 X[47968], X[47666] + 2 X[48126], 2 X[47672] + X[47945], X[47672] + 2 X[48050], X[47945] - 4 X[48050], X[47675] + 2 X[48027], X[47940] + 2 X[48134], X[47975] + 2 X[48125], 2 X[48042] + X[48142], 2 X[48049] + X[48148]

X(48170) lies on these lines: {2, 29362}, {320, 350}, {514, 30709}, {522, 6545}, {523, 7840}, {659, 26985}, {812, 47812}, {1491, 26824}, {1577, 2832}, {3716, 48115}, {3835, 47826}, {3837, 17494}, {4160, 4978}, {4382, 24720}, {4500, 47973}, {4560, 23815}, {4728, 47821}, {4762, 44429}, {4778, 31147}, {4789, 4977}, {4830, 24924}, {4927, 47797}, {4928, 47811}, {4940, 47941}, {4962, 47123}, {6084, 47809}, {6590, 28229}, {14419, 29070}, {23770, 28183}, {23882, 47819}, {25380, 47932}, {25381, 47828}, {26798, 48024}, {27115, 30795}, {28147, 47671}, {28161, 47691}, {28175, 47652}, {28195, 47774}, {28213, 47660}, {28221, 47695}, {29186, 47840}, {29188, 30592}, {29302, 47836}, {31150, 47802}, {31290, 48143}, {39747, 40086}, {45320, 47804}, {46915, 47877}, {47650, 48062}, {47656, 48007}, {47659, 47968}, {47666, 48126}, {47672, 47945}, {47675, 48027}, {47776, 47823}, {47805, 47833}, {47807, 47892}, {47940, 48134}, {47975, 48125}, {48042, 48142}, {48049, 48148}

X(48170) = midpoint of X(i) and X(j) for these {i,j}: {46403, 47834}, {47826, 48119}
X(48170) = reflection of X(i) in X(j) for these {i,j}: {17494, 47827}, {31150, 47802}, {46915, 47877}, {47694, 47834}, {47776, 47823}, {47797, 4927}, {47804, 45320}, {47805, 47833}, {47811, 4928}, {47821, 4728}, {47824, 47812}, {47825, 44429}, {47826, 3835}, {47827, 3837}, {47834, 693}, {47892, 47807}, {47969, 47826}
X(48170) = crossdifference of every pair of points on line {213, 5008}
X(48170) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 46403, 47694}, {693, 47685, 7662}, {693, 48089, 46403}, {3835, 48119, 47969}, {24719, 48098, 7192}, {47672, 48050, 47945}


X(48171) = X(513)X(47772)∩X(523)X(4800)

Barycentrics    (b - c)*(a^3 - a*b^2 + 2*b^3 - 3*a*b*c + 3*b^2*c - a*c^2 + 3*b*c^2 + 2*c^3) : :
X(48171) = 2 X[661] + X[47693], X[693] + 2 X[48088], 4 X[2977] - X[4467], 4 X[3239] - X[47691], 2 X[3716] + X[47700], 4 X[3835] - X[47688], 2 X[3835] + X[48118], X[47688] + 2 X[48118], 2 X[4088] + X[47694], 2 X[4122] + X[17494], X[4122] + 2 X[48056], X[17494] - 4 X[48056], 2 X[4468] + X[47690], 4 X[4468] - X[47969], 2 X[47690] + X[47969], 4 X[4522] - X[46403], 2 X[4522] + X[48094], X[46403] + 2 X[48094], X[4608] + 2 X[47928], 2 X[4824] + X[47659], 2 X[6590] + X[47698], 4 X[18004] - X[20295], 2 X[18004] + X[48103], X[20295] + 2 X[48103], X[24719] + 2 X[48097], 2 X[24720] + X[48117], X[25259] + 2 X[48062], 4 X[25380] - X[47930], X[47653] - 4 X[48030], 2 X[47660] + X[47945], X[47660] + 2 X[48047], X[47945] - 4 X[48047], X[47662] + 2 X[48027], X[47685] + 2 X[48096], X[47687] + 2 X[48055], X[47689] + 2 X[48029], X[47696] + 2 X[48039], X[47706] + 2 X[48099], X[47710] + 2 X[48058], X[47714] + 2 X[48004], X[47718] + 2 X[47966], 2 X[48042] + X[48139], 2 X[48049] + X[48146], 2 X[48050] + X[48130], 2 X[48087] + X[48108]

X(48171) lies on these lines: {513, 47772}, {514, 30709}, {522, 3158}, {523, 4800}, {661, 47693}, {693, 48088}, {824, 47825}, {826, 47793}, {918, 47809}, {1639, 47797}, {2977, 4467}, {3097, 30519}, {3239, 47691}, {3716, 47700}, {3835, 47688}, {4088, 47694}, {4122, 17494}, {4453, 47807}, {4468, 47690}, {4522, 46403}, {4608, 47928}, {4776, 4802}, {4824, 47659}, {4951, 29362}, {6590, 47698}, {14431, 29224}, {18004, 20295}, {23875, 47836}, {24719, 48097}, {24720, 48117}, {25259, 48062}, {25380, 47930}, {28147, 47765}, {28863, 47810}, {28890, 47812}, {29047, 47840}, {29078, 47776}, {29204, 47822}, {29260, 47838}, {29280, 47835}, {29354, 47796}, {29358, 47794}, {29370, 31992}, {30520, 44429}, {47653, 48030}, {47660, 47945}, {47662, 48027}, {47685, 48096}, {47687, 48055}, {47689, 48029}, {47696, 48039}, {47706, 48099}, {47710, 48058}, {47714, 48004}, {47718, 47966}, {47770, 47804}, {47827, 47894}, {47834, 47874}, {47879, 47887}, {48042, 48139}, {48049, 48146}, {48050, 48130}, {48087, 48108}

X(48171) = reflection of X(i) in X(j) for these {i,j}: {4453, 47807}, {47776, 47885}, {47797, 1639}, {47804, 47770}, {47821, 30565}, {47824, 47809}, {47834, 47874}, {47887, 47879}, {47894, 47827}
X(48171) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3835, 48118, 47688}, {4122, 48056, 17494}, {4468, 47690, 47969}, {4522, 48094, 46403}, {18004, 48103, 20295}, {47660, 48047, 47945}


X(48172) = X(2)X(522)∩X(523)X(4800)

Barycentrics    (b - c)*(a^3 - 2*a^2*b + a*b^2 - 2*a^2*c + a*b*c + 3*b^2*c + a*c^2 + 3*b*c^2) : :
X(48172) = 5 X[2] - 4 X[47830], 3 X[2] - 4 X[47831], 5 X[47828] - 6 X[47830], X[47828] - 3 X[47832], 3 X[47830] - 5 X[47831], 2 X[47830] - 5 X[47832], 2 X[47831] - 3 X[47832], X[8] - 4 X[4791], X[145] + 2 X[4474], 4 X[4010] - X[20295], 2 X[4010] + X[47694], 2 X[4106] + X[47697], X[7192] - 4 X[7662], X[7192] + 2 X[48080], X[7253] + 2 X[7650], 2 X[7662] + X[48080], X[20295] + 2 X[47694], 4 X[23813] - X[47685], X[46403] - 4 X[48090], 4 X[4800] - X[47775], 4 X[676] - X[4467], 4 X[1491] - 7 X[27138], 4 X[1577] - X[21302], 2 X[2254] - 5 X[26985], 5 X[3617] - 2 X[4814], 2 X[3700] + X[47695], 2 X[3716] + X[4804], 4 X[3716] - X[17494], 2 X[4804] + X[17494], X[4382] + 2 X[48063], X[47659] + 2 X[47701], 2 X[4500] + X[47972], X[4608] + 2 X[47699], 2 X[4724] + X[26824], 4 X[4806] - X[47945], 8 X[4874] - 5 X[27013], 4 X[4913] - 7 X[27115], 4 X[4940] - X[47940], X[25259] + 2 X[47123], 5 X[26798] - 2 X[48023], 5 X[30835] - 2 X[48017], X[31290] - 4 X[48043], X[31290] + 2 X[48142], 2 X[48043] + X[48142], X[47650] + 2 X[48061], X[47656] + 2 X[48006], X[47941] + 2 X[48134], X[47969] + 2 X[48120], X[47974] + 2 X[48125], 2 X[48037] + X[48141], 2 X[48049] + X[48153]

X(48172) lies on these lines: {2, 522}, {8, 4791}, {145, 4474}, {320, 350}, {523, 4800}, {676, 4467}, {784, 47840}, {812, 47805}, {900, 47824}, {1459, 29814}, {1491, 27138}, {1577, 3887}, {2254, 26985}, {3239, 4024}, {3261, 4441}, {3617, 4814}, {3667, 4379}, {3700, 47695}, {3716, 4804}, {3720, 21173}, {3798, 4962}, {3907, 23057}, {3952, 42722}, {4036, 4651}, {4151, 47793}, {4184, 39199}, {4382, 48063}, {4391, 14077}, {4468, 14779}, {4500, 47972}, {4608, 47699}, {4724, 26824}, {4777, 17264}, {4806, 47945}, {4874, 27013}, {4913, 27115}, {4926, 47823}, {4928, 30765}, {4940, 47940}, {4948, 28187}, {8714, 47796}, {14413, 17496}, {17135, 20293}, {25259, 47123}, {26798, 48023}, {28183, 47827}, {28213, 47944}, {30835, 48017}, {31290, 48043}, {47650, 48061}, {47656, 48006}, {47763, 47813}, {47776, 47804}, {47797, 47894}, {47836, 47875}, {47941, 48134}, {47969, 48120}, {47974, 48125}, {48037, 48141}, {48049, 48153}

X(48172) = anticomplement of X(47828)
X(48172) = midpoint of X(4804) and X(47811)
X(48172) = reflection of X(i) in X(j) for these {i,j}: {2, 47832}, {17494, 47811}, {17496, 14413}, {27486, 47800}, {47763, 47813}, {47775, 47821}, {47776, 47804}, {47780, 47834}, {47808, 47787}, {47811, 3716}, {47821, 4800}, {47824, 47833}, {47825, 47822}, {47828, 47831}, {47836, 47875}, {47894, 47797}
X(48172) = X(28899)-anticomplementary conjugate of X(2)
X(48172) = crossdifference of every pair of points on line {213, 1055}
X(48172) = barycentric product X(4391)*X(8543)
X(48172) = barycentric quotient X(8543)/X(651)
X(48172) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3716, 4804, 17494}, {4010, 47694, 20295}, {7662, 48080, 7192}, {47828, 47831, 2}, {47828, 47832, 47831}, {48043, 48142, 31290}


X(48173) = X(2)X(522)∩X(523)X(47793)

Barycentrics    (b - c)*(a^4 + a^3*b - a^2*b^2 - a*b^3 + a^3*c - 3*a^2*b*c + a*b^2*c + b^3*c - a^2*c^2 + a*b*c^2 + 2*b^2*c^2 - a*c^3 + b*c^3) : :
X(48173) = 2 X[1] + X[20293], X[8] - 4 X[20316], 2 X[26144] + X[47796], 2 X[905] + X[4811], 4 X[1125] - X[21173], 2 X[1459] - 5 X[3616], X[1769] + 2 X[8062], X[27545] + 2 X[47795], 2 X[3716] + X[4017], X[4391] + 2 X[6129], X[4560] + 2 X[7650], X[4581] - 4 X[4874], 2 X[4815] + X[17494], 2 X[4985] + X[17496], X[6332] + 2 X[7661], X[7253] + 2 X[21189], 2 X[17072] + X[42312], X[20294] + 2 X[21185]

X(48173) lies on these lines: {1, 20293}, {2, 522}, {7, 17215}, {8, 20316}, {21, 39199}, {513, 26144}, {523, 47793}, {657, 5296}, {905, 4811}, {1125, 21173}, {1459, 3616}, {1769, 8062}, {2254, 27193}, {3261, 17321}, {3667, 27545}, {3672, 20907}, {3716, 4017}, {4010, 27345}, {4036, 26115}, {4189, 39226}, {4357, 46402}, {4391, 6129}, {4397, 17922}, {4560, 7650}, {4581, 4874}, {4724, 26854}, {4804, 26049}, {4815, 17494}, {4926, 26078}, {4985, 17496}, {5603, 32475}, {6332, 7661}, {7253, 21189}, {7662, 27527}, {8672, 47821}, {11376, 40467}, {17072, 42312}, {17322, 20954}, {20294, 21185}, {20295, 23790}, {23678, 42337}, {23757, 27529}, {27293, 47694}, {28161, 47794}

X(48173) = crosspoint of X(86) and X(6335)
X(48173) = crosssum of X(42) and X(22383)
X(48173) = crossdifference of every pair of points on line {1055, 23222}


X(48174) = X(2)X(4802)∩X(325)X(523)

Barycentrics    (b - c)*(2*a^2*b + 2*a*b^2 + 2*b^3 + 2*a^2*c + a*b*c + b^2*c + 2*a*c^2 + b*c^2 + 2*c^3) : :
X(48174) = 2 X[1491] + X[47692], 2 X[3004] + X[47691], 4 X[3004] - X[47975], 4 X[3837] - X[47689], 2 X[23770] + X[45746], 3 X[44429] - 2 X[47808], 3 X[44435] - X[47808], X[47657] + 2 X[48120], 2 X[47691] + X[47975], 3 X[47797] - 2 X[47800], 4 X[47800] - 3 X[47804], 2 X[650] + X[47688], 2 X[659] + X[47651], 4 X[676] - X[47696], 2 X[2530] + X[47709], 2 X[3716] + X[47923], 2 X[3776] + X[47701], 4 X[3776] - X[48108], 2 X[47701] + X[48108], 2 X[4010] + X[47677], 2 X[4369] + X[47924], 2 X[4458] + X[47958], 4 X[4874] - X[47662], 4 X[4885] - X[47693], 2 X[4932] + X[47902], X[7192] + 2 X[47961], 2 X[7662] + X[47653], 2 X[16892] + X[48080], 2 X[21104] + X[47699], 4 X[21212] - X[48106], 4 X[21260] - X[47706], 4 X[23815] - X[47718], 2 X[24720] + X[47702], 4 X[25666] - X[48118], 5 X[31209] - 2 X[48103], 4 X[31286] - X[48146], X[47665] - 4 X[48090], 2 X[47676] + X[47941], X[47676] + 2 X[47998], X[47941] - 4 X[47998], X[47694] + 2 X[47960], X[47695] + 2 X[48007], X[47697] + 2 X[47968], X[47705] + 2 X[48010], X[47713] + 2 X[48066], X[47717] + 2 X[48012], X[47930] + 2 X[48043], X[47931] + 2 X[48063], X[47939] - 4 X[47990], X[47940] - 4 X[47999], 2 X[47944] + X[48107]

X(48174) lies on these lines: {2, 4802}, {325, 523}, {514, 14413}, {650, 47688}, {659, 47651}, {676, 47696}, {2530, 47709}, {2826, 47708}, {3667, 48015}, {3716, 47923}, {3776, 47701}, {4010, 47677}, {4369, 47924}, {4458, 4778}, {4874, 47662}, {4885, 47693}, {4926, 24719}, {4932, 47902}, {4977, 47798}, {7192, 47961}, {7662, 47653}, {16892, 48080}, {21104, 47699}, {21212, 48106}, {21260, 47706}, {23815, 47718}, {24720, 47702}, {25666, 48118}, {26275, 28213}, {28147, 47757}, {28151, 47802}, {28155, 47806}, {28161, 31131}, {28175, 47771}, {28179, 47807}, {28191, 47766}, {28195, 47805}, {28199, 47773}, {28229, 47801}, {28863, 47832}, {28890, 47826}, {28894, 47834}, {29021, 47819}, {29029, 44550}, {29047, 47814}, {29174, 47893}, {29260, 47816}, {30520, 47821}, {31209, 48103}, {31286, 48146}, {47665, 48090}, {47676, 47941}, {47694, 47960}, {47695, 48007}, {47697, 47968}, {47705, 48010}, {47713, 48066}, {47717, 48012}, {47754, 47824}, {47825, 47880}, {47930, 48043}, {47931, 48063}, {47939, 47990}, {47940, 47999}, {47944, 48107}

X(48174) = reflection of X(i) in X(j) for these {i,j}: {44429, 44435}, {47771, 47799}, {47773, 47803}, {47804, 47797}, {47809, 47757}, {47824, 47754}, {47825, 47880}
X(48174) = crossdifference of every pair of points on line {32, 41423}
X(48174) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3004, 47691, 47975}, {3776, 47701, 48108}, {47676, 47998, 47941}


X(48175) = X(325)X(523)∩X(513)X(14404)

Barycentrics    (b - c)*(4*a*b^2 + 5*a*b*c + b^2*c + 4*a*c^2 + b*c^2) : :
X(48175) = X[693] - 4 X[1491], 5 X[693] - 8 X[3837], X[693] + 2 X[47975], 7 X[693] - 4 X[48120], 5 X[1491] - 2 X[3837], 2 X[1491] + X[47975], 7 X[1491] - X[48120], 4 X[3004] - X[47692], 4 X[3837] - 5 X[44429], 4 X[3837] + 5 X[47975], 14 X[3837] - 5 X[48120], 7 X[44429] - 2 X[48120], 2 X[45746] + X[47689], X[47657] + 2 X[47690], 7 X[47975] + 2 X[48120], 2 X[649] + X[47940], 4 X[650] - X[47697], X[661] + 2 X[48017], 5 X[661] - 2 X[48037], 2 X[4765] + X[48035], 5 X[48017] + X[48037], 2 X[14431] - 3 X[47814], 2 X[2254] + X[47666], 5 X[2254] + X[47904], X[2254] + 2 X[48010], 5 X[47666] - 2 X[47904], X[47666] - 4 X[48010], X[47904] - 10 X[48010], 2 X[2526] + X[17494], 4 X[2526] - X[47685], 2 X[17494] + X[47685], 4 X[2977] - X[47696], X[4088] + 2 X[4818], 2 X[4088] + X[47677], 4 X[4818] - X[47677], X[4380] - 4 X[4913], X[4380] + 2 X[48023], 2 X[4913] + X[48023], X[4391] - 4 X[48012], X[4462] - 4 X[4705], X[4467] + 2 X[48039], 4 X[4522] - X[47665], X[4801] - 4 X[48066], X[4811] - 4 X[47842], 2 X[4824] + X[48108], X[4841] + 2 X[4925], 4 X[48030] - X[48080], X[4979] + 2 X[47985], 2 X[7659] + X[31290], 2 X[21196] + X[48077], 4 X[24720] - X[47675], 2 X[24720] + X[47934], X[47675] + 2 X[47934], 4 X[25380] - X[48142], 5 X[31209] - 2 X[47694], 5 X[31209] - 4 X[47803], 4 X[31286] - X[48153], 2 X[45745] + X[47687], 2 X[46403] + X[47664], X[47651] - 4 X[48007], X[47662] - 4 X[48062], X[47668] + 2 X[47703], 2 X[47679] + X[47718], 2 X[47683] + X[47721], X[47917] + 2 X[48073], X[47932] + 2 X[48042], X[47939] - 4 X[47992], X[47941] - 4 X[48002], 2 X[47945] + X[48107], X[47974] - 4 X[48000], 2 X[48008] + X[48020], 4 X[48027] - X[48079]

X(48175) lies on these lines: {325, 523}, {513, 14404}, {522, 4776}, {649, 47940}, {650, 47697}, {661, 3667}, {784, 14431}, {2254, 4778}, {2526, 17494}, {2977, 47696}, {4010, 28205}, {4088, 4818}, {4160, 44550}, {4380, 4913}, {4391, 48012}, {4462, 4705}, {4467, 48039}, {4522, 47665}, {4560, 28475}, {4728, 28161}, {4789, 47806}, {4801, 48066}, {4802, 36848}, {4811, 47842}, {4824, 28195}, {4841, 4925}, {4926, 48030}, {4948, 29362}, {4979, 47985}, {7659, 31290}, {21146, 28199}, {21196, 48077}, {24720, 28191}, {25380, 48142}, {28147, 47812}, {31209, 47694}, {31286, 48153}, {34258, 35353}, {39386, 48024}, {45323, 47833}, {45745, 47687}, {46403, 47664}, {47651, 48007}, {47662, 48062}, {47668, 47703}, {47679, 47718}, {47683, 47721}, {47762, 47828}, {47784, 47798}, {47802, 47834}, {47804, 47827}, {47813, 47830}, {47820, 47888}, {47917, 48073}, {47932, 48042}, {47939, 47992}, {47941, 48002}, {47945, 48107}, {47974, 48000}, {48008, 48020}, {48027, 48079}

X(48175) = midpoint of X(44429) and X(47975)
X(48175) = reflection of X(i) in X(j) for these {i,j}: {693, 44429}, {4776, 47810}, {4789, 47806}, {31150, 47825}, {44429, 1491}, {47694, 47803}, {47697, 47805}, {47762, 47828}, {47798, 47784}, {47804, 47827}, {47805, 650}, {47813, 47830}, {47820, 47888}, {47833, 45323}, {47834, 47802}
X(48175) = crossdifference of every pair of points on line {32, 16971}
X(48175) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1491, 47975, 693}, {2254, 48010, 47666}, {2526, 17494, 47685}, {4088, 4818, 47677}, {4913, 48023, 4380}, {24720, 47934, 47675}


X(48176) = X(2)X(4802)∩X(523)X(1639)

Barycentrics    (b - c)*(-a^3 + a^2*b + 3*a*b^2 + a^2*c + 6*a*b*c + b^2*c + 3*a*c^2 + b*c^2) : :
X(48176) = X[31150] + 2 X[45676], 3 X[47823] - 4 X[47830], 3 X[47827] - 2 X[47830], 3 X[4893] - X[47832], 3 X[47822] - 2 X[47832], X[649] + 2 X[48002], 2 X[650] + X[4824], X[659] + 2 X[48010], X[1491] + 2 X[48000], 2 X[2977] + X[4841], 2 X[3837] + X[47926], X[4122] + 2 X[45745], 2 X[4369] + X[47928], 2 X[4394] + X[47953], X[4560] + 2 X[47967], 2 X[4782] - 5 X[26777], 2 X[4782] + X[47945], 5 X[26777] + X[47945], X[4784] + 2 X[47996], 2 X[4818] + X[48083], 2 X[4874] + X[47934], 2 X[4913] + X[48024], 2 X[4932] + X[4963], X[7192] + 2 X[47964], 2 X[9508] + X[47666], 2 X[17494] + X[24719], X[17494] + 2 X[48030], X[24719] - 4 X[48030], X[17496] + 2 X[47922], X[21146] + 2 X[47962], 4 X[25380] - X[48143], 4 X[25666] - X[48120], 5 X[26985] - 2 X[48127], 4 X[31287] - X[48134], X[45746] + 2 X[48056], X[47653] + 2 X[48097], X[47663] + 2 X[47999]

X(48176) lies on these lines: {2, 4802}, {513, 14404}, {514, 47823}, {522, 4948}, {523, 1639}, {649, 48002}, {650, 4824}, {659, 48010}, {661, 29328}, {900, 47826}, {1491, 48000}, {2977, 4841}, {3837, 47926}, {4122, 45745}, {4369, 47928}, {4379, 28175}, {4394, 47953}, {4560, 47967}, {4705, 29066}, {4777, 47821}, {4782, 26777}, {4784, 47996}, {4800, 28161}, {4818, 48083}, {4874, 47934}, {4913, 48024}, {4932, 4963}, {4977, 47828}, {7192, 47964}, {9508, 47666}, {17494, 24719}, {17496, 47922}, {21146, 47962}, {25380, 48143}, {25666, 48120}, {26985, 48127}, {28147, 45685}, {28151, 47834}, {28155, 47831}, {28191, 47779}, {28195, 47824}, {28199, 47780}, {29340, 48005}, {29362, 47810}, {31287, 48134}, {45323, 47812}, {45746, 48056}, {47653, 48097}, {47663, 47999}

X(48176) = midpoint of X(47775) and X(47825)
X(48176) = reflection of X(i) in X(j) for these {i,j}: {4379, 47829}, {47812, 45323}, {47822, 4893}, {47823, 47827}, {47833, 47778}
X(48176) = crossdifference of every pair of points on line {4257, 10987}
X(48176) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {17494, 48030, 24719}, {26777, 47945, 4782}


X(48177) = X(2)X(29144)∩X(523)X(1639)

Barycentrics    (b - c)*(-a^3 + 2*a^2*b + a*b^2 + b^3 + 2*a^2*c + 2*a*b*c + a*c^2 + c^3) : :
X(48177) = X[4453] - 3 X[47797], 2 X[1639] - 3 X[47822], 3 X[47832] - X[47873], 2 X[676] + X[47998], X[3801] + 2 X[48099], 2 X[3837] + X[47972], 2 X[4142] + X[48123], 2 X[4458] + X[48024], X[4824] + 2 X[47123], X[4841] + 2 X[47132], 2 X[4874] + X[47701], X[4983] + 2 X[20517], X[21146] + 2 X[48006], 2 X[44902] - 3 X[47799], 4 X[44902] - 3 X[47823], X[47692] + 2 X[48056], X[47695] + 2 X[48030], X[47697] + 2 X[47999], X[47768] - 3 X[47800], X[47772] - 3 X[47821], X[47968] + 2 X[48063]

X(48177) lies on these lines: {2, 29144}, {513, 4453}, {514, 551}, {522, 1491}, {523, 1639}, {659, 28882}, {676, 1459}, {824, 4800}, {826, 47838}, {900, 31147}, {3716, 28863}, {3800, 47835}, {3801, 48099}, {3837, 47972}, {4120, 29370}, {4122, 4944}, {4142, 48123}, {4458, 28855}, {4777, 45342}, {4802, 7662}, {4824, 47123}, {4841, 47132}, {4874, 47701}, {4951, 45661}, {4958, 29078}, {4983, 20517}, {4984, 29328}, {7927, 47794}, {14419, 29132}, {14431, 29192}, {14432, 29172}, {21146, 21183}, {28151, 47770}, {28169, 45343}, {28225, 47983}, {28906, 48043}, {29017, 47840}, {29021, 47839}, {29142, 47841}, {29168, 47795}, {29204, 30565}, {29208, 47793}, {36848, 47757}, {44902, 47799}, {45666, 47771}, {47692, 48056}, {47695, 48030}, {47697, 47999}, {47768, 47800}, {47772, 47821}, {47968, 48063}

X(48177) = midpoint of X(21183) and X(48006)
X(48177) = reflection of X(i) in X(j) for these {i,j}: {4122, 4944}, {4951, 45661}, {21146, 21183}, {36848, 47757}, {47771, 45666}, {47790, 45342}, {47823, 47799}
X(48177) = crossdifference of every pair of points on line {172, 3730}


X(48178) = X(2)X(4977)∩X(325)X(523)

Barycentrics    (b - c)*(a^2*b + 4*a*b^2 + b^3 + a^2*c + 2*a*b*c - b^2*c + 4*a*c^2 - b*c^2 + c^3) : :
X(48178) = 2 X[1491] + X[23770], X[3004] + 2 X[3837], 3 X[44429] - X[47808], 3 X[44435] + X[47808], X[26275] - 4 X[47757], 3 X[26275] - 4 X[47800], 5 X[26275] - 4 X[47801], 3 X[47757] - X[47800], 5 X[47757] - X[47801], 3 X[47799] - 2 X[47800], 5 X[47799] - 2 X[47801], 5 X[47800] - 3 X[47801], 2 X[2977] + X[47652], 2 X[21212] + X[48050], 2 X[3676] + X[48027], 2 X[3776] + X[48047], 2 X[4369] + X[47989], 4 X[4521] - X[48096], X[4841] + 2 X[48098], 2 X[4885] + X[48007], X[7178] + 2 X[48100], 2 X[9508] + X[23729], 3 X[14475] - X[47813], 2 X[17069] + X[24719], X[21104] + 2 X[48030], X[21120] + 2 X[48137], 2 X[21188] + X[48092], 2 X[24720] + X[47998], 5 X[24924] + X[47943], 4 X[25666] - X[48055], 5 X[30795] + X[47968], 5 X[30835] + X[47973], 5 X[31209] + X[47686]

X(48178) lies on these lines: {2, 4977}, {325, 523}, {513, 1638}, {514, 47802}, {900, 47797}, {2530, 2826}, {2977, 47652}, {3667, 21212}, {3676, 48027}, {3776, 48047}, {4369, 4778}, {4521, 48096}, {4802, 47806}, {4841, 48098}, {4885, 48007}, {6084, 47827}, {6545, 47810}, {7178, 48100}, {9508, 23729}, {14475, 47813}, {17069, 24719}, {21104, 48030}, {21120, 48137}, {21146, 30765}, {21188, 48092}, {24720, 47998}, {24924, 47943}, {25666, 48055}, {28175, 30792}, {28183, 31131}, {28195, 47766}, {28209, 47804}, {28213, 47771}, {28217, 47798}, {28292, 48136}, {28882, 47830}, {29162, 47893}, {29288, 47816}, {29362, 47784}, {30574, 48131}, {30795, 47968}, {30835, 47973}, {31095, 47805}, {31209, 47686}, {39386, 44433}, {45677, 47833}, {47825, 47871}, {47829, 47884}

X(48178) = midpoint of X(i) and X(j) for these {i,j}: {6545, 47810}, {30574, 48131}, {44429, 44435}, {47825, 47871}
X(48178) = reflection of X(i) in X(j) for these {i,j}: {26275, 47799}, {47799, 47757}, {47803, 44432}, {47807, 47802}, {47809, 30792}, {47833, 45677}, {47884, 47829}


X(48179) = X(513)X(1638)∩X(523)X(1639)

Barycentrics    (b - c)*(-2*a^3 + 3*a^2*b + 2*a*b^2 + b^3 + 3*a^2*c + 4*a*b*c - b^2*c + 2*a*c^2 - b*c^2 + c^3) : :
X(48179) = 2 X[659] + X[23729], X[661] + 2 X[676], 4 X[2490] - X[48106], X[3004] + 2 X[3716], 2 X[4010] + X[4976], 2 X[4458] + X[48046], X[4824] + 2 X[47132], X[4841] + 2 X[7662], 2 X[4874] + X[47998], 2 X[4885] + X[48006], X[4897] + 2 X[48043], 2 X[4990] + X[21124], X[7178] + 2 X[48099], 4 X[7658] - X[7659], 2 X[13246] + X[48049], 2 X[17069] + X[48080], X[21104] + 2 X[48029], X[21120] + 2 X[48136], 7 X[27138] - X[47687], 5 X[30835] + X[47972], X[31148] - 4 X[45318], 4 X[31287] - X[48069], 2 X[34958] + X[47959]

X(48179) lies on these lines: {513, 1638}, {522, 47760}, {523, 1639}, {525, 47838}, {659, 23729}, {661, 676}, {918, 47797}, {2490, 48106}, {3004, 3716}, {3667, 47882}, {3800, 47794}, {3910, 47840}, {4010, 4976}, {4448, 4977}, {4458, 48046}, {4773, 29328}, {4776, 47798}, {4778, 47891}, {4824, 47132}, {4841, 7662}, {4874, 47998}, {4885, 48006}, {4897, 48043}, {4990, 21124}, {6005, 41800}, {6084, 47811}, {6372, 30724}, {7178, 48099}, {7658, 7659}, {13246, 48049}, {17069, 48080}, {21104, 48029}, {21120, 48136}, {27138, 47687}, {28147, 47770}, {29142, 47839}, {29144, 47807}, {30835, 47972}, {31148, 45318}, {31287, 48069}, {34958, 47959}, {44902, 47824}, {45326, 47809}, {45677, 47812}, {47767, 47803}, {47788, 47831}, {47826, 47887}

X(48179) = midpoint of X(i) and X(j) for these {i,j}: {4776, 47798}, {47797, 47821}, {47826, 47887}
X(48179) = reflection of X(i) in X(j) for these {i,j}: {1638, 47799}, {1639, 47822}, {47767, 47803}, {47788, 47831}, {47809, 45326}, {47812, 45677}, {47824, 44902}


X(48180) = X(2)X(4977)∩X(523)X(1639)

Barycentrics    (b - c)*(2*a^3 - 2*a^2*b - 3*a*b^2 - 2*a^2*c - 6*a*b*c + b^2*c - 3*a*c^2 + b*c^2) : :
X(48180) = X[45314] + 2 X[45315], 3 X[47778] - X[47830], 3 X[47829] - 2 X[47830], 3 X[4893] + X[47832], 3 X[47822] - X[47832], 2 X[650] + X[4806], X[3837] - 4 X[25666], 2 X[4369] + X[47993], X[4784] - 7 X[27115], X[4810] + 5 X[26777], 2 X[4874] + X[48002], X[4992] + 2 X[48003], 2 X[21212] + X[48048], 5 X[24924] + X[47946], 5 X[30795] + X[47969], 5 X[31209] + X[48024], 5 X[31250] + X[47963], 2 X[31286] + X[48028], 2 X[31288] + X[47997], 2 X[45337] + X[45676]

X(48180) lies on these lines: {2, 4977}, {513, 4763}, {523, 1639}, {650, 4806}, {900, 47821}, {3837, 25666}, {4129, 29340}, {4369, 47993}, {4379, 28213}, {4448, 47810}, {4784, 27115}, {4800, 28183}, {4802, 47831}, {4810, 26777}, {4874, 48002}, {4948, 28187}, {4992, 48003}, {21051, 29066}, {21212, 48048}, {24924, 47946}, {28175, 47775}, {28179, 47834}, {28195, 47779}, {28209, 47823}, {28217, 47828}, {29078, 47765}, {29362, 47760}, {30795, 47969}, {31209, 48024}, {31250, 47963}, {31286, 48028}, {31288, 47997}, {45337, 45676}, {45340, 47812}, {47777, 47803}

X(48180) = midpoint of X(i) and X(j) for these {i,j}: {4448, 47810}, {4800, 47825}, {4893, 47822}, {47775, 47833}, {47777, 47803}, {47821, 47827}, {47823, 47826}
X(48180) = reflection of X(i) in X(j) for these {i,j}: {47812, 45340}, {47829, 47778}


X(48181) = X(2)X(513)∩X(523)X(47794)

Barycentrics    (b - c)*(a^4 + a^3*b - a^2*b^2 - a*b^3 + a^3*c - 2*a^2*b*c - a*b^2*c + b^3*c - a^2*c^2 - a*b*c^2 + 2*b^2*c^2 - a*c^3 + b*c^3) : :
X(48181) = 4 X[33528] - X[44426], 2 X[650] + X[30591], X[667] + 2 X[31946], X[2605] + 2 X[20316], X[3733] - 4 X[31288], X[4057] + 2 X[21260], X[4391] + 2 X[31947], 2 X[4874] + X[47842], X[7650] + 2 X[8043], X[7650] + 5 X[31209], 2 X[8043] - 5 X[31209], 5 X[31251] - 2 X[44316]

X(48181) lies on these lines: {2, 513}, {406, 16228}, {451, 33528}, {523, 47794}, {650, 30591}, {667, 31946}, {834, 47839}, {1213, 3063}, {1639, 9209}, {2605, 20316}, {3733, 31288}, {4057, 21260}, {4132, 47835}, {4378, 25512}, {4391, 31947}, {4775, 16828}, {4782, 27293}, {4802, 47793}, {4874, 47842}, {4926, 26144}, {4977, 47795}, {7650, 8043}, {17322, 20906}, {17398, 20980}, {22095, 46838}, {26049, 48090}, {27193, 48098}, {28195, 47796}, {30764, 48057}, {31251, 44316}

X(48181) = {X(7650),X(31209)}-harmonic conjugate of X(8043)


X(48182) = X(2)X(900)∩X(325)X(523)

Barycentrics    (b - c)*(a^2*b - 4*a*b^2 + b^3 + a^2*c - 2*a*b*c + 3*b^2*c - 4*a*c^2 + 3*b*c^2 + c^3) : :
X(48182) = X[26275] - 4 X[30792], X[26275] + 2 X[31131], 3 X[26275] - 2 X[44433], 2 X[30792] + X[31131], 6 X[30792] - X[44433], 3 X[31131] + X[44433], 4 X[3837] - X[23770], 3 X[44429] - X[44435], X[44435] + 3 X[47808], X[47766] - 3 X[47806], 2 X[47766] - 3 X[47807], 4 X[44432] - 3 X[47799], 2 X[44432] - 3 X[47802], 2 X[676] - 5 X[30795], 2 X[2977] + X[46403], X[4010] + 2 X[4925], 2 X[4528] + X[21343], X[47773] - 3 X[47809], 3 X[14430] - X[21129], X[21116] - 3 X[47812], 2 X[24720] + X[48047], 5 X[26985] - 2 X[47132]

X(48182) lies on these lines: {2, 900}, {10, 23888}, {11, 17888}, {119, 120}, {210, 47329}, {325, 523}, {427, 39534}, {513, 1639}, {522, 4928}, {659, 14425}, {676, 30795}, {690, 5988}, {876, 4518}, {918, 36848}, {2254, 4120}, {2526, 47881}, {2786, 45328}, {2977, 46403}, {3290, 4526}, {3667, 3716}, {3766, 30758}, {4010, 4925}, {4049, 23887}, {4088, 21115}, {4448, 45326}, {4522, 30519}, {4528, 21343}, {4773, 9508}, {4777, 47757}, {4778, 47991}, {4784, 39386}, {4809, 44902}, {4926, 47800}, {4977, 47773}, {5020, 44929}, {6084, 10712}, {6550, 28603}, {7179, 43042}, {7484, 39200}, {7485, 39478}, {8889, 44428}, {14430, 21129}, {17069, 30764}, {17072, 28468}, {21116, 47812}, {24097, 39570}, {24720, 28851}, {25380, 45674}, {26985, 47132}, {28183, 47797}, {28195, 48056}, {28209, 47771}, {28217, 47804}, {28221, 47798}, {28294, 30580}, {28481, 47837}, {28602, 47884}, {28890, 45344}, {29126, 31149}, {29142, 47816}, {29144, 47756}, {29226, 44729}, {29278, 47893}, {45323, 47784}

X(48182) = complement of X(44433)
X(48182) = midpoint of X(i) and X(j) for these {i,j}: {2, 31131}, {2254, 4120}, {2526, 47881}, {4088, 21115}, {44429, 47808}, {46403, 47892}
X(48182) = reflection of X(i) in X(j) for these {i,j}: {2, 30792}, {659, 14425}, {4448, 45326}, {4773, 9508}, {4809, 44902}, {4927, 3837}, {23770, 4927}, {25923, 27728}, {26275, 2}, {45674, 25380}, {47784, 45323}, {47799, 47802}, {47807, 47806}, {47884, 28602}, {47892, 2977}
X(48182) = isotomic conjugate of X(9089)
X(48182) = isotomic conjugate of the isogonal conjugate of X(9032)
X(48182) = X(31)-isoconjugate of X(9089)
X(48182) = X(2)-Dao conjugate of X(9089)
X(48182) = crossdifference of every pair of points on line {32, 8649}
X(48182) = barycentric product X(76)*X(9032)
X(48182) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 9089}, {9032, 6}
X(48182) = {X(30792),X(31131)}-harmonic conjugate of X(26275)


X(48183) = X(2)X(900)∩X(523)X(1639)

Barycentrics    (b - c)*(2*a^3 - 2*a^2*b - a*b^2 - 2*a^2*c - 2*a*b*c + 3*b^2*c - a*c^2 + 3*b*c^2) : :
X(48183) = 2 X[3716] + X[3837], X[4806] + 2 X[4874], X[47779] - 3 X[47831], X[4893] - 3 X[47822], X[4893] + 3 X[47832], 2 X[676] + X[18004], X[45314] - 4 X[45337], X[45314] + 2 X[45342], 2 X[45337] + X[45342], X[3251] + 3 X[14431], X[47780] + 3 X[47821], X[47780] - 3 X[47833], 2 X[7662] + X[48002]

X(48183) lies on these lines: {2, 900}, {11, 15614}, {42, 21714}, {513, 3716}, {519, 28603}, {522, 47829}, {523, 1639}, {659, 21297}, {676, 18004}, {812, 45314}, {891, 17793}, {1011, 39478}, {1125, 14422}, {1575, 4526}, {1635, 4010}, {3251, 14431}, {3762, 14421}, {3766, 30963}, {3887, 6702}, {4120, 4809}, {4145, 27799}, {4213, 39534}, {4379, 28209}, {4435, 37673}, {4448, 4728}, {4479, 21433}, {4777, 47778}, {4926, 47830}, {4927, 4977}, {4944, 29370}, {4997, 23352}, {7662, 47777}, {9508, 45675}, {14315, 37691}, {14430, 25574}, {16058, 39200}, {23770, 28175}, {25569, 30709}, {28147, 48056}, {28179, 47775}, {28183, 47827}, {28187, 47825}, {28213, 47826}, {28217, 47823}, {28221, 47828}, {28602, 45326}, {29078, 47800}, {29144, 47879}, {29188, 45324}, {29236, 45316}, {29328, 47803}, {36848, 45340}, {39386, 47824}, {41144, 45338}, {47838, 47875}, {47840, 47872}

X(48183) = midpoint of X(i) and X(j) for these {i,j}: {2, 4800}, {659, 21297}, {1635, 4010}, {3716, 4928}, {3762, 14421}, {4120, 4809}, {4448, 4728}, {7662, 47777}, {25569, 30709}, {45342, 45666}, {47821, 47833}, {47822, 47832}, {47838, 47875}, {47840, 47872}
X(48183) = reflection of X(i) in X(j) for these {i,j}: {3837, 4928}, {9508, 45675}, {14422, 1125}, {28602, 45326}, {36848, 45340}, {45314, 45666}, {45666, 45337}, {48002, 47777}
X(48183) = X(28875)-complementary conjugate of X(2)
X(48183) = crossdifference of every pair of points on line {2176, 4257}
X(48183) = {X(45337),X(45342)}-harmonic conjugate of X(45314)


X(48184) = X(325)X(523)∩X(513)X(4379)

Barycentrics    (b - c)*(-(a*b^2) + a*b*c + 2*b^2*c - a*c^2 + 2*b*c^2) : :
X(48184) = 2 X[693] + X[1491], X[693] + 2 X[3837], 5 X[693] + X[47975], 4 X[693] - X[48120], X[1491] - 4 X[3837], 5 X[1491] - 2 X[47975], 2 X[1491] + X[48120], 10 X[3837] - X[47975], 8 X[3837] + X[48120], 5 X[44429] - X[47975], 4 X[44429] + X[48120], 4 X[47975] + 5 X[48120], 2 X[650] - 5 X[30795], X[659] - 4 X[4885], X[659] + 2 X[48089], 2 X[4885] + X[48089], 4 X[661] - X[47910], 5 X[661] - 2 X[47954], X[661] + 2 X[48098], 2 X[661] + X[48143], 5 X[47910] - 8 X[47954], X[47910] + 8 X[48098], X[47910] + 2 X[48143], X[47954] + 5 X[48098], 4 X[47954] + 5 X[48143], 4 X[48098] - X[48143], X[764] + 2 X[4791], 2 X[1577] + X[3777], X[1577] + 2 X[23815], X[3777] - 4 X[23815], X[2254] + 2 X[48090], X[2530] + 2 X[4823], 4 X[3239] - X[48083], X[4010] + 2 X[24720], 2 X[3776] + X[4122], 2 X[3835] + X[21146], 7 X[3835] - X[47980], 4 X[3835] - X[48024], 7 X[21146] + 2 X[47980], 2 X[21146] + X[48024], 4 X[47980] - 7 X[48024], 2 X[4106] + X[4784], 4 X[4129] - X[47913], 2 X[4369] + X[24719], X[4382] + 2 X[9508], 2 X[4391] + X[23765], X[4490] + 2 X[4978], X[4490] - 4 X[21260], X[4978] + 2 X[21260], 2 X[4782] - 5 X[24924], X[4801] + 2 X[21051], 2 X[4806] + X[48108], X[4810] - 4 X[23813], 2 X[4874] - 5 X[26985], 2 X[4874] + X[46403], 5 X[26985] + X[46403], 5 X[26985] - X[47805], X[4951] + 2 X[6545], X[4963] + 2 X[48133], 2 X[6590] + X[47968], 2 X[18004] + X[47676], 7 X[27138] - X[47969], 2 X[47672] + X[47928], X[47672] + 2 X[48030], X[47928] - 4 X[48030], 5 X[30835] + X[48119], X[31150] - 4 X[45340], 5 X[31251] - 2 X[48003], 2 X[45323] + X[47869], 2 X[47652] + X[48140], 2 X[47660] + X[47925], X[47675] + 2 X[48002], X[47917] + 2 X[48135], X[47934] + 2 X[48127], 2 X[48028] + X[48148]

X(48184) lies on these lines: {2, 29362}, {325, 523}, {513, 4379}, {514, 14431}, {522, 21204}, {650, 30795}, {659, 4885}, {661, 28195}, {764, 4791}, {812, 47823}, {814, 47796}, {1577, 3777}, {2254, 4926}, {2530, 4823}, {2832, 45324}, {3239, 48083}, {3667, 4010}, {3776, 4122}, {3835, 4778}, {4106, 4784}, {4129, 47913}, {4160, 31149}, {4367, 28475}, {4369, 24719}, {4382, 9508}, {4391, 23765}, {4444, 30519}, {4448, 47831}, {4453, 29078}, {4486, 28851}, {4490, 4978}, {4762, 47802}, {4776, 4977}, {4782, 24924}, {4801, 21051}, {4802, 47810}, {4804, 28205}, {4806, 48108}, {4810, 23813}, {4824, 28191}, {4874, 26985}, {4928, 47822}, {4951, 6545}, {4963, 48133}, {6084, 47807}, {6548, 29370}, {6590, 47968}, {8678, 47889}, {14413, 29236}, {14419, 29033}, {18004, 47676}, {21052, 29226}, {21297, 29328}, {23882, 47893}, {27138, 47969}, {28199, 47672}, {28229, 45685}, {29051, 47841}, {29070, 47795}, {29186, 47839}, {29246, 47840}, {29302, 47837}, {29350, 30592}, {30835, 48119}, {31150, 45340}, {31251, 48003}, {35353, 40013}, {39386, 48080}, {45323, 47825}, {45677, 47799}, {47652, 48140}, {47660, 47925}, {47675, 48002}, {47809, 47871}, {47917, 48135}, {47934, 48127}, {48028, 48148}

X(48184) = midpoint of X(i) and X(j) for these {i,j}: {693, 44429}, {4728, 47812}, {21297, 47824}, {46403, 47805}, {47803, 48089}, {47809, 47871}, {47825, 47869}
X(48184) = reflection of X(i) in X(j) for these {i,j}: {659, 47803}, {1491, 44429}, {4448, 47831}, {31150, 47829}, {44429, 3837}, {47799, 45677}, {47803, 4885}, {47805, 4874}, {47822, 4928}, {47825, 45323}, {47827, 47802}, {47829, 45340}, {47833, 45320}, {47885, 47807}
X(48184) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 48098, 48143}, {661, 48143, 47910}, {693, 1491, 48120}, {693, 3837, 1491}, {1577, 23815, 3777}, {3835, 21146, 48024}, {4885, 48089, 659}, {4978, 21260, 4490}, {26985, 46403, 4874}, {47672, 48030, 47928}


X(48185) = X(513)X(30565)∩X(523)X(1639)

Barycentrics    (b - c)*(a^3 - a*b^2 + b^3 - 2*a*b*c + 2*b^2*c - a*c^2 + 2*b*c^2 + c^3) : :
X(48185) = X[4951] + 2 X[10196], X[649] + 2 X[18004], 2 X[650] + X[4122], X[659] + 2 X[4522], X[693] + 2 X[48056], 2 X[2977] + X[3700], 4 X[3239] - X[4010], 2 X[3239] + X[48062], X[4010] + 2 X[48062], 2 X[3776] - 5 X[30795], 2 X[3835] + X[48103], 2 X[3837] + X[48094], X[4064] + 2 X[6133], X[4088] + 2 X[4874], 2 X[4468] + X[21146], X[4490] + 2 X[8045], 2 X[4806] + X[48106], X[4824] + 2 X[6590], 2 X[4885] + X[48088], 2 X[9508] + X[25259], X[24719] + 2 X[47890], 2 X[24720] + X[48083], 7 X[27138] - X[47688], 5 X[30835] + X[48118], X[47652] + 2 X[48097], X[47660] + 2 X[48030], X[47662] + 2 X[47999], 2 X[48048] + X[48108]

X(48185) lies on these lines: {513, 30565}, {514, 14431}, {522, 3971}, {523, 1639}, {525, 47835}, {649, 18004}, {650, 4122}, {659, 4522}, {693, 48056}, {812, 47885}, {824, 47827}, {826, 47794}, {918, 47807}, {1635, 29078}, {2977, 3700}, {3239, 4010}, {3776, 30795}, {3835, 48103}, {3837, 48094}, {4064, 6133}, {4088, 4874}, {4120, 29328}, {4468, 21146}, {4490, 8045}, {4789, 4802}, {4806, 48106}, {4809, 47803}, {4824, 6590}, {4885, 48088}, {6544, 29370}, {6546, 29362}, {7927, 47838}, {9508, 25259}, {14419, 29212}, {21052, 29082}, {23875, 47837}, {23877, 47872}, {24719, 47890}, {24720, 48083}, {27138, 47688}, {28175, 47756}, {28602, 47828}, {28863, 47877}, {29017, 47793}, {29047, 47839}, {29144, 47821}, {29156, 30709}, {29200, 47836}, {29204, 47797}, {29208, 47840}, {29288, 47841}, {29354, 47795}, {30519, 47830}, {30520, 47802}, {30835, 48118}, {36848, 47806}, {45326, 47799}, {45666, 47798}, {47652, 48097}, {47660, 48030}, {47662, 47999}, {47772, 47824}, {47825, 47870}, {47829, 47886}, {47833, 47879}, {48048, 48108}

X(48185) = midpoint of X(i) and X(j) for these {i,j}: {30565, 47809}, {47772, 47824}, {47825, 47870}
X(48185) = reflection of X(i) in X(j) for these {i,j}: {4809, 47803}, {36848, 47806}, {47798, 45666}, {47799, 45326}, {47822, 1639}, {47823, 47807}, {47828, 28602}, {47833, 47879}, {47886, 47829}
X(48185) = {X(3239),X(48062)}-harmonic conjugate of X(4010)


X(48186) = X(2)X(522)∩X(523)X(47794)

Barycentrics    (b - c)*(a^4 + a^3*b - a^2*b^2 - a*b^3 + a^3*c - 2*a^2*b*c + b^3*c - a^2*c^2 + 2*b^2*c^2 - a*c^3 + b*c^3) : :
X(48186) = X[1] + 2 X[20316], 2 X[650] + X[4815], 2 X[905] + X[4985], 4 X[1125] - X[1459], 5 X[3616] + X[20293], 7 X[3624] - X[21173], 2 X[3716] + X[23800], X[4040] + 2 X[47843], X[4064] + 2 X[20517], X[4086] + 2 X[6129], X[7650] + 2 X[14838], 2 X[8062] + X[21189], X[20294] + 2 X[21179], 2 X[20315] + X[21185]

X(48186) lies on these lines: {1, 20316}, {2, 522}, {21, 39226}, {405, 39199}, {513, 47795}, {523, 47794}, {650, 4815}, {657, 5257}, {905, 4985}, {1125, 1459}, {2457, 29304}, {3261, 17322}, {3616, 20293}, {3624, 21173}, {3667, 26144}, {3716, 23800}, {4040, 47843}, {4064, 20517}, {4086, 6129}, {4139, 47835}, {4357, 17215}, {4778, 47796}, {4814, 19874}, {4962, 26078}, {5886, 32475}, {6371, 47841}, {7650, 14838}, {8062, 21189}, {8654, 27732}, {8672, 47822}, {17306, 46399}, {17321, 20907}, {20294, 21179}, {20315, 21185}, {24720, 27193}, {25512, 31947}, {27045, 48142}, {28147, 47793}


X(48187) = X(2)X(4777)∩X(325)X(523)

Barycentrics    (b - c)*(2*a^2*b - 2*a*b^2 + 2*b^3 + 2*a^2*c - a*b*c + 3*b^2*c - 2*a*c^2 + 3*b*c^2 + 2*c^3) : :
X(48187) = 2 X[1491] + X[47689], 4 X[3837] - X[47692], 3 X[44429] - 2 X[44435], X[44435] - 3 X[47808], 2 X[47690] + X[47975], 5 X[44433] - 6 X[47801], 2 X[44433] - 3 X[47804], X[44433] - 3 X[47809], 5 X[47766] - 3 X[47801], 4 X[47766] - 3 X[47804], 2 X[47766] - 3 X[47809], 4 X[47801] - 5 X[47804], 2 X[47801] - 5 X[47809], 2 X[2526] + X[47693], 2 X[2530] + X[47706], 2 X[4088] + X[48108], 4 X[4522] - X[48080], 2 X[4705] + X[47718], X[4801] + 2 X[4808], 2 X[24720] + X[47700], 4 X[21260] - X[47709], 5 X[26985] - 2 X[47131], 4 X[44432] - 3 X[47797], 2 X[44432] - 3 X[47806], X[47685] + 2 X[48103], X[47687] + 2 X[48062], X[47710] + 2 X[48066], X[47714] + 2 X[48012], X[47941] - 4 X[48047], X[47974] - 4 X[48056], 2 X[48042] + X[48146]

X(48187) lies on these lines: {2, 4777}, {10, 21130}, {325, 523}, {513, 47772}, {514, 31131}, {522, 1635}, {900, 4951}, {2254, 30519}, {2526, 47693}, {2530, 47706}, {3667, 48016}, {3681, 9001}, {4088, 28851}, {4120, 4522}, {4411, 31130}, {4705, 47718}, {4776, 29144}, {4778, 47903}, {4782, 4926}, {4801, 4808}, {21115, 24720}, {21260, 47709}, {26985, 47131}, {28161, 44432}, {28165, 47802}, {28169, 47757}, {28183, 47798}, {28187, 47799}, {28195, 47945}, {28205, 47803}, {28294, 47728}, {29021, 47814}, {29047, 47819}, {29110, 44550}, {29128, 31149}, {29164, 47816}, {29204, 36848}, {29250, 47893}, {30580, 47729}, {47685, 48103}, {47687, 47892}, {47694, 47881}, {47710, 48066}, {47714, 48012}, {47941, 48047}, {47974, 48056}, {48042, 48146}

X(48187) = midpoint of X(i) and X(j) for these {i,j}: {21115, 47700}, {47687, 47892}
X(48187) = reflection of X(i) in X(j) for these {i,j}: {4120, 4522}, {21115, 24720}, {21130, 10}, {44429, 47808}, {44433, 47766}, {47691, 4927}, {47694, 47881}, {47729, 30580}, {47797, 47806}, {47798, 47807}, {47804, 47809}, {47892, 48062}, {48080, 4120}
X(48187) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {44433, 47766, 47804}, {44433, 47809, 47766}


X(48188) = X(2)X(29204)∩X(523)X(1639)

Barycentrics    (b - c)*(a^3 + a^2*b - a*b^2 + 2*b^3 + a^2*c - 2*a*b*c + 3*b^2*c - a*c^2 + 3*b*c^2 + 2*c^3) : :
X(48188) = X[4122] + 2 X[48062], 4 X[1639] - 3 X[47822], X[47693] + 2 X[48030], 2 X[3837] + X[48118], X[4453] - 3 X[47809], 2 X[4453] - 3 X[47823], 4 X[4522] - X[24719], 2 X[4522] + X[48103], X[24719] + 2 X[48103], 2 X[4874] + X[47700], 2 X[18004] + X[48106], X[21146] + 2 X[48088], 2 X[44902] - 3 X[47807], X[46403] + 2 X[48097], X[47690] + 2 X[48056], 2 X[48050] + X[48140]

X(48188) lies on these lines: {2, 29204}, {513, 47772}, {514, 31149}, {522, 659}, {523, 1639}, {650, 41269}, {693, 4036}, {812, 4951}, {826, 47835}, {1491, 28863}, {1635, 29370}, {3837, 48118}, {4010, 4944}, {4448, 4664}, {4453, 47809}, {4522, 24719}, {4784, 28906}, {4809, 47766}, {4874, 47700}, {4958, 29328}, {4977, 47908}, {4984, 29078}, {7950, 47794}, {14430, 29172}, {14431, 29160}, {18004, 48106}, {21052, 29332}, {21146, 48088}, {28151, 45676}, {28179, 47756}, {28602, 47886}, {29047, 47841}, {29122, 30709}, {29144, 30565}, {29146, 47793}, {29224, 35352}, {29260, 47839}, {29280, 47836}, {29358, 47837}, {30520, 36848}, {44902, 47807}, {46403, 48097}, {47690, 48056}, {48050, 48140}

X(48188) = reflection of X(i) in X(j) for these {i,j}: {4010, 4944}, {4448, 47770}, {4809, 47766}, {47823, 47809}, {47886, 28602}
X(48188) = crossdifference of every pair of points on line {2275, 4257}
X(48188) = {X(4522),X(48103)}-harmonic conjugate of X(24719)


X(48189) = X(320)X(350)∩X(523)X(1639)

Barycentrics    (b - c)*(a^3 - a^2*b + a*b^2 - a^2*c + 2*a*b*c + 3*b^2*c + a*c^2 + 3*b*c^2) : :
X(48189) = X[4010] + 2 X[7662], X[24719] + 2 X[47694], X[24719] - 4 X[48090], X[47694] + 2 X[48090], X[47780] - 3 X[47834], 4 X[47779] - 3 X[47823], 2 X[47779] - 3 X[47833], 2 X[4893] - 3 X[47822], X[4893] - 3 X[47832], X[4804] + 2 X[4874], X[3700] + 2 X[47132], 2 X[3716] + X[48120], X[4122] + 2 X[47123], 2 X[4806] + X[48142], 5 X[30795] - 2 X[48017], X[47946] + 2 X[48134], X[47969] + 2 X[48127]

X(48189) lies on these lines: {2, 4777}, {10, 4825}, {320, 350}, {514, 4800}, {522, 4809}, {523, 1639}, {676, 28183}, {784, 47841}, {900, 4379}, {1491, 4928}, {1635, 4804}, {3251, 29066}, {3700, 47132}, {3716, 48120}, {3789, 14077}, {4122, 47123}, {4151, 47835}, {4411, 4441}, {4448, 4762}, {4479, 4828}, {4776, 45342}, {4789, 29144}, {4802, 47821}, {4806, 48142}, {4824, 47777}, {4913, 45675}, {4926, 47824}, {4931, 29370}, {4948, 28169}, {23352, 30942}, {28151, 47775}, {28161, 47827}, {28165, 47825}, {28175, 47826}, {28187, 47829}, {28229, 47983}, {29204, 47870}, {29328, 47813}, {30795, 48017}, {31150, 45666}, {36848, 45320}, {47946, 48134}, {47969, 48127}

X(48189) = midpoint of X(i) and X(j) for these {i,j}: {1635, 4804}, {21297, 47694}
X(48189) = reflection of X(i) in X(j) for these {i,j}: {1491, 4928}, {1635, 4874}, {4776, 45342}, {4824, 47777}, {4825, 10}, {4913, 45675}, {4948, 47778}, {21297, 48090}, {24719, 21297}, {31150, 45666}, {36848, 45320}, {47822, 47832}, {47823, 47833}, {47827, 47831}, {47835, 47875}
X(48189) = crossdifference of every pair of points on line {213, 4257}
X(48189) = {X(47694),X(48090)}-harmonic conjugate of X(24719)


X(48190) = X(513)X(14404)∩X(523)X(7625)

Barycentrics    (b - c)*(-a^3 + 7*a*b^2 + 10*a*b*c + 2*b^2*c + 7*a*c^2 + 2*b*c^2) : :
X(48190) = X[7662] + 2 X[47975], X[31150] - 3 X[47825], 3 X[45320] - 4 X[45340], 2 X[45320] - 3 X[47802], 3 X[45323] - 2 X[45340], 4 X[45323] - 3 X[47802], 8 X[45340] - 9 X[47802], 3 X[650] - 2 X[45314], 4 X[1491] - X[48089], 4 X[4948] + X[48089], 2 X[2254] + X[47963], 2 X[45342] - 3 X[47760], 2 X[4913] + X[48027], 2 X[4818] + X[48088], X[7659] + 2 X[48002], 4 X[25380] - X[48134], X[47953] - 4 X[48010], X[31147] - 3 X[47810], X[31148] - 3 X[47828], 3 X[44429] - X[47869], 2 X[44561] - 3 X[47888], 4 X[44567] - 3 X[47803], 2 X[44567] - 3 X[47827], 2 X[45337] - 3 X[47778], 2 X[45663] - 3 X[47830], 2 X[45668] - 3 X[47882], 2 X[45685] - 3 X[47807], 4 X[45691] - 3 X[47761], 2 X[48017] + X[48029]

X(48190) lies on these lines: {2, 7662}, {513, 14404}, {514, 45328}, {522, 45315}, {523, 7625}, {650, 45314}, {784, 45664}, {824, 45344}, {900, 47764}, {1491, 4762}, {2254, 47963}, {4777, 45342}, {4785, 4913}, {4818, 48088}, {4928, 28169}, {6548, 28151}, {7659, 48002}, {8678, 45671}, {23882, 31149}, {25380, 48134}, {28161, 45339}, {28220, 47892}, {28602, 47881}, {28840, 47953}, {31147, 47810}, {31148, 47828}, {44429, 47869}, {44561, 47888}, {44567, 47803}, {45337, 47778}, {45663, 47830}, {45668, 47882}, {45685, 47807}, {45691, 47761}, {48017, 48029}

X(48190) = midpoint of X(i) and X(j) for these {i,j}: {2, 47975}, {1491, 4948}
X(48190) = reflection of X(i) in X(j) for these {i,j}: {7662, 2}, {45320, 45323}, {47803, 47827}, {47881, 28602}
X(48190) = crossdifference of every pair of points on line {1384, 16971}
X(48190) = {X(45320),X(45323)}-harmonic conjugate of X(47802)


X(48191) = X(2)X(28151)∩X(523)X(45326)

Barycentrics    (a - 2*b - 2*c)*(b - c)*(2*a^2 + 3*a*b + 3*a*c + b*c) : :
X(48191) = X[47775] + 3 X[47825], 5 X[47778] - 3 X[47831], 7 X[1491] - X[48115], X[4379] - 3 X[47827], X[4800] - 3 X[4893], X[4800] + 3 X[4948], X[4782] + 2 X[48010], 2 X[4913] + X[48028], 2 X[9508] + X[47964], 4 X[25380] - X[48135]

X(48191) lies on these lines: {2, 28151}, {513, 14404}, {523, 45326}, {812, 48030}, {1491, 48115}, {4379, 4802}, {4448, 47975}, {4705, 29236}, {4770, 4844}, {4777, 4800}, {4782, 48010}, {4824, 47762}, {4913, 48028}, {9508, 47964}, {25380, 48135}, {28147, 47829}, {28165, 47822}, {28175, 47830}, {28179, 47779}, {28195, 47828}, {28199, 47823}, {28205, 47821}, {29144, 47876}, {29148, 47967}, {29178, 48005}, {29204, 47782}, {47760, 48090}

X(48191) = midpoint of X(i) and X(j) for these {i,j}: {4448, 47975}, {4824, 47762}, {4893, 4948}
X(48191) = reflection of X(48090) in X(47760)
X(48191) = crossdifference of every pair of points on line {2163, 16971}
X(48191) = barycentric product X(i)*X(j) for these {i,j}: {4777, 29570}, {5235, 48002}
X(48191) = barycentric quotient X(i)/X(j) for these {i,j}: {29570, 4597}, {48002, 30588}


X(48192) = X(2)X(4802)∩X(523)X(7625)

Barycentrics    (b - c)*(-a^3 + 2*a^2*b + 3*a*b^2 + 2*b^3 + 2*a^2*c + 2*a*b*c + 3*a*c^2 + 2*c^3) : :
X(48192) = X[44433] + 5 X[44435], X[44433] - 5 X[47797], 3 X[44433] - 5 X[47798], 3 X[44435] + X[47798], 3 X[47797] - X[47798], 2 X[30792] - 5 X[47757], 4 X[30792] - 5 X[47802], 6 X[30792] - 5 X[47806], 3 X[47757] - X[47806], 3 X[47802] - 2 X[47806], 2 X[676] + X[48007], 2 X[1491] + X[47131], 2 X[3004] + X[7662], 2 X[3676] + X[47998], 2 X[3776] + X[48029], 2 X[4369] + X[47961], 2 X[4458] + X[48027], 2 X[4874] + X[47960], 2 X[20517] + X[48092], 2 X[21104] + X[47963], 5 X[24924] + X[47924], 4 X[25666] - X[48088], 7 X[31207] - X[48146], 5 X[31209] + X[47688], 4 X[31287] - X[48103]

X(48192) lies on these lines: {2, 4802}, {513, 4453}, {514, 47799}, {523, 7625}, {676, 48007}, {905, 29029}, {1491, 47131}, {2785, 48136}, {3004, 7662}, {3676, 47998}, {3776, 48029}, {4369, 47961}, {4458, 48027}, {4777, 44429}, {4778, 26275}, {4874, 47960}, {4977, 47800}, {20517, 48092}, {21104, 47963}, {21115, 47826}, {24924, 47924}, {25666, 48088}, {28147, 44432}, {28151, 47809}, {28165, 47808}, {28175, 47766}, {28195, 47804}, {28199, 47771}, {28205, 31131}, {28209, 47801}, {28220, 47805}, {28328, 30595}, {28863, 47831}, {28894, 47833}, {30520, 47822}, {30765, 48120}, {31207, 48146}, {31209, 47688}, {31287, 48103}, {44567, 47885}

X(48192) = midpoint of X(i) and X(j) for these {i,j}: {21115, 47826}, {44435, 47797}
X(48192) = reflection of X(i) in X(j) for these {i,j}: {47802, 47757}, {47803, 47799}, {47807, 44432}, {47885, 44567}


X(48193) = X(44)X(513)∩X(523)X(7625)

Barycentrics    a*(b - c)*(a^2 - 5*b^2 - 6*b*c - 5*c^2) : :
X(48193) = 5 X[650] - 2 X[659], X[650] + 2 X[1491], 2 X[650] + X[2526], X[659] + 5 X[1491], 4 X[659] + 5 X[2526], X[659] - 5 X[47827], 2 X[661] + X[7659], 4 X[1491] - X[2526], X[2526] + 4 X[47827], 2 X[4394] + X[48023], X[4790] - 4 X[9508], X[4790] + 2 X[48027], 2 X[9508] + X[48027], X[48026] - 4 X[48030], X[45320] - 4 X[45323], 5 X[45320] - 8 X[45340], 5 X[45323] - 2 X[45340], 4 X[45340] - 5 X[47802], X[905] + 2 X[48012], 2 X[2530] + X[47921], X[47965] + 2 X[48066], 2 X[2977] + X[48007], 4 X[2977] - X[48095], 2 X[48007] + X[48095], X[3669] + 2 X[4705], 4 X[3837] - X[48125], X[4106] + 2 X[4913], 2 X[4824] + X[48133], 2 X[4885] + X[47975], 2 X[4925] + X[48006], 2 X[7662] - 5 X[31250], X[14419] - 3 X[47888], 2 X[17069] + X[48039], 2 X[21146] + X[47920], X[30709] - 3 X[47814], 2 X[24720] + X[47962], 4 X[25380] - X[43067], 2 X[25380] + X[48010], X[43067] + 2 X[48010], 2 X[25666] + X[48017], 5 X[26777] + X[47685], 5 X[27013] + X[47940], 7 X[27115] - X[47697], X[47960] + 2 X[48062], 7 X[31207] - X[48153], 4 X[31287] - X[47694], X[47914] - 4 X[48002], X[47915] - 4 X[48005], X[47919] + 2 X[48103], 2 X[47968] + X[48132], 4 X[48056] - X[48124], 4 X[48059] - X[48128]

X(48193) lies on these lines: {44, 513}, {522, 47760}, {523, 7625}, {905, 4160}, {2512, 4139}, {2530, 47921}, {2832, 47965}, {2977, 28213}, {3004, 28147}, {3667, 45315}, {3669, 4705}, {3837, 48125}, {4106, 4913}, {4500, 4928}, {4762, 44429}, {4778, 45328}, {4802, 6545}, {4824, 48133}, {4885, 47834}, {4925, 48006}, {7662, 31250}, {8678, 14419}, {14838, 30234}, {17069, 48039}, {21146, 47920}, {23880, 30709}, {23882, 47816}, {24720, 47962}, {25380, 43067}, {25666, 48017}, {26777, 47685}, {27013, 47940}, {27115, 47697}, {28175, 47960}, {28195, 45676}, {28205, 45342}, {28229, 47890}, {28475, 45671}, {28894, 47809}, {31207, 48153}, {31287, 47694}, {35057, 42319}, {44567, 47804}, {47761, 47830}, {47782, 47808}, {47803, 47829}, {47807, 47881}, {47914, 48002}, {47915, 48005}, {47919, 48103}, {47968, 48132}, {48056, 48124}, {48059, 48128}

X(48193) = midpoint of X(i) and X(j) for these {i,j}: {1491, 47827}, {2254, 47826}, {44429, 47825}, {47782, 47808}, {47810, 47828}, {47834, 47975}
X(48193) = reflection of X(i) in X(j) for these {i,j}: {650, 47827}, {30234, 14838}, {45320, 47802}, {47761, 47830}, {47802, 45323}, {47803, 47829}, {47804, 44567}, {47834, 4885}, {47881, 47807}
X(48193) = crossdifference of every pair of points on line {1, 1384}
X(48193) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 1491, 2526}, {2977, 48007, 48095}, {9508, 48027, 4790}, {25380, 48010, 43067}


X(48194) = X(44)X(513)∩X(523)X(45326)

Barycentrics    a*(b - c)*(2*a^2 - a*b - 4*b^2 - a*c - 7*b*c - 4*c^2) : :
X(48194) = 4 X[650] - X[4782], 5 X[650] + X[48027], 2 X[650] + X[48030], 5 X[1491] + X[48032], 5 X[4782] + 4 X[48027], X[4782] + 2 X[48030], 5 X[4893] - X[47826], 3 X[4893] + X[47828], 2 X[9508] + X[48028], 5 X[47811] - X[48032], X[47826] + 5 X[47827], 3 X[47826] + 5 X[47828], 3 X[47827] - X[47828], 2 X[48027] - 5 X[48030], 3 X[47778] - X[47831], 2 X[905] + X[47922], 2 X[3004] + X[48097], 2 X[4369] + X[47964], X[4824] + 5 X[31209], 4 X[4885] - X[48127], 2 X[11068] + X[47999], 2 X[14838] + X[47967], X[24719] + 5 X[26777], 5 X[24924] + X[47928], 4 X[25666] - X[48090], 5 X[30795] + X[47926], 2 X[31286] + X[48002], 2 X[44567] + X[45676], 2 X[47962] + X[48135], 2 X[47965] + X[48137], 2 X[48000] + X[48098], 2 X[48003] + X[48100]

X(48194) lies on these lines: {2, 4802}, {44, 513}, {514, 47829}, {523, 45326}, {905, 47922}, {3004, 48097}, {4369, 47964}, {4379, 28199}, {4490, 14413}, {4522, 28183}, {4777, 17264}, {4800, 28205}, {4824, 31209}, {4885, 48127}, {4926, 47821}, {4948, 28165}, {4977, 47830}, {6546, 47877}, {11068, 47999}, {14838, 47967}, {24719, 26777}, {24924, 47928}, {25666, 48090}, {28151, 47833}, {28175, 47779}, {28195, 47775}, {28220, 47824}, {29198, 47888}, {29274, 47814}, {29328, 45315}, {30795, 47926}, {31286, 48002}, {44567, 45676}, {47692, 47834}, {47807, 47876}, {47962, 48135}, {47965, 48137}, {48000, 48098}, {48003, 48100}

X(48194) = midpoint of X(i) and X(j) for these {i,j}: {1491, 47811}, {4490, 14413}, {4893, 47827}, {4948, 47832}, {6546, 47877}, {47775, 47823}, {47807, 47876}, {47822, 47825}
X(48194) = {X(650),X(48030)}-harmonic conjugate of X(4782)


X(48195) = X(2)X(29144)∩X(523)X(45326)

Barycentrics    (b - c)*(-2*a^3 + 2*a^2*b + 2*a*b^2 + b^3 + 2*a^2*c + 3*a*b*c - b^2*c + 2*a*c^2 - b*c^2 + c^3) : :
X(48195) = X[1638] - 3 X[47799], 2 X[676] + X[48030], X[30565] + 3 X[47797], X[30565] - 3 X[47822], 5 X[30795] + X[47972], 2 X[34958] + X[47967]

X(48195) lies on these lines: {2, 29144}, {513, 1638}, {514, 1125}, {522, 45323}, {523, 45326}, {676, 48030}, {900, 3835}, {1639, 29204}, {4010, 27486}, {4448, 44435}, {4776, 4809}, {4777, 47784}, {4800, 47886}, {4806, 28867}, {4977, 45318}, {6006, 13246}, {6590, 28151}, {9508, 46919}, {28220, 47891}, {28855, 45668}, {28863, 45337}, {28882, 45314}, {28902, 48028}, {29017, 47839}, {29200, 47838}, {29208, 47794}, {29284, 47840}, {29328, 45679}, {29370, 45661}, {30565, 47797}, {30795, 47972}, {34958, 47967}

X(48195) = midpoint of X(i) and X(j) for these {i,j}: {4010, 27486}, {4448, 44435}, {4776, 4809}, {4800, 47886}, {26275, 47756}, {47797, 47822}
X(48195) = reflection of X(9508) in X(46919)


X(48196) = X(2)X(514)∩X(525)X(45326)

Barycentrics    (b - c)*(2*a^3 - 2*a*b^2 - 3*a*b*c + 2*b^2*c - 2*a*c^2 + 2*b*c^2) : :
X(48196) = 3 X[2] + X[47793], 5 X[2] - X[47796], X[47793] - 3 X[47794], 5 X[47793] + 3 X[47796], 3 X[47794] + X[47795], 5 X[47794] + X[47796], 5 X[47795] - 3 X[47796], 2 X[650] + X[4823], X[659] + 5 X[31251], X[663] + 5 X[1698], X[1019] - 7 X[31207], 2 X[1125] + X[4147], X[1577] + 5 X[31209], 2 X[3239] + X[21192], 7 X[3624] - X[4449], 8 X[3634] + X[4794], 4 X[3634] - X[17072], X[4794] + 2 X[17072], 2 X[3716] + X[48018], 2 X[3828] + X[45316], 2 X[3835] + X[48011], X[3960] + 2 X[20317], X[4063] + 5 X[30835], X[4129] + 2 X[31286], 2 X[4129] + X[48064], 4 X[31286] - X[48064], 2 X[4369] + X[47997], X[4401] + 2 X[21260], 2 X[4521] + X[21188], X[4724] + 17 X[19872], X[4791] + 2 X[14838], X[4791] + 8 X[31287], X[14838] - 4 X[31287], 2 X[4874] + X[48012], 2 X[4885] + X[48003], 13 X[19877] - X[21302], X[21051] + 2 X[31288], 2 X[44567] + X[45324], X[24720] - 10 X[31253], 5 X[24924] + X[47959], 4 X[25380] - X[48075], 4 X[25666] - X[48054], 5 X[31250] + X[47965]

X(48196) lies on these lines: {2, 514}, {406, 39532}, {474, 39476}, {525, 45326}, {650, 4823}, {659, 31251}, {663, 1698}, {784, 47829}, {830, 47803}, {1019, 31207}, {1125, 4147}, {1577, 31209}, {1635, 29270}, {1639, 23875}, {3239, 21192}, {3624, 4449}, {3634, 4794}, {3667, 26078}, {3716, 48018}, {3828, 45316}, {3835, 48011}, {3960, 20317}, {4063, 30835}, {4129, 31286}, {4151, 47831}, {4369, 47997}, {4401, 21260}, {4521, 21188}, {4546, 5552}, {4724, 19872}, {4763, 29013}, {4791, 14838}, {4874, 48012}, {4885, 48003}, {4928, 29302}, {4932, 27045}, {4944, 23883}, {4962, 27545}, {6002, 45675}, {6004, 45666}, {6005, 47822}, {8714, 47830}, {14431, 29344}, {15309, 47761}, {16408, 44408}, {17749, 22090}, {19877, 21302}, {21051, 31288}, {22154, 37679}, {23879, 47879}, {23882, 44567}, {24720, 31253}, {24924, 47959}, {25380, 48075}, {25666, 48054}, {27529, 44448}, {29021, 47807}, {29047, 47799}, {29164, 47809}, {29216, 45661}, {29260, 47797}, {29350, 47835}, {31250, 47965}, {44429, 47817}, {47804, 47816}, {47814, 47818}, {47827, 47875}, {47836, 47838}, {47872, 47888}

X(48196) = midpoint of X(i) and X(j) for these {i,j}: {2, 47794}, {1639, 41800}, {44429, 47817}, {47793, 47795}, {47804, 47816}, {47814, 47818}, {47822, 47837}, {47827, 47875}, {47835, 47839}, {47836, 47838}, {47872, 47888}
X(48196) = complement of X(47795)
X(48196) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 47793, 47795}, {4129, 31286, 48064}, {47794, 47795, 47793}


X(48197) = X(2)X(513)∩X(523)X(45326)

Barycentrics    (b - c)*(2*a^3 - a^2*b - 2*a*b^2 - a^2*c - 3*a*b*c + 2*b^2*c - 2*a*c^2 + 2*b*c^2) : :
X(48197) = 3 X[2] + X[47821], 5 X[2] - X[47824], X[47821] - 3 X[47822], 5 X[47821] + 3 X[47824], 3 X[47822] + X[47823], 5 X[47822] + X[47824], 5 X[47823] - 3 X[47824], 2 X[650] + X[48090], X[659] + 5 X[30835], 5 X[1698] + X[4775], 7 X[3624] - X[4378], 2 X[3676] + X[48048], 2 X[3835] + X[4782], X[4010] + 5 X[31209], X[4040] + 5 X[31251], X[4129] + 2 X[31288], 2 X[4369] + X[48028], 4 X[4521] - X[48056], X[4724] + 5 X[30795], X[4784] - 7 X[31207], X[4806] + 2 X[31286], X[4874] + 2 X[25666], 2 X[4874] + X[48030], 4 X[25666] - X[48030], 4 X[4885] - X[48098], 3 X[6544] - X[47885], X[9508] - 4 X[31287], X[24719] - 7 X[27138], 5 X[24924] + X[48024], 5 X[31250] + X[48029], 2 X[43067] + X[47954], 2 X[44567] + X[45342], X[45314] + 2 X[45339], X[45323] + 2 X[45337], 2 X[45340] + X[45673], 2 X[48000] + X[48127]

X(48197) lies on these lines: {2, 513}, {522, 47829}, {523, 45326}, {650, 25686}, {659, 30835}, {900, 47830}, {1639, 47799}, {1698, 4775}, {3063, 37673}, {3624, 4378}, {3676, 48048}, {3835, 4782}, {4010, 31209}, {4040, 31251}, {4083, 47794}, {4129, 31288}, {4147, 25574}, {4213, 16228}, {4369, 48028}, {4379, 28195}, {4521, 48056}, {4724, 30795}, {4763, 29328}, {4777, 41310}, {4784, 31207}, {4800, 4926}, {4802, 4893}, {4806, 31286}, {4874, 25666}, {4885, 48098}, {4928, 29362}, {4977, 47779}, {6544, 47885}, {9508, 31287}, {11230, 28537}, {14431, 29236}, {20906, 30963}, {24512, 39521}, {24719, 27138}, {24924, 48024}, {28151, 47834}, {28165, 47825}, {28199, 47775}, {28220, 47826}, {29078, 45661}, {29144, 47807}, {29198, 47795}, {29200, 41800}, {29204, 47797}, {29226, 47793}, {31250, 48029}, {43067, 47954}, {44567, 45342}, {45314, 45339}, {45323, 45337}, {45340, 45673}, {47835, 47840}, {47837, 47838}, {48000, 48127}

X(48197) = midpoint of X(i) and X(j) for these {i,j}: {2, 47822}, {1639, 47799}, {4448, 44429}, {4800, 47828}, {4893, 47833}, {47760, 47803}, {47778, 47831}, {47793, 47841}, {47794, 47839}, {47821, 47823}, {47827, 47832}, {47835, 47840}, {47837, 47838}
X(48197) = complement of X(47823)
X(48197) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 47821, 47823}, {4874, 25666, 48030}, {47822, 47823, 47821}


X(48198) = X(513)X(3716)∩X(523)X(7625)

Barycentrics    (b - c)*(a^3 - 2*a*b^2 + 3*b^2*c - 2*a*c^2 + 3*b*c^2) : :
X(48198) = 2 X[3837] + X[4874], X[3837] + 2 X[4885], X[4874] - 4 X[4885], 2 X[45320] + X[45323], X[45320] + 2 X[45340], X[45323] - 4 X[45340], X[693] + 5 X[30795], 5 X[30795] - X[47827], X[14419] - 3 X[47795], X[1491] + 5 X[26985], 5 X[26985] - X[47834], 2 X[3676] + X[18004], X[4791] + 2 X[19947], X[4978] + 5 X[31251], X[21146] + 5 X[30835], 5 X[30835] - X[47826], X[24719] + 5 X[24924], 2 X[25380] + X[48090], 2 X[25666] + X[48098], 7 X[27138] - X[48024], X[30709] + 3 X[47796], 5 X[31250] + X[48089]

X(48198) lies on these lines: {2, 29362}, {513, 3716}, {523, 7625}, {676, 28221}, {693, 30795}, {814, 14419}, {1491, 26985}, {1638, 29078}, {2832, 23815}, {3667, 45342}, {3676, 18004}, {4160, 21260}, {4728, 29328}, {4762, 47829}, {4778, 45339}, {4789, 47877}, {4791, 19947}, {4926, 45328}, {4927, 47807}, {4977, 47760}, {4978, 31251}, {14475, 29370}, {21146, 30835}, {24719, 24924}, {25380, 48090}, {25666, 48098}, {27138, 48024}, {28191, 45676}, {28195, 45315}, {28213, 47777}, {29246, 47839}, {29324, 30709}, {29366, 47841}, {30519, 45665}, {31250, 48089}, {36848, 47832}, {44429, 47833}, {47812, 47822}, {47814, 47889}, {47819, 47872}, {47871, 47885}

X(48198) = midpoint of X(i) and X(j) for these {i,j}: {693, 47827}, {1491, 47834}, {4728, 47823}, {4789, 47877}, {4927, 47807}, {21146, 47826}, {36848, 47832}, {44429, 47833}, {45320, 47802}, {47812, 47822}, {47814, 47889}, {47819, 47872}, {47871, 47885}
X(48198) = reflection of X(i) in X(j) for these {i,j}: {45323, 47802}, {47802, 45340}
X(48198) = crossdifference of every pair of points on line {1384, 2176}
X(48198) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3837, 4885, 4874}, {45320, 45340, 45323}


X(48199) = X(513)X(1639)∩X(523)X(45326)

Barycentrics    (b - c)*(2*a^3 - 2*a*b^2 + b^3 - 3*a*b*c + 3*b^2*c - 2*a*c^2 + 3*b*c^2 + c^3) : :
X(48199) = 4 X[2490] - X[4782], 2 X[2977] + X[48090], 2 X[3239] + X[9508], X[4122] + 5 X[31209], 2 X[4885] + X[48056], X[18004] + 2 X[31286], 5 X[30795] + X[48094], 5 X[30835] + X[48103], 5 X[31250] + X[48088], 4 X[45334] - X[45342], X[45676] + 2 X[45685]

X(48199) lies on these lines: {513, 1639}, {522, 28602}, {523, 45326}, {824, 47829}, {2490, 4782}, {2977, 48090}, {3239, 9508}, {4122, 31209}, {4448, 47808}, {4728, 47885}, {4763, 29078}, {4802, 47783}, {4885, 48056}, {10196, 29362}, {14431, 29156}, {18004, 31286}, {29017, 47794}, {29144, 47809}, {29200, 47837}, {29204, 47799}, {29208, 47839}, {29280, 41800}, {29284, 47835}, {29328, 45661}, {29370, 45684}, {30565, 47823}, {30795, 48094}, {30835, 48103}, {31250, 48088}, {45334, 45342}, {45676, 45685}, {47770, 47802}, {47827, 47874}

X(48199) = midpoint of X(i) and X(j) for these {i,j}: {1639, 47807}, {4448, 47808}, {4728, 47885}, {30565, 47823}, {47770, 47802}, {47809, 47822}, {47827, 47874}


X(48200) = X(2)X(4777)∩X(523)X(7625)

Barycentrics    (b - c)*(a^3 + 2*a^2*b - 3*a*b^2 + 2*b^3 + 2*a^2*c - 2*a*b*c + 4*b^2*c - 3*a*c^2 + 4*b*c^2 + 2*c^3) : :
X(48200) = X[31131] - 3 X[47808], X[31131] + 3 X[47809], X[47771] + 3 X[47808], X[47771] - 3 X[47809], 2 X[26275] - 3 X[47803], X[26275] - 3 X[47807], 4 X[30792] - 3 X[47802], 2 X[30792] - 3 X[47806], 2 X[47757] - 3 X[47802], X[47757] - 3 X[47806], 4 X[4885] - X[47131], 2 X[48062] + X[48089], X[7659] + 2 X[18004], 3 X[19875] - X[21130], 2 X[24720] + X[48088]

X(48200) lies on these lines: {2, 4777}, {210, 9001}, {513, 30565}, {522, 4763}, {523, 7625}, {650, 28602}, {693, 30758}, {900, 4944}, {905, 29110}, {1491, 21349}, {2517, 30910}, {2786, 4522}, {3263, 4411}, {4802, 44429}, {4885, 30748}, {4926, 47804}, {4951, 28898}, {6084, 48062}, {7659, 18004}, {7662, 47788}, {19875, 21130}, {21260, 29128}, {24720, 28890}, {26985, 30791}, {28151, 44435}, {28161, 47799}, {28165, 47797}, {28169, 44432}, {28183, 47800}, {28205, 47798}, {28220, 47773}, {28221, 47801}, {28319, 30605}, {28851, 45344}, {28859, 48027}, {28878, 48047}, {29144, 47760}, {29204, 47754}, {30519, 45328}, {30520, 36848}, {47690, 47782}, {47786, 48069}, {47792, 47975}

X(48200) = midpoint of X(i) and X(j) for these {i,j}: {31131, 47771}, {47690, 47782}, {47786, 48069}, {47792, 47975}, {47808, 47809}
X(48200) = reflection of X(i) in X(j) for these {i,j}: {650, 28602}, {7662, 47788}, {47757, 30792}, {47802, 47806}, {47803, 47807}, {47880, 45323}
X(48200) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {30792, 47757, 47802}, {31131, 47809, 47771}, {47757, 47806, 30792}, {47771, 47808, 31131}


X(48201) = X(37)X(650)∩X(523)X(45326)

Barycentrics    (b - c)*(2*a^3 + a^2*b - 2*a*b^2 + 2*b^3 + a^2*c - 3*a*b*c + 4*b^2*c - 2*a*c^2 + 4*b*c^2 + 2*c^3) : :
X(48201) = X[30565] + 3 X[47809], 2 X[3837] + X[48097], 2 X[48056] + X[48098], 2 X[4522] + X[4782], X[1638] - 3 X[47807], 5 X[30795] + X[48118], 2 X[48062] + X[48090]

X(48201) lies on these lines: {2, 29204}, {37, 650}, {513, 30565}, {514, 3837}, {522, 45314}, {523, 45326}, {824, 28602}, {900, 4522}, {1635, 4951}, {1638, 47807}, {1639, 29144}, {4036, 30910}, {4122, 27486}, {4763, 29370}, {4789, 28151}, {4802, 30601}, {4948, 47873}, {9508, 28898}, {14431, 29122}, {18004, 28867}, {28209, 47984}, {28220, 48027}, {28863, 45323}, {29078, 45679}, {29146, 47794}, {29202, 47835}, {29280, 47837}, {30795, 48118}, {47787, 48062}

X(48201) = midpoint of X(i) and X(j) for these {i,j}: {1635, 4951}, {4122, 27486}, {4948, 47873}, {47787, 48062}
X(48201) = reflection of X(48090) in X(47787)
X(48201) = crossdifference of every pair of points on line {36, 21793}


X(48202) = X(2)X(4777)∩X(523)X(45326)

Barycentrics    (b - c)*(2*a^3 - a^2*b - a^2*c + a*b*c + 4*b^2*c + 4*b*c^2) : :
X(48202) = X[4379] + 3 X[47832], X[4379] - 3 X[47833], X[4800] - 3 X[47832], X[4800] + 3 X[47833], X[47778] - 3 X[47831], X[4782] - 4 X[4874], X[4782] + 2 X[48090], 2 X[4874] + X[48090], 2 X[3716] + X[48098], X[47775] - 3 X[47822], X[47775] + 3 X[47834], X[4825] - 3 X[19875], 2 X[7662] + X[48030], 2 X[23770] + X[48097], 2 X[48029] + X[48135]

X(48202) lies on these lines: {2, 4777}, {350, 4411}, {513, 4379}, {523, 45326}, {693, 4448}, {812, 4782}, {900, 47779}, {1577, 29236}, {3716, 48098}, {4010, 47762}, {4083, 47875}, {4702, 25393}, {4762, 45666}, {4802, 47770}, {4809, 47790}, {4825, 19875}, {4885, 21264}, {4893, 28151}, {4926, 47823}, {7662, 47760}, {23770, 48097}, {26985, 30998}, {28161, 47829}, {28165, 47827}, {28183, 45318}, {28195, 47821}, {28205, 47828}, {28220, 47780}, {29144, 47788}, {29152, 47820}, {29204, 47874}, {29226, 47872}, {29238, 47818}, {30591, 30910}, {45323, 45678}, {48029, 48135}

X(48202) = midpoint of X(i) and X(j) for these {i,j}: {693, 4448}, {4010, 47762}, {4379, 4800}, {4809, 47790}, {7662, 47760}, {47822, 47834}, {47832, 47833}
X(48202) = reflection of X(i) in X(j) for these {i,j}: {45323, 45678}, {48030, 47760}
X(48202) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4379, 47832, 4800}, {4800, 47833, 4379}, {4874, 48090, 4782}


X(48203) = X(2)X(523)∩X(8)X(47727)

Barycentrics    (b - c)*(-a^3 + 2*a^2*b + a*b^2 + 2*b^3 + 2*a^2*c + a*b*c + b^2*c + a*c^2 + b*c^2 + 2*c^3) : :
X(48203) = 3 X[2] - 4 X[47799], 5 X[2] - 4 X[47807], 3 X[47797] - 2 X[47799], 5 X[47797] - 2 X[47807], 3 X[47797] - X[47809], 5 X[47799] - 3 X[47807], 6 X[47807] - 5 X[47809], X[8] + 2 X[47727], 3 X[47798] - 2 X[47801], 4 X[47801] - 3 X[47805], 2 X[650] + X[47692], 2 X[659] + X[47688], 4 X[676] - X[47660], 2 X[905] + X[47709], 4 X[1125] - X[47726], 2 X[3004] + X[47695], 5 X[3616] - 2 X[47682], 2 X[3776] + X[47972], 2 X[4369] + X[47702], 4 X[4458] - X[7192], 2 X[4458] + X[47701], X[7192] + 2 X[47701], 4 X[4522] - 7 X[27138], X[4560] + 2 X[47712], 2 X[4804] + X[17161], 4 X[4874] - X[47693], 4 X[4885] - X[47689], 3 X[6548] - 2 X[47812], 4 X[7662] - X[47659], 4 X[8689] - X[48139], 4 X[13246] - X[48101], 2 X[14838] + X[47713], X[17494] + 2 X[47691], X[17496] + 2 X[47708], 4 X[23770] - X[26824], 4 X[25666] - X[47700], 5 X[26985] - 2 X[47690], 5 X[27013] - 2 X[48106], 7 X[27115] - 4 X[48062], X[31290] - 4 X[47998], X[45746] + 2 X[47123], 2 X[47131] + X[47975], X[47653] + 2 X[47694], X[47676] + 2 X[48006], X[47697] + 2 X[47960], X[47705] + 2 X[48000], X[47717] + 2 X[48003], X[47923] + 2 X[48063]

X(48203) lies on these lines: {2, 523}, {8, 47727}, {514, 8643}, {522, 21297}, {650, 47692}, {659, 47688}, {676, 47660}, {826, 47840}, {905, 47709}, {1125, 47726}, {2605, 17024}, {3004, 47695}, {3616, 47682}, {3737, 7191}, {3776, 47972}, {4369, 47702}, {4458, 7192}, {4522, 27138}, {4560, 47712}, {4608, 26248}, {4777, 44429}, {4802, 47773}, {4804, 17161}, {4874, 47693}, {4885, 47689}, {4977, 44433}, {6548, 47812}, {7199, 26234}, {7662, 47659}, {7927, 47836}, {7950, 47839}, {8689, 48139}, {13246, 48101}, {14419, 29128}, {14838, 47713}, {16823, 47683}, {17494, 47691}, {17496, 47708}, {23770, 26824}, {25666, 47700}, {26275, 28175}, {26277, 48142}, {26985, 47690}, {27013, 48106}, {27115, 48062}, {28147, 47771}, {28151, 47803}, {28155, 47766}, {28161, 47757}, {28165, 47802}, {28169, 47806}, {28183, 31131}, {29021, 47796}, {29047, 47793}, {29110, 30709}, {29144, 47824}, {29146, 47841}, {29164, 47795}, {29204, 47822}, {29260, 47794}, {29358, 47838}, {31094, 48090}, {31290, 47998}, {45746, 47123}, {47131, 47975}, {47653, 47694}, {47676, 48006}, {47697, 47960}, {47705, 48000}, {47717, 48003}, {47772, 47821}, {47780, 47887}, {47832, 47870}, {47923, 48063}

X(48203) = anticomplement of X(47809)
X(48203) = reflection of X(i) in X(j) for these {i,j}: {2, 47797}, {47771, 47800}, {47772, 47821}, {47773, 47804}, {47780, 47887}, {47792, 47834}, {47805, 47798}, {47808, 47757}, {47809, 47799}, {47870, 47832}
X(48203) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4458, 47701, 7192}, {47797, 47809, 47799}, {47799, 47809, 2}


X(48204) = X(2)X(523)∩X(8)X(2605)

Barycentrics    (b - c)*(a^4 + a^3*b - a^2*b^2 - a*b^3 + a^3*c - a^2*b*c - 3*a*b^2*c + b^3*c - a^2*c^2 - 3*a*b*c^2 + 2*b^2*c^2 - a*c^3 + b*c^3) : :
X(48204) = X[8] + 2 X[2605], 2 X[10] + X[3737], X[26078] + 2 X[47793], X[26144] - 4 X[47794], 2 X[650] + X[2517], 2 X[659] + X[44444], X[1459] + 2 X[4147], X[1491] + 2 X[6133], 2 X[4036] + X[4560], X[4036] + 2 X[8043], X[4560] - 4 X[8043], X[4041] + 2 X[8062], X[4086] + 2 X[14838], X[4088] + 2 X[21187], X[4397] + 5 X[31209], X[4581] + 2 X[47842], 2 X[4705] + X[47844], 2 X[4770] + X[39547], X[6129] - 4 X[31287], 2 X[17072] + X[46385], X[17418] + 2 X[20316], 2 X[20315] + X[47136], 2 X[43927] + X[47945], 4 X[44316] - X[46403], 2 X[45660] + X[45671]

X(48204) lies on these lines: {2, 523}, {8, 2605}, {10, 3737}, {513, 26078}, {522, 14429}, {650, 2517}, {659, 25299}, {966, 3287}, {1329, 8819}, {1459, 4147}, {1491, 6133}, {2345, 3709}, {3085, 44409}, {4036, 4560}, {4041, 8062}, {4086, 14838}, {4088, 21187}, {4132, 47840}, {4139, 47839}, {4397, 31209}, {4581, 47842}, {4705, 47844}, {4770, 39547}, {4802, 47796}, {4840, 26775}, {5046, 46611}, {6129, 31287}, {7199, 28653}, {8672, 47837}, {9508, 27527}, {16828, 47683}, {17072, 46385}, {17418, 20316}, {18116, 26028}, {19784, 47682}, {19836, 47727}, {20315, 28834}, {27193, 48120}, {27345, 48030}, {27545, 28221}, {28147, 47795}, {28423, 48062}, {28623, 47828}, {38469, 47845}, {43927, 47945}, {44316, 46403}, {45660, 45671}

X(48204) = {X(4036),X(8043)}-harmonic conjugate of X(4560)


X(48205) = X(2)X(523)∩X(10)X(2605)

Barycentrics    (b - c)*(a^4 + a^3*b - a^2*b^2 - a*b^3 + a^3*c - a^2*b*c - 2*a*b^2*c + b^3*c - a^2*c^2 - 2*a*b*c^2 + 2*b^2*c^2 - a*c^3 + b*c^3) : :
X(48205) = 2 X[10] + X[2605], X[659] + 2 X[44316], X[1577] + 2 X[8043], 5 X[1698] + X[3737], X[2517] + 5 X[31209], X[3733] + 2 X[21051], X[4036] + 2 X[14838], X[4086] + 2 X[31947], X[43927] + 2 X[48030]

X(48205) lies on these lines: {2, 523}, {10, 2605}, {498, 44409}, {513, 47794}, {650, 24960}, {659, 44316}, {834, 47835}, {1213, 3287}, {1577, 8043}, {1698, 3737}, {2517, 31209}, {2977, 28423}, {3085, 39540}, {3709, 17303}, {3733, 21051}, {3837, 26049}, {4036, 14838}, {4057, 24533}, {4086, 31947}, {4132, 47839}, {4193, 46611}, {4374, 28653}, {4774, 19874}, {4784, 27045}, {4802, 47795}, {4840, 27527}, {4963, 26822}, {4977, 47793}, {5029, 21055}, {16298, 42660}, {17566, 46610}, {19881, 47727}, {26078, 28217}, {26144, 28221}, {28175, 47796}, {28623, 47830}, {43927, 48030}


X(48206) = X(2)X(523)∩X(513)X(3716)

Barycentrics    (b - c)*(2*a^3 - a*b^2 + 3*b^2*c - a*c^2 + 3*b*c^2) : :
X(48206) = 7 X[2] - X[4948], 5 X[2] - X[47825], 3 X[2] + X[47834], 5 X[4948] - 7 X[47825], 3 X[4948] - 7 X[47827], 2 X[4948] - 7 X[47829], X[4948] + 7 X[47833], 3 X[4948] + 7 X[47834], 3 X[47825] - 5 X[47827], 2 X[47825] - 5 X[47829], X[47825] + 5 X[47833], 3 X[47825] + 5 X[47834], 2 X[47827] - 3 X[47829], X[47827] + 3 X[47833], X[47829] + 2 X[47833], 3 X[47829] + 2 X[47834], 3 X[47833] - X[47834], X[3837] + 2 X[4874], X[3837] - 4 X[4885], 2 X[4369] + X[4806], X[4874] + 2 X[4885], X[659] + 5 X[26985], 5 X[3616] + X[4774], 4 X[3634] - X[4770], X[4010] + 5 X[24924], 3 X[4379] + X[47826], 3 X[47822] - X[47826], X[4810] + 5 X[27013], X[4823] + 2 X[31288], X[7662] + 5 X[31250], 4 X[25666] - X[48002], X[45314] + 2 X[45320], 5 X[30795] + X[47694], 5 X[31209] + X[48120], 2 X[31286] + X[48090], 13 X[34595] - X[47683], 2 X[43067] + X[47993], X[45342] + 2 X[45663]

X(48206) lies on these lines: {2, 523}, {513, 3716}, {659, 26985}, {676, 28183}, {814, 30234}, {900, 47823}, {1577, 14419}, {2605, 26102}, {2787, 45324}, {3616, 4774}, {3634, 4770}, {3737, 25502}, {3906, 21181}, {4010, 24924}, {4160, 21051}, {4367, 30709}, {4374, 30963}, {4379, 4977}, {4448, 47812}, {4777, 47830}, {4800, 28217}, {4802, 47778}, {4810, 27013}, {4823, 31288}, {4841, 4893}, {7662, 31250}, {17066, 21264}, {18154, 44451}, {25666, 48002}, {28209, 47821}, {28213, 47780}, {29078, 47787}, {29328, 47761}, {29362, 45314}, {30795, 47694}, {31209, 48120}, {31286, 48090}, {34595, 47683}, {43067, 47993}, {44429, 45340}, {45342, 45663}, {47793, 47889}, {47795, 47875}, {47796, 47872}

X(48206) = midpoint of X(i) and X(j) for these {i,j}: {2, 47833}, {1577, 14419}, {4367, 30709}, {4379, 47822}, {4448, 47812}, {4800, 47824}, {45320, 47803}, {47779, 47831}, {47788, 47799}, {47793, 47889}, {47795, 47875}, {47796, 47872}, {47823, 47832}, {47827, 47834}
X(48206) = reflection of X(i) in X(j) for these {i,j}: {44429, 45340}, {45314, 47803}, {47829, 2}
X(48206) = complement of X(47827)
X(48206) = reflection of X(47829) in the Euler line
X(48206) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 35134}, {35180, 141}
X(48206) = crossdifference of every pair of points on line {187, 2176}
X(48206) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 47834, 47827}, {4874, 4885, 3837}, {47827, 47833, 47834}


X(48207) = X(2)X(523)∩X(513)X(47795)

Barycentrics    (b - c)*(a^4 + a^3*b - a^2*b^2 - a*b^3 + a^3*c - a^2*b*c + b^3*c - a^2*c^2 + 2*b^2*c^2 - a*c^3 + b*c^3) : :
X(48207) = 4 X[1125] - X[2605], X[1577] + 2 X[31947], 7 X[3624] - X[3737], 2 X[3837] + X[4057], X[4367] + 2 X[31946], 2 X[4806] + X[4840], X[4815] + 2 X[8043], X[6129] + 5 X[31250], 2 X[14838] + X[30591], 5 X[30795] - 2 X[44316]

X(48207) lies on these lines: {2, 523}, {499, 44409}, {513, 47795}, {647, 24961}, {834, 47841}, {1125, 2605}, {1577, 31947}, {2457, 14432}, {3086, 39540}, {3287, 17398}, {3624, 3737}, {3837, 4057}, {4132, 47837}, {4193, 46610}, {4367, 31946}, {4374, 17322}, {4657, 17066}, {4784, 27167}, {4802, 47794}, {4806, 4840}, {4815, 8043}, {4874, 25511}, {4977, 47796}, {6129, 31250}, {11374, 34954}, {14838, 30591}, {16299, 42660}, {16777, 21958}, {17566, 46611}, {19863, 39547}, {19881, 47682}, {26078, 28221}, {26144, 28217}, {28175, 47793}, {28623, 47831}, {30795, 31003}

X(48207) = midpoint of X(2457) and X(14432)


X(48208) = X(2)X(523)∩X(513)X(47772)

Barycentrics    (b - c)*(a^3 + 2*a^2*b - a*b^2 + 2*b^3 + 2*a^2*c - a*b*c + 3*b^2*c - a*c^2 + 3*b*c^2 + 2*c^3) : :
X(48208) = 5 X[2] - 4 X[47799], 3 X[2] - 4 X[47807], 5 X[47797] - 6 X[47799], X[47797] - 3 X[47809], 3 X[47799] - 5 X[47807], 2 X[47799] - 5 X[47809], 2 X[47807] - 3 X[47809], X[8] + 2 X[47682], 2 X[10] + X[47726], 2 X[650] + X[47689], 2 X[905] + X[47706], 4 X[1491] - X[47653], 2 X[1491] + X[47693], X[47653] + 2 X[47693], 2 X[2526] + X[47662], 8 X[2977] - 5 X[26777], 5 X[3616] - 2 X[47727], 4 X[3837] - X[47688], 2 X[4088] + X[7192], 2 X[4369] + X[47700], 4 X[4522] - X[20295], 2 X[4522] + X[48106], X[20295] + 2 X[48106], X[4560] + 2 X[47711], X[4608] + 2 X[47934], 2 X[4808] + X[17166], 4 X[4885] - X[47692], 4 X[4913] - X[17161], 2 X[14838] + X[47710], X[17494] + 2 X[47690], X[17494] - 4 X[48062], X[47690] + 2 X[48062], X[17496] + 2 X[47707], 2 X[24720] + X[48118], X[25259] + 2 X[48069], 4 X[25666] - X[47702], 5 X[26985] - 2 X[47691], X[31290] - 4 X[48047], 3 X[31992] - 2 X[47811], 4 X[45344] - X[47774], X[46403] + 2 X[48103], X[47659] + 2 X[47975], X[47685] + 2 X[48095], X[47687] + 2 X[47890], X[47714] + 2 X[48003], X[47718] + 2 X[47965], X[47969] - 4 X[48056], 2 X[48042] + X[48138], 2 X[48050] + X[48146], 2 X[48073] + X[48117], 2 X[48088] + X[48108]

X(48208) lies on these lines: {2, 523}, {8, 47682}, {10, 47726}, {513, 47772}, {514, 47808}, {522, 47771}, {650, 47689}, {826, 47836}, {905, 47706}, {1491, 47653}, {2526, 47662}, {2605, 29815}, {2977, 26777}, {3263, 7199}, {3616, 47727}, {3737, 3920}, {3757, 5214}, {3837, 47688}, {4088, 7192}, {4369, 47700}, {4374, 31130}, {4522, 20295}, {4560, 47711}, {4608, 47934}, {4777, 47804}, {4802, 44429}, {4808, 17166}, {4885, 47692}, {4913, 17161}, {4951, 29328}, {4977, 31131}, {7927, 47840}, {7950, 47837}, {14431, 29128}, {14838, 47710}, {16830, 47683}, {17494, 47690}, {17496, 47707}, {21052, 29116}, {21145, 45332}, {24720, 48118}, {25259, 48069}, {25666, 47702}, {26275, 28187}, {26985, 47691}, {28147, 44435}, {28151, 47802}, {28155, 47757}, {28161, 47766}, {28165, 47803}, {28169, 47800}, {28183, 44433}, {29021, 47793}, {29029, 30709}, {29047, 47796}, {29144, 47821}, {29146, 47835}, {29164, 47794}, {29204, 47823}, {29260, 47795}, {31094, 48030}, {31290, 48047}, {31992, 47811}, {45344, 47774}, {46403, 48103}, {47659, 47975}, {47685, 48095}, {47687, 47890}, {47714, 48003}, {47718, 47965}, {47828, 47894}, {47969, 48056}, {48042, 48138}, {48050, 48146}, {48073, 48117}, {48088, 48108}

X(48208) = reflection of X(i) in X(j) for these {i,j}: {2, 47809}, {21145, 45332}, {44435, 47806}, {46915, 47825}, {47797, 47807}, {47798, 47766}, {47805, 47771}, {47894, 47828}
X(48208) = anticomplement of X(47797)
X(48208) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1491, 47693, 47653}, {4522, 48106, 20295}, {47690, 48062, 17494}, {47797, 47807, 2}, {47797, 47809, 47807}


X(48209) = X(2)X(523)∩X(513)X(26144)

Barycentrics    (b - c)*(a^4 + a^3*b - a^2*b^2 - a*b^3 + a^3*c - a^2*b*c + a*b^2*c + b^3*c - a^2*c^2 + a*b*c^2 + 2*b^2*c^2 - a*c^3 + b*c^3) : :
X(48209) = X[26144] + 2 X[47796], X[26078] - 4 X[47795], X[663] + 2 X[47843], 2 X[905] + X[7650], 4 X[1125] - X[3737], X[2517] - 4 X[4885], X[2517] + 2 X[6129], 2 X[4885] + X[6129], 2 X[2605] - 5 X[3616], 4 X[3837] - X[44444], 2 X[3960] + X[4985], X[4017] + 2 X[8062], 2 X[4057] + X[46403], X[4064] + 2 X[4458], X[4449] + 2 X[20316], X[4491] + 2 X[40086], X[4560] + 2 X[30591], X[4560] - 4 X[31947], X[30591] + 2 X[31947], X[4815] + 2 X[14838], X[17166] + 2 X[47842], 2 X[20315] + X[47123]

X(48209) lies on these lines: {2, 523}, {513, 26144}, {522, 3582}, {659, 26854}, {663, 47843}, {905, 7650}, {1125, 3737}, {1491, 27193}, {2260, 21388}, {2457, 2785}, {2517, 4885}, {2605, 3616}, {3086, 44409}, {3487, 34954}, {3837, 26097}, {3960, 4985}, {4000, 17066}, {4017, 8062}, {4057, 46403}, {4064, 4458}, {4132, 47836}, {4139, 47837}, {4357, 17218}, {4374, 17321}, {4449, 20316}, {4491, 40086}, {4560, 30591}, {4802, 47793}, {4815, 14838}, {4840, 26822}, {4874, 26114}, {5046, 46610}, {5214, 19863}, {6133, 27014}, {7199, 17322}, {7662, 25511}, {8672, 47839}, {8819, 25466}, {14986, 39540}, {17166, 47842}, {17314, 21958}, {19784, 47727}, {19836, 47682}, {19881, 47726}, {20315, 47123}, {24961, 26080}, {25512, 47683}, {26049, 48120}, {27345, 48090}, {27545, 28217}, {28147, 47794}, {28623, 47832}

X(48209) = crosspoint of X(86) and X(15455)
X(48209) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4885, 6129, 2517}, {30591, 31947, 4560}


X(48210) = X(230)X(231)∩X(513)X(14404)

Barycentrics    (b - c)*(-3*a^3 + 5*a*b^2 + 10*a*b*c + 2*b^2*c + 5*a*c^2 + 2*b*c^2) : :
X(48210) = 5 X[650] - 2 X[4874], 4 X[650] - X[7662], 2 X[2977] + X[45745], 8 X[4874] - 5 X[7662], 4 X[4874] - 5 X[47803], 2 X[649] + X[47953], 2 X[4913] + X[48029], 2 X[4394] + X[4824], 2 X[4765] + X[48047], X[47963] - 4 X[48000], X[4790] + 2 X[48002], 2 X[4818] + X[48096], 2 X[9508] + X[47962], 2 X[17494] + X[48089], 2 X[21196] + X[48088], 4 X[25380] - X[48126], 5 X[26777] - X[47805], 5 X[26777] + X[47975], 4 X[31286] - X[48134], 4 X[31287] - X[48120], 2 X[48008] + X[48027]

X(48210) lies on these lines: {230, 231}, {513, 14404}, {649, 47953}, {3667, 4913}, {4369, 28191}, {4394, 4824}, {4705, 28475}, {4762, 47802}, {4763, 28147}, {4765, 48047}, {4778, 47963}, {4790, 48002}, {4802, 47761}, {4818, 48096}, {9508, 28195}, {14431, 23882}, {17494, 44429}, {21196, 48088}, {25380, 48126}, {26777, 47805}, {28165, 45666}, {28199, 43067}, {28894, 47885}, {29328, 47777}, {31286, 48134}, {31287, 48120}, {44567, 47833}, {45320, 47829}, {48008, 48027}

X(48210) = midpoint of X(i) and X(j) for these {i,j}: {17494, 44429}, {31150, 47825}, {47805, 47975}
X(48210) = reflection of X(i) in X(j) for these {i,j}: {7662, 47803}, {45320, 47829}, {47802, 47827}, {47803, 650}, {47833, 44567}, {48089, 44429}
X(48210) = crossdifference of every pair of points on line {3, 16971}


X(48211) = X(2)X(4777)∩X(230)X(231)

Barycentrics    (b - c)*(-3*a^3 + 2*a^2*b + a*b^2 + 2*b^3 + 2*a^2*c + 2*a*b*c + a*c^2 + 2*c^3) : :
X(48211) = 2 X[650] + X[47131], 4 X[676] - X[7662], X[45745] + 2 X[47132], X[47766] - 3 X[47800], 2 X[47766] - 3 X[47803], X[44433] + 3 X[47797], X[44433] - 3 X[47798], X[44435] - 3 X[47797], X[44435] + 3 X[47798], 2 X[44432] - 3 X[47799], 4 X[44432] - 3 X[47802], 2 X[4142] + X[48136], 2 X[4458] + X[48029], X[47773] - 3 X[47804], X[4931] - 3 X[47832], 2 X[6050] + X[47712], 2 X[20517] + X[48099], X[21116] - 3 X[47887]

X(48211) lies on these lines: {1, 21130}, {2, 4777}, {230, 231}, {354, 9001}, {513, 4453}, {514, 26275}, {522, 4928}, {900, 47757}, {3667, 21212}, {3716, 30519}, {3776, 4778}, {4010, 4926}, {4049, 29066}, {4142, 28468}, {4411, 26234}, {4448, 30520}, {4458, 28851}, {4724, 21115}, {4775, 28319}, {4800, 28898}, {4802, 47773}, {4927, 48089}, {4931, 47832}, {4944, 29370}, {4977, 47801}, {6050, 47712}, {20517, 48099}, {21116, 47887}, {28151, 47771}, {28161, 47807}, {28165, 47809}, {28183, 47806}, {28195, 47805}, {28205, 47808}, {28890, 45673}, {29029, 30234}, {29110, 45664}, {29144, 47761}, {29204, 45666}, {47691, 47892}

X(48211) = midpoint of X(i) and X(j) for these {i,j}: {1, 21130}, {4724, 21115}, {44433, 44435}, {47123, 47883}, {47691, 47892}, {47797, 47798}
X(48211) = reflection of X(i) in X(j) for these {i,j}: {47770, 45666}, {47802, 47799}, {47803, 47800}, {47881, 4874}, {48062, 14425}, {48089, 4927}
X(48211) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {44433, 47797, 44435}, {44435, 47798, 44433}


X(48212) = X(2)X(29204)∩X(523)X(44902)

Barycentrics    (b - c)*(-2*a^3 + a^2*b + 2*a*b^2 + 2*b^3 + a^2*c + a*b*c + 2*a*c^2 + 2*c^3) : :
X(48212) = X[4453] + 3 X[47797], X[47878] + 3 X[47887], X[1639] - 3 X[47799], 2 X[4142] + X[48137], 2 X[4458] + X[48030], 2 X[20517] + X[48100], X[47772] - 3 X[47822], 3 X[47833] - X[47873]

X(48212) lies on these lines: {2, 29204}, {513, 4453}, {514, 14422}, {522, 3837}, {523, 44902}, {650, 4802}, {1638, 29144}, {1639, 47799}, {3776, 4977}, {4142, 48137}, {4458, 48030}, {4688, 4777}, {4782, 28882}, {4806, 28906}, {4874, 28863}, {4928, 29370}, {14419, 29122}, {14421, 21130}, {20517, 48100}, {21183, 48098}, {21199, 29350}, {28151, 47782}, {28165, 47131}, {28217, 48042}, {28225, 47990}, {28855, 48028}, {28898, 45342}, {29146, 47795}, {29202, 47841}, {29208, 41800}, {29280, 47839}, {30520, 45666}, {47772, 47822}, {47833, 47873}

X(48212) = midpoint of X(i) and X(j) for these {i,j}: {4809, 44435}, {14421, 21130}
X(48212) = reflection of X(48098) in X(21183)


X(48213) = X(44)X(513)∩X(523)X(44902)

Barycentrics    a*(b - c)*(2*a^2 + a*b - 4*b^2 + a*c - 5*b*c - 4*c^2) : :
X(48213) = 2 X[1491] + X[4782], 7 X[1491] - X[48020], 7 X[1635] + X[48020], 7 X[4782] + 2 X[48020], 7 X[4893] - 3 X[47826], X[4893] - 3 X[47827], X[4893] + 3 X[47828], 2 X[9508] + X[48030], X[47826] - 7 X[47827], X[47826] + 7 X[47828], X[47779] - 3 X[47830], 4 X[2977] - X[48097], X[47780] - 3 X[47823], X[47780] + 3 X[47825], 2 X[4913] + X[48090], 4 X[25380] - X[48098]

X(48213) lies on these lines: {1, 4825}, {2, 4777}, {44, 513}, {522, 47829}, {523, 44902}, {812, 45323}, {824, 28602}, {900, 47778}, {2977, 48097}, {3251, 3795}, {3776, 28175}, {4083, 47888}, {4379, 4948}, {4770, 14422}, {4802, 47754}, {4874, 45675}, {4913, 4928}, {4926, 47822}, {9269, 14077}, {17494, 41836}, {21212, 28147}, {25380, 48098}, {28165, 47833}, {28183, 47831}, {28195, 47824}, {28205, 47832}, {28220, 47775}, {29144, 47784}, {29152, 47814}, {29204, 47886}, {29226, 47893}, {29236, 45671}, {29238, 47816}, {31150, 36848}, {44567, 45666}, {45691, 47761}, {47131, 47689}

X(48213) = midpoint of X(i) and X(j) for these {i,j}: {1, 4825}, {1491, 1635}, {4379, 4948}, {4770, 14422}, {4913, 4928}, {31150, 36848}, {47823, 47825}, {47827, 47828}
X(48213) = reflection of X(i) in X(j) for these {i,j}: {4782, 1635}, {4874, 45675}, {45666, 44567}, {47761, 45691}, {48028, 47777}, {48090, 4928}
X(48213) = X(4825)-line conjugate of X(1)


X(48214) = X(2)X(29362)∩X(230)X(231)

Barycentrics    (b - c)*(3*a^3 - 2*a*b^2 - 4*a*b*c + b^2*c - 2*a*c^2 + b*c^2) : :
X(48214) = 2 X[650] + X[4874], 5 X[650] + X[7662], 5 X[4874] - 2 X[7662], X[7662] - 5 X[47803], 2 X[44567] + X[45314], 4 X[44567] - X[45323], 2 X[45314] + X[45323], X[45673] + 2 X[45691], X[659] + 5 X[31209], 5 X[659] + X[47685], 5 X[31209] - X[44429], 25 X[31209] - X[47685], 5 X[44429] - X[47685], X[14431] - 3 X[47794], X[1491] - 7 X[27115], 7 X[27115] + X[47805], X[3837] - 4 X[31287], 2 X[4394] + X[4806], 4 X[4521] - X[18004], X[4782] + 2 X[25666], 2 X[6050] + X[21051], X[21146] - 7 X[31207], 5 X[26777] + X[48120], 5 X[27013] + X[48024], 2 X[31288] + X[48003]

X(48214) lies on these lines: {2, 29362}, {230, 231}, {513, 4763}, {522, 28602}, {659, 31209}, {814, 14431}, {1491, 27115}, {1635, 29328}, {1639, 29078}, {3667, 9508}, {3716, 4926}, {3837, 31287}, {4369, 28195}, {4394, 4806}, {4448, 47828}, {4521, 18004}, {4778, 31286}, {4782, 25666}, {4913, 28205}, {4977, 47761}, {6050, 21051}, {6544, 29370}, {21146, 31207}, {26777, 48120}, {27013, 48024}, {27929, 30519}, {28199, 48000}, {29246, 47837}, {29324, 47793}, {29366, 47835}, {31150, 47833}, {31288, 48003}, {47797, 47885}, {47799, 47884}, {47804, 47827}, {47811, 47823}, {47815, 47893}, {47817, 47888}

X(48214) = midpoint of X(i) and X(j) for these {i,j}: {650, 47803}, {659, 44429}, {1491, 47805}, {1635, 47822}, {4448, 47828}, {31150, 47833}, {45314, 47829}, {47797, 47885}, {47799, 47884}, {47804, 47827}, {47811, 47823}, {47815, 47893}, {47817, 47888}
X(48214) = reflection of X(i) in X(j) for these {i,j}: {4874, 47803}, {45323, 47829}, {47829, 44567}
X(48214) = {X(44567),X(45314)}-harmonic conjugate of X(45323)


X(48215) = X(513)X(1638)∩X(523)X(44902)

Barycentrics    (b - c)*(-2*a^3 + 2*a*b^2 + b^3 + a*b*c - b^2*c + 2*a*c^2 - b*c^2 + c^3) : :
X(48215) = 4 X[2490] - X[48097], X[4874] + 2 X[21212], 4 X[7658] - X[9508], 2 X[17069] + X[48090], 7 X[31207] - X[48103], 4 X[31287] - X[48056], 2 X[44551] + X[45342], X[45323] + 2 X[45668]

X(48215) lies on these lines: {513, 1638}, {523, 44902}, {2490, 48097}, {4083, 41800}, {4453, 47822}, {4802, 47784}, {4809, 44429}, {4874, 21212}, {4928, 29078}, {7658, 9508}, {14419, 29156}, {17069, 48090}, {21204, 29362}, {28195, 47891}, {28199, 47876}, {29017, 47795}, {29144, 47797}, {29200, 47839}, {29204, 47807}, {29208, 47837}, {29284, 47841}, {29328, 45674}, {31207, 48103}, {31287, 48056}, {36848, 47798}, {44551, 45342}, {45323, 45668}, {47754, 47803}, {47813, 47877}, {47827, 47887}, {47833, 47886}

X(48215) = midpoint of X(i) and X(j) for these {i,j}: {1638, 47799}, {4453, 47822}, {4809, 44429}, {36848, 47798}, {47754, 47803}, {47797, 47823}, {47813, 47877}, {47827, 47887}, {47833, 47886}


X(48216) = X(2)X(513)∩X(523)X(44902)

Barycentrics    (b - c)*(2*a^3 + a^2*b - 2*a*b^2 + a^2*c - a*b*c + 2*b^2*c - 2*a*c^2 + 2*b*c^2) : :
X(48216) = 5 X[2] - X[47821], 3 X[2] + X[47824], 3 X[47821] - 5 X[47822], X[47821] + 5 X[47823], 3 X[47821] + 5 X[47824], X[47822] + 3 X[47823], 3 X[47823] - X[47824], X[649] + 5 X[30795], 2 X[650] + X[48098], 5 X[650] + X[48126], 5 X[48098] - 2 X[48126], X[659] - 7 X[31207], X[1019] + 5 X[31251], X[1491] + 5 X[24924], 5 X[1491] + X[48153], 5 X[24924] - X[47813], 25 X[24924] - X[48153], 5 X[47813] - X[48153], 5 X[1698] + X[4378], 7 X[3624] - X[4775], 2 X[3676] + X[48056], 2 X[3776] + X[48097], 2 X[3837] + X[4782], X[3837] + 2 X[31286], X[4782] - 4 X[31286], 5 X[4369] + X[47992], 2 X[4369] + X[48030], 2 X[47992] - 5 X[48030], 4 X[4521] - X[48048], X[4784] + 5 X[30835], X[4874] + 2 X[25380], 2 X[4885] + X[9508], 4 X[4885] - X[48090], 2 X[9508] + X[48090], X[21146] + 5 X[31209], X[24719] + 5 X[27013], 4 X[25666] - X[48028], 2 X[43067] + X[47964], 2 X[44561] + X[45332], X[45313] + 2 X[45340], X[45320] + 2 X[45691], X[45323] + 2 X[45663], 2 X[48000] + X[48135]

X(48216) lies on these lines: {2, 513}, {514, 47829}, {523, 44902}, {649, 30795}, {650, 48098}, {659, 31207}, {900, 47831}, {1019, 31251}, {1491, 24924}, {1575, 21348}, {1638, 47807}, {1698, 4378}, {2238, 39521}, {3624, 4775}, {3676, 48056}, {3776, 48097}, {3837, 4782}, {4083, 47795}, {4212, 16228}, {4369, 47992}, {4379, 4802}, {4521, 48048}, {4763, 29362}, {4777, 47828}, {4784, 30835}, {4809, 47808}, {4874, 25380}, {4885, 9508}, {4893, 28195}, {4926, 47832}, {4928, 29328}, {4977, 47778}, {6545, 47885}, {11231, 28537}, {14419, 29236}, {20980, 37673}, {21146, 31209}, {24719, 27013}, {25574, 45667}, {25666, 48028}, {28151, 47825}, {28165, 47834}, {28199, 47780}, {29017, 41800}, {29078, 45674}, {29144, 47799}, {29198, 47794}, {29204, 47809}, {29226, 47796}, {43067, 47964}, {44561, 45332}, {45313, 45340}, {45320, 45691}, {45323, 45663}, {47836, 47841}, {48000, 48135}

X(48216) = midpoint of X(i) and X(j) for these {i,j}: {2, 47823}, {1491, 47813}, {1638, 47807}, {4379, 47827}, {4809, 47808}, {6545, 47885}, {36848, 47804}, {47761, 47802}, {47779, 47830}, {47795, 47837}, {47796, 47835}, {47822, 47824}, {47828, 47833}, {47836, 47841}
X(48216) = complement of X(47822)
X(48216) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 47824, 47822}, {3837, 31286, 4782}, {4885, 9508, 48090}, {47822, 47823, 47824}


X(48217) = X(2)X(29144)∩X(523)X(44902)

Barycentrics    (b - c)*(2*a^3 + 2*a^2*b - 2*a*b^2 + b^3 + 2*a^2*c - a*b*c + 3*b^2*c - 2*a*c^2 + 3*b*c^2 + c^3) : :
X(48217) = X[1639] - 3 X[47807], X[47768] + 3 X[47806], 2 X[2977] + X[48098], X[4453] + 3 X[47809], X[4453] - 3 X[47823], 5 X[30795] + X[48106], X[47772] + 3 X[47824], 3 X[47827] - X[47878], 3 X[47828] + X[47873]

X(48217) lies on these lines: {2, 29144}, {513, 1639}, {514, 3828}, {522, 4874}, {523, 44902}, {900, 45313}, {1638, 29204}, {2977, 48098}, {3004, 4802}, {3837, 28882}, {4453, 47809}, {4750, 4951}, {4777, 45691}, {4977, 20316}, {18004, 28906}, {21199, 29318}, {25380, 28863}, {28165, 47123}, {28217, 48063}, {29017, 47837}, {29146, 41800}, {29208, 47795}, {29284, 47836}, {29370, 45674}, {30795, 48106}, {36848, 47771}, {47772, 47824}, {47812, 47885}, {47827, 47878}, {47828, 47873}

X(48217) = midpoint of X(i) and X(j) for these {i,j}: {4750, 4951}, {21183, 48062}, {36848, 47771}, {47809, 47823}, {47812, 47885}
X(48217) = reflection of X(47785) in X(45691)
X(48217) = crossdifference of every pair of points on line {16483, 21008}


X(48218) = X(2)X(514)∩X(525)X(44902)

Barycentrics    (b - c)*(2*a^3 - 2*a*b^2 - a*b*c + 2*b^2*c - 2*a*c^2 + 2*b*c^2) : :
X(48218) = 5 X[2] - X[47793], 3 X[2] + X[47796], 3 X[47793] - 5 X[47794], X[47793] + 5 X[47795], 3 X[47793] + 5 X[47796], X[47794] + 3 X[47795], 3 X[47795] - X[47796], X[663] - 7 X[3624], X[667] + 5 X[30795], 2 X[905] + X[4791], X[905] + 5 X[31250], X[4791] - 10 X[31250], X[1019] + 5 X[30835], 2 X[1125] + X[17072], 5 X[1698] + X[4449], 4 X[3634] - X[4147], 2 X[3716] + X[48075], 2 X[3828] + X[45667], 2 X[3835] + X[48064], 2 X[3837] + X[4401], X[3837] + 2 X[31288], X[4401] - 4 X[31288], X[4040] - 13 X[34595], X[4063] - 7 X[31207], X[4367] + 5 X[31251], 2 X[4369] + X[48054], X[4794] - 10 X[19862], X[4823] - 4 X[4885], X[4823] + 2 X[14838], 2 X[4885] + X[14838], 2 X[4874] + X[48066], X[4978] + 5 X[31209], 11 X[5550] + X[21302], 4 X[7658] - X[21192], X[14349] + 5 X[24924], 8 X[19878] + X[24720], 16 X[19878] - X[48065], 2 X[24720] + X[48065], 2 X[44561] + X[45324], 4 X[25380] - X[48018], 4 X[31286] - X[48011], 4 X[25666] - X[47997], 4 X[31287] - X[48003], 2 X[48049] + X[48074]

X(48218) lies on these lines: {2, 514}, {405, 39476}, {475, 39532}, {525, 44902}, {663, 3624}, {667, 30795}, {830, 47802}, {905, 4791}, {1019, 30835}, {1125, 17072}, {1638, 23875}, {1698, 4449}, {2786, 28779}, {3634, 4147}, {3667, 26144}, {3716, 48075}, {3828, 45667}, {3835, 48064}, {3837, 4401}, {4040, 34595}, {4063, 31207}, {4151, 47830}, {4367, 31251}, {4369, 48054}, {4546, 10527}, {4728, 29270}, {4763, 29302}, {4794, 19862}, {4823, 4885}, {4874, 48066}, {4928, 29013}, {4932, 27167}, {4978, 31209}, {5550, 21302}, {6002, 45678}, {6005, 47823}, {7658, 21192}, {8714, 47831}, {11108, 44408}, {14349, 24924}, {14419, 29344}, {15309, 47760}, {19847, 48063}, {19878, 24720}, {22154, 37674}, {23876, 41800}, {23879, 47882}, {23880, 44561}, {25380, 48018}, {25511, 31286}, {25666, 47997}, {26822, 47984}, {29021, 47799}, {29047, 47807}, {29164, 47797}, {29216, 45674}, {29260, 47809}, {29350, 47837}, {31287, 48003}, {44429, 47818}, {47816, 47820}, {47817, 47819}, {47824, 47838}, {47833, 47888}, {47875, 47893}, {48049, 48074}

X(48218) = midpoint of X(i) and X(j) for these {i,j}: {2, 47795}, {44429, 47818}, {47794, 47796}, {47816, 47820}, {47817, 47819}, {47823, 47839}, {47824, 47838}, {47833, 47888}, {47837, 47841}, {47875, 47893}
X(48218) = complement of X(47794)
X(48218) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 47796, 47794}, {3837, 31288, 4401}, {4885, 14838, 4823}, {47794, 47795, 47796}


X(48219) = X(2)X(4802)∩X(230)X(231)

Barycentrics    (b - c)*(3*a^3 + 2*a^2*b - a*b^2 + 2*b^3 + 2*a^2*c - 2*a*b*c + 4*b^2*c - a*c^2 + 4*b*c^2 + 2*c^3) : :
X(48219) = 2 X[2977] + X[6590], 4 X[4874] - X[47131], X[7662] + 2 X[48062], 3 X[47766] - X[47800], 2 X[47800] - 3 X[47803], X[31131] + 5 X[47771], 3 X[31131] - 5 X[47808], X[31131] - 5 X[47809], 3 X[47771] + X[47808], X[47808] - 3 X[47809], 2 X[3837] + X[48095], X[4122] + 2 X[4394], 2 X[4369] + X[48088], 4 X[4521] - X[47998], X[4790] + 2 X[18004], 2 X[4885] + X[48103], 2 X[6050] + X[47711], 2 X[24720] + X[48096], 5 X[24924] + X[48118], 4 X[25666] - X[47961], 5 X[30795] + X[48140], 5 X[30835] + X[48146], 5 X[31209] + X[47693], X[43067] + 2 X[48056], 2 X[47890] + X[48089]

X(48219) lies on these lines: {2, 4802}, {230, 231}, {513, 30565}, {514, 47802}, {3667, 4522}, {3837, 48095}, {4122, 4394}, {4369, 48088}, {4521, 47998}, {4762, 47885}, {4777, 47804}, {4778, 47991}, {4782, 4926}, {4790, 18004}, {4834, 28328}, {4885, 48103}, {4944, 29328}, {4977, 47806}, {6050, 47711}, {21146, 28195}, {24720, 48096}, {24924, 48118}, {25666, 47961}, {26275, 28161}, {28147, 47799}, {28151, 47797}, {28165, 47798}, {28175, 47757}, {28183, 47801}, {28191, 44432}, {28199, 44435}, {28205, 44433}, {28213, 30792}, {28863, 47830}, {28894, 47827}, {29029, 45664}, {29110, 30234}, {30520, 47823}, {30765, 47928}, {30795, 48140}, {30835, 48146}, {31209, 47693}, {43067, 48056}, {47829, 47880}, {47890, 48089}

X(48219) = midpoint of X(i) and X(j) for these {i,j}: {44429, 47773}, {47771, 47809}
X(48219) = reflection of X(i) in X(j) for these {i,j}: {47802, 47807}, {47803, 47766}, {47880, 47829}


X(48220) = X(230)X(231)∩X(513)X(4379)

Barycentrics    (b - c)*(3*a^3 + a*b^2 + 2*a*b*c + 4*b^2*c + a*c^2 + 4*b*c^2) : :
X(48220) = X[650] - 4 X[4874], X[650] + 2 X[7662], 2 X[676] + X[6590], 2 X[4874] + X[7662], 2 X[47132] + X[48062], 2 X[659] + X[48125], 2 X[1491] - 5 X[31250], X[2526] - 4 X[4885], X[2526] + 2 X[47694], 2 X[4885] + X[47694], 2 X[2533] + X[4162], 4 X[4369] - X[7659], 2 X[3716] + X[43067], X[3803] + 2 X[4823], 2 X[4010] + X[4790], 2 X[4394] + X[4804], X[4500] + 2 X[13246], X[14431] - 3 X[47875], X[17166] + 2 X[20317], 2 X[48029] + X[48133], 2 X[23770] + X[48095], 5 X[26985] + X[47697], 7 X[27138] - X[47940], X[47920] + 2 X[48134], 5 X[30835] + X[48153], 4 X[31287] - X[47975]

X(48220) lies on these lines: {230, 231}, {513, 4379}, {522, 47761}, {659, 48125}, {693, 47805}, {1491, 31250}, {1577, 28475}, {2526, 4885}, {2533, 4162}, {3667, 4369}, {3716, 4778}, {3803, 4823}, {4010, 4790}, {4160, 45664}, {4394, 4804}, {4500, 13246}, {4762, 47804}, {4763, 28161}, {4789, 47798}, {4802, 6546}, {8678, 14431}, {9508, 28205}, {17166, 20317}, {21116, 28195}, {23770, 48095}, {23880, 47820}, {23882, 47818}, {26985, 47697}, {27138, 47940}, {28191, 47962}, {28199, 47920}, {28894, 47797}, {30520, 47887}, {30835, 48153}, {31287, 47975}, {44567, 47825}, {47760, 47831}, {47777, 47822}, {47799, 47880}

X(48220) = midpoint of X(i) and X(j) for these {i,j}: {693, 47805}, {4789, 47798}, {7662, 47803}, {44429, 47694}, {47804, 47834}, {47813, 47832}
X(48220) = reflection of X(i) in X(j) for these {i,j}: {650, 47803}, {2526, 44429}, {44429, 4885}, {45320, 47833}, {47760, 47831}, {47777, 47822}, {47803, 4874}, {47825, 44567}, {47880, 47799}
X(48220) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4874, 7662, 650}, {4885, 47694, 2526}


X(48221) = X(2)X(4802)∩X(523)X(44902)

Barycentrics    (b - c)*(2*a^3 + a^2*b + a^2*c + 3*a*b*c + 4*b^2*c + 4*b*c^2) : :
X(48221) = 5 X[4379] + X[4800], 3 X[4379] + X[47832], 3 X[4800] - 5 X[47832], X[4800] - 5 X[47833], X[47832] - 3 X[47833], 3 X[47779] - X[47830], 2 X[650] + X[48127], 2 X[693] + X[4782], 2 X[4369] + X[48090], 2 X[4874] + X[48098], 4 X[4885] - X[48030], 3 X[14475] - X[47877], 5 X[24924] + X[48120], 4 X[25666] - X[47964], 5 X[30795] + X[48142], 5 X[31250] + X[48134], 2 X[43067] + X[48028]

X(48221) lies on these lines: {2, 4802}, {513, 4379}, {523, 44902}, {650, 48127}, {693, 4782}, {4369, 29328}, {4777, 37756}, {4823, 29340}, {4874, 48098}, {4885, 48030}, {4893, 28199}, {4926, 47824}, {4977, 47831}, {14077, 45332}, {14475, 47877}, {24924, 48120}, {25666, 47964}, {28147, 47829}, {28151, 47827}, {28161, 45668}, {28165, 47828}, {28175, 47778}, {28195, 47780}, {28220, 47821}, {29198, 47875}, {29204, 47887}, {29226, 47889}, {29274, 47820}, {30795, 48142}, {31250, 48134}, {43067, 48028}

X(48221) = midpoint of X(i) and X(j) for these {i,j}: {4379, 47833}, {47780, 47822}, {47823, 47834}


X(48222) = X(230)X(231)∩X(513)X(47772)

Barycentrics    (b - c)*(3*a^3 + 4*a^2*b - a*b^2 + 4*b^3 + 4*a^2*c - 2*a*b*c + 6*b^2*c - a*c^2 + 6*b*c^2 + 4*c^3) : :
X(48222) = 5 X[47766] - 3 X[47800], 4 X[47766] - 3 X[47803], 4 X[47800] - 5 X[47803], X[44433] - 3 X[47771], 2 X[44435] - 3 X[47802], X[44435] - 3 X[47809], 2 X[6050] + X[47710], 2 X[44432] - 3 X[47807], X[47963] - 4 X[48056], X[48089] + 2 X[48103]

X(48222) lies on these lines: {2, 28151}, {230, 231}, {513, 47772}, {4049, 29160}, {4120, 48106}, {4122, 4926}, {4777, 44433}, {4778, 48047}, {4802, 44435}, {4824, 28199}, {4951, 6008}, {6050, 47710}, {21115, 48118}, {21130, 47726}, {26275, 28169}, {28147, 44432}, {28155, 47799}, {28165, 47804}, {28175, 47806}, {28179, 47757}, {28187, 47801}, {28195, 47808}, {28205, 47805}, {28220, 31131}, {28602, 47880}, {28851, 48088}, {28859, 45344}, {29128, 45664}, {29144, 47770}, {29204, 47761}, {47690, 47892}, {47963, 48056}, {48089, 48103}

X(48222) = midpoint of X(i) and X(j) for these {i,j}: {4120, 48106}, {21115, 48118}, {21130, 47726}, {47690, 47892}
X(48222) = reflection of X(i) in X(j) for these {i,j}: {7662, 47881}, {47802, 47809}, {47880, 28602}, {47883, 2977}


X(48223) = X(2)X(4777)∩X(351)X(523)

Barycentrics    (b - c)*(-2*a^3 + 2*a^2*b + 2*b^3 + 2*a^2*c + a*b*c + b^2*c + b*c^2 + 2*c^3) : :
X(48223) = 2 X[26275] - 3 X[47798], 4 X[26275] - 3 X[47804], X[47771] - 3 X[47798], 2 X[47771] - 3 X[47804], 2 X[31131] - 3 X[44429], X[31131] - 3 X[47797], 3 X[44429] - 4 X[47757], 2 X[47757] - 3 X[47797], 2 X[659] + X[47692], 2 X[667] + X[47709], 4 X[676] - X[47690], 4 X[1960] - X[47684], 2 X[4401] + X[47713], 2 X[4458] + X[47972], 4 X[4458] - X[48108], 2 X[47972] + X[48108], 4 X[4874] - X[47689], 4 X[8689] - X[48130], 4 X[13246] - X[48106], X[17494] + 2 X[47131], 2 X[30792] - 3 X[47799], 4 X[30792] - 3 X[47808], 4 X[28602] - 5 X[31209], X[47941] - 4 X[48006], 4 X[34958] - X[47719], 4 X[47132] - X[47656], 2 X[47695] + X[47975], X[47931] + 2 X[48072]

X(48223) lies on these lines: {2, 4777}, {351, 523}, {514, 44433}, {519, 21130}, {522, 4728}, {650, 26242}, {659, 47692}, {667, 29128}, {676, 47690}, {693, 26234}, {900, 44435}, {1960, 47684}, {2786, 48080}, {3873, 9001}, {4391, 29110}, {4401, 47713}, {4448, 29204}, {4458, 47972}, {4724, 28890}, {4800, 29370}, {4802, 47805}, {4809, 29144}, {4874, 47689}, {6084, 47691}, {7662, 47792}, {8643, 29116}, {8689, 48130}, {13246, 48106}, {17494, 26274}, {25569, 29172}, {26248, 47655}, {26277, 47657}, {28147, 47801}, {28151, 47773}, {28161, 47800}, {28165, 47803}, {28169, 47766}, {28183, 30792}, {28187, 47807}, {28205, 47802}, {28602, 31209}, {28859, 47701}, {28878, 47941}, {28894, 47694}, {29021, 47820}, {29047, 47815}, {29126, 47708}, {29164, 47818}, {29250, 47872}, {29260, 47817}, {34958, 47719}, {47132, 47656}, {47695, 47782}, {47931, 48072}

X(48223) = midpoint of X(47695) and X(47782)
X(48223) = reflection of X(i) in X(j) for these {i,j}: {31131, 47757}, {44429, 47797}, {47690, 47788}, {47762, 4809}, {47771, 26275}, {47788, 676}, {47792, 7662}, {47804, 47798}, {47808, 47799}, {47809, 47800}, {47975, 47782}
X(48223) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4458, 47972, 48108}, {26275, 47771, 47804}, {31131, 47757, 44429}, {31131, 47797, 47757}, {47771, 47798, 26275}


X(48224) = X(2)X(29204)∩X(523)X(1638)

Barycentrics    (b - c)*(-a^3 + a^2*b + a*b^2 + 2*b^3 + a^2*c + b^2*c + a*c^2 + b*c^2 + 2*c^3) : :
X(48224) = 4 X[1638] - 3 X[47823], 2 X[4782] + X[47688], 2 X[9508] + X[47692], X[30565] - 3 X[47797], 2 X[30565] - 3 X[47822], 2 X[45326] - 3 X[47799]

X(48224) lies on these lines: {2, 29204}, {75, 693}, {514, 659}, {523, 1638}, {826, 47841}, {900, 24719}, {4010, 28898}, {4122, 30865}, {4448, 30520}, {4453, 29144}, {4728, 29370}, {4782, 47688}, {4800, 30519}, {4802, 31150}, {4928, 4951}, {7950, 47795}, {9508, 47692}, {14413, 29172}, {14419, 29160}, {24623, 27486}, {28151, 46915}, {28179, 47767}, {28209, 47958}, {28871, 48024}, {28902, 47998}, {29047, 47835}, {29146, 47796}, {29260, 47837}, {29280, 47840}, {29358, 47839}, {30565, 47797}, {30913, 31947}, {45326, 47799}, {46919, 48062}

X(48224) = midpoint of X(27486) and X(47691)
X(48224) = reflection of X(i) in X(j) for these {i,j}: {4122, 47787}, {4951, 4928}, {36848, 47754}, {47822, 47797}, {48062, 46919}
X(48224) = crossdifference of every pair of points on line {2251, 2276}


X(48225) = X(2)X(4777)∩X(523)X(1638)

Barycentrics    (b - c)*(-a^3 - a^2*b + 3*a*b^2 - a^2*c + 4*a*b*c + b^2*c + 3*a*c^2 + b*c^2) : :
X(48225) = X[47775] - 3 X[47825], 2 X[4800] - 3 X[47822], X[4800] - 3 X[47827], 4 X[47778] - 3 X[47822], 2 X[47778] - 3 X[47827], 2 X[4379] - 3 X[47823], X[4379] - 3 X[47828], X[659] + 2 X[48017], 5 X[659] - 2 X[48072], 5 X[48017] + X[48072], X[1491] + 2 X[4913], 4 X[1491] - X[24719], 5 X[1491] - 2 X[48050], 8 X[4913] + X[24719], 5 X[4913] + X[48050], 5 X[24719] - 8 X[48050], 5 X[2254] + X[47933], X[4784] + 2 X[48010], 2 X[4818] + X[48103], 2 X[7659] + X[47946], 2 X[9508] + X[47975], 4 X[25380] - X[48120]

X(48225) lies on these lines: {2, 4777}, {513, 14404}, {514, 4948}, {519, 4825}, {522, 4800}, {523, 1638}, {650, 2276}, {659, 48017}, {784, 47835}, {812, 1491}, {900, 4893}, {1734, 29188}, {2254, 47933}, {4010, 47760}, {4151, 47841}, {4560, 29236}, {4705, 29148}, {4728, 45323}, {4762, 36848}, {4784, 48010}, {4802, 47824}, {4809, 47785}, {4818, 48103}, {4926, 47821}, {7659, 47946}, {8043, 30913}, {9508, 47762}, {25380, 48120}, {28151, 47780}, {28161, 44563}, {28165, 47834}, {28169, 47779}, {28183, 47829}, {28217, 47826}, {28602, 47874}, {29144, 47782}, {29178, 48012}, {29204, 47894}, {29328, 47810}, {47759, 48030}

X(48225) = midpoint of X(47762) and X(47975)
X(48225) = reflection of X(i) in X(j) for these {i,j}: {4010, 47760}, {4448, 650}, {4728, 45323}, {4800, 47778}, {4809, 47785}, {47759, 48030}, {47762, 9508}, {47822, 47827}, {47823, 47828}, {47832, 47829}, {47833, 47830}, {47841, 47888}, {47874, 28602}
X(48225) = crossdifference of every pair of points on line {4262, 16971}
X(48225) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4800, 47778, 47822}, {4800, 47827, 47778}


X(48226) = X(44)X(513)∩X(351)X(523)

Barycentrics    a*(b - c)*(2*a^2 - b^2 - 3*b*c - c^2) : :
X(48226) = 2 X[649] + X[48024], 2 X[650] + X[659], 4 X[650] - X[1491], 7 X[650] - X[2526], 2 X[659] + X[1491], 7 X[659] + 2 X[2526], X[661] + 2 X[4782], 7 X[1491] - 4 X[2526], 2 X[2526] - 7 X[47827], 4 X[4394] - X[4784], 2 X[4394] + X[48029], X[4724] + 2 X[9508], X[4784] + 2 X[48029], X[4979] + 2 X[48028], X[31150] + 2 X[45314], X[4951] - 4 X[10196], 2 X[667] + X[4490], X[667] + 2 X[48003], X[4490] - 4 X[48003], X[30709] - 3 X[47793], 4 X[905] - X[23765], 2 X[1019] + X[47913], X[3777] - 4 X[14838], 4 X[3004] - X[47925], 2 X[3798] + X[48040], 2 X[3837] - 5 X[31209], X[4010] + 2 X[48008], 2 X[4025] + X[48083], 2 X[4063] + X[48123], X[4367] - 4 X[6050], X[4367] + 2 X[47965], 2 X[6050] + X[47965], 4 X[4369] - X[48143], X[4380] + 2 X[4806], 2 X[4401] + X[4705], X[4730] + 2 X[4794], 2 X[4830] + X[24719], X[4830] + 2 X[25666], X[24719] - 4 X[25666], X[4834] + 2 X[48058], 2 X[4874] + X[17494], 4 X[4874] - X[48120], 2 X[17494] + X[48120], 2 X[4932] + X[47946], X[4978] - 4 X[31288], X[4983] + 2 X[48011], 2 X[7192] + X[47910], 2 X[8689] + X[48017], 4 X[11068] - X[48103], 2 X[17069] + X[48055], X[21146] - 4 X[31286], 5 X[24924] - 2 X[48098], 5 X[26777] + X[47694], 5 X[27013] + X[47969], 7 X[27115] - X[46403], 4 X[47890] - X[48140], 5 X[30795] - 8 X[31287], 5 X[30795] - 2 X[48089], 4 X[31287] - X[48089], 7 X[31207] - X[48119], X[47928] - 4 X[48000], X[47932] + 2 X[48090], X[47935] + 2 X[48093], X[47944] + 2 X[48060], X[47949] + 2 X[48064], 2 X[47954] + X[48147], 2 X[47957] + X[48149], X[47971] + 2 X[48048], X[47976] + 2 X[48053], 2 X[47990] + X[48104], 2 X[47993] + X[48107], 2 X[47994] + X[48110]

X(48226) lies on these lines: {2, 29362}, {44, 513}, {351, 523}, {514, 14419}, {522, 3971}, {667, 4160}, {784, 47817}, {812, 47822}, {814, 30709}, {905, 23765}, {1019, 47913}, {2832, 3777}, {2977, 28183}, {3004, 28213}, {3667, 45673}, {3798, 48040}, {3837, 31209}, {4010, 48008}, {4025, 48083}, {4063, 48123}, {4367, 6050}, {4369, 48143}, {4380, 4806}, {4401, 4705}, {4730, 4794}, {4762, 47803}, {4763, 47823}, {4778, 45313}, {4802, 47813}, {4830, 24719}, {4834, 48058}, {4874, 17494}, {4932, 47946}, {4977, 47762}, {4978, 31288}, {4983, 48011}, {6084, 47799}, {7192, 47910}, {8689, 48017}, {11068, 28147}, {14077, 25569}, {14425, 47807}, {14430, 29236}, {14431, 29033}, {17069, 48055}, {21052, 29274}, {21146, 31286}, {23882, 47872}, {24924, 48098}, {26777, 47694}, {27013, 47969}, {27115, 46403}, {28161, 48062}, {28175, 47667}, {28195, 31148}, {28229, 47968}, {28602, 47808}, {29051, 47835}, {29070, 47794}, {29078, 30565}, {29186, 47837}, {29246, 47836}, {29302, 47839}, {29328, 47776}, {29370, 31992}, {30795, 31287}, {31207, 48119}, {36848, 47830}, {38348, 45755}, {44429, 47829}, {44567, 47802}, {45666, 47832}, {47797, 47892}, {47805, 47825}, {47928, 48000}, {47932, 48090}, {47935, 48093}, {47944, 48060}, {47949, 48064}, {47954, 48147}, {47957, 48149}, {47971, 48048}, {47976, 48053}, {47990, 48104}, {47993, 48107}, {47994, 48110}

X(48226) = midpoint of X(i) and X(j) for these {i,j}: {649, 47826}, {659, 47827}, {1635, 47811}, {17494, 47834}, {30234, 47965}, {31150, 47804}, {47776, 47821}, {47797, 47892}, {47805, 47825}
X(48226) = reflection of X(i) in X(j) for these {i,j}: {1491, 47827}, {4367, 30234}, {30234, 6050}, {36848, 47830}, {44429, 47829}, {47802, 44567}, {47804, 45314}, {47807, 14425}, {47808, 28602}, {47823, 4763}, {47827, 650}, {47832, 45666}, {47833, 47803}, {47834, 4874}, {47877, 47784}, {47885, 47884}, {48024, 47826}, {48120, 47834}
X(48226) = X(7607)-Ceva conjugate of X(11)
X(48226) = crosssum of X(513) and X(4663)
X(48226) = crossdifference of every pair of points on line {1, 574}
X(48226) = barycentric product X(i)*X(j) for these {i,j}: {513, 29617}, {693, 10987}, {1019, 4527}
X(48226) = barycentric quotient X(i)/X(j) for these {i,j}: {4527, 4033}, {10987, 100}, {29617, 668}
X(48226) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 659, 1491}, {667, 48003, 4490}, {4394, 48029, 4784}, {4830, 25666, 24719}, {4874, 17494, 48120}, {6050, 47965, 4367}, {31287, 48089, 30795}


X(48227) = X(513)X(4453)∩X(523)X(1638)

Barycentrics    (b - c)*(-a^3 + a*b^2 + b^3 + a*c^2 + c^3) : :
X(48227) = X[4809] + 2 X[47754], X[659] + 2 X[3776], 2 X[905] + X[3801], X[1491] + 2 X[4458], X[1491] - 4 X[21212], X[4458] + 2 X[21212], X[2530] + 2 X[20517], X[2533] - 4 X[21188], 4 X[3676] - X[21146], X[3777] + 2 X[4142], X[4010] + 2 X[4025], X[4122] - 4 X[4885], X[4467] + 2 X[48090], 2 X[4522] - 5 X[30795], 2 X[4782] + X[47652], 2 X[4806] + X[47971], 2 X[4874] + X[16892], 2 X[4932] + X[47944], 4 X[7658] - X[48062], 2 X[9508] + X[47691], 2 X[17069] + X[23770], 2 X[18004] - 5 X[30835], 2 X[21196] + X[48120], 5 X[27013] + X[47688], 7 X[31207] - X[48118], 5 X[31209] - 2 X[48056], 4 X[31286] - X[48103], 4 X[31287] - X[48088], X[47661] + 2 X[48127], 2 X[47990] + X[48107]

X(48227) lies on these lines: {513, 4453}, {514, 14419}, {522, 21204}, {523, 1638}, {525, 47841}, {659, 3776}, {824, 47833}, {826, 47795}, {905, 3801}, {918, 47799}, {1491, 4458}, {2530, 20517}, {2533, 21188}, {3676, 21146}, {3777, 4142}, {4010, 4025}, {4122, 4885}, {4448, 47800}, {4467, 48090}, {4522, 30795}, {4728, 29078}, {4750, 29328}, {4763, 47885}, {4782, 47652}, {4802, 47761}, {4806, 47971}, {4874, 16892}, {4932, 47944}, {6545, 29362}, {7658, 48062}, {9508, 47691}, {14431, 29212}, {14475, 29370}, {17069, 23770}, {18004, 30835}, {21115, 47811}, {21121, 21828}, {21196, 48120}, {23875, 47839}, {23877, 47893}, {26747, 31947}, {27013, 47688}, {28175, 47767}, {29017, 47796}, {29047, 47837}, {29144, 47824}, {29200, 47840}, {29204, 47809}, {29208, 47836}, {29252, 47838}, {29288, 41800}, {29354, 47794}, {30519, 47831}, {30520, 47803}, {31207, 48118}, {31209, 48056}, {31286, 48103}, {31287, 48088}, {44902, 47807}, {47661, 48127}, {47827, 47882}, {47834, 47894}, {47990, 48107}

X(48227) = midpoint of X(i) and X(j) for these {i,j}: {4453, 47797}, {21115, 47811}, {47834, 47894}, {47886, 47887}
X(48227) = reflection of X(i) in X(j) for these {i,j}: {4448, 47800}, {47807, 44902}, {47822, 47799}, {47823, 1638}, {47827, 47882}, {47835, 41800}, {47885, 4763}
X(48227) = barycentric product X(514)*X(4655)
X(48227) = barycentric quotient X(4655)/X(190)
X(48227) = {X(4458),X(21212)}-harmonic conjugate of X(1491)


X(48228) = X(2)X(522)∩X(523)X(47795)

Barycentrics    (b - c)*(a^4 + a^3*b - a^2*b^2 - a*b^3 + a^3*c - 2*a*b^2*c + b^3*c - a^2*c^2 - 2*a*b*c^2 + 2*b^2*c^2 - a*c^3 + b*c^3) : :
X(48228) = 2 X[10] + X[1459], 2 X[905] + X[4086], 5 X[1698] - 2 X[20316], 5 X[1698] + X[21173], 2 X[20316] + X[21173], X[1734] + 2 X[8062], X[2517] + 2 X[14838], X[2530] + 2 X[6133], X[3737] + 2 X[17072], 2 X[4401] + X[44444], X[4768] + 2 X[6129], X[4815] - 4 X[4885], 7 X[9780] - X[20293], X[20294] + 2 X[21180], 2 X[20315] + X[21186], X[23800] - 4 X[25380], 2 X[39508] + X[44812], X[44550] + 2 X[45660], X[47844] + 2 X[48012]

X(48228) lies on these lines: {2, 522}, {9, 22443}, {10, 1459}, {404, 39226}, {474, 39199}, {513, 47794}, {523, 47795}, {657, 5750}, {905, 4086}, {965, 23146}, {1698, 20316}, {1734, 8062}, {2517, 14838}, {2530, 6133}, {3261, 28653}, {3667, 26078}, {3737, 17072}, {4036, 16828}, {4139, 47841}, {4401, 44444}, {4474, 19874}, {4768, 6129}, {4778, 47793}, {4815, 4885}, {4913, 25511}, {4962, 26144}, {6371, 47835}, {6586, 17303}, {8672, 47823}, {9000, 38047}, {9780, 20293}, {17306, 21195}, {19863, 31947}, {20294, 21180}, {20315, 21186}, {23684, 25603}, {23800, 25380}, {24720, 26049}, {26446, 32475}, {26822, 47909}, {27167, 48142}, {28147, 47796}, {39508, 44812}, {44550, 45660}, {47844, 48012}

X(48228) = {X(1698),X(21173)}-harmonic conjugate of X(20316)


X(48229) = X(2)X(900)∩X(523)X(1638)

Barycentrics    (b - c)*(2*a^3 + 2*a^2*b - 3*a*b^2 + 2*a^2*c - 2*a*b*c + b^2*c - 3*a*c^2 + b*c^2) : :
X(48229) = X[45314] + 2 X[45328], X[45314] - 4 X[45691], X[45328] + 2 X[45691], 2 X[47778] - 3 X[47829], X[47778] - 3 X[47830], X[4379] - 3 X[47823], X[4379] + 3 X[47828], X[3837] + 2 X[9508], X[3837] - 4 X[25380], X[9508] + 2 X[25380], 7 X[1491] - X[47940], 7 X[47762] + X[47940], X[47775] + 3 X[47824], X[47775] - 3 X[47827], 2 X[31288] + X[48018]

X(48229) lies on these lines: {2, 900}, {513, 4763}, {519, 14422}, {523, 1638}, {665, 1575}, {812, 3837}, {891, 45657}, {918, 28602}, {1491, 47762}, {1635, 36848}, {2254, 4448}, {3828, 28603}, {4191, 39478}, {4212, 39534}, {4728, 45340}, {4777, 47779}, {4784, 47759}, {4806, 47760}, {4893, 28209}, {4926, 47831}, {4948, 28179}, {4977, 47775}, {13588, 42741}, {14315, 43055}, {14413, 25574}, {14838, 29188}, {16059, 39200}, {17072, 29236}, {17754, 22108}, {21051, 29148}, {21260, 29178}, {28161, 45668}, {28175, 47825}, {28183, 47833}, {28187, 47834}, {28217, 47822}, {28221, 47832}, {29078, 47806}, {29144, 47882}, {29328, 47802}, {31288, 48018}, {38238, 47330}, {39386, 47821}, {45342, 45678}, {45666, 45675}, {47836, 47893}

X(48229) = midpoint of X(i) and X(j) for these {i,j}: {1491, 47762}, {1635, 36848}, {2254, 4448}, {4763, 45328}, {4784, 47759}, {4948, 47780}, {26078, 28284}, {47823, 47828}, {47824, 47827}, {47836, 47893}
X(48229) = reflection of X(i) in X(j) for these {i,j}: {4728, 45340}, {4763, 45691}, {4806, 47760}, {28603, 3828}, {45314, 4763}, {45342, 45678}, {45666, 45675}, {47829, 47830}
X(48229) = complement of X(4800)
X(48229) = X(i)-complementary conjugate of X(j) for these (i,j): {291, 15614}, {660, 21251}, {2163, 38989}, {4588, 17793}, {4597, 20542}, {4604, 20333}, {5385, 27854}, {28607, 35119}, {34067, 16590}, {34073, 17755}
X(48229) = crossdifference of every pair of points on line {4262, 8649}
X(48229) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9508, 25380, 3837}, {45328, 45691, 45314}


X(48230) = X(2)X(513)∩X(523)X(47795)

Barycentrics    (b - c)*(a^4 + a^3*b - a^2*b^2 - a*b^3 + a^3*c - a*b^2*c + b^3*c - a^2*c^2 - a*b*c^2 + 2*b^2*c^2 - a*c^3 + b*c^3) : :
X(48230) = X[667] + 2 X[44316], X[693] + 2 X[8043], 2 X[905] + X[4036], X[2517] + 2 X[31947], X[2605] + 2 X[17072], X[3733] + 2 X[21260], X[4057] - 4 X[31288], 4 X[4885] - X[30591], X[8062] + 2 X[25380], 5 X[31251] - 2 X[31946], X[39210] + 2 X[39508], X[43927] + 2 X[48059]

X(48230) lies on these lines: {2, 513}, {37, 22095}, {475, 16228}, {523, 47795}, {667, 44316}, {693, 8043}, {834, 47837}, {905, 4036}, {966, 39521}, {1213, 20980}, {2517, 31947}, {2605, 17072}, {3063, 17398}, {3733, 21260}, {4057, 31288}, {4132, 47841}, {4378, 16828}, {4775, 25512}, {4802, 47796}, {4885, 30591}, {4926, 26078}, {4977, 47794}, {8062, 25380}, {9508, 25511}, {17303, 21348}, {20906, 28653}, {24960, 43060}, {25901, 34948}, {26049, 48098}, {27193, 48090}, {28195, 47793}, {31251, 31946}, {39210, 39508}, {43927, 48059}


X(48231) = X(2)X(4977)∩X(351)X(523)

Barycentrics    (b - c)*(4*a^3 + a^2*b + b^3 + a^2*c - 2*a*b*c + 3*b^2*c + 3*b*c^2 + c^3) : :
X(48231) = X[26275] + 2 X[47771], 3 X[26275] - 2 X[47798], 3 X[47771] + X[47798], X[47798] - 3 X[47804], 3 X[47766] - X[47806], 2 X[47806] - 3 X[47807], 2 X[676] + X[48103], X[1491] - 4 X[2490], 4 X[2527] - X[4784], 2 X[2977] + X[47694], 2 X[3676] + X[48096], X[3700] + 2 X[4782], 2 X[4369] + X[48055], 4 X[4521] - X[48027], 4 X[4874] - X[23770], 2 X[4874] + X[47890], X[23770] + 2 X[47890], 3 X[6544] - X[47810], X[7662] + 2 X[11068], 5 X[24924] + X[48102], 4 X[25666] - X[47989], 7 X[31207] - X[47973], 5 X[31209] + X[47696], 4 X[31287] - X[48007]

X(48231) lies on these lines: {2, 4977}, {351, 523}, {513, 1639}, {514, 47799}, {676, 48103}, {900, 47805}, {1491, 2490}, {2527, 4784}, {2977, 47694}, {3004, 26248}, {3676, 48096}, {3700, 4782}, {4369, 48055}, {4521, 48027}, {4777, 47801}, {4778, 45315}, {4802, 47800}, {4874, 23770}, {6084, 47833}, {6544, 47810}, {6546, 47813}, {7662, 11068}, {14425, 47827}, {24924, 48102}, {25666, 47989}, {28175, 47773}, {28183, 44433}, {28195, 47757}, {28209, 44429}, {28213, 44435}, {28217, 47808}, {28229, 44432}, {28882, 47831}, {29142, 47817}, {29162, 47872}, {29288, 47818}, {29362, 47788}, {30765, 47946}, {31131, 39386}, {31207, 47973}, {31209, 47696}, {31287, 48007}, {47834, 47892}

X(48231) = midpoint of X(i) and X(j) for these {i,j}: {6546, 47813}, {47771, 47804}, {47773, 47797}, {47805, 47809}, {47834, 47892}
X(48231) = reflection of X(i) in X(j) for these {i,j}: {26275, 47804}, {47799, 47803}, {47807, 47766}, {47827, 14425}
X(48231) = crossdifference of every pair of points on line {574, 16483}
X(48231) = {X(4874),X(47890)}-harmonic conjugate of X(23770)


X(48232) = X(513)X(1639)∩X(523)X(1638)

Barycentrics    (b - c)*(2*a^3 + 3*a^2*b - 2*a*b^2 + b^3 + 3*a^2*c + 3*b^2*c - 2*a*c^2 + 3*b*c^2 + c^3) : :
X(48232) = 2 X[676] - 5 X[24924], 4 X[2490] - X[4724], 2 X[2977] + X[21146], X[3004] - 4 X[25380], 2 X[3239] + X[7659], 4 X[3837] - X[23729], 2 X[4522] + X[4897], 2 X[4885] + X[48069], 2 X[4925] + X[47694], X[4976] - 4 X[9508], 2 X[17069] + X[47690], X[21104] + 2 X[48062], 2 X[24720] + X[47890], 5 X[27013] + X[47687], 7 X[31207] - X[47972], 4 X[31287] - X[48006]

X(48232) lies on these lines: {513, 1639}, {522, 47761}, {523, 1638}, {676, 24924}, {918, 47809}, {2490, 4724}, {2977, 21146}, {3004, 25380}, {3239, 7659}, {3667, 47879}, {3800, 47795}, {3837, 23729}, {3910, 47836}, {4522, 4897}, {4809, 28183}, {4885, 48069}, {4925, 47694}, {4976, 9508}, {4977, 6546}, {6084, 47812}, {14425, 47811}, {17069, 47690}, {21104, 48062}, {21116, 28175}, {24720, 47890}, {27013, 47687}, {28147, 47754}, {29021, 41800}, {29142, 47837}, {29144, 47799}, {29288, 30724}, {31207, 47972}, {31287, 48006}, {44902, 47797}, {45326, 47821}, {47756, 47802}, {47762, 47808}, {47784, 47830}, {47827, 47876}

X(48232) = midpoint of X(i) and X(j) for these {i,j}: {47762, 47808}, {47809, 47824}
X(48232) = reflection of X(i) in X(j) for these {i,j}: {1638, 47823}, {1639, 47807}, {47756, 47802}, {47784, 47830}, {47797, 44902}, {47811, 14425}, {47821, 45326}, {47876, 47827}
X(48232) = crossdifference of every pair of points on line {4262, 16483}


X(48233) = X(2)X(4977)∩X(523)X(1638)

Barycentrics    (b - c)*(2*a^3 + 2*a^2*b - a*b^2 + 2*a^2*c + 2*a*b*c + 3*b^2*c - a*c^2 + 3*b*c^2) : :
X(48233) = X[3837] + 2 X[4369], 5 X[3837] - 2 X[48050], 5 X[4369] + X[48050], X[4806] - 4 X[4885], 5 X[24720] + X[48072], 3 X[47779] - X[47831], 3 X[4379] + X[47828], 3 X[47823] - X[47828], X[4784] + 5 X[26985], X[7192] + 5 X[30795], X[21146] + 5 X[24924], 5 X[21146] + X[47933], 5 X[24924] - X[47811], 25 X[24924] - X[47933], 5 X[47811] - X[47933], 4 X[25666] - X[47993], X[31148] + 2 X[45340], 5 X[31209] + X[48143], 2 X[31286] + X[48098], 2 X[43067] + X[48002], X[45314] - 4 X[45663]

X(48233) lies on these lines: {2, 4977}, {513, 3716}, {514, 47829}, {523, 1638}, {900, 47824}, {2490, 4893}, {2533, 14413}, {2977, 3004}, {4784, 26985}, {4800, 39386}, {4802, 47830}, {7192, 30795}, {15584, 35057}, {21146, 24924}, {21181, 29166}, {21212, 28147}, {25666, 47993}, {28179, 47825}, {28183, 47132}, {28195, 47778}, {28209, 47822}, {28217, 47832}, {28229, 47999}, {29078, 47758}, {29328, 45320}, {29362, 47761}, {31148, 45340}, {31209, 48143}, {31286, 48098}, {36848, 47813}, {43067, 48002}, {45314, 45663}, {47791, 47877}, {47807, 47891}, {47826, 47989}, {47836, 47889}

X(48233) = midpoint of X(i) and X(j) for these {i,j}: {2533, 14413}, {4379, 47823}, {21146, 47811}, {36848, 47813}, {47780, 47827}, {47791, 47877}, {47807, 47891}, {47824, 47833}, {47836, 47889}
X(48233) = crossdifference of every pair of points on line {2176, 4262}


X(48234) = X(2)X(1491)∩X(351)X(523)

Barycentrics    (b - c)*(2*a^3 + a*b^2 + a*b*c + 2*b^2*c + a*c^2 + 2*b*c^2) : :
X(48234) = X[1491] - 4 X[4874], 3 X[1491] - 4 X[45323], X[1491] + 2 X[47694], 3 X[4874] - X[45323], 2 X[4874] + X[47694], 2 X[45323] + 3 X[47694], X[31150] - 3 X[47804], 2 X[45314] - 3 X[47804], X[31147] - 3 X[47832], X[31148] - 3 X[47813], 2 X[45320] - 3 X[47833], 2 X[45342] - 3 X[47832], 3 X[4448] - 2 X[45673], X[659] + 2 X[7662], 2 X[659] + X[48120], 4 X[7662] - X[48120], X[45671] - 3 X[47818], X[31149] - 3 X[47875], 2 X[45324] - 3 X[47875], 2 X[2526] - 5 X[30795], 4 X[3716] - X[48024], 2 X[4724] + X[48143], 2 X[3837] + X[47697], 2 X[4782] + X[4804], 3 X[4893] - 2 X[45676], 3 X[45666] - X[45676], 2 X[45664] - 3 X[47872], X[21146] + 2 X[48063], 3 X[47805] + X[47869], 3 X[47834] - X[47869], 3 X[44429] - 4 X[45340], X[44550] - 3 X[47820], 4 X[44561] - 3 X[47893], 2 X[44567] - 3 X[47803], 4 X[44567] - 3 X[47827], 2 X[45315] - 3 X[47822], 4 X[45337] - 3 X[47822], 4 X[45318] - 3 X[47799], 8 X[45318] - 3 X[47877], 2 X[45328] - 3 X[47823], 4 X[45663] - 3 X[47823], 2 X[45339] - 3 X[47831], 4 X[45691] - 3 X[47828], 2 X[47123] + X[48103], 2 X[47132] + X[47890], 2 X[47691] + X[48140], 2 X[47696] + X[47925], X[47705] + 2 X[48097], X[47774] - 3 X[47821], X[47910] - 4 X[48029], X[47928] + 2 X[48142], X[47933] + 2 X[48135], 2 X[48030] + X[48153], X[48032] + 2 X[48098]

X(48234) lies on these lines: {2, 1491}, {351, 523}, {513, 4379}, {514, 551}, {522, 45313}, {599, 9014}, {650, 4948}, {659, 4762}, {784, 45671}, {824, 4809}, {830, 31149}, {900, 47762}, {1635, 4777}, {2526, 30795}, {3251, 4844}, {3716, 28840}, {3720, 4724}, {3837, 47697}, {3840, 24720}, {4010, 4785}, {4782, 4804}, {4789, 44433}, {4802, 47811}, {4824, 43223}, {4893, 45666}, {4927, 28209}, {4951, 47874}, {8678, 45664}, {21146, 48063}, {24768, 43067}, {29362, 47805}, {29370, 47870}, {36848, 47779}, {44429, 45340}, {44550, 47820}, {44561, 47893}, {44567, 47803}, {45315, 45337}, {45318, 47799}, {45328, 45663}, {45339, 47831}, {45691, 47828}, {47123, 48103}, {47132, 47890}, {47691, 48140}, {47696, 47925}, {47705, 48097}, {47774, 47821}, {47910, 48029}, {47928, 48142}, {47933, 48135}, {48030, 48153}, {48032, 48098}

X(48234) = midpoint of X(i) and X(j) for these {i,j}: {2, 47694}, {4789, 44433}, {47805, 47834}
X(48234) = reflection of X(i) in X(j) for these {i,j}: {2, 4874}, {1491, 2}, {4893, 45666}, {4948, 650}, {4951, 47874}, {31147, 45342}, {31149, 45324}, {31150, 45314}, {36848, 47779}, {45315, 45337}, {45328, 45663}, {47827, 47803}, {47877, 47799}
X(48234) = anticomplement of X(45323)
X(48234) = crossdifference of every pair of points on line {574, 8624}
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {659, 7662, 48120}, {4874, 47694, 1491}, {31147, 47832, 45342}, {31149, 47875, 45324}, {31150, 47804, 45314}, {45315, 45337, 47822}, {45328, 45663, 47823}


X(48235) = X(10)X(514)∩X(523)X(1638)

Barycentrics    (b - c)*(a^3 + 2*a^2*b - a*b^2 + b^3 + 2*a^2*c + 2*b^2*c - a*c^2 + 2*b*c^2 + c^3) : :
X(48235) = X[21146] + 2 X[48062], 2 X[24720] + X[48103], X[30565] - 3 X[47809], 2 X[1638] - 3 X[47823], 2 X[3837] + X[48106], X[4010] + 2 X[48069], 2 X[4522] + X[4784], 2 X[9508] + X[47690], 2 X[4782] + X[47687], 2 X[45326] - 3 X[47807], 4 X[45326] - 3 X[47822], 2 X[48056] + X[48108], 2 X[48073] + X[48083]

X(48235) lies on these lines: {2, 29144}, {10, 514}, {513, 30565}, {522, 45313}, {523, 1638}, {649, 900}, {660, 3807}, {2786, 4951}, {3800, 47841}, {3837, 48106}, {4010, 47787}, {4122, 28898}, {4448, 47766}, {4453, 29204}, {4522, 4784}, {4750, 29370}, {4777, 4789}, {4782, 47687}, {4800, 47879}, {4844, 30580}, {4893, 28602}, {6006, 48072}, {7927, 47795}, {14419, 29192}, {14431, 29132}, {21052, 29120}, {21196, 28169}, {28151, 45746}, {28209, 48023}, {28220, 47952}, {28855, 45344}, {28863, 45328}, {28902, 48047}, {29017, 47836}, {29021, 47837}, {29142, 47835}, {29168, 47794}, {29172, 30574}, {29208, 47796}, {30792, 47756}, {45326, 47807}, {48056, 48108}, {48073, 48083}

X(48235) = midpoint of X(i) and X(j) for these {i,j}: {27486, 47690}, {47787, 48069}
X(48235) = reflection of X(i) in X(j) for these {i,j}: {4010, 47787}, {4448, 47766}, {4800, 47879}, {4809, 47761}, {4893, 28602}, {27486, 9508}, {47756, 30792}, {47822, 47807}
X(48235) = crossdifference of every pair of points on line {995, 1914}


X(48236) = X(2)X(4802)∩X(351)X(523)

Barycentrics    (b - c)*(2*a^3 + 2*a^2*b + 2*b^3 + 2*a^2*c - a*b*c + 3*b^2*c + 3*b*c^2 + 2*c^3) : :
X(48236) = 2 X[26275] - 5 X[47771], 6 X[26275] - 5 X[47798], 4 X[26275] - 5 X[47804], 3 X[47771] - X[47798], 2 X[47798] - 3 X[47804], 3 X[44429] - 4 X[47806], 2 X[47806] - 3 X[47809], 2 X[650] + X[47693], 2 X[659] + X[47689], 2 X[667] + X[47706], X[693] + 2 X[48103], 2 X[1491] + X[47662], 4 X[2977] - X[45746], 2 X[3835] + X[48146], 4 X[3837] - X[47651], 2 X[3837] + X[48140], X[47651] + 2 X[48140], 2 X[4122] + X[4380], 2 X[4369] + X[48118], 2 X[4401] + X[47710], 4 X[4468] - X[47941], 2 X[4522] + X[48101], 4 X[4874] - X[47692], 4 X[4885] - X[47688], X[7192] + 2 X[48088], 4 X[9508] - X[47677], 4 X[18004] - X[48079], X[21146] + 2 X[48097], 2 X[24720] + X[48130], 4 X[25380] - X[47923], 4 X[25666] - X[47924], X[46403] + 2 X[48095], 2 X[47660] + X[47975], X[47660] + 2 X[48062], X[47975] - 4 X[48062], X[47666] - 4 X[48056], X[47690] + 2 X[47890], 2 X[48050] + X[48138], 2 X[48073] + X[48113], X[48080] + 2 X[48106], 2 X[48094] + X[48108]

X(48236) lies on these lines: {2, 4802}, {351, 523}, {513, 47772}, {514, 14430}, {650, 47693}, {659, 47689}, {667, 47706}, {693, 48103}, {1491, 47662}, {2977, 45746}, {3835, 48146}, {3837, 47651}, {4122, 4380}, {4369, 48118}, {4391, 29029}, {4401, 47710}, {4468, 47941}, {4522, 48101}, {4777, 47805}, {4778, 31131}, {4874, 47692}, {4885, 47688}, {4977, 47808}, {7192, 48088}, {9508, 47677}, {18004, 48079}, {21146, 48097}, {24720, 48130}, {25380, 47923}, {25666, 47924}, {26248, 47657}, {26277, 47655}, {28147, 47766}, {28151, 47803}, {28155, 47800}, {28161, 44433}, {28169, 47801}, {28175, 44435}, {28179, 47799}, {28191, 47757}, {28199, 45676}, {28602, 47877}, {28863, 47828}, {28894, 47825}, {29021, 47815}, {29047, 47820}, {29164, 47817}, {29174, 47872}, {29260, 47818}, {30520, 47824}, {46403, 48095}, {47660, 47975}, {47666, 48056}, {47690, 47890}, {47770, 47821}, {47834, 47881}, {48050, 48138}, {48073, 48113}, {48080, 48106}, {48094, 48108}

X(48236) = reflection of X(i) in X(j) for these {i,j}: {31150, 47885}, {44429, 47809}, {44435, 47807}, {47797, 47766}, {47804, 47771}, {47821, 47770}, {47834, 47881}, {47877, 28602}
X(48236) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3837, 48140, 47651}, {47660, 48062, 47975}


X(48237) = X(320)X(350)∩X(351)X(523)

Barycentrics    (b - c)*(2*a^3 + 2*a*b^2 + 3*a*b*c + 3*b^2*c + 2*a*c^2 + 3*b*c^2) : :
X(48237) = X[693] - 4 X[7662], 5 X[693] - 2 X[46403], 4 X[693] - X[47685], X[693] + 2 X[47694], 2 X[693] + X[47697], 7 X[693] - 4 X[48089], 4 X[4010] - X[48079], X[4811] + 2 X[47844], 10 X[7662] - X[46403], 16 X[7662] - X[47685], 2 X[7662] + X[47694], 8 X[7662] + X[47697], 7 X[7662] - X[48089], 8 X[46403] - 5 X[47685], X[46403] + 5 X[47694], 4 X[46403] + 5 X[47697], X[46403] - 5 X[47834], 7 X[46403] - 10 X[48089], X[47685] + 8 X[47694], X[47685] + 2 X[47697], X[47685] - 8 X[47834], 7 X[47685] - 16 X[48089], 4 X[47694] - X[47697], 7 X[47694] + 2 X[48089], X[47697] + 4 X[47834], 7 X[47697] + 8 X[48089], 7 X[47834] - 2 X[48089], 2 X[48080] + X[48107], 5 X[31150] - 8 X[45314], 4 X[45314] - 5 X[47804], 4 X[659] - X[47664], 4 X[676] - X[45746], 2 X[14419] - 3 X[47820], 4 X[6590] - X[47689], 2 X[6590] + X[47695], X[47689] + 2 X[47695], 2 X[2526] - 5 X[26985], 4 X[3716] - X[47666], 2 X[3716] + X[48142], X[47666] + 2 X[48142], 4 X[3835] - X[47940], 2 X[3835] + X[48153], X[47940] + 2 X[48153], X[4380] + 2 X[4804], 4 X[4458] - X[47677], X[4462] + 2 X[17166], 2 X[4724] + X[47675], 8 X[4874] - 5 X[31209], 4 X[4874] - X[47975], 5 X[31209] - 4 X[47827], 5 X[31209] - 2 X[47975], 2 X[47123] + X[47660], 4 X[47123] - X[47692], 2 X[47660] + X[47692], 4 X[23770] - X[47651], 2 X[23770] + X[47696], X[47651] + 2 X[47696], 5 X[24924] - 2 X[48017], 8 X[47132] + X[47662], 4 X[47132] - X[47691], X[47662] + 2 X[47691], 2 X[47131] + X[47693], 2 X[47672] + X[47974], X[47672] + 2 X[48063], X[47974] - 4 X[48063], X[47939] - 4 X[48043], X[47969] + 2 X[48134], 2 X[48037] + X[48147], 2 X[48072] + X[48115]

X(48237) lies on these lines: {320, 350}, {351, 523}, {522, 4786}, {659, 47664}, {676, 45746}, {784, 14419}, {1635, 4765}, {2526, 26985}, {2832, 4801}, {3667, 31148}, {3716, 47666}, {3835, 47940}, {4160, 4391}, {4380, 4804}, {4448, 4802}, {4458, 47677}, {4462, 17166}, {4560, 30234}, {4724, 47675}, {4762, 47805}, {4776, 47832}, {4778, 47871}, {4874, 31209}, {4962, 47687}, {8678, 30709}, {21179, 28147}, {23770, 28213}, {24924, 48017}, {28175, 47132}, {28183, 47690}, {28191, 45673}, {28229, 47652}, {44429, 47833}, {47131, 47693}, {47672, 47974}, {47782, 47800}, {47788, 47808}, {47803, 47825}, {47810, 47831}, {47814, 47875}, {47939, 48043}, {47969, 48134}, {48037, 48147}, {48072, 48115}

X(48237) = midpoint of X(i) and X(j) for these {i,j}: {47694, 47834}, {47826, 48142}
X(48237) = reflection of X(i) in X(j) for these {i,j}: {693, 47834}, {4560, 30234}, {4776, 47832}, {31150, 47804}, {44429, 47833}, {47666, 47826}, {47762, 47813}, {47782, 47800}, {47808, 47788}, {47810, 47831}, {47814, 47875}, {47825, 47803}, {47826, 3716}, {47827, 4874}, {47834, 7662}, {47975, 47827}
X(48237) = crossdifference of every pair of points on line {213, 574}
X(48237) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 47694, 47697}, {693, 47697, 47685}, {3716, 48142, 47666}, {3835, 48153, 47940}, {4874, 47975, 31209}, {6590, 47695, 47689}, {7662, 47694, 693}, {23770, 47696, 47651}, {47123, 47660, 47692}, {47672, 48063, 47974}


X(48238) = X(320)X(350)∩X(523)X(1638)

Barycentrics    (b - c)*(a^3 + a^2*b + a*b^2 + a^2*c + 4*a*b*c + 3*b^2*c + a*c^2 + 3*b*c^2) : :
X(48238) = 4 X[693] - X[24719], X[4010] + 2 X[43067], X[7192] + 2 X[48090], 2 X[7662] + X[21146], X[47694] + 2 X[48098], 3 X[47822] - 4 X[47831], 2 X[47831] - 3 X[47833], 3 X[4379] - X[47828], 3 X[47823] - 2 X[47828], 2 X[3716] + X[48143], 2 X[3837] + X[48142], 2 X[4369] + X[48120], 2 X[4782] + X[26824], 2 X[4806] + X[48141], X[4810] + 2 X[4932], X[4824] - 4 X[4885], X[4824] + 2 X[48134], 2 X[4885] + X[48134], 2 X[4874] + X[47672], X[17494] + 2 X[48127], 4 X[25666] - X[47928], 5 X[26985] - 2 X[48030], 5 X[30795] - 2 X[48010], 5 X[30835] - 2 X[48002], X[47946] + 2 X[48133], X[47969] + 2 X[48135]

X(48238) lies on these lines: {2, 4802}, {320, 350}, {514, 47822}, {523, 1638}, {2533, 14077}, {3716, 48143}, {3837, 48142}, {4369, 48120}, {4458, 28161}, {4777, 47824}, {4778, 4800}, {4782, 26824}, {4806, 48141}, {4810, 4932}, {4824, 4885}, {4841, 4893}, {4874, 47672}, {4948, 28155}, {4977, 47832}, {17494, 48127}, {21204, 47877}, {23057, 29366}, {25666, 47928}, {26985, 48030}, {28147, 47779}, {28151, 47825}, {28179, 47829}, {28191, 47778}, {28195, 47821}, {28199, 47775}, {28213, 47826}, {29328, 31148}, {29362, 47813}, {30795, 48010}, {30835, 48002}, {47946, 48133}, {47969, 48135}

X(48238) = midpoint of X(i) and X(j) for these {i,j}: {47672, 47811}, {47780, 47834}
X(48238) = reflection of X(i) in X(j) for these {i,j}: {4948, 47830}, {47811, 4874}, {47822, 47833}, {47823, 4379}, {47827, 47779}, {47877, 21204}
X(48238) = crossdifference of every pair of points on line {213, 4262}
X(48238) = {X(4885),X(48134)}-harmonic conjugate of X(4824)


X(48239) = X(2)X(522)∩X(23)X(385)

Barycentrics    (b - c)*(-3*a^3 + 2*a^2*b - a*b^2 + 2*b^3 + 2*a^2*c + a*b*c + b^2*c - a*c^2 + b*c^2 + 2*c^3) : :
X(48239) = 3 X[2] - 4 X[47800], 5 X[2] - 4 X[47806], 3 X[47798] - 2 X[47800], 5 X[47798] - 2 X[47806], 3 X[47798] - X[47808], 5 X[47800] - 3 X[47806], 6 X[47806] - 5 X[47808], X[17494] + 2 X[47695], 4 X[44433] - X[47773], X[47659] - 4 X[47694], 8 X[676] - 5 X[26985], 4 X[676] - X[47687], 5 X[26985] - 2 X[47687], 2 X[3803] + X[47709], 4 X[4142] - X[21302], X[47676] + 2 X[48014], X[7192] + 2 X[47972], 4 X[8689] - X[48118], 8 X[13246] - 5 X[27013], X[26824] - 4 X[47123], X[31290] - 4 X[48006], X[31291] + 2 X[47708], X[47653] + 2 X[47697], X[47923] + 2 X[48072]

X(48239) lies on these lines: {2, 522}, {23, 385}, {676, 26985}, {900, 47797}, {1459, 17024}, {2826, 17496}, {3667, 4025}, {3803, 47709}, {4010, 4926}, {4024, 4765}, {4142, 21302}, {4375, 30519}, {4430, 9000}, {4777, 47804}, {4778, 47676}, {4809, 47824}, {4962, 47757}, {6636, 39199}, {7191, 21173}, {7192, 47972}, {8689, 48118}, {13246, 27013}, {17161, 26277}, {20293, 33090}, {20954, 26234}, {26275, 28183}, {26824, 47123}, {28161, 47771}, {28195, 47974}, {28205, 47803}, {28221, 31131}, {28537, 47729}, {31290, 48006}, {31291, 47708}, {47653, 47697}, {47923, 48072}

X(48239) = reflection of X(i) in X(j) for these {i,j}: {2, 47798}, {21302, 30574}, {30574, 4142}, {31131, 47799}, {47771, 47801}, {47773, 47805}, {47805, 44433}, {47808, 47800}, {47809, 26275}, {47824, 4809}
X(48239) = anticomplement of X(47808)
X(48239) = anticomplement of the isotomic conjugate of X(9086)
X(48239) = X(9086)-anticomplementary conjugate of X(6327)
X(48239) = X(9086)-Ceva conjugate of X(2)
X(48239) = crossdifference of every pair of points on line {39, 1055}
X(48239) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {676, 47687, 26985}, {47798, 47808, 47800}, {47800, 47808, 2}


X(48240) = X(2)X(29362)∩X(23)X(385)

Barycentrics    (b - c)*(-3*a^3 + a*b^2 + 5*a*b*c + b^2*c + a*c^2 + b*c^2) : :
X(48240) = 2 X[659] + X[17494], 4 X[659] - X[47694], 2 X[17494] + X[47694], X[47693] - 4 X[47890], 2 X[649] + X[47969], 4 X[650] - X[46403], X[661] + 2 X[4830], 2 X[1491] - 5 X[26777], 4 X[2977] - X[47687], X[4724] + 2 X[48008], 2 X[3716] + X[47932], 4 X[3837] - 7 X[27115], X[4380] + 2 X[48029], 4 X[4394] - X[48108], 4 X[4401] - X[17166], X[4467] + 2 X[48055], 2 X[4490] + X[31291], 2 X[4765] + X[48061], 4 X[4782] - X[7192], 2 X[4790] + X[47941], X[4801] - 4 X[6050], 2 X[4818] + X[48105], 4 X[4874] - X[26824], 2 X[4913] + X[48032], 2 X[4932] + X[47927], X[4979] + 2 X[48001], 2 X[7662] + X[47664], 4 X[11068] - X[47690], 4 X[13246] - X[47704], 2 X[14431] - 3 X[47793], 2 X[21146] - 5 X[27013], 2 X[21196] + X[48102], X[21301] - 4 X[48003], 4 X[25380] - X[48115], X[26853] + 2 X[48024], 5 X[31209] - 2 X[48089], 4 X[31286] - X[48119], 4 X[45314] - X[47869], 2 X[45745] + X[47696], 2 X[47663] + X[47688], X[47677] + 2 X[48096], X[47699] + 2 X[48060], X[47945] - 4 X[48000], 2 X[47963] + X[48107]

X(48240) lies on these lines: {2, 29362}, {23, 385}, {513, 14404}, {522, 3158}, {649, 4778}, {650, 44429}, {661, 4830}, {693, 47803}, {812, 47811}, {1491, 26777}, {1635, 47824}, {2832, 45671}, {2977, 47687}, {3667, 4724}, {3684, 32845}, {3716, 47932}, {3837, 27115}, {4041, 28521}, {4380, 48029}, {4394, 48108}, {4401, 17166}, {4467, 48055}, {4490, 31291}, {4762, 47804}, {4763, 47812}, {4765, 48061}, {4781, 46973}, {4782, 7192}, {4785, 47826}, {4790, 47941}, {4801, 6050}, {4818, 48105}, {4874, 26824}, {4913, 48032}, {4932, 47927}, {4977, 47763}, {4979, 48001}, {6084, 47797}, {7662, 47664}, {11068, 47690}, {13246, 47704}, {14431, 29070}, {21146, 27013}, {21196, 48102}, {21297, 47822}, {21301, 48003}, {23882, 47815}, {25380, 48115}, {26853, 48024}, {28191, 47926}, {28475, 47965}, {29033, 30709}, {29078, 47772}, {29186, 47836}, {29302, 47840}, {29370, 44009}, {31209, 48089}, {31286, 48119}, {39954, 47800}, {45314, 47833}, {45745, 47696}, {47663, 47688}, {47677, 48096}, {47699, 48060}, {47799, 47871}, {47809, 47884}, {47945, 48000}, {47963, 48107}

X(48240) = midpoint of X(17494) and X(47805)
X(48240) = reflection of X(i) in X(j) for these {i,j}: {693, 47803}, {21297, 47822}, {44429, 650}, {46403, 44429}, {47694, 47805}, {47805, 659}, {47809, 47884}, {47812, 4763}, {47821, 47811}, {47824, 1635}, {47825, 31150}, {47833, 45314}, {47834, 47804}, {47869, 47833}, {47871, 47799}
X(48240) = crossdifference of every pair of points on line {39, 16971}
X(48240) = {X(659),X(17494)}-harmonic conjugate of X(47694)


X(48241) = X(522)X(6545)∩X(523)X(4453)

Barycentrics    (b - c)*(-a^3 + a*b^2 + 2*b^3 - a*b*c + b^2*c + a*c^2 + b*c^2 + 2*c^3) : :
X(48241) = 2 X[649] + X[47688], 4 X[3004] - X[47945], 4 X[3676] - X[47690], 2 X[3716] + X[47930], 4 X[3776] - X[46403], 2 X[3801] + X[17496], 2 X[4025] + X[47691], X[4088] - 4 X[21212], 2 X[4122] - 5 X[26985], 4 X[4369] - X[47693], 2 X[4458] + X[16892], 4 X[4458] - X[47694], 2 X[16892] + X[47694], X[4467] + 2 X[23770], 2 X[4913] + X[47705], 2 X[4932] + X[47924], 2 X[7662] + X[47677], 4 X[13246] - X[48102], X[17161] + 2 X[48120], 4 X[18004] - 7 X[27138], 4 X[21188] - X[47707], 2 X[21192] + X[47716], 2 X[21196] + X[47704], 4 X[25380] - X[47700], 5 X[27013] - 2 X[48103], 7 X[27115] - 4 X[48056], 5 X[31209] - 2 X[48088], 4 X[31286] - X[48118], X[47657] + 2 X[48134], 2 X[47676] + X[47969], 2 X[47961] + X[48107]

X(48241) lies on these lines: {522, 6545}, {523, 4453}, {649, 47688}, {824, 47834}, {826, 47796}, {918, 47797}, {1638, 47809}, {3004, 47945}, {3676, 47690}, {3716, 47930}, {3776, 46403}, {3801, 17496}, {4025, 47691}, {4088, 21212}, {4122, 26985}, {4369, 47693}, {4458, 16892}, {4467, 23770}, {4802, 46915}, {4809, 47805}, {4913, 47705}, {4932, 47924}, {6548, 29370}, {7662, 47677}, {13246, 48102}, {14419, 29224}, {17161, 48120}, {18004, 27138}, {21188, 47707}, {21192, 47716}, {21196, 47704}, {21297, 29078}, {23875, 47840}, {25380, 47700}, {27013, 48103}, {27115, 48056}, {28147, 47758}, {28191, 47768}, {28863, 47813}, {28890, 47811}, {29047, 47836}, {29204, 47823}, {29212, 30709}, {29280, 47841}, {29354, 47793}, {29358, 47795}, {30519, 47832}, {30520, 47804}, {30565, 47799}, {31209, 48088}, {31286, 48118}, {44429, 47754}, {47657, 48134}, {47676, 47969}, {47772, 47822}, {47825, 47886}, {47833, 47870}, {47961, 48107}

X(48241) = reflection of X(i) in X(j) for these {i,j}: {30565, 47799}, {44429, 47754}, {47772, 47822}, {47805, 4809}, {47809, 1638}, {47821, 47797}, {47824, 4453}, {47825, 47886}, {47834, 47887}, {47870, 47833}
X(48241) = {X(4458),X(16892)}-harmonic conjugate of X(47694)


X(48242) = X(2)X(522)∩X(523)X(4453)

Barycentrics    (b - c)*(-a^3 - 2*a^2*b + 3*a*b^2 - 2*a^2*c + 3*a*b*c + b^2*c + 3*a*c^2 + b*c^2) : :
X(48242) = 3 X[2] - 4 X[47830], 5 X[2] - 4 X[47831], 3 X[47828] - 2 X[47830], 5 X[47828] - 2 X[47831], 3 X[47828] - X[47832], 5 X[47830] - 3 X[47831], 6 X[47831] - 5 X[47832], X[145] + 2 X[4814], X[649] + 2 X[48017], 4 X[1491] - X[20295], 2 X[1734] + X[4560], 4 X[1734] - X[21302], 2 X[4560] + X[21302], X[2254] + 2 X[4913], 2 X[2254] + X[17494], 4 X[4913] - X[17494], 2 X[2526] + X[4380], 5 X[3617] - 2 X[4474], 4 X[3716] - 7 X[27115], 4 X[4010] - 7 X[27138], 2 X[4041] + X[17496], 4 X[4394] - X[47697], 2 X[4724] - 5 X[26777], 2 X[4784] + X[47945], 2 X[4790] + X[47940], 4 X[4791] - 7 X[9780], X[4804] - 4 X[25380], 2 X[4804] - 5 X[26985], 8 X[25380] - 5 X[26985], 4 X[4818] - X[47653], 2 X[4818] + X[48106], X[47653] + 2 X[48106], 2 X[4925] + X[4976], 4 X[4925] - X[47687], 2 X[4976] + X[47687], X[7192] + 2 X[47975], 2 X[7659] + X[47666], 8 X[9508] - 5 X[27013], 4 X[9508] - X[47694], 5 X[27013] - 2 X[47694], 4 X[17069] - X[47695], X[17161] + 2 X[47690], 4 X[24720] - X[26824], X[26853] + 2 X[48023], X[31290] - 4 X[48010], 4 X[45328] - X[47869], X[45746] + 2 X[48069], X[47663] + 2 X[48015], X[47926] + 2 X[48073]

X(48242) lies on these lines: {2, 522}, {42, 21173}, {145, 4814}, {513, 14404}, {523, 4453}, {649, 48017}, {784, 47836}, {900, 47821}, {1459, 17018}, {1491, 20295}, {1635, 47805}, {1734, 4560}, {2254, 4913}, {2526, 4380}, {3617, 4474}, {3667, 4893}, {3716, 27115}, {3887, 45671}, {4010, 27138}, {4041, 17496}, {4151, 47796}, {4210, 39199}, {4379, 28161}, {4394, 47697}, {4651, 20293}, {4724, 26777}, {4777, 37756}, {4784, 47945}, {4790, 47940}, {4791, 9780}, {4800, 28221}, {4804, 25380}, {4818, 47653}, {4925, 4976}, {4926, 47822}, {4948, 4977}, {4962, 47778}, {6006, 47826}, {7192, 47975}, {7659, 47666}, {8714, 47793}, {9508, 27013}, {14077, 44550}, {16755, 30941}, {17069, 47695}, {17161, 47690}, {17759, 21225}, {21297, 44429}, {21301, 29340}, {24720, 26824}, {26853, 48023}, {28183, 47833}, {31290, 48010}, {45328, 47812}, {45746, 48069}, {47663, 48015}, {47759, 47810}, {47809, 47870}, {47840, 47888}, {47926, 48073}

X(48242) = reflection of X(i) in X(j) for these {i,j}: {2, 47828}, {4800, 47829}, {21297, 44429}, {47759, 47810}, {47775, 47825}, {47780, 47824}, {47790, 47806}, {47798, 47785}, {47805, 1635}, {47812, 45328}, {47821, 47827}, {47832, 47830}, {47834, 47823}, {47840, 47888}, {47869, 47812}, {47870, 47809}
X(48242) = anticomplement of X(47832)
X(48242) = crossdifference of every pair of points on line {1055, 16971}
X(48242) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1734, 4560, 21302}, {2254, 4913, 17494}, {4804, 25380, 26985}, {4818, 48106, 47653}, {4925, 4976, 47687}, {9508, 47694, 27013}, {47828, 47832, 47830}, {47830, 47832, 2}


X(48243) = X(2)X(522)∩X(523)X(23678)

Barycentrics    (b - c)*(a^4 + a^3*b - a^2*b^2 - a*b^3 + a^3*c + a^2*b*c - 3*a*b^2*c + b^3*c - a^2*c^2 - 3*a*b*c^2 + 2*b^2*c^2 - a*c^3 + b*c^3) : :
X(48243) = X[8] + 2 X[1459], 4 X[10] - X[20293], 2 X[10] + X[21173], X[20293] + 2 X[21173], 2 X[26078] + X[47793], 2 X[905] + X[4397], 2 X[1491] + X[4581], 2 X[1734] + X[7253], 2 X[2517] + X[4560], 2 X[3737] + X[21302], 2 X[3960] + X[4404], X[4017] - 4 X[25380], 2 X[4086] + X[17496], 2 X[4147] + X[43924], 2 X[4815] - 5 X[26985], 7 X[9780] - 4 X[20316], 2 X[17072] + X[17418], X[20294] + 2 X[21186], 2 X[21172] + X[44448]

X(48243) lies on these lines: {2, 522}, {8, 1459}, {10, 20293}, {404, 39199}, {513, 26078}, {523, 23678}, {657, 5749}, {905, 4397}, {1491, 4581}, {1734, 7253}, {2254, 26049}, {2287, 23146}, {2345, 6586}, {2517, 4560}, {3667, 47794}, {3737, 21302}, {3960, 4404}, {4017, 25380}, {4036, 19874}, {4086, 17496}, {4147, 43924}, {4188, 39226}, {4804, 27193}, {4815, 26985}, {4913, 26114}, {4926, 26144}, {4962, 27545}, {5657, 32475}, {8672, 47824}, {9780, 20316}, {10436, 46402}, {17072, 17418}, {20294, 21186}, {20954, 28653}, {21172, 44448}, {21225, 28604}, {28161, 47795}

X(48243) = {X(10),X(21173)}-harmonic conjugate of X(20293)


X(48244) = X(2)X(900)∩X(523)X(4453)

Barycentrics    a*(b - c)*(a^2 + 2*a*b - 2*b^2 + 2*a*c - b*c - 2*c^2) : :
X(48244) = X[659] + 2 X[2254], X[659] - 4 X[9508], 5 X[659] - 2 X[48032], 2 X[1491] + X[4784], 5 X[1491] - 2 X[48027], 5 X[1635] - X[48032], X[2254] + 2 X[9508], 5 X[2254] + X[48032], 5 X[4784] + 4 X[48027], 5 X[4893] - 3 X[47826], 2 X[4893] - 3 X[47827], X[4893] - 3 X[47828], 2 X[7659] + X[48024], 10 X[9508] - X[48032], 2 X[47826] - 5 X[47827], X[47826] - 5 X[47828], X[3251] - 3 X[14419], 2 X[3251] - 3 X[25569], 2 X[47779] - 3 X[47823], 4 X[47779] - 3 X[47833], X[47780] - 3 X[47824], X[667] + 2 X[48018], 4 X[905] - X[4879], 2 X[1734] + X[4367], 4 X[2977] - X[48083], 4 X[3837] - X[4810], 2 X[3960] + X[4730], 4 X[3960] - X[21343], 2 X[4730] + X[21343], X[4010] - 4 X[25380], 2 X[4010] - 5 X[30795], 4 X[4928] - 5 X[30795], 8 X[25380] - 5 X[30795], X[4834] + 2 X[48066], 2 X[4913] + X[21146], X[4963] - 4 X[48010], 2 X[9269] - 3 X[14413], 3 X[19875] - 2 X[28603]

X(48244) lies on these lines: {1, 14422}, {2, 900}, {44, 513}, {88, 14315}, {100, 4585}, {105, 28535}, {214, 3126}, {291, 876}, {512, 47893}, {514, 4948}, {522, 4809}, {523, 4453}, {665, 2276}, {667, 48018}, {812, 36848}, {905, 4879}, {1734, 4367}, {2977, 48083}, {3667, 47822}, {3716, 45675}, {3738, 11124}, {3837, 4810}, {3960, 4730}, {4010, 4928}, {4151, 47889}, {4184, 42741}, {4191, 39200}, {4196, 39534}, {4210, 39478}, {4212, 44428}, {4378, 4825}, {4379, 4777}, {4435, 14438}, {4448, 4763}, {4458, 28161}, {4776, 45323}, {4802, 21115}, {4834, 48066}, {4913, 21146}, {4926, 47832}, {4951, 28898}, {4962, 13246}, {4963, 48010}, {4977, 47825}, {6005, 47888}, {6006, 47778}, {8027, 47330}, {8714, 47837}, {9269, 14413}, {19875, 28603}, {24396, 24447}, {28175, 47653}, {28183, 47132}, {28209, 47775}, {28217, 47821}, {28602, 30565}, {29078, 47808}, {29144, 47886}, {29150, 47816}, {29170, 47814}, {29178, 31149}, {29188, 45671}, {29328, 44429}, {30656, 30665}, {38325, 44304}, {45666, 45691}

X(48244) = midpoint of X(i) and X(j) for these {i,j}: {1635, 2254}, {4378, 4825}, {4730, 14421}, {7659, 47777}
X(48244) = reflection of X(i) in X(j) for these {i,j}: {1, 14422}, {659, 1635}, {1635, 9508}, {3716, 45675}, {4010, 4928}, {4448, 4763}, {4776, 45323}, {4800, 2}, {4809, 45674}, {4810, 21297}, {4928, 25380}, {14421, 3960}, {21297, 3837}, {21343, 14421}, {23352, 14315}, {25569, 14419}, {28396, 28284}, {30565, 28602}, {36848, 45328}, {45666, 45691}, {47821, 47829}, {47822, 47830}, {47827, 47828}, {47833, 47823}, {47872, 47837}, {48024, 47777}
X(48244) = X(2)-isoconjugate of X(28875)
X(48244) = X(32664)-Dao conjugate of X(28875)
X(48244) = crosssum of X(513) and X(3246)
X(48244) = crossdifference of every pair of points on line {1, 8297}
X(48244) = X(14422)-line conjugate of X(1)
X(48244) = barycentric product X(i)*X(j) for these {i,j}: {513, 17310}, {876, 27949}
X(48244) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 28875}, {17310, 668}, {27949, 874}
X(48244) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2254, 9508, 659}, {3960, 4730, 21343}, {4010, 25380, 30795}


X(48245) = X(513)X(1638)∩X(523)X(4453)

Barycentrics    (b - c)*(-2*a^3 - 3*a^2*b + 2*a*b^2 + b^3 - 3*a^2*c - 2*a*b*c - b^2*c + 2*a*c^2 - b*c^2 + c^3) : :
X(48245) = X[659] - 4 X[2487], 4 X[2490] - X[48083], 2 X[2977] + X[47676], 4 X[3676] - X[23770], 2 X[3798] + X[48089], 2 X[3837] + X[4897], 2 X[4765] + X[48126], 2 X[4932] + X[47989], X[4976] + 2 X[48098], 4 X[7658] - X[48029], 2 X[9508] + X[21104], 2 X[14321] - 5 X[30795], 2 X[17069] + X[21146], 4 X[21212] - X[47998], 4 X[25380] - X[48047], 7 X[31207] - X[48078], 4 X[31286] - X[48055], 4 X[31287] - X[48040], 4 X[43061] - X[48096]

X(48245) lies on these lines: {513, 1638}, {523, 4453}, {659, 2487}, {918, 47807}, {2490, 48083}, {2977, 47676}, {3566, 47796}, {3676, 23770}, {3798, 48089}, {3837, 4897}, {4083, 30724}, {4750, 47812}, {4765, 48126}, {4778, 47882}, {4843, 47889}, {4927, 29328}, {4932, 47989}, {4976, 48098}, {4977, 47762}, {6372, 41800}, {7658, 48029}, {9508, 21104}, {14321, 30795}, {17069, 21146}, {21212, 47998}, {25380, 48047}, {28195, 47768}, {28846, 47802}, {28851, 47830}, {31207, 48078}, {31286, 48055}, {31287, 48040}, {43061, 48096}, {44429, 47755}, {44902, 47822}

X(48245) = midpoint of X(i) and X(j) for these {i,j}: {4453, 47824}, {4750, 47812}, {44429, 47755}
X(48245) = reflection of X(i) in X(j) for these {i,j}: {47799, 1638}, {47807, 47823}, {47822, 44902}


X(48246) = X(2)X(513)∩X(523)X(23678)

Barycentrics    (b - c)*(a^4 + a^3*b - a^2*b^2 - a*b^3 + a^3*c + a^2*b*c - a*b^2*c + b^3*c - a^2*c^2 - a*b*c^2 + 2*b^2*c^2 - a*c^3 + b*c^3) : :
X(48246) = X[26078] + 2 X[47795], X[656] - 4 X[25380], 2 X[667] + X[44444], 2 X[905] + X[2517], X[1459] + 2 X[17072], 2 X[1491] + X[47844], X[2254] + 2 X[8062], 2 X[2605] + X[21302], 2 X[3733] + X[21301], X[3733] + 2 X[44316], X[21301] - 4 X[44316], X[3777] + 2 X[6133], 2 X[3960] + X[4086], 2 X[4036] + X[17496], 4 X[4885] - X[7650], 4 X[8043] - X[17494], X[17418] + 2 X[47843], 2 X[20316] + X[43924], 2 X[24720] + X[46385], 5 X[26985] - 2 X[30591], 2 X[45328] + X[45686]

X(48246) lies on these lines: {2, 513}, {391, 39521}, {475, 44426}, {522, 3582}, {523, 23678}, {656, 25380}, {667, 44444}, {832, 47845}, {834, 47836}, {905, 2517}, {966, 20980}, {1459, 17072}, {1491, 28423}, {2254, 8062}, {2303, 22157}, {2345, 21348}, {2605, 21302}, {3667, 26144}, {3733, 21301}, {3777, 6133}, {3837, 27345}, {3960, 4086}, {4010, 27193}, {4036, 17496}, {4200, 16228}, {4378, 19853}, {4453, 30474}, {4778, 47794}, {4784, 27293}, {4885, 7650}, {4977, 47793}, {5750, 21390}, {6371, 47837}, {8043, 17494}, {9508, 26114}, {17398, 21007}, {17418, 28834}, {20316, 43924}, {20949, 28653}, {21146, 26049}, {21347, 22092}, {23224, 25901}, {23874, 47806}, {24720, 46385}, {25473, 28399}, {26080, 43060}, {26822, 47945}, {26983, 47842}, {26985, 30591}, {27167, 47694}, {30764, 48044}, {45328, 45686}

X(48246) = {X(3733),X(44316)}-harmonic conjugate of X(21301)


X(48247) = X(2)X(28209)∩X(23)X(385)

Barycentrics    (b - c)*(6*a^3 + a^2*b + 2*a*b^2 + b^3 + a^2*c - 2*a*b*c + 3*b^2*c + 2*a*c^2 + 3*b*c^2 + c^3) : :
X(48247) = X[44433] - 3 X[47805], X[47773] + 3 X[47805], 5 X[47766] - 3 X[47806], 4 X[47766] - 3 X[47807], 4 X[47806] - 5 X[47807], 2 X[2977] + X[47697], 2 X[44432] - 3 X[47803], 2 X[44435] - 3 X[47799], X[44435] - 3 X[47804], X[21116] - 3 X[47813], 2 X[47132] + X[47663]

X(48247) lies on these lines: {2, 28209}, {23, 385}, {513, 1639}, {514, 26275}, {900, 4951}, {1491, 14425}, {2977, 47697}, {3667, 4522}, {4369, 4778}, {4773, 4782}, {4802, 47801}, {4874, 4927}, {4977, 44435}, {21104, 28195}, {21115, 48102}, {21116, 47813}, {26248, 47988}, {28175, 47798}, {28213, 47797}, {28217, 47809}, {28220, 47757}, {28225, 47802}, {28851, 48055}, {28859, 45673}, {39386, 47808}, {42028, 47845}, {44429, 48024}, {45314, 47784}, {45666, 47756}, {47132, 47663}

X(48247) = midpoint of X(i) and X(j) for these {i,j}: {21115, 48102}, {44433, 47773}, {47694, 47892}
X(48247) = reflection of X(i) in X(j) for these {i,j}: {1491, 14425}, {4773, 4782}, {4927, 4874}, {47756, 45666}, {47784, 45314}, {47799, 47804}
X(48247) = crossdifference of every pair of points on line {39, 16483}
X(48247) = {X(47773),X(47805)}-harmonic conjugate of X(44433)


X(48248) = X(23)X(385)∩X(513)X(3716)

Barycentrics    (b - c)*(2*a^3 + a*b^2 + b^2*c + a*c^2 + b*c^2) : :
X(48248) = 3 X[659] - X[17494], X[659] - 3 X[47805], X[17494] + 3 X[47694], X[17494] - 9 X[47805], 3 X[44433] + X[47660], X[47694] + 3 X[47805], 3 X[3716] - X[48049], 3 X[3837] - 4 X[4885], 3 X[4806] - 2 X[48049], 3 X[4874] - 2 X[4885], X[4932] + 3 X[48063], 3 X[47831] - X[48042], 2 X[650] - 3 X[45314], X[661] - 3 X[4448], 3 X[4724] + X[48141], 3 X[47887] + X[48105], 3 X[1491] - 5 X[31209], X[1491] - 3 X[47804], 2 X[1491] - 3 X[47829], 5 X[31209] + 3 X[47697], 5 X[31209] - 9 X[47804], 10 X[31209] - 9 X[47829], X[47697] + 3 X[47804], 2 X[47697] + 3 X[47829], 4 X[2490] - 3 X[28602], X[2526] - 3 X[47803], X[2530] - 3 X[47818], X[3004] - 3 X[26275], X[3777] - 3 X[47820], 3 X[4010] - X[48114], 3 X[4367] - X[21222], X[4490] - 3 X[47815], X[4705] - 3 X[47817], 3 X[4800] - X[20295], 3 X[4809] - X[16892], X[4824] - 3 X[47811], 3 X[47811] + X[48153], 3 X[4948] - 5 X[26777], 3 X[7662] - X[48125], X[21146] - 3 X[47813], 3 X[47813] + X[48032], X[21301] - 3 X[47872], X[24719] - 3 X[47832], 5 X[24924] - 3 X[36848], 2 X[25666] - 3 X[45666], 4 X[31287] - 3 X[45323], 3 X[45673] - X[47996], X[46403] - 3 X[47833], X[47696] + 3 X[47798], 3 X[47797] - X[47968], 3 X[47800] - X[48007], 3 X[47822] - X[48023], 3 X[47839] - X[48086], 3 X[47841] - X[48122], X[47939] - 3 X[48024], 2 X[47952] - 3 X[47993], X[47952] - 3 X[48029]

X(48248) lies on these lines: {23, 385}, {86, 4833}, {513, 3716}, {514, 1960}, {522, 4782}, {649, 900}, {650, 45314}, {661, 4448}, {676, 1459}, {784, 4401}, {814, 3803}, {830, 21051}, {918, 4817}, {1491, 31209}, {2490, 26244}, {2526, 47803}, {2530, 47818}, {2533, 48150}, {3004, 26275}, {3777, 47820}, {4010, 48114}, {4367, 21222}, {4490, 47815}, {4705, 47817}, {4761, 6161}, {4777, 48008}, {4778, 47990}, {4784, 28217}, {4800, 20295}, {4809, 16892}, {4824, 47811}, {4948, 26777}, {6084, 47132}, {7662, 29362}, {9013, 15985}, {21146, 47813}, {21185, 29025}, {21201, 29029}, {21301, 47872}, {24623, 47788}, {24719, 47832}, {24924, 36848}, {25666, 45666}, {28175, 48142}, {28179, 47926}, {28195, 48009}, {28213, 47969}, {30865, 47759}, {31287, 45323}, {31288, 48066}, {45673, 47996}, {46403, 47833}, {47131, 48095}, {47692, 48140}, {47696, 47798}, {47797, 47968}, {47800, 48007}, {47822, 48023}, {47839, 48086}, {47841, 48122}, {47939, 48024}, {47952, 47993}, {47974, 48143}

X(48248) = midpoint of X(i) and X(j) for these {i,j}: {659, 47694}, {1491, 47697}, {2533, 48150}, {4761, 6161}, {4824, 48153}, {21146, 48032}, {24720, 48072}, {47131, 48095}, {47692, 48140}, {47695, 48103}, {47974, 48143}
X(48248) = reflection of X(i) in X(j) for these {i,j}: {3837, 4874}, {4806, 3716}, {47829, 47804}, {47993, 48029}, {48066, 31288}
X(48248) = X(28864)-complementary conjugate of X(2)
X(48248) = crossdifference of every pair of points on line {39, 995}
X(48248) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47694, 47805, 659}, {47697, 47804, 1491}, {47811, 48153, 4824}, {47813, 48032, 21146}


X(48249) = X(513)X(1639)∩X(523)X(4453)

Barycentrics    (b - c)*(2*a^3 + 5*a^2*b - 2*a*b^2 + b^3 + 5*a^2*c + 2*a*b*c + 3*b^2*c - 2*a*c^2 + 3*b*c^2 + c^3) : :
X(48249) = 2 X[1639] - 3 X[47807], X[47764] - 3 X[47806], X[4453] - 3 X[47824], 2 X[2977] + X[48108], X[23770] + 2 X[48069], 4 X[25380] - X[47998], 4 X[44902] - 3 X[47799], 2 X[44902] - 3 X[47823], X[47772] - 3 X[47809], 3 X[47828] - X[47878], X[48055] + 2 X[48073]

X(48249) lies on these lines: {513, 1639}, {514, 45328}, {522, 3798}, {523, 4453}, {900, 47762}, {1491, 2977}, {1638, 29144}, {4522, 28906}, {4776, 30792}, {4777, 45669}, {4784, 28217}, {4802, 21104}, {4944, 7659}, {6006, 47879}, {21183, 23770}, {24720, 28882}, {25380, 47998}, {26275, 47761}, {28209, 28602}, {28225, 48027}, {28855, 48047}, {28871, 45344}, {29168, 41800}, {29208, 30724}, {31131, 47763}, {44902, 47799}, {47772, 47809}, {47828, 47878}, {48055, 48073}

X(48249) = midpoint of X(i) and X(j) for these {i,j}: {4944, 7659}, {21183, 48069}, {31131, 47763}
X(48249) = reflection of X(i) in X(j) for these {i,j}: {4776, 30792}, {23770, 21183}, {26275, 47761}, {47799, 47823}
X(48249) = crossdifference of every pair of points on line {2241, 16483}


X(48250) = X(2)X(4977)∩X(23)X(385)

Barycentrics    (b - c)*(3*a^3 + a^2*b + a*b^2 + b^3 + a^2*c - a*b*c + 2*b^2*c + a*c^2 + 2*b*c^2 + c^3) : :
X(48250) = 2 X[659] + X[47660], X[44433] + 2 X[47773], X[47694] + 2 X[47890], X[47695] + 2 X[48103], X[31131] - 4 X[47771], 3 X[31131] - 4 X[47808], 3 X[47771] - X[47808], 2 X[47808] - 3 X[47809], 3 X[47797] - 4 X[47800], 2 X[47800] - 3 X[47804], 2 X[650] + X[47696], 4 X[4521] - X[47982], 2 X[24720] + X[48105], 2 X[48061] + X[48108], 4 X[676] - X[47688], 2 X[3716] + X[48101], 2 X[3776] + X[48139], 2 X[3803] + X[47707], X[4024] + 2 X[4830], 2 X[4369] + X[48102], 2 X[4458] + X[48130], X[4467] - 4 X[4782], 4 X[4874] - X[47652], 4 X[4885] - X[47686], 2 X[4932] + X[48078], X[7192] + 2 X[48055], 2 X[7662] + X[47663], 4 X[8689] - X[47972], 4 X[11068] - X[47975], 4 X[21212] - X[47931], 4 X[25666] - X[47943], 5 X[31209] - 2 X[48007], 4 X[31286] - X[47973], 4 X[43061] - X[48015], X[47676] + 2 X[48096], X[47691] + 2 X[48095], X[47697] + 2 X[48062], 2 X[48040] + X[48107], 2 X[48043] + X[48104], 2 X[48060] + X[48080], 2 X[48063] + X[48106]

X(48250) lies on these lines: {2, 4977}, {23, 385}, {513, 30565}, {514, 14413}, {650, 47696}, {661, 4521}, {676, 47688}, {3667, 48016}, {3716, 48101}, {3776, 48139}, {3803, 47707}, {4024, 4830}, {4122, 4926}, {4369, 48102}, {4458, 48130}, {4467, 4782}, {4474, 28545}, {4789, 29362}, {4802, 47798}, {4874, 47652}, {4885, 47686}, {4932, 48078}, {6084, 47834}, {7192, 48055}, {7662, 47663}, {8689, 47972}, {10196, 47810}, {11068, 47975}, {18004, 39386}, {21212, 47931}, {25666, 47943}, {26248, 28195}, {26275, 28175}, {28147, 47801}, {28209, 47807}, {28213, 47799}, {28220, 47802}, {28225, 47806}, {28229, 47757}, {28537, 47728}, {28859, 47826}, {28882, 47832}, {30765, 47904}, {31209, 48007}, {31286, 47973}, {43061, 48015}, {47676, 48096}, {47691, 48095}, {47697, 48062}, {47767, 47824}, {47825, 47884}, {47833, 47871}, {48040, 48107}, {48043, 48104}, {48060, 48080}, {48063, 48106}

X(48250) = midpoint of X(47773) and X(47805)
X(48250) = reflection of X(i) in X(j) for these {i,j}: {31131, 47809}, {44429, 47766}, {44433, 47805}, {44435, 47803}, {47797, 47804}, {47809, 47771}, {47810, 10196}, {47824, 47767}, {47825, 47884}, {47871, 47833}
X(48250) = crossdifference of every pair of points on line {39, 3915}


X(48251) = X(23)X(385)∩X(513)X(4379)

Barycentrics    (b - c)*(3*a^3 + 2*a*b^2 + a*b*c + 2*b^2*c + 2*a*c^2 + 2*b*c^2) : :
X(48251) = 5 X[659] - 2 X[17494], X[659] + 2 X[47694], X[17494] + 5 X[47694], X[17494] - 5 X[47805], 4 X[45320] - 5 X[47833], 4 X[676] - X[47968], 2 X[14431] - 3 X[47872], 5 X[1491] - 8 X[31287], 4 X[31287] - 5 X[47803], 8 X[4874] - 5 X[30795], 2 X[4874] + X[47697], 5 X[30795] - 4 X[44429], 5 X[30795] + 4 X[47697], X[4963] - 4 X[48029], 2 X[47131] + X[48140]

X(48251) lies on these lines: {23, 385}, {513, 4379}, {514, 25569}, {649, 4820}, {676, 47968}, {830, 14431}, {1491, 31287}, {2533, 28521}, {2605, 4724}, {3667, 4784}, {4778, 47983}, {4782, 28205}, {4817, 30519}, {4874, 30795}, {4927, 7192}, {4963, 48029}, {8689, 28191}, {28183, 47776}, {28199, 48142}, {28217, 47763}, {45314, 47825}, {45666, 47810}, {47131, 48140}, {47800, 47877}, {47804, 47827}, {47818, 47893}

X(48251) = midpoint of X(i) and X(j) for these {i,j}: {44429, 47697}, {47694, 47805}
X(48251) = reflection X(48251) = of X(i) in X(j) for these {i,j}: {659, 47805}, {1491, 47803}, {44429, 4874}, {47810, 45666}, {47825, 45314}, {47827, 47804}, {47877, 47800}, {47893, 47818}


X(48252) = X(513)X(30565)∩X(523)X(4453)

Barycentrics    (b - c)*(a^3 + 3*a^2*b - a*b^2 + b^3 + 3*a^2*c + a*b*c + 2*b^2*c - a*c^2 + 2*b*c^2 + c^3) : :
X(48252) = 2 X[649] + X[47687], X[693] + 2 X[48069], 2 X[2254] + X[47660], 4 X[2977] - X[47969], 4 X[3676] - X[47692], X[3904] + 2 X[4761], 2 X[4025] + X[47689], 4 X[4369] - X[47695], X[4467] + 2 X[47690], 4 X[4522] - X[44449], 4 X[4818] - X[47654], 4 X[4913] - X[47661], 2 X[4913] + X[47703], X[47661] + 2 X[47703], 2 X[4932] + X[48077], 2 X[7659] + X[25259], 4 X[11068] - X[47974], 4 X[21188] - X[47709], 2 X[21192] + X[47714], 4 X[21212] - X[47702], 4 X[24720] - X[47652], 2 X[24720] + X[48106], X[47652] + 2 X[48106], 4 X[25380] - X[47701], 5 X[31209] - 2 X[48006], 4 X[31286] - X[47972], 4 X[43061] - X[48014], X[47662] + 2 X[48015], X[47685] + 2 X[48060], 2 X[48039] + X[48107], 2 X[48042] + X[48104], 2 X[48062] + X[48108], 2 X[48073] + X[48094]

X(48252) lies on these lines: {513, 30565}, {522, 4786}, {523, 4453}, {649, 47687}, {693, 48069}, {2254, 23954}, {2977, 47969}, {3667, 4958}, {3676, 47692}, {3800, 47796}, {3904, 4761}, {4025, 47689}, {4369, 47695}, {4467, 47690}, {4522, 44449}, {4581, 35365}, {4776, 47806}, {4818, 47654}, {4913, 47661}, {4932, 48077}, {7659, 25259}, {11068, 47974}, {21188, 47709}, {21192, 47714}, {21212, 47702}, {24720, 47652}, {25380, 47701}, {28161, 47758}, {29142, 47836}, {29144, 47797}, {29168, 47837}, {31209, 48006}, {31286, 47972}, {43061, 48014}, {47662, 48015}, {47685, 48060}, {47761, 47798}, {47767, 47805}, {47782, 47828}, {47807, 47821}, {47812, 47871}, {48039, 48107}, {48042, 48104}, {48062, 48108}, {48073, 48094}

X(48252) = reflection of X(i) in X(j) for these {i,j}: {4453, 47824}, {4776, 47806}, {30565, 47809}, {47782, 47828}, {47797, 47823}, {47798, 47761}, {47805, 47767}, {47821, 47807}, {47871, 47812}
X(48252) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4913, 47703, 47661}, {24720, 48106, 47652}


X(48253) = X(2)X(4977)∩X(513)X(4379)

Barycentrics    (b - c)*(a^3 + 2*a^2*b + 2*a^2*c + 3*a*b*c + 2*b^2*c + 2*b*c^2) : :
X(48253) = 4 X[4379] - X[4800], 3 X[4379] - X[47832], 3 X[4800] - 4 X[47832], 2 X[47832] - 3 X[47833], 3 X[47823] - 2 X[47830], 3 X[47827] - 4 X[47830], X[649] + 2 X[48098], 2 X[650] + X[48143], X[659] - 4 X[4369], X[659] + 2 X[21146], 2 X[4369] + X[21146], 2 X[661] - 5 X[30795], 2 X[693] + X[4784], 4 X[693] - X[4810], 2 X[4784] + X[4810], X[1491] + 2 X[43067], 2 X[3837] + X[7192], 2 X[4378] + X[4774], 2 X[4394] + X[48126], 2 X[4761] + X[21343], 2 X[4782] + X[48119], 2 X[4806] - 5 X[26985], X[4824] - 4 X[25380], 2 X[4874] + X[48108], 4 X[4885] - X[48024], 2 X[4932] + X[24719], X[4960] + 2 X[48059], X[4963] - 4 X[48030], X[4963] + 2 X[48141], 2 X[48030] + X[48141], 2 X[9508] + X[47672], 2 X[21104] + X[48103], 5 X[24924] + X[48148], 4 X[25666] - X[47946], 5 X[30835] - 2 X[48028], 7 X[31207] - X[47927], 5 X[31251] - 2 X[47997], 4 X[31287] - X[47963], 4 X[45340] - X[47774], X[47926] + 2 X[48135], X[47928] + 2 X[48133]

X(48253) lies on these lines: {2, 4977}, {512, 47889}, {513, 4379}, {514, 47823}, {523, 4453}, {649, 48098}, {650, 48143}, {659, 4369}, {661, 30795}, {693, 4784}, {900, 47834}, {1019, 29340}, {1491, 43067}, {3837, 7192}, {4367, 29066}, {4378, 4774}, {4394, 48126}, {4761, 21343}, {4778, 47779}, {4782, 48119}, {4802, 4948}, {4806, 26985}, {4824, 25380}, {4874, 48108}, {4885, 48024}, {4893, 28195}, {4932, 24719}, {4960, 48059}, {4963, 48030}, {6372, 47872}, {9508, 47672}, {14430, 45332}, {21104, 48103}, {24924, 48148}, {25569, 29188}, {25666, 47946}, {28175, 47825}, {28209, 47821}, {28213, 47775}, {28220, 47826}, {28225, 47831}, {28229, 47778}, {29078, 47755}, {29144, 47887}, {29246, 47820}, {29362, 47762}, {30835, 48028}, {31207, 47927}, {31251, 47997}, {31287, 47963}, {45340, 47774}, {47926, 48135}, {47928, 48133}

X(48253) = midpoint of X(i) and X(j) for these {i,j}: {31148, 47812}, {47780, 47824}
X(48253) = reflection of X(i) in X(j) for these {i,j}: {4800, 47833}, {4948, 47828}, {14430, 45332}, {47775, 47829}, {47822, 47779}, {47827, 47823}, {47833, 4379}
X(48253) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 4784, 4810}, {4369, 21146, 659}, {48030, 48141, 4963}


X(48254) = X(2)X(29144)∩X(523)X(4453)

Barycentrics    (b - c)*(a^3 + 4*a^2*b - a*b^2 + 2*b^3 + 4*a^2*c + a*b*c + 3*b^2*c - a*c^2 + 3*b*c^2 + 2*c^3) : :
X(48254) = X[47690] + 2 X[48069], 2 X[4453] - 3 X[47824], 2 X[1639] - 3 X[47809], 4 X[1639] - 3 X[47821], 2 X[2254] + X[47693], 4 X[24720] - X[47688], 4 X[25380] - X[47702], X[46403] + 2 X[48106], 4 X[44902] - 3 X[47797], 3 X[47825] - 2 X[47878], X[47969] - 4 X[48062], 2 X[48073] + X[48118]

X(48254) lies on these lines: {2, 29144}, {513, 47772}, {514, 3679}, {522, 649}, {523, 4453}, {900, 47870}, {1639, 47809}, {2254, 28863}, {4088, 28855}, {4761, 23884}, {4777, 47762}, {4802, 21146}, {4944, 48080}, {4963, 4977}, {7927, 47796}, {21116, 28147}, {21183, 47691}, {24720, 47688}, {25380, 47702}, {28155, 47704}, {28169, 47758}, {28225, 48039}, {28882, 46403}, {29021, 47836}, {29132, 30709}, {29168, 47793}, {44433, 47767}, {44902, 47797}, {47825, 47878}, {47969, 48062}, {48073, 48118}

X(48254) = reflection of X(i) in X(j) for these {i,j}: {44433, 47767}, {47691, 21183}, {47821, 47809}, {48080, 4944}


X(48255) = X(13)X(15)∩X(11555)X(42945)

Barycentrics    2*sqrt(3)*(6*a^6-19*(b^2+c^2)*a^4+2*(4*b^4-13*b^2*c^2+4*c^4)*a^2+5*(b^4-c^4)*(b^2-c^2))*S+14*a^8-11*(b^2+c^2)*a^6-(33*b^4+52*b^2*c^2+33*c^4)*a^4+43*(b^4-c^4)*(b^2-c^2)*a^2-13*(b^2-c^2)^4 : :

See Kadir Altintas and César Lozada, euclid 4944.

X(48255) lies on these lines: {13, 15}, {11555, 42945}


X(48256) = X(14)X(16)∩X(11556)X(42944)

Barycentrics    -2*sqrt(3)*(6*a^6-19*(b^2+c^2)*a^4+2*(4*b^4-13*b^2*c^2+4*c^4)*a^2+5*(b^4-c^4)*(b^2-c^2))*S+14*a^8-11*(b^2+c^2)*a^6-(33*b^4+52*b^2*c^2+33*c^4)*a^4+43*(b^4-c^4)*(b^2-c^2)*a^2-13*(b^2-c^2)^4 : :

See Kadir Altintas and César Lozada, euclid 4944.

X(48256) lies on these lines: {14, 16}, {11556, 42944}


X(48257) = X(3)X(8706)∩X(100)X(9369)

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

See Kadir Altintas and César Lozada, euclid 4947.

X(48257) lies on the circumcircle and these lines: {3, 8706}, {100, 9369}, {106, 24813}, {109, 9363}, {110, 17539}, {944, 39628}, {1293, 4297}, {12029, 32486}

X(48257) = reflection of X(8706) in X(3)
X(48257) = isogonal conjugate of the circumnormal-isogonal conjugate of X(8706)
X(48257) = circumperp conjugate of X(8706)
X(48257) = circumnormal-isogonal conjugate of X(6363)
X(48257) = circumtangential-isogonal conjugate of the circumnormal-isogonal conjugate of X(8706)
X(48257) = antipode of X(8706) in circumcircle
X(48257) = intersection, other than A, B, C, of circumcircle and circumconic {{A, B, C, X(4), X(6533)}}
X(48257) = trilinear pole of the line {6, 2490}
X(48257) = V-transform of X(i) for these i: {6363, 8706}


X(48258) = X(110)X(8362)∩X(112)X(3867)

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

See Kadir Altintas and César Lozada, euclid 4947.

X(48258) lies on the circumcircle and these lines: {110, 8362}, {112, 3867}, {141, 907}, {827, 3618}

X(48258) = intersection, other than A, B, C, of circumcircle and circumconic {{A, B, C, X(4), X(141)}}
X(48258) = trilinear pole of the line {6, 3806}


X(48259) = X(20)X(805)∩X(107)X(237)

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

See Kadir Altintas and César Lozada, euclid 4947.

X(48259) lies on the circumcircle and these lines: {3, 22456}, {4, 38974}, {20, 805}, {98, 39201}, {99, 44137}, {107, 237}, {110, 401}, {112, 11676}, {419, 1301}, {476, 37918}, {691, 42329}, {935, 37991}, {1298, 15412}, {1304, 1316}, {2713, 6776}, {2715, 11257}, {3288, 26717}, {3331, 26714}, {18858, 38642}

X(48259) = reflection of X(i) in X(j) for these (i, j): (4, 38974), (22456, 3)
X(48259) = isogonal conjugate of the circumnormal-isogonal conjugate of X(22456)
X(48259) = circumperp conjugate of X(22456)
X(48259) = circumnormal-isogonal conjugate of X(39469)
X(48259) = antipode of X(22456) in circumcircle
X(48259) = intersection, other than A, B, C, of circumcircle and circumconic {{A, B, C, X(4), X(401)}}
X(48259) = trilinear pole of the line {6, 6130}
X(48259) = Collings transform of X(38974)
X(48259) = V-transform of X(i) for these i: {22456, 39469}


X(48260) = X(110)X(8598)∩X(376)X(2709)

Barycentrics    (a^8+5*(b^2-c^2)*a^6-(16*b^4-8*b^2*c^2-5*c^4)*a^4+(5*b^6-c^6+2*(4*b^2-5*c^2)*b^2*c^2)*a^2+(b^2-c^2)*(b^4-4*b^2*c^2+c^4)*b^2)*(a^8-5*(b^2-c^2)*a^6+(5*b^4+8*b^2*c^2-16*c^4)*a^4-(b^6-5*c^6+2*(5*b^2-4*c^2)*b^2*c^2)*a^2-(b^2-c^2)*(b^4-4*b^2*c^2+c^4)*c^2) : :

See Kadir Altintas and César Lozada, euclid 4947.

X(48260) lies on the circumcircle and these lines: {3, 9080}, {4, 9193}, {110, 8598}, {376, 2709}, {1302, 35298}

X(48260) = reflection of X(i) in X(j) for these (i, j): (4, 9193), (9080, 3)
X(48260) = isogonal conjugate of the circumnormal-isogonal conjugate of X(9080)
X(48260) = circumperp conjugate of X(9080)
X(48260) = circumnormal-isogonal conjugate of X(9023)
X(48260) = antipode of X(9080) in circumcircle
X(48260) = intersection, other than A, B, C, of circumcircle and circumconic {{A, B, C, X(4), X(8598)}}
X(48260) = trilinear pole of the line {6, 9189}
X(48260) = Collings transform of X(9193)
X(48260) = V-transform of X(i) for these i: {9023, 9080}


X(48261) = (name pending)

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

See Kadir Altintas and César Lozada, euclid 4948.

X(48261) lies on this line: {182, 3518}

X(48261) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(1232)}} and {{A, B, C, X(54), X(140)}}


X(48262) = X(3)X(695)∩X(6)X(382)

Barycentrics    a^2*((b^2+c^2)*a^6-2*(b^4+c^4)*a^4+(b^2+c^2)*(b^4-5*b^2*c^2+c^4)*a^2-(b^2-c^2)^2*b^2*c^2) : :
X(48262) = 3*X(3)-2*X(14134), X(3)+2*X(31989), 3*X(14133)-X(14134), X(14134)+3*X(31989)

See Antreas Hatzipolakis and César Lozada, euclid 4949.

X(48262) lies on these lines: {3, 695}, {4, 30505}, {5, 14822}, {6, 382}, {20, 10339}, {39, 1625}, {54, 2623}, {217, 15048}, {251, 8718}, {512, 42444}, {546, 20965}, {550, 3051}, {631, 8617}, {1180, 6241}, {1194, 40647}, {1993, 33234}, {1994, 33256}, {2211, 13488}, {3016, 9698}, {3094, 18436}, {3124, 12006}, {3231, 3530}, {3520, 35325}, {3528, 9463}, {3981, 37481}, {5254, 41334}, {6102, 20859}, {7592, 44415}, {8041, 11591}, {9605, 12315}, {12605, 14965}, {14042, 34545}, {14153, 37472}, {15484, 38297}, {15700, 36650}, {15720, 21001}, {15806, 41939}, {16881, 20977}, {37665, 41367}, {39024, 43600}, {43613, 45723}, {45956, 46906}

X(48262) = midpoint of X(14133) and X(31989)
X(48262) = reflection of X(i) in X(j) for these (i, j): (3, 14133), (4, 31869)
X(48262) = X(14133)-of-X3-ABC reflections triangle
X(48262) = X(31869)-of-anti-Euler triangle


X(48263) = X(3)X(1615)∩X(9)X(355)

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

See Antreas Hatzipolakis and César Lozada, euclid 4949.

X(48263) lies on these lines: {3, 1615}, {9, 355}, {220, 16202}, {517, 42438}, {672, 31794}, {1174, 3295}, {1212, 24474}, {1385, 8012}, {3730, 12702}, {26285, 32578}

leftri

Points in a [X(514)X(661), X(523)X(661)] coordinate system: X(48264)-X(48280)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1,L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1: a α + b β + c γ = 0.

L2: (a + b)(a + c) α + (b + c)(b + a) β + (c + a)(c + b)γ = 0.

The origin is given by (0,0) = X(661) = b^2 - c^2 : c^2 - a^2 : a^2 - b^2.

Barycentrics u : v : w for a point U = (x,y) in this system are given by

u : v : w = (b - c) (a b + a c - x + (b + c)y) : : ,

where, as functions of a,b,c, the coordinate x is symmetric and homogeneous of degree 2, and y is symmetric and homogeneous of degree 1.

The appearance of {x,y}, k in the following table means that (x,y) = X(k):

{-2 (a^2+b^2+c^2), -((2 (a^2+b^2+c^2))/(a+b+c))}, 48020
{-2 (a b+a c+b c), -((2 (a b+a c+b c))/(a+b+c))}, 48021
{-2 (a+b+c)^2, -2 (a+b+c)}, 48019
{-2 (a^2+b^2+c^2), -((a^2+b^2+c^2)/(a+b+c))}, 47943
{-2 (a b+a c+b c), -a-b-c}, 48082
{-2 (a b+a c+b c), -((a b+a c+b c)/(a+b+c))}, 47946
{-2 (a^2+b^2+c^2), 0}, 47916
{-2 (a b+a c+b c), 0}, 47917
{-((2 a b c)/(a+b+c)), 0}, 47918
{-a^2-b^2-c^2, -((2 (a^2+b^2+c^2))/(a+b+c))}, 48077
{-a b-a c-b c, -2 (a+b+c)}, 47665
{-a b-a c-b c, -((2 (a b+a c+b c))/(a+b+c))}, 48080
{-(a+b+c)^2, -((2 (a b+a c+b c))/(a+b+c))}, 47938
{-a^2-b^2-c^2, -a-b-c}, 4382
{-a^2-b^2-c^2, -((a^2+b^2+c^2)/(a+b+c))}, 48023
{-a b-a c-b c, -a-b-c}, 25259
{-a b-a c-b c, -((a^2+b^2+c^2)/(a+b+c))}, 47698
{-a b-a c-b c, -((a b+a c+b c)/(a+b+c))}, 48024
{-(a+b+c)^2, -a-b-c}, 4813
{-(a+b+c)^2, -((a^2+b^2+c^2)/(a+b+c))}, 47909
{-a^2-b^2-c^2, 1/2 (-a-b-c)}, 23729
{-a^2-b^2-c^2, -((a^2+b^2+c^2)/(2 (a+b+c)))}, 47989
{-a b-a c-b c, 1/2 (-a-b-c)}, 48046
{-a b-a c-b c, -((a b+a c+b c)/(2 (a+b+c)))}, 47993
{-a^2-b^2-c^2, 0}, 47958
{-a b-a c-b c, 0}, 47666
{-((a b c)/(a+b+c)), 0}, 47959
{-a^2-b^2-c^2, (a^2+b^2+c^2)/(a+b+c)}, 47924
{-a b-a c-b c, a+b+c}, 47667
{-a b-a c-b c, (a^2+b^2+c^2)/(a+b+c)}, 47699
{-a b-a c-b c, (a b+a c+b c)/(a+b+c)}, 47928
{-a b-a c-b c, 2 (a+b+c)}, 47668
{1/2 (-a^2-b^2-c^2), -((a^2+b^2+c^2)/(a+b+c))}, 48039
{1/2 (-a b-a c-b c), -((a b+a c+b c)/(a+b+c))}, 48043
{-(1/2) (a+b+c)^2, -((a b+a c+b c)/(a+b+c))}, 47983
{1/2 (-a^2-b^2-c^2), 1/2 (-a-b-c)}, 4106
{1/2 (-a^2-b^2-c^2), -((a^2+b^2+c^2)/(2 (a+b+c)))}, 48027
{1/2 (-a b-a c-b c), -((a b+a c+b c)/(2 (a+b+c)))}, 48028
{-(1/2) (a+b+c)^2, 1/2 (-a-b-c)}, 48026
{-(1/2) (a+b+c)^2, -((a^2+b^2+c^2)/(2 (a+b+c)))}, 47953
{1/2 (-a^2-b^2-c^2), 0}, 47995
{1/2 (-a b-a c-b c), 0}, 47996
{-((a b c)/(2 (a+b+c))), 0}, 47997
{1/2 (-a^2-b^2-c^2), (a^2+b^2+c^2)/(2 (a+b+c))}, 47961
{1/2 (-a b-a c-b c), (a b+a c+b c)/(2 (a+b+c))}, 47964
{0, -2 (a+b+c)}, 4838
{0, -((2 (a^2+b^2+c^2))/(a+b+c))}, 47700
{0, -((2 (a b+a c+b c))/(a+b+c))}, 4804
{0, -a-b-c}, 4024
{0, -((a^2+b^2+c^2)/(a+b+c))}, 4088
{0, -((a b+a c+b c)/(a+b+c))}, 4010
{0, 1/2 (-a-b-c)}, 3700
{0, -((a^2+b^2+c^2)/(2 (a+b+c)))}, 48047
{0, -((a b+a c+b c)/(2 (a+b+c)))}, 4806
{0, 0}, 661
{0, 1/2 (a+b+c)}, 4841
{0, (a^2+b^2+c^2)/(2 (a+b+c))}, 47998
{0, (a b+a c+b c)/(2 (a+b+c))}, 48002
{0, a+b+c}, 4988
{0, (a^2+b^2+c^2)/(a+b+c)}, 47701
{0, (a b+a c+b c)/(a+b+c)}, 4824
{0, 2 (a+b+c)}, 47669
{0, (2 (a^2+b^2+c^2))/(a+b+c)}, 47702
{0, (2 (a b+a c+b c))/(a+b+c)}, 47934
{1/2 (a^2+b^2+c^2), -((a^2+b^2+c^2)/(2 (a+b+c)))}, 48088
{1/2 (a b+a c+b c), 1/2 (-a-b-c)}, 4500
{1/2 (a b+a c+b c), -((a^2+b^2+c^2)/(2 (a+b+c)))}, 4522
{1/2 (a b+a c+b c), -((a b+a c+b c)/(2 (a+b+c)))}, 48090
{1/2 (a^2+b^2+c^2), 0}, 4468
{1/2 (a b+a c+b c), 0}, 3835
{1/2 (a+b+c)^2, 0}, 6590
{(a b c)/(2 (a+b+c)), 0}, 48054
{1/2 (a^2+b^2+c^2), 1/2 (a+b+c)}, 47962
{1/2 (a^2+b^2+c^2), (a^2+b^2+c^2)/(2 (a+b+c))}, 48029
{1/2 (a b+a c+b c), (a b+a c+b c)/(2 (a+b+c))}, 48030
{1/2 (a+b+c)^2, 1/2 (a+b+c)}, 650
{1/2 (a+b+c)^2, (a^2+b^2+c^2)/(2 (a+b+c))}, 7662
{1/2 (a^2+b^2+c^2), (a^2+b^2+c^2)/(a+b+c)}, 48006
{1/2 (a b+a c+b c), (a b+a c+b c)/(a+b+c)}, 48010
{1/2 (a+b+c)^2, a+b+c}, 45745
{1/2 (a+b+c)^2, (a^2+b^2+c^2)/(a+b+c)}, 47123
{1/2 (a+b+c)^2, (a b+a c+b c)/(a+b+c)}, 48062
{a b+a c+b c, -2 (a+b+c)}, 47655
{a b+a c+b c, -((2 (a^2+b^2+c^2))/(a+b+c))}, 47689
{a^2+b^2+c^2, -((a^2+b^2+c^2)/(a+b+c))}, 48118
{a b+a c+b c, -a-b-c}, 47656
{a b+a c+b c, -((a^2+b^2+c^2)/(a+b+c))}, 47690
{a b+a c+b c, -((a b+a c+b c)/(a+b+c))}, 48120
{(a b c)/(a+b+c), -((a b+a c+b c)/(2 (a+b+c)))}, 4992
{a^2+b^2+c^2, 0}, 48094
{a b+a c+b c, 0}, 693
{(a b c)/(a+b+c), 0}, 14349
{a^2+b^2+c^2, (a^2+b^2+c^2)/(2 (a+b+c))}, 48055
{a b+a c+b c, 1/2 (a+b+c)}, 3004
{a b+a c+b c, (a^2+b^2+c^2)/(2 (a+b+c))}, 23770
{a b+a c+b c, (a b+a c+b c)/(2 (a+b+c))}, 3837
{a^2+b^2+c^2, a+b+c}, 47926
{a^2+b^2+c^2, (a^2+b^2+c^2)/(a+b+c)}, 4724
{a b+a c+b c, a+b+c}, 45746
{a b+a c+b c, (a^2+b^2+c^2)/(a+b+c)}, 47691
{a b+a c+b c, (a b+a c+b c)/(a+b+c)}, 1491
{(a+b+c)^2, a+b+c}, 649
{(a+b+c)^2, (a^2+b^2+c^2)/(a+b+c)}, 48142
{a^2+b^2+c^2, (2 (a^2+b^2+c^2))/(a+b+c)}, 47972
{a b+a c+b c, 2 (a+b+c)}, 47657
{a b+a c+b c, (2 (a^2+b^2+c^2))/(a+b+c)}, 47692
{a b+a c+b c, (2 (a b+a c+b c))/(a+b+c)}, 47975
{(a+b+c)^2, (2 (a b+a c+b c))/(a+b+c)}, 48106
{2 (a b+a c+b c), -2 (a+b+c)}, 47670
{2 (a b+a c+b c), -a-b-c}, 47671
{2 (a b+a c+b c), -((a^2+b^2+c^2)/(a+b+c))}, 47703
{2 (a^2+b^2+c^2), 0}, 48130
{2 (a b+a c+b c), 0}, 47672
{(2 a b c)/(a+b+c), 0}, 48131
{2 (a b+a c+b c), 1/2 (a+b+c)}, 21104
{2 (a^2+b^2+c^2), (a^2+b^2+c^2)/(a+b+c)}, 48102
{2 (a b+a c+b c), a+b+c}, 16892
{2 (a b+a c+b c), (a^2+b^2+c^2)/(a+b+c)}, 47704
{2 (a b+a c+b c), (a b+a c+b c)/(a+b+c)}, 21146
{2 (a^2+b^2+c^2), (2 (a^2+b^2+c^2))/(a+b+c)}, 48032
{2 (a b+a c+b c), 2 (a+b+c)}, 47673
{2 (a b+a c+b c), (2 (a^2+b^2+c^2))/(a+b+c)}, 47705
{2 (a b+a c+b c), (2 (a b+a c+b c))/(a+b+c)}, 2254
{2 (a+b+c)^2, 2 (a+b+c)}, 4979
{(-2*a*b*c)/(a + b + c), (-2*(a*b + a*c + b*c))/(a + b + c)}, 48264
{(-2*a*b*c)/(a + b + c), -((a*b + a*c + b*c)/(a + b + c))}, 48265
{-(a + b + c)^2, -2*(a + b + c)}, 48266
{-((a*b*c)/(a + b + c)), -((a*b + a*c + b*c)/(a + b + c))}, 48267
{(-a^2 - b^2 - c^2)/2, -a - b - c}, 48268
{-1/2*(a + b + c)^2, -a - b - c}, 48269
{(-(a*b) - a*c - b*c)/2, (-a - b - c)/2}, 48270
{(a^2 + b^2 + c^2)/2, (-a - b - c)/2}, 48271
{(a*b*c)/(a + b + c), -((a^2 + b^2 + c^2)/(a + b + c))}, 48272
{(a*b*c)/(a + b + c), -((a*b + a*c + b*c)/(a + b + c))}, 48273
{a*b + a*c + b*c, (-a - b - c)/2}, 48274
{(a + b + c)^2, 0}, 48275
{(a + b + c)^2, (a + b + c)/2}, 48276
{(a + b + c)^2, 2*(a + b + c)}, 48277
{(2*a*b*c)/(a + b + c), -((a^2 + b^2 + c^2)/(a + b + c))}, 48278
{(2*a*b*c)/(a + b + c), -((a*b + a*c + b*c)/(a + b + c))}, 48279
{(2*a*b*c)/(a + b + c), (-a - b - c)/2}, 48280


X(48264) = X(514)X(4170)∩X(522)X(3717)

Barycentrics    (a - b - c)*(b - c)*(a*b + a*c + 2*b*c) : :
X(48264) = 3 X[4041] - 4 X[4147], 2 X[4041] - 3 X[14430], 2 X[4147] - 3 X[4391], 8 X[4147] - 9 X[14430], 4 X[4391] - 3 X[14430], 2 X[905] - 3 X[47832], 2 X[1019] - 3 X[47813], 2 X[1734] - 3 X[21052], 4 X[4791] - 3 X[21052], 2 X[2530] - 3 X[4728], 3 X[4010] - 2 X[4992], 4 X[4992] - 3 X[48131], 4 X[4129] - 3 X[47810], 4 X[4823] - 3 X[47812], 2 X[4905] - 3 X[47812], 2 X[4913] - 3 X[47793], 4 X[4990] - 3 X[14432], 2 X[9508] - 3 X[47872], 3 X[14413] - 2 X[17496], X[17496] - 3 X[48172], 5 X[24924] - 6 X[47875], 3 X[31147] - 2 X[48092], 3 X[47814] - 2 X[48017], 3 X[47815] - 2 X[48008]

X(48264) lies on these lines: {514, 4170}, {522, 3717}, {523, 47918}, {525, 21118}, {661, 784}, {663, 23880}, {693, 48151}, {814, 48150}, {824, 47708}, {900, 2533}, {905, 47832}, {1019, 47813}, {1577, 2254}, {1734, 4791}, {2530, 4728}, {3700, 6362}, {3716, 4560}, {3762, 4151}, {3777, 48090}, {3900, 4474}, {3907, 4895}, {3910, 21132}, {4010, 4992}, {4017, 7650}, {4024, 29142}, {4106, 48122}, {4129, 47810}, {4142, 4467}, {4490, 4777}, {4500, 47719}, {4724, 23882}, {4762, 47929}, {4802, 47913}, {4823, 4905}, {4843, 21120}, {4913, 47793}, {4978, 23738}, {4979, 29150}, {4990, 14432}, {6002, 47694}, {6161, 29182}, {6372, 47672}, {7265, 23887}, {7662, 48144}, {9508, 47872}, {14413, 17496}, {23877, 25259}, {24719, 48116}, {24924, 47875}, {28165, 47922}, {29033, 48111}, {29037, 47695}, {29070, 48032}, {29098, 48130}, {29118, 47660}, {29158, 48146}, {29170, 48149}, {29198, 48120}, {29328, 47935}, {29354, 47705}, {29362, 47936}, {31147, 48092}, {42325, 47724}, {47683, 48058}, {47814, 48017}, {47815, 48008}, {47909, 47955}, {47917, 47949}, {47926, 47966}, {47928, 47957}, {47934, 47959}

X(48264) = reflection of X(i) in X(j) for these {i,j}: {1734, 4791}, {2254, 1577}, {3777, 48090}, {4017, 7650}, {4041, 4391}, {4467, 4142}, {4560, 3716}, {4822, 48080}, {4905, 4823}, {6615, 4811}, {14413, 48172}, {17420, 4985}, {23738, 4978}, {47683, 48058}, {47719, 4500}, {47904, 47942}, {47909, 47955}, {47917, 47949}, {47926, 47966}, {47928, 47957}, {47934, 47959}, {48116, 24719}, {48122, 4106}, {48131, 4010}, {48144, 7662}, {48151, 693}
X(48264) = X(i)-Ceva conjugate of X(j) for these (i,j): {2321, 11}, {4436, 21020}, {28660, 2170}
X(48264) = X(i)-isoconjugate of X(j) for these (i,j): {56, 8708}, {109, 40433}, {1415, 32009}, {4559, 40408}
X(48264) = X(i)-Dao conjugate of X(j) for these (i, j): (1, 8708), (11, 40433), (1146, 32009), (3121, 1400), (3739, 4551), (16589, 664), (17205, 1434), (40625, 40439)
X(48264) = crosspoint of X(522) and X(18155)
X(48264) = crossdifference of every pair of points on line {604, 16878}
X(48264) = barycentric product X(i)*X(j) for these {i,j}: {8, 47672}, {312, 6372}, {514, 3706}, {522, 3739}, {650, 20888}, {693, 3691}, {3239, 4059}, {3700, 17175}, {3720, 4391}, {4041, 16748}, {4086, 18166}, {4111, 7199}, {4436, 4858}, {4560, 21020}, {16589, 18155}, {20963, 35519}, {22060, 46110}, {35518, 40975}
X(48264) = barycentric quotient X(i)/X(j) for these {i,j}: {9, 8708}, {522, 32009}, {650, 40433}, {2667, 4559}, {3691, 100}, {3706, 190}, {3720, 651}, {3737, 40408}, {3739, 664}, {4059, 658}, {4111, 1018}, {4436, 4564}, {4560, 40439}, {4754, 6649}, {6372, 57}, {16589, 4551}, {16748, 4625}, {17175, 4573}, {18166, 1414}, {20888, 4554}, {20963, 109}, {21020, 4552}, {21699, 21859}, {22060, 1813}, {39793, 1020}, {40975, 108}, {47672, 7}
X(48264) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1734, 4791, 21052}, {4041, 4391, 14430}, {4823, 4905, 47812}


X(48265) = X(191)X(4063)∩X(355)X(3309)

Barycentrics    (b - c)*(-(a^2*b) - a^2*c - 2*a*b*c + b^2*c + b*c^2) : :
X(48265) = 2 X[667] - 3 X[4448], 2 X[905] - 3 X[47822], 2 X[3669] - 3 X[47841], 2 X[3960] - 3 X[47839], 2 X[4369] - 3 X[47872], 2 X[4504] - 3 X[25569], 3 X[4728] - X[23738], 3 X[4776] - 2 X[48100], 2 X[4782] - 3 X[47815], 2 X[4905] - 3 X[36848], 4 X[21260] - 3 X[36848], 2 X[9508] - 3 X[47793], X[17496] - 3 X[47821], 4 X[20317] - 3 X[47835], X[21222] - 3 X[47840], 4 X[25666] - 3 X[47893]

X(48265) lies on these lines: {191, 4063}, {355, 3309}, {512, 3762}, {513, 2517}, {514, 4010}, {522, 4490}, {523, 47918}, {649, 29170}, {659, 6002}, {663, 4922}, {667, 993}, {693, 29198}, {784, 4824}, {814, 4724}, {891, 4170}, {900, 4041}, {905, 47822}, {918, 3801}, {1577, 6372}, {2254, 21051}, {2530, 4129}, {2787, 4040}, {3566, 21120}, {3667, 4147}, {3669, 11375}, {3716, 4367}, {3777, 3835}, {3837, 48151}, {3869, 4083}, {3960, 47839}, {4122, 29142}, {4140, 4502}, {4162, 37740}, {4369, 47872}, {4474, 29366}, {4498, 29328}, {4504, 25569}, {4705, 8714}, {4707, 29252}, {4728, 23738}, {4776, 48100}, {4777, 47922}, {4782, 47815}, {4801, 48090}, {4806, 48131}, {4874, 48144}, {4905, 7951}, {4977, 47906}, {4985, 8672}, {5155, 18344}, {6362, 48047}, {7265, 29312}, {9508, 47793}, {14288, 28209}, {14430, 28217}, {17496, 47821}, {20317, 26066}, {20512, 21834}, {21118, 48082}, {21222, 47840}, {23880, 48029}, {23882, 47966}, {25259, 29017}, {25666, 47893}, {29025, 48094}, {29070, 47970}, {29074, 47972}, {29118, 48103}, {29144, 47707}, {29162, 48055}, {29168, 47711}, {29174, 48118}, {29204, 47709}, {29344, 48065}, {29354, 47712}, {29362, 47929}, {47666, 47957}, {47967, 47975}

X(48265) = midpoint of X(i) and X(j) for these {i,j}: {4462, 48080}, {21118, 48082}
X(48265) = reflection of X(i) in X(j) for these {i,j}: {2254, 21051}, {2530, 4129}, {2533, 4391}, {3777, 3835}, {4367, 3716}, {4801, 48090}, {4824, 47959}, {4905, 21260}, {4922, 663}, {21146, 1577}, {47666, 47957}, {47946, 47949}, {47975, 47967}, {48123, 48043}, {48131, 4806}, {48144, 4874}, {48151, 3837}
X(48265) = crosspoint of X(668) and X(17758)
X(48265) = crosssum of X(667) and X(4251)
X(48265) = barycentric product X(693)*X(3780)
X(48265) = barycentric quotient X(3780)/X(100)
X(48265) = {X(4905),X(21260)}-harmonic conjugate of X(36848)


X(48266) = X(513)X(4024)∩X(514)X(4838)

Barycentrics    (b - c)*(-a^2 - a*b + b^2 - a*c + 2*b*c + c^2) : :
X(48266) = 2 X[47665] + X[47937], X[47670] + 2 X[48034], X[661] - 3 X[4958], 3 X[661] - 2 X[45745], 5 X[661] - 6 X[47764], 4 X[661] - 3 X[47878], 9 X[4958] - 2 X[45745], 5 X[4958] - 2 X[47764], 4 X[4958] - X[47878], 5 X[45745] - 9 X[47764], 8 X[45745] - 9 X[47878], 8 X[47764] - 5 X[47878], 7 X[649] - 8 X[2527], 5 X[649] - 6 X[47767], 2 X[649] - 3 X[47874], 4 X[2527] - 7 X[3700], 20 X[2527] - 21 X[47767], 16 X[2527] - 21 X[47874], 5 X[3700] - 3 X[47767], 4 X[3700] - 3 X[47874], 4 X[47767] - 5 X[47874], 2 X[650] - 3 X[4120], 3 X[25259] - X[47663], 2 X[47663] - 3 X[48094], 3 X[20295] - X[47653], 2 X[47653] - 3 X[47958], 3 X[1635] - 4 X[3239], 15 X[1635] - 16 X[31182], 5 X[3239] - 4 X[31182], 4 X[2490] - 3 X[4773], 8 X[2516] - 9 X[6544], 4 X[2529] - 3 X[4790], 2 X[3004] - 3 X[31147], 3 X[4931] - X[4979], 3 X[4931] - 2 X[6590], 2 X[3776] - 3 X[21297], 4 X[3798] - 5 X[24924], 2 X[3798] - 3 X[47787], 5 X[24924] - 6 X[47787], 4 X[3835] - 3 X[47886], 2 X[4467] - 3 X[47886], 2 X[4025] - 3 X[4728], 2 X[4369] - 3 X[47790], 3 X[4379] - 2 X[4897], 2 X[4394] - 3 X[4944], 4 X[4394] - 3 X[4984], 3 X[4750] - 4 X[4885], 2 X[4765] - 3 X[47765], 3 X[4776] - 2 X[21196], 4 X[4949] - X[4988], 3 X[4789] - 2 X[4932], 3 X[4893] - 2 X[4976], 3 X[4893] - 4 X[14321], 4 X[4990] - 3 X[8643], 3 X[6545] - 4 X[23813], 4 X[17069] - 5 X[30835], X[17161] - 3 X[47759], 4 X[25666] - 3 X[27486], 5 X[26798] - 3 X[47894], X[26853] - 3 X[47870], 5 X[27013] - 6 X[47879], 7 X[27138] - 6 X[47882], 3 X[30565] - 2 X[48008], 3 X[31148] - 2 X[48013], 5 X[31209] - 6 X[45661], 3 X[47769] - 2 X[48000], 3 X[47887] - 4 X[48090]

X(48266) lies on these lines: {513, 4024}, {514, 4838}, {522, 661}, {523, 4813}, {647, 4526}, {649, 900}, {650, 4120}, {663, 29232}, {667, 29266}, {693, 2786}, {812, 25259}, {824, 20295}, {918, 4382}, {1577, 29216}, {1635, 3239}, {2490, 4773}, {2516, 6544}, {2529, 4790}, {3004, 31147}, {3250, 8714}, {3667, 4931}, {3766, 20909}, {3776, 21297}, {3798, 24924}, {3835, 4467}, {4010, 29078}, {4025, 4728}, {4106, 16892}, {4122, 29328}, {4155, 20983}, {4170, 29062}, {4369, 47790}, {4379, 4897}, {4394, 4944}, {4468, 47932}, {4500, 7192}, {4750, 4885}, {4762, 48082}, {4765, 47765}, {4775, 29058}, {4776, 21196}, {4777, 4949}, {4785, 47660}, {4789, 4932}, {4841, 28183}, {4879, 29230}, {4893, 4976}, {4990, 8643}, {6008, 48101}, {6084, 48117}, {6545, 23813}, {7265, 29013}, {8640, 17989}, {14298, 42462}, {17069, 30835}, {17161, 47759}, {21438, 23794}, {21834, 28623}, {22043, 23803}, {23729, 47923}, {23731, 28894}, {24719, 47973}, {25666, 27486}, {26798, 47894}, {26824, 28851}, {26853, 47870}, {27013, 47879}, {27138, 47882}, {28161, 47669}, {28217, 47873}, {28840, 47656}, {28846, 47672}, {28855, 47675}, {28859, 47659}, {28890, 47650}, {29178, 47682}, {29294, 47712}, {29362, 48078}, {30519, 47652}, {30565, 48008}, {31148, 48013}, {31209, 45661}, {45746, 48049}, {47661, 47996}, {47667, 47991}, {47673, 47995}, {47769, 48000}, {47887, 48090}, {47917, 48038}, {47926, 48046}, {47933, 48036}

X(48266) = midpoint of X(i) and X(j) for these {i,j}: {4838, 48019}, {47655, 47939}, {47665, 48079}, {47670, 47903}
X(48266) = reflection of X(i) in X(j) for these {i,j}: {649, 3700}, {4024, 4820}, {4467, 3835}, {4976, 14321}, {4979, 6590}, {4984, 4944}, {4988, 48026}, {7192, 4500}, {16892, 4106}, {45746, 48049}, {47661, 47996}, {47667, 47991}, {47673, 47995}, {47903, 48034}, {47917, 48038}, {47923, 23729}, {47926, 48046}, {47932, 4468}, {47933, 48036}, {47937, 48079}, {47958, 20295}, {47971, 693}, {47972, 48080}, {47973, 24719}, {48026, 4949}, {48076, 44449}, {48094, 25259}, {48104, 47660}, {48106, 4122}
X(48266) = crossdifference of every pair of points on line {995, 1203}
X(48266) = barycentric product X(i)*X(j) for these {i,j}: {514, 17299}, {522, 24914}
X(48266) = barycentric quotient X(i)/X(j) for these {i,j}: {17299, 190}, {24914, 664}
X(48266) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 3700, 47874}, {3798, 47787, 24924}, {3835, 4467, 47886}, {4931, 4979, 6590}, {4976, 14321, 4893}


X(48267) = X(513)X(1577)∩X(514)X(4010)

Barycentrics    (b - c)*(-(a^2*b) - a^2*c - a*b*c + b^2*c + b*c^2) : :
X(48267) = 2 X[905] - 3 X[47839], 3 X[14431] - 2 X[17072], 2 X[3960] - 3 X[47841], X[4367] - 3 X[4800], 2 X[4369] - 3 X[47875], X[4380] - 3 X[47815], 2 X[4401] - 3 X[4448], X[4560] - 3 X[47821], 3 X[4728] - 2 X[23815], 3 X[4728] - X[48151], X[4729] - 3 X[14430], 3 X[4776] - 2 X[48059], 2 X[4782] - 3 X[47817], X[4784] - 3 X[47872], 2 X[9508] - 3 X[47794], 2 X[14838] - 3 X[47822], X[17166] - 3 X[48172], X[17496] - 3 X[47840], X[21302] - 3 X[30709], 2 X[23789] - 3 X[48184], 4 X[25380] - 5 X[31251], 4 X[25666] - 3 X[47888], 3 X[31147] - X[48122], 3 X[36848] - 2 X[48075], X[47719] - 3 X[47790], 3 X[47813] - X[48149], 3 X[47832] - X[48144]

X(48267) lies on these lines: {1, 29324}, {512, 4391}, {513, 1577}, {514, 4010}, {522, 4705}, {523, 47959}, {649, 29150}, {659, 29013}, {661, 784}, {663, 2787}, {667, 3716}, {693, 6372}, {814, 4040}, {826, 25259}, {891, 4462}, {900, 1734}, {905, 47839}, {1019, 4874}, {1491, 4129}, {1960, 29176}, {2254, 21260}, {2530, 3835}, {2533, 4791}, {2786, 4142}, {3126, 6260}, {3566, 10015}, {3583, 33599}, {3667, 14431}, {3700, 29142}, {3762, 4083}, {3766, 40495}, {3801, 23875}, {3837, 4905}, {3907, 4775}, {3960, 47841}, {4063, 29328}, {4122, 29021}, {4147, 4730}, {4151, 4490}, {4367, 4800}, {4369, 47875}, {4380, 47815}, {4382, 47929}, {4401, 4448}, {4474, 29298}, {4526, 22229}, {4560, 47821}, {4707, 29200}, {4724, 29070}, {4728, 23815}, {4729, 14430}, {4762, 47966}, {4776, 48059}, {4777, 47967}, {4782, 47817}, {4784, 47872}, {4794, 29344}, {4802, 47957}, {4804, 47918}, {4806, 14349}, {4810, 29302}, {4823, 21146}, {4824, 47997}, {4940, 48092}, {4977, 47942}, {4978, 29198}, {6004, 21301}, {6161, 28470}, {6362, 14321}, {7265, 29017}, {7650, 8672}, {7927, 47707}, {7950, 47709}, {8651, 25902}, {8676, 42455}, {9508, 47794}, {14838, 47822}, {16229, 17924}, {17166, 48172}, {17496, 47840}, {21201, 35352}, {21302, 30709}, {23789, 48184}, {23880, 48099}, {23882, 48029}, {25380, 31251}, {25666, 47888}, {29033, 48065}, {29086, 47972}, {29098, 48094}, {29120, 47682}, {29134, 47726}, {29138, 47684}, {29144, 47711}, {29158, 48103}, {29168, 47690}, {29204, 47713}, {29246, 47724}, {29268, 47729}, {29354, 47691}, {29362, 47970}, {31147, 48122}, {36848, 48075}, {47666, 47994}, {47672, 47906}, {47719, 47790}, {47813, 48149}, {47832, 48144}, {47911, 48142}, {47975, 48005}

X(48267) = midpoint of X(i) and X(j) for these {i,j}: {3762, 4170}, {4382, 47929}, {4391, 48080}, {4804, 47918}, {25259, 47708}, {47672, 47906}, {47911, 48142}, {47913, 48120}
X(48267) = reflection of X(i) in X(j) for these {i,j}: {667, 3716}, {1019, 4874}, {1491, 4129}, {1734, 21051}, {2254, 21260}, {2530, 3835}, {2533, 4791}, {4730, 4147}, {4824, 47997}, {4905, 3837}, {4978, 48090}, {4983, 48043}, {14349, 4806}, {21146, 4823}, {47666, 47994}, {47946, 47987}, {47975, 48005}, {48092, 4940}, {48151, 23815}
X(48267) = barycentric product X(514)*X(32915)
X(48267) = barycentric quotient X(32915)/X(190)
X(48267) = {X(4728),X(48151)}-harmonic conjugate of X(23815)


X(48268) = X(2)X(4765)∩X(514)X(4024)

Barycentrics    (b - c)*(-a^2 + b^2 + 4*b*c + c^2) : :
X(48268) = X[4608] + 3 X[20295], X[4608] - 3 X[47656], 2 X[4608] + 3 X[47981], 2 X[47656] + X[47981], 3 X[693] - 2 X[3676], 5 X[693] - 3 X[4453], 3 X[693] - X[4467], 4 X[693] - 3 X[21183], 4 X[3676] - 3 X[4025], 10 X[3676] - 9 X[4453], 8 X[3676] - 9 X[21183], 5 X[4025] - 6 X[4453], 3 X[4025] - 2 X[4467], 2 X[4025] - 3 X[21183], 9 X[4453] - 5 X[4467], 4 X[4453] - 5 X[21183], 4 X[4467] - 9 X[21183], 2 X[649] - 3 X[47789], 5 X[650] - 6 X[45326], 2 X[650] - 3 X[47787], 4 X[45326] - 5 X[47787], 2 X[661] - 3 X[47786], 4 X[4500] - X[48060], 2 X[3239] - 3 X[47790], X[17494] - 3 X[47790], 2 X[3798] - 3 X[4379], 4 X[3835] - 3 X[47783], 2 X[45745] - 3 X[47783], 3 X[4120] - X[47926], 4 X[4369] - 3 X[4786], X[4380] - 3 X[4789], 2 X[4394] - 3 X[47788], 4 X[4521] - 3 X[31150], 3 X[4776] - X[47661], 4 X[4885] - 3 X[47785], 2 X[4976] - 3 X[47785], 2 X[4913] - 3 X[47806], 3 X[4931] - X[48094], 3 X[4958] - X[48076], X[4988] - 3 X[31147], 4 X[7658] - 5 X[26985], 4 X[7658] - 3 X[27486], 5 X[26985] - 3 X[27486], 2 X[11068] - 3 X[47874], 3 X[47874] - X[47932], 2 X[17069] - 3 X[45320], X[17161] - 3 X[44435], 2 X[21196] - 3 X[47757], 3 X[21297] - X[45746], 4 X[25666] - 3 X[47883], 3 X[47766] - 2 X[48008], 5 X[26798] - 3 X[47781], X[26853] - 3 X[47791], 3 X[30565] - X[47664], 4 X[43061] - 3 X[47776], X[47663] - 3 X[47870], X[47667] - 3 X[47759], X[47676] - 3 X[47869], X[47677] - 3 X[47871], 3 X[47764] - 2 X[47996], 3 X[47765] - 2 X[48000], 3 X[47873] - X[48101]

X(48268) lies on these lines: {2, 4765}, {514, 4024}, {522, 693}, {523, 4106}, {649, 47789}, {650, 45326}, {661, 47786}, {812, 4500}, {850, 4151}, {900, 43067}, {918, 4820}, {1577, 25007}, {1734, 23792}, {3004, 4777}, {3239, 17494}, {3261, 17894}, {3667, 5214}, {3669, 26732}, {3700, 4468}, {3798, 4379}, {3835, 45745}, {3910, 43052}, {4010, 48006}, {4120, 47926}, {4369, 4786}, {4380, 4789}, {4394, 47788}, {4521, 31150}, {4560, 24559}, {4776, 47661}, {4778, 48079}, {4802, 47988}, {4838, 47958}, {4841, 4940}, {4885, 4976}, {4897, 4926}, {4913, 47806}, {4927, 28205}, {4931, 48094}, {4958, 48076}, {4962, 47780}, {4977, 47978}, {4988, 31147}, {6006, 48107}, {6008, 48067}, {6009, 48095}, {6332, 23882}, {6362, 9719}, {7658, 26985}, {11068, 47874}, {14321, 47962}, {17069, 45320}, {17161, 44435}, {20954, 35519}, {21104, 28898}, {21185, 29190}, {21186, 23801}, {21196, 47757}, {21297, 28161}, {21832, 28398}, {23729, 28894}, {23874, 48109}, {23880, 30725}, {24719, 47982}, {25666, 47883}, {25924, 45755}, {26248, 47801}, {26277, 47766}, {26798, 47781}, {26853, 47791}, {28147, 47655}, {28169, 47657}, {28292, 47721}, {28846, 47672}, {28878, 44449}, {29362, 48061}, {30565, 47664}, {38357, 40618}, {39771, 39773}, {43061, 47776}, {47652, 47665}, {47663, 47870}, {47667, 47759}, {47676, 47869}, {47677, 47871}, {47764, 47996}, {47765, 48000}, {47873, 48101}, {48015, 48089}

X(48268) = midpoint of X(i) and X(j) for these {i,j}: {4024, 4382}, {4813, 47671}, {4820, 48125}, {4838, 47958}, {20295, 47656}, {25259, 26824}, {31290, 47674}, {44449, 47675}, {47652, 47665}
X(48268) = reflection of X(i) in X(j) for these {i,j}: {3004, 23813}, {4025, 693}, {4467, 3676}, {4468, 3700}, {4841, 4940}, {4976, 4885}, {6590, 4500}, {17494, 3239}, {45745, 3835}, {47932, 11068}, {47962, 14321}, {47981, 20295}, {47982, 24719}, {47995, 4106}, {48006, 4010}, {48013, 43067}, {48015, 48089}, {48060, 6590}
X(48268) = anticomplement of X(4765)
X(48268) = anticomplement of the isotomic conjugate of X(4624)
X(48268) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {109, 41915}, {2334, 37781}, {4606, 3436}, {4614, 20245}, {4624, 6327}, {4627, 3869}, {5545, 75}, {8694, 329}, {25430, 33650}, {34074, 144}
X(48268) = X(4624)-Ceva conjugate of X(2)
X(48268) = X(692)-isoconjugate of X(3296)
X(48268) = X(i)-Dao conjugate of X(j) for these (i, j): (1086, 3296), (40618, 30679), (47965, 4778)
X(48268) = crosspoint of X(i) and X(j) for these (i,j): {190, 32022}, {664, 30598}
X(48268) = crosssum of X(i) and X(j) for these (i,j): {649, 5021}, {8653, 20970}
X(48268) = crossdifference of every pair of points on line {41, 2308}
X(48268) = barycentric product X(i)*X(j) for these {i,j}: {75, 47965}, {514, 42696}, {693, 3305}, {3261, 3295}, {3676, 42032}, {3697, 7199}, {4391, 7190}
X(48268) = barycentric quotient X(i)/X(j) for these {i,j}: {514, 3296}, {3295, 101}, {3305, 100}, {3697, 1018}, {4025, 30679}, {7190, 651}, {42032, 3699}, {42696, 190}, {47965, 1}
X(48268) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 4025, 21183}, {693, 4467, 3676}, {3676, 4467, 4025}, {3835, 45745, 47783}, {4885, 4976, 47785}, {17494, 47790, 3239}, {26985, 27486, 7658}, {47874, 47932, 11068}


X(48269) = X(2)X(3798)∩X(513)X(3700)

Barycentrics    (b - c)*(-a^2 - 2*a*b + b^2 - 2*a*c + 2*b*c + c^2) : :
X(48269) = X[3700] + 2 X[4949], 4 X[4949] + X[6590], X[661] + 3 X[4958], 2 X[661] - 3 X[47764], 5 X[661] - 3 X[47878], 6 X[4958] + X[45745], 2 X[4958] + X[47764], 5 X[4958] + X[47878], X[45745] - 3 X[47764], 5 X[45745] - 6 X[47878], 5 X[47764] - 2 X[47878], X[649] - 3 X[4120], 3 X[649] - 4 X[43061], 2 X[649] - 3 X[47766], 2 X[3239] - 3 X[4120], 3 X[3239] - 2 X[43061], 4 X[3239] - 3 X[47766], 9 X[4120] - 4 X[43061], 8 X[43061] - 9 X[47766], 2 X[650] - 3 X[47765], 4 X[14321] - 3 X[47765], 3 X[1635] - 4 X[4521], 3 X[1639] - 2 X[4394], 4 X[2487] - 5 X[31250], 4 X[2516] - 3 X[4773], 3 X[3835] - 2 X[21212], 4 X[3835] - 3 X[47757], 2 X[3835] - 3 X[47786], 3 X[4025] - 4 X[21212], 2 X[4025] - 3 X[47757], X[4025] - 3 X[47786], 8 X[21212] - 9 X[47757], 4 X[21212] - 9 X[47786], 2 X[3676] - 3 X[4728], 3 X[4728] - X[47971], 4 X[3716] - 3 X[47801], 2 X[4369] - 3 X[47787], 3 X[47787] - X[48013], X[4380] - 3 X[30565], 2 X[11068] - 3 X[30565], X[4467] - 3 X[4776], 2 X[4500] + X[48034], 3 X[4750] - 4 X[7658], 3 X[4750] - 5 X[30835], 4 X[7658] - 5 X[30835], 2 X[4765] - 3 X[4893], 3 X[4931] + X[48019], 3 X[4786] - 4 X[31286], 2 X[31286] - 3 X[45661], 3 X[4789] - X[48107], X[4790] - 3 X[4944], 2 X[4790] - 3 X[47768], 4 X[4885] - 3 X[47758], 2 X[4897] - 3 X[47758], 2 X[4976] - 3 X[47883], 2 X[4932] - 3 X[47789], X[4979] - 3 X[47874], 3 X[4984] - 8 X[14350], 9 X[6544] - 8 X[31182], X[7192] - 3 X[47790], X[16892] - 3 X[31147], 2 X[17069] - 3 X[47760], X[17161] - 3 X[47781], X[17494] - 3 X[47769], 2 X[21196] - 3 X[47783], 3 X[21297] - X[47676], 4 X[25666] - 3 X[47785], 5 X[26798] - 3 X[44435], X[26853] - 3 X[47771], 5 X[26985] - 3 X[47755], 7 X[27138] - 6 X[44432], X[45746] - 3 X[47759], X[47663] - 3 X[47772], X[47667] - 3 X[47774]

X(48269) lies on these lines: {2, 3798}, {4, 38360}, {37, 43060}, {190, 42402}, {513, 3700}, {514, 4024}, {522, 661}, {523, 4820}, {649, 3239}, {650, 900}, {693, 28846}, {812, 4468}, {824, 47995}, {918, 4106}, {1252, 15343}, {1635, 4521}, {1639, 4394}, {2487, 31250}, {2501, 3566}, {2516, 4773}, {2610, 21186}, {2786, 3835}, {3004, 4940}, {3064, 15313}, {3676, 4728}, {3716, 47801}, {3766, 21438}, {4010, 47123}, {4079, 28623}, {4129, 29216}, {4163, 4729}, {4369, 28867}, {4380, 11068}, {4391, 28478}, {4406, 18154}, {4467, 4776}, {4500, 28840}, {4522, 48069}, {4526, 7180}, {4750, 7658}, {4762, 48046}, {4765, 4893}, {4777, 4841}, {4778, 4931}, {4785, 48060}, {4786, 31286}, {4789, 48107}, {4790, 4944}, {4806, 29078}, {4838, 28147}, {4885, 4897}, {4926, 4976}, {4932, 47789}, {4979, 6006}, {4984, 14350}, {4988, 28161}, {5513, 24828}, {6002, 6332}, {6008, 47890}, {6084, 48087}, {6544, 31182}, {6587, 7655}, {6589, 21894}, {7192, 47790}, {8676, 21645}, {16892, 31147}, {17069, 47760}, {17161, 47781}, {17458, 23751}, {17494, 47769}, {18004, 29328}, {21104, 23813}, {21183, 28906}, {21196, 47783}, {21297, 47676}, {21832, 44448}, {23729, 30520}, {23874, 48033}, {25666, 47785}, {26798, 44435}, {26853, 47771}, {26985, 47755}, {27138, 44432}, {28169, 47669}, {28221, 47777}, {28225, 47873}, {28859, 47978}, {28878, 47672}, {28894, 47988}, {28902, 48133}, {29232, 48099}, {29362, 48040}, {39386, 47881}, {45746, 47759}, {47660, 48079}, {47663, 47772}, {47667, 47774}, {48015, 48050}, {48094, 48114}

X(48269) = midpoint of X(i) and X(j) for these {i,j}: {693, 44449}, {4024, 4813}, {4382, 48082}, {4820, 48026}, {20295, 25259}, {31290, 47656}, {47660, 48079}, {47671, 47908}, {47672, 48076}, {48094, 48114}
X(48269) = reflection of X(i) in X(j) for these {i,j}: {649, 3239}, {650, 14321}, {3004, 4940}, {4025, 3835}, {4380, 11068}, {4729, 4163}, {4786, 45661}, {4897, 4885}, {6590, 3700}, {21104, 23813}, {45745, 661}, {47123, 4010}, {47757, 47786}, {47766, 4120}, {47768, 4944}, {47971, 3676}, {47981, 48041}, {47995, 48049}, {48006, 48043}, {48013, 4369}, {48015, 48050}, {48062, 18004}, {48069, 4522}
X(48269) = anticomplement of X(3798)
X(48269) = polar conjugate of the isotomic conjugate of X(20315)
X(48269) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {100, 19583}, {2996, 21293}, {3565, 75}, {8769, 150}, {8770, 149}, {35136, 17137}, {38252, 4440}
X(48269) = X(20315)-Dao conjugate of X(514)
X(48269) = crosspoint of X(i) and X(j) for these (i,j): {4, 190}, {32014, 35136}
X(48269) = crosssum of X(i) and X(j) for these (i,j): {3, 649}, {3057, 46389}, {8651, 20970}, {20283, 20979}
X(48269) = crossdifference of every pair of points on line {999, 1201}
X(48269) = barycentric product X(i)*X(j) for these {i,j}: {4, 20315}, {100, 17888}, {513, 46937}, {514, 17314}, {522, 1788}, {1577, 1778}, {3261, 14974}, {14868, 24006}
X(48269) = barycentric quotient X(i)/X(j) for these {i,j}: {1778, 662}, {1788, 664}, {14868, 4592}, {14974, 101}, {17314, 190}, {17888, 693}, {20315, 69}, {46937, 668}
X(48269) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 3239, 47766}, {649, 4120, 3239}, {650, 14321, 47765}, {3835, 4025, 47757}, {4025, 47786, 3835}, {4380, 30565, 11068}, {4728, 47971, 3676}, {4750, 30835, 7658}, {4885, 4897, 47758}, {45745, 47764, 661}, {47787, 48013, 4369}


X(48270) = X(513)X(4522)∩X(514)X(3700)

Barycentrics    (b - c)*(-2*a*b + b^2 - 2*a*c + b*c + c^2) : :
X(48270) = X[4500] + 2 X[48046], X[649] - 3 X[30565], 3 X[30565] + X[44449], 3 X[661] - X[45746], 5 X[661] - X[47673], X[661] - 3 X[47769], 5 X[661] - 3 X[47781], 3 X[25259] + X[45746], 5 X[25259] + X[47673], X[25259] + 3 X[47769], 5 X[25259] + 3 X[47781], 5 X[45746] - 3 X[47673], X[45746] - 9 X[47769], 5 X[45746] - 9 X[47781], X[47673] - 15 X[47769], X[47673] - 3 X[47781], 5 X[47769] - X[47781], X[693] - 3 X[4120], 5 X[693] - 3 X[21116], 5 X[4120] - X[21116], 3 X[4120] + X[48082], 3 X[21116] + 5 X[48082], X[3776] - 4 X[14321], 3 X[1639] - X[4897], 3 X[1639] - 2 X[31286], 2 X[2487] - 3 X[45326], 4 X[2490] - 3 X[45313], 4 X[2516] - 3 X[45679], 4 X[3239] - 3 X[47879], 2 X[4369] - 3 X[47879], 2 X[3676] - 3 X[4928], 2 X[3798] - 3 X[4763], 4 X[4521] - 3 X[4763], 3 X[4024] - X[47655], X[47655] + 3 X[47666], X[4025] - 3 X[47765], 2 X[4025] - 3 X[47882], 2 X[25666] - 3 X[47765], 4 X[25666] - 3 X[47882], X[4380] - 3 X[6546], 2 X[4394] - 3 X[10196], 3 X[4453] - 5 X[30835], X[4467] - 3 X[4893], 3 X[4728] - X[47676], 3 X[4728] + X[48112], 3 X[4750] - 5 X[31209], 3 X[4776] - X[16892], X[4784] - 3 X[48185], 3 X[4789] - X[48141], X[4790] - 3 X[47770], 2 X[4885] - 3 X[45661], 3 X[4931] - X[47656], 3 X[4931] + X[47917], 3 X[4944] - X[43067], 3 X[4958] + X[47932], X[4979] - 3 X[47771], X[7192] - 3 X[47874], 3 X[47874] + X[48076], 2 X[17069] - 3 X[47778], X[17161] - 3 X[47878], X[20295] + 3 X[47772], 3 X[47772] - X[48094], 2 X[21212] - 3 X[47760], 5 X[24924] - 3 X[47755], 3 X[47764] - X[47995], 3 X[31147] - X[47652], 3 X[31147] + X[48117], 4 X[31287] - 3 X[45674], X[31290] + 3 X[47870], 3 X[44435] - X[47930], X[47659] + 3 X[47774], X[47672] - 3 X[47790], 3 X[47759] - X[47958], 3 X[47766] - X[48013], 3 X[47773] - X[48104], 3 X[47791] - X[48147], 3 X[47873] + X[47908], X[48106] - 3 X[48171]

X(48270) lies on these lines: {2, 47971}, {513, 4522}, {514, 3700}, {522, 48000}, {523, 47964}, {649, 28867}, {650, 2786}, {661, 824}, {693, 4120}, {812, 4468}, {900, 48008}, {918, 3776}, {1639, 4897}, {2487, 45326}, {2490, 45313}, {2516, 45679}, {3004, 30519}, {3239, 4369}, {3566, 4147}, {3667, 11067}, {3676, 4928}, {3762, 28468}, {3798, 4521}, {4024, 47655}, {4025, 25666}, {4063, 28493}, {4088, 48080}, {4122, 48024}, {4129, 23875}, {4380, 6546}, {4394, 10196}, {4453, 30835}, {4467, 4893}, {4728, 47676}, {4750, 31209}, {4776, 16892}, {4784, 48185}, {4785, 47890}, {4789, 48141}, {4790, 47770}, {4804, 47698}, {4813, 28859}, {4818, 48030}, {4820, 47962}, {4822, 47707}, {4838, 47667}, {4885, 45661}, {4931, 47656}, {4940, 30520}, {4944, 28855}, {4949, 6008}, {4958, 47932}, {4977, 47984}, {4979, 47771}, {4988, 47665}, {5592, 28475}, {6590, 28840}, {7192, 28886}, {7265, 47959}, {7658, 14350}, {8034, 21350}, {17069, 47778}, {17161, 47878}, {20295, 28882}, {21051, 29200}, {21196, 28898}, {21212, 47760}, {21260, 29252}, {22037, 23876}, {23731, 47662}, {23879, 47997}, {24719, 48083}, {24924, 47755}, {28217, 48016}, {28507, 48111}, {28863, 47764}, {28871, 47787}, {28890, 47786}, {29037, 48099}, {29062, 48058}, {29190, 48004}, {29216, 48003}, {29328, 48056}, {29362, 48048}, {31147, 47652}, {31287, 45674}, {31290, 47870}, {44435, 47930}, {46403, 48078}, {47659, 47774}, {47663, 48114}, {47672, 47790}, {47686, 48113}, {47690, 48021}, {47693, 47938}, {47703, 47941}, {47711, 48081}, {47715, 47942}, {47719, 47906}, {47759, 47958}, {47766, 48013}, {47773, 48104}, {47791, 48147}, {47873, 47908}, {48079, 48101}, {48106, 48171}

X(48270) = midpoint of X(i) and X(j) for these {i,j}: {649, 44449}, {661, 25259}, {693, 48082}, {3700, 48046}, {4024, 47666}, {4088, 48080}, {4106, 48087}, {4122, 48024}, {4804, 47698}, {4813, 47660}, {4820, 47962}, {4822, 47707}, {4838, 47667}, {4988, 47665}, {6590, 48038}, {7192, 48076}, {7265, 47959}, {20295, 48094}, {23731, 47662}, {24719, 48083}, {46403, 48078}, {47652, 48117}, {47656, 47917}, {47663, 48114}, {47676, 48112}, {47686, 48113}, {47690, 48021}, {47693, 47938}, {47703, 47941}, {47711, 48081}, {47715, 47942}, {47719, 47906}, {48079, 48101}
X(48270) = complement of X(47971)
X(48270) = reflection of X(i) in X(j) for these {i,j}: {3776, 3835}, {3798, 4521}, {3835, 14321}, {4025, 25666}, {4369, 3239}, {4500, 3700}, {4522, 18004}, {4818, 48030}, {4897, 31286}, {7658, 14350}, {47882, 47765}
X(48270) = barycentric product X(514)*X(17242)
X(48270) = barycentric quotient X(17242)/X(190)
X(48270) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 47673, 47781}, {1639, 4897, 31286}, {3239, 4369, 47879}, {3798, 4521, 4763}, {4025, 25666, 47882}, {4025, 47765, 25666}, {4120, 48082, 693}, {4728, 48112, 47676}, {4931, 47917, 47656}, {20295, 47772, 48094}, {25259, 47769, 661}, {30565, 44449, 649}, {31147, 48117, 47652}, {47874, 48076, 7192}


X(48271) = X(513)X(4122)∩X(514)X(3700)

Barycentrics    (b - c)*(a^2 - a*b + 2*b^2 - a*c + 2*b*c + 2*c^2) : :
X(48271) = 5 X[17494] - 9 X[44009], 9 X[44009] + 5 X[47665], X[693] - 3 X[47870], 3 X[25259] - X[44449], X[44449] + 3 X[47660], 3 X[3700] - X[23729], 3 X[4106] - 2 X[23729], 2 X[4500] + X[48124], 5 X[650] - 6 X[10196], 3 X[650] - 2 X[21196], 2 X[650] - 3 X[47770], 9 X[10196] - 5 X[21196], 4 X[10196] - 5 X[47770], 4 X[21196] - 9 X[47770], 4 X[2487] - 3 X[4025], 8 X[2487] - 9 X[47761], 2 X[4025] - 3 X[47761], 4 X[2490] - 3 X[47785], 4 X[2496] - 3 X[48239], 4 X[2516] - 3 X[27486], 4 X[2527] - 3 X[4786], 4 X[2529] - 3 X[47763], 2 X[3004] - 3 X[47760], 4 X[3239] - 3 X[47760], 2 X[3676] - 3 X[47788], 2 X[3776] - 3 X[45320], 2 X[3798] - 3 X[47767], 2 X[3835] - 3 X[4944], 3 X[4944] - X[47960], X[47659] + 3 X[47772], X[47666] - 3 X[47772], 3 X[4120] - 2 X[4940], 3 X[4120] - X[47958], 2 X[4369] - 3 X[47881], 3 X[4379] - X[47930], X[4380] - 3 X[47773], X[4382] - 3 X[4931], 3 X[4931] + X[48130], 2 X[4394] - 3 X[47771], X[4467] - 3 X[47771], 2 X[4458] - 3 X[48220], 4 X[4521] - 3 X[47784], 3 X[4728] - X[47923], 2 X[4765] - 3 X[47884], 3 X[4776] - X[47653], 3 X[4789] - X[47676], 2 X[4818] - 3 X[48193], 10 X[4885] - 9 X[14475], 4 X[4885] - 3 X[47754], 2 X[4885] - 3 X[47874], 9 X[14475] - 5 X[16892], 6 X[14475] - 5 X[47754], 3 X[14475] - 5 X[47874], 2 X[16892] - 3 X[47754], X[16892] - 3 X[47874], 3 X[4893] - X[47673], 3 X[4958] + X[48145], 4 X[7653] - 3 X[47755], 2 X[9508] - 3 X[48219], 2 X[17069] - 3 X[47766], X[17161] - 3 X[31150], 4 X[21212] - 5 X[31250], 2 X[21212] - 3 X[47879], 5 X[31250] - 6 X[47879], 3 X[21297] - X[47651], 2 X[23813] - 3 X[47790], X[47652] - 3 X[47790], 4 X[25666] - 3 X[47880], 3 X[30565] - X[45746], 3 X[31147] - X[47916], 5 X[31209] - 3 X[47894], 4 X[31287] - 3 X[47886], X[47654] - 3 X[47781], X[47657] - 3 X[47775], X[47672] - 3 X[47873], 3 X[47873] + X[48117], X[47675] - 3 X[47792], X[47692] - 3 X[48172], X[47975] - 3 X[48171]

X(48271) lies on these lines: {2, 47677}, {37, 28374}, {75, 30061}, {192, 4777}, {312, 693}, {513, 4122}, {514, 3700}, {522, 4830}, {523, 4468}, {649, 28898}, {650, 824}, {661, 28894}, {768, 21348}, {812, 4820}, {900, 48060}, {918, 6590}, {2487, 4025}, {2490, 47785}, {2496, 48239}, {2509, 23885}, {2516, 27486}, {2526, 4522}, {2527, 4786}, {2529, 47763}, {2786, 4790}, {3004, 3239}, {3057, 11247}, {3175, 4024}, {3309, 47711}, {3669, 8045}, {3676, 47788}, {3776, 45320}, {3798, 47767}, {3803, 29062}, {3835, 4944}, {3900, 47707}, {4010, 4802}, {4120, 4940}, {4369, 30519}, {4379, 47930}, {4380, 4926}, {4382, 4931}, {4391, 20952}, {4394, 4467}, {4408, 20953}, {4411, 20891}, {4458, 48220}, {4521, 47784}, {4728, 47923}, {4765, 47884}, {4776, 47653}, {4789, 47676}, {4804, 48118}, {4806, 47961}, {4810, 48140}, {4818, 48193}, {4838, 47926}, {4885, 14475}, {4893, 47673}, {4949, 48079}, {4958, 48145}, {4976, 11068}, {4977, 48038}, {6008, 48101}, {7653, 47755}, {9001, 43216}, {9508, 48219}, {14321, 47995}, {17069, 47766}, {17161, 31150}, {18004, 48027}, {20295, 47662}, {20317, 21124}, {21212, 31250}, {21297, 47651}, {23813, 47652}, {23879, 47965}, {23883, 48011}, {24562, 25099}, {24719, 28195}, {25666, 47880}, {28151, 47658}, {28165, 47661}, {28205, 47892}, {28209, 48034}, {28217, 48067}, {28220, 47939}, {28851, 48133}, {28882, 48132}, {28910, 48112}, {29204, 47131}, {29362, 48096}, {29370, 48248}, {30565, 45746}, {31147, 47916}, {31209, 47894}, {31287, 47886}, {47654, 47781}, {47657, 47775}, {47672, 47873}, {47675, 47792}, {47692, 48172}, {47693, 48080}, {47703, 48078}, {47963, 48048}, {47975, 48171}, {48113, 48119}, {48114, 48138}

X(48271) = midpoint of X(i) and X(j) for these {i,j}: {4024, 48094}, {4382, 48130}, {4804, 48118}, {4810, 48140}, {4820, 48095}, {4838, 47926}, {17494, 47665}, {20295, 47662}, {25259, 47660}, {47658, 47667}, {47659, 47666}, {47672, 48117}, {47693, 48080}, {47703, 48078}, {48112, 48141}, {48113, 48119}, {48114, 48138}, {48124, 48125}
X(48271) = reflection of X(i) in X(j) for these {i,j}: {2526, 4522}, {3004, 3239}, {3669, 8045}, {4106, 3700}, {4467, 4394}, {4976, 11068}, {16892, 4885}, {21124, 20317}, {43067, 6590}, {47652, 23813}, {47754, 47874}, {47950, 48049}, {47952, 48046}, {47958, 4940}, {47960, 3835}, {47961, 4806}, {47962, 4468}, {47963, 48048}, {47995, 14321}, {48027, 18004}, {48079, 4949}, {48125, 4500}
X(48271) = complement of X(47677)
X(48271) = crossdifference of every pair of points on line {5021, 17798}
X(48271) = barycentric product X(514)*X(17286)
X(48271) = barycentric quotient X(17286)/X(190)
X(48271) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3004, 3239, 47760}, {4120, 47958, 4940}, {4467, 47771, 4394}, {4885, 16892, 47754}, {4931, 48130, 4382}, {4944, 47960, 3835}, {16892, 47874, 4885}, {21212, 47879, 31250}, {47652, 47790, 23813}, {47659, 47772, 47666}, {47873, 48117, 47672}


X(48272) = X(1)X(6332)∩X(2)X(20517)

Barycentrics    (b - c)*(-(a*b^2) + b^3 - a*b*c + b^2*c - a*c^2 + b*c^2 + c^3) : :
X(48272) = X[47726] + 2 X[48039], 5 X[1698] - 4 X[14837], 3 X[3679] - 4 X[4163], 2 X[4142] - 3 X[47794], 2 X[4458] - 3 X[47795], 3 X[4776] - X[47709], 3 X[4809] - 4 X[31288], 2 X[21187] - 3 X[48228], 2 X[21188] - 3 X[47806], 2 X[21192] - 3 X[47828], 3 X[25055] - 4 X[45683]

X(48272) lies on these lines: {1, 6332}, {2, 20517}, {190, 1110}, {514, 4088}, {522, 3465}, {523, 4992}, {525, 1734}, {661, 29021}, {784, 4122}, {826, 1491}, {830, 48077}, {900, 48111}, {918, 4905}, {1577, 4522}, {1698, 14837}, {2254, 23875}, {2340, 8714}, {3239, 21185}, {3261, 19594}, {3679, 4163}, {3762, 3810}, {3777, 29354}, {3801, 21260}, {3835, 47712}, {4041, 23876}, {4063, 48062}, {4083, 4808}, {4091, 6763}, {4129, 47708}, {4142, 47794}, {4391, 23887}, {4397, 23580}, {4458, 47795}, {4467, 29294}, {4468, 47970}, {4490, 29312}, {4560, 29062}, {4705, 29017}, {4707, 17072}, {4730, 29284}, {4770, 29256}, {4776, 47709}, {4777, 48099}, {4791, 21118}, {4802, 48092}, {4809, 31288}, {4983, 29144}, {7927, 48123}, {7950, 48059}, {8678, 47682}, {14208, 17901}, {16892, 29358}, {17494, 29190}, {17496, 29212}, {17899, 23684}, {20295, 29158}, {20516, 29637}, {21124, 29318}, {21173, 23874}, {21187, 48228}, {21188, 47806}, {21192, 47828}, {21302, 29304}, {23687, 23782}, {23789, 47676}, {23879, 47975}, {24719, 29098}, {25055, 45683}, {28481, 47890}, {29047, 47700}, {29142, 47959}, {29146, 48030}, {29164, 47701}, {29166, 48005}, {29168, 48024}, {29186, 47687}, {29204, 48100}, {47666, 47718}, {47679, 48010}, {47727, 48136}, {47938, 48051}, {47942, 48046}, {47958, 48052}, {47972, 48058}, {47977, 48055}, {48116, 48130}

X(48272) = midpoint of X(i) and X(j) for these {i,j}: {47666, 47718}, {47698, 47719}, {47700, 48131}, {47726, 47948}, {48116, 48130}, {48118, 48122}
X(48272) = reflection of X(i) in X(j) for these {i,j}: {1, 6332}, {1577, 4522}, {3801, 21260}, {4063, 48062}, {4707, 17072}, {16892, 48066}, {21118, 4791}, {21124, 48012}, {21185, 3239}, {47676, 23789}, {47679, 48010}, {47701, 48054}, {47708, 4129}, {47712, 3835}, {47727, 48136}, {47938, 48051}, {47942, 48046}, {47948, 48039}, {47958, 48052}, {47959, 48047}, {47970, 4468}, {47972, 48058}, {47977, 48055}
X(48272) = anticomplement of X(20517)
X(48272) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {7087, 149}, {7096, 150}, {7357, 21293}, {40145, 4440}
X(48272) = X(32862)-Ceva conjugate of X(21252)
X(48272) = X(21252)-cross conjugate of X(32862)
X(48272) = X(i)-Dao conjugate of X(j) for these (i, j): (16757, 21178), (21252, 31)
X(48272) = crosspoint of X(190) and X(561)
X(48272) = crosssum of X(560) and X(649)
X(48272) = trilinear pole of line {21252, 21339}
X(48272) = crossdifference of every pair of points on line {2260, 4275}
X(48272) = barycentric product X(i)*X(j) for these {i,j}: {100, 21429}, {190, 21252}, {514, 32862}, {668, 21339}, {1978, 23646}, {4033, 18181}
X(48272) = barycentric quotient X(i)/X(j) for these {i,j}: {18181, 1019}, {21252, 514}, {21339, 513}, {21429, 693}, {22432, 1459}, {23228, 9247}, {23646, 649}, {32862, 190}


X(48273) = X(1)X(814)∩X(512)X(693)

Barycentrics    (b - c)*(-(a^2*b) - a^2*c + a*b*c + b^2*c + b*c^2) : :
X(48273) = X[2530] - 3 X[30592], 2 X[650] - 3 X[47839], 3 X[1635] - 4 X[31288], X[4041] - 3 X[4728], 3 X[4728] - 2 X[21260], 2 X[4147] - 3 X[14431], X[4380] - 3 X[47820], X[4498] - 3 X[47832], 2 X[4770] - 3 X[47814], 3 X[4776] - 2 X[48005], 2 X[4782] - 3 X[47818], X[4784] - 3 X[47889], 4 X[4885] - 3 X[47837], 2 X[4913] - 3 X[47888], 6 X[4928] - 5 X[31251], 2 X[9508] - 3 X[47795], 2 X[14838] - 3 X[47841], X[17494] - 3 X[47840], 2 X[21192] - 3 X[48227], 3 X[21297] - X[21301], 5 X[26985] - 3 X[47836], 3 X[31147] - X[47912], 3 X[36848] - 2 X[48018], X[47707] - 3 X[47790], 3 X[47813] - X[47935], 3 X[47822] - 2 X[48003]

X(48273) lies on these lines: {1, 814}, {512, 693}, {513, 4170}, {514, 4010}, {522, 2530}, {523, 4992}, {525, 23770}, {650, 47839}, {659, 29302}, {663, 4382}, {667, 812}, {784, 4804}, {788, 18081}, {826, 47691}, {830, 24719}, {834, 30591}, {891, 4391}, {900, 4905}, {1019, 29328}, {1491, 4151}, {1577, 4083}, {1635, 31288}, {1734, 3837}, {2084, 17458}, {2254, 23815}, {2517, 4139}, {2533, 4823}, {2787, 4449}, {3261, 4155}, {3309, 48089}, {3700, 29288}, {3762, 29226}, {3777, 8714}, {3801, 23876}, {3835, 4705}, {3900, 23813}, {4040, 29362}, {4041, 4728}, {4063, 4874}, {4106, 8678}, {4122, 29047}, {4129, 4490}, {4147, 14431}, {4367, 4810}, {4369, 4834}, {4378, 6002}, {4380, 47820}, {4498, 47832}, {4507, 18154}, {4522, 4808}, {4707, 29284}, {4730, 17072}, {4762, 48099}, {4770, 47814}, {4775, 29051}, {4776, 48005}, {4777, 14288}, {4782, 47818}, {4784, 47889}, {4801, 6372}, {4802, 48093}, {4806, 47959}, {4811, 6363}, {4822, 47672}, {4824, 48054}, {4879, 29066}, {4885, 47837}, {4913, 47888}, {4922, 29344}, {4928, 31251}, {4940, 47956}, {4961, 48064}, {4977, 48081}, {4990, 6084}, {6004, 46403}, {6005, 21146}, {6367, 45746}, {6371, 7650}, {6373, 23794}, {7265, 47716}, {7654, 28116}, {7927, 47690}, {7950, 47692}, {9313, 48084}, {9508, 47795}, {14838, 47841}, {17166, 20295}, {17494, 47840}, {21192, 48227}, {21297, 21301}, {23882, 48136}, {25259, 29354}, {26985, 47836}, {29017, 47712}, {29025, 47682}, {29074, 47727}, {29082, 47680}, {29144, 47715}, {29146, 47713}, {29150, 48144}, {29166, 47709}, {29168, 47719}, {29174, 47726}, {29182, 47729}, {29184, 47684}, {29204, 47717}, {29208, 47711}, {29252, 47676}, {29312, 47708}, {29332, 47725}, {29336, 47728}, {29366, 47724}, {31147, 47912}, {36848, 48018}, {47666, 48053}, {47707, 47790}, {47813, 47935}, {47822, 48003}, {47975, 48059}, {48121, 48142}

X(48273) = midpoint of X(i) and X(j) for these {i,j}: {663, 4382}, {4170, 4978}, {4367, 4810}, {4801, 48080}, {4804, 48131}, {4822, 47672}, {7265, 47716}, {17166, 20295}, {25259, 47720}, {48120, 48123}, {48121, 48142}
X(48273) = reflection of X(i) in X(j) for these {i,j}: {1577, 48090}, {1734, 3837}, {2254, 23815}, {2533, 4823}, {4041, 21260}, {4063, 4874}, {4490, 4129}, {4705, 3835}, {4730, 17072}, {4808, 4522}, {4824, 48054}, {4834, 4369}, {14349, 4992}, {47666, 48053}, {47946, 48045}, {47949, 48043}, {47956, 4940}, {47959, 4806}, {47975, 48059}
X(48273) = crossdifference of every pair of points on line {1185, 4275}
X(48273) = barycentric product X(514)*X(32860)
X(48273) = barycentric quotient X(32860)/X(190)
X(48273) = {X(4041),X(4728)}-harmonic conjugate of X(21260)


X(48274) = X(325)X(523)∩X(514)X(3700)

Barycentrics    (b - c)*(a*b + b^2 + a*c + 4*b*c + c^2) : :
X(48274) = 4 X[693] - 3 X[4927], 5 X[693] - 3 X[44435], 3 X[693] - X[45746], 3 X[693] + X[47655], 5 X[693] - X[47657], 2 X[3004] - 3 X[4927], 5 X[3004] - 6 X[44435], 3 X[3004] - 2 X[45746], 3 X[3004] + 2 X[47655], X[3004] + 2 X[47656], 5 X[3004] - 2 X[47657], 5 X[4927] - 4 X[44435], 9 X[4927] - 4 X[45746], 9 X[4927] + 4 X[47655], 3 X[4927] + 4 X[47656], 15 X[4927] - 4 X[47657], 9 X[44435] - 5 X[45746], 9 X[44435] + 5 X[47655], 3 X[44435] + 5 X[47656], 3 X[44435] - X[47657], X[45746] + 3 X[47656], 5 X[45746] - 3 X[47657], X[47655] - 3 X[47656], 5 X[47655] + 3 X[47657], 5 X[47656] + X[47657], 4 X[4500] - X[48046], 2 X[650] - 3 X[47788], 2 X[676] - 3 X[47834], 3 X[1638] - 2 X[21196], 3 X[1639] - 2 X[48000], 4 X[2487] - 3 X[27486], 4 X[2490] - 3 X[31150], 4 X[2527] - 3 X[47776], 2 X[4025] - 3 X[47891], 3 X[4120] - X[47917], 3 X[4379] - 2 X[17069], X[4380] - 3 X[47791], 2 X[4394] - 3 X[47789], 3 X[4453] - X[17161], X[4467] - 3 X[47780], X[4608] + 3 X[21297], 3 X[4728] - X[4988], 3 X[4728] + X[47670], 2 X[4765] - 3 X[47761], 3 X[4776] - X[47667], 3 X[4786] - 4 X[7653], 3 X[4789] - X[17494], 2 X[17494] - 3 X[47884], 4 X[4885] - 3 X[47784], 2 X[45745] - 3 X[47784], 2 X[4913] - 3 X[48232], 3 X[4931] - X[48082], 3 X[4944] - X[47920], X[26824] + 3 X[47792], X[47660] - 3 X[47792], 3 X[6545] - X[47673], 2 X[11068] - 3 X[47881], 2 X[14321] + X[47674], 2 X[14321] - 3 X[47790], X[47666] - 3 X[47790], X[47674] + 3 X[47790], 6 X[14425] - 5 X[26777], 3 X[21116] - X[47930], 4 X[25666] - 3 X[47876], 5 X[26985] - 3 X[47782], 5 X[30835] - 3 X[47878], 4 X[31287] - 3 X[47883], X[47652] - 3 X[47869], X[47659] + 3 X[47869], X[47653] - 3 X[47871], X[47658] + 3 X[47871], X[47654] - 3 X[48156], X[47664] - 3 X[47771], X[47668] - 3 X[47781], 3 X[47767] - 2 X[48008], 3 X[47873] - X[48094], 3 X[47874] - X[47926]

X(48274) lies on these lines: {2, 47661}, {325, 523}, {514, 3700}, {522, 4897}, {650, 25084}, {661, 47671}, {676, 47834}, {824, 21104}, {900, 7192}, {918, 4024}, {1638, 21196}, {1639, 48000}, {2487, 27486}, {2490, 31150}, {2527, 47776}, {3239, 47962}, {3676, 28161}, {3835, 4841}, {4025, 4777}, {4077, 23599}, {4120, 47917}, {4369, 4976}, {4379, 17069}, {4380, 47791}, {4394, 47789}, {4411, 17894}, {4453, 17161}, {4467, 28183}, {4522, 28147}, {4608, 18004}, {4728, 4988}, {4762, 6590}, {4765, 47761}, {4776, 47667}, {4786, 7653}, {4789, 17494}, {4802, 23813}, {4804, 47703}, {4820, 28846}, {4838, 16892}, {4885, 45745}, {4913, 48232}, {4926, 48013}, {4931, 48082}, {4944, 47920}, {4949, 48034}, {4977, 20295}, {4978, 47678}, {6009, 48101}, {6084, 26824}, {6362, 47719}, {6545, 47673}, {10015, 23801}, {11068, 47881}, {14321, 47666}, {14425, 26777}, {17166, 29278}, {18199, 46383}, {21116, 47930}, {21183, 28165}, {24560, 25996}, {24622, 29808}, {25008, 25923}, {25259, 47675}, {25666, 47876}, {26248, 26275}, {26277, 48231}, {26732, 48144}, {26985, 47782}, {28169, 47754}, {28195, 47981}, {28209, 48079}, {28217, 48107}, {28220, 47978}, {28902, 44449}, {30181, 43932}, {30804, 47707}, {30835, 47878}, {31287, 47883}, {45677, 46915}, {47650, 47662}, {47652, 47659}, {47653, 47658}, {47654, 48156}, {47664, 47771}, {47665, 47676}, {47668, 47781}, {47680, 47681}, {47767, 48008}, {47873, 48094}, {47874, 47926}, {47998, 48090}

X(48274) = midpoint of X(i) and X(j) for these {i,j}: {661, 47671}, {693, 47656}, {4024, 47672}, {4804, 47703}, {4820, 48133}, {4838, 16892}, {4978, 47678}, {4988, 47670}, {25259, 47675}, {26824, 47660}, {45746, 47655}, {47650, 47662}, {47652, 47659}, {47653, 47658}, {47665, 47676}, {47666, 47674}, {47680, 47681}
X(48274) = reflection of X(i) in X(j) for these {i,j}: {3004, 693}, {3700, 4500}, {4841, 3835}, {4897, 43067}, {4976, 4369}, {45745, 4885}, {46915, 45677}, {47666, 14321}, {47884, 4789}, {47890, 6590}, {47962, 3239}, {47988, 4106}, {47995, 23813}, {47998, 48090}, {48034, 4949}, {48046, 3700}
X(48274) = complement of X(47661)
X(48274) = X(32018)-Ceva conjugate of X(1086)
X(48274) = X(44307)-Dao conjugate of X(4427)
X(48274) = crosspoint of X(693) and X(4608)
X(48274) = crosssum of X(692) and X(35327)
X(48274) = barycentric product X(i)*X(j) for these {i,j}: {75, 47918}, {514, 4967}, {693, 44307}, {1900, 15413}, {4662, 24002}
X(48274) = barycentric quotient X(i)/X(j) for these {i,j}: {1900, 1783}, {4662, 644}, {4967, 190}, {42437, 4115}, {44307, 100}, {47918, 1}
X(48274) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 3004, 4927}, {693, 47655, 45746}, {693, 47657, 44435}, {4728, 47670, 4988}, {4885, 45745, 47784}, {26824, 47792, 47660}, {45746, 47656, 47655}, {47658, 47871, 47653}, {47659, 47869, 47652}, {47666, 47790, 14321}, {47674, 47790, 47666}


X(48275) = X(513)X(4024)∩X(514)X(661)

Barycentrics    (b - c)*(a^2 + a*b + b^2 + a*c + 2*b*c + c^2) : :
X(48275) = 3 X[4024] - 2 X[4820], 3 X[661] - 4 X[3239], 13 X[661] - 16 X[14350], 5 X[661] - 6 X[47765], 2 X[661] - 3 X[47874], 2 X[3239] - 3 X[6590], 13 X[3239] - 12 X[14350], 10 X[3239] - 9 X[47765], 8 X[3239] - 9 X[47874], 2 X[3835] - 3 X[4789], 3 X[4728] - 2 X[47995], 13 X[6590] - 8 X[14350], 5 X[6590] - 3 X[47765], 4 X[6590] - 3 X[47874], 40 X[14350] - 39 X[47765], 32 X[14350] - 39 X[47874], 3 X[30565] - 2 X[47996], 4 X[47765] - 5 X[47874], 7 X[649] - 6 X[4773], 3 X[649] - 2 X[4976], 9 X[4773] - 7 X[4976], 4 X[650] - 3 X[47878], 2 X[4988] - 3 X[47878], 2 X[47656] + X[48104], 2 X[47659] + X[47971], 3 X[1635] - 2 X[45745], 3 X[1635] - X[47669], 4 X[2490] - 3 X[47876], 2 X[3004] - 3 X[4379], 2 X[3700] - 3 X[47873], X[4813] - 3 X[47873], 2 X[3776] - 3 X[47780], X[47653] - 3 X[47780], 2 X[4025] - 3 X[31148], 3 X[31148] - X[47673], 3 X[4120] - 2 X[48026], 2 X[4369] - 3 X[47791], 4 X[4369] - 3 X[47886], X[45746] - 3 X[47791], 2 X[45746] - 3 X[47886], 3 X[4453] - X[47654], 2 X[4932] + X[47658], 2 X[4500] - 3 X[47792], 4 X[4500] - X[47937], X[20295] - 3 X[47792], 6 X[47792] - X[47937], 2 X[4765] - 3 X[47768], 3 X[4931] - X[48019], 2 X[4818] - 3 X[47824], 2 X[4841] - 3 X[4893], 3 X[6545] - 2 X[47960], 3 X[6546] - 2 X[47962], X[14779] - 5 X[26777], X[17161] - 3 X[47763], 2 X[21196] - 3 X[47762], X[47657] - 3 X[47762], 5 X[24924] - 6 X[47789], 4 X[25666] - 3 X[47781], 5 X[27013] - 3 X[46915], 5 X[30835] - 6 X[47788], 3 X[31147] - 2 X[47988], 3 X[31150] - X[47668], 7 X[31207] - 6 X[47784], 4 X[31286] - 3 X[47782], X[31290] - 3 X[47870], 4 X[43061] - 3 X[47883], X[47667] - 3 X[47771], 3 X[47771] - 2 X[48000], X[47670] + 2 X[48060], 3 X[47769] - 2 X[47991], 3 X[47790] - 2 X[48049], 3 X[47809] - 2 X[48010], 3 X[47812] - 2 X[48007], 3 X[47832] - 2 X[47998], 2 X[47999] - 3 X[48184], 2 X[48002] - 3 X[48185], 2 X[48017] - 3 X[48252]

X(48275) lies on these lines: {513, 4024}, {514, 661}, {522, 4838}, {523, 649}, {650, 4802}, {812, 47656}, {824, 7192}, {918, 48141}, {1635, 4458}, {2490, 47876}, {2523, 30600}, {2786, 47665}, {3004, 4379}, {3064, 21127}, {3700, 4813}, {3716, 47699}, {3776, 47653}, {4010, 47938}, {4025, 31148}, {4106, 23731}, {4120, 28195}, {4369, 45746}, {4374, 20909}, {4380, 47655}, {4394, 28151}, {4435, 29208}, {4453, 47654}, {4467, 4932}, {4500, 20295}, {4502, 22044}, {4522, 47945}, {4608, 4817}, {4762, 47671}, {4765, 28155}, {4777, 4790}, {4778, 4931}, {4818, 47824}, {4834, 6367}, {4841, 4893}, {4958, 28225}, {4960, 23875}, {4984, 28165}, {5029, 32193}, {6084, 48138}, {6545, 47960}, {6546, 47962}, {6588, 21102}, {6591, 21108}, {7199, 20952}, {7662, 47701}, {8631, 17166}, {8714, 24089}, {14300, 42462}, {14321, 28213}, {14779, 26777}, {16892, 28894}, {17161, 47763}, {17418, 47135}, {17458, 42664}, {18154, 20949}, {21104, 47923}, {21146, 47973}, {21196, 47657}, {23729, 47907}, {23770, 47924}, {23813, 47950}, {23876, 47681}, {24924, 47789}, {25259, 28840}, {25666, 47781}, {26824, 28882}, {27013, 46915}, {28179, 47767}, {28191, 47766}, {28199, 47881}, {28846, 48147}, {28863, 47676}, {28878, 48112}, {29013, 47678}, {30520, 48133}, {30835, 47788}, {31147, 47988}, {31150, 47668}, {31207, 47784}, {31286, 47782}, {31290, 47870}, {43061, 47883}, {46385, 47124}, {47123, 47702}, {47661, 48008}, {47663, 47674}, {47667, 47771}, {47670, 47932}, {47690, 48077}, {47694, 47972}, {47696, 48105}, {47769, 47991}, {47790, 48049}, {47809, 48010}, {47812, 48007}, {47832, 47998}, {47890, 47926}, {47903, 48038}, {47904, 48040}, {47908, 48046}, {47909, 48047}, {47910, 48048}, {47927, 48055}, {47928, 48056}, {47933, 48061}, {47934, 48062}, {47943, 48089}, {47944, 48090}, {47968, 48098}, {47999, 48184}, {48002, 48185}, {48017, 48252}

X(48275) = midpoint of X(i) and X(j) for these {i,j}: {4380, 47655}, {4467, 47658}, {4608, 17494}, {4838, 4979}, {7192, 47659}, {47662, 47675}, {47663, 47674}, {47665, 48107}, {47670, 47932}, {47671, 48101}
X(48275) = reflection of X(i) in X(j) for these {i,j}: {661, 6590}, {4467, 4932}, {4502, 22044}, {4813, 3700}, {4988, 650}, {16892, 43067}, {20295, 4500}, {23731, 4106}, {45746, 4369}, {47653, 3776}, {47657, 21196}, {47661, 48008}, {47667, 48000}, {47669, 45745}, {47673, 4025}, {47699, 3716}, {47701, 7662}, {47702, 47123}, {47704, 48134}, {47886, 47791}, {47903, 48038}, {47904, 48040}, {47907, 23729}, {47908, 48046}, {47909, 48047}, {47910, 48048}, {47917, 4468}, {47923, 21104}, {47924, 23770}, {47926, 47890}, {47927, 48055}, {47928, 48056}, {47932, 48060}, {47933, 48061}, {47934, 48062}, {47937, 20295}, {47938, 4010}, {47943, 48089}, {47944, 48090}, {47945, 4522}, {47950, 23813}, {47958, 693}, {47968, 48098}, {47971, 7192}, {47972, 47694}, {47973, 21146}, {48076, 25259}, {48077, 47690}, {48094, 47660}, {48105, 47696}
X(48275) = crossdifference of every pair of points on line {31, 35}
X(48275) = barycentric product X(i)*X(j) for these {i,j}: {92, 2523}, {514, 17303}, {522, 10404}, {523, 25526}, {661, 30599}, {693, 5311}, {30600, 30690}
X(48275) = barycentric quotient X(i)/X(j) for these {i,j}: {2523, 63}, {5311, 100}, {10404, 664}, {17303, 190}, {25526, 99}, {30599, 799}, {30600, 3219}
X(48275) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 4988, 47878}, {661, 6590, 47874}, {1635, 47669, 45745}, {4369, 45746, 47886}, {4813, 47873, 3700}, {20295, 47792, 4500}, {31148, 47673, 4025}, {45746, 47791, 4369}, {47653, 47780, 3776}, {47657, 47762, 21196}, {47667, 47771, 48000}


X(48276) = X(241)X(514)∩X(513)X(3700)

Barycentrics    (b - c)*(2*a^2 + a*b + b^2 + a*c + 2*b*c + c^2) : :
X(48276) = 7 X[650] - 8 X[31182], 3 X[650] - 4 X[43061], 2 X[650] - 3 X[47767], 4 X[650] - 3 X[47876], 3 X[1638] - 2 X[3004], 3 X[1638] - 4 X[4369], 9 X[1638] - 8 X[21212], 3 X[3004] - 4 X[21212], 2 X[3776] - 3 X[47891], 3 X[4369] - 2 X[21212], 7 X[4841] - 16 X[31182], 3 X[4841] - 8 X[43061], X[4841] - 3 X[47767], 2 X[4841] - 3 X[47876], 4 X[7658] - 3 X[47880], 6 X[31182] - 7 X[43061], 16 X[31182] - 21 X[47767], 32 X[31182] - 21 X[47876], 4 X[31286] - 3 X[47784], 8 X[43061] - 9 X[47767], 16 X[43061] - 9 X[47876], 3 X[47884] - 2 X[48000], 7 X[3700] - 4 X[4949], 2 X[4949] - 7 X[6590], 4 X[649] - 3 X[4773], 3 X[4773] - 2 X[4976], 2 X[661] - 3 X[1639], 3 X[47812] - X[47943], 2 X[676] - 3 X[47813], X[47701] - 3 X[47813], X[693] - 3 X[47791], X[23729] - 6 X[47791], 2 X[1491] - 3 X[48232], 3 X[1635] - 4 X[2527], 3 X[1635] - X[4988], 4 X[2527] - X[4988], 4 X[2487] - 3 X[47886], 4 X[2490] - 3 X[4893], 4 X[2516] - 3 X[47883], 4 X[2529] - X[45745], 4 X[2529] - 3 X[47768], 2 X[4394] - 3 X[47768], X[45745] - 3 X[47768], 2 X[3239] - 3 X[47881], 3 X[47881] - X[48026], 4 X[3798] - 3 X[45669], 2 X[3835] - 3 X[47788], 3 X[47788] - X[47988], 3 X[4120] - X[48019], 3 X[4379] - X[47958], 3 X[4453] - X[47653], X[4467] - 3 X[47763], X[47659] + 3 X[47763], 4 X[4521] - 3 X[47777], X[4608] + 3 X[47776], X[47661] - 3 X[47776], 3 X[4728] - X[23731], 3 X[4750] - X[47673], 3 X[4789] - X[20295], X[4813] - 3 X[47874], 2 X[14321] - 3 X[47874], 4 X[4874] - 3 X[48179], 2 X[47998] - 3 X[48179], 4 X[4885] - 3 X[47756], 2 X[4885] - 3 X[47789], 3 X[47756] - 2 X[47995], 3 X[47789] - X[47995], 2 X[4925] - 3 X[48252], 2 X[4940] - 3 X[47787], 3 X[47787] - X[47981], 3 X[6545] - X[47916], 3 X[6546] - X[47917], 4 X[7653] - 3 X[47758], X[16892] - 3 X[31148], 2 X[17069] - 3 X[47762], X[45746] - 3 X[47762], X[26853] + 3 X[47792], 5 X[27013] - 3 X[47782], 3 X[27486] - X[47657], 2 X[47999] - 3 X[48178], 3 X[30565] - X[31290], 3 X[31147] - X[47937], 3 X[31150] - X[47667], 5 X[31209] - 3 X[47781], 4 X[31287] - 3 X[47783], X[44449] - 3 X[47870], 3 X[45320] - X[47950], X[47652] - 3 X[47780], X[47654] - 3 X[47894], X[47666] - 3 X[47771], X[47677] - 3 X[47755], X[47698] - 3 X[48236], X[47699] - 3 X[47804], 3 X[47769] - X[47939], 3 X[47770] - X[47952], 3 X[47786] - X[47978], 3 X[47790] - X[48079], 3 X[47807] - 2 X[48030], 3 X[47808] - X[47940], 3 X[47809] - X[47945], 3 X[47832] - X[47938], 3 X[47833] - X[47944], 3 X[47885] - X[47928], 3 X[47887] - X[47924], X[47953] - 3 X[48219], X[47968] - 3 X[48253], X[47969] - 3 X[48250], 2 X[48028] - 3 X[48166]

X(48276) lies on these lines: {241, 514}, {513, 3700}, {522, 4790}, {523, 649}, {661, 1639}, {676, 47701}, {693, 23729}, {824, 4897}, {900, 4024}, {918, 7192}, {1491, 48232}, {1635, 2527}, {2487, 47886}, {2490, 4893}, {2516, 28199}, {2529, 4394}, {2533, 21721}, {2977, 4824}, {3064, 14300}, {3239, 4778}, {3667, 4820}, {3766, 18154}, {3798, 45669}, {3835, 28859}, {4025, 28894}, {4120, 48019}, {4374, 20952}, {4379, 47958}, {4380, 47656}, {4382, 48104}, {4406, 21438}, {4435, 17166}, {4453, 47653}, {4467, 47659}, {4500, 4785}, {4521, 28229}, {4581, 21786}, {4608, 47661}, {4728, 23731}, {4750, 47673}, {4762, 48060}, {4765, 28147}, {4789, 20295}, {4813, 14321}, {4822, 4990}, {4838, 28183}, {4874, 47998}, {4885, 47756}, {4925, 48252}, {4931, 39386}, {4940, 47787}, {4944, 28225}, {4984, 28187}, {6008, 48067}, {6009, 26824}, {6084, 47672}, {6545, 47916}, {6546, 47917}, {6587, 46385}, {7252, 47844}, {7653, 47758}, {7927, 8659}, {9404, 21390}, {14303, 46389}, {16892, 31148}, {17069, 45746}, {17161, 47658}, {20949, 24622}, {25259, 48107}, {26853, 47792}, {27013, 47782}, {27486, 47657}, {28179, 47669}, {28195, 47766}, {28217, 47873}, {28220, 47765}, {28481, 47715}, {28840, 48046}, {28867, 48071}, {28878, 48087}, {28898, 48013}, {28902, 48082}, {30565, 31290}, {31095, 47773}, {31147, 47937}, {31150, 47667}, {31209, 47781}, {31287, 47783}, {44449, 47870}, {45320, 47950}, {47652, 47780}, {47654, 47894}, {47662, 47676}, {47663, 47675}, {47664, 47674}, {47666, 47771}, {47671, 47932}, {47677, 47755}, {47696, 48108}, {47698, 48236}, {47699, 47804}, {47704, 48146}, {47769, 47939}, {47770, 47952}, {47786, 47978}, {47790, 48079}, {47807, 48030}, {47808, 47940}, {47809, 47945}, {47832, 47938}, {47833, 47944}, {47885, 47928}, {47887, 47924}, {47953, 48219}, {47968, 48253}, {47969, 48250}, {48028, 48166}, {48094, 48141}

X(48276) = midpoint of X(i) and X(j) for these {i,j}: {4024, 4979}, {4380, 47656}, {4382, 48104}, {4467, 47659}, {4608, 47661}, {7192, 47660}, {17161, 47658}, {25259, 48107}, {47662, 47676}, {47663, 47675}, {47664, 47674}, {47671, 47932}, {47672, 48101}, {47696, 48108}, {47704, 48146}, {48082, 48147}, {48094, 48141}, {48095, 48133}, {48102, 48148}, {48106, 48142}
X(48276) = reflection of X(i) in X(j) for these {i,j}: {3004, 4369}, {3700, 6590}, {4394, 2529}, {4813, 14321}, {4822, 4990}, {4824, 2977}, {4841, 650}, {4897, 4932}, {4976, 649}, {21104, 43067}, {23729, 693}, {45745, 4394}, {45746, 17069}, {47701, 676}, {47756, 47789}, {47876, 47767}, {47960, 3676}, {47962, 11068}, {47981, 4940}, {47988, 3835}, {47989, 3837}, {47995, 4885}, {47998, 4874}, {48026, 3239}
X(48276) = X(1224)-complementary conjugate of X(21252)
X(48276) = X(3674)-Ceva conjugate of X(4459)
X(48276) = X(9)-isoconjugate of X(29279)
X(48276) = X(478)-Dao conjugate of X(29279)
X(48276) = crosspoint of X(514) and X(4581)
X(48276) = crossdifference of every pair of points on line {55, 386}
X(48276) = barycentric product X(i)*X(j) for these {i,j}: {7, 29278}, {513, 4968}, {514, 5750}, {522, 4298}, {693, 3745}
X(48276) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 29279}, {3745, 100}, {4298, 664}, {4968, 668}, {5750, 190}, {29278, 8}
X(48276) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 4976, 4773}, {650, 4841, 47876}, {2529, 4394, 47768}, {3004, 4369, 1638}, {4608, 47776, 47661}, {4813, 47874, 14321}, {4841, 47767, 650}, {4874, 47998, 48179}, {4885, 47995, 47756}, {45745, 47768, 4394}, {45746, 47762, 17069}, {47659, 47763, 4467}, {47701, 47813, 676}, {47787, 47981, 4940}, {47788, 47988, 3835}, {47789, 47995, 4885}, {47881, 48026, 3239}


X(48277) = X(2)X(4500)∩X(37)X(650)

Barycentrics    (b - c)*(-a^2 + a*b + b^2 + a*c + 2*b*c + c^2) : :
X(48277) = 10 X[650] - 9 X[6544], 4 X[650] - 3 X[47874], 5 X[4024] - 9 X[6544], 2 X[4024] - 3 X[47874], 6 X[6544] - 5 X[47874], 2 X[47657] + X[48104], 2 X[47661] + X[47971], 5 X[661] - 3 X[4958], 7 X[661] - 6 X[47764], 2 X[661] - 3 X[47878], 3 X[4958] - 10 X[45745], 7 X[4958] - 10 X[47764], 2 X[4958] - 5 X[47878], 7 X[45745] - 3 X[47764], 4 X[45745] - 3 X[47878], 4 X[47764] - 7 X[47878], 5 X[649] - 6 X[4773], 3 X[4773] - 5 X[4976], 5 X[693] - 6 X[21204], 3 X[693] - 4 X[21212], 2 X[693] - 3 X[47886], 5 X[21196] - 3 X[21204], 3 X[21196] - 2 X[21212], 4 X[21196] - 3 X[47886], 9 X[21204] - 10 X[21212], 4 X[21204] - 5 X[47886], 8 X[21212] - 9 X[47886], 2 X[17161] + X[48094], 3 X[1635] - 4 X[4765], 3 X[1635] - X[4838], 3 X[1635] - 2 X[6590], 9 X[1635] - 8 X[43061], 4 X[4765] - X[4838], 3 X[4765] - 2 X[43061], 3 X[4838] - 8 X[43061], 3 X[6590] - 4 X[43061], 4 X[13246] - 3 X[48237], 4 X[2516] - 3 X[47881], 4 X[3239] - 3 X[4931], 2 X[3239] - 3 X[47883], 2 X[3700] - 3 X[4893], 2 X[3776] - 3 X[47894], X[26824] - 3 X[47894], 4 X[3798] - 3 X[31148], 4 X[3798] - X[47670], 3 X[31148] - X[47670], 2 X[3835] - 3 X[47782], 3 X[4120] - 2 X[4820], 2 X[4369] - 3 X[27486], 3 X[27486] - X[47656], 3 X[4379] - 4 X[17069], 2 X[4522] - 3 X[47825], X[4608] - 3 X[47763], 3 X[4750] - 2 X[43067], 3 X[4750] - X[47671], 3 X[4789] - 4 X[31286], 2 X[4790] - 3 X[4984], 3 X[6545] - 2 X[48125], 2 X[14321] - 3 X[47876], 2 X[18004] - 3 X[48176], X[20295] - 3 X[46915], 2 X[23813] - 3 X[47880], 5 X[24924] - 6 X[47785], 4 X[25666] - 3 X[47790], 5 X[26777] - 3 X[47870], 5 X[26985] - 6 X[47882], 5 X[27013] - 3 X[47792], 7 X[27115] - 6 X[47879], 5 X[30835] - 6 X[47784], 3 X[31150] - X[47665], 7 X[31207] - 6 X[47788], X[47655] - 3 X[47762], X[47659] - 3 X[47776], X[47674] - 3 X[47755], 3 X[47781] - 2 X[48049], 3 X[47887] - 2 X[48120]

X(48277) lies on these lines: {2, 4500}, {37, 650}, {75, 29771}, {513, 4988}, {514, 4380}, {522, 661}, {523, 649}, {667, 6367}, {693, 4359}, {784, 21832}, {812, 45746}, {824, 17147}, {900, 4813}, {918, 47926}, {1635, 4765}, {2516, 47881}, {2786, 47666}, {2978, 4155}, {3004, 4382}, {3239, 4931}, {3250, 4151}, {3555, 14077}, {3667, 47940}, {3700, 4893}, {3776, 26824}, {3798, 31148}, {3835, 47782}, {4025, 47672}, {4120, 4820}, {4369, 27486}, {4379, 17069}, {4394, 28165}, {4435, 29017}, {4522, 47825}, {4608, 47763}, {4750, 43067}, {4762, 16892}, {4785, 47937}, {4789, 31286}, {4790, 4802}, {4818, 46403}, {4824, 29078}, {4830, 47696}, {4897, 48141}, {4913, 47690}, {4926, 48026}, {5029, 14610}, {6008, 23731}, {6084, 47923}, {6545, 48125}, {7950, 8659}, {8632, 23879}, {14321, 47876}, {18004, 48176}, {19804, 29808}, {20295, 46915}, {20963, 22383}, {21124, 23882}, {23813, 47880}, {23876, 47683}, {24924, 47785}, {25259, 48000}, {25666, 47790}, {26777, 47870}, {26853, 28859}, {26985, 47882}, {27013, 47792}, {27115, 47879}, {28187, 47873}, {28840, 47667}, {28846, 47917}, {28863, 47663}, {28867, 31290}, {28882, 47653}, {28894, 48101}, {28898, 47962}, {29013, 47679}, {29232, 47912}, {29328, 47938}, {29362, 47973}, {30835, 47784}, {31150, 47665}, {31207, 47788}, {44449, 47996}, {47655, 47762}, {47659, 47776}, {47660, 48008}, {47674, 47755}, {47687, 48017}, {47781, 48049}, {47887, 48120}, {47995, 48114}, {48015, 48115}

X(48277) = midpoint of X(i) and X(j) for these {i,j}: {4380, 47657}, {4467, 47661}, {4979, 47669}, {17161, 17494}, {47664, 47677}, {47668, 48107}, {47673, 47932}
X(48277) = reflection of X(i) in X(j) for these {i,j}: {649, 4976}, {661, 45745}, {693, 21196}, {4024, 650}, {4382, 3004}, {4813, 4841}, {4838, 6590}, {4931, 47883}, {6590, 4765}, {25259, 48000}, {26824, 3776}, {44449, 47996}, {46403, 4818}, {47656, 4369}, {47660, 48008}, {47671, 43067}, {47672, 4025}, {47687, 48017}, {47690, 4913}, {47696, 4830}, {47958, 45746}, {47971, 4467}, {48076, 47666}, {48077, 47975}, {48082, 47962}, {48094, 17494}, {48104, 4380}, {48114, 47995}, {48115, 48015}, {48141, 4897}, {48147, 48013}
X(48277) = anticomplement of X(4500)
X(48277) = crossdifference of every pair of points on line {36, 386}
X(48277) = barycentric product X(i)*X(j) for these {i,j}: {514, 17275}, {522, 11375}
X(48277) = barycentric quotient X(i)/X(j) for these {i,j}: {11375, 664}, {17275, 190}
X(48277) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 4024, 47874}, {661, 45745, 47878}, {693, 21196, 47886}, {1635, 4838, 6590}, {4750, 47671, 43067}, {4765, 6590, 1635}, {26824, 47894, 3776}, {27486, 47656, 4369}


X(48278) = X(2)X(4142)∩X(513)X(4064)

Barycentrics    (a - b - c)*(b - c)*(b^2 + c^2) : :
X(48278) = 2 X[47726] + X[47943], 2 X[663] - 3 X[14432], 4 X[6332] - 3 X[14432], X[21302] - 3 X[48169], 4 X[4522] - X[21132], 2 X[3776] - 3 X[47819], 2 X[4458] - 3 X[47796], 3 X[6545] - 4 X[23815], 2 X[10015] - 3 X[21052], 3 X[14430] - 2 X[21120], 2 X[14837] - 3 X[47806], 4 X[17072] - 3 X[30574], 2 X[17072] - 3 X[47808], 2 X[20517] - 3 X[47795], 2 X[21185] - 3 X[47832], 2 X[21187] - 3 X[48246]

X(48278) lies on these lines: {2, 4142}, {190, 9323}, {513, 4064}, {514, 4088}, {522, 663}, {523, 14288}, {525, 2254}, {661, 29142}, {693, 23877}, {764, 29354}, {784, 3250}, {826, 2474}, {830, 47682}, {891, 4808}, {900, 48150}, {905, 37592}, {918, 48151}, {1491, 21124}, {1577, 21118}, {1734, 4424}, {2785, 21302}, {3057, 3900}, {3159, 7265}, {3700, 6362}, {3701, 3810}, {3776, 47819}, {3801, 3837}, {3835, 47708}, {3904, 3907}, {3910, 4041}, {4036, 21102}, {4086, 21119}, {4458, 47796}, {4468, 47929}, {4486, 9237}, {4498, 48062}, {4568, 35333}, {4705, 29312}, {4777, 48136}, {4814, 44448}, {4905, 23875}, {4977, 48116}, {4978, 47704}, {4983, 29168}, {6372, 48082}, {6545, 23815}, {8045, 47694}, {8632, 29106}, {8678, 48077}, {10015, 21052}, {14349, 29021}, {14430, 21120}, {14837, 47806}, {17072, 30574}, {17496, 29037}, {18788, 28487}, {20295, 29118}, {20517, 47795}, {21121, 44316}, {21185, 47832}, {21187, 48246}, {23874, 43924}, {24719, 29025}, {28468, 48187}, {28470, 47728}, {28478, 48069}, {29051, 47687}, {29116, 48050}, {29144, 48123}, {29146, 48100}, {29166, 48059}, {29204, 48137}, {29288, 47700}, {29318, 48066}, {47906, 48046}, {47918, 48047}, {47936, 48055}, {47938, 48091}, {47958, 48092}, {47972, 48099}

X(48278) = midpoint of X(47726) and X(48086)
X(48278) = reflection of X(i) in X(j) for these {i,j}: {663, 6332}, {3801, 3837}, {4391, 4522}, {4498, 48062}, {4814, 44448}, {16892, 2530}, {21102, 4036}, {21118, 1577}, {21119, 4086}, {21121, 44316}, {21124, 1491}, {21132, 4391}, {30574, 47808}, {47694, 8045}, {47701, 14349}, {47703, 47715}, {47704, 4978}, {47708, 3835}, {47906, 48046}, {47912, 48039}, {47918, 48047}, {47929, 4468}, {47936, 48055}, {47938, 48091}, {47943, 48086}, {47958, 48092}, {47972, 48099}
X(48278) = anticomplement of X(4142)
X(48278) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {3497, 150}, {7224, 21293}, {34250, 149}
X(48278) = X(i)-Ceva conjugate of X(j) for these (i,j): {4553, 15523}, {4568, 33299}, {28660, 21044}, {48084, 16892}
X(48278) = X(i)-isoconjugate of X(j) for these (i,j): {57, 4628}, {59, 18108}, {65, 827}, {82, 109}, {83, 1415}, {108, 1176}, {163, 18097}, {226, 34072}, {251, 651}, {664, 46289}, {1400, 4599}, {1402, 4577}, {1409, 42396}, {1428, 36081}, {1441, 4630}, {2149, 10566}, {4554, 46288}, {4565, 18098}, {10547, 18026}, {32085, 36059}, {32674, 34055}
X(48278) = X(i)-Dao conjugate of X(j) for these (i, j): (11, 82), (39, 664), (115, 18097), (141, 109), (339, 349), (650, 10566), (1146, 83), (3124, 1400), (5452, 4628), (6615, 18108), (6741, 18082), (15449, 226), (20620, 32085), (35072, 34055), (38983, 1176), (38991, 251), (39025, 46289), (40582, 4599), (40585, 651), (40602, 827), (40605, 4577), (40624, 3112), (40626, 1799), (40938, 653)
X(48278) = crosspoint of X(i) and X(j) for these (i,j): {190, 7018}, {522, 35519}, {1930, 4568}
X(48278) = crosssum of X(649) and X(7122)
X(48278) = crossdifference of every pair of points on line {251, 1400}
X(48278) = barycentric product X(i)*X(j) for these {i,j}: {8, 16892}, {9, 48084}, {11, 4568}, {29, 2525}, {38, 4391}, {39, 35519}, {141, 522}, {284, 23285}, {312, 2530}, {314, 8061}, {333, 826}, {345, 21108}, {427, 6332}, {514, 3703}, {521, 20883}, {650, 1930}, {652, 1235}, {663, 8024}, {693, 33299}, {2084, 40072}, {3005, 28660}, {3064, 3933}, {3239, 3665}, {3261, 3688}, {3596, 21123}, {3700, 16887}, {3917, 46110}, {3954, 18155}, {4041, 16703}, {4086, 16696}, {4553, 4858}, {4560, 15523}, {4576, 21044}, {8611, 16747}, {14432, 31125}, {17442, 35518}, {23978, 46153}, {25128, 42551}, {34387, 46148}, {40495, 40972}
X(48278) = barycentric quotient X(i)/X(j) for these {i,j}: {11, 10566}, {21, 4599}, {29, 42396}, {38, 651}, {39, 109}, {55, 4628}, {141, 664}, {284, 827}, {314, 4593}, {333, 4577}, {427, 653}, {521, 34055}, {522, 83}, {523, 18097}, {650, 82}, {652, 1176}, {663, 251}, {826, 226}, {1235, 46404}, {1401, 1461}, {1843, 32674}, {1930, 4554}, {1964, 1415}, {2084, 1402}, {2170, 18108}, {2194, 34072}, {2525, 307}, {2530, 57}, {3005, 1400}, {3063, 46289}, {3064, 32085}, {3665, 658}, {3688, 101}, {3700, 18082}, {3703, 190}, {3917, 1813}, {3954, 4551}, {4020, 36059}, {4041, 18098}, {4140, 18099}, {4391, 3112}, {4459, 18111}, {4553, 4564}, {4568, 4998}, {4576, 4620}, {4876, 36081}, {6332, 1799}, {6362, 18087}, {8024, 4572}, {8041, 46153}, {8061, 65}, {10566, 41284}, {15523, 4552}, {16696, 1414}, {16703, 4625}, {16720, 6649}, {16887, 4573}, {16892, 7}, {17187, 4565}, {17442, 108}, {18191, 39179}, {20775, 32660}, {20883, 18026}, {21035, 4559}, {21108, 278}, {21123, 56}, {21126, 7198}, {23285, 349}, {23885, 7247}, {27376, 36127}, {28660, 689}, {33299, 100}, {35519, 308}, {40072, 37204}, {40972, 692}, {42337, 18086}, {42462, 18101}, {46110, 46104}, {46148, 59}, {46149, 36146}, {46152, 7128}, {46153, 1262}, {46387, 1428}, {48084, 85}
X(48278) = {X(663),X(6332)}-harmonic conjugate of X(14432)


X(48279) = X(513)X(4801)∩X(514)X(4010)

Barycentrics    (b - c)*(-(a^2*b) - a^2*c + 2*a*b*c + b^2*c + b*c^2) : :
X(48279) = 2 X[650] - 3 X[47841], 2 X[4382] + X[4922], 2 X[1734] - 3 X[36848], 4 X[23815] - 3 X[36848], 2 X[4369] - 3 X[47889], X[4705] - 3 X[30592], 3 X[4728] - 2 X[21051], X[4729] - 3 X[47812], 2 X[4770] - 3 X[47816], 3 X[4776] - 2 X[47967], 2 X[4782] - 3 X[47820], 3 X[4809] - 4 X[34958], 4 X[4885] - 3 X[47835], 2 X[4913] - 3 X[47893], 2 X[9508] - 3 X[47796], 2 X[17072] - 3 X[48184], X[21302] - 3 X[48170], 3 X[47822] - 2 X[47965], 3 X[47839] - 2 X[48003]

X(48279) lies on these lines: {1, 29070}, {512, 4978}, {513, 4801}, {514, 4010}, {522, 3777}, {523, 14288}, {649, 4839}, {650, 47841}, {661, 4992}, {663, 29362}, {667, 29302}, {693, 2533}, {764, 8714}, {812, 4367}, {814, 4382}, {826, 47716}, {891, 1577}, {900, 48151}, {1734, 23815}, {2530, 4151}, {3566, 21104}, {3801, 3910}, {3835, 4490}, {3837, 4041}, {3900, 48089}, {3907, 21343}, {4122, 29288}, {4170, 6372}, {4369, 47889}, {4378, 29013}, {4391, 19582}, {4498, 4874}, {4705, 30592}, {4728, 21051}, {4729, 47812}, {4762, 48136}, {4770, 47816}, {4775, 29186}, {4776, 47967}, {4777, 48137}, {4782, 47820}, {4802, 48129}, {4806, 47918}, {4809, 34958}, {4810, 6002}, {4815, 6371}, {4822, 4977}, {4824, 14349}, {4879, 29051}, {4885, 47835}, {4913, 47893}, {4990, 48055}, {7199, 9400}, {7265, 29354}, {7662, 8712}, {7927, 47715}, {7950, 47717}, {8045, 48103}, {8678, 24719}, {9508, 47796}, {17072, 48184}, {21302, 48170}, {23813, 30804}, {29017, 47691}, {29086, 47727}, {29094, 47680}, {29098, 47682}, {29144, 47719}, {29146, 47692}, {29154, 47725}, {29166, 47713}, {29198, 48080}, {29200, 47676}, {29208, 47690}, {29244, 47728}, {29246, 48119}, {29274, 47729}, {29298, 47724}, {29312, 47712}, {29328, 48144}, {47666, 48093}, {47822, 47965}, {47839, 48003}, {47975, 48100}

X(48279) = midpoint of X(4382) and X(4449)
X(48279) = reflection of X(i) in X(j) for these {i,j}: {661, 4992}, {1734, 23815}, {2533, 693}, {3801, 23770}, {4041, 3837}, {4391, 48090}, {4490, 3835}, {4498, 4874}, {4824, 14349}, {4922, 4449}, {21146, 4978}, {47666, 48093}, {47913, 48043}, {47918, 4806}, {47946, 4983}, {47975, 48100}, {48055, 4990}, {48103, 8045}
X(48279) = crosspoint of X(596) and X(668)
X(48279) = crosssum of X(595) and X(667)
X(48279) = crossdifference of every pair of points on line {1197, 4264}
X(48279) = {X(1734),X(23815)}-harmonic conjugate of X(36848)


X(48280) = X(86)X(4560)∩X(514)X(3700)

Barycentrics    (b - c)*(-(a^2*b) + b^3 - a^2*c + 4*a*b*c + 3*b^2*c + 3*b*c^2 + c^3) : :
X(48280) = 3 X[1639] - 2 X[47965], 2 X[4025] - 3 X[30724], 2 X[4063] - 3 X[47767], X[4462] - 3 X[47790], 2 X[4467] - 5 X[30722], 2 X[14837] - 3 X[45320], 2 X[17069] - 3 X[47796], 2 X[17496] - 3 X[30726], 2 X[20317] - 3 X[47787]

X(48280) lies on these lines: {86, 4560}, {514, 3700}, {522, 3669}, {523, 14288}, {525, 4978}, {693, 3910}, {900, 48144}, {905, 4976}, {918, 4801}, {1211, 1577}, {1639, 47965}, {2254, 4843}, {3239, 47921}, {3566, 21146}, {3649, 4804}, {3800, 47715}, {4025, 30724}, {4063, 47767}, {4378, 29232}, {4382, 29162}, {4449, 29278}, {4462, 47790}, {4467, 30722}, {4724, 4990}, {4762, 6332}, {4823, 10015}, {4841, 14349}, {4977, 48121}, {4992, 47998}, {6590, 8712}, {8045, 47890}, {14321, 47918}, {14837, 45320}, {17069, 47796}, {17496, 26732}, {20317, 47787}, {20954, 41299}, {23770, 29017}, {23880, 30725}, {28217, 48149}, {28473, 47724}, {28478, 43067}, {29284, 48098}

X(48280) = reflection of X(i) in X(j) for these {i,j}: {4724, 4990}, {4841, 14349}, {4976, 905}, {7178, 693}, {10015, 4823}, {21104, 4978}, {21120, 1577}, {47890, 8045}, {47918, 14321}, {47921, 3239}, {47998, 4992}
X(48280) = barycentric product X(693)*X(25917)
X(48280) = barycentric quotient X(25917)/X(100)

leftri

Points in a [X(1)X(514), X(1)X(523)] coordinate system: X(48281)-X(48307)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1,L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1: (b^2 + c^2 - a b - a c) α + (c^2 + a^2 - b c - b a) β + (a^2 + b^2 - c a - cb) γ = 0.

L2: (b^3 + c^3 - a^2 b - a^2 c) α (c^3 + a^3 - b^2 c - b^2 a) β (a^3 + b^3 - c^2 a - c^2 b) γ = 0.

The origin is given by (0,0) = X(1) = a : b : c.

Barycentrics u : v : w for a point U = (x,y) in this system are given by

u : v : w = (b - c) (a (a - b)(a - c) - x + (b + c)y) : : ,

where, as functions of a,b,c, the coordinate x is symmetric and homogeneous of degree 3, and y is symmetric and homogeneous of degree 2.

The appearance of {x,y}, k in the following table means that (x,y) = X(k):

{-2 (a^2 b+a b^2+a^2 c+b^2 c+a c^2+b c^2), -2 (a b+a c+b c), 21385
{-a b c, -((2 a b c)/(a+b+c))}, 1459
{-a^2 b-a b^2-a^2 c-b^2 c-a c^2-b c^2, -2 (a b+a c+b c)}, 17494
{-a^3-b^3-c^3, -a^2-b^2-c^2}, 47729
{-a^2 b-a b^2-a^2 c-b^2 c-a c^2-b c^2, -a^2-b^2-c^2}, 47695
{-a^2 b-a b^2-a^2 c-b^2 c-a c^2-b c^2, -a b-a c-b c}, 659
{-a^2 b-a b^2-a^2 c-b^2 c-a c^2-b c^2, 1/2 (-a b-a c-b c)}, 48248
{-a b c, 0}, 4449
{-a^3-b^3-c^3, 0}, 47728
{-a^2 b-a b^2-a^2 c-b^2 c-a c^2-b c^2, 0}, 47694
{-a^3-b^3-c^3, a^2+b^2+c^2}, 47684
{-a^2 b-a b^2-a^2 c-b^2 c-a c^2-b c^2, a^2+b^2+c^2}, 47660
{-a^2 b-a b^2-a^2 c-b^2 c-a c^2-b c^2, 2 (a^2+b^2+c^2)}, 47693
{1/2 (-a^2 b-a b^2-a^2 c-b^2 c-a c^2-b c^2), 1/2 (-a b-a c-b c)}, 1960
{0, -2 (a b+a c+b c)}, 47683
{0, -((2 a b c)/(a+b+c))}, 3737
{0, -a^2-b^2-c^2}, 47727
{0, -((a b c)/(a+b+c))}, 2605
{0, 0}, 1
{0, a^2+b^2+c^2}, 47682
{0, 2 (a^2+b^2+c^2)}, 47726
{a b c, -((2 a b c)/(a+b+c))}, 46385
{a^3+b^3+c^3, -2 (a b+a c+b c)}, 45746
{a^3+b^3+c^3, -a^2-b^2-c^2}, 47692
{a b c, 0}, 663
{a^3+b^3+c^3, 0}, 47691
{a^3+b^3+c^3, 1/2 (a^2+b^2+c^2)}, 23770
{a^3+b^3+c^3, a^2+b^2+c^2}, 693
{a^2 b+a b^2+a^2 c+b^2 c+a c^2+b c^2, a^2+b^2+c^2}, 3904
{a^2 b+a b^2+a^2 c+b^2 c+a c^2+b c^2, a b+a c+b c}, 21343
{a^3+b^3+c^3, 2 (a^2+b^2+c^2)}, 47690
{2 a b c, 0}, 4040
{2 (a^3+b^3+c^3), 0}, 47725
{2 (a^3+b^3+c^3), a^2+b^2+c^2}, 47680
{2 (a^3+b^3+c^3), 2 (a^2+b^2+c^2)}, 47724
{-2*a*b*c, (-2*a*b*c)/(a + b + c)}, 48281
{-2*a*b*c, 0}, 48282
{-(a*b*c), -((a*b*c)/(a + b + c))}, 48283
{(-(a^2*b) - a*b^2 - a^2*c - b^2*c - a*c^2 - b*c^2)/2, -(a*b) - a*c - b*c}, 48284
{(-a^3 - b^3 - c^3)/2, (-a^2 - b^2 - c^2)/2}, 48285
{(-(a^2*b) - a*b^2 - a^2*c - b^2*c - a*c^2 - b*c^2)/2, (-a^2 - b^2 - c^2)/2}, 48286
{-1/2*(a*b*c), 0}, 48287
{0, -(a*b) - a*c - b*c}, 48288
{0, (-(a*b) - a*c - b*c)/2}, 48289
{0, (a^2 + b^2 + c^2)/2}, 48290
{0, a*b + a*c + b*c}, 48291
{0, (a*b*c)/(a + b + c)}, 48292
{0, (2*a*b*c)/(a + b + c)}, 48293
{(a*b*c)/2, 0}, 48294
{(a^3 + b^3 + c^3)/2, (a^2 + b^2 + c^2)/2}, 48295
{(a^2*b + a*b^2 + a^2*c + b^2*c + a*c^2 + b*c^2)/2, (a*b + a*c + b*c)/2}, 48296
{a*b*c, -((a*b*c)/(a + b + c))}, 48297
{a^2*b + a*b^2 + a^2*c + b^2*c + a*c^2 + b*c^2, 0}, 48298
{a*b*c, (a^2 + b^2 + c^2)/2}, 48299
{a*b*c, a^2 + b^2 + c^2}, 48300
{a*b*c, a*b + a*c + b*c}, 48301
{a*b*c, (a*b*c)/(a + b + c)}, 48302
{a*b*c, (2*a*b*c)/(a + b + c)}, 48303
{a^2*b + a*b^2 + a^2*c + b^2*c + a*c^2 + b*c^2, 2*(a*b + a*c + b*c)}, 48304
{2*a*b*c, a*b + a*c + b*c}, 48305
{2*a*b*c, (a*b*c)/(a + b + c)}, 48306
{2*a*b*c, (2*a*b*c)/(a + b + c)}, 48307


X(48281) = X(1)X(513)∩X(523)X(21173)

Barycentrics    a*(b - c)*(a^3 - a*b^2 + a*b*c + b^2*c - a*c^2 + b*c^2) : :
X(48281) = 2 X[10] - 3 X[48246], 3 X[1459] - X[46385], 3 X[3737] - 2 X[46385], 3 X[3669] - X[7655], 2 X[7655] - 3 X[23800], 4 X[1125] - 3 X[48165], 5 X[1698] - 6 X[48230], 7 X[3624] - 6 X[48181], 2 X[4147] - 3 X[48228], 3 X[14413] - X[17420], X[20293] - 3 X[47796], 2 X[20316] - 3 X[47795}

X(48281) lies on these lines: {1, 513}, {6, 21390}, {9, 20980}, {10, 48246}, {34, 44426}, {42, 47824}, {43, 47823}, {77, 24002}, {86, 20949}, {242, 514}, {521, 3669}, {522, 4318}, {523, 21173}, {612, 44429}, {614, 47804}, {656, 3960}, {663, 4778}, {832, 3777}, {834, 1019}, {1021, 43060}, {1041, 34492}, {1100, 21007}, {1125, 48165}, {1449, 3063}, {1698, 48230}, {1743, 39521}, {2254, 35057}, {2530, 38469}, {2605, 4040}, {2999, 47761}, {3261, 17218}, {3624, 48181}, {3720, 47821}, {3733, 4063}, {3738, 4017}, {3762, 8062}, {3879, 23790}, {3920, 48164}, {3961, 36848}, {4025, 7203}, {4139, 21343}, {4147, 48228}, {4367, 6371}, {4448, 29820}, {4648, 40474}, {4724, 28229}, {4776, 5287}, {4905, 15313}, {5256, 47762}, {5268, 47802}, {5272, 47803}, {5293, 19947}, {6006, 42312}, {7191, 47805}, {7253, 21222}, {9001, 21189}, {9817, 44923}, {10436, 20906}, {14413, 17420}, {16569, 48216}, {17011, 47763}, {17019, 47759}, {17022, 47760}, {17418, 28147}, {18199, 23189}, {20293, 47796}, {20316, 47795}, {20981, 21389}, {21105, 37558}, {21119, 21180}, {21132, 21179}, {22379, 39210}, {23655, 24720}, {25502, 48197}, {26102, 47822}, {28195, 47970}, {37523, 43052}

X(48281) = midpoint of X(i) and X(j) for these {i,j}: {4449, 43924}, {7253, 21222}, {21103, 23752}
X(48281) = reflection of X(i) in X(j) for these {i,j}: {656, 3960}, {3737, 1459}, {3762, 8062}, {4040, 2605}, {4063, 3733}, {21119, 21180}, {21132, 21179}, {23800, 3669}
X(48281) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {39748, 33650}, {39964, 37781}
X(48281) = X(18026)-Ceva conjugate of X(57)
X(48281) = X(i)-isoconjugate of X(j) for these (i,j): {109, 44040}, {281, 40518}
X(48281) = X(i)-Dao conjugate of X(j) for these (i, j): (11, 44040), (1459, 521)
X(48281) = crosspoint of X(81) and X(664)
X(48281) = crosssum of X(i) and X(j) for these (i,j): {37, 663}, {650, 7069}
X(48281) = crossdifference of every pair of points on line {44, 71}
X(48281) = barycentric product X(i)*X(j) for these {i,j}: {1, 47796}, {57, 20293}, {404, 514}, {513, 32939}, {649, 44139}, {651, 44311}, {757, 21721}, {3261, 44085}, {18026, 39006}
X(48281) = barycentric quotient X(i)/X(j) for these {i,j}: {404, 190}, {603, 40518}, {650, 44040}, {20293, 312}, {21721, 1089}, {32939, 668}, {39006, 521}, {44085, 101}, {44139, 1978}, {44311, 4391}, {47796, 75}
X(48281) = {X(20980),X(21348)}-harmonic conjugate of X(9)


X(48282) = X(1)X(514)∩X(523)X(21173)

Barycentrics    a*(b - c)*(a^2 - a*b - a*c + 3*b*c) : :
X(48282) = 3 X[1] - 2 X[663], 5 X[1] - 2 X[4724], 7 X[1] - 4 X[4794], 7 X[1] - 2 X[47929], 3 X[1] - X[47970], 9 X[1] - 4 X[48065], 4 X[663] - 3 X[4040], X[663] - 3 X[4449], 5 X[663] - 3 X[4724], 7 X[663] - 6 X[4794], 7 X[663] - 3 X[47929], 3 X[663] - 2 X[48065], X[4040] - 4 X[4449], 5 X[4040] - 4 X[4724], 7 X[4040] - 8 X[4794], 7 X[4040] - 4 X[47929], 3 X[4040] - 2 X[47970], 9 X[4040] - 8 X[48065], 5 X[4449] - X[4724], 7 X[4449] - 2 X[4794], 7 X[4449] - X[47929], 6 X[4449] - X[47970], 9 X[4449] - 2 X[48065], 7 X[4724] - 10 X[4794], 7 X[4724] - 5 X[47929], 6 X[4724] - 5 X[47970], 9 X[4724] - 10 X[48065], 12 X[4794] - 7 X[47970], 9 X[4794] - 7 X[48065], 6 X[47929] - 7 X[47970], 9 X[47929] - 14 X[48065], 3 X[47970] - 4 X[48065], 2 X[10] - 3 X[47796], 3 X[1019] - 2 X[4834], 3 X[4378] - X[4834], 3 X[1022] - 2 X[3777], 4 X[1125] - 3 X[47793], 5 X[1698] - 4 X[4147], 5 X[1698] - 6 X[47795], 2 X[4147] - 3 X[47795], 7 X[3624] - 6 X[47794], X[3632] - 4 X[24720], 3 X[3679] - 4 X[17072], 3 X[47948] - 4 X[48052], 2 X[48052] - 3 X[48131], X[4705] - 3 X[14421], 2 X[4770] - 3 X[47893], 2 X[4807] - 3 X[47824], 3 X[14349] - 2 X[47956], 3 X[14413] - 2 X[14838], 3 X[25055] - 4 X[45667], 13 X[34595] - 12 X[48196}

X(48282) lies on these lines: {1, 514}, {10, 47796}, {35, 44408}, {42, 47780}, {43, 4379}, {200, 21183}, {269, 30181}, {512, 21343}, {519, 21302}, {523, 21173}, {612, 44435}, {614, 47771}, {667, 21385}, {693, 32927}, {830, 48116}, {891, 4063}, {1019, 4083}, {1022, 3777}, {1125, 47793}, {1459, 28147}, {1698, 4147}, {1734, 3669}, {2533, 3293}, {2605, 28175}, {2832, 48150}, {2999, 47789}, {3624, 47794}, {3632, 24720}, {3679, 17072}, {3720, 47775}, {3737, 4802}, {3875, 4406}, {3887, 48151}, {3900, 4905}, {3907, 4978}, {3920, 48156}, {3960, 4041}, {3961, 6545}, {3979, 21116}, {4151, 17496}, {4160, 47948}, {4382, 29344}, {4474, 4823}, {4546, 4915}, {4705, 14421}, {4770, 47893}, {4775, 29198}, {4801, 29066}, {4807, 47824}, {4810, 29176}, {4814, 48018}, {4853, 44448}, {4879, 6372}, {4893, 26102}, {4895, 23738}, {4922, 29070}, {5010, 39476}, {5256, 47791}, {5268, 47757}, {5272, 47766}, {5287, 47781}, {5312, 22090}, {6004, 23765}, {6546, 29820}, {7191, 47773}, {8678, 48086}, {8714, 21222}, {9029, 16496}, {14349, 47956}, {14413, 14838}, {16569, 47779}, {17022, 47783}, {17218, 20906}, {17418, 28155}, {20963, 21791}, {21104, 28473}, {21120, 34958}, {21146, 29298}, {23791, 25301}, {25055, 45667}, {25502, 47778}, {28161, 43924}, {28191, 46385}, {28225, 42312}, {29047, 47726}, {29116, 47717}, {29130, 47692}, {29142, 47727}, {29186, 47729}, {29192, 47719}, {29288, 47682}, {29304, 47676}, {29350, 48144}, {34595, 48196}, {47947, 48123}, {47959, 48136}

X(48282) = midpoint of X(4895) and X(23738)
X(48282) = reflection of X(i) in X(j) for these {i,j}: {1, 4449}, {1019, 4378}, {1734, 3669}, {4040, 1}, {4041, 3960}, {4063, 4367}, {4474, 4823}, {4814, 48018}, {21120, 34958}, {21302, 23789}, {21385, 667}, {47724, 4978}, {47725, 47716}, {47929, 4794}, {47947, 48123}, {47948, 48131}, {47959, 48136}, {47970, 663}
X(48282) = reflection of X(4040) in the Soddy line
X(48282) = crossdifference of every pair of points on line {672, 4271}
X(48282) = barycentric product X(1)*X(26985)
X(48282) = barycentric quotient X(26985)/X(75)
X(48282) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 47970, 663}, {663, 47970, 4040}, {4147, 47795, 1698}


X(48283) = X(1)X(513)∩X(523)X(1459)

Barycentrics    a*(b - c)*(a^3 - a*b^2 + b^2*c - a*c^2 + b*c^2) : :
X(48283) = X[8] - 3 X[48246], 2 X[10] - 3 X[48230], 3 X[1459] - X[17418], 3 X[4449] + X[17418], X[656] - 3 X[14413], 4 X[1125] - 3 X[48181], 5 X[3616] - 3 X[48165], 2 X[4147] - 3 X[48205], 3 X[11125] - X[21119], X[20293] - 3 X[48209], 2 X[20316] - 3 X[48207], 2 X[31946] - 3 X[47841}

X(48283) lies on these lines: {1, 513}, {6, 21348}, {8, 48246}, {9, 39521}, {10, 48230}, {34, 16228}, {37, 20980}, {42, 47823}, {43, 48216}, {86, 20906}, {514, 2605}, {521, 14353}, {523, 1459}, {612, 47802}, {614, 47803}, {650, 14399}, {656, 14413}, {663, 4977}, {667, 4694}, {834, 4367}, {900, 30726}, {1100, 3063}, {1125, 48181}, {1442, 24002}, {1449, 21390}, {1734, 8702}, {1735, 23224}, {1870, 44426}, {3050, 22383}, {3616, 48165}, {3669, 15313}, {3720, 47822}, {3733, 4083}, {3737, 4802}, {3837, 23655}, {3920, 44429}, {3938, 36848}, {3960, 35057}, {4040, 28195}, {4147, 48205}, {4411, 17218}, {4724, 28213}, {4776, 17019}, {4777, 21173}, {4794, 28229}, {5256, 47761}, {5287, 47760}, {6129, 9001}, {7191, 47804}, {7649, 21112}, {8674, 23800}, {11125, 21119}, {16884, 21007}, {17011, 47762}, {17018, 47824}, {17024, 47805}, {17394, 20949}, {17458, 20981}, {17478, 29324}, {18199, 25098}, {20293, 48209}, {20316, 48207}, {21102, 21105}, {21103, 21118}, {26102, 48197}, {28175, 46385}, {28217, 42312}, {29814, 47821}, {29815, 48164}, {29820, 45666}, {31946, 47841}, {37696, 44923}

X(48283) = midpoint of X(i) and X(j) for these {i,j}: {1459, 4449}, {21102, 21105}, {21103, 21118}
X(48283) = reflection of X(21112) in X(7649)
X(48283) = crossdifference of every pair of points on line {44, 573}
X(48283) = barycentric product X(i)*X(j) for these {i,j}: {1, 47795}, {513, 32933}, {514, 25440}
X(48283) = barycentric quotient X(i)/X(j) for these {i,j}: {25440, 190}, {32933, 668}, {47795, 75}


X(48284) = X(1)X(17494)∩X(523)X(1960)

Barycentrics    (b - c)*(-2*a^3 + a^2*b + a*b^2 + a^2*c + 2*a*b*c + b^2*c + a*c^2 + b*c^2) : :
X(48284) = X[8] - 5 X[26777], 3 X[31150] + X[47729], 3 X[1635] - X[4761], 5 X[1698] - 7 X[27115], X[2254] - 3 X[45671], 5 X[3616] - X[26824], 7 X[3624] - 5 X[26985], 4 X[3634] - 5 X[31209], 4 X[3634] - X[47721], 5 X[31209] - X[47721], 4 X[3636] + X[47664], X[3762] - 3 X[47811], 3 X[4828] - 5 X[40328], 4 X[4885] - 5 X[19862], 5 X[8656] - X[48142], 3 X[14419] - X[21146], 3 X[14838] - 2 X[25380], 7 X[15808] - 2 X[48125], 3 X[19883] - 2 X[45320], X[21385] - 3 X[48240], 3 X[25055] - X[47869], 3 X[30234] - X[43067], 3 X[44550] + X[47974], X[47680] - 3 X[47797], X[47723] - 3 X[47809], X[47725] - 3 X[48203}

X(48284) lies on these lines: {1, 17494}, {2, 47724}, {8, 26777}, {10, 650}, {513, 23795}, {514, 659}, {519, 31150}, {522, 4794}, {523, 1960}, {551, 4762}, {663, 4151}, {693, 1125}, {814, 4129}, {905, 23789}, {1635, 4761}, {1698, 27115}, {1938, 4084}, {2254, 45671}, {2978, 29350}, {3244, 14077}, {3616, 26824}, {3624, 26985}, {3634, 31209}, {3636, 47664}, {3762, 47811}, {3835, 29033}, {3887, 4913}, {3907, 48003}, {3993, 4777}, {4040, 4560}, {4160, 48000}, {4297, 8760}, {4314, 11934}, {4468, 29212}, {4806, 29340}, {4807, 29366}, {4828, 40328}, {4885, 19862}, {5592, 21196}, {6002, 48058}, {6332, 29190}, {6700, 27417}, {8656, 48142}, {9508, 29188}, {11263, 23806}, {14419, 21146}, {14838, 25380}, {15808, 48125}, {17496, 47970}, {18004, 29058}, {19858, 26049}, {19883, 45320}, {21051, 29182}, {21260, 29274}, {21385, 48240}, {21625, 30235}, {22037, 29078}, {23791, 27648}, {25055, 47869}, {28470, 48012}, {29013, 48099}, {29110, 48056}, {29132, 48006}, {29148, 48029}, {29178, 48043}, {29192, 48062}, {29302, 48136}, {30234, 43067}, {30968, 47778}, {31291, 47948}, {44550, 47974}, {47680, 47797}, {47683, 47694}, {47723, 47809}, {47725, 48203}

X(48284) = midpoint of X(i) and X(j) for these {i,j}: {1, 17494}, {4040, 4560}, {5592, 21196}, {17496, 47970}, {31291, 47948}, {47683, 47694}
X(48284) = reflection of X(i) in X(j) for these {i,j}: {10, 650}, {693, 1125}, {23789, 905}
X(48284) = complement of X(47724)
X(48284) = crossdifference of every pair of points on line {2276, 4286}


X(48285) = X(1)X(693)∩X(523)X(47491)

Barycentrics    (b - c)*(-3*a^3 + 3*a^2*b + 3*a^2*c - 2*a*b*c + b^2*c + b*c^2) : :
X(48285) = 3 X[1] - X[693], 7 X[1] - X[47721], 5 X[1] - X[47724], 7 X[693] - 3 X[47721], 5 X[693] - 3 X[47724], X[693] + 3 X[47729], 5 X[47721] - 7 X[47724], X[47721] + 7 X[47729], X[47724] + 5 X[47729], 3 X[8] - 7 X[27115], 3 X[10] - 4 X[31287], 3 X[145] + 5 X[26777], 3 X[551] - 2 X[4885], 3 X[663] - X[3762], 6 X[1125] - 5 X[31250], 3 X[3241] + X[17494], 3 X[3669] - 2 X[23796], 3 X[3679] - 5 X[31209], X[4814] - 3 X[45671], 5 X[26985] - 9 X[38314], X[47174] - 3 X[47472}

X(48285) lies on these lines: {1, 693}, {8, 27115}, {10, 31287}, {145, 26777}, {514, 47131}, {519, 650}, {523, 47491}, {551, 4885}, {663, 3762}, {993, 8641}, {1125, 31250}, {1938, 3874}, {3241, 17494}, {3244, 14077}, {3309, 23795}, {3669, 23796}, {3679, 31209}, {3814, 15283}, {3907, 4791}, {4160, 47996}, {4162, 8714}, {4369, 4844}, {4449, 29186}, {4504, 6005}, {4669, 44567}, {4775, 4922}, {4814, 45671}, {4879, 29013}, {5493, 8142}, {5882, 8760}, {6738, 30235}, {8674, 23809}, {10006, 15863}, {20517, 28473}, {26985, 38314}, {28834, 45700}, {29160, 47727}, {47174, 47472}

X(48285) = midpoint of X(i) and X(j) for these {i,j}: {1, 47729}, {4775, 4922}, {47727, 47728}
X(48285) = reflection of X(i) in X(j) for these {i,j}: {4669, 44567}, {5493, 8142}, {15863, 10006}


X(48286) = X(1)X(3904)∩X(523)X(1960)

Barycentrics    (b - c)*(-2*a^3 + 2*a^2*b - a*b^2 + b^3 + 2*a^2*c - 2*a*b*c - a*c^2 + c^3) : :
X(48286) = 3 X[1] - X[3904], X[3904] + 3 X[47695], 3 X[10] - 2 X[4528], 3 X[676] - X[4528], 2 X[3754] - 3 X[30691], 3 X[4543] - 7 X[21952], X[4730] - 3 X[4809], X[4768] - 3 X[11125], 3 X[10164] - 4 X[44819], X[21385] - 3 X[44433], X[47723] - 3 X[47834}

X(48286) lies on these lines: {1, 3904}, {10, 676}, {101, 26705}, {106, 2370}, {214, 2804}, {514, 47131}, {519, 10015}, {522, 3960}, {523, 1960}, {535, 42763}, {665, 4151}, {900, 21630}, {928, 3874}, {2799, 41187}, {3239, 6591}, {3244, 6366}, {3754, 30691}, {3800, 8659}, {3887, 4458}, {3900, 20517}, {4024, 14438}, {4162, 29304}, {4297, 9521}, {4543, 21952}, {4669, 44566}, {4707, 4895}, {4730, 4809}, {4768, 11125}, {4820, 29062}, {5029, 9131}, {5168, 9979}, {7662, 29192}, {9033, 41192}, {10164, 44819}, {14422, 28183}, {18613, 23184}, {21343, 23888}, {21385, 44433}, {24009, 24036}, {29066, 47123}, {42662, 44427}, {47694, 47727}, {47716, 48150}, {47720, 48111}, {47723, 47834}

X(48286) = midpoint of X(i) and X(j) for these {i,j}: {1, 47695}, {4707, 4895}, {47694, 47727}, {47716, 48150}, {47720, 48111}
X(48286) = reflection of X(i) in X(j) for these {i,j}: {10, 676}, {4669, 44566}
X(48286) = X(32665)-anticomplementary conjugate of X(17732)
X(48286) = crosspoint of X(903) and X(1897)
X(48286) = crosssum of X(902) and X(1459)
X(48286) = crossdifference of every pair of points on line {1473, 4286}


X(48287) = X(1)X(514)∩X(523)X(17022)

Barycentrics    a*(b - c)*(2*a^2 - 2*a*b - 2*a*c + 3*b*c) : :
X(48287) = 3 X[1] - X[663], 5 X[1] - X[4040], 7 X[1] - X[4724], 4 X[1] - X[4794], 11 X[1] - X[47929], 9 X[1] - X[47970], 6 X[1] - X[48065], 5 X[663] - 3 X[4040], X[663] + 3 X[4449], 7 X[663] - 3 X[4724], 4 X[663] - 3 X[4794], 11 X[663] - 3 X[47929], 3 X[663] - X[47970], X[4040] + 5 X[4449], 7 X[4040] - 5 X[4724], 4 X[4040] - 5 X[4794], 11 X[4040] - 5 X[47929], 9 X[4040] - 5 X[47970], 6 X[4040] - 5 X[48065], 7 X[4449] + X[4724], 4 X[4449] + X[4794], 11 X[4449] + X[47929], 9 X[4449] + X[47970], 6 X[4449] + X[48065], 4 X[4724] - 7 X[4794], 11 X[4724] - 7 X[47929], 9 X[4724] - 7 X[47970], 6 X[4724] - 7 X[48065], 11 X[4794] - 4 X[47929], 9 X[4794] - 4 X[47970], 3 X[4794] - 2 X[48065], X[21118] + 3 X[30573], 9 X[47929] - 11 X[47970], 6 X[47929] - 11 X[48065], 2 X[47970] - 3 X[48065], X[8] - 3 X[47795], 2 X[10] - 3 X[48218], X[145] + 3 X[47796], X[17072] - 3 X[45667], 4 X[1125] - 3 X[48196], 2 X[4147] - 3 X[48196], X[1734] - 3 X[14413], 3 X[3241] + X[21302], 5 X[3616] - 3 X[47794], 7 X[3622] - 3 X[47793], 2 X[3635] + X[24720], X[3777] - 3 X[14421], 2 X[47956] - 3 X[48054], X[47956] - 3 X[48136], 3 X[4367] - X[4834], 2 X[4834] - 3 X[48064], 3 X[8643] - X[21385], 6 X[9269] - X[48066], 3 X[23057] + X[48151}

X(48287) lies on these lines: {1, 514}, {8, 47795}, {10, 48218}, {34, 39532}, {42, 47779}, {55, 39476}, {145, 47796}, {519, 17072}, {612, 44432}, {667, 21343}, {891, 4401}, {1125, 4147}, {1442, 30181}, {1459, 28161}, {1734, 14413}, {1960, 29226}, {2605, 28147}, {3241, 21302}, {3295, 44408}, {3616, 47794}, {3622, 47793}, {3635, 24720}, {3669, 3887}, {3720, 47778}, {3737, 28155}, {3777, 14421}, {3872, 4546}, {3900, 3960}, {3907, 4823}, {3920, 47757}, {3938, 21204}, {3957, 21183}, {4083, 48011}, {4129, 17478}, {4160, 47956}, {4162, 42325}, {4367, 4834}, {4378, 4879}, {4379, 17018}, {4406, 17393}, {4504, 29013}, {4861, 44448}, {4864, 37998}, {4893, 29814}, {4895, 4905}, {4922, 29344}, {4962, 43924}, {4978, 47729}, {6161, 23765}, {6366, 34958}, {7191, 47766}, {8643, 21385}, {8678, 48052}, {9269, 48066}, {14077, 14838}, {17011, 47789}, {17019, 47783}, {17024, 47771}, {21831, 22037}, {23057, 48151}, {24216, 31286}, {29164, 47727}, {29260, 47682}, {29268, 48090}, {29815, 44435}, {37696, 44928}, {47684, 47717}

X(48287) = midpoint of X(i) and X(j) for these {i,j}: {1, 4449}, {667, 21343}, {4378, 4879}, {4895, 4905}, {4978, 47729}, {6161, 23765}, {47684, 47717}, {47716, 47728}
X(48287) = reflection of X(i) in X(j) for these {i,j}: {4147, 1125}, {48018, 3960}, {48054, 48136}, {48064, 4367}, {48065, 663}, {48075, 3669}
X(48287) = crossdifference of every pair of points on line {672, 5036}
X(48287) = barycentric product X(75)*X(39521)
X(48287) = barycentric quotient X(39521)/X(1)
X(48287) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {663, 48065, 4794}, {1125, 4147, 48196}


X(48288) = X(1)X(523)∩X(8)X(4770)

Barycentrics    (b - c)*(-a^3 + a^2*b + a*b^2 + a^2*c + a*b*c + b^2*c + a*c^2 + b*c^2) : :
X(48288) = X[8] - 3 X[47825], 2 X[4770] - 3 X[47825], 2 X[10] - 3 X[47827], X[4774] - 3 X[47827], 4 X[1125] - 3 X[47833], 2 X[1577] - 3 X[47839], 5 X[1698] - 6 X[47829], 2 X[2533] - 3 X[47837], 4 X[14838] - 3 X[47837], 5 X[3616] - 3 X[47834], 7 X[3624] - 6 X[48206], X[4024] - 3 X[14432], 2 X[4369] - 3 X[14419], X[4474] - 3 X[4893], X[4761] - 3 X[45671], 2 X[9508] - 3 X[45671], 2 X[4791] - 3 X[47822], 2 X[4823] - 3 X[47841], 3 X[14413] - X[47672], 3 X[14414] - 2 X[15584], 3 X[14431] - 4 X[25666], 2 X[17072] - 3 X[47888], 4 X[19947] - 3 X[47812], 3 X[44429] - X[47721], 3 X[44435] - X[47722], 3 X[44550] - X[48108}

X(48288) lies on these lines: {1, 523}, {8, 4770}, {10, 4774}, {213, 3287}, {239, 47782}, {274, 4374}, {512, 4560}, {514, 659}, {519, 4948}, {522, 4775}, {661, 2787}, {663, 784}, {690, 4467}, {814, 14349}, {891, 17494}, {1125, 47833}, {1491, 29066}, {1577, 47839}, {1698, 47829}, {1734, 29366}, {1960, 47694}, {2254, 29188}, {2530, 29051}, {2533, 14838}, {2785, 21196}, {3004, 29240}, {3023, 20982}, {3227, 35173}, {3616, 47834}, {3624, 48206}, {3709, 5283}, {3777, 29186}, {3837, 47724}, {3904, 29312}, {3907, 4705}, {3960, 21146}, {4024, 14432}, {4041, 29298}, {4083, 39548}, {4088, 29110}, {4151, 4879}, {4160, 4824}, {4369, 14419}, {4384, 47784}, {4393, 46915}, {4474, 4893}, {4608, 8599}, {4702, 4777}, {4730, 4913}, {4761, 9508}, {4789, 16826}, {4791, 47822}, {4822, 29150}, {4823, 47841}, {4844, 48225}, {4905, 29246}, {4983, 6002}, {6372, 17496}, {7199, 31997}, {8633, 45746}, {14413, 47672}, {14414, 15584}, {14422, 47780}, {14431, 25666}, {16823, 47797}, {16828, 48205}, {16830, 47809}, {16831, 47788}, {16892, 29102}, {17072, 47888}, {19853, 48204}, {19947, 47812}, {20295, 29340}, {21124, 29094}, {21222, 47969}, {21301, 29182}, {23880, 48099}, {23882, 48136}, {24561, 47719}, {24719, 29033}, {25512, 48207}, {27419, 47707}, {28475, 48027}, {28602, 36531}, {29013, 48123}, {29029, 47701}, {29070, 48131}, {29126, 47998}, {29128, 47702}, {29148, 48024}, {29152, 48093}, {29170, 48081}, {29176, 48053}, {29236, 48030}, {29238, 48129}, {29268, 48005}, {29274, 48100}, {29324, 47959}, {29344, 48054}, {29570, 47792}, {39586, 47807}, {44429, 47721}, {44435, 47722}, {44550, 48108}, {47729, 47975}

X(48288) = midpoint of X(i) and X(j) for these {i,j}: {1, 47683}, {4824, 4922}, {21222, 47969}, {45746, 47728}, {47729, 47975}
X(48288) = reflection of X(i) in X(j) for these {i,j}: {8, 4770}, {2533, 14838}, {4730, 4913}, {4761, 9508}, {4774, 10}, {21146, 3960}, {21301, 48059}, {39547, 2605}, {47694, 1960}, {47724, 3837}, {47780, 14422}
X(48288) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {751, 3448}, {30650, 21221}
X(48288) = crossdifference of every pair of points on line {2245, 2276}
X(48288) = barycentric product X(514)*X(32917)
X(48288) = barycentric quotient X(32917)/X(190)
X(48288) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 47825, 4770}, {2533, 14838, 47837}, {4761, 45671, 9508}, {4774, 47827, 10}


X(48289) = X(1)X(523)∩X(2)X(4774)

Barycentrics    (b - c)*(-2*a^3 + 2*a^2*b + a*b^2 + 2*a^2*c + b^2*c + a*c^2 + b*c^2) : :
X(48289) = 3 X[1] + X[47683], 3 X[30580] - X[47682], X[8] - 3 X[47827], 2 X[10] - 3 X[47829], X[145] + 3 X[47825], 3 X[4367] - X[7192], 2 X[4106] - 3 X[4992], X[4106] - 3 X[48136], 4 X[1125] - 3 X[48206], 3 X[2533] - 5 X[24924], 5 X[3616] - 3 X[47833], 7 X[3622] - 3 X[47834], 3 X[21051] - 4 X[25666], X[4122] - 3 X[14432], 3 X[4449] + X[47926], X[4474] - 3 X[47822], 3 X[4504] + X[47991], X[4730] - 3 X[45671], X[4761] - 3 X[14419], 2 X[4791] - 3 X[48183], X[4814] - 3 X[48225], 3 X[14413] - X[21146], X[21302] - 3 X[47893], 3 X[25569] - X[47694], X[43052] - 3 X[48211], X[47721] - 3 X[48184], X[48079] - 3 X[48123}

X(48289) lies on these lines: {1, 523}, {2, 4774}, {8, 47827}, {10, 47829}, {145, 47825}, {239, 47784}, {514, 1960}, {519, 4770}, {661, 4922}, {669, 4367}, {814, 4106}, {900, 4775}, {905, 29366}, {1107, 3709}, {1125, 48206}, {1491, 47729}, {2176, 3287}, {2533, 24924}, {2787, 4806}, {3241, 4948}, {3616, 47833}, {3622, 47834}, {3669, 29246}, {3835, 29236}, {3837, 29066}, {3907, 21051}, {3960, 29188}, {4083, 48008}, {4122, 14432}, {4129, 29268}, {4160, 48002}, {4374, 31997}, {4378, 4977}, {4393, 47782}, {4449, 47926}, {4474, 47822}, {4481, 25423}, {4504, 47991}, {4508, 47756}, {4560, 4879}, {4730, 45671}, {4761, 14419}, {4789, 29570}, {4791, 48183}, {4814, 48225}, {4844, 48229}, {6332, 29074}, {14413, 21146}, {14838, 29298}, {16823, 47799}, {16826, 47788}, {16830, 47807}, {17494, 21343}, {19853, 48205}, {21302, 47893}, {21901, 45902}, {25569, 47694}, {28470, 48100}, {28602, 36480}, {29324, 48099}, {43052, 48211}, {47721, 48184}, {48079, 48123}

X(48289) = midpoint of X(i) and X(j) for these {i,j}: {661, 4922}, {1491, 47729}, {3241, 4948}, {4560, 4879}, {17494, 21343}
X(48289) = reflection of X(i) in X(j) for these {i,j}: {4992, 48136}, {48248, 1960}
X(48289) = complement of X(4774)
X(48289) = X(i)-complementary conjugate of X(j) for these (i,j): {256, 15614}, {2163, 40608}, {3903, 21251}, {29055, 17057}
X(48289) = crosspoint of X(99) and X(996)
X(48289) = crosssum of X(512) and X(995)
X(48289) = crossdifference of every pair of points on line {2245, 21838}


X(48290) = X(1)X(523)∩X(8)X(47809)

Barycentrics    (b - c)*(2*a^3 - a^2*b + b^3 - a^2*c + 2*a*b*c + b^2*c + b*c^2 + c^3) : :
X(48290) = 3 X[1] + X[47726], 3 X[1] - X[47727], 3 X[47682] - X[47726], 3 X[47682] + X[47727], X[8] - 3 X[47809], 2 X[10] - 3 X[47807], X[145] + 3 X[48208], X[47961] - 3 X[48136], 3 X[4367] - 2 X[39545], X[661] - 3 X[14432], 3 X[663] - X[47972], 3 X[693] - X[47722], X[47722] + 3 X[47728], 4 X[1125] - 3 X[47799], 5 X[3616] - 3 X[47797], 7 X[3622] - 3 X[48203], 3 X[4449] + X[48118], X[4474] - 3 X[47874], 3 X[6332] - X[48039], 3 X[14413] - X[16892], 3 X[14419] - 2 X[17069], 5 X[24924] - 3 X[30574], X[43052] - 3 X[48220], X[47943] - 3 X[48131}

X(48290) lies on these lines: {1, 523}, {8, 47809}, {10, 47807}, {145, 48208}, {304, 4374}, {514, 3716}, {525, 4367}, {661, 14432}, {663, 29142}, {667, 3910}, {690, 4897}, {693, 29240}, {891, 47890}, {918, 4378}, {1019, 3566}, {1125, 47799}, {1499, 4784}, {1960, 29312}, {2533, 28473}, {2785, 4369}, {2787, 3700}, {3616, 47797}, {3622, 48203}, {3800, 4879}, {3801, 34958}, {3904, 47694}, {3907, 8045}, {3912, 47788}, {4010, 29126}, {4122, 4922}, {4160, 48047}, {4449, 29288}, {4474, 47874}, {4504, 29037}, {4789, 17316}, {4874, 10015}, {6332, 8678}, {7178, 29094}, {7199, 18156}, {14077, 48062}, {14413, 16892}, {14419, 17069}, {17023, 47784}, {19784, 48205}, {19836, 48207}, {21104, 29102}, {21343, 48103}, {23888, 48247}, {24924, 30574}, {26626, 47782}, {28602, 29659}, {29156, 48090}, {29585, 47792}, {29633, 47829}, {29637, 48206}, {43052, 48220}, {47684, 47691}, {47690, 47729}, {47943, 48131}

X(48290) = midpoint of X(i) and X(j) for these {i,j}: {1, 47682}, {693, 47728}, {3904, 47694}, {4122, 4922}, {21343, 48103}, {47684, 47691}, {47690, 47729}, {47726, 47727}
X(48290) = reflection of X(i) in X(j) for these {i,j}: {3801, 34958}, {10015, 4874}
X(48290) = crosssum of X(512) and X(2242)
X(48290) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 47726, 47727}, {47682, 47727, 47726}


X(48291) = X(1)X(523)∩X(2)X(4770)

Barycentrics    (b - c)*(a^3 - a^2*b + a*b^2 - a^2*c + 3*a*b*c + b^2*c + a*c^2 + b*c^2) : :
X(48291) = 3 X[1] - X[47683], X[8] - 3 X[47834], 2 X[10] - 3 X[47833], X[7192] - 3 X[17166], 3 X[663] - X[47926], 3 X[667] - 2 X[48008], 4 X[1125] - 3 X[47827], 5 X[1698] - 6 X[48206], 5 X[3616] - 3 X[47825], 7 X[3624] - 6 X[47829], 3 X[4041] - 5 X[24924], 2 X[4041] - 3 X[47837], 10 X[24924] - 9 X[47837], 2 X[4147] - 3 X[47875], 3 X[4379] - X[4814], 3 X[4705] - 4 X[25666], 2 X[4705] - 3 X[47839], 8 X[25666] - 9 X[47839], 2 X[4791] - 3 X[48189], 3 X[4822] - X[47903], 2 X[4913] - 3 X[14419], 3 X[4983] - 2 X[47991], 3 X[30592] - 2 X[48050], 3 X[47838] - 2 X[47967], 3 X[47840] - 2 X[48005], 3 X[47841] - 2 X[48012}

X(48291) lies on these lines: {1, 523}, {2, 4770}, {8, 47834}, {10, 47833}, {213, 22044}, {239, 4789}, {512, 7192}, {514, 4775}, {519, 4774}, {522, 4378}, {551, 4948}, {663, 47926}, {667, 48008}, {784, 4449}, {891, 47694}, {1125, 47827}, {1698, 48206}, {1960, 17494}, {2787, 4804}, {3287, 20963}, {3616, 47825}, {3624, 47829}, {3887, 21146}, {4010, 4160}, {4024, 29110}, {4041, 24924}, {4106, 8678}, {4139, 47844}, {4147, 47875}, {4151, 4367}, {4369, 4730}, {4374, 17143}, {4379, 4814}, {4384, 47788}, {4393, 47792}, {4705, 25666}, {4777, 29908}, {4791, 48189}, {4801, 6004}, {4808, 8045}, {4815, 38469}, {4822, 47903}, {4825, 47779}, {4895, 29188}, {4913, 14419}, {4983, 47991}, {4992, 47948}, {7199, 17144}, {7662, 14077}, {10015, 47132}, {16823, 47809}, {16826, 47782}, {16828, 48207}, {16830, 47797}, {16831, 47784}, {19853, 48209}, {21385, 48248}, {25512, 48205}, {29066, 48120}, {29102, 47704}, {29224, 47705}, {29312, 47695}, {29570, 46915}, {30592, 48050}, {39586, 47799}, {47838, 47967}, {47840, 48005}, {47841, 48012}

X(48291) = midpoint of X(4895) and X(47672)
X(48291) = reflection of X(i) in X(j) for these {i,j}: {4730, 4369}, {4808, 8045}, {4825, 47779}, {4948, 551}, {10015, 47132}, {17494, 1960}, {21385, 48248}, {47948, 4992}
X(48291) = anticomplement of X(4770)
X(48291) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {58, 39364}, {89, 21221}, {99, 21291}, {110, 17488}, {2163, 148}, {4556, 30564}, {4588, 1654}, {4597, 1330}, {4604, 2895}, {20569, 21294}, {28607, 21220}, {34073, 1655}, {39704, 3448}
X(48291) = crosspoint of X(i) and X(j) for these (i,j): {99, 32013}, {4597, 32009}
X(48291) = crosssum of X(4775) and X(20963)
X(48291) = crossdifference of every pair of points on line {2245, 20973}


X(48292) = X(1)X(523)∩X(8)X(48209)

Barycentrics    a*(b - c)*(a^3 - a*b^2 - a*b*c + 2*b^2*c - a*c^2 + 2*b*c^2) : :
X(48292) = 3 X[1] - X[3737], 3 X[2605] - 2 X[3737], X[8] - 3 X[48209], 2 X[10] - 3 X[48207], 3 X[4449] + X[42312], 4 X[1125] - 3 X[48205], 5 X[3616] - 3 X[48204], 2 X[4147] - 3 X[48181], X[21103] - 3 X[30573}

X(48292) lies on these lines: {1, 523}, {8, 48209}, {10, 48207}, {42, 47833}, {43, 48206}, {512, 4840}, {513, 4162}, {612, 47799}, {614, 47807}, {656, 8702}, {663, 4802}, {891, 4057}, {1100, 3287}, {1125, 48205}, {1459, 4777}, {2483, 17458}, {3616, 48204}, {3709, 16777}, {3720, 47827}, {3733, 4139}, {3875, 17218}, {3907, 30591}, {3920, 47797}, {4017, 8674}, {4040, 28175}, {4041, 31947}, {4132, 4367}, {4147, 48181}, {4360, 4374}, {4361, 17066}, {4724, 28199}, {4789, 17011}, {4794, 28191}, {4926, 43924}, {5127, 30222}, {5256, 47788}, {5287, 47784}, {5697, 46610}, {6742, 45235}, {7191, 47809}, {7199, 17393}, {8819, 15888}, {17018, 47834}, {17019, 47782}, {17024, 48208}, {17299, 21958}, {17418, 28165}, {17478, 47842}, {21103, 30573}, {21112, 21179}, {21173, 28183}, {21348, 22108}, {21719, 24961}, {21842, 46611}, {23282, 29110}, {23655, 48090}, {26102, 47829}, {28151, 46385}, {28602, 29820}, {29814, 47825}, {29815, 48203}

X(48292) = reflection of X(i) in X(j) for these {i,j}: {2605, 1}, {4041, 31947}, {21112, 21179}
X(48292) = X(32680)-Ceva conjugate of X(2245)
X(48292) = crosspoint of X(1) and X(6742)
X(48292) = crosssum of X(i) and X(j) for these (i,j): {1, 2605}, {523, 7741}
X(48292) = crossdifference of every pair of points on line {1743, 2245}
X(48292) = barycentric product X(4391)*X(18360)
X(48292) = barycentric quotient X(18360)/X(651)


X(48293) = X(1)X(523)∩X(10)X(48209)

Barycentrics    a*(b - c)*(a^3 - a*b^2 - a*b*c + 3*b^2*c - a*c^2 + 3*b*c^2) : :
X(48293) = 3 X[1] - 2 X[2605], 4 X[2605] - 3 X[3737], 2 X[10] - 3 X[48209], 3 X[4449] - X[43924], 4 X[1125] - 3 X[48204], 5 X[1698] - 6 X[48207], 7 X[3624] - 6 X[48205], 2 X[4147] - 3 X[48186], X[21106] - 3 X[30573}

X(48293) lies on these lines: {1, 523}, {10, 48209}, {42, 47834}, {43, 47833}, {75, 17218}, {495, 8819}, {522, 4318}, {612, 47797}, {614, 47809}, {663, 28147}, {1019, 4132}, {1125, 48204}, {1449, 3287}, {1459, 28161}, {1698, 48207}, {2999, 47788}, {3247, 3709}, {3624, 48205}, {3720, 47825}, {3733, 4145}, {3875, 4374}, {3900, 23800}, {3907, 4815}, {3920, 48203}, {4007, 21958}, {4017, 35057}, {4040, 4802}, {4057, 21385}, {4139, 4367}, {4147, 48186}, {4360, 7199}, {4404, 8062}, {4467, 7203}, {4551, 6742}, {4724, 28191}, {4777, 21173}, {4778, 42312}, {4789, 5256}, {4879, 8672}, {5268, 47799}, {5272, 47807}, {5287, 47782}, {5583, 10388}, {6129, 14077}, {6371, 21343}, {7191, 48208}, {11010, 46610}, {11529, 34954}, {14812, 34195}, {16569, 48206}, {17011, 47792}, {17019, 46915}, {17022, 47784}, {17418, 28169}, {21106, 30573}, {21119, 21179}, {25502, 47829}, {26102, 47827}, {28155, 46385}, {28175, 47970}

X(48293) = reflection of X(i) in X(j) for these {i,j}: {3737, 1}, {4404, 8062}, {21119, 21179}, {21385, 4057}
X(48293) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {4565, 18133}, {20615, 3448}, {34594, 3436}, {37205, 21286}, {39949, 33650}
X(48293) = crosspoint of X(664) and X(1255)
X(48293) = crosssum of X(i) and X(j) for these (i,j): {512, 46189}, {523, 7173}, {663, 1100}
X(48293) = crossdifference of every pair of points on line {2245, 2347}


X(48294) = X(1)X(514)∩X(8)X(47794)

Barycentrics    a*(b - c)*(2*a^2 - 2*a*b - 2*a*c + b*c) : :
X(48294) = 3 X[1] + X[4040], 3 X[1] - X[4449], 5 X[1] + X[4724], 2 X[1] + X[4794], 9 X[1] + X[47929], 7 X[1] + X[47970], 4 X[1] + X[48065], 3 X[663] - X[4040], 3 X[663] + X[4449], 5 X[663] - X[4724], 9 X[663] - X[47929], 7 X[663] - X[47970], 4 X[663] - X[48065], 5 X[4040] - 3 X[4724], 2 X[4040] - 3 X[4794], 3 X[4040] - X[47929], 7 X[4040] - 3 X[47970], 4 X[4040] - 3 X[48065], 5 X[4449] + 3 X[4724], 2 X[4449] + 3 X[4794], 3 X[4449] + X[47929], 7 X[4449] + 3 X[47970], 4 X[4449] + 3 X[48065], 2 X[4724] - 5 X[4794], 9 X[4724] - 5 X[47929], 7 X[4724] - 5 X[47970], 4 X[4724] - 5 X[48065], 9 X[4794] - 2 X[47929], 7 X[4794] - 2 X[47970], 7 X[47929] - 9 X[47970], 4 X[47929] - 9 X[48065], 4 X[47970] - 7 X[48065], X[8] - 3 X[47794], 2 X[10] - 3 X[48196], X[145] + 3 X[47793], X[4147] - 3 X[45316], X[667] - 3 X[25569], X[4879] + 3 X[25569], 2 X[4879] + X[48011], 6 X[25569] - X[48011], X[48092] - 3 X[48136], 2 X[4162] + X[48018], 4 X[1125] - 3 X[48218], 2 X[17072] - 3 X[48218], X[2530] + 3 X[3251], 5 X[3616] - X[21302], 5 X[3616] - 3 X[47795], X[21302] - 3 X[47795], 7 X[3622] - 3 X[47796], 4 X[3636] - X[24720], X[4041] + 3 X[23057], X[4063] - 3 X[8643], X[4761] - 3 X[47820], X[4774] - 3 X[47875], X[4905] - 3 X[14413], X[4959] + 3 X[47828], 3 X[14349] - X[47905], 3 X[14421] - X[23765}

X(48294) lies on these lines: {1, 514}, {8, 47794}, {10, 48196}, {33, 39532}, {42, 47778}, {56, 39476}, {78, 4546}, {106, 29348}, {145, 47793}, {512, 48064}, {513, 25405}, {519, 4147}, {522, 2605}, {614, 44432}, {667, 4879}, {676, 28473}, {810, 4129}, {830, 48092}, {905, 3887}, {928, 39541}, {995, 22090}, {999, 44408}, {1125, 17072}, {1191, 22154}, {1279, 37998}, {1386, 9029}, {1459, 3667}, {1577, 47729}, {1734, 4895}, {1960, 4083}, {2530, 3251}, {2533, 4844}, {2785, 20517}, {3309, 3960}, {3616, 21302}, {3622, 47796}, {3636, 24720}, {3669, 42325}, {3720, 47779}, {3737, 28161}, {3777, 6161}, {3900, 14838}, {3907, 4791}, {3920, 47766}, {3938, 10196}, {4010, 29344}, {4041, 23057}, {4063, 8643}, {4160, 47997}, {4170, 29178}, {4367, 4775}, {4379, 29814}, {4406, 17394}, {4458, 29304}, {4504, 29148}, {4511, 44448}, {4761, 47820}, {4774, 47875}, {4807, 31286}, {4823, 29066}, {4874, 29298}, {4893, 17018}, {4905, 14413}, {4959, 47828}, {4962, 21173}, {6003, 6129}, {7191, 47757}, {7269, 30181}, {8045, 29192}, {8678, 48054}, {9577, 23615}, {14077, 48003}, {14282, 17412}, {14349, 47905}, {14421, 23765}, {16969, 21791}, {17011, 47783}, {17019, 47789}, {17024, 44435}, {20691, 40464}, {21183, 29817}, {21188, 28292}, {28155, 46385}, {29164, 47682}, {29182, 48090}, {29260, 47727}, {29815, 47771}, {37697, 44928}, {47684, 47713}

X(48294) = midpoint of X(i) and X(j) for these {i,j}: {1, 663}, {667, 4879}, {905, 4162}, {1577, 47729}, {1734, 4895}, {3777, 6161}, {4040, 4449}, {4367, 4775}, {21173, 42312}, {47684, 47713}, {47712, 47728}
X(48294) = reflection of X(i) in X(j) for these {i,j}: {4401, 1960}, {4794, 663}, {4807, 31286}, {17072, 1125}, {47997, 48099}, {48011, 667}, {48018, 905}, {48065, 4794}, {48075, 3960}
X(48294) = crossdifference of every pair of points on line {672, 16885}
X(48294) = barycentric product X(i)*X(j) for these {i,j}: {1, 31209}, {513, 17336}
X(48294) = barycentric quotient X(i)/X(j) for these {i,j}: {17336, 668}, {31209, 75}
X(48294) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4040, 4449}, {663, 4449, 4040}, {1125, 17072, 48218}, {3616, 21302, 47795}, {4879, 25569, 667}


X(48295) = X(1)X(693)∩X(8)X(26985)

Barycentrics    (b - c)*(a^3 - a^2*b - a^2*c + 2*a*b*c + b^2*c + b*c^2) : :
X(48295) = 5 X[1] + X[47721], 3 X[1] + X[47724], 3 X[1] - X[47729], 5 X[693] - X[47721], 3 X[693] - X[47724], 3 X[693] + X[47729], 3 X[47721] - 5 X[47724], 3 X[47721] + 5 X[47729], X[8] - 5 X[26985], X[47963] - 3 X[48099], X[48134] + 3 X[48136], 3 X[663] + X[48119], 3 X[4978] - X[48119], 3 X[1577] - X[4474], 3 X[4449] + X[4474], X[1734] - 3 X[47796], 5 X[3616] - X[17494], 7 X[3622] + X[26824], 7 X[3624] - 5 X[31209], 4 X[3634] - 5 X[31250], 4 X[3636] + X[48125], X[3762] - 3 X[47832], 3 X[4040] - X[47974], 3 X[4801] + X[47974], X[4041] - 3 X[47795], X[4063] - 3 X[47820], 3 X[4367] + X[4810], 3 X[4379] - X[4761], X[4490] - 3 X[47839], X[4498] - 3 X[47818], X[4705] - 3 X[47841], X[4707] - 3 X[47887], X[4730] - 3 X[47823], X[4804] + 3 X[14413], X[4879] + 3 X[47889], X[4895] + 3 X[47812], 11 X[5550] - 7 X[27115], 2 X[10006] - 3 X[32557], 3 X[14349] - X[47945], 3 X[17166] + X[47945], 3 X[14432] + X[47704], 5 X[19862] - 4 X[31287], 3 X[19883] - 2 X[44567], X[21222] + 3 X[48172], X[21343] + 3 X[47833], X[21385] - 3 X[47804], X[24719] - 3 X[30592], 3 X[25055] - X[31150], 5 X[26777] - 13 X[46934], 3 X[38314] + X[47869], 3 X[47838] - X[47918], 3 X[47840] - X[47959], 3 X[48131] + X[48153}

X(48295) lies on these lines: {1, 693}, {8, 26985}, {10, 4885}, {386, 18154}, {514, 3716}, {519, 45320}, {522, 3960}, {551, 4762}, {650, 1125}, {663, 4978}, {667, 29302}, {740, 4411}, {830, 48042}, {891, 4874}, {900, 39545}, {905, 4151}, {946, 8760}, {978, 30024}, {1386, 9015}, {1459, 4815}, {1577, 4449}, {1734, 47796}, {1938, 3878}, {1960, 29362}, {2787, 48090}, {2832, 48063}, {3309, 23789}, {3616, 17494}, {3622, 26824}, {3624, 31209}, {3634, 31250}, {3636, 48125}, {3669, 8714}, {3700, 29212}, {3743, 25098}, {3762, 47832}, {3835, 4160}, {3887, 24720}, {3907, 4823}, {3910, 20517}, {4010, 4378}, {4040, 4801}, {4041, 47795}, {4063, 47820}, {4170, 48144}, {4367, 4810}, {4369, 29350}, {4379, 4761}, {4458, 23876}, {4490, 47839}, {4498, 47818}, {4504, 29344}, {4705, 47841}, {4707, 47887}, {4730, 47823}, {4775, 21146}, {4777, 24325}, {4804, 14413}, {4879, 47889}, {4895, 47812}, {5550, 27115}, {8045, 29047}, {8062, 28147}, {8583, 25009}, {9366, 15584}, {9373, 21616}, {9397, 15280}, {9443, 10176}, {10006, 32557}, {10198, 28834}, {11934, 12053}, {14349, 17166}, {14421, 48189}, {14432, 47704}, {16828, 21727}, {17749, 29488}, {17793, 48202}, {19853, 27193}, {19858, 25511}, {19861, 26546}, {19862, 31287}, {19883, 44567}, {21212, 44315}, {21214, 30061}, {21222, 48172}, {21343, 47833}, {21385, 47804}, {23813, 28475}, {23887, 47123}, {24541, 26641}, {24719, 30592}, {25055, 31150}, {26777, 46934}, {29130, 47712}, {29160, 47682}, {29188, 48098}, {30117, 30910}, {35057, 47843}, {38314, 47869}, {47680, 47728}, {47684, 47725}, {47690, 47727}, {47692, 47726}, {47838, 47918}, {47840, 47959}, {48131, 48153}

X(48295) = midpoint of X(i) and X(j) for these {i,j}: {1, 693}, {663, 4978}, {1459, 4815}, {1577, 4449}, {4010, 4378}, {4040, 4801}, {4170, 48144}, {4775, 21146}, {14349, 17166}, {14421, 48189}, {47680, 47728}, {47682, 47691}, {47684, 47725}, {47690, 47727}, {47692, 47726}, {47724, 47729}
X(48295) = reflection of X(i) in X(j) for these {i,j}: {10, 4885}, {650, 1125}, {20517, 34958}, {21212, 44315}
X(48295) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 47724, 47729}, {693, 47729, 47724}


X(48296) = X(1)X(659)∩X(10)X(25574)

Barycentrics    a*(b - c)*(2*a^2 - 3*a*b - 3*a*c + 4*b*c) : :
X(48296) = 3 X[1] - X[659], 5 X[1] - X[21385], 5 X[1] - 3 X[25569], 2 X[659] - 3 X[1960], X[659] + 3 X[21343], 5 X[659] - 3 X[21385], 5 X[659] - 9 X[25569], X[1960] + 2 X[21343], 5 X[1960] - 2 X[21385], 5 X[1960] - 6 X[25569], 5 X[21343] + X[21385], 5 X[21343] + 3 X[25569], X[21385] - 3 X[25569], X[4378] - 3 X[4449], 5 X[4378] - 3 X[48144], 5 X[4449] - X[48144], X[2254] - 3 X[14421], 3 X[3241] + X[46403], 3 X[3251] - X[48032], 3 X[3679] - 5 X[30795], X[4730] - 3 X[14413], X[6161] - 3 X[23057], 3 X[9269] - X[9508], 2 X[9508] - 3 X[14422}

X(48296) lies on these lines: {1, 659}, {10, 25574}, {512, 4378}, {519, 3837}, {764, 4895}, {926, 10695}, {1482, 2821}, {2254, 14421}, {2826, 10222}, {3241, 46403}, {3242, 9032}, {3251, 48032}, {3679, 30795}, {4083, 48011}, {4669, 45340}, {4730, 14413}, {4770, 14077}, {4844, 48098}, {4879, 6372}, {4922, 29340}, {5048, 6550}, {6009, 15570}, {6085, 10700}, {6161, 23057}, {9260, 28603}, {9269, 9508}, {11011, 30725}, {15178, 44805}, {17294, 30865}, {24623, 29584}, {29166, 47727}, {29272, 47716}, {48005, 48136}

X(48296) = midpoint of X(i) and X(j) for these {i,j}: {1, 21343}, {764, 4895}
X(48296) = reflection of X(i) in X(j) for these {i,j}: {1960, 1}, {4669, 45340}, {14422, 9269}, {44805, 15178}, {48005, 48136}
X(48296) = crossdifference of every pair of points on line {20331, 37657}
X(48296) = {X(1),X(21385)}-harmonic conjugate of X(25569)


X(48297) = X(1)X(4802)∩X(36)X(238)

Barycentrics    a*(b - c)*(a^3 - a*b^2 - 2*a*b*c - b^2*c - a*c^2 - b*c^2) : :
X(48297) = 3 X[3737] - X[21173], 3 X[4040] + X[21173], 2 X[17072] - 3 X[48205], X[21302] - 3 X[48204], 2 X[31946] - 3 X[47822], 2 X[47843] - 3 X[48207}

X(48297) lies on these lines: {1, 4802}, {36, 238}, {42, 48176}, {43, 48194}, {514, 2605}, {520, 2488}, {522, 4794}, {523, 663}, {612, 48219}, {614, 48192}, {650, 15313}, {659, 834}, {661, 1919}, {676, 1459}, {832, 47842}, {900, 17418}, {1027, 10013}, {1734, 8043}, {1960, 8672}, {3477, 23696}, {3720, 48238}, {3920, 48236}, {4036, 29066}, {4132, 4775}, {4449, 28175}, {4778, 48065}, {6003, 38324}, {6133, 29366}, {7191, 48174}, {8062, 29051}, {8633, 9426}, {17072, 48205}, {21121, 29082}, {21302, 48204}, {23655, 48002}, {26102, 48221}, {28183, 42312}, {28195, 47970}, {28209, 30724}, {28213, 47929}, {30968, 31946}, {35057, 48003}, {47843, 48207}

X(48297) = midpoint of X(i) and X(j) for these {i,j}: {663, 46385}, {1459, 4724}, {3737, 4040}, {4057, 4833}
X(48297) = reflection of X(i) in X(j) for these {i,j}: {1734, 8043}, {23800, 31947}
X(48297) = X(8652)-Ceva conjugate of X(1)
X(48297) = crosspoint of X(i) and X(j) for these (i,j): {58, 28624}, {86, 37211}, {100, 43531}
X(48297) = crosssum of X(i) and X(j) for these (i,j): {10, 28623}, {42, 4813}, {386, 513}
X(48297) = crossdifference of every pair of points on line {37, 579}
X(48297) = barycentric product X(i)*X(j) for these {i,j}: {513, 5278}, {514, 5248}, {584, 693}, {23882, 45128}
X(48297) = barycentric quotient X(i)/X(j) for these {i,j}: {584, 100}, {5248, 190}, {5278, 668}


X(48298) = X(1)X(514)∩X(8)X(1491)

Barycentrics    (b - c)*(-a^3 + 2*a^2*b + a*b^2 + 2*a^2*c - a*b*c + b^2*c + a*c^2 + b*c^2) : :
X(48298) = 3 X[663] - 2 X[48063], 3 X[4449] - X[48142], 3 X[17166] - 2 X[48142], 4 X[905] - 3 X[47836], 4 X[1960] - 3 X[47805], 2 X[2533] - 3 X[47796], 5 X[3616] - 4 X[4874], 2 X[3762] - 3 X[47821], 4 X[3835] - 3 X[30709], 2 X[4474] - 3 X[30709], 3 X[21301] - 4 X[48050], 2 X[48050] - 3 X[48131], 4 X[3960] - 3 X[47824], 2 X[4761] - 3 X[47824], 2 X[4369] - 3 X[14413], 2 X[4391] - 3 X[47840], 3 X[47840] - 4 X[48136], 2 X[4707] - 3 X[48241], 2 X[4730] - 3 X[48242], 3 X[4801] - 2 X[48126], 2 X[10015] - 3 X[47797], 6 X[14419] - 5 X[27013], 3 X[14430] - 4 X[25666], 6 X[14431] - 7 X[27138], 4 X[21212] - 3 X[30574], 2 X[21385] - 3 X[48240], 3 X[25569] - 2 X[48248], 3 X[38314] - 2 X[48234], 2 X[47724] - 3 X[48170}

X(48298) lies on these lines: {1, 514}, {8, 1491}, {512, 17496}, {513, 4922}, {519, 48157}, {523, 3904}, {764, 29188}, {824, 4693}, {891, 17494}, {905, 47836}, {1459, 4581}, {1960, 47805}, {2530, 21302}, {2533, 26115}, {2785, 16892}, {2787, 20295}, {3004, 4477}, {3250, 27241}, {3616, 4874}, {3762, 47821}, {3777, 29366}, {3835, 4474}, {3837, 4774}, {3907, 21301}, {3960, 4761}, {4083, 4560}, {4160, 47945}, {4369, 14413}, {4378, 7192}, {4391, 47840}, {4462, 48099}, {4705, 17751}, {4707, 48241}, {4730, 48242}, {4801, 48126}, {4802, 47684}, {4814, 48017}, {4893, 30942}, {5990, 20045}, {6004, 20041}, {6332, 47707}, {8678, 47940}, {10015, 47797}, {14077, 47975}, {14419, 27013}, {14421, 29822}, {14430, 25666}, {14431, 27138}, {21212, 30574}, {21385, 48240}, {23765, 29246}, {23887, 47727}, {24719, 29236}, {25569, 48248}, {26227, 44435}, {28292, 48015}, {28470, 48122}, {28537, 48174}, {29051, 48115}, {29066, 46403}, {29240, 47652}, {29324, 48123}, {29823, 30580}, {29824, 47775}, {29825, 47779}, {29826, 47766}, {29827, 47778}, {29828, 4775 7}, {38314, 48234}, {47682, 47693}, {47721, 48089}, {47724, 48170}

X(48298) = midpoint of X(21105) and X(47701)
X(48298) = reflection of X(i) in X(j) for these {i,j}: {8, 1491}, {4391, 48136}, {4462, 48099}, {4474, 3835}, {4581, 1459}, {4761, 3960}, {4774, 3837}, {4814, 48017}, {7192, 4378}, {17166, 4449}, {21301, 48131}, {21302, 2530}, {47693, 47682}, {47694, 1}, {47707, 6332}, {47721, 48089}, {47773, 30580}, {47780, 14421}, {48102, 5592}
X(48298) = reflection of X(47694) in the Soddy line
X(48298) = anticomplement of the isotomic conjugate of X(35008)
X(48298) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {35008, 6327}, {35009, 69}
X(48298) = X(35008)-Ceva conjugate of X(2)
X(48298) = crossdifference of every pair of points on line {672, 4274}
X(48298) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3835, 4474, 30709}, {3960, 4761, 47824}, {4391, 48136, 47840}


X(48299) = X(1)X(29288)∩X(523)X(663)

Barycentrics    (b - c)*(2*a^3 - a^2*b + b^3 - a^2*c + b^2*c + b*c^2 + c^3) : :
X(48299) = 3 X[1639] - 2 X[21051], 4 X[2490] - 3 X[47835], 2 X[4142] - 3 X[26275], X[4707] - 3 X[47818], 3 X[14432] - X[48131], 2 X[14837] - 3 X[47803], 2 X[17072] - 3 X[47807], X[21302] - 3 X[47809], X[23755] - 3 X[47813], 4 X[31288] - 3 X[41800}

X(48299) lies on these lines: {1, 29288}, {513, 6332}, {514, 3716}, {523, 663}, {525, 667}, {649, 3566}, {659, 3910}, {676, 3801}, {814, 3700}, {826, 1960}, {900, 48150}, {918, 4367}, {1499, 4834}, {1577, 29240}, {1639, 21051}, {1938, 14344}, {1946, 47194}, {2490, 47835}, {2785, 48231}, {2977, 4041}, {3800, 4775}, {3810, 48063}, {3900, 48062}, {4010, 4990}, {4040, 29142}, {4083, 47890}, {4122, 29278}, {4142, 26275}, {4391, 47728}, {4401, 23876}, {4449, 48094}, {4522, 28470}, {4707, 47818}, {4782, 29284}, {4794, 29021}, {4874, 7178}, {4879, 48103}, {4897, 29200}, {4976, 8632}, {4977, 14432}, {4992, 23729}, {5592, 8045}, {7265, 29232}, {8678, 48047}, {10015, 29094}, {14349, 47989}, {14837, 47803}, {17072, 47807}, {20517, 29220}, {21302, 47809}, {23755, 47813}, {28209, 48122}, {28292, 48219}, {28468, 48247}, {29244, 48090}, {31288, 41800}, {47684, 47708}, {47707, 47729}, {47988, 48093}

X(48299) = midpoint of X(i) and X(j) for these {i,j}: {4040, 47682}, {4391, 47728}, {4449, 48094}, {4879, 48103}, {5592, 8045}, {47684, 47708}, {47707, 47729}
X(48299) = reflection of X(i) in X(j) for these {i,j}: {3801, 676}, {4010, 4990}, {4041, 2977}, {7178, 4874}, {23729, 4992}, {47988, 48093}, {47989, 14349}, {47998, 48099}
X(48299) = crossdifference of every pair of points on line {579, 37581}


X(48300) = X(1)X(29047)∩X(523)X(663)

Barycentrics    (b - c)*(a^3 + b^3 + b^2*c + b*c^2 + c^3) : :
X(48300) = 2 X[1577] - 3 X[47874], 2 X[47682] + X[48094], 2 X[3776] - 3 X[47796], 2 X[47726] + X[47972], 2 X[4142] - 3 X[47804], 2 X[4458] - 3 X[47820], 3 X[14432] - 2 X[48136], 2 X[5592] + X[47689], 3 X[6546] - 2 X[47965], 2 X[14837] - 3 X[47766], 4 X[14838] - 3 X[47886], 2 X[17072] - 3 X[47809], 2 X[20317] - 3 X[47770], 2 X[20517] - 3 X[47818], 2 X[21051] - 3 X[48185], 4 X[21188] - 5 X[24924], X[21302] - 3 X[48208], 7 X[31207] - 6 X[41800], 2 X[47679] - 3 X[47878}

X(48300) lies on these lines: {1, 29047}, {512, 48106}, {513, 4064}, {514, 661}, {522, 48150}, {523, 663}, {525, 649}, {650, 21124}, {659, 29017}, {667, 826}, {690, 4834}, {814, 4122}, {824, 4560}, {830, 48077}, {905, 16892}, {918, 2484}, {1019, 21392}, {1960, 7950}, {2509, 3669}, {2530, 47973}, {2533, 29082}, {2785, 48236}, {3700, 29162}, {3716, 29116}, {3776, 47796}, {3801, 4874}, {3907, 47707}, {3910, 4498}, {4010, 29025}, {4024, 23882}, {4040, 29021}, {4041, 48062}, {4063, 23876}, {4083, 48103}, {4088, 8678}, {4142, 47804}, {4170, 29158}, {4378, 29354}, {4401, 29318}, {4449, 29288}, {4458, 47820}, {4490, 48056}, {4522, 21301}, {4707, 29220}, {4724, 29142}, {4761, 29304}, {4775, 7927}, {4778, 48116}, {4782, 29202}, {4784, 29200}, {4794, 29164}, {4802, 14432}, {4879, 29208}, {4977, 48122}, {4983, 47938}, {5029, 14316}, {5592, 47689}, {6002, 25259}, {6372, 48078}, {6546, 47965}, {7265, 29013}, {8632, 23879}, {8712, 48095}, {14837, 47766}, {14838, 30911}, {15309, 48076}, {17072, 47809}, {17899, 20909}, {18077, 21613}, {20317, 47770}, {20517, 47818}, {21051, 48185}, {21188, 24924}, {21302, 48208}, {23731, 48091}, {23738, 48113}, {23877, 47694}, {26853, 28493}, {28468, 47773}, {28478, 47935}, {28846, 48149}, {29051, 47690}, {29066, 47711}, {29118, 48080}, {29154, 47203}, {29160, 47712}, {29186, 47715}, {29192, 47710}, {29198, 48083}, {29224, 47887}, {29226, 48097}, {29260, 47727}, {30574, 48219}, {31207, 41800}, {47679, 47878}, {47701, 48099}, {47706, 47729}, {47905, 48039}, {47906, 48040}, {47911, 48046}, {47912, 48047}, {47913, 48048}, {47929, 48055}, {47936, 48061}, {47937, 48085}, {47943, 48092}, {47944, 48093}, {47968, 48100}

X(48300) = midpoint of X(i) and X(j) for these {i,j}: {4040, 47726}, {4391, 47684}, {4449, 48118}, {23738, 48113}, {47706, 47729}, {47707, 47728}
X(48300) = reflection of X(i) in X(j) for these {i,j}: {693, 8045}, {3801, 4874}, {4041, 48062}, {4490, 48056}, {4498, 47890}, {16892, 905}, {21124, 650}, {21301, 4522}, {23731, 48091}, {30574, 48219}, {47680, 4823}, {47701, 48099}, {47708, 3716}, {47905, 48039}, {47906, 48040}, {47911, 48046}, {47912, 48047}, {47913, 48048}, {47918, 4468}, {47929, 48055}, {47935, 48060}, {47936, 48061}, {47937, 48085}, {47938, 4983}, {47943, 48092}, {47944, 48093}, {47958, 14349}, {47968, 48100}, {47971, 1019}, {47972, 4040}, {47973, 2530}, {48131, 6332}
X(48300) = X(987)-anticomplementary conjugate of X(150)
X(48300) = X(i)-isoconjugate of X(j) for these (i,j): {6, 833}, {101, 977}
X(48300) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 833), (1015, 977)
X(48300) = crossdifference of every pair of points on line {31, 579}
X(48300) = barycentric product X(i)*X(j) for these {i,j}: {75, 832}, {514, 32777}, {561, 8636}, {693, 976}, {2273, 3261}, {4025, 5090}, {14208, 17520}
X(48300) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 833}, {513, 977}, {832, 1}, {976, 100}, {2273, 101}, {5090, 1897}, {8636, 31}, {17520, 162}, {32777, 190}


X(48301) = X(1)X(784)∩X(523)X(663)

Barycentrics    (b - c)*(a^3 - a^2*b + a*b^2 - a^2*c + 2*a*b*c + b^2*c + a*c^2 + b*c^2) : :
X(48301) = 2 X[10] - 3 X[47875], 4 X[1125] - 3 X[47888], 2 X[1491] - 3 X[47841], 2 X[1577] - 3 X[48189], 2 X[1734] - 3 X[47823], 2 X[4041] - 3 X[47835], 4 X[4874] - 3 X[47835], 2 X[4147] - 3 X[47872], 3 X[4448] - 2 X[47965], 2 X[4705] - 3 X[47822], X[4729] - 3 X[47813], 2 X[4770] - 3 X[47794], 2 X[4808] - 3 X[48188], 2 X[9508] - 3 X[47820], 4 X[14838] - 3 X[48225], 2 X[17072] - 3 X[47833], 2 X[21051] - 3 X[47832], X[21302] - 3 X[47834], 2 X[24720] - 3 X[47889], 4 X[34958] - 3 X[48227], 3 X[47821] - 2 X[47967], 3 X[47838] - 2 X[48005], 3 X[47839] - 2 X[48012], 3 X[47840] - 2 X[48030], 3 X[47893] - 2 X[48017}

X(48301) lies on these lines: {1, 784}, {10, 47875}, {513, 4801}, {514, 4775}, {522, 4367}, {523, 663}, {667, 4151}, {693, 21303}, {814, 4804}, {830, 24719}, {832, 4815}, {885, 7320}, {900, 48144}, {1125, 47888}, {1491, 47841}, {1577, 48189}, {1734, 47823}, {2533, 3900}, {3063, 22044}, {3309, 21146}, {3716, 4490}, {3801, 47123}, {3887, 48238}, {4010, 8678}, {4024, 29074}, {4041, 4874}, {4083, 47694}, {4107, 4500}, {4147, 47872}, {4378, 8714}, {4435, 6590}, {4448, 47965}, {4498, 48248}, {4560, 4777}, {4705, 47822}, {4729, 47813}, {4770, 47794}, {4806, 47912}, {4808, 48188}, {4824, 48099}, {4895, 29366}, {4922, 23880}, {4948, 45316}, {4978, 6004}, {4990, 48047}, {4992, 48023}, {5029, 14610}, {6161, 29186}, {7178, 47132}, {7650, 38469}, {9508, 47820}, {14838, 48225}, {17072, 47833}, {17494, 23506}, {21051, 47832}, {21301, 48090}, {21302, 47834}, {24286, 47715}, {24720, 47889}, {25569, 28161}, {29017, 47695}, {29051, 48120}, {29208, 47660}, {29238, 31291}, {29246, 47672}, {29362, 48150}, {34958, 48227}, {47821, 47967}, {47838, 48005}, {47839, 48012}, {47840, 48030}, {47893, 48017}, {47945, 48093}

X(48301) = reflection of X(i) in X(j) for these {i,j}: {2533, 7662}, {3801, 47123}, {4041, 4874}, {4490, 3716}, {4498, 48248}, {4824, 48099}, {4948, 45316}, {7178, 47132}, {21301, 48090}, {47912, 4806}, {47945, 48093}, {48023, 4992}, {48047, 4990}
X(48301) = X(4041),X(4874)}-harmonic conjugate of X(47835)


X(48302) = X(1)X(513)∩X(523)X(663)

Barycentrics    a*(b - c)*(a^3 - a*b^2 - 2*a*b*c + b^2*c - a*c^2 + b*c^2) : :
X(48302) = X[8] - 3 X[48165], 2 X[10] - 3 X[48181], 3 X[663] - X[46385], 4 X[1125] - 3 X[48230], 5 X[3616] - 3 X[48246], 3 X[4162] + X[7655], 3 X[6129] - X[7655], 2 X[17072] - 3 X[48207], X[17420] + 3 X[23057], X[20293] - 3 X[26144], 2 X[20316] - 3 X[48168], X[21302] - 3 X[48209], 2 X[44316] - 3 X[47841}

X(48302) lies on these lines: {1, 513}, {8, 48165}, {10, 48181}, {33, 16228}, {37, 3063}, {42, 47822}, {43, 48197}, {522, 2605}, {523, 663}, {612, 47803}, {614, 47802}, {656, 4895}, {667, 4132}, {834, 4879}, {900, 1459}, {1100, 20980}, {1125, 48230}, {1449, 39521}, {1734, 31947}, {1919, 21834}, {1946, 23286}, {1960, 4139}, {3247, 21390}, {3616, 48246}, {3720, 47823}, {3737, 4777}, {3920, 47804}, {3938, 4448}, {3946, 40474}, {3961, 45666}, {4040, 4802}, {4057, 4083}, {4162, 6129}, {4360, 20906}, {4435, 6586}, {4449, 4977}, {4724, 28175}, {4776, 17011}, {4794, 28147}, {4806, 23655}, {4926, 21173}, {5256, 47760}, {5287, 47761}, {6198, 44426}, {7191, 44429}, {7269, 24002}, {7650, 47729}, {8632, 17458}, {8674, 21189}, {16777, 21007}, {17018, 47821}, {17019, 47762}, {17024, 48164}, {17072, 48207}, {17393, 20949}, {17418, 28183}, {17420, 23057}, {17478, 29366}, {20293, 26144}, {20316, 48168}, {21111, 21185}, {21302, 48209}, {21831, 23282}, {23886, 24354}, {26102, 48216}, {28191, 48065}, {28199, 47970}, {28217, 43924}, {29066, 30591}, {29814, 47824}, {29815, 47805}, {37697, 44923}, {44316, 47841}

X(48302) = midpoint of X(i) and X(j) for these {i,j}: {656, 4895}, {1459, 42312}, {4162, 6129}, {7650, 47729}
X(48302) = reflection of X(i) in X(j) for these {i,j}: {1734, 31947}, {21111, 21185}
X(48302) = crosssum of X(513) and X(24046)
X(48302) = crossdifference of every pair of points on line {44, 579}
X(48302) = barycentric product X(i)*X(j) for these {i,j}: {1, 47794}, {514, 8715}, {693, 3204}, {4162, 27814}, {18359, 39478}
X(48302) = barycentric quotient X(i)/X(j) for these {i,j}: {3204, 100}, {8715, 190}, {39478, 3218}, {47794, 75}
X(48302) = {X(16777),X(21007)}-harmonic conjugate of X(21348)


X(48303) = X(1)X(522)∩X(523)X(663)

Barycentrics    a*(b - c)*(a^3 - a*b^2 - 2*a*b*c + 2*b^2*c - a*c^2 + 2*b*c^2) : :
X(48303) = 3 X[1] - X[21173], 3 X[1459] - 2 X[21173], X[8] - 3 X[48173], 2 X[20316] - 3 X[48173], 2 X[10] - 3 X[48186], 2 X[4036] - 3 X[47832], 4 X[1125] - 3 X[48228], 5 X[3616] - 3 X[48243], 4 X[31947] - 3 X[47828], 2 X[4147] - 3 X[48165], 3 X[11125] - 2 X[21186], 2 X[17072] - 3 X[48209}

X(48303) lies on these lines: {1, 522}, {8, 20316}, {10, 48186}, {33, 42756}, {35, 39226}, {37, 657}, {42, 4036}, {43, 47831}, {55, 39199}, {75, 17215}, {145, 20293}, {497, 42766}, {513, 4162}, {521, 1769}, {523, 663}, {612, 47800}, {614, 47806}, {649, 3726}, {652, 21347}, {656, 3900}, {659, 23506}, {665, 4501}, {667, 4139}, {676, 4105}, {900, 30726}, {1125, 48228}, {1482, 32475}, {2260, 22443}, {2484, 21834}, {2509, 4171}, {2517, 22090}, {2605, 4777}, {2654, 42768}, {2804, 44409}, {3064, 10397}, {3242, 9000}, {3261, 4360}, {3616, 48243}, {3672, 46402}, {3720, 31947}, {3737, 28161}, {3875, 20907}, {3887, 23800}, {3907, 7650}, {3920, 47798}, {3938, 21119}, {4000, 46399}, {4010, 23655}, {4017, 4895}, {4040, 28147}, {4057, 4498}, {4064, 21831}, {4145, 8643}, {4147, 48165}, {4397, 8062}, {4435, 21348}, {4526, 20980}, {4648, 21195}, {4724, 4802}, {4775, 8672}, {4794, 28155}, {4815, 29066}, {5256, 47787}, {5287, 47785}, {6586, 16777}, {6591, 8611}, {6615, 9001}, {7004, 15635}, {7191, 47808}, {7649, 8058}, {8702, 10459}, {9508, 24666}, {11125, 21186}, {14414, 30235}, {14547, 42767}, {17011, 47790}, {17018, 48172}, {17019, 27486}, {17022, 46919}, {17024, 48169}, {17072, 48209}, {17393, 20954}, {20315, 44448}, {21102, 21185}, {21189, 35057}, {21302, 47843}, {23752, 47123}, {26102, 47830}, {28175, 47929}, {28191, 47970}, {29814, 48242}, {29815, 48239}, {39540, 42337}, {42662, 44427}

X(48303) = midpoint of X(i) and X(j) for these {i,j}: {145, 20293}, {4017, 4895}, {4449, 42312}
X(48303) = reflection of X(i) in X(j) for these {i,j}: {8, 20316}, {656, 6129}, {1459, 1}, {4397, 8062}, {4498, 4057}, {17418, 2605}, {21102, 21185}, {21302, 47843}, {23752, 47123}, {44448, 20315}, {46385, 663}
X(48303) = isogonal conjugate of the isotomic conjugate of X(17894)
X(48303) = X(i)-complementary conjugate of X(j) for these (i,j): {1106, 8054}, {20615, 124}, {40148, 5514}
X(48303) = X(5687)-Ceva conjugate of X(38389)
X(48303) = X(38389)-cross conjugate of X(5687)
X(48303) = crosspoint of X(1) and X(1897)
X(48303) = crosssum of X(1) and X(1459)
X(48303) = crossdifference of every pair of points on line {579, 610}
X(48303) = barycentric product X(i)*X(j) for these {i,j}: {6, 17894}, {63, 16228}, {190, 38389}, {514, 5687}, {522, 34048}
X(48303) = barycentric quotient X(i)/X(j) for these {i,j}: {5687, 190}, {16228, 92}, {17894, 76}, {34048, 664}, {38389, 514}
X(48303) = {X(8),X(48173)}-harmonic conjugate of X(20316)


X(48304) = X(1)X(17494)∩X(523)X(3904)

Barycentrics    (b - c)*(a^3 - 2*a^2*b + a*b^2 - 2*a^2*c + 5*a*b*c + b^2*c + a*c^2 + b*c^2) : :
X(48304) = 4 X[10] - 5 X[26985], 2 X[47724] - 3 X[47869], 4 X[650] - 5 X[3616], 8 X[1125] - 7 X[27115], 4 X[1960] - 3 X[48240], 3 X[3241] - 2 X[47729], 7 X[3622] - 5 X[26777], 2 X[3696] - 3 X[4828], 2 X[3762] - 3 X[48172], 4 X[3960] - 3 X[48242], 3 X[4041] - 4 X[25380], 2 X[4041] - 3 X[47796], 8 X[25380] - 9 X[47796], 2 X[4490] - 3 X[47840], 2 X[4730] - 3 X[47824], 2 X[4761] - 3 X[47780], 8 X[4885] - 7 X[9780], 2 X[4913] - 3 X[14413], 11 X[5550] - 10 X[31209], 8 X[10006] - 9 X[32558], X[20050] + 2 X[47721], X[20050] + 4 X[48125], 7 X[20057] - 2 X[47664], 2 X[21385] - 3 X[47805], 3 X[30709] - 4 X[48090], 2 X[31150] - 3 X[38314}

X(48384) lies on these lines: {1, 17494}, {8, 693}, {10, 26985}, {145, 26824}, {519, 47724}, {522, 21222}, {523, 3904}, {650, 3616}, {891, 47694}, {962, 8760}, {1125, 27115}, {1960, 48240}, {2785, 47704}, {3241, 4762}, {3622, 26777}, {3696, 4828}, {3702, 21611}, {3762, 48172}, {3900, 4801}, {3952, 6633}, {3960, 48242}, {4041, 25380}, {4083, 17166}, {4151, 17496}, {4160, 20295}, {4449, 4560}, {4490, 47840}, {4730, 47824}, {4761, 47780}, {4774, 25574}, {4775, 47969}, {4777, 24349}, {4814, 24720}, {4815, 20293}, {4885, 9780}, {4913, 14413}, {4978, 21302}, {5550, 31209}, {7192, 29350}, {7253, 28147}, {9373, 11415}, {9785, 11934}, {10006, 32558}, {19874, 21727}, {20050, 47721}, {20057, 47664}, {21385, 47805}, {26030, 27139}, {26115, 27346}, {28521, 48115}, {29302, 31291}, {30709, 48090}, {31150, 38314}

X(48304) = midpoint of X(145) and X(26824)
X(48304) = reflection of X(i) in X(j) for these {i,j}: {8, 693}, {4560, 4449}, {4814, 24720}, {17494, 1}, {20293, 4815}, {21302, 4978}, {47721, 48125}, {47969, 4775}


X(48305) = X(513)X(4170)∩X(514)X(4775)

Barycentrics    (b - c)*(a^3 - a^2*b + a*b^2 - a^2*c + a*b*c + b^2*c + a*c^2 + b*c^2) : :
X(48305) = 2 X[10] - 3 X[47872], 4 X[1125] - 3 X[47893], 2 X[1491] - 3 X[47839], 2 X[1734] - 3 X[47837], 4 X[4874] - 3 X[47837], 2 X[4129] - 3 X[4800], 3 X[4448] - 2 X[48003], 2 X[4770] - 3 X[47793], 3 X[4809] - 2 X[21192], 2 X[4823] - 3 X[48189], 2 X[9508] - 3 X[47818], 2 X[17072] - 3 X[47875], 2 X[21260] - 3 X[47832], X[21301] - 3 X[48172], 2 X[23789] - 3 X[47889], 5 X[31251] - 6 X[47831], 4 X[31288] - 3 X[47828], 3 X[47821] - 2 X[48005], 3 X[47822] - 2 X[48012], 3 X[47823] - 2 X[48018], 3 X[47838] - 2 X[48030], 3 X[47840] - 2 X[48059], 3 X[47841] - 2 X[48066], 3 X[47888] - 2 X[48017}

X(48305) lies on these lines: {10, 47872}, {512, 47694}, {513, 4170}, {514, 4775}, {522, 667}, {523, 4040}, {650, 21837}, {659, 4151}, {663, 784}, {693, 6004}, {826, 47695}, {830, 4010}, {832, 7650}, {900, 1019}, {1027, 29288}, {1125, 47893}, {1491, 47839}, {1734, 4874}, {1960, 4560}, {2533, 3887}, {3309, 7662}, {3716, 4705}, {4024, 8632}, {4063, 48248}, {4129, 4800}, {4367, 8714}, {4448, 48003}, {4501, 47129}, {4770, 47793}, {4804, 29070}, {4806, 47948}, {4809, 21192}, {4822, 48153}, {4823, 48189}, {4824, 48058}, {4895, 29298}, {4985, 38469}, {4992, 48086}, {6161, 29051}, {6372, 17166}, {7927, 47660}, {9508, 47818}, {17072, 47875}, {21118, 29094}, {21146, 42325}, {21260, 47832}, {21301, 48172}, {23747, 47123}, {23789, 47889}, {24601, 47790}, {29186, 48120}, {29340, 31291}, {29362, 48111}, {31251, 47831}, {31288, 47828}, {47821, 48005}, {47822, 48012}, {47823, 48018}, {47838, 48030}, {47840, 48059}, {47841, 48066}, {47888, 48017}, {47945, 48053}

X(48305) = midpoint of X(i) and X(j) for these {i,j}: {4804, 48150}, {4822, 48153}
X(48305) = reflection of X(i) in X(j) for these {i,j}: {1734, 4874}, {4063, 48248}, {4560, 1960}, {4705, 3716}, {4824, 48058}, {47945, 48053}, {47948, 4806}, {48086, 4992}
X(48305) = crossdifference of every pair of points on line {583, 2277}
X(48305) = barycentric product X(514)*X(32945)
X(48305) = barycentric quotient X(32945)/X(190)
X(48305) = {X(1734),X(4874)}-harmonic conjugate of X(47837)


X(48306) = X(1)X(4977)∩X(523)X(4040)

Barycentrics    a^2*(b - c)*(a^2 - b^2 - 3*b*c - c^2) : :
X(48306) = 3 X[663] - X[1459], 5 X[663] - X[43924], 2 X[1459] - 3 X[2605], 5 X[1459] - 3 X[43924], 5 X[2605] - 2 X[43924], 2 X[17072] - 3 X[48181], X[21302] - 3 X[48165], 2 X[44316] - 3 X[47839], X[44444] - 3 X[47840}

X(48306) lies on these lines: {1, 4977}, {42, 48162}, {43, 48180}, {512, 4057}, {513, 663}, {522, 4794}, {523, 4040}, {612, 48231}, {614, 48178}, {649, 4826}, {659, 4093}, {786, 4375}, {834, 4775}, {900, 3737}, {1919, 4502}, {1960, 3733}, {2254, 31947}, {2483, 4079}, {2488, 39199}, {3709, 21007}, {3716, 4036}, {3720, 48253}, {3920, 48250}, {4449, 28195}, {4491, 6371}, {4724, 4802}, {4777, 42312}, {4895, 8702}, {4926, 17418}, {7191, 48159}, {7252, 22086}, {8653, 23865}, {8674, 17420}, {17072, 48181}, {21111, 21201}, {21173, 28217}, {21302, 48165}, {23282, 29086}, {23655, 48028}, {26102, 48233}, {28147, 48065}, {28175, 47970}, {28199, 47929}, {29051, 30591}, {44316, 47839}, {44444, 47840}

X(48306) = midpoint of X(42312) and X(46385)
X(48306) = reflection of X(i) in X(j) for these {i,j}: {2254, 31947}, {2605, 663}, {3733, 1960}, {4036, 3716}, {21111, 21201}
X(48306) = X(100)-isoconjugate of X(5557)
X(48306) = X(8054)-Dao conjugate of X(5557)
X(48306) = crosspoint of X(1) and X(8701)
X(48306) = crosssum of X(i) and X(j) for these (i,j): {1, 4977}, {522, 3634}
X(48306) = crossdifference of every pair of points on line {9, 583}
X(48306) = barycentric product X(i)*X(j) for these {i,j}: {1, 48003}, {513, 27065}, {514, 3746}, {649, 5564}, {650, 7269}, {1019, 4015}
X(48306) = barycentric quotient X(i)/X(j) for these {i,j}: {649, 5557}, {3746, 190}, {4015, 4033}, {5564, 1978}, {7269, 4554}, {27065, 668}, {48003, 75}
X(48306) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3709, 21007, 22108}, {4079, 8632, 2483}


X(48307) = X(1)X(513)∩X(523)X(4040)

Barycentrics    a*(a - b - c)*(b - c)*(a^2 + a*b + a*c - b*c) : :
X(48307) = 2 X[10] - 3 X[48165], 3 X[663] - X[17418], 3 X[3737] - 2 X[17418], X[3737] + 2 X[42312], X[17418] + 3 X[42312], 4 X[1125] - 3 X[48246], 5 X[1698] - 6 X[48181], 3 X[6129] - 2 X[14353], 4 X[14353] - 3 X[23800], 7 X[3624] - 6 X[48230], 2 X[17072] - 3 X[48186], X[21302] - 3 X[48173}

X(48307) lies on these lines: {1, 513}, {9, 3063}, {10, 48165}, {33, 44426}, {37, 21007}, {42, 47821}, {43, 47822}, {521, 4162}, {522, 663}, {523, 4040}, {612, 47804}, {614, 44429}, {650, 4501}, {656, 3887}, {659, 4139}, {885, 4336}, {900, 2605}, {1125, 48246}, {1449, 20980}, {1459, 3667}, {1698, 48181}, {1769, 6003}, {2804, 40500}, {2999, 47760}, {3247, 21348}, {3287, 4526}, {3309, 6129}, {3624, 48230}, {3709, 4435}, {3716, 4086}, {3720, 47824}, {3738, 6615}, {3875, 20906}, {3907, 4985}, {3920, 47805}, {3961, 4448}, {4000, 40474}, {4057, 4063}, {4129, 17922}, {4360, 20949}, {4406, 17218}, {4449, 4778}, {4724, 28147}, {4776, 5256}, {4794, 28161}, {4802, 47970}, {4811, 47729}, {4815, 29051}, {4879, 6371}, {4895, 17420}, {5268, 47803}, {5272, 47802}, {5287, 47762}, {6006, 43924}, {7190, 24002}, {7191, 48164}, {7203, 48013}, {7269, 23810}, {7650, 29066}, {7661, 28292}, {8632, 21389}, {14874, 21102}, {15313, 21189}, {16470, 22157}, {16569, 48197}, {16667, 39521}, {17011, 47759}, {17019, 47763}, {17022, 47761}, {17072, 48186}, {19372, 44923}, {21302, 48173}, {23655, 48043}, {25502, 48216}, {26102, 47823}, {28155, 48065}, {28191, 47929}, {29820, 36848}, {30591, 47724}

X(48307) = midpoint of X(i) and X(j) for these {i,j}: {663, 42312}, {4811, 47729}, {4895, 17420}
X(48307) = reflection of X(i) in X(j) for these {i,j}: {3737, 663}, {4063, 4057}, {4086, 3716}, {21102, 21201}, {21173, 2605}, {23800, 6129}, {46385, 4794}, {47724, 30591}
X(48307) = X(i)-Ceva conjugate of X(j) for these (i,j): {646, 9}, {20295, 4063}
X(48307) = X(i)-isoconjugate of X(j) for these (i,j): {7, 40519}, {56, 8050}, {59, 40086}, {65, 34594}, {100, 20615}, {109, 596}, {651, 39798}, {664, 40148}, {1400, 37205}, {1415, 40013}, {4551, 39949}, {4559, 39747}, {4565, 40085}
X(48307) = X(i)-Dao conjugate of X(j) for these (i, j): (1, 8050), (11, 596), (649, 3669), (1146, 40013), (4129, 3676), (6615, 40086), (8054, 20615), (38991, 39798), (39025, 40148), (40582, 37205), (40602, 34594)
X(48307) = crosspoint of X(i) and X(j) for these (i,j): {21, 3699}, {20295, 47793}
X(48307) = crosssum of X(i) and X(j) for these (i,j): {65, 43924}, {513, 24443}
X(48307) = crossdifference of every pair of points on line {44, 583}
X(48307) = barycentric product X(i)*X(j) for these {i,j}: {1, 47793}, {8, 4063}, {9, 20295}, {21, 4129}, {55, 20949}, {78, 17922}, {312, 4057}, {318, 22154}, {333, 4132}, {514, 3871}, {522, 32911}, {595, 4391}, {644, 21208}, {646, 8054}, {650, 4360}, {663, 18140}, {2220, 35519}, {3063, 40087}, {3293, 4560}, {3737, 3995}, {4222, 6332}, {4435, 40093}
X(48307) = barycentric quotient X(i)/X(j) for these {i,j}: {9, 8050}, {21, 37205}, {41, 40519}, {284, 34594}, {522, 40013}, {595, 651}, {649, 20615}, {650, 596}, {663, 39798}, {2170, 40086}, {2220, 109}, {3063, 40148}, {3293, 4552}, {3737, 39747}, {3871, 190}, {4041, 40085}, {4057, 57}, {4063, 7}, {4129, 1441}, {4132, 226}, {4222, 653}, {4360, 4554}, {7252, 39949}, {8054, 3669}, {17922, 273}, {18140, 4572}, {20295, 85}, {20949, 6063}, {21208, 24002}, {22154, 77}, {32911, 664}, {47793, 75}
X(48307) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 21007, 21390}, {8632, 21834, 21389}


X(48308) = ISOGONAL CONJUGATE OF X(46422)

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

X(48308) lies on the cubic K1273 and these lines: {40, 30556}, {198, 2066}, {208, 16232}, {221, 6502}, {1806, 2360}, {2262, 7133}, {30335, 34121}

X(48308) = isogonal conjugate of X(46422)
X(48308) = isogonal conjugate of the anticomplement of X(1659)
X(48308) = X(i)-isoconjugate of X(j) for these (i,j): {1, 46422}, {2, 32555}, {13389, 34909}
X(48308) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 46422), (32664, 32555)
X(48308) = crosssum of X(40) and X(38004)
X(48308) = barycentric product X(i)*X(j) for these {i,j}: {1, 46433}, {2362, 34908}
X(48308) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 46422}, {31, 32555}, {46433, 75}


X(48309) = ISOGONAL CONJUGATE OF X(46421)

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

X(48309) lies on the cubic K1273 and these lines: {40, 30557}, {198, 5414}, {208, 2362}, {221, 2067}, {1805, 2360}, {2262, 42013}, {30336, 34125}

X(48309) = isogonal conjugate of X(46421)
X(48309) = isogonal conjugate of the anticomplement of X(13390)
X(48309) = X(i)-isoconjugate of X(j) for these (i,j): {1, 46421}, {2, 32556}, {13388, 34910}
X(48309) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 46421), (32664, 32556)
X(48309) = barycentric product X(i)*X(j) for these {i,j}: {1, 46434}, {16232, 34907}
X(48309) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 46421}, {31, 32556}, {46434, 75}


X(48310) = COMPLEMENT OF X(21358)

Barycentrics    8*a^2+5*b^2+5*c^2 : :
X(48262) = 5*X(2)+X(6), 13*X(2)-X(69), 4*X(2)-X(141), 2*X(2)+X(597), 7*X(2)-X(599), 11*X(2)+X(1992), X(2)+2*X(3589), 7*X(2)+5*X(3618), 19*X(2)-7*X(3619), 14*X(2)+X(3629), 17*X(2)-2*X(3631), 11*X(2)-5*X(3763), 7*X(2)+X(5032), 11*X(2)+4*X(6329), 8*X(2)+X(8584), 19*X(2)-X(15533), 17*X(2)+X(15534), 5*X(2)-2*X(20582), 13*X(2)+2*X(20583), 5*X(2)-X(21356), 10*X(2)-X(22165), 19*X(2)+2*X(32455), 7*X(2)-4*X(34573), 19*X(2)+8*X(41153), X(2)-7*X(47355)

See Antreas Hatzipolakis and César Lozada, euclid 4963.

X(48310) lies on these lines: {2, 6}, {5, 10168}, {30, 17508}, {140, 5476}, {182, 547}, {373, 9019}, {381, 44882}, {511, 11539}, {518, 19883}, {542, 15699}, {549, 5480}, {576, 16239}, {598, 6656}, {632, 25555}, {1153, 6680}, {1350, 15702}, {1351, 15723}, {1352, 15703}, {1386, 3828}, {1503, 5055}, {1656, 11179}, {1698, 47356}, {3090, 47353}, {3098, 11812}, {3416, 19876}, {3524, 29181}, {3533, 11477}, {3545, 5085}, {3564, 47599}, {3624, 47358}, {3628, 8550}, {3818, 10109}, {3845, 5092}, {3849, 5103}, {4045, 32479}, {4048, 7615}, {4265, 36006}, {4370, 17399}, {4405, 5222}, {4422, 16676}, {4663, 19878}, {4665, 17367}, {4884, 29684}, {4969, 29613}, {5020, 35707}, {5026, 5461}, {5031, 10150}, {5054, 14561}, {5056, 10541}, {5067, 11180}, {5071, 43273}, {5096, 16858}, {5159, 47544}, {5206, 8359}, {5237, 37340}, {5238, 37341}, {5349, 11303}, {5350, 11304}, {5642, 25328}, {5749, 7231}, {5845, 38088}, {5846, 19875}, {5969, 9167}, {6034, 41134}, {6247, 14787}, {6593, 45311}, {6683, 7619}, {6688, 16776}, {6698, 15303}, {6704, 7817}, {6723, 25329}, {7263, 17368}, {7495, 20192}, {7617, 7834}, {7618, 33237}, {7622, 8368}, {7757, 40332}, {7775, 8364}, {7784, 18841}, {7789, 11165}, {7808, 8176}, {7810, 39784}, {7859, 8370}, {7866, 31417}, {7870, 9606}, {7889, 8369}, {7913, 37350}, {8362, 15810}, {8681, 12045}, {8703, 19130}, {8787, 19662}, {9024, 38090}, {9041, 25055}, {9053, 38087}, {9466, 32449}, {9478, 43535}, {9607, 16895}, {9813, 15826}, {9830, 14971}, {9909, 31521}, {10124, 18583}, {10183, 47074}, {10989, 47453}, {11147, 15815}, {11188, 44323}, {12040, 24256}, {13169, 41595}, {14853, 15709}, {15059, 34319}, {15693, 31670}, {15694, 20423}, {15695, 43621}, {15708, 31884}, {15713, 21850}, {16042, 19596}, {16045, 34505}, {16673, 17045}, {16897, 34604}, {17023, 41310}, {17132, 17382}, {17133, 17359}, {17243, 46845}, {17290, 35578}, {17341, 29622}, {17353, 41311}, {17357, 29574}, {17369, 29630}, {17371, 29617}, {17504, 38136}, {17542, 36741}, {19145, 42603}, {19146, 42602}, {19697, 34504}, {19709, 46264}, {21515, 36743}, {21527, 37503}, {21533, 36744}, {22112, 32217}, {22330, 41992}, {22579, 43372}, {22580, 36770}, {23334, 33230}, {24206, 46267}, {25322, 45672}, {25326, 35073}, {25327, 40478}, {28538, 38049}, {29012, 38071}, {29317, 45759}, {29603, 31285}, {31191, 34824}, {32154, 44102}, {33751, 44903}, {34380, 41984}, {34507, 48154}, {37439, 44110}, {39561, 41985}, {39576, 46337}, {42785, 44580}, {44106, 44210}

X(48310) = midpoint of X(i) and X(j) for these {i, j}: {2, 47352}, {6, 21356}, {599, 5032}, {3524, 38072}, {3545, 5085}, {5054, 14561}, {5055, 38064}, {6034, 41134}, {11539, 38079}, {15699, 38110}, {17504, 38136}, {19875, 38023}, {19883, 38089}, {25055, 38047}, {38087, 38314}, {38088, 38093}
X(48310) = reflection of X(i) in X(j) for these (i, j): (597, 47352), (3629, 5032), (5031, 10150), (21167, 5054), (21356, 20582), (22165, 21356), (47352, 3589)
X(48310) = complement of X(21358)
X(48310) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 6, 20582), (2, 597, 141), (2, 599, 34573), (2, 1992, 3763), (2, 3589, 597), (2, 3618, 599), (2, 7792, 11168), (2, 7875, 22329), (2, 11174, 22110), (2, 42849, 44377), (2, 44367, 16988), (6, 11160, 41149), (6, 20582, 22165), (141, 597, 8584), (182, 547, 47354), (597, 22165, 6), (3589, 34573, 3618), (3618, 34573, 3629), (3629, 34573, 141), (3630, 3763, 141), (3763, 6329, 3630), (5092, 25565, 3845), (8362, 19661, 15810), (20582, 22165, 141)


X(48311) = X(2)X(13)∩X(547)X(6771)

Barycentrics    -2*S*(8*a^2+5*b^2+5*c^2)+(4*a^4-11*(b^2+c^2)*a^2+7*(b^2-c^2)^2)*sqrt(3) : :
X(48311) = 5*X(2)+X(13), 13*X(2)-X(616), 4*X(2)-X(618), 2*X(2)+X(5459), 7*X(2)-X(5463), X(2)+2*X(6669), 11*X(2)+4*X(35019), 19*X(2)-X(35751), 17*X(2)+X(35752), 11*X(2)-2*X(36768), 10*X(2)-X(36769), 11*X(2)-5*X(36770), 8*X(2)+X(47865), 13*X(13)+5*X(616), 4*X(13)+5*X(618), 2*X(13)-5*X(5459), 7*X(13)+5*X(5463), X(13)-10*X(6669), X(13)-5*X(22489), 11*X(13)-20*X(35019), 7*X(13)-X(35749), 19*X(13)+5*X(35751), 17*X(13)-5*X(35752), 11*X(13)+10*X(36768), 2*X(13)+X(36769), 8*X(13)-5*X(47865)

See Antreas Hatzipolakis and César Lozada, euclid 4963.

X(48311) lies on these lines: {2, 13}, {531, 14971}, {542, 15699}, {547, 6771}, {549, 5478}, {619, 5461}, {630, 33477}, {635, 9763}, {3090, 41042}, {3545, 21156}, {3763, 22580}, {3828, 11705}, {5055, 41022}, {5460, 6722}, {5464, 14061}, {5470, 41134}, {5473, 15702}, {5617, 15703}, {6671, 31693}, {6673, 37341}, {6772, 43029}, {7486, 41020}, {10109, 22796}, {10124, 20252}, {10187, 42062}, {11305, 13083}, {12781, 19876}, {13103, 15723}, {13917, 32788}, {13982, 32787}, {15694, 25154}, {16001, 16239}, {16645, 47857}, {16963, 47855}, {23303, 41620}, {31274, 31695}, {31696, 42957}, {33560, 35304}, {34508, 47518}, {36521, 42492}, {37786, 40334}, {37835, 47863}, {41745, 43028}, {42035, 43447}, {42124, 47867}, {42923, 47866}

X(48311) = midpoint of X(i) and X(j) for these {i, j}: {2, 22489}, {3545, 21156}, {5470, 41134}
X(48311) = reflection of X(i) in X(j) for these (i, j): (5459, 22489), (22489, 6669)
X(48311) = inverse of X(35749) in inner-Napoleon circle
X(48311) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 5459, 618), (2, 6669, 5459), (13, 5463, 35749), (618, 5459, 47865), (5459, 36769, 13), (6302, 6306, 35019)


X(48312) = X(2)X(14)∩X(547)X(6774)

Barycentrics    2*S*(8*a^2+5*b^2+5*c^2)+(4*a^4-11*(b^2+c^2)*a^2+7*(b^2-c^2)^2)*sqrt(3) : :
X(48312) = 5*X(2)+X(14), 13*X(2)-X(617), 4*X(2)-X(619), 2*X(2)+X(5460), 7*X(2)-X(5464), X(2)+2*X(6670), 11*X(2)+4*X(35020), 19*X(2)-X(36329), 17*X(2)+X(36330), 8*X(2)+X(47866), 10*X(2)-X(47867), 13*X(14)+5*X(617), 4*X(14)+5*X(619), 2*X(14)-5*X(5460), 7*X(14)+5*X(5464), X(14)-10*X(6670), X(14)-5*X(22490), 11*X(14)-20*X(35020), 7*X(14)-X(36327), 19*X(14)+5*X(36329), 17*X(14)-5*X(36330), 8*X(14)-5*X(47866), 2*X(14)+X(47867)

See Antreas Hatzipolakis and César Lozada, euclid 4963.

X(48312) lies on these lines: {2, 14}, {530, 14971}, {542, 15699}, {547, 6774}, {549, 5479}, {618, 5461}, {629, 33476}, {636, 9761}, {671, 36770}, {3090, 41043}, {3545, 21157}, {3763, 22579}, {3828, 11706}, {5055, 41023}, {5459, 6722}, {5463, 14061}, {5469, 41134}, {5474, 15702}, {5613, 15703}, {6672, 31694}, {6674, 37340}, {6775, 43028}, {7486, 41021}, {10109, 22797}, {10124, 20253}, {10188, 42063}, {11306, 13084}, {12780, 19876}, {13102, 15723}, {13916, 32788}, {13981, 32787}, {15694, 25164}, {16002, 16239}, {16644, 47858}, {16962, 47856}, {23302, 41621}, {31274, 31696}, {31695, 36768}, {33561, 35303}, {34509, 47520}, {36521, 42493}, {36769, 42121}, {37785, 40335}, {37832, 47864}, {41746, 43029}, {42036, 43446}, {42922, 47865}

X(48312) = midpoint of X(i) and X(j) for these {i, j}: {2, 22490}, {3545, 21157}, {5469, 41134}
X(48312) = reflection of X(i) in X(j) for these (i, j): (5460, 22490), (22490, 6670)
X(48312) = inverse of X(36327) in outer-Napoleon circle
X(48312) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 5460, 619), (2, 6670, 5460), (14, 5464, 36327), (619, 5460, 47866), (5460, 47867, 14), (6303, 6307, 35020)


X(48313) = X(2)X(14)∩X(549)X(7684)

Barycentrics    -2*S*(8*a^2+5*b^2+5*c^2)+(8*a^4-13*(b^2+c^2)*a^2+5*(b^2-c^2)^2)*sqrt(3) : :
X(48313) = 5*X(2)+X(15), 13*X(2)-X(621), 4*X(2)-X(623), X(2)+2*X(6671), 11*X(2)-5*X(40334), 2*X(2)+X(45879), 13*X(15)+5*X(621), 4*X(15)+5*X(623), X(15)-10*X(6671), 2*X(15)-5*X(45879), 2*X(547)+X(13350), 2*X(549)+X(7684), 5*X(618)+4*X(42496), 4*X(621)-13*X(623), 2*X(621)+13*X(45879), X(623)+8*X(6671), 11*X(623)-20*X(40334), X(623)+2*X(45879), 4*X(6671)-X(45879), 10*X(40334)+11*X(45879)

See Antreas Hatzipolakis and César Lozada, euclid 4963.

X(48313) lies on these lines: {2, 14}, {511, 11539}, {530, 5215}, {547, 13350}, {549, 7684}, {618, 42496}, {629, 9761}, {636, 33475}, {3545, 21158}, {3828, 11707}, {5055, 44666}, {5459, 43416}, {5611, 15723}, {6669, 35304}, {6673, 11304}, {6694, 42948}, {10304, 41036}, {11309, 34508}, {11542, 36769}, {11812, 36755}, {13084, 22238}, {14538, 15702}, {15703, 20428}, {19883, 44659}, {21356, 36757}, {22510, 41134}, {33560, 35931}, {36770, 37786}, {37172, 42921}

X(48313) = midpoint of X(i) and X(j) for these {i, j}: {3545, 21158}, {10304, 41036}, {21356, 36757}, {22510, 41134}
X(48313) = inverse of X(36327) in inner-Napoleon circle
X(48313) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 6671, 45879), (2, 45879, 623), (47361, 47362, 36327)


X(48314) = X(2)X(13)∩X(549)X(7685)

Barycentrics    2*S*(8*a^2+5*b^2+5*c^2)+(8*a^4-13*(b^2+c^2)*a^2+5*(b^2-c^2)^2)*sqrt(3) : :
X(48314) = 5*X(2)+X(16), 13*X(2)-X(622), 4*X(2)-X(624), X(2)+2*X(6672), 11*X(2)-5*X(40335), 2*X(2)+X(45880), 13*X(16)+5*X(622), 4*X(16)+5*X(624), X(16)-10*X(6672), 2*X(16)-5*X(45880), 2*X(547)+X(13349), 2*X(549)+X(7685), 5*X(619)+4*X(42497), 4*X(622)-13*X(624), 2*X(622)+13*X(45880), X(624)+8*X(6672), 11*X(624)-20*X(40335), X(624)+2*X(45880), 4*X(6672)-X(45880), 10*X(40335)+11*X(45880)

See Antreas Hatzipolakis and César Lozada, euclid 4963.

X(48314) lies on these lines: {2, 13}, {511, 11539}, {531, 5215}, {547, 13349}, {549, 7685}, {619, 42497}, {630, 9763}, {635, 33474}, {3545, 21159}, {3828, 11708}, {5055, 44667}, {5460, 43417}, {5615, 15723}, {6670, 35303}, {6674, 11303}, {6695, 42949}, {10304, 41037}, {11310, 34509}, {11543, 47867}, {11812, 36756}, {13083, 22236}, {14539, 15702}, {15703, 20429}, {19883, 44660}, {21356, 36758}, {22511, 41134}, {33561, 35932}, {37173, 42920}

X(48314) = midpoint of X(i) and X(j) for these {i, j}: {3545, 21159}, {10304, 41037}, {21356, 36758}, {22511, 41134}
X(48314) = inverse of X(35749) in outer-Napoleon circle
X(48314) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 6672, 45880), (2, 45880, 624), (47363, 47364, 35749)


X(48315) = CENTER OF THE CIRCUMCONIC OF ABC AND THE TANGENTIAL TRIANGLE-OF-FEUERBACH HYPERBOLA-OF-MEDIAL TRIANGLE

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

See Kadir Altintas, Ivan Pavlov and César Lozada, euclid 4964.

X(48315) lies on the Steiner inellipse and these lines: {2, 14727}, {513, 35508}, {656, 1084}, {1015, 3900}, {1086, 46399}, {1146, 17072}, {1575, 23972}, {3126, 39014}, {13466, 44664}, {35093, 44357}

X(48315) = complement of X(14727)
X(48315) = X(2)-Ceva conjugate of-X(42341)
X(48315) = X(31)-complementary conjugate of-X(42341)
X(48315) = center of the circumconic {{A, B, C, X(2), X(1376)}}
X(48315) = touchpoint of the tripolar of X(42341) and Steiner inellipse
X(48315) = barycentric square of X(42341)


X(48316) = CENTER OF THE CIRCUMCONIC OF ABC AND THE TANGENTIAL TRIANGLE-OF-JERABEK HYPERBOLA-OF-MEDIAL TRIANGLE

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

See Kadir Altintas, Ivan Pavlov and César Lozada, euclid 4964.

X(48316) lies on the Steiner inellipse and these lines: {512, 35071}, {520, 1084}, {3229, 23976}, {35067, 46841}, {38974, 39020}

X(48316) = center of the circumconic {{A, B, C, X(2), X(9306)}}


X(48317) = CENTER OF THE CIRCUMCONIC OF ABC AND THE TANGENTIAL TRIANGLE-OF-FEUERBACH HYPERBOLA-OF-ORTHIC TRIANGLE

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

See Kadir Altintas, Ivan Pavlov and César Lozada, euclid 4964.

X(48317) lies on the nine-point circle and these lines: {2, 40119}, {4, 691}, {25, 14729}, {30, 31842}, {113, 3564}, {114, 403}, {115, 2489}, {120, 37982}, {122, 36189}, {123, 37986}, {125, 3566}, {126, 468}, {127, 14120}, {131, 11799}, {132, 10151}, {136, 16229}, {186, 31843}, {235, 42426}, {381, 42424}, {427, 31655}, {523, 5139}, {868, 16177}, {1560, 3291}, {1596, 25641}, {2971, 45161}, {3143, 38971}, {5512, 8754}, {5866, 37777}, {6623, 18809}, {12294, 33330}, {14568, 44953}, {14852, 18348}, {35235, 46436}, {35968, 37987}, {41360, 47293}

X(48317) = midpoint of X(i) and X(j) for these {i, j}: {4, 40118}, {468, 5203}
X(48317) = complement of the circumperp conjugate of X(40118)
X(48317) = complementary conjugate of the circumnormal-isogonal conjugate of X(40118)
X(48317) = X(2)-Ceva conjugate of-X(14273)
X(48317) = X(i)-complementary conjugate of-X(j) for these (i, j): (31, 14273), (810, 40349)
X(48317) = center of the circumconic {{A, B, C, X(4), X(468)}}
X(48317) = inverse of X(691) in polar circle
X(48317) = inverse of X(40119) in orthoptic circle of Steiner inellipse
X(48317) = orthoassociate of X(691)
X(48317) = orthojoin of X(14273)
X(48317) = Poncelet point of X(i) for these i: {468, 2501, 5203, 10603, 14052, 18020, 40118, 44146}
X(48317) = barycentric product X(338)*X(41616)
X(48317) = trilinear product X(1109)*X(41616)


X(48318) = CENTER OF THE CIRCUMCONIC OF ABC AND THE TANGENTIAL TRIANGLE-OF-JERABEK HYPERBOLA-OF-ORTHIC TRIANGLE

Barycentrics    (b^2-c^2)^2*((b^2+c^2)*a^2-(b^2-c^2)^2)*(a^8-2*(b^2+c^2)*a^6+(b^4+b^2*c^2+c^4)*a^4-(b^2-c^2)^2*b^2*c^2)*(a^12-4*(b^2+c^2)*a^10+3*(2*b^4+3*b^2*c^2+2*c^4)*a^8-2*(b^2+c^2)*(2*b^4+b^2*c^2+2*c^4)*a^6+(b^4+c^4)*(b^2+c^2)^2*a^4-2*(b^4-c^4)*(b^2-c^2)*b^2*c^2*a^2+(b^2-c^2)^4*b^2*c^2)*((b^4+b^2*c^2+c^4)*a^20-2*(b^2+c^2)*(4*b^4+b^2*c^2+4*c^4)*a^18+(28*b^8+28*c^8+(37*b^4+40*b^2*c^2+37*c^4)*b^2*c^2)*a^16-4*(b^2+c^2)*(14*b^8+14*c^8+(3*b^4+16*b^2*c^2+3*c^4)*b^2*c^2)*a^14+(70*b^12+70*c^12+(65*b^8+65*c^8+9*(8*b^4+9*b^2*c^2+8*c^4)*b^2*c^2)*b^2*c^2)*a^12-2*(b^2+c^2)*(28*b^12+28*c^12-(15*b^8+15*c^8-(32*b^4-11*b^2*c^2+32*c^4)*b^2*c^2)*b^2*c^2)*a^10+(28*b^16+28*c^16-(5*b^12+5*c^12-2*(6*b^4+7*b^2*c^2+6*c^4)*(b^4-b^2*c^2+c^4)*b^2*c^2)*b^2*c^2)*a^8-4*(b^4-c^4)*(b^2-c^2)*(2*b^12+2*c^12+(2*b^2-3*b*c+2*c^2)*(2*b^2+3*b*c+2*c^2)*b^4*c^4)*a^6+(b^16+c^16+(2*b^8+2*c^8-(3*b^4+4*b^2*c^2+3*c^4)*b^2*c^2)*b^4*c^4)*(b^2-c^2)^2*a^4+2*(b^4-c^4)*(b^2-c^2)^3*b^6*c^6*a^2-(b^2-c^2)^6*b^6*c^6) : :

See Kadir Altintas, Ivan Pavlov and César Lozada, euclid 4964.

X(48318) lies on the nine-point circle and these lines: { }


X(48319) = CENTER OF THE CIRCUMCONIC OF ABC AND THE TANGENTIAL TRIANGLE-OF-JOHNSON CIRCUMCONIC-OF-ORTHIC TRIANGLE

Barycentrics    (b^2-c^2)^2*((b^2+c^2)*a^2-(b^2-c^2)^2)*(a^12-4*(b^2+c^2)*a^10+(6*b^4+7*b^2*c^2+6*c^4)*a^8-2*(b^2+c^2)*(2*b^4-b^2*c^2+2*c^4)*a^6+(b^4+c^4)^2*a^4-2*(b^4-c^4)*(b^2-c^2)*b^2*c^2*a^2+(b^2-c^2)^4*b^2*c^2)*(a^12-4*(b^2+c^2)*a^10+3*(2*b^4+3*b^2*c^2+2*c^4)*a^8-2*(b^2+c^2)*(2*b^4+b^2*c^2+2*c^4)*a^6+(b^4+c^4)^2*a^4+2*(b^4-c^4)*(b^2-c^2)*b^2*c^2*a^2-(b^2-c^2)^4*b^2*c^2)*((b^4+b^2*c^2+c^4)*a^24-2*(b^2+c^2)*(5*b^4+2*b^2*c^2+5*c^4)*a^22+(45*b^8+45*c^8+4*(18*b^4+19*b^2*c^2+18*c^4)*b^2*c^2)*a^20-12*(b^2+c^2)*(10*b^8+10*c^8+(6*b^4+11*b^2*c^2+6*c^4)*b^2*c^2)*a^18+(210*b^12+210*c^12+(294*b^8+294*c^8+(290*b^4+283*b^2*c^2+290*c^4)*b^2*c^2)*b^2*c^2)*a^16-4*(b^2+c^2)*(63*b^12+63*c^12+(50*b^4-3*b^2*c^2+50*c^4)*b^4*c^4)*a^14+4*(b^2-c^2)^6*(b^2+c^2)*b^6*c^6*a^2+2*(105*b^16+105*c^16+2*(21*b^12+21*c^12+(6*b^8+6*c^8+(12*b^4+11*b^2*c^2+12*c^4)*b^2*c^2)*b^2*c^2)*b^2*c^2)*a^12-(b^2-c^2)^8*b^6*c^6-4*(b^2+c^2)*(30*b^16+30*c^16-(42*b^12+42*c^12-(31*b^8+31*c^8-(25*b^4-24*b^2*c^2+25*c^4)*b^2*c^2)*b^2*c^2)*b^2*c^2)*a^10+(45*b^20+45*c^20-(63*b^16+63*c^16+(11*b^12+11*c^12-2*(23*b^8+23*c^8-(13*b^4-b^2*c^2+13*c^4)*b^2*c^2)*b^2*c^2)*b^2*c^2)*b^2*c^2)*a^8-2*(b^4-c^4)*(b^2-c^2)*(5*b^16+5*c^16-2*(4*b^12+4*c^12-(b^8+c^8+(b^4-5*b^2*c^2+c^4)*b^2*c^2)*b^2*c^2)*b^2*c^2)*a^6+(b^16+c^16-2*(b^8+c^8+(2*b^4+7*b^2*c^2+2*c^4)*b^2*c^2)*b^4*c^4)*(b^2-c^2)^4*a^4) : :

See Kadir Altintas, Ivan Pavlov and César Lozada, euclid 4964.

X(48319) lies on the nine-point circle and these lines: { }

leftri

Points in a [X(1)X(513), X(1)X(514)] coordinate system: X(48320)-X(48340)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1,L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1: b c (2a - b - c) α + c a (2b - c - a) β + a b (2 c - a - b) γ = 0.

L2: (b^2 + c^2 - a b - a c) α (c^2 + a^2 - b c - b a) β (a^2 + b^2 - c a - c b) γ = 0.

The origin is given by (0,0) = X(1) = a : b : c.

Barycentrics u : v : w for a point U = (x,y) in this system are given by

u : v : w = (b - c) (a (a - b)(a - c) - a x - y) : : ,

where, as functions of a,b,c, the coordinate x is symmetric and homogeneous of degree 2, and y is symmetric and homogeneous of degree 3.

The appearance of {x,y}, k in the following table means that (x,y) = X(k):

{-2 (a b+a c+b c), a b c}, 48144}
{-2 (a b+a c+b c), a^3+b^3+c^3}, 47676
{-((2 a b c)/(a+b+c)), a b c}, 1459
{-2 (a b+a c+b c), 2 a b c}, 1019
{-2 (a b+a c+b c), 2 (a+b+c) (a b+a c+b c)}, 47683
{-((2 a b c)/(a+b+c)), 2 a b c}, 3737
{-a b-a c-b c, 0}, 4378
{-a^2-b^2-c^2, a b c}, 48150
{-a^2-b^2-c^2, a^3+b^3+c^3}, 47695
{-a b-a c-b c, a b c}, 4367
{-((a b c)/(a+b+c)), a b c}, 2605
{-a^2-b^2-c^2, 2 a b c}, 48111
{-a b-a c-b c, 2 a b c}, 667
{1/2 (-a^2-b^2-c^2), a^3+b^3+c^3}, 47131
{0, -a b c}, 4449
{0, -a^3-b^3-c^3}, 47728
{0, 0}, 1
{0, a b c}, 663
{0, a^3+b^3+c^3}, 47691
{0, 2 a b c}, 4040
{0, 2 (a^3+b^3+c^3)}, 47725
{1/2 (a^2+b^2+c^2), a b c}, 48136
{1/2 (a^2+b^2+c^2), 2 a b c}, 48099
{a^2+b^2+c^2, -a^3-b^3-c^3}, 3904
{a b+a c+b c, -a b c}, 4879
{a b+a c+b c, 0}, 4775
{a^2+b^2+c^2, a b c}, 48131
{a^2+b^2+c^2, a^3+b^3+c^3}, 47652
{a^2+b^2+c^2, 2 a b c}, 14349
{2 (a^2+b^2+c^2), a b c}, 48122
{2 (a^2+b^2+c^2), a^3+b^3+c^3}, 47686
{2 (a^2+b^2+c^2), 2 a b c}, 48086
{-2*(a*b + a*c + b*c), 0}, 48320
{(-2*a*b*c)/(a + b + c), 0}, 48281
{-2*(a*b + a*c + b*c), (a + b + c)*(a*b + a*c + b*c)}, 48328
{-a^2 - b^2 - c^2, -(a*b*c)}, 48322
{-(a*b) - a*c - b*c, -(a*b*c)}, 48323
{-a^2 - b^2 - c^2, 0}, 48324
{-(a*b) - a*c - b*c, ((a + b + c)*(a*b + a*c + b*c))/2}, 48325
{-(a*b) - a*c - b*c, a^3 + b^3 + c^3}, 48326
{-(a*b) - a*c - b*c, (a + b + c)*(a*b + a*c + b*c)}, 48288
{(-a^2 - b^2 - c^2)/2, 0}, 48327
{(-a^2 - b^2 - c^2)/2, (a^3 + b^3 + c^3)/2}, 48286
{(-(a*b) - a*c - b*c)/2, (a*b*c)/2}, 48328
{(-(a*b) - a*c - b*c)/2, ((a + b + c)*(a*b + a*c + b*c))/2}, 48892
{(-a^2 - b^2 - c^2)/2, a*b*c}, 48329
{(-(a*b) - a*c - b*c)/2, a*b*c}, 48330
{(-(a*b) - a*c - b*c)/2, 2*a*b*c}, 48331
{0, -2*a*b*c}, 48282
{0, (a*b*c)/2}, 48294
{(a^2 + b^2 + c^2)/2, 0}, 48332
{a*b + a*c + b*c, -2*a*b*c}, 48333
{a^2 + b^2 + c^2, -(a*b*c)}, 48344
{a*b + a*c + b*c, -((a + b + c)*(a*b + a*c + b*c))}, 48291
{a^2 + b^2 + c^2, 0}, 48335
{(a*b*c)/(a + b + c), 0}, 48302
{a*b + a*c + b*c, a*b*c}, 48282
{(a*b*c)/(a + b + c), a*b*c}, 48306
{2*(a*b + a*c + b*c), -2*a*b*c}, 48337
{(2*a*b*c)/(a + b + c), -2*a*b*c}, 48293
{2*(a*b + a*c + b*c), -(a*b*c)}, 48338
{2*(a*b + a*c + b*c), -((a + b + c)*(a*b + a*c + b*c))}, 48339
{(2*a*b*c)/(a + b + c), -(a*b*c)}, 48303
{(2*a*b*c)/(a + b + c), 0}, 48307
{(2*a*b*c)/(a + b + c), a*b*c}, 48340
{-2*(a*b + a*c + b*c), -(a*b*c)}, 48341
{(-2*a*b*c)/(a + b + c), -(a*b*c)}, 48342
{-(a*b) - a*c - b*c, (a*b*c)/2}, 48343
{(-(a*b) - a*c - b*c)/2, 0}, 48344
{(-a^2 - b^2 - c^2)/2, (a*b*c)/2}, 48345
{(a^2 + b^2 + c^2)/2, -(a*b*c)}, 48346
{(a*b + a*c + b*c)/2, -1/2*(a*b*c)}, 48347
{(a^2 + b^2 + c^2)/2, (a*b*c)/2}, 48348
{a*b + a*c + b*c, a^3 + b^3 + c^3}, 48349
{(a^3 + b^3 + c^3)/(a + b + c), a*b*c}, 48350
{a*b + a*c + b*c, 2*a*b*c}, 48351
{2*(a*b + a*c + b*c), 0}, 48352
{2*(a*b + a*c + b*c), a*b*c}, 48367


X(48320) = X(1)X(513)∩X(661)X(3960)

Barycentrics    a*(b - c)*(a^2 + a*b + a*c + 3*b*c) : :
X(48320) = 3 X[1] - 2 X[4775], 3 X[4378] - X[4775], 2 X[10] - 3 X[47824], 2 X[649] - 3 X[1019], 4 X[649] - 3 X[4063], 5 X[649] - 3 X[4498], 7 X[649] - 6 X[48011], 5 X[649] - 6 X[48064], X[649] - 3 X[48144], 5 X[1019] - 2 X[4498], 3 X[1019] - X[21385], 7 X[1019] - 4 X[48011], 5 X[1019] - 4 X[48064], 5 X[4063] - 4 X[4498], 3 X[4063] - 2 X[21385], 7 X[4063] - 8 X[48011], 5 X[4063] - 8 X[48064], X[4063] - 4 X[48144], 6 X[4498] - 5 X[21385], 7 X[4498] - 10 X[48011], X[4498] - 5 X[48144], 7 X[21385] - 12 X[48011], 5 X[21385] - 12 X[48064], X[21385] - 6 X[48144], 5 X[48011] - 7 X[48064], 2 X[48011] - 7 X[48144], 2 X[48064] - 5 X[48144], 4 X[1125] - 3 X[47821], 5 X[1698] - 6 X[47823], 4 X[1960] - 3 X[4040], 2 X[1960] - 3 X[4367], 4 X[2516] - 3 X[47965], 7 X[3624] - 6 X[47822], 4 X[3669] - X[47947], 3 X[3669] - X[48026], 3 X[14349] - 2 X[48026], 3 X[47947] - 4 X[48026], 6 X[4129] - 7 X[27138], 2 X[4129] - 3 X[47796], 7 X[27138] - 9 X[47796], 3 X[4379] - 2 X[4791], 3 X[4724] - 5 X[8656], 2 X[4770] - 3 X[48244], 3 X[8643] - 2 X[48065], 3 X[14413] - X[48021], 2 X[48019] - 3 X[48085], X[48019] - 3 X[48131], 4 X[23814] - 3 X[48164], 5 X[30722] - 3 X[47756], 13 X[34595] - 12 X[48197], 3 X[44550] - X[47666], 3 X[45671] - 2 X[48000], 3 X[47888] - 2 X[47967], 3 X[47893] - 2 X[48005}

X(48320) lies on these lines: {1, 513}, {9, 28910}, {10, 47824}, {40, 28537}, {57, 43052}, {239, 514}, {274, 20949}, {512, 21343}, {661, 3960}, {667, 23394}, {693, 29148}, {824, 47681}, {830, 48151}, {870, 4817}, {891, 4784}, {905, 47959}, {918, 47682}, {1018, 6633}, {1125, 47821}, {1577, 29808}, {1698, 47823}, {1960, 4040}, {2254, 4160}, {2401, 39797}, {2515, 30520}, {2516, 47965}, {2530, 47948}, {2787, 21146}, {3294, 16820}, {3306, 23598}, {3624, 47822}, {3669, 14349}, {3762, 4369}, {3768, 28840}, {3777, 48086}, {3803, 47977}, {4129, 27138}, {4379, 4791}, {4382, 29178}, {4384, 47762}, {4401, 47929}, {4449, 6005}, {4508, 31148}, {4724, 8656}, {4770, 48244}, {4776, 16831}, {4801, 29013}, {4834, 29226}, {4905, 8678}, {4922, 29188}, {4978, 6002}, {5214, 28623}, {7659, 14077}, {8643, 48065}, {8672, 21173}, {8712, 47976}, {8714, 17166}, {14413, 48021}, {14838, 47918}, {15309, 29738}, {16552, 21390}, {16823, 47805}, {16826, 47759}, {16828, 48246}, {16830, 23814}, {16832, 47761}, {17175, 17212}, {20906, 32092}, {20963, 21007}, {21104, 29126}, {21301, 23789}, {21389, 28863}, {21391, 28890}, {21392, 47684}, {23796, 36480}, {23876, 47971}, {25512, 48165}, {27673, 47908}, {28398, 47984}, {28758, 47795}, {29029, 47725}, {29033, 48119}, {29037, 47715}, {29062, 47719}, {29066, 48108}, {29118, 47716}, {29132, 47691}, {29150, 48279}, {29158, 47720}, {29170, 48273}, {29196, 47718}, {29212, 47690}, {29487, 43067}, {29545, 48107}, {29807, 47672}, {30722, 47756}, {34595, 48197}, {36531, 36848}, {39577, 44408}, {39586, 44429}, {44550, 47666}, {45671, 48000}, {47888, 47967}, {47893, 48005}, {47906, 48058}, {47911, 48054}, {47912, 48066}, {47942, 48099}, {48081, 48136}

X(48320) = midpoint of X(7192) and X(21222)
X(48320) = reflection of X(i) in X(j) for these {i,j}: {1, 4378}, {661, 3960}, {1019, 48144}, {3762, 4369}, {4040, 4367}, {4063, 1019}, {4498, 48064}, {14349, 3669}, {21301, 23789}, {21385, 649}, {47680, 21104}, {47724, 21146}, {47906, 48058}, {47911, 48054}, {47912, 48066}, {47918, 14838}, {47929, 4401}, {47942, 48099}, {47947, 14349}, {47948, 2530}, {47959, 905}, {47970, 667}, {47977, 3803}, {48081, 48136}, {48085, 48131}, {48086, 3777}
X(48320) = isogonal conjugate of the isotomic conjugate of X(4828)
X(48320) = X(39706)-anticomplementary conjugate of X(21293)
X(48320) = X(4597)-Ceva conjugate of X(1)
X(48320) = X(i)-isoconjugate of X(j) for these (i,j): {55, 46480}, {100, 39974}, {101, 42285}
X(48320) = X(i)-Dao conjugate of X(j) for these (i, j): (223, 46480), (1015, 42285), (4893, 4777), (8054, 39974)
X(48320) = crosspoint of X(i) and X(j) for these (i,j): {81, 4604}, {190, 40434}
X(48320) = crosssum of X(i) and X(j) for these (i,j): {37, 4893}, {513, 17450}, {649, 16666}
X(48320) = crossdifference of every pair of points on line {42, 44}
X(48320) = barycentric product X(i)*X(j) for these {i,j}: {1, 47780}, {6, 4828}, {514, 37633}, {1019, 31025}, {3261, 5035}
X(48320) = barycentric quotient X(i)/X(j) for these {i,j}: {57, 46480}, {513, 42285}, {649, 39974}, {4828, 76}, {5035, 101}, {31025, 4033}, {37633, 190}, {47780, 75}
X(48320) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 21385, 4063}, {1019, 21385, 649}


X(48321) = X(1)X(522)∩X(2)X(4791)

Barycentrics    (b - c)*(-a^3 + a*b^2 + b^2*c + a*c^2 + b*c^2) : :
X(48321) = X[8] - 3 X[48242], 2 X[10] - 3 X[47828], X[4474] - 3 X[47828], 3 X[1019] - 2 X[4932], 3 X[4560] - X[17494], 3 X[4560] + X[21222], X[17494] + 3 X[17496], 3 X[17496] - X[21222], X[48141] - 3 X[48144], 2 X[650] - 3 X[45671], X[3762] - 3 X[45671], 3 X[667] - 2 X[48248], X[693] - 3 X[44550], 2 X[3960] - 3 X[44550], 3 X[905] - 2 X[4885], 4 X[905] - 3 X[47795], 3 X[1577] - 4 X[4885], 2 X[1577] - 3 X[47795], 8 X[4885] - 9 X[47795], 4 X[1125] - 3 X[47832], 5 X[1698] - 6 X[47830], 5 X[3616] - 3 X[48172], 7 X[3624] - 6 X[47831], 3 X[3669] - X[48125], 3 X[4978] - 2 X[48125], 2 X[4036] - 3 X[48228], 3 X[4391] - 5 X[31209], 2 X[4391] - 3 X[47794], 6 X[14838] - 5 X[31209], 4 X[14838] - 3 X[47794], 10 X[31209] - 9 X[47794], 2 X[4770] - 3 X[48225], X[4774] - 3 X[48244], X[4804] - 3 X[14413], 2 X[4823] - 3 X[47796], 2 X[4874] - 3 X[14419], 3 X[14349] - 2 X[48049], 4 X[6050] - 3 X[47817], 2 X[21201] - 3 X[47798], 4 X[19947] - 3 X[48184], 2 X[21051] - 3 X[47888], 2 X[21260] - 3 X[47893], 4 X[31947] - 3 X[48186], X[48114] - 3 X[48131], 5 X[31250] - 6 X[44561], 4 X[31287] - 3 X[45664], 4 X[31288] - 3 X[47872], 3 X[47838] - 2 X[48267}

X(48321) lies on these lines: {1, 522}, {2, 4791}, {8, 48242}, {10, 4474}, {194, 21225}, {239, 514}, {274, 3261}, {330, 1022}, {519, 4814}, {523, 4378}, {525, 36054}, {650, 3762}, {657, 16552}, {661, 29148}, {663, 8714}, {667, 48248}, {693, 3960}, {764, 29362}, {784, 4367}, {814, 2530}, {824, 47682}, {900, 4775}, {905, 1577}, {1125, 47832}, {1491, 2787}, {1698, 47830}, {1734, 3907}, {2254, 29066}, {2526, 28475}, {3004, 29126}, {3227, 35175}, {3616, 48172}, {3624, 47831}, {3669, 4077}, {3737, 28623}, {3776, 47680}, {3777, 29070}, {3887, 47729}, {3904, 4467}, {4036, 16828}, {4088, 29212}, {4151, 4449}, {4160, 47975}, {4170, 48136}, {4382, 23803}, {4384, 47785}, {4391, 14838}, {4462, 48003}, {4508, 47886}, {4705, 29324}, {4770, 48225}, {4774, 48244}, {4777, 29908}, {4804, 14413}, {4823, 47796}, {4874, 14419}, {4905, 29051}, {4976, 30725}, {4983, 29170}, {5283, 6586}, {6002, 14349}, {6050, 47817}, {6332, 7265}, {6603, 28898}, {9534, 20293}, {10015, 17069}, {14422, 48189}, {15309, 47939}, {15420, 47678}, {16815, 21198}, {16823, 21201}, {16825, 21132}, {16826, 47790}, {16830, 47808}, {16831, 47787}, {16832, 46919}, {16834, 43991}, {16975, 24873}, {17175, 17215}, {17899, 41299}, {19853, 48243}, {19947, 48184}, {20295, 29178}, {20517, 21118}, {20907, 32092}, {20954, 31997}, {21051, 47888}, {21260, 47893}, {21301, 29344}, {21302, 48018}, {23598, 24620}, {24719, 29340}, {24720, 47724}, {25512, 31947}, {29013, 48114}, {29033, 46403}, {29037, 48272}, {29062, 48278}, {29132, 47701}, {29150, 48123}, {29152, 48100}, {29176, 48059}, {29186, 48151}, {29238, 48137}, {31250, 44561}, {31287, 45664}, {31288, 47872}, {39586, 47806}, {47677, 47684}, {47838, 48267}

X(48321) = midpoint of X(i) and X(j) for these {i,j}: {3904, 4467}, {4560, 17496}, {4976, 30725}, {17494, 21222}, {47677, 47684}
X(48321) = reflection of X(i) in X(j) for these {i,j}: {693, 3960}, {1577, 905}, {3762, 650}, {4170, 48136}, {4391, 14838}, {4462, 48003}, {4474, 10}, {4707, 4025}, {4978, 3669}, {7265, 6332}, {10015, 17069}, {21118, 20517}, {21301, 48066}, {21302, 48018}, {21385, 48008}, {47680, 3776}, {47724, 24720}, {48189, 14422}
X(48321) = anticomplement of X(4791)
X(48321) = anticomplement of the isogonal conjugate of X(34073)
X(48321) = anticomplement of the isotomic conjugate of X(4604)
X(48321) = complement of the isotomic conjugate of X(46480)
X(48321) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {32, 39364}, {89, 21293}, {101, 21291}, {1576, 30564}, {2163, 150}, {2364, 33650}, {4588, 69}, {4597, 315}, {4604, 6327}, {5385, 21301}, {5549, 3436}, {28607, 149}, {28658, 3448}, {32739, 17488}, {34073, 8}
X(48321) = X(i)-complementary conjugate of X(j) for these (i,j): {39974, 124}, {46480, 2887}
X(48321) = X(4604)-Ceva conjugate of X(2)
X(48321) = X(i)-isoconjugate of X(j) for these (i,j): {100, 46018}, {101, 994}, {163, 45095}
X(48321) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 45095), (1015, 994), (8054, 46018)
X(48321) = crosspoint of X(i) and X(j) for these (i,j): {2, 46480}, {274, 4597}
X(48321) = crosssum of X(213) and X(4775)
X(48321) = crossdifference of every pair of points on line {42, 2183}
X(48321) = barycentric product X(i)*X(j) for these {i,j}: {514, 1150}, {693, 993}, {2278, 3261}, {4025, 5136}, {14299, 18816}
X(48321) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 994}, {523, 45095}, {649, 46018}, {993, 100}, {1150, 190}, {2278, 101}, {5136, 1897}, {14299, 517}
X(48321) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 44550, 3960}, {905, 1577, 47795}, {3762, 45671, 650}, {4391, 14838, 47794}, {4474, 47828, 10}, {4560, 21222, 17494}, {17494, 17496, 21222}


X(48322) = X(1)X(830)∩X(513)X(4162)

Barycentrics    a*(b - c)*(2*a^2 - a*b + b^2 - a*c + 2*b*c + c^2) : :
X(48322) = 4 X[1] - X[48020], 3 X[1] - X[48086], 3 X[48020] - 4 X[48086], 2 X[48086] - 3 X[48131], 2 X[10] - 3 X[47818], 2 X[4895] + X[4979], 2 X[4879] - 3 X[23057], 2 X[47729] + X[48153], 5 X[47936] - 6 X[47977], 2 X[47936] - 3 X[48032], X[47936] - 3 X[48150], 4 X[47977] - 5 X[48032], 3 X[47977] - 5 X[48111], 2 X[47977] - 5 X[48150], 3 X[48032] - 4 X[48111], 2 X[48111] - 3 X[48150], 2 X[650] - 3 X[8643], 3 X[661] - 2 X[47912], 5 X[661] - 4 X[47956], 3 X[661] - 4 X[48099], 3 X[663] - X[47912], 5 X[663] - 2 X[47956], 3 X[663] - 2 X[48099], 5 X[47912] - 6 X[47956], 3 X[47956] - 5 X[48099], 4 X[667] - 3 X[1635], 7 X[667] - 3 X[4825], 3 X[1635] - 2 X[4041], 7 X[1635] - 4 X[4825], 7 X[4041] - 6 X[4825], 4 X[1125] - 3 X[47816], 3 X[1962] - 2 X[42661], 4 X[2490] - 3 X[44729], 2 X[2530] - 3 X[14413], 2 X[2533] - 3 X[47813], 3 X[3251] - X[4983], 3 X[4040] - 2 X[48004], 3 X[47918] - 4 X[48004], 3 X[4120] - 4 X[4990], 2 X[4147] - 3 X[47804], 2 X[4163] - 3 X[47766], 2 X[4490] - 3 X[47811], 3 X[4728] - 2 X[21301], 4 X[4775] - X[48019], 4 X[4874] - 3 X[21052], 4 X[6050] - 5 X[8656], 4 X[17072] - 5 X[24924], 2 X[17072] - 3 X[47820], 5 X[24924] - 6 X[47820}

X(48322) lies on these lines: {1, 830}, {10, 47818}, {512, 4895}, {513, 4162}, {514, 47692}, {649, 3900}, {650, 8643}, {661, 663}, {667, 1635}, {693, 28470}, {788, 23464}, {812, 31291}, {814, 4804}, {832, 4017}, {1019, 3887}, {1125, 47816}, {1769, 9013}, {1960, 4705}, {1962, 42661}, {2254, 4367}, {2484, 4171}, {2490, 44729}, {2530, 14413}, {2533, 47813}, {2787, 48264}, {3251, 4983}, {3309, 48144}, {3803, 4498}, {3907, 47694}, {4024, 29278}, {4040, 4160}, {4120, 4990}, {4147, 47804}, {4163, 47766}, {4369, 21302}, {4378, 6004}, {4462, 48063}, {4490, 47811}, {4504, 17496}, {4546, 43061}, {4728, 21301}, {4775, 4822}, {4794, 47959}, {4801, 48115}, {4874, 21052}, {6005, 48149}, {6050, 8656}, {6161, 6372}, {6332, 48077}, {8645, 21789}, {14349, 47905}, {17072, 24924}, {17166, 29051}, {17420, 38469}, {23755, 23775}, {23877, 47728}, {25569, 47810}, {29208, 48146}, {29246, 48148}, {29274, 48120}, {29288, 48130}, {29350, 47935}, {48023, 48136}

X(48322) = reflection of X(i) in X(j) for these {i,j}: {661, 663}, {2254, 4367}, {4041, 667}, {4462, 48063}, {4498, 3803}, {4546, 43061}, {4705, 1960}, {4729, 649}, {4822, 4775}, {17496, 4504}, {21302, 4369}, {47672, 17166}, {47810, 25569}, {47905, 14349}, {47912, 48099}, {47918, 4040}, {47936, 48111}, {47959, 4794}, {48019, 4822}, {48020, 48131}, {48023, 48136}, {48032, 48150}, {48077, 6332}, {48115, 4801}, {48131, 1}, {48151, 4378}
X(48322) = X(i)-Dao conjugate of X(j) for these (i, j): (15611, 75), (17355, 21580)
X(48322) = crosspoint of X(1) and X(36147)
X(48322) = crosssum of X(i) and X(j) for these (i,j): {1, 48131}, {100, 21362}
X(48322) = crossdifference of every pair of points on line {63, 1743}
X(48322) = barycentric product X(i)*X(j) for these {i,j}: {513, 17355}, {649, 4696}, {650, 10106}, {661, 11115}, {15611, 36147}
X(48322) = barycentric quotient X(i)/X(j) for these {i,j}: {4696, 1978}, {10106, 4554}, {11115, 799}, {15611, 4509}, {17355, 668}
X(48322) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {663, 47912, 48099}, {667, 4041, 1635}, {17072, 47820, 24924}, {47912, 48099, 661}, {47936, 48111, 48032}, {47936, 48150, 48111}


X(48323) = X(1)X(6372)∩X(513)X(4162)

Barycentrics    a*(b - c)*(a^2 + 3*b*c) : :
X(48323) = 3 X[659] - 4 X[667], X[659] - 4 X[4378], 7 X[659] - 8 X[4401], 2 X[667] - 3 X[4367], X[667] - 3 X[4378], 7 X[667] - 6 X[4401], 7 X[4367] - 4 X[4401], 7 X[4378] - 2 X[4401], 4 X[905] - 3 X[47827], 2 X[4490] - 3 X[47827], 3 X[1022] - X[48086], 2 X[1577] - 3 X[47889], 4 X[2530] - 3 X[48160], 2 X[2533] - 3 X[48253], 2 X[3762] - 3 X[47872], 4 X[3960] - 3 X[47893], 2 X[4705] - 3 X[47893], 2 X[4040] - 3 X[25569], 2 X[4041] - 3 X[48244], 2 X[4147] - 3 X[47823], 2 X[4391] - 3 X[47833], 3 X[4800] - 2 X[48265], 3 X[4893] - 2 X[47922], X[4983] - 3 X[14421], 3 X[14413] - X[47918], 2 X[47918] - 3 X[48162], 3 X[14419] - 2 X[48003], 4 X[19947] - 3 X[47816], 4 X[21051] - 5 X[30795], 2 X[21051] - 3 X[47796], 5 X[30795] - 6 X[47796], 2 X[21301] - 3 X[48167], 2 X[47921] - 3 X[48226}

X(48323) lies on these lines: {1, 6372}, {512, 21343}, {513, 4162}, {514, 659}, {523, 17496}, {649, 29226}, {663, 29198}, {693, 29324}, {764, 830}, {814, 4801}, {890, 7192}, {891, 1019}, {905, 4490}, {1022, 48086}, {1491, 3669}, {1577, 47889}, {1960, 47970}, {2530, 4160}, {2533, 48253}, {2787, 4978}, {3733, 28175}, {3762, 47872}, {3777, 8678}, {3907, 21146}, {3960, 4705}, {4040, 25569}, {4041, 48244}, {4057, 28213}, {4083, 4784}, {4147, 47823}, {4382, 29152}, {4391, 47833}, {4462, 4874}, {4491, 4977}, {4800, 48265}, {4810, 6002}, {4813, 48129}, {4893, 47922}, {4922, 29051}, {4948, 44550}, {4983, 14421}, {8650, 48101}, {14413, 47918}, {14419, 48003}, {17166, 21222}, {19947, 47816}, {21051, 30795}, {21105, 23755}, {21301, 48167}, {23880, 48120}, {24533, 43067}, {25537, 47666}, {25926, 47698}, {28399, 47945}, {29025, 47720}, {29029, 47716}, {29074, 47719}, {29082, 47676}, {29110, 47715}, {29120, 47691}, {29128, 47717}, {29134, 47692}, {29138, 47725}, {29148, 48273}, {29168, 47727}, {29246, 47729}, {29250, 47718}, {29268, 47724}, {29274, 48119}, {29284, 47971}, {29354, 47682}, {29366, 48108}, {47911, 48093}, {47912, 48100}, {47913, 48099}, {47921, 48226}, {48023, 48137}, {48024, 48136}

X(48323) = midpoint of X(i) and X(j) for these {i,j}: {17166, 21222}, {21105, 23755}
X(48323) = reflection of X(i) in X(j) for these {i,j}: {659, 4367}, {1491, 3669}, {4367, 4378}, {4462, 4874}, {4490, 905}, {4705, 3960}, {4784, 48144}, {4810, 48279}, {4813, 48129}, {4879, 4449}, {4948, 44550}, {47911, 48093}, {47912, 48100}, {47913, 48099}, {47970, 1960}, {48023, 48137}, {48024, 48136}, {48162, 14413}
X(48323) = crossdifference of every pair of points on line {1743, 2276}
X(48323) = barycentric product X(i)*X(j) for these {i,j}: {513, 17116}, {514, 17122}
X(48323) = barycentric quotient X(i)/X(j) for these {i,j}: {17116, 668}, {17122, 190}
X(48323) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {905, 4490, 47827}, {3960, 4705, 47893}, {21051, 47796, 30795}


X(48324) = X(1)X(513)∩X(8)X(47805)

Barycentrics    a*(b - c)*(2*a^2 - a*b + b^2 - a*c + b*c + c^2) : :
X(48324) = X[8] - 3 X[47805], 2 X[10] - 3 X[47804], 4 X[47936] - 5 X[47977], 3 X[47936] - 5 X[48032], 2 X[47936] - 5 X[48111], X[47936] - 5 X[48150], 3 X[47977] - 4 X[48032], X[47977] - 4 X[48150], 2 X[48032] - 3 X[48111], X[48032] - 3 X[48150], 3 X[663] - X[48023], 5 X[663] - 2 X[48052], 3 X[14349] - 2 X[48023], 5 X[14349] - 4 X[48052], 5 X[48023] - 6 X[48052], 3 X[667] - 2 X[9508], 3 X[1734] - 4 X[9508], 3 X[1019] - 2 X[7659], 4 X[1125] - 3 X[44429], 5 X[1698] - 6 X[47803], 5 X[3616] - 3 X[48164], 7 X[3624] - 6 X[47802], 3 X[4040] - 2 X[48029], 3 X[47959] - 4 X[48029], 2 X[4147] - 3 X[47817], 2 X[4770] - 3 X[48226], X[4774] - 3 X[48251], 3 X[8643] - 2 X[14838], 5 X[8656] - 3 X[47828], 2 X[17072] - 3 X[47818], 3 X[45671] - 2 X[48017], X[47721] - 3 X[48237}

X(48324) lies on these lines: {1, 513}, {8, 47805}, {10, 47804}, {100, 32665}, {512, 47976}, {514, 47692}, {522, 47682}, {649, 3887}, {650, 8657}, {661, 4794}, {663, 830}, {667, 1734}, {832, 21189}, {1019, 3309}, {1125, 44429}, {1491, 1960}, {1577, 28470}, {1698, 47803}, {3063, 5280}, {3616, 48164}, {3624, 47802}, {3762, 48063}, {3803, 3900}, {3912, 47762}, {4040, 8678}, {4041, 4401}, {4147, 47817}, {4160, 4724}, {4367, 4905}, {4369, 28521}, {4448, 29659}, {4729, 48011}, {4730, 4782}, {4770, 48226}, {4774, 48251}, {4776, 17023}, {4777, 47726}, {4804, 29033}, {4817, 40459}, {4895, 29350}, {5299, 20980}, {6005, 48110}, {6590, 47723}, {7662, 47724}, {8643, 14838}, {8656, 47828}, {14077, 21385}, {17072, 47818}, {17166, 29186}, {17212, 33953}, {17284, 47761}, {17316, 47763}, {17742, 21390}, {18108, 23687}, {19784, 48165}, {19836, 48246}, {19881, 48230}, {20949, 39731}, {21130, 44433}, {23887, 47728}, {26626, 47759}, {29013, 31291}, {29066, 47694}, {29192, 47660}, {29344, 48264}, {29598, 47760}, {29633, 47822}, {29637, 47823}, {29660, 36848}, {36478, 45666}, {42325, 48144}, {45671, 48017}, {47123, 47680}, {47131, 47725}, {47721, 48237}, {47905, 48054}, {47912, 48058}, {47918, 48065}, {47948, 48099}, {48086, 48136}

X(48324) = midpoint of X(47697) and X(47729)
X(48324) = reflection of X(i) in X(j) for these {i,j}: {661, 4794}, {1491, 1960}, {1734, 667}, {3762, 48063}, {4041, 4401}, {4063, 3803}, {4729, 48011}, {4730, 4782}, {4905, 4367}, {14349, 663}, {21130, 44433}, {47680, 47123}, {47723, 6590}, {47724, 7662}, {47725, 47131}, {47905, 48054}, {47912, 48058}, {47918, 48065}, {47948, 48099}, {47959, 4040}, {47977, 48111}, {48086, 48136}, {48111, 48150}
X(48324) = crosspoint of X(100) and X(751)
X(48324) = crosssum of X(513) and X(750)
X(48324) = crossdifference of every pair of points on line {44, 4003}
X(48324) = barycentric product X(i)*X(j) for these {i,j}: {1, 47771}, {513, 17354}
X(48324) = barycentric quotient X(i)/X(j) for these {i,j}: {17354, 668}, {47771, 75}


X(48325) = X(1)X(522)∩X(2)X(4474)

Barycentrics    (b - c)*(-2*a^3 + a^2*b + a*b^2 + a^2*c - a*b*c + b^2*c + a*c^2 + b*c^2) : :
X(48325) = X[8] - 3 X[47828], 2 X[10] - 3 X[47830], X[145] + 3 X[48242], X[4814] - 3 X[48242], X[693] - 3 X[14413], 3 X[905] - 2 X[25380], 3 X[17072] - 4 X[25380], 4 X[1125] - 3 X[47831], 2 X[4791] - 3 X[47831], X[2254] - 3 X[44550], 3 X[44550] + X[47729], 5 X[3616] - 3 X[47832], 7 X[3622] - 3 X[48172], 2 X[3716] - 3 X[45316], X[4774] - 3 X[47823], 3 X[6545] - X[47722], 5 X[8656] - 3 X[47805], 3 X[14419] - 2 X[31286], 3 X[14430] - 5 X[31209], 3 X[14432] - X[25259], X[21132] - 3 X[47798], 3 X[30709] - 5 X[30835], X[47721] - 3 X[47812}

X(48325) lies on these lines: {1, 522}, {2, 4474}, {8, 47828}, {10, 47830}, {145, 4814}, {239, 47785}, {274, 20907}, {330, 21225}, {514, 659}, {657, 21384}, {663, 17496}, {693, 14413}, {891, 48008}, {905, 3907}, {1107, 6586}, {1125, 4791}, {1491, 4922}, {1960, 48063}, {2254, 44550}, {2530, 28470}, {2605, 28623}, {2785, 4025}, {2787, 3835}, {2789, 21212}, {3227, 35167}, {3261, 31997}, {3616, 47832}, {3622, 48172}, {3667, 4775}, {3669, 29051}, {3716, 45316}, {3776, 29240}, {3837, 29236}, {3960, 24720}, {4147, 14838}, {4160, 48010}, {4384, 46919}, {4393, 27486}, {4449, 4560}, {4504, 8678}, {4508, 47757}, {4724, 21222}, {4774, 47823}, {4913, 14077}, {4992, 29152}, {6002, 48136}, {6332, 29037}, {6366, 17069}, {6545, 47722}, {8656, 47805}, {14419, 31286}, {14422, 47779}, {14430, 31209}, {14432, 25259}, {16755, 33296}, {16823, 47800}, {16826, 47787}, {16830, 47806}, {16892, 47728}, {17050, 21195}, {19851, 21119}, {19853, 48228}, {20316, 31947}, {21132, 47798}, {21260, 29268}, {23815, 29182}, {28147, 47683}, {28475, 48050}, {28545, 48178}, {29148, 48043}, {29188, 48073}, {29570, 47790}, {30519, 30580}, {30709, 30835}, {31291, 48122}, {47721, 47812}

X(48325) = midpoint of X(i) and X(j) for these {i,j}: {145, 4814}, {663, 17496}, {1491, 4922}, {2254, 47729}, {4449, 4560}, {4724, 21222}, {16892, 47728}, {27486, 30573}, {31291, 48122}
X(48325) = reflection of X(i) in X(j) for these {i,j}: {4147, 14838}, {4791, 1125}, {17072, 905}, {20316, 31947}, {24720, 3960}, {47779, 14422}, {48063, 1960}
X(48325) = complement of X(4474)
X(48325) = X(i)-complementary conjugate of X(j) for these (i,j): {751, 124}, {30650, 26932}
X(48325) = crossdifference of every pair of points on line {2183, 2276}
X(48325) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {145, 48242, 4814}, {1125, 4791, 47831}, {44550, 47729, 2254}


X(48326) = X(1)X(29102)∩X(2)X(48056)

Barycentrics    (b - c)*(b^3 - 2*a*b*c + c^3) : :
X(48326) = 2 X[659] - 3 X[4809], 3 X[659] - 4 X[13246], 4 X[4458] - 3 X[4809], 3 X[4458] - 2 X[13246], 9 X[4809] - 8 X[13246], X[2254] - 3 X[21115], 3 X[21115] + X[47705], 3 X[21116] - X[47703], 2 X[650] - 3 X[48227], 4 X[676] - 3 X[4448], 3 X[4448] - 2 X[48055], 3 X[1638] - 2 X[2977], 4 X[3676] - 3 X[47823], 3 X[47823] - 2 X[48062], 2 X[3837] - 3 X[6545], X[4088] - 3 X[6545], 3 X[4379] - X[48118], 3 X[4453] - 2 X[9508], 2 X[4468] - 3 X[47822], 2 X[4522] - 3 X[48184], 3 X[4728] - 2 X[18004], 2 X[4874] - 3 X[47887], 3 X[47887] - X[48094], 4 X[4885] - 3 X[48185], 2 X[48088] - 3 X[48185], 2 X[5592] - 3 X[25569], 2 X[6590] - 3 X[48238], 2 X[8045] - 3 X[47889], 2 X[10015] - 3 X[21145], X[17494] - 3 X[48241], 4 X[21188] - 3 X[47835], 6 X[21204] - 5 X[30795], 4 X[21212] - 3 X[47827], 5 X[26985] - 3 X[48171], 3 X[31148] - X[48146], 5 X[31209] - 6 X[48215], 4 X[31286] - 3 X[47885], 3 X[44435] - X[47698], 3 X[44435] - 2 X[48030], X[47666] - 3 X[48174], X[47693] - 3 X[47780], X[47700] - 3 X[47812], 3 X[47771] - 2 X[48097], 3 X[47781] - 2 X[47964], 3 X[47813] - X[48130], 3 X[47821] - 2 X[48048], 3 X[47832] - X[48117], 3 X[47877] - 2 X[48010], X[47945] - 3 X[48156], 2 X[47999] - 3 X[48156], X[47969] - 3 X[48203], X[47974] - 3 X[48223], 2 X[48029] - 3 X[48177], X[48124] - 3 X[48220}

X(48326) lies on these lines: {1, 29102}, {2, 48056}, {244, 21112}, {512, 47716}, {513, 41794}, {514, 659}, {523, 2254}, {525, 48279}, {650, 48227}, {676, 4448}, {693, 4122}, {764, 23887}, {824, 48120}, {826, 4978}, {891, 4707}, {900, 4409}, {918, 4010}, {1019, 29098}, {1491, 3776}, {1577, 29354}, {1635, 2527}, {1638, 2977}, {2533, 13259}, {2785, 21343}, {2786, 4810}, {2787, 47680}, {3004, 4824}, {3676, 47823}, {3716, 28890}, {3777, 23877}, {3810, 23765}, {3837, 4088}, {4083, 47720}, {4170, 29252}, {4369, 48103}, {4379, 48118}, {4382, 29078}, {4449, 23747}, {4453, 4802}, {4468, 47822}, {4522, 48184}, {4728, 18004}, {4782, 47663}, {4801, 29017}, {4804, 47930}, {4806, 48082}, {4874, 47887}, {4885, 48088}, {4922, 29240}, {4977, 21125}, {5592, 25569}, {6372, 47712}, {6590, 48238}, {7192, 47688}, {7662, 30520}, {7927, 47717}, {7950, 47715}, {8045, 47889}, {10015, 21145}, {17494, 48241}, {20504, 20507}, {20508, 20510}, {20509, 20511}, {20512, 20515}, {21140, 24136}, {21183, 48188}, {21188, 47835}, {21204, 30795}, {21212, 47827}, {21722, 35352}, {23742, 47123}, {23815, 48272}, {23875, 48273}, {25259, 48090}, {26985, 48171}, {28147, 48244}, {28191, 45674}, {28195, 44433}, {28199, 47667}, {28840, 47944}, {28851, 48024}, {28878, 47983}, {28894, 48134}, {29025, 48144}, {29029, 47725}, {29110, 47724}, {29144, 47692}, {29146, 47719}, {29168, 47713}, {29188, 47727}, {29198, 47708}, {29204, 47690}, {29224, 47682}, {29236, 47722}, {29328, 47971}, {31148, 48146}, {31209, 48215}, {31286, 47885}, {31290, 47990}, {36205, 46409}, {44435, 47698}, {47656, 48127}, {47666, 48174}, {47693, 47780}, {47700, 47812}, {47702, 48148}, {47771, 48097}, {47781, 47964}, {47813, 48130}, {47821, 48048}, {47832, 48117}, {47877, 48010}, {47902, 48147}, {47923, 48142}, {47924, 48141}, {47931, 48153}, {47945, 47999}, {47946, 47998}, {47969, 48203}, {47974, 48223}, {48029, 48177}, {48102, 48248}, {48124, 48220}

X(48326) = midpoint of X(i) and X(j) for these {i,j}: {2254, 47705}, {4804, 47930}, {7192, 47688}, {16892, 47704}, {47676, 47691}, {47692, 48108}, {47702, 48148}, {47902, 48147}, {47923, 48142}, {47924, 48141}, {47931, 48153}
X(48326) = reflection of X(i) in X(j) for these {i,j}: {659, 4458}, {1491, 3776}, {4010, 23770}, {4088, 3837}, {4122, 693}, {4824, 3004}, {21146, 21104}, {25259, 48090}, {31290, 47990}, {47656, 48127}, {47663, 4782}, {47690, 48098}, {47698, 48030}, {47945, 47999}, {47946, 47998}, {48055, 676}, {48062, 3676}, {48082, 4806}, {48083, 3716}, {48088, 4885}, {48094, 4874}, {48102, 48248}, {48103, 4369}, {48188, 21183}, {48272, 23815}
X(48326) = anticomplement of X(48056)
X(48326) = X(39714)-Ceva conjugate of X(1086)
X(48326) = X(3836)-Dao conjugate of X(3573)
X(48326) = crossdifference of every pair of points on line {2276, 4251}
X(48326) = barycentric product X(i)*X(j) for these {i,j}: {513, 20432}, {514, 3836}, {693, 3726}, {3261, 20456}, {3676, 4119}, {7192, 20483}, {7199, 20703}, {20729, 46107}
X(48326) = barycentric quotient X(i)/X(j) for these {i,j}: {3726, 100}, {3836, 190}, {4119, 3699}, {20432, 668}, {20456, 101}, {20483, 3952}, {20703, 1018}, {20729, 1331}
X(48326) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {659, 4458, 4809}, {676, 48055, 4448}, {3676, 48062, 47823}, {4088, 6545, 3837}, {4885, 48088, 48185}, {21115, 47705, 2254}, {21140, 24136, 24193}, {44435, 47698, 48030}, {47887, 48094, 4874}, {47945, 48156, 47999}


X(48327) = X(1)X(513)∩X(8)X(47804)

Barycentrics    a*(b - c)*(3*a^2 - 2*a*b + b^2 - 2*a*c + 2*b*c + c^2) : :
X(48327) = 3 X[3251] - X[4775], X[8] - 3 X[47804], 2 X[10] - 3 X[47803], X[145] + 3 X[47805], 3 X[4162] + X[4790], 3 X[650] - 2 X[4770], 3 X[1960] - X[4770], X[661] - 3 X[663], 5 X[661] - 3 X[47912], 4 X[661] - 3 X[47956], 2 X[661] - 3 X[48099], 5 X[663] - X[47912], 4 X[663] - X[47956], 4 X[47912] - 5 X[47956], 2 X[47912] - 5 X[48099], 3 X[667] - 2 X[4394], 3 X[667] - X[4730], 4 X[1125] - 3 X[47802], X[1491] - 3 X[25569], 3 X[1635] - X[4814], 3 X[1635] - 5 X[8656], X[4814] - 5 X[8656], 5 X[3616] - 3 X[44429], 7 X[3622] - 3 X[48164], X[4041] - 3 X[8643], 2 X[6050] - 3 X[8643], X[4774] - 3 X[48234], 2 X[9508] - 3 X[30234], 3 X[14432] - X[48077], 3 X[17166] - X[47675], X[21302] - 3 X[47820], 2 X[25666] - 3 X[45316], X[47721] - 3 X[47834}

X(48327) lies on these lines: {1, 513}, {8, 47804}, {10, 47803}, {145, 47805}, {512, 4162}, {514, 47131}, {649, 4895}, {650, 1960}, {659, 14077}, {661, 663}, {667, 3900}, {830, 48092}, {832, 6129}, {1125, 47802}, {1491, 25569}, {1635, 4814}, {2490, 4528}, {3309, 4367}, {3616, 44429}, {3622, 48164}, {3669, 6004}, {3803, 4083}, {3887, 7634}, {3912, 47761}, {4010, 28475}, {4040, 47966}, {4041, 6050}, {4160, 4794}, {4448, 36479}, {4449, 48150}, {4729, 4959}, {4774, 48234}, {4776, 26626}, {4777, 47682}, {4802, 47727}, {4820, 29058}, {5299, 39521}, {7662, 29066}, {7718, 44426}, {9029, 43065}, {9508, 30234}, {14432, 48077}, {16502, 20980}, {17023, 47760}, {17072, 24756}, {17166, 47675}, {17316, 47762}, {19784, 48181}, {19836, 48230}, {20906, 39731}, {21302, 47820}, {24720, 28521}, {25666, 45316}, {28165, 47726}, {29110, 48271}, {29188, 43067}, {29240, 47123}, {29585, 47763}, {29633, 48197}, {29637, 48216}, {29659, 45666}, {47694, 47729}, {47695, 47728}, {47721, 47834}

X(48327) = midpoint of X(i) and X(j) for these {i,j}: {649, 4895}, {4378, 6161}, {4449, 48150}, {4729, 4959}, {47694, 47729}, {47695, 47728}
X(48327) = reflection of X(i) in X(j) for these {i,j}: {650, 1960}, {4041, 6050}, {4528, 2490}, {4730, 4394}, {47956, 48099}, {47966, 4040}, {48029, 4794}, {48092, 48136}, {48099, 663}
X(48327) = X(i)-Ceva conjugate of X(j) for these (i,j): {9104, 9}, {36091, 44}, {47845, 47766}
X(48327) = X(i)-isoconjugate of X(j) for these (i,j): {69, 9088}, {664, 3478}
X(48327) = X(39025)-Dao conjugate of X(3478)
X(48327) = crosssum of X(513) and X(3306)
X(48327) = crossdifference of every pair of points on line {44, 63}
X(48327) = barycentric product X(i)*X(j) for these {i,j}: {1, 47766}, {19, 9031}, {37, 47845}, {649, 4737}, {650, 3476}, {661, 4234}
X(48327) = barycentric quotient X(i)/X(j) for these {i,j}: {1973, 9088}, {3063, 3478}, {3476, 4554}, {4234, 799}, {4737, 1978}, {9031, 304}, {47766, 75}, {47845, 274}
X(48327) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {667, 4730, 4394}, {4041, 8643, 6050}, {4814, 8656, 1635}


X(48328) = X(1)X(512)∩X(8)X(47837)

Barycentrics    a*(b - c)*(2*a^2 - a*b - a*c + 2*b*c) : :
X(48328) = 3 X[1] + X[1019], 5 X[1] + X[4784], 3 X[1] - X[4879], X[1019] - 3 X[4367], 5 X[1019] - 3 X[4784], 5 X[4367] - X[4784], 3 X[4367] + X[4879], 3 X[4784] + 5 X[4879], X[8] - 3 X[47837], X[145] + 3 X[47836], 3 X[551] - X[4129], 3 X[667] - X[4498], 3 X[4449] + X[4498], 2 X[905] - 3 X[14422], X[2530] - 3 X[14413], 3 X[2605] - X[4833], 5 X[3616] - 3 X[47839], 7 X[3622] - 3 X[47840], 4 X[3636] - X[4806], X[4040] - 3 X[25569], X[4041] - 3 X[14419], X[4474] - 3 X[47875], X[47724] - 3 X[47889], 2 X[47915] - 3 X[47994], X[47915] - 3 X[48099], X[48091] - 3 X[48136}

X(48328) lies on these lines: {1, 512}, {8, 47837}, {39, 22229}, {145, 47836}, {513, 25405}, {514, 1960}, {517, 44811}, {551, 4129}, {663, 4378}, {667, 891}, {693, 29182}, {764, 48150}, {905, 14422}, {1015, 45902}, {1125, 21051}, {1319, 7178}, {1385, 28473}, {1386, 9040}, {1573, 22222}, {1577, 4922}, {2530, 14413}, {2605, 4833}, {2787, 4504}, {3244, 4807}, {3566, 39545}, {3616, 47839}, {3622, 47840}, {3636, 4806}, {3669, 6004}, {3700, 29264}, {3733, 4139}, {4010, 29176}, {4040, 25569}, {4041, 14419}, {4063, 21343}, {4083, 48011}, {4147, 31288}, {4160, 48005}, {4369, 29298}, {4401, 29226}, {4458, 29094}, {4474, 47875}, {4770, 14838}, {4775, 48144}, {4794, 29198}, {4823, 29236}, {4897, 32478}, {4932, 23506}, {5563, 39577}, {6161, 48151}, {7950, 47682}, {8034, 29818}, {8045, 29110}, {8678, 48059}, {23765, 48111}, {23770, 29336}, {23815, 28470}, {24928, 34958}, {29138, 47712}, {29184, 47691}, {29272, 47728}, {29340, 48273}, {29344, 48090}, {47724, 47889}, {47915, 47994}, {48091, 48136}

X(48328) = midpoint of X(i) and X(j) for these {i,j}: {1, 4367}, {663, 4378}, {667, 4449}, {764, 48150}, {1019, 4879}, {1577, 4922}, {3244, 4807}, {4063, 21343}, {4775, 48144}, {6161, 48151}, {23765, 48111}
X(48328) = reflection of X(i) in X(j) for these {i,j}: {4147, 31288}, {4770, 14838}, {21051, 1125}, {47994, 48099}
X(48328) = crosssum of X(523) and X(11680)
X(48328) = crossdifference of every pair of points on line {2238, 16885}
X(48328) = barycentric product X(i)*X(j) for these {i,j}: {1, 24924}, {513, 17351}
X(48328) = barycentric quotient X(i)/X(j) for these {i,j}: {17351, 668}, {24924, 75}
X(48328) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1019, 4879}, {4367, 4879, 1019}


X(48329) = X(1)X(48111)∩X(3)X(667)

Barycentrics    a*(b - c)*(3*a^2 - 2*a*b + b^2 - 2*a*c + c^2) : :
X(48329) = X[8] - 3 X[47815], 7 X[663] - X[48116], 5 X[663] - X[48122], 3 X[663] - X[48131], X[3777] - 3 X[25569], 5 X[48116] - 7 X[48122], 3 X[48116] - 7 X[48131], 2 X[48116] - 7 X[48136], X[48116] + 7 X[48150], 3 X[48122] - 5 X[48131], 2 X[48122] - 5 X[48136], X[48122] + 5 X[48150], 2 X[48131] - 3 X[48136], X[48131] + 3 X[48150], X[48136] + 2 X[48150], 4 X[4794] - X[48027], 3 X[4794] - X[48054], 3 X[48027] - 4 X[48054], 2 X[48054] - 3 X[48099], X[2254] - 3 X[8643], 5 X[3616] - 3 X[47819], 3 X[4040] - X[47959], 2 X[47959] - 3 X[48029], 3 X[4448] - 2 X[20317], 2 X[14837] - 3 X[26275], 2 X[17072] - 3 X[47803], X[21302] - 3 X[47804}

X(48329) lies on these lines: {1, 48111}, {3, 667}, {8, 47815}, {512, 3803}, {513, 663}, {514, 47131}, {650, 8632}, {659, 3900}, {830, 4794}, {900, 6332}, {905, 1960}, {1429, 17115}, {1633, 4564}, {1734, 6050}, {2254, 8643}, {2478, 21301}, {2977, 44448}, {3057, 4083}, {3250, 4790}, {3616, 47819}, {3716, 28470}, {3887, 4401}, {3907, 48063}, {4040, 8678}, {4057, 15313}, {4063, 5119}, {4160, 47966}, {4186, 18344}, {4187, 21260}, {4448, 20317}, {4449, 48032}, {4491, 9001}, {4498, 4895}, {4782, 37568}, {4820, 29276}, {4879, 8712}, {4905, 37618}, {4926, 48278}, {5592, 23877}, {6872, 31291}, {7662, 29051}, {8654, 24562}, {8657, 24290}, {9010, 37516}, {13724, 28373}, {13747, 31288}, {14837, 26275}, {17072, 28521}, {21185, 29240}, {21302, 47804}, {25875, 25901}, {26249, 35996}, {28475, 48267}, {29074, 48271}, {29186, 48126}, {29208, 48095}, {29246, 43067}, {29288, 48096}, {29366, 48248}, {37828, 47835}, {47956, 48058}

X(48329) = midpoint of X(i) and X(j) for these {i,j}: {1, 48111}, {663, 48150}, {667, 6161}, {4449, 48032}, {4498, 4895}, {31291, 48080}
X(48329) = reflection of X(i) in X(j) for these {i,j}: {905, 1960}, {1734, 6050}, {44448, 2977}, {47956, 48058}, {47966, 48065}, {48027, 48099}, {48029, 4040}, {48099, 4794}, {48136, 663}
X(48329) = crosspoint of X(100) and X(9309)
X(48329) = crosssum of X(513) and X(1376)
X(48329) = crossdifference of every pair of points on line {9, 982}
X(48329) = barycentric product X(i)*X(j) for these {i,j}: {1, 11068}, {513, 26685}, {514, 3749}
X(48329) = barycentric quotient X(i)/X(j) for these {i,j}: {3749, 190}, {11068, 75}, {26685, 668}


X(48330) = X(1)X(667)∩X(8)X(47835)

Barycentrics    a*(b - c)*(2*a^2 - a*b - a*c + b*c) : :
X(48330) = 3 X[1] + X[4063], 2 X[1] + X[4782], 3 X[667] - X[4063], 2 X[4063] - 3 X[4782], X[8] - 3 X[47835], X[663] - 3 X[25569], 3 X[663] + X[48144], X[3777] - 3 X[14413], X[4367] + 3 X[25569], 3 X[4367] - X[48144], 3 X[14413] + X[48150], 9 X[25569] + X[48144], 2 X[48128] - 3 X[48129], X[48128] - 3 X[48136], X[659] - 3 X[8643], X[4449] + 3 X[8643], 2 X[1577] - 3 X[48202], X[1734] - 3 X[14419], X[2533] - 3 X[47820], X[47729] + 3 X[47820], 5 X[3616] - X[21301], 5 X[3616] - 3 X[47841], X[21301] - 3 X[47841], 7 X[3622] - X[24719], 7 X[3622] + X[31291], 7 X[3624] - 5 X[31251], 3 X[4448] - X[4462], X[4474] - 3 X[47872], X[4498] - 5 X[8656], 5 X[8656] + X[21343], 2 X[4705] - 3 X[48194], X[4729] + 3 X[23057], 4 X[14838] - 3 X[48213], 2 X[17072] - 3 X[48216], 2 X[20317] - 3 X[45666], 2 X[21051] - 3 X[48197], X[21120] - 3 X[26275], X[21302] - 3 X[47823], 3 X[25055] - X[31149], 2 X[47955] - 3 X[48028], X[47955] - 3 X[48099], 2 X[48051] - 3 X[48093}

X(48330) lies on these lines: {1, 667}, {8, 47835}, {10, 31288}, {100, 25575}, {241, 8638}, {512, 48064}, {513, 663}, {514, 1960}, {517, 39227}, {518, 42655}, {649, 4879}, {650, 5029}, {659, 4449}, {692, 4564}, {693, 29274}, {764, 48111}, {814, 48090}, {830, 48100}, {885, 2496}, {891, 4401}, {1019, 4775}, {1125, 21260}, {1201, 28373}, {1385, 3309}, {1386, 9010}, {1429, 23865}, {1577, 29236}, {1734, 14419}, {1919, 21348}, {2320, 23836}, {2516, 45755}, {2533, 47729}, {2646, 4162}, {3251, 37525}, {3616, 21301}, {3622, 24719}, {3624, 31251}, {3700, 29230}, {3716, 4504}, {3744, 38238}, {3801, 47728}, {3837, 28470}, {3897, 48265}, {3900, 9508}, {3907, 4874}, {3960, 6004}, {4010, 29152}, {4040, 4378}, {4107, 4885}, {4132, 8639}, {4160, 47967}, {4369, 29366}, {4391, 4922}, {4394, 4435}, {4448, 4462}, {4458, 29082}, {4474, 47872}, {4498, 8656}, {4560, 4777}, {4705, 48194}, {4729, 23057}, {4791, 29268}, {4794, 6372}, {4802, 17166}, {4823, 29182}, {4905, 6161}, {6008, 42819}, {6050, 14077}, {7191, 26249}, {8045, 29074}, {8640, 43931}, {8678, 48030}, {9320, 11712}, {11363, 18344}, {14838, 48213}, {16826, 24601}, {17072, 48216}, {17284, 31208}, {19861, 25901}, {20317, 45666}, {20517, 29094}, {21051, 48197}, {21120, 26275}, {21191, 24673}, {21302, 47823}, {21904, 22224}, {23655, 24532}, {23765, 48032}, {23770, 29244}, {23807, 31997}, {24533, 24666}, {24663, 24674}, {24665, 24676}, {24747, 24749}, {25055, 31149}, {25128, 44451}, {25301, 25636}, {29051, 48098}, {29066, 48221}, {29122, 47712}, {29146, 47682}, {29150, 35016}, {29238, 48273}, {29240, 34958}, {29288, 48097}, {29603, 30836}, {47955, 48028}, {47957, 48058}, {48051, 48093}

X(48330) = midpoint of X(i) and X(j) for these {i,j}: {1, 667}, {649, 4879}, {659, 4449}, {663, 4367}, {764, 48111}, {1019, 4775}, {2533, 47729}, {3716, 4504}, {3777, 48150}, {3801, 47728}, {4040, 4378}, {4391, 4922}, {4498, 21343}, {4905, 6161}, {23765, 48032}, {24719, 31291}
X(48330) = reflection of X(i) in X(j) for these {i,j}: {10, 31288}, {4782, 667}, {21260, 1125}, {47957, 48058}, {48028, 48099}, {48129, 48136}
X(48330) = X(932)-Ceva conjugate of X(17105)
X(48330) = X(100)-isoconjugate of X(3551)
X(48330) = X(i)-Dao conjugate of X(j) for these (i, j): (8054, 3551), (31286, 20906)
X(48330) = crosspoint of X(i) and X(j) for these (i,j): {1, 932}, {934, 7132}
X(48330) = crosssum of X(i) and X(j) for these (i,j): {1, 4083}, {513, 17063}, {514, 20257}, {521, 20254}, {522, 3840}, {3061, 3900}, {20528, 23886}
X(48330) = crossdifference of every pair of points on line {9, 1575}
X(48330) = barycentric product X(i)*X(j) for these {i,j}: {1, 31286}, {75, 23472}, {513, 17350}, {514, 3550}, {649, 24524}, {651, 24840}, {1019, 4090}, {3835, 17105}
X(48330) = barycentric quotient X(i)/X(j) for these {i,j}: {649, 3551}, {3550, 190}, {4090, 4033}, {17105, 4598}, {17350, 668}, {23472, 1}, {24524, 1978}, {24840, 4391}, {31286, 75}
X(48330) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3616, 21301, 47841}, {4367, 25569, 663}, {4449, 8643, 659}, {14413, 48150, 3777}, {23655, 25537, 25142}, {47729, 47820, 2533}


X(48331) = X(1)X(29226)∩X(36)X(238)

Barycentrics    a*(b - c)*(2*a^2 - a*b - a*c - b*c) : :
X(48331) = 3 X[667] - X[1019], X[1019] + 3 X[4040], 3 X[3803] + X[48091], 2 X[3803] + X[48093], 3 X[4057] + X[4833], X[4905] - 3 X[14419], 2 X[48091] - 3 X[48093], X[48091] - 3 X[48099], 3 X[4401] - X[48011], X[4782] + 2 X[4794], 3 X[4782] - 2 X[48011], 3 X[4794] + X[48011], 3 X[659] - X[4498], 3 X[659] + X[4879], 3 X[663] + X[4498], 3 X[663] - X[4879], X[2533] - 3 X[47804], X[3801] - 3 X[47798], X[4041] - 3 X[48226], X[4367] - 3 X[8643], X[4724] + 3 X[8643], X[4391] - 3 X[4448], X[4449] - 3 X[25569], X[4490] - 3 X[47811], 2 X[4823] - 3 X[48202], X[7178] - 3 X[26275], 5 X[8656] - X[48144], 3 X[14413] - X[23765], 3 X[14413] + X[47936], X[21146] - 3 X[47820], 2 X[21260] - 3 X[48197], X[21301] - 3 X[47822], X[21302] - 3 X[47835], X[24719] - 3 X[47840], 4 X[31288] - 3 X[48216], X[31291] + 3 X[47821], X[46403] - 3 X[47841], X[47724] - 3 X[47875], X[47729] + 3 X[47815], 3 X[47889] - X[48119], X[47912] - 3 X[48162], 2 X[47915] - 3 X[47957], X[47915] - 3 X[48029], 2 X[48012] - 3 X[48194}

X(48331) lies on these lines: {1, 29226}, {36, 238}, {512, 4401}, {514, 1960}, {650, 8632}, {659, 663}, {764, 47977}, {814, 3716}, {830, 48030}, {979, 23355}, {1027, 3445}, {1120, 9260}, {1125, 23815}, {1491, 48150}, {1577, 29274}, {1734, 6161}, {2533, 47804}, {3309, 6050}, {3700, 29276}, {3768, 23572}, {3777, 48032}, {3801, 47798}, {3900, 3913}, {4010, 29238}, {4041, 48226}, {4063, 4775}, {4142, 5592}, {4160, 47922}, {4367, 4724}, {4369, 29246}, {4378, 47970}, {4391, 4448}, {4449, 25569}, {4462, 4922}, {4490, 47811}, {4791, 29182}, {4802, 47717}, {4823, 48202}, {4874, 29051}, {4926, 5440}, {6004, 14838}, {6372, 48065}, {7178, 26275}, {8654, 28374}, {8656, 48144}, {8678, 47967}, {14413, 23765}, {17494, 23506}, {20517, 29102}, {21051, 28470}, {21146, 47820}, {21260, 48197}, {21301, 47822}, {21302, 47835}, {24601, 47760}, {24719, 47840}, {28521, 48214}, {29047, 48097}, {29070, 48090}, {29122, 47708}, {29152, 48267}, {29186, 48098}, {29208, 47890}, {31288, 48216}, {31291, 47821}, {39541, 47329}, {46403, 47841}, {47724, 47875}, {47729, 47815}, {47889, 48119}, {47912, 48162}, {47915, 47957}, {48012, 48194}, {48028, 48058}

X(48331) = midpoint of X(i) and X(j) for these {i,j}: {659, 663}, {667, 4040}, {764, 47977}, {1491, 48150}, {1734, 6161}, {2530, 48111}, {3777, 48032}, {3803, 48099}, {4063, 4775}, {4142, 5592}, {4367, 4724}, {4378, 47970}, {4401, 4794}, {4462, 4922}, {4498, 4879}, {23765, 47936}
X(48331) = reflection of X(i) in X(j) for these {i,j}: {4782, 4401}, {9508, 6050}, {23815, 1125}, {47957, 48029}, {48028, 48058}, {48093, 48099}
X(48331) = isogonal conjugate of the isotomic conjugate of X(23794)
X(48331) = X(i)-Ceva conjugate of X(j) for these (i,j): {17349, 23470}, {29227, 1}
X(48331) = X(23470)-cross conjugate of X(17349)
X(48331) = X(i)-isoconjugate of X(j) for these (i,j): {100, 39742}, {190, 39966}
X(48331) = X(i)-Dao conjugate of X(j) for these (i, j): (8054, 39742), (48008, 4408)
X(48331) = crosspoint of X(87) and X(100)
X(48331) = crosssum of X(i) and X(j) for these (i,j): {43, 513}, {3970, 4705}
X(48331) = trilinear pole of line {22215, 23470}
X(48331) = crossdifference of every pair of points on line {37, 982}
X(48331) = barycentric product X(i)*X(j) for these {i,j}: {1, 48008}, {6, 23794}, {99, 22215}, {513, 17349}, {514, 8616}, {649, 17144}, {668, 23470}, {1019, 4685}, {3733, 22016}, {16695, 27438}
X(48331) = barycentric quotient X(i)/X(j) for these {i,j}: {649, 39742}, {667, 39966}, {4685, 4033}, {8616, 190}, {17144, 1978}, {17349, 668}, {22016, 27808}, {22215, 523}, {23470, 513}, {23794, 76}, {48008, 75}
X(48331) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {659, 4879, 4498}, {663, 4498, 4879}, {4724, 8643, 4367}, {14413, 47936, 23765}


X(48332) = X(1)X(513)∩X(8)X(44429)

Barycentrics    a*(b - c)*(a^2 - 2*a*b - b^2 - 2*a*c + 2*b*c - c^2) : :
X(48332) = X[4378] - 3 X[14421], X[8] - 3 X[44429], 2 X[10] - 3 X[47802], X[145] + 3 X[48164], 3 X[3669] - X[7659], 7 X[47966] - 8 X[48004], 3 X[47966] - 4 X[48029], 5 X[47966] - 8 X[48058], X[47966] - 4 X[48136], 6 X[48004] - 7 X[48029], 5 X[48004] - 7 X[48058], 4 X[48004] - 7 X[48099], 2 X[48004] - 7 X[48136], 5 X[48029] - 6 X[48058], 2 X[48029] - 3 X[48099], X[48029] - 3 X[48136], 4 X[48058] - 5 X[48099], 2 X[48058] - 5 X[48136], X[649] - 3 X[14413], 3 X[663] - X[48032], 3 X[905] - 2 X[9508], 4 X[1125] - 3 X[47803], 5 X[3616] - 3 X[47804], 7 X[3622] - 3 X[47805], 2 X[4394] - 3 X[14419], 5 X[4449] + X[47905], 3 X[4449] + X[48023], 2 X[4449] + X[48092], 3 X[47905] - 5 X[48023], 2 X[47905] - 5 X[48092], X[47905] - 5 X[48131], 2 X[48023] - 3 X[48092], X[48023] - 3 X[48131], X[4462] - 3 X[47840], X[4474] - 3 X[4728], 2 X[4770] - 3 X[48193], X[4774] - 3 X[48184], 2 X[4782] - 3 X[30234], 3 X[14430] - 5 X[30835], 3 X[14432] - X[48094], 2 X[20317] - 3 X[47839], X[21302] - 3 X[47819], 2 X[23813] - 3 X[30592], X[47721] - 3 X[48170], X[47722] - 3 X[47871}

X(48332) lies on these lines: {1, 513}, {8, 44429}, {10, 47802}, {145, 48164}, {304, 20906}, {512, 3669}, {514, 3716}, {649, 14413}, {650, 891}, {663, 48032}, {667, 8712}, {905, 4083}, {1125, 47803}, {1491, 14077}, {2530, 3900}, {2785, 3776}, {2787, 4106}, {2832, 4794}, {3063, 16502}, {3309, 3777}, {3616, 47804}, {3622, 47805}, {3904, 47691}, {3912, 47760}, {3960, 29350}, {4160, 48027}, {4162, 6004}, {4394, 14419}, {4449, 8678}, {4458, 28468}, {4462, 47840}, {4474, 4728}, {4498, 6050}, {4770, 48193}, {4774, 48184}, {4776, 17316}, {4777, 47727}, {4782, 30234}, {4802, 47682}, {4922, 24719}, {4992, 29324}, {5280, 39521}, {6129, 6371}, {6332, 29288}, {9260, 32847}, {14349, 47956}, {14430, 30835}, {14432, 48094}, {16781, 21007}, {17023, 47761}, {17284, 30583}, {18156, 20949}, {19784, 48230}, {19836, 48181}, {20317, 47839}, {21222, 48080}, {21302, 47819}, {23813, 30592}, {23815, 29298}, {23880, 48273}, {23882, 48279}, {23887, 47131}, {23888, 48211}, {26626, 47762}, {28151, 47726}, {29066, 48089}, {29226, 47965}, {29585, 47759}, {29633, 48216}, {29637, 48197}, {29660, 45666}, {36479, 36848}, {46403, 47729}, {47652, 47728}, {47684, 47688}, {47721, 48170}, {47722, 47871}, {47915, 48053}, {47955, 48093}, {48091, 48129}

X(48332) = midpoint of X(i) and X(j) for these {i,j}: {764, 4775}, {1491, 21343}, {3777, 4879}, {3904, 47691}, {4449, 48131}, {4922, 24719}, {21222, 48080}, {46403, 47729}, {47652, 47728}, {47684, 47688}
X(48332) = reflection of X(i) in X(j) for these {i,j}: {4498, 6050}, {47915, 48053}, {47955, 48093}, {47956, 14349}, {47966, 48099}, {48091, 48129}, {48092, 48131}, {48099, 48136}
X(48332) = crossdifference of every pair of points on line {44, 4386}
X(48332) = barycentric product X(i)*X(j) for these {i,j}: {1, 47757}, {513, 4419}
X(48332) = barycentric quotient X(i)/X(j) for these {i,j}: {4419, 668}, {47757, 75}


X(48333) = X(1)X(667)∩X(8)X(21260)

Barycentrics    a*(b - c)*(a^2 - 2*a*b - 2*a*c + 2*b*c) : :
X(48333) = 3 X[1] - X[4063], 5 X[1] - 2 X[4782], 3 X[667] - 2 X[4063], 5 X[667] - 4 X[4782], 5 X[4063] - 6 X[4782], 4 X[10] - 5 X[31251], 2 X[10] - 3 X[47841], 5 X[31251] - 6 X[47841], 3 X[4378] - 2 X[48144], 3 X[4449] - X[48144], X[4775] + 2 X[21343], 4 X[1125] - 3 X[47835], 2 X[3669] - 3 X[14421], 2 X[3244] + X[24719], 5 X[3616] - 4 X[31288], 5 X[3623] - X[31291], 2 X[4041] - 3 X[47888], 2 X[4147] - 3 X[47839], 2 X[48051] - 3 X[48123], 3 X[4367] - 2 X[48064], 3 X[4834] - 4 X[48064], 2 X[4401] - 3 X[25569], X[4729] - 3 X[14413], 2 X[4807] - 3 X[47823], 3 X[4983] - 2 X[47955], 4 X[20317] - 3 X[30583], 3 X[10246] - 2 X[39227], 3 X[23057] - X[48150}

X(48333) lies on these lines: {1, 667}, {8, 21260}, {10, 31251}, {145, 21301}, {213, 21836}, {512, 4378}, {514, 4775}, {519, 31149}, {663, 891}, {693, 29298}, {764, 1482}, {905, 4730}, {1125, 47835}, {1459, 4139}, {1960, 4498}, {2098, 4162}, {2099, 3669}, {2530, 3900}, {3063, 17458}, {3242, 9010}, {3244, 24719}, {3616, 31288}, {3623, 31291}, {3661, 30836}, {3777, 3887}, {3907, 48273}, {4040, 29226}, {4041, 47888}, {4147, 47839}, {4160, 48051}, {4170, 29324}, {4367, 4834}, {4382, 29182}, {4393, 24601}, {4401, 25569}, {4501, 21123}, {4705, 14077}, {4729, 14413}, {4774, 4823}, {4801, 29188}, {4807, 47823}, {4808, 6332}, {4810, 29344}, {4833, 28151}, {4867, 9260}, {4895, 6004}, {4905, 11009}, {4922, 29013}, {4978, 29366}, {4983, 47955}, {5289, 20317}, {5425, 9269}, {6008, 42871}, {6363, 42312}, {8678, 48128}, {9320, 10695}, {10246, 39227}, {11396, 18344}, {17023, 31208}, {17135, 30968}, {17143, 23807}, {17762, 21440}, {18197, 23506}, {20055, 31040}, {20980, 21834}, {21051, 25574}, {21302, 23815}, {23057, 48150}, {23765, 42325}, {23770, 28473}, {26249, 29815}, {27758, 31136}, {29017, 47727}, {29066, 48279}, {29070, 47729}, {29082, 47716}, {29094, 47691}, {29098, 47728}, {29102, 47720}, {29150, 34195}, {29154, 47692}, {29172, 47713}, {29208, 47682}, {29264, 48266}, {29332, 47717}, {29667, 30766}, {32478, 47971}, {47948, 48129}

X(48333) = midpoint of X(i) and X(j) for these {i,j}: {145, 21301}, {4879, 21343}
X(48333) = reflection of X(i) in X(j) for these {i,j}: {8, 21260}, {667, 1}, {4378, 4449}, {4498, 1960}, {4705, 48136}, {4730, 905}, {4774, 4823}, {4775, 4879}, {4808, 6332}, {4834, 4367}, {6161, 4162}, {21302, 23815}, {47948, 48129}
X(48333) = crossdifference of every pair of points on line {1575, 16669}
X(48333) = barycentric product X(i)*X(j) for these {i,j}: {1, 30835}, {513, 17262}
X(48333) = barycentric quotient X(i)/X(j) for these {i,j}: {17262, 668}, {30835, 75}
X(48333) = {X(10),X(47841)}-harmonic conjugate of X(31251)


X(48334) = X(1)X(48150)∩X(81)X(1019)

Barycentrics    a*(b - c)*(a*b + b^2 + a*c - 2*b*c + c^2) : :
X(48334) = X[1019] - 3 X[1022], 6 X[1022] - X[47935], 3 X[661] - 4 X[14349], 3 X[661] - 2 X[47918], 5 X[661] - 4 X[47959], 9 X[661] - 8 X[47997], 7 X[661] - 8 X[48054], 2 X[4391] - 3 X[4728], 5 X[14349] - 3 X[47959], 3 X[14349] - 2 X[47997], 7 X[14349] - 6 X[48054], 2 X[14349] - 3 X[48131], 5 X[47918] - 6 X[47959], 3 X[47918] - 4 X[47997], 7 X[47918] - 12 X[48054], X[47918] - 3 X[48131], 9 X[47959] - 10 X[47997], 7 X[47959] - 10 X[48054], 2 X[47959] - 5 X[48131], 7 X[47997] - 9 X[48054], 4 X[47997] - 9 X[48131], 4 X[48054] - 7 X[48131], 2 X[667] - 3 X[14413], 4 X[905] - 3 X[1635], 3 X[1635] - 2 X[4498], 4 X[1125] - 3 X[47817], 4 X[3777] - X[4729], 2 X[2533] - 3 X[47812], 4 X[3837] - 3 X[21052], 2 X[4147] - 3 X[44429], 2 X[4490] - 3 X[47810], 3 X[47810] - 4 X[48100], 3 X[4893] - 2 X[47921], 2 X[21222] + X[48114], 3 X[6545] - 2 X[7178], 3 X[14430] - 4 X[21260], 2 X[17072] - 3 X[47819], 4 X[19947] - 3 X[47837], 4 X[20317] - 5 X[30835], 5 X[24924] - 6 X[47796], 4 X[30723] - 3 X[47758}

X(48334) lies on these lines: {1, 48150}, {81, 1019}, {512, 764}, {513, 4162}, {514, 661}, {525, 47930}, {649, 3669}, {663, 48032}, {667, 14413}, {812, 17496}, {830, 48116}, {891, 2530}, {905, 1635}, {918, 21834}, {1125, 47817}, {1491, 29226}, {1769, 9002}, {2170, 6547}, {2254, 3777}, {2533, 47812}, {2832, 4040}, {3776, 28024}, {3810, 47691}, {3837, 21052}, {3907, 46403}, {3910, 16892}, {3942, 45234}, {3960, 4063}, {4017, 6371}, {4024, 48280}, {4079, 23769}, {4147, 44429}, {4160, 47905}, {4171, 17458}, {4382, 23880}, {4490, 47810}, {4502, 28878}, {4504, 31291}, {4560, 47932}, {4724, 48136}, {4761, 23789}, {4794, 47977}, {4804, 48279}, {4807, 23814}, {4813, 48128}, {4822, 6372}, {4893, 47921}, {4895, 6004}, {4905, 29350}, {4979, 48144}, {4983, 47906}, {4992, 48265}, {6002, 21222}, {6084, 21123}, {6363, 6615}, {6545, 7178}, {8678, 48020}, {14430, 21260}, {14838, 21385}, {16754, 18197}, {17072, 47819}, {17166, 48153}, {17494, 28372}, {19947, 47837}, {20317, 30835}, {21104, 23755}, {21114, 23753}, {21115, 28468}, {21118, 23770}, {21120, 28006}, {23729, 23751}, {23747, 23775}, {23877, 47705}, {23887, 47716}, {24719, 29324}, {24924, 27014}, {25900, 47663}, {26824, 27469}, {27139, 47793}, {28470, 47685}, {28478, 47971}, {28487, 47695}, {29051, 48115}, {29116, 47688}, {29142, 47702}, {29162, 30725}, {29198, 48021}, {29288, 47700}, {30723, 47758}, {34195, 42325}, {47911, 48091}, {47912, 48092}, {47913, 48093}, {47929, 48099}, {48019, 48121}, {48024, 48129}, {48264, 48273}

X(48334) = reflection of X(i) in X(j) for these {i,j}: {649, 3669}, {661, 48131}, {1491, 48137}, {2254, 3777}, {4024, 48280}, {4041, 2530}, {4063, 3960}, {4462, 3835}, {4490, 48100}, {4498, 905}, {4724, 48136}, {4729, 2254}, {4761, 23789}, {4804, 48279}, {4807, 23814}, {4813, 48128}, {4979, 48144}, {21118, 23770}, {21385, 14838}, {23738, 23765}, {23755, 21104}, {31291, 4504}, {47672, 4801}, {47700, 48278}, {47705, 47720}, {47905, 48086}, {47906, 4983}, {47911, 48091}, {47912, 48092}, {47913, 48093}, {47918, 14349}, {47929, 48099}, {47932, 4560}, {47935, 1019}, {47936, 4040}, {47977, 4794}, {48019, 48121}, {48020, 48122}, {48021, 48123}, {48024, 48129}, {48032, 663}, {48094, 6332}, {48150, 1}, {48151, 764}, {48153, 17166}, {48264, 48273}, {48265, 4992}
X(48334) = X(i)-Ceva conjugate of X(j) for these (i,j): {7, 244}, {514, 21120}, {2051, 1086}, {21272, 4642}, {21362, 3752}, {21580, 3663}, {32023, 3123}
X(48334) = X(i)-isoconjugate of X(j) for these (i,j): {6, 8706}, {100, 23617}, {101, 1222}, {220, 6613}, {644, 1476}, {651, 1261}, {692, 32017}, {3451, 3699}, {3939, 40420}, {4587, 40446}, {31615, 40528}
X(48334) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 8706), (1015, 1222), (1086, 32017), (2170, 8), (3452, 190), (3752, 646), (8054, 23617), (12640, 6558), (24237, 14829), (38991, 1261), (40617, 40420)
X(48334) = crosspoint of X(i) and X(j) for these (i,j): {514, 3669}, {3663, 21580}, {3752, 21362}, {18600, 21272}
X(48334) = crosssum of X(i) and X(j) for these (i,j): {1, 48150}, {101, 644}
X(48334) = crossdifference of every pair of points on line {31, 200}
X(48334) = barycentric product X(i)*X(j) for these {i,j}: {7, 6615}, {57, 21120}, {75, 6363}, {244, 21272}, {269, 42337}, {513, 3663}, {514, 3752}, {522, 1122}, {649, 26563}, {661, 18600}, {693, 1201}, {1015, 21580}, {1019, 4415}, {1086, 21362}, {1111, 23845}, {1432, 28006}, {1828, 4025}, {2347, 24002}, {3057, 3676}, {3261, 20228}, {3452, 3669}, {3596, 42336}, {3835, 27499}, {3942, 17906}, {4017, 17183}, {4521, 45205}, {4642, 7192}, {4862, 46004}, {6736, 43932}, {7178, 18163}, {7199, 21796}, {7203, 21031}, {14284, 19604}, {14837, 42549}, {17096, 21809}, {20895, 43924}, {22344, 46107}
X(48334) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 8706}, {269, 6613}, {513, 1222}, {514, 32017}, {649, 23617}, {663, 1261}, {764, 40451}, {1122, 664}, {1201, 100}, {1828, 1897}, {2347, 644}, {3057, 3699}, {3452, 646}, {3663, 668}, {3669, 40420}, {3752, 190}, {4415, 4033}, {4642, 3952}, {6363, 1}, {6615, 8}, {14284, 44720}, {17183, 7257}, {18163, 645}, {18600, 799}, {20228, 101}, {21120, 312}, {21272, 7035}, {21362, 1016}, {21580, 31625}, {21796, 1018}, {21809, 30730}, {22072, 4571}, {22344, 1331}, {23845, 765}, {26563, 1978}, {27499, 4598}, {28006, 17787}, {42336, 56}, {42337, 341}, {42549, 44327}, {43923, 40446}, {43924, 1476}, {45219, 43290}
X(48334) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {905, 4498, 1635}, {4490, 48100, 47810}, {14349, 47918, 661}, {17458, 48033, 4171}, {47918, 48131, 14349}


X(48335) = X(1)X(513)∩X(8)X(48164)

Barycentrics    a*(b - c)*(a*b + b^2 + a*c - b*c + c^2) : :
X(48335) = X[8] - 3 X[48164], 2 X[10] - 3 X[44429], 2 X[661] - 3 X[14349], 5 X[661] - 3 X[47918], 4 X[661] - 3 X[47959], 7 X[661] - 6 X[47997], 5 X[661] - 6 X[48054], X[661] - 3 X[48131], 3 X[4728] - 2 X[4791], 3 X[4801] - X[47675], 5 X[14349] - 2 X[47918], 7 X[14349] - 4 X[47997], 5 X[14349] - 4 X[48054], 4 X[47918] - 5 X[47959], 7 X[47918] - 10 X[47997], X[47918] - 5 X[48131], 7 X[47959] - 8 X[47997], 5 X[47959] - 8 X[48054], X[47959] - 4 X[48131], 5 X[47997] - 7 X[48054], 2 X[47997] - 7 X[48131], 2 X[48054] - 5 X[48131], 3 X[1491] - 2 X[4770], 3 X[905] - 2 X[4394], 3 X[4063] - 4 X[4394], 3 X[1019] - 2 X[4790], 3 X[3669] - X[4790], 4 X[3669] - X[47976], 4 X[4790] - 3 X[47976], 4 X[1125] - 3 X[47804], 5 X[1698] - 6 X[47802], 3 X[1734] - 2 X[4730], X[1734] - 4 X[48137], 3 X[2530] - X[4730], X[4730] - 6 X[48137], 5 X[3616] - 3 X[47805], 7 X[3624] - 6 X[47803], X[47977] - 4 X[48136], 2 X[4147] - 3 X[47816], X[4380] - 3 X[44550], X[4774] - 3 X[48167], 2 X[4782] - 3 X[14419], X[47942] - 4 X[48129], 2 X[23765] + X[48081], 2 X[8689] - 3 X[45316], 3 X[14432] - X[48102], 4 X[19947] - 3 X[47823], 3 X[45671] - 2 X[48008], 3 X[30592] - 2 X[48090}

X(48335) lies on these lines: {1, 513}, {8, 48164}, {10, 44429}, {304, 20949}, {512, 3777}, {514, 661}, {522, 47727}, {649, 3960}, {650, 21385}, {663, 48111}, {784, 48279}, {830, 4449}, {834, 23800}, {891, 1491}, {905, 4063}, {1019, 1429}, {1125, 47804}, {1698, 47802}, {1734, 2530}, {1930, 20906}, {2254, 29350}, {2526, 14077}, {2533, 23815}, {2787, 24719}, {2832, 4724}, {3063, 5299}, {3616, 47805}, {3624, 47803}, {3667, 38329}, {3674, 24002}, {3776, 4707}, {3810, 47712}, {3970, 4079}, {4040, 47977}, {4041, 48066}, {4147, 47816}, {4160, 48023}, {4380, 44550}, {4382, 27469}, {4448, 29660}, {4481, 4762}, {4490, 48059}, {4498, 14838}, {4502, 28855}, {4560, 29302}, {4705, 29226}, {4729, 48018}, {4761, 24720}, {4774, 48167}, {4782, 14419}, {4794, 48032}, {4802, 47726}, {4822, 23738}, {4867, 9001}, {4879, 6004}, {4983, 29198}, {4992, 48267}, {5280, 20980}, {6005, 48151}, {6371, 21189}, {6372, 23765}, {7146, 43052}, {7216, 30723}, {8678, 48086}, {8689, 45316}, {14432, 48102}, {14825, 17192}, {15309, 48121}, {16502, 21007}, {16892, 23876}, {17023, 47762}, {17284, 47760}, {17316, 47759}, {17458, 28863}, {17496, 29013}, {18081, 40495}, {18197, 28374}, {19784, 48246}, {19836, 48165}, {19881, 48181}, {19947, 29633}, {20295, 21222}, {21130, 23888}, {21834, 30519}, {23729, 29126}, {23877, 47716}, {23887, 47691}, {26626, 47763}, {27647, 47926}, {28372, 45671}, {28894, 47681}, {29047, 48278}, {29066, 46403}, {29160, 47688}, {29178, 48114}, {29192, 47687}, {29288, 48272}, {29598, 47761}, {29637, 47822}, {29659, 36848}, {30592, 48090}, {42664, 47676}, {47685, 47729}, {47686, 47728}, {47724, 48089}, {47906, 48045}, {47911, 48051}, {47912, 48052}, {47913, 48053}, {47929, 48058}, {47935, 48064}, {47936, 48065}, {47947, 48091}, {47948, 48092}, {47949, 48093}, {47970, 48099}, {48085, 48128}, {48110, 48144}

X(48335) = midpoint of X(i) and X(j) for these {i,j}: {3904, 47652}, {4449, 48122}, {4822, 23738}, {20295, 21222}, {23729, 30725}, {23765, 48123}, {47651, 47684}, {47685, 47729}, {47686, 47728}
X(48335) = reflection of X(i) in X(j) for these {i,j}: {649, 3960}, {1019, 3669}, {1734, 2530}, {2530, 48137}, {2533, 23815}, {3762, 3835}, {4040, 48136}, {4041, 48066}, {4063, 905}, {4462, 4129}, {4490, 48059}, {4498, 14838}, {4705, 48100}, {4707, 3776}, {4729, 48018}, {4761, 24720}, {4905, 3777}, {4983, 48129}, {14349, 48131}, {21130, 44435}, {21385, 650}, {47724, 48089}, {47906, 48045}, {47911, 48051}, {47912, 48052}, {47913, 48053}, {47918, 48054}, {47929, 48058}, {47935, 48064}, {47936, 48065}, {47942, 4983}, {47947, 48091}, {47948, 48092}, {47949, 48093}, {47959, 14349}, {47970, 48099}, {47976, 1019}, {47977, 4040}, {48032, 4794}, {48081, 48123}, {48085, 48128}, {48110, 48144}, {48111, 663}, {48267, 4992}
X(48335) = X(i)-Ceva conjugate of X(j) for these (i,j): {514, 21130}, {39704, 244}
X(48335) = X(i)-isoconjugate of X(j) for these (i,j): {6, 9059}, {44, 36091}, {100, 40401}, {101, 996}, {519, 32686}
X(48335) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 9059), (1015, 996), (8054, 40401), (40595, 36091)
X(48335) = crosssum of X(101) and X(4752)
X(48335) = crossdifference of every pair of points on line {31, 44}
X(48335) = barycentric product X(i)*X(j) for these {i,j}: {1, 44435}, {75, 9002}, {88, 23888}, {89, 21130}, {513, 4389}, {514, 4850}, {649, 33934}, {661, 16712}, {693, 995}, {1019, 26580}, {3669, 5233}, {3676, 3877}, {4247, 14208}, {4266, 24002}, {4424, 7192}, {23206, 46107}
X(48335) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 9059}, {106, 36091}, {513, 996}, {649, 40401}, {995, 100}, {3877, 3699}, {4247, 162}, {4266, 644}, {4389, 668}, {4424, 3952}, {4850, 190}, {5233, 646}, {9002, 1}, {9456, 32686}, {16712, 799}, {17461, 4767}, {20973, 4752}, {21130, 4671}, {23206, 1331}, {23888, 4358}, {26580, 4033}, {33934, 1978}, {44435, 75}


X(48336) = X(1)X(6372)∩X(512)X(659)

Barycentrics    a*(b - c)*(a^2 - 2*a*b - 2*a*c - b*c) : :
X(48336) = 3 X[659] - 2 X[4063], 3 X[4040] - X[4063], 4 X[663] - 3 X[25569], 3 X[663] - X[48144], 2 X[4367] - 3 X[25569], 3 X[4367] - 2 X[48144], 9 X[25569] - 4 X[48144], 3 X[48123] - 2 X[48128], 4 X[4775] - X[21343], 3 X[667] - 2 X[48064], X[4784] - 4 X[4794], 3 X[4784] - 4 X[48064], 3 X[4794] - X[48064], 3 X[4983] - 2 X[48051], 3 X[6161] + 2 X[48051], 2 X[1577] - 3 X[4800], 2 X[1734] - 3 X[47827], 2 X[2254] - 3 X[47893], 2 X[2533] - 3 X[47872], 4 X[3716] - 3 X[47872], 2 X[3837] - 3 X[47840], 2 X[4705] - 3 X[48162], 4 X[48058] - 3 X[48162], 2 X[4162] + X[47913], X[4729] - 3 X[47811], X[4959] + 2 X[47922], 2 X[47955] - 3 X[48024], 4 X[14838] - 3 X[48244], 2 X[17072] - 3 X[47822], 2 X[21051] - 3 X[47821], X[21302] - 3 X[47821], 2 X[21146] - 3 X[47889], 2 X[21260] - 3 X[47838], 2 X[24720] - 3 X[47841], 5 X[30795] - 6 X[47839], 3 X[47826] - 2 X[47967], 3 X[47888] - 2 X[48018], 4 X[48059] - 3 X[48160}

X(48336) lies on these lines: {1, 6372}, {512, 659}, {513, 663}, {514, 4775}, {661, 4435}, {667, 4784}, {693, 29246}, {814, 48080}, {830, 4983}, {885, 17097}, {891, 47970}, {900, 4560}, {1019, 1960}, {1491, 3309}, {1577, 4800}, {1734, 47827}, {2254, 47893}, {2530, 42325}, {2533, 3716}, {3287, 4502}, {3762, 29298}, {3800, 48103}, {3837, 47840}, {3887, 4705}, {3900, 4490}, {3907, 48265}, {4010, 29051}, {4057, 8639}, {4083, 4724}, {4107, 48049}, {4160, 47949}, {4162, 47913}, {4170, 4810}, {4391, 4774}, {4401, 4834}, {4449, 29198}, {4729, 47811}, {4730, 48003}, {4806, 21301}, {4895, 47918}, {4959, 47922}, {4977, 17166}, {4979, 5029}, {4992, 46403}, {5592, 29118}, {6004, 14349}, {7265, 29086}, {8678, 47955}, {14077, 47966}, {14838, 48244}, {17072, 47822}, {18107, 47759}, {21051, 21302}, {21146, 47889}, {21260, 47838}, {24286, 48086}, {24720, 47841}, {25259, 29074}, {28470, 48043}, {29017, 47972}, {29066, 48267}, {29082, 47708}, {29102, 47712}, {29120, 47728}, {29134, 47684}, {29168, 47682}, {29186, 48273}, {29208, 48094}, {29224, 47713}, {29226, 47929}, {29276, 48266}, {29288, 48083}, {29324, 47729}, {29332, 47709}, {29350, 48065}, {29354, 47727}, {30795, 47839}, {47826, 47967}, {47888, 48018}, {47912, 48028}, {47948, 48053}, {48023, 48093}, {48059, 48160}

X(48336) = midpoint of X(i) and X(j) for these {i,j}: {4822, 48150}, {4895, 47918}, {4983, 6161}
X(48336) = reflection of X(i) in X(j) for these {i,j}: {659, 4040}, {667, 4794}, {1019, 1960}, {1491, 48099}, {2533, 3716}, {3777, 48136}, {4367, 663}, {4490, 48029}, {4705, 48058}, {4730, 48003}, {4774, 4391}, {4784, 667}, {4810, 4170}, {4834, 4401}, {4879, 4775}, {21301, 4806}, {21302, 21051}, {21343, 4879}, {46403, 4992}, {47912, 48028}, {47948, 48053}, {48023, 48093}, {48122, 48129}
X(48336) = crosspoint of X(1) and X(8708)
X(48336) = crosssum of X(1) and X(6372)
X(48336) = crossdifference of every pair of points on line {9, 24512}
X(48336) = barycentric product X(i)*X(j) for these {i,j}: {1, 48000}, {513, 17260}, {514, 3750}
X(48336) = barycentric quotient X(i)/X(j) for these {i,j}: {3750, 190}, {17260, 668}, {48000, 75}
X(48336) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {663, 4367, 25569}, {2533, 3716, 47872}, {4705, 48058, 48162}, {21302, 47821, 21051}


X(48337) = X(1)X(512)∩X(2)X(4807)

Barycentrics    a*(b - c)*(a^2 - 3*a*b - 3*a*c + b*c) : :
X(48337) = 3 X[1] - 2 X[4367], 5 X[1] - 2 X[4784], 3 X[1019] - 4 X[4367], 5 X[1019] - 4 X[4784], X[1019] - 4 X[4879], 5 X[4367] - 3 X[4784], X[4367] - 3 X[4879], X[4784] - 5 X[4879], 2 X[10] - 3 X[47840], 3 X[663] - 2 X[4401], 3 X[4063] - 4 X[4401], 3 X[1022] - 2 X[48151], 4 X[1125] - 3 X[47836], 5 X[1698] - 6 X[47839], 7 X[3624] - 6 X[47837], X[3632] - 4 X[4806], 3 X[3679] - 4 X[21051], 4 X[4775] - X[21385], 2 X[4147] - 3 X[47838], 3 X[8643] - 2 X[48011}

X(48337) lies on these lines: {1, 512}, {2, 4807}, {8, 4129}, {10, 47840}, {55, 39577}, {525, 47727}, {663, 4063}, {830, 4895}, {891, 47970}, {1018, 3903}, {1021, 42664}, {1022, 48151}, {1125, 47836}, {1698, 47839}, {1734, 48136}, {2785, 47712}, {3340, 7178}, {3624, 47837}, {3632, 4806}, {3679, 21051}, {3737, 4132}, {3776, 28579}, {3800, 47682}, {3887, 48131}, {3900, 14349}, {3907, 4170}, {3979, 8034}, {4010, 29298}, {4040, 4083}, {4145, 4833}, {4147, 47838}, {4151, 47683}, {4160, 4822}, {4449, 6005}, {4498, 4794}, {4729, 14838}, {4810, 29182}, {4814, 48012}, {4922, 29150}, {4959, 48023}, {4960, 17166}, {6372, 21343}, {7927, 47726}, {7962, 29126}, {7982, 28473}, {7983, 40459}, {8643, 48011}, {8678, 48085}, {8712, 48111}, {9040, 16496}, {9331, 22229}, {11529, 34958}, {14077, 47959}, {17159, 17218}, {29013, 47729}, {29082, 47725}, {29158, 47728}, {29188, 48279}, {29220, 47692}, {29304, 47691}, {29366, 47724}, {34195, 42325}, {35338, 46162}, {47948, 48123}

X(48337) = midpoint of X(4959) and X(48023)
X(48337) = reflection of X(i) in X(j) for these {i,j}: {1, 4879}, {8, 4129}, {1019, 1}, {1734, 48136}, {4040, 4775}, {4063, 663}, {4498, 4794}, {4729, 14838}, {4814, 48012}, {4960, 17166}, {21385, 4040}, {47724, 48273}, {47947, 4822}, {47948, 48123}
X(48337) = anticomplement of X(4807)
X(48337) = Evans inverse of X(4367)
X(48337) = crossdifference of every pair of points on line {2238, 16669}


X(48338) = X(1)X(6005)∩X(187)X(237)

Barycentrics    a^2*(a - 3*b - 3*c)*(b - c) : :
X(48338) = 2 X[10] - 3 X[47838], X[145] + 2 X[48037], 3 X[649] - 4 X[667], 5 X[649] - 8 X[1960], X[649] - 4 X[4775], 5 X[649] - 4 X[4834], 2 X[649] - 3 X[8643], 7 X[649] - 10 X[8656], 3 X[663] - 2 X[667], 5 X[663] - 4 X[1960], 5 X[663] - 2 X[4834], 4 X[663] - 3 X[8643], 7 X[663] - 5 X[8656], 5 X[667] - 6 X[1960], X[667] - 3 X[4775], 5 X[667] - 3 X[4834], 8 X[667] - 9 X[8643], 14 X[667] - 15 X[8656], 2 X[1960] - 5 X[4775], 16 X[1960] - 15 X[8643], 28 X[1960] - 25 X[8656], 5 X[4775] - X[4834], 8 X[4775] - 3 X[8643], 14 X[4775] - 5 X[8656], 8 X[4834] - 15 X[8643], 14 X[4834] - 25 X[8656], 21 X[8643] - 20 X[8656], 2 X[2533] - 3 X[47832], 2 X[4041] - 3 X[4893], 3 X[4893] - 4 X[48099], 2 X[4147] - 3 X[47821], 2 X[4163] - 3 X[47765], 2 X[4490] - 3 X[47826], 2 X[4807] - 3 X[47794], X[4813] + 2 X[4895], X[4959] + 2 X[4983], 4 X[4990] - 3 X[47874], 4 X[17072] - 5 X[30835], 2 X[17072] - 3 X[47840], 5 X[30835] - 6 X[47840], 2 X[21301] - 3 X[31147], 7 X[31207] - 6 X[47836}

X(48338) lies on these lines: {1, 6005}, {10, 47838}, {145, 48037}, {187, 237}, {513, 4162}, {650, 4729}, {657, 4079}, {661, 3900}, {830, 48121}, {834, 4491}, {891, 47929}, {926, 4502}, {2254, 48136}, {2484, 4826}, {2499, 4105}, {2533, 47832}, {2785, 47708}, {3309, 38329}, {3667, 17496}, {3803, 47935}, {3835, 21302}, {3887, 14349}, {3907, 48080}, {3910, 47972}, {4010, 29366}, {4040, 4498}, {4041, 4893}, {4063, 4794}, {4083, 4724}, {4132, 46385}, {4147, 47821}, {4160, 47911}, {4163, 47765}, {4170, 29066}, {4382, 29051}, {4474, 29298}, {4490, 47826}, {4705, 4814}, {4785, 31291}, {4807, 47794}, {4810, 29274}, {4813, 4822}, {4843, 48277}, {4922, 29170}, {4959, 4983}, {4990, 47874}, {6002, 47729}, {6004, 48122}, {7265, 29192}, {8712, 48032}, {14077, 47918}, {17072, 30835}, {17159, 17215}, {17166, 48141}, {20295, 28470}, {21301, 31147}, {21343, 29198}, {21385, 48065}, {23755, 47123}, {23875, 47727}, {29118, 47728}, {29188, 48273}, {29208, 48118}, {29220, 47713}, {29246, 48119}, {29278, 48266}, {29288, 48117}, {29304, 47712}, {31207, 47836}, {47905, 48091}, {48020, 48128}, {48023, 48123}

X(48338) = midpoint of X(i) and X(j) for these {i,j}: {4822, 4895}, {4959, 47912}
X(48338) = reflection of X(i) in X(j) for these {i,j}: {649, 663}, {663, 4775}, {2254, 48136}, {4041, 48099}, {4063, 4794}, {4449, 4879}, {4474, 48267}, {4498, 4040}, {4729, 650}, {4813, 4822}, {4814, 4705}, {4834, 1960}, {21302, 3835}, {21385, 48065}, {23755, 47123}, {47905, 48091}, {47911, 48081}, {47912, 4983}, {47935, 3803}, {48020, 48128}, {48023, 48123}, {48119, 48279}, {48141, 17166}, {48144, 1}
X(48338) = isogonal conjugate of the isotomic conjugate of X(28161)
X(48338) = X(i)-Ceva conjugate of X(j) for these (i,j): {10390, 244}, {28162, 6}
X(48338) = X(i)-isoconjugate of X(j) for these (i,j): {75, 28162}, {99, 31503}, {100, 30712}, {190, 39980}
X(48338) = X(i)-Dao conjugate of X(j) for these (i, j): (206, 28162), (8054, 30712), (11530, 668), (38986, 31503)
X(48338) = crosspoint of X(i) and X(j) for these (i,j): {6, 28162}, {101, 2334}
X(48338) = crosssum of X(i) and X(j) for these (i,j): {1, 48144}, {2, 28161}, {514, 3616}
X(48338) = crossdifference of every pair of points on line {2, 1743}
X(48338) = barycentric product X(i)*X(j) for these {i,j}: {6, 28161}, {513, 3731}, {649, 3617}, {650, 3340}, {663, 5226}, {667, 42034}, {3445, 14350}, {3733, 4058}, {3984, 6591}, {4394, 10563}
X(48338) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 28162}, {649, 30712}, {667, 39980}, {798, 31503}, {3340, 4554}, {3617, 1978}, {3731, 668}, {4058, 27808}, {5226, 4572}, {28161, 76}, {42034, 6386}
X(48338) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 663, 8643}, {4041, 48099, 4893}, {17072, 47840, 30835}


X(48339) = X(1)X(522)∩X(8)X(4791)

Barycentrics    (b - c)*(a^3 - 2*a^2*b + a*b^2 - 2*a^2*c + 2*a*b*c + b^2*c + a*c^2 + b*c^2) : :
X(48339) = X[8] - 3 X[48172], 2 X[4791] - 3 X[48172], 2 X[10] - 3 X[47832], X[4814] - 3 X[47832], 4 X[1125] - 3 X[47828], 5 X[1698] - 6 X[47831], 3 X[1734] - 4 X[25380], 2 X[1734] - 3 X[47795], 8 X[25380] - 9 X[47795], 5 X[3616] - 3 X[48242], 7 X[3624] - 6 X[47830], 2 X[4041] - 3 X[47794], 2 X[4705] - 3 X[47838], 2 X[4770] - 3 X[47822], 3 X[47796] - 2 X[48018], 3 X[47840] - 2 X[48012}

X(48339) lies on these lines: {1, 522}, {8, 4791}, {10, 4814}, {239, 47790}, {519, 4474}, {523, 4775}, {657, 3294}, {663, 4151}, {693, 3887}, {784, 4879}, {824, 47727}, {900, 4378}, {1125, 47828}, {1577, 3900}, {1698, 47831}, {1734, 25380}, {3261, 17143}, {3309, 4978}, {3616, 48242}, {3624, 47830}, {3762, 14077}, {4024, 29192}, {4041, 47794}, {4160, 48080}, {4162, 23882}, {4170, 8678}, {4384, 47787}, {4449, 8714}, {4500, 47723}, {4702, 4777}, {4705, 47838}, {4707, 47123}, {4730, 4874}, {4761, 7662}, {4770, 47822}, {4794, 17494}, {4801, 42325}, {4804, 4895}, {4815, 15313}, {4823, 21302}, {4825, 48183}, {6004, 48279}, {6005, 17166}, {6161, 29362}, {7253, 28161}, {7650, 35057}, {16823, 47808}, {16826, 27486}, {16828, 48186}, {16830, 47798}, {16831, 47785}, {17144, 20954}, {17753, 46402}, {19853, 48173}, {20907, 32104}, {21385, 48063}, {23876, 47695}, {25512, 48228}, {29188, 48120}, {29270, 31291}, {29302, 48150}, {29350, 47694}, {39586, 47800}, {47796, 48018}, {47840, 48012}

X(48339) = midpoint of X(4804) and X(4895)
X(48339) = reflection of X(i) in X(j) for these {i,j}: {8, 4791}, {4707, 47123}, {4730, 4874}, {4761, 7662}, {4814, 10}, {4825, 48183}, {17494, 4794}, {21302, 4823}, {21385, 48063}, {47723, 4500}
X(48339) = crossdifference of every pair of points on line {2183, 5165}
X(48339) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 48172, 4791}, {4814, 47832, 10}


X(48340) = X(1)X(4778)∩X(513)X(663)

Barycentrics    a^2*(b - c)*(a^2 - b^2 - 4*b*c - c^2) : :
X(48340) = 3 X[663] - 2 X[2605], 3 X[663] - X[43924], 3 X[1459] - 4 X[2605], 3 X[1459] - 2 X[43924], 2 X[3733] - 3 X[8643], 3 X[4448] - 2 X[6133], 2 X[17072] - 3 X[48165], 2 X[21187] - 3 X[47798], 2 X[24720] - 3 X[48209], 5 X[30835] - 4 X[44316], 2 X[47843] - 3 X[48173}

X(48340) lies on these lines: {1, 4778}, {42, 47826}, {513, 663}, {522, 3465}, {523, 4724}, {649, 4057}, {652, 33525}, {656, 3309}, {657, 21007}, {667, 23226}, {832, 1245}, {834, 4491}, {900, 17418}, {2424, 34821}, {2484, 4502}, {2517, 3716}, {3667, 3737}, {3733, 8643}, {3835, 44444}, {4132, 4498}, {4406, 17215}, {4448, 6133}, {4449, 4977}, {4775, 6371}, {4802, 47929}, {4815, 29186}, {4959, 8702}, {4985, 29066}, {6006, 21173}, {7650, 29051}, {7661, 8713}, {15313, 17420}, {17072, 48165}, {17159, 26277}, {20316, 21302}, {21185, 23752}, {21187, 47798}, {22090, 48099}, {23655, 48024}, {23800, 42325}, {24720, 48209}, {28147, 47970}, {28161, 48065}, {30835, 44316}, {47843, 48173}

X(48340) = midpoint of X(4724) and X(42312)
X(48340) = reflection of X(i) in X(j) for these {i,j}: {649, 4057}, {1459, 663}, {2517, 3716}, {3737, 4794}, {21302, 20316}, {23752, 21185}, {43924, 2605}, {44444, 3835}, {46385, 4040}
X(48340) = isogonal conjugate of the isotomic conjugate of X(48268)
X(48340) = X(i)-Ceva conjugate of X(j) for these (i,j): {29187, 42}, {48074, 649}
X(48340) = X(i)-isoconjugate of X(j) for these (i,j): {100, 3296}, {1783, 30679}
X(48340) = X(i)-Dao conjugate of X(j) for these (i, j): (8054, 3296), (39006, 30679)
X(48340) = crosspoint of X(i) and X(j) for these (i,j): {1, 8694}, {1171, 5545}
X(48340) = crosssum of X(i) and X(j) for these (i,j): {1, 4778}, {513, 4646}, {514, 4648}, {522, 1698}, {1213, 4843}
X(48340) = crossdifference of every pair of points on line {9, 1125}
X(48340) = barycentric product X(i)*X(j) for these {i,j}: {1, 47965}, {6, 48268}, {513, 3305}, {514, 3295}, {649, 42696}, {650, 7190}, {1019, 3697}, {42032, 43924}
X(48340) = barycentric quotient X(i)/X(j) for these {i,j}: {649, 3296}, {1459, 30679}, {3295, 190}, {3305, 668}, {3697, 4033}, {7190, 4554}, {42696, 1978}, {47965, 75}, {48268, 76}
X(48340) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {663, 43924, 2605}, {2605, 43924, 1459}, {4502, 8632, 2484}


X(48341) = X(239)X(514)∩X(513)X(4162)

Barycentrics    a*(b - c)*(a^2 + a*b + a*c + 4*b*c) : :
X(48341) = 3 X[649] - 4 X[1019], 5 X[649] - 4 X[4063], 3 X[649] - 2 X[4498], 7 X[649] - 4 X[21385], 9 X[649] - 8 X[48011], 7 X[649] - 8 X[48064], X[649] - 4 X[48320], 5 X[1019] - 3 X[4063], 7 X[1019] - 3 X[21385], 3 X[1019] - 2 X[48011], 7 X[1019] - 6 X[48064], 2 X[1019] - 3 X[48144], X[1019] - 3 X[48320], 6 X[4063] - 5 X[4498], 7 X[4063] - 5 X[21385], 9 X[4063] - 10 X[48011], 7 X[4063] - 10 X[48064], 2 X[4063] - 5 X[48144], X[4063] - 5 X[48320], 7 X[4498] - 6 X[21385], 3 X[4498] - 4 X[48011], 7 X[4498] - 12 X[48064], X[4498] - 3 X[48144], X[4498] - 6 X[48320], 2 X[21222] + X[48141], 9 X[21385] - 14 X[48011], 2 X[21385] - 7 X[48144], X[21385] - 7 X[48320], 7 X[48011] - 9 X[48064], 4 X[48011] - 9 X[48144], 2 X[48011] - 9 X[48320], 4 X[48064] - 7 X[48144], 2 X[48064] - 7 X[48320], 3 X[4449] - 2 X[4879], X[4879] - 3 X[48323], 4 X[4879] - 3 X[48338], 4 X[48323] - X[48338], 3 X[661] - 2 X[47915], 3 X[3669] - X[47915], 3 X[663] - 4 X[48328], 3 X[4378] - 2 X[48328], 4 X[905] - 3 X[4893], 3 X[4893] - 2 X[47918], 3 X[1022] - X[48085], 3 X[1459] - 2 X[4833], 3 X[1635] - 2 X[47921], 2 X[4147] - 3 X[47824], 4 X[4367] - 3 X[8643], 3 X[4367] - 2 X[48331], 2 X[4724] - 3 X[8643], 3 X[4724] - 4 X[48331], 9 X[8643] - 8 X[48331], 3 X[4379] - 2 X[4391], 2 X[4490] - 3 X[47828], 3 X[4813] - 4 X[48091], 2 X[48091] - 3 X[48131], 3 X[14413] - X[47906], 3 X[14413] - 2 X[48099], 4 X[20317] - 5 X[24924], 4 X[30723] - 3 X[47757], 5 X[30835] - 6 X[47796], 7 X[31207] - 6 X[47793], 3 X[47826] - 2 X[47913], 3 X[47827] - 2 X[47922], 3 X[47832] - 2 X[48265], 3 X[47893] - 2 X[47967]

X(48341) lies on these lines: {239, 514}, {513, 4162}, {661, 3669}, {663, 4378}, {667, 47929}, {764, 48122}, {814, 48119}, {905, 4893}, {1022, 27789}, {1459, 4833}, {1635, 47921}, {2484, 30520}, {2530, 47912}, {3777, 48023}, {3803, 47936}, {3907, 48108}, {3910, 47971}, {3960, 47959}, {4147, 47824}, {4160, 4905}, {4367, 4724}, {4369, 4462}, {4379, 4391}, {4382, 4801}, {4490, 47828}, {4729, 7659}, {4784, 29226}, {4813, 48091}, {4822, 48332}, {4922, 29246}, {4978, 29148}, {4979, 8712}, {6005, 48282}, {6332, 48082}, {8672, 43924}, {8678, 48151}, {14349, 47911}, {14413, 47906}, {15309, 48121}, {20317, 24924}, {21146, 29324}, {21302, 48073}, {23880, 47672}, {28398, 31290}, {28878, 30719}, {29037, 47719}, {29118, 47720}, {29120, 48326}, {29132, 47716}, {29170, 48279}, {29212, 47715}, {30723, 47757}, {30835, 47796}, {31207, 47793}, {47826, 47913}, {47827, 47922}, {47832, 48265}, {47893, 47967}, {48019, 48128}, {48021, 48136}, {48078, 48299}, {48117, 48300}, {48266, 48280}

X(48341) = reflection of X(i) in X(j) for these {i,j}: {649, 48144}, {661, 3669}, {663, 4378}, {4382, 4801}, {4449, 48323}, {4462, 4369}, {4498, 1019}, {4724, 4367}, {4729, 7659}, {4813, 48131}, {4822, 48332}, {21302, 48073}, {21385, 48064}, {47906, 48099}, {47911, 14349}, {47912, 2530}, {47918, 905}, {47926, 4560}, {47929, 667}, {47936, 3803}, {47959, 3960}, {48019, 48128}, {48021, 48136}, {48023, 3777}, {48078, 48299}, {48082, 6332}, {48117, 48300}, {48121, 48335}, {48122, 764}, {48144, 48320}, {48266, 48280}, {48338, 4449}
X(48341) = crosssum of X(649) and X(16667)
X(48341) = crossdifference of every pair of points on line {42, 1743}
X(48341) = barycentric product X(i)*X(j) for these {i,j}: {513, 25590}, {514, 37674}, {3261, 5042}, {4025, 4214}
X(48341) = barycentric quotient X(i)/X(j) for these {i,j}: {4214, 1897}, {5042, 101}, {25590, 668}, {37674, 190}
X(48341) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {905, 47918, 4893}, {1019, 4498, 649}, {4367, 4724, 8643}, {4498, 48144, 1019}, {14413, 47906, 48099}


X(48342) = X(242)X(514)∩X(513)X(4162)

Barycentrics    a*(b - c)*(a^3 - a*b^2 + 2*a*b*c + 2*b^2*c - a*c^2 + 2*b*c^2) : :
X(48342) = 3 X[1459] - 2 X[3737], 4 X[3737] - 3 X[46385], X[3737] - 3 X[48281], X[46385] - 4 X[48281], 3 X[4449] - X[42312], 3 X[4449] - 2 X[48292], 2 X[42312] - 3 X[48303], 4 X[48292] - 3 X[48303], 2 X[4840] - 3 X[48144], 3 X[2457] - 4 X[3676], 2 X[4147] - 3 X[48246], 2 X[20316] - 3 X[47796]

X(48342) lies on these lines: {1, 4778}, {242, 514}, {513, 4162}, {522, 48282}, {523, 7286}, {656, 3669}, {663, 4977}, {764, 832}, {834, 4840}, {2457, 3676}, {2605, 4724}, {3667, 48293}, {3720, 47826}, {3733, 4498}, {3777, 38469}, {4017, 9001}, {4040, 28229}, {4147, 48246}, {4378, 6371}, {4462, 8062}, {4802, 17418}, {4905, 35057}, {4985, 48295}, {15313, 48151}, {17215, 20949}, {20293, 47843}, {20316, 47796}, {21106, 47704}, {21146, 23655}, {21173, 28147}, {21222, 28623}, {28209, 48302}, {28213, 47929}, {28220, 48306}, {28225, 48287}

X(48342) = midpoint of X(21106) and X(47704)
X(48342) = reflection of X(i) in X(j) for these {i,j}: {656, 3669}, {663, 48283}, {1459, 48281}, {4462, 8062}, {4498, 3733}, {4724, 2605}, {4985, 48295}, {20293, 47843}, {42312, 48292}, {46385, 1459}, {47929, 48297}, {48303, 4449}, {48307, 48287}, {48340, 1}
X(48342) = crosspoint of X(1219) and X(8050)
X(48342) = crosssum of X(i) and X(j) for these (i,j): {1, 48340}, {1191, 4057}
X(48342) = crossdifference of every pair of points on line {71, 380}
X(48342) = barycentric product X(i)*X(j) for these {i,j}: {474, 514}, {649, 44147}, {3261, 44104}
X(48342) = barycentric quotient X(i)/X(j) for these {i,j}: {474, 190}, {44104, 101}, {44147, 1978}
X(48342) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4449, 42312, 48292}, {42312, 48292, 48303}


X(48343) = X(513)X(25405)∩X(514)X(659)

Barycentrics    a*(b - c)*(2*a^2 + 3*b*c) : :
X(48343) = 3 X[1] - X[48338], 3 X[48144] + X[48338], 3 X[659] - 5 X[667], X[659] - 5 X[4367], X[659] + 5 X[4378], 4 X[659] - 5 X[4401], 3 X[659] + 5 X[48323], X[667] - 3 X[4367], X[667] + 3 X[4378], 4 X[667] - 3 X[4401], 4 X[4367] - X[4401], 3 X[4367] + X[48323], 4 X[4378] + X[4401], 3 X[4378] - X[48323], 3 X[4401] + 4 X[48323], 5 X[905] - 3 X[48193], 5 X[48012] - 6 X[48193], 5 X[3616] - 3 X[47838], 4 X[3636] - X[48037], X[3762] - 3 X[47820], X[4462] - 3 X[47818], X[4490] - 3 X[14419], 3 X[8643] - X[47970], X[14349] - 3 X[14413], 3 X[14422] - X[48005], 2 X[21051] - 3 X[48218], 5 X[21260] - 6 X[45340], 3 X[30234] - X[47921]

X(48343) lies on these lines: {1, 6005}, {512, 48287}, {513, 25405}, {514, 659}, {649, 48282}, {663, 48320}, {693, 29344}, {830, 3669}, {890, 4932}, {891, 48011}, {905, 4160}, {1019, 4449}, {1960, 29198}, {2787, 4823}, {2832, 3803}, {3616, 47838}, {3636, 48037}, {3733, 28147}, {3762, 47820}, {3910, 39545}, {3960, 8678}, {4057, 28229}, {4083, 48064}, {4462, 47818}, {4490, 14419}, {4491, 4778}, {4504, 29066}, {4784, 48333}, {4791, 29324}, {4794, 6372}, {4834, 21343}, {4905, 48322}, {4978, 29033}, {6002, 48295}, {8045, 29212}, {8637, 23394}, {8643, 47970}, {8650, 48060}, {9266, 32106}, {14349, 14413}, {14422, 48005}, {15309, 48136}, {15599, 28473}, {17166, 48321}, {17212, 20907}, {21051, 48218}, {21260, 45340}, {23738, 48111}, {23770, 29114}, {23789, 28470}, {23875, 48290}, {28537, 44811}, {29140, 47691}, {29176, 48090}, {29178, 48273}, {29182, 48098}, {29270, 48279}, {29358, 47682}, {30234, 47921}, {42325, 48327}, {47987, 48099}, {48151, 48324}

X(48343) = midpoint of X(i) and X(j) for these {i,j}: {1, 48144}, {649, 48282}, {663, 48320}, {667, 48323}, {1019, 4449}, {4367, 4378}, {4784, 48333}, {4834, 21343}, {4905, 48322}, {17166, 48321}, {23738, 48111}, {48151, 48324}
X(48343) = reflection of X(i) in X(j) for these {i,j}: {4794, 48330}, {47987, 48099}, {48012, 905}, {48065, 1960}, {48066, 3960}, {48294, 48328}
X(48343) = crossdifference of every pair of points on line {2276, 16885}
X(48343) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {667, 4378, 48323}, {4367, 48323, 667}


X(48344) = X(1)X(513)∩X(514)X(1960)

Barycentrics    a*(b - c)*(2*a^2 - a*b - a*c + 3*b*c) : :
X(48344) = 3 X[1] - X[4775], 3 X[1] + X[48320], 3 X[4378] + X[4775], 3 X[4378] - X[48320], 3 X[14421] - X[48335], X[8] - 3 X[47823], 2 X[10] - 3 X[48216], X[145] + 3 X[47824], X[1960] - 3 X[48328], 2 X[1960] - 3 X[48330], 4 X[1960] - 3 X[48331], 4 X[48328] - X[48331], X[649] - 3 X[4367], X[649] + 3 X[4449], 3 X[4367] + X[21343], 3 X[4449] - X[21343], 3 X[659] - 5 X[8656], 3 X[667] - X[21385], X[21385] + 3 X[48282], 4 X[1125] - 3 X[48197], X[1491] - 3 X[14413], 5 X[3616] - 3 X[47822], 7 X[3622] - 3 X[47821], X[3835] - 3 X[45667], 3 X[4379] - X[4774], X[4474] - 3 X[47833], X[4724] - 3 X[25569], X[4770] - 3 X[14422], 2 X[4770] - 3 X[48213], 2 X[4791] - 3 X[48202], X[4814] - 3 X[48244], 7 X[27138] - 9 X[47841], X[48019] - 3 X[48123], 2 X[48026] - 3 X[48093], X[48026] - 3 X[48136]

X(48344) lies on these lines: {1, 513}, {8, 47823}, {10, 48216}, {145, 47824}, {213, 39521}, {239, 9260}, {512, 48287}, {514, 1960}, {523, 48325}, {649, 4083}, {650, 14438}, {659, 8656}, {663, 29198}, {667, 21385}, {693, 4922}, {814, 4504}, {830, 48137}, {891, 4782}, {1019, 48333}, {1107, 21348}, {1125, 48197}, {1319, 43052}, {1385, 28537}, {1491, 14413}, {2176, 20980}, {2787, 48090}, {3616, 47822}, {3622, 47821}, {3777, 48322}, {3835, 45667}, {4160, 48030}, {4379, 4774}, {4393, 47762}, {4474, 47833}, {4508, 45320}, {4724, 25569}, {4770, 14422}, {4776, 29570}, {4777, 29908}, {4791, 48202}, {4802, 48288}, {4814, 48244}, {4823, 29268}, {4879, 48144}, {4926, 48339}, {4978, 29274}, {6372, 48294}, {6588, 47967}, {7192, 23506}, {8640, 23394}, {8678, 48100}, {9443, 22108}, {9508, 14077}, {16823, 47803}, {16826, 47760}, {16830, 47802}, {17212, 33296}, {17496, 48301}, {19853, 48230}, {20906, 31997}, {21146, 47729}, {23765, 48150}, {23770, 29156}, {24331, 45666}, {27138, 47841}, {28151, 47683}, {28910, 42819}, {29066, 48098}, {29122, 47691}, {29152, 48273}, {29188, 48285}, {29204, 47682}, {29238, 48279}, {29276, 48280}, {29350, 48296}, {36534, 36848}, {47728, 48326}, {47957, 48099}, {48019, 48123}, {48026, 48093}

X(48344) = midpoint of X(i) and X(j) for these {i,j}: {1, 4378}, {649, 21343}, {663, 48323}, {667, 48282}, {693, 4922}, {764, 48324}, {1019, 48333}, {3777, 48322}, {4367, 4449}, {4775, 48320}, {4879, 48144}, {17496, 48301}, {21146, 47729}, {23765, 48150}, {47728, 48326}, {48291, 48321}
X(48344) = reflection of X(i) in X(j) for these {i,j}: {47957, 48099}, {48090, 48295}, {48093, 48136}, {48213, 14422}, {48330, 48328}, {48331, 48330}
X(48344) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {932, 21291}, {7121, 39364}, {34073, 21219}
X(48344) = X(47779)-Dao conjugate of X(4777)
X(48344) = crosspoint of X(1) and X(4597)
X(48344) = crosssum of X(i) and X(j) for these (i,j): {1, 4775}, {649, 23540}
X(48344) = crossdifference of every pair of points on line {43, 44}
X(48344) = barycentric product X(1)*X(47779)
X(48344) = barycentric quotient X(47779)/X(75)
X(48344) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 48320, 4775}, {649, 4449, 21343}, {4367, 21343, 649}, {4378, 4775, 48320}


X(48345) = X(513)X(25405)∩X(514)X(47131)

Barycentrics    a*(b - c)*(3*a^2 - 2*a*b + b^2 - 2*a*c + b*c + c^2) : :
X(48345) = 3 X[1] - X[48334], 3 X[48150] + X[48334], X[8] - 3 X[47817], 3 X[663] - X[14349], 5 X[663] - X[48023], 4 X[663] - X[48052], 5 X[14349] - 3 X[48023], 4 X[14349] - 3 X[48052], X[14349] + 3 X[48324], 4 X[48023] - 5 X[48052], X[48023] + 5 X[48324], X[48052] + 4 X[48324], X[1734] - 3 X[8643], X[2530] - 3 X[25569], 3 X[3251] - X[4879], 3 X[4040] - X[47918], 2 X[47918] - 3 X[48004], X[47918] + 3 X[48322], X[48004] + 2 X[48322], 3 X[4794] - X[47997], 2 X[47997] - 3 X[48058], X[21302] - 3 X[47818]

X(48345) lies on these lines: {1, 48150}, {8, 47817}, {512, 3743}, {513, 25405}, {514, 47131}, {663, 830}, {667, 3887}, {1019, 4653}, {1734, 8643}, {1960, 14838}, {2530, 25569}, {2832, 4449}, {3251, 4879}, {3309, 44811}, {3803, 4162}, {3900, 4401}, {3960, 6004}, {4040, 4160}, {4057, 35057}, {4063, 4895}, {4170, 31291}, {4367, 6161}, {4794, 8678}, {4885, 28585}, {15309, 48336}, {21302, 47818}, {29298, 48248}, {40459, 41193}, {48003, 48331}, {48032, 48282}

X(48345) = midpoint of X(i) and X(j) for these {i,j}: {1, 48150}, {663, 48324}, {3803, 4162}, {4040, 48322}, {4063, 4895}, {4170, 31291}, {4367, 6161}, {4449, 48111}, {48032, 48282}, {48327, 48329}
X(48345) = reflection of X(i) in X(j) for these {i,j}: {3960, 48330}, {14838, 1960}, {48003, 48331}, {48004, 4040}, {48058, 4794}
X(48345) = crossdifference of every pair of points on line {5282, 16885}


X(48346) = X(513)X(4162)∩X(514)X(3716)

Barycentrics    a*(b - c)*(a^2 - 2*a*b - b^2 - 2*a*c + 4*b*c - c^2) : :
X(48346) = 3 X[1] - X[48111], 2 X[48111] - 3 X[48329], X[8] - 3 X[47819], 3 X[4449] - X[48322], X[48322] + 3 X[48334], 9 X[47966] - 10 X[48004], 4 X[47966] - 5 X[48029], 7 X[47966] - 10 X[48058], 3 X[47966] - 5 X[48099], 2 X[47966] - 5 X[48136], X[47966] - 5 X[48332], 8 X[48004] - 9 X[48029], 7 X[48004] - 9 X[48058], 2 X[48004] - 3 X[48099], 4 X[48004] - 9 X[48136], 2 X[48004] - 9 X[48332], 7 X[48029] - 8 X[48058], 3 X[48029] - 4 X[48099], X[48029] - 4 X[48332], 6 X[48058] - 7 X[48099], 4 X[48058] - 7 X[48136], 2 X[48058] - 7 X[48332], 2 X[48099] - 3 X[48136], X[48099] - 3 X[48332], 3 X[663] - X[47936], X[667] - 3 X[14421], 3 X[1022] - X[4905], 5 X[3616] - 3 X[47815], 2 X[4147] - 3 X[47802], 2 X[4163] - 3 X[48182], X[4498] - 3 X[14413], X[48126] + 2 X[48298], X[48086] + 3 X[48282], X[48086] - 3 X[48335], 2 X[20317] - 3 X[47841], 3 X[30583] - 5 X[31251], 4 X[30723] - 3 X[48245], 3 X[47777] - 2 X[47922], 2 X[47912] - 3 X[48027], X[47912] - 3 X[48131]

X(48346) lies on these lines: {1, 48111}, {8, 47819}, {65, 876}, {513, 4162}, {514, 3716}, {650, 29226}, {663, 47936}, {667, 999}, {764, 1482}, {891, 905}, {1022, 4905}, {1769, 9048}, {2526, 48137}, {2530, 14077}, {2832, 48294}, {3338, 4063}, {3616, 47815}, {3777, 3900}, {3803, 48328}, {3810, 47131}, {3904, 47720}, {3907, 48089}, {4106, 29324}, {4147, 47802}, {4160, 48092}, {4163, 48182}, {4367, 8712}, {4498, 14413}, {4801, 48126}, {6004, 48296}, {6050, 21385}, {6332, 48088}, {8678, 48086}, {17757, 21260}, {20317, 25681}, {20323, 48330}, {20517, 23888}, {23880, 48279}, {30583, 31251}, {30723, 48245}, {34647, 48265}, {37535, 39227}, {47777, 47922}, {47912, 48027}, {47915, 48093}, {48026, 48129}, {48287, 48327}

X(48346) = midpoint of X(i) and X(j) for these {i,j}: {764, 48333}, {3777, 21343}, {3904, 47720}, {4449, 48334}, {4801, 48298}, {4879, 23765}, {23738, 48338}, {48282, 48335}
X(48346) = reflection of X(i) in X(j) for these {i,j}: {2526, 48137}, {3803, 48328}, {21385, 6050}, {47915, 48093}, {48026, 48129}, {48027, 48131}, {48029, 48136}, {48088, 6332}, {48096, 48299}, {48126, 4801}, {48136, 48332}, {48327, 48287}, {48329, 1}
X(48346) = crosssum of X(1) and X(48329)
X(48346) = crossdifference of every pair of points on line {1743, 3550}


X(48347) = X(1)X(512)∩X(663)X(891)

Barycentrics    a*(b - c)*(2*a^2 - 3*a*b - 3*a*c + 2*b*c) : :
X(48347) = 5 X[1] - X[1019], 3 X[1] - X[4367], 7 X[1] - X[4784], 3 X[1] + X[48337], 3 X[1019] - 5 X[4367], 7 X[1019] - 5 X[4784], X[1019] + 5 X[4879], 2 X[1019] - 5 X[48328], 3 X[1019] + 5 X[48337], 7 X[4367] - 3 X[4784], X[4367] + 3 X[4879], 2 X[4367] - 3 X[48328], X[4784] + 7 X[4879], 2 X[4784] - 7 X[48328], 3 X[4784] + 7 X[48337], 2 X[4879] + X[48328], 3 X[4879] - X[48337], 3 X[48328] + 2 X[48337], X[8] - 3 X[47839], X[145] + 3 X[47840], 3 X[551] - X[4807], 3 X[1960] - 2 X[4401], X[4401] - 3 X[48294], 3 X[3251] - X[48150], 5 X[3616] - 3 X[47837], 7 X[3622] - 3 X[47836], 2 X[3635] + X[4806], X[4063] - 3 X[25569], X[4729] - 3 X[14419], X[4808] - 3 X[14432], X[4814] - 3 X[47888], 3 X[14421] - X[48151], 3 X[23057] + X[48131]

X(48347) lies on these lines: {1, 512}, {8, 47839}, {145, 47840}, {513, 48287}, {514, 48296}, {519, 21051}, {551, 4807}, {663, 891}, {814, 48285}, {1500, 45902}, {1960, 4083}, {2530, 4895}, {2605, 4139}, {3244, 4129}, {3251, 48150}, {3616, 47837}, {3622, 47836}, {3635, 4806}, {4010, 29268}, {4040, 21343}, {4063, 25569}, {4151, 48289}, {4160, 48053}, {4162, 6004}, {4170, 4922}, {4378, 48338}, {4449, 4775}, {4504, 29150}, {4729, 14419}, {4794, 29226}, {4808, 14432}, {4814, 47888}, {6161, 48334}, {6363, 48307}, {6371, 48302}, {7178, 11011}, {7927, 48290}, {7950, 47727}, {8672, 48292}, {10222, 28473}, {14421, 48151}, {15178, 44811}, {23057, 48131}, {29182, 47729}, {29184, 47728}, {29272, 47691}, {29350, 48330}, {29366, 48295}, {48059, 48136}, {48282, 48336}, {48298, 48305}

X(48347) = midpoint of X(i) and X(j) for these {i,j}: {1, 4879}, {663, 48333}, {2530, 4895}, {3244, 4129}, {4040, 21343}, {4162, 48332}, {4170, 4922}, {4367, 48337}, {4378, 48338}, {4449, 4775}, {6161, 48334}, {47729, 48273}, {48282, 48336}, {48298, 48305}
X(48347) = reflection of X(i) in X(j) for these {i,j}: {1960, 48294}, {44811, 15178}, {48059, 48136}, {48328, 1}
X(48347) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 48337, 4367}, {4367, 4879, 48337}


X(48348) = X(1)X(830)∩X(512)X(3960)

Barycentrics    a*(b - c)*(a^2 - 2*a*b - b^2 - 2*a*c + b*c - c^2) : :
X(48348) = 5 X[1] + X[48020], 3 X[1] + X[48086], 3 X[1] - X[48322], 3 X[48020] - 5 X[48086], X[48020] - 5 X[48131], 3 X[48020] + 5 X[48322], X[48086] - 3 X[48131], 3 X[48131] + X[48322], X[8] - 3 X[47816], 6 X[47966] - 7 X[48004], 5 X[47966] - 7 X[48029], 4 X[47966] - 7 X[48058], 3 X[47966] - 7 X[48099], X[47966] - 7 X[48136], X[47966] + 7 X[48332], 5 X[48004] - 6 X[48029], 2 X[48004] - 3 X[48058], X[48004] - 6 X[48136], X[48004] + 6 X[48332], 4 X[48029] - 5 X[48058], 3 X[48029] - 5 X[48099], X[48029] - 5 X[48136], X[48029] + 5 X[48332], 3 X[48058] - 4 X[48099], X[48058] - 4 X[48136], X[48058] + 4 X[48332], X[48099] - 3 X[48136], X[48099] + 3 X[48332], 3 X[663] - X[48111], X[48111] + 3 X[48335], X[1019] - 3 X[14413], 3 X[1022] - X[23738], 3 X[4040] - X[47936], X[47936] + 3 X[48334], 5 X[3616] - 3 X[47818], X[3762] - 3 X[47840], 3 X[4449] + X[47912], 3 X[14349] - X[47912], X[4462] - 3 X[47838], X[4730] - 3 X[47893], X[4761] - 3 X[47796], X[4983] + 3 X[14421], 3 X[14421] - X[48323], X[48052] + 2 X[48287]

X(48348) lies on these lines: {1, 830}, {8, 47816}, {512, 3960}, {513, 25405}, {514, 3716}, {661, 48282}, {663, 48111}, {758, 42661}, {764, 48336}, {891, 48003}, {905, 29350}, {1019, 14413}, {1022, 23738}, {1491, 48333}, {1577, 48298}, {2254, 48337}, {2530, 3887}, {2787, 4992}, {2832, 4040}, {3616, 47818}, {3669, 6005}, {3762, 47840}, {3776, 29304}, {3777, 4775}, {3801, 23884}, {3837, 29298}, {3900, 48066}, {3904, 47712}, {4083, 14838}, {4106, 29344}, {4160, 4449}, {4170, 17496}, {4378, 15309}, {4401, 8712}, {4462, 47838}, {4705, 21343}, {4730, 47893}, {4761, 47796}, {4807, 25380}, {4822, 48320}, {4905, 48338}, {4983, 14421}, {5216, 16754}, {6004, 48137}, {6332, 29047}, {8678, 48052}, {14077, 48012}, {20517, 28468}, {23815, 29366}, {28470, 48285}, {29013, 48325}, {29070, 48289}, {47727, 48278}, {48059, 48296}, {48122, 48324}, {48279, 48288}

X(48348) = midpoint of X(i) and X(j) for these {i,j}: {1, 48131}, {661, 48282}, {663, 48335}, {764, 48336}, {1491, 48333}, {1577, 48298}, {2254, 48337}, {2530, 4879}, {3777, 4775}, {3904, 47712}, {4040, 48334}, {4170, 17496}, {4378, 48123}, {4449, 14349}, {4705, 21343}, {4822, 48320}, {4905, 48338}, {4983, 48323}, {47727, 48278}, {48059, 48296}, {48086, 48322}, {48122, 48324}, {48136, 48332}, {48279, 48288}
X(48348) = reflection of X(i) in X(j) for these {i,j}: {4807, 25380}, {48004, 48099}
X(48348) = barycentric product X(513)*X(17258)
X(48348) = barycentric quotient X(17258)/X(668)
X(48348) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 48086, 48322}, {4983, 14421, 48323}, {48004, 48099, 48058}, {48131, 48322, 48086}


X(48349) = X(1)X(29029)∩X(512)X(3801)

Barycentrics    (b - c)*(b + c)*(2*a^2 + b^2 - b*c + c^2) : :
X(48349) = 3 X[3801] - 2 X[4707], X[4707] - 3 X[47712], X[47676] - 3 X[47691], 2 X[47676] - 3 X[48326], 2 X[3700] - 3 X[4010], 4 X[3700] - 3 X[4122], 3 X[4804] - X[4838], X[4838] + 3 X[47702], X[4988] - 3 X[47701], 2 X[649] - 3 X[4809], 2 X[650] - 3 X[48177], 3 X[676] - 2 X[2527], 2 X[2977] - 3 X[48179], 4 X[3239] - 3 X[48188], 2 X[4025] - 3 X[48224], X[4380] - 3 X[48223], 2 X[4394] - 3 X[48211], 3 X[4448] - 2 X[47890], 8 X[4521] - 9 X[47822], 4 X[4521] - 3 X[48062], 3 X[47822] - 2 X[48062], 2 X[4782] - 3 X[47798], 4 X[4885] - 3 X[48235], 2 X[4925] - 3 X[48178], 2 X[6590] - 3 X[48189], 2 X[9508] - 3 X[47797], X[17494] - 3 X[48158], 4 X[21212] - 3 X[48244], 5 X[26985] - 3 X[48254], 5 X[31209] - 6 X[48195], X[47693] - 3 X[48172], 3 X[47821] - 2 X[48056], 3 X[47823] - 2 X[48069], 3 X[47877] - 2 X[48017]

X(48349) lies on these lines: {1, 29029}, {512, 3801}, {513, 41794}, {514, 4775}, {522, 4810}, {523, 661}, {649, 4809}, {650, 48177}, {663, 29025}, {667, 29158}, {676, 2527}, {693, 29144}, {826, 4170}, {900, 16892}, {1577, 7927}, {2533, 3800}, {2787, 47727}, {2977, 48179}, {3005, 21249}, {3239, 48188}, {3716, 48103}, {4025, 48224}, {4040, 29098}, {4083, 47708}, {4106, 4777}, {4129, 4808}, {4367, 29118}, {4378, 29132}, {4380, 48223}, {4391, 29208}, {4394, 48211}, {4448, 47890}, {4449, 29120}, {4458, 4784}, {4521, 47822}, {4761, 12073}, {4782, 47798}, {4802, 47699}, {4834, 20517}, {4874, 48106}, {4885, 48235}, {4922, 29126}, {4925, 48178}, {4977, 47704}, {4978, 29168}, {4992, 48278}, {6370, 8663}, {6372, 47716}, {6590, 48189}, {7265, 7950}, {9508, 47797}, {17494, 48158}, {21146, 23770}, {21212, 48244}, {23877, 48123}, {25259, 29204}, {26985, 48254}, {28151, 47658}, {28209, 47900}, {29017, 47709}, {29021, 48273}, {29047, 48267}, {29082, 48338}, {29094, 48337}, {29102, 47725}, {29122, 47728}, {29128, 47682}, {29140, 48294}, {29142, 48279}, {29156, 47729}, {29174, 48300}, {29188, 47680}, {29198, 47720}, {29288, 48265}, {29354, 47717}, {29362, 47972}, {29370, 48266}, {31095, 48203}, {31209, 48195}, {47132, 48276}, {47690, 48090}, {47692, 48080}, {47693, 48172}, {47698, 48028}, {47705, 48021}, {47821, 48056}, {47823, 48069}, {47877, 48017}, {47945, 47990}, {48101, 48248}

X(48349) = midpoint of X(i) and X(j) for these {i,j}: {4170, 47713}, {4804, 47702}, {47692, 48080}, {47705, 48021}, {47902, 48153}
X(48349) = reflection of X(i) in X(j) for these {i,j}: {3801, 47712}, {4088, 4806}, {4122, 4010}, {4784, 4458}, {4808, 4129}, {4824, 47998}, {4834, 20517}, {21146, 23770}, {47690, 48090}, {47698, 48028}, {47700, 18004}, {47945, 47990}, {48101, 48248}, {48103, 3716}, {48106, 4874}, {48276, 47132}, {48278, 4992}, {48326, 47691}
X(48349) = X(81)-isoconjugate of X(28883)
X(48349) = X(40586)-Dao conjugate of X(28883)
X(48349) = crossdifference of every pair of points on line {58, 7296}
X(48349) = barycentric product X(i)*X(j) for these {i,j}: {10, 28882}, {514, 4085}, {523, 17367}, {693, 46907}, {850, 5332}, {4064, 31908}
X(48349) = barycentric quotient X(i)/X(j) for these {i,j}: {42, 28883}, {4085, 190}, {5332, 110}, {17367, 99}, {28882, 86}, {46907, 100}


X(48350) = X(1)X(9013)∩X(513)X(663)

Barycentrics    a*(b - c)*(b + c)*(a*b + b^2 + a*c - b*c + c^2) : :
X(48350) = 3 X[4017] + X[4822], 3 X[4086] - 4 X[21714], 2 X[4705] - 3 X[47842], 2 X[21714] - 3 X[31946], 3 X[656] - X[4729], 5 X[3616] - 3 X[47845], X[4581] - 3 X[48209], X[4768] - 3 X[47816], 2 X[6133] - 3 X[48181]

X(48350) lies on these lines: {1, 9013}, {37, 661}, {513, 663}, {522, 14288}, {523, 1577}, {656, 4132}, {764, 28209}, {832, 48302}, {834, 21189}, {900, 2530}, {1001, 4833}, {1491, 4728}, {2849, 44408}, {3005, 21249}, {3616, 47845}, {3739, 30765}, {3801, 6370}, {4026, 4761}, {4041, 4145}, {4057, 22160}, {4077, 41003}, {4369, 4657}, {4444, 24357}, {4490, 28151}, {4581, 48209}, {4768, 47816}, {4854, 48163}, {4879, 8674}, {4934, 17463}, {6133, 48181}, {7192, 17321}, {8061, 21834}, {8672, 48053}, {9001, 48332}, {9002, 48335}, {17279, 25666}, {17302, 31095}, {17322, 26248}, {17384, 24924}, {21348, 48025}, {23765, 28220}, {25887, 25900}, {27565, 27574}, {27697, 27710}, {28022, 28024}, {28169, 48012}, {28358, 28372}, {28840, 41312}, {31148, 41311}, {38469, 48292}, {41313, 45315}, {42758, 47756}

X(48350) = midpoint of X(1769) and X(48131)
X(48350) = reflection of X(4086) in X(31946)
X(48350) = X(i)-Ceva conjugate of X(j) for these (i,j): {30588, 3125}, {45095, 3120}
X(48350) = X(i)-isoconjugate of X(j) for these (i,j): {58, 9059}, {110, 996}, {662, 40401}, {16704, 32686}
X(48350) = X(i)-Dao conjugate of X(j) for these (i, j): (10, 9059), (244, 996), (1084, 40401)
X(48350) = crosspoint of X(i) and X(j) for these (i,j): {1, 9070}, {44435, 48335}
X(48350) = crosssum of X(1) and X(9013)
X(48350) = crossdifference of every pair of points on line {9, 609}
X(48350) = barycentric product X(i)*X(j) for these {i,j}: {10, 48335}, {37, 44435}, {321, 9002}, {512, 33934}, {513, 26580}, {514, 4424}, {523, 4850}, {661, 4389}, {995, 1577}, {3877, 7178}, {4017, 5233}, {4077, 4266}, {4674, 23888}, {4705, 16712}, {14618, 23206}
X(48350) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 9059}, {512, 40401}, {661, 996}, {995, 662}, {3877, 645}, {4266, 643}, {4389, 799}, {4424, 190}, {4850, 99}, {5233, 7257}, {9002, 81}, {16712, 4623}, {23206, 4558}, {23888, 30939}, {26580, 668}, {33934, 670}, {44435, 274}, {48335, 86}


X(48351) = X(36)X(238)∩X(512)X(4498)

Barycentrics    a*(b - c)*(a^2 - 2*a*b - 2*a*c - 2*b*c) : :
X(48351) = 3 X[667] - 2 X[1019], 3 X[667] - 4 X[48331], X[1019] - 3 X[4040], 3 X[4040] - 2 X[48331], 3 X[4983] - 2 X[48091], X[4498] - 3 X[4724], 3 X[4775] - 2 X[4879], 5 X[4775] - 2 X[21343], 5 X[4879] - 3 X[21343], 4 X[4879] - 3 X[48333], X[4879] - 3 X[48336], 4 X[21343] - 5 X[48333], X[21343] - 5 X[48336], X[48333] - 4 X[48336], 3 X[659] - 2 X[48011], 3 X[4834] - 4 X[48011], X[4834] - 4 X[48065], X[48011] - 3 X[48065], 3 X[663] - 2 X[48328], 3 X[4378] - 4 X[48328], 3 X[6161] + 2 X[47915], 2 X[47915] - 3 X[47949], 2 X[2254] - 3 X[47888], 4 X[3716] - 3 X[47875], 2 X[3837] - 3 X[47838], 4 X[4129] - 3 X[31149], 3 X[4800] - 2 X[4823], 2 X[21260] - 3 X[47821], 2 X[23789] - 3 X[47841], 2 X[23815] - 3 X[47840], 2 X[24720] - 3 X[47839], 5 X[31251] - 6 X[47822], 4 X[31288] - 3 X[47824], 3 X[47826] - 2 X[48005], 3 X[47827] - 2 X[48018], 3 X[47893] - 2 X[48075], 2 X[48012] - 3 X[48162]

X(48351) lies on these lines: {1, 29198}, {36, 238}, {512, 4498}, {514, 4775}, {659, 4834}, {661, 6004}, {663, 4378}, {764, 48136}, {826, 47972}, {830, 48024}, {891, 47929}, {1027, 2334}, {1491, 42325}, {1577, 29246}, {1960, 48144}, {2254, 47888}, {3309, 4705}, {3716, 47875}, {3762, 29366}, {3800, 48055}, {3837, 47838}, {3887, 4490}, {3900, 47966}, {4010, 29186}, {4083, 47970}, {4129, 31149}, {4160, 47913}, {4170, 29362}, {4367, 4794}, {4391, 29188}, {4401, 4784}, {4462, 29298}, {4468, 4808}, {4730, 47965}, {4800, 4823}, {4813, 8632}, {4822, 48032}, {6050, 7659}, {7927, 48094}, {8657, 48019}, {8672, 48340}, {9002, 39548}, {21260, 47821}, {23789, 47841}, {23815, 47840}, {24601, 47759}, {24720, 47839}, {25259, 29086}, {29047, 48083}, {29051, 48267}, {29066, 48265}, {29070, 48080}, {29102, 47708}, {29168, 48300}, {29224, 47709}, {29226, 48337}, {29354, 48078}, {31251, 47822}, {31288, 47824}, {47826, 48005}, {47827, 48018}, {47893, 48075}, {47906, 48322}, {47912, 47994}, {47942, 48324}, {47948, 48028}, {48012, 48162}, {48021, 48150}, {48023, 48053}, {48294, 48323}, {48320, 48330}

X(48351) = midpoint of X(i) and X(j) for these {i,j}: {4822, 48032}, {6161, 47949}, {47906, 48322}, {47929, 48338}, {47942, 48324}, {48021, 48150}, {48081, 48111}
X(48351) = reflection of X(i) in X(j) for these {i,j}: {659, 48065}, {667, 4040}, {764, 48136}, {1019, 48331}, {1491, 48058}, {2530, 48099}, {4367, 4794}, {4378, 663}, {4490, 48004}, {4705, 48029}, {4730, 47965}, {4775, 48336}, {4784, 4401}, {4808, 4468}, {4834, 659}, {7659, 6050}, {47912, 47994}, {47948, 48028}, {48023, 48053}, {48086, 48093}, {48144, 1960}, {48320, 48330}, {48323, 48294}, {48333, 4775}
X(48351) = X(29199)-Ceva conjugate of X(1)
X(48351) = X(i)-isoconjugate of X(j) for these (i,j): {100, 39739}, {190, 39965}
X(48351) = X(8054)-Dao conjugate of X(39739)
X(48351) = crosspoint of X(100) and X(10013)
X(48351) = crosssum of X(513) and X(17018)
X(48351) = crossdifference of every pair of points on line {37, 3873}
X(48351) = barycentric product X(i)*X(j) for these {i,j}: {1, 47926}, {513, 17259}, {649, 32104}
X(48351) = barycentric quotient X(i)/X(j) for these {i,j}: {649, 39739}, {667, 39965}, {17259, 668}, {32104, 1978}, {47926, 75}
X(48351) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1019, 4040, 48331}, {1019, 48331, 667}


X(48352) = X(1)X(513)∩X(512)X(659)

Barycentrics    a*(b - c)*(a^2 - 3*a*b - 3*a*c - b*c) : :
X(48352) = 3 X[1] - 2 X[4378], 3 X[1022] - 4 X[48332], X[4378] - 3 X[4775], 4 X[4378] - 3 X[48320], 4 X[4775] - X[48320], 2 X[10] - 3 X[47821], 2 X[659] - 3 X[4040], 4 X[659] - 3 X[4063], X[659] - 3 X[48336], X[4063] - 4 X[48336], 4 X[1125] - 3 X[47824], 5 X[1698] - 6 X[47822], 2 X[2526] - 3 X[14349], 7 X[3624] - 6 X[47823], 2 X[4770] - 3 X[48162], 2 X[4807] - 3 X[47793], X[4814] - 3 X[47826], 3 X[4879] - 2 X[48296], 3 X[48282] - 4 X[48296], X[4959] + 2 X[47987], 3 X[8643] - 2 X[48064], 2 X[17072] - 3 X[47838], 13 X[34595] - 12 X[48216]

X(48352) lies on these lines: {1, 513}, {10, 47821}, {213, 21007}, {239, 47759}, {512, 659}, {514, 48304}, {522, 47683}, {649, 4794}, {661, 3887}, {663, 1019}, {830, 4822}, {900, 48288}, {918, 47727}, {1125, 47824}, {1698, 47822}, {1734, 48099}, {1960, 4784}, {2499, 2821}, {2526, 3309}, {3243, 28910}, {3294, 4079}, {3340, 43052}, {3624, 47823}, {3667, 48321}, {3700, 47723}, {3716, 4761}, {3803, 47976}, {3900, 47959}, {4010, 29188}, {4041, 48058}, {4083, 47970}, {4129, 21302}, {4160, 4895}, {4170, 29051}, {4384, 4776}, {4448, 36531}, {4474, 4844}, {4498, 48065}, {4502, 16552}, {4724, 21385}, {4729, 48003}, {4770, 48162}, {4807, 47793}, {4814, 47826}, {4826, 21389}, {4834, 48331}, {4879, 6372}, {4905, 48136}, {4959, 47987}, {4977, 48291}, {4983, 47948}, {6003, 38329}, {6004, 48086}, {6006, 48325}, {7982, 28537}, {8643, 48064}, {8678, 47947}, {8712, 47977}, {12073, 48103}, {15309, 48322}, {16823, 48164}, {16826, 47763}, {16828, 48165}, {16830, 47805}, {16831, 47762}, {16832, 47760}, {17072, 47838}, {17143, 20949}, {20906, 32104}, {21130, 28319}, {23876, 47972}, {25259, 29192}, {25512, 48246}, {28217, 48289}, {28521, 48049}, {29066, 48080}, {29102, 47725}, {29132, 47728}, {29144, 47726}, {29148, 47729}, {29198, 48333}, {29220, 47709}, {29246, 48273}, {29298, 48265}, {29304, 47708}, {29366, 48267}, {34595, 48216}, {37998, 45751}, {39586, 47804}, {42325, 48131}, {47905, 48051}, {47912, 48045}, {48108, 48295}, {48144, 48294}

X(48352) = midpoint of X(4895) and X(48021)
X(48352) = reflection of X(i) in X(j) for these {i,j}: {1, 4775}, {649, 4794}, {1019, 663}, {1734, 48099}, {4040, 48336}, {4041, 48058}, {4063, 4040}, {4498, 48065}, {4729, 48003}, {4761, 3716}, {4784, 1960}, {4834, 48331}, {4905, 48136}, {21302, 4129}, {21385, 4724}, {47723, 3700}, {47724, 4010}, {47905, 48051}, {47912, 48045}, {47947, 48081}, {47948, 4983}, {47976, 3803}, {48085, 4822}, {48086, 48123}, {48108, 48295}, {48144, 48294}, {48282, 4879}, {48320, 1}, {48337, 48338}
X(48352) = reflection of X(48320) in the OI line
X(48352) = X(4379)-Dao conjugate of X(4411)
X(48352) = crosssum of X(513) and X(46904)
X(48352) = crossdifference of every pair of points on line {44, 24512}
X(48352) = barycentric product X(1)*X(47775)
X(48352) = barycentric quotient X(47775)/X(75)


X(48353) = X(13)X(46856)∩X(14)X(21466)

Barycentrics    (-6*sqrt(3)*((b^2+c^2)*a^4+b^2*c^2*a^2-(b^4-c^4)*(b^2-c^2))*S+2*a^8-3*(b^2+c^2)*a^6-(b^4+19*b^2*c^2+c^4)*a^4+(b^2+c^2)*(3*b^4-7*b^2*c^2+3*c^4)*a^2-(b^4-16*b^2*c^2+c^4)*(b^2-c^2)^2)*(2*S+(a^2-b^2+c^2)*sqrt(3))*(2*S+(a^2+b^2-c^2)*sqrt(3)) : :
Barycentrics    (S+sqrt(3)*SC)*(S+sqrt(3)*SB)*(-3*sqrt(3)*((3*R^2-SW)*S^2-SB*SC*SW)+S*(6*S^2-27*R^2*SA+6*SA^2+3*SB*SC+SW^2)) : :

See Kadir Altintas and César Lozada, euclid 4960.

X(48353) lies on the Kiepert circumhyperbola and these lines: {2, 11537}, {13, 46856}, {14, 21466}, {671, 16770}, {8014, 12817}, {11078, 42035}, {11080, 36316}, {36969, 42001}

X(48353) = isogonal conjugate of X(48354)
X(48353) = X(13)-reciprocal conjugate of-X(5463)
X(48353) = trilinear pole of the line {523, 11625}
X(48353) = barycentric quotient X(13)/X(5463)


X(48354) = ISOGONAL CONJUGATE OF X(48353)

Barycentrics    a^2*(2*S+sqrt(3)*(-a^2+b^2+c^2))*(-6*sqrt(3)*(a^6-b^2*a^4-(b^4+b^2*c^2+c^4)*a^2+(b^4-c^4)*b^2)*S+a^8-3*(6*b^2+c^2)*a^6+(34*b^4+4*b^2*c^2+c^4)*a^4-(18*b^6-3*c^6-(4*b^2+19*c^2)*b^2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)*(b^2-2*c^2))*(-6*sqrt(3)*(a^6-c^2*a^4-(b^4+b^2*c^2+c^4)*a^2-(b^4-c^4)*c^2)*S+a^8-3*(b^2+6*c^2)*a^6+(b^4+4*b^2*c^2+34*c^4)*a^4+(3*b^6-18*c^6+(19*b^2+4*c^2)*b^2*c^2)*a^2-(b^4-c^4)*(b^2-c^2)*(2*b^2-c^2)) : :

See Kadir Altintas and César Lozada, euclid 4960.

X(48354) lies on these lines: {3, 6}, {396, 21466}, {5191, 14173}, {9145, 32302}, {9761, 11092}, {11131, 17402}, {14172, 35329}, {15768, 47141}, {16645, 30465}, {18777, 36967}, {35931, 45331}, {41476, 47053}

X(48354) = isogonal conjugate of X(48354)
X(48354) = crossdifference of every pair of points on line {X(523), X(11625)}
X(48354) = barycentric quotient X(13)/X(5463)


X(48355) = X(13)X(21467)∩X(14)X(46857)

Barycentrics    (6*sqrt(3)*((b^2+c^2)*a^4+b^2*c^2*a^2-(b^4-c^4)*(b^2-c^2))*S+2*a^8-3*(b^2+c^2)*a^6-(b^4+19*b^2*c^2+c^4)*a^4+(b^2+c^2)*(3*b^4-7*b^2*c^2+3*c^4)*a^2-(b^4-16*b^2*c^2+c^4)*(b^2-c^2)^2)*(-2*S+(a^2-b^2+c^2)*sqrt(3))*(-2*S+(a^2+b^2-c^2)*sqrt(3)) : :
Barycentrics    (-S+sqrt(3)*SC)*(-S+sqrt(3)*SB)*(-3*sqrt(3)*((3*R^2-SW)*S^2-SB*SC*SW)-S*(6*S^2-27*R^2*SA+6*SA^2+3*SB*SC+SW^2)) : :

See Kadir Altintas and César Lozada, euclid 4960.

X(48355) lies on the Kiepert circumhyperbola and these lines: {2, 11549}, {13, 21467}, {14, 46857}, {671, 16771}, {8015, 12816}, {11085, 36317}, {11092, 42036}, {36970, 42002}

X(48355) = isogonal conjugate of X(48356)
X(48355) = X(14)-reciprocal conjugate of-X(5464)
X(48355) = trilinear pole of the line {523, 11627}
X(48355) = barycentric quotient X(14)/X(5464)


X(48356) = ISOGONAL CONJUGATE OF X(48355)

Barycentrics    a^2*(-2*S+sqrt(3)*(-a^2+b^2+c^2))*(6*sqrt(3)*(a^6-b^2*a^4-(b^4+b^2*c^2+c^4)*a^2+(b^4-c^4)*b^2)*S+a^8-3*(6*b^2+c^2)*a^6+(34*b^4+4*b^2*c^2+c^4)*a^4-(18*b^6-3*c^6-(4*b^2+19*c^2)*b^2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)*(b^2-2*c^2))*(6*sqrt(3)*(a^6-c^2*a^4-(b^4+b^2*c^2+c^4)*a^2-(b^4-c^4)*c^2)*S+a^8-3*(b^2+6*c^2)*a^6+(b^4+4*b^2*c^2+34*c^4)*a^4+(3*b^6-18*c^6+(19*b^2+4*c^2)*b^2*c^2)*a^2-(b^4-c^4)*(b^2-c^2)*(2*b^2-c^2)) : :

See Kadir Altintas and César Lozada, euclid 4960.

X(48356) lies on these lines: {3, 6}, {395, 21467}, {5191, 14179}, {9145, 32301}, {9763, 11078}, {11130, 17403}, {14171, 35330}, {15769, 47142}, {16644, 30468}, {18776, 36968}, {35932, 45331}, {44250, 47322}

X(48356) = isogonal conjugate of X(48355)
X(48356) = crossdifference of every pair of points on line {X(523), X(11627)}
X(48356) = barycentric product X(16)*X(5464)


X(48357) = X(11)X(57)∩X(40)X(5514)

Barycentrics    (a^3+a^2 b-a b^2-b^3+a^2 c-2 a b c+b^2 c-a c^2+b c^2-c^3) (a^4-a^3 b-a b^3+b^4+2 a^2 b c+2 a b^2 c-2 a^2 c^2-a b c^2-2 b^2 c^2+c^4) (a^4-2 a^2 b^2+b^4-a^3 c+2 a^2 b c-a b^2 c+2 a b c^2-2 b^2 c^2-a c^3+c^4) : :
X(48357) = 3*X(1699)-2*X(44993), 5*X(8227)-4*X(40555), 2*X(28344)-3*X(38036)

See Antreas Hatzipolakis and Ercole Suppa, euclid 4979.

X(48357) lies on these lines: {1,13529}, {11,57}, {40,5514}, {189,9812}, {223,38357}, {515,44978}, {516,972}, {934,946}, {3345,41869}, {3434,15499}, {5057,15633}, {6366,14217}, {8227,40555}, {28344,38036}

X(48357) = isogonal conjugate of X(39558)
X(48357) = antigonal conjugate of X(40)
X(48357) = reflection of X(i) in X(j) for these (i,j): (40,5514),(934,946)
X(48357) = X(3)-Dao conjugate of X(39558)
X(48357) = trilinear pole of the line: {6129, 40943}
X(48357) = symgonal image of X(946)


X(48358) = X(4)X(12016)∩X(282)X(5514)

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

See Antreas Hatzipolakis and Ercole Suppa, euclid 4979.

X(48358) lies on these lines: {4,12016}, {282,5514}, {1490,13612}

X(48358) = reflection of X(1490) in X(13612)
X(48358) = isogonal conjugate of the circumperp conjugate of X(3182)
X(48358) = antigonal conjugate of X(1490)
X(48358) = symgonal image of X(6245)


X(48359) = X(223)X(13612)∩X(3345)X(5514)

Barycentrics    (a^10-a^9 b-3 a^8 b^2+4 a^7 b^3+2 a^6 b^4-6 a^5 b^5+2 a^4 b^6+4 a^3 b^7-3 a^2 b^8-a b^9+b^10+8 a^8 b c-4 a^7 b^2 c-4 a^6 b^3 c-4 a^3 b^6 c-4 a^2 b^7 c+8 a b^8 c-5 a^8 c^2+8 a^6 b^2 c^2-6 a^4 b^4 c^2+8 a^2 b^6 c^2-5 b^8 c^2-16 a^6 b c^3+8 a^5 b^2 c^3+8 a^4 b^3 c^3+8 a^3 b^4 c^3+8 a^2 b^5 c^3-16 a b^6 c^3+10 a^6 c^4-2 a^5 b c^4-2 a^4 b^2 c^4-12 a^3 b^3 c^4-2 a^2 b^4 c^4-2 a b^5 c^4+10 b^6 c^4+8 a^4 b c^5-4 a^3 b^2 c^5-4 a^2 b^3 c^5+8 a b^4 c^5-10 a^4 c^6+8 a^3 b c^6-8 a^2 b^2 c^6+8 a b^3 c^6-10 b^4 c^6+5 a^2 c^8-5 a b c^8+5 b^2 c^8-c^10) (a^10-5 a^8 b^2+10 a^6 b^4-10 a^4 b^6+5 a^2 b^8-b^10-a^9 c+8 a^8 b c-16 a^6 b^3 c-2 a^5 b^4 c+8 a^4 b^5 c+8 a^3 b^6 c-5 a b^8 c-3 a^8 c^2-4 a^7 b c^2+8 a^6 b^2 c^2+8 a^5 b^3 c^2-2 a^4 b^4 c^2-4 a^3 b^5 c^2-8 a^2 b^6 c^2+5 b^8 c^2+4 a^7 c^3-4 a^6 b c^3+8 a^4 b^3 c^3-12 a^3 b^4 c^3-4 a^2 b^5 c^3+8 a b^6 c^3+2 a^6 c^4-6 a^4 b^2 c^4+8 a^3 b^3 c^4-2 a^2 b^4 c^4+8 a b^5 c^4-10 b^6 c^4-6 a^5 c^5+8 a^2 b^3 c^5-2 a b^4 c^5+2 a^4 c^6-4 a^3 b c^6+8 a^2 b^2 c^6-16 a b^3 c^6+10 b^4 c^6+4 a^3 c^7-4 a^2 b c^7-3 a^2 c^8+8 a b c^8-5 b^2 c^8-a c^9+c^10) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 4979.

X(48359) lies on these lines: {223,13612}, {3345,5514}

X(48359) = reflection of X(3345) in X(5514)
X(48359) = isogonal conjugate of the circumperp conjugate of X(84)
X(48359) = antigonal conjugate of X(3345)


X(48360) = X(80)X(1776)∩X(1156)X(6905)

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

See Antreas Hatzipolakis and Ercole Suppa, euclid 4979.

X(48360) lies on Feuerbach circumhyperbola and these lines: {79,11219}, {80,1776}, {1156,6905}, {1768,5561}, {2320,6265}, {3427,12248}

X(48360) = antigonal conjugate of the isogonal conjugate of X(32613)


X(48361) = TRILINEAR POLE OF THE LINE X(6587)X(6749)

Barycentrics   (a^2+b^2-c^2) (a^2-b^2+c^2) (2 a^12+a^10 b^2-22 a^8 b^4+38 a^6 b^6-22 a^4 b^8+a^2 b^10+2 b^12-8 a^10 c^2+16 a^8 b^2 c^2-8 a^6 b^4 c^2-8 a^4 b^6 c^2+16 a^2 b^8 c^2-8 b^10 c^2+11 a^8 c^4-26 a^6 b^2 c^4+30 a^4 b^4 c^4-26 a^2 b^6 c^4+11 b^8 c^4-4 a^6 c^6+4 a^4 b^2 c^6+4 a^2 b^4 c^6-4 b^6 c^6-4 a^4 c^8+a^2 b^2 c^8-4 b^4 c^8+4 a^2 c^10+4 b^2 c^10-c^12) (2 a^12-8 a^10 b^2+11 a^8 b^4-4 a^6 b^6-4 a^4 b^8+4 a^2 b^10-b^12+a^10 c^2+16 a^8 b^2 c^2-26 a^6 b^4 c^2+4 a^4 b^6 c^2+a^2 b^8 c^2+4 b^10 c^2-22 a^8 c^4-8 a^6 b^2 c^4+30 a^4 b^4 c^4+4 a^2 b^6 c^4-4 b^8 c^4+38 a^6 c^6-8 a^4 b^2 c^6-26 a^2 b^4 c^6-4 b^6 c^6-22 a^4 c^8+16 a^2 b^2 c^8+11 b^4 c^8+a^2 c^10-8 b^2 c^10+2 c^12) : :
Barycentrics    SB SC (-144 R^4+S^2+48 R^2 SB+6 SB SC+6 SC^2+40 R^2 SW-12 SB SW-6 SC SW-SW^2) (144 R^4+5 S^2-48 R^2 SC+6 SC^2-40 R^2 SW+6 SC SW+SW^2) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 4979.

X(48361) lies these lines: { }

X(48361) = isogonal conjugate of the circumperp conjugate of X(11204)
X(48361) = antigonal conjugate of the isogonal conjugate of X(11202)
X(48361) = trilinear pole of the line: {6587, 6749}


X(48362) = ISOGONAL CONJUGATE OF X(11799)

Barycentrics    a^2 (a^10-3 a^8 b^2+2 a^6 b^4+2 a^4 b^6-3 a^2 b^8+b^10-2 a^8 c^2+8 a^6 b^2 c^2-12 a^4 b^4 c^2+8 a^2 b^6 c^2-2 b^8 c^2+2 a^4 b^2 c^4+2 a^2 b^4 c^4+2 a^4 c^6-6 a^2 b^2 c^6+2 b^4 c^6-a^2 c^8-b^2 c^8) (a^10-2 a^8 b^2+2 a^4 b^6-a^2 b^8-3 a^8 c^2+8 a^6 b^2 c^2+2 a^4 b^4 c^2-6 a^2 b^6 c^2-b^8 c^2+2 a^6 c^4-12 a^4 b^2 c^4+2 a^2 b^4 c^4+2 b^6 c^4+2 a^4 c^6+8 a^2 b^2 c^6-3 a^2 c^8-2 b^2 c^8+c^10) : :
Barycentrics    (SB+SC) (S^2 (3 R^2-SW)+SA SC (9 R^2-SW)) (2 S^2 (6 R^2-SW)+SC (9 R^2-SW) (SC-SW)) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 4979.

X(48362) lies on Jerabek circumhyperbola and these lines: {3,19403}, {6,15463}, {68,9140}, {69,11579}, {110,4846}, {186,1177}, {265,858}, {879,11653}, {895,43574}, {1176,15035}, {3426,12292}, {3431,13198}, {3521,5655}, {5486,5622}, {7464,34802}, {10293,10295}, {11413,45788}, {11744,15139}, {12244,35512}, {12302,34801}, {13603,43391}, {14457,37119}, {15136,40112}, {15462,43697}, {15472,45088}, {18550,38789}, {35471,43695}, {41737,43578}

X(48362) = midpoint of X(3) and X(19403)
X(48362) = isogonal conjugate of X(11799)
X(48362) = antigonal conjugate of the isogonal conjugate of X(6644)
X(48362) = X(3)-Dao conjugate of X(11799)
X(48362) = X(i)-vertex conjugate of X(j) for these (i,j): (4,1177), (1177,4)
X(48362) = trilinear pole of the line: {647, 5063}
X(48362) = 1st Saragossa point of X(10293)


X(48363) = X(4)X(9)∩X(46)X(944)

Barycentrics    a (a^6-3 a^4 b^2+3 a^2 b^4-b^6-3 a^4 b c+4 a^3 b^2 c-4 a b^4 c+3 b^5 c-3 a^4 c^2+4 a^3 b c^2-6 a^2 b^2 c^2+4 a b^3 c^2+b^4 c^2+4 a b^2 c^3-6 b^3 c^3+3 a^2 c^4-4 a b c^4+b^2 c^4+3 b c^5-c^6) : :
X(48363) = 3*X(36)-2*X(11715),3*X(484)-X(1768),3*X(4511)-4*X(22935),3*X(6905)-X(10698)

See Antreas Hatzipolakis and Ercole Suppa, euclid 4979.

X(48363) lies on these lines: {1,6942}, {3,3897}, {4,9}, {8,6934}, {36,11715}, {46,944}, {57,7966}, {65,11491}, {80,1776}, {84,41348}, {100,517}, {104,1155}, {119,5057}, {145,37532}, {165,6950}, {376,3359}, {392,6946}, {411,37562}, {484,515}, {518,38665}, {519,5535}, {535,12751}, {580,3987}, {602,24440}, {631,24541}, {946,6949}, {952,3218}, {962,6834}, {1006,3753}, {1385,4004}, {1389,2646}, {1519,15017}, {1532,28174}, {1537,28212}, {1697,10595}, {1788,12116}, {1936,24028}, {2078,12736}, {2093,18446}, {2800,3245}, {2933,3417}, {3072,4642}, {3090,5250}, {3149,12702}, {3219,5790}, {3309,13266}, {3336,5882}, {3337,13607}, {3474,12115}, {3528,37560}, {3577,35445}, {3579,6906}, {3587,6935}, {3617,26921}, {3651,31788}, {3746,31870}, {3754,10902}, {3869,11499}, {3871,24474}, {3877,6911}, {3885,10680}, {3935,12331}, {4295,10786}, {4861,26286}, {5067,31435}, {5119,5218}, {5126,37789}, {5176,5841}, {5183,6001}, {5450,37572}, {5536,5541}, {5537,35204}, {5554,6868}, {5690,37468}, {5691,40256}, {5709,12245}, {5842,40663}, {5883,34486}, {5903,6796}, {6684,6952}, {6830,26446}, {6848,20070}, {6875,19860}, {6901,24987}, {6902,24982}, {6927,27385}, {6928,25005}, {6938,9778}, {6940,31786}, {6941,12699}, {6967,26062}, {6968,9812}, {7098,10573}, {7672,18450}, {7686,37568}, {8227,20104}, {8256,11827}, {8715,37625}, {9352,10269}, {9623,21165}, {9957,45977}, {10246,27003}, {10711,28534}, {10860,11001}, {10914,37623}, {11249,14923}, {11500,37567}, {12515,28160}, {12528,18518}, {13464,37563}, {14988,18524}, {16139,18259}, {17531,31838}, {17768,37725}, {18391,37000}, {18514,40265}, {20119,37787}, {21669,22937}, {22765,38460}, {27065,38042}, {32141,34772}, {33814,35459}, {35448,37302}

X(48363) = midpoint of X(i) and X(j) for these {i,j}: {3245,44425}, {5536,5541}, {8072,8073}
X(48363) = reflection of X(i) in X(j) for these (i,j): (4,1512), (104,1155), (944,21578), (3935,12331), (5057,119), (35459,33814), (38460,22765)
X(48363) = trilinear quotient X(i)/X(j) for these (i,j): (46,944, 26877), (5903,6796,21740)


X(48364) = X(4)X(6)∩X(107)X(6000)

Barycentrics    (a^2+b^2-c^2) (a^2-b^2+c^2) (a^12-6 a^10 b^2+14 a^8 b^4-16 a^6 b^6+9 a^4 b^8-2 a^2 b^10-6 a^10 c^2-a^8 b^2 c^2+8 a^6 b^4 c^2+10 a^4 b^6 c^2-10 a^2 b^8 c^2-b^10 c^2+14 a^8 c^4+8 a^6 b^2 c^4-38 a^4 b^4 c^4+12 a^2 b^6 c^4+4 b^8 c^4-16 a^6 c^6+10 a^4 b^2 c^6+12 a^2 b^4 c^6-6 b^6 c^6+9 a^4 c^8-10 a^2 b^2 c^8+4 b^4 c^8-2 a^2 c^10-b^2 c^10) : ;
Barycentrics    SB SC (144 R^4+3 S^2-2 SB SC-40 R^2 SW+SW^2) : :
X(48364) = 4*X(107)-3*X(40664),3*X(6760)-2*X(38621),3*X(23239)-2*X(34109)

See Antreas Hatzipolakis and Ercole Suppa, euclid 4979.

X(48364) lies on these lines: {4,6}, {30,34186}, {107,6000}, {421,12133}, {436,11455}, {450,14915}, {1075,12315}, {1294,34147}, {1559,6761}, {3426,37070}, {6760,38621}, {16261,37124}, {23239,34109}

X(48364) = reflection of X(i) in X(j) for these (i,j): (4,1515), (1294,34147), (6761,1559)
X(48364) = trilinear quotient X(4)/X(12112)


X(48365) = EULER LINE INTERCEPT OF X(15)X(1511)

Barycentrics   a^2*(sqrt(3)*(a^8-2*(b^2+c^2)*a^6+4*b^2*c^2*a^4+2*(b^4-3*b^2*c^2+c^4)*(b^2+c^2)*a^2-(b^4+c^4)*(b^2-c^2)^2)-8*S^3*(-a^2+b^2+c^2)) : :
Barycentrics    (SB+SC) (3 S^2+2 Sqrt[3] S SA+3 SA (6 R^2+SA-2 SW)) : :

As a point on the Euler line, X(48365) has Shinagawa coefficients (3 e-12 f+4 Sqrt[3] S, 3 e+12 f-4 Sqrt[3] S).

See Kadir Altintas, César Lozada and Ercole Suppa euclid 4982 and euclid 4983.

X(48365) lies on these lines: {2, 3}, {15, 1511}, {62, 5946}, {298, 14368}, {568, 11126}, {1154, 44718}, {1605, 47610}, {3581, 11131}, {5334, 21311}, {5463, 15361}, {5961, 6671}, {6104, 11080}, {6670, 41460}, {10654, 11141}, {11127, 22115}, {11179, 14179}, {13350, 47035}, {14169, 40280}, {14805, 41477}, {14816, 34394}, {21158, 34317}, {22236, 47391}, {34425, 43584}

X(48365) = midpoint of X(3) and X(3129)
X(48365) = crossdifference of every pair of points on line {X(647), X(23283)}
X(48365) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(11086)}} and {{A, B, C, X(15), X(471)}}
X(48365) = trilinear quotient X(i)/X(j) for these (i,j): (3,381,35470), (3,2070,34008), (186,11146,3)
X(48365) = {X(186), X(11146)}-harmonic conjugate of X(3)


X(48366) = EULER LINE INTERCEPT OF X(16)X(1511)

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

See Kadir Altintas and César Lozada euclid 4982.

X(48366) lies on these lines: {2, 3}, {16, 1511}, {61, 5946}, {299, 14369}, {568, 11127}, {1154, 44719}, {1606, 47611}, {3581, 11130}, {5335, 21310}, {5464, 15361}, {5961, 6672}, {6105, 11085}, {6669, 41459}, {10653, 11142}, {11126, 22115}, {11179, 14173}, {13349, 47036}, {14170, 40280}, {14805, 41478}, {14817, 34395}, {21159, 34318}, {22238, 47391}, {34424, 43584}

X(48366) = midpoint of X(3) and X(3130)
X(48366) = crossdifference of every pair of points on line {X(647), X(23284)}
X(48366) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(11081)}} and {{A, B, C, X(16), X(470)}}
X(48366) = {X(186), X(11145)}-harmonic conjugate of X(3)


X(48367) = X(512)X(4498)∩X(513)X(663)

Barycentrics    a*(b - c)*(a^2 - 3*a*b - 3*a*c - 2*b*c) : :
X(48367) = 3 X[663] - 2 X[4367], 7 X[663] - 6 X[25569], 5 X[663] - 4 X[48330], 7 X[4367] - 9 X[25569], 4 X[4367] - 3 X[48144], 5 X[4367] - 6 X[48330], X[4367] - 3 X[48336], 12 X[25569] - 7 X[48144], 15 X[25569] - 14 X[48330], 3 X[25569] - 7 X[48336], 5 X[48144] - 8 X[48330], X[48144] - 4 X[48336], 2 X[48330] - 5 X[48336], 2 X[48337] - 3 X[48338], 3 X[649] - 4 X[4401], 3 X[4040] - 2 X[4401], 2 X[1019] - 3 X[8643], 4 X[4794] - 3 X[8643], 2 X[1734] - 3 X[4893], 3 X[4893] - 4 X[48058], 2 X[4705] - 3 X[47826], X[4959] + 2 X[47913], 2 X[17072] - 3 X[47821], 2 X[24720] - 3 X[47840], 5 X[30835] - 6 X[47838], 3 X[47796] - 2 X[48073]

X(48367) lies on these lines: {512, 4498}, {513, 663}, {514, 48304}, {525, 47972}, {649, 2664}, {661, 3309}, {830, 4813}, {885, 5665}, {1019, 4794}, {1734, 4893}, {2254, 48099}, {3667, 4560}, {3800, 48094}, {3803, 4979}, {3887, 47959}, {3900, 47918}, {4010, 29246}, {4041, 48029}, {4063, 48065}, {4083, 47929}, {4107, 48041}, {4151, 47926}, {4160, 47942}, {4170, 4382}, {4435, 47905}, {4449, 4775}, {4474, 29366}, {4490, 4814}, {4705, 47826}, {4729, 47965}, {4778, 17166}, {4784, 48331}, {4879, 29198}, {4895, 47906}, {4959, 47913}, {4977, 48301}, {4983, 6004}, {5029, 9811}, {7927, 48118}, {8672, 42312}, {8678, 47911}, {8712, 47936}, {14349, 42325}, {15309, 48324}, {17072, 47821}, {21124, 48006}, {21185, 23755}, {21301, 48043}, {23738, 48332}, {24720, 47840}, {28470, 48037}, {28478, 48014}, {29047, 48117}, {29051, 48080}, {29188, 48267}, {29208, 48083}, {29288, 48078}, {29350, 47970}, {30835, 47838}, {47796, 48073}, {47912, 48024}, {47948, 48045}, {48020, 48091}, {48119, 48273}, {48142, 48305}, {48294, 48320}

X(48367) = midpoint of X(4895) and X(47906)
X(48367) = reflection of X(i) in X(j) for these {i,j}: {649, 4040}, {663, 48336}, {1019, 4794}, {1734, 48058}, {2254, 48099}, {4041, 48029}, {4063, 48065}, {4382, 4170}, {4449, 4775}, {4474, 48265}, {4498, 4724}, {4729, 47965}, {4784, 48331}, {4813, 48081}, {4814, 4490}, {4979, 3803}, {21124, 48006}, {21301, 48043}, {23738, 48332}, {23755, 21185}, {47905, 48026}, {47911, 48021}, {47912, 48024}, {47948, 48045}, {48020, 48091}, {48023, 4983}, {48116, 48128}, {48119, 48273}, {48121, 4822}, {48122, 48123}, {48142, 48305}, {48144, 663}, {48151, 48136}, {48320, 48294}
X(48367) = crosssum of X(522) and X(26037)
X(48367) = crossdifference of every pair of points on line {9, 3720}
X(48367) = barycentric product X(1)*X(47962)
X(48367) = barycentric quotient X(47962)/X(75)
X(48367) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1019, 4794, 8643}, {1734, 48058, 4893}


X(48368) = EULER LINE INTERCEPT OF X(541)X(20773)

Barycentrics    8*a^10-15*(b^2+c^2)*a^8-2*(b^4-10*b^2*c^2+c^4)*a^6+2*(b^2+c^2)*(8*b^4-13*b^2*c^2+8*c^4)*a^4-2*(b^2-c^2)^2*(3*b^4+5*b^2*c^2+3*c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3 : : :
X(48368) = X(2)-3*X(18324), 2*X(2)-3*X(34477), 2*X(548)+X(17714), 5*X(549)-4*X(5498), X(550)+2*X(12107)

See Antreas Hatzipolakis and César Lozada euclid 4986.

X(48368) lies on these lines: {2, 3}, {541, 20773}, {3581, 41628}, {11265, 41946}, {11266, 41945}, {11267, 42943}, {11268, 42942}, {14831, 21660}

X(48368) = midpoint of X(i) and X(j) for these {i, j}: {26, 376}, {44213, 44242}
X(48368) = reflection of X(i) in X(j) for these (i, j): (5, 15330), (381, 10020), (549, 15331), (11250, 34200), (13371, 549), (15686, 15332), (15687, 13406), (15761, 44213), (18377, 547), (31181, 23336), (34477, 18324), (44213, 1658)


X(48369) = EULER LINE INTERCEPT OF X(11438)X(17330)

Barycentrics    8*a^10-2*(b+c)*a^9-(15*b^2+2*b*c+15*c^2)*a^8+8*(b+c)*(b^2+c^2)*a^7-2*(b^4+c^4-4*(b^2+5*b*c+c^2)*b*c)*a^6-4*(b+c)*(3*b^4+2*b^2*c^2+3*c^4)*a^5+4*(4*b^4+4*c^4-(11*b^2-10*b*c+11*c^2)*b*c)*(b+c)^2*a^4+8*(b^4-c^4)*(b^2-c^2)*(b+c)*a^3-2*(b^2-c^2)^2*(3*b^4+3*c^4-4*(b^2-b*c+c^2)*b*c)*a^2-2*(b^2-c^2)^4*(b+c)*a-(b^2-c^2)^4*(b+c)^2 : :
X(48368) = X(2)-3*X(21162)

See Antreas Hatzipolakis and César Lozada euclid 4986.

X(48369) lies on these lines: {2, 3}, {11438, 17330}, {17271, 44683}

X(48369) = midpoint of X(27) and X(376)
X(48369) = reflection of X(i) in X(j) for these (i, j): (381, 6678), (440, 549)


X(48370) = EULER LINE INTERCEPT OF X(15940)X(18481)

Barycentrics    8*a^10+2*(b+c)*a^7*b*c-(15*b^2+2*b*c+15*c^2)*a^8-2*(b+c)*(3*b^2-2*b*c+3*c^2)*a^5*b*c-2*(b^4+c^4-3*(b^2+6*b*c+c^2)*b*c)*a^6+2*(b^2-c^2)*(b-c)*(3*b^2+2*b*c+3*c^2)*a^3*b*c+2*(8*b^4+8*c^4-(19*b^2-18*b*c+19*c^2)*b*c)*(b+c)^2*a^4-2*(b^2-c^2)^3*(b-c)*a*b*c-2*(b^4-c^4)*(b^2-c^2)*(3*b^2-b*c+3*c^2)*a^2-(b^4-c^4)*(b^2-c^2)^3 : :

See Antreas Hatzipolakis and César Lozada euclid 4986.

X(48370) lies on these lines: {2, 3}, {15940, 18481}

X(48370) = midpoint of X(28) and X(376)
X(48370) = reflection of X(21530) in X(549)


X(48371) = CENTER OF CIRCUMCONIC {{A, B, C, X(4), X(31726)}}

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

See Antreas Hatzipolakis and César Lozada euclid 5001.

X(48371) lies on the nine-point circle and these lines: {113, 40111}, {25641, 44235}

X(48371) = center of the circumconic {{A, B, C, X(4), X(31726)}}
X(48371) = Poncelet point of X(31726)


X(48372) = PERSPECTOR OF CIRCUMCONIC {{A, B, C, X(4), X(31726)}}

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

See Antreas Hatzipolakis and César Lozada euclid 5001.

X(48372) lies on this line: {230, 231}

X(48372) = crossdifference of every pair of points on line {X(3), X(3047)}
X(48372) = perspector of the circumconic {{A, B, C, X(4), X(31726)}}
X(48372) = barycentric product X(523)*X(31726)
X(48372) = trilinear product X(661)*X(31726)
X(48372) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1637, 12077, 46425), (1637, 47236, 647)


X(48373) = TRILINEAR POLE OF LINE X(3)X(113)

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

See Antreas Hatzipolakis and César Lozada euclid 5001.

X(48373) lies on the MacBeath circumconic and these lines: {110, 8057}, {287, 37784}, {476, 39461}, {525, 46639}, {895, 1503}, {2407, 43755}, {2986, 15262}, {3580, 14919}, {4558, 20580}, {9033, 32715}, {13573, 46426}, {16237, 44769}

X(48373) = reflection of X(476) in X(39461)
X(48373) = isogonal conjugate of X(46425)
X(48373) = isotomic conjugate of the anticomplement of X(41077)
X(48373) = crosspoint of X(i) and X(j) for these (i, j): {2, 41077}, {99, 5502}, {476, 32640}
X(48373) = X(i)-isoconjugate-of-X(j) for these {i, j}: {656, 15262}, {661, 2071}, {822, 34170}
X(48373) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (107, 34170), (110, 2071), (112, 15262), (1304, 38937)
X(48373) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(15459)}} and {{A, B, C, X(6), X(32715)}}
X(48373) = trilinear pole of line {3, 113}
X(48373) = barycentric product X(i)*X(j) for these {i, j}: {69, 22239}, {99, 11744}
X(48373) = barycentric quotient X(i)/X(j) for these (i, j): (107, 34170), (110, 2071), (112, 15262), (1304, 38937)
X(48373) = trilinear product X(i)*X(j) for these {i, j}: {63, 22239}, {662, 11744}, {823, 40082}
X(48373) = trilinear quotient X(i)/X(j) for these (i, j): (162, 15262), (662, 2071), (823, 34170)


X(48374) = X(265)X(6000)∩X(328)X(43090)

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

See Antreas Hatzipolakis and César Lozada euclid 5001.

X(48374) lies on these lines: {265, 6000}, {328, 43090}, {1141, 22239}, {6644, 12028}

X(48374) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(31726)}} and {{A, B, C, X(6), X(403)}}
X(48374) = barycentric product X(94)*X(11744)


X(48375) = X(3)X(113)∩X(125)X(3523)

Barycentrics    10*a^10-22*(b^2+c^2)*a^8+(5*b^4+48*b^2*c^2+5*c^4)*a^6+(b^2+c^2)*(17*b^4-46*b^2*c^2+17*c^4)*a^4-(b^2-c^2)^2*(11*b^4+16*b^2*c^2+11*c^4)*a^2+(b^2+c^2)*(b^2-c^2)^4 : :
X(48375) = 5*X(3)+X(113), 2*X(3)+X(5972), 11*X(3)+X(7728), 3*X(3)+X(14643), 7*X(3)-X(16111), 13*X(3)-X(20127), 4*X(3)-X(37853), 5*X(3)-X(38788), 7*X(3)+X(38789), 8*X(3)+X(38791), 4*X(3)+X(38792), 7*X(3)+5*X(38794), 13*X(3)+5*X(38795), 2*X(113)-5*X(5972), 11*X(113)-5*X(7728), 3*X(113)-5*X(14643), 7*X(113)+5*X(16111), 13*X(113)+5*X(20127), 4*X(113)+5*X(37853), 7*X(113)-5*X(38789), 8*X(113)-5*X(38791), 4*X(113)-5*X(38792), X(113)-5*X(38793)

See Antreas Hatzipolakis and César Lozada euclid 5001.

X(48375) lies on these lines: {3, 113}, {74, 10299}, {110, 15717}, {125, 3523}, {140, 7687}, {186, 29317}, {376, 36518}, {511, 16227}, {541, 17504}, {542, 3524}, {548, 46686}, {549, 17702}, {550, 12900}, {631, 6723}, {974, 17704}, {1112, 13348}, {1350, 32300}, {1503, 16976}, {1511, 15712}, {1539, 46853}, {3522, 13202}, {3526, 12295}, {3530, 6699}, {3619, 32250}, {3819, 5663}, {5054, 23515}, {5447, 14708}, {5504, 37515}, {5642, 15055}, {5655, 15716}, {6053, 12041}, {6409, 13990}, {6410, 8998}, {7485, 32607}, {7516, 12901}, {9729, 41673}, {9826, 15644}, {10113, 14869}, {10303, 10733}, {10706, 15715}, {10721, 21735}, {11723, 31663}, {11793, 44573}, {12108, 20304}, {12121, 15042}, {12383, 38729}, {13198, 13347}, {14093, 15046}, {14156, 37968}, {15020, 24981}, {15023, 15059}, {15040, 16003}, {15041, 15706}, {15061, 15693}, {15113, 16196}, {15473, 32534}, {15700, 32609}, {15707, 38724}, {16254, 39084}, {16657, 41674}, {20126, 38638}, {20397, 34153}, {25563, 43898}, {29323, 47090}, {30714, 38728}, {34200, 34584}, {38725, 41983}

X(48375) = midpoint of X(i) and X(j) for these {i, j}: {3, 38793}, {113, 38788}, {376, 36518}, {5642, 15055}, {14644, 16163}, {15035, 38727}, {16111, 38789}, {23515, 38723}, {37853, 38792}
X(48375) = reflection of X(i) in X(j) for these (i, j): (5972, 38793), (14644, 6723), (38791, 38792), (38792, 5972)
X(48375) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 5972, 37853), (3, 38794, 16111), (140, 38726, 7687), (631, 15036, 16163), (631, 16163, 6723), (3523, 15051, 125), (3524, 15035, 38727), (5054, 38723, 23515), (5972, 37853, 38791), (15042, 15720, 12121)


X(48376) = X(2970)X(10419)∩X(7728)X(13417)

Barycentrics    b^2*c^2*(a^12-4*b^2*a^10+(5*b^4+2*b^2*c^2-2*c^4)*a^8-2*(5*b^4-3*b^2*c^2-c^4)*c^2*a^6-(b^2-c^2)*(5*b^6-2*c^6-(13*b^2-4*c^2)*b^2*c^2)*a^4+2*(b^2-c^2)^3*(2*b^2-c^2)*b^2*a^2-(b^2+c^2)*(b^2-c^2)^5)*(a^12-4*c^2*a^10-(2*b^4-2*b^2*c^2-5*c^4)*a^8+2*(b^4+3*b^2*c^2-5*c^4)*b^2*a^6-(b^2-c^2)*(2*b^6-5*c^6-(4*b^2-13*c^2)*b^2*c^2)*a^4+2*(b^2-c^2)^3*(b^2-2*c^2)*c^2*a^2+(b^2+c^2)*(b^2-c^2)^5) : :

See Antreas Hatzipolakis and César Lozada euclid 5001.

X(48376) lies on these lines: {2970, 10419}, {7728, 13417}, {14264, 37197}

X(48376) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(403)}} and {{A, B, C, X(4), X(31726)}}


X(48377) = X(5663)X(31726)∩X(22467)X(39986)

Barycentrics    b^2*c^2*(a^12-(2*b-c)*(2*b+c)*a^10+(5*b^4-2*c^4)*a^8-(10*b^2-9*c^2)*b^2*c^2*a^6-(b^2-c^2)*(5*b^6-2*c^6-(15*b^2-7*c^2)*b^2*c^2)*a^4+(4*b^2+c^2)*(b^2-c^2)^4*a^2-(b^2+c^2)*(b^2-c^2)^5)*(a^12+(b-2*c)*(b+2*c)*a^10-(2*b^4-5*c^4)*a^8+(9*b^2-10*c^2)*b^2*c^2*a^6-(b^2-c^2)*(2*b^6-5*c^6-(7*b^2-15*c^2)*b^2*c^2)*a^4+(b^2+4*c^2)*(b^2-c^2)^4*a^2+(b^2+c^2)*(b^2-c^2)^5) : :

See Antreas Hatzipolakis and César Lozada euclid 5001.

X(48377) lies on these lines: {5663, 31726}, {22467, 39986}, {34209, 44235}

X(48377) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(31726)}} and {{A, B, C, X(5), X(46428)}}


X(48378) = X(2)X(7687)∩X(3)X(113)

Barycentrics    6*a^10-14*(b^2+c^2)*a^8+(5*b^4+28*b^2*c^2+5*c^4)*a^6+(b^2+c^2)*(9*b^4-26*b^2*c^2+9*c^4)*a^4-(b^2-c^2)^2*(7*b^4+8*b^2*c^2+7*c^4)*a^2+(b^2+c^2)*(b^2-c^2)^4 : :
X(48378) = 9*X(2)-X(10733), 3*X(2)+5*X(15051), 3*X(2)+X(16163), 3*X(3)+X(113), 7*X(3)+X(7728), 5*X(3)+3*X(14643), 5*X(3)-X(16111), 9*X(3)-X(20127), 3*X(3)-X(37853), 11*X(3)-3*X(38788), 13*X(3)+3*X(38789), 15*X(3)+X(38790), 5*X(3)+X(38791), 7*X(3)+3*X(38792), X(3)+3*X(38793), 3*X(3)+5*X(38794), 7*X(3)+5*X(38795), 3*X(7687)-X(10733), X(7687)+5*X(15051), X(10733)+15*X(15051), X(10733)+3*X(16163), 5*X(15051)-X(16163)

See Antreas Hatzipolakis and César Lozada euclid 5001.

X(48378) lies on these lines: {2, 7687}, {3, 113}, {4, 15036}, {5, 38726}, {20, 36518}, {30, 12900}, {74, 3524}, {110, 3523}, {125, 631}, {140, 6723}, {141, 542}, {146, 15692}, {182, 5486}, {186, 15473}, {265, 5054}, {376, 13202}, {381, 15042}, {389, 41673}, {394, 12227}, {399, 15693}, {511, 9826}, {541, 10272}, {550, 46686}, {632, 10113}, {974, 16836}, {1112, 15644}, {1151, 13990}, {1152, 8998}, {1216, 14708}, {1368, 32743}, {1531, 44280}, {1533, 2071}, {1539, 8703}, {1568, 37941}, {1656, 12295}, {1986, 3917}, {2931, 31521}, {3091, 15023}, {3448, 15020}, {3525, 14644}, {3526, 12121}, {3528, 10721}, {3530, 5663}, {3538, 13203}, {3579, 11723}, {3580, 44673}, {3819, 12358}, {5085, 5181}, {5095, 10519}, {5432, 46683}, {5433, 46687}, {5609, 22251}, {5622, 32114}, {5650, 21650}, {5655, 15700}, {5892, 12236}, {5907, 44573}, {6000, 16976}, {6593, 21167}, {6643, 19506}, {6644, 19130}, {6676, 46265}, {7393, 12302}, {7484, 19457}, {7509, 32607}, {7514, 12901}, {7575, 29317}, {7722, 7999}, {7998, 12219}, {8994, 10820}, {9033, 44818}, {9140, 15708}, {9306, 10193}, {10164, 11720}, {10165, 11735}, {10192, 11598}, {10212, 14128}, {10257, 18400}, {10299, 10990}, {10303, 15059}, {10564, 32223}, {10610, 22966}, {10625, 16222}, {10628, 13416}, {10706, 15698}, {10819, 13969}, {11202, 46264}, {11430, 37648}, {11438, 37645}, {11566, 29181}, {11693, 15707}, {11694, 41983}, {11695, 11746}, {11807, 41670}, {11812, 40685}, {12041, 15712}, {12108, 20397}, {12140, 37118}, {12317, 15719}, {12893, 15115}, {13198, 37515}, {13348, 41671}, {14156, 15646}, {14499, 38708}, {14500, 38709}, {14677, 17504}, {14683, 15057}, {14869, 34128}, {15034, 24981}, {15040, 15061}, {15055, 15063}, {15078, 18388}, {15081, 15702}, {15088, 16239}, {15118, 33851}, {15122, 29012}, {15462, 19126}, {15463, 43652}, {15472, 35486}, {16003, 32609}, {16278, 21166}, {17928, 22109}, {18440, 23329}, {18579, 19924}, {18580, 24206}, {20773, 43586}, {21970, 37497}, {22104, 47084}, {23236, 38638}, {23583, 38605}, {23698, 36177}, {25487, 34477}, {31378, 46632}, {31945, 32417}, {32250, 40330}, {32263, 37476}, {33511, 33813}, {33923, 34584}, {38246, 40477}, {40805, 46301}, {43615, 43839}, {44872, 44912}

X(48378) = midpoint of X(i) and X(j) for these {i, j}: {3, 5972}, {5, 38726}, {74, 6053}, {110, 20417}, {113, 37853}, {389, 41673}, {550, 46686}, {1112, 15644}, {1216, 14708}, {1511, 6699}, {3579, 11723}, {5907, 44573}, {7687, 16163}, {10564, 32223}, {12041, 16534}, {12042, 33512}, {12893, 15115}, {13348, 41671}, {14156, 15646}, {15118, 33851}, {16111, 38791}, {22104, 47084}, {33511, 33813}, {34153, 36253}
X(48378) = reflection of X(i) in X(j) for these (i, j): (6723, 140), (11746, 11695), (15088, 16239), (44872, 44912)
X(48378) = complement of X(7687)
X(48378) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 15051, 16163), (2, 16163, 7687), (3, 113, 37853), (3, 14643, 16111), (3, 38793, 5972), (3, 38794, 113), (74, 5642, 6053), (110, 3523, 38727), (110, 38727, 20417), (113, 16111, 38790), (113, 38790, 38791), (113, 38793, 38794), (113, 38794, 5972), (549, 1511, 6699), (631, 15035, 125), (1656, 38723, 12295), (3526, 12121, 23515), (5972, 37853, 113), (5972, 38791, 14643), (5972, 38792, 38795), (7728, 38795, 38792), (10564, 44214, 32223), (14643, 16111, 38791), (14643, 38790, 113), (14869, 34153, 34128), (15040, 15720, 15061), (32609, 38728, 16003), (34128, 34153, 36253)


X(48379) = ISOGONAL CONJUGATE OF X(3047)

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

See Antreas Hatzipolakis and César Lozada euclid 5001.

X(48379) lies on these lines: {232, 19656}, {338, 46426}, {511, 31726}, {1485, 30715}, {5968, 30744}, {10255, 14356}, {19189, 19651}, {35488, 35908}

X(48379) = isogonal conjugate of X(3047)
X(48379) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(31726)}} and {{A, B, C, X(5), X(10419)}}


X(48380) = ISOTOMIC CONJUGATE OF X(2990)

Barycentrics    b*c*(a^3*b - a^2*b^2 - a*b^3 + b^4 + a^3*c + a*b^2*c - a^2*c^2 + a*b*c^2 - 2*b^2*c^2 - a*c^3 + c^4) : :
X(48380) = 3 X[2] - 4 X[26011]

X(48380) lies on these lines: {2, 37}, {8, 10629}, {78, 20320}, {92, 1947}, {110, 422}, {145, 23528}, {226, 14213}, {297, 525}, {306, 20237}, {313, 26579}, {314, 26637}, {318, 12649}, {320, 20920}, {343, 3782}, {517, 38952}, {519, 23580}, {527, 14206}, {651, 37790}, {655, 3218}, {726, 26013}, {851, 29010}, {908, 4858}, {1089, 24982}, {1109, 20360}, {1214, 17479}, {1230, 26609}, {1441, 31019}, {1733, 3011}, {1738, 17888}, {1824, 20242}, {1897, 37782}, {1985, 20430}, {1993, 3187}, {2052, 43675}, {2987, 43189}, {2990, 13136}, {3120, 23690}, {3262, 3936}, {3695, 25962}, {3701, 25005}, {3868, 37235}, {3870, 17860}, {3977, 20881}, {4008, 26228}, {4054, 20236}, {4066, 8582}, {4365, 25941}, {4385, 5554}, {4442, 23541}, {4647, 24987}, {5249, 6358}, {5392, 40149}, {5422, 26223}, {5745, 20879}, {6057, 25973}, {10030, 20940}, {13407, 23555}, {14570, 18609}, {15066, 26651}, {17184, 37636}, {17484, 30807}, {17871, 33144}, {18750, 20078}, {20076, 20220}, {20256, 21318}, {20883, 30687}, {20895, 33077}, {20911, 26541}, {23661, 34772}, {23689, 33143}, {23989, 40704}, {24026, 26015}, {26005, 26611}, {26625, 26659}, {29028, 46550}, {29077, 46551}, {30273, 35980}, {31623, 40571}, {32859, 45794}

X(48380) = isogonal conjugate of X(32655)
X(48380) = isotomic conjugate of X(2990)
X(48380) = polar conjugate of X(915)
X(48380) = anticomplement of the isotomic conjugate of X(16082)
X(48380) = isotomic conjugate of the isogonal conjugate of X(8609)
X(48380) = polar conjugate of the isogonal conjugate of X(912)
X(48380) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {19, 153}, {34, 36918}, {104, 4329}, {909, 20}, {1309, 20295}, {1795, 6527}, {10428, 3007}, {14776, 514}, {16082, 6327}, {32641, 20294}, {32702, 522}, {34234, 1370}, {34858, 6360}, {36110, 693}, {36123, 69}, {39294, 3888}, {41933, 10538}, {43933, 150}
X(48380) = X(i)-Ceva conjugate of X(j) for these (i,j): {264, 34332}, {13136, 4391}, {16082, 2}, {18816, 14266}, {46405, 693}
X(48380) = X(34332)-cross conjugate of X(264)
X(48380) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32655}, {3, 913}, {6, 36052}, {31, 2990}, {48, 915}, {163, 3657}, {184, 37203}, {604, 45393}, {649, 6099}, {909, 39173}, {1459, 32698}, {2183, 15381}, {9247, 46133}, {22383, 36106}
X(48380) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 2990), (3, 32655), (9, 36052), (115, 3657), (119, 6), (1249, 915), (1737, 2323), (3161, 45393), (5375, 6099), (8609, 517), (23980, 39173), (36103, 913), (39002, 22383), (39175, 14578), (42769, 1015)
X(48380) = cevapoint of X(912) and X(8609)
X(48380) = crosspoint of X(76) and X(18816)
X(48380) = crosssum of X(1977) and X(23220)
X(48380) = trilinear pole of line {119, 34332}
X(48380) = crossdifference of every pair of points on line {184, 667}
X(48380) = barycentric product X(i)*X(j) for these {i,j}: {75, 1737}, {76, 8609}, {92, 914}, {119, 18816}, {264, 912}, {850, 3658}, {1969, 2252}, {3262, 14266}, {3596, 18838}, {11570, 20566}, {34332, 46133}
X(48380) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 36052}, {2, 2990}, {4, 915}, {6, 32655}, {8, 45393}, {19, 913}, {92, 37203}, {100, 6099}, {104, 15381}, {119, 517}, {264, 46133}, {517, 39173}, {523, 3657}, {912, 3}, {914, 63}, {1158, 10692}, {1737, 1}, {1783, 32698}, {1897, 36106}, {2252, 48}, {3658, 110}, {8609, 6}, {11570, 36}, {12665, 2077}, {12831, 1155}, {12832, 1319}, {14266, 104}, {18838, 56}, {34332, 912}, {39991, 2687}, {42769, 8677}
X(48380) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 312, 17740}, {312, 37758, 4358}, {321, 1229, 4671}, {321, 17862, 2}, {321, 20905, 26591}, {3936, 20887, 3262}, {4671, 28605, 4461}, {17862, 26591, 20905}, {20905, 26591, 2}, {26538, 26587, 2}, {26567, 26612, 2}


X(48381) = ISOTOMIC CONJUGATE OF X(2989)

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

X(48381) lies on these lines: {1, 2}, {19, 21270}, {37, 25000}, {40, 31015}, {69, 26651}, {75, 26540}, {110, 423}, {125, 46534}, {141, 20905}, {150, 7291}, {297, 525}, {319, 37659}, {321, 13567}, {343, 1231}, {355, 379}, {445, 45038}, {448, 6740}, {515, 14953}, {516, 47107}, {517, 857}, {594, 25001}, {610, 20074}, {674, 21045}, {677, 2989}, {944, 24580}, {946, 31014}, {952, 1375}, {962, 31042}, {1086, 17895}, {1108, 5740}, {1146, 30807}, {1385, 24581}, {1441, 16608}, {1482, 30808}, {1483, 31186}, {1730, 21072}, {1826, 17220}, {1839, 20289}, {1855, 5905}, {1952, 18359}, {1953, 20305}, {1959, 33864}, {2170, 26012}, {2183, 21091}, {2321, 25019}, {3007, 4466}, {3262, 37796}, {3668, 40903}, {3868, 37448}, {3936, 26011}, {3969, 25091}, {4358, 26005}, {4445, 25878}, {4566, 5236}, {4968, 26550}, {5015, 26678}, {5224, 24554}, {5250, 31049}, {5295, 25017}, {5422, 23126}, {5657, 14021}, {5690, 30810}, {5839, 26668}, {5882, 35290}, {6515, 17911}, {6684, 31016}, {8287, 17444}, {8756, 9028}, {11433, 26223}, {11491, 36016}, {12245, 30809}, {12645, 31184}, {16603, 17451}, {17229, 25067}, {17233, 26669}, {17863, 21933}, {18589, 21271}, {20110, 27382}, {21011, 34830}, {24608, 34627}, {24635, 33298}, {24682, 31163}, {24993, 26543}, {26530, 26665}, {26591, 37648}, {27249, 37529}, {27300, 37699}, {29081, 46548}, {29331, 37165}, {29961, 35631}, {30844, 34631}, {31048, 31162}, {31909, 41723}, {37781, 40862}, {40905, 45738}, {40937, 40999}

X(48381) = anticomplement of X(26006)
X(48381) = reflection of X(i) in X(j) for these {i,j}: {3007, 4466}, {14543, 8756}
X(48381) = isotomic conjugate of X(2989)
X(48381) = anticomplement of X(26006)
X(48381) = polar conjugate of X(917)
X(48381) = isotomic conjugate of the isogonal conjugate of X(8608)
X(48381) = polar conjugate of the isogonal conjugate of X(916)
X(48381) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {19, 152}, {103, 4329}, {911, 20}, {36039, 20294}, {36056, 6527}, {36101, 1370}, {36109, 3261}, {36122, 69}, {40116, 513}
X(48381) = X(i)-Ceva conjugate of X(j) for these (i,j): {264, 34335}, {677, 25259}
X(48381) = X(34335)-cross conjugate of X(264)
X(48381) = X(i)-isoconjugate of X(j) for these (i,j): {31, 2989}, {48, 917}, {513, 35182}, {905, 32699}, {910, 15380}, {1459, 36107}
X(48381) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 2989), (118, 6), (1249, 917), (8608, 516), (39003, 1459), (39026, 35182)
X(48381) = cevapoint of X(916) and X(8608)
X(48381) = crosspoint of X(76) and X(18025)
X(48381) = trilinear pole of line {118, 34335}
X(48381) = crossdifference of every pair of points on line {184, 649}
X(48381) = barycentric product X(i)*X(j) for these {i,j}: {75, 1736}, {76, 8608}, {118, 18025}, {264, 916}, {850, 4243}, {1969, 2253}
X(48381) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2989}, {4, 917}, {101, 35182}, {103, 15380}, {118, 516}, {916, 3}, {1736, 1}, {1783, 36107}, {2253, 48}, {4243, 110}, {8608, 6}, {8750, 32699}, {21102, 35363}, {34335, 916}
X(48381) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 28757, 40863}, {10, 25935, 2}, {343, 17862, 17184}, {594, 25964, 25001}, {2321, 25019, 25243}, {3661, 26531, 2}, {3912, 26001, 2}, {26526, 26575, 2}, {26532, 26581, 2}, {26544, 26610, 2}, {26548, 26599, 2}, {26559, 26595, 2}, {26560, 26597, 2}, {26570, 26594, 2}

leftri

Points in a [X(2)X(513), X(2)X(523)] coordinate system: X(48156)-X(48254)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1,L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1 = the line X(3)X(513) with coefficients given by the barycentrics for the isotomic conjugate of X(2990), shown at X(48380)

L2 = the line X(3)X(514) with coefficients given by the barycentrics for the isotomic conjugate of X(2989), shown at X(48381)

The origin is given by (0,0) = X(3), the circumcenter.

Barycentrics u : v : w for a point U = (x,y) in this system are given by

u : v : w = (b - c) (a^2(a - b)(a - c)(a^2 - b^2 - c^2) + a x - y]) : : ,

where, as functions of a,b,c, the coordinate x is symmetric and homogeneous of degree 5, and y is symmetric and homogeneous of degree 6.

The appearance of {x,y}, k in the following list means that (x,y) = X(k):

{-((2 a^2 b^2 c^2)/(a+b+c)), -a^2 b^2 c^2}, 39226
{0,-2 a^2 b^2 c^2}, 44408
{0,-a^2 b^2 c^2}, 39476
{0,0},3}
{(-2*a^2*b^2*c^2)/(a + b + c), -2*a^2*b^2*c^2}, 48382
{(-2*a^2*b^2*c^2)/(a + b + c), 0},48383
{-((a^2*b^2*c^2)/(a + b + c)), -(a^2*b^2*c^2)}, 48384
{-a^5 - b^5 - c^5, a*b*c*(a^3 + b^3 + c^3)}, 48385
{0, a^2*b^2*c^2}, 48386
{0, 2*a^2*b^2*c^2}, 48387
{0, 2*a*b*c*(a^3 + b^3 + c^3)}, 48388
{(a^2*b^2*c^2)/(a + b + c), a^2*b^2*c^2}, 48389
{(2*a^2*b^2*c^2)/(a + b + c), 0}, 48390
{(2*a^2*b^2*c^2)/(a + b + c), 2*a^2*b^2*c^2}, 48391


X(48382) = X(3)X(523)∩X(36)X(238)

Barycentrics    a^2*(b - c)*(a^5 - 2*a^3*b^2 + a*b^4 - a^3*b*c + a^2*b^2*c + a*b^3*c - b^4*c - 2*a^3*c^2 + a^2*b*c^2 + 2*a*b^2*c^2 + b^3*c^2 + a*b*c^3 + b^2*c^3 + a*c^4 - b*c^4) : :
X(48382) = X[4057] - 3 X[39199], 2 X[4057] - 3 X[39200], X[4057] + 3 X[44408], X[39200] + 2 X[44408]

X(48382) lies on these lines: {3, 523}, {21, 48209}, {22, 47797}, {25, 47799}, {35, 48293}, {36, 238}, {55, 48292}, {56, 2605}, {404, 48204}, {405, 48207}, {474, 48205}, {514, 39226}, {522, 39476}, {900, 35451}, {1011, 47833}, {2178, 3709}, {3287, 36743}, {4017, 23226}, {4184, 47834}, {4191, 47827}, {4210, 47825}, {4778, 39225}, {4977, 39478}, {5959, 17524}, {6372, 39480}, {6636, 48203}, {7354, 8819}, {7484, 47807}, {7485, 47809}, {8071, 44409}, {11340, 47782}, {11350, 47784}, {15246, 48208}, {16058, 48206}, {16059, 47829}, {16453, 18116}, {37557, 47727}

X(48382) = midpoint of X(39199) and X(44408)
X(48382) = reflection of X(39200) in X(39199)
X(48382) = X(38340)-Ceva conjugate of X(6)
X(48382) = X(1897)-isoconjugate of X(34800)
X(48382) = X(34467)-Dao conjugate of X(34800)
X(48382) = crosspoint of X(i) and X(j) for these (i,j): {58, 26700}, {10419, 36064}
X(48382) = crosssum of X(i) and X(j) for these (i,j): {10, 35057}, {522, 25639}, {526, 6739}
X(48382) = crossdifference of every pair of points on line {37, 3003}
X(48382) = barycentric product X(905)*X(7414)
X(48382) = barycentric quotient X(i)/X(j) for these {i,j}: {7414, 6335}, {22383, 34800}


X(48383) = X(3)X(513)∩X(186)X(523)

Barycentrics    a^2*(b - c)*(a^5 - 2*a^3*b^2 + a*b^4 - a^3*b*c + a^2*b^2*c + a*b^3*c - b^4*c - 2*a^3*c^2 + a^2*b*c^2 - b^3*c^2 + a*b*c^3 - b^2*c^3 + a*c^4 - b*c^4) : :
X(48383) = X[16228] - 3 X[47803]

X(48383) lies on these lines: {3, 513}, {21, 48165}, {22, 47804}, {24, 44426}, {25, 16228}, {35, 48307}, {36, 48281}, {55, 48302}, {56, 48283}, {186, 523}, {404, 48246}, {405, 48181}, {474, 48230}, {512, 39480}, {514, 39226}, {521, 34948}, {522, 39200}, {656, 8648}, {667, 15313}, {900, 4057}, {1011, 47822}, {1030, 21007}, {1624, 37966}, {2178, 21348}, {2476, 34962}, {3063, 36744}, {3738, 39210}, {4184, 47821}, {4191, 47823}, {4210, 47824}, {4261, 22157}, {4448, 16064}, {4778, 39476}, {4874, 23864}, {4977, 44408}, {5120, 39521}, {6636, 47805}, {7484, 47802}, {7485, 44429}, {8193, 48327}, {9001, 23224}, {9818, 44923}, {11340, 47762}, {11350, 47761}, {13558, 47199}, {15246, 48164}, {16058, 48197}, {16059, 48216}, {17420, 23226}, {18610, 23399}, {20834, 45666}, {20980, 36743}, {21308, 39483}, {22160, 31947}, {37557, 48324}

X(48383) = reflection of X(i) in X(j) for these {i,j}: {34948, 39227}, {39199, 39478}, {39200, 39225}
X(48383) = circumcircle-inverse of X(31847)
X(48383) = isogonal conjugate of the anticomplement of X(34467)
X(48383) = X(6335)-Ceva conjugate of X(6)
X(48383) = X(22383)-Dao conjugate of X(905)
X(48383) = crosspoint of X(i) and X(j) for these (i,j): {54, 100}, {108, 3450}, {1309, 15381}
X(48383) = crosssum of X(i) and X(j) for these (i,j): {5, 513}, {119, 8677}, {514, 20305}, {520, 21530}, {521, 1329}, {525, 21245}
X(48383) = crossdifference of every pair of points on line {216, 7561}
X(48383) = barycentric product X(6335)*X(34467)
X(48383) = barycentric quotient X(34467)/X(905)


X(48384) = X(3)X(523)∩X(36)X(2605)

Barycentrics    a^2*(b - c)*(a^5 - 2*a^3*b^2 + a*b^4 - a^3*b*c + a^2*b^2*c + a*b^3*c - b^4*c - 2*a^3*c^2 + a^2*b*c^2 + 2*a*b^2*c^2 + a*b*c^3 + a*c^4 - b*c^4) : :
X(48384) = X[39225] - 3 X[39226], X[39225] + 3 X[39476], 2 X[39225] - 3 X[39478], 2 X[39476] + X[39478]

X(48384) lies on these lines: {3, 523}, {21, 48207}, {22, 47799}, {35, 48292}, {36, 2605}, {404, 48205}, {513, 23961}, {900, 18861}, {1011, 48206}, {3287, 5124}, {3737, 7280}, {4057, 8660}, {4184, 47833}, {4188, 48204}, {4189, 48209}, {4191, 47829}, {4210, 47827}, {4367, 5957}, {4977, 44408}, {5010, 48293}, {6636, 47797}, {7485, 47807}, {8071, 39540}, {8819, 15326}, {11340, 47784}, {14793, 44409}, {15246, 47809}, {28217, 39200}

X(48384) = midpoint of X(39226) and X(39476)
X(48384) = reflection of X(39478) in X(39226)


X(48385) = X(39)X(661)∩X(513)X(7626)

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

X(48385) lies on these lines: {39, 661}, {114, 31841}, {182, 9013}, {513, 7626}, {3788, 4369}, {6004, 39212}, {7192, 7763}, {7834, 25666}, {7874, 24924}


X(48386) = X(3)X(514)∩X(36)X(4449)

Barycentrics    a^2*(b - c)*(a^4 - a^3*b - a^2*b^2 + a*b^3 - a^3*c + a^2*b*c + a*b^2*c - b^3*c - a^2*c^2 + a*b*c^2 - b^2*c^2 + a*c^3 - b*c^3) : :
X(48386) = 3 X[3] - X[44408], 3 X[39476] - 2 X[44408], 2 X[39200] - 3 X[39225]

X(48386) lies on these lines: {3, 514}, {21, 47794}, {22, 47766}, {25, 39532}, {35, 663}, {36, 4449}, {55, 48294}, {56, 48287}, {404, 47795}, {405, 48196}, {474, 48218}, {521, 39210}, {522, 39200}, {523, 15646}, {649, 39577}, {667, 3887}, {993, 4147}, {1011, 47778}, {1734, 8648}, {1946, 14838}, {3900, 39227}, {3960, 22091}, {4040, 5010}, {4057, 4962}, {4184, 4893}, {4188, 47796}, {4189, 47793}, {4191, 47779}, {4210, 4379}, {4255, 22154}, {4256, 22090}, {4777, 39478}, {4794, 5217}, {4843, 5926}, {6362, 44805}, {6366, 44811}, {6367, 39477}, {6636, 47771}, {7280, 48282}, {7484, 44432}, {7485, 47757}, {7634, 48329}, {8676, 44827}, {9818, 44928}, {10196, 16064}, {11340, 47789}, {15246, 44435}, {17072, 25440}, {17166, 39578}, {19525, 21198}, {21196, 22388}, {23864, 31286}, {23879, 39201}, {28161, 39199}, {34948, 35057}, {36152, 47123}, {45684, 47523}

X(48386) = midpoint of X(7634) and X(48329)
X(48386) = reflection of X(39476) in X(3)
X(48386) = crosssum of X(513) and X(17605)


X(48387) = X(3)X(514)∩X(55)X(663)

Barycentrics    a^2*(a - b - c)*(b - c)*(a^3 - a*b^2 + a*b*c + b^2*c - a*c^2 + b*c^2) : :
X(48387) = 3 X[3] - 2 X[39476], 4 X[39476] - 3 X[44408], 3 X[39199] - 4 X[39478], X[4705] - 3 X[11124], 3 X[14414] - X[48131]

X(48387) lies on these lines: {3, 514}, {21, 47793}, {22, 47771}, {25, 47766}, {35, 4040}, {36, 48282}, {55, 663}, {56, 4449}, {100, 21302}, {101, 14723}, {186, 523}, {386, 22154}, {404, 47796}, {405, 47794}, {474, 47795}, {513, 2077}, {521, 3733}, {522, 1324}, {649, 8676}, {650, 1946}, {659, 6362}, {667, 3900}, {669, 4843}, {958, 4147}, {999, 48287}, {1011, 4893}, {1376, 17072}, {1598, 39532}, {3295, 48294}, {3309, 7634}, {3669, 22091}, {3939, 40519}, {4041, 8648}, {4063, 39577}, {4091, 9000}, {4139, 39480}, {4184, 47775}, {4191, 4379}, {4210, 47780}, {4255, 22090}, {4367, 6366}, {4428, 45316}, {4477, 21005}, {4705, 11124}, {4724, 5217}, {4777, 39200}, {4874, 23383}, {5010, 47970}, {5172, 21118}, {6004, 15625}, {6050, 6182}, {6367, 14270}, {6544, 47523}, {6546, 16064}, {6636, 47773}, {7484, 47757}, {7485, 44435}, {8069, 21185}, {8713, 15599}, {9029, 12329}, {9366, 48330}, {10196, 20834}, {11108, 48196}, {11340, 47791}, {11350, 47789}, {11479, 44928}, {14077, 39227}, {14414, 48131}, {14838, 22160}, {15246, 48156}, {15280, 31288}, {15584, 29070}, {16058, 47778}, {16059, 47779}, {16408, 48218}, {16419, 44432}, {16678, 17166}, {16695, 23880}, {18755, 21791}, {20988, 23615}, {21183, 37309}, {21196, 23093}, {22388, 45745}, {23187, 39210}, {23843, 48062}, {28147, 39226}, {28161, 39225}, {37579, 47123}, {40726, 45667}

X(48387) = reflection of X(i) in X(j) for these {i,j}: {15280, 31288}, {23187, 39210}, {44408, 3}
X(48387) = circumcircle-inverse of X(31852)
X(48387) = Stammler-circle-inverse of X(18329)
X(48387) = isogonal conjugate of the anticomplement of X(39006)
X(48387) = isogonal conjugate of the isotomic conjugate of X(20293)
X(48387) = X(1897)-Ceva conjugate of X(6)
X(48387) = X(i)-isoconjugate of X(j) for these (i,j): {92, 40518}, {934, 44040}
X(48387) = X(i)-Dao conjugate of X(j) for these (i, j): (1459, 4025), (14714, 44040), (22391, 40518), (44311, 311)
X(48387) = crosspoint of X(i) and X(j) for these (i,j): {54, 101}, {100, 284}, {108, 3451}, {112, 3453}, {15380, 40116}
X(48387) = crosssum of X(i) and X(j) for these (i,j): {5, 514}, {118, 39470}, {226, 513}, {440, 520}, {521, 3452}, {522, 41883}, {525, 3454}, {6364, 31591}, {6365, 31590}
X(48387) = crossdifference of every pair of points on line {216, 1108}
X(48387) = barycentric product X(i)*X(j) for these {i,j}: {6, 20293}, {9, 48281}, {55, 47796}, {60, 21721}, {101, 44311}, {404, 650}, {663, 32939}, {1897, 39006}, {3063, 44139}, {4391, 44085}
X(48387) = barycentric quotient X(i)/X(j) for these {i,j}: {184, 40518}, {404, 4554}, {657, 44040}, {20293, 76}, {21721, 34388}, {32939, 4572}, {39006, 4025}, {44085, 651}, {44311, 3261}, {47796, 6063}, {48281, 85}
X(48387) = {X(650),X(1946)}-harmonic conjugate of X(21789)


X(48388) = X(3)X(514)∩X(35)X(47725)

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

X(48388) lies on these lines: {3, 514}, {35, 47725}, {55, 47691}, {56, 47728}, {659, 17069}, {663, 37549}, {1376, 48062}, {3670, 4040}, {4057, 13246}, {4202, 47793}, {4458, 23865}, {4724, 17595}, {16158, 48241}, {21488, 47791}, {35984, 47775}


X(48389) = X(3)X(523)∩X(21)X(48205)

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

X(48389) lies on these lines: {3, 523}, {21, 48205}, {22, 47807}, {35, 2605}, {36, 48292}, {404, 48207}, {522, 39478}, {900, 4057}, {1011, 47829}, {1030, 3287}, {3737, 5010}, {4184, 47827}, {4188, 48209}, {4189, 48204}, {4191, 48206}, {4210, 47833}, {4777, 39226}, {4802, 39476}, {4926, 39225}, {6097, 18116}, {6636, 47809}, {7280, 48293}, {7485, 47799}, {8069, 39540}, {8674, 39210}, {11340, 47788}, {15246, 47797}, {16064, 28602}, {28175, 44408}, {28183, 39199}, {28221, 39200}, {37557, 48290}

X(48389) = X(i)-Ceva conjugate of X(j) for these (i,j): {99, 32933}, {4555, 323}
X(48389) = crosspoint of X(99) and X(40214)
X(48389) = crosssum of X(i) and X(j) for these (i,j): {512, 8818}, {513, 9955}
X(48389) = crossdifference of every pair of points on line {3003, 17053}
X(48389) = barycentric product X(i)*X(j) for these {i,j}: {35, 47795}, {2605, 32933}, {3219, 48283}, {14838, 25440}
X(48389) = barycentric quotient X(i)/X(j) for these {i,j}: {25440, 15455}, {47795, 20565}, {48283, 30690}


X(48390) = X(3)X(513)∩X(6)X(22095)

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

X(48390) lies on these lines: {3, 513}, {6, 22095}, {21, 48246}, {22, 44429}, {25, 47802}, {35, 48281}, {36, 48307}, {55, 48283}, {56, 48302}, {378, 44426}, {404, 48165}, {405, 48230}, {474, 48181}, {522, 39476}, {523, 2071}, {900, 18861}, {1011, 47823}, {1333, 22157}, {1593, 16228}, {2254, 23226}, {3063, 36743}, {3309, 34948}, {3667, 39200}, {3733, 8636}, {4057, 27086}, {4184, 47824}, {4191, 47822}, {4210, 47821}, {4254, 39521}, {4776, 11340}, {5124, 21007}, {6006, 39225}, {6636, 48164}, {6642, 44923}, {6830, 34962}, {7484, 47803}, {7485, 47804}, {8193, 48332}, {8674, 23187}, {11350, 47760}, {15246, 47805}, {15313, 23224}, {16058, 48216}, {16059, 48197}, {16064, 36848}, {20980, 36744}, {37557, 48335}

X(48390) = reflection of X(i) in X(j) for these {i,j}: {4057, 39478}, {39200, 39226}
X(48390) = crosssum of X(496) and X(513)
X(48390) = crossdifference of every pair of points on line {800, 8609}


X(48391) = X(3)X(523)∩X(21)X(48204)

Barycentrics    a^2*(b - c)*(a^5 - 2*a^3*b^2 + a*b^4 - a^3*b*c + a^2*b^2*c + a*b^3*c - b^4*c - 2*a^3*c^2 + a^2*b*c^2 + 2*a*b^2*c^2 - 3*b^3*c^2 + a*b*c^3 - 3*b^2*c^3 + a*c^4 - b*c^4) : :
X(48391) = 3 X[39200] - 4 X[39225]

X(48391) lies on these lines: {3, 523}, {21, 48204}, {22, 47809}, {25, 47807}, {35, 3737}, {36, 48293}, {55, 2605}, {56, 48292}, {404, 48209}, {405, 48205}, {474, 48207}, {513, 2077}, {522, 39200}, {1011, 47827}, {3287, 36744}, {3733, 8674}, {3900, 34948}, {4041, 23226}, {4057, 4926}, {4184, 47825}, {4191, 47833}, {4210, 47834}, {4777, 39199}, {4789, 11340}, {4802, 44408}, {4948, 19346}, {5432, 8819}, {6636, 48208}, {7484, 47799}, {7485, 47797}, {8043, 21789}, {8069, 44409}, {8193, 48290}, {9508, 23864}, {11350, 47788}, {15246, 48203}, {16058, 47829}, {16059, 48206}, {20834, 28602}, {28147, 39476}, {28161, 39226}, {28183, 39478}, {35057, 39210}, {37557, 47682}

X(48391) = crosssum of X(513) and X(12047)
X(48391) = crossdifference of every pair of points on line {1108, 3003}

leftri

Points in a [L(31),L(32)] coordinate system: X(48392)-X(48410)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1,L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1 = the line L(32) = X(325)X(523) = [a^2, b^2, c^2];

L2 = the line L(31) = X(514)X(661) = [a,b,c].

The origin is given by (0,0) = X(693) = b c (b + c) : : .

Barycentrics u : v : w for a point U = (x,y) in this system are given by

u : v : w = (b - c) (b c - (b+c) x + y) : : ,

where, as functions of a,b,c, the coordinate x is symmetric and homogeneous of degree 1, and y is symmetric and homogeneous of degree 2.

Note that the (L(31),L(32)) coordinate system is not the same as the (L(32),L(31) system; see the preamble just before X(47650).,

The appearance of {x,y}, k in the following table means that (x,y) = X(k):

{-2 (a+b+c), -2 (a b+a c+b c)}, 47665)
{-((2 (a^2+b^2+c^2))/(a+b+c)), -2 (a^2+b^2+c^2)), 47685)
{-((2 (a^2+b^2+c^2))/(a+b+c)), -((2 a b c)/(a+b+c))}, 47706)
{-((2 (a b+a c+b c))/(a+b+c)), -2 (a b+a c+b c)}, 48080)
{-2 (a+b+c), -a b-a c-b c}, 4838)
{-((2 (a^2+b^2+c^2))/(a+b+c)), -a^2-b^2-c^2}, 47687)
{-((2 (a^2+b^2+c^2))/(a+b+c)), -a b-a c-b c}, 47700)
{-((2 (a^2+b^2+c^2))/(a+b+c)), -((a b c)/(a+b+c))}, 47710)
{-((2 (a b+a c+b c))/(a+b+c)), -a b-a c-b c}, 4804)
{-2 (a+b+c), 0}, 47655)
{-((2 (a^2+b^2+c^2))/(a+b+c)), 0}, 47689)
{-2 (a+b+c), a^2+b^2+c^2}, 47658)
{-2 (a+b+c), a b+a c+b c}, 47670)
{-((2 (a^2+b^2+c^2))/(a+b+c)), (a b c)/(a+b+c)}, 47714)
{-((2 (a^2+b^2+c^2))/(a+b+c)), (2 a b c)/(a+b+c)}, 47718)
{-a-b-c, -2 (a^2+b^2+c^2)}, 47650)
{-a-b-c, -2 (a b+a c+b c)}, 25259)
{-((a^2+b^2+c^2)/(a+b+c)), -2 (a^2+b^2+c^2)}, 47686)
{-((a^2+b^2+c^2)/(a+b+c)), -2 (a b+a c+b c)}, 47698)
{-((a^2+b^2+c^2)/(a+b+c)), -((2 a b c)/(a+b+c))}, 47707)
{-((a b+a c+b c)/(a+b+c)), -2 (a b+a c+b c)}, 48024)
{-a-b-c, -a^2-b^2-c^2}, 26824)
{-a-b-c, -a b-a c-b c}, 4024)
{-a-b-c, -((a b c)/(a+b+c))}, 47678)
{-((a^2+b^2+c^2)/(a+b+c)), -a^2-b^2-c^2}, 46403)
{-((a^2+b^2+c^2)/(a+b+c)), -a b-a c-b c}, 4088)
{-((a^2+b^2+c^2)/(a+b+c)), -((a b c)/(a+b+c))}, 47711)
{-((a b+a c+b c)/(a+b+c)), -a b-a c-b c}, 4010)
{-a-b-c, 0}, 47656)
{-((a^2+b^2+c^2)/(a+b+c)), 0}, 47690)
{-((a b+a c+b c)/(a+b+c)), 0}, 48120)
{-a-b-c, a^2+b^2+c^2}, 47659)
{-a-b-c, a b+a c+b c}, 47671)
{-((a^2+b^2+c^2)/(a+b+c)), a^2+b^2+c^2}, 47693)
{-((a^2+b^2+c^2)/(a+b+c)), a b+a c+b c}, 47703)
{-((a^2+b^2+c^2)/(a+b+c)), (a b c)/(a+b+c)}, 47715)
{-a-b-c, 2 (a b+a c+b c)}, 47674)
{-((a^2+b^2+c^2)/(a+b+c)), (2 a b c)/(a+b+c)}, 47719)
{1/2 (-a-b-c), -2 (a b+a c+b c)}, 48046)
{-((a b+a c+b c)/(2 (a+b+c))), -2 (a b+a c+b c)}, 47993)
{1/2 (-a-b-c), -a b-a c-b c}, 3700)
{-((a^2+b^2+c^2)/(2 (a+b+c))), -a b-a c-b c}, 48047)
{-((a b+a c+b c)/(2 (a+b+c))), -a b-a c-b c}, 4806)
{1/2 (-a-b-c), 1/2 (-a^2-b^2-c^2)}, 48125)
{1/2 (-a-b-c), 1/2 (-a b-a c-b c)}, 4500)
{-((a^2+b^2+c^2)/(2 (a+b+c))), 1/2 (-a^2-b^2-c^2)}, 48089)
{-((a^2+b^2+c^2)/(2 (a+b+c))), 1/2 (-a b-a c-b c)}, 4522)
{-((a b+a c+b c)/(2 (a+b+c))), 1/2 (-a b-a c-b c)}, 48090)
{1/2 (-a-b-c), 0}, 48274)
{-((a b+a c+b c)/(2 (a+b+c))), 1/2 (a b+a c+b c)}, 48127)
{0, -2 (a^2+b^2+c^2)}, 47651)
{0, -2 (a b+a c+b c)}, 47666)
{0, -((2 a b c)/(a+b+c))}, 4391)
{0, -a^2-b^2-c^2}, 47652)
{0, -a b-a c-b c}, 661)
{0, -((a b c)/(a+b+c))}, 1577)
{0, 1/2 (-a b-a c-b c)}, 3835)
{0, -((a b c)/(2 (a+b+c)))}, 4823)
{0, 0}, 693)
{0, 1/2 (a^2+b^2+c^2)}, 6590)
{0, a^2+b^2+c^2}, 47660)
{0, a b+a c+b c}, 47672)
{0, (a b c)/(a+b+c)}, 4978)
{0, 2 (a^2+b^2+c^2)}, 47662)
{0, 2 (a b+a c+b c)}, 47675)
{0, (2 a b c)/(a+b+c)}, 4801)
{1/2 (a+b+c), -a b-a c-b c}, 4841)
{(a^2+b^2+c^2)/(2 (a+b+c)), -a b-a c-b c}, 47998)
{(a b+a c+b c)/(2 (a+b+c)), -a b-a c-b c}, 48002)
{(a b+a c+b c)/(2 (a+b+c)), -((a b c)/(a+b+c))}, 21051)
{1/2 (a+b+c), 1/2 (-a^2-b^2-c^2)}, 47960)
{(a b+a c+b c)/(2 (a+b+c)), 1/2 (-a b-a c-b c)}, 48030)
{(a b+a c+b c)/(2 (a+b+c)), -((a b c)/(2 (a+b+c)))}, 21260)
{1/2 (a+b+c), 0}, 3004)
{(a^2+b^2+c^2)/(2 (a+b+c)), 0}, 23770)
{(a b+a c+b c)/(2 (a+b+c)), 0}, 3837)
{1/2 (a+b+c), 1/2 (a^2+b^2+c^2)}, 650)
{1/2 (a+b+c), 1/2 (a b+a c+b c)}, 3776)
{(a^2+b^2+c^2)/(2 (a+b+c)), 1/2 (a^2+b^2+c^2)}, 7662)
{(a b+a c+b c)/(2 (a+b+c)), 1/2 (a b+a c+b c)}, 48098)
{(a b+a c+b c)/(2 (a+b+c)), (a b c)/(2 (a+b+c))}, 23815)
{1/2 (a+b+c), a^2+b^2+c^2}, 47890)
{1/2 (a+b+c), a b+a c+b c}, 21104)
{a+b+c, -2 (a b+a c+b c)}, 47667)
{(a^2+b^2+c^2)/(a+b+c), -2 (a b+a c+b c)}, 47699)
{(a^2+b^2+c^2)/(a+b+c), -((2 a b c)/(a+b+c))}, 47708)
{(a b+a c+b c)/(a+b+c), -2 (a^2+b^2+c^2)}, 47925)
{(a b+a c+b c)/(a+b+c), -2 (a b+a c+b c)}, 47928)
{(a b+a c+b c)/(a+b+c), -((2 a b c)/(a+b+c))}, 4490)
{a+b+c, -a^2-b^2-c^2}, 47653)
{a+b+c, -a b-a c-b c}, 4988)
{a+b+c, -((a b c)/(a+b+c))}, 47679)
{(a^2+b^2+c^2)/(a+b+c), -a^2-b^2-c^2}, 47688)
{(a^2+b^2+c^2)/(a+b+c), -a b-a c-b c}, 47701)
{(a^2+b^2+c^2)/(a+b+c), -((a b c)/(a+b+c))}, 47712)
{(a b+a c+b c)/(a+b+c), -a^2-b^2-c^2}, 47968)
{(a b+a c+b c)/(a+b+c), -a b-a c-b c}, 4824)
{(a b+a c+b c)/(a+b+c), -((a b c)/(a+b+c))}, 4705)
{(a b+a c+b c)/(a+b+c), 1/2 (-a^2-b^2-c^2)}, 48007)
{(a b+a c+b c)/(a+b+c), 1/2 (-a b-a c-b c)}, 48010)
{(a b+a c+b c)/(a+b+c), -((a b c)/(2 (a+b+c)))}, 48012)
{a+b+c, 0}, 45746)
{(a^2+b^2+c^2)/(a+b+c), 0}, 47691)
{(a b+a c+b c)/(a+b+c), 0}, 1491)
{a+b+c, 1/2 (a^2+b^2+c^2)}, 45745)
{(a^2+b^2+c^2)/(a+b+c), 1/2 (a^2+b^2+c^2)}, 47123)
{(a b+a c+b c)/(a+b+c), 1/2 (a^2+b^2+c^2)}, 48062)
{(a b+a c+b c)/(a+b+c), 1/2 (a b+a c+b c)}, 24720)
{(a b+a c+b c)/(a+b+c), (a b c)/(2 (a+b+c))}, 48066)
{a+b+c, a^2+b^2+c^2}, 17494)
{a+b+c, a b+a c+b c}, 16892)
{(a^2+b^2+c^2)/(a+b+c), a^2+b^2+c^2}, 47694)
{(a^2+b^2+c^2)/(a+b+c), a b+a c+b c}, 47704)
{(a^2+b^2+c^2)/(a+b+c), (a b c)/(a+b+c)}, 47716)
{(a b+a c+b c)/(a+b+c), a^2+b^2+c^2}, 48103)
{(a b+a c+b c)/(a+b+c), a b+a c+b c}, 21146)
{(a b+a c+b c)/(a+b+c), (a b c)/(a+b+c)}, 2530)
{a+b+c, 2 (a^2+b^2+c^2)}, 47663)
{a+b+c, 2 (a b+a c+b c)}, 47676)
{(a^2+b^2+c^2)/(a+b+c), 2 (a^2+b^2+c^2)}, 47696)
{(a^2+b^2+c^2)/(a+b+c), (2 a b c)/(a+b+c)}, 47720)
{(a b+a c+b c)/(a+b+c), 2 (a^2+b^2+c^2)}, 48140)
{(a b+a c+b c)/(a+b+c), 2 (a b+a c+b c)}, 48143)
{(a b+a c+b c)/(a+b+c), (2 a b c)/(a+b+c)}, 3777)
{2 (a+b+c), -2 (a b+a c+b c)}, 47668)
{(2 (a^2+b^2+c^2))/(a+b+c), -((2 a b c)/(a+b+c))}, 47709)
{2 (a+b+c), -a^2-b^2-c^2}, 47654)
{2 (a+b+c), -a b-a c-b c}, 47669)
{(2 (a^2+b^2+c^2))/(a+b+c), -a b-a c-b c}, 47702)
{(2 (a^2+b^2+c^2))/(a+b+c), -((a b c)/(a+b+c))}, 47713)
{(2 (a b+a c+b c))/(a+b+c), -a b-a c-b c}, 47934)
{2 (a+b+c), 0}, 47657)
{(2 (a^2+b^2+c^2))/(a+b+c), 0}, 47692)
{(2 (a b+a c+b c))/(a+b+c), 0}, 47975)
{(2 (a b+a c+b c))/(a+b+c), 1/2 (a b+a c+b c)}, 48017)
{2 (a+b+c), a^2+b^2+c^2}, 47661)
{2 (a+b+c), a b+a c+b c}, 47673)
{(2 (a^2+b^2+c^2))/(a+b+c), a^2+b^2+c^2}, 47695)
{(2 (a^2+b^2+c^2))/(a+b+c), a b+a c+b c}, 47705)
{(2 (a^2+b^2+c^2))/(a+b+c), (a b c)/(a+b+c)}, 47717)
{(2 (a b+a c+b c))/(a+b+c), a b+a c+b c}, 2254)
{2 (a+b+c), 2 (a^2+b^2+c^2)}, 47664)
{2 (a+b+c), 2 (a b+a c+b c)}, 47677)
{(2 (a^2+b^2+c^2))/(a+b+c), 2 (a^2+b^2+c^2)}, 47697)
{(2 (a b+a c+b c))/(a+b+c), 2 (a b+a c+b c)}, 48108)
{-((a*b + a*c + b*c)/(a + b + c)), (-2*a*b*c)/(a + b + c)}, 48392
{-((a*b + a*c + b*c)/(a + b + c)), -((a*b*c)/(a + b + c))}, 48393
{-((a*b + a*c + b*c)/(a + b + c)), (-(a*b) - a*c - b*c)/2}, 48394
{-1/2*(a^2 + b^2 + c^2)/(a + b + c), -((a*b*c)/(a + b + c))}, 48395
{-1/2*(a^2 + b^2 + c^2)/(a + b + c), 0}, 48396
{(-a - b - c)/2, (a^2 + b^2 + c^2)/2}, 48397
{0, (-a^2 - b^2 - c^2)/2}, 48398
{0, (a*b + a*c + b*c)/2}, 48399
{(a^2 + b^2 + c^2)/(2*(a + b + c)), (-2*a*b*c)/(a + b + c)}, 48400
{(a*b + a*c + b*c)/(2*(a + b + c)), (-2*a*b*c)/(a + b + c)}, 48401
{(a + b + c)/2, -((a*b*c)/(a + b + c))}, 48402
{(a^2 + b^2 + c^2)/(2*(a + b + c)), -((a*b*c)/(a + b + c))}, 48403
{(a + b + c)/2, (-(a*b) - a*c - b*c)/2}, 48404
{(a*b + a*c + b*c)/(2*(a + b + c)), (a^2 + b^2 + c^2)/2}, 48405
{(a*b + a*c + b*c)/(2*(a + b + c)), (a*b*c)/(a + b + c)}, 48406
{(2*(a*b + a*c + b*c))/(a + b + c), -((a*b*c)/(a + b + c))}, 48407
{(2*(a*b + a*c + b*c))/(a + b + c), a^2 + b^2 + c^2}, 48408
{(2*(a*b + a*c + b*c))/(a + b + c), (a*b*c)/(a + b + c)}, 48409
{(2*(a*b + a*c + b*c))/(a + b + c), (2*a*b*c)/(a + b + c)}, 48410


X(48392) = X(513)X(48264)∩X(514)X(4010)

Barycentrics    (b - c)*(a*b^2 + a*b*c + 2*b^2*c + a*c^2 + 2*b*c^2) : :
X(48392) = 2 X[650] - 3 X[47872], 2 X[667] - 3 X[48234], 3 X[1491] - 4 X[21260], 5 X[1491] - 6 X[47816], 3 X[1577] - 2 X[21260], 5 X[1577] - 3 X[47816], 10 X[21260] - 9 X[47816], X[31291] - 3 X[47694], 2 X[905] - 3 X[47833], 2 X[2530] - 3 X[48184], 4 X[4823] - 3 X[48184], 2 X[3669] - 3 X[47889], 2 X[3803] - 3 X[48251], 3 X[4728] - 2 X[48100], 3 X[4800] - 2 X[48099], 4 X[4885] - 3 X[47893], 2 X[4913] - 3 X[47835], 3 X[4951] - 2 X[48272], 3 X[14431] - 2 X[48012], 2 X[14838] - 3 X[47875], X[17496] - 3 X[47834], 5 X[31251] - 6 X[45324], 4 X[31288] - 3 X[45671]

X(48392) lies on these lines: {513, 48264}, {514, 4010}, {522, 2533}, {523, 4391}, {650, 47872}, {659, 23882}, {667, 48234}, {693, 3777}, {784, 1491}, {814, 31291}, {824, 3801}, {905, 47833}, {1769, 4041}, {2530, 4823}, {3669, 47889}, {3803, 48251}, {3810, 4500}, {3900, 4774}, {3907, 48301}, {4024, 21118}, {4083, 4804}, {4122, 23877}, {4147, 28161}, {4367, 7662}, {4560, 4874}, {4705, 4791}, {4728, 48100}, {4800, 48099}, {4802, 47918}, {4885, 47893}, {4913, 47835}, {4948, 45664}, {4951, 48272}, {4963, 47955}, {4978, 23765}, {6004, 47724}, {6372, 48143}, {7192, 29170}, {14430, 28165}, {14431, 48012}, {14838, 47875}, {17166, 29324}, {17496, 47834}, {21051, 47975}, {23755, 29200}, {28151, 47922}, {28195, 47906}, {29025, 47660}, {29066, 48305}, {29074, 47695}, {29098, 48140}, {29174, 47693}, {29182, 48324}, {29198, 47672}, {29236, 48322}, {29274, 48150}, {29298, 48339}, {31251, 45324}, {31288, 45671}, {47917, 47957}, {47928, 47959}, {47934, 47967}, {48090, 48131}, {48098, 48151}

X(48392) = midpoint of X(4024) and X(21118)
X(48392) = reflection of X(i) in X(j) for these {i,j}: {1491, 1577}, {2530, 4823}, {3777, 693}, {4367, 7662}, {4490, 4391}, {4560, 4874}, {4705, 4791}, {4948, 45664}, {4963, 47955}, {23765, 4978}, {47910, 47949}, {47913, 48265}, {47917, 47957}, {47928, 47959}, {47934, 47967}, {47975, 21051}, {48024, 48267}, {48123, 4010}, {48131, 48090}, {48151, 48098}
X(48392) = crossdifference of every pair of points on line {5019, 16778}
X(48392) = {X(2530),X(4823)}-harmonic conjugate of X(48184)


X(48393) = X(513)X(4960)∩X(514)X(4010)

Barycentrics    (b - c)*(b + c)*(a*b + a*c + 2*b*c) : :
X(48393) = 4 X[1577] - 3 X[14431], 3 X[1577] - 2 X[21051], 2 X[4705] - 3 X[14431], 3 X[4705] - 4 X[21051], 9 X[14431] - 8 X[21051], 2 X[650] - 3 X[47875], 3 X[693] - 2 X[23815], 5 X[693] - 3 X[47819], 3 X[2530] - 4 X[23815], 5 X[2530] - 6 X[47819], 10 X[23815] - 9 X[47819], 3 X[2533] - 2 X[4807], 3 X[4730] - 4 X[4807], 2 X[3960] - 3 X[47889], 2 X[4401] - 3 X[48234], 2 X[4560] - 3 X[14419], X[4560] - 3 X[47834], 3 X[4728] - 2 X[48059], 2 X[4770] - 3 X[21052], 3 X[4800] - 2 X[48058], 4 X[4885] - 3 X[47888], 2 X[4913] - 3 X[47837], 2 X[6050] - 3 X[48220], 2 X[14838] - 3 X[47833], 3 X[30592] - 2 X[48131], X[47664] - 3 X[47815], 3 X[47872] - 2 X[48003], 2 X[48066] - 3 X[48184]

X(48393) lies on these lines: {512, 4804}, {513, 4960}, {514, 4010}, {522, 30595}, {523, 1577}, {650, 47875}, {661, 21836}, {667, 7662}, {690, 23755}, {693, 784}, {764, 4978}, {826, 4024}, {1491, 4823}, {1734, 4777}, {2533, 4151}, {2787, 17166}, {3801, 23879}, {3907, 48291}, {3960, 47889}, {4129, 4824}, {4145, 22320}, {4378, 23880}, {4401, 48234}, {4455, 4762}, {4490, 4791}, {4500, 23877}, {4560, 14419}, {4567, 36239}, {4728, 48059}, {4770, 21052}, {4800, 48058}, {4802, 47959}, {4885, 47888}, {4905, 48098}, {4913, 47837}, {4948, 45324}, {6050, 48220}, {6161, 29051}, {6367, 21124}, {6372, 47672}, {6538, 31010}, {7192, 29150}, {8714, 21146}, {14349, 48090}, {14838, 47833}, {17072, 28161}, {21118, 29312}, {21260, 47975}, {23813, 48092}, {24287, 29118}, {28151, 47967}, {28195, 47942}, {28199, 47957}, {29066, 48301}, {29070, 47694}, {29086, 47695}, {29098, 47660}, {29128, 47792}, {29142, 48274}, {29168, 47703}, {29182, 48322}, {29198, 48127}, {29274, 48324}, {29354, 47704}, {29366, 48339}, {30592, 48131}, {47656, 47708}, {47664, 47815}, {47872, 48003}, {47917, 47994}, {47928, 47997}, {47934, 48005}, {48066, 48184}

X(48393) = midpoint of X(i) and X(j) for these {i,j}: {47656, 47708}, {47672, 48264}, {47678, 47712}
X(48393) = reflection of X(i) in X(j) for these {i,j}: {667, 7662}, {764, 4978}, {1491, 4823}, {2530, 693}, {4490, 4791}, {4705, 1577}, {4730, 2533}, {4824, 4129}, {4905, 48098}, {4948, 45324}, {4983, 4010}, {6161, 48305}, {14349, 48090}, {14419, 47834}, {47910, 47987}, {47917, 47994}, {47928, 47997}, {47934, 48005}, {47949, 48267}, {47975, 21260}, {48092, 23813}
X(48393) = X(i)-Ceva conjugate of X(j) for these (i,j): {76, 3125}, {594, 3120}, {40216, 16732}
X(48393) = X(i)-isoconjugate of X(j) for these (i,j): {58, 8708}, {101, 40408}, {110, 40433}, {163, 32009}, {692, 40439}
X(48393) = X(i)-Dao conjugate of X(j) for these (i, j): (10, 8708), (115, 32009), (244, 40433), (1015, 40408), (1086, 40439), (2486, 1621), (3121, 6), (3739, 100), (16589, 99), (17205, 1509)
X(48393) = crosspoint of X(523) and X(693)
X(48393) = crosssum of X(110) and X(692)
X(48393) = X(48393) = crossdifference of every pair of points on line {1333, 2205}
X(48393) = barycentric product X(i)*X(j) for these {i,j}: {10, 47672}, {226, 48264}, {321, 6372}, {514, 21020}, {523, 3739}, {661, 20888}, {693, 16589}, {826, 18089}, {850, 20963}, {1577, 3720}, {2667, 3261}, {3691, 4077}, {3700, 4059}, {3706, 7178}, {4024, 17175}, {4036, 18166}, {4111, 24002}, {4391, 39793}, {4436, 16732}, {4705, 16748}, {7199, 21699}, {14208, 40975}, {14618, 22060}, {21753, 40495}
X(48393) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 8708}, {513, 40408}, {514, 40439}, {523, 32009}, {661, 40433}, {2667, 101}, {3691, 643}, {3706, 645}, {3720, 662}, {3739, 99}, {4059, 4573}, {4111, 644}, {4436, 4567}, {6372, 81}, {16589, 100}, {16748, 4623}, {17175, 4610}, {18089, 4577}, {20888, 799}, {20963, 110}, {21020, 190}, {21699, 1018}, {21753, 692}, {21820, 4557}, {22060, 4558}, {22369, 906}, {39793, 651}, {40975, 162}, {47672, 86}, {48264, 333}
X(48393) = {X(1577),X(4705)}-harmonic conjugate of X(14431)


X(48394) = X(514)X(4010)∩X(522)X(693)

Barycentrics    (b - c)*(-(a^2*b) + a*b^2 - a^2*c + 3*a*b*c + 3*b^2*c + a*c^2 + 3*b*c^2) : :
X(48394) = 7 X[4010] - X[47910], 5 X[4010] - X[47946], 4 X[4010] - X[47986], 3 X[4010] - X[48024], 5 X[47910] - 7 X[47946], 4 X[47910] - 7 X[47986], 3 X[47910] - 7 X[48024], 2 X[47910] - 7 X[48043], X[47910] + 7 X[48120], 4 X[47946] - 5 X[47986], 3 X[47946] - 5 X[48024], 2 X[47946] - 5 X[48043], X[47946] + 5 X[48120], 3 X[47986] - 4 X[48024], X[47986] + 4 X[48120], 2 X[48024] - 3 X[48043], X[48024] + 3 X[48120], X[48043] + 2 X[48120], 3 X[693] - X[2254], 5 X[693] - 3 X[47812], X[2254] + 3 X[4804], 2 X[2254] - 3 X[24720], 5 X[2254] - 9 X[47812], X[4467] - 3 X[47887], 2 X[4804] + X[24720], 5 X[4804] + 3 X[47812], 5 X[24720] - 6 X[47812], 3 X[3835] - 2 X[48030], 3 X[48010] - 4 X[48030], X[48010] - 4 X[48090], X[48030] - 3 X[48090], X[649] - 3 X[47834], 2 X[650] - 3 X[47831], X[659] - 3 X[48189], 2 X[2977] - 3 X[47879], 4 X[3716] - 3 X[45673], X[4088] - 3 X[47790], 3 X[4120] - X[47698], X[4380] - 3 X[47813], X[4724] - 3 X[48172], X[26824] + 3 X[48172], 3 X[4728] - X[47975], 3 X[4776] - X[47934], X[4784] - 3 X[48238], 3 X[4789] - X[48106], 4 X[4885] - 3 X[47830], 2 X[4913] - 3 X[47830], 3 X[4931] + X[47705], X[48037] + 2 X[48127], 2 X[9508] - 3 X[47779], X[17494] - 3 X[47832], 3 X[21297] - X[48023], 2 X[25380] - 3 X[45320], 5 X[26985] - 3 X[47828], 5 X[30795] - 3 X[48225], 5 X[30835] - 3 X[47825], 3 X[31147] - X[47945], 2 X[31286] - 3 X[47833], 3 X[45316] - 2 X[48284], 3 X[45667] - 4 X[48295], 3 X[45667] - 2 X[48325], X[47664] - 3 X[47811], X[47673] - 3 X[48174], X[47693] - 3 X[47873], 3 X[47759] - X[47909], 3 X[47797] - X[48277], 3 X[47804] - X[47932], 3 X[47821] - X[47926], 3 X[47869] - X[48119], 3 X[47870] - X[48118], 3 X[47871] - X[47973]

X(48394) lies on these lines: {514, 4010}, {522, 693}, {523, 3835}, {649, 47834}, {650, 47831}, {659, 48189}, {661, 28147}, {812, 7662}, {824, 23770}, {900, 48073}, {1491, 28161}, {1577, 4147}, {2977, 47879}, {3667, 21146}, {3716, 4762}, {3810, 48280}, {3837, 4777}, {4024, 47691}, {4088, 47790}, {4120, 47698}, {4151, 4823}, {4380, 47813}, {4382, 47694}, {4474, 48304}, {4724, 26824}, {4728, 28169}, {4776, 47934}, {4778, 47672}, {4784, 48238}, {4785, 4810}, {4789, 48106}, {4801, 48264}, {4802, 4806}, {4824, 28155}, {4874, 48008}, {4885, 4913}, {4895, 47721}, {4931, 47705}, {4932, 29328}, {4940, 47992}, {4948, 45339}, {4977, 48037}, {6006, 48108}, {9508, 47779}, {14315, 23817}, {17494, 47832}, {20295, 48142}, {21297, 48023}, {23655, 48293}, {23813, 48050}, {25259, 47704}, {25380, 45320}, {26049, 48186}, {26985, 47828}, {27193, 48228}, {28151, 48002}, {28175, 48028}, {28179, 47964}, {28191, 47666}, {28195, 47980}, {28199, 47993}, {28209, 48135}, {28225, 48143}, {28229, 47675}, {28470, 48301}, {28840, 48134}, {29362, 48063}, {30519, 48326}, {30795, 48225}, {30835, 47825}, {31147, 47945}, {31286, 47833}, {45316, 48284}, {45667, 48295}, {47650, 48102}, {47656, 47701}, {47659, 47924}, {47664, 47811}, {47671, 47699}, {47673, 48174}, {47693, 47873}, {47724, 48339}, {47759, 47909}, {47797, 48277}, {47804, 47932}, {47821, 47926}, {47869, 48119}, {47870, 48118}, {47871, 47973}

X(48394) = midpoint of X(i) and X(j) for these {i,j}: {693, 4804}, {4010, 48120}, {4024, 47691}, {4382, 47694}, {4474, 48304}, {4724, 26824}, {4801, 48264}, {4895, 47721}, {20295, 48142}, {25259, 47704}, {47123, 48268}, {47650, 48102}, {47656, 47701}, {47659, 47924}, {47671, 47699}, {47672, 48080}, {47675, 48021}, {47724, 48339}
X(48394) = reflection of X(i) in X(j) for these {i,j}: {3835, 48090}, {4147, 1577}, {4913, 4885}, {4948, 45339}, {17072, 4823}, {24720, 693}, {47986, 48043}, {47992, 4940}, {47996, 4806}, {48008, 4874}, {48010, 3835}, {48017, 3837}, {48043, 4010}, {48050, 23813}, {48073, 48098}, {48325, 48295}
X(48394) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4885, 4913, 47830}, {26824, 48172, 4724}, {48295, 48325, 45667}


X(48395) = X(512)X(3700)∩X(514)X(4522)

Barycentrics    (b - c)*(b + c)*(a^2 + b^2 + 2*b*c + c^2) : :
X(48395) = 3 X[1577] + X[47710], 3 X[1577] - X[47712], 5 X[1577] - X[47713], X[47710] - 3 X[47711], 5 X[47710] + 3 X[47713], 3 X[47711] + X[47712], 5 X[47711] + X[47713], 5 X[47712] - 3 X[47713], X[663] - 3 X[47874], 2 X[676] - 3 X[47875], 3 X[693] - X[47720], 3 X[47707] + X[47720], 3 X[4120] - X[4822], 3 X[4391] + X[47718], 3 X[47690] - X[47718], 2 X[4401] - 3 X[48231], X[4467] - 3 X[47836], X[4560] - 3 X[47809], X[4729] + 3 X[4931], 2 X[4770] - 3 X[44729], 3 X[4789] - X[17166], 2 X[6050] - 3 X[47766], 2 X[14838] - 3 X[47807], 2 X[17069] - 3 X[47837], 3 X[21052] - X[21124], X[21302] + 3 X[47870], 2 X[34958] - 3 X[47833], X[45746] - 3 X[47814], 2 X[48058] - 3 X[48166], 2 X[48066] - 3 X[48182]

X(48395) lies on these lines: {10, 23879}, {512, 3700}, {514, 4522}, {523, 1577}, {525, 2533}, {649, 29232}, {663, 47874}, {667, 29278}, {676, 47875}, {693, 29288}, {824, 17072}, {826, 7178}, {891, 48280}, {900, 4834}, {2501, 4024}, {3004, 21260}, {3239, 48099}, {3566, 4761}, {3762, 47715}, {3800, 4010}, {3907, 8045}, {4040, 47723}, {4120, 4822}, {4129, 47998}, {4369, 29037}, {4391, 29142}, {4401, 48231}, {4462, 47719}, {4467, 47836}, {4524, 14308}, {4560, 47809}, {4729, 4931}, {4730, 4843}, {4770, 6367}, {4774, 28473}, {4775, 4990}, {4777, 21185}, {4782, 29276}, {4789, 17166}, {4791, 29021}, {4823, 23770}, {4841, 48005}, {4874, 29074}, {4897, 29090}, {4983, 14321}, {6050, 47766}, {6590, 8678}, {8639, 17989}, {10015, 29017}, {14838, 47807}, {17069, 47837}, {20517, 29196}, {21052, 21124}, {21104, 29354}, {21120, 29312}, {21301, 47660}, {21302, 47870}, {23882, 48062}, {29058, 47767}, {29066, 48299}, {29070, 47890}, {29110, 47788}, {29186, 48055}, {29208, 48090}, {29240, 48300}, {34958, 47833}, {45746, 47814}, {47689, 47708}, {47691, 47706}, {47703, 47918}, {47912, 48275}, {48058, 48166}, {48066, 48182}

X(48395) = midpoint of X(i) and X(j) for these {i,j}: {693, 47707}, {1577, 47711}, {2533, 4122}, {3762, 47715}, {4024, 4041}, {4040, 47723}, {4391, 47690}, {4462, 47719}, {4761, 7265}, {21301, 47660}, {47689, 47708}, {47691, 47706}, {47703, 47918}, {47710, 47712}, {47912, 48275}
X(48395) = reflection of X(i) in X(j) for these {i,j}: {3004, 21260}, {4775, 4990}, {4841, 48005}, {4983, 14321}, {23770, 4823}, {47998, 4129}, {48099, 3239}, {48290, 8045}
X(48395) = X(i)-isoconjugate of X(j) for these (i,j): {58, 1310}, {99, 1472}, {662, 2221}, {1036, 1414}, {1333, 37215}, {1444, 32691}, {1790, 36099}, {2281, 4610}, {2339, 4565}
X(48395) = X(i)-Dao conjugate of X(j) for these (i, j): (10, 1310), (37, 37215), (1084, 2221), (5515, 86), (6741, 30479), (17421, 1444), (38986, 1472), (40181, 662), (40608, 1036)
X(48395) = crosspoint of X(i) and X(j) for these (i,j): {1018, 7162}, {2517, 6590}
X(48395) = crosssum of X(1019) and X(3338)
X(48395) = crossdifference of every pair of points on line {1333, 1790}
X(48395) = barycentric product X(i)*X(j) for these {i,j}: {10, 6590}, {37, 2517}, {313, 2484}, {321, 8678}, {388, 3700}, {523, 2345}, {525, 7102}, {594, 47844}, {612, 1577}, {661, 4385}, {1010, 4024}, {1826, 23874}, {2285, 4086}, {2303, 4036}, {2522, 41013}, {3610, 7649}, {3974, 7178}, {4079, 44154}, {4397, 8898}, {5227, 24006}, {7085, 14618}, {8646, 27801}, {14594, 21044}
X(48395) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 37215}, {37, 1310}, {388, 4573}, {512, 2221}, {612, 662}, {798, 1472}, {1010, 4610}, {1460, 4565}, {1824, 36099}, {2285, 1414}, {2333, 32691}, {2345, 99}, {2484, 58}, {2517, 274}, {2522, 1444}, {3610, 4561}, {3700, 30479}, {3709, 1036}, {3974, 645}, {4041, 2339}, {4079, 1245}, {4320, 4637}, {4385, 799}, {5227, 4592}, {6590, 86}, {7085, 4558}, {7102, 648}, {7365, 4616}, {8646, 1333}, {8678, 81}, {8898, 934}, {10376, 4617}, {14594, 4620}, {23874, 17206}, {26933, 15419}, {44119, 4556}, {47844, 1509}
X(48395) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1577, 47710, 47712}, {47711, 47712, 47710}


X(48396) = X(513)X(3700)∩X(514)X(4522)

Barycentrics    (b - c)*(a^2*b + b^3 + a^2*c + 2*a*b*c + 3*b^2*c + 3*b*c^2 + c^3) : :
X(48396) = 3 X[693] + X[47689], 3 X[693] - X[47691], 5 X[693] - X[47692], 2 X[1491] - 3 X[48182], 2 X[3004] - 3 X[48178], 4 X[3837] - 3 X[48178], 3 X[23770] + 2 X[47689], X[23770] + 2 X[47690], 3 X[23770] - 2 X[47691], 5 X[23770] - 2 X[47692], 3 X[44429] - X[45746], X[47655] + 3 X[48175], X[47656] + 3 X[47808], X[47689] - 3 X[47690], 5 X[47689] + 3 X[47692], 3 X[47690] + X[47691], 5 X[47690] + X[47692], 5 X[47691] - 3 X[47692], 3 X[47808] - X[47975], 2 X[650] - 3 X[47807], 2 X[659] - 3 X[48231], 2 X[676] - 3 X[47833], 3 X[4789] + X[47687], 3 X[4789] - X[47694], 4 X[2490] - 3 X[48226], 2 X[2977] - 3 X[47809], X[17494] - 3 X[47809], 4 X[3239] - 3 X[48166], 2 X[48029] - 3 X[48166], 2 X[4025] - 3 X[48245], 3 X[4120] - X[48021], X[4467] - 3 X[47824], X[4724] - 3 X[47874], 3 X[4728] - X[47701], 3 X[4776] - X[47699], 2 X[4782] - 3 X[47767], 4 X[4874] - 3 X[26275], 2 X[4874] - 3 X[47788], 4 X[4885] - 3 X[47799], 3 X[4951] + X[48143], X[4976] - 3 X[48232], 2 X[9508] - 3 X[48232], X[4988] - 3 X[47810], X[5592] - 3 X[8045], 2 X[5592] - 3 X[48299], 2 X[11068] - 3 X[48219], X[16892] - 3 X[47812], 2 X[17069] - 3 X[47823], X[26824] + 3 X[48208], 5 X[26985] - 3 X[47797], X[47652] - 3 X[48170], X[47693] + 3 X[48170], X[47688] - 3 X[47871], 2 X[47132] - 3 X[47834], X[47695] - 3 X[47834], 2 X[48007] - 3 X[48163], 3 X[30565] - X[47969], 3 X[31147] - X[47938], X[45745] - 3 X[47806], X[47653] - 3 X[48159], X[47659] + 3 X[48164], X[47661] - 3 X[47825], X[47663] - 3 X[48236], X[47679] - 3 X[47816], 3 X[47769] - X[47941], 3 X[47786] - X[47979], 3 X[47787] - X[48006], 3 X[47790] - X[48080], 3 X[47828] - X[48277], 3 X[47832] - X[47972], X[47968] - 3 X[48167]

X(48396) lies on these lines: {1, 47723}, {325, 523}, {513, 3700}, {514, 4522}, {522, 3798}, {650, 47807}, {659, 48231}, {661, 47703}, {676, 47833}, {824, 24720}, {900, 4784}, {918, 4122}, {1019, 29232}, {1577, 29142}, {1638, 4777}, {2254, 4024}, {2490, 48226}, {2533, 3910}, {2977, 17494}, {3239, 48029}, {3800, 48273}, {3835, 47998}, {4025, 48245}, {4083, 48280}, {4088, 47672}, {4120, 48021}, {4367, 29278}, {4382, 48106}, {4391, 47719}, {4467, 47824}, {4724, 47874}, {4728, 47701}, {4762, 48062}, {4774, 6366}, {4776, 47699}, {4778, 48270}, {4782, 47767}, {4801, 47707}, {4802, 47999}, {4820, 7659}, {4823, 29021}, {4841, 48030}, {4874, 26275}, {4885, 47799}, {4897, 29078}, {4940, 47983}, {4951, 48143}, {4976, 9508}, {4977, 18004}, {4978, 29288}, {4988, 47810}, {4990, 48336}, {5592, 8045}, {6084, 48103}, {7178, 29017}, {10015, 29312}, {11068, 48219}, {14321, 48024}, {16892, 47812}, {17069, 47823}, {21104, 48098}, {21196, 25380}, {21212, 28161}, {25259, 48108}, {26824, 48208}, {26985, 47797}, {28175, 47652}, {28179, 47688}, {28183, 47132}, {28209, 47685}, {28213, 47662}, {28217, 47697}, {28221, 48237}, {28894, 48007}, {29066, 48290}, {29144, 48090}, {29192, 48295}, {29240, 47682}, {29362, 47890}, {29370, 47891}, {30565, 47969}, {30792, 47782}, {31095, 48169}, {31131, 47792}, {31147, 47938}, {45745, 47806}, {47653, 48159}, {47659, 48164}, {47661, 47825}, {47663, 48236}, {47671, 47934}, {47675, 47698}, {47679, 47816}, {47680, 47726}, {47684, 47722}, {47700, 47704}, {47706, 47720}, {47708, 47718}, {47710, 47716}, {47712, 47714}, {47721, 47728}, {47769, 47941}, {47786, 47979}, {47787, 48006}, {47790, 48080}, {47828, 48277}, {47832, 47972}, {47881, 48247}, {47968, 48167}, {48023, 48275}, {48069, 48268}, {48077, 48142}, {48082, 48148}, {48094, 48119}, {48102, 48115}

X(48396) = midpoint of X(i) and X(j) for these {i,j}: {1, 47723}, {661, 47703}, {693, 47690}, {1577, 47715}, {2254, 4024}, {4088, 47672}, {4122, 21146}, {4382, 48106}, {4391, 47719}, {4801, 47707}, {4820, 7659}, {4978, 47711}, {25259, 48108}, {31131, 47792}, {46403, 47660}, {47652, 47693}, {47656, 47975}, {47662, 47686}, {47671, 47934}, {47675, 47698}, {47680, 47726}, {47682, 47724}, {47684, 47722}, {47685, 47696}, {47687, 47694}, {47689, 47691}, {47700, 47704}, {47706, 47720}, {47708, 47718}, {47710, 47716}, {47712, 47714}, {47721, 47728}, {48023, 48275}, {48069, 48268}, {48077, 48142}, {48082, 48148}, {48088, 48126}, {48094, 48119}, {48102, 48115}
X(48396) = reflection of X(i) in X(j) for these {i,j}: {3004, 3837}, {4841, 48030}, {4976, 9508}, {17494, 2977}, {21104, 48098}, {21196, 25380}, {23770, 693}, {26275, 47788}, {47695, 47132}, {47782, 30792}, {47983, 4940}, {47989, 48050}, {47998, 3835}, {48024, 14321}, {48029, 3239}, {48046, 18004}, {48047, 4522}, {48247, 47881}, {48299, 8045}, {48336, 4990}
X(48396) = crossdifference of every pair of points on line {32, 16466}
X(48396) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 47689, 47691}, {3004, 3837, 48178}, {3239, 48029, 48166}, {4789, 47687, 47694}, {4976, 48232, 9508}, {17494, 47809, 2977}, {47656, 47808, 47975}, {47690, 47691, 47689}, {47693, 48170, 47652}, {47695, 47834, 47132}


X(48397) = X(230)X(231)∩X(513)X(4024)

Barycentrics    (b - c)*(a^2 + a*b + 2*b^2 + a*c + 4*b*c + 2*c^2) : :
X(48397) = 7 X[650] - 8 X[2490], 11 X[650] - 12 X[14425], 3 X[650] - 2 X[45745], 5 X[650] - 6 X[47766], 2 X[650] - 3 X[47881], 7 X[650] - 6 X[47883], 4 X[2490] - 7 X[6590], 22 X[2490] - 21 X[14425], 12 X[2490] - 7 X[45745], 20 X[2490] - 21 X[47766], 16 X[2490] - 21 X[47881], 4 X[2490] - 3 X[47883], 11 X[6590] - 6 X[14425], 3 X[6590] - X[45745], 5 X[6590] - 3 X[47766], 4 X[6590] - 3 X[47881], 7 X[6590] - 3 X[47883], 18 X[14425] - 11 X[45745], 10 X[14425] - 11 X[47766], 8 X[14425] - 11 X[47881], 14 X[14425] - 11 X[47883], 5 X[45745] - 9 X[47766], 4 X[45745] - 9 X[47881], 7 X[45745] - 9 X[47883], 4 X[47766] - 5 X[47881], 7 X[47766] - 5 X[47883], 7 X[47881] - 4 X[47883], 3 X[4024] - X[48266], 3 X[4820] - 2 X[48266], X[4820] + 2 X[48275], X[48266] + 3 X[48275], 4 X[4500] - X[47950], 3 X[649] - 4 X[2529], 4 X[2529] + 3 X[4838], 2 X[661] - 3 X[4944], X[661] - 3 X[47873], 3 X[693] - X[47653], X[693] - 3 X[47792], 5 X[693] - 3 X[48156], X[47653] + 3 X[47659], X[47653] - 9 X[47792], 2 X[47653] - 3 X[47960], 5 X[47653] - 9 X[48156], X[47659] + 3 X[47792], 2 X[47659] + X[47960], 5 X[47659] + 3 X[48156], 6 X[47792] - X[47960], 5 X[47792] - X[48156], 5 X[47960] - 6 X[48156], 2 X[3004] - 3 X[45320], 4 X[3239] - 3 X[47777], 2 X[4841] - 3 X[47777], 3 X[4379] - X[47673], X[4467] - 3 X[47791], 4 X[4521] - 3 X[47876], X[4608] + 3 X[47870], X[47666] - 3 X[47870], 3 X[4750] - 4 X[7653], 3 X[47656] + X[47663], 2 X[47656] + X[48095], 3 X[47660] - X[47663], 2 X[47663] - 3 X[48095], 2 X[4765] - 3 X[47767], 3 X[4789] - 2 X[4885], 3 X[4789] - X[45746], 3 X[4789] + X[47658], 2 X[4885] + X[47658], 4 X[4885] - 3 X[47880], 2 X[45746] - 3 X[47880], 2 X[47658] + 3 X[47880], X[4813] - 3 X[4931], 3 X[4893] - X[47669], 2 X[4940] - 3 X[47790], X[4988] - 3 X[47874], 2 X[17069] - 3 X[47789], X[17161] - 3 X[47762], 2 X[21196] - 3 X[47761], 3 X[30565] - X[47667], 5 X[31209] - 3 X[46915], 5 X[31250] - 6 X[47788], 4 X[31287] - 3 X[47782], X[43052] + 2 X[47681], 3 X[44435] - X[47654], X[47651] - 3 X[47869], X[47661] - 3 X[47771], X[47664] - 3 X[47773], X[47668] - 3 X[47775], X[47677] - 3 X[47780], 3 X[47770] - 2 X[48000]

X(48397) lies on these lines: {2, 47657}, {230, 231}, {513, 4024}, {514, 3700}, {522, 4790}, {649, 2529}, {661, 4802}, {693, 20950}, {824, 43067}, {918, 48133}, {1639, 28155}, {3004, 45320}, {3239, 4841}, {4120, 28199}, {4379, 47673}, {4394, 28165}, {4411, 20909}, {4467, 47791}, {4468, 47920}, {4521, 47876}, {4608, 47666}, {4750, 7653}, {4762, 47656}, {4765, 28169}, {4789, 4885}, {4813, 4931}, {4893, 47669}, {4926, 4979}, {4940, 47790}, {4949, 28220}, {4976, 28161}, {4977, 48269}, {4988, 28151}, {5214, 7252}, {6084, 48132}, {7192, 28898}, {7199, 21438}, {14321, 28175}, {17069, 47789}, {17161, 47762}, {17494, 47655}, {18004, 47953}, {18154, 20906}, {21196, 47761}, {23813, 47958}, {23882, 47678}, {26824, 47662}, {28179, 47765}, {28187, 47768}, {29013, 31010}, {30520, 47672}, {30565, 47667}, {31209, 46915}, {31250, 47788}, {31287, 47782}, {43052, 47681}, {44435, 47654}, {47651, 47869}, {47661, 47771}, {47664, 47773}, {47668, 47775}, {47670, 47926}, {47671, 48094}, {47677, 47780}, {47770, 48000}

X(48397) = midpoint of X(i) and X(j) for these {i,j}: {649, 4838}, {693, 47659}, {4024, 48275}, {4608, 47666}, {7192, 47665}, {17494, 47655}, {26824, 47662}, {45746, 47658}, {47656, 47660}, {47670, 47926}, {47671, 48094}
X(48397) = reflection of X(i) in X(j) for these {i,j}: {650, 6590}, {4106, 4500}, {4790, 48276}, {4820, 4024}, {4841, 3239}, {4944, 47873}, {45746, 4885}, {47880, 4789}, {47914, 48046}, {47920, 4468}, {47950, 4106}, {47952, 48270}, {47953, 18004}, {47958, 23813}, {47960, 693}, {47961, 48090}, {48019, 4949}, {48026, 3700}, {48087, 48271}, {48095, 47660}, {48125, 48274}, {48277, 4394}
X(48397) = complement of X(47657)
X(48397) = crossdifference of every pair of points on line {3, 1203}
X(48397) = barycentric product X(i)*X(j) for these {i,j}: {75, 47912}, {522, 5290}, {523, 14005}
X(48397) = barycentric quotient X(i)/X(j) for these {i,j}: {5290, 664}, {14005, 99}, {47912, 1}
X(48397) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 6590, 47881}, {2490, 47883, 650}, {3239, 4841, 47777}, {4608, 47870, 47666}, {4789, 45746, 4885}, {4789, 47658, 45746}, {4885, 45746, 47880}, {47659, 47792, 693}


X(48398) = X(513)X(11934)∩X(514)X(661)

Barycentrics    (b - c)*(a^2 + b^2 - 2*b*c + c^2) : :
X(48398) = X[649] - 3 X[6545], 2 X[649] - 3 X[47758], 2 X[3676] - 3 X[6545], 4 X[3676] - 3 X[47758], 5 X[693] - 3 X[4789], 3 X[693] + X[47651], 3 X[693] - X[47660], 5 X[693] - X[47662], X[693] - 3 X[47871], 2 X[3239] - 3 X[4728], 4 X[3835] - 3 X[47765], 2 X[4468] - 3 X[47765], 3 X[4728] - X[48094], 6 X[4789] - 5 X[6590], 9 X[4789] + 5 X[47651], 3 X[4789] + 5 X[47652], 9 X[4789] - 5 X[47660], 3 X[4789] - X[47662], X[4789] - 5 X[47871], 3 X[6590] + 2 X[47651], X[6590] + 2 X[47652], 3 X[6590] - 2 X[47660], 5 X[6590] - 2 X[47662], X[6590] - 6 X[47871], X[47651] - 3 X[47652], 5 X[47651] + 3 X[47662], X[47651] + 9 X[47871], 3 X[47652] + X[47660], 5 X[47652] + X[47662], X[47652] + 3 X[47871], 5 X[47660] - 3 X[47662], X[47660] - 9 X[47871], X[47662] - 15 X[47871], 3 X[47874] - X[48130], 2 X[650] - 3 X[47757], 2 X[659] - 3 X[47800], 4 X[676] - 3 X[47801], 3 X[1635] - 4 X[7658], 3 X[1638] - 2 X[4394], 4 X[2490] - 5 X[31250], 2 X[2490] - 3 X[45677], 5 X[31250] - 6 X[45677], 2 X[2977] - 3 X[47802], 3 X[21115] - X[47971], 3 X[21115] + X[48114], 2 X[3798] - 3 X[4453], X[4380] - 3 X[4453], 4 X[3837] - 3 X[47806], 3 X[47806] - 2 X[48062], 3 X[4120] - X[48117], 2 X[4369] - 3 X[21183], 4 X[4369] - 3 X[47768], 3 X[21183] - X[48060], 3 X[47768] - 2 X[48060], 3 X[4379] - X[48101], 4 X[4521] - 3 X[6546], 4 X[4521] - 5 X[30835], 3 X[6546] - 5 X[30835], 2 X[4765] - 3 X[47886], 3 X[47886] - X[47932], 3 X[21116] + X[23731], 3 X[21116] - X[48141], 2 X[4885] - 3 X[4927], 4 X[4885] - 3 X[47766], 3 X[4927] - X[47890], 3 X[47766] - 2 X[47890], 4 X[4940] - 3 X[47764], 3 X[47764] - 2 X[48046], 3 X[4944] - X[48124], 2 X[17069] - 3 X[47754], 9 X[6548] - 5 X[27013], 9 X[14475] - 7 X[31207], X[17494] - 3 X[44435], 2 X[17494] - 3 X[47883], 3 X[44435] + X[47650], 2 X[47650] + 3 X[47883], 3 X[21204] - 2 X[31286], 4 X[21212] - 3 X[47785], 3 X[47785] - 2 X[48008], 3 X[21297] - X[25259], 5 X[24924] - 4 X[43061], 5 X[26798] - 3 X[47769], X[26824] + 3 X[48156], X[45746] - 3 X[48156], X[26853] - 3 X[47755], 5 X[26985] - 3 X[47771], X[47688] + 3 X[48170], X[47690] - 3 X[48170], X[47696] - 3 X[47834], 3 X[31147] - X[48082], 3 X[47786] - 2 X[48270], 5 X[30795] - 3 X[47885], 3 X[31148] - X[48104], 5 X[31209] - 6 X[44432], 5 X[31209] - 3 X[47892], 4 X[31287] - 3 X[47884], 3 X[45320] - X[48095], X[47653] + 3 X[47869], X[47656] - 3 X[47869], X[47664] - 3 X[47782], 3 X[47783] - 2 X[48000], 3 X[47812] - X[48106], 3 X[47832] - X[48102], 3 X[47881] - X[48132], X[47974] - 3 X[48161], X[47975] - 3 X[48159], X[48103] - 3 X[48184]

X(48398) lies on these lines: {2, 11068}, {57, 649}, {513, 11934}, {514, 661}, {516, 28589}, {522, 4382}, {523, 2525}, {650, 6084}, {659, 47800}, {676, 47801}, {812, 3776}, {824, 48268}, {891, 4524}, {900, 47131}, {918, 4106}, {1635, 7658}, {1638, 4394}, {2170, 24198}, {2254, 23687}, {2490, 31250}, {2977, 47802}, {3004, 4762}, {3064, 40166}, {3261, 18071}, {3310, 43051}, {3667, 21115}, {3669, 6591}, {3700, 23813}, {3716, 48061}, {3733, 46542}, {3798, 4380}, {3803, 34958}, {3837, 47806}, {3960, 16757}, {4024, 47923}, {4063, 21188}, {4083, 20507}, {4120, 48117}, {4369, 21183}, {4379, 48101}, {4498, 14837}, {4500, 28863}, {4521, 6546}, {4765, 47886}, {4778, 21116}, {4785, 48013}, {4802, 47999}, {4804, 47973}, {4806, 48040}, {4813, 28878}, {4885, 4927}, {4897, 6008}, {4932, 48067}, {4940, 47764}, {4944, 48124}, {4977, 7662}, {5537, 15599}, {5563, 18108}, {5903, 29350}, {5905, 20295}, {6009, 17069}, {6548, 27013}, {7178, 8712}, {7982, 28292}, {8713, 48338}, {9313, 23811}, {14321, 48087}, {14475, 31190}, {17115, 21107}, {17494, 44435}, {17658, 44318}, {17894, 20908}, {18197, 23788}, {20237, 20909}, {20928, 20952}, {20950, 29739}, {21120, 40137}, {21204, 31286}, {21206, 30095}, {21212, 24623}, {21297, 25259}, {21301, 47720}, {23726, 23760}, {23751, 23777}, {23765, 23780}, {23789, 29158}, {23815, 29098}, {23865, 33925}, {24719, 48326}, {24720, 48069}, {24924, 43061}, {26798, 47769}, {26824, 45746}, {26853, 47755}, {26985, 47771}, {27064, 29004}, {27286, 27293}, {28042, 40134}, {28147, 47671}, {28155, 47670}, {28161, 47673}, {28191, 47693}, {28195, 47990}, {28209, 47132}, {28225, 47697}, {28229, 47696}, {28609, 31147}, {28840, 47981}, {28851, 48038}, {28855, 48034}, {28890, 47786}, {28894, 48274}, {29240, 48332}, {30006, 30023}, {30078, 30094}, {30795, 47885}, {31148, 48104}, {31209, 44432}, {31287, 47884}, {45320, 48095}, {47653, 47656}, {47654, 47655}, {47664, 47782}, {47701, 48119}, {47703, 47924}, {47704, 48023}, {47705, 48077}, {47722, 48298}, {47783, 48000}, {47812, 48106}, {47832, 48102}, {47881, 48132}, {47930, 48266}, {47938, 48148}, {47943, 48142}, {47944, 48143}, {47951, 48134}, {47961, 48126}, {47968, 48120}, {47972, 48115}, {47974, 48161}, {47975, 48159}, {48035, 48042}, {48036, 48043}, {48039, 48050}, {48063, 48068}, {48103, 48184}

X(48398) = midpoint of X(i) and X(j) for these {i,j}: {693, 47652}, {4024, 47923}, {4382, 16892}, {4804, 47973}, {17494, 47650}, {20295, 47676}, {21104, 23729}, {21301, 47720}, {23731, 48141}, {24719, 48326}, {26824, 45746}, {46403, 47691}, {47651, 47660}, {47653, 47656}, {47654, 47655}, {47672, 47958}, {47680, 48335}, {47685, 47695}, {47686, 47694}, {47687, 47692}, {47688, 47690}, {47701, 48119}, {47703, 47924}, {47704, 48023}, {47705, 48077}, {47722, 48298}, {47916, 48275}, {47930, 48266}, {47937, 48147}, {47938, 48148}, {47943, 48142}, {47944, 48143}, {47950, 48133}, {47951, 48134}, {47960, 48125}, {47961, 48126}, {47968, 48120}, {47971, 48114}, {47972, 48115}
X(48398) = reflection of X(i) in X(j) for these {i,j}: {649, 3676}, {3700, 23813}, {3803, 34958}, {4025, 3776}, {4063, 21188}, {4380, 3798}, {4468, 3835}, {4498, 14837}, {6590, 693}, {45745, 3004}, {47123, 23770}, {47130, 3261}, {47663, 11068}, {47758, 6545}, {47766, 4927}, {47768, 21183}, {47883, 44435}, {47890, 4885}, {47892, 44432}, {47932, 4765}, {48008, 21212}, {48034, 48041}, {48035, 48042}, {48036, 48043}, {48038, 48049}, {48039, 48050}, {48040, 4806}, {48046, 4940}, {48060, 4369}, {48061, 3716}, {48062, 3837}, {48067, 4932}, {48068, 48063}, {48069, 24720}, {48087, 14321}, {48094, 3239}, {48269, 4106}
X(48398) = complement of X(47663)
X(48398) = anticomplement of X(11068)
X(48398) = orthic-isogonal conjugate of X(1086)
X(48398) = X(i)-Ceva conjugate of X(j) for these (i,j): {4, 1086}, {1088, 244}, {3732, 4000}, {46740, 1111}
X(48398) = X(i)-isoconjugate of X(j) for these (i,j): {100, 7123}, {184, 42384}, {190, 7084}, {220, 8269}, {644, 1037}, {692, 30701}, {1041, 4587}, {1110, 48070}, {3939, 7131}, {4557, 40403}, {14935, 31615}
X(48398) = X(i)-Dao conjugate of X(j) for these (i, j): (514, 48070), (1086, 30701), (1565, 69), (4000, 6558), (6554, 190), (8054, 7123), (14936, 200), (15487, 100), (17463, 4006), (18589, 1018), (40615, 8817), (40617, 7131)
X(48398) = crosspoint of X(i) and X(j) for these (i,j): {3732, 4000}, {7199, 17925}
X(48398) = crossdifference of every pair of points on line {31, 218}
X(48398) = barycentric product X(i)*X(j) for these {i,j}: {27, 21107}, {497, 3676}, {513, 3673}, {514, 4000}, {522, 7195}, {614, 693}, {661, 16750}, {1086, 3732}, {1088, 17115}, {1111, 1633}, {1473, 46107}, {1851, 4025}, {2082, 24002}, {3261, 16502}, {3914, 7192}, {4077, 5324}, {4211, 14208}, {4391, 28017}, {7199, 16583}, {7289, 17924}, {7649, 17170}, {17925, 18589}, {18155, 40961}, {21450, 30804}
X(48398) = barycentric quotient X(i)/X(j) for these {i,j}: {92, 42384}, {269, 8269}, {497, 3699}, {514, 30701}, {614, 100}, {649, 7123}, {667, 7084}, {1019, 40403}, {1040, 4571}, {1086, 48070}, {1473, 1331}, {1633, 765}, {1851, 1897}, {2082, 644}, {3669, 7131}, {3673, 668}, {3676, 8817}, {3732, 1016}, {3914, 3952}, {4000, 190}, {4211, 162}, {4319, 4578}, {5324, 643}, {6554, 6558}, {7083, 3939}, {7124, 4587}, {7195, 664}, {7289, 1332}, {16502, 101}, {16583, 1018}, {16750, 799}, {17115, 200}, {17170, 4561}, {17925, 40411}, {21107, 306}, {21450, 37223}, {23620, 4574}, {28017, 651}, {40934, 4557}, {40961, 4551}, {40965, 4069}, {43923, 1041}, {43924, 1037}
X(48398) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 47663, 11068}, {649, 3676, 47758}, {649, 6545, 3676}, {693, 47651, 47660}, {693, 47662, 4789}, {2490, 45677, 31250}, {3835, 4468, 47765}, {3837, 48062, 47806}, {4369, 48060, 47768}, {4380, 4453, 3798}, {4728, 48094, 3239}, {4885, 47890, 47766}, {4927, 47890, 4885}, {4940, 48046, 47764}, {6546, 30835, 4521}, {20950, 29739, 35519}, {21115, 48114, 47971}, {21116, 23731, 48141}, {21183, 48060, 4369}, {21212, 48008, 47785}, {26824, 48156, 45746}, {44435, 47650, 17494}, {47652, 47660, 47651}, {47652, 47871, 693}, {47653, 47869, 47656}, {47688, 48170, 47690}, {47886, 47932, 4765}


X(48399) = X(514)X(661)∩X(523)X(3776)

Barycentrics    (b - c)*(a*b + a*c + 3*b*c) : :
X(48399) = X[661] - 3 X[693], 2 X[661] - 3 X[3835], 5 X[661] - 9 X[4728], 7 X[661] - 9 X[4776], 5 X[661] - 3 X[47666], X[661] + 3 X[47672], 7 X[661] - 3 X[47917], 4 X[661] - 3 X[47996], 5 X[693] - 3 X[4728], 7 X[693] - 3 X[4776], 5 X[693] - X[47666], 3 X[693] + X[47675], 7 X[693] - X[47917], 4 X[693] - X[47996], 5 X[3835] - 6 X[4728], 7 X[3835] - 6 X[4776], 5 X[3835] - 2 X[47666], X[3835] + 2 X[47672], 3 X[3835] + 2 X[47675], 7 X[3835] - 2 X[47917], 7 X[4728] - 5 X[4776], 3 X[4728] - X[47666], 3 X[4728] + 5 X[47672], 9 X[4728] + 5 X[47675], 21 X[4728] - 5 X[47917], 12 X[4728] - 5 X[47996], 15 X[4776] - 7 X[47666], 3 X[4776] + 7 X[47672], 9 X[4776] + 7 X[47675], 3 X[4776] - X[47917], 12 X[4776] - 7 X[47996], 3 X[4789] - X[48094], 3 X[4978] - X[48335], 8 X[14350] - 9 X[45661], X[47666] + 5 X[47672], 3 X[47666] + 5 X[47675], 7 X[47666] - 5 X[47917], 4 X[47666] - 5 X[47996], 3 X[47672] - X[47675], 7 X[47672] + X[47917], 4 X[47672] + X[47996], 7 X[47675] + 3 X[47917], 4 X[47675] + 3 X[47996], 3 X[47871] - X[47958], 4 X[47917] - 7 X[47996], X[48073] + 2 X[48120], X[24720] + 2 X[48127], X[48017] - 4 X[48098], X[48017] + 4 X[48127], X[649] - 3 X[47780], X[26824] + 3 X[47780], 5 X[650] - 6 X[45675], 2 X[650] - 3 X[47779], 4 X[45675] - 5 X[47779], X[659] - 3 X[48238], 2 X[4790] - 3 X[4932], X[4790] - 3 X[43067], 4 X[4790] - 3 X[48016], X[4790] + 3 X[48125], X[4932] + 2 X[48125], 4 X[43067] - X[48016], X[48016] + 4 X[48125], 3 X[1635] - X[47664], X[48037] + 2 X[48143], X[4024] + 3 X[21116], 3 X[21116] - X[47676], X[48041] + 2 X[48133], 3 X[4369] - 2 X[4394], 4 X[4369] - 3 X[45313], 8 X[4394] - 9 X[45313], 4 X[4394] - 3 X[48008], 3 X[45313] - 2 X[48008], 3 X[4379] - X[17494], 3 X[4379] - 2 X[31286], X[4380] - 3 X[31148], X[4382] - 3 X[47869], 2 X[4382] + X[48071], X[7192] + 3 X[47869], 6 X[47869] + X[48071], 3 X[4453] - X[48277], X[4608] + 3 X[48156], X[4724] - 3 X[47834], 2 X[4765] - 3 X[45674], 2 X[4770] - 3 X[17072], X[4813] - 3 X[21297], X[4824] - 3 X[48184], X[4838] + 3 X[21115], 3 X[21115] - X[47677], X[4841] - 3 X[4927], 4 X[4885] - 3 X[47778], 3 X[47778] - 2 X[48000], 3 X[4893] - 5 X[26985], X[4976] - 3 X[47891], X[47980] - 4 X[48090], X[47980] + 4 X[48135], X[48043] + 2 X[48135], X[4988] - 3 X[44435], 3 X[44435] + X[47674], 3 X[6545] - X[45746], 3 X[6545] + X[47671], X[48063] + 2 X[48126], 2 X[8689] - 3 X[48234], 3 X[21183] - 2 X[21212], 3 X[21183] - X[45745], 4 X[23813] - X[47984], 5 X[24924] - 3 X[31150], 2 X[25666] - 3 X[45320], 3 X[45320] - X[47962], 5 X[26777] - 7 X[31207], 3 X[47812] - X[47975], 5 X[30795] - 3 X[48176], 5 X[30835] - 3 X[47775], 3 X[31147] - X[31290], 3 X[44429] - X[47934], 3 X[45667] - 2 X[48289], X[47650] + 3 X[47791], 3 X[47791] - X[48101], X[47661] - 3 X[47886], X[48072] + 2 X[48119], 3 X[47759] - X[47908], 3 X[47760] - X[47920], 3 X[47762] - X[47932], 3 X[47790] - X[48082], 3 X[47821] - X[47927], 3 X[47832] - X[47969], 3 X[47870] - X[48117], X[48023] - 3 X[48170], X[48032] - 3 X[48237], X[48042] + 2 X[48134]

X(48399) lies on these lines: {2, 47926}, {514, 661}, {522, 21146}, {523, 3776}, {649, 17029}, {650, 45675}, {659, 48238}, {812, 4790}, {824, 21104}, {918, 4500}, {1491, 28147}, {1635, 47664}, {2254, 28161}, {2786, 48268}, {3667, 4804}, {3676, 7212}, {3700, 28851}, {3716, 48009}, {3837, 4802}, {4010, 4778}, {4024, 21116}, {4106, 28840}, {4369, 4394}, {4379, 17494}, {4380, 31148}, {4382, 4785}, {4453, 48277}, {4608, 48156}, {4724, 47834}, {4765, 45674}, {4770, 17072}, {4806, 28195}, {4813, 21297}, {4824, 28191}, {4838, 21115}, {4841, 4927}, {4885, 47778}, {4893, 26985}, {4940, 47991}, {4976, 47891}, {4977, 47980}, {4988, 44435}, {6545, 25381}, {7199, 29739}, {7662, 48063}, {8689, 48234}, {16892, 47656}, {17166, 28470}, {20295, 48141}, {21183, 21212}, {23301, 23815}, {23655, 48282}, {23729, 28859}, {23791, 25128}, {23813, 47984}, {24924, 31150}, {25666, 45320}, {26049, 47795}, {26777, 31207}, {27193, 47794}, {27674, 48003}, {28155, 47812}, {28175, 48030}, {28199, 48002}, {28213, 48028}, {28225, 48080}, {28229, 48024}, {28855, 48269}, {28882, 48276}, {28890, 48271}, {28906, 48266}, {29051, 48327}, {29807, 48144}, {30795, 48176}, {30835, 47775}, {31147, 31290}, {44429, 47934}, {45667, 48289}, {46403, 48142}, {47650, 47791}, {47655, 47673}, {47657, 47670}, {47659, 47923}, {47661, 47886}, {47665, 47930}, {47685, 48153}, {47689, 47705}, {47690, 47704}, {47691, 47703}, {47694, 48072}, {47697, 48115}, {47759, 47908}, {47760, 47920}, {47762, 47932}, {47790, 48082}, {47821, 47927}, {47832, 47969}, {47870, 48117}, {47985, 48050}, {48023, 48170}, {48032, 48237}, {48042, 48089}, {48079, 48147}, {48107, 48114}

X(48399) = midpoint of X(i) and X(j) for these {i,j}: {649, 26824}, {661, 47675}, {693, 47672}, {4010, 48143}, {4024, 47676}, {4106, 48133}, {4382, 7192}, {4804, 48108}, {4838, 47677}, {4988, 47674}, {7662, 48126}, {16892, 47656}, {20295, 48141}, {21104, 48274}, {21146, 48120}, {43067, 48125}, {45746, 47671}, {46403, 48142}, {47650, 48101}, {47652, 48275}, {47655, 47673}, {47657, 47670}, {47659, 47923}, {47665, 47930}, {47685, 48153}, {47689, 47705}, {47690, 47704}, {47691, 47703}, {47694, 48119}, {47697, 48115}, {48079, 48147}, {48080, 48148}, {48089, 48134}, {48090, 48135}, {48098, 48127}, {48107, 48114}
X(48399) = reflection of X(i) in X(j) for these {i,j}: {3835, 693}, {4932, 43067}, {17494, 31286}, {21196, 3676}, {24720, 48098}, {45745, 21212}, {47962, 25666}, {47980, 48043}, {47984, 48049}, {47985, 48050}, {47986, 4806}, {47991, 4940}, {47996, 3835}, {48000, 4885}, {48008, 4369}, {48009, 3716}, {48010, 3837}, {48016, 4932}, {48017, 24720}, {48037, 4010}, {48041, 4106}, {48042, 48089}, {48043, 48090}, {48049, 23813}, {48063, 7662}, {48071, 7192}, {48072, 47694}, {48073, 21146}
X(48399) = complement of X(47926)
X(48399) = X(i)-complementary conjugate of X(j) for these (i,j): {39739, 116}, {39965, 11}
X(48399) = X(i)-isoconjugate of X(j) for these (i,j): {6, 29199}, {101, 39972}, {692, 39738}
X(48399) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 29199), (1015, 39972), (1086, 39738)
X(48399) = barycentric product X(i)*X(j) for these {i,j}: {75, 29198}, {514, 4699}, {693, 26102}
X(48399) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 29199}, {513, 39972}, {514, 39738}, {4699, 190}, {26102, 100}, {29198, 1}
X(48399) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 47672, 47675}, {693, 47666, 4728}, {693, 47675, 661}, {4024, 21116, 47676}, {4369, 48008, 45313}, {4379, 17494, 31286}, {4838, 21115, 47677}, {4885, 48000, 47778}, {6545, 47671, 45746}, {7192, 47869, 4382}, {21183, 45745, 21212}, {26824, 47780, 649}, {44435, 47674, 4988}, {45320, 47962, 25666}, {47650, 47791, 48101}


X(48400) = X(513)X(1835)∩X(514)X(3716)

Barycentrics    (b - c)*(a^2*b + b^3 + a^2*c + 2*a*b*c - b^2*c - b*c^2 + c^3) : :
X(48400) = 5 X[4391] - X[47706], 3 X[4391] - X[47707], 3 X[4391] + X[47709], 3 X[47706] - 5 X[47707], X[47706] + 5 X[47708], 3 X[47706] + 5 X[47709], X[47707] + 3 X[47708], 3 X[47708] - X[47709], 2 X[667] - 3 X[26275], 2 X[905] - 3 X[47799], 3 X[1577] - X[47715], 2 X[2530] - 3 X[48178], 2 X[2977] - 3 X[47793], 3 X[3762] + X[47717], 3 X[47712] - X[47717], X[3904] - 3 X[47840], 3 X[4800] - 2 X[4990], 3 X[6545] - X[23738], X[17496] - 3 X[47797], 4 X[21188] - 3 X[48245], 4 X[21260] - 3 X[48182], X[31291] - 3 X[44433], 3 X[47756] - 2 X[48100], 3 X[47887] - X[48341]

X(48400) lies on these lines: {512, 10015}, {513, 1835}, {514, 3716}, {523, 4391}, {525, 48267}, {659, 21789}, {661, 21118}, {667, 26275}, {676, 4367}, {830, 21201}, {885, 17097}, {900, 21301}, {905, 47799}, {918, 3801}, {1491, 6362}, {1577, 29142}, {2530, 2826}, {2977, 47793}, {3004, 3766}, {3566, 48080}, {3700, 29017}, {3762, 29288}, {3777, 30804}, {3810, 3835}, {3904, 47840}, {3910, 4010}, {4040, 29240}, {4083, 21120}, {4129, 23887}, {4142, 6002}, {4378, 34958}, {4401, 29114}, {4462, 47691}, {4775, 28473}, {4782, 29124}, {4791, 29021}, {4800, 4990}, {4833, 4977}, {4874, 29120}, {4879, 6366}, {4897, 29170}, {6545, 23738}, {8678, 21185}, {17166, 47132}, {17496, 47797}, {20317, 48062}, {20517, 29148}, {21104, 29198}, {21124, 48264}, {21132, 48131}, {21188, 48245}, {21260, 48182}, {23755, 48021}, {23877, 48047}, {28183, 30709}, {28487, 48050}, {28490, 48325}, {29025, 47890}, {29029, 48231}, {29156, 48331}, {31291, 44433}, {47134, 48022}, {47680, 47970}, {47756, 48100}, {47887, 48341}, {48090, 48280}

X(48400) = midpoint of X(i) and X(j) for these {i,j}: {661, 21118}, {3762, 47712}, {3801, 48265}, {4391, 47708}, {4462, 47691}, {21124, 48264}, {21132, 48131}, {23755, 48021}, {47680, 47970}, {47707, 47709}
X(48400) = reflection of X(i) in X(j) for these {i,j}: {4367, 676}, {4378, 34958}, {17166, 47132}, {48062, 20317}, {48280, 48090}, {48299, 3716}
X(48400) = X(4516)-Dao conjugate of X(210)
X(48400) = crossdifference of every pair of points on line {219, 5019}
X(48400) = barycentric product X(i)*X(j) for these {i,j}: {514, 24210}, {693, 41015}, {7199, 23668}, {11997, 24002}, {16680, 23989}, {16727, 22280}
X(48400) = barycentric quotient X(i)/X(j) for these {i,j}: {11997, 644}, {16680, 1252}, {23668, 1018}, {24210, 190}, {41015, 100}
X(48400) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4391, 47709, 47707}, {47707, 47708, 47709}


X(48401) = X(513)X(4147)∩X(514)X(3837)

Barycentrics    (b - c)*(-(a*b^2) - 4*a*b*c + b^2*c - a*c^2 + b*c^2) : :
X(48401) = 3 X[3837] - 4 X[21260], 5 X[3837] - 4 X[23815], 3 X[21051] - 2 X[21260], 5 X[21051] - 2 X[23815], 5 X[21260] - 3 X[23815], 3 X[659] - X[31291], 2 X[667] - 3 X[45314], X[764] - 3 X[47816], 2 X[905] - 3 X[47829], X[2533] - 3 X[14430], 3 X[14430] + X[47918], X[3777] - 3 X[47814], X[4367] - 3 X[47793], X[4378] - 3 X[47794], 3 X[4448] - X[48322], X[4449] - 3 X[47822], X[4879] - 3 X[47821], X[4978] - 3 X[14431], X[4983] + 3 X[30583], X[17166] - 3 X[47872], X[17496] - 3 X[47827], 3 X[21052] - X[21146], X[21222] - 3 X[47893], X[21343] - 3 X[47840], X[23738] - 3 X[36848], X[23765] - 3 X[44429], 3 X[47760] - X[48346], 3 X[47823] - X[48341], 3 X[47835] - X[48144], 3 X[47837] - X[48320], 3 X[47838] - X[48333], 3 X[47839] - X[48282]

X(48401) lies on these lines: {2, 48323}, {8, 48336}, {10, 6372}, {513, 4147}, {514, 3837}, {523, 4391}, {650, 29324}, {659, 31291}, {667, 45314}, {764, 47816}, {814, 47965}, {891, 4129}, {900, 4041}, {905, 47829}, {1491, 4462}, {2533, 4977}, {2787, 48003}, {3762, 4705}, {3777, 47814}, {3835, 29226}, {3910, 18004}, {4083, 4806}, {4367, 47793}, {4378, 47794}, {4448, 48322}, {4449, 47822}, {4468, 29082}, {4761, 47949}, {4770, 8714}, {4833, 21300}, {4874, 20317}, {4879, 25574}, {4978, 14431}, {4983, 30583}, {8678, 48248}, {17072, 29198}, {17166, 47872}, {17496, 47827}, {21052, 21146}, {21120, 48047}, {21222, 47893}, {21343, 47840}, {23301, 47666}, {23738, 36848}, {23765, 44429}, {25126, 43067}, {28175, 31946}, {28183, 48264}, {28209, 47913}, {28213, 44316}, {29118, 32212}, {29120, 48062}, {29152, 48008}, {29188, 48004}, {29246, 47966}, {29268, 48284}, {29284, 48270}, {29298, 48058}, {29332, 48088}, {29362, 47921}, {29366, 48029}, {31288, 48343}, {47760, 48346}, {47823, 48341}, {47835, 48144}, {47837, 48320}, {47838, 48333}, {47839, 48282}, {47959, 47993}

X(48401) = midpoint of X(i) and X(j) for these {i,j}: {8, 48336}, {1491, 4462}, {2533, 47918}, {3762, 4705}, {4041, 48265}, {4391, 4490}, {4761, 47949}, {21120, 48047}
X(48401) = reflection of X(i) in X(j) for these {i,j}: {3837, 21051}, {4874, 20317}, {4992, 4129}, {47993, 47959}, {48002, 47967}, {48343, 31288}
X(48401) = complement of X(48323)
X(48401) = crossdifference of every pair of points on line {5019, 21785}
X(48401) = {X(14430),X(47918)}-harmonic conjugate of X(2533)


X(48402) = X(241)X(514)∩X(525)X(661)

Barycentrics    (b^2 - c^2)*(a^2 + 2*a*b + b^2 + 2*a*c + c^2) : :
X(48402) = X[3669] - 3 X[47880], 2 X[4369] - 3 X[41800], 2 X[14838] - 3 X[47784], 3 X[1577] - X[47678], 3 X[4705] - X[4808], X[47678] + 3 X[47679], X[3777] - 3 X[47877], X[4560] - 3 X[47782], 3 X[4750] - X[48149], X[4801] - 3 X[44435], 3 X[4893] - X[48300], 2 X[4990] - 3 X[47838], X[6332] - 3 X[47783], X[17166] - 3 X[47797], 2 X[34958] - 3 X[47797], 2 X[23815] - 3 X[48178], 3 X[44429] - X[47719], X[47660] - 3 X[47793], X[47690] - 3 X[47814], X[47696] - 3 X[47815], X[47715] - 3 X[47816], X[47718] - 3 X[47808], X[47720] - 3 X[48174], 3 X[47756] - X[48280], 3 X[47810] - X[48278], 3 X[47886] - X[48144], 3 X[48177] - X[48301]

X(48402) lies on these lines: {241, 514}, {512, 47998}, {523, 1577}, {525, 661}, {690, 48053}, {826, 48005}, {918, 47959}, {1019, 17069}, {1491, 29142}, {1499, 4822}, {2483, 4063}, {3309, 48006}, {3566, 4983}, {3700, 4129}, {3777, 47877}, {3800, 4041}, {3801, 4824}, {3910, 14349}, {4170, 4843}, {4391, 45746}, {4490, 29288}, {4498, 47958}, {4560, 29126}, {4750, 48149}, {4770, 7927}, {4801, 44435}, {4823, 48274}, {4893, 48300}, {4897, 15309}, {4913, 29118}, {4976, 29013}, {4988, 27731}, {4990, 47838}, {6002, 21196}, {6332, 47783}, {7265, 14321}, {8045, 25666}, {16892, 47918}, {17166, 34958}, {20317, 28894}, {23729, 29302}, {23731, 47935}, {23815, 48178}, {23875, 47997}, {23876, 48054}, {23877, 48010}, {23882, 45745}, {25684, 47682}, {28478, 48091}, {28481, 48023}, {28493, 48041}, {28846, 47955}, {29017, 48030}, {29021, 48012}, {29200, 48028}, {29252, 47994}, {29284, 48093}, {29312, 48059}, {44429, 47719}, {47660, 47793}, {47690, 47814}, {47696, 47815}, {47708, 47975}, {47715, 47816}, {47718, 47808}, {47720, 48174}, {47756, 48280}, {47810, 48278}, {47886, 48144}, {47911, 47971}, {47929, 47973}, {48177, 48301}

X(48402) = midpoint of X(i) and X(j) for these {i,j}: {661, 21124}, {1577, 47679}, {3801, 4824}, {4041, 47701}, {4391, 45746}, {4498, 47958}, {4841, 7178}, {16892, 47918}, {23731, 47935}, {47708, 47975}, {47911, 47971}, {47921, 47960}, {47929, 47973}
X(48402) = reflection of X(i) in X(j) for these {i,j}: {1019, 17069}, {3700, 4129}, {4897, 21192}, {7265, 14321}, {8045, 25666}, {17166, 34958}, {43067, 21188}, {47890, 48003}, {48046, 47997}, {48047, 48005}, {48274, 4823}
X(48402) = crossdifference of every pair of points on line {55, 1333}
X(48402) = barycentric product X(i)*X(j) for these {i,j}: {10, 47995}, {523, 17321}, {693, 3931}, {850, 16466}, {1577, 5256}, {4025, 39579}, {4077, 5250}, {4194, 17094}, {7178, 14555}, {7713, 14208}
X(48402) = barycentric quotient X(i)/X(j) for these {i,j}: {3931, 100}, {4194, 36797}, {4254, 5546}, {5250, 643}, {5256, 662}, {7713, 162}, {14555, 645}, {16466, 110}, {17321, 99}, {39579, 1897}, {47995, 86}
X(48402) = {X(17166),X(47797)}-harmonic conjugate of X(34958)


X(48403) = X(513)X(5570)∩X(514)X(3716)

Barycentrics    (b^2 - c^2)*(a^2 + b^2 - 2*b*c + c^2) : :
X(48403) = 5 X[1577] - X[47710], 3 X[1577] - X[47711], 3 X[1577] + X[47713], X[4808] - 3 X[14431], 3 X[47710] - 5 X[47711], X[47710] + 5 X[47712], 3 X[47710] + 5 X[47713], X[47711] + 3 X[47712], 3 X[47712] - X[47713], 3 X[693] - X[47719], 3 X[47708] + X[47719], 2 X[2977] - 3 X[47794], 3 X[4049] - X[4807], 2 X[4401] - 3 X[26275], X[4560] - 3 X[47797], 3 X[4728] - X[48278], X[4729] - 3 X[30574], 3 X[4927] - 2 X[23815], 2 X[6050] - 3 X[47800], 3 X[6545] - X[48151], 2 X[9508] - 3 X[41800], 2 X[14838] - 3 X[47799], X[47663] - 3 X[47815], 3 X[47756] - 2 X[48059], 3 X[47832] - X[48300], 3 X[47872] - X[48103], 3 X[47887] - X[48144], 2 X[48066] - 3 X[48178]

X(48403) lies on these lines: {65, 512}, {513, 5570}, {514, 3716}, {523, 1577}, {525, 3801}, {659, 22160}, {663, 29240}, {667, 676}, {693, 29142}, {784, 3004}, {812, 4142}, {826, 3700}, {891, 21120}, {918, 48267}, {999, 4367}, {1019, 3338}, {1482, 4879}, {1499, 21145}, {1960, 29336}, {2499, 6372}, {2530, 6362}, {2533, 3800}, {2826, 3777}, {2977, 47794}, {3566, 4170}, {3762, 47716}, {3835, 23877}, {3910, 48273}, {4017, 44705}, {4040, 47680}, {4049, 4807}, {4083, 10015}, {4129, 21077}, {4369, 29118}, {4391, 29288}, {4401, 26275}, {4458, 6002}, {4462, 47720}, {4560, 47797}, {4728, 48278}, {4729, 30574}, {4784, 5708}, {4791, 29047}, {4804, 21124}, {4822, 23755}, {4823, 29021}, {4874, 29025}, {4897, 29150}, {4922, 28533}, {4927, 23815}, {5048, 48347}, {6050, 47800}, {6366, 48333}, {6545, 48151}, {8045, 29116}, {8678, 47123}, {9508, 41800}, {14838, 47799}, {16892, 48264}, {17115, 21107}, {20323, 48328}, {20517, 29013}, {21118, 48131}, {21132, 48334}, {21301, 47695}, {24719, 28481}, {25415, 48337}, {25681, 47839}, {29017, 48090}, {29098, 47890}, {29128, 47788}, {29156, 48330}, {29244, 48331}, {29312, 48280}, {37535, 44811}, {47663, 47815}, {47690, 47709}, {47692, 47707}, {47704, 47918}, {47756, 48059}, {47832, 48300}, {47872, 48103}, {47887, 48144}, {48066, 48178}, {48265, 48326}

X(48403) = midpoint of X(i) and X(j) for these {i,j}: {693, 47708}, {1577, 47712}, {2533, 48349}, {3762, 47716}, {3801, 4010}, {4040, 47680}, {4170, 4707}, {4391, 47691}, {4462, 47720}, {4804, 21124}, {4822, 23755}, {16892, 48264}, {21118, 48131}, {21132, 48334}, {21301, 47695}, {47690, 47709}, {47692, 47707}, {47704, 47918}, {47711, 47713}, {48265, 48326}
X(48403) = reflection of X(i) in X(j) for these {i,j}: {667, 676}, {4367, 34958}, {48047, 4129}
X(48403) = polar conjugate of the isotomic conjugate of X(21107)
X(48403) = X(i)-Ceva conjugate of X(j) for these (i,j): {1446, 3125}, {1826, 3120}, {46886, 2969}
X(48403) = X(i)-isoconjugate of X(j) for these (i,j): {99, 7084}, {101, 40403}, {163, 30701}, {643, 1037}, {662, 7123}, {906, 40411}, {2328, 8269}, {5546, 7131}
X(48403) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 30701), (1015, 40403), (1084, 7123), (1565, 17206), (4000, 7256), (4988, 48070), (5190, 40411), (6554, 99), (14936, 2287), (15487, 662), (16583, 4561), (17463, 3681), (18589, 100), (36908, 8269), (38986, 7084), (40622, 8817)
X(48403) = crosspoint of X(693) and X(7649)
X(48403) = crosssum of X(692) and X(1331)
X(48403) = crossdifference of every pair of points on line {1333, 1801}
X(48403) = barycentric product X(i)*X(j) for these {i,j}: {4, 21107}, {497, 7178}, {514, 3914}, {523, 4000}, {525, 1851}, {614, 1577}, {661, 3673}, {693, 16583}, {850, 16502}, {1446, 17115}, {1473, 14618}, {1633, 16732}, {2082, 4077}, {2501, 17170}, {3120, 3732}, {3261, 40934}, {3700, 7195}, {4086, 28017}, {4391, 40961}, {4705, 16750}, {6591, 20235}, {7289, 24006}, {7649, 18589}, {17441, 17924}, {17925, 21015}, {18084, 21108}, {21750, 40495}, {23620, 46107}, {24002, 40965}
X(48403) = barycentric quotient X(i)/X(j) for these {i,j}: {497, 645}, {512, 7123}, {513, 40403}, {523, 30701}, {614, 662}, {798, 7084}, {1427, 8269}, {1473, 4558}, {1633, 4567}, {1851, 648}, {2082, 643}, {3120, 48070}, {3673, 799}, {3732, 4600}, {3914, 190}, {4000, 99}, {4017, 7131}, {4319, 7259}, {5324, 4612}, {6554, 7256}, {7083, 5546}, {7178, 8817}, {7180, 1037}, {7195, 4573}, {7289, 4592}, {7649, 40411}, {8020, 8750}, {16502, 110}, {16583, 100}, {16750, 4623}, {17115, 2287}, {17170, 4563}, {17441, 1332}, {18589, 4561}, {21107, 69}, {21750, 692}, {21813, 4557}, {22363, 906}, {23620, 1331}, {28017, 1414}, {40934, 101}, {40961, 651}, {40965, 644}, {41013, 42384}
X(48403) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1577, 47713, 47711}, {47711, 47712, 47713}


X(48404) = X(241)X(514)∩X(513)X(4818)

Barycentrics    (b - c)*(2*a*b + b^2 + 2*a*c + b*c + c^2) : :
X(48404) = 3 X[3004] - X[21104], X[3776] + 2 X[4841], 3 X[3776] - 2 X[21104], 3 X[4369] - 4 X[7658], 2 X[4369] - 3 X[47882], 3 X[4841] + X[21104], 8 X[7658] - 9 X[47882], 2 X[21212] - 3 X[47880], 2 X[31286] - 3 X[47784], X[43067] - 3 X[47880], 3 X[47754] - X[48133], 3 X[47784] - X[48276], 3 X[47876] - X[47890], X[649] - 3 X[47782], 3 X[661] - X[25259], 3 X[661] + X[47673], 5 X[661] - 3 X[47769], X[661] - 3 X[47781], X[25259] + 3 X[45746], 5 X[25259] - 9 X[47769], X[25259] - 9 X[47781], 2 X[25259] - 3 X[48270], 3 X[45746] - X[47673], 5 X[45746] + 3 X[47769], X[45746] + 3 X[47781], 2 X[45746] + X[48270], 5 X[47673] + 9 X[47769], X[47673] + 9 X[47781], 2 X[47673] + 3 X[48270], X[47769] - 5 X[47781], 6 X[47769] - 5 X[48270], 6 X[47781] - X[48270], 3 X[693] + X[47668], 3 X[693] - X[47671], 3 X[4988] - X[47668], 3 X[4988] + X[47671], 2 X[3239] - 3 X[45315], X[4024] - 3 X[4776], 3 X[4776] + X[47657], 3 X[4120] - X[47665], 3 X[4453] - X[48141], X[4608] - 5 X[26985], 3 X[4728] - X[47656], 3 X[4728] + X[47669], 3 X[4750] - X[48107], 3 X[4789] - 5 X[30835], X[4838] - 3 X[47790], 3 X[4893] - X[47660], X[4979] - 3 X[27486], 3 X[6545] - X[47675], 3 X[6546] - X[47662], X[6590] - 3 X[47783], 2 X[6590] - 3 X[47879], 2 X[25666] - 3 X[47783], 4 X[25666] - 3 X[47879], X[7192] - 3 X[47886], X[17161] + 3 X[47759], 3 X[47759] - X[48266], X[17494] - 3 X[47878], 3 X[47878] + X[47958], X[20295] + 3 X[46915], 3 X[46915] - X[48277], X[21146] - 3 X[47877], 5 X[24924] - 3 X[47791], 7 X[27138] - 3 X[47792], X[31290] + 3 X[47894], 3 X[47894] - X[47971], 3 X[30565] + X[47654], 3 X[44435] + X[47667], 3 X[44435] - X[47672], 3 X[31150] - X[48101], 3 X[44429] - X[47703], X[47653] + 3 X[47775], 3 X[47775] - X[48094], X[47658] - 3 X[47873], X[47659] - 3 X[47874], X[47690] - 3 X[47810], X[47696] - 3 X[47811], X[47704] - 3 X[48174], 3 X[47755] - X[48147], 3 X[47756] - X[48274], 3 X[47774] - X[48076], 3 X[47776] - X[48104], 3 X[47777] - X[48271], 3 X[47797] - X[48142], 3 X[47798] - X[48153], 3 X[47825] - X[48106], 3 X[47883] - X[48060], 3 X[47892] - X[48138], X[48103] - 3 X[48176], X[48119] - 3 X[48159], X[48134] - 3 X[48192]

X(48404) lies on these lines: {2, 48275}, {241, 514}, {513, 4818}, {522, 47998}, {523, 3835}, {649, 28859}, {661, 824}, {693, 4988}, {812, 45745}, {900, 48041}, {918, 47996}, {2254, 47699}, {2487, 28213}, {2512, 21261}, {2530, 23768}, {2786, 48026}, {3239, 45315}, {3798, 4778}, {4024, 4776}, {4025, 28840}, {4120, 47665}, {4380, 23731}, {4382, 47661}, {4453, 48141}, {4467, 4813}, {4468, 28863}, {4608, 26985}, {4728, 47656}, {4750, 48107}, {4777, 4940}, {4782, 4932}, {4785, 4976}, {4789, 30835}, {4802, 4885}, {4838, 47790}, {4842, 20907}, {4893, 47660}, {4928, 23770}, {4979, 27486}, {6545, 47675}, {6546, 47662}, {6590, 25666}, {7192, 47886}, {14349, 47679}, {16892, 28851}, {17161, 47759}, {17494, 28882}, {20295, 46915}, {20505, 29946}, {20949, 25667}, {21146, 47877}, {21828, 27648}, {23879, 48054}, {24287, 47959}, {24924, 47791}, {26853, 47937}, {27138, 47792}, {27854, 42760}, {28175, 47779}, {28179, 48201}, {28191, 44432}, {28195, 45674}, {28209, 48071}, {28493, 48085}, {28846, 47991}, {28855, 47952}, {28886, 31290}, {29037, 47956}, {29190, 48052}, {29216, 48051}, {29328, 47990}, {29362, 47999}, {30519, 48046}, {30565, 47654}, {30764, 47809}, {30765, 44435}, {31150, 48101}, {44429, 47703}, {47652, 47926}, {47653, 47775}, {47658, 47873}, {47659, 47874}, {47663, 47916}, {47676, 47917}, {47677, 48082}, {47690, 47810}, {47691, 47934}, {47696, 47811}, {47701, 47975}, {47704, 48174}, {47755, 48147}, {47756, 48274}, {47774, 48076}, {47776, 48104}, {47777, 48271}, {47797, 48142}, {47798, 48153}, {47825, 48106}, {47883, 48060}, {47892, 48138}, {47928, 48326}, {47969, 47973}, {48103, 48176}, {48119, 48159}, {48134, 48192}

X(48404) = complement of X(48275)
X(48404) = midpoint of X(i) and X(j) for these {i,j}: {661, 45746}, {693, 4988}, {2254, 47699}, {3004, 4841}, {4024, 47657}, {4380, 23731}, {4382, 47661}, {4467, 4813}, {4976, 47988}, {14349, 47679}, {16892, 47666}, {17161, 48266}, {17494, 47958}, {20295, 48277}, {25259, 47673}, {26853, 47937}, {31290, 47971}, {45745, 47995}, {47652, 47926}, {47653, 48094}, {47656, 47669}, {47663, 47916}, {47667, 47672}, {47668, 47671}, {47676, 47917}, {47677, 48082}, {47691, 47934}, {47701, 47975}, {47928, 48326}, {47960, 47962}, {47969, 47973}
X(48404) = reflection of X(i) in X(j) for these {i,j}: {3776, 3004}, {4500, 3835}, {4522, 48030}, {4932, 17069}, {6590, 25666}, {43067, 21212}, {47879, 47783}, {48270, 661}, {48276, 31286}
X(48404) = X(39736)-Ceva conjugate of X(1086)
X(48404) = barycentric product X(i)*X(j) for these {i,j}: {75, 48123}, {514, 17248}, {693, 17592}
X(48404) = barycentric quotient X(i)/X(j) for these {i,j}: {17248, 190}, {17592, 100}, {48123, 1}
X(48404) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 47673, 25259}, {693, 47668, 47671}, {4728, 47669, 47656}, {4776, 47657, 4024}, {4988, 47671, 47668}, {6590, 25666, 47879}, {6590, 47783, 25666}, {17161, 47759, 48266}, {20295, 46915, 48277}, {25259, 45746, 47673}, {31290, 47894, 47971}, {43067, 47880, 21212}, {44435, 47667, 47672}, {45746, 47781, 661}, {47653, 47775, 48094}, {47784, 48276, 31286}, {47878, 47958, 17494}


X(48405) = X(230)X(231)∩X(513)X(4522)

Barycentrics    (b - c)*(a^3 + a^2*b + b^3 + a^2*c + 2*b^2*c + 2*b*c^2 + c^3) : :
X(48405) = 3 X[2] + X[47693], X[650] - 3 X[48219], 2 X[676] - 3 X[4874], 4 X[2490] - 3 X[48214], X[7662] - 3 X[47881], X[7662] + 3 X[48222], X[47131] - 3 X[48220], X[48030] - 3 X[48201], X[659] - 3 X[47771], X[47690] + 3 X[47771], X[661] - 3 X[48185], X[693] + 3 X[48236], X[48103] - 3 X[48236], X[1491] - 3 X[47809], X[47660] + 3 X[47809], 3 X[1639] - X[47998], X[2254] - 3 X[48235], X[2526] - 3 X[48200], X[3004] - 3 X[47807], 2 X[3676] - 3 X[48233], X[4010] - 3 X[47874], 3 X[47874] + X[48106], X[4088] - 3 X[48188], 3 X[4379] + X[48118], 3 X[4379] - X[48326], 3 X[4448] - X[47972], 4 X[4521] - 3 X[48180], 3 X[4728] + X[48146], 3 X[4776] - X[47944], 3 X[4789] - X[48120], X[4810] - 3 X[47790], X[4988] - 3 X[48176], 3 X[6546] + X[47703], X[7192] + 3 X[48171], X[16892] - 3 X[47823], X[17494] - 3 X[47885], X[21124] - 3 X[47835], 2 X[21212] - 3 X[48216], X[23770] - 3 X[47788], 5 X[24924] - 3 X[48227], 2 X[25380] - 3 X[48217], 2 X[25666] - 3 X[48199], 5 X[26985] - X[47688], 3 X[30565] - X[48024], 5 X[30795] - 3 X[44435], 5 X[30835] - X[47924], 5 X[31250] - 3 X[48192], 3 X[36848] - X[47973], 3 X[44429] + X[47662], 3 X[44429] - X[47968], X[45746] - 3 X[47827], X[46403] + 3 X[47773], X[47652] - 3 X[48184], X[48140] + 3 X[48184], X[47653] - 3 X[47877], X[47659] + 3 X[47825], X[47676] - 3 X[48253], X[47686] - 3 X[48167], X[47687] + 3 X[48250], X[47689] + 3 X[47804], X[47691] - 3 X[47833], X[47694] + 3 X[48208], X[47695] - 3 X[48234], X[47696] + 3 X[47808], X[47697] + 3 X[48187], X[47698] + 3 X[47791], X[47699] - 3 X[48162], X[47700] + 3 X[47813], X[47701] - 3 X[47822], X[47702] - 3 X[48177], X[47704] - 3 X[48238], X[47706] + 3 X[47820], X[47708] - 3 X[47872], X[47710] + 3 X[47818], X[47712] - 3 X[47875], X[47714] + 3 X[47817], X[47718] + 3 X[47815], X[47720] - 3 X[47889], 3 X[47760] - X[47961], 3 X[47765] - X[47983], 3 X[47770] - X[48029], 3 X[47802] - X[47960], 3 X[47806] - X[48007], 3 X[47812] + X[48130], 3 X[47832] - X[48349], X[47925] - 3 X[48159]

X(48405) lies on these lines: {2, 47693}, {230, 231}, {513, 4522}, {514, 3837}, {522, 4782}, {649, 4122}, {659, 26249}, {661, 48185}, {667, 29074}, {693, 48103}, {824, 9508}, {900, 48069}, {1491, 47660}, {1577, 29025}, {1639, 47998}, {1960, 29192}, {2254, 48235}, {2526, 48200}, {2533, 29082}, {3004, 47807}, {3239, 4806}, {3676, 48233}, {3700, 29328}, {3716, 29144}, {4010, 47874}, {4083, 8045}, {4088, 48188}, {4142, 29146}, {4367, 47707}, {4379, 48118}, {4391, 29120}, {4401, 29086}, {4448, 47972}, {4458, 29204}, {4468, 4977}, {4521, 48180}, {4728, 48146}, {4774, 47728}, {4776, 47944}, {4778, 48048}, {4784, 25259}, {4789, 48120}, {4791, 29029}, {4802, 4885}, {4810, 47790}, {4823, 29098}, {4824, 48275}, {4834, 7265}, {4988, 48176}, {6546, 47703}, {7178, 29332}, {7192, 48171}, {7950, 20517}, {10015, 29172}, {16892, 47823}, {17494, 47885}, {21124, 47835}, {21146, 48094}, {21212, 48216}, {23770, 47788}, {24719, 48101}, {24924, 48227}, {25380, 28863}, {25666, 48199}, {26985, 47688}, {28147, 48194}, {28151, 45684}, {28175, 48198}, {28209, 48040}, {28602, 28894}, {29090, 48064}, {29106, 48011}, {29362, 47890}, {29366, 48299}, {29370, 47767}, {30565, 48024}, {30795, 44435}, {30835, 47924}, {30865, 47781}, {31250, 48192}, {36848, 47973}, {43067, 48088}, {44429, 47662}, {45746, 47827}, {46403, 47773}, {47652, 48140}, {47653, 47877}, {47659, 47825}, {47676, 48253}, {47686, 48167}, {47687, 48250}, {47689, 47804}, {47691, 47833}, {47694, 48208}, {47695, 48234}, {47696, 47808}, {47697, 48187}, {47698, 47791}, {47699, 48162}, {47700, 47813}, {47701, 47822}, {47702, 48177}, {47704, 48238}, {47706, 47820}, {47708, 47872}, {47710, 47818}, {47712, 47875}, {47714, 47817}, {47718, 47815}, {47720, 47889}, {47760, 47961}, {47765, 47983}, {47770, 48029}, {47802, 47960}, {47806, 48007}, {47812, 48130}, {47832, 48349}, {47925, 48159}, {48047, 48276}, {48083, 48108}, {48089, 48095}

X(48405) = midpoint of X(i) and X(j) for these {i,j}: {649, 4122}, {659, 47690}, {667, 47711}, {693, 48103}, {1491, 47660}, {2533, 48300}, {4010, 48106}, {4367, 47707}, {4774, 47728}, {4784, 25259}, {4824, 48275}, {4834, 7265}, {6590, 48062}, {21146, 48094}, {24719, 48101}, {43067, 48088}, {47652, 48140}, {47662, 47968}, {47881, 48222}, {48047, 48276}, {48083, 48108}, {48089, 48095}, {48097, 48098}, {48118, 48326}
X(48405) = reflection of X(4806) in X(3239)
X(48405) = crossdifference of every pair of points on line {3, 21793}
X(48405) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 48236, 48103}, {4379, 48118, 48326}, {44429, 47662, 47968}, {47660, 47809, 1491}, {47690, 47771, 659}, {47874, 48106, 4010}, {48140, 48184, 47652}


X(48406) = X(513)X(4992)∩X(514)X(3837)

Barycentrics    (b - c)*(-(a*b^2) + 2*a*b*c + b^2*c - a*c^2 + b*c^2) : :
X(48406) = 3 X[3837] - 2 X[21260], 3 X[21051] - 4 X[21260], X[21051] - 4 X[23815], X[21260] - 3 X[23815], X[659] - 3 X[47796], X[1491] - 3 X[47819], X[4801] + 3 X[47819], X[2533] - 3 X[47812], 3 X[47812] + X[48334], X[3801] - 3 X[6545], X[4041] - 3 X[36848], X[4170] - 3 X[30592], 3 X[4367] - X[31291], X[31291] + 3 X[46403], X[4391] - 3 X[48184], X[23765] + 3 X[48184], 3 X[4448] - X[47936], X[4490] - 3 X[44429], X[4498] - 3 X[47823], X[4724] - 3 X[47841], 3 X[4728] + X[23738], 3 X[4728] - X[48265], 3 X[4776] - X[47913], X[17494] - 3 X[47893], X[17496] + 3 X[48170], X[21301] - 3 X[48167], 3 X[48167] + X[48323], X[21385] - 3 X[47837], 5 X[26985] - 3 X[47872], 5 X[30795] - 3 X[47793], 5 X[31251] - 6 X[45340], 4 X[31288] - 3 X[45314], X[47694] - 3 X[47889], 3 X[47802] - X[47921], 3 X[47822] - X[47929], 3 X[47829] - 2 X[48003], 3 X[47839] - X[47970]

X(48406) lies on these lines: {512, 23789}, {513, 4992}, {514, 3837}, {523, 2530}, {659, 47796}, {693, 3777}, {764, 1577}, {814, 3669}, {900, 4905}, {905, 29362}, {1491, 4801}, {2254, 48279}, {2533, 47812}, {2832, 48206}, {3261, 20512}, {3776, 29017}, {3801, 6545}, {3835, 29198}, {3960, 29070}, {4010, 48151}, {4041, 36848}, {4083, 24720}, {4106, 29170}, {4151, 23814}, {4170, 28217}, {4367, 31291}, {4374, 18081}, {4391, 23765}, {4448, 47936}, {4490, 44429}, {4498, 47823}, {4724, 47841}, {4728, 23738}, {4776, 47913}, {4778, 48093}, {4806, 6372}, {4977, 14349}, {4983, 28209}, {6004, 48295}, {14838, 19947}, {17072, 29226}, {17494, 47893}, {17496, 48170}, {21146, 48131}, {21301, 48167}, {21302, 21343}, {21385, 47837}, {23301, 47672}, {24719, 48144}, {25126, 48000}, {26985, 47872}, {28175, 44316}, {28213, 31946}, {28470, 48344}, {29051, 48289}, {29188, 48348}, {29246, 48136}, {29274, 48325}, {29366, 48332}, {30795, 47793}, {31251, 45340}, {31288, 45314}, {47694, 47889}, {47802, 47921}, {47822, 47929}, {47829, 48003}, {47839, 47970}, {47993, 48054}, {48108, 48123}, {48278, 48326}

X(48406) = midpoint of X(i) and X(j) for these {i,j}: {693, 3777}, {764, 1577}, {1491, 4801}, {2254, 48279}, {2530, 4978}, {2533, 48334}, {3669, 48089}, {4010, 48151}, {4367, 46403}, {4391, 23765}, {4905, 48273}, {21146, 48131}, {21301, 48323}, {21302, 21343}, {23738, 48265}, {24719, 48144}, {48098, 48137}, {48108, 48123}, {48278, 48326}
X(48406) = reflection of X(i) in X(j) for these {i,j}: {3837, 23815}, {14838, 19947}, {21051, 3837}, {47993, 48054}, {48002, 48059}
X(48406) = X(561)-Ceva conjugate of X(1086)
X(48406) = X(2209)-isoconjugate of X(35572)
X(48406) = X(i)-Dao conjugate of X(j) for these (i, j): (3248, 31), (16604, 4595), (34832, 100)
X(48406) = crossdifference of every pair of points on line {2220, 21793}
X(48406) = barycentric product X(i)*X(j) for these {i,j}: {330, 21128}, {514, 24165}, {523, 16710}, {693, 16604}, {20899, 43931}, {21757, 40495}
X(48406) = barycentric quotient X(i)/X(j) for these {i,j}: {330, 35572}, {16604, 100}, {16710, 99}, {20899, 36863}, {21128, 192}, {21757, 692}, {21827, 4557}, {22378, 906}, {24165, 190}, {34832, 4595}
X(48406) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4728, 23738, 48265}, {4801, 47819, 1491}, {23765, 48184, 4391}, {47812, 48334, 2533}, {48167, 48323, 21301}


X(48407) = X(512)X(4824)∩X(514)X(1734)

Barycentrics    (b - c)*(b + c)*(2*a*b + 2*a*c + b*c) : :
X(48407) = 3 X[4041] - 2 X[4807], 3 X[4761] - 4 X[4807], X[4761] + 2 X[47934], 2 X[4807] + 3 X[47934], 5 X[1577] - 6 X[14431], 3 X[1577] - 4 X[21051], 5 X[4705] - 3 X[14431], 3 X[4705] - 2 X[21051], 9 X[14431] - 10 X[21051], 4 X[650] - 3 X[47818], 2 X[693] - 3 X[47816], 3 X[47816] - 4 X[48012], 3 X[1491] - 2 X[23815], 3 X[4978] - 4 X[23815], X[4367] - 3 X[4948], 2 X[4367] - 3 X[45671], 2 X[4401] - 3 X[31150], X[4801] - 3 X[48175], 2 X[48066] - 3 X[48175], 2 X[4823] - 3 X[47814], 2 X[6050] - 3 X[48210], 2 X[7662] - 3 X[47794], 2 X[14838] - 3 X[47825], X[17166] - 3 X[47825], 2 X[34958] - 3 X[47784], 2 X[47694] - 3 X[47817], 3 X[47817] - 4 X[48003], 3 X[47775] - 2 X[48058], 3 X[48176] - X[48301]

X(48407) lies on these lines: {512, 4824}, {514, 1734}, {522, 47959}, {523, 1577}, {650, 47818}, {661, 4151}, {693, 47816}, {784, 3762}, {812, 47948}, {830, 17494}, {900, 47949}, {1019, 4913}, {1491, 4978}, {2533, 4770}, {3004, 47716}, {3309, 47962}, {3667, 47942}, {3800, 4841}, {3907, 47683}, {4010, 48005}, {4040, 48000}, {4088, 23879}, {4122, 6367}, {4129, 4804}, {4160, 4560}, {4367, 4948}, {4401, 31150}, {4777, 47967}, {4801, 48066}, {4823, 47814}, {4926, 47957}, {4961, 48079}, {4983, 48002}, {6005, 47666}, {6050, 48210}, {7265, 48047}, {7662, 47794}, {8714, 47918}, {14349, 48010}, {14838, 17166}, {17072, 28147}, {21260, 48120}, {23875, 47698}, {29013, 47912}, {29047, 45746}, {29062, 48277}, {29186, 47926}, {29190, 48077}, {29302, 48023}, {34958, 47784}, {42325, 47969}, {47657, 47706}, {47694, 47817}, {47775, 48058}, {47905, 47932}, {47992, 48085}, {47996, 48081}, {47997, 48080}, {48030, 48273}, {48059, 48279}, {48099, 48339}, {48176, 48301}, {48284, 48322}, {48304, 48348}

X(48407) = midpoint of X(i) and X(j) for these {i,j}: {4041, 47934}, {47657, 47706}, {47905, 47932}
X(48407) = reflection of X(i) in X(j) for these {i,j}: {693, 48012}, {1019, 4913}, {1577, 4705}, {2533, 4770}, {3762, 4490}, {4010, 48005}, {4040, 48000}, {4170, 661}, {4761, 4041}, {4801, 48066}, {4804, 4129}, {4815, 47842}, {4905, 48017}, {4978, 1491}, {4983, 48002}, {7265, 48047}, {14349, 48010}, {17166, 14838}, {45671, 4948}, {47694, 48003}, {47710, 4808}, {47716, 3004}, {48080, 47997}, {48081, 47996}, {48085, 47992}, {48108, 48018}, {48120, 21260}, {48267, 47967}, {48273, 48030}, {48279, 48059}, {48304, 48348}, {48322, 48284}, {48339, 48099}
X(48407) = X(i)-isoconjugate of X(j) for these (i,j): {58, 6013}, {110, 10013}
X(48407) = X(i)-Dao conjugate of X(j) for these (i, j): (10, 6013), (244, 10013)
X(48407) = crosspoint of X(3952) and X(5936)
X(48407) = crossdifference of every pair of points on line {1333, 2280}
X(48407) = barycentric product X(i)*X(j) for these {i,j}: {10, 47666}, {321, 6005}, {523, 4687}, {1577, 17018}, {8655, 27801}
X(48407) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 6013}, {661, 10013}, {4024, 46772}, {4687, 99}, {6005, 81}, {8655, 1333}, {8672, 17110}, {16878, 4565}, {17018, 662}, {39673, 4556}, {47666, 86}
X(48407) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 48012, 47816}, {4801, 48175, 48066}, {17166, 47825, 14838}, {47694, 48003, 47817}


X(48408) = X(2)X(2977)∩X(514)X(1734)

Barycentrics    (b - c)*(a^3 + a^2*b - a*b^2 + b^3 + a^2*c - 3*a*b*c - a*c^2 + c^3) : :
X(48408) = 3 X[2] - 4 X[2977], 4 X[659] - 3 X[44433], 2 X[659] - 3 X[47892], 3 X[44433] - 2 X[47695], 2 X[47694] - 3 X[48250], X[47695] - 3 X[47892], 4 X[47890] - 3 X[48250], 4 X[650] - 3 X[47797], 2 X[47691] - 3 X[47797], 2 X[676] - 3 X[47884], 2 X[693] - 3 X[47809], 3 X[47809] - 4 X[48062], 4 X[1491] - 3 X[48159], 2 X[47652] - 3 X[48159], 3 X[1635] - 2 X[4458], 3 X[1635] - X[47705], 2 X[3004] - 3 X[47825], X[47688] - 3 X[47825], 2 X[3700] - 3 X[48171], 2 X[3716] - 3 X[6546], 2 X[3776] - 3 X[47828], 4 X[3837] - 3 X[47871], 2 X[4010] - 3 X[30565], 3 X[30565] - 4 X[48056], 3 X[4453] - 4 X[9508], 3 X[4453] - 2 X[48326], 3 X[4789] - 2 X[48120], 2 X[4874] - 3 X[47885], 3 X[31131] - 2 X[46403], 3 X[6545] - 4 X[25380], 2 X[6590] - 3 X[48236], 2 X[7662] - 3 X[47771], 4 X[11068] - 3 X[47804], 2 X[47123] - 3 X[47804], 3 X[14430] - 4 X[32212], 4 X[17069] - 3 X[48241], 2 X[21104] - 3 X[47824], 2 X[21146] - 3 X[48252], 2 X[21185] - 3 X[47815], 5 X[26777] - 3 X[48203], X[26824] - 3 X[48208], 5 X[26985] - 6 X[47807], 7 X[27115] - 6 X[47799], 6 X[28602] - 5 X[30795], 3 X[30580] - 2 X[48296], 3 X[31150] - X[47692], 4 X[31286] - 3 X[47887], 2 X[47131] - 3 X[47798], 2 X[47132] - 3 X[48231], X[47650] - 3 X[47808], 3 X[47808] - 2 X[48089], X[47651] - 3 X[48175], 2 X[48007] - 3 X[48175], 3 X[47775] - 2 X[47998], 3 X[47781] - 2 X[47961], 3 X[47791] - 2 X[48134], 2 X[48090] - 3 X[48185], 2 X[48098] - 3 X[48235], 3 X[48161] - 2 X[48349]

X(48408) lies on these lines: {2, 2977}, {8, 29240}, {10, 47680}, {23, 385}, {100, 13397}, {105, 15344}, {513, 47663}, {514, 1734}, {522, 47700}, {650, 47691}, {676, 47884}, {693, 47809}, {812, 4088}, {824, 48118}, {891, 3904}, {900, 20058}, {905, 47720}, {1491, 47652}, {1635, 4458}, {2526, 47686}, {2804, 13266}, {2826, 38665}, {3004, 47688}, {3667, 48078}, {3700, 48171}, {3716, 6546}, {3776, 47828}, {3837, 47871}, {4010, 30565}, {4369, 47704}, {4382, 4522}, {4453, 4802}, {4468, 48080}, {4490, 29025}, {4498, 23877}, {4560, 29288}, {4705, 29098}, {4730, 29102}, {4762, 47690}, {4777, 48097}, {4778, 48145}, {4789, 48120}, {4808, 29070}, {4809, 28151}, {4810, 18004}, {4818, 47923}, {4874, 47885}, {4895, 5592}, {4913, 16892}, {6084, 20344}, {6545, 25380}, {6590, 48236}, {7662, 47771}, {11068, 47123}, {13246, 28155}, {14077, 47728}, {14430, 32212}, {14838, 47716}, {17069, 48241}, {17166, 45695}, {20295, 48047}, {20999, 44428}, {21104, 47824}, {21115, 28191}, {21146, 48252}, {21185, 47815}, {21385, 23887}, {23731, 47992}, {23882, 47707}, {25259, 48088}, {26777, 48203}, {26824, 48208}, {26985, 47807}, {27115, 47799}, {28175, 47653}, {28179, 46915}, {28602, 30795}, {28859, 47909}, {28882, 48023}, {29118, 47918}, {29158, 47959}, {29302, 48272}, {29328, 44449}, {29362, 47687}, {30580, 48296}, {31150, 47692}, {31286, 47887}, {47131, 47798}, {47132, 48231}, {47650, 47808}, {47651, 48007}, {47664, 47689}, {47696, 48095}, {47699, 47962}, {47701, 48000}, {47708, 47965}, {47712, 48003}, {47727, 48284}, {47775, 47998}, {47781, 47961}, {47791, 48134}, {47938, 47996}, {47944, 48002}, {47958, 48010}, {48090, 48185}, {48098, 48235}, {48161, 48349}, {48290, 48304}

X(48408) = midpoint of X(i) and X(j) for these {i,j}: {47664, 47689}, {47700, 47932}, {47934, 48146}
X(48408) = reflection of X(i) in X(j) for these {i,j}: {693, 48062}, {4010, 48056}, {4382, 4522}, {4810, 18004}, {4895, 5592}, {16892, 4913}, {20295, 48047}, {23731, 47992}, {23770, 2977}, {25259, 48088}, {44433, 47892}, {47123, 11068}, {47650, 48089}, {47651, 48007}, {47652, 1491}, {47660, 48103}, {47680, 10}, {47686, 2526}, {47688, 3004}, {47691, 650}, {47694, 47890}, {47695, 659}, {47696, 48095}, {47699, 47962}, {47701, 48000}, {47704, 4369}, {47705, 4458}, {47708, 47965}, {47712, 48003}, {47716, 14838}, {47720, 905}, {47727, 48284}, {47923, 4818}, {47938, 47996}, {47944, 48002}, {47958, 48010}, {47973, 48017}, {48080, 4468}, {48108, 48069}, {48304, 48290}, {48326, 9508}
X(48408) = anticomplement of X(23770)
X(48408) = anticomplement of the isotomic conjugate of X(35574)
X(48408) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2991, 150}, {35574, 6327}
X(48408) = X(35574)-Ceva conjugate of X(2)
X(48408) = crosssum of X(667) and X(20752)
X(48408) = crossdifference of every pair of points on line {39, 2280}
X(48408) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 47691, 47797}, {659, 47695, 44433}, {693, 48062, 47809}, {1491, 47652, 48159}, {1635, 47705, 4458}, {2977, 23770, 2}, {4010, 48056, 30565}, {9508, 48326, 4453}, {11068, 47123, 47804}, {47650, 47808, 48089}, {47651, 48175, 48007}, {47688, 47825, 3004}, {47694, 47890, 48250}, {47695, 47892, 659}


X(48409) = X(514)X(1734)∩X(522)X(4170)

Barycentrics    (b - c)*(2*a*b^2 + 2*a*b*c + b^2*c + 2*a*c^2 + b*c^2) : :
X(48409) = X[4761] - 4 X[48017], 4 X[650] - 3 X[47817], 2 X[667] - 3 X[45671], 3 X[1491] - 2 X[21260], 4 X[1491] - 3 X[47816], 3 X[1577] - 4 X[21260], 2 X[1577] - 3 X[47816], 8 X[21260] - 9 X[47816], 3 X[4560] - X[31291], 2 X[4129] - 3 X[47810], 3 X[47810] - X[48264], X[4391] - 3 X[48175], 2 X[48012] - 3 X[48175], 2 X[4791] - 3 X[47814], 2 X[4823] - 3 X[44429], 2 X[4874] - 3 X[47888], 2 X[7662] - 3 X[47795], 4 X[14838] - 3 X[47818], 2 X[47694] - 3 X[47818], 4 X[19947] - 3 X[47889], 2 X[20517] - 3 X[47886], X[21301] - 3 X[48157], 2 X[23795] + X[47917], 5 X[31251] - 6 X[45323], 4 X[31288] - 3 X[48234], 3 X[44550] - 2 X[48343], 3 X[47775] - 2 X[48004], 3 X[47825] - 2 X[48003]

X(48409) lies on these lines: {514, 1734}, {522, 4170}, {523, 2530}, {650, 47817}, {661, 8714}, {667, 45671}, {693, 48066}, {784, 1491}, {812, 48086}, {824, 48272}, {830, 4560}, {900, 4983}, {2526, 23882}, {3004, 47712}, {3667, 48081}, {3762, 4705}, {3960, 17166}, {4010, 48059}, {4063, 4913}, {4129, 47810}, {4151, 48131}, {4160, 17496}, {4391, 48012}, {4401, 47697}, {4777, 14288}, {4791, 47814}, {4818, 23877}, {4823, 44429}, {4824, 6372}, {4874, 47888}, {4926, 48093}, {4976, 28481}, {4985, 47842}, {4992, 28183}, {6002, 47948}, {7662, 47795}, {8678, 48321}, {14838, 47694}, {15309, 47945}, {19947, 47889}, {20295, 48052}, {20517, 47886}, {21124, 23887}, {21301, 48157}, {23789, 47672}, {23795, 47917}, {23815, 48120}, {23879, 48278}, {28187, 30592}, {29013, 48023}, {29021, 45746}, {29051, 47683}, {29062, 48077}, {29098, 47968}, {29142, 47679}, {29148, 47912}, {29158, 47958}, {29190, 48277}, {29302, 48122}, {29358, 47677}, {31251, 45323}, {31288, 48234}, {44550, 48343}, {47657, 47718}, {47775, 48004}, {47825, 48003}, {47932, 48116}, {47942, 47996}, {47947, 47992}, {47949, 48002}, {47959, 48010}, {47970, 48000}, {48005, 48265}, {48030, 48267}, {48054, 48080}, {48136, 48339}, {48150, 48284}

X(48409) = midpoint of X(i) and X(j) for these {i,j}: {47657, 47718}, {47932, 48116}, {47934, 48151}
X(48409) = reflection of X(i) in X(j) for these {i,j}: {693, 48066}, {1577, 1491}, {1734, 48017}, {3762, 4705}, {4010, 48059}, {4063, 4913}, {4170, 14349}, {4391, 48012}, {4761, 1734}, {4978, 2530}, {4985, 47842}, {17166, 3960}, {20295, 48052}, {47672, 23789}, {47694, 14838}, {47697, 4401}, {47712, 3004}, {47942, 47996}, {47947, 47992}, {47949, 48002}, {47959, 48010}, {47970, 48000}, {48080, 48054}, {48108, 48075}, {48120, 23815}, {48150, 48284}, {48264, 4129}, {48265, 48005}, {48267, 48030}, {48273, 48100}, {48339, 48136}
X(48409) = crossdifference of every pair of points on line {2220, 2280}
X(48409) = barycentric product X(i)*X(j) for these {i,j}: {514, 4981}, {693, 25092}
X(48409) = barycentric quotient X(i)/X(j) for these {i,j}: {4981, 190}, {25092, 100}
X(48409) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1491, 1577, 47816}, {4391, 48175, 48012}, {14838, 47694, 47818}, {47810, 48264, 4129}


X(48410) = X(513)X(4560)∩X(514)X(1734)

Barycentrics    (b - c)*(2*a*b^2 + a*b*c + b^2*c + 2*a*c^2 + b*c^2) : :
X(48410) = 3 X[1734] - 2 X[4807], 4 X[650] - 3 X[47815], 3 X[693] - 4 X[23815], 2 X[693] - 3 X[47819], 3 X[2530] - 2 X[23815], 4 X[2530] - 3 X[47819], 8 X[23815] - 9 X[47819], 4 X[905] - 3 X[47820], 2 X[47694] - 3 X[47820], 3 X[1491] - 2 X[21051], 4 X[1491] - 3 X[47814], 3 X[4391] - 4 X[21051], 2 X[4391] - 3 X[47814], 8 X[21051] - 9 X[47814], 2 X[1577] - 3 X[44429], 3 X[44429] - 4 X[48066], 2 X[4142] - 3 X[47886], 2 X[4367] - 3 X[44550], 2 X[4401] - 3 X[45671], X[4462] - 3 X[48175], 2 X[4705] - 3 X[48175], 3 X[4776] - 4 X[48059], 3 X[4776] - 2 X[48267], 2 X[4791] - 3 X[47816], 2 X[4874] - 3 X[47893], 4 X[6050] - 3 X[47805], 2 X[7662] - 3 X[47796], 4 X[14838] - 3 X[47804], 2 X[20317] - 3 X[48193], 2 X[21185] - 3 X[47797], 5 X[31209] - 6 X[47888], 2 X[47711] - 3 X[48187], 2 X[47712] - 3 X[48174], 3 X[47775] - 2 X[47966], 3 X[47825] - 2 X[47965]

X(48410) lies on these lines: {513, 4560}, {514, 1734}, {522, 48131}, {523, 3777}, {650, 47815}, {667, 47697}, {693, 784}, {812, 48122}, {824, 48278}, {826, 47677}, {830, 48321}, {900, 48123}, {905, 47694}, {1491, 4391}, {1577, 44429}, {2526, 21301}, {3004, 6362}, {3667, 4822}, {3669, 17166}, {3762, 48012}, {3810, 4818}, {3835, 48264}, {3900, 48298}, {4010, 48100}, {4142, 47886}, {4151, 48335}, {4367, 44550}, {4401, 45671}, {4462, 4705}, {4498, 4913}, {4776, 48059}, {4777, 48137}, {4791, 47816}, {4824, 22320}, {4874, 47893}, {4926, 48129}, {6002, 48023}, {6004, 48288}, {6050, 47805}, {6372, 47666}, {7662, 47796}, {8678, 17496}, {8714, 14349}, {14838, 47804}, {16892, 23877}, {20295, 48092}, {20317, 48193}, {21185, 47797}, {21196, 28487}, {23882, 46403}, {29013, 48086}, {29025, 47968}, {29037, 48077}, {29070, 47685}, {29098, 47651}, {29118, 47958}, {29142, 45746}, {29148, 47948}, {29150, 48079}, {29186, 47683}, {31209, 47888}, {47711, 48187}, {47712, 48174}, {47775, 47966}, {47825, 47965}, {47906, 47996}, {47911, 47992}, {47913, 48002}, {47918, 48010}, {47929, 48000}, {48030, 48265}, {48111, 48284}, {48304, 48346}, {48322, 48325}, {48339, 48348}

X(48410) = midpoint of X(23738) and X(47934)
X(48410) = reflection of X(i) in X(j) for these {i,j}: {693, 2530}, {1577, 48066}, {3762, 48012}, {4010, 48100}, {4041, 48017}, {4391, 1491}, {4462, 4705}, {4498, 4913}, {4761, 48018}, {4801, 3777}, {17166, 3669}, {20295, 48092}, {21124, 4818}, {21301, 2526}, {47694, 905}, {47697, 667}, {47708, 3004}, {47906, 47996}, {47911, 47992}, {47913, 48002}, {47918, 48010}, {47929, 48000}, {48080, 14349}, {48108, 4905}, {48111, 48284}, {48264, 3835}, {48265, 48030}, {48267, 48059}, {48279, 48137}, {48304, 48346}, {48322, 48325}, {48339, 48348}
X(48410) = X(1918)-isoconjugate of X(35565)
X(48410) = X(34021)-Dao conjugate of X(35565)
X(48410) = crossdifference of every pair of points on line {2205, 2280}
X(48410) = barycentric product X(274)*X(2512)
X(48410) = barycentric quotient X(i)/X(j) for these {i,j}: {274, 35565}, {2512, 37}
X(48410) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 2530, 47819}, {905, 47694, 47820}, {1491, 4391, 47814}, {1577, 48066, 44429}, {4462, 48175, 4705}, {48059, 48267, 4776}


X(48411) = 73RD HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10 - 3*a^8*c^2 + 3*a^6*b^2*c^2 + 3*a^4*b^4*c^2 - 3*b^8*c^2 + 2*a^6*c^4 + 3*a^4*b^2*c^4 + 6*a^2*b^4*c^4 + 2*b^6*c^4 + 2*a^4*c^6 + 2*b^4*c^6 - 3*a^2*c^8 - 3*b^2*c^8 + c^10 : :
X(48411) = X[3] + 2 X[5576], 2 X[5] + X[14118], 4 X[140] - X[7512], 2 X[140] + X[33332], 5 X[632] - 2 X[34004], 5 X[1656] - 2 X[13160], 5 X[1656] + X[14130], 7 X[3090] - X[34007], 7 X[3526] - 4 X[7568], 7 X[3526] - X[13564], 7 X[3526] + 2 X[15559], 8 X[3628] + X[14865], 13 X[5079] + 2 X[34005], X[7512] + 2 X[33332], 4 X[7568] - X[13564], 2 X[7568] + X[15559], 2 X[13160] + X[14130], X[13564] + 2 X[15559], 5 X[15694] - X[34006], 4 X[34002] - 13 X[46219], 4 X[34002] - X[47748], 13 X[46219] - X[47748], 2 X[1209] + X[37472]

See Antreas Hatzipolakis and Peter Moses euclid 5015.

X(48411) lies on these lines: {2, 3}, {66, 38064}, {542, 11597}, {567, 21243}, {570, 1989}, {1209, 37472}, {1352, 9703}, {3580, 15038}, {3589, 45016}, {5655, 21650}, {5892, 15061}, {9220, 14806}, {10264, 40640}, {11562, 20126}, {12824, 34128}, {13434, 34826}, {13561, 43651}, {14389, 15087}, {14805, 18474}, {15037, 37649}, {15047, 26879}, {20299, 37471}, {23329, 40280}, {34319, 46267}, {35283, 45082}

X(48411) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14787, 5055}, {2, 18281, 5054}, {5, 140, 44802}, {140, 5133, 2070}, {140, 33332, 7512}, {381, 2070, 13490}, {381, 5054, 14070}, {1656, 9818, 10254}, {1656, 14130, 13160}, {3526, 13564, 7568}, {3545, 18568, 381}, {5054, 34609, 3}, {5054, 45735, 34477}, {5133, 13490, 381}, {6639, 7404, 3851}, {6640, 14786, 5070}, {7527, 46029, 31726}, {7568, 15559, 13564}, {14118, 44802, 7512}, {15246, 44802, 186}, {15699, 34331, 2}, {15765, 18585, 7488}, {35921, 39504, 7574}

leftri

Odd minor triangle centers: X(48412)-X(48438)

rightri

A triangle center P = p(a,b,c) : q(a,b,c) : r(a,b,c) is even if p(a,b,c) = p(a,c,b) and odd if p(a,b,c) = - p(a,c,b); or equivalently, p(a,b,c) = (b - c) u(a,b,c), where u(a,b,c) : u(b,c,a) : u(c,a,b) is even. These definitions follow C. Kimberling, "Functional equations associated with triangle geometry," Aequationes Mathematicae 45 (1993) 127-152. The triangle center P is minor if p(a,b,c) is invariant of a. (This definition is not closely related to "major" triangle center, defined elsewhere as a center that can be expressed in barycentrics m(A,B,C) : m(B,C,A) : m(C,A,B) such that m(A,B,C) is invariant of B and C.)

The odd minor centers in this section are all polynomial centers of degree 3, with first barycentric given by the form (b - c)(h*(b^2 + c^2) + k* b c), where h and k are real numbers, not both zero.

The appearance of {h,k,i} in the following list means that X(i) = (b - c)(h*(b^2 + c^2) + k* b c)::

{0,1}, 693}
{1,-2}, 6545}
{1,-1}, 3776}
{1,0}, 16892}
{1,1}, 824}
{1,2}, 4024}
{1,3}, 4500}
{2,1}, 47677}
{2,3}, 47665}
{1,-6}, 48412}
{1,-5}, 48413}
{1,-4}, 48414}
{1,-3}, 48415}
{1,4}, 48416}
{1,5}, 48417}
{1,6}, 48418}
{1,7}, 48419}
{2,-5}, 48420}
{2,-3}, 48421}
{2,-1}, 48422}
{2,5}, 48423}
{2,7}, 48424}
{3,-2}, 48425}
{3,-1}, 48426}
{3,1}, 48427}
{3,2}, 48428}
{3,4}, 48429}
{3,5}, 48430}
{3,7}, 48431}
{4,-3}, 48432}
{4,-1}, 48433}
{4,1}, 48434}
{4,3}, 48435}
{4,5}, 48436}
{4,7}, 48437}
{5,6}, 48438}


X(48412) = X(321)X(693)∩X(514)X(27138)

Barycentrics    (b - c)*(b^2 - 6*b*c + c^2) : :
X(48412) = 5 X[693] + 2 X[3776], 8 X[693] - X[4024], 9 X[693] - 2 X[4500], 4 X[693] + 3 X[6545], 6 X[693] + X[16892], 15 X[693] - X[47665], 13 X[693] + X[47677], 16 X[3776] + 5 X[4024], 9 X[3776] + 5 X[4500], 8 X[3776] - 15 X[6545], 12 X[3776] - 5 X[16892], 6 X[3776] + X[47665], 26 X[3776] - 5 X[47677], 9 X[4024] - 16 X[4500], X[4024] + 6 X[6545], 3 X[4024] + 4 X[16892], 15 X[4024] - 8 X[47665], 13 X[4024] + 8 X[47677], 8 X[4500] + 27 X[6545], 4 X[4500] + 3 X[16892], 10 X[4500] - 3 X[47665], 26 X[4500] + 9 X[47677], 9 X[6545] - 2 X[16892], 45 X[6545] + 4 X[47665], 39 X[6545] - 4 X[47677], 5 X[16892] + 2 X[47665], 13 X[16892] - 6 X[47677], 13 X[47665] + 15 X[47677], 16 X[2487] - 9 X[14435], 6 X[3004] + X[47670], 4 X[3798] + 3 X[4382], 16 X[3798] - 9 X[4984], 2 X[3798] - 9 X[21183], 4 X[4382] + 3 X[4984], X[4382] + 6 X[21183], X[4984] - 8 X[21183], 4 X[3835] + 3 X[21116], 3 X[4120] + 4 X[21104], 9 X[4120] - 2 X[48112], 6 X[21104] + X[48112], 9 X[4379] - 2 X[48060], 9 X[4728] - 2 X[48046], 16 X[4885] - 9 X[6544], 6 X[4927] + X[47672], 3 X[6546] - 10 X[26985], 9 X[6548] - 2 X[21196], 9 X[14475] - 2 X[17494], 6 X[21204] + X[26824], 4 X[21212] + 3 X[47869], X[23731] + 6 X[47780], 9 X[31147] - 2 X[48034], 6 X[43067] + X[47937], 6 X[44435] + X[47671], X[47650] + 6 X[47779], X[47704] + 6 X[48184], 6 X[47871] + X[48101], 9 X[47874] - 2 X[48124], 6 X[47891] + X[48114], X[47943] + 6 X[48238]

X(48412) lies on these lines: {321, 693}, {514, 27138}, {2487, 14435}, {3004, 47670}, {3798, 4382}, {3835, 21116}, {4120, 21104}, {4379, 48060}, {4728, 48046}, {4885, 6544}, {4927, 47672}, {6546, 26985}, {6548, 21196}, {14475, 17494}, {21204, 26824}, {21212, 47869}, {23731, 47780}, {31147, 48034}, {43067, 47937}, {44435, 47671}, {47650, 47779}, {47704, 48184}, {47871, 48101}, {47874, 48124}, {47891, 48114}, {47943, 48238}

X(48412) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 6545, 4024}, {3776, 47665, 16892}


X(48413) = X(321)X(693)∩X(514)X(1639)

Barycentrics    (b - c)*(b^2 - 5*b*c + c^2) : :
X(48413) = 2 X[693] + X[3776], 7 X[693] - X[4024], 4 X[693] - X[4500], 5 X[693] + X[16892], 13 X[693] - X[47665], 11 X[693] + X[47677], 7 X[3776] + 2 X[4024], 2 X[3776] + X[4500], 5 X[3776] - 2 X[16892], 13 X[3776] + 2 X[47665], 11 X[3776] - 2 X[47677], 4 X[4024] - 7 X[4500], X[4024] + 7 X[6545], 5 X[4024] + 7 X[16892], 13 X[4024] - 7 X[47665], 11 X[4024] + 7 X[47677], X[4500] + 4 X[6545], 5 X[4500] + 4 X[16892], 13 X[4500] - 4 X[47665], 11 X[4500] + 4 X[47677], 5 X[6545] - X[16892], 13 X[6545] + X[47665], 11 X[6545] - X[47677], 13 X[16892] + 5 X[47665], 11 X[16892] - 5 X[47677], 11 X[47665] + 13 X[47677], 3 X[4927] - X[47756], 3 X[45320] - X[47770], 2 X[47770] - 3 X[47879], X[4786] - 5 X[21183], 3 X[4786] - 5 X[47758], 3 X[21183] - X[47758], 3 X[4728] - X[47769], 3 X[6548] + X[47869], 3 X[6548] - X[47886], 3 X[14475] - X[31150], 2 X[21104] + X[48270], 2 X[21212] + X[48125], 5 X[24924] + X[47650]

X(48413) lies on these lines: {321, 693}, {514, 1639}, {812, 4786}, {4379, 28882}, {4728, 28851}, {4762, 21204}, {4776, 21116}, {4785, 47891}, {4885, 10196}, {4951, 48326}, {4977, 48202}, {4978, 30910}, {6009, 45313}, {6084, 47779}, {6548, 47869}, {14475, 31150}, {21104, 48270}, {21115, 47790}, {21212, 48125}, {21297, 28867}, {24924, 47650}, {28147, 48178}, {28175, 48201}, {28859, 47780}, {28871, 47786}, {28886, 31147}, {28890, 47787}, {45677, 47778}, {47672, 47781}, {47887, 48170}

X(48413) = midpoint of X(i) and X(j) for these {i,j}: {693, 6545}, {4379, 47871}, {4776, 21116}, {4951, 48326}, {21115, 47790}, {47672, 47781}, {47869, 47886}, {47887, 48170}
X(48413) = reflection of X(i) in X(j) for these {i,j}: {3776, 6545}, {10196, 4885}, {47778, 45677}, {47879, 45320}, {47882, 21204}
X(48413) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 3776, 4500}, {6548, 47869, 47886}


X(48414) = X(321)X(693)∩X(514)X(17266)

Barycentrics    (b - c)*(b^2 - 4*b*c + c^2) : :
X(48414) = 3 X[693] + 2 X[3776], 6 X[693] - X[4024], 7 X[693] - 2 X[4500], 2 X[693] + 3 X[6545], 4 X[693] + X[16892], 11 X[693] - X[47665], 9 X[693] + X[47677], 4 X[3776] + X[4024], 7 X[3776] + 3 X[4500], 4 X[3776] - 9 X[6545], 8 X[3776] - 3 X[16892], 22 X[3776] + 3 X[47665], 6 X[3776] - X[47677], 7 X[4024] - 12 X[4500], X[4024] + 9 X[6545], 2 X[4024] + 3 X[16892], 11 X[4024] - 6 X[47665], 3 X[4024] + 2 X[47677], 4 X[4500] + 21 X[6545], 8 X[4500] + 7 X[16892], 22 X[4500] - 7 X[47665], 18 X[4500] + 7 X[47677], 6 X[6545] - X[16892], 33 X[6545] + 2 X[47665], 27 X[6545] - 2 X[47677], 11 X[16892] + 4 X[47665], 9 X[16892] - 4 X[47677], 9 X[47665] + 11 X[47677], X[649] - 6 X[21183], 4 X[650] - 9 X[14475], X[661] - 6 X[4927], 2 X[661] + 3 X[21116], 4 X[4927] + X[21116], 4 X[676] + X[48115], 6 X[1638] - X[47932], 6 X[3004] - X[47669], 4 X[3004] + X[47671], 2 X[47669] + 3 X[47671], 4 X[3676] + X[4382], 8 X[3676] - 3 X[4750], 2 X[4382] + 3 X[4750], 2 X[3700] + 3 X[21115], 4 X[3837] + X[47704], X[4088] - 6 X[48184], 3 X[4120] + 2 X[47676], 2 X[4369] + 3 X[47871], 6 X[4379] - X[48101], 2 X[4458] + 3 X[48170], 9 X[4728] - 4 X[14321], 3 X[4728] + 2 X[21104], 6 X[4728] - X[48082], 2 X[14321] + 3 X[21104], 8 X[14321] - 3 X[48082], 4 X[21104] + X[48082], 2 X[4841] + 3 X[47672], 8 X[4885] - 3 X[6546], X[4979] - 6 X[47891], X[4988] - 6 X[44435], 3 X[4988] + 2 X[47674], 9 X[44435] + X[47674], 9 X[6548] - 4 X[21212], 9 X[6548] + X[26824], 4 X[21212] + X[26824], X[17494] - 6 X[21204], 2 X[21196] + 3 X[47869], 2 X[23729] + 3 X[31148], X[23731] + 4 X[43067], 2 X[23770] + 3 X[47812], 4 X[23813] + X[47971], 16 X[31182] - 21 X[31207], 4 X[31286] + X[47650], 4 X[44314] + X[48304], 6 X[45320] - X[48094], X[47663] - 6 X[47779], X[47664] - 6 X[47882], X[47701] + 4 X[48098], 6 X[47754] - X[48277], 6 X[47756] - X[47917], 6 X[47757] - X[47926], 6 X[47787] - X[48117], 6 X[47788] - X[48130], 6 X[47789] - X[48138], 6 X[47833] - X[48102], 3 X[47877] + 2 X[48127], 3 X[47886] + 2 X[48125], 3 X[47887] + 2 X[48089], X[47933] - 6 X[48179], X[47934] - 6 X[48178], X[48105] - 6 X[48220]

X(48414) lies on these lines: {321, 693}, {514, 17266}, {649, 21183}, {650, 14475}, {661, 4927}, {676, 48115}, {1638, 47932}, {3004, 47669}, {3676, 4382}, {3700, 21115}, {3837, 47704}, {4088, 48184}, {4120, 47676}, {4369, 47871}, {4379, 48101}, {4458, 48170}, {4728, 14321}, {4841, 47672}, {4885, 6546}, {4979, 47891}, {4988, 44435}, {6084, 24924}, {6548, 21212}, {15283, 21132}, {17494, 21204}, {21196, 47869}, {23729, 31148}, {23731, 43067}, {23770, 47812}, {23813, 47971}, {26798, 28855}, {31182, 31207}, {31286, 47650}, {44314, 48304}, {45320, 48094}, {47663, 47779}, {47664, 47882}, {47701, 48098}, {47754, 48277}, {47756, 47917}, {47757, 47926}, {47787, 48117}, {47788, 48130}, {47789, 48138}, {47833, 48102}, {47877, 48127}, {47886, 48125}, {47887, 48089}, {47933, 48179}, {47934, 48178}, {48105, 48220}

X(48414) = barycentric product X(514)*X(7263)
X(48414) = barycentric quotient X(7263)/X(190)
X(48414) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 3776, 4024}, {693, 6545, 16892}, {3676, 4382, 4750}, {3776, 4024, 16892}, {4024, 6545, 3776}, {4728, 21104, 48082}, {6548, 26824, 21212}


X(48415) = X(321)X(693)∩X(514)X(4521)

Barycentrics    (b - c)*(b^2 - 3*b*c + c^2) : :
X(48415) = 5 X[693] - X[4024], 3 X[693] - X[4500], X[693] + 3 X[6545], 3 X[693] + X[16892], 9 X[693] - X[47665], 7 X[693] + X[47677], 5 X[3776] + X[4024], 3 X[3776] + X[4500], X[3776] - 3 X[6545], 3 X[3776] - X[16892], 9 X[3776] + X[47665], 7 X[3776] - X[47677], 3 X[4024] - 5 X[4500], X[4024] + 15 X[6545], 3 X[4024] + 5 X[16892], 9 X[4024] - 5 X[47665], 7 X[4024] + 5 X[47677], X[4500] + 9 X[6545], 3 X[4500] - X[47665], 7 X[4500] + 3 X[47677], 9 X[6545] - X[16892], 27 X[6545] + X[47665], 21 X[6545] - X[47677], 3 X[16892] + X[47665], 7 X[16892] - 3 X[47677], 7 X[47665] + 9 X[47677], 2 X[4521] - 3 X[45678], X[649] + 3 X[47871], X[650] - 3 X[21204], 3 X[3676] - X[3798], 3 X[1635] + X[47650], 3 X[1638] - X[48008], X[3835] - 3 X[4927], 3 X[3835] - X[48046], 3 X[4927] + X[21104], 9 X[4927] - X[48046], 3 X[21104] + X[48046], X[4369] - 3 X[21183], 5 X[4369] - 3 X[47768], 3 X[4369] - X[48060], 5 X[21183] - X[47768], 9 X[21183] - X[48060], 9 X[47768] - 5 X[48060], 3 X[4379] + X[47652], 9 X[4379] - X[48138], 3 X[47652] + X[48138], X[4382] + 3 X[4453], X[4468] - 3 X[4928], X[4522] - 3 X[48184], 3 X[48184] + X[48326], 3 X[4728] + X[47676], 9 X[4728] - X[48112], 3 X[4728] - X[48270], 3 X[47676] + X[48112], X[48112] - 3 X[48270], 3 X[4789] + X[47923], X[4932] - 3 X[47891], X[23729] + 3 X[47891], 9 X[6548] - X[17494], 3 X[6548] - X[47882], X[17494] - 3 X[47882], 3 X[7192] + X[47937], 3 X[10196] - 5 X[31250], 3 X[14413] + X[47722], 9 X[14475] - 5 X[31209], 3 X[21115] + X[25259], 3 X[21116] + X[47666], X[21196] - 3 X[47754], 3 X[47754] + X[48125], 3 X[21297] + X[47971], 5 X[24924] - X[47663], 5 X[26798] - X[48076], X[26824] + 3 X[47886], 5 X[26985] - 3 X[47879], 5 X[26985] - X[48094], 3 X[47879] - X[48094], 3 X[43067] + X[47950], X[48034] - 3 X[48049], 9 X[44435] - X[47667], 3 X[44435] + X[47672], X[47667] + 3 X[47672], 7 X[31207] - 3 X[47892], 2 X[43061] - 3 X[45663], 3 X[44429] + X[47704], 9 X[45320] - X[48124], 3 X[45661] - X[48087], 3 X[45746] + X[47670], X[46403] + 3 X[47887], X[47686] + 3 X[47813], X[47691] + 3 X[47812], X[47703] + 3 X[48174], X[47705] + 3 X[47808], 3 X[47755] + X[48114], 3 X[47756] - X[47996], 3 X[47757] - X[48000], 3 X[47779] - X[47890], 3 X[47780] + X[47958], 3 X[47790] + X[47930], 3 X[47791] + X[47916], 3 X[47797] + X[48119], 3 X[47798] + X[48115], 3 X[47831] - X[48055], 3 X[47834] + X[47973], 3 X[47869] + X[48277], X[47968] + 3 X[48238], X[48009] - 3 X[48179], X[48010] - 3 X[48178], X[48056] - 3 X[48198], X[48126] + 3 X[48192], X[48142] + 3 X[48159], 3 X[48156] + X[48275]

X(48415) lies on these lines: {321, 693}, {514, 4521}, {649, 47871}, {650, 21204}, {812, 3676}, {1635, 47650}, {1638, 48008}, {2487, 6009}, {2786, 23813}, {3239, 28890}, {3835, 4927}, {4106, 28867}, {4369, 21183}, {4379, 47652}, {4382, 4453}, {4458, 48089}, {4468, 4928}, {4522, 48184}, {4728, 47676}, {4762, 21212}, {4789, 47923}, {4818, 48120}, {4932, 23729}, {4940, 28855}, {6084, 31286}, {6548, 17494}, {7192, 47937}, {10196, 31250}, {14077, 44314}, {14413, 47722}, {14475, 31209}, {21115, 25259}, {21116, 47666}, {21191, 23743}, {21196, 47754}, {21297, 47971}, {23770, 24720}, {23792, 24417}, {23815, 23877}, {24924, 47663}, {26798, 48076}, {26824, 47886}, {26985, 47879}, {28504, 48287}, {28859, 43067}, {28886, 48034}, {30765, 44435}, {31207, 47892}, {43061, 45663}, {44429, 47704}, {45320, 48124}, {45661, 48087}, {45746, 47670}, {46403, 47887}, {47686, 47813}, {47691, 47812}, {47703, 48174}, {47705, 47808}, {47755, 48114}, {47756, 47996}, {47757, 48000}, {47779, 47890}, {47780, 47958}, {47790, 47930}, {47791, 47916}, {47797, 48119}, {47798, 48115}, {47831, 48055}, {47834, 47973}, {47869, 48277}, {47968, 48238}, {48009, 48179}, {48010, 48178}, {48056, 48198}, {48126, 48192}, {48142, 48159}, {48156, 48275}

X(48415) = midpoint of X(i) and X(j) for these {i,j}: {693, 3776}, {3835, 21104}, {4458, 48089}, {4500, 16892}, {4522, 48326}, {4818, 48120}, {4932, 23729}, {21191, 23743}, {21196, 48125}, {23770, 24720}, {47676, 48270}
X(48415) = X(1110)-isoconjugate of X(25576)
X(48415) = X(i)-Dao conjugate of X(j) for these (i, j): (514, 25576), (4014, 9310)
X(48415) = crossdifference of every pair of points on line {2210, 3052}
X(48415) = barycentric product X(i)*X(j) for these {i,j}: {75, 23765}, {693, 17063}, {1111, 4499}, {4051, 24002}, {7199, 21951}, {23524, 40495}, {23989, 25577}
X(48415) = barycentric quotient X(i)/X(j) for these {i,j}: {1086, 25576}, {4051, 644}, {4499, 765}, {7240, 4579}, {17063, 100}, {21951, 1018}, {22172, 4557}, {23524, 692}, {23765, 1}, {25577, 1252}
X(48415) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 6545, 3776}, {693, 16892, 4500}, {3776, 4500, 16892}, {4728, 47676, 48270}, {4927, 21104, 3835}, {23729, 47891, 4932}, {26985, 48094, 47879}, {47754, 48125, 21196}, {48184, 48326, 4522}


X(48416) = X(321)X(693)∩X(514)X(4120)

Barycentrics    (b - c)*(b^2 + 4*b*c + c^2) : :
X(48416) = 5 X[693] - 2 X[3776], 2 X[693] + X[4024], X[693] + 2 X[4500], 4 X[693] - X[16892], 5 X[693] + X[47665], 7 X[693] - X[47677], 4 X[3776] + 5 X[4024], X[3776] + 5 X[4500], 4 X[3776] - 5 X[6545], 8 X[3776] - 5 X[16892], 2 X[3776] + X[47665], 14 X[3776] - 5 X[47677], X[4024] - 4 X[4500], 2 X[4024] + X[16892], 5 X[4024] - 2 X[47665], 7 X[4024] + 2 X[47677], 4 X[4500] + X[6545], 8 X[4500] + X[16892], 10 X[4500] - X[47665], 14 X[4500] + X[47677], 5 X[6545] + 2 X[47665], 7 X[6545] - 2 X[47677], 5 X[16892] + 4 X[47665], 7 X[16892] - 4 X[47677], 7 X[47665] + 5 X[47677], 3 X[4120] - 2 X[47769], 2 X[45343] + X[47869], X[47769] - 3 X[47790], 3 X[4379] - 2 X[47758], 3 X[4750] - 4 X[47758], 3 X[4728] - 2 X[47756], X[649] + 2 X[48268], 2 X[661] + X[47671], X[661] + 2 X[48274], X[47671] - 4 X[48274], 2 X[4931] + X[21116], 2 X[3004] + X[4838], 4 X[3239] - X[47926], 2 X[3700] + X[47672], 4 X[3700] - X[48082], 2 X[47672] + X[48082], 4 X[3835] - X[4988], 2 X[3835] + X[47656], X[4988] + 2 X[47656], 2 X[4010] + X[47703], X[4088] + 2 X[48120], 4 X[4106] - X[23731], 2 X[4106] + X[48275], X[23731] + 2 X[48275], 2 X[4122] + X[47704], X[4382] + 2 X[6590], 2 X[4382] + X[48101], 4 X[6590] - X[48101], X[4608] + 5 X[26798], 3 X[14475] - 4 X[45320], 3 X[14475] - 2 X[47886], 3 X[6546] - 4 X[47770], 2 X[47770] - 3 X[47874], 4 X[4765] - 7 X[31207], 2 X[4820] + X[47971], 4 X[4823] - X[21124], 2 X[4841] + X[47670], 4 X[4885] - X[48277], 2 X[4976] - 5 X[24924], 3 X[6544] - 2 X[31150], 3 X[6544] - 4 X[47879], 4 X[14321] - X[47917], 3 X[14435] - 4 X[45313], X[17161] - 4 X[21212], 2 X[21196] - 5 X[26985], 4 X[23813] - X[47958], 4 X[25666] - X[47661], 5 X[30835] - 2 X[45745], 2 X[43067] + X[48266], X[47674] + 2 X[47996], X[47675] + 2 X[48270], X[47701] - 4 X[48090], X[48076] + 2 X[48133], X[48078] + 2 X[48126], X[48094] + 2 X[48125], X[48114] + 2 X[48276], X[48141] + 2 X[48269]

X(48416) lies on these lines: {321, 693}, {514, 4120}, {522, 4379}, {523, 4728}, {649, 47789}, {661, 47671}, {812, 4789}, {900, 31148}, {918, 4931}, {1635, 47788}, {1638, 28183}, {2786, 47780}, {3004, 4838}, {3239, 47926}, {3700, 47672}, {3835, 4988}, {4010, 47703}, {4088, 4951}, {4106, 23731}, {4122, 47704}, {4382, 6590}, {4508, 48291}, {4608, 26798}, {4688, 4777}, {4762, 6546}, {4765, 31207}, {4785, 47791}, {4820, 47971}, {4823, 21124}, {4841, 47670}, {4885, 48277}, {4893, 47787}, {4928, 47782}, {4976, 24924}, {4984, 47762}, {6367, 9148}, {6544, 31150}, {10196, 17494}, {14321, 47917}, {14435, 45313}, {17161, 21212}, {21196, 26985}, {21204, 47894}, {23813, 47958}, {25666, 47661}, {27486, 47779}, {28161, 47757}, {28165, 47880}, {28187, 45677}, {28863, 47871}, {29078, 48238}, {30835, 45745}, {43067, 48266}, {45661, 47775}, {47674, 47996}, {47675, 48270}, {47701, 48090}, {47760, 47878}, {48076, 48133}, {48078, 48126}, {48094, 48125}, {48114, 48276}, {48141, 48269}

X(48416) = midpoint of X(i) and X(j) for these {i,j}: {4024, 6545}, {4951, 48120}, {21297, 47792}, {47656, 47781}, {47789, 48268}, {47869, 47870}
X(48416) = reflection of X(i) in X(j) for these {i,j}: {649, 47789}, {1635, 47788}, {4088, 4951}, {4120, 47790}, {4750, 4379}, {4893, 47787}, {4984, 47762}, {4988, 47781}, {6545, 693}, {6546, 47874}, {16892, 6545}, {17494, 10196}, {27486, 47779}, {31150, 47879}, {47775, 45661}, {47781, 3835}, {47782, 4928}, {47870, 45343}, {47878, 47760}, {47886, 45320}, {47894, 21204}
X(48416) = crossdifference of every pair of points on line {2210, 21747}
X(48416) = barycentric product X(514)*X(4665)
X(48416) = barycentric quotient X(4665)/X(190)
X(48416) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 48274, 47671}, {693, 4024, 16892}, {693, 4500, 4024}, {693, 47665, 3776}, {3700, 47672, 48082}, {3835, 47656, 4988}, {4106, 48275, 23731}, {4382, 6590, 48101}, {31150, 47879, 6544}, {45320, 47886, 14475}


X(48417) = X(321)X(693)∩X(514)X(4940)

Barycentrics    (b - c)*(b^2 + 5*b*c + c^2) : :
X(48417) = 3 X[693] - X[3776], 3 X[693] + X[4024], 7 X[693] - 3 X[6545], 5 X[693] - X[16892], 7 X[693] + X[47665], 9 X[693] - X[47677], X[3776] + 3 X[4500], 7 X[3776] - 9 X[6545], 5 X[3776] - 3 X[16892], 7 X[3776] + 3 X[47665], 3 X[3776] - X[47677], X[4024] - 3 X[4500], 7 X[4024] + 9 X[6545], 5 X[4024] + 3 X[16892], 7 X[4024] - 3 X[47665], 3 X[4024] + X[47677], 7 X[4500] + 3 X[6545], 5 X[4500] + X[16892], 7 X[4500] - X[47665], 9 X[4500] + X[47677], 15 X[6545] - 7 X[16892], 3 X[6545] + X[47665], 27 X[6545] - 7 X[47677], 7 X[16892] + 5 X[47665], 9 X[16892] - 5 X[47677], 9 X[47665] + 7 X[47677], 7 X[650] - 9 X[45684], 3 X[661] + X[47674], 3 X[3835] - X[4841], X[4841] + 3 X[48274], 3 X[4120] + X[47675], 5 X[4369] - 3 X[4786], 3 X[4786] + 5 X[48268], X[4382] + 3 X[4789], 3 X[4728] + X[47656], 9 X[4728] - X[47669], 3 X[47656] + X[47669], 3 X[4776] + X[47671], X[4818] - 3 X[48184], X[4838] + 3 X[44435], 3 X[4928] - X[45745], 3 X[4931] + X[47676], X[4976] - 3 X[47779], X[17494] - 3 X[47879], X[21196] - 3 X[45320], 3 X[21297] + X[48275], 7 X[26824] + 9 X[44009], X[26824] + 3 X[47874], 3 X[44009] - 7 X[47874], 5 X[26985] - 3 X[47882], 5 X[26985] - X[48277], 3 X[47882] - X[48277], 7 X[27138] - 3 X[47878], 5 X[30835] - X[47661], 3 X[45343] - X[48271], 3 X[45661] - X[47962], X[47652] + 3 X[47873], X[47670] + 3 X[47781], X[47672] + 3 X[47790], 3 X[47790] - X[48270], 3 X[47780] + X[48266], 3 X[47786] - X[47991], 3 X[47787] - X[48000], 3 X[47788] - X[48008], 3 X[47791] + X[48114], 3 X[47792] + X[47958], 3 X[47869] + X[48094]

X(48417) lies on these lines: {321, 693}, {514, 4940}, {522, 47132}, {650, 45684}, {661, 47674}, {3700, 28851}, {3835, 4841}, {4106, 28859}, {4120, 47675}, {4369, 4786}, {4382, 4789}, {4522, 48120}, {4728, 47656}, {4739, 4777}, {4776, 47671}, {4818, 48184}, {4838, 44435}, {4928, 45745}, {4931, 47676}, {4976, 47779}, {6590, 28882}, {17494, 47879}, {18004, 48127}, {21196, 45320}, {21297, 48275}, {26824, 44009}, {26985, 47882}, {27138, 47878}, {28867, 43067}, {28886, 48269}, {30835, 47661}, {45343, 48271}, {45661, 47962}, {47652, 47873}, {47670, 47781}, {47672, 47790}, {47780, 48266}, {47786, 47991}, {47787, 48000}, {47788, 48008}, {47791, 48114}, {47792, 47958}, {47869, 48094}

X(48417) = midpoint of X(i) and X(j) for these {i,j}: {693, 4500}, {3776, 4024}, {3835, 48274}, {4369, 48268}, {4522, 48120}, {18004, 48127}, {47672, 48270}
X(48417) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 4024, 3776}, {693, 47665, 6545}, {3776, 4500, 4024}, {26985, 48277, 47882}, {47672, 47790, 48270}


X(48418) = X(321)X(693)∩X(514)X(26798)

Barycentrics    (b - c)*(b^2 + 6*b*c + c^2) : :
X(48418) = 7 X[693] - 2 X[3776], 4 X[693] + X[4024], 3 X[693] + 2 X[4500], 8 X[693] - 3 X[6545], 6 X[693] - X[16892], 9 X[693] + X[47665], 11 X[693] - X[47677], 8 X[3776] + 7 X[4024], 3 X[3776] + 7 X[4500], 16 X[3776] - 21 X[6545], 12 X[3776] - 7 X[16892], 18 X[3776] + 7 X[47665], 22 X[3776] - 7 X[47677], 3 X[4024] - 8 X[4500], 2 X[4024] + 3 X[6545], 3 X[4024] + 2 X[16892], 9 X[4024] - 4 X[47665], 11 X[4024] + 4 X[47677], 16 X[4500] + 9 X[6545], 4 X[4500] + X[16892], 6 X[4500] - X[47665], 22 X[4500] + 3 X[47677], 9 X[6545] - 4 X[16892], 27 X[6545] + 8 X[47665], 33 X[6545] - 8 X[47677], 3 X[16892] + 2 X[47665], 11 X[16892] - 6 X[47677], 11 X[47665] + 9 X[47677], 6 X[3700] - X[48112], 4 X[3798] - 9 X[4379], 2 X[3798] + 3 X[48268], 3 X[4379] + 2 X[48268], 6 X[3835] - X[47667], 4 X[3835] + X[47671], 2 X[47667] + 3 X[47671], 6 X[4106] - X[47937], 3 X[4120] + 2 X[47672], 9 X[4120] - 4 X[48046], 3 X[47672] + 2 X[48046], 8 X[4369] - 3 X[4984], 3 X[4382] + 2 X[48060], 6 X[4728] - X[4988], 9 X[4728] + X[47670], 3 X[4728] + 2 X[48274], 3 X[4988] + 2 X[47670], X[4988] + 4 X[48274], X[47670] - 6 X[48274], 6 X[4789] - X[48101], 6 X[4927] - X[47673], 6 X[4928] - X[47661], 3 X[4931] + 2 X[21104], 9 X[6544] - 4 X[17494], 3 X[6546] + 2 X[26824], 6 X[6590] - X[48138], 9 X[14475] - 4 X[21196], X[17161] - 6 X[21204], 3 X[21116] + 2 X[25259], 6 X[21297] - X[23731], 6 X[23813] - X[47950], 4 X[23813] + X[48275], 2 X[47950] + 3 X[48275], 6 X[45320] - X[48277], X[47664] - 6 X[47879], X[47669] - 6 X[47756], X[47703] + 4 X[48090], 6 X[47786] - X[47908], 6 X[47787] - X[47926], 6 X[47788] - X[47932], 6 X[47790] - X[48082], 3 X[47874] + 2 X[48125], 2 X[48034] + 3 X[48141]

X(48418) lies on these lines: {321, 693}, {514, 26798}, {3700, 48112}, {3798, 4379}, {3835, 47667}, {4106, 47937}, {4120, 47672}, {4369, 4984}, {4382, 48060}, {4728, 4988}, {4789, 48101}, {4927, 47673}, {4928, 47661}, {4931, 21104}, {6544, 17494}, {6546, 26824}, {6590, 48138}, {14475, 21196}, {17161, 21204}, {21116, 25259}, {21297, 23731}, {23813, 47950}, {45320, 48277}, {47664, 47879}, {47669, 47756}, {47703, 48090}, {47786, 47908}, {47787, 47926}, {47788, 47932}, {47790, 48082}, {47874, 48125}, {48034, 48141}

X(48418) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 4024, 6545}, {693, 4500, 16892}, {4500, 16892, 4024}, {4728, 48274, 4988}


X(48419) = X(321)X(693)∩X(514)X(4944)

Barycentrics    (b - c)*(b^2 + 7*b*c + c^2) : :
X(48419) = 4 X[693] - X[3776], 5 X[693] + X[4024], 2 X[693] + X[4500], 3 X[693] - X[6545], 7 X[693] - X[16892], 11 X[693] + X[47665], 13 X[693] - X[47677], 5 X[3776] + 4 X[4024], X[3776] + 2 X[4500], 3 X[3776] - 4 X[6545], 7 X[3776] - 4 X[16892], 11 X[3776] + 4 X[47665], 13 X[3776] - 4 X[47677], 2 X[4024] - 5 X[4500], 3 X[4024] + 5 X[6545], 7 X[4024] + 5 X[16892], 11 X[4024] - 5 X[47665], 13 X[4024] + 5 X[47677], 3 X[4500] + 2 X[6545], 7 X[4500] + 2 X[16892], 11 X[4500] - 2 X[47665], 13 X[4500] + 2 X[47677], 7 X[6545] - 3 X[16892], 11 X[6545] + 3 X[47665], 13 X[6545] - 3 X[47677], 11 X[16892] + 7 X[47665], 13 X[16892] - 7 X[47677], 13 X[47665] + 11 X[47677], 3 X[47768] - 5 X[47789], 3 X[4728] - X[47781], 2 X[10196] - 3 X[47879]

X(48419) lies on these lines: {321, 693}, {514, 4944}, {522, 48245}, {812, 47768}, {4728, 47781}, {4762, 10196}, {4777, 21204}, {4789, 28882}, {21297, 28859}, {28169, 48182}, {28851, 47790}, {28867, 47780}, {30520, 45343}, {45320, 47882}, {45339, 47876}, {45678, 47883}, {47672, 47769}, {47756, 48274}, {47758, 48268}, {47770, 48125}, {47869, 47874}, {47871, 47873}

X(48419) = midpoint of X(i) and X(j) for these {i,j}: {47672, 47769}, {47756, 48274}, {47758, 48268}, {47770, 48125}, {47869, 47874}, {47871, 47873}
X(48419) = reflection of X(i) in X(j) for these {i,j}: {47876, 45339}, {47882, 45320}, {47883, 45678}
X(48419) = {X(693),X(4500)}-harmonic conjugate of X(3776)


X(48420) = X(321)X(693)∩X(650)X(6548)

Barycentrics    (b - c)*(-5*b*c + 2*(b^2 + c^2)) : :
X(48420) = 3 X[693] + 4 X[3776], 9 X[693] - 2 X[4024], 11 X[693] - 4 X[4500], X[693] + 6 X[6545], 5 X[693] + 2 X[16892], 8 X[693] - X[47665], 6 X[693] + X[47677], 6 X[3776] + X[4024], 11 X[3776] + 3 X[4500], 2 X[3776] - 9 X[6545], 10 X[3776] - 3 X[16892], 32 X[3776] + 3 X[47665], 8 X[3776] - X[47677], 11 X[4024] - 18 X[4500], X[4024] + 27 X[6545], 5 X[4024] + 9 X[16892], 16 X[4024] - 9 X[47665], 4 X[4024] + 3 X[47677], 2 X[4500] + 33 X[6545], 10 X[4500] + 11 X[16892], 32 X[4500] - 11 X[47665], 24 X[4500] + 11 X[47677], 15 X[6545] - X[16892], 48 X[6545] + X[47665], 36 X[6545] - X[47677], 16 X[16892] + 5 X[47665], 12 X[16892] - 5 X[47677], 3 X[47665] + 4 X[47677], 2 X[650] - 9 X[6548], 6 X[1638] + X[47650], 8 X[3004] - X[47668], 6 X[3004] + X[47674], 3 X[47668] + 4 X[47674], 8 X[3676] - X[4380], 10 X[3676] - 3 X[4786], 4 X[3676] + 3 X[47871], 5 X[4380] - 12 X[4786], X[4380] + 6 X[47871], 2 X[4786] + 5 X[47871], 6 X[4379] + X[47651], 3 X[4776] + 4 X[21104], 2 X[4841] - 9 X[44435], 4 X[4841] + 3 X[47675], 6 X[44435] + X[47675], 9 X[4927] - 2 X[14321], 6 X[4927] + X[47676], 4 X[14321] + 3 X[47676], 6 X[21183] + X[47652], 12 X[21204] - 5 X[31209], 8 X[21212] - X[47664], X[26824] + 6 X[47754], 16 X[31182] - 9 X[47892], X[47685] + 6 X[47887], X[47692] + 6 X[47812], 4 X[48098] + 3 X[48174]

X(48420) lies on these lines: {321, 693}, {650, 6548}, {1638, 47650}, {3004, 47668}, {3676, 4380}, {4379, 47651}, {4776, 21104}, {4841, 44435}, {4927, 14321}, {20057, 28321}, {21183, 47652}, {21204, 31209}, {21212, 47664}, {26824, 47754}, {26985, 30861}, {31182, 47892}, {47685, 47887}, {47692, 47812}, {48098, 48174}

X(48420) = barycentric product X(i)*X(j) for these {i,j}: {693, 9335}, {3261, 9336}
X(48420) = barycentric quotient X(i)/X(j) for these {i,j}: {9335, 100}, {9336, 101}
X(48420) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 3776, 47677}, {3676, 47871, 4380}


X(48421) = X(321)X(693)∩X(514)X(24924)

Barycentrics    (b - c)*(-3*b*c + 2*(b^2 + c^2)) : :
X(48421) = X[693] + 4 X[3776], 7 X[693] - 2 X[4024], 9 X[693] - 4 X[4500], X[693] - 6 X[6545], 3 X[693] + 2 X[16892], 6 X[693] - X[47665], 4 X[693] + X[47677], 14 X[3776] + X[4024], 9 X[3776] + X[4500], 2 X[3776] + 3 X[6545], 6 X[3776] - X[16892], 24 X[3776] + X[47665], 16 X[3776] - X[47677], 9 X[4024] - 14 X[4500], X[4024] - 21 X[6545], 3 X[4024] + 7 X[16892], 12 X[4024] - 7 X[47665], 8 X[4024] + 7 X[47677], 2 X[4500] - 27 X[6545], 2 X[4500] + 3 X[16892], 8 X[4500] - 3 X[47665], 16 X[4500] + 9 X[47677], 9 X[6545] + X[16892], 36 X[6545] - X[47665], 24 X[6545] + X[47677], 4 X[16892] + X[47665], 8 X[16892] - 3 X[47677], 2 X[47665] + 3 X[47677], 6 X[1638] - X[47663], 6 X[3004] - X[47667], 4 X[3004] + X[47675], 2 X[47667] + 3 X[47675], 4 X[3676] + X[47652], 8 X[3676] - 3 X[47762], 6 X[3676] - X[48060], 2 X[47652] + 3 X[47762], 3 X[47652] + 2 X[48060], 9 X[47762] - 4 X[48060], 8 X[3798] - 3 X[4380], 4 X[3798] - 9 X[4453], X[4380] - 6 X[4453], 2 X[3835] + 3 X[21115], 6 X[3835] - X[48112], 9 X[21115] + X[48112], 2 X[4025] + 3 X[47871], 4 X[4369] + X[47651], 6 X[4369] - X[48138], 3 X[47651] + 2 X[48138], 6 X[4379] - X[47662], 4 X[4458] + X[47685], 3 X[4776] + 2 X[47676], 9 X[4776] - 4 X[48046], 3 X[47676] + 2 X[48046], 4 X[4885] - 9 X[6548], 6 X[4885] - X[48124], 27 X[6548] - 2 X[48124], 6 X[4927] - X[25259], 6 X[4928] - X[48117], 3 X[7192] + 2 X[47950], 8 X[7658] - 3 X[47892], 4 X[17069] + X[47650], X[17494] - 6 X[47754], 2 X[21104] + 3 X[44435], 4 X[21104] + X[47666], 6 X[44435] - X[47666], 2 X[21146] + 3 X[48174], 6 X[21183] - X[47660], 6 X[21204] - X[48094], 8 X[21212] - 3 X[31150], 2 X[23729] + 3 X[47755], 4 X[23789] + X[47709], 4 X[24720] + X[47692], 7 X[27138] - 2 X[48087], 2 X[43067] + 3 X[48156], 3 X[44429] + 2 X[48326], 3 X[44550] + 2 X[47680], 3 X[47657] + 2 X[47670], X[47664] - 6 X[47886], X[47668] + 4 X[47672], X[47689] - 6 X[47812], X[47697] - 6 X[47887], X[47698] - 6 X[48178], 2 X[47704] + 3 X[48175], 6 X[47779] - X[48130], 3 X[47780] + 2 X[47960], 6 X[47797] - X[47974], 6 X[47831] - X[48113], 3 X[47894] + 2 X[48125], 2 X[47937] + 3 X[48107], X[47940] - 6 X[48159], X[47969] - 6 X[48192], 2 X[47973] + 3 X[48237], 2 X[48089] + 3 X[48241], X[48140] - 6 X[48233]

X(48421) lies on these lines: {321, 693}, {514, 24924}, {1638, 47663}, {3004, 47667}, {3676, 47652}, {3798, 4380}, {3835, 21115}, {4025, 47871}, {4369, 47651}, {4379, 47662}, {4458, 47685}, {4776, 47676}, {4777, 4821}, {4885, 6548}, {4927, 25259}, {4928, 48117}, {7192, 47950}, {7658, 47892}, {17069, 47650}, {17494, 24620}, {21104, 44435}, {21146, 48174}, {21183, 47660}, {21204, 48094}, {21212, 31150}, {23729, 47755}, {23789, 47709}, {24720, 47692}, {26985, 30520}, {27138, 48087}, {28890, 30835}, {43067, 48156}, {44429, 48326}, {44550, 47680}, {47657, 47670}, {47664, 47886}, {47668, 47672}, {47689, 47812}, {47697, 47887}, {47698, 48178}, {47704, 48175}, {47779, 48130}, {47780, 47960}, {47797, 47974}, {47831, 48113}, {47894, 48125}, {47937, 48107}, {47940, 48159}, {47969, 48192}, {47973, 48237}, {48089, 48241}, {48140, 48233}

X(48421) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 16892, 47665}, {3676, 47652, 47762}, {3776, 6545, 693}, {16892, 47665, 47677}, {21104, 44435, 47666}


X(48422) = X(321)X(693)∩X(514)X(1635)

Barycentrics    (b - c)*(-(b*c) + 2*(b^2 + c^2)) : :
X(48422) = 3 X[47754] - X[47770], X[693] - 4 X[3776], 5 X[693] - 2 X[4024], 7 X[693] - 4 X[4500], X[693] + 2 X[16892], 4 X[693] - X[47665], 2 X[693] + X[47677], 10 X[3776] - X[4024], 7 X[3776] - X[4500], 2 X[3776] + X[16892], 16 X[3776] - X[47665], 8 X[3776] + X[47677], 7 X[4024] - 10 X[4500], X[4024] - 5 X[6545], X[4024] + 5 X[16892], 8 X[4024] - 5 X[47665], 4 X[4024] + 5 X[47677], 2 X[4500] - 7 X[6545], 2 X[4500] + 7 X[16892], 16 X[4500] - 7 X[47665], 8 X[4500] + 7 X[47677], 8 X[6545] - X[47665], 4 X[6545] + X[47677], 8 X[16892] + X[47665], 4 X[16892] - X[47677], X[47665] + 2 X[47677], 3 X[4453] - 2 X[47758], 5 X[4453] - 2 X[47768], 4 X[47758] - 3 X[47762], 5 X[47758] - 3 X[47768], 5 X[47762] - 4 X[47768], 2 X[649] + X[47651], 3 X[4776] - 4 X[47756], 3 X[4776] - 2 X[47769], 3 X[44435] - 2 X[47756], 3 X[44435] - X[47769], 2 X[2254] + X[47692], 4 X[3004] - X[47666], 2 X[3004] + X[47676], X[47666] + 2 X[47676], 4 X[3676] - X[47660], 2 X[3835] + X[47930], 4 X[3960] - X[47684], 4 X[4025] - X[4380], 2 X[4025] + X[47652], X[4380] + 2 X[47652], 4 X[4369] - X[47662], 2 X[4369] + X[47923], X[47662] + 2 X[47923], 4 X[4458] - X[47697], 2 X[4458] + X[47973], X[47697] + 2 X[47973], 2 X[4818] + X[47704], 2 X[4905] + X[47709], 2 X[4932] + X[47916], 2 X[4976] + X[47650], 3 X[6548] - 2 X[45320], 3 X[6548] - X[47870], X[7192] + 2 X[47960], 4 X[10196] - 5 X[31209], 8 X[21212] - 5 X[31209], 4 X[21212] - X[48094], 5 X[31209] - 2 X[48094], 4 X[13246] - X[48105], 3 X[14475] - 2 X[47879], 4 X[17069] - X[47663], X[17161] + 2 X[48125], 2 X[21104] + X[45746], 8 X[21104] + X[47668], 4 X[21104] - X[47675], 4 X[45746] - X[47668], 2 X[45746] + X[47675], X[47668] + 2 X[47675], 4 X[21196] - X[47664], 4 X[23789] - X[47718], 4 X[24720] - X[47689], 4 X[25380] - X[48118], 4 X[25666] - X[48117], 5 X[26985] - 2 X[48271], 5 X[27013] - 2 X[48095], 4 X[31286] - X[48130], 4 X[31287] - X[48124], 3 X[31992] - 4 X[44567], 2 X[43067] + X[47653], X[47655] + 2 X[47673], X[47657] + 2 X[47672], X[47695] + 2 X[48015], X[47702] + 2 X[48073], X[47705] + 2 X[48017], X[47713] + 2 X[48075], X[47717] + 2 X[48018], X[47900] + 2 X[48071], X[47939] - 4 X[47995], X[47940] - 4 X[48007], 2 X[47958] + X[48107], 2 X[47971] + X[48079], X[47975] + 2 X[48326]

X(48422) lies on these lines: {2, 30520}, {321, 693}, {513, 48156}, {514, 1635}, {522, 47871}, {649, 47651}, {826, 47819}, {905, 30913}, {918, 4776}, {1638, 47771}, {2254, 47692}, {3004, 47666}, {3676, 47660}, {3835, 47930}, {3837, 4951}, {3960, 47684}, {4025, 4380}, {4369, 47662}, {4379, 28863}, {4440, 31512}, {4448, 48212}, {4458, 47697}, {4728, 30519}, {4740, 4777}, {4750, 28882}, {4762, 47894}, {4789, 21183}, {4802, 47824}, {4818, 47704}, {4893, 28890}, {4905, 47709}, {4927, 47790}, {4932, 47916}, {4976, 47650}, {6009, 45669}, {6084, 27486}, {6546, 47882}, {6548, 45320}, {7192, 47960}, {10196, 21212}, {13246, 48105}, {14475, 47879}, {17069, 47663}, {17161, 48125}, {17490, 17494}, {21104, 45746}, {21196, 47664}, {21204, 47874}, {21297, 28898}, {23789, 47718}, {24720, 47689}, {25380, 48118}, {25666, 48117}, {26985, 48271}, {27013, 48095}, {28147, 48252}, {28151, 48254}, {28175, 48245}, {28179, 48249}, {28894, 47780}, {28910, 47774}, {29204, 36848}, {29354, 47814}, {29370, 48167}, {30565, 47757}, {31286, 48130}, {31287, 48124}, {31992, 44567}, {43067, 47653}, {47655, 47673}, {47657, 47672}, {47695, 48015}, {47702, 48073}, {47705, 48017}, {47713, 48075}, {47717, 48018}, {47760, 47772}, {47761, 47773}, {47775, 47880}, {47791, 47891}, {47802, 48171}, {47804, 48227}, {47821, 48192}, {47823, 48236}, {47887, 48237}, {47900, 48071}, {47939, 47995}, {47940, 48007}, {47958, 48107}, {47971, 48079}, {47975, 48326}

X(48422) = midpoint of X(i) and X(j) for these {i,j}: {6545, 16892}, {47676, 47781}
X(48422) = reflection of X(i) in X(j) for these {i,j}: {2, 47754}, {693, 6545}, {4448, 48212}, {4776, 44435}, {4789, 21183}, {4951, 3837}, {6545, 3776}, {6546, 47882}, {10196, 21212}, {30565, 47757}, {31150, 47886}, {47660, 47789}, {47666, 47781}, {47762, 4453}, {47769, 47756}, {47771, 1638}, {47772, 47760}, {47773, 47761}, {47775, 47880}, {47781, 3004}, {47789, 3676}, {47790, 4927}, {47791, 47891}, {47804, 48227}, {47821, 48192}, {47870, 45320}, {47874, 21204}, {47892, 47785}, {48094, 10196}, {48171, 47802}, {48187, 36848}, {48223, 48224}, {48236, 47823}, {48237, 47887}
X(48422) = anticomplement of X(47770)
X(48422) = crossdifference of every pair of points on line {2177, 2210}
X(48422) = barycentric product X(i)*X(j) for these {i,j}: {514, 17227}, {693, 4392}
X(48422) = barycentric quotient X(i)/X(j) for these {i,j}: {4392, 100}, {4735, 4557}, {17227, 190}
X(48422) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 16892, 47677}, {693, 47677, 47665}, {3004, 47676, 47666}, {3776, 16892, 693}, {4025, 47652, 4380}, {4369, 47923, 47662}, {4458, 47973, 47697}, {6548, 47870, 45320}, {21104, 45746, 47675}, {21212, 48094, 31209}, {44435, 47769, 47756}, {45746, 47675, 47668}, {47756, 47769, 4776}


X(48423) = X(321)X(693)∩X(514)X(4931)

Barycentrics    (b - c)*(5*b*c + 2*(b^2 + c^2)) : :
X(48423) = 7 X[693] - 4 X[3776], X[693] + 2 X[4024], X[693] - 4 X[4500], 3 X[693] - 2 X[6545], 5 X[693] - 2 X[16892], 2 X[693] + X[47665], 4 X[693] - X[47677], 2 X[3776] + 7 X[4024], X[3776] - 7 X[4500], 6 X[3776] - 7 X[6545], 10 X[3776] - 7 X[16892], 8 X[3776] + 7 X[47665], 16 X[3776] - 7 X[47677], X[4024] + 2 X[4500], 3 X[4024] + X[6545], 5 X[4024] + X[16892], 4 X[4024] - X[47665], 8 X[4024] + X[47677], 6 X[4500] - X[6545], 10 X[4500] - X[16892], 8 X[4500] + X[47665], 16 X[4500] - X[47677], 5 X[6545] - 3 X[16892], 4 X[6545] + 3 X[47665], 8 X[6545] - 3 X[47677], 4 X[16892] + 5 X[47665], 8 X[16892] - 5 X[47677], 2 X[47665] + X[47677], 2 X[4786] - 5 X[4789], 4 X[4786] - 5 X[47762], 3 X[4786] - 5 X[47789], 3 X[4789] - 2 X[47789], 3 X[47762] - 4 X[47789], 3 X[4776] - 2 X[47781], X[47781] - 3 X[47790], 2 X[661] + X[47655], 4 X[661] - X[47668], 2 X[47655] + X[47668], 4 X[3239] - X[47661], 2 X[3700] + X[47656], 4 X[3700] - X[47666], 2 X[47656] + X[47666], 2 X[3835] + X[4838], 4 X[3835] - X[47657], 2 X[4838] + X[47657], 2 X[4106] + X[47659], X[4380] - 4 X[6590], 2 X[4382] + X[47662], X[4608] + 2 X[48026], 2 X[4804] + X[47689], 2 X[4820] + X[7192], 4 X[4885] - X[17161], 4 X[10196] - 3 X[31150], X[10196] - 3 X[45343], 2 X[10196] - 3 X[47874], X[31150] - 4 X[45343], 4 X[14321] - X[47667], X[14349] + 2 X[31010], 4 X[23813] - X[47653], 2 X[25259] + X[47675], X[25259] + 2 X[48274], X[47675] - 4 X[48274], X[26824] + 2 X[48271], 5 X[31209] - 2 X[48277], X[47658] + 2 X[47995], X[47660] + 2 X[48268], X[47670] + 2 X[47996], X[47671] + 2 X[48270], X[47674] + 2 X[48046], X[47939] - 4 X[48269], X[48079] + 2 X[48275], X[48107] + 2 X[48266]

X(48423) lies on these lines: {2, 4777}, {321, 693}, {513, 47792}, {514, 4931}, {522, 4786}, {523, 4776}, {661, 47655}, {812, 47873}, {900, 47791}, {3239, 47661}, {3681, 14077}, {3700, 47656}, {3835, 4838}, {4106, 47659}, {4380, 6590}, {4382, 47662}, {4411, 28605}, {4467, 47758}, {4608, 48026}, {4762, 47870}, {4802, 47759}, {4804, 47689}, {4820, 7192}, {4828, 42029}, {4885, 17161}, {4926, 47763}, {4944, 47775}, {6367, 47814}, {10196, 31150}, {14321, 47667}, {14349, 31010}, {17494, 41839}, {21297, 28894}, {23813, 47653}, {25259, 47675}, {26824, 48271}, {27486, 28183}, {28147, 47786}, {28161, 47782}, {28165, 46915}, {28169, 47783}, {28187, 47784}, {28205, 47761}, {28898, 47780}, {29066, 32915}, {30520, 47869}, {31209, 48277}, {32771, 48295}, {32937, 48304}, {45320, 47894}, {45661, 47878}, {45746, 47756}, {47658, 47995}, {47660, 48268}, {47670, 47996}, {47671, 48270}, {47674, 48046}, {47776, 47881}, {47939, 48269}, {48079, 48275}, {48107, 48266}

X(48423) = midpoint of X(47656) and X(47769)
X(48423) = reflection of X(i) in X(j) for these {i,j}: {4467, 47758}, {4776, 47790}, {17494, 47770}, {27486, 47788}, {31150, 47874}, {45746, 47756}, {46915, 47760}, {47666, 47769}, {47762, 4789}, {47769, 3700}, {47775, 4944}, {47776, 47881}, {47782, 47787}, {47874, 45343}, {47878, 45661}, {47894, 45320}, {48223, 48189}
X(48423) = barycentric product X(i)*X(j) for these {i,j}: {693, 9330}, {3261, 9331}
X(48423) = barycentric quotient X(i)/X(j) for these {i,j}: {9330, 100}, {9331, 101}
X(48423) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 47655, 47668}, {693, 4024, 47665}, {693, 47665, 47677}, {3700, 47656, 47666}, {3835, 4838, 47657}, {4024, 4500, 693}, {25259, 48274, 47675}


X(48424) = X(321)X(693)∩X(3700)X(47675)

Barycentrics    (b - c)*(7*b*c + 2*(b^2 + c^2)) : :
X(48424) = 9 X[693] - 4 X[3776], 3 X[693] + 2 X[4024], X[693] + 4 X[4500], 11 X[693] - 6 X[6545], 7 X[693] - 2 X[16892], 4 X[693] + X[47665], 6 X[693] - X[47677], 2 X[3776] + 3 X[4024], X[3776] + 9 X[4500], 22 X[3776] - 27 X[6545], 14 X[3776] - 9 X[16892], 16 X[3776] + 9 X[47665], 8 X[3776] - 3 X[47677], X[4024] - 6 X[4500], 11 X[4024] + 9 X[6545], 7 X[4024] + 3 X[16892], 8 X[4024] - 3 X[47665], 4 X[4024] + X[47677], 22 X[4500] + 3 X[6545], 14 X[4500] + X[16892], 16 X[4500] - X[47665], 24 X[4500] + X[47677], 21 X[6545] - 11 X[16892], 24 X[6545] + 11 X[47665], 36 X[6545] - 11 X[47677], 8 X[16892] + 7 X[47665], 12 X[16892] - 7 X[47677], 3 X[47665] + 2 X[47677], 4 X[3700] + X[47675], 4 X[3835] + X[47655], 6 X[3835] - X[47669], 3 X[47655] + 2 X[47669], 2 X[4106] + 3 X[47792], X[4380] - 6 X[4789], X[4380] + 4 X[48268], 3 X[4789] + 2 X[48268], X[4608] + 4 X[4940], 6 X[4728] - X[47657], 9 X[4776] - 4 X[4841], 3 X[4776] + 2 X[47656], 6 X[4776] - X[47668], 2 X[4841] + 3 X[47656], 8 X[4841] - 3 X[47668], 4 X[47656] + X[47668], 2 X[4820] + 3 X[47780], 8 X[14321] - 3 X[47666], 4 X[14321] + X[47674], 4 X[14321] - 9 X[47790], 2 X[14321] + 3 X[48274], 3 X[47666] + 2 X[47674], X[47666] - 6 X[47790], X[47666] + 4 X[48274], X[47674] + 9 X[47790], X[47674] - 6 X[48274], 3 X[47790] + 2 X[48274], X[17161] - 6 X[45320], 4 X[23813] + X[47659], 6 X[45343] - X[48094], X[47661] - 6 X[47787], X[47662] - 6 X[47873], X[47664] - 6 X[47874], 3 X[47869] + 2 X[48271], 3 X[47870] + 2 X[48125]

X(48424) lies on these lines: {321, 693}, {3700, 47675}, {3835, 47655}, {4106, 47792}, {4380, 4789}, {4608, 4940}, {4699, 4777}, {4728, 47657}, {4776, 4841}, {4802, 26798}, {4820, 47780}, {14321, 47666}, {17161, 45320}, {23813, 47659}, {31094, 48174}, {45343, 48094}, {47661, 47787}, {47662, 47873}, {47664, 47874}, {47869, 48271}, {47870, 48125}

X(48424) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 4024, 47677}, {4024, 47677, 47665}, {4776, 47656, 47668}, {4789, 48268, 4380}, {14321, 47674, 47666}, {14321, 48274, 47674}, {47674, 47790, 14321}, {47790, 48274, 47666}


X(48425) = X(321)X(693)∩X(514)X(26777)

Barycentrics    (b - c)*(-2*b*c + 3*(b^2 + c^2)) : :
X(48425) = X[693] - 6 X[3776], 8 X[693] - 3 X[4024], 11 X[693] - 6 X[4500], 4 X[693] - 9 X[6545], 2 X[693] + 3 X[16892], 13 X[693] - 3 X[47665], 7 X[693] + 3 X[47677], 16 X[3776] - X[4024], 11 X[3776] - X[4500], 8 X[3776] - 3 X[6545], 4 X[3776] + X[16892], 26 X[3776] - X[47665], 14 X[3776] + X[47677], 11 X[4024] - 16 X[4500], X[4024] - 6 X[6545], X[4024] + 4 X[16892], 13 X[4024] - 8 X[47665], 7 X[4024] + 8 X[47677], 8 X[4500] - 33 X[6545], 4 X[4500] + 11 X[16892], 26 X[4500] - 11 X[47665], 14 X[4500] + 11 X[47677], 3 X[6545] + 2 X[16892], 39 X[6545] - 4 X[47665], 21 X[6545] + 4 X[47677], 13 X[16892] + 2 X[47665], 7 X[16892] - 2 X[47677], 7 X[47665] + 13 X[47677], 6 X[1638] - X[48130], 2 X[3004] + 3 X[21115], 6 X[3004] - X[47917], 9 X[21115] + X[47917], 4 X[3676] + X[47923], 8 X[4025] - 3 X[4984], 3 X[4120] + 2 X[47930], 6 X[4453] - X[48101], 3 X[4750] + 2 X[47652], X[4988] + 4 X[21104], 27 X[6544] - 32 X[31287], 3 X[6544] - 8 X[47754], 9 X[6544] - 4 X[48094], 4 X[31287] - 9 X[47754], 8 X[31287] - 3 X[48094], 6 X[47754] - X[48094], 3 X[6546] - 8 X[21212], 9 X[6546] - 14 X[27115], 12 X[21212] - 7 X[27115], 3 X[21116] + 2 X[45746], X[23731] - 6 X[48156], 2 X[23795] + 3 X[47712], 6 X[44435] - X[48082], 3 X[47676] + 2 X[47996], 6 X[47756] - X[48112], 6 X[47757] - X[48117], 6 X[47758] - X[48138], 6 X[47799] - X[48113], X[48078] - 6 X[48192], X[48102] - 6 X[48227], X[48146] - 6 X[48245]

X(48425) lies on these lines: {321, 693}, {514, 26777}, {1638, 48130}, {3004, 21115}, {3676, 47923}, {4025, 4984}, {4120, 47930}, {4453, 48101}, {4750, 47652}, {4988, 21104}, {6544, 31287}, {6546, 21212}, {21116, 45746}, {23731, 48156}, {23795, 47712}, {30520, 31250}, {44435, 48082}, {47676, 47996}, {47756, 48112}, {47757, 48117}, {47758, 48138}, {47799, 48113}, {48078, 48192}, {48102, 48227}, {48146, 48245}

X(48425) = barycentric product X(693)*X(42038)
X(48425) = barycentric quotient X(42038)/X(100)
X(48425) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3776, 16892, 6545}, {6545, 16892, 4024}


X(48426) = X(321)X(693)∩X(514)X(4394)

Barycentrics    (b - c)*(-(b*c) + 3*(b^2 + c^2)) : :
X(48426) = X[693] - 3 X[3776], 7 X[693] - 3 X[4024], 5 X[693] - 3 X[4500], 5 X[693] - 9 X[6545], X[693] + 3 X[16892], 11 X[693] - 3 X[47665], 5 X[693] + 3 X[47677], 7 X[3776] - X[4024], 5 X[3776] - X[4500], 5 X[3776] - 3 X[6545], 11 X[3776] - X[47665], 5 X[3776] + X[47677], 5 X[4024] - 7 X[4500], 5 X[4024] - 21 X[6545], X[4024] + 7 X[16892], 11 X[4024] - 7 X[47665], 5 X[4024] + 7 X[47677], X[4500] - 3 X[6545], X[4500] + 5 X[16892], 11 X[4500] - 5 X[47665], 3 X[6545] + 5 X[16892], 33 X[6545] - 5 X[47665], 3 X[6545] + X[47677], 11 X[16892] + X[47665], 5 X[16892] - X[47677], 5 X[47665] + 11 X[47677], 3 X[3004] - X[47996], 3 X[4453] + X[47923], 3 X[4750] + X[47651], 3 X[10196] - X[48124], 3 X[21115] + X[45746], 3 X[21116] + X[47657], 3 X[21204] - X[48271], 3 X[21212] - 2 X[31287], 5 X[26777] - 9 X[47886], 35 X[27115] - 27 X[31992], 7 X[27115] - 9 X[47882], 7 X[27115] - 3 X[48094], 3 X[31992] - 5 X[47882], 9 X[31992] - 5 X[48094], 3 X[47882] - X[48094], 5 X[31250] - 9 X[47754], 3 X[44435] + X[47930], 3 X[44435] - X[48270], 3 X[45674] - X[48095], 3 X[47676] + X[47917], 3 X[47755] + X[47916], X[47971] + 3 X[48156], X[47973] + 3 X[48241]

X(48426) lies on these lines: {321, 693}, {514, 4394}, {3004, 28851}, {3676, 28863}, {4025, 28882}, {4453, 47923}, {4750, 47651}, {4818, 48326}, {10196, 48124}, {21115, 45746}, {21116, 47657}, {21204, 48271}, {21212, 30520}, {23796, 29021}, {26777, 47886}, {27115, 31992}, {28859, 47960}, {28886, 47995}, {31250, 47754}, {44435, 47930}, {45674, 48095}, {47676, 47917}, {47755, 47916}, {47971, 48156}, {47973, 48241}

X(48426) = midpoint of X(i) and X(j) for these {i,j}: {3776, 16892}, {4500, 47677}, {4818, 48326}, {47930, 48270}
X(48426) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3776, 4500, 6545}, {6545, 16892, 47677}, {6545, 47677, 4500}, {44435, 47930, 48270}


X(48427) = X(321)X(693)∩X(514)X(4790)

Barycentrics    (b - c)*(b*c + 3*(b^2 + c^2)) : :
X(48427) = 2 X[693] - 3 X[3776], 5 X[693] - 3 X[4024], 4 X[693] - 3 X[4500], 7 X[693] - 9 X[6545], X[693] - 3 X[16892], 7 X[693] - 3 X[47665], X[693] + 3 X[47677], 5 X[3776] - 2 X[4024], 7 X[3776] - 6 X[6545], 7 X[3776] - 2 X[47665], X[3776] + 2 X[47677], 4 X[4024] - 5 X[4500], 7 X[4024] - 15 X[6545], X[4024] - 5 X[16892], 7 X[4024] - 5 X[47665], X[4024] + 5 X[47677], 7 X[4500] - 12 X[6545], X[4500] - 4 X[16892], 7 X[4500] - 4 X[47665], X[4500] + 4 X[47677], 3 X[6545] - 7 X[16892], 3 X[6545] - X[47665], 3 X[6545] + 7 X[47677], 7 X[16892] - X[47665], X[47665] + 7 X[47677], 5 X[4025] - 3 X[47768], 3 X[4750] - X[47662], 3 X[21115] - X[47656], 3 X[21116] - X[47655], 6 X[21212] - 5 X[31250], 4 X[21212] - 3 X[47879], 10 X[31250] - 9 X[47879], 5 X[31250] - 3 X[48271], 3 X[47879] - 2 X[48271], 35 X[26777] - 27 X[44009], 5 X[26777] - 9 X[47894], 5 X[26777] - 3 X[48094], 3 X[44009] - 7 X[47894], 9 X[44009] - 7 X[48094], 3 X[47894] - X[48094], 7 X[27115] - 9 X[47886], 3 X[27486] - X[48130], 3 X[45746] - X[47917], X[47917] + 3 X[47930], 28 X[31287] - 27 X[45684], 8 X[31287] - 9 X[47882], 6 X[45684] - 7 X[47882], 3 X[47781] - X[48112], 3 X[47782] - X[48117], 3 X[48156] - X[48266]

X(48427) lies on these lines: {321, 693}, {514, 4790}, {523, 48073}, {918, 47996}, {2786, 47960}, {3004, 30519}, {4025, 28863}, {4467, 28882}, {4750, 47662}, {21115, 47656}, {21116, 47655}, {21196, 30520}, {21212, 31250}, {23795, 29021}, {26777, 44009}, {27115, 47886}, {27486, 48130}, {28851, 45746}, {28859, 47653}, {28867, 47958}, {28890, 45745}, {28906, 47988}, {31287, 45684}, {47654, 48141}, {47673, 47676}, {47781, 48112}, {47782, 48117}, {48156, 48266}

X(48427) = midpoint of X(i) and X(j) for these {i,j}: {4467, 47923}, {16892, 47677}, {45746, 47930}, {47653, 47971}, {47654, 48141}, {47673, 47676}
X(48427) = reflection of X(i) in X(j) for these {i,j}: {3776, 16892}, {4500, 3776}, {48270, 3004}, {48271, 21212}
X(48427) = {X(21212),X(48271)}-harmonic conjugate of X(47879)


X(48428) = X(321)X(693)∩X(514)X(14779)

Barycentrics    (b - c)*(2*b*c + 3*(b^2 + c^2)) : :
X(48428) = 5 X[693] - 6 X[3776], 4 X[693] - 3 X[4024], 7 X[693] - 6 X[4500], 8 X[693] - 9 X[6545], 2 X[693] - 3 X[16892], 5 X[693] - 3 X[47665], X[693] - 3 X[47677], 8 X[3776] - 5 X[4024], 7 X[3776] - 5 X[4500], 16 X[3776] - 15 X[6545], 4 X[3776] - 5 X[16892], 2 X[3776] - 5 X[47677], 7 X[4024] - 8 X[4500], 2 X[4024] - 3 X[6545], 5 X[4024] - 4 X[47665], X[4024] - 4 X[47677], 16 X[4500] - 21 X[6545], 4 X[4500] - 7 X[16892], 10 X[4500] - 7 X[47665], 2 X[4500] - 7 X[47677], 3 X[6545] - 4 X[16892], 15 X[6545] - 8 X[47665], 3 X[6545] - 8 X[47677], 5 X[16892] - 2 X[47665], X[47665] - 5 X[47677], 3 X[4988] - 2 X[47917], 3 X[47673] - X[47917], 4 X[3004] - 3 X[4120], 4 X[3676] - 3 X[47873], 2 X[3762] - 3 X[21124], 4 X[4467] - 3 X[4984], 3 X[4984] - 2 X[48101], 3 X[4750] - 2 X[47660], 27 X[6544] - 28 X[27115], 3 X[6544] - 4 X[47894], 7 X[27115] - 9 X[47894], 3 X[6546] - 4 X[21196], 9 X[6546] - 10 X[26777], 6 X[21196] - 5 X[26777], 3 X[21115] - 2 X[48274], 3 X[21116] - 2 X[47656], 4 X[21212] - 3 X[47870], 4 X[23796] - 3 X[47715], 3 X[45746] - 2 X[47996], 4 X[47996] - 3 X[48082], 10 X[31250] - 9 X[47874], 8 X[31287] - 9 X[47886], 4 X[31287] - 3 X[48271], 3 X[47886] - 2 X[48271], 3 X[47878] - 2 X[48087]

X(48428) lies on these lines: {321, 693}, {514, 14779}, {522, 47686}, {523, 47930}, {900, 47916}, {918, 4988}, {2786, 23731}, {3004, 4120}, {3667, 47907}, {3676, 47873}, {3762, 21124}, {4467, 4984}, {4750, 47660}, {4838, 21104}, {4841, 48112}, {4926, 47919}, {4976, 48130}, {6544, 27115}, {6546, 21196}, {21115, 48274}, {21116, 47656}, {21212, 47870}, {23764, 29312}, {23796, 47715}, {28217, 47900}, {28840, 47654}, {28851, 47657}, {28890, 47661}, {28894, 47971}, {28898, 47958}, {29078, 47943}, {30519, 45746}, {30520, 48277}, {31250, 47874}, {31287, 47886}, {45745, 48117}, {47671, 47676}, {47878, 48087}, {47960, 48266}

X(48428) = reflection of X(i) in X(j) for these {i,j}: {4024, 16892}, {4838, 21104}, {4988, 47673}, {16892, 47677}, {23731, 47653}, {47665, 3776}, {47671, 47676}, {48082, 45746}, {48101, 4467}, {48112, 4841}, {48117, 45745}, {48130, 4976}, {48266, 47960}
X(48428) = barycentric product X(693)*X(42039)
X(48428) = barycentric quotient X(42039)/X(100)
X(48428) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4024, 16892, 6545}, {4467, 48101, 4984}


X(48429) = X(321)X(693)∩X(522)X(47693)

Barycentrics    (b - c)*(4*b*c + 3*(b^2 + c^2)) : :
X(48429) = 7 X[693] - 6 X[3776], 2 X[693] - 3 X[4024], 5 X[693] - 6 X[4500], 10 X[693] - 9 X[6545], 4 X[693] - 3 X[16892], X[693] - 3 X[47665], 5 X[693] - 3 X[47677], 4 X[3776] - 7 X[4024], 5 X[3776] - 7 X[4500], 20 X[3776] - 21 X[6545], 8 X[3776] - 7 X[16892], 2 X[3776] - 7 X[47665], 10 X[3776] - 7 X[47677], 5 X[4024] - 4 X[4500], 5 X[4024] - 3 X[6545], 5 X[4024] - 2 X[47677], 4 X[4500] - 3 X[6545], 8 X[4500] - 5 X[16892], 2 X[4500] - 5 X[47665], 6 X[6545] - 5 X[16892], 3 X[6545] - 10 X[47665], 3 X[6545] - 2 X[47677], X[16892] - 4 X[47665], 5 X[16892] - 4 X[47677], 5 X[47665] - X[47677], 2 X[47917] - 3 X[48082], 2 X[3004] - 3 X[4931], 2 X[4025] - 3 X[47873], 3 X[4120] - 2 X[45746], 3 X[4750] - 4 X[6590], 4 X[4791] - 3 X[21124], 3 X[4958] - 2 X[47988], 3 X[4988] - 4 X[47996], 3 X[25259] - 2 X[47996], 3 X[6546] - 4 X[48271], 3 X[6546] - 2 X[48277], 3 X[17161] - 5 X[26777], 5 X[17161] - 9 X[31992], 25 X[26777] - 27 X[31992], 3 X[21116] - 2 X[47930], 3 X[21116] - 4 X[48274], 6 X[21196] - 7 X[27115], 2 X[21196] - 3 X[47870], 7 X[27115] - 9 X[47870], 2 X[23795] - 3 X[47715], 5 X[26985] - 6 X[45343], 10 X[31250] - 9 X[47886], 8 X[31287] - 9 X[47874]

X(48429) lies on these lines: {321, 693}, {522, 47693}, {523, 47917}, {918, 4838}, {2786, 47659}, {3004, 4931}, {3700, 47673}, {3762, 23879}, {4025, 47873}, {4120, 45746}, {4608, 28855}, {4718, 4777}, {4750, 6590}, {4791, 21124}, {4802, 48076}, {4820, 47958}, {4926, 48104}, {4958, 47988}, {4988, 25259}, {6546, 48271}, {17161, 26777}, {21116, 47930}, {21196, 27115}, {23731, 28894}, {23795, 47715}, {26985, 45343}, {28147, 47908}, {28161, 47926}, {28165, 48087}, {28175, 47903}, {28183, 47932}, {28205, 48095}, {28840, 47658}, {28851, 47655}, {28898, 48275}, {30519, 47656}, {31250, 47886}, {31287, 47874}, {47654, 48049}, {47657, 48270}, {47669, 48046}, {47923, 48268}

X(48429) = reflection of X(i) in X(j) for these {i,j}: {4024, 47665}, {4988, 25259}, {16892, 4024}, {23731, 48266}, {47654, 48049}, {47657, 48270}, {47669, 48046}, {47671, 4838}, {47673, 3700}, {47677, 4500}, {47923, 48268}, {47930, 48274}, {47958, 4820}, {48277, 48271}
X(48429) = barycentric product X(693)*X(42041)
X(48429) = barycentric quotient X(42041)/X(100)
X(48429) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4024, 6545, 4500}, {4500, 47677, 6545}, {6545, 47677, 16892}, {47930, 48274, 21116}, {48271, 48277, 6546}


X(48430) = X(321)X(693)∩X(514)X(4820)

Barycentrics    (b - c)*(5*b*c + 3*(b^2 + c^2)) : :
X(48430) = 4 X[693] - 3 X[3776], X[693] - 3 X[4024], 2 X[693] - 3 X[4500], 11 X[693] - 9 X[6545], 5 X[693] - 3 X[16892], X[693] + 3 X[47665], 7 X[693] - 3 X[47677], X[3776] - 4 X[4024], 11 X[3776] - 12 X[6545], 5 X[3776] - 4 X[16892], X[3776] + 4 X[47665], 7 X[3776] - 4 X[47677], 11 X[4024] - 3 X[6545], 5 X[4024] - X[16892], 7 X[4024] - X[47677], 11 X[4500] - 6 X[6545], 5 X[4500] - 2 X[16892], X[4500] + 2 X[47665], 7 X[4500] - 2 X[47677], 15 X[6545] - 11 X[16892], 3 X[6545] + 11 X[47665], 21 X[6545] - 11 X[47677], X[16892] + 5 X[47665], 7 X[16892] - 5 X[47677], 7 X[47665] + X[47677], 2 X[47996] - 3 X[48270], 3 X[4120] - X[47657], X[4467] - 3 X[47873], 3 X[4786] - 5 X[6590], 3 X[4838] + X[47917], 3 X[25259] - X[47917], 2 X[4885] - 3 X[45343], 3 X[4931] - X[45746], 3 X[17161] - 7 X[27115], X[17161] - 3 X[47874], 7 X[27115] - 9 X[47874], 3 X[21196] - 4 X[31287], 2 X[21196] - 3 X[47879], 8 X[31287] - 9 X[47879], 5 X[26777] - 9 X[47870], 5 X[26777] - 3 X[48277], 3 X[47870] - X[48277], 3 X[31147] - X[47654], 10 X[31250] - 9 X[47882], X[47669] - 3 X[47769], X[47673] - 3 X[47790], 3 X[47792] - X[47971]

X(48430) lies on these lines: {321, 693}, {514, 4820}, {523, 47964}, {4120, 47657}, {4467, 47873}, {4608, 48076}, {4681, 4777}, {4786, 6590}, {4791, 23879}, {4813, 47658}, {4838, 25259}, {4885, 45343}, {4931, 45746}, {17161, 27115}, {21196, 31287}, {23875, 31010}, {26777, 47870}, {28147, 47991}, {28161, 48000}, {28175, 47984}, {28183, 48008}, {28221, 48016}, {28851, 47656}, {28859, 47659}, {28863, 48268}, {28867, 48275}, {30519, 48274}, {31147, 47654}, {31250, 47882}, {47655, 48082}, {47669, 47769}, {47673, 47790}, {47674, 48112}, {47792, 47971}

X(48430) = midpoint of X(i) and X(j) for these {i,j}: {4024, 47665}, {4608, 48076}, {4813, 47658}, {4838, 25259}, {47655, 48082}, {47659, 48266}, {47674, 48112}
X(48430) = reflection of X(i) in X(j) for these {i,j}: {3776, 4500}, {4500, 4024}


X(48431) = X(321)X(693)∩X(650)X(45343)

Barycentrics    (b - c)*(7*b*c + 3*(b^2 + c^2)) : :
X(48431) = 5 X[693] - 3 X[3776], X[693] + 3 X[4024], X[693] - 3 X[4500], 13 X[693] - 9 X[6545], 7 X[693] - 3 X[16892], 5 X[693] + 3 X[47665], 11 X[693] - 3 X[47677], X[3776] + 5 X[4024], X[3776] - 5 X[4500], 13 X[3776] - 15 X[6545], 7 X[3776] - 5 X[16892], 11 X[3776] - 5 X[47677], 13 X[4024] + 3 X[6545], 7 X[4024] + X[16892], 5 X[4024] - X[47665], 11 X[4024] + X[47677], 13 X[4500] - 3 X[6545], 7 X[4500] - X[16892], 5 X[4500] + X[47665], 11 X[4500] - X[47677], 21 X[6545] - 13 X[16892], 15 X[6545] + 13 X[47665], 33 X[6545] - 13 X[47677], 5 X[16892] + 7 X[47665], 11 X[16892] - 7 X[47677], 11 X[47665] + 5 X[47677], X[650] - 3 X[45343], 3 X[3700] - X[47996], 3 X[4120] + X[47655], X[4838] + 3 X[47790], 3 X[4931] + X[47656], 9 X[4931] - X[47917], 3 X[4931] - X[48270], 3 X[47656] + X[47917], X[47917] - 3 X[48270], X[17161] - 3 X[47882], 3 X[21196] - 5 X[31250], 5 X[26777] - 9 X[47874], 7 X[27115] - 9 X[47879], 7 X[27115] - 3 X[48277], 3 X[47879] - X[48277], 3 X[31147] + X[47658], X[47670] + 3 X[47769], 3 X[47792] + X[48266]

X(48431) lies on these lines: {321, 693}, {650, 45343}, {3700, 47996}, {4120, 47655}, {4698, 4777}, {4820, 28867}, {4838, 47790}, {4931, 47656}, {17161, 47882}, {21196, 31250}, {25666, 28161}, {26777, 47874}, {27115, 47879}, {28183, 31286}, {28851, 48274}, {28882, 48268}, {31147, 47658}, {47670, 47769}, {47792, 48266}

X(48431) = midpoint of X(i) and X(j) for these {i,j}: {3776, 47665}, {4024, 4500}, {47656, 48270}
X(48431) = {X(4931),X(47656)}-harmonic conjugate of X(48270)


X(48432) = X(321)X(693)∩X(3676)X(47662)

Barycentrics    (b - c)*(-3*b*c + 4*(b^2 + c^2)) : :
X(48432) = 9 X[2] - 2 X[48124], X[693] - 8 X[3776], 11 X[693] - 4 X[4024], 15 X[693] - 8 X[4500], 5 X[693] - 12 X[6545], 3 X[693] + 4 X[16892], 9 X[693] - 2 X[47665], 5 X[693] + 2 X[47677], 22 X[3776] - X[4024], 15 X[3776] - X[4500], 10 X[3776] - 3 X[6545], 6 X[3776] + X[16892], 36 X[3776] - X[47665], 20 X[3776] + X[47677], 15 X[4024] - 22 X[4500], 5 X[4024] - 33 X[6545], 3 X[4024] + 11 X[16892], 18 X[4024] - 11 X[47665], 10 X[4024] + 11 X[47677], 2 X[4500] - 9 X[6545], 2 X[4500] + 5 X[16892], 12 X[4500] - 5 X[47665], 4 X[4500] + 3 X[47677], 9 X[6545] + 5 X[16892], 54 X[6545] - 5 X[47665], 6 X[6545] + X[47677], 6 X[16892] + X[47665], 10 X[16892] - 3 X[47677], 5 X[47665] + 9 X[47677], 8 X[3676] - X[47662], 4 X[3798] + 3 X[47652], 6 X[4453] + X[47651], 9 X[4453] - 2 X[48060], 3 X[47651] + 4 X[48060], 9 X[4776] - 2 X[48112], 9 X[6548] - 2 X[48271], 6 X[21104] + X[47667], 6 X[21115] + X[47666], 6 X[21116] + X[47668], 25 X[31209] - 18 X[31992], 5 X[31209] - 12 X[47754], 3 X[31992] - 10 X[47754], 9 X[44435] - 2 X[48046], X[47685] + 6 X[48241], 9 X[47762] - 2 X[48138], 4 X[47950] + 3 X[48107], 2 X[47950] - 9 X[48156], X[48107] + 6 X[48156], 3 X[48175] + 4 X[48326]

X(48432) lies on these lines: {2, 48124}, {321, 693}, {3676, 47662}, {3798, 47652}, {4453, 47651}, {4776, 48112}, {6548, 48271}, {21104, 47667}, {21115, 47666}, {21116, 47668}, {31209, 31233}, {44435, 48046}, {47685, 48241}, {47762, 48138}, {47950, 48107}, {48175, 48326}

X(48432) = crossdifference of every pair of points on line {2210, 17782}
X(48432) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4500, 16892, 47677}, {6545, 16892, 4500}, {6545, 47677, 693}


X(48433) = X(321)X(693)∩X(650)X(44009)

Barycentrics    (b - c)*(-(b*c) + 4*(b^2 + c^2)) : :
X(48433) = 3 X[693] - 8 X[3776], 9 X[693] - 4 X[4024], 13 X[693] - 8 X[4500], 7 X[693] - 12 X[6545], X[693] + 4 X[16892], 7 X[693] - 2 X[47665], 3 X[693] + 2 X[47677], 6 X[3776] - X[4024], 13 X[3776] - 3 X[4500], 14 X[3776] - 9 X[6545], 2 X[3776] + 3 X[16892], 28 X[3776] - 3 X[47665], 4 X[3776] + X[47677], 13 X[4024] - 18 X[4500], 7 X[4024] - 27 X[6545], X[4024] + 9 X[16892], 14 X[4024] - 9 X[47665], 2 X[4024] + 3 X[47677], 14 X[4500] - 39 X[6545], 2 X[4500] + 13 X[16892], 28 X[4500] - 13 X[47665], 12 X[4500] + 13 X[47677], 3 X[6545] + 7 X[16892], 6 X[6545] - X[47665], 18 X[6545] + 7 X[47677], 14 X[16892] + X[47665], 6 X[16892] - X[47677], 3 X[47665] + 7 X[47677], 14 X[650] - 9 X[44009], 4 X[4025] + X[47651], 6 X[4453] - X[47662], 3 X[4776] + 2 X[47930], 2 X[4841] + 3 X[47676], 4 X[14321] - 9 X[44435], 4 X[21104] + X[47657], 6 X[21104] - X[47674], 3 X[47657] + 2 X[47674], 9 X[21115] + X[47669], 6 X[21115] - X[47675], 2 X[47669] + 3 X[47675], 14 X[21212] - 9 X[45684], 7 X[27115] - 2 X[48124], X[47664] - 6 X[47894], X[47697] - 6 X[48241], 3 X[47762] + 2 X[47923], 3 X[47763] + 2 X[47919], 4 X[47960] + X[48107], X[48079] - 6 X[48156]

X(48433) lies on these lines: {321, 693}, {650, 44009}, {4025, 47651}, {4453, 47662}, {4776, 47930}, {4841, 47676}, {14321, 44435}, {21104, 47657}, {21115, 47669}, {21212, 45684}, {27115, 48124}, {30520, 31209}, {47664, 47894}, {47697, 48241}, {47762, 47923}, {47763, 47919}, {47960, 48107}, {48079, 48156}

X(48433) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3776, 16892, 47677}, {3776, 47677, 693}, {6545, 47665, 693}


X(48434) = X(321)X(693)∩X(918)X(47781)

Barycentrics    (b - c)*(b*c + 4*(b^2 + c^2)) : :
X(48434) = 5 X[693] - 8 X[3776], 7 X[693] - 4 X[4024], 11 X[693] - 8 X[4500], 3 X[693] - 4 X[6545], X[693] - 4 X[16892], 5 X[693] - 2 X[47665], X[693] + 2 X[47677], 14 X[3776] - 5 X[4024], 11 X[3776] - 5 X[4500], 6 X[3776] - 5 X[6545], 2 X[3776] - 5 X[16892], 4 X[3776] - X[47665], 4 X[3776] + 5 X[47677], 11 X[4024] - 14 X[4500], 3 X[4024] - 7 X[6545], X[4024] - 7 X[16892], 10 X[4024] - 7 X[47665], 2 X[4024] + 7 X[47677], 6 X[4500] - 11 X[6545], 2 X[4500] - 11 X[16892], 20 X[4500] - 11 X[47665], 4 X[4500] + 11 X[47677], X[6545] - 3 X[16892], 10 X[6545] - 3 X[47665], 2 X[6545] + 3 X[47677], 10 X[16892] - X[47665], 2 X[16892] + X[47677], X[47665] + 5 X[47677], 4 X[4025] - X[47662], X[4380] + 2 X[47923], 3 X[4453] - 2 X[47789], 2 X[4467] + X[47651], 2 X[4951] - 3 X[44429], 2 X[10196] - 3 X[47886], 4 X[21104] - X[47655], 5 X[26777] - 2 X[48124], X[26853] + 2 X[47919], 5 X[31209] - 4 X[47770], 2 X[47653] + X[48107], X[47657] + 2 X[47676], X[47666] + 2 X[47930], 2 X[47673] + X[47675], 4 X[47960] - X[48079]

X(48434) lies on these lines: {321, 693}, {918, 47781}, {3004, 47769}, {4025, 47662}, {4380, 47923}, {4453, 47789}, {4467, 47651}, {4776, 30519}, {4951, 44429}, {10196, 47886}, {14077, 30613}, {21104, 47655}, {25259, 47756}, {26777, 48124}, {26853, 47919}, {28863, 47762}, {28898, 48156}, {30520, 31150}, {31209, 47770}, {47653, 48107}, {47657, 47676}, {47660, 47758}, {47666, 47930}, {47673, 47675}, {47754, 47870}, {47772, 47880}, {47960, 48079}, {48237, 48241}

X(48434) = reflection of X(i) in X(j) for these {i,j}: {25259, 47756}, {31150, 47894}, {47660, 47758}, {47769, 3004}, {47772, 47880}, {47870, 47754}, {48237, 48241}
X(48434) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3776, 47665, 693}, {16892, 47677, 693}


X(48435) = X(321)X(693)∩X(522)X(47651)

Barycentrics    (b - c)*(3*b*c + 4*(b^2 + c^2)) : :
X(48435) = 7 X[693] - 8 X[3776], 5 X[693] - 4 X[4024], 9 X[693] - 8 X[4500], 11 X[693] - 12 X[6545], 3 X[693] - 4 X[16892], 3 X[693] - 2 X[47665], 10 X[3776] - 7 X[4024], 9 X[3776] - 7 X[4500], 22 X[3776] - 21 X[6545], 6 X[3776] - 7 X[16892], 12 X[3776] - 7 X[47665], 4 X[3776] - 7 X[47677], 9 X[4024] - 10 X[4500], 11 X[4024] - 15 X[6545], 3 X[4024] - 5 X[16892], 6 X[4024] - 5 X[47665], 2 X[4024] - 5 X[47677], 22 X[4500] - 27 X[6545], 2 X[4500] - 3 X[16892], 4 X[4500] - 3 X[47665], 4 X[4500] - 9 X[47677], 9 X[6545] - 11 X[16892], 18 X[6545] - 11 X[47665], 6 X[6545] - 11 X[47677], 2 X[16892] - 3 X[47677], X[47665] - 3 X[47677], 3 X[47657] - 2 X[47667], 4 X[3798] - 3 X[47660], 10 X[3798] - 9 X[47768], 5 X[47660] - 6 X[47768], 3 X[4380] - 2 X[48138], 3 X[4467] - 2 X[48060], 3 X[47662] - 4 X[48060], 2 X[4820] - 3 X[48156], 3 X[17494] - 2 X[48124], 3 X[47653] - 2 X[47950], 4 X[47950] - 3 X[48079], 3 X[47666] - 2 X[48112], 3 X[47673] - X[48112], 5 X[31209] - 6 X[47894], 5 X[31209] - 4 X[48271], 3 X[47894] - 2 X[48271], 3 X[45746] - 2 X[48046], 3 X[46915] - 2 X[48087], 2 X[47670] - 3 X[47675], X[47670] - 3 X[47930]

X(48435) lies on these lines: {321, 693}, {522, 47651}, {918, 47657}, {2786, 47937}, {3798, 47660}, {4380, 28863}, {4467, 47662}, {4764, 4777}, {4820, 48156}, {17161, 30520}, {17494, 48124}, {28183, 47650}, {28846, 47654}, {28851, 47668}, {28894, 48107}, {28898, 47653}, {30519, 47666}, {31209, 47894}, {45746, 48046}, {46915, 48087}, {47655, 47676}, {47670, 47675}

X(48435) = reflection of X(i) in X(j) for these {i,j}: {693, 47677}, {47655, 47676}, {47662, 4467}, {47664, 17161}, {47665, 16892}, {47666, 47673}, {47675, 47930}, {48079, 47653}
X(48435) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16892, 47665, 693}, {47665, 47677, 16892}, {47894, 48271, 31209}


X(48436) = X(321)X(693)∩X(522)X(47662)

Barycentrics    (b - c)*(5*b*c + 4*(b^2 + c^2)) : :
X(48436) = 9 X[693] - 8 X[3776], 3 X[693] - 4 X[4024], 7 X[693] - 8 X[4500], 13 X[693] - 12 X[6545], 5 X[693] - 4 X[16892], 3 X[693] - 2 X[47677], 2 X[3776] - 3 X[4024], 7 X[3776] - 9 X[4500], 26 X[3776] - 27 X[6545], 10 X[3776] - 9 X[16892], 4 X[3776] - 9 X[47665], 4 X[3776] - 3 X[47677], 7 X[4024] - 6 X[4500], 13 X[4024] - 9 X[6545], 5 X[4024] - 3 X[16892], 2 X[4024] - 3 X[47665], 26 X[4500] - 21 X[6545], 10 X[4500] - 7 X[16892], 4 X[4500] - 7 X[47665], 12 X[4500] - 7 X[47677], 15 X[6545] - 13 X[16892], 6 X[6545] - 13 X[47665], 18 X[6545] - 13 X[47677], 2 X[16892] - 5 X[47665], 6 X[16892] - 5 X[47677], 3 X[47665] - X[47677], 3 X[47655] - 2 X[47674], 4 X[4122] - 3 X[48175], 5 X[4467] - 6 X[4786], 3 X[4776] - 2 X[47673], 2 X[4841] - 3 X[25259], 4 X[4841] - 3 X[47657], 4 X[14321] - 3 X[45746], 2 X[17161] - 3 X[31150], 3 X[31150] - 4 X[48271], 5 X[31209] - 6 X[47870], 3 X[47666] - 2 X[47669]

X(48436) lies on these lines: {321, 693}, {522, 47662}, {523, 47910}, {918, 47655}, {3644, 4777}, {4122, 48175}, {4462, 23879}, {4467, 4786}, {4776, 47673}, {4820, 47653}, {4838, 30519}, {4841, 25259}, {14321, 45746}, {14779, 47914}, {17161, 31150}, {28183, 47663}, {28846, 47658}, {28894, 48079}, {28898, 47659}, {31209, 47870}, {47654, 48269}, {47666, 47669}, {47668, 48082}

X(48436) = reflection of X(i) in X(j) for these {i,j}: {693, 47665}, {14779, 47914}, {17161, 48271}, {47653, 4820}, {47654, 48269}, {47657, 25259}, {47668, 48082}, {47675, 4838}, {47677, 4024}, {48107, 47659}
X(48436) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4024, 47677, 693}, {17161, 48271, 31150}, {47665, 47677, 4024}


X(48437) = X(321)X(693)∩X(514)X(4958)

Barycentrics    (b - c)*(7*b*c + 4*(b^2 + c^2)) : :
X(48437) = 11 X[693] - 8 X[3776], X[693] - 4 X[4024], 5 X[693] - 8 X[4500], 5 X[693] - 4 X[6545], 7 X[693] - 4 X[16892], X[693] + 2 X[47665], 5 X[693] - 2 X[47677], 2 X[3776] - 11 X[4024], 5 X[3776] - 11 X[4500], 10 X[3776] - 11 X[6545], 14 X[3776] - 11 X[16892], 4 X[3776] + 11 X[47665], 20 X[3776] - 11 X[47677], 5 X[4024] - 2 X[4500], 5 X[4024] - X[6545], 7 X[4024] - X[16892], 2 X[4024] + X[47665], 10 X[4024] - X[47677], 14 X[4500] - 5 X[16892], 4 X[4500] + 5 X[47665], 4 X[4500] - X[47677], 7 X[6545] - 5 X[16892], 2 X[6545] + 5 X[47665], 2 X[16892] + 7 X[47665], 10 X[16892] - 7 X[47677], 5 X[47665] + X[47677], 4 X[3700] - X[47657], 5 X[31150] - 6 X[31992], 3 X[31150] - 4 X[47770], 9 X[31992] - 10 X[47770], 3 X[31992] - 5 X[47870], 2 X[47770] - 3 X[47870], 3 X[4789] - 2 X[47758], 2 X[4820] + X[47659], 4 X[4820] - X[48079], 2 X[47659] + X[48079], 2 X[4838] + X[47666], 2 X[17161] - 5 X[31209], 2 X[25259] + X[47655], X[47651] - 4 X[48268], X[47658] + 2 X[48269], X[47664] - 4 X[48271], X[47668] - 4 X[48270], 2 X[47756] - 3 X[47790]

X(48437) lies on these lines: {321, 693}, {514, 4958}, {523, 47769}, {3700, 47657}, {4448, 4664}, {4467, 47789}, {4776, 4931}, {4789, 47758}, {4820, 47659}, {4838, 47666}, {4944, 46915}, {4951, 47975}, {10196, 48277}, {17161, 31209}, {25259, 47655}, {28151, 47774}, {28161, 30565}, {28165, 47775}, {28183, 47771}, {28205, 47776}, {28898, 47792}, {45343, 47886}, {47651, 48268}, {47658, 48269}, {47664, 48271}, {47668, 48270}, {47756, 47790}, {47762, 47873}

X(48437) = reflection of X(i) in X(j) for these {i,j}: {4467, 47789}, {4776, 4931}, {6545, 4500}, {31150, 47870}, {46915, 4944}, {47657, 47781}, {47677, 6545}, {47762, 47873}, {47781, 3700}, {47886, 45343}, {47975, 4951}, {48277, 10196}
X(48437) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4024, 47665, 693}, {4500, 47677, 693}, {4820, 47659, 48079}


X(48438) = X(321)X(693)∩X(522)X(48138)

Barycentrics    (b - c)*(6*b*c + 5*(b^2 + c^2)) : :
X(48438) = 11 X[693] - 10 X[3776], 4 X[693] - 5 X[4024], 9 X[693] - 10 X[4500], 16 X[693] - 15 X[6545], 6 X[693] - 5 X[16892], 3 X[693] - 5 X[47665], 7 X[693] - 5 X[47677], 8 X[3776] - 11 X[4024], 9 X[3776] - 11 X[4500], 32 X[3776] - 33 X[6545], 12 X[3776] - 11 X[16892], 6 X[3776] - 11 X[47665], 14 X[3776] - 11 X[47677], 9 X[4024] - 8 X[4500], 4 X[4024] - 3 X[6545], 3 X[4024] - 2 X[16892], 3 X[4024] - 4 X[47665], 7 X[4024] - 4 X[47677], 32 X[4500] - 27 X[6545], 4 X[4500] - 3 X[16892], 2 X[4500] - 3 X[47665], 14 X[4500] - 9 X[47677], 9 X[6545] - 8 X[16892], 9 X[6545] - 16 X[47665], 21 X[6545] - 16 X[47677], 7 X[16892] - 6 X[47677], 7 X[47665] - 3 X[47677], 3 X[4120] - 2 X[47673], 3 X[4984] - 4 X[47660], 3 X[4988] - 4 X[48046], 9 X[6544] - 8 X[21196], 3 X[6546] - 2 X[17161], 2 X[47667] - 3 X[48082], 2 X[47950] - 3 X[48266]

X(48438) lies on these lines: {321, 693}, {522, 48138}, {523, 47904}, {918, 47670}, {4120, 47673}, {4777, 48124}, {4984, 47660}, {4988, 48046}, {6544, 21196}, {6546, 17161}, {28161, 48117}, {28183, 48130}, {28221, 48145}, {28894, 47937}, {30519, 47671}, {47667, 48082}, {47950, 48266}

X(48438) = reflection of X(16892) in X(47665)
X(48438) = {X(16892),X(47665)}-harmonic conjugate of X(4024)


X(48439) = X(2)X(39)∩X(125)X(5031)

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

X(48439) lies on the cubic K1274 and these lines: {2, 39}, {125, 5031}, {511, 13518}, {669, 9148}, {3222, 5970}, {22329, 36950}, {39080, 47638}

X(48439) = reflection of X(32526) in X(32530)
X(48439) = complement of X(32526)
X(48439) = anticomplement of X(32530)
X(48439) = orthoptic-circle-of-Steiner-inellipse-inverse of X(76)
X(48439) = orthoptic-circle-of-Steiner-circumellipse-inverse of X(20081)
X(48439) = Neuberg-circles-radical-circle-inverse of X(2)
X(48439) = psi-transform of X(18906)
X(48439) = X(9148)-lineconjugate of X(669)
X(48439) = {X(2),X(32526)}-harmonic conjugate of X(32530)


X(48440) = X(2)X(32)∩X(3005)X(14420)

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

X(48440) lies on the cubic K1274 and these lines: {2, 32}, {3005, 14420}, {3291, 35971}, {5976, 39079}, {13519, 29012}, {15449, 22329}

X(48440) = orthoptic-circle-of-Steiner-inellipse-inverse of X(83)
X(48440) = orthoptic-circle-of-Steiner-circumellipse-inverse of X(20088)
X(48440) = X(14420)-line conjugate of X(3005)


X(48441) = X(2)X(17)∩X(23)X(31939)

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

X(48441) lies on the cubic K1274 and these lines: {2, 17}, {23, 31939}, {6109, 33500}, {22739, 44666}

X(48441) = orthoptic-circle-of-Steiner-inellipse-inverse of X(17)
X(48441) = orthoptic-circle-of-Steiner-circumellipse-inverse of X(22113)


X(48442) = X(2)X(18)∩X(23)X(31940)

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

X(48442) lies on the cubic K1274 and these lines: {2, 18}, {23, 31940}, {6108, 33498}, {22738, 44667}

X(48442) = orthoptic circle of the Steiner inellipe inverse of X(18)
X(48442) = orthoptic circle of the Steiner circumellipe inverse of X(22114)


X(48443) = X(2)X(846)∩X(86)X(9432)

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

X(48443) lies on the cubic K1274 and these lines: {2, 846}, {86, 9432}, {87, 7312}, {106, 16823}, {242, 468}, {244, 27912}, {524, 3756}, {740, 5205}, {1213, 39059}, {1357, 1447}, {2789, 5029}, {2802, 16830}, {5121, 17770}, {7292, 8054}, {20098, 39581}, {24627, 24697}, {27064, 40533}

X(48443) = orthoptic-circle-of-Steiner-inellipse-inverse of X(11599)
X(48443) = X(2789)-lineconjugate of X(5029)


X(48444) = X(2)X(694)∩X(468)X(42068)

Barycentrics    a^6*b^4 + 2*a^4*b^6 - 4*a^6*b^2*c^2 + a^4*b^4*c^2 - 3*a^2*b^6*c^2 + a^6*c^4 + a^4*b^2*c^4 + b^6*c^4 + 2*a^4*c^6 - 3*a^2*b^2*c^6 + b^4*c^6 : :
X(48444) = 3 X[2] + X[9998]

X(48444) lies on the cubics K796 and K1274 and these lines: {2, 694}, {468, 42068}, {511, 32530}, {729, 1078}, {732, 32526}, {3231, 38996}, {3491, 5972}, {3589, 6786}, {5027, 11176}, {5152, 20998}, {6292, 35971}

X(48444) = midpoint of X(9998) and X(13518)
X(48444) = complement of X(13518)
X(48444) = orthoptic-circle-of-Steiner-inellipse-inverse of X(1916)
X(48444) = psi-transform of X(194)
X(48444) = X(11176)-lineconjugate of X(5027)
X(48444) = {X(2),X(9998)}-harmonic conjugate of X(13518)


X(48445) = X(6)X(30496)∩X(20)X(185)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^4*b^4 + a^2*b^6 - 4*a^4*b^2*c^2 - b^6*c^2 + a^4*c^4 + 2*b^4*c^4 + a^2*c^6 - b^2*c^6) : :
X(48445) = 4 X[1691] - 3 X[47638]

X(48445) lies on these lines: {6, 30496}, {20, 185}, {125, 5031}, {184, 1613}, {217, 1692}, {287, 34238}, {512, 1570}, {1899, 5207}, {2076, 19459}, {3491, 39141}, {8779, 46627}, {8858, 12215}, {10602, 15514}, {10605, 35456}, {14912, 40254}, {19125, 35006}, {23526, 41532}, {35388, 39643}

X(48445) = midpoint of X(193) and X(32529)
X(48445) = reflection of X(5167) in X(1692)
X(48445) = Neuberg-circles-radical-circle-inverse of X(20)
X(48445) = X(18829)-Ceva conjugate of X(647)
X(48445) = crosssum of X(419) and X(9308)
X(48445) = crossdifference of every pair of points on line {193, 2451}
X(48445) = X(i)-lineconjugate of X(j) for these (i,j): {20, 193}, {512, 2451}


X(48446) = ANTIGONAL CONJUGATE OF X(25411)

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

See Kadir Altintas and César Lozada euclid 5023.

X(48446) lies on this line: {354, 3254}

X(48446) = antigonal conjugate of X(25411)
X(48446) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(25411)}} and {{A, B, C, X(7), X(15346)}}


X(48447) = ANTIGONAL CONJUGATE OF X(25412)

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

See Kadir Altintas and César Lozada euclid 5023.

X(48447) lies on this line: {3057, 12641}

X(48447) = antigonal conjugate of X(25412)
X(48447) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(25412)}} and {{A, B, C, X(8), X(15347)}}


X(48448) = X(3)X(10229)∩X(122)X(154)

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

See Kadir Altintas and César Lozada euclid 5023.

X(48448) lies on these lines: {3, 10229}, {122, 154}, {2867, 16096}, {3532, 10991}

X(48448) = inverse of X(10229) in circumcircle
X(48448) = intersection, other than A, B, C, of circumconics {{A, B, C, X(20), X(14572)}} and {{A, B, C, X(122), X(13611)}}


X(48449) = X(6)X(661)∩X(32)X(38938)

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

X(48449) lies on the cubic K222 and these lines: {6, 661}, {32, 38938}, {80, 5291}, {115, 34172}, {187, 759}, {385, 14616}, {919, 19628}, {1411, 17962}, {2161, 17735}, {3724, 6187}, {4386, 36815}, {24624, 35466}, {36716, 45926}

X(48449) = barycentric product X(5202)*X(14616)
X(48449) = barycentric quotient X(5202)/X(758)


X(48450) = X(6)X(351)∩X(110)X(187)

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

X(48450) lies on the cubic K222 and these lines: {6, 351}, {110, 187}, {111, 21906}, {232, 17968}, {385, 18823}, {543, 37859}, {574, 15566}, {2434, 9155}, {2482, 5468}, {2502, 40282}, {3455, 9215}, {5467, 39689}, {5967, 9125}, {9123, 35606}, {9147, 9180}, {9156, 14609}

X(48450) = isogonal conjugate of X(17948)
X(48450) = X(i)-isoconjugate of X(j) for these (i,j): {1, 17948}, {2, 17955}, {75, 17964}, {543, 897}, {661, 34760}, {662, 18007}, {799, 17993}, {923, 45809}, {1577, 23348}, {2502, 46277}, {8371, 36085}, {9182, 23894}
X(48450) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 17948), (206, 17964), (1084, 18007), (2482, 45809), (6593, 543), (32664, 17955), (36830, 34760), (38988, 8371), (38996, 17993)
X(48450) = crosssum of X(543) and X(1641)
X(48450) = crossdifference of every pair of points on line {543, 8371}
X(48450) = X(37859)-lineconjugate of X(543)
X(48450) = barycentric product X(i)*X(j) for these {i,j}: {110, 34763}, {187, 18823}, {351, 9170}, {524, 843}, {5467, 9180}
X(48450) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 17948}, {31, 17955}, {32, 17964}, {110, 34760}, {187, 543}, {351, 8371}, {512, 18007}, {524, 45809}, {669, 17993}, {843, 671}, {1576, 23348}, {5467, 9182}, {14567, 2502}, {18823, 18023}, {34763, 850}, {39689, 1641}


X(48451) = X(6)X(647)∩X(74)X(187)

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

X(48451) lies on the cubic K222 and these lines: {6, 647}, {32, 14264}, {39, 14385}, {50, 46147}, {74, 187}, {111, 232}, {115, 34150}, {230, 12079}, {323, 3284}, {385, 1494}, {511, 46233}, {543, 38894}, {1495, 3003}, {2394, 35906}, {3163, 14611}, {3258, 6128}, {3470, 5007}, {5008, 39239}, {5191, 47427}, {6000, 46232}, {6103, 17986}, {7735, 36875}, {8779, 18877}, {10311, 35908}, {10317, 44715}, {14999, 23967}, {36896, 40135}, {39174, 39643}

X(48451) = isogonal conjugate of the polar conjugate of X(17986)
X(48451) = X(i)-isoconjugate of X(j) for these (i,j): {842, 14206}, {2173, 5641}, {5649, 36035}, {5664, 36096}, {24001, 35909}
X(48451) = X(i)-Dao conjugate of X(j) for these (i, j): (23967, 3260), (36896, 5641), (42426, 46106)
X(48451) = crossdifference of every pair of points on line {30, 5664}
X(48451) = barycentric product X(i)*X(j) for these {i,j}: {3, 17986}, {74, 542}, {1494, 5191}, {1640, 44769}, {2247, 2349}, {2433, 14999}, {6103, 14919}, {7473, 14380}, {9139, 45662}, {9717, 16092}, {14385, 43087}, {18312, 32640}, {32112, 34761}, {34369, 35910}
X(48451) = barycentric quotient X(i)/X(j) for these {i,j}: {74, 5641}, {542, 3260}, {1640, 41079}, {2247, 14206}, {2433, 14223}, {5191, 30}, {6041, 1637}, {6103, 46106}, {17986, 264}, {32112, 34765}, {32640, 5649}, {40352, 842}, {44769, 6035}
X(48451) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {74, 32640, 187}, {1304, 8749, 232}


X(48452) = X(6)X(523)∩X(98)X(187)

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

X(48452) lies on the cubic K222 and these lines: {6, 523}, {32, 14265}, {98, 187}, {111, 6037}, {115, 34175}, {230, 237}, {232, 419}, {248, 290}, {287, 39099}, {384, 14382}, {543, 37858}, {2549, 37991}, {2698, 13137}, {2715, 19627}, {7735, 36874}, {12215, 39941}, {15014, 22456}, {15993, 20021}, {31636, 39101}, {34156, 39646}, {46237, 47388}

X(48452) = X(i)-isoconjugate of X(j) for these (i,j): {1755, 46142}, {1959, 2698}, {23997, 46040}
X(48452) = X(36899)-Dao conjugate of X(46142)
X(48452) = barycentric product X(i)*X(j) for these {i,j}: {98, 2782}, {14382, 16068}
X(48452) = barycentric quotient X(i)/X(j) for these {i,j}: {98, 46142}, {1976, 2698}, {2395, 46040}, {2782, 325}, {6071, 44114}, {16068, 40810}, {40820, 16069}
X(48452) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {290, 2966, 385}, {2966, 41932, 248}, {36897, 36899, 39095}


X(48453) = X(6)X(526)∩X(30)X(41392)

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

X(48453) lies on the cubic K222 and these lines: {6, 526}, {30, 41392}, {32, 38939}, {50, 34370}, {74, 2088}, {111, 248}, {112, 186}, {115, 34174}, {385, 5641}, {1511, 2420}, {1637, 35906}, {1989, 38393}, {2407, 3163}, {2493, 5191}, {5649, 46787}, {8749, 34568}, {9717, 47230}, {23347, 39176}

X(48453) = X(23969)-Ceva conjugate of X(14998)
X(48453) = X(i)-isoconjugate of X(j) for these (i,j): {63, 17986}, {542, 2349}, {1494, 2247}, {5191, 33805}, {18312, 36034}
X(48453) = X(i)-Dao conjugate of X(j) for these (i, j): (3162, 17986), (3258, 18312)
X(48453) = barycentric product X(i)*X(j) for these {i,j}: {30, 842}, {1495, 5641}, {1637, 5649}, {2407, 14998}, {2420, 14223}, {4240, 35909}, {5664, 23969}, {6035, 14398}, {35906, 46787}
X(48453) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 17986}, {842, 1494}, {1495, 542}, {1637, 18312}, {2420, 14999}, {9406, 2247}, {9407, 5191}, {14398, 1640}, {14581, 6103}, {14583, 43087}, {14998, 2394}, {23347, 7473}, {23969, 39290}, {35906, 46786}, {35909, 34767}
X(48453) = {X(2492),X(23350)}-harmonic conjugate of X(14998)

leftri

Centers related to anti-Auriga triangles: X(48454)-X(48542)

rightri

This preamble and centers X(48454)-X(48542) were contributed by César Eliud Lozada, May 12, 2022.

1st- and 2nd- anti-Auriga triangles were introduced in the preamble just before X(45345).


X(48454) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO ABC

Barycentrics    -4*a*(-a+b+c)*(a+b-c)*(a-b+c)*S*sqrt(R*(4*R+r))+2*a^7-2*(b+c)*a^6-3*(b^2+c^2)*a^5+(b+c)*(3*b^2-2*b*c+3*c^2)*a^4+(b^4-c^4)*(b^2-c^2)*a-(b^2-c^2)^3*(b-c) : :
X(48454) = 3*X(45696)-2*X(48460) = 3*X(45696)-4*X(48519)

The reciprocal orthologic center of these triangles is X(4).

X(48454) lies on these lines: {1, 5842}, {3, 18496}, {4, 5597}, {5, 26398}, {20, 26290}, {30, 45696}, {40, 26382}, {55, 26327}, {56, 26387}, {382, 45369}, {485, 45365}, {486, 45366}, {511, 48515}, {515, 45711}, {516, 48487}, {517, 48493}, {528, 48465}, {542, 48470}, {674, 48490}, {944, 26395}, {946, 26365}, {1478, 45371}, {1479, 45373}, {1503, 45724}, {1587, 26385}, {1588, 26384}, {2777, 48472}, {2781, 48529}, {2794, 48462}, {2800, 48501}, {2829, 48464}, {3070, 44582}, {3071, 44583}, {3434, 26291}, {3575, 26371}, {5598, 37000}, {5663, 48483}, {5691, 26296}, {5840, 48533}, {5870, 26344}, {5871, 26334}, {6256, 26400}, {6284, 26351}, {6934, 26425}, {7354, 26380}, {7680, 8186}, {9835, 45354}, {9838, 45362}, {9839, 45361}, {9873, 26310}, {11366, 36999}, {11500, 26389}, {12110, 26379}, {12113, 26383}, {12114, 26319}, {12115, 26402}, {12116, 26401}, {13748, 45345}, {13749, 45348}, {13754, 48485}, {15311, 48513}, {17702, 48535}, {18400, 48521}, {18499, 26410}, {23698, 48531}, {26360, 37820}, {26391, 48468}, {26392, 48469}, {26396, 48476}, {26397, 48477}, {26399, 48482}, {29012, 48517}, {35820, 45357}, {35821, 45360}, {41022, 48456}, {41023, 48458}, {44666, 48499}, {44667, 48497}, {45349, 48466}, {45352, 48467}

X(48454) = reflection of X(i) in X(j) for these (i, j): (48455, 1), (48460, 48519), (48487, 48511), (48489, 45724)
X(48454) = X(48455)-of-5th mixtilinear triangle
X(48454) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 18496, 26386), (3, 26386, 26359), (4, 5597, 26326), (4, 26381, 5597), (20, 26394, 26290), (26398, 45355, 5), (48460, 48519, 45696)


X(48455) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO ABC

Barycentrics    4*a*(-a+b+c)*(a+b-c)*(a-b+c)*S*sqrt(R*(4*R+r))+2*a^7-2*(b+c)*a^6-3*(b^2+c^2)*a^5+(b+c)*(3*b^2-2*b*c+3*c^2)*a^4+(b^4-c^4)*(b^2-c^2)*a-(b^2-c^2)^3*(b-c) : :
X(48455) = 3*X(45697)-2*X(48461) = 3*X(45697)-4*X(48520)

The reciprocal orthologic center of these triangles is X(4).

X(48455) lies on these lines: {1, 5842}, {3, 18498}, {4, 5598}, {5, 26422}, {20, 26291}, {30, 45697}, {40, 26406}, {55, 26326}, {56, 26411}, {382, 45370}, {485, 45368}, {486, 45367}, {511, 48516}, {515, 45712}, {516, 48488}, {517, 48494}, {528, 48464}, {542, 48471}, {674, 48489}, {944, 26419}, {946, 26366}, {1478, 45372}, {1479, 45374}, {1503, 45725}, {1587, 26409}, {1588, 26408}, {2777, 48473}, {2781, 48530}, {2794, 48463}, {2800, 48502}, {2829, 48465}, {3070, 44584}, {3071, 44585}, {3434, 26290}, {3575, 26372}, {5597, 37000}, {5663, 48484}, {5691, 26297}, {5840, 48534}, {5870, 26345}, {5871, 26335}, {6256, 26424}, {6284, 26352}, {6934, 26401}, {7354, 26404}, {7680, 8187}, {9834, 45353}, {9838, 45364}, {9839, 45363}, {9873, 26311}, {11367, 36999}, {11500, 26413}, {12110, 26403}, {12113, 26407}, {12114, 26320}, {12115, 26426}, {12116, 26425}, {13748, 45347}, {13749, 45346}, {13754, 48486}, {15311, 48514}, {17702, 48536}, {18400, 48522}, {18499, 26386}, {23698, 48532}, {26359, 37820}, {26415, 48468}, {26416, 48469}, {26420, 48476}, {26421, 48477}, {26423, 48482}, {29012, 48518}, {35820, 45359}, {35821, 45358}, {41022, 48457}, {41023, 48459}, {44666, 48500}, {44667, 48498}, {45350, 48467}, {45351, 48466}

X(48455) = reflection of X(i) in X(j) for these (i, j): (48454, 1), (48461, 48520), (48488, 48512), (48490, 45725)
X(48455) = X(48454)-of-5th mixtilinear triangle
X(48455) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 18498, 26410), (3, 26410, 26360), (4, 5598, 26327), (4, 26405, 5598), (20, 26418, 26291), (26422, 45356, 5), (48461, 48520, 45697)


X(48456) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 1st ALTINTAS-ISODYNAMIC

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

The reciprocal orthologic center of these triangles is X(4).

X(48456) lies on these lines: {1, 48457}, {13, 5597}, {530, 45696}, {531, 48470}, {542, 45724}, {616, 26394}, {618, 26359}, {5473, 26290}, {5478, 26326}, {5617, 26386}, {6268, 26344}, {6270, 26334}, {6770, 26381}, {6771, 26398}, {7975, 26395}, {9901, 26296}, {9916, 26302}, {9982, 26310}, {10062, 45371}, {10078, 45373}, {11705, 26365}, {12142, 26371}, {12205, 26379}, {12337, 26393}, {12473, 45354}, {12781, 26382}, {12793, 26383}, {12922, 26390}, {12932, 26389}, {12942, 26388}, {12952, 26387}, {12990, 45362}, {12991, 45361}, {13076, 26351}, {13103, 45369}, {13105, 26402}, {13107, 26401}, {13917, 45365}, {13982, 45366}, {18974, 26380}, {19073, 26384}, {19074, 26385}, {22773, 26319}, {22796, 45355}, {35753, 45357}, {35754, 45360}, {41022, 48454}, {41023, 48462}, {48460, 48499}, {48497, 48519}

X(48456) = X(48457)-of-5th mixtilinear triangle
X(48456) = reflection of X(48457) in X(1)


X(48457) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 1st ALTINTAS-ISODYNAMIC

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

The reciprocal orthologic center of these triangles is X(4).

X(48457) lies on these lines: {1, 48456}, {13, 5598}, {530, 45697}, {531, 48471}, {542, 45725}, {616, 26418}, {618, 26360}, {5473, 26291}, {5478, 26327}, {5617, 26410}, {6268, 26345}, {6270, 26335}, {6770, 26405}, {6771, 26422}, {7975, 26419}, {9901, 26297}, {9916, 26303}, {9982, 26311}, {10062, 45372}, {10078, 45374}, {11705, 26366}, {12142, 26372}, {12205, 26403}, {12337, 26417}, {12472, 45353}, {12781, 26406}, {12793, 26407}, {12922, 26414}, {12932, 26413}, {12942, 26412}, {12952, 26411}, {12990, 45364}, {12991, 45363}, {13076, 26352}, {13103, 45370}, {13105, 26426}, {13107, 26425}, {13917, 45368}, {13982, 45367}, {18974, 26404}, {19073, 26408}, {19074, 26409}, {22773, 26320}, {22796, 45356}, {35753, 45359}, {35754, 45358}, {41022, 48455}, {41023, 48463}, {48461, 48500}, {48498, 48520}

X(48457) = X(48456)-of-5th mixtilinear triangle
X(48457) = reflection of X(48456) in X(1)


X(48458) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 2nd ALTINTAS-ISODYNAMIC

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

The reciprocal orthologic center of these triangles is X(4).

X(48458) lies on these lines: {1, 48459}, {14, 5597}, {530, 48470}, {531, 45696}, {542, 45724}, {617, 26394}, {619, 26359}, {5474, 26290}, {5479, 26326}, {5613, 26386}, {6269, 26344}, {6271, 26334}, {6773, 26381}, {6774, 26398}, {7974, 26395}, {9900, 26296}, {9915, 26302}, {9981, 26310}, {10061, 45371}, {10077, 45373}, {11706, 26365}, {12141, 26371}, {12204, 26379}, {12336, 26393}, {12471, 45354}, {12780, 26382}, {12792, 26383}, {12921, 26390}, {12931, 26389}, {12941, 26388}, {12951, 26387}, {12988, 45362}, {12989, 45361}, {13075, 26351}, {13102, 45369}, {13104, 26402}, {13106, 26401}, {13916, 45365}, {13981, 45366}, {18975, 26380}, {19075, 26384}, {19076, 26385}, {22774, 26319}, {22797, 45355}, {35850, 45357}, {35851, 45360}, {41022, 48462}, {41023, 48454}, {48460, 48497}, {48499, 48519}

X(48458) = X(48459)-of-5th mixtilinear triangle
X(48458) = reflection of X(48459) in X(1)


X(48459) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 2nd ALTINTAS-ISODYNAMIC

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

The reciprocal orthologic center of these triangles is X(4).

X(48459) lies on these lines: {1, 48458}, {14, 5598}, {530, 48471}, {531, 45697}, {542, 45725}, {617, 26418}, {619, 26360}, {5474, 26291}, {5479, 26327}, {5613, 26410}, {6269, 26345}, {6271, 26335}, {6773, 26405}, {6774, 26422}, {7974, 26419}, {9900, 26297}, {9915, 26303}, {9981, 26311}, {10061, 45372}, {10077, 45374}, {11706, 26366}, {12141, 26372}, {12204, 26403}, {12336, 26417}, {12470, 45353}, {12780, 26406}, {12792, 26407}, {12921, 26414}, {12931, 26413}, {12941, 26412}, {12951, 26411}, {12988, 45364}, {12989, 45363}, {13075, 26352}, {13102, 45370}, {13104, 26426}, {13106, 26425}, {13916, 45368}, {13981, 45367}, {18975, 26404}, {19075, 26408}, {19076, 26409}, {22774, 26320}, {22797, 45356}, {35850, 45359}, {35851, 45358}, {41022, 48463}, {41023, 48455}, {48461, 48498}, {48500, 48520}

X(48459) = X(48458)-of-5th mixtilinear triangle
X(48459) = reflection of X(48458) in X(1)


X(48460) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO ANTI-ASCELLA

Barycentrics    a*(-4*(-a+b+c)*(a-b+c)*(a+b-c)*S*sqrt(R*(4*R+r))+2*a*b*c*((b+c)*a^2-2*b*c*a-(b^2-c^2)*(b-c))) : :
X(48460) = 3*X(45696)-X(48454) = 3*X(45696)-2*X(48519)

The reciprocal orthologic center of these triangles is X(1593).

X(48460) lies on these lines: {1, 3}, {4, 26371}, {5, 26326}, {20, 26381}, {30, 45696}, {355, 26382}, {371, 44582}, {372, 44583}, {382, 18496}, {511, 45724}, {515, 48511}, {542, 48529}, {952, 48464}, {971, 48495}, {1154, 48521}, {1160, 26344}, {1161, 26334}, {1478, 26388}, {1479, 26387}, {2782, 48462}, {3311, 26385}, {3312, 26384}, {3398, 26379}, {3434, 26410}, {3564, 48489}, {5663, 48472}, {6000, 48513}, {7387, 26302}, {8981, 45365}, {9732, 45348}, {9733, 45345}, {9738, 45352}, {9739, 45349}, {9821, 26310}, {10525, 26390}, {10526, 26389}, {10669, 45362}, {10673, 45361}, {11251, 26383}, {13966, 45366}, {17702, 48483}, {18400, 48505}, {20075, 26405}, {28915, 48541}, {37820, 45356}, {44665, 48485}, {48456, 48499}, {48458, 48497}, {48474, 48537}, {48491, 48517}

X(48460) = midpoint of X(i) and X(j) for these {i, j}: {45711, 48487}, {48462, 48531}, {48464, 48533}, {48472, 48535}, {48474, 48537}
X(48460) = reflection of X(i) in X(j) for these (i, j): (48454, 48519), (48461, 1)
X(48460) = center of circle {{X(48462), X(48464), X(48472)}}
X(48460) = X(48461)-of-5th mixtilinear triangle
X(48460) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 5119, 26352), (1, 25415, 26404), (3, 5597, 26398), (3, 10246, 26366), (3, 45369, 5597), (4, 26386, 45355), (4, 26394, 26386), (371, 45357, 44582), (372, 45360, 44583), (1385, 18443, 48461), (5597, 26290, 3), (9819, 26087, 48461), (11529, 46920, 48461), (11567, 18421, 48461), (15178, 30503, 48461), (26290, 45369, 26398), (26326, 26359, 5), (26351, 26380, 1), (26400, 26423, 26393), (45696, 48454, 48519)


X(48461) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO ANTI-ASCELLA

Barycentrics    a*(4*(-a+b+c)*(a-b+c)*(a+b-c)*S*sqrt(R*(4*R+r))+2*a*b*c*((b+c)*a^2-2*b*c*a-(b^2-c^2)*(b-c))) : :
X(48461) = 3*X(45697)-X(48455) = 3*X(45697)-2*X(48520)

The reciprocal orthologic center of these triangles is X(1593).

X(48461) lies on these lines: {1, 3}, {4, 26372}, {5, 26327}, {20, 26405}, {30, 45697}, {355, 26406}, {371, 44584}, {372, 44585}, {382, 18498}, {511, 45725}, {515, 48512}, {542, 48530}, {952, 48465}, {971, 48496}, {1154, 48522}, {1160, 26345}, {1161, 26335}, {1478, 26412}, {1479, 26411}, {2782, 48463}, {3311, 26409}, {3312, 26408}, {3398, 26403}, {3434, 26386}, {3564, 48490}, {5663, 48473}, {6000, 48514}, {7387, 26303}, {8981, 45368}, {9732, 45346}, {9733, 45347}, {9738, 45350}, {9739, 45351}, {9821, 26311}, {10525, 26389}, {10526, 26413}, {10669, 45364}, {10673, 45363}, {11251, 26407}, {13966, 45367}, {17702, 48484}, {18400, 48506}, {20075, 26381}, {28915, 48542}, {37820, 45355}, {44665, 48486}, {48457, 48500}, {48459, 48498}, {48475, 48538}, {48492, 48518}

X(48461) = midpoint of X(i) and X(j) for these {i, j}: {45712, 48488}, {48463, 48532}, {48465, 48534}, {48473, 48536}, {48475, 48538}
X(48461) = reflection of X(i) in X(j) for these (i, j): (48455, 48520), (48460, 1)
X(48461) = center of circle {{X(48463), X(48465), X(48473)}}
X(48461) = X(48460)-of-5th mixtilinear triangle
X(48461) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 5119, 26351), (1, 25415, 26380), (3, 5598, 26422), (3, 10246, 26365), (3, 45370, 5598), (4, 26410, 45356), (4, 26418, 26410), (371, 45359, 44584), (372, 45358, 44585), (1385, 18443, 48460), (5598, 26291, 3), (9819, 26087, 48460), (11529, 46920, 48460), (11567, 18421, 48460), (15178, 30503, 48460), (26291, 45370, 26422), (26327, 26360, 5), (26352, 26404, 1), (26399, 26424, 26417), (45697, 48455, 48520)


X(48462) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 1st ANTI-BROCARD

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

The reciprocal orthologic center of these triangles is X(5999).

X(48462) lies on the circumcircle of 1st anti-Auriga triangle and these lines: {1, 48463}, {30, 48470}, {98, 5597}, {99, 26290}, {114, 26359}, {115, 26326}, {147, 26394}, {517, 48532}, {542, 45696}, {690, 48472}, {2782, 48460}, {2783, 48533}, {2784, 48511}, {2787, 48464}, {2794, 48454}, {2795, 48541}, {2799, 48474}, {3023, 26380}, {3027, 26351}, {6033, 26386}, {6226, 26344}, {6227, 26334}, {7970, 26395}, {8980, 45365}, {9860, 26296}, {9861, 26302}, {9862, 26310}, {9864, 26382}, {10053, 45371}, {10069, 45373}, {11710, 26365}, {12042, 26398}, {12131, 26371}, {12176, 26379}, {12178, 26393}, {12180, 45354}, {12181, 26383}, {12182, 26390}, {12183, 26389}, {12184, 26388}, {12185, 26387}, {12186, 45362}, {12187, 45361}, {12188, 45369}, {12189, 26402}, {12190, 26401}, {13967, 45366}, {18496, 38744}, {19055, 26384}, {19056, 26385}, {22504, 26319}, {22505, 45355}, {35824, 45357}, {35825, 45360}, {41022, 48458}, {41023, 48456}, {45724, 48491}, {48517, 48519}

X(48462) = X(48463)-of-5th mixtilinear triangle
X(48462) = reflection of X(i) in X(j) for these (i, j): (48463, 1), (48531, 48460)


X(48463) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 1st ANTI-BROCARD

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

The reciprocal orthologic center of these triangles is X(5999).

X(48463) lies on the circumcircle of 2nd anti-Auriga triangle and these lines: {1, 48462}, {30, 48471}, {98, 5598}, {99, 26291}, {114, 26360}, {115, 26327}, {147, 26418}, {517, 48531}, {542, 45697}, {690, 48473}, {2782, 48461}, {2783, 48534}, {2784, 48512}, {2787, 48465}, {2794, 48455}, {2795, 48542}, {2799, 48475}, {3023, 26404}, {3027, 26352}, {6033, 26410}, {6226, 26345}, {6227, 26335}, {7970, 26419}, {8980, 45368}, {9860, 26297}, {9861, 26303}, {9862, 26311}, {9864, 26406}, {10053, 45372}, {10069, 45374}, {11710, 26366}, {12042, 26422}, {12131, 26372}, {12176, 26403}, {12178, 26417}, {12179, 45353}, {12181, 26407}, {12182, 26414}, {12183, 26413}, {12184, 26412}, {12185, 26411}, {12186, 45364}, {12187, 45363}, {12188, 45370}, {12189, 26426}, {12190, 26425}, {13967, 45367}, {18498, 38744}, {19055, 26408}, {19056, 26409}, {22504, 26320}, {22505, 45356}, {35824, 45359}, {35825, 45358}, {41022, 48459}, {41023, 48457}, {45725, 48492}, {48518, 48520}

X(48463) = X(48462)-of-5th mixtilinear triangle
X(48463) = reflection of X(i) in X(j) for these (i, j): (48462, 1), (48532, 48461)


X(48464) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO ANTI-INNER-GARCIA

Barycentrics    a*(4*(a+b-c)*(-a+b+c)*(a-b+c)*(a^3-(b+c)*a^2-(b^2-3*b*c+c^2)*a+(b^2-c^2)*(b-c))*S*sqrt(R*(4*R+r))+b*c*(2*a^7-6*(b+c)*a^6+(b^2+16*b*c+c^2)*a^5+(b+c)*(11*b^2-26*b*c+11*c^2)*a^4-8*(b^2+3*b*c+c^2)*(b-c)^2*a^3-4*(b^2-c^2)*(b-c)*(b^2-4*b*c+c^2)*a^2+(5*b^2-8*b*c+5*c^2)*(b^2-c^2)^2*a-(b^2-c^2)^3*(b-c))) : :

The reciprocal orthologic center of these triangles is X(2077).

X(48464) lies on the circumcircle of 1st anti-Auriga triangle and these lines: {1, 11219}, {11, 26326}, {100, 26290}, {104, 5597}, {119, 26359}, {153, 26394}, {515, 48501}, {517, 48534}, {528, 48455}, {952, 48460}, {1317, 26351}, {1768, 26296}, {2771, 48535}, {2783, 48531}, {2787, 48462}, {2800, 45711}, {2802, 48487}, {2806, 48474}, {2829, 48454}, {2831, 48537}, {5848, 48489}, {8674, 48472}, {9913, 26302}, {10058, 45371}, {10074, 45373}, {10698, 26395}, {10742, 26386}, {11715, 26365}, {12138, 26371}, {12199, 26379}, {12248, 26381}, {12332, 26393}, {12463, 45354}, {12499, 26310}, {12751, 26382}, {12752, 26383}, {12753, 26334}, {12754, 26344}, {12761, 26390}, {12762, 26389}, {12763, 26388}, {12764, 26387}, {12765, 45362}, {12766, 45361}, {12773, 45369}, {12775, 26402}, {12776, 26401}, {13913, 45365}, {13977, 45366}, {18496, 38756}, {19081, 26384}, {19082, 26385}, {22775, 26319}, {22799, 45355}, {26398, 38602}, {35856, 45357}, {35857, 45360}

X(48464) = X(48465)-of-5th mixtilinear triangle
X(48464) = reflection of X(i) in X(j) for these (i, j): (48465, 1), (48533, 48460)


X(48465) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO ANTI-INNER-GARCIA

Barycentrics    a*(-4*(a+b-c)*(-a+b+c)*(a-b+c)*(a^3-(b+c)*a^2-(b^2-3*b*c+c^2)*a+(b^2-c^2)*(b-c))*S*sqrt(R*(4*R+r))+b*c*(2*a^7-6*(b+c)*a^6+(b^2+16*b*c+c^2)*a^5+(b+c)*(11*b^2-26*b*c+11*c^2)*a^4-8*(b^2+3*b*c+c^2)*(b-c)^2*a^3-4*(b^2-c^2)*(b-c)*(b^2-4*b*c+c^2)*a^2+(5*b^2-8*b*c+5*c^2)*(b^2-c^2)^2*a-(b^2-c^2)^3*(b-c))) : :

The reciprocal orthologic center of these triangles is X(2077).

X(48465) lies on the circumcircle of 2nd anti-Auriga triangle and these lines: {1, 11219}, {11, 26327}, {100, 26291}, {104, 5598}, {119, 26360}, {153, 26418}, {515, 48502}, {517, 48533}, {528, 48454}, {952, 48461}, {1317, 26352}, {1768, 26297}, {2771, 48536}, {2783, 48532}, {2787, 48463}, {2800, 45712}, {2802, 48488}, {2806, 48475}, {2829, 48455}, {2831, 48538}, {5848, 48490}, {8674, 48473}, {9913, 26303}, {10058, 45372}, {10074, 45374}, {10698, 26419}, {10742, 26410}, {11715, 26366}, {12138, 26372}, {12199, 26403}, {12248, 26405}, {12332, 26417}, {12462, 45353}, {12499, 26311}, {12751, 26406}, {12752, 26407}, {12753, 26335}, {12754, 26345}, {12761, 26414}, {12762, 26413}, {12763, 26412}, {12764, 26411}, {12765, 45364}, {12766, 45363}, {12773, 45370}, {12775, 26426}, {12776, 26425}, {13913, 45368}, {13977, 45367}, {18498, 38756}, {19081, 26408}, {19082, 26409}, {22775, 26320}, {22799, 45356}, {26422, 38602}, {35856, 45359}, {35857, 45358}

X(48465) = X(48464)-of-5th mixtilinear triangle
X(48465) = reflection of X(i) in X(j) for these (i, j): (48464, 1), (48534, 48461)


X(48466) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 1st ANTI-AURIGA

Barycentrics    2*((b^2+c^2)*a^2-(b^2-c^2)^2)*S+2*a^6-(b^2+c^2)*a^4-(b^2+c^2)*(b^2-c^2)^2 : :
X(48466) = 3*X(2)+X(5870) = 5*X(4)-X(48477) = 3*X(376)+X(48476) = 3*X(381)-X(13749) = X(487)-3*X(9758) = 3*X(591)-X(1160) = X(1160)+3*X(36733) = 7*X(3090)+X(14227) = 5*X(3091)-X(5871) = 9*X(3545)-X(14242) = 5*X(3618)-X(39888) = 3*X(3845)-2*X(14235) = 2*X(9739)-3*X(41490)

The reciprocal orthologic center of these triangles is X(48454).

X(48466) lies on these lines: {2, 5870}, {3, 639}, {4, 372}, {5, 182}, {6, 36656}, {20, 3593}, {30, 9739}, {39, 3071}, {40, 45546}, {55, 45560}, {56, 45562}, {69, 6278}, {114, 642}, {115, 3070}, {141, 6214}, {184, 8968}, {193, 6280}, {371, 6811}, {376, 45522}, {381, 13749}, {382, 45578}, {485, 6776}, {487, 9742}, {489, 7763}, {490, 11185}, {492, 11825}, {515, 45715}, {524, 5874}, {542, 44475}, {546, 14230}, {550, 7690}, {591, 1160}, {615, 36714}, {637, 11824}, {640, 1352}, {944, 45572}, {946, 45500}, {1328, 45102}, {1478, 45580}, {1479, 45582}, {1587, 45515}, {1588, 7374}, {2794, 43121}, {3068, 10784}, {3090, 14227}, {3091, 5871}, {3103, 38383}, {3312, 45440}, {3332, 36689}, {3366, 41020}, {3391, 41021}, {3545, 14242}, {3575, 45502}, {3618, 39888}, {3627, 14239}, {3845, 14235}, {5085, 11313}, {5418, 12257}, {5480, 7584}, {5490, 12124}, {5590, 36701}, {5691, 45530}, {5921, 6281}, {6119, 9756}, {6200, 26441}, {6201, 7586}, {6215, 23312}, {6256, 45528}, {6284, 45570}, {6290, 18440}, {6561, 21736}, {6564, 22618}, {6566, 42259}, {6813, 10577}, {7354, 45506}, {7389, 45552}, {7583, 8550}, {7745, 18993}, {7759, 42858}, {8414, 13882}, {8721, 37343}, {9732, 9766}, {9835, 45536}, {9838, 45569}, {9839, 45566}, {9873, 45538}, {10133, 32588}, {10514, 39887}, {10516, 11314}, {10576, 45511}, {10783, 31412}, {11257, 14234}, {11500, 45520}, {12007, 19117}, {12110, 45504}, {12113, 45548}, {12114, 45540}, {12115, 45584}, {12116, 45586}, {13785, 36711}, {13925, 45869}, {13951, 36712}, {14245, 19058}, {15765, 41022}, {18585, 41023}, {18762, 36657}, {19116, 44474}, {21737, 26468}, {22700, 44364}, {23261, 44526}, {23267, 26330}, {23311, 44882}, {26346, 45473}, {26920, 44637}, {33430, 35824}, {35821, 45565}, {36655, 36990}, {39874, 42277}, {42216, 45862}, {43118, 45438}, {45349, 48454}, {45351, 48455}, {45516, 48469}, {45519, 48468}, {45526, 48482}

X(48466) = midpoint of X(i) and X(j) for these {i, j}: {3, 13748}, {591, 36733}
X(48466) = reflection of X(i) in X(j) for these (i, j): (3627, 14239), (14230, 546), (48467, 5)
X(48466) = complement of the complement of X(5870)
X(48466) = center of circle {{X(3), X(13748), X(18338)}}
X(48466) = X(4)-of-1st anti-Kenmotu-free-vertices triangle
X(48466) = X(13748)-of-anti-X3-ABC reflections triangle
X(48466) = X(13749)-of-Ehrmann-mid triangle
X(48466) = X(13934)-of-outer-Vecten triangle, when ABC is acute
X(48466) = X(48467)-of-Johnson triangle
X(48466) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6289, 639), (3, 45377, 45554), (3, 45554, 641), (4, 372, 45544), (4, 6565, 6251), (4, 8982, 35820), (4, 12256, 6560), (4, 45510, 372), (20, 45508, 45498), (182, 45542, 5), (372, 486, 45577), (3071, 36709, 45545), (6811, 45406, 371), (7584, 36658, 5480), (8550, 45861, 7583), (13785, 36711, 45441), (18762, 36657, 45860), (36990, 42262, 36655)


X(48467) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 1st ANTI-AURIGA

Barycentrics    -2*((b^2+c^2)*a^2-(b^2-c^2)^2)*S+2*a^6-(b^2+c^2)*a^4-(b^2+c^2)*(b^2-c^2)^2 : :
X(48467) = 3*X(2)+X(5871) = 5*X(4)-X(48476) = 3*X(376)+X(48477) = 3*X(381)-X(13748) = X(488)-3*X(9757) = X(1161)-3*X(1991) = X(1161)+3*X(36719) = 7*X(3090)+X(14242) = 5*X(3091)-X(5870) = 9*X(3545)-X(14227) = 5*X(3618)-X(39887) = 3*X(3845)-2*X(14239) = 2*X(9738)-3*X(41491)

The reciprocal orthologic center of these triangles is X(48454).

X(48467) lies on these lines: {2, 5871}, {3, 640}, {4, 371}, {5, 182}, {6, 36655}, {20, 3595}, {30, 9738}, {39, 3070}, {40, 45547}, {55, 45561}, {56, 45563}, {69, 6281}, {114, 641}, {115, 3071}, {141, 6215}, {193, 6279}, {372, 6813}, {376, 45523}, {381, 13748}, {382, 45579}, {427, 8968}, {486, 6776}, {488, 9742}, {489, 11185}, {490, 7763}, {491, 11824}, {515, 45716}, {524, 5875}, {542, 44476}, {546, 14233}, {550, 7692}, {590, 36709}, {638, 11825}, {639, 1352}, {944, 45573}, {946, 45501}, {1161, 1991}, {1327, 45101}, {1478, 45581}, {1479, 45583}, {1587, 7000}, {1588, 45514}, {2794, 43120}, {3069, 10783}, {3090, 14242}, {3091, 5870}, {3102, 38383}, {3311, 45441}, {3332, 36688}, {3367, 41020}, {3392, 41021}, {3545, 14227}, {3575, 45503}, {3618, 39887}, {3627, 14235}, {3845, 14239}, {5085, 11314}, {5418, 21736}, {5420, 12256}, {5480, 7583}, {5491, 12123}, {5591, 36703}, {5691, 45531}, {5921, 6278}, {6118, 9756}, {6202, 7585}, {6214, 23311}, {6256, 45529}, {6284, 45571}, {6289, 18440}, {6396, 8982}, {6565, 22587}, {6567, 42258}, {6811, 10576}, {7354, 45507}, {7388, 45553}, {7584, 8550}, {7745, 18994}, {7759, 42859}, {8406, 13934}, {8721, 37342}, {8911, 44638}, {8976, 36711}, {9733, 9766}, {9834, 45535}, {9835, 45537}, {9838, 45567}, {9839, 45568}, {9873, 45539}, {10132, 32587}, {10515, 39888}, {10516, 11313}, {10577, 45510}, {10784, 42561}, {11257, 14238}, {11500, 45521}, {12007, 19116}, {12110, 45505}, {12113, 45549}, {12114, 45541}, {12115, 45585}, {12116, 45587}, {13665, 36712}, {13993, 45868}, {14231, 19057}, {15765, 41023}, {18538, 36658}, {18585, 41022}, {19117, 44473}, {22699, 44365}, {23251, 44526}, {23273, 26331}, {23312, 44882}, {26336, 45472}, {33431, 35825}, {35820, 45564}, {36656, 36990}, {39874, 42274}, {42215, 45863}, {43119, 45439}, {45350, 48455}, {45352, 48454}, {45517, 48468}, {45518, 48469}, {45527, 48482}

X(48467) = midpoint of X(i) and X(j) for these {i, j}: {3, 13749}, {1991, 36719}
X(48467) = reflection of X(i) in X(j) for these (i, j): (3627, 14235), (14233, 546), (48466, 5)
X(48467) = complement of the complement of X(5871)
X(48467) = center of circle {{X(3), X(13749), X(18338)}}
X(48467) = X(13748)-of-Ehrmann-mid triangle
X(48467) = X(13749)-of-anti-X3-ABC reflections triangle
X(48467) = X(13934)-of-inner-Vecten triangle, when ABC is obtuse
X(48467) = X(45407)-of-1st anti-Kenmotu-free-vertices triangle
X(48467) = X(48466)-of-Johnson triangle
X(48467) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6290, 640), (3, 45378, 45555), (3, 45429, 8989), (3, 45555, 642), (4, 371, 45545), (4, 6564, 6250), (4, 12257, 6561), (4, 26441, 35821), (4, 45511, 371), (20, 45509, 45499), (182, 45543, 5), (371, 485, 45576), (3070, 36714, 45544), (6813, 45407, 372), (7583, 36657, 5480), (8550, 45860, 7584), (13665, 36712, 45440), (18538, 36658, 45861), (36990, 42265, 36656)


X(48468) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 1st ANTI-AURIGA

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

The reciprocal orthologic center of these triangles is X(48454).

X(48468) lies on these lines: {3, 5490}, {4, 493}, {5, 26498}, {20, 26292}, {30, 45699}, {40, 26442}, {55, 26477}, {56, 26471}, {382, 45610}, {485, 18926}, {486, 45606}, {515, 45718}, {944, 26495}, {946, 26367}, {1478, 45612}, {1479, 45614}, {1503, 45727}, {1587, 26460}, {1588, 26454}, {3070, 45597}, {3071, 45596}, {3575, 26373}, {5691, 26298}, {5870, 26347}, {5871, 26337}, {6256, 26500}, {6284, 26353}, {6464, 48469}, {7354, 26433}, {7487, 8948}, {8884, 24244}, {9834, 45589}, {9835, 45591}, {9839, 45603}, {9873, 26312}, {10318, 26329}, {11500, 26483}, {12110, 26427}, {12113, 26447}, {12114, 26322}, {12115, 45615}, {12116, 26501}, {13748, 19498}, {13749, 45413}, {26391, 48454}, {26415, 48455}, {26496, 48476}, {26497, 48477}, {26499, 48482}, {35820, 45601}, {35821, 45600}, {45517, 48467}, {45519, 48466}

X(48468) = X(4)-of-anti-Lucas(+1) homothetic triangle
X(48468) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 18521, 26466), (3, 26466, 5490), (4, 493, 26328), (4, 26439, 493), (20, 26494, 26292), (26498, 45593, 5)


X(48469) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 1st ANTI-AURIGA

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

The reciprocal orthologic center of these triangles is X(48454).

X(48469) lies on these lines: {3, 5491}, {4, 494}, {5, 26507}, {20, 26293}, {30, 45698}, {40, 26443}, {55, 26478}, {56, 26472}, {382, 45609}, {485, 45605}, {486, 18927}, {515, 45717}, {944, 26504}, {946, 26368}, {1478, 45611}, {1479, 45613}, {1503, 45726}, {1587, 26461}, {1588, 26455}, {3070, 45595}, {3071, 45598}, {3575, 26374}, {5691, 26299}, {5870, 26338}, {5871, 45594}, {6256, 26509}, {6284, 26354}, {6464, 48468}, {7354, 26434}, {7487, 8946}, {8884, 8982}, {9834, 45588}, {9835, 45590}, {9838, 45604}, {9873, 26313}, {10318, 26328}, {11500, 26484}, {12110, 26428}, {12113, 26448}, {12114, 26323}, {12115, 26511}, {12116, 26510}, {13748, 45412}, {13749, 19499}, {26392, 48454}, {26416, 48455}, {26505, 48476}, {26506, 48477}, {26508, 48482}, {35820, 45599}, {35821, 45602}, {45516, 48466}, {45518, 48467}

X(48469) = X(4)-of-anti-Lucas(-1) homothetic triangle
X(48469) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 18523, 26467), (3, 26467, 5491), (4, 494, 26329), (4, 26440, 494), (20, 26503, 26293), (26507, 45592, 5)


X(48470) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO ANTI-MCCAY

Barycentrics    12*a*(a^4-(b^2+c^2)*a^2+b^4-b^2*c^2+c^4)*S*sqrt(R*(4*R+r))+(a+b+c)*(4*a^7-4*(b+c)*a^6-5*(b^2+c^2)*a^5+(b+c)*(5*b^2-2*b*c+5*c^2)*a^4+2*(b^2+c^2)^2*a^3-2*(b^3+c^3)*(b^2+c^2)*a^2+(b^2-2*c^2)*(2*b^2-c^2)*(b^2+c^2)*a-(b^2-c^2)*(b-c)*(2*b^2-c^2)*(b^2-2*c^2)) : :

The reciprocal orthologic center of these triangles is X(9855).

X(48470) lies on these lines: {1, 48471}, {30, 48462}, {528, 48532}, {530, 48458}, {531, 48456}, {542, 48454}, {543, 45696}, {671, 5597}, {2482, 26359}, {2782, 48491}, {2796, 48511}, {5969, 48515}, {8591, 26394}, {8724, 26386}, {9830, 45724}, {9875, 26296}, {9876, 26302}, {9878, 26310}, {9880, 26326}, {9881, 26382}, {9882, 26334}, {9883, 26344}, {9884, 26395}, {10054, 45371}, {10070, 45373}, {12117, 26290}, {12132, 26371}, {12191, 26379}, {12243, 26381}, {12258, 26365}, {12326, 26393}, {12346, 45354}, {12347, 26383}, {12348, 26390}, {12349, 26389}, {12350, 26388}, {12351, 26387}, {12352, 45362}, {12353, 45361}, {12354, 26351}, {12355, 45369}, {12356, 26402}, {12357, 26401}, {13908, 45365}, {13968, 45366}, {18969, 26380}, {19057, 26384}, {19058, 26385}, {22565, 26319}, {22566, 45355}, {35698, 45357}, {35699, 45360}

X(48470) = X(48471)-of-5th mixtilinear triangle
X(48470) = reflection of X(i) in X(j) for these (i, j): (48471, 1), (48531, 45696)


X(48471) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO ANTI-MCCAY

Barycentrics    -12*a*(a^4-(b^2+c^2)*a^2+b^4-b^2*c^2+c^4)*S*sqrt(R*(4*R+r))+(a+b+c)*(4*a^7-4*(b+c)*a^6-5*(b^2+c^2)*a^5+(b+c)*(5*b^2-2*b*c+5*c^2)*a^4+2*(b^2+c^2)^2*a^3-2*(b^3+c^3)*(b^2+c^2)*a^2+(b^2-2*c^2)*(2*b^2-c^2)*(b^2+c^2)*a-(b^2-c^2)*(b-c)*(2*b^2-c^2)*(b^2-2*c^2)) : :

The reciprocal orthologic center of these triangles is X(9855).

X(48471) lies on these lines: {1, 48470}, {30, 48463}, {528, 48531}, {530, 48459}, {531, 48457}, {542, 48455}, {543, 45697}, {671, 5598}, {2482, 26360}, {2782, 48492}, {2796, 48512}, {5969, 48516}, {8591, 26418}, {8724, 26410}, {9830, 45725}, {9875, 26297}, {9876, 26303}, {9878, 26311}, {9880, 26327}, {9881, 26406}, {9882, 26335}, {9883, 26345}, {9884, 26419}, {10054, 45372}, {10070, 45374}, {12117, 26291}, {12132, 26372}, {12191, 26403}, {12243, 26405}, {12258, 26366}, {12326, 26417}, {12345, 45353}, {12347, 26407}, {12348, 26414}, {12349, 26413}, {12350, 26412}, {12351, 26411}, {12352, 45364}, {12353, 45363}, {12354, 26352}, {12355, 45370}, {12356, 26426}, {12357, 26425}, {13908, 45368}, {13968, 45367}, {18969, 26404}, {19057, 26408}, {19058, 26409}, {22565, 26320}, {22566, 45356}, {35698, 45359}, {35699, 45358}

X(48471) = X(48470)-of-5th mixtilinear triangle
X(48471) = reflection of X(i) in X(j) for these (i, j): (48470, 1), (48532, 45697)


X(48472) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO ANTI-ORTHOCENTROIDAL

Barycentrics    a*(4*(a+b-c)*(-a+b+c)*(a-b+c)*(a^6-(b^2+c^2)*a^4-(b^4-3*b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2))*S*sqrt(R*(4*R+r))+a*((b^2+c^2)*a^9-(b+c)^3*a^8-4*(b^4-b^2*c^2+c^4)*a^7+2*(2*b^2-3*b*c+2*c^2)*(b+c)^3*a^6+(b^2+c^2)*(6*b^4-11*b^2*c^2+6*c^4)*a^5-(6*b^4+6*c^4-b*c*(18*b^2-25*b*c+18*c^2))*(b+c)^3*a^4-2*(b^2-c^2)^2*(2*b^4+7*b^2*c^2+2*c^4)*a^3+2*(b^3+c^3)*(b^2-c^2)^2*(2*b^2-3*b*c+2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)*(b^4+7*b^2*c^2+c^4)*a-(b^2-c^2)^3*(b-c)*(b^2-b*c+c^2)^2)) : :

The reciprocal orthologic center of these triangles is X(12112).

X(48472) lies on the circumcircle of 1st anti-Auriga triangle and these lines: {1, 48473}, {30, 48483}, {74, 5597}, {110, 26290}, {113, 26359}, {125, 26326}, {146, 26394}, {517, 48536}, {541, 45696}, {542, 48531}, {690, 48462}, {1503, 48529}, {1539, 45355}, {2771, 48533}, {2777, 48454}, {2781, 45724}, {2836, 48541}, {3024, 26380}, {3028, 26351}, {5663, 48460}, {7725, 26334}, {7726, 26344}, {7728, 26386}, {7978, 26395}, {8674, 48464}, {8994, 45365}, {9517, 48474}, {9904, 26296}, {9919, 26302}, {9984, 26310}, {10065, 45371}, {10081, 45373}, {10620, 45369}, {10628, 48521}, {11709, 26365}, {12041, 26398}, {12133, 26371}, {12192, 26379}, {12244, 26381}, {12327, 26393}, {12366, 45354}, {12368, 26382}, {12369, 26383}, {12371, 26390}, {12372, 26389}, {12373, 26388}, {12374, 26387}, {12377, 45362}, {12378, 45361}, {12381, 26402}, {12382, 26401}, {13969, 45366}, {17702, 48485}, {18496, 38790}, {19059, 26384}, {19060, 26385}, {22583, 26319}, {35826, 45357}, {35827, 45360}

X(48472) = X(48473)-of-5th mixtilinear triangle
X(48472) = reflection of X(i) in X(j) for these (i, j): (48473, 1), (48535, 48460)


X(48473) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO ANTI-ORTHOCENTROIDAL

Barycentrics    a*(-4*(a+b-c)*(-a+b+c)*(a-b+c)*(a^6-(b^2+c^2)*a^4-(b^4-3*b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2))*S*sqrt(R*(4*R+r))+a*((b^2+c^2)*a^9-(b+c)^3*a^8-4*(b^4-b^2*c^2+c^4)*a^7+2*(2*b^2-3*b*c+2*c^2)*(b+c)^3*a^6+(b^2+c^2)*(6*b^4-11*b^2*c^2+6*c^4)*a^5-(6*b^4+6*c^4-b*c*(18*b^2-25*b*c+18*c^2))*(b+c)^3*a^4-2*(b^2-c^2)^2*(2*b^4+7*b^2*c^2+2*c^4)*a^3+2*(b^3+c^3)*(b^2-c^2)^2*(2*b^2-3*b*c+2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)*(b^4+7*b^2*c^2+c^4)*a-(b^2-c^2)^3*(b-c)*(b^2-b*c+c^2)^2)) : :

The reciprocal orthologic center of these triangles is X(12112).

X(48473) lies on the circumcircle of 2nd anti-Auriga triangle and these lines: {1, 48472}, {30, 48484}, {74, 5598}, {110, 26291}, {113, 26360}, {125, 26327}, {146, 26418}, {517, 48535}, {541, 45697}, {542, 48532}, {690, 48463}, {1503, 48530}, {1539, 45356}, {2771, 48534}, {2777, 48455}, {2781, 45725}, {2836, 48542}, {3024, 26404}, {3028, 26352}, {5663, 48461}, {7725, 26335}, {7726, 26345}, {7728, 26410}, {7978, 26419}, {8674, 48465}, {8994, 45368}, {9517, 48475}, {9904, 26297}, {9919, 26303}, {9984, 26311}, {10065, 45372}, {10081, 45374}, {10620, 45370}, {10628, 48522}, {11709, 26366}, {12041, 26422}, {12133, 26372}, {12192, 26403}, {12244, 26405}, {12327, 26417}, {12365, 45353}, {12368, 26406}, {12369, 26407}, {12371, 26414}, {12372, 26413}, {12373, 26412}, {12374, 26411}, {12377, 45364}, {12378, 45363}, {12381, 26426}, {12382, 26425}, {13969, 45367}, {17702, 48486}, {18498, 38790}, {19059, 26408}, {19060, 26409}, {22583, 26320}, {35826, 45359}, {35827, 45358}

X(48473) = X(48472)-of-5th mixtilinear triangle
X(48473) = reflection of X(i) in X(j) for these (i, j): (48472, 1), (48536, 48461)


X(48474) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a*(4*(a+b-c)*(a-b+c)*(-a+b+c)*(a^10-(b^2+c^2)*a^8+b^2*c^2*a^6-(b^6-c^6)*(b^2-c^2)*a^2+(b^8-c^8)*(b^2-c^2))*S*sqrt(R*(4*R+r))+a*((b^2+c^2)*a^13-(b+c)^3*a^12-2*(b^4+c^4)*a^11+2*(b^3+c^3)*(b+c)^2*a^10-(b^4-3*b^2*c^2+c^4)*(b^2+c^2)*a^9+(b^4+c^4-b*c*(2*b^2-b*c+2*c^2))*(b+c)^3*a^8+4*(b^6-c^6)*(b^2-c^2)*a^7-4*(b^2-c^2)^2*(b+c)*(b^4+c^4-b*c*(b^2-b*c+c^2))*a^6-(b^8-c^8)*a^5*(b^2-c^2)+(b^2-c^2)^3*(b-c)*(b^4+c^4)*a^4-2*(b^4-c^4)^2*(b^2+c^2)^2*a^3+2*(b^2-c^2)^2*(b-c)^2*(b^3-c^3)*(b^4-c^4)*a^2+(b^4-c^4)*(b^2-c^2)*(b^8+c^8+b^2*c^2*(5*b^4+4*b^2*c^2+5*c^4))*a-(b^2-c^2)^3*(b-c)^5*(b^2+b*c+c^2)^2)) : :

The reciprocal orthologic center of these triangles is X(19158).

X(48474) lies on the circumcircle of 1st anti-Auriga triangle and these lines: {1, 48475}, {112, 26290}, {127, 26326}, {132, 26359}, {517, 48538}, {1297, 5597}, {2781, 48535}, {2794, 48531}, {2799, 48462}, {2806, 48464}, {2831, 48533}, {2838, 48541}, {3320, 26351}, {6020, 26380}, {9517, 48472}, {9530, 45696}, {12145, 26371}, {12207, 26379}, {12253, 26381}, {12265, 26365}, {12340, 26393}, {12384, 26394}, {12408, 26296}, {12413, 26302}, {12479, 45354}, {12503, 26310}, {12784, 26382}, {12796, 26383}, {12805, 26334}, {12806, 26344}, {12918, 26386}, {12925, 26390}, {12935, 26389}, {12945, 26388}, {12955, 26387}, {12996, 45362}, {12997, 45361}, {13099, 26395}, {13115, 45369}, {13116, 45371}, {13117, 45373}, {13118, 26402}, {13119, 26401}, {13918, 45365}, {13985, 45366}, {19093, 26384}, {19094, 26385}, {19159, 26319}, {19160, 45355}, {26398, 38624}, {35828, 45357}, {35829, 45360}, {48460, 48537}

X(48474) = X(48475)-of-5th mixtilinear triangle
X(48474) = reflection of X(i) in X(j) for these (i, j): (48475, 1), (48537, 48460)


X(48475) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a*(-4*(a+b-c)*(a-b+c)*(-a+b+c)*(a^10-(b^2+c^2)*a^8+b^2*c^2*a^6-(b^6-c^6)*(b^2-c^2)*a^2+(b^8-c^8)*(b^2-c^2))*S*sqrt(R*(4*R+r))+a*((b^2+c^2)*a^13-(b+c)^3*a^12-2*(b^4+c^4)*a^11+2*(b^3+c^3)*(b+c)^2*a^10-(b^4-3*b^2*c^2+c^4)*(b^2+c^2)*a^9+(b^4+c^4-b*c*(2*b^2-b*c+2*c^2))*(b+c)^3*a^8+4*(b^6-c^6)*(b^2-c^2)*a^7-4*(b^2-c^2)^2*(b+c)*(b^4+c^4-b*c*(b^2-b*c+c^2))*a^6-(b^8-c^8)*a^5*(b^2-c^2)+(b^2-c^2)^3*(b-c)*(b^4+c^4)*a^4-2*(b^4-c^4)^2*(b^2+c^2)^2*a^3+2*(b^2-c^2)^2*(b-c)^2*(b^3-c^3)*(b^4-c^4)*a^2+(b^4-c^4)*(b^2-c^2)*(b^8+c^8+b^2*c^2*(5*b^4+4*b^2*c^2+5*c^4))*a-(b^2-c^2)^3*(b-c)^5*(b^2+b*c+c^2)^2)) : :

The reciprocal orthologic center of these triangles is X(19158).

X(48475) lies on the circumcircle of 2nd anti-Auriga triangle and these lines: {1, 48474}, {112, 26291}, {127, 26327}, {132, 26360}, {517, 48537}, {1297, 5598}, {2781, 48536}, {2794, 48532}, {2799, 48463}, {2806, 48465}, {2831, 48534}, {2838, 48542}, {3320, 26352}, {6020, 26404}, {9517, 48473}, {9530, 45697}, {12145, 26372}, {12207, 26403}, {12253, 26405}, {12265, 26366}, {12340, 26417}, {12384, 26418}, {12408, 26297}, {12413, 26303}, {12478, 45353}, {12503, 26311}, {12784, 26406}, {12796, 26407}, {12805, 26335}, {12806, 26345}, {12918, 26410}, {12925, 26414}, {12935, 26413}, {12945, 26412}, {12955, 26411}, {12996, 45364}, {12997, 45363}, {13099, 26419}, {13115, 45370}, {13116, 45372}, {13117, 45374}, {13118, 26426}, {13119, 26425}, {13918, 45368}, {13985, 45367}, {19093, 26408}, {19094, 26409}, {19159, 26320}, {19160, 45356}, {26422, 38624}, {35828, 45359}, {35829, 45358}, {48461, 48538}

X(48475) = X(48474)-of-5th mixtilinear triangle
X(48475) = reflection of X(i) in X(j) for these (i, j): (48474, 1), (48538, 48461)


X(48476) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO 1st ANTI-AURIGA

Barycentrics    (5*a^4-2*(b^2+c^2)*a^2-3*(b^2-c^2)^2)*S+2*a^6-(b^2+c^2)*a^4-(b^4-c^4)*(b^2-c^2) : :
X(48476) = 3*X(2)-4*X(14233) = 5*X(4)-4*X(48467) = 3*X(376)-4*X(48466) = 3*X(3543)-2*X(13749) = 7*X(3832)-8*X(14239) = 4*X(5874)-3*X(26288) = 4*X(14230)-5*X(17578) = X(14242)-3*X(15682)

The reciprocal orthologic center of these triangles is X(48454).

X(48476) lies on these lines: {2, 14233}, {3, 18539}, {4, 371}, {5, 26516}, {20, 492}, {30, 1160}, {40, 26444}, {55, 26479}, {56, 26473}, {193, 1503}, {230, 7000}, {376, 45522}, {382, 5871}, {489, 32006}, {515, 45719}, {944, 26514}, {946, 26369}, {1007, 26295}, {1384, 23259}, {1587, 26462}, {1588, 18907}, {3070, 44594}, {3071, 44595}, {3543, 13749}, {3575, 26375}, {3832, 14239}, {5691, 26300}, {6201, 42215}, {6256, 26518}, {6284, 26355}, {6289, 33364}, {6460, 45406}, {6560, 10784}, {6776, 9974}, {6811, 42638}, {7354, 26435}, {7374, 42258}, {7582, 45544}, {7585, 45862}, {8982, 42414}, {9541, 36656}, {9873, 26314}, {10515, 26619}, {10783, 35820}, {11500, 26485}, {12110, 26429}, {12113, 26449}, {12114, 26324}, {12115, 26520}, {12116, 26519}, {12323, 44365}, {13687, 14241}, {14227, 33703}, {14230, 17578}, {14242, 15682}, {23263, 36655}, {26396, 48454}, {26420, 48455}, {26496, 48468}, {26505, 48469}, {26517, 48482}, {29012, 39887}, {31670, 39888}, {36709, 43408}, {36711, 42225}, {36990, 42271}, {42637, 45510}

X(48476) = midpoint of X(14227) and X(33703)
X(48476) = reflection of X(i) in X(j) for these (i, j): (20, 13748), (5871, 382), (39888, 31670), (48477, 3146)
X(48476) = anticomplement of the anticomplement of X(14233)
X(48476) = X(4)-of-3rd anti-tri-squares-central triangle
X(48476) = X(22617)-of-1st half-squares triangle, when ABC is acute
X(48476) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 18539, 26468), (3, 26468, 26361), (4, 3068, 26330), (4, 12257, 31412), (4, 13886, 6250), (4, 26441, 3068), (20, 492, 26294), (6289, 35945, 33364), (7000, 23261, 26331)


X(48477) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO 1st ANTI-AURIGA

Barycentrics    -(5*a^4-2*(b^2+c^2)*a^2-3*(b^2-c^2)^2)*S+2*a^6-(b^2+c^2)*a^4-(b^4-c^4)*(b^2-c^2) : :
X(48477) = 3*X(2)-4*X(14230) = 5*X(4)-4*X(48466) = 3*X(376)-4*X(48467) = 3*X(3543)-2*X(13748) = 7*X(3832)-8*X(14235) = 4*X(5875)-3*X(26289) = X(14227)-3*X(15682) = 4*X(14233)-5*X(17578)

The reciprocal orthologic center of these triangles is X(48454).

X(48477) lies on these lines: {2, 14230}, {3, 26307}, {4, 372}, {5, 26521}, {20, 491}, {30, 1161}, {40, 26445}, {55, 26480}, {56, 26474}, {193, 1503}, {230, 7374}, {376, 45523}, {382, 5870}, {490, 32006}, {515, 45720}, {944, 26515}, {946, 26370}, {1007, 26294}, {1384, 23249}, {1587, 18907}, {1588, 26457}, {3070, 44596}, {3071, 44597}, {3543, 13748}, {3575, 26376}, {3832, 14235}, {5691, 26301}, {6202, 42216}, {6256, 26523}, {6284, 26356}, {6290, 33365}, {6459, 45407}, {6561, 10783}, {6776, 9975}, {6813, 42637}, {7000, 42259}, {7354, 26436}, {7581, 45545}, {7586, 45863}, {9873, 26315}, {10514, 26620}, {10784, 35821}, {11500, 26486}, {12110, 26430}, {12113, 26450}, {12114, 26325}, {12115, 26525}, {12116, 26524}, {12322, 44364}, {13807, 14226}, {14227, 15682}, {14233, 17578}, {14242, 33703}, {21736, 31412}, {23253, 36656}, {26397, 48454}, {26421, 48455}, {26441, 42413}, {26497, 48468}, {26506, 48469}, {26522, 48482}, {29012, 39888}, {31670, 39887}, {36712, 42226}, {36714, 43407}, {36990, 42272}, {42638, 45511}

X(48477) = midpoint of X(14242) and X(33703)
X(48477) = reflection of X(i) in X(j) for these (i, j): (20, 13749), (5870, 382), (39887, 31670), (48476, 3146)
X(48477) = anticomplement of the anticomplement of X(14230)
X(48477) = X(22617)-of-2nd half-squares triangle, when ABC is obtuse
X(48477) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 26438, 26469), (3, 26469, 26362), (4, 3069, 26331), (4, 8982, 3069), (4, 12256, 42561), (4, 13939, 6251), (20, 491, 26295), (6290, 35944, 33365), (7374, 23251, 26330)


X(48478) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 3rd ANTI-TRI-SQUARES

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

The reciprocal orthologic center of these triangles is X(486).

X(48478) lies on these lines: {1, 48479}, {4, 26397}, {30, 48527}, {486, 5597}, {487, 26394}, {642, 26359}, {3564, 45724}, {6251, 26326}, {6280, 26344}, {6281, 26334}, {6290, 26386}, {7980, 26395}, {9906, 26296}, {9921, 26302}, {9986, 26310}, {10067, 45371}, {10083, 45373}, {12123, 26290}, {12147, 26371}, {12210, 26379}, {12256, 26381}, {12268, 26365}, {12343, 26393}, {12485, 45354}, {12601, 45369}, {12787, 26382}, {12799, 26383}, {12928, 26390}, {12938, 26389}, {12948, 26388}, {12958, 26387}, {13002, 45362}, {13003, 45361}, {13081, 26351}, {13132, 26402}, {13133, 26401}, {13921, 45365}, {13933, 45366}, {18989, 26380}, {19104, 26384}, {19105, 26385}, {22595, 26319}, {22596, 45355}, {32419, 45696}, {35830, 45357}, {35833, 45360}, {44583, 44648}

X(48478) = reflection of X(48479) in X(1)
X(48478) = X(48479)-of-5th mixtilinear triangle
X(48478) = {X(45724), X(48519)}-harmonic conjugate of X(48480)


X(48479) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 3rd ANTI-TRI-SQUARES

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

The reciprocal orthologic center of these triangles is X(486).

X(48479) lies on these lines: {1, 48478}, {4, 26421}, {30, 48528}, {486, 5598}, {487, 26418}, {642, 26360}, {3564, 45725}, {6251, 26327}, {6280, 26345}, {6281, 26335}, {6290, 26410}, {7980, 26419}, {9906, 26297}, {9921, 26303}, {9986, 26311}, {10067, 45372}, {10083, 45374}, {12123, 26291}, {12147, 26372}, {12210, 26403}, {12256, 26405}, {12268, 26366}, {12343, 26417}, {12484, 45353}, {12601, 45370}, {12787, 26406}, {12799, 26407}, {12928, 26414}, {12938, 26413}, {12948, 26412}, {12958, 26411}, {13002, 45364}, {13003, 45363}, {13081, 26352}, {13132, 26426}, {13133, 26425}, {13921, 45368}, {13933, 45367}, {18989, 26404}, {19104, 26408}, {19105, 26409}, {22595, 26320}, {22596, 45356}, {32419, 45697}, {35830, 45359}, {35833, 45358}, {44585, 44648}

X(48479) = reflection of X(48478) in X(1)
X(48479) = X(48478)-of-5th mixtilinear triangle
X(48479) = {X(45725), X(48520)}-harmonic conjugate of X(48481)


X(48480) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 4th ANTI-TRI-SQUARES

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

The reciprocal orthologic center of these triangles is X(485).

X(48480) lies on these lines: {1, 48481}, {4, 26396}, {30, 48525}, {485, 5597}, {488, 26394}, {641, 26359}, {3564, 45724}, {6250, 26326}, {6278, 26344}, {6279, 26334}, {6289, 26386}, {7981, 26395}, {9907, 26296}, {9922, 26302}, {9987, 26310}, {10068, 45371}, {10084, 45373}, {12124, 26290}, {12148, 26371}, {12211, 26379}, {12257, 26381}, {12269, 26365}, {12344, 26393}, {12487, 45354}, {12602, 45369}, {12788, 26382}, {12800, 26383}, {12929, 26390}, {12939, 26389}, {12949, 26388}, {12959, 26387}, {13004, 45362}, {13005, 45361}, {13082, 26351}, {13134, 26402}, {13135, 26401}, {13879, 45365}, {13880, 45366}, {18988, 26380}, {19102, 26384}, {19103, 26385}, {22624, 26319}, {22625, 45355}, {32421, 45696}, {35831, 45360}, {35832, 45357}, {44582, 44647}

X(48480) = reflection of X(48481) in X(1)
X(48480) = X(48481)-of-5th mixtilinear triangle
X(48480) = {X(45724), X(48519)}-harmonic conjugate of X(48478)


X(48481) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 4th ANTI-TRI-SQUARES

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

The reciprocal orthologic center of these triangles is X(485).

X(48481) lies on these lines: {1, 48480}, {4, 26420}, {30, 48526}, {485, 5598}, {488, 26418}, {641, 26360}, {3564, 45725}, {6250, 26327}, {6278, 26345}, {6279, 26335}, {6289, 26410}, {7981, 26419}, {9907, 26297}, {9922, 26303}, {9987, 26311}, {10068, 45372}, {10084, 45374}, {12124, 26291}, {12148, 26372}, {12211, 26403}, {12257, 26405}, {12269, 26366}, {12344, 26417}, {12486, 45353}, {12602, 45370}, {12788, 26406}, {12800, 26407}, {12929, 26414}, {12939, 26413}, {12949, 26412}, {12959, 26411}, {13004, 45364}, {13005, 45363}, {13082, 26352}, {13134, 26426}, {13135, 26425}, {13879, 45368}, {13880, 45367}, {18988, 26404}, {19102, 26408}, {19103, 26409}, {22624, 26320}, {22625, 45356}, {32421, 45697}, {35831, 45358}, {35832, 45359}, {44584, 44647}

X(48481) = reflection of X(48480) in X(1)
X(48481) = X(48480)-of-5th mixtilinear triangle
X(48481) = {X(45725), X(48520)}-harmonic conjugate of X(48479)


X(48482) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 1st ANTI-AURIGA

Barycentrics    a^7-(b+c)*a^6-(b+c)^2*a^5+(b+c)*(b^2+c^2)*a^4-(b-c)^2*(b^2+c^2)*a^3+(b^4-c^4)*(b-c)*a^2+(b^4-c^4)*(b^2-c^2)*a-(b^2-c^2)^3*(b-c) : :
X(48482) = 3*X(4)-X(12667) = 3*X(354)-X(12671) = 3*X(381)-2*X(18242) = X(1490)-3*X(1699) = 3*X(1699)-2*X(12608) = 5*X(3623)-4*X(32905) = 3*X(3830)-X(40267) = 3*X(5603)-2*X(40257) = 3*X(5886)-2*X(37837) = 3*X(5927)-2*X(32159) = 3*X(6256)-2*X(12667) = X(6361)-3*X(14647) = X(6869)-4*X(24387) = 4*X(10943)-3*X(45700) = 2*X(11249)-3*X(45700) = 3*X(14647)-2*X(40256) = X(16127)-4*X(22793)

The reciprocal orthologic center of these triangles is X(48454).

X(48482) lies on these lines: {1, 4}, {2, 6796}, {3, 2886}, {5, 1001}, {7, 12005}, {8, 6840}, {10, 6827}, {11, 3149}, {20, 5450}, {30, 10525}, {35, 6833}, {36, 6934}, {40, 3434}, {55, 6831}, {56, 26475}, {84, 10431}, {100, 6943}, {104, 4299}, {119, 18518}, {149, 151}, {165, 6899}, {283, 14956}, {354, 12671}, {355, 960}, {377, 3576}, {381, 16202}, {382, 2829}, {411, 11680}, {443, 10165}, {485, 45650}, {486, 45651}, {495, 10894}, {496, 20420}, {498, 6830}, {499, 6905}, {516, 1158}, {518, 5812}, {528, 10306}, {580, 33137}, {602, 1714}, {908, 17857}, {938, 31870}, {942, 45654}, {952, 10526}, {956, 11827}, {958, 31789}, {971, 16127}, {993, 6868}, {1006, 19854}, {1012, 6284}, {1071, 1836}, {1076, 8270}, {1125, 6826}, {1210, 37550}, {1376, 6922}, {1385, 3824}, {1484, 22775}, {1503, 45728}, {1512, 10826}, {1532, 10896}, {1537, 13274}, {1538, 18782}, {1587, 26464}, {1588, 26458}, {1593, 10835}, {1621, 6828}, {1657, 35252}, {1698, 6947}, {1788, 10265}, {2077, 6890}, {2078, 6848}, {2475, 5731}, {2478, 5587}, {2550, 5705}, {2949, 5759}, {3070, 19050}, {3071, 19049}, {3072, 5156}, {3085, 6844}, {3086, 37583}, {3091, 34486}, {3146, 10529}, {3254, 10309}, {3295, 7680}, {3419, 14110}, {3421, 47745}, {3427, 6598}, {3428, 24390}, {3436, 5881}, {3543, 11240}, {3575, 26377}, {3616, 6839}, {3623, 32905}, {3624, 6854}, {3627, 32214}, {3813, 22770}, {3816, 6918}, {3817, 6849}, {3822, 6867}, {3825, 6944}, {3830, 12001}, {3832, 10587}, {3841, 6989}, {4190, 37561}, {4294, 6847}, {4295, 5768}, {4297, 6850}, {4300, 33104}, {4302, 6906}, {4309, 6845}, {5010, 6977}, {5056, 26127}, {5057, 12528}, {5081, 20220}, {5082, 11362}, {5084, 10175}, {5218, 6956}, {5231, 6705}, {5248, 6824}, {5251, 6936}, {5252, 10953}, {5259, 6832}, {5284, 6991}, {5506, 5818}, {5534, 21077}, {5536, 40265}, {5556, 34485}, {5572, 5805}, {5584, 31140}, {5657, 6903}, {5693, 11415}, {5704, 45043}, {5707, 29207}, {5720, 21616}, {5721, 16466}, {5722, 7686}, {5777, 24703}, {5787, 5878}, {5794, 31786}, {5799, 45898}, {5800, 39870}, {5806, 18527}, {5870, 26349}, {5871, 26342}, {5880, 9940}, {5886, 24299}, {5895, 13095}, {5927, 32159}, {6264, 36977}, {6361, 14647}, {6643, 18589}, {6825, 25639}, {6834, 7741}, {6835, 8227}, {6862, 32613}, {6864, 26105}, {6869, 24387}, {6882, 11499}, {6889, 15931}, {6891, 25440}, {6893, 19925}, {6894, 40259}, {6896, 7988}, {6897, 7987}, {6898, 7989}, {6908, 31418}, {6911, 10200}, {6923, 18481}, {6924, 26492}, {6927, 10589}, {6929, 18480}, {6950, 14794}, {6957, 18492}, {6971, 18524}, {6986, 33108}, {6987, 19843}, {7354, 10959}, {7491, 22758}, {7497, 11365}, {7580, 15908}, {7681, 9669}, {7728, 12906}, {7951, 10786}, {7971, 31162}, {7982, 41575}, {7992, 45648}, {8557, 10445}, {8727, 11496}, {9580, 12705}, {9655, 30283}, {9670, 37447}, {9799, 9812}, {9834, 45625}, {9835, 45626}, {9838, 45645}, {9873, 26317}, {10167, 18260}, {10172, 17559}, {10246, 11281}, {10303, 26060}, {10310, 37374}, {10483, 37002}, {10599, 37719}, {10721, 12382}, {10722, 12190}, {10723, 13190}, {10724, 13279}, {10728, 12776}, {10733, 13218}, {10735, 13314}, {10864, 12687}, {10947, 12672}, {10966, 12953}, {10993, 35251}, {11219, 11661}, {11230, 40262}, {11248, 37356}, {11269, 37530}, {11375, 33597}, {11401, 12173}, {11826, 37022}, {12110, 26431}, {12113, 26452}, {12547, 45656}, {12595, 36990}, {12609, 18443}, {12664, 14054}, {12675, 45636}, {12677, 34791}, {12679, 18839}, {12684, 16150}, {12691, 41686}, {12750, 34789}, {12761, 22938}, {12943, 18967}, {13106, 36962}, {13107, 36961}, {13119, 44988}, {13748, 45422}, {13749, 45423}, {13907, 31412}, {13965, 42561}, {15177, 37231}, {15726, 18238}, {15909, 41861}, {16216, 18482}, {17556, 34746}, {17647, 37611}, {18525, 37821}, {18761, 37290}, {18962, 37740}, {19537, 21154}, {21279, 22464}, {23251, 44645}, {23261, 44646}, {23541, 27378}, {24316, 29069}, {25524, 37281}, {26118, 29639}, {26399, 48454}, {26423, 48455}, {26499, 48468}, {26508, 48469}, {26517, 48476}, {26522, 48477}, {28146, 34862}, {28174, 33899}, {28194, 34744}, {28204, 34647}, {35820, 45640}, {35821, 45641}, {37162, 40260}, {37411, 42842}, {45526, 48466}, {45527, 48467}

X(48482) = midpoint of X(i) and X(j) for these {i, j}: {84, 41869}, {5691, 12650}, {5787, 12699}
X(48482) = reflection of X(i) in X(j) for these (i, j): (20, 5450), (40, 12616), (1158, 6245), (1490, 12608), (5534, 21077), (5709, 10916), (6256, 4), (6260, 18483), (6261, 946), (6361, 40256), (9942, 13374), (11248, 37356), (11249, 10943), (11500, 5), (12761, 22938), (22770, 3813), (22775, 1484), (31730, 6705)
X(48482) = anticomplement of X(6796)
X(48482) = X(4)-of-anti-inner-Yff triangle
X(48482) = X(3149)-of-inner-Johnson triangle
X(48482) = X(5449)-of-2nd Conway triangle, when ABC is acute
X(48482) = X(6256)-of-outer-Yff tangents triangle
X(48482) = X(11500)-of-Johnson triangle
X(48482) = X(12116)-of-anti-outer-Yff triangle
X(48482) = X(18242)-of-anti-Ehrmann-mid triangle
X(48482) = X(37468)-of-2nd circumperp tangential triangle
X(48482) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 4, 26332), (3, 18544, 26470), (3, 26470, 26363), (4, 497, 946), (4, 944, 1478), (4, 1479, 26333), (4, 10531, 1699), (4, 10806, 10532), (4, 12115, 3585), (4, 12116, 1), (5, 10267, 10198), (11, 6253, 3149), (20, 10527, 11012), (56, 36999, 37468), (149, 6895, 962), (382, 18543, 10680), (496, 20420, 22753), (962, 12649, 37625), (1490, 1699, 12608), (1699, 4857, 10531), (3434, 6836, 40), (3583, 5691, 4), (6830, 11491, 498), (6833, 37000, 35), (6934, 10785, 36), (7741, 44425, 6834), (8227, 18406, 6835), (9669, 19541, 7681), (10267, 45630, 5), (10532, 10806, 1), (10532, 12116, 10806), (10680, 18543, 37726), (10943, 11249, 45700), (18514, 41698, 4), (31418, 43161, 6908)


X(48483) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO AAOA

Barycentrics    -4*a*(a+b-c)*(a-b+c)*(-a+b+c)*(a^6-(b^2+c^2)*a^4-(b^4-3*b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2))*S*sqrt(R*(4*R+r))+2*a^13-2*(b+c)*a^12-6*(b^2+c^2)*a^11+2*(b+c)*(3*b^2-b*c+3*c^2)*a^10+(5*b^4+12*b^2*c^2+5*c^4)*a^9-(b+c)*(5*b^4+5*c^4-4*b*c*(b^2-3*b*c+c^2))*a^8-8*(b^2+c^2)*b^2*c^2*a^7-2*(b+c)*(b^4+c^4-b*c*(4*b^2-3*b*c+4*c^2))*b*c*a^6+2*(b^4+c^4)*b^2*c^2*a^5+2*(b^2-c^2)*(b-c)*(b^4+c^4+b*c*(b^2+b*c+c^2))*b*c*a^4-2*(b^8-c^8)*a^3*(b^2-c^2)+2*(b^2-c^2)^3*(b-c)*(b^4+c^4)*a^2+(b^4-c^4)^2*(b^2-c^2)^2*a-(b^2-c^2)^5*(b-c)*(b^2+c^2) : :

The reciprocal orthologic center of these triangles is X(7574).

X(48483) lies on these lines: {1, 48484}, {30, 48472}, {110, 26386}, {113, 45355}, {125, 26398}, {265, 5597}, {399, 18496}, {511, 48529}, {542, 45724}, {1511, 26359}, {2771, 48501}, {2777, 48513}, {3448, 26381}, {5663, 48454}, {10088, 26388}, {10091, 26387}, {10113, 26326}, {10628, 48505}, {12121, 26290}, {12140, 26371}, {12201, 26379}, {12261, 26365}, {12334, 26393}, {12383, 26394}, {12407, 26296}, {12412, 26302}, {12467, 45354}, {12501, 26310}, {12778, 26382}, {12790, 26383}, {12803, 26334}, {12804, 26344}, {12889, 26390}, {12890, 26389}, {12894, 45362}, {12895, 45361}, {12896, 26351}, {12898, 26395}, {12902, 45369}, {12903, 45371}, {12904, 45373}, {12905, 26402}, {12906, 26401}, {13915, 45365}, {13979, 45366}, {17702, 48460}, {18968, 26380}, {19051, 26384}, {19052, 26385}, {19478, 26319}, {32423, 48519}, {35834, 45357}, {35835, 45360}

X(48483) = X(48484)-of-5th mixtilinear triangle
X(48483) = reflection of X(i) in X(j) for these (i, j): (48484, 1), (48535, 48519)


X(48484) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO AAOA

Barycentrics    4*a*(a+b-c)*(a-b+c)*(-a+b+c)*(a^6-(b^2+c^2)*a^4-(b^4-3*b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2))*S*sqrt(R*(4*R+r))+2*a^13-2*(b+c)*a^12-6*(b^2+c^2)*a^11+2*(b+c)*(3*b^2-b*c+3*c^2)*a^10+(5*b^4+12*b^2*c^2+5*c^4)*a^9-(b+c)*(5*b^4+5*c^4-4*b*c*(b^2-3*b*c+c^2))*a^8-8*(b^2+c^2)*b^2*c^2*a^7-2*(b+c)*(b^4+c^4-b*c*(4*b^2-3*b*c+4*c^2))*b*c*a^6+2*(b^4+c^4)*b^2*c^2*a^5+2*(b^2-c^2)*(b-c)*(b^4+c^4+b*c*(b^2+b*c+c^2))*b*c*a^4-2*(b^8-c^8)*a^3*(b^2-c^2)+2*(b^2-c^2)^3*(b-c)*(b^4+c^4)*a^2+(b^4-c^4)^2*(b^2-c^2)^2*a-(b^2-c^2)^5*(b-c)*(b^2+c^2) : :

The reciprocal orthologic center of these triangles is X(7574).

X(48484) lies on these lines: {1, 48483}, {30, 48473}, {110, 26410}, {113, 45356}, {125, 26422}, {265, 5598}, {399, 18498}, {511, 48530}, {542, 45725}, {1511, 26360}, {2771, 48502}, {2777, 48514}, {3448, 26405}, {5663, 48455}, {10088, 26412}, {10091, 26411}, {10113, 26327}, {10628, 48506}, {12121, 26291}, {12140, 26372}, {12201, 26403}, {12261, 26366}, {12334, 26417}, {12383, 26418}, {12407, 26297}, {12412, 26303}, {12466, 45353}, {12501, 26311}, {12778, 26406}, {12790, 26407}, {12803, 26335}, {12804, 26345}, {12889, 26414}, {12890, 26413}, {12894, 45364}, {12895, 45363}, {12896, 26352}, {12898, 26419}, {12902, 45370}, {12903, 45372}, {12904, 45374}, {12905, 26426}, {12906, 26425}, {13915, 45368}, {13979, 45367}, {17702, 48461}, {18968, 26404}, {19051, 26408}, {19052, 26409}, {19478, 26320}, {32423, 48520}, {35834, 45359}, {35835, 45358}

X(48484) = X(48483)-of-5th mixtilinear triangle
X(48484) = reflection of X(i) in X(j) for these (i, j): (48483, 1), (48536, 48520)


X(48485) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO ARIES

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

The reciprocal orthologic center of these triangles is X(9833).

X(48485) lies on these lines: {1, 48486}, {30, 48513}, {68, 5597}, {155, 26386}, {539, 45696}, {1069, 26387}, {1147, 26359}, {1154, 48505}, {3157, 26388}, {3564, 45724}, {6193, 26394}, {9896, 26296}, {9908, 26302}, {9923, 26310}, {9927, 26326}, {9928, 26382}, {9929, 26334}, {9930, 26344}, {9933, 26395}, {10055, 45371}, {10071, 45373}, {11411, 26381}, {12118, 26290}, {12134, 26371}, {12164, 18496}, {12193, 26379}, {12259, 26365}, {12328, 26393}, {12359, 26398}, {12416, 45354}, {12418, 26383}, {12422, 26390}, {12423, 26389}, {12426, 45362}, {12427, 45361}, {12428, 26351}, {12429, 45369}, {12430, 26402}, {12431, 26401}, {13754, 48454}, {13909, 45365}, {13970, 45366}, {14984, 48529}, {17702, 48472}, {18970, 26380}, {19061, 26384}, {19062, 26385}, {22659, 26319}, {22660, 45355}, {35836, 45357}, {35837, 45360}, {44665, 48460}

X(48485) = X(48486)-of-5th mixtilinear triangle
X(48485) = reflection of X(48486) in X(1)


X(48486) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO ARIES

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

The reciprocal orthologic center of these triangles is X(9833).

X(48486) lies on these lines: {1, 48485}, {30, 48514}, {68, 5598}, {155, 26410}, {539, 45697}, {1069, 26411}, {1147, 26360}, {1154, 48506}, {3157, 26412}, {3564, 45725}, {6193, 26418}, {9896, 26297}, {9908, 26303}, {9923, 26311}, {9927, 26327}, {9928, 26406}, {9929, 26335}, {9930, 26345}, {9933, 26419}, {10055, 45372}, {10071, 45374}, {11411, 26405}, {12118, 26291}, {12134, 26372}, {12164, 18498}, {12193, 26403}, {12259, 26366}, {12328, 26417}, {12359, 26422}, {12415, 45353}, {12418, 26407}, {12422, 26414}, {12423, 26413}, {12426, 45364}, {12427, 45363}, {12428, 26352}, {12429, 45370}, {12430, 26426}, {12431, 26425}, {13754, 48455}, {13909, 45368}, {13970, 45367}, {14984, 48530}, {17702, 48473}, {18970, 26404}, {19061, 26408}, {19062, 26409}, {22659, 26320}, {22660, 45356}, {35836, 45359}, {35837, 45358}, {44665, 48461}

X(48486) = X(48485)-of-5th mixtilinear triangle
X(48486) = reflection of X(48485) in X(1)


X(48487) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO BEVAN ANTIPODAL

Barycentrics    a*(4*(-a+b+c)*(a-b+c)*(a+b-c)*S*sqrt(R*(4*R+r))+((b+c)*a^2-2*b*c*a-(b^2-c^2)*(b-c))*(a^3-(b+c)*a^2-(b+c)^2*a+(b^2-c^2)*(b-c))) : :

The reciprocal orthologic center of these triangles is X(1).

X(48487) lies on these lines: {1, 3}, {4, 26382}, {10, 26326}, {515, 48493}, {516, 48454}, {946, 26359}, {962, 26394}, {1702, 26385}, {1703, 26384}, {1836, 26388}, {1902, 26371}, {2800, 48533}, {2802, 48464}, {2809, 48541}, {5812, 26389}, {5840, 48501}, {5847, 48489}, {6001, 48513}, {6361, 26381}, {9911, 26302}, {12197, 26379}, {12497, 26310}, {12696, 26383}, {12697, 26334}, {12698, 26344}, {12699, 26386}, {12700, 26390}, {12701, 26387}, {13912, 45365}, {13975, 45366}, {22793, 45355}, {22841, 45362}, {22842, 45361}, {28174, 48519}, {28194, 45696}, {35610, 45357}, {35611, 45360}

X(48487) = reflection of X(i) in X(j) for these (i, j): (45711, 48460), (48454, 48511), (48488, 1)
X(48487) = X(48488)-of-5th mixtilinear triangle
X(48487) = {X(1), X(41338)}-harmonic conjugate of X(26291)


X(48488) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO BEVAN ANTIPODAL

Barycentrics    a*(-4*(-a+b+c)*(a-b+c)*(a+b-c)*S*sqrt(R*(4*R+r))+((b+c)*a^2-2*b*c*a-(b^2-c^2)*(b-c))*(a^3-(b+c)*a^2-(b+c)^2*a+(b^2-c^2)*(b-c))) : :

The reciprocal orthologic center of these triangles is X(1).

X(48488) lies on these lines: {1, 3}, {4, 26406}, {10, 26327}, {515, 48494}, {516, 48455}, {946, 26360}, {962, 26418}, {1702, 26409}, {1703, 26408}, {1836, 26412}, {1902, 26372}, {2800, 48534}, {2802, 48465}, {2809, 48542}, {5812, 26413}, {5840, 48502}, {5847, 48490}, {6001, 48514}, {6361, 26405}, {9911, 26303}, {12197, 26403}, {12497, 26311}, {12696, 26407}, {12697, 26335}, {12698, 26345}, {12699, 26410}, {12700, 26414}, {12701, 26411}, {13912, 45368}, {13975, 45367}, {22793, 45356}, {22841, 45364}, {22842, 45363}, {28174, 48520}, {28194, 45697}, {35610, 45359}, {35611, 45358}

X(48488) = reflection of X(i) in X(j) for these (i, j): (45712, 48461), (48455, 48512), (48487, 1)
X(48488) = X(48487)-of-5th mixtilinear triangle
X(48488) = {X(1), X(41338)}-harmonic conjugate of X(26290)


X(48489) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 9th BROCARD

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

The reciprocal orthologic center of these triangles is X(4).

X(48489) lies on these lines: {1, 48490}, {6, 26326}, {69, 26290}, {542, 45696}, {674, 48455}, {1352, 26359}, {1503, 45724}, {3564, 48460}, {5597, 6776}, {5847, 48487}, {5848, 48464}, {5921, 26394}, {18440, 26386}, {19145, 45365}, {19146, 45366}, {26296, 39878}, {26302, 39879}, {26310, 39882}, {26319, 39883}, {26334, 39887}, {26344, 39888}, {26351, 39897}, {26365, 39870}, {26371, 39871}, {26379, 39872}, {26380, 39873}, {26381, 39874}, {26382, 39885}, {26383, 39886}, {26384, 39875}, {26385, 39876}, {26387, 39892}, {26388, 39891}, {26389, 39890}, {26390, 39889}, {26393, 39877}, {26395, 39898}, {26401, 39903}, {26402, 39902}, {39881, 45354}, {39884, 45355}, {39893, 45357}, {39894, 45360}, {39895, 45362}, {39896, 45361}, {39899, 45369}, {39900, 45371}, {39901, 45373}

X(48489) = X(48490)-of-5th mixtilinear triangle
X(48489) = reflection of X(i) in X(j) for these (i, j): (48454, 45724), (48490, 1)


X(48490) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 9th BROCARD

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

The reciprocal orthologic center of these triangles is X(4).

X(48490) lies on these lines: {1, 48489}, {6, 26327}, {69, 26291}, {542, 45697}, {674, 48454}, {1352, 26360}, {1503, 45725}, {3564, 48461}, {5598, 6776}, {5847, 48488}, {5848, 48465}, {5921, 26418}, {18440, 26410}, {19145, 45368}, {19146, 45367}, {26297, 39878}, {26303, 39879}, {26311, 39882}, {26320, 39883}, {26335, 39887}, {26345, 39888}, {26352, 39897}, {26366, 39870}, {26372, 39871}, {26403, 39872}, {26404, 39873}, {26405, 39874}, {26406, 39885}, {26407, 39886}, {26408, 39875}, {26409, 39876}, {26411, 39892}, {26412, 39891}, {26413, 39890}, {26414, 39889}, {26417, 39877}, {26419, 39898}, {26425, 39903}, {26426, 39902}, {39880, 45353}, {39884, 45356}, {39893, 45359}, {39894, 45358}, {39895, 45364}, {39896, 45363}, {39899, 45370}, {39900, 45372}, {39901, 45374}

X(48490) = X(48489)-of-5th mixtilinear triangle
X(48490) = reflection of X(i) in X(j) for these (i, j): (48455, 45725), (48489, 1)


X(48491) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 1st BROCARD-REFLECTED

Barycentrics    -12*a*(a+b-c)*(a-b+c)*(-a+b+c)*((b^2+c^2)*a^2+b^2*c^2)*S*sqrt(R*(4*R+r))+3*(b^2+c^2)*a^9-3*(b+c)*(b^2+c^2)*a^8-4*(b^4+b^2*c^2+c^4)*a^7+4*(b^3+c^3)*(b^2+b*c+c^2)*a^6-(b^2+c^2)*(b^4+13*b^2*c^2+c^4)*a^5+(b+c)*(b^6+c^6-2*(2*b^4+2*c^4-b*c*(7*b^2-5*b*c+7*c^2))*b*c)*a^4+2*(b^2-c^2)^2*(b^4+3*b^2*c^2+c^4)*a^3-2*(b^2-c^2)^2*(b+c)*(b^2-b*c+c^2)^2*a^2+(b^4-c^4)*(b^2-c^2)*b^2*c^2*a-(b^2-c^2)^3*(b-c)*b^2*c^2 : :
X(48491) = X(48515)-4*X(48519)

The reciprocal orthologic center of these triangles is X(3).

X(48491) lies on these lines: {1, 48492}, {262, 5597}, {511, 45696}, {2782, 48470}, {6194, 26394}, {7697, 26386}, {7709, 26381}, {15819, 26359}, {18971, 26380}, {19063, 26384}, {19064, 26385}, {22475, 26365}, {22480, 26371}, {22521, 26379}, {22556, 26393}, {22650, 26296}, {22655, 26302}, {22672, 45354}, {22676, 26290}, {22678, 26310}, {22680, 26319}, {22681, 45355}, {22682, 26326}, {22697, 26382}, {22698, 26383}, {22699, 26334}, {22700, 26344}, {22703, 26390}, {22704, 26389}, {22705, 26388}, {22706, 26387}, {22709, 45362}, {22710, 45361}, {22711, 26351}, {22713, 26395}, {22720, 45365}, {22721, 45366}, {22728, 45369}, {22729, 45371}, {22730, 45373}, {22731, 26402}, {22732, 26401}, {26398, 40108}, {32515, 48515}, {35838, 45357}, {35839, 45360}, {45724, 48462}, {48460, 48517}

X(48491) = X(48492)-of-5th mixtilinear triangle
X(48491) = reflection of X(48492) in X(1)


X(48492) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 1st BROCARD-REFLECTED

Barycentrics    12*a*(a+b-c)*(a-b+c)*(-a+b+c)*((b^2+c^2)*a^2+b^2*c^2)*S*sqrt(R*(4*R+r))+3*(b^2+c^2)*a^9-3*(b+c)*(b^2+c^2)*a^8-4*(b^4+b^2*c^2+c^4)*a^7+4*(b^3+c^3)*(b^2+b*c+c^2)*a^6-(b^2+c^2)*(b^4+13*b^2*c^2+c^4)*a^5+(b+c)*(b^6+c^6-2*(2*b^4+2*c^4-b*c*(7*b^2-5*b*c+7*c^2))*b*c)*a^4+2*(b^2-c^2)^2*(b^4+3*b^2*c^2+c^4)*a^3-2*(b^2-c^2)^2*(b+c)*(b^2-b*c+c^2)^2*a^2+(b^4-c^4)*(b^2-c^2)*b^2*c^2*a-(b^2-c^2)^3*(b-c)*b^2*c^2 : :
X(48492) = X(48516)-4*X(48520)

The reciprocal orthologic center of these triangles is X(3).

X(48492) lies on these lines: {1, 48491}, {262, 5598}, {511, 45697}, {2782, 48471}, {6194, 26418}, {7697, 26410}, {7709, 26405}, {15819, 26360}, {18971, 26404}, {19063, 26408}, {19064, 26409}, {22475, 26366}, {22480, 26372}, {22521, 26403}, {22556, 26417}, {22650, 26297}, {22655, 26303}, {22668, 45353}, {22676, 26291}, {22678, 26311}, {22680, 26320}, {22681, 45356}, {22682, 26327}, {22697, 26406}, {22698, 26407}, {22699, 26335}, {22700, 26345}, {22703, 26414}, {22704, 26413}, {22705, 26412}, {22706, 26411}, {22709, 45364}, {22710, 45363}, {22711, 26352}, {22713, 26419}, {22720, 45368}, {22721, 45367}, {22728, 45370}, {22729, 45372}, {22730, 45374}, {22731, 26426}, {22732, 26425}, {26422, 40108}, {32515, 48516}, {35838, 45359}, {35839, 45358}, {45725, 48463}, {48461, 48518}

X(48492) = X(48491)-of-5th mixtilinear triangle
X(48492) = reflection of X(48491) in X(1)


X(48493) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO EXCENTERS-MIDPOINTS

Barycentrics    -4*S*sqrt(R*(4*R+r))*a+(-a+b+c)*(2*a^3-(b^2+c^2)*a+(b^2-c^2)*(b-c)) : :
X(48493) = 3*X(45696)-2*X(45711) = 3*X(45696)-4*X(48511)

The reciprocal orthologic center of these triangles is X(10).

X(48493) lies on these lines: {1, 442}, {8, 5597}, {10, 26365}, {145, 26394}, {355, 26326}, {515, 48487}, {517, 48454}, {519, 45696}, {758, 48503}, {944, 26290}, {952, 48460}, {1482, 26386}, {2098, 26387}, {2099, 26388}, {2802, 48501}, {3434, 26419}, {3632, 26296}, {3913, 26393}, {5690, 26398}, {5844, 48519}, {5846, 45724}, {8148, 18496}, {10573, 45373}, {10912, 26390}, {10944, 26380}, {10950, 26351}, {12135, 26371}, {12195, 26379}, {12245, 26381}, {12410, 26302}, {12455, 45354}, {12495, 26310}, {12513, 26319}, {12626, 26383}, {12627, 26334}, {12628, 26344}, {12635, 26389}, {12636, 45362}, {12637, 45361}, {12645, 45369}, {12647, 45371}, {12648, 26402}, {12649, 26401}, {13911, 45365}, {13973, 45366}, {14839, 48515}, {19065, 26384}, {19066, 26385}, {22791, 45355}, {26327, 37533}, {35842, 45357}, {35843, 45360}

X(48493) = reflection of X(i) in X(j) for these (i, j): (45711, 48511), (48494, 1)
X(48493) = X(48494)-of-5th mixtilinear triangle
X(48493) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 3419, 26360), (1, 26382, 26359), (145, 26394, 26395), (45711, 48511, 45696)


X(48494) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO EXCENTERS-MIDPOINTS

Barycentrics    4*S*sqrt(R*(4*R+r))*a+(-a+b+c)*(2*a^3-(b^2+c^2)*a+(b^2-c^2)*(b-c)) : :
X(48494) = 3*X(45697)-2*X(45712) = 3*X(45697)-4*X(48512)

The reciprocal orthologic center of these triangles is X(10).

X(48494) lies on these lines: {1, 442}, {8, 5598}, {10, 26366}, {145, 26418}, {355, 26327}, {515, 48488}, {517, 48455}, {519, 45697}, {758, 48504}, {944, 26291}, {952, 48461}, {1482, 26410}, {2098, 26411}, {2099, 26412}, {2802, 48502}, {3434, 26395}, {3632, 26297}, {3913, 26417}, {5690, 26422}, {5844, 48520}, {5846, 45725}, {8148, 18498}, {10573, 45374}, {10912, 26414}, {10944, 26404}, {10950, 26352}, {12135, 26372}, {12195, 26403}, {12245, 26405}, {12410, 26303}, {12454, 45353}, {12495, 26311}, {12513, 26320}, {12626, 26407}, {12627, 26335}, {12628, 26345}, {12635, 26413}, {12636, 45364}, {12637, 45363}, {12645, 45370}, {12647, 45372}, {12648, 26426}, {12649, 26425}, {13911, 45368}, {13973, 45367}, {14839, 48516}, {19065, 26408}, {19066, 26409}, {22791, 45356}, {26326, 37533}, {35842, 45359}, {35843, 45358}

X(48494) = reflection of X(i) in X(j) for these (i, j): (45712, 48512), (48493, 1)
X(48494) = X(48493)-of-5th mixtilinear triangle
X(48494) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 3419, 26359), (1, 26406, 26360), (145, 26418, 26419), (45712, 48512, 45697)


X(48495) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO EXTOUCH

Barycentrics    a*(-4*(a-b+c)^2*(-a+b+c)^2*(a+b-c)^2*S*sqrt(R*(4*R+r))+(b+c)*a^8-2*(b^2-b*c+c^2)*a^7-2*(b+c)^3*a^6+2*(b^2-b*c+c^2)*(3*b^2+2*b*c+3*c^2)*a^5+8*(b^2-c^2)*(b-c)*b*c*a^4-2*(3*b^4+3*c^4+b*c*(7*b^2+12*b*c+7*c^2))*(b-c)^2*a^3+2*(b^2-c^2)*(b-c)*(b^4+6*b^2*c^2+c^4)*a^2+2*(b^2-c^2)^2*(b+c)^2*(b^2-b*c+c^2)*a-(b^2-c^2)^4*(b+c)) : :

The reciprocal orthologic center of these triangles is X(40).

X(48495) lies on these lines: {1, 12664}, {84, 5597}, {515, 48487}, {971, 48460}, {1490, 26290}, {1709, 45371}, {2829, 48501}, {6001, 45711}, {6223, 26394}, {6245, 26326}, {6257, 26344}, {6258, 26334}, {6259, 26386}, {6260, 26359}, {7971, 26395}, {7992, 26296}, {8987, 45365}, {9910, 26302}, {10085, 45373}, {12114, 26365}, {12136, 26371}, {12196, 26379}, {12246, 26381}, {12330, 26393}, {12457, 45354}, {12496, 26310}, {12667, 26382}, {12668, 26383}, {12676, 26390}, {12677, 26389}, {12678, 26388}, {12679, 26387}, {12680, 26351}, {12684, 45369}, {12686, 26402}, {12687, 26401}, {12688, 26380}, {13974, 45366}, {18237, 26319}, {18245, 45362}, {18246, 45361}, {19067, 26384}, {19068, 26385}, {22792, 45355}, {26398, 34862}, {35844, 45357}, {35845, 45360}

X(48495) = X(48496)-of-5th mixtilinear triangle
X(48495) = reflection of X(48496) in X(1)


X(48496) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO EXTOUCH

Barycentrics    a*(4*(a-b+c)^2*(-a+b+c)^2*(a+b-c)^2*S*sqrt(R*(4*R+r))+(b+c)*a^8-2*(b^2-b*c+c^2)*a^7-2*(b+c)^3*a^6+2*(b^2-b*c+c^2)*(3*b^2+2*b*c+3*c^2)*a^5+8*(b^2-c^2)*(b-c)*b*c*a^4-2*(3*b^4+3*c^4+b*c*(7*b^2+12*b*c+7*c^2))*(b-c)^2*a^3+2*(b^2-c^2)*(b-c)*(b^4+6*b^2*c^2+c^4)*a^2+2*(b^2-c^2)^2*(b+c)^2*(b^2-b*c+c^2)*a-(b^2-c^2)^4*(b+c)) : :

The reciprocal orthologic center of these triangles is X(40).

X(48496) lies on these lines: {1, 12664}, {84, 5598}, {515, 48488}, {971, 48461}, {1490, 26291}, {1709, 45372}, {2829, 48502}, {6001, 45712}, {6223, 26418}, {6245, 26327}, {6257, 26345}, {6258, 26335}, {6259, 26410}, {6260, 26360}, {7971, 26419}, {7992, 26297}, {8987, 45368}, {9910, 26303}, {10085, 45374}, {12114, 26366}, {12136, 26372}, {12196, 26403}, {12246, 26405}, {12330, 26417}, {12456, 45353}, {12496, 26311}, {12667, 26406}, {12668, 26407}, {12676, 26414}, {12677, 26413}, {12678, 26412}, {12679, 26411}, {12680, 26352}, {12684, 45370}, {12686, 26426}, {12687, 26425}, {12688, 26404}, {13974, 45367}, {18237, 26320}, {18245, 45364}, {18246, 45363}, {19067, 26408}, {19068, 26409}, {22792, 45356}, {26422, 34862}, {35844, 45359}, {35845, 45358}

X(48496) = X(48495)-of-5th mixtilinear triangle
X(48496) = reflection of X(48495) in X(1)


X(48497) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO INNER-FERMAT

Barycentrics    8*(-10*S+sqrt(3)*(a^2+b^2+c^2))*sqrt(3)*S^2*a*sqrt(R*(4*R+r))+2*(6*a^2*((b^2+c^2)*a-b^3-c^3)*S+(2*a^7-2*(b+c)*a^6-3*(b^2+c^2)*a^5+(b+c)*(3*b^2+b*c+3*c^2)*a^4-6*b^2*c^2*a^3-3*(b^2-c^2)*(b-c)*b*c*a^2+(b^4-c^4)*(b^2-c^2)*a-(b^2-c^2)^3*(b-c))*sqrt(3))*(a+b+c) : :

The reciprocal orthologic center of these triangles is X(3).

X(48497) lies on these lines: {1, 48498}, {18, 5597}, {533, 45696}, {628, 26394}, {630, 26359}, {5965, 45724}, {11740, 26365}, {16627, 26386}, {16628, 45369}, {18972, 26380}, {19069, 26384}, {19072, 26385}, {22481, 26371}, {22522, 26379}, {22531, 26381}, {22557, 26393}, {22651, 26296}, {22656, 26302}, {22673, 45354}, {22745, 26310}, {22771, 26319}, {22794, 45355}, {22831, 26326}, {22843, 26290}, {22851, 26382}, {22852, 26383}, {22853, 26334}, {22854, 26344}, {22857, 26390}, {22858, 26389}, {22859, 26388}, {22860, 26387}, {22863, 45362}, {22864, 45361}, {22865, 26351}, {22867, 26395}, {22876, 45365}, {22877, 45366}, {22884, 45371}, {22885, 45373}, {22886, 26402}, {22887, 26401}, {35846, 45357}, {35849, 45360}, {44667, 48454}, {48456, 48519}, {48458, 48460}

X(48497) = X(48498)-of-5th mixtilinear triangle
X(48497) = reflection of X(48498) in X(1)


X(48498) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO INNER-FERMAT

Barycentrics    -8*(-10*S+sqrt(3)*(a^2+b^2+c^2))*sqrt(3)*S^2*a*sqrt(R*(4*R+r))+2*(6*a^2*((b^2+c^2)*a-b^3-c^3)*S+(2*a^7-2*(b+c)*a^6-3*(b^2+c^2)*a^5+(b+c)*(3*b^2+b*c+3*c^2)*a^4-6*b^2*c^2*a^3-3*(b^2-c^2)*(b-c)*b*c*a^2+(b^4-c^4)*(b^2-c^2)*a-(b^2-c^2)^3*(b-c))*sqrt(3))*(a+b+c) : :

The reciprocal orthologic center of these triangles is X(3).

X(48498) lies on these lines: {1, 48497}, {18, 5598}, {533, 45697}, {628, 26418}, {630, 26360}, {5965, 45725}, {11740, 26366}, {16627, 26410}, {16628, 45370}, {18972, 26404}, {19069, 26408}, {19072, 26409}, {22481, 26372}, {22522, 26403}, {22531, 26405}, {22557, 26417}, {22651, 26297}, {22656, 26303}, {22669, 45353}, {22745, 26311}, {22771, 26320}, {22794, 45356}, {22831, 26327}, {22843, 26291}, {22851, 26406}, {22852, 26407}, {22853, 26335}, {22854, 26345}, {22857, 26414}, {22858, 26413}, {22859, 26412}, {22860, 26411}, {22863, 45364}, {22864, 45363}, {22865, 26352}, {22867, 26419}, {22876, 45368}, {22877, 45367}, {22884, 45372}, {22885, 45374}, {22886, 26426}, {22887, 26425}, {35846, 45359}, {35849, 45358}, {44667, 48455}, {48457, 48520}, {48459, 48461}

X(48498) = X(48497)-of-5th mixtilinear triangle
X(48498) = reflection of X(48497) in X(1)


X(48499) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO OUTER-FERMAT

Barycentrics    -8*(10*S+sqrt(3)*(a^2+b^2+c^2))*sqrt(3)*S^2*a*sqrt(R*(4*R+r))+2*(-6*a^2*((b^2+c^2)*a-b^3-c^3)*S+(2*a^7-2*(b+c)*a^6-3*(b^2+c^2)*a^5+(b+c)*(3*b^2+b*c+3*c^2)*a^4-6*b^2*c^2*a^3-3*(b^2-c^2)*(b-c)*b*c*a^2+(b^4-c^4)*(b^2-c^2)*a-(b^2-c^2)^3*(b-c))*sqrt(3))*(a+b+c) : :

The reciprocal orthologic center of these triangles is X(3).

X(48499) lies on these lines: {1, 48500}, {17, 5597}, {532, 45696}, {627, 26394}, {629, 26359}, {5965, 45724}, {11739, 26365}, {16626, 26386}, {16629, 45369}, {18973, 26380}, {19070, 26385}, {19071, 26384}, {22482, 26371}, {22523, 26379}, {22532, 26381}, {22558, 26393}, {22652, 26296}, {22657, 26302}, {22674, 45354}, {22746, 26310}, {22772, 26319}, {22795, 45355}, {22832, 26326}, {22890, 26290}, {22896, 26382}, {22897, 26383}, {22898, 26334}, {22899, 26344}, {22902, 26390}, {22903, 26389}, {22904, 26388}, {22905, 26387}, {22908, 45362}, {22909, 45361}, {22910, 26351}, {22912, 26395}, {22921, 45365}, {22922, 45366}, {22929, 45371}, {22930, 45373}, {22931, 26402}, {22932, 26401}, {35847, 45360}, {35848, 45357}, {44666, 48454}, {48456, 48460}, {48458, 48519}

X(48499) = X(48500)-of-5th mixtilinear triangle
X(48499) = reflection of X(48500) in X(1)


X(48500) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO OUTER-FERMAT

Barycentrics    8*(10*S+sqrt(3)*(a^2+b^2+c^2))*sqrt(3)*S^2*a*sqrt(R*(4*R+r))+2*(-6*a^2*((b^2+c^2)*a-b^3-c^3)*S+(2*a^7-2*(b+c)*a^6-3*(b^2+c^2)*a^5+(b+c)*(3*b^2+b*c+3*c^2)*a^4-6*b^2*c^2*a^3-3*(b^2-c^2)*(b-c)*b*c*a^2+(b^4-c^4)*(b^2-c^2)*a-(b^2-c^2)^3*(b-c))*sqrt(3))*(a+b+c) : :

The reciprocal orthologic center of these triangles is X(3).

X(48500) lies on these lines: {1, 48499}, {17, 5598}, {532, 45697}, {627, 26418}, {629, 26360}, {5965, 45725}, {11739, 26366}, {16626, 26410}, {16629, 45370}, {18973, 26404}, {19070, 26409}, {19071, 26408}, {22482, 26372}, {22523, 26403}, {22532, 26405}, {22558, 26417}, {22652, 26297}, {22657, 26303}, {22670, 45353}, {22746, 26311}, {22772, 26320}, {22795, 45356}, {22832, 26327}, {22890, 26291}, {22896, 26406}, {22897, 26407}, {22898, 26335}, {22899, 26345}, {22902, 26414}, {22903, 26413}, {22904, 26412}, {22905, 26411}, {22908, 45364}, {22909, 45363}, {22910, 26352}, {22912, 26419}, {22921, 45368}, {22922, 45367}, {22929, 45372}, {22930, 45374}, {22931, 26426}, {22932, 26425}, {35847, 45358}, {35848, 45359}, {44666, 48455}, {48457, 48461}, {48459, 48520}

X(48500) = X(48499)-of-5th mixtilinear triangle
X(48500) = reflection of X(48499) in X(1)


X(48501) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(48501) lies on these lines: {1, 48502}, {11, 26365}, {80, 5597}, {100, 26382}, {214, 26359}, {515, 48464}, {528, 45712}, {952, 45711}, {2771, 48483}, {2800, 48454}, {2802, 48493}, {2829, 48495}, {5840, 48487}, {6224, 26394}, {6246, 26326}, {6262, 26344}, {6263, 26334}, {6265, 26386}, {7972, 26395}, {8988, 45365}, {9897, 26296}, {9912, 26302}, {10057, 45371}, {10073, 45373}, {12119, 26290}, {12137, 26371}, {12198, 26379}, {12247, 26381}, {12331, 26393}, {12461, 45354}, {12498, 26310}, {12611, 45355}, {12619, 26398}, {12729, 26383}, {12737, 26390}, {12738, 26389}, {12739, 26388}, {12740, 26387}, {12741, 45362}, {12742, 45361}, {12743, 26351}, {12747, 45369}, {12749, 26402}, {12750, 26401}, {12751, 26400}, {12773, 26319}, {13976, 45366}, {18976, 26380}, {19077, 26384}, {19078, 26385}, {35852, 45357}, {35853, 45360}, {48511, 48533}

X(48501) = X(48502)-of-5th mixtilinear triangle
X(48501) = reflection of X(i) in X(j) for these (i, j): (48502, 1), (48533, 48511)


X(48502) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(48502) lies on these lines: {1, 48501}, {11, 26366}, {80, 5598}, {100, 26406}, {214, 26360}, {515, 48465}, {528, 45711}, {952, 45712}, {2771, 48484}, {2800, 48455}, {2802, 48494}, {2829, 48496}, {5840, 48488}, {6224, 26418}, {6246, 26327}, {6262, 26345}, {6263, 26335}, {6265, 26410}, {7972, 26419}, {8988, 45368}, {9897, 26297}, {9912, 26303}, {10057, 45372}, {10073, 45374}, {12119, 26291}, {12137, 26372}, {12198, 26403}, {12247, 26405}, {12331, 26417}, {12460, 45353}, {12498, 26311}, {12611, 45356}, {12619, 26422}, {12729, 26407}, {12737, 26414}, {12738, 26413}, {12739, 26412}, {12740, 26411}, {12741, 45364}, {12742, 45363}, {12743, 26352}, {12747, 45370}, {12749, 26426}, {12750, 26425}, {12751, 26424}, {12773, 26320}, {13976, 45367}, {18976, 26404}, {19077, 26408}, {19078, 26409}, {35852, 45359}, {35853, 45358}, {48512, 48534}

X(48502) = X(48501)-of-5th mixtilinear triangle
X(48502) = reflection of X(i) in X(j) for these (i, j): (48501, 1), (48534, 48512)


X(48503) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 2nd FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(48503) lies on these lines: {1, 48504}, {30, 45711}, {79, 5597}, {758, 48493}, {2771, 48483}, {3647, 26359}, {3648, 26394}, {3649, 26365}, {3652, 26386}, {5441, 26395}, {11684, 26382}, {13743, 26319}, {16113, 26290}, {16114, 26371}, {16115, 26379}, {16116, 26381}, {16117, 26393}, {16118, 26296}, {16119, 26302}, {16122, 45354}, {16123, 26310}, {16125, 26326}, {16129, 26383}, {16130, 26334}, {16131, 26344}, {16138, 26390}, {16139, 26389}, {16140, 26388}, {16141, 26387}, {16142, 26351}, {16148, 45365}, {16149, 45366}, {16150, 45369}, {16152, 45371}, {16153, 45373}, {16154, 26402}, {16155, 26401}, {16161, 45362}, {16162, 45361}, {18977, 26380}, {19079, 26384}, {19080, 26385}, {22798, 45355}, {35854, 45357}, {35855, 45360}, {45712, 48509}

X(48503) = X(48504)-of-5th mixtilinear triangle
X(48503) = reflection of X(48504) in X(1)


X(48504) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 2nd FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(48504) lies on these lines: {1, 48503}, {30, 45712}, {79, 5598}, {758, 48494}, {2771, 48484}, {3647, 26360}, {3648, 26418}, {3649, 26366}, {3652, 26410}, {5441, 26419}, {11684, 26406}, {13743, 26320}, {16113, 26291}, {16114, 26372}, {16115, 26403}, {16116, 26405}, {16117, 26417}, {16118, 26297}, {16119, 26303}, {16121, 45353}, {16123, 26311}, {16125, 26327}, {16129, 26407}, {16130, 26335}, {16131, 26345}, {16138, 26414}, {16139, 26413}, {16140, 26412}, {16141, 26411}, {16142, 26352}, {16148, 45368}, {16149, 45367}, {16150, 45370}, {16152, 45372}, {16153, 45374}, {16154, 26426}, {16155, 26425}, {16161, 45364}, {16162, 45363}, {18977, 26404}, {19079, 26408}, {19080, 26409}, {22798, 45356}, {35854, 45359}, {35855, 45358}, {45711, 48510}

X(48504) = X(48503)-of-5th mixtilinear triangle
X(48504) = reflection of X(48503) in X(1)


X(48505) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO HATZIPOLAKIS-MOSES

Barycentrics    4*a*(a+b-c)*(a-b+c)*(-a+b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(-a^2+b^2+c^2)*(a^6-(b^2+c^2)*a^4-(b^4+b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2))*S*sqrt(R*(4*R+r))+2*a^19-2*(b+c)*a^18-8*(b^2+c^2)*a^17+2*(b+c)*(4*b^2-b*c+4*c^2)*a^16+(9*b^4+20*b^2*c^2+9*c^4)*a^15-(b+c)*(9*b^4+9*c^4-2*(3*b-c)*(b-3*c)*b*c)*a^14+(b^2+c^2)*(3*b^4-14*b^2*c^2+3*c^4)*a^13-(b+c)*(3*b^6+3*c^6+(4*b^4+4*c^4-(11*b^2-10*b*c+11*c^2)*b*c)*b*c)*a^12-(11*b^8+11*c^8+2*(2*b^4-3*b^2*c^2+2*c^4)*b^2*c^2)*a^11+(b+c)*(11*b^8+11*c^8-2*(b^6+c^6-(2*b^4+2*c^4+b*c*(b^2-3*b*c+c^2))*b*c)*b*c)*a^10+3*(b^4-c^4)^2*(b^2+c^2)*a^9-(b^2-c^2)^2*(b+c)*(3*b^6+3*c^6+b^2*c^2*(9*b^2-4*b*c+9*c^2))*a^8+(3*b^4-4*b^2*c^2+3*c^4)*(b^4-c^4)^2*a^7-(b^4-c^4)*(b^2-c^2)*(b+c)*(3*b^6+3*c^6-(2*b^4+2*c^4+b*c*(b^2-4*b*c+c^2))*b*c)*a^6+(b^2-c^2)^2*(b^2+c^2)^5*a^5-(b^2-c^2)^3*(b-c)*(b^8+c^8-2*(b^6+c^6+b^2*c^2*(2*b^2-b*c+2*c^2))*b*c)*a^4-(b^4-c^4)^2*(b^2-c^2)^2*(3*b^4+2*b^2*c^2+3*c^4)*a^3+(b^2-c^2)^5*(b-c)*(b^2+c^2)*(3*b^4+2*b^2*c^2+3*c^4)*a^2+(b^2+c^2)^3*(b^2-c^2)^6*a-(b^2-c^2)^7*(b-c)*(b^2+c^2)^2 : :

The reciprocal orthologic center of these triangles is X(6146).

X(48505) lies on these lines: {1, 48506}, {1154, 48485}, {5597, 6145}, {10628, 48483}, {18400, 48460}, {26290, 32330}, {26296, 32356}, {26302, 32357}, {26310, 32362}, {26319, 32363}, {26326, 32369}, {26334, 32373}, {26344, 32374}, {26351, 32390}, {26359, 32391}, {26365, 32331}, {26371, 32332}, {26379, 32335}, {26380, 32336}, {26381, 32337}, {26382, 32371}, {26383, 32372}, {26384, 32342}, {26385, 32343}, {26386, 32379}, {26387, 32383}, {26388, 32382}, {26389, 32381}, {26390, 32380}, {26393, 32347}, {26394, 32354}, {26395, 32394}, {26401, 32406}, {26402, 32405}, {32361, 45354}, {32364, 45355}, {32388, 45362}, {32389, 45361}, {32399, 45365}, {32400, 45366}, {32402, 45369}, {32403, 45371}, {32404, 45373}, {35858, 45357}, {35859, 45360}

X(48505) = X(48506)-of-5th mixtilinear triangle
X(48505) = reflection of X(48506) in X(1)


X(48506) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO HATZIPOLAKIS-MOSES

Barycentrics    -4*a*(a+b-c)*(a-b+c)*(-a+b+c)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(-a^2+b^2+c^2)*(a^6-(b^2+c^2)*a^4-(b^4+b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2))*S*sqrt(R*(4*R+r))+2*a^19-2*(b+c)*a^18-8*(b^2+c^2)*a^17+2*(b+c)*(4*b^2-b*c+4*c^2)*a^16+(9*b^4+20*b^2*c^2+9*c^4)*a^15-(b+c)*(9*b^4+9*c^4-2*(3*b-c)*(b-3*c)*b*c)*a^14+(b^2+c^2)*(3*b^4-14*b^2*c^2+3*c^4)*a^13-(b+c)*(3*b^6+3*c^6+(4*b^4+4*c^4-(11*b^2-10*b*c+11*c^2)*b*c)*b*c)*a^12-(11*b^8+11*c^8+2*(2*b^4-3*b^2*c^2+2*c^4)*b^2*c^2)*a^11+(b+c)*(11*b^8+11*c^8-2*(b^6+c^6-(2*b^4+2*c^4+b*c*(b^2-3*b*c+c^2))*b*c)*b*c)*a^10+3*(b^4-c^4)^2*(b^2+c^2)*a^9-(b^2-c^2)^2*(b+c)*(3*b^6+3*c^6+b^2*c^2*(9*b^2-4*b*c+9*c^2))*a^8+(3*b^4-4*b^2*c^2+3*c^4)*(b^4-c^4)^2*a^7-(b^4-c^4)*(b^2-c^2)*(b+c)*(3*b^6+3*c^6-(2*b^4+2*c^4+b*c*(b^2-4*b*c+c^2))*b*c)*a^6+(b^2-c^2)^2*(b^2+c^2)^5*a^5-(b^2-c^2)^3*(b-c)*(b^8+c^8-2*(b^6+c^6+b^2*c^2*(2*b^2-b*c+2*c^2))*b*c)*a^4-(b^4-c^4)^2*(b^2-c^2)^2*(3*b^4+2*b^2*c^2+3*c^4)*a^3+(b^2-c^2)^5*(b-c)*(b^2+c^2)*(3*b^4+2*b^2*c^2+3*c^4)*a^2+(b^2+c^2)^3*(b^2-c^2)^6*a-(b^2-c^2)^7*(b-c)*(b^2+c^2)^2 : :

The reciprocal orthologic center of these triangles is X(6146).

X(48506) lies on these lines: {1, 48505}, {1154, 48486}, {5598, 6145}, {10628, 48484}, {18400, 48461}, {26291, 32330}, {26297, 32356}, {26303, 32357}, {26311, 32362}, {26320, 32363}, {26327, 32369}, {26335, 32373}, {26345, 32374}, {26352, 32390}, {26360, 32391}, {26366, 32331}, {26372, 32332}, {26403, 32335}, {26404, 32336}, {26405, 32337}, {26406, 32371}, {26407, 32372}, {26408, 32342}, {26409, 32343}, {26410, 32379}, {26411, 32383}, {26412, 32382}, {26413, 32381}, {26414, 32380}, {26417, 32347}, {26418, 32354}, {26419, 32394}, {26425, 32406}, {26426, 32405}, {32360, 45353}, {32364, 45356}, {32388, 45364}, {32389, 45363}, {32399, 45368}, {32400, 45367}, {32402, 45370}, {32403, 45372}, {32404, 45374}, {35858, 45359}, {35859, 45358}

X(48506) = X(48505)-of-5th mixtilinear triangle
X(48506) = reflection of X(48505) in X(1)


X(48507) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 3rd HATZIPOLAKIS

Barycentrics    -4*a*(a+b-c)*(a-b+c)*(-a+b+c)*(a^12-2*(b^2+c^2)*a^10-(b^2-3*b*c-c^2)*(b^2+3*b*c-c^2)*a^8+(b^2+c^2)*(4*b^4-13*b^2*c^2+4*c^4)*a^6-(b^8+c^8+b^2*c^2*(9*b^4-28*b^2*c^2+9*c^4))*a^4-(b^4-c^4)*(b^2-c^2)*(2*b^4-9*b^2*c^2+2*c^4)*a^2+(b^4-c^4)^2*(b^2-c^2)^2)*S*sqrt(R*(4*R+r))+2*a^19-2*(b+c)*a^18-8*(b^2+c^2)*a^17+2*(b+c)*(4*b^2-b*c+4*c^2)*a^16+9*(b^4+4*b^2*c^2+c^4)*a^15-3*(b+c)*(3*b^4+3*c^4-2*(b^2-6*b*c+c^2)*b*c)*a^14+(b^2+c^2)*(3*b^4-58*b^2*c^2+3*c^4)*a^13-(b+c)*(3*b^6+3*c^6+(4*b^4+4*c^4-(55*b^2-26*b*c+55*c^2)*b*c)*b*c)*a^12-(11*b^8+11*c^8-2*(10*b^4+47*b^2*c^2+10*c^4)*b^2*c^2)*a^11+(b+c)*(11*b^8+11*c^8-2*(b^6+c^6+(10*b^4+10*c^4-(13*b^2-47*b*c+13*c^2)*b*c)*b*c)*b*c)*a^10+(b^2+c^2)*(3*b^8+3*c^8+2*(12*b^4-43*b^2*c^2+12*c^4)*b^2*c^2)*a^9-(b+c)*(3*b^10+3*c^10+(27*b^6+27*c^6-2*(6*b^4+6*c^4+b*c*(31*b^2-28*b*c+31*c^2))*b*c)*b^2*c^2)*a^8+(3*b^8+3*c^8-2*b^2*c^2*(7*b^4+13*b^2*c^2+7*c^4))*(b^2-c^2)^2*a^7-(b^2-c^2)^2*(b+c)*(3*b^8+3*c^8-2*(b^6+c^6+(7*b^4+7*c^4-b*c*(5*b^2-13*b*c+5*c^2))*b*c)*b*c)*a^6+((b^2-c^2)^2-4*b^2*c^2)*(b^2-c^2)^3*(b^4-c^4)*a^5-(b^2-c^2)^4*(b+c)*(b^6+c^6-(4*b^4+4*c^4+5*b*c*(b-c)^2)*b*c)*a^4-3*(b^2+c^2)^2*(b^2-c^2)^6*a^3+3*(b^2-c^2)^7*(b-c)*(b^2+c^2)*a^2+(b^2+c^2)^3*(b^2-c^2)^6*a-(b^2-c^2)^7*(b-c)*(b^2+c^2)^2 : :

The reciprocal orthologic center of these triangles is X(12241).

X(48507) lies on these lines: {1, 48508}, {5597, 22466}, {18978, 26380}, {19083, 26384}, {19084, 26385}, {22476, 26365}, {22483, 26371}, {22524, 26379}, {22533, 26381}, {22559, 26393}, {22647, 26394}, {22653, 26296}, {22658, 26302}, {22675, 45354}, {22747, 26310}, {22776, 26319}, {22800, 45355}, {22833, 26326}, {22941, 26382}, {22943, 26383}, {22945, 26334}, {22947, 26344}, {22951, 26290}, {22955, 26386}, {22956, 26390}, {22957, 26389}, {22958, 26388}, {22959, 26387}, {22963, 45362}, {22964, 45361}, {22965, 26351}, {22966, 26359}, {22969, 26395}, {22976, 45365}, {22977, 45366}, {22979, 45369}, {22980, 45371}, {22981, 45373}, {22982, 26402}, {22983, 26401}, {35860, 45357}, {35861, 45360}

X(48507) = X(48508)-of-5th mixtilinear triangle
X(48507) = reflection of X(48508) in X(1)


X(48508) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 3rd HATZIPOLAKIS

Barycentrics    4*a*(a+b-c)*(a-b+c)*(-a+b+c)*(a^12-2*(b^2+c^2)*a^10-(b^2-3*b*c-c^2)*(b^2+3*b*c-c^2)*a^8+(b^2+c^2)*(4*b^4-13*b^2*c^2+4*c^4)*a^6-(b^8+c^8+b^2*c^2*(9*b^4-28*b^2*c^2+9*c^4))*a^4-(b^4-c^4)*(b^2-c^2)*(2*b^4-9*b^2*c^2+2*c^4)*a^2+(b^4-c^4)^2*(b^2-c^2)^2)*S*sqrt(R*(4*R+r))+2*a^19-2*(b+c)*a^18-8*(b^2+c^2)*a^17+2*(b+c)*(4*b^2-b*c+4*c^2)*a^16+9*(b^4+4*b^2*c^2+c^4)*a^15-3*(b+c)*(3*b^4+3*c^4-2*(b^2-6*b*c+c^2)*b*c)*a^14+(b^2+c^2)*(3*b^4-58*b^2*c^2+3*c^4)*a^13-(b+c)*(3*b^6+3*c^6+(4*b^4+4*c^4-(55*b^2-26*b*c+55*c^2)*b*c)*b*c)*a^12-(11*b^8+11*c^8-2*(10*b^4+47*b^2*c^2+10*c^4)*b^2*c^2)*a^11+(b+c)*(11*b^8+11*c^8-2*(b^6+c^6+(10*b^4+10*c^4-(13*b^2-47*b*c+13*c^2)*b*c)*b*c)*b*c)*a^10+(b^2+c^2)*(3*b^8+3*c^8+2*(12*b^4-43*b^2*c^2+12*c^4)*b^2*c^2)*a^9-(b+c)*(3*b^10+3*c^10+(27*b^6+27*c^6-2*(6*b^4+6*c^4+b*c*(31*b^2-28*b*c+31*c^2))*b*c)*b^2*c^2)*a^8+(3*b^8+3*c^8-2*b^2*c^2*(7*b^4+13*b^2*c^2+7*c^4))*(b^2-c^2)^2*a^7-(b^2-c^2)^2*(b+c)*(3*b^8+3*c^8-2*(b^6+c^6+(7*b^4+7*c^4-b*c*(5*b^2-13*b*c+5*c^2))*b*c)*b*c)*a^6+((b^2-c^2)^2-4*b^2*c^2)*(b^2-c^2)^3*(b^4-c^4)*a^5-(b^2-c^2)^4*(b+c)*(b^6+c^6-(4*b^4+4*c^4+5*b*c*(b-c)^2)*b*c)*a^4-3*(b^2+c^2)^2*(b^2-c^2)^6*a^3+3*(b^2-c^2)^7*(b-c)*(b^2+c^2)*a^2+(b^2+c^2)^3*(b^2-c^2)^6*a-(b^2-c^2)^7*(b-c)*(b^2+c^2)^2 : :

The reciprocal orthologic center of these triangles is X(12241).

X(48508) lies on these lines: {1, 48507}, {5598, 22466}, {18978, 26404}, {19083, 26408}, {19084, 26409}, {22476, 26366}, {22483, 26372}, {22524, 26403}, {22533, 26405}, {22559, 26417}, {22647, 26418}, {22653, 26297}, {22658, 26303}, {22671, 45353}, {22747, 26311}, {22776, 26320}, {22800, 45356}, {22833, 26327}, {22941, 26406}, {22943, 26407}, {22945, 26335}, {22947, 26345}, {22951, 26291}, {22955, 26410}, {22956, 26414}, {22957, 26413}, {22958, 26412}, {22959, 26411}, {22963, 45364}, {22964, 45363}, {22965, 26352}, {22966, 26360}, {22969, 26419}, {22976, 45368}, {22977, 45367}, {22979, 45370}, {22980, 45372}, {22981, 45374}, {22982, 26426}, {22983, 26425}, {35860, 45359}, {35861, 45358}

X(48508) = X(48507)-of-5th mixtilinear triangle
X(48508) = reflection of X(48507) in X(1)


X(48509) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO HUTSON EXTOUCH

Barycentrics    a*(-4*(a^6-2*(b+c)*a^5-(b^2+10*b*c+c^2)*a^4+4*(b+c)^3*a^3-(b^4+c^4-2*b*c*(6*b^2+5*b*c+6*c^2))*a^2-2*(b^2-c^2)*(b-c)*(b^2+6*b*c+c^2)*a+(b^2-c^2)^2*(b-c)^2)*S*sqrt(R*(4*R+r))+(b+c)*a^8-2*(b^2-b*c+c^2)*a^7-2*(b+c)^3*a^6+2*(b^2-b*c+c^2)*(3*b^2+2*b*c+3*c^2)*a^5+8*(b^2-c^2)*(b-c)*b*c*a^4-2*(3*b^4+3*c^4+b*c*(7*b^2+12*b*c+7*c^2))*(b-c)^2*a^3+2*(b^2-c^2)*(b-c)*(b^4+6*b^2*c^2+c^4)*a^2+2*(b^2-c^2)^2*(b+c)^2*a*(b^2-b*c+c^2)-(b^2-c^2)^4*(b+c)) : :

The reciprocal orthologic center of these triangles is X(40).

X(48509) lies on these lines: {1, 12664}, {5597, 7160}, {8000, 26395}, {9874, 26394}, {9898, 26296}, {10059, 45371}, {10075, 45373}, {12120, 26290}, {12139, 26371}, {12200, 26379}, {12249, 26381}, {12260, 26365}, {12333, 26393}, {12411, 26302}, {12465, 45354}, {12500, 26310}, {12599, 26326}, {12777, 26382}, {12789, 26383}, {12801, 26334}, {12802, 26344}, {12856, 26386}, {12857, 26390}, {12858, 26389}, {12859, 26388}, {12860, 26387}, {12861, 45362}, {12862, 45361}, {12863, 26351}, {12864, 26359}, {12872, 45369}, {12874, 26402}, {12875, 26401}, {13914, 45365}, {13978, 45366}, {18979, 26380}, {19085, 26384}, {19086, 26385}, {22777, 26319}, {22801, 45355}, {35862, 45357}, {35863, 45360}, {45712, 48503}

X(48509) = X(48510)-of-5th mixtilinear triangle
X(48509) = reflection of X(48510) in X(1)


X(48510) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO HUTSON EXTOUCH

Barycentrics    a*(4*(a^6-2*(b+c)*a^5-(b^2+10*b*c+c^2)*a^4+4*(b+c)^3*a^3-(b^4+c^4-2*b*c*(6*b^2+5*b*c+6*c^2))*a^2-2*(b^2-c^2)*(b-c)*(b^2+6*b*c+c^2)*a+(b^2-c^2)^2*(b-c)^2)*S*sqrt(R*(4*R+r))+(b+c)*a^8-2*(b^2-b*c+c^2)*a^7-2*(b+c)^3*a^6+2*(b^2-b*c+c^2)*(3*b^2+2*b*c+3*c^2)*a^5+8*(b^2-c^2)*(b-c)*b*c*a^4-2*(3*b^4+3*c^4+b*c*(7*b^2+12*b*c+7*c^2))*(b-c)^2*a^3+2*(b^2-c^2)*(b-c)*(b^4+6*b^2*c^2+c^4)*a^2+2*(b^2-c^2)^2*(b+c)^2*a*(b^2-b*c+c^2)-(b^2-c^2)^4*(b+c)) : :

The reciprocal orthologic center of these triangles is X(40).

X(48510) lies on these lines: {1, 12664}, {5598, 7160}, {8000, 26419}, {9874, 26418}, {9898, 26297}, {10059, 45372}, {10075, 45374}, {12120, 26291}, {12139, 26372}, {12200, 26403}, {12249, 26405}, {12260, 26366}, {12333, 26417}, {12411, 26303}, {12464, 45353}, {12500, 26311}, {12599, 26327}, {12777, 26406}, {12789, 26407}, {12801, 26335}, {12802, 26345}, {12856, 26410}, {12857, 26414}, {12858, 26413}, {12859, 26412}, {12860, 26411}, {12861, 45364}, {12862, 45363}, {12863, 26352}, {12864, 26360}, {12872, 45370}, {12874, 26426}, {12875, 26425}, {13914, 45368}, {13978, 45367}, {18979, 26404}, {19085, 26408}, {19086, 26409}, {22777, 26320}, {22801, 45356}, {35862, 45359}, {35863, 45358}, {45711, 48504}

X(48510) = X(48509)-of-5th mixtilinear triangle
X(48510) = reflection of X(48509) in X(1)


X(48511) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 1st JENKINS

Barycentrics    8*a*S*sqrt(R*(4*R+r))+2*a^4-(b+c)*a^3-(b+c)^2*a^2+(b+c)*(b^2+c^2)*a-(b^2-c^2)^2 : :
X(48511) = 3*X(45696)-X(45711) = 3*X(45696)+X(48493)

The reciprocal orthologic center of these triangles is X(10).

X(48511) lies on these lines: {1, 224}, {8, 26296}, {10, 5597}, {40, 26381}, {226, 26388}, {355, 45369}, {515, 48460}, {516, 48454}, {517, 48519}, {519, 45696}, {726, 48515}, {946, 26386}, {950, 26351}, {1125, 26359}, {1210, 45373}, {2784, 48462}, {2796, 48470}, {3244, 26395}, {3419, 11366}, {4297, 26290}, {5847, 45724}, {6684, 26398}, {8666, 26319}, {8715, 26393}, {10106, 26380}, {10915, 26400}, {10916, 26399}, {12053, 26387}, {12699, 18496}, {13883, 44582}, {13936, 44583}, {17766, 48517}, {18483, 45355}, {19925, 26326}, {20075, 26297}, {21077, 26389}, {31397, 45371}, {48501, 48533}

X(48511) = midpoint of X(i) and X(j) for these {i, j}: {45711, 48493}, {48454, 48487}, {48501, 48533}
X(48511) = reflection of X(48512) in X(1)
X(48511) = X(48512)-of-5th mixtilinear triangle
X(48511) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5597, 26382, 10), (26359, 26365, 1125), (45696, 48493, 45711)


X(48512) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 1st JENKINS

Barycentrics    -8*a*S*sqrt(R*(4*R+r))+2*a^4-(b+c)*a^3-(b+c)^2*a^2+(b+c)*(b^2+c^2)*a-(b^2-c^2)^2 : :
X(48512) = 3*X(45697)-X(45712) = 3*X(45697)+X(48494)

The reciprocal orthologic center of these triangles is X(10).

X(48512) lies on these lines: {1, 224}, {8, 26297}, {10, 5598}, {40, 26405}, {226, 26412}, {355, 45370}, {515, 48461}, {516, 48455}, {517, 48520}, {519, 45697}, {726, 48516}, {946, 26410}, {950, 26352}, {1125, 26360}, {1210, 45374}, {2784, 48463}, {2796, 48471}, {3244, 26419}, {3419, 11367}, {4297, 26291}, {5847, 45725}, {6684, 26422}, {8666, 26320}, {8715, 26417}, {10106, 26404}, {10915, 26424}, {10916, 26423}, {12053, 26411}, {12699, 18498}, {13883, 44584}, {13936, 44585}, {17766, 48518}, {18483, 45356}, {19925, 26327}, {20075, 26296}, {21077, 26413}, {31397, 45372}, {48502, 48534}

X(48512) = midpoint of X(i) and X(j) for these {i, j}: {45712, 48494}, {48455, 48488}, {48502, 48534}
X(48512) = reflection of X(48511) in X(1)
X(48512) = X(48511)-of-5th mixtilinear triangle
X(48512) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5598, 26406, 10), (26360, 26366, 1125), (45697, 48494, 45712)


X(48513) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO MIDHEIGHT

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

The reciprocal orthologic center of these triangles is X(4).

X(48513) lies on these lines: {1, 48514}, {30, 48485}, {64, 5597}, {1498, 26290}, {2777, 48483}, {2883, 26359}, {3357, 26398}, {5878, 26386}, {6000, 48460}, {6001, 48487}, {6225, 26394}, {6247, 26326}, {6266, 26344}, {6267, 26334}, {6285, 26380}, {7355, 26351}, {7973, 26395}, {8991, 45365}, {9899, 26296}, {9914, 26302}, {10060, 45371}, {10076, 45373}, {11381, 26371}, {12202, 26379}, {12250, 26381}, {12262, 26365}, {12335, 26393}, {12469, 45354}, {12502, 26310}, {12779, 26382}, {12791, 26383}, {12920, 26390}, {12930, 26389}, {12940, 26388}, {12950, 26387}, {12986, 45362}, {12987, 45361}, {13093, 45369}, {13094, 26402}, {13095, 26401}, {13980, 45366}, {15311, 48454}, {19087, 26384}, {19088, 26385}, {22778, 26319}, {22802, 45355}, {34146, 45724}, {35864, 45357}, {35865, 45360}, {36201, 48529}

X(48513) = X(48514)-of-5th mixtilinear triangle
X(48513) = reflection of X(48514) in X(1)


X(48514) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO MIDHEIGHT

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

The reciprocal orthologic center of these triangles is X(4).

X(48514) lies on these lines: {1, 48513}, {30, 48486}, {64, 5598}, {1498, 26291}, {2777, 48484}, {2883, 26360}, {3357, 26422}, {5878, 26410}, {6000, 48461}, {6001, 48488}, {6225, 26418}, {6247, 26327}, {6266, 26345}, {6267, 26335}, {6285, 26404}, {7355, 26352}, {7973, 26419}, {8991, 45368}, {9899, 26297}, {9914, 26303}, {10060, 45372}, {10076, 45374}, {11381, 26372}, {12202, 26403}, {12250, 26405}, {12262, 26366}, {12335, 26417}, {12468, 45353}, {12502, 26311}, {12779, 26406}, {12791, 26407}, {12920, 26414}, {12930, 26413}, {12940, 26412}, {12950, 26411}, {12986, 45364}, {12987, 45363}, {13093, 45370}, {13094, 26426}, {13095, 26425}, {13980, 45367}, {15311, 48455}, {19087, 26408}, {19088, 26409}, {22778, 26320}, {22802, 45356}, {34146, 45725}, {35864, 45359}, {35865, 45358}, {36201, 48530}

X(48514) = X(48513)-of-5th mixtilinear triangle
X(48514) = reflection of X(48513) in X(1)


X(48515) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 1st NEUBERG

Barycentrics    4*a*((b^2+c^2)*a^2+b^2*c^2)*S*sqrt(R*(4*R+r))+(a+b+c)*((b^2+c^2)*a^5-(b+c)*(b^2+c^2)*a^4+(b^2+c^2)*b^2*c^2*a-(b^2-c^2)*(b-c)*b^2*c^2) : :
X(48515) = 3*X(48491)-4*X(48519)

The reciprocal orthologic center of these triangles is X(3).

X(48515) lies on these lines: {1, 48516}, {39, 26359}, {76, 5597}, {194, 26394}, {384, 26379}, {511, 48454}, {538, 45696}, {726, 48511}, {730, 45711}, {732, 45724}, {2782, 48460}, {3095, 26386}, {5969, 48470}, {6248, 26326}, {6272, 26344}, {6273, 26334}, {7976, 26395}, {8992, 45365}, {9902, 26296}, {9917, 26302}, {9983, 26310}, {10063, 45371}, {10079, 45373}, {11257, 26290}, {12143, 26371}, {12251, 26381}, {12263, 26365}, {12338, 26393}, {12475, 45354}, {12782, 26382}, {12794, 26383}, {12836, 26387}, {12837, 26388}, {12923, 26390}, {12933, 26389}, {12992, 45362}, {12993, 45361}, {13077, 26351}, {13108, 45369}, {13109, 26402}, {13110, 26401}, {13983, 45366}, {14839, 48493}, {14881, 45355}, {18982, 26380}, {19089, 26384}, {19090, 26385}, {22779, 26319}, {32515, 48491}, {35866, 45357}, {35867, 45360}

X(48515) = X(48516)-of-5th mixtilinear triangle
X(48515) = reflection of X(48516) in X(1)


X(48516) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 1st NEUBERG

Barycentrics    -4*a*((b^2+c^2)*a^2+b^2*c^2)*S*sqrt(R*(4*R+r))+(a+b+c)*((b^2+c^2)*a^5-(b+c)*(b^2+c^2)*a^4+(b^2+c^2)*b^2*c^2*a-(b^2-c^2)*(b-c)*b^2*c^2) : :
X(48516) = 3*X(48492)-4*X(48520)

The reciprocal orthologic center of these triangles is X(3).

X(48516) lies on these lines: {1, 48515}, {39, 26360}, {76, 5598}, {194, 26418}, {384, 26403}, {511, 48455}, {538, 45697}, {726, 48512}, {730, 45712}, {732, 45725}, {2782, 48461}, {3095, 26410}, {5969, 48471}, {6248, 26327}, {6272, 26345}, {6273, 26335}, {7976, 26419}, {8992, 45368}, {9902, 26297}, {9917, 26303}, {9983, 26311}, {10063, 45372}, {10079, 45374}, {11257, 26291}, {12143, 26372}, {12251, 26405}, {12263, 26366}, {12338, 26417}, {12474, 45353}, {12782, 26406}, {12794, 26407}, {12836, 26411}, {12837, 26412}, {12923, 26414}, {12933, 26413}, {12992, 45364}, {12993, 45363}, {13077, 26352}, {13108, 45370}, {13109, 26426}, {13110, 26425}, {13983, 45367}, {14839, 48494}, {14881, 45356}, {18982, 26404}, {19089, 26408}, {19090, 26409}, {22779, 26320}, {32515, 48492}, {35866, 45359}, {35867, 45358}

X(48516) = X(48515)-of-5th mixtilinear triangle
X(48516) = reflection of X(48515) in X(1)


X(48517) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 2nd NEUBERG

Barycentrics    4*a*(a^4+3*(b^2+c^2)*a^2+b^4+3*b^2*c^2+c^4)*S*sqrt(R*(4*R+r))+(a+b+c)*(3*(b^2+c^2)*a^5-(b+c)*(3*b^2-2*b*c+3*c^2)*a^4+2*(b^2+c^2)^2*a^3-2*(b^3+c^3)*(b^2+c^2)*a^2+(b^2+c^2)*b^2*c^2*a-(b^2-c^2)*(b-c)*b^2*c^2) : :

The reciprocal orthologic center of these triangles is X(3).

X(48517) lies on these lines: {1, 48518}, {83, 5597}, {732, 45724}, {754, 45696}, {2896, 26310}, {6249, 26326}, {6274, 26344}, {6275, 26334}, {6287, 26386}, {6292, 26359}, {7977, 26395}, {8993, 45365}, {9903, 26296}, {9918, 26302}, {10064, 45371}, {10080, 45373}, {12122, 26290}, {12144, 26371}, {12206, 26379}, {12252, 26381}, {12264, 26365}, {12339, 26393}, {12477, 45354}, {12783, 26382}, {12795, 26383}, {12924, 26390}, {12934, 26389}, {12944, 26388}, {12954, 26387}, {12994, 45362}, {12995, 45361}, {13078, 26351}, {13111, 45369}, {13112, 26402}, {13113, 26401}, {13984, 45366}, {17766, 48511}, {18983, 26380}, {19091, 26384}, {19092, 26385}, {22780, 26319}, {22803, 45355}, {29012, 48454}, {35868, 45357}, {35869, 45360}, {48460, 48491}, {48462, 48519}

X(48517) = X(48518)-of-5th mixtilinear triangle
X(48517) = reflection of X(48518) in X(1)


X(48518) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 2nd NEUBERG

Barycentrics    -4*a*(a^4+3*(b^2+c^2)*a^2+b^4+3*b^2*c^2+c^4)*S*sqrt(R*(4*R+r))+(a+b+c)*(3*(b^2+c^2)*a^5-(b+c)*(3*b^2-2*b*c+3*c^2)*a^4+2*(b^2+c^2)^2*a^3-2*(b^3+c^3)*(b^2+c^2)*a^2+(b^2+c^2)*b^2*c^2*a-(b^2-c^2)*(b-c)*b^2*c^2) : :

The reciprocal orthologic center of these triangles is X(3).

X(48518) lies on these lines: {1, 48517}, {83, 5598}, {732, 45725}, {754, 45697}, {2896, 26311}, {6249, 26327}, {6274, 26345}, {6275, 26335}, {6287, 26410}, {6292, 26360}, {7977, 26419}, {8993, 45368}, {9903, 26297}, {9918, 26303}, {10064, 45372}, {10080, 45374}, {12122, 26291}, {12144, 26372}, {12206, 26403}, {12252, 26405}, {12264, 26366}, {12339, 26417}, {12476, 45353}, {12783, 26406}, {12795, 26407}, {12924, 26414}, {12934, 26413}, {12944, 26412}, {12954, 26411}, {12994, 45364}, {12995, 45363}, {13078, 26352}, {13111, 45370}, {13112, 26426}, {13113, 26425}, {13984, 45367}, {17766, 48512}, {18983, 26404}, {19091, 26408}, {19092, 26409}, {22780, 26320}, {22803, 45356}, {29012, 48455}, {35868, 45359}, {35869, 45358}, {48461, 48492}, {48463, 48520}

X(48518) = X(48517)-of-5th mixtilinear triangle
X(48518) = reflection of X(48517) in X(1)


X(48519) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO ORTHIC AXES

Barycentrics    -8*a*(a+b-c)*(-a+b+c)*(a-b+c)*S*sqrt(R*(4*R+r))+2*a^7-2*(b+c)*a^6-3*(b^2+c^2)*a^5+3*(b^2+c^2)*(b+c)*a^4-4*b^2*c^2*a^3-2*(b^2-c^2)*(b-c)*b*c*a^2+(b^4-c^4)*(b^2-c^2)*a-(b^2-c^2)^3*(b-c) : :
X(48519) = 3*X(45696)+X(48454) = 3*X(45696)-X(48460) = 3*X(48491)+X(48515)

The reciprocal orthologic center of these triangles is X(4).

X(48519) lies on these lines: {1, 48520}, {3, 26381}, {4, 18496}, {5, 5597}, {26, 26302}, {30, 45696}, {140, 26359}, {355, 26296}, {495, 26388}, {496, 26387}, {517, 48511}, {546, 26326}, {550, 26290}, {952, 45711}, {1483, 26395}, {3070, 45357}, {3071, 45360}, {3564, 45724}, {5690, 26382}, {5844, 48493}, {5874, 26344}, {5875, 26334}, {5901, 26365}, {6756, 26371}, {7583, 44582}, {7584, 44583}, {10942, 26389}, {10943, 26390}, {11366, 37820}, {13925, 45365}, {13993, 45366}, {15171, 26351}, {18990, 26380}, {19116, 26384}, {19117, 26385}, {20075, 45370}, {26310, 32151}, {26319, 32153}, {26379, 32134}, {26383, 32162}, {26393, 32141}, {26401, 32214}, {26402, 32213}, {28174, 48487}, {32147, 45354}, {32177, 45362}, {32178, 45361}, {32423, 48483}, {32515, 48491}, {48456, 48497}, {48458, 48499}, {48462, 48517}

X(48519) = midpoint of X(i) and X(j) for these {i, j}: {48454, 48460}, {48483, 48535}
X(48519) = reflection of X(48520) in X(1)
X(48519) = X(48520)-of-5th mixtilinear triangle
X(48519) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5597, 26386, 5), (18496, 45369, 4), (26326, 45355, 546), (26359, 26398, 140), (26381, 26394, 3), (26387, 45373, 496), (26388, 45371, 495), (45696, 48454, 48460), (48478, 48480, 45724)


X(48520) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO ORTHIC AXES

Barycentrics    8*a*(a+b-c)*(-a+b+c)*(a-b+c)*S*sqrt(R*(4*R+r))+2*a^7-2*(b+c)*a^6-3*(b^2+c^2)*a^5+3*(b^2+c^2)*(b+c)*a^4-4*b^2*c^2*a^3-2*(b^2-c^2)*(b-c)*b*c*a^2+(b^4-c^4)*(b^2-c^2)*a-(b^2-c^2)^3*(b-c) : :
X(48520) = 3*X(45697)+X(48455) = 3*X(45697)-X(48461) = 3*X(48492)+X(48516)

The reciprocal orthologic center of these triangles is X(4).

X(48520) lies on these lines: {1, 48519}, {3, 26405}, {4, 18498}, {5, 5598}, {26, 26303}, {30, 45697}, {140, 26360}, {355, 26297}, {495, 26412}, {496, 26411}, {517, 48512}, {546, 26327}, {550, 26291}, {952, 45712}, {1483, 26419}, {3070, 45359}, {3071, 45358}, {3564, 45725}, {5690, 26406}, {5844, 48494}, {5874, 26345}, {5875, 26335}, {5901, 26366}, {6756, 26372}, {7583, 44584}, {7584, 44585}, {10942, 26413}, {10943, 26414}, {11367, 37820}, {13925, 45368}, {13993, 45367}, {15171, 26352}, {18990, 26404}, {19116, 26408}, {19117, 26409}, {20075, 45369}, {26311, 32151}, {26320, 32153}, {26403, 32134}, {26407, 32162}, {26417, 32141}, {26425, 32214}, {26426, 32213}, {28174, 48488}, {32146, 45353}, {32177, 45364}, {32178, 45363}, {32423, 48484}, {32515, 48492}, {48457, 48498}, {48459, 48500}, {48463, 48518}

X(48520) = midpoint of X(i) and X(j) for these {i, j}: {48455, 48461}, {48484, 48536}
X(48520) = reflection of X(48519) in X(1)
X(48520) = X(48519)-of-5th mixtilinear triangle
X(48520) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5598, 26410, 5), (18498, 45370, 4), (26327, 45356, 546), (26360, 26422, 140), (26405, 26418, 3), (26411, 45374, 496), (26412, 45372, 495), (45697, 48455, 48461), (48479, 48481, 45725)


X(48521) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO REFLECTION

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

The reciprocal orthologic center of these triangles is X(4).

X(48521) lies on these lines: {1, 48522}, {54, 5597}, {195, 45369}, {539, 45696}, {1154, 48460}, {1209, 26359}, {2888, 26394}, {3574, 26326}, {6276, 26344}, {6277, 26334}, {6288, 26386}, {7691, 26290}, {7979, 26395}, {8995, 45365}, {9905, 26296}, {9920, 26302}, {9985, 26310}, {10066, 45371}, {10082, 45373}, {10610, 26398}, {10628, 48472}, {11576, 26371}, {12208, 26379}, {12254, 26381}, {12266, 26365}, {12341, 26393}, {12481, 45354}, {12785, 26382}, {12797, 26383}, {12926, 26390}, {12936, 26389}, {12946, 26388}, {12956, 26387}, {12965, 45357}, {12971, 45360}, {12998, 45362}, {12999, 45361}, {13079, 26351}, {13121, 26402}, {13122, 26401}, {13986, 45366}, {18400, 48454}, {18984, 26380}, {19095, 26384}, {19096, 26385}, {22781, 26319}, {22804, 45355}, {32423, 48483}, {44668, 45724}

X(48521) = X(48522)-of-5th mixtilinear triangle
X(48521) = reflection of X(48522) in X(1)


X(48522) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO REFLECTION

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

The reciprocal orthologic center of these triangles is X(4).

X(48522) lies on these lines: {1, 48521}, {54, 5598}, {195, 45370}, {539, 45697}, {1154, 48461}, {1209, 26360}, {2888, 26418}, {3574, 26327}, {6276, 26345}, {6277, 26335}, {6288, 26410}, {7691, 26291}, {7979, 26419}, {8995, 45368}, {9905, 26297}, {9920, 26303}, {9985, 26311}, {10066, 45372}, {10082, 45374}, {10610, 26422}, {10628, 48473}, {11576, 26372}, {12208, 26403}, {12254, 26405}, {12266, 26366}, {12341, 26417}, {12480, 45353}, {12785, 26406}, {12797, 26407}, {12926, 26414}, {12936, 26413}, {12946, 26412}, {12956, 26411}, {12965, 45359}, {12971, 45358}, {12998, 45364}, {12999, 45363}, {13079, 26352}, {13121, 26426}, {13122, 26425}, {13986, 45367}, {18400, 48455}, {18984, 26404}, {19095, 26408}, {19096, 26409}, {22781, 26320}, {22804, 45356}, {32423, 48484}, {44668, 45725}

X(48522) = X(48521)-of-5th mixtilinear triangle
X(48522) = reflection of X(48521) in X(1)


X(48523) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 1st SCHIFFLER

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

The reciprocal orthologic center of these triangles is X(79).

X(48523) lies on these lines: {1, 48524}, {5597, 10266}, {12146, 26371}, {12209, 26379}, {12255, 26381}, {12267, 26365}, {12342, 26393}, {12409, 26296}, {12414, 26302}, {12483, 45354}, {12504, 26310}, {12556, 26290}, {12600, 26326}, {12786, 26382}, {12798, 26383}, {12807, 26334}, {12808, 26344}, {12849, 26394}, {12919, 26386}, {12927, 26390}, {12937, 26389}, {12947, 26388}, {12957, 26387}, {13000, 45362}, {13001, 45361}, {13080, 26351}, {13089, 26359}, {13100, 26395}, {13126, 45369}, {13128, 45371}, {13129, 45373}, {13130, 26402}, {13131, 26401}, {13919, 45365}, {13987, 45366}, {18985, 26380}, {19097, 26384}, {19098, 26385}, {22782, 26319}, {22805, 45355}, {35870, 45357}, {35871, 45360}

X(48523) = X(48524)-of-5th mixtilinear triangle
X(48523) = reflection of X(48524) in X(1)


X(48524) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 1st SCHIFFLER

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

The reciprocal orthologic center of these triangles is X(79).

X(48524) lies on these lines: {1, 48523}, {5598, 10266}, {12146, 26372}, {12209, 26403}, {12255, 26405}, {12267, 26366}, {12342, 26417}, {12409, 26297}, {12414, 26303}, {12482, 45353}, {12504, 26311}, {12556, 26291}, {12600, 26327}, {12786, 26406}, {12798, 26407}, {12807, 26335}, {12808, 26345}, {12849, 26418}, {12919, 26410}, {12927, 26414}, {12937, 26413}, {12947, 26412}, {12957, 26411}, {13000, 45364}, {13001, 45363}, {13080, 26352}, {13089, 26360}, {13100, 26419}, {13126, 45370}, {13128, 45372}, {13129, 45374}, {13130, 26426}, {13131, 26425}, {13919, 45368}, {13987, 45367}, {18985, 26404}, {19097, 26408}, {19098, 26409}, {22782, 26320}, {22805, 45356}, {35870, 45359}, {35871, 45358}

X(48524) = X(48523)-of-5th mixtilinear triangle
X(48524) = reflection of X(48523) in X(1)


X(48525) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 1st TRI-SQUARES-CENTRAL

Barycentrics    24*a*S^2*(a^2+c^2+b^2+4*S)*sqrt(R*(4*R+r))+(a+b+c)*(12*a^2*((b^2+c^2)*a-b^3-c^3)*S-10*a^7+10*(b+c)*a^6+15*(b^2+c^2)*a^5-(b+c)*(15*b^2-8*b*c+15*c^2)*a^4+4*b^2*c^2*a^3+2*(b^2-c^2)*(b-c)*b*c*a^2-5*(b^4-c^4)*(b^2-c^2)*a+5*(b^2-c^2)^3*(b-c)) : :

The reciprocal orthologic center of these triangles is X(13665).

X(48525) lies on these lines: {1, 48526}, {30, 48480}, {1327, 5597}, {13666, 26290}, {13667, 26365}, {13668, 26371}, {13672, 26379}, {13674, 26381}, {13675, 26393}, {13678, 26394}, {13679, 26296}, {13680, 26302}, {13683, 45354}, {13685, 26310}, {13687, 26326}, {13688, 26382}, {13689, 26383}, {13690, 26334}, {13691, 26344}, {13692, 26386}, {13693, 26390}, {13694, 26389}, {13695, 26388}, {13696, 26387}, {13697, 45362}, {13698, 45361}, {13699, 26351}, {13701, 26359}, {13702, 26395}, {13713, 45369}, {13714, 45371}, {13715, 45373}, {13716, 26402}, {13717, 26401}, {13920, 45365}, {13988, 45366}, {15682, 26396}, {18986, 26380}, {19099, 26384}, {22541, 26385}, {22783, 26319}, {22806, 45355}, {35872, 45357}, {35873, 45360}, {45724, 48527}

X(48525) = X(48526)-of-5th mixtilinear triangle
X(48525) = reflection of X(48526) in X(1)


X(48526) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 1st TRI-SQUARES-CENTRAL

Barycentrics    -24*a*S^2*(a^2+c^2+b^2+4*S)*sqrt(R*(4*R+r))+(a+b+c)*(12*a^2*((b^2+c^2)*a-b^3-c^3)*S-10*a^7+10*(b+c)*a^6+15*(b^2+c^2)*a^5-(b+c)*(15*b^2-8*b*c+15*c^2)*a^4+4*b^2*c^2*a^3+2*(b^2-c^2)*(b-c)*b*c*a^2-5*(b^4-c^4)*(b^2-c^2)*a+5*(b^2-c^2)^3*(b-c)) : :

The reciprocal orthologic center of these triangles is X(13665).

X(48526) lies on these lines: {1, 48525}, {30, 48481}, {1327, 5598}, {13666, 26291}, {13667, 26366}, {13668, 26372}, {13672, 26403}, {13674, 26405}, {13675, 26417}, {13678, 26418}, {13679, 26297}, {13680, 26303}, {13682, 45353}, {13685, 26311}, {13687, 26327}, {13688, 26406}, {13689, 26407}, {13690, 26335}, {13691, 26345}, {13692, 26410}, {13693, 26414}, {13694, 26413}, {13695, 26412}, {13696, 26411}, {13697, 45364}, {13698, 45363}, {13699, 26352}, {13701, 26360}, {13702, 26419}, {13713, 45370}, {13714, 45372}, {13715, 45374}, {13716, 26426}, {13717, 26425}, {13920, 45368}, {13988, 45367}, {15682, 26420}, {18986, 26404}, {19099, 26408}, {22541, 26409}, {22783, 26320}, {22806, 45356}, {35872, 45359}, {35873, 45358}, {45725, 48528}

X(48526) = X(48525)-of-5th mixtilinear triangle
X(48526) = reflection of X(48525) in X(1)


X(48527) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    -24*a*S^2*(a^2+c^2+b^2-4*S)*sqrt(R*(4*R+r))+(a+b+c)*(-12*a^2*((b^2+c^2)*a-b^3-c^3)*S-10*a^7+10*(b+c)*a^6+15*(b^2+c^2)*a^5-(b+c)*(15*b^2-8*b*c+15*c^2)*a^4+4*b^2*c^2*a^3+2*(b^2-c^2)*(b-c)*b*c*a^2-5*(b^4-c^4)*(b^2-c^2)*a+5*(b^2-c^2)^3*(b-c)) : :

The reciprocal orthologic center of these triangles is X(13785).

X(48527) lies on these lines: {1, 48528}, {30, 48478}, {1328, 5597}, {13786, 26290}, {13787, 26365}, {13788, 26371}, {13792, 26379}, {13794, 26381}, {13795, 26393}, {13798, 26394}, {13799, 26296}, {13800, 26302}, {13803, 45354}, {13805, 26310}, {13807, 26326}, {13808, 26382}, {13809, 26383}, {13810, 26334}, {13811, 26344}, {13812, 26386}, {13813, 26390}, {13814, 26389}, {13815, 26388}, {13816, 26387}, {13817, 45362}, {13818, 45361}, {13819, 26351}, {13821, 26359}, {13822, 26395}, {13836, 45369}, {13837, 45371}, {13838, 45373}, {13839, 26402}, {13840, 26401}, {13848, 45365}, {13849, 45366}, {15682, 26397}, {18987, 26380}, {19100, 26385}, {19101, 26384}, {22784, 26319}, {22807, 45355}, {35874, 45357}, {35875, 45360}, {45724, 48525}

X(48527) = X(48528)-of-5th mixtilinear triangle
X(48527) = reflection of X(48528) in X(1)


X(48528) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    24*a*S^2*(a^2+c^2+b^2-4*S)*sqrt(R*(4*R+r))+(a+b+c)*(-12*a^2*((b^2+c^2)*a-b^3-c^3)*S-10*a^7+10*(b+c)*a^6+15*(b^2+c^2)*a^5-(b+c)*(15*b^2-8*b*c+15*c^2)*a^4+4*b^2*c^2*a^3+2*(b^2-c^2)*(b-c)*b*c*a^2-5*(b^4-c^4)*(b^2-c^2)*a+5*(b^2-c^2)^3*(b-c)) : :

The reciprocal orthologic center of these triangles is X(13785).

X(48528) lies on these lines: {1, 48527}, {30, 48479}, {1328, 5598}, {13786, 26291}, {13787, 26366}, {13788, 26372}, {13792, 26403}, {13794, 26405}, {13795, 26417}, {13798, 26418}, {13799, 26297}, {13800, 26303}, {13802, 45353}, {13805, 26311}, {13807, 26327}, {13808, 26406}, {13809, 26407}, {13810, 26335}, {13811, 26345}, {13812, 26410}, {13813, 26414}, {13814, 26413}, {13815, 26412}, {13816, 26411}, {13817, 45364}, {13818, 45363}, {13819, 26352}, {13821, 26360}, {13822, 26419}, {13836, 45370}, {13837, 45372}, {13838, 45374}, {13839, 26426}, {13840, 26425}, {13848, 45368}, {13849, 45367}, {15682, 26421}, {18987, 26404}, {19100, 26409}, {19101, 26408}, {22784, 26320}, {22807, 45356}, {35874, 45359}, {35875, 45358}, {45725, 48526}

X(48528) = X(48527)-of-5th mixtilinear triangle
X(48528) = reflection of X(48527) in X(1)


X(48529) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(48529) lies on these lines: {1, 48530}, {67, 5597}, {511, 48483}, {542, 48460}, {1503, 48472}, {2781, 48454}, {6593, 26359}, {9970, 26386}, {11061, 26394}, {14984, 48485}, {26290, 32233}, {26296, 32261}, {26302, 32262}, {26310, 32268}, {26319, 32270}, {26326, 32274}, {26334, 32280}, {26344, 32281}, {26351, 32297}, {26365, 32238}, {26371, 32239}, {26379, 32242}, {26380, 32243}, {26381, 32247}, {26382, 32278}, {26383, 32279}, {26384, 32252}, {26385, 32253}, {26387, 32290}, {26388, 32289}, {26389, 32288}, {26390, 32287}, {26393, 32256}, {26395, 32298}, {26401, 32310}, {26402, 32309}, {32266, 45354}, {32271, 45355}, {32295, 45362}, {32296, 45361}, {32303, 45365}, {32304, 45366}, {32306, 45369}, {32307, 45371}, {32308, 45373}, {35876, 45357}, {35877, 45360}, {36201, 48513}

X(48529) = X(48530)-of-5th mixtilinear triangle
X(48529) = reflection of X(48530) in X(1)


X(48530) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(48530) lies on these lines: {1, 48529}, {67, 5598}, {511, 48484}, {542, 48461}, {1503, 48473}, {2781, 48455}, {6593, 26360}, {9970, 26410}, {11061, 26418}, {14984, 48486}, {26291, 32233}, {26297, 32261}, {26303, 32262}, {26311, 32268}, {26320, 32270}, {26327, 32274}, {26335, 32280}, {26345, 32281}, {26352, 32297}, {26366, 32238}, {26372, 32239}, {26403, 32242}, {26404, 32243}, {26405, 32247}, {26406, 32278}, {26407, 32279}, {26408, 32252}, {26409, 32253}, {26411, 32290}, {26412, 32289}, {26413, 32288}, {26414, 32287}, {26417, 32256}, {26419, 32298}, {26425, 32310}, {26426, 32309}, {32265, 45353}, {32271, 45356}, {32295, 45364}, {32296, 45363}, {32303, 45368}, {32304, 45367}, {32306, 45370}, {32307, 45372}, {32308, 45374}, {35876, 45359}, {35877, 45358}, {36201, 48514}

X(48530) = X(48529)-of-5th mixtilinear triangle
X(48530) = reflection of X(48529) in X(1)


X(48531) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 1st ANTI-BROCARD

Barycentrics    4*a*(a^4-(b^2+c^2)*a^2+b^4-b^2*c^2+c^4)*S*sqrt(R*(4*R+r))+(a+b+c)*((b^2+c^2)*a^5-(b^2-c^2)*(b-c)*a^4-4*b^2*c^2*a^3-2*(b^2-c^2)*(b-c)*b*c*a^2+(b^2+c^2)*b^2*c^2*a-(b^2-c^2)*(b-c)*b^2*c^2) : :

The reciprocal parallelogic center of these triangles is X(385).

X(48531) lies on the circumcircle of 1st anti-Auriga triangle and these lines: {1, 48532}, {98, 26290}, {99, 5597}, {114, 26326}, {115, 26359}, {148, 26394}, {517, 48463}, {528, 48471}, {542, 48472}, {543, 45696}, {690, 48535}, {2782, 48460}, {2783, 48464}, {2787, 48533}, {2788, 48541}, {2794, 48474}, {2799, 48537}, {3023, 26351}, {3027, 26380}, {4027, 26379}, {5186, 26371}, {5969, 45724}, {6319, 26334}, {6320, 26344}, {6321, 26386}, {7983, 26395}, {8782, 26310}, {8997, 45365}, {10086, 45371}, {10089, 45373}, {11711, 26365}, {13172, 26381}, {13173, 26393}, {13174, 26296}, {13175, 26302}, {13177, 45354}, {13178, 26382}, {13179, 26383}, {13180, 26390}, {13181, 26389}, {13182, 26388}, {13183, 26387}, {13184, 45362}, {13185, 45361}, {13188, 45369}, {13189, 26402}, {13190, 26401}, {13989, 45366}, {18496, 38733}, {19108, 26384}, {19109, 26385}, {22514, 26319}, {22515, 45355}, {23698, 48454}, {26398, 33813}, {35878, 45357}, {35879, 45360}

X(48531) = X(48532)-of-5th mixtilinear triangle
X(48531) = reflection of X(i) in X(j) for these (i, j): (48462, 48460), (48470, 45696), (48532, 1)


X(48532) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 1st ANTI-BROCARD

Barycentrics    -4*a*(a^4-(b^2+c^2)*a^2+b^4-b^2*c^2+c^4)*S*sqrt(R*(4*R+r))+(a+b+c)*((b^2+c^2)*a^5-(b^2-c^2)*(b-c)*a^4-4*b^2*c^2*a^3-2*(b^2-c^2)*(b-c)*b*c*a^2+(b^2+c^2)*b^2*c^2*a-(b^2-c^2)*(b-c)*b^2*c^2) : :

The reciprocal parallelogic center of these triangles is X(385).

X(48532) lies on the circumcircle of 2nd anti-Auriga triangle and these lines: {1, 48531}, {98, 26291}, {99, 5598}, {114, 26327}, {115, 26360}, {148, 26418}, {517, 48462}, {528, 48470}, {542, 48473}, {543, 45697}, {690, 48536}, {2782, 48461}, {2783, 48465}, {2787, 48534}, {2788, 48542}, {2794, 48475}, {2799, 48538}, {3023, 26352}, {3027, 26404}, {4027, 26403}, {5186, 26372}, {5969, 45725}, {6319, 26335}, {6320, 26345}, {6321, 26410}, {7983, 26419}, {8782, 26311}, {8997, 45368}, {10086, 45372}, {10089, 45374}, {11711, 26366}, {13172, 26405}, {13173, 26417}, {13174, 26297}, {13175, 26303}, {13176, 45353}, {13178, 26406}, {13179, 26407}, {13180, 26414}, {13181, 26413}, {13182, 26412}, {13183, 26411}, {13184, 45364}, {13185, 45363}, {13188, 45370}, {13189, 26426}, {13190, 26425}, {13989, 45367}, {18498, 38733}, {19108, 26408}, {19109, 26409}, {22514, 26320}, {22515, 45356}, {23698, 48455}, {26422, 33813}, {35878, 45359}, {35879, 45358}

X(48532) = X(48531)-of-5th mixtilinear triangle
X(48532) = reflection of X(i) in X(j) for these (i, j): (48463, 48461), (48471, 45697), (48531, 1)


X(48533) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO ANTI-INNER-GARCIA

Barycentrics    a*(4*(a^3-(b+c)*a^2-(b^2-3*b*c+c^2)*a+(b^2-c^2)*(b-c))*S*sqrt(R*(4*R+r))+b*c*(a+b+c)*(2*a^3-2*(b+c)*a^2+(b^2+c^2)*a-(b^2-c^2)*(b-c))) : :

The reciprocal parallelogic center of these triangles is X(36).

X(48533) lies on the circumcircle of 1st anti-Auriga triangle and these lines: {1, 528}, {11, 26351}, {80, 26382}, {100, 5597}, {104, 26290}, {119, 26326}, {149, 26394}, {214, 26365}, {517, 48465}, {952, 48460}, {1317, 26380}, {1320, 26395}, {1862, 26371}, {2771, 48472}, {2783, 48462}, {2787, 48531}, {2800, 48487}, {2802, 45711}, {2806, 48537}, {2826, 48541}, {2831, 48474}, {5541, 26296}, {5840, 48454}, {8674, 48535}, {9024, 45724}, {10087, 45371}, {10090, 45373}, {10738, 26386}, {12331, 45369}, {13194, 26379}, {13199, 26381}, {13205, 26393}, {13222, 26302}, {13230, 45354}, {13235, 26310}, {13268, 26383}, {13269, 26334}, {13270, 26344}, {13271, 26390}, {13272, 26389}, {13273, 26388}, {13274, 26387}, {13275, 45362}, {13276, 45361}, {13278, 26402}, {13279, 26401}, {13922, 45365}, {13991, 45366}, {19112, 26384}, {19113, 26385}, {22560, 26319}, {22938, 45355}, {25438, 26400}, {26398, 33814}, {35882, 45357}, {35883, 45360}, {48501, 48511}

X(48533) = X(48534)-of-5th mixtilinear triangle
X(48533) = reflection of X(i) in X(j) for these (i, j): (48464, 48460), (48501, 48511), (48534, 1)


X(48534) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO ANTI-INNER-GARCIA

Barycentrics    a*(-4*(a^3-(b+c)*a^2-(b^2-3*b*c+c^2)*a+(b^2-c^2)*(b-c))*S*sqrt(R*(4*R+r))+b*c*(a+b+c)*(2*a^3-2*(b+c)*a^2+(b^2+c^2)*a-(b^2-c^2)*(b-c))) : :

The reciprocal parallelogic center of these triangles is X(36).

X(48534) lies on the circumcircle of 2nd anti-Auriga triangle and these lines: {1, 528}, {11, 26352}, {80, 26406}, {100, 5598}, {104, 26291}, {119, 26327}, {149, 26418}, {214, 26366}, {517, 48464}, {952, 48461}, {1317, 26404}, {1320, 26419}, {1862, 26372}, {2771, 48473}, {2783, 48463}, {2787, 48532}, {2800, 48488}, {2802, 45712}, {2806, 48538}, {2826, 48542}, {2831, 48475}, {5541, 26297}, {5840, 48455}, {8674, 48536}, {9024, 45725}, {10087, 45372}, {10090, 45374}, {10738, 26410}, {12331, 45370}, {13194, 26403}, {13199, 26405}, {13205, 26417}, {13222, 26303}, {13228, 45353}, {13235, 26311}, {13268, 26407}, {13269, 26335}, {13270, 26345}, {13271, 26414}, {13272, 26413}, {13273, 26412}, {13274, 26411}, {13275, 45364}, {13276, 45363}, {13278, 26426}, {13279, 26425}, {13922, 45368}, {13991, 45367}, {19112, 26408}, {19113, 26409}, {22560, 26320}, {22938, 45356}, {25438, 26424}, {26422, 33814}, {35882, 45359}, {35883, 45358}, {48502, 48512}

X(48534) = X(48533)-of-5th mixtilinear triangle
X(48534) = reflection of X(i) in X(j) for these (i, j): (48465, 48461), (48502, 48512), (48533, 1)


X(48535) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO ANTI-ORTHOCENTROIDAL

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

The reciprocal parallelogic center of these triangles is X(323).

X(48535) lies on the circumcircle of 1st anti-Auriga triangle and these lines: {1, 48536}, {74, 26290}, {110, 5597}, {113, 26326}, {125, 26359}, {265, 26386}, {399, 45369}, {517, 48473}, {542, 45696}, {690, 48531}, {1112, 26371}, {1511, 26398}, {2771, 48464}, {2775, 48541}, {2781, 48474}, {2854, 45724}, {2948, 26296}, {3024, 26351}, {3028, 26380}, {3448, 26394}, {5663, 48460}, {7732, 26334}, {7733, 26344}, {7984, 26395}, {8674, 48533}, {8998, 45365}, {9517, 48537}, {10088, 45371}, {10091, 45373}, {10113, 45355}, {11720, 26365}, {12310, 26302}, {12375, 45357}, {12376, 45360}, {12383, 26381}, {12902, 18496}, {12903, 26388}, {12904, 26387}, {13193, 26379}, {13204, 26393}, {13209, 45354}, {13210, 26310}, {13211, 26382}, {13212, 26383}, {13213, 26390}, {13214, 26389}, {13215, 45362}, {13216, 45361}, {13217, 26402}, {13218, 26401}, {13990, 45366}, {17702, 48454}, {19110, 26384}, {19111, 26385}, {22586, 26319}, {32423, 48483}

X(48535) = X(48536)-of-5th mixtilinear triangle
X(48535) = reflection of X(i) in X(j) for these (i, j): (48472, 48460), (48483, 48519), (48536, 1)


X(48536) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO ANTI-ORTHOCENTROIDAL

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

The reciprocal parallelogic center of these triangles is X(323).

X(48536) lies on the circumcircle of 2nd anti-Auriga triangle and these lines: {1, 48535}, {74, 26291}, {110, 5598}, {113, 26327}, {125, 26360}, {265, 26410}, {399, 45370}, {517, 48472}, {542, 45697}, {690, 48532}, {1112, 26372}, {1511, 26422}, {2771, 48465}, {2775, 48542}, {2781, 48475}, {2854, 45725}, {2948, 26297}, {3024, 26352}, {3028, 26404}, {3448, 26418}, {5663, 48461}, {7732, 26335}, {7733, 26345}, {7984, 26419}, {8674, 48534}, {8998, 45368}, {9517, 48538}, {10088, 45372}, {10091, 45374}, {10113, 45356}, {11720, 26366}, {12310, 26303}, {12375, 45359}, {12376, 45358}, {12383, 26405}, {12902, 18498}, {12903, 26412}, {12904, 26411}, {13193, 26403}, {13204, 26417}, {13208, 45353}, {13210, 26311}, {13211, 26406}, {13212, 26407}, {13213, 26414}, {13214, 26413}, {13215, 45364}, {13216, 45363}, {13217, 26426}, {13218, 26425}, {13990, 45367}, {17702, 48455}, {19110, 26408}, {19111, 26409}, {22586, 26320}, {32423, 48484}

X(48536) = X(48535)-of-5th mixtilinear triangle
X(48536) = reflection of X(i) in X(j) for these (i, j): (48473, 48461), (48484, 48520), (48535, 1)


X(48537) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a*(4*(a^10-(b^2+c^2)*a^8+b^2*c^2*a^6-(b^6-c^6)*(b^2-c^2)*a^2+(b^8-c^8)*(b^2-c^2))*S*sqrt(R*(4*R+r))+a*(a+b+c)*((b^2+c^2)*a^9-(b^2-c^2)*(b-c)*a^8-4*b^2*c^2*a^7-2*(b^2-c^2)*(b-c)*b*c*a^6-(2*b^2-c^2)*(b^2-2*c^2)*(b^2+c^2)*a^5+(b^2-c^2)*(b-c)*(2*b^4+2*c^4+b*c*(2*b^2-b*c+2*c^2))*a^4+2*(b^2-c^2)^2*b^2*c^2*a^3+2*(b^3+c^3)*b*c*(b^2-c^2)^2*a^2+(b^6+c^6)*(b^2-c^2)^2*a-(b^2-c^2)^2*(b+c)^3*(b^2-b*c+c^2)^2)) : :

The reciprocal parallelogic center of these triangles is X(10313).

X(48537) lies on the circumcircle of 1st anti-Auriga triangle and these lines: {1, 48538}, {112, 5597}, {127, 26359}, {132, 26326}, {517, 48475}, {1297, 26290}, {2781, 45724}, {2794, 48454}, {2799, 48531}, {2806, 48533}, {2831, 48464}, {3320, 26380}, {6020, 26351}, {9517, 48535}, {9523, 48541}, {10705, 26395}, {10749, 26386}, {11641, 26302}, {11722, 26365}, {13166, 26371}, {13195, 26379}, {13200, 26381}, {13206, 26393}, {13219, 26394}, {13221, 26296}, {13231, 45354}, {13236, 26310}, {13280, 26382}, {13281, 26383}, {13282, 26334}, {13283, 26344}, {13294, 26390}, {13295, 26389}, {13296, 26388}, {13297, 26387}, {13298, 45362}, {13299, 45361}, {13310, 45369}, {13311, 45371}, {13312, 45373}, {13313, 26402}, {13314, 26401}, {13923, 45365}, {13992, 45366}, {19114, 26384}, {19115, 26385}, {19162, 26319}, {19163, 45355}, {26398, 38608}, {35880, 45357}, {35881, 45360}, {48460, 48474}

X(48537) = X(48538)-of-5th mixtilinear triangle
X(48537) = reflection of X(i) in X(j) for these (i, j): (48474, 48460), (48538, 1)


X(48538) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a*(-4*(a^10-(b^2+c^2)*a^8+b^2*c^2*a^6-(b^6-c^6)*(b^2-c^2)*a^2+(b^8-c^8)*(b^2-c^2))*S*sqrt(R*(4*R+r))+a*(a+b+c)*((b^2+c^2)*a^9-(b^2-c^2)*(b-c)*a^8-4*b^2*c^2*a^7-2*(b^2-c^2)*(b-c)*b*c*a^6-(2*b^2-c^2)*(b^2-2*c^2)*(b^2+c^2)*a^5+(b^2-c^2)*(b-c)*(2*b^4+2*c^4+b*c*(2*b^2-b*c+2*c^2))*a^4+2*(b^2-c^2)^2*b^2*c^2*a^3+2*(b^3+c^3)*b*c*(b^2-c^2)^2*a^2+(b^6+c^6)*(b^2-c^2)^2*a-(b^2-c^2)^2*(b+c)^3*(b^2-b*c+c^2)^2)) : :

The reciprocal parallelogic center of these triangles is X(10313).

X(48538) lies on the circumcircle of 2nd anti-Auriga triangle and these lines: {1, 48537}, {112, 5598}, {127, 26360}, {132, 26327}, {517, 48474}, {1297, 26291}, {2781, 45725}, {2794, 48455}, {2799, 48532}, {2806, 48534}, {2831, 48465}, {3320, 26404}, {6020, 26352}, {9517, 48536}, {9523, 48542}, {10705, 26419}, {10749, 26410}, {11641, 26303}, {11722, 26366}, {13166, 26372}, {13195, 26403}, {13200, 26405}, {13206, 26417}, {13219, 26418}, {13221, 26297}, {13229, 45353}, {13236, 26311}, {13280, 26406}, {13281, 26407}, {13282, 26335}, {13283, 26345}, {13294, 26414}, {13295, 26413}, {13296, 26412}, {13297, 26411}, {13298, 45364}, {13299, 45363}, {13310, 45370}, {13311, 45372}, {13312, 45374}, {13313, 26426}, {13314, 26425}, {13923, 45368}, {13992, 45367}, {19114, 26408}, {19115, 26409}, {19162, 26320}, {19163, 45356}, {26422, 38608}, {35880, 45359}, {35881, 45358}, {48461, 48475}

X(48538) = X(48537)-of-5th mixtilinear triangle
X(48538) = reflection of X(i) in X(j) for these (i, j): (48475, 48461), (48537, 1)


X(48539) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 1st ANTI-AURIGA

Barycentrics    (a^4-2*(b^2+c^2)*a^2+3*(b^2-c^2)^2)*(a^2-c^2)*(a^2-b^2) : :
X(48539) = 3*X(99)-2*X(9145) = 3*X(14639)-4*X(18122) = 3*X(21166)-2*X(40879) = 3*X(44375)-4*X(47113)

The reciprocal parallelogic center of these triangles is X(48454).

X(48539) lies on these lines: {3, 48540}, {99, 523}, {110, 925}, {384, 12039}, {513, 47747}, {522, 45709}, {524, 12117}, {525, 45722}, {648, 5467}, {1296, 30247}, {1350, 42329}, {2847, 14981}, {2854, 23235}, {8547, 11257}, {9142, 38664}, {9155, 47285}, {9202, 23872}, {9203, 23873}, {9216, 9979}, {14639, 18122}, {21166, 40879}, {33813, 36207}, {35278, 35357}, {35520, 36163}, {41254, 46127}, {44375, 47113}

X(48539) = reflection of X(i) in X(j) for these (i, j): (36207, 33813), (38664, 9142), (48540, 3)
X(48539) = barycentric product X(99)*X(43620)
X(48539) = trilinear product X(662)*X(43620)
X(48539) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {20, 14360, 36173}, {13556, 22338, 23236}
X(48539) = reflection of X(110) in the line X(14687)X(17702)
X(48539) = X(48540)-of-ABC-X3 reflections triangle
X(48539) = X(4)-of-1st anti-Parry triangle
X(48539) = crossdifference of every pair of points on line {X(21906), X(47421)}


X(48540) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO 1st ANTI-AURIGA

Barycentrics    a^8-(b^2+c^2)*a^6-(b^4-3*b^2*c^2+c^4)*a^4+(b^4-c^4)*(b^2-c^2)*a^2-3*(b^2-c^2)^2*b^2*c^2 : :
X(48540) = 3*X(98)-2*X(9142) = 2*X(187)-3*X(44375) = 5*X(14061)-4*X(18122)

The reciprocal parallelogic center of these triangles is X(48454).

X(48540) lies on these lines: {2, 3018}, {3, 48539}, {4, 5505}, {6, 264}, {67, 17983}, {74, 1300}, {76, 19221}, {94, 323}, {98, 523}, {99, 40879}, {111, 2373}, {187, 44375}, {298, 21469}, {299, 21468}, {316, 524}, {522, 45710}, {525, 45723}, {543, 45772}, {571, 40896}, {729, 2367}, {1494, 1989}, {1632, 5191}, {1990, 14165}, {1995, 15363}, {2378, 23872}, {2379, 23873}, {2393, 38294}, {2453, 35278}, {2770, 8599}, {2782, 36207}, {2847, 10991}, {2854, 38664}, {2970, 15106}, {3016, 44155}, {4563, 45809}, {5916, 23870}, {5917, 23871}, {6128, 39358}, {7417, 9769}, {7668, 11596}, {8744, 37778}, {9003, 22265}, {9035, 41079}, {9131, 9215}, {9140, 9214}, {9145, 23235}, {12094, 44468}, {14061, 18122}, {14590, 38872}, {14685, 47208}, {20080, 44128}, {43656, 43658}

X(48540) = reflection of X(i) in X(j) for these (i, j): (99, 40879), (23235, 9145), (48539, 3)
X(48540) = crossdifference of every pair of points on line {X(39469), X(47405)}
X(48540) = center of circle {{X(20), X(3448), X(36174)}}
X(48540) = reflection of X(74) in the line X(15919)X(17702)
X(48540) = X(4)-of-2nd anti-Parry triangle
X(48540) = X(48539)-of-ABC-X3 reflections triangle
X(48540) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 338, 41254), (264, 648, 41253), (648, 41254, 6), (5191, 47285, 1632), (9512, 47285, 5191)


X(48541) = CYCLOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-AURIGA TO 2nd ANTI-AURIGA

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

The reciprocal cyclologic center of these triangles is X(48542).

X(48541) lies on the circumcircle of 1st anti-Auriga triangle and these lines: {1, 48542}, {105, 26290}, {120, 26326}, {528, 48455}, {1292, 5597}, {1358, 26351}, {2775, 48535}, {2788, 48531}, {2795, 48462}, {2809, 48487}, {2826, 48533}, {2836, 48472}, {2838, 48474}, {3021, 26380}, {5511, 26359}, {9523, 48537}, {15521, 26386}, {26394, 34547}, {26398, 38619}, {28915, 48460}, {38589, 45369}

X(48541) = X(48542)-of-5th mixtilinear triangle
X(48541) = reflection of X(48542) in X(1)


X(48542) = CYCLOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-AURIGA TO 1st ANTI-AURIGA

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

The reciprocal cyclologic center of these triangles is X(48541).

X(48542) lies on the circumcircle of 2nd anti-Auriga triangle and these lines: {1, 48541}, {105, 26291}, {120, 26327}, {528, 48454}, {1292, 5598}, {1358, 26352}, {2775, 48536}, {2788, 48532}, {2795, 48463}, {2809, 48488}, {2826, 48534}, {2836, 48473}, {2838, 48475}, {3021, 26404}, {5511, 26360}, {9523, 48538}, {15521, 26410}, {26418, 34547}, {26422, 38619}, {28915, 48461}, {38589, 45370}

X(48542) = X(48541)-of-5th mixtilinear triangle
X(48542) = reflection of X(48541) in X(1)

leftri

Points in a [X(2)X(513), X(2)X(514)] coordinate system: X(48543)-X(48580)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1,L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1: (2bc-ab-ac) α + (2ca-bc-ba) β + (2ab-ca-cb) γ = 0.

L2: (2a-b-c) α + (2b-c-a) β + (2c-a-b) γ = 0.

The origin is given by (0,0) = X(2) = 1 : 1 : 1 .

Barycentrics u : v : w for a point U = (x,y) in this system are given by

u : v : w = (b - c) ((a-b)(a-c) + ax + y) : : ,

where, as functions of a,b,c, the coordinate x is symmetric and homogeneous of degree 1, and y is symmetric and homogeneous of degree 2.

For the "reversed" coordinate system, [L2,L1], see X(47754) - X(47845).

The appearance of {x,y},k in the following list means that (x,y) = X(k):

{-2 (a+b+c), -2 (a b+a c+b c)}, 47774
{-((2 (a b+a c+b c))/(a+b+c)), -a b-a c-b c}, 47826
{-2 (a+b+c), 0}, 47759
{-((2 (a^2+b^2+c^2))/(a+b+c)), 0}, 48164
{-((2 (a b+a c+b c))/(a+b+c)), 0}, 47821
{-2 (a+b+c), 1/2 (a^2+b^2+c^2)}, 47764
{-2 (a+b+c), a^2+b^2+c^2}, 47769
{-2 (a+b+c), a b+a c+b c}, 31147
{-((2 (a^2+b^2+c^2))/(a+b+c)), a^2+b^2+c^2}, 47808
{-((2 (a b+a c+b c))/(a+b+c)), (a b c)/(a+b+c)}, 47838
{-((2 (a b+a c+b c))/(a+b+c)), a b+a c+b c}, 47832
{-2 (a+b+c), 2 (a^2+b^2+c^2)}, 47772
{-2 (a+b+c), 2 (a b+a c+b c)}, 21297
{-((2 (a^2+b^2+c^2))/(a+b+c)), 2 (a^2+b^2+c^2)}, 48208
{-((2 (a b+a c+b c))/(a+b+c)), (2 a b c)/(a+b+c)}, 47840
{-((2 (a b+a c+b c))/(a+b+c)), 2 (a b+a c+b c)}, 47834
{-((a^2+b^2+c^2)/(a+b+c)), -((2 a b c)/(a+b+c))}, 47814
{-a-b-c, -a b-a c-b c}, 661
{-((a^2+b^2+c^2)/(a+b+c)), -a^2-b^2-c^2}, 48159
{-((a^2+b^2+c^2)/(a+b+c)), -((a b c)/(a+b+c))}, 47816
{-((a^2+b^2+c^2)/(a+b+c)), -a b-a c-b c}, 47810
{-((a b+a c+b c)/(a+b+c)), -a b-a c-b c}, 48162
{-a-b-c, 0}, 4776
{-((a^2+b^2+c^2)/(a+b+c)), 0}, 44429
{-((a b+a c+b c)/(a+b+c)), 0}, 47822
{-a-b-c, 1/2 (a^2+b^2+c^2)}, 47765
{-a-b-c, 1/2 (a b+a c+b c)}, 3835
{-((a^2+b^2+c^2)/(a+b+c)), 1/2 (a^2+b^2+c^2)}, 47806
{-((a b+a c+b c)/(a+b+c)), 1/2 (a b+a c+b c)}, 47831
{-a-b-c, a^2+b^2+c^2}, 30565
{-a-b-c, a b+a c+b c}, 4728
{-((a^2+b^2+c^2)/(a+b+c)), a^2+b^2+c^2}, 47809
{-((a^2+b^2+c^2)/(a+b+c)), a b+a c+b c}, 47812
{-((a b+a c+b c)/(a+b+c)), (a b c)/(a+b+c)}, 47839
{-((a b+a c+b c)/(a+b+c)), a b+a c+b c}, 47833
{-a-b-c, 2 (a b+a c+b c)}, 693
{-((a^2+b^2+c^2)/(a+b+c)), 2 (a^2+b^2+c^2)}, 48236
{-((a^2+b^2+c^2)/(a+b+c)), (2 a b c)/(a+b+c)}, 47819
{-((a b+a c+b c)/(a+b+c)), (2 a b c)/(a+b+c)}, 47841
{-((a b+a c+b c)/(a+b+c)), 2 (a b+a c+b c)}, 48238
{1/2 (-a-b-c), -a b-a c-b c}, 47777
{1/2 (-a-b-c), 1/2 (-a^2-b^2-c^2)}, 47756
{1/2 (-a-b-c), 1/2 (-a b-a c-b c)}, 45315
{-((a^2+b^2+c^2)/(2 (a+b+c))), 1/2 (-a^2-b^2-c^2)}, 48178
{-((a b+a c+b c)/(2 (a+b+c))), 1/2 (-a b-a c-b c)}, 48180
{1/2 (-a-b-c), 0}, 47760
{-((a^2+b^2+c^2)/(2 (a+b+c))), 0}, 47802
{-((a b+a c+b c)/(2 (a+b+c))), 0}, 48197
{1/2 (-a-b-c), 1/2 (a^2+b^2+c^2)}, 1639
{1/2 (-a-b-c), 1/2 (a b+a c+b c)}, 4928
{-((a^2+b^2+c^2)/(2 (a+b+c))), 1/2 (a^2+b^2+c^2)}, 47807
{-((a b+a c+b c)/(2 (a+b+c))), 1/2 (a b+a c+b c)}, 48206
{1/2 (-a-b-c), a^2+b^2+c^2}, 47770
{1/2 (-a-b-c), a b+a c+b c}, 45320
{-((a^2+b^2+c^2)/(2 (a+b+c))), a^2+b^2+c^2}, 48219
{-((a b+a c+b c)/(2 (a+b+c))), a b+a c+b c}, 48221
{0, -2 (a^2+b^2+c^2)}, 48156
{0, -((2 a b c)/(a+b+c))}, 47793
{0, -2 (a b+a c+b c)}, 47775
{0, -a^2-b^2-c^2}, 44435
{0, -((a b c)/(a+b+c))}, 47794
{0, -a b-a c-b c}, 4893
{0, 1/2 (-a^2-b^2-c^2)}, 47757
{0, -((a b c)/(2 (a+b+c)))}, 48196
{0, 1/2 (-a b-a c-b c)}, 47778
{0, 0}, 2
{0, 1/2 (a^2+b^2+c^2)}, 47766
{0, (a b c)/(2 (a+b+c))}, 48218
{0, 1/2 (a b+a c+b c)}, 47779
{0, a^2+b^2+c^2}, 47771
{0, (a b c)/(a+b+c)}, 47795
{0, a b+a c+b c}, 4379
{0, 2 (a^2+b^2+c^2)}, 47773
{0, (2 a b c)/(a+b+c)}, 47796
{0, 2 (a b+a c+b c)}, 47780
{1/2 (a+b+c), -a^2-b^2-c^2}, 47754
{1/2 (a+b+c), -a b-a c-b c}, 650
{(a^2+b^2+c^2)/(2 (a+b+c)), -a^2-b^2-c^2}, 48192
{(a b+a c+b c)/(2 (a+b+c)), -a b-a c-b c}, 48194
{1/2 (a+b+c), 1/2 (-a^2-b^2-c^2)}, 1638
{1/2 (a+b+c), 1/2 (-a b-a c-b c)}, 4763
{(a^2+b^2+c^2)/(2 (a+b+c)), 1/2 (-a^2-b^2-c^2)}, 47799
{(a b+a c+b c)/(2 (a+b+c)), 1/2 (-a b-a c-b c)}, 47829
{1/2 (a+b+c), 0}, 47761
{(a^2+b^2+c^2)/(2 (a+b+c)), 0}, 47803
{(a b+a c+b c)/(2 (a+b+c)), 0}, 48216
{1/2 (a+b+c), 1/2 (a^2+b^2+c^2)}, 47767
{1/2 (a+b+c), 1/2 (a b+a c+b c)}, 4369
{(a^2+b^2+c^2)/(2 (a+b+c)), 1/2 (a^2+b^2+c^2)}, 48231
{(a b+a c+b c)/(2 (a+b+c)), 1/2 (a b+a c+b c)}, 48233
{1/2 (a+b+c), 2 (a b+a c+b c)}, 43067
{a+b+c, -2 (a b+a c+b c)}, 31150
{(a^2+b^2+c^2)/(a+b+c), -2 (a^2+b^2+c^2)}, 48174
{(a^2+b^2+c^2)/(a+b+c), -((2 a b c)/(a+b+c))}, 47815
{(a b+a c+b c)/(a+b+c), -((2 a b c)/(a+b+c))}, 47835
{(a b+a c+b c)/(a+b+c), -2 (a b+a c+b c)}, 48176
{a+b+c, -a^2-b^2-c^2}, 4453
{a+b+c, -a b-a c-b c}, 1635
{(a^2+b^2+c^2)/(a+b+c), -a^2-b^2-c^2}, 47797
{(a^2+b^2+c^2)/(a+b+c), -((a b c)/(a+b+c))}, 47817
{(a^2+b^2+c^2)/(a+b+c), -a b-a c-b c}, 47811
{(a b+a c+b c)/(a+b+c), -((a b c)/(a+b+c))}, 47837
{(a b+a c+b c)/(a+b+c), -a b-a c-b c}, 47827
{a+b+c, 1/2 (-a^2-b^2-c^2)}, 47758
{a+b+c, 1/2 (-a b-a c-b c)}, 45313
{(a^2+b^2+c^2)/(a+b+c), 1/2 (-a^2-b^2-c^2)}, 47800
{(a b+a c+b c)/(a+b+c), 1/2 (-a b-a c-b c)}, 47830
{a+b+c, 0}, 47762
{(a^2+b^2+c^2)/(a+b+c), 0}, 47804
{(a b+a c+b c)/(a+b+c), 0}, 47823
{a+b+c, 1/2 (a^2+b^2+c^2)}, 47768
{a+b+c, a b+a c+b c}, 31148
{(a^2+b^2+c^2)/(a+b+c), a^2+b^2+c^2}, 48250
{(a^2+b^2+c^2)/(a+b+c), (a b c)/(a+b+c)}, 47818
{(a^2+b^2+c^2)/(a+b+c), a b+a c+b c}, 47813
{(a b+a c+b c)/(a+b+c), a b+a c+b c}, 48253
{(a^2+b^2+c^2)/(a+b+c), (2 a b c)/(a+b+c)}, 47820
{2 (a+b+c), -2 (a b+a c+b c)}, 47776
{(2 (a^2+b^2+c^2))/(a+b+c), -2 (a^2+b^2+c^2)}, 48203
{(2 (a b+a c+b c))/(a+b+c), -((2 a b c)/(a+b+c))}, 47836
{(2 (a b+a c+b c))/(a+b+c), -2 (a b+a c+b c)}, 47825
{2 (a+b+c), -a^2-b^2-c^2}, 47755
{2 (a+b+c), -a b-a c-b c}, 649
{(2 (a^2+b^2+c^2))/(a+b+c), -a^2-b^2-c^2}, 47798
{(2 (a b+a c+b c))/(a+b+c), -a b-a c-b c}, 47828
{(2 (a^2+b^2+c^2))/(a+b+c), 1/2 (-a^2-b^2-c^2)}, 47801
{2 (a+b+c), 0}, 47763
{(2 (a^2+b^2+c^2))/(a+b+c), 0}, 47805
{(2 (a b+a c+b c))/(a+b+c), 0}, 47824
{2 (a+b+c), 1/2 (a b+a c+b c)}, 4932
{2 (a+b+c), 2 (a b+a c+b c)}, 7192
{-2*(a + b + c), -a^2 - b^2 - c^2}, 48543
{-2*(a + b + c), -(a*b) - a*c - b*c}, 48544
{(-2*(a^2 + b^2 + c^2))/(a + b + c), (a^2 + b^2 + c^2)/2}, 48545
{(-2*(a*b + a*c + b*c))/(a + b + c), (a^2 + b^2 + c^2)/2}, 48546
{(-2*(a*b + a*c + b*c))/(a + b + c), (a*b + a*c + b*c)/2}, 48547
{-a - b - c, -2*(a*b + a*c + b*c)}, 48548
{-((a^2 + b^2 + c^2)/(a + b + c)), -2*(a*b + a*c + b*c)}, 48549
{-a - b - c, -a^2 - b^2 - c^2}, 48550
{-a - b - c, -((a*b*c)/(a + b + c))}, 48551
{-((a*b + a*c + b*c)/(a + b + c)), -a^2 - b^2 - c^2}, 48552
{-((a*b + a*c + b*c)/(a + b + c)), -((a*b*c)/(a + b + c))}, 48553
{-a - b - c, (-a^2 - b^2 - c^2)/2}, 48554
{-((a*b + a*c + b*c)/(a + b + c)), (-a^2 - b^2 - c^2)/2}, 48555
{-((a^2 + b^2 + c^2)/(a + b + c)), (a*b*c)/(a + b + c)}, 48556
{-a - b - c, 2*(a^2 + b^2 + c^2)}, 48557
{(-a - b - c)/2, -a^2 - b^2 - c^2}, 48558
{(a + b + c)/2, (-2*a*b*c)/(a + b + c)}, 48559
{(a + b + c)/2, -2*(a*b + a*c + b*c)}, 48560
{(a^2 + b^2 + c^2)/(2*(a + b + c)), -((a*b*c)/(a + b + c))}, 48561
{(a^2 + b^2 + c^2)/(2*(a + b + c)), (-(a*b) - a*c - b*c)/2}, 48562
{(a + b + c)/2, a*b + a*c + b*c}, 48563
{(a^2 + b^2 + c^2)/(2*(a + b + c)), (a*b*c)/(a + b + c)}, 48564
{a + b + c, (-2*a*b*c)/(a + b + c)}, 48565
{a + b + c, -((a*b*c)/(a + b + c))}, 48566
{a + b + c, a^2 + b^2 + c^2}, 48567
{a + b + c, (a*b*c)/(a + b + c)}, 48568
{(a*b + a*c + b*c)/(a + b + c), (a*b*c)/(a + b + c)}, 48569
{a + b + c, (2*a*b*c)/(a + b + c)}, 48570
{2*(a + b + c), -2*(a^2 + b^2 + c^2)}, 48571
{(2*(a^2 + b^2 + c^2))/(a + b + c), -(a*b) - a*c - b*c}, 48572
{(2*(a*b + a*c + b*c))/(a + b + c), -((a*b*c)/(a + b + c))}, 48573
{2*(a + b + c), (-a^2 - b^2 - c^2)/2}, 48574
{(2*(a*b + a*c + b*c))/(a + b + c), (-(a*b) - a*c - b*c)/2}, 48575
{2*(a + b + c), (a^2 + b^2 + c^2)/2}, 48576
{2*(a + b + c), a*b + a*c + b*c}, 48577
{(2*(a^2 + b^2 + c^2))/(a + b + c), a*b + a*c + b*c}, 48578
{(2*(a*b + a*c + b*c))/(a + b + c), a*b + a*c + b*c}, 48579
{2*(a + b + c), (2*a*b*c)/(a + b + c)}, 48580


X(48543) = X(513)X(4453)∩X(514)X(4120)

Barycentrics    (b - c)*(2*a^2 + 3*a*b + b^2 + 3*a*c - b*c + c^2) : :
X(48543) = 2 X[4453] - 3 X[44435], 5 X[4453] - 6 X[47754], 4 X[4453] - 3 X[47755], 5 X[44435] - 4 X[47754], 8 X[47754] - 5 X[47755], 3 X[47798] - 4 X[48177], 5 X[31147] - 2 X[45343], 3 X[31147] - X[47873], 4 X[45343] - 5 X[47790], 6 X[45343] - 5 X[47873], 3 X[47759] - 2 X[47764], 3 X[47759] - X[47772], 4 X[47764] - 3 X[47769], 3 X[47769] - 2 X[47772], 3 X[47790] - 2 X[47873], X[17161] + 5 X[20295], 2 X[17161] - 5 X[45746], X[17161] - 10 X[47995], 2 X[20295] + X[45746], X[20295] + 2 X[47995], X[45746] - 4 X[47995], 4 X[661] - X[47663], X[693] + 2 X[47988], 4 X[4806] - X[47696], X[47686] + 2 X[48024], 3 X[47781] - 2 X[47878], 2 X[1639] - 3 X[4776], 4 X[1639] - 3 X[47771], 2 X[3004] + X[48079], 2 X[3676] + X[47978], 2 X[3776] + X[48019], 2 X[3835] + X[23731], 4 X[4106] - X[47656], 2 X[4369] + X[47937], 2 X[4382] + X[47667], 2 X[4522] + X[47902], 2 X[4984] - 3 X[27486], 2 X[4813] + X[47676], 2 X[4820] + X[47654], 4 X[4940] - X[47660], 2 X[4940] + X[47950], X[47660] + 2 X[47950], 2 X[6590] - 5 X[26798], X[7192] + 2 X[47981], 4 X[14321] - X[47662], X[16892] + 2 X[48041], 2 X[21104] + X[47939], 4 X[23729] - X[47650], 2 X[23729] + X[47666], X[47650] + 2 X[47666], 2 X[24719] + X[47699], X[24719] + 2 X[47990], X[47699] - 4 X[47990], X[25259] + 2 X[47958], X[25259] - 4 X[48049], X[47958] + 2 X[48049], 4 X[25666] - X[48104], 5 X[27013] - 2 X[48067], X[31290] + 2 X[48398], 3 X[44429] - 2 X[48249], X[44449] + 2 X[47960], 2 X[44902] - 3 X[47756], 4 X[44902] - 3 X[47762], X[46403] + 2 X[47983], X[47651] + 2 X[48046], X[47652] + 2 X[48026], X[47653] + 2 X[48269], X[47690] + 2 X[47944], 3 X[47808] - 2 X[48254], X[47916] + 2 X[48270], X[47938] + 2 X[48050], X[47943] + 2 X[48043], 2 X[47989] + X[48080], X[48114] + 2 X[48504]

X(48543) lies on these lines: {2, 47768}, {513, 4453}, {514, 4120}, {522, 17161}, {661, 28882}, {693, 4806}, {812, 47781}, {824, 4958}, {1639, 4776}, {3004, 28217}, {3667, 47894}, {3676, 47978}, {3776, 48019}, {3835, 23731}, {4106, 4122}, {4369, 47937}, {4382, 47667}, {4522, 47902}, {4728, 28859}, {4778, 47780}, {4785, 4984}, {4813, 28855}, {4820, 47654}, {4927, 28209}, {4940, 4944}, {6008, 47782}, {6590, 26798}, {7192, 17218}, {14321, 47662}, {16892, 28906}, {21104, 47939}, {21115, 28886}, {23729, 47650}, {24719, 47699}, {25259, 28863}, {25666, 48104}, {27013, 48067}, {28155, 48268}, {28187, 47657}, {28220, 45342}, {28846, 48156}, {31290, 48398}, {44429, 48249}, {44449, 47960}, {44902, 47756}, {46403, 47983}, {47651, 48046}, {47652, 48026}, {47653, 48269}, {47690, 47944}, {47757, 47763}, {47765, 47773}, {47776, 47783}, {47777, 47892}, {47808, 48254}, {47916, 48270}, {47938, 48050}, {47943, 48043}, {47989, 48080}, {48114, 48504}

X(48543) = midpoint of X(i) and X(j) for these {i,j}: {4944, 47950}, {21183, 47981}
X(48543) = reflection of X(i) in X(j) for these {i,j}: {4944, 4940}, {7192, 21183}, {47660, 4944}, {47755, 44435}, {47762, 47756}, {47763, 47757}, {47769, 47759}, {47771, 4776}, {47772, 47764}, {47773, 47765}, {47776, 47783}, {47790, 31147}, {47791, 4728}, {47870, 47786}, {47892, 47777}
X(48543) = anticomplement of X(47768)
X(48543) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4940, 47950, 47660}, {20295, 47995, 45746}, {23729, 47666, 47650}, {24719, 47990, 47699}, {47759, 47772, 47764}, {47764, 47772, 47769}, {47958, 48049, 25259}


X(48544) = X(44)X(513)∩X(514)X(4120)

Barycentrics    a*(b - c)*(a + 4*b + 4*c) : :
X(48544) = 5 X[649] - 8 X[650], X[649] - 4 X[661], 3 X[649] - 4 X[1635], 23 X[649] - 32 X[2516], 13 X[649] - 16 X[4394], 11 X[649] - 8 X[4790], X[649] + 2 X[4813], 7 X[649] - 4 X[4979], 3 X[649] - 8 X[47777], 5 X[649] + 4 X[48019], X[649] + 8 X[48026], 2 X[650] - 5 X[661], 6 X[650] - 5 X[1635], 23 X[650] - 20 X[2516], 13 X[650] - 10 X[4394], 11 X[650] - 5 X[4790], 4 X[650] + 5 X[4813], 4 X[650] - 5 X[4893], 14 X[650] - 5 X[4979], 3 X[650] - 5 X[47777], 2 X[650] + X[48019], X[650] + 5 X[48026], 3 X[661] - X[1635], 23 X[661] - 8 X[2516], 13 X[661] - 4 X[4394], 11 X[661] - 2 X[4790], 2 X[661] + X[4813], 7 X[661] - X[4979], 3 X[661] - 2 X[47777], 5 X[661] + X[48019], X[661] + 2 X[48026], 23 X[1635] - 24 X[2516], 13 X[1635] - 12 X[4394], 11 X[1635] - 6 X[4790], 2 X[1635] + 3 X[4813], 2 X[1635] - 3 X[4893], 7 X[1635] - 3 X[4979], 5 X[1635] + 3 X[48019], X[1635] + 6 X[48026], 26 X[2516] - 23 X[4394], 44 X[2516] - 23 X[4790], 16 X[2516] + 23 X[4813], 16 X[2516] - 23 X[4893], 56 X[2516] - 23 X[4979], 12 X[2516] - 23 X[47777], 40 X[2516] + 23 X[48019], 4 X[2516] + 23 X[48026], and many others

X(48544) lies on these lines: {44, 513}, {512, 4825}, {514, 4120}, {663, 48053}, {693, 47908}, {900, 47878}, {1639, 28209}, {2786, 47781}, {3004, 48076}, {3572, 14434}, {3700, 28175}, {3835, 31290}, {4010, 47909}, {4024, 28147}, {4088, 47983}, {4106, 47917}, {4369, 47939}, {4379, 4776}, {4382, 47666}, {4449, 48093}, {4453, 28886}, {4468, 23731}, {4498, 47997}, {4750, 47783}, {4777, 4958}, {4778, 47765}, {4785, 47775}, {4802, 4931}, {4804, 47953}, {4806, 48142}, {4810, 47964}, {4820, 47669}, {4822, 47956}, {4851, 28183}, {4885, 48147}, {4932, 31207}, {4940, 47672}, {4944, 28195}, {4959, 4983}, {4962, 45745}, {4963, 48090}, {4977, 47874}, {4984, 6006}, {4988, 28161}, {5029, 14422}, {6544, 47768}, {6545, 28878}, {6590, 28229}, {7192, 30835}, {11068, 47978}, {14321, 28213}, {14349, 47911}, {14437, 23352}, {16892, 48038}, {17494, 48041}, {20295, 47926}, {21115, 28910}, {23813, 47914}, {24719, 47927}, {25666, 48107}, {26777, 48016}, {26798, 48399}, {27013, 48071}, {28217, 47876}, {28220, 47881}, {28221, 48277}, {28225, 47766}, {28855, 44435}, {28859, 30565}, {28867, 47782}, {28902, 47756}, {28906, 47894}, {31148, 47760}, {43067, 47903}, {44449, 48504}, {45315, 45675}, {45661, 47791}, {46403, 47986}, {47763, 47778}, {47890, 47937}, {47900, 48095}, {47902, 48088}, {47904, 48089}, {47906, 48092}, {47907, 47988}, {47915, 48334}, {47916, 48087}, {47918, 48091}, {47923, 47995}, {47924, 47990}, {47929, 47994}, {47938, 48047}, {47941, 48050}, {47942, 48052}, {47943, 48040}, {47944, 48118}, {47945, 48043}, {47946, 48119}, {47947, 48054}, {47948, 48045}, {47949, 48122}, {47950, 48130}, {47951, 48113}, {47955, 48131}, {47958, 48046}, {47959, 48051}, {47960, 48112}, {47962, 48114}, {47981, 48101}, {47987, 48086}, {47989, 48078}, {47992, 48080}, {48000, 48079}, {48048, 48139}

X(48544) = midpoint of X(i) and X(j) for these {i,j}: {4813, 4893}, {31290, 47780}, {47759, 47774}, {47779, 47984}
X(48544) = reflection of X(i) in X(j) for these {i,j}: {649, 4893}, {1635, 47777}, {4120, 47764}, {4379, 4776}, {4750, 47783}, {4784, 48213}, {4893, 661}, {4984, 47883}, {7192, 47779}, {31147, 47759}, {31148, 47760}, {47762, 45315}, {47763, 47778}, {47780, 3835}, {47791, 45661}, {47873, 4120}, {48141, 47780}, {48142, 48189}, {48189, 4806}, {48244, 48030}
X(48544) = X(2)-isoconjugate of X(28152)
X(48544) = X(32664)-Dao conjugate of X(28152)
X(48544) = crosssum of X(649) and X(5313)
X(48544) = crossdifference of every pair of points on line {1, 21747}
X(48544) = barycentric product X(i)*X(j) for these {i,j}: {1, 28151}, {513, 19875}, {514, 16672}
X(48544) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 28152}, {16672, 190}, {19875, 668}, {28151, 75}
X(48544) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 1635, 47777}, {661, 4813, 649}, {661, 48019, 650}, {661, 48026, 4813}, {693, 47991, 47908}, {1635, 47777, 4893}, {3835, 31290, 48141}, {4468, 23731, 48138}, {4940, 47952, 47672}, {4983, 47912, 48338}, {14349, 47911, 48341}, {20295, 47996, 47926}, {24719, 47993, 47927}, {47666, 48049, 4382}, {47947, 48054, 48144}, {47948, 48045, 48367}, {47958, 48046, 48117}, {47959, 48051, 48121}, {47988, 48094, 47907}, {47995, 48082, 47923}, {47997, 48085, 4498}


X(48545) = X(2)X(3667)∩X(513)X(1639)

Barycentrics    (b - c)*(-a^3 + a^2*b - 5*a*b^2 + b^3 + a^2*c - 2*a*b*c + 3*b^2*c - 5*a*c^2 + 3*b*c^2 + c^3) : :
X(48545) = X[7649] - 4 X[44316], 3 X[47766] - 4 X[47807], X[47766] - 4 X[48182], 5 X[47766] - 4 X[48231], 7 X[47766] - 4 X[48247], 3 X[47806] - 2 X[47807], 5 X[47806] - 2 X[48231], 7 X[47806] - 2 X[48247], X[47807] - 3 X[48182], 5 X[47807] - 3 X[48231], 7 X[47807] - 3 X[48247], 5 X[48182] - X[48231], 7 X[48182] - X[48247], 7 X[48231] - 5 X[48247], 3 X[47808] - X[48208], 3 X[48164] + X[48208], 2 X[31131] + X[47757], 3 X[31131] + X[47797], 5 X[31131] + X[48223], 3 X[44429] - X[47797], 5 X[44429] - X[48223], 3 X[47757] - 2 X[47797], 5 X[47757] - 2 X[48223], 5 X[47797] - 3 X[48223], 4 X[1491] - X[45745], 2 X[2254] + X[48269], 2 X[2505] + X[14321], 2 X[2526] + X[6590], 2 X[3676] + X[48077], 4 X[3837] - X[47123], X[4106] + 2 X[4925], 2 X[4163] + X[48334], 2 X[4369] + X[48035], 4 X[4521] - X[48032], 2 X[4522] + X[48015], 2 X[20315] + X[44444], 2 X[11068] + X[47685], 2 X[24720] + X[48039], 4 X[25666] - X[48014], 2 X[48017] + X[48268], X[48038] + 2 X[48073], 2 X[48042] + X[48060], 2 X[48050] + X[48069]

X(48545) lies on these lines: {2, 3667}, {427, 7649}, {513, 1639}, {514, 47808}, {522, 4728}, {523, 47311}, {612, 43924}, {614, 42312}, {900, 47800}, {1491, 45745}, {2254, 48269}, {2505, 14321}, {2526, 6590}, {3676, 48077}, {3798, 30764}, {3837, 47123}, {4057, 7485}, {4106, 4925}, {4163, 48334}, {4369, 48035}, {4521, 48032}, {4522, 48015}, {4777, 48178}, {4778, 47809}, {4802, 48163}, {4926, 47799}, {4962, 44432}, {4977, 48200}, {5133, 39508}, {6006, 47804}, {7179, 31605}, {7378, 16231}, {7386, 20315}, {7392, 44925}, {7396, 20294}, {7485, 39225}, {8642, 25926}, {11068, 47685}, {23764, 39570}, {24720, 48039}, {25666, 48014}, {28147, 48159}, {28155, 48156}, {28161, 44435}, {28169, 48174}, {28183, 48192}, {28209, 48219}, {28213, 48222}, {28217, 30792}, {28221, 48211}, {28225, 47771}, {28229, 48236}, {47883, 48193}, {48017, 48268}, {48038, 48073}, {48042, 48060}, {48050, 48069}

X(48545) = midpoint of X(i) and X(j) for these {i,j}: {31131, 44429}, {44435, 48169}, {47808, 48164}, {48159, 48187}
X(48545) = reflection of X(i) in X(j) for these {i,j}: {47757, 44429}, {47766, 47806}, {47768, 48232}, {47798, 44432}, {47800, 47802}, {47801, 2}, {47803, 30792}, {47806, 48182}, {47883, 48193}
X(48545) = reflection of X(47801) in the Nagel line
X(48545) = crossdifference of every pair of points on line {16483, 21309}


X(48546) = X(513)X(1639)∩X(514)X(14432)

Barycentrics    (b - c)*(3*a^3 - 3*a^2*b - a*b^2 + b^3 - 3*a^2*c - 6*a*b*c + 3*b^2*c - a*c^2 + 3*b*c^2 + c^3) : :
X(48546) = 2 X[659] + X[48269], 2 X[676] + X[48087], X[2254] - 4 X[4521], 4 X[2490] - X[7659], 2 X[3239] + X[4724], 2 X[3676] + X[48078], 2 X[3716] + X[4468], 4 X[3716] - X[47123], 2 X[4468] + X[47123], 2 X[3835] + X[48061], 2 X[4369] + X[48036], 2 X[4522] + X[48014], 2 X[4874] + X[48040], 2 X[4990] + X[47921], X[6590] + 2 X[48029], 2 X[11068] + X[48080], 4 X[25666] - X[48015], X[48039] + 2 X[48063], 2 X[48043] + X[48060], 2 X[48050] + X[48068], 2 X[48055] + X[48398]

X(48546) lies on these lines: {165, 3667}, {513, 1639}, {514, 14432}, {522, 14392}, {659, 48269}, {676, 48087}, {918, 47800}, {2254, 4521}, {2490, 7659}, {3239, 4724}, {3676, 48078}, {3716, 4468}, {3835, 48061}, {4369, 48036}, {4448, 47801}, {4522, 48014}, {4776, 4778}, {4874, 48040}, {4977, 45320}, {4990, 47921}, {6590, 48029}, {8713, 21052}, {11068, 48080}, {14430, 28292}, {21183, 47831}, {25666, 48015}, {28147, 48161}, {28155, 48158}, {28161, 48171}, {28225, 45334}, {28478, 47815}, {28846, 47804}, {28878, 47813}, {30520, 48179}, {47757, 47822}, {47758, 47803}, {47769, 47805}, {47772, 47798}, {48039, 48063}, {48043, 48060}, {48050, 48068}, {48055, 48398}

X(48546) = midpoint of X(i) and X(j) for these {i,j}: {47769, 47805}, {47772, 47798}
X(48546) = reflection of X(i) in X(j) for these {i,j}: {21183, 47831}, {47757, 47822}, {47758, 47803}, {47765, 48166}, {47768, 48231}, {47801, 4448}, {47806, 1639}
X(48546) = {X(3716),X(4468)}-harmonic conjugate of X(47123)


X(48547) = X(513)X(3716)∩X(514)X(14432)

Barycentrics    (b - c)*(2*a^3 - 3*a^2*b - a*b^2 - 3*a^2*c - 3*a*b*c + 3*b^2*c - a*c^2 + 3*b*c^2) : :
X(48547) = 2 X[3716] + X[3835], 8 X[3716] + X[48042], 5 X[3716] + X[48050], 4 X[3716] - X[48063], 10 X[3716] - X[48072], 4 X[3835] - X[48042], 5 X[3835] - 2 X[48050], 2 X[3835] + X[48063], 5 X[3835] + X[48072], 2 X[4369] + X[48037], 4 X[4806] - X[48041], 4 X[4874] - X[4932], 2 X[4874] + X[48043], 4 X[4885] - X[48073], X[4932] + 2 X[48043], X[47779] - 4 X[48183], 3 X[47779] - 4 X[48206], 5 X[47779] - 4 X[48233], 3 X[47831] - 2 X[48206], 5 X[47831] - 2 X[48233], 5 X[48042] - 8 X[48050], X[48042] + 2 X[48063], 5 X[48042] + 4 X[48072], 4 X[48050] + 5 X[48063], 2 X[48050] + X[48072], 5 X[48063] - 2 X[48072], 3 X[48183] - X[48206], 5 X[48183] - X[48233], 5 X[48206] - 3 X[48233], 3 X[47821] - X[47826], 3 X[47821] + X[47834], X[47826] + 3 X[47832], 3 X[47832] - X[47834], 2 X[4800] + X[47778], 3 X[4800] + X[47827], 5 X[4800] + X[48225], 3 X[47778] - 2 X[47827], 5 X[47778] - 2 X[48225], 3 X[47822] - X[47827], 5 X[47822] - X[48225], 5 X[47827] - 3 X[48225], 2 X[676] + X[48270], 5 X[693] + X[47933], 2 X[693] + X[48009], 2 X[47933] - 5 X[48009], 2 X[4010] + X[48008], 2 X[7662] + X[47996], 2 X[8689] + X[24719], 2 X[13246] + X[48269], 4 X[25666] - X[48017], 2 X[45342] + X[45673], 2 X[31286] + X[48080], 2 X[43067] + X[47980], X[45313] - 4 X[45337], 2 X[47694] + X[47985], 2 X[48029] + X[48399]

X(48547) lies on these lines: {2, 3667}, {43, 42312}, {513, 3716}, {514, 14432}, {522, 4800}, {661, 48237}, {663, 30709}, {676, 48270}, {693, 47933}, {824, 48179}, {900, 47830}, {1011, 39225}, {2786, 47800}, {2787, 45316}, {3239, 4024}, {4010, 48008}, {4057, 16058}, {4120, 47798}, {4207, 16231}, {4213, 7649}, {4379, 28225}, {4486, 47811}, {4522, 28183}, {4724, 48170}, {4777, 48180}, {4778, 47833}, {4785, 47804}, {4926, 47829}, {4962, 47828}, {4977, 48202}, {6002, 30234}, {6006, 47823}, {6822, 44444}, {7662, 47996}, {8643, 28525}, {8689, 24719}, {13246, 48269}, {14419, 48267}, {25666, 48017}, {26102, 43924}, {28147, 48162}, {28155, 47775}, {28169, 48176}, {28187, 48191}, {28209, 48221}, {28217, 48216}, {28221, 48213}, {28229, 48238}, {28840, 48220}, {29328, 45666}, {29362, 45342}, {30519, 47797}, {31147, 47805}, {31286, 48080}, {37355, 44316}, {39508, 47513}, {43067, 47980}, {44429, 45339}, {45313, 45337}, {47694, 47985}, {47874, 48161}, {48029, 48399}

X(48547) = midpoint of X(i) and X(j) for these {i,j}: {661, 48237}, {663, 30709}, {4010, 48226}, {4120, 47798}, {4724, 48170}, {4800, 47822}, {4893, 48172}, {14419, 48267}, {31147, 47805}, {47786, 47801}, {47821, 47832}, {47826, 47834}, {47874, 48161}, {48162, 48189}
X(48547) = reflection of X(i) in X(j) for these {i,j}: {24720, 48198}, {44429, 45339}, {45313, 47803}, {47778, 47822}, {47779, 47831}, {47803, 45337}, {47830, 48197}, {47831, 48183}, {48008, 48226}, {48017, 48193}, {48193, 25666}
X(48547) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3716, 3835, 48063}, {3835, 48063, 48042}, {3835, 48072, 48050}, {4874, 48043, 4932}, {47821, 47834, 47826}, {47826, 47832, 47834}


X(48548) = X(513)X(14404)∩X(514)X(661)

Barycentrics    (b - c)*(4*a*b + 4*a*c + b*c) : :
X(48548) = X[31150] + 2 X[47774], 3 X[31150] - 2 X[47776], 3 X[47774] + X[47776], 3 X[47775] - X[47776], 4 X[661] - X[693], 5 X[661] - 2 X[3835], 3 X[661] - X[4728], 2 X[661] + X[47666], 7 X[661] - X[47672], 10 X[661] - X[47675], 5 X[661] + X[47917], X[661] + 2 X[47996], 11 X[661] - 2 X[48399], 5 X[693] - 8 X[3835], 3 X[693] - 4 X[4728], X[693] + 2 X[47666], 7 X[693] - 4 X[47672], 5 X[693] - 2 X[47675], 5 X[693] + 4 X[47917], X[693] + 8 X[47996], 11 X[693] - 8 X[48399], 6 X[3835] - 5 X[4728], 4 X[3835] - 5 X[4776], 4 X[3835] + 5 X[47666], 14 X[3835] - 5 X[47672], 4 X[3835] - X[47675], 2 X[3835] + X[47917], X[3835] + 5 X[47996], 11 X[3835] - 5 X[48399], X[4391] - 4 X[47997], X[4462] - 4 X[47959], 4 X[4468] - X[47662], 2 X[4728] - 3 X[4776], 2 X[4728] + 3 X[47666], 7 X[4728] - 3 X[47672], 10 X[4728] - 3 X[47675], 5 X[4728] + 3 X[47917], X[4728] + 6 X[47996], 11 X[4728] - 6 X[48399], 7 X[4776] - 2 X[47672], 5 X[4776] - X[47675], 5 X[4776] + 2 X[47917], X[4776] + 4 X[47996], 11 X[4776] - 4 X[48399], X[4801] - 4 X[48054], X[47651] - 4 X[47995], 7 X[47666] + 2 X[47672], 5 X[47666] + X[47675], 5 X[47666] - 2 X[47917], X[47666] - 4 X[47996], 11 X[47666] + 4 X[48399], 10 X[47672] - 7 X[47675], 5 X[47672] + 7 X[47917], X[47672] + 14 X[47996], 11 X[47672] - 14 X[48399], X[47675] + 2 X[47917], X[47675] + 20 X[47996], 11 X[47675] - 20 X[48399], X[47917] - 10 X[47996], 11 X[47917] + 10 X[48399], 11 X[47996] + X[48399], 2 X[649] + X[47939], X[649] + 2 X[47991], X[47939] - 4 X[47991], 2 X[650] + X[31290], 4 X[650] - X[48107], 2 X[31290] + X[48107], X[47975] - 4 X[48002], X[47975] + 2 X[48024], 2 X[48002] + X[48024], 2 X[1491] + X[47941], X[1491] + 2 X[47993], X[47941] - 4 X[47993], X[2254] + 2 X[47986], 4 X[3700] - X[47655], 2 X[3700] + X[47667], X[47655] + 2 X[47667], 2 X[3716] + X[47909], 2 X[3837] + X[47910], X[4010] + 2 X[47964], 2 X[4024] + X[47668], 2 X[4369] + X[47908], 3 X[4379] - 4 X[45678], 3 X[45315] - 2 X[45678], X[4380] + 2 X[4813], X[4380] - 4 X[48000], X[4813] + 2 X[48000], X[4467] + 2 X[48038], X[4560] + 2 X[47955], 2 X[4724] + X[47940], X[4724] + 2 X[47992], X[47940] - 4 X[47992], 2 X[4763] - 3 X[4893], 4 X[4763] - 3 X[47762], 2 X[4765] + X[48034], X[4824] + 2 X[48028], 2 X[4824] + X[48080], 4 X[48028] - X[48080], 2 X[4790] - 5 X[26777], 2 X[4806] + X[47928], 2 X[4851] + X[25259], 4 X[4851] - X[47657], 2 X[25259] + X[47657], 2 X[4874] + X[4963], 2 X[4885] + X[47914], 2 X[4932] + X[47903], 4 X[4940] - X[26824], 2 X[4940] + X[47920], X[26824] + 2 X[47920], X[4979] + 2 X[47984], 2 X[4988] + X[47665], X[4988] + 2 X[48270], X[47665] - 4 X[48270], 2 X[48010] + X[48021], X[17494] + 2 X[48026], 2 X[17494] + X[48079], 4 X[48026] - X[48079], 5 X[7192] - 8 X[7653], 2 X[7192] - 5 X[31209], X[7192] + 2 X[47952], 16 X[7653] - 25 X[31209], 4 X[7653] - 5 X[47761], 4 X[7653] + 5 X[47952], 5 X[31209] - 4 X[47761], 5 X[31209] + 4 X[47952], 4 X[14321] - X[47656], X[17496] + 2 X[47915], 2 X[20295] + X[47664], X[20295] + 2 X[47962], X[47664] - 4 X[47962], X[21146] + 2 X[47954], 2 X[21196] + X[48076], 2 X[24720] + X[47904], 4 X[25666] - X[48141], 5 X[26798] - 2 X[48125], 5 X[26985] - 2 X[48133], X[47934] + 2 X[48043], X[47946] + 2 X[48030], 2 X[47946] + X[48108], 4 X[48030] - X[48108], 4 X[31286] - X[48147], X[44449] + 2 X[45745], X[45746] + 2 X[48046], X[46403] + 2 X[47963], X[47653] + 2 X[48087], X[47661] + 2 X[48269], X[47663] + 2 X[47988], X[47677] + 2 X[48082], X[47677] - 4 X[48504], X[48082] + 2 X[48504], X[47685] + 2 X[47969], X[47685] - 4 X[48027], X[47969] + 2 X[48027], X[47689] + 2 X[47699], X[47689] - 4 X[48047], X[47699] + 2 X[48047], X[47692] + 2 X[47698], X[47692] - 4 X[47998], X[47698] + 2 X[47998], X[47694] + 2 X[47953], X[47697] + 2 X[47945], X[47697] - 4 X[48029], X[47945] + 2 X[48029], X[47926] + 2 X[48049], X[47927] + 2 X[48050], X[47932] + 2 X[48041], X[47933] + 2 X[48042], 2 X[47949] + X[48510], X[47974] - 4 X[48001], X[47974] + 2 X[48023], 2 X[48001] + X[48023], 2 X[47983] + X[48508], 2 X[47985] + X[48032], 2 X[47987] + X[48509], 2 X[48008] + X[48019], 2 X[48009] + X[48020], 2 X[48045] + X[48507]

X(48548) lies on these lines: {2, 47777}, {513, 14404}, {514, 661}, {523, 47769}, {649, 47939}, {650, 31290}, {900, 47975}, {918, 47781}, {1491, 28209}, {1639, 47791}, {2254, 47986}, {2786, 47878}, {3700, 47655}, {3716, 47909}, {3837, 47910}, {4010, 28151}, {4024, 47668}, {4369, 47908}, {4379, 45315}, {4380, 4813}, {4444, 6544}, {4453, 28878}, {4467, 48038}, {4560, 47955}, {4724, 47940}, {4750, 28886}, {4762, 47759}, {4763, 4893}, {4765, 48034}, {4777, 4824}, {4778, 47810}, {4790, 26777}, {4802, 47870}, {4806, 28179}, {4851, 25259}, {4874, 4963}, {4885, 47914}, {4932, 47903}, {4940, 26824}, {4944, 47792}, {4977, 30792}, {4979, 47984}, {4988, 47665}, {6006, 48010}, {6008, 17494}, {6546, 28859}, {7192, 7653}, {14321, 47656}, {17496, 47915}, {20295, 47664}, {21146, 47954}, {21196, 48076}, {24720, 47904}, {25666, 48141}, {26798, 48125}, {26985, 48133}, {27486, 47876}, {28169, 47934}, {28195, 47770}, {28213, 48184}, {28220, 31992}, {28229, 45670}, {28846, 47782}, {28855, 47886}, {28894, 47772}, {28898, 46915}, {28902, 47755}, {28910, 47880}, {30583, 35353}, {31148, 47778}, {31286, 48147}, {44449, 45745}, {45746, 48046}, {46403, 47963}, {47653, 48087}, {47661, 48269}, {47663, 47988}, {47677, 48082}, {47685, 47969}, {47689, 47699}, {47692, 47698}, {47694, 47953}, {47697, 47945}, {47760, 47780}, {47804, 48162}, {47821, 48237}, {47926, 48049}, {47927, 48050}, {47932, 48041}, {47933, 48042}, {47949, 48510}, {47974, 48001}, {47983, 48508}, {47985, 48032}, {47987, 48509}, {48008, 48019}, {48009, 48020}, {48045, 48507}

X(48548) = midpoint of X(i) and X(j) for these {i,j}: {4776, 47666}, {31290, 47763}, {36848, 47946}, {47761, 47952}, {47774, 47775}
X(48548) = reflection of X(i) in X(j) for these {i,j}: {2, 47777}, {693, 4776}, {4379, 45315}, {4453, 47783}, {4776, 661}, {4789, 47765}, {7192, 47761}, {27486, 47876}, {31148, 47778}, {31150, 47775}, {36848, 48030}, {47755, 47784}, {47762, 4893}, {47763, 650}, {47780, 47760}, {47791, 1639}, {47792, 4944}, {47804, 48162}, {48107, 47763}, {48108, 36848}, {48225, 45676}, {48237, 47821}
X(48548) = crossdifference of every pair of points on line {31, 9346}
X(48548) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 47991, 47939}, {650, 31290, 48107}, {661, 47666, 693}, {661, 47917, 3835}, {661, 47996, 47666}, {1491, 47993, 47941}, {3700, 47667, 47655}, {3835, 47675, 693}, {3835, 47917, 47675}, {4724, 47992, 47940}, {4813, 48000, 4380}, {4824, 48028, 48080}, {4851, 25259, 47657}, {4940, 47920, 26824}, {4988, 48270, 47665}, {17494, 48026, 48079}, {20295, 47962, 47664}, {47666, 47675, 47917}, {47698, 47998, 47692}, {47699, 48047, 47689}, {47945, 48029, 47697}, {47946, 48030, 48108}, {47969, 48027, 47685}, {48001, 48023, 47974}, {48002, 48024, 47975}, {48082, 48504, 47677}


X(48549) = X(513)X(14404)∩X(514)X(14430)

Barycentrics    (b - c)*(2*a^2*b + 4*a*b^2 + 2*a^2*c + 7*a*b*c + b^2*c + 4*a*c^2 + b*c^2) : :
X(48549) = X[31150] - 4 X[45676], X[47774] + 2 X[48190], 3 X[44429] - 2 X[47812], 3 X[47810] - X[47812], 2 X[661] + X[47975], X[661] + 2 X[48010], 5 X[661] - 2 X[48043], 4 X[661] - X[48080], X[47975] - 4 X[48010], 5 X[47975] + 4 X[48043], 2 X[47975] + X[48080], 5 X[48010] + X[48043], 8 X[48010] + X[48080], 8 X[48043] - 5 X[48080], X[649] + 2 X[47992], 2 X[650] + X[47945], 2 X[659] + X[47940], X[693] + 2 X[4824], X[693] - 4 X[48030], 7 X[693] - 4 X[48127], X[4824] + 2 X[48030], 7 X[4824] + 2 X[48127], 7 X[48030] - X[48127], 2 X[1491] + X[47666], 5 X[1491] + X[47910], X[1491] + 2 X[48002], 4 X[1491] - X[48108], 5 X[47666] - 2 X[47910], X[47666] - 4 X[48002], 2 X[47666] + X[48108], X[47910] - 10 X[48002], 4 X[47910] + 5 X[48108], 8 X[48002] + X[48108], 2 X[2254] + X[47941], X[2254] + 2 X[47996], X[47941] - 4 X[47996], 2 X[2526] + X[47969], 2 X[3004] + X[47698], 2 X[3835] + X[47934], 4 X[3837] - X[47675], 2 X[3837] + X[47928], X[47675] + 2 X[47928], X[4088] + 2 X[48504], 2 X[4122] + X[47657], 2 X[4369] + X[47909], X[4391] - 4 X[48005], X[4462] - 4 X[47967], 2 X[4522] + X[4988], X[4560] + 2 X[47956], 2 X[4784] + X[47939], X[4801] - 4 X[48059], X[4813] + 2 X[4913], 2 X[4818] + X[48082], 2 X[4851] + X[47690], X[7192] + 2 X[47953], 4 X[9508] - X[48107], X[17494] + 2 X[48027], 4 X[18004] - X[47665], X[21146] + 2 X[47964], 2 X[24719] + X[47664], 2 X[24720] + X[47917], 4 X[25380] - X[48141], 4 X[25666] - X[48142], 5 X[26985] - 2 X[48134], X[45746] + 2 X[48047], X[46403] + 2 X[47962], X[47651] - 4 X[47999], X[47653] + 2 X[48088], X[47662] - 4 X[48056], X[47663] + 2 X[47989], X[47667] + 2 X[48396], X[47904] + 2 X[48073], X[47926] + 2 X[48050], 2 X[47959] + X[48510], 2 X[47995] + X[48508], 2 X[47997] + X[48509], 2 X[48000] + X[48023], 2 X[48017] + X[48021], 2 X[48054] + X[48507]

X(48549) lies on these lines: {513, 14404}, {514, 14430}, {522, 661}, {523, 4776}, {649, 47992}, {650, 47945}, {659, 47940}, {693, 4036}, {1491, 2977}, {2254, 28225}, {2526, 47969}, {3004, 47698}, {3835, 28155}, {3837, 47675}, {4010, 28165}, {4088, 48504}, {4122, 47657}, {4369, 47909}, {4391, 48005}, {4462, 47967}, {4522, 4988}, {4560, 47956}, {4728, 28147}, {4784, 47939}, {4801, 48059}, {4806, 28187}, {4813, 4913}, {4818, 48082}, {4851, 47690}, {4893, 47804}, {4948, 29328}, {7192, 47953}, {9508, 48107}, {17494, 48027}, {18004, 47665}, {21146, 47964}, {24719, 47664}, {24720, 47917}, {25380, 48141}, {25666, 48142}, {26985, 48134}, {28175, 48184}, {28195, 36848}, {28217, 48024}, {28840, 47828}, {28894, 48171}, {31148, 47830}, {45315, 47832}, {45323, 48253}, {45746, 48047}, {46403, 47962}, {47651, 47999}, {47653, 48088}, {47662, 48056}, {47663, 47989}, {47667, 48396}, {47760, 47834}, {47762, 47827}, {47777, 47821}, {47778, 47813}, {47780, 47802}, {47783, 47797}, {47791, 47807}, {47822, 48237}, {47824, 48193}, {47880, 48241}, {47904, 48073}, {47926, 48050}, {47959, 48510}, {47995, 48508}, {47997, 48509}, {48000, 48023}, {48017, 48021}, {48054, 48507}, {48180, 48234}

X(48549) = midpoint of X(47774) and X(48242)
X(48549) = reflection of X(i) in X(j) for these {i,j}: {31148, 47830}, {31150, 48176}, {44429, 47810}, {47762, 47827}, {47776, 48210}, {47780, 47802}, {47791, 47807}, {47797, 47783}, {47804, 4893}, {47813, 47778}, {47821, 47777}, {47824, 48193}, {47832, 45315}, {47834, 47760}, {48176, 45676}, {48234, 48180}, {48237, 47822}, {48241, 47880}, {48242, 48190}, {48253, 45323}
X(48549) = crossdifference of every pair of points on line {1468, 2241}
X(48549) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 47975, 48080}, {661, 48010, 47975}, {1491, 47666, 48108}, {1491, 48002, 47666}, {2254, 47996, 47941}, {3837, 47928, 47675}, {4824, 48030, 693}


X(48550) = X(513)X(4453)∩X(514)X(661)

Barycentrics    (b - c)*(a^2 + 2*a*b + b^2 + 2*a*c - b*c + c^2) : :
X(48550) = 3 X[47756] - X[47767], 3 X[6548] - X[7192], 3 X[6548] - 2 X[47891], 3 X[6548] + 2 X[47988], X[7192] + 2 X[47988], 3 X[4453] - 4 X[47754], 3 X[4453] - 2 X[47755], 2 X[4809] - 3 X[47797], 3 X[44435] - 2 X[47754], 3 X[44435] - X[47755], 2 X[661] + X[47652], X[693] + 2 X[47995], 4 X[3239] - X[47662], 4 X[3835] - X[47660], 2 X[3835] + X[47958], 2 X[4468] + X[47651], 3 X[4776] - 2 X[47765], 3 X[30565] - 4 X[47765], X[47660] + 2 X[47958], X[47666] + 2 X[48398], 4 X[3004] - X[4467], 2 X[3004] + X[20295], X[4467] + 2 X[20295], 2 X[3676] + X[47981], 4 X[3676] - X[48107], 2 X[47981] + X[48107], 2 X[3700] - 5 X[26798], 2 X[3700] + X[47653], 5 X[26798] + X[47653], 2 X[3716] + X[47943], 2 X[3776] + X[4813], 2 X[3837] + X[47944], X[4010] + 2 X[47999], 2 X[4024] + X[47654], 2 X[4025] + X[48079], 2 X[4106] + X[45746], 2 X[4369] - 3 X[14475], 2 X[4369] + X[23731], 3 X[14475] + X[23731], 2 X[4382] + X[47661], X[4382] + 2 X[48504], X[47661] - 4 X[48504], 4 X[4500] - X[47658], 2 X[4522] + X[47924], 2 X[4806] + X[47968], 2 X[4851] + X[26824], 2 X[4885] + X[47950], and many others

X(48550) lies on these lines: {2, 47756}, {86, 4833}, {513, 4453}, {514, 661}, {523, 21297}, {649, 47882}, {812, 47782}, {824, 31147}, {850, 21606}, {900, 3004}, {918, 47759}, {1638, 31095}, {1639, 47773}, {3676, 47981}, {3700, 26798}, {3716, 47943}, {3776, 4813}, {3837, 47944}, {4010, 47999}, {4024, 47654}, {4025, 6006}, {4106, 4777}, {4120, 28863}, {4369, 14475}, {4379, 28859}, {4382, 47661}, {4500, 47658}, {4522, 47924}, {4762, 47781}, {4778, 21183}, {4785, 47886}, {4806, 47968}, {4851, 26824}, {4885, 47950}, {4893, 28882}, {4927, 4977}, {4932, 47937}, {4940, 25259}, {4979, 21212}, {6008, 27486}, {6009, 17494}, {6084, 47775}, {6544, 25666}, {6545, 28840}, {6546, 45315}, {7658, 48067}, {16892, 44449}, {17069, 26853}, {21104, 31290}, {21115, 28855}, {21146, 47990}, {21196, 48114}, {21204, 31148}, {21208, 38979}, {23770, 47945}, {23813, 28151}, {24720, 47938}, {24924, 47900}, {26248, 45666}, {26277, 48195}, {26985, 48276}, {27647, 29985}, {28169, 47657}, {28175, 48171}, {28179, 48274}, {28213, 48166}, {28220, 43067}, {28894, 47790}, {28910, 47676}, {29144, 31131}, {29328, 47877}, {30091, 30094}, {30520, 47769}, {30832, 31992}, {30835, 47907}, {31150, 47783}, {31209, 48060}, {31286, 48104}, {44429, 48252}, {44432, 47768}, {45320, 47791}, {45684, 48145}, {46403, 47998}, {47123, 47940}, {47650, 47962}, {47667, 48125}, {47677, 48269}, {47685, 48006}, {47686, 48029}, {47687, 47701}, {47688, 48047}, {47690, 47961}, {47691, 48027}, {47692, 48039}, {47694, 47989}, {47695, 48023}, {47696, 47951}, {47697, 47982}, {47699, 48089}, {47704, 47992}, {47708, 48092}, {47712, 48052}, {47720, 47956}, {47757, 47762}, {47760, 47771}, {47776, 47784}, {47805, 48179}, {47822, 48250}, {47824, 48178}, {47923, 48270}, {47971, 48041}, {47972, 48042}, {47973, 48043}, {47983, 48108}, {48007, 48080}, {48030, 48508}, {48182, 48254}

X(48550) = midpoint of X(i) and X(j) for these {i,j}: {20295, 47894}, {23729, 47876}, {47759, 48156}, {47874, 47958}, {47891, 47988}
X(48550) = reflection of X(i) in X(j) for these {i,j}: {2, 47756}, {649, 47882}, {4453, 44435}, {4467, 47894}, {4789, 4728}, {6546, 45315}, {7192, 47891}, {17494, 47876}, {27486, 47880}, {30565, 4776}, {31148, 21204}, {31150, 47783}, {44433, 48177}, {47660, 47874}, {47755, 47754}, {47762, 47757}, {47763, 1638}, {47768, 44432}, {47771, 47760}, {47773, 1639}, {47776, 47784}, {47780, 4927}, {47791, 45320}, {47805, 48179}, {47824, 48178}, {47874, 3835}, {47892, 4893}, {47894, 3004}, {48250, 47822}, {48252, 44429}, {48254, 48182}
X(48550) = anticomplement of X(47767)
X(48550) = barycentric product X(i)*X(j) for these {i,j}: {514, 17320}, {693, 17012}, {3261, 5315}, {4868, 7199}
X(48550) = barycentric quotient X(i)/X(j) for these {i,j}: {4868, 1018}, {5315, 101}, {17012, 100}, {17320, 190}, {27776, 4767}
X(48550) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3004, 20295, 4467}, {3676, 47981, 48107}, {3835, 47958, 47660}, {4382, 48504, 47661}, {4940, 47960, 25259}, {6548, 7192, 47891}, {16892, 48049, 44449}, {26798, 47653, 3700}, {44435, 47755, 47754}, {47701, 48050, 47687}, {47754, 47755, 4453}


X(48551) = X(513)X(47794)∩X(514)X(661)

Barycentrics    (b - c)*(b + c)*(-2*a^2 - 2*a*b - 2*a*c + b*c) : :
X(48551) = 2 X[10] + X[4822], 2 X[661] + X[1577], X[661] + 2 X[4129], X[693] + 2 X[47997], X[1577] - 4 X[4129], X[3762] + 2 X[14349], 4 X[3835] - X[4978], 2 X[3835] + X[47959], X[4391] + 2 X[48054], 2 X[4823] + X[47666], X[4978] + 2 X[47959], X[1019] - 4 X[25666], X[1734] + 2 X[48043], X[2533] + 2 X[48053], 2 X[3700] + X[47679], 2 X[3716] + X[47948], 2 X[3837] + X[47949], X[4010] + 2 X[48005], 2 X[4010] + X[48507], 4 X[48005] - X[48507], X[4063] + 2 X[48049], 2 X[4088] + X[47713], X[4170] + 2 X[4705], X[4170] - 4 X[4806], X[4705] + 2 X[4806], 2 X[4369] + X[47947], 4 X[4522] - X[47714], 5 X[4707] - 8 X[7657], X[4761] + 2 X[4983], X[4761] - 4 X[21051], X[4983] + 2 X[21051], 2 X[4851] + X[47678], 2 X[4885] + X[47955], 2 X[4940] + X[47965], X[4960] + 2 X[47991], 4 X[45315] - X[45671], X[7265] - 4 X[14321], X[7265] + 2 X[48502], 2 X[14321] + X[48502], 2 X[17072] + X[48081], X[20295] + 2 X[48003], 2 X[20317] + X[48091], X[21146] + 2 X[47994], 2 X[21188] + X[48038], 2 X[21192] + X[44449], 2 X[21260] + X[48024], X[21301] + 2 X[48058], 2 X[23789] + X[47906], 2 X[23815] + X[47913], 2 X[24720] + X[47942], 5 X[30835] + X[47911], 2 X[31010] + X[47669], 5 X[31209] - 2 X[48064], 4 X[31286] - X[48110], 2 X[45324] + X[47774], X[46403] + 2 X[48004], 2 X[47701] + X[47710], X[47711] + 2 X[47998], X[47712] + 2 X[48047], 2 X[47967] + X[48273], X[47970] + 2 X[48050], X[47976] + 2 X[48041], X[47977] + 2 X[48042], 2 X[47987] + X[48108], 2 X[48002] + X[48393], 2 X[48011] + X[48079], 2 X[48012] + X[48080], 2 X[48030] + X[48267], 4 X[48030] - X[48509], 2 X[48267] + X[48509], 2 X[48059] + X[48265]

X(48551) lies on these lines: {2, 15309}, {10, 4822}, {513, 47794}, {514, 661}, {656, 6006}, {830, 47821}, {900, 47842}, {1019, 25666}, {1734, 48043}, {2533, 48053}, {3700, 47679}, {3716, 47948}, {3837, 47949}, {4010, 48005}, {4063, 48049}, {4088, 47713}, {4120, 23879}, {4160, 47840}, {4170, 4705}, {4369, 47947}, {4522, 47714}, {4707, 7657}, {4750, 27574}, {4761, 4983}, {4851, 47678}, {4885, 47955}, {4893, 29013}, {4940, 47965}, {4960, 47991}, {4964, 48337}, {6002, 45315}, {6005, 47814}, {7265, 14321}, {8061, 28867}, {8678, 47838}, {8714, 47810}, {17072, 48081}, {20295, 48003}, {20317, 48091}, {21146, 47994}, {21188, 48038}, {21192, 44449}, {21260, 48024}, {21301, 48058}, {23789, 47906}, {23815, 47913}, {23875, 47769}, {23882, 47777}, {24720, 47942}, {27045, 47763}, {28209, 31946}, {29070, 48162}, {29150, 47827}, {29170, 47888}, {29186, 47826}, {29246, 31149}, {29270, 31150}, {29302, 31147}, {30835, 47911}, {31010, 47669}, {31209, 48064}, {31286, 48110}, {34959, 41800}, {45324, 47774}, {46403, 48004}, {47701, 47710}, {47711, 47998}, {47712, 48047}, {47759, 47793}, {47760, 47795}, {47762, 48196}, {47818, 47822}, {47967, 48273}, {47970, 48050}, {47976, 48041}, {47977, 48042}, {47987, 48108}, {48002, 48393}, {48011, 48079}, {48012, 48080}, {48030, 48267}, {48059, 48265}

X(48551) = midpoint of X(47759) and X(47793)
X(48551) = reflection of X(i) in X(j) for these {i,j}: {47762, 48196}, {47795, 47760}, {47818, 47822}
X(48551) = X(i)-complementary conjugate of X(j) for these (i,j): {2334, 17761}, {4606, 3741}, {8694, 3739}, {34074, 1125}, {34820, 34589}
X(48551) = X(163)-isoconjugate of X(39711)
X(48551) = X(115)-Dao conjugate of X(39711)
X(48551) = barycentric product X(i)*X(j) for these {i,j}: {10, 48079}, {321, 48011}, {523, 17393}
X(48551) = barycentric quotient X(i)/X(j) for these {i,j}: {523, 39711}, {17393, 99}, {48011, 81}, {48079, 86}
X(48551) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 4129, 1577}, {3835, 47959, 4978}, {4010, 48005, 48507}, {4705, 4806, 4170}, {4983, 21051, 4761}, {14321, 48502, 7265}, {48030, 48267, 48509}


X(48552) = X(513)X(4453)∩X(514)X(47822)

Barycentrics    (b - c)*(2*a^2*b + 2*a*b^2 + b^3 + 2*a^2*c + 2*a*b*c + 2*a*c^2 + c^3) : :
X(48552) = 2 X[661] + X[48326], 2 X[676] + X[47989], 2 X[1491] + X[48349], 2 X[3004] + X[4010], 2 X[3676] + X[47983], 2 X[3716] + X[47968], 2 X[3776] + X[48024], X[3801] + 2 X[14349], 4 X[3835] - X[4122], 2 X[3837] + X[47701], 2 X[4369] + X[47944], X[4784] - 4 X[21212], 2 X[4806] + X[16892], X[4810] + 2 X[21196], X[4824] + 2 X[23770], 2 X[4874] + X[47958], 2 X[4885] + X[47961], 2 X[4992] + X[21124], X[7192] + 2 X[47990], 3 X[14475] - 2 X[48233], 2 X[21104] + X[47946], X[21146] + 2 X[47998], 5 X[24924] + X[47902], 4 X[25666] - X[48103], 7 X[27138] - X[47693], 5 X[30835] + X[47924], 5 X[30835] - 2 X[48505], X[47924] + 2 X[48505], X[45746] + 2 X[48090], X[47667] + 2 X[48127], X[47676] + 2 X[48028], X[47688] + 2 X[48056], X[47691] + 2 X[48030], X[47694] + 2 X[47999], X[47699] + 2 X[48098], X[47704] + 2 X[48002], X[47708] + 2 X[48100], X[47712] + 2 X[48059], X[47716] + 2 X[48005], X[47720] + 2 X[47967], X[47943] + 2 X[48248], X[48120] + 2 X[48504], X[48279] + 2 X[48502]

X(48552) lies on these lines: {513, 4453}, {514, 47822}, {522, 47877}, {523, 4728}, {661, 48326}, {676, 47989}, {1491, 48349}, {1639, 28175}, {3004, 4010}, {3676, 47983}, {3716, 47968}, {3776, 48024}, {3801, 14349}, {3835, 4122}, {3837, 47701}, {4369, 47944}, {4448, 4977}, {4776, 48174}, {4784, 21212}, {4789, 4802}, {4806, 16892}, {4810, 21196}, {4824, 23770}, {4874, 47958}, {4885, 47961}, {4992, 21124}, {6546, 48180}, {7192, 47990}, {7927, 47816}, {14475, 48233}, {21104, 47946}, {21116, 28213}, {21146, 47998}, {21204, 48253}, {24924, 47902}, {25666, 48103}, {27138, 47693}, {28147, 48188}, {28199, 47770}, {28882, 48226}, {29078, 31147}, {29118, 47893}, {29144, 44429}, {29158, 47888}, {29192, 31149}, {29208, 47814}, {29328, 47886}, {30835, 47924}, {36848, 48178}, {45666, 48250}, {45746, 48090}, {47667, 48127}, {47676, 48028}, {47688, 48056}, {47691, 48030}, {47694, 47999}, {47699, 48098}, {47704, 48002}, {47708, 48100}, {47712, 48059}, {47716, 48005}, {47720, 47967}, {47757, 47823}, {47759, 48241}, {47762, 48215}, {47771, 48197}, {47778, 47885}, {47783, 48176}, {47791, 48221}, {47802, 48235}, {47804, 48195}, {47821, 48156}, {47943, 48248}, {48120, 48504}, {48158, 48164}, {48199, 48236}, {48279, 48502}

X(48552) = midpoint of X(i) and X(j) for these {i,j}: {4776, 48174}, {47759, 48241}, {47821, 48156}, {48158, 48164}, {48159, 48161}
X(48552) = reflection of X(i) in X(j) for these {i,j}: {4448, 48179}, {4809, 47797}, {6546, 48180}, {36848, 48178}, {47762, 48215}, {47771, 48197}, {47791, 48221}, {47804, 48195}, {47823, 47757}, {47885, 47778}, {48176, 47783}, {48185, 47760}, {48227, 48192}, {48235, 47802}, {48236, 48199}, {48250, 45666}, {48253, 21204}
X(48552) = {X(30835),X(47924)}-harmonic conjugate of X(48505)


X(48553) = X(513)X(47794)∩X(514)X(47822)

Barycentrics    (b - c)*(a^3 - a^2*b - a*b^2 - a^2*c - 3*a*b*c + b^2*c - a*c^2 + b*c^2) : :
X(48553) = X[1] + 2 X[48501], 2 X[10] + X[48336], 3 X[47822] - X[47841], 3 X[47839] - 2 X[47841], 2 X[650] + X[48267], X[659] + 2 X[4129], 4 X[1125] - X[48323], X[2530] - 4 X[25666], X[2533] + 2 X[48058], 2 X[3716] + X[4705], 4 X[3716] - X[48305], 2 X[4705] + X[48305], 2 X[3837] + X[47970], X[4010] + 2 X[48003], X[4040] + 2 X[21051], X[4063] + 2 X[4806], 2 X[4147] + X[4775], 2 X[4369] + X[47949], 2 X[4391] + X[48288], 2 X[4490] + X[48291], X[4724] + 2 X[21260], X[4834] + 2 X[48043], 2 X[4874] + X[47959], 2 X[4885] + X[47966], X[4960] + 2 X[47993], 2 X[4992] + X[21385], X[7192] + 2 X[47994], 2 X[14838] + X[48265], 2 X[17072] + X[48351], 4 X[19947] - X[23738], 2 X[20317] + X[48099], X[21146] + 2 X[48004], 2 X[21188] + X[48040], 2 X[23789] - 5 X[30795], 2 X[23815] - 5 X[30835], 2 X[23815] + X[47929], 5 X[30835] + X[47929], 2 X[24720] - 5 X[31251], 5 X[24924] + X[47906], X[31149] + 2 X[45673], 4 X[31288] - X[48144], X[47694] + 2 X[48005], X[47712] + 2 X[48056], X[47948] + 2 X[48248], 2 X[47965] + X[48273], 2 X[48000] + X[48393]

X(48553) lies on these lines: {1, 48501}, {2, 6372}, {10, 48336}, {512, 47793}, {513, 47794}, {514, 47822}, {525, 48166}, {650, 48267}, {659, 4129}, {784, 4893}, {826, 30565}, {830, 4448}, {891, 47840}, {1125, 48323}, {1635, 29150}, {1639, 29142}, {2530, 25666}, {2533, 48058}, {3716, 4705}, {3837, 47970}, {4010, 48003}, {4040, 21051}, {4063, 4806}, {4083, 47838}, {4120, 29106}, {4147, 4775}, {4151, 4800}, {4369, 47949}, {4391, 48288}, {4490, 48291}, {4724, 21260}, {4776, 47815}, {4834, 48043}, {4874, 47959}, {4885, 47966}, {4960, 47993}, {4992, 21385}, {6004, 47814}, {6005, 47835}, {6546, 29098}, {7192, 47994}, {7927, 48161}, {7950, 48171}, {8672, 48165}, {8714, 47827}, {10196, 29118}, {14430, 29298}, {14431, 29051}, {14838, 48265}, {17072, 48351}, {19947, 23738}, {20317, 48099}, {21052, 29188}, {21146, 48004}, {21188, 48040}, {23789, 30795}, {23815, 30835}, {24720, 31251}, {24924, 47906}, {29013, 48226}, {29021, 48185}, {29047, 48177}, {29070, 47811}, {29158, 47885}, {29164, 48188}, {29168, 47809}, {29170, 48214}, {29182, 30709}, {29198, 47795}, {29288, 48179}, {29354, 47797}, {31149, 45673}, {31288, 48144}, {45666, 47818}, {47694, 48005}, {47712, 48056}, {47778, 47888}, {47823, 48196}, {47948, 48248}, {47965, 48273}, {48000, 48393}

X(48553) = midpoint of X(i) and X(j) for these {i,j}: {4776, 47815}, {47793, 47821}, {47872, 48162}
X(48553) = reflection of X(i) in X(j) for these {i,j}: {47795, 48197}, {47818, 45666}, {47823, 48196}, {47837, 47794}, {47839, 47822}, {47888, 47778}
X(48553) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3716, 4705, 48305}, {30835, 47929, 23815}


X(48554) = X(513)X(1638)∩X(514)X(661)

Barycentrics    (b - c)*(a^2 + 4*a*b + b^2 + 4*a*c - 2*b*c + c^2) : :
X(48554) = X[1638] - 3 X[47756], 2 X[1638] - 3 X[47757], 4 X[1638] - 3 X[47758], 4 X[47756] - X[47758], 3 X[47800] - 4 X[48195], 2 X[661] + X[48398], 2 X[3239] + X[47958], 4 X[3835] - X[6590], 2 X[3835] + X[47995], 3 X[4776] - X[30565], X[6590] + 2 X[47995], 2 X[30565] - 3 X[47765], X[3004] + 2 X[4940], 2 X[3004] + X[48269], 4 X[4940] - X[48269], 2 X[3676] + X[4813], 2 X[3716] + X[47982], 2 X[3776] + X[48038], 2 X[3798] + X[48079], 2 X[3837] + X[47983], X[4025] + 2 X[48049], 2 X[4106] + X[45745], 2 X[4369] + X[47981], 4 X[4521] - X[48101], 2 X[4765] + X[48114], 2 X[45679] - 3 X[47785], 2 X[4806] + X[48007], X[4851] + 2 X[23813], 2 X[4885] + X[47988], 2 X[4932] + X[47978], X[4979] - 4 X[7658], 2 X[14321] + X[47960], 2 X[14837] + X[48121], X[21185] + 2 X[48052], 2 X[21188] + X[48085], 4 X[21212] - X[48013], 2 X[21212] + X[48041], X[48013] + 2 X[48041], X[23731] + 5 X[30835], 2 X[24720] + X[47979], 5 X[24924] + X[47937], 4 X[25666] - X[48060], 5 X[26798] + X[45746], 4 X[31286] - X[48067], 4 X[43061] - X[48104], 2 X[45326] - 3 X[47760], 4 X[45326] - 3 X[47766], X[47123] + 2 X[48027], 3 X[47806] - 2 X[48235], X[48006] + 2 X[48050], X[48014] + 2 X[48042], X[48015] + 2 X[48043], X[48268] + 2 X[48504]

X(48554) lies on these lines: {2, 47768}, {513, 1638}, {514, 661}, {522, 31147}, {649, 46919}, {812, 47783}, {824, 47786}, {900, 2526}, {918, 47764}, {3004, 4940}, {3667, 47886}, {3676, 4813}, {3716, 47982}, {3776, 28871}, {3798, 48079}, {3837, 47983}, {4025, 28867}, {4106, 45745}, {4369, 47981}, {4379, 4778}, {4521, 48101}, {4750, 6006}, {4765, 48114}, {4785, 45679}, {4786, 47882}, {4806, 48007}, {4851, 23813}, {4874, 28209}, {4885, 47988}, {4928, 28859}, {4932, 47978}, {4977, 45320}, {4979, 7658}, {6008, 47784}, {6084, 47777}, {6545, 28878}, {14321, 47960}, {14475, 36834}, {14837, 48121}, {20295, 27486}, {21183, 28840}, {21185, 48052}, {21188, 48085}, {21212, 48013}, {21297, 47781}, {23731, 30835}, {24720, 47979}, {24924, 47937}, {25666, 48060}, {26277, 47763}, {26798, 45746}, {28191, 48171}, {28195, 48166}, {28225, 31148}, {28846, 44435}, {28882, 45315}, {28902, 48026}, {31286, 48067}, {43061, 48104}, {44432, 47762}, {45326, 47760}, {47123, 48027}, {47769, 48156}, {47806, 48235}, {48006, 48050}, {48014, 48042}, {48015, 48043}, {48268, 48504}

X(48554) = midpoint of X(i) and X(j) for these {i,j}: {20295, 27486}, {21297, 47781}, {44435, 47759}, {47769, 48156}, {47787, 47995}
X(48554) = reflection of X(i) in X(j) for these {i,j}: {649, 46919}, {4786, 47882}, {6590, 47787}, {47757, 47756}, {47758, 47757}, {47762, 44432}, {47765, 4776}, {47766, 47760}, {47768, 2}, {47787, 3835}, {47789, 4928}, {47801, 48179}, {47883, 47783}
X(48554) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3004, 4940, 48269}, {3835, 47995, 6590}, {21212, 48041, 48013}


X(48555) = X(513)X(1638)∩X(514)X(47822)

Barycentrics    (b - c)*(-a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 3*a^2*c + 4*a*b*c - b^2*c + 3*a*c^2 - b*c^2 + c^3) : :
X(48555) = 2 X[676] + X[48027], 2 X[3676] + X[48024], 2 X[3716] + X[48007], 2 X[3776] + X[48040], 2 X[3837] + X[48006], X[4025] + 2 X[4806], 2 X[4369] + X[47983], 4 X[4521] - X[48103], 2 X[4765] + X[4810], X[4784] - 4 X[7658], 2 X[4874] + X[47995], 2 X[4885] + X[47998], X[4983] + 2 X[21188], 2 X[14837] + X[48123], X[21185] + 2 X[48059], 2 X[21212] + X[48043], 5 X[24924] + X[47938], 4 X[25666] - X[48062], 5 X[26985] + X[47699], 7 X[27138] - X[47690], 5 X[30835] + X[47701], 2 X[34958] + X[47956], X[45745] + 2 X[48090], X[47123] + 2 X[48030], X[47764] + 2 X[48212], X[47982] + 2 X[48248]

X(48555) lies on these lines: {513, 1638}, {514, 47822}, {522, 1491}, {523, 47760}, {661, 47887}, {676, 48027}, {918, 48192}, {1639, 4802}, {3676, 48024}, {3716, 48007}, {3776, 48040}, {3837, 48006}, {4025, 4806}, {4129, 29212}, {4369, 47983}, {4448, 4778}, {4521, 48103}, {4765, 4810}, {4776, 47797}, {4784, 7658}, {4800, 47877}, {4874, 4977}, {4885, 47998}, {4983, 21188}, {6332, 29172}, {6366, 48136}, {6545, 47826}, {14837, 48123}, {21185, 48059}, {21212, 48043}, {24924, 47938}, {25666, 48062}, {26985, 47699}, {27138, 47690}, {28147, 48185}, {28155, 48188}, {28175, 47770}, {28846, 48227}, {29078, 47786}, {29144, 47806}, {29328, 47785}, {30520, 48166}, {30565, 48174}, {30835, 47701}, {34958, 47956}, {44429, 48161}, {44432, 47823}, {44435, 47821}, {45326, 48219}, {45745, 48090}, {47123, 48030}, {47764, 48212}, {47766, 48197}, {47769, 48241}, {47781, 47834}, {47789, 48206}, {47808, 48158}, {47982, 48248}

X(48555) = midpoint of X(i) and X(j) for these {i,j}: {661, 47887}, {4776, 47797}, {4800, 47877}, {6545, 47826}, {30565, 48174}, {44429, 48161}, {44435, 47821}, {47756, 48179}, {47769, 48241}, {47781, 47834}, {47808, 48158}
X(48555) = reflection of X(i) in X(j) for these {i,j}: {47758, 48215}, {47766, 48197}, {47789, 48206}, {47800, 48195}, {47823, 44432}, {48219, 45326}
X(48555) = crossdifference of every pair of points on line {172, 14974}


X(48556) = X(513)X(47795)∩X(514)X(14430)

Barycentrics    (b - c)*(-2*a*b^2 + b^2*c - 2*a*c^2 + b*c^2) : :
X(48556) = 2 X[10] + X[48334], 3 X[44429] - X[47814], 2 X[47814] - 3 X[47816], X[47814] + 3 X[47819], X[47816] + 2 X[47819], X[661] + 2 X[23789], X[693] + 2 X[48066], 2 X[693] + X[48509], 4 X[48066] - X[48509], X[764] + 2 X[21051], X[1019] + 2 X[48050], 4 X[1125] - X[48150], 2 X[1491] + X[4978], X[1491] + 2 X[23815], 4 X[1491] - X[48507], X[4978] - 4 X[23815], 2 X[4978] + X[48507], 8 X[23815] + X[48507], X[1577] + 2 X[2530], X[1577] - 4 X[3837], X[2530] + 2 X[3837], 2 X[2254] + X[4170], 2 X[3004] + X[47715], 5 X[3616] - 2 X[48345], X[3762] + 2 X[3777], X[3762] - 4 X[21260], X[3777] + 2 X[21260], 2 X[3776] + X[48272], 2 X[3835] + X[4905], 2 X[3960] + X[21301], X[4063] - 4 X[25380], X[4086] - 4 X[44316], X[4129] + 2 X[23814], 2 X[4129] + X[48151], 4 X[23814] - X[48151], X[4367] - 4 X[19947], 2 X[4369] + X[48086], 2 X[4401] + X[47685], X[4705] + 2 X[48506], X[4761] + 2 X[48131], X[4801] + 2 X[48012], 2 X[4823] + X[48510], X[7192] + 2 X[48052], X[14349] + 2 X[24720], 2 X[14838] + X[46403], 2 X[17072] + X[48335], X[21146] + 2 X[48059], X[21302] + 2 X[48348], 5 X[24924] + X[48116], 4 X[25666] - X[47970], X[45671] + 2 X[48167], 2 X[40086] + X[47842], 2 X[48054] + X[48108], 2 X[48073] + X[48081], 2 X[48075] + X[48080]

X(48556) lies on these lines: {2, 47817}, {10, 48334}, {512, 36848}, {513, 47795}, {514, 14430}, {661, 23789}, {693, 48066}, {764, 21051}, {784, 48184}, {830, 47796}, {1019, 25526}, {1125, 48150}, {1491, 4978}, {1577, 2530}, {1638, 28481}, {2254, 4170}, {2832, 47793}, {3004, 47715}, {3616, 48345}, {3762, 3777}, {3776, 48272}, {3835, 4905}, {3960, 21301}, {4063, 25380}, {4086, 44316}, {4129, 23814}, {4367, 19947}, {4369, 48086}, {4401, 47685}, {4705, 48506}, {4728, 8714}, {4761, 48131}, {4801, 48012}, {4823, 48510}, {5996, 6545}, {6004, 47841}, {7192, 48052}, {14349, 24720}, {14838, 46403}, {17072, 48335}, {21146, 48059}, {21302, 48348}, {23791, 28372}, {24924, 48116}, {25666, 47970}, {26725, 42325}, {29021, 44435}, {29047, 47808}, {29070, 45671}, {29142, 48178}, {29164, 48174}, {29190, 47886}, {29260, 48187}, {29288, 48182}, {29302, 47828}, {29324, 31149}, {29344, 44550}, {29362, 47888}, {40086, 47842}, {47794, 47802}, {47804, 48218}, {47815, 48196}, {47875, 48198}, {47889, 48160}, {48054, 48108}, {48073, 48081}, {48075, 48080}

X(48556) = midpoint of X(i) and X(j) for these {i,j}: {44429, 47819}, {47796, 48164}, {47889, 48160}, {47893, 48167}
X(48556) = reflection of X(i) in X(j) for these {i,j}: {45671, 47893}, {47794, 47802}, {47804, 48218}, {47815, 48196}, {47816, 44429}, {47817, 2}, {47818, 47795}, {47875, 48198}
X(48556) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 48066, 48509}, {1491, 4978, 48507}, {1491, 23815, 4978}, {2530, 3837, 1577}, {3777, 21260, 3762}, {4129, 23814, 48151}


X(48557) = X(513)X(47772)∩X(514)X(661)

Barycentrics    (b - c)*(2*a^2 - 2*a*b + 2*b^2 - 2*a*c + b*c + 2*c^2) : :
X(48557) = X[47754] - 3 X[47770], X[17494] - 3 X[44009], 2 X[17494] + X[47665], X[17494] + 2 X[48271], 6 X[44009] + X[47665], 3 X[44009] + 2 X[48271], X[47665] - 4 X[48271], 2 X[661] + X[47662], X[693] + 2 X[48094], 4 X[3239] - X[47652], 2 X[3762] + X[47684], 4 X[3835] - X[47651], 2 X[3835] + X[48130], X[4462] + 2 X[48300], 2 X[4468] + X[47660], 4 X[4468] - X[47666], 3 X[4776] - 4 X[47765], 4 X[6590] - X[47675], 3 X[30565] - 2 X[47765], X[47651] + 2 X[48130], 2 X[47660] + X[47666], 2 X[650] - 3 X[31992], 4 X[650] - X[47677], 6 X[31992] - X[47677], 3 X[31992] - X[47894], X[4380] + 2 X[25259], X[4380] - 4 X[47890], X[25259] + 2 X[47890], 2 X[47755] - 3 X[47762], X[47755] - 3 X[47771], 3 X[47762] - 4 X[47767], 2 X[47767] - 3 X[47771], 2 X[3700] + X[47663], 4 X[3716] - X[47692], 2 X[3716] + X[48118], X[47692] + 2 X[48118], 2 X[3776] - 3 X[14475], X[4010] + 2 X[48097], 2 X[4024] + X[47664], 2 X[4040] + X[47706], 2 X[4088] + X[47697], 2 X[4369] + X[48117], X[4467] - 4 X[11068], 4 X[4522] - X[47685], 2 X[4522] + X[48102], X[47685] + 2 X[48102], X[4608] + 2 X[47920], 2 X[4724] + X[47689], and many others

X(48557) lies on these lines: {2, 30520}, {192, 4777}, {513, 47772}, {514, 661}, {522, 47892}, {650, 4850}, {659, 29370}, {824, 6546}, {826, 47815}, {900, 4380}, {918, 47755}, {1635, 30519}, {1639, 44435}, {3700, 6009}, {3716, 47692}, {3776, 14475}, {4010, 48097}, {4024, 47664}, {4040, 47706}, {4088, 47697}, {4120, 28882}, {4369, 48117}, {4379, 28890}, {4448, 29204}, {4453, 47766}, {4467, 11068}, {4522, 47685}, {4608, 47920}, {4724, 47689}, {4762, 47870}, {4802, 47821}, {4806, 48140}, {4809, 47804}, {4828, 20923}, {4885, 6548}, {4893, 28863}, {4932, 48112}, {4940, 48132}, {4944, 21297}, {6006, 44449}, {6084, 47790}, {6544, 16892}, {6545, 47879}, {7192, 28910}, {10196, 47886}, {17498, 47845}, {20295, 48095}, {20892, 30061}, {21115, 47779}, {21212, 45684}, {24720, 48113}, {25666, 47923}, {26854, 27291}, {26985, 30861}, {27486, 47884}, {28147, 48161}, {28151, 47659}, {28169, 47661}, {28175, 48166}, {28179, 47667}, {28209, 47939}, {28220, 31290}, {28886, 48082}, {28894, 47775}, {28898, 47776}, {29354, 47820}, {29358, 47817}, {31286, 47930}, {36848, 48201}, {44429, 48185}, {45666, 48224}, {45670, 47783}, {45746, 47876}, {46403, 48096}, {47655, 47926}, {47657, 48000}, {47676, 47891}, {47687, 48061}, {47690, 47974}, {47693, 48029}, {47694, 48088}, {47696, 47940}, {47700, 48063}, {47710, 48065}, {47718, 47970}, {47760, 48156}, {47780, 47881}, {47803, 48241}, {47822, 48174}, {47824, 48219}, {47941, 48048}, {47975, 48056}, {48041, 48145}, {48043, 48146}, {48049, 48138}, {48050, 48139}, {48079, 48101}, {48080, 48103}, {48083, 48108}

X(48557) = midpoint of X(i) and X(j) for these {i,j}: {47772, 47773}, {47874, 48094}
X(48557) = reflection of X(i) in X(j) for these {i,j}: {2, 47770}, {693, 47874}, {4453, 47766}, {4776, 30565}, {6545, 47879}, {16892, 47882}, {21115, 47779}, {21297, 4944}, {27486, 47884}, {31150, 6546}, {36848, 48201}, {44429, 48185}, {44435, 1639}, {45746, 47876}, {47676, 47891}, {47677, 47894}, {47755, 47767}, {47762, 47771}, {47780, 47881}, {47783, 45670}, {47824, 48219}, {47871, 47787}, {47886, 10196}, {47894, 650}, {48156, 47760}, {48174, 47822}, {48187, 48188}, {48223, 4448}, {48224, 45666}, {48241, 47803}, {48254, 48222}
X(48557) = anticomplement of X(47754)
X(48557) = barycentric product X(514)*X(17342)
X(48557) = barycentric quotient X(17342)/X(190)
X(48557) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3716, 48118, 47692}, {3835, 48130, 47651}, {4468, 47660, 47666}, {4522, 48102, 47685}, {6544, 16892, 47882}, {6544, 47882, 31209}, {17494, 48271, 47665}, {25259, 47890, 4380}, {31992, 47894, 650}, {47659, 47962, 47668}, {47690, 48055, 47974}, {47696, 48047, 47940}, {47755, 47767, 47762}, {47755, 47771, 47767}, {48083, 48505, 48108}, {48101, 48270, 48079}


X(48558) = X(513)X(4453)∩X(514)X(1639)

Barycentrics    (b - c)*(a^2 + 3*a*b + 2*b^2 + 3*a*c - 2*b*c + 2*c^2) : :
X(48558) = X[4453] - 3 X[44435], 2 X[4453] - 3 X[47754], 5 X[4453] - 3 X[47755], 5 X[44435] - X[47755], 5 X[47754] - 2 X[47755], 3 X[48192] - 2 X[48212], X[1639] - 3 X[47756], 2 X[1639] - 3 X[47760], 4 X[1639] - 3 X[47770], 4 X[47756] - X[47770], 2 X[3004] + X[4106], 2 X[676] + X[47982], 7 X[693] - X[4608], 4 X[2487] - X[48067], 2 X[3676] + X[47988], 2 X[3776] + X[48026], 2 X[3835] + X[47960], 4 X[3835] - X[48271], 2 X[47960] + X[48271], 2 X[3837] + X[47961], 2 X[4369] + X[47950], 3 X[4728] - X[47873], 3 X[4776] - X[47772], X[47772] + 3 X[48156], X[4790] - 4 X[21212], 2 X[4874] + X[47951], X[43067] + 2 X[47995], 2 X[4885] + X[47958], 2 X[4940] + X[16892], X[4958] - 3 X[31147], X[4984] - 3 X[47886], X[7662] + 2 X[47999], 2 X[21104] + X[47952], 2 X[23813] + X[45746], 5 X[24924] + X[47907], 4 X[25666] - X[48095], 5 X[26798] + X[47677], 7 X[27138] - X[47662], 5 X[30835] + X[47916], 7 X[31207] - X[48145], 4 X[31287] - X[48101], 3 X[44429] - X[48254], 2 X[44902] - 3 X[47757], 4 X[44902] - 3 X[47761], 3 X[47757] - X[47768], 3 X[47761] - 2 X[47768], 3 X[47802] - 2 X[48217], X[47962] + 2 X[48398], X[48125] + 2 X[48504], 3 X[48178] - X[48249]

X(48558) lies on these lines: {513, 4453}, {514, 1639}, {522, 2526}, {650, 28882}, {676, 47982}, {693, 4036}, {812, 47880}, {918, 47764}, {2487, 48067}, {3676, 28225}, {3776, 28855}, {3835, 4944}, {3837, 47961}, {4025, 28217}, {4083, 22314}, {4369, 47950}, {4448, 6548}, {4728, 28894}, {4762, 47878}, {4776, 30520}, {4777, 21297}, {4778, 47891}, {4790, 21212}, {4874, 4977}, {4885, 47958}, {4926, 47894}, {4940, 16892}, {4958, 28898}, {4984, 6008}, {6009, 47883}, {6084, 47783}, {7662, 47999}, {21104, 47952}, {21115, 28910}, {21204, 28859}, {23813, 28165}, {24924, 47907}, {25666, 48095}, {26798, 47677}, {27138, 47662}, {28155, 48274}, {28187, 48268}, {28195, 47780}, {28199, 48185}, {28906, 48049}, {30835, 47916}, {31207, 48145}, {31287, 48101}, {44429, 48254}, {44432, 47767}, {44902, 47757}, {45677, 47789}, {47781, 47871}, {47802, 48217}, {47962, 48398}, {48125, 48504}, {48178, 48249}

X(48558) = midpoint of X(i) and X(j) for these {i,j}: {4776, 48156}, {4944, 47960}, {21183, 47995}, {47781, 47871}
X(48558) = reflection of X(i) in X(j) for these {i,j}: {4944, 3835}, {43067, 21183}, {47754, 44435}, {47760, 47756}, {47761, 47757}, {47767, 44432}, {47768, 44902}, {47770, 47760}, {47789, 45677}, {47881, 4928}, {48271, 4944}
X(48558) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3835, 47960, 48271}, {44902, 47768, 47761}, {47757, 47768, 44902}


X(48559) = X(2)X(8712)∩X(241)X(514)

Barycentrics    (b - c)*(3*a^3 + 2*a^2*b - a*b^2 + 2*a^2*c - 4*a*b*c + 2*b^2*c - a*c^2 + 2*b*c^2) : :
X(48559) = 2 X[10] + X[3803], X[3669] - 4 X[31286], 2 X[4369] + X[47921], X[7178] + 2 X[11068], 2 X[14837] + X[47890], X[43067] + 2 X[47965], X[47962] - 4 X[48003], X[649] + 2 X[20317], 4 X[2490] - X[6332], 4 X[2516] - X[4560], 2 X[4063] + X[4106], X[4391] + 2 X[4394], X[4462] + 5 X[27013], X[4498] + 2 X[4885], 2 X[4932] + X[47915], 2 X[4940] + X[47935], 4 X[25666] - X[48128], 7 X[31207] - X[48334], 4 X[31287] - X[48131], 4 X[31288] - X[48332]

X(48559) lies on these lines: {2, 8712}, {10, 3803}, {241, 514}, {513, 26078}, {525, 47770}, {649, 20317}, {798, 6008}, {900, 6133}, {1635, 23880}, {1639, 28478}, {2490, 6332}, {2516, 4560}, {3309, 47817}, {3900, 47804}, {3910, 47766}, {4063, 4106}, {4083, 47803}, {4391, 4394}, {4462, 27013}, {4498, 4885}, {4776, 26049}, {4932, 47915}, {4940, 47935}, {14077, 47818}, {21198, 29114}, {25666, 48128}, {29013, 45664}, {29017, 48219}, {29146, 48222}, {29208, 48211}, {29366, 45314}, {30061, 47776}, {31207, 48334}, {31287, 48131}, {31288, 48332}, {31359, 45666}, {47760, 47794}

X(48559) = midpoint of X(47815) and X(47836)
X(48559) = reflection of X(i) in X(j) for these {i,j}: {47754, 41800}, {47760, 47794}


X(48560) = X(241)X(514)∩X(513)X(14404)

Barycentrics    (b - c)*(-3*a^2 + 5*a*b + 5*a*c + 2*b*c) : :
X(48560) = 5 X[650] - 2 X[4369], 3 X[650] - 2 X[4763], 7 X[650] - 4 X[31286], 4 X[650] - X[43067], 5 X[650] + X[47920], 2 X[650] + X[47962], X[650] + 2 X[48000], 7 X[650] - X[48133], 3 X[4369] - 5 X[4763], 7 X[4369] - 10 X[31286], 8 X[4369] - 5 X[43067], 4 X[4369] - 5 X[47761], 2 X[4369] + X[47920], 4 X[4369] + 5 X[47962], X[4369] + 5 X[48000], 14 X[4369] - 5 X[48133], 7 X[4763] - 6 X[31286], 8 X[4763] - 3 X[43067], 4 X[4763] - 3 X[47761], 10 X[4763] + 3 X[47920], 4 X[4763] + 3 X[47962], X[4763] + 3 X[48000], 14 X[4763] - 3 X[48133], X[4851] + 2 X[11068], 16 X[31286] - 7 X[43067], 8 X[31286] - 7 X[47761], 20 X[31286] + 7 X[47920], 8 X[31286] + 7 X[47962], 2 X[31286] + 7 X[48000], 4 X[31286] - X[48133], 5 X[43067] + 4 X[47920], X[43067] + 2 X[47962], X[43067] + 8 X[48000], 7 X[43067] - 4 X[48133], 5 X[47761] + 2 X[47920], X[47761] + 4 X[48000], 7 X[47761] - 2 X[48133], 2 X[47920] - 5 X[47962], X[47920] - 10 X[48000], 7 X[47920] + 5 X[48133], X[47962] - 4 X[48000], 7 X[47962] + 2 X[48133], 14 X[48000] + X[48133], X[48095] + 2 X[48504], 5 X[31150] + X[47774], 3 X[31150] - X[47776], X[47774] - 5 X[47775], 3 X[47774] + 5 X[47776], 3 X[47775] + X[47776], 5 X[649] + X[47903], 2 X[649] + X[47952], 2 X[47903] - 5 X[47952], 4 X[2516] - X[7192], X[4106] + 2 X[17494], 7 X[4106] - 10 X[26798], 7 X[4776] - 5 X[26798], 7 X[17494] + 5 X[26798], 2 X[4394] - 5 X[26777], 2 X[4394] + X[47666], 5 X[26777] + X[47666], 5 X[26777] - X[47763], 4 X[4521] - X[48274], X[4728] - 3 X[4893], 2 X[4728] - 3 X[47760], 2 X[4765] + X[48046], 2 X[4782] + X[47953], X[4790] + 2 X[47996], 2 X[4885] + X[47926], 2 X[4932] + X[47914], 2 X[4940] + X[47932], X[7659] + 2 X[48001], 2 X[9508] + X[47963], 2 X[21196] + X[48087], 2 X[23813] + X[47664], 4 X[25666] - X[48125], 7 X[27115] - X[47675], 5 X[31250] - 2 X[48399], 4 X[31287] - X[47672], 3 X[45320] - 4 X[45678], 2 X[45678] - 3 X[47778], 2 X[45745] + X[48271], 2 X[48008] + X[48026]

X(48560) lies on these lines: {241, 514}, {513, 14404}, {523, 47770}, {649, 47903}, {661, 6008}, {812, 47777}, {900, 48014}, {918, 47883}, {2516, 7192}, {3716, 28169}, {4106, 4776}, {4122, 4777}, {4379, 44567}, {4394, 26777}, {4521, 48274}, {4728, 4762}, {4750, 28910}, {4765, 48046}, {4782, 47953}, {4786, 28902}, {4790, 47996}, {4802, 47771}, {4874, 28179}, {4885, 47926}, {4913, 6006}, {4926, 47769}, {4932, 47914}, {4940, 47932}, {6084, 47783}, {6546, 28894}, {7659, 48001}, {7662, 28151}, {9508, 28220}, {10196, 47881}, {14425, 47789}, {21196, 48087}, {23813, 47664}, {25666, 48125}, {27115, 47675}, {28147, 48220}, {28161, 45670}, {28165, 47870}, {28175, 48214}, {28886, 45679}, {30520, 47782}, {31250, 48399}, {31287, 47672}, {45320, 45678}, {45745, 48271}, {47781, 47892}, {47802, 48194}, {48008, 48026}

X(48560) = midpoint of X(i) and X(j) for these {i,j}: {4776, 17494}, {6546, 47878}, {31150, 47775}, {47666, 47763}, {47761, 47962}, {47781, 47892}
X(48560) = reflection of X(i) in X(j) for these {i,j}: {4106, 4776}, {4379, 44567}, {7662, 45666}, {43067, 47761}, {45320, 47778}, {47754, 47784}, {47760, 4893}, {47761, 650}, {47763, 4394}, {47789, 14425}, {47802, 48194}, {47881, 10196}, {47891, 46919}, {48190, 48191}
X(48560) = crossdifference of every pair of points on line {55, 16971}
X(48560) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 47920, 4369}, {650, 47962, 43067}, {650, 48000, 47962}, {650, 48133, 31286}, {26777, 47666, 4394}


X(48561) = X(513)X(47794)∩X(514)X(47799)

Barycentrics    (b - c)*(3*a^3 - a*b^2 - 4*a*b*c + 2*b^2*c - a*c^2 + 2*b*c^2) : :
X(48561) = 3 X[47815] + X[47819], 2 X[10] + X[48329], 3 X[47794] - X[47816], X[47816] + 3 X[47817], X[667] + 2 X[20317], 2 X[45314] + X[45664], 4 X[1125] - X[48346], 5 X[1698] + X[48111], X[2530] - 4 X[31287], 2 X[2977] + X[21185], X[3669] - 4 X[31288], X[3803] + 2 X[21051], 2 X[4147] + X[48327], 2 X[4369] + X[47966], X[4391] + 2 X[6050], 2 X[4394] + X[48267], 2 X[4874] + X[47965], X[7662] + 2 X[48003], 2 X[11068] + X[48503], 2 X[20517] + X[48088], 2 X[21188] + X[48055], 2 X[23815] - 5 X[31250], 5 X[24924] + X[47929], 4 X[25666] - X[48092], 7 X[27115] - X[48510], 7 X[31207] - X[48151]

X(48561) lies on these lines: {2, 47815}, {10, 48329}, {392, 4083}, {513, 47794}, {514, 47799}, {650, 784}, {667, 958}, {814, 45314}, {826, 47770}, {1125, 48346}, {1698, 48111}, {2530, 31287}, {2832, 48218}, {2977, 21185}, {3309, 4448}, {3669, 5433}, {3803, 21051}, {4147, 48327}, {4369, 47966}, {4391, 6050}, {4394, 48267}, {4762, 47875}, {4874, 47965}, {4944, 29106}, {6362, 14425}, {6372, 47761}, {7662, 48003}, {8643, 14430}, {8678, 47793}, {8712, 47839}, {10196, 23877}, {11068, 48503}, {20517, 48088}, {21188, 48055}, {23815, 31250}, {23882, 47872}, {24924, 47929}, {25666, 48092}, {27115, 48510}, {29021, 48219}, {29047, 48211}, {29142, 47766}, {29164, 48222}, {29288, 47800}, {29324, 30234}, {31207, 48151}, {44567, 47888}, {47802, 48196}, {47805, 47814}

X(48561) = midpoint of X(i) and X(j) for these {i,j}: {2, 47815}, {4448, 47835}, {8643, 14430}, {47793, 47804}, {47794, 47817}, {47805, 47814}, {47872, 48226}
X(48561) = reflection of X(i) in X(j) for these {i,j}: {47802, 48196}, {47888, 44567}
X(48561) = complement of X(47819)


X(48562) = X(513)X(4763)∩X(514)X(47799)

Barycentrics    (b - c)*(-a + b + c)*(-3*a^2 - 2*a*b - 2*a*c + b*c) : :
X(48562) = 3 X[47811] + X[47812], 4 X[44567] - X[45328], 2 X[44567] + X[45673], 2 X[45314] + X[45315], X[45328] + 2 X[45673], 2 X[650] + X[3716], 4 X[650] - X[4913], 2 X[3716] + X[4913], 4 X[4521] - X[4522], X[659] + 2 X[25666], 2 X[659] + X[48050], 4 X[25666] - X[48050], X[2254] - 7 X[27115], X[2526] + 2 X[8689], 2 X[3835] + X[4830], X[14430] - 3 X[47793], 2 X[4369] + X[48001], 2 X[4394] + X[48043], X[4504] + 2 X[48501], X[4724] + 2 X[25380], X[4724] + 5 X[31209], 2 X[25380] - 5 X[31209], 2 X[4782] + X[48049], 2 X[4874] + X[48000], X[4804] + 5 X[26777], 3 X[6544] - X[47809], 2 X[13246] + X[48047], 2 X[21212] + X[48055], X[24720] - 4 X[31287], 5 X[24924] + X[47969], 5 X[27013] + X[48021], 2 X[31286] + X[48029], X[30592] - 3 X[47839], X[31150] + 2 X[45337], 7 X[31207] - X[48108], 3 X[31992] + X[48203]

X(48562) lies on these lines: {2, 47811}, {333, 3737}, {513, 4763}, {514, 47799}, {522, 650}, {523, 10180}, {659, 25666}, {812, 47822}, {1635, 47821}, {2254, 27115}, {2526, 8689}, {2786, 48166}, {3835, 4830}, {3907, 14430}, {4369, 4977}, {4394, 48043}, {4448, 47827}, {4504, 48501}, {4724, 25380}, {4728, 48240}, {4762, 47831}, {4778, 47761}, {4782, 48049}, {4802, 4874}, {4804, 26777}, {4893, 47804}, {4928, 29362}, {6544, 47809}, {6546, 47797}, {7662, 28155}, {9508, 28217}, {13246, 48047}, {14077, 45316}, {21212, 48055}, {24720, 31287}, {24924, 47969}, {27013, 48021}, {27929, 28863}, {28147, 48220}, {28161, 48210}, {28175, 45318}, {28225, 31286}, {28840, 48162}, {28890, 48227}, {29051, 47794}, {29186, 48196}, {30592, 47839}, {31150, 45337}, {31207, 48108}, {31992, 48203}, {45663, 48253}, {45675, 47823}, {45678, 48184}, {47762, 47826}, {47775, 47813}, {47805, 47810}, {47884, 48179}, {47885, 48177}, {48176, 48234}

X(48562) = midpoint of X(i) and X(j) for these {i,j}: {2, 47811}, {1635, 47821}, {4448, 47827}, {4728, 48240}, {4893, 47804}, {6546, 47797}, {31150, 47832}, {45314, 48180}, {45673, 47830}, {47762, 47826}, {47775, 47813}, {47805, 47810}, {47822, 48226}, {47884, 48179}, {47885, 48177}, {48176, 48234}
X(48562) = reflection of X(i) in X(j) for these {i,j}: {4763, 48214}, {4928, 48197}, {45315, 48180}, {45328, 47830}, {47823, 45675}, {47830, 44567}, {47832, 45337}, {48184, 45678}, {48253, 45663}
X(48562) = complement of X(47812)
X(48562) = barycentric product X(i)*X(j) for these {i,j}: {522, 29584}, {4391, 16477}
X(48562) = barycentric quotient X(i)/X(j) for these {i,j}: {16477, 651}, {29584, 664}
X(48562) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 3716, 4913}, {659, 25666, 48050}, {4724, 31209, 25380}, {44567, 45673, 45328}


X(48563) = X(241)X(514)∩X(513)X(4379)

Barycentrics    (b - c)*(3*a^2 + a*b + a*c + 4*b*c) : :
X(48563) = X[650] - 4 X[4369], 3 X[650] - 4 X[4763], 5 X[650] - 8 X[31286], X[650] + 2 X[43067], 4 X[650] - X[47920], 5 X[650] - 2 X[47962], 7 X[650] - 4 X[48000], 2 X[650] + X[48133], 4 X[3676] - X[47960], 2 X[3676] + X[48276], 4 X[3776] - X[47919], 3 X[4369] - X[4763], 5 X[4369] - 2 X[31286], 2 X[4369] + X[43067], 16 X[4369] - X[47920], 10 X[4369] - X[47962], 7 X[4369] - X[48000], 8 X[4369] + X[48133], 5 X[4763] - 6 X[31286], 2 X[4763] + 3 X[43067], 2 X[4763] - 3 X[47761], 16 X[4763] - 3 X[47920], 10 X[4763] - 3 X[47962], 7 X[4763] - 3 X[48000], 8 X[4763] + 3 X[48133], X[4851] - 4 X[7658], 2 X[21104] + X[48095], 4 X[31286] + 5 X[43067], 4 X[31286] - 5 X[47761], 32 X[31286] - 5 X[47920], 4 X[31286] - X[47962], 14 X[31286] - 5 X[48000], 16 X[31286] + 5 X[48133], 8 X[43067] + X[47920], 5 X[43067] + X[47962], 7 X[43067] + 2 X[48000], 4 X[43067] - X[48133], 8 X[47761] - X[47920], 5 X[47761] - X[47962], 7 X[47761] - 2 X[48000], 4 X[47761] + X[48133], 5 X[47920] - 8 X[47962], 7 X[47920] - 16 X[48000], X[47920] + 2 X[48133], X[47960] + 2 X[48276], 7 X[47962] - 10 X[48000], and many others

X(48563) lies on these lines: {2, 47777}, {241, 514}, {513, 4379}, {523, 47758}, {649, 7653}, {661, 31250}, {693, 4790}, {900, 7659}, {918, 47789}, {1639, 28878}, {2487, 45745}, {2516, 47926}, {2526, 36848}, {2529, 48101}, {3798, 48274}, {4025, 48397}, {4106, 4932}, {4394, 47672}, {4453, 28894}, {4750, 4777}, {4762, 47762}, {4776, 4885}, {4778, 47756}, {4782, 48126}, {4789, 28898}, {4802, 47886}, {4820, 4897}, {4874, 28209}, {4940, 26985}, {4944, 28846}, {4977, 47757}, {4979, 23813}, {6084, 47768}, {7655, 47844}, {9508, 28151}, {14475, 28220}, {21204, 28859}, {24924, 47914}, {25666, 47952}, {27013, 47675}, {28147, 44551}, {28161, 45669}, {28175, 48210}, {28213, 48214}, {28840, 45678}, {28851, 47770}, {28855, 47879}, {28886, 45661}, {28902, 47765}, {28910, 30565}, {30835, 48147}, {31207, 47917}, {31287, 47666}, {44567, 47775}, {44902, 47783}, {45663, 47778}, {45691, 48191}, {47676, 48124}, {47802, 48233}, {47823, 48193}, {48190, 48229}

X(48563) = midpoint of X(i) and X(j) for these {i,j}: {693, 47763}, {4379, 31148}, {4453, 47791}, {4776, 7192}, {4789, 47755}, {43067, 47761}, {47762, 47780}
X(48563) = reflection of X(i) in X(j) for these {i,j}: {650, 47761}, {2526, 36848}, {4776, 4885}, {4790, 47763}, {4944, 47788}, {45320, 4379}, {47760, 47779}, {47761, 4369}, {47775, 44567}, {47777, 2}, {47778, 45663}, {47783, 44902}, {47802, 48233}, {47876, 46919}, {47880, 1638}, {47881, 47789}, {48026, 4776}, {48029, 45666}, {48190, 48229}, {48191, 45691}, {48193, 47823}
X(48563) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 43067, 48133}, {650, 48133, 47920}, {3676, 48276, 47960}, {4369, 43067, 650}, {4885, 7192, 48026}, {7192, 27138, 47939}, {26985, 48107, 4940}, {31286, 47962, 650}


X(48564) = X(513)X(47795)∩X(514)X(47799)

Barycentrics    (b - c)*(3*a^3 - a*b^2 + 2*b^2*c - a*c^2 + 2*b*c^2) : :
X(48564) = X[47814] + 3 X[47820], X[650] - 4 X[31288], X[663] + 5 X[24924], X[667] + 2 X[4885], X[693] + 2 X[6050], X[30234] + 2 X[48206], X[905] + 2 X[4874], 4 X[1125] - X[48136], 2 X[2487] + X[4990], 7 X[3624] - X[14349], X[3803] + 2 X[3837], X[4041] - 7 X[31207], 2 X[4369] + X[48099], X[4378] + 2 X[20317], 2 X[4394] + X[48273], 2 X[4401] + X[48089], X[4705] - 4 X[31287], X[7662] + 2 X[14838], 2 X[14837] + X[48290], 2 X[17072] + X[48327], X[17166] + 5 X[31209], 10 X[19862] - X[48027], 2 X[21188] + X[48299], 2 X[21260] - 5 X[31250], 4 X[25666] - X[47956], 13 X[34595] - X[47948], 2 X[34958] + X[48062], 2 X[44561] + X[48234], X[45316] + 2 X[45663]

X(48564) lies on these lines: {2, 8678}, {512, 47761}, {513, 47795}, {514, 47799}, {650, 31288}, {663, 24924}, {667, 4885}, {693, 6050}, {784, 48220}, {810, 24666}, {814, 30234}, {830, 47802}, {905, 4874}, {1125, 48136}, {2487, 4990}, {3309, 47823}, {3624, 14349}, {3803, 3837}, {3900, 47837}, {4041, 31207}, {4160, 48196}, {4369, 48099}, {4378, 20317}, {4394, 48273}, {4401, 48089}, {4705, 31287}, {4944, 29090}, {6002, 47831}, {7662, 14838}, {14077, 47835}, {14419, 23880}, {14837, 48290}, {17072, 24756}, {17166, 31209}, {19862, 48027}, {21181, 29220}, {21188, 48299}, {21260, 31250}, {23882, 47833}, {25666, 47956}, {29021, 48211}, {29037, 47879}, {29047, 48219}, {29051, 47779}, {29070, 45320}, {29142, 47800}, {29170, 48183}, {29198, 45666}, {29232, 47787}, {29246, 48233}, {29260, 48222}, {29288, 47766}, {29324, 45664}, {29344, 45324}, {29354, 47770}, {34595, 47948}, {34958, 48062}, {44561, 47893}, {45316, 45663}, {47762, 47840}, {47796, 47804}, {47805, 47819}, {47889, 48226}

X(48564) = midpoint of X(i) and X(j) for these {i,j}: {2, 47820}, {14419, 47875}, {47762, 47840}, {47795, 47818}, {47796, 47804}, {47805, 47819}, {47889, 48226}, {47893, 48234}
X(48564) = reflection of X(i) in X(j) for these {i,j}: {47802, 48218}, {47893, 44561}
X(48564) = complement of X(47814)


X(48565) = X(513)X(26078)∩X(514)X(1635)

Barycentrics    (b - c)*(2*a^3 + 2*a^2*b + 2*a^2*c - a*b*c + b^2*c + b*c^2) : :
X(48565) = X[44550] - 4 X[45313], 2 X[649] + X[4391], 4 X[667] - X[47729], X[693] + 2 X[4063], 2 X[905] - 5 X[27013], 2 X[1019] + X[4462], 2 X[1577] + X[4380], X[1577] + 2 X[48011], X[4380] - 4 X[48011], 2 X[1734] + X[47697], X[2533] + 2 X[4782], 4 X[2533] - X[47721], 8 X[4782] + X[47721], X[3762] + 2 X[48064], 2 X[3803] + X[21302], 2 X[3835] + X[47935], 2 X[4129] + X[47976], 4 X[4129] - X[48079], 2 X[47976] + X[48079], 4 X[4142] - X[47709], 2 X[4142] + X[48106], X[47709] + 2 X[48106], 2 X[4369] + X[4498], 4 X[4369] - X[4801], 2 X[4498] + X[4801], 4 X[4394] - X[4560], 2 X[4401] + X[4761], X[4790] + 2 X[20317], 2 X[4807] + X[48324], 2 X[4834] + X[48080], 2 X[4932] + X[47918], X[6332] - 4 X[43061], X[7192] + 2 X[47965], 4 X[9508] - X[48510], 2 X[14349] - 5 X[31209], 2 X[14837] + X[48060], 4 X[20517] - X[47692], 4 X[21188] - X[47652], 4 X[21192] - X[47677], 4 X[25380] - X[48122], 4 X[25666] - X[48121], 4 X[31286] - X[48131], 4 X[31287] - X[48128], X[47666] - 4 X[48003], X[47936] + 2 X[48073], X[47939] - 4 X[47997], X[47940] - 4 X[48012], 2 X[47959] + X[48107]

X(48565) lies on these lines: {512, 47804}, {513, 26078}, {514, 1635}, {525, 47771}, {649, 4391}, {659, 29246}, {667, 16158}, {693, 4063}, {826, 48236}, {905, 27013}, {1019, 4462}, {1577, 4380}, {1734, 47697}, {2533, 4782}, {3309, 47805}, {3566, 48231}, {3762, 48064}, {3800, 47798}, {3803, 21302}, {3835, 47935}, {3910, 47767}, {4083, 47820}, {4120, 28493}, {4129, 47976}, {4142, 47709}, {4151, 48237}, {4369, 4498}, {4394, 4560}, {4401, 4761}, {4773, 26732}, {4776, 47794}, {4790, 20317}, {4807, 48324}, {4809, 29208}, {4834, 48080}, {4932, 47918}, {6005, 47817}, {6332, 43061}, {7192, 47965}, {7927, 48223}, {8712, 47761}, {9508, 48510}, {14349, 31209}, {14837, 48060}, {20517, 47692}, {21188, 47652}, {21192, 47677}, {23882, 47776}, {25380, 48122}, {25666, 48121}, {28478, 47766}, {28481, 47808}, {29328, 47872}, {29350, 47818}, {31286, 48131}, {31287, 48128}, {41800, 44435}, {44429, 47837}, {47666, 48003}, {47803, 47840}, {47819, 47823}, {47936, 48073}, {47939, 47997}, {47940, 48012}, {47959, 48107}

X(48565) = reflection of X(i) in X(j) for these {i,j}: {4776, 47794}, {44429, 47837}, {44435, 41800}, {47796, 47761}, {47814, 47835}, {47819, 47823}, {47840, 47803}
X(48565) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1577, 48011, 4380}, {4129, 47976, 48079}, {4142, 48106, 47709}, {4369, 4498, 4801}


X(48566) = X(513)X(47794)∩X(514)X(1635)

Barycentrics    (b - c)*(2*a^3 + 2*a^2*b + 2*a^2*c + b^2*c + b*c^2) : :
X(48566) = 4 X[45313] - X[45671], 2 X[649] + X[1577], 2 X[667] + X[4761], X[693] + 2 X[48011], 2 X[1019] + X[3762], 8 X[2527] + X[4707], 2 X[3835] + X[47976], X[4063] + 2 X[4369], 2 X[4063] + X[4978], 4 X[4369] - X[4978], 2 X[4129] + X[4979], X[4170] + 2 X[4834], X[4170] - 4 X[4874], X[4834] + 2 X[4874], X[4380] + 2 X[4823], X[4391] + 2 X[48064], 4 X[4458] - X[47717], 2 X[4807] + X[48322], 2 X[4932] + X[47959], X[4960] + 2 X[48000], 2 X[4976] + X[47678], X[7192] + 2 X[48003], 4 X[9508] - X[48509], X[14349] - 4 X[31286], 2 X[14838] - 5 X[27013], 4 X[20517] - X[47713], 2 X[20517] + X[48106], X[47713] + 2 X[48106], 2 X[21188] + X[48060], 2 X[21192] + X[47660], 5 X[24924] + X[47935], 4 X[25380] - X[48086], 4 X[25666] - X[48085], 7 X[31207] - X[48121], 5 X[31209] - 2 X[48054], 4 X[31287] - X[48091], 4 X[31288] - X[48123], X[47679] + 2 X[48276], X[47697] + 2 X[48018], X[47977] + 2 X[48073], 2 X[47997] + X[48107]

X(48566) lies on these lines: {512, 47818}, {513, 47794}, {514, 1635}, {525, 47767}, {649, 1577}, {667, 4761}, {693, 48011}, {812, 29485}, {830, 47836}, {1019, 3762}, {2527, 4707}, {2533, 29182}, {3835, 47976}, {4063, 4369}, {4129, 4979}, {4151, 47813}, {4170, 4834}, {4379, 29302}, {4380, 4823}, {4391, 48064}, {4458, 47717}, {4776, 48196}, {4807, 48322}, {4809, 7927}, {4932, 47959}, {4960, 48000}, {4976, 47678}, {6005, 47804}, {7192, 48003}, {9508, 48509}, {14349, 31286}, {14838, 27013}, {15309, 47763}, {20517, 47713}, {21145, 29184}, {21188, 48060}, {21192, 47660}, {23875, 47771}, {23883, 47870}, {24924, 47935}, {25380, 48086}, {25666, 48085}, {28481, 48232}, {28493, 47879}, {29150, 47872}, {29216, 47874}, {29328, 47875}, {29350, 47820}, {29358, 48236}, {31207, 48121}, {31209, 48054}, {31287, 48091}, {31288, 48123}, {42325, 47805}, {47679, 48276}, {47697, 48018}, {47761, 47795}, {47803, 47838}, {47977, 48073}, {47997, 48107}

X(48566) = midpoint of X(47763) and X(47793)
X(48566) = reflection of X(i) in X(j) for these {i,j}: {4776, 48196}, {47795, 47761}, {47816, 47837}, {47838, 47803}
X(48566) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4063, 4369, 4978}, {4834, 4874, 4170}, {20517, 48106, 47713}


X(48567) = X(513)X(30565)∩X(514)X(1635)

Barycentrics    (b - c)*(3*a^2 + b^2 + b*c + c^2) : :
X(48567) = X[47756] - 3 X[47767], X[7192] + 2 X[47890], 3 X[30565] - 2 X[47769], 3 X[30565] - 4 X[47770], X[47769] - 3 X[47771], 2 X[47770] - 3 X[47771], 3 X[4453] - 4 X[47758], X[4453] - 4 X[47768], 2 X[47758] - 3 X[47762], X[47758] - 3 X[47768], 4 X[649] - X[4467], 2 X[649] + X[47660], X[4467] + 2 X[47660], X[693] + 2 X[48060], 4 X[2490] - X[47988], 4 X[2527] - X[3004], 8 X[2527] - 5 X[27013], 2 X[3004] - 5 X[27013], 4 X[2529] - X[43067], 8 X[2529] + X[47663], 2 X[43067] + X[47663], 4 X[2977] - X[47945], 2 X[3239] + X[48067], 4 X[3239] - X[48079], 2 X[48067] + X[48079], 4 X[3676] - X[47651], 2 X[3700] + X[26853], 2 X[3776] + X[48138], 4 X[3798] - X[47677], 2 X[3835] + X[48104], 2 X[4025] + X[47662], 4 X[4369] - X[47652], 2 X[4369] + X[48101], X[47652] + 2 X[48101], X[4380] + 2 X[6590], 4 X[4394] - X[45746], 2 X[4458] + X[48146], 2 X[4468] + X[48107], 4 X[4521] - X[47981], 4 X[4765] - X[47657], 2 X[4790] + X[25259], 2 X[4830] + X[47703], 2 X[4851] - 5 X[26777], 2 X[4932] + X[48094], 2 X[4976] + X[47659], 2 X[4979] + X[44449], 3 X[6544] - 2 X[45315], 2 X[8045] + X[47935], 4 X[11068] - X[47666], 4 X[13246] - X[47702], 3 X[14475] - 4 X[45663], 4 X[17069] - X[47653], X[17494] + 2 X[48276], 4 X[21196] - X[47654], 4 X[21212] - X[47916], 2 X[23729] - 5 X[26985], X[23731] - 4 X[25666], 5 X[24924] + X[48145], 4 X[25380] - X[47943], 3 X[31992] - X[47774], 7 X[31207] - X[47907], 5 X[31209] - 8 X[43061], 5 X[31209] - 2 X[47995], 4 X[43061] - X[47995], 4 X[31286] - X[47958], 4 X[31287] - X[47950], X[47658] + 2 X[48277], X[47661] - 4 X[48008], X[47661] + 2 X[48275], 2 X[48008] + X[48275], X[47676] + 2 X[48095], X[47695] + 2 X[48106], X[47697] + 2 X[48069], 2 X[48016] + X[48266], 2 X[48071] + X[48076], 2 X[48073] + X[48105]

X(48567) lies on these lines: {2, 47756}, {333, 7192}, {513, 30565}, {514, 1635}, {523, 47776}, {649, 824}, {650, 47781}, {661, 10196}, {693, 47789}, {812, 4789}, {900, 47870}, {918, 47763}, {1638, 48156}, {1639, 47759}, {2490, 47988}, {2527, 3004}, {2529, 43067}, {2977, 47945}, {3239, 48067}, {3676, 47651}, {3700, 26853}, {3776, 48138}, {3798, 47677}, {3805, 8027}, {3835, 48104}, {4025, 47662}, {4369, 6545}, {4379, 28882}, {4380, 6590}, {4394, 45746}, {4458, 48146}, {4468, 48107}, {4521, 47981}, {4750, 28863}, {4762, 47791}, {4765, 47657}, {4776, 47766}, {4778, 47810}, {4785, 47874}, {4790, 25259}, {4830, 47703}, {4851, 26777}, {4893, 28859}, {4932, 48094}, {4951, 48505}, {4976, 47659}, {4977, 47775}, {4979, 44449}, {6008, 47790}, {6009, 47869}, {6084, 47780}, {6544, 45315}, {6546, 28840}, {8045, 47935}, {11068, 47666}, {13246, 47702}, {14475, 45663}, {17069, 47653}, {17494, 48276}, {21196, 47654}, {21212, 47916}, {21297, 47788}, {23729, 26985}, {23731, 25666}, {24924, 48145}, {25380, 47943}, {26275, 48158}, {27486, 28894}, {28175, 48241}, {28209, 28602}, {28213, 48245}, {29144, 44433}, {30520, 47755}, {31147, 47879}, {31207, 47907}, {31209, 43061}, {31286, 47958}, {31287, 47950}, {44435, 47761}, {47658, 48277}, {47661, 48008}, {47676, 48095}, {47695, 48106}, {47697, 48069}, {47804, 48161}, {47821, 48231}, {47823, 48159}, {48016, 48266}, {48071, 48076}, {48073, 48105}, {48164, 48232}

X(48567) = midpoint of X(i) and X(j) for these {i,j}: {6545, 48101}, {47763, 47773}, {47789, 48060}
X(48567) = reflection of X(i) in X(j) for these {i,j}: {2, 47767}, {661, 10196}, {693, 47789}, {4453, 47762}, {4776, 47766}, {4951, 48505}, {6545, 4369}, {21297, 47788}, {30565, 47771}, {31131, 48235}, {31147, 47879}, {44435, 47761}, {47652, 6545}, {47759, 1639}, {47762, 47768}, {47769, 47770}, {47775, 47884}, {47781, 650}, {47782, 1635}, {47790, 47881}, {47821, 48231}, {47871, 4379}, {47886, 45313}, {48156, 1638}, {48158, 26275}, {48159, 47823}, {48161, 47804}, {48164, 48232}
X(48567) = anticomplement of X(47756)
X(48567) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 47660, 4467}, {2527, 3004, 27013}, {3239, 48067, 48079}, {4369, 48101, 47652}, {43061, 47995, 31209}, {47769, 47770, 30565}, {47769, 47771, 47770}, {48008, 48275, 47661}


X(48568) = X(513)X(47795)∩X(514)X(1635)

Barycentrics    (b - c)*(2*a^3 + 2*a^2*b + 2*a^2*c + 2*a*b*c + b^2*c + b*c^2) : :
X(48568) = 2 X[31148] + X[45671], 2 X[649] + X[4978], X[693] + 2 X[48064], 2 X[1019] + X[1577], X[1019] + 2 X[4369], X[1577] - 4 X[4369], 4 X[1125] - X[4822], 4 X[2487] - X[48502], X[3762] + 2 X[48144], 2 X[3835] + X[48110], 2 X[4129] - 5 X[24924], 2 X[4129] + X[48149], 5 X[24924] + X[48149], X[4170] + 2 X[4784], 2 X[4367] + X[4761], 2 X[4401] + X[48108], 4 X[4458] - X[47713], X[4801] + 2 X[48011], 2 X[4897] + X[7265], 2 X[4932] + X[14349], X[7192] + 2 X[14838], 8 X[7653] + X[48321], 4 X[9508] - X[48507], 4 X[17069] - X[47679], 4 X[23814] - X[48116], 4 X[25380] - X[47948], 4 X[25666] - X[47947], 5 X[27013] - 2 X[48003], 7 X[31207] - X[47911], 5 X[31209] - 2 X[47997], 4 X[31286] - X[47959], 4 X[31287] - X[47955], 4 X[31288] - X[48024], X[47697] + 2 X[48075], X[47717] + 2 X[48106], 2 X[48054] + X[48107], 2 X[48073] + X[48111], 2 X[48074] + X[48079]

X(48568) lies on these lines: {2, 15309}, {513, 47795}, {514, 1635}, {649, 4978}, {667, 29246}, {693, 29270}, {812, 29803}, {830, 47824}, {1019, 1577}, {1125, 4822}, {2487, 48502}, {2533, 29268}, {3762, 48144}, {3835, 48110}, {4129, 24924}, {4160, 47836}, {4170, 4784}, {4367, 4761}, {4379, 29013}, {4401, 48108}, {4444, 43527}, {4458, 47713}, {4750, 23879}, {4776, 48218}, {4801, 48011}, {4809, 29168}, {4897, 7265}, {4932, 14349}, {6005, 47820}, {6006, 45686}, {6372, 47817}, {7192, 14838}, {7653, 48321}, {8714, 47813}, {9508, 48507}, {17069, 47679}, {21145, 29138}, {23814, 48116}, {23875, 47755}, {24920, 47842}, {25380, 47948}, {25666, 47947}, {27013, 48003}, {29070, 48253}, {29150, 47833}, {29158, 47887}, {29170, 47875}, {31207, 47911}, {31209, 47997}, {31286, 47959}, {31287, 47955}, {31288, 48024}, {47697, 48075}, {47717, 48106}, {47761, 47794}, {47763, 47796}, {47816, 47823}, {48054, 48107}, {48073, 48111}, {48074, 48079}

X(48568) = midpoint of X(47763) and X(47796)
X(48568) = reflection of X(i) in X(j) for these {i,j}: {4776, 48218}, {47794, 47761}, {47816, 47823}, {47842, 24920}
X(48568) = crosspoint of X(799) and X(30598)
X(48568) = crossdifference of every pair of points on line {2177, 3725}
X(48568) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1019, 4369, 1577}, {24924, 48149, 4129}


X(48569) = X(513)X(47795)∩X(514)X(47823)

Barycentrics    (b - c)*(a^3 + a^2*b - a*b^2 + a^2*c + a*b*c + b^2*c - a*c^2 + b*c^2) : :
X(48569) = 2 X[10] + X[48323], 3 X[47795] - X[47838], 2 X[47838] - 3 X[47839], 3 X[47823] - X[47835], 2 X[47835] - 3 X[47837], X[649] + 2 X[23815], X[659] + 2 X[23789], X[667] + 2 X[24720], 4 X[905] - X[48288], X[1019] + 2 X[3837], 4 X[1125] - X[48336], 5 X[1698] - 2 X[48501], 2 X[1734] + X[48291], 2 X[2254] + X[48305], X[2530] + 2 X[4369], X[2533] + 2 X[3960], X[4063] + 2 X[48506], 2 X[4129] - 5 X[30795], X[4378] + 2 X[17072], X[4705] - 4 X[25380], X[4724] - 4 X[31288], 2 X[4807] + X[21343], 2 X[4874] + X[4905], 4 X[4885] - X[48267], X[4978] + 2 X[9508], X[7192] + 2 X[48059], 2 X[14838] + X[21146], 4 X[19947] - X[48131], 2 X[21051] + X[48320], 2 X[21260] + X[48144], X[21302] + 2 X[48328], X[24719] + 2 X[48064], 5 X[24924] + X[48151], 4 X[25666] - X[47949], 7 X[31207] - X[47929], 4 X[31287] - X[47966], 2 X[48018] + X[48301], 2 X[48073] + X[48351]

X(48569) lies on these lines: {2, 6372}, {10, 48323}, {512, 47796}, {513, 47795}, {514, 47823}, {525, 48245}, {649, 23815}, {659, 23789}, {667, 24720}, {784, 4379}, {826, 4453}, {830, 36848}, {891, 47836}, {905, 48288}, {1019, 3837}, {1125, 48336}, {1638, 29142}, {1698, 48501}, {1734, 48291}, {2254, 48305}, {2530, 4369}, {2533, 3960}, {3800, 48249}, {4063, 48506}, {4129, 30795}, {4151, 47889}, {4378, 17072}, {4705, 25380}, {4724, 31288}, {4728, 29150}, {4750, 29106}, {4807, 21343}, {4874, 4905}, {4885, 48267}, {4978, 9508}, {6004, 47820}, {6005, 47841}, {6545, 29098}, {7192, 48059}, {7927, 48252}, {7950, 48241}, {8672, 48246}, {8714, 47833}, {14413, 29298}, {14419, 29051}, {14838, 21146}, {19947, 48131}, {21051, 48320}, {21204, 29118}, {21260, 48144}, {21302, 48328}, {24719, 48064}, {24924, 48151}, {25666, 47949}, {29013, 48184}, {29021, 48227}, {29047, 48235}, {29070, 47812}, {29164, 48224}, {29168, 47797}, {29170, 48198}, {29198, 47794}, {29288, 30724}, {29354, 47809}, {31207, 47929}, {31287, 47966}, {47762, 47819}, {47779, 47875}, {47822, 48218}, {48018, 48301}, {48073, 48351}

X(48569) = midpoint of X(i) and X(j) for these {i,j}: {30724, 48232}, {47762, 47819}, {47796, 47824}, {47889, 48244}, {47893, 48253}
X(48569) = reflection of X(i) in X(j) for these {i,j}: {47794, 48216}, {47822, 48218}, {47837, 47823}, {47839, 47795}, {47875, 47779}
X(48569) = barycentric product X(514)*X(32940)
X(48569) = barycentric quotient X(32940)/X(190)


X(48570) = X(513)X(26144)∩X(514)X(1635)

Barycentrics    (b - c)*(2*a^3 + 2*a^2*b + 2*a^2*c + 3*a*b*c + b^2*c + b*c^2) : :
X(48570) = 2 X[31148] + X[44550], 2 X[649] + X[4801], 2 X[667] + X[48108], X[693] + 2 X[1019], 2 X[905] + X[7192], 4 X[1125] - X[48081], 2 X[3835] + X[48149], 4 X[4367] - X[47729], 4 X[4369] - X[4391], 2 X[4369] + X[48144], X[4391] + 2 X[48144], X[4380] + 2 X[4978], X[4380] - 4 X[48064], X[4978] + 2 X[48064], 4 X[4401] - X[47974], 4 X[4458] - X[47709], X[4462] + 2 X[48320], X[4560] + 2 X[43067], X[4761] + 2 X[48343], 2 X[4905] + X[47697], 2 X[4932] + X[48131], 4 X[6050] - X[47969], 8 X[7653] + X[21222], 2 X[8045] + X[47971], 2 X[14349] + X[48107], 4 X[14838] - X[47666], 4 X[23789] - X[47685], 4 X[25380] - X[47912], 4 X[25666] - X[47911], 5 X[27013] - 2 X[47965], 5 X[31209] - 2 X[47959], 4 X[31286] - X[47918], 4 X[31287] - X[47915], 4 X[31288] - X[47949], 4 X[44561] - X[47774], X[47939] - 4 X[48054], X[47940] - 4 X[48066], 2 X[48073] + X[48150], X[48079] + 2 X[48110]

X(48570) lies on these lines: {513, 26144}, {514, 1635}, {525, 47755}, {649, 4801}, {667, 48108}, {693, 1019}, {814, 48253}, {905, 7192}, {1125, 48081}, {3835, 48149}, {4367, 29366}, {4369, 4391}, {4379, 6002}, {4380, 4978}, {4401, 47974}, {4458, 47709}, {4462, 48320}, {4560, 43067}, {4761, 48343}, {4776, 15309}, {4905, 47697}, {4932, 48131}, {6050, 47969}, {6372, 47804}, {7653, 21222}, {8045, 47971}, {8678, 47824}, {8714, 48237}, {14349, 48107}, {14838, 47666}, {23789, 47685}, {23882, 47780}, {25380, 47912}, {25666, 47911}, {27013, 47965}, {29118, 47887}, {29162, 47891}, {29168, 48223}, {29170, 47833}, {29182, 47721}, {29198, 47815}, {29328, 47889}, {29354, 48236}, {31209, 47959}, {31286, 47918}, {31287, 47915}, {31288, 47949}, {44561, 47774}, {47761, 47793}, {47814, 47823}, {47939, 48054}, {47940, 48066}, {48073, 48150}, {48079, 48110}

X(48570) = reflection of X(i) in X(j) for these {i,j}: {4776, 47795}, {47793, 47761}, {47814, 47823}
X(48570) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4369, 48144, 4391}, {4978, 48064, 4380}


X(48571) = X(239)X(514)∩X(513)X(48156)

Barycentrics    (b - c)*(-a^2 - a*b + 2*b^2 - a*c - b*c + 2*c^2) : :
X(48571) = 3 X[2] - 4 X[1638], 5 X[2] - 4 X[1639], 7 X[2] - 8 X[44902], 9 X[2] - 8 X[45326], 5 X[1638] - 3 X[1639], 2 X[1638] - 3 X[4453], 7 X[1638] - 6 X[44902], 3 X[1638] - 2 X[45326], 8 X[1638] - 3 X[47772], 2 X[1639] - 5 X[4453], 6 X[1639] - 5 X[30565], 7 X[1639] - 10 X[44902], 9 X[1639] - 10 X[45326], 8 X[1639] - 5 X[47772], 3 X[4453] - X[30565], 7 X[4453] - 4 X[44902], 9 X[4453] - 4 X[45326], 4 X[4453] - X[47772], 7 X[30565] - 12 X[44902], 3 X[30565] - 4 X[45326], 4 X[30565] - 3 X[47772], 9 X[44902] - 7 X[45326], 16 X[44902] - 7 X[47772], 16 X[45326] - 9 X[47772], 4 X[3798] - X[47663], 5 X[4025] - 2 X[4765], 4 X[4025] - X[17494], 2 X[4025] + X[47676], 2 X[4707] + X[21222], 5 X[4750] - 3 X[14435], 3 X[4750] - 2 X[45679], 8 X[4765] - 5 X[17494], 4 X[4765] - 5 X[27486], 4 X[4765] + 5 X[47676], 2 X[4932] + X[47923], X[7192] + 2 X[16892], 2 X[7192] + X[47653], 9 X[14435] - 10 X[45679], 6 X[14435] - 5 X[47776], 4 X[16892] - X[47653], X[17494] + 2 X[47676], 4 X[45679] - 3 X[47776], 2 X[4728] - 3 X[6548], 2 X[48158] - 3 X[48203], X[48158] - 3 X[48241], 3 X[48203] - 4 X[48224], and many others

X(48571) lies on these lines: {2, 918}, {149, 900}, {239, 514}, {335, 4080}, {513, 48156}, {522, 47869}, {661, 28871}, {693, 4820}, {812, 21115}, {824, 47780}, {926, 4430}, {1025, 4552}, {1635, 28890}, {2610, 31037}, {2785, 30573}, {2786, 6545}, {3004, 28902}, {3676, 25259}, {3776, 20295}, {4120, 21204}, {4369, 47930}, {4379, 30519}, {4467, 21104}, {4468, 27115}, {4608, 47673}, {4661, 42341}, {4763, 31992}, {4776, 47754}, {4777, 21146}, {4784, 47688}, {4789, 47891}, {4790, 47651}, {4897, 26853}, {6009, 20092}, {6366, 39357}, {6546, 45674}, {7226, 24462}, {7659, 47692}, {14475, 45661}, {16727, 16732}, {17069, 26777}, {17155, 20525}, {17161, 47672}, {17483, 46401}, {21183, 47790}, {21212, 48082}, {23875, 47796}, {25666, 48112}, {26798, 44449}, {27013, 48094}, {27138, 48270}, {28169, 47703}, {28209, 47968}, {28220, 47974}, {28846, 44435}, {28851, 47775}, {28855, 47774}, {28863, 31148}, {28878, 47781}, {28906, 31147}, {28910, 47880}, {29078, 48170}, {29204, 48254}, {29252, 47840}, {29354, 47836}, {30520, 47762}, {30577, 44009}, {31209, 48087}, {31286, 48117}, {43067, 47659}, {47657, 48133}, {47757, 47769}, {47758, 47771}, {47809, 48245}, {47821, 48195}, {47823, 48171}, {47824, 48208}, {47887, 48172}, {47907, 48071}, {47943, 48014}, {47960, 48107}

X(48571) = midpoint of X(27486) and X(47676)
X(48571) = reflection of X(i) in X(j) for these {i,j}: {2, 4453}, {4120, 21204}, {4468, 46919}, {4776, 47754}, {4789, 47891}, {6546, 45674}, {17494, 27486}, {21297, 6545}, {25259, 47787}, {27486, 4025}, {30565, 1638}, {46915, 47894}, {47759, 44435}, {47763, 47755}, {47769, 47757}, {47771, 47758}, {47772, 2}, {47773, 47762}, {47775, 47886}, {47776, 4750}, {47787, 3676}, {47790, 21183}, {47792, 47780}, {47809, 48245}, {47821, 48227}, {47870, 4379}, {48158, 48224}, {48171, 47823}, {48172, 47887}, {48203, 48241}, {48208, 47824}
X(48571) = anticomplement of X(30565)
X(48571) = anticomplement of the isotomic conjugate of X(37143)
X(48571) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1308, 69}, {34578, 21293}, {35171, 315}, {37143, 6327}
X(48571) = X(37143)-Ceva conjugate of X(2)
X(48571) = crosspoint of X(274) and X(35171)
X(48571) = crosssum of X(213) and X(8645)
X(48571) = crossdifference of every pair of points on line {42, 38365}
X(48571) = barycentric product X(i)*X(j) for these {i,j}: {514, 17297}, {3261, 5030}
X(48571) = barycentric quotient X(i)/X(j) for these {i,j}: {5030, 101}, {17297, 190}
X(48571) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1638, 30565, 2}, {3676, 25259, 26985}, {3776, 47971, 20295}, {4025, 47676, 17494}, {4453, 30565, 1638}, {4467, 21104, 26824}, {4897, 47652, 26853}, {7192, 16892, 47653}, {43067, 47677, 47659}, {48158, 48224, 48203}, {48158, 48241, 48224}


X(48572) = X(44)X(513)∩X(514)X(8643)

Barycentrics    a*(b - c)*(3*a^2 - a*b - a*c - 4*b*c) : :
X(48572) = X[649] - 4 X[659], X[649] + 2 X[4724], 5 X[649] - 8 X[4782], 7 X[649] - 4 X[4784], 2 X[650] + X[48032], 2 X[659] + X[4724], 5 X[659] - 2 X[4782], 7 X[659] - X[4784], 5 X[4724] + 4 X[4782], 7 X[4724] + 2 X[4784], 14 X[4782] - 5 X[4784], X[4813] - 4 X[48029], 3 X[4893] - 2 X[47810], X[47810] - 3 X[47811], 5 X[663] - 2 X[48333], 7 X[663] - 4 X[48347], 7 X[48333] - 10 X[48347], 2 X[667] + X[47929], 4 X[667] - X[48341], 2 X[47929] + X[48341], 2 X[905] + X[47936], 2 X[3004] + X[48105], 4 X[3716] - X[4382], 2 X[3803] + X[47918], 2 X[4040] + X[4498], 4 X[4040] - X[48338], 2 X[4498] + X[48338], X[4063] + 2 X[48065], 2 X[4063] + X[48367], 4 X[48065] - X[48367], 2 X[4369] + X[47974], 2 X[4378] - 5 X[8656], 2 X[4401] + X[47970], 4 X[4401] - X[48144], 2 X[47970] + X[48144], X[4449] - 4 X[48331], 2 X[4794] + X[21385], X[4814] + 2 X[6161], 2 X[4830] + X[48080], 4 X[4874] - X[48119], 4 X[4885] - X[48115], 4 X[6050] - X[48151], 3 X[6544] - 2 X[47806], X[7192] + 2 X[48009], 4 X[8689] - X[47694], 8 X[8689] + X[47926], 2 X[47694] + X[47926], 2 X[11068] + X[48014], 4 X[13246] - X[47676], 2 X[14838] + X[47977], X[16892] + 2 X[48061], X[17494] + 2 X[48063], 4 X[24720] - 7 X[31207], 4 X[25666] - X[47685], 5 X[26777] - 2 X[48017], X[26853] + 2 X[48037], 5 X[27013] - 2 X[48073], X[48142] - 4 X[48248], 2 X[47969] + X[48141], 5 X[30835] - 2 X[46403], X[31147] - 4 X[45673], 3 X[31992] - X[48169], 2 X[43067] + X[47933], X[47697] + 2 X[48000], 2 X[47701] + X[48138], X[47702] + 2 X[48095], 2 X[47890] + X[47972], X[47907] - 4 X[47998], X[47908] - 4 X[48001], X[47911] - 4 X[48004], 2 X[47921] + X[48322], X[47923] + 2 X[48102], 2 X[47962] + X[48153], 2 X[47965] + X[48150], 2 X[48003] + X[48111], 2 X[48006] + X[48101], 4 X[48055] - X[48117], 4 X[48058] - X[48121]

X(48572) lies on these lines: {44, 513}, {514, 8643}, {522, 3158}, {663, 891}, {667, 47929}, {905, 47936}, {3004, 48105}, {3667, 47769}, {3716, 4382}, {3803, 47918}, {4040, 4498}, {4063, 48065}, {4369, 47974}, {4375, 48172}, {4378, 8656}, {4379, 47804}, {4401, 47970}, {4448, 29362}, {4449, 25569}, {4778, 47758}, {4794, 21385}, {4802, 48251}, {4814, 6161}, {4830, 48080}, {4874, 48119}, {4885, 48115}, {4962, 48008}, {4977, 48227}, {6050, 48151}, {6544, 47806}, {6545, 47800}, {7192, 48009}, {8056, 21173}, {8689, 28147}, {10196, 47808}, {11068, 48014}, {13246, 47676}, {14838, 47977}, {16892, 48061}, {17494, 28161}, {24720, 31207}, {25666, 47685}, {26275, 47887}, {26277, 47780}, {26777, 48017}, {26853, 48037}, {27013, 48073}, {28175, 48142}, {28213, 47927}, {28225, 47763}, {28229, 47969}, {28882, 48161}, {29051, 47815}, {29186, 47817}, {30835, 46403}, {31147, 45673}, {31992, 48169}, {36848, 48214}, {43067, 47933}, {45314, 47823}, {45666, 48184}, {47697, 48000}, {47701, 48138}, {47702, 48095}, {47778, 48164}, {47803, 47812}, {47831, 48170}, {47890, 47972}, {47907, 47998}, {47908, 48001}, {47911, 48004}, {47921, 48322}, {47923, 48102}, {47962, 48153}, {47965, 48150}, {48003, 48111}, {48006, 48101}, {48055, 48117}, {48058, 48121}, {48167, 48197}

X(48572) = reflection of X(i) in X(j) for these {i,j}: {4379, 47804}, {4449, 25569}, {4893, 47811}, {6545, 47800}, {25569, 48331}, {31147, 47821}, {36848, 48214}, {47808, 10196}, {47812, 47803}, {47821, 45673}, {47823, 45314}, {47828, 48226}, {47832, 4448}, {47887, 26275}, {48160, 48194}, {48164, 47778}, {48167, 48197}, {48170, 47831}, {48184, 45666}
X(48572) = crossdifference of every pair of points on line {1, 23649}
X(48572) = barycentric product X(513)*X(16833)
X(48572) = barycentric quotient X(16833)/X(668)
X(48572) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {659, 4724, 649}, {667, 47929, 48341}, {4040, 4498, 48338}, {4063, 48065, 48367}, {4401, 47970, 48144}


X(48573) = X(513)X(47794)∩X(514)X(30574)

Barycentrics    (b - c)*(a^3 + 2*a^2*b - a*b^2 + 2*a^2*c + b^2*c - a*c^2 + b*c^2) : :
X(48573) = X[8] + 2 X[48343], 2 X[10] + X[48144], 3 X[47795] - 2 X[47841], 3 X[47823] - X[47841], 2 X[905] + X[4761], X[1019] + 2 X[17072], 4 X[1125] - X[48338], X[1734] + 2 X[4369], 2 X[2533] + X[48321], 4 X[3676] - X[47716], 2 X[3837] + X[4834], 2 X[4025] + X[47711], X[4040] - 4 X[31286], X[4063] + 2 X[24720], 2 X[4147] + X[48320], X[4170] - 4 X[4885], 2 X[4401] - 5 X[27013], X[4449] + 2 X[4807], X[4498] + 2 X[23789], X[4729] + 2 X[48295], X[4784] + 2 X[21260], 2 X[4806] - 5 X[31251], 2 X[4932] + X[47948], X[4960] + 2 X[48010], X[7192] + 2 X[48012], X[14349] - 4 X[25380], 4 X[21188] - X[47712], 2 X[21188] + X[48069], X[47712] + 2 X[48069], 2 X[21192] + X[47690], X[21301] + 2 X[48064], 4 X[25666] - X[48081], 7 X[31207] - X[48367], 5 X[31209] - 2 X[48058], 4 X[31288] - X[48336], 2 X[43067] + X[48507], X[46403] + 2 X[48011], X[47694] + 2 X[48018], X[47970] + 2 X[48073], X[47976] + 2 X[48050], 2 X[48003] + X[48108]

X(48573) lies on these lines: {2, 6005}, {8, 48343}, {10, 48144}, {512, 47795}, {513, 47794}, {514, 30574}, {525, 48232}, {649, 23791}, {784, 48244}, {826, 48235}, {830, 47762}, {900, 47875}, {905, 4761}, {1019, 17072}, {1125, 48338}, {1635, 29186}, {1638, 3800}, {1734, 4369}, {2533, 48321}, {3309, 47761}, {3676, 47716}, {3837, 4834}, {3887, 47820}, {4025, 47711}, {4040, 31286}, {4063, 24720}, {4147, 48320}, {4151, 4379}, {4170, 4885}, {4401, 27013}, {4449, 4807}, {4453, 29047}, {4498, 23789}, {4729, 48295}, {4750, 29062}, {4784, 21260}, {4806, 31251}, {4932, 47948}, {4960, 48010}, {4961, 21297}, {6372, 47835}, {7192, 48012}, {7927, 48227}, {14349, 25380}, {14419, 29366}, {14431, 29170}, {15309, 47814}, {21052, 29148}, {21188, 47712}, {21192, 47690}, {21301, 48064}, {21390, 22443}, {23875, 47809}, {25666, 48081}, {29021, 48252}, {29142, 48249}, {29164, 48254}, {29200, 48217}, {29252, 48185}, {29260, 48241}, {29288, 48245}, {29302, 47812}, {29350, 47796}, {29358, 48208}, {31207, 48367}, {31209, 48058}, {31288, 48336}, {42325, 47804}, {43067, 48507}, {46403, 48011}, {47694, 48018}, {47821, 48196}, {47839, 48216}, {47840, 48218}, {47888, 48229}, {47970, 48073}, {47976, 48050}, {48003, 48108}

X(48573) = midpoint of X(47824) and X(47836)
X(48573) = reflection of X(i) in X(j) for these {i,j}: {47794, 47837}, {47795, 47823}, {47818, 47761}, {47821, 48196}, {47838, 2}, {47839, 48216}, {47840, 48218}, {47888, 48229}
X(48573) = crosspoint of X(5936) and X(8050)
X(48573) = {X(21188),X(48069)}-harmonic conjugate of X(47712)


X(48574) = X(239)X(514)∩X(513)X(1638)

Barycentrics    (b - c)*(-5*a^2 - 2*a*b + b^2 - 2*a*c - 2*b*c + c^2) : :
X(48574) = 2 X[3798] + X[7192], 4 X[3798] - X[45745], 10 X[3798] - X[47667], X[4025] + 2 X[4932], 2 X[4765] + X[48141], 3 X[4786] - 2 X[45679], 2 X[7192] + X[45745], 5 X[7192] + X[47667], 5 X[27486] - X[47667], 5 X[45745] - 2 X[47667], 5 X[1638] - 3 X[47756], 4 X[1638] - 3 X[47757], 2 X[1638] - 3 X[47758], 4 X[47756] - 5 X[47757], 2 X[47756] - 5 X[47758], 4 X[2487] - X[48026], 4 X[2527] - X[48087], 2 X[3676] + X[4979], X[3700] - 4 X[7653], 2 X[3776] + X[48067], 2 X[4369] + X[48013], 4 X[4369] - X[48269], 2 X[48013] + X[48269], 4 X[4521] - X[48076], 2 X[4784] + X[47123], 2 X[4790] + X[48398], X[4813] - 4 X[7658], 2 X[4850] + X[7649], 2 X[4897] + X[6590], 2 X[14837] + X[48149], 2 X[21188] + X[48110], 4 X[21212] - X[47981], 2 X[21212] + X[48071], X[47981] + 2 X[48071], 4 X[25666] - X[48034], X[30565] - 3 X[47762], 2 X[30565] - 3 X[47766], 4 X[31286] - X[48038], 4 X[43061] - X[48082], 2 X[45326] - 3 X[47761], 4 X[45326] - 3 X[47765]

X(48574) lies on these lines: {2, 47764}, {239, 514}, {513, 1638}, {522, 31148}, {650, 28902}, {661, 46919}, {900, 7659}, {918, 47768}, {1635, 28878}, {2487, 48026}, {2527, 48087}, {2786, 47789}, {3667, 4379}, {3676, 4979}, {3700, 7653}, {3776, 48067}, {4369, 28867}, {4468, 28871}, {4521, 48076}, {4728, 6006}, {4763, 28886}, {4776, 30765}, {4778, 47886}, {4784, 47123}, {4785, 21183}, {4790, 48398}, {4802, 45669}, {4813, 7658}, {4850, 7649}, {4897, 6590}, {6008, 47891}, {14475, 48042}, {14837, 48149}, {21188, 48110}, {21212, 47981}, {25666, 48034}, {28209, 47880}, {28217, 45320}, {28225, 44551}, {28840, 47785}, {28846, 30565}, {28855, 45313}, {28910, 47884}, {30724, 43932}, {31286, 48038}, {43061, 48082}, {44432, 47759}, {45326, 47761}, {45674, 47783}, {47779, 47786}, {47982, 48032}

X(48574) = midpoint of X(i) and X(j) for these {i,j}: {7192, 27486}, {47755, 47763}, {47787, 48013}
X(48574) = reflection of X(i) in X(j) for these {i,j}: {661, 46919}, {27486, 3798}, {45745, 27486}, {47757, 47758}, {47759, 44432}, {47764, 2}, {47765, 47761}, {47766, 47762}, {47783, 45674}, {47786, 47779}, {47787, 4369}, {48269, 47787}
X(48574) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3798, 7192, 45745}, {4369, 48013, 48269}, {21212, 48071, 47981}


X(48575) = X(513)X(4763)∩X(514)X(30574)

Barycentrics    (b - c)*(2*a^3 + 3*a^2*b - 3*a*b^2 + 3*a^2*c - a*b*c + b^2*c - 3*a*c^2 + b*c^2) : :
X(48575) = X[45313] + 2 X[45328], X[45673] - 4 X[45691], 3 X[47778] - 4 X[47829], 5 X[47778] - 4 X[48180], X[47778] - 4 X[48229], 2 X[47829] - 3 X[47830], 5 X[47829] - 3 X[48180], X[47829] - 3 X[48229], 5 X[47830] - 2 X[48180], X[48180] - 5 X[48229], 3 X[47824] + X[47825], X[47825] - 3 X[47828], 3 X[47779] - 2 X[47833], 5 X[47779] - 2 X[48189], X[47779] + 2 X[48244], 3 X[47823] - X[47833], 5 X[47823] - X[48189], 5 X[47833] - 3 X[48189], X[47833] + 3 X[48244], X[48189] + 5 X[48244], 2 X[649] + X[48042], 4 X[650] - X[48009], 2 X[650] + X[48073], X[48009] + 2 X[48073], 2 X[1491] + X[4932], 4 X[1491] - X[47985], 2 X[4932] + X[47985], X[2254] + 2 X[31286], 2 X[2254] + X[48063], 4 X[31286] - X[48063], 2 X[2487] + X[4925], X[3835] - 4 X[25380], 2 X[4369] + X[48017], 2 X[4784] + X[48041], 2 X[4913] + X[48399], X[7659] + 2 X[25666], 2 X[7659] + X[48037], 4 X[25666] - X[48037], 2 X[9508] + X[24720], 4 X[9508] - X[48008], 2 X[24720] + X[48008], 2 X[21212] + X[48069], X[47984] - 4 X[48030], X[48016] + 2 X[48050], 2 X[48027] + X[48071]

X(48575) lies on these lines: {2, 3667}, {43, 43924}, {513, 4763}, {514, 30574}, {522, 4809}, {649, 48042}, {650, 48009}, {824, 48232}, {900, 47831}, {1491, 4932}, {2254, 31286}, {2487, 4925}, {2786, 47806}, {2787, 17072}, {3136, 39508}, {3835, 25380}, {4057, 16059}, {4191, 39225}, {4196, 16231}, {4212, 7649}, {4369, 48017}, {4379, 28161}, {4750, 47808}, {4777, 48233}, {4778, 47827}, {4784, 48041}, {4785, 44429}, {4893, 28225}, {4913, 48399}, {4926, 48206}, {4948, 28191}, {4962, 47832}, {4977, 48213}, {6006, 47822}, {6821, 44444}, {7659, 25666}, {9508, 24720}, {21212, 48069}, {26102, 42312}, {28147, 48225}, {28155, 47780}, {28169, 48238}, {28183, 48221}, {28209, 48194}, {28213, 48191}, {28217, 48197}, {28221, 48202}, {28229, 48176}, {28521, 30234}, {28840, 48193}, {30519, 47809}, {31148, 48175}, {44316, 47514}, {45663, 48220}, {47886, 48252}, {47984, 48030}, {48016, 48050}, {48027, 48071}

X(48575) = midpoint of X(i) and X(j) for these {i,j}: {649, 48164}, {2254, 47804}, {4379, 48242}, {4750, 47808}, {31148, 48175}, {47823, 48244}, {47824, 47828}, {47886, 48252}, {48225, 48253}
X(48575) = reflection of X(i) in X(j) for these {i,j}: {3835, 47802}, {45673, 48214}, {47778, 47830}, {47779, 47823}, {47802, 25380}, {47804, 31286}, {47830, 48229}, {47831, 48216}, {48042, 48164}, {48063, 47804}, {48214, 45691}, {48220, 45663}
X(48575) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 48073, 48009}, {1491, 4932, 47985}, {2254, 31286, 48063}, {7659, 25666, 48037}, {9508, 24720, 48008}


X(48576) = X(239)X(514)∩X(513)X(1639)

Barycentrics    (b - c)*(7*a^2 + 2*a*b + b^2 + 2*a*c + 2*b*c + c^2) : :
X(48576) = 5 X[649] - 2 X[4765], 7 X[649] - X[4988], 11 X[649] - 8 X[14351], 5 X[649] - 3 X[14435], 4 X[649] - X[45745], 14 X[4765] - 5 X[4988], 11 X[4765] - 20 X[14351], 2 X[4765] - 3 X[14435], 8 X[4765] - 5 X[45745], 2 X[4932] + X[48060], 11 X[4988] - 56 X[14351], 5 X[4988] - 21 X[14435], 4 X[4988] - 7 X[45745], 40 X[14351] - 33 X[14435], 32 X[14351] - 11 X[45745], 12 X[14435] - 5 X[45745], X[47755] - 3 X[47763], 8 X[1639] - 5 X[47764], 6 X[1639] - 5 X[47765], 4 X[1639] - 5 X[47766], 3 X[1639] - 5 X[47767], 2 X[1639] - 5 X[47768], 3 X[47764] - 4 X[47765], 3 X[47764] - 8 X[47767], X[47764] - 4 X[47768], 2 X[47765] - 3 X[47766], X[47765] - 3 X[47768], 3 X[47766] - 4 X[47767], 2 X[47767] - 3 X[47768], 5 X[4790] + X[4820], 2 X[4790] + X[6590], 2 X[4820] - 5 X[6590], 4 X[2487] - X[47950], 4 X[2527] - X[48026], 4 X[2529] - X[3700], 2 X[3676] + X[48104], 2 X[4369] + X[48067], 4 X[4521] - X[48019], X[4813] - 3 X[6544], X[4813] - 4 X[43061], 3 X[6544] - 4 X[43061], 2 X[4979] + X[48269], 4 X[7653] - X[23729], 4 X[7658] - X[23731], 2 X[11068] + X[48107], 4 X[25666] - X[47978], 4 X[31286] - X[47981], 2 X[47754] - 3 X[47758], 2 X[48016] + X[48268], X[48038] + 2 X[48071]

X(48576) lies on these lines: {239, 514}, {513, 1639}, {650, 28209}, {900, 4790}, {1635, 4778}, {2487, 47950}, {2527, 48026}, {2529, 3700}, {3676, 48104}, {4369, 48067}, {4394, 28220}, {4468, 28886}, {4521, 48019}, {4773, 4802}, {4777, 48276}, {4785, 47789}, {4813, 6544}, {4893, 28225}, {4944, 39386}, {4962, 47873}, {4976, 28151}, {4977, 47883}, {4979, 6006}, {4984, 28161}, {6009, 43067}, {7653, 23729}, {7658, 23731}, {11068, 48107}, {25666, 47978}, {28169, 48275}, {28217, 47881}, {28229, 47878}, {28859, 47785}, {28910, 47890}, {31286, 47981}, {45313, 47783}, {47754, 47758}, {47757, 47762}, {47882, 47995}, {47891, 48398}, {48016, 48268}, {48038, 48071}

X(48576) = midpoint of X(4979) and X(47874)
X(48576) = reflection of X(i) in X(j) for these {i,j}: {47757, 47762}, {47764, 47766}, {47765, 47767}, {47766, 47768}, {47783, 45313}, {47876, 4394}, {47894, 3798}, {47995, 47882}, {48269, 47874}, {48398, 47891}
X(48576) = crossdifference of every pair of points on line {42, 6767}
X(48576) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47765, 47767, 47766}, {47765, 47768, 47767}


X(48577) = X(239)X(514)∩X(513)X(4379)

Barycentrics    (b - c)*(3*a^2 + 2*a*b + 2*a*c + 2*b*c) : :
X(48577) = X[649] - 4 X[4932], X[649] + 2 X[7192], 5 X[649] - 2 X[17494], 3 X[649] - 2 X[47776], 4 X[649] - X[47926], 7 X[649] - 4 X[48008], 2 X[649] + X[48141], 4 X[3798] - X[4988], 2 X[4932] + X[7192], 10 X[4932] - X[17494], 6 X[4932] - X[47776], 16 X[4932] - X[47926], 7 X[4932] - X[48008], 8 X[4932] + X[48141], X[4960] + 2 X[48064], 5 X[7192] + X[17494], 3 X[7192] + X[47776], 8 X[7192] + X[47926], 7 X[7192] + 2 X[48008], 4 X[7192] - X[48141], X[17494] - 5 X[47763], 3 X[17494] - 5 X[47776], 8 X[17494] - 5 X[47926], 7 X[17494] - 10 X[48008], 4 X[17494] + 5 X[48141], 2 X[47676] + X[48138], 3 X[47763] - X[47776], 8 X[47763] - X[47926], 7 X[47763] - 2 X[48008], 4 X[47763] + X[48141], 8 X[47776] - 3 X[47926], 7 X[47776] - 6 X[48008], 4 X[47776] + 3 X[48141], 7 X[47926] - 16 X[48008], X[47926] + 2 X[48141], 8 X[48008] + 7 X[48141], 3 X[4379] - 2 X[4728], 5 X[4379] - 4 X[45320], 4 X[4728] - 3 X[31147], X[4728] - 3 X[31148], 5 X[4728] - 6 X[45320], X[31147] - 4 X[31148], 5 X[31147] - 8 X[45320], 5 X[31148] - 2 X[45320], 4 X[650] - X[47908], 2 X[650] + X[48147], and many others

X(48577) lies on these lines: {239, 514}, {513, 4379}, {650, 47908}, {659, 28220}, {661, 31207}, {890, 4378}, {1638, 4724}, {2516, 47914}, {2529, 48087}, {2786, 47791}, {3676, 23731}, {3776, 47907}, {4024, 48013}, {4120, 47789}, {4369, 4776}, {4375, 6548}, {4382, 4979}, {4394, 47917}, {4453, 28859}, {4763, 4893}, {4777, 4784}, {4778, 47758}, {4782, 47927}, {4785, 47780}, {4789, 28867}, {4790, 47672}, {4885, 48019}, {4897, 48275}, {4977, 47886}, {6006, 47694}, {6546, 28878}, {7653, 24924}, {7659, 48153}, {9508, 47909}, {14433, 43928}, {14475, 36834}, {20295, 48071}, {21104, 48104}, {25666, 47939}, {26824, 48016}, {26853, 48399}, {26985, 48041}, {27013, 47996}, {28175, 45669}, {28225, 47757}, {28229, 48240}, {28855, 47771}, {28886, 30565}, {28902, 47767}, {28906, 47870}, {31209, 47991}, {31286, 31290}, {35119, 43922}, {36848, 48023}, {45313, 47775}, {45666, 48024}, {45674, 47781}, {45677, 48248}, {47759, 47779}, {47774, 47778}, {47932, 48133}, {47971, 48276}

X(48577) = midpoint of X(i) and X(j) for these {i,j}: {4776, 48107}, {7192, 47763}
X(48577) = reflection of X(i) in X(j) for these {i,j}: {649, 47763}, {661, 47761}, {4120, 47789}, {4379, 31148}, {4776, 4369}, {4813, 4776}, {4893, 47762}, {6546, 47768}, {31147, 4379}, {47759, 47779}, {47763, 4932}, {47774, 47778}, {47775, 45313}, {47781, 45674}, {47873, 47791}, {48023, 36848}, {48024, 45666}
X(48577) = crossdifference of every pair of points on line {42, 9331}
X(48577) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 7192, 48141}, {649, 48141, 47926}, {650, 48147, 47908}, {4369, 4813, 30835}, {4369, 48107, 4813}, {4932, 7192, 649}, {4979, 43067, 4382}, {7653, 48026, 24924}


X(48578) = X(513)X(4379)∩X(514)X(8643)

Barycentrics    (b - c)*(3*a^3 + a^2*b + 2*a*b^2 + a^2*c + 2*a*b*c + 2*b^2*c + 2*a*c^2 + 2*b*c^2) : :
X(48578) = 3 X[4379] - 2 X[47812], 5 X[31147] - 8 X[45342], X[31147] - 4 X[48234], 4 X[45342] - 5 X[47832], 2 X[45342] - 5 X[48234], X[47812] - 3 X[47813], X[649] + 2 X[47694], 2 X[650] + X[48153], 4 X[659] - X[47926], 2 X[659] + X[48142], X[47705] + 2 X[48095], X[47926] + 2 X[48142], 4 X[676] - X[47958], 2 X[4724] + X[48141], X[4724] - 4 X[48248], 2 X[21104] + X[48105], X[48141] + 8 X[48248], 4 X[1491] - 7 X[31207], 2 X[2526] - 5 X[24924], 4 X[3716] - X[4813], 2 X[4369] + X[47697], X[4382] - 4 X[7662], 2 X[4458] + X[47696], 4 X[4458] - X[47923], 2 X[47696] + X[47923], 8 X[4874] - 5 X[30835], 4 X[4874] - X[48023], 5 X[30835] - 2 X[48023], 4 X[4885] - X[48020], X[4960] + 2 X[48065], X[7192] + 2 X[48063], 5 X[8656] - 2 X[48288], 4 X[8689] - X[47969], 4 X[13246] - X[45746], 4 X[25666] - X[47940], 5 X[26985] - 2 X[48042], 5 X[27013] - 2 X[48017], 2 X[43067] + X[48032], 2 X[43927] + X[48340], 2 X[47123] + X[48101], 2 X[47131] + X[48146], 2 X[47691] + X[48138], X[47908] - 4 X[48029], X[47933] + 2 X[48133], X[47972] + 2 X[48276], X[48139] + 2 X[48326]

X(48578) lies on these lines: {513, 4379}, {514, 8643}, {522, 649}, {650, 48153}, {659, 4802}, {676, 1459}, {812, 48237}, {1491, 31207}, {2526, 24924}, {3667, 47763}, {3716, 4813}, {4369, 47697}, {4382, 7662}, {4448, 47826}, {4458, 47696}, {4763, 48175}, {4778, 6545}, {4782, 28165}, {4785, 48172}, {4817, 28863}, {4874, 30835}, {4885, 48020}, {4893, 47804}, {4960, 48065}, {4962, 45343}, {7192, 17218}, {8656, 48288}, {8678, 14430}, {8689, 47969}, {13246, 45746}, {17494, 28155}, {25666, 47940}, {26985, 48042}, {27013, 48017}, {28147, 48240}, {28161, 47776}, {28859, 48161}, {43067, 48032}, {43927, 48340}, {45313, 48242}, {45314, 48176}, {47123, 48101}, {47131, 48146}, {47691, 48138}, {47779, 48164}, {47803, 47810}, {47830, 48157}, {47908, 48029}, {47933, 48133}, {47972, 48276}, {48139, 48326}, {48160, 48216}

X(48578) = reflection of X(i) in X(j) for these {i,j}: {4379, 47813}, {4728, 48220}, {4893, 47804}, {31147, 47832}, {47810, 47803}, {47826, 4448}, {47832, 48234}, {48157, 47830}, {48160, 48216}, {48164, 47779}, {48167, 48221}, {48175, 4763}, {48176, 45314}, {48242, 45313}
X(48578) = crossdifference of every pair of points on line {1193, 3730}
X(48578) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {659, 48142, 47926}, {4458, 47696, 47923}, {4874, 48023, 30835}


X(48579) = X(513)X(4379)∩X(514)X(30574)

Barycentrics    (b - c)*(a^3 + 3*a^2*b + 3*a^2*c + 4*a*b*c + 2*b^2*c + 2*b*c^2) : :
X(48579) = 5 X[4379] - 2 X[4800], 3 X[4379] - 2 X[47833], 7 X[4379] - 4 X[48202], 5 X[4379] - 4 X[48221], 4 X[4800] - 5 X[47832], 3 X[4800] - 5 X[47833], 7 X[4800] - 10 X[48202], X[4800] - 5 X[48253], 3 X[47832] - 4 X[47833], 7 X[47832] - 8 X[48202], 5 X[47832] - 8 X[48221], X[47832] - 4 X[48253], 7 X[47833] - 6 X[48202], 5 X[47833] - 6 X[48221], X[47833] - 3 X[48253], 5 X[48202] - 7 X[48221], 2 X[48202] - 7 X[48253], 2 X[48221] - 5 X[48253], 3 X[47824] - X[47825], 2 X[47825] - 3 X[47828], X[649] + 2 X[21146], 2 X[649] + X[48119], 4 X[21146] - X[48119], 4 X[650] - X[47927], 2 X[650] + X[48148], X[47927] + 2 X[48148], 4 X[1491] - X[47909], 2 X[1491] + X[48141], X[47909] + 2 X[48141], X[2254] + 2 X[43067], 2 X[2254] + X[48142], 4 X[43067] - X[48142], 2 X[2533] + X[48341], 4 X[3676] - X[47701], 4 X[3776] - X[47924], 4 X[3837] - X[4813], 2 X[4025] + X[47703], 4 X[4369] - X[4724], 2 X[4369] + X[48108], X[4724] + 2 X[48108], X[4382] + 2 X[4784], X[4382] - 4 X[48098], X[4784] + 2 X[48098], X[4474] + 2 X[48320], X[4804] + 2 X[7659], 4 X[4885] - X[48021], 3 X[4893] - 4 X[47829], 3 X[47823] - 2 X[47829], 2 X[4913] + X[47675], 2 X[4932] + X[46403], X[4960] + 2 X[48066], X[4979] + 2 X[48089], X[7192] + 2 X[24720], 2 X[7192] + X[48023], 4 X[24720] - X[48023], 4 X[9508] - X[47926], 2 X[9508] + X[48143], X[47926] + 2 X[48143], 2 X[21104] + X[48106], 4 X[21212] - X[47699], 4 X[21260] - X[47911], 4 X[23789] - X[48122], 4 X[23815] - X[48121], 5 X[24924] - 2 X[48029], 4 X[25380] - X[47666], 4 X[25666] - X[47941], 5 X[26985] - 2 X[48043], 5 X[30795] - 2 X[48028], 5 X[30835] - 2 X[48024], 5 X[31209] - 2 X[48001], 5 X[31251] - 2 X[47994], 4 X[31286] - X[47969], 2 X[47676] + X[48118], X[47694] + 2 X[48073], X[47704] + 2 X[48069], X[47908] - 4 X[48030], X[47932] + 2 X[48126], X[47934] + 2 X[48133], X[47971] + 2 X[48396], X[47973] + 2 X[48276], 2 X[48027] + X[48147], 2 X[48050] + X[48107], X[48117] - 4 X[48505]

X(48579) lies on these lines: {2, 4778}, {42, 48342}, {513, 4379}, {514, 30574}, {522, 47755}, {649, 21146}, {650, 47927}, {661, 47802}, {900, 48238}, {1019, 29033}, {1491, 47909}, {2254, 43067}, {2533, 48341}, {2787, 48144}, {3667, 47834}, {3676, 47701}, {3720, 48340}, {3776, 47924}, {3837, 4813}, {4025, 47703}, {4369, 4724}, {4382, 4784}, {4474, 48320}, {4785, 48170}, {4802, 21115}, {4804, 7659}, {4885, 48021}, {4893, 4977}, {4913, 47675}, {4932, 46403}, {4948, 28199}, {4960, 48066}, {4979, 48089}, {6006, 48172}, {7192, 24720}, {8643, 29246}, {8672, 9148}, {9508, 47926}, {21104, 48106}, {21212, 47699}, {21260, 47911}, {23789, 48122}, {23815, 48121}, {24924, 48029}, {25380, 47666}, {25666, 47941}, {26985, 48043}, {28147, 48242}, {28175, 48225}, {28195, 47827}, {28209, 47822}, {28213, 48176}, {28217, 48189}, {28220, 48162}, {28225, 47779}, {28229, 47775}, {28840, 44429}, {28851, 47809}, {28859, 48159}, {28878, 47806}, {28890, 48236}, {30795, 48028}, {30835, 48024}, {31209, 48001}, {31251, 47994}, {31286, 47969}, {45313, 48240}, {45328, 48175}, {47676, 48118}, {47694, 48073}, {47704, 48069}, {47761, 47811}, {47886, 48245}, {47887, 47891}, {47908, 48030}, {47932, 48126}, {47934, 48133}, {47971, 48396}, {47973, 48276}, {48027, 48147}, {48050, 48107}, {48117, 48505}

X(48579) = midpoint of X(i) and X(j) for these {i,j}: {7192, 48164}, {47804, 48108}
X(48579) = reflection of X(i) in X(j) for these {i,j}: {661, 47802}, {4379, 48253}, {4724, 47804}, {4800, 48221}, {4893, 47823}, {31147, 48184}, {47775, 47830}, {47804, 4369}, {47811, 47761}, {47821, 47779}, {47822, 48233}, {47826, 2}, {47828, 47824}, {47832, 4379}, {47886, 48245}, {47887, 47891}, {48023, 48164}, {48162, 48216}, {48164, 24720}, {48175, 45328}, {48176, 48229}, {48240, 45313}
X(48579) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 21146, 48119}, {650, 48148, 47927}, {1491, 48141, 47909}, {2254, 43067, 48142}, {4369, 48108, 4724}, {4784, 48098, 4382}, {7192, 24720, 48023}, {9508, 48143, 47926}


X(48580) = X(239)X(514)∩X(513)X(26144)

Barycentrics    (a + b)*(b - c)*(a + c)*(3*a + b + c) : :
X(48580) = 4 X[1019] - X[4560], 5 X[1019] + X[4960], 2 X[1019] + X[7192], 7 X[1019] - X[47683], 5 X[4560] + 4 X[4960], X[4560] + 2 X[7192], 7 X[4560] - 4 X[47683], 8 X[4932] + X[21222], 2 X[4932] + X[48144], 2 X[4960] - 5 X[7192], 7 X[4960] + 5 X[47683], 7 X[7192] + 2 X[47683], X[17494] - 4 X[48064], X[21222] - 4 X[48144], 2 X[4850] + X[47844], 2 X[905] + X[48107], 5 X[3616] - 2 X[4822], 2 X[4369] + X[48149], 2 X[4784] + X[17166], 2 X[4790] + X[4801], 2 X[4978] + X[26853], 4 X[6050] - X[47941], 4 X[14838] - X[31290], X[20295] + 2 X[48110], 5 X[27013] - 2 X[47959], 7 X[27115] - 4 X[47997], 5 X[31209] - 2 X[47955], 4 X[31286] - X[47911], 2 X[48071] + X[48121]

X(48580) lies on these lines: {2, 15309}, {239, 514}, {513, 26144}, {900, 4850}, {905, 48107}, {3616, 4822}, {3733, 28209}, {4369, 48149}, {4784, 17166}, {4790, 4801}, {4978, 26853}, {6002, 31148}, {6006, 7253}, {6008, 7199}, {6050, 47941}, {14838, 31290}, {17096, 30724}, {20295, 48110}, {27013, 47959}, {27115, 47997}, {27527, 47761}, {29013, 47780}, {29150, 47834}, {29270, 47869}, {31209, 47955}, {31286, 47911}, {47759, 47795}, {47762, 47793}, {48071, 48121}

X(48580) = reflection of X(i) in X(j) for these {i,j}: {47759, 47795}, {47793, 47762}
X(48580) = X(39711)-anticomplementary conjugate of X(21294)
X(48580) = X(i)-Ceva conjugate of X(j) for these (i,j): {4633, 86}, {37870, 16726}
X(48580) = X(i)-isoconjugate of X(j) for these (i,j): {10, 34074}, {37, 8694}, {42, 4606}, {756, 4627}, {872, 4633}, {1018, 2334}, {1500, 4614}, {4551, 34820}, {4557, 25430}, {4559, 4866}
X(48580) = X(i)-Dao conjugate of X(j) for these (i, j): (40589, 8694), (40592, 4606), (40620, 5936)
X(48580) = cevapoint of X(4778) and X(4790)
X(48580) = crosspoint of X(86) and X(4633)
X(48580) = crosssum of X(42) and X(4832)
X(48580) = crossdifference of every pair of points on line {42, 7064}
X(48580) = barycentric product X(i)*X(j) for these {i,j}: {81, 4801}, {86, 4778}, {274, 4790}, {333, 30723}, {391, 17096}, {514, 42028}, {552, 4853}, {757, 4815}, {873, 4822}, {1014, 4811}, {1019, 19804}, {1434, 4765}, {1449, 7199}, {1509, 4851}, {3361, 18155}, {3616, 7192}, {4025, 31903}, {4560, 21454}, {4673, 7203}, {4830, 18827}, {4835, 17212}
X(48580) = barycentric quotient X(i)/X(j) for these {i,j}: {58, 8694}, {81, 4606}, {391, 30730}, {593, 4627}, {757, 4614}, {1019, 25430}, {1333, 34074}, {1434, 4624}, {1449, 1018}, {1509, 4633}, {3361, 4551}, {3616, 3952}, {3733, 2334}, {3737, 4866}, {4512, 4069}, {4700, 4169}, {4765, 2321}, {4773, 3943}, {4778, 10}, {4790, 37}, {4801, 321}, {4811, 3701}, {4815, 1089}, {4818, 3773}, {4822, 756}, {4827, 4515}, {4830, 740}, {4832, 1500}, {4839, 4037}, {4851, 594}, {4853, 6057}, {5257, 4103}, {7192, 5936}, {7199, 40023}, {7252, 34820}, {7341, 5545}, {8653, 7064}, {16726, 47915}, {17553, 4767}, {19804, 4033}, {21454, 4552}, {30723, 226}, {31903, 1897}, {37593, 40521}, {42028, 190}
X(48580) = {X(1019),X(7192)}-harmonic conjugate of X(4560)


X(48581) = EULER LINE INTERCEPT OF X(9707)X(41481)

Barycentrics    3*a^16-11*(b^2+c^2)*a^14-27*(b^2+c^2)*a^10*b^2*c^2+6*(b^2+2*c^2)*(2*b^2+c^2)*a^12-(5*b^8+5*c^8-(5*b^4+16*b^2*c^2+5*c^4)*b^2*c^2)*a^8-(b^4-c^4)*(b^2-c^2)*(3*b^4-8*b^2*c^2+3*c^4)*a^6+2*(b^2-c^2)^2*(3*b^8+2*b^4*c^4+3*c^8)*a^4+(b^2-c^2)^6*b^2*c^2-(b^4-c^4)*(b^2-c^2)^3*(2*b^4+3*b^2*c^2+2*c^4)*a^2 : :

See Kadir Altintas and César Lozada euclid 5030.

X(48581) lies on these lines: {2, 3}, {9707, 41481}

X(48581) = {X(3), X(37070)}-harmonic conjugate of X(5)

leftri

Points in the [ [bc,ca,ab], [a,b,c] ] coordinate system: X(48582)-X(48626)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1,L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1: bc α + ca β + ab γ = 0.

L2: a α + b β + c γ = 0.

The origin is given by (0,0) = X(661) = a(b^2-c^2) : b(c^2-a^2) :c(a^2-b^2).

Barycentrics u : v : w for a point U = (x,y) in this system are given by

u : v : w = (b - c) (ab + ac - a x - y) : : ,

where, as functions of a,b,c, the coordinate x is symmetric and homogeneous of degree 1, and y is symmetric and homogeneous of degree 2.

For the "reversed" coordinate system, [L2,L1], see X(47900) - X(48151).

The appearance of {x,y},k in the following list means that (x,y) = X(k) and that k ≥ 48582.

{-2*(a + b + c), (-2*a*b*c)/(a + b + c)}, 48582 {(-2*(a^2 + b^2 + c^2))/(a + b + c), -2*(a*b + a*c + b*c)}, 48583 {-2*(a + b + c), -((a*b*c)/(a + b + c))}, 48584 {(-2*(a^2 + b^2 + c^2))/(a + b + c), -a^2 - b^2 - c^2}, 48585 {(-2*(a^2 + b^2 + c^2))/(a + b + c), -((a*b*c)/(a + b + c))}, 48586 {-2*(a + b + c), -1/2*(a*b*c)/(a + b + c)}, 48587 {-2*(a + b + c), (-(a*b) - a*c - b*c)/2}, 48588 {(-2*(a^2 + b^2 + c^2))/(a + b + c), (-a^2 - b^2 - c^2)/2}, 48589 {(-2*(a^2 + b^2 + c^2))/(a + b + c), (-(a*b) - a*c - b*c)/2}, 48590 {(-2*(a*b + a*c + b*c))/(a + b + c), -1/2*(a*b*c)/(a + b + c)}, 48591 {-2*(a + b + c), (a*b + a*c + b*c)/2}, 48592 {(-2*(a^2 + b^2 + c^2))/(a + b + c), (a*b + a*c + b*c)/2}, 48593 {(-2*(a*b + a*c + b*c))/(a + b + c), (a*b*c)/(2*(a + b + c))}, 48594 {-2*(a + b + c), (a*b*c)/(a + b + c)}, 48595 {(-2*(a^2 + b^2 + c^2))/(a + b + c), (a*b*c)/(a + b + c)}, 48596 {-2*(a + b + c), (2*a*b*c)/(a + b + c)}, 48597 {-((a^2 + b^2 + c^2)/(a + b + c)), -2*(a^2 + b^2 + c^2)}, 48598 {-((a*b + a*c + b*c)/(a + b + c)), -2*(a^2 + b^2 + c^2)}, 48599 {-a - b - c, -1/2*(a*b*c)/(a + b + c)}, 48600 {-((a^2 + b^2 + c^2)/(a + b + c)), -1/2*(a*b*c)/(a + b + c)}, 48601 {-a - b - c, (a*b*c)/(2*(a + b + c))}, 48602 {-((a^2 + b^2 + c^2)/(a + b + c)), (a*b*c)/(2*(a + b + c))}, 48603 {-((a*b + a*c + b*c)/(a + b + c)), 2*(a^2 + b^2 + c^2)}, 48604 {(-a - b - c)/2, -2*(a^2 + b^2 + c^2)}, 48605 {-1/2*(a^2 + b^2 + c^2)/(a + b + c), -2*(a^2 + b^2 + c^2)}, 48606 {-1/2*(a^2 + b^2 + c^2)/(a + b + c), (-2*a*b*c)/(a + b + c)}, 48607 {-1/2*(a^2 + b^2 + c^2)/(a + b + c), -2*(a*b + a*c + b*c)}, 48608 {-1/2*(a*b + a*c + b*c)/(a + b + c), (-2*a*b*c)/(a + b + c)}, 48608 {-1/2*(a*b + a*c + b*c)/(a + b + c), -2*(a*b + a*c + b*c)}, 48610 {-1/2*(a*b + a*c + b*c)/(a + b + c), -a^2 - b^2 - c^2}, 48611 {(-a - b - c)/2, -1/2*(a*b*c)/(a + b + c)}, 48612 {-1/2*(a^2 + b^2 + c^2)/(a + b + c), -1/2*(a*b*c)/(a + b + c)}, 48613 {-1/2*(a*b + a*c + b*c)/(a + b + c), a^2 + b^2 + c^2}, 48614 {-1/2*(a^2 + b^2 + c^2)/(a + b + c), 2*(a^2 + b^2 + c^2)}, 48615 {-1/2*(a^2 + b^2 + c^2)/(a + b + c), (2*a*b*c)/(a + b + c)}, 48616 {(a^2 + b^2 + c^2)/(2*(a + b + c)), -2*(a^2 + b^2 + c^2)}, 48617 {(a^2 + b^2 + c^2)/(2*(a + b + c)), (-2*a*b*c)/(a + b + c)}, 48618 {(a^2 + b^2 + c^2)/(2*(a + b + c)), -2*(a*b + a*c + b*c)}, 48619 {(a*b + a*c + b*c)/(2*(a + b + c)), -2*(a*b + a*c + b*c)}, 48620 {(a*b + a*c + b*c)/(2*(a + b + c)), -a^2 - b^2 - c^2}, 48621 {(a^2 + b^2 + c^2)/(2*(a + b + c)), 2*(a^2 + b^2 + c^2)}, 48622 {(a^2 + b^2 + c^2)/(a + b + c), -1/2*(a*b*c)/(a + b + c)}, 48623 {2*(a + b + c), -1/2*(a*b*c)/(a + b + c)}, 48624 {(2*(a^2 + b^2 + c^2))/(a + b + c), (-(a*b) - a*c - b*c)/2}, 48625 {(2*(a^2 + b^2 + c^2))/(a + b + c), 2*(a^2 + b^2 + c^2)}, 48626


X(48582) = X(513)X(4041)∩X(514)X(4838)

Barycentrics    a*(b - c)*(2*a^2 + 5*a*b + 3*b^2 + 5*a*c + 8*b*c + 3*c^2) : :
X(48582) = X[4498] - 3 X[47911], 2 X[4498] - 3 X[47918], 5 X[4498] - 6 X[47921], 4 X[4498] - 3 X[47935], 3 X[47911] - 2 X[47915], 5 X[47911] - 2 X[47921], 4 X[47911] - X[47935], 4 X[47915] - 3 X[47918], 5 X[47915] - 3 X[47921], 8 X[47915] - 3 X[47935], 5 X[47918] - 4 X[47921], 8 X[47921] - 5 X[47935], 3 X[661] - 2 X[1019], 5 X[661] - 4 X[14838], 5 X[1019] - 6 X[14838], X[1019] - 3 X[47947], 4 X[1019] - 3 X[48149], 2 X[14838] - 5 X[47947], 8 X[14838] - 5 X[48149], 4 X[47947] - X[48149], 2 X[905] - 3 X[48544], 3 X[1635] - 4 X[47997], 3 X[1635] - 2 X[48110], 4 X[4129] - 3 X[31148], 3 X[4813] - 2 X[48091], 3 X[4813] - X[48341], 4 X[48091] - 3 X[48131], 3 X[48131] - 2 X[48341], 3 X[4822] - 2 X[4879], 3 X[4979] - 4 X[48011], 3 X[47959] - 2 X[48011], 3 X[4983] - 2 X[48328], 3 X[14413] - 4 X[48093], 5 X[24924] - 6 X[48551], 4 X[25666] - 3 X[48580], 3 X[47811] - 4 X[47994], 3 X[48021] - 2 X[48351], 3 X[48150] - 4 X[48351], 3 X[48024] - 2 X[48331], 2 X[48071] - 3 X[48565]

X(48582) lies on these lines: {513, 4041}, {514, 4838}, {649, 47955}, {661, 1019}, {905, 48544}, {1577, 48147}, {1635, 47997}, {4129, 31148}, {4560, 47991}, {4801, 48041}, {4813, 48091}, {4822, 4879}, {4979, 47959}, {4983, 48328}, {6002, 31290}, {6372, 48116}, {14413, 48093}, {17217, 28840}, {23882, 47908}, {24924, 48551}, {25666, 48580}, {29013, 47917}, {29070, 47904}, {29150, 47934}, {29238, 47910}, {29354, 47902}, {47811, 47994}, {47942, 48032}, {48021, 48150}, {48024, 48331}, {48026, 48144}, {48038, 48300}, {48051, 48320}, {48071, 48565}, {48081, 48322}, {48085, 48334}

X(48582) = reflection of X(i) in X(j) for these {i,j}: {649, 47955}, {661, 47947}, {4498, 47915}, {4560, 47991}, {4801, 48041}, {4979, 47959}, {47918, 47911}, {47935, 47918}, {47936, 47906}, {48032, 47942}, {48110, 47997}, {48131, 4813}, {48144, 48026}, {48147, 1577}, {48149, 661}, {48150, 48021}, {48300, 48038}, {48320, 48051}, {48322, 48081}, {48334, 48085}, {48341, 48091}
X(48582) = crossdifference of every pair of points on line {1449, 1962}
X(48582) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4498, 47911, 47915}, {4498, 47915, 47918}, {4813, 48341, 48091}, {47997, 48110, 1635}, {48091, 48341, 48131}


X(48583) = X(513)X(4963)∩X(514)X(47685)

Barycentrics    (b - c)*(2*a^3 + 3*a^2*b + 5*a*b^2 + 3*a^2*c + 8*a*b*c + 2*b^2*c + 5*a*c^2 + 2*b*c^2) : :
X(48583) = 3 X[47909] - X[47927], 4 X[47909] - X[47933], 3 X[47917] - 2 X[47927], 4 X[47927] - 3 X[47933], X[47685] - 3 X[47940], 2 X[47685] - 3 X[48020], 4 X[47685] - 3 X[48115], 4 X[47940] - X[48115], 5 X[661] - 4 X[3716], 3 X[661] - 2 X[47694], 7 X[661] - 6 X[47821], 3 X[661] - 4 X[47992], 6 X[3716] - 5 X[47694], 14 X[3716] - 15 X[47821], 2 X[3716] - 5 X[47945], 3 X[3716] - 5 X[47992], 8 X[3716] - 5 X[48153], 7 X[47694] - 9 X[47821], X[47694] - 3 X[47945], 4 X[47694] - 3 X[48153], 3 X[47821] - 7 X[47945], 9 X[47821] - 14 X[47992], 12 X[47821] - 7 X[48153], 3 X[47945] - 2 X[47992], 4 X[47945] - X[48153], 8 X[47992] - 3 X[48153], 4 X[1491] - 3 X[31148], 3 X[1635] - 4 X[48010], 3 X[4728] - 4 X[48027], 3 X[4728] - 2 X[48142], 2 X[4932] - 3 X[48175], 3 X[21115] - 4 X[48007], 5 X[24924] - 6 X[47810], 3 X[47666] - 2 X[48009], 4 X[48009] - 3 X[48032], 3 X[47672] - 4 X[48089], 3 X[48023] - 2 X[48089], 3 X[47811] - 4 X[48002], 3 X[47813] - 4 X[48030], 2 X[48063] - 3 X[48548]

X(48583) lies on these lines: {513, 4963}, {514, 47685}, {522, 47669}, {523, 23731}, {661, 3716}, {693, 47985}, {1491, 31148}, {1635, 48010}, {2254, 48147}, {2526, 48141}, {3667, 47661}, {4724, 47953}, {4728, 48027}, {4778, 48145}, {4932, 48175}, {4977, 48146}, {4979, 47975}, {21115, 48007}, {24924, 47810}, {28161, 48079}, {47666, 48009}, {47672, 48023}, {47675, 48042}, {47697, 47996}, {47698, 48130}, {47704, 47989}, {47705, 47958}, {47811, 48002}, {47813, 48030}, {47935, 48407}, {48017, 48107}, {48039, 48275}, {48063, 48548}, {48149, 48409}

X(48583) = reflection of X(i) in X(j) for these {i,j}: {661, 47945}, {693, 47985}, {4724, 47953}, {4979, 47975}, {47672, 48023}, {47675, 48042}, {47694, 47992}, {47697, 47996}, {47704, 47989}, {47705, 47958}, {47904, 4963}, {47917, 47909}, {47932, 47934}, {47933, 47917}, {47935, 48407}, {48020, 47940}, {48032, 47666}, {48107, 48017}, {48115, 48020}, {48130, 47698}, {48141, 2526}, {48142, 48027}, {48145, 48408}, {48147, 2254}, {48149, 48409}, {48153, 661}, {48275, 48039}
X(48583) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47694, 47945, 47992}, {47694, 47992, 661}, {48027, 48142, 4728}


X(48584) = X(484)X(513)∩X(514)X(4838)

Barycentrics    a*(b - c)*(2*a^2 + 5*a*b + 3*b^2 + 5*a*c + 7*b*c + 3*c^2) : :
X(48584) = X[4063] - 3 X[47947], 2 X[4063] - 3 X[47959], 5 X[4063] - 6 X[47965], 4 X[4063] - 3 X[47976], 3 X[47947] - 2 X[47955], 5 X[47947] - 2 X[47965], 4 X[47947] - X[47976], 4 X[47955] - 3 X[47959], 5 X[47955] - 3 X[47965], 8 X[47955] - 3 X[47976], 5 X[47959] - 4 X[47965], 8 X[47965] - 5 X[47976], 3 X[661] - 2 X[48064], 4 X[48064] - 3 X[48110], 3 X[1635] - 2 X[48074], 2 X[3960] - 5 X[4813], 4 X[3960] - 5 X[14349], 3 X[3960] - 5 X[48051], 6 X[3960] - 5 X[48144], 3 X[4813] - 2 X[48051], 3 X[4813] - X[48144], 3 X[14349] - 4 X[48051], 3 X[14349] - 2 X[48144], 5 X[4822] - 3 X[23057], 2 X[4932] - 3 X[48551], 3 X[4983] - 2 X[48330], 2 X[14838] - 3 X[48544], 2 X[48071] - 3 X[48566], 3 X[48081] - 2 X[48336], 3 X[48324] - 4 X[48336], 3 X[48085] - 2 X[48128], 4 X[48128] - 3 X[48335]

X(48584) lies on these lines: {484, 513}, {514, 4838}, {661, 48064}, {1019, 48026}, {1635, 48074}, {3960, 4813}, {4129, 48107}, {4822, 23057}, {4823, 48147}, {4932, 48551}, {4978, 48041}, {4979, 47997}, {4983, 48330}, {14838, 48544}, {21385, 47915}, {28867, 47679}, {29013, 31290}, {29270, 47917}, {48021, 48111}, {48054, 48149}, {48071, 48566}, {48081, 48324}, {48085, 48128}, {48091, 48320}

X(48584) = reflection of X(i) in X(j) for these {i,j}: {1019, 48026}, {4063, 47955}, {4978, 48041}, {4979, 47997}, {14349, 4813}, {21385, 47915}, {47959, 47947}, {47976, 47959}, {47977, 47942}, {48107, 4129}, {48110, 661}, {48111, 48021}, {48144, 48051}, {48147, 4823}, {48149, 48054}, {48320, 48091}, {48324, 48081}, {48335, 48085}
X(48584) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4063, 47947, 47955}, {4063, 47955, 47959}, {4813, 48144, 48051}, {48051, 48144, 14349}


X(48585) = X(513)X(16892)∩X(514)X(47685)

Barycentrics    (b - c)*(3*a^3 + 2*a^2*b + 4*a*b^2 + b^3 + 2*a^2*c + 2*a*b*c + b^2*c + 4*a*c^2 + b*c^2 + c^3) : :
X(48585) = X[47701] - 3 X[47943], 2 X[47701] - 3 X[47958], 5 X[47701] - 6 X[47961], 4 X[47701] - 3 X[47972], 3 X[47943] - 2 X[47951], 5 X[47943] - 2 X[47961], 4 X[47943] - X[47972], 4 X[47951] - 3 X[47958], 5 X[47951] - 3 X[47961], 8 X[47951] - 3 X[47972], 5 X[47958] - 4 X[47961], 8 X[47961] - 5 X[47972], X[47700] + 3 X[47901], X[47700] - 3 X[48020], 2 X[47700] - 3 X[48077], 3 X[47901] + 2 X[48035], 2 X[47901] + X[48077], 3 X[48020] - 2 X[48035], 4 X[48035] - 3 X[48077], 3 X[661] - 2 X[48061], 3 X[47982] - X[48061], 4 X[47982] - X[48105], 4 X[48061] - 3 X[48105], 3 X[48023] - 2 X[48047], 3 X[48023] - X[48139], 4 X[48047] - 3 X[48094], 3 X[48094] - 2 X[48139], 2 X[47696] - 3 X[47874], 3 X[47874] - 4 X[48050], 3 X[47886] - 4 X[48007], 2 X[48063] - 3 X[48550], 2 X[48072] - 3 X[48161]

X(48585) lies on these lines: {513, 16892}, {514, 47685}, {522, 47916}, {661, 4521}, {900, 47924}, {1638, 4724}, {2254, 48104}, {2526, 48101}, {3667, 47677}, {4088, 28195}, {4453, 13246}, {4977, 47908}, {4979, 48015}, {28213, 48118}, {28220, 48027}, {28229, 48039}, {46403, 48275}, {47660, 48042}, {47696, 47874}, {47886, 48007}, {48063, 48550}, {48069, 48145}, {48072, 48161}, {48086, 48300}, {48153, 48398}

X(48585) = midpoint of X(47901) and X(48020)
X(48585) = reflection of X(i) in X(j) for these {i,j}: {661, 47982}, {4724, 47989}, {4979, 48015}, {47660, 48042}, {47696, 48050}, {47700, 48035}, {47701, 47951}, {47958, 47943}, {47971, 47973}, {47972, 47958}, {48032, 47995}, {48077, 48020}, {48094, 48023}, {48101, 2526}, {48102, 48027}, {48104, 2254}, {48105, 661}, {48130, 48039}, {48139, 48047}, {48145, 48069}, {48153, 48398}, {48275, 46403}, {48300, 48086}
X(48585) = crossdifference of every pair of points on line {3915, 5280}
X(48585) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47696, 48050, 47874}, {47700, 48020, 48035}, {47700, 48035, 48077}, {47701, 47943, 47951}, {47701, 47951, 47958}, {48023, 48139, 48047}, {48047, 48139, 48094}


X(48586) = X(484)X(513)∩X(514)X(47685)

Barycentrics    a*(b - c)*(2*a^2 + a*b + 3*b^2 + a*c + 3*b*c + 3*c^2) : :
X(48586) = 3 X[1734] - 2 X[4834], 4 X[4834] - 3 X[47976], 3 X[47948] - 2 X[47956], 5 X[47948] - 2 X[47966], 3 X[47948] - X[47970], 4 X[47948] - X[47977], 4 X[47956] - 3 X[47959], 5 X[47956] - 3 X[47966], 8 X[47956] - 3 X[47977], 5 X[47959] - 4 X[47966], 3 X[47959] - 2 X[47970], 6 X[47966] - 5 X[47970], 8 X[47966] - 5 X[47977], 4 X[47970] - 3 X[47977], 3 X[47905] + X[48116], 3 X[48020] - X[48116], 3 X[661] - 2 X[48065], 4 X[48065] - 3 X[48111], 2 X[663] - 3 X[14349], X[663] - 3 X[48023], 4 X[663] - 3 X[48324], 7 X[663] - 6 X[48345], 3 X[14349] - 4 X[48052], 7 X[14349] - 4 X[48345], 3 X[48023] - 2 X[48052], 4 X[48023] - X[48324], 7 X[48023] - 2 X[48345], 8 X[48052] - 3 X[48324], 7 X[48052] - 3 X[48345], 7 X[48324] - 8 X[48345], 2 X[4401] - 3 X[47810], 3 X[48086] - X[48282], 5 X[48086] - 2 X[48346], 2 X[48282] - 3 X[48335], 5 X[48282] - 6 X[48346], 5 X[48335] - 4 X[48346], 2 X[48063] - 3 X[48551], 3 X[48131] - 2 X[48287]

X(48586) lies on these lines: {1, 48092}, {484, 513}, {514, 47685}, {661, 48065}, {663, 830}, {1019, 2526}, {2254, 48110}, {3309, 48085}, {3887, 48121}, {4040, 48027}, {4129, 47697}, {4160, 48122}, {4401, 47810}, {4813, 42325}, {4823, 48153}, {4978, 48042}, {4979, 48018}, {6004, 48081}, {6161, 48093}, {8678, 48086}, {28507, 48404}, {29047, 47943}, {29186, 47945}, {29196, 47653}, {29260, 47916}, {47997, 48032}, {48051, 48367}, {48054, 48150}, {48063, 48551}, {48075, 48149}, {48091, 48352}, {48128, 48337}, {48131, 48287}

X(48586) = midpoint of X(47905) and X(48020)
X(48586) = reflection of X(i) in X(j) for these {i,j}: {1, 48092}, {663, 48052}, {1019, 2526}, {4040, 48027}, {4978, 48042}, {4979, 48018}, {6161, 48093}, {14349, 48023}, {47697, 4129}, {47959, 47948}, {47970, 47956}, {47976, 1734}, {47977, 47959}, {48032, 47997}, {48110, 2254}, {48111, 661}, {48149, 48075}, {48150, 48054}, {48153, 4823}, {48324, 14349}, {48335, 48086}, {48337, 48128}, {48352, 48091}, {48367, 48051}
X(48586) = crossdifference of every pair of points on line {1100, 5282}
X(48586) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {663, 48023, 48052}, {663, 48052, 14349}, {47948, 47970, 47956}, {47956, 47970, 47959}


X(48587) = X(513)X(47987)∩X(514)X(4838)

Barycentrics    a*(b - c)*(2*a + 3*b + 2*c)*(2*a + 2*b + 3*c) : :
X(48587) = 5 X[47997] - 4 X[48003], 3 X[47997] - 2 X[48011], 6 X[48003] - 5 X[48011], X[1019] - 3 X[4813], 2 X[1019] - 3 X[48054], 3 X[1022] - 7 X[48085], 9 X[1022] - 7 X[48341], 3 X[48085] - X[48341], 3 X[3669] - 5 X[48091], X[4498] - 3 X[47947], 3 X[48045] - 2 X[48331]

X(48587) lies on these lines: {513, 47987}, {514, 4838}, {661, 48074}, {1019, 4813}, {1022, 27789}, {1308, 28196}, {3669, 15309}, {4498, 47947}, {4562, 32106}, {4823, 7199}, {29270, 31290}, {48026, 48064}, {48045, 48331}

X(48587) = reflection of X(i) in X(j) for these {i,j}: {48054, 4813}, {48064, 48026}, {48074, 661}
X(48587) = X(47959)-cross conjugate of X(514)
X(48587) = X(i)-isoconjugate of X(j) for these (i,j): {100, 16884}, {101, 3624}, {109, 4034}, {163, 42031}, {1252, 28195}, {4557, 42025}, {4567, 48053}, {4570, 47669}, {4574, 31901}
X(48587) = X(i)-Dao conjugate of X(j) for these (i, j): (11, 4034), (115, 42031), (661, 28195), (1015, 3624), (8054, 16884), (40627, 48053)
X(48587) = cevapoint of X(513) and X(48026)
X(48587) = crosssum of X(46845) and X(48026)
X(48587) = barycentric product X(i)*X(j) for these {i,j}: {513, 28650}, {514, 27789}, {1111, 28196}
X(48587) = barycentric quotient X(i)/X(j) for these {i,j}: {244, 28195}, {513, 3624}, {523, 42031}, {649, 16884}, {650, 4034}, {1019, 42025}, {3122, 48053}, {3125, 47669}, {27789, 190}, {28196, 765}, {28650, 668}, {47959, 28651}


X(48588) = X(513)X(4507)∩X(514)X(4838)

Barycentrics    (b - c)*(4*a^2 + 7*a*b + 7*a*c + b*c) : :
X(48588) = 3 X[47984] - 2 X[47991], 5 X[47984] - 2 X[48000], 3 X[47984] - X[48008], 4 X[47984] - X[48016], 4 X[47991] - 3 X[47996], 5 X[47991] - 3 X[48000], 8 X[47991] - 3 X[48016], 5 X[47996] - 4 X[48000], 3 X[47996] - 2 X[48008], 6 X[48000] - 5 X[48008], 8 X[48000] - 5 X[48016], 4 X[48008] - 3 X[48016], X[47903] - 3 X[47939], X[47903] + 3 X[48019], 5 X[47903] + 3 X[48114], 3 X[47939] + X[48079], 5 X[47939] + X[48114], 3 X[48019] - X[48079], 5 X[48019] - X[48114], 5 X[48079] - 3 X[48114], 4 X[661] - 3 X[45313], 3 X[45313] - 2 X[48071], 7 X[3835] - 6 X[4379], 3 X[3835] - 2 X[7192], 11 X[3835] - 10 X[26985], 5 X[3835] - 6 X[47759], 3 X[4379] - 7 X[4813], 9 X[4379] - 7 X[7192], 33 X[4379] - 35 X[26985], 5 X[4379] - 7 X[47759], 3 X[4813] - X[7192], 11 X[4813] - 5 X[26985], 5 X[4813] - 3 X[47759], 11 X[7192] - 15 X[26985], 5 X[7192] - 9 X[47759], 25 X[26985] - 33 X[47759], 2 X[4106] - 3 X[48041], 5 X[4106] - 3 X[48133], 4 X[4106] - 3 X[48399], 5 X[48041] - 2 X[48133], 4 X[48133] - 5 X[48399], 3 X[31290] - X[47926], 3 X[4932] - 4 X[25666], 5 X[4932] - 6 X[47761], 10 X[25666] - 9 X[47761], 2 X[25666] - 3 X[48026], 3 X[47761] - 5 X[48026], 2 X[8689] - 3 X[48024], 5 X[24924] - 3 X[48107], 2 X[31286] - 3 X[48544]

X(48588) lies on these lines: {513, 4507}, {514, 4838}, {661, 45313}, {812, 47914}, {3835, 4379}, {4106, 28840}, {4785, 31290}, {4932, 25666}, {8689, 48024}, {24924, 48107}, {28209, 48270}, {28213, 48430}, {28225, 48036}, {28855, 47981}, {28871, 47950}, {28886, 47988}, {29738, 48341}, {31286, 48544}, {48020, 48068}, {48021, 48072}

X(48588) = midpoint of X(i) and X(j) for these {i,j}: {47903, 48079}, {47939, 48019}
X(48588) = reflection of X(i) in X(j) for these {i,j}: {3835, 4813}, {4932, 48026}, {47996, 47984}, {48008, 47991}, {48016, 47996}, {48071, 661}, {48072, 48021}, {48399, 48041}
X(48588) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 48071, 45313}, {47903, 48019, 48079}, {47939, 48079, 47903}, {47984, 48008, 47991}, {47991, 48008, 47996}


X(48589) = X(513)X(3004)∩X(514)X(47685)

Barycentrics    (b - c)*(5*a^3 + 3*a^2*b + 7*a*b^2 + b^3 + 3*a^2*c + 4*a*b*c + b^2*c + 7*a*c^2 + b*c^2 + c^3) : :
X(48589) = 3 X[47982] - 2 X[47989], 5 X[47982] - 2 X[47998], 3 X[47982] - X[48006], 4 X[47982] - X[48014], 4 X[47989] - 3 X[47995], 5 X[47989] - 3 X[47998], 8 X[47989] - 3 X[48014], 5 X[47995] - 4 X[47998], 3 X[47995] - 2 X[48006], 6 X[47998] - 5 X[48006], 8 X[47998] - 5 X[48014], 4 X[48006] - 3 X[48014], 3 X[47700] + 5 X[47901], X[47700] - 5 X[48020], 2 X[47700] - 5 X[48035], 3 X[47700] - 5 X[48077], X[47901] + 3 X[48020], 2 X[47901] + 3 X[48035], 3 X[48020] - X[48077], 3 X[48035] - 2 X[48077], X[47924] - 3 X[47943], 3 X[4468] - 2 X[48102], 3 X[48023] - X[48102], 3 X[48039] - 2 X[48088], 3 X[47787] - 4 X[48050], 2 X[48063] - 3 X[48554]

X(48589) lies on these lines: {513, 3004}, {514, 47685}, {522, 47653}, {661, 28225}, {900, 47951}, {2254, 48067}, {2526, 48060}, {3667, 47958}, {4088, 28229}, {4468, 4778}, {4724, 46919}, {4962, 47702}, {4977, 48039}, {6006, 47701}, {6332, 48086}, {6590, 48042}, {28161, 47916}, {28209, 48027}, {28217, 47961}, {28220, 48047}, {45674, 48032}, {47787, 48050}, {48029, 48214}, {48063, 48554}

X(48589) = midpoint of X(47901) and X(48077)
X(48589) = reflection of X(i) in X(j) for these {i,j}: {4468, 48023}, {6332, 48086}, {6590, 48042}, {47995, 47982}, {48006, 47989}, {48013, 48015}, {48014, 47995}, {48035, 48020}, {48060, 2526}, {48061, 48027}, {48067, 2254}, {48068, 661}
X(48589) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47901, 48020, 48077}, {47982, 48006, 47989}, {47989, 48006, 47995}


X(48590) = X(513)X(4507)∩X(514)X(47685)

Barycentrics    (b - c)*(4*a^3 + 3*a^2*b + 7*a*b^2 + 3*a^2*c + 7*a*b*c + b^2*c + 7*a*c^2 + b*c^2) : :
X(48590) = 3 X[47985] - 2 X[47992], 5 X[47985] - 2 X[48001], 3 X[47985] - X[48009], 4 X[47992] - 3 X[47996], 5 X[47992] - 3 X[48001], 5 X[47996] - 4 X[48001], 3 X[47996] - 2 X[48009], 6 X[48001] - 5 X[48009], X[47685] + 3 X[47940], X[47685] - 3 X[48020], 5 X[47685] - 3 X[48115], 5 X[47940] + X[48115], 5 X[48020] - X[48115], 4 X[1491] - 3 X[45313], 3 X[3835] - 2 X[47694], 7 X[3835] - 6 X[47832], 7 X[47694] - 9 X[47832], X[47694] - 3 X[48023], 3 X[47832] - 7 X[48023], X[47927] - 3 X[47945], 3 X[48042] - 2 X[48089], 5 X[48042] - 2 X[48134], 5 X[48089] - 3 X[48134], 4 X[48089] - 3 X[48399], 4 X[48134] - 5 X[48399]

X(48590) lies on these lines: {513, 4507}, {514, 47685}, {522, 47944}, {661, 48072}, {1491, 45313}, {2254, 48071}, {2526, 4932}, {3667, 47979}, {3835, 47694}, {4778, 48103}, {4962, 48079}, {28225, 48069}, {47878, 48019}, {47892, 47939}, {47927, 47945}, {48027, 48063}, {48042, 48089}

X(48590) = midpoint of X(47940) and X(48020)
X(48590) = reflection of X(i) in X(j) for these {i,j}: {3835, 48023}, {4932, 2526}, {47996, 47985}, {48009, 47992}, {48016, 48017}, {48063, 48027}, {48071, 2254}, {48072, 661}, {48399, 48042}
X(48590) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47985, 48009, 47992}, {47992, 48009, 47996}


X(48591) = X(513)X(47987)∩X(514)X(4170)

Barycentrics    a*(b - c)*(6*a*b + 2*b^2 + 6*a*c + 9*b*c + 2*c^2) : :
X(48591) = 3 X[47987] - 2 X[47994], 5 X[47987] - 2 X[48005], 3 X[47987] - X[48012], 4 X[47987] - X[48018], 4 X[47994] - 3 X[47997], 5 X[47994] - 3 X[48005], 8 X[47994] - 3 X[48018], 5 X[47997] - 4 X[48005], 3 X[47997] - 2 X[48012], 6 X[48005] - 5 X[48012], 8 X[48005] - 5 X[48018], 4 X[48012] - 3 X[48018], 3 X[4822] + 5 X[47906], X[4822] + 5 X[47942], X[4822] - 5 X[48021], 3 X[4822] - 5 X[48081], X[47906] - 3 X[47942], X[47906] + 3 X[48021], 3 X[47942] + X[48081], 3 X[48021] - X[48081], X[2530] - 3 X[48024], 2 X[2530] - 3 X[48054], 2 X[3803] - 3 X[48065], 5 X[4490] - 3 X[4730], X[4490] - 3 X[47949], X[4730] - 5 X[47949], 3 X[4983] - X[23765], 3 X[48045] - 2 X[48093], 5 X[48045] - 2 X[48137], 5 X[48093] - 3 X[48137]

X(48591) lies on these lines: {513, 47987}, {514, 4170}, {659, 48074}, {661, 48075}, {2530, 48024}, {3803, 15309}, {3887, 47915}, {4129, 28225}, {4490, 4730}, {4778, 4823}, {4983, 23765}, {6372, 48045}, {8714, 47986}, {29164, 48082}, {29270, 47969}, {29350, 47913}, {42325, 47955}, {47977, 48019}, {48028, 48066}, {48029, 48064}

X(48591) = midpoint of X(i) and X(j) for these {i,j}: {47906, 48081}, {47942, 48021}, {47977, 48019}
X(48591) = reflection of X(i) in X(j) for these {i,j}: {47997, 47987}, {48011, 48004}, {48012, 47994}, {48018, 47997}, {48054, 48024}, {48064, 48029}, {48066, 48028}, {48074, 659}, {48075, 661}
X(48591) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47906, 48021, 48081}, {47942, 48081, 47906}, {47987, 48012, 47994}, {47994, 48012, 47997}


X(48592) = X(513)X(3716)∩X(514)X(4838)

Barycentrics    (b - c)*(-4*a^2 - 5*a*b - 5*a*c + b*c) : :
X(48592) = 5 X[3835] - 4 X[4369], 9 X[3835] - 8 X[4885], 13 X[3835] - 12 X[4928], 3 X[3835] - 2 X[4932], 7 X[3835] - 8 X[4940], 21 X[3835] - 16 X[7653], 7 X[3835] - 6 X[47779], 3 X[3835] - 4 X[48049], 9 X[4369] - 10 X[4885], 13 X[4369] - 15 X[4928], 6 X[4369] - 5 X[4932], 7 X[4369] - 10 X[4940], 21 X[4369] - 20 X[7653], 14 X[4369] - 15 X[47779], 2 X[4369] - 5 X[48041], 3 X[4369] - 5 X[48049], 8 X[4369] - 5 X[48071], 26 X[4885] - 27 X[4928], 4 X[4885] - 3 X[4932], 7 X[4885] - 9 X[4940], 7 X[4885] - 6 X[7653], 28 X[4885] - 27 X[47779], 4 X[4885] - 9 X[48041], 2 X[4885] - 3 X[48049], 16 X[4885] - 9 X[48071], 18 X[4928] - 13 X[4932], 21 X[4928] - 26 X[4940], 63 X[4928] - 52 X[7653], 14 X[4928] - 13 X[47779], 6 X[4928] - 13 X[48041], 9 X[4928] - 13 X[48049], 24 X[4928] - 13 X[48071], 7 X[4932] - 12 X[4940], 7 X[4932] - 8 X[7653], 7 X[4932] - 9 X[47779], X[4932] - 3 X[48041], 4 X[4932] - 3 X[48071], 3 X[4940] - 2 X[7653], 4 X[4940] - 3 X[47779], 4 X[4940] - 7 X[48041], 6 X[4940] - 7 X[48049], 16 X[4940] - 7 X[48071], 8 X[7653] - 9 X[47779], 8 X[7653] - 21 X[48041], 4 X[7653] - 7 X[48049], 32 X[7653] - 21 X[48071], 3 X[47779] - 7 X[48041], 9 X[47779] - 14 X[48049], 12 X[47779] - 7 X[48071], 3 X[48041] - 2 X[48049], 4 X[48041] - X[48071], 3 X[48043] - 2 X[48248], 8 X[48049] - 3 X[48071], X[47658] - 3 X[48266], 3 X[47903] - 5 X[47939], X[47903] - 5 X[48019], X[47903] + 5 X[48079], 3 X[47903] + 5 X[48114], X[47939] - 3 X[48019], X[47939] + 3 X[48079], 3 X[48019] + X[48114], 3 X[48079] - X[48114], 3 X[47920] - 5 X[47952], 2 X[47920] - 5 X[47984], 2 X[47952] - 3 X[47984], 3 X[4813] - X[17494], 5 X[4813] - 3 X[47774], 5 X[17494] - 9 X[47774], 2 X[17494] - 3 X[47996], 6 X[47774] - 5 X[47996], 2 X[4790] - 3 X[47778], 3 X[4979] - 5 X[31209], 2 X[4979] - 3 X[45313], 10 X[31209] - 9 X[45313], 3 X[20295] - X[48141], 2 X[48141] - 3 X[48399], X[21222] - 3 X[48121], 5 X[26798] - 3 X[48577], X[26853] - 3 X[48544], 2 X[31286] - 3 X[47759], 5 X[48008] - 6 X[48560], 5 X[48026] - 3 X[48560], 3 X[48085] - X[48321]

X(48592) lies on these lines: {513, 3716}, {514, 4838}, {661, 48016}, {812, 47920}, {2786, 47981}, {3667, 47979}, {4500, 28209}, {4785, 4813}, {4790, 47778}, {4962, 47940}, {4979, 31209}, {6006, 21196}, {6008, 47991}, {20295, 48141}, {21222, 48121}, {23729, 28886}, {23731, 30519}, {26798, 48577}, {26853, 48544}, {28217, 48404}, {28840, 48125}, {28867, 47988}, {28906, 47958}, {29738, 48144}, {31286, 47759}, {48008, 48026}, {48014, 48020}, {48085, 48321}

X(48592) = midpoint of X(i) and X(j) for these {i,j}: {44449, 47937}, {47939, 48114}, {48019, 48079}
X(48592) = reflection of X(i) in X(j) for these {i,j}: {3835, 48041}, {4932, 48049}, {47996, 4813}, {48008, 48026}, {48016, 661}, {48071, 3835}, {48072, 48037}, {48399, 20295}
X(48592) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4932, 47779, 7653}, {4932, 48041, 48049}, {4932, 48049, 3835}, {4940, 47779, 3835}, {47939, 48079, 48114}, {48019, 48114, 47939}


X(48593) = X(513)X(3716)∩X(514)X(47685)

Barycentrics    (b - c)*(-4*a^3 - a^2*b - 5*a*b^2 - a^2*c - a*b*c + b^2*c - 5*a*c^2 + b*c^2) : :
X(48593) = 4 X[3716] - 5 X[3835], 2 X[3716] - 5 X[48042], 3 X[3716] - 5 X[48050], 6 X[3716] - 5 X[48063], 8 X[3716] - 5 X[48072], 14 X[3716] - 15 X[48547], 3 X[3835] - 4 X[48050], 3 X[3835] - 2 X[48063], 7 X[3835] - 6 X[48547], 3 X[48042] - 2 X[48050], 3 X[48042] - X[48063], 4 X[48042] - X[48072], 7 X[48042] - 3 X[48547], 8 X[48050] - 3 X[48072], 14 X[48050] - 9 X[48547], 4 X[48063] - 3 X[48072], 7 X[48063] - 9 X[48547], 7 X[48072] - 12 X[48547], 3 X[47685] + X[47940], 3 X[47685] - X[48115], X[47940] - 3 X[48020], 3 X[48020] + X[48115], 3 X[48122] - X[48298], 2 X[31286] - 3 X[48164], 3 X[46403] - X[48142], 2 X[48142] - 3 X[48399], 2 X[47953] - 3 X[47985], 2 X[47969] - 3 X[47996], X[47969] - 3 X[48023], X[48138] - 3 X[48169]

X(48593) lies on these lines: {513, 3716}, {514, 47685}, {522, 47968}, {2254, 48016}, {2526, 48008}, {3239, 48019}, {3667, 48015}, {4453, 48013}, {4522, 28209}, {4778, 48083}, {4962, 48114}, {28225, 48036}, {28470, 48122}, {31286, 48164}, {46403, 48142}, {47953, 47985}, {47969, 47996}, {48009, 48027}, {48138, 48169}

X(48593) = midpoint of X(i) and X(j) for these {i,j}: {47685, 48020}, {47689, 47901}, {47940, 48115}
X(48593) = reflection of X(i) in X(j) for these {i,j}: {3835, 48042}, {47996, 48023}, {48008, 2526}, {48009, 48027}, {48016, 2254}, {48063, 48050}, {48071, 48073}, {48072, 3835}, {48399, 46403}
X(48593) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47685, 47940, 48115}, {48020, 48115, 47940}, {48042, 48063, 48050}, {48050, 48063, 3835}


X(48594) = X(513)X(4401)∩X(514)X(4170)

Barycentrics    a*(b - c)*(6*a*b + 2*b^2 + 6*a*c + 7*b*c + 2*c^2) : :
X(48594) = 3 X[47922] - 5 X[47957], 2 X[47922] - 5 X[47987], 2 X[47957] - 3 X[47987], 2 X[6050] - 3 X[48058], 4 X[6050] - 3 X[48064], 3 X[48045] - 2 X[48053], 5 X[48045] - 2 X[48059], 3 X[48045] - X[48066], 4 X[48045] - X[48075], 4 X[48053] - 3 X[48054], 5 X[48053] - 3 X[48059], 8 X[48053] - 3 X[48075], 5 X[48054] - 4 X[48059], 3 X[48054] - 2 X[48066], 6 X[48059] - 5 X[48066], 8 X[48059] - 5 X[48075], 4 X[48066] - 3 X[48075], 5 X[4822] + 3 X[47906], X[4822] + 3 X[48021], X[4822] - 3 X[48081], 3 X[47906] - 5 X[47942], X[47906] - 5 X[48021], X[47906] + 5 X[48081], X[47942] - 3 X[48021], X[47942] + 3 X[48081], X[3777] - 3 X[4983], 2 X[4705] - 3 X[47997], X[4705] - 3 X[48024], X[4729] - 3 X[47959]

X(48594) lies on these lines: {512, 47922}, {513, 4401}, {514, 4170}, {661, 48018}, {3777, 4983}, {3887, 47955}, {4151, 47986}, {4705, 6005}, {4729, 47959}, {4778, 30591}, {4794, 15309}, {4823, 48043}, {6372, 48129}, {29260, 48082}, {29350, 47949}, {42325, 48026}, {47911, 48352}, {47947, 48367}, {48011, 48029}, {48012, 48028}, {48019, 48111}

X(48594) = midpoint of X(i) and X(j) for these {i,j}: {4170, 47941}, {4822, 47942}, {47911, 48352}, {47947, 48367}, {48019, 48111}, {48021, 48081}
X(48594) = reflection of X(i) in X(j) for these {i,j}: {4823, 48043}, {47997, 48024}, {48011, 48029}, {48012, 48028}, {48018, 661}, {48054, 48045}, {48064, 48058}, {48066, 48053}, {48074, 4401}, {48075, 48054}
X(48594) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4822, 48021, 47942}, {47942, 48081, 4822}, {48045, 48066, 48053}, {48053, 48066, 48054}


X(48595) = X(36)X(238)∩X(514)X(4838)

Barycentrics    a*(b - c)*(2*a^2 + 5*a*b + 3*b^2 + 5*a*c + 5*b*c + 3*c^2) : :
X(48595) = 6 X[905] - 5 X[1019], 4 X[905] - 5 X[14349], 2 X[905] - 5 X[48085], 3 X[905] - 5 X[48091], 8 X[905] - 5 X[48110], 2 X[1019] - 3 X[14349], X[1019] - 3 X[48085], 4 X[1019] - 3 X[48110], 3 X[4983] - 2 X[48331], 3 X[14349] - 4 X[48091], 3 X[48081] - 2 X[48351], 3 X[48085] - 2 X[48091], 4 X[48085] - X[48110], 8 X[48091] - 3 X[48110], 3 X[48111] - 4 X[48351], 3 X[661] - 2 X[48011], 3 X[47976] - 4 X[48011], X[4498] - 3 X[4813], 2 X[4498] - 3 X[47959], 3 X[48121] - X[48341], 3 X[48335] - 2 X[48341], 2 X[47915] - 3 X[47947], 2 X[48003] - 3 X[48544], 2 X[48071] - 3 X[48568], 3 X[48123] - 2 X[48328]

X(48595) lies on these lines: {36, 238}, {514, 4838}, {649, 48051}, {661, 47976}, {1577, 48041}, {4063, 48026}, {4106, 4960}, {4498, 4813}, {4822, 48324}, {4961, 47934}, {4978, 23794}, {4979, 48054}, {7265, 28859}, {15309, 48121}, {21385, 47955}, {23731, 23875}, {28493, 47679}, {29302, 31290}, {29358, 47902}, {47915, 47947}, {47935, 47997}, {47977, 48021}, {48003, 48544}, {48071, 48568}, {48123, 48328}, {48128, 48320}

X(48595) = reflection of X(i) in X(j) for these {i,j}: {649, 48051}, {1019, 48091}, {1577, 48041}, {4063, 48026}, {4960, 4106}, {4979, 48054}, {14349, 48085}, {21385, 47955}, {47935, 47997}, {47959, 4813}, {47976, 661}, {47977, 48021}, {48110, 14349}, {48111, 48081}, {48320, 48128}, {48324, 4822}, {48335, 48121}
X(48595) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1019, 48085, 48091}, {1019, 48091, 14349}


X(48596) = X(36)X(238)∩X(514)X(47685)

Barycentrics    a*(b - c)*(2*a^2 + a*b + 3*b^2 + a*c + b*c + 3*c^2) : :
X(48596) = 2 X[4040] - 3 X[14349], X[4040] - 3 X[48086], 5 X[4040] - 6 X[48099], 4 X[4040] - 3 X[48111], 3 X[14349] - 4 X[48092], 5 X[14349] - 4 X[48099], 3 X[48086] - 2 X[48092], 5 X[48086] - 2 X[48099], 4 X[48086] - X[48111], 5 X[48092] - 3 X[48099], 8 X[48092] - 3 X[48111], 8 X[48099] - 5 X[48111], X[47905] - 3 X[48020], X[47905] + 3 X[48116], X[4449] - 3 X[48122], 2 X[4449] - 3 X[48335], 2 X[20517] - 3 X[48159], 4 X[23814] - 3 X[48570], 2 X[47929] - 3 X[47959], X[47929] - 3 X[48023], 3 X[48131] - 2 X[48294], 4 X[48294] - 3 X[48324]

X(48596) lies on these lines: {36, 238}, {514, 47685}, {661, 47977}, {830, 4449}, {1577, 48042}, {2254, 47976}, {2526, 4063}, {2832, 47912}, {4724, 48052}, {4977, 48272}, {4979, 48075}, {6161, 48129}, {7950, 47925}, {20517, 48159}, {23814, 48570}, {29021, 47943}, {29164, 47916}, {29358, 47931}, {42325, 48121}, {47929, 47959}, {47935, 48018}, {47936, 47997}, {47970, 48027}, {48032, 48054}, {48128, 48352}, {48131, 48294}

X(48596) = midpoint of X(48020) and X(48116)
X(48596) = reflection of X(i) in X(j) for these {i,j}: {1577, 48042}, {4040, 48092}, {4063, 2526}, {4724, 48052}, {4979, 48075}, {6161, 48129}, {14349, 48086}, {47935, 48018}, {47936, 47997}, {47959, 48023}, {47970, 48027}, {47976, 2254}, {47977, 661}, {48032, 48054}, {48110, 4905}, {48111, 14349}, {48324, 48131}, {48335, 48122}, {48352, 48128}
X(48596) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4040, 48086, 48092}, {4040, 48092, 14349}


X(48597) = X(513)X(663)∩X(514)X(4838)

Barycentrics    a*(b - c)*(2*a^2 + 5*a*b + 3*b^2 + 5*a*c + 4*b*c + 3*c^2) : :
X(48597) = 2 X[3669] - 5 X[48121], 3 X[3669] - 5 X[48128], 4 X[3669] - 5 X[48131], 6 X[3669] - 5 X[48144], 8 X[3669] - 5 X[48149], 3 X[4822] - 2 X[48336], 3 X[14413] - 4 X[48129], 3 X[48121] - 2 X[48128], 3 X[48121] - X[48144], 4 X[48121] - X[48149], 3 X[48123] - 2 X[48330], 4 X[48128] - 3 X[48131], 8 X[48128] - 3 X[48149], 3 X[48131] - 2 X[48144], 4 X[48144] - 3 X[48149], 3 X[48150] - 4 X[48336], 3 X[661] - 2 X[4063], 5 X[661] - 4 X[48003], 3 X[661] - 4 X[48051], 4 X[4063] - 3 X[47935], 5 X[4063] - 6 X[48003], X[4063] - 3 X[48085], 5 X[47935] - 8 X[48003], 3 X[47935] - 8 X[48051], X[47935] - 4 X[48085], 3 X[48003] - 5 X[48051], 2 X[48003] - 5 X[48085], 2 X[48051] - 3 X[48085], 3 X[1635] - 2 X[47976], 3 X[1635] - 4 X[48054], 3 X[4813] - 2 X[47955], 3 X[47918] - 4 X[47955], 2 X[4834] - 3 X[47810], 3 X[4979] - 4 X[48064], 3 X[14349] - 2 X[48064], 3 X[47811] - 4 X[48053], 2 X[47965] - 3 X[48544], 2 X[48071] - 3 X[48570]

X(48597) lies on these lines: {512, 47905}, {513, 663}, {514, 4838}, {525, 23731}, {649, 48091}, {661, 4063}, {826, 47902}, {1635, 47976}, {4170, 48153}, {4391, 48041}, {4498, 48026}, {4729, 47948}, {4813, 47918}, {4834, 47810}, {4978, 48147}, {4979, 14349}, {6005, 48020}, {8712, 47911}, {15309, 48334}, {21124, 47988}, {23875, 47916}, {28209, 48280}, {28478, 47981}, {28493, 45746}, {29216, 47673}, {29252, 47931}, {29302, 47917}, {47811, 48053}, {47936, 48021}, {47965, 48544}, {48032, 48081}, {48071, 48570}

X(48597) = reflection of X(i) in X(j) for these {i,j}: {649, 48091}, {661, 48085}, {4063, 48051}, {4391, 48041}, {4498, 48026}, {4729, 47948}, {4979, 14349}, {21124, 47988}, {47918, 4813}, {47935, 661}, {47936, 48021}, {47976, 48054}, {48032, 48081}, {48131, 48121}, {48144, 48128}, {48147, 4978}, {48149, 48131}, {48150, 4822}, {48153, 4170}
X(48597) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4063, 48051, 661}, {4063, 48085, 48051}, {47976, 48054, 1635}, {48121, 48144, 48128}, {48128, 48144, 48131}


X(48598) = X(513)X(47702)∩X(514)X(4088)

Barycentrics    (b - c)*(3*a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3 + 3*a^2*c + 2*a*b*c + 2*b^2*c + 4*a*c^2 + 2*b*c^2 + 2*c^3) : :
X(48598) = X[47702] + 3 X[47901], X[47702] - 3 X[47916], 2 X[47702] - 3 X[47924], 2 X[47901] + X[47924], X[4088] - 3 X[47943], 2 X[4088] - 3 X[48023], 5 X[4088] - 6 X[48039], 4 X[4088] - 3 X[48118], 3 X[47943] - 2 X[47982], 5 X[47943] - 2 X[48039], 4 X[47943] - X[48118], 4 X[47982] - 3 X[48023], 5 X[47982] - 3 X[48039], 8 X[47982] - 3 X[48118], 5 X[48023] - 4 X[48039], 8 X[48039] - 5 X[48118], 3 X[661] - 2 X[48096], 3 X[47951] - X[48096], 4 X[47951] - X[48139], 4 X[48096] - 3 X[48139], 3 X[4724] - 4 X[47998], 3 X[4724] - 2 X[48105], 3 X[47958] - 2 X[47998], 3 X[47958] - X[48105], 3 X[47701] - 2 X[48014], 3 X[4893] - 4 X[47999], 4 X[4925] - 3 X[48106], 3 X[47826] - 4 X[47995], 3 X[47826] - 2 X[48102], 2 X[47696] - 3 X[47832], 3 X[47810] - 2 X[48095], 3 X[47828] - 4 X[48007], 3 X[47828] - 2 X[48101], 2 X[48072] - 3 X[48158], 2 X[48083] - 3 X[48544]

X(48598) lies on these lines: {513, 47702}, {514, 4088}, {649, 47968}, {661, 28195}, {676, 1459}, {1491, 48138}, {2526, 48146}, {4778, 47676}, {4802, 48020}, {4893, 47999}, {4925, 48106}, {28175, 48077}, {28191, 48035}, {28199, 47700}, {28209, 47972}, {28213, 47989}, {28220, 47961}, {28229, 47780}, {47652, 48142}, {47662, 48050}, {47696, 47832}, {47810, 48095}, {47828, 48007}, {47950, 48021}, {47988, 48078}, {48026, 48113}, {48027, 48130}, {48072, 48158}, {48083, 48544}

X(48598) = midpoint of X(47901) and X(47916)
X(48598) = reflection of X(i) in X(j) for these {i,j}: {649, 47968}, {661, 47951}, {4088, 47982}, {4724, 47958}, {47662, 48050}, {47693, 48042}, {47923, 47925}, {47924, 47916}, {48021, 47950}, {48023, 47943}, {48032, 47961}, {48078, 47988}, {48094, 47989}, {48101, 48007}, {48102, 47995}, {48105, 47998}, {48113, 48026}, {48118, 48023}, {48119, 47686}, {48130, 48027}, {48138, 1491}, {48139, 661}, {48142, 47652}, {48146, 2526}
X(48598) = crossdifference of every pair of points on line {3730, 21764}
X(48598) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4088, 47943, 47982}, {4088, 47982, 48023}, {47958, 48105, 47998}, {47995, 48102, 47826}, {47998, 48105, 4724}, {48007, 48101, 47828}


X(48599) = X(513)X(47702)∩X(514)X(4010)

Barycentrics    (b - c)*(2*a^3 + 4*a^2*b + 3*a*b^2 + 2*b^3 + 4*a^2*c + 3*a*b*c + 2*b^2*c + 3*a*c^2 + 2*b*c^2 + 2*c^3) : :
X(48599) = 2 X[47902] + X[47925], 3 X[47902] + X[47931], 3 X[47916] - X[47931], 3 X[47925] - 2 X[47931], 3 X[47944] - 2 X[47983], 5 X[47944] - 2 X[48040], 3 X[47944] - X[48083], 4 X[47983] - 3 X[48024], 5 X[47983] - 3 X[48040], 5 X[48024] - 4 X[48040], 3 X[48024] - 2 X[48083], 6 X[48040] - 5 X[48083], 3 X[661] - 2 X[48097], 4 X[48097] - 3 X[48140], 3 X[1491] - 4 X[47999], 3 X[1491] - 2 X[48106], 3 X[47958] - 2 X[47999], 3 X[47958] - X[48106], 3 X[4951] - 2 X[47693], 2 X[18004] - 3 X[48543], 5 X[30795] - 6 X[48558], 3 X[47968] - 2 X[48015], 2 X[48095] - 3 X[48162], 2 X[48101] - 3 X[48226], 2 X[48405] - 3 X[48550]

X(48599) lies on these lines: {513, 47702}, {514, 4010}, {523, 47940}, {659, 47961}, {661, 48097}, {1491, 47958}, {2976, 4977}, {4382, 4802}, {4782, 48145}, {4784, 47960}, {4806, 47662}, {4810, 28894}, {4931, 28199}, {4951, 47693}, {18004, 48543}, {28175, 47656}, {28195, 48142}, {28859, 48326}, {29144, 47943}, {29328, 47653}, {30795, 48558}, {47652, 48143}, {47968, 48015}, {47990, 48094}, {47995, 48103}, {48028, 48130}, {48030, 48146}, {48095, 48162}, {48101, 48226}, {48405, 48550}

X(48599) = midpoint of X(i) and X(j) for these {i,j}: {47902, 47916}, {47907, 47924}
X(48599) = reflection of X(i) in X(j) for these {i,j}: {659, 47961}, {1491, 47958}, {4784, 47960}, {47662, 4806}, {47925, 47916}, {48024, 47944}, {48083, 47983}, {48094, 47990}, {48103, 47995}, {48106, 47999}, {48130, 48028}, {48140, 661}, {48143, 47652}, {48145, 4782}, {48146, 48030}
X(48599) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47944, 48083, 47983}, {47958, 48106, 47999}, {47983, 48083, 48024}, {47999, 48106, 1491}


X(48600) = X(513)X(47987)∩X(514)X(4024)

Barycentrics    a*(b - c)*(2*a^2 + 6*a*b + 4*b^2 + 6*a*c + 9*b*c + 4*c^2) : :
X(48600) = 3 X[47997] - 2 X[48003], 4 X[48003] - 3 X[48011], 3 X[4813] + X[47911], 3 X[4813] - X[48085], 5 X[4813] - X[48121], X[47911] - 3 X[47947], 5 X[47911] + 3 X[48121], 3 X[47947] + X[48085], 5 X[47947] + X[48121], 5 X[48085] - 3 X[48121], 3 X[661] - X[48110], 3 X[48064] - 2 X[48110], X[905] - 3 X[48026], 2 X[905] - 3 X[48054], X[1019] - 3 X[48544], 2 X[4932] - 3 X[48196], X[47921] - 3 X[47955], X[47935] - 3 X[47959], X[47935] + 3 X[48019], X[48107] - 3 X[48551]

X(48600) lies on these lines: {513, 47987}, {514, 4024}, {650, 48074}, {661, 48064}, {905, 15309}, {1019, 48544}, {1577, 47939}, {4129, 21191}, {4401, 48028}, {4794, 48045}, {4823, 28840}, {4932, 27045}, {4983, 48294}, {29013, 47991}, {29260, 47938}, {29270, 47666}, {47921, 47955}, {47935, 47959}, {48024, 48065}, {48027, 48075}, {48093, 48343}, {48107, 48551}

X(48600) = midpoint of X(i) and X(j) for these {i,j}: {1577, 47939}, {4813, 47947}, {47911, 48085}, {47959, 48019}
X(48600) = reflection of X(i) in X(j) for these {i,j}: {4401, 48028}, {4794, 48045}, {48011, 47997}, {48054, 48026}, {48064, 661}, {48065, 48024}, {48074, 650}, {48075, 48027}, {48294, 4983}, {48343, 48093}
X(48600) = crossdifference of every pair of points on line {2308, 16884}
X(48600) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4813, 47911, 48085}, {47947, 48085, 47911}


X(48601) = X(513)X(47987)∩X(514)X(4088)

Barycentrics    a*(b - c)*(2*a^2 + 2*a*b + 4*b^2 + 2*a*c + 5*b*c + 4*c^2) : :
X(48601) = 3 X[47997] - 2 X[48004], X[47912] - 3 X[47948], X[47912] + 3 X[48023], 5 X[47912] + 3 X[48122], 3 X[47948] + X[48086], 5 X[47948] + X[48122], 3 X[48023] - X[48086], 5 X[48023] - X[48122], 5 X[48086] - 3 X[48122], 3 X[661] - X[48111], 3 X[48065] - 2 X[48111], X[4794] - 4 X[48027], 3 X[4794] - 4 X[48099], 5 X[4794] - 4 X[48329], 3 X[48027] - X[48099], 5 X[48027] - X[48329], 3 X[48054] - 2 X[48099], 5 X[48054] - 2 X[48329], 5 X[48099] - 3 X[48329], 3 X[48092] - X[48346], 4 X[48052] - X[48287], 3 X[48052] - X[48348], 3 X[48287] - 4 X[48348], 3 X[14349] - X[48322], 2 X[47905] + X[48294], 3 X[47905] + X[48322], 3 X[48294] - 2 X[48322], X[47697] - 3 X[48551], X[47936] - 3 X[47959], X[47936] + 3 X[48020]

X(48601) lies on these lines: {513, 47987}, {514, 4088}, {661, 48065}, {830, 4794}, {1491, 48064}, {1577, 47940}, {2526, 15309}, {3309, 48051}, {3887, 48091}, {4160, 48092}, {4401, 48030}, {6004, 48045}, {8678, 48052}, {14349, 47905}, {29047, 47989}, {29164, 48077}, {29178, 48409}, {29186, 47992}, {29260, 47958}, {29270, 47975}, {42325, 48026}, {47697, 48551}, {47936, 47959}, {48100, 48343}

X(48601) = midpoint of X(i) and X(j) for these {i,j}: {1577, 47940}, {14349, 47905}, {47912, 48086}, {47948, 48023}, {47959, 48020}
X(48601) = reflection of X(i) in X(j) for these {i,j}: {4401, 48030}, {4794, 48054}, {48011, 48012}, {48054, 48027}, {48064, 1491}, {48065, 661}, {48075, 2526}, {48294, 14349}, {48343, 48100}
X(48601) = crossdifference of every pair of points on line {16884, 21764}
X(48601) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47912, 48023, 48086}, {47948, 48086, 47912}


X(48602) = X(513)X(4401)∩X(514)X(4024)

Barycentrics    a*(b - c)*(2*a^2 + 6*a*b + 4*b^2 + 6*a*c + 7*b*c + 4*c^2) : :
X(48602) = X[14838] - 3 X[48051], 2 X[14838] - 3 X[48054], 4 X[14838] - 3 X[48064], 4 X[48051] - X[48064], 6 X[48051] - X[48074], 3 X[48054] - X[48074], 3 X[48064] - 2 X[48074], 5 X[4813] - X[47911], 3 X[4813] - X[47947], 3 X[4813] + X[48121], 3 X[47911] - 5 X[47947], X[47911] + 5 X[48085], 3 X[47911] + 5 X[48121], X[47947] + 3 X[48085], 3 X[48085] - X[48121], 3 X[661] - X[47976], 2 X[47976] - 3 X[48011], X[3669] - 3 X[48091], X[4063] - 3 X[48544], 2 X[4932] - 3 X[48218], X[4960] - 3 X[31147], 3 X[14349] - X[48149], 3 X[48019] + X[48149], 2 X[47965] - 3 X[47997], X[47965] - 3 X[48026]

X(48602) lies on these lines: {513, 4401}, {514, 4024}, {661, 47976}, {3669, 15309}, {4063, 48544}, {4794, 4983}, {4823, 48049}, {4824, 4961}, {4932, 27167}, {4960, 31147}, {4978, 47939}, {14349, 48019}, {23875, 47988}, {29164, 47938}, {29270, 48079}, {29302, 47991}, {29358, 47944}, {47965, 47997}, {48018, 48027}, {48123, 48287}

X(48602) = midpoint of X(i) and X(j) for these {i,j}: {4813, 48085}, {4978, 47939}, {14349, 48019}, {47947, 48121}
X(48602) = reflection of X(i) in X(j) for these {i,j}: {4401, 48053}, {4794, 4983}, {4823, 48049}, {47997, 48026}, {48011, 661}, {48018, 48027}, {48054, 48051}, {48064, 48054}, {48065, 48045}, {48074, 14838}, {48075, 48052}, {48287, 48123}
X(48602) = crossdifference of every pair of points on line {2308, 16777}
X(48602) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4813, 48121, 47947}, {14838, 48074, 48064}, {47947, 48085, 48121}, {48054, 48074, 14838}


X(48603) = X(513)X(4401)∩X(514)X(4088)

Barycentrics    a*(b - c)*(2*a^2 + 2*a*b + 4*b^2 + 2*a*c + 3*b*c + 4*c^2) : :
X(48603) = 3 X[48052] - X[48058], 4 X[48052] - X[48065], 3 X[48054] - 2 X[48058], 4 X[48058] - 3 X[48065], 3 X[47912] - 5 X[47948], X[47912] - 5 X[48023], X[47912] + 5 X[48086], 3 X[47912] + 5 X[48122], X[47948] - 3 X[48023], X[47948] + 3 X[48086], 3 X[48023] + X[48122], 3 X[48086] - X[48122], 3 X[661] - X[47977], 3 X[48092] - X[48136], 4 X[48092] - X[48294], 5 X[48092] - X[48327], 4 X[48136] - 3 X[48294], 5 X[48136] - 3 X[48327], 5 X[48294] - 4 X[48327], X[4794] + 2 X[48020], 3 X[4794] - 2 X[48150], 3 X[14349] - X[48150], 3 X[48020] + X[48150], X[4834] - 3 X[48160], 2 X[47966] - 3 X[47997], X[47966] - 3 X[48027]

X(48603) lies on these lines: {513, 4401}, {514, 4088}, {661, 47977}, {830, 48092}, {1491, 48011}, {2526, 48018}, {2832, 47956}, {3887, 48128}, {4794, 14349}, {4823, 48050}, {4834, 48160}, {4978, 47940}, {28591, 47979}, {29021, 47989}, {29164, 47958}, {29178, 48410}, {29260, 48077}, {29270, 48409}, {29358, 47968}, {42325, 48091}, {47905, 48335}, {47959, 48116}, {47966, 47997}, {48131, 48287}

X(48603) = midpoint of X(i) and X(j) for these {i,j}: {4978, 47940}, {14349, 48020}, {28591, 47979}, {47905, 48335}, {47943, 48272}, {47948, 48122}, {47959, 48116}, {48023, 48086}
X(48603) = reflection of X(i) in X(j) for these {i,j}: {4401, 48059}, {4794, 14349}, {4823, 48050}, {47997, 48027}, {48011, 1491}, {48018, 2526}, {48054, 48052}, {48064, 48066}, {48065, 48054}, {48287, 48131}
X(48603) = crossdifference of every pair of points on line {16777, 21764}
X(48603) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47948, 48086, 48122}, {48023, 48122, 47948}


X(48604) = X(513)X(47700)∩X(514)X(4010)

Barycentrics    (b - c)*(2*a^3 + a*b^2 + 2*b^3 - 3*a*b*c + 2*b^2*c + a*c^2 + 2*b*c^2 + 2*c^3) : :
(48604) = 2 X[48113] + X[48140], 3 X[48113] + X[48146], 3 X[48130] - X[48146], 3 X[48140] - 2 X[48146], 5 X[47944] - 6 X[47983], 2 X[47944] - 3 X[48024], X[47944] - 3 X[48083], 4 X[47983] - 5 X[48024], 3 X[47983] - 5 X[48040], 2 X[47983] - 5 X[48083], 3 X[48024] - 4 X[48040], 2 X[48040] - 3 X[48083], 3 X[1491] - 2 X[47973], 3 X[1491] - 4 X[48056], X[47973] - 3 X[48094], 2 X[48056] - 3 X[48094], 2 X[3837] - 3 X[48557], 3 X[4951] - 2 X[46403], 2 X[16892] - 3 X[48226], 5 X[30795] - 6 X[47770], 2 X[47960] - 3 X[48162], 2 X[48069] - 3 X[48103], 6 X[48206] - 5 X[48421], 6 X[48215] - 5 X[48425], 3 X[48234] - 2 X[48326]

X(48604) lies on these lines: {513, 47700}, {514, 4010}, {523, 47974}, {659, 30520}, {661, 47925}, {1491, 47973}, {2254, 48097}, {3837, 48557}, {4468, 47968}, {4782, 47930}, {4784, 48095}, {4802, 47927}, {4806, 47651}, {4951, 46403}, {4977, 47662}, {7950, 47977}, {16892, 48226}, {18004, 47686}, {23765, 48300}, {28195, 47908}, {28213, 48046}, {29146, 47936}, {29204, 48032}, {30795, 47770}, {47660, 48143}, {47873, 48026}, {47916, 48028}, {47931, 48030}, {47958, 48048}, {47960, 48162}, {48069, 48103}, {48206, 48421}, {48215, 48425}, {48234, 48326}

(48604) = midpoint of X(i) and X(j) for these {i,j}: {48113, 48130}, {48117, 48139}
(48604) = reflection of X(i) in X(j) for these {i,j}: {659, 48096}, {1491, 48094}, {2254, 48097}, {4784, 48095}, {23765, 48300}, {47651, 4806}, {47686, 18004}, {47916, 48028}, {47925, 661}, {47930, 4782}, {47931, 48030}, {47944, 48040}, {47958, 48048}, {47968, 4468}, {47973, 48056}, {48024, 48083}, {48140, 48130}, {48143, 47660}
(48604) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47944, 48040, 48024}, {47944, 48083, 48040}, {47973, 48056, 1491}, {47973, 48094, 48056}


X(48605) = X(513)X(47702)∩X(514)X(3700)

Barycentrics    (b - c)*(5*a^2 + 3*a*b + 4*b^2 + 3*a*c + 4*c^2) : :
X(48605) = X[47900] - 3 X[47907], X[47900] + 3 X[47916], 2 X[47900] + 3 X[47919], 5 X[47900] + 3 X[47930], 2 X[47907] + X[47919], 3 X[47907] + X[47923], 5 X[47907] + X[47930], 3 X[47916] - X[47923], 5 X[47916] - X[47930], 3 X[47919] - 2 X[47923], 5 X[47919] - 2 X[47930], 5 X[47923] - 3 X[47930], 3 X[47950] - 2 X[47988], 5 X[47950] - 2 X[48046], 3 X[47950] - X[48087], 4 X[47950] - X[48124], 4 X[47988] - 3 X[48026], 5 X[47988] - 3 X[48046], 8 X[47988] - 3 X[48124], 5 X[48026] - 4 X[48046], 3 X[48026] - 2 X[48087], 6 X[48046] - 5 X[48087], 8 X[48046] - 5 X[48124], 4 X[48087] - 3 X[48124], 3 X[650] - 2 X[48101], 3 X[47958] - X[48101], 4 X[4025] - 3 X[4790], 2 X[4025] - 3 X[47960], 5 X[4025] - 3 X[48067], 5 X[4790] - 4 X[48067], 5 X[47960] - 2 X[48067], 3 X[23731] - X[48076], 5 X[31250] - 6 X[48558], 3 X[47777] - 4 X[47995], 3 X[47777] - 2 X[48095], 3 X[47880] - 2 X[48060], 4 X[47999] - 3 X[48193]

X(48605) lies on these lines: {513, 47702}, {514, 3700}, {650, 47958}, {661, 48132}, {918, 47978}, {2526, 47951}, {4025, 4790}, {4394, 48145}, {4762, 47668}, {4940, 47662}, {4977, 47123}, {6008, 47653}, {7659, 47968}, {23731, 30520}, {28195, 47944}, {28213, 47983}, {31250, 48558}, {47652, 48133}, {47777, 47995}, {47880, 48060}, {47990, 48096}, {47999, 48193}, {48024, 48127}

X(48605) = midpoint of X(i) and X(j) for these {i,j}: {47900, 47923}, {47907, 47916}
X(48605) = reflection of X(i) in X(j) for these {i,j}: {650, 47958}, {2526, 47951}, {4790, 47960}, {7659, 47968}, {47662, 4940}, {47919, 47916}, {48026, 47950}, {48087, 47988}, {48095, 47995}, {48096, 47990}, {48124, 48026}, {48132, 661}, {48133, 47652}, {48145, 4394}, {48397, 23729}
X(48605) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47900, 47916, 47923}, {47907, 47923, 47900}, {47950, 48087, 47988}, {47988, 48087, 48026}, {47995, 48095, 47777}


X(48606) = X(513)X(47702)∩X(514)X(4522)

Barycentrics    (b - c)*(5*a^3 + 6*a^2*b + 7*a*b^2 + 4*b^3 + 6*a^2*c + 4*a*b*c + 4*b^2*c + 7*a*c^2 + 4*b*c^2 + 4*c^3) : :
X(48606) = 3 X[47702] + 5 X[47901], X[47702] - 5 X[47916], 3 X[47702] - 5 X[47924], X[47901] + 3 X[47916], 3 X[47916] - X[47924], 3 X[47951] - 2 X[47989], 5 X[47951] - 2 X[48047], 3 X[47951] - X[48088], 4 X[47989] - 3 X[48027], 5 X[47989] - 3 X[48047], 5 X[48027] - 4 X[48047], 3 X[48027] - 2 X[48088], 6 X[48047] - 5 X[48088], 3 X[47943] - X[48077], 3 X[47961] - 2 X[48006], 5 X[47961] - 2 X[48068], 5 X[48006] - 3 X[48068], 3 X[47958] - X[48102], 3 X[48029] - 2 X[48102]

X(48606) lies on these lines: {513, 47702}, {514, 4522}, {661, 48135}, {4802, 47943}, {4977, 47961}, {21116, 28195}, {28151, 48020}, {28175, 47982}, {28179, 48035}, {28199, 48023}, {28213, 47995}, {28220, 47701}, {28229, 47998}, {47652, 48134}, {47999, 48095}, {48030, 48132}

X(48606) = midpoint of X(i) and X(j) for these {i,j}: {47901, 47924}, {47907, 47931}
X(48606) = reflection of X(i) in X(j) for these {i,j}: {48027, 47951}, {48029, 47958}, {48088, 47989}, {48095, 47999}, {48096, 47995}, {48132, 48030}, {48134, 47652}
X(48606) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47901, 47916, 47924}, {47951, 48088, 47989}, {47989, 48088, 48027}


X(48607) = X(513)X(4041)∩X(514)X(4522)

Barycentrics    a*(b - c)*(a^2 + 2*a*b + 3*b^2 + 2*a*c + 8*b*c + 3*c^2) : :
X(48607) = X[47905] - 3 X[47912], X[47905] + 3 X[47918], 5 X[47905] + 3 X[47936], 3 X[47912] + X[47929], 5 X[47912] + X[47936], 3 X[47918] - X[47929], 5 X[47918] - X[47936], 5 X[47929] - 3 X[47936], 5 X[47956] - 2 X[48052], 3 X[47956] - X[48092], 5 X[48027] - 4 X[48052], 3 X[48027] - 2 X[48092], 6 X[48052] - 5 X[48092], 3 X[661] - X[4449], 2 X[4449] - 3 X[48136], X[4040] - 3 X[47959], 2 X[4040] - 3 X[48029], 5 X[4040] - 3 X[48324], 4 X[4040] - 3 X[48329], 5 X[47959] - X[48324], 4 X[47959] - X[48329], 5 X[48029] - 2 X[48324], 4 X[48324] - 5 X[48329], 3 X[47997] - X[48294], 3 X[48099] - 2 X[48294], X[17496] - 3 X[48549], 3 X[21052] - X[48141], 3 X[47810] - X[48341], 3 X[47826] - X[48322]

X(48607) lies on these lines: {512, 47955}, {513, 4041}, {514, 4522}, {650, 47967}, {661, 4449}, {814, 47962}, {830, 47966}, {891, 48091}, {905, 48005}, {1577, 48134}, {2526, 29198}, {3309, 47949}, {3566, 48038}, {3669, 48030}, {3887, 47987}, {3900, 48024}, {3907, 47996}, {4040, 8678}, {4064, 4802}, {4083, 48026}, {4147, 28840}, {4160, 47997}, {4462, 47945}, {4824, 23880}, {4940, 48279}, {4983, 14077}, {14349, 48346}, {17496, 48549}, {21051, 43067}, {21052, 48141}, {21302, 47941}, {28470, 48001}, {29051, 47963}, {29226, 48128}, {29288, 47961}, {29324, 48002}, {29366, 47993}, {47810, 48341}, {47826, 48322}, {48054, 48332}, {48058, 48327}

X(48607) = midpoint of X(i) and X(j) for these {i,j}: {4041, 47911}, {4462, 47945}, {21302, 47941}, {47905, 47929}, {47912, 47918}
X(48607) = reflection of X(i) in X(j) for these {i,j}: {650, 47967}, {905, 48005}, {3669, 48030}, {43067, 21051}, {47921, 47922}, {48027, 47956}, {48029, 47959}, {48099, 47997}, {48134, 1577}, {48136, 661}, {48279, 4940}, {48327, 48058}, {48329, 48029}, {48332, 48054}, {48346, 14349}
X(48607) = crossdifference of every pair of points on line {1449, 1707}
X(48607) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47905, 47918, 47929}, {47912, 47929, 47905}


X(48608) = X(513)X(4963)∩X(514)X(4522)

Barycentrics    (b - c)*(a^3 + 6*a^2*b + 7*a*b^2 + 6*a^2*c + 16*a*b*c + 4*b^2*c + 7*a*c^2 + 4*b*c^2) : :
X(48608) = 3 X[47909] + X[47927], 5 X[47909] + X[47933], 3 X[47917] - X[47927], 5 X[47917] - X[47933], 5 X[47927] - 3 X[47933], 3 X[47953] - 2 X[47992], 5 X[47953] - 2 X[48050], 3 X[47953] - X[48089], 4 X[47953] - X[48126], 4 X[47992] - 3 X[48027], 5 X[47992] - 3 X[48050], 8 X[47992] - 3 X[48126], 5 X[48027] - 4 X[48050], 3 X[48027] - 2 X[48089], 6 X[48050] - 5 X[48089], 8 X[48050] - 5 X[48126], 4 X[48089] - 3 X[48126], 5 X[4824] - 3 X[48225], 2 X[4932] - 3 X[48210], 5 X[7662] - 6 X[48547], 5 X[47996] - 3 X[48547], 5 X[43067] - 6 X[48233], 5 X[48002] - 3 X[48233], 3 X[47666] - X[47694], 2 X[47694] - 3 X[48029], X[47685] - 3 X[47945], 3 X[47963] - 2 X[48009], 5 X[47963] - 2 X[48072], 5 X[48009] - 3 X[48072]

X(48608) lies on these lines: {513, 4963}, {514, 4522}, {523, 47952}, {650, 47964}, {661, 48134}, {2526, 28195}, {4024, 4802}, {4106, 28175}, {4824, 48225}, {4932, 48210}, {4977, 48069}, {7662, 47996}, {28147, 47991}, {28191, 48049}, {28199, 48125}, {43067, 48002}, {47666, 47694}, {47685, 47945}, {47963, 48009}, {48030, 48133}

X(48608) = midpoint of X(i) and X(j) for these {i,j}: {4963, 47928}, {47908, 47934}, {47909, 47917}
X(48608) = reflection of X(i) in X(j) for these {i,j}: {650, 47964}, {7662, 47996}, {43067, 48002}, {48027, 47953}, {48029, 47666}, {48089, 47992}, {48126, 48027}, {48133, 48030}, {48134, 661}
X(48608) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47953, 48089, 47992}, {47992, 48089, 48027}


X(48609) = X(513)X(4041)∩X(514)X(4806)

Barycentrics    a*(b - c)*(3*a*b + 2*b^2 + 3*a*c + 9*b*c + 2*c^2) : :
X(48609) = 3 X[4041] - 5 X[4490], 3 X[4041] + 5 X[47906], X[4041] + 5 X[47913], X[4041] - 5 X[47918], 2 X[4041] - 5 X[47922], X[4490] + 3 X[47913], X[4490] - 3 X[47918], 2 X[4490] - 3 X[47922], X[47906] - 3 X[47913], X[47906] + 3 X[47918], 2 X[47906] + 3 X[47922], 2 X[47913] + X[47922], 3 X[47957] - 2 X[47994], 5 X[47957] - 2 X[48053], 3 X[47957] - X[48093], 4 X[47957] - X[48129], 4 X[47994] - 3 X[48028], 5 X[47994] - 3 X[48053], 8 X[47994] - 3 X[48129], 5 X[48028] - 4 X[48053], 3 X[48028] - 2 X[48093], 6 X[48053] - 5 X[48093], 8 X[48053] - 5 X[48129], 4 X[48093] - 3 X[48129], 3 X[661] - X[23765], 2 X[23765] - 3 X[48137], X[2530] - 3 X[47959], 2 X[2530] - 3 X[48030], X[3803] - 3 X[47966], 3 X[47949] - X[48081], 3 X[47967] - 2 X[48012], 5 X[47967] - 2 X[48075], 5 X[48012] - 3 X[48075], 3 X[47826] - X[48323], 3 X[48162] - X[48341]

X(48609) lies on these lines: {513, 4041}, {514, 4806}, {661, 23765}, {891, 47987}, {1577, 48135}, {2530, 29198}, {2533, 28220}, {3803, 47966}, {4083, 47949}, {4147, 28209}, {4391, 28195}, {4462, 47946}, {4778, 48401}, {4802, 48265}, {6372, 47967}, {28151, 48264}, {28199, 48392}, {29202, 48082}, {29226, 48024}, {29274, 47969}, {29324, 48001}, {47826, 48323}, {47997, 48100}, {48004, 48331}, {48029, 48330}, {48058, 48344}, {48162, 48341}

X(48609) = midpoint of X(i) and X(j) for these {i,j}: {4462, 47946}, {4490, 47906}, {47913, 47918}
X(48609) = reflection of X(i) in X(j) for these {i,j}: {47922, 47918}, {48028, 47957}, {48030, 47959}, {48093, 47994}, {48100, 47997}, {48129, 48028}, {48135, 1577}, {48137, 661}, {48330, 48029}, {48331, 48004}, {48344, 48058}
X(48609) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4490, 47913, 47906}, {47906, 47918, 4490}, {47957, 48093, 47994}, {47994, 48093, 48028}


X(48610) = X(513)X(4963)∩X(514)X(4806)

Barycentrics    (b - c)*(7*a^2*b + 6*a*b^2 + 7*a^2*c + 17*a*b*c + 4*b^2*c + 6*a*c^2 + 4*b*c^2) : :
X(48610) = X[47904] - 3 X[47910], X[47904] + 3 X[47917], 5 X[47904] + 3 X[47934], 3 X[47910] + X[47928], 5 X[47910] + X[47934], 3 X[47917] - X[47928], 5 X[47917] - X[47934], 5 X[47928] - 3 X[47934], 2 X[4806] - 5 X[47954], 3 X[4806] - 5 X[47993], 4 X[4806] - 5 X[48028], 6 X[4806] - 5 X[48090], 8 X[4806] - 5 X[48127], 3 X[47954] - 2 X[47993], 3 X[47954] - X[48090], 4 X[47954] - X[48127], 4 X[47993] - 3 X[48028], 8 X[47993] - 3 X[48127], 3 X[48028] - 2 X[48090], 4 X[48090] - 3 X[48127], 3 X[47946] - X[48080], 3 X[47964] - 2 X[48010], 5 X[47964] - 2 X[48073], 5 X[48010] - 3 X[48073], 7 X[21146] - 9 X[44429], X[21146] - 3 X[47666], 2 X[21146] - 3 X[48030], 3 X[44429] - 7 X[47666], 6 X[44429] - 7 X[48030], 2 X[48133] - 3 X[48221]

X(48610) lies on these lines: {513, 4963}, {514, 4806}, {523, 47980}, {661, 48135}, {4777, 47941}, {4802, 47946}, {4824, 28220}, {4977, 47964}, {21146, 28195}, {28151, 48021}, {28175, 47986}, {28179, 48037}, {28199, 48024}, {28213, 47996}, {28229, 48002}, {48133, 48221}

X(48610) = midpoint of X(i) and X(j) for these {i,j}: {4963, 47927}, {47904, 47928}, {47910, 47917}
X(48610) = reflection of X(i) in X(j) for these {i,j}: {48028, 47954}, {48030, 47666}, {48090, 47993}, {48098, 47996}, {48127, 48028}, {48135, 661}
X(48610) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47904, 47917, 47928}, {47910, 47928, 47904}, {47954, 48090, 47993}, {47993, 48090, 48028}


X(48611) = X(513)X(16892)∩X(514)X(4806)

Barycentrics    (b - c)*(2*a^3 + 5*a^2*b + 4*a*b^2 + 2*b^3 + 5*a^2*c + 5*a*b*c + 2*b^2*c + 4*a*c^2 + 2*b*c^2 + 2*c^3) : :
X(48611) = X[47938] - 3 X[47944], X[47938] + 3 X[47958], 5 X[47938] + 3 X[47973], 3 X[47944] + X[47968], 5 X[47944] + X[47973], 3 X[47958] - X[47968], 5 X[47958] - X[47973], 5 X[47968] - 3 X[47973], 3 X[47990] - X[48048], 3 X[48028] - 2 X[48048], 3 X[661] - X[48140], 3 X[48097] - 2 X[48140], X[4122] - 3 X[48543], 3 X[47916] + X[48113], 3 X[48024] - X[48113], 3 X[47983] - X[48036], 3 X[47995] - X[48062], 3 X[48030] - 2 X[48062], X[48138] - 3 X[48162], X[48145] - 3 X[48226], 3 X[48221] - 2 X[48276]

X(48611) lies on these lines: {513, 16892}, {514, 4806}, {523, 47985}, {659, 47907}, {661, 48097}, {1491, 47902}, {2496, 28220}, {4106, 4122}, {4120, 28199}, {4500, 28175}, {4977, 48063}, {7662, 28195}, {29144, 47989}, {29202, 48121}, {29204, 47924}, {29280, 48085}, {47651, 47946}, {47916, 48024}, {47925, 48021}, {47983, 48036}, {47995, 48030}, {48135, 48398}, {48138, 48162}, {48145, 48226}, {48221, 48276}

X(48611) = midpoint of X(i) and X(j) for these {i,j}: {659, 47907}, {1491, 47902}, {47651, 47946}, {47916, 48024}, {47925, 48021}, {47938, 47968}, {47944, 47958}, {47950, 47961}
X(48611) = reflection of X(i) in X(j) for these {i,j}: {48028, 47990}, {48030, 47995}, {48097, 661}, {48135, 48398}
X(48611) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47938, 47958, 47968}, {47944, 47968, 47938}


X(48612) = X(513)X(47987)∩X(514)X(3700)

Barycentrics    a*(b - c)*(a^2 + 4*a*b + 3*b^2 + 4*a*c + 7*b*c + 3*c^2) : :
X(48612) = 3 X[47997] - X[48011], 3 X[48003] - 2 X[48011], X[47915] - 3 X[47955], X[47915] + 3 X[48026], 2 X[47915] + 3 X[48051], 5 X[47915] + 3 X[48128], 2 X[47955] + X[48051], 3 X[47955] + X[48091], 5 X[47955] + X[48128], 3 X[48026] - X[48091], 5 X[48026] - X[48128], 3 X[48051] - 2 X[48091], 5 X[48051] - 2 X[48128], 5 X[48091] - 3 X[48128], 3 X[661] - X[1019], 5 X[661] - X[48149], 2 X[1019] - 3 X[14838], X[1019] + 3 X[47947], 5 X[1019] - 3 X[48149], X[14838] + 2 X[47947], 5 X[14838] - 2 X[48149], 5 X[47947] + X[48149], 3 X[48024] - X[48351], 4 X[4129] - 3 X[45324], X[4879] - 3 X[4983], X[4498] + 3 X[4813], X[4498] - 3 X[47959], 3 X[4893] - X[48110], X[4978] - 3 X[47759], X[7192] - 3 X[48551], 3 X[14349] - X[48341], X[14349] - 3 X[48544], 3 X[47911] + X[48341], X[47911] + 3 X[48544], X[48341] - 9 X[48544], 3 X[47794] - X[48107], 3 X[48028] - X[48331], 3 X[48058] - 2 X[48331], 3 X[48053] - X[48328]

X(48612) lies on these lines: {513, 47987}, {514, 3700}, {661, 1019}, {830, 48024}, {1577, 31290}, {2832, 47913}, {3887, 47912}, {3960, 48054}, {4063, 48019}, {4129, 28840}, {4160, 4879}, {4394, 48074}, {4498, 4813}, {4893, 48110}, {4960, 47903}, {4963, 48393}, {4978, 47759}, {6005, 47956}, {6372, 48052}, {7192, 48551}, {8678, 48045}, {8714, 47992}, {14349, 47911}, {23803, 47984}, {23875, 48038}, {23883, 44449}, {29013, 47996}, {29047, 47983}, {29070, 47993}, {29150, 48002}, {29186, 47986}, {29270, 47962}, {29302, 48041}, {29354, 47990}, {42325, 47948}, {47794, 48107}, {47906, 48086}, {47918, 48085}, {47942, 48023}, {48028, 48058}, {48053, 48328}, {48093, 48348}

X(48612) = midpoint of X(i) and X(j) for these {i,j}: {661, 47947}, {1577, 31290}, {4063, 48019}, {4813, 47959}, {4960, 47903}, {4963, 48393}, {14349, 47911}, {44449, 47679}, {47906, 48086}, {47912, 48081}, {47915, 48091}, {47918, 48085}, {47942, 48023}, {47948, 48021}, {47955, 48026}
X(48612) = reflection of X(i) in X(j) for these {i,j}: {3960, 48054}, {14838, 661}, {48003, 47997}, {48004, 47994}, {48051, 48026}, {48058, 48028}, {48074, 4394}, {48348, 48093}
X(48612) = crossdifference of every pair of points on line {1962, 16884}
X(48612) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47911, 48544, 14349}, {47915, 48026, 48091}, {47955, 48091, 47915}


X(48613) = X(513)X(47987)∩X(514)X(4522)

Barycentrics    a*(b - c)*(a^2 + 2*a*b + 3*b^2 + 2*a*c + 5*b*c + 3*c^2) : :
X(48613) = 2 X[47956] + X[48052], 3 X[47956] + X[48092], 3 X[48027] - X[48092], 3 X[48052] - 2 X[48092], 3 X[661] - X[4040], 3 X[661] + X[47905], 5 X[661] - X[48150], X[4040] + 3 X[47948], 2 X[4040] - 3 X[48058], 5 X[4040] - 3 X[48150], X[47905] - 3 X[47948], 2 X[47905] + 3 X[48058], 5 X[47905] + 3 X[48150], 2 X[47948] + X[48058], 5 X[47948] + X[48150], 5 X[48058] - 2 X[48150], X[1019] - 3 X[47810], X[3803] - 3 X[47777], X[4449] - 3 X[14349], X[4449] + 3 X[47912], 2 X[4449] - 3 X[48348], 2 X[47912] + X[48348], X[4170] - 3 X[47759], X[7192] - 3 X[47816], 3 X[48054] - X[48294], X[47694] - 3 X[48551], X[47716] - 3 X[48550], 3 X[47826] - X[48111], 3 X[47828] - X[48110], X[47929] - 3 X[47959], X[47929] + 3 X[48023], X[48081] - 3 X[48544], X[48107] - 3 X[48573]

X(48613) lies on these lines: {512, 48051}, {513, 47987}, {514, 4522}, {661, 830}, {1019, 47810}, {1491, 15309}, {1577, 47945}, {1734, 4813}, {2254, 47947}, {2526, 47955}, {2832, 47918}, {3309, 48045}, {3803, 47777}, {3887, 4983}, {3960, 48059}, {4041, 48085}, {4151, 48049}, {4160, 4449}, {4170, 47759}, {4808, 47944}, {4905, 47911}, {6004, 48028}, {6005, 48026}, {7192, 47816}, {7927, 47990}, {8678, 48054}, {14838, 48030}, {20295, 48407}, {29013, 48010}, {29021, 48039}, {29047, 47995}, {29062, 48404}, {29070, 48002}, {29186, 47996}, {29260, 47961}, {29350, 48091}, {29354, 47999}, {42325, 48024}, {47694, 48551}, {47716, 48550}, {47826, 48111}, {47828, 48110}, {47929, 47959}, {47970, 48020}, {48081, 48544}, {48099, 48345}, {48107, 48573}

X(48613) = midpoint of X(i) and X(j) for these {i,j}: {661, 47948}, {1577, 47945}, {1734, 4813}, {2254, 47947}, {2526, 47955}, {4040, 47905}, {4041, 48085}, {4808, 47944}, {4905, 47911}, {14349, 47912}, {20295, 48407}, {47918, 48086}, {47956, 48027}, {47959, 48023}, {47970, 48020}
X(48613) = reflection of X(i) in X(j) for these {i,j}: {3960, 48059}, {14838, 48030}, {48003, 48005}, {48004, 47997}, {48052, 48027}, {48058, 661}, {48345, 48099}, {48348, 14349}
X(48613) = crossdifference of every pair of points on line {38, 16884}
X(48613) = barycentric product X(1)*X(47658)
X(48613) = barycentric quotient X(47658)/X(75)
X(48613) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 47905, 4040}, {4040, 47948, 47905}


X(48614) = X(513)X(4088)∩X(514)X(4806)

Barycentrics    (b - c)*(2*a^3 - a^2*b + 2*b^3 - a^2*c - 5*a*b*c + 2*b^2*c + 2*b*c^2 + 2*c^3) : :
X(48614) = X[48078] - 3 X[48083], X[48078] + 3 X[48094], 2 X[48078] + 3 X[48097], 5 X[48078] + 3 X[48106], 2 X[48083] + X[48097], 3 X[48083] + X[48103], 5 X[48083] + X[48106], 3 X[48094] - X[48103], 5 X[48094] - X[48106], 3 X[48097] - 2 X[48103], 5 X[48097] - 2 X[48106], 5 X[48103] - 3 X[48106], 2 X[47990] - 3 X[48028], X[47990] - 3 X[48048], 3 X[661] - X[47925], 2 X[3776] - 3 X[48197], 3 X[4468] - X[48007], 2 X[48007] - 3 X[48030], 2 X[4818] - 3 X[48191], 3 X[4951] - X[48115], 2 X[21104] - 3 X[48221], X[21146] - 3 X[48557], X[24719] - 3 X[47772], 2 X[24720] - 3 X[48201], X[47902] - 3 X[48024], X[47902] + 3 X[48130], X[47923] - 3 X[48162], X[47930] - 3 X[48226], X[47979] - 3 X[48040]

X(48614) lies on these lines: {513, 4088}, {514, 4806}, {523, 48009}, {659, 48117}, {661, 47925}, {918, 4782}, {1491, 48113}, {3776, 48197}, {4468, 48007}, {4522, 4977}, {4724, 29204}, {4802, 47699}, {4818, 48191}, {4874, 28890}, {4926, 48408}, {4944, 48275}, {4951, 48115}, {6590, 48135}, {21104, 48221}, {21146, 48557}, {24719, 47772}, {24720, 48201}, {28195, 47660}, {29146, 47970}, {29354, 48331}, {47662, 47946}, {47902, 48024}, {47923, 48162}, {47930, 48226}, {47979, 48040}, {48021, 48140}, {48029, 48124}

X(48614) = midpoint of X(i) and X(j) for these {i,j}: {659, 48117}, {1491, 48113}, {47662, 47946}, {48021, 48140}, {48024, 48130}, {48029, 48124}, {48078, 48103}, {48083, 48094}, {48087, 48096}
X(48614) = reflection of X(i) in X(j) for these {i,j}: {48028, 48048}, {48030, 4468}, {48097, 48094}, {48135, 6590}
X(48614) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {48078, 48094, 48103}, {48083, 48103, 48078}


X(48615) = X(513)X(47700)∩X(514)X(4522)

Barycentrics    (b - c)*(3*a^3 + 2*a^2*b + a*b^2 + 4*b^3 + 2*a^2*c - 4*a*b*c + 4*b^2*c + a*c^2 + 4*b*c^2 + 4*c^3) : :
X(48615) = X[47700] - 3 X[48118], X[47700] + 3 X[48130], 3 X[48118] + X[48139], 3 X[48130] - X[48139], 5 X[47951] - 6 X[47989], 2 X[47951] - 3 X[48027], X[47951] - 3 X[48088], 4 X[47989] - 5 X[48027], 3 X[47989] - 5 X[48047], 2 X[47989] - 5 X[48088], 3 X[48027] - 4 X[48047], 2 X[48047] - 3 X[48088], 3 X[48014] - 5 X[48061], 2 X[48014] - 5 X[48096], 2 X[48061] - 3 X[48096], 2 X[3776] - 3 X[48219], 2 X[47701] - 3 X[48029], X[47701] - 3 X[48094], 2 X[24720] - 3 X[48222], X[47651] - 3 X[48171], X[47688] - 3 X[48557]

X(48615) lies on these lines: {513, 47700}, {514, 4522}, {523, 2976}, {650, 48097}, {661, 28199}, {3776, 48219}, {4088, 28195}, {4468, 28175}, {4724, 28151}, {4777, 48102}, {4802, 47701}, {4926, 48105}, {4977, 48035}, {24720, 48222}, {28147, 48055}, {28165, 48032}, {28179, 48006}, {28183, 48068}, {28191, 47998}, {28213, 48039}, {28220, 48077}, {29047, 48329}, {30520, 48103}, {47651, 48171}, {47660, 48134}, {47688, 48557}, {47919, 48030}, {47960, 48056}, {48300, 48346}

X(48615) = midpoint of X(i) and X(j) for these {i,j}: {47700, 48139}, {48117, 48146}, {48118, 48130}
X(48615) = reflection of X(i) in X(j) for these {i,j}: {650, 48097}, {47919, 48030}, {47951, 48047}, {47960, 48056}, {47961, 4468}, {48027, 48088}, {48029, 48094}, {48134, 47660}, {48346, 48300}
X(48615) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47700, 48130, 48139}, {47951, 48047, 48027}, {47951, 48088, 48047}, {48118, 48139, 47700}


X(48616) = X(513)X(663)∩X(514)X(4522)

Barycentrics    a*(b - c)*(a^2 + 2*a*b + 3*b^2 + 2*a*c + 3*c^2) : :
X(48616) = X[663] + 3 X[48122], X[663] - 3 X[48131], 2 X[663] - 3 X[48136], 5 X[663] - 3 X[48150], 4 X[663] - 3 X[48329], X[48116] - 3 X[48122], X[48116] + 3 X[48131], 2 X[48116] + 3 X[48136], 5 X[48116] + 3 X[48150], 4 X[48116] + 3 X[48329], 2 X[48122] + X[48136], 5 X[48122] + X[48150], 4 X[48122] + X[48329], 5 X[48131] - X[48150], 4 X[48131] - X[48329], 5 X[48136] - 2 X[48150], 4 X[48150] - 5 X[48329], 2 X[47956] - 3 X[48027], X[47956] - 3 X[48092], 3 X[48027] - 4 X[48052], 2 X[48052] - 3 X[48092], 2 X[48287] - 3 X[48332], 3 X[2530] - X[4834], 2 X[4142] - 3 X[48192], 2 X[4394] - 3 X[47893], 3 X[48086] + X[48282], 2 X[48086] + X[48346], X[48282] - 3 X[48335], 2 X[48282] - 3 X[48346], 3 X[14349] - X[47970], 2 X[47970] - 3 X[48029], 2 X[14837] - 3 X[48178], 2 X[48065] - 3 X[48099]

X(48616) lies on these lines: {513, 663}, {514, 4522}, {650, 48100}, {830, 48287}, {1491, 8712}, {2526, 4083}, {2530, 4834}, {2832, 47966}, {3250, 23751}, {3566, 48015}, {3907, 48042}, {3910, 48007}, {4142, 48192}, {4394, 47893}, {4449, 48020}, {4778, 48299}, {4802, 48278}, {4813, 23738}, {4940, 48265}, {4977, 6332}, {4978, 48134}, {6372, 48091}, {8678, 48086}, {14349, 47970}, {14837, 48178}, {23813, 48392}, {23880, 24719}, {28195, 48300}, {29017, 47960}, {29142, 47961}, {43067, 48406}, {47921, 48030}, {47965, 48059}, {48023, 48334}, {48065, 48099}, {48327, 48348}

X(48616) = midpoint of X(i) and X(j) for these {i,j}: {663, 48116}, {4449, 48020}, {4813, 23738}, {48023, 48334}, {48086, 48335}, {48121, 48151}, {48122, 48131}
X(48616) = reflection of X(i) in X(j) for these {i,j}: {650, 48100}, {3669, 48137}, {43067, 48406}, {47921, 48030}, {47956, 48052}, {47965, 48059}, {47966, 48054}, {48027, 48092}, {48029, 14349}, {48134, 4978}, {48136, 48131}, {48265, 4940}, {48327, 48348}, {48329, 48136}, {48346, 48335}, {48392, 23813}
X(48616) = crossdifference of every pair of points on line {9, 17716}
X(48616) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {663, 48122, 48116}, {47956, 48052, 48027}, {47956, 48092, 48052}, {48116, 48131, 663}


X(48617) = X(513)X(47702)∩X(514)X(3716)

Barycentrics    (b - c)*(3*a^3 + 6*a^2*b + 5*a*b^2 + 4*b^3 + 6*a^2*c + 4*a*b*c + 4*b^2*c + 5*a*c^2 + 4*b*c^2 + 4*c^3) : :
X(48617) = 5 X[47702] + 3 X[47901], X[47702] + 3 X[47916], X[47702] - 3 X[47924], X[47901] - 5 X[47916], X[47901] + 5 X[47924], 3 X[47961] - 2 X[47998], 5 X[47961] - 2 X[48055], 3 X[47961] - X[48096], 4 X[47998] - 3 X[48029], 5 X[47998] - 3 X[48055], 5 X[48029] - 4 X[48055], 3 X[48029] - 2 X[48096], 6 X[48055] - 5 X[48096], 3 X[47951] - 2 X[47982], 5 X[47951] - 2 X[48035], 5 X[47982] - 3 X[48035], X[4088] - 3 X[47958], 2 X[4088] - 3 X[48027], 2 X[4925] - 3 X[48007], 3 X[47701] - X[48105], 3 X[47777] - 2 X[48097], 2 X[48405] - 3 X[48558]

X(48617) lies on these lines: {513, 47702}, {514, 3716}, {523, 47951}, {661, 28199}, {4088, 4802}, {4777, 47943}, {4925, 48007}, {4977, 48014}, {28147, 47989}, {28151, 48023}, {28165, 48020}, {28175, 47995}, {28179, 48039}, {28191, 48047}, {28195, 47701}, {28213, 48006}, {28220, 47972}, {30520, 47944}, {47652, 48126}, {47777, 48097}, {47990, 48087}, {48028, 48124}, {48405, 48558}

X(48617) = midpoint of X(i) and X(j) for these {i,j}: {47902, 47923}, {47916, 47924}
X(48617) = reflection of X(i) in X(j) for these {i,j}: {48027, 47958}, {48029, 47961}, {48087, 47990}, {48088, 47995}, {48096, 47998}, {48124, 48028}, {48126, 47652}
X(48617) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47961, 48096, 47998}, {47998, 48096, 48029}


X(48618) = X(513)X(4041)∩X(514)X(3716)

Barycentrics    a*(b - c)*(a^2 - 2*a*b - b^2 - 2*a*c - 8*b*c - c^2) : :
X(48618) = 3 X[47905] - 5 X[47912], X[47905] - 5 X[47918], X[47905] + 5 X[47929], 3 X[47905] + 5 X[47936], X[47912] - 3 X[47918], X[47912] + 3 X[47929], 3 X[47918] + X[47936], 3 X[47929] - X[47936], 3 X[47966] - 2 X[48004], 5 X[47966] - 2 X[48058], 3 X[47966] - X[48099], 4 X[47966] - X[48136], 5 X[47966] - X[48332], 6 X[47966] - X[48346], 9 X[47966] - 2 X[48348], 4 X[48004] - 3 X[48029], 5 X[48004] - 3 X[48058], 8 X[48004] - 3 X[48136], 10 X[48004] - 3 X[48332], 4 X[48004] - X[48346], 3 X[48004] - X[48348], 5 X[48029] - 4 X[48058], 3 X[48029] - 2 X[48099], 5 X[48029] - 2 X[48332], 3 X[48029] - X[48346], 9 X[48029] - 4 X[48348], 6 X[48058] - 5 X[48099], 8 X[48058] - 5 X[48136], 12 X[48058] - 5 X[48346], 9 X[48058] - 5 X[48348], 4 X[48099] - 3 X[48136], 5 X[48099] - 3 X[48332], 3 X[48099] - 2 X[48348], 5 X[48136] - 4 X[48332], 3 X[48136] - 2 X[48346], 9 X[48136] - 8 X[48348], 6 X[48332] - 5 X[48346], 9 X[48332] - 10 X[48348], 3 X[48346] - 4 X[48348], 3 X[4724] - X[48322], 2 X[48322] - 3 X[48329], 3 X[4893] - X[23738], 3 X [47970] - X[48111], X[23765] - 3 X[48162], 3 X[47760] - 2 X[48406], 3 X[47777] - 2 X[48100], 3 X[47811] - X[48341], 3 X[47826] - X[48334], 3 X[47959] - X[48086], 3 X[48027] - 2 X[48086]

X(48618) lies on these lines: {513, 4041}, {514, 3716}, {650, 29198}, {1577, 48126}, {2526, 47967}, {2832, 47997}, {3566, 48036}, {3907, 48009}, {3910, 48040}, {4462, 47969}, {4724, 48322}, {4762, 48265}, {4893, 23738}, {4977, 6133}, {6050, 48320}, {6372, 47965}, {8678, 47970}, {8712, 48024}, {14077, 48351}, {20317, 21146}, {21385, 47942}, {23765, 48162}, {29017, 48087}, {29142, 48088}, {47760, 48406}, {47777, 48100}, {47811, 48341}, {47826, 48334}, {47957, 48026}, {47959, 48027}, {47994, 48091}, {48028, 48128}, {48065, 48327}

X(48618) = midpoint of X(i) and X(j) for these {i,j}: {4462, 47969}, {4498, 47906}, {21385, 47942}, {47912, 47936}, {47918, 47929}
X(48618) = reflection of X(i) in X(j) for these {i,j}: {2526, 47967}, {21146, 20317}, {48026, 47957}, {48027, 47959}, {48029, 47966}, {48091, 47994}, {48092, 47997}, {48099, 48004}, {48126, 1577}, {48128, 48028}, {48136, 48029}, {48320, 6050}, {48327, 48065}, {48329, 4724}, {48332, 48058}, {48346, 48099}
X(48618) = crossdifference of every pair of points on line {1449, 3750}
X(48618) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47912, 47929, 47936}, {47918, 47936, 47912}, {47966, 48099, 48004}, {48004, 48099, 48029}, {48029, 48346, 48099}, {48099, 48346, 48136}


X(48619) = X(513)X(4963)∩X(514)X(3716)

Barycentrics    (b - c)*(-a^3 + 6*a^2*b + 5*a*b^2 + 6*a^2*c + 16*a*b*c + 4*b^2*c + 5*a*c^2 + 4*b*c^2) : :
X(48619) = X[47909] - 3 X[47917], X[47909] + 3 X[47927], 3 X[47917] + X[47933], 3 X[47927] - X[47933], 6 X[3716] - 5 X[7662], 2 X[3716] - 5 X[47963], 3 X[3716] - 5 X[48001], 4 X[3716] - 5 X[48029], 8 X[3716] - 5 X[48134], X[7662] - 3 X[47963], 2 X[7662] - 3 X[48029], 4 X[7662] - 3 X[48134], 3 X[47963] - 2 X[48001], 4 X[47963] - X[48134], 4 X[48001] - 3 X[48029], 8 X[48001] - 3 X[48134], 5 X[30795] - 3 X[48143], 3 X[45320] - 2 X[48135], X[46403] - 3 X[47666], 2 X[46403] - 3 X[48027], X[47697] - 3 X[47969], 3 X[47777] - 2 X[48098], 3 X[47953] - 2 X[47985], 2 X[48073] - 3 X[48190]

X(48619) lies on these lines: {513, 4963}, {514, 3716}, {523, 48036}, {650, 2457}, {661, 48126}, {2526, 47964}, {4106, 47993}, {4762, 47946}, {4802, 48083}, {4977, 47962}, {7659, 28220}, {28213, 43067}, {28229, 48000}, {29362, 47952}, {30795, 48143}, {45320, 48135}, {46403, 47666}, {47697, 47969}, {47777, 48098}, {47953, 47985}, {47954, 48026}, {47996, 48089}, {48028, 48125}, {48048, 48397}, {48073, 48190}

X(48619) = midpoint of X(i) and X(j) for these {i,j}: {47904, 47926}, {47909, 47933}, {47917, 47927}
X(48619) = reflection of X(i) in X(j) for these {i,j}: {2526, 47964}, {4106, 47993}, {7662, 48001}, {48026, 47954}, {48027, 47666}, {48029, 47963}, {48089, 47996}, {48125, 48028}, {48126, 661}, {48134, 48029}, {48397, 48048}
X(48619) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7662, 47963, 48001}, {7662, 48001, 48029}, {47909, 47927, 47933}, {47917, 47933, 47909}


X(48620) = X(513)X(4963)∩X(514)X(3837)

Barycentrics    (b - c)*(5*a^2*b + 6*a*b^2 + 5*a^2*c + 15*a*b*c + 4*b^2*c + 6*a*c^2 + 4*b*c^2) : :
X(48620) = 3 X[47904] - 5 X[47910], X[47904] - 5 X[47917], X[47904] + 5 X[47928], 3 X[47904] + 5 X[47934], X[47910] - 3 X[47917], X[47910] + 3 X[47928], 3 X[47917] + X[47934], 3 X[47928] - X[47934], 2 X[3837] - 5 X[47964], 3 X[3837] - 5 X[48002], 4 X[3837] - 5 X[48030], 6 X[3837] - 5 X[48098], 8 X[3837] - 5 X[48135], 3 X[47964] - 2 X[48002], 3 X[47964] - X[48098], 4 X[47964] - X[48135], 4 X[48002] - 3 X[48030], 8 X[48002] - 3 X[48135], 3 X[48030] - 2 X[48098], 4 X[48098] - 3 X[48135], 3 X[47954] - 2 X[47986], 5 X[47954] - 2 X[48037], 5 X[47986] - 3 X[48037], X[4010] - 3 X[47666], 2 X[4010] - 3 X[48028], 3 X[4824] - X[48108], 5 X[4824] - 3 X[48175], 5 X[48108] - 9 X[48175], 2 X[43067] - 3 X[48194], 2 X[48134] - 3 X[48202]

X(48620) lies on these lines: {513, 4963}, {514, 3837}, {523, 47954}, {661, 28199}, {1491, 48132}, {4010, 4802}, {4777, 47946}, {4782, 47962}, {4806, 28191}, {4824, 28195}, {4926, 47941}, {4977, 48017}, {28147, 47993}, {28151, 48024}, {28165, 48021}, {28175, 47996}, {28179, 48043}, {28183, 47980}, {28213, 48010}, {28220, 47975}, {43067, 48194}, {48134, 48202}

X(48620) = midpoint of X(i) and X(j) for these {i,j}: {4963, 47926}, {47910, 47934}, {47917, 47928}
X(48620) = reflection of X(i) in X(j) for these {i,j}: {4782, 47962}, {48028, 47666}, {48030, 47964}, {48090, 47996}, {48098, 48002}, {48127, 661}, {48135, 48030}
X(48620) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47910, 47928, 47934}, {47917, 47934, 47910}, {47964, 48098, 48002}, {48002, 48098, 48030}


X(48621) = X(513)X(16892)∩X(514)X(3837)

Barycentrics    (b - c)*(2*a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3 + 3*a^2*c + 3*a*b*c + 2*b^2*c + 4*a*c^2 + 2*b*c^2 + 2*c^3) : :
X(48621) = 3 X[47938] - 5 X[47944], X[47938] - 5 X[47958], X[47938] + 5 X[47968], 3 X[47938] + 5 X[47973], X[47944] - 3 X[47958], X[47944] + 3 X[47968], 3 X[47958] + X[47973], 3 X[47968] - X[47973], 3 X[47999] - X[48056], 4 X[47999] - X[48097], 3 X[48030] - 2 X[48056], 4 X[48056] - 3 X[48097], 3 X[1491] - X[48146], 3 X[47916] + X[48146], X[47696] - 3 X[48552], 3 X[47810] - X[48140], 3 X[47827] - X[48138], 3 X[47877] - X[48101], 2 X[47890] - 3 X[48194], 3 X[47995] - X[48040], 3 X[48028] - 2 X[48040], 3 X[48007] - X[48069], X[48139] - 3 X[48162]

X(48621) lies on these lines: {513, 16892}, {514, 3837}, {523, 48042}, {661, 47925}, {1491, 47916}, {3004, 4782}, {3776, 4977}, {4784, 47907}, {4802, 47652}, {4809, 28220}, {4824, 47651}, {24719, 47653}, {26248, 28195}, {28213, 47779}, {29146, 48086}, {29204, 48023}, {47696, 48552}, {47810, 48140}, {47827, 48138}, {47877, 48101}, {47890, 48194}, {47919, 48027}, {47931, 48024}, {47995, 48028}, {48007, 48069}, {48127, 48398}, {48139, 48162}

X(48621) = midpoint of X(i) and X(j) for these {i,j}: {661, 47925}, {1491, 47916}, {4784, 47907}, {4824, 47651}, {24719, 47653}, {47919, 48027}, {47931, 48024}, {47944, 47973}, {47951, 47960}, {47958, 47968}
X(48621) = reflection of X(i) in X(j) for these {i,j}: {4782, 3004}, {48028, 47995}, {48030, 47999}, {48097, 48030}, {48127, 48398}
X(48621) = crossdifference of every pair of points on line {5280, 21793}
X(48621) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47944, 47968, 47973}, {47958, 47973, 47944}


X(48622) = X(513)X(47700)∩X(514)X(3716)

Barycentrics    (b - c)*(5*a^3 + 2*a^2*b + 3*a*b^2 + 4*b^3 + 2*a^2*c - 4*a*b*c + 4*b^2*c + 3*a*c^2 + 4*b*c^2 + 4*c^3) : :
X(48622) = 3 X[47700] - 5 X[48118], X[47700] - 5 X[48130], X[47700] + 5 X[48139], X[48118] - 3 X[48130], X[48118] + 3 X[48139], 5 X[47961] - 6 X[47998], 2 X[47961] - 3 X[48029], X[47961] - 3 X[48096], 4 X[47998] - 5 X[48029], 3 X[47998] - 5 X[48055], 2 X[47998] - 5 X[48096], 3 X[48029] - 4 X[48055], 2 X[48055] - 3 X[48096], 4 X[48290] - 3 X[48346], X[47972] - 3 X[48102], 2 X[48039] - 3 X[48088], 2 X[47943] - 3 X[48027], X[47943] - 3 X[48094], 2 X[47727] - 3 X[48329]

X(48622) lies on these lines: {513, 47700}, {514, 3716}, {523, 48068}, {661, 48135}, {2526, 48097}, {4088, 28220}, {4468, 28213}, {4724, 28199}, {4777, 48105}, {4802, 47972}, {4977, 48039}, {28151, 48032}, {28175, 48061}, {28179, 48014}, {28195, 47914}, {28229, 48047}, {47660, 48126}, {47727, 48329}, {47950, 48048}

X(48622) = midpoint of X(i) and X(j) for these {i,j}: {48113, 48138}, {48130, 48139}
X(48622) = reflection of X(i) in X(j) for these {i,j}: {2526, 48097}, {47950, 48048}, {47951, 4468}, {47961, 48055}, {48027, 48094}, {48029, 48096}, {48126, 47660}
X(48622) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47961, 48055, 48029}, {47961, 48096, 48055}


X(48623) = X(1)X(514)∩X(513)X(47987)

Barycentrics    a*(b - c)*(2*a^2 - 2*a*b - 2*a*c - 5*b*c) : :
X(48623) = 5 X[1] - 7 X[663], 3 X[1] - 7 X[4040], 9 X[1] - 7 X[4449], X[1] - 7 X[4724], 4 X[1] - 7 X[4794], 3 X[1] + 7 X[47929], X[1] + 7 X[47970], 2 X[1] - 7 X[48065], 11 X[1] - 7 X[48282], 8 X[1] - 7 X[48287], 6 X[1] - 7 X[48294], 3 X[663] - 5 X[4040], 9 X[663] - 5 X[4449], X[663] - 5 X[4724], 4 X[663] - 5 X[4794], 3 X[663] + 5 X[47929], X[663] + 5 X[47970], 2 X[663] - 5 X[48065], 11 X[663] - 5 X[48282], 8 X[663] - 5 X[48287], 6 X[663] - 5 X[48294], 3 X[4040] - X[4449], X[4040] - 3 X[4724], 4 X[4040] - 3 X[4794], X[4040] + 3 X[47970], 2 X[4040] - 3 X[48065], 11 X[4040] - 3 X[48282], 8 X[4040] - 3 X[48287], X[4449] - 9 X[4724], 4 X[4449] - 9 X[4794], X[4449] + 3 X[47929], X[4449] + 9 X[47970], 2 X[4449] - 9 X[48065], 11 X[4449] - 9 X[48282], 8 X[4449] - 9 X[48287], 2 X[4449] - 3 X[48294], 4 X[4724] - X[4794], 3 X[4724] + X[47929], 11 X[4724] - X[48282], 8 X[4724] - X[48287], 6 X[4724] - X[48294], 3 X[4794] + 4 X[47929], X[4794] + 4 X[47970], 11 X[4794] - 4 X[48282], 3 X[4794] - 2 X[48294], X[47929] - 3 X[47970], 2 X[47929] + 3 X[48065], 11 X[47929] + 3 X[48282], 8 X[47929] + 3 X[48287], 2 X[47929] + X[48294], 2 X[47970] + X[48065], 11 X[47970] + X[48282], 8 X[47970] + X[48287], 6 X[47970] + X[48294], 11 X[48065] - 2 X[48282], 4 X[48065] - X[48287], 3 X[48065] - X[48294], 8 X[48282] - 11 X[48287], 6 X[48282] - 11 X[48294], 3 X[48287] - 4 X[48294], X[1019] - 3 X[48572], 7 X[4147] - 6 X[4745], X[4905] - 3 X[47811], 2 X[23789] - 3 X[48218], 7 X[24720] - 10 X[31253], 2 X[24720] - 3 X[48196], 20 X[31253] - 21 X[48196], 8 X[41150] - 7 X[45667], 17 X[46932] - 21 X[47793], X[47685] - 3 X[48551], X[47714] - 3 X[48557], 3 X[47817] - X[48108], 3 X[47826] - X[48086], X[47905] - 3 X[47959], X[47905] + 3 X[48032], 3 X[48029] - X[48092], 3 X[48054] - 2 X[48092]

X(48623) lies on these lines: {1, 514}, {513, 47987}, {650, 48075}, {659, 48064}, {661, 47977}, {830, 47966}, {1019, 48572}, {1577, 47974}, {2832, 48099}, {3887, 47921}, {4147, 4745}, {4401, 6372}, {4778, 21188}, {4791, 29186}, {4905, 47811}, {14349, 47936}, {21385, 48367}, {23789, 48218}, {24720, 31253}, {28155, 48340}, {28191, 48306}, {28225, 46385}, {28229, 48297}, {29021, 48055}, {29033, 48265}, {29164, 48094}, {29260, 47972}, {29350, 48351}, {29358, 48083}, {41150, 45667}, {42325, 47965}, {46932, 47793}, {47685, 48551}, {47714, 48557}, {47817, 48108}, {47826, 48086}, {47905, 47959}, {47918, 48111}, {48029, 48054}, {48331, 48343}

X(48623) = midpoint of X(i) and X(j) for these {i,j}: {661, 47977}, {1577, 47974}, {4040, 47929}, {4724, 47970}, {14349, 47936}, {21385, 48367}, {47918, 48111}, {47959, 48032}
X(48623) = reflection of X(i) in X(j) for these {i,j}: {4794, 48065}, {47997, 48004}, {48018, 48003}, {48054, 48029}, {48064, 659}, {48065, 4724}, {48075, 650}, {48287, 4794}, {48294, 4040}, {48343, 48331}
X(48623) = crossdifference of every pair of points on line {672, 16884}
X(48623) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4040, 47970, 47929}, {4040, 48294, 4794}, {4724, 47929, 4040}, {48065, 48294, 4040}


X(48624) = X(513)X(47987)∩X(514)X(4380)

Barycentrics    a*(b - c)*(4*a^2 + 6*a*b + 2*b^2 + 6*a*c + 3*b*c + 2*c^2) : :
X(48624) = 3 X[47997] - 4 X[48003], 2 X[48003] - 3 X[48011], 3 X[4979] + X[47935], 3 X[4979] - X[48110], 5 X[4979] - X[48149], X[47935] - 3 X[47976], 2 X[47935] + 3 X[48074], 5 X[47935] + 3 X[48149], 2 X[47976] + X[48074], 3 X[47976] + X[48110], 5 X[47976] + X[48149], 3 X[48074] - 2 X[48110], 5 X[48074] - 2 X[48149], 5 X[48110] - 3 X[48149], 3 X[649] - X[48085], 3 X[48054] - 2 X[48085], X[905] - 3 X[4790], 2 X[905] - 3 X[48064], 5 X[905] - 3 X[48128], 5 X[4790] - X[48128], 5 X[48064] - 2 X[48128], 3 X[4063] - X[47911], 2 X[48049] - 3 X[48196], X[48079] - 3 X[48566]

X(48624) lies on these lines: {513, 47987}, {514, 4380}, {649, 48054}, {905, 4790}, {4063, 47911}, {4394, 48051}, {4782, 48045}, {4784, 48075}, {4785, 4823}, {15309, 47921}, {26853, 29270}, {48049, 48196}, {48079, 48566}

X(48624) = midpoint of X(i) and X(j) for these {i,j}: {4979, 47976}, {47935, 48110}
X(48624) = reflection of X(i) in X(j) for these {i,j}: {47997, 48011}, {48045, 4782}, {48051, 4394}, {48054, 649}, {48064, 4790}, {48074, 4979}, {48075, 4784}
X(48624) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4979, 47935, 48110}, {47976, 48110, 47935}


X(48625) = X(513)X(4507)∩X(514)X(47692)

Barycentrics    (b - c)*(-4*a^3 + 3*a^2*b - a*b^2 + 3*a^2*c + 7*a*b*c + b^2*c - a*c^2 + b*c^2) : :
X(48625) = 5 X[47985] - 6 X[47992], 2 X[47985] - 3 X[47996], X[47985] - 3 X[48009], 4 X[47992] - 5 X[47996], 3 X[47992] - 5 X[48001], 2 X[47992] - 5 X[48009], 3 X[47996] - 4 X[48001], 2 X[48001] - 3 X[48009], X[47697] + 3 X[47974], X[47697] - 3 X[48032], 2 X[47697] - 3 X[48072], 5 X[47697] - 3 X[48153], X[47933] - 3 X[47974], X[47933] + 3 X[48032], 2 X[47933] + 3 X[48072], 5 X[47933] + 3 X[48153], 2 X[47974] + X[48072], 5 X[47974] + X[48153], 5 X[48032] - X[48153], 5 X[48072] - 2 X[48153], 4 X[659] - 3 X[45313], 3 X[45313] - 2 X[48073], 3 X[3835] - 2 X[46403], 5 X[3835] - 6 X[47821], 3 X[4724] - X[46403], 5 X[4724] - 3 X[47821], 5 X[46403] - 9 X[47821], 2 X[3837] - 3 X[45673], 2 X[7662] - 3 X[48063], 5 X[7662] - 3 X[48126], 4 X[7662] - 3 X[48399], 5 X[48063] - 2 X[48126], 4 X[48126] - 5 X[48399], 5 X[24720] - 6 X[48216], 2 X[31286] - 3 X[48572], X[47909] - 3 X[47969], 2 X[48089] - 3 X[48547]

X(48625) lies on these lines: {513, 4507}, {514, 47692}, {522, 48083}, {659, 45313}, {3667, 48036}, {3798, 28225}, {3835, 4724}, {3837, 45673}, {4380, 48034}, {4778, 47968}, {4962, 47932}, {4979, 47883}, {7662, 48063}, {8689, 21146}, {24720, 48216}, {28470, 47929}, {31286, 48572}, {47909, 47969}, {48029, 48042}, {48089, 48547}

X(48625) = midpoint of X(i) and X(j) for these {i,j}: {47697, 47933}, {47974, 48032}
X(48625) = reflection of X(i) in X(j) for these {i,j}: {3835, 4724}, {21146, 8689}, {47985, 48001}, {47996, 48009}, {48042, 48029}, {48072, 48032}, {48073, 659}, {48399, 48063}
X(48625) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {659, 48073, 45313}, {47697, 47974, 47933}, {47933, 48032, 47697}, {47985, 48001, 47996}, {47985, 48009, 48001}


X(48626) = X(513)X(47700)∩X(514)X(47692)

Barycentrics    (b - c)*(4*a^3 + a^2*b + 3*a*b^2 + 2*b^3 + a^2*c - 2*a*b*c + 2*b^2*c + 3*a*c^2 + 2*b*c^2 + 2*c^3) : :
X(48626) = 3 X[47700] - 4 X[48118], X[47700] - 4 X[48139], 2 X[48118] - 3 X[48130], X[48118] - 3 X[48139], 3 X[47702] - 4 X[47972], 5 X[47702] - 8 X[48014], 3 X[47702] - 8 X[48068], X[47702] - 4 X[48105], 2 X[47727] - 3 X[48150], 5 X[47972] - 6 X[48014], 2 X[47972] - 3 X[48032], X[47972] - 3 X[48105], 4 X[48014] - 5 X[48032], 3 X[48014] - 5 X[48068], 2 X[48014] - 5 X[48105], 3 X[48032] - 4 X[48068], 2 X[48068] - 3 X[48105], 3 X[661] - 2 X[47943], 5 X[661] - 4 X[47989], 3 X[661] - 4 X[48055], 3 X[47901] - 4 X[47943], 5 X[47901] - 8 X[47989], 3 X[47901] - 8 X[48055], X[47901] - 4 X[48102], 5 X[47943] - 6 X[47989], X[47943] - 3 X[48102], 3 X[47989] - 5 X[48055], 2 X[47989] - 5 X[48102], 2 X[48055] - 3 X[48102], 3 X[1635] - 2 X[47973], 3 X[4724] - 2 X[47961], 3 X[47916] - 4 X[47961], 3 X[4728] - 2 X[47686], 3 X[48020] - 4 X[48039], 2 X[48039] - 3 X[48094], 4 X[8689] - 3 X[48174], 5 X[24924] - 6 X[48250], 3 X[47811] - 2 X[47968], 3 X[47826] - 2 X[47951], 2 X[47960] - 3 X[48572], 2 X[48042] - 3 X[48557], 4 X[48290] - 3 X[48334]

X(48626) lies on these lines: {513, 47700}, {514, 47692}, {659, 47931}, {661, 1639}, {1635, 47973}, {2605, 4724}, {4088, 28209}, {4728, 47686}, {4778, 47903}, {4838, 29362}, {8689, 48174}, {23745, 29122}, {24924, 48250}, {28213, 47701}, {28220, 48023}, {28225, 48077}, {28229, 47958}, {47651, 48063}, {47660, 48115}, {47672, 47696}, {47811, 47968}, {47826, 47951}, {47900, 48021}, {47937, 48036}, {47960, 48572}, {48019, 48078}, {48042, 48557}, {48290, 48334}

X(48626) = reflection of X(i) in X(j) for these {i,j}: {661, 48102}, {47651, 48063}, {47672, 47696}, {47692, 48072}, {47700, 48130}, {47702, 48032}, {47705, 47697}, {47900, 48021}, {47901, 661}, {47916, 4724}, {47931, 659}, {47937, 48036}, {47943, 48055}, {47958, 48061}, {47972, 48068}, {48019, 48078}, {48020, 48094}, {48023, 48096}, {48032, 48105}, {48112, 48113}, {48115, 47660}, {48130, 48139}
X(48626) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47943, 48055, 661}, {47943, 48102, 48055}, {47972, 48068, 48032}, {47972, 48105, 48068}

leftri

2nd degree even minor triangle centers: X(48627)-X(48640)

rightri

Centers in this section are of the form h*(b^2 + c^2) + k* b c, where h and k are real numbers, not both 0. All such points lie on the line X(75)X(141).

The appearance of {h,k},i in the following list means that h*(b^2 + c^2) + k* b c = X(i).

{0,1}, 75
{1,-4}, 7263
{1,-2}, 1086
{1,-1}, 3662
{1,0}, 141
{1,2}, 594
{1,4}, 4665
{2,-1}, 17227
{2,1}, 17228
{1, -3}, 48627
{1, 3}, 48628
{2, -3}, 48629
{2, 3}, 48630
{3, -4}, 48631
{3, -2}, 48632
{3, -1}, 48633
{3, 1}, 48634
{3, 2}, 48635
{3, 4}, 48636
{4, -3}, 48637
{4, -1}, 48638
{4, 1}, 48639


X(48627) = X(1)X(26806)∩X(75)X(141)

Barycentrics    b^2 - 3*b*c + c^2 : :
X(48627) = 4 X[17234] - 3 X[29582], 2 X[17242] - 3 X[29582]

X(48627) lies on these lines: {1, 26806}, {2, 2415}, {6, 7321}, {7, 193}, {8, 7613}, {9, 4440}, {10, 4772}, {37, 4398}, {69, 4371}, {75, 141}, {76, 20892}, {86, 17301}, {87, 27846}, {142, 192}, {145, 5542}, {190, 17278}, {194, 17050}, {226, 17490}, {274, 17202}, {312, 40688}, {319, 7232}, {320, 4361}, {330, 7185}, {346, 17266}, {519, 17375}, {527, 17349}, {536, 17234}, {538, 30056}, {545, 17336}, {553, 37683}, {599, 5564}, {894, 3618}, {903, 17276}, {908, 24620}, {940, 19796}, {966, 17254}, {982, 21242}, {1213, 17249}, {1267, 26361}, {1278, 3912}, {1447, 17008}, {1654, 17274}, {1738, 24349}, {1743, 29590}, {1958, 7225}, {1999, 19789}, {2321, 4740}, {2345, 17291}, {2643, 18168}, {2796, 15485}, {3008, 17350}, {3120, 24230}, {3123, 17065}, {3187, 26842}, {3210, 5249}, {3218, 16551}, {3241, 4780}, {3247, 29622}, {3264, 18144}, {3306, 37759}, {3620, 29615}, {3622, 4356}, {3644, 17243}, {3664, 4393}, {3671, 20036}, {3672, 16826}, {3673, 47286}, {3686, 4741}, {3705, 7897}, {3739, 4389}, {3758, 6329}, {3759, 4395}, {3782, 5241}, {3790, 3836}, {3834, 4686}, {3872, 20098}, {3875, 6173}, {3914, 29843}, {3943, 4764}, {3945, 29584}, {3946, 17379}, {3948, 30090}, {3950, 4788}, {3980, 29634}, {4021, 29570}, {4080, 24184}, {4085, 31178}, {4292, 19851}, {4346, 16815}, {4357, 4699}, {4359, 27184}, {4360, 4675}, {4363, 16706}, {4364, 4751}, {4384, 4862}, {4399, 17360}, {4416, 4887}, {4419, 17260}, {4431, 4821}, {4441, 31028}, {4442, 4890}, {4452, 17316}, {4454, 26685}, {4461, 29579}, {4472, 17400}, {4475, 17891}, {4644, 17121}, {4648, 17319}, {4659, 17280}, {4664, 17245}, {4670, 17380}, {4687, 17246}, {4688, 5224}, {4704, 29571}, {4726, 17231}, {4739, 17237}, {4851, 17160}, {4852, 17378}, {4869, 17310}, {4888, 16834}, {4902, 16833}, {4904, 26530}, {4912, 15492}, {4941, 17063}, {4967, 17238}, {4971, 17386}, {4980, 33172}, {5222, 17120}, {5271, 26840}, {5391, 26362}, {5590, 32797}, {5591, 32798}, {5749, 29630}, {5750, 17383}, {5845, 32096}, {5880, 32922}, {6383, 18891}, {6542, 17151}, {6650, 33869}, {7179, 7777}, {7227, 17371}, {7238, 17361}, {7240, 23524}, {7790, 33940}, {9776, 30699}, {10029, 41792}, {10436, 17302}, {14839, 25279}, {15668, 17320}, {16020, 24280}, {16710, 17197}, {16823, 24248}, {16825, 32857}, {16827, 17753}, {17030, 26812}, {17045, 41847}, {17067, 17353}, {17118, 17289}, {17140, 33131}, {17147, 27186}, {17155, 29641}, {17178, 17205}, {17255, 17256}, {17258, 17259}, {17262, 17263}, {17264, 17265}, {17271, 28634}, {17273, 17275}, {17279, 27191}, {17281, 17283}, {17287, 42696}, {17297, 17299}, {17303, 17305}, {17306, 28604}, {17312, 17314}, {17313, 17315}, {17317, 17318}, {17321, 29612}, {17322, 17323}, {17325, 28653}, {17329, 17330}, {17334, 17335}, {17340, 17341}, {17345, 17346}, {17347, 17348}, {17351, 17352}, {17354, 17356}, {17369, 17370}, {17372, 31138}, {17376, 17377}, {17381, 17382}, {17387, 17388}, {17392, 17393}, {17394, 17395}, {17398, 17399}, {17495, 31019}, {17759, 30949}, {18134, 42051}, {18230, 20073}, {19785, 29841}, {20059, 24599}, {20081, 30030}, {20236, 26567}, {20340, 24182}, {20880, 26538}, {20888, 24190}, {21442, 33930}, {24077, 42713}, {24181, 25242}, {24200, 25385}, {24325, 33149}, {24443, 25024}, {24589, 33151}, {24598, 28358}, {24617, 27958}, {24621, 30097}, {24789, 32939}, {25351, 33165}, {25728, 31183}, {26627, 33155}, {26724, 32933}, {26817, 27255}, {26971, 27107}, {26976, 27311}, {27641, 29979}, {28968, 37771}, {30036, 40908}, {30044, 30830}, {30089, 31198}, {31229, 33129}, {32029, 47595}, {32801, 45472}, {32802, 45473}, {32865, 42055}, {33141, 42053}, {37800, 40862}

X(48627) = reflection of X(i) in X(j) for these {i,j}: {17242, 17234}, {17336, 17337}, {25269, 25101}
X(48627) = complement of X(25269)
X(48627) = anticomplement of X(25101)
X(48627) = X(21951)-cross conjugate of X(17063)
X(48627) = X(692)-isoconjugate of X(25576)
X(48627) = X(i)-Dao conjugate of X(j) for these (i, j): (1086, 25576), (4014, 20980), (17063, 3208)
X(48627) = cevapoint of X(4051) and X(17063)
X(48627) = crosspoint of X(75) and X(7209)
X(48627) = trilinear pole of line {23765, 48415}
X(48627) = barycentric product X(i)*X(j) for these {i,j}: {75, 17063}, {85, 4051}, {190, 48415}, {274, 21951}, {310, 22172}, {561, 23524}, {668, 23765}, {693, 4499}, {3261, 25577}, {4941, 6384}, {7018, 7240}
X(48627) = barycentric quotient X(i)/X(j) for these {i,j}: {514, 25576}, {4051, 9}, {4499, 100}, {4941, 43}, {7240, 171}, {17063, 1}, {21951, 37}, {22172, 42}, {23524, 31}, {23765, 513}, {25577, 101}, {48415, 514}
X(48627) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3663, 17247}, {2, 3729, 17339}, {2, 25269, 25101}, {2, 31995, 17116}, {7, 239, 17364}, {7, 4402, 193}, {37, 27147, 29581}, {69, 17117, 29617}, {75, 1086, 3662}, {75, 3662, 3661}, {75, 17227, 594}, {75, 17228, 4665}, {86, 17301, 17396}, {142, 192, 17244}, {142, 1266, 192}, {190, 17278, 17338}, {193, 4402, 239}, {320, 4361, 17363}, {894, 4000, 17367}, {903, 17277, 17276}, {1086, 7263, 75}, {1958, 7225, 27950}, {2321, 17232, 29577}, {2345, 17291, 29613}, {3618, 7222, 894}, {3618, 42697, 7222}, {3620, 32087, 29615}, {3663, 24199, 2}, {3729, 4859, 2}, {3739, 4389, 17248}, {3834, 4686, 17233}, {3875, 6173, 17300}, {3875, 17300, 17389}, {3980, 33147, 29634}, {4000, 7222, 3618}, {4000, 42697, 894}, {4357, 4699, 29576}, {4359, 33146, 27184}, {4360, 4675, 17391}, {4363, 16706, 17368}, {4384, 4862, 6646}, {4384, 6646, 17331}, {4395, 17365, 3759}, {4431, 21255, 17230}, {4659, 17282, 17280}, {4688, 17235, 5224}, {4740, 17232, 2321}, {4764, 17241, 3943}, {4772, 17236, 10}, {4788, 29572, 3950}, {4821, 17230, 4431}, {4888, 16834, 20090}, {4941, 17063, 22172}, {7228, 17366, 3758}, {7232, 17119, 319}, {7238, 17362, 17361}, {7321, 37756, 6}, {10436, 17302, 17397}, {17118, 17290, 17289}, {17151, 17298, 6542}, {17234, 17242, 29582}, {17246, 34824, 4687}, {17276, 17277, 17333}, {17280, 17282, 29629}, {17304, 25590, 2}, {17306, 28604, 29608}, {17312, 17314, 29618}, {17340, 40480, 17341}, {17889, 24165, 3705}, {29590, 31300, 1743}


X(48628) = X(1)X(28604)∩X(75)X(141)

Barycentrics    b^2 + 3*b*c + c^2 : :

X(48628) lies on these lines: {1, 28604}, {2, 2321}, {6, 5564}, {7, 17287}, {8, 193}, {9, 41841}, {10, 192}, {37, 28633}, {43, 21803}, {69, 7222}, {75, 141}, {86, 17299}, {142, 4772}, {144, 4678}, {148, 1654}, {190, 17275}, {239, 2345}, {312, 5241}, {319, 4363}, {320, 4445}, {321, 3596}, {344, 16815}, {346, 17260}, {519, 17379}, {527, 17343}, {536, 5224}, {545, 17329}, {599, 7321}, {940, 19797}, {966, 17261}, {1211, 42029}, {1213, 4664}, {1266, 4821}, {1267, 26362}, {1269, 30473}, {1278, 4357}, {1449, 20016}, {1574, 27641}, {1655, 42437}, {1698, 6541}, {1958, 4390}, {1999, 19822}, {2959, 14712}, {3008, 17358}, {3030, 7064}, {3617, 3717}, {3620, 31995}, {3621, 4923}, {3626, 4416}, {3644, 4364}, {3663, 4740}, {3664, 17373}, {3672, 17326}, {3681, 4111}, {3686, 17350}, {3705, 7777}, {3706, 29843}, {3728, 12782}, {3739, 17233}, {3758, 7227}, {3759, 4399}, {3763, 37756}, {3778, 46032}, {3840, 41836}, {3879, 4060}, {3912, 4058}, {3943, 4687}, {3950, 24603}, {4000, 17292}, {4007, 6542}, {4078, 9780}, {4360, 17303}, {4361, 17289}, {4384, 17280}, {4385, 47286}, {4389, 4686}, {4393, 5750}, {4395, 17370}, {4398, 4726}, {4419, 17252}, {4422, 32096}, {4440, 17272}, {4472, 17388}, {4478, 17360}, {4643, 32025}, {4648, 17310}, {4651, 24514}, {4657, 17160}, {4659, 6646}, {4668, 20072}, {4670, 17377}, {4675, 17295}, {4688, 17229}, {4690, 17347}, {4704, 5257}, {4708, 4718}, {4709, 29659}, {4727, 28639}, {4732, 33165}, {4739, 17231}, {4751, 17243}, {4764, 17246}, {4852, 17381}, {4898, 29597}, {4971, 17393}, {4980, 32782}, {5232, 17254}, {5391, 26361}, {5590, 32798}, {5591, 32797}, {5743, 42034}, {5749, 17121}, {5839, 17120}, {6535, 26037}, {6539, 17147}, {7081, 17008}, {7179, 7897}, {7228, 17361}, {7237, 17891}, {7790, 33941}, {8013, 32925}, {14554, 27797}, {15668, 17315}, {16706, 17119}, {16777, 28653}, {16816, 17353}, {16826, 17314}, {16998, 32945}, {17000, 32941}, {17030, 20501}, {17065, 22167}, {17151, 17302}, {17163, 29667}, {17232, 24199}, {17240, 17245}, {17241, 34824}, {17251, 17258}, {17256, 17262}, {17259, 17264}, {17263, 17269}, {17271, 17276}, {17277, 17281}, {17278, 17285}, {17279, 29628}, {17282, 29587}, {17288, 42697}, {17291, 29611}, {17294, 17300}, {17296, 26806}, {17301, 17307}, {17306, 29591}, {17309, 17317}, {17312, 29616}, {17318, 17322}, {17320, 17327}, {17321, 29610}, {17328, 17334}, {17330, 17336}, {17335, 17340}, {17337, 17342}, {17346, 17351}, {17348, 17354}, {17349, 17355}, {17352, 17359}, {17366, 17371}, {17372, 17378}, {17380, 17385}, {17383, 29604}, {17386, 17392}, {17390, 41847}, {17395, 17400}, {17759, 31330}, {17868, 33299}, {19732, 42033}, {19808, 29841}, {20080, 35578}, {21020, 29641}, {21241, 21829}, {22008, 31025}, {22016, 30830}, {24688, 31337}, {25001, 26531}, {25298, 34283}, {26227, 46918}, {26758, 31053}, {26971, 27091}, {27113, 27192}, {27184, 28605}, {27569, 33932}, {27790, 28651}, {27798, 33092}, {31090, 32865}, {31229, 32779}, {32801, 45473}, {32802, 45472}, {32935, 42334}, {41809, 42044}

X(48628) = reflection of X(i) in X(j) for these {i,j}: {17247, 5224}, {17393, 17398}
X(48628) = trilinear pole of line {4490, 4500}
X(48628) = barycentric product X(i)*X(j) for these {i,j}: {190, 4500}, {312, 7201}, {334, 4489}, {668, 4490}, {1978, 4502}, {4507, 6386}, {6376, 7275}, {27450, 40848}
X(48628) = barycentric quotient X(i)/X(j) for these {i,j}: {4489, 238}, {4490, 513}, {4500, 514}, {4502, 649}, {4507, 667}, {7201, 57}, {7275, 87}, {27450, 39914}
X(48628) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 2321, 17242}, {2, 3875, 17396}, {2, 32087, 17117}, {6, 5564, 29617}, {8, 894, 17363}, {8, 7229, 193}, {10, 192, 17248}, {10, 4431, 192}, {75, 594, 3661}, {75, 3661, 3662}, {75, 4110, 3963}, {75, 17227, 7263}, {75, 17228, 1086}, {75, 17786, 20913}, {86, 17299, 17389}, {190, 17275, 17331}, {193, 7229, 894}, {239, 2345, 17368}, {319, 4363, 17364}, {321, 21810, 24077}, {594, 4665, 75}, {1278, 29593, 4357}, {1654, 3729, 17333}, {2321, 4967, 2}, {2345, 4371, 3618}, {2345, 42696, 239}, {3617, 4461, 17257}, {3618, 4371, 239}, {3618, 42696, 4371}, {3679, 3729, 1654}, {3739, 17233, 17244}, {3879, 4060, 20055}, {3912, 4699, 27147}, {3950, 24603, 27268}, {4007, 10436, 6542}, {4360, 17303, 17397}, {4361, 17289, 17367}, {4384, 17280, 17338}, {4399, 17369, 3759}, {4445, 17118, 320}, {4472, 17388, 17394}, {4478, 17365, 17360}, {4659, 17270, 6646}, {4686, 17239, 4389}, {4688, 17229, 17234}, {4726, 17237, 4398}, {4740, 17238, 3663}, {4751, 17243, 29581}, {4764, 17250, 17246}, {4772, 17230, 142}, {4821, 17236, 1266}, {6542, 10436, 17391}, {7227, 17362, 3758}, {16706, 17293, 29613}, {16777, 28653, 29612}, {17116, 29615, 69}, {17119, 17293, 16706}, {17151, 17308, 17302}, {17229, 17234, 29577}, {17240, 17245, 29582}, {17277, 17281, 17339}, {17278, 17285, 29629}, {17281, 28634, 17277}, {17294, 25590, 17300}, {17309, 17317, 29618}, {24199, 29594, 17232}


X(48629) = X(2)X(4912)∩X(75)X(141)

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

X(48629) lies on these lines: {2, 4912}, {7, 3618}, {9, 27191}, {37, 29599}, {69, 4402}, {75, 141}, {86, 6173}, {142, 4389}, {190, 4862}, {192, 3834}, {193, 320}, {239, 7232}, {312, 33146}, {319, 4371}, {344, 4346}, {527, 17352}, {536, 17232}, {545, 17339}, {599, 17117}, {894, 17290}, {903, 3729}, {908, 31233}, {982, 21241}, {1266, 4764}, {1278, 17231}, {1760, 28017}, {1999, 19830}, {3008, 17347}, {3218, 31229}, {3619, 31995}, {3620, 5564}, {3631, 29617}, {3644, 3912}, {3663, 4098}, {3664, 17380}, {3672, 17317}, {3673, 7790}, {3739, 17236}, {3763, 17116}, {3769, 33147}, {3782, 18743}, {3823, 31302}, {3875, 17297}, {3946, 17378}, {4310, 32850}, {4357, 4751}, {4360, 17298}, {4361, 17288}, {4363, 17291}, {4364, 27147}, {4384, 17273}, {4393, 17376}, {4395, 17363}, {4416, 17067}, {4417, 24177}, {4419, 17263}, {4429, 24231}, {4440, 17279}, {4479, 30945}, {4648, 17320}, {4657, 26806}, {4659, 17285}, {4670, 17383}, {4675, 17302}, {4676, 32857}, {4681, 29572}, {4686, 17230}, {4688, 17238}, {4699, 17237}, {4739, 29593}, {4740, 17229}, {4741, 17348}, {4772, 17239}, {4852, 17375}, {4859, 17274}, {4869, 17315}, {4887, 17353}, {4888, 46922}, {5224, 24199}, {5241, 27184}, {5590, 32801}, {5591, 32802}, {6329, 17365}, {6376, 24190}, {6646, 17278}, {7225, 18042}, {7227, 29613}, {7228, 17368}, {7229, 17289}, {7238, 17364}, {7897, 33891}, {7937, 33940}, {10436, 17305}, {14829, 23681}, {15668, 17324}, {16674, 29620}, {16675, 29626}, {16732, 26567}, {16815, 17253}, {16816, 17344}, {16826, 17323}, {16885, 29607}, {17118, 17292}, {17119, 17287}, {17151, 17295}, {17160, 17296}, {17184, 19804}, {17192, 39731}, {17244, 17246}, {17245, 17247}, {17248, 34824}, {17254, 17259}, {17255, 17260}, {17261, 17265}, {17262, 17266}, {17300, 17301}, {17307, 25590}, {17312, 17318}, {17313, 17319}, {17327, 31139}, {17332, 29628}, {17333, 17337}, {17334, 17338}, {17340, 29629}, {17345, 17349}, {17350, 17356}, {17379, 17382}, {17391, 17395}, {17392, 17396}, {17889, 21242}, {18133, 30090}, {18144, 20892}, {20255, 20943}, {20923, 39995}, {21251, 24168}, {21356, 32087}, {24063, 27697}, {24076, 27727}, {24169, 33103}, {24182, 25121}, {24789, 26840}, {25269, 41310}, {25505, 27017}, {26361, 32791}, {26362, 32792}, {26842, 32774}, {26997, 28748}, {30598, 39720}, {30829, 33151}, {33172, 42029}

X(48629) = reflection of X(17240) in X(17232)
X(48629) = barycentric product X(190)*X(48421)
X(48629) = barycentric quotient X(i)/X(j) for these {i,j}: {7287, 4557}, {48421, 514}
X(48629) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17235, 17249}, {2, 17276, 17336}, {7, 16706, 3758}, {75, 3662, 17227}, {75, 17227, 17228}, {75, 18150, 17786}, {86, 17304, 17399}, {142, 4389, 4687}, {190, 17282, 17341}, {192, 3834, 17241}, {239, 7232, 17361}, {320, 4000, 3759}, {894, 17290, 17370}, {903, 17283, 3729}, {1086, 3662, 75}, {1266, 17233, 4764}, {1266, 21255, 17233}, {3661, 7263, 75}, {3663, 17234, 4664}, {3729, 17283, 17342}, {3739, 17236, 17250}, {3875, 17297, 17386}, {3912, 4398, 3644}, {4360, 17298, 17387}, {4361, 17288, 17360}, {4363, 17291, 17371}, {4384, 17273, 17328}, {4657, 26806, 41847}, {4675, 17302, 17394}, {4852, 31138, 17375}, {4859, 17274, 17277}, {4862, 17282, 190}, {6173, 17304, 86}, {6646, 17278, 17335}, {7238, 17366, 17364}, {10436, 17305, 17400}, {17274, 17277, 17329}, {17300, 17301, 17393}, {17334, 40480, 17338}


X(48630) = X(2)X(3723)∩X(75)X(141)

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

X(48630) lies on these lines: {2, 3723}, {6, 29615}, {8, 1386}, {9, 32025}, {10, 4687}, {37, 29593}, {69, 7229}, {75, 141}, {86, 17294}, {190, 17270}, {192, 17239}, {193, 319}, {239, 17293}, {320, 7222}, {321, 30473}, {344, 3617}, {346, 17256}, {519, 17381}, {536, 17238}, {599, 17116}, {894, 4445}, {966, 17264}, {1100, 20055}, {1211, 42034}, {1213, 17242}, {1268, 16831}, {1278, 17237}, {1654, 17281}, {1999, 19827}, {2321, 4664}, {3589, 29617}, {3619, 32087}, {3620, 7321}, {3626, 17353}, {3644, 4058}, {3679, 4595}, {3681, 21865}, {3686, 17354}, {3729, 17271}, {3731, 31144}, {3739, 17230}, {3763, 17117}, {3834, 4772}, {3875, 17307}, {3912, 4751}, {3943, 17248}, {4007, 4360}, {4022, 46032}, {4043, 6376}, {4060, 17023}, {4361, 17292}, {4363, 17287}, {4384, 17285}, {4385, 7790}, {4389, 4431}, {4390, 18042}, {4393, 17385}, {4399, 17367}, {4402, 16706}, {4472, 17391}, {4478, 17363}, {4657, 29591}, {4659, 17273}, {4670, 17373}, {4686, 17236}, {4688, 17232}, {4690, 17350}, {4699, 17231}, {4704, 4708}, {4725, 37677}, {4727, 25498}, {4740, 17235}, {4745, 25072}, {4851, 28604}, {4967, 17234}, {4971, 17396}, {5232, 17258}, {5241, 18743}, {5590, 32802}, {5591, 32801}, {5743, 20942}, {5750, 17377}, {6329, 17362}, {6542, 17303}, {7199, 21958}, {7227, 17364}, {7777, 30179}, {7937, 33941}, {10436, 17295}, {15668, 17310}, {16777, 29610}, {16815, 17267}, {16816, 17357}, {16826, 17309}, {17045, 29608}, {17118, 17288}, {17119, 17291}, {17143, 18044}, {17144, 18046}, {17151, 17305}, {17160, 17306}, {17243, 29576}, {17245, 29577}, {17251, 17261}, {17252, 17262}, {17259, 17268}, {17260, 17269}, {17275, 17280}, {17278, 29587}, {17297, 25590}, {17314, 17322}, {17316, 28653}, {17317, 29616}, {17318, 17326}, {17319, 17327}, {17330, 17339}, {17331, 17340}, {17343, 17351}, {17346, 17355}, {17348, 17358}, {17349, 17359}, {17366, 29613}, {17372, 17379}, {17375, 39704}, {17380, 29604}, {17388, 17397}, {17389, 17398}, {18041, 33299}, {18065, 32104}, {19742, 42030}, {19875, 31248}, {21242, 32778}, {21356, 31995}, {24547, 26610}, {25505, 27044}, {26361, 32792}, {26362, 32791}, {28593, 31330}, {29569, 43985}, {29570, 30598}, {29572, 31238}, {32782, 42029}

X(48630) = reflection of X(17249) in X(17238)
X(48630) = trilinear pole of line {47665, 48012}
X(48630) = barycentric product X(i)*X(j) for these {i,j}: {190, 47665}, {668, 48012}, {5216, 27808}
X(48630) = barycentric quotient X(i)/X(j) for these {i,j}: {5216, 3733}, {47665, 514}, {48012, 513}
X(48630) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17229, 17240}, {2, 17299, 17393}, {8, 17289, 3759}, {10, 17233, 4687}, {75, 3661, 17228}, {75, 17228, 17227}, {86, 17294, 17386}, {190, 17270, 17328}, {192, 17239, 17250}, {239, 17293, 17371}, {319, 2345, 3758}, {321, 30473, 30596}, {594, 3661, 75}, {894, 4445, 17360}, {1654, 17281, 17336}, {2321, 5224, 4664}, {3619, 32087, 37756}, {3662, 4665, 75}, {3679, 17286, 17277}, {3729, 17271, 17329}, {3739, 17230, 17241}, {3875, 17307, 17399}, {4007, 17308, 4360}, {4360, 17308, 17400}, {4361, 17292, 17370}, {4363, 17287, 17361}, {4384, 17285, 17341}, {4389, 4431, 4764}, {4478, 17369, 17363}, {4851, 28604, 41847}, {4967, 29594, 17234}, {6542, 17303, 17394}, {10436, 17295, 17387}, {17275, 17280, 17335}, {17277, 17286, 17342}, {29611, 42696, 16706}


X(48631) = X(2)X(7228)∩X(75)X(141)

Barycentrics    -4*b*c + 3*(b^2 + c^2) : :
X(48631) = 3 X[4000] + X[21296], 3 X[7232] - X[21296], X[4072] - 5 X[21255]

X(48631) lies on these lines: {2, 7228}, {6, 7238}, {7, 3589}, {9, 40480}, {69, 4395}, {75, 141}, {142, 3986}, {239, 3630}, {319, 4405}, {320, 3629}, {346, 28297}, {524, 4000}, {527, 17356}, {536, 4072}, {545, 4862}, {597, 16706}, {599, 4399}, {903, 17280}, {940, 19823}, {1213, 17236}, {1266, 17231}, {1743, 28333}, {1999, 19828}, {2345, 20582}, {3008, 17345}, {3619, 17118}, {3620, 4478}, {3631, 4361}, {3663, 3834}, {3664, 17382}, {3672, 17313}, {3763, 7227}, {3782, 4358}, {3821, 25557}, {3879, 31138}, {3912, 4718}, {3943, 4398}, {3946, 17376}, {4310, 9053}, {4346, 17262}, {4357, 31238}, {4363, 34573}, {4370, 17341}, {4389, 17245}, {4409, 29629}, {4415, 30829}, {4419, 17265}, {4422, 17276}, {4440, 17283}, {4452, 17309}, {4454, 36606}, {4472, 17306}, {4643, 4859}, {4644, 6329}, {4648, 17323}, {4657, 6173}, {4671, 33146}, {4675, 17045}, {4704, 17234}, {4726, 29594}, {4764, 29577}, {4869, 17318}, {4884, 25957}, {4887, 17351}, {4957, 26567}, {4966, 33149}, {4969, 17361}, {4971, 17296}, {4972, 17146}, {5222, 32455}, {5356, 27003}, {5743, 17184}, {6381, 20255}, {6646, 17337}, {6707, 17325}, {7179, 15491}, {7231, 7321}, {7277, 17367}, {8584, 17364}, {10022, 17385}, {11246, 33123}, {17067, 17348}, {17237, 24199}, {17249, 27147}, {17273, 17330}, {17274, 17278}, {17281, 36525}, {17288, 17362}, {17293, 31995}, {17297, 17388}, {17298, 17301}, {17300, 17395}, {17302, 17392}, {17305, 17398}, {17329, 29628}, {17370, 48310}, {19945, 21330}, {20195, 31285}, {20335, 25350}, {25101, 31243}, {25349, 30949}, {31647, 36230}, {32799, 45472}, {32800, 45473}, {37650, 45789}

X(48631) = midpoint of X(i) and X(j) for these {i,j}: {4000, 7232}, {4452, 17309}, {4862, 17279}
X(48631) = barycentric product X(75)*X(42040)
X(48631) = barycentric quotient X(42040)/X(1)
X(48631) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 17290, 3589}, {141, 1086, 7263}, {141, 7263, 4665}, {142, 17235, 4364}, {320, 17366, 3629}, {594, 17227, 141}, {1086, 3662, 141}, {3620, 17119, 4478}, {3663, 3834, 17243}, {3763, 42697, 7227}, {4398, 17232, 3943}, {4440, 17283, 17340}, {4675, 17304, 17045}, {6646, 27191, 17337}, {7321, 17291, 17369}, {7321, 17369, 7231}, {16706, 17365, 597}, {17184, 40688, 5743}, {17274, 17278, 17332}, {17276, 17282, 4422}, {17288, 17362, 22165}, {17288, 37756, 17362}, {17298, 17301, 17390}, {17305, 26806, 17398}


X(48632) = X(2)X(7232)∩X(75)X(141)

Barycentrics    -2*b*c + 3*(b^2 + c^2) : :
X(48632) = 3 X[16706] - X[17121], X[17121] + 3 X[17288]

X(48632) lies on these lines: {2, 7232}, {6, 21296}, {7, 3763}, {37, 21255}, {69, 4969}, {75, 141}, {142, 1213}, {239, 3631}, {319, 4395}, {320, 3589}, {344, 17255}, {524, 16706}, {527, 17357}, {545, 17280}, {597, 17364}, {599, 4000}, {894, 7238}, {1211, 24589}, {1266, 17229}, {1654, 27191}, {1999, 19829}, {2245, 29812}, {2345, 21358}, {3008, 17344}, {3619, 4363}, {3620, 4361}, {3629, 17361}, {3630, 3759}, {3644, 29577}, {3663, 3943}, {3664, 17384}, {3672, 17311}, {3729, 4409}, {3756, 25760}, {3782, 4671}, {3821, 4966}, {3834, 4357}, {3844, 24231}, {3879, 17382}, {3912, 4681}, {3945, 26104}, {3946, 17374}, {4358, 4415}, {4364, 17234}, {4370, 17274}, {4389, 4704}, {4398, 17230}, {4399, 17287}, {4416, 17356}, {4419, 17267}, {4422, 6646}, {4440, 17285}, {4445, 21356}, {4472, 17307}, {4478, 17117}, {4643, 17282}, {4644, 47355}, {4648, 17325}, {4657, 17298}, {4675, 17306}, {4686, 29594}, {4741, 17352}, {4788, 17233}, {4851, 17304}, {4859, 17275}, {4862, 17281}, {4869, 16777}, {4971, 17295}, {4972, 17145}, {5222, 40341}, {5224, 34824}, {5590, 32799}, {5591, 32800}, {5852, 33159}, {6173, 17303}, {6329, 29630}, {6381, 21025}, {6666, 31243}, {6703, 19832}, {6707, 17326}, {7227, 7321}, {7228, 17289}, {11246, 24943}, {14210, 17192}, {16669, 31191}, {16674, 29621}, {16675, 29627}, {17023, 17376}, {17045, 17300}, {17061, 33085}, {17118, 29611}, {17239, 24199}, {17241, 17247}, {17244, 17249}, {17250, 27147}, {17254, 17263}, {17257, 17265}, {17258, 17266}, {17262, 29579}, {17272, 17278}, {17276, 17284}, {17277, 40480}, {17293, 42697}, {17296, 17301}, {17297, 17302}, {17312, 17320}, {17313, 17321}, {17316, 17323}, {17317, 17324}, {17328, 29628}, {17329, 17338}, {17333, 17341}, {17336, 29629}, {17345, 17353}, {17351, 29596}, {17363, 22165}, {17375, 17380}, {17378, 17383}, {17387, 17396}, {17391, 17399}, {17724, 33086}, {17768, 29637}, {19945, 22167}, {25527, 37646}, {25557, 32784}, {26840, 44416}, {27017, 27106}, {27184, 30829}, {29802, 34282}, {30991, 37651}, {32782, 40688}, {32795, 45472}, {32796, 45473}, {33124, 44419}

X(48632) = midpoint of X(16706) and X(17288)
X(48632) = barycentric product X(i)*X(j) for these {i,j}: {75, 42038}, {190, 48425}
X(48632) = barycentric quotient X(i)/X(j) for these {i,j}: {42038, 1}, {48425, 514}
X(48632) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7232, 17365}, {2, 17273, 17332}, {7, 3763, 17369}, {69, 17290, 17366}, {69, 17366, 4969}, {141, 1086, 594}, {141, 3662, 1086}, {141, 4665, 17228}, {141, 7263, 3661}, {142, 17237, 1213}, {320, 3589, 7277}, {320, 17291, 3589}, {599, 4000, 17362}, {3662, 17227, 141}, {3663, 17231, 3943}, {3834, 4357, 17245}, {3912, 17235, 17246}, {4389, 17232, 17243}, {4643, 17282, 17337}, {4657, 17298, 17392}, {4675, 17306, 17398}, {4851, 17304, 17395}, {6646, 17283, 4422}, {7228, 20582, 17289}, {7238, 34573, 894}, {7321, 17292, 7227}, {17234, 17236, 4364}, {17272, 17278, 17330}, {17274, 17279, 17334}, {17276, 17284, 17340}, {17279, 17334, 4370}, {17287, 37756, 4399}, {17296, 17301, 17388}, {17297, 17302, 17390}, {17300, 17305, 17045}, {17307, 26806, 4472}, {17361, 17367, 3629}, {17364, 17370, 597}, {17384, 31138, 3664}


X(48633) = X(2)X(1743)∩X(75)X(141)

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

X(48633) lies on these lines: {2, 1743}, {7, 17292}, {9, 29629}, {37, 29582}, {69, 17121}, {75, 141}, {142, 17238}, {192, 29577}, {193, 29630}, {239, 3620}, {319, 17290}, {320, 3763}, {344, 17254}, {391, 29607}, {524, 17370}, {527, 17358}, {599, 16706}, {894, 3619}, {940, 19832}, {1278, 29594}, {1654, 17282}, {1999, 19823}, {3008, 17343}, {3247, 29623}, {3589, 17361}, {3631, 3759}, {3663, 4788}, {3672, 17310}, {3729, 29587}, {3758, 34573}, {3834, 5224}, {3840, 30989}, {3879, 17383}, {3912, 4098}, {3945, 29614}, {3946, 17373}, {3986, 29599}, {4000, 17287}, {4058, 4821}, {4357, 17232}, {4358, 27184}, {4364, 17241}, {4389, 4681}, {4398, 17229}, {4419, 17268}, {4422, 17329}, {4440, 17286}, {4445, 37756}, {4643, 17283}, {4648, 17326}, {4657, 17297}, {4671, 17184}, {4675, 17307}, {4698, 17234}, {4718, 17233}, {4741, 17353}, {4851, 17305}, {4869, 16826}, {5232, 16815}, {5296, 29626}, {5590, 32795}, {5591, 32796}, {5847, 26150}, {6173, 28604}, {6542, 17304}, {6646, 17284}, {7179, 16986}, {7232, 17289}, {7321, 17293}, {10436, 29608}, {16673, 29589}, {17023, 17375}, {17045, 17387}, {17116, 29611}, {17146, 29667}, {17202, 30965}, {17240, 17246}, {17243, 17249}, {17245, 17250}, {17253, 17263}, {17255, 17264}, {17256, 17265}, {17257, 17266}, {17258, 17267}, {17261, 29579}, {17271, 17278}, {17273, 17279}, {17274, 17280}, {17275, 27191}, {17276, 17285}, {17295, 17301}, {17296, 17302}, {17300, 17306}, {17308, 26806}, {17311, 17320}, {17312, 17321}, {17313, 17322}, {17315, 17323}, {17316, 17324}, {17317, 17325}, {17319, 29618}, {17328, 17337}, {17332, 17341}, {17334, 17342}, {17344, 17352}, {17345, 17354}, {17346, 17356}, {17347, 17357}, {17350, 29596}, {17360, 17366}, {17365, 17371}, {17374, 17380}, {17376, 17381}, {17377, 17382}, {17378, 17384}, {17385, 31138}, {17386, 17395}, {17390, 17399}, {17392, 17400}, {20090, 29598}, {20290, 29666}, {21240, 30044}, {24090, 27727}, {24199, 29593}, {24589, 32782}, {25590, 29591}, {27017, 27091}, {27106, 27145}, {28626, 29609}, {29634, 33085}, {31004, 31028}, {38204, 46933}

X(48633) = barycentric product X(190)*X(48426)
X(48633) = barycentric quotient X(48426)/X(514)
X(48633) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17272, 17331}, {2, 17288, 17364}, {2, 21296, 17120}, {69, 17291, 17367}, {141, 1086, 17228}, {141, 3662, 3661}, {141, 17227, 3662}, {142, 17238, 29576}, {320, 3763, 17368}, {599, 16706, 17363}, {894, 3619, 29613}, {1654, 17282, 29628}, {3834, 5224, 27147}, {3912, 17236, 17247}, {4000, 17287, 29617}, {4000, 21356, 17287}, {4357, 17232, 17244}, {4389, 17231, 17242}, {4643, 17283, 17338}, {4648, 17326, 29612}, {4657, 17297, 17391}, {4851, 17305, 17396}, {6646, 17284, 17339}, {7232, 21358, 17289}, {17120, 17288, 21296}, {17120, 21296, 17364}, {17234, 17237, 17248}, {17234, 17248, 29581}, {17273, 17279, 17333}, {17296, 17302, 17389}, {17300, 17306, 17397}, {17365, 20582, 17371}


X(48634) = X(2)X(1449)∩X(75)X(141)

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

X(48634) lies on these lines: {2, 1449}, {6, 29613}, {8, 17291}, {9, 29587}, {10, 17232}, {37, 29577}, {69, 17120}, {75, 141}, {86, 29608}, {142, 29593}, {192, 4072}, {239, 3619}, {319, 3763}, {320, 17293}, {344, 17252}, {346, 17254}, {519, 17383}, {524, 17371}, {599, 17289}, {894, 3620}, {966, 17266}, {1211, 30829}, {1213, 17241}, {1654, 17284}, {2321, 4788}, {2345, 17288}, {3589, 17360}, {3631, 3758}, {3679, 27295}, {3705, 16986}, {3759, 34573}, {3912, 3986}, {3943, 17249}, {3946, 20055}, {4000, 29615}, {4029, 4357}, {4034, 29590}, {4058, 4740}, {4358, 32782}, {4364, 17240}, {4389, 4718}, {4416, 17358}, {4422, 17328}, {4445, 16706}, {4643, 17285}, {4648, 29610}, {4657, 17295}, {4671, 27184}, {4681, 17233}, {4687, 29582}, {4690, 17352}, {4698, 5224}, {4699, 21255}, {4741, 17355}, {4851, 17307}, {5232, 17260}, {5257, 29572}, {5564, 17290}, {5590, 32796}, {5591, 32795}, {5750, 17375}, {5839, 29630}, {6542, 17306}, {6646, 17286}, {10436, 29591}, {16777, 29618}, {17023, 17373}, {17045, 17386}, {17145, 29667}, {17234, 17239}, {17243, 17250}, {17251, 17263}, {17253, 17264}, {17256, 17267}, {17257, 17268}, {17258, 17269}, {17271, 17279}, {17272, 17280}, {17273, 17281}, {17275, 17283}, {17277, 29629}, {17278, 32025}, {17294, 17302}, {17297, 17303}, {17298, 28604}, {17299, 17305}, {17300, 17308}, {17309, 17320}, {17310, 17321}, {17311, 17322}, {17313, 28653}, {17314, 17324}, {17315, 17325}, {17316, 17326}, {17317, 17327}, {17319, 29616}, {17329, 17340}, {17330, 17341}, {17332, 17342}, {17343, 17353}, {17344, 17354}, {17346, 17357}, {17347, 17359}, {17349, 29596}, {17361, 17369}, {17362, 17370}, {17372, 17380}, {17374, 17381}, {17377, 17384}, {17378, 17385}, {17379, 29604}, {17387, 17398}, {17388, 17399}, {17390, 17400}, {17772, 25539}, {19832, 29841}, {24589, 33172}, {25624, 46843}, {26083, 34379}, {27091, 27145}, {27191, 28634}, {32108, 40480}

X(48634) = barycentric product X(190)*X(48427)
X(48634) = barycentric quotient X(48427)/X(514)
X(48634) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17287, 17363}, {2, 17296, 17391}, {2, 32099, 17121}, {10, 17232, 27147}, {69, 17292, 17368}, {141, 594, 17227}, {141, 3661, 3662}, {141, 17228, 3661}, {319, 3763, 17367}, {599, 17289, 17364}, {1213, 17241, 29581}, {1654, 17284, 17338}, {2345, 21356, 17288}, {3620, 29611, 894}, {3912, 17238, 17248}, {4357, 17230, 17242}, {4445, 16706, 29617}, {4445, 21358, 16706}, {4643, 17285, 17339}, {4657, 17295, 17389}, {4851, 17307, 17397}, {5224, 17231, 17244}, {5232, 29579, 17260}, {6542, 17306, 17396}, {17121, 17287, 32099}, {17121, 32099, 17363}, {17233, 17237, 17247}, {17234, 17239, 29576}, {17271, 17279, 17331}, {17272, 17280, 17333}, {17275, 17283, 29628}, {17317, 17327, 29612}, {17362, 20582, 17370}


X(48635) = X(2)X(4445)∩X(75)X(141)

Barycentrics    2*b*c + 3*(b^2 + c^2) : :
X(48635) = X[17120] + 3 X[17287], X[17120] - 3 X[17289]

X(48635) lies on these lines: {2, 4445}, {6, 29611}, {8, 3763}, {10, 4966}, {37, 29594}, {45, 5232}, {69, 7277}, {75, 141}, {86, 29591}, {239, 4478}, {319, 3589}, {320, 7227}, {344, 17251}, {346, 17253}, {519, 17384}, {524, 17120}, {545, 17273}, {597, 17363}, {599, 2345}, {894, 3631}, {966, 17267}, {1100, 29604}, {1211, 4358}, {1213, 3912}, {1654, 4422}, {1999, 19832}, {2321, 4718}, {3619, 4361}, {3620, 4363}, {3629, 17360}, {3630, 3758}, {3634, 5625}, {3679, 17278}, {3686, 17357}, {3759, 29613}, {3775, 3932}, {3834, 4967}, {3836, 4733}, {3879, 17385}, {3943, 4357}, {4000, 21358}, {4007, 17301}, {4021, 4727}, {4046, 32781}, {4058, 4686}, {4364, 4704}, {4370, 17271}, {4389, 4788}, {4395, 5564}, {4399, 16706}, {4415, 4671}, {4416, 17359}, {4431, 17235}, {4472, 17300}, {4643, 17286}, {4657, 17294}, {4687, 29577}, {4688, 21255}, {4690, 17353}, {4691, 31243}, {4748, 16675}, {4851, 17308}, {4971, 17302}, {5224, 17230}, {5590, 32800}, {5591, 32799}, {5743, 30829}, {5749, 40341}, {5750, 17374}, {5839, 47355}, {6381, 21024}, {6542, 17045}, {6707, 17317}, {7228, 17288}, {7232, 21356}, {7238, 17116}, {16738, 26774}, {16777, 29616}, {17023, 17372}, {17232, 34824}, {17234, 29593}, {17240, 17248}, {17241, 29576}, {17242, 17250}, {17252, 17264}, {17256, 17268}, {17257, 17269}, {17259, 29579}, {17270, 17279}, {17272, 17281}, {17275, 17284}, {17277, 29587}, {17282, 28634}, {17290, 42696}, {17296, 17303}, {17297, 28604}, {17299, 17306}, {17309, 17321}, {17310, 17322}, {17312, 28653}, {17314, 17325}, {17315, 17326}, {17316, 17327}, {17328, 17339}, {17331, 17342}, {17343, 17354}, {17344, 17355}, {17346, 17358}, {17348, 29596}, {17364, 22165}, {17370, 29617}, {17373, 17381}, {17380, 20055}, {17386, 17397}, {17389, 17400}, {17394, 29608}, {25498, 29574}, {26543, 26594}, {26979, 27044}, {30942, 31337}, {32795, 45473}, {32796, 45472}, {37653, 44416}

X(48635) = midpoint of X(17287) and X(17289)
X(48635) = barycentric product X(i)*X(j) for these {i,j}: {75, 42039}, {190, 48428}
X(48635) = barycentric quotient X(i)/X(j) for these {i,j}: {42039, 1}, {48428, 514}
X(48635) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4445, 17362}, {2, 17295, 17390}, {8, 3763, 17366}, {10, 17231, 17245}, {69, 17293, 17369}, {69, 17369, 7277}, {141, 594, 1086}, {141, 3661, 594}, {141, 4665, 3662}, {141, 7263, 17227}, {319, 3589, 4969}, {319, 17292, 3589}, {599, 2345, 17365}, {1654, 17285, 4422}, {2321, 17237, 17246}, {3661, 17228, 141}, {3912, 17239, 1213}, {4357, 17229, 3943}, {4399, 20582, 16706}, {4478, 34573, 239}, {4643, 17286, 17340}, {4657, 17294, 17388}, {4851, 17308, 17398}, {5224, 17230, 17243}, {5564, 17291, 4395}, {6542, 17307, 17045}, {16706, 29615, 4399}, {17233, 17238, 4364}, {17270, 17279, 17330}, {17271, 17280, 17332}, {17272, 17281, 17334}, {17275, 17284, 17337}, {17280, 17332, 4370}, {17296, 17303, 17392}, {17299, 17306, 17395}, {17317, 29610, 6707}, {17360, 17368, 3629}, {17363, 17371, 597}


X(48636) = X(2)X(4399)∩X(75)X(141)

Barycentrics    4*b*c + 3*(b^2 + c^2) : :
X(48636) = 3 X[2345] + X[32099], 3 X[4445] - X[32099]

X(48636) lies on these lines: {2, 4399}, {6, 4478}, {8, 3589}, {10, 4698}, {69, 7227}, {75, 141}, {312, 43285}, {319, 3629}, {320, 7231}, {346, 17251}, {519, 17385}, {524, 2345}, {536, 4058}, {545, 17272}, {597, 17121}, {599, 7228}, {894, 3630}, {966, 17269}, {1211, 4671}, {1213, 17233}, {1268, 29569}, {1449, 28337}, {1654, 17340}, {2321, 4364}, {3247, 25358}, {3617, 17259}, {3619, 17119}, {3620, 7238}, {3626, 17348}, {3631, 4363}, {3664, 10022}, {3672, 28309}, {3679, 17279}, {3686, 17359}, {3705, 15491}, {3739, 29594}, {3763, 4395}, {3815, 30179}, {3912, 31238}, {3943, 4704}, {3950, 4708}, {4000, 20582}, {4007, 4657}, {4060, 4852}, {4357, 4718}, {4358, 5743}, {4360, 29591}, {4361, 29611}, {4370, 17331}, {4405, 5564}, {4422, 17275}, {4431, 17237}, {4461, 17255}, {4470, 30712}, {4472, 4851}, {4678, 37650}, {4690, 17355}, {4691, 6666}, {4733, 29674}, {4739, 21255}, {4751, 29577}, {4788, 17238}, {4967, 17231}, {4969, 17368}, {5232, 17262}, {5749, 32455}, {5750, 17372}, {5839, 6329}, {6539, 18139}, {6542, 17398}, {6707, 17316}, {7277, 17360}, {7300, 27065}, {8584, 17363}, {15668, 29616}, {17045, 17299}, {17230, 17245}, {17240, 29576}, {17270, 17281}, {17271, 17334}, {17280, 17330}, {17284, 28634}, {17285, 17337}, {17287, 17365}, {17290, 32087}, {17294, 17303}, {17295, 17392}, {17307, 17395}, {17310, 28653}, {17314, 17327}, {17315, 29610}, {17371, 29617}, {17381, 20055}, {17393, 29608}, {21705, 23901}, {28633, 29571}, {28635, 29627}, {28640, 29602}, {32799, 45473}, {32800, 45472}

X(48636) = midpoint of X(i) and X(j) for these {i,j}: {2345, 4445}, {4007, 4657}, {4461, 17255}
X(48636) = barycentric product X(i)*X(j) for these {i,j}: {75, 42041}, {190, 48429}
X(48636) = barycentric quotient X(i)/X(j) for these {i,j}: {42041, 1}, {48429, 514}
X(48636) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 17293, 3589}, {10, 17229, 17243}, {141, 594, 4665}, {141, 4665, 7263}, {319, 17369, 3629}, {594, 3661, 141}, {1086, 17228, 141}, {2321, 17239, 4364}, {3620, 17118, 7238}, {3763, 42696, 4395}, {4060, 29604, 4852}, {4361, 29611, 34573}, {4967, 17231, 34824}, {5564, 17292, 17366}, {5564, 17366, 4405}, {17233, 29593, 1213}, {17270, 17281, 17332}, {17275, 17286, 4422}, {17280, 32025, 17330}, {17287, 17365, 22165}, {17289, 17362, 597}, {17289, 29615, 17362}, {17294, 17303, 17390}, {17295, 28604, 17392}, {17299, 17308, 17045}


X(48637) = X(2)X(15492)∩X(75)X(141)

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

X(48637) lies on these lines: {2, 15492}, {7, 17371}, {75, 141}, {142, 17250}, {193, 16706}, {319, 4402}, {320, 3618}, {903, 17286}, {3619, 7229}, {3620, 4371}, {3644, 17231}, {3663, 17240}, {3673, 7937}, {3758, 7232}, {3759, 17288}, {3834, 4687}, {4000, 17360}, {4389, 17241}, {4664, 17232}, {4675, 17400}, {4741, 17356}, {4751, 17237}, {4764, 17230}, {4859, 17271}, {4862, 17285}, {4869, 17320}, {5564, 21356}, {6173, 17307}, {6329, 17364}, {6646, 17341}, {7222, 17289}, {7228, 29613}, {7238, 17368}, {17116, 21358}, {17184, 18743}, {17192, 18156}, {17234, 17249}, {17238, 28633}, {17254, 17265}, {17255, 17266}, {17272, 27191}, {17273, 17282}, {17274, 17283}, {17276, 17342}, {17278, 17328}, {17297, 17304}, {17298, 17305}, {17300, 17399}, {17301, 17386}, {17302, 17387}, {17306, 41847}, {17312, 17323}, {17313, 17324}, {17331, 40480}, {17334, 29629}, {17339, 36522}, {17367, 32455}, {17375, 17382}, {17376, 17383}, {17379, 31138}, {17381, 39704}, {20943, 21240}, {26361, 32803}, {26362, 32804}, {33172, 42034}

X(48637) = barycentric product X(190)*X(48432)
X(48637) = barycentric quotient X(48432)/X(514)
X(48637) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1086, 17228, 75}, {3662, 17227, 75}, {3834, 17236, 4687}, {4389, 21255, 17241}, {7232, 17291, 3758}, {17232, 17235, 4664}, {17273, 17282, 17335}, {17274, 17283, 17336}, {17288, 17290, 3759}, {17297, 17304, 17393}, {17298, 17305, 17394}


X(48638) = X(2)X(16669)∩X(75)X(141)

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

X(48638) lies on these lines: {2, 16669}, {69, 17370}, {75, 141}, {319, 21356}, {320, 3619}, {599, 3759}, {894, 21358}, {3620, 5839}, {3631, 17367}, {3644, 17230}, {3758, 3763}, {3834, 4751}, {3912, 17249}, {3950, 4389}, {4357, 17241}, {4398, 29594}, {4643, 17341}, {4657, 17387}, {4664, 17231}, {4687, 17232}, {4741, 17357}, {4764, 17229}, {4851, 17399}, {4859, 32025}, {4869, 17322}, {5224, 21255}, {5257, 17234}, {5590, 32803}, {5591, 32804}, {5750, 39704}, {6646, 17342}, {7232, 17292}, {7321, 29611}, {17184, 42034}, {17246, 29577}, {17252, 17265}, {17253, 17266}, {17254, 17267}, {17255, 17268}, {17258, 29579}, {17270, 27191}, {17271, 17282}, {17272, 17283}, {17273, 17284}, {17274, 17285}, {17276, 29587}, {17279, 17329}, {17287, 17290}, {17295, 17304}, {17296, 17305}, {17297, 17306}, {17298, 17307}, {17300, 17400}, {17302, 17386}, {17310, 17323}, {17311, 17324}, {17312, 17325}, {17313, 17326}, {17332, 29629}, {17343, 17356}, {17345, 17358}, {17347, 29596}, {17364, 34573}, {17365, 29613}, {17368, 20582}, {17373, 17382}, {17374, 17383}, {17375, 17384}, {18743, 26580}, {20195, 31144}, {20942, 27184}, {25505, 27106}, {29630, 40341}

X(48638) = barycentric product X(190)*X(48433)
X(48638) = barycentric quotient X(48433)/X(514)
X(48638) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {141, 3662, 17228}, {141, 17227, 75}, {320, 3619, 17371}, {599, 17291, 3759}, {3620, 16706, 17360}, {3661, 3662, 7263}, {3662, 17228, 75}, {3763, 17288, 3758}, {3834, 17238, 4751}, {17227, 17228, 3662}, {17230, 17235, 3644}, {17231, 17236, 4664}, {17232, 17237, 4687}, {17272, 17283, 17335}, {17273, 17284, 17336}, {17296, 17305, 17393}, {17297, 17306, 17394}, {17298, 17307, 41847}


X(48639) = X(2)X(4690)∩X(75)X(141)

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

X(48639) lies on these lines: {2, 4690}, {69, 17371}, {75, 141}, {239, 21358}, {319, 3619}, {320, 21356}, {524, 29613}, {599, 3758}, {1654, 17341}, {3620, 4644}, {3631, 17368}, {3644, 17229}, {3679, 27191}, {3759, 3763}, {3834, 29593}, {3912, 17250}, {4098, 4357}, {4364, 29577}, {4389, 29594}, {4407, 29674}, {4445, 17291}, {4473, 4643}, {4657, 17386}, {4664, 17230}, {4675, 29591}, {4687, 4708}, {4741, 17359}, {4751, 17232}, {4764, 17235}, {4798, 17300}, {4851, 17400}, {4869, 28653}, {5224, 17241}, {5232, 17263}, {5590, 32804}, {5591, 32803}, {6542, 17399}, {17233, 17249}, {17234, 24603}, {17251, 17266}, {17252, 17267}, {17253, 17268}, {17254, 17269}, {17256, 29579}, {17270, 17283}, {17271, 17284}, {17272, 17285}, {17273, 17286}, {17279, 17328}, {17280, 17329}, {17282, 32025}, {17288, 17293}, {17290, 29615}, {17294, 17305}, {17295, 17306}, {17296, 17307}, {17297, 17308}, {17309, 17324}, {17310, 17325}, {17311, 17326}, {17312, 17327}, {17313, 29610}, {17320, 29616}, {17322, 29624}, {17330, 29629}, {17343, 17357}, {17344, 17358}, {17346, 29596}, {17363, 34573}, {17367, 20582}, {17372, 17383}, {17373, 17384}, {17375, 17385}, {17378, 29604}, {17382, 20055}, {17392, 29608}, {18743, 32782}, {25358, 29622}, {25503, 29580}, {26738, 31017}, {30818, 31056}, {33151, 42034}, {41141, 41848}

X(48639) = barycentric product X(190)*X(48434)
X(48639) = barycentric quotient X(48434)/X(514)
X(48639) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {141, 3661, 17227}, {141, 17228, 75}, {319, 3619, 17370}, {599, 17292, 3758}, {3620, 17289, 17361}, {3661, 3662, 4665}, {3661, 17227, 75}, {3763, 17287, 3759}, {4643, 29587, 17342}, {4708, 17231, 29572}, {4708, 29572, 4687}, {17227, 17228, 3661}, {17229, 17236, 3644}, {17230, 17237, 4664}, {17231, 17238, 4687}, {17232, 17239, 4751}, {17238, 29572, 4708}, {17271, 17284, 17335}, {17272, 17285, 17336}, {17295, 17306, 17393}, {17296, 17307, 17394}, {17297, 17308, 41847}, {21356, 29611, 320}


X(48640) = X(2)X(4916)∩X(75)X(141)

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

X(48640) lies on these lines: {2, 4916}, {8, 17370}, {10, 17241}, {75, 141}, {193, 17289}, {319, 3618}, {320, 7229}, {1211, 20942}, {1213, 29577}, {1654, 17342}, {2321, 17249}, {2345, 17361}, {3619, 4402}, {3620, 7222}, {3644, 17237}, {3679, 17283}, {3758, 17287}, {3759, 4445}, {3763, 29615}, {3986, 5224}, {4007, 17305}, {4029, 17233}, {4058, 4398}, {4072, 4357}, {4371, 16706}, {4385, 7937}, {4478, 17367}, {4664, 17229}, {4687, 17230}, {4690, 17358}, {4751, 17231}, {4764, 17236}, {4851, 29591}, {5232, 17264}, {6329, 17363}, {6542, 17400}, {7321, 21356}, {16832, 32101}, {17117, 21358}, {17251, 17268}, {17252, 17269}, {17270, 17285}, {17271, 17286}, {17275, 17341}, {17280, 17328}, {17281, 17329}, {17284, 32025}, {17294, 17307}, {17295, 17308}, {17296, 41847}, {17299, 17399}, {17303, 17387}, {17309, 17326}, {17310, 17327}, {17311, 29610}, {17322, 29616}, {17343, 17359}, {17362, 29613}, {17368, 32455}, {17373, 17385}, {17377, 29604}, {17384, 20055}, {17390, 29608}, {25072, 41848}, {26361, 32804}, {26362, 32803}, {29617, 34573}, {32782, 42034}

X(48640) = barycentric product X(190)*X(48435)
X(48640) = barycentric quotient X(48435)/X(514)
X(48640) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {319, 29611, 17371}, {594, 17227, 75}, {3661, 17228, 75}, {4445, 17292, 3759}, {5224, 29594, 17240}, {17229, 17238, 4664}, {17230, 17239, 4687}, {17231, 29593, 4751}, {17270, 17285, 17335}, {17271, 17286, 17336}, {17275, 29587, 17341}, {17287, 17293, 3758}, {17294, 17307, 17393}, {17295, 17308, 17394}

leftri

3rd degree even minor triangle centers: X(48641)-X(48682)

rightri

Centers in this section are of the form h*(b^3 + c^3) + k* b c (b + c), where h and k are real numbers, not both 0. All such points lie on the line X(321)X(28871).

The appearance of {h,k},i in the following list means that h*(b^3 + c^3) + k* b c (b + c) = X(i).

{1,-1}, 3120
{1,0}, 2887}
{1,2}, 3773}
{1,3}, 6535}
{1, -4}, 48641
{1,-3}, 48642
{1, -2}, 48643
{1,4}, 48644
{2,-3}, 48645
{2,-1}, 48646
{2,1}, 48647
{2,3}, 48648
{3,-2}, 48649
{3,1}, 48650
{3,2}, 48651
{3,4}, 48622


X(48641) = X(262)X(4133)∩X(321)X(2887)

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

X(48641) lies on these lines: {226, 4133}, {321, 2887}, {536, 25385}, {726, 21242}, {740, 4054}, {1150, 17767}, {1215, 3755}, {1278, 17717}, {2321, 4892}, {3644, 29657}, {3696, 21093}, {3756, 24165}, {3775, 33151}, {3836, 4671}, {3846, 28605}, {3925, 4135}, {3936, 4527}, {3944, 42029}, {4052, 4104}, {4085, 4442}, {4398, 29827}, {4414, 28542}, {4415, 4733}, {4439, 33108}, {4457, 21060}, {4656, 27798}, {4726, 5087}, {4743, 46897}, {4871, 7263}, {5718, 28522}, {17764, 26227}, {17769, 33104}, {17772, 24725}, {17889, 42034}, {22034, 29653}, {25354, 31993}, {25496, 30699}, {28516, 29639}

X(48641) = barycentric product X(3952)*X(48413)
X(48641) = barycentric quotient X(48413)/X(7192)
X(48641) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {321, 3120, 3773}, {3120, 3773, 2887}


X(48642) = X(42)X(4054)∩X(75)X(25960)

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

X(48642) lies on these lines: {42, 4054}, {75, 25960}, {192, 29682}, {226, 4062}, {312, 25961}, {321, 2887}, {536, 33105}, {726, 29690}, {756, 21027}, {1215, 4442}, {1278, 29849}, {1647, 24165}, {3663, 31241}, {3685, 29689}, {3706, 32856}, {3729, 24892}, {3838, 32848}, {3846, 4980}, {3925, 3994}, {3944, 28605}, {3969, 4892}, {4080, 17163}, {4362, 20064}, {4415, 21020}, {4418, 29683}, {4425, 31025}, {4651, 21093}, {4671, 17889}, {4686, 17605}, {5695, 33127}, {6057, 21026}, {6536, 31993}, {8013, 26580}, {10129, 32855}, {11679, 33098}, {17017, 30699}, {17064, 33161}, {17116, 29845}, {17147, 25385}, {17281, 31237}, {17355, 29867}, {19785, 29684}, {19796, 32944}, {20653, 42031}, {23681, 29677}, {25760, 42029}, {25957, 42034}, {29685, 33134}, {29686, 33143}, {30957, 48627}, {33111, 42044}, {33132, 41242}, {33145, 44417}

X(48642) = barycentric product X(i)*X(j) for these {i,j}: {10, 7263}, {3952, 48414}
X(48642) = barycentric quotient X(i)/X(j) for these {i,j}: {7263, 86}, {48414, 7192}
X(48642) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {226, 4365, 4062}, {321, 2887, 6535}, {321, 3120, 15523}, {2887, 6535, 15523}, {3120, 6535, 2887}, {4418, 37759, 29683}, {4671, 17889, 29687}, {17147, 25385, 29688}


X(48643) = X(2)X(17593)∩X(8)X(33101)

Barycentrics    b^3 + c^3 - 2*b*c*(b + c) : :
X(48643) = 3 X[226] - X[4028], 3 X[2886] - X[4884], X[17156] + 3 X[31164]

X(48643) lies on these lines: {2, 17593}, {8, 33101}, {10, 3967}, {11, 24165}, {38, 21242}, {42, 4442}, {55, 17764}, {63, 17767}, {75, 3846}, {149, 32923}, {171, 37759}, {190, 33138}, {192, 33111}, {210, 21093}, {226, 740}, {239, 33096}, {306, 4527}, {312, 3836}, {321, 2887}, {333, 33099}, {519, 39542}, {536, 3838}, {537, 4847}, {596, 24387}, {726, 2886}, {752, 1836}, {894, 33135}, {1086, 3840}, {1150, 33098}, {1215, 3914}, {1266, 24239}, {1278, 32855}, {1463, 35626}, {1999, 33097}, {2321, 4138}, {2796, 4640}, {2901, 11263}, {3159, 3841}, {3175, 29653}, {3187, 24725}, {3210, 17717}, {3434, 17765}, {3454, 42031}, {3663, 6682}, {3666, 25385}, {3685, 33130}, {3703, 21241}, {3706, 33064}, {3729, 4438}, {3741, 3782}, {3757, 33095}, {3771, 5695}, {3772, 3923}, {3775, 27184}, {3791, 41011}, {3816, 7263}, {3821, 44417}, {3825, 24176}, {3842, 4656}, {3891, 33104}, {3925, 3971}, {3932, 4135}, {3936, 4365}, {3980, 17720}, {3993, 17056}, {4011, 24789}, {4035, 4133}, {4080, 4651}, {4104, 4732}, {4363, 29635}, {4387, 29642}, {4398, 17591}, {4407, 31330}, {4418, 33133}, {4425, 31993}, {4439, 29641}, {4441, 30953}, {4654, 39594}, {4655, 11679}, {4671, 25957}, {4672, 40940}, {4693, 29839}, {4703, 5271}, {4710, 27792}, {4854, 43223}, {4865, 17769}, {4871, 40688}, {4920, 20888}, {4941, 17063}, {4956, 29817}, {4970, 5718}, {4999, 8720}, {5057, 32914}, {5263, 33152}, {5268, 24693}, {5745, 28526}, {5880, 29649}, {5905, 17771}, {6147, 35633}, {6541, 22034}, {6690, 28530}, {7081, 24715}, {7283, 24161}, {10129, 29849}, {10453, 33103}, {11019, 42053}, {11235, 29844}, {11680, 17155}, {11814, 16602}, {13405, 28580}, {14829, 32857}, {16592, 21345}, {16606, 39786}, {16825, 24703}, {16888, 21927}, {17070, 44416}, {17123, 17777}, {17135, 32856}, {17147, 33105}, {17156, 31164}, {17164, 21935}, {17165, 33136}, {17301, 29650}, {17483, 32919}, {17484, 32864}, {17605, 42051}, {17719, 32932}, {17763, 20292}, {17772, 32946}, {19785, 25496}, {19796, 29821}, {19962, 24250}, {21020, 26580}, {21080, 21926}, {21101, 21956}, {21324, 21833}, {23812, 37595}, {24169, 30818}, {24210, 24325}, {24248, 32916}, {24349, 33141}, {24552, 33143}, {24892, 32933}, {25006, 42054}, {25422, 25502}, {25760, 28605}, {26015, 42055}, {26098, 30699}, {26223, 33128}, {26227, 33094}, {27064, 33132}, {29643, 42044}, {29674, 42034}, {29843, 31178}, {29850, 41242}, {29862, 42033}, {30942, 33146}, {31019, 32915}, {31053, 32860}, {32771, 33134}, {32772, 33155}, {32778, 42029}, {32865, 32937}, {32917, 33100}, {32918, 33102}, {32922, 33106}, {32924, 33107}, {32925, 33108}, {32926, 33109}, {32927, 33110}, {32928, 33112}, {32929, 33127}, {32930, 33129}, {32931, 33131}, {32935, 33137}, {32938, 33139}, {32939, 33140}, {32940, 33142}, {32941, 33144}, {32942, 33147}, {32943, 33148}, {32944, 33150}, {32945, 33153}

X(48643) = midpoint of X(i) and X(j) for these {i,j}: {1836, 4362}, {3434, 32920}, {5905, 32853}
X(48643) = reflection of X(29671) in X(3838)
X(48643) = complement of X(32934)
X(48643) = isotomic conjugate of the isogonal conjugate of X(22172)
X(48643) = X(48627)-Ceva conjugate of X(21951)
X(48643) = X(163)-isoconjugate of X(25576)
X(48643) = X(115)-Dao conjugate of X(25576)
X(48643) = barycentric product X(i)*X(j) for these {i,j}: {10, 48627}, {75, 21951}, {76, 22172}, {321, 17063}, {850, 25577}, {1441, 4051}, {1577, 4499}, {3952, 48415}, {4033, 23765}, {23524, 27801}
X(48643) = barycentric quotient X(i)/X(j) for these {i,j}: {523, 25576}, {4051, 21}, {4499, 662}, {4941, 27644}, {17063, 81}, {21951, 1}, {22172, 6}, {23524, 1333}, {23765, 1019}, {25577, 110}, {48415, 7192}, {48627, 86}
X(48643) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 3944, 3846}, {312, 17889, 3836}, {321, 2887, 3773}, {321, 3120, 2887}, {1215, 3914, 4085}, {3729, 17064, 4438}, {3772, 3923, 6679}, {3914, 4054, 1215}, {3967, 21949, 10}, {4011, 24789, 31289}, {26098, 30699, 32921}


X(48644) = X(10)X(3175)∩X(42)X(4527)

Barycentrics    b^3 + c^3 + 4*b*c*(b + c) : :

X(48644) lies on these lines: {10, 3175}, {42, 4527}, {306, 4535}, {321, 2887}, {594, 3971}, {1089, 30713}, {1211, 4135}, {1215, 2321}, {1278, 33174}, {3159, 6538}, {3626, 4126}, {3703, 21242}, {3741, 4884}, {3775, 32925}, {3791, 17355}, {3836, 28605}, {3846, 4671}, {3943, 43223}, {3950, 10180}, {3967, 21085}, {4046, 4090}, {4058, 4104}, {4078, 27798}, {4085, 4365}, {4362, 17281}, {4425, 22034}, {4439, 31330}, {4445, 4942}, {4519, 29655}, {4669, 13996}, {4686, 24169}, {4980, 29687}, {6541, 31993}, {17229, 33064}, {17230, 33103}, {17269, 29642}, {17285, 33147}, {17286, 26128}, {17359, 29654}, {17764, 33074}, {17767, 33080}, {17769, 24552}, {17772, 26223}, {28542, 32950}, {29674, 42029}, {32778, 42034}

X(48644) = barycentric product X(i)*X(j) for these {i,j}: {10, 48628}, {3701, 7201}, {3952, 4500}, {4033, 4490}, {4502, 27808}
X(48644) = barycentric quotient X(i)/X(j) for these {i,j}: {4490, 1019}, {4500, 7192}, {4502, 3733}, {7201, 1014}, {48628, 86}
X(48644) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {321, 3773, 2887}, {321, 6535, 3773}


X(48645) = X(210)X(4080)∩X(226)X(3896)

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

X(48645) lies on these lines: {210, 4080}, {226, 3896}, {321, 2887}, {1836, 20064}, {1962, 30588}, {3210, 10129}, {3782, 46909}, {3838, 17147}, {3914, 46897}, {3944, 4359}, {3952, 21949}, {3969, 4138}, {4054, 4972}, {4135, 21026}, {4358, 17889}, {4365, 4892}, {4398, 29680}, {4640, 44006}, {4980, 25760}, {4981, 33151}, {17025, 19830}, {17064, 32933}, {17495, 17605}, {17777, 26724}, {19796, 33107}, {20292, 37759}, {25385, 33145}, {25958, 42029}, {25959, 42034}, {30699, 33070}, {33132, 41241}

X(48645) = barycentric product X(i)*X(j) for these {i,j}: {313, 9336}, {321, 9335}, {3952, 48420}
X(48645) = barycentric quotient X(i)/X(j) for these {i,j}: {9335, 81}, {9336, 58}, {48420, 7192}
X(48645) = {X(226),X(4442)}-harmonic conjugate of X(3896)


X(48646) = X(2)X(1155)∩X(38)X(21241)

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

X(48646) lies on these lines: {2, 1155}, {38, 21241}, {42, 4892}, {75, 25958}, {149, 33124}, {190, 29873}, {226, 4972}, {306, 4442}, {312, 25959}, {320, 33142}, {321, 2887}, {997, 17679}, {1150, 17064}, {1707, 31229}, {1738, 5741}, {2886, 17184}, {3006, 3782}, {3011, 4450}, {3434, 26132}, {3452, 24988}, {3662, 11680}, {3696, 31037}, {3705, 33146}, {3706, 31017}, {3744, 21282}, {3758, 29868}, {3771, 33094}, {3772, 6327}, {3821, 33105}, {3846, 24589}, {3896, 3914}, {3923, 31237}, {3925, 26580}, {3944, 4358}, {3967, 4080}, {3971, 21026}, {4202, 12047}, {4359, 17889}, {4362, 31134}, {4388, 33129}, {4389, 29664}, {4417, 33131}, {4429, 31053}, {4432, 29869}, {4438, 33098}, {4463, 40961}, {4511, 17678}, {4514, 33148}, {4641, 17491}, {4645, 33133}, {4651, 21949}, {4655, 24892}, {4660, 33127}, {4672, 29867}, {4683, 33138}, {4697, 29863}, {4722, 31177}, {4797, 24724}, {4865, 33143}, {4920, 21432}, {4980, 32778}, {4981, 27184}, {5014, 33144}, {5025, 26562}, {5051, 12609}, {5905, 33114}, {9342, 30867}, {9955, 26094}, {16706, 33107}, {16727, 16891}, {17211, 20880}, {17483, 33121}, {17484, 33118}, {17594, 30834}, {17673, 26689}, {17674, 21616}, {17676, 28628}, {17717, 33125}, {17719, 32948}, {17869, 34825}, {18134, 33134}, {18139, 24210}, {19785, 33070}, {19786, 33112}, {19796, 32842}, {24248, 33113}, {24552, 25527}, {24593, 29662}, {24690, 25383}, {24696, 29978}, {24715, 29846}, {24725, 25453}, {25378, 25502}, {25385, 32781}, {26098, 32774}, {26128, 33104}, {27002, 31272}, {29631, 33097}, {29632, 33095}, {29641, 33151}, {29643, 33154}, {29671, 33145}, {29673, 32856}, {29849, 33149}, {29850, 33096}, {29857, 32933}, {29861, 32940}, {29862, 32936}, {29872, 32939}, {30588, 43223}, {30811, 32929}, {30831, 32932}, {31019, 32773}, {32775, 33109}, {32776, 33111}, {32843, 33132}, {32844, 33147}, {32850, 33153}, {32851, 33102}, {32857, 33119}, {32859, 33137}, {32865, 33065}, {32946, 33128}, {32947, 33130}, {32949, 33135}, {33064, 33136}, {33066, 33139}, {33067, 33140}, {33069, 33141}, {33071, 33150}, {33072, 33152}, {33073, 33155}, {33078, 37759}, {33099, 33115}, {33100, 33116}, {33101, 33117}, {33103, 33120}, {33106, 33123}, {33110, 33126}

X(48646) = barycentric product X(i)*X(j) for these {i,j}: {10, 48629}, {3261, 7287}, {3952, 48421}
X(48646) = barycentric quotient X(i)/X(j) for these {i,j}: {7287, 101}, {48421, 7192}, {48629, 86}
X(48646) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {226, 4972, 46897}, {2886, 17184, 46909}, {2887, 3120, 321}, {3434, 26132, 33122}, {3914, 3936, 3896}, {3914, 4138, 3936}, {3944, 25957, 4358}, {17889, 25760, 4359}, {27184, 33108, 4981}, {29850, 33096, 41241}


X(48647) = X(2)X(1386)∩X(8)X(33122)

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

X(48647) lies on these lines: {2, 1386}, {8, 33122}, {10, 2650}, {42, 28595}, {69, 33114}, {75, 25959}, {141, 3006}, {210, 31037}, {306, 3755}, {312, 25958}, {313, 35532}, {319, 33139}, {320, 33170}, {321, 2887}, {333, 29873}, {345, 32950}, {518, 31017}, {984, 27476}, {1150, 29857}, {2321, 4442}, {2895, 33118}, {3454, 3701}, {3617, 28629}, {3661, 33108}, {3662, 33089}, {3703, 17184}, {3705, 33172}, {3744, 28599}, {3771, 33074}, {3790, 33151}, {3791, 29867}, {3821, 32848}, {3836, 24589}, {3840, 36951}, {3846, 29687}, {3883, 24542}, {3891, 25527}, {3914, 3969}, {3923, 31134}, {3925, 4733}, {3932, 26580}, {4062, 4085}, {4358, 25760}, {4359, 25957}, {4362, 31237}, {4388, 33157}, {4392, 4735}, {4417, 29679}, {4429, 33077}, {4438, 33080}, {4514, 33173}, {4641, 20290}, {4645, 32779}, {4646, 27558}, {4655, 33161}, {4660, 33156}, {4683, 33164}, {4851, 29829}, {4865, 24943}, {4966, 29835}, {4980, 17889}, {4981, 29641}, {5014, 33171}, {5057, 17280}, {5249, 39597}, {5297, 30832}, {5718, 26251}, {5846, 26230}, {5847, 30768}, {6327, 32777}, {7081, 30831}, {7292, 17283}, {14829, 29872}, {16706, 32842}, {17025, 17370}, {17162, 17372}, {17163, 21949}, {17231, 29824}, {17233, 33134}, {17289, 33112}, {17351, 17491}, {17726, 34573}, {18134, 29667}, {19786, 33093}, {19875, 31179}, {20336, 21249}, {21747, 28498}, {24723, 32849}, {25354, 29653}, {25453, 32852}, {26034, 33113}, {26061, 32946}, {26128, 32854}, {26227, 30811}, {27184, 32862}, {29631, 32846}, {29632, 33076}, {29637, 32844}, {29643, 32784}, {29671, 32781}, {29673, 33081}, {29828, 30834}, {29846, 33079}, {29849, 33174}, {29850, 32861}, {29861, 32919}, {29862, 32917}, {30632, 35543}, {31034, 38047}, {32773, 32858}, {32774, 33088}, {32775, 32847}, {32776, 33092}, {32780, 32949}, {32783, 33072}, {32843, 33159}, {32850, 33175}, {32851, 33086}, {32855, 33125}, {32859, 33163}, {32863, 33121}, {32866, 33123}, {32947, 33158}, {32948, 33160}, {33064, 33162}, {33065, 33165}, {33066, 33166}, {33067, 33167}, {33068, 33168}, {33069, 33169}, {33082, 33115}, {33083, 33116}, {33084, 33117}, {33085, 33119}, {33087, 33120}, {33090, 33124}, {33091, 33126}, {33100, 42033}

X(48647) = midpoint of X(31017) and X(31079)
X(48647) = isotomic conjugate of the isogonal conjugate of X(4735)
X(48647) = barycentric product X(i)*X(j) for these {i,j}: {10, 17227}, {76, 4735}, {321, 4392}, {3952, 48422}
X(48647) = barycentric quotient X(i)/X(j) for these {i,j}: {4392, 81}, {4735, 6}, {17227, 86}, {48422, 7192}
X(48647) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 3936, 46897}, {141, 3006, 46909}, {306, 4972, 3896}, {2887, 3773, 3120}, {2887, 15523, 321}, {3120, 3773, 321}, {3120, 15523, 3773}, {25760, 29674, 4358}, {25957, 32778, 4359}, {29641, 32782, 4981}, {32843, 33159, 41241}


X(48648) = X(8)X(13742)∩X(10)X(1962)

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

X(48648) lies on these lines: {8, 13742}, {10, 1962}, {306, 46897}, {319, 33166}, {321, 2887}, {2321, 4972}, {3416, 20064}, {3661, 4981}, {3701, 40603}, {3703, 46909}, {3706, 31079}, {3790, 32782}, {3844, 17147}, {3873, 17230}, {3967, 31037}, {4078, 41809}, {4358, 25960}, {4359, 25961}, {4365, 4535}, {4980, 25957}, {5284, 17268}, {6057, 26580}, {6327, 17281}, {7191, 17285}, {7226, 17228}, {15481, 43990}, {17135, 17229}, {17140, 17231}, {17233, 29667}, {17240, 29814}, {17280, 33075}, {17286, 24552}, {17289, 33093}, {17351, 20290}, {17769, 29686}, {19877, 28651}, {20017, 38047}, {24589, 29687}, {25958, 42034}, {25959, 42029}, {32861, 41241}, {33083, 42033}

X(48648) = barycentric product X(i)*X(j) for these {i,j}: {10, 17228}, {321, 7226}, {3952, 47677}, {4033, 48066}
X(48648) = barycentric quotient X(i)/X(j) for these {i,j}: {7226, 81}, {17228, 86}, {47677, 7192}, {48066, 1019}
X(48648) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 3969, 3896}, {2887, 3773, 6535}, {2887, 6535, 321}, {3661, 32862, 4981}, {3773, 15523, 321}, {4535, 28595, 4365}, {6535, 15523, 2887}


X(48649) = X(226)X(4085)∩X(321)X(2887)

Barycentrics    -2*b*c*(b + c) + 3*(b^3 + c^3) : :
X(48649) = X[4035] - 3 X[4138]

X(48649) lies on these lines: {226, 4085}, {321, 2887}, {345, 28542}, {550, 1125}, {740, 4035}, {752, 3772}, {1836, 6679}, {3452, 25351}, {3771, 17764}, {3782, 21241}, {3821, 3838}, {3829, 48631}, {3836, 3944}, {3846, 17889}, {3914, 4743}, {4054, 28595}, {4407, 27184}, {4438, 17767}, {4655, 17064}, {4920, 20893}, {10129, 33125}, {17184, 21242}, {17211, 20894}, {17605, 24169}, {17765, 33144}, {17771, 33137}, {24692, 37646}, {24703, 31289}, {26132, 32941}


X(48650) = X(10)X(31037)∩X(42)X(4035)

Barycentrics    b*c*(b + c) + 3*(b^3 + c^3) : :

X(48650) lies on these lines: {10, 31037}, {42, 4035}, {141, 29690}, {306, 4780}, {321, 2887}, {902, 20106}, {1211, 21026}, {2308, 30768}, {3416, 31237}, {3454, 3992}, {3844, 33105}, {3883, 29869}, {3925, 8013}, {3936, 28595}, {4062, 4972}, {4642, 21712}, {4714, 20653}, {4865, 29686}, {5847, 29867}, {6536, 29653}, {18134, 29685}, {18743, 25760}, {19804, 25957}, {21249, 42713}, {21701, 21944}, {25527, 32854}, {25958, 29674}, {25959, 32778}, {28599, 29656}, {29673, 31017}, {29682, 32784}, {29683, 33078}, {29684, 33070}, {29688, 32781}, {29689, 33076}, {29857, 33080}, {29861, 32863}, {29862, 33083}, {29872, 33085}, {29873, 33082}, {30811, 33074}, {30831, 33079}, {31079, 33064}, {31134, 32777}, {42038, 48632}

X(48650) = barycentric product X(i)*X(j) for these {i,j}: {10, 48632}, {321, 42038}, {3952, 48425}
X(48650) = barycentric quotient X(i)/X(j) for these {i,j}: {42038, 81}, {48425, 7192}, {48632, 86}
X(48650) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2887, 15523, 3120}, {3120, 15523, 6535}


X(48651) = X(10)X(4035)∩X(306)X(4085)

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

X(48651) lies on these lines: {10, 4035}, {306, 4085}, {321, 2887}, {752, 32777}, {3416, 6679}, {3454, 4125}, {3775, 29641}, {3791, 30768}, {3836, 19804}, {3844, 29671}, {3846, 18743}, {3914, 4527}, {3966, 31289}, {4407, 32782}, {4439, 27184}, {4743, 4972}, {4914, 29672}, {17230, 33141}, {17231, 29655}, {17285, 33106}, {17765, 33171}, {17769, 26128}, {17771, 33163}, {17772, 25453}, {21255, 42053}, {24325, 39597}, {31017, 33162}, {31079, 33081}

X(48651) = barycentric product X(i)*X(j) for these {i,j}: {10, 48633}, {3952, 48426}
X(48651) = barycentric quotient X(i)/X(j) for these {i,j}: {48426, 7192}, {48633, 86}
X(48651) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {306, 28595, 4085}, {2887, 15523, 3773}


X(48652) = X(10)X(4046)∩X(321)X(2887)

Barycentrics    4*b*c*(b + c) + 3*(b^3 + c^3) : :

X(48652) lies on these lines: {10, 4046}, {321, 2887}, {1215, 4035}, {2321, 28595}, {3775, 32862}, {3914, 4535}, {3969, 4085}, {4439, 32782}, {4527, 4972}, {4865, 17286}, {17229, 29673}, {17230, 33169}, {17285, 32866}, {17598, 29587}, {17769, 24943}, {17772, 26061}, {18743, 32778}, {19804, 29674}

X(48652) = barycentric product X(i)*X(j) for these {i,j}: {10, 48634}, {3952, 48427}
X(48652) = barycentric quotient X(i)/X(j) for these {i,j}: {48427, 7192}, {48634, 86}
X(48652) = {X(3773),X(15523)}-harmonic conjugate of X(2887)


X(48653) = X(6)X(512)∩X(115)X(524)

Barycentrics    a^2*(2*a^8*b^2 - 3*a^6*b^4 + 5*a^2*b^8 + 2*a^8*c^2 - 10*a^6*b^2*c^2 + 12*a^4*b^4*c^2 - 19*a^2*b^6*c^2 - b^8*c^2 - 3*a^6*c^4 + 12*a^4*b^2*c^4 + 12*a^2*b^4*c^4 + 3*b^6*c^4 - 19*a^2*b^2*c^6 + 3*b^4*c^6 + 5*a^2*c^8 - b^2*c^8) : :

X(48653) lies on the cubic K1275 and these lines: {6, 512}, {110, 41936}, {115, 524}, {187, 1084}, {511, 3124}, {691, 36696}, {2030, 9427}, {5104, 14990}, {9181, 32740}, {10630, 10765}, {10754, 14607}, {15899, 39024}, {16188, 47571}, {35606, 45329}, {46124, 47587}, {47242, 47574}

X(48653) = midpoint of X(10754) and X(14607)
X(48653) = crossdifference of every pair of points on line {524, 5652}
X(48653) = X(115)-lineconjugate of X(524)


X(48654) = X(6)X(690)∩X(187)X(524)

Barycentrics    (2*a^2 - b^2 - c^2)*(2*a^10 - 4*a^8*b^2 - 3*a^6*b^4 + 2*a^4*b^6 - a^2*b^8 - 4*a^8*c^2 + 18*a^6*b^2*c^2 - 6*a^4*b^4*c^2 + 11*a^2*b^6*c^2 - 3*b^8*c^2 - 3*a^6*c^4 - 6*a^4*b^2*c^4 - 18*a^2*b^4*c^4 + 3*b^6*c^4 + 2*a^4*c^6 + 11*a^2*b^2*c^6 + 3*b^4*c^6 - a^2*c^8 - 3*b^2*c^8) : :
X(48654) = 3 X[5182] - X[5468], X[14444] + 2 X[41672]

X(48654) lies on the cubic K1275 and these lines: {6, 690}, {99, 10765}, {114, 24855}, {115, 28662}, {187, 524}, {542, 1648}, {2793, 35606}, {5182, 5468}, {5967, 9125}, {8593, 35356}, {11179, 47082}, {14444, 41672}

X(48654) = crosssum of X(6) and X(15566)
X(48654) = crossdifference of every pair of points on line {2854, 5653}
X(48654) = barycentric product X(524)*X(5912)
X(48654) = barycentric quotient X(5912)/X(671)

leftri

Centers related to anti-Ehrmann-mid triangle: X(48655)-X(48720)

rightri

This preamble and centers X(48655)-X(48720) were contributed by César Eliud Lozada, May 13, 2022.

Anti-Ehrmann-mid triangle is introduced in the preamble just before X(45345)..


X(48655) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO 1st ALTINTAS-ISODYNAMIC

Barycentrics    2*(a^4+(b^2+c^2)*a^2-2*(b^2-c^2)^2)*S+(3*a^6-2*(b^2+c^2)*a^4+(b^2+c^2)^2*a^2-2*(b^4-c^4)*(b^2-c^2))*sqrt(3) : :
X(48655) = 3*X(3)-4*X(618) = 2*X(13)-3*X(381) = 7*X(13)-6*X(32907) = X(13)-3*X(41042) = 3*X(381)-4*X(22796) = 7*X(381)-4*X(32907) = 2*X(618)-3*X(5617) = 5*X(1656)-4*X(6771) = 5*X(1656)-6*X(36765) = 5*X(1656)-2*X(41020) = 5*X(3091)-4*X(20252) = 7*X(3526)-6*X(21156) = X(3830)+2*X(36363) = 5*X(3843)-4*X(5478) = 2*X(6771)-3*X(36765) = 2*X(11121)-3*X(16628) = 7*X(22796)-3*X(32907) = 2*X(22796)-3*X(41042) = 2*X(32907)-7*X(41042) = 3*X(36765)-X(41020)

The reciprocal orthologic center of these triangles is X(4).

X(48655) lies on these lines: {2, 47610}, {3, 618}, {4, 3181}, {5, 6770}, {6, 13}, {30, 298}, {147, 1080}, {376, 34540}, {382, 5864}, {395, 37332}, {530, 3830}, {531, 6298}, {617, 30471}, {623, 24303}, {999, 12952}, {1656, 6771}, {1657, 5473}, {2782, 13102}, {3091, 20252}, {3104, 36970}, {3129, 11092}, {3295, 12942}, {3526, 21156}, {3534, 5463}, {3543, 40900}, {3564, 20425}, {3843, 5478}, {3845, 36344}, {3851, 35019}, {5054, 36770}, {5055, 6669}, {5066, 36318}, {5072, 20415}, {5339, 46855}, {5459, 19709}, {5479, 38732}, {5613, 38743}, {5663, 16259}, {5965, 41024}, {5978, 5989}, {5979, 7788}, {5980, 14458}, {5981, 6054}, {6115, 11485}, {6302, 22872}, {6306, 22874}, {6321, 41060}, {6582, 9761}, {6782, 11486}, {7837, 46708}, {7975, 18526}, {9654, 10062}, {9655, 18974}, {9668, 13076}, {9669, 10078}, {9749, 9756}, {9862, 11300}, {9901, 18480}, {9982, 18503}, {10654, 37333}, {11295, 14904}, {11302, 12042}, {11305, 14880}, {11480, 36766}, {11705, 18493}, {12101, 35749}, {12142, 18494}, {12205, 18501}, {12337, 18524}, {12383, 46470}, {12472, 45379}, {12473, 45380}, {12702, 12781}, {12793, 18508}, {12922, 18519}, {12932, 18518}, {12990, 45381}, {12991, 45382}, {13105, 18545}, {13107, 18543}, {13917, 45384}, {13982, 45385}, {14269, 25154}, {14651, 20253}, {15685, 36769}, {15695, 36768}, {16530, 22238}, {18358, 37351}, {18496, 48456}, {18498, 48457}, {18581, 22847}, {18586, 33353}, {18587, 33350}, {19106, 25235}, {19924, 22493}, {20428, 22507}, {22511, 42153}, {22598, 48659}, {22627, 48660}, {22684, 41038}, {22773, 26321}, {22868, 48673}, {22870, 34508}, {22894, 36967}, {22998, 42155}, {23005, 42093}, {23006, 42127}, {23251, 35753}, {23261, 35754}, {33699, 35750}, {36771, 42817}, {36782, 36836}, {37170, 39874}, {39884, 41017}, {42094, 47859}, {42095, 46054}

X(48655) = reflection of X(i) in X(j) for these (i, j): (3, 5617), (13, 22796), (381, 41042), (382, 36961), (1657, 5473), (3534, 5463), (5611, 1080), (6321, 41060), (6770, 5), (6778, 22797), (9862, 47611), (9901, 18480), (12188, 14), (12702, 12781), (13103, 4), (18508, 12793), (18526, 7975), (20425, 41016), (36383, 5459), (41020, 6771), (48656, 6033)
X(48655) = anticomplement of X(47610)
X(48655) = inverse of X(22797) in orthocentroidal circle
X(48655) = orthologic center (anti-Ehrmann-mid, T) for these triangles T: {1st Altintas-isodynamic, Bankoff, 3rd Fermat-Dao, 7th Fermat-Dao, 11th Fermat-Dao, 15th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi, 1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi, 1st half-diamonds-central, 1st isodynamic-Dao, 3rd isodynamic-Dao, Largest-circumscribed-equilateral, 1st Lemoine-Dao, outer-Napoleon}
X(48655) = X(13)-of-anti-Ehrmann-mid triangle
X(48655) = X(5617)-of-X3-ABC reflections triangle
X(48655) = X(6770)-of-Johnson triangle
X(48655) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (13, 22796, 381), (13, 41042, 22796), (14, 3818, 381), (381, 18440, 48656), (381, 39899, 42974), (6771, 36765, 1656), (6782, 22513, 11486), (16809, 22797, 381), (31862, 31863, 22797), (36765, 41020, 6771)


X(48656) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO 2nd ALTINTAS-ISODYNAMIC

Barycentrics    -2*(a^4+(b^2+c^2)*a^2-2*(b^2-c^2)^2)*S+(3*a^6-2*(b^2+c^2)*a^4+(b^2+c^2)^2*a^2-2*(b^4-c^4)*(b^2-c^2))*sqrt(3) : :
X(48656) = 3*X(3)-4*X(619) = 2*X(14)-3*X(381) = 7*X(14)-6*X(32909) = X(14)-3*X(41043) = 3*X(381)-4*X(22797) = 7*X(381)-4*X(32909) = 2*X(619)-3*X(5613) = 5*X(1656)-4*X(6774) = 5*X(1656)-2*X(41021) = 5*X(3091)-4*X(20253) = 7*X(3526)-6*X(21157) = X(3830)+2*X(36362) = 5*X(3843)-4*X(5479) = 2*X(3845)+X(36319) = 9*X(5055)-8*X(6670) = 4*X(5066)-X(36320) = 2*X(11122)-3*X(16629) = 7*X(22797)-3*X(32909) = 2*X(22797)-3*X(41043) = 2*X(32909)-7*X(41043)

The reciprocal orthologic center of these triangles is X(4).

X(48656) lies on these lines: {2, 47611}, {3, 619}, {4, 3180}, {5, 6773}, {6, 13}, {30, 299}, {147, 383}, {376, 34541}, {382, 5865}, {396, 37333}, {530, 6299}, {531, 3830}, {616, 30472}, {624, 24304}, {999, 12951}, {1656, 6774}, {1657, 5474}, {2782, 13103}, {3091, 20253}, {3105, 36969}, {3130, 11078}, {3295, 12941}, {3526, 21157}, {3534, 5464}, {3543, 40901}, {3564, 20426}, {3843, 5479}, {3845, 36319}, {3851, 35020}, {5055, 6670}, {5066, 36320}, {5072, 20416}, {5340, 46854}, {5460, 19709}, {5478, 38732}, {5617, 38743}, {5663, 16260}, {5965, 41025}, {5978, 7788}, {5979, 5989}, {5980, 6054}, {5981, 14458}, {6114, 11486}, {6295, 9763}, {6303, 22917}, {6307, 22919}, {6321, 41061}, {6783, 11485}, {7837, 46709}, {7974, 18526}, {9654, 10061}, {9655, 18975}, {9668, 13075}, {9669, 10077}, {9750, 9756}, {9862, 11299}, {9900, 18480}, {9981, 18503}, {10653, 37332}, {11296, 14905}, {11301, 12042}, {11306, 14880}, {11706, 18493}, {12101, 36327}, {12141, 18494}, {12204, 18501}, {12336, 18524}, {12383, 46471}, {12470, 45379}, {12471, 45380}, {12702, 12780}, {12792, 18508}, {12921, 18519}, {12931, 18518}, {12988, 45381}, {12989, 45382}, {13104, 18545}, {13106, 18543}, {13188, 36776}, {13916, 45384}, {13981, 45385}, {14269, 25164}, {14651, 20252}, {15685, 47867}, {16529, 22236}, {18358, 37352}, {18496, 48458}, {18498, 48459}, {18582, 22893}, {18586, 33352}, {18587, 33351}, {19107, 25236}, {19924, 22494}, {20429, 22509}, {22510, 42156}, {22600, 48659}, {22629, 48660}, {22686, 41039}, {22774, 26321}, {22850, 36968}, {22913, 48673}, {22915, 34509}, {22997, 42154}, {23004, 42094}, {23013, 42126}, {23251, 35850}, {23261, 35851}, {25560, 36765}, {33699, 36331}, {37171, 39874}, {37785, 44289}, {39884, 41016}, {42093, 47860}, {42098, 46053}, {42913, 44219}

X(48656) = reflection of X(i) in X(j) for these (i, j): (3, 5613), (14, 22797), (381, 41043), (382, 36962), (1657, 5474), (3534, 5464), (5615, 383), (6321, 41061), (6773, 5), (6777, 22796), (9862, 47610), (9900, 18480), (12188, 13), (12702, 12780), (13102, 4), (13188, 36776), (18508, 12792), (18526, 7974), (20426, 41017), (36382, 5460), (37785, 44289), (41021, 6774), (48655, 6033)
X(48656) = anticomplement of X(47611)
X(48656) = inverse of X(22796) in orthocentroidal circle
X(48656) = orthologic center (anti-Ehrmann-mid, T) for these triangles T: {2nd Altintas-isodynamic, 4th Fermat-Dao, 8th Fermat-Dao, 12th Fermat-Dao, 16th Fermat-Dao, 1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi, 3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi, 2nd half-diamonds-central, 2nd isodynamic-Dao, 4th isodynamic-Dao, 2nd Lemoine-Dao, inner-Napoleon}
X(48656) = X(14)-of-anti-Ehrmann-mid triangle
X(48656) = X(5613)-of-X3-ABC reflections triangle
X(48656) = X(6773)-of-Johnson triangle
X(48656) = X(40706)-of-outer-Fermat triangle
X(48656) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (13, 3818, 381), (14, 22797, 381), (14, 41043, 22797), (381, 18440, 48655), (381, 39899, 42975), (6783, 22512, 11485), (16808, 22796, 381), (31862, 31863, 22796)


X(48657) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO ANTI-MCCAY

Barycentrics    a^8+6*(b^2+c^2)*a^6-(8*b^4+11*b^2*c^2+8*c^4)*a^4+(b^2+c^2)*(3*b^4+b^2*c^2+3*c^4)*a^2-2*(b^4-c^4)^2 : :
X(48657) = 3*X(3)-4*X(2482) = 7*X(3)-4*X(10991) = 3*X(3)-2*X(14830) = X(3)-4*X(14981) = 3*X(4)-X(8596) = 3*X(147)+X(8591) = 5*X(147)+X(13172) = 2*X(147)+X(13188) = 4*X(147)-X(38744) = 2*X(2482)-3*X(8724) = 7*X(2482)-3*X(10991) = X(2482)-3*X(14981) = 5*X(8591)-3*X(13172) = 2*X(8591)-3*X(13188) = 4*X(8591)+3*X(38744) = 2*X(8596)-3*X(12355) = 7*X(8724)-2*X(10991) = 3*X(8724)-X(14830) = 6*X(10991)-7*X(14830) = X(10991)-7*X(14981) = X(14830)-6*X(14981)

The reciprocal orthologic center of these triangles is X(9855).

X(48657) lies on the cubic K330 and these lines: {2, 7711}, {3, 67}, {4, 8596}, {5, 12243}, {30, 147}, {39, 25561}, {98, 5054}, {99, 3534}, {114, 5055}, {115, 18584}, {148, 3845}, {237, 44555}, {262, 381}, {382, 23235}, {399, 2421}, {524, 9301}, {530, 6299}, {531, 6298}, {543, 3830}, {547, 14651}, {549, 11177}, {620, 15701}, {999, 12351}, {1003, 34682}, {1656, 23234}, {1657, 12117}, {1992, 22143}, {2784, 3655}, {2794, 15681}, {2796, 12699}, {3295, 12350}, {3524, 5984}, {3564, 37461}, {3656, 21636}, {3843, 9880}, {4027, 33220}, {5024, 11646}, {5066, 41135}, {5070, 11623}, {5182, 33237}, {5459, 33423}, {5460, 33422}, {5477, 21309}, {5613, 33390}, {5617, 33391}, {5969, 6309}, {5987, 47596}, {5989, 7799}, {6034, 9605}, {6055, 15561}, {6311, 48660}, {6315, 48659}, {6321, 14269}, {6777, 41101}, {6778, 41100}, {7783, 9878}, {7813, 19924}, {7841, 11152}, {7870, 14880}, {8593, 11156}, {8703, 9862}, {8787, 11842}, {9140, 9155}, {9143, 45662}, {9167, 38739}, {9654, 10054}, {9655, 18969}, {9668, 12354}, {9669, 10070}, {9760, 33460}, {9762, 33461}, {9830, 9888}, {9855, 10811}, {9875, 18480}, {9881, 12702}, {9882, 26336}, {9883, 26346}, {9884, 18526}, {9885, 36363}, {9886, 36362}, {9892, 13710}, {9894, 13830}, {10620, 11006}, {10992, 17800}, {11171, 11178}, {11645, 35002}, {11656, 14643}, {12042, 15693}, {12132, 18494}, {12191, 18501}, {12258, 18493}, {12326, 18524}, {12345, 45379}, {12346, 45380}, {12347, 18508}, {12348, 18519}, {12349, 18518}, {12352, 45381}, {12353, 45382}, {12356, 18545}, {12357, 18543}, {13102, 41042}, {13103, 41043}, {13174, 28198}, {13846, 35824}, {13847, 35825}, {13908, 45384}, {13968, 45385}, {14093, 21166}, {14849, 45311}, {15300, 15685}, {15360, 37914}, {15682, 20094}, {15684, 23698}, {15688, 33813}, {15689, 38741}, {15695, 36521}, {15700, 34473}, {15703, 38224}, {15707, 38750}, {15718, 38634}, {15810, 43150}, {18496, 48470}, {18498, 48471}, {18510, 19057}, {18512, 19058}, {20399, 46219}, {22505, 38335}, {22565, 26321}, {22871, 48665}, {22916, 48666}, {23251, 35698}, {23261, 35699}, {31982, 34511}, {32552, 36383}, {32553, 36382}, {37956, 39828}, {38635, 38742}

X(48657) = midpoint of X(i) and X(j) for these {i, j}: {11632, 14692}, {15682, 20094}
X(48657) = reflection of X(i) in X(j) for these (i, j): (3, 8724), (148, 3845), (381, 6054), (671, 22566), (1657, 12117), (3534, 99), (3656, 21636), (3830, 6033), (8724, 14981), (9862, 8703), (9875, 18480), (9880, 38745), (10620, 11006), (11177, 549), (11632, 114), (11646, 25562), (12188, 2), (12243, 5), (12355, 4), (12702, 9881), (13102, 41042), (13103, 41043), (14830, 2482), (15685, 38730), (18508, 12347), (18526, 9884), (35002, 39785), (36382, 32553), (36383, 32552), (38730, 15300), (38732, 38743), (38733, 3830), (38749, 36521), (39899, 8593)
X(48657) = circumtangential-isogonal conjugate of the Gibert-circumtangential conjugate of X(9999)
X(48657) = inverse of X(2930) in Stammler circle
X(48657) = orthologic center (anti-Ehrmann-mid, T) for these triangles T: {anti-McCay, McCay, Moses-Steiner osculatory}
X(48657) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {99, 110, 47288}, {32526, 39157, 43460}
X(48657) = reflection of X(67) in the line X(690)X(18309)
X(48657) = X(671)-of-these triangles: {anti-Ehrmann-mid, 2nd Neuberg}
X(48657) = X(7775)-of-anti-McCay triangle
X(48657) = X(8724)-of-X3-ABC reflections triangle
X(48657) = X(12243)-of-Johnson triangle
X(48657) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (114, 11632, 5055), (147, 13188, 38744), (381, 6054, 38743), (671, 6054, 22566), (671, 22566, 381), (2482, 14830, 3), (6055, 15561, 15694), (8724, 14830, 2482), (12042, 41134, 15693)


X(48658) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    3*a^14-2*(b^2+c^2)*a^12-(3*b^4-5*b^2*c^2+3*c^4)*a^10-(2*b^2-c^2)*(b^2-2*c^2)*(b^2+c^2)*a^8+(b^4-3*b^2*c^2+c^4)*(b^2-c^2)^2*a^6+3*(b^4-c^4)*(b^2-c^2)*(2*b^4+b^2*c^2+2*c^4)*a^4-(b^4-c^4)^2*(b^4+4*b^2*c^2+c^4)*a^2-2*(b^4-c^4)*(b^2-c^2)^3*(b^4+c^4) : :
X(48658) = 3*X(3)-4*X(132) = 7*X(3)-8*X(6720) = 4*X(127)-5*X(3843) = 7*X(132)-6*X(6720) = 2*X(132)-3*X(12918) = 3*X(381)-2*X(1297) = 3*X(381)-4*X(19160) = 3*X(382)-2*X(10735) = 5*X(1656)-4*X(38624) = 7*X(3526)-6*X(38717) = 3*X(3534)-4*X(38608) = 3*X(3830)-2*X(10749) = 9*X(5055)-8*X(34841) = 5*X(5076)-4*X(19163) = 5*X(5076)-2*X(38689) = 4*X(6720)-7*X(12918) = X(10735)-3*X(44988) = 4*X(10735)-3*X(48681) = 3*X(12384)-X(13200) = 2*X(13200)-3*X(13310) = 4*X(44988)-X(48681)

The reciprocal orthologic center of these triangles is X(19158).

X(48658) lies on the circumcircle of anti-Ehrmann-mid triangle and these lines: {3, 132}, {4, 13115}, {5, 12253}, {30, 12384}, {112, 1657}, {127, 3843}, {381, 1297}, {382, 10735}, {999, 12955}, {1656, 38624}, {2781, 12902}, {2794, 5073}, {2799, 38744}, {2806, 38756}, {2831, 48680}, {3295, 12945}, {3320, 9668}, {3526, 38717}, {3534, 38608}, {3627, 13219}, {3830, 9530}, {5055, 34841}, {5076, 19163}, {5899, 19165}, {6020, 9655}, {6407, 13923}, {6408, 13992}, {9517, 38790}, {9518, 38768}, {9532, 38780}, {9654, 13116}, {9669, 13117}, {10718, 38335}, {12083, 14983}, {12145, 18494}, {12207, 18501}, {12265, 18493}, {12340, 18524}, {12408, 18480}, {12478, 45379}, {12479, 45380}, {12503, 18503}, {12702, 12784}, {12796, 18508}, {12805, 26336}, {12806, 26346}, {12925, 18519}, {12935, 18518}, {12996, 45381}, {12997, 45382}, {13099, 18526}, {13118, 18545}, {13119, 18543}, {13221, 28146}, {13918, 45384}, {13985, 45385}, {14689, 15681}, {15696, 38699}, {18496, 48474}, {18498, 48475}, {18510, 19093}, {18512, 19094}, {19159, 26321}, {23251, 35828}, {23261, 35829}, {35880, 42263}, {35881, 42264}

X(48658) = reflection of X(i) in X(j) for these (i, j): (3, 12918), (382, 44988), (1297, 19160), (1657, 112), (12083, 14983), (12253, 5), (12408, 18480), (12702, 12784), (13115, 4), (13219, 3627), (13310, 12384), (18508, 12796), (18526, 13099), (38689, 19163), (48681, 382)
X(48658) = inverse of X(34131) in Stammler circle
X(48658) = orthologic center (anti-Ehrmann-mid, T) for these triangles T: {1st anti-orthosymmedial, 1st orthosymmedial}
X(48658) = X(1297)-of-anti-Ehrmann-mid triangle
X(48658) = X(12253)-of-Johnson triangle
X(48658) = X(12918)-of-X3-ABC reflections triangle
X(48658) = {X(1297), X(19160)}-harmonic conjugate of X(381)


X(48659) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO 3rd ANTI-TRI-SQUARES

Barycentrics    3*a^6-2*(b^2+c^2)*a^4+(b^2+c^2)^2*a^2-4*S*(a^2+b^2-c^2)*(a^2-b^2+c^2)-2*(b^2+c^2)*(b^2-c^2)^2 : :
X(48659) = 3*X(3)-4*X(642) = 3*X(4)-X(12221) = 3*X(381)-2*X(486) = 3*X(381)-4*X(22596) = X(382)+2*X(6281) = 2*X(642)-3*X(6290) = 3*X(3830)-X(22809) = 5*X(3843)-4*X(6251) = 9*X(5055)-8*X(6119) = 3*X(9742)-X(12510) = 2*X(12221)-3*X(12601) = 4*X(12268)-5*X(18493)

The reciprocal orthologic center of these triangles is X(486).

X(48659) lies on these lines: {3, 640}, {4, 193}, {5, 12256}, {30, 487}, {372, 45439}, {381, 486}, {382, 1161}, {542, 9975}, {638, 33878}, {999, 12958}, {1152, 45543}, {1352, 14230}, {1586, 8780}, {1657, 12123}, {3071, 39899}, {3146, 12509}, {3167, 32587}, {3295, 12948}, {3627, 12296}, {3818, 23251}, {3830, 22809}, {3843, 6251}, {3851, 45377}, {5050, 45407}, {5055, 6119}, {5093, 45441}, {6033, 45488}, {6280, 26346}, {6315, 48657}, {6398, 13934}, {6406, 13754}, {6423, 6564}, {6560, 32494}, {6561, 22592}, {7388, 12017}, {7517, 12972}, {7581, 14848}, {7980, 18526}, {9654, 10067}, {9655, 18989}, {9668, 13081}, {9669, 10083}, {9742, 12510}, {9906, 18480}, {9986, 18503}, {12147, 18494}, {12210, 18501}, {12268, 18493}, {12299, 34382}, {12303, 47527}, {12314, 36655}, {12343, 18524}, {12484, 45379}, {12485, 45380}, {12702, 12787}, {12799, 18508}, {12928, 18519}, {12938, 18518}, {12978, 18534}, {13002, 45381}, {13003, 45382}, {13132, 18545}, {13133, 18543}, {13665, 30435}, {13748, 48662}, {13785, 32498}, {13921, 45384}, {13933, 45385}, {14244, 37343}, {18496, 48478}, {18498, 48479}, {18510, 19104}, {18512, 19105}, {19461, 44413}, {22591, 22625}, {22595, 26321}, {22598, 48655}, {22600, 48656}, {22617, 42283}, {22817, 31723}, {35786, 45438}, {42022, 44665}, {43511, 45079}

X(48659) = midpoint of X(3146) and X(12509)
X(48659) = reflection of X(i) in X(j) for these (i, j): (3, 6290), (486, 22596), (1152, 45543), (1657, 12123), (9906, 18480), (12256, 5), (12296, 3627), (12314, 36655), (12601, 4), (12702, 12787), (18508, 12799), (18526, 7980), (22591, 22625), (23261, 22820)
X(48659) = orthologic center (anti-Ehrmann-mid, T) for these triangles T: {3rd anti-tri-squares, 2nd half-squares, 4th tri-squares, inner-Vecten}
X(48659) = X(486)-of-anti-Ehrmann-mid triangle
X(48659) = X(6290)-of-X3-ABC reflections triangle
X(48659) = X(12256)-of-Johnson triangle
X(48659) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 12222, 21850), (4, 18440, 48660), (486, 22596, 381), (486, 45023, 3070), (32498, 44648, 13785)


X(48660) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO 4th ANTI-TRI-SQUARES

Barycentrics    3*a^6-2*(b^2+c^2)*a^4+(b^2+c^2)^2*a^2+4*S*(a^2+b^2-c^2)*(a^2-b^2+c^2)-2*(b^2+c^2)*(b^2-c^2)^2 : :
X(48660) = 3*X(3)-4*X(641) = 3*X(4)-X(12222) = 3*X(381)-2*X(485) = 3*X(381)-4*X(22625) = X(382)+2*X(6278) = 2*X(641)-3*X(6289) = 3*X(3830)-X(22810) = 5*X(3843)-4*X(6250) = 9*X(5055)-8*X(6118) = 3*X(9742)-X(12509) = 2*X(12222)-3*X(12602) = 4*X(12269)-5*X(18493)

The reciprocal orthologic center of these triangles is X(485).

X(48660) lies on these lines: {3, 639}, {4, 193}, {5, 12257}, {30, 488}, {371, 45438}, {381, 485}, {382, 1160}, {542, 9974}, {637, 33878}, {999, 12959}, {1151, 45542}, {1352, 14233}, {1585, 8780}, {1657, 12124}, {3070, 39899}, {3146, 12510}, {3167, 32588}, {3295, 12949}, {3627, 12297}, {3818, 23261}, {3830, 22810}, {3843, 6250}, {3851, 45378}, {5050, 45406}, {5055, 6118}, {5093, 45440}, {6033, 45489}, {6221, 13882}, {6279, 26336}, {6291, 13754}, {6311, 48657}, {6424, 6565}, {6560, 22591}, {6561, 32497}, {7389, 12017}, {7517, 12973}, {7582, 14848}, {7981, 18526}, {9654, 10068}, {9655, 18988}, {9668, 13082}, {9669, 10084}, {9742, 12509}, {9907, 18480}, {9987, 18503}, {12148, 18494}, {12211, 18501}, {12269, 18493}, {12298, 34382}, {12304, 47527}, {12313, 36656}, {12344, 18524}, {12486, 45379}, {12487, 45380}, {12702, 12788}, {12800, 18508}, {12929, 18519}, {12939, 18518}, {12979, 18534}, {13004, 45381}, {13005, 45382}, {13134, 18545}, {13135, 18543}, {13665, 32499}, {13749, 48662}, {13785, 30435}, {13879, 45384}, {13880, 45385}, {14229, 37342}, {18496, 48480}, {18498, 48481}, {18510, 19102}, {18512, 19103}, {19462, 44413}, {22592, 22596}, {22624, 26321}, {22627, 48655}, {22629, 48656}, {22646, 42284}, {22818, 31723}, {35787, 45439}, {43512, 45078}, {44665, 45593}

X(48660) = midpoint of X(3146) and X(12510)
X(48660) = reflection of X(i) in X(j) for these (i, j): (3, 6289), (485, 22625), (1151, 45542), (1657, 12124), (9907, 18480), (12257, 5), (12297, 3627), (12313, 36656), (12602, 4), (12702, 12788), (18508, 12800), (18526, 7981), (22592, 22596), (23251, 22819)
X(48660) = orthologic center (anti-Ehrmann-mid, T) for these triangles T: {4th anti-tri-squares, 1st half-squares, 3rd tri-squares, outer-Vecten}
X(48660) = X(485)-of-anti-Ehrmann-mid triangle
X(48660) = X(6289)-of-X3-ABC reflections triangle
X(48660) = X(12257)-of-Johnson triangle
X(48660) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 12221, 21850), (4, 18440, 48659), (485, 22625, 381), (485, 45024, 3071), (32499, 44647, 13665)


X(48661) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO BEVAN ANTIPODAL

Barycentrics    3*a^4+2*(b+c)*a^3-(b^2+4*b*c+c^2)*a^2-2*(b^2-c^2)*(b-c)*a-2*(b^2-c^2)^2 : :
X(48661) = 3*X(2)-4*X(40273) = 3*X(3)-4*X(946) = 7*X(3)-8*X(1125) = 5*X(3)-6*X(5886) = 11*X(3)-12*X(10165) = 9*X(3)-8*X(12512) = 4*X(3)-5*X(18493) = 5*X(3)-4*X(31730) = 7*X(946)-6*X(1125) = 10*X(946)-9*X(5886) = 11*X(946)-9*X(10165) = 3*X(946)-2*X(12512) = 2*X(946)-3*X(12699) = 16*X(946)-15*X(18493) = 5*X(946)-3*X(31730) = 9*X(1125)-7*X(12512) = 4*X(1125)-7*X(12699) = 10*X(1125)-7*X(31730) = 11*X(5886)-10*X(10165) = 3*X(5886)-5*X(12699) = 3*X(5886)-2*X(31730)

The reciprocal orthologic center of these triangles is X(1).

X(48661) lies on these lines: {1, 1657}, {2, 40273}, {3, 142}, {4, 3617}, {5, 6361}, {7, 15172}, {8, 3627}, {10, 3843}, {20, 10246}, {30, 944}, {40, 381}, {46, 9669}, {55, 37731}, {65, 9668}, {79, 3303}, {140, 9778}, {145, 28186}, {165, 3526}, {191, 31140}, {354, 4338}, {355, 3830}, {376, 5901}, {382, 517}, {390, 6147}, {484, 10896}, {496, 3474}, {497, 5708}, {515, 5073}, {519, 15684}, {535, 10912}, {546, 5657}, {548, 3616}, {550, 5603}, {551, 15689}, {631, 38034}, {942, 9580}, {950, 1159}, {952, 3146}, {999, 1770}, {1058, 24470}, {1319, 4333}, {1385, 3534}, {1387, 38754}, {1388, 4316}, {1478, 45081}, {1479, 36279}, {1519, 35251}, {1537, 6934}, {1656, 1699}, {1698, 5072}, {1702, 18512}, {1703, 18510}, {1836, 3295}, {1902, 18494}, {2095, 6851}, {2098, 10483}, {2800, 40265}, {2802, 38756}, {2807, 6243}, {2809, 38768}, {2817, 38780}, {3057, 9655}, {3149, 35000}, {3242, 29317}, {3244, 28172}, {3245, 18514}, {3336, 11238}, {3339, 18527}, {3428, 13743}, {3434, 3927}, {3475, 11544}, {3487, 10386}, {3522, 38028}, {3529, 28182}, {3543, 12245}, {3576, 15696}, {3583, 37567}, {3622, 17538}, {3628, 9779}, {3649, 4309}, {3653, 15695}, {3654, 14269}, {3655, 15685}, {3656, 4297}, {3679, 38335}, {3817, 5070}, {3832, 38042}, {3845, 5818}, {3850, 9780}, {3851, 5493}, {3861, 38112}, {3940, 11415}, {4190, 35272}, {4292, 7373}, {4294, 39542}, {4295, 15171}, {4301, 10247}, {4312, 5045}, {4318, 8144}, {4324, 34471}, {4428, 11263}, {4640, 31493}, {4857, 5221}, {5054, 8227}, {5055, 6684}, {5057, 5687}, {5059, 7967}, {5076, 7991}, {5079, 11231}, {5119, 9654}, {5131, 45035}, {5180, 5730}, {5183, 10826}, {5204, 15228}, {5217, 18393}, {5250, 17528}, {5274, 34753}, {5550, 15712}, {5697, 12943}, {5698, 31419}, {5709, 18544}, {5711, 33095}, {5731, 15704}, {5752, 29309}, {5812, 12693}, {5840, 48667}, {5847, 48662}, {5882, 28158}, {5902, 9670}, {5903, 12953}, {5918, 13373}, {6001, 48672}, {6407, 8983}, {6408, 13971}, {6767, 10624}, {6848, 38752}, {6849, 35514}, {6861, 15911}, {6985, 11849}, {6999, 29589}, {7489, 35239}, {7580, 37621}, {7743, 15803}, {7957, 31937}, {7973, 18400}, {7982, 18526}, {7984, 34584}, {7987, 15688}, {8158, 12700}, {9579, 9957}, {9614, 37582}, {9616, 13903}, {9624, 17502}, {9657, 16118}, {9709, 24703}, {9856, 37585}, {9961, 24475}, {10164, 46219}, {10222, 28154}, {10267, 16117}, {10283, 12103}, {10306, 18524}, {10310, 37251}, {10679, 37411}, {10724, 12747}, {10860, 37612}, {10895, 11010}, {11230, 15720}, {11237, 37563}, {11249, 18515}, {11260, 34740}, {11278, 28168}, {11396, 18560}, {11522, 13624}, {11529, 31795}, {11531, 28204}, {11723, 38723}, {11724, 38731}, {11725, 38742}, {11726, 38766}, {11727, 38778}, {11735, 38788}, {12017, 38035}, {12101, 38074}, {12102, 38138}, {12197, 18501}, {12261, 15041}, {12331, 34789}, {12410, 47527}, {12433, 18221}, {12458, 45379}, {12459, 45380}, {12497, 18503}, {12565, 37615}, {12571, 19709}, {12651, 37533}, {12696, 18508}, {12697, 26336}, {12698, 26346}, {12703, 18545}, {12704, 18543}, {12705, 37584}, {12773, 14217}, {12778, 38789}, {12782, 22728}, {13465, 37433}, {13912, 45384}, {13975, 45385}, {14093, 25055}, {14130, 15177}, {15338, 37606}, {15640, 34631}, {15686, 38314}, {15693, 16192}, {15718, 19883}, {16189, 32900}, {16417, 41012}, {16466, 33094}, {16853, 40998}, {17564, 26129}, {17733, 28494}, {18482, 38121}, {18496, 48487}, {18498, 48488}, {18990, 30305}, {19541, 35448}, {19708, 38022}, {21000, 24160}, {21735, 46934}, {22770, 26321}, {22841, 45381}, {22842, 45382}, {23251, 35610}, {23261, 35611}, {24390, 44447}, {26332, 47032}, {28164, 37727}, {28228, 31673}, {28452, 31777}, {29229, 35631}, {29349, 37482}, {30424, 40270}, {31443, 31467}, {31479, 37568}, {31726, 47321}, {31798, 31822}, {32141, 36002}, {33699, 34627}, {34864, 37557}, {35238, 45976}, {35641, 42263}, {35642, 42264}, {37022, 37535}, {41722, 44438}, {41854, 43166}, {42266, 44635}, {42267, 44636}

X(48661) = midpoint of X(i) and X(j) for these {i, j}: {145, 33703}, {5073, 8148}, {9589, 41869}, {15640, 34631}
X(48661) = reflection of X(i) in X(j) for these (i, j): (3, 12699), (8, 3627), (20, 22791), (40, 22793), (382, 41869), (1482, 962), (1657, 1), (3529, 34773), (3534, 31162), (5493, 18483), (5881, 33697), (5904, 31828), (6361, 5), (7957, 31937), (7991, 18480), (8158, 12700), (9961, 24475), (12331, 34789), (12645, 5691), (12702, 4), (12747, 10724), (12773, 14217), (13465, 37433), (15681, 3656), (15685, 3655), (17800, 18481), (18481, 4301), (18508, 12696), (18525, 382), (18526, 7982), (20070, 5690), (31798, 31822), (34627, 33699), (34632, 3845), (34718, 3830), (37585, 9856)
X(48661) = anticomplement of the anticomplement of X(40273)
X(48661) = orthologic center (anti-Ehrmann-mid, T) for these triangles T: {Bevan antipodal, 3rd extouch}
X(48661) = center of circle {{X(145), X(33703), X(36171)}}
X(48661) = X(40)-of-anti-Ehrmann-mid triangle
X(48661) = X(1657)-of-5th mixtilinear triangle
X(48661) = X(6361)-of-Johnson triangle
X(48661) = X(10627)-of-2nd Conway triangle, when ABC is acute
X(48661) = X(12699)-of-X3-ABC reflections triangle
X(48661) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 12702, 5790), (4, 20070, 5690), (20, 22791, 10246), (40, 22793, 381), (165, 9955, 3526), (382, 12645, 5691), (496, 3474, 37545), (1699, 3579, 1656), (1770, 12701, 999), (3487, 30332, 10386), (3653, 34638, 15695), (3656, 4297, 37624), (3845, 34632, 38066), (4295, 15171, 15934), (4301, 18481, 10247), (5493, 18483, 26446), (5690, 20070, 12702), (5691, 12645, 18525), (5818, 10248, 3845), (5886, 31730, 3), (6361, 9812, 5), (8227, 31663, 5054), (10247, 17800, 18481), (10248, 34632, 5818), (11230, 35242, 15720), (15681, 37624, 4297), (18483, 26446, 3851), (18499, 40266, 18525)


X(48662) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO 9th BROCARD

Barycentrics    7*a^6-4*(b^2+c^2)*a^4+(b^2+c^2)^2*a^2-4*(b^4-c^4)*(b^2-c^2) : :
X(48662) = 7*X(3)-8*X(141) = 3*X(3)-4*X(1352) = 9*X(3)-8*X(44882) = 5*X(3)-4*X(46264) = 3*X(4)-2*X(1353) = 4*X(4)-3*X(5093) = 4*X(6)-5*X(3843) = 6*X(141)-7*X(1352) = 4*X(141)-7*X(18440) = 9*X(141)-7*X(44882) = 10*X(141)-7*X(46264) = 2*X(1352)-3*X(18440) = 3*X(1352)-2*X(44882) = 5*X(1352)-3*X(46264) = 8*X(1353)-9*X(5093) = 4*X(1353)-3*X(39899) = 3*X(5093)-2*X(39899) = 9*X(18440)-4*X(44882) = 5*X(18440)-2*X(46264) = 10*X(44882)-9*X(46264)

The reciprocal orthologic center of these triangles is X(4).

X(48662) lies on these lines: {3, 66}, {4, 1353}, {5, 39874}, {6, 3843}, {25, 3448}, {30, 5921}, {49, 19124}, {69, 1657}, {182, 5055}, {193, 3627}, {265, 32250}, {381, 6776}, {382, 3564}, {399, 19139}, {511, 5073}, {524, 15684}, {542, 1351}, {546, 14912}, {548, 3620}, {599, 15689}, {999, 39892}, {1350, 11645}, {1539, 32234}, {1843, 34783}, {1853, 5972}, {1992, 38335}, {2777, 32272}, {3146, 34380}, {3167, 11550}, {3295, 39891}, {3426, 17702}, {3517, 32140}, {3526, 18358}, {3527, 10116}, {3534, 11180}, {3618, 5072}, {3818, 3851}, {3855, 33748}, {5020, 18911}, {5032, 14893}, {5054, 40330}, {5070, 10516}, {5076, 21850}, {5079, 38110}, {5085, 18553}, {5094, 46818}, {5480, 14269}, {5644, 6997}, {5663, 6403}, {5847, 48661}, {5848, 38756}, {5868, 20429}, {5869, 20428}, {5876, 12220}, {5899, 37488}, {6391, 12293}, {6759, 19129}, {7716, 37490}, {9654, 39900}, {9655, 39873}, {9668, 39897}, {9669, 39901}, {9909, 11442}, {9967, 18435}, {10113, 39562}, {10255, 23300}, {10519, 15696}, {10575, 14913}, {10691, 44833}, {11178, 15701}, {11179, 19709}, {11216, 25329}, {11318, 39141}, {11381, 34382}, {11403, 34799}, {11479, 34224}, {11646, 40825}, {12007, 14848}, {12162, 18438}, {12272, 12290}, {12283, 15305}, {12429, 16655}, {12702, 39885}, {13748, 48659}, {13749, 48660}, {14093, 21356}, {14157, 19154}, {14530, 34776}, {14683, 31133}, {14810, 15695}, {15059, 35264}, {15069, 17800}, {15516, 38072}, {15694, 24206}, {15703, 47354}, {15718, 21358}, {16111, 35450}, {16659, 39568}, {18404, 36851}, {18405, 18449}, {18474, 32063}, {18480, 39878}, {18493, 39870}, {18494, 39871}, {18496, 48489}, {18498, 48490}, {18501, 39872}, {18503, 39882}, {18508, 39886}, {18510, 39875}, {18512, 39876}, {18518, 39890}, {18519, 39889}, {18524, 39877}, {18526, 39898}, {18543, 39903}, {18545, 39902}, {19145, 45384}, {19146, 45385}, {19588, 47527}, {19924, 35400}, {20080, 33703}, {20127, 32275}, {20423, 35403}, {20850, 31383}, {22728, 32451}, {23049, 38789}, {23251, 39893}, {23261, 39894}, {26321, 39883}, {26336, 39887}, {26346, 39888}, {29317, 40341}, {30771, 32064}, {31726, 32220}, {31884, 43150}, {32139, 39588}, {32244, 34584}, {32257, 38788}, {33414, 33415}, {37485, 47748}, {39880, 45379}, {39881, 45380}, {39895, 45381}, {39896, 45382}, {45554, 48677}, {45555, 48678}

X(48662) = midpoint of X(i) and X(j) for these {i, j}: {12272, 12290}, {20080, 33703}
X(48662) = reflection of X(i) in X(j) for these (i, j): (3, 18440), (193, 3627), (265, 32250), (399, 41737), (1351, 36990), (1657, 69), (3534, 11180), (6391, 12293), (6776, 39884), (10575, 14913), (11898, 5921), (12220, 5876), (12702, 39885), (17800, 33878), (18438, 12162), (18508, 39886), (18526, 39898), (20127, 32275), (32234, 1539), (33878, 15069), (34783, 1843), (39874, 5), (39878, 18480), (39899, 4), (44456, 382)
X(48662) = orthologic center (anti-Ehrmann-mid, 9th Brocard)
X(48662) = X(6776)-of-anti-Ehrmann-mid triangle
X(48662) = X(18440)-of-X3-ABC reflections triangle
X(48662) = X(39874)-of-Johnson triangle
X(48662) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 39899, 5093), (1351, 36990, 3830), (3818, 5050, 3851), (6776, 39884, 381), (10516, 12017, 5070), (12134, 34780, 3), (18358, 25406, 3526)


X(48663) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO 1st BROCARD-REFLECTED

Barycentrics    3*(b^2+c^2)*a^6-(b^4+b^2*c^2+c^4)*a^4-(b^2+c^2)*(2*b^4-7*b^2*c^2+2*c^4)*a^2-4*(b^2-c^2)^2*b^2*c^2 : :
X(48663) = 5*X(3)-8*X(3934) = X(3)-4*X(6248) = 3*X(3)-4*X(15819) = 2*X(4)+X(13108) = 5*X(4)+X(20081) = 3*X(4)-X(44434) = 4*X(4)-X(48673) = 2*X(3934)-5*X(6248) = 4*X(3934)-5*X(7697) = 6*X(3934)-5*X(15819) = 3*X(6248)-X(15819) = 3*X(7697)-2*X(15819) = 5*X(13108)-2*X(20081) = 3*X(13108)+2*X(44434) = 2*X(13108)+X(48673) = 2*X(20081)+5*X(22728) = 3*X(20081)+5*X(44434) = 4*X(20081)+5*X(48673) = 3*X(22728)-2*X(44434) = 4*X(44434)-3*X(48673)

The reciprocal orthologic center of these triangles is X(3).

X(48663) lies on these lines: {3, 3734}, {4, 7779}, {5, 7709}, {30, 6194}, {39, 3851}, {76, 382}, {148, 10335}, {194, 546}, {262, 381}, {511, 3830}, {538, 14269}, {550, 31276}, {736, 34505}, {999, 22706}, {1350, 44774}, {1503, 31958}, {1569, 18424}, {1634, 18575}, {1656, 7919}, {1657, 22676}, {3090, 32516}, {3091, 32448}, {3095, 3843}, {3097, 38140}, {3146, 32521}, {3295, 22705}, {3407, 9755}, {3534, 22712}, {3627, 12251}, {3628, 32522}, {3818, 6321}, {5055, 11171}, {5070, 13334}, {5072, 11272}, {5073, 9821}, {5079, 7786}, {5085, 32149}, {5188, 17800}, {6287, 7748}, {7710, 37348}, {7754, 13111}, {7770, 10131}, {9466, 15681}, {9654, 13077}, {9655, 10079}, {9668, 10063}, {9669, 18982}, {9772, 13188}, {9902, 22793}, {10516, 11261}, {10796, 38664}, {10847, 35938}, {10848, 35939}, {11164, 15688}, {12702, 22697}, {14881, 32520}, {15022, 32523}, {15694, 21163}, {16808, 32465}, {16809, 32466}, {18440, 38744}, {18480, 22650}, {18493, 22475}, {18494, 22480}, {18496, 48491}, {18498, 48492}, {18501, 22521}, {18503, 22678}, {18508, 22698}, {18510, 19063}, {18512, 19064}, {18518, 22704}, {18519, 22703}, {18524, 22556}, {18526, 22713}, {18543, 22732}, {18545, 22731}, {18553, 44453}, {18906, 39884}, {22668, 45379}, {22672, 45380}, {22680, 26321}, {22684, 41038}, {22686, 41039}, {22699, 26336}, {22700, 26346}, {22709, 45381}, {22710, 45382}, {22720, 45384}, {22721, 45385}, {22726, 48677}, {22727, 48678}, {23251, 35838}, {23261, 35839}, {32470, 42273}, {32471, 42270}, {39266, 47618}

X(48663) = midpoint of X(13108) and X(22728)
X(48663) = reflection of X(i) in X(j) for these (i, j): (3, 7697), (262, 22681), (1350, 44774), (1657, 22676), (3095, 22682), (3097, 38140), (3534, 22712), (7697, 6248), (7709, 5), (11257, 40108), (12188, 43532), (12702, 22697), (13188, 9772), (18508, 22698), (18526, 22713), (22650, 18480), (22728, 4), (32447, 381), (32519, 262), (48673, 22728)
X(48663) = orthologic center (anti-Ehrmann-mid, 1st Brocard-reflected)
X(48663) = X(262)-of-anti-Ehrmann-mid triangle
X(48663) = X(7697)-of-X3-ABC reflections triangle
X(48663) = X(7709)-of-Johnson triangle
X(48663) = X(32519)-of-Ehrmann-mid triangle
X(48663) = X(33683)-of-Artzt triangle
X(48663) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 13108, 48673), (262, 22681, 381), (262, 32519, 32447), (381, 32519, 262), (12188, 35930, 11842)


X(48664) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO EXTOUCH

Barycentrics    3*a^7-(b+c)*a^6-2*(3*b^2-7*b*c+3*c^2)*a^5-2*(b+c)*b*c*a^4+3*(b^2+c^2)*(b-c)^2*a^3+(b^2-c^2)*(b-c)*(3*b^2+4*b*c+3*c^2)*a^2-8*(b^2-c^2)^2*b*c*a-2*(b^2-c^2)^3*(b-c) : :
X(48664) = 3*X(3)-4*X(6260) = 2*X(84)-3*X(381) = 3*X(381)-4*X(22792) = 2*X(550)-3*X(5658) = 5*X(1656)-4*X(34862) = 3*X(3830)-2*X(5787) = 5*X(3843)-4*X(6245) = 9*X(5055)-8*X(6705) = 3*X(5790)-4*X(6256) = 3*X(6259)-2*X(6260) = 4*X(12114)-5*X(18493)

The reciprocal orthologic center of these triangles is X(40).

X(48664) lies on these lines: {3, 3452}, {4, 5708}, {5, 12246}, {20, 9945}, {30, 5758}, {84, 381}, {382, 971}, {515, 5073}, {550, 5658}, {999, 12679}, {1490, 1657}, {1656, 34862}, {1709, 9654}, {1864, 9579}, {2096, 37545}, {2829, 16127}, {3295, 12678}, {3627, 9799}, {3830, 5787}, {3843, 6245}, {3927, 6925}, {5055, 6705}, {5225, 41556}, {5730, 9809}, {5779, 6850}, {5780, 28458}, {5790, 6256}, {6001, 18525}, {6257, 26346}, {6258, 26336}, {6938, 41543}, {7971, 18526}, {7992, 18480}, {8987, 45384}, {9655, 12688}, {9668, 12680}, {9669, 10085}, {10572, 41706}, {10864, 22793}, {12114, 18493}, {12136, 18494}, {12196, 18501}, {12330, 18524}, {12433, 36996}, {12456, 45379}, {12457, 45380}, {12496, 18503}, {12667, 12702}, {12668, 18508}, {12675, 18530}, {12676, 18519}, {12677, 18518}, {12686, 18545}, {12687, 18543}, {12773, 46435}, {12953, 17660}, {13974, 45385}, {15071, 37001}, {15239, 37532}, {18237, 26321}, {18245, 45381}, {18246, 45382}, {18496, 48495}, {18498, 48496}, {18499, 48671}, {18510, 19067}, {18512, 19068}, {23251, 35844}, {23261, 35845}

X(48664) = reflection of X(i) in X(j) for these (i, j): (3, 6259), (84, 22792), (1657, 1490), (7992, 18480), (9799, 3627), (10864, 22793), (12246, 5), (12684, 4), (12702, 12667), (12773, 46435), (18508, 12668), (18525, 40267), (18526, 7971)
X(48664) = orthologic center (anti-Ehrmann-mid, T) for these triangles T: {extouch, 1st Zaniah}
X(48664) = X(84)-of-anti-Ehrmann-mid triangle
X(48664) = X(6259)-of-X3-ABC reflections triangle
X(48664) = X(12246)-of-Johnson triangle
X(48664) = {X(84), X(22792)}-harmonic conjugate of X(381)


X(48665) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO INNER-FERMAT

Barycentrics    -2*(7*a^4-(b^2+c^2)*a^2-6*(b^2-c^2)^2)*S+sqrt(3)*(3*a^6-2*(b^2+c^2)*a^4+(b^2+c^2)^2*a^2-2*(b^4-c^4)*(b^2-c^2)) : :
X(48665) = 3*X(3)-4*X(630) = 3*X(4)-X(22114) = 2*X(18)-3*X(381) = 3*X(381)-4*X(22794) = 3*X(382)+2*X(22845) = 2*X(630)-3*X(16627) = 5*X(3843)-4*X(22831) = 9*X(5055)-8*X(6674) = 4*X(11740)-5*X(18493) = 4*X(12101)-X(33627) = 9*X(14269)-4*X(33464) = 3*X(16628)-2*X(22114) = X(33624)+2*X(33699)

The reciprocal orthologic center of these triangles is X(3).

X(48665) lies on these lines: {3, 624}, {4, 3181}, {5, 22531}, {14, 37008}, {18, 381}, {30, 628}, {382, 5865}, {533, 3830}, {622, 44777}, {999, 22860}, {1657, 22843}, {3053, 42128}, {3295, 22859}, {3843, 22831}, {5055, 6674}, {5076, 5965}, {5318, 22861}, {5869, 22683}, {7773, 11133}, {8260, 10653}, {9654, 22884}, {9655, 18972}, {9668, 22865}, {9669, 22885}, {10612, 42989}, {11486, 31706}, {11603, 12188}, {11740, 18493}, {12101, 33627}, {12702, 22851}, {13111, 16001}, {14269, 33464}, {18480, 22651}, {18494, 22481}, {18496, 48497}, {18498, 48498}, {18501, 22522}, {18503, 22745}, {18508, 22852}, {18510, 19069}, {18512, 19072}, {18518, 22858}, {18519, 22857}, {18524, 22557}, {18526, 22867}, {18543, 22887}, {18545, 22886}, {19106, 22850}, {19107, 22855}, {22669, 45379}, {22673, 45380}, {22736, 37825}, {22771, 26321}, {22797, 42158}, {22846, 42813}, {22853, 26336}, {22854, 26346}, {22856, 42093}, {22862, 42127}, {22863, 45381}, {22864, 45382}, {22871, 48657}, {22876, 45384}, {22877, 45385}, {22882, 48677}, {22883, 48678}, {23251, 35846}, {23261, 35849}, {31703, 42094}, {33624, 33699}, {35746, 42282}, {36994, 47068}, {37332, 42165}, {37333, 42162}

X(48665) = reflection of X(i) in X(j) for these (i, j): (3, 16627), (18, 22794), (1657, 22843), (12188, 11603), (12702, 22851), (16628, 4), (18508, 22852), (18526, 22867), (22531, 5), (22651, 18480)
X(48665) = orthologic center (anti-Ehrmann-mid, T) for these triangles T: {inner-Fermat, 1st half-diamonds}
X(48665) = X(18)-of-anti-Ehrmann-mid triangle
X(48665) = X(16627)-of-X3-ABC reflections triangle
X(48665) = X(22531)-of-Johnson triangle
X(48665) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (18, 22794, 381), (5076, 18440, 48666)


X(48666) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO OUTER-FERMAT

Barycentrics    2*(7*a^4-(b^2+c^2)*a^2-6*(b^2-c^2)^2)*S+sqrt(3)*(3*a^6-2*(b^2+c^2)*a^4+(b^2+c^2)^2*a^2-2*(b^4-c^4)*(b^2-c^2)) : :
X(48666) = 3*X(3)-4*X(629) = 3*X(4)-X(22113) = 2*X(17)-3*X(381) = 3*X(381)-4*X(22795) = 3*X(382)+2*X(22844) = 2*X(629)-3*X(16626) = 5*X(3843)-4*X(22832) = 9*X(5055)-8*X(6673) = 4*X(11739)-5*X(18493) = 4*X(12101)-X(33626) = 9*X(14269)-4*X(33465) = 3*X(16629)-2*X(22113) = X(33622)+2*X(33699)

The reciprocal orthologic center of these triangles is X(3).

X(48666) lies on these lines: {3, 623}, {4, 3180}, {5, 22532}, {13, 37007}, {17, 381}, {30, 627}, {382, 5864}, {532, 3830}, {621, 44776}, {999, 22905}, {1657, 22890}, {3053, 42125}, {3295, 22904}, {3843, 22832}, {5055, 6673}, {5076, 5965}, {5321, 22907}, {5868, 22685}, {7773, 11132}, {8259, 10654}, {9654, 22929}, {9655, 18973}, {9668, 22910}, {9669, 22930}, {10611, 42988}, {11485, 31705}, {11602, 12188}, {11739, 18493}, {12101, 33626}, {12702, 22896}, {13111, 16002}, {14269, 33465}, {18480, 22652}, {18494, 22482}, {18496, 48499}, {18498, 48500}, {18501, 22523}, {18503, 22746}, {18508, 22897}, {18510, 19071}, {18512, 19070}, {18518, 22903}, {18519, 22902}, {18524, 22558}, {18526, 22912}, {18543, 22932}, {18545, 22931}, {19106, 22901}, {19107, 22894}, {22670, 45379}, {22674, 45380}, {22737, 37824}, {22772, 26321}, {22796, 36782}, {22891, 42814}, {22898, 26336}, {22899, 26346}, {22900, 42094}, {22906, 42126}, {22908, 45381}, {22909, 45382}, {22916, 48657}, {22921, 45384}, {22922, 45385}, {22927, 48677}, {22928, 48678}, {23251, 35848}, {23261, 35847}, {31704, 42093}, {33622, 33699}, {36992, 47066}, {37332, 42159}, {37333, 42164}

X(48666) = reflection of X(i) in X(j) for these (i, j): (3, 16626), (17, 22795), (1657, 22890), (12188, 11602), (12702, 22896), (16629, 4), (18508, 22897), (18526, 22912), (22532, 5), (22652, 18480), (36782, 22796)
X(48666) = orthologic center (anti-Ehrmann-mid, T) for these triangles T: {outer-Fermat, 2nd half-diamonds}
X(48666) = X(17)-of-anti-Ehrmann-mid triangle
X(48666) = X(16626)-of-X3-ABC reflections triangle
X(48666) = X(22532)-of-Johnson triangle
X(48666) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (17, 22795, 381), (5076, 18440, 48665)


X(48667) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO FUHRMANN

Barycentrics    a*(a^6-3*(b+c)*a^5+7*b*c*a^4+6*(b^2-c^2)*(b-c)*a^3-(3*b^4+3*c^4+b*c*(5*b^2-14*b*c+5*c^2))*a^2-3*(b^2-c^2)*(b-c)^3*a+2*(b^2-c^2)*(b-c)*(b^3+c^3)) : :
X(48667) = 3*X(3)-4*X(214) = 3*X(3)-2*X(12515) = 5*X(3)-4*X(46684) = 3*X(4)-X(20085) = 4*X(11)-5*X(18493) = 2*X(80)-3*X(381) = 2*X(104)-3*X(10246) = 2*X(214)-3*X(6265) = 5*X(214)-3*X(46684) = 3*X(381)-4*X(12611) = 2*X(1320)-3*X(1482) = X(1320)-3*X(10698) = 3*X(1537)-X(12690) = 2*X(3065)-3*X(13743) = 3*X(6265)-X(12515) = 5*X(6265)-2*X(46684) = 3*X(10246)-4*X(19907) = 3*X(10738)-2*X(12690) = 5*X(12515)-6*X(46684) = 3*X(12747)-2*X(20085)

The reciprocal orthologic center of these triangles is X(3).

X(48667) lies on these lines: {1, 399}, {3, 214}, {4, 145}, {5, 12247}, {8, 11698}, {11, 18493}, {30, 5180}, {40, 22935}, {56, 11571}, {80, 381}, {100, 5730}, {104, 1621}, {119, 2886}, {355, 21635}, {382, 34789}, {515, 16128}, {517, 3689}, {528, 4930}, {546, 1389}, {758, 22560}, {944, 9809}, {956, 12532}, {999, 11570}, {1012, 9964}, {1145, 3940}, {1159, 12736}, {1317, 3058}, {1319, 1727}, {1385, 1768}, {1387, 15934}, {1388, 15446}, {1484, 5603}, {1656, 12619}, {1657, 12119}, {2098, 7972}, {2801, 10247}, {2802, 8148}, {2829, 16127}, {2932, 4511}, {2975, 13465}, {3218, 14988}, {3295, 12739}, {3306, 17654}, {3340, 6797}, {3476, 34698}, {3576, 12767}, {3579, 15015}, {3655, 33812}, {3656, 21630}, {3711, 5660}, {3843, 6246}, {3870, 17652}, {3877, 37286}, {3884, 33858}, {3895, 37700}, {3899, 35204}, {4189, 38602}, {5055, 6702}, {5079, 38182}, {5083, 7373}, {5119, 41541}, {5330, 12248}, {5425, 39782}, {5440, 35460}, {5531, 7982}, {5690, 6960}, {5694, 11014}, {5697, 41689}, {5722, 41558}, {5840, 48661}, {5886, 10265}, {5901, 6888}, {5903, 37251}, {6262, 26346}, {6263, 26336}, {6264, 10222}, {6767, 15558}, {6859, 9952}, {6862, 11729}, {6863, 38752}, {6892, 13226}, {6910, 34123}, {6913, 12691}, {6933, 34122}, {6954, 38762}, {7171, 7971}, {7993, 16200}, {8988, 45384}, {9654, 10057}, {9655, 18976}, {9669, 10073}, {9708, 18254}, {9897, 11009}, {9955, 37718}, {9956, 15017}, {9957, 37736}, {10090, 36279}, {10703, 34586}, {10711, 12531}, {11011, 31937}, {11224, 18528}, {11278, 12653}, {11715, 37624}, {12137, 18494}, {12198, 18501}, {12460, 45379}, {12461, 45380}, {12498, 18503}, {12551, 37620}, {12645, 12751}, {12699, 48680}, {12729, 18508}, {12741, 45381}, {12742, 45382}, {12749, 18545}, {12750, 18543}, {12755, 42884}, {13199, 28174}, {13205, 22836}, {13976, 45385}, {14217, 18499}, {16117, 34600}, {16134, 48671}, {16145, 48676}, {16160, 34195}, {17636, 25415}, {18481, 33337}, {18496, 48501}, {18498, 48502}, {18510, 19077}, {18512, 19078}, {20400, 38128}, {21740, 37621}, {23251, 35852}, {23261, 35853}, {25413, 45770}, {26726, 41711}, {30305, 34745}, {32198, 45701}, {35004, 45976}, {35856, 44635}, {35857, 44636}, {38133, 46219}, {38753, 43161}

X(48667) = midpoint of X(i) and X(j) for these {i, j}: {944, 9809}, {5531, 7982}, {6326, 13253}
X(48667) = reflection of X(i) in X(j) for these (i, j): (3, 6265), (8, 11698), (40, 22935), (80, 12611), (104, 19907), (149, 22791), (355, 21635), (382, 34789), (1482, 10698), (1657, 12119), (1768, 1385), (6264, 10222), (9803, 1484), (9897, 18480), (10738, 1537), (12247, 5), (12248, 34773), (12331, 6326), (12515, 214), (12645, 12751), (12653, 11278), (12702, 100), (12737, 25485), (12747, 4), (12773, 1), (13205, 22836), (16117, 34600), (18481, 33337), (18508, 12729), (18525, 10742), (18526, 7972), (19914, 119), (22775, 40257), (35000, 4511), (35460, 5440), (38756, 16128), (48680, 12699)
X(48667) = orthologic center (anti-Ehrmann-mid, T) for these triangles T: {Fuhrmann, K798i}
X(48667) = center of circle {{X(100), X(109), X(14513)}}
X(48667) = reflection of X(i) in the line X(j)X(k) for these (i, j, k): (1, 8674, 35050), (4, 900, 35050)
X(48667) = X(80)-of-anti-Ehrmann-mid triangle
X(48667) = X(6265)-of-X3-ABC reflections triangle
X(48667) = X(11561)-of-2nd Conway triangle, when ABC is acute
X(48667) = X(11571)-of-2nd circumperp tangential triangle
X(48667) = X(12247)-of-Johnson triangle
X(48667) = X(12773)-of-5th mixtilinear triangle
X(48667) = X(12902)-of-2nd circumperp triangle, when ABC is acute
X(48667) = X(18524)-of-inner-Garcia triangle
X(48667) = X(18525)-of-anti-inner-Garcia triangle
X(48667) = X(34153)-of-hexyl triangle, when ABC is acute
X(48667) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 40266, 26321), (80, 12611, 381), (104, 19907, 10246), (119, 19914, 5790), (214, 12515, 3), (355, 21635, 38755), (5603, 9803, 1484), (6265, 12515, 214), (11570, 12740, 999), (12737, 25485, 10247), (12739, 12758, 3295), (26321, 40266, 48668)


X(48668) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO 2nd FUHRMANN

Barycentrics    a*(a^6+(b+c)*a^5-(4*b^2-3*b*c+4*c^2)*a^4-2*(b^2-c^2)*(b-c)*a^3+(5*b^4+5*c^4-b*c*(b+c)^2)*a^2+(b^2-c^2)*(b-c)^3*a+(b+c)*(b^2-c^2)*(2*c^3-2*b^3)) : :
X(48668) = X(1)-3*X(7701) = 2*X(1)-3*X(13743) = 3*X(3)-4*X(3647) = 3*X(4)-X(20084) = 2*X(79)-3*X(381) = 3*X(191)-2*X(3579) = 3*X(381)-4*X(22798) = X(382)+2*X(41691) = 3*X(442)-X(16006) = 3*X(2475)-4*X(18357) = 4*X(3579)-3*X(16117) = 2*X(3647)-3*X(3652) = 3*X(7701)-2*X(26202) = X(8148)-6*X(16138) = 2*X(10308)+X(12702) = 2*X(10308)+3*X(13465) = 2*X(11684)-3*X(13465) = X(12702)-3*X(13465) = 3*X(13743)-4*X(26202) = 3*X(16150)-2*X(20084)

The reciprocal orthologic center of these triangles is X(3).

X(48668) lies on these lines: {1, 399}, {3, 3647}, {4, 16150}, {5, 9782}, {8, 30}, {21, 18515}, {79, 381}, {191, 210}, {355, 38756}, {382, 41691}, {442, 10940}, {517, 11524}, {758, 8148}, {999, 16141}, {1260, 35251}, {1482, 4430}, {1657, 16113}, {1749, 37251}, {1768, 45976}, {2475, 10742}, {2932, 45392}, {3295, 16140}, {3649, 10072}, {3651, 19919}, {3683, 13624}, {3843, 16112}, {4420, 35000}, {4860, 33592}, {5055, 6701}, {5220, 16139}, {5302, 33669}, {5441, 18526}, {5499, 9780}, {5550, 10021}, {5708, 6841}, {5779, 37401}, {5790, 6256}, {5901, 13243}, {7489, 15071}, {9654, 16152}, {9655, 18977}, {9668, 16142}, {9669, 16153}, {10246, 31649}, {10943, 37447}, {11849, 12528}, {12699, 28646}, {12731, 48671}, {12738, 12937}, {12745, 48676}, {14450, 16160}, {15677, 34773}, {16114, 18494}, {16115, 18501}, {16118, 18480}, {16121, 45379}, {16122, 45380}, {16123, 18503}, {16129, 18508}, {16130, 26336}, {16131, 26346}, {16143, 22937}, {16148, 45384}, {16149, 45385}, {16154, 18545}, {16155, 18543}, {16159, 18483}, {16161, 45381}, {16162, 45382}, {17768, 31671}, {18496, 48503}, {18498, 48504}, {18510, 19079}, {18512, 19080}, {18516, 36279}, {23251, 35854}, {23261, 35855}, {28444, 33857}, {28453, 33858}, {31937, 32636}, {31938, 35448}, {37234, 41695}

X(48668) = midpoint of X(10308) and X(11684)
X(48668) = reflection of X(i) in X(j) for these (i, j): (1, 26202), (3, 3652), (79, 22798), (1482, 21669), (1657, 16113), (3651, 19919), (12702, 11684), (12773, 3065), (13743, 7701), (14450, 16160), (16116, 5), (16117, 191), (16118, 18480), (16132, 22936), (16143, 22937), (16150, 4), (18508, 16129), (18526, 5441)
X(48668) = orthologic center (anti-Ehrmann-mid, T) for these triangles T: {2nd Fuhrmann, K798e}
X(48668) = X(79)-of-anti-Ehrmann-mid triangle
X(48668) = X(3519)-of-Fuhrmann triangle, when ABC is acute
X(48668) = X(3652)-of-X3-ABC reflections triangle
X(48668) = X(16116)-of-Johnson triangle
X(48668) = X(26202)-of-Aquila triangle
X(48668) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 7701, 26202), (1, 26202, 13743), (79, 22798, 381), (12702, 13465, 11684), (16132, 22936, 28443), (26321, 40266, 48667)


X(48669) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO HATZIPOLAKIS-MOSES

Barycentrics    a^2*(a^14-5*(b^2+c^2)*a^12+(9*b^4+7*b^2*c^2+9*c^4)*a^10-(b^2+c^2)*(5*b^4-6*b^2*c^2+5*c^4)*a^8-(b^4+c^4)*(5*b^4-4*b^2*c^2+5*c^4)*a^6+(b^4-c^4)*(b^2-c^2)*(9*b^4-4*b^2*c^2+9*c^4)*a^4-5*(b^4-c^4)^2*(b^4-b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2)^3*(b^4+4*b^2*c^2+c^4)) : :
X(48669) = 3*X(3)-4*X(32391) = 2*X(54)+X(12315) = 3*X(154)-2*X(23358) = X(195)+2*X(1498) = 3*X(381)-2*X(6145) = 3*X(381)-4*X(32364) = X(382)+2*X(32359) = 4*X(2883)-X(48675) = 4*X(3574)-X(34780) = 5*X(3843)-4*X(32369) = 4*X(6759)-X(12307) = 2*X(7691)-5*X(14530) = 4*X(8254)-X(12324) = X(9920)-3*X(32063) = 4*X(10610)-X(13093) = 2*X(18381)-3*X(32395) = 5*X(18493)-4*X(32331) = 2*X(20424)+X(34781) = X(32338)+2*X(44544) = 3*X(32379)-2*X(32391)

The reciprocal orthologic center of these triangles is X(6146).

X(48669) lies on these lines: {3, 32357}, {4, 19362}, {5, 32337}, {22, 41726}, {30, 32354}, {54, 1593}, {64, 32349}, {154, 23358}, {195, 382}, {381, 6145}, {399, 2917}, {973, 1598}, {999, 32383}, {1154, 7387}, {1181, 3574}, {1209, 18451}, {1503, 45034}, {1657, 32330}, {2070, 41725}, {2781, 47748}, {2883, 48675}, {3089, 32334}, {3295, 32382}, {3575, 43590}, {3581, 32392}, {3843, 32369}, {5656, 32423}, {5878, 18562}, {6000, 10274}, {6288, 18440}, {7691, 9715}, {8254, 12324}, {9654, 32403}, {9655, 32336}, {9668, 32390}, {9669, 32404}, {9919, 32338}, {9968, 48679}, {10540, 48670}, {10610, 13093}, {11414, 41590}, {11597, 18466}, {11743, 18535}, {11802, 46261}, {12084, 47360}, {12234, 15811}, {12254, 18560}, {12289, 19504}, {12291, 43580}, {12300, 32333}, {12316, 39879}, {12702, 32371}, {13621, 41589}, {14157, 32339}, {14216, 32351}, {14627, 41362}, {15038, 18383}, {15047, 23325}, {15087, 32365}, {15106, 21844}, {15137, 17800}, {15138, 35498}, {15139, 43809}, {17814, 32348}, {18381, 32395}, {18404, 45016}, {18480, 32356}, {18493, 32331}, {18494, 32332}, {18496, 48505}, {18498, 48506}, {18501, 32335}, {18503, 32362}, {18508, 32372}, {18510, 32342}, {18512, 32343}, {18518, 32381}, {18519, 32380}, {18524, 32347}, {18526, 32394}, {18543, 32406}, {18545, 32405}, {19361, 25739}, {19468, 43581}, {20424, 32346}, {23251, 35858}, {23261, 35859}, {26321, 32363}, {26336, 32373}, {26346, 32374}, {26883, 32352}, {32360, 45379}, {32361, 45380}, {32388, 45381}, {32389, 45382}, {32393, 36753}, {32396, 37514}, {32399, 45384}, {32400, 45385}

X(48669) = midpoint of X(i) and X(j) for these {i, j}: {1498, 17824}, {32346, 34781}
X(48669) = reflection of X(i) in X(j) for these (i, j): (3, 32379), (64, 32401), (195, 17824), (1657, 32330), (2917, 6759), (6145, 32364), (12084, 47360), (12307, 2917), (12702, 32371), (14216, 32351), (18508, 32372), (18526, 32394), (32337, 5), (32345, 10274), (32346, 20424), (32356, 18480), (32402, 4)
X(48669) = orthologic center (anti-Ehrmann-mid, Hatzipolakis-Moses)
X(48669) = X(6145)-of-anti-Ehrmann-mid triangle
X(48669) = X(32337)-of-Johnson triangle
X(48669) = X(32379)-of-X3-ABC reflections triangle
X(48669) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6145, 32364, 381), (6293, 6759, 2937), (15800, 18445, 195)


X(48670) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO 3rd HATZIPOLAKIS

Barycentrics    (a^14-5*(b^2+c^2)*a^12+3*(3*b^4+5*b^2*c^2+3*c^4)*a^10-(b^2+c^2)*(5*b^4+18*b^2*c^2+5*c^4)*a^8-(5*b^8+5*c^8-2*(14*b^4-b^2*c^2+14*c^4)*b^2*c^2)*a^6+(b^2+c^2)*(3*b^4-8*b^2*c^2+3*c^4)*(3*b^4-2*b^2*c^2+3*c^4)*a^4-(b^2-c^2)^2*(5*b^8+5*c^8+(5*b^4-16*b^2*c^2+5*c^4)*b^2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)^3*(b^4+4*b^2*c^2+c^4))*a^2 : :
X(48670) = 3*X(3)-4*X(22966) = 3*X(381)-2*X(22466) = 3*X(381)-4*X(22800) = 5*X(3843)-4*X(22833) = 5*X(18493)-4*X(22476) = 3*X(22955)-2*X(22966)

The reciprocal orthologic center of these triangles is X(12241).

X(48670) lies on these lines: {3, 22658}, {4, 22979}, {5, 19361}, {25, 5889}, {30, 22647}, {113, 195}, {155, 22970}, {381, 15317}, {382, 13419}, {399, 2929}, {403, 22663}, {999, 22959}, {1657, 22951}, {1993, 45014}, {3295, 22958}, {3426, 12085}, {3843, 22833}, {5562, 37928}, {5907, 32345}, {7529, 22530}, {8549, 18440}, {8780, 32139}, {9654, 22980}, {9655, 18978}, {9668, 22965}, {9669, 22981}, {10540, 48669}, {12134, 18403}, {12162, 18859}, {12429, 18385}, {12702, 22941}, {17505, 42016}, {17814, 17822}, {18480, 22653}, {18493, 22476}, {18494, 22483}, {18496, 48507}, {18498, 48508}, {18501, 22524}, {18503, 22747}, {18508, 22943}, {18510, 19083}, {18512, 19084}, {18518, 22957}, {18519, 22956}, {18524, 22559}, {18526, 22969}, {18543, 22983}, {18545, 22982}, {18565, 38790}, {18569, 22555}, {22535, 43598}, {22585, 22978}, {22671, 45379}, {22675, 45380}, {22776, 26321}, {22945, 26336}, {22947, 26346}, {22963, 45381}, {22964, 45382}, {22968, 36749}, {22973, 36752}, {22976, 45384}, {22977, 45385}, {23251, 35860}, {23261, 35861}, {32375, 43821}, {41595, 45016}

X(48670) = reflection of X(i) in X(j) for these (i, j): (3, 22955), (1657, 22951), (12702, 22941), (18508, 22943), (18526, 22969), (22466, 22800), (22533, 5), (22550, 22750), (22653, 18480), (22979, 4)
X(48670) = crosssum of X(3) and X(43616)
X(48670) = orthologic center (anti-Ehrmann-mid, 3rd Hatzipolakis)
X(48670) = X(22466)-of-anti-Ehrmann-mid triangle
X(48670) = X(22533)-of-Johnson triangle
X(48670) = X(22955)-of-X3-ABC reflections triangle
X(48670) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (17814, 17837, 22834), (22466, 22800, 381)


X(48671) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO HUTSON EXTOUCH

Barycentrics    3*a^10-4*(b+c)*a^9-2*(4*b^2+13*b*c+4*c^2)*a^8+2*(b+c)*(5*b^2+12*b*c+5*c^2)*a^7+2*(4*b^2+9*b*c+4*c^2)*(b+c)^2*a^6-2*(b+c)*(3*b^4+3*c^4+2*b*c*(8*b^2+5*b*c+8*c^2))*a^5-2*(3*b^6+3*c^6-(7*b^4+7*c^4-3*b*c*(3*b^2-14*b*c+3*c^2))*b*c)*a^4-2*(b^2-c^2)*(b-c)^3*(b^2+8*b*c+c^2)*a^3+(5*b^4+5*c^4-2*b*c*(13*b^2+11*b*c+13*c^2))*(b^2-c^2)^2*a^2+2*(b^2-c^2)^3*(b-c)*(b^2+10*b*c+c^2)*a-2*(b^2-c^2)^4*(b-c)^2 : :
X(48671) = 3*X(3)-4*X(12864) = 3*X(381)-2*X(7160) = 3*X(381)-4*X(22801) = 5*X(3843)-4*X(12599) = 4*X(12260)-5*X(18493) = 3*X(12856)-2*X(12864)

The reciprocal orthologic center of these triangles is X(40).

X(48671) lies on these lines: {3, 12411}, {4, 12872}, {5, 12249}, {30, 9874}, {381, 7160}, {999, 12860}, {1657, 12120}, {3295, 12859}, {3843, 12599}, {8000, 18526}, {9654, 10059}, {9655, 18979}, {9668, 12863}, {9669, 10075}, {9898, 18480}, {12139, 18494}, {12200, 18501}, {12260, 18493}, {12333, 18524}, {12464, 45379}, {12465, 45380}, {12500, 18503}, {12631, 12858}, {12702, 12777}, {12731, 48668}, {12789, 18508}, {12801, 26336}, {12802, 26346}, {12857, 18519}, {12861, 45381}, {12862, 45382}, {12874, 18545}, {12875, 18543}, {13914, 45384}, {13978, 45385}, {16134, 48667}, {18496, 48509}, {18498, 48510}, {18499, 48664}, {18510, 19085}, {18512, 19086}, {22777, 26321}, {23251, 35862}, {23261, 35863}

X(48671) = reflection of X(i) in X(j) for these (i, j): (3, 12856), (1657, 12120), (7160, 22801), (9898, 18480), (12249, 5), (12631, 12858), (12702, 12777), (12872, 4), (18508, 12789), (18526, 8000)
X(48671) = orthologic center (anti-Ehrmann-mid, Hutson extouch)
X(48671) = X(7160)-of-anti-Ehrmann-mid triangle
X(48671) = X(12249)-of-Johnson triangle
X(48671) = X(12856)-of-X3-ABC reflections triangle
X(48671) = {X(7160), X(22801)}-harmonic conjugate of X(381)


X(48672) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO MIDHEIGHT

Barycentrics    3*a^10-4*(4*b^4-7*b^2*c^2+4*c^4)*a^6+18*(b^4-c^4)*(b^2-c^2)*a^4-(b^2-c^2)^2*(3*b^4+22*b^2*c^2+3*c^4)*a^2-2*(b^4-c^4)*(b^2-c^2)^3 : :
X(48672) = 3*X(3)-4*X(2883) = 5*X(3)-4*X(5894) = 11*X(3)-12*X(10192) = 7*X(3)-8*X(16252) = 3*X(3)-2*X(20427) = 4*X(5)-3*X(35450) = 2*X(2883)-3*X(5878) = 5*X(2883)-3*X(5894) = 11*X(2883)-9*X(10192) = 7*X(2883)-6*X(16252) = 5*X(5878)-2*X(5894) = 11*X(5878)-6*X(10192) = 7*X(5878)-4*X(16252) = 3*X(5878)-X(20427) = 11*X(5894)-15*X(10192) = 7*X(5894)-10*X(16252) = 6*X(5894)-5*X(20427) = 18*X(10192)-11*X(20427) = 2*X(12250)-3*X(35450) = 12*X(16252)-7*X(20427)

The reciprocal orthologic center of these triangles is X(4).

X(48672) lies on these lines: {3, 1661}, {4, 3426}, {5, 12250}, {20, 25712}, {26, 9919}, {30, 6193}, {52, 382}, {64, 381}, {133, 42457}, {146, 11413}, {154, 15696}, {399, 1498}, {403, 34469}, {541, 12163}, {550, 5656}, {999, 12950}, {1012, 25713}, {1147, 34622}, {1503, 5073}, {1514, 26937}, {1597, 45089}, {1656, 3357}, {3089, 32601}, {3295, 12940}, {3515, 32111}, {3526, 10606}, {3534, 5925}, {3627, 12324}, {3830, 14216}, {3843, 6247}, {3851, 5893}, {3853, 32064}, {4846, 11479}, {5055, 6696}, {5072, 40686}, {5076, 18381}, {5079, 23329}, {5663, 12429}, {6001, 48661}, {6241, 44438}, {6266, 26346}, {6267, 26336}, {6285, 9655}, {6624, 36965}, {7355, 9668}, {7387, 25715}, {7539, 43613}, {7973, 18526}, {8567, 15720}, {8780, 44240}, {8907, 11414}, {8991, 45384}, {9654, 10060}, {9669, 10076}, {9833, 17800}, {9899, 18480}, {9920, 12082}, {9937, 39568}, {10620, 11744}, {10675, 42130}, {10676, 42131}, {10721, 13148}, {11206, 15704}, {11381, 18494}, {11432, 13488}, {11455, 43599}, {12173, 12290}, {12174, 18560}, {12202, 18501}, {12244, 32534}, {12262, 18493}, {12335, 18524}, {12468, 45379}, {12469, 45380}, {12502, 18503}, {12702, 12779}, {12791, 18508}, {12920, 18519}, {12930, 18518}, {12986, 45381}, {12987, 45382}, {13094, 18545}, {13095, 18543}, {13491, 41715}, {13568, 18535}, {13980, 45385}, {15063, 35602}, {15681, 34782}, {15688, 17821}, {18383, 38335}, {18436, 36982}, {18439, 18440}, {18496, 48513}, {18498, 48514}, {18510, 19087}, {18512, 19088}, {18536, 46850}, {18913, 44226}, {18931, 44960}, {21851, 36990}, {22778, 26321}, {23251, 35864}, {23261, 35865}, {23328, 46219}, {26864, 35491}, {26917, 37197}, {30443, 40647}, {31978, 37481}, {33878, 41735}, {33923, 35260}, {34664, 44750}, {36201, 48679}

X(48672) = reflection of X(i) in X(j) for these (i, j): (3, 5878), (64, 22802), (382, 5895), (1657, 1498), (5925, 6759), (6241, 44544), (9899, 18480), (10620, 11744), (12250, 5), (12315, 6225), (12324, 3627), (12702, 12779), (13093, 4), (15105, 5893), (17800, 9833), (18436, 36982), (18508, 12791), (18526, 7973), (20427, 2883), (30443, 40647), (33878, 41735), (34780, 382)
X(48672) = orthologic center (anti-Ehrmann-mid, midheight)
X(48672) = X(64)-of-anti-Ehrmann-mid triangle
X(48672) = X(5878)-of-X3-ABC reflections triangle
X(48672) = X(12250)-of-Johnson triangle
X(48672) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5, 12250, 35450), (64, 22802, 381), (550, 5656, 14530), (2883, 20427, 3), (5878, 20427, 2883), (5925, 6759, 3534)


X(48673) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO 1st NEUBERG

Barycentrics    a^2*((b^2+c^2)*a^4+(b^4+5*b^2*c^2+c^4)*a^2-(b^2+c^2)*(2*b^4-b^2*c^2+2*c^4)) : :
X(48673) = 3*X(3)-4*X(39) = 5*X(3)-4*X(5188) = 3*X(3)-2*X(9821) = 5*X(3)-6*X(11171) = 7*X(3)-8*X(13334) = 11*X(3)-12*X(21163) = 2*X(3)-3*X(32447) = 2*X(39)-3*X(3095) = 5*X(39)-3*X(5188) = 10*X(39)-9*X(11171) = 7*X(39)-6*X(13334) = 11*X(39)-9*X(21163) = 8*X(39)-9*X(32447) = 3*X(1351)-2*X(13330) = 5*X(3095)-2*X(5188) = 3*X(3095)-X(9821) = 5*X(3095)-3*X(11171) = 7*X(3095)-4*X(13334) = 11*X(3095)-6*X(21163) = 4*X(3095)-3*X(32447)

The reciprocal orthologic center of these triangles is X(3).

X(48673) lies on these lines: {2, 32521}, {3, 6}, {4, 7779}, {5, 3314}, {20, 32448}, {30, 194}, {76, 381}, {140, 6194}, {262, 1656}, {298, 37333}, {299, 37332}, {315, 37243}, {376, 32516}, {382, 2782}, {384, 18501}, {524, 31981}, {538, 3830}, {542, 7890}, {548, 32522}, {550, 7709}, {698, 7758}, {726, 12699}, {730, 18525}, {732, 18440}, {999, 12836}, {1147, 19558}, {1154, 32444}, {1569, 38730}, {1657, 11257}, {1843, 22152}, {1916, 7754}, {1993, 6660}, {1994, 46546}, {3060, 11328}, {3097, 3579}, {3202, 9703}, {3295, 12837}, {3526, 11272}, {3534, 7757}, {3543, 20105}, {3552, 10351}, {3734, 18502}, {3818, 7855}, {3843, 6248}, {3851, 7697}, {3933, 18906}, {3934, 5055}, {5054, 7786}, {5476, 7822}, {5858, 6294}, {5859, 6581}, {5889, 31952}, {5969, 6309}, {6033, 7759}, {6179, 12042}, {6272, 26346}, {6273, 26336}, {6287, 34507}, {6314, 48678}, {6318, 48677}, {6683, 15694}, {7470, 7839}, {7750, 34734}, {7760, 14880}, {7767, 37345}, {7768, 9996}, {7778, 18806}, {7785, 40279}, {7787, 44224}, {7794, 19130}, {7795, 20423}, {7796, 9993}, {7845, 37004}, {7877, 9873}, {7882, 18500}, {7893, 32151}, {7896, 10356}, {7905, 43460}, {7906, 8782}, {7976, 18526}, {8148, 14839}, {8149, 9766}, {8667, 32189}, {8725, 41749}, {8992, 45384}, {9466, 19709}, {9654, 10063}, {9655, 18982}, {9668, 13077}, {9669, 10079}, {9902, 18480}, {9983, 18503}, {10335, 13571}, {11002, 37338}, {12143, 18494}, {12263, 18493}, {12338, 18524}, {12474, 45379}, {12475, 45380}, {12702, 12782}, {12773, 32454}, {12794, 18508}, {12923, 18519}, {12933, 18518}, {12992, 45381}, {12993, 45382}, {13109, 18545}, {13110, 18543}, {13111, 35930}, {13983, 45385}, {14984, 19597}, {15066, 21513}, {15681, 32450}, {15701, 44562}, {15703, 31239}, {15720, 40108}, {15819, 46219}, {16981, 37465}, {18496, 48515}, {18498, 48516}, {18510, 19089}, {18512, 19090}, {20854, 33586}, {21969, 36212}, {22486, 33237}, {22779, 26321}, {22868, 48655}, {22913, 48656}, {23251, 35866}, {23261, 35867}, {32134, 35925}, {32449, 46264}, {32451, 39899}, {32465, 42157}, {32466, 42158}, {32470, 42258}, {32471, 42259}, {33015, 42788}, {34938, 41481}, {37915, 38583}, {38383, 38743}, {38907, 39093}, {44437, 45186}, {44460, 47517}, {44464, 47519}

X(48673) = midpoint of X(i) and X(j) for these {i, j}: {382, 32520}, {7877, 9873}
X(48673) = reflection of X(i) in X(j) for these (i, j): (3, 3095), (20, 32448), (76, 14881), (1657, 11257), (3534, 7757), (7893, 32151), (9821, 39), (9902, 18480), (12188, 1916), (12251, 5), (12702, 12782), (12773, 32454), (13108, 4), (18508, 12794), (18526, 7976), (18906, 21850), (22728, 44434), (33878, 3094), (38730, 1569), (39899, 32451), (46264, 32449), (48663, 22728)
X(48673) = anticomplement of X(32521)
X(48673) = inverse of X(2076) in Stammler circle
X(48673) = inverse of X(5092) in 2nd Brocard circle
X(48673) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(43688)}} and {{A, B, C, X(32), X(14492)}}
X(48673) = orthologic center (anti-Ehrmann-mid, 1st Neuberg)
X(48673) = X(76)-of-anti-Ehrmann-mid triangle
X(48673) = X(3095)-of-X3-ABC reflections triangle
X(48673) = X(12251)-of-Johnson triangle
X(48673) = X(48673)-of-circumsymmedial triangle
X(48673) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 3095, 32447), (4, 13108, 48663), (32, 35002, 3), (39, 9821, 3), (39, 13330, 30435), (76, 14881, 381), (576, 30270, 3398), (1351, 35458, 6), (1351, 47618, 11842), (1657, 32519, 11257), (1670, 1671, 5092), (1689, 1690, 5007), (2080, 9737, 3), (3094, 46305, 9605), (3095, 9821, 39), (3098, 7772, 12054), (3098, 12054, 3), (3102, 3103, 13331), (3104, 3105, 6), (3398, 30270, 3), (3933, 21850, 44230), (5092, 35248, 3), (5111, 37517, 1351), (5188, 11171, 3), (7785, 43453, 40279), (9605, 33878, 3), (11272, 22712, 3526), (13108, 22728, 4), (32452, 46313, 6), (38596, 38597, 2076)


X(48674) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO 2nd NEUBERG

Barycentrics    3*a^8+2*(b^2+c^2)*a^6+3*b^2*c^2*a^4-(b^2+c^2)*(3*b^4-7*b^2*c^2+3*c^4)*a^2-2*(b^4-c^4)^2 : :
X(48674) = 3*X(3)-4*X(6292) = 3*X(3)-2*X(8725) = 3*X(4)-X(20088) = 2*X(83)-3*X(381) = 3*X(381)-4*X(22803) = 7*X(3526)-6*X(9751) = 5*X(3843)-4*X(6249) = 9*X(5054)-10*X(31268) = 9*X(5055)-8*X(6704) = 3*X(6287)-2*X(6292) = 3*X(6287)-X(8725) = 4*X(12206)-3*X(34682) = 4*X(12264)-5*X(18493) = 3*X(13111)-2*X(20088) = 5*X(31982)-3*X(34511)

The reciprocal orthologic center of these triangles is X(3).

X(48674) lies on these lines: {3, 2916}, {4, 5984}, {5, 12252}, {30, 2896}, {76, 382}, {83, 381}, {546, 7797}, {550, 46226}, {732, 18440}, {754, 3830}, {999, 12954}, {1657, 12122}, {3295, 12944}, {3526, 9751}, {3534, 31168}, {3627, 43453}, {3843, 6249}, {3851, 7834}, {3933, 5207}, {5054, 31268}, {5055, 6704}, {5079, 7943}, {5309, 14269}, {5989, 7752}, {6033, 35701}, {6274, 26346}, {6275, 26336}, {6313, 48678}, {6317, 48677}, {7861, 40238}, {7864, 40250}, {7977, 18526}, {8993, 45384}, {9654, 10064}, {9655, 18983}, {9668, 13078}, {9669, 10080}, {9821, 44772}, {9903, 18480}, {9990, 32151}, {11178, 35248}, {11645, 12054}, {12144, 18494}, {12206, 18501}, {12264, 18493}, {12339, 18524}, {12476, 45379}, {12477, 45380}, {12699, 17766}, {12702, 12783}, {12795, 18508}, {12924, 18519}, {12934, 18518}, {12994, 45381}, {12995, 45382}, {13112, 18545}, {13113, 18543}, {13984, 45385}, {15687, 19570}, {15688, 47005}, {18496, 48517}, {18498, 48518}, {18510, 19091}, {18512, 19092}, {22780, 26321}, {22870, 34508}, {22915, 34509}, {23251, 35868}, {23261, 35869}, {31982, 34511}, {35700, 38733}, {37332, 47611}, {37333, 47610}

X(48674) = reflection of X(i) in X(j) for these (i, j): (3, 6287), (83, 22803), (1657, 12122), (3534, 31168), (8725, 6292), (9821, 44772), (9903, 18480), (9990, 32151), (12188, 11606), (12252, 5), (12702, 12783), (13111, 4), (18508, 12795), (18526, 7977), (24273, 3818)
X(48674) = orthologic center (anti-Ehrmann-mid, 2nd Neuberg)
X(48674) = X(83)-of-anti-Ehrmann-mid triangle
X(48674) = X(6287)-of-X3-ABC reflections triangle
X(48674) = X(12252)-of-Johnson triangle
X(48674) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (83, 22803, 381), (6287, 8725, 6292), (6292, 8725, 3)


X(48675) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO REFLECTION

Barycentrics    3*a^10-6*(b^2+c^2)*a^8+(2*b^4+7*b^2*c^2+2*c^4)*a^6-3*(b^2+c^2)*b^2*c^2*a^4+(3*b^4+2*b^2*c^2+3*c^4)*(b^2-c^2)^2*a^2-2*(b^4-c^4)*(b^2-c^2)^3 : :
X(48675) = 3*X(3)-4*X(1209) = 7*X(3)-8*X(32348) = 7*X(4)-4*X(11803) = 3*X(4)-2*X(20424) = 2*X(54)-3*X(381) = 7*X(195)-8*X(11803) = 3*X(195)-4*X(20424) = 3*X(381)-4*X(22804) = 2*X(548)-3*X(21357) = 3*X(568)-4*X(11808) = 2*X(1209)-3*X(6288) = 7*X(1209)-6*X(32348) = 3*X(2917)-2*X(34785) = 3*X(3830)-X(12316) = 3*X(3830)-2*X(15800) = 3*X(3830)-4*X(32340) = 7*X(6288)-4*X(32348) = 6*X(11803)-7*X(20424) = X(12316)-4*X(32340) = 4*X(20299)-3*X(32345)

The reciprocal orthologic center of these triangles is X(4).

X(48675) lies on these lines: {3, 161}, {4, 195}, {5, 12254}, {20, 21230}, {30, 2888}, {54, 156}, {185, 6153}, {265, 13621}, {382, 1154}, {539, 3830}, {546, 36966}, {548, 21357}, {568, 11808}, {999, 12956}, {1539, 43580}, {1656, 10610}, {1657, 7691}, {2883, 48669}, {3090, 20584}, {3091, 8254}, {3146, 12325}, {3295, 12946}, {3426, 3519}, {3448, 45971}, {3526, 13565}, {3574, 3843}, {3845, 22051}, {3851, 10619}, {3853, 11271}, {5055, 6689}, {5076, 15801}, {5449, 37922}, {5663, 13368}, {5876, 32338}, {5889, 32196}, {5898, 17702}, {5965, 36990}, {6102, 7730}, {6146, 15037}, {6152, 12173}, {6242, 35480}, {6276, 26346}, {6277, 26336}, {6286, 12953}, {7356, 12943}, {7507, 9703}, {7547, 47360}, {7979, 18526}, {8995, 45384}, {9654, 10066}, {9655, 18984}, {9668, 13079}, {9669, 10082}, {9905, 18480}, {9908, 32332}, {9927, 18378}, {9985, 18503}, {10024, 32354}, {10224, 32609}, {10255, 32351}, {10274, 10540}, {10539, 11597}, {10620, 33565}, {10628, 18439}, {10677, 42094}, {10678, 42093}, {10733, 32137}, {10895, 47378}, {11442, 41596}, {11572, 22115}, {11576, 18494}, {11801, 21451}, {11804, 44235}, {12084, 15124}, {12134, 18403}, {12208, 18501}, {12266, 18493}, {12278, 34514}, {12291, 45959}, {12295, 22979}, {12300, 44438}, {12341, 18524}, {12480, 45379}, {12481, 45380}, {12702, 12785}, {12797, 18508}, {12926, 18519}, {12936, 18518}, {12965, 23251}, {12971, 23261}, {12998, 45381}, {12999, 45382}, {13121, 18545}, {13122, 18543}, {13365, 15043}, {13561, 37955}, {13986, 45385}, {14049, 46686}, {14130, 30522}, {14516, 31724}, {14627, 44076}, {15038, 45970}, {15087, 34799}, {15089, 46261}, {16655, 18325}, {17846, 18561}, {18350, 18383}, {18356, 18559}, {18404, 32346}, {18435, 34786}, {18440, 22815}, {18451, 32365}, {18496, 48521}, {18498, 48522}, {18510, 19095}, {18512, 19096}, {18513, 35197}, {18565, 20427}, {19468, 21659}, {21308, 43582}, {22781, 26321}, {22816, 42016}, {25739, 43809}, {26917, 38724}, {32063, 32359}, {32352, 34783}, {34798, 43895}, {34864, 41171}, {40632, 44870}, {43845, 45731}, {44407, 47748}

X(48675) = midpoint of X(i) and X(j) for these {i, j}: {3146, 12325}, {12111, 13423}
X(48675) = reflection of X(i) in X(j) for these (i, j): (3, 6288), (20, 21230), (54, 22804), (185, 6153), (195, 4), (1657, 7691), (5889, 32196), (9905, 18480), (10620, 33565), (12254, 5), (12307, 2888), (12316, 15800), (12702, 12785), (14049, 46686), (15800, 32340), (18508, 12797), (18526, 7979), (32338, 5876), (32339, 13368), (34783, 32352), (36966, 546), (40632, 44870), (42016, 22816), (43580, 1539)
X(48675) = orthologic center (anti-Ehrmann-mid, reflection)
X(48675) = X(54)-of-anti-Ehrmann-mid triangle
X(48675) = X(6288)-of-X3-ABC reflections triangle
X(48675) = X(12254)-of-Johnson triangle
X(48675) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 9920, 44515), (54, 22804, 381), (265, 45286, 13621), (3830, 12316, 15800), (11597, 18430, 32395), (15800, 32340, 3830)


X(48676) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO 1st SCHIFFLER

Barycentrics    a*(a^9+2*(b+c)*a^8-2*(5*b^2-4*b*c+5*c^2)*a^7-2*(b+c)*(b^2+b*c+c^2)*a^6+(24*b^4+24*c^4-(22*b^2-9*b*c+22*c^2)*b*c)*a^5-2*(b^2-c^2)*(b-c)*(3*b^2+4*b*c+3*c^2)*a^4-(22*b^6+22*c^6-(20*b^4+20*c^4+(b^2-8*b*c+c^2)*b*c)*b*c)*a^3+2*(b^2-c^2)*(b-c)*(5*b^4+5*c^4+b*c*(9*b^2+4*b*c+9*c^2))*a^2+(b^4-c^4)*(b^2-c^2)*(7*b^2-6*b*c+7*c^2)*a-4*(b^2-c^2)^4*(b+c)) : :
X(48676) = 3*X(3)-4*X(13089) = 3*X(381)-2*X(10266) = 3*X(381)-4*X(22805) = 5*X(3843)-4*X(12600) = 4*X(12267)-5*X(18493) = 3*X(12919)-2*X(13089)

The reciprocal orthologic center of these triangles is X(79).

X(48676) lies on these lines: {3, 7701}, {4, 13126}, {5, 12255}, {30, 12849}, {381, 10266}, {999, 12957}, {1657, 12556}, {3295, 12947}, {3843, 12600}, {6595, 12773}, {9654, 13128}, {9655, 18985}, {9668, 13080}, {9669, 13129}, {10896, 18244}, {12146, 18494}, {12209, 18501}, {12247, 38756}, {12267, 18493}, {12342, 18524}, {12409, 18480}, {12482, 45379}, {12483, 45380}, {12504, 18503}, {12702, 12786}, {12745, 48668}, {12798, 18508}, {12807, 26336}, {12808, 26346}, {12927, 18519}, {12937, 18518}, {13000, 45381}, {13001, 45382}, {13100, 18526}, {13130, 18545}, {13131, 18543}, {13919, 45384}, {13987, 45385}, {16138, 23015}, {16145, 48667}, {18496, 48523}, {18498, 48524}, {18510, 19097}, {18512, 19098}, {22782, 26321}, {23251, 35870}, {23261, 35871}

X(48676) = reflection of X(i) in X(j) for these (i, j): (3, 12919), (1657, 12556), (10266, 22805), (12255, 5), (12409, 18480), (12702, 12786), (12773, 6595), (13126, 4), (18508, 12798), (18526, 13100)
X(48676) = orthologic center (anti-Ehrmann-mid, 1st Schiffler)
X(48676) = X(10266)-of-anti-Ehrmann-mid triangle
X(48676) = X(12255)-of-Johnson triangle
X(48676) = X(12919)-of-X3-ABC reflections triangle
X(48676) = {X(10266), X(22805)}-harmonic conjugate of X(381)


X(48677) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO 1st TRI-SQUARES-CENTRAL

Barycentrics    16*S^3+9*a^6-6*(b^2+c^2)*a^4+3*(b^2+c^2)^2*a^2-6*(b^4-c^4)*(b^2-c^2) : :
X(48677) = 3*X(3)-4*X(13701) = 3*X(381)-2*X(1327) = 3*X(381)-4*X(22806) = X(3534)+2*X(13691) = 5*X(3843)-4*X(13687) = 4*X(13667)-5*X(18493) = 3*X(13692)-2*X(13701)

The reciprocal orthologic center of these triangles is X(13665).

X(48677) lies on these lines: {2, 8780}, {3, 13680}, {4, 13713}, {5, 13674}, {30, 488}, {381, 486}, {542, 8980}, {591, 3830}, {999, 13696}, {1503, 9757}, {1657, 13666}, {3295, 13695}, {3534, 13691}, {3818, 13847}, {3843, 13687}, {3845, 33456}, {5055, 45377}, {6231, 38744}, {6302, 22872}, {6303, 22917}, {6317, 48674}, {6318, 48673}, {9654, 13714}, {9655, 18986}, {9668, 13699}, {9669, 13715}, {9892, 13710}, {12702, 13688}, {13667, 18493}, {13668, 18494}, {13672, 18501}, {13675, 18524}, {13679, 18480}, {13682, 45379}, {13683, 45380}, {13685, 18503}, {13689, 18508}, {13690, 26336}, {13693, 18519}, {13694, 18518}, {13697, 45381}, {13698, 45382}, {13702, 18526}, {13716, 18545}, {13717, 18543}, {13920, 45384}, {13988, 45385}, {15682, 18539}, {15703, 45378}, {18496, 48525}, {18498, 48526}, {18510, 19099}, {18512, 22541}, {19709, 45376}, {22726, 48663}, {22783, 26321}, {22807, 42274}, {22882, 48665}, {22927, 48666}, {23251, 35872}, {23261, 35873}, {26438, 41099}, {32787, 39899}, {32808, 33878}, {45554, 48662}

X(48677) = midpoint of X(13691) and X(13712)
X(48677) = reflection of X(i) in X(j) for these (i, j): (3, 13692), (1327, 22806), (1657, 13666), (3534, 13712), (12702, 13688), (13674, 5), (13679, 18480), (13713, 4), (18508, 13689), (18526, 13702), (33456, 3845)
X(48677) = orthologic center (anti-Ehrmann-mid, 1st tri-squares-central)
X(48677) = X(1327)-of-anti-Ehrmann-mid triangle
X(48677) = X(13674)-of-Johnson triangle
X(48677) = X(13692)-of-X3-ABC reflections triangle
X(48677) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 18440, 48678), (1327, 22616, 32788), (1327, 22806, 381)


X(48678) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    -16*S^3+9*a^6-6*(b^2+c^2)*a^4+3*(b^2+c^2)^2*a^2-6*(b^4-c^4)*(b^2-c^2) : :
X(48678) = 3*X(3)-4*X(13821) = 3*X(381)-2*X(1328) = 3*X(381)-4*X(22807) = X(3534)+2*X(13810) = 5*X(3843)-4*X(13807) = 4*X(13787)-5*X(18493) = 3*X(13812)-2*X(13821)

The reciprocal orthologic center of these triangles is X(13785).

X(48678) lies on these lines: {2, 8780}, {3, 13800}, {4, 13836}, {5, 13794}, {30, 487}, {381, 485}, {542, 13847}, {999, 13816}, {1503, 9758}, {1657, 13786}, {1991, 3830}, {3295, 13815}, {3534, 13810}, {3818, 13846}, {3843, 13807}, {3845, 33457}, {5055, 45378}, {6230, 38744}, {6306, 22874}, {6307, 22919}, {6313, 48674}, {6314, 48673}, {9654, 13837}, {9655, 18987}, {9668, 13819}, {9669, 13838}, {9894, 13830}, {12702, 13808}, {13787, 18493}, {13788, 18494}, {13792, 18501}, {13795, 18524}, {13799, 18480}, {13802, 45379}, {13803, 45380}, {13805, 18503}, {13809, 18508}, {13811, 26346}, {13813, 18519}, {13814, 18518}, {13817, 45381}, {13818, 45382}, {13822, 18526}, {13839, 18545}, {13840, 18543}, {13848, 45384}, {13849, 45385}, {15682, 26438}, {15703, 45377}, {18496, 48527}, {18498, 48528}, {18510, 19101}, {18512, 19100}, {18539, 41099}, {19709, 45375}, {22727, 48663}, {22784, 26321}, {22806, 42277}, {22883, 48665}, {22928, 48666}, {23251, 35874}, {23261, 35875}, {32788, 39899}, {32809, 33878}, {45555, 48662}

X(48678) = midpoint of X(13810) and X(13835)
X(48678) = reflection of X(i) in X(j) for these (i, j): (3, 13812), (1328, 22807), (1657, 13786), (3534, 13835), (12702, 13808), (13794, 5), (13799, 18480), (13836, 4), (18508, 13809), (18526, 13822), (33457, 3845)
X(48678) = orthologic center (anti-Ehrmann-mid, 2nd tri-squares-central)
X(48678) = X(1328)-of-anti-Ehrmann-mid triangle
X(48678) = X(13794)-of-Johnson triangle
X(48678) = X(13812)-of-X3-ABC reflections triangle
X(48678) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 18440, 48677), (1328, 22645, 32787), (1328, 22807, 381)


X(48679) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO WALSMITH

Barycentrics    a^2*(a^10-7*(b^2+c^2)*a^8+(10*b^4+b^2*c^2+10*c^4)*a^6+2*(b^4-3*b^2*c^2+c^4)*(b^2+c^2)*a^4-(11*b^8+11*c^8-b^2*c^2*(11*b^4-4*b^2*c^2+11*c^4))*a^2+(b^4-c^4)*(b^2-c^2)*(5*b^4+4*b^2*c^2+5*c^4)) : :
X(48679) = 3*X(3)-4*X(6593) = 5*X(3)-6*X(15462) = 2*X(3)-3*X(45016) = 3*X(6)-2*X(32305) = 2*X(67)-3*X(381) = 2*X(74)-3*X(5050) = 3*X(113)-2*X(32257) = 4*X(182)-3*X(15041) = 3*X(381)-4*X(32271) = 3*X(399)-2*X(2930) = 4*X(575)-3*X(5621) = 4*X(576)-3*X(39562) = 2*X(6593)-3*X(9970) = 10*X(6593)-9*X(15462) = 8*X(6593)-9*X(45016) = 5*X(9970)-3*X(15462) = 4*X(9970)-3*X(45016) = 3*X(10620)-4*X(32305) = 4*X(15462)-5*X(45016) = 2*X(16010)-3*X(39562)

The reciprocal orthologic center of these triangles is X(125).

X(48679) lies on these lines: {3, 1177}, {4, 32306}, {5, 32247}, {6, 10620}, {23, 45082}, {30, 11061}, {67, 381}, {74, 5050}, {110, 33878}, {113, 32257}, {146, 3564}, {182, 15041}, {382, 542}, {399, 511}, {524, 18325}, {541, 5095}, {575, 5621}, {576, 16010}, {895, 1351}, {999, 32290}, {1350, 19140}, {1352, 38789}, {1503, 38790}, {1593, 11482}, {1597, 34802}, {1657, 32233}, {1995, 15106}, {2777, 32264}, {2854, 12308}, {2892, 10297}, {2937, 15039}, {3098, 15040}, {3292, 37928}, {3295, 32289}, {3448, 21850}, {3534, 34319}, {3843, 32274}, {5055, 6698}, {5085, 25556}, {5093, 11579}, {5102, 9976}, {5181, 5655}, {5480, 38724}, {5609, 7387}, {5864, 13859}, {5865, 13858}, {6293, 8538}, {7545, 37473}, {7728, 18440}, {8542, 18435}, {9143, 37900}, {9654, 32307}, {9655, 32243}, {9668, 32297}, {9669, 32308}, {9715, 15034}, {9968, 48669}, {10117, 34779}, {10264, 14853}, {10272, 10519}, {10510, 35001}, {10605, 34470}, {10706, 32244}, {11179, 41595}, {11284, 12824}, {11422, 19504}, {11511, 11562}, {11799, 47558}, {11898, 14982}, {12017, 12041}, {12164, 12271}, {12167, 12292}, {12244, 25321}, {12702, 32278}, {12902, 31670}, {14677, 25406}, {14848, 15118}, {15046, 24206}, {15081, 38136}, {15681, 40342}, {18374, 37958}, {18449, 34146}, {18480, 32261}, {18493, 32238}, {18494, 32239}, {18496, 48529}, {18498, 48530}, {18501, 32242}, {18503, 32268}, {18508, 32279}, {18510, 32252}, {18512, 32253}, {18518, 32288}, {18519, 32287}, {18524, 32256}, {18526, 32298}, {18543, 32310}, {18545, 32309}, {18570, 43697}, {20423, 25328}, {21358, 25566}, {22151, 37950}, {23251, 35876}, {23261, 35877}, {25329, 46264}, {25335, 32273}, {26321, 32270}, {26336, 32280}, {26346, 32281}, {30714, 34726}, {31861, 32251}, {32063, 38885}, {32265, 45379}, {32266, 45380}, {32275, 38791}, {32295, 45381}, {32296, 45382}, {32303, 45384}, {32304, 45385}, {32313, 44206}, {35458, 38661}, {36201, 48672}

X(48679) = midpoint of X(12308) and X(44456)
X(48679) = reflection of X(i) in X(j) for these (i, j): (3, 9970), (67, 32271), (1350, 19140), (1351, 10752), (1657, 32233), (3448, 21850), (3534, 34319), (10117, 34779), (10620, 6), (11898, 14982), (12702, 32278), (12902, 31670), (16010, 576), (18440, 7728), (18508, 32279), (18526, 32298), (25335, 32273), (32247, 5), (32254, 14094), (32261, 18480), (32275, 38791), (32306, 4), (33878, 110), (35001, 10510), (44206, 32313), (46264, 25329)
X(48679) = orthologic center (anti-Ehrmann-mid, Walsmith)
X(48679) = X(67)-of-anti-Ehrmann-mid triangle
X(48679) = X(9970)-of-X3-ABC reflections triangle
X(48679) = X(32247)-of-Johnson triangle
X(48679) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 9970, 45016), (67, 32271, 381), (576, 16010, 39562), (1350, 19140, 32609)


X(48680) = PARALLELOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO ANTI-INNER-GARCIA

Barycentrics    3*a^7-3*(b+c)*a^6-(4*b^2-5*b*c+4*c^2)*a^5+2*(b+c)*(2*b^2-b*c+2*c^2)*a^4-(b^2+c^2)*(b^2+b*c+c^2)*a^3+(b^4-c^4)*(b-c)*a^2+2*(b^2-c^2)^2*(b-c)^2*a-2*(b^2-c^2)^3*(b-c) : :
X(48680) = 3*X(3)-4*X(11) = 7*X(3)-8*X(6713) = 11*X(3)-12*X(21154) = 5*X(3)-4*X(24466) = 3*X(4)-2*X(11698) = 3*X(4)-X(20095) = 4*X(4)-3*X(38755) = 7*X(11)-6*X(6713) = 2*X(11)-3*X(10738) = 11*X(11)-9*X(21154) = 5*X(11)-3*X(24466) = 4*X(6713)-7*X(10738) = 10*X(6713)-7*X(24466) = 11*X(10738)-6*X(21154) = 5*X(10738)-2*X(24466) = 4*X(11698)-3*X(12331) = 8*X(11698)-9*X(38755) = 3*X(12331)-2*X(20095) = 2*X(12331)-3*X(38755) = 15*X(21154)-11*X(24466)

The reciprocal parallelogic center of these triangles is X(36).

X(48680) lies on the circumcircle of anti-Ehrmann-mid triangle and these lines: {3, 11}, {4, 11698}, {5, 13199}, {20, 1484}, {30, 149}, {80, 12702}, {100, 381}, {104, 1657}, {119, 3843}, {153, 3627}, {214, 18493}, {382, 952}, {390, 6923}, {399, 10767}, {517, 9897}, {528, 3830}, {999, 13274}, {1317, 9655}, {1320, 18526}, {1387, 4305}, {1482, 7972}, {1656, 33814}, {1699, 22935}, {1768, 28146}, {1862, 18494}, {2771, 3901}, {2783, 38744}, {2787, 38733}, {2800, 40265}, {2801, 38768}, {2802, 18525}, {2806, 48681}, {2829, 5073}, {2830, 38800}, {2831, 48658}, {2886, 28453}, {2932, 37251}, {3035, 5055}, {3065, 24468}, {3295, 13273}, {3476, 10247}, {3526, 34474}, {3534, 10707}, {3579, 37718}, {3583, 35000}, {3586, 6797}, {3656, 33337}, {3738, 38780}, {3851, 10993}, {4316, 22765}, {5054, 31272}, {5070, 23513}, {5072, 38141}, {5076, 22799}, {5083, 18541}, {5218, 6980}, {5528, 18482}, {5541, 18480}, {5727, 25413}, {5759, 5825}, {5790, 6246}, {5848, 44456}, {6154, 14269}, {6174, 19709}, {6224, 22791}, {6264, 28160}, {6326, 22793}, {6407, 13913}, {6408, 13977}, {6667, 15694}, {7489, 33108}, {7951, 11849}, {8674, 12902}, {9024, 18440}, {9654, 10087}, {9670, 16173}, {9955, 15015}, {10073, 36279}, {10246, 12119}, {10620, 10778}, {10711, 38335}, {10755, 39899}, {10768, 13188}, {10769, 12188}, {10770, 38574}, {10771, 38579}, {10772, 38572}, {10773, 38589}, {10774, 38590}, {10775, 38591}, {10776, 38592}, {10777, 38573}, {10779, 38593}, {10780, 13115}, {10781, 15155}, {10782, 15154}, {11235, 18515}, {11604, 16117}, {12247, 28174}, {12653, 28204}, {12699, 48667}, {12764, 35448}, {13194, 18501}, {13205, 18524}, {13228, 45379}, {13230, 45380}, {13235, 18503}, {13268, 18508}, {13269, 26336}, {13270, 26346}, {13271, 18519}, {13272, 18518}, {13275, 45381}, {13276, 45382}, {13278, 18545}, {13279, 18543}, {13665, 48714}, {13785, 48715}, {13922, 45384}, {13991, 45385}, {15171, 47032}, {15310, 18330}, {15681, 38761}, {15696, 38693}, {15701, 45310}, {15703, 31235}, {15718, 38069}, {15720, 34126}, {15723, 38084}, {15863, 34718}, {17800, 37726}, {18240, 18530}, {18481, 21630}, {18496, 48533}, {18498, 48534}, {18510, 19112}, {18512, 19113}, {18521, 48707}, {18523, 48708}, {18539, 48711}, {18542, 25438}, {18544, 48713}, {20418, 38754}, {22560, 26321}, {23251, 35882}, {23261, 35883}, {25416, 34748}, {26438, 48712}, {28459, 45043}, {31512, 38586}, {34789, 36999}, {35251, 39692}, {35856, 42263}, {35857, 42264}, {38637, 38759}, {38760, 46219}, {45375, 48703}, {45376, 48704}, {45377, 48705}, {45378, 48706}

X(48680) = reflection of X(i) in X(j) for these (i, j): (3, 10738), (20, 1484), (100, 22938), (153, 3627), (382, 10724), (399, 10767), (1482, 14217), (1657, 104), (3534, 10707), (5528, 18482), (5541, 18480), (6224, 22791), (6326, 22793), (10620, 10778), (12188, 10769), (12331, 4), (12702, 80), (12773, 149), (13115, 10780), (13188, 10768), (13199, 5), (15154, 10782), (15155, 10781), (16117, 11604), (17800, 38753), (18481, 21630), (18508, 13268), (18526, 1320), (20095, 11698), (35000, 3583), (35448, 12764), (38572, 10772), (38573, 10777), (38574, 10770), (38579, 10771), (38586, 31512), (38589, 10773), (38590, 10774), (38591, 10775), (38592, 10776), (38593, 10779), (38665, 22799), (38753, 37726), (38756, 382), (39899, 10755), (48667, 12699)
X(48680) = inverse of X(14667) in Stammler circle
X(48680) = parallelogic center (anti-Ehrmann-mid, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48680) = X(100)-of-anti-Ehrmann-mid triangle
X(48680) = X(10738)-of-X3-ABC reflections triangle
X(48680) = X(13199)-of-Johnson triangle
X(48680) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 12331, 38755), (4, 20095, 11698), (100, 22938, 381), (5070, 38636, 38762), (11698, 20095, 12331), (23513, 38762, 5070)


X(48681) = PARALLELOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    (-a^2+b^2+c^2)*(3*a^12-3*(b^2+c^2)*a^10-(2*b^4-7*b^2*c^2+2*c^4)*a^8+4*(b^4-c^4)*(b^2-c^2)*a^6-(b^2-c^2)^2*(3*b^4-b^2*c^2+3*c^4)*a^4-(b^8-c^8)*a^2*(b^2-c^2)+2*(b^4+c^4)*(b^2-c^2)^4) : :
X(48681) = 3*X(3)-4*X(127) = 5*X(3)-4*X(14689) = 7*X(3)-8*X(34841) = 2*X(112)-3*X(381) = 2*X(127)-3*X(10749) = 5*X(127)-3*X(14689) = 7*X(127)-6*X(34841) = 4*X(132)-5*X(3843) = 3*X(381)-4*X(19163) = 3*X(382)-2*X(44988) = 5*X(1656)-4*X(38608) = 7*X(3526)-6*X(38699) = 3*X(10735)-X(44988) = 4*X(10735)-X(48658) = 5*X(10749)-2*X(14689) = 7*X(10749)-4*X(34841) = 2*X(12253)-3*X(13115) = X(12253)-3*X(13219) = 7*X(14689)-10*X(34841) = 4*X(44988)-3*X(48658)

The reciprocal parallelogic center of these triangles is X(10313).

X(48681) lies on the circumcircle of anti-Ehrmann-mid triangle and these lines: {3, 114}, {4, 13310}, {5, 13200}, {30, 12253}, {112, 381}, {132, 3843}, {339, 10722}, {382, 10735}, {999, 13297}, {1297, 1657}, {1656, 38608}, {2781, 18440}, {2799, 38733}, {2806, 48680}, {2825, 38768}, {2831, 38756}, {2853, 38780}, {3014, 15905}, {3295, 13296}, {3320, 9655}, {3526, 38699}, {3534, 10718}, {3627, 12384}, {3830, 12918}, {3851, 14900}, {5055, 6720}, {5070, 38639}, {5076, 19160}, {6020, 9668}, {6407, 13918}, {6408, 13985}, {9517, 12902}, {9530, 15684}, {9654, 13311}, {9669, 13312}, {10705, 18526}, {10766, 39899}, {10780, 12773}, {11722, 18493}, {12408, 28146}, {12702, 13280}, {13166, 18494}, {13195, 18501}, {13206, 18524}, {13221, 18480}, {13229, 45379}, {13231, 45380}, {13236, 18503}, {13281, 18508}, {13282, 26336}, {13283, 26346}, {13294, 18519}, {13295, 18518}, {13298, 45381}, {13299, 45382}, {13313, 18545}, {13314, 18543}, {13923, 45384}, {13992, 45385}, {15696, 38717}, {18437, 18564}, {18496, 48537}, {18498, 48538}, {18510, 19114}, {18512, 19115}, {19162, 26321}, {23251, 35880}, {23261, 35881}, {34163, 38321}, {35828, 42263}, {35829, 42264}

X(48681) = reflection of X(i) in X(j) for these (i, j): (3, 10749), (112, 19163), (382, 10735), (1657, 1297), (3534, 10718), (12384, 3627), (12702, 13280), (12773, 10780), (13115, 13219), (13200, 5), (13221, 18480), (13310, 4), (18508, 13281), (18526, 10705), (38676, 19160), (39899, 10766), (48658, 382)
X(48681) = inverse of X(39857) in Stammler circle
X(48681) = parallelogic center (anti-Ehrmann-mid, T) for these triangles T: {1st anti-orthosymmedial, 1st orthosymmedial}
X(48681) = X(112)-of-anti-Ehrmann-mid triangle
X(48681) = X(10749)-of-X3-ABC reflections triangle
X(48681) = X(13200)-of-Johnson triangle
X(48681) = {X(112), X(19163)}-harmonic conjugate of X(381)


X(48682) = CYCLOLOGIC CENTER OF THESE TRIANGLES: ANTI-EHRMANN-MID TO ANTI-EULER

Barycentrics    3*a^16-3*(b^2+c^2)*a^14-(19*b^4-32*b^2*c^2+19*c^4)*a^12+(b^2+c^2)*(37*b^4-68*b^2*c^2+37*c^4)*a^10-(5*b^8+5*c^8+(64*b^4-141*b^2*c^2+64*c^4)*b^2*c^2)*a^8-(b^2+c^2)*(33*b^8+33*c^8-(130*b^4-197*b^2*c^2+130*c^4)*b^2*c^2)*a^6+(23*b^8+23*c^8+2*(16*b^4-31*b^2*c^2+16*c^4)*b^2*c^2)*(b^2-c^2)^2*a^4-(b^4-c^4)*(b^2-c^2)^3*(b^4+26*b^2*c^2+c^4)*a^2-2*(b^4+3*b^2*c^2+c^4)*(b^2-c^2)^6 : :

The reciprocal cyclologic center of these triangles is X(48683).

X(48682) lies on the circumcircle of anti-Ehrmann-mid triangle and these lines: {4, 10264}, {5, 48683}

X(48682) = cyclologic center (anti-Ehrmann-mid, anti-Euler)
X(48682) = X(48683)-of-Johnson triangle
X(48682) = reflection of X(48683) in X(5)


X(48683) = CYCLOLOGIC CENTER OF THESE TRIANGLES: ANTI-EULER TO ANTI-EHRMANN-MID

Barycentrics    3*a^16-4*(b^2+c^2)*a^14-6*(3*b^4-5*b^2*c^2+3*c^4)*a^12+2*(b^2+c^2)*(23*b^4-42*b^2*c^2+23*c^4)*a^10-3*(10*b^8+10*c^8+b^2*c^2*(10*b^4-41*b^2*c^2+10*c^4))*a^8-2*(b^2+c^2)*(4*b^8+4*c^8-b^2*c^2*(41*b^4-76*b^2*c^2+41*c^4))*a^6+(14*b^8-43*b^4*c^4+14*c^8)*(b^2-c^2)^2*a^4-2*(b^4-c^4)*(b^2-c^2)^3*(b^4+7*b^2*c^2+c^4)*a^2-(b^2+c^2)^2*(b^2-c^2)^6 : :

The reciprocal cyclologic center of these triangles is X(48682).

X(48683) lies on the circumcircle of anti-Euler triangle and these lines: {3, 146}, {5, 48682}, {376, 827}

X(48683) = cyclologic center (anti-Euler, anti-Ehrmann-mid)
X(48683) = X(48682)-of-Johnson triangle
X(48683) = reflection of X(48682) in X(5)

leftri

Centers related to anti-inner-Garcia triangle: X(48684)-X(48720)

rightri

This preamble and centers X(48684)-X(48720) were contributed by César Eliud Lozada, May 13, 2022.

Anti-inner-Garcia triangle was introduced in the preamble just before X(45345).


X(48684) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU CENTERS TO ANTI-INNER-GARCIA

Barycentrics    a*(2*(a^3-c*a^2-(b-c)^2*a-(b^2-c^2)*c)*(a^3-b*a^2-(b-c)^2*a+(b^2-c^2)*b)*S+2*(b^2+b*c+c^2)*a^6-2*(b+c)*(b^2+b*c+c^2)*a^5-(4*b^4+4*c^4-7*b*c*(b^2+c^2))*a^4+4*(b^2-c^2)*(b-c)*(b^2+b*c+c^2)*a^3+2*(b^4+c^4-2*b*c*(b^2+b*c+c^2))*(b-c)^2*a^2-2*(b^2-c^2)*(b-c)^3*(b^2+b*c+c^2)*a-(b^2-c^2)^2*b*c*(b^2+c^2)) : :
X(48684) = 3*X(104)-X(12753) = X(12753)+3*X(12754) = 2*X(12753)-3*X(48685) = 2*X(12754)+X(48685)

The reciprocal orthologic center of these triangles is X(2077).

X(48684) lies on the circumcircle of 1st anti-Kenmotu centers triangle and these lines: {3, 48686}, {6, 104}, {11, 45404}, {100, 12305}, {119, 45472}, {153, 492}, {952, 9733}, {1317, 45470}, {1768, 45426}, {2800, 45713}, {2829, 13748}, {3102, 35857}, {6289, 10742}, {9913, 45428}, {10058, 45490}, {10074, 45492}, {10698, 45476}, {11715, 45398}, {12138, 45400}, {12199, 45402}, {12248, 45406}, {12332, 45416}, {12462, 45430}, {12463, 45432}, {12499, 45434}, {12751, 45444}, {12752, 45446}, {12761, 45454}, {12762, 45456}, {12763, 45458}, {12764, 45460}, {12765, 45467}, {12766, 45464}, {12773, 45488}, {12775, 45494}, {12776, 45496}, {13913, 45484}, {13977, 45487}, {22775, 45436}, {22799, 45438}, {35856, 45462}, {38602, 43119}, {38756, 45375}, {45345, 48464}, {45347, 48465}, {45411, 48687}, {45412, 48689}, {45415, 48688}, {45421, 48693}, {45422, 48694}, {45424, 48695}

X(48684) = midpoint of X(i) and X(j) for these {i, j}: {104, 12754}, {153, 48692}
X(48684) = reflection of X(i) in X(j) for these (i, j): (3, 48686), (48685, 104), (48703, 9733)
X(48684) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48684) = X(104)-of-1st anti-Kenmotu centers triangle
X(48684) = X(48686)-of-X3-ABC reflections triangle
X(48684) = {X(104), X(10759)}-harmonic conjugate of X(48700)


X(48685) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU CENTERS TO ANTI-INNER-GARCIA

Barycentrics    a*(-2*(a^3-c*a^2-(b-c)^2*a-(b^2-c^2)*c)*(a^3-b*a^2-(b-c)^2*a+(b^2-c^2)*b)*S+2*(b^2+b*c+c^2)*a^6-2*(b+c)*(b^2+b*c+c^2)*a^5-(4*b^4+4*c^4-7*b*c*(b^2+c^2))*a^4+4*(b^2-c^2)*(b-c)*(b^2+b*c+c^2)*a^3+2*(b^4+c^4-2*b*c*(b^2+b*c+c^2))*(b-c)^2*a^2-2*(b^2-c^2)*(b-c)^3*(b^2+b*c+c^2)*a-(b^2-c^2)^2*b*c*(b^2+c^2)) : :
X(48685) = 3*X(104)-X(12754) = 3*X(12753)+X(12754) = 2*X(12753)+X(48684) = 2*X(12754)-3*X(48684)

The reciprocal orthologic center of these triangles is X(2077).

X(48685) lies on the circumcircle of 2nd anti-Kenmotu centers triangle and these lines: {3, 48687}, {6, 104}, {11, 45405}, {100, 12306}, {119, 45473}, {153, 491}, {952, 9732}, {1317, 45471}, {1768, 45427}, {2800, 45714}, {2829, 13749}, {3103, 35856}, {6290, 10742}, {9913, 45429}, {10058, 45491}, {10074, 45493}, {10698, 45477}, {11715, 45399}, {12138, 45401}, {12199, 45403}, {12248, 45407}, {12332, 45417}, {12462, 45431}, {12463, 45433}, {12499, 45435}, {12751, 45445}, {12752, 45447}, {12761, 45455}, {12762, 45457}, {12763, 45459}, {12764, 45461}, {12765, 45465}, {12766, 45466}, {12773, 45489}, {12775, 45495}, {12776, 45497}, {13913, 45486}, {13977, 45485}, {22775, 45437}, {22799, 45439}, {35857, 45463}, {38602, 43118}, {38756, 45376}, {45346, 48465}, {45348, 48464}, {45410, 48686}, {45413, 48688}, {45414, 48689}, {45420, 48692}, {45423, 48694}, {45425, 48695}

X(48685) = midpoint of X(i) and X(j) for these {i, j}: {104, 12753}, {153, 48693}
X(48685) = reflection of X(i) in X(j) for these (i, j): (3, 48687), (48684, 104), (48704, 9732)
X(48685) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48685) = X(104)-of-2nd anti-Kenmotu centers triangle
X(48685) = X(48687)-of-X3-ABC reflections triangle
X(48685) = {X(104), X(10759)}-harmonic conjugate of X(48701)


X(48686) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO ANTI-INNER-GARCIA

Barycentrics    2*a*S*((4*a^6-4*(b+c)*a^5-8*(b-c)^2*a^4+4*(b+c)*(2*b^2-3*b*c+2*c^2)*a^3+2*(2*b^4+2*c^4-b*c*(7*b^2-8*b*c+7*c^2))*a^2-4*(b^3+c^3)*(b-c)^2*a-2*(b^2-c^2)^2*b*c)*S+2*(b^2+b*c+c^2)*a^6-2*(b+c)*(b^2+b*c+c^2)*a^5-(4*b^4+4*c^4-7*b*c*(b^2+c^2))*a^4+4*(b^3-c^3)*(b^2-c^2)*a^3+2*(b^4+c^4-2*b*c*(b^2+b*c+c^2))*(b-c)^2*a^2-2*(b^2-c^2)*(b-c)^2*(b^3-c^3)*a-(b^4-c^4)*(b^2-c^2)*b*c) : :
X(48686) = X(12754)+3*X(38693)

The reciprocal orthologic center of these triangles is X(2077).

X(48686) lies on the circumcircle of 1st anti-Kenmotu-free-vertices triangle and these lines: {3, 48684}, {11, 45506}, {39, 48701}, {100, 45498}, {104, 372}, {119, 641}, {153, 45508}, {182, 38602}, {952, 9739}, {1317, 45570}, {1768, 45530}, {2800, 45715}, {2829, 48466}, {5062, 48700}, {6566, 48715}, {7690, 33814}, {9737, 48706}, {9913, 45532}, {10058, 45580}, {10074, 45582}, {10698, 45572}, {10742, 45554}, {11715, 45500}, {12138, 45502}, {12199, 45504}, {12248, 45510}, {12332, 45520}, {12462, 45534}, {12463, 45536}, {12499, 45538}, {12751, 45546}, {12752, 45548}, {12753, 45550}, {12754, 38693}, {12761, 45556}, {12762, 45558}, {12763, 45560}, {12764, 45562}, {12765, 45569}, {12766, 45566}, {12773, 45578}, {12775, 45584}, {12776, 45586}, {13913, 45574}, {13977, 45577}, {19081, 45512}, {19082, 45515}, {22775, 45540}, {22799, 45542}, {35857, 45565}, {38756, 45377}, {45349, 48464}, {45351, 48465}, {45410, 48685}, {45516, 48689}, {45519, 48688}, {45522, 48692}, {45525, 48693}, {45526, 48694}, {45528, 48695}

X(48686) = midpoint of X(3) and X(48684)
X(48686) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48686) = X(48684)-of-anti-X3-ABC reflections triangle
X(48686) = X(104)-of-1st anti-Kenmotu-free-vertices triangle
X(48686) = reflection of X(i) in X(j) for these (i, j): (48687, 38602), (48705, 9739)


X(48687) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO ANTI-INNER-GARCIA

Barycentrics    -2*a*S*(-(4*a^6-4*(b+c)*a^5-8*(b-c)^2*a^4+4*(b+c)*(2*b^2-3*b*c+2*c^2)*a^3+2*(2*b^4+2*c^4-b*c*(7*b^2-8*b*c+7*c^2))*a^2-4*(b^3+c^3)*(b-c)^2*a-2*(b^2-c^2)^2*b*c)*S+2*(b^2+b*c+c^2)*a^6-2*(b+c)*(b^2+b*c+c^2)*a^5-(4*b^4+4*c^4-7*b*c*(b^2+c^2))*a^4+4*(b^3-c^3)*(b^2-c^2)*a^3+2*(b^4+c^4-2*b*c*(b^2+b*c+c^2))*(b-c)^2*a^2-2*(b^2-c^2)*(b-c)^2*(b^3-c^3)*a-(b^4-c^4)*(b^2-c^2)*b*c) : :
X(48687) = X(12753)+3*X(38693)

The reciprocal orthologic center of these triangles is X(2077).

X(48687) lies on the circumcircle of 2nd anti- Kenmotu-free-vertices triangle and these lines: {3, 48685}, {11, 45507}, {39, 48700}, {100, 45499}, {104, 371}, {119, 642}, {153, 45509}, {182, 38602}, {952, 9738}, {1317, 45571}, {1768, 45531}, {2800, 45716}, {2829, 48467}, {5058, 48701}, {6567, 48714}, {7692, 33814}, {9737, 48705}, {9913, 45533}, {10058, 45581}, {10074, 45583}, {10698, 45573}, {10742, 45555}, {11715, 45501}, {12138, 45503}, {12199, 45505}, {12248, 45511}, {12332, 45521}, {12462, 45535}, {12463, 45537}, {12499, 45539}, {12751, 45547}, {12752, 45549}, {12753, 38693}, {12754, 45551}, {12761, 45557}, {12762, 45559}, {12763, 45561}, {12764, 45563}, {12765, 45567}, {12766, 45568}, {12773, 45579}, {12775, 45585}, {12776, 45587}, {13913, 45576}, {13977, 45575}, {19081, 45514}, {19082, 45513}, {22775, 45541}, {22799, 45543}, {35856, 45564}, {38756, 45378}, {45350, 48465}, {45352, 48464}, {45411, 48684}, {45517, 48688}, {45518, 48689}, {45523, 48693}, {45524, 48692}, {45527, 48694}, {45529, 48695}

X(48687) = midpoint of X(3) and X(48685)
X(48687) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48687) = X(48685)-of-anti-X3-ABC reflections triangle
X(48687) = reflection of X(i) in X(j) for these (i, j): (48686, 38602), (48706, 9738)


X(48688) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO ANTI-INNER-GARCIA

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

The reciprocal orthologic center of these triangles is X(2077).

X(48688) lies on the circumcircle of anti-Lucas(+1) homothetic triangle and these lines: {11, 26328}, {100, 26292}, {104, 493}, {119, 5490}, {153, 26494}, {952, 48707}, {1317, 26353}, {1768, 26298}, {2800, 45718}, {2829, 48468}, {6464, 48689}, {9913, 26304}, {10058, 45612}, {10074, 45614}, {10698, 26495}, {10742, 26466}, {11715, 26367}, {12138, 26373}, {12199, 26427}, {12248, 26439}, {12332, 26493}, {12462, 45589}, {12463, 45591}, {12499, 26312}, {12751, 26442}, {12752, 26447}, {12753, 26337}, {12754, 26347}, {12761, 26488}, {12762, 26483}, {12763, 26477}, {12764, 26471}, {12766, 45603}, {12773, 45610}, {12775, 45615}, {12776, 26501}, {13913, 45607}, {13977, 45606}, {18521, 38756}, {19081, 26454}, {19082, 26460}, {22775, 26322}, {22799, 45593}, {26391, 48464}, {26415, 48465}, {26496, 48692}, {26497, 48693}, {26498, 38602}, {26499, 48694}, {26500, 48695}, {35856, 45601}, {35857, 45600}, {45413, 48685}, {45415, 48684}, {45517, 48687}, {45519, 48686}, {45596, 48701}, {45597, 48700}

X(48688) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48688) = X(104)-of-anti-Lucas(+1) homothetic triangle


X(48689) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO ANTI-INNER-GARCIA

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

The reciprocal orthologic center of these triangles is X(2077).

X(48689) lies on the circumcircle of anti-Lucas(-1) homothetic triangle and these lines: {11, 26329}, {100, 26293}, {104, 494}, {119, 5491}, {153, 26503}, {952, 48708}, {1317, 26354}, {1768, 26299}, {2800, 45717}, {2829, 48469}, {6464, 48688}, {9913, 26305}, {10058, 45611}, {10074, 45613}, {10698, 26504}, {10742, 26467}, {11715, 26368}, {12138, 26374}, {12199, 26428}, {12248, 26440}, {12332, 26502}, {12462, 45588}, {12463, 45590}, {12499, 26313}, {12751, 26443}, {12752, 26448}, {12753, 45594}, {12754, 26338}, {12761, 26489}, {12762, 26484}, {12763, 26478}, {12764, 26472}, {12765, 45604}, {12773, 45609}, {12775, 26511}, {12776, 26510}, {13913, 45605}, {13977, 45608}, {18523, 38756}, {19081, 26455}, {19082, 26461}, {22775, 26323}, {22799, 45592}, {26392, 48464}, {26416, 48465}, {26505, 48692}, {26506, 48693}, {26507, 38602}, {26508, 48694}, {26509, 48695}, {35856, 45599}, {35857, 45602}, {45412, 48684}, {45414, 48685}, {45516, 48686}, {45518, 48687}, {45595, 48700}, {45598, 48701}

X(48689) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48689) = X(104)-of-anti-Lucas(-1) homothetic triangle


X(48690) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO ANTI-INNER-GARCIA

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

The reciprocal orthologic center of these triangles is X(36).

X(48690) lies on the circumcircle of 1st anti-Parry triangle and these lines: {3, 48691}, {21, 104}, {99, 2826}, {100, 1296}, {900, 9145}, {2827, 45709}, {2854, 48710}, {9216, 9980}

X(48690) = orthologic center (1st anti-Parry, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48690) = X(48691)-of-ABC-X3 reflections triangle
X(48690) = X(100)-of-1st anti-Parry triangle
X(48690) = reflection of X(i) in X(j) for these (i, j): (48691, 3), (48709, 9145)


X(48691) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO ANTI-INNER-GARCIA

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

The reciprocal orthologic center of these triangles is X(36).

X(48691) lies on the circumcircle of 2nd anti-Parry triangle and these lines: {3, 48690}, {72, 74}, {98, 2826}, {104, 111}, {900, 9142}, {2827, 45710}, {2854, 48709}, {9215, 9978}

X(48691) = orthologic center (2nd anti-Parry, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48691) = reflection of X(74) in the line X(8674)X(9142)
X(48691) = X(48690)-of-ABC-X3 reflections triangle
X(48691) = X(100)-of-2nd anti-Parry triangle
X(48691) = reflection of X(i) in X(j) for these (i, j): (48690, 3), (48710, 9142)


X(48692) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO ANTI-INNER-GARCIA

Barycentrics    (3*a^7-3*(b+c)*a^6-(5*b^2-17*b*c+5*c^2)*a^5+(b+c)*(5*b^2-14*b*c+5*c^2)*a^4+(b^4+c^4-2*b*c*(5*b^2-11*b*c+5*c^2))*a^3-(b^2-c^2)*(b-c)*(b^2-10*b*c+c^2)*a^2+(b^2-7*b*c+c^2)*(b^2-c^2)^2*a-(b^2-c^2)^3*(b-c))*S+a*(2*(b^2+b*c+c^2)*a^6-2*(b+c)*(b^2+b*c+c^2)*a^5-(4*b^4+4*c^4-7*(b^2+c^2)*b*c)*a^4+4*(b^3-c^3)*(b^2-c^2)*a^3+2*(b^4+c^4-2*b*c*(b^2+b*c+c^2))*(b-c)^2*a^2-2*(b^2-c^2)*(b-c)^2*(b^3-c^3)*a-(b^4-c^4)*(b^2-c^2)*b*c) : :

The reciprocal orthologic center of these triangles is X(2077).

X(48692) lies on the circumcircle of 3rd anti-tri-squares-central triangle and these lines: {11, 26330}, {100, 26294}, {104, 3068}, {119, 26361}, {153, 492}, {193, 48693}, {952, 48711}, {1317, 26355}, {1768, 26300}, {2800, 45719}, {2829, 48476}, {5860, 12754}, {9913, 26306}, {10698, 26514}, {10742, 26468}, {11715, 26369}, {12138, 26375}, {12199, 26429}, {12248, 26441}, {12332, 26512}, {12499, 26314}, {12751, 26444}, {12752, 26449}, {12753, 26339}, {12761, 26490}, {12762, 26485}, {12763, 26479}, {12764, 26473}, {12775, 26520}, {12776, 26519}, {18539, 38756}, {19081, 26456}, {19082, 26462}, {22775, 26324}, {26396, 48464}, {26420, 48465}, {26496, 48688}, {26505, 48689}, {26516, 38602}, {26517, 48694}, {26518, 48695}, {35857, 39660}, {44594, 48700}, {44595, 48701}, {45420, 48685}, {45522, 48686}, {45524, 48687}

X(48692) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48692) = X(104)-of-3rd anti-tri-squares-central triangle
X(48692) = reflection of X(153) in X(48684)


X(48693) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO ANTI-INNER-GARCIA

Barycentrics    -(3*a^7-3*(b+c)*a^6-(5*b^2-17*b*c+5*c^2)*a^5+(b+c)*(5*b^2-14*b*c+5*c^2)*a^4+(b^4+c^4-2*b*c*(5*b^2-11*b*c+5*c^2))*a^3-(b^2-c^2)*(b-c)*(b^2-10*b*c+c^2)*a^2+(b^2-7*b*c+c^2)*(b^2-c^2)^2*a-(b^2-c^2)^3*(b-c))*S+a*(2*(b^2+b*c+c^2)*a^6-2*(b+c)*(b^2+b*c+c^2)*a^5-(4*b^4+4*c^4-7*(b^2+c^2)*b*c)*a^4+4*(b^3-c^3)*(b^2-c^2)*a^3+2*(b^4+c^4-2*b*c*(b^2+b*c+c^2))*(b-c)^2*a^2-2*(b^2-c^2)*(b-c)^2*(b^3-c^3)*a-(b^4-c^4)*(b^2-c^2)*b*c) : :

The reciprocal orthologic center of these triangles is X(2077).

X(48693) lies on the circumcircle of 4th anti-tri-squares-central triangle and these lines: {11, 26331}, {100, 26295}, {104, 3069}, {119, 26362}, {153, 491}, {193, 48692}, {952, 48712}, {1317, 26356}, {1768, 26301}, {2800, 45720}, {2829, 48477}, {5861, 12753}, {8982, 12248}, {9913, 26307}, {10698, 26515}, {10742, 26469}, {11715, 26370}, {12138, 26376}, {12199, 26430}, {12332, 26513}, {12499, 26315}, {12751, 26445}, {12752, 26450}, {12754, 26340}, {12761, 26491}, {12762, 26486}, {12763, 26480}, {12764, 26474}, {12775, 26525}, {12776, 26524}, {19081, 26457}, {19082, 26463}, {22775, 26325}, {26397, 48464}, {26421, 48465}, {26438, 38756}, {26497, 48688}, {26506, 48689}, {26521, 38602}, {26522, 48694}, {26523, 48695}, {35856, 39661}, {44596, 48700}, {44597, 48701}, {45421, 48684}, {45523, 48687}, {45525, 48686}

X(48693) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48693) = reflection of X(153) in X(48685)


X(48694) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO ANTI-INNER-GARCIA

Barycentrics    a*(a^9-2*(b+c)*a^8-(2*b^2-9*b*c+2*c^2)*a^7+3*(2*b-c)*(b-2*c)*(b+c)*a^6-(11*b^2-30*b*c+11*c^2)*b*c*a^5-(b+c)*(6*b^4+6*c^4-b*c*(29*b^2-48*b*c+29*c^2))*a^4+(2*b^2+7*b*c+2*c^2)*(b^2-4*b*c+c^2)*(b-c)^2*a^3+(b^2-c^2)*(b-c)*(2*b^4+2*c^4-b*c*(9*b^2-20*b*c+9*c^2))*a^2-(b^4+c^4-b*c*(7*b^2-10*b*c+7*c^2))*(b^2-c^2)^2*a-(b^2-c^2)^3*(b-c)*b*c) : :
X(48694) = 3*X(104)-2*X(5450) = 4*X(5450)-3*X(48695) = 3*X(11219)-2*X(12616) = X(11500)-3*X(22775)

The reciprocal orthologic center of these triangles is X(2077).

X(48694) lies on the circumcircle of anti-inner-Yff triangle and these lines: {1, 104}, {5, 12762}, {11, 26332}, {100, 11012}, {119, 15843}, {153, 10527}, {382, 2829}, {515, 13279}, {528, 22770}, {692, 1385}, {952, 11249}, {956, 37725}, {960, 6265}, {999, 7680}, {1317, 26357}, {1320, 37625}, {1387, 45654}, {1537, 18967}, {1728, 12691}, {1788, 10090}, {2801, 6261}, {2802, 5709}, {2975, 5693}, {3428, 10609}, {3632, 6796}, {5258, 5660}, {5563, 11219}, {5715, 16174}, {5851, 42842}, {6256, 45700}, {6264, 12704}, {6326, 46685}, {6713, 10198}, {6734, 12751}, {6905, 41684}, {8068, 10599}, {8256, 19914}, {9708, 20400}, {9711, 38752}, {9913, 26308}, {10267, 12332}, {10742, 26470}, {10902, 38693}, {10943, 12761}, {10966, 45634}, {12019, 22753}, {12114, 22791}, {12116, 12248}, {12138, 26377}, {12199, 26431}, {12331, 35252}, {12462, 45625}, {12463, 45626}, {12499, 26317}, {12687, 45632}, {12737, 24474}, {12738, 37837}, {12752, 26452}, {12753, 26342}, {12754, 26349}, {12763, 26481}, {12764, 26475}, {12765, 45645}, {12766, 45644}, {12831, 22759}, {13913, 45650}, {13977, 45651}, {18544, 38756}, {18861, 36152}, {19049, 48701}, {19050, 48700}, {19081, 26458}, {19082, 26464}, {22799, 45630}, {26200, 34862}, {26399, 48464}, {26423, 48465}, {26499, 48688}, {26508, 48689}, {26517, 48692}, {26522, 48693}, {33597, 41701}, {35856, 45640}, {35857, 45641}, {45422, 48684}, {45423, 48685}, {45526, 48686}, {45527, 48687}

X(48694) = reflection of X(i) in X(j) for these (i, j): (12332, 38602), (12738, 37837), (12762, 5), (38665, 6796), (48482, 37726), (48695, 104), (48713, 11249)
X(48694) = orthologic center (anti-inner-Yff, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48694) = X(104)-of-anti-inner-Yff triangle
X(48694) = X(12762)-of-Johnson triangle
X(48694) = X(12776)-of-anti-outer-Yff triangle
X(48694) = X(48695)-of-outer-Yff tangents triangle
X(48694) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (104, 10698, 10058), (104, 12776, 1), (10680, 12773, 37726)


X(48695) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO ANTI-INNER-GARCIA

Barycentrics    a*(a^9-2*(b+c)*a^8-(2*b^2-9*b*c+2*c^2)*a^7+(b+c)*(6*b^2-11*b*c+6*c^2)*a^6-(15*b^2-22*b*c+15*c^2)*b*c*a^5-(b+c)*(6*b^4+6*c^4-7*b*c*(3*b^2-4*b*c+3*c^2))*a^4+(2*b^4+2*c^4+b*c*(7*b^2-4*b*c+7*c^2))*(b-c)^2*a^3+(b^2-c^2)*(b-c)*(2*b^4+2*c^4-b*c*(5*b^2-8*b*c+5*c^2))*a^2-(b^4+c^4-3*(b-c)^2*b*c)*(b^2-c^2)^2*a-(b^2-c^2)^3*(b-c)*b*c) : :
X(48695) = X(1490)-3*X(15015) = 4*X(5450)-X(48694) = 2*X(6796)-3*X(34474) = X(12247)-3*X(14647) = 2*X(18242)-3*X(38752) = X(33898)-3*X(38752) = 3*X(38755)-X(40267)

The reciprocal orthologic center of these triangles is X(2077).

X(48695) lies on the circumcircle of anti-outer-Yff triangle and these lines: {1, 104}, {3, 119}, {4, 10090}, {5, 12761}, {11, 1012}, {20, 4996}, {21, 10165}, {35, 12749}, {36, 1519}, {40, 39776}, {55, 45635}, {56, 1537}, {78, 12665}, {80, 12616}, {84, 224}, {100, 515}, {153, 5552}, {214, 6261}, {405, 21154}, {944, 10087}, {952, 3913}, {971, 22935}, {993, 3359}, {999, 45637}, {1001, 6914}, {1006, 15017}, {1071, 12739}, {1145, 10310}, {1317, 26358}, {1387, 11496}, {1490, 15015}, {2771, 34862}, {2801, 3358}, {2932, 37725}, {2975, 40256}, {3560, 6713}, {3576, 12686}, {4316, 6905}, {5218, 6950}, {5440, 17661}, {5533, 10785}, {5541, 12650}, {5840, 48482}, {5851, 42843}, {5854, 10306}, {6001, 6265}, {6264, 12703}, {6667, 6913}, {6705, 10265}, {6796, 34474}, {6831, 13273}, {6833, 8068}, {6912, 31272}, {6924, 22799}, {6938, 14793}, {6986, 32633}, {7330, 18254}, {7987, 45649}, {10179, 24927}, {10679, 12773}, {10738, 35451}, {10882, 45629}, {10942, 12762}, {11219, 46816}, {11500, 33814}, {11552, 45977}, {12138, 26378}, {12199, 26432}, {12247, 14647}, {12331, 35251}, {12462, 45627}, {12463, 45628}, {12499, 26318}, {12515, 37562}, {12611, 32612}, {12672, 12740}, {12680, 41541}, {12737, 23340}, {12752, 26453}, {12753, 26343}, {12754, 26350}, {12763, 26482}, {12764, 26476}, {12765, 45647}, {12766, 45646}, {12832, 22760}, {13278, 38669}, {13279, 14217}, {13913, 45652}, {13977, 45653}, {19047, 48701}, {19048, 48700}, {19081, 26459}, {19082, 26465}, {19914, 26321}, {21164, 37306}, {23513, 37234}, {24466, 37022}, {26400, 48464}, {26424, 48465}, {26500, 48688}, {26509, 48689}, {26518, 48692}, {26523, 48693}, {31849, 36058}, {34758, 37437}, {35856, 45642}, {35857, 45643}, {45424, 48684}, {45425, 48685}, {45528, 48686}, {45529, 48687}

X(48695) = midpoint of X(i) and X(j) for these {i, j}: {1, 2950}, {84, 6326}, {5541, 12650}, {12114, 12332}
X(48695) = reflection of X(i) in X(j) for these (i, j): (80, 12616), (104, 5450), (6256, 119), (6261, 214), (10265, 6705), (11500, 33814), (12761, 5), (22775, 38602), (25438, 11248), (33898, 18242), (46435, 12608), (48694, 104)
X(48695) = orthologic center (anti-outer-Yff, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48695) = X(104)-of-anti-outer-Yff triangle
X(48695) = X(1158)-of-anti-inner-Garcia triangle
X(48695) = X(1537)-of-2nd circumperp tangential triangle
X(48695) = X(2950)-of-anti-Aquila triangle
X(48695) = X(5504)-of-2nd circumperp triangle, when ABC is acute
X(48695) = X(12761)-of-Johnson triangle
X(48695) = X(12775)-of-anti-inner-Yff triangle
X(48695) = X(46085)-of-hexyl triangle, when ABC is acute
X(48695) = X(48694)-of-inner-Yff tangents triangle
X(48695) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 18861, 10090), (104, 6906, 10058), (104, 10698, 10074), (104, 12775, 1), (1012, 1470, 26333), (2077, 12751, 100), (11729, 38602, 10269), (33898, 38752, 18242)


X(48696) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-GARCIA TO EXCENTERS-MIDPOINTS

Barycentrics    a*(a^3-(b^2+3*b*c+c^2)*a+2*(b+c)*b*c) : :
X(48696) = 4*X(11)-5*X(31263) = 5*X(36)-6*X(13587) = 5*X(100)-3*X(13587) = 2*X(1319)-3*X(15015) = 2*X(1519)-3*X(5660) = 4*X(3035)-3*X(3582) = X(3245)+2*X(3935) = 2*X(3583)-3*X(31160) = 4*X(3689)-X(4867) = 2*X(3689)+X(5541) = X(4867)+2*X(5541) = 4*X(5123)-3*X(37718) = 4*X(5440)-X(41702) = X(5537)+2*X(38665) = 3*X(6174)-2*X(15325) = 3*X(12331)-X(18524) = 4*X(12331)-X(44425) = 4*X(17757)-3*X(31160) = 4*X(18524)-3*X(44425)

The reciprocal orthologic center of these triangles is X(214).

X(48696) lies on these lines: {1, 474}, {2, 25439}, {3, 3632}, {8, 35}, {10, 1621}, {11, 31263}, {21, 3626}, {30, 6154}, {36, 100}, {40, 912}, {43, 5315}, {46, 6765}, {55, 3679}, {56, 3633}, {72, 11010}, {78, 5697}, {80, 6735}, {145, 5563}, {149, 3814}, {165, 18452}, {171, 16474}, {191, 34790}, {197, 37546}, {200, 5119}, {214, 38460}, {238, 31855}, {404, 3244}, {484, 518}, {495, 34612}, {497, 34719}, {498, 5082}, {515, 5537}, {517, 3689}, {521, 1734}, {528, 3583}, {529, 4316}, {595, 3214}, {659, 33905}, {758, 3245}, {899, 40091}, {910, 5525}, {952, 2077}, {956, 4421}, {958, 4668}, {960, 37563}, {997, 3895}, {1001, 19536}, {1006, 38127}, {1012, 37712}, {1018, 3684}, {1054, 4694}, {1125, 9342}, {1145, 32760}, {1203, 3293}, {1259, 37711}, {1260, 3586}, {1317, 5193}, {1319, 15015}, {1320, 24302}, {1324, 23858}, {1329, 4857}, {1385, 3893}, {1478, 17784}, {1479, 7080}, {1519, 5660}, {1575, 16784}, {1698, 3295}, {1737, 5853}, {1768, 13528}, {2078, 40663}, {2177, 30116}, {2550, 10056}, {2551, 4309}, {2771, 35460}, {2800, 48697}, {2802, 4511}, {2886, 3584}, {2900, 18397}, {2932, 33956}, {2975, 3625}, {3035, 3582}, {3058, 3820}, {3086, 12632}, {3149, 11531}, {3174, 18412}, {3189, 10573}, {3196, 4908}, {3216, 37588}, {3241, 37602}, {3256, 5252}, {3303, 3624}, {3315, 24168}, {3336, 3555}, {3337, 34791}, {3340, 11501}, {3421, 4302}, {3434, 7951}, {3496, 4006}, {3501, 17745}, {3579, 6763}, {3585, 12607}, {3612, 4853}, {3617, 5248}, {3621, 8666}, {3635, 5253}, {3636, 17531}, {3654, 7688}, {3685, 3992}, {3693, 5540}, {3722, 4695}, {3757, 4714}, {3811, 5903}, {3822, 33110}, {3828, 5284}, {3833, 29817}, {3870, 5902}, {3872, 37525}, {3878, 4420}, {3885, 30144}, {3892, 27003}, {3894, 36279}, {3899, 3940}, {3901, 37567}, {3920, 4868}, {3921, 15254}, {3930, 5011}, {3956, 27065}, {3957, 5883}, {3961, 4424}, {4007, 36744}, {4060, 38871}, {4072, 38869}, {4188, 20050}, {4262, 4390}, {4276, 4720}, {4293, 34690}, {4386, 16785}, {4413, 6767}, {4433, 32847}, {4515, 17744}, {4557, 4693}, {4691, 5260}, {4692, 32932}, {4701, 5267}, {4727, 19297}, {4816, 5217}, {4855, 21842}, {4861, 24926}, {4863, 26446}, {4882, 41229}, {4900, 30392}, {4901, 7295}, {4915, 30282}, {4917, 18398}, {4975, 5205}, {5048, 12653}, {5080, 20095}, {5100, 30171}, {5123, 37718}, {5172, 36920}, {5176, 37006}, {5264, 17977}, {5275, 9331}, {5280, 20691}, {5310, 33091}, {5312, 5710}, {5432, 34720}, {5445, 10916}, {5531, 6001}, {5552, 7741}, {5587, 10679}, {5657, 15931}, {5659, 6684}, {5690, 10902}, {5691, 10306}, {5720, 12703}, {5844, 13996}, {5881, 11248}, {6174, 15325}, {6361, 16127}, {6600, 17057}, {6736, 10572}, {6745, 30384}, {6796, 12245}, {6905, 28234}, {6906, 47745}, {6909, 28236}, {6911, 16200}, {6912, 38155}, {6940, 13607}, {7280, 12513}, {7489, 38176}, {7962, 11502}, {7971, 7991}, {7982, 11499}, {8167, 19876}, {8227, 37622}, {8301, 45765}, {8668, 11517}, {9581, 26358}, {9624, 12000}, {9668, 31141}, {9780, 25542}, {9897, 13205}, {10039, 47033}, {10090, 26726}, {10197, 33108}, {10459, 33771}, {10528, 37719}, {10584, 26364}, {10591, 27525}, {10609, 38455}, {10915, 37710}, {11009, 14923}, {11012, 32141}, {11224, 22753}, {11236, 18513}, {11278, 37251}, {11329, 29605}, {11362, 11491}, {11496, 37714}, {11508, 41709}, {11509, 37709}, {11524, 15178}, {11525, 13384}, {12629, 37618}, {12645, 18515}, {12736, 45395}, {13278, 16173}, {13405, 26725}, {15017, 22835}, {15171, 21031}, {15733, 41700}, {15808, 17535}, {15863, 46816}, {16202, 31423}, {16371, 34747}, {16412, 29602}, {16453, 23391}, {16470, 21858}, {16858, 38098}, {17460, 47622}, {17549, 34641}, {17572, 20057}, {17734, 33136}, {17751, 35206}, {18491, 31162}, {18518, 41869}, {18526, 36972}, {18838, 37736}, {19843, 31452}, {20054, 37307}, {21060, 34639}, {23169, 23832}, {24387, 27529}, {27385, 37735}, {28174, 38629}, {28204, 35000}, {28228, 36002}, {31140, 31479}, {31393, 46917}, {33179, 45976}, {35636, 45394}, {37561, 37727}, {37583, 41687}, {37722, 47742}, {37725, 41698}

X(48696) = midpoint of X(5080) and X(20095)
X(48696) = reflection of X(i) in X(j) for these (i, j): (1, 5440), (36, 100), (80, 6735), (149, 3814), (238, 46973), (1768, 13528), (3583, 17757), (3632, 44784), (4880, 484), (12653, 5048), (30384, 6745), (37006, 5176), (38460, 214), (41684, 1145), (41698, 37725), (41702, 1)
X(48696) = cevapoint of X(9) and X(2990)
X(48696) = crosssum of X(9) and X(8609)
X(48696) = orthologic center (anti-inner-Garcia, T) for these triangles T: {excenters-midpoints, Garcia-reflection, 2nd Schiffler}
X(48696) = X(1320)-of-anti-inner-Garcia triangle
X(48696) = X(5440)-of-Aquila triangle
X(48696) = X(41702)-of-5th mixtilinear triangle
X(48696) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 3632, 5288), (8, 35, 5258), (8, 8715, 35), (10, 3746, 5259), (10, 3871, 3746), (40, 5534, 15071), (43, 37610, 5315), (55, 3679, 5251), (145, 25440, 5563), (200, 5119, 5692), (956, 4421, 5010), (956, 8168, 4677), (1018, 3684, 5526), (3293, 5255, 1203), (3303, 9709, 3624), (3421, 34607, 4302), (3434, 7951, 31159), (3434, 45701, 7951), (3689, 5541, 4867), (3722, 4695, 30117), (3811, 5903, 41696), (3913, 5687, 1), (4413, 6767, 25055), (4421, 8168, 956), (4677, 5010, 956), (14923, 22836, 11009), (17784, 34619, 1478), (18491, 44455, 31162), (34790, 37568, 191), (36279, 41711, 3894)


X(48697) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-GARCIA TO EXTOUCH

Barycentrics    a*(a^9-3*(b+c)*a^8+7*b*c*a^7+(b+c)*(8*b^2-13*b*c+8*c^2)*a^6-(6*b^4+6*c^4+(7*b^2-10*b*c+7*c^2)*b*c)*a^5-(b+c)*(6*b^4+6*c^4-b*c*(25*b^2-34*b*c+25*c^2))*a^4+(8*b^4+8*c^4+b*c*(9*b^2-2*b*c+9*c^2))*(b-c)^2*a^3-(b^2-c^2)*(b-c)*(11*b^2-6*b*c+11*c^2)*b*c*a^2-(b^2-c^2)^2*(3*b^4+3*c^4-b*c*(7*b^2-4*b*c+7*c^2))*a+(b^3-c^3)*(b^2-c^2)^3) : :
X(48697) = 3*X(4881)-4*X(37837)

The reciprocal orthologic center of these triangles is X(12665).

X(48697) lies on these lines: {1, 4}, {3, 12666}, {100, 2745}, {2800, 48696}, {2829, 4511}, {4881, 18239}, {5720, 14647}, {5842, 45395}, {6909, 34256}, {11015, 18243}, {11220, 37300}, {22792, 37733}

X(48697) = reflection of X(41698) in X(6260)
X(48697) = orthologic center (anti-inner-Garcia, T) for these triangles T: {extouch, 1st Zaniah}
X(48697) = X(46435)-of-anti-inner-Garcia triangle
X(48697) = {X(1490), X(6261)}-harmonic conjugate of X(12667)


X(48698) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-GARCIA TO 2nd FUHRMANN

Barycentrics    a*(a^6-(b+c)*a^5-2*(b^2-b*c+c^2)*a^4+2*(b+c)*(b^2+c^2)*a^3+(b^4+c^4-b*c*(b^2-b*c+c^2))*a^2-(b^3+c^3)*(b^2+b*c+c^2)*a-(b^2-c^2)^2*b*c) : :
X(48698) = 2*X(15325)-3*X(15670)

The reciprocal orthologic center of these triangles is X(16128).

X(48698) lies on these lines: {1, 21}, {3, 3648}, {8, 13743}, {30, 100}, {55, 15677}, {72, 22936}, {78, 7701}, {79, 404}, {329, 37286}, {355, 21669}, {411, 16113}, {442, 9342}, {519, 46816}, {908, 35204}, {956, 28453}, {960, 45065}, {1001, 15672}, {1259, 37433}, {1376, 2475}, {2771, 4511}, {3065, 47320}, {3218, 41542}, {3233, 42746}, {3436, 15680}, {3649, 5253}, {3650, 5303}, {3651, 45392}, {3652, 5694}, {3871, 5441}, {4188, 20084}, {4420, 26202}, {4423, 15674}, {4855, 16143}, {5172, 17484}, {5176, 37006}, {5260, 18253}, {5284, 15325}, {5427, 35596}, {5499, 27529}, {5730, 13465}, {5844, 31649}, {6173, 16133}, {6175, 7951}, {6326, 6909}, {6701, 17531}, {6796, 33557}, {6915, 16125}, {6924, 16150}, {10032, 21161}, {10543, 38455}, {11375, 27186}, {12531, 44669}, {12866, 16761}, {13145, 22937}, {14450, 37308}, {16118, 25440}, {17637, 34772}, {17768, 27086}, {33668, 34758}

X(48698) = reflection of X(i) in X(j) for these (i, j): (1749, 3647), (3218, 41542), (40663, 18253)
X(48698) = orthologic center (anti-inner-Garcia, T) for these triangles T: {2nd Fuhrmann, K798e}
X(48698) = X(3065)-of-anti-inner-Garcia triangle
X(48698) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (21, 11684, 2975), (191, 3869, 11684), (16118, 25440, 35982)


X(48699) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-GARCIA TO HUTSON EXTOUCH

Barycentrics    a*(a^9-3*(b+c)*a^8-9*b*c*a^7+(b+c)*(8*b^2+19*b*c+8*c^2)*a^6-3*(2*b^2+b*c+2*c^2)*(b-c)^2*a^5-(b+c)*(6*b^4+6*c^4+b*c*(39*b^2+2*b*c+39*c^2))*a^4+(8*b^6+8*c^6+(9*b^4+9*c^4+2*b*c*(2*b^2+11*b*c+2*c^2))*b*c)*a^3+(b+c)*(21*b^4+21*c^4-2*(2*b^2+b*c+2*c^2)*b*c)*b*c*a^2-(b^2-c^2)^2*(3*b^4+3*c^4+b*c*(9*b^2+4*b*c+9*c^2))*a+(b^3-c^3)*(b^2-c^2)^3) : :

The reciprocal orthologic center of these triangles is X(12757).

X(48699) lies on these lines: {1, 12521}, {3, 12756}, {35204, 41553}

X(48699) = orthologic center (anti-inner-Garcia, Hutson extouch)


X(48700) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO ANTI-INNER-GARCIA

Barycentrics    a*((a^3-c*a^2-(b-c)^2*a-(b^2-c^2)*c)*(a^3-b*a^2-(b-c)^2*a+(b^2-c^2)*b)-2*S*a*(a^3-(b+c)*a^2-(b^2-3*b*c+c^2)*a+(b^2-c^2)*(b-c))) : :
X(48700) = 3*X(371)-X(35882) = 3*X(35856)+X(35882) = 2*X(35856)+X(48714) = 2*X(35882)-3*X(48714)

The reciprocal orthologic center of these triangles is X(2077).

X(48700) lies on the circumcircle of 1st Kenmotu-centers triangle and these lines: {3, 48715}, {6, 104}, {11, 2067}, {39, 48687}, {100, 1151}, {119, 590}, {149, 6459}, {153, 3068}, {371, 952}, {372, 38602}, {485, 10742}, {528, 41945}, {615, 6713}, {1124, 10074}, {1152, 19112}, {1317, 2066}, {1335, 10058}, {1387, 35768}, {1484, 42215}, {1587, 12248}, {1702, 6264}, {1768, 18991}, {1862, 11473}, {2800, 7969}, {2829, 3070}, {3035, 31453}, {3311, 12773}, {3592, 19113}, {5062, 48686}, {5412, 12138}, {5418, 38752}, {5541, 9616}, {5840, 42258}, {6200, 33814}, {6221, 12331}, {6326, 9583}, {6409, 34474}, {6419, 35857}, {6425, 38665}, {6560, 38753}, {6561, 10738}, {6564, 22799}, {6567, 48706}, {6667, 42583}, {7968, 11715}, {8976, 38755}, {8981, 11698}, {8983, 21635}, {9541, 13199}, {9615, 15015}, {9661, 39692}, {9913, 44598}, {10577, 34126}, {10698, 44635}, {10711, 13846}, {10724, 42263}, {10728, 23251}, {11219, 19077}, {12199, 44586}, {12332, 44590}, {12462, 44600}, {12463, 44602}, {12499, 44604}, {12515, 35774}, {12735, 35808}, {12737, 35775}, {12751, 13911}, {12752, 44610}, {12761, 44618}, {12762, 44620}, {12763, 31472}, {12764, 44623}, {12765, 44627}, {12766, 44629}, {12775, 44643}, {12776, 44645}, {13665, 38756}, {13922, 31454}, {13977, 32788}, {13991, 21154}, {19048, 48695}, {19050, 48694}, {19907, 35763}, {20095, 43512}, {22775, 44606}, {22938, 35821}, {23513, 42270}, {31272, 42262}, {35787, 38141}, {38754, 42261}, {38757, 43879}, {38761, 42259}, {44582, 48464}, {44584, 48465}, {44594, 48692}, {44596, 48693}, {45595, 48689}, {45597, 48688}

X(48700) = midpoint of X(371) and X(35856)
X(48700) = reflection of X(48714) in X(371)
X(48700) = inverse of X(35856) in Kenmotu circle
X(48700) = orthologic center (1st Kenmotu-centers, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48700) = X(104)-of-1st Kenmotu-centers triangle
X(48700) = X(38602)-of-1st Kenmotu-free-vertices triangle
X(48700) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 104, 48701), (104, 10759, 48684), (104, 19082, 6), (119, 13913, 590), (6200, 35883, 33814), (19112, 38693, 1152)


X(48701) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO ANTI-INNER-GARCIA

Barycentrics    a*((a^3-c*a^2-(b-c)^2*a-(b^2-c^2)*c)*(a^3-b*a^2-(b-c)^2*a+(b^2-c^2)*b)+2*S*a*(a^3-(b+c)*a^2-(b^2-3*b*c+c^2)*a+(b^2-c^2)*(b-c))) : :
X(48701) = 3*X(372)-X(35883) = 3*X(35857)+X(35883) = 2*X(35857)+X(48715) = 2*X(35883)-3*X(48715)

The reciprocal orthologic center of these triangles is X(2077).

X(48701) lies on the circumcircle of 2nd Kenmotu-centers triangle and these lines: {3, 48714}, {6, 104}, {11, 3070}, {39, 48686}, {100, 1152}, {119, 615}, {149, 6460}, {153, 3069}, {371, 38602}, {372, 952}, {486, 10742}, {528, 41946}, {590, 6713}, {1124, 10058}, {1151, 19113}, {1317, 5414}, {1335, 10074}, {1387, 35769}, {1484, 42216}, {1588, 12248}, {1703, 6264}, {1768, 18992}, {1862, 11474}, {2800, 7968}, {2829, 3071}, {3312, 12773}, {3594, 19112}, {5058, 48687}, {5413, 12138}, {5420, 38752}, {5840, 42259}, {6396, 33814}, {6398, 12331}, {6410, 34474}, {6420, 35856}, {6426, 38665}, {6560, 10738}, {6561, 38753}, {6565, 22799}, {6566, 48705}, {6667, 42582}, {7969, 11715}, {9913, 44599}, {10576, 34126}, {10698, 44636}, {10711, 13847}, {10724, 42264}, {10728, 23261}, {11219, 19078}, {11698, 13966}, {12199, 44587}, {12332, 44591}, {12462, 44601}, {12463, 44603}, {12499, 44605}, {12515, 35775}, {12735, 35809}, {12737, 35774}, {12751, 13973}, {12752, 44611}, {12761, 44619}, {12762, 44621}, {12763, 44622}, {12764, 44624}, {12765, 44628}, {12766, 44630}, {12775, 44644}, {12776, 44646}, {13785, 38756}, {13913, 32787}, {13922, 21154}, {13951, 38755}, {13971, 21635}, {13991, 37725}, {19047, 48695}, {19049, 48694}, {19907, 35762}, {20095, 43511}, {22775, 44607}, {22938, 35820}, {23513, 42273}, {31272, 42265}, {35786, 38141}, {38754, 42260}, {38757, 43880}, {38761, 42258}, {44583, 48464}, {44585, 48465}, {44595, 48692}, {44597, 48693}, {45596, 48688}, {45598, 48689}

X(48701) = midpoint of X(372) and X(35857)
X(48701) = reflection of X(48715) in X(372)
X(48701) = orthologic center (2nd Kenmotu-centers, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48701) = X(104)-of-2nd Kenmotu-centers triangle
X(48701) = X(10506)-of-2nd Kenmotu diagonals triangle
X(48701) = X(38602)-of-2nd Kenmotu-free-vertices triangle
X(48701) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 104, 48700), (104, 10759, 48685), (104, 19081, 6), (119, 13977, 615), (6396, 35882, 33814), (19113, 38693, 1151)


X(48702) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-GARCIA TO 1st SCHIFFLER

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

The reciprocal orthologic center of these triangles is X(3065).

X(48702) lies on these lines: {1, 6597}, {3, 12769}, {100, 15228}

X(48702) = orthologic center (anti-inner-Garcia, 1st Schiffler)
X(48702) = X(6595)-of-anti-inner-Garcia triangle


X(48703) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU CENTERS TO ANTI-INNER-GARCIA

Barycentrics    a*(2*(a-b)*(a-c)*S+2*(b^2-b*c+c^2)*a^2-2*(b^3+c^3)*a+(b^2+c^2)*b*c) : :
X(48703) = 3*X(100)-X(13269) = X(13269)+3*X(13270) = 2*X(13269)-3*X(48704) = 2*X(13270)+X(48704)

The reciprocal parallelogic center of these triangles is X(36).

X(48703) lies on the circumcircle of 1st anti-Kenmotu centers triangle and these lines: {3, 48705}, {6, 100}, {11, 45470}, {80, 45444}, {104, 12305}, {119, 45440}, {149, 492}, {214, 45398}, {528, 591}, {952, 9733}, {1317, 45404}, {1320, 45476}, {1862, 45400}, {2802, 45713}, {3102, 35883}, {5541, 45426}, {5840, 13748}, {6289, 10738}, {10087, 45490}, {10090, 45492}, {12331, 45488}, {13194, 45402}, {13199, 45406}, {13205, 45416}, {13222, 45428}, {13228, 45430}, {13230, 45432}, {13235, 45434}, {13268, 45446}, {13271, 45454}, {13272, 45456}, {13273, 45458}, {13274, 45460}, {13275, 45467}, {13276, 45464}, {13278, 45494}, {13279, 45496}, {13922, 45484}, {13991, 45487}, {22560, 45436}, {22938, 45438}, {25438, 45424}, {33814, 43119}, {35882, 45462}, {45345, 48533}, {45347, 48534}, {45375, 48680}, {45411, 48706}, {45412, 48708}, {45415, 48707}, {45421, 48712}, {45422, 48713}

X(48703) = midpoint of X(i) and X(j) for these {i, j}: {100, 13270}, {149, 48711}
X(48703) = reflection of X(i) in X(j) for these (i, j): (3, 48705), (48684, 9733), (48704, 100)
X(48703) = parallelogic center (1st anti-Kenmotu centers, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48703) = X(100)-of-1st anti-Kenmotu centers triangle
X(48703) = X(48705)-of-X3-ABC reflections triangle
X(48703) = {X(100), X(10755)}-harmonic conjugate of X(48714)


X(48704) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU CENTERS TO ANTI-INNER-GARCIA

Barycentrics    a*(-2*(a-b)*(a-c)*S+2*(b^2-b*c+c^2)*a^2-2*(b^3+c^3)*a+(b^2+c^2)*b*c) : :
X(48704) = 3*X(100)-X(13270) = 3*X(13269)+X(13270) = 2*X(13269)+X(48703) = 2*X(13270)-3*X(48703)

The reciprocal parallelogic center of these triangles is X(36).

X(48704) lies on the circumcircle of 2nd anti-Kenmotu centers triangle and these lines: {3, 48706}, {6, 100}, {11, 45471}, {80, 45445}, {104, 12306}, {119, 45441}, {149, 491}, {214, 45399}, {528, 1991}, {952, 9732}, {1317, 45405}, {1320, 45477}, {1862, 45401}, {2802, 45714}, {3103, 35882}, {5541, 45427}, {5840, 13749}, {6290, 10738}, {10087, 45491}, {10090, 45493}, {12331, 45489}, {13194, 45403}, {13199, 45407}, {13205, 45417}, {13222, 45429}, {13228, 45431}, {13230, 45433}, {13235, 45435}, {13268, 45447}, {13271, 45455}, {13272, 45457}, {13273, 45459}, {13274, 45461}, {13275, 45465}, {13276, 45466}, {13278, 45495}, {13279, 45497}, {13922, 45486}, {13991, 45485}, {22560, 45437}, {22938, 45439}, {25438, 45425}, {33814, 43118}, {35883, 45463}, {45346, 48534}, {45348, 48533}, {45376, 48680}, {45410, 48705}, {45413, 48707}, {45414, 48708}, {45420, 48711}, {45423, 48713}

X(48704) = midpoint of X(i) and X(j) for these {i, j}: {100, 13269}, {149, 48712}
X(48704) = reflection of X(i) in X(j) for these (i, j): (3, 48706), (48685, 9732), (48703, 100)
X(48704) = parallelogic center (2nd anti-Kenmotu centers, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48704) = X(100)-of-2nd anti-Kenmotu centers triangle
X(48704) = X(48706)-of-X3-ABC reflections triangle
X(48704) = {X(100), X(10755)}-harmonic conjugate of X(48715)


X(48705) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO ANTI-INNER-GARCIA

Barycentrics    a*(-2*(2*(b^2-b*c+c^2)*a^2-2*(b^3+c^3)*a+(b^2+c^2)*b*c)*S+2*a^6-2*(b+c)*a^5-4*(b^2-b*c+c^2)*a^4+2*(b+c)*(2*b^2-b*c+2*c^2)*a^3+(2*b^4+2*c^4-5*(b^2+c^2)*b*c)*a^2-2*(b^2-c^2)*(b-c)*(b^2+b*c+c^2)*a+(b^2-c^2)^2*b*c) : :
X(48705) = X(13270)+3*X(34474)

The reciprocal parallelogic center of these triangles is X(36).

X(48705) lies on the circumcircle of 1st anti-Kenmotu-free-vertices triangle and these lines: {3, 48703}, {11, 641}, {39, 48715}, {80, 45546}, {100, 372}, {104, 45498}, {119, 45544}, {149, 45508}, {182, 9024}, {214, 45500}, {528, 41490}, {952, 9739}, {1317, 45506}, {1320, 45572}, {1862, 45502}, {2802, 45715}, {5062, 48714}, {5541, 45530}, {5840, 48466}, {6566, 48701}, {7690, 38602}, {9737, 48687}, {10087, 45580}, {10090, 45582}, {10738, 45554}, {12331, 45578}, {13194, 45504}, {13199, 45510}, {13205, 45520}, {13222, 45532}, {13228, 45534}, {13230, 45536}, {13235, 45538}, {13268, 45548}, {13269, 45550}, {13270, 34474}, {13271, 45556}, {13272, 45558}, {13273, 45560}, {13274, 45562}, {13275, 45569}, {13276, 45566}, {13278, 45584}, {13279, 45586}, {13922, 45574}, {13991, 45577}, {19112, 45512}, {19113, 45515}, {22560, 45540}, {22938, 45542}, {25438, 45528}, {35883, 45565}, {45349, 48533}, {45351, 48534}, {45377, 48680}, {45410, 48704}, {45516, 48708}, {45519, 48707}, {45522, 48711}, {45525, 48712}, {45526, 48713}

X(48705) = midpoint of X(3) and X(48703)
X(48705) = parallelogic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48705) = X(48703)-of-anti-X3-ABC reflections triangle
X(48705) = X(100)-of-1st anti-Kenmotu-free-vertices triangle
X(48705) = reflection of X(i) in X(j) for these (i, j): (48686, 9739), (48706, 33814)


X(48706) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO ANTI-INNER-GARCIA

Barycentrics    a*(2*(2*(b^2-b*c+c^2)*a^2-2*(b^3+c^3)*a+(b^2+c^2)*b*c)*S+2*a^6-2*(b+c)*a^5-4*(b^2-b*c+c^2)*a^4+2*(b+c)*(2*b^2-b*c+2*c^2)*a^3+(2*b^4+2*c^4-5*(b^2+c^2)*b*c)*a^2-2*(b^2-c^2)*(b-c)*(b^2+b*c+c^2)*a+(b^2-c^2)^2*b*c) : :
X(48706) = X(13269)+3*X(34474)

The reciprocal parallelogic center of these triangles is X(36).

X(48706) lies on the circumcircle of 2nd anti- Kenmotu-free-vertices triangle and these lines: {3, 48704}, {11, 642}, {39, 48714}, {80, 45547}, {100, 371}, {104, 45499}, {119, 45545}, {149, 45509}, {182, 9024}, {214, 45501}, {528, 41491}, {952, 9738}, {1317, 45507}, {1320, 45573}, {1862, 45503}, {2802, 45716}, {5058, 48715}, {5541, 45531}, {5840, 48467}, {6567, 48700}, {7692, 38602}, {9737, 48686}, {10087, 45581}, {10090, 45583}, {10738, 45555}, {12331, 45579}, {13194, 45505}, {13199, 45511}, {13205, 45521}, {13222, 45533}, {13228, 45535}, {13230, 45537}, {13235, 45539}, {13268, 45549}, {13269, 34474}, {13270, 45551}, {13271, 45557}, {13272, 45559}, {13273, 45561}, {13274, 45563}, {13275, 45567}, {13276, 45568}, {13278, 45585}, {13279, 45587}, {13922, 45576}, {13991, 45575}, {19112, 45514}, {19113, 45513}, {22560, 45541}, {22938, 45543}, {25438, 45529}, {35882, 45564}, {45350, 48534}, {45352, 48533}, {45378, 48680}, {45411, 48703}, {45517, 48707}, {45518, 48708}, {45523, 48712}, {45524, 48711}, {45527, 48713}

X(48706) = midpoint of X(3) and X(48704)
X(48706) = parallelogic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48706) = X(48704)-of-anti-X3-ABC reflections triangle
X(48706) = reflection of X(i) in X(j) for these (i, j): (48687, 9738), (48705, 33814)


X(48707) = PARALLELOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO ANTI-INNER-GARCIA

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

The reciprocal parallelogic center of these triangles is X(36).

X(48707) lies on the circumcircle of anti-Lucas(+1) homothetic triangle and these lines: {11, 5490}, {80, 26442}, {100, 493}, {104, 26292}, {119, 26328}, {149, 26494}, {214, 26367}, {528, 45699}, {952, 48688}, {1317, 26433}, {1320, 26495}, {1862, 26373}, {2802, 45718}, {5541, 26298}, {5840, 48468}, {6464, 48708}, {9024, 45727}, {10087, 45612}, {10090, 45614}, {10738, 26466}, {12331, 45610}, {13194, 26427}, {13199, 26439}, {13205, 26493}, {13222, 26304}, {13228, 45589}, {13230, 45591}, {13235, 26312}, {13268, 26447}, {13269, 26337}, {13270, 26347}, {13271, 26488}, {13272, 26483}, {13273, 26477}, {13274, 26471}, {13276, 45603}, {13278, 45615}, {13279, 26501}, {13922, 45607}, {13991, 45606}, {18521, 48680}, {19112, 26454}, {19113, 26460}, {22560, 26322}, {22938, 45593}, {25438, 26500}, {26391, 48533}, {26415, 48534}, {26496, 48711}, {26497, 48712}, {26498, 33814}, {26499, 48713}, {35882, 45601}, {35883, 45600}, {45413, 48704}, {45415, 48703}, {45517, 48706}, {45519, 48705}, {45596, 48715}, {45597, 48714}

X(48707) = parallelogic center (anti-Lucas(+1) homothetic, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48707) = X(100)-of-anti-Lucas(+1) homothetic triangle


X(48708) = PARALLELOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO ANTI-INNER-GARCIA

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

The reciprocal parallelogic center of these triangles is X(36).

X(48708) lies on the circumcircle of anti-Lucas(-1) homothetic triangle and these lines: {11, 5491}, {80, 26443}, {100, 494}, {104, 26293}, {119, 26329}, {149, 26503}, {214, 26368}, {528, 45698}, {952, 48689}, {1317, 26434}, {1320, 26504}, {1862, 26374}, {2802, 45717}, {5541, 26299}, {5840, 48469}, {6464, 48707}, {9024, 45726}, {10087, 45611}, {10090, 45613}, {10738, 26467}, {12331, 45609}, {13194, 26428}, {13199, 26440}, {13205, 26502}, {13222, 26305}, {13228, 45588}, {13230, 45590}, {13235, 26313}, {13268, 26448}, {13269, 45594}, {13270, 26338}, {13271, 26489}, {13272, 26484}, {13273, 26478}, {13274, 26472}, {13275, 45604}, {13278, 26511}, {13279, 26510}, {13922, 45605}, {13991, 45608}, {18523, 48680}, {19112, 26455}, {19113, 26461}, {22560, 26323}, {22938, 45592}, {25438, 26509}, {26392, 48533}, {26416, 48534}, {26505, 48711}, {26506, 48712}, {26507, 33814}, {26508, 48713}, {35882, 45599}, {35883, 45602}, {45412, 48703}, {45414, 48704}, {45516, 48705}, {45518, 48706}, {45595, 48714}, {45598, 48715}

X(48708) = parallelogic center (anti-Lucas(-1) homothetic, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48708) = X(100)-of-anti-Lucas(-1) homothetic triangle


X(48709) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO ANTI-INNER-GARCIA

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

The reciprocal parallelogic center of these triangles is X(2077).

X(48709) lies on the circumcircle of 1st anti-Parry triangle and these lines: {3, 48710}, {100, 110}, {104, 1296}, {900, 9145}, {2804, 48539}, {2854, 48691}, {3738, 45709}, {9216, 9978}

X(48709) = parallelogic center (1st anti-Parry, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48709) = X(48710)-of-ABC-X3 reflections triangle
X(48709) = X(104)-of-1st anti-Parry triangle
X(48709) = reflection of X(i) in X(j) for these (i, j): (48690, 9145), (48710, 3)


X(48710) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO ANTI-INNER-GARCIA

Barycentrics    a*(a^10-(b+c)*a^9-(2*b^2-3*b*c+2*c^2)*a^8+2*(b^3+c^3)*a^7+(3*b^4+3*c^4-b*c*(3*b^2+b*c+3*c^2))*a^6-(b+c)*(3*b^4+3*c^4+b*c*(4*b^2-13*b*c+4*c^2))*a^5-(4*b^6+4*c^6-3*(3*b^4+3*c^4+b*c*(b^2-5*b*c+c^2))*b*c)*a^4+(b^2-c^2)*(b-c)*(4*b^4+4*c^4+b*c*(10*b^2+b*c+10*c^2))*a^3+(b^4-c^4)*(b^2-c^2)*(2*b^2-9*b*c+2*c^2)*a^2-2*(b^3+c^3)*(b-c)^2*(b^4+c^4+b*c*(b^2-b*c+c^2))*a+3*(b^2-c^2)^2*b^3*c^3) : :

The reciprocal parallelogic center of these triangles is X(2077).

X(48710) lies on the circumcircle of 2nd anti-Parry triangle and these lines: {3, 48709}, {37, 100}, {74, 104}, {900, 9142}, {2804, 48540}, {2854, 48690}, {3738, 45710}, {9215, 9980}

X(48710) = parallelogic center (2nd anti-Parry, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48710) = reflection of X(74) in the line X(2771)X(9142)
X(48710) = X(48709)-of-ABC-X3 reflections triangle
X(48710) = X(104)-of-2nd anti-Parry triangle
X(48710) = reflection of X(i) in X(j) for these (i, j): (48691, 9142), (48709, 3)


X(48711) = PARALLELOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO ANTI-INNER-GARCIA

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

The reciprocal parallelogic center of these triangles is X(36).

X(48711) lies on the circumcircle of 3rd anti-tri-squares-central triangle and these lines: {11, 26355}, {80, 26444}, {100, 3068}, {104, 26294}, {119, 26330}, {149, 492}, {193, 9024}, {214, 26369}, {528, 5860}, {952, 48692}, {1317, 26435}, {1320, 26514}, {1862, 26375}, {2802, 45719}, {5541, 26300}, {5840, 48476}, {6154, 13269}, {10738, 26468}, {13194, 26429}, {13199, 26441}, {13205, 26512}, {13222, 26306}, {13235, 26314}, {13268, 26449}, {13271, 26490}, {13272, 26485}, {13273, 26479}, {13274, 26473}, {13278, 26520}, {13279, 26519}, {18539, 48680}, {19112, 26456}, {19113, 26462}, {22560, 26324}, {25438, 26518}, {26396, 48533}, {26420, 48534}, {26496, 48707}, {26505, 48708}, {26516, 33814}, {26517, 48713}, {35883, 39660}, {44594, 48714}, {44595, 48715}, {45420, 48704}, {45522, 48705}, {45524, 48706}

X(48711) = parallelogic center (3rd anti-tri-squares-central, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48711) = X(100)-of-3rd anti-tri-squares-central triangle
X(48711) = reflection of X(i) in X(j) for these (i, j): (149, 48703), (13269, 6154), (48712, 20095)


X(48712) = PARALLELOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO ANTI-INNER-GARCIA

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

The reciprocal parallelogic center of these triangles is X(36).

X(48712) lies on the circumcircle of 4th anti-tri-squares-central triangle and these lines: {11, 26356}, {80, 26445}, {100, 3069}, {104, 26295}, {119, 26331}, {149, 491}, {193, 9024}, {214, 26370}, {528, 5861}, {952, 48693}, {1317, 26436}, {1320, 26515}, {1862, 26376}, {2802, 45720}, {5541, 26301}, {5840, 48477}, {6154, 13270}, {8982, 13199}, {10738, 26469}, {13194, 26430}, {13205, 26513}, {13222, 26307}, {13235, 26315}, {13268, 26450}, {13271, 26491}, {13272, 26486}, {13273, 26480}, {13274, 26474}, {13278, 26525}, {13279, 26524}, {19112, 26457}, {19113, 26463}, {22560, 26325}, {25438, 26523}, {26397, 48533}, {26421, 48534}, {26438, 48680}, {26497, 48707}, {26506, 48708}, {26521, 33814}, {26522, 48713}, {35882, 39661}, {44596, 48714}, {44597, 48715}, {45421, 48703}, {45523, 48706}, {45525, 48705}

X(48712) = parallelogic center (4th anti-tri-squares-central, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48712) = reflection of X(i) in X(j) for these (i, j): (149, 48704), (13270, 6154), (48711, 20095)


X(48713) = PARALLELOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO ANTI-INNER-GARCIA

Barycentrics    a*(a^6-(b+c)*a^5-(2*b^2-b*c+2*c^2)*a^4+2*(b^3+c^3)*a^3+(b^4+c^4-2*b*c*(b^2-3*b*c+c^2))*a^2-(b+c)*(b^4+c^4-2*b*c*(b-c)^2)*a+(b^2-c^2)^2*b*c) : :
X(48713) = 3*X(100)-2*X(8715) = 3*X(5660)-2*X(21077) = 3*X(6326)-X(11523) = 4*X(8715)-3*X(25438) = 3*X(10707)-4*X(24387) = X(12513)-3*X(22560) = 2*X(37726)-3*X(45700)

The reciprocal parallelogic center of these triangles is X(36).

X(48713) lies on the circumcircle of anti-inner-Yff triangle and these lines: {1, 88}, {3, 528}, {5, 13272}, {11, 405}, {21, 4857}, {36, 12750}, {56, 10609}, {80, 5258}, {104, 3651}, {119, 11929}, {149, 4189}, {411, 8666}, {474, 6174}, {518, 12738}, {519, 6905}, {535, 36002}, {758, 5536}, {943, 1125}, {952, 11249}, {958, 12019}, {993, 1005}, {1145, 10966}, {1317, 26437}, {1484, 5428}, {1490, 2801}, {1768, 12565}, {1862, 26377}, {2800, 5709}, {2829, 37411}, {2932, 6154}, {3035, 10198}, {3058, 19525}, {3086, 37313}, {3149, 37725}, {3434, 14793}, {3555, 41701}, {3738, 38324}, {3829, 7489}, {3881, 14151}, {3887, 13256}, {3913, 6924}, {4188, 11240}, {4239, 29639}, {5187, 39692}, {5440, 18839}, {5533, 43740}, {5563, 35979}, {5660, 21077}, {5687, 13996}, {5705, 6702}, {5840, 48482}, {5854, 10680}, {5856, 22753}, {6224, 10074}, {6265, 24474}, {6326, 11523}, {6667, 16853}, {6911, 45701}, {6914, 11235}, {6918, 20400}, {6933, 8068}, {6940, 34486}, {7171, 43178}, {7972, 41575}, {9024, 45728}, {10072, 37300}, {10267, 13205}, {10529, 17100}, {10530, 31295}, {10698, 37625}, {10738, 13743}, {10902, 34474}, {10912, 32141}, {10943, 13271}, {11108, 45310}, {11269, 11322}, {11344, 31458}, {11491, 22837}, {11510, 12732}, {11849, 13463}, {12116, 13199}, {12260, 25524}, {12575, 21630}, {12607, 37251}, {12739, 33598}, {12773, 35252}, {12775, 14217}, {13194, 26431}, {13222, 26308}, {13228, 45625}, {13230, 45626}, {13235, 26317}, {13268, 26452}, {13269, 26342}, {13270, 26349}, {13273, 26481}, {13274, 26475}, {13275, 45645}, {13276, 45644}, {13922, 45650}, {13991, 45651}, {14054, 17660}, {16173, 24541}, {16371, 33925}, {16864, 31235}, {17536, 31272}, {18524, 38455}, {18544, 48680}, {18967, 25416}, {19049, 48715}, {19050, 48714}, {19112, 26458}, {19113, 26464}, {19541, 38757}, {19843, 45043}, {20066, 34758}, {22765, 44669}, {22938, 45630}, {24390, 37564}, {26399, 48533}, {26423, 48534}, {26499, 48707}, {26508, 48708}, {26517, 48711}, {26522, 48712}, {31146, 35977}, {31157, 37286}, {33140, 35992}, {34485, 34894}, {34600, 39772}, {35882, 45640}, {35883, 45641}, {37308, 37722}, {45422, 48703}, {45423, 48704}, {45526, 48705}, {45527, 48706}

X(48713) = reflection of X(i) in X(j) for these (i, j): (13205, 33814), (13272, 5), (25438, 100), (38669, 8666), (48694, 11249)
X(48713) = parallelogic center (anti-inner-Yff, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48713) = center of circle {{X(2651), X(36002), X(37960)}}
X(48713) = X(100)-of-anti-inner-Yff triangle
X(48713) = X(3811)-of-anti-inner-Garcia triangle
X(48713) = X(10609)-of-2nd circumperp tangential triangle
X(48713) = X(13272)-of-Johnson triangle
X(48713) = X(13279)-of-anti-outer-Yff triangle
X(48713) = X(25438)-of-outer-Yff tangents triangle
X(48713) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (100, 1320, 10087), (100, 13279, 1), (149, 4996, 10058)


X(48714) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO ANTI-INNER-GARCIA

Barycentrics    a*(2*(a-b)*(a-c)*S+a*(a^3-(b+c)*a^2-(b^2-3*b*c+c^2)*a+(b^2-c^2)*(b-c))) : :
X(48714) = 3*X(371)-X(35856) = X(35856)+3*X(35882) = 2*X(35856)-3*X(48700) = 2*X(35882)+X(48700)

The reciprocal parallelogic center of these triangles is X(36).

X(48714) lies on the circumcircle of 1st Kenmotu-centers triangle and these lines: {3, 48701}, {6, 100}, {11, 590}, {39, 48706}, {80, 13911}, {104, 1151}, {119, 3071}, {149, 3068}, {153, 6459}, {214, 7968}, {371, 952}, {372, 33814}, {485, 10738}, {486, 38752}, {528, 32787}, {615, 3035}, {1124, 10090}, {1152, 19081}, {1317, 2067}, {1320, 44635}, {1335, 10087}, {1387, 35808}, {1484, 8981}, {1587, 13199}, {1702, 6326}, {1768, 9616}, {1862, 5412}, {2771, 31439}, {2802, 7969}, {2829, 42258}, {3036, 31453}, {3070, 5840}, {3311, 12331}, {3592, 19082}, {5062, 48705}, {5415, 6154}, {5420, 38762}, {5533, 9661}, {5541, 18991}, {6174, 13991}, {6200, 35857}, {6221, 12773}, {6224, 19066}, {6264, 9583}, {6265, 35775}, {6409, 38693}, {6419, 35883}, {6425, 38669}, {6561, 10742}, {6564, 22938}, {6567, 48687}, {6667, 32789}, {7585, 20095}, {8068, 9646}, {8253, 31272}, {8983, 21630}, {9541, 12248}, {9679, 19047}, {10265, 13912}, {10707, 13846}, {10724, 23251}, {10728, 42263}, {11473, 12138}, {11698, 42215}, {11729, 45643}, {12735, 35768}, {12739, 16232}, {13194, 44586}, {13205, 44590}, {13222, 44598}, {13228, 44600}, {13230, 44602}, {13235, 44604}, {13268, 44610}, {13271, 44618}, {13272, 44620}, {13273, 31472}, {13274, 44623}, {13275, 44627}, {13276, 44629}, {13278, 44643}, {13279, 44645}, {13665, 48680}, {13893, 37718}, {13913, 31454}, {13973, 19077}, {13977, 38760}, {15015, 18992}, {19048, 25438}, {19050, 48713}, {19907, 35642}, {20418, 41963}, {22560, 44606}, {22799, 35821}, {23513, 42582}, {24466, 42259}, {31235, 32790}, {35788, 35853}, {38753, 42260}, {38763, 43880}, {44582, 48533}, {44584, 48534}, {44594, 48711}, {44596, 48712}, {45595, 48708}, {45597, 48707}

X(48714) = midpoint of X(371) and X(35882)
X(48714) = reflection of X(48700) in X(371)
X(48714) = inverse of X(35882) in Kenmotu circle
X(48714) = parallelogic center (1st Kenmotu-centers, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48714) = X(100)-of-1st Kenmotu-centers triangle
X(48714) = X(33814)-of-1st Kenmotu-free-vertices triangle
X(48714) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 100, 48715), (11, 13922, 590), (100, 10755, 48703), (100, 19113, 6), (6200, 35857, 38602), (19081, 34474, 1152)


X(48715) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO ANTI-INNER-GARCIA

Barycentrics    a*(-2*(a-b)*(a-c)*S+a*(a^3-(b+c)*a^2-(b^2-3*b*c+c^2)*a+(b^2-c^2)*(b-c))) : :
X(48715) = 3*X(372)-X(35857) = X(35857)+3*X(35883) = 2*X(35857)-3*X(48701) = 2*X(35883)+X(48701)

The reciprocal parallelogic center of these triangles is X(36).

X(48715) lies on the circumcircle of 2nd Kenmotu-centers triangle and these lines: {3, 48700}, {6, 100}, {11, 615}, {39, 48705}, {80, 13973}, {104, 1152}, {119, 3070}, {149, 3069}, {153, 6460}, {214, 7969}, {371, 33814}, {372, 952}, {485, 38752}, {486, 10738}, {528, 32788}, {590, 3035}, {1124, 10087}, {1151, 19082}, {1317, 6502}, {1320, 44636}, {1335, 10090}, {1387, 35809}, {1484, 13966}, {1588, 13199}, {1703, 6326}, {1862, 5413}, {2362, 12739}, {2802, 7968}, {2829, 42259}, {3071, 5840}, {3312, 12331}, {3594, 19081}, {5058, 48706}, {5416, 6154}, {5418, 38762}, {5541, 18992}, {6174, 13922}, {6224, 19065}, {6265, 35774}, {6396, 35856}, {6398, 12773}, {6410, 38693}, {6420, 35882}, {6426, 38669}, {6560, 10742}, {6565, 22938}, {6566, 48686}, {6667, 32790}, {7586, 20095}, {8252, 31272}, {10265, 13975}, {10707, 13847}, {10724, 23261}, {10728, 42264}, {11474, 12138}, {11698, 42216}, {11729, 45642}, {12735, 35769}, {13194, 44587}, {13205, 44591}, {13222, 44599}, {13228, 44601}, {13230, 44603}, {13235, 44605}, {13268, 44611}, {13271, 44619}, {13272, 44621}, {13273, 44622}, {13274, 44624}, {13275, 44628}, {13276, 44630}, {13278, 44644}, {13279, 44646}, {13785, 48680}, {13911, 19078}, {13913, 38760}, {13947, 37718}, {13971, 21630}, {13977, 37726}, {15015, 18991}, {19047, 25438}, {19049, 48713}, {19907, 35641}, {20418, 41964}, {22560, 44607}, {22799, 35820}, {23513, 42583}, {24466, 42258}, {31235, 32789}, {35789, 35852}, {38753, 42261}, {38763, 43879}, {44583, 48533}, {44585, 48534}, {44595, 48711}, {44597, 48712}, {45596, 48707}, {45598, 48708}

X(48715) = midpoint of X(372) and X(35883)
X(48715) = reflection of X(48701) in X(372)
X(48715) = parallelogic center (2nd Kenmotu-centers, T) for these triangles T: {anti-inner-Garcia, inner-Garcia}
X(48715) = X(100)-of-2nd Kenmotu-centers triangle
X(48715) = X(10501)-of-2nd Kenmotu diagonals triangle
X(48715) = X(33814)-of-2nd Kenmotu-free-vertices triangle
X(48715) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 100, 48714), (11, 13991, 615), (100, 10755, 48704), (100, 19112, 6), (6396, 35856, 38602), (19082, 34474, 1151)


X(48716) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 10th BROCARD TO 7th BROCARD

Barycentrics    (b^2+c^2)*a^10-3*(b^4+b^2*c^2+c^4)*a^8+3*(b^2+c^2)*(b^4+c^4)*a^6-(b^4+c^4)*(b^2+c^2)^2*a^4+2*(b^4-c^4)*(b^2-c^2)*b^2*c^2*a^2-(b^2-c^2)^4*b^2*c^2 : :
X(48716) = 4*X(182)-3*X(39906) = 3*X(182)-2*X(39912) = 3*X(39906)-2*X(39910) = 9*X(39906)-8*X(39912) = 3*X(39910)-4*X(39912)

The reciprocal orthologic center of these triangles is X(39910).

X(48716) lies on these lines: {3, 311}, {4, 28728}, {30, 41716}, {69, 32428}, {76, 42329}, {98, 16276}, {182, 39906}, {1352, 36790}, {1975, 33971}, {2782, 6776}, {2790, 5921}, {14570, 30258}, {36212, 39530}

X(48716) = reflection of X(39910) in X(182)
X(48716) = orthologic center (10th Brocard, 7th Brocard)
X(48716) = X(20)-of-7th Brocard triangle
X(48716) = X(5889)-of-1st Brocard triangle
X(48716) = {X(182), X(39910)}-harmonic conjugate of X(39906)


X(48717) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 8th MIXTILINEAR TO 4th MIXTILINEAR

Barycentrics    a*(-a+b+c)*(4*a^8-8*(b+c)*a^7-3*(8*b^2+3*b*c+8*c^2)*a^6+2*(b+c)*(35*b^2-47*b*c+35*c^2)*a^5-(26*b^4+26*c^4-b*c*(79*b^2+114*b*c+79*c^2))*a^4-12*(b^2-c^2)*(b-c)*(5*b^2+3*b*c+5*c^2)*a^3+(52*b^4+52*c^4+b*c*(29*b^2-126*b*c+29*c^2))*(b-c)^2*a^2-2*(b^2-c^2)*(b-c)^3*(b^2+7*b*c+c^2)*a-3*(b+2*c)*(2*b+c)*(b-c)^6) : :

The reciprocal orthologic center of these triangles is X(31980).

X(48717) lies on these lines: {55, 31980}

X(48717) = orthologic center (8th mixtilinear, 4th mixtilinear)


X(48718) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 9th MIXTILINEAR TO 3rd MIXTILINEAR

Barycentrics    a*(4*a^12-8*(b+c)*a^11-(32*b^2-23*b*c+32*c^2)*a^10+2*(b+c)*(29*b^2+42*b*c+29*c^2)*a^9+(82*b^4+82*c^4-b*c*(429*b^2+518*b*c+429*c^2))*a^8-4*(b+c)*(38*b^4+38*c^4+7*b*c*(b^2-52*b*c+c^2))*a^7-2*(44*b^6+44*c^6-(561*b^4+561*c^4-2*b*c*(143*b^2+899*b*c+143*c^2))*b*c)*a^6+4*(b+c)*(47*b^6+47*c^6-(105*b^4+105*c^4+b*c*(627*b^2-1642*b*c+627*c^2))*b*c)*a^5+2*(16*b^8+16*c^8-(511*b^6+511*c^6-(1372*b^4+1372*c^4+3*b*c*(325*b^2-1416*b*c+325*c^2))*b*c)*b*c)*a^4-4*(b+c)*(28*b^8+28*c^8-(147*b^6+147*c^6+(88*b^4+88*c^4-b*c*(1499*b^2-2616*b*c+1499*c^2))*b*c)*b*c)*a^3+(8*b^6+8*c^6+(279*b^4+279*c^4-2*b*c*(794*b^2-1357*b*c+794*c^2))*b*c)*(b^2-c^2)^2*a^2+2*(b^2-c^2)^3*(b-c)*(b^2-4*b*c+c^2)*(13*b^2-34*b*c+13*c^2)*a-3*(b^2-c^2)^4*(b-c)^2*(2*b-c)*(b-2*c)) : :

The reciprocal orthologic center of these triangles is X(31979).

X(48718) lies on these lines: {56, 31979}

X(48718) = orthologic center (9th mixtilinear, 3rd mixtilinear)


X(48719) = PERSPECTOR OF THESE TRIANGLES: BEVAN ANTIPODAL AND DAO

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

X(48719) lies on these lines: {223, 20226}, {1001, 10571}, {1419, 2293}, {4853, 21147}, {16713, 18623}

X(48719) = cevapoint of X(57) and X(1043)
X(48719) = perspector (Bevan antipodal, Dao)
X(48719) = crosssum of X(57) and X(1042)


X(48720) = PERSPECTOR OF THESE TRIANGLES: DAO AND X-PARABOLA-TANGENTIAL

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

X(48720) lies on these lines: {}

X(48720) = cevapoint of X(115) and X(1043)
X(48720) = crosssum of X(115) and X(1042)
X(48720) = perspector (Dao, X-parabola-tangential)
X(48720) = X(1043)-Ceva conjugate of-X(115)


X(48721) = X(6)X(523)∩X(30)X(115)

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

X(48721) lies on the cubic K1275 and these lines: {6, 523}, {30, 115}, {111, 7471}, {574, 36177}, {842, 36899}, {1384, 46633}, {2502, 3233}, {2549, 47084}, {2966, 41254}, {3054, 11007}, {3815, 34094}, {5024, 46634}, {5112, 47239}, {6128, 44398}, {6531, 7473}, {7735, 16092}, {9154, 35278}, {11580, 36188}, {11594, 47561}, {16303, 28662}, {18907, 34209}, {20976, 30221}, {36181, 37689}, {36194, 37637}, {46992, 47169}

X(48721) = reflection of X(i) in X(j) for these {i,j}: {5112, 47239}, {46986, 34094}, {46987, 36177}
X(48721) = crossdifference of every pair of points on line {511, 34291}
X(48721) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {115, 187, 5915}, {115, 23967, 230}, {35606, 35906, 6}

leftri

Centers related to anti-Kenmotu-free-vertices triangles: X(48722)-X(48793)

rightri

This preamble and centers X(48722)-X(48793) were contributed by César Eliud Lozada, May 14, 2022.

Anti-Kenmotu-free-vertices triangles were introduced in the preamble just before X(45345)..


X(48722) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 1st ALTINTAS-ISODYNAMIC

Barycentrics    -a^2*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)*sqrt(3)+8*S^3+2*a^6-2*(b^2+c^2)*a^4+(b^4+c^4)*a^2-(b^2+c^2)*(b^2-c^2)^2 : :
X(48722) = X(6268)+3*X(21156)

The reciprocal orthologic center of these triangles is X(4).

X(48722) lies on these lines: {2, 98}, {5, 6302}, {13, 372}, {530, 36439}, {531, 48728}, {590, 6782}, {615, 6115}, {616, 45508}, {618, 641}, {2043, 22796}, {2044, 9739}, {2046, 33441}, {2782, 6303}, {5473, 45498}, {5478, 45544}, {6268, 21156}, {6270, 45550}, {6306, 48750}, {6811, 41071}, {7975, 45572}, {9901, 45530}, {9916, 45532}, {9982, 45538}, {10062, 45580}, {10078, 45582}, {11705, 45500}, {12142, 45502}, {12205, 45504}, {12337, 45520}, {12472, 45534}, {12473, 45536}, {12781, 45546}, {12793, 45548}, {12922, 45556}, {12932, 45558}, {12942, 45560}, {12952, 45562}, {12990, 45569}, {12991, 45566}, {13076, 45570}, {13103, 45578}, {13105, 45584}, {13107, 45586}, {13765, 42974}, {13917, 45574}, {13982, 45577}, {14136, 32788}, {14813, 48734}, {15765, 41022}, {16001, 35732}, {18587, 36765}, {18974, 45506}, {19073, 45512}, {19074, 45515}, {22773, 45540}, {25154, 36454}, {33392, 34551}, {35754, 45565}, {36457, 48778}, {41023, 48726}, {45349, 48456}, {45351, 48457}, {45377, 48655}

X(48722) = midpoint of X(2044) and X(33440)
X(48722) = reflection of X(48723) in X(6771)
X(48722) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {1st Altintas-isodynamic, Bankoff, 3rd Fermat-Dao, 7th Fermat-Dao, 11th Fermat-Dao, 15th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi, 1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi, 1st half-diamonds-central, 1st isodynamic-Dao, 3rd isodynamic-Dao, Largest-circumscribed-equilateral, 1st Lemoine-Dao, outer-Napoleon}
X(48722) = X(13)-of-1st anti-Kenmotu-free-vertices triangle
X(48722) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 5617, 48723), (2, 45554, 48724)


X(48723) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 1st ALTINTAS-ISODYNAMIC

Barycentrics    a^2*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)*sqrt(3)-8*S^3+2*a^6-2*(b^2+c^2)*a^4+(b^4+c^4)*a^2-(b^2+c^2)*(b^2-c^2)^2 : :
X(48723) = X(6270)+3*X(21156)

The reciprocal orthologic center of these triangles is X(4).

X(48723) lies on these lines: {2, 98}, {5, 6306}, {13, 371}, {530, 36457}, {531, 48729}, {590, 6115}, {615, 6782}, {616, 45509}, {618, 642}, {2043, 9738}, {2044, 22796}, {2045, 33440}, {2782, 6307}, {5473, 45499}, {5478, 45545}, {6268, 45551}, {6270, 21156}, {6302, 48751}, {6813, 41071}, {7975, 45573}, {9901, 45531}, {9916, 45533}, {9982, 45539}, {10062, 45581}, {10078, 45583}, {11705, 45501}, {12142, 45503}, {12205, 45505}, {12337, 45521}, {12472, 45535}, {12473, 45537}, {12781, 45547}, {12793, 45549}, {12922, 45557}, {12932, 45559}, {12942, 45561}, {12952, 45563}, {12990, 45567}, {12991, 45568}, {13076, 45571}, {13103, 45579}, {13105, 45585}, {13107, 45587}, {13646, 42974}, {13917, 45576}, {13982, 45575}, {14136, 32787}, {14814, 48735}, {16001, 42282}, {18585, 41022}, {18586, 36765}, {18974, 45507}, {19073, 45514}, {19074, 45513}, {22773, 45541}, {25154, 36436}, {33394, 34552}, {35753, 45564}, {36439, 48779}, {41023, 48727}, {45350, 48457}, {45352, 48456}, {45378, 48655}

X(48723) = midpoint of X(2043) and X(33441)
X(48723) = reflection of X(48722) in X(6771)
X(48723) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {1st Altintas-isodynamic, Bankoff, 3rd Fermat-Dao, 7th Fermat-Dao, 11th Fermat-Dao, 15th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi, 1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi, 1st half-diamonds-central, 1st isodynamic-Dao, 3rd isodynamic-Dao, Largest-circumscribed-equilateral, 1st Lemoine-Dao, outer-Napoleon}
X(48723) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 5617, 48722), (2, 45555, 48725)


X(48724) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 2nd ALTINTAS-ISODYNAMIC

Barycentrics    a^2*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)*sqrt(3)+8*S^3+2*a^6-2*(b^2+c^2)*a^4+(b^4+c^4)*a^2-(b^2+c^2)*(b^2-c^2)^2 : :
X(48724) = X(6269)+3*X(21157)

The reciprocal orthologic center of these triangles is X(4).

X(48724) lies on these lines: {2, 98}, {4, 35759}, {5, 6303}, {14, 372}, {530, 48728}, {531, 36457}, {590, 6783}, {615, 6114}, {617, 45508}, {619, 641}, {2043, 9739}, {2044, 22797}, {2045, 33443}, {2782, 6302}, {5474, 45498}, {5479, 45544}, {6269, 21157}, {6271, 45550}, {6307, 48752}, {6811, 41070}, {7974, 45572}, {9900, 45530}, {9915, 45532}, {9981, 45538}, {10061, 45580}, {10077, 45582}, {11706, 45500}, {12141, 45502}, {12204, 45504}, {12336, 45520}, {12470, 45534}, {12471, 45536}, {12780, 45546}, {12792, 45548}, {12921, 45556}, {12931, 45558}, {12941, 45560}, {12951, 45562}, {12988, 45569}, {12989, 45566}, {13075, 45570}, {13102, 45578}, {13104, 45584}, {13106, 45586}, {13764, 42975}, {13916, 45574}, {13981, 45577}, {14137, 32788}, {14814, 48734}, {16002, 42282}, {18585, 41023}, {18975, 45506}, {19075, 45512}, {19076, 45515}, {22774, 45540}, {25164, 36436}, {33395, 34552}, {35851, 45565}, {36439, 48778}, {41022, 48726}, {45349, 48458}, {45351, 48459}, {45377, 48656}

X(48724) = midpoint of X(2043) and X(33442)
X(48724) = reflection of X(48725) in X(6774)
X(48724) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {2nd Altintas-isodynamic, 4th Fermat-Dao, 8th Fermat-Dao, 12th Fermat-Dao, 16th Fermat-Dao, 1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi, 3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi, 2nd half-diamonds-central, 2nd isodynamic-Dao, 4th isodynamic-Dao, 2nd Lemoine-Dao, inner-Napoleon}
X(48724) = X(14)-of-1st anti-Kenmotu-free-vertices triangle
X(48724) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 5613, 48725), (2, 45554, 48722)


X(48725) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 2nd ALTINTAS-ISODYNAMIC

Barycentrics    -a^2*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)*sqrt(3)-8*S^3+2*a^6-2*(b^2+c^2)*a^4+(b^4+c^4)*a^2-(b^2+c^2)*(b^2-c^2)^2 : :
X(48725) = X(6271)+3*X(21157)

The reciprocal orthologic center of these triangles is X(4).

X(48725) lies on these lines: {2, 98}, {5, 6307}, {14, 371}, {530, 48729}, {531, 36439}, {590, 6114}, {615, 6783}, {617, 45509}, {619, 642}, {2043, 22797}, {2044, 9738}, {2046, 33442}, {2782, 6306}, {5474, 45499}, {5479, 45545}, {6269, 45551}, {6271, 21157}, {6303, 48753}, {6813, 41070}, {7974, 45573}, {9900, 45531}, {9915, 45533}, {9981, 45539}, {10061, 45581}, {10077, 45583}, {11706, 45501}, {12141, 45503}, {12204, 45505}, {12336, 45521}, {12470, 45535}, {12471, 45537}, {12780, 45547}, {12792, 45549}, {12921, 45557}, {12931, 45559}, {12941, 45561}, {12951, 45563}, {12988, 45567}, {12989, 45568}, {13075, 45571}, {13102, 45579}, {13104, 45585}, {13106, 45587}, {13645, 42975}, {13916, 45576}, {13981, 45575}, {14137, 32787}, {14813, 35742}, {15765, 41023}, {16002, 35732}, {18975, 45507}, {19075, 45514}, {19076, 45513}, {22774, 45541}, {25164, 36454}, {33393, 34551}, {35850, 45564}, {36457, 48779}, {41022, 48727}, {45350, 48459}, {45352, 48458}, {45378, 48656}

X(48725) = midpoint of X(2044) and X(33443)
X(48725) = reflection of X(48724) in X(6774)
X(48725) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {2nd Altintas-isodynamic, 4th Fermat-Dao, 8th Fermat-Dao, 12th Fermat-Dao, 16th Fermat-Dao, 1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi, 3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi, 2nd half-diamonds-central, 2nd isodynamic-Dao, 4th isodynamic-Dao, 2nd Lemoine-Dao, inner-Napoleon}
X(48725) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 5613, 48724), (2, 45555, 48723)


X(48726) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 1st ANTI-BROCARD

Barycentrics    3*(b^2+c^2)*a^8-4*(b^4+b^2*c^2+c^4)*a^6+3*(b^6+c^6)*a^4-2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*b^2*c^2+2*S*(2*a^8-3*(b^2+c^2)*a^6+3*(b^4+c^4)*a^4-(b^2+c^2)*(2*b^4-3*b^2*c^2+2*c^4)*a^2-(b^2-c^2)^2*b^2*c^2) : :
X(48726) = X(6226)+3*X(34473)

The reciprocal orthologic center of these triangles is X(5999).

X(48726) lies on the circumcircle of 1st anti-Kenmotu-free-vertices triangle and these lines: {30, 48728}, {98, 372}, {99, 45498}, {114, 641}, {115, 45544}, {147, 45508}, {182, 10007}, {542, 41490}, {690, 48730}, {2023, 18993}, {2782, 9739}, {2783, 48705}, {2784, 48764}, {2787, 48686}, {2794, 43121}, {2799, 48732}, {3023, 45506}, {3027, 45570}, {6033, 45554}, {6226, 34473}, {6227, 45550}, {7690, 33813}, {7970, 45572}, {8980, 45574}, {9737, 48785}, {9860, 45530}, {9861, 45532}, {9862, 45510}, {9864, 45546}, {10053, 45580}, {10069, 45582}, {10352, 45552}, {10991, 13989}, {11710, 45500}, {12131, 45502}, {12176, 45504}, {12178, 45520}, {12179, 45534}, {12180, 45536}, {12181, 45548}, {12182, 45556}, {12183, 45558}, {12184, 45560}, {12185, 45562}, {12186, 45569}, {12187, 45566}, {12188, 45578}, {12189, 45584}, {12190, 45586}, {13967, 45577}, {19055, 45512}, {19056, 45515}, {22504, 45540}, {22505, 45542}, {33370, 33430}, {35825, 45565}, {38744, 45377}, {41022, 48724}, {41023, 48722}, {45349, 48462}, {45351, 48463}, {48770, 48772}

X(48726) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard}
X(48726) = X(98)-of-1st anti-Kenmotu-free-vertices triangle
X(48726) = reflection of X(i) in X(j) for these (i, j): (48727, 12042), (48784, 9739)


X(48727) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 1st ANTI-BROCARD

Barycentrics    3*(b^2+c^2)*a^8-4*(b^4+b^2*c^2+c^4)*a^6+3*(b^6+c^6)*a^4-2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*b^2*c^2-2*S*(2*a^8-3*(b^2+c^2)*a^6+3*(b^4+c^4)*a^4-(b^2+c^2)*(2*b^4-3*b^2*c^2+2*c^4)*a^2-(b^2-c^2)^2*b^2*c^2) : :
X(48727) = X(6227)+3*X(34473)

The reciprocal orthologic center of these triangles is X(5999).

X(48727) lies on the circumcircle of 2nd anti- Kenmotu-free-vertices triangle and these lines: {30, 48729}, {98, 371}, {99, 45499}, {114, 642}, {115, 45545}, {147, 45509}, {182, 10007}, {542, 41491}, {690, 48731}, {2023, 18994}, {2782, 9738}, {2783, 48706}, {2784, 48765}, {2787, 48687}, {2794, 43120}, {2799, 48733}, {3023, 45507}, {3027, 45571}, {6033, 45555}, {6226, 45551}, {6227, 34473}, {7692, 33813}, {7970, 45573}, {8980, 45576}, {8997, 10991}, {9737, 48784}, {9860, 45531}, {9861, 45533}, {9862, 45511}, {9864, 45547}, {10053, 45581}, {10069, 45583}, {10352, 45553}, {11710, 45501}, {12131, 45503}, {12176, 45505}, {12178, 45521}, {12179, 45535}, {12180, 45537}, {12181, 45549}, {12182, 45557}, {12183, 45559}, {12184, 45561}, {12185, 45563}, {12186, 45567}, {12187, 45568}, {12188, 45579}, {12189, 45585}, {12190, 45587}, {13967, 45575}, {19055, 45514}, {19056, 45513}, {22504, 45541}, {22505, 45543}, {33371, 33431}, {35824, 45564}, {38744, 45378}, {41022, 48725}, {41023, 48723}, {45350, 48463}, {45352, 48462}, {48771, 48773}

X(48727) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard}
X(48727) = reflection of X(i) in X(j) for these (i, j): (48726, 12042), (48785, 9738)


X(48728) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO ANTI-MCCAY

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

The reciprocal orthologic center of these triangles is X(9855).

X(48728) lies on these lines: {30, 48726}, {76, 13684}, {114, 41491}, {182, 7606}, {325, 32419}, {372, 671}, {530, 48724}, {531, 48722}, {542, 44475}, {543, 41490}, {638, 22562}, {641, 2482}, {2782, 48744}, {2796, 48764}, {5418, 33343}, {5969, 48768}, {8591, 45508}, {8724, 45554}, {8787, 44656}, {9875, 45530}, {9876, 45532}, {9878, 45538}, {9880, 45544}, {9881, 45546}, {9882, 45550}, {9883, 45553}, {9884, 45572}, {10054, 45580}, {10070, 45582}, {12117, 45498}, {12132, 45502}, {12191, 45504}, {12243, 45510}, {12258, 45500}, {12326, 45520}, {12345, 45534}, {12346, 45536}, {12347, 45548}, {12348, 45556}, {12349, 45558}, {12350, 45560}, {12351, 45562}, {12352, 45569}, {12353, 45566}, {12354, 45570}, {12355, 45578}, {12356, 45584}, {12357, 45586}, {13843, 13968}, {13908, 45574}, {18969, 45506}, {19057, 45512}, {19058, 45515}, {22565, 45540}, {22566, 45542}, {35699, 45565}, {45349, 48470}, {45351, 48471}, {45377, 48657}

X(48728) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {anti-McCay, McCay, Moses-Steiner osculatory}
X(48728) = X(671)-of-1st anti-Kenmotu-free-vertices triangle
X(48728) = reflection of X(48784) in X(41490)


X(48729) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO ANTI-MCCAY

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

The reciprocal orthologic center of these triangles is X(9855).

X(48729) lies on these lines: {30, 48727}, {76, 13804}, {114, 41490}, {182, 7606}, {325, 32421}, {371, 671}, {530, 48725}, {531, 48723}, {542, 44476}, {543, 41491}, {637, 22563}, {642, 2482}, {2782, 48745}, {2796, 48765}, {5420, 33342}, {5969, 48769}, {8591, 45509}, {8724, 45555}, {8787, 44657}, {9875, 45531}, {9876, 45533}, {9878, 45539}, {9880, 45545}, {9881, 45547}, {9882, 45552}, {9883, 45551}, {9884, 45573}, {10054, 45581}, {10070, 45583}, {12117, 45499}, {12132, 45503}, {12191, 45505}, {12243, 45511}, {12258, 45501}, {12326, 45521}, {12345, 45535}, {12346, 45537}, {12347, 45549}, {12348, 45557}, {12349, 45559}, {12350, 45561}, {12351, 45563}, {12352, 45567}, {12353, 45568}, {12354, 45571}, {12355, 45579}, {12356, 45585}, {12357, 45587}, {13720, 13908}, {13968, 45575}, {18969, 45507}, {19057, 45514}, {19058, 45513}, {22565, 45541}, {22566, 45543}, {35698, 45564}, {45350, 48471}, {45352, 48470}, {45378, 48657}

X(48729) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {anti-McCay, McCay, Moses-Steiner osculatory}
X(48729) = reflection of X(48785) in X(41491)


X(48730) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*(3*(b^2+c^2)*a^8-6*(b^4+c^4)*a^6+3*(b^2+c^2)*b^2*c^2*a^4+6*(b^6-c^6)*(b^2-c^2)*a^2-3*(b^4-c^4)*(b^6-c^6)+2*S*(2*a^8-3*(b^2+c^2)*a^6-3*(b^4-4*b^2*c^2+c^4)*a^4+(b^2+c^2)*(7*b^4-15*b^2*c^2+7*c^4)*a^2-(3*b^4+7*b^2*c^2+3*c^4)*(b^2-c^2)^2)) : :
X(48730) = X(7725)-5*X(15021) = X(7726)+3*X(15055)

The reciprocal orthologic center of these triangles is X(12112).

X(48730) lies on the circumcircle of 1st anti-Kenmotu-free-vertices triangle and these lines: {30, 48736}, {74, 372}, {110, 5408}, {113, 641}, {125, 45544}, {146, 45508}, {182, 2781}, {541, 41490}, {542, 48784}, {690, 48726}, {1503, 48782}, {1511, 7690}, {1539, 45542}, {2771, 48705}, {2777, 48466}, {3024, 45506}, {3028, 45570}, {5663, 9739}, {7725, 15021}, {7726, 15055}, {7728, 45554}, {7978, 45572}, {8674, 48686}, {8994, 45574}, {9517, 48732}, {9737, 48787}, {9904, 45530}, {9919, 45532}, {9984, 45538}, {10065, 45580}, {10081, 45582}, {10620, 45578}, {10628, 48774}, {10990, 48734}, {11709, 45500}, {12133, 45502}, {12192, 45504}, {12244, 45510}, {12327, 45520}, {12365, 45534}, {12366, 45536}, {12368, 45546}, {12369, 45548}, {12371, 45556}, {12372, 45558}, {12373, 45560}, {12374, 45562}, {12377, 45569}, {12378, 45566}, {12381, 45584}, {12382, 45586}, {13969, 45577}, {15041, 45410}, {17702, 48738}, {19059, 45512}, {19060, 45515}, {22583, 45540}, {35827, 45565}, {38790, 45377}, {45349, 48472}, {45351, 48473}

X(48730) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {anti-orthocentroidal, orthocentroidal}
X(48730) = X(74)-of-1st anti-Kenmotu-free-vertices triangle
X(48730) = reflection of X(i) in X(j) for these (i, j): (48731, 12041), (48786, 9739)


X(48731) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*(3*(b^2+c^2)*a^8-6*(b^4+c^4)*a^6+3*(b^2+c^2)*b^2*c^2*a^4+6*(b^6-c^6)*(b^2-c^2)*a^2-3*(b^4-c^4)*(b^6-c^6)-2*S*(2*a^8-3*(b^2+c^2)*a^6-3*(b^4-4*b^2*c^2+c^4)*a^4+(b^2+c^2)*(7*b^4-15*b^2*c^2+7*c^4)*a^2-(3*b^4+7*b^2*c^2+3*c^4)*(b^2-c^2)^2)) : :
X(48731) = X(7725)+3*X(15055) = X(7726)-5*X(15021)

The reciprocal orthologic center of these triangles is X(12112).

X(48731) lies on the circumcircle of 2nd anti- Kenmotu-free-vertices triangle and these lines: {30, 48737}, {74, 371}, {110, 5409}, {113, 642}, {125, 45545}, {146, 45509}, {182, 2781}, {541, 41491}, {542, 48785}, {690, 48727}, {1503, 48783}, {1511, 7692}, {1539, 45543}, {2771, 48706}, {2777, 48467}, {3024, 45507}, {3028, 45571}, {5663, 9738}, {7725, 15055}, {7726, 15021}, {7728, 45555}, {7978, 45573}, {8674, 48687}, {8994, 45576}, {9517, 48733}, {9737, 48786}, {9904, 45531}, {9919, 45533}, {9984, 45539}, {10065, 45581}, {10081, 45583}, {10620, 45579}, {10628, 48775}, {10990, 48735}, {11709, 45501}, {12133, 45503}, {12192, 45505}, {12244, 45511}, {12327, 45521}, {12365, 45535}, {12366, 45537}, {12368, 45547}, {12369, 45549}, {12371, 45557}, {12372, 45559}, {12373, 45561}, {12374, 45563}, {12377, 45567}, {12378, 45568}, {12381, 45585}, {12382, 45587}, {13969, 45575}, {15041, 45411}, {17702, 48739}, {19059, 45514}, {19060, 45513}, {22583, 45541}, {35826, 45564}, {38790, 45378}, {45350, 48473}, {45352, 48472}

X(48731) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {anti-orthocentroidal, orthocentroidal}
X(48731) = reflection of X(i) in X(j) for these (i, j): (48730, 12041), (48787, 9738)


X(48732) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*(3*(b^2+c^2)*a^12-4*(b^4+b^2*c^2+c^4)*a^10-(b^2+c^2)*(b^4-5*b^2*c^2+c^4)*a^8-4*(b^2-c^2)^2*b^2*c^2*a^6+(b^8-c^8)*(b^2-c^2)*a^4+4*(b^4-c^4)^2*(b^4+c^4)*a^2+(b^4-c^4)*(b^2-c^2)*(-3*b^8-3*c^8-(b^4+8*b^2*c^2+c^4)*b^2*c^2)+2*S*(2*a^12-3*(b^2+c^2)*a^10+(b^4+4*b^2*c^2+c^4)*a^8-(b^2+c^2)*(2*b^4-3*b^2*c^2+2*c^4)*a^6-(b^2-c^2)^2*b^2*c^2*a^4+(b^4-c^4)*(b^2-c^2)*(5*b^4+3*b^2*c^2+5*c^4)*a^2+(b^6-c^6)*(b^2-c^2)*(-3*b^4-2*b^2*c^2-3*c^4))) : :
X(48732) = X(12806)+3*X(38717)

The reciprocal orthologic center of these triangles is X(19158).

X(48732) lies on the circumcircle of 1st anti-Kenmotu-free-vertices triangle and these lines: {112, 45498}, {127, 45544}, {132, 641}, {182, 38624}, {372, 1297}, {2781, 48786}, {2794, 48784}, {2799, 48726}, {2806, 48686}, {2831, 48705}, {3320, 45570}, {6020, 45506}, {7690, 38608}, {9517, 48730}, {9530, 41490}, {9733, 19165}, {9737, 48789}, {9739, 48788}, {12145, 45502}, {12207, 45504}, {12253, 45510}, {12265, 45500}, {12340, 45520}, {12384, 45508}, {12408, 45530}, {12413, 45532}, {12478, 45534}, {12479, 45536}, {12503, 45538}, {12784, 45546}, {12796, 45548}, {12805, 45550}, {12806, 38717}, {12918, 45554}, {12925, 45556}, {12935, 45558}, {12945, 45560}, {12955, 45562}, {12996, 45569}, {12997, 45566}, {13099, 45572}, {13115, 45578}, {13116, 45580}, {13117, 45582}, {13118, 45584}, {13119, 45586}, {13918, 45574}, {13985, 45577}, {19093, 45512}, {19094, 45515}, {19159, 45540}, {19160, 45542}, {34217, 42859}, {35829, 45565}, {45349, 48474}, {45351, 48475}, {45377, 48658}

X(48732) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {1st anti-orthosymmedial, 1st orthosymmedial}
X(48732) = X(1297)-of-1st anti-Kenmotu-free-vertices triangle
X(48732) = reflection of X(i) in X(j) for these (i, j): (48733, 38624), (48788, 9739)


X(48733) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*(3*(b^2+c^2)*a^12-4*(b^4+b^2*c^2+c^4)*a^10-(b^2+c^2)*(b^4-5*b^2*c^2+c^4)*a^8-4*(b^2-c^2)^2*b^2*c^2*a^6+(b^8-c^8)*(b^2-c^2)*a^4+4*(b^4-c^4)^2*(b^4+c^4)*a^2+(b^4-c^4)*(b^2-c^2)*(-3*b^8-3*c^8-(b^4+8*b^2*c^2+c^4)*b^2*c^2)-2*S*(2*a^12-3*(b^2+c^2)*a^10+(b^4+4*b^2*c^2+c^4)*a^8-(b^2+c^2)*(2*b^4-3*b^2*c^2+2*c^4)*a^6-(b^2-c^2)^2*b^2*c^2*a^4+(b^4-c^4)*(b^2-c^2)*(5*b^4+3*b^2*c^2+5*c^4)*a^2+(b^6-c^6)*(b^2-c^2)*(-3*b^4-2*b^2*c^2-3*c^4))) : :
X(48733) = X(12805)+3*X(38717)

The reciprocal orthologic center of these triangles is X(19158).

X(48733) lies on the circumcircle of 2nd anti- Kenmotu-free-vertices triangle and these lines: {112, 45499}, {127, 45545}, {132, 642}, {182, 38624}, {371, 1297}, {2781, 48787}, {2794, 48785}, {2799, 48727}, {2806, 48687}, {2831, 48706}, {3320, 45571}, {6020, 45507}, {7692, 38608}, {8989, 9732}, {9517, 48731}, {9530, 41491}, {9737, 48788}, {9738, 48789}, {12145, 45503}, {12207, 45505}, {12253, 45511}, {12265, 45501}, {12340, 45521}, {12384, 45509}, {12408, 45531}, {12413, 45533}, {12478, 45535}, {12479, 45537}, {12503, 45539}, {12784, 45547}, {12796, 45549}, {12805, 38717}, {12806, 45551}, {12918, 45555}, {12925, 45557}, {12935, 45559}, {12945, 45561}, {12955, 45563}, {12996, 45567}, {12997, 45568}, {13099, 45573}, {13115, 45579}, {13116, 45581}, {13117, 45583}, {13118, 45585}, {13119, 45587}, {13918, 45576}, {13985, 45575}, {19093, 45514}, {19094, 45513}, {19159, 45541}, {19160, 45543}, {34217, 42858}, {35828, 45564}, {45350, 48475}, {45352, 48474}, {45378, 48658}

X(48733) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {1st anti-orthosymmedial, 1st orthosymmedial}
X(48733) = reflection of X(i) in X(j) for these (i, j): (48732, 38624), (48789, 9738)


X(48734) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 3rd ANTI-TRI-SQUARES

Barycentrics    4*a^6-5*(b^2+c^2)*a^4+2*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)-2*S*(2*a^4-3*(b^2+c^2)*a^2+(b^2-c^2)^2) : :
X(48734) = X(4)-3*X(486) = 2*X(4)-3*X(6251) = X(4)+3*X(12256) = 4*X(140)-3*X(642) = 3*X(487)-7*X(3523) = 5*X(1656)-6*X(6119) = 5*X(1656)-3*X(6290) = X(1657)+3*X(12601) = 5*X(3522)-3*X(12123) = 5*X(3522)+3*X(12221) = 7*X(3523)+3*X(6280) = 4*X(3850)-3*X(22596) = 7*X(3851)-3*X(48659) = X(5059)+3*X(12296) = X(6251)+2*X(12256) = 3*X(7612)-X(22592) = 3*X(12268)-2*X(13464) = 3*X(12509)-11*X(21735) = 3*X(13847)-X(36655)

The reciprocal orthologic center of these triangles is X(486).

X(48734) lies on these lines: {2, 6281}, {3, 591}, {4, 372}, {5, 48778}, {30, 48781}, {39, 44648}, {114, 8184}, {140, 141}, {376, 22484}, {487, 1270}, {492, 45552}, {550, 9739}, {615, 48467}, {639, 43118}, {1503, 13966}, {1587, 13711}, {1588, 13770}, {1656, 6119}, {1657, 12601}, {2045, 6300}, {2046, 6301}, {3070, 39565}, {3071, 7756}, {3517, 9921}, {3522, 12123}, {3594, 36656}, {3850, 22596}, {3851, 45377}, {5059, 12296}, {5062, 7755}, {5304, 9758}, {5418, 14912}, {5420, 6776}, {5493, 48740}, {5871, 13941}, {5882, 45715}, {6201, 42523}, {6215, 45872}, {6250, 42216}, {6278, 11291}, {6279, 32806}, {6395, 45440}, {6396, 45406}, {6398, 13748}, {6399, 13934}, {6420, 6811}, {6813, 35813}, {7583, 45869}, {7584, 45545}, {7612, 10195}, {7690, 33923}, {7980, 45572}, {8960, 13638}, {8981, 12007}, {9540, 13650}, {9906, 45530}, {9986, 45538}, {10067, 45580}, {10083, 45582}, {10194, 14244}, {10299, 45522}, {10577, 45407}, {10619, 48774}, {10783, 32786}, {10990, 48730}, {10991, 13989}, {10992, 48784}, {10993, 48705}, {11316, 15069}, {12147, 45502}, {12210, 45504}, {12268, 13464}, {12343, 45520}, {12484, 45534}, {12485, 45536}, {12509, 21735}, {12787, 45546}, {12799, 45548}, {12928, 45556}, {12938, 45558}, {12948, 45560}, {12958, 45562}, {13002, 45569}, {13003, 45566}, {13081, 45570}, {13132, 45584}, {13133, 45586}, {13687, 13932}, {13749, 13951}, {13847, 36655}, {13880, 13967}, {13993, 45860}, {14230, 18762}, {14239, 42226}, {14813, 48722}, {14814, 48724}, {14900, 48788}, {15105, 48766}, {18989, 45506}, {19104, 45512}, {22591, 39647}, {22595, 45540}, {22605, 42278}, {22606, 42279}, {26288, 42024}, {26341, 45472}, {30714, 48786}, {32490, 38740}, {32788, 36709}, {35743, 48752}, {35833, 45565}, {36371, 36437}, {36374, 36455}, {39387, 45551}, {43174, 48764}, {43510, 45077}, {45349, 48478}, {45351, 48479}

X(48734) = midpoint of X(i) and X(j) for these {i, j}: {376, 22484}, {486, 12256}, {487, 6280}, {12123, 12221}, {22591, 39647}, {26288, 42024}
X(48734) = reflection of X(i) in X(j) for these (i, j): (6251, 486), (6290, 6119), (13687, 13932), (45860, 13993)
X(48734) = complement of X(6281)
X(48734) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {3rd anti-tri-squares, 2nd half-squares, 4th tri-squares, inner-Vecten}
X(48734) = X(486)-of-1st anti-Kenmotu-free-vertices triangle
X(48734) = X(15294)-of-outer-Vecten triangle, when ABC is acute
X(48734) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 45525, 372), (140, 8550, 48735), (182, 48772, 641), (372, 45510, 48466), (372, 48466, 45544), (45510, 45525, 4)


X(48735) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 4th ANTI-TRI-SQUARES

Barycentrics    4*a^6-5*(b^2+c^2)*a^4+2*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)+2*S*(2*a^4-3*(b^2+c^2)*a^2+(b^2-c^2)^2) : :
X(48735) = X(4)-3*X(485) = 2*X(4)-3*X(6250) = X(4)+3*X(12257) = 4*X(140)-3*X(641) = 3*X(488)-7*X(3523) = 5*X(1656)-6*X(6118) = 5*X(1656)-3*X(6289) = X(1657)+3*X(12602) = 5*X(3522)-3*X(12124) = 5*X(3522)+3*X(12222) = 7*X(3523)+3*X(6279) = 4*X(3850)-3*X(22625) = 7*X(3851)-3*X(48660) = X(5059)+3*X(12297) = X(6250)+2*X(12257) = 3*X(7612)-X(22591) = 3*X(12269)-2*X(13464) = 3*X(12510)-11*X(21735) = 3*X(13846)-X(36656)

The reciprocal orthologic center of these triangles is X(485).

X(48735) lies on these lines: {2, 6278}, {3, 1991}, {4, 371}, {5, 48779}, {30, 48780}, {39, 44647}, {114, 8180}, {140, 141}, {376, 22485}, {488, 1271}, {491, 45553}, {550, 9738}, {590, 48466}, {640, 43119}, {1503, 8981}, {1587, 13651}, {1588, 13834}, {1656, 6118}, {1657, 12602}, {2045, 6305}, {2046, 6304}, {3070, 7756}, {3071, 39565}, {3517, 9922}, {3522, 12124}, {3592, 36655}, {3850, 22625}, {3851, 45378}, {5058, 7755}, {5059, 12297}, {5304, 9757}, {5418, 6776}, {5420, 14912}, {5493, 48741}, {5870, 8972}, {5882, 45716}, {6199, 45441}, {6200, 45407}, {6202, 42522}, {6214, 45871}, {6221, 13749}, {6222, 13882}, {6251, 42215}, {6280, 32805}, {6281, 11292}, {6419, 6813}, {6811, 35812}, {7583, 45544}, {7584, 45868}, {7612, 10194}, {7692, 33923}, {7981, 45573}, {8976, 13748}, {8980, 13921}, {8997, 10991}, {9907, 45531}, {9987, 45539}, {10068, 45581}, {10084, 45583}, {10195, 14229}, {10299, 45523}, {10576, 45406}, {10619, 48775}, {10784, 32785}, {10990, 48731}, {10992, 48785}, {10993, 48706}, {11315, 15069}, {11623, 43142}, {12007, 13966}, {12148, 45503}, {12211, 45505}, {12269, 13464}, {12344, 45521}, {12486, 45535}, {12487, 45537}, {12510, 21735}, {12788, 45547}, {12800, 45549}, {12929, 45557}, {12939, 45559}, {12949, 45561}, {12959, 45563}, {13004, 45567}, {13005, 45568}, {13082, 45571}, {13134, 45585}, {13135, 45587}, {13758, 13880}, {13771, 13935}, {13807, 13850}, {13846, 36656}, {13925, 45861}, {14233, 18538}, {14235, 42225}, {14813, 35742}, {14814, 48723}, {14900, 48789}, {15105, 48767}, {18988, 45507}, {19103, 45513}, {21736, 22645}, {22592, 39647}, {22624, 45541}, {22634, 42279}, {22635, 42278}, {26289, 42023}, {26348, 45473}, {30714, 48787}, {31454, 36709}, {31487, 36712}, {32491, 38740}, {32787, 36714}, {35832, 45564}, {36370, 36455}, {36372, 36437}, {39388, 45550}, {43174, 48765}, {43509, 45076}, {45350, 48481}, {45352, 48480}

X(48735) = midpoint of X(i) and X(j) for these {i, j}: {376, 22485}, {485, 12257}, {488, 6279}, {12124, 12222}, {22592, 39647}, {26289, 42023}
X(48735) = reflection of X(i) in X(j) for these (i, j): (6250, 485), (6289, 6118), (13807, 13850), (45861, 13925)
X(48735) = complement of X(6278)
X(48735) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {4th anti-tri-squares, 1st half-squares, 3rd tri-squares, outer-Vecten}
X(48735) = X(15294)-of-inner-Vecten triangle, when ABC is obtuse
X(48735) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 45524, 371), (140, 8550, 48734), (182, 48773, 642), (371, 45511, 48467), (371, 48467, 45545), (45511, 45524, 4)


X(48736) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO AAOA

Barycentrics    (a^6-(b^2+c^2)*a^4-(b^4+c^4)*a^2+(b^4-c^4)*(b^2-c^2))*(2*a^6-2*(b^2+c^2)*a^4+(b^4+c^4)*a^2-(b^4-c^4)*(b^2-c^2))+8*(b^2-c^2)^2*S^3*(-a^2+b^2+c^2) : :
X(48736) = X(12803)-5*X(15027) = X(12804)+3*X(15061)

The reciprocal orthologic center of these triangles is X(7574).

X(48736) lies on these lines: {2, 98}, {30, 48730}, {113, 45542}, {265, 372}, {399, 45377}, {511, 48782}, {641, 1511}, {2771, 48754}, {2777, 48766}, {5663, 48466}, {7690, 16163}, {9739, 17702}, {10088, 45560}, {10091, 45562}, {10113, 45544}, {10628, 48758}, {12121, 45498}, {12140, 45502}, {12201, 45504}, {12261, 45500}, {12334, 45520}, {12383, 45508}, {12407, 45530}, {12412, 45532}, {12466, 45534}, {12467, 45536}, {12501, 45538}, {12778, 45546}, {12790, 45548}, {12803, 15027}, {12804, 15061}, {12889, 45556}, {12890, 45558}, {12894, 45569}, {12895, 45566}, {12896, 45570}, {12898, 45572}, {12902, 45578}, {12903, 45580}, {12904, 45582}, {12905, 45584}, {12906, 45586}, {13915, 45574}, {13979, 45577}, {18968, 45506}, {19051, 45512}, {19052, 45515}, {19478, 45540}, {32423, 48772}, {35835, 45565}, {38724, 45410}, {44656, 46688}, {45349, 48483}, {45351, 48484}

X(48736) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {antiAOA, AOA, 1st Hyacinth}
X(48736) = X(265)-of-1st anti-Kenmotu-free-vertices triangle
X(48736) = reflection of X(i) in X(j) for these (i, j): (48737, 125), (48786, 48772)


X(48737) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO AAOA

Barycentrics    (a^6-(b^2+c^2)*a^4-(b^4+c^4)*a^2+(b^4-c^4)*(b^2-c^2))*(2*a^6-2*(b^2+c^2)*a^4+(b^4+c^4)*a^2-(b^4-c^4)*(b^2-c^2))-8*(b^2-c^2)^2*S^3*(-a^2+b^2+c^2) : :
X(48737) = X(12803)+3*X(15061) = X(12804)-5*X(15027)

The reciprocal orthologic center of these triangles is X(7574).

X(48737) lies on these lines: {2, 98}, {30, 48731}, {113, 45543}, {265, 371}, {399, 45378}, {511, 48783}, {642, 1511}, {2771, 48755}, {2777, 48767}, {5663, 48467}, {7692, 16163}, {9738, 17702}, {10088, 45561}, {10091, 45563}, {10113, 45545}, {10628, 48759}, {12121, 45499}, {12140, 45503}, {12201, 45505}, {12261, 45501}, {12334, 45521}, {12383, 45509}, {12407, 45531}, {12412, 45533}, {12466, 45535}, {12467, 45537}, {12501, 45539}, {12778, 45547}, {12790, 45549}, {12803, 15061}, {12804, 15027}, {12889, 45557}, {12890, 45559}, {12894, 45567}, {12895, 45568}, {12896, 45571}, {12898, 45573}, {12902, 45579}, {12903, 45581}, {12904, 45583}, {12905, 45585}, {12906, 45587}, {13915, 45576}, {13979, 45575}, {18968, 45507}, {19051, 45514}, {19052, 45513}, {19478, 45541}, {32423, 48773}, {35834, 45564}, {38724, 45411}, {44657, 46689}, {45350, 48484}, {45352, 48483}

X(48737) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {antiAOA, AOA, 1st Hyacinth}
X(48737) = reflection of X(i) in X(j) for these (i, j): (48736, 125), (48787, 48773)


X(48738) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO ARIES

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

The reciprocal orthologic center of these triangles is X(9833).

X(48738) lies on these lines: {3, 45408}, {30, 48766}, {68, 372}, {140, 141}, {155, 45554}, {539, 41490}, {1069, 45562}, {1154, 48758}, {1899, 5408}, {3157, 45560}, {6193, 45508}, {8968, 21243}, {9739, 44665}, {9896, 45530}, {9908, 45532}, {9923, 45538}, {9927, 45544}, {9928, 45546}, {9929, 45550}, {9930, 45553}, {9933, 45572}, {10055, 45580}, {10071, 45582}, {11411, 45510}, {12118, 45498}, {12134, 45502}, {12164, 45377}, {12193, 45504}, {12256, 13430}, {12259, 45500}, {12328, 45520}, {12415, 45534}, {12416, 45536}, {12418, 45548}, {12422, 45556}, {12423, 45558}, {12426, 45569}, {12427, 45566}, {12428, 45570}, {12429, 45578}, {12430, 45584}, {12431, 45586}, {13754, 48466}, {13909, 45574}, {13970, 45577}, {14984, 48782}, {17702, 48730}, {18970, 45506}, {19061, 45512}, {19062, 45515}, {22659, 45540}, {22660, 45542}, {35837, 45565}, {45349, 48485}, {45351, 48486}

X(48738) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {Aries, 2nd Hyacinth}
X(48738) = X(68)-of-1st anti-Kenmotu-free-vertices triangle
X(48738) = reflection of X(48739) in X(12359)


X(48739) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO ARIES

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

The reciprocal orthologic center of these triangles is X(9833).

X(48739) lies on these lines: {3, 45409}, {30, 48767}, {68, 371}, {140, 141}, {155, 45555}, {539, 41491}, {1069, 45563}, {1154, 48759}, {1899, 5409}, {3157, 45561}, {6193, 45509}, {9738, 44665}, {9896, 45531}, {9908, 45533}, {9923, 45539}, {9927, 45545}, {9928, 45547}, {9929, 45552}, {9930, 45551}, {9933, 45573}, {10055, 45581}, {10071, 45583}, {11411, 45511}, {12118, 45499}, {12134, 45503}, {12164, 45378}, {12193, 45505}, {12257, 13441}, {12259, 45501}, {12328, 45521}, {12415, 45535}, {12416, 45537}, {12418, 45549}, {12422, 45557}, {12423, 45559}, {12426, 45567}, {12427, 45568}, {12428, 45571}, {12429, 45579}, {12430, 45585}, {12431, 45587}, {13754, 48467}, {13909, 45576}, {13970, 45575}, {14984, 48783}, {17702, 48731}, {18970, 45507}, {19061, 45514}, {19062, 45513}, {22659, 45541}, {22660, 45543}, {35836, 45564}, {45350, 48486}, {45352, 48485}

X(48739) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {Aries, 2nd Hyacinth}
X(48739) = reflection of X(48738) in X(12359)


X(48740) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO BEVAN ANTIPODAL

Barycentrics    a*((b+c)*a^4+2*(b^2-b*c+c^2)*a^3+2*(b+c)*b*c*a^2-2*(b^3+c^3)*(b+c)*a-(b^4-c^4)*(b-c)+2*S*(2*a^3+(b+c)*a^2-2*(b^2+b*c+c^2)*a-(b^2-c^2)*(b-c))) : :
X(48740) = 3*X(165)+X(12698)

The reciprocal orthologic center of these triangles is X(1).

X(48740) lies on these lines: {1, 45498}, {3, 45398}, {4, 45546}, {10, 45544}, {40, 372}, {46, 45582}, {65, 45570}, {165, 12698}, {182, 3579}, {515, 48746}, {516, 48466}, {517, 9739}, {641, 946}, {962, 45508}, {1385, 7690}, {1702, 45515}, {1703, 45512}, {1836, 45560}, {1902, 45502}, {2800, 48705}, {2802, 48686}, {3057, 45506}, {5119, 45580}, {5493, 48734}, {5603, 45522}, {5709, 45526}, {5812, 45558}, {5840, 48754}, {5847, 48742}, {6001, 48766}, {6361, 45510}, {6566, 7968}, {7982, 45572}, {7991, 45530}, {9737, 45716}, {9911, 45532}, {10306, 45520}, {12197, 45504}, {12458, 45534}, {12459, 45536}, {12497, 45538}, {12696, 45548}, {12697, 45550}, {12699, 45554}, {12700, 45556}, {12701, 45562}, {12702, 45578}, {12703, 45584}, {12704, 45586}, {13912, 45574}, {13975, 45577}, {22770, 45540}, {22793, 45542}, {22841, 45569}, {22842, 45566}, {28174, 48772}, {28194, 41490}, {31439, 44656}, {35611, 45565}, {45349, 48487}, {45351, 48488}, {45377, 48661}

X(48740) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {Bevan antipodal, 3rd extouch}
X(48740) = X(40)-of-1st anti-Kenmotu-free-vertices triangle
X(48740) = reflection of X(i) in X(j) for these (i, j): (45715, 9739), (48466, 48764), (48741, 3579)


X(48741) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO BEVAN ANTIPODAL

Barycentrics    a*((b+c)*a^4+2*(b^2-b*c+c^2)*a^3+2*(b+c)*b*c*a^2-2*(b^3+c^3)*(b+c)*a-(b^4-c^4)*(b-c)-2*S*(2*a^3+(b+c)*a^2-2*(b^2+b*c+c^2)*a-(b^2-c^2)*(b-c))) : :
X(48741) = 3*X(165)+X(12697)

The reciprocal orthologic center of these triangles is X(1).

X(48741) lies on these lines: {1, 45499}, {3, 45399}, {4, 45547}, {10, 45545}, {40, 371}, {46, 45583}, {65, 45571}, {165, 12697}, {182, 3579}, {515, 48747}, {516, 48467}, {517, 9738}, {642, 946}, {962, 45509}, {1385, 7692}, {1702, 45513}, {1703, 45514}, {1836, 45561}, {1902, 45503}, {2800, 48706}, {2802, 48687}, {3057, 45507}, {5119, 45581}, {5493, 48735}, {5603, 45523}, {5709, 45527}, {5812, 45559}, {5840, 48755}, {5847, 48743}, {6001, 48767}, {6361, 45511}, {6567, 7969}, {7982, 45573}, {7991, 45531}, {9737, 45715}, {9911, 45533}, {10306, 45521}, {12197, 45505}, {12458, 45535}, {12459, 45537}, {12497, 45539}, {12696, 45549}, {12698, 45551}, {12699, 45555}, {12700, 45557}, {12701, 45563}, {12702, 45579}, {12703, 45585}, {12704, 45587}, {13912, 45576}, {13975, 45575}, {22770, 45541}, {22793, 45543}, {22841, 45567}, {22842, 45568}, {28174, 48773}, {28194, 41491}, {35610, 45564}, {45350, 48488}, {45352, 48487}, {45378, 48661}

X(48741) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {Bevan antipodal, 3rd extouch}
X(48741) = reflection of X(i) in X(j) for these (i, j): (45716, 9738), (48467, 48765), (48740, 3579)


X(48742) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 9th BROCARD

Barycentrics    (a^2+b^2+c^2)*(2*a^6-(b^2+c^2)*a^4-(b^4-c^4)*(b^2-c^2))-2*S*(-a^2+b^2+c^2)*(4*a^4+(b^2+c^2)*a^2+(b^2-c^2)^2) : :
X(48742) = 3*X(5050)-X(13748) = 2*X(14239)-3*X(38136) = 3*X(25406)+X(39888)

The reciprocal orthologic center of these triangles is X(4).

X(48742) lies on these lines: {5, 182}, {6, 45544}, {69, 45498}, {372, 6776}, {542, 41490}, {641, 1352}, {1692, 3071}, {3564, 9739}, {5050, 13748}, {5062, 36714}, {5085, 11315}, {5480, 44656}, {5847, 48740}, {5848, 48686}, {5921, 45508}, {6399, 13934}, {9757, 32805}, {11292, 25406}, {12007, 44474}, {14233, 18583}, {14239, 38136}, {18440, 45554}, {19145, 45574}, {19146, 45577}, {22594, 46264}, {26441, 35841}, {29012, 44475}, {29181, 44472}, {32786, 39874}, {39870, 45500}, {39871, 45502}, {39872, 45504}, {39873, 45506}, {39875, 45512}, {39876, 45515}, {39877, 45520}, {39878, 45530}, {39879, 45532}, {39880, 45534}, {39881, 45536}, {39882, 45538}, {39883, 45540}, {39885, 45546}, {39886, 45548}, {39887, 45550}, {39889, 45556}, {39890, 45558}, {39891, 45560}, {39892, 45562}, {39894, 45565}, {39895, 45569}, {39896, 45566}, {39897, 45570}, {39898, 45572}, {39899, 45578}, {39900, 45580}, {39901, 45582}, {39902, 45584}, {39903, 45586}, {45349, 48489}, {45351, 48490}, {45377, 48662}, {47353, 48778}

X(48742) = orthologic center (1st anti-Kenmotu-free-vertices, 9th Brocard)
X(48742) = X(6776)-of-1st anti-Kenmotu-free-vertices triangle
X(48742) = reflection of X(i) in X(j) for these (i, j): (14233, 18583), (48466, 182)


X(48743) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 9th BROCARD

Barycentrics    (a^2+b^2+c^2)*(2*a^6-(b^2+c^2)*a^4-(b^4-c^4)*(b^2-c^2))+2*S*(-a^2+b^2+c^2)*(4*a^4+(b^2+c^2)*a^2+(b^2-c^2)^2) : :
X(48743) = 3*X(5050)-X(13749) = 2*X(14235)-3*X(38136) = 3*X(25406)+X(39887)

The reciprocal orthologic center of these triangles is X(4).

X(48743) lies on these lines: {5, 182}, {6, 45545}, {69, 45499}, {371, 6776}, {542, 41491}, {642, 1352}, {1692, 3070}, {3564, 9738}, {5050, 13749}, {5058, 36709}, {5085, 11316}, {5480, 44657}, {5847, 48741}, {5848, 48687}, {5921, 45509}, {6222, 13882}, {8982, 35840}, {9758, 32806}, {11291, 25406}, {12007, 44473}, {14230, 18583}, {14235, 38136}, {18440, 45555}, {19145, 45576}, {19146, 45575}, {22623, 46264}, {29012, 44476}, {29181, 44471}, {32785, 39874}, {39870, 45501}, {39871, 45503}, {39872, 45505}, {39873, 45507}, {39875, 45514}, {39876, 45513}, {39877, 45521}, {39878, 45531}, {39879, 45533}, {39880, 45535}, {39881, 45537}, {39882, 45539}, {39883, 45541}, {39885, 45547}, {39886, 45549}, {39888, 45551}, {39889, 45557}, {39890, 45559}, {39891, 45561}, {39892, 45563}, {39893, 45564}, {39895, 45567}, {39896, 45568}, {39897, 45571}, {39898, 45573}, {39899, 45579}, {39900, 45581}, {39901, 45583}, {39902, 45585}, {39903, 45587}, {45350, 48490}, {45352, 48489}, {45378, 48662}, {47353, 48779}

X(48743) = orthologic center (2nd anti- Kenmotu-free-vertices, 9th Brocard)
X(48743) = reflection of X(i) in X(j) for these (i, j): (14230, 18583), (48467, 182)


X(48744) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 1st BROCARD-REFLECTED

Barycentrics    3*(b^2+c^2)*a^8-4*(b^4+b^2*c^2+c^4)*a^6+3*(b^6+c^6)*a^4-2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*b^2*c^2-2*S*(3*(b^2+c^2)*a^6-(5*b^4+8*b^2*c^2+5*c^4)*a^4+(b^2+c^2)*(2*b^4-7*b^2*c^2+2*c^4)*a^2+(b^2-c^2)^2*b^2*c^2) : :
X(48744) = 5*X(7786)-X(22699) = X(48768)-4*X(48772)

The reciprocal orthologic center of these triangles is X(3).

X(48744) lies on these lines: {39, 44648}, {182, 10007}, {262, 372}, {511, 41490}, {641, 15819}, {2782, 48728}, {6194, 45508}, {7697, 45554}, {7709, 45510}, {7786, 22699}, {9739, 48770}, {18971, 45506}, {19063, 45512}, {19064, 45515}, {22475, 45500}, {22480, 45502}, {22521, 45504}, {22556, 45520}, {22650, 45530}, {22655, 45532}, {22668, 45534}, {22672, 45536}, {22676, 45498}, {22678, 45538}, {22680, 45540}, {22681, 45542}, {22682, 45544}, {22697, 45546}, {22698, 45548}, {22700, 45553}, {22703, 45556}, {22704, 45558}, {22705, 45560}, {22706, 45562}, {22709, 45569}, {22710, 45566}, {22711, 45570}, {22713, 45572}, {22720, 45574}, {22721, 45577}, {22728, 45578}, {22729, 45580}, {22730, 45582}, {22731, 45584}, {22732, 45586}, {32515, 48768}, {35839, 45565}, {45349, 48491}, {45351, 48492}, {45377, 48663}

X(48744) = orthologic center (1st anti-Kenmotu-free-vertices, 1st Brocard-reflected)
X(48744) = X(262)-of-1st anti-Kenmotu-free-vertices triangle
X(48744) = reflection of X(48745) in X(40108)


X(48745) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 1st BROCARD-REFLECTED

Barycentrics    3*(b^2+c^2)*a^8-4*(b^4+b^2*c^2+c^4)*a^6+3*(b^6+c^6)*a^4-2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*b^2*c^2+2*S*(3*(b^2+c^2)*a^6-(5*b^4+8*b^2*c^2+5*c^4)*a^4+(b^2+c^2)*(2*b^4-7*b^2*c^2+2*c^4)*a^2+(b^2-c^2)^2*b^2*c^2) : :
X(48745) = 5*X(7786)-X(22700) = X(48769)-4*X(48773)

The reciprocal orthologic center of these triangles is X(3).

X(48745) lies on these lines: {39, 44647}, {182, 10007}, {262, 371}, {511, 41491}, {642, 15819}, {2782, 48729}, {6194, 45509}, {7697, 45555}, {7709, 45511}, {7786, 22700}, {9738, 48771}, {18971, 45507}, {19063, 45514}, {19064, 45513}, {22475, 45501}, {22480, 45503}, {22521, 45505}, {22556, 45521}, {22650, 45531}, {22655, 45533}, {22668, 45535}, {22672, 45537}, {22676, 45499}, {22678, 45539}, {22680, 45541}, {22681, 45543}, {22682, 45545}, {22697, 45547}, {22698, 45549}, {22699, 45552}, {22703, 45557}, {22704, 45559}, {22705, 45561}, {22706, 45563}, {22709, 45567}, {22710, 45568}, {22711, 45571}, {22713, 45573}, {22720, 45576}, {22721, 45575}, {22728, 45579}, {22729, 45581}, {22730, 45583}, {22731, 45585}, {22732, 45587}, {32515, 48769}, {35838, 45564}, {45350, 48492}, {45352, 48491}, {45378, 48663}

X(48745) = orthologic center (2nd anti- Kenmotu-free-vertices, 1st Brocard-reflected)
X(48745) = reflection of X(48744) in X(40108)


X(48746) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO EXCENTERS-MIDPOINTS

Barycentrics    2*(2*a^3+(b^2+c^2)*a-(b+c)*(b^2+c^2))*S+(a+b+c)*(2*(b+c)*a^3-(b^2+4*b*c+c^2)*a^2-2*(b^2-c^2)*(b-c)*a+(b^2-c^2)^2) : :
X(48746) = 3*X(5657)+X(12628) = 3*X(41490)-2*X(45715) = 3*X(41490)-4*X(48764)

The reciprocal orthologic center of these triangles is X(10).

X(48746) lies on these lines: {1, 641}, {8, 372}, {10, 45500}, {145, 45508}, {182, 5690}, {355, 45544}, {515, 48740}, {517, 48466}, {519, 41490}, {639, 45444}, {758, 48756}, {944, 45498}, {952, 9739}, {1482, 45554}, {2098, 45562}, {2099, 45560}, {2802, 48754}, {3632, 45530}, {3656, 48778}, {3913, 45520}, {5657, 12628}, {5844, 48772}, {7690, 34773}, {7763, 45573}, {7967, 45522}, {8148, 45377}, {10573, 45582}, {10912, 45556}, {10944, 45506}, {10950, 45570}, {12135, 45502}, {12195, 45504}, {12245, 45510}, {12410, 45532}, {12454, 45534}, {12455, 45536}, {12495, 45538}, {12513, 45540}, {12626, 45548}, {12627, 45550}, {12635, 45558}, {12636, 45569}, {12637, 45566}, {12645, 45578}, {12647, 45580}, {12648, 45584}, {12649, 45586}, {13911, 45574}, {13973, 45577}, {14839, 48768}, {19065, 45512}, {19066, 45515}, {22791, 45542}, {35843, 45565}, {45349, 48493}, {45351, 48494}

X(48746) = reflection of X(i) in X(j) for these (i, j): (45715, 48764), (48747, 5690)
X(48746) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {excenters-midpoints, Garcia-reflection, 2nd Schiffler}
X(48746) = X(8)-of-1st anti-Kenmotu-free-vertices triangle
X(48746) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 45546, 641), (145, 45508, 45572), (45715, 48764, 41490)


X(48747) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO EXCENTERS-MIDPOINTS

Barycentrics    -2*(2*a^3+(b^2+c^2)*a-(b+c)*(b^2+c^2))*S+(a+b+c)*(2*(b+c)*a^3-(b^2+4*b*c+c^2)*a^2-2*(b^2-c^2)*(b-c)*a+(b^2-c^2)^2) : :
X(48747) = 3*X(5657)+X(12627) = 3*X(41491)-2*X(45716) = 3*X(41491)-4*X(48765)

The reciprocal orthologic center of these triangles is X(10).

X(48747) lies on these lines: {1, 642}, {8, 371}, {10, 45501}, {145, 45509}, {182, 5690}, {355, 45545}, {515, 48741}, {517, 48467}, {519, 41491}, {640, 45445}, {758, 48757}, {944, 45499}, {952, 9738}, {1482, 45555}, {2098, 45563}, {2099, 45561}, {2802, 48755}, {3632, 45531}, {3656, 48779}, {3913, 45521}, {5657, 12627}, {5844, 48773}, {7692, 34773}, {7763, 45572}, {7967, 45523}, {8148, 45378}, {10573, 45583}, {10912, 45557}, {10944, 45507}, {10950, 45571}, {12135, 45503}, {12195, 45505}, {12245, 45511}, {12410, 45533}, {12454, 45535}, {12455, 45537}, {12495, 45539}, {12513, 45541}, {12626, 45549}, {12628, 45551}, {12635, 45559}, {12636, 45567}, {12637, 45568}, {12645, 45579}, {12647, 45581}, {12648, 45585}, {12649, 45587}, {13911, 45576}, {13973, 45575}, {14839, 48769}, {19065, 45514}, {19066, 45513}, {22791, 45543}, {35842, 45564}, {45350, 48494}, {45352, 48493}

X(48747) = reflection of X(i) in X(j) for these (i, j): (45716, 48765), (48746, 5690)
X(48747) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {excenters-midpoints, Garcia-reflection, 2nd Schiffler}
X(48747) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 45547, 642), (145, 45509, 45573), (45716, 48765, 41491)


X(48748) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO EXTOUCH

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

The reciprocal orthologic center of these triangles is X(40).

X(48748) lies on these lines: {84, 372}, {182, 34862}, {515, 48740}, {641, 6260}, {971, 9739}, {1490, 45498}, {1709, 45580}, {2829, 48754}, {5658, 45522}, {6001, 45715}, {6223, 45508}, {6245, 45544}, {6257, 45553}, {6258, 45550}, {6259, 45554}, {7971, 45572}, {7992, 45530}, {8987, 45574}, {9910, 45532}, {10085, 45582}, {12114, 45500}, {12136, 45502}, {12196, 45504}, {12246, 45510}, {12330, 45520}, {12456, 45534}, {12457, 45536}, {12496, 45538}, {12667, 45546}, {12668, 45548}, {12676, 45556}, {12677, 45558}, {12678, 45560}, {12679, 45562}, {12680, 45570}, {12684, 45578}, {12686, 45584}, {12687, 45586}, {12688, 45506}, {13974, 45577}, {18237, 45540}, {18245, 45569}, {18246, 45566}, {19067, 45512}, {19068, 45515}, {22792, 45542}, {35845, 45565}, {45349, 48495}, {45351, 48496}, {45377, 48664}

X(48748) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {extouch, 1st Zaniah}
X(48748) = X(84)-of-1st anti-Kenmotu-free-vertices triangle
X(48748) = reflection of X(48749) in X(34862)


X(48749) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO EXTOUCH

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

The reciprocal orthologic center of these triangles is X(40).

X(48749) lies on these lines: {84, 371}, {182, 34862}, {515, 48741}, {642, 6260}, {971, 9738}, {1490, 45499}, {1709, 45581}, {2829, 48755}, {5658, 45523}, {6001, 45716}, {6223, 45509}, {6245, 45545}, {6257, 45551}, {6258, 45552}, {6259, 45555}, {7971, 45573}, {7992, 45531}, {8987, 45576}, {9910, 45533}, {10085, 45583}, {12114, 45501}, {12136, 45503}, {12196, 45505}, {12246, 45511}, {12330, 45521}, {12456, 45535}, {12457, 45537}, {12496, 45539}, {12667, 45547}, {12668, 45549}, {12676, 45557}, {12677, 45559}, {12678, 45561}, {12679, 45563}, {12680, 45571}, {12684, 45579}, {12686, 45585}, {12687, 45587}, {12688, 45507}, {13974, 45575}, {18237, 45541}, {18245, 45567}, {18246, 45568}, {19067, 45514}, {19068, 45513}, {22792, 45543}, {35844, 45564}, {45350, 48496}, {45352, 48495}, {45378, 48664}

X(48749) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {extouch, 1st Zaniah}
X(48749) = reflection of X(48748) in X(34862)


X(48750) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO INNER-FERMAT

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

The reciprocal orthologic center of these triangles is X(3).

X(48750) lies on these lines: {18, 372}, {54, 69}, {533, 41490}, {630, 641}, {2043, 9739}, {6306, 48722}, {11740, 45500}, {16627, 35732}, {16628, 45578}, {18972, 45506}, {19069, 45512}, {19072, 45515}, {22481, 45502}, {22522, 45504}, {22531, 45510}, {22557, 45520}, {22651, 45530}, {22656, 45532}, {22669, 45534}, {22673, 45536}, {22745, 45538}, {22771, 45540}, {22794, 45542}, {22831, 45544}, {22843, 45498}, {22851, 45546}, {22852, 45548}, {22853, 45550}, {22854, 45553}, {22857, 45556}, {22858, 45558}, {22859, 45560}, {22860, 45562}, {22863, 45569}, {22864, 45566}, {22865, 45570}, {22867, 45572}, {22876, 45574}, {22877, 45577}, {22884, 45580}, {22885, 45582}, {22886, 45584}, {22887, 45586}, {35849, 45565}, {44667, 48466}, {45349, 48497}, {45351, 48498}, {45377, 48665}

X(48750) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {inner-Fermat, 1st half-diamonds}
X(48750) = X(18)-of-1st anti-Kenmotu-free-vertices triangle


X(48751) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO INNER-FERMAT

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

The reciprocal orthologic center of these triangles is X(3).

X(48751) lies on these lines: {18, 371}, {54, 69}, {533, 41491}, {630, 642}, {2044, 9738}, {6302, 48723}, {11740, 45501}, {16627, 42282}, {16628, 45579}, {18972, 45507}, {19069, 45514}, {19072, 45513}, {22481, 45503}, {22522, 45505}, {22531, 45511}, {22557, 45521}, {22651, 45531}, {22656, 45533}, {22669, 45535}, {22673, 45537}, {22745, 45539}, {22771, 45541}, {22794, 45543}, {22831, 45545}, {22843, 45499}, {22851, 45547}, {22852, 45549}, {22853, 45552}, {22854, 45551}, {22857, 45557}, {22858, 45559}, {22859, 45561}, {22860, 45563}, {22863, 45567}, {22864, 45568}, {22865, 45571}, {22867, 45573}, {22876, 45576}, {22877, 45575}, {22883, 35746}, {22884, 45581}, {22885, 45583}, {22886, 45585}, {22887, 45587}, {35846, 45564}, {44667, 48467}, {45350, 48498}, {45352, 48497}, {45378, 48665}

X(48751) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {inner-Fermat, 1st half-diamonds}


X(48752) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO OUTER-FERMAT

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

The reciprocal orthologic center of these triangles is X(3).

X(48752) lies on these lines: {17, 372}, {54, 69}, {532, 41490}, {629, 641}, {2044, 9739}, {6307, 48724}, {11739, 45500}, {16626, 42282}, {16629, 45578}, {18973, 45506}, {19070, 45515}, {19071, 45512}, {22113, 35747}, {22482, 45502}, {22523, 45504}, {22532, 45510}, {22558, 45520}, {22652, 45530}, {22657, 45532}, {22670, 45534}, {22674, 45536}, {22746, 45538}, {22772, 45540}, {22795, 45542}, {22832, 45544}, {22890, 45498}, {22896, 45546}, {22897, 45548}, {22898, 45550}, {22899, 45553}, {22902, 45556}, {22903, 45558}, {22904, 45560}, {22905, 45562}, {22908, 45569}, {22909, 45566}, {22910, 45570}, {22912, 45572}, {22921, 45574}, {22922, 45577}, {22929, 45580}, {22930, 45582}, {22931, 45584}, {22932, 45586}, {35743, 48734}, {35847, 45565}, {44666, 48466}, {45349, 48499}, {45351, 48500}, {45377, 48666}

X(48752) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {outer-Fermat, 2nd half-diamonds}
X(48752) = X(17)-of-1st anti-Kenmotu-free-vertices triangle


X(48753) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO OUTER-FERMAT

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

The reciprocal orthologic center of these triangles is X(3).

X(48753) lies on these lines: {17, 371}, {54, 69}, {532, 41491}, {629, 642}, {2043, 9738}, {6303, 48725}, {11739, 45501}, {16626, 35732}, {16629, 45579}, {18973, 45507}, {19070, 45513}, {19071, 45514}, {22482, 45503}, {22523, 45505}, {22532, 45511}, {22558, 45521}, {22652, 45531}, {22657, 45533}, {22670, 45535}, {22674, 45537}, {22746, 45539}, {22772, 45541}, {22795, 45543}, {22832, 45545}, {22890, 45499}, {22896, 45547}, {22897, 45549}, {22898, 45552}, {22899, 45551}, {22902, 45557}, {22903, 45559}, {22904, 45561}, {22905, 45563}, {22908, 45567}, {22909, 45568}, {22910, 45571}, {22912, 45573}, {22921, 45576}, {22922, 45575}, {22929, 45581}, {22930, 45583}, {22931, 45585}, {22932, 45587}, {35848, 45564}, {44666, 48467}, {45350, 48500}, {45352, 48499}, {45378, 48666}

X(48753) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {outer-Fermat, 2nd half-diamonds}


X(48754) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(48754) lies on these lines: {11, 5405}, {80, 372}, {100, 45546}, {182, 12619}, {214, 641}, {515, 48686}, {952, 45715}, {2771, 48736}, {2800, 48466}, {2802, 48746}, {2829, 48748}, {5840, 48740}, {6224, 45508}, {6246, 45544}, {6262, 45553}, {6263, 45550}, {6265, 45554}, {7972, 45572}, {8988, 45574}, {9897, 45530}, {9912, 45532}, {10057, 45580}, {10073, 45582}, {12119, 45498}, {12137, 45502}, {12198, 45504}, {12247, 45510}, {12331, 45520}, {12460, 45534}, {12461, 45536}, {12498, 45538}, {12611, 45542}, {12729, 45548}, {12737, 45556}, {12738, 45558}, {12739, 45560}, {12740, 45562}, {12741, 45569}, {12742, 45566}, {12743, 45570}, {12747, 45578}, {12749, 45584}, {12750, 45586}, {12751, 45528}, {12773, 45540}, {13976, 45577}, {18976, 45506}, {19077, 45512}, {19078, 45515}, {35853, 45565}, {45349, 48501}, {45351, 48502}, {45377, 48667}, {48705, 48764}

X(48754) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {Fuhrmann, K798i}
X(48754) = X(80)-of-1st anti-Kenmotu-free-vertices triangle
X(48754) = reflection of X(i) in X(j) for these (i, j): (48705, 48764), (48755, 12619)


X(48755) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(48755) lies on these lines: {11, 5393}, {80, 371}, {100, 45547}, {182, 12619}, {214, 642}, {515, 48687}, {952, 45716}, {2771, 48737}, {2800, 48467}, {2802, 48747}, {2829, 48749}, {5840, 48741}, {6224, 45509}, {6246, 45545}, {6262, 45551}, {6263, 45552}, {6265, 45555}, {7972, 45573}, {8988, 45576}, {9897, 45531}, {9912, 45533}, {10057, 45581}, {10073, 45583}, {12119, 45499}, {12137, 45503}, {12198, 45505}, {12247, 45511}, {12331, 45521}, {12460, 45535}, {12461, 45537}, {12498, 45539}, {12611, 45543}, {12729, 45549}, {12737, 45557}, {12738, 45559}, {12739, 45561}, {12740, 45563}, {12741, 45567}, {12742, 45568}, {12743, 45571}, {12747, 45579}, {12749, 45585}, {12750, 45587}, {12751, 45529}, {12773, 45541}, {13976, 45575}, {18976, 45507}, {19077, 45514}, {19078, 45513}, {35852, 45564}, {45350, 48502}, {45352, 48501}, {45378, 48667}, {48706, 48765}

X(48755) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {Fuhrmann, K798i}
X(48755) = reflection of X(i) in X(j) for these (i, j): (48706, 48765), (48754, 12619)


X(48756) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 2nd FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(48756) lies on these lines: {30, 45715}, {79, 372}, {182, 48757}, {641, 3647}, {758, 48746}, {2771, 48736}, {3648, 45508}, {3649, 45500}, {3652, 45554}, {5441, 45572}, {6841, 31555}, {11684, 45546}, {13743, 45540}, {16113, 45498}, {16114, 45502}, {16115, 45504}, {16116, 45510}, {16117, 45520}, {16118, 45530}, {16119, 45532}, {16121, 45534}, {16122, 45536}, {16123, 45538}, {16125, 45544}, {16129, 45548}, {16130, 45550}, {16131, 45553}, {16138, 45556}, {16139, 45558}, {16140, 45560}, {16141, 45562}, {16142, 45570}, {16148, 45574}, {16149, 45577}, {16150, 45578}, {16152, 45580}, {16153, 45582}, {16154, 45584}, {16155, 45586}, {16161, 45569}, {16162, 45566}, {18977, 45506}, {19079, 45512}, {19080, 45515}, {22798, 45542}, {35855, 45565}, {45349, 48503}, {45351, 48504}, {45377, 48668}

X(48756) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {2nd Fuhrmann, K798e}
X(48756) = X(79)-of-1st anti-Kenmotu-free-vertices triangle


X(48757) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 2nd FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(48757) lies on these lines: {30, 45716}, {79, 371}, {182, 48756}, {642, 3647}, {758, 48747}, {2771, 48737}, {3648, 45509}, {3649, 45501}, {3652, 45555}, {5441, 45573}, {6841, 31556}, {11684, 45547}, {13743, 45541}, {16113, 45499}, {16114, 45503}, {16115, 45505}, {16116, 45511}, {16117, 45521}, {16118, 45531}, {16119, 45533}, {16121, 45535}, {16122, 45537}, {16123, 45539}, {16125, 45545}, {16129, 45549}, {16130, 45552}, {16131, 45551}, {16138, 45557}, {16139, 45559}, {16140, 45561}, {16141, 45563}, {16142, 45571}, {16148, 45576}, {16149, 45575}, {16150, 45579}, {16152, 45581}, {16153, 45583}, {16154, 45585}, {16155, 45587}, {16161, 45567}, {16162, 45568}, {18977, 45507}, {19079, 45514}, {19080, 45513}, {22798, 45543}, {35854, 45564}, {45350, 48504}, {45352, 48503}, {45378, 48668}

X(48757) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {2nd Fuhrmann, K798e}


X(48758) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO HATZIPOLAKIS-MOSES

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

The reciprocal orthologic center of these triangles is X(6146).

X(48758) lies on these lines: {182, 6689}, {372, 6145}, {641, 32391}, {1154, 48738}, {9739, 18400}, {10628, 48736}, {32330, 45498}, {32331, 45500}, {32332, 45502}, {32335, 45504}, {32336, 45506}, {32337, 45510}, {32342, 45512}, {32343, 45515}, {32347, 45520}, {32354, 45508}, {32356, 45530}, {32357, 45532}, {32360, 45534}, {32361, 45536}, {32362, 45538}, {32363, 45540}, {32364, 45542}, {32369, 45544}, {32371, 45546}, {32372, 45548}, {32373, 45550}, {32374, 45553}, {32379, 45554}, {32380, 45556}, {32381, 45558}, {32382, 45560}, {32383, 45562}, {32388, 45569}, {32389, 45566}, {32390, 45570}, {32394, 45572}, {32399, 45574}, {32400, 45577}, {32402, 45578}, {32403, 45580}, {32404, 45582}, {32405, 45584}, {32406, 45586}, {35859, 45565}, {45349, 48505}, {45351, 48506}, {45377, 48669}

X(48758) = orthologic center (1st anti-Kenmotu-free-vertices, Hatzipolakis-Moses)
X(48758) = X(6145)-of-1st anti-Kenmotu-free-vertices triangle


X(48759) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO HATZIPOLAKIS-MOSES

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

The reciprocal orthologic center of these triangles is X(6146).

X(48759) lies on these lines: {182, 6689}, {371, 6145}, {642, 32391}, {1154, 48739}, {9738, 18400}, {10628, 48737}, {32330, 45499}, {32331, 45501}, {32332, 45503}, {32335, 45505}, {32336, 45507}, {32337, 45511}, {32342, 45514}, {32343, 45513}, {32347, 45521}, {32354, 45509}, {32356, 45531}, {32357, 45533}, {32360, 45535}, {32361, 45537}, {32362, 45539}, {32363, 45541}, {32364, 45543}, {32369, 45545}, {32371, 45547}, {32372, 45549}, {32373, 45552}, {32374, 45551}, {32379, 45555}, {32380, 45557}, {32381, 45559}, {32382, 45561}, {32383, 45563}, {32388, 45567}, {32389, 45568}, {32390, 45571}, {32394, 45573}, {32399, 45576}, {32400, 45575}, {32402, 45579}, {32403, 45581}, {32404, 45583}, {32405, 45585}, {32406, 45587}, {35858, 45564}, {45350, 48506}, {45352, 48505}, {45378, 48669}

X(48759) = orthologic center (2nd anti- Kenmotu-free-vertices, Hatzipolakis-Moses)


X(48760) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 3rd HATZIPOLAKIS

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

The reciprocal orthologic center of these triangles is X(12241).

X(48760) lies on these lines: {182, 44516}, {372, 22466}, {641, 22966}, {18978, 45506}, {19083, 45512}, {19084, 45515}, {22476, 45500}, {22483, 45502}, {22524, 45504}, {22533, 45510}, {22559, 45520}, {22647, 45508}, {22653, 45530}, {22658, 45532}, {22671, 45534}, {22675, 45536}, {22747, 45538}, {22776, 45540}, {22800, 45542}, {22833, 45544}, {22941, 45546}, {22943, 45548}, {22945, 45550}, {22947, 45553}, {22951, 45498}, {22955, 45554}, {22956, 45556}, {22957, 45558}, {22958, 45560}, {22959, 45562}, {22963, 45569}, {22964, 45566}, {22965, 45570}, {22969, 45572}, {22976, 45574}, {22977, 45577}, {22979, 45578}, {22980, 45580}, {22981, 45582}, {22982, 45584}, {22983, 45586}, {35861, 45565}, {45349, 48507}, {45351, 48508}, {45377, 48670}

X(48760) = orthologic center (1st anti-Kenmotu-free-vertices, 3rd Hatzipolakis)
X(48760) = X(22466)-of-1st anti-Kenmotu-free-vertices triangle


X(48761) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 3rd HATZIPOLAKIS

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

The reciprocal orthologic center of these triangles is X(12241).

X(48761) lies on these lines: {182, 44516}, {371, 22466}, {642, 22966}, {18978, 45507}, {19083, 45514}, {19084, 45513}, {22476, 45501}, {22483, 45503}, {22524, 45505}, {22533, 45511}, {22559, 45521}, {22647, 45509}, {22653, 45531}, {22658, 45533}, {22671, 45535}, {22675, 45537}, {22747, 45539}, {22776, 45541}, {22800, 45543}, {22833, 45545}, {22941, 45547}, {22943, 45549}, {22945, 45552}, {22947, 45551}, {22951, 45499}, {22955, 45555}, {22956, 45557}, {22957, 45559}, {22958, 45561}, {22959, 45563}, {22963, 45567}, {22964, 45568}, {22965, 45571}, {22969, 45573}, {22976, 45576}, {22977, 45575}, {22979, 45579}, {22980, 45581}, {22981, 45583}, {22982, 45585}, {22983, 45587}, {35860, 45564}, {45350, 48508}, {45352, 48507}, {45378, 48670}

X(48761) = orthologic center (2nd anti- Kenmotu-free-vertices, 3rd Hatzipolakis)


X(48762) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO HUTSON EXTOUCH

Barycentrics    a*(-2*((b+c)*a^7+(b^2+4*b*c+c^2)*a^6-(b+c)*(3*b^2-2*b*c+3*c^2)*a^5-(b^2+c^2)*(3*b^2+26*b*c+3*c^2)*a^4+(b+c)*(3*b^4+3*c^4-2*b*c*(2*b^2+15*b*c+2*c^2))*a^3+(b^2+6*b*c+c^2)*(3*b^4+3*c^4+2*b*c*(3*b^2-b*c+3*c^2))*a^2-(b^2-c^2)^3*(b-c)*a-(b^2-c^2)*(b+c)^2*(b^4-c^4))*S+(a+b+c)*(2*a^9-3*(b+c)*a^8-6*(b^2+3*b*c+c^2)*a^7+2*(b+c)*(5*b^2+8*b*c+5*c^2)*a^6+2*(3*b^4+3*c^4+b*c*(19*b^2+16*b*c+19*c^2))*a^5-4*(b+c)*(3*b^4+3*c^4+2*b*c*(4*b^2+b*c+4*c^2))*a^4-2*(b^6+c^6+(11*b^4+11*c^4+b*c*(11*b^2-14*b*c+11*c^2))*b*c)*a^3+2*(b^2-c^2)^2*(b+c)*(3*b^2+8*b*c+3*c^2)*a^2+2*(b^2-c^2)^2*(b-c)^2*b*c*a-(b^2-c^2)^4*(b+c))) : :

The reciprocal orthologic center of these triangles is X(40).

X(48762) lies on these lines: {182, 48763}, {372, 7160}, {641, 12864}, {8000, 45572}, {9874, 45508}, {9898, 45530}, {10059, 45580}, {10075, 45582}, {12120, 45498}, {12139, 45502}, {12200, 45504}, {12249, 45510}, {12260, 45500}, {12333, 45520}, {12411, 45532}, {12464, 45534}, {12465, 45536}, {12500, 45538}, {12599, 45544}, {12777, 45546}, {12789, 45548}, {12801, 45550}, {12802, 45553}, {12856, 45554}, {12857, 45556}, {12858, 45558}, {12859, 45560}, {12860, 45562}, {12861, 45569}, {12862, 45566}, {12863, 45570}, {12872, 45578}, {12874, 45584}, {12875, 45586}, {13914, 45574}, {13978, 45577}, {18979, 45506}, {19085, 45512}, {19086, 45515}, {22777, 45540}, {22801, 45542}, {35863, 45565}, {45349, 48509}, {45351, 48510}, {45377, 48671}

X(48762) = orthologic center (1st anti-Kenmotu-free-vertices, Hutson extouch)
X(48762) = X(7160)-of-1st anti-Kenmotu-free-vertices triangle


X(48763) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO HUTSON EXTOUCH

Barycentrics    a*(2*((b+c)*a^7+(b^2+4*b*c+c^2)*a^6-(b+c)*(3*b^2-2*b*c+3*c^2)*a^5-(b^2+c^2)*(3*b^2+26*b*c+3*c^2)*a^4+(b+c)*(3*b^4+3*c^4-2*b*c*(2*b^2+15*b*c+2*c^2))*a^3+(b^2+6*b*c+c^2)*(3*b^4+3*c^4+2*b*c*(3*b^2-b*c+3*c^2))*a^2-(b^2-c^2)^3*(b-c)*a-(b^2-c^2)*(b+c)^2*(b^4-c^4))*S+(a+b+c)*(2*a^9-3*(b+c)*a^8-6*(b^2+3*b*c+c^2)*a^7+2*(b+c)*(5*b^2+8*b*c+5*c^2)*a^6+2*(3*b^4+3*c^4+b*c*(19*b^2+16*b*c+19*c^2))*a^5-4*(b+c)*(3*b^4+3*c^4+2*b*c*(4*b^2+b*c+4*c^2))*a^4-2*(b^6+c^6+(11*b^4+11*c^4+b*c*(11*b^2-14*b*c+11*c^2))*b*c)*a^3+2*(b^2-c^2)^2*(b+c)*(3*b^2+8*b*c+3*c^2)*a^2+2*(b^2-c^2)^2*(b-c)^2*b*c*a-(b^2-c^2)^4*(b+c))) : :

The reciprocal orthologic center of these triangles is X(40).

X(48763) lies on these lines: {182, 48762}, {371, 7160}, {642, 12864}, {8000, 45573}, {9874, 45509}, {9898, 45531}, {10059, 45581}, {10075, 45583}, {12120, 45499}, {12139, 45503}, {12200, 45505}, {12249, 45511}, {12260, 45501}, {12333, 45521}, {12411, 45533}, {12464, 45535}, {12465, 45537}, {12500, 45539}, {12599, 45545}, {12777, 45547}, {12789, 45549}, {12801, 45552}, {12802, 45551}, {12856, 45555}, {12857, 45557}, {12858, 45559}, {12859, 45561}, {12860, 45563}, {12861, 45567}, {12862, 45568}, {12863, 45571}, {12872, 45579}, {12874, 45585}, {12875, 45587}, {13914, 45576}, {13978, 45575}, {18979, 45507}, {19085, 45514}, {19086, 45513}, {22777, 45541}, {22801, 45543}, {35862, 45564}, {45350, 48510}, {45352, 48509}, {45378, 48671}

X(48763) = orthologic center (2nd anti- Kenmotu-free-vertices, Hutson extouch)


X(48764) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 1st JENKINS

Barycentrics    2*(2*a^3+(b+c)*a^2-(b^2+c^2)*(b+c))*S+(a+b+c)*(2*a^4+(b+c)*a^3-(3*b^2+2*b*c+3*c^2)*a^2-(b^2-c^2)*(b-c)*a+(b^2-c^2)^2) : :
X(48764) = 3*X(41490)-X(45715) = 3*X(41490)+X(48746)

The reciprocal orthologic center of these triangles is X(10).

X(48764) lies on these lines: {1, 45508}, {8, 45530}, {10, 372}, {39, 13936}, {40, 45510}, {182, 5847}, {226, 45560}, {355, 45578}, {515, 9739}, {516, 48466}, {517, 48772}, {519, 41490}, {641, 1125}, {726, 48768}, {946, 45554}, {950, 45570}, {1152, 45444}, {1210, 45582}, {2784, 48726}, {2796, 48728}, {3244, 45572}, {3576, 45522}, {4297, 45498}, {5062, 13883}, {5405, 24210}, {8666, 45540}, {8715, 45520}, {10106, 45506}, {10164, 45553}, {10915, 45528}, {10916, 45526}, {12053, 45562}, {12699, 45377}, {17766, 48770}, {18483, 45542}, {19925, 45544}, {21077, 45558}, {26446, 45410}, {31397, 45580}, {43174, 48734}, {45349, 48511}, {45351, 48512}, {48705, 48754}

X(48764) = midpoint of X(i) and X(j) for these {i, j}: {45715, 48746}, {48466, 48740}, {48705, 48754}
X(48764) = reflection of X(48765) in X(6684)
X(48764) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {1st Jenkins, 1st Savin}
X(48764) = X(10)-of-1st anti-Kenmotu-free-vertices triangle
X(48764) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (372, 45546, 10), (641, 45500, 1125), (41490, 48746, 45715)


X(48765) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 1st JENKINS

Barycentrics    -2*(2*a^3+(b+c)*a^2-(b^2+c^2)*(b+c))*S+(a+b+c)*(2*a^4+(b+c)*a^3-(3*b^2+2*b*c+3*c^2)*a^2-(b^2-c^2)*(b-c)*a+(b^2-c^2)^2) : :
X(48765) = 3*X(41491)-X(45716) = 3*X(41491)+X(48747)

The reciprocal orthologic center of these triangles is X(10).

X(48765) lies on these lines: {1, 45509}, {8, 45531}, {10, 371}, {39, 13883}, {40, 45511}, {182, 5847}, {226, 45561}, {355, 45579}, {515, 9738}, {516, 48467}, {517, 48773}, {519, 41491}, {642, 1125}, {726, 48769}, {946, 45555}, {950, 45571}, {1151, 45445}, {1210, 45583}, {2784, 48727}, {2796, 48729}, {3244, 45573}, {3576, 45523}, {3931, 38487}, {4297, 45499}, {5058, 13936}, {5393, 24210}, {8666, 45541}, {8715, 45521}, {10106, 45507}, {10164, 45552}, {10915, 45529}, {10916, 45527}, {12053, 45563}, {12699, 45378}, {17766, 48771}, {18483, 45543}, {19925, 45545}, {21077, 45559}, {26446, 45411}, {31397, 45581}, {43174, 48735}, {45350, 48512}, {45352, 48511}, {48706, 48755}

X(48765) = midpoint of X(i) and X(j) for these {i, j}: {45716, 48747}, {48467, 48741}, {48706, 48755}
X(48765) = reflection of X(48764) in X(6684)
X(48765) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {1st Jenkins, 1st Savin}
X(48765) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (371, 45547, 10), (642, 45501, 1125), (41491, 48747, 45716)


X(48766) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO MIDHEIGHT

Barycentrics    a^2*((b^2+c^2)*a^8-2*(b^4-b^2*c^2+c^4)*a^6+2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)^2*(b^2+c^2)+S*(a^8-(b^2+c^2)*a^6-(3*b^4-8*b^2*c^2+3*c^4)*a^4+5*(b^4-c^4)*(b^2-c^2)*a^2-2*(b^4+3*b^2*c^2+c^4)*(b^2-c^2)^2)) : :
X(48766) = X(6266)+3*X(10606)

The reciprocal orthologic center of these triangles is X(4).

X(48766) lies on these lines: {30, 48738}, {64, 372}, {182, 3357}, {641, 2883}, {1498, 45498}, {2777, 48736}, {2781, 44472}, {5656, 45522}, {5878, 45554}, {6000, 9739}, {6001, 48740}, {6225, 45508}, {6247, 45544}, {6266, 10606}, {6267, 45550}, {6285, 45506}, {6566, 12970}, {6759, 7690}, {7355, 45570}, {7973, 45572}, {8991, 45574}, {9899, 45530}, {9914, 45532}, {10060, 45580}, {10076, 45582}, {11381, 45502}, {12202, 45504}, {12250, 45510}, {12262, 45500}, {12335, 45520}, {12468, 45534}, {12469, 45536}, {12502, 45538}, {12779, 45546}, {12791, 45548}, {12920, 45556}, {12930, 45558}, {12940, 45560}, {12950, 45562}, {12986, 45569}, {12987, 45566}, {13093, 45578}, {13094, 45584}, {13095, 45586}, {13980, 45577}, {15105, 48734}, {15311, 48466}, {19087, 45512}, {19088, 45515}, {22778, 45540}, {22802, 45542}, {35450, 45410}, {35865, 45565}, {36201, 48782}, {45349, 48513}, {45351, 48514}, {45377, 48672}

X(48766) = orthologic center (1st anti-Kenmotu-free-vertices, midheight)
X(48766) = X(64)-of-1st anti-Kenmotu-free-vertices triangle
X(48766) = reflection of X(48767) in X(3357)


X(48767) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO MIDHEIGHT

Barycentrics    a^2*((b^2+c^2)*a^8-2*(b^4-b^2*c^2+c^4)*a^6+2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)^2*(b^2+c^2)-S*(a^8-(b^2+c^2)*a^6-(3*b^4-8*b^2*c^2+3*c^4)*a^4+5*(b^4-c^4)*(b^2-c^2)*a^2-2*(b^4+3*b^2*c^2+c^4)*(b^2-c^2)^2)) : :
X(48767) = X(6267)+3*X(10606)

The reciprocal orthologic center of these triangles is X(4).

X(48767) lies on these lines: {30, 48739}, {64, 371}, {182, 3357}, {642, 2883}, {1498, 45499}, {2777, 48737}, {2781, 44471}, {5656, 45523}, {5878, 45555}, {6000, 9738}, {6001, 48741}, {6225, 45509}, {6247, 45545}, {6266, 45551}, {6267, 10606}, {6285, 45507}, {6567, 12964}, {6759, 7692}, {7355, 45571}, {7973, 45573}, {8991, 45576}, {9899, 45531}, {9914, 45533}, {10060, 45581}, {10076, 45583}, {11381, 45503}, {12202, 45505}, {12250, 45511}, {12262, 45501}, {12335, 45521}, {12468, 45535}, {12469, 45537}, {12502, 45539}, {12779, 45547}, {12791, 45549}, {12920, 45557}, {12930, 45559}, {12940, 45561}, {12950, 45563}, {12986, 45567}, {12987, 45568}, {13093, 45579}, {13094, 45585}, {13095, 45587}, {13980, 45575}, {15105, 48735}, {15311, 48467}, {19087, 45514}, {19088, 45513}, {22778, 45541}, {22802, 45543}, {35450, 45411}, {35864, 45564}, {36201, 48783}, {45350, 48514}, {45352, 48513}, {45378, 48672}

X(48767) = orthologic center (2nd anti- Kenmotu-free-vertices, midheight)
X(48767) = reflection of X(48766) in X(3357)


X(48768) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 1st NEUBERG

Barycentrics    2*(b^2+c^2)*(a^4-b^2*c^2)*S+(b^2+c^2)*a^6-(b^4+c^4)*a^4-3*(b^2+c^2)*b^2*c^2*a^2+(b^2-c^2)^2*b^2*c^2 : :
X(48768) = X(6272)+3*X(22712) = 3*X(48744)-4*X(48772)

The reciprocal orthologic center of these triangles is X(3).

X(48768) lies on these lines: {39, 615}, {76, 372}, {182, 732}, {194, 45508}, {325, 639}, {384, 45504}, {486, 1916}, {511, 48466}, {538, 41490}, {726, 48764}, {730, 45715}, {736, 43121}, {2782, 9739}, {3095, 45554}, {5969, 48728}, {6118, 22717}, {6248, 45544}, {6272, 22712}, {6273, 45550}, {7709, 45522}, {7976, 45572}, {8992, 45574}, {9902, 45530}, {9917, 45532}, {9983, 45538}, {10063, 45580}, {10079, 45582}, {11257, 45498}, {12143, 45502}, {12251, 45510}, {12263, 45500}, {12338, 45520}, {12474, 45534}, {12475, 45536}, {12782, 45546}, {12794, 45548}, {12836, 45562}, {12837, 45560}, {12923, 45556}, {12933, 45558}, {12992, 45569}, {12993, 45566}, {13077, 45570}, {13108, 45578}, {13109, 45584}, {13110, 45586}, {14839, 48746}, {14881, 45542}, {18982, 45506}, {19089, 45512}, {19090, 45515}, {22779, 45540}, {32515, 48744}, {35867, 45565}, {44422, 48778}, {45349, 48515}, {45351, 48516}, {45377, 48673}

X(48768) = orthologic center (1st anti-Kenmotu-free-vertices, 1st Neuberg)
X(48768) = X(76)-of-1st anti-Kenmotu-free-vertices triangle
X(48768) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (39, 13983, 45577), (182, 8149, 48769)


X(48769) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 1st NEUBERG

Barycentrics    -2*(b^2+c^2)*(a^4-b^2*c^2)*S+(b^2+c^2)*a^6-(b^4+c^4)*a^4-3*(b^2+c^2)*b^2*c^2*a^2+(b^2-c^2)^2*b^2*c^2 : :
X(48769) = X(6273)+3*X(22712) = 3*X(48745)-4*X(48773)

The reciprocal orthologic center of these triangles is X(3).

X(48769) lies on these lines: {39, 590}, {76, 371}, {182, 732}, {194, 45509}, {325, 640}, {384, 45505}, {485, 1916}, {511, 48467}, {538, 41491}, {726, 48765}, {730, 45716}, {736, 43120}, {2782, 9738}, {3095, 45555}, {5969, 48729}, {6119, 22719}, {6248, 45545}, {6272, 45551}, {6273, 22712}, {7709, 45523}, {7976, 45573}, {9902, 45531}, {9917, 45533}, {9983, 45539}, {10063, 45581}, {10079, 45583}, {11257, 45499}, {12143, 45503}, {12251, 45511}, {12263, 45501}, {12338, 45521}, {12474, 45535}, {12475, 45537}, {12782, 45547}, {12794, 45549}, {12836, 45563}, {12837, 45561}, {12923, 45557}, {12933, 45559}, {12992, 45567}, {12993, 45568}, {13077, 45571}, {13108, 45579}, {13109, 45585}, {13110, 45587}, {13983, 45575}, {14839, 48747}, {14881, 45543}, {18982, 45507}, {19089, 45514}, {19090, 45513}, {22779, 45541}, {32515, 48745}, {35866, 45564}, {44422, 48779}, {45350, 48516}, {45352, 48515}, {45378, 48673}

X(48769) = orthologic center (2nd anti- Kenmotu-free-vertices, 1st Neuberg)
X(48769) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (39, 8992, 45576), (182, 8149, 48768)


X(48770) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 2nd NEUBERG

Barycentrics    2*(b^2+c^2)*(a^4-b^2*c^2)*S+2*a^8+(b^2+c^2)*a^6-(3*b^4+8*b^2*c^2+3*c^4)*a^4-7*(b^2+c^2)*b^2*c^2*a^2+(b^2-c^2)^2*b^2*c^2 : :
X(48770) = X(6274)+3*X(9751)

The reciprocal orthologic center of these triangles is X(3).

X(48770) lies on these lines: {83, 372}, {182, 732}, {641, 6292}, {754, 41490}, {2896, 45508}, {6119, 9478}, {6249, 45544}, {6274, 6316}, {6275, 45550}, {6287, 45554}, {7977, 45572}, {8993, 45574}, {9739, 48744}, {9903, 45530}, {9918, 45532}, {10064, 45580}, {10080, 45582}, {12122, 45498}, {12144, 45502}, {12206, 45504}, {12252, 45510}, {12264, 45500}, {12339, 45520}, {12476, 45534}, {12477, 45536}, {12783, 45546}, {12795, 45548}, {12924, 45556}, {12934, 45558}, {12944, 45560}, {12954, 45562}, {12994, 45569}, {12995, 45566}, {13078, 45570}, {13111, 45578}, {13112, 45584}, {13113, 45586}, {13984, 45577}, {17766, 48764}, {18983, 45506}, {19091, 45512}, {19092, 45515}, {22780, 45540}, {22803, 45542}, {29012, 48466}, {35701, 43118}, {35869, 45565}, {45349, 48517}, {45351, 48518}, {45377, 48674}, {48726, 48772}

X(48770) = orthologic center (1st anti-Kenmotu-free-vertices, 2nd Neuberg)
X(48770) = X(83)-of-1st anti-Kenmotu-free-vertices triangle


X(48771) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 2nd NEUBERG

Barycentrics    -2*(b^2+c^2)*(a^4-b^2*c^2)*S+2*a^8+(b^2+c^2)*a^6-(3*b^4+8*b^2*c^2+3*c^4)*a^4-7*(b^2+c^2)*b^2*c^2*a^2+(b^2-c^2)^2*b^2*c^2 : :
X(48771) = X(6275)+3*X(9751)

The reciprocal orthologic center of these triangles is X(3).

X(48771) lies on these lines: {83, 371}, {182, 732}, {642, 6292}, {754, 41491}, {2896, 45509}, {6118, 9478}, {6249, 45545}, {6274, 45551}, {6275, 6312}, {6287, 45555}, {7977, 45573}, {8993, 45576}, {9738, 48745}, {9903, 45531}, {9918, 45533}, {10064, 45581}, {10080, 45583}, {12122, 45499}, {12144, 45503}, {12206, 45505}, {12252, 45511}, {12264, 45501}, {12339, 45521}, {12476, 45535}, {12477, 45537}, {12783, 45547}, {12795, 45549}, {12924, 45557}, {12934, 45559}, {12944, 45561}, {12954, 45563}, {12994, 45567}, {12995, 45568}, {13078, 45571}, {13111, 45579}, {13112, 45585}, {13113, 45587}, {13984, 45575}, {17766, 48765}, {18983, 45507}, {19091, 45514}, {19092, 45513}, {22780, 45541}, {22803, 45543}, {29012, 48467}, {35701, 43119}, {35868, 45564}, {45350, 48518}, {45352, 48517}, {45378, 48674}, {48727, 48773}

X(48771) = orthologic center (2nd anti- Kenmotu-free-vertices, 2nd Neuberg)


X(48772) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO ORTHIC AXES

Barycentrics    (-a^2+b^2+c^2)*(2*a^4-(b^2+c^2)*a^2+(b^2-c^2)^2)+2*S*(2*a^4-3*(b^2+c^2)*a^2+(b^2-c^2)^2) : :
X(48772) = 3*X(549)+X(5874) = 3*X(591)+X(9732) = 5*X(632)-X(5875) = X(9739)-3*X(41490) = 3*X(41490)+X(48466) = 3*X(48744)+X(48768)

The reciprocal orthologic center of these triangles is X(4).

X(48772) lies on these lines: {2, 45410}, {3, 489}, {4, 45377}, {5, 372}, {26, 45532}, {30, 9739}, {39, 7584}, {114, 6215}, {140, 141}, {230, 5062}, {355, 45530}, {486, 2549}, {488, 32828}, {495, 45560}, {496, 45562}, {517, 48764}, {524, 44475}, {546, 22820}, {548, 7690}, {549, 5874}, {550, 45498}, {591, 9732}, {632, 5875}, {639, 43121}, {952, 45715}, {1152, 6289}, {1352, 5420}, {1353, 8981}, {1483, 45572}, {1656, 45525}, {3069, 37343}, {3071, 45565}, {3103, 44392}, {3312, 13758}, {3593, 21737}, {3628, 45872}, {3850, 45868}, {5050, 11315}, {5066, 48778}, {5690, 45546}, {5844, 48746}, {5901, 45500}, {6119, 6722}, {6214, 35256}, {6290, 8252}, {6306, 48722}, {6307, 48724}, {6566, 13449}, {6756, 45502}, {6811, 45488}, {10942, 45528}, {10943, 45526}, {12256, 32805}, {12314, 36656}, {13692, 13847}, {13925, 45574}, {13935, 37342}, {13972, 18583}, {13993, 45577}, {15171, 45570}, {15884, 37242}, {15886, 32152}, {18990, 45506}, {19116, 45512}, {19117, 45515}, {19146, 37466}, {28174, 48740}, {32134, 45504}, {32141, 45520}, {32146, 45534}, {32147, 45536}, {32151, 45538}, {32153, 45540}, {32162, 45548}, {32177, 45569}, {32178, 45566}, {32213, 45584}, {32214, 45586}, {32419, 43144}, {32423, 48736}, {32515, 48744}, {32807, 45407}, {34200, 48781}, {35833, 42215}, {39387, 45411}, {43118, 45472}, {45349, 48519}, {45351, 48520}, {48726, 48770}

X(48772) = midpoint of X(i) and X(j) for these {i, j}: {9739, 48466}, {48736, 48786}
X(48772) = reflection of X(48773) in X(140)
X(48772) = orthologic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {orthic axes, Yiu tangents}
X(48772) = X(5)-of-1st anti-Kenmotu-free-vertices triangle
X(48772) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (141, 10104, 48773), (182, 641, 140), (372, 45554, 5), (641, 48734, 182), (41490, 48466, 9739), (45377, 45578, 4), (45508, 45510, 3), (45542, 45544, 546), (45560, 45580, 495), (45562, 45582, 496)


X(48773) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO ORTHIC AXES

Barycentrics    (-a^2+b^2+c^2)*(2*a^4-(b^2+c^2)*a^2+(b^2-c^2)^2)-2*S*(2*a^4-3*(b^2+c^2)*a^2+(b^2-c^2)^2) : :
X(48773) = 3*X(549)+X(5875) = 5*X(632)-X(5874) = 3*X(1991)+X(9733) = X(9738)-3*X(41491) = 3*X(41491)+X(48467) = 3*X(48745)+X(48769)

The reciprocal orthologic center of these triangles is X(4).

X(48773) lies on these lines: {2, 45411}, {3, 490}, {4, 45378}, {5, 371}, {26, 45533}, {30, 9738}, {39, 7583}, {114, 6214}, {140, 141}, {230, 5058}, {355, 45531}, {485, 2549}, {487, 32828}, {495, 45561}, {496, 45563}, {517, 48765}, {524, 44476}, {546, 22819}, {548, 7692}, {549, 5875}, {550, 45499}, {632, 5874}, {639, 43142}, {640, 43120}, {952, 45716}, {1151, 6290}, {1352, 5418}, {1353, 13966}, {1483, 45573}, {1656, 45524}, {1991, 9733}, {3068, 37342}, {3070, 45564}, {3102, 44394}, {3311, 13638}, {3628, 45871}, {3850, 45869}, {5050, 11316}, {5066, 48779}, {5690, 45547}, {5844, 48747}, {5901, 45501}, {6118, 6722}, {6215, 35255}, {6289, 8253}, {6302, 48723}, {6303, 48725}, {6567, 13449}, {6756, 45503}, {6813, 45489}, {9540, 37343}, {9541, 26469}, {10942, 45529}, {10943, 45527}, {12257, 32806}, {12313, 36655}, {13812, 13846}, {13910, 18583}, {13925, 45576}, {13993, 45575}, {15171, 45571}, {15883, 37242}, {15885, 32152}, {18990, 45507}, {19116, 45514}, {19117, 45513}, {19145, 37466}, {28174, 48741}, {32134, 45505}, {32141, 45521}, {32146, 45535}, {32147, 45537}, {32151, 45539}, {32153, 45541}, {32162, 45549}, {32177, 45567}, {32178, 45568}, {32213, 45585}, {32214, 45587}, {32421, 43141}, {32423, 48737}, {32515, 48745}, {34200, 48780}, {35832, 42216}, {39388, 45410}, {43119, 45473}, {45350, 48520}, {45352, 48519}, {48727, 48771}

X(48773) = midpoint of X(i) and X(j) for these {i, j}: {9738, 48467}, {48737, 48787}
X(48773) = reflection of X(48772) in X(140)
X(48773) = orthologic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {orthic axes, Yiu tangents}
X(48773) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (141, 10104, 48772), (182, 642, 140), (371, 45555, 5), (642, 48735, 182), (41491, 48467, 9738), (45378, 45579, 4), (45509, 45511, 3), (45543, 45545, 546), (45561, 45581, 495), (45563, 45583, 496)


X(48774) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO REFLECTION

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

The reciprocal orthologic center of these triangles is X(4).

X(48774) lies on these lines: {54, 372}, {182, 9977}, {195, 45578}, {539, 41490}, {641, 1209}, {1154, 9739}, {2888, 45508}, {3574, 45544}, {6276, 45553}, {6277, 45550}, {6288, 45554}, {7691, 45498}, {7979, 45572}, {8995, 45574}, {9905, 45530}, {9920, 45532}, {9985, 45538}, {10066, 45580}, {10082, 45582}, {10619, 48734}, {10628, 48730}, {11576, 45502}, {12208, 45504}, {12254, 45510}, {12266, 45500}, {12341, 45520}, {12480, 45534}, {12481, 45536}, {12785, 45546}, {12797, 45548}, {12926, 45556}, {12936, 45558}, {12946, 45560}, {12956, 45562}, {12971, 45565}, {12998, 45569}, {12999, 45566}, {13079, 45570}, {13121, 45584}, {13122, 45586}, {13986, 45577}, {18400, 48466}, {18984, 45506}, {19095, 45512}, {19096, 45515}, {22781, 45540}, {22804, 45542}, {32423, 48736}, {45349, 48521}, {45351, 48522}, {45377, 48675}

X(48774) = orthologic center (1st anti-Kenmotu-free-vertices, reflection)
X(48774) = X(54)-of-1st anti-Kenmotu-free-vertices triangle
X(48774) = reflection of X(48775) in X(10610)


X(48775) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO REFLECTION

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

The reciprocal orthologic center of these triangles is X(4).

X(48775) lies on these lines: {54, 371}, {182, 9977}, {195, 45579}, {539, 41491}, {642, 1209}, {1154, 9738}, {2888, 45509}, {3574, 45545}, {6276, 45551}, {6277, 45552}, {6288, 45555}, {7691, 45499}, {7979, 45573}, {8995, 45576}, {9905, 45531}, {9920, 45533}, {9985, 45539}, {10066, 45581}, {10082, 45583}, {10619, 48735}, {10628, 48731}, {11576, 45503}, {12208, 45505}, {12254, 45511}, {12266, 45501}, {12341, 45521}, {12480, 45535}, {12481, 45537}, {12785, 45547}, {12797, 45549}, {12926, 45557}, {12936, 45559}, {12946, 45561}, {12956, 45563}, {12965, 45564}, {12998, 45567}, {12999, 45568}, {13079, 45571}, {13121, 45585}, {13122, 45587}, {13986, 45575}, {18400, 48467}, {18984, 45507}, {19095, 45514}, {19096, 45513}, {22781, 45541}, {22804, 45543}, {32423, 48737}, {45350, 48522}, {45352, 48521}, {45378, 48675}

X(48775) = orthologic center (2nd anti- Kenmotu-free-vertices, reflection)
X(48775) = reflection of X(48774) in X(10610)


X(48776) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 1st SCHIFFLER

Barycentrics    -2*(2*a^9-5*(b^2+c^2)*a^7+(b+c)*(b^2+c^2)*a^6+(3*b^4+3*c^4+8*b*c*(b^2+c^2))*a^5-(b^2-c^2)*(b-c)*(3*b^2+4*b*c+3*c^2)*a^4+(b^6+c^6-8*b*c*(b^4+c^4))*a^3+(b+c)*(b^2+c^2)*(3*b^4+3*c^4-b*c*(4*b^2-b*c+4*c^2))*a^2-(b^4-c^4)^2*a-(b^4-c^4)*(b^2-c^2)^2*(b-c))*S+(a+b+c)*(2*(b+c)*a^9-(3*b^2-4*b*c+3*c^2)*a^8-6*(b+c)*(b^2+c^2)*a^7+2*(5*b^4+5*c^4-6*b*c*(b^2+c^2))*a^6+2*(b+c)*(3*b^4+3*c^4-b*c*(b^2-5*b*c+c^2))*a^5-(12*b^6+12*c^6-(14*b^4+14*c^4+9*b*c*(b^2+c^2))*b*c)*a^4-2*(b^2-c^2)*(b-c)*(b^4+3*b^2*c^2+c^4)*a^3+(6*b^4+6*c^4-b*c*(8*b^2-3*b*c+8*c^2))*(b^2-c^2)^2*a^2-2*(b^2-c^2)^3*(b-c)*b*c*a-(b^2-c^2)^4*(b-c)^2) : :

The reciprocal orthologic center of these triangles is X(79).

X(48776) lies on these lines: {182, 48777}, {372, 10266}, {641, 13089}, {12146, 45502}, {12209, 45504}, {12255, 45510}, {12267, 45500}, {12342, 45520}, {12409, 45530}, {12414, 45532}, {12482, 45534}, {12483, 45536}, {12504, 45538}, {12556, 45498}, {12600, 45544}, {12786, 45546}, {12798, 45548}, {12807, 45550}, {12808, 45553}, {12849, 45508}, {12919, 45554}, {12927, 45556}, {12937, 45558}, {12947, 45560}, {12957, 45562}, {13000, 45569}, {13001, 45566}, {13080, 45570}, {13100, 45572}, {13126, 45578}, {13128, 45580}, {13129, 45582}, {13130, 45584}, {13131, 45586}, {13919, 45574}, {13987, 45577}, {18985, 45506}, {19097, 45512}, {19098, 45515}, {22782, 45540}, {22805, 45542}, {35871, 45565}, {45349, 48523}, {45351, 48524}, {45377, 48676}

X(48776) = orthologic center (1st anti-Kenmotu-free-vertices, 1st Schiffler)
X(48776) = X(10266)-of-1st anti-Kenmotu-free-vertices triangle


X(48777) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 1st SCHIFFLER

Barycentrics    2*(2*a^9-5*(b^2+c^2)*a^7+(b+c)*(b^2+c^2)*a^6+(3*b^4+3*c^4+8*b*c*(b^2+c^2))*a^5-(b^2-c^2)*(b-c)*(3*b^2+4*b*c+3*c^2)*a^4+(b^6+c^6-8*b*c*(b^4+c^4))*a^3+(b+c)*(b^2+c^2)*(3*b^4+3*c^4-b*c*(4*b^2-b*c+4*c^2))*a^2-(b^4-c^4)^2*a-(b^4-c^4)*(b^2-c^2)^2*(b-c))*S+(a+b+c)*(2*(b+c)*a^9-(3*b^2-4*b*c+3*c^2)*a^8-6*(b+c)*(b^2+c^2)*a^7+2*(5*b^4+5*c^4-6*b*c*(b^2+c^2))*a^6+2*(b+c)*(3*b^4+3*c^4-b*c*(b^2-5*b*c+c^2))*a^5-(12*b^6+12*c^6-(14*b^4+14*c^4+9*b*c*(b^2+c^2))*b*c)*a^4-2*(b^2-c^2)*(b-c)*(b^4+3*b^2*c^2+c^4)*a^3+(6*b^4+6*c^4-b*c*(8*b^2-3*b*c+8*c^2))*(b^2-c^2)^2*a^2-2*(b^2-c^2)^3*(b-c)*b*c*a-(b^2-c^2)^4*(b-c)^2) : :

The reciprocal orthologic center of these triangles is X(79).

X(48777) lies on these lines: {182, 48776}, {371, 10266}, {642, 13089}, {12146, 45503}, {12209, 45505}, {12255, 45511}, {12267, 45501}, {12342, 45521}, {12409, 45531}, {12414, 45533}, {12482, 45535}, {12483, 45537}, {12504, 45539}, {12556, 45499}, {12600, 45545}, {12786, 45547}, {12798, 45549}, {12807, 45552}, {12808, 45551}, {12849, 45509}, {12919, 45555}, {12927, 45557}, {12937, 45559}, {12947, 45561}, {12957, 45563}, {13000, 45567}, {13001, 45568}, {13080, 45571}, {13100, 45573}, {13126, 45579}, {13128, 45581}, {13129, 45583}, {13130, 45585}, {13131, 45587}, {13919, 45576}, {13987, 45575}, {18985, 45507}, {19097, 45514}, {19098, 45513}, {22782, 45541}, {22805, 45543}, {35870, 45564}, {45350, 48524}, {45352, 48523}, {45378, 48676}

X(48777) = orthologic center (2nd anti- Kenmotu-free-vertices, 1st Schiffler)


X(48778) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 1st TRI-SQUARES-CENTRAL

Barycentrics    4*a^6-(b^2+c^2)*a^4+2*(b^4+6*b^2*c^2+c^4)*a^2-2*(2*a^4-7*(b^2+c^2)*a^2+5*(b^2-c^2)^2)*S-5*(b^2+c^2)*(b^2-c^2)^2 : :
X(48778) = 5*X(2)+X(13691) = 5*X(381)-X(13713) = 4*X(547)-X(48780) = 5*X(641)-2*X(7690) = X(641)+2*X(45542) = X(1327)-3*X(3545) = 5*X(3091)-X(33456) = 3*X(3839)+X(13678) = 3*X(5055)+X(48677) = 11*X(5056)-X(13690) = 5*X(5071)-X(13674) = 5*X(6289)+X(12313) = X(7690)+5*X(45542) = 3*X(11147)-X(13786) = X(13687)+2*X(13692) = 5*X(13687)-2*X(13713) = 5*X(13692)+X(13713) = X(13701)+2*X(22806)

The reciprocal orthologic center of these triangles is X(13665).

X(48778) lies on these lines: {2, 5870}, {4, 13712}, {5, 48734}, {30, 641}, {114, 41491}, {182, 547}, {372, 1327}, {381, 13687}, {485, 22616}, {591, 11917}, {3091, 33456}, {3543, 13666}, {3544, 45525}, {3656, 48746}, {3839, 13678}, {3845, 9739}, {5055, 45377}, {5056, 13690}, {5066, 48772}, {5071, 13674}, {6251, 13710}, {6289, 12313}, {9770, 13681}, {9880, 48784}, {11147, 13786}, {11180, 42602}, {11237, 13696}, {11238, 13695}, {13667, 45500}, {13668, 45502}, {13672, 45504}, {13675, 45520}, {13679, 45530}, {13680, 45532}, {13682, 45534}, {13683, 45536}, {13685, 45538}, {13688, 31162}, {13689, 45548}, {13693, 45556}, {13694, 45558}, {13697, 45569}, {13698, 45566}, {13699, 45570}, {13702, 34627}, {13704, 36455}, {13706, 36437}, {13714, 45580}, {13715, 45582}, {13716, 45584}, {13717, 45586}, {13920, 45574}, {13932, 42262}, {13988, 45577}, {15682, 45522}, {18986, 45506}, {19099, 45512}, {22165, 44472}, {22541, 45515}, {22783, 45540}, {35247, 36733}, {35873, 45565}, {36439, 48724}, {36457, 48722}, {36724, 45860}, {38426, 42274}, {44422, 48768}, {45349, 48525}, {45351, 48526}, {47353, 48742}

X(48778) = midpoint of X(i) and X(j) for these {i, j}: {4, 13712}, {381, 13692}, {3543, 13666}, {13688, 31162}, {13702, 34627}
X(48778) = reflection of X(13687) in X(381)
X(48778) = orthologic center (1st anti-Kenmotu-free-vertices, 1st tri-squares-central)
X(48778) = X(1327)-of-1st anti-Kenmotu-free-vertices triangle
X(48778) = X(13712)-of-Euler triangle
X(48778) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (381, 41490, 45544), (381, 45554, 41490), (547, 47354, 48779)


X(48779) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    4*a^6-(b^2+c^2)*a^4+2*(b^4+6*b^2*c^2+c^4)*a^2+2*(2*a^4-7*(b^2+c^2)*a^2+5*(b^2-c^2)^2)*S-5*(b^2+c^2)*(b^2-c^2)^2 : :
X(48779) = 5*X(2)+X(13810) = 5*X(381)-X(13836) = 4*X(547)-X(48781) = 5*X(642)-2*X(7692) = X(642)+2*X(45543) = X(1328)-3*X(3545) = 5*X(3091)-X(33457) = 3*X(3839)+X(13798) = 3*X(5055)+X(48678) = 11*X(5056)-X(13811) = 5*X(5071)-X(13794) = 5*X(6290)+X(12314) = X(7692)+5*X(45543) = 3*X(11147)-X(13666) = X(13807)+2*X(13812) = 5*X(13807)-2*X(13836) = 5*X(13812)+X(13836) = X(13821)+2*X(22807)

The reciprocal orthologic center of these triangles is X(13785).

X(48779) lies on these lines: {2, 5871}, {4, 13835}, {5, 48735}, {30, 642}, {114, 41490}, {182, 547}, {371, 1328}, {381, 13807}, {486, 22645}, {1991, 11916}, {3091, 33457}, {3543, 13786}, {3544, 45524}, {3656, 48747}, {3839, 13798}, {3845, 9738}, {5055, 45378}, {5056, 13811}, {5066, 48773}, {5071, 13794}, {6250, 13830}, {6290, 12314}, {9770, 13801}, {9880, 48785}, {11147, 13666}, {11180, 42603}, {11237, 13816}, {11238, 13815}, {13787, 45501}, {13788, 45503}, {13792, 45505}, {13795, 45521}, {13799, 45531}, {13800, 45533}, {13802, 45535}, {13803, 45537}, {13805, 45539}, {13808, 31162}, {13809, 45549}, {13813, 45557}, {13814, 45559}, {13817, 45567}, {13818, 45568}, {13819, 45571}, {13822, 34627}, {13824, 36437}, {13826, 36455}, {13837, 45581}, {13838, 45583}, {13839, 45585}, {13840, 45587}, {13848, 45576}, {13849, 45575}, {13850, 42265}, {15682, 45523}, {18987, 45507}, {19100, 45513}, {19101, 45514}, {22165, 44471}, {22784, 45541}, {35246, 36719}, {35874, 45564}, {36439, 48723}, {36457, 48725}, {36725, 45861}, {38425, 42277}, {44422, 48769}, {45350, 48528}, {45352, 48527}, {47353, 48743}

X(48779) = midpoint of X(i) and X(j) for these {i, j}: {4, 13835}, {381, 13812}, {3543, 13786}, {13808, 31162}, {13822, 34627}
X(48779) = reflection of X(13807) in X(381)
X(48779) = orthologic center (2nd anti- Kenmotu-free-vertices, 2nd tri-squares-central)
X(48779) = X(13835)-of-Euler triangle
X(48779) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (381, 41491, 45545), (381, 45555, 41491), (547, 47354, 48778)


X(48780) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 1st TRI-SQUARES-CENTRAL

Barycentrics    16*a^6-13*(b^2+c^2)*a^4+2*((b^2-c^2)^2-4*b^2*c^2)*a^2+2*(2*a^4-7*(b^2+c^2)*a^2+5*(b^2-c^2)^2)*S-5*(b^2+c^2)*(b^2-c^2)^2 : :
X(48780) = 5*X(376)-3*X(13666) = X(376)+3*X(13674) = 4*X(547)-3*X(48778) = 4*X(549)-3*X(13701) = 3*X(1327)-X(3543) = 3*X(3545)-X(13691) = 4*X(11737)-3*X(22806) = X(13666)+5*X(13674) = 3*X(13687)-2*X(15687) = 3*X(13690)+7*X(15702) = 3*X(13692)-5*X(15694) = 3*X(13712)-5*X(15692) = X(15683)+3*X(33456) = 7*X(15703)-3*X(48677)

The reciprocal orthologic center of these triangles is X(13665).

X(48780) lies on these lines: {30, 48735}, {182, 547}, {371, 1131}, {376, 13666}, {381, 13748}, {549, 642}, {3545, 13691}, {9738, 15686}, {11737, 22806}, {12305, 32421}, {13667, 45501}, {13668, 45503}, {13672, 45505}, {13675, 45521}, {13678, 45509}, {13679, 45531}, {13680, 45533}, {13682, 45535}, {13683, 45537}, {13685, 45539}, {13687, 15687}, {13688, 45547}, {13689, 45549}, {13690, 15702}, {13692, 15694}, {13693, 45557}, {13694, 45559}, {13695, 45561}, {13696, 45563}, {13697, 45567}, {13698, 45568}, {13699, 45571}, {13702, 45573}, {13712, 15692}, {13713, 45579}, {13714, 45581}, {13715, 45583}, {13716, 45585}, {13717, 45587}, {13920, 45576}, {13988, 45575}, {14244, 32419}, {15682, 45524}, {15683, 33456}, {15703, 45378}, {18986, 45507}, {19099, 45514}, {22541, 45513}, {22783, 45541}, {34200, 48773}, {35872, 45564}, {45350, 48526}, {45352, 48525}

X(48780) = orthologic center (2nd anti- Kenmotu-free-vertices, 1st tri-squares-central)


X(48781) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    16*a^6-13*(b^2+c^2)*a^4+2*((b^2-c^2)^2-4*b^2*c^2)*a^2-2*(2*a^4-7*(b^2+c^2)*a^2+5*(b^2-c^2)^2)*S-5*(b^2+c^2)*(b^2-c^2)^2 : :
X(48781) = 5*X(376)-3*X(13786) = X(376)+3*X(13794) = 4*X(547)-3*X(48779) = 4*X(549)-3*X(13821) = 3*X(1328)-X(3543) = 3*X(3545)-X(13810) = 4*X(11737)-3*X(22807) = X(13786)+5*X(13794) = 3*X(13807)-2*X(15687) = 3*X(13811)+7*X(15702) = 3*X(13812)-5*X(15694) = 3*X(13835)-5*X(15692) = X(15683)+3*X(33457) = 7*X(15703)-3*X(48678)

The reciprocal orthologic center of these triangles is X(13785).

X(48781) lies on these lines: {30, 48734}, {182, 547}, {372, 1132}, {376, 13786}, {381, 13749}, {549, 641}, {3545, 13810}, {9739, 15686}, {11737, 22807}, {12306, 32419}, {13787, 45500}, {13788, 45502}, {13792, 45504}, {13795, 45520}, {13798, 45508}, {13799, 45530}, {13800, 45532}, {13802, 45534}, {13803, 45536}, {13805, 45538}, {13807, 15687}, {13808, 45546}, {13809, 45548}, {13811, 15702}, {13812, 15694}, {13813, 45556}, {13814, 45558}, {13815, 45560}, {13816, 45562}, {13817, 45569}, {13818, 45566}, {13819, 45570}, {13822, 45572}, {13835, 15692}, {13836, 45578}, {13837, 45580}, {13838, 45582}, {13839, 45584}, {13840, 45586}, {13848, 45574}, {13849, 45577}, {14229, 32421}, {15682, 45525}, {15683, 33457}, {15703, 45377}, {18987, 45506}, {19100, 45515}, {19101, 45512}, {22784, 45540}, {34200, 48772}, {35875, 45565}, {45349, 48527}, {45351, 48528}

X(48781) = orthologic center (1st anti-Kenmotu-free-vertices, 2nd tri-squares-central)
X(48781) = X(1328)-of-1st anti-Kenmotu-free-vertices triangle


X(48782) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(48782) lies on these lines: {67, 372}, {182, 6699}, {511, 48736}, {542, 9739}, {641, 6593}, {1503, 48730}, {2781, 48466}, {5095, 44656}, {9970, 45554}, {11061, 45508}, {14984, 48738}, {15118, 44474}, {32233, 45498}, {32238, 45500}, {32239, 45502}, {32242, 45504}, {32243, 45506}, {32247, 45510}, {32252, 45512}, {32253, 45515}, {32256, 45520}, {32261, 45530}, {32262, 45532}, {32265, 45534}, {32266, 45536}, {32268, 45538}, {32270, 45540}, {32271, 45542}, {32274, 45544}, {32278, 45546}, {32279, 45548}, {32280, 45550}, {32281, 45553}, {32287, 45556}, {32288, 45558}, {32289, 45560}, {32290, 45562}, {32295, 45569}, {32296, 45566}, {32297, 45570}, {32298, 45572}, {32303, 45574}, {32304, 45577}, {32306, 45578}, {32307, 45580}, {32308, 45582}, {32309, 45584}, {32310, 45586}, {35877, 45565}, {36201, 48766}, {45349, 48529}, {45351, 48530}, {45377, 48679}

X(48782) = orthologic center (1st anti-Kenmotu-free-vertices, Walsmith)
X(48782) = X(67)-of-1st anti-Kenmotu-free-vertices triangle


X(48783) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(48783) lies on these lines: {67, 371}, {182, 6699}, {511, 48737}, {542, 9738}, {642, 6593}, {1503, 48731}, {2781, 48467}, {5095, 44657}, {9970, 45555}, {11061, 45509}, {14984, 48739}, {15118, 44473}, {32233, 45499}, {32238, 45501}, {32239, 45503}, {32242, 45505}, {32243, 45507}, {32247, 45511}, {32252, 45514}, {32253, 45513}, {32256, 45521}, {32261, 45531}, {32262, 45533}, {32265, 45535}, {32266, 45537}, {32268, 45539}, {32270, 45541}, {32271, 45543}, {32274, 45545}, {32278, 45547}, {32279, 45549}, {32280, 45552}, {32281, 45551}, {32287, 45557}, {32288, 45559}, {32289, 45561}, {32290, 45563}, {32295, 45567}, {32296, 45568}, {32297, 45571}, {32298, 45573}, {32303, 45576}, {32304, 45575}, {32306, 45579}, {32307, 45581}, {32308, 45583}, {32309, 45585}, {32310, 45587}, {35876, 45564}, {36201, 48767}, {45350, 48530}, {45352, 48529}, {45378, 48679}

X(48783) = orthologic center (2nd anti- Kenmotu-free-vertices, Walsmith)


X(48784) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 1st ANTI-BROCARD

Barycentrics    -2*((b^2+c^2)*a^4-2*(b^4+c^4)*a^2+b^2*c^2*(b^2+c^2))*S+2*a^8-5*(b^2+c^2)*a^6+(5*b^4+4*b^2*c^2+5*c^4)*a^4-(b^2+c^2)*(2*b^4-b^2*c^2+2*c^4)*a^2+(b^2-c^2)^2*b^2*c^2 : :
X(48784) = X(6230)-3*X(9894) = X(6320)+3*X(21166)

The reciprocal parallelogic center of these triangles is X(385).

X(48784) lies on the circumcircle of 1st anti-Kenmotu-free-vertices triangle and these lines: {98, 13708}, {99, 372}, {114, 45544}, {115, 641}, {148, 45508}, {182, 5969}, {542, 48730}, {543, 41490}, {690, 48786}, {2782, 9739}, {2783, 48686}, {2787, 48705}, {2794, 48732}, {2799, 48788}, {3023, 45570}, {3027, 45506}, {4027, 45504}, {5186, 45502}, {6230, 9894}, {6319, 45550}, {6320, 21166}, {6321, 45554}, {6560, 33341}, {7690, 12042}, {7983, 45572}, {8294, 9865}, {8782, 45538}, {8997, 45574}, {9737, 48727}, {9880, 48778}, {10086, 45580}, {10089, 45582}, {10992, 48734}, {11711, 45500}, {13172, 45510}, {13173, 45520}, {13174, 45530}, {13175, 45532}, {13176, 45534}, {13177, 45536}, {13178, 45546}, {13179, 45548}, {13180, 45556}, {13181, 45558}, {13182, 45560}, {13183, 45562}, {13184, 45569}, {13185, 45566}, {13188, 45578}, {13189, 45584}, {13190, 45586}, {13989, 45577}, {14651, 45522}, {19108, 45512}, {19109, 45515}, {22514, 45540}, {22515, 45542}, {23698, 48466}, {35879, 45565}, {38733, 45377}, {45349, 48531}, {45351, 48532}

X(48784) = parallelogic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard}
X(48784) = X(99)-of-1st anti-Kenmotu-free-vertices triangle
X(48784) = reflection of X(i) in X(j) for these (i, j): (48726, 9739), (48728, 41490), (48785, 33813)


X(48785) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 1st ANTI-BROCARD

Barycentrics    2*((b^2+c^2)*a^4-2*(b^4+c^4)*a^2+b^2*c^2*(b^2+c^2))*S+2*a^8-5*(b^2+c^2)*a^6+(5*b^4+4*b^2*c^2+5*c^4)*a^4-(b^2+c^2)*(2*b^4-b^2*c^2+2*c^4)*a^2+(b^2-c^2)^2*b^2*c^2 : :
X(48785) = X(6231)-3*X(9892) = X(6319)+3*X(21166)

The reciprocal parallelogic center of these triangles is X(385).

X(48785) lies on the circumcircle of 2nd anti- Kenmotu-free-vertices triangle and these lines: {98, 13828}, {99, 371}, {114, 45545}, {115, 642}, {148, 45509}, {182, 5969}, {542, 48731}, {543, 41491}, {690, 48787}, {2782, 9738}, {2783, 48687}, {2787, 48706}, {2794, 48733}, {2799, 48789}, {3023, 45571}, {3027, 45507}, {4027, 45505}, {5186, 45503}, {6231, 9892}, {6319, 21166}, {6320, 45551}, {6321, 45555}, {6561, 33340}, {7692, 12042}, {7983, 45573}, {8293, 9865}, {8782, 45539}, {8997, 45576}, {9737, 48726}, {9880, 48779}, {10086, 45581}, {10089, 45583}, {10992, 48735}, {11711, 45501}, {13172, 45511}, {13173, 45521}, {13174, 45531}, {13175, 45533}, {13176, 45535}, {13177, 45537}, {13178, 45547}, {13179, 45549}, {13180, 45557}, {13181, 45559}, {13182, 45561}, {13183, 45563}, {13184, 45567}, {13185, 45568}, {13188, 45579}, {13189, 45585}, {13190, 45587}, {13989, 45575}, {14651, 45523}, {19108, 45514}, {19109, 45513}, {22514, 45541}, {22515, 45543}, {23698, 48467}, {35878, 45564}, {38733, 45378}, {45350, 48532}, {45352, 48531}

X(48785) = parallelogic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard}
X(48785) = reflection of X(i) in X(j) for these (i, j): (48727, 9738), (48729, 41491), (48784, 33813)


X(48786) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*(-2*((b^2+c^2)*a^4-4*b^2*c^2*a^2-(b^4-3*b^2*c^2+c^4)*(b^2+c^2))*S+(2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)*((-a^2+b^2+c^2)^2-b^2*c^2)) : :
X(48786) = X(7732)-5*X(15034) = X(7733)+3*X(15035)

The reciprocal parallelogic center of these triangles is X(323).

X(48786) lies on the circumcircle of 1st anti-Kenmotu-free-vertices triangle and these lines: {74, 45498}, {110, 372}, {113, 45544}, {125, 641}, {182, 1511}, {265, 45554}, {399, 45578}, {542, 41490}, {690, 48784}, {895, 10819}, {1112, 45502}, {2771, 48686}, {2781, 48732}, {2948, 45530}, {3024, 45570}, {3028, 45506}, {3448, 45508}, {5663, 9739}, {7690, 12041}, {7732, 15034}, {7733, 15035}, {7984, 45572}, {8674, 48705}, {8998, 45574}, {9517, 48788}, {9737, 48731}, {10088, 45580}, {10091, 45582}, {10113, 45542}, {11720, 45500}, {12310, 45532}, {12376, 45565}, {12383, 45510}, {12902, 45377}, {12903, 45560}, {12904, 45562}, {13193, 45504}, {13204, 45520}, {13208, 45534}, {13209, 45536}, {13210, 45538}, {13211, 45546}, {13212, 45548}, {13213, 45556}, {13214, 45558}, {13215, 45569}, {13216, 45566}, {13217, 45584}, {13218, 45586}, {13990, 45577}, {17702, 48466}, {19110, 45512}, {19111, 45515}, {22586, 45540}, {30714, 48734}, {32423, 48736}, {32609, 45410}, {45349, 48535}, {45351, 48536}

X(48786) = parallelogic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {anti-orthocentroidal, orthocentroidal}
X(48786) = X(110)-of-1st anti-Kenmotu-free-vertices triangle
X(48786) = reflection of X(i) in X(j) for these (i, j): (48730, 9739), (48736, 48772), (48787, 1511)


X(48787) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*(2*((b^2+c^2)*a^4-4*b^2*c^2*a^2-(b^4-3*b^2*c^2+c^4)*(b^2+c^2))*S+(2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)*((-a^2+b^2+c^2)^2-b^2*c^2)) : :
X(48787) = X(7732)+3*X(15035) = X(7733)-5*X(15034)

The reciprocal parallelogic center of these triangles is X(323).

X(48787) lies on the circumcircle of 2nd anti- Kenmotu-free-vertices triangle and these lines: {74, 45499}, {110, 371}, {113, 45545}, {125, 642}, {182, 1511}, {265, 45555}, {399, 45579}, {542, 41491}, {690, 48785}, {895, 10820}, {1112, 45503}, {2771, 48687}, {2781, 48733}, {2948, 45531}, {3024, 45571}, {3028, 45507}, {3448, 45509}, {5663, 9738}, {7692, 12041}, {7732, 15035}, {7733, 15034}, {7984, 45573}, {8674, 48706}, {8998, 45576}, {9517, 48789}, {9737, 48730}, {10088, 45581}, {10091, 45583}, {10113, 45543}, {11720, 45501}, {12310, 45533}, {12375, 45564}, {12383, 45511}, {12902, 45378}, {12903, 45561}, {12904, 45563}, {13193, 45505}, {13204, 45521}, {13208, 45535}, {13209, 45537}, {13210, 45539}, {13211, 45547}, {13212, 45549}, {13213, 45557}, {13214, 45559}, {13215, 45567}, {13216, 45568}, {13217, 45585}, {13218, 45587}, {13990, 45575}, {17702, 48467}, {19110, 45514}, {19111, 45513}, {22586, 45541}, {30714, 48735}, {32423, 48737}, {32609, 45411}, {45350, 48536}, {45352, 48535}

X(48787) = parallelogic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {anti-orthocentroidal, orthocentroidal}
X(48787) = reflection of X(i) in X(j) for these (i, j): (48731, 9738), (48737, 48773), (48786, 1511)


X(48788) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*(-2*((b^2+c^2)*a^8-2*(b^4+c^4)*a^6+(b^2+c^2)*b^2*c^2*a^4+2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*(b^4+b^2*c^2+c^4))*S+2*a^12-5*(b^2+c^2)*a^10+(3*b^4+8*b^2*c^2+3*c^4)*a^8+(b^2+c^2)*(2*b^4-7*b^2*c^2+2*c^4)*a^6-(4*b^4+3*b^2*c^2+4*c^4)*(b^2-c^2)^2*a^4+(b^4-c^4)*(b^2-c^2)*(3*b^4+b^2*c^2+3*c^4)*a^2-(b^8+c^8+3*b^2*c^2*(b^4+c^4))*(b^2-c^2)^2) : :
X(48788) = X(13283)+3*X(38699)

The reciprocal parallelogic center of these triangles is X(10313).

X(48788) lies on the circumcircle of 1st anti-Kenmotu-free-vertices triangle and these lines: {112, 372}, {127, 641}, {132, 45544}, {182, 2781}, {1297, 45498}, {2794, 43121}, {2799, 48784}, {2806, 48705}, {2831, 48686}, {3320, 45506}, {6020, 45570}, {7690, 38624}, {9517, 48786}, {9737, 48733}, {9739, 48732}, {10705, 45572}, {10749, 45554}, {11641, 45532}, {11722, 45500}, {12975, 34217}, {13166, 45502}, {13195, 45504}, {13200, 45510}, {13206, 45520}, {13219, 45508}, {13221, 45530}, {13229, 45534}, {13231, 45536}, {13236, 45538}, {13280, 45546}, {13281, 45548}, {13282, 45550}, {13283, 38699}, {13294, 45556}, {13295, 45558}, {13296, 45560}, {13297, 45562}, {13298, 45569}, {13299, 45566}, {13310, 45578}, {13311, 45580}, {13312, 45582}, {13313, 45584}, {13314, 45586}, {13923, 45574}, {13992, 45577}, {14900, 48734}, {19114, 45512}, {19115, 45515}, {19162, 45540}, {19163, 45542}, {35881, 45565}, {45349, 48537}, {45351, 48538}, {45377, 48681}

X(48788) = parallelogic center (1st anti-Kenmotu-free-vertices, T) for these triangles T: {1st anti-orthosymmedial, 1st orthosymmedial}
X(48788) = X(112)-of-1st anti-Kenmotu-free-vertices triangle
X(48788) = reflection of X(i) in X(j) for these (i, j): (48732, 9739), (48789, 38608)


X(48789) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*(2*((b^2+c^2)*a^8-2*(b^4+c^4)*a^6+(b^2+c^2)*b^2*c^2*a^4+2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*(b^4+b^2*c^2+c^4))*S+2*a^12-5*(b^2+c^2)*a^10+(3*b^4+8*b^2*c^2+3*c^4)*a^8+(b^2+c^2)*(2*b^4-7*b^2*c^2+2*c^4)*a^6-(4*b^4+3*b^2*c^2+4*c^4)*(b^2-c^2)^2*a^4+(b^4-c^4)*(b^2-c^2)*(3*b^4+b^2*c^2+3*c^4)*a^2-(b^8+c^8+3*b^2*c^2*(b^4+c^4))*(b^2-c^2)^2) : :
X(48789) = X(13282)+3*X(38699)

The reciprocal parallelogic center of these triangles is X(10313).

X(48789) lies on the circumcircle of 2nd anti- Kenmotu-free-vertices triangle and these lines: {112, 371}, {127, 642}, {132, 45545}, {182, 2781}, {1297, 45499}, {2794, 43120}, {2799, 48785}, {2806, 48706}, {2831, 48687}, {3320, 45507}, {6020, 45571}, {7692, 38624}, {9517, 48787}, {9737, 48732}, {9738, 48733}, {10705, 45573}, {10749, 45555}, {11641, 45533}, {11722, 45501}, {12974, 34217}, {13166, 45503}, {13195, 45505}, {13200, 45511}, {13206, 45521}, {13219, 45509}, {13221, 45531}, {13229, 45535}, {13231, 45537}, {13236, 45539}, {13280, 45547}, {13281, 45549}, {13282, 38699}, {13283, 45551}, {13294, 45557}, {13295, 45559}, {13296, 45561}, {13297, 45563}, {13298, 45567}, {13299, 45568}, {13310, 45579}, {13311, 45581}, {13312, 45583}, {13313, 45585}, {13314, 45587}, {13923, 45576}, {13992, 45575}, {14900, 48735}, {19114, 45514}, {19115, 45513}, {19162, 45541}, {19163, 45543}, {35880, 45564}, {45350, 48538}, {45352, 48537}, {45378, 48681}

X(48789) = parallelogic center (2nd anti- Kenmotu-free-vertices, T) for these triangles T: {1st anti-orthosymmedial, 1st orthosymmedial}
X(48789) = reflection of X(i) in X(j) for these (i, j): (48733, 9738), (48788, 38608)


X(48790) = CYCLOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-FREE-VERTICES TO OUTER-VECTEN

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

The reciprocal cyclologic center of these triangles is X(48791).

X(48790) lies on the circumcircle of 1st anti-Kenmotu-free-vertices triangle and these lines: {110, 5408}, {114, 641}, {136, 45544}, {372, 3563}, {1147, 2909}, {8968, 47200}, {9733, 19165}, {9739, 30428}, {14769, 15234}

X(48790) = cyclologic center (1st anti-Kenmotu-free-vertices, outer-Vecten)
X(48790) = X(39383)-of-1st anti-Kenmotu-free-vertices triangle


X(48791) = CYCLOLOGIC CENTER OF THESE TRIANGLES: OUTER-VECTEN TO 1st ANTI-KENMOTU-FREE-VERTICES

Barycentrics    2*(a^12-5*(b^2+c^2)*a^10+5*(b^4-b^2*c^2+c^4)*a^8-2*((b^2-c^2)^2-4*b^2*c^2)*(b^2+c^2)*a^6-(b^8+c^8+b^2*c^2*(7*b^4-4*b^2*c^2+7*c^4))*a^4+3*(b^4-c^4)*(b^2-c^2)*(b^4+4*b^2*c^2+c^4)*a^2-(b^2-c^2)^2*(b^4-2*b^2*c^2-c^4)*(b^4+2*b^2*c^2-c^4))*S+a^14-(7*b^4+17*b^2*c^2+7*c^4)*a^10+(b^2+c^2)*(14*b^4-3*b^2*c^2+14*c^4)*a^8-(15*b^8+15*c^8-b^2*c^2*(b^4+16*b^2*c^2+c^4))*a^6+(b^2+c^2)*(10*b^8+10*c^8-b^2*c^2*(17*b^4-10*b^2*c^2+17*c^4))*a^4-(b^4-c^4)^2*(3*b^4-16*b^2*c^2+3*c^4)*a^2-4*(b^4-c^4)*(b^2-c^2)^3*b^2*c^2 : :

The reciprocal cyclologic center of these triangles is X(48790).

X(48791) lies on the outer-Vecten circle and these lines: {3, 42009}, {492, 1306}

X(48791) = cyclologic center (outer-Vecten, 1st anti-Kenmotu-free-vertices)
X(48791) = X(39384)-of-outer-Vecten triangle, when ABC is acute


X(48792) = CYCLOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-FREE-VERTICES TO INNER-VECTEN

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

The reciprocal cyclologic center of these triangles is X(48793).

X(48792) lies on the circumcircle of 2nd anti- Kenmotu-free-vertices triangle and these lines: {110, 5409}, {114, 642}, {136, 8968}, {371, 3563}, {1147, 2909}, {8989, 9732}, {9738, 30427}, {14769, 15233}

X(48792) = cyclologic center (2nd anti- Kenmotu-free-vertices, inner-Vecten)


X(48793) = CYCLOLOGIC CENTER OF THESE TRIANGLES: INNER-VECTEN TO 2nd ANTI-KENMOTU-FREE-VERTICES

Barycentrics    -2*(a^12-5*(b^2+c^2)*a^10+5*(b^4-b^2*c^2+c^4)*a^8-2*((b^2-c^2)^2-4*b^2*c^2)*(b^2+c^2)*a^6-(b^8+c^8+b^2*c^2*(7*b^4-4*b^2*c^2+7*c^4))*a^4+3*(b^4-c^4)*(b^2-c^2)*(b^4+4*b^2*c^2+c^4)*a^2-(b^2-c^2)^2*(b^4-2*b^2*c^2-c^4)*(b^4+2*b^2*c^2-c^4))*S+a^14-(7*b^4+17*b^2*c^2+7*c^4)*a^10+(b^2+c^2)*(14*b^4-3*b^2*c^2+14*c^4)*a^8-(15*b^8+15*c^8-b^2*c^2*(b^4+16*b^2*c^2+c^4))*a^6+(b^2+c^2)*(10*b^8+10*c^8-b^2*c^2*(17*b^4-10*b^2*c^2+17*c^4))*a^4-(b^4-c^4)^2*(3*b^4-16*b^2*c^2+3*c^4)*a^2-4*(b^4-c^4)*(b^2-c^2)^3*b^2*c^2 : :

The reciprocal cyclologic center of these triangles is X(48792).

X(48793) lies on the inner-Vecten circle and these lines: {3, 42060}, {491, 1307}

X(48793) = cyclologic center (inner-Vecten, 2nd anti- Kenmotu-free-vertices)
X(48793) = X(39384)-of-inner-Vecten triangle, when ABC is obtuse


X(48794) = EULER LINE INTERCEPT OF X(13)X(1338)

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

See Kadir Altintas and César Lozada euclid 5040.

X(48794) lies on these lines: {2, 3}, {13, 1338}, {18, 34425}, {62, 36305}, {621, 22648}, {3060, 16965}, {5012, 16964}, {5611, 11671}, {6151, 22862}, {15080, 19107}, {15107, 19106}, {16809, 41473}, {23004, 34394}, {33529, 44667}, {34424, 36967}, {36969, 45826}, {41472, 42099}

X(48794) = {X(5), X(15778)}-harmonic conjugate of X(2)


X(48795) = X(1)X(18)∩X(3)X(1277)

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

See Kadir Altintas and César Lozada euclid 5040.

X(48795) lies on the cubic K005 and these lines: {1, 18}, {3, 1277}, {4, 5673}, {5, 44072}, {54, 6192}, {61, 3467}, {3459, 21011}, {3461, 8837}, {3469, 8918}, {3490, 6191}, {7344, 39261}

X(48795) = cevapoint of X(1277) and X(44072)
X(48795) = X(5)-Ceva conjugate of-X(6192)
X(48795) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(8454)}} and {{A, B, C, X(4), X(16883)}}


X(48796) = EULER LINE INTERCEPT OF X(14)X(1337)

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

See Kadir Altintas and César Lozada euclid 5040.

X(48796) lies these lines: {2, 3}, {14, 1337}, {17, 34424}, {61, 36304}, {622, 22649}, {2981, 22906}, {3060, 16964}, {5012, 16965}, {5615, 11671}, {15080, 19106}, {15107, 19107}, {16808, 41472}, {23005, 34395}, {33530, 44666}, {34425, 36968}, {36970, 45827}, {41473, 42100}

X(48796) = {X(5), X(15802)}-harmonic conjugate of X(2)


X(48797) = X(1)X(17)∩X(3)X(1276)

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

See Kadir Altintas and César Lozada euclid 5040.

X(48797) lies on the cubic K005 and these lines: {1, 17}, {3, 1276}, {4, 5672}, {5, 44071}, {54, 6191}, {62, 1251}, {3459, 21011}, {3461, 8839}, {3469, 8919}, {3489, 6192}, {7345, 39262}

X(48797) = cevapoint of X(1276) and X(44071)
X(48797) = X(5)-Ceva conjugate of-X(6191)
X(48797) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(8444)}} and {{A, B, C, X(4), X(16882)}}

leftri

Points in the [ [b-c,c-a,a-b], [(b^2 - c^2)(a^2 - b^2 - c^2), (c^2 - a^2)(b^2 - c^2 - a^2), (a^2 - b^2)(c^2 - a^2 - b^2)] ] coordinate system: X(48798) - X(48833)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1,L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1 = Nagel line: (b-c) α + (c-a) β + (a-b) γ = 0.

L2 = Euler line: (b^2 - c^2)(a^2 - b^2 - c^2) α + (c^2 - a^2)(b^2 - c^2 - a^2) β + (a^2 - b^2)(c^2 - a^2 - b^2) γ = 0.

The origin is given by (0,0) = X(2) = 1 : 1 : 1.

Barycentrics u : v : w for a triangle center U = (x,y) in this system are given by

u : v : w = (b-c)(a-b)(a-c) (a+b+c)^2 + (2a-b-c) x + (2 a^4-a^2 b^2-b^4-a^2 c^2+2 b^2 c^2-c^4) y : : ,

where, as functions of a,b,c, the coordinate x is antisymmetric and homogeneous of degree 1, and y is antisymmetric and homogeneous of degree 2n; viz., x and y are of the form (b-c)(a-b)(a-c)z(a,b,c), where z(a,b,c) is symmetric in a,b,c..

The appearance of {x,y},k in the following list means that (x,y) = X(k).

{-2 (a-b) (a-c) (b-c) (a+b+c), 0}, 8
{-((a-b) (a-c) (b-c) (a+b+c)), 0}, 3679
{-(1/2) (a-b) (a-c) (b-c) (a+b+c), 0}, 10
{0, -(((a-b) (a-c) (b-c))/(a^2+b^2+c^2))}, 11359
{0, 0}, 2
{0, ((a-b) (a-c) (b-c))/(a^2+b^2+c^2)}, 11354
{0, ((a-b) (a-c) (b-c))/(a+b+c)^2}, 19277
{1/2 (a-b) (a-c) (b-c) (a+b+c), 0}, 551
{(a-b) (a-c) (b-c) (a+b+c), 0}, 1
{2 (a-b) (a-c) (b-c) (a+b+c), 0}, 3241
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), (-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48798
{(-2*a*(a - b)*b*(a - c)*(b - c)*c)/(a^2 + b^2 + c^2), (-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48799
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), -(((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2))}, 48800
{(-2*a*(a - b)*b*(a - c)*(b - c)*c)/(a^2 + b^2 + c^2), -(((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2))}, 48801
{(-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c), 0}, 48802
{(-2*a*(a - b)*b*(a - c)*(b - c)*c)/(a^2 + b^2 + c^2), 0}, 48803
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48804
{(-2*a*(a - b)*b*(a - c)*(b - c)*c)/(a^2 + b^2 + c^2), ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48805
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), (2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48806
{-((a - b)*(a - c)*(b - c)*(a + b + c)), (-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48807
{-((a*(a - b)*b*(a - c)*(b - c)*c)/(a^2 + b^2 + c^2)), -(((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2))}, 48808
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)), 0}, 48809
{-((a*(a - b)*b*(a - c)*(b - c)*c)/(a^2 + b^2 + c^2)), ((a - b)*(a - c)*(b - c))/(2*(a^2 + b^2 + c^2))}, 48810
{-((a*(a - b)*b*(a - c)*(b - c)*c)/(a^2 + b^2 + c^2)), ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48811
{-((a - b)*(a - c)*(b - c)*(a + b + c)), (2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48812
{0, (-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48813
{0, -(((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c))}, 48814
{0, -1/2*((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48815
{0, ((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 48816
{0, (2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48817
{(a - b)*(a - c)*(b - c)*(a + b + c), (-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48818
{(a - b)*(a - c)*(b - c)*(a + b + c), -(((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2))}, 48819
{(a - b)*(a - c)*(b - c)*(a + b + c), -1/2*((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48820
{(a*(a - b)*b*(a - c)*(b - c)*c)/(a^2 + b^2 + c^2), -1/2*((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48821
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c), 0}, 48822
{(a - b)*(a - c)*(b - c)*(a + b + c), ((a - b)*(a - c)*(b - c))/(2*(a*b + a*c + b*c))}, 48823
{(a - b)*(a - c)*(b - c)*(a + b + c), ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48824
{(a - b)*(a - c)*(b - c)*(a + b + c), ((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 48825
{(a*(a - b)*b*(a - c)*(b - c)*c)/(a^2 + b^2 + c^2), ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48826
{(a - b)*(a - c)*(b - c)*(a + b + c), (2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48827
{(a - b)*(a - c)*(b - c)*(a + b + c), (2*(a - b)*(a - c)*(b - c))/(a + b + c)^2}, 48828
{(2*a*(a - b)*b*(a - c)*(b - c)*c)/(a^2 + b^2 + c^2), -(((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2))}, 48829
{(2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c), 0}, 48830
{(2*a*(a - b)*b*(a - c)*(b - c)*c)/(a^2 + b^2 + c^2), 0}, 48831
{(2*a*(a - b)*b*(a - c)*(b - c)*c)/(a^2 + b^2 + c^2), ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48832
{(2*a*(a - b)*b*(a - c)*(b - c)*c)/(a^2 + b^2 + c^2), (2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 48833


X(48798) = X(8)X(30)∩X(69)X(519)

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

X(48798) = X(488) lies on these lines: {2, 5015}, {8, 30}, {69, 519}, {319, 32836}, {3241, 11359}, {3524, 3705}, {3543, 4385}, {3545, 7081}, {3839, 7172}, {4000, 7865}, {4030, 11237}, {4294, 42033}, {4371, 7761}, {4680, 10056}, {4894, 10072}, {5278, 11354}, {5839, 7739}, {14033, 29615}, {14929, 31995}, {17561, 29641}, {18139, 38314}, {24280, 28202}, {29617, 32986}, {30179, 33255}

X(48798) = reflection of X(3241) in X(11359)


X(48799) = X(2)X(36)∩X(69)X(519)

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

X(48799) lies on these lines: {2, 36}, {69, 519}, {529, 11359}, {551, 26098}, {2549, 17281}, {3241, 6327}, {3679, 26034}, {4299, 16393}, {4317, 5051}, {5432, 16402}, {7354, 16394}, {9657, 13728}, {11194, 16052}, {12647, 32950}, {15326, 16401}, {17677, 45700}, {37635, 38314}


X(48800) = X(8)X(30)∩X(519)X(599)

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

X(48800) lies on these lines: {8, 30}, {381, 5015}, {519, 599}, {1724, 3679}, {3545, 7172}, {3695, 10385}, {3705, 5054}, {3729, 28202}, {3830, 4385}, {4030, 10056}, {4361, 7865}, {4680, 11237}, {4894, 11238}, {5055, 7081}, {5300, 44217}, {5814, 36721}, {7739, 17362}, {11286, 29615}, {11287, 29617}, {11297, 40713}, {11298, 40714}, {14929, 32087}, {15171, 42032}, {30179, 33220}

X(48800) = reflection of X(11354) in X(3679)


X(48801) = X(2)X(12)∩X(519)X(599)

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

X(48801) lies on these lines: {2, 12}, {515, 10516}, {519, 599}, {535, 11354}, {540, 16790}, {551, 5717}, {964, 9657}, {1056, 4026}, {1626, 16370}, {2099, 17184}, {3303, 17676}, {3304, 5051}, {3670, 3679}, {3704, 42049}, {3913, 4201}, {4234, 34620}, {4428, 37038}, {5289, 27184}, {10197, 19279}, {11113, 34634}, {11235, 17677}, {12513, 16062}, {12943, 24552}, {16052, 45700}, {17274, 24471}, {38315, 38456}


X(48802) = X(1)X(2)∩X(517)X(3789)

Barycentrics    a^3 - a^2*b + 5*a*b^2 + b^3 - a^2*c + 6*a*b*c + 5*b^2*c + 5*a*c^2 + 5*b*c^2 + c^3 : :
X(48802) = X[8] + 2 X[36480], 4 X[10] - X[36479], 4 X[4407] - X[4419]

X(48802) lies on these lines: {1, 2}, {517, 3789}, {528, 17251}, {966, 32941}, {1211, 31140}, {2094, 3980}, {2550, 3775}, {3242, 4733}, {3475, 27798}, {3672, 4709}, {3696, 17301}, {3820, 30959}, {3913, 16850}, {3923, 6172}, {4000, 4732}, {4104, 31142}, {4301, 36695}, {4407, 4419}, {4643, 28534}, {4660, 5232}, {4688, 47358}, {4967, 16496}, {4980, 17871}, {5263, 17346}, {6174, 37660}, {7982, 36672}, {8299, 9708}, {11354, 14968}, {11355, 34606}, {13633, 38066}, {17254, 24248}, {21283, 27081}, {21356, 31151}


X(48803) = X(1)X(2)∩X(392)X(41581)

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

X(48803) lies on these lines: {1, 2}, {392, 41581}, {528, 11359}, {529, 11354}, {966, 16488}, {1211, 16483}, {1478, 24552}, {3303, 13728}, {3902, 32774}, {4026, 6767}, {4309, 17676}, {4317, 11115}, {4647, 19819}, {4717, 30699}, {5258, 17526}, {5315, 5739}, {5434, 16394}, {7739, 17281}, {8666, 37176}, {9709, 25914}, {11235, 16052}, {12513, 17698}, {16470, 37654}, {17306, 31393}, {17321, 33936}, {18613, 19266}, {19290, 37538}, {23888, 26144}, {26034, 37610}, {28423, 48285}


X(48804) = X(6)X(519)∩X(8)X(30)

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

X(48804) lies on these lines: {6, 519}, {8, 30}, {381, 4385}, {594, 7739}, {986, 3679}, {1089, 11238}, {3295, 42033}, {3524, 7172}, {3703, 10056}, {3705, 5055}, {3729, 28198}, {3790, 6767}, {3830, 5015}, {4445, 7865}, {4692, 11237}, {4696, 5827}, {4968, 44217}, {5054, 7081}, {5295, 36721}, {7788, 33941}, {11286, 29617}, {11287, 29615}, {11297, 40714}, {11298, 40713}, {15170, 42032}, {22253, 48628}, {30179, 33219}, {32836, 42696}, {34790, 36731}

X(48804) = reflection of X(11359) in X(3679)


X(48805) = X(1)X(536)∩X(2)X(11)

Barycentrics    3*a^3 - a^2*b + 2*a*b^2 - a^2*c + 2*b^2*c + 2*a*c^2 + 2*b*c^2 : :
X(48805) = 2 X[1] + X[5695], X[6] + 2 X[32941], X[3242] + 2 X[3923], 2 X[1386] + X[3886], 5 X[3763] - 2 X[4660], 4 X[4085] - 7 X[47355], 2 X[4852] - 5 X[16491], 2 X[17382] - 3 X[25055], X[16496] + 2 X[17351]

X(48058) lies on these lines: {1, 536}, {2, 11}, {6, 519}, {8, 17354}, {31, 31136}, {36, 16401}, {45, 4432}, {56, 16393}, {86, 16711}, {88, 24344}, {171, 31137}, {190, 36534}, {238, 3679}, {392, 44670}, {474, 15625}, {516, 31884}, {527, 47358}, {537, 3242}, {551, 4356}, {599, 752}, {740, 38315}, {894, 42871}, {902, 37660}, {940, 32943}, {958, 13735}, {964, 3303}, {1027, 4762}, {1125, 24693}, {1279, 4688}, {1386, 3886}, {1486, 19322}, {1617, 16398}, {1944, 5289}, {2783, 10246}, {3052, 3741}, {3240, 4954}, {3241, 28503}, {3246, 4384}, {3286, 4234}, {3304, 11115}, {3416, 29594}, {3632, 16477}, {3655, 37474}, {3685, 4664}, {3696, 7290}, {3749, 44417}, {3763, 4660}, {3813, 37176}, {3913, 13740}, {3920, 4387}, {3938, 31161}, {4011, 42056}, {4042, 17127}, {4085, 47355}, {4195, 12513}, {4217, 34606}, {4307, 4966}, {4309, 13728}, {4383, 32945}, {4418, 17597}, {4442, 29831}, {4676, 5220}, {4677, 16468}, {4689, 29826}, {4740, 32922}, {4852, 16491}, {4859, 15668}, {4863, 5294}, {5010, 16402}, {5051, 9670}, {5204, 16397}, {5259, 19871}, {5737, 8616}, {5750, 30331}, {5793, 37588}, {5853, 38047}, {6057, 20020}, {8053, 16370}, {8692, 17277}, {9710, 13742}, {10436, 42819}, {11114, 34653}, {11358, 18613}, {14621, 17310}, {15485, 17259}, {15569, 29597}, {15571, 21010}, {16371, 20470}, {16395, 16678}, {16396, 23853}, {16399, 17798}, {16404, 37577}, {16475, 28581}, {16494, 40587}, {16496, 17351}, {16506, 36872}, {17269, 32847}, {17274, 28534}, {17290, 24715}, {17293, 33076}, {17294, 28538}, {17342, 20179}, {17369, 36479}, {17542, 19870}, {17599, 32929}, {17677, 34706}, {19326, 20872}, {20155, 29574}, {21000, 32916}, {21242, 31187}, {21358, 28562}, {24441, 36554}, {24695, 28333}, {25377, 31202}, {25590, 35227}, {26223, 41711}, {29584, 31317}, {29686, 33094}, {30811, 33104}, {30942, 37540}, {34718, 37510}, {36224, 40882}

X(48805) = midpoint of X(3886) and X(16834)
X(48805) = reflection of X(i) in X(j) for these {i,j}: {3416, 29594}, {3679, 17359}, {16834, 1386}, {17301, 551}
X(48805) = crossdifference of every pair of points on line {665, 9002}
X(48805) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4693, 17318}, {4432, 36480, 45}, {24715, 29660, 17290}


X(48806) = X(8)X(30)∩X(519)X(1992)

Barycentrics    a^4 - 2*a^2*b^2 + b^4 + 6*a^2*b*c + 6*b^3*c - 2*a^2*c^2 + 10*b^2*c^2 + 6*b*c^3 + c^4 : :

X(48806) lies on these lines: {1, 42032}, {2, 3701}, {8, 30}, {75, 32836}, {345, 4692}, {519, 1992}, {1056, 3790}, {1089, 10072}, {1930, 17079}, {1997, 4125}, {2345, 7739}, {3241, 11354}, {3524, 7081}, {3543, 5015}, {3545, 3705}, {3582, 28808}, {3673, 32869}, {3679, 42020}, {3703, 11237}, {3729, 28194}, {3734, 4371}, {3757, 17561}, {5564, 32815}, {5815, 36731}, {7172, 10304}, {7229, 22253}, {7283, 10385}, {14033, 29617}, {24280, 28198}, {29615, 32986}, {30179, 33251}, {32833, 33941}, {34625, 42034}

X(48806) = reflection of X(3241) in X(11354)


X(48807) = X(30)X(40)∩X(69)X(519)

Barycentrics    5*a^4 - a^3*b - 3*a^2*b^2 - a*b^3 - 4*b^4 - a^3*c - 4*a^2*b*c - a*b^2*c - 4*b^3*c - 3*a^2*c^2 - a*b*c^2 - a*c^3 - 4*b*c^3 - 4*c^4 : :
X(48807) = 2 X[11354] - 3 X[19875]

X(48807) lies on these lines: {1, 11359}, {2, 4339}, {30, 40}, {69, 519}, {540, 3751}, {988, 5015}, {2549, 4034}, {2959, 3849}, {3550, 11354}, {3586, 33079}, {4680, 17594}, {4888, 14929}, {11287, 16833}

X(48807) = reflection of X(1) in X(11359)


X(48808) = X(2)X(36)∩X(519)X(599)

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

X(48808) lies on these lines: {1, 31134}, {2, 36}, {10, 17595}, {38, 3679}, {519, 599}, {551, 4138}, {752, 16796}, {758, 17274}, {1054, 10713}, {1626, 16418}, {3828, 4438}, {4201, 8715}, {4217, 19836}, {5248, 37038}, {8666, 16062}, {28164, 36721}, {30116, 31151}


X(48809) = X(1)X(2)∩X(355)X(13632)

Barycentrics    a^3 + a^2*b + 4*a*b^2 + b^3 + a^2*c + 6*a*b*c + 4*b^2*c + 4*a*c^2 + 4*b*c^2 + c^3 : :
X(48809) = 2 X[10] + X[36480], 7 X[9780] - X[36479], X[4363] + 2 X[4407]

X(48809) lies on these lines: {1, 2}, {355, 13632}, {535, 47039}, {599, 3775}, {740, 41312}, {752, 17251}, {758, 3789}, {1213, 32941}, {1992, 33682}, {3696, 41311}, {3826, 20582}, {3836, 21358}, {3842, 41313}, {3886, 25354}, {3913, 16846}, {4085, 17327}, {4301, 36672}, {4363, 4407}, {4643, 28558}, {4657, 4732}, {4660, 5224}, {4709, 17321}, {4733, 32921}, {4974, 38023}, {5263, 31144}, {7991, 36693}, {8616, 26044}, {8715, 16850}, {11237, 16603}, {13633, 26446}, {17237, 24693}, {17250, 24715}, {17303, 47359}, {24325, 47358}, {24441, 28542}, {27081, 33104}, {27812, 33143}, {31143, 32946}

X(48809) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3679, 29617}, {10, 19868, 16825}


X(48810) = X(1)X(3943)∩X(2)X(11)

Barycentrics    4*a^3 + 3*a*b^2 + b^3 + 3*b^2*c + 3*a*c^2 + 3*b*c^2 + c^3 : :
X(48810) = 2 X[3589] + X[32941], 5 X[3616] + X[5695], X[4660] - 4 X[34573], 5 X[16491] + X[17299], X[16834] - 3 X[38023], X[17301] - 3 X[25055]

X(48810) lies on these lines: {1, 3943}, {2, 11}, {10, 3246}, {141, 752}, {238, 17330}, {516, 21167}, {519, 597}, {529, 11354}, {536, 551}, {545, 3923}, {966, 8692}, {984, 4370}, {1086, 29660}, {1125, 17067}, {1213, 15485}, {2783, 38028}, {3011, 27747}, {3589, 32941}, {3616, 5695}, {3679, 7290}, {3685, 17320}, {3696, 41140}, {3782, 29686}, {3813, 17698}, {3932, 17342}, {4353, 28301}, {4364, 4432}, {4407, 4759}, {4422, 36480}, {4472, 24331}, {4660, 34573}, {4676, 17333}, {4693, 17395}, {4702, 17023}, {4854, 29648}, {4966, 17378}, {5192, 9711}, {5749, 42871}, {5750, 42819}, {6057, 29815}, {11112, 34657}, {12607, 13740}, {15254, 19868}, {16484, 17398}, {16491, 17299}, {16834, 38023}, {17070, 29855}, {17274, 17768}, {17301, 24342}, {17354, 36534}, {17726, 33156}, {19861, 38336}, {24693, 40480}, {24943, 31134}, {25466, 37150}, {28309, 32921}, {28538, 29594}, {28581, 38049}, {29032, 38034}, {29637, 31151}, {29652, 44416}, {36722, 42356}

X(48810) = midpoint of X(1) and X(17281)
X(48810) = reflection of X(17382) in X(1125)


X(48811) = X(2)X(35)∩X(6)X(519)

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

X(48811) lies on these lines: {1, 42044}, {2, 35}, {6, 519}, {551, 16394}, {595, 3679}, {993, 24552}, {1001, 19277}, {1125, 19276}, {1717, 19861}, {4195, 8666}, {4234, 4278}, {4653, 5333}, {5263, 33309}, {8616, 19875}, {8715, 13740}, {11113, 34666}, {16418, 23361}, {16861, 19871}, {19290, 19883}, {24387, 37176}, {28198, 41455}, {30142, 35652}


X(48812) = X(1)X(3175)∩X(30)X(40)

Barycentrics    3*a^4 + a^3*b - a^2*b^2 + a*b^3 + a^3*c + 4*a^2*b*c + a*b^2*c + 4*b^3*c - a^2*c^2 + a*b*c^2 + 8*b^2*c^2 + a*c^3 + 4*b*c^3 : :
X(48812) = 2 X[11359] - 3 X[19875]

X(48812) lies on these lines: {1, 3175}, {2, 988}, {30, 40}, {519, 1992}, {529, 5227}, {3247, 24275}, {3586, 33169}, {3701, 19336}, {3729, 25898}, {3749, 4692}, {3828, 8720}, {4034, 7737}, {4234, 4385}, {4967, 32815}, {4968, 11346}, {5268, 19290}, {5271, 11352}, {5587, 33167}, {5774, 16570}, {11286, 16833}, {11359, 17596}

X(48812) = reflection of X(1) in X(11354)


X(48813) = X(2)X(3)∩X(69)X(519)

Barycentrics    3*a^4 - 2*a^3*b - 4*a^2*b^2 - 2*a*b^3 - 3*b^4 - 2*a^3*c - 2*a^2*b*c - 2*a*b^2*c - 2*b^3*c - 4*a^2*c^2 - 2*a*b*c^2 + 2*b^2*c^2 - 2*a*c^3 - 2*b*c^3 - 3*c^4 : :
X(48813) = X[11354] - 3 X[11359]

X(48813) lies on these lines: {2, 3}, {8, 32950}, {69, 519}, {315, 16712}, {387, 41629}, {391, 15048}, {529, 5800}, {540, 1992}, {966, 2549}, {1213, 44526}, {3488, 3662}, {3616, 48646}, {3679, 42020}, {4045, 37650}, {4259, 44663}, {4293, 32773}, {4304, 25527}, {4340, 42028}, {4419, 16086}, {4648, 7761}, {5082, 5484}, {5224, 32815}, {7739, 37654}, {10483, 19784}, {14548, 17179}, {16711, 45962}, {17271, 32836}, {18391, 33068}, {19722, 19766}, {24275, 43619}, {24929, 26132}, {25055, 33106}, {26244, 43448}

X(48813) = reflection of X(2) in X(11359)
X(48813) = anticomplement of X(11354)
X(48813) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20, 4234}, {2, 4190, 19336}, {2, 4234, 37176}, {2, 6872, 11346}, {2, 11346, 13742}, {2, 13736, 11357}, {3, 16052, 2}, {20, 16062, 37176}, {377, 13725, 37153}, {377, 17676, 13725}, {442, 16351, 2}, {4197, 17553, 2}, {4202, 6872, 13742}, {4202, 11346, 2}, {4205, 19332, 2}, {4234, 16062, 2}, {5051, 19336, 2}, {8728, 11357, 2}, {11112, 11113, 10691}, {13745, 44217, 2}, {17678, 37038, 2}


X(48814) = X(1)X(4703)∩X(2)X(3)

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

X(48814) lies on these lines: {1, 4703}, {2, 3}, {8, 33761}, {45, 16086}, {519, 751}, {540, 17196}, {986, 12579}, {3060, 3877}, {3488, 17257}, {3679, 42033}, {4389, 30117}, {4417, 4653}, {5251, 32773}, {5722, 38000}, {6284, 19853}, {6646, 15934}, {10483, 25512}, {10572, 31359}, {18541, 26806}, {25055, 26128}

X(48814) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11111, 4234}, {2, 15677, 16393}, {2, 31156, 13735}, {2, 37299, 19336}, {4, 13736, 11110}, {382, 16844, 26051}, {405, 26117, 16062}, {452, 13725, 13740}, {5047, 17676, 33833}, {6872, 37314, 1010}, {11113, 13745, 2}, {11357, 17528, 2}, {11359, 16857, 2}, {16351, 17556, 2}, {17553, 17577, 2}


X(48815) = X(2)X(3)∩X(10)X(4884)

Barycentrics    4*a^3*b + 5*a^2*b^2 + 4*a*b^3 + 3*b^4 + 4*a^3*c + 4*a^2*b*c + 4*a*b^2*c + 4*b^3*c + 5*a^2*c^2 + 4*a*b*c^2 + 2*b^2*c^2 + 4*a*c^3 + 4*b*c^3 + 3*c^4 : :
X(48815) = X[11354] + 3 X[11359]

X(48815) lies on these lines: {2, 3}, {10, 4884}, {86, 14929}, {141, 519}, {540, 597}, {1213, 15048}, {2885, 3828}, {3782, 19867}, {3933, 16712}, {5719, 25527}, {5749, 18541}, {6284, 19881}, {6707, 7761}, {10593, 19864}, {15171, 19836}, {15935, 17291}, {16086, 17305}, {17398, 18907}, {18139, 38314}, {18990, 19784}, {19875, 37716}, {33174, 37715}

X(48815) = midpoint of X(2) and X(11359)
X(48815) = complement of X(11354)
X(48815) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 443, 19332}, {2, 4201, 4234}, {2, 4234, 17698}, {2, 13725, 11357}, {2, 16052, 5}, {2, 16062, 16052}, {2, 16351, 6675}, {2, 17676, 11346}, {2, 17678, 37150}, {4201, 17698, 550}, {4202, 13728, 8728}


X(48816) = X(2)X(3)∩X(75)X(519)

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

X(48816) lies on these lines: {1, 19796}, {2, 3}, {10, 4650}, {75, 519}, {540, 17346}, {551, 23537}, {1770, 31359}, {3241, 19819}, {3679, 7270}, {4252, 25446}, {4363, 16086}, {4421, 19845}, {6646, 18541}, {7354, 19853}, {10483, 16828}, {11194, 19844}, {15934, 26806}, {19785, 38314}, {19786, 25055}, {19808, 19875}, {19812, 19883}

X(48816) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 377, 17678}, {2, 17579, 37038}, {2, 17678, 16062}, {20, 37153, 11110}, {377, 1010, 16062}, {1010, 17678, 2}, {7270, 19797, 3679}, {11359, 19277, 2}, {14005, 17676, 37039}, {16394, 44217, 2}, {17528, 19276, 2}, {17532, 19290, 2}, {37090, 37241, 17512}


X(48817) = X(2)X(3)∩X(69)X(540)

Barycentrics    5*a^4 + 2*a^3*b + 2*a*b^3 - b^4 + 2*a^3*c + 2*a^2*b*c + 2*a*b^2*c + 2*b^3*c + 2*a*b*c^2 + 6*b^2*c^2 + 2*a*c^3 + 2*b*c^3 - c^4 : :
X(48817) = 3 X[11354] - X[11359]

X(48817) lies on these lines: {2, 3}, {69, 540}, {86, 32815}, {391, 18907}, {519, 1992}, {894, 3488}, {966, 7737}, {1220, 4294}, {3241, 42044}, {3419, 26065}, {3734, 4648}, {3849, 20558}, {3944, 25055}, {4293, 32942}, {4339, 4385}, {4352, 32822}, {5712, 24271}, {5716, 7283}, {7804, 37650}, {10483, 19836}, {15933, 35578}, {17378, 32836}, {17398, 44526}, {30117, 42697}, {30761, 32827}

X(48817) = reflection of X(2) in X(11354)
X(48817) = anticomplement of X(11359)
X(48817) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3543, 17677}, {2, 35927, 21937}, {4, 4195, 37176}, {377, 11319, 13742}, {964, 6872, 13725}, {7737, 24275, 966}, {11113, 16394, 2}, {11114, 17579, 34603}, {11286, 11354, 33309}, {16418, 37150, 2}


X(48818) = X(1)X(30)∩X(2)X(988)

Barycentrics    a^4 - 3*a^3*b - 5*a^2*b^2 - 3*a*b^3 - 2*b^4 - 3*a^3*c - 3*a*b^2*c - 5*a^2*c^2 - 3*a*b*c^2 + 4*b^2*c^2 - 3*a*c^3 - 2*c^4 : :
X(48818) = 2 X[11354] - 3 X[25055]

X(48818) lies on these lines: {1, 30}, {2, 988}, {9, 7739}, {69, 519}, {376, 37552}, {381, 37592}, {529, 17301}, {986, 3679}, {2549, 3247}, {3534, 5266}, {3545, 24239}, {3576, 33152}, {3586, 17598}, {3666, 11237}, {3723, 44526}, {3731, 15048}, {3872, 33145}, {3944, 38021}, {3976, 36721}, {4310, 15933}, {4339, 15683}, {4357, 32836}, {5054, 37599}, {5290, 36731}, {5298, 17720}, {5587, 17591}, {7865, 17296}, {9623, 33149}, {10056, 17594}, {11287, 29573}, {11354, 19701}, {15672, 29681}, {15688, 37589}, {17593, 31434}, {17725, 30282}, {18193, 37715}, {19875, 37716}, {24248, 28194}, {29574, 32986}

X(48818) = reflection of X(3679) in X(11359)


X(48819) = X(1)X(30)∩X(2)X(3701)

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

X(48819) lies on these lines: {1, 30}, {2, 3701}, {37, 7739}, {376, 5266}, {381, 13161}, {519, 599}, {529, 998}, {538, 41312}, {549, 988}, {551, 3445}, {553, 5711}, {986, 3654}, {2549, 3723}, {3247, 15048}, {3295, 28037}, {3524, 37599}, {3582, 17720}, {3653, 37617}, {3663, 28194}, {3666, 10056}, {3677, 37715}, {4339, 11001}, {4851, 7865}, {5055, 24239}, {5298, 17602}, {5722, 17598}, {5725, 11237}, {5886, 33152}, {5988, 48657}, {8703, 37552}, {10304, 37589}, {10371, 43993}, {11287, 29574}, {15671, 29681}, {16466, 17781}, {17321, 32836}, {17591, 26446}, {21620, 36731}, {23536, 44217}, {24248, 28198}, {24929, 28108}

X(48819) = reflection of X(11354) in X(551)
X(48819) = {X(3058),X(5434)}-harmonic conjugate of X(34634)


X(48820) = X(1)X(30)∩X(141)X(519)

Barycentrics    4*a^4 + 6*a^3*b + 7*a^2*b^2 + 6*a*b^3 + b^4 + 6*a^3*c + 6*a*b^2*c + 7*a^2*c^2 + 6*a*b*c^2 - 2*b^2*c^2 + 6*a*c^3 + c^4 : :
X(48820) = X[11354] - 3 X[38314]

X(48820) lies on these lines: {1, 30}, {141, 519}, {549, 37592}, {551, 35652}, {961, 7373}, {988, 12100}, {3241, 11359}, {3582, 17602}, {3663, 28198}, {3723, 15048}, {3845, 13161}, {4339, 15681}, {4353, 28194}, {5266, 8703}, {7739, 16777}, {7865, 17390}, {10056, 17599}, {11354, 19684}, {15699, 24239}, {17504, 37599}, {25055, 25430}, {33152, 38034}, {34200, 37552}, {37589, 45759}

X(48820) = midpoint of X(3241) and X(11359)


X(48821) = X(2)X(11)∩X(141)X(519)

Barycentrics    4*a^2*b + a*b^2 + 3*b^3 + 4*a^2*c + b^2*c + a*c^2 + b*c^2 + 3*c^3 : :
X(48821) = X[141] + 2 X[4085], X[17281] - 3 X[19875], 2 X[3589] + X[4660], X[3755] + 2 X[3844], X[4780] + 2 X[17229], X[5695] - 7 X[9780], X[32941] - 4 X[34573]

X(48821) lies on these lines: {2, 11}, {8, 17305}, {10, 536}, {30, 24309}, {141, 519}, {529, 11359}, {537, 3821}, {551, 3836}, {597, 752}, {1086, 29659}, {1213, 3731}, {1738, 4688}, {2783, 38042}, {3241, 4966}, {3246, 31191}, {3416, 16834}, {3589, 4660}, {3679, 7174}, {3755, 3844}, {3775, 4669}, {3782, 31161}, {3823, 4755}, {3828, 17359}, {3932, 4664}, {4030, 32774}, {4425, 42056}, {4472, 24693}, {4645, 46922}, {4655, 28333}, {4689, 30768}, {4702, 29596}, {4709, 48636}, {4780, 17229}, {4854, 29679}, {4954, 33175}, {5051, 9711}, {5224, 32087}, {5695, 9780}, {9710, 13728}, {12607, 16062}, {15569, 29600}, {16394, 19784}, {16594, 25378}, {17070, 29828}, {17224, 17251}, {17234, 38314}, {17245, 25055}, {17246, 33165}, {17274, 47359}, {17290, 36479}, {17366, 33076}, {17369, 24715}, {17392, 31151}, {17395, 32847}, {17768, 38047}, {24331, 40480}, {25351, 34824}, {25453, 44419}, {28562, 48310}, {28566, 38049}, {28582, 38191}, {29685, 40688}, {31136, 32781}, {31137, 33174}, {32941, 34573}

X(48821) = midpoint of X(i) and X(j) for these {i,j}: {3416, 16834}, {3679, 17301}, {3755, 29594}, {17274, 47359}
X(48821) = reflection of X(i) in X(j) for these {i,j}: {17359, 3828}, {29594, 3844}
X(48821) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4026, 4429, 3826}, {24715, 36478, 17369}


X(48822) = X(1)X(2)∩X(86)X(4660)

Barycentrics    a^3 + 5*a^2*b + 2*a*b^2 + b^3 + 5*a^2*c + 6*a*b*c + 2*b^2*c + 2*a*c^2 + 2*b*c^2 + c^3 : :
X(48822) = 4 X[1125] - X[36480], 5 X[3616] + X[36479]

X(48822) lies on these lines: {1, 2}, {86, 4660}, {148, 41193}, {517, 28600}, {535, 40718}, {537, 41312}, {3416, 5625}, {3653, 13633}, {3656, 13632}, {3748, 41850}, {3751, 25354}, {3821, 6173}, {4026, 17392}, {4085, 15668}, {4363, 28542}, {4425, 31164}, {4439, 16672}, {4649, 17346}, {4670, 28534}, {4795, 28558}, {4865, 37869}, {8666, 16850}, {11355, 43531}, {12513, 16846}, {15569, 17359}, {16370, 17798}, {16484, 17381}, {17297, 32784}, {17301, 24325}, {17320, 31178}, {17394, 33076}, {17398, 32941}, {18613, 19263}, {19701, 31140}, {19740, 33104}, {24715, 41847}, {25507, 32865}, {27811, 33161}, {28599, 30562}

X(48822) = {X(1),X(3679)}-harmonic conjugate of X(17389)


X(48823) = X(1)X(30)∩X(495)X(4038)

Barycentrics    2*a^4 + 6*a^3*b + 5*a^2*b^2 - b^4 + 6*a^3*c + 18*a^2*b*c + 6*a*b^2*c + 5*a^2*c^2 + 6*a*b*c^2 + 2*b^2*c^2 - c^4 : :

X(48823) lies on these lines: {1, 30}, {495, 4038}, {519, 3696}, {549, 37607}, {551, 1104}, {553, 3931}, {940, 10056}, {999, 21321}, {1468, 15670}, {3017, 25466}, {3241, 19819}, {3582, 5718}, {3664, 28194}, {4340, 10385}, {4349, 28854}, {4995, 37522}, {5717, 36722}, {6051, 17781}, {7373, 28386}, {8703, 37573}, {9345, 17757}, {11237, 37715}, {12100, 37608}, {21620, 36728}, {34200, 37574}, {37150, 42057}


X(48824) = X(1)X(30)∩X(6)X(519)

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

X(48824) lies on these lines: {1, 30}, {2, 5015}, {6, 519}, {376, 4339}, {540, 47358}, {549, 37552}, {551, 11359}, {582, 3654}, {754, 41312}, {988, 8703}, {1100, 7739}, {3241, 42044}, {3247, 18907}, {3419, 17469}, {3524, 37589}, {3582, 17721}, {3723, 7737}, {3744, 5725}, {3830, 13161}, {3931, 10385}, {4344, 15933}, {4657, 7865}, {5054, 24239}, {5717, 36721}, {5722, 17716}, {10072, 37539}, {10304, 37599}, {11286, 29574}, {15671, 29664}, {16498, 33109}, {24248, 28202}

X(48824) = reflection of X(11359) in X(551)
X(48824) = crossdifference of every pair of points on line {9002, 9404}


X(48825) = X(1)X(30)∩X(75)X(519)

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

X(48825) lies on these lines: {1, 30}, {2, 1468}, {75, 519}, {171, 10056}, {376, 37573}, {495, 37604}, {529, 17392}, {549, 37608}, {553, 986}, {940, 11237}, {1478, 4038}, {3578, 31339}, {3582, 17717}, {3584, 37522}, {3679, 10371}, {3976, 5717}, {4298, 44733}, {4307, 28854}, {4340, 5255}, {4995, 37603}, {5045, 36490}, {5080, 9345}, {5290, 36728}, {5298, 5718}, {5712, 37617}, {8703, 37574}, {11112, 42042}, {15671, 29661}, {16474, 32865}, {28458, 37529}, {36730, 37594}, {38314, 41825}


X(48826) = X(2)X(36)∩X(6)X(519)

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

X(48826) lies on these lines: {1, 3994}, {2, 36}, {6, 519}, {10, 16394}, {30, 24309}, {31, 3679}, {106, 4945}, {551, 25496}, {1168, 36815}, {1220, 5248}, {3734, 17382}, {3828, 19276}, {4195, 8715}, {4234, 4276}, {5206, 25629}, {5235, 19875}, {5260, 19871}, {8666, 13740}, {11112, 34653}, {16393, 25440}, {16397, 26030}, {17508, 28160}, {30117, 31178}


X(48827) = X(1)X(30)∩X(2)X(4339)

Barycentrics    7*a^4 + 3*a^3*b + a^2*b^2 + 3*a*b^3 - 2*b^4 + 3*a^3*c + 3*a*b^2*c + a^2*c^2 + 3*a*b*c^2 + 4*b^2*c^2 + 3*a*c^3 - 2*c^4 : :
X(48827) = 2 X[11359] - 3 X[25055]

X(48827) lies on these lines: {1, 30}, {2, 4339}, {376, 988}, {381, 5266}, {519, 1992}, {989, 4217}, {1449, 7739}, {1724, 3679}, {3247, 7737}, {3524, 24239}, {3534, 37592}, {3543, 13161}, {3586, 17716}, {3731, 18907}, {3744, 11237}, {3749, 10056}, {3879, 32836}, {4034, 24275}, {4307, 15933}, {5054, 37589}, {5298, 17721}, {5429, 24392}, {5716, 10385}, {7865, 17306}, {11238, 37539}, {11286, 29573}, {11355, 42042}, {11359, 25055}, {14033, 29574}, {15672, 29664}, {15688, 37599}, {16485, 33109}, {16498, 23681}, {17722, 30282}, {19875, 37717}, {33106, 38021}

X(48827) = reflection of X(3679) in X(11354)


X(48828) = X(1)X(30)∩X(2)X(1453)

Barycentrics    7*a^4 + 9*a^3*b + 7*a^2*b^2 + 3*a*b^3 - 2*b^4 + 9*a^3*c + 18*a^2*b*c + 9*a*b^2*c + 7*a^2*c^2 + 9*a*b*c^2 + 4*b^2*c^2 + 3*a*c^3 - 2*c^4 : :

X(48828) lies on these lines: {1, 30}, {2, 1453}, {381, 37594}, {519, 4349}, {553, 4340}, {3545, 39595}, {3586, 37595}, {3679, 5711}, {3745, 11237}, {3945, 15933}, {4307, 28194}, {4658, 12625}, {5269, 10056}, {5298, 17723}, {5725, 19875}, {11354, 29573}, {26098, 38021}

X(48828) = reflection of X(3679) in X(19277)


X(48829) = X(1)X(3834)∩X(2)X(11)

Barycentrics    a^3 - 3*a^2*b - 2*b^3 - 3*a^2*c - 2*c^3 : :
X(48829) = X[6] - 4 X[4085], X[6] + 2 X[4660], 2 X[4085] + X[4660], 4 X[10] - X[5695], X[3242] - 4 X[3821], X[3416] + 2 X[3755], 5 X[3763] - 2 X[32941], 4 X[3844] - X[3886], 2 X[4780] + X[17299], X[16496] - 4 X[17235], 2 X[17359] - 3 X[19875]

X(48829) lies on these lines: {1, 3834}, {2, 11}, {6, 752}, {8, 4389}, {10, 45}, {42, 31134}, {405, 23855}, {516, 36721}, {518, 17274}, {519, 599}, {527, 47359}, {529, 5800}, {535, 38530}, {536, 984}, {545, 24248}, {903, 24349}, {940, 32948}, {958, 37038}, {1058, 25914}, {1086, 36479}, {2177, 30811}, {2783, 5790}, {2796, 38087}, {3052, 25453}, {3241, 17297}, {3303, 4202}, {3662, 42871}, {3685, 17342}, {3711, 26580}, {3751, 4715}, {3753, 44670}, {3763, 32941}, {3786, 17196}, {3844, 3886}, {3883, 41140}, {3913, 16062}, {4030, 19785}, {4042, 33083}, {4201, 12513}, {4217, 6284}, {4234, 34626}, {4361, 33076}, {4363, 24715}, {4383, 32947}, {4387, 29679}, {4450, 42058}, {4484, 24464}, {4645, 17378}, {4689, 29857}, {4693, 17269}, {4702, 17284}, {4733, 9791}, {4780, 17299}, {4854, 10327}, {4860, 29835}, {5014, 17599}, {5192, 9670}, {5220, 17333}, {5737, 32865}, {6679, 21000}, {7672, 36589}, {8692, 17352}, {9458, 25378}, {9710, 13725}, {10896, 26030}, {11112, 34634}, {11236, 17677}, {12953, 17537}, {16052, 45701}, {16475, 28566}, {16484, 17265}, {16496, 17235}, {16834, 28538}, {17184, 41711}, {17262, 33165}, {17282, 42819}, {17305, 36534}, {17318, 32847}, {17320, 32850}, {17325, 36480}, {17359, 19875}, {17595, 33120}, {17597, 33125}, {17601, 29861}, {17766, 38315}, {17782, 29865}, {18185, 33730}, {20182, 33072}, {24325, 31139}, {24331, 25351}, {24342, 24452}, {25760, 27739}, {27747, 29828}, {28526, 38191}, {28562, 47352}, {29057, 38144}, {29631, 37540}, {33136, 37660}, {33137, 44419}

X(48829) = reflection of X(i) in X(j) for these {i,j}: {1, 17382}, {5695, 17281}, {17281, 10}
X(48829) = crossdifference of every pair of points on line {665, 9011}
X(48829) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 31151, 17313}, {4085, 4660, 6}, {24715, 29659, 4363}


X(48830) = X(1)X(2)∩X(37)X(47359)

Barycentrics    a^3 + 7*a^2*b + a*b^2 + b^3 + 7*a^2*c + 6*a*b*c + b^2*c + a*c^2 + b*c^2 + c^3 : :
X(48830) = 2 X[1] + X[36479], 5 X[3616] - 2 X[36480]

X(48830) lies on these lines: {1, 2}, {37, 47359}, {390, 33682}, {517, 10186}, {518, 41312}, {597, 1001}, {599, 4026}, {758, 1002}, {1009, 3303}, {1279, 38023}, {1482, 13632}, {1992, 4649}, {2267, 16503}, {2796, 35578}, {3058, 11355}, {3618, 16484}, {3880, 28600}, {3932, 38087}, {3945, 4660}, {4085, 4648}, {4184, 37546}, {4307, 28562}, {4356, 17132}, {4644, 28558}, {4780, 25590}, {4795, 28534}, {4863, 37869}, {4948, 48290}, {4966, 21358}, {5485, 40718}, {5772, 6541}, {5881, 36672}, {6329, 8692}, {6767, 8299}, {8193, 19346}, {10246, 13633}, {11160, 33082}, {12513, 16850}, {13464, 36670}, {15569, 41313}, {16370, 37580}, {16785, 37657}, {17045, 42871}, {17549, 37576}, {17740, 21806}, {17754, 31393}, {19740, 21283}, {20423, 31394}, {21356, 32784}, {24203, 37632}, {38047, 41310}, {38049, 38316}, {41311, 47358}

X(48830) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3679, 29574}, {1, 29659, 17316}, {1, 32847, 29585}


X(48831) = X(1)X(2)∩X(345)X(4868)

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

X(48831) lies on these lines: {1, 2}, {345, 4868}, {517, 14561}, {528, 11354}, {529, 11359}, {1478, 4972}, {1766, 28194}, {2049, 9710}, {3718, 17320}, {3746, 17526}, {3753, 11213}, {3913, 17698}, {4026, 9708}, {4309, 11319}, {4424, 33163}, {4692, 19785}, {4714, 19822}, {4737, 19786}, {5119, 5294}, {5955, 21896}, {7373, 25914}, {8715, 37176}, {11236, 16052}, {16370, 37577}, {16394, 34612}, {18421, 28739}, {18613, 19267}, {19270, 31458}, {23888, 26078}, {37325, 37546}


X(48832) = X(2)X(12)∩X(6)X(519)

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

X(48832) lies on these lines: {1, 3967}, {2, 12}, {6, 519}, {10, 4252}, {405, 18613}, {515, 5085}, {535, 11359}, {993, 19279}, {1001, 33309}, {2099, 26223}, {3058, 4217}, {3241, 42032}, {3303, 11319}, {3304, 5192}, {3679, 5247}, {3913, 4195}, {4202, 9657}, {4234, 4267}, {4387, 17015}, {4428, 13735}, {4972, 12943}, {5204, 26030}, {5252, 5294}, {5289, 27064}, {5724, 33163}, {5737, 19290}, {8055, 38314}, {9708, 19277}, {10404, 25904}, {12513, 13740}, {12607, 37176}, {15888, 17526}, {16371, 23361}, {17016, 42044}, {17054, 42053}, {17579, 34666}, {17677, 34739}


X(48833) = X(1)X(4217)∩X(2)X(36)

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

X(48833) lies on these lines: {1, 4217}, {2, 36}, {8, 42058}, {519, 1992}, {529, 11354}, {551, 33144}, {958, 37150}, {1220, 37038}, {1479, 17537}, {1707, 3679}, {3241, 17165}, {4234, 45701}, {4317, 5192}, {5270, 17526}, {6174, 16401}, {9711, 19274}, {11114, 34657}, {11717, 17777}, {16052, 34739}, {16394, 34606}, {17539, 31452}, {28160, 38047}

leftri

Points in a [Euler line, Nagel line] coordinate system: X(48834)-X(48870)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1,L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1 = Euler line: (b^2 - c^2)(a^2 - b^2 - c^2) α + (c^2 - a^2)(b^2 - c^2 - a^2) β + (a^2 - b^2)(c^2 - a^2 - b^2) γ = 0.
L2= Nagel line: (b-c) α + (c-a) β + (a-b) γ = 0.

The origin is given by (0,0) = X(2) = 1 : 1 : 1.

Barycentrics u : v : w for a point U = (x,y) in this system are given by

u : v : w = (a - b) (a - c) (b - c) (a + b + c)^2 + (2 a^4 - a^2 b^2 - b^4 - a^2 c^2 + 2 b^2 c^2 - c^4) x + (2 a - b - c) y,

where, as functions of a,b,c, the coordinate x is antisymmetric and homogeneous of degree 1, and y is antisymmetric and homogeneous of degree 2. For a [Nagel line, Euler line] coordinate system, see trhe preamble just before X(48798).

The appearance of {x,y},k in the following list means that (x,y) = X(k).

{-((2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2)), -2 (a-b) (a-c) (b-c) (a+b+c)}, 48798
{-((2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2)), -((a-b) (a-c) (b-c) (a+b+c))}, 48807
{-((2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2)), 0}, 48813
{-((2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2)), (a-b) (a-c) (b-c) (a+b+c)}, 48818
{-(((a-b) (a-c) (b-c))/(a^2+b^2+c^2)), -2 (a-b) (a-c) (b-c) (a+b+c)}, 48800
{-(((a-b) (a-c) (b-c))/(a^2+b^2+c^2)), -((2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2))}, 599
{-(((a-b) (a-c) (b-c))/(a b+a c+b c)), -((2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a b+a c+b c))}, 17346
{-(((a-b) (a-c) (b-c))/(a^2+b^2+c^2)), 0}, 11359
{-(((a-b) (a-c) (b-c))/(a b+a c+b c)), 0}, 48814
{-(((a-b) (a-c) (b-c))/(a^2+b^2+c^2)), (a-b) (a-c) (b-c) (a+b+c)}, 48819
{-(((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2))), -(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2))}, 141
{-(((a-b) (a-c) (b-c))/(2 (a b+a c+b c))), -(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a b+a c+b c))}, 17330
{-(((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2))), 0}, 48815
{-(((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2))), (a-b) (a-c) (b-c) (a+b+c)}, 48820
{0, -2 (a-b) (a-c) (b-c) (a+b+c)}, 8
{0, -((2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c))}, 48802
{0, -((a-b) (a-c) (b-c) (a+b+c))}, 3679
{0, -(((a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c))}, 48809
{0, -(1/2) (a-b) (a-c) (b-c) (a+b+c)}, 10
{0, 0}, 2
{0, 1/2 (a-b) (a-c) (b-c) (a+b+c)}, 551
{0, (a-b) (a-c) (b-c) (a+b+c)}, 1
{0, ((a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c)}, 48822
{0, 2 (a-b) (a-c) (b-c) (a+b+c)}, 3241
{0, (2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c)}, 48830
{((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2)), ((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)}, 597
{((a-b) (a-c) (b-c))/(2 (a b+a c+b c)), (a-b) (a-c) (b-c) (a+b+c)}, 48823
{((a-b) (a-c) (b-c))/(2 (a b+a c+b c)), ((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a b+a c+b c)}, 17392
{((a-b) (a-c) (b-c))/(a^2+b^2+c^2), -2 (a-b) (a-c) (b-c) (a+b+c)}, 48804
{((a-b) (a-c) (b-c))/(a^2+b^2+c^2), 0}, 11354
{((a-b) (a-c) (b-c))/(a b+a c+b c), 0}, 48816
{((a-b) (a-c) (b-c))/(a+b+c)^2, 0}, 19277
{((a-b) (a-c) (b-c))/(a^2+b^2+c^2), (a-b) (a-c) (b-c) (a+b+c)}, 48824
{((a-b) (a-c) (b-c))/(a b+a c+b c), (a-b) (a-c) (b-c) (a+b+c)}, 48825
{((a-b) (a-c) (b-c))/(a^2+b^2+c^2), (2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)}, 6
{((a-b) (a-c) (b-c))/(a b+a c+b c), (2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a b+a c+b c)}, 17378
{(2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2), -2 (a-b) (a-c) (b-c) (a+b+c)}, 48806
{(2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2), -((a-b) (a-c) (b-c) (a+b+c))}, 48812
{(2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2), 0}, 48817
{(2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2), (a-b) (a-c) (b-c) (a+b+c)}, 48827
{(2 (a-b) (a-c) (b-c))/(a+b+c)^2, (a-b) (a-c) (b-c) (a+b+c)}, 48828
{(-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), (-2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)}, 48834
{(-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), -(((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2))}, 48835
{(-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(2*(a^2 + b^2 + c^2))}, 48836
{(-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), (2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)}, 48837
{(-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), (2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c)}, 48838
{-(((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)), -(((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c))}, 48839
{-(((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)), ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c)}, 48840
{-(((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)), ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c)}, 48841
{-(((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)), (2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)}, 48842
{-1/2*((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(2*(a^2 + b^2 + c^2))}, 48843
{-1/2*((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(2*(a*b + a*c + b*c))}, 48844
{-1/2*((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)}, 48845
{-1/2*((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c), ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c)}, 48846
{-1/2*((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), (2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)}, 48847
{-1/2*((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c), (2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)}, 48848
{0, (-2*(a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c)}, 48849
{0, (-2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c)}, 48850
{0, -(((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c))}, 48851
{0, -(((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c))}, 48852
{0, -1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c)}, 48853
{0, ((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c)}, 48854
{0, ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c)}, 48855
{0, (2*(a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c)}, 48856
{0, (2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)}, 48857
{0, (2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c)}, 48858
{((a - b)*(a - c)*(b - c))/(2*(a^2 + b^2 + c^2)), -(((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2))}, 48859
{((a - b)*(a - c)*(b - c))/(2*(a^2 + b^2 + c^2)), -1/2*((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c)}, 48860
{((a - b)*(a - c)*(b - c))/(2*(a^2 + b^2 + c^2)), (2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)}, 48861
{((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), (-2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)}, 48862
{((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), -(((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2))}, 48863
{((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), -(((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c))}, 48864
{((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), -1/2*((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)}, 48865
{((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(2*(a^2 + b^2 + c^2))}, 48866
{((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)}, 48867
{((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c), ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c)}, 48868
{(2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), (-2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c)}, 48869
{(2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), (2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)}, 48870


X(48834) = X(2)X(58)∩X(30)X(599)

Barycentrics    3*a^4 + 2*a^3*b - 2*a^2*b^2 - 4*a*b^3 - 3*b^4 + 2*a^3*c + 2*a^2*b*c - 4*a*b^2*c - 4*b^3*c - 2*a^2*c^2 - 4*a*b*c^2 - 2*b^2*c^2 - 4*a*c^3 - 4*b*c^3 - 3*c^4 : :
X(48834) = 3 X[21356] - X[48817]

X(48834) lies on these lines: {2, 58}, {6, 48815}, {30, 599}, {69, 519}, {141, 11354}, {377, 3679}, {524, 11359}, {551, 13725}, {594, 18541}, {752, 48803}, {1211, 19290}, {1478, 33080}, {1714, 4921}, {3241, 17676}, {3578, 17679}, {3828, 37153}, {4302, 33081}, {4741, 16086}, {5292, 16052}, {7854, 36474}, {9041, 48800}, {13728, 19722}, {16062, 41629}, {17179, 45962}, {17271, 48816}, {17297, 48814}, {19266, 40726}, {21356, 48817}, {28538, 48819}, {31137, 37193}, {37169, 41141}

X(48834) = midpoint of X(69) and X(48813)
X(48834) = reflection of X(i) in X(j) for these {i,j}: {6, 48815}, {11354, 141}


X(48835) = X(1)X(6327)∩X(2)X(4257)

Barycentrics    a^4 - a^2*b^2 - a*b^3 - b^4 - a*b^2*c - b^3*c - a^2*c^2 - a*b*c^2 - a*c^3 - b*c^3 - c^4 : :
X(48835) = X[6] - 3 X[11359], X[69] + 3 X[48813], X[16496] + 3 X[48807], 2 X[3589] - 3 X[48815], 7 X[3619] - 3 X[48817], 5 X[3763] - 3 X[11354]

X(48835) lies on these lines: {1, 6327}, {2, 4257}, {3, 3454}, {6, 540}, {8, 20068}, {10, 46}, {30, 141}, {36, 25760}, {38, 4680}, {58, 16062}, {69, 519}, {315, 16887}, {333, 17678}, {386, 1330}, {464, 20106}, {495, 44419}, {529, 996}, {626, 36477}, {752, 16796}, {758, 4259}, {986, 36974}, {993, 2887}, {995, 4388}, {1125, 4138}, {1211, 11112}, {1227, 24715}, {1724, 4202}, {2475, 10479}, {2979, 18417}, {3017, 37683}, {3286, 19258}, {3583, 30942}, {3589, 48815}, {3619, 48817}, {3634, 37153}, {3662, 30117}, {3670, 5016}, {3679, 32948}, {3763, 11354}, {3771, 37175}, {3821, 38456}, {3822, 32916}, {3831, 37191}, {3840, 37193}, {3846, 19266}, {3934, 36663}, {4189, 25645}, {4252, 6693}, {4256, 4417}, {4276, 37467}, {4278, 37030}, {4302, 33171}, {4363, 18541}, {4424, 32950}, {4450, 37610}, {4645, 30116}, {4653, 18134}, {4683, 5692}, {4692, 33074}, {4703, 10176}, {4805, 24690}, {5010, 29846}, {5051, 37522}, {5080, 33086}, {5224, 48816}, {5251, 25957}, {5278, 17679}, {5313, 32843}, {5737, 17528}, {5793, 9655}, {5799, 31774}, {5902, 33067}, {6646, 16086}, {6700, 37180}, {6763, 36568}, {7232, 15934}, {7748, 21024}, {7800, 36474}, {7802, 33954}, {7951, 32918}, {9598, 21070}, {11114, 33172}, {12572, 37179}, {13728, 43531}, {14829, 17677}, {16052, 37646}, {16370, 30811}, {16552, 26085}, {16857, 17265}, {16910, 29433}, {17034, 33832}, {17205, 45962}, {17234, 48814}, {17272, 18655}, {17283, 33309}, {17284, 31015}, {17327, 19277}, {17532, 37660}, {17549, 30831}, {17550, 29473}, {17579, 32782}, {17733, 31964}, {18252, 44662}, {19732, 44217}, {19867, 26223}, {24632, 33736}, {27184, 30115}

X(48835) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {58, 16062, 20083}, {1330, 4201, 386}, {1478, 26034, 10}, {18134, 37038, 4653}, {25527, 37817, 1125}


X(48836) = X(30)X(3589)∩X(69)X(519)

Barycentrics    2*a^4 - 2*a^3*b - 3*a^2*b^2 - a*b^3 - 2*b^4 - 2*a^3*c - 2*a^2*b*c - a*b^2*c - b^3*c - 3*a^2*c^2 - a*b*c^2 + 2*b^2*c^2 - a*c^3 - b*c^3 - 2*c^4 : :
X(48836) = X[69] - 9 X[48813], X[996] - 3 X[48829], 5 X[3763] - 9 X[11359], X[32941] - 3 X[48808]

X(48836) lies on these lines: {1, 21282}, {4, 20108}, {10, 3977}, {20, 20083}, {30, 3589}, {69, 519}, {377, 1125}, {535, 4085}, {540, 3629}, {550, 6693}, {551, 33104}, {996, 48829}, {3240, 21291}, {3634, 13725}, {3763, 11359}, {3816, 6715}, {4256, 17677}, {4316, 29631}, {4653, 17678}, {4803, 17271}, {6686, 37193}, {7802, 17200}, {7844, 36477}, {15935, 48631}, {19878, 37153}, {25441, 37256}, {30811, 47040}, {31015, 31191}, {32941, 48808}


X(48837) = X(1)X(224)∩X(6)X(10)

Barycentrics    a^4 - 2*a^3*b - 2*a^2*b^2 - b^4 - 2*a^3*c - 2*a^2*b*c - 2*a^2*c^2 + 2*b^2*c^2 - c^4 : :
X(48837) = X[69] - 3 X[48813], X[16496] - 3 X[48818], 2 X[141] - 3 X[11359], 4 X[3589] - 3 X[11354], 5 X[3618] - 3 X[48817], 5 X[3763] - 6 X[48815], 4 X[4085] - 3 X[48831], 5 X[16491] - 3 X[48827], 2 X[32941] - 3 X[48803]

X(48837) lies on these lines: {1, 224}, {2, 4256}, {3, 1834}, {4, 386}, {5, 4255}, {6, 30}, {8, 4424}, {10, 345}, {20, 58}, {21, 1714}, {31, 4302}, {35, 5230}, {36, 11269}, {39, 36474}, {42, 1478}, {43, 37193}, {69, 519}, {81, 17579}, {86, 48816}, {141, 11359}, {192, 16086}, {193, 540}, {213, 9598}, {315, 33296}, {333, 37038}, {355, 4646}, {376, 3017}, {381, 37662}, {390, 40091}, {442, 19765}, {447, 17907}, {464, 4304}, {497, 995}, {498, 21935}, {515, 990}, {517, 4259}, {550, 4252}, {580, 6868}, {581, 6850}, {595, 4294}, {631, 45939}, {758, 24248}, {938, 24046}, {940, 11112}, {944, 15955}, {950, 1040}, {952, 5820}, {988, 10916}, {991, 6916}, {993, 33137}, {997, 24210}, {1012, 5721}, {1043, 16062}, {1072, 37569}, {1086, 15934}, {1125, 17064}, {1191, 15171}, {1193, 1479}, {1210, 37180}, {1265, 3159}, {1330, 20018}, {1376, 19266}, {1448, 5930}, {1468, 4299}, {1616, 15172}, {1711, 12514}, {1724, 6872}, {1735, 18391}, {1785, 37189}, {2092, 5816}, {2177, 10056}, {2271, 5254}, {2331, 15942}, {2332, 41361}, {2334, 9657}, {2475, 19767}, {2478, 3216}, {2548, 36663}, {2550, 30116}, {2594, 18961}, {2811, 21109}, {2999, 3586}, {3008, 37169}, {3058, 16483}, {3085, 33771}, {3240, 5080}, {3293, 3436}, {3419, 3666}, {3488, 4000}, {3553, 18506}, {3583, 5313}, {3585, 5312}, {3587, 8557}, {3589, 11354}, {3618, 48817}, {3670, 12649}, {3752, 5722}, {3763, 48815}, {3767, 18755}, {3772, 24929}, {3811, 13161}, {3915, 4309}, {3931, 5794}, {3940, 4415}, {3987, 5554}, {4085, 48831}, {4189, 24883}, {4190, 37522}, {4201, 10449}, {4251, 5286}, {4253, 7738}, {4258, 5305}, {4262, 7735}, {4276, 19262}, {4340, 4658}, {4383, 11113}, {4417, 17677}, {4511, 33134}, {4642, 10573}, {4680, 33088}, {4720, 32782}, {4803, 5232}, {5084, 17749}, {5218, 17734}, {5222, 31015}, {5358, 13730}, {5396, 6923}, {5400, 6957}, {5440, 17720}, {5703, 24160}, {5706, 37468}, {5713, 6917}, {5718, 17532}, {5774, 44419}, {5841, 44414}, {6256, 37699}, {6284, 16466}, {6703, 19276}, {6744, 24171}, {6857, 24880}, {6871, 37693}, {6934, 37530}, {6948, 37469}, {6987, 13329}, {7491, 36754}, {7748, 20970}, {7791, 17034}, {9534, 26117}, {9597, 20963}, {9840, 19763}, {10198, 37573}, {10448, 19854}, {10596, 32486}, {11114, 32911}, {11185, 37678}, {11239, 24222}, {11509, 34030}, {12433, 17054}, {12437, 34937}, {13745, 19732}, {14548, 17205}, {15170, 16486}, {15973, 19755}, {16043, 29455}, {16370, 35466}, {16371, 37634}, {16491, 48827}, {16857, 17337}, {17056, 17528}, {17277, 48814}, {17352, 33309}, {17365, 18541}, {17398, 19277}, {17556, 37663}, {17678, 18134}, {17679, 18139}, {18178, 37482}, {19762, 37425}, {19766, 43531}, {20075, 37610}, {20083, 37176}, {20894, 34284}, {22836, 36250}, {24790, 26101}, {25092, 26036}, {26127, 27625}, {26332, 37529}, {31775, 36746}, {31789, 36745}, {32941, 48803}, {33141, 37617}, {37241, 37538}, {37375, 37651}, {37716, 45701}, {40965, 44662}

X(48837) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 23537, 24159}, {1, 23681, 26728}, {3, 1834, 5292}, {20, 387, 58}, {213, 9598, 17732}, {376, 37642, 4257}, {1074, 3914, 23537}, {3017, 4257, 37642}, {3488, 4000, 30117}, {4304, 40940, 37817}, {23537, 26728, 23681}, {23681, 26728, 24159}, {33141, 37617, 45700}


X(48838) = X(2)X(39)∩X(69)X(519)

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

X(48838) lies on these lines: {2, 39}, {30, 10446}, {69, 519}, {81, 11352}, {86, 11354}, {192, 20924}, {304, 3175}, {1975, 4234}, {2549, 17300}, {3210, 33934}, {3666, 20925}, {3674, 4654}, {3734, 17379}, {3933, 16052}, {3945, 32815}, {4045, 17232}, {4419, 40859}, {4704, 20569}, {5224, 48815}, {7737, 20090}, {7751, 22267}, {7760, 17691}, {7761, 17375}, {7788, 17677}, {7798, 17349}, {7804, 37677}, {8667, 21937}, {8682, 27480}, {10436, 48812}, {11286, 46922}, {11287, 17297}, {11359, 17271}, {15048, 17234}, {17078, 30545}, {17179, 30962}, {17277, 22253}, {17320, 48819}, {17697, 33955}, {19582, 41805}, {19870, 32092}, {24296, 37684}, {27253, 32026}, {30116, 42697}

X(48838) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4352, 16712}, {76, 16712, 2}


X(48839) = X(2)X(58)∩X(30)X(573)

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

X(48839) lies on these lines: {2, 58}, {10, 7262}, {30, 573}, {519, 751}, {551, 16478}, {599, 16857}, {754, 11354}, {995, 41002}, {1707, 19875}, {3060, 5692}, {3578, 14020}, {3679, 5086}, {3929, 7713}, {4256, 14555}, {4257, 5743}, {4643, 30117}, {4653, 5739}, {4658, 37314}, {13735, 41816}, {16858, 31143}, {17271, 33309}

X(48839) = midpoint of X(17346) and X(48814)


X(48840) = X(2)X(39)∩X(519)X(599)

Barycentrics    a^3*b + a^2*b^2 + a*b^3 + a^3*c + a^2*b*c + a*b^2*c + b^3*c + a^2*c^2 + a*b*c^2 - 2*b^2*c^2 + a*c^3 + b*c^3 : :
X(48840) = 2 X[3997] + X[17276]

X(48840) lies on these lines: {2, 39}, {30, 991}, {86, 3734}, {519, 599}, {754, 17378}, {1086, 30116}, {1111, 41269}, {1573, 4000}, {2549, 4648}, {3945, 7737}, {3997, 17276}, {4045, 17234}, {4201, 7854}, {4389, 40859}, {4713, 30106}, {5007, 17691}, {6173, 48818}, {7751, 16060}, {7760, 33827}, {7761, 17300}, {7765, 33838}, {7768, 33832}, {7772, 17681}, {7780, 22267}, {7781, 16061}, {7794, 16062}, {7796, 33834}, {7798, 17277}, {7804, 17379}, {7818, 17677}, {7848, 17375}, {7865, 17297}, {7908, 30761}, {11287, 17313}, {13740, 17130}, {15048, 17245}, {15668, 24275}, {16916, 33955}, {17131, 26244}, {17259, 22253}, {17290, 30109}, {17399, 24731}, {17750, 24214}, {20943, 27324}, {24296, 37633}, {30112, 30997}


X(48841) = X(1)X(535)∩X(2)X(4256)

Barycentrics    2*a^4 - 3*a^3*b - 4*a^2*b^2 - b^4 - 3*a^3*c - 7*a^2*b*c - 4*a*b^2*c - 4*a^2*c^2 - 4*a*b*c^2 + 2*b^2*c^2 - c^4 : :
X(48841) = X[17346] - 3 X[48814]

X(48841) lies on these lines: {1, 535}, {2, 4256}, {30, 991}, {58, 11111}, {381, 45944}, {519, 751}, {528, 30116}, {544, 3488}, {551, 24210}, {966, 4803}, {968, 3679}, {975, 34701}, {2328, 31156}, {3017, 16418}, {3830, 45924}, {4316, 9345}, {4658, 6872}, {7761, 17313}, {10459, 34719}, {11159, 20155}, {11237, 38945}, {15935, 17246}, {17301, 30117}, {17556, 19765}, {33148, 38314}, {36005, 37633}, {37299, 37522}, {40091, 47357}, {48830, 48833}


X(48842) = X(6)X(30)∩X(519)X(599)

Barycentrics    a^4 - 6*a^3*b - 5*a^2*b^2 - 2*b^4 - 6*a^3*c - 6*a^2*b*c - 5*a^2*c^2 + 4*b^2*c^2 - 2*c^4 : :
X(48842) = X(48842) = 2 X[11354] - 3 X[47352], 3 X[21358] - 4 X[48815], 3 X[38315] - 2 X[48824]

X(48842) lies on these lines: {1, 21949}, {2, 1043}, {3, 3017}, {6, 30}, {42, 11237}, {58, 3534}, {376, 387}, {377, 37631}, {381, 386}, {518, 48818}, {519, 599}, {524, 48813}, {540, 15534}, {549, 5292}, {597, 48817}, {1100, 48828}, {1126, 9655}, {1191, 3058}, {1193, 11238}, {1386, 48827}, {1616, 15170}, {1714, 15670}, {2271, 5309}, {3241, 17679}, {3488, 17366}, {3524, 37646}, {3545, 37662}, {3578, 17676}, {3679, 4646}, {4000, 15933}, {4256, 5054}, {4257, 15688}, {4258, 5306}, {4995, 5230}, {5298, 11269}, {5846, 48798}, {6175, 19767}, {7788, 33296}, {8959, 13846}, {10304, 37642}, {11236, 42043}, {11354, 47352}, {11648, 20970}, {14636, 19760}, {15694, 45939}, {16086, 17318}, {21358, 48815}, {28458, 36746}, {28459, 36745}, {28538, 48807}, {38315, 48824}

X(48842) = reflection of X(i) in X(j) for these {i,j}: {599, 11359}, {3242, 48819}, {48817, 597}, {48827, 1386}


X(48843) = X(1)X(4202)∩X(6)X(550)

Barycentrics    2*a^3*b + 2*a^2*b^2 + a*b^3 + b^4 + 2*a^3*c + 2*a^2*b*c + a*b^2*c + b^3*c + 2*a^2*c^2 + a*b*c^2 + a*c^3 + b*c^3 + c^4 : :
X(48843) = X[6] + 3 X[11359], X[141] - 3 X[48815], X[996] - 3 X[48831], 5 X[3618] + 3 X[48813], 3 X[11354] - 7 X[47355], 5 X[16491] + 3 X[48807]

X(48843) lies on these lines: {1, 4202}, {2, 4256}, {3, 6693}, {5, 20108}, {6, 540}, {8, 43993}, {10, 3666}, {30, 3589}, {36, 29631}, {58, 4201}, {141, 519}, {321, 19867}, {377, 43531}, {386, 3454}, {387, 37655}, {404, 25441}, {496, 1125}, {758, 3821}, {993, 25453}, {995, 32773}, {996, 48831}, {1698, 33113}, {1724, 17676}, {3017, 14829}, {3216, 5051}, {3583, 32944}, {3618, 48813}, {3822, 6685}, {4425, 10176}, {4429, 30116}, {4680, 17017}, {4694, 29835}, {4737, 18136}, {5132, 19258}, {5251, 29850}, {5313, 25760}, {5315, 32947}, {5692, 32776}, {5883, 24169}, {5902, 33125}, {7750, 17200}, {7808, 36663}, {7834, 36477}, {10448, 19846}, {11354, 47355}, {12609, 40677}, {15792, 25526}, {15934, 17290}, {16052, 37662}, {16056, 29635}, {16086, 17302}, {16491, 48807}, {16706, 30117}, {17023, 37096}, {17352, 48814}, {17381, 48816}, {17679, 19684}, {19270, 24880}, {19279, 31187}, {19701, 44217}, {19786, 30115}, {20913, 29659}, {24995, 25599}, {25440, 37255}, {25468, 48822}, {25499, 36480}, {26590, 30106}, {26978, 36479}, {27714, 28611}, {30810, 31191}, {37676, 48808}

X(48843) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 20083, 6693}, {386, 16062, 3454}


X(48844) = X(2)X(39)∩X(30)X(6176)

Barycentrics    2*a^3*b + a^2*b^2 + 2*a*b^3 + 2*a^3*c + 2*a^2*b*c + 2*a*b^2*c + 2*b^3*c + a^2*c^2 + 2*a*b*c^2 - 2*b^2*c^2 + 2*a*c^3 + 2*b*c^3 : :
X(48844) = X[3997] + 2 X[17235]

X(48844) lies on these lines: {2, 39}, {30, 6176}, {37, 20893}, {86, 7804}, {141, 519}, {551, 17758}, {626, 16052}, {754, 17392}, {1573, 16706}, {3734, 11354}, {3997, 17235}, {4045, 17245}, {4234, 7816}, {4648, 7761}, {5007, 33827}, {7780, 16060}, {7798, 17259}, {7821, 33834}, {7848, 17300}, {7849, 16062}, {7865, 11359}, {7873, 33832}, {11346, 25497}, {17179, 24512}, {17290, 30116}, {17305, 40859}, {19870, 24790}, {21937, 46893}

X(48844) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 16712, 39}, {11359, 17313, 7865}


X(48845) = X(2)X(1043)∩X(30)X(182)

Barycentrics    8*a^3*b + 7*a^2*b^2 + 2*a*b^3 + 3*b^4 + 8*a^3*c + 8*a^2*b*c + 2*a*b^2*c + 2*b^3*c + 7*a^2*c^2 + 2*a*b*c^2 - 2*b^2*c^2 + 2*a*c^3 + 2*b*c^3 + 3*c^4 : :
X(48845) = 3 X[38023] - X[48827], 3 X[38047] - X[48812], 3 X[38087] - X[48806], 3 X[47352] - X[48817]

X(48845) lies on these lines: {2, 1043}, {6, 48813}, {30, 182}, {141, 519}, {377, 19722}, {386, 16052}, {524, 11359}, {540, 8584}, {551, 3813}, {1714, 16351}, {3241, 4202}, {3589, 11354}, {3679, 13728}, {4201, 41629}, {4260, 44663}, {6703, 19290}, {7478, 13394}, {9041, 48819}, {16056, 40726}, {16086, 17395}, {17679, 37631}, {24366, 48830}, {25055, 33141}, {33184, 46913}, {38023, 48827}, {38047, 48812}, {38087, 48806}, {47352, 48817}, {47359, 48818}

X(48845) = midpoint of X(i) and X(j) for these {i,j}: {6, 48813}, {47359, 48818}
X(48845) = reflection of X(i) in X(j) for these {i,j}: {141, 48815}, {11354, 3589}


X(48846) = X(1)X(529)∩X(2)X(1043)

Barycentrics    2*a^4 - 6*a^3*b - 7*a^2*b^2 - b^4 - 6*a^3*c - 14*a^2*b*c - 8*a*b^2*c - 7*a^2*c^2 - 8*a*b*c^2 + 2*b^2*c^2 - c^4 : :

X(48846) lies on these lines: {1, 529}, {2, 1043}, {30, 991}, {37, 519}, {51, 5919}, {225, 4870}, {524, 48814}, {535, 48823}, {551, 37150}, {597, 33309}, {2654, 3058}, {3193, 31156}, {3241, 14020}, {3303, 13724}, {3488, 16777}, {3772, 25055}, {4217, 19722}, {4271, 31393}, {4322, 5434}, {4653, 37646}, {5718, 37375}, {7739, 11354}, {9345, 15326}, {10197, 37715}, {10448, 31157}, {10459, 34699}, {11114, 37631}, {14033, 20155}, {15934, 17246}, {17056, 17532}, {17313, 48813}, {17395, 30117}, {36004, 37633}, {48830, 48832}


X(48847) = X(5)X(386)∩X(6)X(30)

Barycentrics    4*a^3*b + 3*a^2*b^2 + b^4 + 4*a^3*c + 4*a^2*b*c + 3*a^2*c^2 - 2*b^2*c^2 + c^4 : :
X(48847) = X[69] - 3 X[11359], 2 X[141] - 3 X[48815], X[193] + 3 X[48813], 5 X[3618] - 3 X[11354], 5 X[16491] - 3 X[48824], X[16496] - 3 X[48819]

X(48847) lies on these lines: {1, 3925}, {2, 4720}, {3, 387}, {4, 45100}, {5, 386}, {6, 30}, {8, 13728}, {11, 5313}, {12, 5312}, {42, 495}, {43, 3820}, {58, 550}, {69, 11359}, {81, 11112}, {140, 4255}, {141, 519}, {145, 4202}, {193, 48813}, {376, 37666}, {442, 19767}, {496, 1193}, {517, 3755}, {540, 3629}, {548, 4252}, {549, 3017}, {581, 37424}, {595, 10386}, {632, 45939}, {942, 24177}, {956, 37329}, {999, 16056}, {1043, 17698}, {1062, 37730}, {1191, 15172}, {1203, 6284}, {1483, 15955}, {1596, 3192}, {1714, 6675}, {2049, 19766}, {2257, 3587}, {2271, 5305}, {2999, 5722}, {3058, 5315}, {3216, 17527}, {3240, 17757}, {3241, 18139}, {3419, 5256}, {3488, 5222}, {3618, 11354}, {3772, 5719}, {3914, 39542}, {3933, 33296}, {4000, 15934}, {4205, 9534}, {4257, 8703}, {4360, 16086}, {4393, 37096}, {4417, 16052}, {4644, 18541}, {4646, 5690}, {4719, 10916}, {4854, 5692}, {4868, 16579}, {5254, 20970}, {5278, 13745}, {5396, 6907}, {5434, 16474}, {5453, 44222}, {5687, 37255}, {5706, 20420}, {5707, 37281}, {5712, 17528}, {5721, 8727}, {5841, 39523}, {5930, 37544}, {6147, 23537}, {7483, 24883}, {7491, 37509}, {8362, 17034}, {9605, 36474}, {9708, 16850}, {10592, 21935}, {10950, 33178}, {11113, 32911}, {11269, 15325}, {15170, 16483}, {15171, 16466}, {15935, 17366}, {16062, 20018}, {16370, 24597}, {16491, 48824}, {16496, 48819}, {16857, 37650}, {17349, 48814}, {17379, 48816}, {17533, 37651}, {17563, 37522}, {17564, 37634}, {17579, 37685}, {17678, 17778}, {17785, 25650}, {19783, 37153}, {19785, 39544}, {20204, 44342}, {24929, 40940}, {28452, 45923}, {31775, 36742}, {31782, 37415}, {31789, 36754}, {37038, 37652}, {37241, 44094}, {37716, 42043}

X(48847) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {43, 37715, 3820}, {386, 1834, 5}, {1714, 19765, 6675}, {3017, 4256, 37646}, {4255, 5292, 140}, {4256, 37646, 549}, {16062, 20018, 41014}


X(48848) = X(6)X(30)∩X(37)X(519)

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

X(48848) lies on these lines: {2, 2271}, {6, 30}, {37, 519}, {213, 3058}, {218, 11113}, {376, 5021}, {386, 9300}, {549, 18755}, {1100, 48823}, {1449, 48825}, {1834, 5309}, {2176, 15170}, {3017, 4251}, {3755, 28854}, {5434, 20963}, {7753, 20970}, {8703, 33863}, {10385, 14974}, {16972, 48824}, {16973, 48819}, {17034, 37671}, {37654, 48814}

X(48848) = {X(3017),X(4251)}-harmonic conjugate of X(5306)


X(48849) = X(1)X(2)∩X(7)X(31178)

Barycentrics    3*a^3 - 5*a^2*b + a*b^2 - 3*b^3 - 5*a^2*c - 6*a*b*c - 5*b^2*c + a*c^2 - 5*b*c^2 - 3*c^3 : :
X(48849) = X[8] + 2 X[36479], 7 X[9780] - 4 X[36480], 3 X[38314] - 4 X[48822]

X(48849) lies on these lines: {1, 2}, {7, 31178}, {100, 19325}, {105, 9708}, {238, 5772}, {329, 31161}, {517, 44431}, {529, 42048}, {752, 35578}, {944, 13634}, {956, 19322}, {1111, 48799}, {2345, 48805}, {2550, 4688}, {2975, 19326}, {4000, 48821}, {4085, 4402}, {4339, 16394}, {4447, 40726}, {4660, 31995}, {4914, 5712}, {5232, 16496}, {5258, 37254}, {5273, 33169}, {5423, 42056}, {5657, 13635}, {5687, 19323}, {5881, 7390}, {7407, 7982}, {9041, 17251}, {9746, 28236}, {9776, 33074}, {11354, 26035}, {17281, 47357}, {18230, 33165}, {26978, 48815}, {34284, 48813}, {37654, 47359}, {38025, 41310}, {48798, 48816}, {48806, 48814}

X(48849) = reflection of X(3241) in X(48830)
X(48849) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3679, 29594}, {8, 5308, 32847}


X(48850) = X(1)X(2)∩X(30)X(17346)

Barycentrics    3*a^3*b - 3*a*b^3 + 3*a^3*c - a^2*b*c - 7*a*b^2*c - 3*b^3*c - 7*a*b*c^2 - 6*b^2*c^2 - 3*a*c^3 - 3*b*c^3 : :
X(48850) = 5 X[3617] - 2 X[30116]

X(48850) lies on these lines: {1, 2}, {30, 17346}, {72, 42029}, {333, 16370}, {524, 48816}, {538, 48813}, {1043, 16418}, {1150, 13587}, {3419, 4886}, {3578, 17579}, {3696, 44663}, {3913, 16289}, {4113, 4737}, {4720, 5278}, {4803, 17349}, {4921, 16393}, {5044, 20942}, {5233, 17533}, {5295, 42034}, {6534, 31302}, {11359, 17271}, {13735, 19723}, {14829, 16417}, {16857, 17277}, {17330, 48814}, {19276, 41629}, {19277, 46922}, {21300, 45671}, {37654, 48817}

X(48850) = reflection of X(48814) in X(17330)
X(48850) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 9534, 10449}, {3679, 42043, 10}


X(48851) = X(1)X(2)∩X(515)X(17251)

Barycentrics    a^3 - 4*a^2*b - a*b^2 - 2*b^3 - 4*a^2*c - 6*a*b*c - 4*b^2*c - a*c^2 - 4*b*c^2 - 2*c^3 : :
X(48851) = 2 X[10] + X[36479], 5 X[1698] - 2 X[36480], 3 X[19875] - 2 X[48809]

X(48851) lies on these lines: {1, 2}, {515, 9746}, {518, 17251}, {528, 24358}, {1001, 17359}, {1215, 31142}, {2345, 47357}, {3243, 3775}, {3416, 17392}, {3673, 48818}, {3749, 19808}, {3751, 17346}, {3761, 26234}, {3836, 38093}, {3842, 4901}, {3913, 16849}, {4026, 17301}, {4301, 7407}, {4356, 28313}, {4363, 28534}, {4426, 48832}, {4439, 16676}, {4659, 28542}, {4660, 25590}, {4688, 48829}, {4780, 32087}, {4825, 48200}, {4914, 19701}, {5224, 16496}, {5251, 26241}, {5258, 19310}, {5337, 19290}, {5881, 6998}, {6173, 24325}, {7179, 18421}, {7379, 7991}, {7380, 7982}, {7385, 37714}, {10436, 33076}, {12245, 39605}, {12513, 16852}, {16370, 37586}, {16484, 17286}, {16491, 17381}, {17239, 42871}, {17250, 24841}, {17254, 24349}, {17274, 31178}, {17293, 42819}, {17330, 47359}, {17399, 32922}, {17798, 19322}, {28228, 44431}, {28503, 41312}, {28595, 41867}, {31140, 31993}, {31164, 32771}, {38057, 38191}, {48807, 48816}, {48812, 48814}

X(48851) = midpoint of X(36479) and X(48802)
X(48851) = reflection of X(i) in X(j) for these {i,j}: {1, 48822}, {48802, 10}
X(48851) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3679, 17294}, {10, 24331, 17284}


X(48852) = X(1)X(2)∩X(30)X(573)

Barycentrics    a^3*b - a^2*b^2 - 2*a*b^3 + a^3*c - 3*a^2*b*c - 6*a*b^2*c - 2*b^3*c - a^2*c^2 - 6*a*b*c^2 - 4*b^2*c^2 - 2*a*c^3 - 2*b*c^3 : :
X(48852) = 4 X[10] - X[30116], 8 X[4732] + X[17461]

X(48852) lies on these lines: {1, 2}, {4, 9568}, {6, 19277}, {30, 573}, {58, 19276}, {181, 11237}, {238, 48811}, {333, 4257}, {381, 970}, {538, 11359}, {540, 17346}, {579, 17275}, {599, 4260}, {671, 3029}, {994, 44663}, {1573, 4261}, {1682, 11238}, {1685, 35823}, {1686, 35822}, {2051, 3545}, {3030, 10713}, {3031, 9140}, {3032, 10707}, {3033, 10708}, {3034, 10712}, {3058, 9555}, {3091, 9569}, {3534, 35203}, {3830, 9566}, {3839, 9535}, {3878, 31327}, {3913, 16288}, {4256, 5737}, {4276, 16370}, {4279, 11354}, {4421, 16300}, {4653, 19732}, {4658, 16458}, {4732, 17461}, {4803, 17259}, {4995, 31496}, {5055, 9567}, {5132, 9708}, {5156, 48832}, {5258, 16451}, {5295, 35652}, {5434, 9552}, {5587, 10440}, {5692, 21020}, {6054, 34454}, {8715, 16289}, {9549, 38021}, {9560, 11648}, {9570, 44837}, {10706, 34453}, {10709, 34455}, {10710, 34457}, {10711, 34458}, {10715, 34456}, {10716, 34459}, {10974, 17528}, {16394, 19723}, {16418, 19763}, {16456, 28620}, {16857, 37502}, {17277, 33309}, {17678, 41816}, {34627, 44039}

X(48852) = midpoint of X(17346) and X(48816)
X(48852) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 9534, 386}


X(48853) = X(1)X(2)∩X(993)X(19322)

Barycentrics    7*a^2*b + 4*a*b^2 + 3*b^3 + 7*a^2*c + 12*a*b*c + 7*b^2*c + 4*a*c^2 + 7*b*c^2 + 3*c^3 : :
X(48853) = 5 X[1698] + X[36479], 4 X[3634] - X[36480], 3 X[19875] - X[48802]

X(48853) lies on these lines: {1, 2}, {993, 19322}, {3739, 48821}, {4026, 4688}, {4078, 4755}, {4297, 13634}, {4301, 7380}, {4357, 31178}, {4780, 4967}, {5267, 19326}, {5493, 7379}, {5881, 7410}, {8666, 16852}, {8715, 16849}, {9746, 28164}, {10022, 28534}, {10164, 13635}, {11057, 48816}, {17303, 48805}, {19323, 25440}

X(48853) = midpoint of X(3679) and X(48830)
X(48853) = reflection of X(48809) in X(3828)
X(48853) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 551, 29594}, {24603, 29659, 10}


X(48854) = X(1)X(2)∩X(35)X(19326)

Barycentrics    3*a^3 + 2*a^2*b + 5*a*b^2 + 2*a^2*c + 6*a*b*c + 2*b^2*c + 5*a*c^2 + 2*b*c^2 : :
X(48854) = X[1] + 2 X[36480], 4 X[1125] - X[36479], 3 X[25055] - 2 X[48822]

X(48854) lies on these lines: {1, 2}, {35, 19326}, {36, 19325}, {37, 48805}, {40, 13634}, {55, 19322}, {56, 19323}, {86, 16496}, {515, 10186}, {517, 9746}, {528, 41312}, {537, 7174}, {944, 39605}, {980, 19290}, {1001, 4755}, {1107, 48832}, {1390, 36871}, {1447, 18421}, {2223, 16370}, {3185, 4428}, {3230, 5275}, {3247, 32941}, {3303, 19309}, {3304, 19313}, {3576, 13635}, {3746, 19310}, {3751, 46922}, {3842, 7290}, {3913, 16852}, {4301, 7390}, {4432, 16676}, {4657, 48821}, {4659, 28554}, {4664, 5263}, {4702, 16672}, {5223, 33682}, {5283, 11354}, {5563, 19314}, {5819, 47357}, {5881, 7380}, {6998, 7982}, {7322, 25496}, {7385, 11522}, {10180, 10389}, {10436, 31178}, {11194, 37609}, {12513, 16849}, {16371, 37575}, {16418, 37590}, {16491, 17277}, {16858, 23407}, {16972, 17330}, {16973, 47359}, {17251, 28538}, {17392, 47358}, {19328, 26241}, {21372, 40131}, {24036, 48826}, {24441, 28534}, {24841, 41847}, {25499, 48815}, {28164, 44431}, {28639, 42871}, {37869, 41711}, {38049, 38057}, {38053, 38187}, {41311, 48829}, {41313, 48810}, {48814, 48827}, {48816, 48818}

X(48854) = reflection of X(i) in X(j) for these {i,j}: {3679, 48809}, {48830, 551}
X(48854) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3679, 16834}, {1, 16830, 39586}, {1, 36531, 4384}, {3241, 29580, 1}, {16826, 36534, 1}


X(48855) = X(1)X(2)∩X(30)X(991)

Barycentrics    a*(3*a^2*b + 3*a*b^2 + 3*a^2*c + 7*a*b*c + 4*b^2*c + 3*a*c^2 + 4*b*c^2) : :
X(48855) = 2 X[1] + X[30116], X[573] - 4 X[6176]

X(48855) lies on these lines: {1, 2}, {6, 16857}, {30, 991}, {36, 9345}, {58, 16418}, {81, 16858}, {381, 581}, {405, 4658}, {500, 3830}, {529, 48823}, {535, 48825}, {538, 5145}, {540, 17196}, {553, 37523}, {573, 6176}, {579, 15934}, {810, 45324}, {940, 4257}, {964, 28619}, {993, 4038}, {1064, 38021}, {1453, 39948}, {1573, 16884}, {1724, 16861}, {1962, 5902}, {2049, 28620}, {2650, 27785}, {2901, 42029}, {3247, 3997}, {3303, 16453}, {3304, 16287}, {3736, 19277}, {3746, 16451}, {3845, 5453}, {3894, 3989}, {4245, 18185}, {4256, 16417}, {4262, 40750}, {4306, 4654}, {4383, 19536}, {4428, 5711}, {4870, 10571}, {5055, 5396}, {5056, 22392}, {5071, 37732}, {5132, 6767}, {5156, 40091}, {5165, 16672}, {5563, 16452}, {5707, 28466}, {5718, 17533}, {5733, 6987}, {5883, 17592}, {5904, 42041}, {6051, 31165}, {6534, 24349}, {6928, 45933}, {7865, 11359}, {8666, 16289}, {9275, 9306}, {10441, 14636}, {11113, 37631}, {11194, 16300}, {11286, 20155}, {11518, 13726}, {12513, 16288}, {13587, 37633}, {13735, 42028}, {14020, 42045}, {15178, 19543}, {15569, 44663}, {16371, 19765}, {16396, 19715}, {16431, 19758}, {16436, 19761}, {17547, 32911}, {17549, 37522}, {18145, 37632}, {18154, 48285}, {18398, 42038}, {20150, 32941}, {21161, 37530}, {28443, 45931}, {28444, 37469}, {31424, 39980}, {33309, 46922}, {37819, 41311}

X(48855) = midpoint of X(17378) and X(48814)
X(48855) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3720, 995}, {1, 5287, 30115}, {940, 4653, 4257}, {17749, 19767, 386}


X(48856) = X(1)X(2)∩X(37)X(47357)

Barycentrics    5*a^3 + a^2*b + 7*a*b^2 - b^3 + a^2*c + 6*a*b*c + b^2*c + 7*a*c^2 + b*c^2 - c^3 : :
X(48856) = X[8] - 4 X[36480], 5 X[3616] - 2 X[36479], 5 X[3616] - 4 X[48822], 3 X[38314] - 2 X[48830], X[4307] + 2 X[7174]

X(48856) lies on these lines: {1, 2}, {37, 47357}, {38, 2094}, {105, 6767}, {277, 48820}, {515, 11200}, {527, 4307}, {529, 42050}, {537, 35578}, {948, 11237}, {984, 4344}, {1000, 40127}, {1279, 38025}, {1738, 38092}, {2550, 17301}, {3242, 17392}, {3303, 4223}, {3598, 18421}, {3746, 37254}, {3945, 16496}, {4310, 6173}, {4339, 11111}, {4353, 7613}, {4419, 28534}, {4759, 31722}, {5055, 15251}, {5273, 17716}, {5283, 14968}, {5328, 17722}, {5423, 25496}, {5686, 16475}, {5716, 34606}, {5734, 7385}, {5846, 17251}, {5881, 7407}, {7390, 7982}, {7967, 44430}, {16487, 25072}, {16491, 37681}, {16601, 48824}, {16673, 30331}, {17399, 32850}, {20344, 34578}, {24452, 36588}, {31393, 40131}, {38053, 38185}, {38057, 38315}

X(48856) = reflection of X(i) in X(j) for these {i,j}: {8, 48802}, {36479, 48822}, {48802, 36480}
X(48856) = {X(145),X(16830)}-harmonic conjugate of X(39581)


X(48857) = X(1)X(2)∩X(6)X(30)

Barycentrics    a^4 + 6*a^3*b + 4*a^2*b^2 + b^4 + 6*a^3*c + 6*a^2*b*c + 4*a^2*c^2 - 2*b^2*c^2 + c^4 : :
X(48857) = 3 X[16475] - X[48827]

X(48857) lies on these lines: {1, 2}, {6, 30}, {58, 376}, {381, 1834}, {388, 1126}, {443, 4658}, {500, 44284}, {518, 48819}, {524, 11359}, {540, 1992}, {549, 4255}, {579, 3587}, {595, 10385}, {597, 11354}, {599, 48815}, {1191, 15170}, {1386, 48824}, {1449, 48828}, {1724, 31156}, {2271, 5306}, {2308, 4302}, {2901, 42032}, {3058, 16466}, {3242, 48820}, {3524, 4256}, {3654, 4646}, {3751, 48818}, {3755, 28194}, {3913, 16298}, {4252, 8703}, {4257, 10304}, {4649, 48825}, {4653, 17561}, {4654, 23537}, {5054, 37646}, {5055, 37662}, {5309, 20970}, {5319, 36477}, {5733, 6826}, {5846, 48800}, {6838, 22392}, {7277, 18541}, {7772, 36474}, {11214, 44662}, {12513, 16299}, {13745, 19723}, {14636, 19763}, {15670, 19765}, {15934, 17366}, {16475, 48827}, {17679, 42045}, {28458, 36742}, {28459, 36754}, {32833, 33296}, {37631, 44217}, {46922, 48816}

X(48857) = midpoint of X(i) and X(j) for these {i,j}: {1992, 48813}, {3751, 48818}
X(48857) = reflection of X(i) in X(j) for these {i,j}: {599, 48815}, {3242, 48820}, {11354, 597}, {48824, 1386}
X(48857) = crossdifference of every pair of points on line {649, 8675}
X(48857) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 387, 3017}, {2, 3017, 5292}, {386, 387, 5292}, {386, 3017, 2}


X(48858) = X(1)X(2)∩X(6)X(33309)

Barycentrics    5*a^3*b + 4*a^2*b^2 - a*b^3 + 5*a^3*c + 9*a^2*b*c + 3*a*b^2*c - b^3*c + 4*a^2*c^2 + 3*a*b*c^2 - 2*b^2*c^2 - a*c^3 - b*c^3 : :
X(48858) = X[145] + 2 X[30116]

X(48858) lies on these lines: {1, 2}, {6, 33309}, {30, 10446}, {86, 19277}, {376, 10441}, {524, 48814}, {538, 48817}, {1043, 19276}, {1764, 10304}, {1992, 10477}, {3543, 10454}, {3655, 35631}, {3839, 10478}, {4195, 4658}, {4360, 15934}, {4653, 37683}, {4734, 5883}, {5731, 10439}, {7967, 39550}, {8591, 38481}, {9143, 38482}, {10385, 10480}, {10470, 15692}, {11114, 42045}, {11354, 46922}, {11359, 17297}, {12435, 34632}, {12513, 16289}, {12545, 34628}, {14829, 19279}, {15677, 35637}, {16394, 42028}, {16418, 41629}, {16574, 31393}, {17392, 48816}, {18185, 19260}, {31179, 37375}, {35892, 47357}

X(48858) = reflection of X(48816) in X(17392)
X(48858) = {X({}),X(1)}-harmonic conjugate of X({}[[1]][[3]])


X(48859) = X(2)X(1043)∩X(30)X(141)

Barycentrics    4*a^4 + a^2*b^2 + 6*a*b^3 + b^4 + 6*a*b^2*c + 6*b^3*c + a^2*c^2 + 6*a*b*c^2 + 10*b^2*c^2 + 6*a*c^3 + 6*b*c^3 + c^4 : :
X(48859) = 3 X[21358] - X[48813]

X(48859) lies on these lines: {2, 1043}, {30, 141}, {519, 597}, {524, 11354}, {540, 22165}, {599, 48817}, {964, 37631}, {2345, 15933}, {3017, 17698}, {3242, 48806}, {3416, 48827}, {3454, 3845}, {3488, 17293}, {3578, 11319}, {4665, 30117}, {4851, 48828}, {4966, 48825}, {5298, 30942}, {5306, 21024}, {5737, 17561}, {5846, 48824}, {7227, 15934}, {9053, 48804}, {10479, 15670}, {11237, 33171}, {11359, 20582}, {17330, 33309}, {21358, 48813}, {33954, 37671}, {47358, 48812}

X(48859) = midpoint of X(i) and X(j) for these {i,j}: {599, 48817}, {3242, 48806}, {3416, 48827}, {47358, 48812}
X(48859) = reflection of X(11359) in X(20582)


X(48860) = X(2)X(39)∩X(519)X(597)

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

X(48860) lies on these lines: {2, 39}, {519, 597}, {754, 17330}, {966, 7761}, {1213, 4045}, {1573, 17289}, {1654, 7848}, {2108, 19875}, {3734, 17259}, {3849, 20666}, {4279, 11354}, {5007, 17688}, {7780, 16061}, {7798, 15668}, {7804, 17277}, {7821, 33835}, {7829, 17698}, {7849, 33838}, {7853, 31090}, {7865, 17251}, {7873, 33818}, {17369, 30109}

X(48860) = {X(17277),X(24275)}-harmonic conjugate of X(7804)


X(48861) = X(2)X(41014)∩X(6)X(30)

Barycentrics    4*a^4 + 12*a^3*b + 7*a^2*b^2 + b^4 + 12*a^3*c + 12*a^2*b*c + 7*a^2*c^2 - 2*b^2*c^2 + c^4 : :
X(48861) = 3 X[5032] + X[48813], 3 X[16475] - X[48824]

X(48861) lies on these lines: {2, 41014}, {5, 3017}, {6, 30}, {58, 8703}, {381, 387}, {386, 549}, {518, 48820}, {519, 597}, {524, 48815}, {540, 8584}, {547, 5292}, {1203, 3058}, {1834, 3845}, {1992, 11359}, {3524, 37666}, {3578, 13728}, {3751, 48819}, {3755, 28198}, {4252, 34200}, {4255, 12100}, {4256, 17504}, {4257, 45759}, {4649, 48823}, {4995, 5312}, {5032, 48813}, {5054, 37642}, {5298, 5313}, {5306, 20970}, {8728, 37631}, {11539, 37646}, {15170, 16466}, {15670, 19767}, {15673, 19765}, {15699, 37662}, {16475, 48824}, {16667, 48828}, {28458, 36750}, {28459, 37509}

X(48861) = midpoint of X(i) and X(j) for these {i,j}: {1992, 11359}, {3751, 48819}


X(48862) = X(2)X(1043)∩X(6)X(519)

Barycentrics    3*a^4 - 2*a^3*b - a^2*b^2 + 4*a*b^3 - 2*a^3*c - 2*a^2*b*c + 4*a*b^2*c + 4*b^3*c - a^2*c^2 + 4*a*b*c^2 + 8*b^2*c^2 + 4*a*c^3 + 4*b*c^3 : :
X(48862) = 5 X[3763] - 4 X[48815], 2 X[11359] - 3 X[21358]

X(48862) lies on these lines: {2, 1043}, {6, 519}, {8, 11346}, {10, 11357}, {30, 599}, {141, 48813}, {145, 19738}, {405, 3679}, {518, 48812}, {524, 48817}, {529, 11355}, {540, 15533}, {551, 2049}, {594, 3488}, {964, 3241}, {1011, 31136}, {1724, 4677}, {3736, 19277}, {3763, 48815}, {3828, 16844}, {4195, 41629}, {4234, 4252}, {4258, 21024}, {4267, 16418}, {4383, 4720}, {4421, 19760}, {5774, 21000}, {5802, 17330}, {7478, 35259}, {9041, 48806}, {10477, 44663}, {10479, 16351}, {11194, 19759}, {11319, 31145}, {11351, 17230}, {11358, 31137}, {11359, 21358}, {12943, 33081}, {15934, 17118}, {16086, 17269}, {16486, 32943}, {16857, 37502}, {17119, 30117}, {17251, 48814}, {17310, 19281}, {17313, 48816}, {17678, 19838}, {19279, 47040}, {19290, 37674}, {19701, 38314}, {19744, 19875}, {27739, 37375}, {28538, 48827}, {31146, 37059}, {37075, 41141}

X(48862) = reflection of X(i) in X(j) for these {i,j}: {6, 11354}, {48813, 141}
X(48862) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 11346, 19723}, {964, 3241, 19722}


X(48863) = X(1)X(321)∩X(6)X(519)

Barycentrics    a^4 + a*b^3 + a*b^2*c + b^3*c + a*b*c^2 + 2*b^2*c^2 + a*c^3 + b*c^3 : :
X(48863) = X[6] - 3 X[11354], X[996] + 2 X[32941], X[69] + 3 X[48817], 7 X[3619] - 3 X[48813], 5 X[3763] - 3 X[11359], X[16496] + 3 X[48812], 4 X[34573] - 3 X[48815]

X(48863) lies on these lines: {1, 321}, {2, 4256}, {4, 3430}, {6, 519}, {8, 595}, {10, 55}, {21, 10479}, {30, 141}, {32, 21024}, {33, 997}, {36, 11322}, {58, 4195}, {69, 540}, {75, 30117}, {76, 33954}, {145, 19743}, {264, 447}, {312, 30115}, {333, 13735}, {379, 17284}, {386, 1043}, {515, 12618}, {535, 11355}, {551, 19701}, {626, 36663}, {758, 3923}, {936, 27394}, {940, 16394}, {960, 10570}, {976, 1089}, {993, 1011}, {995, 32942}, {1010, 19792}, {1104, 5295}, {1125, 2049}, {1210, 37065}, {1211, 11113}, {1376, 4245}, {1478, 33171}, {1714, 17526}, {1726, 12514}, {1834, 17698}, {1975, 16887}, {1985, 3814}, {2077, 37069}, {2161, 4432}, {2345, 3488}, {2476, 25645}, {3052, 5774}, {3216, 5192}, {3241, 19717}, {3244, 19739}, {3295, 5793}, {3583, 25760}, {3619, 48813}, {3626, 39589}, {3634, 16844}, {3635, 19748}, {3661, 11320}, {3679, 5278}, {3714, 5266}, {3763, 11359}, {3771, 3822}, {3773, 10791}, {3828, 11357}, {3831, 13738}, {3840, 11358}, {3894, 32940}, {3912, 19281}, {3914, 19869}, {3924, 4647}, {3934, 36477}, {3938, 4692}, {3980, 5883}, {4011, 10176}, {4185, 5101}, {4217, 5739}, {4234, 4257}, {4255, 20108}, {4262, 26244}, {4276, 19260}, {4297, 37062}, {4302, 26034}, {4304, 16368}, {4363, 15934}, {4384, 11342}, {4418, 5902}, {4424, 32929}, {4669, 19723}, {4673, 15955}, {4680, 15523}, {4720, 32911}, {4803, 17349}, {5010, 32918}, {5080, 11330}, {5132, 19243}, {5224, 48814}, {5235, 16858}, {5251, 31330}, {5259, 31339}, {5263, 30116}, {5264, 17751}, {5267, 37057}, {5283, 28594}, {5292, 6693}, {5313, 32944}, {5440, 30818}, {5563, 19769}, {5692, 32930}, {5737, 16418}, {5799, 31782}, {5835, 37730}, {6700, 7532}, {6737, 16471}, {7227, 15935}, {7229, 15933}, {7232, 18541}, {7478, 10546}, {7522, 20106}, {7795, 36474}, {7951, 29846}, {8666, 19762}, {9534, 17697}, {10448, 19863}, {10454, 37399}, {11019, 37059}, {11114, 32782}, {11115, 37522}, {11679, 37817}, {13741, 17749}, {14020, 41809}, {14377, 21240}, {15668, 19277}, {16061, 29455}, {16086, 17280}, {16370, 37660}, {16496, 48812}, {16783, 26035}, {16857, 17259}, {16919, 29473}, {17034, 17688}, {17054, 24176}, {17056, 37150}, {17234, 48816}, {17277, 33309}, {17532, 30811}, {17537, 31037}, {17577, 30831}, {17579, 33172}, {19276, 37674}, {19714, 42057}, {19719, 29574}, {19740, 38314}, {19749, 19883}, {19750, 34641}, {19751, 38098}, {19755, 24387}, {19838, 23537}, {20172, 30109}, {20888, 24549}, {21616, 39579}, {24291, 33936}, {24929, 44417}, {25639, 37056}, {29433, 33819}, {29611, 37076}, {31036, 36534}, {33160, 37717}, {33953, 34284}, {34573, 48815}

X(48863) = crossdifference of every pair of points on line {9002, 43060}
X(48863) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 964, 43531}, {8, 11319, 1724}, {405, 3419, 1751}, {1043, 13740, 386}, {1834, 17698, 20083}, {3419, 32777, 10}, {4195, 10449, 58}, {4234, 14829, 4257}, {5292, 37176, 6693}


X(48864) = X(2)X(39)∩X(6)X(519)

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

X(48864) lies on these lines: {2, 39}, {6, 519}, {8, 14968}, {9, 48812}, {30, 573}, {32, 4234}, {86, 7798}, {391, 7737}, {574, 26244}, {754, 17346}, {966, 2549}, {1213, 15048}, {1573, 2345}, {1654, 7761}, {3501, 3679}, {3734, 17277}, {4045, 5224}, {4195, 5007}, {4253, 21024}, {4363, 30109}, {5235, 24296}, {5254, 16052}, {5275, 19290}, {5277, 19336}, {5278, 11352}, {5319, 37176}, {7751, 16061}, {7760, 17688}, {7765, 16062}, {7768, 33818}, {7772, 13740}, {7781, 16060}, {7790, 31090}, {7794, 33838}, {7796, 33835}, {7804, 17349}, {7844, 30761}, {7848, 17343}, {7865, 17271}, {8682, 27474}, {11287, 17251}, {11648, 17677}, {15668, 22253}, {17130, 17681}, {17155, 46902}, {17179, 30945}, {17354, 40859}, {17369, 30116}, {17389, 19738}, {19722, 29574}, {32939, 36283}, {37654, 48817}

X(48864) = crossdifference of every pair of points on line {669, 9002}
X(48864) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 194, 16712}, {26035, 26770, 5283}


X(48865) = X(6)X(519)∩X(10)X(11346)

Barycentrics    6*a^4 + 2*a^3*b + a^2*b^2 + 5*a*b^3 + 2*a^3*c + 2*a^2*b*c + 5*a*b^2*c + 5*b^3*c + a^2*c^2 + 5*a*b*c^2 + 10*b^2*c^2 + 5*a*c^3 + 5*b*c^3 : :
X(48865) = X[6] - 5 X[11354], 3 X[21356] + 5 X[48817]

X(48865) lies on these lines: {6, 519}, {10, 11346}, {30, 14810}, {405, 3828}, {540, 22165}, {551, 964}, {1724, 4669}, {3244, 19738}, {3626, 19723}, {3634, 11357}, {3679, 11319}, {4276, 16858}, {5278, 38098}, {11351, 29596}, {19281, 41141}, {21356, 48817}


X(48866) = X(6)X(519)∩X(10)X(31)

Barycentrics    2*a^4 + 2*a^3*b + a^2*b^2 + a*b^3 + 2*a^3*c + 2*a^2*b*c + a*b^2*c + b^3*c + a^2*c^2 + a*b*c^2 + 2*b^2*c^2 + a*c^3 + b*c^3 : :
X(48866) = X[6] + 3 X[11354], X[996] - 3 X[48832], X[32941] - 3 X[48811], 5 X[3618] + 3 X[48817], 3 X[11359] - 7 X[47355], 5 X[16491] + 3 X[48812]

X(48866) lies on these lines: {1, 3159}, {2, 4257}, {3, 20108}, {4, 20083}, {5, 6693}, {6, 519}, {10, 31}, {30, 3589}, {36, 32944}, {56, 226}, {58, 13740}, {76, 17200}, {86, 33309}, {141, 540}, {379, 31191}, {386, 4195}, {447, 36794}, {551, 4656}, {595, 1220}, {758, 4672}, {894, 30117}, {1011, 6685}, {1395, 1877}, {2049, 3634}, {2267, 8804}, {3008, 19281}, {3216, 11115}, {3241, 19743}, {3286, 19243}, {3454, 17698}, {3583, 11330}, {3618, 48817}, {3626, 19750}, {3636, 19747}, {3679, 19742}, {3821, 24288}, {3822, 6679}, {3828, 19732}, {4075, 30142}, {4203, 4276}, {4234, 4256}, {4383, 16394}, {4653, 13735}, {4692, 17469}, {4697, 5883}, {4745, 19723}, {5046, 25441}, {5047, 25526}, {5192, 37522}, {5251, 32772}, {5333, 16861}, {5361, 10479}, {6686, 11358}, {6700, 37065}, {7478, 10545}, {7535, 12436}, {7808, 36477}, {7834, 36663}, {10198, 28776}, {11320, 17023}, {11342, 29571}, {11359, 47355}, {12512, 37062}, {14621, 30109}, {15668, 16857}, {16474, 32943}, {16491, 48812}, {16552, 36480}, {16844, 19878}, {16974, 22011}, {17259, 19277}, {17290, 18541}, {17352, 48816}, {17381, 48814}, {17697, 18169}, {17758, 25497}, {19276, 37679}, {19740, 25055}, {19741, 38314}, {19869, 41011}, {20103, 37059}, {24295, 38456}, {27064, 30115}, {29598, 37076}

X(48866) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {405, 43531, 1125}, {964, 1724, 10}, {993, 25496, 1125}, {4680, 26061, 10}


X(48867) = X(2)X(58)∩X(6)X(519)

Barycentrics    3*a^4 + 4*a^3*b + 2*a^2*b^2 + a*b^3 + 4*a^3*c + 4*a^2*b*c + a*b^2*c + b^3*c + 2*a^2*c^2 + a*b*c^2 + 2*b^2*c^2 + a*c^3 + b*c^3 : :
X(48867) = 5 X[3618] - X[48813], X[11359] - 3 X[47352], 3 X[16475] + X[48812], 3 X[38023] - X[48819], 3 X[38087] - X[48800]

X(48867) lies on these lines: {1, 11346}, {2, 58}, {6, 519}, {10, 19723}, {30, 182}, {386, 4234}, {405, 551}, {964, 3679}, {979, 42042}, {1003, 46913}, {1125, 11357}, {1751, 17532}, {2049, 3828}, {3216, 19336}, {3241, 11319}, {3589, 48815}, {3618, 48813}, {3758, 30117}, {4096, 30142}, {4245, 40726}, {4252, 20108}, {4383, 19290}, {4658, 17697}, {4921, 10479}, {5047, 42025}, {5278, 19875}, {5640, 7478}, {7829, 36663}, {11351, 17367}, {11359, 47352}, {13740, 41629}, {16052, 20083}, {16475, 48812}, {16783, 48830}, {16859, 28619}, {19281, 41140}, {19684, 25055}, {19701, 19883}, {19717, 38314}, {19750, 38098}, {33309, 46922}, {38023, 48819}, {38087, 48800}

X(48867) = midpoint of X(i) and X(j) for these {i,j}: {6, 11354}, {47359, 48824}
X(48867) = reflection of X(48815) in X(3589)
X(48867) = crossdifference of every pair of points on line {9002, 42664}
X(48867) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {405, 19722, 551}, {11346, 19738, 1}


X(48868) = X(2)X(58)∩X(30)X(991)

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

X(48868) lies on these lines: {1, 11015}, {2, 58}, {3, 45933}, {30, 991}, {75, 519}, {171, 10197}, {222, 11237}, {255, 3584}, {377, 4658}, {381, 36746}, {528, 48823}, {529, 30116}, {551, 37038}, {553, 37591}, {581, 28452}, {599, 19277}, {754, 11359}, {940, 17532}, {975, 28609}, {1448, 4654}, {2979, 5902}, {3017, 17528}, {3583, 9345}, {3822, 37604}, {4255, 19706}, {4256, 5712}, {4257, 17056}, {4306, 5434}, {4307, 40091}, {4675, 30117}, {4973, 29657}, {5717, 24046}, {5733, 6916}, {6173, 48828}, {10459, 34690}, {11112, 37631}, {11287, 20155}, {11354, 17313}, {13725, 28620}, {16777, 18541}, {17676, 28619}, {17678, 42028}, {24160, 37554}, {25055, 37817}, {36004, 37635}, {37375, 37633}

X(48868) = midpoint of X(17378) and X(48816)


X(48869) = X(2)X(39)∩X(30)X(17346)

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

X(48869) lies on these lines: {2, 39}, {30, 17346}, {86, 22253}, {391, 32815}, {519, 1992}, {1654, 2549}, {3177, 33935}, {3496, 3929}, {3570, 16383}, {3734, 17349}, {4045, 17238}, {4195, 7760}, {4234, 14614}, {5224, 15048}, {7761, 17343}, {7781, 22267}, {7798, 17379}, {8716, 21937}, {11287, 17271}, {11354, 46922}, {11359, 31144}, {14033, 37654}, {24271, 37652}, {25242, 33941}, {26244, 31859}, {27340, 33939}, {27474, 35102}, {29574, 42032}, {30109, 42697}, {31169, 42029}

X(48869) = {X(7798),X(24275)}-harmonic conjugate of X(17379)


X(48870) = X(2)X(58)∩X(6)X(30)

Barycentrics    5*a^4 + 6*a^3*b + 2*a^2*b^2 - b^4 + 6*a^3*c + 6*a^2*b*c + 2*a^2*c^2 + 2*b^2*c^2 - c^4 : :
X(48870) = 3 X[16475] - X[48818], 3 X[38315] - 2 X[48820], 3 X[47352] - 2 X[48815]

X(48870) lies on these lines: {1, 17781}, {2, 58}, {4, 3017}, {6, 30}, {9, 48828}, {31, 10056}, {238, 48825}, {376, 386}, {381, 5292}, {387, 3543}, {405, 37631}, {452, 4658}, {518, 48824}, {519, 1992}, {524, 11354}, {549, 4252}, {582, 44284}, {597, 11359}, {752, 48831}, {964, 3578}, {1001, 48823}, {1126, 4294}, {1386, 48819}, {1453, 4654}, {1468, 10072}, {1478, 2308}, {1714, 6175}, {1834, 3830}, {3524, 4257}, {3545, 37642}, {3839, 37666}, {4255, 8703}, {4256, 10304}, {4644, 30117}, {5007, 36474}, {5021, 9300}, {5054, 37662}, {5055, 37646}, {5071, 45939}, {5319, 36663}, {5325, 5717}, {5434, 16466}, {5712, 17561}, {5733, 6913}, {5846, 48804}, {7277, 15934}, {11346, 42045}, {13745, 19722}, {14636, 19762}, {15677, 19767}, {16475, 48818}, {16857, 17392}, {17330, 19277}, {17366, 18541}, {17378, 33309}, {17525, 19765}, {28458, 36754}, {28459, 36742}, {38315, 48820}, {46922, 48814}, {47352, 48815}

X(48870) = midpoint of X(i) and X(j) for these {i,j}: {1992, 48817}, {3751, 48827}
X(48870) = reflection of X(i) in X(j) for these {i,j}: {11359, 597}, {48819, 1386}
X(48870) = crossdifference of every pair of points on line {8675, 42664}


X(48871) = EULER LINE INTERCEPT OF X(6)X(5649)

Barycentrics    a^2 (a^12-4 a^10 b^2+5 a^8 b^4-5 a^4 b^8+4 a^2 b^10-b^12-4 a^10 c^2+5 a^8 b^2 c^2-5 a^6 b^4 c^2+7 a^4 b^6 c^2+a^2 b^8 c^2-4 b^10 c^2+5 a^8 c^4-5 a^6 b^2 c^4-2 a^4 b^4 c^4-5 a^2 b^6 c^4+7 b^8 c^4+7 a^4 b^2 c^6-5 a^2 b^4 c^6-4 b^6 c^6-5 a^4 c^8+a^2 b^2 c^8+7 b^4 c^8+4 a^2 c^10-4 b^2 c^10-c^12) : :
Barycentrics    (SB+SC) (9 (4 R^2-SW) (SB-SW) (SC-SW) SW+S^2 (-36 R^2 SA+3 SB SC+11 SA SW)) : :

As a point on the Euler line, X(48871) has Shinagawa coefficients (9E*F*(E+F)-2*(E+4*F)*S^2,(-E+8*F)*S^2).

See Kadir Altintas and Ercole Suppa euclid 5052.

X(48871) lies on these lines: {2,3}, {6,5649}, {99,36789}, {112,14919}, {287,16010}, {2420,15066}, {5664,31859}, {12584,15595}, {32254,40867}, {32305,41145}

X(48871) = trilinear quotient X(i)/X(j) for these (i,j): (2,40856,458), (3,1995,36176), (3,37921,7492), (7496,37918,3)

leftri

Points in a [Brocard axis, Euler line] coordinate system: X(48872)-X(48910)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1, L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1 = Brocard axis: b^2 c^2 (b^2 - c^2) α + c^2 a^2 (c^2 - a^2) β + a^2 b^2 (a^2 - b^2) γ = 0.

L2 = Euler line: (b^2 - c^2)(a^2 - b^2 - c^2) α + (c^2 - a^2)(b^2 - c^2 - a^2) β + (a^2 - b^2)(c^2 - a^2 - b^2) γ = 0.

The origin is given by (0, 0) = X(3) = a^2(a^2-b^2-c^2) : : .

Barycentrics u : v : w for a point U = (x, y) in this system are given by

u : v : w = a^2(a^2-b^2-c^2)(b^2-c^2)(c^2-a^2)(a^2-b^2) - a^2(a^2(b^2+c^2) - b^4 - c^4) x + (a^2(-2a^2+b^2+c^2) + (b^2-c^2)^2)y : : ,

where, as functions of a, b, c, the coordinate x is antisymmetric and homogeneous of degree 4, and y is antisymmetric and homogeneous of degree 6.

The appearance of {x, y}, k in the following list means that (x, y) = X(k).

{-2 (a-b) (a-c) (b-c) (a+b+c), -2 a (a-b) b (a-c) (b-c) c}, 12702
{-((2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)), 0}, 1350
{-((2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)), (a^2-b^2) (a^2-c^2) (b^2-c^2)}, 1352
{-((2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)), 2 (a^2-b^2) (a^2-c^2) (b^2-c^2)}, 36990
{-((a-b) (a-c) (b-c) (a+b+c)), -a (a-b) b (a-c) (b-c) c}, 40
{-(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)), 0}, 3098
{-(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a b+a c+b c)), 0}, 573
{-(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)), 1/2 (a^2-b^2) (a^2-c^2) (b^2-c^2)}, 141
{-(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)), (a^2-b^2) (a^2-c^2) (b^2-c^2)}, 3818
{-(1/2) (a-b) (a-c) (b-c) (a+b+c), -(1/2) a (a-b) b (a-c) (b-c) c}, 3579
{-(1/2) (a-b) (a-c) (b-c) (a+b+c), 0}, 35203
{-(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(2 (a^2+b^2+c^2))), 0}, 14810
{-(1/2) (a-b) (a-c) (b-c) (a+b+c), 1/2 (a-b) (a-c) (b-c) (a+b+c)^3}, 46976
{-(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(2 (a^2+b^2+c^2))), 1/2 (a^2-b^2) (a^2-c^2) (b^2-c^2)}, 24206
{0, -2 (a^2-b^2) (a^2-c^2) (b^2-c^2)}, 1657
{0, -a (a-b) b (a-c) (b-c) c}, 37425
{0, -((a^2-b^2) (a^2-c^2) (b^2-c^2))}, 20
{0, -(1/2) (a^2-b^2) (a^2-c^2) (b^2-c^2)}, 550
{0, 0}, 3
{0, 1/2 (a^2-b^2) (a^2-c^2) (b^2-c^2)}, 5
{0, a (a-b) b (a-c) (b-c) c}, 9840
{0, (a^2-b^2) (a^2-c^2) (b^2-c^2)}, 4
{0, 2 (a^2-b^2) (a^2-c^2) (b^2-c^2)}, 382
{((a^2-b^2) (a^2-c^2) (b^2-c^2))/(2 (a^2+b^2+c^2)), 0}, 5092
{1/2 (a-b) (a-c) (b-c) (a+b+c), 1/2 a (a-b) b (a-c) (b-c) c}, 1385
{((a^2-b^2) (a^2-c^2) (b^2-c^2))/(2 (a^2+b^2+c^2)), 1/2 (a^2-b^2) (a^2-c^2) (b^2-c^2)}, 19130
{((a^2-b^2) (a^2-c^2) (b^2-c^2))/(2 (a b+a c+b c)), 1/2 (a^2-b^2) (a^2-c^2) (b^2-c^2)}, 24220
{((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2), -(1/2) (a^2-b^2) (a^2-c^2) (b^2-c^2)}, 44882
{(a-b) (a-c) (b-c) (a+b+c), 0}, 500
{((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2), 0}, 182
{((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a b+a c+b c), 0}, 991
{(a-b) (a-c) (b-c) (a+b+c), 1/2 a (a-b) b (a-c) (b-c) c}, 5453
{((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2), 1/2 (a^2-b^2) (a^2-c^2) (b^2-c^2)}, 5480
{(a-b) (a-c) (b-c) (a+b+c), a (a-b) b (a-c) (b-c) c}, 1
{2 (a-b) (a-c) (b-c) (a+b+c), -((a-b) (a-c) (b-c) (a^3+b^3+c^3))}, 46483
{(2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2), -((a^2-b^2) (a^2-c^2) (b^2-c^2))}, 46264
{(2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2), 0}, 6
{(2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2), 1/2 (a^2-b^2) (a^2-c^2) (b^2-c^2)}, 21850
{(2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2), (a^2-b^2) (a^2-c^2) (b^2-c^2)}, 31670
{(2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a b+a c+b c), (a^2-b^2) (a^2-c^2) (b^2-c^2)}, 10446
{2 (a-b) (a-c) (b-c) (a+b+c), 2 a (a-b) b (a-c) (b-c) c}, 1482
{(-2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2), -2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)}, 48872
{(-2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2), -((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))}, 48873
{(-2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2), -1/2*((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))}, 48874
{(-2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c), 0}, 48875
{(-2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2), ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/2}, 48876
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), (a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)}, 48877
{(-2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c), (a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)}, 48878
{-(((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)), -2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)}, 48879
{-(((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)), -((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))}, 48880
{-(((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)), -1/2*((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))}, 48881
{-((a - b)*(a - c)*(b - c)*(a + b + c)), 0}, 48882
{-((a - b)*(a - c)*(b - c)*(a + b + c)), a*(a - b)*b*(a - c)*(b - c)*c}, 48883
{-(((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)), 2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)}, 48884
{-1/2*((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2), -1/2*((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))}, 48885
{-1/2*((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c), 0}, 48886
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/2}, 48887
{-1/2*((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c), ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/2}, 48888
{-1/2*((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2), (a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)}, 48889
{0, -((a - b)*(a - c)*(b - c)*(a^3 + b^3 + c^3))}, 48890
{((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(2*(a^2 + b^2 + c^2)), -((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))}, 48891
{((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(2*(a^2 + b^2 + c^2)), -1/2*((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))}, 48892
{((a - b)*(a - c)*(b - c)*(a + b + c))/2, 0}, 48883
{((a - b)*(a - c)*(b - c)*(a + b + c))/2, a*(a - b)*b*(a - c)*(b - c)*c}, 48894
{((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(2*(a^2 + b^2 + c^2)), (a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)}, 48895
{((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2), -2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)}, 48896
{(a - b)*(a - c)*(b - c)*(a + b + c), -(a*(a - b)*b*(a - c)*(b - c)*c)}, 48897
{((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2), -((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))}, 48898
{(a - b)*(a - c)*(b - c)*(a + b + c), (a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)}, 48899
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c), ((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c)^2)/(a + b + c)}, 48900
{((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2), (a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)}, 48901
{((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c), (a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)}, 48902
{(a - b)*(a - c)*(b - c)*(a + b + c), 2*a*(a - b)*b*(a - c)*(b - c)*c}, 48903
{((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2), 2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)}, 48904
{(2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2), -2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)}, 48905
{(2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2), -1/2*((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))}, 48906
{2*(a - b)*(a - c)*(b - c)*(a + b + c), 0}, 48907
{(2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c), 0}, 48908
{2*(a - b)*(a - c)*(b - c)*(a + b + c), a*(a - b)*b*(a - c)*(b - c)*c}, 48909
{(2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2), 2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)}, 48910


X(48872) = X(6)X(20)∩X(30)X(599)

Barycentrics    5*a^6 + 4*a^4*b^2 - 7*a^2*b^4 - 2*b^6 + 4*a^4*c^2 - 2*a^2*b^2*c^2 + 2*b^4*c^2 - 7*a^2*c^4 + 2*b^2*c^4 - 2*c^6 : :
X(48872) = 5 X[3] - 4 X[19130], 7 X[3] - 6 X[38317], 8 X[3] - 7 X[47355], 14 X[19130] - 15 X[38317], 32 X[19130] - 35 X[47355], 48 X[38317] - 49 X[47355], 4 X[4] - 5 X[3763], 2 X[4] - 3 X[31884], 5 X[3763] - 6 X[31884], 5 X[6] - 6 X[25406], 17 X[6] - 18 X[33748], 3 X[6] - 4 X[44882], 5 X[20] - 3 X[25406], 17 X[20] - 9 X[33748], 3 X[20] - 2 X[44882], 17 X[25406] - 15 X[33748], 9 X[25406] - 10 X[44882], 27 X[33748] - 34 X[44882], 3 X[599] - 4 X[1350], 9 X[599] - 8 X[1352], 3 X[599] - 2 X[36990], 21 X[599] - 16 X[39884], 5 X[599] - 4 X[47353], 3 X[1350] - 2 X[1352], 7 X[1350] - 4 X[39884], 5 X[1350] - 3 X[47353], 4 X[1352] - 3 X[36990], 7 X[1352] - 6 X[39884], 10 X[1352] - 9 X[47353], 7 X[36990] - 8 X[39884], 5 X[36990] - 6 X[47353], 20 X[39884] - 21 X[47353], 4 X[74] - 3 X[25330], 2 X[182] - 3 X[3534], 10 X[182] - 9 X[14848], 5 X[3534] - 3 X[14848], 3 X[376] - 2 X[5480], 4 X[376] - 3 X[47352], 8 X[5480] - 9 X[47352], 3 X[381] - 4 X[14810], 2 X[382] - 3 X[10516], 4 X[3098] - 3 X[10516], 8 X[1657] - X[6144], 5 X[1657] - X[39899], 5 X[6144] - 8 X[39899], X[14927] - 3 X[15683], 4 X[548] - 3 X[14561], 4 X[550] - 3 X[5085], 3 X[550] - 2 X[18583], and many others

X(48872) lies on these lines: {3, 7889}, {4, 3763}, {5, 43621}, {6, 20}, {30, 599}, {69, 5059}, {74, 25330}, {141, 3146}, {159, 5895}, {182, 3534}, {376, 5480}, {381, 14810}, {382, 3098}, {394, 20062}, {511, 1657}, {516, 3242}, {524, 14927}, {542, 15685}, {548, 14561}, {550, 5085}, {611, 4324}, {613, 4316}, {1351, 15681}, {1353, 11477}, {1370, 26958}, {1503, 3529}, {1885, 7716}, {2076, 44518}, {2777, 2930}, {2781, 15102}, {2916, 11414}, {3091, 21167}, {3416, 28164}, {3522, 3589}, {3543, 21358}, {3579, 38144}, {3619, 17578}, {3818, 5073}, {3830, 24206}, {3832, 34573}, {4265, 7580}, {4297, 38315}, {5017, 14532}, {5092, 15696}, {5096, 37022}, {5116, 44541}, {5189, 37638}, {5476, 15689}, {5621, 16111}, {5894, 36851}, {5921, 15533}, {5972, 9909}, {5999, 37637}, {6034, 38747}, {6776, 11001}, {6781, 40825}, {7354, 10387}, {7464, 15578}, {7500, 17811}, {7667, 17810}, {7706, 35243}, {7728, 44457}, {7778, 40236}, {8266, 31952}, {8567, 23300}, {8703, 38072}, {9053, 20070}, {9855, 39141}, {10168, 15695}, {10519, 33703}, {10541, 14853}, {10721, 33851}, {11179, 19710}, {11495, 38185}, {11645, 11898}, {11821, 16656}, {12007, 46333}, {12082, 15577}, {12088, 35228}, {12103, 21850}, {12294, 37196}, {12512, 38047}, {12584, 38790}, {13910, 42638}, {13972, 42637}, {15041, 32273}, {15066, 20063}, {15069, 17800}, {15682, 40330}, {15686, 20423}, {15690, 38064}, {15707, 25565}, {16010, 20127}, {17702, 25335}, {17845, 34146}, {18382, 40686}, {18440, 29323}, {18911, 33586}, {19149, 44831}, {20987, 39568}, {22676, 24256}, {23042, 32903}, {23699, 37751}, {25331, 32233}, {26543, 31295}, {30739, 31860}, {31489, 37182}, {31830, 33543}, {32271, 38723}, {33532, 40909}, {33923, 38136}, {34638, 47359}, {34726, 37480}, {35259, 37900}, {37899, 41424}, {38110, 44245}, {44246, 47581}, {44280, 47453}

X(48872) = midpoint of X(i) and X(j) for these {i,j}: {69, 5059}, {17800, 33878}
X(48872) = reflection of X(i) in X(j) for these {i,j}: {6, 20}, {382, 3098}, {3146, 141}, {5073, 3818}, {5895, 159}, {10721, 33851}, {11179, 19710}, {11477, 46264}, {15069, 33878}, {16010, 20127}, {20423, 15686}, {21850, 12103}, {31670, 550}, {36851, 5894}, {36990, 1350}, {38790, 12584}, {40909, 33532}, {43273, 15681}, {43621, 5}, {44526, 14532}, {46264, 15704}, {47359, 34638}
X(48872) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 31884, 3763}, {20, 13568, 16936}, {382, 3098, 10516}, {550, 31670, 5085}, {1350, 36990, 599}


X(48873) = X(6)X(550)∩X(30)X(599)

Barycentrics    3*a^6 + 3*a^4*b^2 - 5*a^2*b^4 - b^6 + 3*a^4*c^2 - 2*a^2*b^2*c^2 + b^4*c^2 - 5*a^2*c^4 + b^2*c^4 - c^6 : :
X(48873) = 3 X[2] - 4 X[14810], 5 X[3] - 4 X[3589], 3 X[3] - 2 X[5480], 4 X[3] - 3 X[14561], 6 X[3589] - 5 X[5480], 16 X[3589] - 15 X[14561], 8 X[3589] - 5 X[31670], 8 X[5480] - 9 X[14561], 4 X[5480] - 3 X[31670], 3 X[14561] - 2 X[31670], 5 X[4] - 7 X[3619], 3 X[4] - 4 X[24206], 10 X[3098] - 7 X[3619], 3 X[3098] - 2 X[24206], 4 X[3098] - X[43621], 21 X[3619] - 20 X[24206], 14 X[3619] - 5 X[43621], 8 X[24206] - 3 X[43621], 2 X[5] - 3 X[31884], 5 X[20] - X[193], 3 X[20] - X[6776], 3 X[193] - 5 X[6776], 2 X[193] - 5 X[46264], 2 X[6776] - 3 X[46264], 3 X[599] - 5 X[1350], 6 X[599] - 5 X[1352], 9 X[599] - 5 X[36990], 3 X[599] - 2 X[39884], 7 X[599] - 5 X[47353], 3 X[1350] - X[36990], 5 X[1350] - 2 X[39884], 7 X[1350] - 3 X[47353], 3 X[1352] - 2 X[36990], 5 X[1352] - 4 X[39884], 7 X[1352] - 6 X[47353], 5 X[36990] - 6 X[39884], 7 X[36990] - 9 X[47353], 14 X[39884] - 15 X[47353], 2 X[182] - 3 X[376], 4 X[182] - 3 X[20423], 3 X[182] - 4 X[33751], 9 X[376] - 8 X[33751], 9 X[20423] - 16 X[33751], 3 X[11001] - X[14927], 4 X[546] - 5 X[3763], 4 X[548] - 3 X[5085], 3 X[5085] - 2 X[21850], 2 X[576] - 5 X[17538], 2 X[576] - 3 X[25406], and many others

X(48873) lies on these lines: {2, 14488}, {3, 3589}, {4, 3096}, {5, 31884}, {6, 550}, {20, 185}, {30, 599}, {69, 3529}, {125, 1370}, {141, 382}, {146, 12584}, {159, 5878}, {182, 376}, {524, 15681}, {542, 11001}, {546, 3763}, {548, 5085}, {576, 17538}, {597, 15688}, {611, 15338}, {613, 15326}, {631, 19130}, {698, 14023}, {1351, 3534}, {1353, 15686}, {1469, 4302}, {1503, 1657}, {1656, 21167}, {2076, 3767}, {2549, 5017}, {2777, 38885}, {2781, 12121}, {2810, 38765}, {2854, 20127}, {2937, 35228}, {2979, 20062}, {3056, 4299}, {3066, 43957}, {3094, 7737}, {3146, 3818}, {3242, 28174}, {3357, 36851}, {3416, 28160}, {3522, 5092}, {3523, 38317}, {3528, 3618}, {3530, 38136}, {3543, 40330}, {3564, 15704}, {3579, 38116}, {3620, 18553}, {3627, 10516}, {3819, 6995}, {3851, 34573}, {3917, 7500}, {4846, 33532}, {5026, 38731}, {5028, 6781}, {5039, 7738}, {5050, 15696}, {5059, 29323}, {5068, 42786}, {5104, 43619}, {5286, 41413}, {5476, 10304}, {5596, 34785}, {5800, 47038}, {5921, 11645}, {5925, 9924}, {5965, 39874}, {5969, 38741}, {5999, 17004}, {6249, 16045}, {6403, 35481}, {6449, 13910}, {6450, 13972}, {6593, 38723}, {7391, 43653}, {7470, 35424}, {7487, 13348}, {7519, 7998}, {7667, 33586}, {7716, 13488}, {7728, 33851}, {7739, 12212}, {7791, 12122}, {7803, 35422}, {7863, 30270}, {8550, 44456}, {8703, 18583}, {9024, 38753}, {9306, 34608}, {9833, 10625}, {9909, 15448}, {9970, 16163}, {10168, 19708}, {10387, 18990}, {10483, 12588}, {10691, 17810}, {10990, 46349}, {11178, 15682}, {11477, 12103}, {11579, 16111}, {11821, 44870}, {12082, 32111}, {12083, 15577}, {12085, 37485}, {12100, 38072}, {12177, 38738}, {12294, 18533}, {12605, 15812}, {13201, 14683}, {13624, 38035}, {14216, 34778}, {14269, 20582}, {14677, 16010}, {14688, 38798}, {14848, 15695}, {14907, 18906}, {14912, 37517}, {14982, 34584}, {14994, 32815}, {15035, 32271}, {15041, 25328}, {15066, 37900}, {15107, 16063}, {15311, 39879}, {15462, 38726}, {15516, 15697}, {15578, 18859}, {15644, 31305}, {15646, 47453}, {15684, 47354}, {15685, 48662}, {15687, 21358}, {15700, 48310}, {15709, 25565}, {15759, 38079}, {16051, 32223}, {17712, 18951}, {17800, 18440}, {18931, 46730}, {19128, 35503}, {19149, 37483}, {20063, 33884}, {20190, 33750}, {21243, 33522}, {21312, 37488}, {21735, 25555}, {22330, 33748}, {22486, 33207}, {22676, 31958}, {24248, 29032}, {28202, 47358}, {30552, 44470}, {31152, 32269}, {31663, 38047}, {32522, 44423}, {33265, 39141}, {33703, 40107}, {33923, 38110}, {34200, 47352}, {34417, 46336}, {34511, 47618}, {34815, 42353}, {34938, 46728}, {35259, 37899}, {35268, 37645}, {35491, 39588}, {36757, 42434}, {36758, 42433}, {37182, 43461}, {37638, 46517}, {37910, 41424}, {41716, 44831}, {44267, 47450}, {44280, 47581}, {45823, 46027}

X(48873) = midpoint of X(i) and X(j) for these {i,j}: {69, 3529}, {1657, 33878}, {5925, 9924}, {17800, 18440}
X(48873) = reflection of X(i) in X(j) for these {i,j}: {4, 3098}, {6, 550}, {146, 12584}, {382, 141}, {1351, 44882}, {1352, 1350}, {3146, 3818}, {4846, 33532}, {5596, 34785}, {5878, 159}, {7728, 33851}, {9970, 16163}, {11179, 3534}, {11579, 16111}, {12177, 38738}, {14216, 34778}, {15682, 11178}, {15684, 47354}, {16010, 14677}, {20423, 376}, {21850, 548}, {31670, 3}, {31958, 22676}, {36851, 3357}, {43273, 15686}, {43621, 4}, {44456, 8550}, {46264, 20}
X(48873) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 31670, 14561}, {548, 21850, 5085}, {599, 39884, 1352}, {1351, 3534, 44882}, {1351, 44882, 11179}, {2979, 20062, 31383}, {3146, 10519, 3818}, {3522, 14853, 5092}, {3528, 3618, 17508}, {3530, 38136, 47355}, {33522, 44442, 21243}, {36993, 36995, 36998}


X(48874) = X(6)X(548)∩X(30)X(599)

Barycentrics    4*a^6 + 5*a^4*b^2 - 8*a^2*b^4 - b^6 + 5*a^4*c^2 - 4*a^2*b^2*c^2 + b^4*c^2 - 8*a^2*c^4 + b^2*c^4 - c^6 : :
X(48874) = 7 X[3] - 5 X[3618], 5 X[3] - 3 X[14853], 3 X[3] - 2 X[18583], 4 X[3] - 3 X[38110], 25 X[3618] - 21 X[14853], 15 X[3618] - 14 X[18583], 10 X[3618] - 7 X[21850], 20 X[3618] - 21 X[38110], 9 X[14853] - 10 X[18583], 6 X[14853] - 5 X[21850], 4 X[14853] - 5 X[38110], 4 X[18583] - 3 X[21850], 8 X[18583] - 9 X[38110], 2 X[21850] - 3 X[38110], 7 X[5] - 8 X[34573], 13 X[5] - 14 X[42786], 7 X[3098] - 4 X[34573], 13 X[3098] - 7 X[42786], 52 X[34573] - 49 X[42786], 7 X[20] + X[20080], 5 X[20] - X[39874], X[20080] - 7 X[33878], 5 X[20080] + 7 X[39874], 5 X[33878] + X[39874], 3 X[599] - 7 X[1350], 9 X[599] - 7 X[1352], 15 X[599] - 7 X[36990], 12 X[599] - 7 X[39884], 11 X[599] - 7 X[47353], 3 X[1350] - X[1352], 5 X[1350] - X[36990], 4 X[1350] - X[39884], 11 X[1350] - 3 X[47353], 5 X[1352] - 3 X[36990], 4 X[1352] - 3 X[39884], 11 X[1352] - 9 X[47353], 4 X[36990] - 5 X[39884], 11 X[36990] - 15 X[47353], 11 X[39884] - 12 X[47353], 3 X[69] - X[48662], 3 X[1657] + X[48662], 2 X[140] - 3 X[31884], 4 X[140] - 3 X[38136], X[31670] - 3 X[31884], 2 X[31670] - 3 X[38136], 2 X[182] - 3 X[8703], X[193] - 5 X[17538], 3 X[376] - X[1351], 7 X[376] - 3 X[5032], and many others

X(48874) lies on these lines: {3, 3618}, {5, 3098}, {6, 548}, {20, 3564}, {30, 599}, {69, 1657}, {140, 31670}, {141, 3627}, {182, 8703}, {193, 17538}, {376, 1351}, {382, 10519}, {511, 550}, {524, 15686}, {542, 19710}, {549, 5480}, {597, 45759}, {632, 19130}, {895, 38788}, {1176, 37495}, {1368, 32269}, {1503, 15704}, {1992, 15689}, {2781, 34153}, {2854, 14677}, {3094, 18907}, {3242, 28212}, {3416, 28186}, {3522, 5050}, {3528, 12017}, {3529, 18440}, {3530, 14561}, {3534, 6776}, {3589, 15712}, {3619, 3843}, {3620, 33703}, {3763, 3850}, {3830, 40330}, {3845, 24206}, {3853, 10516}, {4316, 39897}, {4324, 39873}, {5017, 15048}, {5085, 33923}, {5092, 46853}, {5097, 33751}, {5102, 41981}, {5181, 34584}, {5447, 7715}, {5476, 17504}, {5921, 11001}, {5972, 10154}, {6101, 34146}, {6995, 44833}, {7667, 18911}, {7734, 17810}, {7998, 10301}, {8598, 39141}, {9924, 20427}, {9967, 36987}, {10168, 15711}, {10323, 31802}, {10691, 33586}, {10752, 38723}, {10753, 38731}, {10754, 38742}, {10755, 38754}, {10756, 38766}, {10757, 38778}, {10765, 38798}, {11160, 46333}, {11178, 33699}, {11179, 15690}, {11180, 15685}, {11477, 44245}, {11645, 44903}, {11812, 38072}, {11898, 14927}, {12084, 37485}, {12100, 38079}, {12103, 34380}, {12108, 47355}, {12294, 37458}, {13340, 41716}, {13391, 19161}, {13624, 38040}, {14848, 19708}, {14869, 38317}, {14891, 47352}, {14893, 21358}, {14984, 16111}, {15066, 37899}, {15107, 30739}, {15462, 48368}, {15578, 37950}, {15585, 22802}, {15646, 47581}, {15684, 21356}, {15691, 43273}, {15696, 25406}, {15759, 38064}, {16063, 47582}, {18438, 44240}, {18560, 41584}, {19139, 37483}, {20423, 34200}, {20582, 23046}, {31804, 37484}, {32218, 43893}, {32220, 44246}, {33522, 34609}, {33884, 37900}, {35259, 37910}, {35404, 47354}, {35481, 39871}, {37477, 44261}, {37638, 47315}, {41464, 43599}, {43576, 44285}, {44267, 47569}

X(48874) = midpoint of X(i) and X(j) for these {i,j}: {20, 33878}, {69, 1657}, {3529, 18440}, {9924, 20427}, {11180, 15685}, {11898, 14927}
X(48874) = reflection of X(i) in X(j) for these {i,j}: {5, 3098}, {6, 548}, {382, 18358}, {1353, 44882}, {3627, 141}, {5097, 33751}, {5480, 14810}, {11179, 15690}, {20423, 34200}, {21850, 3}, {22802, 15585}, {31670, 140}, {33699, 11178}, {35404, 47354}, {38136, 31884}, {43273, 15691}, {43621, 3853}, {44267, 47569}, {46264, 12103}
X(48874) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 21850, 38110}, {140, 31670, 38136}, {382, 10519, 18358}, {550, 1353, 44882}, {5480, 14810, 549}, {10516, 43621, 3853}, {11898, 15681, 14927}, {15696, 44456, 25406}, {19130, 21167, 632}, {31670, 31884, 140}


X(48875) = X(3)X(6)∩X(4)X(1654)

Barycentrics    a^2*(a^3*b + 2*a^2*b^2 - a*b^3 - 2*b^4 + a^3*c + a^2*b*c - a*b^2*c - b^3*c + 2*a^2*c^2 - a*b*c^2 - a*c^3 - b*c^3 - 2*c^4) : :
X(48875) = 3 X[3] - 2 X[991], 3 X[573] - X[991], 5 X[1656] - 4 X[24220]

X(48875) lies on these lines: {3, 6}, {4, 1654}, {5, 5224}, {25, 22139}, {30, 17346}, {40, 1757}, {51, 16058}, {69, 36674}, {75, 29369}, {103, 28907}, {140, 17381}, {198, 17976}, {199, 1993}, {220, 41323}, {355, 382}, {381, 17251}, {440, 41588}, {517, 984}, {940, 19516}, {966, 36659}, {1011, 3060}, {1352, 36716}, {1482, 29311}, {1656, 17327}, {1742, 3579}, {1764, 5400}, {2183, 3781}, {2323, 23095}, {2807, 38572}, {2979, 4191}, {3056, 37590}, {3295, 21746}, {3664, 5708}, {3819, 16409}, {3882, 10477}, {3917, 16059}, {3927, 4416}, {5232, 36671}, {5480, 36530}, {5640, 16373}, {5650, 16421}, {5725, 36279}, {6244, 20670}, {6767, 39543}, {9018, 45729}, {9047, 15624}, {9535, 37365}, {12699, 45305}, {13632, 20423}, {13723, 15988}, {16466, 23659}, {17238, 36651}, {17271, 36729}, {17330, 36730}, {17349, 36697}, {17362, 29235}, {19549, 34466}, {20760, 26893}, {20834, 33586}, {21363, 37521}, {21969, 22080}, {22076, 28383}, {22161, 37581}, {25898, 33745}, {29331, 30273}, {31670, 36707}

X(48875) = reflection of X(i) in X(j) for these {i,j}: {3, 573}, {1482, 31394}, {1742, 3579}, {10446, 5}, {12699, 45305}, {36730, 17330}
X(48875) = crosssum of X(11) and X(4782)
X(48875) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {581, 35203, 3}, {2245, 37516, 37507}, {3098, 13329, 3}, {4259, 4271, 37502}, {11477, 37499, 37474}, {37474, 37499, 3}


X(48876) = X(3)X(69)∩X(30)X(599)

Barycentrics    (a^2 - b^2 - c^2)*(3*a^2*b^2 - b^4 + 3*a^2*c^2 + 2*b^2*c^2 - c^4) : :
X(48876) = 5 X[2] - 3 X[14848], 4 X[2] - 3 X[38079], 5 X[1351] - 9 X[14848], 4 X[1351] - 9 X[38079], 9 X[14848] - 10 X[18583], 4 X[14848] - 5 X[38079], 8 X[18583] - 9 X[38079], 3 X[3] - X[6776], X[3] - 3 X[10519], 3 X[3] + X[11898], 5 X[3] - 3 X[25406], 11 X[3] - 9 X[33750], 5 X[3] - X[39899], 3 X[69] + X[6776], X[69] + 3 X[10519], 3 X[69] - X[11898], 5 X[69] + 3 X[25406], 11 X[69] + 9 X[33750], 5 X[69] + X[39899], X[6776] - 9 X[10519], 5 X[6776] - 9 X[25406], 11 X[6776] - 27 X[33750], 5 X[6776] - 3 X[39899], 9 X[10519] + X[11898], 5 X[10519] - X[25406], 11 X[10519] - 3 X[33750], 15 X[10519] - X[39899], 5 X[11898] + 9 X[25406], 11 X[11898] + 27 X[33750], 5 X[11898] + 3 X[39899], 11 X[25406] - 15 X[33750], 3 X[25406] - X[39899], 45 X[33750] - 11 X[39899], X[4] - 5 X[3620], 5 X[3620] - 2 X[18358], 5 X[3620] + X[33878], 2 X[18358] + X[33878], 3 X[5] - 2 X[5480], 5 X[5] - 4 X[19130], 3 X[5] - 4 X[24206], 4 X[5] - 3 X[38136], X[5] - 4 X[40107], 3 X[141] - X[5480], 5 X[141] - 2 X[19130], 4 X[141] - X[21850], 3 X[141] - 2 X[24206], 8 X[141] - 3 X[38136], 5 X[5480] - 6 X[19130], 4 X[5480] - 3 X[21850], 8 X[5480] - 9 X[38136], and many others

X(48876) lies on these lines: {2, 1351}, {3, 69}, {4, 3620}, {5, 141}, {6, 140}, {10, 38165}, {20, 18440}, {26, 13562}, {30, 599}, {35, 39873}, {36, 39897}, {49, 1176}, {66, 34787}, {67, 32423}, {68, 15812}, {98, 37671}, {110, 44210}, {125, 343}, {142, 38164}, {155, 16197}, {159, 31831}, {182, 524}, {193, 631}, {230, 5028}, {235, 11444}, {323, 7495}, {325, 22712}, {376, 5921}, {378, 39871}, {381, 21356}, {385, 37450}, {394, 6676}, {399, 32247}, {427, 2979}, {468, 15066}, {495, 1469}, {496, 3056}, {518, 5690}, {526, 44813}, {542, 8703}, {546, 10516}, {547, 20423}, {548, 15069}, {550, 1503}, {575, 3629}, {576, 632}, {590, 35840}, {597, 5097}, {613, 15325}, {615, 35841}, {616, 44250}, {732, 32448}, {858, 33884}, {895, 15061}, {952, 3416}, {1078, 2456}, {1092, 19131}, {1125, 38040}, {1147, 19126}, {1154, 19161}, {1160, 37342}, {1161, 37343}, {1211, 37521}, {1385, 5847}, {1386, 38028}, {1483, 5846}, {1484, 9024}, {1511, 41729}, {1513, 3314}, {1570, 7749}, {1595, 1843}, {1596, 5891}, {1598, 11487}, {1654, 21554}, {1656, 3619}, {1799, 42065}, {1899, 10691}, {1906, 15056}, {1992, 5054}, {1993, 7499}, {1995, 47582}, {2080, 8369}, {2782, 14994}, {2794, 7848}, {2854, 10264}, {2895, 19649}, {2896, 35456}, {3054, 5107}, {3060, 37439}, {3094, 15048}, {3095, 8362}, {3147, 19118}, {3167, 7494}, {3242, 5844}, {3292, 13394}, {3313, 10627}, {3519, 41435}, {3522, 39874}, {3523, 7906}, {3524, 11160}, {3525, 11482}, {3526, 3618}, {3530, 5085}, {3534, 11180}, {3541, 12167}, {3546, 18919}, {3549, 28419}, {3580, 7998}, {3627, 3818}, {3628, 3763}, {3630, 5092}, {3634, 38167}, {3751, 26446}, {3781, 26932}, {3784, 26942}, {3815, 5052}, {3819, 13567}, {3844, 38042}, {3845, 11178}, {4220, 32863}, {4259, 37438}, {4265, 7508}, {4299, 39891}, {4302, 39892}, {4851, 46475}, {4966, 31394}, {5017, 18907}, {5032, 15702}, {5095, 38793}, {5102, 16239}, {5157, 32046}, {5159, 37638}, {5171, 7789}, {5181, 5663}, {5182, 38750}, {5188, 7794}, {5204, 39901}, {5217, 39900}, {5227, 24467}, {5408, 8964}, {5447, 11574}, {5476, 15699}, {5477, 38748}, {5562, 6823}, {5611, 37340}, {5615, 37341}, {5622, 15089}, {5650, 37648}, {5651, 32269}, {5739, 16434}, {5762, 47595}, {5848, 33814}, {5876, 34146}, {6036, 13468}, {6090, 7493}, {6144, 12108}, {6147, 24471}, {6210, 33087}, {6221, 39876}, {6243, 7405}, {6247, 13348}, {6329, 15520}, {6398, 39875}, {6467, 11577}, {6515, 7484}, {6636, 13171}, {6639, 28408}, {6642, 37491}, {6644, 37488}, {6656, 12251}, {6661, 10788}, {6666, 38166}, {6667, 38168}, {6668, 38169}, {6677, 17811}, {6684, 34379}, {6697, 34826}, {6755, 40684}, {6756, 37486}, {6759, 15585}, {6771, 33458}, {6774, 33459}, {6883, 37492}, {6907, 10477}, {6998, 17300}, {7289, 26921}, {7380, 17238}, {7383, 12160}, {7386, 40911}, {7395, 13142}, {7399, 11412}, {7400, 12164}, {7403, 37484}, {7413, 37653}, {7483, 15988}, {7485, 11245}, {7492, 46818}, {7496, 37779}, {7502, 15577}, {7512, 46442}, {7516, 13292}, {7542, 20806}, {7568, 44480}, {7575, 47569}, {7616, 17006}, {7667, 11442}, {7690, 48742}, {7692, 48743}, {7750, 35383}, {7761, 44395}, {7763, 35429}, {7771, 44369}, {7778, 10011}, {7779, 37455}, {7788, 9744}, {7801, 8722}, {7810, 18860}, {7813, 21163}, {7854, 30270}, {7855, 37479}, {7868, 9753}, {7934, 39663}, {7999, 26156}, {8229, 31017}, {8353, 13172}, {8548, 16196}, {8584, 10168}, {8728, 26543}, {8780, 10565}, {9019, 41714}, {9306, 10154}, {9825, 17834}, {9863, 44251}, {9909, 14826}, {9924, 14216}, {9970, 10272}, {10104, 13355}, {10109, 38072}, {10124, 47352}, {10128, 17810}, {10256, 39764}, {10257, 41614}, {10282, 34774}, {10301, 15107}, {10387, 15172}, {10616, 16773}, {10617, 16772}, {10752, 14643}, {10753, 15561}, {10754, 38224}, {10758, 38764}, {10759, 38752}, {10764, 38776}, {10983, 16043}, {11008, 15720}, {11061, 32609}, {11171, 32451}, {11179, 12100}, {11188, 13340}, {11272, 35439}, {11291, 12314}, {11292, 12313}, {11331, 41371}, {11433, 16419}, {11459, 32111}, {11585, 18438}, {11645, 15686}, {11694, 34319}, {11812, 15534}, {12054, 39872}, {12121, 44249}, {12233, 21851}, {12244, 44458}, {12317, 32254}, {12362, 18396}, {12383, 32306}, {12588, 18990}, {12589, 15171}, {12702, 39898}, {13391, 29959}, {13624, 39870}, {13860, 16990}, {13910, 44502}, {13972, 44501}, {14019, 26530}, {14389, 23061}, {14913, 15644}, {14929, 35387}, {15035, 32244}, {15051, 32234}, {15068, 16618}, {15118, 34128}, {15246, 45968}, {15462, 34477}, {15526, 42353}, {15578, 34152}, {15583, 20299}, {15687, 19924}, {15704, 29012}, {15760, 23039}, {15980, 18906}, {15983, 19514}, {16003, 32114}, {16163, 32275}, {16238, 44492}, {16252, 34779}, {16619, 47449}, {16659, 41464}, {17004, 40336}, {17508, 44682}, {17702, 32257}, {17710, 34115}, {17714, 20987}, {17792, 31419}, {18374, 44213}, {18481, 39885}, {18553, 29317}, {18911, 21766}, {18935, 26944}, {19116, 45575}, {19117, 45574}, {19125, 47525}, {19127, 40111}, {19128, 46444}, {19145, 35255}, {19146, 35256}, {19154, 34351}, {19659, 38597}, {19660, 38596}, {19710, 41152}, {20113, 32191}, {20127, 41737}, {20300, 37938}, {20368, 33084}, {20425, 37352}, {20426, 37351}, {20576, 33185}, {21230, 23300}, {21970, 40132}, {22251, 25329}, {22861, 42117}, {22907, 42118}, {23046, 25561}, {24390, 25304}, {25338, 47450}, {26869, 46336}, {27377, 37124}, {30258, 42313}, {31837, 34381}, {32110, 44273}, {32134, 42534}, {32220, 44214}, {32272, 38723}, {32455, 39561}, {32782, 37360}, {32808, 45510}, {32809, 45511}, {33971, 44134}, {34200, 43273}, {34417, 35283}, {34540, 37463}, {34541, 37464}, {34573, 37517}, {35238, 39877}, {35239, 39883}, {35241, 39886}, {35242, 39878}, {35243, 39879}, {35244, 39880}, {35245, 39881}, {35246, 39887}, {35247, 39888}, {35248, 39882}, {35249, 39889}, {35250, 39890}, {35251, 39902}, {35252, 39903}, {35259, 37897}, {35297, 39141}, {35424, 44224}, {35458, 37334}, {35937, 40867}, {36696, 38806}, {37174, 43999}, {37345, 47618}, {37458, 37478}, {37477, 41721}, {37644, 40916}, {41198, 47613}, {41199, 47612}, {41398, 44280}, {41424, 47630}, {41462, 41724}, {44234, 47453}, {44266, 47556}, {44282, 47581}, {44324, 44439}, {44452, 47457}, {46981, 47565}, {47090, 47278}

X(48876) = midpoint of X(i) and X(j) for these {i,j}: {3, 69}, {4, 33878}, {20, 18440}, {66, 34787}, {399, 32247}, {1350, 1352}, {1843, 10625}, {3098, 34507}, {3534, 11180}, {3630, 8550}, {5562, 37511}, {6776, 11898}, {9924, 14216}, {11179, 15533}, {11188, 13340}, {11411, 19588}, {12317, 32254}, {12383, 32306}, {12702, 39898}, {14913, 15644}, {14927, 48662}, {15069, 46264}, {16003, 32114}, {16163, 32275}, {18481, 39885}, {20127, 41737}, {35241, 39886}, {37477, 41721}, {46981, 47565}
X(48876) = reflection of X(i) in X(j) for these {i,j}: {4, 18358}, {5, 141}, {6, 140}, {141, 40107}, {550, 3098}, {576, 3589}, {1351, 18583}, {1353, 182}, {3313, 10627}, {3627, 3818}, {3629, 575}, {3845, 11178}, {5446, 9822}, {5476, 20582}, {5480, 24206}, {6759, 15585}, {7575, 47569}, {8550, 5092}, {8584, 10168}, {9970, 10272}, {10263, 9969}, {11179, 12100}, {11574, 5447}, {15074, 11574}, {15583, 20299}, {15687, 47354}, {16619, 47449}, {20423, 547}, {21850, 5}, {31670, 546}, {34153, 33851}, {34319, 11694}, {34507, 3631}, {34774, 10282}, {34779, 16252}, {35389, 20576}, {35439, 11272}, {39870, 13624}, {39884, 1352}, {43273, 34200}, {44266, 47556}, {44882, 14810}, {46264, 548}
X(48876) = complement of X(1351)
X(48876) = anticomplement of X(18583)
X(48876) = complement of the isogonal conjugate of X(7612)
X(48876) = isotomic conjugate of the polar conjugate of X(3815)
X(48876) = X(i)-complementary conjugate of X(j) for these (i,j): {7612, 10}, {42298, 20305}, {47735, 226}
X(48876) = X(19)-isoconjugate of X(30535)
X(48876) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 30535), (3815, 458), (15819, 4)
X(48876) = crosspoint of X(69) and X(42313)
X(48876) = crosssum of X(25) and X(10311)
X(48876) = crossdifference of every pair of points on line {2489, 3050}
X(48876) = barycentric product X(i)*X(j) for these {i,j}: {69, 3815}, {72, 16740}, {305, 5052}, {15819, 42313}
X(48876) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 30535}, {3815, 4}, {5052, 25}, {15819, 458}, {16740, 286}
X(48876) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1351, 18583}, {3, 11898, 6776}, {3, 39899, 25406}, {5, 21850, 38136}, {6, 140, 38110}, {69, 6393, 3933}, {69, 6776, 11898}, {69, 10519, 3}, {141, 5480, 24206}, {193, 631, 5050}, {325, 22712, 37451}, {343, 3917, 1368}, {394, 43653, 6676}, {549, 1353, 182}, {599, 1350, 1352}, {599, 16789, 8263}, {1656, 44456, 14853}, {2979, 37636, 427}, {3314, 6194, 1513}, {3523, 14912, 12017}, {3523, 20080, 14912}, {3526, 5093, 3618}, {3534, 48662, 14927}, {3580, 7998, 30739}, {3619, 14853, 1656}, {3620, 33878, 18358}, {3630, 21167, 8550}, {3763, 11477, 14561}, {3763, 14561, 3628}, {5092, 21167, 15712}, {5418, 5420, 44535}, {5476, 20582, 15699}, {5480, 24206, 5}, {5650, 41586, 37648}, {5651, 32269, 44212}, {6515, 7484, 45298}, {7399, 11412, 31802}, {7485, 45794, 11245}, {8550, 21167, 5092}, {10516, 31670, 546}, {11180, 14927, 48662}, {14810, 44882, 8703}, {14826, 33522, 9909}, {15069, 31884, 46264}, {18911, 21766, 43957}, {20423, 21358, 547}, {31884, 46264, 548}


X(48877) = X(4)X(69)∩X(8)X(30)

Barycentrics    a^6*b - a^5*b^2 - 2*a^4*b^3 + 2*a^3*b^4 + a^2*b^5 - a*b^6 + a^6*c + 2*a^5*b*c - a^4*b^2*c + a^2*b^4*c - 2*a*b^5*c - b^6*c - a^5*c^2 - a^4*b*c^2 + 2*a^2*b^3*c^2 + a*b^4*c^2 - b^5*c^2 - 2*a^4*c^3 + 2*a^2*b^2*c^3 + 4*a*b^3*c^3 + 2*b^4*c^3 + 2*a^3*c^4 + a^2*b*c^4 + a*b^2*c^4 + 2*b^3*c^4 + a^2*c^5 - 2*a*b*c^5 - b^2*c^5 - a*c^6 - b*c^6 : :
X(48877) = 3 X[376] - 4 X[35203], 5 X[3616] - 4 X[5453], 3 X[5657] - 2 X[37425], 5 X[5818] - 4 X[15973], 4 X[8143] - 3 X[27804], 4 X[10035] - 5 X[31272], 9 X[27811] - 8 X[32167]

X(48877) lies on these lines: {2, 500}, {3, 5278}, {4, 69}, {5, 18139}, {8, 30}, {10, 35338}, {321, 40263}, {333, 3651}, {355, 5300}, {376, 9534}, {582, 19742}, {938, 15936}, {944, 9840}, {1043, 21669}, {1071, 15970}, {1150, 6985}, {1943, 6198}, {2771, 17164}, {2894, 37781}, {2895, 37433}, {3434, 13754}, {3579, 4651}, {3616, 5453}, {3652, 4427}, {3673, 15982}, {3702, 31937}, {3936, 6841}, {4359, 13369}, {4417, 6845}, {4552, 35194}, {5015, 15983}, {5080, 13391}, {5082, 6000}, {5086, 34800}, {5271, 41854}, {5495, 27529}, {5657, 37425}, {5739, 6851}, {5741, 37356}, {5810, 36496}, {5818, 15973}, {6327, 18517}, {6358, 41562}, {6896, 18141}, {6899, 14555}, {6990, 18134}, {8143, 27804}, {8728, 15937}, {9799, 28638}, {9955, 29824}, {9958, 10327}, {10035, 31272}, {11001, 48850}, {12649, 13408}, {12699, 17135}, {14206, 31938}, {16159, 17491}, {17751, 18480}, {20108, 37732}, {22798, 27558}, {27811, 32167}, {37151, 37474}, {37447, 41014}, {41492, 41804}

X(48877) = reflection of X(i) in X(j) for these {i,j}: {944, 9840}, {15971, 355}
X(48877) = anticomplement of X(500)
X(48877) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {79, 2894}, {943, 3648}, {2982, 41808}


X(48878) = X(4)X(69)∩X(8)X(144)

Barycentrics    a^5*b - 2*a^4*b^2 + 2*a^2*b^4 - a*b^5 + a^5*c + a^4*b*c - a*b^4*c - b^5*c - 2*a^4*c^2 + 2*a*b^3*c^2 + 2*a*b^2*c^3 + 2*b^3*c^3 + 2*a^2*c^4 - a*b*c^4 - a*c^5 - b*c^5 : :
X(48878) = 5 X[3091] - 4 X[24220]

X(48878) lies on these lines: {1, 26125}, {2, 991}, {3, 17277}, {4, 69}, {5, 17234}, {6, 13727}, {8, 144}, {10, 1742}, {20, 391}, {24, 28712}, {27, 33586}, {30, 17346}, {33, 1943}, {51, 6817}, {75, 971}, {85, 5728}, {141, 36652}, {152, 2807}, {182, 36489}, {190, 5779}, {192, 29016}, {193, 3332}, {239, 990}, {312, 5927}, {319, 31672}, {320, 5805}, {333, 7580}, {341, 9947}, {344, 5817}, {355, 15310}, {381, 17297}, {388, 21746}, {394, 14004}, {461, 37669}, {515, 3883}, {938, 3664}, {944, 31394}, {946, 4684}, {962, 29311}, {966, 36706}, {984, 28850}, {1056, 39543}, {1150, 36002}, {1160, 36713}, {1161, 36710}, {1350, 6996}, {1441, 10394}, {1444, 36012}, {1699, 10453}, {1709, 32932}, {1730, 37109}, {1750, 11679}, {1754, 37652}, {2801, 24349}, {3091, 4869}, {3098, 36697}, {3212, 32118}, {3560, 28980}, {3619, 36682}, {3661, 12618}, {3692, 7283}, {3696, 15726}, {3819, 6822}, {3882, 33536}, {3886, 11372}, {3917, 6818}, {3923, 9355}, {3936, 10883}, {4229, 37499}, {4300, 19853}, {4359, 11220}, {4384, 5732}, {4417, 8727}, {4648, 36660}, {4651, 9778}, {4673, 9856}, {4966, 42356}, {5092, 36705}, {5233, 37374}, {5278, 7411}, {5480, 7377}, {5695, 16112}, {5733, 20090}, {5739, 10431}, {5762, 17347}, {5816, 7379}, {5881, 29698}, {5943, 6821}, {6837, 25650}, {6908, 25446}, {6998, 37474}, {7988, 30947}, {8226, 18134}, {9732, 36708}, {9733, 36715}, {9779, 29824}, {9812, 17135}, {10157, 18743}, {10164, 26038}, {10167, 19804}, {10171, 26103}, {10519, 36670}, {10861, 20905}, {10884, 16817}, {12245, 29309}, {12520, 16824}, {12649, 17364}, {12669, 20880}, {13329, 17349}, {14810, 36699}, {14829, 19541}, {15064, 27538}, {17263, 38108}, {17271, 36721}, {17298, 38150}, {17335, 31658}, {17361, 18482}, {17378, 36722}, {19130, 36651}, {20430, 29331}, {24199, 43177}, {24206, 36473}, {25252, 44694}, {30326, 30568}, {30807, 41228}, {36996, 42697}

X(48878) = reflection of X(i) in X(j) for these {i,j}: {1, 45305}, {20, 573}, {944, 31394}, {1742, 10}, {10446, 4}, {17378, 36722}
X(48878) = anticomplement of X(991)


X(48879) = X(20)X(182)∩X(30)X(141)

Barycentrics    5*a^6 + 3*a^4*b^2 - 6*a^2*b^4 - 2*b^6 + 3*a^4*c^2 - 2*a^2*b^2*c^2 + 2*b^4*c^2 - 6*a^2*c^4 + 2*b^2*c^4 - 2*c^6 : :
X(48879) = X[6] - 3 X[15681], 7 X[20] - 3 X[14853], 3 X[20] - X[31670], 7 X[182] - 6 X[14853], 3 X[182] - 2 X[31670], 9 X[14853] - 7 X[31670], 4 X[141] - 5 X[3098], 6 X[141] - 5 X[3818], 16 X[141] - 15 X[11178], 11 X[141] - 10 X[18358], 17 X[141] - 15 X[47354], 3 X[3098] - 2 X[3818], 4 X[3098] - 3 X[11178], 11 X[3098] - 8 X[18358], 17 X[3098] - 12 X[47354], 8 X[3818] - 9 X[11178], 11 X[3818] - 12 X[18358], 17 X[3818] - 18 X[47354], 33 X[11178] - 32 X[18358], 17 X[11178] - 16 X[47354], 34 X[18358] - 33 X[47354], X[69] + 3 X[3529], 3 X[376] - 2 X[19130], 3 X[376] - X[43621], 3 X[382] - 5 X[3763], 5 X[3763] - 6 X[14810], 15 X[1657] - X[6144], 9 X[1657] - X[39899], 3 X[6144] - 5 X[39899], 15 X[15683] + X[20080], 4 X[548] - 3 X[38317], 3 X[550] - 2 X[3589], 4 X[550] - 3 X[17508], 5 X[550] - 3 X[38136], 8 X[3589] - 9 X[17508], 10 X[3589] - 9 X[38136], 5 X[17508] - 4 X[38136], 7 X[576] - 8 X[12007], X[576] - 4 X[15704], 2 X[12007] - 7 X[15704], 3 X[1350] - 2 X[43150], 3 X[17800] + 2 X[43150], X[1992] - 5 X[11001], 6 X[1992] - 5 X[37517], 3 X[1992] - 5 X[46264], 6 X[11001] - X[37517], 3 X[11001] - X[46264], 3 X[3534] - 2 X[5092], 5 X[3534] - 3 X[47352], 10 X[5092] - 9 X[47352], 6 X[3845] - 7 X[42786], 2 X[3853] - 3 X[21167], X[5073] - 3 X[31884], 3 X[11204] - 2 X[18382], X[15533] + 5 X[15685], 3 X[15533] - 5 X[33878], 3 X[15685] + X[33878], 3 X[14561] - 5 X[17538], 3 X[14561] - 4 X[33751], 5 X[17538] - 4 X[33751], 3 X[15687] - 4 X[34573], 9 X[15688] - 7 X[47355], 12 X[15691] - 7 X[42785], 5 X[19708] - 4 X[25565], 3 X[19710] - X[21850], 2 X[20301] - 3 X[38788], X[20423] - 3 X[46333], 5 X[22234] - 6 X[25406], 3 X[23041] - 4 X[32903], 5 X[31730] - 3 X[38191], 3 X[39561] - 4 X[44882]

X(48879) lies on these lines: {3, 39784}, {6, 15681}, {20, 182}, {30, 141}, {69, 3529}, {376, 19130}, {382, 3763}, {511, 1657}, {542, 15683}, {548, 38317}, {550, 3589}, {576, 12007}, {1350, 17800}, {1352, 5059}, {1370, 32223}, {1531, 12082}, {1974, 13619}, {1992, 11001}, {3146, 24206}, {3534, 5092}, {3845, 42786}, {3853, 21167}, {5039, 7756}, {5073, 31884}, {5476, 15686}, {5480, 12103}, {5651, 20063}, {5965, 14927}, {6781, 41412}, {7470, 7918}, {7519, 16187}, {7693, 22112}, {7772, 8725}, {9306, 20062}, {11204, 18382}, {11645, 15533}, {12584, 34584}, {14532, 35424}, {14561, 17538}, {15687, 34573}, {15688, 47355}, {15691, 42785}, {16111, 32273}, {16163, 44831}, {19708, 25565}, {19710, 21850}, {20301, 38788}, {20423, 46333}, {22234, 25406}, {23041, 32903}, {31730, 38191}, {35001, 35257}, {36711, 43127}, {36712, 43126}, {39561, 44882}, {41413, 44526}, {42258, 42833}, {42259, 42832}

X(48879) = midpoint of X(i) and X(j) for these {i,j}: {1350, 17800}, {1352, 5059}
X(48879) = reflection of X(i) in X(j) for these {i,j}: {182, 20}, {382, 14810}, {3146, 24206}, {5476, 15686}, {5480, 12103}, {32273, 16111}, {37517, 46264}, {43621, 19130}
X(48879) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 43621, 19130}, {14561, 17538, 33751}


X(48880) = X(20)X(185)∩X(30)X(141)

Barycentrics    3*a^6 + 2*a^4*b^2 - 4*a^2*b^4 - b^6 + 2*a^4*c^2 - 2*a^2*b^2*c^2 + b^4*c^2 - 4*a^2*c^4 + b^2*c^4 - c^6 : :
X(48880) = 3 X[3] - 2 X[19130], 4 X[3] - 3 X[38317], 9 X[3] - 7 X[47355], 8 X[19130] - 9 X[38317], 6 X[19130] - 7 X[47355], 27 X[38317] - 28 X[47355], X[6] - 3 X[3534], 9 X[20] - X[193], 5 X[20] - X[6776], 3 X[20] - X[46264], 5 X[193] - 9 X[6776], X[193] - 3 X[46264], 3 X[6776] - 5 X[46264], 3 X[32429] - 2 X[41622], 2 X[141] - 3 X[3098], 4 X[141] - 3 X[3818], 10 X[141] - 9 X[11178], 7 X[141] - 6 X[18358], 11 X[141] - 9 X[47354], 5 X[3098] - 3 X[11178], 7 X[3098] - 4 X[18358], 11 X[3098] - 6 X[47354], 5 X[3818] - 6 X[11178], 7 X[3818] - 8 X[18358], 11 X[3818] - 12 X[47354], 21 X[11178] - 20 X[18358], 11 X[11178] - 10 X[47354], 22 X[18358] - 21 X[47354], X[69] + 3 X[11001], 9 X[182] - 8 X[6329], 3 X[182] - 2 X[21850], 9 X[550] - 4 X[6329], 3 X[550] - X[21850], 4 X[6329] - 3 X[21850], 9 X[376] - 5 X[3618], 3 X[376] - 2 X[5092], 3 X[376] - X[31670], 5 X[376] - 3 X[38064], 7 X[376] - 4 X[46267], 5 X[3618] - 6 X[5092], 10 X[3618] - 9 X[5476], 5 X[3618] - 3 X[31670], 25 X[3618] - 27 X[38064], 35 X[3618] - 36 X[46267], 4 X[5092] - 3 X[5476], 10 X[5092] - 9 X[38064], 7 X[5092] - 6 X[46267], 3 X[5476] - 2 X[31670], 5 X[5476] - 6 X[38064], and many others

X(48880) lies on these lines: {2, 43621}, {3, 7889}, {4, 7937}, {6, 3534}, {20, 185}, {30, 141}, {69, 11001}, {99, 34616}, {113, 12083}, {159, 2777}, {182, 550}, {376, 3618}, {378, 32600}, {381, 42786}, {382, 24206}, {524, 19710}, {542, 15681}, {546, 21167}, {548, 5480}, {575, 17538}, {576, 12103}, {597, 15690}, {599, 15685}, {1176, 43576}, {1350, 1657}, {1352, 3529}, {1469, 4324}, {1503, 15704}, {1531, 28408}, {1533, 12082}, {1843, 35481}, {1974, 10295}, {2076, 7748}, {2549, 41413}, {2781, 34776}, {3056, 4316}, {3522, 14561}, {3589, 8703}, {3619, 15682}, {3763, 3830}, {3819, 7500}, {3844, 33697}, {3845, 34573}, {3917, 20062}, {4265, 16117}, {5017, 7756}, {5059, 10519}, {5073, 10516}, {5085, 15696}, {5097, 25406}, {5102, 33749}, {5189, 7703}, {5650, 7519}, {5651, 37900}, {5925, 39879}, {5999, 17006}, {6697, 18376}, {7470, 7790}, {7667, 37648}, {7822, 35248}, {7897, 43460}, {7998, 20063}, {8177, 47101}, {8725, 41749}, {10168, 15688}, {10301, 16187}, {10546, 37901}, {11173, 11742}, {11204, 23300}, {11511, 47308}, {12017, 15689}, {12041, 32273}, {12294, 35471}, {13348, 31305}, {14070, 48378}, {14093, 38072}, {14532, 23698}, {14853, 20190}, {15055, 20301}, {15332, 19154}, {15577, 22802}, {15683, 43150}, {15686, 32455}, {15693, 25565}, {15695, 47352}, {15759, 48310}, {16111, 32305}, {16163, 19140}, {17800, 36990}, {18382, 23329}, {18400, 34778}, {18583, 44245}, {19124, 35491}, {19126, 44249}, {19457, 21312}, {20582, 33699}, {20987, 44457}, {24728, 29032}, {31152, 32223}, {32271, 38726}, {32431, 36732}, {33524, 34563}, {33851, 34584}, {34146, 34785}, {35243, 40909}, {36718, 45439}, {36734, 45438}, {36987, 44831}, {37342, 43126}, {37343, 43127}, {38136, 46853}, {39874, 46333}, {43273, 44456}, {45303, 47095}

X(48880) = midpoint of X(i) and X(j) for these {i,j}: {599, 15685}, {1350, 1657}, {1352, 3529}, {5925, 39879}, {17800, 36990}
X(48880) = reflection of X(i) in X(j) for these {i,j}: {4, 14810}, {182, 550}, {382, 24206}, {576, 44882}, {597, 15690}, {3818, 3098}, {5476, 376}, {5480, 548}, {15682, 25561}, {18583, 44245}, {19140, 16163}, {19154, 15332}, {22802, 15577}, {31670, 5092}, {32271, 38726}, {32273, 12041}, {32305, 16111}, {33697, 3844}, {33699, 20582}, {34507, 1350}, {36990, 40107}, {44882, 12103}
X(48880) = complement of X(43621)
X(48880) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 31670, 5092}, {382, 31884, 24206}, {548, 5480, 17508}, {5085, 15696, 33751}, {5092, 31670, 5476}


X(48881) = X(6)X(376)∩X(20)X(64)

Barycentrics    4*a^6 + 3*a^4*b^2 - 6*a^2*b^4 - b^6 + 3*a^4*c^2 - 4*a^2*b^2*c^2 + b^4*c^2 - 6*a^2*c^4 + b^2*c^4 - c^6 : :
X(48881) = 3 X[3] - 2 X[3589], 5 X[3] - 3 X[14561], 3 X[3] - X[31670], 4 X[3589] - 3 X[5480], 10 X[3589] - 9 X[14561], 5 X[5480] - 6 X[14561], 3 X[5480] - 2 X[31670], 9 X[14561] - 5 X[31670], 3 X[4] - 5 X[3763], X[4] - 3 X[31884], 5 X[3763] - 9 X[31884], 2 X[5] - 3 X[21167], 4 X[14810] - 3 X[21167], X[6] - 3 X[376], 3 X[20] + X[69], 7 X[20] + X[5921], 5 X[20] - X[14927], 5 X[20] + X[15069], X[69] - 3 X[1350], 7 X[69] - 3 X[5921], 5 X[69] + 3 X[14927], 5 X[69] - 3 X[15069], 7 X[1350] - X[5921], 5 X[1350] + X[14927], 5 X[1350] - X[15069], 5 X[5921] + 7 X[14927], 5 X[5921] - 7 X[15069], 3 X[10192] - 4 X[35228], 3 X[141] - 2 X[3818], 7 X[141] - 6 X[11178], 5 X[141] - 4 X[18358], 4 X[141] - 3 X[47354], 3 X[3098] - X[3818], 7 X[3098] - 3 X[11178], 5 X[3098] - 2 X[18358], 8 X[3098] - 3 X[47354], 7 X[3818] - 9 X[11178], 5 X[3818] - 6 X[18358], 8 X[3818] - 9 X[47354], 15 X[11178] - 14 X[18358], 8 X[11178] - 7 X[47354], 16 X[18358] - 15 X[47354], X[193] - 3 X[43273], 3 X[381] - 4 X[34573], 3 X[381] - X[43621], 4 X[34573] - X[43621], 5 X[550] - X[1353], 6 X[550] - X[3629], 4 X[550] - X[8550], 6 X[1353] - 5 X[3629], 4 X[1353] - 5 X[8550], and many others

X(48881) lies on these lines: {2, 31860}, {3, 3589}, {4, 3763}, {5, 14810}, {6, 376}, {20, 64}, {22, 10192}, {30, 141}, {53, 35474}, {159, 15311}, {182, 548}, {193, 43273}, {206, 37480}, {378, 3867}, {381, 34573}, {511, 550}, {518, 31730}, {524, 3534}, {542, 3630}, {549, 19130}, {575, 33751}, {576, 44245}, {577, 44248}, {597, 5092}, {599, 11001}, {698, 9821}, {1351, 15696}, {1352, 1657}, {1368, 32223}, {1370, 18382}, {1469, 15338}, {1853, 33522}, {1974, 37931}, {1992, 15697}, {2076, 5254}, {2777, 33851}, {2781, 3313}, {2810, 38773}, {2854, 16111}, {2883, 11414}, {2930, 12244}, {2979, 46818}, {3056, 15326}, {3094, 44251}, {3146, 7928}, {3242, 6361}, {3424, 46944}, {3522, 5085}, {3524, 47355}, {3528, 14853}, {3529, 10519}, {3530, 38317}, {3543, 3619}, {3564, 12103}, {3618, 10304}, {3620, 15683}, {3627, 24206}, {3631, 15681}, {3651, 4265}, {3830, 20582}, {3844, 31673}, {4259, 44238}, {4293, 10387}, {4304, 24471}, {4846, 35243}, {5026, 38736}, {5066, 42786}, {5096, 37403}, {5189, 45303}, {5476, 34200}, {5562, 44762}, {5650, 10301}, {5651, 37899}, {5846, 18481}, {5925, 41735}, {5969, 38749}, {5999, 37688}, {6144, 6776}, {6200, 13910}, {6201, 36702}, {6202, 36717}, {6247, 44683}, {6329, 12017}, {6390, 30270}, {6393, 7802}, {6396, 13972}, {6403, 35491}, {6409, 40288}, {6410, 40289}, {6560, 13644}, {6561, 13763}, {6593, 38726}, {6636, 14389}, {6697, 23324}, {6698, 12295}, {7492, 13394}, {7496, 7693}, {7519, 21766}, {7667, 13567}, {7703, 47314}, {7712, 40112}, {7931, 40236}, {7987, 38035}, {7998, 37900}, {8266, 47620}, {8356, 34616}, {8584, 15690}, {8705, 35257}, {9019, 37511}, {9021, 37585}, {9024, 38761}, {9053, 12702}, {9530, 42459}, {9607, 12212}, {9967, 44240}, {9970, 38723}, {10168, 45759}, {10323, 12233}, {10541, 33750}, {10546, 47313}, {10564, 44261}, {10606, 36851}, {11179, 15689}, {11180, 46333}, {11257, 41747}, {11413, 15578}, {11477, 12007}, {11574, 44241}, {11579, 38788}, {11645, 19710}, {11821, 15811}, {12041, 25328}, {12082, 20987}, {12100, 48310}, {12177, 38731}, {12220, 16386}, {13568, 37198}, {13634, 17398}, {13635, 17337}, {14093, 38064}, {14654, 37751}, {14688, 38803}, {14891, 42785}, {14928, 38738}, {14982, 41464}, {15048, 41413}, {15107, 37648}, {15160, 15163}, {15161, 15162}, {15321, 41171}, {15582, 33524}, {15583, 21312}, {15585, 35513}, {15644, 34146}, {15682, 21358}, {15692, 38072}, {15704, 29012}, {15712, 38136}, {15713, 25565}, {15714, 38079}, {15988, 37299}, {16063, 32269}, {17508, 18583}, {17579, 26543}, {17811, 34608}, {18325, 32218}, {18438, 44246}, {18917, 37486}, {19708, 47352}, {20427, 39879}, {21737, 45862}, {23300, 23328}, {25561, 33699}, {29323, 39884}, {31152, 47296}, {31827, 32150}, {32191, 45186}, {32217, 47335}, {33268, 39141}, {33532, 35707}, {33703, 40330}, {33844, 37428}, {34417, 43957}, {35242, 38047}, {35248, 44230}, {35481, 41585}, {36701, 45441}, {36703, 45440}, {36740, 37426}, {37348, 43128}, {38110, 46853}, {39561, 41981}, {39874, 40341}

X(48881) = midpoint of X(i) and X(j) for these {i,j}: {20, 1350}, {599, 11001}, {1352, 1657}, {2930, 12244}, {3242, 6361}, {3529, 36990}, {5925, 41735}, {14654, 37751}, {14927, 15069}, {15160, 15163}, {15161, 15162}, {15683, 47353}, {20427, 39879}, {33878, 46264}, {39874, 40341}
X(48881) = reflection of X(i) in X(j) for these {i,j}: {5, 14810}, {141, 3098}, {182, 548}, {575, 33751}, {597, 8703}, {2883, 15577}, {3627, 24206}, {3830, 20582}, {5026, 38736}, {5476, 34200}, {5480, 3}, {6593, 38726}, {8550, 44882}, {11477, 12007}, {12295, 6698}, {14688, 38803}, {15583, 44883}, {18325, 32218}, {18440, 3631}, {18583, 33923}, {21850, 5092}, {25328, 12041}, {31670, 3589}, {31673, 3844}, {31827, 32150}, {32217, 47335}, {33699, 25561}, {39884, 40107}, {44456, 32455}, {44882, 550}, {45186, 32191}
X(48881) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 31670, 3589}, {5, 14810, 21167}, {3529, 10519, 36990}, {3534, 33878, 46264}, {3589, 31670, 5480}, {5092, 21850, 597}, {7519, 21766, 35283}, {8703, 21850, 5092}, {11179, 44456, 32455}, {11477, 25406, 12007}, {12017, 20423, 6329}, {18583, 33923, 17508}, {21312, 37485, 44883}


X(48882) = X(3)X(6)∩X(30)X(40)

Barycentrics    a^2*(a^4*b + 2*a^3*b^2 - 2*a*b^4 - b^5 + a^4*c + 2*a^3*b*c + a^2*b^2*c - 2*a*b^3*c - 2*b^4*c + 2*a^3*c^2 + a^2*b*c^2 - 2*a*b^2*c^2 - b^3*c^2 - 2*a*b*c^3 - b^2*c^3 - 2*a*c^4 - 2*b*c^4 - c^5) : :
X(48882) = X[500] - 4 X[35203], 2 X[8143] - 3 X[11203], 2 X[1385] - 3 X[14636], 3 X[3576] - 2 X[5453], 3 X[5657] - X[15971], 2 X[15973] - 3 X[26446], 2 X[10035] - 3 X[21154]

X(48882) lies on these lines: {3, 6}, {4, 26064}, {5, 1764}, {10, 46704}, {23, 35193}, {30, 40}, {46, 5725}, {51, 16287}, {63, 5814}, {71, 31445}, {102, 39630}, {140, 21363}, {165, 37699}, {199, 1437}, {283, 2915}, {373, 16296}, {517, 2292}, {540, 46617}, {859, 22076}, {896, 3214}, {942, 22097}, {946, 25359}, {1154, 11012}, {1385, 14636}, {1400, 37594}, {1715, 37424}, {1730, 8728}, {1753, 46467}, {2077, 6097}, {2183, 5044}, {2328, 20831}, {2360, 22136}, {2979, 16451}, {3060, 16452}, {3338, 37631}, {3428, 13754}, {3576, 5453}, {3647, 35468}, {3792, 35206}, {3819, 16414}, {3882, 10461}, {3917, 16453}, {4205, 17185}, {5250, 13745}, {5562, 7420}, {5650, 16297}, {5657, 15971}, {5707, 37320}, {5709, 13408}, {5835, 12514}, {5886, 10476}, {5943, 16286}, {6000, 7959}, {6210, 12699}, {6688, 16291}, {6763, 32861}, {7609, 38330}, {9548, 15973}, {10035, 21154}, {10434, 37698}, {13731, 37536}, {16528, 44245}, {17209, 37023}, {17524, 22080}, {18180, 37225}, {19513, 28273}, {20367, 24470}, {20836, 22139}, {28369, 37592}, {33586, 37284}, {37422, 41810}

X(48882) = reflection of X(i) in X(j) for these {i,j}: {3, 35203}, {500, 3}, {37425, 3579}, {46704, 10}
X(48882) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5752, 5396}, {3, 36750, 572}, {40, 7701, 2941}, {371, 372, 4275}, {3882, 10461, 41014}, {36746, 37499, 3}


X(48883) = X(1)X(256)∩X(30)X(40)

Barycentrics    a*(a^5*b + 2*a^4*b^2 - 2*a^2*b^4 - a*b^5 + a^5*c + a^3*b^2*c - a^2*b^3*c - 2*a*b^4*c + b^5*c + 2*a^4*c^2 + a^3*b*c^2 - 2*a^2*b^2*c^2 - a*b^3*c^2 - a^2*b*c^3 - a*b^2*c^3 - 2*b^3*c^3 - 2*a^2*c^4 - 2*a*b*c^4 - a*c^5 + b*c^5) : :
X(48883) = 3 X[165] - 4 X[35203], 3 X[165] - 2 X[37425], 2 X[500] - 3 X[3576], 5 X[1698] - 4 X[15973], 2 X[3743] - 3 X[11203], 3 X[5587] - 2 X[46704], 5 X[7987] - 6 X[14636]

X(48883) lies on these lines: {1, 256}, {3, 1724}, {4, 1764}, {9, 13442}, {10, 15971}, {20, 391}, {21, 3430}, {30, 40}, {51, 47521}, {58, 4220}, {63, 5016}, {72, 21362}, {78, 21361}, {165, 6048}, {377, 1730}, {405, 1350}, {500, 3576}, {517, 5492}, {524, 6762}, {540, 46483}, {548, 16528}, {581, 10470}, {758, 12713}, {855, 22076}, {936, 28381}, {950, 22097}, {970, 37331}, {1009, 5188}, {1018, 7283}, {1020, 4296}, {1043, 3882}, {1154, 11014}, {1265, 29497}, {1330, 10461}, {1698, 15973}, {1699, 10476}, {1715, 6850}, {1736, 37613}, {1746, 37088}, {1753, 46468}, {1834, 18163}, {1935, 5285}, {2328, 28029}, {2938, 46198}, {2944, 9355}, {3098, 13732}, {3271, 28265}, {3293, 37619}, {3454, 8229}, {3743, 11203}, {3917, 13724}, {4253, 14930}, {4267, 6045}, {4292, 15970}, {4297, 46362}, {4300, 29353}, {4340, 7390}, {4647, 29057}, {5051, 7683}, {5400, 19513}, {5480, 13728}, {5587, 46704}, {6003, 21306}, {6211, 29317}, {6998, 25526}, {7373, 10108}, {7379, 46196}, {7609, 19924}, {7741, 15974}, {7987, 14636}, {9579, 24310}, {11031, 35650}, {11097, 14538}, {11098, 14539}, {11101, 15107}, {12545, 45305}, {12704, 13408}, {13329, 37328}, {13723, 30270}, {13745, 31435}, {16192, 36634}, {17185, 26117}, {17194, 37225}, {17810, 19520}, {18206, 20077}, {18860, 37023}, {19544, 37522}, {19782, 33878}, {20122, 37558}, {26064, 37456}, {29301, 46895}, {33586, 37228}, {35193, 37919}, {36746, 37320}, {37402, 37508}

X(48883) = reflection of X(i) in X(j) for these {i,j}: {1, 9840}, {15971, 10}, {37425, 35203}
X(48883) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {40, 7330, 21375}, {581, 19262, 10470}, {1284, 10544, 1}, {35203, 37425, 165}


X(48884) = X(4)X(83)∩X(30)X(141)

Barycentrics    3*a^6 + a^4*b^2 - 2*a^2*b^4 - 2*b^6 + a^4*c^2 + 2*a^2*b^2*c^2 + 2*b^4*c^2 - 2*a^2*c^4 + 2*b^2*c^4 - 2*c^6 : :
X(48884) = 9 X[4] - 5 X[3618], 5 X[4] - 3 X[14561], 5 X[4] - X[14927], 3 X[4] - 2 X[19130], 7 X[4] - 3 X[25406], 7 X[4] - 4 X[25555], 3 X[4] - X[46264], 9 X[182] - 10 X[3618], 5 X[182] - 6 X[14561], 5 X[182] - 2 X[14927], 3 X[182] - 4 X[19130], 7 X[182] - 6 X[25406], 7 X[182] - 8 X[25555], 3 X[182] - 2 X[46264], 25 X[3618] - 27 X[14561], 25 X[3618] - 9 X[14927], 5 X[3618] - 6 X[19130], 35 X[3618] - 27 X[25406], 35 X[3618] - 36 X[25555], 5 X[3618] - 3 X[46264], 3 X[14561] - X[14927], 9 X[14561] - 10 X[19130], 7 X[14561] - 5 X[25406], 21 X[14561] - 20 X[25555], 9 X[14561] - 5 X[46264], 3 X[14927] - 10 X[19130], 7 X[14927] - 15 X[25406], 7 X[14927] - 20 X[25555], 3 X[14927] - 5 X[46264], 14 X[19130] - 9 X[25406], 7 X[19130] - 6 X[25555], 3 X[25406] - 4 X[25555], 9 X[25406] - 7 X[46264], 12 X[25555] - 7 X[46264], 4 X[5] - 3 X[17508], X[6] - 3 X[3830], 4 X[141] - 3 X[3098], 2 X[141] - 3 X[3818], 8 X[141] - 9 X[11178], 5 X[141] - 6 X[18358], 7 X[141] - 9 X[47354], 2 X[3098] - 3 X[11178], 5 X[3098] - 8 X[18358], 7 X[3098] - 12 X[47354], 4 X[3818] - 3 X[11178], 5 X[3818] - 4 X[18358], 7 X[3818] - 6 X[47354], 15 X[11178] - 16 X[18358], and many others

X(48884) lies on these lines: {3, 29323}, {4, 83}, {5, 17508}, {6, 3830}, {20, 24206}, {23, 7703}, {30, 141}, {66, 2777}, {69, 13603}, {113, 31723}, {115, 41412}, {125, 7519}, {146, 148}, {206, 44288}, {381, 5092}, {382, 511}, {385, 14458}, {428, 37648}, {518, 33697}, {524, 33699}, {546, 38317}, {549, 42786}, {575, 5076}, {576, 1353}, {597, 12101}, {631, 33751}, {1350, 5073}, {1352, 3146}, {1428, 18514}, {1495, 31133}, {1531, 20806}, {1539, 19140}, {1657, 10516}, {1843, 35480}, {1853, 21970}, {1992, 33623}, {2330, 18513}, {3070, 42833}, {3071, 42832}, {3313, 16194}, {3357, 11819}, {3534, 3763}, {3580, 11550}, {3589, 3845}, {3619, 11001}, {3620, 15640}, {3839, 10168}, {3843, 5085}, {3853, 5480}, {3860, 48310}, {4048, 7825}, {4232, 6723}, {5039, 7747}, {5059, 40330}, {5068, 33750}, {5094, 32237}, {5169, 35268}, {5189, 5651}, {5476, 6329}, {5972, 31099}, {6000, 34775}, {6321, 35389}, {6697, 11204}, {6772, 42085}, {6775, 42086}, {6776, 15520}, {7391, 9306}, {7470, 7937}, {7500, 21243}, {7502, 32600}, {7528, 13347}, {7530, 23325}, {7533, 22112}, {7540, 11438}, {7553, 46730}, {7777, 43460}, {7872, 42534}, {7898, 34681}, {7902, 42421}, {7935, 18500}, {8177, 18546}, {8703, 34573}, {9752, 35021}, {9821, 44772}, {9873, 14712}, {9969, 14915}, {10113, 32305}, {10296, 12220}, {10546, 10989}, {11477, 48662}, {11511, 18323}, {12017, 14269}, {12102, 18583}, {12103, 21167}, {12294, 35490}, {12295, 32273}, {12974, 36709}, {12975, 36714}, {13346, 13419}, {13491, 32191}, {14853, 22234}, {14881, 32429}, {15578, 37440}, {15684, 33878}, {15685, 21358}, {16063, 16187}, {16163, 28408}, {16625, 34780}, {17800, 31884}, {18376, 23300}, {18382, 36201}, {18509, 36734}, {18511, 36718}, {18533, 37853}, {18539, 42859}, {19710, 20582}, {20423, 39874}, {22260, 32472}, {22615, 44473}, {22644, 44474}, {25565, 41099}, {26438, 42858}, {29181, 34507}, {31074, 44082}, {31383, 37645}, {31725, 44470}, {32274, 34584}, {32431, 36490}, {33703, 40107}, {35403, 38072}, {35422, 35930}, {35426, 39646}, {36362, 40901}, {36363, 40900}, {36711, 43120}, {36712, 43121}, {36719, 45438}, {36733, 45439}, {37349, 43650}, {37485, 44454}, {37511, 43129}, {37899, 45303}, {38335, 43273}, {38734, 46034}, {44441, 48378}, {44938, 44984}, {44939, 44987}

X(48884) = midpoint of X(i) and X(j) for these {i,j}: {69, 43621}, {382, 36990}, {1350, 5073}, {1352, 3146}, {11477, 48662}, {15684, 47353}
X(48884) = reflection of X(i) in X(j) for these {i,j}: {20, 24206}, {182, 4}, {597, 12101}, {1350, 18553}, {1657, 14810}, {3098, 3818}, {3534, 25561}, {5476, 15687}, {5480, 3853}, {13491, 32191}, {18583, 12102}, {19140, 1539}, {19710, 20582}, {32273, 12295}, {32305, 10113}, {32429, 14881}, {33878, 43150}, {34507, 39884}, {37511, 43129}, {37517, 31670}, {44882, 546}, {46264, 19130}
X(48884) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 14927, 14561}, {4, 46264, 19130}, {69, 15682, 43621}, {546, 44882, 38317}, {1657, 10516, 14810}, {3098, 3818, 11178}, {19130, 46264, 182}, {25406, 25555, 182}, {33878, 47353, 43150}, {36969, 36970, 11648}


X(48885) = X(3)X(7889)∩X(182)X(376)

Barycentrics    4*a^6 + 2*a^4*b^2 - 5*a^2*b^4 - b^6 + 2*a^4*c^2 - 4*a^2*b^2*c^2 + b^4*c^2 - 5*a^2*c^4 + b^2*c^4 - c^6 : :
X(48885) = 5 X[3] - 3 X[38317], 11 X[3] - 7 X[47355], 5 X[19130] - 6 X[38317], 11 X[19130] - 14 X[47355], 33 X[38317] - 35 X[47355], X[6] - 5 X[15696], 3 X[20] + X[1352], 11 X[20] + 5 X[3620], 5 X[20] + 3 X[10519], 2 X[20] + X[40107], X[1352] - 3 X[3098], 11 X[1352] - 15 X[3620], 5 X[1352] - 9 X[10519], 2 X[1352] - 3 X[40107], 11 X[3098] - 5 X[3620], 5 X[3098] - 3 X[10519], 25 X[3620] - 33 X[10519], 10 X[3620] - 11 X[40107], 6 X[10519] - 5 X[40107], 11 X[14810] - 6 X[20582], 7 X[14810] - 3 X[25561], 12 X[20582] - 11 X[24206], 14 X[20582] - 11 X[25561], 7 X[24206] - 6 X[25561], X[182] - 3 X[376], 5 X[182] - 3 X[20423], 5 X[376] - X[20423], 3 X[376] - 2 X[33751], 3 X[20423] - 10 X[33751], 9 X[550] - X[1353], 11 X[550] - X[3629], 7 X[550] - X[8550], 3 X[550] - X[44882], 11 X[1353] - 9 X[3629], 7 X[1353] - 9 X[8550], X[1353] - 3 X[44882], 7 X[3629] - 11 X[8550], 3 X[3629] - 11 X[44882], 3 X[8550] - 7 X[44882], X[1350] + 3 X[3534], 5 X[1350] - X[11898], 11 X[1350] - 3 X[15533], 15 X[3534] + X[11898], 11 X[3534] + X[15533], 11 X[11898] - 15 X[15533], 3 X[548] - X[18583], 3 X[5092] - 2 X[18583], X[575] - 4 X[44245], 5 X[631] - X[43621], X[1351] - 9 X[15689], X[1657] + 3 X[31884], X[3818] - 3 X[31884], 5 X[3522] - 3 X[17508], 5 X[3522] - 2 X[25555], 5 X[3522] - X[31670], 3 X[17508] - 2 X[25555], 3 X[17508] - X[31670], 3 X[3524] - 2 X[25565], 7 X[3528] - 3 X[14561], X[3627] - 3 X[21167], 5 X[3763] - X[5073], 5 X[3843] - 7 X[42786], X[5097] - 6 X[15690], X[5476] - 3 X[15688], X[5480] - 3 X[8703], 2 X[5480] - 3 X[10168], 7 X[5480] - 9 X[38079], 7 X[8703] - 3 X[38079], 7 X[10168] - 6 X[38079], 5 X[17538] - X[46264], 3 X[10193] - 2 X[20300], 3 X[10516] + X[17800], X[11179] - 5 X[15697], 3 X[15055] - X[32273], 3 X[15681] + X[36990], 3 X[15683] + 5 X[40330], 5 X[15714] - 3 X[48310], X[19140] - 3 X[38723], 3 X[19710] + X[39884], 3 X[25406] - 2 X[33749], 3 X[25406] - X[37517], X[32305] - 3 X[38788], 3 X[34507] - X[48662], 13 X[35421] - 4 X[41153]

X(48885) lies on these lines: {3, 7889}, {6, 15696}, {20, 1352}, {22, 5972}, {30, 14810}, {141, 15704}, {182, 376}, {511, 550}, {524, 15691}, {542, 1350}, {548, 5092}, {575, 44245}, {631, 43621}, {1351, 15689}, {1503, 12103}, {1657, 3818}, {1843, 35491}, {1974, 35503}, {2076, 7756}, {2777, 15577}, {2979, 24981}, {3094, 6781}, {3522, 17508}, {3524, 25565}, {3528, 14561}, {3589, 33923}, {3627, 21167}, {3763, 5073}, {3843, 42786}, {3844, 28168}, {3853, 34573}, {5097, 15690}, {5476, 15688}, {5480, 8703}, {5650, 37900}, {5965, 12254}, {6723, 31152}, {7470, 35375}, {7555, 10182}, {7667, 32269}, {9541, 42833}, {9967, 44246}, {10193, 20300}, {10295, 12294}, {10301, 15082}, {10516, 17800}, {10627, 45185}, {11001, 11178}, {11179, 15697}, {11574, 44240}, {11645, 15686}, {11649, 16386}, {12584, 20127}, {15055, 32273}, {15681, 36990}, {15683, 40330}, {15714, 48310}, {16063, 32223}, {16163, 41716}, {18382, 25563}, {19140, 38723}, {19710, 39884}, {20063, 41462}, {20190, 21850}, {22676, 38749}, {25406, 33749}, {32305, 38788}, {34507, 48662}, {34778, 34785}, {35421, 41153}, {35475, 46026}, {36709, 43127}, {36714, 43126}, {41435, 43613}, {44903, 47354}

X(48885) = midpoint of X(i) and X(j) for these {i,j}: {20, 3098}, {141, 15704}, {1657, 3818}, {11001, 11178}, {12584, 20127}, {34778, 34785}, {44903, 47354}
X(48885) = reflection of X(i) in X(j) for these {i,j}: {182, 33751}, {3589, 33923}, {3853, 34573}, {5092, 548}, {10168, 8703}, {18382, 25563}, {19130, 3}, {21850, 20190}, {24206, 14810}, {31670, 25555}, {37517, 33749}, {40107, 3098}
X(48885) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 12122, 32152}, {182, 376, 33751}, {1657, 31884, 3818}, {3522, 31670, 17508}, {17508, 31670, 25555}, {25406, 37517, 33749}


X(48886) = X(3)X(6)∩X(5)X(516)

Barycentrics    a^2*(2*a^3*b + a^2*b^2 - 2*a*b^3 - b^4 + 2*a^3*c + 2*a^2*b*c - 2*a*b^2*c - 2*b^3*c + a^2*c^2 - 2*a*b*c^2 - 2*a*c^3 - 2*b*c^3 - c^4) : :
X(48886) = 3 X[3] - X[991], 3 X[573] + X[991], 3 X[165] + X[6210], 5 X[631] - X[10446], X[1742] - 5 X[35242]

X(48886) lies on these lines: {2, 22080}, {3, 6}, {5, 516}, {30, 48860}, {35, 21746}, {40, 13731}, {51, 4184}, {55, 39543}, {103, 28856}, {140, 6707}, {165, 2108}, {184, 11340}, {517, 6176}, {631, 10446}, {1011, 5943}, {1155, 5718}, {1352, 36698}, {1385, 29311}, {1730, 8731}, {1742, 35242}, {1790, 34986}, {2051, 10164}, {2269, 37609}, {2807, 38599}, {3664, 37582}, {3818, 36674}, {3819, 4191}, {3916, 4416}, {3917, 4210}, {4297, 9568}, {4640, 5743}, {6688, 16058}, {7816, 24267}, {9052, 15624}, {9306, 11350}, {10434, 39551}, {15310, 31663}, {16451, 22076}, {17594, 45897}, {19346, 21849}, {19513, 28252}, {24047, 41323}, {29343, 30273}, {31670, 36706}, {31730, 45305}, {37572, 37693}

X(48886) = midpoint of X(i) and X(j) for these {i,j}: {3, 573}, {40, 31394}, {31730, 45305}
X(48886) = reflection of X(i) in X(j) for these {i,j}: {24220, 140}, {41430, 31663}
X(48886) = crosssum of X(11) and X(4784)
X(48886) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 9566, 581}, {3, 13329, 5092}, {3, 37510, 572}, {40, 13731, 15488}, {165, 21363, 4192}, {572, 37510, 575}, {2245, 5132, 4260}, {13329, 37508, 3}


X(48887) = X(5)X(141)∩X(10)X(30)

Barycentrics    a^5*b^2 - 2*a^3*b^4 + a*b^6 - 2*a^3*b^3*c - a^2*b^4*c + 2*a*b^5*c + b^6*c + a^5*c^2 - 2*a^3*b^2*c^2 - 3*a^2*b^3*c^2 - a*b^4*c^2 + b^5*c^2 - 2*a^3*b*c^3 - 3*a^2*b^2*c^3 - 4*a*b^3*c^3 - 2*b^4*c^3 - 2*a^3*c^4 - a^2*b*c^4 - a*b^2*c^4 - 2*b^3*c^4 + 2*a*b*c^5 + b^2*c^5 + a*c^6 + b*c^6 : :
X(48887) = 3 X[5587] - X[46704], 5 X[5818] - X[15971], 3 X[10180] - 2 X[32167], 3 X[14636] - X[18481], 3 X[26446] - X[37425]

X(48887) lies on these lines: {2, 500}, {3, 1746}, {4, 26064}, {5, 141}, {10, 30}, {323, 3615}, {355, 9840}, {381, 10479}, {524, 10916}, {582, 5278}, {740, 8143}, {966, 6851}, {1125, 5453}, {1154, 25639}, {1211, 6841}, {1861, 46467}, {2886, 13754}, {3136, 18180}, {3651, 5235}, {3652, 4418}, {3739, 13369}, {3741, 9955}, {3814, 13391}, {4259, 19754}, {4647, 5492}, {4683, 16159}, {5051, 45926}, {5587, 46704}, {5737, 6985}, {5743, 37356}, {5818, 15971}, {6000, 20306}, {6097, 25440}, {6358, 35194}, {6667, 10035}, {6734, 13408}, {6990, 32782}, {9710, 14915}, {9956, 15973}, {10180, 32167}, {12699, 31330}, {13745, 24987}, {14636, 18481}, {15974, 26470}, {17188, 22136}, {19716, 36742}, {19755, 37516}, {22076, 37357}, {22793, 45305}, {26446, 37425}, {31737, 39583}, {31993, 40263}, {34466, 37365}, {41797, 47742}

X(48887) = complement of X(500)
X(48887) = midpoint of X(i) and X(j) for these {i,j}: {355, 9840}, {4647, 5492}
X(48887) = reflection of X(i) in X(j) for these {i,j}: {5453, 1125}, {10035, 6667}, {15973, 9956}
X(48887) = X(i)-complementary conjugate of X(j) for these (i,j): {943, 3647}, {2259, 16585}


X(48888) = X(4)X(9)∩X(5)X(141)

Barycentrics    a^4*b^2 - a^3*b^3 - a^2*b^4 + a*b^5 - a^3*b^2*c - a^2*b^3*c + a*b^4*c + b^5*c + a^4*c^2 - a^3*b*c^2 - 2*a*b^3*c^2 - a^3*c^3 - a^2*b*c^3 - 2*a*b^2*c^3 - 2*b^3*c^3 - a^2*c^4 + a*b*c^4 + a*c^5 + b*c^5 : :
X(48888) = 3 X[5587] + X[6210], 5 X[1698] - X[1742], 5 X[3091] - X[10446]

X(48888) lies on these lines: {2, 991}, {3, 17259}, {4, 9}, {5, 141}, {12, 21746}, {30, 48860}, {37, 29016}, {51, 3136}, {69, 36660}, {92, 22027}, {116, 25365}, {118, 124}, {142, 5751}, {165, 26037}, {182, 36477}, {193, 5733}, {355, 31394}, {381, 17251}, {391, 3332}, {442, 25964}, {495, 39543}, {572, 6998}, {581, 1125}, {941, 4356}, {946, 5752}, {971, 3739}, {990, 4384}, {993, 7420}, {1210, 3664}, {1211, 8226}, {1215, 15064}, {1352, 36526}, {1376, 41797}, {1441, 1736}, {1656, 17265}, {1698, 1742}, {1699, 31330}, {1737, 5823}, {1746, 4220}, {1754, 5278}, {1765, 15970}, {1834, 4263}, {2328, 14004}, {2476, 26540}, {2801, 24325}, {3060, 17167}, {3091, 5232}, {3190, 27287}, {3741, 3817}, {3755, 4277}, {3784, 40687}, {3818, 36661}, {3819, 37355}, {3823, 9956}, {3840, 10171}, {3842, 28850}, {3917, 47513}, {4300, 16828}, {4363, 5779}, {4416, 5906}, {4643, 5805}, {4847, 5739}, {5224, 36652}, {5235, 36002}, {5241, 37374}, {5690, 29309}, {5691, 31339}, {5712, 11019}, {5713, 10916}, {5732, 16832}, {5737, 19541}, {5743, 8727}, {5762, 17332}, {5843, 7228}, {5927, 31993}, {5943, 47514}, {6201, 36691}, {6202, 36690}, {6358, 7069}, {6684, 41430}, {6826, 48835}, {6884, 25645}, {6894, 26064}, {6913, 48863}, {7232, 38107}, {7489, 14663}, {7522, 17810}, {7580, 19732}, {7747, 20666}, {7988, 30942}, {9355, 24342}, {10157, 44417}, {10164, 37400}, {10175, 29353}, {13329, 13727}, {13478, 19544}, {14853, 36672}, {15599, 25627}, {16609, 32118}, {17197, 37516}, {17272, 38150}, {17279, 38108}, {17330, 36722}, {20090, 45942}, {20236, 44694}, {21635, 25385}, {21935, 23659}, {22000, 26893}, {23821, 24248}, {26005, 37363}, {26015, 31034}, {29349, 38042}, {29395, 32850}, {31657, 34824}, {31670, 36659}, {32917, 44425}, {42425, 45162}

X(48888) = midpoint of X(i) and X(j) for these {i,j}: {4, 573}, {10, 45305}, {355, 31394}, {17330, 36722}
X(48888) = reflection of X(i) in X(j) for these {i,j}: {24220, 5}, {41430, 6684}
X(48888) = complement of X(991)
X(48888) = crossdifference of every pair of points on line {1459, 3050}
X(48888) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 20262, 31897}, {13727, 17277, 13329}


X(48889) = X(4)X(69)∩X(182)X(381)

Barycentrics    2*a^6 + a^4*b^2 - a^2*b^4 - 2*b^6 + a^4*c^2 + 4*a^2*b^2*c^2 + 2*b^4*c^2 - a^2*c^4 + 2*b^2*c^4 - 2*c^6 : :
X(48889) = 7 X[4] + X[69], 3 X[4] + X[1352], 2 X[4] + X[18553], 5 X[4] - X[31670], 5 X[4] + X[34507], 4 X[4] + X[43150], 3 X[69] - 7 X[1352], X[69] - 7 X[3818], 2 X[69] - 7 X[18553], 5 X[69] + 7 X[31670], 5 X[69] - 7 X[34507], 4 X[69] - 7 X[43150], X[1352] - 3 X[3818], 2 X[1352] - 3 X[18553], 5 X[1352] + 3 X[31670], 5 X[1352] - 3 X[34507], 4 X[1352] - 3 X[43150], 5 X[3818] + X[31670], 5 X[3818] - X[34507], 4 X[3818] - X[43150], 9 X[16261] - X[41716], 5 X[18553] + 2 X[31670], 5 X[18553] - 2 X[34507], 4 X[31670] + 5 X[43150], 4 X[34507] - 5 X[43150], 3 X[5] - X[44882], 3 X[5092] - 2 X[44882], X[6] - 5 X[3843], 3 X[6] + X[48662], 15 X[3843] + X[48662], 7 X[14810] - 12 X[20582], X[14810] - 3 X[25561], 6 X[20582] - 7 X[24206], 4 X[20582] - 7 X[25561], 2 X[24206] - 3 X[25561], X[182] - 3 X[381], 5 X[182] - 3 X[43273], 5 X[182] - 6 X[46267], 7 X[182] - 9 X[47352], 3 X[381] + X[36990], 5 X[381] - X[43273], 5 X[381] - 2 X[46267], 7 X[381] - 3 X[47352], 5 X[36990] + 3 X[43273], 5 X[36990] + 6 X[46267], 7 X[36990] + 9 X[47352], 7 X[43273] - 15 X[47352], 14 X[46267] - 15 X[47352], 3 X[262] - X[32429], X[382] + 3 X[10516], X[3098] - 3 X[10516], X[1353] - 9 X[3845], and many others

X(48889) lies on these lines: {2, 32237}, {3, 29323}, {4, 69}, {5, 5092}, {6, 3843}, {30, 14810}, {51, 3448}, {66, 22802}, {141, 3627}, {147, 44422}, {159, 34786}, {182, 381}, {206, 7564}, {262, 32429}, {265, 22336}, {373, 7533}, {382, 3098}, {427, 5972}, {428, 21243}, {524, 14893}, {542, 1353}, {546, 575}, {548, 34573}, {549, 33751}, {576, 18440}, {597, 23046}, {599, 38335}, {625, 4048}, {631, 42786}, {732, 7843}, {1350, 3830}, {1351, 14269}, {1469, 18513}, {1495, 5169}, {1539, 32274}, {1656, 17508}, {1657, 3763}, {1691, 39565}, {1974, 35488}, {2030, 18424}, {2916, 34864}, {3056, 18514}, {3091, 20190}, {3398, 48674}, {3410, 21969}, {3543, 40330}, {3545, 14927}, {3564, 3861}, {3589, 3850}, {3619, 7910}, {3819, 7391}, {3821, 29113}, {3832, 11572}, {3839, 5476}, {3844, 28146}, {3851, 5085}, {3853, 18358}, {3855, 25406}, {3857, 38110}, {3858, 25555}, {5031, 7816}, {5052, 11646}, {5064, 9306}, {5066, 10168}, {5072, 47355}, {5073, 31884}, {5116, 7603}, {5188, 6287}, {5189, 5650}, {5318, 36252}, {5321, 36251}, {5462, 14864}, {5651, 31133}, {5663, 32191}, {5846, 40273}, {5921, 18392}, {5943, 7394}, {5965, 21850}, {6000, 7706}, {6033, 22682}, {6683, 40278}, {6688, 6997}, {6697, 31830}, {6698, 34584}, {6723, 44212}, {6759, 34775}, {7392, 10219}, {7401, 17704}, {7403, 13419}, {7486, 33750}, {7488, 32600}, {7528, 9729}, {7544, 46850}, {7547, 19124}, {7566, 26883}, {7687, 20301}, {7703, 14002}, {7728, 16194}, {7747, 41413}, {7785, 41622}, {7817, 42421}, {7845, 22728}, {7853, 24273}, {7861, 42534}, {8550, 38136}, {9738, 36711}, {9739, 36712}, {9967, 18403}, {9976, 41737}, {10151, 47581}, {10301, 32223}, {10519, 17578}, {10546, 31857}, {10575, 14861}, {10733, 12584}, {11179, 41099}, {11442, 21849}, {11574, 18404}, {12101, 41152}, {12106, 15578}, {12188, 35426}, {12212, 14537}, {13335, 44230}, {13349, 37332}, {13350, 37333}, {13473, 47468}, {13566, 13630}, {13570, 18390}, {13595, 15059}, {13665, 42833}, {13785, 42832}, {13861, 32767}, {13881, 41412}, {14216, 15012}, {14644, 32305}, {14853, 22330}, {14982, 32273}, {15038, 45730}, {15069, 37517}, {15082, 16063}, {15520, 39899}, {15577, 31861}, {15684, 21358}, {15687, 19924}, {15704, 21167}, {15819, 40236}, {15820, 20998}, {16111, 38321}, {16163, 35484}, {16187, 31152}, {16264, 39569}, {18377, 46852}, {18394, 39874}, {18405, 39879}, {18509, 42858}, {18511, 42859}, {18535, 37488}, {19136, 44872}, {20300, 36201}, {22352, 37353}, {22681, 24256}, {22796, 41017}, {22797, 41016}, {23293, 44106}, {24981, 34986}, {25565, 38071}, {29959, 31726}, {31236, 44082}, {32149, 37348}, {32369, 34774}, {33749, 43865}, {34146, 46849}, {35283, 46517}, {35424, 36997}, {36655, 45542}, {36656, 45543}, {36709, 43144}, {36714, 43141}, {38010, 43620}, {38064, 41106}, {42268, 44481}, {42269, 44482}, {43226, 44498}, {43227, 44497}, {44091, 44958}

X(48889) = midpoint of X(i) and X(j) for these {i,j}: {4, 3818}, {66, 22802}, {141, 3627}, {159, 34786}, {182, 36990}, {382, 3098}, {576, 18440}, {1539, 32274}, {3830, 11178}, {3853, 18358}, {5480, 39884}, {6759, 34775}, {9976, 41737}, {10733, 12584}, {12294, 41714}, {14982, 32273}, {15069, 37517}, {15687, 47354}, {31670, 34507}, {35424, 36997}
X(48889) = reflection of X(i) in X(j) for these {i,j}: {548, 34573}, {575, 19130}, {3589, 3850}, {5092, 5}, {5097, 5480}, {6776, 15516}, {10168, 5066}, {14810, 24206}, {18553, 3818}, {19130, 546}, {20301, 7687}, {40107, 18358}, {43150, 18553}, {43273, 46267}, {44883, 32767}, {46264, 20190}
X(48889) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 16261, 1531}, {381, 36990, 182}, {382, 10516, 3098}, {3091, 46264, 38317}, {3845, 39884, 5480}, {5476, 6776, 15516}, {7394, 11550, 5943}, {10301, 45303, 32223}, {10519, 17578, 43621}, {14810, 25561, 24206}, {20428, 20429, 6248}, {38317, 46264, 20190}


X(48890) = X(2)X(3)∩X(7)X(5716)

Barycentrics    (2*a^3 + a^2*b + b^3 + a^2*c - b^2*c - b*c^2 + c^3)*(a^4 - b^4 + a^2*b*c - b^3*c - b*c^3 - c^4) : :
X(48890) = 5 X[5818] - 4 X[9958], 3 X[21020] - 2 X[35099]

X(48890) lies on these lines: {2, 3}, {7, 5716}, {8, 1503}, {40, 5300}, {63, 5016}, {321, 3429}, {500, 18444}, {511, 3868}, {515, 4968}, {516, 2292}, {529, 12642}, {950, 17863}, {1281, 2794}, {1284, 6284}, {1441, 1891}, {2829, 12746}, {3101, 5174}, {3430, 3936}, {3670, 4292}, {4297, 23536}, {4712, 12527}, {5279, 7270}, {5818, 9958}, {5840, 13265}, {7354, 8240}, {8235, 41869}, {8822, 21287}, {9579, 18655}, {9589, 11533}, {9959, 28146}, {10483, 30366}, {11043, 15171}, {11203, 28150}, {11518, 15936}, {11520, 42045}, {12579, 28158}, {12699, 30285}, {17741, 29012}, {19752, 48837}, {21020, 35099}, {26085, 37499}

X(48890) = anticomplement of X(13442)
X(48890) = X(75)-Ceva conjugate of X(40940)
X(48890) = X(1257)-isoconjugate of X(8615)
X(48890) = X(i)-Dao conjugate of X(j) for these (i, j): (440, 15314), (1104, 1)
X(48890) = crosspoint of X(75) and X(2064)
X(48890) = barycentric product X(i)*X(j) for these {i,j}: {1104, 2064}, {5279, 17863}, {7270, 40940}
X(48890) = barycentric quotient X(i)/X(j) for these {i,j}: {5279, 1257}, {5285, 2983}, {40940, 15314}
X(48890) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 20, 19645}, {4, 4220, 5051}, {20, 6839, 37088}, {20, 37433, 37422}, {20, 37437, 412}, {20, 37443, 21}, {28, 37098, 25015}, {377, 4198, 379}, {2475, 31293, 27}, {4220, 36029, 37311}, {15970, 15971, 377}


X(48891) = X(3)X(29323)∩X(20)X(185)

Barycentrics    6*a^6 + a^4*b^2 - 5*a^2*b^4 - 2*b^6 + a^4*c^2 - 4*a^2*b^2*c^2 + 2*b^4*c^2 - 5*a^2*c^4 + 2*b^2*c^4 - 2*c^6 : :
X(48891) = X[6] + 3 X[15681], 15 X[20] + X[193], 7 X[20] + X[6776], 3 X[20] + X[46264], 7 X[193] - 15 X[6776], X[193] - 5 X[46264], 3 X[6776] - 7 X[46264], 4 X[3589] - 5 X[5092], 14 X[3589] - 15 X[10168], 6 X[3589] - 5 X[19130], 7 X[5092] - 6 X[10168], 3 X[5092] - 2 X[19130], 9 X[10168] - 7 X[19130], X[141] - 3 X[550], 2 X[141] - 3 X[14810], 4 X[141] - 3 X[18553], 5 X[141] - 3 X[39884], 4 X[550] - X[18553], 5 X[550] - X[39884], 5 X[14810] - 2 X[39884], 5 X[18553] - 4 X[39884], 15 X[376] - 7 X[3619], 3 X[376] - X[3818], 7 X[3619] - 5 X[3818], X[382] - 3 X[17508], 3 X[382] - 7 X[47355], 9 X[17508] - 7 X[47355], X[3630] - 15 X[15686], X[575] + 2 X[15704], 3 X[575] - 2 X[21850], 3 X[15704] + X[21850], X[21850] - 3 X[44882], 3 X[599] - 5 X[3098], X[599] - 5 X[3534], 9 X[599] - 5 X[18440], 6 X[599] - 5 X[43150], X[3098] - 3 X[3534], 3 X[3098] - X[18440], 9 X[3534] - X[18440], 6 X[3534] - X[43150], 2 X[18440] - 3 X[43150], X[1352] - 5 X[17538], X[3146] - 3 X[38317], 9 X[3524] - 7 X[42786], 3 X[3529] + 5 X[3618], X[3529] + 2 X[20190], 5 X[3618] - 6 X[20190], 5 X[3763] - 9 X[15688], X[5059] + 3 X[14561], 3 X[5085] + X[17800], 3 X[5476] - X[43621], and many others

X(48891) lies on these lines: {3, 29323}, {5, 33751}, {6, 15681}, {20, 185}, {30, 3589}, {39, 8725}, {141, 550}, {182, 1657}, {373, 20063}, {376, 3619}, {382, 17508}, {542, 3630}, {548, 24206}, {575, 15704}, {599, 3098}, {1352, 17538}, {1503, 12103}, {1843, 13619}, {2916, 18859}, {3146, 38317}, {3313, 20127}, {3524, 42786}, {3529, 3618}, {3763, 15688}, {5059, 14561}, {5085, 17800}, {5097, 29181}, {5476, 15683}, {5943, 20062}, {6240, 46026}, {6636, 32600}, {6688, 7500}, {6781, 41413}, {6995, 10219}, {7470, 7911}, {7492, 7703}, {7712, 13857}, {8584, 19710}, {8703, 25561}, {11001, 31670}, {11178, 15689}, {11179, 46333}, {11204, 34775}, {12017, 15685}, {12055, 14537}, {12383, 36987}, {14927, 34507}, {15516, 25406}, {15577, 32903}, {15578, 18383}, {15690, 18358}, {15696, 36990}, {16063, 32237}, {17704, 31305}, {25565, 33699}, {33532, 44883}, {34200, 34573}, {34236, 46518}, {37517, 43273}, {37853, 44239}, {38010, 43619}, {38064, 42785}, {40341, 44748}, {41412, 44526}

X(48891) = midpoint of X(i) and X(j) for these {i,j}: {182, 1657}, {5476, 15683}, {14927, 34507}, {15704, 44882}
X(48891) = reflection of X(i) in X(j) for these {i,j}: {5, 33751}, {575, 44882}, {14810, 550}, {15577, 32903}, {18383, 15578}, {18553, 14810}, {24206, 548}, {25561, 8703}, {33699, 25565}, {43150, 3098}


X(48892) = X(3)X(2916)∩X(20)X(182)

Barycentrics    4*a^6 - 3*a^2*b^4 - b^6 - 4*a^2*b^2*c^2 + b^4*c^2 - 3*a^2*c^4 + b^2*c^4 - c^6 : :
X(48892) = 9 X[3] - 5 X[3763], 3 X[3] - X[3818], 7 X[3] - 3 X[10516], 5 X[3] - X[36990], 5 X[3763] - 3 X[3818], 35 X[3763] - 27 X[10516], 10 X[3763] - 9 X[24206], 5 X[3763] - 18 X[33751], 25 X[3763] - 9 X[36990], 7 X[3818] - 9 X[10516], 2 X[3818] - 3 X[24206], X[3818] - 6 X[33751], 5 X[3818] - 3 X[36990], 6 X[10516] - 7 X[24206], 3 X[10516] - 14 X[33751], 15 X[10516] - 7 X[36990], X[15321] - 3 X[32600], X[24206] - 4 X[33751], 5 X[24206] - 2 X[36990], 10 X[33751] - X[36990], X[4] - 3 X[17508], X[6] + 3 X[3534], 5 X[20] + 3 X[14853], 3 X[20] + X[31670], 5 X[182] - 3 X[14853], 3 X[182] - X[31670], 9 X[14853] - 5 X[31670], 2 X[3589] - 3 X[5092], 8 X[3589] - 9 X[10168], 4 X[3589] - 3 X[19130], 4 X[5092] - 3 X[10168], 3 X[10168] - 2 X[19130], X[66] - 3 X[11204], X[69] - 9 X[376], X[69] - 3 X[3098], 5 X[69] + 3 X[39874], X[69] + 3 X[46264], 3 X[376] - X[3098], 15 X[376] + X[39874], 3 X[376] + X[46264], 5 X[3098] + X[39874], X[14928] + 3 X[38749], X[39874] - 5 X[46264], X[141] - 3 X[8703], X[193] + 15 X[15697], X[382] - 3 X[38317], 7 X[550] + X[1353], 9 X[550] + X[3629], 5 X[550] + X[8550], 9 X[1353] - 7 X[3629], 5 X[1353] - 7 X[8550], X[1353] - 7 X[44882], and many others

X(48892) lies on these lines: {3, 2916}, {4, 17508}, {5, 29323}, {6, 3534}, {20, 182}, {22, 32223}, {30, 3589}, {66, 11204}, {69, 74}, {125, 7492}, {141, 8703}, {193, 15697}, {206, 2777}, {316, 7470}, {373, 37900}, {382, 38317}, {511, 550}, {524, 15690}, {543, 8177}, {548, 1503}, {575, 12103}, {576, 17538}, {597, 19710}, {599, 15695}, {858, 32124}, {1350, 5965}, {1351, 33749}, {1352, 3522}, {1428, 4324}, {1657, 5085}, {1691, 7756}, {1843, 10295}, {1974, 35481}, {2330, 4316}, {2549, 41412}, {2793, 13232}, {3146, 33750}, {3313, 14855}, {3357, 36989}, {3528, 14927}, {3529, 14561}, {3564, 44245}, {3618, 11001}, {3619, 19708}, {3830, 25565}, {3917, 46818}, {4048, 7830}, {5054, 42786}, {5096, 16117}, {5116, 7747}, {5447, 45185}, {5476, 12017}, {5480, 15704}, {5642, 7712}, {5972, 16063}, {6000, 35254}, {6036, 9754}, {6144, 15689}, {6459, 42832}, {6460, 42833}, {6636, 21243}, {6697, 10193}, {6699, 7502}, {6723, 7493}, {6772, 42086}, {6775, 42085}, {7387, 44862}, {7512, 43608}, {7519, 22112}, {7525, 15578}, {7667, 11064}, {7693, 20063}, {7753, 12055}, {7777, 9774}, {7794, 35248}, {7931, 43460}, {9821, 32429}, {10300, 15448}, {10304, 11178}, {10323, 44829}, {10545, 37901}, {11179, 37517}, {11574, 44249}, {11649, 37511}, {11676, 35422}, {12100, 25561}, {12121, 32305}, {12203, 43453}, {12294, 35491}, {12584, 38723}, {13347, 31305}, {13355, 32135}, {13910, 42226}, {13972, 42225}, {14093, 47353}, {14389, 22352}, {14458, 16986}, {15683, 38064}, {15685, 42785}, {15686, 21850}, {15688, 18440}, {15759, 20582}, {15988, 36005}, {16111, 35257}, {16661, 21659}, {18358, 34200}, {18400, 44883}, {18553, 33923}, {18559, 46026}, {18917, 46728}, {19124, 35471}, {19140, 20127}, {19910, 38738}, {20062, 43650}, {21167, 39884}, {21734, 40330}, {22802, 23041}, {23055, 41151}, {23329, 34775}, {24309, 29315}, {24981, 33884}, {25564, 35228}, {26156, 44280}, {30739, 32237}, {31884, 34507}, {32002, 35474}, {32068, 33586}, {32233, 38788}, {32476, 41623}, {33699, 48310}, {34682, 41749}, {34776, 34778}, {35464, 38742}, {35707, 38726}, {36382, 40900}, {36383, 40901}, {38747, 43152}, {40825, 44519}, {44903, 46267}, {45759, 47354}

X(48892) = midpoint of X(i) and X(j) for these {i,j}: {20, 182}, {550, 44882}, {597, 19710}, {3098, 46264}, {3357, 36989}, {5476, 15681}, {5480, 15704}, {9821, 32429}, {12121, 32305}, {19140, 20127}, {34776, 34778}
X(48892) = reflection of X(i) in X(j) for these {i,j}: {3, 33751}, {1351, 33749}, {3830, 25565}, {5480, 20190}, {14810, 548}, {19130, 5092}, {20299, 15578}, {20582, 15759}, {24206, 3}, {25561, 12100}, {40107, 14810}
X(48892) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 46264, 3098}, {3618, 11001, 43621}, {5092, 19130, 10168}, {7525, 17712, 20299}, {16063, 35268, 5972}, {39884, 46853, 21167}


X(48893) = X(3)X(6)∩X(30)X(551)

Barycentrics    a^2*(2*a^4*b + a^3*b^2 - 3*a^2*b^3 - a*b^4 + b^5 + 2*a^4*c + 4*a^3*b*c - a^2*b^2*c - 4*a*b^3*c - b^4*c + a^3*c^2 - a^2*b*c^2 - 4*a*b^2*c^2 - 2*b^3*c^2 - 3*a^2*c^3 - 4*a*b*c^3 - 2*b^2*c^3 - a*c^4 - b*c^4 + c^5) : :
X(48893) = 2 X[500] + X[35203], 3 X[3576] - X[9840], 3 X[5731] + X[15971], 5 X[7987] - 3 X[14636]

X(48893) lies on these lines: {1, 37425}, {3, 6}, {4, 6176}, {21, 25897}, {30, 551}, {35, 3955}, {40, 42042}, {51, 16451}, {65, 15447}, {81, 46623}, {184, 37285}, {228, 29958}, {515, 15973}, {517, 5453}, {1154, 33862}, {1437, 37286}, {1490, 15972}, {1790, 3145}, {2360, 20834}, {3271, 35206}, {3292, 35193}, {3576, 9840}, {3651, 37527}, {3819, 16287}, {3917, 16452}, {4184, 22076}, {5044, 24036}, {5495, 32612}, {5731, 15971}, {5732, 15979}, {5840, 10035}, {5943, 16453}, {6000, 10267}, {6097, 13754}, {6688, 16414}, {7175, 37573}, {7416, 46850}, {7420, 13598}, {7987, 14636}, {9306, 37284}, {10441, 37400}, {10470, 37331}, {12109, 14547}, {13391, 23961}, {13408, 24299}, {13745, 17614}, {15082, 16296}, {16132, 30285}, {17194, 28258}, {17768, 42443}, {18481, 46704}, {19782, 37062}, {20840, 32237}, {28369, 37552}, {37080, 37631}, {41854, 46475}

X(48893) = midpoint of X(i) and X(j) for these {i,j}: {1, 37425}, {3, 500}, {18481, 46704}
X(48893) = reflection of X(35203) in X(3)
X(48893) = isogonal conjugate of the polar conjugate of X(25986)
X(48893) = barycentric product X(3)*X(25986)
X(48893) = barycentric quotient X(25986)/X(264)
X(48893) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 581, 970}, {3, 5396, 15489}, {3, 37474, 13323}


X(48894) = X(1)X(256)∩X(3)X(4653)

Barycentrics    a*(2*a^5*b + a^4*b^2 - 3*a^3*b^3 - a^2*b^4 + a*b^5 + 2*a^5*c - a^3*b^2*c - 2*a^2*b^3*c - a*b^4*c + 2*b^5*c + a^4*c^2 - a^3*b*c^2 - 4*a^2*b^2*c^2 - 2*a*b^3*c^2 - 3*a^3*c^3 - 2*a^2*b*c^3 - 2*a*b^2*c^3 - 4*b^3*c^3 - a^2*c^4 - a*b*c^4 + a*c^5 + 2*b*c^5) : :
X(48894) = X[40] - 3 X[14636], X[500] - 3 X[10246], X[2650] + 3 X[11203], 3 X[3576] - X[37425], 5 X[3616] - X[15971], 3 X[5886] - X[46704]

X(48894) lies on these lines: {1, 256}, {3, 4653}, {12, 15974}, {21, 37527}, {30, 551}, {40, 14636}, {98, 19312}, {182, 405}, {500, 10246}, {517, 3743}, {524, 11260}, {542, 13745}, {575, 1724}, {758, 9959}, {1008, 6248}, {1009, 13334}, {1043, 6998}, {1104, 15976}, {1125, 15973}, {1154, 33281}, {1352, 13725}, {1495, 11101}, {2646, 24210}, {2650, 11203}, {2654, 22347}, {2782, 41193}, {2792, 12579}, {3098, 19782}, {3560, 6759}, {3576, 37425}, {3616, 15971}, {3819, 47521}, {3838, 37836}, {3897, 46483}, {4192, 10470}, {4195, 11257}, {4300, 29349}, {4313, 15970}, {5092, 13732}, {5171, 19761}, {5436, 15972}, {5453, 10105}, {5603, 10465}, {5886, 46704}, {5943, 13724}, {6036, 37047}, {6097, 32612}, {6776, 13736}, {7379, 43460}, {9306, 37228}, {9737, 19758}, {10441, 19262}, {11097, 13350}, {11098, 13349}, {13335, 13723}, {13442, 29012}, {13464, 43164}, {13728, 24206}, {13731, 15489}, {13734, 46850}, {14561, 19766}, {14853, 19783}, {15447, 37605}, {19544, 19765}, {19771, 34417}, {20323, 37631}, {25579, 37531}, {26117, 37823}, {29093, 35099}, {29181, 42819}, {37023, 47113}, {37055, 43976}, {42443, 44669}

X(48894) = midpoint of X(1) and X(9840)
X(48894) = reflection of X(i) in X(j) for these {i,j}: {5453, 15178}, {15973, 1125}
X(48894) = {X(1),X(30366)}-harmonic conjugate of X(10544)


X(48895) = X(2)X(43621)∩X(4)X(69)

Barycentrics    2*a^6 + 3*a^4*b^2 - 3*a^2*b^4 - 2*b^6 + 3*a^4*c^2 + 4*a^2*b^2*c^2 + 2*b^4*c^2 - 3*a^2*c^4 + 2*b^2*c^4 - 2*c^6 : :
X(48895) = 3 X[2] + X[43621], 9 X[4] - X[69], 5 X[4] - X[1352], 3 X[4] - X[3818], 4 X[4] - X[18553], 3 X[4] + X[31670], 7 X[4] - X[34507], 6 X[4] - X[43150], 5 X[69] - 9 X[1352], X[69] - 3 X[3818], 4 X[69] - 9 X[18553], X[69] + 3 X[31670], 7 X[69] - 9 X[34507], 2 X[69] - 3 X[43150], 3 X[1352] - 5 X[3818], 4 X[1352] - 5 X[18553], 3 X[1352] + 5 X[31670], 7 X[1352] - 5 X[34507], 6 X[1352] - 5 X[43150], 4 X[3818] - 3 X[18553], 7 X[3818] - 3 X[34507], 3 X[18553] + 4 X[31670], 7 X[18553] - 4 X[34507], 3 X[18553] - 2 X[43150], 7 X[31670] + 3 X[34507], 2 X[31670] + X[43150], 6 X[34507] - 7 X[43150], 5 X[5] - 3 X[21167], 5 X[14810] - 6 X[21167], X[6] + 3 X[3830], X[20] - 3 X[38317], 4 X[3589] - 3 X[5092], 10 X[3589] - 9 X[10168], 2 X[3589] - 3 X[19130], 5 X[5092] - 6 X[10168], 3 X[10168] - 5 X[19130], X[66] - 3 X[18376], X[141] - 3 X[3845], 2 X[141] - 3 X[25561], 3 X[381] - X[3098], 9 X[381] - 5 X[3763], 3 X[3098] - 5 X[3763], X[3629] + 9 X[15687], X[3629] - 3 X[21850], 3 X[15687] + X[21850], X[575] + 2 X[3627], X[576] + 5 X[5076], 3 X[576] - X[39899], 5 X[5076] - X[36990], 15 X[5076] + X[39899], 3 X[36990] + X[39899], and many others

X(48895) lies on these lines: {2, 43621}, {3, 39784}, {4, 69}, {5, 14810}, {6, 3830}, {20, 38317}, {30, 3589}, {66, 18376}, {115, 41413}, {141, 3845}, {143, 14864}, {146, 32062}, {148, 41622}, {182, 382}, {265, 11807}, {373, 5189}, {381, 3098}, {427, 32223}, {428, 11064}, {524, 12101}, {542, 1539}, {546, 24206}, {575, 3627}, {576, 5076}, {597, 33699}, {698, 7843}, {1350, 3843}, {1370, 6688}, {1386, 33697}, {1469, 18514}, {1503, 3853}, {1657, 17508}, {1974, 35480}, {2076, 39565}, {2777, 20301}, {2916, 37924}, {3054, 32414}, {3056, 18513}, {3094, 39590}, {3146, 14561}, {3329, 14492}, {3534, 47355}, {3543, 5476}, {3545, 42786}, {3564, 12102}, {3618, 15682}, {3619, 41099}, {3819, 7394}, {3849, 8177}, {3851, 31884}, {3860, 20582}, {3861, 40107}, {3917, 37349}, {4846, 43726}, {5039, 44518}, {5064, 37638}, {5066, 34573}, {5073, 5085}, {5102, 48662}, {5103, 7816}, {5446, 34514}, {5650, 7533}, {5943, 7391}, {5965, 39884}, {5972, 10301}, {6000, 18382}, {6144, 18440}, {6321, 35439}, {6776, 22330}, {7386, 10219}, {7519, 32237}, {7527, 32600}, {7528, 13348}, {7540, 11430}, {7576, 16163}, {7703, 32225}, {7728, 32273}, {7766, 14458}, {7806, 9993}, {7820, 44230}, {7842, 24256}, {7873, 18500}, {8703, 25565}, {9738, 36712}, {9739, 36711}, {9969, 44288}, {10151, 47569}, {10296, 19121}, {10545, 10989}, {10546, 13857}, {10721, 32305}, {10733, 19140}, {11178, 14269}, {11550, 21849}, {11649, 44283}, {12017, 15684}, {12045, 46336}, {12295, 32271}, {12317, 14831}, {13111, 35426}, {13473, 47571}, {13570, 18531}, {13623, 14855}, {13860, 43152}, {13910, 42225}, {13972, 42226}, {14389, 34603}, {14848, 35434}, {14853, 15516}, {14893, 18358}, {14928, 39809}, {14957, 34236}, {15704, 33751}, {16625, 18917}, {16776, 18572}, {17704, 34938}, {17710, 44267}, {18383, 21852}, {18403, 37511}, {18559, 44091}, {19124, 35490}, {19149, 34786}, {19710, 48310}, {21243, 47582}, {21969, 37779}, {22615, 44482}, {22644, 44481}, {22803, 32521}, {23049, 44490}, {23325, 34778}, {25555, 38136}, {31074, 44106}, {31133, 34417}, {31725, 44479}, {32149, 37242}, {34775, 34779}, {34986, 46818}, {35403, 44456}, {35427, 38744}, {35431, 36997}, {36709, 43141}, {36714, 43144}, {36755, 37333}, {36756, 37332}, {38010, 43618}, {38144, 48661}, {42874, 44228}, {43460, 44422}

X(48895) = midpoint of X(i) and X(j) for these {i,j}: {182, 382}, {576, 36990}, {597, 33699}, {1386, 33697}, {3543, 5476}, {3627, 5480}, {3818, 31670}, {7728, 32273}, {10721, 32305}, {10733, 19140}, {12295, 32271}, {18440, 37517}, {19149, 34786}, {34775, 34779}, {35431, 36997}
X(48895) = reflection of X(i) in X(j) for these {i,j}: {575, 5480}, {5092, 19130}, {6776, 22330}, {8703, 25565}, {14810, 5}, {15704, 33751}, {20582, 3860}, {24206, 546}, {25561, 3845}, {43150, 3818}, {44882, 25555}
X(48895) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 31670, 3818}, {621, 622, 7768}, {3818, 43150, 18553}, {36969, 36970, 14537}, {38136, 44882, 25555}


X(48896) = X(2)X(33751)∩X(30)X(182)

Barycentrics    5*a^6 + a^4*b^2 - 4*a^2*b^4 - 2*b^6 + a^4*c^2 - 2*a^2*b^2*c^2 + 2*b^4*c^2 - 4*a^2*c^4 + 2*b^2*c^4 - 2*c^6 : :
X(48896) = 3 X[2] - 4 X[33751], 2 X[4] - 3 X[17508], 3 X[20] - X[1352], 13 X[20] - 5 X[3620], 7 X[20] - 3 X[10519], 5 X[20] - 2 X[40107], 2 X[1352] - 3 X[3098], 13 X[1352] - 15 X[3620], 7 X[1352] - 9 X[10519], 5 X[1352] - 6 X[40107], 13 X[3098] - 10 X[3620], 7 X[3098] - 6 X[10519], 5 X[3098] - 4 X[40107], 35 X[3620] - 39 X[10519], 25 X[3620] - 26 X[40107], 15 X[10519] - 14 X[40107], 13 X[182] - 12 X[597], 7 X[182] - 6 X[5476], 5 X[182] - 4 X[5480], 9 X[182] - 8 X[18583], 3 X[182] - 4 X[44882], 14 X[597] - 13 X[5476], 15 X[597] - 13 X[5480], 27 X[597] - 26 X[18583], 9 X[597] - 13 X[44882], 15 X[5476] - 14 X[5480], 27 X[5476] - 28 X[18583], 9 X[5476] - 14 X[44882], 9 X[5480] - 10 X[18583], 3 X[5480] - 5 X[44882], 2 X[18583] - 3 X[44882], 3 X[376] - 2 X[24206], 13 X[1657] + X[6144], 7 X[1657] + X[39899], 7 X[6144] - 13 X[39899], 3 X[11001] + X[14927], X[576] + 2 X[3529], 5 X[576] - 6 X[14912], 5 X[3529] + 3 X[14912], 3 X[14912] - 5 X[46264], X[1350] - 3 X[15681], 3 X[1350] - X[48662], 9 X[15681] - X[48662], X[1351] + 3 X[15685], 4 X[1353] - 3 X[37517], 8 X[3530] - 7 X[42786], 3 X[3534] - 2 X[14810], 3 X[3534] - X[36990], and many others

X(48896) lies on these lines: {2, 33751}, {3, 29323}, {4, 17508}, {6, 17800}, {20, 1352}, {30, 182}, {141, 12103}, {376, 24206}, {382, 5092}, {511, 1657}, {524, 44903}, {542, 11001}, {550, 3818}, {576, 3529}, {1350, 11645}, {1351, 15685}, {1353, 29181}, {1370, 5972}, {1386, 28154}, {1503, 15704}, {2777, 36989}, {3146, 19130}, {3530, 42786}, {3534, 11178}, {3618, 11541}, {3627, 38317}, {5059, 31670}, {5073, 5085}, {5076, 47355}, {5097, 43273}, {5189, 35268}, {6560, 42833}, {6561, 42832}, {6776, 15683}, {7525, 32600}, {7553, 13347}, {7748, 41412}, {8725, 37479}, {10168, 15682}, {10516, 15696}, {11704, 12088}, {12584, 15580}, {13394, 47095}, {14561, 33703}, {15059, 37913}, {15578, 23325}, {15640, 38064}, {15686, 39884}, {15688, 25561}, {15691, 47354}, {17578, 33750}, {18430, 47748}, {18553, 31884}, {18565, 19131}, {18911, 20062}, {19124, 34797}, {19140, 34584}, {19710, 41152}, {20063, 34417}, {21167, 44245}, {21850, 22234}, {25406, 43621}, {31152, 32237}, {34573, 46853}, {34786, 44883}, {35400, 46267}, {42852, 43618}

X(48896) = midpoint of X(i) and X(j) for these {i,j}: {6, 17800}, {3529, 46264}, {5059, 31670}
X(48896) = reflection of X(i) in X(j) for these {i,j}: {141, 12103}, {382, 5092}, {576, 46264}, {3098, 20}, {3146, 19130}, {3818, 550}, {11178, 3534}, {15682, 10168}, {34786, 44883}, {36990, 14810}, {47354, 15691}
X(48896) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3534, 36990, 14810}, {14810, 36990, 11178}


X(48897) = X(1)X(30)∩X(40)X(511)

Barycentrics    a*(a^5*b - 2*a^3*b^3 + a*b^5 + a^5*c + 4*a^4*b*c - a^3*b^2*c - 3*a^2*b^3*c - b^5*c - a^3*b*c^2 - 2*a^2*b^2*c^2 - a*b^3*c^2 - 2*a^3*c^3 - 3*a^2*b*c^3 - a*b^2*c^3 + 2*b^3*c^3 + a*c^5 - b*c^5) : :
X(48897) = 3 X[1] - 4 X[5453], 3 X[500] - 2 X[5453], 4 X[35203] - 5 X[35242], 3 X[4300] - X[10459], 3 X[3576] - 2 X[9840], 3 X[5587] - 4 X[15973], 4 X[10035] - 3 X[16173]

X(48897) lies on these lines: {1, 30}, {3, 1724}, {4, 991}, {6, 37426}, {10, 35338}, {20, 581}, {33, 46468}, {35, 1935}, {40, 511}, {42, 31730}, {43, 35203}, {55, 1777}, {58, 3651}, {73, 4304}, {81, 33557}, {140, 5400}, {165, 37699}, {201, 41562}, {283, 35989}, {284, 30267}, {376, 386}, {387, 37427}, {411, 37469}, {442, 17194}, {484, 13391}, {501, 3737}, {515, 4300}, {524, 6765}, {540, 3811}, {548, 22392}, {550, 5396}, {580, 7411}, {846, 7701}, {940, 37411}, {942, 15937}, {947, 23696}, {950, 4303}, {971, 37528}, {978, 14636}, {1044, 11529}, {1064, 4297}, {1066, 4314}, {1071, 15852}, {1154, 11010}, {1210, 22053}, {1350, 37062}, {1385, 32486}, {1490, 13442}, {1697, 6000}, {1739, 40296}, {1745, 3601}, {1754, 36742}, {1764, 37482}, {1778, 37508}, {1818, 12572}, {1961, 46976}, {2293, 21620}, {2360, 28029}, {2475, 17173}, {2594, 15338}, {2635, 13411}, {3073, 15931}, {3100, 8555}, {3149, 37501}, {3293, 3579}, {3295, 6180}, {3303, 10105}, {3336, 47749}, {3430, 4221}, {3488, 4306}, {3524, 17749}, {3576, 9840}, {3586, 37523}, {3670, 13369}, {3720, 18483}, {4256, 37403}, {4257, 6876}, {4276, 7421}, {4278, 7430}, {4292, 14547}, {4305, 10571}, {4337, 10572}, {4415, 41543}, {4644, 6361}, {4653, 21669}, {4674, 13145}, {5010, 6097}, {5119, 13754}, {5247, 7688}, {5482, 19648}, {5499, 45926}, {5587, 15973}, {5663, 37563}, {5691, 46704}, {5713, 10431}, {5721, 37424}, {5732, 29181}, {6003, 14812}, {6767, 10108}, {6985, 37522}, {7299, 34879}, {7580, 36746}, {8583, 13745}, {9275, 43576}, {9958, 18528}, {10035, 16173}, {12053, 15368}, {15107, 37405}, {15447, 15803}, {15682, 48855}, {15792, 36001}, {15970, 24181}, {17056, 37447}, {17104, 43574}, {17810, 37273}, {18591, 40979}, {24468, 32913}, {26131, 37433}, {30282, 37694}, {37356, 37693}

X(48897) = reflection of X(i) in X(j) for these {i,j}: {1, 500}, {40, 37425}, {5691, 46704}
X(48897) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1464, 10543, 1}, {4337, 10572, 37558}, {7580, 36746, 37530}, {26131, 37433, 45924}


X(48898) = X(20)X(185)∩X(30)X(182)

Barycentrics    3*a^6 - 2*a^2*b^4 - b^6 - 2*a^2*b^2*c^2 + b^4*c^2 - 2*a^2*c^4 + b^2*c^4 - c^6 : :
X(48898) = 7 X[3] - 5 X[3763], 5 X[3] - 3 X[10516], 3 X[3] - 2 X[24206], 3 X[3] - 4 X[33751], 3 X[3] - X[36990], 10 X[3763] - 7 X[3818], 25 X[3763] - 21 X[10516], 15 X[3763] - 14 X[24206], 15 X[3763] - 28 X[33751], 15 X[3763] - 7 X[36990], 5 X[3818] - 6 X[10516], 3 X[3818] - 4 X[24206], 3 X[3818] - 8 X[33751], 3 X[3818] - 2 X[36990], 9 X[10516] - 10 X[24206], 9 X[10516] - 20 X[33751], 9 X[10516] - 5 X[36990], 4 X[33751] - X[36990], 2 X[4] - 3 X[38317], 4 X[5092] - 3 X[38317], 2 X[5] - 3 X[17508], 7 X[20] + X[193], 3 X[20] + X[6776], 3 X[193] - 7 X[6776], X[193] - 7 X[46264], X[6776] - 3 X[46264], 7 X[182] - 6 X[597], 4 X[182] - 3 X[5476], 3 X[182] - 2 X[5480], 5 X[182] - 4 X[18583], 8 X[597] - 7 X[5476], 9 X[597] - 7 X[5480], 15 X[597] - 14 X[18583], 3 X[597] - 7 X[44882], 9 X[5476] - 8 X[5480], 15 X[5476] - 16 X[18583], 3 X[5476] - 8 X[44882], 5 X[5480] - 6 X[18583], X[5480] - 3 X[44882], 2 X[18583] - 5 X[44882], X[67] - 3 X[38788], X[69] - 5 X[17538], 8 X[140] - 7 X[42786], 3 X[376] - X[1352], 3 X[376] - 2 X[14810], 3 X[376] + X[14927], 7 X[376] - 3 X[21356], 7 X[1352] - 9 X[21356], 2 X[14810] + X[14927], 14 X[14810] - 9 X[21356], and many others

X(48898) lies on these lines: {2, 32237}, {3, 2916}, {4, 5092}, {5, 17508}, {6, 1657}, {20, 185}, {22, 125}, {26, 17712}, {30, 182}, {51, 20062}, {67, 38788}, {69, 13452}, {140, 42786}, {141, 548}, {206, 22802}, {373, 7519}, {376, 1352}, {382, 5085}, {524, 15686}, {542, 1350}, {550, 1503}, {575, 3529}, {576, 12007}, {599, 15689}, {858, 35268}, {1351, 15681}, {1353, 19710}, {1368, 15448}, {1386, 28146}, {1469, 4316}, {1495, 16063}, {1598, 44862}, {1691, 7748}, {1843, 35471}, {1974, 18560}, {1992, 46333}, {2030, 43619}, {2330, 10483}, {2777, 15141}, {2979, 14683}, {3056, 4324}, {3091, 33750}, {3146, 14561}, {3313, 10575}, {3522, 18553}, {3524, 25561}, {3564, 12103}, {3589, 3627}, {3618, 33703}, {3619, 21735}, {3788, 40278}, {3819, 31383}, {3830, 10168}, {3843, 47355}, {3923, 29113}, {4048, 7761}, {4549, 6000}, {5017, 6781}, {5050, 17800}, {5059, 14853}, {5073, 12017}, {5093, 33749}, {5097, 11001}, {5116, 5475}, {5189, 15080}, {5207, 7782}, {5254, 41412}, {5596, 20427}, {5621, 12902}, {5640, 20063}, {5943, 7500}, {5965, 33878}, {5972, 31152}, {5984, 33706}, {5999, 17005}, {6030, 31074}, {6240, 19124}, {6403, 13619}, {6593, 34584}, {6636, 11550}, {6688, 6995}, {6756, 13347}, {7391, 22352}, {7398, 10219}, {7487, 17704}, {7502, 15578}, {7553, 37515}, {7667, 9306}, {7699, 46450}, {7802, 12215}, {8550, 37517}, {8703, 11178}, {8719, 38736}, {9729, 31305}, {9833, 13348}, {9862, 22676}, {9863, 12122}, {9977, 39588}, {10304, 40330}, {10519, 41482}, {10721, 15462}, {10733, 20301}, {11180, 15697}, {11414, 18396}, {11646, 38742}, {12083, 18390}, {12203, 39750}, {12244, 15102}, {12252, 44423}, {12294, 35481}, {12584, 16163}, {13293, 15577}, {13394, 46517}, {14093, 21358}, {14269, 25565}, {14641, 34146}, {14826, 40911}, {14855, 19161}, {14893, 48310}, {14907, 14994}, {14982, 38723}, {15088, 44278}, {15516, 15683}, {15595, 35941}, {15682, 38064}, {15684, 47352}, {15688, 47353}, {15696, 18440}, {15712, 34573}, {16187, 43957}, {16618, 23325}, {17702, 32305}, {17834, 17848}, {18358, 21167}, {18374, 18564}, {18376, 20300}, {18381, 44883}, {18400, 35243}, {18418, 18531}, {18565, 19129}, {19145, 42264}, {19146, 42263}, {20127, 32233}, {20299, 34775}, {20582, 45759}, {21659, 33524}, {21850, 39561}, {22862, 42096}, {22906, 42097}, {23300, 34786}, {24257, 29032}, {24309, 29020}, {24728, 29097}, {31726, 47453}, {32113, 44246}, {32216, 32267}, {33264, 39141}, {34200, 47354}, {34417, 37900}, {34603, 43650}, {34726, 37475}, {36757, 43633}, {36758, 43632}, {36883, 38798}, {37648, 37899}, {38010, 43448}, {38029, 41869}, {38315, 48661}, {38654, 38749}, {40341, 44796}, {40825, 44526}, {42215, 42832}, {42216, 42833}, {42353, 44248}, {43407, 44482}, {43408, 44481}

X(48898) = midpoint of X(i) and X(j) for these {i,j}: {6, 1657}, {20, 46264}, {1352, 14927}, {3313, 10575}, {3529, 31670}, {5059, 43621}, {5596, 20427}, {11001, 11179}, {15681, 43273}, {15683, 20423}, {20127, 32233}
X(48898) = reflection of X(i) in X(j) for these {i,j}: {4, 5092}, {141, 548}, {182, 44882}, {382, 19130}, {1352, 14810}, {3098, 550}, {3627, 3589}, {3818, 3}, {3830, 10168}, {10733, 20301}, {11178, 8703}, {12584, 16163}, {18358, 33923}, {18381, 44883}, {18440, 40107}, {22802, 206}, {24206, 33751}, {31670, 575}, {34507, 3098}, {34775, 20299}, {34786, 23300}, {36990, 24206}, {37517, 8550}, {47354, 34200}
X(48898) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 36990, 24206}, {4, 5092, 38317}, {376, 1352, 14810}, {376, 14927, 1352}, {382, 5085, 19130}, {3529, 25406, 31670}, {5059, 14853, 43621}, {15696, 18440, 31884}, {18358, 33923, 21167}, {18440, 31884, 40107}, {24206, 33751, 3}, {24206, 36990, 3818}, {25406, 31670, 575}, {36993, 36995, 11257}, {42266, 42267, 7756}


X(48899) = X(1)X(30)∩X(4)X(69)

Barycentrics    a^6*b + 2*a^5*b^2 + a^4*b^3 - a^3*b^4 - 2*a^2*b^5 - a*b^6 + a^6*c + 2*a^5*b*c + 2*a^4*b^2*c - 2*a^2*b^4*c - 2*a*b^5*c - b^6*c + 2*a^5*c^2 + 2*a^4*b*c^2 + 2*a^2*b^3*c^2 + a*b^4*c^2 - b^5*c^2 + a^4*c^3 + 2*a^2*b^2*c^3 + 4*a*b^3*c^3 + 2*b^4*c^3 - a^3*c^4 - 2*a^2*b*c^4 + a*b^2*c^4 + 2*b^3*c^4 - 2*a^2*c^5 - 2*a*b*c^5 - b^2*c^5 - a*c^6 - b*c^6 : :
X(48899) = 4 X[1125] - 3 X[14636]

X(48899) lies on these lines: {1, 30}, {2, 35203}, {3, 10478}, {4, 69}, {5, 1764}, {10, 24705}, {40, 15973}, {355, 12435}, {381, 10479}, {382, 10454}, {442, 17185}, {497, 35620}, {516, 37425}, {517, 4647}, {540, 17733}, {550, 10470}, {764, 6002}, {946, 4425}, {952, 11521}, {962, 15971}, {1125, 14636}, {1402, 1770}, {1478, 10480}, {1479, 10473}, {1699, 10476}, {1999, 46976}, {2051, 19513}, {2300, 23537}, {3741, 18483}, {4205, 10455}, {4292, 15979}, {5057, 46975}, {5208, 37433}, {5603, 10465}, {5787, 12547}, {5805, 10442}, {5812, 10888}, {5814, 10447}, {5886, 10882}, {6033, 38481}, {6851, 35612}, {7009, 46468}, {7413, 46623}, {7681, 15974}, {7728, 38482}, {9812, 39550}, {9955, 19863}, {10035, 38761}, {10451, 37468}, {10461, 37447}, {10474, 10572}, {10475, 30384}, {10525, 17617}, {10738, 35649}, {10741, 38479}, {10742, 35636}, {10887, 26446}, {12555, 37822}, {13161, 28369}, {13244, 16128}, {13323, 19645}, {13391, 38474}, {13731, 24220}, {15522, 38478}, {15682, 48858}, {15945, 21530}, {17167, 37225}, {17188, 20836}, {17738, 30077}, {18417, 37230}, {20788, 37482}, {22793, 35631}, {23536, 28368}, {25058, 26131}, {27000, 30065}, {29181, 39553}, {31730, 43223}, {34789, 35638}, {35623, 45924}

X(48899) = midpoint of X(962) and X(15971)
X(48899) = reflection of X(i) in X(j) for these {i,j}: {40, 15973}, {9840, 946}, {18481, 5453}, {38761, 10035}
X(48899) = anticomplement of X(35203)
X(48899) = crossdifference of every pair of points on line {3049, 9404}
X(48899) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 10446, 10441}, {946, 12545, 37620}


X(48900) = X(1)X(85)∩X(3)X(142)

Barycentrics    a^5 - a^4*b - a^2*b^3 + a*b^4 - a^4*c + b^4*c - 2*a*b^2*c^2 - b^3*c^2 - a^2*c^3 - b^2*c^3 + a*c^4 + b*c^4 : :
X(48900) = X[40] - 3 X[9746], 5 X[3616] - 3 X[10186], 7 X[3622] - 3 X[11200]

X(48900) lies on these lines: {1, 85}, {2, 9441}, {3, 142}, {4, 1973}, {5, 40561}, {6, 45305}, {8, 28870}, {10, 220}, {30, 48822}, {40, 6998}, {41, 13576}, {86, 1742}, {226, 28053}, {355, 2784}, {517, 24455}, {740, 3811}, {752, 45700}, {936, 27384}, {962, 28862}, {990, 24325}, {1441, 4336}, {1698, 28874}, {1699, 6996}, {1709, 4697}, {1721, 10436}, {1802, 2550}, {1836, 17798}, {1944, 24341}, {2271, 3755}, {2486, 47373}, {3332, 19843}, {3434, 20769}, {3589, 42356}, {3616, 10186}, {3622, 11200}, {3758, 9355}, {3817, 31191}, {3923, 25066}, {4229, 25526}, {4307, 14986}, {4343, 5736}, {4349, 21625}, {4356, 34937}, {4364, 38454}, {4670, 15726}, {4847, 23151}, {4920, 24248}, {5587, 28877}, {5603, 28885}, {5657, 28889}, {5703, 37573}, {5750, 21629}, {5790, 28909}, {5901, 11730}, {6684, 28881}, {6685, 19541}, {7580, 43223}, {8226, 25453}, {8227, 21554}, {8727, 29635}, {9440, 26125}, {9779, 32944}, {9780, 43984}, {9812, 32772}, {10883, 29631}, {11231, 28913}, {11680, 24591}, {12047, 37576}, {12263, 32941}, {12558, 20083}, {12571, 14535}, {13634, 31162}, {13635, 38021}, {14953, 35267}, {15486, 29207}, {16054, 17188}, {16876, 17167}, {17889, 24781}, {18480, 28901}, {19314, 41012}, {19545, 37619}, {20358, 36488}, {20544, 24264}, {22793, 28897}, {24283, 37597}, {24315, 44670}, {24715, 40861}, {25352, 26446}, {27399, 32932}, {28125, 30807}, {29054, 46475}, {29066, 42455}, {29633, 36652}, {32935, 35026}

X(48900) = crossdifference of every pair of points on line {6586, 46388}


X(48901) = X(4)X(69)∩X(30)X(182)

Barycentrics    a^6 + 2*a^4*b^2 - 2*a^2*b^4 - b^6 + 2*a^4*c^2 + 2*a^2*b^2*c^2 + b^4*c^2 - 2*a^2*c^4 + b^2*c^4 - c^6 : :
X(48901) = 2 X[3] - 3 X[38317], 5 X[3] - 7 X[47355], 4 X[19130] - 3 X[38317], 10 X[19130] - 7 X[47355], 15 X[38317] - 14 X[47355], 5 X[4] - X[69], 3 X[4] - X[1352], 5 X[4] - 2 X[18553], 4 X[4] - X[34507], 7 X[4] - 2 X[43150], 3 X[69] - 5 X[1352], 2 X[69] - 5 X[3818], X[69] + 5 X[31670], 4 X[69] - 5 X[34507], 7 X[69] - 10 X[43150], 2 X[1352] - 3 X[3818], 5 X[1352] - 6 X[18553], X[1352] + 3 X[31670], 4 X[1352] - 3 X[34507], 7 X[1352] - 6 X[43150], 5 X[3818] - 4 X[18553], X[3818] + 2 X[31670], 7 X[3818] - 4 X[43150], 2 X[18553] + 5 X[31670], 8 X[18553] - 5 X[34507], 7 X[18553] - 5 X[43150], 4 X[31670] + X[34507], 7 X[31670] + 2 X[43150], 7 X[34507] - 8 X[43150], 5 X[5] - 4 X[34573], 8 X[5] - 7 X[42786], 5 X[3098] - 8 X[34573], 4 X[3098] - 7 X[42786], 32 X[34573] - 35 X[42786], 5 X[6] - 4 X[33749], 5 X[382] + 4 X[33749], X[20] - 3 X[14561], 5 X[20] - 9 X[33750], 2 X[20] - 7 X[42785], 2 X[5092] - 3 X[14561], 10 X[5092] - 9 X[33750], 4 X[5092] - 7 X[42785], 2 X[5092] + X[43621], 5 X[14561] - 3 X[33750], 6 X[14561] - 7 X[42785], 3 X[14561] + X[43621], 18 X[33750] - 35 X[42785], 9 X[33750] + 5 X[43621], 7 X[42785] + 2 X[43621], , and many others

X(48901) lies on these lines: {2, 14488}, {3, 7889}, {4, 69}, {5, 3098}, {6, 382}, {20, 5092}, {22, 40913}, {25, 5972}, {30, 182}, {51, 7391}, {66, 18383}, {74, 20301}, {113, 12584}, {115, 5017}, {125, 31133}, {141, 546}, {148, 32451}, {184, 34603}, {206, 11819}, {262, 40236}, {373, 16063}, {381, 1350}, {427, 32269}, {428, 9306}, {518, 22793}, {524, 15687}, {542, 1351}, {550, 3589}, {573, 36707}, {575, 3146}, {576, 1353}, {578, 7553}, {599, 14269}, {611, 12953}, {613, 12943}, {698, 7759}, {858, 34417}, {991, 36716}, {1370, 5943}, {1386, 28160}, {1428, 10483}, {1469, 3583}, {1495, 7519}, {1513, 37647}, {1539, 2854}, {1595, 46730}, {1596, 18418}, {1597, 37488}, {1656, 31884}, {1657, 5085}, {1885, 44470}, {1899, 21849}, {1974, 6240}, {1993, 24981}, {2030, 43618}, {2076, 7746}, {2393, 44276}, {2777, 23049}, {2781, 10113}, {2794, 35431}, {2930, 38789}, {2979, 37349}, {3056, 3585}, {3060, 3448}, {3066, 31152}, {3094, 5475}, {3357, 23300}, {3529, 3618}, {3534, 10168}, {3543, 5032}, {3564, 3853}, {3619, 3855}, {3628, 21167}, {3763, 3851}, {3767, 41413}, {3788, 5103}, {3819, 6997}, {3832, 10519}, {3839, 25561}, {3843, 10516}, {3844, 38140}, {3845, 11178}, {3861, 18358}, {3867, 13488}, {3917, 7394}, {3923, 29032}, {4846, 38005}, {5039, 5254}, {5050, 5073}, {5054, 25565}, {5064, 21243}, {5076, 5965}, {5094, 32223}, {5102, 39899}, {5104, 18424}, {5169, 15107}, {5189, 5640}, {5309, 12212}, {5446, 18381}, {5663, 32273}, {5878, 36851}, {5969, 22505}, {5984, 14458}, {5999, 9993}, {6033, 22728}, {6034, 38741}, {6249, 7770}, {6287, 7854}, {6361, 38116}, {6688, 7386}, {6756, 13346}, {7401, 13348}, {7403, 46728}, {7526, 32600}, {7528, 15644}, {7530, 15577}, {7533, 7998}, {7540, 13352}, {7761, 24256}, {7801, 47618}, {7834, 35422}, {7876, 12122}, {7878, 12252}, {8541, 32220}, {8550, 15520}, {8705, 44267}, {8722, 37345}, {9019, 44263}, {9024, 22799}, {9654, 10387}, {9729, 34938}, {9732, 36712}, {9733, 36711}, {9735, 41034}, {9736, 41035}, {9738, 36714}, {9739, 36709}, {9744, 44422}, {9815, 17704}, {9969, 18569}, {9970, 10733}, {9971, 18403}, {9976, 13202}, {10110, 14790}, {10151, 47468}, {10301, 11064}, {10721, 11579}, {10723, 12177}, {10982, 44829}, {11001, 38064}, {11179, 14927}, {11257, 44423}, {11261, 22682}, {11442, 21969}, {11563, 32218}, {11649, 31726}, {11898, 38335}, {12002, 21852}, {12007, 33699}, {12017, 17800}, {12102, 34380}, {12110, 39750}, {12173, 44469}, {12225, 44491}, {12605, 19126}, {12702, 38144}, {12897, 34117}, {13394, 37899}, {13419, 36747}, {13446, 46450}, {13473, 39871}, {13570, 18537}, {14216, 16625}, {14389, 35268}, {14538, 37333}, {14539, 37332}, {14693, 35375}, {14864, 18951}, {14893, 47354}, {14912, 22330}, {15059, 31074}, {15069, 44456}, {15080, 20063}, {15462, 18559}, {15579, 34798}, {15681, 47352}, {15683, 46267}, {15684, 43273}, {15704, 38110}, {15980, 35387}, {16001, 41039}, {16002, 41038}, {16010, 38790}, {16264, 44704}, {16621, 31802}, {16981, 41724}, {16982, 18356}, {17702, 19139}, {17810, 34609}, {18388, 18534}, {18390, 19161}, {18400, 19149}, {18404, 37511}, {18481, 38035}, {18560, 19124}, {18562, 19129}, {18563, 19131}, {19123, 40242}, {19128, 34797}, {19137, 31833}, {19145, 42263}, {19146, 42264}, {19710, 38079}, {20062, 22352}, {20192, 47311}, {20299, 34778}, {20300, 23329}, {20582, 38071}, {21736, 43141}, {22615, 44502}, {22644, 44501}, {22676, 32149}, {22681, 44774}, {23048, 36201}, {24220, 36661}, {24257, 29113}, {24309, 29211}, {25406, 33703}, {25556, 32233}, {30270, 44230}, {31105, 32225}, {31383, 34986}, {31724, 37473}, {31730, 38146}, {31822, 34381}, {34155, 35480}, {34200, 48310}, {34236, 37190}, {35228, 37440}, {35389, 36997}, {35490, 39588}, {35502, 46026}, {36657, 45543}, {36658, 45542}, {36757, 42432}, {36758, 42431}, {37200, 39569}, {37334, 43152}, {37648, 46517}, {37984, 47569}, {38147, 38761}, {38749, 39656}, {39522, 44407}, {42104, 44498}, {42105, 44497}, {42160, 44512}, {42161, 44511}, {42215, 42833}, {42216, 42832}, {42271, 44656}, {42272, 44657}, {44271, 44668}, {45303, 47582}

X(48901) = midpoint of X(i) and X(j) for these {i,j}: {4, 31670}, {6, 382}, {20, 43621}, {1351, 36990}, {3146, 46264}, {3543, 20423}, {3627, 21850}, {5878, 36851}, {9970, 10733}, {10721, 11579}, {10723, 12177}, {11179, 15682}, {11477, 18440}, {15069, 44456}, {15684, 43273}, {16010, 38790}, {34779, 34786}, {35389, 36997}
X(48901) = anticomplement of X(14810)
X(48901) = reflection of X(i) in X(j) for these {i,j}: {3, 19130}, {20, 5092}, {66, 18383}, {69, 18553}, {74, 20301}, {141, 546}, {182, 5480}, {550, 3589}, {576, 21850}, {1350, 24206}, {3098, 5}, {3357, 23300}, {3534, 10168}, {3818, 4}, {6776, 5097}, {7761, 40250}, {11178, 3845}, {11257, 44423}, {11261, 22682}, {12584, 113}, {17508, 38136}, {18358, 3861}, {18381, 18382}, {19140, 32271}, {21852, 12002}, {22676, 32149}, {32233, 25556}, {33878, 40107}, {34507, 3818}, {34776, 34117}, {34778, 20299}, {34785, 206}, {44774, 22681}, {44882, 18583}, {46264, 575}, {47354, 14893}, {47569, 37984}
X(48901) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 19130, 38317}, {20, 14561, 5092}, {182, 5480, 5476}, {381, 1350, 24206}, {550, 3589, 17508}, {550, 38136, 3589}, {621, 622, 7850}, {1351, 3830, 36990}, {3146, 14853, 46264}, {3534, 38072, 10168}, {3830, 13102, 36961}, {3830, 13103, 36962}, {3843, 33878, 10516}, {5064, 33586, 21243}, {5480, 44882, 18583}, {6776, 20423, 5097}, {10516, 33878, 40107}, {14389, 37900, 35268}, {14561, 43621, 20}, {14853, 46264, 575}, {18583, 44882, 182}, {35820, 35821, 7747}


X(48902) = X(4)X(69)∩X(30)X(991)

Barycentrics    a^5*b + a^4*b^2 - a^2*b^4 - a*b^5 + a^5*c + a^4*b*c - a*b^4*c - b^5*c + a^4*c^2 + 2*a*b^3*c^2 + 2*a*b^2*c^3 + 2*b^3*c^3 - a^2*c^4 - a*b*c^4 - a*c^5 - b*c^5 : :
X(48902) = 3 X[1699] - X[6210]

X(48902) lies on these lines: {2, 22080}, {3, 142}, {4, 69}, {5, 573}, {27, 9306}, {30, 991}, {182, 6996}, {343, 430}, {355, 29311}, {381, 17251}, {394, 1889}, {469, 21243}, {497, 35612}, {517, 3696}, {940, 1836}, {962, 29309}, {964, 17202}, {980, 24248}, {1011, 17167}, {1086, 37819}, {1150, 5057}, {1479, 21746}, {1699, 1764}, {1738, 27623}, {1742, 41869}, {1754, 29105}, {1765, 5735}, {1899, 7381}, {2048, 45554}, {2051, 19540}, {2792, 11599}, {2807, 10739}, {3098, 13727}, {3332, 46264}, {3685, 29981}, {3819, 6817}, {4192, 10478}, {4301, 4780}, {5092, 36697}, {5138, 5327}, {5224, 36687}, {5480, 36654}, {5482, 29229}, {5737, 24703}, {5788, 5812}, {5816, 36675}, {5943, 6818}, {6289, 36679}, {6290, 36678}, {6688, 6822}, {6776, 7406}, {6994, 14826}, {7377, 24206}, {7534, 17814}, {7746, 20666}, {9554, 17717}, {9732, 36713}, {9733, 36710}, {9738, 36715}, {9739, 36708}, {9812, 29349}, {10444, 46475}, {10470, 11522}, {11322, 17174}, {11358, 17182}, {12701, 19765}, {14561, 36670}, {14810, 36489}, {15310, 22793}, {16159, 45931}, {16345, 40998}, {16548, 24332}, {17197, 37507}, {18483, 45305}, {19130, 36652}, {19645, 29841}, {20430, 29069}, {20760, 22000}, {20788, 39551}, {24045, 41323}, {27000, 29999}, {29054, 31395}, {29097, 37530}, {32431, 36686}

X(48902) = midpoint of X(i) and X(j) for these {i,j}: {4, 10446}, {1742, 41869}
X(48902) = reflection of X(i) in X(j) for these {i,j}: {3, 24220}, {573, 5}, {31394, 946}, {45305, 18483}
X(48902) = crossdifference of every pair of points on line {3049, 6586}


X(48903) = X(1)X(30)∩X(3)X(4653)

Barycentrics    a*(a^5*b - 2*a^3*b^3 + a*b^5 + a^5*c - 2*a^4*b*c - a^3*b^2*c + 2*b^5*c - a^3*b*c^2 - 2*a^2*b^2*c^2 - a*b^3*c^2 - 2*a^3*c^3 - a*b^2*c^3 - 4*b^3*c^3 + a*c^5 + 2*b*c^5) : :
X(48903) = 3 X[1] - 2 X[5453], 3 X[500] - 4 X[5453], 2 X[3579] - 3 X[14636], 3 X[5603] - X[15971], 3 X[5886] - 2 X[15973]

X(48903) lies on these lines: {1, 30}, {3, 4653}, {4, 5396}, {5, 3216}, {6, 37234}, {34, 46467}, {36, 6097}, {37, 37585}, {42, 18480}, {58, 13743}, {60, 14157}, {65, 1725}, {81, 21669}, {94, 6740}, {355, 37529}, {381, 386}, {382, 581}, {405, 582}, {511, 1482}, {517, 2292}, {540, 22837}, {542, 15955}, {546, 37732}, {580, 7489}, {758, 5492}, {846, 16139}, {855, 18180}, {896, 22936}, {942, 2654}, {946, 36250}, {990, 37615}, {991, 1657}, {995, 18493}, {1012, 5707}, {1046, 3652}, {1064, 22793}, {1154, 11009}, {1193, 9955}, {1385, 37425}, {1387, 46419}, {1458, 31776}, {1478, 5399}, {1498, 36742}, {1780, 3560}, {1834, 6841}, {1854, 6000}, {1870, 46468}, {2099, 13754}, {2594, 3585}, {2650, 2771}, {3100, 15938}, {3120, 33592}, {3293, 18357}, {3332, 6868}, {3534, 48855}, {3579, 14636}, {3720, 13624}, {3850, 5400}, {3861, 22392}, {4252, 28444}, {4256, 37251}, {4272, 32431}, {4300, 28146}, {4306, 18541}, {5055, 17749}, {5312, 18492}, {5425, 17705}, {5603, 15971}, {5663, 22461}, {5691, 37698}, {5713, 6923}, {5718, 37406}, {5886, 15973}, {6003, 24457}, {6842, 45944}, {6883, 37537}, {6913, 36754}, {6914, 37530}, {6985, 19765}, {7986, 14915}, {10540, 17104}, {12047, 34586}, {12702, 30116}, {13745, 19860}, {15447, 37618}, {15556, 35194}, {15952, 37527}, {15979, 37594}, {16617, 35466}, {16948, 28461}, {17056, 37401}, {18524, 33771}, {37230, 45924}, {37331, 37536}, {37403, 37633}, {37469, 45931}, {37571, 47749}, {44229, 48837}

X(48903) = reflection of X(i) in X(j) for these {i,j}: {500, 1}, {2292, 8143}, {12702, 35203}, {37425, 1385}, {46704, 946}
X(48903) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 79, 1464}, {1834, 6841, 45926}, {3560, 5706, 5398}, {13743, 45923, 58}


X(48904) = X(3)X(39784)∩X(30)X(182)

Barycentrics    3*a^6 + 3*a^4*b^2 - 4*a^2*b^4 - 2*b^6 + 3*a^4*c^2 + 2*a^2*b^2*c^2 + 2*b^4*c^2 - 4*a^2*c^4 + 2*b^2*c^4 - 2*c^6 : :
X(48904) = 11 X[4] - 7 X[3619], 3 X[4] - 2 X[24206], 11 X[3098] - 14 X[3619], 3 X[3098] - 4 X[24206], X[3098] + 2 X[43621], 21 X[3619] - 22 X[24206], 7 X[3619] + 11 X[43621], 2 X[24206] + 3 X[43621], 2 X[20] - 3 X[17508], 3 X[20] - 4 X[33751], 3 X[17508] - 4 X[19130], 9 X[17508] - 8 X[33751], 3 X[19130] - 2 X[33751], 11 X[182] - 12 X[597], 5 X[182] - 6 X[5476], 3 X[182] - 4 X[5480], 7 X[182] - 8 X[18583], 5 X[182] - 4 X[44882], 10 X[597] - 11 X[5476], 9 X[597] - 11 X[5480], 21 X[597] - 22 X[18583], 15 X[597] - 11 X[44882], 9 X[5476] - 10 X[5480], 21 X[5476] - 20 X[18583], 3 X[5476] - 2 X[44882], 7 X[5480] - 6 X[18583], 5 X[5480] - 3 X[44882], 10 X[18583] - 7 X[44882], 3 X[381] - 2 X[14810], 9 X[382] - X[11898], 7 X[382] - X[15069], 5 X[382] - X[18440], 3 X[382] - X[36990], 11 X[382] - X[40341], 7 X[11898] - 9 X[15069], 5 X[11898] - 9 X[18440], X[11898] - 3 X[36990], 11 X[11898] - 9 X[40341], 5 X[15069] - 7 X[18440], 3 X[15069] - 7 X[36990], 11 X[15069] - 7 X[40341], 3 X[18440] - 5 X[36990], 11 X[18440] - 5 X[40341], 11 X[36990] - 3 X[40341], 2 X[550] - 3 X[38317], X[576] + 2 X[3146], 3 X[576] - 2 X[6776], 3 X[3146] + X[6776], and many others

X(48904) lies on these lines: {3, 39784}, {4, 3096}, {6, 5073}, {20, 17508}, {30, 182}, {69, 46848}, {125, 7391}, {141, 3853}, {381, 14810}, {382, 511}, {524, 35404}, {542, 10721}, {550, 38317}, {576, 3146}, {1350, 3830}, {1351, 11645}, {1352, 3543}, {1386, 28168}, {1503, 34788}, {1539, 12584}, {1657, 5092}, {1843, 35490}, {1974, 34797}, {2777, 32273}, {3357, 18382}, {3529, 14561}, {3589, 15704}, {3627, 3818}, {3843, 31884}, {3850, 21167}, {3858, 34573}, {5039, 7748}, {5059, 25555}, {5076, 10516}, {5085, 17800}, {5189, 34417}, {6560, 42832}, {6561, 42833}, {7540, 37480}, {7553, 13346}, {7690, 36709}, {7692, 36714}, {7699, 37925}, {9306, 34603}, {10168, 11001}, {10304, 25565}, {10539, 40113}, {11179, 15640}, {11204, 20300}, {11541, 25406}, {11648, 12212}, {12007, 15520}, {12294, 35480}, {13570, 18536}, {13598, 18396}, {14927, 20423}, {15516, 43273}, {15685, 38072}, {15691, 48310}, {15696, 47355}, {17578, 40107}, {18383, 34778}, {18553, 33878}, {18562, 19131}, {18563, 19126}, {20063, 35268}, {20127, 20301}, {21358, 35403}, {25561, 38335}, {31099, 32223}, {32111, 34613}, {32305, 34584}, {33699, 39884}, {33703, 39561}, {34146, 34786}, {37648, 47095}, {38110, 42785}, {40236, 43461}, {41413, 44518}, {42271, 44474}, {42272, 44473}, {42852, 43619}, {44971, 44972}

X(48904) = midpoint of X(i) and X(j) for these {i,j}: {4, 43621}, {6, 5073}, {3146, 31670}, {11179, 15640}, {33703, 46264}
X(48904) = reflection of X(i) in X(j) for these {i,j}: {20, 19130}, {141, 3853}, {576, 31670}, {1657, 5092}, {3098, 4}, {3357, 18382}, {3818, 3627}, {11001, 10168}, {11178, 3830}, {12584, 1539}, {15704, 3589}, {20127, 20301}, {33878, 18553}, {34778, 18383}
X(48904) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 19130, 17508}, {3850, 21167, 42786}, {5476, 44882, 182}, {36992, 36994, 36997}


X(48905) = X(6)X(30)∩X(20)X(64)

Barycentrics    5*a^6 - 3*a^2*b^4 - 2*b^6 - 2*a^2*b^2*c^2 + 2*b^4*c^2 - 3*a^2*c^4 + 2*b^2*c^4 - 2*c^6 : :
X(48905) = 6 X[3] - 5 X[3763], 3 X[3] - 2 X[3818], 4 X[3] - 3 X[10516], 5 X[3] - 4 X[24206], 7 X[3] - 8 X[33751], 5 X[3763] - 4 X[3818], 10 X[3763] - 9 X[10516], 25 X[3763] - 24 X[24206], 35 X[3763] - 48 X[33751], 5 X[3763] - 3 X[36990], 8 X[3818] - 9 X[10516], 5 X[3818] - 6 X[24206], 7 X[3818] - 12 X[33751], 4 X[3818] - 3 X[36990], 15 X[10516] - 16 X[24206], 21 X[10516] - 32 X[33751], 3 X[10516] - 2 X[36990], 5 X[15321] - 6 X[18488], 7 X[24206] - 10 X[33751], 8 X[24206] - 5 X[36990], 16 X[33751] - 7 X[36990], 3 X[4] - 4 X[3589], 2 X[4] - 3 X[5085], 8 X[3589] - 9 X[5085], 2 X[3589] - 3 X[44882], 3 X[5085] - 4 X[44882], 5 X[6] - 6 X[11179], 7 X[6] - 6 X[20423], 5 X[6] - 4 X[21850], 3 X[6] - 2 X[31670], 2 X[6] - 3 X[43273], 5 X[6] - 2 X[43621], 7 X[11179] - 5 X[20423], 3 X[11179] - 2 X[21850], 9 X[11179] - 5 X[31670], 4 X[11179] - 5 X[43273], 3 X[11179] - X[43621], 3 X[11179] - 5 X[46264], 15 X[20423] - 14 X[21850], 9 X[20423] - 7 X[31670], 4 X[20423] - 7 X[43273], 15 X[20423] - 7 X[43621], 3 X[20423] - 7 X[46264], 6 X[21850] - 5 X[31670], 8 X[21850] - 15 X[43273], 2 X[21850] - 5 X[46264], 4 X[31670] - 9 X[43273], and many others

X(48905) lies on these lines: {2, 41424}, {3, 2916}, {4, 3589}, {6, 30}, {20, 64}, {22, 1853}, {66, 10606}, {67, 16111}, {141, 376}, {146, 17812}, {154, 1370}, {159, 2935}, {160, 47620}, {182, 382}, {193, 15683}, {206, 1531}, {265, 5621}, {316, 47619}, {381, 5092}, {394, 46818}, {428, 17825}, {511, 1657}, {516, 32921}, {524, 11001}, {542, 15681}, {548, 39884}, {550, 1352}, {597, 15682}, {599, 3098}, {611, 10483}, {621, 5868}, {622, 5869}, {1351, 17800}, {1386, 41869}, {1428, 12953}, {1495, 31152}, {1498, 36989}, {1539, 15462}, {1656, 17508}, {1691, 44518}, {1843, 37196}, {1899, 47582}, {1974, 44438}, {2071, 35228}, {2330, 12943}, {2777, 11820}, {2781, 12220}, {2794, 14532}, {2930, 12121}, {3066, 7519}, {3090, 33750}, {3094, 44519}, {3146, 5480}, {3242, 18481}, {3313, 6000}, {3416, 31730}, {3524, 34573}, {3528, 21167}, {3529, 3629}, {3537, 15435}, {3543, 3618}, {3564, 15704}, {3619, 10304}, {3627, 10541}, {3630, 46333}, {3631, 11180}, {3796, 7391}, {3830, 12017}, {3843, 38317}, {3844, 35242}, {3853, 38110}, {4048, 7470}, {4302, 10387}, {5026, 10722}, {5050, 5073}, {5059, 5102}, {5064, 22352}, {5076, 20190}, {5094, 35268}, {5096, 6985}, {5157, 18494}, {5189, 6800}, {5476, 15684}, {5596, 15311}, {5646, 35283}, {5691, 38144}, {5695, 29040}, {5846, 6361}, {5895, 12225}, {5925, 34146}, {5999, 8350}, {6030, 31236}, {6034, 39809}, {6053, 32063}, {6389, 44248}, {6390, 8721}, {6564, 36733}, {6565, 36719}, {6593, 10721}, {6642, 17712}, {6699, 14070}, {7396, 10192}, {7464, 35707}, {7488, 15578}, {7500, 17810}, {7553, 37514}, {7667, 17811}, {7703, 47596}, {7712, 10989}, {7716, 18533}, {7748, 40825}, {7778, 43460}, {7806, 40236}, {8177, 34505}, {8703, 18358}, {9715, 40686}, {9756, 37182}, {9774, 42849}, {9786, 31305}, {9909, 26958}, {9970, 34584}, {9971, 14855}, {9973, 37511}, {10117, 26283}, {10168, 14269}, {10245, 44673}, {10249, 18382}, {10323, 41171}, {10519, 17538}, {10565, 23332}, {10574, 32191}, {10601, 34603}, {10605, 44831}, {10620, 25335}, {10734, 14688}, {11178, 15688}, {11413, 15577}, {11425, 34938}, {11438, 34726}, {11646, 38749}, {11750, 37488}, {12054, 44000}, {12082, 18396}, {12173, 19124}, {12279, 41716}, {12283, 22535}, {12362, 15811}, {12588, 15338}, {12589, 15326}, {12699, 38315}, {12902, 25330}, {13394, 31099}, {13442, 19753}, {13445, 41464}, {13567, 34608}, {13634, 17327}, {13635, 17265}, {13665, 36734}, {13785, 36718}, {13910, 23249}, {13972, 23259}, {14216, 44683}, {14641, 37473}, {14791, 46817}, {14810, 15696}, {14853, 33703}, {15055, 32274}, {15080, 31133}, {15448, 16051}, {15533, 19710}, {15534, 15685}, {15576, 44704}, {15581, 41482}, {15687, 38064}, {15693, 25561}, {15694, 42786}, {15697, 21356}, {15812, 44241}, {16010, 17702}, {16063, 35259}, {16496, 34628}, {16621, 33537}, {16936, 31829}, {17834, 18917}, {17907, 42854}, {18400, 37485}, {18405, 23300}, {18550, 19151}, {18911, 37900}, {19121, 23049}, {19127, 35480}, {19128, 35490}, {19140, 38790}, {19145, 35820}, {19146, 35821}, {19161, 46850}, {19708, 20582}, {20062, 33586}, {21852, 40647}, {21971, 45979}, {22728, 44423}, {22793, 38029}, {23041, 37444}, {23292, 44442}, {24309, 29321}, {25331, 48679}, {25712, 34782}, {28150, 39870}, {28343, 44988}, {28662, 44987}, {31255, 44082}, {31673, 38047}, {31859, 34624}, {31860, 37648}, {32002, 37200}, {32113, 47308}, {32429, 48673}, {32444, 41328}, {33256, 39141}, {33560, 41026}, {33561, 41027}, {33851, 41737}, {34507, 48662}, {34780, 46728}, {34785, 39879}, {34797, 39588}, {35243, 44407}, {35434, 46267}, {35513, 36851}, {36711, 45553}, {36712, 45552}, {36741, 37411}, {36757, 42431}, {36758, 42432}, {36761, 38738}, {36883, 38805}, {37751, 38797}, {39568, 44829}, {39646, 43453}, {39875, 43408}, {39876, 43407}, {40949, 44573}, {41099, 48310}, {44246, 47569}, {47031, 47449}, {47309, 47455}, {47310, 47454}, {47333, 47452}, {47335, 47450}, {47336, 47453}

X(48905) = midpoint of X(i) and X(j) for these {i,j}: {20, 14927}, {1351, 17800}, {3529, 6776}, {12279, 41716}
X(48905) = reflection of X(i) in X(j) for these {i,j}: {4, 44882}, {6, 46264}, {67, 16111}, {382, 182}, {599, 3534}, {1350, 20}, {1352, 550}, {1498, 36989}, {2930, 12121}, {3146, 5480}, {3242, 18481}, {3416, 31730}, {5895, 19149}, {6144, 39899}, {9971, 14855}, {9973, 37511}, {10721, 6593}, {10722, 5026}, {10734, 14688}, {11477, 6776}, {11646, 38749}, {12902, 32305}, {14982, 16163}, {15069, 1350}, {15682, 597}, {15684, 5476}, {18440, 3098}, {19161, 46850}, {24273, 8725}, {25335, 10620}, {32113, 47308}, {34775, 44883}, {35480, 19127}, {36883, 38805}, {36990, 3}, {37751, 38797}, {38790, 19140}, {39879, 34785}, {39884, 548}, {40341, 33878}, {40949, 44573}, {41735, 34782}, {41737, 33851}, {41869, 1386}, {43621, 21850}, {44987, 28662}, {44988, 28343}, {47353, 376}, {48662, 34507}, {48673, 32429}
X(48905) = crossdifference of every pair of points on line {8675, 39520}
X(48905) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3818, 3763}, {3, 36990, 10516}, {4, 44882, 5085}, {6, 46264, 43273}, {20, 46349, 20725}, {381, 5092, 47355}, {550, 1352, 31884}, {3098, 18440, 599}, {3146, 25406, 5480}, {3528, 40330, 21167}, {3534, 18440, 3098}, {3763, 3818, 10516}, {3763, 36990, 3818}, {3830, 12017, 19130}, {6560, 6561, 15048}, {7667, 31383, 17811}, {11179, 21850, 6}, {11179, 43621, 21850}, {12017, 19130, 47352}, {12902, 32305, 25330}, {34775, 44883, 1853}, {42263, 42264, 44526}, {43621, 46264, 11179}


X(48906) = X(3)X(69)∩X(6)X(30)

Barycentrics    (a^2 - b^2 - c^2)*(4*a^4 + a^2*b^2 + b^4 + a^2*c^2 - 2*b^2*c^2 + c^4) : :
X(48906) = 3 X[2] - 5 X[12017], 3 X[2] + X[39874], 5 X[12017] - 2 X[18358], 5 X[12017] - X[18440], 5 X[12017] + X[39874], 2 X[18358] + X[39874], 3 X[3] - X[69], 5 X[3] - 3 X[10519], 5 X[3] - X[11898], X[3] - 3 X[25406], 7 X[3] - 9 X[33750], 3 X[3] + X[39899], X[69] + 3 X[6776], 5 X[69] - 9 X[10519], 5 X[69] - 3 X[11898], X[69] - 9 X[25406], 7 X[69] - 27 X[33750], 5 X[6776] + 3 X[10519], 5 X[6776] + X[11898], X[6776] + 3 X[25406], 7 X[6776] + 9 X[33750], 3 X[6776] - X[39899], 3 X[10519] - X[11898], X[10519] - 5 X[25406], 7 X[10519] - 15 X[33750], 9 X[10519] + 5 X[39899], X[11898] - 15 X[25406], 7 X[11898] - 45 X[33750], 3 X[11898] + 5 X[39899], 7 X[25406] - 3 X[33750], 9 X[25406] + X[39899], 27 X[33750] + 7 X[39899], X[4] - 3 X[5050], 2 X[4] - 3 X[38136], 3 X[5050] - 2 X[18583], 4 X[18583] - 3 X[38136], 3 X[5] - 4 X[3589], 3 X[5] - 2 X[3818], 2 X[5] - 3 X[38110], 5 X[5] - 6 X[38317], 3 X[182] - 2 X[3589], 3 X[182] - X[3818], 4 X[182] - 3 X[38110], 5 X[182] - 3 X[38317], 4 X[182] - X[39884], 8 X[3589] - 9 X[38110], 10 X[3589] - 9 X[38317], 8 X[3589] - 3 X[39884], 4 X[3818] - 9 X[38110], 5 X[3818] - 9 X[38317], 4 X[3818] - 3 X[39884], and many others

X(48906) lies on these lines: {2, 8780}, {3, 69}, {4, 5050}, {5, 182}, {6, 30}, {20, 1351}, {22, 11245}, {24, 39871}, {25, 45298}, {35, 39897}, {36, 39873}, {55, 39901}, {56, 39900}, {66, 10249}, {68, 16197}, {74, 44285}, {98, 35705}, {110, 30739}, {125, 13394}, {140, 1352}, {141, 542}, {146, 40640}, {147, 7931}, {154, 6677}, {159, 6644}, {160, 44221}, {184, 1368}, {185, 9967}, {186, 41584}, {193, 376}, {194, 44251}, {217, 14965}, {230, 5033}, {235, 19128}, {265, 1176}, {302, 6773}, {303, 6770}, {316, 2456}, {343, 22352}, {355, 38165}, {381, 3618}, {382, 14853}, {389, 21852}, {394, 10691}, {397, 36757}, {398, 36758}, {427, 5012}, {428, 5422}, {441, 18437}, {468, 6800}, {495, 2330}, {496, 1428}, {498, 39891}, {499, 39892}, {511, 550}, {516, 4991}, {517, 39870}, {518, 34773}, {524, 3098}, {546, 14561}, {547, 38064}, {548, 1350}, {569, 1595}, {575, 3627}, {576, 12007}, {597, 3845}, {599, 12100}, {611, 18990}, {613, 15171}, {631, 5921}, {632, 20190}, {698, 32429}, {732, 32521}, {858, 11003}, {879, 47256}, {895, 12121}, {946, 38040}, {952, 16799}, {974, 6467}, {1154, 3313}, {1181, 12362}, {1205, 11562}, {1370, 11402}, {1386, 22791}, {1495, 37648}, {1513, 7806}, {1531, 21637}, {1539, 36201}, {1570, 7756}, {1596, 1974}, {1654, 13634}, {1656, 48662}, {1657, 5093}, {1692, 5254}, {1843, 9730}, {1899, 3796}, {1907, 13434}, {1992, 3534}, {1993, 7667}, {2080, 39872}, {2433, 47261}, {2781, 14677}, {2782, 13354}, {2854, 34153}, {2916, 7555}, {3054, 6055}, {3070, 35831}, {3071, 35830}, {3094, 32516}, {3146, 33748}, {3164, 44252}, {3167, 7386}, {3311, 39875}, {3312, 39876}, {3448, 7495}, {3524, 3620}, {3526, 40330}, {3529, 11482}, {3530, 15069}, {3543, 14848}, {3575, 39588}, {3576, 39878}, {3579, 5847}, {3580, 15080}, {3581, 44261}, {3619, 5054}, {3628, 10516}, {3630, 45759}, {3631, 17504}, {3655, 16496}, {3656, 16491}, {3751, 18481}, {3858, 25555}, {3867, 44407}, {3972, 34624}, {4048, 44224}, {4173, 48445}, {4220, 37656}, {4672, 29040}, {5020, 11206}, {5032, 11001}, {5034, 7745}, {5066, 47352}, {5095, 16111}, {5097, 29317}, {5135, 37356}, {5182, 6033}, {5188, 41756}, {5305, 40825}, {5462, 7715}, {5476, 6329}, {5477, 38749}, {5596, 9818}, {5640, 10301}, {5650, 24981}, {5805, 38164}, {5848, 38602}, {5890, 12220}, {5892, 9822}, {5894, 32392}, {5899, 45967}, {5901, 38029}, {5946, 9969}, {5965, 14810}, {5967, 11007}, {5984, 37455}, {6000, 34774}, {6090, 46336}, {6146, 6823}, {6200, 39894}, {6396, 39893}, {6403, 10574}, {6636, 37779}, {6642, 39879}, {6643, 19347}, {6656, 39141}, {6756, 36752}, {7399, 34224}, {7400, 12429}, {7403, 13353}, {7404, 34780}, {7405, 37471}, {7426, 7712}, {7470, 7762}, {7493, 26869}, {7496, 14683}, {7499, 11442}, {7500, 9777}, {7514, 13562}, {7516, 31831}, {7525, 43588}, {7540, 15037}, {7553, 36753}, {7575, 35707}, {7583, 19145}, {7584, 19146}, {7592, 31802}, {7693, 15018}, {7710, 37071}, {7734, 17811}, {7748, 39764}, {7783, 35456}, {7792, 43460}, {8356, 9862}, {8362, 12054}, {8369, 26316}, {8546, 37950}, {8547, 47335}, {8548, 19467}, {8549, 31833}, {8584, 19710}, {8593, 11155}, {9033, 44205}, {9140, 32227}, {9715, 18916}, {9729, 34782}, {9755, 37182}, {9774, 22329}, {9821, 32451}, {9825, 9833}, {9830, 16509}, {9909, 11433}, {9924, 37475}, {9955, 38049}, {9956, 38118}, {10113, 15118}, {10128, 17825}, {10154, 13567}, {10168, 15699}, {10246, 39898}, {10267, 39877}, {10269, 39883}, {10272, 14982}, {10304, 20080}, {10565, 18950}, {10575, 12294}, {10601, 31383}, {10620, 11061}, {10645, 22997}, {10646, 22998}, {10752, 20127}, {10753, 38741}, {10754, 38730}, {10758, 38765}, {10759, 38753}, {10762, 23240}, {10764, 38777}, {10784, 21737}, {10991, 21163}, {11002, 37900}, {11008, 15688}, {11112, 15988}, {11160, 19708}, {11178, 11539}, {11185, 35429}, {11188, 40280}, {11202, 15585}, {11414, 13142}, {11426, 34938}, {11427, 34609}, {11432, 31305}, {11456, 26206}, {11464, 26156}, {11477, 12103}, {11479, 34781}, {11550, 37649}, {11574, 13754}, {11579, 32233}, {11695, 45185}, {11812, 21358}, {12022, 19121}, {12087, 43838}, {12106, 20987}, {12134, 13336}, {12167, 18533}, {12168, 12317}, {12233, 44829}, {12244, 25321}, {12252, 43453}, {12272, 20791}, {12359, 18128}, {12370, 44470}, {12589, 15325}, {12699, 16475}, {12902, 25320}, {13292, 37488}, {13369, 34381}, {13383, 18952}, {13491, 34146}, {13630, 19161}, {13635, 17300}, {14096, 25046}, {14216, 37476}, {14641, 44495}, {14643, 41737}, {14645, 38736}, {14805, 44218}, {14826, 16419}, {14855, 40673}, {14893, 38072}, {14913, 16836}, {15041, 32247}, {15055, 32234}, {15066, 43957}, {15072, 46444}, {15073, 44240}, {15311, 34779}, {15321, 40441}, {15516, 29323}, {15533, 15759}, {15534, 15690}, {15577, 37814}, {15583, 18400}, {15646, 35228}, {15686, 32455}, {15693, 21356}, {15711, 22165}, {15712, 17508}, {15713, 20582}, {15740, 38263}, {15812, 47391}, {16196, 19357}, {16202, 39903}, {16203, 39902}, {16238, 23041}, {16264, 36794}, {16659, 43651}, {16776, 43129}, {17907, 44228}, {18323, 18550}, {18357, 38047}, {18374, 46030}, {18382, 44263}, {18404, 41257}, {18420, 36851}, {18438, 35257}, {18445, 20806}, {18510, 36719}, {18512, 36733}, {18531, 19125}, {18537, 32063}, {18553, 44516}, {18570, 44883}, {18571, 32113}, {18579, 47449}, {18932, 45170}, {19126, 44665}, {19132, 44920}, {19149, 44503}, {19662, 26614}, {19925, 38167}, {20576, 40278}, {21167, 40107}, {22112, 35283}, {22249, 47450}, {22338, 36696}, {23327, 34775}, {23335, 32046}, {23515, 32250}, {25561, 48310}, {25738, 34002}, {26341, 37342}, {26348, 37343}, {26398, 48489}, {26422, 48490}, {26446, 39885}, {26451, 39886}, {26487, 39890}, {26492, 39889}, {27377, 35474}, {31152, 37645}, {31267, 44911}, {31884, 33923}, {32145, 43839}, {32269, 35268}, {32272, 38728}, {32275, 38727}, {32300, 46686}, {32305, 32600}, {32490, 45378}, {32491, 45377}, {32515, 41747}, {32618, 47613}, {32619, 47612}, {32807, 45510}, {34200, 40341}, {34545, 34603}, {34783, 41716}, {35243, 37491}, {35439, 41623}, {35840, 42259}, {35841, 42258}, {36709, 45411}, {36714, 45410}, {37351, 48656}, {37352, 48655}, {37470, 44273}, {37473, 44242}, {37784, 44458}, {38035, 40273}, {39880, 45620}, {39881, 45621}, {39895, 45623}, {39896, 45624}, {43575, 43810}, {43630, 44497}, {43631, 44498}, {44267, 47581}, {44491, 45731}, {44762, 44870}, {44961, 47455}, {47031, 47281}, {47277, 47308}, {47279, 47333}, {47309, 47459}, {47332, 47456}, {47334, 47454}, {47336, 47457}

X(48906) = midpoint of X(i) and X(j) for these {i,j}: {3, 6776}, {6, 46264}, {20, 1351}, {69, 39899}, {185, 9967}, {193, 33878}, {382, 14927}, {550, 1353}, {895, 12121}, {1205, 11562}, {1992, 3534}, {3751, 18481}, {5095, 16111}, {5477, 38749}, {6467, 37511}, {8549, 36989}, {8550, 44882}, {8593, 14830}, {9821, 32451}, {10575, 12294}, {10620, 11061}, {10752, 20127}, {10753, 38741}, {10754, 38730}, {10758, 38765}, {10759, 38753}, {10762, 23240}, {10764, 38777}, {11179, 43273}, {11579, 32233}, {12244, 48679}, {14855, 40673}, {18440, 39874}, {34783, 41716}, {47277, 47308}, {48742, 48743}
X(48906) = reflection of X(i) in X(j) for these {i,j}: {4, 18583}, {5, 182}, {141, 5092}, {550, 44882}, {576, 12007}, {599, 12100}, {1350, 548}, {1352, 140}, {1353, 8550}, {3094, 32516}, {3627, 5480}, {3818, 3589}, {3845, 597}, {5097, 33749}, {5480, 575}, {10113, 15118}, {14982, 10272}, {15687, 5476}, {18440, 18358}, {19161, 13630}, {21850, 6}, {22791, 1386}, {24206, 20190}, {32113, 18571}, {36990, 546}, {37517, 32455}, {38136, 5050}, {39884, 5}, {44267, 47581}, {46686, 32300}, {47336, 47457}, {47353, 547}, {47354, 10168}
X(48906) = complement of X(18440)
X(48906) = anticomplement of X(18358)
X(48906) = circumcircle-inverse of X(35463)
X(48906) = isotomic conjugate of the polar conjugate of X(5306)
X(48906) = X(5306)-Dao conjugate of X(11331)
X(48906) = crossdifference of every pair of points on line {2489, 8675}
X(48906) = barycentric product X(69)*X(5306)
X(48906) = barycentric quotient X(5306)/X(4)
X(48906) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 18440, 18358}, {2, 39874, 18440}, {3, 11898, 10519}, {3, 18917, 44683}, {3, 35463, 34883}, {3, 39899, 69}, {4, 5050, 18583}, {4, 18583, 38136}, {5, 182, 38110}, {6, 43273, 46264}, {20, 14912, 1351}, {22, 11245, 41588}, {22, 37644, 47582}, {69, 6776, 39899}, {141, 5092, 549}, {182, 3818, 3589}, {193, 376, 33878}, {206, 3818, 46817}, {1176, 5622, 19129}, {1352, 5085, 140}, {1495, 37648, 44212}, {1899, 3796, 6676}, {3580, 15080, 44210}, {3589, 3818, 5}, {6146, 10984, 6823}, {6560, 6561, 44526}, {6776, 25406, 3}, {6800, 18911, 468}, {9833, 37514, 9825}, {10168, 47354, 15699}, {11179, 46264, 6}, {11245, 47582, 37644}, {12017, 18440, 2}, {12017, 39874, 18358}, {12244, 25321, 48679}, {14561, 36990, 546}, {14853, 14927, 382}, {14982, 15462, 10272}, {18914, 44683, 18917}, {37644, 47582, 41588}, {38064, 47353, 547}, {38110, 39884, 5}, {41979, 41980, 2549}, {42215, 42216, 15048}, {47610, 47611, 549}


X(48907) = X(1)X(10108)∩X(3)X(6)

Barycentrics    a^2*(a^4*b - a^3*b^2 - 3*a^2*b^3 + a*b^4 + 2*b^5 + a^4*c + 2*a^3*b*c - 2*a^2*b^2*c - 2*a*b^3*c + b^4*c - a^3*c^2 - 2*a^2*b*c^2 - 2*a*b^2*c^2 - b^3*c^2 - 3*a^2*c^3 - 2*a*b*c^3 - b^2*c^3 + a*c^4 + b*c^4 + 2*c^5) : :
X(48907) = 5 X[3] - 4 X[35203], 5 X[500] - 2 X[35203], 4 X[5453] - 3 X[10246], 2 X[9840] - 3 X[10246], 3 X[5790] - 4 X[15973]

X(48907) lies on these lines: {1, 10108}, {3, 6}, {5, 18139}, {30, 944}, {51, 16414}, {110, 20840}, {382, 10454}, {540, 12635}, {952, 15971}, {1154, 5495}, {1210, 15368}, {1437, 20918}, {2979, 16287}, {3060, 16453}, {3819, 16291}, {3917, 16286}, {3970, 40263}, {5453, 9840}, {5482, 37732}, {5640, 16297}, {5716, 15934}, {5790, 15973}, {5889, 7416}, {6003, 23345}, {7998, 16296}, {10105, 37615}, {10679, 13754}, {11573, 14547}, {12160, 37287}, {12702, 37425}, {13391, 22765}, {18525, 46704}, {19648, 37536}, {20432, 29331}, {20470, 31757}, {20834, 22136}, {22139, 37292}, {22458, 26892}, {23061, 35193}

X(48907) = reflection of X(i) in X(j) for these {i,j}: {3, 500}, {9840, 5453}, {12702, 37425}, {18525, 46704}
X(48907) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {581, 37482, 3}, {991, 5752, 3}, {5453, 9840, 10246}


X(48908) = X(1)X(1463)∩X(3)X(6)

Barycentrics    a^2*(a^3*b - 2*a^2*b^2 - a*b^3 + 2*b^4 + a^3*c + a^2*b*c - a*b^2*c - b^3*c - 2*a^2*c^2 - a*b*c^2 - a*c^3 - b*c^3 + 2*c^4) : :
X(48908) = 3 X[3] - 2 X[573], X[573] - 3 X[991], 3 X[381] - 4 X[24220], 3 X[5886] - 2 X[45305], 3 X[10246] - 2 X[31394]

X(48908) lies on these lines: {1, 1463}, {3, 6}, {4, 17300}, {5, 17234}, {7, 24833}, {20, 20090}, {30, 10446}, {51, 16059}, {55, 7186}, {69, 36474}, {75, 29331}, {86, 36477}, {101, 28908}, {104, 29237}, {140, 17352}, {141, 36530}, {184, 20841}, {373, 16421}, {381, 17313}, {394, 20834}, {405, 26657}, {516, 1482}, {517, 1742}, {942, 41777}, {971, 20430}, {999, 21746}, {1011, 2979}, {1352, 36707}, {1385, 6210}, {1469, 37590}, {1486, 36942}, {1654, 36543}, {1656, 17265}, {1993, 16064}, {2801, 31395}, {2807, 10679}, {3060, 4191}, {3190, 22149}, {3207, 41323}, {3220, 23095}, {3306, 22067}, {3526, 16500}, {3560, 28965}, {3664, 15934}, {3784, 14547}, {3792, 20992}, {3917, 16058}, {3940, 4416}, {4360, 24813}, {4585, 6914}, {4648, 36526}, {5482, 19549}, {5886, 45305}, {5943, 16409}, {7373, 39543}, {7998, 16373}, {8148, 29309}, {9037, 15624}, {9777, 37309}, {10222, 29229}, {10246, 29353}, {10247, 29349}, {10391, 20254}, {12635, 17770}, {12702, 29311}, {13633, 20423}, {15066, 47523}, {15668, 36527}, {17232, 36473}, {17243, 24828}, {17262, 24844}, {17297, 36551}, {17365, 29243}, {17379, 36489}, {17392, 36490}, {17976, 24320}, {19515, 37651}, {19540, 37521}, {20760, 26892}, {20835, 22139}, {24817, 31300}, {26540, 37165}, {29369, 30273}, {31670, 36716}, {36280, 42843}

X(48908) = reflection of X(i) in X(j) for these {i,j}: {3, 991}, {6210, 1385}, {36490, 17392}
X(48908) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 1351, 37510}, {500, 37482, 3}, {572, 3098, 3}, {1350, 37474, 3}


X(48909) = X(1)X(256)∩X(3)X(81)

Barycentrics    a*(a^5*b - a^4*b^2 - 3*a^3*b^3 + a^2*b^4 + 2*a*b^5 + a^5*c - 2*a^3*b^2*c - a^2*b^3*c + a*b^4*c + b^5*c - a^4*c^2 - 2*a^3*b*c^2 - 2*a^2*b^2*c^2 - a*b^3*c^2 - 3*a^3*c^3 - a^2*b*c^3 - a*b^2*c^3 - 2*b^3*c^3 + a^2*c^4 + a*b*c^4 + 2*a*c^5 + b*c^5) : :
X(48909) = 3 X[42045] - X[46483], 4 X[1385] - 3 X[14636], 3 X[3576] - 2 X[35203], 3 X[1962] - 2 X[9959]

X(48909) lies on these lines: {1, 256}, {3, 81}, {4, 17778}, {5, 3936}, {6, 13732}, {8, 15973}, {20, 20090}, {21, 22139}, {30, 944}, {40, 42042}, {72, 1959}, {140, 5754}, {145, 15971}, {323, 11101}, {386, 19514}, {405, 1351}, {496, 15974}, {500, 517}, {524, 12635}, {576, 1724}, {581, 4192}, {631, 9567}, {764, 6003}, {851, 41723}, {946, 42057}, {952, 46704}, {1008, 12251}, {1009, 3095}, {1012, 12164}, {1064, 35631}, {1071, 15979}, {1385, 14636}, {1656, 30831}, {1695, 3576}, {1962, 9959}, {1993, 13733}, {2080, 37023}, {2360, 46548}, {2392, 5496}, {2979, 47521}, {3060, 13724}, {3061, 15984}, {3145, 3193}, {3167, 37052}, {3191, 29958}, {3430, 4658}, {3564, 13442}, {3580, 27685}, {3792, 28265}, {3924, 28368}, {5396, 19513}, {5482, 19335}, {5611, 11097}, {5615, 11098}, {5707, 19548}, {5730, 34380}, {5752, 13731}, {5797, 30448}, {5889, 13734}, {5904, 31395}, {5965, 41696}, {6097, 11849}, {6986, 37510}, {7379, 7779}, {7380, 31089}, {7985, 32515}, {8227, 31137}, {8731, 22076}, {9777, 25875}, {10519, 19766}, {11036, 15970}, {11095, 20425}, {11096, 20426}, {12528, 20430}, {13754, 37533}, {15066, 19771}, {15447, 37567}, {15507, 42450}, {15981, 16466}, {18180, 28258}, {18210, 39772}, {19546, 37732}, {22136, 36011}, {28381, 34772}, {29181, 42871}, {31778, 37698}, {37331, 37482}, {37360, 41014}, {39598, 45126}

X(48909) = midpoint of X(145) and X(15971)
X(48909) = reflection of X(i) in X(j) for these {i,j}: {3, 5453}, {8, 15973}, {9840, 1}, {37425, 500}
X(48909) = crosssum of X(1) and X(30362)
X(48909) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 19782, 13732}, {386, 37521, 19514}, {581, 10441, 4192}, {3430, 4658, 37527}, {5396, 37536, 19513}


X(48910) = X(4)X(141)∩X(6)X(30)

Barycentrics    3*a^6 + 4*a^4*b^2 - 5*a^2*b^4 - 2*b^6 + 4*a^4*c^2 + 2*a^2*b^2*c^2 + 2*b^4*c^2 - 5*a^2*c^4 + 2*b^2*c^4 - 2*c^6 : :
X(48910) = 3 X[3] - 4 X[19130], 5 X[3] - 6 X[38317], 6 X[3] - 7 X[47355], 10 X[19130] - 9 X[38317], 8 X[19130] - 7 X[47355], 36 X[38317] - 35 X[47355], 3 X[4] - 2 X[141], 4 X[4] - 3 X[10516], 5 X[4] - 3 X[10519], 7 X[4] - 5 X[40330], 4 X[141] - 3 X[1350], 8 X[141] - 9 X[10516], 10 X[141] - 9 X[10519], 14 X[141] - 15 X[40330], 2 X[1350] - 3 X[10516], 5 X[1350] - 6 X[10519], 7 X[1350] - 10 X[40330], 5 X[10516] - 4 X[10519], 21 X[10516] - 20 X[40330], 21 X[10519] - 25 X[40330], 4 X[5] - 3 X[31884], 7 X[6] - 6 X[11179], 5 X[6] - 6 X[20423], 3 X[6] - 4 X[21850], 4 X[6] - 3 X[43273], X[6] + 2 X[43621], 3 X[6] - 2 X[46264], 5 X[11179] - 7 X[20423], 9 X[11179] - 14 X[21850], 3 X[11179] - 7 X[31670], 8 X[11179] - 7 X[43273], 3 X[11179] + 7 X[43621], 9 X[11179] - 7 X[46264], 9 X[20423] - 10 X[21850], 3 X[20423] - 5 X[31670], 8 X[20423] - 5 X[43273], 3 X[20423] + 5 X[43621], 9 X[20423] - 5 X[46264], 2 X[21850] - 3 X[31670], 16 X[21850] - 9 X[43273], 2 X[21850] + 3 X[43621], 8 X[31670] - 3 X[43273], 3 X[31670] - X[46264], 3 X[43273] + 8 X[43621], 9 X[43273] - 8 X[46264], 3 X[43621] + X[46264], 3 X[20] - 5 X[3618], 2 X[20] - 3 X[5085], and many others

X(48910) lies on these lines: {2, 31860}, {3, 7889}, {4, 141}, {5, 31884}, {6, 30}, {20, 3618}, {23, 35228}, {40, 38144}, {66, 18405}, {67, 12295}, {69, 3543}, {113, 18534}, {154, 7500}, {159, 1533}, {182, 1657}, {193, 1503}, {297, 42854}, {376, 3589}, {381, 3098}, {382, 511}, {394, 34603}, {428, 17811}, {516, 32935}, {518, 41869}, {524, 15682}, {542, 6144}, {548, 38136}, {550, 14561}, {576, 29323}, {597, 11001}, {599, 3818}, {613, 10483}, {1351, 5073}, {1352, 3627}, {1370, 17810}, {1469, 12953}, {1478, 10387}, {1593, 35240}, {1597, 37485}, {1656, 14810}, {1843, 44438}, {1853, 3580}, {1974, 37196}, {1992, 15640}, {2076, 13881}, {2777, 16010}, {2781, 10733}, {2810, 10727}, {2854, 10721}, {2916, 12083}, {2930, 7728}, {3056, 12943}, {3066, 16063}, {3090, 21167}, {3242, 12699}, {3313, 18494}, {3416, 31673}, {3529, 6329}, {3534, 5092}, {3545, 34573}, {3586, 24471}, {3619, 3839}, {3620, 47354}, {3629, 39874}, {3630, 11180}, {3796, 20062}, {3843, 24206}, {3844, 18492}, {3845, 21358}, {4265, 6985}, {4297, 38035}, {5017, 44518}, {5050, 17800}, {5059, 25406}, {5102, 6776}, {5241, 26118}, {5476, 12017}, {5621, 20127}, {5732, 38143}, {5965, 48662}, {5969, 10722}, {6034, 38749}, {6403, 35490}, {6564, 36719}, {6565, 36733}, {6800, 20063}, {7000, 26362}, {7374, 26361}, {7409, 33522}, {7519, 35259}, {7533, 21766}, {7540, 37483}, {7553, 37498}, {7667, 17825}, {7703, 15107}, {7777, 40236}, {8266, 32444}, {8550, 14927}, {9019, 35480}, {9024, 10728}, {9541, 13910}, {9756, 17008}, {9766, 43460}, {9786, 34938}, {9971, 37511}, {10168, 15689}, {10541, 15704}, {10606, 23300}, {10620, 25330}, {10748, 37751}, {10750, 15163}, {10751, 15162}, {10996, 45816}, {11064, 41424}, {11178, 38335}, {11425, 31305}, {11430, 34726}, {11541, 14912}, {11579, 34584}, {11645, 15534}, {11646, 39809}, {11824, 36712}, {11825, 36711}, {12086, 15578}, {12103, 38110}, {12121, 32271}, {12173, 12294}, {12244, 25328}, {12305, 36709}, {12306, 36714}, {12512, 38146}, {12584, 38789}, {12902, 25335}, {13202, 14982}, {13473, 41584}, {13567, 44442}, {13598, 19161}, {13665, 36718}, {13785, 36734}, {14532, 35423}, {15041, 20301}, {15311, 36851}, {15321, 18474}, {15533, 33699}, {15686, 38064}, {15687, 18358}, {15691, 38079}, {15696, 17508}, {15701, 25565}, {16491, 34628}, {17845, 19149}, {18481, 38315}, {18502, 44000}, {19145, 42266}, {19146, 42267}, {19696, 39141}, {19708, 48310}, {19709, 42786}, {20304, 31181}, {20582, 41099}, {21970, 26958}, {22802, 39879}, {23041, 31304}, {23049, 44883}, {23292, 34608}, {25336, 48679}, {26926, 44935}, {28172, 39870}, {31099, 32269}, {31152, 34417}, {31255, 44106}, {31383, 37672}, {31730, 38047}, {32113, 47309}, {34146, 45186}, {34505, 43453}, {34733, 39882}, {34777, 36201}, {35707, 37946}, {36474, 37499}, {36740, 37411}, {36757, 43632}, {36758, 43633}, {37488, 47527}, {38147, 38759}, {41756, 48673}, {44946, 44972}, {47031, 47454}, {47308, 47455}, {47310, 47449}, {47332, 47452}, {47335, 47453}, {47336, 47450}

X(48910) = midpoint of X(i) and X(j) for these {i,j}: {1351, 5073}, {1992, 15640}, {6776, 33703}, {31670, 43621}
X(48910) = reflection of X(i) in X(j) for these {i,j}: {6, 31670}, {20, 5480}, {67, 12295}, {599, 3830}, {1350, 4}, {1352, 3627}, {1657, 182}, {2930, 7728}, {3242, 12699}, {3416, 31673}, {3529, 44882}, {6144, 44456}, {10620, 32273}, {11001, 597}, {11646, 39809}, {12121, 32271}, {12244, 25328}, {14927, 8550}, {14982, 13202}, {15069, 36990}, {15162, 10751}, {15163, 10750}, {15681, 5476}, {15704, 18583}, {17845, 19149}, {19161, 13598}, {25335, 12902}, {25336, 48679}, {32113, 47309}, {33534, 4846}, {33878, 3818}, {34778, 18382}, {36990, 382}, {37751, 10748}, {39874, 3629}, {39879, 22802}, {39899, 37517}, {40341, 18440}, {46264, 21850}, {47353, 3543}
X(48910) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 19130, 47355}, {4, 1350, 10516}, {20, 5480, 5085}, {381, 3098, 3763}, {3529, 14853, 44882}, {3818, 33878, 599}, {3830, 33878, 3818}, {6560, 6561, 18907}, {7391, 33586, 1853}, {10620, 32273, 25330}, {15107, 31133, 37638}, {18382, 34778, 1853}, {18440, 40341, 15069}, {21850, 46264, 6}, {31670, 46264, 21850}, {36990, 40341, 18440}, {37517, 39899, 15534}


X(48911) = X(187)X(11058)∩X(599)X(5092)

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

See Antreas Hatzipolakis and Peter Moses euclid 5061.

X(48911) lies on these lines: {187, 11058}, {599, 5092}, {7669, 35472}, {7771, 40829}, {8667, 42008}, {9464, 37671}, {11057, 18023}, {14537, 18575}, {16264, 18559}, {36882, 47101}, {40344, 44558}

X(48911) = isogonal conjugate of X(48912)
X(48911) = isotomic conjugate of X(48913)


X(48912) = X(2)X(3098)∩X(6)X(23)

Barycentrics    a^2*(2*a^4 + 2*a^2*b^2 - 4*b^4 + 2*a^2*c^2 + 5*b^2*c^2 - 4*c^4) : :
X(48912) = 2 X[10546] - 3 X[14002]

See Antreas Hatzipolakis and Peter Moses euclid 5061.

X(48912) lies on these lines: {2, 3098}, {4, 3581}, {6, 23}, {20, 37470}, {22, 12017}, {25, 323}, {51, 15080}, {74, 3543}, {110, 16981}, {193, 9143}, {317, 13485}, {511, 10546}, {671, 14479}, {1350, 16042}, {1351, 9716}, {1495, 3060}, {1511, 47485}, {1992, 12367}, {1993, 41424}, {1994, 26864}, {1995, 33878}, {2070, 3431}, {2979, 44106}, {3066, 7496}, {3091, 37478}, {3146, 11438}, {3410, 6995}, {3448, 7519}, {3522, 43584}, {3523, 38848}, {3545, 33533}, {3818, 15360}, {3839, 4550}, {3854, 7691}, {5092, 5640}, {5104, 8617}, {5169, 32269}, {5189, 43621}, {5446, 11464}, {5643, 17508}, {6636, 17810}, {7391, 37643}, {7426, 21850}, {7517, 15032}, {7530, 12112}, {7556, 14805}, {7703, 32225}, {7714, 45794}, {9545, 37440}, {9781, 37513}, {9909, 34545}, {10594, 15052}, {10620, 11738}, {11422, 32237}, {12086, 37487}, {12106, 37496}, {13321, 37947}, {13595, 15066}, {13603, 46202}, {14169, 34755}, {14170, 34754}, {14491, 15038}, {15019, 35268}, {15022, 46728}, {15037, 17714}, {15053, 15683}, {15068, 34484}, {15081, 31723}, {18358, 47582}, {18374, 18882}, {18440, 44555}, {18911, 20063}, {19570, 41443}, {20423, 37909}, {21849, 26881}, {21970, 31133}, {31074, 47296}, {31861, 41398}, {35002, 37465}, {35237, 37945}, {35606, 36181}, {37483, 44802}, {37644, 39874}, {37901, 46264}, {37939, 39522}, {37940, 44413}, {38942, 47486}, {40914, 41617}, {41448, 43574}, {42085, 44466}, {42086, 44462}

X(48912) = isogonal conjugate of X(48911)
X(48912) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 23, 7712}, {6, 7712, 11003}, {23, 11002, 11003}, {1351, 35265, 9716}, {1495, 3060, 11004}, {1495, 11004, 9544}, {3098, 10545, 2}, {3098, 34417, 10545}, {7712, 11002, 6}, {10545, 15107, 3098}, {15066, 31860, 13595}, {15107, 34417, 2}, {31860, 33586, 15066}


X(48913) = X(2)X(187)∩X(4)X(7799)

Barycentrics    2*a^4 + 2*a^2*b^2 - 4*b^4 + 2*a^2*c^2 + 5*b^2*c^2 - 4*c^4 : :
X(48913) = 4 X[7752] - X[7782], X[7900] + 2 X[39565]

See Antreas Hatzipolakis and Peter Moses euclid 5061.

X(48913) lies on these lines: {2, 187}, {4, 7799}, {5, 7811}, {23, 14558}, {30, 7752}, {69, 25561}, {76, 381}, {83, 33219}, {99, 3830}, {115, 7837}, {183, 19709}, {194, 39563}, {298, 16808}, {299, 16809}, {302, 41100}, {303, 41101}, {315, 3545}, {325, 3845}, {376, 7769}, {385, 18362}, {491, 1328}, {492, 1327}, {546, 7796}, {547, 7750}, {549, 7802}, {626, 47005}, {671, 9766}, {1007, 15682}, {1078, 5055}, {1506, 7910}, {1975, 14269}, {2548, 7918}, {3091, 7768}, {3314, 43457}, {3543, 7763}, {3788, 19686}, {3832, 32836}, {3839, 7871}, {3854, 32874}, {3861, 32820}, {3933, 23046}, {5025, 7753}, {5066, 7850}, {5068, 32885}, {5071, 32006}, {5207, 5476}, {5306, 7812}, {5309, 7785}, {5503, 17503}, {6033, 14458}, {6179, 7843}, {6390, 12101}, {6661, 7930}, {7739, 7858}, {7745, 7942}, {7747, 7940}, {7757, 7775}, {7759, 19570}, {7764, 14062}, {7767, 11737}, {7772, 14045}, {7779, 18424}, {7780, 33011}, {7781, 14044}, {7786, 7825}, {7790, 9300}, {7818, 18806}, {7821, 33018}, {7827, 16041}, {7840, 18546}, {7847, 33278}, {7854, 33024}, {7859, 33223}, {7863, 14066}, {7865, 7885}, {7870, 11361}, {7873, 33002}, {7880, 7912}, {7883, 44543}, {7888, 14042}, {7899, 33220}, {7900, 39565}, {7902, 33289}, {7919, 15484}, {7922, 16044}, {7936, 16921}, {9166, 14614}, {10109, 37688}, {10989, 11059}, {11058, 18023}, {11185, 41099}, {11286, 34885}, {11318, 12150}, {12100, 37647}, {14568, 33006}, {14893, 32819}, {15683, 32829}, {15694, 43459}, {18146, 37375}, {18575, 40829}, {19099, 45420}, {19100, 45421}, {19106, 30472}, {19107, 30471}, {19708, 34803}, {31401, 33263}, {34681, 38907}, {37350, 41624}, {39266, 44422}

X(48913) = isotomic conjugate of X(48911)
X(48913) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 316, 11057}, {2, 7898, 40344}, {2, 11057, 7771}, {2, 14537, 3972}, {2, 14976, 46893}, {2, 19569, 187}, {381, 7773, 7809}, {381, 7809, 76}, {625, 14537, 2}, {671, 9766, 11055}, {3839, 32816, 32833}, {5025, 7753, 7884}, {7603, 40344, 2}, {7753, 7884, 7878}, {7775, 14041, 7757}, {7776, 15031, 76}, {7843, 32966, 6179}


X(48914) = X(30)X(52)∩X(51)X(186)

Barycentrics    a^2*(-a^2+b^2+c^2)*((b^2+c^2)*a^10-3*(b^2+c^2)^2*a^8+(b^2+c^2)*(2*b^4+b^2*c^2+2*c^4)*a^6+2*(b^2-c^2)^2*(b^4+3*b^2*c^2+c^4)*a^4-3*(b^6+c^6)*(b^2-c^2)^2*a^2+(b^2-c^2)^6) : :
X(48914) = 3*X(2)-4*X(13376), 3*X(51)-2*X(186), 9*X(373)-8*X(44452), 4*X(2072)-3*X(3917), 5*X(3567)-3*X(35489), 4*X(5462)-3*X(37955), 4*X(10095)-3*X(16532), 4*X(10110)-3*X(37943), 2*X(10296)+X(14531), 4*X(13446)-3*X(46451), 9*X(14845)-8*X(15350), 4*X(18323)-X(45187), 4*X(34152)-3*X(36987)

See Antreas Hatzipolakis and César Lozada euclid 5063.

X(48914) lies on these lines: {2, 13376}, {3, 11692}, {4, 13418}, {30, 52}, {51, 186}, {125, 13391}, {184, 5899}, {373, 44452}, {389, 13619}, {511, 3153}, {578, 37932}, {1154, 21650}, {1181, 37949}, {1204, 35452}, {1531, 45780}, {1843, 10151}, {2070, 5446}, {2072, 3917}, {2914, 11807}, {3567, 35489}, {3581, 18859}, {5462, 37955}, {5562, 18403}, {6000, 7731}, {6467, 37945}, {8705, 47094}, {10095, 16532}, {10110, 37943}, {10295, 32411}, {10296, 14531}, {10619, 44056}, {10625, 37938}, {11424, 37954}, {11649, 47096}, {12902, 13754}, {13403, 32352}, {13417, 18400}, {13446, 46451}, {14845, 15350}, {17701, 43574}, {18323, 45187}, {19357, 37956}, {19362, 37924}, {20424, 21660}, {34152, 36987}

X(48914) = reflection of X(i) in X(j) for these (i, j): (3, 11692), (2070, 5446), (5562, 18403), (10295, 32411), (10625, 37938), (13619, 389), (14157, 11807)
X(48914) = anticomplement of the anticomplement of X(13376)

leftri

Points in a [Euler line, Brocard axis] coordinate system: X(48915)-X(48944)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1, L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1 = Euler line: (b^2 - c^2)(a^2 - b^2 - c^2) α + (c^2 - a^2)(b^2 - c^2 - a^2) β + (a^2 - b^2)(c^2 - a^2 - b^2) γ = 0.

L2 = Brocard axis: b^2 c^2 (b^2 - c^2) α + c^2 a^2 (c^2 - a^2) β + a^2 b^2 (a^2 - b^2) γ = 0.

The origin is given by (0, 0) = X(3) = a^2(a^2-b^2-c^2) : : .

Barycentrics u : v : w for a triangle center U = (x, y) in this system are given by

u : v : w = a^2(a^2-b^2-c^2)(b^2-c^2)(c^2-a^2)(a^2-b^2) + (a^2(-2a^2+b^2+c^2) + (b^2-c^2)^2)x - a^2(a^2(b^2+c^2) - b^4 - c^4) y : : ,

where, as polynomials in a, b, c, the coordinate x is antisymmetric and homogeneous of degree 6, and y is antisymmetric and homogeneous of degree 4.

The appearance of {x, y}, k in the following list means that (x, y) = X(k).

{-2 a (a-b) b (a-c) (b-c) c, -2 (a-b) (a-c) (b-c) (a+b+c)}, 12702}
{-2 (a^2-b^2) (a^2-c^2) (b^2-c^2), -((2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2))}, 48872
{-2 (a^2-b^2) (a^2-c^2) (b^2-c^2), -(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2))}, 48879
{-2 (a^2-b^2) (a^2-c^2) (b^2-c^2), 0}, 1657
{-2 (a^2-b^2) (a^2-c^2) (b^2-c^2), ((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)}, 48896
{-2 (a^2-b^2) (a^2-c^2) (b^2-c^2), (2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)}, 48905
{-((a^2-b^2) (a^2-c^2) (b^2-c^2)), -((2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2))}, 48873
{-a (a-b) b (a-c) (b-c) c, -((a-b) (a-c) (b-c) (a+b+c))}, 40
{-((a^2-b^2) (a^2-c^2) (b^2-c^2)), -(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2))}, 48880
{-((a-b) (a-c) (b-c) (a^3+b^3+c^3)), 0}, 48890
{-a (a-b) b (a-c) (b-c) c, 0}, 37425
{-((a^2-b^2) (a^2-c^2) (b^2-c^2)), 0}, 20
{-((a^2-b^2) (a^2-c^2) (b^2-c^2)), ((a^2-b^2) (a^2-c^2) (b^2-c^2))/(2 (a^2+b^2+c^2))}, 48891
{-a (a-b) b (a-c) (b-c) c, (a-b) (a-c) (b-c) (a+b+c)}, 48897
{-((a^2-b^2) (a^2-c^2) (b^2-c^2)), ((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)}, 48898
{-((a-b) (a-c) (b-c) (a^3+b^3+c^3)), 2 (a-b) (a-c) (b-c) (a+b+c)}, 46483
{-((a^2-b^2) (a^2-c^2) (b^2-c^2)), (2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)}, 46264
{-(1/2) (a^2-b^2) (a^2-c^2) (b^2-c^2), -((2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2))}, 48874
{-(1/2) (a^2-b^2) (a^2-c^2) (b^2-c^2), -(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2))}, 48881
{-(1/2) a (a-b) b (a-c) (b-c) c, -(1/2) (a-b) (a-c) (b-c) (a+b+c)}, 3579
{-(1/2) (a^2-b^2) (a^2-c^2) (b^2-c^2), -(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(2 (a^2+b^2+c^2)))}, 48885
{-(1/2) (a^2-b^2) (a^2-c^2) (b^2-c^2), 0}, 550
{-(1/2) (a^2-b^2) (a^2-c^2) (b^2-c^2), ((a^2-b^2) (a^2-c^2) (b^2-c^2))/(2 (a^2+b^2+c^2))}, 48892
{-(1/2) (a^2-b^2) (a^2-c^2) (b^2-c^2), ((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)}, 44882
{-(1/2) (a^2-b^2) (a^2-c^2) (b^2-c^2), (2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)}, 48906
{0, -((2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2))}, 1350
{0, -((2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a b+a c+b c))}, 48875
{0, -((a-b) (a-c) (b-c) (a+b+c))}, 48882
{0, -(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2))}, 3098
{0, -(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a b+a c+b c))}, 573
{0, -(1/2) (a-b) (a-c) (b-c) (a+b+c)}, 35203
{0, -(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(2 (a^2+b^2+c^2)))}, 14810
{0, -(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(2 (a b+a c+b c)))}, 48886
{0, 0}, 3
{0, 1/2 (a-b) (a-c) (b-c) (a+b+c)}, 48893
{0, ((a^2-b^2) (a^2-c^2) (b^2-c^2))/(2 (a^2+b^2+c^2))}, 5092
{0, (a-b) (a-c) (b-c) (a+b+c)}, 500
{0, ((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)}, 182
{0, ((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a b+a c+b c)}, 991
{0, 2 (a-b) (a-c) (b-c) (a+b+c)}, 48907
{0, (2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)}, 6
{0, (2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a b+a c+b c)}, 48908
{1/2 (a^2-b^2) (a^2-c^2) (b^2-c^2), -((2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2))}, 48876
{1/2 (a^2-b^2) (a^2-c^2) (b^2-c^2), -(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2))}, 141
{1/2 (a-b) (a-c) (b-c) (a+b+c)^3, -(1/2) (a-b) (a-c) (b-c) (a+b+c)}, 46976
{1/2 (a^2-b^2) (a^2-c^2) (b^2-c^2), -(1/2) (a-b) (a-c) (b-c) (a+b+c)}, 48887
{1/2 (a^2-b^2) (a^2-c^2) (b^2-c^2), -(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(2 (a^2+b^2+c^2)))}, 24206
{1/2 (a^2-b^2) (a^2-c^2) (b^2-c^2), -(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(2 (a b+a c+b c)))}, 48888
{1/2 (a^2-b^2) (a^2-c^2) (b^2-c^2), 0}, 5
{1/2 a (a-b) b (a-c) (b-c) c, 1/2 (a-b) (a-c) (b-c) (a+b+c)}, 1385
{1/2 (a^2-b^2) (a^2-c^2) (b^2-c^2), ((a^2-b^2) (a^2-c^2) (b^2-c^2))/(2 (a^2+b^2+c^2))}, 19130
{1/2 (a^2-b^2) (a^2-c^2) (b^2-c^2), ((a^2-b^2) (a^2-c^2) (b^2-c^2))/(2 (a b+a c+b c))}, 24220
{1/2 a (a-b) b (a-c) (b-c) c, (a-b) (a-c) (b-c) (a+b+c)}, 5453
{1/2 (a^2-b^2) (a^2-c^2) (b^2-c^2), ((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)}, 5480
{1/2 (a^2-b^2) (a^2-c^2) (b^2-c^2), (2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)}, 21850
{(a^2-b^2) (a^2-c^2) (b^2-c^2), -2 (a-b) (a-c) (b-c) (a+b+c)}, 48877
{(a^2-b^2) (a^2-c^2) (b^2-c^2), -((2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2))}, 1352
{(a^2-b^2) (a^2-c^2) (b^2-c^2), -((2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a b+a c+b c))}, 48878
{a (a-b) b (a-c) (b-c) c, -((a-b) (a-c) (b-c) (a+b+c))}, 48883
{(a^2-b^2) (a^2-c^2) (b^2-c^2), -(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2))}, 3818
{(a^2-b^2) (a^2-c^2) (b^2-c^2), -(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(2 (a^2+b^2+c^2)))}, 48889
{a (a-b) b (a-c) (b-c) c, 0}, 9840
{(a^2-b^2) (a^2-c^2) (b^2-c^2), 0}, 4
{a (a-b) b (a-c) (b-c) c, 1/2 (a-b) (a-c) (b-c) (a+b+c)}, 48894
{(a^2-b^2) (a^2-c^2) (b^2-c^2), ((a^2-b^2) (a^2-c^2) (b^2-c^2))/(2 (a^2+b^2+c^2))}, 48895
{a (a-b) b (a-c) (b-c) c, (a-b) (a-c) (b-c) (a+b+c)}, 1
{(a^2-b^2) (a^2-c^2) (b^2-c^2), (a-b) (a-c) (b-c) (a+b+c)}, 48899
{(a^2-b^2) (a^2-c^2) (b^2-c^2), ((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)}, 48901
{(a^2-b^2) (a^2-c^2) (b^2-c^2), ((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a b+a c+b c)}, 48902
{((a-b) (a-c) (b-c) (a b+a c+b c)^2)/(a+b+c), ((a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c)}, 48900
{a (a-b) b (a-c) (b-c) c, 2 (a-b) (a-c) (b-c) (a+b+c)}, 48909
{(a^2-b^2) (a^2-c^2) (b^2-c^2), (2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)}, 31670
{(a^2-b^2) (a^2-c^2) (b^2-c^2), (2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a b+a c+b c)}, 10446
{2 (a^2-b^2) (a^2-c^2) (b^2-c^2), -((2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2))}, 36990
{2 (a^2-b^2) (a^2-c^2) (b^2-c^2), -(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2))}, 48884
{2 (a^2-b^2) (a^2-c^2) (b^2-c^2), 0}, 382
{2 a (a-b) b (a-c) (b-c) c, (a-b) (a-c) (b-c) (a+b+c)}, 48903
{2 (a^2-b^2) (a^2-c^2) (b^2-c^2), ((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)}, 48904
{2 a (a-b) b (a-c) (b-c) c, 2 (a-b) (a-c) (b-c) (a+b+c)}, 1482
{2 (a^2-b^2) (a^2-c^2) (b^2-c^2), (2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)}, 48910
{-2*a*(a - b)*b*(a - c)*(b - c)*c, -((a - b)*(a - c)*(b - c)*(a + b + c))}, 48915
{-2*a*(a - b)*b*(a - c)*(b - c)*c, (a - b)*(a - c)*(b - c)*(a + b + c)}, 48916
{-(a*(a - b)*b*(a - c)*(b - c)*c), -2*(a - b)*(a - c)*(b - c)*(a + b + c)}, 48917
{-((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)), (-2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c)}, 48918
{-(a*(a - b)*b*(a - c)*(b - c)*c), -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))}, 48919
{-((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)), -1/2*((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)}, 48920
{-(a*(a - b)*b*(a - c)*(b - c)*c), 2*(a - b)*(a - c)*(b - c)*(a + b + c)}, 48921
{-(a*(a - b)*b*(a - c)*(b - c)*c), (2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)}, 48922
{-((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2)), 2*(a - b)*(a - c)*(b - c)*(a + b + c)}, 48923
{-1/2*(a*(a - b)*b*(a - c)*(b - c)*c), -((a - b)*(a - c)*(b - c)*(a + b + c))}, 48924
{-1/2*((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c)^2)/(a + b + c), -1/2*((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)}, 48925
{-1/2*(a*(a - b)*b*(a - c)*(b - c)*c), ((a - b)*(a - c)*(b - c)*(a + b + c))/2}, 48926
{-1/2*(a*(a - b)*b*(a - c)*(b - c)*c), (a - b)*(a - c)*(b - c)*(a + b + c)}, 48927
{0, -2*(a - b)*(a - c)*(b - c)*(a + b + c)}, 48928
{0, ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(2*(a*b + a*c + b*c))}, 48929
{(a*(a - b)*b*(a - c)*(b - c)*c)/2, 0}, 48930
{((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/2, ((a - b)*(a - c)*(b - c)*(a + b + c))/2}, 48931
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c)^2)/(2*(a + b + c)), ((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(2*(a + b + c))}, 48932
{((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/2, (a - b)*(a - c)*(b - c)*(a + b + c)}, 48933
{((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/2, ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c)}, 48934
{(a - b)*(a - c)*(b - c)*(a^3 + b^3 + c^3), -2*(a - b)*(a - c)*(b - c)*(a + b + c)}, 48935
{a*(a - b)*b*(a - c)*(b - c)*c, -2*(a - b)*(a - c)*(b - c)*(a + b + c)}, 48936
{(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2), -((a - b)*(a - c)*(b - c)*(a + b + c))}, 48937
{(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2), -(((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a*b + a*c + b*c))}, 48938
{a*(a - b)*b*(a - c)*(b - c)*c, -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))}, 48939
{(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2), ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(2*(a*b + a*c + b*c))}, 48940
{(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2), 2*(a - b)*(a - c)*(b - c)*(a + b + c)}, 48941
{2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2), -1/2*((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2)}, 48942
{2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2), ((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(2*(a^2 + b^2 + c^2))}, 48943
{(2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c)^2)/(a + b + c), (2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)}, 48944


X(48915) = X(1)X(15447)∩X(30)X(40)

Barycentrics    a*(a^5*b + 2*a^4*b^2 - 2*a^2*b^4 - a*b^5 + a^5*c + 6*a^4*b*c + a^3*b^2*c - 4*a^2*b^3*c - 2*a*b^4*c - 2*b^5*c + 2*a^4*c^2 + a^3*b*c^2 - 2*a^2*b^2*c^2 - a*b^3*c^2 - 4*a^2*b*c^3 - a*b^2*c^3 + 4*b^3*c^3 - 2*a^2*c^4 - 2*a*b*c^4 - a*c^5 - 2*b*c^5) : :
X(48915) = 3 X[3] - 2 X[48894], 4 X[48894] - 3 X[48903], 3 X[40] - X[48883], 3 X[48882] - 2 X[48883], 3 X[500] - 2 X[48909], 3 X[37425] - X[48909], 3 X[5657] - 2 X[48887], 3 X[14636] - 4 X[31663]

X(48915) lies on these lines: {1, 15447}, {3, 4653}, {30, 40}, {382, 573}, {500, 517}, {511, 12702}, {516, 46704}, {546, 21363}, {550, 1764}, {1482, 48893}, {3430, 16117}, {3579, 9840}, {5453, 7982}, {5657, 48887}, {6097, 11012}, {6361, 15971}, {7991, 48897}, {12433, 20367}, {12699, 15973}, {14636, 31663}, {15489, 19648}, {15952, 46623}, {20605, 48263}, {24474, 30271}, {28174, 48899}

X(48915) = midpoint of X(i) and X(j) for these {i,j}: {6361, 15971}, {7991, 48897}
X(48915) = reflection of X(i) in X(j) for these {i,j}: {500, 37425}, {1482, 48893}, {7982, 5453}, {9840, 3579}, {12699, 15973}, {48882, 40}, {48903, 3}


X(48916) = X(1)X(30)∩X(3)X(17749)

Barycentrics    a*(a^5*b - 2*a^3*b^3 + a*b^5 + a^5*c + 6*a^4*b*c - a^3*b^2*c - 4*a^2*b^3*c - 2*b^5*c - a^3*b*c^2 - 2*a^2*b^2*c^2 - a*b^3*c^2 - 2*a^3*c^3 - 4*a^2*b*c^3 - a*b^2*c^3 + 4*b^3*c^3 + a*c^5 - 2*b*c^5) : :
X(48916) = 2 X[1] - 3 X[500], 5 X[1] - 6 X[5453], X[1] - 3 X[48897], 4 X[1] - 3 X[48903], 5 X[500] - 4 X[5453], 2 X[5453] - 5 X[48897], 8 X[5453] - 5 X[48903], 4 X[48897] - X[48903], 2 X[3579] - 3 X[37425], 4 X[3579] - 3 X[48882], 5 X[3617] - 3 X[48877], X[8148] - 3 X[48907], 7 X[9780] - 6 X[48887], 3 X[9840] - 4 X[13624], 2 X[11278] - 3 X[48909], 2 X[31673] - 3 X[46704], 5 X[35242] - 3 X[48883]

X(48916) lies on these lines: {1, 30}, {3, 17749}, {20, 5396}, {58, 16117}, {60, 43576}, {355, 1742}, {382, 991}, {386, 3534}, {511, 12702}, {548, 37732}, {581, 1657}, {582, 37426}, {846, 16138}, {896, 3214}, {1458, 31795}, {2594, 4324}, {3000, 31794}, {3216, 8703}, {3245, 13391}, {3530, 5400}, {3617, 48877}, {3651, 16948}, {4300, 28160}, {4302, 5399}, {6097, 45885}, {8148, 48907}, {9780, 48887}, {9840, 13624}, {10459, 28208}, {11001, 19767}, {11278, 48909}, {14131, 19546}, {14636, 27627}, {17104, 37477}, {21674, 22798}, {29181, 43178}, {31673, 46704}, {35242, 48883}, {37401, 45926}, {37524, 47749}

X(48916) = reflection of X(i) in X(j) for these {i,j}: {500, 48897}, {48882, 37425}, {48903, 500}


X(48917) = X(3)X(81)∩X(8)X(30)

Barycentrics    a*(a^5*b + 3*a^4*b^2 + a^3*b^3 - 3*a^2*b^4 - 2*a*b^5 + a^5*c + 4*a^4*b*c + 2*a^3*b^2*c - 3*a^2*b^3*c - 3*a*b^4*c - b^5*c + 3*a^4*c^2 + 2*a^3*b*c^2 - 2*a^2*b^2*c^2 - a*b^3*c^2 + a^3*c^3 - 3*a^2*b*c^3 - a*b^2*c^3 + 2*b^3*c^3 - 3*a^2*c^4 - 3*a*b*c^4 - 2*a*c^5 - b*c^5) : :
X(48917) = 2 X[1] - 3 X[14636], 3 X[14636] - 4 X[35203], 3 X[3] - 2 X[5453], 4 X[5453] - 3 X[48909], 3 X[40] - X[48897], 3 X[37425] - 2 X[48897], 3 X[165] - 2 X[48893], 3 X[9840] - 2 X[48903], 3 X[48882] - X[48903], 3 X[5657] - 2 X[15973]

X(48917) lies on these lines: {1, 14636}, {2, 9566}, {3, 81}, {4, 1654}, {5, 41809}, {8, 30}, {10, 24705}, {28, 22139}, {40, 511}, {42, 500}, {63, 15979}, {165, 48893}, {199, 3193}, {323, 37405}, {376, 20018}, {517, 2292}, {524, 24683}, {573, 10441}, {942, 2269}, {970, 1764}, {986, 28369}, {1351, 37062}, {1695, 10476}, {2245, 18178}, {3167, 37408}, {3430, 46623}, {3496, 15984}, {3580, 27553}, {3882, 10381}, {4192, 5752}, {4658, 37508}, {5221, 37631}, {5657, 15973}, {5690, 46704}, {5889, 37409}, {6097, 35000}, {6197, 15975}, {7102, 46467}, {7982, 48894}, {7991, 48883}, {8731, 18180}, {9122, 12164}, {9955, 30970}, {12699, 31330}, {13391, 35460}, {13754, 26893}, {15489, 19335}, {15945, 41340}, {17976, 38856}, {19546, 34466}, {22076, 28258}, {24443, 28368}, {33878, 37426}, {37225, 41723}, {37431, 37510}, {38430, 42045}

X(48917) = midpoint of X(i) and X(j) for these {i,j}: {6361, 48877}, {7991, 48883}
X(48917) = reflection of X(i) in X(j) for these {i,j}: {1, 35203}, {500, 3579}, {7982, 48894}, {9840, 48882}, {12699, 48887}, {37425, 40}, {42045, 38430}, {46704, 5690}, {48899, 10}, {48909, 3}
X(48917) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 35203, 14636}, {573, 10441, 13731}, {970, 1764, 19513}


X(48918) = X(3)X(86)∩X(4)X(9)

Barycentrics    3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 2*a^2*b^4 - a*b^5 + 3*a^5*c + 3*a^4*b*c - 2*a^3*b^2*c - 2*a^2*b^3*c - a*b^4*c - b^5*c + 2*a^4*c^2 - 2*a^3*b*c^2 + 2*a*b^3*c^2 - 2*a^3*c^3 - 2*a^2*b*c^3 + 2*a*b^2*c^3 + 2*b^3*c^3 - 2*a^2*c^4 - a*b*c^4 - a*c^5 - b*c^5 : :
X(48918) = 3 X[2] - 4 X[48886], 3 X[4] - 4 X[48888], 3 X[573] - 2 X[48888], 3 X[376] - 2 X[991], 5 X[631] - 4 X[24220]

X(48918) lies on these lines: {2, 22080}, {3, 86}, {4, 9}, {20, 185}, {30, 17346}, {165, 10478}, {182, 37416}, {184, 7560}, {376, 991}, {390, 39543}, {517, 30273}, {550, 48908}, {581, 1742}, {631, 24220}, {941, 4307}, {944, 29311}, {962, 31394}, {1045, 24695}, {1213, 36687}, {1352, 6999}, {1899, 3151}, {2792, 13174}, {3474, 5712}, {3651, 5757}, {3767, 20666}, {4192, 9535}, {4229, 37474}, {4294, 21746}, {5327, 36744}, {5739, 32932}, {5752, 15310}, {6996, 20154}, {6998, 37499}, {7991, 10454}, {9778, 37400}, {10605, 30266}, {13329, 36697}, {19642, 37652}, {20070, 29309}, {33971, 37420}

X(48918) = reflection of X(i) in X(j) for these {i,j}: {4, 573}, {962, 31394}, {1742, 31730}, {10446, 3}, {41869, 45305}, {48878, 48875}, {48902, 48886}, {48908, 550}
X(48918) = anticomplement of X(48902)
X(48918) = crossdifference of every pair of points on line {1459, 2451}
X(48918) = {X(48886),X(48902)}-harmonic conjugate of X(2)


X(48919) = X(10)X(30)∩X(40)X(511)

Barycentrics    a*(2*a^5*b + 3*a^4*b^2 - a^3*b^3 - 3*a^2*b^4 - a*b^5 + 2*a^5*c + 8*a^4*b*c + a^3*b^2*c - 6*a^2*b^3*c - 3*a*b^4*c - 2*b^5*c + 3*a^4*c^2 + a^3*b*c^2 - 4*a^2*b^2*c^2 - 2*a*b^3*c^2 - a^3*c^3 - 6*a^2*b*c^3 - 2*a*b^2*c^3 + 4*b^3*c^3 - 3*a^2*c^4 - 3*a*b*c^4 - a*c^5 - 2*b*c^5) : :
X(48919) = 3 X[3] - X[48903], 3 X[48894] - 2 X[48903], 3 X[40] + X[48897], 3 X[37425] - X[48897], 3 X[165] - X[9840], 2 X[5453] - 3 X[48893], 3 X[9778] + X[15971], 3 X[14636] - 5 X[35242]

X(48919) lies on these lines: {3, 4653}, {4, 48886}, {10, 30}, {40, 511}, {165, 9840}, {182, 37062}, {376, 10449}, {500, 12702}, {516, 15973}, {517, 5453}, {1495, 37405}, {2475, 22080}, {3057, 15447}, {3098, 37426}, {3216, 4192}, {3651, 10381}, {4221, 46623}, {6361, 48899}, {7991, 48909}, {9778, 15971}, {11471, 15975}, {14636, 35242}, {14915, 47749}, {16589, 37508}, {19767, 37400}, {37402, 37527}, {37409, 46850}

X(48919) = midpoint of X(i) and X(j) for these {i,j}: {40, 37425}, {500, 12702}, {6361, 48899}, {7991, 48909}
X(48919) = reflection of X(i) in X(j) for these {i,j}: {35203, 3579}, {46976, 9958}, {48894, 3}


X(48920) = X(3)X(39784)∩X(20)X(185)

Barycentrics    6*a^6 + 3*a^4*b^2 - 7*a^2*b^4 - 2*b^6 + 3*a^4*c^2 - 4*a^2*b^2*c^2 + 2*b^4*c^2 - 7*a^2*c^4 + 2*b^2*c^4 - 2*c^6 : :
X(48920) = 3 X[3] - X[48904], 2 X[48879] + X[48895], 3 X[48879] + X[48904], 3 X[48895] - 2 X[48904], 5 X[4] - 7 X[42786], 17 X[20] - X[193], 9 X[20] - X[6776], 5 X[20] - X[46264], 3 X[20] + X[48873], 3 X[20] - X[48898], 9 X[193] - 17 X[6776], 5 X[193] - 17 X[46264], 3 X[193] + 17 X[48873], X[193] + 17 X[48880], 2 X[193] - 17 X[48891], 3 X[193] - 17 X[48898], 5 X[6776] - 9 X[46264], X[6776] + 3 X[48873], X[6776] + 9 X[48880], 2 X[6776] - 9 X[48891], X[6776] - 3 X[48898], 3 X[46264] + 5 X[48873], X[46264] + 5 X[48880], 2 X[46264] - 5 X[48891], 3 X[46264] - 5 X[48898], X[48873] - 3 X[48880], 2 X[48873] + 3 X[48891], 2 X[48880] + X[48891], 3 X[48880] + X[48898], 3 X[48891] - 2 X[48898], 17 X[14810] - 12 X[20582], 3 X[14810] - 2 X[24206], 5 X[14810] - 3 X[25561], 18 X[20582] - 17 X[24206], 20 X[20582] - 17 X[25561], 6 X[20582] - 17 X[48885], and many others

X(48920) lies on these lines: {3, 39784}, {4, 42786}, {6, 42994}, {20, 185}, {30, 14810}, {182, 3534}, {206, 32903}, {376, 48901}, {542, 19710}, {548, 19130}, {550, 5092}, {575, 12103}, {1350, 11645}, {1352, 11001}, {1657, 3098}, {3522, 38317}, {3529, 3818}, {3589, 44245}, {3819, 20062}, {5039, 44519}, {5097, 15686}, {5650, 20063}, {7519, 15082}, {7756, 41413}, {10168, 15690}, {11178, 15685}, {11898, 48905}, {12086, 32600}, {12294, 13619}, {14927, 46333}, {15691, 18583}, {15696, 17508}, {15704, 29012}, {17538, 20190}, {17800, 31884}, {20301, 37853}, {22330, 25406}, {25565, 45759}, {32273, 38788}, {39884, 44903}

X(48920) = midpoint of X(i) and X(j) for these {i,j}: {3, 48879}, {20, 48880}, {182, 48872}, {1350, 48896}, {1657, 3098}, {3529, 3818}, {11178, 15685}, {15704, 48881}, {17800, 48884}, {48873, 48898}
X(48920) = reflection of X(i) in X(j) for these {i,j}: {206, 32903}, {575, 48892}, {3589, 44245}, {5092, 550}, {5097, 44882}, {5480, 33751}, {10168, 15690}, {14810, 48885}, {18553, 3098}, {19130, 548}, {20301, 37853}, {31670, 20190}, {48889, 14810}, {48891, 20}, {48892, 12103}, {48895, 3}
X(48920) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 48873, 48898}, {550, 5480, 33751}, {1350, 15681, 48896}, {3522, 43621, 38317}, {3534, 48872, 182}, {5480, 33751, 5092}, {15696, 48910, 17508}, {17800, 31884, 48884}, {48880, 48898, 48873}


X(48921) = X(30)X(944)∩X(40)X(511)

Barycentrics    a*(a^5*b - a^4*b^2 - 3*a^3*b^3 + a^2*b^4 + 2*a*b^5 + a^5*c + 4*a^4*b*c - 2*a^3*b^2*c - 3*a^2*b^3*c + a*b^4*c - b^5*c - a^4*c^2 - 2*a^3*b*c^2 - 2*a^2*b^2*c^2 - a*b^3*c^2 - 3*a^3*c^3 - 3*a^2*b*c^3 - a*b^2*c^3 + 2*b^3*c^3 + a^2*c^4 + a*b*c^4 + 2*a*c^5 - b*c^5) : :
X(48921) = X[1482] - 3 X[48907], 2 X[1482] - 3 X[48909], 2 X[40] - 3 X[37425], X[40] - 3 X[48897], 3 X[500] - 2 X[1385], 4 X[1385] - 3 X[9840], 6 X[5453] - 5 X[37624], 5 X[5818] - 6 X[15973], 5 X[5818] - 3 X[48877], 10 X[7987] - 9 X[14636], 5 X[7987] - 3 X[48883], 5 X[7987] - 6 X[48893], 3 X[14636] - 2 X[48883], 3 X[14636] - 4 X[48893], 7 X[16192] - 6 X[35203], 4 X[31663] - 3 X[48882], 4 X[33179] - 3 X[48903]

X(48921) lies on these lines: {1, 33551}, {3, 16948}, {4, 17300}, {30, 944}, {40, 511}, {474, 5544}, {500, 1064}, {548, 5754}, {581, 37331}, {991, 13731}, {1351, 37426}, {1437, 46549}, {3522, 9567}, {3667, 4065}, {4192, 37482}, {5453, 37624}, {5482, 19546}, {5818, 15973}, {7987, 14636}, {16192, 35203}, {19335, 37732}, {19548, 36746}, {19646, 37521}, {23841, 35338}, {31663, 48882}, {33179, 48903}, {33878, 37062}, {42043, 47639}

X(48921) = reflection of X(i) in X(j) for these {i,j}: {9840, 500}, {37425, 48897}, {48877, 15973}, {48883, 48893}, {48909, 48907}
X(48921) = {X(48883),X(48893)}-harmonic conjugate of X(14636)


X(48922) = X(6)X(30)∩X(40)X(511)

Barycentrics    a*(a^7*b + a^6*b^2 - 2*a^5*b^3 - 2*a^4*b^4 + a^3*b^5 + a^2*b^6 + a^7*c + 4*a^6*b*c - a^5*b^2*c - 3*a^4*b^3*c - a^3*b^4*c + a*b^6*c - b^7*c + a^6*c^2 - a^5*b*c^2 - 4*a^4*b^2*c^2 - 4*a^3*b^3*c^2 - a^2*b^4*c^2 + a*b^5*c^2 - 2*a^5*c^3 - 3*a^4*b*c^3 - 4*a^3*b^2*c^3 - 4*a^2*b^3*c^3 - 2*a*b^4*c^3 + b^5*c^3 - 2*a^4*c^4 - a^3*b*c^4 - a^2*b^2*c^4 - 2*a*b^3*c^4 + a^3*c^5 + a*b^2*c^5 + b^3*c^5 + a^2*c^6 + a*b*c^6 - b*c^7) : :
X(48922) = 4 X[5092] - 3 X[14636], 3 X[38029] - 2 X[48894], 3 X[38047] - 2 X[48887]

X(48922) lies on these lines: {6, 30}, {40, 511}, {182, 1724}, {500, 518}, {542, 6126}, {1352, 15973}, {1386, 48903}, {1503, 13408}, {3098, 37676}, {3242, 5453}, {3564, 12430}, {4265, 6097}, {5092, 14636}, {6776, 15971}, {38029, 48894}, {38047, 48887}

X(48922) = midpoint of X(i) and X(j) for these {i,j}: {3751, 48897}, {6776, 15971}
X(48922) = reflection of X(i) in X(j) for these {i,j}: {1352, 15973}, {3242, 5453}, {9840, 182}, {48903, 1386}


X(48923) = X(2)X(48893)∩X(3)X(5278)

Barycentrics    3*a^6*b + a^5*b^2 - 4*a^4*b^3 + a^2*b^5 - a*b^6 + 3*a^6*c + 6*a^5*b*c - a^4*b^2*c - 4*a^3*b^3*c - a^2*b^4*c - 2*a*b^5*c - b^6*c + a^5*c^2 - a^4*b*c^2 - 4*a^3*b^2*c^2 + a*b^4*c^2 - b^5*c^2 - 4*a^4*c^3 - 4*a^3*b*c^3 + 4*a*b^3*c^3 + 2*b^4*c^3 - a^2*b*c^4 + a*b^2*c^4 + 2*b^3*c^4 + a^2*c^5 - 2*a*b*c^5 - b^2*c^5 - a*c^6 - b*c^6 : :
X(48923) = 3 X[2] - 4 X[48893], 3 X[376] - 2 X[48882], 5 X[631] - 4 X[48887], 5 X[3522] - 4 X[35203], 4 X[5453] - 3 X[5603], 3 X[5731] - 2 X[9840], 3 X[7967] - 2 X[48903]

X(48923) lies on these lines: {2, 48893}, {3, 5278}, {4, 500}, {8, 37425}, {20, 185}, {30, 944}, {376, 48882}, {515, 4300}, {524, 3189}, {631, 48887}, {1788, 15447}, {2360, 37009}, {3146, 48899}, {3522, 35203}, {4297, 46362}, {4339, 28369}, {5453, 5603}, {5731, 9840}, {7967, 48903}, {10430, 15979}, {10884, 15970}, {12528, 30273}, {13754, 37000}, {15937, 20420}, {16704, 46623}, {19752, 37492}, {41723, 46519}

X(48923) = reflection of X(i) in X(j) for these {i,j}: {4, 500}, {8, 37425}, {962, 48909}, {3146, 48899}, {15971, 48897}, {48877, 3}, {48883, 4297}


X(48924) = X(3)X(81)∩X(30)X(40)

Barycentrics    a*(2*a^5*b + 4*a^4*b^2 - 4*a^2*b^4 - 2*a*b^5 + 2*a^5*c + 6*a^4*b*c + 2*a^3*b^2*c - 5*a^2*b^3*c - 4*a*b^4*c - b^5*c + 4*a^4*c^2 + 2*a^3*b*c^2 - 4*a^2*b^2*c^2 - 2*a*b^3*c^2 - 5*a^2*b*c^3 - 2*a*b^2*c^3 + 2*b^3*c^3 - 4*a^2*c^4 - 4*a*b*c^4 - 2*a*c^5 - b*c^5) : :
X(48924) = 3 X[3] - X[48909], 3 X[5453] - 2 X[48909], 3 X[40] + X[48883], 3 X[48882] - X[48883], 3 X[165] - X[500], 3 X[35203] - X[48894], X[1482] - 3 X[14636], 3 X[5657] - X[46704], 3 X[9778] + X[48877], 3 X[26446] - X[48899], X[46483] - 3 X[46617]

X(48924) lies on these lines: {3, 81}, {5, 573}, {30, 40}, {140, 1764}, {165, 500}, {323, 37294}, {333, 41810}, {511, 3579}, {516, 48887}, {517, 3743}, {1482, 14636}, {1817, 22136}, {3336, 37631}, {3628, 21363}, {5036, 5292}, {5657, 46704}, {5707, 37499}, {6097, 10310}, {6147, 24310}, {7991, 48903}, {8251, 15945}, {9548, 38042}, {9566, 19543}, {9778, 48877}, {9840, 12702}, {10476, 38028}, {10887, 26446}, {13391, 13528}, {15447, 37572}, {18180, 22080}, {18253, 35468}, {22097, 24470}, {31663, 48893}, {37536, 48886}, {46483, 46617}

X(48924) = midpoint of X(i) and X(j) for these {i,j}: {40, 48882}, {7991, 48903}, {9840, 12702}
X(48924) = reflection of X(i) in X(j) for these {i,j}: {5453, 3}, {48893, 31663}


X(48925) = X(3)X(142)∩X(99)X(103)

Barycentrics    2*a^5 + 4*a^4*b - 3*a^3*b^2 - 2*a^2*b^3 - a*b^4 + 4*a^4*c - 3*a^2*b^2*c - b^4*c - 3*a^3*c^2 - 3*a^2*b*c^2 + 2*a*b^2*c^2 + b^3*c^2 - 2*a^2*c^3 + b^2*c^3 - a*c^4 - b*c^4 : :
X(48925) = 3 X[3] - X[48900], X[6361] + 3 X[10186], 3 X[9746] - 7 X[16192]

X(48925) lies on these lines: {3, 142}, {10, 24047}, {40, 7709}, {99, 103}, {165, 4384}, {519, 8716}, {550, 28845}, {740, 8720}, {2702, 2724}, {3579, 28850}, {3755, 33863}, {4307, 37574}, {4349, 37573}, {4356, 37607}, {4512, 37274}, {6361, 10186}, {6996, 10164}, {7618, 28562}, {8703, 28854}, {9441, 12194}, {9746, 16192}, {9778, 26626}, {11329, 40998}, {12545, 37402}, {13634, 34638}, {14953, 35270}, {17687, 38204}, {19925, 24275}, {21997, 35263}, {28150, 36477}, {28870, 34773}, {34848, 36028}, {35242, 36697}, {37508, 45305}


X(48926) = X(3)X(1724)∩X(30)X(551)

Barycentrics    a*(2*a^5*b + a^4*b^2 - 3*a^3*b^3 - a^2*b^4 + a*b^5 + 2*a^5*c + 6*a^4*b*c - a^3*b^2*c - 5*a^2*b^3*c - a*b^4*c - b^5*c + a^4*c^2 - a^3*b*c^2 - 4*a^2*b^2*c^2 - 2*a*b^3*c^2 - 3*a^3*c^3 - 5*a^2*b*c^3 - 2*a*b^2*c^3 + 2*b^3*c^3 - a^2*c^4 - a*b*c^4 + a*c^5 - b*c^5) : :
X(48926) = 3 X[3] - X[48883], X[48883] + 3 X[48897], 3 X[1385] - 2 X[48894], 3 X[48893] - X[48894], 3 X[500] - X[48909], 3 X[37425] + X[48909], 3 X[11231] - 2 X[48887], 3 X[26446] - X[48877]

X(48926) lies on these lines: {3, 1724}, {30, 551}, {40, 48907}, {500, 517}, {511, 3579}, {516, 43972}, {548, 9569}, {991, 37536}, {1437, 35989}, {3295, 10108}, {3627, 6176}, {3651, 43576}, {4192, 5482}, {4303, 45022}, {5453, 10222}, {5495, 35004}, {5709, 15937}, {5810, 36706}, {6097, 33862}, {9840, 13624}, {10225, 13391}, {10440, 35203}, {10624, 15368}, {11231, 48887}, {14131, 19513}, {15107, 37294}, {15178, 48903}, {15447, 37582}, {15622, 32613}, {15971, 18481}, {15973, 18480}, {16117, 37527}, {26446, 48877}, {28146, 48899}, {28160, 46704}, {31663, 48882}, {37400, 37482}

X(48926) = midpoint of X(i) and X(j) for these {i,j}: {3, 48897}, {40, 48907}, {500, 37425}, {15971, 18481}
X(48926) = reflection of X(i) in X(j) for these {i,j}: {1385, 48893}, {9840, 13624}, {10222, 5453}, {18480, 15973}, {48882, 31663}, {48903, 15178}


X(48927) = X(1)X(30)∩X(3)X(16948)

Barycentrics    a*(2*a^5*b - 4*a^3*b^3 + 2*a*b^5 + 2*a^5*c + 6*a^4*b*c - 2*a^3*b^2*c - 5*a^2*b^3*c - b^5*c - 2*a^3*b*c^2 - 4*a^2*b^2*c^2 - 2*a*b^3*c^2 - 4*a^3*c^3 - 5*a^2*b*c^3 - 2*a*b^2*c^3 + 2*b^3*c^3 + 2*a*c^5 - b*c^5) : :
X(48927) = X[1] - 3 X[500], 2 X[1] - 3 X[5453], X[1] + 3 X[48897], 5 X[1] - 3 X[48903], 5 X[500] - X[48903], X[5453] + 2 X[48897], 5 X[5453] - 2 X[48903], 5 X[48897] + X[48903], 4 X[3634] - 3 X[48887], X[8148] - 3 X[48909], 7 X[9780] - 3 X[48877], X[12702] - 3 X[37425], X[12702] + 3 X[48907], 2 X[13624] - 3 X[48893], 3 X[15973] - 2 X[18357], 5 X[35242] - 3 X[48882]

X(48927) lies on these lines: {1, 30}, {3, 16948}, {5, 991}, {60, 37477}, {81, 16117}, {386, 8703}, {511, 3579}, {548, 5396}, {549, 17749}, {550, 581}, {952, 4300}, {1154, 37568}, {1155, 13391}, {1742, 37698}, {3216, 12100}, {3530, 37732}, {3534, 19767}, {3634, 48887}, {4303, 12433}, {4306, 15935}, {4337, 37730}, {5217, 6097}, {5221, 47749}, {5400, 16239}, {5708, 15937}, {6924, 37501}, {7411, 36750}, {8148, 48909}, {9780, 48877}, {9840, 28370}, {11277, 35466}, {12702, 37425}, {13624, 48893}, {14547, 24470}, {15447, 37524}, {15852, 24475}, {15973, 18357}, {16160, 17056}, {22053, 34753}, {33557, 45923}, {33699, 48855}, {35242, 48882}

X(48927) = midpoint of X(i) and X(j) for these {i,j}: {500, 48897}, {37425, 48907}
X(48927) = reflection of X(5453) in X(500)


X(48928) = X(3)X(6)∩X(8)X(30)

Barycentrics    a^2*(a^4*b + 3*a^3*b^2 + a^2*b^3 - 3*a*b^4 - 2*b^5 + a^4*c + 2*a^3*b*c + 2*a^2*b^2*c - 2*a*b^3*c - 3*b^4*c + 3*a^3*c^2 + 2*a^2*b*c^2 - 2*a*b^2*c^2 - b^3*c^2 + a^2*c^3 - 2*a*b*c^3 - b^2*c^3 - 3*a*c^4 - 3*b*c^4 - 2*c^5) : :
X(48928) = 3 X[3] - 2 X[500], 3 X[3] - 4 X[35203], 5 X[3] - 4 X[48893], X[500] - 3 X[48882], 5 X[500] - 6 X[48893], 4 X[500] - 3 X[48907], 2 X[35203] - 3 X[48882], 5 X[35203] - 3 X[48893], 8 X[35203] - 3 X[48907], 5 X[48882] - 2 X[48893], 4 X[48882] - X[48907], 8 X[48893] - 5 X[48907], 3 X[381] - 4 X[48887], 3 X[381] - 2 X[48899], 2 X[5453] - 3 X[14636], 3 X[5790] - 2 X[46704], 3 X[10246] - 2 X[48909], 3 X[10247] - 4 X[48894]

X(48928) lies on these lines: {3, 6}, {8, 30}, {51, 16286}, {283, 20918}, {381, 10479}, {517, 5492}, {1201, 14815}, {1482, 9840}, {1764, 19648}, {2979, 16453}, {3060, 16287}, {3293, 3579}, {3333, 10108}, {3917, 16414}, {4643, 12699}, {5453, 14636}, {5482, 21363}, {5640, 16296}, {5690, 15971}, {5790, 46704}, {5943, 16291}, {7420, 11412}, {7998, 16297}, {8148, 48903}, {10246, 48909}, {10247, 48894}, {13391, 35000}, {13754, 42461}, {15107, 20840}, {20040, 34773}, {20831, 22139}, {20836, 22136}, {22458, 26893}

X(48928) = reflection of X(i) in X(j) for these {i,j}: {3, 48882}, {500, 35203}, {1482, 9840}, {8148, 48903}, {15971, 5690}, {48897, 3579}, {48899, 48887}, {48907, 3}
X(48928) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 5752, 5754}, {500, 35203, 3}, {500, 48882, 35203}, {573, 37482, 3}, {582, 3098, 3}, {15107, 35193, 20840}, {48887, 48899, 381}


X(48929) = X(1)X(29309)∩X(3)X(6)

Barycentrics    a^2*(2*a^3*b - a^2*b^2 - 2*a*b^3 + b^4 + 2*a^3*c + 2*a^2*b*c - 2*a*b^2*c - 2*b^3*c - a^2*c^2 - 2*a*b*c^2 - 2*a*c^3 - 2*b*c^3 + c^4) : :
X(48929) = 3 X[3] - X[573], 5 X[3] - X[48875], 3 X[3] + X[48908], X[573] + 3 X[991], 5 X[573] - 3 X[48875], 2 X[573] - 3 X[48886], 5 X[991] + X[48875], 2 X[991] + X[48886], 3 X[991] - X[48908], 2 X[48875] - 5 X[48886], 3 X[48875] + 5 X[48908], 3 X[48886] + 2 X[48908], 3 X[376] + X[10446], 5 X[631] - X[48878], X[1742] + 3 X[3576], 3 X[3576] - X[31394], X[6210] - 5 X[7987], 3 X[10165] - X[45305]

X(48929) lies on these lines: {1, 29309}, {3, 6}, {20, 48894}, {30, 6176}, {36, 21746}, {51, 4210}, {56, 39543}, {75, 29343}, {101, 28857}, {104, 29189}, {140, 48888}, {376, 10446}, {516, 550}, {517, 13476}, {631, 48878}, {1011, 3819}, {1352, 36706}, {1742, 3576}, {1790, 16064}, {2807, 32613}, {2810, 15624}, {2979, 22080}, {3218, 22068}, {3246, 13624}, {3579, 29311}, {3664, 24929}, {3818, 36474}, {3917, 4184}, {4191, 5943}, {4416, 5440}, {5732, 46475}, {6210, 7987}, {6688, 16059}, {7411, 37527}, {7430, 36987}, {9306, 20835}, {10165, 45305}, {10219, 16409}, {10882, 39551}, {12045, 16421}, {13731, 48897}, {15082, 16373}, {15488, 37425}, {16056, 17194}, {17245, 36654}, {17502, 29353}, {24325, 29073}, {31670, 36698}, {36674, 48901}, {36707, 48889}, {36716, 48895}, {37400, 37521}

X(48929) = midpoint of X(i) and X(j) for these {i,j}: {3, 991}, {20, 48902}, {573, 48908}, {1742, 31394}
X(48929) = reflection of X(i) in X(j) for these {i,j}: {48886, 3}, {48888, 140}
X(48929) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 500, 970}, {3, 572, 5092}, {3, 581, 15489}, {3, 15937, 5755}, {3, 33878, 37499}, {3, 37474, 182}, {3, 37482, 35203}, {3, 48908, 573}, {573, 991, 48908}, {1742, 3576, 31394}


X(48930) = X(1)X(48882)∩X(2)X(3)

Barycentrics    a*(2*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 2*a^2*b^4 + 2*a^5*c + 2*a^4*b*c - 3*a^2*b^3*c - 2*a*b^4*c + b^5*c + 2*a^4*c^2 - 4*a^2*b^2*c^2 - 2*a*b^3*c^2 - 2*a^3*c^3 - 3*a^2*b*c^3 - 2*a*b^2*c^3 - 2*b^3*c^3 - 2*a^2*c^4 - 2*a*b*c^4 + b*c^5) : :
X(48930) = X[3] - 3 X[14636], 3 X[3] - X[37425], 5 X[631] - X[15971], X[9840] + 3 X[14636], 3 X[9840] + X[37425], 9 X[14636] - X[37425], X[500] - 3 X[3576], 3 X[3576] + X[48883], X[5492] - 3 X[11203], 3 X[5731] + X[48877], 3 X[5886] - X[48899], 5 X[7987] - X[48897], 3 X[10246] - X[48909]

X(48930) lies on these lines: {1, 48882}, {2, 3}, {35, 37715}, {40, 48903}, {355, 10434}, {500, 3576}, {511, 1385}, {515, 48887}, {517, 3743}, {524, 8666}, {1834, 4276}, {3704, 5690}, {3712, 37619}, {3846, 5267}, {5396, 10470}, {5492, 11203}, {5563, 37631}, {5731, 48877}, {5886, 10882}, {5901, 37620}, {6176, 37536}, {7280, 15447}, {7354, 39578}, {7987, 48897}, {10246, 48909}, {11012, 13408}, {13624, 48893}, {16678, 18990}, {19760, 48837}, {19763, 48847}, {22791, 31394}, {31445, 40660}

X(48930) = midpoint of X(i) and X(j) for these {i,j}: {1, 48882}, {3, 9840}, {40, 48903}, {500, 48883}, {35203, 48894}
X(48930) = reflection of X(i) in X(j) for these {i,j}: {5453, 1385}, {15973, 140}, {48893, 13624}
X(48930) = complement of X(46704)
X(48930) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 382, 37400}, {3, 7489, 37399}, {3, 13731, 140}, {3, 13743, 4221}, {3, 19547, 6924}, {3, 37234, 37062}, {3, 37331, 548}, {859, 37225, 6675}, {3576, 48883, 500}, {9840, 14636, 3}, {9840, 15981, 15976}, {13726, 28376, 16418}, {19260, 37030, 17698}


X(48931) = X(4)X(500)∩X(5)X(141)

Barycentrics    a^5*b^2 + 2*a^4*b^3 - 2*a^2*b^5 - a*b^6 + 2*a^4*b^2*c + 2*a^3*b^3*c - a^2*b^4*c - 2*a*b^5*c - b^6*c + a^5*c^2 + 2*a^4*b*c^2 + 2*a^3*b^2*c^2 + 3*a^2*b^3*c^2 + a*b^4*c^2 - b^5*c^2 + 2*a^4*c^3 + 2*a^3*b*c^3 + 3*a^2*b^2*c^3 + 4*a*b^3*c^3 + 2*b^4*c^3 - a^2*b*c^4 + a*b^2*c^4 + 2*b^3*c^4 - 2*a^2*c^5 - 2*a*b*c^5 - b^2*c^5 - a*c^6 - b*c^6 : :
X(48931) = 3 X[381] + X[48907], 3 X[1699] + X[48897], 5 X[3091] - X[48877], 3 X[5603] + X[15971], 3 X[5603] - X[48903], 3 X[5886] - X[9840], 5 X[8227] - X[48883]

X(48931) lies on these lines: {1, 46704}, {2, 48882}, {3, 10478}, {4, 500}, {5, 141}, {23, 3615}, {30, 551}, {40, 41812}, {140, 2051}, {226, 37594}, {355, 48909}, {381, 48907}, {442, 17167}, {515, 5453}, {517, 15973}, {524, 21077}, {1699, 48897}, {1746, 36750}, {1770, 15447}, {2475, 18465}, {2829, 10035}, {3091, 48877}, {3109, 47327}, {3142, 18180}, {3564, 9958}, {3824, 34830}, {4205, 17182}, {4259, 19755}, {4892, 9955}, {5051, 17174}, {5482, 37365}, {5603, 15971}, {5799, 37438}, {5810, 36659}, {5812, 15972}, {5886, 9840}, {7680, 13754}, {8143, 29057}, {8227, 48883}, {12699, 37425}, {13407, 37631}, {13408, 13442}, {13745, 41012}, {17188, 20831}, {19754, 37516}, {22076, 47515}, {30055, 46937}, {30436, 41586}, {30984, 37482}, {32515, 34475}, {34753, 40687}

X(48931) = midpoint of X(i) and X(j) for these {i,j}: {1, 46704}, {3, 48899}, {4, 500}, {355, 48909}, {12699, 37425}, {13408, 13442}, {15971, 48903}
X(48931) = reflection of X(i) in X(j) for these {i,j}: {35203, 140}, {48887, 5}, {48894, 5901}
X(48931) = complement of X(48882)
X(48931) = {X(5603),X(15971)}-harmonic conjugate of X(48903)


X(48932) = X(3)X(142)∩X(10)X(98)

Barycentrics    2*a^5 - a^3*b^2 - 2*a^2*b^3 + a*b^4 - a^2*b^2*c + b^4*c - a^3*c^2 - a^2*b*c^2 - 2*a*b^2*c^2 - b^3*c^2 - 2*a^2*c^3 - b^2*c^3 + a*c^4 + b*c^4 : :
X(48932) = X[1] + 3 X[9746], 11 X[5550] - 3 X[44431]

X(48932) lies on these lines: {1, 1447}, {3, 142}, {5, 28845}, {10, 98}, {103, 43168}, {165, 16831}, {226, 17798}, {379, 35267}, {515, 36477}, {519, 8667}, {549, 28854}, {551, 13634}, {572, 45305}, {726, 31981}, {740, 8669}, {894, 8245}, {927, 2700}, {991, 32462}, {1281, 17760}, {1284, 18758}, {1385, 28850}, {1699, 29603}, {1742, 25528}, {2796, 9888}, {3576, 24331}, {3634, 9756}, {3741, 25940}, {3755, 18755}, {3817, 6996}, {3923, 40923}, {4220, 43223}, {4229, 32014}, {4297, 13727}, {4307, 5265}, {4349, 37607}, {4356, 37573}, {4660, 39647}, {4847, 20769}, {5550, 44431}, {5690, 28870}, {5847, 43149}, {5988, 8295}, {6210, 33682}, {6308, 17766}, {6684, 28849}, {6685, 19544}, {7385, 29633}, {8182, 28562}, {8227, 36697}, {8301, 20257}, {8424, 20258}, {9441, 10164}, {9751, 19862}, {9840, 40718}, {9955, 28897}, {9956, 28901}, {10175, 36527}, {10186, 36705}, {10436, 24728}, {11230, 28866}, {11231, 28877}, {13405, 37580}, {13411, 37576}, {13635, 19883}, {16367, 40998}, {16826, 18788}, {17687, 38059}, {19522, 37619}, {19649, 25501}, {19857, 35099}, {22791, 28862}, {24684, 44670}, {26232, 30059}, {26446, 28909}, {28885, 38028}, {30142, 37529}, {31016, 35270}, {35291, 37233}

X(48932) = midpoint of X(3) and X(48900)


X(48933) = X(1)X(30)∩X(5)X(141)

Barycentrics    2*a^5*b^2 + 3*a^4*b^3 - a^3*b^4 - 3*a^2*b^5 - a*b^6 + 3*a^4*b^2*c + 2*a^3*b^3*c - 2*a^2*b^4*c - 2*a*b^5*c - b^6*c + 2*a^5*c^2 + 3*a^4*b*c^2 + 2*a^3*b^2*c^2 + 3*a^2*b^3*c^2 + a*b^4*c^2 - b^5*c^2 + 3*a^4*c^3 + 2*a^3*b*c^3 + 3*a^2*b^2*c^3 + 4*a*b^3*c^3 + 2*b^4*c^3 - a^3*c^4 - 2*a^2*b*c^4 + a*b^2*c^4 + 2*b^3*c^4 - 3*a^2*c^5 - 2*a*b*c^5 - b^2*c^5 - a*c^6 - b*c^6 : :
X(48933) = 3 X[5] - 2 X[48887], 3 X[381] - X[48877], 3 X[549] - 2 X[35203], 3 X[5886] - X[48883], 3 X[10283] - 2 X[48894]

X(48933) lies on these lines: {1, 30}, {3, 19684}, {4, 48907}, {5, 141}, {140, 21363}, {381, 48877}, {442, 17173}, {516, 43972}, {524, 9958}, {549, 35203}, {550, 48893}, {952, 46704}, {1482, 15971}, {2051, 5482}, {3579, 4670}, {3615, 15107}, {4292, 15368}, {5690, 15973}, {5886, 48883}, {5901, 9840}, {6851, 15937}, {8143, 29301}, {10035, 38602}, {10108, 21620}, {10283, 48894}, {10478, 37482}, {17751, 18357}, {20330, 29181}, {28174, 37425}, {31657, 43169}

X(48933) = midpoint of X(i) and X(j) for these {i,j}: {4, 48907}, {500, 48899}, {1482, 15971}, {12699, 48897}, {46704, 48909}
X(48933) = reflection of X(i) in X(j) for these {i,j}: {550, 48893}, {5690, 15973}, {9840, 5901}, {34773, 5453}, {38602, 10035}, {48882, 140}
X(48933) = crossdifference of every pair of points on line {3050, 9404}


X(48934) = X(3)X(86)∩X(5)X(141)

Barycentrics    2*a^4*b^2 + a^3*b^3 - 2*a^2*b^4 - a*b^5 + a^3*b^2*c + a^2*b^3*c - a*b^4*c - b^5*c + 2*a^4*c^2 + a^3*b*c^2 + 2*a*b^3*c^2 + a^3*c^3 + a^2*b*c^3 + 2*a*b^2*c^3 + 2*b^3*c^3 - 2*a^2*c^4 - a*b*c^4 - a*c^5 - b*c^5 : :
X(48934) = 3 X[5] - 2 X[48888], 3 X[24220] - X[48888], 3 X[381] - X[48878], 3 X[549] - 2 X[48886], 3 X[5886] - X[6210]

X(48934) lies on these lines: {2, 48875}, {3, 86}, {4, 17300}, {5, 141}, {30, 991}, {37, 29369}, {51, 37355}, {69, 36659}, {140, 573}, {335, 20430}, {343, 34119}, {355, 32846}, {381, 17297}, {496, 21746}, {516, 550}, {517, 24325}, {549, 48886}, {946, 15310}, {1350, 36477}, {1352, 36663}, {1482, 32922}, {1656, 17307}, {1742, 12699}, {2979, 3136}, {3060, 47513}, {3620, 36673}, {3664, 4920}, {3917, 17167}, {4260, 17197}, {4648, 36674}, {4869, 36671}, {5603, 37331}, {5690, 29311}, {5733, 46264}, {5805, 24827}, {5886, 6210}, {5901, 31394}, {6996, 20132}, {9955, 45305}, {10441, 15973}, {10478, 37365}, {11112, 18465}, {13728, 17202}, {16850, 17183}, {17000, 21554}, {17232, 36651}, {17238, 36676}, {17313, 36729}, {17378, 36730}, {17379, 36697}, {17390, 29235}, {18583, 19512}, {29353, 38034}, {31670, 36661}, {34282, 41014}, {43169, 46475}

X(48934) = midpoint of X(i) and X(j) for these {i,j}: {3, 10446}, {4, 48908}, {991, 48902}, {1742, 12699}, {17378, 36730}
X(48934) = reflection of X(i) in X(j) for these {i,j}: {5, 24220}, {573, 140}, {31394, 5901}, {45305, 9955}
X(48934) = complement of X(48875)
X(48934) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3917, 17167, 47514}, {10478, 37521, 37365}


X(48935) = X(4)X(333)∩X(8)X(30)

Barycentrics    2*a^7 - a^6*b - 4*a^5*b^2 + a^4*b^3 + 2*a^3*b^4 + a^2*b^5 - b^7 - a^6*c - 2*a^5*b*c - 2*a^4*b^2*c + 2*a^3*b^3*c + 3*a^2*b^4*c - 4*a^5*c^2 - 2*a^4*b*c^2 + 4*a^3*b^2*c^2 + 2*b^5*c^2 + a^4*c^3 + 2*a^3*b*c^3 - b^4*c^3 + 2*a^3*c^4 + 3*a^2*b*c^4 - b^3*c^4 + a^2*c^5 + 2*b^2*c^5 - c^7 : :
X(48935) = 4 X[5453] - 3 X[42045]

X(48935) lies on these lines: {2, 13408}, {3, 3936}, {4, 333}, {8, 30}, {20, 2895}, {40, 36974}, {283, 860}, {500, 34772}, {540, 3811}, {582, 4202}, {631, 41878}, {944, 3564}, {1330, 1792}, {3085, 37540}, {3090, 31205}, {3869, 13754}, {4417, 6876}, {5016, 37584}, {5278, 44229}, {5279, 15945}, {5453, 42045}, {5739, 6869}, {5758, 13442}, {6327, 35239}, {6868, 11411}, {6897, 28980}, {6900, 17277}, {6903, 14829}, {9840, 30055}, {11491, 37425}, {14206, 41013}, {15680, 37779}, {21161, 25650}, {24432, 24851}, {35203, 45048}, {37823, 46623}, {41014, 44238}, {48882, 48890}

X(48935) = reflection of X(i) in X(j) for these {i,j}: {46483, 3}, {48890, 48882}
X(48935) = anticomplement of X(13408)


X(48936) = X(1)X(256)∩X(8)X(30)

Barycentrics    a*(a^5*b + 3*a^4*b^2 + a^3*b^3 - 3*a^2*b^4 - 2*a*b^5 + a^5*c + 2*a^3*b^2*c - a^2*b^3*c - 3*a*b^4*c + b^5*c + 3*a^4*c^2 + 2*a^3*b*c^2 - 2*a^2*b^2*c^2 - a*b^3*c^2 + a^3*c^3 - a^2*b*c^3 - a*b^2*c^3 - 2*b^3*c^3 - 3*a^2*c^4 - 3*a*b*c^4 - 2*a*c^5 + b*c^5) : :
X(48936) = 2 X[1] - 3 X[9840], X[1] - 3 X[48883], 5 X[1] - 6 X[48894], 4 X[1] - 3 X[48909], 5 X[9840] - 4 X[48894], 5 X[48883] - 2 X[48894], 4 X[48883] - X[48909], 8 X[48894] - 5 X[48909], 6 X[35203] - 5 X[35242], 5 X[35242] - 3 X[48897], 3 X[500] - 4 X[13624], 2 X[500] - 3 X[14636], 8 X[13624] - 9 X[14636], 4 X[3579] - 3 X[37425], 2 X[3579] - 3 X[48882], 5 X[3617] - 3 X[15971], 4 X[18483] - 3 X[48899], 7 X[9780] - 6 X[15973], 2 X[11278] - 3 X[48903], 4 X[18357] - 3 X[46704]

X(48936) lies on these lines: {1, 256}, {3, 16948}, {4, 37653}, {8, 30}, {20, 48875}, {43, 35203}, {283, 46549}, {376, 9566}, {405, 33878}, {500, 1193}, {758, 12642}, {896, 3214}, {1009, 9821}, {1350, 13732}, {1724, 3098}, {2979, 13724}, {3060, 47521}, {3617, 15971}, {3647, 18235}, {3741, 18483}, {4647, 29301}, {4683, 12699}, {4685, 31730}, {5220, 29181}, {5302, 17792}, {5752, 37331}, {9780, 15973}, {10593, 15974}, {11278, 48903}, {13391, 35459}, {13728, 21850}, {13731, 37482}, {17749, 19514}, {18357, 46704}, {19335, 34466}, {22139, 28029}, {35002, 37023}, {37328, 37510}

X(48936) = reflection of X(i) in X(j) for these {i,j}: {9840, 48883}, {37425, 48882}, {48897, 35203}, {48909, 9840}
X(48936) = {X(1756),X(10544)}-harmonic conjugate of X(11043)


X(48937) = X(4)X(69)∩X(5)X(500)

Barycentrics    a^6*b - a^4*b^3 + a^3*b^4 - a*b^6 + a^6*c + 2*a^5*b*c - 2*a*b^5*c - b^6*c + 2*a^2*b^3*c^2 + a*b^4*c^2 - b^5*c^2 - a^4*c^3 + 2*a^2*b^2*c^3 + 4*a*b^3*c^3 + 2*b^4*c^3 + a^3*c^4 + a*b^2*c^4 + 2*b^3*c^4 - 2*a*b*c^5 - b^2*c^5 - a*c^6 - b*c^6 : :
X(48937) = 2 X[48877] + X[48899], 3 X[381] - X[48907], 2 X[4297] - 3 X[14636], 2 X[5453] - 3 X[5886], 3 X[5587] - 2 X[15973], 3 X[5587] - X[48897], 2 X[10035] - 3 X[23513]

X(48937) lies on these lines: {2, 48893}, {3, 1746}, {4, 69}, {5, 500}, {10, 37425}, {20, 35203}, {30, 40}, {333, 46623}, {381, 48907}, {515, 9840}, {942, 1111}, {944, 48894}, {946, 42057}, {952, 48903}, {3578, 5178}, {4297, 14636}, {4641, 41506}, {5453, 5886}, {5587, 15973}, {5788, 7580}, {9799, 15970}, {10035, 23513}, {10108, 18527}, {13478, 19548}, {13731, 48888}, {13754, 37820}, {14956, 22076}, {15447, 24914}, {18480, 46704}, {20242, 23154}, {30449, 45926}, {37365, 37732}

X(48937) = midpoint of X(i) and X(j) for these {i,j}: {4, 48877}, {5691, 48883}
X(48937) = reflection of X(i) in X(j) for these {i,j}: {3, 48887}, {20, 35203}, {500, 5}, {944, 48894}, {37425, 10}, {46704, 18480}, {48897, 15973}, {48899, 4}, {48909, 946}
X(48937) = anticomplement of X(48893)
X(48937) = {X(5587),X(48897)}-harmonic conjugate of X(15973)


X(48938) = X(4)X(69)∩X(5)X(991)

Barycentrics    a^5*b - a^4*b^2 + a^2*b^4 - a*b^5 + a^5*c + a^4*b*c - a*b^4*c - b^5*c - a^4*c^2 + 2*a*b^3*c^2 + 2*a*b^2*c^3 + 2*b^3*c^3 + a^2*c^4 - a*b*c^4 - a*c^5 - b*c^5 : :
X(48938) = 3 X[4] - X[10446], X[10446] + 3 X[48878], 2 X[10446] - 3 X[48902], 2 X[48878] + X[48902], 3 X[381] - 2 X[24220], 3 X[381] - X[48908], X[1742] - 3 X[5587], 3 X[26446] - 2 X[41430]

X(48938) lies on these lines: {3, 17259}, {4, 69}, {5, 991}, {8, 29309}, {20, 48886}, {30, 573}, {141, 36654}, {182, 13727}, {192, 29343}, {355, 382}, {381, 17313}, {388, 39543}, {515, 31394}, {572, 36477}, {984, 29073}, {1478, 21746}, {1742, 5587}, {1889, 33586}, {2807, 10741}, {3098, 6996}, {3419, 4416}, {3664, 5722}, {3819, 6818}, {4263, 48837}, {5092, 36489}, {5691, 6210}, {5788, 37411}, {5816, 36474}, {5943, 6817}, {6688, 6821}, {7377, 19130}, {9306, 14004}, {9732, 36710}, {9733, 36713}, {9738, 36708}, {9739, 36715}, {12699, 29311}, {14810, 36697}, {15310, 18480}, {20430, 29016}, {24206, 36652}, {26446, 41430}, {28850, 31395}, {32431, 36663}

X(48938) = midpoint of X(i) and X(j) for these {i,j}: {4, 48878}, {382, 48875}, {5691, 6210}
X(48938) = reflection of X(i) in X(j) for these {i,j}: {3, 48888}, {20, 48886}, {991, 5}, {31394, 45305}, {48902, 4}, {48908, 24220}
X(48938) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 48877, 10441}, {381, 48908, 24220}


X(48939) = X(1)X(256)∩X(10)X(30)

Barycentrics    a*(2*a^5*b + 3*a^4*b^2 - a^3*b^3 - 3*a^2*b^4 - a*b^5 + 2*a^5*c + a^3*b^2*c - 2*a^2*b^3*c - 3*a*b^4*c + 2*b^5*c + 3*a^4*c^2 + a^3*b*c^2 - 4*a^2*b^2*c^2 - 2*a*b^3*c^2 - a^3*c^3 - 2*a^2*b*c^3 - 2*a*b^2*c^3 - 4*b^3*c^3 - 3*a^2*c^4 - 3*a*b*c^4 - a*c^5 + 2*b*c^5) : :
X(48939) = X[1] - 3 X[9840], X[1] + 3 X[48883], 2 X[1] - 3 X[48894], 5 X[1] - 3 X[48909], 5 X[9840] - X[48909], 2 X[48883] + X[48894], 5 X[48883] + X[48909], 5 X[48894] - 2 X[48909], 2 X[3579] - 3 X[35203], 2 X[18357] - 3 X[48887], 3 X[14636] - X[48897], 4 X[3634] - 3 X[15973], X[8148] - 3 X[48903], 7 X[9780] - 3 X[15971], X[12702] - 3 X[48882], 4 X[13624] - 3 X[48893], 5 X[35242] - 3 X[37425]

X(48939) lies on these lines: {1, 256}, {3, 17749}, {10, 30}, {20, 48886}, {405, 3098}, {500, 995}, {978, 14636}, {1724, 5092}, {3214, 37619}, {3634, 15973}, {3819, 13724}, {4220, 16948}, {5943, 47521}, {6176, 37482}, {7173, 15974}, {8148, 48903}, {9780, 15971}, {11097, 36755}, {11098, 36756}, {12702, 48882}, {13442, 29317}, {13624, 48893}, {13725, 31670}, {13728, 19130}, {13732, 14810}, {13745, 19924}, {15254, 29181}, {15489, 37331}, {15680, 22080}, {19766, 20423}, {24239, 32636}, {29113, 35099}, {35242, 37425}, {37443, 37823}

X(48939) = midpoint of X(9840) and X(48883)
X(48939) = reflection of X(48894) in X(9840)


X(48940) = X(4)X(69)∩X(5)X(516)

Barycentrics    2*a^5*b + a^4*b^2 - a^2*b^4 - 2*a*b^5 + 2*a^5*c + 2*a^4*b*c - 2*a*b^4*c - 2*b^5*c + a^4*c^2 + 4*a*b^3*c^2 + 4*a*b^2*c^3 + 4*b^3*c^3 - a^2*c^4 - 2*a*b*c^4 - 2*a*c^5 - 2*b*c^5 : :
X(48940) = 3 X[4] + X[10446], 5 X[4] - X[48878], 5 X[10446] + 3 X[48878], X[10446] - 3 X[48902], X[48878] + 5 X[48902], 3 X[381] - X[573], 3 X[1699] - X[31394], 3 X[3830] + X[48908], 5 X[3843] - X[48875]

X(48940) lies on these lines: {4, 69}, {5, 516}, {30, 6176}, {381, 573}, {382, 991}, {430, 21243}, {517, 4793}, {546, 48888}, {970, 12699}, {1479, 39543}, {1699, 4192}, {1889, 9306}, {3583, 21746}, {3830, 48908}, {3843, 48875}, {5092, 6996}, {5755, 31671}, {6688, 6818}, {6822, 10219}, {7402, 42786}, {7406, 46264}, {9738, 36713}, {9739, 36710}, {9812, 26038}, {13727, 14810}, {13731, 41869}, {18480, 29311}, {19130, 36654}, {20666, 39565}, {28146, 41430}, {36527, 37508}, {36670, 38317}, {36678, 45543}, {36679, 45542}, {36708, 43141}, {36715, 43144}

X(48940) = midpoint of X(i) and X(j) for these {i,j}: {4, 48902}, {382, 991}
X(48940) = reflection of X(i) in X(j) for these {i,j}: {48886, 5}, {48888, 546}


X(48941) = X(4)X(69)∩X(20)X(500)

Barycentrics    a^6*b + 3*a^5*b^2 + 2*a^4*b^3 - 2*a^3*b^4 - 3*a^2*b^5 - a*b^6 + a^6*c + 2*a^5*b*c + 3*a^4*b^2*c - 3*a^2*b^4*c - 2*a*b^5*c - b^6*c + 3*a^5*c^2 + 3*a^4*b*c^2 + 2*a^2*b^3*c^2 + a*b^4*c^2 - b^5*c^2 + 2*a^4*c^3 + 2*a^2*b^2*c^3 + 4*a*b^3*c^3 + 2*b^4*c^3 - 2*a^3*c^4 - 3*a^2*b*c^4 + a*b^2*c^4 + 2*b^3*c^4 - 3*a^2*c^5 - 2*a*b*c^5 - b^2*c^5 - a*c^6 - b*c^6 : :
X(48941) = X[48877] - 4 X[48899], 3 X[376] - 4 X[48893], 5 X[631] - 4 X[35203], 5 X[3091] - 4 X[48887], 4 X[5453] - 3 X[5731], 3 X[5603] - 2 X[9840], 3 X[5657] - 4 X[15973], 4 X[10035] - 3 X[38693], 5 X[10595] - 4 X[48894]

X(48941) lies on these lines: {2, 48882}, {3, 19684}, {4, 69}, {8, 46704}, {20, 500}, {30, 944}, {376, 48893}, {515, 11521}, {516, 48897}, {517, 4968}, {631, 9535}, {946, 48883}, {1064, 12545}, {2096, 15979}, {3091, 48887}, {4205, 17183}, {4295, 37614}, {4385, 15983}, {4911, 15982}, {5453, 5731}, {5603, 9840}, {5657, 15973}, {5758, 13442}, {5814, 20245}, {6361, 37425}, {10035, 38693}, {10595, 48894}, {12699, 17491}, {13408, 48890}, {18656, 24701}, {19645, 36742}, {37402, 41810}

X(48941) = reflection of X(i) in X(j) for these {i,j}: {4, 48899}, {8, 46704}, {20, 500}, {944, 48909}, {6361, 37425}, {48877, 4}, {48883, 946}, {48890, 13408}
X(48941) = anticomplement of X(48882)


X(48942) = X(4)X(5092)∩X(382)X(511)

Barycentrics    6*a^6 + 3*a^4*b^2 - 5*a^2*b^4 - 4*b^6 + 3*a^4*c^2 + 4*a^2*b^2*c^2 + 4*b^4*c^2 - 5*a^2*c^4 + 4*b^2*c^4 - 4*c^6 : :
X(48942) = 5 X[4] - 3 X[38317], 3 X[4] - X[48898], 5 X[5092] - 6 X[38317], 3 X[5092] - 2 X[48898], 9 X[38317] - 5 X[48898], 3 X[5] - 2 X[33751], 4 X[33751] - 3 X[48891], 19 X[14810] - 24 X[20582], 3 X[14810] - 4 X[24206], 2 X[14810] - 3 X[25561], 5 X[14810] - 4 X[48885], 18 X[20582] - 19 X[24206], 16 X[20582] - 19 X[25561], 30 X[20582] - 19 X[48885], 12 X[20582] - 19 X[48889], 8 X[24206] - 9 X[25561], 5 X[24206] - 3 X[48885], 2 X[24206] - 3 X[48889], 15 X[25561] - 8 X[48885], 3 X[25561] - 4 X[48889], 2 X[48885] - 5 X[48889], X[182] - 3 X[3830], 7 X[182] - 9 X[38072], 7 X[3830] - 3 X[38072], 3 X[381] - X[48896], 15 X[382] + X[11898], 11 X[382] + X[15069], 7 X[382] + X[18440], 3 X[382] + X[36990], 19 X[382] + X[40341], 3 X[382] - X[48904], and many others

X(48942) lies on these lines: {4, 5092}, {5, 33751}, {30, 14810}, {125, 34603}, {182, 3830}, {381, 48896}, {382, 511}, {542, 33699}, {546, 48892}, {575, 3627}, {1350, 15684}, {1352, 15682}, {3098, 5073}, {3146, 3818}, {3522, 42786}, {3543, 5032}, {3589, 12102}, {3843, 17508}, {3853, 19130}, {5076, 20190}, {5476, 14927}, {10168, 12101}, {10516, 48879}, {10721, 44943}, {11178, 48872}, {12088, 32600}, {15640, 40330}, {15687, 44882}, {17578, 46264}, {18553, 29317}, {19924, 35404}, {21358, 35400}, {29181, 43150}, {31133, 32237}, {33703, 48880}, {34507, 43621}, {35434, 43273}

X(48942) = midpoint of X(i) and X(j) for these {i,j}: {382, 48884}, {3098, 5073}, {3146, 3818}, {33703, 48880}, {34507, 43621}, {36990, 48904}
X(48942) = reflection of X(i) in X(j) for these {i,j}: {575, 48895}, {3589, 12102}, {5092, 4}, {5097, 48901}, {10168, 12101}, {14810, 48889}, {19130, 3853}, {48891, 5}, {48892, 546}, {48895, 3627}, {48905, 20190}
X(48942) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {382, 36990, 48904}, {14810, 48889, 25561}, {36990, 48910, 11898}, {48884, 48904, 36990}


X(48943) = X(4)X(7937)∩X(382)X(511)

Barycentrics    6*a^6 + 5*a^4*b^2 - 7*a^2*b^4 - 4*b^6 + 5*a^4*c^2 + 4*a^2*b^2*c^2 + 4*b^4*c^2 - 7*a^2*c^4 + 4*b^2*c^4 - 4*c^6 : :
X(48943) = 3 X[4] - X[48880], 3 X[14810] - 2 X[48880], X[6] + 3 X[15684], 8 X[3589] - 7 X[5092], 22 X[3589] - 21 X[10168], 6 X[3589] - 7 X[19130], 12 X[3589] - 7 X[48891], 10 X[3589] - 7 X[48892], 4 X[3589] - 7 X[48895], 11 X[5092] - 12 X[10168], 3 X[5092] - 4 X[19130], 3 X[5092] - 2 X[48891], 5 X[5092] - 4 X[48892], 9 X[10168] - 11 X[19130], 18 X[10168] - 11 X[48891], 15 X[10168] - 11 X[48892], 6 X[10168] - 11 X[48895], 5 X[19130] - 3 X[48892], 2 X[19130] - 3 X[48895], 5 X[48891] - 6 X[48892], X[48891] - 3 X[48895], 2 X[48892] - 5 X[48895], X[141] - 3 X[3627], 5 X[141] - 3 X[48874], 2 X[141] - 3 X[48889], 5 X[3627] - X[48874], 2 X[48874] - 5 X[48889], 3 X[381] - X[48879], 17 X[382] - X[11898], 13 X[382] - X[15069], 9 X[382] - X[18440], and many others

X(48943) lies on these lines: {4, 7937}, {6, 15684}, {30, 3589}, {141, 3627}, {182, 5073}, {381, 48879}, {382, 511}, {542, 35404}, {546, 48885}, {575, 3146}, {1533, 34613}, {1657, 47355}, {1992, 11645}, {3098, 3830}, {3529, 38317}, {3543, 3620}, {3618, 33703}, {3763, 38335}, {3839, 42786}, {3853, 24206}, {5076, 48872}, {5097, 8550}, {10541, 35407}, {13596, 32600}, {14893, 34573}, {15687, 48881}, {17508, 17800}, {17578, 48873}, {18553, 29181}, {18560, 46026}, {19710, 25565}, {19924, 22165}, {20190, 48896}, {35400, 38072}, {38228, 43148}, {42785, 46267}

X(48943) = midpoint of X(i) and X(j) for these {i,j}: {182, 5073}, {382, 48904}, {3146, 48901}, {3818, 43621}, {33703, 48898}, {48884, 48910}
X(48943) = reflection of X(i) in X(j) for these {i,j}: {575, 48901}, {5092, 48895}, {14810, 4}, {19710, 25565}, {24206, 3853}, {25561, 3830}, {48885, 546}, {48889, 3627}, {48891, 19130}, {48896, 20190}
X(48943) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {382, 48910, 48884}, {3543, 43621, 3818}, {19130, 48891, 5092}, {48884, 48904, 48910}, {48891, 48895, 19130}


X(48944) = X(3)X(142)∩X(4)X(218)

Barycentrics    a^5 - 3*a^4*b + a^3*b^2 - a^2*b^3 + 2*a*b^4 - 3*a^4*c + a^2*b^2*c + 2*b^4*c + a^3*c^2 + a^2*b*c^2 - 4*a*b^2*c^2 - 2*b^3*c^2 - a^2*c^3 - 2*b^2*c^3 + 2*a*c^4 + 2*b*c^4 : :
X(48944) = 2 X[3579] - 3 X[9746], 4 X[5901] - 3 X[10186], 5 X[10595] - 3 X[11200]

X(48955) lies on these lines: {1, 4059}, {3, 142}, {4, 218}, {10, 28881}, {30, 48830}, {40, 3294}, {355, 28849}, {379, 35273}, {381, 28854}, {382, 28845}, {962, 13727}, {1058, 4307}, {1482, 28850}, {1490, 37529}, {1699, 9441}, {1836, 37580}, {2784, 18525}, {3332, 29207}, {3434, 23151}, {3579, 9746}, {4229, 17201}, {4349, 40270}, {5587, 28913}, {5690, 28905}, {5691, 28901}, {5790, 28858}, {5901, 10186}, {6361, 6998}, {6996, 9812}, {10595, 11200}, {11500, 40515}, {12645, 28870}, {14942, 17753}, {16783, 28897}, {17318, 29036}, {21554, 44431}, {22791, 28915}, {28174, 36477}

X(48944) = reflection of X(3) in X(48900)


X(48945) = X(2)X(6)∩X(112)X(5095)

Barycentrics    3*a^8 - 6*a^6*b^2 - 4*a^4*b^4 + 4*a^2*b^6 - b^8 - 6*a^6*c^2 + 23*a^4*b^2*c^2 - 7*a^2*b^4*c^2 - 4*a^4*c^4 - 7*a^2*b^2*c^4 + 2*b^4*c^4 + 4*a^2*c^6 - c^8 : :
X(48945) = 5 X[3618] - 4 X[32525], 3 X[5166] - 2 X[5913], 2 X[6791] - 3 X[36696]

X(48945) lies on the cubics K870 and K1276 and these lines: {2, 6}, {112, 5095}, {115, 895}, {542, 10765}, {843, 2696}, {1499, 6776}, {2452, 15048}, {2770, 5486}, {5477, 41720}, {6791, 36696}, {7472, 32220}, {8288, 25320}, {9214, 34169}, {10602, 35902}, {11006, 48654}, {14120, 47277}, {14832, 14833}, {18346, 39899}, {18440, 43964}, {20094, 25052}, {20382, 43697}

X(48945) = midpoint of X(i) and X(j) for these {i,j}: {193, 38940}, {18346, 39899}
X(48945) = reflection of X(i) in X(j) for these {i,j}: {69, 5108}, {6792, 6}, {18440, 43964}
X(48945) = 2nd-Lemoine-circle-inverse of X(22151)
X(48945) = orthoptic-circle-of-Steiner-inellipse-inverse of X(24855)
X(48945) = psi-transform of X(10418)
X(48945) = crossdifference of every pair of points on line {512, 32127}

X(48946) = X(3)X(67)∩X(111)X(125)

Barycentrics    2*a^12 - 4*a^10*b^2 - 5*a^8*b^4 + 6*a^6*b^6 + 2*a^4*b^8 - 2*a^2*b^10 + b^12 - 4*a^10*c^2 + 22*a^8*b^2*c^2 - 10*a^6*b^4*c^2 + 5*a^4*b^6*c^2 - 11*a^2*b^8*c^2 + 2*b^10*c^2 - 5*a^8*c^4 - 10*a^6*b^2*c^4 - 12*a^4*b^4*c^4 + 13*a^2*b^6*c^4 - b^8*c^4 + 6*a^6*c^6 + 5*a^4*b^2*c^6 + 13*a^2*b^4*c^6 - 4*b^6*c^6 + 2*a^4*c^8 - 11*a^2*b^2*c^8 - b^4*c^8 - 2*a^2*c^10 + 2*b^2*c^10 + c^12 : :
X(48946) = X[67] - 3 X[15357], 3 X[2482] - X[2930], 3 X[5621] - X[10991], 3 X[99] + X[32255], 2 X[5095] - 3 X[41672], X[895] + 3 X[11006], 3 X[5477] - X[16176], 4 X[6698] - 3 X[19662], X[11061] - 3 X[18800]

X(48946) lies on the cubics K418 and K1276 and these lines: {3, 67}, {99, 32255}, {111, 125}, {112, 5095}, {543, 25328}, {690, 2492}, {895, 11006}, {3448, 14928}, {5477, 16176}, {6698, 19662}, {11061, 18800}, {20301, 38734}, {23698, 32273}

X(48946) = midpoint of X(i) and X(j) for these {i,j}: {3448, 14928}, {14981, 16010}
X(48946) = reflection of X(38734) in X(20301)
X(48946) = crossdifference of every pair of points on line {2492, 2930}
X(48946) = X(i)-line conjugate of X(j) for these (i,j): {3, 2930}, {690, 2492}

leftri

Centers related to 1st anti-Parry triangle: X(48947)-X(48979)

rightri

This preamble and centers X(48947)-X(48979) were contributed by César Eliud Lozada, May 18, 2022.

1st anti-Parry triangle was introduced in the preamble just before X(45345).


X(48947) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 1st ANTI-BROCARD

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

The reciprocal orthologic center of these triangles is X(385).

X(48947) lies on the circumcircle of 1st anti-Parry triangle and these lines: {2, 98}, {3, 48980}, {99, 1296}, {381, 23348}, {690, 48953}, {804, 9145}, {892, 8704}, {1499, 9182}, {2407, 15342}, {2709, 14607}, {2782, 48983}, {2783, 48690}, {2787, 48709}, {2794, 45772}, {2799, 48954}, {2854, 48982}, {4590, 32472}, {5996, 32583}, {6233, 9066}, {8289, 9966}, {9147, 9216}, {31998, 32473}

X(48947) = reflection of X(i) in X(j) for these (i, j): (48951, 9145), (48952, 99), (48980, 3)
X(48947) = reflection of X(98) in the line X(690)X(40879)
X(48947) = orthologic center (1st anti-Parry, T) for these triangles T: {1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard}
X(48947) = center of circle {{X(2), X(8591), X(44372)}}
X(48947) = X(99)-of-1st anti-Parry triangle
X(48947) = X(48980)-of-ABC-X3 reflections triangle
X(48947) = X(48982)-of-anti-Artzt triangle
X(48947) = {X(98), X(6054)}-harmonic conjugate of X(9775)


X(48948) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 1st ANTI-ORTHOSYMMEDIAL

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

The reciprocal orthologic center of these triangles is X(10313).

X(48948) lies on the circumcircle of 1st anti-Parry triangle and these lines: {3, 48981}, {22, 110}, {112, 1296}, {2794, 45772}, {2799, 48539}, {2806, 48709}, {2831, 48690}, {2854, 48985}, {2881, 9145}, {9216, 13114}, {9517, 45722}, {9530, 38738}

X(48948) = orthologic center (1st anti-Parry, T) for these triangles T: {1st anti-orthosymmedial, 1st orthosymmedial}
X(48948) = X(48981)-of-ABC-X3 reflections triangle
X(48948) = X(112)-of-1st anti-Parry triangle
X(48948) = reflection of X(i) in X(j) for these (i, j): (48954, 9145), (48981, 3)


X(48949) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 1st ALTINTAS-ISODYNAMIC

Barycentrics    (-2*sqrt(3)*(3*(b^2+c^2)*a^6-(4*b^4+13*b^2*c^2+4*c^4)*a^4+(b^2+c^2)*(7*b^4-20*b^2*c^2+7*c^4)*a^2-(b^4-4*b^2*c^2+c^4)*(b^2-c^2)^2)*S+2*a^10-7*(b^2+c^2)*a^8+3*(3*b^4-5*b^2*c^2+3*c^4)*a^6-(b^2+c^2)*(7*b^4-55*b^2*c^2+7*c^4)*a^4-4*(b^8+c^8+(7*b^4-18*b^2*c^2+7*c^4)*b^2*c^2)*a^2+3*(b^4-c^4)*(b^2-c^2)^3)*(a^2-b^2)*(a^2-c^2) : :

The reciprocal parallelogic center of these triangles is X(4).

X(48949) lies on these lines: {3, 5916}, {99, 9203}, {110, 13305}, {523, 9202}, {530, 5474}, {690, 45722}, {9145, 48964}, {9200, 9216}, {23870, 48539}, {23871, 48951}, {27550, 48952}, {48963, 48974}

X(48949) = parallelogic center (1st anti-Parry, T) for these triangles T: {1st Altintas-isodynamic, Bankoff, 3rd Fermat-Dao, 7th Fermat-Dao, 11th Fermat-Dao, 15th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi, 1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi, 1st half-diamonds-central, 1st isodynamic-Dao, 3rd isodynamic-Dao, Largest-circumscribed-equilateral, 1st Lemoine-Dao, outer-Napoleon}
X(48949) = X(5916)-of-ABC-X3 reflections triangle
X(48949) = X(13)-of-1st anti-Parry triangle
X(48949) = reflection of X(5916) in X(3)


X(48950) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 2nd ALTINTAS-ISODYNAMIC

Barycentrics    (2*sqrt(3)*(3*(b^2+c^2)*a^6-(4*b^4+13*b^2*c^2+4*c^4)*a^4+(b^2+c^2)*(7*b^4-20*b^2*c^2+7*c^4)*a^2-(b^4-4*b^2*c^2+c^4)*(b^2-c^2)^2)*S+2*a^10-7*(b^2+c^2)*a^8+3*(3*b^4-5*b^2*c^2+3*c^4)*a^6-(b^2+c^2)*(7*b^4-55*b^2*c^2+7*c^4)*a^4-4*(b^8+c^8+(7*b^4-18*b^2*c^2+7*c^4)*b^2*c^2)*a^2+3*(b^4-c^4)*(b^2-c^2)^3)*(a^2-b^2)*(a^2-c^2) : :

The reciprocal parallelogic center of these triangles is X(4).

X(48950) lies on these lines: {3, 5917}, {99, 9202}, {110, 13304}, {523, 9203}, {531, 5473}, {690, 45722}, {9145, 48963}, {9201, 9216}, {23870, 48951}, {23871, 48539}, {27551, 48952}, {48964, 48974}

X(48950) = parallelogic center (1st anti-Parry, T) for these triangles T: {2nd Altintas-isodynamic, 4th Fermat-Dao, 8th Fermat-Dao, 12th Fermat-Dao, 16th Fermat-Dao, 1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi, 3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi, 2nd half-diamonds-central, 2nd isodynamic-Dao, 4th isodynamic-Dao, 2nd Lemoine-Dao, inner-Napoleon}
X(48950) = X(5917)-of-ABC-X3 reflections triangle
X(48950) = X(14)-of-1st anti-Parry triangle
X(48950) = reflection of X(5917) in X(3)


X(48951) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 1st ANTI-BROCARD

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

The reciprocal parallelogic center of these triangles is X(5999).

X(48951) lies on the circumcircle of 1st anti-Parry triangle and these lines: {2, 9216}, {3, 48982}, {98, 376}, {99, 110}, {115, 35922}, {523, 48952}, {542, 48953}, {804, 9145}, {2783, 48709}, {2786, 48970}, {2787, 48690}, {2794, 48954}, {2799, 48539}, {2854, 48980}, {2966, 9181}, {5467, 40866}, {7492, 14931}, {9479, 48973}, {14960, 31953}, {23870, 48950}, {23871, 48949}, {32583, 36900}, {40879, 48983}, {45722, 48961}

X(48951) = reflection of X(98) in the line X(2793)X(40879)
X(48951) = parallelogic center (1st anti-Parry, T) for these triangles T: {1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard}
X(48951) = X(48982)-of-ABC-X3 reflections triangle
X(48951) = X(98)-of-1st anti-Parry triangle
X(48951) = reflection of X(i) in X(j) for these (i, j): (48947, 9145), (48982, 3), (48983, 40879)


X(48952) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO ANTI-MCCAY

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

The reciprocal parallelogic center of these triangles is X(9855).

X(48952) lies on these lines: {3, 48983}, {20, 542}, {99, 1296}, {110, 9485}, {523, 48951}, {671, 38675}, {690, 48539}, {804, 48961}, {842, 5999}, {2782, 48980}, {2789, 48970}, {4226, 40866}, {5466, 9216}, {9146, 44010}, {9966, 11152}, {14570, 15342}, {27550, 48949}, {27551, 48950}, {32472, 33799}, {38738, 45772}

X(48952) = parallelogic center (1st anti-Parry, T) for these triangles T: {anti-McCay, McCay, Moses-Steiner osculatory}
X(48952) = center of circle {{X(148), X(14683), X(20094)}}
X(48952) = X(48983)-of-ABC-X3 reflections triangle
X(48952) = X(671)-of-1st anti-Parry triangle
X(48952) = reflection of X(i) in X(j) for these (i, j): (45772, 38738), (48947, 99), (48983, 3)


X(48953) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*(a^8-3*(b^2+c^2)*a^6-(2*b^4-13*b^2*c^2+2*c^4)*a^4+(b^2+c^2)*(9*b^4-20*b^2*c^2+9*c^4)*a^2-(5*b^4+7*b^2*c^2+5*c^4)*(b^2-c^2)^2)*(a^2-c^2)*(a^2-b^2) : :
X(48953) = 2*X(9142)-3*X(15055)

The reciprocal parallelogic center of these triangles is X(12112).

X(48953) lies on the circumcircle of 1st anti-Parry triangle and these lines: {3, 48984}, {74, 1296}, {99, 9003}, {110, 351}, {520, 9181}, {523, 48957}, {525, 48979}, {542, 48951}, {690, 48947}, {691, 8675}, {2771, 48709}, {2781, 48954}, {5505, 17430}, {8674, 48690}, {9033, 48539}, {9142, 15055}, {9146, 45808}, {9517, 45722}, {11579, 34383}, {22265, 40879}, {35053, 45709}

X(48953) = parallelogic center (1st anti-Parry, T) for these triangles T: {anti-orthocentroidal, orthocentroidal}
X(48953) = center of circle {{X(3), X(399), X(35447)}}
X(48953) = X(48984)-of-ABC-X3 reflections triangle
X(48953) = X(74)-of-1st anti-Parry triangle
X(48953) = reflection of X(i) in X(j) for these (i, j): (110, 9145), (22265, 40879), (48984, 3)


X(48954) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 1st ANTI-ORTHOSYMMEDIAL

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

The reciprocal parallelogic center of these triangles is X(19158).

X(48954) lies on the circumcircle of 1st anti-Parry triangle and these lines: {3, 48985}, {99, 2848}, {110, 112}, {1296, 1297}, {2781, 48953}, {2794, 48951}, {2799, 48947}, {2806, 48690}, {2831, 48709}, {2854, 48981}, {2881, 9145}, {9157, 9216}, {10718, 34518}

X(48954) = parallelogic center (1st anti-Parry, T) for these triangles T: {1st anti-orthosymmedial, 1st orthosymmedial}
X(48954) = X(48985)-of-ABC-X3 reflections triangle
X(48954) = X(1297)-of-1st anti-Parry triangle
X(48954) = reflection of X(i) in X(j) for these (i, j): (48948, 9145), (48985, 3)


X(48955) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 3rd ANTI-TRI-SQUARES

Barycentrics    ((a^4-(b^2+c^2)*a^2+4*b^4-16*b^2*c^2+4*c^4)*a^2-2*(2*a^4-4*(b^2+c^2)*a^2+3*(b^2-c^2)^2)*S)*(a^2-c^2)*(a^2-b^2) : :

The reciprocal parallelogic center of these triangles is X(486).

X(48955) lies on these lines: {3, 48986}, {110, 13316}, {523, 48978}, {3566, 45722}, {9216, 13319}

X(48955) = reflection of X(48986) in X(3)
X(48955) = parallelogic center (1st anti-Parry, T) for these triangles T: {3rd anti-tri-squares, 2nd half-squares, 4th tri-squares, inner-Vecten}
X(48955) = X(486)-of-1st anti-Parry triangle
X(48955) = X(48986)-of-ABC-X3 reflections triangle
X(48955) = {X(45722), X(48974)}-harmonic conjugate of X(48956)


X(48956) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 4th ANTI-TRI-SQUARES

Barycentrics    ((a^4-(b^2+c^2)*a^2+4*b^4-16*b^2*c^2+4*c^4)*a^2+2*(2*a^4-4*(b^2+c^2)*a^2+3*(b^2-c^2)^2)*S)*(a^2-c^2)*(a^2-b^2) : :

The reciprocal parallelogic center of these triangles is X(485).

X(48956) lies on these lines: {3, 48987}, {110, 13317}, {523, 48977}, {3566, 45722}, {9216, 13320}

X(48956) = reflection of X(48987) in X(3)
X(48956) = parallelogic center (1st anti-Parry, T) for these triangles T: {4th anti-tri-squares, 1st half-squares, 3rd tri-squares, outer-Vecten}
X(48956) = X(485)-of-1st anti-Parry triangle
X(48956) = X(48987)-of-ABC-X3 reflections triangle
X(48956) = {X(45722), X(48974)}-harmonic conjugate of X(48955)


X(48957) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO AAOA

Barycentrics    (a^10-3*(b^2+c^2)*a^8+(b^4+7*b^2*c^2+c^4)*a^6+2*(b^2+c^2)*(3*b^4-7*b^2*c^2+3*c^4)*a^4-2*(b^2-c^2)^2*(2*b^2-3*b*c+2*c^2)*(2*b^2+3*b*c+2*c^2)*a^2+3*(b^4-c^4)*(b^2-c^2)^3)*(a^2-c^2)*(a^2-b^2) : :
X(48957) = 3*X(15055)-2*X(49006)

The reciprocal parallelogic center of these triangles is X(7574).

X(48957) lies on these lines: {3, 48988}, {110, 930}, {512, 48979}, {523, 48953}, {526, 48539}, {690, 45722}, {8674, 48965}, {9033, 48971}, {9216, 13291}, {12219, 45616}, {15055, 49006}

X(48957) = parallelogic center (1st anti-Parry, T) for these triangles T: {antiAOA, AOA, 1st Hyacinth}
X(48957) = X(48988)-of-ABC-X3 reflections triangle
X(48957) = X(265)-of-1st anti-Parry triangle
X(48957) = reflection of X(i) in X(j) for these (i, j): (110, 48974), (48988, 3)


X(48958) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO ARIES

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

The reciprocal parallelogic center of these triangles is X(9833).

X(48958) lies on these lines: {3, 48989}, {99, 20184}, {110, 13223}, {523, 48971}, {924, 48539}, {1510, 48967}, {3566, 45722}, {9216, 13224}

X(48958) = parallelogic center (1st anti-Parry, T) for these triangles T: {Aries, 2nd Hyacinth}
X(48958) = X(48989)-of-ABC-X3 reflections triangle
X(48958) = X(68)-of-1st anti-Parry triangle
X(48958) = reflection of X(48989) in X(3)


X(48959) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO BEVAN ANTIPODAL

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

The reciprocal parallelogic center of these triangles is X(1).

X(48959) lies on these lines: {3, 48990}, {99, 4778}, {110, 9811}, {513, 9145}, {514, 48539}, {521, 48971}, {522, 47747}, {2827, 48709}, {2854, 45710}, {3738, 48690}, {4977, 48974}, {8713, 48969}, {9216, 9810}, {28478, 48960}

X(48959) = parallelogic center (1st anti-Parry, T) for these triangles T: {Bevan antipodal, 3rd extouch}
X(48959) = X(48990)-of-ABC-X3 reflections triangle
X(48959) = X(40)-of-1st anti-Parry triangle
X(48959) = reflection of X(i) in X(j) for these (i, j): (45709, 9145), (48539, 48970), (48990, 3)


X(48960) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 9th BROCARD

Barycentrics    (a^6-(b^2+c^2)*a^4+(7*b^4-22*b^2*c^2+7*c^4)*a^2-3*(b^4-c^4)*(b^2-c^2))*(a^2-c^2)*(a^2-b^2) : :

The reciprocal parallelogic center of these triangles is X(4).

X(48960) lies on these lines: {3, 48991}, {99, 110}, {525, 45722}, {543, 6776}, {671, 18911}, {2790, 11820}, {3566, 9145}, {5656, 14981}, {6054, 32111}, {6233, 30247}, {8593, 32220}, {9216, 39905}, {11456, 23235}, {14928, 41719}, {15072, 38664}, {28478, 48959}

X(48960) = parallelogic center (1st anti-Parry, 9th Brocard)
X(48960) = X(48991)-of-ABC-X3 reflections triangle
X(48960) = X(6776)-of-1st anti-Parry triangle
X(48960) = reflection of X(i) in X(j) for these (i, j): (48539, 45722), (48991, 3)


X(48961) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 1st BROCARD-REFLECTED

Barycentrics    ((b^2+c^2)*a^6-(b^4+5*b^2*c^2+c^4)*a^4+2*(b^4-3*b^2*c^2+c^4)*(b^2+c^2)*a^2+(b^2-c^2)^2*b^2*c^2)*(a^2-c^2)*(a^2-b^2) : :
X(48961) = X(48972)-4*X(48974)

The reciprocal parallelogic center of these triangles is X(3).

X(48961) lies on these lines: {3, 48992}, {99, 512}, {110, 22733}, {804, 48952}, {3849, 12117}, {4785, 48970}, {9145, 48973}, {9216, 22734}, {23878, 48539}, {25423, 48972}, {45722, 48951}

X(48961) = parallelogic center (1st anti-Parry, 1st Brocard-reflected)
X(48961) = X(48992)-of-ABC-X3 reflections triangle
X(48961) = X(262)-of-1st anti-Parry triangle
X(48961) = reflection of X(48992) in X(3)


X(48962) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO EXTOUCH

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

The reciprocal parallelogic center of these triangles is X(40).

X(48962) lies on these lines: {3, 48994}, {110, 13254}, {521, 45709}, {522, 47747}, {2804, 48965}, {3900, 9145}, {8058, 48539}, {9216, 13255}

X(48962) = parallelogic center (1st anti-Parry, T) for these triangles T: {extouch, 1st Zaniah}
X(48962) = X(48994)-of-ABC-X3 reflections triangle
X(48962) = X(84)-of-1st anti-Parry triangle
X(48962) = reflection of X(48994) in X(3)


X(48963) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO INNER-FERMAT

Barycentrics    ((a^4-(b^2+c^2)*a^2+4*b^4-16*b^2*c^2+4*c^4)*sqrt(3)*a^2-2*(5*a^4-10*(b^2+c^2)*a^2+6*(b^2-c^2)^2)*S)*(a^2-b^2)*(a^2-c^2) : :

The reciprocal parallelogic center of these triangles is X(3).

X(48963) lies on these lines: {3, 48995}, {110, 22888}, {9145, 48950}, {9202, 30216}, {9203, 23873}, {9216, 22889}, {32478, 45722}, {48949, 48974}

X(48963) = parallelogic center (1st anti-Parry, T) for these triangles T: {inner-Fermat, 1st half-diamonds}
X(48963) = X(48995)-of-ABC-X3 reflections triangle
X(48963) = X(18)-of-1st anti-Parry triangle
X(48963) = reflection of X(48995) in X(3)


X(48964) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO OUTER-FERMAT

Barycentrics    ((a^4-(b^2+c^2)*a^2+4*b^4-16*b^2*c^2+4*c^4)*sqrt(3)*a^2+2*(5*a^4-10*(b^2+c^2)*a^2+6*(b^2-c^2)^2)*S)*(a^2-b^2)*(a^2-c^2) : :

The reciprocal parallelogic center of these triangles is X(3).

X(48964) lies on these lines: {3, 48996}, {110, 22933}, {9145, 48949}, {9202, 23872}, {9203, 30215}, {9216, 22934}, {32478, 45722}, {48950, 48974}

X(48964) = parallelogic center (1st anti-Parry, T) for these triangles T: {outer-Fermat, 2nd half-diamonds}
X(48964) = X(48996)-of-ABC-X3 reflections triangle
X(48964) = X(17)-of-1st anti-Parry triangle
X(48964) = reflection of X(48996) in X(3)


X(48965) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO FUHRMANN

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

The reciprocal parallelogic center of these triangles is X(3).

X(48965) lies on these lines: {3, 48997}, {110, 13263}, {522, 48709}, {900, 45709}, {2804, 48962}, {2827, 47747}, {3738, 48539}, {8674, 48957}, {9216, 13264}, {48690, 48970}

X(48965) = parallelogic center (1st anti-Parry, T) for these triangles T: {Fuhrmann, K798i}
X(48965) = X(48997)-of-ABC-X3 reflections triangle
X(48965) = X(80)-of-1st anti-Parry triangle
X(48965) = reflection of X(i) in X(j) for these (i, j): (48690, 48970), (48997, 3)


X(48966) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 2nd FUHRMANN

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

The reciprocal parallelogic center of these triangles is X(3).

X(48966) lies on these lines: {3, 48998}, {110, 16156}, {523, 45709}, {6003, 47747}, {8674, 48957}, {9216, 16157}, {35057, 48539}

X(48966) = parallelogic center (1st anti-Parry, T) for these triangles T: {2nd Fuhrmann, K798e}
X(48966) = X(48998)-of-ABC-X3 reflections triangle
X(48966) = X(79)-of-1st anti-Parry triangle
X(48966) = reflection of X(48998) in X(3)


X(48967) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO HATZIPOLAKIS-MOSES

Barycentrics    (-a^2+b^2+c^2)*(a^14-3*(b^2+c^2)*a^12+5*b^2*c^2*a^10+3*(b^2+c^2)*(3*b^4-4*b^2*c^2+3*c^4)*a^8-(b^2-c^2)^2*(9*b^4+7*b^2*c^2+9*c^4)*a^6-3*(b^4-c^4)^2*(b^2+c^2)*a^4+2*(b^2-c^2)^4*(4*b^4+5*b^2*c^2+4*c^4)*a^2-3*(b^2+c^2)*(b^2-c^2)^6)*(a^2-c^2)*(a^2-b^2) : :

The reciprocal parallelogic center of these triangles is X(6146).

X(48967) lies on these lines: {3, 48999}, {110, 32407}, {1510, 48958}, {6368, 9145}, {9216, 32408}

X(48967) = parallelogic center (1st anti-Parry, Hatzipolakis-Moses)
X(48967) = X(48999)-of-ABC-X3 reflections triangle
X(48967) = X(6145)-of-1st anti-Parry triangle
X(48967) = reflection of X(48999) in X(3)


X(48968) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 3rd HATZIPOLAKIS

Barycentrics    (a^16-4*(b^2+c^2)*a^14+(3*b^4+19*b^2*c^2+3*c^4)*a^12+(b^2+c^2)*(9*b^4-41*b^2*c^2+9*c^4)*a^10-(18*b^8+18*c^8-(5*b^2+4*b*c+5*c^2)*(5*b^2-4*b*c+5*c^2)*b^2*c^2)*a^8+(b^2+c^2)*(6*b^8+6*c^8+(13*b^4-54*b^2*c^2+13*c^4)*b^2*c^2)*a^6+(b^2-c^2)^2*(b^4-4*b^2*c^2+c^4)*(11*b^4-2*b^2*c^2+11*c^4)*a^4-(b^4-c^4)*(b^2-c^2)^3*(11*b^4-20*b^2*c^2+11*c^4)*a^2+3*(b^2+c^2)^2*(b^2-c^2)^6)*(a^2-c^2)*(a^2-b^2) : :

The reciprocal parallelogic center of these triangles is X(12241).

X(48968) lies on these lines: {3, 49000}, {110, 22984}, {9216, 22985}

X(48968) = parallelogic center (1st anti-Parry, 3rd Hatzipolakis)
X(48968) = X(49000)-of-ABC-X3 reflections triangle
X(48968) = X(22466)-of-1st anti-Parry triangle
X(48968) = reflection of X(49000) in X(3)


X(48969) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO HUTSON EXTOUCH

Barycentrics    a*(a^9-2*(b+c)*a^8-(b+3*c)*(3*b+c)*a^7+(b+c)*(5*b^2+14*b*c+5*c^2)*a^6+(7*b^4+7*c^4+2*(16*b^2+b*c+16*c^2)*b*c)*a^5-(b+c)*(b^2+6*b*c+c^2)*(7*b^2-6*b*c+7*c^2)*a^4-(9*b^6+9*c^6+(26*b^4+26*c^4+(7*b^2+44*b*c+7*c^2)*b*c)*b*c)*a^3+(b^2-c^2)*(b-c)*(7*b^4+7*c^4+2*(18*b^2+61*b*c+18*c^2)*b*c)*a^2+4*(b^2-c^2)^2*(b-c)^2*(b^2+3*b*c+c^2)*a-3*(b^2-c^2)^4*(b+c))*(a^2-c^2)*(a^2-b^2) : :

The reciprocal parallelogic center of these triangles is X(40).

X(48969) lies on these lines: {3, 49001}, {110, 13284}, {8713, 48959}, {9216, 13285}

X(48969) = parallelogic center (1st anti-Parry, Hutson extouch)
X(48969) = X(49001)-of-ABC-X3 reflections triangle
X(48969) = X(7160)-of-1st anti-Parry triangle
X(48969) = reflection of X(49001) in X(3)


X(48970) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 1st JENKINS

Barycentrics    (2*a^4-4*(b^2+c^2)*a^2-3*(b^2-c^2)*(b-c)*a+3*(b^2-c^2)^2)*(a^2-c^2)*(a^2-b^2) : :
X(48970) = 3*X(99)-X(45709) = 3*X(99)+X(47747)

The reciprocal parallelogic center of these triangles is X(10).

X(48970) lies on these lines: {3, 49002}, {99, 2705}, {513, 48974}, {514, 48539}, {522, 9145}, {2786, 48951}, {2789, 48952}, {4785, 48961}, {23235, 45710}, {28470, 48972}, {28478, 45722}, {28487, 48973}, {48690, 48965}

X(48970) = midpoint of X(i) and X(j) for these {i, j}: {23235, 45710}, {45709, 47747}, {48539, 48959}, {48690, 48965}
X(48970) = reflection of X(49002) in X(3)
X(48970) = parallelogic center (1st anti-Parry, T) for these triangles T: {1st Jenkins, 1st Savin}
X(48970) = X(10)-of-1st anti-Parry triangle
X(48970) = X(49002)-of-ABC-X3 reflections triangle
X(48970) = {X(99), X(47747)}-harmonic conjugate of X(45709)


X(48971) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO MIDHEIGHT

Barycentrics    a^2*(-a^2+b^2+c^2)*(a^6-2*(b^2+c^2)*a^4-7*(b^2-c^2)^2*a^2+8*(b^4-c^4)*(b^2-c^2))*(a^2-c^2)*(a^2-b^2) : :
X(48971) = 4*X(9145)-3*X(32661)

The reciprocal parallelogic center of these triangles is X(4).

X(48971) lies on these lines: {3, 49003}, {110, 13302}, {520, 9145}, {521, 48959}, {523, 48958}, {8057, 48539}, {8673, 45722}, {9007, 48974}, {9033, 48957}, {9216, 13303}

X(48971) = parallelogic center (1st anti-Parry, midheight)
X(48971) = X(49003)-of-ABC-X3 reflections triangle
X(48971) = X(64)-of-1st anti-Parry triangle
X(48971) = reflection of X(49003) in X(3)


X(48972) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 1st NEUBERG

Barycentrics    ((b^2+c^2)*a^6-(5*b^4-3*b^2*c^2+5*c^4)*a^4-2*(b^2+c^2)*b^2*c^2*a^2+3*(b^2-c^2)^2*b^2*c^2)*(a^2-c^2)*(a^2-b^2) : :
X(48972) = 3*X(48961)-4*X(48974)

The reciprocal parallelogic center of these triangles is X(3).

X(48972) lies on these lines: {3, 49004}, {99, 32472}, {110, 13306}, {512, 48539}, {804, 9145}, {9216, 13307}, {11645, 12117}, {25423, 48961}, {28470, 48970}, {45722, 48973}

X(48972) = parallelogic center (1st anti-Parry, 1st Neuberg)
X(48972) = X(49004)-of-ABC-X3 reflections triangle
X(48972) = X(76)-of-1st anti-Parry triangle
X(48972) = reflection of X(49004) in X(3)


X(48973) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 2nd NEUBERG

Barycentrics    (a^8+(b^2+c^2)*a^6-(2*b^4+15*b^2*c^2+2*c^4)*a^4+2*(b^2+c^2)*(2*b^4-9*b^2*c^2+2*c^4)*a^2+3*(b^2-c^2)^2*b^2*c^2)*(a^2-c^2)*(a^2-b^2) : :

The reciprocal parallelogic center of these triangles is X(3).

X(48973) lies on these lines: {3, 49005}, {99, 32473}, {110, 13308}, {826, 48539}, {9145, 48961}, {9216, 13309}, {9479, 48951}, {12117, 12177}, {14718, 14810}, {28487, 48970}, {45722, 48972}

X(48973) = parallelogic center (1st anti-Parry, 2nd Neuberg)
X(48973) = X(49005)-of-ABC-X3 reflections triangle
X(48973) = X(83)-of-1st anti-Parry triangle
X(48973) = reflection of X(49005) in X(3)


X(48974) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO ORTHIC AXES

Barycentrics    (2*a^4-4*(b^2+c^2)*a^2+3*(b^2-c^2)^2)*(a^2-c^2)*(a^2-b^2) : :
X(48974) = 3*X(99)-X(9145) = 3*X(99)+X(48539) = 3*X(15035)-X(48988) = 3*X(48961)+X(48972)

The reciprocal parallelogic center of these triangles is X(4).

X(48974) lies on these lines: {3, 49006}, {5, 14662}, {99, 523}, {110, 930}, {513, 48970}, {900, 45709}, {1296, 44061}, {3566, 45722}, {4226, 35357}, {4977, 48959}, {5467, 14570}, {7816, 12039}, {9007, 48971}, {9027, 15301}, {9142, 23235}, {9216, 32193}, {9479, 48951}, {15035, 48988}, {25423, 48961}, {28217, 47747}, {48949, 48963}, {48950, 48964}

X(48974) = midpoint of X(i) and X(j) for these {i, j}: {110, 48957}, {9142, 23235}, {9145, 48539}
X(48974) = reflection of X(49006) in X(3)
X(48974) = inverse of X(13315) in Stammler hyperbola
X(48974) = parallelogic center (1st anti-Parry, T) for these triangles T: {orthic axes, Yiu tangents}
X(48974) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {126, 128, 30714}, {137, 5512, 24981}
X(48974) = X(5)-of-1st anti-Parry triangle
X(48974) = X(49006)-of-ABC-X3 reflections triangle
X(48974) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (99, 48539, 9145), (48955, 48956, 45722)


X(48975) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO REFLECTION

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

The reciprocal parallelogic center of these triangles is X(4).

X(48975) lies on these lines: {3, 49007}, {99, 20184}, {110, 930}, {1510, 9145}, {6368, 48539}, {9216, 13318}

X(48975) = reflection of X(49007) in X(3)
X(48975) = parallelogic center (1st anti-Parry, reflection)
X(48975) = X(49007)-of-ABC-X3 reflections triangle
X(48975) = X(54)-of-1st anti-Parry triangle
X(48975) = inverse of X(14610) in Stammler hyperbola


X(48976) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 1st SCHIFFLER

Barycentrics    (a^10-2*(b+c)*a^9-3*(b^2+c^2)*a^8+14*(b^3+c^3)*a^7-(2*b-c)*(b-2*c)*(4*b^2+9*b*c+4*c^2)*a^6-2*(b+c)*(11*b^4+11*c^4-5*(3*b^2-4*b*c+3*c^2)*b*c)*a^5+2*(12*b^6+12*c^6-(3*b^4+3*c^4+(17*b^2+2*b*c+17*c^2)*b*c)*b*c)*a^4+2*(b^2-c^2)*(b-c)*(5*b^4+5*c^4-(b^2-b*c+c^2)*b*c)*a^3-(b^2-c^2)^2*(17*b^4+17*c^4-(10*b^2+17*b*c+10*c^2)*b*c)*a^2+6*(b^2-c^2)^3*(b-c)*b*c*a+3*(b^2-c^2)^4*(b-c)^2)*(a^2-c^2)*(a^2-b^2) : :

The reciprocal parallelogic center of these triangles is X(79).

X(48976) lies on these lines: {3, 49008}, {110, 23035}, {8702, 48539}, {9216, 23036}, {30200, 47747}

X(48976) = parallelogic center (1st anti-Parry, 1st Schiffler)
X(48976) = X(49008)-of-ABC-X3 reflections triangle
X(48976) = X(10266)-of-1st anti-Parry triangle
X(48976) = reflection of X(49008) in X(3)


X(48977) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 1st TRI-SQUARES-CENTRAL

Barycentrics    ((a^4-(b^2+c^2)*a^2+4*b^4-16*b^2*c^2+4*c^4)*a^2+2*(2*a^4-4*(b^2+c^2)*a^2+5*(b^2-c^2)^2)*S)*(a^2-c^2)*(a^2-b^2) : :

The reciprocal parallelogic center of these triangles is X(13665).

X(48977) lies on these lines: {3, 49009}, {110, 13718}, {523, 48956}, {9216, 13719}, {12117, 32421}, {45722, 48978}

X(48977) = parallelogic center (1st anti-Parry, 1st tri-squares-central)
X(48977) = X(49009)-of-ABC-X3 reflections triangle
X(48977) = X(1327)-of-1st anti-Parry triangle
X(48977) = reflection of X(49009) in X(3)


X(48978) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    ((a^4-(b^2+c^2)*a^2+4*b^4-16*b^2*c^2+4*c^4)*a^2-2*(2*a^4-4*(b^2+c^2)*a^2+5*(b^2-c^2)^2)*S)*(a^2-c^2)*(a^2-b^2) : :

The reciprocal parallelogic center of these triangles is X(13785).

X(48978) lies on these lines: {3, 49010}, {110, 13841}, {523, 48955}, {9216, 13842}, {12117, 32419}, {45722, 48977}

X(48978) = parallelogic center (1st anti-Parry, 2nd tri-squares-central)
X(48978) = X(49010)-of-ABC-X3 reflections triangle
X(48978) = X(1328)-of-1st anti-Parry triangle
X(48978) = reflection of X(49010) in X(3)


X(48979) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-PARRY TO WALSMITH

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

The reciprocal parallelogic center of these triangles is X(125).

X(48979) lies on these lines: {3, 49011}, {99, 32228}, {110, 32312}, {512, 48957}, {525, 48953}, {690, 9145}, {1499, 47293}, {9216, 32313}, {9517, 48539}

X(48979) = parallelogic center (1st anti-Parry, Walsmith)
X(48979) = X(49011)-of-ABC-X3 reflections triangle
X(48979) = X(67)-of-1st anti-Parry triangle
X(48979) = reflection of X(49011) in X(3)

leftri

Centers related to 2nd anti-Parry triangle: X(48980)-X(49011)

rightri

This preamble and centers X(48980)-X(49011) were contributed by César Eliud Lozada, May 18, 2022.

2nd anti-Parry triangle was introduced in the preamble just before X(45345).


X(48980) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO 1st ANTI-BROCARD

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

The reciprocal orthologic center of these triangles is X(385).

X(48980) lies on the circumcircle of 2nd anti-Parry triangle and these lines: {2, 9215}, {3, 48947}, {69, 74}, {98, 111}, {147, 31128}, {690, 48984}, {804, 9142}, {2782, 48952}, {2783, 48691}, {2787, 48710}, {2794, 48981}, {2799, 48985}, {2854, 48951}, {4027, 9999}, {5191, 40866}

X(48980) = reflection of X(i) in X(j) for these (i, j): (45772, 38749), (48947, 3), (48982, 9142), (48983, 98)
X(48980) = reflection of X(74) in the line X(690)X(9142)
X(48980) = orthologic center (2nd anti-Parry, T) for these triangles T: {1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard}
X(48980) = center of circle {{X(148), X(38940), X(44373)}}
X(48980) = X(48947)-of-ABC-X3 reflections triangle
X(48980) = X(99)-of-2nd anti-Parry triangle
X(48980) = crossdifference of every pair of points on line {X(9155), X(14398)}


X(48981) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*(a^16-2*(b^2+c^2)*a^14+6*b^2*c^2*a^12-(b^2+c^2)*(b^4+c^4)*a^10+(7*b^8+7*c^8-b^2*c^2*(9*b^4-5*b^2*c^2+9*c^4))*a^8-2*(b^4-c^4)*(b^2-c^2)*(b^2+2*c^2)*(2*b^2+c^2)*a^6-2*(b^2-c^2)^2*(3*b^8+3*c^8-b^2*c^2*(7*b^4+6*b^2*c^2+7*c^4))*a^4+(b^4-c^4)*(b^2-c^2)*(7*b^8+7*c^8-2*b^2*c^2*(4*b^4+b^2*c^2+4*c^4))*a^2-(b^2-c^2)^4*(b^4+3*b^2*c^2+c^4)*(2*b^4+b^2*c^2+2*c^4)) : :

The reciprocal orthologic center of these triangles is X(10313).

X(48981) lies on the circumcircle of 2nd anti-Parry triangle and these lines: {3, 48948}, {6, 74}, {111, 1297}, {115, 9530}, {2794, 48980}, {2799, 48540}, {2806, 48710}, {2831, 48691}, {2854, 48954}, {2881, 9142}, {6103, 45280}, {9157, 9215}, {9517, 45723}

X(48981) = reflection of X(i) in X(j) for these (i, j): (48948, 3), (48985, 9142)
X(48981) = reflection of X(74) in the line X(9142)X(9517)
X(48981) = orthologic center (2nd anti-Parry, T) for these triangles T: {1st anti-orthosymmedial, 1st orthosymmedial}
X(48981) = X(48948)-of-ABC-X3 reflections triangle
X(48981) = X(112)-of-2nd anti-Parry triangle
X(48981) = crossdifference of every pair of points on line {X(9033), X(35282)}


X(48982) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO 1st ANTI-BROCARD

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

The reciprocal parallelogic center of these triangles is X(5999).

X(48982) lies on the circumcircle of 2nd anti-Parry triangle and these lines: {2, 99}, {3, 48951}, {6, 40866}, {74, 98}, {114, 7687}, {187, 2966}, {523, 48983}, {525, 5915}, {542, 48984}, {804, 9142}, {842, 43654}, {1916, 11060}, {2407, 10754}, {2783, 48710}, {2786, 49002}, {2787, 48691}, {2794, 48985}, {2799, 48540}, {2854, 48947}, {4235, 6531}, {5916, 23871}, {5917, 23870}, {5939, 32221}, {5969, 40879}, {8781, 12066}, {9147, 9215}, {9479, 49005}, {16278, 47200}, {45723, 48992}

X(48982) = reflection of X(74) in the line X(542)X(9142)
X(48982) = parallelogic center (2nd anti-Parry, T) for these triangles T: {1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard}
X(48982) = X(48951)-of-ABC-X3 reflections triangle
X(48982) = X(48947)-of-Artzt triangle
X(48982) = X(40879)-of-1st anti-Brocard triangle
X(48982) = X(98)-of-2nd anti-Parry triangle
X(48982) = reflection of X(i) in X(j) for these (i, j): (48951, 3), (48980, 9142)


X(48983) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO ANTI-MCCAY

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

The reciprocal parallelogic center of these triangles is X(9855).

X(48983) lies on these lines: {3, 48952}, {4, 542}, {30, 17948}, {74, 39450}, {98, 111}, {114, 30786}, {147, 31125}, {511, 892}, {523, 48982}, {690, 48540}, {691, 11676}, {804, 48992}, {1316, 40866}, {1513, 16092}, {2782, 48947}, {2789, 49002}, {2790, 14908}, {5182, 46512}, {5916, 27550}, {5917, 27551}, {5968, 13860}, {6054, 42008}, {7422, 14977}, {9215, 9485}, {10723, 45774}, {12117, 38688}, {14263, 39646}, {16093, 23698}, {19924, 39061}, {23348, 34810}, {40879, 48951}

X(48983) = midpoint of X(10723) and X(45774)
X(48983) = reflection of X(i) in X(j) for these (i, j): (48951, 40879), (48952, 3), (48980, 98)
X(48983) = barycentric product X(i)*X(j) for these {i, j}: {111, 44155}, {671, 1316}, {892, 47229}
X(48983) = barycentric quotient X(111)/X(9513)
X(48983) = trilinear product X(i)*X(j) for these {i, j}: {897, 1316}, {923, 44155}
X(48983) = trilinear quotient X(897)/X(9513)
X(48983) = trilinear pole of the line {1316, 47229}
X(48983) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(1316)}} and {{A, B, C, X(74), X(46249)}}
X(48983) = X(111)-Hirst inverse of-X(5466)
X(48983) = X(896)-isoconjugate-of-X(9513)
X(48983) = reflection of X(98) in the line X(543)X(40879)
X(48983) = parallelogic center (2nd anti-Parry, T) for these triangles T: {anti-McCay, McCay, Moses-Steiner osculatory}
X(48983) = X(48952)-of-ABC-X3 reflections triangle
X(48983) = X(671)-of-2nd anti-Parry triangle
X(48983) = X(111)-reciprocal conjugate of-X(9513)


X(48984) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*(a^12-2*(b^2+c^2)*a^10+(5*b^4-4*b^2*c^2+5*c^4)*a^8-(b^2+c^2)*(11*b^4-20*b^2*c^2+11*c^4)*a^6+(8*b^8+8*c^8+3*b^2*c^2*(3*b^4-11*b^2*c^2+3*c^4))*a^4+(b^4-c^4)*(b^2-c^2)*(b^2-4*b*c-c^2)*(b^2+4*b*c-c^2)*a^2-(b^2-c^2)^2*(2*b^8+2*c^8-b^2*c^2*(3*b^4+7*b^2*c^2+3*c^4))) : :
X(48984) = 2*X(9145)-3*X(15035) = 3*X(22265)-2*X(48988)

The reciprocal parallelogic center of these triangles is X(12112).

X(48984) lies on the circumcircle of 2nd anti-Parry triangle and these lines: {3, 48953}, {6, 110}, {74, 526}, {98, 9003}, {523, 22265}, {525, 49011}, {542, 48982}, {690, 48980}, {842, 8675}, {2771, 48710}, {2781, 48985}, {2871, 10752}, {5505, 11653}, {8674, 48691}, {9033, 48540}, {9138, 9215}, {9145, 15035}, {9517, 45723}, {15364, 34210}, {35053, 45710}

X(48984) = reflection of X(i) in X(j) for these (i, j): (74, 9142), (48953, 3)
X(48984) = perspector of the circumconic {{A, B, C, X(691), X(40384)}}
X(48984) = parallelogic center (2nd anti-Parry, T) for these triangles T: {anti-orthocentroidal, orthocentroidal}
X(48984) = X(48953)-of-ABC-X3 reflections triangle
X(48984) = X(74)-of-2nd anti-Parry triangle
X(48984) = crossdifference of every pair of points on line {X(690), X(3163)}


X(48985) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*(a^16-2*(b^2+c^2)*a^14+6*(b^4-b^2*c^2+c^4)*a^12-(b^2+c^2)*(7*b^4-12*b^2*c^2+7*c^4)*a^10-(5*b^8+5*c^8-b^2*c^2*(15*b^4-19*b^2*c^2+15*c^4))*a^8+8*(b^6-c^6)*(b^4-c^4)*a^6-2*(b^2-c^2)^2*(8*b^4+9*b^2*c^2+8*c^4)*b^2*c^2*a^4+(b^4-c^4)*(b^2-c^2)*(b^8+c^8-2*b^2*c^2*(b^4-5*b^2*c^2+c^4))*a^2-(b^2-c^2)^4*(2*b^4+3*b^2*c^2+2*c^4)*(b^4-b^2*c^2+c^4)) : :

The reciprocal parallelogic center of these triangles is X(19158).

X(48985) lies on the circumcircle of 2nd anti-Parry triangle and these lines: {3, 48954}, {25, 111}, {74, 1297}, {98, 2848}, {2781, 48984}, {2794, 48982}, {2799, 48980}, {2806, 48691}, {2831, 48710}, {2854, 48948}, {2881, 9142}, {8744, 32649}, {9215, 13114}

X(48985) = reflection of X(i) in X(j) for these (i, j): (48954, 3), (48981, 9142)
X(48985) = reflection of X(74) in the line X(2781)X(9142)
X(48985) = parallelogic center (2nd anti-Parry, T) for these triangles T: {1st anti-orthosymmedial, 1st orthosymmedial}
X(48985) = X(48954)-of-ABC-X3 reflections triangle
X(48985) = X(1297)-of-2nd anti-Parry triangle
X(48985) = crossdifference of every pair of points on line {X(6793), X(14417)}


X(48986) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO 3rd ANTI-TRI-SQUARES

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

The reciprocal parallelogic center of these triangles is X(486).

X(48986) lies on these lines: {3, 48955}, {111, 13319}, {523, 49010}, {3566, 45723}, {9215, 13316}

X(48986) = reflection of X(48955) in X(3)
X(48986) = parallelogic center (2nd anti-Parry, T) for these triangles T: {3rd anti-tri-squares, 2nd half-squares, 4th tri-squares, inner-Vecten}
X(48986) = X(486)-of-2nd anti-Parry triangle
X(48986) = X(48955)-of-ABC-X3 reflections triangle
X(48986) = {X(45723), X(49006)}-harmonic conjugate of X(48987)


X(48987) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO 4th ANTI-TRI-SQUARES

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

The reciprocal parallelogic center of these triangles is X(485).

X(48987) lies on these lines: {3, 48956}, {111, 13320}, {523, 49009}, {3566, 45723}, {9215, 13317}

X(48987) = reflection of X(48956) in X(3)
X(48987) = parallelogic center (2nd anti-Parry, T) for these triangles T: {4th anti-tri-squares, 1st half-squares, 3rd tri-squares, outer-Vecten}
X(48987) = X(485)-of-2nd anti-Parry triangle
X(48987) = X(48956)-of-ABC-X3 reflections triangle
X(48987) = {X(45723), X(49006)}-harmonic conjugate of X(48986)


X(48988) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO AAOA

Barycentrics    a^14-2*(b^2+c^2)*a^12+2*(b^4+b^2*c^2+c^4)*a^10-(b^2+c^2)*(5*b^4-8*b^2*c^2+5*c^4)*a^8+(8*b^8+8*c^8-3*b^2*c^2*(3*b^4-b^2*c^2+3*c^4))*a^6-5*(b^8-c^8)*a^4*(b^2-c^2)+(b^2-c^2)^2*(b^8+c^8+2*b^2*c^2*(3*b^4-4*b^2*c^2+3*c^4))*a^2-3*(b^4-c^4)*(b^2-c^2)^3*b^2*c^2 : :
X(48988) = 3*X(14850)-4*X(44386) = 3*X(15035)-2*X(48974) = 3*X(22265)-X(48984)

The reciprocal parallelogic center of these triangles is X(7574).

X(48988) lies on these lines: {3, 48957}, {74, 1141}, {111, 13291}, {512, 49011}, {523, 22265}, {526, 48540}, {690, 5916}, {7722, 45618}, {8674, 48997}, {9033, 49003}, {9140, 38393}, {9215, 13290}, {14850, 44386}, {15035, 48974}

X(48988) = parallelogic center (2nd anti-Parry, T) for these triangles T: {antiAOA, AOA, 1st Hyacinth}
X(48988) = X(48957)-of-ABC-X3 reflections triangle
X(48988) = X(265)-of-2nd anti-Parry triangle
X(48988) = reflection of X(i) in X(j) for these (i, j): (74, 49006), (48957, 3)


X(48989) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO ARIES

Barycentrics    a^14-2*(b^2+c^2)*a^12+5*(b^4-b^2*c^2+c^4)*a^10-(b^2+c^2)*(14*b^4-27*b^2*c^2+14*c^4)*a^8+(b^2-c^2)^2*(17*b^4+20*b^2*c^2+17*c^4)*a^6-4*(b^4-c^4)*(b^2-c^2)*(2*b^4+b^2*c^2+2*c^4)*a^4+(b^2-c^2)^2*(b^4-b^2*c^2+c^4)*(b^4+10*b^2*c^2+c^4)*a^2-3*(b^4-c^4)*(b^2-c^2)^3*b^2*c^2 : :

The reciprocal parallelogic center of these triangles is X(9833).

X(48989) lies on these lines: {3, 48958}, {74, 45781}, {98, 20184}, {111, 13224}, {523, 49003}, {924, 48540}, {1510, 48999}, {3566, 45723}, {9215, 13223}

X(48989) = parallelogic center (2nd anti-Parry, T) for these triangles T: {Aries, 2nd Hyacinth}
X(48989) = X(48958)-of-ABC-X3 reflections triangle
X(48989) = X(68)-of-2nd anti-Parry triangle
X(48989) = reflection of X(48958) in X(3)


X(48990) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO BEVAN ANTIPODAL

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

The reciprocal parallelogic center of these triangles is X(1).

X(48990) lies on these lines: {3, 48959}, {74, 35053}, {98, 4778}, {111, 9810}, {513, 9142}, {514, 48540}, {521, 49003}, {522, 48993}, {2827, 48710}, {2854, 45709}, {3738, 48691}, {4977, 49006}, {8713, 49001}, {9215, 9811}, {28478, 48991}

X(48990) = parallelogic center (2nd anti-Parry, T) for these triangles T: {Bevan antipodal, 3rd extouch}
X(48990) = X(48959)-of-ABC-X3 reflections triangle
X(48990) = X(40)-of-2nd anti-Parry triangle
X(48990) = reflection of X(i) in X(j) for these (i, j): (45710, 9142), (48540, 49002), (48959, 3)


X(48991) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO 9th BROCARD

Barycentrics    a^10-(8*b^4-13*b^2*c^2+8*c^4)*a^6+(b^2+c^2)*(12*b^4-23*b^2*c^2+12*c^4)*a^4-(b^2-c^2)^2*(5*b^4+19*b^2*c^2+5*c^4)*a^2+3*(b^4-c^4)*(b^2-c^2)*b^2*c^2 : :

The reciprocal parallelogic center of these triangles is X(4).

X(48991) lies on these lines: {3, 48960}, {69, 543}, {74, 98}, {99, 15066}, {111, 39905}, {115, 37643}, {525, 45723}, {671, 3580}, {2373, 6323}, {2790, 3426}, {3566, 9142}, {7618, 15596}, {9215, 39904}, {10754, 41617}, {11459, 23235}, {11623, 18931}, {28478, 48990}

X(48991) = reflection of X(98) in the line X(542)X(5486)
X(48991) = parallelogic center (2nd anti-Parry, 9th Brocard)
X(48991) = X(48960)-of-ABC-X3 reflections triangle
X(48991) = X(6776)-of-2nd anti-Parry triangle
X(48991) = reflection of X(i) in X(j) for these (i, j): (48540, 45723), (48960, 3)


X(48992) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO 1st BROCARD-REFLECTED

Barycentrics    (b^2+c^2)*a^10-(2*b^4-b^2*c^2+2*c^4)*a^8+(b^4-c^4)*(b^2-c^2)*a^6+b^4*c^4*a^4-3*(b^4-c^4)*(b^2-c^2)*b^2*c^2*a^2-(b^2-c^2)^2*b^4*c^4 : :
X(48992) = X(49004)-4*X(49006)

The reciprocal parallelogic center of these triangles is X(3).

X(48992) lies on these lines: {2, 3016}, {3, 48961}, {98, 512}, {111, 22734}, {385, 671}, {804, 48983}, {4785, 49002}, {9142, 49005}, {9215, 22733}, {9830, 40879}, {10033, 10706}, {11645, 44375}, {23878, 48540}, {25423, 49004}, {32761, 40870}, {45723, 48982}

X(48992) = parallelogic center (2nd anti-Parry, 1st Brocard-reflected)
X(48992) = X(48961)-of-ABC-X3 reflections triangle
X(48992) = X(262)-of-2nd anti-Parry triangle
X(48992) = reflection of X(48961) in X(3)


X(48993) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO EXCENTERS-MIDPOINTS

Barycentrics    a^8-(b^2+c^2)*a^6+6*(b^2-c^2)*(b-c)*a^5-(b^4-3*b^2*c^2+c^4)*a^4-6*(b^4-c^4)*(b-c)*a^3+(b^4-c^4)*(b^2-c^2)*a^2+6*(b^2-c^2)*(b-c)*b^2*c^2*a-3*(b^2-c^2)^2*b^2*c^2 : :
X(48993) = 3*X(98)-2*X(45710) = 3*X(98)-4*X(49002)

The reciprocal parallelogic center of these triangles is X(10).

X(48993) lies on these lines: {3, 47747}, {98, 2712}, {111, 13251}, {513, 48540}, {522, 48990}, {900, 9142}, {2827, 48997}, {6003, 48998}, {9215, 13250}, {23235, 45709}, {28217, 49006}, {28481, 45723}, {30200, 49008}

X(48993) = reflection of X(i) in X(j) for these (i, j): (23235, 45709), (45710, 49002), (47747, 3)
X(48993) = parallelogic center (2nd anti-Parry, T) for these triangles T: {excenters-midpoints, Garcia-reflection, 2nd Schiffler}
X(48993) = X(8)-of-2nd anti-Parry triangle
X(48993) = X(47747)-of-ABC-X3 reflections triangle
X(48993) = {X(45710), X(49002)}-harmonic conjugate of X(98)


X(48994) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO EXTOUCH

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

The reciprocal parallelogic center of these triangles is X(40).

X(48994) lies on these lines: {3, 48962}, {111, 13255}, {521, 45710}, {522, 48990}, {2804, 48997}, {3900, 9142}, {9215, 13254}

X(48994) = parallelogic center (2nd anti-Parry, T) for these triangles T: {extouch, 1st Zaniah}
X(48994) = X(48962)-of-ABC-X3 reflections triangle
X(48994) = X(84)-of-2nd anti-Parry triangle
X(48994) = reflection of X(48962) in X(3)


X(48995) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO INNER-FERMAT

Barycentrics    a^2*(a^8-(5*b^4-7*b^2*c^2+5*c^4)*a^4+(b^2+c^2)*(6*b^4-11*b^2*c^2+6*c^4)*a^2-2*(b^4+5*b^2*c^2+c^4)*(b^2-c^2)^2)*sqrt(3)-2*S*(5*a^8-5*(b^2+c^2)*a^6+(4*b^4-3*b^2*c^2+4*c^4)*a^4-4*(b^4-c^4)*(b^2-c^2)*a^2-6*(b^2-c^2)^2*b^2*c^2) : :

The reciprocal parallelogic center of these triangles is X(3).

X(48995) lies on these lines: {3, 48963}, {74, 39433}, {111, 22889}, {2378, 30216}, {2379, 23873}, {5916, 49006}, {5917, 9142}, {9215, 22888}, {10646, 32037}, {32478, 45723}

X(48995) = parallelogic center (2nd anti-Parry, T) for these triangles T: {inner-Fermat, 1st half-diamonds}
X(48995) = X(48963)-of-ABC-X3 reflections triangle
X(48995) = X(18)-of-2nd anti-Parry triangle
X(48995) = reflection of X(48963) in X(3)


X(48996) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO OUTER-FERMAT

Barycentrics    a^2*(a^8-(5*b^4-7*b^2*c^2+5*c^4)*a^4+(b^2+c^2)*(6*b^4-11*b^2*c^2+6*c^4)*a^2-2*(b^4+5*b^2*c^2+c^4)*(b^2-c^2)^2)*sqrt(3)+2*S*(5*a^8-5*(b^2+c^2)*a^6+(4*b^4-3*b^2*c^2+4*c^4)*a^4-4*(b^4-c^4)*(b^2-c^2)*a^2-6*(b^2-c^2)^2*b^2*c^2) : :

The reciprocal parallelogic center of these triangles is X(3).

X(48996) lies on these lines: {3, 48964}, {74, 39432}, {111, 22934}, {2378, 23872}, {2379, 30215}, {5916, 9142}, {5917, 49006}, {9215, 22933}, {10645, 32036}, {32478, 45723}

X(48996) = parallelogic center (2nd anti-Parry, T) for these triangles T: {outer-Fermat, 2nd half-diamonds}
X(48996) = X(48964)-of-ABC-X3 reflections triangle
X(48996) = X(17)-of-2nd anti-Parry triangle
X(48996) = reflection of X(48964) in X(3)


X(48997) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO FUHRMANN

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

The reciprocal parallelogic center of these triangles is X(3).

X(48997) lies on these lines: {3, 48965}, {111, 13264}, {522, 48710}, {900, 45710}, {2804, 48994}, {2827, 48993}, {3738, 48540}, {8674, 48988}, {9215, 13263}, {48691, 49002}

X(48997) = parallelogic center (2nd anti-Parry, T) for these triangles T: {Fuhrmann, K798i}
X(48997) = X(48965)-of-ABC-X3 reflections triangle
X(48997) = X(80)-of-2nd anti-Parry triangle
X(48997) = reflection of X(i) in X(j) for these (i, j): (48691, 49002), (48965, 3)


X(48998) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO 2nd FUHRMANN

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

The reciprocal parallelogic center of these triangles is X(3).

X(48998) lies on these lines: {3, 48966}, {111, 16157}, {523, 45710}, {6003, 48993}, {8674, 48988}, {9215, 16156}, {35057, 48540}

X(48998) = parallelogic center (2nd anti-Parry, T) for these triangles T: {2nd Fuhrmann, K798e}
X(48998) = X(48966)-of-ABC-X3 reflections triangle
X(48998) = X(79)-of-2nd anti-Parry triangle
X(48998) = reflection of X(48966) in X(3)


X(48999) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO HATZIPOLAKIS-MOSES

Barycentrics    (-a^2+b^2+c^2)*(a^18-2*(b^2+c^2)*a^16+(b^4+c^4)*a^14-(b^2+c^2)*(3*b^4-8*b^2*c^2+3*c^4)*a^12+(6*b^8+6*c^8-5*(b^4+b^2*c^2+c^4)*b^2*c^2)*a^10-4*(b^4-c^4)*(b^2-c^2)*b^2*c^2*a^8-(b^2-c^2)^2*(7*b^8+7*c^8-5*b^2*c^2*(b^4-b^2*c^2+c^4))*a^6+(b^6+c^6)*(b^2-c^2)^2*(5*b^4-4*b^2*c^2+5*c^4)*a^4-(b^2-c^2)^4*(b^8+c^8+2*b^2*c^2*(3*b^4+2*b^2*c^2+3*c^4))*a^2+3*(b^2-c^2)^6*b^2*c^2*(b^2+c^2)) : :

The reciprocal parallelogic center of these triangles is X(6146).

X(48999) lies on these lines: {3, 48967}, {111, 32408}, {1510, 48989}, {6368, 9142}, {9215, 32407}

X(48999) = parallelogic center (2nd anti-Parry, Hatzipolakis-Moses)
X(48999) = X(48967)-of-ABC-X3 reflections triangle
X(48999) = X(6145)-of-2nd anti-Parry triangle
X(48999) = reflection of X(48967) in X(3)


X(49000) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO 3rd HATZIPOLAKIS

Barycentrics    a^20-3*(b^2+c^2)*a^18+3*(b^4+4*b^2*c^2+c^4)*a^16-4*(b^2+c^2)^3*a^14+(3*b^4+3*c^4+b*c*(9*b^2+13*b*c+9*c^2))*(3*b^4+3*c^4-b*c*(9*b^2-13*b*c+9*c^2))*a^12-(b^2+c^2)*(6*b^8+6*c^8+b^2*c^2*(3*b^4-5*b^2*c^2+3*c^4))*a^10-(7*b^12+7*c^12-(51*b^8+51*c^8-2*b^2*c^2*(41*b^4-42*b^2*c^2+41*c^4))*b^2*c^2)*a^8+(b^4-c^4)*(b^2-c^2)*(12*b^8+12*c^8-b^2*c^2*(42*b^4-43*b^2*c^2+42*c^4))*a^6-3*(b^2-c^2)^6*(2*b^4+7*b^2*c^2+2*c^4)*a^4+(b^4-c^4)*(b^2-c^2)^3*(b^8+c^8+b^2*c^2*(9*b^4-26*b^2*c^2+9*c^4))*a^2-3*(b^2-c^2)^6*b^2*c^2*(b^2+c^2)^2 : :

The reciprocal parallelogic center of these triangles is X(12241).

X(49000) lies on these lines: {3, 48968}, {111, 22985}, {9215, 22984}

X(49000) = parallelogic center (2nd anti-Parry, 3rd Hatzipolakis)
X(49000) = X(48968)-of-ABC-X3 reflections triangle
X(49000) = X(22466)-of-2nd anti-Parry triangle
X(49000) = reflection of X(48968) in X(3)


X(49001) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO HUTSON EXTOUCH

Barycentrics    a*(a^13-2*(b+c)*a^12-2*(b^2+5*b*c+c^2)*a^11+(b+c)*(9*b^2+2*b*c+9*c^2)*a^10-(4*b^4+4*c^4-b*c*(22*b^2+21*b*c+22*c^2))*a^9-2*(b+c)*(8*b^4+8*c^4-b*c*(b^2-3*b*c+c^2))*a^8+(16*b^6+16*c^6-(34*b^4+34*c^4+5*b*c*(5*b^2-2*b*c+5*c^2))*b*c)*a^7+(b+c)*(14*b^6+14*c^6+b*c*(6*b^2-11*b*c+6*c^2)*(b^2-14*b*c+c^2))*a^6-(19*b^8+19*c^8-(46*b^6+46*c^6+(41*b^4+41*c^4-2*b*c*(17*b^2+18*b*c+17*c^2))*b*c)*b*c)*a^5-(b^2-c^2)*(b-c)*(6*b^6+6*c^6+(38*b^4+38*c^4-b*c*(57*b^2-10*b*c+57*c^2))*b*c)*a^4+(b^2-c^2)^2*(10*b^6+10*c^6-(28*b^4+28*c^4+b*c*(13*b^2+42*b*c+13*c^2))*b*c)*a^3+(b^2-c^2)*(b-c)*(b^8+c^8+(18*b^6+18*c^6-(3*b^4+3*c^4+2*b*c*(15*b^2+58*b*c+15*c^2))*b*c)*b*c)*a^2-2*(b^2-c^2)^4*(b^4+c^4-b*c*(2*b-c)*(b-2*c))*a+3*(b^2-c^2)^4*(b+c)*b^2*c^2) : :

The reciprocal parallelogic center of these triangles is X(40).

X(49001) lies on these lines: {3, 48969}, {111, 13285}, {8713, 48990}, {9215, 13284}

X(49001) = parallelogic center (2nd anti-Parry, Hutson extouch)
X(49001) = X(48969)-of-ABC-X3 reflections triangle
X(49001) = X(7160)-of-2nd anti-Parry triangle
X(49001) = reflection of X(48969) in X(3)


X(49002) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO 1st JENKINS

Barycentrics    2*a^8-2*(b^2+c^2)*a^6+3*(b^2-c^2)*(b-c)*a^5+(b^4+c^4)*a^4-3*(b^4-c^4)*(b-c)*a^3-(b^4-c^4)*(b^2-c^2)*a^2+3*(b^2-c^2)*(b-c)*b^2*c^2*a-3*(b^2-c^2)^2*b^2*c^2 : :
X(49002) = 3*X(98)-X(45710) = 3*X(98)+X(48993)

The reciprocal parallelogic center of these triangles is X(10).

X(49002) lies on these lines: {3, 48970}, {74, 2372}, {98, 2712}, {190, 37508}, {513, 49006}, {514, 48540}, {522, 9142}, {671, 37792}, {2786, 48982}, {2789, 48983}, {4785, 48992}, {28470, 49004}, {28478, 45723}, {28487, 49005}, {38664, 45709}, {48691, 48997}

X(49002) = midpoint of X(i) and X(j) for these {i, j}: {38664, 45709}, {45710, 48993}, {48540, 48990}, {48691, 48997}
X(49002) = reflection of X(48970) in X(3)
X(49002) = parallelogic center (2nd anti-Parry, T) for these triangles T: {1st Jenkins, 1st Savin}
X(49002) = X(10)-of-2nd anti-Parry triangle
X(49002) = X(48970)-of-ABC-X3 reflections triangle
X(49002) = {X(98), X(48993)}-harmonic conjugate of X(45710)


X(49003) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO MIDHEIGHT

Barycentrics    a^2*(-a^2+b^2+c^2)*(a^10-(b^2+c^2)*a^8+(7*b^4-13*b^2*c^2+7*c^4)*a^6-13*(b^4-c^4)*(b^2-c^2)*a^4+(b^2-c^2)^2*(4*b^4+21*b^2*c^2+4*c^4)*a^2+(b^4-c^4)*(b^2-c^2)*(2*b^4-10*b^2*c^2+2*c^4)) : :

The reciprocal parallelogic center of these triangles is X(4).

X(49003) lies on these lines: {3, 48971}, {74, 5896}, {111, 13303}, {520, 9142}, {521, 48990}, {523, 48989}, {8057, 48540}, {8673, 45723}, {8681, 9132}, {9007, 49006}, {9033, 48988}, {9215, 13302}

X(49003) = parallelogic center (2nd anti-Parry, midheight)
X(49003) = X(48971)-of-ABC-X3 reflections triangle
X(49003) = X(64)-of-2nd anti-Parry triangle
X(49003) = reflection of X(48971) in X(3)


X(49004) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO 1st NEUBERG

Barycentrics    (b^2+c^2)*a^10+(2*b^4-7*b^2*c^2+2*c^4)*a^8-(b^4-c^4)*(b^2-c^2)*a^6-(2*b^8+2*c^8-b^2*c^2*(2*b^4+b^2*c^2+2*c^4))*a^4+(b^4-c^4)*(b^2-c^2)*b^2*c^2*a^2-3*(b^2-c^2)^2*b^4*c^4 : :
X(49004) = 3*X(48992)-4*X(49006)

The reciprocal parallelogic center of these triangles is X(3).

X(49004) lies on these lines: {3, 48972}, {74, 2367}, {98, 5970}, {111, 13307}, {512, 48540}, {670, 3098}, {671, 11645}, {804, 9142}, {9215, 13306}, {9774, 10717}, {25051, 39874}, {25423, 48992}, {28470, 49002}, {45723, 49005}

X(49004) = parallelogic center (2nd anti-Parry, 1st Neuberg)
X(49004) = X(48972)-of-ABC-X3 reflections triangle
X(49004) = X(76)-of-2nd anti-Parry triangle
X(49004) = reflection of X(48972) in X(3)


X(49005) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO 2nd NEUBERG

Barycentrics    a^12+2*(b^2+c^2)*a^10-3*(b^4+c^4)*a^8-2*(b^2+c^2)*b^2*c^2*a^6+(2*b^8+2*c^8-b^2*c^2*(3*b^4-7*b^2*c^2+3*c^4))*a^4-(b^4-c^4)*(b^2-c^2)*(2*b^4+9*b^2*c^2+2*c^4)*a^2-3*(b^2-c^2)^2*b^4*c^4 : :

The reciprocal parallelogic center of these triangles is X(3).

X(49005) lies on these lines: {3, 48973}, {74, 39427}, {98, 32473}, {111, 13309}, {671, 9302}, {826, 48540}, {4577, 5092}, {9142, 48992}, {9215, 13308}, {9479, 48982}, {28487, 49002}, {45723, 49004}

X(49005) = parallelogic center (2nd anti-Parry, 2nd Neuberg)
X(49005) = X(48973)-of-ABC-X3 reflections triangle
X(49005) = X(83)-of-2nd anti-Parry triangle
X(49005) = reflection of X(48973) in X(3)


X(49006) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO ORTHIC AXES

Barycentrics    2*a^8-2*(b^2+c^2)*a^6+(b^4+c^4)*a^4-(b^4-c^4)*(b^2-c^2)*a^2-3*(b^2-c^2)^2*b^2*c^2 : :
X(49006) = 3*X(98)-X(9142) = 3*X(98)+X(48540) = X(9301)-3*X(44376) = 3*X(15055)-X(48957) = 3*X(48992)+X(49004)

The reciprocal parallelogic center of these triangles is X(4).

X(49006) lies on these lines: {3, 48974}, {5, 19140}, {6, 3613}, {30, 15364}, {74, 1141}, {98, 523}, {111, 9076}, {338, 5191}, {513, 49002}, {900, 45710}, {1576, 41254}, {1989, 38393}, {3566, 45723}, {4977, 48990}, {5916, 48995}, {5917, 48996}, {7669, 47285}, {9007, 49003}, {9140, 14559}, {9145, 38664}, {9215, 14610}, {9301, 44376}, {9479, 48982}, {12188, 40879}, {15055, 48957}, {15107, 46155}, {25423, 48992}, {28217, 48993}, {35357, 46512}

X(49006) = midpoint of X(i) and X(j) for these {i, j}: {74, 48988}, {9142, 48540}, {9145, 38664}, {12188, 40879}
X(49006) = reflection of X(48974) in X(3)
X(49006) = parallelogic center (2nd anti-Parry, T) for these triangles T: {orthic axes, Yiu tangents}
X(49006) = center of circle {{X(9145), X(38664), X(47290)}}
X(49006) = X(5)-of-2nd anti-Parry triangle
X(49006) = X(48974)-of-ABC-X3 reflections triangle
X(49006) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (98, 48540, 9142), (48986, 48987, 45723)


X(49007) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO REFLECTION

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

The reciprocal parallelogic center of these triangles is X(4).

X(49007) lies on these lines: {3, 48975}, {74, 1141}, {98, 20184}, {111, 13318}, {1510, 9142}, {6368, 48540}, {9019, 41404}, {9215, 13315}

X(49007) = parallelogic center (2nd anti-Parry, reflection)
X(49007) = X(48975)-of-ABC-X3 reflections triangle
X(49007) = X(54)-of-2nd anti-Parry triangle
X(49007) = reflection of X(48975) in X(3)


X(49008) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO 1st SCHIFFLER

Barycentrics    a^14-2*(b+c)*a^13-2*(b^2+c^2)*a^12+10*(b+c)*b*c*a^11+(11*b^4+11*c^4+2*b*c*(b^2-6*b*c+c^2))*a^10+2*(b+c)*(4*b^4+4*c^4-b*c*(16*b^2-17*b*c+16*c^2))*a^9-2*(16*b^6+16*c^6+(2*b^4+2*c^4-13*b*c*(b^2+c^2))*b*c)*a^8-2*(b+c)*(2*b^6+2*c^6-(18*b^4+18*c^4-b*c*(30*b^2-31*b*c+30*c^2))*b*c)*a^7+(35*b^8+35*c^8-(25*b^4+25*c^4-b*c*(2*b^2-15*b*c+2*c^2))*b^2*c^2)*a^6-2*(b^3-c^3)*(b^2-c^2)*(3*b^4+3*c^4+b*c*(11*b^2-13*b*c+11*c^2))*a^5-(b^2-c^2)^2*(14*b^6+14*c^6-(4*b^4+4*c^4-b*c*(25*b^2+2*b*c+25*c^2))*b*c)*a^4+2*(b^2-c^2)*(b-c)*(2*b^8+2*c^8+(5*b^6+5*c^6-b*c*(3*b^2+5*b*c+3*c^2)*(b^2-b*c+c^2))*b*c)*a^3+(b^2-c^2)^2*(b^8+c^8-(2*b^6+2*c^6-(15*b^4+15*c^4-b*c*(4*b^2+23*b*c+4*c^2))*b*c)*b*c)*a^2-6*(b^2-c^2)^3*(b-c)*b^3*c^3*a-3*(b^2-c^2)^4*(b-c)^2*b^2*c^2 : :

The reciprocal parallelogic center of these triangles is X(79).

X(49008) lies on these lines: {3, 48976}, {111, 23036}, {8702, 48540}, {9215, 23035}, {30200, 48993}

X(49008) = parallelogic center (2nd anti-Parry, 1st Schiffler)
X(49008) = X(48976)-of-ABC-X3 reflections triangle
X(49008) = X(10266)-of-2nd anti-Parry triangle
X(49008) = reflection of X(48976) in X(3)


X(49009) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO 1st TRI-SQUARES-CENTRAL

Barycentrics    (a^8-(5*b^4-7*b^2*c^2+5*c^4)*a^4+(b^2+c^2)*(6*b^4-11*b^2*c^2+6*c^4)*a^2-2*(b^4+5*b^2*c^2+c^4)*(b^2-c^2)^2)*a^2+2*(2*a^8-2*(b^2+c^2)*a^6-(b^4-4*b^2*c^2+c^4)*a^4+(b^4-c^4)*(b^2-c^2)*a^2-5*(b^2-c^2)^2*b^2*c^2)*S : :

The reciprocal parallelogic center of these triangles is X(13665).

X(49009) lies on these lines: {3, 48977}, {111, 13719}, {523, 48987}, {671, 32421}, {9215, 13718}, {45723, 49010}

X(49009) = parallelogic center (2nd anti-Parry, 1st tri-squares-central)
X(49009) = X(48977)-of-ABC-X3 reflections triangle
X(49009) = X(1327)-of-2nd anti-Parry triangle
X(49009) = reflection of X(48977) in X(3)


X(49010) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    (a^8-(5*b^4-7*b^2*c^2+5*c^4)*a^4+(b^2+c^2)*(6*b^4-11*b^2*c^2+6*c^4)*a^2-2*(b^4+5*b^2*c^2+c^4)*(b^2-c^2)^2)*a^2-2*(2*a^8-2*(b^2+c^2)*a^6-(b^4-4*b^2*c^2+c^4)*a^4+(b^4-c^4)*(b^2-c^2)*a^2-5*(b^2-c^2)^2*b^2*c^2)*S : :

The reciprocal parallelogic center of these triangles is X(13785).

X(49010) lies on these lines: {3, 48978}, {111, 13842}, {523, 48986}, {671, 32419}, {9215, 13841}, {45723, 49009}

X(49010) = parallelogic center (2nd anti-Parry, 2nd tri-squares-central)
X(49010) = X(48978)-of-ABC-X3 reflections triangle
X(49010) = X(1328)-of-2nd anti-Parry triangle
X(49010) = reflection of X(48978) in X(3)


X(49011) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-PARRY TO WALSMITH

Barycentrics    a^16-(b^2+c^2)*a^14+2*(3*b^4-7*b^2*c^2+3*c^4)*a^12-(3*b^2-5*c^2)*(5*b^2-3*c^2)*(b^2+c^2)*a^10+(3*b^8+3*c^8+(25*b^4-63*b^2*c^2+25*c^4)*b^2*c^2)*a^8+(b^2+c^2)*(15*b^8+15*c^8-(59*b^4-89*b^2*c^2+59*c^4)*b^2*c^2)*a^6-2*(b^2-c^2)^2*(5*b^8+5*c^8+b^2*c^2*(5*b^4-6*b^2*c^2+5*c^4))*a^4+(b^4-c^4)*(b^2-c^2)*(b^8+c^8+b^2*c^2*(9*b^4-14*b^2*c^2+9*c^4))*a^2-3*(b^4-c^4)^2*(b^2-c^2)^2*b^2*c^2 : :

The reciprocal parallelogic center of these triangles is X(125).

X(49011) lies on these lines: {3, 48979}, {74, 9076}, {98, 32228}, {111, 32313}, {512, 48988}, {525, 48984}, {542, 42007}, {690, 9142}, {1499, 22265}, {9215, 32312}, {9517, 48540}, {18907, 34319}, {19140, 43977}

X(49011) = parallelogic center (2nd anti-Parry, Walsmith)
X(49011) = X(48979)-of-ABC-X3 reflections triangle
X(49011) = X(67)-of-2nd anti-Parry triangle
X(49011) = reflection of X(48979) in X(3)

leftri

Centers related to 3rd- and 4th- anti-tri-squares-central triangles: X(49012)-X(49101)

rightri

This preamble and centers X(49012)-X(49101) were contributed by César Eliud Lozada, May 18, 2022.

3rd- and 4th- anti-tri-squares-central triangles were introduced in the preamble just before X(45345).


X(49012) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL AND 1st AURIGA

Barycentrics    -4*((3*a-b-c)*S-a*((b+c)*a-b^2-c^2))*S*sqrt(R*(4*R+r))+a^2*(a+b+c)*(-a+b+c)*(a^2+4*S+b^2+c^2) : :

X(49012) lies on these lines: {4, 12486}, {55, 45719}, {193, 12452}, {492, 5601}, {3068, 5597}, {5598, 26514}, {5599, 26361}, {5860, 8199}, {8186, 26300}, {8190, 26306}, {8196, 26330}, {8197, 26444}, {8198, 26339}, {8200, 26468}, {8201, 49020}, {8202, 49022}, {9834, 48476}, {11252, 49038}, {11366, 26369}, {11384, 26375}, {11492, 26512}, {11493, 26324}, {11822, 26294}, {11837, 26429}, {11843, 26441}, {11861, 26314}, {11863, 26449}, {11865, 26490}, {11867, 26485}, {11869, 26479}, {11871, 26473}, {11873, 26355}, {11875, 49028}, {11877, 49030}, {11879, 49032}, {11881, 26520}, {11883, 26519}, {12179, 49040}, {12345, 49042}, {12365, 49044}, {12415, 49052}, {12454, 49060}, {12456, 49062}, {12458, 49054}, {12460, 49068}, {12462, 48692}, {12464, 49076}, {12466, 49050}, {12468, 49080}, {12470, 49036}, {12472, 49034}, {12474, 49082}, {12476, 49084}, {12478, 49046}, {12480, 49088}, {12482, 49090}, {12484, 49048}, {13176, 49096}, {13208, 49098}, {13228, 48711}, {13229, 49100}, {13682, 15682}, {13802, 49092}, {13944, 49026}, {16121, 49070}, {18495, 49016}, {18539, 45379}, {18955, 26435}, {19007, 26456}, {19008, 26462}, {22668, 49058}, {22669, 49064}, {22670, 49066}, {22671, 49074}, {26420, 45353}, {26496, 45589}, {26505, 45588}, {26516, 45620}, {26517, 45625}, {26518, 45627}, {32146, 49086}, {32265, 49094}, {32360, 49072}, {35778, 49018}, {35781, 39660}, {39880, 49056}, {44594, 44600}, {44595, 44601}, {45420, 45431}, {45522, 45534}, {45524, 45535}

X(49012) = homothetic center (3rd anti-tri-squares-central, 1st Auriga)
X(49012) = X(45365)-of-these triangles: {3rd anti-tri-squares-central, 1st Auriga}
X(49012) = {X(55), X(45719)}-harmonic conjugate of X(49014)


X(49013) = HOMOTHETIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL AND 1st AURIGA

Barycentrics    -4*(-(3*a-b-c)*S-a*((b+c)*a-b^2-c^2))*S*sqrt(R*(4*R+r))+a^2*(a+b+c)*(-a+b+c)*(a^2-4*S+b^2+c^2) : :

X(49013) lies on these lines: {4, 12484}, {55, 45720}, {193, 12452}, {491, 5601}, {3069, 5597}, {5598, 26515}, {5599, 26362}, {5861, 8198}, {8186, 26301}, {8190, 26307}, {8196, 26331}, {8197, 26445}, {8199, 26340}, {8200, 26469}, {8201, 49021}, {8202, 49023}, {8982, 11843}, {9834, 48477}, {11252, 49039}, {11366, 26370}, {11384, 26376}, {11492, 26513}, {11493, 26325}, {11822, 26295}, {11837, 26430}, {11861, 26315}, {11863, 26450}, {11865, 26491}, {11867, 26486}, {11869, 26480}, {11871, 26474}, {11873, 26356}, {11875, 49029}, {11877, 49031}, {11879, 49033}, {11881, 26525}, {11883, 26524}, {12179, 49041}, {12345, 49043}, {12365, 49045}, {12415, 49053}, {12454, 49061}, {12456, 49063}, {12458, 49055}, {12460, 49069}, {12462, 48693}, {12464, 49077}, {12466, 49051}, {12468, 49081}, {12470, 49037}, {12472, 49035}, {12474, 49083}, {12476, 49085}, {12478, 49047}, {12480, 49089}, {12482, 49091}, {12486, 49049}, {13176, 49097}, {13208, 49099}, {13228, 48712}, {13229, 49101}, {13682, 49093}, {13802, 15682}, {13890, 49027}, {16121, 49071}, {18495, 49017}, {18955, 26436}, {19007, 26457}, {19008, 26463}, {22668, 49059}, {22669, 49065}, {22670, 49067}, {22671, 49075}, {26421, 45353}, {26438, 45379}, {26497, 45589}, {26506, 45588}, {26521, 45620}, {26522, 45625}, {26523, 45627}, {32146, 49087}, {32265, 49095}, {32360, 49073}, {35778, 39661}, {35781, 49019}, {39880, 49057}, {44596, 44600}, {44597, 44601}, {45421, 45430}, {45523, 45535}, {45525, 45534}

X(49013) = homothetic center (4th anti-tri-squares-central, 1st Auriga)
X(49013) = X(45366)-of-1st Auriga triangle
X(49013) = {X(55), X(45720)}-harmonic conjugate of X(49015)


X(49014) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL AND 2nd AURIGA

Barycentrics    4*((3*a-b-c)*S-a*((b+c)*a-b^2-c^2))*S*sqrt(R*(4*R+r))+a^2*(a+b+c)*(-a+b+c)*(a^2+4*S+b^2+c^2) : :

X(49014) lies on these lines: {4, 12487}, {55, 45719}, {193, 12453}, {492, 5602}, {3068, 5598}, {5597, 26514}, {5600, 26361}, {5860, 8206}, {8187, 26300}, {8191, 26306}, {8203, 26330}, {8204, 26444}, {8205, 26339}, {8207, 26468}, {8208, 49020}, {8209, 49022}, {9835, 48476}, {11253, 49038}, {11367, 26369}, {11385, 26375}, {11492, 26324}, {11493, 26512}, {11823, 26294}, {11838, 26429}, {11844, 26441}, {11862, 26314}, {11864, 26449}, {11866, 26490}, {11868, 26485}, {11870, 26479}, {11872, 26473}, {11874, 26355}, {11876, 49028}, {11878, 49030}, {11880, 49032}, {11882, 26520}, {11884, 26519}, {12180, 49040}, {12346, 49042}, {12366, 49044}, {12416, 49052}, {12455, 49060}, {12457, 49062}, {12459, 49054}, {12461, 49068}, {12463, 48692}, {12465, 49076}, {12467, 49050}, {12469, 49080}, {12471, 49036}, {12473, 49034}, {12475, 49082}, {12477, 49084}, {12479, 49046}, {12481, 49088}, {12483, 49090}, {12485, 49048}, {13177, 49096}, {13209, 49098}, {13230, 48711}, {13231, 49100}, {13683, 15682}, {13803, 49092}, {13945, 49026}, {16122, 49070}, {18497, 49016}, {18539, 45380}, {18956, 26435}, {19009, 26456}, {19010, 26462}, {22672, 49058}, {22673, 49064}, {22674, 49066}, {22675, 49074}, {26396, 45354}, {26496, 45591}, {26505, 45590}, {26516, 45621}, {26517, 45626}, {26518, 45628}, {32147, 49086}, {32266, 49094}, {32361, 49072}, {35779, 39660}, {35780, 49018}, {39881, 49056}, {44594, 44602}, {44595, 44603}, {45420, 45433}, {45522, 45536}, {45524, 45537}

X(49014) = homothetic center (3rd anti-tri-squares-central, 2nd Auriga)
X(49014) = X(45368)-of-these triangles: {3rd anti-tri-squares-central, 2nd Auriga}
X(49014) = {X(55), X(45719)}-harmonic conjugate of X(49012)


X(49015) = HOMOTHETIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL AND 2nd AURIGA

Barycentrics    4*(-(3*a-b-c)*S-a*((b+c)*a-b^2-c^2))*S*sqrt(R*(4*R+r))+a^2*(a+b+c)*(-a+b+c)*(a^2-4*S+b^2+c^2) : :

X(49015) lies on these lines: {4, 12485}, {55, 45720}, {193, 12453}, {491, 5602}, {3069, 5598}, {5597, 26515}, {5600, 26362}, {5861, 8205}, {8187, 26301}, {8191, 26307}, {8203, 26331}, {8204, 26445}, {8206, 26340}, {8207, 26469}, {8208, 49021}, {8209, 49023}, {8982, 11844}, {9835, 48477}, {11253, 49039}, {11367, 26370}, {11385, 26376}, {11492, 26325}, {11493, 26513}, {11823, 26295}, {11838, 26430}, {11862, 26315}, {11864, 26450}, {11866, 26491}, {11868, 26486}, {11870, 26480}, {11872, 26474}, {11874, 26356}, {11876, 49029}, {11878, 49031}, {11880, 49033}, {11882, 26525}, {11884, 26524}, {12180, 49041}, {12346, 49043}, {12366, 49045}, {12416, 49053}, {12455, 49061}, {12457, 49063}, {12459, 49055}, {12461, 49069}, {12463, 48693}, {12465, 49077}, {12467, 49051}, {12469, 49081}, {12471, 49037}, {12473, 49035}, {12475, 49083}, {12477, 49085}, {12479, 49047}, {12481, 49089}, {12483, 49091}, {12487, 49049}, {13177, 49097}, {13209, 49099}, {13230, 48712}, {13231, 49101}, {13683, 49093}, {13803, 15682}, {13891, 49027}, {16122, 49071}, {18497, 49017}, {18956, 26436}, {19009, 26457}, {19010, 26463}, {22672, 49059}, {22673, 49065}, {22674, 49067}, {22675, 49075}, {26397, 45354}, {26438, 45380}, {26497, 45591}, {26506, 45590}, {26521, 45621}, {26522, 45626}, {26523, 45628}, {32147, 49087}, {32266, 49095}, {32361, 49073}, {35779, 49019}, {35780, 39661}, {39881, 49057}, {44596, 44602}, {44597, 44603}, {45421, 45432}, {45523, 45537}, {45525, 45536}

X(49015) = homothetic center (4th anti-tri-squares-central, 2nd Auriga)
X(49015) = X(45367)-of-2nd Auriga triangle
X(49015) = {X(55), X(45720)}-harmonic conjugate of X(49013)


X(49016) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL AND EHRMANN-MID

Barycentrics    (5*a^4+2*(b^2+c^2)*a^2-7*(b^2-c^2)^2)*S+2*a^6+4*b^2*c^2*a^2-2*(b^4-c^4)*(b^2-c^2) : :
X(49016) = 3*X(381)-X(45384)

X(49016) lies on these lines: {4, 488}, {5, 26516}, {20, 22819}, {30, 26361}, {113, 49050}, {193, 3818}, {381, 3068}, {382, 26294}, {546, 5875}, {1478, 26473}, {1479, 26479}, {1539, 49044}, {3091, 26441}, {3146, 45522}, {3583, 26355}, {3585, 26435}, {3843, 49028}, {3845, 5860}, {3854, 45524}, {6564, 13651}, {6565, 44595}, {9818, 26306}, {9955, 26369}, {10113, 49098}, {10895, 49030}, {10896, 49032}, {12611, 49068}, {12699, 26444}, {13665, 26462}, {13785, 26456}, {14881, 49082}, {15682, 22806}, {18480, 45719}, {18483, 49078}, {18491, 26512}, {18492, 26300}, {18495, 49012}, {18497, 49014}, {18500, 26314}, {18502, 26429}, {18507, 26449}, {18516, 26490}, {18517, 26485}, {18520, 49020}, {18522, 49022}, {18525, 26514}, {18542, 26520}, {18544, 26519}, {18761, 26324}, {18762, 49026}, {19160, 49046}, {19163, 49100}, {22505, 49040}, {22515, 49096}, {22566, 49042}, {22596, 49048}, {22660, 49052}, {22681, 49058}, {22791, 49060}, {22792, 49062}, {22793, 49054}, {22794, 49064}, {22795, 49066}, {22796, 49034}, {22797, 49036}, {22798, 49070}, {22799, 48692}, {22800, 49074}, {22801, 49076}, {22802, 49080}, {22803, 49084}, {22804, 49088}, {22805, 49090}, {22807, 49092}, {22938, 48711}, {23249, 45375}, {26396, 45355}, {26420, 45356}, {26496, 45593}, {26505, 45592}, {26517, 45630}, {26518, 45631}, {31412, 48660}, {32271, 49094}, {32364, 49072}, {35786, 49018}, {35787, 39660}, {39884, 49056}, {41099, 45420}, {43407, 45377}

X(49016) = homothetic center (3rd anti-tri-squares-central, Ehrmann-mid)
X(49016) = X(45384)-of-these triangles: {3rd anti-tri-squares-central, Ehrmann-mid}
X(49016) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 26468, 49038), (5, 48476, 26516), (381, 18539, 3068), (546, 49086, 26330), (3818, 3839, 49017)


X(49017) = HOMOTHETIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL AND EHRMANN-MID

Barycentrics    -(5*a^4+2*(b^2+c^2)*a^2-7*(b^2-c^2)^2)*S+2*a^6+4*b^2*c^2*a^2-2*(b^4-c^4)*(b^2-c^2) : :
X(49017) = 3*X(381)-X(45385)

X(49017) lies on these lines: {4, 487}, {5, 26521}, {20, 22820}, {30, 26362}, {113, 49051}, {193, 3818}, {381, 3069}, {382, 26295}, {546, 5874}, {1478, 26474}, {1479, 26480}, {1539, 49045}, {3091, 8982}, {3146, 45523}, {3583, 26356}, {3585, 26436}, {3843, 49029}, {3845, 5861}, {3854, 45525}, {6564, 44596}, {6565, 13770}, {9818, 26307}, {9955, 26370}, {10113, 49099}, {10895, 49031}, {10896, 49033}, {12611, 49069}, {12699, 26445}, {13665, 26463}, {13785, 26457}, {14881, 49083}, {15682, 22807}, {18480, 45720}, {18483, 49079}, {18491, 26513}, {18492, 26301}, {18495, 49013}, {18497, 49015}, {18500, 26315}, {18502, 26430}, {18507, 26450}, {18516, 26491}, {18517, 26486}, {18520, 49021}, {18522, 49023}, {18525, 26515}, {18538, 49027}, {18542, 26525}, {18544, 26524}, {18761, 26325}, {19160, 49047}, {19163, 49101}, {22505, 49041}, {22515, 49097}, {22566, 49043}, {22625, 49049}, {22660, 49053}, {22681, 49059}, {22791, 49061}, {22792, 49063}, {22793, 49055}, {22794, 49065}, {22795, 49067}, {22796, 49035}, {22797, 49037}, {22798, 49071}, {22799, 48693}, {22800, 49075}, {22801, 49077}, {22802, 49081}, {22803, 49085}, {22804, 49089}, {22805, 49091}, {22806, 49093}, {22938, 48712}, {23259, 45376}, {26397, 45355}, {26421, 45356}, {26497, 45593}, {26506, 45592}, {26522, 45630}, {26523, 45631}, {32271, 49095}, {32364, 49073}, {35786, 39661}, {35787, 49019}, {39884, 49057}, {41099, 45421}, {42561, 48659}, {43408, 45378}

X(49017) = homothetic center (4th anti-tri-squares-central, Ehrmann-mid)
X(49017) = X(45385)-of-Ehrmann-mid triangle
X(49017) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 26469, 49039), (5, 48477, 26521), (381, 26438, 3069), (546, 49087, 26331), (3818, 3839, 49016)


X(49018) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL AND 1st KENMOTU-FREE-VERTICES

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

X(49018) lies on these lines: {4, 22646}, {6, 39660}, {193, 637}, {230, 3312}, {371, 12124}, {372, 631}, {485, 492}, {3070, 9974}, {3103, 7757}, {5093, 7745}, {5319, 6418}, {5860, 35794}, {6200, 26294}, {6278, 6564}, {6396, 26516}, {6419, 26462}, {6420, 44595}, {6560, 26441}, {6565, 26330}, {9733, 44647}, {10576, 26361}, {10783, 35820}, {12375, 49098}, {12965, 49088}, {15682, 35872}, {18539, 23251}, {19117, 39679}, {23267, 35830}, {26300, 35774}, {26306, 35776}, {26314, 35782}, {26324, 35784}, {26339, 35792}, {26355, 35808}, {26369, 35762}, {26375, 35764}, {26396, 45357}, {26420, 45359}, {26429, 35766}, {26435, 35768}, {26444, 35788}, {26449, 35790}, {26456, 35770}, {26473, 35802}, {26479, 35800}, {26485, 35798}, {26490, 35796}, {26496, 45601}, {26505, 45599}, {26512, 35772}, {26514, 35810}, {26517, 45640}, {26518, 45642}, {26519, 35818}, {26520, 35816}, {31411, 45488}, {31412, 49049}, {35610, 49054}, {35641, 45719}, {35698, 49042}, {35753, 49034}, {35769, 49032}, {35778, 49012}, {35780, 49014}, {35786, 49016}, {35804, 49020}, {35806, 49022}, {35809, 49030}, {35814, 49026}, {35824, 49040}, {35826, 49044}, {35828, 49046}, {35834, 49050}, {35836, 49052}, {35838, 49058}, {35842, 49060}, {35844, 49062}, {35846, 49064}, {35848, 49066}, {35850, 49036}, {35852, 49068}, {35854, 49070}, {35856, 48692}, {35858, 49072}, {35860, 49074}, {35862, 49076}, {35864, 49080}, {35866, 49082}, {35868, 49084}, {35870, 49090}, {35874, 49092}, {35876, 49094}, {35878, 49096}, {35880, 49100}, {35882, 48711}, {45524, 45564}

X(49018) = homothetic center (3rd anti-tri-squares-central, 1st Kenmotu-free-vertices)
X(49018) = X(45574)-of-these triangles: {3rd anti-tri-squares-central, 1st Kenmotu-free-vertices}
X(49018) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 49028, 39660), (1587, 35840, 39661), (3068, 45522, 5418), (5093, 7745, 49019), (44594, 49038, 371)


X(49019) = HOMOTHETIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL AND 2nd KENMOTU-FREE-VERTICES

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

X(49019) lies on these lines: {4, 22617}, {6, 39661}, {193, 638}, {230, 3311}, {371, 631}, {372, 12123}, {486, 491}, {3071, 9975}, {3102, 7757}, {5093, 7745}, {5319, 6417}, {5861, 35795}, {6200, 26521}, {6281, 6565}, {6396, 26295}, {6419, 44596}, {6420, 26457}, {6561, 8982}, {6564, 26331}, {9732, 44648}, {10577, 26362}, {10784, 35821}, {12376, 49099}, {12971, 49089}, {15682, 35875}, {19116, 39648}, {23261, 26438}, {23273, 35831}, {26301, 35775}, {26307, 35777}, {26315, 35783}, {26325, 35785}, {26340, 35793}, {26356, 35809}, {26370, 35763}, {26376, 35765}, {26397, 45360}, {26421, 45358}, {26430, 35767}, {26436, 35769}, {26445, 35789}, {26450, 35791}, {26463, 35771}, {26474, 35803}, {26480, 35801}, {26486, 35799}, {26491, 35797}, {26497, 45600}, {26506, 45602}, {26513, 35773}, {26515, 35811}, {26522, 45641}, {26523, 45643}, {26524, 35819}, {26525, 35817}, {35611, 49055}, {35642, 45720}, {35699, 49043}, {35754, 49035}, {35768, 49033}, {35779, 49015}, {35781, 49013}, {35787, 49017}, {35805, 49023}, {35807, 49021}, {35808, 49031}, {35815, 49027}, {35825, 49041}, {35827, 49045}, {35829, 49047}, {35835, 49051}, {35837, 49053}, {35839, 49059}, {35843, 49061}, {35845, 49063}, {35847, 49067}, {35849, 49065}, {35851, 49037}, {35853, 49069}, {35855, 49071}, {35857, 48693}, {35859, 49073}, {35861, 49075}, {35863, 49077}, {35865, 49081}, {35867, 49083}, {35869, 49085}, {35871, 49091}, {35873, 49093}, {35877, 49095}, {35879, 49097}, {35881, 49101}, {35883, 48712}, {42561, 49048}, {45525, 45565}

X(49019) = homothetic center (4th anti-tri-squares-central, 2nd Kenmotu-free-vertices)
X(49019) = X(45575)-of-2nd Kenmotu-free-vertices triangle
X(49019) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 49029, 39661), (1588, 35841, 39660), (3069, 45523, 5420), (5093, 7745, 49018), (44597, 49039, 372)


X(49020) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL AND LUCAS(+1) HOMOTHETIC

Barycentrics    3*a^8+12*(b^2+c^2)*a^6-2*(17*b^4+32*b^2*c^2+17*c^4)*a^4+4*(5*a^4-10*(b^2+c^2)*a^2+b^4-22*b^2*c^2+c^4)*S*a^2+4*(b^2+c^2)*(5*b^4-12*b^2*c^2+5*c^4)*a^2-(b^4-c^4)^2 : :

X(49020) lies on these lines: {4, 13004}, {193, 12590}, {393, 493}, {492, 6462}, {5860, 8218}, {6459, 45478}, {6461, 49022}, {8188, 26300}, {8194, 26306}, {8201, 49012}, {8208, 49014}, {8210, 26514}, {8212, 26330}, {8214, 26444}, {8216, 26339}, {8220, 26468}, {8222, 26361}, {9838, 48476}, {10669, 49038}, {10875, 26314}, {10945, 26490}, {10951, 26485}, {11377, 26369}, {11394, 26375}, {11503, 26512}, {11828, 26294}, {11840, 26429}, {11846, 26441}, {11907, 26449}, {11930, 26479}, {11932, 26473}, {11947, 26355}, {11949, 49028}, {11951, 49030}, {11953, 49032}, {11955, 26520}, {11957, 26519}, {12186, 49040}, {12352, 49042}, {12377, 49044}, {12426, 49052}, {12440, 45719}, {12636, 49060}, {12741, 49068}, {12765, 48692}, {12861, 49076}, {12894, 49050}, {12986, 49080}, {12988, 49036}, {12990, 49034}, {12992, 49082}, {12994, 49084}, {12996, 49046}, {12998, 49088}, {13000, 49090}, {13002, 49048}, {13184, 49096}, {13215, 49098}, {13275, 48711}, {13298, 49100}, {13697, 15682}, {13817, 49092}, {13956, 49026}, {16161, 49070}, {18245, 49062}, {18520, 49016}, {18539, 45381}, {18963, 26435}, {19031, 26456}, {19032, 26462}, {22709, 49058}, {22761, 26324}, {22841, 49054}, {22863, 49064}, {22908, 49066}, {22963, 49074}, {26396, 45362}, {26420, 45364}, {26505, 45604}, {26516, 45623}, {26517, 45645}, {26518, 45647}, {32177, 49086}, {32295, 49094}, {32388, 49072}, {35804, 49018}, {35807, 39660}, {39895, 49056}, {44594, 44627}, {44595, 44628}, {45420, 45465}, {45522, 45569}, {45524, 45567}

X(49020) = homothetic center (3rd anti-tri-squares-central, Lucas(+1) homothetic)
X(49020) = X(45607)-of-these triangles: {3rd anti-tri-squares-central, Lucas(+1) homothetic}


X(49021) = HOMOTHETIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL AND LUCAS(+1) HOMOTHETIC

Barycentrics    -5*a^8+20*(b^2+c^2)*a^6-2*(13*b^4+24*b^2*c^2+13*c^4)*a^4+4*(3*a^4-6*(b^2+c^2)*a^2+7*b^4-10*b^2*c^2+7*c^4)*S*a^2+12*(b^2+c^2)*(b^4+c^4)*a^2-(b^4-c^4)^2 : :

X(49021) lies on these lines: {4, 13002}, {193, 12590}, {491, 6462}, {493, 3069}, {5861, 8216}, {6461, 49023}, {8188, 26301}, {8194, 26307}, {8201, 49013}, {8208, 49015}, {8210, 26515}, {8212, 26331}, {8214, 26445}, {8218, 26340}, {8220, 26469}, {8222, 26362}, {8982, 11846}, {9838, 48477}, {10669, 49039}, {10875, 26315}, {10945, 26491}, {10951, 26486}, {11377, 26370}, {11394, 26376}, {11503, 26513}, {11828, 26295}, {11840, 26430}, {11907, 26450}, {11930, 26480}, {11932, 26474}, {11947, 26356}, {11949, 49029}, {11951, 49031}, {11953, 49033}, {11955, 26525}, {11957, 26524}, {12186, 49041}, {12352, 49043}, {12377, 49045}, {12426, 49053}, {12440, 45720}, {12636, 49061}, {12741, 49069}, {12765, 48693}, {12861, 49077}, {12894, 49051}, {12986, 49081}, {12988, 49037}, {12990, 49035}, {12992, 49083}, {12994, 49085}, {12996, 49047}, {12998, 49089}, {13000, 49091}, {13004, 49049}, {13184, 49097}, {13215, 49099}, {13275, 48712}, {13298, 49101}, {13697, 49093}, {13817, 15682}, {13899, 49027}, {16161, 49071}, {18245, 49063}, {18520, 49017}, {18963, 26436}, {19031, 26457}, {19032, 26463}, {22709, 49059}, {22761, 26325}, {22841, 49055}, {22863, 49065}, {22908, 49067}, {22963, 49075}, {26397, 45362}, {26421, 45364}, {26438, 45381}, {26506, 45604}, {26521, 45623}, {26522, 45645}, {26523, 45647}, {32177, 49087}, {32295, 49095}, {32388, 49073}, {35804, 39661}, {35807, 49019}, {39895, 49057}, {44596, 44627}, {44597, 44628}, {45421, 45467}, {45523, 45567}, {45525, 45569}

X(49021) = homothetic center (4th anti-tri-squares-central, Lucas(+1) homothetic)
X(49021) = X(45606)-of-Lucas(+1) homothetic triangle


X(49022) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL AND LUCAS(-1) HOMOTHETIC

Barycentrics    -5*a^8+20*(b^2+c^2)*a^6-2*(13*b^4+24*b^2*c^2+13*c^4)*a^4-4*(3*a^4-6*(b^2+c^2)*a^2+7*b^4-10*b^2*c^2+7*c^4)*S*a^2+12*(b^2+c^2)*(b^4+c^4)*a^2-(b^4-c^4)^2 : :

X(49022) lies on these lines: {4, 13005}, {193, 12591}, {492, 6463}, {494, 3068}, {5860, 8219}, {6461, 49020}, {8189, 26300}, {8195, 26306}, {8202, 49012}, {8209, 49014}, {8211, 26514}, {8213, 26330}, {8215, 26444}, {8217, 26339}, {8221, 26468}, {8223, 26361}, {10673, 49038}, {10876, 26314}, {10946, 26490}, {10952, 26485}, {11378, 26369}, {11395, 26375}, {11504, 26512}, {11829, 26294}, {11841, 26429}, {11847, 26441}, {11908, 26449}, {11931, 26479}, {11933, 26473}, {11948, 26355}, {11950, 49028}, {11952, 49030}, {11954, 49032}, {11956, 26520}, {11958, 26519}, {12187, 49040}, {12353, 49042}, {12378, 49044}, {12427, 49052}, {12441, 45719}, {12637, 49060}, {12742, 49068}, {12766, 48692}, {12862, 49076}, {12895, 49050}, {12987, 49080}, {12989, 49036}, {12991, 49034}, {12993, 49082}, {12995, 49084}, {12997, 49046}, {12999, 49088}, {13001, 49090}, {13003, 49048}, {13185, 49096}, {13216, 49098}, {13276, 48711}, {13299, 49100}, {13698, 15682}, {13818, 49092}, {13957, 49026}, {16162, 49070}, {18246, 49062}, {18522, 49016}, {18539, 45382}, {18964, 26435}, {19033, 26456}, {19034, 26462}, {22710, 49058}, {22762, 26324}, {22842, 49054}, {22864, 49064}, {22909, 49066}, {22964, 49074}, {26396, 45361}, {26420, 45363}, {26496, 45603}, {26516, 45624}, {26517, 45644}, {26518, 45646}, {32178, 49086}, {32296, 49094}, {32389, 49072}, {35805, 39660}, {35806, 49018}, {39896, 49056}, {44594, 44629}, {44595, 44630}, {45420, 45466}, {45522, 45566}, {45524, 45568}

X(49022) = homothetic center (3rd anti-tri-squares-central, Lucas(-1) homothetic)
X(49022) = X(45605)-of-these triangles: {3rd anti-tri-squares-central, Lucas(-1) homothetic}


X(49023) = HOMOTHETIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL AND LUCAS(-1) HOMOTHETIC

Barycentrics    3*a^8+12*(b^2+c^2)*a^6-2*(17*b^4+32*b^2*c^2+17*c^4)*a^4-4*(5*a^4-10*(b^2+c^2)*a^2+b^4-22*b^2*c^2+c^4)*S*a^2+4*(b^2+c^2)*(5*b^4-12*b^2*c^2+5*c^4)*a^2-(b^4-c^4)^2 : :

X(49023) lies on these lines: {4, 13003}, {193, 12591}, {393, 494}, {491, 6463}, {5861, 8217}, {6460, 45479}, {6461, 49021}, {8189, 26301}, {8195, 26307}, {8202, 49013}, {8209, 49015}, {8211, 26515}, {8213, 26331}, {8215, 26445}, {8219, 26340}, {8221, 26469}, {8223, 26362}, {8982, 11847}, {10673, 49039}, {10876, 26315}, {10946, 26491}, {10952, 26486}, {11378, 26370}, {11395, 26376}, {11504, 26513}, {11829, 26295}, {11841, 26430}, {11908, 26450}, {11931, 26480}, {11933, 26474}, {11948, 26356}, {11950, 49029}, {11952, 49031}, {11954, 49033}, {11956, 26525}, {11958, 26524}, {12187, 49041}, {12353, 49043}, {12378, 49045}, {12427, 49053}, {12441, 45720}, {12637, 49061}, {12742, 49069}, {12766, 48693}, {12862, 49077}, {12895, 49051}, {12987, 49081}, {12989, 49037}, {12991, 49035}, {12993, 49083}, {12995, 49085}, {12997, 49047}, {12999, 49089}, {13001, 49091}, {13005, 49049}, {13185, 49097}, {13216, 49099}, {13276, 48712}, {13299, 49101}, {13698, 49093}, {13818, 15682}, {13900, 49027}, {16162, 49071}, {18246, 49063}, {18522, 49017}, {18964, 26436}, {19033, 26457}, {19034, 26463}, {22710, 49059}, {22762, 26325}, {22842, 49055}, {22864, 49065}, {22909, 49067}, {22964, 49075}, {26397, 45361}, {26421, 45363}, {26438, 45382}, {26497, 45603}, {26521, 45624}, {26522, 45644}, {26523, 45646}, {32178, 49087}, {32296, 49095}, {32389, 49073}, {35805, 49019}, {35806, 39661}, {39896, 49057}, {44596, 44629}, {44597, 44630}, {45421, 45464}, {45523, 45568}, {45525, 45566}

X(49023) = homothetic center (4th anti-tri-squares-central, Lucas(-1) homothetic)
X(49023) = X(45608)-of-Lucas(-1) homothetic triangle


X(49024) = PERSPECTOR OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL AND INNER-SQUARES

Barycentrics    (5*a^6-43*(b^2+c^2)*a^4+(11*b^4-94*b^2*c^2+11*c^4)*a^2+11*(b^4-c^4)*(b^2-c^2))*S+7*a^8-4*(b^2+c^2)*a^6-2*(13*b^4+32*b^2*c^2+13*c^4)*a^4+4*(b^2+c^2)*(7*b^4-16*b^2*c^2+7*c^4)*a^2-(5*b^4-14*b^2*c^2+5*c^4)*(b^2-c^2)^2 : :

X(49024) lies on these lines: {485, 26361}

X(49024) = perspector (3rd anti-tri-squares-central, inner-squares)


X(49025) = PERSPECTOR OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL AND OUTER-SQUARES

Barycentrics    -(5*a^6-43*(b^2+c^2)*a^4+(11*b^4-94*b^2*c^2+11*c^4)*a^2+11*(b^4-c^4)*(b^2-c^2))*S+7*a^8-4*(b^2+c^2)*a^6-2*(13*b^4+32*b^2*c^2+13*c^4)*a^4+4*(b^2+c^2)*(7*b^4-16*b^2*c^2+7*c^4)*a^2-(5*b^4-14*b^2*c^2+5*c^4)*(b^2-c^2)^2 : :

X(49025) lies on these lines: {486, 26362}

X(49025) = perspector (4th anti-tri-squares-central, outer-squares)


X(49026) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL AND 4th TRI-SQUARES-CENTRAL

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

X(49026) lies on these lines: {2, 6}, {4, 13880}, {372, 26330}, {486, 48476}, {7584, 26516}, {13849, 49092}, {13933, 49048}, {13935, 26294}, {13936, 26369}, {13937, 26375}, {13938, 26429}, {13939, 26441}, {13940, 26512}, {13942, 26300}, {13943, 26306}, {13944, 49012}, {13945, 49014}, {13946, 26314}, {13947, 26444}, {13948, 26449}, {13951, 26468}, {13952, 26490}, {13953, 26485}, {13954, 26479}, {13955, 26473}, {13956, 49020}, {13957, 49022}, {13958, 26355}, {13959, 26514}, {13961, 49028}, {13962, 49030}, {13963, 49032}, {13964, 26520}, {13965, 26519}, {13966, 49038}, {13967, 49040}, {13968, 49042}, {13969, 49044}, {13970, 49052}, {13971, 45719}, {13973, 49060}, {13974, 49062}, {13975, 49054}, {13976, 49068}, {13977, 48692}, {13978, 49076}, {13979, 49050}, {13980, 49080}, {13981, 49036}, {13982, 49034}, {13983, 49082}, {13984, 49084}, {13985, 49046}, {13986, 49088}, {13987, 49090}, {13988, 15682}, {13989, 49096}, {13990, 49098}, {13991, 48711}, {13992, 49100}, {13993, 40287}, {16149, 49070}, {18539, 45385}, {18762, 49016}, {18966, 26435}, {19146, 49056}, {22721, 49058}, {22764, 26324}, {22877, 49064}, {22922, 49066}, {22977, 49074}, {26288, 43291}, {26396, 45366}, {26420, 45367}, {26496, 45606}, {26505, 45608}, {26517, 45651}, {26518, 45653}, {32304, 49094}, {32400, 49072}, {35813, 38426}, {35814, 49018}, {45522, 45577}, {45524, 45575}

X(49026) = homothetic center (3rd anti-tri-squares-central, 4th tri-squares-central)
X(49026) = X(49027)-of-these triangles: {3rd anti-tri-squares-central, 4th tri-squares-central}
X(49026) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 26456, 3068), (2, 45484, 32785), (230, 5860, 3068), (615, 44595, 26361), (13847, 13950, 3069), (13941, 45487, 3069), (26361, 44595, 3068)


X(49027) = HOMOTHETIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL AND 3rd TRI-SQUARES-CENTRAL

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

X(49027) lies on these lines: {2, 6}, {4, 13921}, {371, 26331}, {485, 48477}, {7583, 26521}, {8976, 26469}, {8980, 49041}, {8981, 49039}, {8982, 13886}, {8983, 45720}, {8987, 49063}, {8988, 49069}, {8991, 49081}, {8992, 49083}, {8993, 49085}, {8994, 49045}, {8995, 49089}, {8997, 49097}, {8998, 49099}, {9540, 26295}, {13848, 15682}, {13879, 49049}, {13883, 26370}, {13884, 26376}, {13885, 26430}, {13887, 26513}, {13888, 26301}, {13889, 26307}, {13890, 49013}, {13891, 49015}, {13892, 26315}, {13893, 26445}, {13894, 26450}, {13895, 26491}, {13896, 26486}, {13897, 26480}, {13898, 26474}, {13899, 49021}, {13900, 49023}, {13901, 26356}, {13902, 26515}, {13903, 49029}, {13904, 49031}, {13905, 49033}, {13906, 26525}, {13907, 26524}, {13908, 49043}, {13909, 49053}, {13911, 49061}, {13912, 49055}, {13913, 48693}, {13914, 49077}, {13915, 49051}, {13916, 49037}, {13917, 49035}, {13918, 49047}, {13919, 49091}, {13920, 49093}, {13922, 48712}, {13923, 49101}, {13925, 40286}, {16148, 49071}, {18538, 49017}, {18965, 26436}, {19145, 49057}, {22720, 49059}, {22763, 26325}, {22876, 49065}, {22921, 49067}, {22976, 49075}, {26289, 43291}, {26397, 45365}, {26421, 45368}, {26438, 45384}, {26497, 45607}, {26506, 45605}, {26522, 45650}, {26523, 45652}, {32303, 49095}, {32399, 49073}, {35812, 38425}, {35815, 49019}, {45523, 45576}, {45525, 45574}

X(49027) = homothetic center (4th anti-tri-squares-central, 3rd tri-squares-central)
X(49027) = X(49026)-of-3rd tri-squares-central triangle
X(49027) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 26463, 3069), (2, 45485, 32786), (230, 5861, 3069), (590, 44596, 26362), (8972, 45486, 3068), (8974, 13846, 3068), (26362, 44596, 3069)


X(49028) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL AND X3-ABC REFLECTIONS

Barycentrics    -2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*S+a^2*(a^4-4*(b^2+c^2)*a^2+3*b^4-2*b^2*c^2+3*c^4) : :
X(49028) = 3*X(381)-2*X(6214) = X(11825)-3*X(35822) = X(26441)-3*X(45420) = 3*X(32787)-2*X(43120)

X(49028) lies on these lines: {2, 12314}, {3, 1587}, {4, 193}, {5, 492}, {6, 39660}, {20, 12313}, {30, 26441}, {52, 44637}, {140, 45522}, {155, 45478}, {195, 49088}, {230, 372}, {355, 49078}, {371, 12961}, {381, 5860}, {382, 5871}, {399, 49098}, {427, 13439}, {485, 9733}, {488, 9752}, {511, 3070}, {517, 26300}, {524, 45862}, {550, 45524}, {576, 3071}, {590, 9739}, {637, 34380}, {999, 26435}, {1160, 13665}, {1352, 45440}, {1353, 45406}, {1482, 45719}, {1585, 41588}, {1588, 5093}, {1598, 26375}, {1656, 26361}, {3060, 6400}, {3093, 10665}, {3095, 13647}, {3167, 5200}, {3295, 26355}, {3311, 18907}, {3312, 5305}, {3629, 14233}, {3843, 49016}, {3933, 37342}, {5050, 7581}, {5102, 23261}, {5254, 35840}, {5491, 10840}, {5611, 14814}, {5615, 14813}, {5790, 26444}, {5864, 42249}, {5865, 42248}, {5870, 39899}, {5874, 45375}, {6278, 45438}, {6290, 9766}, {6417, 26462}, {6418, 26456}, {6459, 22810}, {6515, 32588}, {6560, 9732}, {6811, 43133}, {7388, 18583}, {7389, 48876}, {7517, 26306}, {7582, 11482}, {7745, 35841}, {8960, 45498}, {9301, 26314}, {9654, 26479}, {9669, 26473}, {9738, 42259}, {10246, 26369}, {10247, 26514}, {10620, 49044}, {10679, 26518}, {10680, 26517}, {11477, 23251}, {11825, 35822}, {11842, 26429}, {11849, 26512}, {11875, 49012}, {11876, 49014}, {11911, 26449}, {11928, 26490}, {11929, 26485}, {11949, 49020}, {11950, 49022}, {12000, 26520}, {12001, 26519}, {12017, 36701}, {12188, 49040}, {12296, 33456}, {12323, 14853}, {12331, 48711}, {12355, 49042}, {12645, 49060}, {12684, 49062}, {12702, 49054}, {12747, 49068}, {12773, 48692}, {12872, 49076}, {12902, 49050}, {12974, 31454}, {12975, 41946}, {13019, 44665}, {13093, 49080}, {13102, 49036}, {13103, 49034}, {13108, 49082}, {13111, 49084}, {13115, 49046}, {13126, 49090}, {13188, 49096}, {13310, 49100}, {13713, 15682}, {13749, 31670}, {13836, 49092}, {13961, 49026}, {15765, 20425}, {16150, 49070}, {16628, 49064}, {16629, 49066}, {18585, 20426}, {19117, 45411}, {20423, 45441}, {21737, 23267}, {22728, 49058}, {22765, 26324}, {22979, 49074}, {23249, 44456}, {26396, 45369}, {26420, 45370}, {26496, 45610}, {26505, 45609}, {32306, 49094}, {32402, 49072}, {32515, 33435}, {32787, 43120}, {36657, 45376}, {37517, 42284}, {42252, 47068}, {42253, 47066}, {45554, 45861}

X(49028) = reflection of X(3) in X(7583)
X(49028) = homothetic center (3rd anti-tri-squares-central, X3-ABC reflections)
X(49028) = X(6214)-of-anti-Ehrmann-mid triangle
X(49028) = X(7583)-of-these triangles: {3rd anti-tri-squares-central, X3-ABC reflections}
X(49028) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 193, 49086), (4, 1351, 49029), (4, 12222, 49087), (4, 49049, 5921), (4, 49086, 18539), (1351, 12602, 4), (3068, 26294, 26516), (3068, 49038, 3), (5860, 26330, 26468), (8960, 45498, 49104), (26294, 26516, 3), (26330, 26468, 381), (26355, 49030, 3295), (26435, 49032, 999), (26516, 49038, 26294), (39660, 49018, 6)


X(49029) = HOMOTHETIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL AND X3-ABC REFLECTIONS

Barycentrics    2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*S+a^2*(a^4-4*(b^2+c^2)*a^2+3*b^4-2*b^2*c^2+3*c^4) : :
X(49029) = 3*X(381)-2*X(6215) = X(8982)-3*X(45421) = X(11824)-3*X(35823) = 3*X(32788)-2*X(43121)

X(49029) lies on these lines: {2, 12313}, {3, 1588}, {4, 193}, {5, 491}, {6, 39661}, {20, 12314}, {30, 8982}, {52, 44638}, {140, 45523}, {141, 45870}, {155, 45479}, {195, 49089}, {230, 371}, {355, 49079}, {372, 12966}, {381, 5861}, {382, 5870}, {399, 49099}, {427, 13428}, {486, 9732}, {487, 9752}, {511, 3071}, {517, 26301}, {524, 45863}, {550, 45525}, {576, 3070}, {615, 9738}, {638, 34380}, {999, 26436}, {1161, 13785}, {1352, 45441}, {1353, 45407}, {1482, 45720}, {1586, 41588}, {1587, 5093}, {1598, 26376}, {1656, 26362}, {3060, 6239}, {3092, 10666}, {3095, 13766}, {3295, 26356}, {3311, 5305}, {3312, 18907}, {3629, 14230}, {3843, 49017}, {3933, 37343}, {5050, 7582}, {5102, 23251}, {5254, 35841}, {5490, 10839}, {5611, 14813}, {5615, 14814}, {5790, 26445}, {5864, 42247}, {5865, 42246}, {5871, 39899}, {5875, 45376}, {6281, 45439}, {6289, 9766}, {6417, 26463}, {6418, 26457}, {6460, 22809}, {6515, 32587}, {6561, 9733}, {6813, 43134}, {7388, 48876}, {7389, 18583}, {7517, 26307}, {7581, 11482}, {7745, 35840}, {8780, 19219}, {9301, 26315}, {9654, 26480}, {9669, 26474}, {9739, 42258}, {10246, 26370}, {10247, 26515}, {10620, 49045}, {10679, 26523}, {10680, 26522}, {10983, 21736}, {11477, 23261}, {11824, 35823}, {11842, 26430}, {11849, 26513}, {11875, 49013}, {11876, 49015}, {11911, 26450}, {11928, 26491}, {11929, 26486}, {11949, 49021}, {11950, 49023}, {12000, 26525}, {12001, 26524}, {12017, 36703}, {12188, 49041}, {12297, 33457}, {12322, 14853}, {12331, 48712}, {12355, 49043}, {12645, 49061}, {12684, 49063}, {12702, 49055}, {12747, 49069}, {12773, 48693}, {12872, 49077}, {12902, 49051}, {12974, 41945}, {13020, 44665}, {13093, 49081}, {13102, 49037}, {13103, 49035}, {13108, 49083}, {13111, 49085}, {13115, 49047}, {13126, 49091}, {13188, 49097}, {13310, 49101}, {13713, 49093}, {13748, 31670}, {13836, 15682}, {13903, 49027}, {15765, 20426}, {16150, 49071}, {16628, 49065}, {16629, 49067}, {18585, 20425}, {19116, 45410}, {20423, 45440}, {22728, 49059}, {22765, 26325}, {22979, 49075}, {23259, 44456}, {23273, 33878}, {26397, 45369}, {26421, 45370}, {26497, 45610}, {26506, 45609}, {32306, 49095}, {32402, 49073}, {32515, 33434}, {32788, 43121}, {36658, 45375}, {37517, 42283}, {42250, 47068}, {42251, 47066}, {45499, 49103}, {45555, 45860}

X(49029) = reflection of X(3) in X(7584)
X(49029) = homothetic center (4th anti-tri-squares-central, X3-ABC reflections)
X(49029) = X(6215)-of-anti-Ehrmann-mid triangle
X(49029) = X(7584)-of-X3-ABC reflections triangle
X(49029) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 193, 49087), (4, 1351, 49028), (4, 12221, 49086), (4, 49048, 5921), (4, 49087, 26438), (1351, 12601, 4), (3069, 26295, 26521), (3069, 49039, 3), (5861, 26331, 26469), (7582, 21737, 5050), (26295, 26521, 3), (26331, 26469, 381), (26356, 49031, 3295), (26436, 49033, 999), (26521, 49039, 26295), (39661, 49019, 6)


X(49030) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL AND INNER-YFF

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

X(49030) lies on these lines: {1, 1336}, {3, 26435}, {4, 10068}, {5, 26473}, {12, 26468}, {35, 26294}, {55, 49038}, {56, 26516}, {193, 611}, {230, 3297}, {388, 26441}, {492, 3085}, {495, 26479}, {498, 26361}, {1124, 44595}, {1335, 44594}, {1478, 48476}, {1479, 26330}, {1709, 49062}, {3295, 26355}, {3299, 26456}, {3301, 26462}, {5119, 49054}, {5218, 45522}, {5860, 10041}, {9654, 18539}, {10037, 26306}, {10038, 26314}, {10039, 26444}, {10040, 26339}, {10053, 49040}, {10054, 49042}, {10055, 49052}, {10057, 49068}, {10058, 48692}, {10059, 49076}, {10060, 49080}, {10061, 49036}, {10062, 49034}, {10063, 49082}, {10064, 49084}, {10065, 49044}, {10066, 49088}, {10067, 49048}, {10084, 13886}, {10086, 49096}, {10087, 48711}, {10088, 49098}, {10523, 26490}, {10801, 26429}, {10895, 49016}, {10954, 26485}, {11398, 26375}, {11507, 26512}, {11877, 49012}, {11878, 49014}, {11912, 26449}, {11951, 49020}, {11952, 49022}, {12647, 49060}, {12903, 49050}, {13116, 49046}, {13128, 49090}, {13311, 49100}, {13714, 15682}, {13715, 14241}, {13837, 49092}, {13962, 49026}, {16152, 49070}, {18988, 35945}, {22729, 49058}, {22766, 26324}, {22884, 49064}, {22929, 49066}, {22980, 49074}, {26396, 45371}, {26420, 45372}, {26496, 45612}, {26505, 45611}, {31397, 49078}, {32307, 49094}, {32403, 49072}, {35808, 39660}, {35809, 49018}, {39900, 49056}, {45420, 45491}, {45524, 45581}

X(49030) = homothetic center (3rd anti-tri-squares-central, inner-Yff)
X(49030) = X(45650)-of-these triangles: {3rd anti-tri-squares-central, inner-Yff}
X(49030) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 3068, 49032), (495, 49086, 26479), (3068, 26514, 26517), (3068, 26520, 45719), (3295, 49028, 26355)


X(49031) = HOMOTHETIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL AND INNER-YFF

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

X(49031) lies on these lines: {1, 1123}, {3, 26436}, {4, 10067}, {5, 26474}, {12, 26469}, {35, 26295}, {55, 49039}, {56, 26521}, {193, 611}, {230, 3298}, {388, 8982}, {491, 3085}, {495, 26480}, {498, 26362}, {1124, 44597}, {1335, 44596}, {1478, 48477}, {1479, 26331}, {1709, 49063}, {3295, 26356}, {3299, 26457}, {3301, 26463}, {5119, 49055}, {5218, 45523}, {5861, 10040}, {9654, 26438}, {10037, 26307}, {10038, 26315}, {10039, 26445}, {10041, 26340}, {10053, 49041}, {10054, 49043}, {10055, 49053}, {10057, 49069}, {10058, 48693}, {10059, 49077}, {10060, 49081}, {10061, 49037}, {10062, 49035}, {10063, 49083}, {10064, 49085}, {10065, 49045}, {10066, 49089}, {10068, 49049}, {10083, 13939}, {10086, 49097}, {10087, 48712}, {10088, 49099}, {10523, 26491}, {10801, 26430}, {10895, 49017}, {10954, 26486}, {11398, 26376}, {11507, 26513}, {11877, 49013}, {11878, 49015}, {11912, 26450}, {11951, 49021}, {11952, 49023}, {12647, 49061}, {12903, 49051}, {13116, 49047}, {13128, 49091}, {13311, 49101}, {13714, 49093}, {13837, 15682}, {13838, 14226}, {13904, 49027}, {16152, 49071}, {18989, 35944}, {22729, 49059}, {22766, 26325}, {22884, 49065}, {22929, 49067}, {22980, 49075}, {26397, 45371}, {26421, 45372}, {26497, 45612}, {26506, 45611}, {31397, 49079}, {32307, 49095}, {32403, 49073}, {35808, 49019}, {35809, 39661}, {39900, 49057}, {45421, 45490}, {45525, 45580}

X(49031) = homothetic center (4th anti-tri-squares-central, inner-Yff)
X(49031) = X(45651)-of-inner-Yff triangle
X(49031) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 3069, 49033), (495, 49087, 26480), (3069, 26515, 26522), (3069, 26525, 45720), (3295, 49029, 26356)


X(49032) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL AND OUTER-YFF

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

X(49032) lies on these lines: {1, 1336}, {3, 26355}, {4, 10084}, {5, 26479}, {11, 26468}, {36, 26294}, {46, 49054}, {55, 26516}, {56, 49038}, {193, 613}, {230, 3298}, {492, 3086}, {496, 26473}, {497, 26441}, {499, 26361}, {999, 26435}, {1124, 44594}, {1210, 49078}, {1335, 44595}, {1478, 26330}, {1479, 48476}, {1737, 26444}, {3299, 26462}, {3301, 26456}, {5860, 10049}, {7288, 45522}, {9669, 18539}, {10046, 26306}, {10047, 26314}, {10048, 26339}, {10068, 13886}, {10069, 49040}, {10070, 49042}, {10071, 49052}, {10073, 49068}, {10074, 48692}, {10075, 49076}, {10076, 49080}, {10077, 49036}, {10078, 49034}, {10079, 49082}, {10080, 49084}, {10081, 49044}, {10082, 49088}, {10083, 49048}, {10085, 49062}, {10089, 49096}, {10090, 48711}, {10091, 49098}, {10523, 26485}, {10573, 49060}, {10802, 26429}, {10896, 49016}, {10948, 26490}, {11399, 26375}, {11508, 26512}, {11879, 49012}, {11880, 49014}, {11913, 26449}, {11953, 49020}, {11954, 49022}, {12904, 49050}, {13082, 35945}, {13117, 49046}, {13129, 49090}, {13312, 49100}, {13714, 14241}, {13715, 15682}, {13838, 49092}, {13963, 49026}, {16153, 49070}, {22730, 49058}, {22767, 26324}, {22885, 49064}, {22930, 49066}, {22981, 49074}, {26396, 45373}, {26420, 45374}, {26496, 45614}, {26505, 45613}, {32308, 49094}, {32404, 49072}, {35768, 39660}, {35769, 49018}, {39901, 49056}, {45420, 45493}, {45524, 45583}

X(49032) = homothetic center (3rd anti-tri-squares-central, outer-Yff)
X(49032) = X(45652)-of-these triangles: {3rd anti-tri-squares-central, outer-Yff}
X(49032) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 3068, 49030), (496, 49086, 26473), (613, 14986, 49033), (999, 49028, 26435), (3068, 26514, 26518), (3068, 26519, 45719)


X(49033) = HOMOTHETIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL AND OUTER-YFF

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

X(49033) lies on these lines: {1, 1123}, {3, 26356}, {4, 10083}, {5, 26480}, {11, 26469}, {36, 26295}, {46, 49055}, {55, 26521}, {56, 49039}, {193, 613}, {230, 3297}, {491, 3086}, {496, 26474}, {497, 8982}, {499, 26362}, {999, 26436}, {1124, 44596}, {1210, 49079}, {1335, 44597}, {1478, 26331}, {1479, 48477}, {1737, 26445}, {3299, 26463}, {3301, 26457}, {5861, 10048}, {7288, 45523}, {9669, 26438}, {10046, 26307}, {10047, 26315}, {10049, 26340}, {10067, 13939}, {10069, 49041}, {10070, 49043}, {10071, 49053}, {10073, 49069}, {10074, 48693}, {10075, 49077}, {10076, 49081}, {10077, 49037}, {10078, 49035}, {10079, 49083}, {10080, 49085}, {10081, 49045}, {10082, 49089}, {10084, 49049}, {10085, 49063}, {10089, 49097}, {10090, 48712}, {10091, 49099}, {10523, 26486}, {10573, 49061}, {10802, 26430}, {10896, 49017}, {10948, 26491}, {11399, 26376}, {11508, 26513}, {11879, 49013}, {11880, 49015}, {11913, 26450}, {11953, 49021}, {11954, 49023}, {12904, 49051}, {13081, 35944}, {13117, 49047}, {13129, 49091}, {13312, 49101}, {13715, 49093}, {13837, 14226}, {13838, 15682}, {13905, 49027}, {16153, 49071}, {22730, 49059}, {22767, 26325}, {22885, 49065}, {22930, 49067}, {22981, 49075}, {26397, 45373}, {26421, 45374}, {26497, 45614}, {26506, 45613}, {32308, 49095}, {32404, 49073}, {35768, 49019}, {35769, 39661}, {39901, 49057}, {45421, 45492}, {45525, 45582}

X(49033) = homothetic center (4th anti-tri-squares-central, outer-Yff)
X(49033) = X(45653)-of-outer-Yff triangle
X(49033) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 3069, 49031), (496, 49087, 26474), (613, 14986, 49032), (999, 49029, 26436), (3069, 26515, 26523), (3069, 26524, 45720)


X(49034) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO 1st ALTINTAS-ISODYNAMIC

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

The reciprocal orthologic center of these triangles is X(4).

X(49034) lies on these lines: {4, 22634}, {13, 3068}, {146, 148}, {492, 616}, {530, 5860}, {531, 49042}, {618, 26361}, {5473, 26294}, {5478, 26330}, {5617, 26468}, {6270, 26339}, {6306, 21156}, {6770, 26441}, {6771, 26516}, {7975, 26514}, {9901, 26300}, {9916, 26306}, {9982, 26314}, {10062, 49030}, {10078, 49032}, {11705, 26369}, {12142, 26375}, {12205, 26429}, {12337, 26512}, {12472, 49012}, {12473, 49014}, {12781, 26444}, {12793, 26449}, {12922, 26490}, {12932, 26485}, {12942, 26479}, {12952, 26473}, {12990, 49020}, {12991, 49022}, {13076, 26355}, {13103, 49028}, {13105, 26520}, {13107, 26519}, {13982, 49026}, {15682, 36340}, {18539, 48655}, {18587, 49064}, {18974, 26435}, {19073, 26456}, {19074, 26462}, {22773, 26324}, {22796, 49016}, {26396, 48456}, {26420, 48457}, {35753, 49018}, {35754, 39660}, {41022, 48476}, {41023, 49040}, {45522, 48722}, {45524, 48723}, {49038, 49066}

X(49034) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {1st Altintas-isodynamic, Bankoff, 3rd Fermat-Dao, 7th Fermat-Dao, 11th Fermat-Dao, 15th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi, 1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi, 1st half-diamonds-central, 1st isodynamic-Dao, 3rd isodynamic-Dao, Largest-circumscribed-equilateral, 1st Lemoine-Dao, outer-Napoleon}
X(49034) = X(13)-of-3rd anti-tri-squares-central triangle
X(49034) = X(22601)-of-1st half-squares triangle, when ABC is acute


X(49035) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO 1st ALTINTAS-ISODYNAMIC

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

The reciprocal orthologic center of these triangles is X(4).

X(49035) lies on these lines: {4, 22605}, {13, 3069}, {146, 148}, {491, 616}, {530, 5861}, {531, 49043}, {618, 26362}, {5473, 26295}, {5478, 26331}, {5617, 26469}, {6268, 26340}, {6302, 21156}, {6770, 8982}, {6771, 26521}, {7975, 26515}, {9901, 26301}, {9916, 26307}, {9982, 26315}, {10062, 49031}, {10078, 49033}, {11705, 26370}, {12142, 26376}, {12205, 26430}, {12337, 26513}, {12472, 49013}, {12473, 49015}, {12781, 26445}, {12793, 26450}, {12922, 26491}, {12932, 26486}, {12942, 26480}, {12952, 26474}, {12990, 49021}, {12991, 49023}, {13076, 26356}, {13103, 49029}, {13105, 26525}, {13107, 26524}, {13917, 49027}, {15682, 36342}, {18586, 49065}, {18974, 26436}, {19073, 26457}, {19074, 26463}, {22773, 26325}, {22796, 49017}, {26397, 48456}, {26421, 48457}, {26438, 48655}, {35753, 39661}, {35754, 49019}, {41022, 48477}, {41023, 49041}, {45523, 48723}, {45525, 48722}, {49039, 49067}

X(49035) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {1st Altintas-isodynamic, Bankoff, 3rd Fermat-Dao, 7th Fermat-Dao, 11th Fermat-Dao, 15th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi, 1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi, 1st half-diamonds-central, 1st isodynamic-Dao, 3rd isodynamic-Dao, Largest-circumscribed-equilateral, 1st Lemoine-Dao, outer-Napoleon}
X(49035) = X(22603)-of-2nd half-squares triangle, when ABC is obtuse


X(49036) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO 2nd ALTINTAS-ISODYNAMIC

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

The reciprocal orthologic center of these triangles is X(4).

X(49036) lies on these lines: {4, 22635}, {14, 3068}, {146, 148}, {492, 617}, {530, 49042}, {531, 5860}, {619, 26361}, {5474, 26294}, {5479, 26330}, {5613, 26468}, {6271, 26339}, {6307, 21157}, {6773, 26441}, {6774, 26516}, {7974, 26514}, {9900, 26300}, {9915, 26306}, {9981, 26314}, {10061, 49030}, {10077, 49032}, {11706, 26369}, {12141, 26375}, {12204, 26429}, {12336, 26512}, {12470, 49012}, {12471, 49014}, {12780, 26444}, {12792, 26449}, {12921, 26490}, {12931, 26485}, {12941, 26479}, {12951, 26473}, {12988, 49020}, {12989, 49022}, {13075, 26355}, {13102, 49028}, {13104, 26520}, {13106, 26519}, {13981, 49026}, {15682, 36341}, {18539, 48656}, {18586, 49066}, {18975, 26435}, {19075, 26456}, {19076, 26462}, {22774, 26324}, {22797, 49016}, {26396, 48458}, {26420, 48459}, {35850, 49018}, {35851, 39660}, {41022, 49040}, {41023, 48476}, {45522, 48724}, {45524, 48725}, {49038, 49064}

X(49036) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {2nd Altintas-isodynamic, 4th Fermat-Dao, 8th Fermat-Dao, 12th Fermat-Dao, 16th Fermat-Dao, 1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi, 3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi, 2nd half-diamonds-central, 2nd isodynamic-Dao, 4th isodynamic-Dao, 2nd Lemoine-Dao, inner-Napoleon}
X(49036) = X(14)-of-3rd anti-tri-squares-central triangle
X(49036) = X(22603)-of-1st half-squares triangle, when ABC is acute


X(49037) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO 2nd ALTINTAS-ISODYNAMIC

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

The reciprocal orthologic center of these triangles is X(4).

X(49037) lies on these lines: {4, 22606}, {14, 3069}, {146, 148}, {491, 617}, {530, 49043}, {531, 5861}, {619, 26362}, {5474, 26295}, {5479, 26331}, {5613, 26469}, {6269, 26340}, {6303, 21157}, {6773, 8982}, {6774, 26521}, {7974, 26515}, {9900, 26301}, {9915, 26307}, {9981, 26315}, {10061, 49031}, {10077, 49033}, {11706, 26370}, {12141, 26376}, {12204, 26430}, {12336, 26513}, {12470, 49013}, {12471, 49015}, {12780, 26445}, {12792, 26450}, {12921, 26491}, {12931, 26486}, {12941, 26480}, {12951, 26474}, {12988, 49021}, {12989, 49023}, {13075, 26356}, {13102, 49029}, {13104, 26525}, {13106, 26524}, {13916, 49027}, {15682, 36343}, {18587, 49067}, {18975, 26436}, {19075, 26457}, {19076, 26463}, {22774, 26325}, {22797, 49017}, {26397, 48458}, {26421, 48459}, {26438, 48656}, {35850, 39661}, {35851, 49019}, {41022, 49041}, {41023, 48477}, {45523, 48725}, {45525, 48724}, {49039, 49065}

X(49037) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {2nd Altintas-isodynamic, 4th Fermat-Dao, 8th Fermat-Dao, 12th Fermat-Dao, 16th Fermat-Dao, 1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi, 3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi, 2nd half-diamonds-central, 2nd isodynamic-Dao, 4th isodynamic-Dao, 2nd Lemoine-Dao, inner-Napoleon}
X(49037) = X(22601)-of-2nd half-squares triangle, when ABC is obtuse


X(49038) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO ANTI-ASCELLA

Barycentrics    (3*a^4-2*(b^2+c^2)*a^2-(b^2-c^2)^2)*S+2*a^2*((b^2+c^2)*a^2-b^4-c^4) : :
X(49038) = 3*X(2)-4*X(9739) = 3*X(376)-2*X(9732) = 3*X(591)-2*X(14233) = 5*X(3522)-4*X(9738) = 7*X(3523)-8*X(43141) = 3*X(5860)-X(48476) = 3*X(5860)-2*X(49086) = X(5870)-3*X(26288) = 9*X(10304)-8*X(43144) = 3*X(11179)-2*X(44472)

The reciprocal orthologic center of these triangles is X(1593).

X(49038) lies on these lines: {1, 26355}, {2, 9739}, {3, 1587}, {4, 488}, {5, 26330}, {20, 185}, {30, 1160}, {40, 26300}, {55, 49030}, {56, 49032}, {230, 1152}, {355, 26444}, {371, 12124}, {372, 5286}, {376, 9732}, {382, 18539}, {485, 45498}, {487, 44365}, {515, 49078}, {517, 45719}, {542, 49094}, {550, 1161}, {591, 14233}, {638, 3926}, {952, 48692}, {971, 49062}, {1007, 6813}, {1154, 49088}, {1217, 11474}, {1350, 42259}, {1351, 6459}, {1385, 26369}, {1478, 26479}, {1479, 26473}, {1482, 26514}, {1588, 45488}, {2782, 49040}, {3069, 12314}, {3070, 12305}, {3127, 11090}, {3311, 26462}, {3312, 26456}, {3398, 26429}, {3522, 9738}, {3523, 43141}, {3529, 49048}, {3564, 49056}, {3767, 6566}, {5200, 5408}, {5663, 49044}, {6000, 49080}, {6201, 37343}, {6231, 39809}, {6400, 26376}, {6560, 11825}, {7387, 26306}, {7581, 43119}, {7585, 43120}, {8416, 15048}, {9541, 45489}, {9737, 12222}, {9766, 13749}, {9821, 26314}, {10304, 43144}, {10519, 11293}, {10525, 26490}, {10526, 26485}, {10669, 49020}, {10673, 49022}, {10679, 26520}, {10680, 26519}, {11179, 44472}, {11248, 26512}, {11249, 26324}, {11251, 26449}, {11252, 49012}, {11253, 49014}, {11294, 14853}, {11477, 42258}, {11824, 35944}, {11917, 42215}, {12221, 23698}, {12257, 35947}, {12313, 42638}, {12602, 31412}, {13886, 49104}, {13935, 45578}, {13966, 49026}, {14241, 49114}, {17702, 49050}, {18400, 49072}, {26396, 48460}, {26420, 48461}, {31400, 45565}, {31670, 42859}, {36701, 43118}, {36709, 43140}, {43121, 43511}, {43510, 49103}, {44665, 49052}, {45472, 45862}, {49034, 49066}, {49036, 49064}, {49046, 49100}, {49058, 49084}

X(49038) = midpoint of X(i) and X(j) for these {i, j}: {45719, 49054}, {48692, 48711}, {49040, 49096}, {49044, 49098}, {49046, 49100}
X(49038) = reflection of X(i) in X(j) for these (i, j): (4, 9733), (1161, 550), (31670, 42859), (48476, 49086), (49039, 20)
X(49038) = anticomplement of the anticomplement of X(9739)
X(49038) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {anti-Ascella, anti-Atik, 1st anti-circumperp, anti-Conway, 2nd anti-Conway, 3rd anti-Euler, 4th anti-Euler, anti-excenters-reflections, 2nd anti-extouch, anti-Honsberger, anti-Hutson intouch, anti-incircle-circles, anti-inverse-in-incircle, 6th anti-mixtilinear, 1st anti-Sharygin, anti-tangential-midarc, anti-Ursa minor, anti-Wasat, circumorthic, Ehrmann-side, Ehrmann-vertex, 2nd Ehrmann, 2nd Euler, 1st excosine, extangents, intangents, 1st Kenmotu diagonals, 2nd Kenmotu diagonals, Kosnita, Lucas antipodal tangents, Lucas(-1) antipodal tangents, orthic, submedial, tangential, inner tri-equilateral, outer tri-equilateral, Trinh}
X(49038) = center of circle {{X(48692), X(48711), X(49040)}}
X(49038) = X(3)-of-3rd anti-tri-squares-central triangle
X(49038) = X(9733)-of-anti-Euler triangle
X(49038) = X(32498)-of-1st half-squares triangle, when ABC is acute
X(49038) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 3068, 26516), (3, 49028, 3068), (4, 492, 26468), (4, 12510, 490), (4, 26468, 49016), (20, 193, 26441), (20, 43133, 6776), (371, 12124, 35945), (371, 49018, 44594), (372, 39660, 44595), (3068, 26294, 3), (5860, 48476, 49086), (6560, 11825, 21737), (6813, 12323, 26469), (11824, 42261, 35944), (26294, 49028, 26516), (26330, 26361, 5), (26355, 26435, 1)


X(49039) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO ANTI-ASCELLA

Barycentrics    -(3*a^4-2*(b^2+c^2)*a^2-(b^2-c^2)^2)*S+2*a^2*((b^2+c^2)*a^2-b^4-c^4) : :
X(49039) = 3*X(2)-4*X(9738) = 3*X(376)-2*X(9733) = 3*X(1991)-2*X(14230) = 5*X(3522)-4*X(9739) = 7*X(3523)-8*X(43144) = 3*X(5861)-X(48477) = 3*X(5861)-2*X(49087) = X(5871)-3*X(26289) = 9*X(10304)-8*X(43141) = 3*X(11179)-2*X(44471)

The reciprocal orthologic center of these triangles is X(1593).

X(49039) lies on these lines: {1, 26356}, {2, 9738}, {3, 1588}, {4, 487}, {5, 26331}, {20, 185}, {30, 1161}, {40, 26301}, {55, 49031}, {56, 49033}, {230, 1151}, {355, 26445}, {371, 5286}, {372, 12123}, {376, 9733}, {382, 26438}, {393, 26875}, {486, 45499}, {488, 44364}, {515, 49079}, {517, 45720}, {542, 49095}, {550, 1160}, {637, 3926}, {952, 48693}, {971, 49063}, {1007, 6811}, {1154, 49089}, {1217, 11473}, {1350, 42258}, {1351, 6460}, {1385, 26370}, {1478, 26480}, {1479, 26474}, {1482, 26515}, {1587, 45489}, {1991, 14230}, {2782, 49041}, {3068, 12313}, {3071, 12306}, {3128, 11091}, {3311, 26463}, {3312, 26457}, {3398, 26430}, {3522, 9739}, {3523, 43144}, {3529, 49049}, {3564, 49057}, {3767, 6567}, {5663, 49045}, {6000, 49081}, {6202, 37342}, {6230, 39809}, {6239, 26375}, {6561, 11824}, {7387, 26307}, {7582, 43118}, {7586, 43121}, {8396, 15048}, {8981, 49027}, {9540, 45579}, {9737, 12221}, {9766, 13748}, {9821, 26315}, {10304, 43141}, {10519, 11294}, {10525, 26491}, {10526, 26486}, {10669, 49021}, {10673, 49023}, {10679, 26525}, {10680, 26524}, {11179, 44471}, {11248, 26513}, {11249, 26325}, {11251, 26450}, {11252, 49013}, {11253, 49015}, {11293, 14853}, {11477, 42259}, {11825, 35945}, {11916, 42216}, {12222, 23698}, {12256, 35946}, {12314, 42637}, {12601, 42561}, {13939, 49103}, {14226, 49115}, {17702, 49051}, {18400, 49073}, {26397, 48460}, {26421, 48461}, {31400, 45564}, {31670, 42858}, {36703, 43119}, {36714, 43137}, {43120, 43512}, {43509, 49104}, {44665, 49053}, {45473, 45863}, {49035, 49067}, {49037, 49065}, {49047, 49101}, {49059, 49085}

X(49039) = midpoint of X(i) and X(j) for these {i, j}: {45720, 49055}, {48693, 48712}, {49041, 49097}, {49045, 49099}, {49047, 49101}
X(49039) = reflection of X(i) in X(j) for these (i, j): (4, 9732), (1160, 550), (31670, 42858), (48477, 49087), (49038, 20)
X(49039) = anticomplement of the anticomplement of X(9738)
X(49039) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {anti-Ascella, anti-Atik, 1st anti-circumperp, anti-Conway, 2nd anti-Conway, 3rd anti-Euler, 4th anti-Euler, anti-excenters-reflections, 2nd anti-extouch, anti-Honsberger, anti-Hutson intouch, anti-incircle-circles, anti-inverse-in-incircle, 6th anti-mixtilinear, 1st anti-Sharygin, anti-tangential-midarc, anti-Ursa minor, anti-Wasat, circumorthic, Ehrmann-side, Ehrmann-vertex, 2nd Ehrmann, 2nd Euler, 1st excosine, extangents, intangents, 1st Kenmotu diagonals, 2nd Kenmotu diagonals, Kosnita, Lucas antipodal tangents, Lucas(-1) antipodal tangents, orthic, submedial, tangential, inner tri-equilateral, outer tri-equilateral, Trinh}
X(49039) = center of circle {{X(48693), X(48712), X(49041)}}
X(49039) = X(9732)-of-anti-Euler triangle
X(49039) = X(12313)-of-3rd anti-tri-squares-central triangle
X(49039) = X(32498)-of-2nd half-squares triangle, when ABC is obtuse
X(49039) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 3069, 26521), (3, 49029, 3069), (4, 491, 26469), (4, 12509, 489), (4, 26469, 49017), (20, 193, 8982), (20, 43134, 6776), (371, 39661, 44596), (372, 12123, 35944), (372, 49019, 44597), (3069, 26295, 3), (5861, 48477, 49087), (6811, 12322, 26468), (11825, 42260, 35945), (26295, 49029, 26521), (26331, 26362, 5), (26356, 26436, 1)


X(49040) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO 1st ANTI-BROCARD

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

The reciprocal orthologic center of these triangles is X(5999).

X(49040) lies on the circumcircle of 3rd anti-tri-squares-central triangle and these lines: {4, 32495}, {30, 49042}, {98, 3068}, {99, 26294}, {114, 26361}, {115, 26330}, {147, 492}, {193, 1916}, {542, 5860}, {690, 49044}, {2782, 49038}, {2783, 48711}, {2784, 49078}, {2787, 48692}, {2794, 48476}, {2799, 49046}, {3023, 26435}, {3027, 26355}, {5999, 44365}, {6033, 26468}, {6227, 26339}, {7970, 26514}, {9860, 26300}, {9861, 26306}, {9862, 26314}, {9864, 26444}, {10053, 49030}, {10069, 49032}, {11177, 45420}, {11710, 26369}, {12042, 26516}, {12131, 26375}, {12176, 26429}, {12178, 26512}, {12179, 49012}, {12180, 49014}, {12181, 26449}, {12182, 26490}, {12183, 26485}, {12184, 26479}, {12185, 26473}, {12186, 49020}, {12187, 49022}, {12188, 49028}, {12189, 26520}, {12190, 26519}, {13967, 49026}, {18539, 38744}, {19055, 26456}, {19056, 26462}, {22504, 26324}, {22505, 49016}, {26396, 48462}, {26420, 48463}, {35824, 49018}, {35825, 39660}, {39809, 48477}, {41022, 49036}, {41023, 49034}, {45522, 48726}, {45524, 48727}, {49084, 49086}

X(49040) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard}
X(49040) = X(98)-of-3rd anti-tri-squares-central triangle
X(49040) = reflection of X(i) in X(j) for these (i, j): (49041, 5984), (49096, 49038)


X(49041) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO 1st ANTI-BROCARD

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

The reciprocal orthologic center of these triangles is X(5999).

X(49041) lies on the circumcircle of 4th anti-tri-squares-central triangle and these lines: {4, 32492}, {30, 49043}, {98, 3069}, {99, 26295}, {114, 26362}, {115, 26331}, {147, 491}, {193, 1916}, {542, 5861}, {690, 49045}, {2782, 49039}, {2783, 48712}, {2784, 49079}, {2787, 48693}, {2794, 48477}, {2799, 49047}, {3023, 26436}, {3027, 26356}, {5999, 44364}, {6033, 26469}, {6226, 26340}, {7970, 26515}, {8980, 49027}, {8982, 9862}, {9860, 26301}, {9861, 26307}, {9864, 26445}, {10053, 49031}, {10069, 49033}, {11177, 45421}, {11710, 26370}, {12042, 26521}, {12131, 26376}, {12176, 26430}, {12178, 26513}, {12179, 49013}, {12180, 49015}, {12181, 26450}, {12182, 26491}, {12183, 26486}, {12184, 26480}, {12185, 26474}, {12186, 49021}, {12187, 49023}, {12188, 49029}, {12189, 26525}, {12190, 26524}, {19055, 26457}, {19056, 26463}, {22504, 26325}, {22505, 49017}, {26397, 48462}, {26421, 48463}, {26438, 38744}, {35824, 39661}, {35825, 49019}, {39809, 48476}, {41022, 49037}, {41023, 49035}, {45523, 48727}, {45525, 48726}, {49085, 49087}

X(49041) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard}
X(49041) = reflection of X(i) in X(j) for these (i, j): (49040, 5984), (49097, 49039)


X(49042) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO ANTI-MCCAY

Barycentrics    (7*a^4-7*(b^2+c^2)*a^2-5*b^4+17*b^2*c^2-5*c^4)*S+4*a^6-3*(b^2+c^2)*a^4-(2*b^2-c^2)*(b^2-2*c^2)*(b^2+c^2) : :

The reciprocal orthologic center of these triangles is X(9855).

X(49042) lies on these lines: {4, 33432}, {30, 49040}, {148, 45420}, {193, 8596}, {492, 8591}, {530, 49036}, {531, 49034}, {542, 48476}, {543, 5860}, {671, 3068}, {2482, 26361}, {2782, 49058}, {2796, 49078}, {5861, 39809}, {5969, 49082}, {8597, 44365}, {8724, 26468}, {9766, 49097}, {9875, 26300}, {9876, 26306}, {9878, 26314}, {9880, 26330}, {9881, 26444}, {9882, 26339}, {9884, 26514}, {10054, 49030}, {10070, 49032}, {12117, 26294}, {12132, 26375}, {12191, 26429}, {12243, 26441}, {12258, 26369}, {12326, 26512}, {12345, 49012}, {12346, 49014}, {12347, 26449}, {12348, 26490}, {12349, 26485}, {12350, 26479}, {12351, 26473}, {12352, 49020}, {12353, 49022}, {12354, 26355}, {12355, 49028}, {12356, 26520}, {12357, 26519}, {13968, 49026}, {18539, 48657}, {18969, 26435}, {19057, 26456}, {19058, 26462}, {22565, 26324}, {22566, 49016}, {26396, 48470}, {26420, 48471}, {26516, 49102}, {35698, 49018}, {35699, 39660}, {45522, 48728}, {45524, 48729}

X(49042) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {anti-McCay, McCay, Moses-Steiner osculatory}
X(49042) = X(671)-of-3rd anti-tri-squares-central triangle
X(49042) = reflection of X(i) in X(j) for these (i, j): (49043, 8596), (49096, 5860)


X(49043) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO ANTI-MCCAY

Barycentrics    -(7*a^4-7*(b^2+c^2)*a^2-5*b^4+17*b^2*c^2-5*c^4)*S+4*a^6-3*(b^2+c^2)*a^4-(2*b^2-c^2)*(b^2-2*c^2)*(b^2+c^2) : :

The reciprocal orthologic center of these triangles is X(9855).

X(49043) lies on these lines: {4, 33433}, {30, 49041}, {148, 45421}, {193, 8596}, {491, 8591}, {530, 49037}, {531, 49035}, {542, 48477}, {543, 5861}, {671, 3069}, {2482, 26362}, {2782, 49059}, {2796, 49079}, {5860, 39809}, {5969, 49083}, {8597, 44364}, {8724, 26469}, {8982, 12243}, {9766, 49096}, {9875, 26301}, {9876, 26307}, {9878, 26315}, {9880, 26331}, {9881, 26445}, {9883, 26340}, {9884, 26515}, {10054, 49031}, {10070, 49033}, {12117, 26295}, {12132, 26376}, {12191, 26430}, {12258, 26370}, {12326, 26513}, {12345, 49013}, {12346, 49015}, {12347, 26450}, {12348, 26491}, {12349, 26486}, {12350, 26480}, {12351, 26474}, {12352, 49021}, {12353, 49023}, {12354, 26356}, {12355, 49029}, {12356, 26525}, {12357, 26524}, {13908, 49027}, {18969, 26436}, {19057, 26457}, {19058, 26463}, {22565, 26325}, {22566, 49017}, {26397, 48470}, {26421, 48471}, {26438, 48657}, {26521, 49102}, {35698, 39661}, {35699, 49019}, {45523, 48729}, {45525, 48728}

X(49043) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {anti-McCay, McCay, Moses-Steiner osculatory}
X(49043) = reflection of X(i) in X(j) for these (i, j): (49042, 8596), (49097, 5861)


X(49044) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO ANTI-ORTHOCENTROIDAL

Barycentrics    (3*a^10-(b^2+c^2)*a^8-(14*b^4-23*b^2*c^2+14*c^4)*a^6+2*(b^2+c^2)*(9*b^4-17*b^2*c^2+9*c^4)*a^4-(b^2-c^2)^2*(5*b^4+19*b^2*c^2+5*c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3)*S+3*a^2*((b^2+c^2)*a^8-2*(b^4+c^4)*a^6+(b^2+c^2)*b^2*c^2*a^4+2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*(b^4+b^2*c^2+c^4)) : :

The reciprocal orthologic center of these triangles is X(12112).

X(49044) lies on the circumcircle of 3rd anti-tri-squares-central triangle and these lines: {30, 49050}, {74, 3068}, {110, 26294}, {113, 26361}, {125, 26330}, {146, 492}, {193, 2781}, {541, 5860}, {542, 49096}, {690, 49040}, {1503, 49094}, {1539, 49016}, {2771, 48711}, {2777, 48476}, {3024, 26435}, {3028, 26355}, {5663, 49038}, {7725, 26339}, {7728, 26468}, {7978, 26514}, {8674, 48692}, {9517, 49046}, {9904, 26300}, {9919, 26306}, {9984, 26314}, {10065, 49030}, {10081, 49032}, {10620, 49028}, {10628, 49088}, {11709, 26369}, {12041, 26516}, {12133, 26375}, {12192, 26429}, {12244, 26441}, {12327, 26512}, {12365, 49012}, {12366, 49014}, {12368, 26444}, {12369, 26449}, {12371, 26490}, {12372, 26485}, {12373, 26479}, {12374, 26473}, {12377, 49020}, {12378, 49022}, {12381, 26520}, {12382, 26519}, {13969, 49026}, {17702, 49052}, {18539, 38790}, {19059, 26456}, {19060, 26462}, {22583, 26324}, {26396, 48472}, {26420, 48473}, {35826, 49018}, {35827, 39660}, {45522, 48730}, {45524, 48731}

X(49044) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {anti-orthocentroidal, orthocentroidal}
X(49044) = X(74)-of-3rd anti-tri-squares-central triangle
X(49044) = reflection of X(49098) in X(49038)


X(49045) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO ANTI-ORTHOCENTROIDAL

Barycentrics    -(3*a^10-(b^2+c^2)*a^8-(14*b^4-23*b^2*c^2+14*c^4)*a^6+2*(b^2+c^2)*(9*b^4-17*b^2*c^2+9*c^4)*a^4-(b^2-c^2)^2*(5*b^4+19*b^2*c^2+5*c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3)*S+3*a^2*((b^2+c^2)*a^8-2*(b^4+c^4)*a^6+(b^2+c^2)*b^2*c^2*a^4+2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*(b^4+b^2*c^2+c^4)) : :

The reciprocal orthologic center of these triangles is X(12112).

X(49045) lies on the circumcircle of 4th anti-tri-squares-central triangle and these lines: {30, 49051}, {74, 3069}, {110, 26295}, {113, 26362}, {125, 26331}, {146, 491}, {193, 2781}, {541, 5861}, {542, 49097}, {690, 49041}, {1503, 49095}, {1539, 49017}, {2771, 48712}, {2777, 48477}, {3024, 26436}, {3028, 26356}, {5663, 49039}, {7726, 26340}, {7728, 26469}, {7978, 26515}, {8674, 48693}, {8982, 12244}, {8994, 49027}, {9517, 49047}, {9904, 26301}, {9919, 26307}, {9984, 26315}, {10065, 49031}, {10081, 49033}, {10620, 49029}, {10628, 49089}, {11709, 26370}, {12041, 26521}, {12133, 26376}, {12192, 26430}, {12327, 26513}, {12365, 49013}, {12366, 49015}, {12368, 26445}, {12369, 26450}, {12371, 26491}, {12372, 26486}, {12373, 26480}, {12374, 26474}, {12377, 49021}, {12378, 49023}, {12381, 26525}, {12382, 26524}, {17702, 49053}, {19059, 26457}, {19060, 26463}, {22583, 26325}, {26397, 48472}, {26421, 48473}, {26438, 38790}, {35826, 39661}, {35827, 49019}, {45523, 48731}, {45525, 48730}

X(49045) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {anti-orthocentroidal, orthocentroidal}
X(49045) = reflection of X(49099) in X(49039)


X(49046) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    (3*(b^2+c^2)*a^12-4*(b^4+b^2*c^2+c^4)*a^10-4*(b^2-c^2)^2*b^2*c^2*a^6-(b^2+c^2)*(b^4-5*b^2*c^2+c^4)*a^8+(b^8-c^8)*(b^2-c^2)*a^4+4*(b^4-c^4)^2*(b^4+c^4)*a^2+(b^4-c^4)*(b^2-c^2)*(-3*b^8-3*c^8-(b^4+8*b^2*c^2+c^4)*b^2*c^2))*a^2+(3*a^14-(b^2+c^2)*a^12-(3*b^4-b^2*c^2+3*c^4)*a^10-(b^2+c^2)*(7*b^4-16*b^2*c^2+7*c^4)*a^8+5*(b^2-c^2)^2*(b^4+c^4)*a^6+3*(b^4-c^4)*(b^2-c^2)*(3*b^4+2*b^2*c^2+3*c^4)*a^4-(b^2-c^2)^2*(5*b^8+5*c^8+(9*b^4+20*b^2*c^2+9*c^4)*b^2*c^2)*a^2-(b^8-c^8)*(b^2-c^2)^3)*S : :

The reciprocal orthologic center of these triangles is X(19158).

X(49046) lies on the circumcircle of 3rd anti-tri-squares-central triangle and these lines: {112, 26294}, {127, 26330}, {132, 26361}, {193, 49047}, {492, 12384}, {1297, 3068}, {2781, 49098}, {2794, 49096}, {2799, 49040}, {2806, 48692}, {2831, 48711}, {3320, 26355}, {5860, 9530}, {6020, 26435}, {9517, 49044}, {12145, 26375}, {12207, 26429}, {12253, 26441}, {12265, 26369}, {12340, 26512}, {12408, 26300}, {12413, 26306}, {12478, 49012}, {12479, 49014}, {12503, 26314}, {12784, 26444}, {12796, 26449}, {12805, 26339}, {12918, 26468}, {12925, 26490}, {12935, 26485}, {12945, 26479}, {12955, 26473}, {12996, 49020}, {12997, 49022}, {13099, 26514}, {13115, 49028}, {13116, 49030}, {13117, 49032}, {13118, 26520}, {13119, 26519}, {13985, 49026}, {18539, 48658}, {19093, 26456}, {19094, 26462}, {19159, 26324}, {19160, 49016}, {26396, 48474}, {26420, 48475}, {26516, 38624}, {35828, 49018}, {35829, 39660}, {45522, 48732}, {45524, 48733}, {49038, 49100}

X(49046) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {1st anti-orthosymmedial, 1st orthosymmedial}
X(49046) = X(1297)-of-3rd anti-tri-squares-central triangle
X(49046) = reflection of X(49100) in X(49038)


X(49047) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    (3*(b^2+c^2)*a^12-4*(b^4+b^2*c^2+c^4)*a^10-4*(b^2-c^2)^2*b^2*c^2*a^6-(b^2+c^2)*(b^4-5*b^2*c^2+c^4)*a^8+(b^8-c^8)*(b^2-c^2)*a^4+4*(b^4-c^4)^2*(b^4+c^4)*a^2+(b^4-c^4)*(b^2-c^2)*(-3*b^8-3*c^8-(b^4+8*b^2*c^2+c^4)*b^2*c^2))*a^2-(3*a^14-(b^2+c^2)*a^12-(3*b^4-b^2*c^2+3*c^4)*a^10-(b^2+c^2)*(7*b^4-16*b^2*c^2+7*c^4)*a^8+5*(b^2-c^2)^2*(b^4+c^4)*a^6+3*(b^4-c^4)*(b^2-c^2)*(3*b^4+2*b^2*c^2+3*c^4)*a^4-(b^2-c^2)^2*(5*b^8+5*c^8+(9*b^4+20*b^2*c^2+9*c^4)*b^2*c^2)*a^2-(b^8-c^8)*(b^2-c^2)^3)*S : :

The reciprocal orthologic center of these triangles is X(19158).

X(49047) lies on the circumcircle of 4th anti-tri-squares-central triangle and these lines: {112, 26295}, {127, 26331}, {132, 26362}, {193, 49046}, {491, 12384}, {1297, 3069}, {2781, 49099}, {2794, 49097}, {2799, 49041}, {2806, 48693}, {2831, 48712}, {3320, 26356}, {5861, 9530}, {6020, 26436}, {8982, 12253}, {9517, 49045}, {12145, 26376}, {12207, 26430}, {12265, 26370}, {12340, 26513}, {12408, 26301}, {12413, 26307}, {12478, 49013}, {12479, 49015}, {12503, 26315}, {12784, 26445}, {12796, 26450}, {12806, 26340}, {12918, 26469}, {12925, 26491}, {12935, 26486}, {12945, 26480}, {12955, 26474}, {12996, 49021}, {12997, 49023}, {13099, 26515}, {13115, 49029}, {13116, 49031}, {13117, 49033}, {13118, 26525}, {13119, 26524}, {13918, 49027}, {19093, 26457}, {19094, 26463}, {19159, 26325}, {19160, 49017}, {26397, 48474}, {26421, 48475}, {26438, 48658}, {26521, 38624}, {35828, 39661}, {35829, 49019}, {45523, 48733}, {45525, 48732}, {49039, 49101}

X(49047) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {1st anti-orthosymmedial, 1st orthosymmedial}
X(49047) = reflection of X(49101) in X(49039)


X(49048) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO 3rd ANTI-TRI-SQUARES

Barycentrics    7*a^6-13*(b^2+c^2)*a^4+(9*b^4-2*b^2*c^2+9*c^4)*a^2-3*(b^4-c^4)*(b^2-c^2)+4*S*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :
X(49048) = 3*X(4)-4*X(12601) = 5*X(4)-4*X(48659) = 3*X(376)-8*X(6280) = 9*X(376)-8*X(12123) = 3*X(376)-4*X(12256) = 3*X(376)-2*X(12509) = 8*X(486)-7*X(3090) = 4*X(487)-5*X(631) = 3*X(487)-4*X(49103) = 15*X(631)-16*X(49103) = 16*X(642)-17*X(3533) = 9*X(3545)-8*X(6290) = 11*X(3855)-8*X(6281) = 3*X(6280)-X(12123) = 4*X(6280)-X(12509) = 2*X(12123)-3*X(12256) = 4*X(12123)-3*X(12509) = 3*X(12221)-2*X(12601) = 5*X(12221)-2*X(48659) = 5*X(12601)-3*X(48659)

The reciprocal orthologic center of these triangles is X(486).

X(49048) lies on these lines: {4, 193}, {30, 49092}, {230, 13939}, {371, 22591}, {376, 5860}, {486, 3068}, {487, 492}, {511, 12285}, {637, 14912}, {642, 3533}, {3146, 22809}, {3529, 49038}, {3545, 6290}, {3855, 6281}, {5491, 44365}, {5874, 21736}, {5965, 12323}, {6144, 14233}, {6251, 22484}, {6400, 8681}, {7464, 12303}, {7556, 12972}, {7980, 26514}, {9906, 26300}, {9921, 26306}, {9986, 26314}, {10067, 49030}, {10083, 49032}, {10299, 45522}, {10323, 12169}, {10625, 12274}, {11180, 45441}, {12082, 12311}, {12088, 12978}, {12147, 26375}, {12210, 26429}, {12245, 49078}, {12268, 26369}, {12296, 15682}, {12343, 26512}, {12484, 49012}, {12485, 49014}, {12787, 26444}, {12799, 26449}, {12928, 26490}, {12938, 26485}, {12948, 26479}, {12958, 26473}, {13002, 49020}, {13003, 49022}, {13081, 26355}, {13132, 26520}, {13133, 26519}, {13881, 13886}, {13933, 49026}, {14227, 33703}, {14242, 49056}, {15534, 45862}, {18989, 26435}, {19104, 26456}, {19105, 26462}, {22592, 31412}, {22595, 26324}, {22596, 49016}, {23267, 35830}, {23273, 35833}, {26396, 48478}, {26420, 48479}, {32810, 43120}, {42561, 49019}, {44595, 44648}

X(49048) = reflection of X(i) in X(j) for these (i, j): (4, 12221), (3146, 22809), (12256, 6280), (12274, 10625), (12509, 12256)
X(49048) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {3rd anti-tri-squares, 2nd half-squares, 4th tri-squares, inner-Vecten}
X(49048) = X(486)-of-3rd anti-tri-squares-central triangle
X(49048) = X(12221)-of-anti-Euler triangle
X(49048) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (193, 49086, 4), (5921, 49029, 4), (12256, 12509, 376)


X(49049) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO 4th ANTI-TRI-SQUARES

Barycentrics    7*a^6-13*(b^2+c^2)*a^4+(9*b^4-2*b^2*c^2+9*c^4)*a^2-3*(b^4-c^4)*(b^2-c^2)-4*S*(a^2+b^2-c^2)*(a^2-b^2+c^2) : :
X(49049) = 3*X(4)-4*X(12602) = 5*X(4)-4*X(48660) = 3*X(376)-8*X(6279) = 9*X(376)-8*X(12124) = 3*X(376)-4*X(12257) = 3*X(376)-2*X(12510) = 8*X(485)-7*X(3090) = 4*X(488)-5*X(631) = 3*X(488)-4*X(49104) = 15*X(631)-16*X(49104) = 16*X(641)-17*X(3533) = 9*X(3545)-8*X(6289) = 11*X(3855)-8*X(6278) = 3*X(6279)-X(12124) = 4*X(6279)-X(12510) = 2*X(12124)-3*X(12257) = 4*X(12124)-3*X(12510) = 3*X(12222)-2*X(12602) = 5*X(12222)-2*X(48660) = 5*X(12602)-3*X(48660)

The reciprocal orthologic center of these triangles is X(485).

X(49049) lies on these lines: {4, 193}, {30, 49093}, {230, 13886}, {372, 22592}, {376, 5861}, {485, 3069}, {488, 491}, {511, 12286}, {638, 14912}, {641, 3533}, {3146, 22810}, {3529, 49039}, {3545, 6289}, {3855, 6278}, {5490, 44364}, {5965, 12322}, {6144, 14230}, {6239, 8681}, {6250, 22485}, {7464, 12304}, {7556, 12973}, {7981, 26515}, {9907, 26301}, {9922, 26307}, {9987, 26315}, {10068, 49031}, {10084, 49033}, {10299, 45523}, {10323, 12170}, {10625, 12275}, {11180, 45440}, {12082, 12312}, {12088, 12979}, {12148, 26376}, {12211, 26430}, {12245, 49079}, {12269, 26370}, {12297, 15682}, {12344, 26513}, {12486, 49013}, {12487, 49015}, {12788, 26445}, {12800, 26450}, {12929, 26491}, {12939, 26486}, {12949, 26480}, {12959, 26474}, {13004, 49021}, {13005, 49023}, {13082, 26356}, {13134, 26525}, {13135, 26524}, {13879, 49027}, {13881, 13939}, {14227, 49057}, {14242, 33703}, {15534, 45863}, {18988, 26436}, {19102, 26457}, {19103, 26463}, {22591, 42561}, {22624, 26325}, {22625, 49017}, {23267, 35832}, {23273, 35831}, {26397, 48480}, {26421, 48481}, {31412, 49018}, {32811, 43121}, {44596, 44647}

X(49049) = reflection of X(i) in X(j) for these (i, j): (4, 12222), (3146, 22810), (12257, 6279), (12275, 10625), (12510, 12257)
X(49049) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {4th anti-tri-squares, 1st half-squares, 3rd tri-squares, outer-Vecten}
X(49049) = X(12222)-of-anti-Euler triangle
X(49049) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (193, 49087, 4), (5921, 49028, 4), (12257, 12510, 376)


X(49050) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO AAOA

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

The reciprocal orthologic center of these triangles is X(7574).

X(49050) lies on these lines: {30, 49044}, {110, 26468}, {113, 49016}, {125, 26516}, {146, 148}, {265, 3068}, {399, 18539}, {492, 12383}, {511, 49094}, {1511, 26361}, {2771, 49068}, {2777, 49080}, {3448, 26441}, {5663, 48476}, {5860, 12804}, {10088, 26479}, {10091, 26473}, {10113, 26330}, {10628, 49072}, {12121, 26294}, {12140, 26375}, {12201, 26429}, {12261, 26369}, {12334, 26512}, {12407, 26300}, {12412, 26306}, {12466, 49012}, {12467, 49014}, {12501, 26314}, {12778, 26444}, {12790, 26449}, {12803, 26339}, {12889, 26490}, {12890, 26485}, {12894, 49020}, {12895, 49022}, {12896, 26355}, {12898, 26514}, {12902, 49028}, {12903, 49030}, {12904, 49032}, {12905, 26520}, {12906, 26519}, {13979, 49026}, {17702, 49038}, {18968, 26435}, {19051, 26456}, {19052, 26462}, {19478, 26324}, {26396, 48483}, {26420, 48484}, {32423, 49086}, {35834, 49018}, {35835, 39660}, {45522, 48736}, {45524, 48737}

X(49050) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {antiAOA, AOA, 1st Hyacinth}
X(49050) = X(265)-of-3rd anti-tri-squares-central triangle
X(49050) = reflection of X(49098) in X(49086)


X(49051) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO AAOA

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

The reciprocal orthologic center of these triangles is X(7574).

X(49051) lies on these lines: {30, 49045}, {110, 26469}, {113, 49017}, {125, 26521}, {146, 148}, {265, 3069}, {399, 26438}, {491, 12383}, {511, 49095}, {1511, 26362}, {2771, 49069}, {2777, 49081}, {3448, 8982}, {5663, 48477}, {5861, 12803}, {10088, 26480}, {10091, 26474}, {10113, 26331}, {10628, 49073}, {12121, 26295}, {12140, 26376}, {12201, 26430}, {12261, 26370}, {12334, 26513}, {12407, 26301}, {12412, 26307}, {12466, 49013}, {12467, 49015}, {12501, 26315}, {12778, 26445}, {12790, 26450}, {12804, 26340}, {12889, 26491}, {12890, 26486}, {12894, 49021}, {12895, 49023}, {12896, 26356}, {12898, 26515}, {12902, 49029}, {12903, 49031}, {12904, 49033}, {12905, 26525}, {12906, 26524}, {13915, 49027}, {17702, 49039}, {18968, 26436}, {19051, 26457}, {19052, 26463}, {19478, 26325}, {26397, 48483}, {26421, 48484}, {32423, 49087}, {35834, 39661}, {35835, 49019}, {45523, 48737}, {45525, 48736}

X(49051) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {antiAOA, AOA, 1st Hyacinth}
X(49051) = reflection of X(49099) in X(49087)


X(49052) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO ARIES

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

The reciprocal orthologic center of these triangles is X(9833).

X(49052) lies on these lines: {4, 193}, {30, 49080}, {68, 3068}, {155, 26468}, {492, 6193}, {539, 5860}, {1069, 26473}, {1147, 26361}, {1154, 49072}, {3157, 26479}, {9896, 26300}, {9908, 26306}, {9923, 26314}, {9927, 26330}, {9928, 26444}, {9929, 26339}, {9933, 26514}, {10055, 49030}, {10071, 49032}, {11411, 26441}, {12118, 26294}, {12134, 26375}, {12193, 26429}, {12259, 26369}, {12328, 26512}, {12359, 26516}, {12415, 49012}, {12416, 49014}, {12418, 26449}, {12422, 26490}, {12423, 26485}, {12426, 49020}, {12427, 49022}, {12428, 26355}, {12430, 26520}, {12431, 26519}, {13754, 48476}, {13970, 49026}, {14984, 49094}, {17702, 49044}, {18970, 26435}, {19061, 26456}, {19062, 26462}, {22659, 26324}, {22660, 49016}, {26396, 48485}, {26420, 48486}, {35836, 49018}, {35837, 39660}, {44665, 49038}, {45522, 48738}, {45524, 48739}

X(49052) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {Aries, 2nd Hyacinth}
X(49052) = X(68)-of-3rd anti-tri-squares-central triangle


X(49053) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO ARIES

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

The reciprocal orthologic center of these triangles is X(9833).

X(49053) lies on these lines: {4, 193}, {30, 49081}, {68, 3069}, {155, 26469}, {491, 6193}, {539, 5861}, {1069, 26474}, {1147, 26362}, {1154, 49073}, {3157, 26480}, {8982, 11411}, {9896, 26301}, {9908, 26307}, {9923, 26315}, {9927, 26331}, {9928, 26445}, {9930, 26340}, {9933, 26515}, {10055, 49031}, {10071, 49033}, {12118, 26295}, {12134, 26376}, {12193, 26430}, {12259, 26370}, {12328, 26513}, {12359, 26521}, {12415, 49013}, {12416, 49015}, {12418, 26450}, {12422, 26491}, {12423, 26486}, {12426, 49021}, {12427, 49023}, {12428, 26356}, {12430, 26525}, {12431, 26524}, {13754, 48477}, {13909, 49027}, {14984, 49095}, {17702, 49045}, {18970, 26436}, {19061, 26457}, {19062, 26463}, {22659, 26325}, {22660, 49017}, {26397, 48485}, {26421, 48486}, {35836, 39661}, {35837, 49019}, {44665, 49039}, {45523, 48739}, {45525, 48738}

X(49053) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {Aries, 2nd Hyacinth}


X(49054) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO BEVAN ANTIPODAL

Barycentrics    (3*a^4+4*(b+c)*a^3-2*(b^2+4*b*c+c^2)*a^2-4*(b^2-c^2)*(b-c)*a-(b^2-c^2)^2)*S+a*((b+c)*a^4+2*(b^2-b*c+c^2)*a^3+2*(b+c)*b*c*a^2-2*(b^3+c^3)*(b+c)*a-(b^4-c^4)*(b-c)) : :
X(49054) = 3*X(5603)-4*X(48740)

The reciprocal orthologic center of these triangles is X(1).

X(49054) lies on these lines: {1, 26294}, {3, 26369}, {4, 12788}, {10, 26330}, {40, 3068}, {46, 49032}, {65, 26355}, {193, 20070}, {492, 962}, {515, 49060}, {516, 48476}, {517, 45719}, {946, 26361}, {1702, 26462}, {1703, 26456}, {1836, 26479}, {1902, 26375}, {2800, 48711}, {2802, 48692}, {3057, 26435}, {3579, 26516}, {5119, 49030}, {5603, 45522}, {5709, 26517}, {5812, 26485}, {5840, 49068}, {5847, 49056}, {5860, 12698}, {6001, 49080}, {6361, 26441}, {7982, 26514}, {7991, 26300}, {9911, 26306}, {10306, 26512}, {12197, 26429}, {12458, 49012}, {12459, 49014}, {12497, 26314}, {12696, 26449}, {12697, 26339}, {12699, 26468}, {12700, 26490}, {12701, 26473}, {12702, 49028}, {12703, 26520}, {12704, 26519}, {13975, 49026}, {18539, 48661}, {22770, 26324}, {22793, 49016}, {22841, 49020}, {22842, 49022}, {26396, 48487}, {26420, 48488}, {28174, 49086}, {34632, 45420}, {35610, 49018}, {35611, 39660}, {45524, 48741}

X(49054) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {Bevan antipodal, 3rd extouch}
X(49054) = X(40)-of-3rd anti-tri-squares-central triangle
X(49054) = reflection of X(i) in X(j) for these (i, j): (45719, 49038), (48476, 49078), (49055, 20070)


X(49055) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO BEVAN ANTIPODAL

Barycentrics    -(3*a^4+4*(b+c)*a^3-2*(b^2+4*b*c+c^2)*a^2-4*(b^2-c^2)*(b-c)*a-(b^2-c^2)^2)*S+a*((b+c)*a^4+2*(b^2-b*c+c^2)*a^3+2*(b+c)*b*c*a^2-2*(b^3+c^3)*(b+c)*a-(b^4-c^4)*(b-c)) : :
X(49055) = 3*X(5603)-4*X(48741)

The reciprocal orthologic center of these triangles is X(1).

X(49055) lies on these lines: {1, 26295}, {3, 26370}, {4, 12787}, {10, 26331}, {40, 3069}, {46, 49033}, {65, 26356}, {193, 20070}, {491, 962}, {515, 49061}, {516, 48477}, {517, 45720}, {946, 26362}, {1702, 26463}, {1703, 26457}, {1836, 26480}, {1902, 26376}, {2800, 48712}, {2802, 48693}, {3057, 26436}, {3579, 26521}, {5119, 49031}, {5603, 45523}, {5709, 26522}, {5812, 26486}, {5840, 49069}, {5847, 49057}, {5861, 12697}, {6001, 49081}, {6361, 8982}, {7982, 26515}, {7991, 26301}, {9911, 26307}, {10306, 26513}, {12197, 26430}, {12458, 49013}, {12459, 49015}, {12497, 26315}, {12696, 26450}, {12698, 26340}, {12699, 26469}, {12700, 26491}, {12701, 26474}, {12702, 49029}, {12703, 26525}, {12704, 26524}, {13912, 49027}, {22770, 26325}, {22793, 49017}, {22841, 49021}, {22842, 49023}, {26397, 48487}, {26421, 48488}, {26438, 48661}, {28174, 49087}, {34632, 45421}, {35610, 39661}, {35611, 49019}, {45525, 48740}

X(49055) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {Bevan antipodal, 3rd extouch}
X(49055) = reflection of X(i) in X(j) for these (i, j): (45720, 49039), (48477, 49079), (49054, 20070)


X(49056) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO 9th BROCARD

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

The reciprocal orthologic center of these triangles is X(4).

X(49056) lies on these lines: {4, 22646}, {6, 26330}, {69, 26294}, {193, 1503}, {492, 5921}, {542, 5860}, {1352, 26361}, {3068, 6776}, {3564, 49038}, {5847, 49054}, {5848, 48692}, {5870, 39899}, {5871, 49086}, {10784, 39660}, {14242, 49048}, {18440, 26468}, {18539, 48662}, {19146, 49026}, {26300, 39878}, {26306, 39879}, {26314, 39882}, {26324, 39883}, {26339, 39887}, {26355, 39897}, {26369, 39870}, {26375, 39871}, {26396, 48489}, {26420, 48490}, {26429, 39872}, {26435, 39873}, {26441, 39874}, {26444, 39885}, {26449, 39886}, {26456, 39875}, {26462, 39876}, {26473, 39892}, {26479, 39891}, {26485, 39890}, {26490, 39889}, {26512, 39877}, {26514, 39898}, {26516, 48906}, {26519, 39903}, {26520, 39902}, {39880, 49012}, {39881, 49014}, {39884, 49016}, {39895, 49020}, {39896, 49022}, {39900, 49030}, {39901, 49032}, {45522, 48742}, {45524, 48743}

X(49056) = orthologic center (3rd anti-tri-squares-central, 9th Brocard)
X(49056) = X(6776)-of-3rd anti-tri-squares-central triangle
X(49056) = reflection of X(i) in X(j) for these (i, j): (5870, 39899), (48476, 193)


X(49057) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO 9th BROCARD

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

The reciprocal orthologic center of these triangles is X(4).

X(49057) lies on these lines: {4, 22617}, {6, 26331}, {69, 26295}, {193, 1503}, {491, 5921}, {542, 5861}, {1352, 26362}, {3069, 6776}, {3564, 49039}, {5847, 49055}, {5848, 48693}, {5870, 49087}, {5871, 39899}, {8982, 39874}, {10783, 39661}, {14227, 49049}, {18440, 26469}, {19145, 49027}, {26301, 39878}, {26307, 39879}, {26315, 39882}, {26325, 39883}, {26340, 39888}, {26356, 39897}, {26370, 39870}, {26376, 39871}, {26397, 48489}, {26421, 48490}, {26430, 39872}, {26436, 39873}, {26438, 48662}, {26445, 39885}, {26450, 39886}, {26457, 39875}, {26463, 39876}, {26474, 39892}, {26480, 39891}, {26486, 39890}, {26491, 39889}, {26513, 39877}, {26515, 39898}, {26521, 48906}, {26524, 39903}, {26525, 39902}, {39880, 49013}, {39881, 49015}, {39884, 49017}, {39895, 49021}, {39896, 49023}, {39900, 49031}, {39901, 49033}, {45523, 48743}, {45525, 48742}

X(49057) = orthologic center (4th anti-tri-squares-central, 9th Brocard)
X(49057) = reflection of X(i) in X(j) for these (i, j): (5871, 39899), (48477, 193)


X(49058) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO 1st BROCARD-REFLECTED

Barycentrics    (3*(b^2+c^2)*a^6+(2*b^4+11*b^2*c^2+2*c^4)*a^4-(b^2+c^2)*(5*b^4-4*b^2*c^2+5*c^4)*a^2-(b^2-c^2)^2*b^2*c^2)*S+3*(b^2+c^2)*a^8-4*(b^4+b^2*c^2+c^4)*a^6+3*(b^6+c^6)*a^4-2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*b^2*c^2 : :
X(49058) = X(49082)-4*X(49086)

The reciprocal orthologic center of these triangles is X(3).

X(49058) lies on these lines: {4, 33434}, {193, 1916}, {262, 3068}, {492, 6194}, {511, 5860}, {2782, 49042}, {6226, 37517}, {7697, 26468}, {7709, 26441}, {15819, 26361}, {18539, 48663}, {18971, 26435}, {19063, 26456}, {19064, 26462}, {22475, 26369}, {22480, 26375}, {22521, 26429}, {22556, 26512}, {22650, 26300}, {22655, 26306}, {22668, 49012}, {22672, 49014}, {22676, 26294}, {22678, 26314}, {22680, 26324}, {22681, 49016}, {22682, 26330}, {22697, 26444}, {22698, 26449}, {22699, 26339}, {22703, 26490}, {22704, 26485}, {22705, 26479}, {22706, 26473}, {22709, 49020}, {22710, 49022}, {22711, 26355}, {22713, 26514}, {22721, 49026}, {22728, 49028}, {22729, 49030}, {22730, 49032}, {22731, 26520}, {22732, 26519}, {26396, 48491}, {26420, 48492}, {26516, 40108}, {32515, 49082}, {35838, 49018}, {35839, 39660}, {45522, 48744}, {45524, 48745}, {49038, 49084}

X(49058) = orthologic center (3rd anti-tri-squares-central, 1st Brocard-reflected)
X(49058) = X(262)-of-3rd anti-tri-squares-central triangle
X(49058) = reflection of X(49059) in X(44434)


X(49059) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO 1st BROCARD-REFLECTED

Barycentrics    -(3*(b^2+c^2)*a^6+(2*b^4+11*b^2*c^2+2*c^4)*a^4-(b^2+c^2)*(5*b^4-4*b^2*c^2+5*c^4)*a^2-(b^2-c^2)^2*b^2*c^2)*S+3*(b^2+c^2)*a^8-4*(b^4+b^2*c^2+c^4)*a^6+3*(b^6+c^6)*a^4-2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*b^2*c^2 : :
X(49059) = X(49083)-4*X(49087)

The reciprocal orthologic center of these triangles is X(3).

X(49059) lies on these lines: {4, 33435}, {193, 1916}, {262, 3069}, {491, 6194}, {511, 5861}, {2782, 49043}, {6227, 37517}, {7697, 26469}, {7709, 8982}, {15819, 26362}, {18971, 26436}, {19063, 26457}, {19064, 26463}, {22475, 26370}, {22480, 26376}, {22521, 26430}, {22556, 26513}, {22650, 26301}, {22655, 26307}, {22668, 49013}, {22672, 49015}, {22676, 26295}, {22678, 26315}, {22680, 26325}, {22681, 49017}, {22682, 26331}, {22697, 26445}, {22698, 26450}, {22700, 26340}, {22703, 26491}, {22704, 26486}, {22705, 26480}, {22706, 26474}, {22709, 49021}, {22710, 49023}, {22711, 26356}, {22713, 26515}, {22720, 49027}, {22728, 49029}, {22729, 49031}, {22730, 49033}, {22731, 26525}, {22732, 26524}, {26397, 48491}, {26421, 48492}, {26438, 48663}, {26521, 40108}, {32515, 49083}, {35838, 39661}, {35839, 49019}, {45523, 48745}, {45525, 48744}, {49039, 49085}

X(49059) = orthologic center (4th anti-tri-squares-central, 1st Brocard-reflected)
X(49059) = reflection of X(49058) in X(44434)


X(49060) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO EXCENTERS-MIDPOINTS

Barycentrics    (5*a-3*b-3*c)*S+2*a^3+(b^2+c^2)*a-(b+c)*(b^2+c^2) : :
X(49060) = 3*X(5860)-2*X(45719) = 3*X(5860)-4*X(49078) = 3*X(7967)-4*X(48746)

The reciprocal orthologic center of these triangles is X(10).

X(49060) lies on these lines: {1, 26361}, {8, 3068}, {10, 26369}, {145, 492}, {193, 3621}, {355, 26330}, {515, 49054}, {517, 48476}, {519, 3640}, {758, 49070}, {944, 26294}, {952, 48692}, {1007, 26515}, {1482, 26468}, {2098, 26473}, {2099, 26479}, {2802, 49068}, {3632, 5589}, {3913, 26512}, {5690, 26516}, {5844, 49086}, {7967, 45522}, {8148, 18539}, {10573, 49032}, {10912, 26490}, {10944, 26435}, {10950, 26355}, {12135, 26375}, {12195, 26429}, {12245, 26441}, {12410, 26306}, {12454, 49012}, {12455, 49014}, {12495, 26314}, {12513, 26324}, {12626, 26449}, {12635, 26485}, {12636, 49020}, {12637, 49022}, {12645, 49028}, {12647, 49030}, {12648, 26520}, {12649, 26519}, {12788, 33364}, {13973, 49026}, {14839, 49082}, {19065, 26456}, {19066, 26462}, {22791, 49016}, {26396, 48493}, {26420, 48494}, {31145, 45420}, {35842, 49018}, {35843, 39660}, {45524, 48747}

X(49060) = reflection of X(i) in X(j) for these (i, j): (12627, 3632), (45719, 49078), (49061, 3621)
X(49060) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {excenters-midpoints, Garcia-reflection, 2nd Schiffler}
X(49060) = X(8)-of-3rd anti-tri-squares-central triangle
X(49060) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 26444, 26361), (145, 492, 26514), (45719, 49078, 5860)


X(49061) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO EXCENTERS-MIDPOINTS

Barycentrics    -(5*a-3*b-3*c)*S+2*a^3+(b^2+c^2)*a-(b+c)*(b^2+c^2) : :
X(49061) = 3*X(5861)-2*X(45720) = 3*X(5861)-4*X(49079) = 3*X(7967)-4*X(48747)

The reciprocal orthologic center of these triangles is X(10).

X(49061) lies on these lines: {1, 26362}, {8, 3069}, {10, 26370}, {145, 491}, {193, 3621}, {355, 26331}, {515, 49055}, {517, 48477}, {519, 3641}, {758, 49071}, {944, 26295}, {952, 48693}, {1007, 26514}, {1482, 26469}, {2098, 26474}, {2099, 26480}, {2802, 49069}, {3632, 5588}, {3913, 26513}, {5690, 26521}, {5844, 49087}, {7967, 45523}, {8148, 26438}, {8982, 12245}, {10573, 49033}, {10912, 26491}, {10944, 26436}, {10950, 26356}, {12135, 26376}, {12195, 26430}, {12410, 26307}, {12454, 49013}, {12455, 49015}, {12495, 26315}, {12513, 26325}, {12626, 26450}, {12635, 26486}, {12636, 49021}, {12637, 49023}, {12645, 49029}, {12647, 49031}, {12648, 26525}, {12649, 26524}, {12787, 33365}, {13911, 49027}, {14839, 49083}, {19065, 26457}, {19066, 26463}, {22791, 49017}, {26397, 48493}, {26421, 48494}, {31145, 45421}, {35842, 39661}, {35843, 49019}, {45525, 48746}

X(49061) = reflection of X(i) in X(j) for these (i, j): (12628, 3632), (45720, 49079), (49060, 3621)
X(49061) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {excenters-midpoints, Garcia-reflection, 2nd Schiffler}
X(49061) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 26445, 26362), (145, 491, 26515), (45720, 49079, 5861)


X(49062) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO EXTOUCH

Barycentrics    (3*a^7+(b+c)*a^6-(9*b^2-22*b*c+9*c^2)*a^5-(b+c)*(3*b^2-2*b*c+3*c^2)*a^4+3*(b-c)^2*(3*b^2+2*b*c+3*c^2)*a^3+(b^2-c^2)*(b-c)*(3*b^2+2*b*c+3*c^2)*a^2-(b^2-c^2)^2*(b+3*c)*(3*b+c)*a-(b^2-c^2)^3*(b-c))*S+a*((b+c)*a^7+(b^2+4*b*c+c^2)*a^6-(b+c)*(3*b^2-2*b*c+3*c^2)*a^5-3*(b^2+c^2)*(b-c)^2*a^4+(b^2-c^2)*(b-c)*(3*b^2+2*b*c+3*c^2)*a^3+(3*b^2+4*b*c+3*c^2)*(b-c)^4*a^2-(b^2-c^2)^3*(b-c)*a-(b^4-c^4)*(b^2-c^2)*(b+c)^2) : :
X(49062) = 3*X(5658)-4*X(48748)

The reciprocal orthologic center of these triangles is X(40).

X(49062) lies on these lines: {84, 3068}, {193, 49063}, {492, 6223}, {515, 49054}, {971, 49038}, {1490, 26294}, {1709, 49030}, {2829, 49068}, {5658, 45522}, {5860, 6257}, {6001, 45719}, {6245, 26330}, {6258, 26339}, {6259, 26468}, {6260, 26361}, {7971, 26514}, {7992, 26300}, {9910, 26306}, {10085, 49032}, {12114, 26369}, {12136, 26375}, {12196, 26429}, {12246, 26441}, {12330, 26512}, {12456, 49012}, {12457, 49014}, {12496, 26314}, {12667, 26444}, {12668, 26449}, {12676, 26490}, {12677, 26485}, {12678, 26479}, {12679, 26473}, {12680, 26355}, {12684, 49028}, {12686, 26520}, {12687, 26519}, {12688, 26435}, {13974, 49026}, {18237, 26324}, {18245, 49020}, {18246, 49022}, {18539, 48664}, {19067, 26456}, {19068, 26462}, {22792, 49016}, {26396, 48495}, {26420, 48496}, {26516, 34862}, {35844, 49018}, {35845, 39660}, {45524, 48749}

X(49062) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {extouch, 1st Zaniah}
X(49062) = X(84)-of-3rd anti-tri-squares-central triangle


X(49063) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO EXTOUCH

Barycentrics    -(3*a^7+(b+c)*a^6-(9*b^2-22*b*c+9*c^2)*a^5-(b+c)*(3*b^2-2*b*c+3*c^2)*a^4+3*(b-c)^2*(3*b^2+2*b*c+3*c^2)*a^3+(b^2-c^2)*(b-c)*(3*b^2+2*b*c+3*c^2)*a^2-(b^2-c^2)^2*(b+3*c)*(3*b+c)*a-(b^2-c^2)^3*(b-c))*S+a*((b+c)*a^7+(b^2+4*b*c+c^2)*a^6-(b+c)*(3*b^2-2*b*c+3*c^2)*a^5-3*(b^2+c^2)*(b-c)^2*a^4+(b^2-c^2)*(b-c)*(3*b^2+2*b*c+3*c^2)*a^3+(3*b^2+4*b*c+3*c^2)*(b-c)^4*a^2-(b^2-c^2)^3*(b-c)*a-(b^4-c^4)*(b^2-c^2)*(b+c)^2) : :
X(49063) = 3*X(5658)-4*X(48749)

The reciprocal orthologic center of these triangles is X(40).

X(49063) lies on these lines: {84, 3069}, {193, 49062}, {491, 6223}, {515, 49055}, {971, 49039}, {1490, 26295}, {1709, 49031}, {2829, 49069}, {5658, 45523}, {5861, 6258}, {6001, 45720}, {6245, 26331}, {6257, 26340}, {6259, 26469}, {6260, 26362}, {7971, 26515}, {7992, 26301}, {8982, 12246}, {8987, 49027}, {9910, 26307}, {10085, 49033}, {12114, 26370}, {12136, 26376}, {12196, 26430}, {12330, 26513}, {12456, 49013}, {12457, 49015}, {12496, 26315}, {12667, 26445}, {12668, 26450}, {12676, 26491}, {12677, 26486}, {12678, 26480}, {12679, 26474}, {12680, 26356}, {12684, 49029}, {12686, 26525}, {12687, 26524}, {12688, 26436}, {18237, 26325}, {18245, 49021}, {18246, 49023}, {19067, 26457}, {19068, 26463}, {22792, 49017}, {26397, 48495}, {26421, 48496}, {26438, 48664}, {26521, 34862}, {35844, 39661}, {35845, 49019}, {45525, 48748}

X(49063) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {extouch, 1st Zaniah}


X(49064) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO INNER-FERMAT

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

The reciprocal orthologic center of these triangles is X(3).

X(49064) lies on these lines: {4, 33436}, {18, 3068}, {193, 576}, {492, 628}, {533, 5860}, {630, 26361}, {11740, 26369}, {16628, 49028}, {18539, 48665}, {18587, 49034}, {18972, 26435}, {19069, 26456}, {19072, 26462}, {22481, 26375}, {22522, 26429}, {22531, 26441}, {22557, 26512}, {22651, 26300}, {22656, 26306}, {22669, 49012}, {22673, 49014}, {22745, 26314}, {22771, 26324}, {22794, 49016}, {22831, 26330}, {22843, 26294}, {22851, 26444}, {22852, 26449}, {22853, 26339}, {22857, 26490}, {22858, 26485}, {22859, 26479}, {22860, 26473}, {22863, 49020}, {22864, 49022}, {22865, 26355}, {22867, 26514}, {22877, 49026}, {22884, 49030}, {22885, 49032}, {22886, 26520}, {22887, 26519}, {26396, 48497}, {26420, 48498}, {26516, 49105}, {35846, 49018}, {35849, 39660}, {44667, 48476}, {45522, 48750}, {45524, 48751}, {49036, 49038}

X(49064) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {inner-Fermat, 1st half-diamonds}
X(49064) = X(18)-of-3rd anti-tri-squares-central triangle
X(49064) = reflection of X(i) in X(j) for these (i, j): (22853, 33464), (49065, 22114)


X(49065) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO INNER-FERMAT

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

The reciprocal orthologic center of these triangles is X(3).

X(49065) lies on these lines: {4, 33437}, {18, 3069}, {193, 576}, {491, 628}, {533, 5861}, {630, 26362}, {8982, 22531}, {11740, 26370}, {16628, 49029}, {18586, 49035}, {18972, 26436}, {19069, 26457}, {19072, 26463}, {22481, 26376}, {22522, 26430}, {22557, 26513}, {22651, 26301}, {22656, 26307}, {22669, 49013}, {22673, 49015}, {22745, 26315}, {22771, 26325}, {22794, 49017}, {22831, 26331}, {22843, 26295}, {22851, 26445}, {22852, 26450}, {22854, 26340}, {22857, 26491}, {22858, 26486}, {22859, 26480}, {22860, 26474}, {22863, 49021}, {22864, 49023}, {22865, 26356}, {22867, 26515}, {22876, 49027}, {22884, 49031}, {22885, 49033}, {22886, 26525}, {22887, 26524}, {26397, 48497}, {26421, 48498}, {26438, 48665}, {26521, 49105}, {35846, 39661}, {35849, 49019}, {44667, 48477}, {45523, 48751}, {45525, 48750}, {49037, 49039}

X(49065) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {inner-Fermat, 1st half-diamonds}
X(49065) = reflection of X(i) in X(j) for these (i, j): (22854, 33464), (49064, 22114)


X(49066) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO OUTER-FERMAT

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

The reciprocal orthologic center of these triangles is X(3).

X(49066) lies on these lines: {4, 33438}, {17, 3068}, {193, 576}, {492, 627}, {532, 5860}, {629, 26361}, {11739, 26369}, {16629, 49028}, {18539, 48666}, {18586, 49036}, {18973, 26435}, {19070, 26462}, {19071, 26456}, {22482, 26375}, {22523, 26429}, {22532, 26441}, {22558, 26512}, {22652, 26300}, {22657, 26306}, {22670, 49012}, {22674, 49014}, {22746, 26314}, {22772, 26324}, {22795, 49016}, {22832, 26330}, {22890, 26294}, {22896, 26444}, {22897, 26449}, {22898, 26339}, {22902, 26490}, {22903, 26485}, {22904, 26479}, {22905, 26473}, {22908, 49020}, {22909, 49022}, {22910, 26355}, {22912, 26514}, {22922, 49026}, {22929, 49030}, {22930, 49032}, {22931, 26520}, {22932, 26519}, {26396, 48499}, {26420, 48500}, {26516, 49106}, {35847, 39660}, {35848, 49018}, {44666, 48476}, {45522, 48752}, {45524, 48753}, {49034, 49038}

X(49066) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {outer-Fermat, 2nd half-diamonds}
X(49066) = X(17)-of-3rd anti-tri-squares-central triangle
X(49066) = reflection of X(i) in X(j) for these (i, j): (22898, 33465), (49067, 22113)


X(49067) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO OUTER-FERMAT

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

The reciprocal orthologic center of these triangles is X(3).

X(49067) lies on these lines: {4, 33439}, {17, 3069}, {193, 576}, {491, 627}, {532, 5861}, {629, 26362}, {8982, 22532}, {11739, 26370}, {16629, 49029}, {18587, 49037}, {18973, 26436}, {19070, 26463}, {19071, 26457}, {22482, 26376}, {22523, 26430}, {22558, 26513}, {22652, 26301}, {22657, 26307}, {22670, 49013}, {22674, 49015}, {22746, 26315}, {22772, 26325}, {22795, 49017}, {22832, 26331}, {22890, 26295}, {22896, 26445}, {22897, 26450}, {22899, 26340}, {22902, 26491}, {22903, 26486}, {22904, 26480}, {22905, 26474}, {22908, 49021}, {22909, 49023}, {22910, 26356}, {22912, 26515}, {22921, 49027}, {22929, 49031}, {22930, 49033}, {22931, 26525}, {22932, 26524}, {26397, 48499}, {26421, 48500}, {26438, 48666}, {26521, 49106}, {35847, 49019}, {35848, 39661}, {44666, 48477}, {45523, 48753}, {45525, 48752}, {49035, 49039}

X(49067) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {outer-Fermat, 2nd half-diamonds}
X(49067) = reflection of X(i) in X(j) for these (i, j): (22899, 33465), (49066, 22113)


X(49068) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(49068) lies on these lines: {11, 26369}, {80, 3068}, {100, 26444}, {193, 20085}, {214, 26361}, {492, 6224}, {515, 48692}, {952, 45719}, {2771, 49050}, {2800, 48476}, {2802, 49060}, {2829, 49062}, {5840, 49054}, {5860, 6262}, {6246, 26330}, {6263, 26339}, {6265, 26468}, {7972, 26514}, {9897, 26300}, {9912, 26306}, {10057, 49030}, {10073, 49032}, {12119, 26294}, {12137, 26375}, {12198, 26429}, {12247, 26441}, {12331, 26512}, {12460, 49012}, {12461, 49014}, {12498, 26314}, {12611, 49016}, {12619, 26516}, {12729, 26449}, {12737, 26490}, {12738, 26485}, {12739, 26479}, {12740, 26473}, {12741, 49020}, {12742, 49022}, {12743, 26355}, {12747, 49028}, {12749, 26520}, {12750, 26519}, {12751, 26518}, {12773, 26324}, {13976, 49026}, {18539, 48667}, {18976, 26435}, {19077, 26456}, {19078, 26462}, {26396, 48501}, {26420, 48502}, {35852, 49018}, {35853, 39660}, {45522, 48754}, {45524, 48755}, {48711, 49078}

X(49068) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {Fuhrmann, K798i}
X(49068) = X(80)-of-3rd anti-tri-squares-central triangle
X(49068) = reflection of X(i) in X(j) for these (i, j): (48711, 49078), (49069, 20085)


X(49069) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(49069) lies on these lines: {11, 26370}, {80, 3069}, {100, 26445}, {193, 20085}, {214, 26362}, {491, 6224}, {515, 48693}, {952, 45720}, {2771, 49051}, {2800, 48477}, {2802, 49061}, {2829, 49063}, {5840, 49055}, {5861, 6263}, {6246, 26331}, {6262, 26340}, {6265, 26469}, {7972, 26515}, {8982, 12247}, {8988, 49027}, {9897, 26301}, {9912, 26307}, {10057, 49031}, {10073, 49033}, {12119, 26295}, {12137, 26376}, {12198, 26430}, {12331, 26513}, {12460, 49013}, {12461, 49015}, {12498, 26315}, {12611, 49017}, {12619, 26521}, {12729, 26450}, {12737, 26491}, {12738, 26486}, {12739, 26480}, {12740, 26474}, {12741, 49021}, {12742, 49023}, {12743, 26356}, {12747, 49029}, {12749, 26525}, {12750, 26524}, {12751, 26523}, {12773, 26325}, {18976, 26436}, {19077, 26457}, {19078, 26463}, {26397, 48501}, {26421, 48502}, {26438, 48667}, {35852, 39661}, {35853, 49019}, {45523, 48755}, {45525, 48754}, {48712, 49079}

X(49069) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {Fuhrmann, K798i}
X(49069) = reflection of X(i) in X(j) for these (i, j): (48712, 49079), (49068, 20085)


X(49070) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO 2nd FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(49070) lies on these lines: {30, 45719}, {79, 3068}, {193, 20084}, {492, 3648}, {758, 49060}, {2771, 49050}, {3647, 26361}, {3649, 26369}, {3652, 26468}, {5441, 26514}, {5860, 16131}, {11684, 26444}, {13743, 26324}, {16113, 26294}, {16114, 26375}, {16115, 26429}, {16116, 26441}, {16117, 26512}, {16118, 26300}, {16119, 26306}, {16121, 49012}, {16122, 49014}, {16123, 26314}, {16125, 26330}, {16129, 26449}, {16130, 26339}, {16138, 26490}, {16139, 26485}, {16140, 26479}, {16141, 26473}, {16142, 26355}, {16149, 49026}, {16150, 49028}, {16152, 49030}, {16153, 49032}, {16154, 26520}, {16155, 26519}, {16161, 49020}, {16162, 49022}, {18539, 48668}, {18977, 26435}, {19079, 26456}, {19080, 26462}, {22798, 49016}, {26396, 48503}, {26420, 48504}, {26516, 49107}, {35854, 49018}, {35855, 39660}, {45522, 48756}, {45524, 48757}

X(49070) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {2nd Fuhrmann, K798e}
X(49070) = X(79)-of-3rd anti-tri-squares-central triangle
X(49070) = reflection of X(49071) in X(20084)


X(49071) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO 2nd FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(49071) lies on these lines: {30, 45720}, {79, 3069}, {193, 20084}, {491, 3648}, {758, 49061}, {2771, 49051}, {3647, 26362}, {3649, 26370}, {3652, 26469}, {5441, 26515}, {5861, 16130}, {8982, 16116}, {11684, 26445}, {13743, 26325}, {16113, 26295}, {16114, 26376}, {16115, 26430}, {16117, 26513}, {16118, 26301}, {16119, 26307}, {16121, 49013}, {16122, 49015}, {16123, 26315}, {16125, 26331}, {16129, 26450}, {16131, 26340}, {16138, 26491}, {16139, 26486}, {16140, 26480}, {16141, 26474}, {16142, 26356}, {16148, 49027}, {16150, 49029}, {16152, 49031}, {16153, 49033}, {16154, 26525}, {16155, 26524}, {16161, 49021}, {16162, 49023}, {18977, 26436}, {19079, 26457}, {19080, 26463}, {22798, 49017}, {26397, 48503}, {26421, 48504}, {26438, 48668}, {26521, 49107}, {35854, 39661}, {35855, 49019}, {45523, 48757}, {45525, 48756}

X(49071) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {2nd Fuhrmann, K798e}
X(49071) = reflection of X(49070) in X(20084)


X(49072) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO HATZIPOLAKIS-MOSES

Barycentrics    (5*a^16-16*(b^2+c^2)*a^14+(12*b^4+29*b^2*c^2+12*c^4)*a^12+(b^2+c^2)*(8*b^4-15*b^2*c^2+8*c^4)*a^10-2*(5*b^8+5*c^8+b^2*c^2*(5*b^4-8*b^2*c^2+5*c^4))*a^8+10*(b^4-c^4)*(b^2-c^2)*b^2*c^2*a^6-(b^2-c^2)^2*(4*b^8+4*c^8+b^2*c^2*(7*b^4+18*b^2*c^2+7*c^4))*a^4+(b^4-c^4)*(b^2-c^2)^3*(8*b^4+5*b^2*c^2+8*c^4)*a^2-3*(b^2+c^2)^2*(b^2-c^2)^6)*S+(a^6-(b^2+c^2)*a^4-(b^2+c^2)^2*a^2+(b^4-c^4)*(b^2-c^2))*(2*a^12-4*(b^2+c^2)*a^10+(b^4+4*b^2*c^2+c^4)*a^8+2*(b^4-c^4)*(b^2-c^2)*a^6-2*(b^6-c^6)*(b^2-c^2)*a^4+2*(b^8-c^8)*a^2*(b^2-c^2)-(b^4-c^4)^2*(b^2-c^2)^2) : :

The reciprocal orthologic center of these triangles is X(6146).

X(49072) lies on these lines: {193, 49073}, {492, 32354}, {1154, 49052}, {3068, 6145}, {5860, 32374}, {10628, 49050}, {18400, 49038}, {18539, 48669}, {26294, 32330}, {26300, 32356}, {26306, 32357}, {26314, 32362}, {26324, 32363}, {26330, 32369}, {26339, 32373}, {26355, 32390}, {26361, 32391}, {26369, 32331}, {26375, 32332}, {26396, 48505}, {26420, 48506}, {26429, 32335}, {26435, 32336}, {26441, 32337}, {26444, 32371}, {26449, 32372}, {26456, 32342}, {26462, 32343}, {26468, 32379}, {26473, 32383}, {26479, 32382}, {26485, 32381}, {26490, 32380}, {26512, 32347}, {26514, 32394}, {26516, 49108}, {26519, 32406}, {26520, 32405}, {32360, 49012}, {32361, 49014}, {32364, 49016}, {32388, 49020}, {32389, 49022}, {32400, 49026}, {32402, 49028}, {32403, 49030}, {32404, 49032}, {35858, 49018}, {35859, 39660}, {45522, 48758}, {45524, 48759}

X(49072) = orthologic center (3rd anti-tri-squares-central, Hatzipolakis-Moses)
X(49072) = X(6145)-of-3rd anti-tri-squares-central triangle


X(49073) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO HATZIPOLAKIS-MOSES

Barycentrics    -(5*a^16-16*(b^2+c^2)*a^14+(12*b^4+29*b^2*c^2+12*c^4)*a^12+(b^2+c^2)*(8*b^4-15*b^2*c^2+8*c^4)*a^10-2*(5*b^8+5*c^8+b^2*c^2*(5*b^4-8*b^2*c^2+5*c^4))*a^8+10*(b^4-c^4)*(b^2-c^2)*b^2*c^2*a^6-(b^2-c^2)^2*(4*b^8+4*c^8+b^2*c^2*(7*b^4+18*b^2*c^2+7*c^4))*a^4+(b^4-c^4)*(b^2-c^2)^3*(8*b^4+5*b^2*c^2+8*c^4)*a^2-3*(b^2+c^2)^2*(b^2-c^2)^6)*S+(a^6-(b^2+c^2)*a^4-(b^2+c^2)^2*a^2+(b^4-c^4)*(b^2-c^2))*(2*a^12-4*(b^2+c^2)*a^10+(b^4+4*b^2*c^2+c^4)*a^8+2*(b^4-c^4)*(b^2-c^2)*a^6-2*(b^6-c^6)*(b^2-c^2)*a^4+2*(b^8-c^8)*a^2*(b^2-c^2)-(b^4-c^4)^2*(b^2-c^2)^2) : :

The reciprocal orthologic center of these triangles is X(6146).

X(49073) lies on these lines: {193, 49072}, {491, 32354}, {1154, 49053}, {3069, 6145}, {5861, 32373}, {8982, 32337}, {10628, 49051}, {18400, 49039}, {26295, 32330}, {26301, 32356}, {26307, 32357}, {26315, 32362}, {26325, 32363}, {26331, 32369}, {26340, 32374}, {26356, 32390}, {26362, 32391}, {26370, 32331}, {26376, 32332}, {26397, 48505}, {26421, 48506}, {26430, 32335}, {26436, 32336}, {26438, 48669}, {26445, 32371}, {26450, 32372}, {26457, 32342}, {26463, 32343}, {26469, 32379}, {26474, 32383}, {26480, 32382}, {26486, 32381}, {26491, 32380}, {26513, 32347}, {26515, 32394}, {26521, 49108}, {26524, 32406}, {26525, 32405}, {32360, 49013}, {32361, 49015}, {32364, 49017}, {32388, 49021}, {32389, 49023}, {32399, 49027}, {32402, 49029}, {32403, 49031}, {32404, 49033}, {35858, 39661}, {35859, 49019}, {45523, 48759}, {45525, 48758}

X(49073) = orthologic center (4th anti-tri-squares-central, Hatzipolakis-Moses)


X(49074) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO 3rd HATZIPOLAKIS

Barycentrics    (5*a^16-16*(b^2+c^2)*a^14+3*(4*b^4+23*b^2*c^2+4*c^4)*a^12+(b^2+c^2)*(8*b^4-87*b^2*c^2+8*c^4)*a^10-2*(5*b^8+5*c^8+b^2*c^2*(5*b^4-76*b^2*c^2+5*c^4))*a^8+2*(b^2+c^2)*(21*b^4-50*b^2*c^2+21*c^4)*b^2*c^2*a^6-(b^2-c^2)^2*(4*b^8+4*c^8-b^2*c^2*(17*b^4-58*b^2*c^2+17*c^4))*a^4+(b^4-c^4)*(b^2-c^2)^3*(8*b^4-19*b^2*c^2+8*c^4)*a^2-3*(b^2+c^2)^2*(b^2-c^2)^6)*S-(a^2+b^2-c^2)*(a^2-b^2+c^2)*(-a^2+b^2+c^2)*(2*a^12-4*(b^2+c^2)*a^10+(b^4+12*b^2*c^2+c^4)*a^8+2*(b^2+c^2)*(b^4-4*b^2*c^2+c^4)*a^6-2*(b^6-c^6)*(b^2-c^2)*a^4+2*(b^4-c^4)*(b^2-c^2)^3*a^2-(b^4-c^4)^2*(b^2-c^2)^2) : :

The reciprocal orthologic center of these triangles is X(12241).

X(49074) lies on these lines: {193, 49075}, {492, 22647}, {3068, 22466}, {5860, 22947}, {18539, 48670}, {18978, 26435}, {19083, 26456}, {19084, 26462}, {22476, 26369}, {22483, 26375}, {22524, 26429}, {22533, 26441}, {22559, 26512}, {22653, 26300}, {22658, 26306}, {22671, 49012}, {22675, 49014}, {22747, 26314}, {22776, 26324}, {22800, 49016}, {22833, 26330}, {22941, 26444}, {22943, 26449}, {22945, 26339}, {22951, 26294}, {22955, 26468}, {22956, 26490}, {22957, 26485}, {22958, 26479}, {22959, 26473}, {22963, 49020}, {22964, 49022}, {22965, 26355}, {22966, 26361}, {22969, 26514}, {22977, 49026}, {22979, 49028}, {22980, 49030}, {22981, 49032}, {22982, 26520}, {22983, 26519}, {26396, 48507}, {26420, 48508}, {26516, 49109}, {35860, 49018}, {35861, 39660}, {45522, 48810}, {45524, 48811}

X(49074) = orthologic center (3rd anti-tri-squares-central, 3rd Hatzipolakis)
X(49074) = X(22466)-of-3rd anti-tri-squares-central triangle


X(49075) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO 3rd HATZIPOLAKIS

Barycentrics    -(5*a^16-16*(b^2+c^2)*a^14+3*(4*b^4+23*b^2*c^2+4*c^4)*a^12+(b^2+c^2)*(8*b^4-87*b^2*c^2+8*c^4)*a^10-2*(5*b^8+5*c^8+b^2*c^2*(5*b^4-76*b^2*c^2+5*c^4))*a^8+2*(b^2+c^2)*(21*b^4-50*b^2*c^2+21*c^4)*b^2*c^2*a^6-(b^2-c^2)^2*(4*b^8+4*c^8-b^2*c^2*(17*b^4-58*b^2*c^2+17*c^4))*a^4+(b^4-c^4)*(b^2-c^2)^3*(8*b^4-19*b^2*c^2+8*c^4)*a^2-3*(b^2+c^2)^2*(b^2-c^2)^6)*S-(a^2+b^2-c^2)*(a^2-b^2+c^2)*(-a^2+b^2+c^2)*(2*a^12-4*(b^2+c^2)*a^10+(b^4+12*b^2*c^2+c^4)*a^8+2*(b^2+c^2)*(b^4-4*b^2*c^2+c^4)*a^6-2*(b^6-c^6)*(b^2-c^2)*a^4+2*(b^4-c^4)*(b^2-c^2)^3*a^2-(b^4-c^4)^2*(b^2-c^2)^2) : :

The reciprocal orthologic center of these triangles is X(12241).

X(49075) lies on these lines: {193, 49074}, {491, 22647}, {3069, 22466}, {5861, 22945}, {8982, 22533}, {18978, 26436}, {19083, 26457}, {19084, 26463}, {22476, 26370}, {22483, 26376}, {22524, 26430}, {22559, 26513}, {22653, 26301}, {22658, 26307}, {22671, 49013}, {22675, 49015}, {22747, 26315}, {22776, 26325}, {22800, 49017}, {22833, 26331}, {22941, 26445}, {22943, 26450}, {22947, 26340}, {22951, 26295}, {22955, 26469}, {22956, 26491}, {22957, 26486}, {22958, 26480}, {22959, 26474}, {22963, 49021}, {22964, 49023}, {22965, 26356}, {22966, 26362}, {22969, 26515}, {22976, 49027}, {22979, 49029}, {22980, 49031}, {22981, 49033}, {22982, 26525}, {22983, 26524}, {26397, 48507}, {26421, 48508}, {26438, 48670}, {26521, 49109}, {35860, 39661}, {35861, 49019}, {45523, 48811}, {45525, 48810}

X(49075) = orthologic center (4th anti-tri-squares-central, 3rd Hatzipolakis)


X(49076) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO HUTSON EXTOUCH

Barycentrics    -(-a+b+c)*(3*a^6+4*(b+c)*a^5-(5*b^2+18*b*c+5*c^2)*a^4-8*(b+c)^3*a^3+(b^4+c^4-6*b*c*(2*b^2-9*b*c+2*c^2))*a^2+4*(b^2-c^2)*(b-c)^3*a+(b^2-c^2)^2*(b-c)^2)*S+a*((b+c)*a^7+(b^2+4*b*c+c^2)*a^6-(b+c)*(3*b^2-2*b*c+3*c^2)*a^5-(b^2+c^2)*(3*b^2+26*b*c+3*c^2)*a^4+(b+c)*(3*b^4+3*c^4-2*b*c*(2*b^2+15*b*c+2*c^2))*a^3+(b^2+6*b*c+c^2)*(3*b^4+3*c^4+2*b*c*(3*b^2-b*c+3*c^2))*a^2-(b^2-c^2)^3*(b-c)*a-(b^4-c^4)*(b^2-c^2)*(b+c)^2) : :

The reciprocal orthologic center of these triangles is X(40).

X(49076) lies on these lines: {193, 49077}, {492, 9874}, {3068, 7160}, {5860, 12802}, {8000, 26514}, {9898, 26300}, {10059, 49030}, {10075, 49032}, {12120, 26294}, {12139, 26375}, {12200, 26429}, {12249, 26441}, {12260, 26369}, {12333, 26512}, {12411, 26306}, {12464, 49012}, {12465, 49014}, {12500, 26314}, {12599, 26330}, {12777, 26444}, {12789, 26449}, {12801, 26339}, {12856, 26468}, {12857, 26490}, {12858, 26485}, {12859, 26479}, {12860, 26473}, {12861, 49020}, {12862, 49022}, {12863, 26355}, {12864, 26361}, {12872, 49028}, {12874, 26520}, {12875, 26519}, {13978, 49026}, {18539, 48671}, {18979, 26435}, {19085, 26456}, {19086, 26462}, {22777, 26324}, {22801, 49016}, {26396, 48509}, {26420, 48510}, {26516, 49110}, {35862, 49018}, {35863, 39660}, {45522, 48812}, {45524, 48813}

X(49076) = orthologic center (3rd anti-tri-squares-central, Hutson extouch)
X(49076) = X(7160)-of-3rd anti-tri-squares-central triangle


X(49077) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO HUTSON EXTOUCH

Barycentrics    (-a+b+c)*(3*a^6+4*(b+c)*a^5-(5*b^2+18*b*c+5*c^2)*a^4-8*(b+c)^3*a^3+(b^4+c^4-6*b*c*(2*b^2-9*b*c+2*c^2))*a^2+4*(b^2-c^2)*(b-c)^3*a+(b^2-c^2)^2*(b-c)^2)*S+a*((b+c)*a^7+(b^2+4*b*c+c^2)*a^6-(b+c)*(3*b^2-2*b*c+3*c^2)*a^5-(b^2+c^2)*(3*b^2+26*b*c+3*c^2)*a^4+(b+c)*(3*b^4+3*c^4-2*b*c*(2*b^2+15*b*c+2*c^2))*a^3+(b^2+6*b*c+c^2)*(3*b^4+3*c^4+2*b*c*(3*b^2-b*c+3*c^2))*a^2-(b^2-c^2)^3*(b-c)*a-(b^4-c^4)*(b^2-c^2)*(b+c)^2) : :

The reciprocal orthologic center of these triangles is X(40).

X(49077) lies on these lines: {193, 49076}, {491, 9874}, {3069, 7160}, {5861, 12801}, {8000, 26515}, {8982, 12249}, {9898, 26301}, {10059, 49031}, {10075, 49033}, {12120, 26295}, {12139, 26376}, {12200, 26430}, {12260, 26370}, {12333, 26513}, {12411, 26307}, {12464, 49013}, {12465, 49015}, {12500, 26315}, {12599, 26331}, {12777, 26445}, {12789, 26450}, {12802, 26340}, {12856, 26469}, {12857, 26491}, {12858, 26486}, {12859, 26480}, {12860, 26474}, {12861, 49021}, {12862, 49023}, {12863, 26356}, {12864, 26362}, {12872, 49029}, {12874, 26525}, {12875, 26524}, {13914, 49027}, {18979, 26436}, {19085, 26457}, {19086, 26463}, {22777, 26325}, {22801, 49017}, {26397, 48509}, {26421, 48510}, {26438, 48671}, {26521, 49110}, {35862, 39661}, {35863, 49019}, {45523, 48813}, {45525, 48812}

X(49077) = orthologic center (4th anti-tri-squares-central, Hutson extouch)


X(49078) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO 1st JENKINS

Barycentrics    -2*(-a+b+c)*S+2*a^3+(b+c)*a^2-(b+c)*(b^2+c^2) : :
X(49078) = 3*X(3576)-4*X(48814) = 3*X(5860)-X(45719) = 3*X(5860)+X(49060)

The reciprocal orthologic center of these triangles is X(10).

X(49078) lies on these lines: {1, 492}, {8, 193}, {10, 3068}, {40, 26441}, {226, 26479}, {230, 13973}, {355, 49028}, {371, 12788}, {515, 49038}, {516, 48476}, {517, 49086}, {519, 3640}, {726, 49082}, {946, 26468}, {950, 26355}, {1125, 26361}, {1210, 49032}, {2784, 49040}, {2796, 49042}, {3244, 26514}, {3576, 45522}, {3626, 26339}, {3679, 45420}, {4297, 26294}, {6684, 26516}, {7969, 45444}, {8666, 26324}, {8715, 26512}, {9766, 45714}, {10106, 26435}, {10915, 26518}, {10916, 26517}, {12053, 26473}, {12245, 49048}, {12699, 18539}, {13883, 44594}, {13936, 44595}, {17766, 49084}, {18483, 49016}, {19925, 26330}, {21077, 26485}, {24244, 26442}, {26396, 48511}, {26420, 48512}, {31397, 49030}, {45524, 48815}, {48711, 49068}

X(49078) = midpoint of X(i) and X(j) for these {i, j}: {45719, 49060}, {48476, 49054}, {48711, 49068}
X(49078) = reflection of X(49079) in X(8)
X(49078) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {1st Jenkins, 1st Savin}
X(49078) = X(10)-of-3rd anti-tri-squares-central triangle
X(49078) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (8, 193, 26300), (3068, 26444, 10), (5860, 49060, 45719), (26361, 26369, 1125)


X(49079) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO 1st JENKINS

Barycentrics    2*(-a+b+c)*S+2*a^3+(b+c)*a^2-(b+c)*(b^2+c^2) : :
X(49079) = 3*X(3576)-4*X(48815) = 3*X(5861)-X(45720) = 3*X(5861)+X(49061)

The reciprocal orthologic center of these triangles is X(10).

X(49079) lies on these lines: {1, 491}, {8, 193}, {10, 3069}, {40, 8982}, {226, 26480}, {230, 13911}, {355, 49029}, {372, 12787}, {515, 49039}, {516, 48477}, {517, 49087}, {519, 3641}, {726, 49083}, {946, 26469}, {950, 26356}, {1125, 26362}, {1210, 49033}, {1707, 13461}, {2784, 49041}, {2796, 49043}, {3244, 26515}, {3576, 45523}, {3626, 26340}, {3679, 45421}, {4297, 26295}, {6684, 26521}, {7968, 45445}, {8666, 26325}, {8715, 26513}, {9766, 45713}, {10106, 26436}, {10915, 26523}, {10916, 26522}, {12053, 26474}, {12245, 49049}, {12699, 26438}, {13883, 44596}, {13936, 44597}, {17766, 49085}, {18483, 49017}, {19925, 26331}, {21077, 26486}, {24243, 26443}, {26397, 48511}, {26421, 48512}, {31397, 49031}, {45525, 48814}, {48712, 49069}

X(49079) = midpoint of X(i) and X(j) for these {i, j}: {45720, 49061}, {48477, 49055}, {48712, 49069}
X(49079) = reflection of X(49078) in X(8)
X(49079) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {1st Jenkins, 1st Savin}
X(49079) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (8, 193, 26301), (3069, 26445, 10), (5861, 49061, 45720), (26362, 26370, 1125)


X(49080) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO MIDHEIGHT

Barycentrics    (3*a^10+3*(b^2+c^2)*a^8-2*(13*b^4-22*b^2*c^2+13*c^4)*a^6+30*(b^4-c^4)*(b^2-c^2)*a^4-(b^2-c^2)^2*(9*b^4+38*b^2*c^2+9*c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3)*S+4*a^2*((b^2+c^2)*a^8-2*(b^4-b^2*c^2+c^4)*a^6+2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)^2*(b^2+c^2)) : :
X(49080) = 3*X(5656)-4*X(48816)

The reciprocal orthologic center of these triangles is X(4).

X(49080) lies on these lines: {30, 49052}, {64, 3068}, {193, 34146}, {492, 6225}, {1498, 26294}, {2777, 49050}, {2883, 26361}, {3357, 26516}, {5656, 45522}, {5860, 6266}, {5878, 26468}, {6000, 49038}, {6001, 49054}, {6247, 26330}, {6267, 26339}, {6285, 26435}, {7355, 26355}, {7973, 26514}, {9899, 26300}, {9914, 26306}, {10060, 49030}, {10076, 49032}, {11381, 26375}, {12202, 26429}, {12250, 26441}, {12262, 26369}, {12335, 26512}, {12468, 49012}, {12469, 49014}, {12502, 26314}, {12779, 26444}, {12791, 26449}, {12920, 26490}, {12930, 26485}, {12940, 26479}, {12950, 26473}, {12986, 49020}, {12987, 49022}, {13093, 49028}, {13094, 26520}, {13095, 26519}, {13980, 49026}, {15311, 48476}, {18539, 48672}, {19087, 26456}, {19088, 26462}, {22778, 26324}, {22802, 49016}, {26396, 48513}, {26420, 48514}, {35864, 49018}, {35865, 39660}, {36201, 49094}, {45524, 48817}

X(49080) = orthologic center (3rd anti-tri-squares-central, midheight)
X(49080) = X(64)-of-3rd anti-tri-squares-central triangle


X(49081) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO MIDHEIGHT

Barycentrics    -(3*a^10+3*(b^2+c^2)*a^8-2*(13*b^4-22*b^2*c^2+13*c^4)*a^6+30*(b^4-c^4)*(b^2-c^2)*a^4-(b^2-c^2)^2*(9*b^4+38*b^2*c^2+9*c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3)*S+4*a^2*((b^2+c^2)*a^8-2*(b^4-b^2*c^2+c^4)*a^6+2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)^2*(b^2+c^2)) : :
X(49081) = 3*X(5656)-4*X(48817)

The reciprocal orthologic center of these triangles is X(4).

X(49081) lies on these lines: {30, 49053}, {64, 3069}, {193, 34146}, {491, 6225}, {1498, 26295}, {2777, 49051}, {2883, 26362}, {3357, 26521}, {5656, 45523}, {5861, 6267}, {5878, 26469}, {6000, 49039}, {6001, 49055}, {6247, 26331}, {6266, 26340}, {6285, 26436}, {7355, 26356}, {7973, 26515}, {8982, 12250}, {8991, 49027}, {9899, 26301}, {9914, 26307}, {10060, 49031}, {10076, 49033}, {11381, 26376}, {12202, 26430}, {12262, 26370}, {12335, 26513}, {12468, 49013}, {12469, 49015}, {12502, 26315}, {12779, 26445}, {12791, 26450}, {12920, 26491}, {12930, 26486}, {12940, 26480}, {12950, 26474}, {12986, 49021}, {12987, 49023}, {13093, 49029}, {13094, 26525}, {13095, 26524}, {15311, 48477}, {19087, 26457}, {19088, 26463}, {22778, 26325}, {22802, 49017}, {26397, 48513}, {26421, 48514}, {26438, 48672}, {35864, 39661}, {35865, 49019}, {36201, 49095}, {45525, 48816}

X(49081) = orthologic center (4th anti-tri-squares-central, midheight)


X(49082) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO 1st NEUBERG

Barycentrics    ((b^2+c^2)*a^2-3*b^2*c^2)*S+(b^2+c^2)*(a^4-b^2*c^2) : :
X(49082) = 3*X(7709)-4*X(48818) = 3*X(49058)-4*X(49086)

The reciprocal orthologic center of these triangles is X(3).

X(49082) lies on these lines: {4, 33452}, {39, 26361}, {76, 3068}, {193, 732}, {194, 492}, {384, 26429}, {511, 48476}, {538, 5860}, {726, 49078}, {730, 45719}, {2782, 49038}, {3095, 26468}, {5969, 49042}, {6248, 26330}, {6273, 26339}, {6274, 7798}, {6275, 17130}, {6314, 11292}, {7709, 45522}, {7976, 26514}, {9902, 26300}, {9917, 26306}, {9983, 26314}, {10063, 49030}, {10079, 49032}, {11257, 26294}, {12143, 26375}, {12251, 26441}, {12263, 26369}, {12338, 26512}, {12474, 49012}, {12475, 49014}, {12782, 26444}, {12794, 26449}, {12836, 26473}, {12837, 26479}, {12923, 26490}, {12933, 26485}, {12992, 49020}, {12993, 49022}, {13077, 26355}, {13108, 49028}, {13109, 26520}, {13110, 26519}, {13983, 49026}, {14839, 49060}, {14881, 49016}, {18539, 48673}, {18982, 26435}, {19089, 26456}, {19090, 26462}, {22779, 26324}, {26396, 48515}, {26420, 48516}, {26516, 49111}, {32515, 49058}, {35866, 49018}, {35867, 39660}, {45524, 48819}

X(49082) = orthologic center (3rd anti-tri-squares-central, 1st Neuberg)
X(49082) = X(76)-of-3rd anti-tri-squares-central triangle
X(49082) = reflection of X(49083) in X(20081)


X(49083) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO 1st NEUBERG

Barycentrics    -((b^2+c^2)*a^2-3*b^2*c^2)*S+(b^2+c^2)*(a^4-b^2*c^2) : :
X(49083) = 3*X(7709)-4*X(48819) = 3*X(49059)-4*X(49087)

The reciprocal orthologic center of these triangles is X(3).

X(49083) lies on these lines: {4, 33453}, {39, 26362}, {76, 3069}, {193, 732}, {194, 491}, {384, 26430}, {511, 48477}, {538, 5861}, {726, 49079}, {730, 45720}, {2782, 49039}, {3095, 26469}, {5969, 49043}, {6248, 26331}, {6272, 26340}, {6274, 17130}, {6275, 7798}, {6318, 11291}, {7709, 45523}, {7976, 26515}, {8982, 12251}, {8992, 49027}, {9902, 26301}, {9917, 26307}, {9983, 26315}, {10063, 49031}, {10079, 49033}, {11257, 26295}, {12143, 26376}, {12263, 26370}, {12338, 26513}, {12474, 49013}, {12475, 49015}, {12782, 26445}, {12794, 26450}, {12836, 26474}, {12837, 26480}, {12923, 26491}, {12933, 26486}, {12992, 49021}, {12993, 49023}, {13077, 26356}, {13108, 49029}, {13109, 26525}, {13110, 26524}, {14839, 49061}, {14881, 49017}, {18982, 26436}, {19089, 26457}, {19090, 26463}, {22779, 26325}, {26397, 48515}, {26421, 48516}, {26438, 48673}, {26521, 49111}, {32515, 49059}, {35866, 39661}, {35867, 49019}, {45525, 48818}

X(49083) = orthologic center (4th anti-tri-squares-central, 1st Neuberg)
X(49083) = reflection of X(49082) in X(20081)


X(49084) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO 2nd NEUBERG

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

The reciprocal orthologic center of these triangles is X(3).

X(49084) lies on these lines: {4, 33454}, {83, 3068}, {193, 732}, {492, 2896}, {637, 754}, {6249, 26330}, {6275, 26339}, {6287, 26468}, {6292, 26361}, {6313, 11291}, {7977, 26514}, {9903, 26300}, {9918, 26306}, {10064, 49030}, {10080, 49032}, {12122, 26294}, {12144, 26375}, {12206, 26429}, {12252, 26441}, {12264, 26369}, {12339, 26512}, {12476, 49012}, {12477, 49014}, {12783, 26444}, {12795, 26449}, {12924, 26490}, {12934, 26485}, {12944, 26479}, {12954, 26473}, {12994, 49020}, {12995, 49022}, {13078, 26355}, {13111, 49028}, {13112, 26520}, {13113, 26519}, {13984, 49026}, {17766, 49078}, {18539, 48674}, {18983, 26435}, {19091, 26456}, {19092, 26462}, {22780, 26324}, {22803, 49016}, {26396, 48517}, {26420, 48518}, {26516, 49112}, {29012, 39887}, {35868, 49018}, {35869, 39660}, {45522, 48770}, {45524, 48771}, {49038, 49058}, {49040, 49086}

X(49084) = orthologic center (3rd anti-tri-squares-central, 2nd Neuberg)
X(49084) = X(83)-of-3rd anti-tri-squares-central triangle
X(49084) = reflection of X(49085) in X(20088)


X(49085) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO 2nd NEUBERG

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

The reciprocal orthologic center of these triangles is X(3).

X(49085) lies on these lines: {4, 33455}, {83, 3069}, {193, 732}, {491, 2896}, {638, 754}, {6249, 26331}, {6274, 26340}, {6287, 26469}, {6292, 26362}, {6317, 11292}, {7977, 26515}, {8982, 12252}, {8993, 49027}, {9903, 26301}, {9918, 26307}, {10064, 49031}, {10080, 49033}, {12122, 26295}, {12144, 26376}, {12206, 26430}, {12264, 26370}, {12339, 26513}, {12476, 49013}, {12477, 49015}, {12783, 26445}, {12795, 26450}, {12924, 26491}, {12934, 26486}, {12944, 26480}, {12954, 26474}, {12994, 49021}, {12995, 49023}, {13078, 26356}, {13111, 49029}, {13112, 26525}, {13113, 26524}, {17766, 49079}, {18983, 26436}, {19091, 26457}, {19092, 26463}, {22780, 26325}, {22803, 49017}, {26397, 48517}, {26421, 48518}, {26438, 48674}, {26521, 49112}, {29012, 39888}, {35868, 39661}, {35869, 49019}, {45523, 48771}, {45525, 48770}, {49039, 49059}, {49041, 49087}

X(49085) = orthologic center (4th anti-tri-squares-central, 2nd Neuberg)
X(49085) = reflection of X(49084) in X(20088)


X(49086) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO ORTHIC AXES

Barycentrics    -2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*S+(-a^2+b^2+c^2)*(2*a^4-(b^2+c^2)*a^2+(b^2-c^2)^2) : :
X(49086) = 3*X(3)-4*X(48772) = 3*X(591)-2*X(9739) = 5*X(1656)-4*X(48773) = 3*X(5860)+X(48476) = 3*X(5860)-X(49038) = 3*X(49058)+X(49082)

The reciprocal orthologic center of these triangles is X(4).

X(49086) lies on these lines: {3, 489}, {4, 193}, {5, 1588}, {25, 13428}, {26, 26306}, {30, 1160}, {52, 45478}, {68, 1322}, {114, 371}, {140, 26361}, {155, 3092}, {230, 486}, {355, 26300}, {376, 49092}, {381, 45420}, {487, 1007}, {495, 26479}, {496, 26473}, {511, 13748}, {517, 49078}, {524, 14233}, {542, 13749}, {546, 5875}, {550, 26294}, {576, 45440}, {591, 9739}, {638, 11898}, {639, 43119}, {952, 45719}, {1151, 45554}, {1352, 3071}, {1353, 1587}, {1483, 26514}, {1585, 3167}, {1656, 45524}, {1993, 32588}, {3070, 9974}, {3629, 45862}, {3818, 45441}, {5050, 7389}, {5200, 41588}, {5690, 26444}, {5844, 49060}, {5871, 49056}, {5889, 6239}, {5901, 26369}, {6193, 24244}, {6214, 37343}, {6251, 45439}, {6278, 6561}, {6279, 42269}, {6280, 6560}, {6281, 42268}, {6290, 6565}, {6400, 12272}, {6756, 26375}, {6776, 12322}, {6805, 45298}, {6811, 12313}, {7375, 38110}, {7582, 18583}, {7583, 44594}, {7584, 30435}, {9732, 9766}, {10784, 21737}, {10845, 12257}, {10942, 26485}, {10943, 26490}, {11313, 45411}, {11442, 32587}, {12188, 33431}, {13993, 40287}, {15069, 23261}, {15171, 26355}, {18358, 23273}, {18586, 49036}, {18587, 49034}, {18990, 26435}, {19116, 26456}, {19117, 26462}, {26314, 32151}, {26324, 32153}, {26346, 36711}, {26396, 48519}, {26420, 48520}, {26429, 32134}, {26449, 32162}, {26512, 32141}, {26519, 32214}, {26520, 32213}, {28174, 49054}, {32146, 49012}, {32147, 49014}, {32177, 49020}, {32178, 49022}, {32423, 49050}, {32515, 49058}, {33372, 48657}, {35830, 39894}, {35837, 39530}, {36656, 45375}, {37489, 48738}, {39899, 45407}, {42262, 45555}, {43120, 45472}, {43125, 45487}, {45377, 45579}, {49040, 49084}

X(49086) = midpoint of X(i) and X(j) for these {i, j}: {48476, 49038}, {49050, 49098}
X(49086) = reflection of X(i) in X(j) for these (i, j): (5875, 546), (9732, 48466), (49087, 4)
X(49086) = orthologic center (3rd anti-tri-squares-central, T) for these triangles T: {orthic axes, Yiu tangents}
X(49086) = X(5)-of-3rd anti-tri-squares-central triangle
X(49086) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 193, 49028), (4, 12221, 49029), (4, 49048, 193), (489, 45510, 3), (492, 26441, 3), (637, 45406, 3), (1351, 48660, 4), (3068, 26468, 5), (5860, 48476, 49038), (6214, 42215, 37343), (6811, 43134, 12313), (10784, 21737, 48906), (12601, 18440, 4), (18539, 49028, 4), (26330, 49016, 546), (26361, 26516, 140), (26473, 49032, 496), (26479, 49030, 495), (45375, 45489, 36656)


X(49087) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO ORTHIC AXES

Barycentrics    2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*S+(-a^2+b^2+c^2)*(2*a^4-(b^2+c^2)*a^2+(b^2-c^2)^2) : :
X(49087) = 3*X(3)-4*X(48773) = 5*X(1656)-4*X(48772) = 3*X(1991)-2*X(9738) = 3*X(5861)+X(48477) = 3*X(5861)-X(49039) = 3*X(49059)+X(49083)

The reciprocal orthologic center of these triangles is X(4).

X(49087) lies on these lines: {3, 490}, {4, 193}, {5, 1587}, {25, 13439}, {26, 26307}, {30, 1161}, {52, 45479}, {68, 1321}, {114, 372}, {140, 26362}, {155, 3093}, {230, 485}, {355, 26301}, {376, 49093}, {381, 45421}, {488, 1007}, {495, 26480}, {496, 26474}, {511, 13749}, {517, 49079}, {524, 14230}, {542, 13748}, {546, 5874}, {550, 26295}, {576, 45441}, {637, 11898}, {640, 43118}, {952, 45720}, {1152, 45555}, {1352, 3070}, {1353, 1588}, {1483, 26515}, {1586, 3167}, {1656, 45525}, {1991, 9738}, {1993, 32587}, {3071, 9975}, {3629, 45863}, {3818, 45440}, {5050, 7388}, {5690, 26445}, {5844, 49061}, {5870, 49057}, {5889, 6400}, {5901, 26370}, {6193, 24243}, {6215, 37342}, {6239, 12272}, {6250, 45438}, {6278, 42269}, {6279, 6561}, {6280, 42268}, {6281, 6560}, {6289, 6564}, {6756, 26376}, {6776, 12323}, {6806, 45298}, {6813, 12314}, {7376, 38110}, {7581, 18583}, {7583, 30435}, {7584, 44597}, {9733, 9766}, {10783, 48906}, {10846, 12256}, {10942, 26486}, {10943, 26491}, {11314, 45410}, {11442, 32588}, {12188, 33430}, {13925, 40286}, {15069, 23251}, {15171, 26356}, {18358, 23267}, {18586, 49035}, {18587, 49037}, {18990, 26436}, {19116, 26457}, {19117, 26463}, {21737, 48876}, {26315, 32151}, {26325, 32153}, {26336, 36712}, {26397, 48519}, {26421, 48520}, {26430, 32134}, {26450, 32162}, {26513, 32141}, {26524, 32214}, {26525, 32213}, {28174, 49055}, {32146, 49013}, {32147, 49015}, {32177, 49021}, {32178, 49023}, {32423, 49051}, {32455, 45870}, {32515, 49059}, {33373, 48657}, {35831, 39893}, {35836, 39530}, {36655, 45376}, {37489, 48739}, {39899, 45406}, {42265, 45554}, {43121, 45473}, {43124, 45486}, {45378, 45578}, {49041, 49085}

X(49087) = midpoint of X(i) and X(j) for these {i, j}: {48477, 49039}, {49051, 49099}
X(49087) = reflection of X(i) in X(j) for these (i, j): (5874, 546), (9733, 48467), (49086, 4)
X(49087) = orthologic center (4th anti-tri-squares-central, T) for these triangles T: {orthic axes, Yiu tangents}
X(49087) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 193, 49029), (4, 12222, 49028), (4, 49049, 193), (490, 45511, 3), (491, 8982, 3), (638, 45407, 3), (1351, 48659, 4), (3069, 26469, 5), (5861, 48477, 49039), (6215, 42216, 37342), (6813, 43133, 12314), (12602, 18440, 4), (26331, 49017, 546), (26362, 26521, 140), (26438, 49029, 4), (26474, 49033, 496), (26480, 49031, 495), (45376, 45488, 36655)


X(49088) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO REFLECTION

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

The reciprocal orthologic center of these triangles is X(4).

X(49088) lies on these lines: {54, 3068}, {193, 31304}, {195, 49028}, {492, 2888}, {539, 5860}, {1154, 49038}, {1209, 26361}, {3574, 26330}, {6277, 26339}, {6288, 26468}, {7691, 26294}, {7979, 26514}, {9905, 26300}, {9920, 26306}, {9985, 26314}, {10066, 49030}, {10082, 49032}, {10610, 26516}, {10628, 49044}, {11576, 26375}, {12208, 26429}, {12254, 26441}, {12266, 26369}, {12341, 26512}, {12480, 49012}, {12481, 49014}, {12785, 26444}, {12797, 26449}, {12926, 26490}, {12936, 26485}, {12946, 26479}, {12956, 26473}, {12965, 49018}, {12971, 39660}, {12998, 49020}, {12999, 49022}, {13079, 26355}, {13121, 26520}, {13122, 26519}, {13986, 49026}, {18400, 48476}, {18539, 48675}, {18984, 26435}, {19095, 26456}, {19096, 26462}, {22781, 26324}, {22804, 49016}, {26396, 48521}, {26420, 48522}, {32423, 49050}, {45522, 48774}, {45524, 48775}

X(49088) = orthologic center (3rd anti-tri-squares-central, reflection)
X(49088) = X(54)-of-3rd anti-tri-squares-central triangle


X(49089) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO REFLECTION

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

The reciprocal orthologic center of these triangles is X(4).

X(49089) lies on these lines: {54, 3069}, {193, 31304}, {195, 49029}, {491, 2888}, {539, 5861}, {1154, 49039}, {1209, 26362}, {3574, 26331}, {6276, 26340}, {6288, 26469}, {7691, 26295}, {7979, 26515}, {8982, 12254}, {8995, 49027}, {9905, 26301}, {9920, 26307}, {9985, 26315}, {10066, 49031}, {10082, 49033}, {10610, 26521}, {10628, 49045}, {11576, 26376}, {12208, 26430}, {12266, 26370}, {12341, 26513}, {12480, 49013}, {12481, 49015}, {12785, 26445}, {12797, 26450}, {12926, 26491}, {12936, 26486}, {12946, 26480}, {12956, 26474}, {12965, 39661}, {12971, 49019}, {12998, 49021}, {12999, 49023}, {13079, 26356}, {13121, 26525}, {13122, 26524}, {18400, 48477}, {18984, 26436}, {19095, 26457}, {19096, 26463}, {22781, 26325}, {22804, 49017}, {26397, 48521}, {26421, 48522}, {26438, 48675}, {32423, 49051}, {45523, 48775}, {45525, 48774}

X(49089) = orthologic center (4th anti-tri-squares-central, reflection)


X(49090) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO 1st SCHIFFLER

Barycentrics    (5*a^7+3*(b+c)*a^6-3*(5*b^2-4*b*c+5*c^2)*a^5-3*(b+c)*(3*b^2-2*b*c+3*c^2)*a^4+(15*b^4+15*c^4-b*c*(8*b^2+9*b*c+8*c^2))*a^3+(b+c)*(9*b^4+9*c^4-b*c*(12*b^2-11*b*c+12*c^2))*a^2-(b^2-c^2)^2*(5*b^2+4*b*c+5*c^2)*a-3*(b^2-c^2)^3*(b-c))*S+2*a^9-5*(b^2+c^2)*a^7+(b+c)*(b^2+c^2)*a^6+(3*b^4+3*c^4+8*b*c*(b^2+c^2))*a^5-(b^2-c^2)*(b-c)*(3*b^2+4*b*c+3*c^2)*a^4+(b^6+c^6-8*b*c*(b^4+c^4))*a^3+(b+c)*(b^2+c^2)*(3*b^4+3*c^4-b*c*(4*b^2-b*c+4*c^2))*a^2-(b^4-c^4)^2*a-(b^4-c^4)*(b^2-c^2)^2*(b-c) : :

The reciprocal orthologic center of these triangles is X(79).

X(49090) lies on these lines: {193, 49091}, {492, 12849}, {3068, 10266}, {5860, 12808}, {12146, 26375}, {12209, 26429}, {12255, 26441}, {12267, 26369}, {12342, 26512}, {12409, 26300}, {12414, 26306}, {12482, 49012}, {12483, 49014}, {12504, 26314}, {12556, 26294}, {12600, 26330}, {12786, 26444}, {12798, 26449}, {12807, 26339}, {12919, 26468}, {12927, 26490}, {12937, 26485}, {12947, 26479}, {12957, 26473}, {13000, 49020}, {13001, 49022}, {13080, 26355}, {13089, 26361}, {13100, 26514}, {13126, 49028}, {13128, 49030}, {13129, 49032}, {13130, 26520}, {13131, 26519}, {13987, 49026}, {18539, 48676}, {18985, 26435}, {19097, 26456}, {19098, 26462}, {22782, 26324}, {22805, 49016}, {26396, 48523}, {26420, 48524}, {26516, 49113}, {35870, 49018}, {35871, 39660}, {45522, 48776}, {45524, 48777}

X(49090) = orthologic center (3rd anti-tri-squares-central, 1st Schiffler)
X(49090) = X(10266)-of-3rd anti-tri-squares-central triangle


X(49091) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO 1st SCHIFFLER

Barycentrics    -(5*a^7+3*(b+c)*a^6-3*(5*b^2-4*b*c+5*c^2)*a^5-3*(b+c)*(3*b^2-2*b*c+3*c^2)*a^4+(15*b^4+15*c^4-b*c*(8*b^2+9*b*c+8*c^2))*a^3+(b+c)*(9*b^4+9*c^4-b*c*(12*b^2-11*b*c+12*c^2))*a^2-(b^2-c^2)^2*(5*b^2+4*b*c+5*c^2)*a-3*(b^2-c^2)^3*(b-c))*S+2*a^9-5*(b^2+c^2)*a^7+(b+c)*(b^2+c^2)*a^6+(3*b^4+3*c^4+8*b*c*(b^2+c^2))*a^5-(b^2-c^2)*(b-c)*(3*b^2+4*b*c+3*c^2)*a^4+(b^6+c^6-8*b*c*(b^4+c^4))*a^3+(b+c)*(b^2+c^2)*(3*b^4+3*c^4-b*c*(4*b^2-b*c+4*c^2))*a^2-(b^4-c^4)^2*a-(b^4-c^4)*(b^2-c^2)^2*(b-c) : :

The reciprocal orthologic center of these triangles is X(79).

X(49091) lies on these lines: {193, 49090}, {491, 12849}, {3069, 10266}, {5861, 12807}, {8982, 12255}, {12146, 26376}, {12209, 26430}, {12267, 26370}, {12342, 26513}, {12409, 26301}, {12414, 26307}, {12482, 49013}, {12483, 49015}, {12504, 26315}, {12556, 26295}, {12600, 26331}, {12786, 26445}, {12798, 26450}, {12808, 26340}, {12919, 26469}, {12927, 26491}, {12937, 26486}, {12947, 26480}, {12957, 26474}, {13000, 49021}, {13001, 49023}, {13080, 26356}, {13089, 26362}, {13100, 26515}, {13126, 49029}, {13128, 49031}, {13129, 49033}, {13130, 26525}, {13131, 26524}, {13919, 49027}, {18985, 26436}, {19097, 26457}, {19098, 26463}, {22782, 26325}, {22805, 49017}, {26397, 48523}, {26421, 48524}, {26438, 48676}, {26521, 49113}, {35870, 39661}, {35871, 49019}, {45523, 48777}, {45525, 48776}

X(49091) = orthologic center (4th anti-tri-squares-central, 1st Schiffler)


X(49092) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    4*(11*a^4-4*(b^2+c^2)*a^2-7*(b^2-c^2)^2)*S+29*a^6-35*(b^2+c^2)*a^4+(19*b^4-6*b^2*c^2+19*c^4)*a^2-13*(b^4-c^4)*(b^2-c^2) : :
X(49092) = 3*X(4)-4*X(33457) = 8*X(1328)-7*X(41106) = 3*X(3524)-4*X(13794) = 9*X(3524)-8*X(13835) = 17*X(3544)-16*X(48779) = 3*X(11001)-8*X(13811) = 3*X(13794)-2*X(13835) = 4*X(13798)-5*X(19708) = 5*X(41099)-4*X(48678)

The reciprocal orthologic center of these triangles is X(13785).

X(49092) lies on these lines: {4, 33457}, {30, 49048}, {193, 15682}, {230, 14226}, {376, 49086}, {492, 13798}, {1328, 3068}, {3524, 13794}, {3544, 45524}, {5860, 11001}, {13786, 26294}, {13787, 26369}, {13788, 26375}, {13792, 26429}, {13795, 26512}, {13799, 26300}, {13800, 26306}, {13802, 49012}, {13803, 49014}, {13805, 26314}, {13807, 26330}, {13808, 26444}, {13809, 26449}, {13810, 26339}, {13812, 26468}, {13813, 26490}, {13814, 26485}, {13815, 26479}, {13816, 26473}, {13817, 49020}, {13818, 49022}, {13819, 26355}, {13821, 26361}, {13822, 26514}, {13836, 49028}, {13837, 49030}, {13838, 49032}, {13839, 26520}, {13840, 26519}, {13849, 49026}, {18539, 41099}, {18987, 26435}, {19100, 26462}, {19101, 26456}, {22784, 26324}, {22807, 49016}, {26396, 48527}, {26420, 48528}, {26516, 49115}, {35874, 49018}, {35875, 39660}, {43386, 44594}, {43387, 44595}, {45522, 48781}

X(49092) = orthologic center (3rd anti-tri-squares-central, 2nd tri-squares-central)
X(49092) = X(1328)-of-3rd anti-tri-squares-central triangle


X(49093) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO 1st TRI-SQUARES-CENTRAL

Barycentrics    -4*(11*a^4-4*(b^2+c^2)*a^2-7*(b^2-c^2)^2)*S+29*a^6-35*(b^2+c^2)*a^4+(19*b^4-6*b^2*c^2+19*c^4)*a^2-13*(b^4-c^4)*(b^2-c^2) : :
X(49093) = 3*X(4)-4*X(33456) = 8*X(1327)-7*X(41106) = 3*X(3524)-4*X(13674) = 9*X(3524)-8*X(13712) = 17*X(3544)-16*X(48778) = 3*X(11001)-8*X(13690) = 3*X(13674)-2*X(13712) = 4*X(13678)-5*X(19708) = 5*X(41099)-4*X(48677)

The reciprocal orthologic center of these triangles is X(13665).

X(49093) lies on these lines: {4, 33456}, {30, 49049}, {193, 15682}, {230, 14241}, {376, 49087}, {491, 13678}, {1327, 3069}, {3524, 8982}, {3544, 45525}, {5861, 11001}, {13666, 26295}, {13667, 26370}, {13668, 26376}, {13672, 26430}, {13675, 26513}, {13679, 26301}, {13680, 26307}, {13682, 49013}, {13683, 49015}, {13685, 26315}, {13687, 26331}, {13688, 26445}, {13689, 26450}, {13691, 26340}, {13692, 26469}, {13693, 26491}, {13694, 26486}, {13695, 26480}, {13696, 26474}, {13697, 49021}, {13698, 49023}, {13699, 26356}, {13701, 26362}, {13702, 26515}, {13713, 49029}, {13714, 49031}, {13715, 49033}, {13716, 26525}, {13717, 26524}, {13920, 49027}, {18986, 26436}, {19099, 26457}, {22541, 26463}, {22783, 26325}, {22806, 49017}, {26397, 48525}, {26421, 48526}, {26438, 41099}, {26521, 49114}, {35872, 39661}, {35873, 49019}, {43386, 44596}, {43387, 44597}, {45523, 48780}

X(49093) = orthologic center (4th anti-tri-squares-central, 1st tri-squares-central)


X(49094) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(49094) lies on these lines: {66, 193}, {67, 3068}, {492, 11061}, {511, 49050}, {542, 49038}, {1503, 49044}, {2781, 48476}, {5860, 32281}, {6593, 26361}, {9970, 26468}, {14984, 49052}, {18539, 48679}, {26294, 32233}, {26300, 32261}, {26306, 32262}, {26314, 32268}, {26324, 32270}, {26330, 32274}, {26339, 32280}, {26355, 32297}, {26369, 32238}, {26375, 32239}, {26396, 48529}, {26420, 48530}, {26429, 32242}, {26435, 32243}, {26441, 32247}, {26444, 32278}, {26449, 32279}, {26456, 32252}, {26462, 32253}, {26473, 32290}, {26479, 32289}, {26485, 32288}, {26490, 32287}, {26512, 32256}, {26514, 32298}, {26516, 49116}, {26519, 32310}, {26520, 32309}, {32265, 49012}, {32266, 49014}, {32271, 49016}, {32295, 49020}, {32296, 49022}, {32304, 49026}, {32306, 49028}, {32307, 49030}, {32308, 49032}, {35876, 49018}, {35877, 39660}, {36201, 49080}, {45522, 48782}, {45524, 48783}

X(49094) = orthologic center (3rd anti-tri-squares-central, Walsmith)
X(49094) = X(67)-of-3rd anti-tri-squares-central triangle


X(49095) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(49095) lies on these lines: {66, 193}, {67, 3069}, {491, 11061}, {511, 49051}, {542, 49039}, {1503, 49045}, {2781, 48477}, {5861, 32280}, {6593, 26362}, {8982, 32247}, {9970, 26469}, {14984, 49053}, {26295, 32233}, {26301, 32261}, {26307, 32262}, {26315, 32268}, {26325, 32270}, {26331, 32274}, {26340, 32281}, {26356, 32297}, {26370, 32238}, {26376, 32239}, {26397, 48529}, {26421, 48530}, {26430, 32242}, {26436, 32243}, {26438, 48679}, {26445, 32278}, {26450, 32279}, {26457, 32252}, {26463, 32253}, {26474, 32290}, {26480, 32289}, {26486, 32288}, {26491, 32287}, {26513, 32256}, {26515, 32298}, {26521, 49116}, {26524, 32310}, {26525, 32309}, {32265, 49013}, {32266, 49015}, {32271, 49017}, {32295, 49021}, {32296, 49023}, {32303, 49027}, {32306, 49029}, {32307, 49031}, {32308, 49033}, {35876, 39661}, {35877, 49019}, {36201, 49081}, {45523, 48783}, {45525, 48782}

X(49095) = orthologic center (4th anti-tri-squares-central, Walsmith)


X(49096) = PARALLELOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO 1st ANTI-BROCARD

Barycentrics    (3*a^4-3*(b^2+c^2)*a^2-b^4+5*b^2*c^2-c^4)*S+(b^2+c^2)*a^4-2*(b^4+c^4)*a^2+b^2*c^2*(b^2+c^2) : :
X(49096) = 3*X(14651)-4*X(48784)

The reciprocal parallelogic center of these triangles is X(385).

X(49096) lies on the circumcircle of 3rd anti-tri-squares-central triangle and these lines: {98, 26294}, {99, 3068}, {114, 26330}, {115, 26361}, {148, 492}, {193, 5969}, {542, 49044}, {543, 5860}, {690, 49098}, {2782, 49038}, {2783, 48692}, {2787, 48711}, {2794, 49046}, {2799, 49100}, {3023, 26355}, {3027, 26435}, {4027, 26429}, {5186, 26375}, {6319, 26339}, {6321, 26468}, {7983, 26514}, {8591, 45420}, {8782, 26314}, {9766, 49043}, {10086, 49030}, {10089, 49032}, {11711, 26369}, {12510, 33430}, {13172, 26441}, {13173, 26512}, {13174, 26300}, {13175, 26306}, {13176, 49012}, {13177, 49014}, {13178, 26444}, {13179, 26449}, {13180, 26490}, {13181, 26485}, {13182, 26479}, {13183, 26473}, {13184, 49020}, {13185, 49022}, {13188, 49028}, {13189, 26520}, {13190, 26519}, {13989, 49026}, {14651, 45522}, {18539, 38733}, {19108, 26456}, {19109, 26462}, {22514, 26324}, {22515, 49016}, {23698, 48476}, {26396, 48531}, {26420, 48532}, {26516, 33813}, {35878, 49018}, {35879, 39660}, {45524, 48785}

X(49096) = parallelogic center (3rd anti-tri-squares-central, T) for these triangles T: {1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard}
X(49096) = X(99)-of-3rd anti-tri-squares-central triangle
X(49096) = reflection of X(i) in X(j) for these (i, j): (49040, 49038), (49042, 5860), (49097, 20094)


X(49097) = PARALLELOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO 1st ANTI-BROCARD

Barycentrics    -(3*a^4-3*(b^2+c^2)*a^2-b^4+5*b^2*c^2-c^4)*S+(b^2+c^2)*a^4-2*(b^4+c^4)*a^2+b^2*c^2*(b^2+c^2) : :
X(49097) = 3*X(14651)-4*X(48785)

The reciprocal parallelogic center of these triangles is X(385).

X(49097) lies on the circumcircle of 4th anti-tri-squares-central triangle and these lines: {98, 26295}, {99, 3069}, {114, 26331}, {115, 26362}, {148, 491}, {193, 5969}, {542, 49045}, {543, 5861}, {690, 49099}, {2782, 49039}, {2783, 48693}, {2787, 48712}, {2794, 49047}, {2799, 49101}, {3023, 26356}, {3027, 26436}, {4027, 26430}, {5186, 26376}, {6320, 26340}, {6321, 26469}, {7983, 26515}, {8591, 45421}, {8782, 26315}, {8982, 13172}, {8997, 49027}, {9766, 49042}, {10086, 49031}, {10089, 49033}, {11711, 26370}, {12509, 33431}, {13173, 26513}, {13174, 26301}, {13175, 26307}, {13176, 49013}, {13177, 49015}, {13178, 26445}, {13179, 26450}, {13180, 26491}, {13181, 26486}, {13182, 26480}, {13183, 26474}, {13184, 49021}, {13185, 49023}, {13188, 49029}, {13189, 26525}, {13190, 26524}, {14651, 45523}, {19108, 26457}, {19109, 26463}, {22514, 26325}, {22515, 49017}, {23698, 48477}, {26397, 48531}, {26421, 48532}, {26438, 38733}, {26521, 33813}, {35878, 39661}, {35879, 49019}, {45525, 48784}

X(49097) = parallelogic center (4th anti-tri-squares-central, T) for these triangles T: {1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard}
X(49097) = reflection of X(i) in X(j) for these (i, j): (49041, 49039), (49043, 5861), (49096, 20094)


X(49098) = PARALLELOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO ANTI-ORTHOCENTROIDAL

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

The reciprocal parallelogic center of these triangles is X(323).

X(49098) lies on the circumcircle of 3rd anti-tri-squares-central triangle and these lines: {74, 26294}, {110, 3068}, {113, 26330}, {125, 26361}, {193, 2854}, {265, 26468}, {399, 49028}, {492, 3448}, {542, 5860}, {690, 49096}, {1112, 26375}, {1511, 26516}, {2771, 48692}, {2781, 49046}, {2948, 26300}, {3024, 26355}, {3028, 26435}, {5663, 49038}, {7732, 24981}, {7984, 26514}, {8674, 48711}, {9143, 45420}, {9517, 49100}, {10088, 49030}, {10091, 49032}, {10113, 49016}, {11720, 26369}, {12310, 26306}, {12375, 49018}, {12376, 39660}, {12383, 26441}, {12902, 18539}, {12903, 26479}, {12904, 26473}, {13193, 26429}, {13204, 26512}, {13208, 49012}, {13209, 49014}, {13210, 26314}, {13211, 26444}, {13212, 26449}, {13213, 26490}, {13214, 26485}, {13215, 49020}, {13216, 49022}, {13217, 26520}, {13218, 26519}, {13990, 49026}, {17702, 48476}, {19110, 26456}, {19111, 26462}, {22586, 26324}, {26396, 48535}, {26420, 48536}, {32423, 49050}, {45522, 48786}, {45524, 48787}

X(49098) = parallelogic center (3rd anti-tri-squares-central, T) for these triangles T: {anti-orthocentroidal, orthocentroidal}
X(49098) = X(110)-of-3rd anti-tri-squares-central triangle
X(49098) = reflection of X(i) in X(j) for these (i, j): (7732, 24981), (49044, 49038), (49050, 49086), (49099, 14683)


X(49099) = PARALLELOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO ANTI-ORTHOCENTROIDAL

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

The reciprocal parallelogic center of these triangles is X(323).

X(49099) lies on the circumcircle of 4th anti-tri-squares-central triangle and these lines: {74, 26295}, {110, 3069}, {113, 26331}, {125, 26362}, {193, 2854}, {265, 26469}, {399, 49029}, {491, 3448}, {542, 5861}, {690, 49097}, {1112, 26376}, {1511, 26521}, {2771, 48693}, {2781, 49047}, {2948, 26301}, {3024, 26356}, {3028, 26436}, {5663, 49039}, {7733, 24981}, {7984, 26515}, {8674, 48712}, {8982, 12383}, {8998, 49027}, {9143, 45421}, {9517, 49101}, {10088, 49031}, {10091, 49033}, {10113, 49017}, {11720, 26370}, {12310, 26307}, {12375, 39661}, {12376, 49019}, {12902, 26438}, {12903, 26480}, {12904, 26474}, {13193, 26430}, {13204, 26513}, {13208, 49013}, {13209, 49015}, {13210, 26315}, {13211, 26445}, {13212, 26450}, {13213, 26491}, {13214, 26486}, {13215, 49021}, {13216, 49023}, {13217, 26525}, {13218, 26524}, {17702, 48477}, {19110, 26457}, {19111, 26463}, {22586, 26325}, {26397, 48535}, {26421, 48536}, {32423, 49051}, {45523, 48787}, {45525, 48786}

X(49099) = parallelogic center (4th anti-tri-squares-central, T) for these triangles T: {anti-orthocentroidal, orthocentroidal}
X(49099) = reflection of X(i) in X(j) for these (i, j): (7733, 24981), (49045, 49039), (49051, 49087), (49098, 14683)


X(49100) = PARALLELOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES-CENTRAL TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    (3*a^10-3*(b^2+c^2)*a^8-(4*b^4-11*b^2*c^2+4*c^4)*a^6+4*(b^4-c^4)*(b^2-c^2)*a^4+(b^4-3*b^2*c^2+c^4)*(b^2-c^2)^2*a^2+(b^8-c^8)*(-b^2+c^2))*S+a^2*((b^2+c^2)*a^8-2*(b^4+c^4)*a^6+(b^2+c^2)*b^2*c^2*a^4+2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*(b^4+b^2*c^2+c^4)) : :

The reciprocal parallelogic center of these triangles is X(10313).

X(49100) lies on the circumcircle of 3rd anti-tri-squares-central triangle and these lines: {112, 3068}, {127, 26361}, {132, 26330}, {193, 2781}, {492, 13219}, {1297, 26294}, {2794, 48476}, {2799, 49096}, {2806, 48711}, {2831, 48692}, {3320, 26435}, {5860, 13283}, {6020, 26355}, {9517, 49098}, {10705, 26514}, {10749, 26468}, {11641, 26306}, {11722, 26369}, {13166, 26375}, {13195, 26429}, {13200, 26441}, {13206, 26512}, {13221, 26300}, {13229, 49012}, {13231, 49014}, {13236, 26314}, {13280, 26444}, {13281, 26449}, {13282, 26339}, {13294, 26490}, {13295, 26485}, {13296, 26479}, {13297, 26473}, {13298, 49020}, {13299, 49022}, {13310, 49028}, {13311, 49030}, {13312, 49032}, {13313, 26520}, {13314, 26519}, {13992, 49026}, {18539, 48681}, {19114, 26456}, {19115, 26462}, {19162, 26324}, {19163, 49016}, {26396, 48537}, {26420, 48538}, {26516, 38608}, {35880, 49018}, {35881, 39660}, {45522, 48788}, {45524, 48789}, {49038, 49046}

X(49100) = parallelogic center (3rd anti-tri-squares-central, T) for these triangles T: {1st anti-orthosymmedial, 1st orthosymmedial}
X(49100) = X(112)-of-3rd anti-tri-squares-central triangle
X(49100) = reflection of X(49046) in X(49038)


X(49101) = PARALLELOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES-CENTRAL TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    -(3*a^10-3*(b^2+c^2)*a^8-(4*b^4-11*b^2*c^2+4*c^4)*a^6+4*(b^4-c^4)*(b^2-c^2)*a^4+(b^4-3*b^2*c^2+c^4)*(b^2-c^2)^2*a^2+(b^8-c^8)*(-b^2+c^2))*S+a^2*((b^2+c^2)*a^8-2*(b^4+c^4)*a^6+(b^2+c^2)*b^2*c^2*a^4+2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*(b^4+b^2*c^2+c^4)) : :

The reciprocal parallelogic center of these triangles is X(10313).

X(49101) lies on the circumcircle of 4th anti-tri-squares-central triangle and these lines: {112, 3069}, {127, 26362}, {132, 26331}, {193, 2781}, {491, 13219}, {1297, 26295}, {2794, 48477}, {2799, 49097}, {2806, 48712}, {2831, 48693}, {3320, 26436}, {5861, 13282}, {6020, 26356}, {8982, 13200}, {9517, 49099}, {10705, 26515}, {10749, 26469}, {11641, 26307}, {11722, 26370}, {13166, 26376}, {13195, 26430}, {13206, 26513}, {13221, 26301}, {13229, 49013}, {13231, 49015}, {13236, 26315}, {13280, 26445}, {13281, 26450}, {13283, 26340}, {13294, 26491}, {13295, 26486}, {13296, 26480}, {13297, 26474}, {13298, 49021}, {13299, 49023}, {13310, 49029}, {13311, 49031}, {13312, 49033}, {13313, 26525}, {13314, 26524}, {13923, 49027}, {19114, 26457}, {19115, 26463}, {19162, 26325}, {19163, 49017}, {26397, 48537}, {26421, 48538}, {26438, 48681}, {26521, 38608}, {35880, 39661}, {35881, 49019}, {45523, 48789}, {45525, 48788}, {49039, 49047}

X(49101) = parallelogic center (4th anti-tri-squares-central, T) for these triangles T: {1st anti-orthosymmedial, 1st orthosymmedial}
X(49101) = reflection of X(49047) in X(49039)

leftri

Centers related to anti-X3-ABC reflections triangle: X(49102)-X(49120)

rightri

This preamble and centers X(49102)-X(49120) were contributed by César Eliud Lozada, May 18, 2022.

Anti-X3-ABC reflections triangle was introduced in the preamble just before X(45345).


X(49102) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS TO ANTI-MCCAY

Barycentrics    2*a^8-3*(b^2+c^2)*a^6+(5*b^4-4*b^2*c^2+5*c^4)*a^4-(b^2+c^2)*(6*b^4-11*b^2*c^2+6*c^4)*a^2+(b^2-c^2)^2*(2*b^2-c^2)*(b^2-2*c^2) : :
X(49102) = 3*X(2)+X(12243) = X(2)+3*X(14651) = 5*X(2)-3*X(15561) = 2*X(2)-3*X(34127) = X(2)-3*X(38224) = X(8724)+3*X(11632) = X(8724)+9*X(14651) = 5*X(8724)-9*X(15561) = 2*X(8724)-9*X(34127) = X(8724)-9*X(38224) = X(11152)-3*X(11171) = X(11152)+3*X(43532) = 3*X(11632)-X(12243) = X(11632)-3*X(14651) = 5*X(11632)+3*X(15561) = 2*X(11632)+3*X(34127) = X(11632)+3*X(38224) = X(12243)-9*X(14651) = 5*X(12243)+9*X(15561) = 2*X(12243)+9*X(34127) = X(12243)+9*X(38224)

The reciprocal orthologic center of these triangles is X(9855).

X(49102) lies on these lines: {2, 2782}, {3, 671}, {4, 8587}, {5, 542}, {6, 19905}, {13, 41094}, {14, 41098}, {24, 12132}, {30, 115}, {35, 12354}, {36, 18969}, {55, 10070}, {56, 10054}, {98, 381}, {99, 5054}, {111, 11628}, {114, 547}, {125, 11656}, {140, 2482}, {147, 5071}, {148, 3524}, {182, 7606}, {376, 6321}, {498, 12350}, {499, 12351}, {517, 12258}, {530, 6774}, {531, 6771}, {543, 549}, {546, 10991}, {550, 38734}, {620, 11539}, {631, 8591}, {632, 22247}, {804, 9175}, {1499, 9183}, {1656, 23234}, {2023, 5309}, {2080, 8859}, {2790, 44275}, {2794, 3845}, {2796, 6684}, {3023, 3582}, {3027, 3584}, {3090, 38627}, {3311, 19057}, {3312, 19058}, {3398, 33013}, {3455, 12106}, {3523, 8596}, {3525, 38628}, {3526, 23235}, {3530, 10992}, {3534, 34473}, {3543, 38741}, {3545, 6033}, {3564, 8355}, {3576, 9875}, {3628, 14981}, {3655, 13178}, {3656, 38220}, {3767, 6034}, {3830, 14639}, {3839, 9862}, {5026, 10168}, {5050, 8593}, {5055, 6054}, {5066, 23514}, {5465, 5663}, {5469, 16630}, {5470, 16631}, {5613, 22489}, {5617, 22490}, {5622, 14833}, {5655, 14849}, {5969, 49111}, {6130, 45321}, {6200, 35699}, {6396, 35698}, {6642, 9876}, {6722, 15491}, {7583, 13908}, {7584, 13968}, {7603, 14159}, {7753, 12829}, {7797, 9302}, {7809, 39093}, {7827, 11272}, {7841, 10104}, {7844, 11178}, {7870, 13108}, {7983, 34718}, {8590, 11645}, {8597, 21445}, {8703, 23698}, {8997, 43211}, {9140, 18332}, {9144, 20126}, {9167, 10124}, {9214, 20975}, {9512, 41720}, {9855, 38225}, {9860, 38021}, {9878, 26316}, {9881, 26446}, {9882, 26341}, {9883, 26348}, {9884, 10246}, {9888, 34505}, {10053, 11238}, {10069, 11237}, {10109, 36519}, {10267, 12326}, {10269, 22565}, {10304, 38730}, {10485, 11179}, {10722, 14269}, {10723, 15681}, {10753, 14848}, {11001, 38742}, {11006, 15061}, {11710, 28204}, {11724, 38022}, {11812, 15300}, {12100, 38737}, {12176, 14041}, {12177, 47352}, {12345, 45620}, {12346, 45621}, {12347, 26451}, {12348, 26492}, {12349, 26487}, {12352, 45623}, {12353, 45624}, {12356, 16203}, {12357, 16202}, {13172, 15692}, {13188, 15694}, {13335, 47617}, {13857, 21531}, {13881, 14880}, {13989, 43212}, {14443, 16220}, {14693, 37461}, {14762, 32135}, {14791, 39120}, {14893, 39838}, {15685, 38634}, {15686, 38747}, {15687, 35021}, {15688, 38733}, {15693, 21166}, {15702, 38750}, {15708, 20094}, {15711, 41147}, {15713, 36521}, {15722, 38635}, {15980, 22329}, {16239, 38751}, {16324, 47334}, {18424, 40277}, {19708, 38731}, {19710, 41154}, {20379, 31854}, {25559, 32909}, {25560, 32907}, {26398, 48470}, {26422, 48471}, {26516, 49042}, {26521, 49043}, {31274, 47598}, {32479, 47113}, {33460, 49106}, {33461, 49105}, {33699, 41151}, {34094, 47200}, {34200, 38738}, {36196, 46633}, {37459, 44401}, {38736, 45759}, {41022, 44289}, {46236, 46951}

X(49102) = midpoint of X(i) and X(j) for these {i, j}: {2, 11632}, {3, 671}, {4, 14830}, {6, 19905}, {98, 381}, {115, 6055}, {125, 11656}, {376, 6321}, {3543, 38741}, {3655, 13178}, {5461, 11623}, {6033, 11177}, {6054, 12188}, {7983, 34718}, {8724, 12243}, {9140, 18332}, {9144, 20126}, {9888, 34505}, {10723, 15681}, {11171, 43532}, {11179, 11646}, {12117, 12355}, {14443, 16220}, {14651, 38224}, {15980, 22329}, {25559, 32909}, {25560, 32907}, {34473, 38732}, {36196, 46633}, {38664, 48657}, {46082, 46083}, {48728, 48729}
X(49102) = reflection of X(i) in X(j) for these (i, j): (5, 5461), (114, 547), (549, 6036), (2482, 140), (5026, 10168), (5461, 20398), (8787, 575), (12042, 6055), (15686, 38747), (22505, 381), (22566, 5), (32135, 46267), (33813, 549), (34127, 38224), (37459, 44401), (37461, 14693), (38229, 38735), (38738, 34200), (39838, 14893)
X(49102) = complement of X(8724)
X(49102) = inverse of X(182) in McCay circle
X(49102) = inverse of X(187) in Kiepert circumhyperbola
X(49102) = inverse of X(14650) in van Lamoen circle
X(49102) = inverse of X(20301) in nine-point circle
X(49102) = crossdifference of every pair of points on line {X(34291), X(39232)}
X(49102) = reflection of X(2) in the line X(804)X(11621)
X(49102) = orthologic center (anti-X3-ABC reflections, T) for these triangles T: {anti-McCay, McCay, Moses-Steiner osculatory}
X(49102) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {2, 5465, 11632}, {3, 671, 31854}, {98, 381, 36166}, {99, 33638, 47291}, {111, 5912, 9169}, {115, 125, 6055}, {7426, 15980, 22329}
X(49102) = X(187)-of-McCay triangle
X(49102) = X(671)-of-anti-X3-ABC reflections triangle
X(49102) = X(1153)-of-anti-McCay triangle
X(49102) = X(5026)-of-Artzt triangle
X(49102) = X(14830)-of-Euler triangle
X(49102) = X(22566)-of-Johnson triangle
X(49102) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 12243, 8724), (2, 14651, 11632), (3, 12355, 12117), (98, 9166, 381), (114, 14971, 547), (115, 12042, 22515), (376, 41135, 6321), (381, 11842, 598), (549, 6036, 26614), (671, 12117, 12355), (1656, 48657, 23234), (3545, 11177, 6033), (5055, 12188, 6054), (6054, 14061, 5055), (7841, 10104, 34510), (8724, 11632, 12243), (11623, 20398, 5), (11632, 38224, 2), (13188, 15694, 41134), (23234, 38664, 48657), (26614, 33813, 549)


X(49103) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS TO 3rd ANTI-TRI-SQUARES

Barycentrics    a^2*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)-S*(2*a^4-3*(b^2+c^2)*a^2+(b^2-c^2)^2) : :
X(49103) = 3*X(2)+X(12256) = 3*X(3)-X(12123) = 3*X(3)+X(12601) = 7*X(3)+X(22809) = 2*X(140)+X(48734) = 3*X(376)+X(12296) = 3*X(486)+X(12123) = 3*X(486)-X(12601) = 7*X(486)-X(22809) = X(487)-5*X(631) = 3*X(487)+X(49048) = X(488)+3*X(7612) = 15*X(631)+X(49048) = 5*X(1656)-X(48659) = 7*X(3523)+X(12221) = 9*X(3524)-X(12509) = 4*X(6119)-X(22596) = 7*X(12123)+3*X(22809) = 7*X(12601)-3*X(22809) = 2*X(12975)+3*X(49115)

The reciprocal orthologic center of these triangles is X(486).

X(49103) lies on these lines: {2, 6290}, {3, 486}, {4, 26521}, {5, 6119}, {24, 12147}, {30, 6251}, {35, 13081}, {36, 18989}, {55, 10083}, {56, 10067}, {115, 15886}, {140, 141}, {157, 45532}, {183, 45508}, {230, 372}, {371, 44648}, {376, 12296}, {487, 492}, {488, 5491}, {498, 12948}, {499, 12958}, {511, 13966}, {517, 12268}, {524, 13087}, {549, 32419}, {550, 45868}, {575, 8981}, {590, 45410}, {597, 44486}, {639, 13335}, {640, 6036}, {1152, 13881}, {1161, 13961}, {1352, 11316}, {1656, 48659}, {2080, 12210}, {3069, 9732}, {3311, 19104}, {3312, 19105}, {3523, 12221}, {3524, 12509}, {3526, 6281}, {3530, 12974}, {3538, 12320}, {3576, 9906}, {3767, 15884}, {5050, 5418}, {5054, 6280}, {6200, 35833}, {6221, 13770}, {6229, 44390}, {6289, 11291}, {6300, 15765}, {6301, 18585}, {6316, 35684}, {6396, 35830}, {6398, 13711}, {6642, 9921}, {6643, 22817}, {6771, 33447}, {6774, 33445}, {7583, 13921}, {7584, 9738}, {7692, 13993}, {7980, 10246}, {8406, 37637}, {9733, 13758}, {9737, 45577}, {9739, 35256}, {9986, 26316}, {10168, 44484}, {10267, 12343}, {10269, 22595}, {11824, 35813}, {12229, 37515}, {12237, 15644}, {12306, 13847}, {12484, 45620}, {12485, 45621}, {12787, 26446}, {12799, 26451}, {12928, 26492}, {12938, 26487}, {13002, 45623}, {13003, 45624}, {13132, 16203}, {13133, 16202}, {13468, 41490}, {13783, 45441}, {13939, 49039}, {15693, 22484}, {19145, 31401}, {21737, 32786}, {22605, 36457}, {22606, 36439}, {23005, 35739}, {23698, 43141}, {26398, 48478}, {26422, 48479}, {26468, 26620}, {32498, 42262}, {32788, 45489}, {33449, 49106}, {33451, 49105}, {35944, 42561}, {36701, 45079}, {36702, 43375}, {39388, 45510}, {40107, 44483}, {41964, 45578}, {42215, 43144}, {42277, 45023}, {43510, 49038}, {45499, 49029}

X(49103) = midpoint of X(i) and X(j) for these {i, j}: {3, 486}, {642, 48734}, {6289, 39647}, {6290, 12256}, {6316, 35684}, {12123, 12601}, {12237, 15644}
X(49103) = reflection of X(i) in X(j) for these (i, j): (5, 6119), (642, 140), (22596, 5)
X(49103) = complement of X(6290)
X(49103) = orthologic center (anti-X3-ABC reflections, T) for these triangles T: {3rd anti-tri-squares, 2nd half-squares, 4th tri-squares, inner-Vecten}
X(49103) = X(486)-of-anti-X3-ABC reflections triangle
X(49103) = X(6251)-of-inner-Vecten triangle, when ABC is obtuse
X(49103) = X(9732)-of-4th tri-squares-central triangle
X(49103) = X(13968)-of-McCay triangle
X(49103) = X(22596)-of-Johnson triangle
X(49103) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 12256, 6290), (3, 12601, 12123), (140, 182, 49104), (140, 48772, 141), (486, 5420, 13934), (486, 12123, 12601), (486, 42260, 22617), (6119, 8184, 45872)


X(49104) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS TO 4th ANTI-TRI-SQUARES

Barycentrics    a^2*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)+S*(2*a^4-3*(b^2+c^2)*a^2+(b^2-c^2)^2) : :
X(49104) = 3*X(2)+X(12257) = 3*X(3)-X(12124) = 3*X(3)+X(12602) = 7*X(3)+X(22810) = 2*X(140)+X(48735) = 3*X(376)+X(12297) = 3*X(485)+X(12124) = 3*X(485)-X(12602) = 7*X(485)-X(22810) = X(487)+3*X(7612) = X(488)-5*X(631) = 3*X(488)+X(49049) = 15*X(631)+X(49049) = 5*X(1656)-X(48660) = 7*X(3523)+X(12222) = 9*X(3524)-X(12510) = 4*X(6118)-X(22625) = 7*X(12124)+3*X(22810) = 7*X(12602)-3*X(22810) = 2*X(12974)+3*X(49114)

The reciprocal orthologic center of these triangles is X(485).

X(49104) lies on these lines: {2, 6222}, {3, 485}, {4, 26516}, {5, 6118}, {24, 12148}, {30, 6250}, {35, 13082}, {36, 18988}, {55, 10084}, {56, 10068}, {115, 15885}, {140, 141}, {157, 45533}, {183, 45509}, {230, 371}, {372, 44647}, {376, 12297}, {487, 5490}, {488, 491}, {498, 12949}, {499, 12959}, {511, 8981}, {517, 12269}, {524, 13088}, {549, 32421}, {550, 45869}, {575, 13966}, {597, 44485}, {615, 45411}, {639, 6036}, {640, 13335}, {1151, 13881}, {1160, 13903}, {1352, 11315}, {1656, 48660}, {2080, 12211}, {3068, 9733}, {3311, 19102}, {3312, 19103}, {3523, 12222}, {3524, 12510}, {3526, 6278}, {3530, 12975}, {3538, 12321}, {3576, 9907}, {3767, 15883}, {5050, 5420}, {5054, 6279}, {6200, 35831}, {6221, 13834}, {6228, 44391}, {6290, 11292}, {6304, 18585}, {6305, 15765}, {6312, 35685}, {6396, 35832}, {6398, 13651}, {6642, 9922}, {6643, 22818}, {6771, 33446}, {6774, 33444}, {7583, 9739}, {7584, 13880}, {7690, 13925}, {7981, 10246}, {8414, 37637}, {8960, 45498}, {9540, 9732}, {9600, 39661}, {9737, 45576}, {9738, 35255}, {9987, 26316}, {10168, 44483}, {10267, 12344}, {10269, 22624}, {11825, 35812}, {11917, 31487}, {12230, 37515}, {12238, 15644}, {12305, 13846}, {12486, 45620}, {12487, 45621}, {12788, 26446}, {12800, 26451}, {12929, 26492}, {12939, 26487}, {13004, 45623}, {13005, 45624}, {13134, 16203}, {13135, 16202}, {13468, 41491}, {13663, 45440}, {13886, 49038}, {15693, 22485}, {19146, 31401}, {21737, 26295}, {22634, 36439}, {22635, 36457}, {23698, 43144}, {26398, 48480}, {26422, 48481}, {26469, 26619}, {31412, 35945}, {31454, 45489}, {31463, 39679}, {32499, 42265}, {32787, 45488}, {33448, 49106}, {33450, 49105}, {36703, 45078}, {36717, 43374}, {39387, 45511}, {40107, 44484}, {41963, 45579}, {42216, 43141}, {42274, 45024}, {43509, 49039}

X(49104) = midpoint of X(i) and X(j) for these {i, j}: {3, 485}, {641, 48735}, {6289, 12257}, {6290, 39647}, {6312, 35685}, {12124, 12602}, {12238, 15644}
X(49104) = reflection of X(i) in X(j) for these (i, j): (5, 6118), (641, 140), (22625, 5)
X(49104) = complement of X(6289)
X(49104) = orthologic center (anti-X3-ABC reflections, T) for these triangles T: {4th anti-tri-squares, 1st half-squares, 3rd tri-squares, outer-Vecten}
X(49104) = X(485)-of-anti-X3-ABC reflections triangle
X(49104) = X(6251)-of-outer-Vecten triangle, when ABC is acute
X(49104) = X(9733)-of-3rd tri-squares-central triangle
X(49104) = X(13908)-of-McCay triangle
X(49104) = X(22625)-of-Johnson triangle
X(49104) = X(44647)-of-1st anti-Kenmotu-free-vertices triangle
X(49104) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 12257, 6289), (3, 12602, 12124), (140, 182, 49103), (140, 48773, 141), (485, 5418, 13882), (485, 12124, 12602), (485, 42261, 22646), (6118, 8180, 45871), (8960, 45498, 49028)


X(49105) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS TO INNER-FERMAT

Barycentrics    a^2*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)*sqrt(3)-2*S*(3*a^4-4*(b^2+c^2)*a^2+(b^2-c^2)^2) : :
X(49105) = 3*X(2)+X(22531) = 3*X(3)+X(16628) = 3*X(3)-X(22843) = X(17)-3*X(38226) = 3*X(18)-X(16628) = 3*X(18)+X(22843) = X(628)-5*X(631) = 5*X(1656)-X(48665) = 7*X(3523)+X(22114) = 4*X(3530)+X(33464) = 3*X(3576)+X(22651) = 4*X(6674)-X(22794) = 3*X(10246)-X(22867) = X(11603)-3*X(38224) = 3*X(13084)+X(22866) = 5*X(15693)+X(36368) = 7*X(15701)-X(36388) = 11*X(15719)+X(33627) = 11*X(15720)-X(22845) = X(22851)-3*X(26446)

The reciprocal orthologic center of these triangles is X(3).

X(49105) lies on these lines: {2, 16627}, {3, 14}, {5, 6672}, {16, 7749}, {17, 38226}, {24, 22481}, {30, 22831}, {35, 22865}, {36, 18972}, {54, 69}, {55, 22885}, {56, 22884}, {140, 618}, {498, 22859}, {499, 22860}, {511, 8260}, {517, 11740}, {533, 549}, {542, 33377}, {575, 16772}, {626, 33381}, {1656, 48665}, {2041, 33359}, {2042, 33360}, {2080, 22522}, {3311, 19069}, {3312, 19072}, {3411, 5611}, {3523, 22114}, {3526, 33387}, {3530, 13350}, {3576, 22651}, {5050, 42490}, {5237, 12815}, {5872, 22736}, {5980, 5983}, {6108, 16001}, {6200, 35849}, {6396, 35846}, {6642, 22656}, {6680, 33391}, {7583, 22876}, {7584, 22877}, {7756, 46053}, {9698, 36759}, {9735, 40694}, {10246, 22867}, {10267, 22557}, {10269, 22771}, {10645, 22856}, {10646, 31703}, {11305, 33375}, {11308, 24206}, {11481, 22862}, {11603, 38224}, {12042, 25560}, {13084, 22866}, {15561, 25559}, {15693, 36368}, {15701, 36388}, {15719, 33627}, {15720, 22845}, {15778, 33529}, {16202, 22887}, {16203, 22886}, {16653, 33379}, {20415, 42488}, {21159, 42489}, {22669, 45620}, {22673, 45621}, {22745, 26316}, {22847, 31710}, {22851, 26446}, {22852, 26451}, {22853, 26341}, {22854, 26348}, {22857, 26492}, {22858, 26487}, {22861, 42089}, {22863, 45623}, {22864, 45624}, {22869, 35688}, {23303, 31706}, {26398, 48497}, {26422, 48498}, {26516, 49064}, {26521, 49065}, {33383, 42673}, {33393, 43121}, {33395, 43120}, {33450, 49104}, {33451, 49103}, {33461, 49102}, {33463, 40108}, {33467, 49111}, {33469, 49112}, {33471, 34551}, {33473, 34552}, {36756, 42121}, {37464, 41057}, {42149, 47068}, {42599, 44250}

X(49105) = midpoint of X(i) and X(j) for these {i, j}: {3, 18}, {16627, 22531}, {16628, 22843}, {22869, 35688}, {48750, 48751}
X(49105) = reflection of X(i) in X(j) for these (i, j): (5, 6674), (630, 140), (22794, 5)
X(49105) = complement of X(16627)
X(49105) = orthologic center (anti-X3-ABC reflections, T) for these triangles T: {inner-Fermat, 1st half-diamonds}
X(49105) = X(18)-of-anti-X3-ABC reflections triangle
X(49105) = X(22794)-of-Johnson triangle
X(49105) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 22531, 16627), (3, 16628, 22843), (18, 22843, 16628), (182, 631, 49106), (8260, 16773, 14139)


X(49106) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS TO OUTER-FERMAT

Barycentrics    a^2*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)*sqrt(3)+2*S*(3*a^4-4*(b^2+c^2)*a^2+(b^2-c^2)^2) : :
X(49106) = 3*X(2)+X(22532) = 3*X(3)+X(16629) = 3*X(3)-X(22890) = 3*X(17)-X(16629) = 3*X(17)+X(22890) = X(18)-3*X(38226) = X(627)-5*X(631) = 5*X(1656)-X(48666) = 7*X(3523)+X(22113) = 4*X(3530)+X(33465) = 3*X(3576)+X(22652) = 4*X(6673)-X(22795) = 3*X(10246)-X(22912) = X(11602)-3*X(38224) = 3*X(13083)+X(22911) = 5*X(15693)+X(36366) = 7*X(15701)-X(36386) = 11*X(15719)+X(33626) = 11*X(15720)-X(22844) = 3*X(21156)+X(36782)

The reciprocal orthologic center of these triangles is X(3).

X(49106) lies on these lines: {2, 16626}, {3, 13}, {5, 6671}, {15, 7749}, {18, 38226}, {24, 22482}, {30, 22832}, {35, 22910}, {36, 18973}, {54, 69}, {55, 22930}, {56, 22929}, {140, 619}, {498, 22904}, {499, 22905}, {511, 8259}, {517, 11739}, {532, 549}, {542, 33376}, {575, 16773}, {626, 33380}, {1656, 48666}, {2041, 33358}, {2042, 33361}, {2080, 22523}, {3311, 19071}, {3312, 19070}, {3412, 5615}, {3523, 22113}, {3526, 33386}, {3530, 13349}, {3576, 22652}, {5050, 42491}, {5238, 12815}, {5873, 22737}, {5981, 5982}, {6109, 16002}, {6200, 35847}, {6396, 35848}, {6642, 22657}, {6680, 33390}, {6694, 44223}, {7583, 22921}, {7584, 22922}, {7756, 46054}, {9698, 36760}, {9736, 40693}, {10246, 22912}, {10267, 22558}, {10269, 22772}, {10645, 31704}, {10646, 22900}, {11306, 33374}, {11307, 24206}, {11480, 22906}, {11602, 38224}, {12042, 25559}, {13083, 22911}, {15561, 25560}, {15693, 36366}, {15701, 36386}, {15719, 33626}, {15720, 22844}, {15802, 33530}, {16202, 22932}, {16203, 22931}, {16652, 33378}, {20416, 42489}, {21158, 42488}, {22670, 45620}, {22674, 45621}, {22746, 26316}, {22893, 31709}, {22896, 26446}, {22897, 26451}, {22898, 26341}, {22899, 26348}, {22902, 26492}, {22903, 26487}, {22907, 42092}, {22908, 45623}, {22909, 45624}, {22914, 35689}, {23302, 31705}, {26398, 48499}, {26422, 48500}, {26516, 49066}, {26521, 49067}, {33382, 42672}, {33392, 43120}, {33394, 43121}, {33448, 49104}, {33449, 49103}, {33460, 49102}, {33462, 40108}, {33466, 49111}, {33468, 49112}, {33470, 34552}, {33472, 34551}, {36755, 42124}, {37463, 41056}, {42152, 47066}

X(49106) = midpoint of X(i) and X(j) for these {i, j}: {3, 17}, {16626, 22532}, {16629, 22890}, {22914, 35689}, {48752, 48753}
X(49106) = reflection of X(i) in X(j) for these (i, j): (5, 6673), (629, 140), (22795, 5)
X(49106) = complement of X(16626)
X(49106) = orthologic center (anti-X3-ABC reflections, T) for these triangles T: {outer-Fermat, 2nd half-diamonds}
X(49106) = X(17)-of-anti-X3-ABC reflections triangle
X(49106) = X(22795)-of-Johnson triangle
X(49106) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 22532, 16626), (3, 16629, 22890), (17, 22890, 16629), (182, 631, 49105), (8259, 16772, 14138)


X(49107) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS TO 2nd FUHRMANN

Barycentrics    (b+c)*a^6+2*b*c*a^5-3*(b^3+c^3)*a^4-2*(b^2+b*c+c^2)*b*c*a^3+(b^2-c^2)*(b-c)*(3*b^2+b*c+3*c^2)*a^2-(b^2-c^2)^3*(b-c) : :
X(49107) = 3*X(2)+X(16116) = 3*X(3)-X(16113) = 3*X(3)+X(16150) = 3*X(79)+X(16113) = 3*X(79)-X(16150) = 3*X(191)-7*X(31423) = X(355)-3*X(6175) = 3*X(442)-2*X(9956) = 5*X(631)-X(3648) = X(944)+3*X(2475) = X(944)-3*X(33858) = X(946)-3*X(11263) = 2*X(946)-3*X(33592) = 5*X(1656)-X(48668) = 7*X(3523)+X(20084) = 7*X(3526)-X(41691) = X(3579)+2*X(11544) = 3*X(5499)-X(5690) = X(5690)+3*X(33668) = 4*X(6701)-X(22798)

The reciprocal orthologic center of these triangles is X(3).

X(49107) lies on these lines: {1, 47032}, {2, 3652}, {3, 79}, {5, 3833}, {12, 13145}, {21, 32612}, {24, 16114}, {30, 551}, {35, 16142}, {36, 18977}, {55, 16153}, {56, 16152}, {119, 125}, {140, 3647}, {182, 48756}, {191, 31142}, {226, 3579}, {355, 6175}, {498, 16140}, {499, 16141}, {500, 3120}, {517, 3649}, {582, 24725}, {631, 3648}, {758, 5499}, {908, 3650}, {944, 2475}, {1125, 12611}, {1656, 48668}, {2080, 16115}, {3065, 35010}, {3311, 19079}, {3312, 19080}, {3523, 20084}, {3526, 41691}, {3576, 16118}, {3628, 21635}, {3651, 16159}, {3653, 15678}, {3655, 15679}, {3824, 31936}, {3838, 13369}, {3918, 11698}, {4854, 32167}, {5249, 9955}, {5428, 23961}, {5441, 9670}, {5453, 36250}, {5691, 16132}, {5694, 37438}, {5703, 35249}, {5762, 13159}, {5885, 6842}, {5886, 21669}, {6200, 35855}, {6260, 38140}, {6396, 35854}, {6583, 15908}, {6642, 16119}, {6675, 22936}, {6713, 10021}, {6841, 9940}, {6863, 41697}, {6920, 16128}, {6923, 33857}, {6940, 48698}, {6951, 37733}, {6958, 41695}, {6980, 15016}, {7583, 16148}, {7584, 16149}, {7701, 37534}, {7987, 28460}, {8143, 17056}, {10165, 12104}, {10202, 17637}, {10222, 16137}, {10225, 11277}, {10267, 16117}, {10269, 13743}, {10308, 27186}, {10543, 15178}, {11230, 12608}, {11231, 18253}, {11278, 21620}, {11491, 35982}, {11684, 26446}, {11813, 35598}, {12047, 13624}, {12512, 33862}, {12609, 18480}, {12612, 49110}, {12615, 49113}, {12645, 47033}, {12699, 31019}, {13607, 33281}, {14450, 16139}, {16121, 45620}, {16122, 45621}, {16123, 26316}, {16129, 26451}, {16130, 26341}, {16131, 26348}, {16138, 26492}, {16143, 18443}, {16154, 16203}, {16155, 16202}, {16160, 31657}, {16161, 45623}, {16162, 45624}, {17525, 41012}, {17768, 22937}, {18516, 28629}, {26201, 26470}, {26398, 48503}, {26422, 48504}, {26516, 49070}, {26521, 49071}, {35000, 37731}, {38607, 38618}

X(49107) = midpoint of X(i) and X(j) for these {i, j}: {1, 47032}, {3, 79}, {2475, 33858}, {3649, 37401}, {3651, 16159}, {3652, 16116}, {3655, 15679}, {5499, 33668}, {6923, 33857}, {12699, 33557}, {14450, 16139}, {16113, 16150}, {16132, 37230}, {48756, 48757}
X(49107) = reflection of X(i) in X(j) for these (i, j): (5, 6701), (3647, 140), (10222, 16137), (10543, 15178), (22798, 5), (22936, 6675), (26202, 16617), (31649, 1125), (33592, 11263), (33856, 6713), (37447, 9955)
X(49107) = complement of X(3652)
X(49107) = orthologic center (anti-X3-ABC reflections, T) for these triangles T: {2nd Fuhrmann, K798e}
X(49107) = center of circle {{X(1), X(3109), X(47032)}}
X(49107) = X(79)-of-anti-X3-ABC reflections triangle
X(49107) = X(1493)-of-Wasat triangle, when ABC is acute
X(49107) = X(2914)-of-K798i triangle, when ABC is acute
X(49107) = X(3519)-of-3rd Euler triangle, when ABC is acute
X(49107) = X(22798)-of-Johnson triangle
X(49107) = X(47032)-of-anti-Aquila triangle
X(49107) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 16116, 3652), (3, 16150, 16113), (79, 16113, 16150), (11230, 26202, 16617)


X(49108) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS TO HATZIPOLAKIS-MOSES

Barycentrics    (b^2-c^2)^2*a^12-2*(b^2+c^2)*(2*b^4-3*b^2*c^2+2*c^4)*a^10+(5*b^8+5*c^8+2*b^2*c^2*(b^4-b^2*c^2+c^4))*a^8-2*(b^4-c^4)*(b^2-c^2)*b^2*c^2*a^6-(b^2-c^2)^2*(5*b^8+5*c^8+6*(b^4+b^2*c^2+c^4)*b^2*c^2)*a^4+4*(b^6-c^6)*(b^2-c^2)^2*(b^4-c^4)*a^2-(b^2+c^2)^2*(b^2-c^2)^6 : :
X(49108) = 3*X(2)+X(32337) = 3*X(3)-X(32330) = 3*X(3)+X(32402) = 5*X(631)-X(32354) = X(1209)+2*X(20299) = 5*X(1656)-X(48669) = 3*X(1853)+X(2917) = 7*X(3526)-X(32359) = X(3574)-4*X(32767) = 3*X(3576)+X(32356) = 3*X(6145)+X(32330) = 3*X(6145)-X(32402) = X(6247)+2*X(13565) = X(6288)+5*X(40686) = X(18381)+2*X(32348) = 3*X(23325)-X(32365) = 3*X(23325)-2*X(32393) = 3*X(23329)-X(32401) = 3*X(23332)-X(32351) = X(32345)-5*X(40686)

The reciprocal orthologic center of these triangles is X(6146).

X(49108) lies on these lines: {2, 32337}, {3, 161}, {5, 32364}, {24, 32332}, {30, 32369}, {35, 32390}, {36, 32336}, {54, 70}, {55, 32404}, {56, 32403}, {66, 32344}, {125, 389}, {140, 32391}, {182, 6689}, {427, 973}, {498, 32382}, {499, 32383}, {517, 32331}, {539, 18281}, {631, 32354}, {858, 15606}, {1154, 12359}, {1493, 15116}, {1503, 7568}, {1595, 11743}, {1656, 48669}, {2080, 32335}, {2777, 18488}, {2781, 33332}, {3311, 32342}, {3312, 32343}, {3357, 43577}, {3526, 32359}, {3576, 32356}, {5094, 12242}, {5449, 18569}, {5965, 44469}, {6000, 13160}, {6153, 49116}, {6200, 35859}, {6240, 32340}, {6247, 13565}, {6396, 35858}, {6642, 32357}, {6696, 12041}, {7495, 14864}, {7558, 14216}, {7583, 32399}, {7584, 32400}, {7691, 23293}, {8889, 32334}, {10111, 15089}, {10246, 32394}, {10264, 32184}, {10267, 32347}, {10269, 32363}, {10610, 20376}, {10619, 37118}, {11472, 22802}, {12225, 18383}, {15800, 32395}, {15805, 32396}, {16202, 32406}, {16203, 32405}, {17824, 36752}, {18428, 19506}, {21230, 23300}, {23041, 24206}, {23327, 32368}, {23328, 44242}, {23336, 32423}, {26316, 32362}, {26341, 32373}, {26348, 32374}, {26398, 48505}, {26422, 48506}, {26446, 32371}, {26451, 32372}, {26487, 32381}, {26492, 32380}, {26516, 49072}, {26521, 49073}, {32346, 47528}, {32360, 45620}, {32361, 45621}, {32388, 45623}, {32389, 45624}, {34826, 44201}, {43817, 45622}, {44287, 46374}

X(49108) = midpoint of X(i) and X(j) for these {i, j}: {3, 6145}, {66, 32344}, {6288, 32345}, {14076, 20299}, {18381, 23358}, {32330, 32402}, {32337, 32379}, {48758, 48759}
X(49108) = reflection of X(i) in X(j) for these (i, j): (1209, 14076), (10274, 6689), (10610, 20376), (23358, 32348), (32364, 5), (32365, 32393), (32391, 140)
X(49108) = complement of X(32379)
X(49108) = orthologic center (anti-X3-ABC reflections, Hatzipolakis-Moses)
X(49108) = X(6145)-of-anti-X3-ABC reflections triangle
X(49108) = X(32364)-of-Johnson triangle
X(49108) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 32337, 32379), (3, 32402, 32330), (6145, 32330, 32402), (20299, 21243, 18381), (21243, 32348, 1209), (23325, 32365, 32393)


X(49109) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS TO 3rd HATZIPOLAKIS

Barycentrics    (b^2-c^2)^2*a^12-2*(2*b^2-c^2)*(b^2-2*c^2)*(b^2+c^2)*a^10+(5*b^8+5*c^8-2*b^2*c^2*(b^4+9*b^2*c^2+c^4))*a^8-2*(b^2+c^2)*(7*b^4-18*b^2*c^2+7*c^4)*b^2*c^2*a^6-(b^2-c^2)^2*(5*b^8+5*c^8-2*b^2*c^2*(7*b^4+b^2*c^2+7*c^4))*a^4+4*(b^6+c^6)*(b^2-c^2)^4*a^2-(b^2+c^2)^2*(b^2-c^2)^6 : :
X(49109) = 3*X(2)+X(22533) = 3*X(3)-X(22951) = 3*X(3)+X(22979) = 5*X(631)-X(22647) = 5*X(1656)-X(48670) = 3*X(3576)+X(22653) = 3*X(10246)-X(22969) = 3*X(22466)+X(22951) = 3*X(22466)-X(22979) = X(22941)-3*X(26446) = X(22943)-3*X(26451)

The reciprocal orthologic center of these triangles is X(12241).

X(49109) lies on these lines: {2, 22533}, {3, 2929}, {5, 22800}, {24, 22483}, {30, 22833}, {35, 22965}, {36, 18978}, {55, 22981}, {56, 22980}, {125, 5907}, {140, 22966}, {182, 44516}, {403, 9729}, {498, 22958}, {499, 22959}, {517, 22476}, {631, 22647}, {1209, 6723}, {1656, 48670}, {2080, 22524}, {3311, 19083}, {3312, 19084}, {3357, 22816}, {3576, 22653}, {6200, 35861}, {6396, 35860}, {6642, 22658}, {7505, 22750}, {7583, 22976}, {7584, 22977}, {9826, 32364}, {10246, 22969}, {10267, 22559}, {10269, 22776}, {10610, 44452}, {11440, 26913}, {11472, 20299}, {11585, 22530}, {11591, 12359}, {14156, 31985}, {15805, 22973}, {16202, 22983}, {16203, 22982}, {18560, 22538}, {19360, 19460}, {22528, 44440}, {22671, 45620}, {22675, 45621}, {22747, 26316}, {22941, 26446}, {22943, 26451}, {22945, 26341}, {22947, 26348}, {22956, 26492}, {22957, 26487}, {22963, 45623}, {22964, 45624}, {22971, 37475}, {22972, 37514}, {26398, 48507}, {26422, 48508}, {26516, 49074}, {26521, 49075}, {32375, 43839}

X(49109) = midpoint of X(i) and X(j) for these {i, j}: {3, 22466}, {2929, 22808}, {22533, 22955}, {22951, 22979}, {48810, 48811}
X(49109) = reflection of X(i) in X(j) for these (i, j): (22800, 5), (22966, 140), (22978, 22581)
X(49109) = complement of X(22955)
X(49109) = orthologic center (anti-X3-ABC reflections, 3rd Hatzipolakis)
X(49109) = X(22466)-of-anti-X3-ABC reflections triangle
X(49109) = X(22800)-of-Johnson triangle
X(49109) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 22533, 22955), (3, 22979, 22951), (22466, 22951, 22979)


X(49110) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS TO HUTSON EXTOUCH

Barycentrics    a*(2*a^9-3*(b+c)*a^8-6*(b^2+3*b*c+c^2)*a^7+2*(b+c)*(5*b^2+8*b*c+5*c^2)*a^6+2*(3*b^4+3*c^4+b*c*(19*b^2+16*b*c+19*c^2))*a^5-4*(b+c)*(3*b^4+3*c^4+2*b*c*(4*b^2+b*c+4*c^2))*a^4-2*(b^6+c^6+(11*b^4+11*c^4+b*c*(11*b^2-14*b*c+11*c^2))*b*c)*a^3+2*(b^2-c^2)^2*(b+c)*(3*b^2+8*b*c+3*c^2)*a^2+2*(b^2-c^2)^2*(b-c)^2*b*c*a-(b^2-c^2)^4*(b+c)) : :
X(49110) = 3*X(2)+X(12249) = 3*X(3)-X(12120) = 3*X(3)+X(12872) = 5*X(631)-X(9874) = 5*X(1656)-X(48671) = 3*X(3576)+X(9898) = 3*X(7160)+X(12120) = 3*X(7160)-X(12872) = X(8000)-3*X(10246) = X(12777)-3*X(26446) = X(12789)-3*X(26451)

The reciprocal orthologic center of these triangles is X(40).

X(49110) lies on these lines: {2, 12249}, {3, 7091}, {5, 22801}, {24, 12139}, {30, 12599}, {35, 12863}, {36, 18979}, {55, 10075}, {56, 10059}, {140, 12864}, {182, 48812}, {498, 12859}, {499, 12860}, {517, 12260}, {631, 9874}, {1656, 48671}, {2080, 12200}, {3311, 19085}, {3312, 19086}, {3576, 9898}, {3579, 31657}, {5534, 31445}, {6200, 35863}, {6396, 35862}, {6600, 10267}, {6642, 12411}, {7583, 13914}, {7584, 13978}, {8000, 10246}, {10269, 22777}, {12464, 45620}, {12465, 45621}, {12500, 26316}, {12612, 49107}, {12619, 12620}, {12777, 26446}, {12789, 26451}, {12801, 26341}, {12802, 26348}, {12857, 26492}, {12858, 26487}, {12861, 45623}, {12862, 45624}, {12874, 16203}, {12875, 16202}, {26398, 48509}, {26422, 48510}, {26516, 49076}, {26521, 49077}, {32613, 34862}

X(49110) = midpoint of X(i) and X(j) for these {i, j}: {3, 7160}, {12120, 12872}, {12249, 12856}, {48812, 48813}
X(49110) = reflection of X(i) in X(j) for these (i, j): (12864, 140), (22801, 5)
X(49110) = complement of X(12856)
X(49110) = orthologic center (anti-X3-ABC reflections, Hutson extouch)
X(49110) = X(7160)-of-anti-X3-ABC reflections triangle
X(49110) = X(22801)-of-Johnson triangle
X(49110) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 12249, 12856), (3, 12872, 12120), (7160, 12120, 12872)


X(49111) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS TO 1st NEUBERG

Barycentrics    (b^2+c^2)*a^6-(b^4+c^4)*a^4-3*(b^2+c^2)*b^2*c^2*a^2+(b^2-c^2)^2*b^2*c^2 : :
X(49111) = 3*X(2)+X(12251) = 3*X(3)-X(11257) = 3*X(3)+X(13108) = X(3)-3*X(22712) = X(4)+3*X(6194) = X(4)-3*X(7697) = 2*X(4)-3*X(22681) = X(4)-5*X(31276) = 3*X(76)+X(11257) = 3*X(76)-X(13108) = X(76)+3*X(22712) = 3*X(6194)-X(9821) = 2*X(6194)+X(22681) = 3*X(6194)+5*X(31276) = X(6287)-3*X(42006) = 3*X(7697)+X(9821) = 3*X(7697)-5*X(31276) = X(11257)-9*X(22712) = 2*X(11272)+X(12251) = X(13108)+9*X(22712)

The reciprocal orthologic center of these triangles is X(3).

X(49111) lies on these lines: {2, 3095}, {3, 76}, {4, 2896}, {5, 141}, {17, 3105}, {18, 3104}, {24, 12143}, {30, 5188}, {35, 13077}, {36, 18982}, {39, 140}, {55, 10079}, {56, 10063}, {114, 7794}, {115, 46283}, {148, 19910}, {157, 1607}, {182, 732}, {194, 631}, {262, 1656}, {311, 22062}, {315, 37348}, {381, 7883}, {384, 2080}, {385, 3398}, {498, 12837}, {499, 12836}, {517, 12263}, {538, 549}, {547, 44422}, {550, 15598}, {575, 7805}, {576, 7808}, {590, 3103}, {599, 22566}, {615, 3102}, {632, 6683}, {726, 6684}, {730, 1385}, {736, 7780}, {1232, 20775}, {1506, 46313}, {1569, 38748}, {1657, 22676}, {1916, 38224}, {2023, 7746}, {2450, 37636}, {2548, 13330}, {2794, 32151}, {2937, 38946}, {2979, 37988}, {3094, 3767}, {3096, 40252}, {3097, 31423}, {3311, 19089}, {3312, 19090}, {3314, 37446}, {3456, 17714}, {3523, 7709}, {3524, 32522}, {3526, 7786}, {3530, 21163}, {3564, 13354}, {3576, 9902}, {3628, 31239}, {3734, 5171}, {3815, 46305}, {3850, 22682}, {3851, 22728}, {3917, 21531}, {3933, 37451}, {4857, 22711}, {5050, 32451}, {5052, 34380}, {5054, 7757}, {5056, 44434}, {5270, 18971}, {5319, 13331}, {5613, 25167}, {5617, 25157}, {5690, 14839}, {5891, 44227}, {5969, 49102}, {5984, 12252}, {6036, 32189}, {6179, 11842}, {6200, 35867}, {6272, 26348}, {6273, 26341}, {6321, 6655}, {6396, 35866}, {6642, 9917}, {6704, 25555}, {6771, 33483}, {6774, 33482}, {7467, 39998}, {7583, 8992}, {7584, 13983}, {7607, 10290}, {7610, 13085}, {7745, 46321}, {7750, 39266}, {7754, 41651}, {7761, 22515}, {7766, 10359}, {7767, 35430}, {7770, 10350}, {7789, 37459}, {7793, 35925}, {7795, 37466}, {7796, 43461}, {7800, 37242}, {7804, 32134}, {7807, 14693}, {7815, 9737}, {7819, 20576}, {7829, 44423}, {7830, 23698}, {7832, 38227}, {7834, 10007}, {7836, 15561}, {7854, 22505}, {7873, 13449}, {7889, 35437}, {7911, 14639}, {7914, 11261}, {7934, 15092}, {7976, 10246}, {8704, 31744}, {8722, 17130}, {8782, 10357}, {9301, 12110}, {9865, 12054}, {9983, 26316}, {10267, 12338}, {10269, 22779}, {10519, 18906}, {11007, 47207}, {11055, 15701}, {11331, 47202}, {11539, 44562}, {11623, 42787}, {11676, 17128}, {12100, 14711}, {12474, 45620}, {12475, 45621}, {12782, 26446}, {12794, 26451}, {12923, 26492}, {12933, 26487}, {12992, 45623}, {12993, 45624}, {13109, 16203}, {13110, 16202}, {13172, 33260}, {13325, 31862}, {13326, 31863}, {13881, 22677}, {14023, 18769}, {14561, 40332}, {14670, 44262}, {14869, 32450}, {15720, 32519}, {16321, 16619}, {17131, 37479}, {17508, 32429}, {18321, 38527}, {18583, 35439}, {19522, 20913}, {20794, 44149}, {21243, 21536}, {21359, 36365}, {21360, 36364}, {21443, 29010}, {22138, 36794}, {22416, 39000}, {22564, 33013}, {22684, 22696}, {22686, 22695}, {26398, 48515}, {26422, 48516}, {26516, 49082}, {26521, 49083}, {28417, 44716}, {31981, 35700}, {33259, 38750}, {33466, 49106}, {33467, 49105}, {34507, 44774}, {35002, 37334}, {35431, 42534}, {35458, 45804}, {37182, 40278}, {37336, 43453}, {42548, 43843}

X(49111) = midpoint of X(i) and X(j) for these {i, j}: {3, 76}, {4, 9821}, {5, 32521}, {148, 19910}, {381, 33706}, {3095, 12251}, {5188, 6248}, {6194, 7697}, {7751, 8149}, {11257, 13108}, {13354, 14994}, {18321, 38527}, {22676, 48663}, {31981, 35700}, {48818, 48819}
X(49111) = reflection of X(i) in X(j) for these (i, j): (5, 3934), (39, 140), (3095, 11272), (10263, 27375), (14881, 5), (22681, 7697), (32448, 13334), (32516, 3530), (34510, 7810), (35436, 20576), (35439, 18583), (40108, 15819), (44422, 547)
X(49111) = complement of X(3095)
X(49111) = anticomplement of X(11272)
X(49111) = anticomplementary conjugate of the anticomplement of X(592)
X(49111) = complementary conjugate of the complement of X(3406)
X(49111) = circumperp conjugate of X(35464)
X(49111) = perspector of the circumconic {{A, B, C, X(11794), X(43187)}}
X(49111) = inverse of X(13188) in 2nd Brocard circle
X(49111) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(39684)}} and {{A, B, C, X(4), X(39685)}}
X(49111) = crossdifference of every pair of points on line {X(2491), X(3050)}
X(49111) = X(592)-anticomplementary conjugate of-X(8)
X(49111) = orthologic center (anti-X3-ABC reflections, 1st Neuberg)
X(49111) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {3, 76, 31848}, {4, 9821, 31850}
X(49111) = X(76)-of-anti-X3-ABC reflections triangle
X(49111) = X(575)-of-6th Brocard triangle
X(49111) = X(9821)-of-Euler triangle
X(49111) = X(14881)-of-Johnson triangle
X(49111) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 3095, 11272), (2, 12251, 3095), (3, 183, 10104), (3, 10104, 12042), (3, 12188, 12203), (3, 13108, 11257), (4, 6194, 9821), (4, 31276, 7697), (39, 140, 40108), (39, 15819, 140), (76, 11257, 13108), (76, 22712, 3), (194, 631, 11171), (549, 32448, 13334), (639, 640, 5031), (1656, 48673, 262), (3523, 20081, 7709), (3526, 32447, 7786), (3530, 32516, 21163), (3934, 18806, 24256), (3934, 32521, 14881), (5188, 9466, 6248), (5403, 5404, 24206), (6194, 31276, 4), (7697, 9821, 4), (7746, 32452, 2023), (21166, 43459, 3), (32481, 32482, 13188)


X(49112) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS TO 2nd NEUBERG

Barycentrics    2*a^8+(b^2+c^2)*a^6-(3*b^4+8*b^2*c^2+3*c^4)*a^4-7*(b^2+c^2)*b^2*c^2*a^2+(b^2-c^2)^2*b^2*c^2 : :
X(49112) = 3*X(2)+X(12252) = X(3)-3*X(9751) = 3*X(3)-X(12122) = 3*X(3)+X(13111) = X(83)+3*X(9751) = 3*X(83)+X(12122) = 3*X(83)-X(13111) = 5*X(631)-X(2896) = 5*X(1656)-X(48674) = 7*X(3523)+X(20088) = 7*X(3526)-5*X(31268) = 3*X(3576)+X(9903) = 3*X(5054)-X(31168) = 3*X(5085)+X(24273) = 4*X(6704)-X(22803) = X(7751)-5*X(8150) = X(7977)-3*X(10246) = 9*X(9751)-X(12122) = 9*X(9751)+X(13111) = 5*X(12054)+X(17128)

The reciprocal orthologic center of these triangles is X(3).

X(49112) lies on these lines: {2, 6287}, {3, 83}, {4, 8725}, {5, 5092}, {24, 12144}, {30, 6249}, {35, 13078}, {36, 18983}, {55, 10080}, {56, 10064}, {114, 140}, {182, 732}, {187, 3530}, {498, 12944}, {499, 12954}, {517, 12264}, {549, 754}, {550, 7804}, {575, 32521}, {631, 2896}, {1656, 48674}, {2080, 12206}, {2782, 8290}, {3311, 19091}, {3312, 19092}, {3398, 37455}, {3523, 20088}, {3526, 31268}, {3576, 9903}, {3934, 5026}, {5054, 31168}, {5085, 14880}, {5976, 40238}, {6200, 35869}, {6274, 26348}, {6275, 26341}, {6308, 35701}, {6396, 35868}, {6642, 9918}, {6656, 22505}, {6684, 17766}, {6771, 33485}, {6774, 33484}, {7583, 8993}, {7584, 13984}, {7771, 7776}, {7808, 17508}, {7944, 38743}, {7977, 10246}, {8716, 13085}, {9478, 34127}, {9821, 10359}, {10007, 35422}, {10256, 12108}, {10267, 12339}, {10269, 22780}, {11171, 32476}, {11606, 38224}, {12006, 14962}, {12156, 15693}, {12476, 45620}, {12477, 45621}, {12783, 26446}, {12795, 26451}, {12924, 26492}, {12934, 26487}, {12994, 45623}, {12995, 45624}, {13112, 16203}, {13113, 16202}, {13334, 33813}, {15819, 44772}, {26398, 48517}, {26422, 48518}, {26516, 49084}, {26521, 49085}, {33021, 38741}, {33468, 49106}, {33469, 49105}, {34510, 36998}, {39214, 44821}

X(49112) = midpoint of X(i) and X(j) for these {i, j}: {3, 83}, {4, 8725}, {6287, 12252}, {6308, 35701}, {12122, 13111}, {48770, 48771}
X(49112) = reflection of X(i) in X(j) for these (i, j): (5, 6704), (6292, 140), (22803, 5)
X(49112) = complement of X(6287)
X(49112) = orthologic center (anti-X3-ABC reflections, 2nd Neuberg)
X(49112) = X(83)-of-anti-X3-ABC reflections triangle
X(49112) = X(8725)-of-Euler triangle
X(49112) = X(22803)-of-Johnson triangle
X(49112) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 12252, 6287), (3, 13111, 12122), (3, 18501, 22676), (83, 9751, 3), (83, 12122, 13111), (13334, 44224, 33813)


X(49113) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS TO 1st SCHIFFLER

Barycentrics    2*(b+c)*a^9-(3*b^2-4*b*c+3*c^2)*a^8-6*(b+c)*(b^2+c^2)*a^7+2*(5*b^4+5*c^4-6*b*c*(b^2+c^2))*a^6+2*(b+c)*(3*b^4+3*c^4-b*c*(b^2-5*b*c+c^2))*a^5-(12*b^6+12*c^6-(14*b^4+14*c^4+9*b*c*(b^2+c^2))*b*c)*a^4-2*(b^2-c^2)*(b-c)*(b^4+3*b^2*c^2+c^4)*a^3+(6*b^4+6*c^4-b*c*(8*b^2-3*b*c+8*c^2))*(b^2-c^2)^2*a^2-2*(b^2-c^2)^3*(b-c)*b*c*a-(b^2-c^2)^4*(b-c)^2 : :
X(49113) = 3*X(2)+X(12255) = 3*X(3)-X(12556) = 3*X(3)+X(13126) = 5*X(631)-X(12849) = 5*X(1656)-X(48676) = 3*X(3576)+X(12409) = 3*X(10246)-X(13100) = 3*X(10266)+X(12556) = 3*X(10266)-X(13126) = X(12786)-3*X(26446) = X(12798)-3*X(26451)

The reciprocal orthologic center of these triangles is X(79).

X(49113) lies on these lines: {2, 12255}, {3, 10266}, {5, 22805}, {21, 33860}, {24, 12146}, {30, 12600}, {35, 13080}, {36, 18985}, {55, 13129}, {56, 13128}, {140, 13089}, {182, 48776}, {498, 12947}, {499, 12957}, {517, 12267}, {631, 12849}, {1385, 33668}, {1656, 48676}, {1749, 11277}, {2080, 12209}, {3311, 19097}, {3312, 19098}, {3576, 12409}, {5499, 12619}, {6200, 35871}, {6396, 35870}, {6642, 12414}, {7583, 13919}, {7584, 13987}, {10246, 13100}, {10267, 12342}, {10269, 22782}, {12482, 45620}, {12483, 45621}, {12504, 26316}, {12615, 49107}, {12786, 26446}, {12798, 26451}, {12807, 26341}, {12808, 26348}, {12913, 37621}, {12927, 26492}, {12937, 26487}, {13000, 45623}, {13001, 45624}, {13130, 16203}, {13131, 16202}, {13995, 37563}, {26398, 48523}, {26422, 48524}, {26516, 49090}, {26521, 49091}

X(49113) = midpoint of X(i) and X(j) for these {i, j}: {3, 10266}, {12255, 12919}, {12556, 13126}, {48776, 48777}
X(49113) = reflection of X(i) in X(j) for these (i, j): (13089, 140), (22805, 5)
X(49113) = complement of X(12919)
X(49113) = orthologic center (anti-X3-ABC reflections, 1st Schiffler)
X(49113) = X(10266)-of-anti-X3-ABC reflections triangle
X(49113) = X(22805)-of-Johnson triangle
X(49113) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 12255, 12919), (3, 13126, 12556), (35, 18244, 13080), (10266, 12556, 13126)


X(49114) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS TO 1st TRI-SQUARES-CENTRAL

Barycentrics    3*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)*a^2+(2*a^4-7*(b^2+c^2)*a^2+5*(b^2-c^2)^2)*S : :
X(49114) = 3*X(2)+X(13674) = 3*X(3)-X(13666) = 3*X(3)+X(13713) = 2*X(547)+X(48780) = 5*X(631)-X(13678) = 3*X(1327)+X(13666) = 3*X(1327)-X(13713) = 5*X(1656)-X(48677) = 3*X(3524)+X(33456) = 3*X(3576)+X(13679) = 3*X(5054)-X(13712) = 3*X(10246)-X(13702) = 2*X(12974)-5*X(49104) = X(13688)-3*X(26446) = X(13689)-3*X(26451)

The reciprocal orthologic center of these triangles is X(13665).

X(49114) lies on these lines: {2, 6290}, {3, 1327}, {5, 22806}, {24, 13668}, {30, 6250}, {35, 13699}, {36, 18986}, {55, 13715}, {56, 13714}, {140, 13701}, {182, 547}, {498, 13695}, {499, 13696}, {517, 13667}, {631, 13678}, {1656, 48677}, {2080, 13672}, {3311, 19099}, {3312, 22541}, {3524, 33456}, {3545, 43119}, {3576, 13679}, {3845, 43120}, {5050, 42603}, {5054, 13712}, {6200, 35873}, {6396, 35872}, {6642, 13680}, {6771, 33487}, {6774, 33486}, {7583, 13920}, {7584, 13988}, {9738, 43211}, {9771, 41490}, {10246, 13702}, {10267, 13675}, {10269, 22783}, {10515, 48678}, {11539, 43121}, {11812, 12975}, {12042, 45871}, {13682, 45620}, {13683, 45621}, {13685, 26316}, {13688, 26446}, {13689, 26451}, {13690, 26341}, {13691, 26348}, {13693, 26492}, {13694, 26487}, {13697, 45623}, {13698, 45624}, {13708, 35702}, {13716, 16203}, {13717, 16202}, {14241, 49038}, {15682, 26516}, {15764, 36400}, {15765, 22872}, {18585, 22917}, {22165, 44486}, {26398, 48525}, {26422, 48526}, {26521, 49093}, {33470, 34552}, {33471, 34551}

X(49114) = midpoint of X(i) and X(j) for these {i, j}: {3, 1327}, {13666, 13713}, {13674, 13692}, {13708, 35702}, {48778, 48780}
X(49114) = reflection of X(i) in X(j) for these (i, j): (13701, 140), (22806, 5), (48778, 547)
X(49114) = complement of X(13692)
X(49114) = orthologic center (anti-X3-ABC reflections, 1st tri-squares-central)
X(49114) = X(1327)-of-anti-X3-ABC reflections triangle
X(49114) = X(8997)-of-McCay triangle
X(49114) = X(22806)-of-Johnson triangle
X(49114) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 13674, 13692), (3, 13713, 13666), (182, 547, 49115), (1327, 13666, 13713)


X(49115) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    3*(a^4-(b^2+c^2)*a^2-2*b^2*c^2)*a^2-(2*a^4-7*(b^2+c^2)*a^2+5*(b^2-c^2)^2)*S : :
X(49115) = 3*X(2)+X(13794) = 3*X(3)-X(13786) = 3*X(3)+X(13836) = 2*X(547)+X(48781) = 5*X(631)-X(13798) = 3*X(1328)+X(13786) = 3*X(1328)-X(13836) = 5*X(1656)-X(48678) = 3*X(3524)+X(33457) = 3*X(3576)+X(13799) = 3*X(5054)-X(13835) = 3*X(10246)-X(13822) = 2*X(12975)-5*X(49103) = X(13808)-3*X(26446) = X(13809)-3*X(26451)

The reciprocal orthologic center of these triangles is X(13785).

X(49115) lies on these lines: {2, 6222}, {3, 1328}, {5, 22807}, {24, 13788}, {30, 6251}, {35, 13819}, {36, 18987}, {55, 13838}, {56, 13837}, {140, 13821}, {182, 547}, {498, 13815}, {499, 13816}, {517, 13787}, {631, 13798}, {1656, 48678}, {2080, 13792}, {3311, 19101}, {3312, 19100}, {3524, 33457}, {3545, 43118}, {3576, 13799}, {3845, 43121}, {5050, 42602}, {5054, 13835}, {6200, 35875}, {6396, 35874}, {6642, 13800}, {6771, 33489}, {6774, 33488}, {7583, 13848}, {7584, 13849}, {9739, 43212}, {9771, 41491}, {10246, 13822}, {10267, 13795}, {10269, 22784}, {10514, 48677}, {11539, 43120}, {11812, 12974}, {12042, 45872}, {13802, 45620}, {13803, 45621}, {13805, 26316}, {13808, 26446}, {13809, 26451}, {13810, 26341}, {13811, 26348}, {13813, 26492}, {13814, 26487}, {13817, 45623}, {13818, 45624}, {13828, 35703}, {13839, 16203}, {13840, 16202}, {14226, 49039}, {15682, 26521}, {15764, 36397}, {15765, 22919}, {18585, 22874}, {22165, 44485}, {26398, 48527}, {26422, 48528}, {26516, 49092}, {33472, 34551}, {33473, 34552}

X(49115) = midpoint of X(i) and X(j) for these {i, j}: {3, 1328}, {13786, 13836}, {13794, 13812}, {13828, 35703}, {48779, 48781}
X(49115) = reflection of X(i) in X(j) for these (i, j): (13821, 140), (22807, 5), (48779, 547)
X(49115) = complement of X(13812)
X(49115) = orthologic center (anti-X3-ABC reflections, 2nd tri-squares-central)
X(49115) = X(1328)-of-anti-X3-ABC reflections triangle
X(49115) = X(13989)-of-McCay triangle
X(49115) = X(22807)-of-Johnson triangle
X(49115) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 13794, 13812), (3, 13836, 13786), (182, 547, 49114), (1328, 13786, 13836)


X(49116) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS TO WALSMITH

Barycentrics    2*(b^2+c^2)*a^10-(5*b^4+2*b^2*c^2+5*c^4)*a^8+2*(b^4+b^2*c^2+c^4)*(b^2+c^2)*a^6+2*(2*b^8+2*c^8-b^2*c^2*(b^4+4*b^2*c^2+c^4))*a^4-4*(b^6-c^6)*(b^4-c^4)*a^2+(b^4-c^4)^2*(b^2-c^2)^2 : :
X(49116) = 3*X(2)+X(32247) = 3*X(3)-X(32233) = 3*X(3)+X(32306) = X(6)-3*X(15061) = 3*X(67)+X(32233) = 3*X(67)-X(32306) = 3*X(74)+X(41737) = 3*X(125)-2*X(20301) = X(146)-5*X(40330) = 3*X(182)-X(41731) = 3*X(599)+X(16010) = 3*X(1352)-X(41737) = 3*X(5621)+X(15069) = 3*X(5648)-X(32254) = 4*X(6698)-X(32271) = 6*X(6699)-X(41731) = X(16003)+2*X(40107) = X(16010)-3*X(20126) = 2*X(20417)+X(34507) = 2*X(32257)+X(32305)

The reciprocal orthologic center of these triangles is X(125).

X(49116) lies on these lines: {2, 9970}, {3, 67}, {5, 2781}, {6, 15061}, {24, 32239}, {30, 8262}, {35, 32297}, {36, 32243}, {55, 32308}, {56, 32307}, {69, 11579}, {74, 1352}, {113, 24206}, {125, 511}, {140, 6593}, {141, 5663}, {146, 40330}, {182, 6699}, {265, 1350}, {498, 32289}, {499, 32290}, {517, 32238}, {524, 15122}, {541, 11178}, {575, 5095}, {576, 15118}, {631, 11061}, {690, 18312}, {1503, 12041}, {1656, 48679}, {2080, 32242}, {2777, 3818}, {2836, 31837}, {2854, 10264}, {3098, 17702}, {3311, 32252}, {3312, 32253}, {3357, 34118}, {3448, 10519}, {3526, 45016}, {3576, 32261}, {3589, 34128}, {3763, 14643}, {5054, 34319}, {5085, 38728}, {5092, 38727}, {5094, 5476}, {5480, 20304}, {5544, 6723}, {5622, 15057}, {5642, 7495}, {5655, 21358}, {5907, 15063}, {5965, 15089}, {5969, 15535}, {5972, 15106}, {6153, 49108}, {6200, 35877}, {6396, 35876}, {6642, 32262}, {7574, 19924}, {7579, 19130}, {7583, 32303}, {7584, 32304}, {7687, 48901}, {7728, 10516}, {9140, 16063}, {9517, 44813}, {10065, 12589}, {10081, 12588}, {10113, 29181}, {10168, 15303}, {10246, 32298}, {10267, 32256}, {10269, 32270}, {10295, 11645}, {10620, 14982}, {10627, 12359}, {10733, 48873}, {10752, 14561}, {10990, 18553}, {11006, 19905}, {11179, 13169}, {12121, 31884}, {12295, 29317}, {12585, 32283}, {13202, 48889}, {13371, 16982}, {13399, 44280}, {13561, 40929}, {13754, 19510}, {14216, 38885}, {14644, 31670}, {14677, 39884}, {14791, 32273}, {14810, 16163}, {14869, 40342}, {15041, 18440}, {15055, 46264}, {15136, 40919}, {15141, 15805}, {16111, 29012}, {16202, 32310}, {16203, 32309}, {18400, 45619}, {18583, 40685}, {19360, 32251}, {19378, 22581}, {20127, 36990}, {23699, 36832}, {26316, 32268}, {26341, 32280}, {26348, 32281}, {26398, 48529}, {26422, 48530}, {26446, 32278}, {26451, 32279}, {26487, 32288}, {26492, 32287}, {26516, 49094}, {26521, 49095}, {32265, 45620}, {32266, 45621}, {32276, 44503}, {32295, 45623}, {32296, 45624}, {32423, 33851}, {33878, 38724}, {37473, 45622}, {37517, 38725}, {37853, 48898}, {38064, 41720}, {38788, 48905}, {47296, 47581}

X(49116) = midpoint of X(i) and X(j) for these {i, j}: {3, 67}, {69, 11579}, {74, 1352}, {265, 1350}, {599, 20126}, {5181, 16003}, {9970, 32247}, {10264, 48876}, {10620, 14982}, {10733, 48873}, {11006, 19905}, {11179, 13169}, {14216, 38885}, {14677, 39884}, {20127, 36990}, {20417, 32257}, {23236, 25335}, {32233, 32306}, {32305, 34507}, {48782, 48783}
X(49116) = reflection of X(i) in X(j) for these (i, j): (5, 6698), (113, 24206), (182, 6699), (576, 15118), (5095, 575), (5181, 40107), (5476, 45311), (5480, 20304), (6593, 140), (12585, 32283), (13202, 48889), (15118, 20397), (15303, 10168), (16163, 14810), (18583, 40685), (19140, 5972), (25328, 20379), (32271, 5), (32273, 36253), (32305, 20417), (34507, 32257), (47581, 47296), (48898, 37853), (48901, 7687)
X(49116) = complement of X(9970)
X(49116) = orthologic center (anti-X3-ABC reflections, Walsmith)
X(49116) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {2, 11006, 19905}, {74, 98, 1352}, {10620, 12188, 14982}, {11161, 11179, 13169}
X(49116) = X(67)-of-anti-X3-ABC reflections triangle
X(49116) = X(32271)-of-Johnson triangle
X(49116) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 32247, 9970), (3, 32306, 32233), (67, 32233, 32306), (631, 11061, 15462), (10752, 15059, 14561), (15057, 32244, 5622), (15141, 44480, 34155)


X(49117) = CYCLOLOGIC CENTER OF THESE TRIANGLES: EHRMANN-MID TO ANTI-X3-ABC REFLECTIONS

Barycentrics    2*a^16-3*(b^2+c^2)*a^14-(7*b^4-20*b^2*c^2+7*c^4)*a^12+(3*b^2-4*c^2)*(4*b^2-3*c^2)*(b^2+c^2)*a^10+(b^2-c^2)^2*(2*b^2-5*c^2)*(5*b^2-2*c^2)*a^8-9*(b^4-c^4)*(b^2-c^2)*(3*b^4-4*b^2*c^2+3*c^4)*a^6+(13*b^8+13*c^8+6*b^2*c^2*(4*b^4-7*b^2*c^2+4*c^4))*(b^2-c^2)^2*a^4+(b^4-c^4)*(b^2-c^2)^3*(2*b^4-17*b^2*c^2+2*c^4)*a^2-(b^2-c^2)^6*(b^2+2*c^2)*(2*b^2+c^2) : :
X(49117) = 3*X(4)-X(22337) = 3*X(4)+X(34186) = 5*X(4)-X(34549) = 3*X(5)-2*X(6716) = X(107)-3*X(381) = 2*X(140)-3*X(36520) = 5*X(1656)-3*X(23239) = X(1657)-3*X(38714) = 5*X(3091)-X(5667) = X(3184)-3*X(36520) = 7*X(3526)-X(23241) = 3*X(3830)+X(38591) = 3*X(3830)-X(44985) = 4*X(6716)-3*X(38605) = 3*X(10714)-X(38591) = 3*X(10714)+X(44985) = 3*X(10745)+X(22337) = 3*X(10745)-X(34186) = 5*X(10745)+X(34549) = 5*X(22337)-3*X(34549) = 5*X(34186)+3*X(34549)

The reciprocal cyclologic center of these triangles is X(38605).

X(49117) lies on the circumcircle of Ehrmann-mid triangle and these lines: {2, 23240}, {3, 10152}, {4, 2972}, {5, 1539}, {30, 122}, {107, 381}, {133, 546}, {140, 3184}, {382, 1294}, {402, 16111}, {550, 33531}, {1656, 23239}, {1657, 38714}, {2790, 22505}, {2797, 22515}, {2803, 22938}, {2816, 19925}, {2828, 22799}, {2848, 19163}, {3091, 5667}, {3324, 3585}, {3526, 23241}, {3583, 7158}, {3627, 20329}, {3830, 10714}, {3843, 38577}, {3845, 9530}, {3853, 38956}, {5076, 38686}, {7526, 14703}, {9033, 10113}, {9818, 14673}, {9955, 11718}, {10701, 18525}, {10742, 10775}, {10762, 18440}, {11250, 40082}, {11732, 34773}, {14670, 22823}, {37243, 38649}

X(49117) = midpoint of X(i) and X(j) for these {i, j}: {3, 10152}, {4, 10745}, {382, 1294}, {3830, 10714}, {10701, 18525}, {10742, 10775}, {10762, 18440}, {22337, 34186}, {38591, 44985}
X(49117) = reflection of X(i) in X(j) for these (i, j): (133, 546), (550, 34842), (3184, 140), (11718, 9955), (34773, 11732), (38605, 5), (38621, 122), (38956, 3853)
X(49117) = complement of X(23240)
X(49117) = reflection of X(5) in the line X(7687)X(9033)
X(49117) = cyclologic center (Ehrmann-mid, anti-X3-ABC reflections)
X(49117) = center of circle {{X(4), X(1552), X(10745)}}
X(49117) = X(107)-of-Ehrmann-mid triangle
X(49117) = X(10152)-of-anti-X3-ABC reflections triangle
X(49117) = X(10745)-of-Euler triangle
X(49117) = X(38605)-of-Johnson triangle
X(49117) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 34186, 22337), (3184, 36520, 140), (3830, 38591, 44985), (10714, 44985, 38591), (10745, 22337, 34186)


X(49118) = CYCLOLOGIC CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS TO K798E

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

The reciprocal cyclologic center of these triangles is X(5).

X(49118) lies on the cubic K798 and these lines: {3, 501}, {106, 22765}, {110, 27086}, {517, 38612}, {758, 1385}, {1006, 6176}, {1511, 23961}, {23341, 26086}, {43574, 48893}

X(49118) = cyclologic center (anti-X3-ABC reflections, K798e)
X(49118) = X(5127)-of-anti-X3-ABC reflections triangle
X(49118) = midpoint of X(3) and X(5127)


X(49119) = CYCLOLOGIC CENTER OF THESE TRIANGLES: ANTI-X3-ABC REFLECTIONS TO MCCAY

Barycentrics    a^2*(32*a^12-152*(b^2+c^2)*a^10+2*(134*b^4+237*b^2*c^2+134*c^4)*a^8-(b^2+c^2)*(212*b^4+297*b^2*c^2+212*c^4)*a^6+(40*b^8+40*c^8+7*(43*b^4+36*b^2*c^2+43*c^4)*b^2*c^2)*a^4+(b^2+c^2)*(40*b^8+40*c^8-(214*b^4-221*b^2*c^2+214*c^4)*b^2*c^2)*a^2-16*b^12-16*c^12+(64*b^8+64*c^8-(59*b^4-46*b^2*c^2+59*c^4)*b^2*c^2)*b^2*c^2) : :
X(49119) = 3*X(381)-X(45156)

The reciprocal cyclologic center of these triangles is X(49120).

X(49119) lies on the circumcircle of anti-X3-ABC reflections triangle and these lines: {3, 8600}, {30, 45166}, {140, 16938}, {381, 45156}, {575, 14650}, {7622, 12042}

X(49119) = midpoint of X(3) and X(8600)
X(49119) = cyclologic center (anti-X3-ABC reflections, McCay)
X(49119) = X(45156)-of-Ehrmann-mid triangle
X(49119) = X(33601)-of-McCay triangle
X(49119) = X(8600)-of-anti-X3-ABC reflections triangle
X(49119) = reflection of X(16938) in X(140)


X(49120) = CYCLOLOGIC CENTER OF THESE TRIANGLES: MCCAY TO ANTI-X3-ABC REFLECTIONS

Barycentrics    16*a^14-84*(b^2+c^2)*a^12+(442*b^4-419*b^2*c^2+442*c^4)*a^10-(b^2+c^2)*(974*b^4-2103*b^2*c^2+974*c^4)*a^8+(1198*b^8+1198*c^8-(2469*b^4-262*b^2*c^2+2469*c^4)*b^2*c^2)*a^6-(b^2+c^2)*(854*b^8+854*c^8-(3669*b^4-5102*b^2*c^2+3669*c^4)*b^2*c^2)*a^4+4*(72*b^12+72*c^12-(371*b^8+371*c^8-2*(365*b^4-447*b^2*c^2+365*c^4)*b^2*c^2)*b^2*c^2)*a^2-8*(b^4-c^4)*(b^2-c^2)*(b^2-2*c^2)^2*(2*b^2-c^2)^2 : :

The reciprocal cyclologic center of these triangles is X(49119).

X(49120) lies on the McCay circle and these lines: {3, 25409}, {140, 16939}

X(49120) = midpoint of X(3) and X(25409)
X(49120) = cyclologic center (McCay, anti-X3-ABC reflections)
X(49120) = X(25409)-of-anti-X3-ABC reflections triangle
X(49120) = reflection of X(16939) in X(140)


X(49121) = (name pending)

Barycentrics    (3*(b^2+c^2)*a^24-6*(5*b^4+12*b^2*c^2+5*c^4)*a^22+66*(b^2+2*c^2)*(2*b^2+c^2)*(b^2+c^2)*a^20-(330*b^8+330*c^8+(1453*b^4+2038*b^2*c^2+1453*c^4)*b^2*c^2)*a^18+(b^2+c^2)*(495*b^8+495*c^8+(2195*b^4+1964*b^2*c^2+2195*c^4)*b^2*c^2)*a^16-(396*b^12+396*c^12+(3260*b^8+3260*c^8+(4309*b^4+4722*b^2*c^2+4309*c^4)*b^2*c^2)*b^2*c^2)*a^14+2*(b^2+c^2)*(1512*b^8+1512*c^8-(676*b^4-1607*b^2*c^2+676*c^4)*b^2*c^2)*b^2*c^2*a^12+(396*b^16+396*c^16-(2782*b^12+2782*c^12-(1691*b^8+1691*c^8-(b^4-132*b^2*c^2+c^4)*b^2*c^2)*b^2*c^2)*b^2*c^2)*a^10-(b^2+c^2)*(495*b^16+495*c^16-(3178*b^12+3178*c^12-(7360*b^8+7360*c^8-(8995*b^4-9311*b^2*c^2+8995*c^4)*b^2*c^2)*b^2*c^2)*b^2*c^2)*a^8+(330*b^16+330*c^16-(1440*b^12+1440*c^12-(1781*b^8+1781*c^8+(143*b^4+379*b^2*c^2+143*c^4)*b^2*c^2)*b^2*c^2)*b^2*c^2)*(b^2-c^2)^2*a^6-(b^4-c^4)*(b^2-c^2)^3*(132*b^12+132*c^12-(686*b^8+686*c^8-(1284*b^4-965*b^2*c^2+1284*c^4)*b^2*c^2)*b^2*c^2)*a^4+(30*b^12+30*c^12-(137*b^8+137*c^8-(151*b^4+120*b^2*c^2+151*c^4)*b^2*c^2)*b^2*c^2)*(b^2-c^2)^6*a^2-(b^2-c^2)^8*(b^2+c^2)*(3*b^8+3*c^8-(19*b^4-40*b^2*c^2+19*c^4)*b^2*c^2))*a^2 : :

In the plane of a triangle ABC, let
OaObOc = pedal triangle of O;
A'B'C' = reflection triangle;
A* = orthogonal projection of A' on OOa, and define B* and C* cyclically;
A"B"C" = the pedal triangle of N = X(5) [of ABC] wrt triangle A*B*C*.

Conjecture: the Euler lines of A*B"C", B*C"A", C*A"B" concur. If this is true, then N is one [of 9] intersections of the Napoleon-Feuerbach cubic K005 of ABC and A*B*C*.

See Antreas Hatzipolakis and César Lozada euclid 5069.

X(49121) lies on these lines: { }


X(49122) = X(4)X(69)∩X(111)X(694)

Barycentrics    a^2*(a^6*b^4 - a^2*b^8 + a^6*b^2*c^2 - a^4*b^4*c^2 + 2*a^2*b^6*c^2 + a^6*c^4 - a^4*b^2*c^4 - a^2*b^4*c^4 - b^6*c^4 + 2*a^2*b^2*c^6 - b^4*c^6 - a^2*c^8) : :
X(49122) = 2 X[5104] - 3 X[11673], 5 X[3618] - 4 X[35060]

X(49122) lies on the cubic K1277 and these lines: {4, 69}, {111, 694}, {148, 2393}, {385, 2882}, {1691, 19121}, {2387, 10754}, {2998, 14712}, {3618, 35060}, {11675, 15745}, {18322, 21850}

(49122) = reflection of X(i) in X(j) for these {i,j}: {69, 5167}, {18322, 21850}, {32529, 1691}
(49122) = reflection of X(69) in the Lemoine axis
(49122) = crossdifference of every pair of points on line {3049, 11183}


X(49123) = X(2)X(5866)∩X(5)X(6)

Barycentrics    a^8*b^2 - 2*a^6*b^4 + 2*a^2*b^8 - b^10 + a^8*c^2 - 2*a^6*b^2*c^2 + 2*a^4*b^4*c^2 - 8*a^2*b^6*c^2 + 3*b^8*c^2 - 2*a^6*c^4 + 2*a^4*b^2*c^4 + 12*a^2*b^4*c^4 - 2*b^6*c^4 - 8*a^2*b^2*c^6 - 2*b^4*c^6 + 2*a^2*c^8 + 3*b^2*c^8 - c^10 : :
X(49123) = 2 X[9721] - 3 X[15538], 2 X[9721] + X[45769], 3 X[15538] + X[45769], 3 X[381] + X[35463]

X(49123) lies on the Moses-Parry circle, the cubic K1277, and these lines: {2, 5866}, {4, 21397}, {5, 6}, {30, 2079}, {111, 858}, {112, 230}, {113, 36472}, {115, 2072}, {187, 11799}, {232, 40234}, {235, 3053}, {381, 35463}, {427, 5203}, {468, 8428}, {1368, 44526}, {1560, 3291}, {2450, 3566}, {2493, 5523}, {3548, 44528}, {5133, 6032}, {5576, 39565}, {6823, 44535}, {7737, 46030}, {7746, 10024}, {7748, 37452}, {8426, 46698}, {8427, 46699}, {8429, 36189}, {8430, 47138}, {8744, 16306}, {10257, 34866}, {10297, 44533}, {11585, 15075}, {12362, 44525}, {12605, 44523}, {15760, 37637}, {16868, 41370}, {18404, 44527}, {18531, 44524}, {28419, 32972}, {28708, 39143}, {32654, 47108}, {34512, 37648}, {37361, 44517}, {44249, 44538}

X(49123) = reflection of X(14729) in X(468)
X(49123) = reflection of X(2079) in the Orthic axis
X(49123) = nine-point-circle-inverse of X(6)
X(49123) = polar-circle-inverse of X(21397)
X(49123) = complement of X(5866)
X(49123) = complement of the isogonal conjugate of X(41521)
X(49123) = X(i)-complementary conjugate of X(j) for these (i,j): {40347, 18589}, {41521, 10}
X(49123) = crosspoint of X(671) and X(847)
X(49123) = crosssum of X(i) and X(j) for these (i,j): {6, 41615}, {187, 1147}
X(49123) = crossdifference of every pair of points on line {924, 9306}
X(49123) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {485, 486, 8548}, {2165, 43620, 13881}


X(49124) = X(4)X(39)∩X(147)X(14961)

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

X(49124) lies on the cubic K1277 and these lines: {4, 39}, {147, 14961}, {1297, 35002}, {1691, 5622}, {3267, 7799}, {3269, 11674}, {5116, 15577}, {7836, 14376}

X(49124) = polar-circle-inverse of X(3199)


X(49125) = X(6)X(110)∩X(74)X(1352)

Barycentrics    a^2*(a^12 + a^10*b^2 - 4*a^8*b^4 - 2*a^6*b^6 + 5*a^4*b^8 + a^2*b^10 - 2*b^12 + a^10*c^2 - a^8*b^2*c^2 + 12*a^6*b^4*c^2 - 6*a^4*b^6*c^2 - 13*a^2*b^8*c^2 + 7*b^10*c^2 - 4*a^8*c^4 + 12*a^6*b^2*c^4 - 24*a^4*b^4*c^4 + 18*a^2*b^6*c^4 + 2*b^8*c^4 - 2*a^6*c^6 - 6*a^4*b^2*c^6 + 18*a^2*b^4*c^6 - 14*b^6*c^6 + 5*a^4*c^8 - 13*a^2*b^2*c^8 + 2*b^4*c^8 + a^2*c^10 + 7*b^2*c^10 - 2*c^12) : :
X(49125) = X[895] - 4 X[1995], 2 X[5181] + X[7519]

X(49125) lies on the cubic K1277 and these lines: {6, 110}, {74, 1352}, {858, 12367}, {2892, 3620}, {5181, 7519}, {9306, 41743}, {10752, 15068}, {14982, 38323}, {15051, 15577}, {15107, 32113}, {15116, 16063}, {20772, 41614}, {25320, 40132}, {35264, 41612}, {37777, 41617}, {41721, 47552}

X(49125) = {X(110),X(11188)}-harmonic conjugate of X(895)


X(49126) = X(30)X(2076)∩X(111)X(694)

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

X(49126) lies on the cubic K1277 and these lines: {30, 2076}, {111, 694}, {511, 18371}, {1691, 5622}, {5017, 7418}, {9210, 20403}

X(49126) = reflection of X(18371) in the Lemoine axis

leftri

Combos (1+h)*X(3) - h*X(4) on the Euler line: X(49127)-X(49140)

rightri

If h is a constant or other function symmetric in a,b,c and of degree 0 of homogeneity, then (1+h)*X(3)-h*X(4), like every combo of points on the Euler line, is also on the Euler line. The combo (1+h)*X(3)-h*X(4) can also be expressed as X(3) + h*X(30).

In the following list, the appearance of h,k means that (1+h)*X(3)-h*X(4) = X(k).

-10, 49133
-9,11541
-8, 49134
-7, 49135
-6, 49136
-5,33703
-4,5073
-3,3146
-2,382
-1,4
-2/3,381
-1/2,5
-1/3,2
0,3
1/3,376
1/2,550
2/3,3534
1,20
2,1657
3,3529
4,17800
5,5059
6, 49137
7, 49138
8, 49139
9, 49140
(-(a*b*c)/(a^3 + b^3 + c^3)), 49127
(a*b*c)/(a^3 + b^3 + c^3), 49128
(a*b + a*c + b*c)/(a^2 + b^2 + c^2), 49129
(2*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), 49130
-1/2*(a^2 + b^2 + c^2)/(a*b + a*c + b*c), 49131
(a^2 + b^2 + c^2)/(2*(a*b + a*c + b*c)), 49132


X(49127) = X(2)X(3)∩X(31)X(15310)

Barycentrics    a*(a^5 - a^4*b + a^2*b^3 - a*b^4 - a^4*c + b^4*c - b^3*c^2 + a^2*c^3 - b^2*c^3 - a*c^4 + b*c^4) : :
X(49127) = 5 X[3] - 3 X[28464], 4 X[5] - 3 X[36583], 3 X[165] - X[21375]

X(49127) lies on these lines: {2, 3}, {31, 15310}, {40, 3961}, {55, 3782}, {81, 48908}, {100, 11689}, {165, 6211}, {355, 33117}, {511, 1754}, {515, 29673}, {516, 29656}, {517, 3938}, {545, 4421}, {741, 991}, {902, 28388}, {946, 29672}, {982, 36509}, {983, 1423}, {1283, 17889}, {1292, 9082}, {1376, 24320}, {1626, 2886}, {1647, 32612}, {1715, 46730}, {1746, 48938}, {1764, 3098}, {1936, 3784}, {3100, 20254}, {3187, 29331}, {3223, 32462}, {3295, 39544}, {3434, 20999}, {3576, 29820}, {3749, 28039}, {4297, 29655}, {5285, 36482}, {5687, 42461}, {5706, 48909}, {5886, 29853}, {10902, 29675}, {11012, 29676}, {11495, 36528}, {12511, 36480}, {12699, 29638}, {13323, 48897}, {15931, 31394}, {16678, 36488}, {18163, 47038}, {18481, 33120}, {24309, 24326}, {24813, 32939}, {24833, 33146}, {29326, 33637}, {29327, 32929}, {29651, 39552}, {29652, 37620}, {29860, 41869}, {33119, 36506}, {33163, 36497}, {36742, 48921}

X(49127) = reflection of X(4) in X(30448)
X(49127) = barycentric product X(100)*X(24793)
X(49127) = barycentric quotient X(24793)/X(693)
X(49127) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 4, 13732}, {3, 1657, 15952}, {3, 3149, 19514}, {3, 6911, 19335}, {3, 6985, 19513}, {3, 7580, 4192}, {3, 19517, 21487}, {3, 19540, 19649}, {3, 19541, 16434}, {3, 36558, 631}, {3, 37411, 37415}, {20, 36510, 3}, {25, 1004, 16056}, {404, 28029, 28383}, {411, 37328, 3}, {1005, 37261, 16058}, {4220, 7411, 3}, {4224, 35990, 47522}, {5004, 5005, 17522}, {7465, 35989, 1011}, {9909, 11347, 46548}, {16056, 46549, 25}, {16434, 19541, 19546}, {17579, 37311, 37397}, {19649, 36002, 19540}, {20841, 47522, 4224}, {33849, 35977, 16059}, {35979, 35998, 28348}, {35996, 36003, 4191}


X(49128) = X(1)X(987)∩X(2)X(3)

Barycentrics    a*(a^6 - a^4*b^2 + a^3*b^3 - a*b^5 + 2*a^4*b*c - a^2*b^3*c - b^5*c - a^4*c^2 - a*b^3*c^2 + a^3*c^3 - a^2*b*c^3 - a*b^2*c^3 + 2*b^3*c^3 - a*c^5 - b*c^5) : :
X(49128) = X[3] - 3 X[28464], 2 X[4] - 3 X[36583]

X(49128) lies on these lines: {1, 987}, {2, 3}, {31, 517}, {36, 3944}, {55, 5724}, {56, 3782}, {58, 10441}, {104, 932}, {105, 39631}, {511, 30487}, {515, 4112}, {545, 11194}, {572, 4653}, {573, 759}, {958, 5835}, {960, 2217}, {970, 1724}, {993, 3923}, {999, 4310}, {1064, 2309}, {1329, 2933}, {1385, 6051}, {1468, 35631}, {1766, 5336}, {1870, 20254}, {2051, 48866}, {2268, 24929}, {2551, 38903}, {2975, 32933}, {3428, 20992}, {3576, 7611}, {5886, 32772}, {9549, 16468}, {9567, 32911}, {10457, 37536}, {13478, 48863}, {14987, 29325}, {15310, 30269}, {15488, 37530}, {19133, 37569}, {19782, 36746}, {26446, 32917}, {36742, 48909}, {37469, 37521}, {40980, 48917}

X(49128) = midpoint of X(1) and X(21375)
X(49128) = anticomplement of X(30448)
X(49128) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 4, 19548}, {3, 405, 13731}, {3, 1012, 37331}, {3, 3560, 9840}, {3, 6913, 19544}, {3, 16434, 19335}, {3, 19540, 6905}, {3, 19549, 404}, {3, 37415, 19513}, {21, 37231, 28348}, {21, 37399, 3}, {22, 26096, 36571}, {1006, 4221, 3}, {4185, 37248, 28258}, {6906, 37431, 3}, {6909, 19649, 3}, {7520, 28376, 20836}, {16370, 16435, 3}, {17512, 19260, 13723}, {37106, 37400, 3}, {37241, 37249, 16056}


X(49129) = X(1)X(24296)∩X(2)X(3)

Barycentrics    a^6 + 2*a^5*b - a^3*b^3 - a^2*b^4 - a*b^5 + 2*a^5*c + 2*a^4*b*c - a^3*b^2*c - a^2*b^3*c - a*b^4*c - b^5*c - a^3*b*c^2 - 2*a^2*b^2*c^2 + 2*a*b^3*c^2 - a^3*c^3 - a^2*b*c^3 + 2*a*b^2*c^3 + 2*b^3*c^3 - a^2*c^4 - a*b*c^4 - a*c^5 - b*c^5 : :
X(49129) = 2 X[4] - 3 X[36551], 4 X[5] - 3 X[36729], X[382] - 3 X[36721], 5 X[1656] - 3 X[36731], 7 X[3851] - 6 X[36727], 2 X[36685] - 3 X[36729]

X(49129) lies on these lines: {1, 24296}, {2, 3}, {40, 29365}, {182, 516}, {572, 48902}, {582, 3073}, {1479, 17798}, {1766, 29010}, {2271, 18907}, {2549, 5292}, {3454, 7761}, {3824, 25500}, {3916, 24591}, {4045, 20083}, {5021, 15048}, {5651, 18653}, {6284, 37576}, {6684, 48925}, {7737, 18755}, {9566, 41810}, {10444, 29369}, {10479, 24271}, {12717, 29327}, {15171, 37580}, {17731, 32515}, {17732, 20672}, {18483, 48932}, {22793, 28897}, {37474, 48934}, {37510, 48918}

X(49129) = reflection of X(36685) in X(5)
X(49129) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36675, 5}, {3, 4, 36477}, {3, 381, 6998}, {3, 382, 13727}, {3, 19648, 19545}, {4, 631, 36693}, {4, 37416, 3}, {5, 36685, 36729}, {20, 36670, 36674}, {20, 36697, 3}, {4229, 6996, 21554}, {4229, 21554, 3}, {14784, 14785, 6999}, {36670, 36674, 5}


X(49130) = X(2)X(3)∩X(6)X(516)

Barycentrics    a^6 + 4*a^5*b - 2*a^3*b^3 - a^2*b^4 - 2*a*b^5 + 4*a^5*c + 4*a^4*b*c - 2*a^3*b^2*c - 2*a^2*b^3*c - 2*a*b^4*c - 2*b^5*c - 2*a^3*b*c^2 - 2*a^2*b^2*c^2 + 4*a*b^3*c^2 - 2*a^3*c^3 - 2*a^2*b*c^3 + 4*a*b^2*c^3 + 4*b^3*c^3 - a^2*c^4 - 2*a*b*c^4 - 2*a*c^5 - 2*b*c^5 : :
X(49130) = 2 X[4] - 3 X[36721], 4 X[5] - 3 X[36731], 3 X[381] - 2 X[36685], 5 X[3843] - 6 X[36551], 7 X[3851] - 6 X[36729]

X(49130) lies on these lines: {2, 3}, {6, 516}, {10, 42316}, {40, 16552}, {165, 19732}, {387, 15048}, {950, 5808}, {971, 10444}, {1699, 19701}, {1724, 9441}, {1730, 10860}, {1834, 2549}, {2268, 5765}, {2271, 7737}, {4061, 5814}, {4314, 5717}, {5278, 9778}, {5691, 24271}, {5728, 18655}, {6284, 37580}, {6361, 28915}, {7988, 19749}, {9812, 19684}, {10164, 19744}, {10476, 10864}, {12651, 37529}, {12702, 29365}, {12953, 17798}, {16783, 28897}, {17206, 32815}, {18653, 35259}, {19765, 24296}, {19925, 24275}, {28158, 48866}, {28164, 48863}, {33863, 44526}, {37474, 48902}, {37499, 48888}, {43174, 48864}, {43531, 48900}

X(49130) = crossdifference of every pair of points on line {647, 9000}
X(49130) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4229, 3}, {3, 3843, 36527}, {4, 376, 7390}, {4, 631, 36695}, {4, 7380, 381}, {4, 7390, 36722}, {4, 36673, 546}, {4, 37062, 2049}, {20, 6996, 3}, {376, 21554, 3}, {405, 37063, 37064}, {405, 37075, 16844}, {964, 37076, 405}, {1011, 1889, 7522}, {3146, 37416, 13727}, {13727, 37416, 3}


X(49131) = X(1)X(1565)∩X(2)X(3)

Barycentrics    2*a^6 - 2*a^5*b + a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - b^6 - 2*a^5*c - 2*a^4*b*c + 2*a^3*b^2*c + 2*a^2*b^3*c + a^4*c^2 + 2*a^3*b*c^2 + b^4*c^2 + 2*a^3*c^3 + 2*a^2*b*c^3 - 2*a^2*c^4 + b^2*c^4 - c^6 : :
X(49131) = 2 X[4] - 3 X[36728], 4 X[5] - 3 X[36722], X[382] - 3 X[36730], 5 X[1656] - 3 X[36490], X[1657] + 3 X[36732], 7 X[3526] - 3 X[36720]

X(49131) lies on these lines: {1, 1565}, {2, 3}, {165, 32780}, {516, 24325}, {572, 44882}, {573, 29181}, {950, 37597}, {991, 1503}, {1043, 3933}, {1742, 29207}, {2223, 7354}, {3100, 41007}, {3564, 48908}, {4026, 24309}, {4297, 28845}, {4301, 28854}, {5266, 21620}, {5290, 37552}, {5480, 13329}, {6284, 37575}, {7079, 40616}, {7675, 41004}, {7772, 48848}, {15338, 37586}, {17365, 29307}, {18990, 37590}, {21850, 37510}, {29012, 48929}, {29024, 41430}, {29291, 31394}, {29317, 48886}, {37474, 46264}, {37499, 48872}

X(49131) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 382, 36674}, {3, 36530, 140}, {3, 36707, 5}, {4, 21554, 5}, {20, 4229, 550}, {20, 7379, 13727}, {20, 36706, 3}, {1010, 37044, 17698}, {1370, 20835, 440}, {7379, 13727, 5}, {7411, 37456, 19542}


X(49132) = X(1)X(5244)∩X(2)X(3)

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

X(49132) = 2 X[4] - 3 X[36722], 4 X[5] - 3 X[36728], X[382] - 3 X[36490], 5 X[1656] - 3 X[36730], X[1657] + 3 X[36720], 7 X[3526] - 3 X[36732]

X(49132) lies on these lines: {1, 5244}, {2, 3}, {10, 910}, {12, 37586}, {32, 1834}, {37, 516}, {40, 728}, {57, 5808}, {165, 32777}, {387, 30435}, {572, 5480}, {573, 1503}, {991, 29181}, {1104, 4297}, {1330, 3933}, {1427, 4298}, {1530, 21062}, {1565, 24701}, {1754, 44115}, {1763, 5814}, {1890, 40937}, {1892, 6356}, {2223, 6284}, {2968, 24611}, {3198, 5295}, {3555, 17441}, {3564, 48875}, {4254, 5800}, {4292, 37597}, {4314, 5266}, {4675, 43169}, {5007, 48848}, {5493, 28854}, {5728, 18650}, {5805, 10444}, {6210, 29207}, {7354, 37575}, {7767, 10449}, {9778, 17776}, {12572, 25066}, {13329, 44882}, {15171, 37590}, {16552, 39690}, {16783, 44081}, {17362, 29219}, {29012, 48886}, {29050, 41430}, {29317, 48929}, {31670, 37474}, {36990, 37499}, {37510, 48906}

X(49132) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 382, 36474}, {3, 36716, 5}, {4, 631, 7407}, {4, 6998, 5}, {4, 7410, 36673}, {4, 36672, 381}, {4, 36687, 546}, {4, 37320, 4205}, {4, 37412, 1536}, {20, 7385, 6996}, {20, 36698, 3}, {199, 427, 7536}, {405, 2915, 36018}, {405, 37326, 17698}, {464, 6995, 13615}, {4205, 33745, 17698}, {6996, 7385, 5}, {7410, 36673, 1656}, {23512, 37443, 8727}, {26054, 37390, 47510}, {37320, 37412, 25}


X(49133) = X(2)X(3)∩X(397)X(42112)

Barycentrics    19*a^4 - 9*a^2*b^2 - 10*b^4 - 9*a^2*c^2 + 20*b^2*c^2 - 10*c^4 : :
X(49133) = 30 X[2] - 29 X[3], 27 X[2] - 29 X[4], 57 X[2] - 58 X[5], 33 X[2] - 29 X[20], 31 X[2] - 29 X[376], 28 X[2] - 29 X[381], 24 X[2] - 29 X[382], 59 X[2] - 58 X[549], 63 X[2] - 58 X[550], 36 X[2] - 29 X[1657], 21 X[2] - 29 X[3146], 89 X[2] - 87 X[3524], 39 X[2] - 29 X[3529], 32 X[2] - 29 X[3534], 25 X[2] - 29 X[3543], 85 X[2] - 87 X[3545], 51 X[2] - 58 X[3627], 26 X[2] - 29 X[3830], 83 X[2] - 87 X[3839], 55 X[2] - 58 X[3845], 88 X[2] - 87 X[5054], 86 X[2] - 87 X[5055], 45 X[2] - 29 X[5059], 18 X[2] - 29 X[5073], 61 X[2] - 58 X[8703], 91 X[2] - 87 X[10304], 35 X[2] - 29 X[11001], 3 X[2] - 29 X[11541], 82 X[2] - 87 X[14269], 17 X[2] - 29 X[15640], 34 X[2] - 29 X[15681], 23 X[2] - 29 X[15682], 37 X[2] - 29 X[15683], 22 X[2] - 29 X[15684], 38 X[2] - 29 X[15685], 65 X[2] - 58 X[15686], 53 X[2] - 58 X[15687], 92 X[2] - 87 X[15688], 94 X[2] - 87 X[15689], 69 X[2] - 58 X[15704], 42 X[2] - 29 X[17800], 67 X[2] - 58 X[19710], 49 X[2] - 58 X[33699], 15 X[2] - 29 X[33703], 64 X[2] - 65 X[35382], 76 X[2] - 145 X[35384], 10 X[2] - 29 X[35400], 10 X[2] - 11 X[35401], 47 X[2] - 58 X[35404], 78 X[2] - 145 X[35407], 49 X[2] - 116 X[35408], 53 X[2] - 87 X[35409], 80 X[2] - 87 X[38335], 71 X[2] - 58 X[44903], 101 X[2] - 87 X[46333], 9 X[3] - 10 X[4], 19 X[3] - 20 X[5], 11 X[3] - 10 X[20], 39 X[3] - 40 X[140], 31 X[3] - 30 X[376], 14 X[3] - 15 X[381], 4 X[3] - 5 X[382], 37 X[3] - 40 X[546], 23 X[3] - 24 X[547], 41 X[3] - 40 X[548], 59 X[3] - 60 X[549], 21 X[3] - 20 X[550], 49 X[3] - 50 X[631], 97 X[3] - 100 X[632], 24 X[3] - 25 X[1656], 6 X[3] - 5 X[1657], 67 X[3] - 70 X[3090], 47 X[3] - 50 X[3091], 7 X[3] - 10 X[3146], 51 X[3] - 50 X[3522], 69 X[3] - 70 X[3523], 89 X[3] - 90 X[3524], 34 X[3] - 35 X[3526], 71 X[3] - 70 X[3528], 13 X[3] - 10 X[3529], 79 X[3] - 80 X[3530], 33 X[3] - 34 X[3533], 16 X[3] - 15 X[3534], 5 X[3] - 6 X[3543], 17 X[3] - 18 X[3545], 17 X[3] - 20 X[3627], 77 X[3] - 80 X[3628], 13 X[3] - 15 X[3830], 13 X[3] - 14 X[3832], 83 X[3] - 90 X[3839], 23 X[3] - 25 X[3843], 11 X[3] - 12 X[3845], 15 X[3] - 16 X[3850], 33 X[3] - 35 X[3851], and many others

X(49133) lies on these lines: {2, 3}, {397, 42112}, {398, 42113}, {485, 41961}, {486, 41962}, {1131, 9691}, {1327, 6519}, {1328, 6522}, {1482, 28172}, {3581, 11999}, {5041, 44526}, {5097, 48910}, {5339, 34755}, {5340, 34754}, {5349, 42115}, {5350, 42116}, {5365, 42123}, {5366, 42122}, {5925, 14864}, {6199, 42413}, {6241, 13421}, {6395, 42414}, {6429, 8960}, {6433, 8976}, {6434, 13951}, {6437, 42266}, {6438, 42267}, {6445, 23253}, {6446, 23263}, {6447, 43210}, {6448, 43209}, {6451, 10195}, {6452, 10194}, {6480, 23251}, {6481, 23261}, {6482, 13846}, {6483, 13847}, {6560, 41955}, {6561, 41956}, {8148, 28190}, {8550, 43621}, {11278, 28168}, {11488, 42907}, {11489, 42906}, {11531, 28160}, {11738, 14841}, {11898, 29317}, {12002, 37481}, {12645, 28146}, {12702, 28158}, {12953, 37587}, {13321, 46850}, {13432, 18400}, {13903, 22644}, {13961, 22615}, {14490, 26861}, {16200, 32900}, {16267, 43422}, {16268, 43423}, {16964, 43244}, {16965, 43245}, {18493, 31662}, {18510, 42271}, {18512, 42272}, {18525, 28154}, {18526, 28164}, {18553, 48872}, {19106, 42988}, {19107, 42989}, {22793, 30392}, {29323, 37517}, {31454, 43432}, {33179, 41869}, {33541, 37494}, {35770, 42264}, {35771, 42263}, {36836, 42430}, {36843, 42429}, {39561, 48905}, {41947, 42283}, {41948, 42284}, {41973, 42155}, {41974, 42154}, {41977, 42125}, {41978, 42128}, {42090, 42794}, {42091, 42793}, {42096, 42431}, {42097, 42432}, {42099, 42817}, {42100, 42818}, {42108, 42151}, {42109, 42150}, {42126, 42158}, {42127, 42157}, {42140, 42924}, {42141, 42925}, {42144, 42998}, {42145, 42999}, {42153, 42908}, {42156, 42909}, {42779, 43636}, {42780, 43637}, {42974, 43632}, {42975, 43633}, {42992, 43194}, {42993, 43193}, {43336, 43516}, {43337, 43515}, {43787, 43882}, {43788, 43881}

X(49133) = reflection of X(i) in X(j) for these {i,j}: {3, 33703}, {1657, 5073}, {14093, 35384}, {15681, 15640}, {15696, 35407}, {17800, 3146}, {33699, 35408}
X(49133) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 382, 38335}, {3, 3545, 3526}, {3, 3830, 3832}, {3, 3843, 547}, {3, 3851, 3533}, {3, 3853, 381}, {3, 5059, 1657}, {3, 5070, 15708}, {3, 15686, 15696}, {3, 17800, 11001}, {3, 35400, 33703}, {3, 35406, 3146}, {4, 20, 15712}, {4, 376, 46935}, {4, 550, 46219}, {4, 3522, 35018}, {4, 15712, 3851}, {4, 46219, 381}, {4, 46935, 3858}, {20, 3533, 41981}, {20, 3628, 15695}, {20, 3845, 3}, {20, 5076, 5054}, {20, 15684, 5076}, {140, 550, 10304}, {140, 5072, 1656}, {140, 15711, 3523}, {376, 16239, 3}, {381, 1657, 550}, {381, 3146, 382}, {381, 15695, 5054}, {382, 1657, 1656}, {382, 3529, 15700}, {382, 5054, 5076}, {382, 5072, 3830}, {546, 14890, 5}, {548, 15702, 3}, {548, 41991, 15702}, {550, 3853, 5056}, {550, 5056, 3}, {550, 12100, 3522}, {550, 17800, 1657}, {631, 3146, 33699}, {1656, 1657, 3534}, {1656, 15700, 140}, {1657, 5073, 382}, {2043, 2044, 15711}, {3146, 5059, 5056}, {3146, 11001, 3853}, {3146, 17800, 381}, {3528, 12102, 19709}, {3528, 41983, X(49133) = 3}, {3529, 3830, 15696}, {3529, 3832, 15686}, {3529, 5071, 20}, {3533, 3845, 3851}, {3533, 5056, 3628}, {3533, 41981, 3}, {3534, 38335, 15723}, {3543, 11001, 11539}, {3544, 3843, 381}, {3627, 15681, 3526}, {3627, 35018, 4}, {3628, 3853, 3845}, {3830, 10304, 381}, {3830, 15696, 5072}, {3832, 15686, 3}, {3832, 46936, 3545}, {3843, 15704, 15688}, {3845, 11001, 15695}, {3845, 41981, 3533}, {3850, 11539, 5056}, {3851, 5054, 1656}, {3851, 5073, 15684}, {3853, 11001, 3}, {3859, 12100, 3628}, {5054, 14093, 15698}, {5056, 5059, 11001}, {5056, 11001, 550}, {5059, 35400, 35405}, {5059, 35405, 382}, {5067, 15690, 3}, {5072, 15696, 15700}, {5073, 33703, 35405}, {5076, 15684, 382}, {5076, 15696, 5071}, {10304, 11001, 15686}, {11001, 33703, 3146}, {12100, 15721, 15707}, {12102, 44903, 3528}, {12103, 17578, 5055}, {15681, 46936, 15696}, {15682, 15704, 3843}, {15682, 15711, 3830}, {15684, 17800, 3628}, {15687, 17538, 5070}, {17800, 35400, 35406}, {19710, 35403, 15706}, {20478, 20479, 35499}, {33699, 35413, 10304}


X(49134) = X(2)X(3)∩X(485)X(9690)

Barycentrics    15*a^4 - 7*a^2*b^2 - 8*b^4 - 7*a^2*c^2 + 16*b^2*c^2 - 8*c^4 : :
X(49134) = 24 X[2] - 23 X[3], 21 X[2] - 23 X[4], 45 X[2] - 46 X[5], 27 X[2] - 23 X[20], 93 X[2] - 92 X[140], 25 X[2] - 23 X[376], 22 X[2] - 23 X[381], 18 X[2] - 23 X[382], 87 X[2] - 92 X[546], 91 X[2] - 92 X[547], 99 X[2] - 92 X[548], 47 X[2] - 46 X[549], 51 X[2] - 46 X[550], 30 X[2] - 23 X[1657], 15 X[2] - 23 X[3146], 71 X[2] - 69 X[3524], 33 X[2] - 23 X[3529], 26 X[2] - 23 X[3534], 19 X[2] - 23 X[3543], 67 X[2] - 69 X[3545], 39 X[2] - 46 X[3627], 20 X[2] - 23 X[3830], 65 X[2] - 69 X[3839], 43 X[2] - 46 X[3845], 81 X[2] - 92 X[3853], 70 X[2] - 69 X[5054], 68 X[2] - 69 X[5055], 39 X[2] - 23 X[5059], 89 X[2] - 92 X[5066], 12 X[2] - 23 X[5073], 49 X[2] - 46 X[8703], 73 X[2] - 69 X[10304], 29 X[2] - 23 X[11001], 3 X[2] + 23 X[11541], 95 X[2] - 92 X[12100], 83 X[2] - 92 X[12101], 105 X[2] - 92 X[12103], 64 X[2] - 69 X[14269], 85 X[2] - 92 X[14893], 11 X[2] - 23 X[15640], 28 X[2] - 23 X[15681], 17 X[2] - 23 X[15682], 31 X[2] - 23 X[15683], 16 X[2] - 23 X[15684], 32 X[2] - 23 X[15685], 53 X[2] - 46 X[15686], 41 X[2] - 46 X[15687], 74 X[2] - 69 X[15688], 76 X[2] - 69 X[15689], 101 X[2] - 92 X[15690], 103 X[2] - 92 X[15691], 57 X[2] - 46 X[15704], 99 X[2] - 115 X[17578], 36 X[2] - 23 X[17800], 55 X[2] - 46 X[19710], 37 X[2] - 46 X[33699], 9 X[2] - 23 X[33703], 97 X[2] - 92 X[34200], 2 X[2] - 5 X[35384], 4 X[2] - 23 X[35400], 35 X[2] - 46 X[35404], 48 X[2] - 115 X[35407], 25 X[2] - 92 X[35408], 35 X[2] - 69 X[35409], 98 X[2] - 115 X[35434], 62 X[2] - 69 X[38335], 47 X[2] - 48 X[41986], 39 X[2] - 40 X[41989], 21 X[2] - 22 X[41991], 59 X[2] - 46 X[44903], 83 X[2] - 69 X[46333], 7 X[3] - 8 X[4], 15 X[3] - 16 X[5], 9 X[3] - 8 X[20], 31 X[3] - 32 X[140], 25 X[3] - 24 X[376], 11 X[3] - 12 X[381], 3 X[3] - 4 X[382], 29 X[3] - 32 X[546], 91 X[3] - 96 X[547], 33 X[3] - 32 X[548], 47 X[3] - 48 X[549], 17 X[3] - 16 X[550], 39 X[3] - 40 X[631], 77 X[3] - 80 X[632], 19 X[3] - 20 X[1656], 5 X[3] - 4 X[1657], 53 X[3] - 56 X[3090], 37 X[3] - 40 X[3091], 5 X[3] - 8 X[3146], 41 X[3] - 40 X[3522], 55 X[3] - 56 X[3523], 71 X[3] - 72 X[3524], 85 X[3] - 88 X[3525], 27 X[3] - 28 X[3526], 57 X[3] - 56 X[3528], 11 X[3] - 8 X[3529], and many others

X(49134) lies on these lines: {2, 3}, {485, 9690}, {486, 43415}, {1131, 9693}, {1159, 4338}, {1351, 29323}, {1482, 28168}, {3068, 6474}, {3069, 6475}, {3411, 19107}, {3412, 19106}, {3521, 44731}, {4301, 28172}, {4302, 31480}, {4309, 9655}, {4317, 9668}, {4325, 12953}, {4330, 12943}, {5050, 48904}, {5085, 48943}, {5093, 48910}, {5881, 28146}, {6199, 35820}, {6279, 22810}, {6280, 22809}, {6395, 35821}, {6407, 23251}, {6408, 23261}, {6409, 42558}, {6410, 42557}, {6417, 42263}, {6418, 42264}, {6445, 35812}, {6446, 35813}, {6451, 35786}, {6452, 35787}, {6472, 9541}, {6473, 42571}, {6500, 6561}, {6501, 6560}, {6564, 42568}, {6565, 42569}, {6767, 9657}, {7373, 9670}, {7748, 21309}, {7765, 43136}, {8148, 9589}, {9607, 22246}, {9680, 42284}, {9681, 13665}, {9691, 22644}, {9692, 13925}, {9698, 44519}, {10247, 41869}, {11362, 28158}, {11485, 43632}, {11486, 43633}, {11742, 31455}, {12017, 48896}, {12174, 40242}, {12645, 28178}, {12702, 28154}, {13340, 13474}, {13961, 17851}, {13993, 43508}, {14531, 14915}, {15037, 33534}, {15057, 38633}, {15069, 29317}, {15606, 18435}, {16772, 42105}, {16773, 42104}, {16964, 42097}, {16965, 42096}, {18510, 43407}, {18512, 43408}, {18525, 28150}, {18526, 28190}, {22236, 43645}, {22238, 43646}, {23236, 38790}, {23241, 38577}, {23698, 40268}, {28164, 37727}, {29012, 44456}, {29181, 48662}, {31487, 42258}, {31884, 48942}, {33697, 37714}, {34786, 35450}, {36967, 43332}, {36968, 43333}, {36969, 43331}, {36970, 43330}, {40107, 48872}, {40693, 42109}, {40694, 42108}, {42093, 42433}, {42094, 42434}, {42099, 42156}, {42100, 42153}, {42112, 42127}, {42113, 42126}, {42115, 42814}, {42116, 42813}, {42122, 43328}, {42123, 43329}, {42150, 43401}, {42151, 43402}, {42154, 42990}, {42155, 42991}, {42260, 45384}, {42261, 45385}, {42431, 42799}, {42432, 42800}, {42490, 42930}, {42491, 42931}, {42514, 43108}, {42515, 43109}, {42584, 42818}, {42585, 42817}, {42936, 43399}, {42937, 43400}, {42940, 42989}, {42941, 42988}, {42976, 43424}, {42977, 43425}

X(49134) = reflection of X(i) in X(j) for these {i,j}: {3, 5073}, {381, 15640}, {382, 33703}, {1657, 3146}, {5054, 35409}, {5059, 3627}, {15685, 15684}, {17800, 382}
X(49134) = orthocentroidal-circle-inverse of X(41991)
X(49134) = Stammler-circle-inverse of X(15646)
X(49134) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 41991}, {3, 4, 19709}, {3, 5073, 15684}, {3, 35403, 3851}, {3, 46219, 15722}, {4, 20, 3530}, {4, 376, 46936}, {4, 632, 381}, {4, 3091, 41987}, {4, 3146, 35404}, {4, 8703, 5079}, {4, 12103, 5054}, {4, 15681, 3}, {4, 15692, 12811}, {4, 15696, 5070}, {4, 15719, 3091}, {4, 21734, 5}, {4, 35409, 3146}, {4, 41981, 1656}, {4, 46936, 3860}, {5, 382, 3830}, {5, 548, 3523}, {5, 3146, 382}, {5, 5054, 5070}, {5, 12103, 21734}, {5, 14893, 3832}, {5, 19710, 548}, {5, 21734, 5054}, {5, 33923, 631}, {5, 44682, 10124}, {20, 382, 3843}, {20, 3530, 15696}, {20, 3843, 3}, {20, 3853, 3526}, {20, 3855, 46853}, {20, 5067, 548}, {20, 17578, 5067}, {140, 15695, 3}, {376, 3854, 12108}, {376, 3860, 5054}, {376, 46219, 3}, {381, 382, 17578}, {381, 3534, 17504}, {381, 11812, 5055}, {381, 15022, 3851}, {382, 1657, 5}, {382, 3526, 3853}, {382, 15696, 4}, {382, 17800, 3}, {382, 33703, 5073}, {547, 3627, 4}, {547, 12103, 33923}, {548, 12102, 5}, {548, 17578, 381}, {549, 41986, 2}, {550, 5055, 3}, {550, 5076, 5055}, {550, 12811, 15692}, {550, 14893, 3525}, {550, 15682, 5076}, {631, 3839, 5}, {631, 15717, 44580}, {632, 3523, 5054}, {1593, 47748, 3}, {1656, 15689, 3}, {1656, 15704, 15689}, {1657, 3146, 3830}, {1657, 3627, 15718}, {1657, 3830, 3}, {1657, 5054, 12103}, {1657, 12103, 15681}, {2043, 2044, 14891}, {3146, 3529, 12102}, {3146, 5059, 3839}, {3522, 5072, 15701}, {3522, 15687, 5072}, {3522, 15701, 3}, {3523, 3525, 11812}, {3523, 3529, 19710}, {3523, 3839, 15022}, {3523, 12102, 381}, {3523, 15640, 3146}, {3525, 3832, 5}, {3526, 3853, 3843}, {3528, 3543, 3861}, {3528, 3861, 1656}, {3529, 5067, 20}, {3529, 17578, 548}, {3529, 19710, 1657}, {3530, 3856, 547}, {3530, 12811, 48154}, {3534, 3627, 3851}, {3534, 3839, 15718}, {3534, 3851, 3}, {3534, 5076, 46935}, {3534, 35381, 8703}, {3543, 11001, 41985}, {3543, 15704, 1656}, {3627, 3851, 35403}, {3627, 5059, 3534}, {3627, 33923, 3839}, {3830, 3839, 35403}, {3830, 5055, 14893}, {3830, 5073, 3146}, {3830, 15681, 5054}, {3830, 15695, 41106}, {3830, 15703, 14269}, {3830, 15718, 3839}, {3843, 3851, 3856}, {3843, 17800, 20}, {3845, 17538, 15720}, {3853, 46853, 3855}, {3855, 46853, 3526}, {3856, 17504, 5067}, {3857, 15691, 10299}, {3861, 12100, 5}, {3861, 15704, 3528}, {5054, 15696, 21734}, {5054, 19709, 15703}, {5054, 35404, 3830}, {5054, 46936, 46219}, {5059, 33923, 1657}, {5070, 15681, 15696}, {5070, 15696, 3}, {5070, 17800, 15681}, {5073, 17800, 382}, {5073, 35406, 15640}, {5076, 48154, 3843}, {5079, 35434, 4}, {5899, 12085, 3}, {7387, 12085, 46939}, {7517, 35452, 3}, {10124, 15719, 5054}, {11001, 44580, 3534}, {12100, 12103, 41981}, {12101, 46333, 15700}, {12102, 12103, 632}, {12102, 19710, 3523}, {12103, 21734, 15696}, {12103, 35404, 4}, {13621, 21312, 3}, {15154, 15155, 15646}, {15681, 15684, 35401}, {15682, 46935, 3627}, {15683, 38335, 15695}, {15684, 15685, 14269}, {15684, 35407, 5073}, {15696, 35434, 3859}, {15704, 38071, 41981}, {15709, 17578, 3861}, {15716, 35402, 23046}, {15718, 33923, 3}, {19709, 35401, 14269}, {19710, 47599, 376}, {35421, 41987, 10124}, {44457, 47527, 3}


X(49135) = X(2)X(3)∩X(8)X(28150)

Barycentrics    13*a^4 - 6*a^2*b^2 - 7*b^4 - 6*a^2*c^2 + 14*b^2*c^2 - 7*c^4 : :
X(49135) = 21 X[2] - 20 X[3], 9 X[2] - 10 X[4], 39 X[2] - 40 X[5], 6 X[2] - 5 X[20], 81 X[2] - 80 X[140], 11 X[2] - 10 X[376], 19 X[2] - 20 X[381], 3 X[2] - 4 X[382], 15 X[2] - 16 X[546], 79 X[2] - 80 X[547], 87 X[2] - 80 X[548], 41 X[2] - 40 X[549], 9 X[2] - 8 X[550], 51 X[2] - 50 X[631], 99 X[2] - 100 X[1656], 27 X[2] - 20 X[1657], 69 X[2] - 70 X[3090], 24 X[2] - 25 X[3091], 3 X[2] - 5 X[3146], 27 X[2] - 25 X[3522], 36 X[2] - 35 X[3523], 31 X[2] - 30 X[3524], 15 X[2] - 14 X[3528], 33 X[2] - 32 X[3530], 23 X[2] - 20 X[3534], 4 X[2] - 5 X[3543], 33 X[2] - 34 X[3544], 29 X[2] - 30 X[3545], 33 X[2] - 40 X[3627], 17 X[2] - 20 X[3830], 33 X[2] - 35 X[3832], 14 X[2] - 15 X[3839], 93 X[2] - 100 X[3843], 37 X[2] - 40 X[3845], 27 X[2] - 28 X[3851], 69 X[2] - 80 X[3853], 81 X[2] - 85 X[3854], 21 X[2] - 22 X[3855], 61 X[2] - 60 X[5054], 59 X[2] - 60 X[5055], 54 X[2] - 55 X[5056], 9 X[2] - 5 X[5059], 77 X[2] - 80 X[5066], 63 X[2] - 65 X[5068], 49 X[2] - 50 X[5071], 9 X[2] - 20 X[5073], 87 X[2] - 100 X[5076], 51 X[2] - 52 X[5079], 84 X[2] - 85 X[7486], 43 X[2] - 40 X[8703], 27 X[2] - 26 X[10299], 66 X[2] - 65 X[10303], 16 X[2] - 15 X[10304], 13 X[2] - 10 X[11001], 3 X[2] + 10 X[11541], 31 X[2] - 32 X[11737], 83 X[2] - 80 X[12100], 71 X[2] - 80 X[12101], 93 X[2] - 80 X[12103], 11 X[2] - 12 X[14269], 57 X[2] - 56 X[14869], 73 X[2] - 80 X[14893], 93 X[2] - 95 X[15022], 2 X[2] - 5 X[15640], 5 X[2] - 4 X[15681], 7 X[2] - 10 X[15682], 7 X[2] - 5 X[15683], 13 X[2] - 20 X[15684], 29 X[2] - 20 X[15685], 47 X[2] - 40 X[15686], 7 X[2] - 8 X[15687], 13 X[2] - 12 X[15688], 67 X[2] - 60 X[15689], 89 X[2] - 80 X[15690], 91 X[2] - 80 X[15691], 26 X[2] - 25 X[15692], 28 X[2] - 25 X[15697], 73 X[2] - 70 X[15698], 29 X[2] - 28 X[15700], 71 X[2] - 70 X[15702], 51 X[2] - 40 X[15704], 47 X[2] - 45 X[15705], 37 X[2] - 36 X[15707], 46 X[2] - 45 X[15708], 91 X[2] - 90 X[15709], 19 X[2] - 18 X[15710], 23 X[2] - 22 X[15715], 57 X[2] - 55 X[15717], 45 X[2] - 44 X[15720], 56 X[2] - 55 X[15721], 25 X[2] - 24 X[17504], 57 X[2] - 50 X[17538], 21 X[2] - 25 X[17578], 33 X[2] - 20 X[17800], 53 X[2] - 50 X[19708], 97 X[2] - 100 X[19709], and many others

X(49135) lies on these lines: {2, 3}, {8, 28150}, {15, 5366}, {16, 5365}, {17, 42105}, {18, 42104}, {61, 42803}, {62, 42804}, {145, 28160}, {146, 24981}, {153, 6154}, {193, 29012}, {253, 340}, {316, 32825}, {397, 42096}, {398, 42097}, {485, 9542}, {486, 43508}, {515, 20050}, {516, 3632}, {517, 20054}, {590, 43786}, {615, 43785}, {938, 4031}, {944, 28168}, {962, 3244}, {1131, 8960}, {1132, 22615}, {1495, 38942}, {1503, 11008}, {1587, 42275}, {1588, 42276}, {1699, 15808}, {1990, 45245}, {2393, 36983}, {2889, 11469}, {2979, 13474}, {2996, 14712}, {3060, 13382}, {3070, 42413}, {3071, 42414}, {3357, 15107}, {3411, 43425}, {3412, 43424}, {3424, 43676}, {3532, 43699}, {3567, 12002}, {3576, 10248}, {3583, 5265}, {3585, 5281}, {3590, 9540}, {3591, 12819}, {3600, 10483}, {3620, 18553}, {3621, 28174}, {3622, 22793}, {3626, 5493}, {3631, 36990}, {3636, 5731}, {3982, 9579}, {4293, 4857}, {4294, 5270}, {4299, 5274}, {4302, 5261}, {4316, 10591}, {4324, 10590}, {5286, 43618}, {5304, 7748}, {5334, 42113}, {5335, 42112}, {5339, 42108}, {5340, 421 09}, {5343, 19107}, {5344, 19106}, {5349, 11489}, {5350, 11488}, {5351, 43478}, {5352, 43477}, {5447, 16261}, {5656, 45185}, {5657, 33697}, {5882, 20057}, {5895, 44762}, {5921, 29181}, {5925, 32064}, {6102, 16981}, {6284, 8162}, {6329, 25406}, {6361, 28154}, {6459, 6470}, {6460, 6471}, {6468, 23251}, {6469, 23261}, {6744, 11034}, {6776, 29323}, {7320, 10624}, {7581, 42225}, {7582, 42226}, {7585, 35820}, {7586, 35821}, {7620, 7780}, {7747, 37665}, {7752, 32887}, {7764, 23334}, {7768, 32815}, {7802, 15589}, {7860, 32824}, {7991, 34641}, {7999, 46849}, {8550, 14927}, {8717, 43651}, {8718, 11003}, {8972, 23253}, {9543, 13886}, {9588, 34638}, {9589, 34747}, {9613, 30332}, {9681, 43883}, {9692, 13846}, {9693, 14241}, {9742, 43460}, {9778, 31673}, {9781, 14855}, {9812, 13464}, {10194, 35787}, {10195, 35786}, {10513, 32822}, {10519, 48884}, {10539, 43576}, {10625, 11455}, {10653, 41973}, {10654, 41974}, {10721, 30714}, {10722, 10992}, {10723, 10991}, {10725, 33521}, {10727, 33520}, {10728, 10993}, {10733, 10990}, {10982, 33534}, {11002, 40647}, {11148, 32479}, {11185, 32886}, {11439, 15644}, {11444, 32062}, {11480, 42494}, {11481, 42495}, {11485, 43487}, {11486, 43488}, {11542, 43556}, {11543, 43557}, {12112, 16266}, {12245, 28178}, {12250, 41724}, {12279, 45186}, {12953, 14986}, {13340, 32137}, {13421, 34783}, {13598, 15072}, {13603, 42021}, {13847, 43414}, {13941, 23263}, {14491, 14861}, {14561, 48943}, {14853, 48904}, {14864, 20427}, {14900, 44988}, {15052, 15811}, {15056, 36987}, {15058, 33884}, {15516, 33748}, {15520, 31670}, {15741, 40196}, {16808, 42798}, {16809, 42797}, {17129, 43681}, {18220, 21578}, {18525, 28182}, {18581, 43196}, {18582, 43195}, {20014, 28224}, {20070, 28146}, {22236, 43401}, {22238, 43402}, {23249, 42266}, {23259, 42267}, {23267, 43519}, {23273, 43520}, {25555, 48896}, {28190, 48661}, {28202, 31145}, {31361, 38808}, {31412, 41963}, {31414, 41945}, {31663, 46932}, {32006, 32820}, {32787, 42641}, {32788, 42642}, {32789, 43405}, {32790, 43406}, {33750, 48891}, {34170, 34286}, {34549, 45037}, {35021, 39809}, {35022, 39838}, {36967, 42939}, {36968, 42938}, {38140, 46931}, {40330, 48880}, {41112, 42635}, {41113, 42636}, {41964, 42561}, {42085, 42431}, {42086, 42432}, {42099, 42134}, {42100, 42133}, {42101, 42776}, {42102, 42775}, {42107, 42774}, {42110, 42773}, {42111, 43367}, {42114, 43366}, {42125, 43474}, {42126, 42924}, {42127, 42925}, {42128, 43473}, {42136, 42989}, {42137, 42988}, {42139, 42944}, {42142, 42945}, {42159, 42908}, {42160, 43419}, {42161, 43418}, {42162, 42909}, {42283, 42637}, {42284, 42638}, {42429, 42814}, {42430, 42813}, {42480, 42546}, {42481, 42545}, {42514, 43228}, {42515, 43229}, {42570, 43438}, {42571, 43439}, {42580, 43400}, {42581, 43399}, {42612, 42995}, {42613, 42994}, {42625, 42793}, {42626, 42794}, {42645, 42730}, {42646, 42729}, {42682, 43774}, {42683, 43773}, {42920, 42978}, {42921, 42979}, {42940, 43193}, {42941, 43194}, {42946, 43230}, {42947, 43231}, {42972, 43427}, {42973, 43426}, {43577, 43837}

X(49135) = midpoint of X(11541) and X(33703)
X(49135) = reflection of X(i) in X(j) for these {i,j}: {4, 5073}, {20, 3146}, {3146, 33703}, {3529, 382}, {3543, 15640}, {5059, 4}, {6776, 43621}, {11001, 15684}, {12279, 45186}, {14927, 48910}, {15683, 15682}, {15685, 35404}, {17800, 3627}, {35414, 41099}, {35732, 2041}, {42282, 2042}
X(49135) = anticomplement of X(3529)
X(49135) = anticomplement of the isogonal conjugate of X(43719)
X(49135) = X(43719)-anticomplementary conjugate of X(8)
X(49135) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3146, 382}, {2, 3522, 10299}, {2, 3529, 20}, {2, 3530, 10303}, {2, 3832, 3544}, {2, 3851, 5056}, {2, 5068, 35018}, {2, 15687, 3839}, {2, 15688, 15692}, {2, 15715, 15708}, {2, 15717, 14869}, {3, 4, 5068}, {3, 5, 15709}, {3, 20, 15697}, {3, 381, 48154}, {3, 382, 15687}, {3, 3526, 44580}, {3, 3839, 7486}, {3, 3855, 2}, {3, 3861, 5071}, {3, 7486, 15721}, {3, 15682, 17578}, {3, 15683, 20}, {3, 15687, 3855}, {3, 15699, 631}, {3, 17578, 3839}, {3, 41989, 3525}, {4, 20, 3523}, {4, 140, 3854}, {4, 376, 1656}, {4, 550, 2}, {4, 631, 3850}, {4, 1656, 3832}, {4, 1657, 3522}, {4, 3522, 5056}, {4, 3523, 3091}, {4, 3529, 550}, {4, 3533, 381}, {4, 5059, 20}, {4, 5068, 3839}, {4, 5073, 3146}, {4, 10299, 3851}, {4, 11001, 21735}, {4, 17538, 3533}, {4, 21735, 5}, {4, 33703, 5073}, {5, 15691, 3}, {5, 35409, 3146}, {15, 5366, 22235}, {16, 5365, 22237}, {20, 3091, 10304}, {20, 3146, 3543}, {20, 3543, 3091}, {20, 3839, 3}, {20, 5056, 3522}, {20, 10303, 376}, {20, 15640, 3146}, {20, 17578, 7486}, {140, 3854, 5056}, {376, 3524, 46332}, {376, 3544, 3530}, {376, 3627, 3832}, {376, 3832, 10303}, {376, 14269, 2}, {378, 12087, 38435}, {381, 15710, 2}, {381, 15717, 46936}, {381, 17538, 15717}, {381, 33923, 3533}, {382, 550, 4}, {382, 1657, 3851}, {382, 3529, 2}, {382, 3855, 17578}, {382, 5079, 3830}, {382, 14269, 3627}, {382, 15681, 546}, {382, 15700, 5076}, {382, 17800, 3530}, {397, 42096, 43770}, {398, 42097, 43769}, {546, 550, 15720}, {546, 3528, 2}, {546, 15681, 3528}, {548, 5076, 3545}, {548, 15713, 3}, {548, 35404, 5076}, {548, 35413, 15704}, {550, 3851, 10299}, {550, 10299, 3522}, {550, 14869, 33923}, {550, 15687, 35018}, {550, 15720, 3528}, {550, 35018, 3}, {550, 38071, 15712}, {631, 5079, 2}, {1003, 33200, 33183}, {1597, 33524, 37126}, {1656, 3627, 4}, {1657, 3522, 20}, {1657, 3851, 550}, {2043, 2044, 15698}, {3090, 3534, 21734}, {3090, 21734, 15708}, {3091, 3523, 46935}, {3091, 15721, 7486}, {3146, 5059, 4}, {3146, 15683, 17578}, {3146, 17578, 15682}, {3146, 33703, 15640}, {3522, 3854, 140}, {3522, 5056, 3523}, {3522, 5059, 1657}, {3522, 17578, 3858}, {3523, 3543, 4}, {3524, 3843, 15022}, {3524, 11737, 2}, {3525, 46333, 15696}, {3526, 12102, 41099}, {3528, 3529, 15681}, {3529, 15682, 3855}, {3530, 3544, 2}, {3530, 3627, 14269}, {3530, 14269, 3544}, {3533, 17538, 33923}, {3533, 33923, 15717}, {3534, 3853, 3090}, {3534, 38071, 15715}, {3543, 15683, 15721}, {3543, 15697, 3839}, {3544, 3855, 5066}, {3544, 14269, 3832}, {3545, 15700, 2}, {3627, 17800, 376}, {3627, 46332, 3843}, {3830, 3850, 4}, {3830, 15704, 631}, {3830, 35421, 41106}, {3832, 15711, 46936}, {3832, 17800, 20}, {3839, 7486, 3091}, {3839, 15682, 3543}, {3839, 15683, 15697}, {3839, 15697, 15721}, {3843, 12103, 3524}, {3845, 15696, 3525}, {3850, 33923, 11540}, {3851, 3858, 3855}, {3851, 10299, 2}, {3855, 35018, 5068}, {3858, 35018, 3851}, {3861, 19710, 3}, {4232, 5189, 7396}, {5066, 10303, 7486}, {5066, 15687, 14269}, {5068, 15721, 46935}, {5068, 17578, 4}, {5072, 46853, 15702}, {5076, 15685, 548}, {5079, 34200, 631}, {5189, 7500, 4232}, {6658, 33192, 32974}, {7387, 12086, 10298}, {7486, 15697, 3}, {7802, 32826, 15589}, {7841, 33201, 33182}, {7860, 32824, 37668}, {9541, 22644, 1131}, {10304, 46935, 3523}, {11001, 15709, 15691}, {11001, 35409, 15684}, {11114, 37435, 5129}, {11361, 33271, 33023}, {12082, 47527, 14118}, {12101, 46853, 5072}, {12102, 15686, 3526}, {12102, 35414, 20}, {12103, 33699, 3843}, {14033, 19695, 33025}, {14035, 19691, 33272}, {14035, 33272, 33202}, {14042, 33253, 2}, {14062, 33254, 2}, {14063, 35927, 33203}, {14066, 33008, 32991}, {14068, 33264, 32990}, {14784, 14785, 12103}, {14813, 14814, 15696}, {14869, 15710, 15717}, {14869, 15711, 3530}, {15156, 15157, 37957}, {15681, 15720, 550}, {15682, 15683, 3839}, {15683, 17578, 3}, {15684, 15692, 3543}, {15685, 35404, 3545}, {15686, 41099, 15705}, {15688, 41983, 15710}, {15697, 15721, 10304}, {15697, 17578, 3091}, {15706, 15723, 15701}, {15706, 17800, 15704}, {15708, 15712, 3523}, {15715, 38071, 2}, {16041, 33250, 33205}, {19106, 42150, 5344}, {19107, 42151, 5343}, {19687, 33238, 2}, {19696, 33017, 32981}, {19697, 33232, 2}, {21735, 41981, 3522}, {23249, 42266, 43512}, {23253, 42260, 8972}, {23259, 42267, 43511}, {23263, 42261, 13941}, {32966, 33214, 35287}, {32981, 33017, 33180}, {32982, 33007, 33181}, {32996, 33265, 32989}, {33019, 33193, 32973}, {33229, 33239, 2}, {33256, 33280, 2}, {33257, 33279, 2}, {33923, 46936, 3523}, {34725, 47338, 4}, {35415, 44245, 17538}, {35820, 43408, 7585}, {35821, 43407, 7586}, {38335, 44903, 19708}, {42085, 42431, 42998}, {42086, 42432, 42999}, {42101, 43239, 42776}, {42102, 43238, 42775}, {42140, 43769, 398}, {42141, 43770, 397}, {42157, 42629, 42779}, {42158, 42630, 42780}, {42431, 42998, 43465}, {42432, 42999, 43466}


X(49136) = X(2)X(3)∩X(8)X(28182)

Barycentrics    11*a^4 - 5*a^2*b^2 - 6*b^4 - 5*a^2*c^2 + 12*b^2*c^2 - 6*c^4 : :
X(49136) = 18 X[2] - 17 X[3], 15 X[2] - 17 X[4], 33 X[2] - 34 X[5], 21 X[2] - 17 X[20], 69 X[2] - 68 X[140], 19 X[2] - 17 X[376], 16 X[2] - 17 X[381], 12 X[2] - 17 X[382], 63 X[2] - 68 X[546], 67 X[2] - 68 X[547], 75 X[2] - 68 X[548], 35 X[2] - 34 X[549], 39 X[2] - 34 X[550], 87 X[2] - 85 X[631], 84 X[2] - 85 X[1656], 24 X[2] - 17 X[1657], 81 X[2] - 85 X[3091], 9 X[2] - 17 X[3146], 93 X[2] - 85 X[3522], 53 X[2] - 51 X[3524], 27 X[2] - 17 X[3529], 20 X[2] - 17 X[3534], 13 X[2] - 17 X[3543], 49 X[2] - 51 X[3545], 27 X[2] - 34 X[3627], 14 X[2] - 17 X[3830], 47 X[2] - 51 X[3839], 78 X[2] - 85 X[3843], 31 X[2] - 34 X[3845], 57 X[2] - 68 X[3853], 15 X[2] - 16 X[3856], 52 X[2] - 51 X[5054], 50 X[2] - 51 X[5055], 33 X[2] - 17 X[5059], 65 X[2] - 68 X[5066], 83 X[2] - 85 X[5071], 6 X[2] - 17 X[5073], 72 X[2] - 85 X[5076], 37 X[2] - 34 X[8703], 55 X[2] - 51 X[10304], 23 X[2] - 17 X[11001], 9 X[2] + 17 X[11541], 71 X[2] - 68 X[12100], 59 X[2] - 68 X[12101], 81 X[2] - 68 X[12103], 92 X[2] - 85 X[14093], 46 X[2] - 51 X[14269], 61 X[2] - 68 X[14893], 5 X[2] - 17 X[15640], 22 X[2] - 17 X[15681], 11 X[2] - 17 X[15682], 25 X[2] - 17 X[15683], 10 X[2] - 17 X[15684], 26 X[2] - 17 X[15685], 41 X[2] - 34 X[15686], 29 X[2] - 34 X[15687], 56 X[2] - 51 X[15688], 58 X[2] - 51 X[15689], 77 X[2] - 68 X[15690], 79 X[2] - 68 X[15691], 89 X[2] - 85 X[15692], 88 X[2] - 85 X[15693], 86 X[2] - 85 X[15694], 94 X[2] - 85 X[15695], 96 X[2] - 85 X[15696], 97 X[2] - 85 X[15697], 45 X[2] - 34 X[15704], 99 X[2] - 85 X[17538], 69 X[2] - 85 X[17578], 30 X[2] - 17 X[17800], 91 X[2] - 85 X[19708], 82 X[2] - 85 X[19709], 43 X[2] - 34 X[19710], 95 X[2] - 102 X[23046], 25 X[2] - 34 X[33699], 3 X[2] - 17 X[33703], 73 X[2] - 68 X[34200], 16 X[2] - 85 X[35384], 2 X[2] + 17 X[35400], 74 X[2] - 85 X[35403], 23 X[2] - 34 X[35404], 48 X[2] - 187 X[35405], 54 X[2] - 221 X[35406], 18 X[2] - 85 X[35407], X[2] - 68 X[35408], X[2] - 3 X[35409], 173 X[2] - 85 X[35414], 4 X[2] - 5 X[35434], 97 X[2] - 102 X[38071], 44 X[2] - 51 X[38335], 79 X[2] - 85 X[41099], 13 X[2] - 12 X[41982], 11 X[2] - 12 X[41987], 9 X[2] - 8 X[44245], 47 X[2] - 34 X[44903], and many others

X(49136) lies on these lines: {2, 3}, {8, 28182}, {17, 42430}, {18, 42429}, {61, 42096}, {62, 42097}, {64, 32608}, {265, 43691}, {355, 28158}, {397, 42968}, {398, 42969}, {399, 37498}, {485, 6519}, {486, 6522}, {516, 12645}, {575, 48904}, {576, 29323}, {962, 28190}, {1181, 34563}, {1351, 43621}, {1482, 28164}, {1539, 15034}, {1614, 11935}, {1620, 7687}, {2777, 34780}, {2979, 32137}, {3068, 43340}, {3069, 43341}, {3303, 9655}, {3304, 9668}, {3311, 42272}, {3312, 42271}, {3592, 18512}, {3594, 18510}, {3746, 12943}, {3763, 48920}, {4324, 31479}, {5093, 14927}, {5237, 42093}, {5238, 42094}, {5339, 43019}, {5340, 43018}, {5351, 42129}, {5352, 42132}, {5365, 42913}, {5366, 42912}, {5368, 7748}, {5563, 12953}, {5609, 10721}, {5691, 28154}, {5790, 33697}, {5881, 28202}, {5925, 34786}, {6101, 11455}, {6199, 43408}, {6221, 22644}, {6243, 14915}, {6395, 43407}, {6398, 22615}, {6417, 42225}, {6418, 42226}, {6419, 42263}, {6420, 42264}, {6425, 13665}, {6426, 13785}, {6427, 6561}, {6428, 6560}, {6445, 31412}, {6446, 42561}, {6447, 42258}, {6448, 42259}, {6449, 42284}, {6450, 42283}, {6451, 42273}, {6452, 42270}, {6453, 13903}, {6454, 13961}, {6455, 42269}, {6456, 42268}, {6496, 42277}, {6497, 42274}, {7583, 42413}, {7584, 42414}, {7756, 15484}, {7772, 44526}, {7909, 11164}, {7936, 10302}, {7982, 18526}, {7991, 18525}, {8148, 28186}, {8567, 18376}, {8717, 37471}, {9589, 28208}, {9605, 43619}, {9680, 43568}, {9690, 13925}, {9691, 13886}, {9812, 37624}, {10113, 15021}, {10147, 35812}, {10148, 35813}, {10222, 28168}, {10248, 38028}, {10263, 12279}, {10516, 48879}, {10541, 48898}, {10575, 16625}, {10627, 11439}, {11381, 37484}, {11441, 37496}, {11477, 29012}, {11480, 42962}, {11481, 42963}, {11482, 12007}, {11485, 42109}, {11486, 42108}, {11518, 18541}, {11742, 15515}, {11820, 37493}, {11898, 29181}, {12041, 15044}, {12121, 15039}, {12290, 13391}, {12295, 15027}, {12307, 15605}, {12699, 13607}, {12702, 28150}, {12902, 15054}, {13202, 32609}, {13321, 40647}, {13474, 23039}, {13491, 16982}, {13993, 43415}, {14094, 38790}, {14641, 37481}, {14692, 23698}, {15046, 38726}, {15081, 38633}, {15107, 32138}, {16194, 40247}, {16261, 32142}, {16267, 42587}, {16268, 42586}, {17505, 43713}, {18400, 48672}, {18439, 45187}, {18440, 29317}, {18491, 44846}, {18493, 30389}, {18530, 31776}, {18581, 42685}, {18582, 42684}, {19106, 22236}, {19107, 22238}, {20127, 36253}, {20190, 48896}, {22234, 43273}, {22334, 34483}, {23235, 38744}, {23253, 45384}, {23263, 45385}, {26883, 37477}, {30435, 43618}, {31454, 43526}, {31652, 44519}, {32533, 44763}, {33534, 36752}, {34754, 43636}, {34755, 43637}, {35007, 44518}, {35237, 36753}, {35450, 41362}, {36836, 42099}, {36843, 42100}, {36969, 42988}, {36970, 42989}, {36987, 46849}, {36990, 43150}, {38628, 48657}, {38664, 38733}, {38665, 38756}, {38666, 38768}, {38667, 38780}, {38669, 48680}, {38675, 38800}, {38676, 48658}, {38689, 48681}, {38723, 38795}, {38729, 38788}, {38730, 38745}, {38731, 38751}, {38734, 38741}, {38740, 38742}, {40693, 43401}, {40694, 43402}, {41945, 43342}, {41946, 43343}, {41979, 43624}, {41980, 43625}, {42085, 42165}, {42086, 42164}, {42087, 42162}, {42088, 42159}, {42090, 42598}, {42091, 42599}, {42103, 42951}, {42104, 42115}, {42105, 42116}, {42106, 42950}, {42133, 42584}, {42134, 42585}, {42140, 42145}, {42141, 42144}, {42150, 42941}, {42151, 42940}, {42154, 42431}, {42155, 42432}, {42157, 42974}, {42158, 42975}, {42260, 43879}, {42261, 43880}, {42476, 42919}, {42477, 42918}, {42580, 42954}, {42581, 42955}, {42592, 43399}, {42593, 43400}, {42612, 43301}, {42613, 43300}, {42625, 42694}, {42626, 42695}, {42629, 43302}, {42630, 43303}, {42801, 43330}, {42802, 43331}, {42982, 43647}, {42983, 43648}, {43195, 43298}, {43196, 43299}, {43380, 43794}, {43381, 43793}, {43420, 43551}, {43421, 43550}, {43845, 44413}, {48872, 48884}

X(49136) = midpoint of X(3146) and X(11541)
X(49136) = reflection of X(i) in X(j) for these {i,j}: {3, 3146}, {382, 5073}, {1351, 43621}, {1657, 382}, {3529, 3627}, {3534, 15684}, {5059, 5}, {5073, 33703}, {5925, 34786}, {11001, 35404}, {12279, 10263}, {15681, 15682}, {15683, 33699}, {15684, 15640}, {15685, 3543}, {17800, 4}, {18526, 48661}, {35414, 15713}, {37484, 11381}, {48872, 48884}, {48879, 48942}, {48896, 48943}, {48905, 48904}
X(49136) = orthocentroidal-circle-inverse of X(3856)
X(49136) = Stammler-circle-inverse of X(37955)
X(49136) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 3856}, {2, 44245, 3}, {3, 4, 5072}, {3, 382, 5076}, {3, 546, 1656}, {3, 3090, 5054}, {3, 3146, 382}, {3, 3830, 546}, {3, 3843, 3090}, {3, 3851, 632}, {3, 5055, 10303}, {3, 5070, 12108}, {3, 5072, 3526}, {3, 5073, 3146}, {3, 5076, 381}, {3, 12108, 15700}, {3, 15681, 17538}, {3, 15704, 3534}, {3, 17800, 15704}, {3, 35407, 5073}, {4, 20, 549}, {4, 376, 7486}, {4, 548, 5055}, {4, 3522, 44904}, {4, 3526, 381}, {4, 3534, 3526}, {4, 5066, 3843}, {4, 7486, 23046}, {4, 10303, 3857}, {4, 10304, 5}, {4, 15022, 546}, {4, 15683, 548}, {4, 15684, 382}, {4, 15704, 3}, {4, 15717, 5066}, {4, 17800, 3534}, {4, 33703, 15640}, {4, 46333, 15717}, {5, 550, 14891}, {5, 5059, 15681}, {5, 15690, 10299}, {5, 17538, 3}, {20, 546, 3}, {20, 1656, 15688}, {20, 3543, 3854}, {20, 3545, 33923}, {20, 3830, 1656}, {20, 3854, 19708}, {20, 10299, 15690}, {20, 19708, 550}, {140, 382, 35402}, {140, 17578, 14269}, {140, 35404, 17578}, {376, 632, 3}, {376, 3853, 3851}, {381, 1657, 15696}, {381, 3534, 15706}, {381, 15696, 15720}, {382, 1656, 3830}, {382, 1657, 381}, {382, 3529, 5079}, {382, 3534, 4}, {382, 5059, 15693}, {382, 17800, 3526}, {546, 549, 15022}, {546, 47599, 12811}, {548, 3857, 10303}, {548, 10303, 3}, {548, 33699, 4}, {549, 1656, 3526}, {549, 3534, 15688}, {549, 3628, 3525}, {549, 15690, 10304}, {549, 23046, 10109}, {550, 3090, 3}, {550, 3543, 3843}, {550, 3627, 41991}, {550, 3843, 5054}, {550, 5066, 15717}, {550, 12102, 3090}, {550, 16239, 19708}, {1593, 44457, 13564}, {1656, 5054, 16239}, {1656, 5072, 15022}, {1657, 3526, 3534}, {1657, 5076, 3}, {1657, 15688, 20}, {2043, 2044, 17504}, {3090, 3543, 12102}, {3090, 12102, 3843}, {3091, 3529, 12103}, {3091, 12103, 3}, {3146, 3529, 3627}, {3146, 3861, 35419}, {3522, 3544, 12108}, {3522, 3845, 5070}, {3522, 5070, 15700}, {3522, 12108, 3}, {3523, 3861, 19709}, {3525, 3529, 20}, {3525, 15022, 3628}, {3526, 5079, 3628}, {3526, 15706, 15720}, {3528, 3850, 15694}, {3529, 3627, 3}, {3529, 35416, 5054}, {3534, 5072, 3}, {3534, 17800, 1657}, {3543, 15685, 5054}, {3543, 15717, 4}, {3543, 46333, 5066}, {3544, 12108, 5070}, {3627, 3628, 4}, {3627, 12103, 3091}, {3627, 15704, 3628}, {3627, 41991, 12102}, {3628, 5072, 5079}, {3830, 15685, 19708}, {3830, 15688, 381}, {3832, 8703, 46219}, {3839, 15695, 15723}, {3839, 44903, 15695}, {3843, 15685, 550}, {3843, 19708, 1656}, {3845, 12108, 3544}, {3850, 19710, 3528}, {3853, 23046, 4}, {3854, 19708, 16239}, {3855, 15712, 15703}, {3857, 5055, 5072}, {3857, 10303, 5055}, {3857, 15704, 548}, {3861, 15686, 3523}, {5054, 14891, 15693}, {5054, 41991, 5079}, {5055, 15683, 3534}, {5055, 15684, 33699}, {5056, 46853, 15701}, {5059, 15682, 5}, {5066, 15685, 3534}, {5073, 17800, 15684}, {7464, 37440, 3}, {7486, 23046, 3851}, {10304, 15681, 3534}, {11001, 14269, 14093}, {11001, 17578, 140}, {11001, 35404, 14269}, {11541, 15640, 15704}, {11541, 33703, 3146}, {11541, 35407, 382}, {12083, 47527, 14130}, {12086, 17714, 3}, {12086, 37946, 17714}, {12101, 15712, 3855}, {12102, 15704, 15717}, {12102, 16239, 546}, {12121, 38791, 15039}, {14093, 35402, 381}, {14093, 35404, 35402}, {14893, 46853, 5056}, {15154, 15155, 37955}, {15156, 15157, 7575}, {15681, 15682, 38335}, {15681, 38335, 15693}, {15682, 15690, 3830}, {15683, 33699, 5055}, {15684, 17800, 4}, {15691, 41099, 15707}, {15693, 38335, 381}, {15697, 38071, 15718}, {15700, 44904, 3526}, {15704, 33699, 3857}, {15705, 35404, 3830}, {15707, 35401, 41099}, {15709, 44904, 5070}, {15717, 46333, 550}, {15759, 47599, 549}, {18586, 18587, 35403}, {19106, 42130, 42815}, {19107, 42131, 42816}, {19695, 33280, 11286}, {22615, 43336, 43431}, {22644, 43337, 43430}, {31725, 34938, 7574}, {31861, 33524, 3}, {33250, 33279, 11318}, {33699, 35435, 15706}, {35400, 35407, 11541}, {35403, 46219, 3832}, {35471, 47341, 3}, {35732, 42282, 11001}, {36969, 43194, 42988}, {36970, 43193, 42989}, {37950, 44879, 3}, {42108, 42113, 11486}, {42109, 42112, 11485}, {42271, 42276, 3312}, {42272, 42275, 3311}, {42280, 42281, 3543}, {47752, 47753, 15646}, {48879, 48942, 10516}


X(49137) = X(2)X(3)∩X(6)X(43324)

Barycentrics    13*a^4 - 7*a^2*b^2 - 6*b^4 - 7*a^2*c^2 + 12*b^2*c^2 - 6*c^4 : :
X(49137) = 18 X[2] - 19 X[3], 21 X[2] - 19 X[4], 39 X[2] - 38 X[5], 15 X[2] - 19 X[20], 75 X[2] - 76 X[140], 17 X[2] - 19 X[376], 20 X[2] - 19 X[381], 24 X[2] - 19 X[382], 81 X[2] - 76 X[546], 77 X[2] - 76 X[547], 69 X[2] - 76 X[548], 37 X[2] - 38 X[549], 33 X[2] - 38 X[550], 93 X[2] - 95 X[631], 96 X[2] - 95 X[1656], 12 X[2] - 19 X[1657], 99 X[2] - 95 X[3091], 27 X[2] - 19 X[3146], 87 X[2] - 95 X[3522], 55 X[2] - 57 X[3524], 9 X[2] - 19 X[3529], 16 X[2] - 19 X[3534], 23 X[2] - 19 X[3543], 59 X[2] - 57 X[3545], 45 X[2] - 38 X[3627], 22 X[2] - 19 X[3830], 61 X[2] - 57 X[3839], 102 X[2] - 95 X[3843], 41 X[2] - 38 X[3845], 87 X[2] - 76 X[3853], 21 X[2] - 20 X[3859], 56 X[2] - 57 X[5054], 58 X[2] - 57 X[5055], 3 X[2] - 19 X[5059], 79 X[2] - 76 X[5066], 97 X[2] - 95 X[5071], 30 X[2] - 19 X[5073], 108 X[2] - 95 X[5076], 35 X[2] - 38 X[8703], 53 X[2] - 57 X[10304], 13 X[2] - 19 X[11001], 45 X[2] - 19 X[11541], 73 X[2] - 76 X[12100], 85 X[2] - 76 X[12101], 9 X[2] - 8 X[12102], 63 X[2] - 76 X[12103], 88 X[2] - 95 X[14093], 62 X[2] - 57 X[14269], 83 X[2] - 76 X[14893], 31 X[2] - 19 X[15640], 14 X[2] - 19 X[15681], 25 X[2] - 19 X[15682], 11 X[2] - 19 X[15683], 26 X[2] - 19 X[15684], 10 X[2] - 19 X[15685], 31 X[2] - 38 X[15686], 43 X[2] - 38 X[15687], 52 X[2] - 57 X[15688], 50 X[2] - 57 X[15689], 67 X[2] - 76 X[15690], 65 X[2] - 76 X[15691], 91 X[2] - 95 X[15692], 92 X[2] - 95 X[15693], 94 X[2] - 95 X[15694], 86 X[2] - 95 X[15695], 84 X[2] - 95 X[15696], 83 X[2] - 95 X[15697], 27 X[2] - 38 X[15704], 81 X[2] - 95 X[17538], 111 X[2] - 95 X[17578], 6 X[2] - 19 X[17800], 89 X[2] - 95 X[19708], 98 X[2] - 95 X[19709], 29 X[2] - 38 X[19710], 47 X[2] - 38 X[33699], 33 X[2] - 19 X[33703], 71 X[2] - 76 X[34200], 164 X[2] - 95 X[35384], 106 X[2] - 95 X[35403], 49 X[2] - 38 X[35404], 162 X[2] - 95 X[35407], 143 X[2] - 76 X[35408], 91 X[2] - 57 X[35409], 40 X[2] - 209 X[35410], 50 X[2] - 247 X[35411], 74 X[2] - 247 X[35412], 7 X[2] - 95 X[35414], 112 X[2] - 95 X[35434], 68 X[2] - 247 X[35435], 64 X[2] - 57 X[38335], 101 X[2] - 95 X[41099], 25 X[2] - 38 X[44903], 43 X[2] - 57 X[46333], 7 X[3] - 6 X[4], 13 X[3] - 12 X[5], 5 X[3] - 6 X[20], and many others

X(49137) lies on these lines: {2, 3}, {6, 43324}, {13, 43421}, {14, 43420}, {15, 42900}, {16, 42901}, {61, 42097}, {62, 42096}, {156, 43576}, {516, 18526}, {568, 14641}, {575, 48896}, {576, 48905}, {944, 28182}, {1482, 28150}, {1539, 15020}, {1699, 31666}, {3070, 6447}, {3071, 6448}, {3303, 10483}, {3311, 42276}, {3312, 42275}, {3592, 42266}, {3594, 42267}, {3746, 9655}, {3763, 48942}, {4316, 9669}, {4324, 9654}, {5007, 44526}, {5050, 43621}, {5085, 42785}, {5237, 42125}, {5238, 42128}, {5351, 42093}, {5352, 42094}, {5563, 9668}, {5609, 38790}, {5691, 38176}, {5890, 16982}, {5925, 34780}, {6053, 12121}, {6199, 42575}, {6221, 42272}, {6361, 28190}, {6395, 42574}, {6398, 42271}, {6407, 23249}, {6408, 23259}, {6417, 42226}, {6418, 42225}, {6419, 42264}, {6420, 42263}, {6425, 35820}, {6426, 35821}, {6427, 6560}, {6428, 6561}, {6449, 22644}, {6450, 22615}, {6451, 42269}, {6452, 42268}, {6453, 13665}, {6454, 13785}, {6455, 42284}, {6456, 42283}, {6488, 35812}, {6489, 35813}, {6496, 42273}, {6497, 42270}, {6519, 13903}, {6522, 13961}, {7728, 15039}, {7747, 22332}, {7748, 22331}, {7843, 11165}, {7922, 11164}, {7982, 28146}, {7991, 12645}, {8148, 28178}, {8717, 13353}, {9541, 43316}, {9605, 43618}, {9690, 13886}, {9692, 14241}, {9693, 43376}, {10222, 28154}, {10516, 48920}, {10541, 48901}, {10620, 17834}, {10627, 11455}, {10991, 12355}, {11381, 13340}, {11477, 29317}, {11482, 46264}, {11485, 42113}, {11486, 42112}, {11742, 37512}, {11801, 38633}, {11898, 29012}, {11935, 37495}, {12279, 13391}, {12702, 28164}, {13202, 15040}, {13321, 13598}, {13419, 22334}, {13939, 43415}, {14094, 34584}, {14855, 15012}, {14915, 37484}, {14927, 44456}, {15021, 38724}, {15027, 16111}, {15034, 38789}, {15041, 36253}, {15042, 36518}, {15178, 41869}, {15484, 44519}, {16808, 42930}, {16809, 42931}, {16964, 42429}, {16965, 42430}, {17845, 48672}, {18440, 29323}, {18481, 28158}, {18510, 42259}, {18512, 42258}, {18525, 28168}, {19106, 36836}, {19107, 36843}, {20190, 48904}, {20397, 38788}, {20398, 38742}, {20399, 38731}, {20725, 32533}, {22115, 44788}, {22236, 42099}, {22238, 42100}, {22330, 43273}, {22793, 30389}, {23269, 43883}, {23275, 43884}, {29181, 39899}, {30435, 43619}, {31371, 44731}, {31454, 43786}, {32139, 37496}, {32609, 38791}, {33534, 36747}, {34754, 42965}, {34755, 42964}, {35237, 36749}, {36967, 42988}, {36968, 42989}, {36969, 42892}, {36970, 42893}, {36990, 48879}, {38795, 41427}, {39590, 44541}, {41107, 42587}, {41108, 42586}, {41943, 42909}, {41944, 42908}, {41973, 46334}, {41974, 46335}, {42087, 42161}, {42088, 42160}, {42090, 42166}, {42091, 42163}, {42095, 42593}, {42098, 42592}, {42104, 42599}, {42105, 42598}, {42108, 42115}, {42109, 42116}, {42136, 43329}, {42137, 43328}, {42140, 42584}, {42141, 42585}, {42149, 43402}, {42152, 43401}, {42154, 42800}, {42155, 42799}, {42157, 43009}, {42158, 43008}, {42215, 42414}, {42216, 42413}, {42431, 42974}, {42432, 42975}, {42480, 42990}, {42481, 42991}, {42490, 43489}, {42491, 43490}, {42508, 42994}, {42509, 42995}, {42625, 42814}, {42626, 42813}, {42629, 43334}, {42630, 43335}, {42637, 45385}, {42638, 45384}, {42779, 43645}, {42780, 43646}, {42797, 43545}, {42798, 43544}, {42922, 43243}, {42923, 43242}, {42934, 43485}, {42935, 43486}, {42942, 43773}, {42943, 43774}, {43366, 43467}, {43367, 43468}, {43377, 43522}, {43465, 43630}, {43466, 43631}, {43497, 43781}, {43498, 43782}

X(49137) = reflection of X(i) in X(j) for these {i,j}: {3, 3529}, {381, 15685}, {382, 1657}, {1657, 17800}, {3146, 15704}, {3830, 15683}, {5073, 20}, {11541, 3627}, {15640, 15686}, {15682, 44903}, {15684, 11001}, {17800, 5059}, {18440, 48872}, {33703, 550}, {34780, 5925}, {35400, 2}, {35407, 17538}, {35408, 15759}, {36990, 48879}, {44456, 14927}, {48672, 17845}, {48910, 48896}
X(49137) = orthocentroidal-circle-inverse of X(3859)
X(49137) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 3859}, {3, 4, 5079}, {3, 3091, 3526}, {3, 3146, 5076}, {3, 3525, 15693}, {3, 3529, 1657}, {3, 3627, 381}, {3, 3628, 15720}, {3, 3830, 3091}, {3, 3843, 3628}, {3, 3851, 3525}, {3, 5055, 14869}, {3, 5073, 3627}, {3, 5076, 5072}, {3, 5079, 5054}, {3, 12103, 15696}, {3, 15681, 12103}, {3, 17800, 3529}, {3, 35406, 3543}, {3, 37923, 35479}, {4, 20, 8703}, {4, 382, 35434}, {4, 3530, 19709}, {4, 5070, 381}, {4, 8703, 5070}, {4, 12103, 3}, {4, 15681, 15696}, {4, 15692, 5}, {4, 15696, 5054}, {4, 21734, 547}, {4, 38071, 3843}, {4, 46936, 41991}, {5, 550, 15759}, {5, 15691, 21735}, {5, 15723, 1656}, {5, 21735, 15701}, {5, 41981, 15692}, {20, 140, 15689}, {20, 3090, 44245}, {20, 3146, 3090}, {20, 3524, 550}, {20, 3627, 3}, {20, 5068, 376}, {20, 5070, 15696}, {20, 5073, 381}, {20, 11541, 3627}, {20, 15682, 140}, {20, 15685, 1657}, {20, 21735, 15691}, {20, 33703, 3861}, {140, 44903, 20}, {376, 3628, 3}, {376, 3843, 15720}, {376, 5068, 44682}, {381, 1657, 20}, {381, 3090, 5072}, {381, 5073, 382}, {381, 5079, 12811}, {381, 8703, 5054}, {381, 15688, 15701}, {381, 15689, 15716}, {381, 15693, 15699}, {382, 1656, 38335}, {382, 1657, 3534}, {382, 3534, 1656}, {382, 5054, 4}, {382, 5072, 5076}, {546, 15704, 17538}, {546, 17538, 3}, {547, 550, 21734}, {547, 8703, 3524}, {547, 12108, 632}, {547, 15683, 15681}, {548, 3525, 3}, {548, 3543, 3851}, {548, 3851, 15693}, {548, 45762, 140}, {549, 35381, 5054}, {550, 3091, 3}, {550, 3526, 14093}, {550, 3830, 3526}, {550, 3861, 3524}, {550, 33703, 3830}, {632, 3090, 5070}, {632, 12811, 3090}, {632, 15704, 12103}, {1657, 15696, 15681}, {1657, 33703, 14093}, {1657, 35384, 3528}, {1657, 35405, 3522}, {2043, 2044, 45759}, {3090, 3146, 3627}, {3090, 11541, 3146}, {3090, 44245, 3}, {3146, 3529, 15704}, {3146, 5076, 382}, {3146, 12108, 3830}, {3146, 15704, 3}, {3146, 17538, 546}, {3522, 3853, 5055}, {3522, 14869, 3}, {3524, 3830, 381}, {3526, 15696, 21734}, {3526, 15720, 15713}, {3526, 33703, 382}, {3528, 3845, 46219}, {3528, 46219, 15706}, {3529, 11541, 20}, {3530, 35404, 4}, {3530, 41991, 46936}, {3534, 15723, 15688}, {3534, 35434, 5054}, {3534, 38335, 15700}, {3543, 15710, 3860}, {3627, 8703, 12811}, {3627, 11541, 5073}, {3627, 12811, 4}, {3627, 15704, 44245}, {3627, 44245, 3090}, {3832, 33923, 15694}, {3843, 5059, 35435}, {3843, 5068, 381}, {3843, 35401, 4}, {3853, 19710, 3522}, {3856, 45759, 3533}, {3858, 15690, 15717}, {3858, 15717, 15703}, {3861, 15713, 5068}, {3861, 21734, 5070}, {3861, 44245, 12108}, {5054, 15681, 3534}, {5055, 35405, 382}, {5068, 12101, 3843}, {5070, 12811, 5079}, {5072, 14093, 12108}, {5072, 15704, 3534}, {5073, 15681, 5070}, {5073, 15685, 20}, {5073, 17800, 15685}, {5073, 44245, 5076}, {5076, 15696, 632}, {5079, 15696, 3}, {7464, 17714, 3}, {7555, 35475, 3}, {8703, 35404, 41987}, {8703, 41984, 15692}, {9693, 43521, 43376}, {10109, 14269, 381}, {11001, 15684, 15688}, {11001, 21735, 20}, {11001, 35409, 15692}, {12085, 44457, 2937}, {12101, 15691, 41983}, {12101, 44682, 5068}, {12103, 12811, 8703}, {12103, 35404, 46936}, {12811, 41987, 41991}, {13154, 41463, 3}, {14893, 15697, 15707}, {15156, 15157, 37950}, {15640, 15686, 14269}, {15681, 15684, 15692}, {15681, 35401, 376}, {15682, 15689, 381}, {15682, 44903, 15689}, {15683, 33703, 550}, {15684, 15691, 381}, {15685, 15689, 44903}, {15685, 15701, 11001}, {15687, 46333, 15695}, {15688, 15696, 41981}, {15688, 15759, 14093}, {15689, 45762, 15693}, {15691, 15701, 15688}, {15691, 41984, 8703}, {15692, 41984, 15701}, {15696, 35434, 1656}, {15703, 41988, 381}, {15704, 44245, 20}, {15713, 38071, 547}, {17538, 35407, 5076}, {19687, 33271, 5077}, {19696, 33234, 11159}, {19709, 41987, 381}, {19709, 46936, 5079}, {31649, 35986, 3}, {33532, 35502, 3}, {33699, 33923, 3832}, {35384, 46219, 382}, {41989, 44245, 14891}, {41991, 46936, 19709}, {42225, 43407, 6418}, {42226, 43408, 6417}, {42280, 42281, 17578}, {42431, 43194, 42974}, {42432, 43193, 42975}, {43324, 43325, 6}, {47752, 47753, 34152}


X(49138) = X(2)X(3)∩X(8)X(28168)

Barycentrics    15*a^4 - 8*a^2*b^2 - 7*b^4 - 8*a^2*c^2 + 14*b^2*c^2 - 7*c^4 : :
X(49138) = 21 X[2] - 22 X[3], 12 X[2] - 11 X[4], 45 X[2] - 44 X[5], 9 X[2] - 11 X[20], 87 X[2] - 88 X[140], 10 X[2] - 11 X[376], 23 X[2] - 22 X[381], 27 X[2] - 22 X[382], 93 X[2] - 88 X[546], 89 X[2] - 88 X[547], 81 X[2] - 88 X[548], 43 X[2] - 44 X[549], 39 X[2] - 44 X[550], 54 X[2] - 55 X[631], 15 X[2] - 22 X[1657], 78 X[2] - 77 X[3090], 57 X[2] - 55 X[3091], 15 X[2] - 11 X[3146], 51 X[2] - 55 X[3522], 75 X[2] - 77 X[3523], 32 X[2] - 33 X[3524], 72 X[2] - 77 X[3528], 6 X[2] - 11 X[3529], 19 X[2] - 22 X[3534], 13 X[2] - 11 X[3543], 34 X[2] - 33 X[3545], 51 X[2] - 44 X[3627], 25 X[2] - 22 X[3830], 81 X[2] - 77 X[3832], 35 X[2] - 33 X[3839], 47 X[2] - 44 X[3845], 9 X[2] - 8 X[3853], 21 X[2] - 20 X[3858], 65 X[2] - 66 X[5054], 67 X[2] - 66 X[5055], 3 X[2] - 11 X[5059], 91 X[2] - 88 X[5066], 56 X[2] - 55 X[5071], 41 X[2] - 44 X[8703], 31 X[2] - 33 X[10304], 8 X[2] - 11 X[11001], 24 X[2] - 11 X[11541], 85 X[2] - 88 X[12100], 97 X[2] - 88 X[12101], 75 X[2] - 88 X[12103], 33 X[2] - 32 X[12811], 71 X[2] - 66 X[14269], 95 X[2] - 88 X[14893], 17 X[2] - 11 X[15640], 17 X[2] - 22 X[15681], 14 X[2] - 11 X[15682], 7 X[2] - 11 X[15683], 29 X[2] - 22 X[15684], 13 X[2] - 22 X[15685], 37 X[2] - 44 X[15686], 49 X[2] - 44 X[15687], 61 X[2] - 66 X[15688], 59 X[2] - 66 X[15689], 79 X[2] - 88 X[15690], 7 X[2] - 8 X[15691], 53 X[2] - 55 X[15692], 9 X[2] - 10 X[15696], 49 X[2] - 55 X[15697], 74 X[2] - 77 X[15698], 76 X[2] - 77 X[15702], 3 X[2] - 4 X[15704], 95 X[2] - 99 X[15705], 97 X[2] - 99 X[15708], 98 X[2] - 99 X[15709], 94 X[2] - 99 X[15710], 19 X[2] - 20 X[15714], 48 X[2] - 55 X[17538], 63 X[2] - 55 X[17578], 9 X[2] - 22 X[17800], 52 X[2] - 55 X[19708], 35 X[2] - 44 X[19710], 53 X[2] - 44 X[33699], 18 X[2] - 11 X[33703], 15 X[2] - 16 X[33923], 83 X[2] - 88 X[34200], 41 X[2] - 22 X[35400], 11 X[2] - 10 X[35403], 5 X[2] - 4 X[35404], 155 X[2] - 88 X[35408], 50 X[2] - 33 X[35409], 73 X[2] - 242 X[35410], 89 X[2] - 286 X[35411], X[2] - 5 X[35414], 95 X[2] - 104 X[35421], 73 X[2] - 66 X[38335], 58 X[2] - 55 X[41099], 80 X[2] - 77 X[41106], 27 X[2] - 28 X[44682], 31 X[2] - 44 X[44903], 57 X[2] - 56 X[44904], and many others

X(49138) lies on these lines: {2, 3}, {8, 28168}, {69, 29323}, {145, 28178}, {388, 4330}, {497, 4325}, {625, 39142}, {944, 9589}, {962, 28154}, {1056, 4309}, {1058, 4317}, {1131, 9692}, {1285, 5319}, {1568, 27082}, {1587, 6470}, {1588, 6471}, {3060, 14641}, {3068, 9693}, {3098, 43613}, {3316, 42284}, {3317, 42283}, {3411, 42160}, {3412, 42161}, {3474, 37721}, {3486, 4338}, {3532, 15153}, {3618, 48904}, {3619, 48885}, {4293, 9670}, {4294, 9657}, {4296, 9644}, {4301, 7967}, {4316, 5225}, {4324, 5229}, {4701, 5881}, {5237, 43494}, {5238, 43493}, {5334, 42970}, {5335, 42971}, {5343, 42943}, {5344, 42942}, {5349, 42625}, {5350, 42626}, {5351, 42495}, {5352, 42494}, {5365, 36843}, {5366, 36836}, {5493, 34627}, {5691, 38127}, {5734, 18481}, {6241, 14531}, {6459, 42276}, {6460, 42275}, {6468, 23249}, {6469, 23259}, {6560, 42413}, {6561, 42414}, {6759, 43576}, {7317, 37708}, {7354, 8162}, {7581, 41956}, {7582, 41955}, {7712, 43394}, {7738, 43618}, {7759, 9741}, {7765, 43619}, {7871, 32006}, {7998, 46849}, {7999, 32062}, {8164, 9656}, {8717, 13434}, {8976, 43507}, {9541, 23269}, {9588, 31673}, {9606, 44519}, {9671, 15326}, {9680, 31412}, {9681, 31414}, {9705, 13346}, {10187, 42544}, {10188, 42543}, {10248, 13624}, {10595, 41869}, {10653, 43770}, {10654, 43769}, {10721, 20125}, {11270, 43699}, {11362, 28172}, {11381, 15606}, {11431, 13568}, {11455, 15644}, {11480, 42693}, {11481, 42692}, {11488, 42434}, {11489, 42433}, {12245, 28160}, {12254, 40196}, {12295, 15057}, {12943, 31410}, {13886, 42260}, {13939, 42261}, {13951, 43508}, {14491, 15740}, {14912, 48905}, {14927, 29317}, {15032, 33534}, {15058, 36987}, {15318, 33702}, {15516, 31670}, {15520, 33749}, {16241, 42775}, {16242, 42776}, {16772, 42134}, {16773, 42133}, {16964, 42112}, {16965, 42113}, {19925, 31425}, {20070, 28186}, {20396, 38788}, {20421, 43907}, {21740, 41860}, {22615, 35813}, {22644, 35812}, {23236, 34584}, {23241, 36965}, {23251, 43509}, {23253, 41950}, {23261, 43510}, {23263, 41949}, {23267, 42258}, {23273, 42259}, {23275, 42271}, {25406, 43621}, {28146, 37727}, {29181, 39874}, {31487, 43512}, {31730, 37714}, {32601, 34224}, {32822, 32890}, {32823, 32891}, {33604, 42973}, {33605, 42972}, {33884, 45959}, {34089, 42277}, {34091, 42274}, {35822, 42538}, {35823, 42537}, {37640, 42430}, {37641, 42429}, {40107, 48879}, {40693, 42099}, {40694, 42100}, {41945, 43386}, {41946, 43387}, {42085, 42991}, {42086, 42990}, {42090, 42813}, {42091, 42814}, {42096, 42148}, {42097, 42147}, {42101, 42491}, {42102, 42490}, {42108, 42153}, {42109, 42156}, {42122, 42986}, {42123, 42987}, {42130, 43465}, {42131, 43466}, {42157, 43204}, {42158, 43203}, {42159, 42981}, {42162, 42980}, {42262, 43375}, {42265, 43374}, {42268, 42557}, {42269, 42558}, {42516, 42779}, {42517, 42780}, {42528, 42920}, {42529, 42921}, {42572, 43521}, {42573, 43522}, {42816, 43253}, {42908, 43202}, {42909, 43201}, {42998, 43482}, {42999, 43481}, {43105, 43777}, {43106, 43778}, {43244, 43776}, {43245, 43775}, {43413, 43432}, {43414, 43433}, {44518, 46453}

X(49138) = reflection of X(i) in X(j) for these {i,j}: {4, 3529}, {20, 17800}, {3146, 1657}, {3529, 5059}, {3543, 15685}, {5073, 15704}, {10109, 35413}, {11541, 4}, {15640, 15681}, {15682, 15683}, {33703, 20}, {35400, 8703}, {43621, 48896}
X(49138) = anticomplement of X(5073)
X(49138) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20, 15696}, {2, 3091, 44904}, {2, 44682, 631}, {3, 4, 5071}, {3, 382, 3861}, {3, 1657, 19710}, {3, 3858, 2}, {3, 3861, 7486}, {3, 5068, 15709}, {3, 7486, 631}, {3, 10124, 3523}, {3, 15682, 4}, {3, 15687, 5068}, {3, 17578, 3855}, {3, 35018, 15721}, {4, 20, 3528}, {4, 376, 3525}, {4, 3524, 3544}, {4, 3525, 41106}, {4, 3528, 5067}, {4, 3529, 11001}, {4, 11001, 17538}, {4, 15702, 3091}, {4, 17538, 3524}, {4, 19708, 3090}, {4, 35503, 38282}, {5, 20, 376}, {5, 1657, 20}, {5, 3525, 5067}, {5, 3526, 46936}, {5, 3530, 46219}, {5, 3839, 3855}, {5, 3843, 3854}, {5, 12100, 3526}, {5, 12102, 3843}, {5, 21734, 631}, {5, 35404, 3853}, {5, 46853, 12108}, {20, 382, 631}, {20, 858, 45771}, {20, 3146, 5}, {20, 3528, 17538}, {20, 3543, 15717}, {20, 3832, 548}, {20, 5059, 17800}, {20, 15717, 550}, {20, 17578, 3}, {20, 17800, 3529}, {20, 33703, 4}, {376, 631, 21734}, {376, 3146, 4}, {376, 3529, 1657}, {376, 3545, 12100}, {376, 5054, 19708}, {376, 14893, 15702}, {376, 15682, 3839}, {376, 35409, 3830}, {376, 41106, 3524}, {382, 548, 3832}, {382, 631, 4}, {382, 3861, 17578}, {546, 10304, 3533}, {548, 3832, 631}, {550, 3090, 19708}, {550, 3543, 3090}, {550, 3843, 15717}, {550, 5066, 3}, {550, 12102, 5054}, {550, 41991, 14891}, {631, 3090, 16239}, {631, 3855, 7486}, {631, 33703, 382}, {1657, 3146, 376}, {1657, 3830, 12103}, {1657, 5073, 33923}, {1657, 11541, 41106}, {2041, 2042, 3543}, {3090, 3543, 4}, {3090, 46333, 550}, {3091, 3534, 21735}, {3091, 15705, 46219}, {3091, 21735, 15702}, {3146, 3523, 3830}, {3146, 3854, 3543}, {3146, 46936, 3627}, {3522, 3627, 3545}, {3522, 3859, 631}, {3522, 15640, 3627}, {3522, 15721, 3}, {3522, 46936, 12100}, {3523, 12103, 376}, {3525, 11541, 3146}, {3528, 5067, 3524}, {3528, 11001, 20}, {3529, 3533, 44903}, {3529, 11541, 17538}, {3529, 33703, 20}, {3530, 14893, 5}, {3534, 14893, 15705}, {3534, 15705, 376}, {3543, 3854, 12102}, {3543, 15685, 46333}, {3543, 15717, 3843}, {3543, 46333, 19708}, {3545, 3627, 4}, {3552, 33285, 33236}, {3627, 15681, 3522}, {3830, 10124, 3839}, {3830, 12103, 3523}, {3839, 5071, 41106}, {3839, 15683, 19710}, {3839, 15705, 15699}, {3839, 19710, 376}, {3843, 5054, 5}, {3843, 15717, 3090}, {3843, 17800, 15685}, {3851, 44245, 15692}, {3853, 15696, 2}, {3853, 15704, 15696}, {3853, 33923, 5}, {3854, 5054, 3090}, {3854, 19708, 3525}, {3855, 15682, 17578}, {3855, 17578, 4}, {3855, 33703, 15682}, {3857, 15693, 46935}, {3857, 41981, 15693}, {3858, 15691, 3}, {3858, 15704, 15691}, {3861, 7486, 3855}, {3861, 15691, 44682}, {3861, 16239, 5066}, {3861, 35018, 3859}, {5054, 12102, 3854}, {5054, 41982, 15705}, {5066, 15683, 46333}, {5067, 17538, 3528}, {5067, 41106, 5}, {5068, 15697, 3}, {5073, 15696, 3853}, {5073, 15704, 2}, {5073, 35404, 3146}, {5076, 8703, 5056}, {5365, 36843, 43543}, {5366, 36836, 43542}, {6353, 35490, 4}, {6655, 14039, 33232}, {6658, 33271, 32986}, {7387, 7464, 21844}, {7486, 17578, 3861}, {7556, 12084, 23040}, {9541, 42272, 23269}, {9681, 35820, 31414}, {11001, 11541, 4}, {11001, 33703, 5067}, {11361, 33209, 33226}, {11361, 33226, 32957}, {11413, 37925, 44879}, {12084, 12087, 7556}, {12085, 12088, 35473}, {12103, 35409, 4}, {14042, 33207, 32978}, {14062, 33208, 32977}, {14068, 33267, 33215}, {14269, 15712, 15022}, {14784, 14785, 15681}, {14893, 46219, 3091}, {15640, 15681, 3545}, {15682, 15709, 15687}, {15683, 15721, 15681}, {15683, 17578, 20}, {15685, 19708, 11001}, {15687, 15697, 15709}, {15696, 15704, 20}, {15697, 17578, 48154}, {15702, 46219, 3525}, {15704, 35404, 33923}, {15704, 44904, 3534}, {15714, 35404, 14893}, {15717, 16239, 631}, {19687, 33272, 32956}, {19691, 33007, 33238}, {19695, 32981, 33190}, {19696, 32997, 14033}, {32982, 33250, 33191}, {32985, 33019, 33292}, {32996, 33268, 33216}, {33007, 33238, 14069}, {33017, 33239, 32951}, {33192, 33257, 14064}, {33193, 33256, 14001}, {33229, 35927, 33189}, {33264, 33280, 16043}, {33265, 33279, 32970}, {33524, 47527, 35921}, {33699, 44245, 3851}, {33703, 46333, 3843}, {35408, 44903, 15703}, {35435, 46935, 3529}, {36836, 43401, 5366}, {36843, 43402, 5365}, {42263, 43407, 7582}, {42264, 43408, 7581}, {43621, 48896, 25406}


X(49139) = X(2)X(3)∩X(6)X(43485)

Barycentrics    17*a^4 - 9*a^2*b^2 - 8*b^4 - 9*a^2*c^2 + 16*b^2*c^2 - 8*c^4 : :
X(49139) = 24 X[2] - 25 X[3], 27 X[2] - 25 X[4], 51 X[2] - 50 X[5], 21 X[2] - 25 X[20], 99 X[2] - 100 X[140], 23 X[2] - 25 X[376], 26 X[2] - 25 X[381], 6 X[2] - 5 X[382], 21 X[2] - 20 X[546], 93 X[2] - 100 X[548], 49 X[2] - 50 X[549], 9 X[2] - 10 X[550], 18 X[2] - 25 X[1657], 33 X[2] - 25 X[3146], 73 X[2] - 75 X[3524], 33 X[2] - 35 X[3528], 3 X[2] - 5 X[3529], 39 X[2] - 40 X[3530], 22 X[2] - 25 X[3534], 29 X[2] - 25 X[3543], 87 X[2] - 85 X[3544], 77 X[2] - 75 X[3545], 57 X[2] - 50 X[3627], 28 X[2] - 25 X[3830], 79 X[2] - 75 X[3839], 53 X[2] - 50 X[3845], 36 X[2] - 35 X[3851], 57 X[2] - 55 X[3855], 74 X[2] - 75 X[5054], 76 X[2] - 75 X[5055], 9 X[2] - 25 X[5059], 36 X[2] - 25 X[5073], 66 X[2] - 65 X[5079], 47 X[2] - 50 X[8703], 63 X[2] - 65 X[10299], 71 X[2] - 75 X[10304], 19 X[2] - 25 X[11001], 51 X[2] - 25 X[11541], 41 X[2] - 40 X[11737], 97 X[2] - 100 X[12100], 87 X[2] - 100 X[12103], 16 X[2] - 15 X[14269], 69 X[2] - 70 X[14869], 37 X[2] - 25 X[15640], 4 X[2] - 5 X[15681], 31 X[2] - 25 X[15682], 17 X[2] - 25 X[15683], 32 X[2] - 25 X[15684], 16 X[2] - 25 X[15685], 43 X[2] - 50 X[15686], 11 X[2] - 10 X[15687], 14 X[2] - 15 X[15688], 68 X[2] - 75 X[15689], 91 X[2] - 100 X[15690], 89 X[2] - 100 X[15691], 34 X[2] - 35 X[15700], 39 X[2] - 50 X[15704], 44 X[2] - 45 X[15707], 43 X[2] - 45 X[15710], 53 X[2] - 55 X[15715], 54 X[2] - 55 X[15720], 29 X[2] - 30 X[17504], 12 X[2] - 25 X[17800], 41 X[2] - 50 X[19710], 59 X[2] - 50 X[33699], 39 X[2] - 25 X[33703], 19 X[2] - 20 X[34200], 81 X[2] - 80 X[35018], 44 X[2] - 25 X[35400], 61 X[2] - 50 X[35404], 109 X[2] - 75 X[35409], 37 X[2] - 125 X[35414], 31 X[2] - 30 X[38071], 82 X[2] - 75 X[38335], 37 X[2] - 50 X[44903], 61 X[2] - 75 X[46333], 61 X[2] - 60 X[47478], 9 X[3] - 8 X[4], 17 X[3] - 16 X[5], 7 X[3] - 8 X[20], 33 X[3] - 32 X[140], 23 X[3] - 24 X[376], 13 X[3] - 12 X[381], 5 X[3] - 4 X[382], 35 X[3] - 32 X[546], 101 X[3] - 96 X[547], 31 X[3] - 32 X[548], 49 X[3] - 48 X[549], 15 X[3] - 16 X[550], 41 X[3] - 40 X[631], 83 X[3] - 80 X[632], 21 X[3] - 20 X[1656], 3 X[3] - 4 X[1657], 59 X[3] - 56 X[3090], 43 X[3] - 40 X[3091], 11 X[3] - 8 X[3146], and many others

X(49139) lies on these lines: {2, 3}, {6, 43485}, {64, 14841}, {397, 42113}, {398, 42112}, {590, 12818}, {615, 12819}, {1482, 28154}, {1498, 37496}, {1506, 11742}, {1539, 38638}, {1990, 33636}, {3068, 6472}, {3069, 6473}, {3244, 28150}, {3631, 48873}, {3632, 28160}, {5050, 48896}, {5093, 48905}, {5237, 42908}, {5238, 42909}, {5339, 42100}, {5340, 42099}, {5343, 42123}, {5344, 42122}, {5349, 42091}, {5350, 42090}, {5365, 42818}, {5366, 42817}, {5368, 21309}, {5493, 18525}, {5882, 28158}, {5895, 45185}, {6199, 42266}, {6395, 42267}, {6407, 8960}, {6417, 42264}, {6418, 42263}, {6445, 23251}, {6446, 23261}, {6474, 9541}, {6496, 35786}, {6497, 35787}, {6500, 6560}, {6501, 6561}, {6767, 10483}, {7746, 15603}, {8148, 28146}, {9680, 43409}, {9690, 42260}, {9691, 13665}, {10113, 38633}, {10145, 13903}, {10146, 13961}, {10187, 42774}, {10188, 42773}, {10990, 12902}, {10991, 38733}, {10992, 38744}, {10993, 38756}, {11485, 42431}, {11486, 42432}, {12017, 48904}, {12174, 12316}, {12308, 34584}, {12645, 28190}, {12702, 28168}, {12820, 42529}, {12821, 42528}, {14864, 35450}, {14900, 48658}, {15105, 34780}, {15605, 48675}, {16966, 43292}, {16967, 43293}, {17851, 23259}, {18526, 28178}, {18553, 48879}, {18581, 42793}, {18582, 42794}, {19106, 43004}, {19107, 43005}, {19160, 38639}, {20050, 28174}, {20054, 28224}, {22236, 43418}, {22238, 43419}, {22246, 43618}, {22505, 38635}, {22515, 38634}, {22615, 41964}, {22644, 41963}, {22799, 38636}, {22938, 38637}, {28202, 34747}, {29012, 40341}, {29317, 44456}, {29323, 33878}, {30714, 38790}, {33520, 38768}, {33586, 43807}, {34507, 48872}, {35021, 38732}, {35022, 38743}, {35023, 38755}, {35024, 38767}, {36969, 42939}, {36970, 42938}, {37624, 41869}, {41973, 42994}, {41974, 42995}, {42085, 43106}, {42086, 43105}, {42087, 42988}, {42088, 42989}, {42093, 43026}, {42094, 43027}, {42096, 42158}, {42097, 42157}, {42104, 42944}, {42105, 42945}, {42108, 42149}, {42109, 42152}, {42117, 43769}, {42118, 43770}, {42126, 42151}, {42127, 42150}, {42144, 42999}, {42145, 42998}, {42225, 42414}, {42226, 42413}, {42261, 43415}, {42429, 43193}, {42430, 43194}, {42584, 42816}, {42585, 42815}, {42643, 43512}, {42644, 43511}, {42797, 43239}, {42798, 43238}, {42813, 43231}, {42814, 43230}, {42918, 43367}, {42919, 43366}, {43136, 44526}, {43636, 43776}, {43637, 43775}, {44762, 48672}

X(49139) = reflection of X(i) in X(j) for these {i,j}: {3, 17800}, {382, 3529}, {1657, 5059}, {5073, 1657}, {11541, 5}, {15640, 44903}, {15684, 15685}, {33703, 15704}, {35400, 3534}
X(49139) = Stammler-circle-inverse of X(34152)
X(49139) = crosspoint of X(43570) and X(43571)
X(49139) = crosssum of X(6453) and X(6454)
X(49139) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 382, 14269}, {3, 3843, 15703}, {3, 17800, 15685}, {3, 18535, 22462}, {3, 35403, 5}, {4, 20, 33923}, {4, 550, 15720}, {4, 15720, 3851}, {4, 33923, 1656}, {5, 15689, 3}, {20, 546, 15688}, {20, 3146, 3545}, {20, 3525, 15690}, {20, 3627, 15716}, {20, 3830, 3}, {20, 10299, 550}, {20, 15022, 376}, {20, 16239, 15696}, {140, 550, 3528}, {140, 3545, 1656}, {376, 5070, 3}, {376, 5076, 5070}, {376, 45761, 14093}, {381, 3534, 45759}, {381, 15713, 5055}, {382, 546, 3830}, {382, 550, 3851}, {382, 1657, 550}, {382, 3528, 3843}, {382, 3529, 15681}, {382, 3534, 5079}, {382, 5079, 15687}, {382, 15681, 3}, {382, 15688, 546}, {382, 15696, 3855}, {382, 15720, 4}, {546, 550, 10299}, {546, 1656, 3851}, {546, 10299, 1656}, {546, 14869, 15022}, {546, 15690, 3530}, {546, 34200, 16239}, {548, 15694, 3}, {548, 41989, 19711}, {549, 3854, 1656}, {550, 1657, 15681}, {550, 3529, 1657}, {550, 3530, 3522}, {550, 3851, 3}, {550, 3858, 17504}, {550, 10299, 15688}, {550, 15687, 140}, {1656, 1657, 20}, {1656, 15688, 10299}, {1657, 5059, 17800}, {1657, 5073, 3}, {2043, 2044, 15759}, {2045, 2046, 47598}, {3146, 3528, 15687}, {3146, 3534, 3843}, {3146, 15687, 382}, {3525, 3545, 7486}, {3526, 12103, 15695}, {3526, 15695, 3}, {3528, 5079, 15707}, {3528, 7486, 3530}, {3528, 15687, 5079}, {3528, 15707, 3}, {3529, 3855, 11001}, {3530, 33703, 382}, {3530, 47598, 14869}, {3534, 3843, 3}, {3534, 5079, 3528}, {3534, 15687, 15707}, {3543, 12103, 3526}, {3543, 21735, 3858}, {3544, 17504, 3526}, {3545, 15688, 15707}, {3627, 11001, 15696}, {3627, 15696, 5055}, {3627, 34200, 3855}, {3830, 15681, 15688}, {3830, 15695, 10109}, {3832, 44245, 15693}, {3832, 46333, 44245}, {3843, 15694, 41989}, {3843, 15707, 5079}, {3843, 35400, 3146}, {3851, 5073, 382}, {3851, 15681, 550}, {3851, 46219, 35018}, {3853, 17538, 5054}, {3853, 44903, 17538}, {3858, 12103, 21735}, {3858, 21735, 3526}, {3860, 11001, 3534}, {5055, 15696, 3}, {5055, 35412, 15685}, {5073, 15681, 3851}, {5073, 17800, 1657}, {5079, 15687, 3843}, {7387, 35452, 3}, {7486, 15704, 3534}, {8703, 17578, 5072}, {11541, 15683, 5}, {14269, 15685, 15681}, {14813, 14814, 17538}, {15154, 15155, 34152}, {15640, 17538, 3853}, {15640, 44903, 5054}, {15681, 15707, 3534}, {15681, 17800, 3529}, {15681, 35400, 15687}, {15683, 15700, 15681}, {15687, 19711, 38071}, {15688, 15700, 19708}, {15688, 15716, 34200}, {15690, 15704, 20}, {15703, 35400, 15684}, {15703, 45759, 15722}, {15704, 33703, 381}, {15713, 16239, 3525}, {15720, 35018, 46219}, {18378, 21312, 3}, {21570, 21577, 37269}, {21572, 21575, 11340}, {35404, 44245, 3832}, {35404, 46333, 15693}, {42260, 43570, 43523}, {42261, 43571, 43524}, {42278, 42279, 3146}, {43485, 43486, 6}, {43515, 43523, 43570}, {43516, 43524, 43571}


X(49140) = X(2)X(3)∩X(8)X(28172)

Barycentrics    19*a^4 - 10*a^2*b^2 - 9*b^4 - 10*a^2*c^2 + 18*b^2*c^2 - 9*c^4 : :
X(49140) = 27 X[2] - 28 X[3], 15 X[2] - 14 X[4], 57 X[2] - 56 X[5], 6 X[2] - 7 X[20], 13 X[2] - 14 X[376], 29 X[2] - 28 X[381], 33 X[2] - 28 X[382], 15 X[2] - 16 X[548], 55 X[2] - 56 X[549], 51 X[2] - 56 X[550], 69 X[2] - 70 X[631], 3 X[2] - 4 X[1657], 99 X[2] - 98 X[3090], 36 X[2] - 35 X[3091], 9 X[2] - 7 X[3146], 33 X[2] - 35 X[3522], 48 X[2] - 49 X[3523], 41 X[2] - 42 X[3524], 93 X[2] - 98 X[3528], 9 X[2] - 14 X[3529], 25 X[2] - 28 X[3534], 8 X[2] - 7 X[3543], 43 X[2] - 42 X[3545], 9 X[2] - 8 X[3627], 31 X[2] - 28 X[3830], 51 X[2] - 49 X[3832], 22 X[2] - 21 X[3839], 21 X[2] - 20 X[3843], 59 X[2] - 56 X[3845], 33 X[2] - 32 X[3850], 83 X[2] - 84 X[5054], 85 X[2] - 84 X[5055], 78 X[2] - 77 X[5056], 3 X[2] - 7 X[5059], 93 X[2] - 91 X[5068], 71 X[2] - 70 X[5071], 45 X[2] - 44 X[5072], 39 X[2] - 28 X[5073], 53 X[2] - 56 X[8703], 90 X[2] - 91 X[10303], 20 X[2] - 21 X[10304], 11 X[2] - 14 X[11001], 27 X[2] - 14 X[11541], 99 X[2] - 112 X[12103], 63 X[2] - 64 X[12108], 81 X[2] - 80 X[12812], 19 X[2] - 20 X[14093], 89 X[2] - 84 X[14269], 95 X[2] - 96 X[14890], 31 X[2] - 32 X[14891], 49 X[2] - 48 X[14892], 17 X[2] - 16 X[14893], 10 X[2] - 7 X[15640], 23 X[2] - 28 X[15681], 17 X[2] - 14 X[15682], 5 X[2] - 7 X[15683], 5 X[2] - 4 X[15684], 19 X[2] - 28 X[15685], 7 X[2] - 8 X[15686], 61 X[2] - 56 X[15687], 79 X[2] - 84 X[15688], 11 X[2] - 12 X[15689], 34 X[2] - 35 X[15692], 32 X[2] - 35 X[15697], 95 X[2] - 98 X[15698], 97 X[2] - 98 X[15702], 45 X[2] - 56 X[15704], 61 X[2] - 63 X[15705], 35 X[2] - 36 X[15706], 62 X[2] - 63 X[15708], 39 X[2] - 40 X[15712], 75 X[2] - 77 X[15717], 43 X[2] - 44 X[15718], 76 X[2] - 77 X[15721], 9 X[2] - 10 X[17538], 39 X[2] - 35 X[17578], 15 X[2] - 28 X[17800], 67 X[2] - 70 X[19708], 47 X[2] - 56 X[19710], 87 X[2] - 91 X[21734], 21 X[2] - 22 X[21735], 25 X[2] - 24 X[23046], 65 X[2] - 56 X[33699], 47 X[2] - 28 X[35400], 67 X[2] - 56 X[35404], 59 X[2] - 42 X[35409], 13 X[2] - 35 X[35414], 31 X[2] - 33 X[35418], 13 X[2] - 12 X[38335], 73 X[2] - 70 X[41099], 101 X[2] - 98 X[41106], 47 X[2] - 48 X[41983], 43 X[2] - 56 X[44903], 97 X[2] - 96 X[45757], 23 X[2] - 24 X[45759], 61 X[2] - 64 X[46332], and many others

X(49140) lies on these lines: {2, 3}, {8, 28172}, {61, 42113}, {62, 42112}, {99, 32876}, {145, 28146}, {193, 29317}, {315, 32875}, {371, 43337}, {372, 43336}, {390, 10483}, {515, 20053}, {516, 3633}, {535, 12632}, {575, 43621}, {944, 28154}, {962, 3635}, {1131, 9542}, {1132, 42261}, {3068, 43339}, {3069, 43338}, {3284, 45245}, {3590, 9680}, {3621, 28186}, {3623, 48661}, {3625, 7991}, {3630, 5921}, {4114, 11518}, {4316, 5265}, {4324, 5281}, {4691, 5691}, {5007, 43619}, {5237, 42133}, {5238, 42134}, {5334, 42964}, {5335, 42965}, {5343, 36968}, {5344, 36967}, {5351, 42104}, {5352, 42105}, {5734, 34628}, {6144, 29181}, {6361, 28168}, {6419, 42276}, {6420, 42275}, {6425, 42272}, {6426, 42271}, {6427, 42226}, {6428, 42225}, {6453, 23249}, {6454, 23259}, {6455, 43788}, {6456, 43787}, {6488, 42638}, {6489, 42637}, {6519, 13886}, {6522, 13939}, {7583, 43519}, {7584, 43520}, {7585, 42266}, {7586, 42267}, {7737, 41940}, {7756, 37665}, {7758, 11148}, {7772, 43618}, {7802, 32878}, {7982, 28150}, {8972, 22644}, {8976, 43560}, {9540, 43507}, {9541, 35815}, {9543, 13665}, {9681, 43342}, {9692, 43786}, {9862, 38627}, {10147, 23251}, {10148, 23261}, {10519, 48879}, {10645, 43364}, {10646, 43365}, {10653, 42934}, {10654, 42935}, {11439, 36987}, {11477, 14927}, {12007, 48905}, {12244, 38626}, {12245, 28190}, {12248, 38631}, {12383, 38632}, {13172, 38628}, {13199, 38629}, {13202, 15020}, {13935, 43508}, {13941, 22615}, {13951, 43561}, {14023, 32479}, {14683, 34584}, {14692, 20094}, {14853, 48896}, {14929, 32880}, {15023, 36518}, {15025, 37853}, {15072, 16625}, {15077, 43691}, {15589, 32888}, {16241, 43477}, {16242, 43478}, {18296, 43713}, {18581, 42928}, {18582, 42929}, {20014, 28212}, {20050, 28232}, {20070, 28160}, {22234, 31670}, {22235, 36969}, {22236, 42141}, {22237, 36970}, {22238, 42140}, {22330, 46264}, {22728, 32523}, {31666, 46934}, {32605, 44788}, {33750, 48895}, {34638, 37714}, {35007, 43448}, {35814, 43884}, {35820, 43512}, {35821, 43511}, {36836, 42109}, {36843, 42108}, {40693, 43022}, {40694, 43023}, {41945, 42538}, {41946, 42537}, {41963, 43380}, {41964, 43381}, {42093, 42686}, {42094, 42687}, {42099, 42161}, {42100, 42160}, {42103, 42954}, {42106, 42955}, {42119, 42165}, {42120, 42164}, {42130, 42689}, {42131, 42688}, {42147, 42803}, {42148, 42804}, {42149, 43012}, {42150, 42430}, {42151, 42429}, {42152, 43013}, {42154, 43769}, {42155, 43770}, {42163, 42685}, {42166, 42684}, {42258, 42522}, {42259, 42523}, {42263, 42414}, {42264, 42413}, {42433, 43404}, {42434, 43403}, {42694, 43545}, {42695, 43544}, {42791, 43201}, {42792, 43202}, {42998, 43632}, {42999, 43633}, {43150, 48873}, {43226, 43467}, {43227, 43468}, {43300, 43636}, {43301, 43637}

X(49140) = reflection of X(i) in X(j) for these {i,j}: {4, 17800}, {20, 5059}, {3146, 3529}, {11541, 3}, {15640, 15683}, {33703, 1657}, {35400, 19710}
X(49140) = anticomplement of X(33703)
X(49140) = anticomplement of the isogonal conjugate of X(44763)
X(49140) = X(44763)-anticomplementary conjugate of X(8)
X(49140) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1657, 20}, {2, 3146, 3627}, {2, 12812, 46936}, {2, 14891, 15708}, {2, 15683, 46333}, {2, 35418, 14891}, {3, 4, 15022}, {3, 5076, 12811}, {3, 11541, 3146}, {3, 12102, 3544}, {3, 12811, 3525}, {3, 15022, 10303}, {4, 20, 10304}, {4, 376, 3526}, {4, 548, 2}, {4, 631, 5066}, {4, 3529, 15704}, {4, 3534, 15717}, {4, 5055, 3832}, {4, 10303, 3091}, {4, 10304, 7486}, {4, 15683, 20}, {4, 15698, 5}, {4, 17800, 15683}, {4, 33699, 17578}, {4, 33703, 15684}, {4, 46333, 548}, {20, 3146, 3091}, {20, 3523, 15697}, {20, 3543, 3523}, {20, 3839, 3522}, {20, 5056, 376}, {20, 15640, 4}, {20, 15682, 46935}, {20, 15692, 550}, {376, 5073, 17578}, {376, 17578, 5056}, {376, 38335, 2}, {382, 549, 4}, {382, 1657, 15689}, {382, 3522, 3839}, {382, 11001, 3522}, {382, 12103, 3090}, {382, 15689, 3850}, {382, 46219, 12101}, {546, 3627, 38335}, {546, 5056, 3091}, {546, 41992, 19709}, {548, 1657, 46333}, {548, 3627, 5072}, {548, 3850, 549}, {548, 15684, 4}, {548, 15706, 21735}, {549, 15704, 12103}, {550, 3832, 15692}, {550, 5076, 3525}, {550, 12811, 3}, {550, 15682, 3832}, {1131, 42260, 9542}, {1657, 3627, 17538}, {1657, 3843, 15686}, {1657, 5073, 15712}, {1657, 15684, 548}, {1657, 33703, 2}, {2043, 2044, 15710}, {3090, 3525, 48154}, {3090, 3529, 11001}, {3090, 3839, 3091}, {3090, 11001, 12103}, {3090, 12103, 3522}, {3091, 3146, 3543}, {3091, 10303, 7486}, {3091, 10304, 10303}, {3146, 3529, 20}, {3146, 5059, 3529}, {3146, 12103, 3839}, {3146, 15704, 10303}, {3522, 11001, 20}, {3522, 17578, 19709}, {3522, 21734, 41982}, {3522, 48154, 15692}, {3524, 3853, 3854}, {3525, 5076, 3832}, {3525, 15682, 5076}, {3526, 5073, 33699}, {3526, 33699, 4}, {3528, 3830, 5068}, {3528, 5068, 15708}, {3529, 11541, 3}, {3529, 15704, 15683}, {3529, 17538, 1657}, {3529, 33703, 17538}, {3534, 15684, 23046}, {3543, 7486, 4}, {3545, 15718, 2}, {3627, 5072, 4}, {3627, 12108, 3843}, {3627, 14893, 5076}, {3627, 15686, 12108}, {3627, 15689, 3090}, {3627, 15704, 548}, {3627, 15712, 546}, {3627, 17538, 2}, {3627, 33703, 3146}, {3628, 15704, 3534}, {3628, 15717, 10303}, {3628, 23046, 5072}, {3830, 3856, 4}, {3832, 11812, 5056}, {3832, 15692, 46935}, {3839, 15708, 47478}, {3843, 15686, 21735}, {3843, 21735, 2}, {3857, 12812, 5072}, {3861, 15688, 3533}, {5055, 46935, 7486}, {5059, 15683, 17800}, {5072, 15684, 3627}, {5072, 15704, 17538}, {5073, 19709, 382}, {5076, 15692, 3091}, {6658, 33272, 33198}, {7486, 10304, 3523}, {8597, 33254, 32980}, {9855, 33279, 439}, {10304, 15640, 3543}, {10304, 15721, 15698}, {11001, 33703, 3850}, {12082, 12086, 38435}, {12085, 12087, 10298}, {12103, 15689, 17538}, {14093, 14890, 15698}, {14893, 48154, 3850}, {15156, 15157, 2071}, {15640, 15683, 10304}, {15640, 15704, 3091}, {15684, 17800, 1657}, {15684, 38335, 33699}, {15684, 46333, 2}, {15702, 45757, 2}, {15704, 17800, 3529}, {17538, 33703, 3627}, {19691, 33193, 32974}, {19696, 33271, 2}, {19709, 41992, 3090}, {32981, 33256, 33210}, {33019, 35927, 33199}, {33703, 46333, 4}, {35732, 42282, 5059}, {47752, 47753, 37948}


X(49141) = X(2)X(47350)∩X(25)X(111)

Barycentrics    a^2*(a^8 - 2*a^6*b^2 - 4*a^4*b^4 + 2*a^2*b^6 + 3*b^8 - 2*a^6*c^2 + 13*a^4*b^2*c^2 - 3*a^2*b^4*c^2 - 12*b^6*c^2 - 4*a^4*c^4 - 3*a^2*b^2*c^4 + 18*b^4*c^4 + 2*a^2*c^6 - 12*b^2*c^6 + 3*c^8) : :

X(49141) lies on on the cubic K1276 and these lines: {2, 47350}, {25, 111}, {542, 1351}, {9777, 14163}, {10602, 35902}


X(49142) = 74TH HATZIPOLAKIS-MOSES-EULER POINT

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

See Antreas Hatzipolakis and Peter Moses euclid 5084.

X(49142) lies on these lines: {2, 3}, {517, 21011}

leftri

Centers related to anti-inner-Yff and anti-outer-Yff triangles: X(49143)-X(49207)

rightri

This preamble and centers X(49143)-X(49207) were contributed by César Eliud Lozada, May 20, 2022.

Anti-inner-Yff and anti-outer-Yff triangles were introduced in the preamble just before X(45345).


X(49143) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 1st ALTINTAS-ISODYNAMIC

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

The reciprocal orthologic center of these triangles is X(4).

X(49143) lies on these lines: {1, 13}, {5, 12932}, {530, 45700}, {531, 49149}, {542, 45728}, {616, 10527}, {618, 26363}, {5473, 11012}, {5478, 26332}, {5617, 26470}, {6268, 26349}, {6270, 26342}, {6669, 10198}, {6734, 12781}, {6770, 12116}, {6771, 10267}, {6778, 13106}, {9916, 26308}, {9982, 26317}, {10680, 13103}, {10902, 21156}, {10943, 12922}, {11249, 22772}, {12142, 26377}, {12205, 26431}, {12472, 45625}, {12473, 45626}, {12793, 26452}, {12942, 26481}, {12952, 26475}, {12990, 45645}, {12991, 45644}, {13076, 26357}, {13917, 45650}, {13982, 45651}, {18544, 48655}, {18974, 26437}, {19049, 49209}, {19050, 49208}, {19073, 26458}, {19074, 26464}, {22796, 45630}, {26399, 48456}, {26423, 48457}, {26517, 49034}, {26522, 49035}, {35753, 45640}, {35754, 45641}, {41022, 48482}, {41023, 49147}, {45526, 48722}, {45527, 48723}

X(49143) = reflection of X(i) in X(j) for these (i, j): (12337, 6771), (12932, 5), (49144, 13)
X(49143) = orthologic center (anti-inner-Yff, T) for these triangles T: 1st Altintas-isodynamic, Bankoff, 3rd Fermat-Dao, 7th Fermat-Dao, 11th Fermat-Dao, 15th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi, 1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi, 1st half-diamonds-central, 1st isodynamic-Dao, 3rd isodynamic-Dao, Largest-circumscribed-equilateral, 1st Lemoine-Dao, outer-Napoleon
X(49143) = X(13)-of-anti-inner-Yff triangle
X(49143) = X(12932)-of-Johnson triangle
X(49143) = X(13107)-of-anti-outer-Yff triangle
X(49143) = X(49144)-of-outer-Yff tangents triangle
X(49143) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (13, 7975, 10062), (13, 13107, 1)


X(49144) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 1st ALTINTAS-ISODYNAMIC

Barycentrics    2*sqrt(3)*(a^4-2*(b^2+c^2)*a^2+2*(b+c)*b*c*a+b^4+c^4-2*(b^2+b*c+c^2)*b*c)*S*a^2+(a+b+c)*(a^7-(b+c)*a^6+10*b*c*a^5-8*(b+c)*b*c*a^4-(3*b^4+3*c^4+2*(b^2-7*b*c+c^2)*b*c)*a^3+(b^2-c^2)*(b-c)*(3*b+c)*(b+3*c)*a^2+2*(b^2-c^2)^2*(b^2-4*b*c+c^2)*a-2*(b^2-c^2)^3*(b-c)) : :

The reciprocal orthologic center of these triangles is X(4).

X(49144) lies on these lines: {1, 13}, {5, 12922}, {119, 5617}, {530, 45701}, {531, 49150}, {542, 45729}, {616, 5552}, {618, 26364}, {1470, 18974}, {2077, 5473}, {5478, 26333}, {6256, 41022}, {6268, 26350}, {6270, 26343}, {6669, 10200}, {6735, 12781}, {6770, 12115}, {6771, 10269}, {6778, 13104}, {9916, 26309}, {9982, 26318}, {10679, 13103}, {10942, 12932}, {11248, 12337}, {12142, 26378}, {12205, 26432}, {12472, 45627}, {12473, 45628}, {12793, 26453}, {12942, 26482}, {12952, 26476}, {12990, 45647}, {12991, 45646}, {13076, 26358}, {13917, 45652}, {13982, 45653}, {16001, 37622}, {18542, 48655}, {19047, 49209}, {19048, 49208}, {19073, 26459}, {19074, 26465}, {21156, 37561}, {22796, 45631}, {26400, 48456}, {26424, 48457}, {26518, 49034}, {26523, 49035}, {35753, 45642}, {35754, 45643}, {36961, 41698}, {41023, 49148}, {45528, 48722}, {45529, 48723}

X(49144) = reflection of X(i) in X(j) for these (i, j): (12922, 5), (22773, 6771), (49143, 13)
X(49144) = orthologic center (anti-outer-Yff, T) for these triangles T: 1st Altintas-isodynamic, Bankoff, 3rd Fermat-Dao, 7th Fermat-Dao, 11th Fermat-Dao, 15th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi, 1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi, 1st half-diamonds-central, 1st isodynamic-Dao, 3rd isodynamic-Dao, Largest-circumscribed-equilateral, 1st Lemoine-Dao, outer-Napoleon
X(49144) = X(13)-of-anti-outer-Yff triangle
X(49144) = X(12922)-of-Johnson triangle
X(49144) = X(13105)-of-anti-inner-Yff triangle
X(49144) = X(49143)-of-inner-Yff tangents triangle
X(49144) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (13, 7975, 10078), (13, 13105, 1)


X(49145) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 2nd ALTINTAS-ISODYNAMIC

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

The reciprocal orthologic center of these triangles is X(4).

X(49145) lies on these lines: {1, 14}, {5, 12931}, {530, 49149}, {531, 45700}, {542, 45728}, {617, 10527}, {619, 26363}, {5474, 11012}, {5479, 26332}, {5613, 26470}, {6269, 26349}, {6271, 26342}, {6670, 10198}, {6734, 12780}, {6773, 12116}, {6774, 10267}, {6777, 13107}, {9915, 26308}, {9981, 26317}, {10680, 13102}, {10902, 21157}, {10943, 12921}, {11249, 22771}, {12141, 26377}, {12204, 26431}, {12470, 45625}, {12471, 45626}, {12792, 26452}, {12941, 26481}, {12951, 26475}, {12988, 45645}, {12989, 45644}, {13075, 26357}, {13916, 45650}, {13981, 45651}, {18544, 48656}, {18975, 26437}, {19049, 49211}, {19050, 49210}, {19075, 26458}, {19076, 26464}, {22797, 45630}, {26399, 48458}, {26423, 48459}, {26517, 49036}, {26522, 49037}, {35850, 45640}, {35851, 45641}, {41022, 49147}, {41023, 48482}, {45526, 48724}, {45527, 48725}

X(49145) = reflection of X(i) in X(j) for these (i, j): (12336, 6774), (12931, 5), (49146, 14)
X(49145) = orthologic center (anti-inner-Yff, T) for these triangles T: 2nd Altintas-isodynamic, 4th Fermat-Dao, 8th Fermat-Dao, 12th Fermat-Dao, 16th Fermat-Dao, 1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi, 3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi, 2nd half-diamonds-central, 2nd isodynamic-Dao, 4th isodynamic-Dao, 2nd Lemoine-Dao, inner-Napoleon
X(49145) = X(14)-of-anti-inner-Yff triangle
X(49145) = X(12931)-of-Johnson triangle
X(49145) = X(13106)-of-anti-outer-Yff triangle
X(49145) = X(49146)-of-outer-Yff tangents triangle
X(49145) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (14, 7974, 10061), (14, 13106, 1)


X(49146) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 2nd ALTINTAS-ISODYNAMIC

Barycentrics    -2*sqrt(3)*(a^4-2*(b^2+c^2)*a^2+2*(b+c)*b*c*a+b^4+c^4-2*(b^2+b*c+c^2)*b*c)*S*a^2+(a+b+c)*(a^7-(b+c)*a^6+10*b*c*a^5-8*(b+c)*b*c*a^4-(3*b^4+3*c^4+2*(b^2-7*b*c+c^2)*b*c)*a^3+(b^2-c^2)*(b-c)*(3*b+c)*(b+3*c)*a^2+2*(b^2-c^2)^2*(b^2-4*b*c+c^2)*a-2*(b^2-c^2)^3*(b-c)) : :

The reciprocal orthologic center of these triangles is X(4).

X(49146) lies on these lines: {1, 14}, {5, 12921}, {119, 5613}, {530, 49150}, {531, 45701}, {542, 45729}, {617, 5552}, {619, 26364}, {1470, 18975}, {2077, 5474}, {5479, 26333}, {6256, 41023}, {6269, 26350}, {6271, 26343}, {6670, 10200}, {6735, 12780}, {6773, 12115}, {6774, 10269}, {6777, 13105}, {9981, 26318}, {10679, 13102}, {10942, 12931}, {11248, 12336}, {12141, 26378}, {12204, 26432}, {12470, 45627}, {12471, 45628}, {12792, 26453}, {12941, 26482}, {12951, 26476}, {12988, 45647}, {12989, 45646}, {13075, 26358}, {13916, 45652}, {13981, 45653}, {16002, 37622}, {18542, 48656}, {19047, 49211}, {19048, 49210}, {19075, 26459}, {19076, 26465}, {21157, 37561}, {22797, 45631}, {26400, 48458}, {26424, 48459}, {26518, 49036}, {26523, 49037}, {35850, 45642}, {35851, 45643}, {36962, 41698}, {41022, 49148}, {45528, 48724}, {45529, 48725}

X(49146) = reflection of X(i) in X(j) for these (i, j): (12921, 5), (22774, 6774), (49145, 14)
X(49146) = orthologic center (anti-outer-Yff, T) for these triangles T: 2nd Altintas-isodynamic, 4th Fermat-Dao, 8th Fermat-Dao, 12th Fermat-Dao, 16th Fermat-Dao, 1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi, 3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi, 2nd half-diamonds-central, 2nd isodynamic-Dao, 4th isodynamic-Dao, 2nd Lemoine-Dao, inner-Napoleon
X(49146) = X(14)-of-anti-outer-Yff triangle
X(49146) = X(12921)-of-Johnson triangle
X(49146) = X(13104)-of-anti-inner-Yff triangle
X(49146) = X(49145)-of-inner-Yff tangents triangle
X(49146) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (14, 7974, 10077), (14, 13104, 1)


X(49147) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 1st ANTI-BROCARD

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

The reciprocal orthologic center of these triangles is X(5999).

X(49147) lies on the circumcircle of anti-inner-Yff triangle and these lines: {1, 98}, {5, 12183}, {30, 49149}, {58, 946}, {99, 11012}, {114, 26363}, {115, 26332}, {147, 10527}, {542, 45700}, {690, 49151}, {2782, 11249}, {2783, 48713}, {2784, 10916}, {2787, 48694}, {2794, 48482}, {2799, 49153}, {3023, 26437}, {3027, 26357}, {5984, 10529}, {6033, 26470}, {6036, 10198}, {6226, 26349}, {6227, 26342}, {6734, 9864}, {7983, 37625}, {8980, 45650}, {9861, 26308}, {9862, 12116}, {10267, 12042}, {10532, 14651}, {10680, 12188}, {10902, 34473}, {10943, 12182}, {11177, 11240}, {12131, 26377}, {12176, 26431}, {12179, 45625}, {12180, 45626}, {12181, 26452}, {12184, 26481}, {12185, 26475}, {12186, 45645}, {12187, 45644}, {12382, 22265}, {12704, 24469}, {13188, 35252}, {13190, 38664}, {13967, 45651}, {18544, 38744}, {19049, 49213}, {19050, 49212}, {19055, 26458}, {19056, 26464}, {22505, 45630}, {26399, 48462}, {26423, 48463}, {26517, 49040}, {26522, 49041}, {35824, 45640}, {35825, 45641}, {41022, 49145}, {41023, 49143}, {45526, 48726}, {45527, 48727}, {45728, 49166}

X(49147) = reflection of X(i) in X(j) for these (i, j): (12178, 12042), (12183, 5), (49148, 98), (49201, 11249)
X(49147) = orthologic center (anti-inner-Yff, T) for these triangles T: 1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard
X(49147) = X(98)-of-anti-inner-Yff triangle
X(49147) = X(12183)-of-Johnson triangle
X(49147) = X(12190)-of-anti-outer-Yff triangle
X(49147) = X(49148)-of-outer-Yff tangents triangle
X(49147) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (98, 7970, 10053), (98, 12190, 1)


X(49148) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 1st ANTI-BROCARD

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

The reciprocal orthologic center of these triangles is X(5999).

X(49148) lies on the circumcircle of anti-outer-Yff triangle and these lines: {1, 98}, {5, 12182}, {30, 49150}, {99, 2077}, {114, 26364}, {115, 26333}, {119, 6033}, {147, 5552}, {542, 45701}, {690, 49152}, {1470, 3023}, {2782, 11248}, {2783, 25438}, {2784, 10915}, {2787, 48695}, {2791, 49207}, {2794, 6256}, {2799, 49154}, {3027, 26358}, {5554, 5985}, {5984, 10528}, {6036, 10200}, {6226, 26350}, {6227, 26343}, {6735, 9864}, {8980, 45652}, {9861, 26309}, {9862, 12115}, {10086, 38498}, {10269, 12042}, {10531, 14651}, {10679, 12188}, {10722, 41698}, {10768, 39692}, {10942, 12183}, {11177, 11239}, {12131, 26378}, {12176, 26432}, {12179, 45627}, {12180, 45628}, {12181, 26453}, {12184, 26482}, {12185, 26476}, {12186, 45647}, {12187, 45646}, {12381, 22265}, {13188, 35251}, {13189, 38664}, {13967, 45653}, {18542, 38744}, {19047, 49213}, {19048, 49212}, {19055, 26459}, {19056, 26465}, {22505, 45631}, {26400, 48462}, {26424, 48463}, {26518, 49040}, {26523, 49041}, {34473, 37561}, {35824, 45642}, {35825, 45643}, {41022, 49146}, {41023, 49144}, {45528, 48726}, {45529, 48727}, {45729, 49167}

X(49148) = reflection of X(i) in X(j) for these (i, j): (12182, 5), (22504, 12042), (49147, 98), (49202, 11248)
X(49148) = orthologic center (anti-outer-Yff, T) for these triangles T: 1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard
X(49148) = X(98)-of-anti-outer-Yff triangle
X(49148) = X(12182)-of-Johnson triangle
X(49148) = X(12189)-of-anti-inner-Yff triangle
X(49148) = X(49147)-of-inner-Yff tangents triangle
X(49148) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (98, 7970, 10069), (98, 12189, 1)


X(49149) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO ANTI-MCCAY

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

The reciprocal orthologic center of these triangles is X(9855).

X(49149) lies on these lines: {1, 671}, {5, 12349}, {30, 49147}, {148, 11240}, {530, 49145}, {531, 49143}, {542, 48482}, {543, 45700}, {2482, 26363}, {2782, 49166}, {2796, 10916}, {5461, 10198}, {5969, 49187}, {6734, 9881}, {8591, 10527}, {8596, 10529}, {8724, 26470}, {9830, 45728}, {9876, 26308}, {9878, 26317}, {9880, 26332}, {9882, 26342}, {9883, 26349}, {10267, 12326}, {10680, 12355}, {10943, 12348}, {11012, 12117}, {11249, 22565}, {12116, 12243}, {12132, 26377}, {12191, 26431}, {12345, 45625}, {12346, 45626}, {12347, 26452}, {12350, 26481}, {12351, 26475}, {12352, 45645}, {12353, 45644}, {12354, 26357}, {13908, 45650}, {13968, 45651}, {18544, 48657}, {18969, 26437}, {19049, 49215}, {19050, 49214}, {19057, 26458}, {19058, 26464}, {22566, 45630}, {26399, 48470}, {26423, 48471}, {26517, 49042}, {26522, 49043}, {35698, 45640}, {35699, 45641}, {45526, 48728}, {45527, 48729}

X(49149) = reflection of X(i) in X(j) for these (i, j): (12326, 49102), (12349, 5), (49150, 671), (49201, 45700)
X(49149) = orthologic center (anti-inner-Yff, T) for these triangles T: anti-McCay, McCay, Moses-Steiner osculatory
X(49149) = X(671)-of-anti-inner-Yff triangle
X(49149) = X(12349)-of-Johnson triangle
X(49149) = X(12357)-of-anti-outer-Yff triangle
X(49149) = X(49150)-of-outer-Yff tangents triangle
X(49149) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (671, 9884, 10054), (671, 12357, 1)


X(49150) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO ANTI-MCCAY

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

The reciprocal orthologic center of these triangles is X(9855).

X(49150) lies on these lines: {1, 671}, {5, 12348}, {30, 49148}, {119, 8724}, {148, 11239}, {530, 49146}, {531, 49144}, {542, 6256}, {543, 45701}, {1470, 18969}, {2077, 12117}, {2482, 26364}, {2782, 49167}, {2796, 10915}, {5461, 10200}, {5552, 8591}, {5969, 49188}, {6735, 9881}, {8596, 10528}, {9830, 45729}, {9876, 26309}, {9878, 26318}, {9880, 26333}, {9882, 26343}, {9883, 26350}, {10269, 22565}, {10679, 12355}, {10942, 12349}, {11248, 12326}, {12115, 12243}, {12132, 26378}, {12191, 26432}, {12345, 45627}, {12346, 45628}, {12347, 26453}, {12350, 26482}, {12351, 26476}, {12352, 45647}, {12353, 45646}, {12354, 26358}, {13908, 45652}, {13968, 45653}, {18542, 48657}, {19047, 49215}, {19048, 49214}, {19057, 26459}, {19058, 26465}, {22566, 45631}, {26400, 48470}, {26424, 48471}, {26518, 49042}, {26523, 49043}, {35698, 45642}, {35699, 45643}, {45528, 48728}, {45529, 48729}

X(49150) = reflection of X(i) in X(j) for these (i, j): (12348, 5), (22565, 49102), (49149, 671), (49202, 45701)
X(49150) = orthologic center (anti-outer-Yff, T) for these triangles T: anti-McCay, McCay, Moses-Steiner osculatory
X(49150) = X(671)-of-anti-outer-Yff triangle
X(49150) = X(12348)-of-Johnson triangle
X(49150) = X(12356)-of-anti-inner-Yff triangle
X(49150) = X(49149)-of-inner-Yff tangents triangle
X(49150) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (671, 9884, 10070), (671, 12356, 1)


X(49151) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*(a^11-(b+c)*a^10-2*(b^2-b*c+c^2)*a^9+2*(b^2-c^2)*(b-c)*a^8-(2*b^4+2*c^4+b*c*(4*b^2-13*b*c+4*c^2))*a^7+(b+c)*(2*b^4+2*c^4+b*c*(3*b-2*c)*(2*b-3*c))*a^6+(8*b^4+8*c^4+b*c*(16*b^2+11*b*c+16*c^2))*(b-c)^2*a^5-(b+c)*(8*b^6+8*c^6-(6*b^4+6*c^4+b*c*(13*b^2-24*b*c+13*c^2))*b*c)*a^4-(7*b^6+7*c^6+2*(5*b^4+5*c^4+b*c*(9*b^2+16*b*c+9*c^2))*b*c)*(b-c)^2*a^3+(b^2-c^2)*(b-c)*(7*b^6+7*c^6-2*b^2*c^2*(b^2-6*b*c+c^2))*a^2+(b^4-c^4)*(b^2-c^2)*(2*b^4+2*c^4-b*c*(2*b^2-9*b*c+2*c^2))*a-(b^2-c^2)^3*(b-c)*(2*b^4+2*c^4-b*c*(2*b-c)*(b-2*c))) : :

The reciprocal orthologic center of these triangles is X(12112).

X(49151) lies on the circumcircle of anti-inner-Yff triangle and these lines: {1, 74}, {5, 12372}, {30, 49159}, {102, 110}, {113, 26363}, {125, 26332}, {146, 10527}, {399, 35252}, {541, 45700}, {542, 49201}, {690, 49147}, {1503, 49199}, {1539, 45630}, {2771, 48713}, {2777, 48482}, {2778, 12262}, {2781, 45728}, {3024, 26437}, {3028, 26357}, {5663, 11249}, {6699, 10198}, {6734, 12368}, {7725, 26342}, {7726, 26349}, {7728, 26470}, {7984, 37625}, {8674, 48694}, {8994, 45650}, {9517, 49153}, {9919, 26308}, {9984, 26317}, {10117, 13095}, {10267, 12041}, {10620, 10680}, {10628, 49191}, {10902, 15055}, {10943, 12371}, {12116, 12244}, {12133, 26377}, {12192, 26431}, {12365, 45625}, {12366, 45626}, {12369, 26452}, {12373, 26481}, {12374, 26475}, {12377, 45645}, {12378, 45644}, {12704, 33535}, {12906, 20127}, {13218, 15054}, {13969, 45651}, {15021, 34486}, {15041, 16202}, {17702, 49161}, {18544, 38790}, {19049, 49217}, {19050, 49216}, {19059, 26458}, {19060, 26464}, {26399, 48472}, {26423, 48473}, {26517, 49044}, {26522, 49045}, {32247, 39903}, {35826, 45640}, {35827, 45641}, {43806, 43862}, {45526, 48730}, {45527, 48731}

X(49151) = reflection of X(i) in X(j) for these (i, j): (12327, 12041), (12372, 5), (49152, 74), (49203, 11249)
X(49151) = orthologic center (anti-inner-Yff, T) for these triangles T: anti-orthocentroidal, orthocentroidal
X(49151) = X(74)-of-anti-inner-Yff triangle
X(49151) = X(12372)-of-Johnson triangle
X(49151) = X(12382)-of-anti-outer-Yff triangle
X(49151) = X(49152)-of-outer-Yff tangents triangle
X(49151) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (74, 7978, 10065), (74, 12382, 1)


X(49152) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*(a^11-(b+c)*a^10-2*(b^2-b*c+c^2)*a^9+2*(b+c)*(b^2+c^2)*a^8-(2*b^2-c^2)*(b^2-2*c^2)*a^7+(b+c)*(2*b^4+2*c^4-b*c*(b+2*c)*(2*b+c))*a^6+(8*b^4+8*c^4+(4*b^2-5*b*c+4*c^2)*b*c)*(b-c)^2*a^5-(b+c)*(8*b^6+8*c^6-(6*b^4+6*c^4+b*c*(5*b^2-4*b*c+5*c^2))*b*c)*a^4-(7*b^6+7*c^6-2*(b^4+c^4+b*c*(7*b^2+6*b*c+7*c^2))*b*c)*(b-c)^2*a^3+(b^2-c^2)*(b-c)*(7*b^6+7*c^6+2*(4*b^4+4*c^4+b*c*(3*b^2+4*b*c+3*c^2))*b*c)*a^2+(2*b^6+2*c^6-(6*b^4+6*c^4-b*c*(3*b^2-16*b*c+3*c^2))*b*c)*(b^2-c^2)^2*a-(b^2-c^2)^3*(b-c)*(2*b^4+2*c^4+b*c*(b+2*c)*(2*b+c))) : :

The reciprocal orthologic center of these triangles is X(12112).

X(49152) lies on the circumcircle of anti-outer-Yff triangle and these lines: {1, 74}, {5, 12371}, {30, 49160}, {110, 2077}, {113, 26364}, {119, 7728}, {125, 26333}, {146, 5552}, {399, 35251}, {541, 45701}, {542, 49202}, {690, 49148}, {1470, 3024}, {1503, 49200}, {1539, 45631}, {2771, 25438}, {2777, 6256}, {2778, 37562}, {2779, 13217}, {2781, 45729}, {3028, 26358}, {5663, 11248}, {6699, 10200}, {6735, 12368}, {7725, 26343}, {7726, 26350}, {8674, 48695}, {8994, 45652}, {9517, 49154}, {9919, 26309}, {9984, 26318}, {10088, 38497}, {10117, 13094}, {10269, 12041}, {10620, 10679}, {10628, 49192}, {10721, 41698}, {10767, 39692}, {10942, 12372}, {12115, 12244}, {12133, 26378}, {12192, 26432}, {12365, 45627}, {12366, 45628}, {12369, 26453}, {12373, 26482}, {12374, 26476}, {12377, 45647}, {12378, 45646}, {12703, 33535}, {12905, 20127}, {13969, 45653}, {15041, 16203}, {15055, 37561}, {17702, 49162}, {18542, 38790}, {19047, 49217}, {19048, 49216}, {19059, 26459}, {19060, 26465}, {26400, 48472}, {26424, 48473}, {26518, 49044}, {26523, 49045}, {32247, 39902}, {35826, 45642}, {35827, 45643}, {43806, 43861}, {45528, 48730}, {45529, 48731}

X(49152) = reflection of X(i) in X(j) for these (i, j): (12371, 5), (22583, 12041), (49151, 74), (49204, 11248)
X(49152) = orthologic center (anti-outer-Yff, T) for these triangles T: anti-orthocentroidal, orthocentroidal
X(49152) = X(74)-of-anti-outer-Yff triangle
X(49152) = X(12371)-of-Johnson triangle
X(49152) = X(12381)-of-anti-inner-Yff triangle
X(49152) = X(49151)-of-inner-Yff tangents triangle
X(49152) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (74, 7978, 10081), (74, 12381, 1)


X(49153) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*(a^15-(b+c)*a^14-2*(b^2-b*c+c^2)*a^13+2*(b^2-c^2)*(b-c)*a^12+(b^4+c^4-(4*b^2-7*b*c+4*c^2)*b*c)*a^11-(b^3+c^3)*(b^2-5*b*c+c^2)*a^10-(2*b^4+2*c^4+(b+2*c)*(2*b+c)*b*c)*(b-c)^2*a^9+(b+c)*(2*b^6+2*c^6-(2*b^4+2*c^4-(3*b^2-8*b*c+3*c^2)*b*c)*b*c)*a^8+(3*b^6+3*c^6+(6*b^4+6*c^4+(7*b^2+6*b*c+7*c^2)*b*c)*b*c)*(b-c)^2*a^7-(b^2-c^2)*(b-c)*(3*b^6+3*c^6+(2*b^2+3*b*c+2*c^2)*(b-c)^2*b*c)*a^6+2*(b+c)*(b^2-c^2)*(b^2-b*c+c^2)^2*(b^3-c^3)*a^5-2*(b^2-c^2)^2*(b+c)*(b^6+c^6+(2*b^2-b*c+2*c^2)*b^2*c^2)*a^4-(b^4-c^4)*(b^2-c^2)*(5*b^6+5*c^6-2*(2*b^2+b*c+2*c^2)*(b^2-3*b*c+c^2)*b*c)*a^3+(b^4-c^4)*(b^2-c^2)*(b+c)*(5*b^6+5*c^6-2*(5*b^4+5*c^4-(5*b^2-3*b*c+5*c^2)*b*c)*b*c)*a^2+(b^4-c^4)*(b^2-c^2)*(2*b^8+2*c^8-(2*b^6+2*c^6-(7*b^4+7*c^4-2*(b^2-3*b*c+c^2)*b*c)*b*c)*b*c)*a-(b^2-c^2)^3*(b-c)*(2*b^8+2*c^8-(b^2+c^2)*(2*b^4+2*c^4-3*(b^2+c^2)*b*c)*b*c)) : :

The reciprocal orthologic center of these triangles is X(19158).

X(49153) lies on the circumcircle of anti-inner-Yff triangle and these lines: {1, 1297}, {5, 12935}, {112, 11012}, {127, 26332}, {132, 26363}, {2781, 49203}, {2794, 49201}, {2799, 49147}, {2806, 48694}, {2831, 48713}, {3320, 26357}, {6020, 26437}, {6734, 12784}, {9517, 49151}, {9530, 45700}, {10198, 34841}, {10267, 12340}, {10527, 12384}, {10680, 13115}, {10705, 37625}, {10902, 38717}, {10943, 12925}, {11249, 19159}, {12116, 12253}, {12145, 26377}, {12207, 26431}, {12413, 26308}, {12478, 45625}, {12479, 45626}, {12503, 26317}, {12796, 26452}, {12805, 26342}, {12806, 26349}, {12918, 26470}, {12945, 26481}, {12955, 26475}, {12996, 45645}, {12997, 45644}, {13310, 35252}, {13314, 38689}, {13918, 45650}, {13985, 45651}, {18544, 48658}, {19049, 49219}, {19050, 49218}, {19093, 26458}, {19094, 26464}, {19160, 45630}, {26399, 48474}, {26423, 48475}, {26517, 49046}, {26522, 49047}, {35828, 45640}, {35829, 45641}, {45526, 48732}, {45527, 48733}

X(49153) = reflection of X(i) in X(j) for these (i, j): (12340, 38624), (12935, 5), (49154, 1297), (49205, 11249)
X(49153) = orthologic center (anti-inner-Yff, T) for these triangles T: 1st anti-orthosymmedial, 1st orthosymmedial
X(49153) = X(1297)-of-anti-inner-Yff triangle
X(49153) = X(12935)-of-Johnson triangle
X(49153) = X(13119)-of-anti-outer-Yff triangle
X(49153) = X(49154)-of-outer-Yff tangents triangle
X(49153) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1297, 13099, 13116), (1297, 13119, 1)


X(49154) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*(a^15-(b+c)*a^14-2*(b^2-b*c+c^2)*a^13+2*(b+c)*(b^2+c^2)*a^12+(b^4-b^2*c^2+c^4)*a^11-(b^3+c^3)*(b^2+3*b*c+c^2)*a^10-(2*b^4+2*c^4+b*c*(6*b^2+5*b*c+6*c^2))*(b-c)^2*a^9+(b+c)*(b^2+c^2)*(2*b^4+2*c^4+b*c*(2*b^2-7*b*c+2*c^2))*a^8+(3*b^6+3*c^6-(2*b^4+2*c^4+3*b*c*(3*b^2+2*b*c+3*c^2))*b*c)*(b-c)^2*a^7-(b^2-c^2)*(b-c)*(3*b^6+3*c^6+(2*b^4+2*c^4-b*c*(b-c)^2)*b*c)*a^6+2*(b^2-c^2)^2*(b^6+c^6+b*c*(3*b^2+5*b*c+3*c^2)*(b^2-b*c+c^2))*a^5-2*(b^2-c^2)^2*(b+c)*(b^6+c^6+(2*b^4+2*c^4+b*c*(2*b^2+b*c+2*c^2))*b*c)*a^4-(b^2-c^2)^2*(5*b^8+5*c^8-(8*b^6+8*c^6-(7*b^4+7*c^4-2*b*c*(7*b^2-6*b*c+7*c^2))*b*c)*b*c)*a^3+(b^6-c^6)*(b^2-c^2)*(b+c)*(5*b^4+5*c^4-2*(b^2-b*c+c^2)*b*c)*a^2+(2*b^10+2*c^10-(6*b^8+6*c^8-(b^6+c^6-(8*b^4+8*c^4-5*b*c*(b^2-4*b*c+c^2))*b*c)*b*c)*b*c)*(b^2-c^2)^2*a-(b^2-c^2)^3*(b-c)*(2*b^8+2*c^8+(b^2+c^2)*(2*b^4+2*c^4+3*(b^2+c^2)*b*c)*b*c)) : :

The reciprocal orthologic center of these triangles is X(19158).

X(49154) lies on the circumcircle of anti-outer-Yff triangle and these lines: {1, 1297}, {5, 12925}, {112, 2077}, {119, 12918}, {127, 26333}, {132, 26364}, {1470, 6020}, {2781, 49204}, {2794, 49202}, {2799, 49148}, {2806, 48695}, {2831, 25438}, {3320, 26358}, {5552, 12384}, {6735, 12784}, {9517, 49152}, {9530, 45701}, {10200, 34841}, {10269, 19159}, {10679, 13115}, {10942, 12935}, {11248, 12340}, {12115, 12253}, {12145, 26378}, {12207, 26432}, {12413, 26309}, {12478, 45627}, {12479, 45628}, {12503, 26318}, {12796, 26453}, {12805, 26343}, {12806, 26350}, {12945, 26482}, {12955, 26476}, {12996, 45647}, {12997, 45646}, {13310, 35251}, {13311, 38519}, {13313, 38689}, {13918, 45652}, {13985, 45653}, {18542, 48658}, {19047, 49219}, {19048, 49218}, {19093, 26459}, {19094, 26465}, {19160, 45631}, {26400, 48474}, {26424, 48475}, {26518, 49046}, {26523, 49047}, {35828, 45642}, {35829, 45643}, {37561, 38717}, {41698, 44988}, {45528, 48732}, {45529, 48733}

X(49154) = reflection of X(i) in X(j) for these (i, j): (12925, 5), (19159, 38624), (49153, 1297), (49206, 11248)
X(49154) = orthologic center (anti-outer-Yff, T) for these triangles T: 1st anti-orthosymmedial, 1st orthosymmedial
X(49154) = X(1297)-of-anti-outer-Yff triangle
X(49154) = X(12925)-of-Johnson triangle
X(49154) = X(13118)-of-anti-inner-Yff triangle
X(49154) = X(49153)-of-inner-Yff tangents triangle
X(49154) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1297, 13099, 13117), (1297, 13118, 1)


X(49155) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 3rd ANTI-TRI-SQUARES

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

The reciprocal orthologic center of these triangles is X(486).

X(49155) lies on these lines: {1, 486}, {4, 26522}, {5, 12938}, {30, 49197}, {487, 10527}, {642, 26363}, {3564, 10943}, {6119, 10198}, {6251, 26332}, {6280, 26349}, {6281, 26342}, {6290, 26470}, {6734, 12787}, {9921, 26308}, {9986, 26317}, {10267, 12343}, {10529, 12221}, {10680, 12601}, {11012, 12123}, {11249, 22595}, {12116, 12256}, {12147, 26377}, {12210, 26431}, {12484, 45625}, {12485, 45626}, {12799, 26452}, {12948, 26481}, {12958, 26475}, {13002, 45645}, {13003, 45644}, {13081, 26357}, {13135, 22591}, {13881, 44645}, {13921, 45650}, {13933, 45651}, {18544, 48659}, {18989, 26437}, {19049, 44648}, {19050, 49220}, {19104, 26458}, {19105, 26464}, {22596, 45630}, {26399, 48478}, {26423, 48479}, {26517, 49048}, {26524, 42561}, {32419, 45700}, {35830, 45640}, {35833, 45641}, {37726, 45422}, {45526, 48734}

X(49155) = reflection of X(i) in X(j) for these (i, j): (12343, 49103), (12938, 5), (49156, 486)
X(49155) = orthologic center (anti-inner-Yff, T) for these triangles T: 3rd anti-tri-squares, 2nd half-squares, 4th tri-squares, inner-Vecten
X(49155) = X(486)-of-anti-inner-Yff triangle
X(49155) = X(12938)-of-Johnson triangle
X(49155) = X(13133)-of-anti-outer-Yff triangle
X(49155) = X(49156)-of-outer-Yff tangents triangle
X(49155) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (486, 7980, 10067), (486, 13133, 1), (10943, 45728, 49157)


X(49156) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 3rd ANTI-TRI-SQUARES

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

The reciprocal orthologic center of these triangles is X(486).

X(49156) lies on these lines: {1, 486}, {4, 26523}, {5, 12928}, {30, 49198}, {119, 6290}, {487, 5552}, {642, 26364}, {1470, 18989}, {2077, 12123}, {3564, 10942}, {6119, 10200}, {6251, 26333}, {6280, 26350}, {6281, 26343}, {6735, 12787}, {9921, 26309}, {9986, 26318}, {10269, 22595}, {10528, 12221}, {10679, 12601}, {11248, 12343}, {12115, 12256}, {12147, 26378}, {12210, 26432}, {12484, 45627}, {12485, 45628}, {12799, 26453}, {12948, 26482}, {12958, 26476}, {13002, 45647}, {13003, 45646}, {13081, 26358}, {13134, 22591}, {13881, 44643}, {13921, 45652}, {13933, 45653}, {18542, 48659}, {19047, 44648}, {19048, 49220}, {19104, 26459}, {19105, 26465}, {22596, 45631}, {26400, 48478}, {26424, 48479}, {26518, 49048}, {26525, 42561}, {32419, 45701}, {35830, 45642}, {35833, 45643}, {45528, 48734}

X(49156) = reflection of X(i) in X(j) for these (i, j): (12928, 5), (22595, 49103), (49155, 486)
X(49156) = orthologic center (anti-outer-Yff, T) for these triangles T: 3rd anti-tri-squares, 2nd half-squares, 4th tri-squares, inner-Vecten
X(49156) = X(486)-of-anti-outer-Yff triangle
X(49156) = X(12928)-of-Johnson triangle
X(49156) = X(13132)-of-anti-inner-Yff triangle
X(49156) = X(49155)-of-inner-Yff tangents triangle
X(49156) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (486, 7980, 10083), (486, 13132, 1), (10942, 45729, 49158)


X(49157) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 4th ANTI-TRI-SQUARES

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

The reciprocal orthologic center of these triangles is X(485).

X(49157) lies on these lines: {1, 485}, {4, 26517}, {5, 12939}, {30, 49195}, {488, 10527}, {641, 26363}, {3564, 10943}, {6118, 10198}, {6250, 26332}, {6278, 26349}, {6279, 26342}, {6289, 26470}, {6734, 12788}, {9922, 26308}, {9987, 26317}, {10267, 12344}, {10529, 12222}, {10680, 12602}, {11012, 12124}, {11249, 22624}, {12116, 12257}, {12148, 26377}, {12211, 26431}, {12486, 45625}, {12487, 45626}, {12800, 26452}, {12949, 26481}, {12959, 26475}, {13004, 45645}, {13005, 45644}, {13082, 26357}, {13133, 22592}, {13879, 45650}, {13880, 45651}, {13881, 44646}, {18544, 48660}, {18988, 26437}, {19049, 49221}, {19050, 44647}, {19102, 26458}, {19103, 26464}, {22625, 45630}, {26399, 48480}, {26423, 48481}, {26519, 31412}, {26522, 49049}, {31484, 45715}, {32421, 45700}, {35831, 45641}, {35832, 45640}, {37726, 45423}, {45527, 48735}

X(49157) = reflection of X(i) in X(j) for these (i, j): (12344, 49104), (12939, 5), (49158, 485)
X(49157) = orthologic center (anti-inner-Yff, T) for these triangles T: 4th anti-tri-squares, 1st half-squares, 3rd tri-squares, outer-Vecten
X(49157) = X(485)-of-anti-inner-Yff triangle
X(49157) = X(12939)-of-Johnson triangle
X(49157) = X(13135)-of-anti-outer-Yff triangle
X(49157) = X(49158)-of-outer-Yff tangents triangle
X(49157) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (485, 7981, 10068), (485, 13135, 1), (10943, 45728, 49155)


X(49158) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 4th ANTI-TRI-SQUARES

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

The reciprocal orthologic center of these triangles is X(485).

X(49158) lies on these lines: {1, 485}, {4, 26518}, {5, 12929}, {30, 49196}, {119, 6289}, {488, 5552}, {641, 26364}, {1470, 18988}, {2077, 12124}, {3564, 10942}, {6118, 10200}, {6250, 26333}, {6278, 26350}, {6279, 26343}, {6735, 12788}, {9922, 26309}, {9987, 26318}, {10269, 22624}, {10528, 12222}, {10679, 12602}, {11248, 12344}, {12115, 12257}, {12148, 26378}, {12211, 26432}, {12486, 45627}, {12487, 45628}, {12800, 26453}, {12949, 26482}, {12959, 26476}, {13004, 45647}, {13005, 45646}, {13082, 26358}, {13132, 22592}, {13879, 45652}, {13880, 45653}, {13881, 44644}, {18542, 48660}, {19047, 49221}, {19048, 44647}, {19102, 26459}, {19103, 26465}, {22625, 45631}, {26400, 48480}, {26424, 48481}, {26520, 31412}, {26523, 49049}, {32421, 45701}, {35831, 45643}, {35832, 45642}, {45529, 48735}

X(49158) = reflection of X(i) in X(j) for these (i, j): (12929, 5), (22624, 49104), (49157, 485)
X(49158) = orthologic center (anti-outer-Yff, T) for these triangles T: 4th anti-tri-squares, 1st half-squares, 3rd tri-squares, outer-Vecten
X(49158) = X(485)-of-anti-outer-Yff triangle
X(49158) = X(12929)-of-Johnson triangle
X(49158) = X(13134)-of-anti-inner-Yff triangle
X(49158) = X(49157)-of-inner-Yff tangents triangle
X(49158) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (485, 7981, 10084), (485, 13134, 1), (10942, 45729, 49156)


X(49159) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO AAOA

Barycentrics    a^13-(b+c)*a^12-(3*b^2+2*b*c+3*c^2)*a^11+3*(b+c)*(b^2+c^2)*a^10+(3*b^4+3*c^4+b*c*(4*b^2+3*b*c+4*c^2))*a^9-3*(b^3+c^3)*(b^2+b*c+c^2)*a^8-2*(b^6+5*b^3*c^3+c^6)*a^7+2*(b+c)*(b^6+c^6-(b^2-c^2)^2*b*c)*a^6+(3*b^8+3*c^8-(4*b^6+4*c^6-(b^4+c^4+2*b*c*(3*b^2-4*b*c+3*c^2))*b*c)*b*c)*a^5-(b^2-c^2)^2*(b+c)*(3*b^4+3*c^4-b*c*(6*b^2-7*b*c+6*c^2))*a^4-(b^4-c^4)*(b^2-c^2)*(3*b^4+3*c^4-2*(b^2-b*c+c^2)*b*c)*a^3+(b^2-c^2)^3*(b-c)*(3*b^4+2*b^2*c^2+3*c^4)*a^2+(b^4-c^4)^2*(b^2-c^2)^2*a-(b^2-c^2)^5*(b-c)*(b^2+c^2) : :

The reciprocal orthologic center of these triangles is X(7574).

X(49159) lies on these lines: {1, 265}, {5, 12890}, {30, 49151}, {110, 26470}, {113, 45630}, {125, 10267}, {399, 18544}, {511, 49199}, {542, 45728}, {952, 13214}, {1511, 26363}, {2771, 7728}, {2777, 49185}, {3448, 12116}, {5663, 48482}, {6734, 12778}, {10088, 26481}, {10091, 26475}, {10113, 26332}, {10198, 20304}, {10527, 12383}, {10628, 49179}, {10680, 12902}, {10733, 12382}, {10778, 13218}, {10902, 15061}, {10943, 12889}, {11012, 12121}, {11249, 17702}, {12140, 26377}, {12201, 26431}, {12412, 26308}, {12466, 45625}, {12467, 45626}, {12501, 26317}, {12790, 26452}, {12803, 26342}, {12804, 26349}, {12894, 45645}, {12895, 45644}, {12896, 26357}, {13915, 45650}, {13979, 45651}, {15027, 34486}, {16202, 38724}, {18968, 26437}, {19049, 49223}, {19050, 49222}, {19051, 26458}, {19052, 26464}, {26399, 48483}, {26423, 48484}, {26517, 49050}, {26522, 49051}, {35834, 45640}, {35835, 45641}, {45526, 48736}, {45527, 48737}

X(49159) = reflection of X(i) in X(j) for these (i, j): (12334, 125), (12890, 5), (49160, 265), (49203, 10943)
X(49159) = orthologic center (anti-inner-Yff, T) for these triangles T: antiAOA, AOA, 1st Hyacinth
X(49159) = X(265)-of-anti-inner-Yff triangle
X(49159) = X(12890)-of-Johnson triangle
X(49159) = X(12906)-of-anti-outer-Yff triangle
X(49159) = X(49160)-of-outer-Yff tangents triangle
X(49159) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (265, 12898, 12903), (265, 12906, 1)


X(49160) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO AAOA

Barycentrics    a^13-(b+c)*a^12-3*(b-c)^2*a^11+(b+c)*(3*b^2-4*b*c+3*c^2)*a^10+(3*b^4+3*c^4-b*c*(12*b^2-11*b*c+12*c^2))*a^9-(b^3+c^3)*(3*b^2-5*b*c+3*c^2)*a^8-2*(b^6+c^6-(2*b^4+2*c^4-b*c*(4*b^2-11*b*c+4*c^2))*b*c)*a^7+2*(b^2-c^2)*(b-c)*(b^4+c^4+b*c*(b^2+5*b*c+c^2))*a^6+(3*b^8+3*c^8-(7*b^4+7*c^4+2*b*c*(3*b^2-8*b*c+3*c^2))*b^2*c^2)*a^5-(b^2-c^2)*(b-c)*(3*b^6+3*c^6+2*(4*b^4+4*c^4+b*c*(3*b^2-b*c+3*c^2))*b*c)*a^4-(b^2-c^2)^2*(3*b^6+3*c^6-(6*b^4+6*c^4+b*c*(3*b^2-4*b*c+3*c^2))*b*c)*a^3+(b^2-c^2)^4*(b+c)*(3*b^2-2*b*c+3*c^2)*a^2+(b^4-c^4)*(b^2-c^2)^3*(b^2-4*b*c+c^2)*a-(b^2-c^2)^5*(b-c)*(b^2+c^2) : :

The reciprocal orthologic center of these triangles is X(7574).

X(49160) lies on these lines: {1, 265}, {5, 12889}, {30, 49152}, {110, 119}, {113, 45631}, {125, 10269}, {399, 18542}, {511, 49200}, {542, 45729}, {952, 13213}, {1470, 18968}, {1511, 26364}, {2077, 12121}, {2771, 12751}, {2777, 49186}, {3448, 12115}, {5552, 12383}, {5663, 6256}, {6735, 12778}, {7728, 41698}, {10088, 26482}, {10091, 26476}, {10113, 26333}, {10200, 20304}, {10628, 49180}, {10679, 12902}, {10733, 12381}, {10942, 12890}, {11248, 12334}, {12140, 26378}, {12201, 26432}, {12412, 26309}, {12466, 45627}, {12467, 45628}, {12501, 26318}, {12790, 26453}, {12803, 26343}, {12804, 26350}, {12894, 45647}, {12895, 45646}, {12896, 26358}, {13915, 45652}, {13979, 45653}, {15061, 37561}, {16203, 38724}, {19047, 49223}, {19048, 49222}, {19051, 26459}, {19052, 26465}, {26400, 48483}, {26424, 48484}, {26518, 49050}, {26523, 49051}, {35834, 45642}, {35835, 45643}, {45528, 48736}, {45529, 48737}

X(49160) = reflection of X(i) in X(j) for these (i, j): (12889, 5), (19478, 125), (49159, 265), (49204, 10942)
X(49160) = orthologic center (anti-outer-Yff, T) for these triangles T: antiAOA, AOA, 1st Hyacinth
X(49160) = X(265)-of-anti-outer-Yff triangle
X(49160) = X(12889)-of-Johnson triangle
X(49160) = X(12905)-of-anti-inner-Yff triangle
X(49160) = X(49159)-of-inner-Yff tangents triangle
X(49160) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (265, 12898, 12904), (265, 12905, 1)


X(49161) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO ARIES

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

The reciprocal orthologic center of these triangles is X(9833).

X(49161) lies on these lines: {1, 68}, {4, 912}, {5, 12423}, {30, 49185}, {155, 26470}, {539, 45700}, {1069, 26475}, {1147, 26363}, {1154, 49179}, {3157, 26481}, {3564, 10943}, {5449, 10198}, {6193, 10527}, {6734, 9928}, {9908, 26308}, {9923, 26317}, {9927, 26332}, {9929, 26342}, {9930, 26349}, {10267, 12328}, {10680, 12429}, {11012, 12118}, {11249, 22659}, {11411, 12116}, {12134, 26377}, {12164, 18544}, {12193, 26431}, {12415, 45625}, {12416, 45626}, {12418, 26452}, {12426, 45645}, {12427, 45644}, {12428, 26357}, {13754, 48482}, {13909, 45650}, {13970, 45651}, {14984, 49199}, {17702, 49151}, {18970, 26437}, {19049, 49225}, {19050, 49224}, {19061, 26458}, {19062, 26464}, {22660, 45630}, {26399, 48485}, {26423, 48486}, {26517, 49052}, {26522, 49053}, {35836, 45640}, {35837, 45641}, {45526, 48738}, {45527, 48739}

X(49161) = reflection of X(i) in X(j) for these (i, j): (12328, 12359), (12423, 5), (49162, 68)
X(49161) = orthologic center (anti-inner-Yff, T) for these triangles T: Aries, 2nd Hyacinth
X(49161) = X(68)-of-anti-inner-Yff triangle
X(49161) = X(12423)-of-Johnson triangle
X(49161) = X(12431)-of-anti-outer-Yff triangle
X(49161) = X(49162)-of-outer-Yff tangents triangle
X(49161) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (68, 9933, 10055), (68, 12431, 1)


X(49162) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO ARIES

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

The reciprocal orthologic center of these triangles is X(9833).

X(49162) lies on these lines: {1, 68}, {5, 12422}, {8, 912}, {30, 49186}, {119, 155}, {539, 45701}, {1069, 26476}, {1147, 26364}, {1154, 49180}, {1470, 18970}, {2077, 12118}, {3157, 26482}, {3564, 10942}, {5449, 10200}, {5552, 6193}, {6256, 13754}, {6735, 9928}, {9908, 26309}, {9923, 26318}, {9927, 26333}, {9929, 26343}, {9930, 26350}, {10269, 12359}, {10679, 12429}, {11248, 12328}, {12134, 26378}, {12164, 18542}, {12193, 26432}, {12415, 45627}, {12416, 45628}, {12418, 26453}, {12426, 45647}, {12427, 45646}, {12428, 26358}, {13909, 45652}, {13970, 45653}, {14984, 49200}, {17702, 49152}, {19047, 49225}, {19048, 49224}, {19061, 26459}, {19062, 26465}, {22660, 45631}, {26400, 48485}, {26424, 48486}, {26518, 49052}, {26523, 49053}, {35836, 45642}, {35837, 45643}, {45528, 48738}, {45529, 48739}

X(49162) = reflection of X(i) in X(j) for these (i, j): (12422, 5), (22659, 12359), (49161, 68)
X(49162) = orthologic center (anti-outer-Yff, T) for these triangles T: Aries, 2nd Hyacinth
X(49162) = X(68)-of-anti-outer-Yff triangle
X(49162) = X(12422)-of-Johnson triangle
X(49162) = X(12430)-of-anti-inner-Yff triangle
X(49162) = X(49161)-of-inner-Yff tangents triangle
X(49162) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (68, 9933, 10071), (68, 12430, 1)


X(49163) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO BEVAN ANTIPODAL

Barycentrics    a*(a^6-(3*b^2+2*b*c+3*c^2)*a^4+8*(b+c)*b*c*a^3+(3*b^4-14*b^2*c^2+3*c^4)*a^2-8*(b^2-c^2)*(b-c)*b*c*a-(b^2-c^2)^2*(b-c)^2) : :
X(49163) = 5*X(40)-X(6766) = 3*X(165)-2*X(11249) = 3*X(3158)-X(7971) = 3*X(3158)-2*X(37700) = 3*X(3576)-4*X(26285) = 3*X(4421)-2*X(37837) = 3*X(5587)-2*X(10525) = 5*X(5709)-2*X(6766) = 3*X(16200)-4*X(46920) = 4*X(26286)-5*X(35242)

The reciprocal orthologic center of these triangles is X(1).

X(49163) lies on these lines: {1, 3}, {4, 6735}, {5, 1706}, {8, 7330}, {9, 5690}, {10, 6893}, {20, 12648}, {30, 12686}, {34, 24028}, {63, 12245}, {84, 952}, {90, 41684}, {104, 36846}, {119, 12699}, {200, 5887}, {355, 12705}, {452, 5554}, {515, 12640}, {516, 6256}, {519, 1158}, {912, 6765}, {944, 3895}, {946, 6944}, {962, 1519}, {1012, 10914}, {1376, 45776}, {1702, 26465}, {1703, 26459}, {1709, 5881}, {1750, 18518}, {1753, 1877}, {1766, 4266}, {1768, 3633}, {1836, 26482}, {1872, 7713}, {1902, 26378}, {2057, 5687}, {2800, 3811}, {2802, 48695}, {2829, 32049}, {3158, 7971}, {3243, 24475}, {3306, 10595}, {3358, 5853}, {3560, 9623}, {3646, 11231}, {3656, 17564}, {3868, 13278}, {3871, 18446}, {3872, 6906}, {3880, 12114}, {3885, 6909}, {3913, 5534}, {3929, 34718}, {4301, 6970}, {4421, 37837}, {4853, 22758}, {5084, 5250}, {5123, 10893}, {5252, 11826}, {5437, 5901}, {5541, 5691}, {5587, 10525}, {5603, 17567}, {5758, 10528}, {5762, 32213}, {5763, 28212}, {5795, 6930}, {5812, 10942}, {5836, 11496}, {5844, 6762}, {5847, 49165}, {6261, 8715}, {6361, 12115}, {6684, 10200}, {6705, 21627}, {6827, 10624}, {6842, 31434}, {6850, 31397}, {6882, 9614}, {6891, 12053}, {6916, 16004}, {6923, 9578}, {6926, 9785}, {6927, 27385}, {6928, 9580}, {6948, 10106}, {6961, 44675}, {7160, 37424}, {7681, 37828}, {7966, 9841}, {7995, 40263}, {9911, 26309}, {10483, 12749}, {10526, 41698}, {10573, 30223}, {10860, 18481}, {10864, 28204}, {11239, 34632}, {11372, 18480}, {11523, 14988}, {12197, 26432}, {12497, 26318}, {12608, 28194}, {12679, 37725}, {12688, 18528}, {12696, 26453}, {12697, 26343}, {12698, 26350}, {12701, 26476}, {12775, 39776}, {13912, 45652}, {13975, 45653}, {14217, 39692}, {15952, 18163}, {17527, 26446}, {17857, 48696}, {18542, 48661}, {19047, 49227}, {19048, 49226}, {22793, 45631}, {22841, 45647}, {22842, 45646}, {26492, 37704}, {26518, 49054}, {26523, 49055}, {28234, 40256}, {31436, 37401}, {34918, 37290}, {35610, 45642}, {35611, 45643}, {45528, 48740}, {45529, 48741}

X(49163) = midpoint of X(i) and X(j) for these {i, j}: {84, 2136}, {5758, 20070}, {6769, 7991}
X(49163) = reflection of X(i) in X(j) for these (i, j): (1, 11248), (5534, 3913), (5709, 40), (6256, 10915), (6261, 8715), (6762, 24467), (7971, 37700), (8158, 37623), (12700, 5), (21627, 6705), (22770, 3579), (37531, 10306), (41869, 10526)
X(49163) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(3359)}} and {{A, B, C, X(9), X(37561)}}
X(49163) = orthologic center (anti-outer-Yff, T) for these triangles T: Bevan antipodal, 3rd extouch
X(49163) = X(40)-of-anti-outer-Yff triangle
X(49163) = X(5709)-of-inner-Yff tangents triangle
X(49163) = X(11248)-of-Aquila triangle
X(49163) = X(12084)-of-excentral triangle, when ABC is acute
X(49163) = X(12700)-of-Johnson triangle
X(49163) = X(12703)-of-anti-inner-Yff triangle
X(49163) = X(15761)-of-6th mixtilinear triangle, when ABC is acute
X(49163) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 40, 3359), (1, 3359, 37534), (1, 10270, 10269), (1, 15803, 5193), (1, 21164, 16203), (3, 1482, 24928), (3, 12702, 31798), (3, 23340, 1), (3, 24474, 1467), (40, 1697, 3), (40, 7982, 46), (40, 12703, 1), (40, 12704, 484), (40, 31393, 37560), (40, 37569, 37550), (65, 26358, 1), (484, 11531, 12704), (1470, 3057, 1), (3295, 31788, 18443), (3579, 10269, 10270), (5687, 41389, 2057), (7991, 11010, 40), (10202, 12000, 1), (10679, 37562, 1), (10965, 18838, 1), (10965, 37567, 18838), (25413, 37533, 3340), (31393, 37560, 1385), (34339, 37622, 1), (37526, 37556, 10246), (37585, 40294, 1)


X(49164) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 9th BROCARD

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

The reciprocal orthologic center of these triangles is X(4).

X(49164) lies on these lines: {1, 6776}, {5, 39890}, {6, 26332}, {69, 11012}, {182, 10198}, {542, 45700}, {1352, 26363}, {1503, 45728}, {3564, 11249}, {5709, 5847}, {5848, 48694}, {5921, 10527}, {6261, 9028}, {6734, 39885}, {10267, 39877}, {10532, 14912}, {10680, 39899}, {10902, 25406}, {10943, 39889}, {11898, 35252}, {12116, 39874}, {12382, 32234}, {18440, 26470}, {18544, 48662}, {19049, 49229}, {19050, 49228}, {19145, 45650}, {19146, 45651}, {26308, 39879}, {26317, 39882}, {26342, 39887}, {26349, 39888}, {26357, 39897}, {26377, 39871}, {26399, 48489}, {26423, 48490}, {26431, 39872}, {26437, 39873}, {26452, 39886}, {26458, 39875}, {26464, 39876}, {26475, 39892}, {26481, 39891}, {26517, 49056}, {26522, 49057}, {39880, 45625}, {39881, 45626}, {39884, 45630}, {39893, 45640}, {39894, 45641}, {39895, 45645}, {39896, 45644}, {45526, 48742}, {45527, 48743}

X(49164) = reflection of X(i) in X(j) for these (i, j): (39877, 48906), (39890, 5), (48482, 45728), (49165, 6776)
X(49164) = orthologic center (anti-inner-Yff, 9th Brocard)
X(49164) = X(6776)-of-anti-inner-Yff triangle
X(49164) = X(39890)-of-Johnson triangle
X(49164) = X(39903)-of-anti-outer-Yff triangle
X(49164) = X(49165)-of-outer-Yff tangents triangle
X(49164) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6776, 39898, 39900), (6776, 39903, 1)


X(49165) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 9th BROCARD

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

The reciprocal orthologic center of these triangles is X(4).

X(49165) lies on these lines: {1, 6776}, {5, 39889}, {6, 26333}, {69, 2077}, {119, 18440}, {182, 10200}, {542, 45701}, {1352, 26364}, {1470, 39873}, {1503, 6256}, {3564, 11248}, {5552, 5921}, {5847, 49163}, {5848, 48695}, {6735, 39885}, {10269, 39883}, {10531, 14912}, {10679, 39899}, {10942, 39890}, {11898, 35251}, {12115, 39874}, {12381, 32234}, {18542, 48662}, {19047, 49229}, {19048, 49228}, {19145, 45652}, {19146, 45653}, {25406, 37561}, {26309, 39879}, {26318, 39882}, {26343, 39887}, {26350, 39888}, {26358, 39897}, {26378, 39871}, {26400, 48489}, {26424, 48490}, {26432, 39872}, {26453, 39886}, {26459, 39875}, {26465, 39876}, {26476, 39892}, {26482, 39891}, {26518, 49056}, {26523, 49057}, {39880, 45627}, {39881, 45628}, {39884, 45631}, {39893, 45642}, {39894, 45643}, {39895, 45647}, {39896, 45646}, {45528, 48742}, {45529, 48743}

X(49165) = reflection of X(i) in X(j) for these (i, j): (6256, 45729), (39883, 48906), (39889, 5), (49164, 6776)
X(49165) = orthologic center (anti-outer-Yff, 9th Brocard)
X(49165) = X(6776)-of-anti-outer-Yff triangle
X(49165) = X(39889)-of-Johnson triangle
X(49165) = X(39902)-of-anti-inner-Yff triangle
X(49165) = X(49164)-of-inner-Yff tangents triangle
X(49165) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6776, 39898, 39901), (6776, 39902, 1)


X(49166) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 1st BROCARD-REFLECTED

Barycentrics    (2*b^4+2*c^4-b*c*(6*b^2-5*b*c+6*c^2))*a^7-(b+c)*(2*b^4+2*c^4-b*c*(6*b^2-5*b*c+6*c^2))*a^6-(4*b^6+4*c^6-(6*b^4+6*c^4-b*c*(17*b^2-6*b*c+17*c^2))*b*c)*a^5+(b+c)*(4*b^6+4*c^6-(10*b^4+10*c^4-b*c*(17*b^2-16*b*c+17*c^2))*b*c)*a^4+(2*b^6+2*c^6+(4*b^4+4*c^4+b*c*(5*b^2+12*b*c+5*c^2))*b*c)*(b-c)^2*a^3-(b^2-c^2)*(b-c)*(2*b^6+2*c^6-b^2*c^2*(3*b^2-4*b*c+3*c^2))*a^2+(b^4-c^4)*(b^2-c^2)*b^2*c^2*a-(b^2-c^2)^3*(b-c)*b^2*c^2 : :
X(49166) = 4*X(10943)-X(49187)

The reciprocal orthologic center of these triangles is X(3).

X(49166) lies on these lines: {1, 262}, {5, 22704}, {511, 45700}, {2782, 49149}, {3095, 37726}, {6194, 10527}, {6734, 22697}, {7697, 26470}, {7709, 12116}, {7786, 34486}, {7976, 49176}, {10267, 22556}, {10529, 44434}, {10680, 22728}, {10943, 12923}, {11012, 22676}, {11249, 22680}, {15819, 26363}, {18543, 32519}, {18544, 48663}, {18971, 26437}, {19049, 49231}, {19050, 49230}, {19063, 26458}, {19064, 26464}, {22480, 26377}, {22521, 26431}, {22655, 26308}, {22668, 45625}, {22672, 45626}, {22678, 26317}, {22681, 45630}, {22682, 26332}, {22698, 26452}, {22699, 26342}, {22700, 26349}, {22705, 26481}, {22706, 26475}, {22709, 45645}, {22710, 45644}, {22711, 26357}, {22720, 45650}, {22721, 45651}, {26399, 48491}, {26423, 48492}, {26517, 49058}, {26522, 49059}, {35838, 45640}, {35839, 45641}, {45526, 48744}, {45527, 48745}, {45728, 49147}

X(49166) = reflection of X(i) in X(j) for these (i, j): (22556, 40108), (22704, 5), (49167, 262)
X(49166) = orthologic center (anti-inner-Yff, 1st Brocard-reflected)
X(49166) = X(262)-of-anti-inner-Yff triangle
X(49166) = X(22704)-of-Johnson triangle
X(49166) = X(22732)-of-anti-outer-Yff triangle
X(49166) = X(49167)-of-outer-Yff tangents triangle
X(49166) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (262, 22713, 22729), (262, 22732, 1)


X(49167) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 1st BROCARD-REFLECTED

Barycentrics    (2*b^4+2*c^4+(6*b^2+5*b*c+6*c^2)*b*c)*a^7-(b+c)*(2*b^4+2*c^4+(6*b^2+5*b*c+6*c^2)*b*c)*a^6-(4*b^6+4*c^6-(2*b^4+2*c^4+7*(b+c)^2*b*c)*b*c)*a^5+(b+c)*(4*b^6+4*c^6+(2*b^4+2*c^4-(7*b^2+4*b*c+7*c^2)*b*c)*b*c)*a^4+(2*b^6+2*c^6-(4*b^4+4*c^4+b*c*(11*b^2+16*b*c+11*c^2))*b*c)*(b-c)^2*a^3-(b^2-c^2)*(b-c)*(2*b^6+2*c^6-b^2*c^2*(3*b^2+8*b*c+3*c^2))*a^2+(b^2-c^2)^2*(b^2-4*b*c+c^2)*b^2*c^2*a-(b^2-c^2)^3*(b-c)*b^2*c^2 : :
X(49167) = 4*X(10942)-X(49188)

The reciprocal orthologic center of these triangles is X(3).

X(49167) lies on these lines: {1, 262}, {5, 22703}, {119, 7697}, {511, 45701}, {1470, 18971}, {2077, 22676}, {2782, 49150}, {5552, 6194}, {6735, 22697}, {7709, 12115}, {10269, 22680}, {10528, 44434}, {10679, 22728}, {10942, 12933}, {11248, 12339}, {14881, 37622}, {15819, 26364}, {18542, 48663}, {18545, 32519}, {19047, 49231}, {19048, 49230}, {19063, 26459}, {19064, 26465}, {22480, 26378}, {22521, 26432}, {22655, 26309}, {22668, 45627}, {22672, 45628}, {22678, 26318}, {22681, 45631}, {22682, 26333}, {22698, 26453}, {22699, 26343}, {22700, 26350}, {22705, 26482}, {22706, 26476}, {22709, 45647}, {22710, 45646}, {22711, 26358}, {22720, 45652}, {22721, 45653}, {26400, 48491}, {26424, 48492}, {26518, 49058}, {26523, 49059}, {35838, 45642}, {35839, 45643}, {45528, 48744}, {45529, 48745}, {45729, 49148}

X(49167) = reflection of X(i) in X(j) for these (i, j): (22680, 40108), (22703, 5), (49166, 262)
X(49167) = orthologic center (anti-outer-Yff, 1st Brocard-reflected)
X(49167) = X(262)-of-anti-outer-Yff triangle
X(49167) = X(22703)-of-Johnson triangle
X(49167) = X(22731)-of-anti-inner-Yff triangle
X(49167) = X(49166)-of-inner-Yff tangents triangle
X(49167) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (262, 22713, 22730), (262, 22731, 1)


X(49168) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO EXCENTERS-MIDPOINTS

Barycentrics    a^4-2*(b+c)*a^3+2*(b^3+c^3)*a-(b^2-c^2)^2 : :
X(49168) = 2*X(1)-3*X(45700) = 3*X(8)+X(6764) = 4*X(10)-3*X(45701) = X(145)-3*X(34625) = 5*X(3617)-3*X(34619) = 3*X(3679)-X(6765) = 3*X(3679)-2*X(10915) = 2*X(3811)-3*X(45701) = 3*X(4677)+X(11519) = 2*X(6764)+3*X(49169) = 4*X(10916)-3*X(45700) = 2*X(22837)-3*X(34625)

The reciprocal orthologic center of these triangles is X(10).

X(49168) lies on these lines: {1, 2}, {3, 44669}, {4, 758}, {5, 12635}, {11, 5730}, {20, 1768}, {40, 12625}, {57, 17647}, {63, 10572}, {65, 3419}, {69, 17861}, {72, 1837}, {80, 3436}, {100, 36152}, {142, 17706}, {158, 5081}, {191, 6872}, {214, 7288}, {218, 40997}, {226, 12559}, {281, 2323}, {329, 4067}, {355, 518}, {377, 5902}, {382, 17768}, {388, 3874}, {405, 21677}, {443, 5883}, {496, 5289}, {497, 3878}, {515, 5709}, {517, 48482}, {524, 13408}, {527, 31673}, {528, 12702}, {529, 18525}, {540, 48877}, {674, 31778}, {740, 45131}, {908, 10826}, {912, 6256}, {942, 5794}, {944, 6876}, {946, 6866}, {950, 12514}, {952, 11249}, {956, 10950}, {958, 37730}, {960, 5722}, {966, 25081}, {986, 48837}, {993, 3486}, {1001, 12433}, {1056, 3881}, {1058, 3884}, {1145, 11510}, {1329, 3940}, {1478, 3868}, {1479, 3869}, {1482, 3813}, {1512, 17857}, {1788, 25440}, {1836, 4018}, {1936, 32853}, {2098, 26475}, {2099, 24390}, {2271, 21965}, {2321, 8557}, {2342, 38955}, {2476, 34195}, {2478, 5692}, {2550, 3754}, {2551, 3678}, {2771, 16127}, {2801, 12667}, {2802, 6903}, {2949, 6987}, {3057, 45634}, {3176, 15499}, {3189, 5657}, {3193, 13746}, {3218, 4299}, {3254, 43734}, {3336, 4190}, {3434, 5903}, {3485, 25639}, {3487, 3822}, {3488, 5248}, {3555, 5252}, {3583, 11415}, {3585, 3901}, {3586, 12526}, {3647, 11111}, {3649, 17532}, {3694, 8609}, {3817, 5804}, {3829, 4930}, {3833, 17582}, {3841, 28629}, {3893, 36920}, {3894, 5270}, {3899, 4857}, {3913, 5690}, {4084, 4295}, {4208, 18221}, {4253, 24247}, {4297, 5768}, {4305, 5267}, {4313, 5775}, {4361, 16608}, {4848, 37550}, {4863, 10914}, {4867, 7741}, {4880, 10483}, {5082, 12432}, {5084, 10176}, {5119, 41709}, {5177, 11263}, {5187, 37718}, {5204, 10609}, {5221, 11112}, {5288, 37706}, {5295, 42708}, {5440, 24914}, {5450, 5770}, {5535, 6934}, {5538, 6890}, {5587, 10599}, {5603, 6873}, {5687, 37579}, {5694, 6929}, {5715, 19925}, {5735, 5850}, {5738, 18698}, {5790, 12607}, {5818, 25568}, {5836, 45654}, {5844, 10912}, {5846, 45728}, {5851, 48664}, {5853, 11362}, {5854, 19914}, {5880, 31794}, {5881, 6762}, {5884, 6850}, {5887, 26333}, {6326, 6834}, {6361, 34744}, {6600, 16202}, {6684, 12437}, {6826, 31870}, {6827, 31806}, {6857, 35016}, {6863, 37733}, {6871, 16126}, {6891, 10265}, {6893, 20117}, {6897, 15016}, {6900, 10532}, {6910, 37571}, {6916, 45084}, {6923, 49193}, {6925, 15071}, {6931, 15079}, {6933, 37701}, {7469, 47321}, {7951, 41696}, {7982, 24392}, {7991, 45648}, {8148, 13463}, {8275, 10936}, {8668, 25438}, {9578, 41863}, {9581, 21616}, {9799, 28164}, {9955, 34647}, {10268, 43174}, {10404, 24473}, {10522, 41686}, {10525, 14988}, {10543, 16370}, {10585, 17057}, {10591, 11813}, {10680, 12645}, {10944, 26437}, {11010, 20075}, {11114, 11684}, {11194, 34773}, {11235, 22791}, {11236, 18357}, {11260, 37727}, {11278, 34640}, {11520, 13407}, {11529, 12609}, {11682, 30384}, {12135, 26377}, {12195, 26431}, {12410, 26308}, {12435, 45656}, {12454, 45625}, {12455, 45626}, {12495, 26317}, {12531, 13279}, {12563, 45039}, {12616, 37531}, {12626, 26452}, {12627, 26342}, {12628, 26349}, {12636, 45645}, {12637, 45644}, {12640, 49183}, {12690, 12953}, {12699, 44663}, {13464, 24386}, {13750, 16465}, {13911, 45650}, {13973, 45651}, {14798, 48696}, {14839, 49187}, {15733, 31788}, {15829, 36922}, {15934, 25466}, {16418, 18253}, {17151, 22464}, {17362, 21933}, {17559, 45085}, {17614, 17728}, {17770, 48878}, {18492, 28609}, {18526, 35252}, {19049, 49233}, {19050, 49232}, {19065, 26458}, {19066, 26464}, {21627, 28234}, {22021, 26063}, {24299, 26446}, {24929, 26066}, {26399, 48493}, {26423, 48494}, {26517, 49060}, {26522, 49061}, {28646, 33697}, {31435, 37723}, {31458, 37724}, {34688, 34700}, {34701, 35242}, {35842, 45640}, {35843, 45641}, {36977, 37707}, {37229, 41574}, {37721, 41229}, {39585, 40950}, {45526, 48746}, {45527, 48747}

X(49168) = midpoint of X(i) and X(j) for these {i, j}: {40, 12625}, {3632, 12629}, {5881, 6762}
X(49168) = reflection of X(i) in X(j) for these (i, j): (1, 10916), (145, 22837), (944, 8666), (1482, 3813), (3189, 8715), (3811, 10), (3913, 5690), (4930, 3829), (6765, 10915), (8148, 13463), (11523, 21077), (12437, 6684), (12635, 5), (37531, 12616), (37727, 11260), (49169, 8)
X(49168) = anticomplement of X(22836)
X(49168) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(34772)}} and {{A, B, C, X(78), X(6598)}}
X(49168) = X(i)-beth conjugate of-X(j) for these (i, j): (8, 3811), (643, 36152)
X(49168) = orthologic center (anti-inner-Yff, T) for these triangles T: excenters-midpoints, Garcia-reflection, 2nd Schiffler
X(49168) = X(8)-of-anti-inner-Yff triangle
X(49168) = X(3811)-of-outer-Garcia triangle
X(49168) = X(5730)-of-inner-Johnson triangle
X(49168) = X(10916)-of-Aquila triangle
X(49168) = X(12635)-of-Johnson triangle
X(49168) = X(12649)-of-anti-outer-Yff triangle
X(49168) = X(18383)-of-2nd Conway triangle, when ABC is acute
X(49168) = X(40285)-of-intouch triangle, when ABC is acute
X(49168) = X(41725)-of-excentral triangle, when ABC is acute
X(49168) = X(49169)-of-outer-Yff tangents triangle
X(49168) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 10, 10198), (1, 3679, 24987), (1, 5705, 1125), (1, 6734, 26363), (1, 10916, 45700), (8, 145, 12647), (8, 5554, 3679), (8, 12649, 1), (8, 18391, 10), (10, 3244, 13405), (10, 3625, 6743), (10, 3811, 45701), (10, 30143, 2), (78, 1737, 26364), (80, 5904, 3436), (145, 10527, 1), (145, 34625, 22837), (355, 24474, 26332), (944, 24477, 8666), (997, 1210, 10200), (1210, 6737, 997), (3189, 5657, 8715), (3585, 3901, 5905), (3617, 19855, 10), (3632, 41684, 8), (3679, 6765, 10915), (3868, 5086, 1478), (5692, 37702, 2478), (5902, 47033, 377), (6734, 41575, 1)


X(49169) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO EXCENTERS-MIDPOINTS

Barycentrics    a^4-2*(b+c)*a^3+8*b*c*a^2+2*(b+c)*(b^2-3*b*c+c^2)*a-(b^2-c^2)^2 : :
X(49169) = 2*X(1)-3*X(45701) = 5*X(8)-X(6764) = 4*X(10)-3*X(45700) = X(145)-3*X(34619) = 5*X(3617)-3*X(34625) = 3*X(3679)-2*X(10916) = 3*X(3679)-X(12629) = 5*X(4668)-X(11519) = 2*X(6764)-5*X(49168) = 4*X(10915)-3*X(45701) = 2*X(22836)-3*X(34619)

The reciprocal orthologic center of these triangles is X(10).

X(49169) lies on these lines: {1, 2}, {3, 32157}, {4, 2802}, {5, 10912}, {36, 36977}, {40, 37002}, {55, 36972}, {56, 1145}, {65, 44784}, {80, 10043}, {119, 1482}, {355, 3880}, {381, 13463}, {405, 45081}, {484, 20076}, {515, 12640}, {517, 6256}, {518, 37562}, {528, 18525}, {529, 12702}, {535, 6361}, {758, 12115}, {908, 30323}, {942, 45637}, {944, 2077}, {952, 3913}, {962, 41698}, {999, 8256}, {1000, 2551}, {1056, 3754}, {1320, 11681}, {1470, 5687}, {1478, 14923}, {1479, 3885}, {1519, 7982}, {1788, 5193}, {1837, 17622}, {2098, 17757}, {2099, 26482}, {2136, 5881}, {3057, 41389}, {3359, 11362}, {3419, 3893}, {3421, 3878}, {3434, 37710}, {3436, 5697}, {3476, 25440}, {3486, 25439}, {3555, 18838}, {3680, 5587}, {3813, 5790}, {3816, 33559}, {3894, 10940}, {3895, 10572}, {3897, 31452}, {3898, 5084}, {3956, 45085}, {3968, 17582}, {4345, 5828}, {4421, 34773}, {4865, 34029}, {5123, 11373}, {5252, 10914}, {5288, 14803}, {5440, 37738}, {5499, 32213}, {5559, 5692}, {5657, 8666}, {5690, 10269}, {5730, 10958}, {5818, 24387}, {5836, 45655}, {5844, 10942}, {5846, 45729}, {5853, 47745}, {5886, 33895}, {5903, 10052}, {6264, 10785}, {6702, 47743}, {6705, 12437}, {6872, 37563}, {6924, 22560}, {6929, 10284}, {6931, 16173}, {6958, 12737}, {6961, 11715}, {7354, 13996}, {7741, 41702}, {7962, 21616}, {7991, 45649}, {8148, 18542}, {8275, 10935}, {8668, 22758}, {9709, 22754}, {9955, 34640}, {10270, 43174}, {10591, 21630}, {10679, 12645}, {10786, 11014}, {10950, 26358}, {11037, 33815}, {11235, 18357}, {11236, 22791}, {11256, 12619}, {11260, 24927}, {11278, 34647}, {11499, 48713}, {12000, 42843}, {12135, 26378}, {12195, 26432}, {12410, 26309}, {12435, 45629}, {12454, 45627}, {12455, 45628}, {12495, 26318}, {12531, 13278}, {12608, 28234}, {12626, 26453}, {12627, 26343}, {12628, 26350}, {12636, 45647}, {12637, 45646}, {12773, 32198}, {13911, 45652}, {13973, 45653}, {14839, 49188}, {17647, 37709}, {17765, 23693}, {18519, 27870}, {18526, 35251}, {19047, 49233}, {19048, 49232}, {19065, 26459}, {19066, 26465}, {19582, 21290}, {19914, 20418}, {20323, 37829}, {24391, 37534}, {24928, 37828}, {25466, 40587}, {26400, 48493}, {26424, 48494}, {26518, 49060}, {26523, 49061}, {33956, 37727}, {34716, 35242}, {34717, 34741}, {35842, 45642}, {35843, 45643}, {37707, 48696}, {41540, 41863}, {45528, 48746}, {45529, 48747}

X(49169) = midpoint of X(i) and X(j) for these {i, j}: {2136, 5881}, {3632, 6765}, {12641, 12751}
X(49169) = reflection of X(i) in X(j) for these (i, j): (1, 10915), (145, 22836), (355, 32537), (944, 8715), (1482, 12607), (7982, 21077), (10912, 5), (11256, 12619), (12513, 5690), (12629, 10916), (12773, 32198), (47746, 33895), (49168, 8)
X(49169) = anticomplement of X(22837)
X(49169) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(38460)}} and {{A, B, C, X(78), X(12641)}}
X(49169) = orthologic center (anti-outer-Yff, T) for these triangles T: excenters-midpoints, Garcia-reflection, 2nd Schiffler
X(49169) = X(8)-of-anti-outer-Yff triangle
X(49169) = X(10912)-of-Johnson triangle
X(49169) = X(10915)-of-Aquila triangle
X(49169) = X(12648)-of-anti-inner-Yff triangle
X(49169) = X(13463)-of-anti-Ehrmann-mid triangle
X(49169) = X(36983)-of-4th Euler triangle, when ABC is acute
X(49169) = X(49168)-of-inner-Yff tangents triangle
X(49169) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 10, 10200), (1, 2057, 997), (1, 3679, 24982), (1, 6735, 26364), (1, 10915, 45701), (8, 145, 10573), (8, 12648, 1), (8, 12649, 41684), (145, 5552, 1), (145, 34619, 22836), (355, 23340, 26333), (1000, 2551, 3884), (3633, 41684, 12649), (3679, 8583, 10), (3679, 12629, 10916), (3872, 10039, 26363), (3885, 5176, 1479), (3913, 11248, 25438), (5886, 47746, 33895)


X(49170) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO EXTOUCH

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

The reciprocal orthologic center of these triangles is X(40).

X(49170) lies on these lines: {1, 84}, {3, 49183}, {5, 12677}, {9, 37837}, {56, 12664}, {515, 5709}, {946, 45654}, {958, 9942}, {971, 11249}, {993, 6261}, {1158, 4297}, {1490, 11012}, {1728, 22775}, {2829, 10864}, {2975, 9960}, {3333, 5715}, {3358, 5450}, {3359, 17647}, {3427, 3600}, {3428, 12671}, {4293, 37550}, {4298, 6245}, {5019, 8557}, {5705, 18242}, {6223, 10527}, {6257, 26349}, {6258, 26342}, {6259, 26470}, {6260, 26363}, {6705, 10198}, {6734, 12667}, {8987, 45650}, {9841, 10268}, {9910, 26308}, {10267, 12330}, {10309, 10529}, {10396, 22753}, {10680, 12684}, {10943, 12676}, {12116, 12246}, {12136, 26377}, {12196, 26431}, {12456, 45625}, {12457, 45626}, {12496, 26317}, {12608, 18540}, {12616, 37534}, {12650, 37625}, {12668, 26452}, {12678, 26481}, {12679, 26475}, {12680, 26357}, {12688, 26437}, {13974, 45651}, {14647, 24987}, {18245, 45645}, {18246, 45644}, {18544, 48664}, {19049, 49235}, {19050, 49234}, {19067, 26458}, {19068, 26464}, {21370, 44075}, {22792, 45630}, {26399, 48495}, {26423, 48496}, {26517, 49062}, {26522, 49063}, {35844, 45640}, {35845, 45641}, {45526, 48748}, {45527, 48749}

X(49170) = reflection of X(i) in X(j) for these (i, j): (12330, 34862), (12677, 5), (49171, 84)
X(49170) = orthologic center (anti-inner-Yff, T) for these triangles T: extouch, 1st Zaniah
X(49170) = X(84)-of-anti-inner-Yff triangle
X(49170) = X(12664)-of-2nd circumperp tangential triangle
X(49170) = X(12677)-of-Johnson triangle
X(49170) = X(12687)-of-anti-outer-Yff triangle
X(49170) = X(49171)-of-outer-Yff tangents triangle
X(49170) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (84, 7971, 1709), (84, 12687, 1)


X(49171) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO EXTOUCH

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

The reciprocal orthologic center of these triangles is X(40).

X(49171) lies on these lines: {1, 84}, {2, 10309}, {5, 12676}, {9, 10270}, {10, 1158}, {40, 1145}, {46, 41698}, {57, 7681}, {78, 12666}, {90, 1768}, {100, 34256}, {119, 6259}, {142, 3358}, {214, 6261}, {442, 7701}, {515, 12640}, {517, 15347}, {946, 45655}, {971, 6600}, {1470, 12688}, {1490, 2077}, {1519, 3086}, {1728, 15239}, {2057, 10310}, {2092, 3330}, {4640, 49183}, {4855, 48697}, {5552, 6223}, {6245, 26333}, {6257, 26350}, {6258, 26343}, {6260, 26364}, {6594, 6796}, {6735, 12667}, {8583, 37561}, {8987, 45652}, {9841, 37837}, {9910, 26309}, {10269, 18237}, {10427, 18243}, {10679, 12631}, {10860, 11500}, {10864, 12703}, {10942, 12677}, {11509, 12664}, {12115, 12246}, {12136, 26378}, {12196, 26432}, {12456, 45627}, {12457, 45628}, {12496, 26318}, {12616, 18540}, {12639, 49194}, {12668, 26453}, {12678, 26482}, {12679, 26476}, {12680, 26358}, {13974, 45653}, {14647, 24982}, {15348, 15726}, {16127, 41540}, {16143, 35204}, {16209, 45649}, {17437, 34789}, {18242, 37560}, {18245, 45647}, {18246, 45646}, {18542, 48664}, {19047, 49235}, {19048, 49234}, {19067, 26459}, {19068, 26465}, {22792, 45631}, {26400, 48495}, {26424, 48496}, {26518, 49062}, {26523, 49063}, {35844, 45642}, {35845, 45643}, {37022, 41389}, {37562, 40587}, {45528, 48748}, {45529, 48749}

X(49171) = midpoint of X(100) and X(34256)
X(49171) = reflection of X(i) in X(j) for these (i, j): (12676, 5), (18237, 34862), (49170, 84)
X(49171) = complement of X(10309)
X(49171) = complementary conjugate of X(7681)
X(49171) = center of the circumconic {{A, B, C, X(100), X(34256)}}
X(49171) = intersection, other than A, B, C, of circumconics {{A, B, C, X(84), X(2057)}} and {{A, B, C, X(222), X(1767)}}
X(49171) = X(i)-Ceva conjugate of-X(j) for these (i, j): (2, 3554), (100, 30201)
X(49171) = X(i)-complementary conjugate of-X(j) for these (i, j): (1, 7681), (31, 3554), (109, 30201), (212, 268)
X(49171) = X(3)-Zayin conjugate of-X(40)
X(49171) = orthologic center (anti-outer-Yff, T) for these triangles T: extouch, 1st Zaniah
X(49171) = X(84)-of-anti-outer-Yff triangle
X(49171) = X(12676)-of-Johnson triangle
X(49171) = X(12686)-of-anti-inner-Yff triangle
X(49171) = X(49170)-of-inner-Yff tangents triangle
X(49171) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (84, 7971, 10085), (84, 12686, 1), (84, 12705, 12114), (1158, 6256, 3359), (6705, 12608, 10200)


X(49172) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO INNER-FERMAT

Barycentrics    2*sqrt(3)*(a^4-2*(b^2+c^2)*a^2-2*(b+c)*b*c*a+b^4+c^4+2*(b^2-b*c+c^2)*b*c)*S*a^2+(a+b+c)*(a^7-(b+c)*a^6-2*(2*b-c)*(b-2*c)*a^5+4*(b+c)*(b^2-3*b*c+c^2)*a^4+(5*b^4+5*c^4-2*(5*b^2-11*b*c+5*c^2)*b*c)*a^3-(b^2-c^2)*(b-c)*(5*b^2-6*b*c+5*c^2)*a^2-2*(b^4-c^4)*(b^2-c^2)*a+2*(b^2-c^2)^3*(b-c)) : :

The reciprocal orthologic center of these triangles is X(3).

X(49172) lies on these lines: {1, 18}, {5, 22858}, {533, 45700}, {628, 10527}, {630, 26363}, {5965, 45728}, {6674, 10198}, {6734, 22851}, {10267, 22557}, {10529, 22114}, {10680, 16628}, {10943, 12922}, {11012, 22843}, {11249, 22771}, {12116, 22531}, {16627, 26470}, {18544, 48665}, {18972, 26437}, {19049, 49237}, {19050, 49236}, {19069, 26458}, {19072, 26464}, {22481, 26377}, {22522, 26431}, {22656, 26308}, {22669, 45625}, {22673, 45626}, {22745, 26317}, {22794, 45630}, {22831, 26332}, {22852, 26452}, {22853, 26342}, {22854, 26349}, {22859, 26481}, {22860, 26475}, {22863, 45645}, {22864, 45644}, {22865, 26357}, {22876, 45650}, {22877, 45651}, {26399, 48497}, {26423, 48498}, {26517, 49064}, {26522, 49065}, {35846, 45640}, {35849, 45641}, {44667, 48482}, {45526, 48750}, {45527, 48751}

X(49172) = reflection of X(i) in X(j) for these (i, j): (22557, 49105), (22858, 5), (49173, 18)
X(49172) = orthologic center (anti-inner-Yff, T) for these triangles T: inner-Fermat, 1st half-diamonds
X(49172) = X(18)-of-anti-inner-Yff triangle
X(49172) = X(22858)-of-Johnson triangle
X(49172) = X(22887)-of-anti-outer-Yff triangle
X(49172) = X(49173)-of-outer-Yff tangents triangle
X(49172) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (18, 22867, 22884), (18, 22887, 1)


X(49173) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO INNER-FERMAT

Barycentrics    2*sqrt(3)*(a^4-2*(b^2+c^2)*a^2+2*(b+c)*b*c*a+b^4+c^4-2*(b^2+b*c+c^2)*b*c)*S*a^2+(a+b+c)*(a^7-(b+c)*a^6-2*(2*b^2+3*b*c+2*c^2)*a^5+4*(b+c)^3*a^4+(5*b^4+5*c^4-2*b*c*(b^2+9*b*c+c^2))*a^3-(b^2-c^2)*(b-c)*(5*b^2+14*b*c+5*c^2)*a^2-2*(b^2-c^2)^2*(b^2-4*b*c+c^2)*a+2*(b^2-c^2)^3*(b-c)) : :

The reciprocal orthologic center of these triangles is X(3).

X(49173) lies on these lines: {1, 18}, {5, 22857}, {119, 16627}, {533, 45701}, {628, 5552}, {630, 26364}, {1470, 18972}, {2077, 22843}, {5965, 45729}, {6256, 44667}, {6674, 10200}, {6735, 22851}, {10269, 22771}, {10528, 22114}, {10679, 16628}, {10942, 12932}, {11248, 12336}, {12115, 22531}, {18542, 48665}, {19047, 49237}, {19048, 49236}, {19069, 26459}, {19072, 26465}, {22481, 26378}, {22522, 26432}, {22656, 26309}, {22669, 45627}, {22673, 45628}, {22745, 26318}, {22794, 45631}, {22831, 26333}, {22852, 26453}, {22853, 26343}, {22854, 26350}, {22859, 26482}, {22860, 26476}, {22863, 45647}, {22864, 45646}, {22865, 26358}, {22876, 45652}, {22877, 45653}, {26400, 48497}, {26424, 48498}, {26518, 49064}, {26523, 49065}, {35846, 45642}, {35849, 45643}, {45528, 48750}, {45529, 48751}

X(49173) = reflection of X(i) in X(j) for these (i, j): (22771, 49105), (22857, 5), (49172, 18)
X(49173) = orthologic center (anti-outer-Yff, T) for these triangles T: inner-Fermat, 1st half-diamonds
X(49173) = X(18)-of-anti-outer-Yff triangle
X(49173) = X(22857)-of-Johnson triangle
X(49173) = X(22886)-of-anti-inner-Yff triangle
X(49173) = X(49172)-of-inner-Yff tangents triangle
X(49173) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (18, 22867, 22885), (18, 22886, 1)


X(49174) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO OUTER-FERMAT

Barycentrics    -2*sqrt(3)*(a^4-2*(b^2+c^2)*a^2-2*(b+c)*b*c*a+b^4+c^4+2*(b^2-b*c+c^2)*b*c)*S*a^2+(a+b+c)*(a^7-(b+c)*a^6-2*(2*b-c)*(b-2*c)*a^5+4*(b+c)*(b^2-3*b*c+c^2)*a^4+(5*b^4+5*c^4-2*(5*b^2-11*b*c+5*c^2)*b*c)*a^3-(b^2-c^2)*(b-c)*(5*b^2-6*b*c+5*c^2)*a^2-2*(b^4-c^4)*(b^2-c^2)*a+2*(b^2-c^2)^3*(b-c)) : :

The reciprocal orthologic center of these triangles is X(3).

X(49174) lies on these lines: {1, 17}, {5, 22903}, {532, 45700}, {627, 10527}, {629, 26363}, {5965, 45728}, {6673, 10198}, {6734, 22896}, {10267, 22558}, {10529, 22113}, {10680, 16629}, {10943, 12921}, {11012, 22890}, {11249, 22772}, {12116, 22532}, {13107, 36782}, {16626, 26470}, {18544, 48666}, {18973, 26437}, {19049, 49239}, {19050, 49238}, {19070, 26464}, {19071, 26458}, {22482, 26377}, {22523, 26431}, {22657, 26308}, {22670, 45625}, {22674, 45626}, {22746, 26317}, {22795, 45630}, {22832, 26332}, {22897, 26452}, {22898, 26342}, {22899, 26349}, {22904, 26481}, {22905, 26475}, {22908, 45645}, {22909, 45644}, {22910, 26357}, {22921, 45650}, {22922, 45651}, {26399, 48499}, {26423, 48500}, {26517, 49066}, {26522, 49067}, {35847, 45641}, {35848, 45640}, {44666, 48482}, {45526, 48752}, {45527, 48753}

X(49174) = reflection of X(i) in X(j) for these (i, j): (22558, 49106), (22903, 5), (49175, 17)
X(49174) = orthologic center (anti-inner-Yff, T) for these triangles T: outer-Fermat, 2nd half-diamonds
X(49174) = X(17)-of-anti-inner-Yff triangle
X(49174) = X(22903)-of-Johnson triangle
X(49174) = X(22932)-of-anti-outer-Yff triangle
X(49174) = X(49175)-of-outer-Yff tangents triangle
X(49174) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (17, 22912, 22929), (17, 22932, 1)


X(49175) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO OUTER-FERMAT

Barycentrics    -2*sqrt(3)*(a^4-2*(b^2+c^2)*a^2+2*(b+c)*b*c*a+b^4+c^4-2*(b^2+b*c+c^2)*b*c)*S*a^2+(a+b+c)*(a^7-(b+c)*a^6-2*(2*b^2+3*b*c+2*c^2)*a^5+4*(b+c)^3*a^4+(5*b^4+5*c^4-2*b*c*(b^2+9*b*c+c^2))*a^3-(b^2-c^2)*(b-c)*(5*b^2+14*b*c+5*c^2)*a^2-2*(b^2-c^2)^2*(b^2-4*b*c+c^2)*a+2*(b^2-c^2)^3*(b-c)) : :

The reciprocal orthologic center of these triangles is X(3).

X(49175) lies on these lines: {1, 17}, {5, 22902}, {119, 16626}, {532, 45701}, {627, 5552}, {629, 26364}, {1470, 18973}, {2077, 22890}, {5965, 45729}, {6256, 44666}, {6673, 10200}, {6735, 22896}, {10269, 22772}, {10528, 22113}, {10679, 16629}, {10942, 12931}, {11248, 12337}, {12115, 22532}, {13105, 36782}, {18542, 48666}, {19047, 49239}, {19048, 49238}, {19070, 26465}, {19071, 26459}, {22482, 26378}, {22523, 26432}, {22657, 26309}, {22670, 45627}, {22674, 45628}, {22746, 26318}, {22795, 45631}, {22832, 26333}, {22897, 26453}, {22898, 26343}, {22899, 26350}, {22904, 26482}, {22905, 26476}, {22908, 45647}, {22909, 45646}, {22910, 26358}, {22921, 45652}, {22922, 45653}, {26400, 48499}, {26424, 48500}, {26518, 49066}, {26523, 49067}, {35847, 45643}, {35848, 45642}, {45528, 48752}, {45529, 48753}

X(49175) = reflection of X(i) in X(j) for these (i, j): (22772, 49106), (22902, 5), (49174, 17)
X(49175) = orthologic center (anti-outer-Yff, T) for these triangles T: outer-Fermat, 2nd half-diamonds
X(49175) = X(17)-of-anti-outer-Yff triangle
X(49175) = X(22902)-of-Johnson triangle
X(49175) = X(22931)-of-anti-inner-Yff triangle
X(49175) = X(49174)-of-inner-Yff tangents triangle
X(49175) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (17, 22912, 22930), (17, 22931, 1)


X(49176) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO FUHRMANN

Barycentrics    a^7-2*(b+c)*a^6+b*c*a^5+3*(b^3+c^3)*a^4-(3*b^4+3*c^4-(b^2+c^2)*b*c)*a^3+(b^2-c^2)*(b-c)*b*c*a^2+2*(b^2-c^2)*(b-c)*(b^3+c^3)*a-(b^2-c^2)^3*(b-c) : :
X(49176) = 4*X(5)-3*X(5660) = 6*X(11)-5*X(8227) = 3*X(80)-2*X(355) = 6*X(119)-7*X(7989) = 2*X(119)-3*X(37718) = 4*X(355)-3*X(12751) = 4*X(1483)-3*X(7972) = 2*X(1483)-3*X(12737) = 3*X(1484)-2*X(5901) = 4*X(1484)-3*X(16173) = 3*X(5531)-7*X(7989) = X(5531)-3*X(37718) = 3*X(5587)-4*X(12019) = 3*X(5587)-2*X(37725) = 3*X(5660)-2*X(12738) = 4*X(5901)-3*X(6265) = 8*X(5901)-9*X(16173) = 2*X(6265)-3*X(16173) = 3*X(6326)-5*X(8227) = 7*X(7989)-9*X(37718)

The reciprocal orthologic center of these triangles is X(3).

X(49176) lies on these lines: {1, 5}, {3, 11219}, {4, 2801}, {10, 34486}, {30, 5536}, {40, 528}, {79, 24475}, {100, 5178}, {104, 3651}, {149, 151}, {153, 6246}, {165, 10993}, {214, 26363}, {515, 13279}, {518, 13272}, {912, 3583}, {938, 45043}, {942, 38543}, {944, 45700}, {946, 10707}, {1071, 49178}, {1145, 49183}, {1320, 41575}, {1385, 47033}, {1479, 5693}, {1737, 2078}, {1768, 5709}, {1998, 37569}, {2095, 36999}, {2323, 5179}, {2475, 12005}, {2771, 7728}, {2802, 6903}, {2826, 47680}, {2829, 10864}, {3035, 5705}, {3085, 41553}, {3333, 41556}, {3419, 3576}, {3555, 12762}, {3678, 6902}, {3813, 11014}, {3893, 19914}, {3894, 37826}, {4294, 41166}, {4302, 5770}, {4423, 5790}, {4466, 10708}, {4857, 5887}, {4863, 13996}, {5083, 12757}, {5086, 5882}, {5445, 32141}, {5535, 5842}, {5690, 34720}, {5715, 13257}, {5735, 5851}, {5787, 7992}, {5811, 12665}, {5902, 37820}, {5904, 6928}, {6154, 10268}, {6174, 31423}, {6224, 10527}, {6262, 26349}, {6263, 26342}, {6583, 37230}, {6702, 10198}, {6713, 15015}, {6763, 7491}, {6917, 18398}, {6965, 15064}, {7976, 49166}, {8988, 45650}, {9612, 12831}, {9809, 10248}, {9912, 26308}, {9945, 21154}, {9963, 38693}, {9964, 11604}, {10031, 13607}, {10090, 37583}, {10246, 31245}, {10267, 12331}, {10525, 15071}, {10529, 20085}, {10680, 12747}, {10698, 21630}, {10711, 19925}, {10724, 13243}, {10806, 15863}, {11249, 12773}, {11570, 45638}, {12137, 26377}, {12198, 26431}, {12460, 45625}, {12461, 45626}, {12498, 26317}, {12551, 45656}, {12571, 21635}, {12611, 45630}, {12729, 26452}, {12736, 45654}, {12741, 45645}, {12742, 45644}, {12743, 26357}, {12758, 45634}, {12764, 15094}, {12767, 45648}, {12832, 37550}, {13199, 46684}, {13226, 24466}, {13271, 17654}, {13273, 17660}, {13274, 17638}, {13976, 45651}, {14151, 21620}, {15908, 16132}, {16116, 49193}, {16127, 43740}, {16128, 22938}, {17536, 24987}, {17590, 34122}, {18492, 38757}, {18543, 26726}, {18544, 48667}, {18976, 26437}, {19049, 49241}, {19050, 49240}, {19077, 26458}, {19078, 26464}, {20118, 37579}, {21740, 24387}, {22935, 24299}, {24541, 31254}, {26201, 47032}, {26399, 48501}, {26423, 48502}, {26517, 49068}, {26522, 49069}, {33519, 37822}, {35852, 45640}, {35853, 45641}, {37531, 41709}, {45526, 48754}, {45527, 48755}

X(49176) = midpoint of X(i) and X(j) for these {i, j}: {149, 9803}, {7993, 9897}, {10724, 13243}
X(49176) = reflection of X(i) in X(j) for these (i, j): (1, 37726), (100, 10265), (153, 6246), (5531, 119), (6224, 11715), (6265, 1484), (6326, 11), (7972, 12737), (10609, 20418), (10698, 21630), (12119, 104), (12331, 12619), (12738, 5), (12751, 80), (12757, 5083), (13199, 46684), (14217, 149), (16128, 22938), (24466, 13226), (34789, 10738), (37725, 12019), (38665, 10), (47034, 11604), (48713, 10916)
X(49176) = inverse of X(5587) in Fuhrmann circle
X(49176) = X(8)-beth conjugate of-X(38665)
X(49176) = reflection of X(i) in the line X(j)X(k) for these (i, j, k): (4, 3887, 4010), (40, 2826, 10015), (104, 4458, 13277)
X(49176) = orthologic center (anti-inner-Yff, T) for these triangles T: Fuhrmann, K798i
X(49176) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {4, 10767, 18341}, {149, 150, 9803}
X(49176) = X(23)-of-Fuhrmann triangle, when ABC is acute
X(49176) = X(80)-of-anti-inner-Yff triangle
X(49176) = X(12738)-of-Johnson triangle
X(49176) = X(12750)-of-anti-outer-Yff triangle
X(49176) = X(12751)-of-outer-Yff tangents triangle
X(49176) = X(36253)-of-2nd Conway triangle, when ABC is acute
X(49176) = X(37726)-of-Aquila triangle
X(49176) = X(38665)-of-outer-Garcia triangle
X(49176) = X(41701)-of-outer-Johnson triangle
X(49176) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5, 12738, 5660), (80, 7972, 10057), (80, 12750, 1), (104, 48713, 11012), (1484, 6265, 16173), (5531, 37718, 119), (10609, 20418, 3576), (12019, 37725, 5587), (12649, 48482, 37625), (13279, 38669, 48694), (26470, 37726, 1484)


X(49177) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 2nd FUHRMANN

Barycentrics    a^7-(2*b^2+3*b*c+2*c^2)*a^5-(b^3+c^3)*a^4+(b^3+c^3)*(b+c)*a^3+(b^2-c^2)*(b-c)*(2*b^2+b*c+2*c^2)*a^2+2*(b^2-c^2)^2*b*c*a-(b^2-c^2)^3*(b-c) : :
X(49177) = 2*X(3)-3*X(26725) = X(79)+2*X(12699) = X(191)-3*X(1699) = 4*X(946)-X(16113) = X(962)+2*X(16125) = 4*X(1125)-3*X(21161) = 3*X(1699)-2*X(6841) = 3*X(3576)-4*X(11281) = 3*X(3576)-2*X(44238) = 7*X(3624)-6*X(28465) = 2*X(3649)+X(41869) = X(3652)-4*X(40273) = 3*X(5426)-5*X(11522) = 2*X(5428)-3*X(5886) = X(5441)-4*X(22791) = 3*X(6598)-2*X(49168) = X(11684)-4*X(18483) = 4*X(12699)+X(49178) = 4*X(16159)-X(49178) = 3*X(26725)-4*X(33592)

The reciprocal orthologic center of these triangles is X(3).

X(49177) lies on these lines: {1, 30}, {3, 26725}, {4, 758}, {5, 16139}, {11, 41697}, {21, 946}, {40, 442}, {72, 18406}, {191, 1699}, {283, 37369}, {497, 10122}, {515, 34195}, {516, 3651}, {517, 37230}, {962, 2475}, {1125, 21161}, {1482, 36999}, {1770, 10058}, {1839, 2323}, {1858, 3583}, {2077, 35979}, {2292, 45924}, {2771, 7728}, {2779, 41723}, {2800, 11604}, {2886, 24468}, {2949, 8226}, {3086, 41547}, {3149, 42843}, {3254, 10308}, {3336, 37356}, {3434, 31938}, {3576, 11281}, {3624, 28465}, {3647, 5698}, {3648, 10527}, {3650, 5231}, {3652, 5536}, {3683, 9955}, {3853, 16128}, {3958, 32431}, {3962, 18480}, {4301, 10698}, {5057, 6734}, {5426, 11522}, {5427, 11376}, {5428, 5886}, {5443, 14794}, {5499, 28174}, {5535, 6831}, {5587, 5812}, {5603, 35016}, {5691, 16126}, {5692, 44229}, {5705, 18253}, {5735, 7701}, {5758, 40661}, {5762, 15909}, {5805, 6675}, {5840, 34600}, {5880, 35242}, {5883, 6903}, {5884, 6895}, {5904, 18517}, {6175, 24987}, {6326, 20420}, {6361, 6701}, {6684, 31254}, {6796, 31660}, {6836, 15016}, {6839, 31806}, {6840, 31870}, {6894, 20117}, {6900, 10176}, {7688, 12609}, {7982, 44669}, {9589, 37401}, {9799, 9812}, {10021, 38034}, {10266, 34485}, {10267, 16117}, {10529, 20084}, {10680, 16150}, {10740, 34300}, {10943, 16138}, {10957, 14883}, {11218, 37621}, {11249, 13743}, {11496, 37286}, {12116, 16116}, {12119, 39778}, {12616, 41557}, {12757, 12866}, {13274, 33667}, {13465, 22798}, {15670, 38021}, {16114, 26377}, {16115, 26431}, {16119, 26308}, {16121, 45625}, {16122, 45626}, {16123, 26317}, {16129, 26452}, {16130, 26342}, {16131, 26349}, {16140, 26481}, {16141, 26475}, {16142, 26357}, {16148, 45650}, {16149, 45651}, {16161, 45645}, {16162, 45644}, {18493, 28443}, {18544, 48668}, {18977, 26437}, {19049, 49243}, {19050, 49242}, {19079, 26458}, {19080, 26464}, {20292, 31730}, {22753, 37308}, {22837, 34617}, {24299, 28146}, {25055, 44255}, {26200, 47032}, {26399, 48503}, {26423, 48504}, {26517, 49070}, {26522, 49071}, {28178, 31651}, {28453, 35252}, {29097, 37530}, {31435, 44256}, {31673, 41575}, {33557, 34486}, {33594, 35204}, {35854, 45640}, {35855, 45641}, {37005, 46816}, {45526, 48756}, {45527, 48757}

X(49177) = midpoint of X(i) and X(j) for these {i, j}: {962, 2475}, {5691, 16126}, {12699, 16159}, {14217, 47034}, {14450, 37433}, {16117, 48661}, {16132, 41869}
X(49177) = reflection of X(i) in X(j) for these (i, j): (3, 33592), (21, 946), (40, 442), (79, 16159), (191, 6841), (2475, 16125), (3651, 11263), (3652, 16160), (7701, 37447), (12119, 39778), (13465, 22798), (16113, 21), (16117, 49107), (16132, 3649), (16139, 5), (16160, 40273), (22937, 9955), (35204, 33594), (41691, 7701), (44238, 11281), (47033, 37230), (49178, 79)
X(49177) = orthologic center (anti-inner-Yff, T) for these triangles T: 2nd Fuhrmann, K798e
X(49177) = X(79)-of-anti-inner-Yff triangle
X(49177) = X(6689)-of-2nd Conway triangle, when ABC is acute
X(49177) = X(16139)-of-Johnson triangle
X(49177) = X(16155)-of-anti-outer-Yff triangle
X(49177) = X(33592)-of-X3-ABC reflections triangle
X(49177) = X(41590)-of-hexyl triangle, when ABC is acute
X(49177) = X(41697)-of-inner-Johnson triangle
X(49177) = X(49178)-of-outer-Yff tangents triangle
X(49177) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 33592, 26725), (79, 5441, 16152), (79, 16155, 1), (191, 1699, 6841), (1836, 3649, 79), (1836, 12699, 41869), (3649, 6284, 33857), (6284, 33857, 5441), (9812, 14450, 37433), (11281, 44238, 3576)


X(49178) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 2nd FUHRMANN

Barycentrics    a^7-(2*b-c)*(b-2*c)*a^5-(b^3+c^3)*a^4+(b^4+c^4-3*(b^2+c^2)*b*c)*a^3+(b^2-c^2)*(b-c)*(2*b^2+b*c+2*c^2)*a^2-2*(b^2-c^2)^2*b*c*a-(b^2-c^2)^3*(b-c) : :
X(49178) = 5*X(21)-6*X(10165) = 5*X(79)-2*X(12699) = 3*X(79)-2*X(16159) = 5*X(191)-7*X(9588) = 4*X(1125)-3*X(28461) = 5*X(3651)-4*X(12512) = 7*X(9588)-10*X(37401) = 14*X(9588)-5*X(41691) = 7*X(10248)-10*X(16125) = 7*X(10248)-5*X(37433) = X(12245)+5*X(16116) = 8*X(12512)-5*X(16113) = 3*X(12699)-5*X(16159) = 4*X(12699)-5*X(49177) = 5*X(13465)-9*X(38066) = 2*X(13743)-3*X(26725) = 4*X(16159)-3*X(49177) = 2*X(19919)-3*X(26446) = 3*X(26725)-4*X(49107) = 4*X(37401)-X(41691)

The reciprocal orthologic center of these triangles is X(3).

X(49178) lies on these lines: {1, 30}, {4, 3255}, {5, 16138}, {10, 10711}, {12, 41695}, {21, 10165}, {40, 12607}, {119, 3652}, {140, 15017}, {191, 3359}, {355, 41706}, {377, 16127}, {442, 7701}, {758, 12115}, {1071, 49176}, {1125, 28461}, {1385, 34789}, {1470, 18977}, {1519, 11263}, {1768, 6842}, {1770, 3256}, {2077, 3651}, {2475, 5554}, {2771, 12751}, {3065, 39692}, {3085, 41546}, {3336, 37406}, {3583, 13369}, {3586, 7702}, {3647, 26364}, {3648, 5552}, {3922, 18480}, {5553, 6598}, {5587, 6259}, {5693, 6850}, {5880, 18492}, {5881, 12678}, {5882, 14217}, {5884, 37437}, {6001, 17653}, {6175, 24982}, {6260, 35990}, {6326, 31775}, {6675, 21164}, {6701, 10200}, {6735, 11684}, {6841, 37534}, {6901, 31871}, {6923, 15071}, {6925, 37625}, {6940, 21635}, {6951, 31803}, {8227, 12679}, {9809, 20117}, {10122, 45655}, {10248, 10430}, {10269, 13743}, {10528, 20084}, {10679, 16150}, {10738, 26201}, {10742, 13145}, {10902, 35989}, {10942, 16139}, {10958, 41697}, {11112, 18243}, {11248, 16117}, {11604, 15528}, {12119, 21740}, {12703, 49184}, {13465, 38066}, {16005, 30513}, {16114, 26378}, {16115, 26432}, {16119, 26309}, {16121, 45627}, {16122, 45628}, {16123, 26318}, {16129, 26453}, {16130, 26343}, {16131, 26350}, {16133, 21620}, {16140, 26482}, {16141, 26476}, {16142, 26358}, {16148, 45652}, {16149, 45653}, {16160, 35010}, {16161, 45647}, {16162, 45646}, {16203, 33592}, {17637, 18838}, {18542, 48668}, {19047, 49243}, {19048, 49242}, {19079, 26459}, {19080, 26465}, {19919, 26446}, {20292, 31673}, {22798, 45631}, {22836, 37430}, {26400, 48503}, {26424, 48504}, {26518, 49070}, {26523, 49071}, {31423, 37822}, {34300, 38777}, {34339, 37230}, {35854, 45642}, {35855, 45643}, {37426, 42843}, {37569, 41571}, {37616, 38761}, {40263, 41690}, {45528, 48756}, {45529, 48757}

X(49178) = midpoint of X(16118) and X(16143)
X(49178) = reflection of X(i) in X(j) for these (i, j): (191, 37401), (3652, 5499), (5441, 33858), (7701, 442), (13743, 49107), (16113, 3651), (16138, 5), (21669, 11263), (37433, 16125), (37569, 41571), (41691, 191), (47033, 47032), (49177, 79)
X(49178) = orthologic center (anti-outer-Yff, T) for these triangles T: 2nd Fuhrmann, K798e
X(49178) = X(79)-of-anti-outer-Yff triangle
X(49178) = X(16138)-of-Johnson triangle
X(49178) = X(16154)-of-anti-inner-Yff triangle
X(49178) = X(41695)-of-outer-Johnson triangle
X(49178) = X(49177)-of-inner-Yff tangents triangle
X(49178) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (79, 5441, 16153), (79, 16154, 1), (9809, 37163, 20117), (13743, 49107, 26725)


X(49179) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO HATZIPOLAKIS-MOSES

Barycentrics    a^19-(b+c)*a^18-2*(2*b^2+b*c+2*c^2)*a^17+4*(b+c)*(b^2+c^2)*a^16+(5*b^4+5*c^4+b*c*(6*b^2+7*b*c+6*c^2))*a^15-(b+c)*(5*b^4+7*b^2*c^2+5*c^4)*a^14-(b^6+c^6+2*b*c*(b^4+7*b^2*c^2+c^4))*a^13+(b+c)*(b^6+c^6-2*(b^2-c^2)^2*b*c)*a^12-(b^8+c^8+2*(5*b^6+5*c^6-(b^4+c^4+3*(b^2-b*c+c^2)*b*c)*b*c)*b*c)*a^11+(b+c)*(b^8+c^8+2*(4*b^6+4*c^6-(b^4+c^4+b*c*(2*b^2-3*b*c+2*c^2))*b*c)*b*c)*a^10-(b^8+c^8-2*(4*b^6+4*c^6+3*b*c*(b^2+b*c+c^2)^2)*b*c)*(b-c)^2*a^9+(b^2-c^2)*(b-c)*(b^8+c^8-2*(4*b^6+4*c^6+(3*b^4+3*c^4+b*c*(4*b^2+5*b*c+4*c^2))*b*c)*b*c)*a^8-(b^4-c^4)*(b^2-c^2)*(b^6+c^6-2*b*c*(b^2+3*b*c+c^2)*(b-c)^2)*a^7+(b^4-c^4)*(b^2-c^2)*(b^3+c^3)*(b^4+c^4+(b-c)^2*b*c)*a^6+(5*b^6+5*c^6-2*(3*b^4+3*c^4-b*c*(b^2+3*b*c+c^2))*b*c)*(b^4-c^4)^2*a^5-(b^2-c^2)^3*(b-c)*(5*b^8+5*c^8+(7*b^4+7*c^4+2*b*c*(b^2+4*b*c+c^2))*b^2*c^2)*a^4-2*(b^4-c^4)^2*(b^2-c^2)^2*(2*b^4+2*c^4-(b-c)^2*b*c)*a^3+4*(b^2-c^2)^5*(b-c)*(b^2+c^2)*(b^4+b^2*c^2+c^4)*a^2+(b^2+c^2)^3*(b^2-c^2)^6*a-(b^2-c^2)^7*(b-c)*(b^2+c^2)^2 : :

The reciprocal orthologic center of these triangles is X(6146).

X(49179) lies on these lines: {1, 6145}, {5, 32381}, {1154, 49161}, {6734, 32371}, {10267, 32347}, {10527, 32354}, {10628, 49159}, {10680, 32402}, {10943, 32380}, {11012, 32330}, {11249, 18400}, {12116, 32337}, {18544, 48669}, {19049, 49245}, {19050, 49244}, {26308, 32357}, {26317, 32362}, {26332, 32369}, {26342, 32373}, {26349, 32374}, {26357, 32390}, {26363, 32391}, {26377, 32332}, {26399, 48505}, {26423, 48506}, {26431, 32335}, {26437, 32336}, {26452, 32372}, {26458, 32342}, {26464, 32343}, {26470, 32379}, {26475, 32383}, {26481, 32382}, {26517, 49072}, {26522, 49073}, {32360, 45625}, {32361, 45626}, {32364, 45630}, {32388, 45645}, {32389, 45644}, {32399, 45650}, {32400, 45651}, {35858, 45640}, {35859, 45641}, {45526, 48758}, {45527, 48759}

X(49179) = reflection of X(i) in X(j) for these (i, j): (32347, 49108), (32381, 5), (49180, 6145)
X(49179) = orthologic center (anti-inner-Yff, Hatzipolakis-Moses)
X(49179) = X(6145)-of-anti-inner-Yff triangle
X(49179) = X(32381)-of-Johnson triangle
X(49179) = X(32406)-of-anti-outer-Yff triangle
X(49179) = X(49180)-of-outer-Yff tangents triangle
X(49179) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6145, 32394, 32403), (6145, 32406, 1)


X(49180) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO HATZIPOLAKIS-MOSES

Barycentrics    a^19-(b+c)*a^18-2*(2*b^2-3*b*c+2*c^2)*a^17+4*(b^3+c^3)*a^16+(5*b^4+5*c^4-3*b*c*(6*b^2-5*b*c+6*c^2))*a^15-(b+c)*(5*b^4+5*c^4-3*b*c*(4*b^2-5*b*c+4*c^2))*a^14-(b^6+c^6-2*(5*b^4+5*c^4-b*c*(8*b^2-17*b*c+8*c^2))*b*c)*a^13+(b+c)*(b^2-3*b*c+c^2)*(b^4+c^4-3*(b-c)^2*b*c)*a^12-(b^8+c^8-2*(7*b^6+7*c^6-(3*b^4+3*c^4+b*c*(5*b^2-9*b*c+5*c^2))*b*c)*b*c)*a^11+(b+c)*(b^8+c^8-2*(6*b^6+6*c^6-b*c*(b^2+3*b*c+c^2)*(3*b^2-5*b*c+3*c^2))*b*c)*a^10-(b^8+c^8+2*(6*b^6+6*c^6+(b^4+c^4+b*c*(4*b^2+11*b*c+4*c^2))*b*c)*b*c)*(b-c)^2*a^9+(b^2-c^2)*(b-c)*(b^8+c^8+2*(3*b^2-b*c+3*c^2)*(2*b^4+2*c^4+(b^2-b*c+c^2)*b*c)*b*c)*a^8-(b^2-c^2)^2*(b^8+c^8+(2*b^2-3*b*c+2*c^2)*(3*b^4+3*c^4+4*b*c*(2*b^2+b*c+2*c^2))*b*c)*a^7+(b^2-c^2)^2*(b+c)*(b^8+c^8+(4*b^6+4*c^6+(7*b^4+7*c^4-4*b*c*(2*b-c)*(b-2*c))*b*c)*b*c)*a^6+(b^2-c^2)*(b-c)*(b^3+c^3)*(5*b^8+5*c^8+3*(b^6+c^6-(2*b^4+2*c^4+b*c*(5*b^2+2*b*c+5*c^2))*b*c)*b*c)*a^5-(b^2-c^2)^3*(b-c)*(5*b^8+5*c^8+3*(4*b^6+4*c^6+(5*b^4+5*c^4+2*b*c*(3*b^2+4*b*c+3*c^2))*b*c)*b*c)*a^4-2*(b^4-c^4)*(b^2-c^2)^3*(2*b^6+2*c^6-b*c*(5*b^4+2*b^2*c^2+5*c^4))*a^3+4*(b^2-c^2)^5*(b-c)*(b^2+c^2)*(b^4+c^4+(b^2+b*c+c^2)*b*c)*a^2+(b^2-4*b*c+c^2)*(b^2+c^2)^2*(b^2-c^2)^6*a-(b^2-c^2)^7*(b-c)*(b^2+c^2)^2 : :

The reciprocal orthologic center of these triangles is X(6146).

X(49180) lies on these lines: {1, 6145}, {5, 32380}, {119, 32379}, {1154, 49162}, {1470, 32336}, {2077, 32330}, {5552, 32354}, {6735, 32371}, {10269, 32363}, {10628, 49160}, {10679, 32402}, {10942, 32381}, {11248, 18400}, {12115, 32337}, {18542, 48669}, {19047, 49245}, {19048, 49244}, {26309, 32357}, {26318, 32362}, {26333, 32369}, {26343, 32373}, {26350, 32374}, {26358, 32390}, {26364, 32391}, {26378, 32332}, {26400, 48505}, {26424, 48506}, {26432, 32335}, {26453, 32372}, {26459, 32342}, {26465, 32343}, {26476, 32383}, {26482, 32382}, {26518, 49072}, {26523, 49073}, {32360, 45627}, {32361, 45628}, {32364, 45631}, {32388, 45647}, {32389, 45646}, {32399, 45652}, {32400, 45653}, {35858, 45642}, {35859, 45643}, {45528, 48758}, {45529, 48759}

X(49180) = reflection of X(i) in X(j) for these (i, j): (32363, 49108), (32380, 5), (49179, 6145)
X(49180) = orthologic center (anti-outer-Yff, Hatzipolakis-Moses)
X(49180) = X(6145)-of-anti-outer-Yff triangle
X(49180) = X(32380)-of-Johnson triangle
X(49180) = X(32405)-of-anti-inner-Yff triangle
X(49180) = X(49179)-of-inner-Yff tangents triangle
X(49180) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6145, 32394, 32404), (6145, 32405, 1)


X(49181) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 3rd HATZIPOLAKIS

Barycentrics    a^19-(b+c)*a^18-2*(2*b^2+b*c+2*c^2)*a^17+4*(b+c)*(b^2+c^2)*a^16+(5*b^4+5*c^4+3*b*c*(b+2*c)*(2*b+c))*a^15-5*(b+c)*(b^4+3*b^2*c^2+c^4)*a^14-(b^6+c^6+2*(b^4+c^4+5*b*c*(2*b^2+3*b*c+2*c^2))*b*c)*a^13+(b+c)*(b^6+c^6-2*(b^4+c^4-2*b*c*(5*b^2+b*c+5*c^2))*b*c)*a^12-(b^8+c^8+2*(5*b^6+5*c^6-(5*b^4+5*c^4+b*c*(19*b^2+5*b*c+19*c^2))*b*c)*b*c)*a^11+(b+c)*(b^8+c^8+2*(4*b^6+4*c^6-(5*b^4+5*c^4+b*c*(6*b^2+5*b*c+6*c^2))*b*c)*b*c)*a^10-(b^10+c^10-(10*b^8+10*c^8-(3*b^6+3*c^6-4*(2*b^4+2*c^4+b*c*(2*b^2-23*b*c+2*c^2))*b*c)*b*c)*b*c)*a^9+(b+c)*(b^10+c^10-(10*b^8+10*c^8-(3*b^6+3*c^6+4*(b^4+c^4-b*c*(2*b^2-9*b*c+2*c^2))*b*c)*b*c)*b*c)*a^8-(b^10+c^10-(12*b^6+12*c^6-(18*b^4+18*c^4+b*c*(47*b^2+20*b*c+47*c^2))*b*c)*b^2*c^2)*(b-c)^2*a^7+(b^2-c^2)*(b-c)*(b^10+c^10+(2*b^8+2*c^8-(8*b^6+8*c^6-(10*b^4+10*c^4+27*(b^2+c^2)*b*c)*b*c)*b*c)*b*c)*a^6+(b^4-c^4)*(b^2-c^2)*(b-c)^2*(5*b^6+5*c^6+2*(2*b^4+2*c^4-b*c*(5*b^2+4*b*c+5*c^2))*b*c)*a^5-(b^2-c^2)^3*(b-c)*(5*b^8+5*c^8-(13*b^4+13*c^4-2*(b^2+c^2)*b*c)*b^2*c^2)*a^4-2*(b^4-c^4)^2*(b^2-c^2)^2*(b-c)^2*(2*b^2+3*b*c+2*c^2)*a^3+4*(b^6+c^6)*(b^2-c^2)^5*(b-c)*a^2+(b^2+c^2)^3*(b^2-c^2)^6*a-(b^2-c^2)^7*(b-c)*(b^2+c^2)^2 : :

The reciprocal orthologic center of these triangles is X(12241).

X(49181) lies on these lines: {1, 22466}, {5, 22957}, {6734, 22941}, {10267, 22559}, {10527, 22647}, {10680, 22979}, {10943, 22956}, {11012, 22951}, {11249, 22776}, {12116, 22533}, {18544, 48670}, {18978, 26437}, {19049, 49247}, {19050, 49246}, {19083, 26458}, {19084, 26464}, {22483, 26377}, {22524, 26431}, {22658, 26308}, {22671, 45625}, {22675, 45626}, {22747, 26317}, {22800, 45630}, {22833, 26332}, {22943, 26452}, {22945, 26342}, {22947, 26349}, {22955, 26470}, {22958, 26481}, {22959, 26475}, {22963, 45645}, {22964, 45644}, {22965, 26357}, {22966, 26363}, {22976, 45650}, {22977, 45651}, {26399, 48507}, {26423, 48508}, {26517, 49074}, {26522, 49075}, {35860, 45640}, {35861, 45641}, {45526, 48810}, {45527, 48811}

X(49181) = reflection of X(i) in X(j) for these (i, j): (22559, 49109), (22957, 5), (49182, 22466)
X(49181) = orthologic center (anti-inner-Yff, 3rd Hatzipolakis)
X(49181) = X(22466)-of-anti-inner-Yff triangle
X(49181) = X(22957)-of-Johnson triangle
X(49181) = X(22983)-of-anti-outer-Yff triangle
X(49181) = X(49182)-of-outer-Yff tangents triangle
X(49181) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (22466, 22969, 22980), (22466, 22983, 1)


X(49182) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 3rd HATZIPOLAKIS

Barycentrics    a^19-(b+c)*a^18-2*(2*b^2-3*b*c+2*c^2)*a^17+4*(b^3+c^3)*a^16+(b^2-b*c+c^2)*(5*b^2-13*b*c+5*c^2)*a^15-(b+c)*(5*b^4+5*c^4-b*c*(12*b^2-23*b*c+12*c^2))*a^14-(b^6+c^6-2*(5*b^4+5*c^4-b*c*(18*b^2-41*b*c+18*c^2))*b*c)*a^13+(b+c)*(b^6+c^6-2*(3*b^4+3*c^4-2*b*c*(9*b^2-14*b*c+9*c^2))*b*c)*a^12-(b^8+c^8-2*(7*b^6+7*c^6+(b^4+c^4-b*c*(45*b^2-49*b*c+45*c^2))*b*c)*b*c)*a^11+(b+c)*(b^8+c^8-2*(6*b^6+6*c^6+(b^4+c^4-b*c*(32*b^2-49*b*c+32*c^2))*b*c)*b*c)*a^10-(b^10+c^10+(10*b^8+10*c^8-(29*b^6+29*c^6-4*(8*b^4+8*c^4+b*c*(16*b^2-51*b*c+16*c^2))*b*c)*b*c)*b*c)*a^9+(b+c)*(b^10+c^10+(10*b^8+10*c^8-(29*b^6+29*c^6-4*(5*b^4+5*c^4+b*c*(16*b^2-37*b*c+16*c^2))*b*c)*b*c)*b*c)*a^8-(b^10+c^10+(8*b^8+8*c^8+(12*b^6+12*c^6-(54*b^4+54*c^4+b*c*(49*b^2-36*b*c+49*c^2))*b*c)*b*c)*b*c)*(b-c)^2*a^7+(b^2-c^2)*(b-c)*(b^10+c^10+(6*b^8+6*c^8+(8*b^6+8*c^6-(46*b^4+46*c^4+b*c*(29*b^2-56*b*c+29*c^2))*b*c)*b*c)*b*c)*a^6+(b^2-c^2)^2*(b-c)^2*(5*b^8+5*c^8+(8*b^6+8*c^6-(13*b^4+13*c^4+4*b*c*(2*b^2-9*b*c+2*c^2))*b*c)*b*c)*a^5-(b^2-c^2)^3*(b-c)*(5*b^8+5*c^8+(12*b^6+12*c^6-(5*b^4+5*c^4+2*b*c*(7*b^2-8*b*c+7*c^2))*b*c)*b*c)*a^4-2*(b^4-c^4)*(b^2-c^2)^3*(b-c)^2*(2*b^4+2*c^4-b*c*(b^2+8*b*c+c^2))*a^3+4*(b^2-c^2)^5*(b-c)*(b^2+c^2)*(b^4+c^4+(b^2-b*c+c^2)*b*c)*a^2+(b^2-c^2)^6*(b^2+c^2)^2*(b^2-4*b*c+c^2)*a-(b^2-c^2)^7*(b-c)*(b^2+c^2)^2 : :

The reciprocal orthologic center of these triangles is X(12241).

X(49182) lies on these lines: {1, 22466}, {5, 22956}, {119, 22955}, {1470, 18978}, {2077, 22951}, {5552, 22647}, {6735, 22941}, {10269, 22776}, {10679, 22979}, {10942, 22957}, {11248, 22559}, {12115, 22533}, {18542, 48670}, {19047, 49247}, {19048, 49246}, {19083, 26459}, {19084, 26465}, {22483, 26378}, {22524, 26432}, {22658, 26309}, {22671, 45627}, {22675, 45628}, {22747, 26318}, {22800, 45631}, {22833, 26333}, {22943, 26453}, {22945, 26343}, {22947, 26350}, {22958, 26482}, {22959, 26476}, {22963, 45647}, {22964, 45646}, {22965, 26358}, {22966, 26364}, {22976, 45652}, {22977, 45653}, {26400, 48507}, {26424, 48508}, {26518, 49074}, {26523, 49075}, {35860, 45642}, {35861, 45643}, {45528, 48810}, {45529, 48811}

X(49182) = reflection of X(i) in X(j) for these (i, j): (22776, 49109), (22956, 5), (49181, 22466)
X(49182) = orthologic center (anti-outer-Yff, 3rd Hatzipolakis)
X(49182) = X(22466)-of-anti-outer-Yff triangle
X(49182) = X(22956)-of-Johnson triangle
X(49182) = X(22982)-of-anti-inner-Yff triangle
X(49182) = X(49181)-of-inner-Yff tangents triangle
X(49182) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (22466, 22969, 22981), (22466, 22982, 1)


X(49183) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO HUTSON EXTOUCH

Barycentrics    a*(a^4-2*(b+c)^2*a^2+(b^2-c^2)^2)*(a^5-(b+c)*a^4-2*(b+c)^2*a^3+2*(b+c)*(b^2+c^2)*a^2+(b^4+c^4+2*b*c*(2*b^2-b*c+2*c^2))*a-(b^2-c^2)^2*(b+c)) : :
X(49183) = 3*X(7160)+X(12842) = 2*X(12842)+3*X(49184)

The reciprocal orthologic center of these triangles is X(40).

X(49183) lies on these lines: {1, 5920}, {3, 49170}, {5, 12858}, {9, 10268}, {10, 6827}, {40, 442}, {142, 5709}, {200, 10902}, {214, 48694}, {1145, 49176}, {1158, 43182}, {1709, 13089}, {2092, 8557}, {3072, 34261}, {3085, 37550}, {3359, 41540}, {3579, 15346}, {3647, 7330}, {4640, 49171}, {5531, 35204}, {6260, 12514}, {6600, 10267}, {6734, 12777}, {6867, 18483}, {7686, 31435}, {7989, 17057}, {9874, 10527}, {10427, 37560}, {10680, 12872}, {10806, 15998}, {10943, 12857}, {11012, 12120}, {11249, 22754}, {11491, 12867}, {12116, 12249}, {12139, 26377}, {12200, 26431}, {12411, 26308}, {12464, 45625}, {12465, 45626}, {12500, 26317}, {12599, 26332}, {12631, 16202}, {12639, 49193}, {12640, 49168}, {12658, 34486}, {12789, 26452}, {12801, 26342}, {12802, 26349}, {12855, 45654}, {12856, 26470}, {12859, 26481}, {12860, 26475}, {12861, 45645}, {12862, 45644}, {12863, 26357}, {12864, 26363}, {13405, 45636}, {13914, 45650}, {13978, 45651}, {15298, 15932}, {16208, 45648}, {18391, 45634}, {18544, 48671}, {18979, 26437}, {19049, 49249}, {19050, 49248}, {19085, 26458}, {19086, 26464}, {22801, 45630}, {26399, 48509}, {26423, 48510}, {26517, 49076}, {26522, 49077}, {35862, 45640}, {35863, 45641}, {45526, 48812}, {45527, 48813}

X(49183) = reflection of X(i) in X(j) for these (i, j): (12333, 49110), (12858, 5), (49184, 7160)
X(49183) = X(2)-Ceva conjugate of-X(3553)
X(49183) = X(31)-complementary conjugate of-X(3553)
X(49183) = orthologic center (anti-inner-Yff, Hutson extouch)
X(49183) = X(7160)-of-anti-inner-Yff triangle
X(49183) = X(12858)-of-Johnson triangle
X(49183) = X(12875)-of-anti-outer-Yff triangle
X(49183) = X(49184)-of-outer-Yff tangents triangle
X(49183) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (7160, 8000, 10059), (7160, 12875, 1)


X(49184) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO HUTSON EXTOUCH

Barycentrics    a*(a^9-(b+c)*a^8-4*(b+c)^2*a^7+4*(b+c)*(b^2+3*b*c+c^2)*a^6+2*(3*b^4+3*c^4+2*b*c*(3*b^2+5*b*c+3*c^2))*a^5-6*(b+c)^5*a^4-4*(b^6+c^6+3*b^2*c^2*(b^2-8*b*c+c^2))*a^3+4*(b^2-c^2)*(b-c)*(b^4+c^4+b*c*(5*b^2+16*b*c+5*c^2))*a^2+(b^4+c^4-2*b*c*(2*b^2+b*c+2*c^2))*(b^2-c^2)^2*a-(b^2-c^2)^4*(b+c)) : :
X(49184) = 5*X(7160)-X(12842) = 2*X(12842)-5*X(49183)

The reciprocal orthologic center of these triangles is X(40).

X(49184) lies on these lines: {1, 5920}, {5, 12857}, {119, 12856}, {1470, 18979}, {2077, 12120}, {3359, 32051}, {5552, 9874}, {6735, 12777}, {10269, 22777}, {10596, 15998}, {10679, 12631}, {10942, 12858}, {11248, 12333}, {12115, 12249}, {12139, 26378}, {12200, 26432}, {12411, 26309}, {12464, 45627}, {12465, 45628}, {12500, 26318}, {12521, 48695}, {12599, 26333}, {12690, 12751}, {12703, 49178}, {12789, 26453}, {12801, 26343}, {12802, 26350}, {12855, 45655}, {12859, 26482}, {12860, 26476}, {12861, 45647}, {12862, 45646}, {12863, 26358}, {12864, 26364}, {13914, 45652}, {13978, 45653}, {18542, 48671}, {19047, 49249}, {19048, 49248}, {19085, 26459}, {19086, 26465}, {22801, 45631}, {26400, 48509}, {26424, 48510}, {26518, 49076}, {26523, 49077}, {35862, 45642}, {35863, 45643}, {45528, 48812}, {45529, 48813}

X(49184) = midpoint of X(12631) and X(12872)
X(49184) = reflection of X(i) in X(j) for these (i, j): (12857, 5), (22777, 49110), (49183, 7160)
X(49184) = orthologic center (anti-outer-Yff, Hutson extouch)
X(49184) = X(7160)-of-anti-outer-Yff triangle
X(49184) = X(12857)-of-Johnson triangle
X(49184) = X(12874)-of-anti-inner-Yff triangle
X(49184) = X(49183)-of-inner-Yff tangents triangle
X(49184) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (7160, 8000, 10075), (7160, 12874, 1)


X(49185) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO MIDHEIGHT

Barycentrics    a^2*(a^11-(b+c)*a^10-(b-c)^2*a^9+(b+c)*(b^2-4*b*c+c^2)*a^8-2*(3*b^4+3*c^4+2*b*c*(b^2-4*b*c+c^2))*a^7+2*(b+c)*(3*b^4+3*c^4+2*b*c*(b^2-4*b*c+c^2))*a^6+2*(7*b^4+7*c^4+2*b*c*(7*b^2+6*b*c+7*c^2))*(b-c)^2*a^5-2*(b^2-c^2)*(b-c)*(7*b^4+7*c^4+8*(b^2+c^2)*b*c)*a^4-(b^2-c^2)^2*(11*b^4+11*c^4-2*b*c*(2*b^2-15*b*c+2*c^2))*a^3+(b^2-c^2)^2*(b+c)*(11*b^4+11*c^4-10*b*c*(2*b^2-3*b*c+2*c^2))*a^2+(b^4-c^4)*(b^2-c^2)*(3*b^4+3*c^4-2*(b^2-7*b*c+c^2)*b*c)*a+(b^2-c^2)^3*(b-c)*(-3*b^4-3*c^4+2*(b^2-5*b*c+c^2)*b*c)) : :

The reciprocal orthologic center of these triangles is X(4).

X(49185) lies on these lines: {1, 64}, {3, 14529}, {5, 12930}, {30, 49161}, {1498, 11012}, {2777, 49159}, {2883, 26363}, {3357, 10267}, {5709, 6001}, {5878, 26470}, {6000, 11249}, {6225, 10527}, {6247, 26332}, {6266, 26349}, {6267, 26342}, {6285, 26437}, {6696, 10198}, {6734, 12779}, {7355, 26357}, {8991, 45650}, {9914, 26308}, {10606, 10902}, {10680, 13093}, {10943, 12920}, {11381, 26377}, {12116, 12250}, {12202, 26431}, {12315, 35252}, {12468, 45625}, {12469, 45626}, {12502, 26317}, {12791, 26452}, {12940, 26481}, {12950, 26475}, {12986, 45645}, {12987, 45644}, {13980, 45651}, {15311, 48482}, {16202, 35450}, {18544, 48672}, {19049, 49251}, {19050, 49250}, {19087, 26458}, {19088, 26464}, {22802, 45630}, {26399, 48513}, {26423, 48514}, {26517, 49080}, {26522, 49081}, {34146, 45728}, {35864, 45640}, {35865, 45641}, {36201, 49199}, {45526, 48816}, {45527, 48817}

X(49185) = reflection of X(i) in X(j) for these (i, j): (12335, 3357), (12930, 5), (49186, 64)
X(49185) = orthologic center (anti-inner-Yff, midheight)
X(49185) = X(64)-of-anti-inner-Yff triangle
X(49185) = X(12930)-of-Johnson triangle
X(49185) = X(13095)-of-anti-outer-Yff triangle
X(49185) = X(49186)-of-outer-Yff tangents triangle
X(49185) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (64, 7973, 10060), (64, 13095, 1)


X(49186) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO MIDHEIGHT

Barycentrics    a^2*(a^11-(b+c)*a^10-(b-c)^2*a^9+(b+c)*(b^2+c^2)*a^8-2*(3*b^4+3*c^4-2*b*c*(b+c)^2)*a^7+2*(b+c)*(3*b^4+3*c^4-2*b*c*(b+c)^2)*a^6+2*(7*b^4+7*c^4+2*b*c*(b^2-4*b*c+c^2))*(b-c)^2*a^5-2*(b^2-c^2)*(b-c)*(7*b^4+7*c^4+4*b*c*(2*b^2+b*c+2*c^2))*a^4-(b^4-c^4)*(b^2-c^2)*(11*b^2-28*b*c+11*c^2)*a^3+(b^4-c^4)*(b^2-c^2)*(b+c)*(11*b^2-12*b*c+11*c^2)*a^2+(b^2-c^2)^2*(3*b^6+3*c^6-(10*b^4+10*c^4-9*b*c*(b^2-4*b*c+c^2))*b*c)*a+(b^2-c^2)^3*(b-c)*(-3*b^4-3*c^4-2*(b^2+5*b*c+c^2)*b*c)) : :

The reciprocal orthologic center of these triangles is X(4).

X(49186) lies on these lines: {1, 64}, {5, 12920}, {30, 49162}, {119, 5878}, {1470, 6285}, {1498, 2077}, {2777, 49160}, {2883, 26364}, {3357, 10269}, {3913, 5534}, {5552, 6225}, {5895, 41698}, {6000, 11248}, {6247, 26333}, {6256, 15311}, {6266, 26350}, {6267, 26343}, {6696, 10200}, {6735, 12779}, {7355, 26358}, {8991, 45652}, {9914, 26309}, {10605, 40953}, {10606, 37561}, {10679, 13093}, {10942, 12930}, {11381, 26378}, {12115, 12250}, {12202, 26432}, {12315, 35251}, {12468, 45627}, {12469, 45628}, {12502, 26318}, {12791, 26453}, {12940, 26482}, {12950, 26476}, {12986, 45647}, {12987, 45646}, {13980, 45653}, {16203, 35450}, {18542, 48672}, {19047, 49251}, {19048, 49250}, {19087, 26459}, {19088, 26465}, {22802, 45631}, {26400, 48513}, {26424, 48514}, {26518, 49080}, {26523, 49081}, {34146, 45729}, {35864, 45642}, {35865, 45643}, {36201, 49200}, {45528, 48816}, {45529, 48817}

X(49186) = reflection of X(i) in X(j) for these (i, j): (12920, 5), (22778, 3357), (49185, 64)
X(49186) = orthologic center (anti-outer-Yff, midheight)
X(49186) = X(64)-of-anti-outer-Yff triangle
X(49186) = X(12920)-of-Johnson triangle
X(49186) = X(13094)-of-anti-inner-Yff triangle
X(49186) = X(49185)-of-inner-Yff tangents triangle
X(49186) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (64, 7973, 10076), (64, 13094, 1)


X(49187) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 1st NEUBERG

Barycentrics    ((2*b^2+b*c+2*c^2)*a^4-2*(b^2+c^2)*b*c*a^2-2*(b+c)*b^2*c^2*a+(b^2-c^2)^2*b*c)/a : :
X(49187) = 4*X(10943)-3*X(49166)

The reciprocal orthologic center of these triangles is X(3).

X(49187) lies on these lines: {1, 76}, {5, 12933}, {39, 26363}, {194, 10527}, {384, 26431}, {511, 48482}, {538, 45700}, {726, 10916}, {732, 45728}, {946, 46180}, {2782, 11249}, {3095, 26470}, {3734, 10804}, {3934, 10198}, {5969, 49149}, {6248, 26332}, {6272, 26349}, {6273, 26342}, {6734, 12782}, {8992, 45650}, {9917, 26308}, {9983, 26317}, {10267, 12338}, {10529, 20081}, {10680, 13108}, {10902, 22712}, {10943, 12923}, {11012, 11257}, {12116, 12251}, {12143, 26377}, {12474, 45625}, {12475, 45626}, {12794, 26452}, {12836, 26475}, {12837, 26481}, {12992, 45645}, {12993, 45644}, {13077, 26357}, {13983, 45651}, {14839, 49168}, {14881, 45630}, {18544, 48673}, {18982, 26437}, {19049, 49253}, {19050, 49252}, {19089, 26458}, {19090, 26464}, {26399, 48515}, {26423, 48516}, {26517, 49082}, {26522, 49083}, {35866, 45640}, {35867, 45641}, {45526, 48818}, {45527, 48819}

X(49187) = reflection of X(i) in X(j) for these (i, j): (12338, 49111), (12933, 5), (49188, 76)
X(49187) = orthologic center (anti-inner-Yff, 1st Neuberg)
X(49187) = X(76)-of-anti-inner-Yff triangle
X(49187) = X(12933)-of-Johnson triangle
X(49187) = X(13110)-of-anti-outer-Yff triangle
X(49187) = X(49188)-of-outer-Yff tangents triangle
X(49187) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (76, 7976, 10063), (76, 13110, 1)


X(49188) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 1st NEUBERG

Barycentrics    ((2*b^2-b*c+2*c^2)*a^4+2*(b^2+c^2)*b*c*a^2-2*(b+c)*b^2*c^2*a-(b^2-c^2)^2*b*c)/a : :
X(49188) = 4*X(10942)-3*X(49167)

The reciprocal orthologic center of these triangles is X(3).

X(49188) lies on these lines: {1, 76}, {5, 12923}, {39, 26364}, {119, 3095}, {194, 5552}, {384, 26432}, {511, 6256}, {538, 45701}, {726, 10915}, {732, 45729}, {1470, 18982}, {2077, 11257}, {2782, 11248}, {3734, 10803}, {3934, 10200}, {5969, 49150}, {6248, 26333}, {6272, 26350}, {6273, 26343}, {6735, 12782}, {8992, 45652}, {9917, 26309}, {9983, 26318}, {10269, 22779}, {10528, 20081}, {10679, 13108}, {10942, 12933}, {12115, 12251}, {12143, 26378}, {12474, 45627}, {12475, 45628}, {12794, 26453}, {12836, 26476}, {12837, 26482}, {12992, 45647}, {12993, 45646}, {13077, 26358}, {13983, 45653}, {14839, 49169}, {14881, 45631}, {18542, 48673}, {19047, 49253}, {19048, 49252}, {19089, 26459}, {19090, 26465}, {22712, 37561}, {26400, 48515}, {26424, 48516}, {26518, 49082}, {26523, 49083}, {32454, 39692}, {35866, 45642}, {35867, 45643}, {45528, 48818}, {45529, 48819}

X(49188) = reflection of X(i) in X(j) for these (i, j): (12923, 5), (22779, 49111), (49187, 76)
X(49188) = orthologic center (anti-outer-Yff, 1st Neuberg)
X(49188) = X(76)-of-anti-outer-Yff triangle
X(49188) = X(12923)-of-Johnson triangle
X(49188) = X(13109)-of-anti-inner-Yff triangle
X(49188) = X(49187)-of-inner-Yff tangents triangle
X(49188) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (76, 7976, 10079), (76, 13109, 1)


X(49189) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 2nd NEUBERG

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

The reciprocal orthologic center of these triangles is X(3).

X(49189) lies on these lines: {1, 83}, {5, 12934}, {732, 45728}, {754, 45700}, {2896, 10527}, {3072, 10916}, {6249, 26332}, {6274, 26349}, {6275, 26342}, {6287, 26470}, {6292, 26363}, {6704, 10198}, {6734, 12783}, {8993, 45650}, {9751, 10902}, {9918, 26308}, {10267, 12339}, {10529, 20088}, {10680, 13111}, {10943, 12182}, {11012, 12122}, {11249, 22680}, {12116, 12252}, {12144, 26377}, {12206, 26431}, {12476, 45625}, {12477, 45626}, {12595, 24273}, {12795, 26452}, {12944, 26481}, {12954, 26475}, {12994, 45645}, {12995, 45644}, {13078, 26357}, {13984, 45651}, {18544, 48674}, {18983, 26437}, {19049, 49255}, {19050, 49254}, {19091, 26458}, {19092, 26464}, {22803, 45630}, {26399, 48517}, {26423, 48518}, {26517, 49084}, {26522, 49085}, {29012, 48482}, {35868, 45640}, {35869, 45641}, {45526, 48770}, {45527, 48771}

X(49189) = reflection of X(i) in X(j) for these (i, j): (12339, 49112), (12934, 5), (49190, 83)
X(49189) = orthologic center (anti-inner-Yff, 2nd Neuberg)
X(49189) = X(83)-of-anti-inner-Yff triangle
X(49189) = X(12934)-of-Johnson triangle
X(49189) = X(13113)-of-anti-outer-Yff triangle
X(49189) = X(49190)-of-outer-Yff tangents triangle
X(49189) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (83, 7977, 10064), (83, 13113, 1)


X(49190) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 2nd NEUBERG

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

The reciprocal orthologic center of these triangles is X(3).

X(49190) lies on these lines: {1, 83}, {5, 12924}, {119, 6287}, {732, 45729}, {754, 45701}, {1470, 18983}, {2077, 12122}, {2896, 5552}, {6249, 26333}, {6256, 29012}, {6274, 26350}, {6275, 26343}, {6292, 26364}, {6704, 10200}, {6735, 12783}, {8993, 45652}, {9751, 37561}, {9918, 26309}, {10269, 22780}, {10528, 20088}, {10679, 13111}, {10915, 12618}, {10942, 12183}, {11248, 12339}, {12115, 12252}, {12144, 26378}, {12206, 26432}, {12476, 45627}, {12477, 45628}, {12594, 24273}, {12795, 26453}, {12944, 26482}, {12954, 26476}, {12994, 45647}, {12995, 45646}, {13078, 26358}, {13984, 45653}, {18542, 48674}, {19047, 49255}, {19048, 49254}, {19091, 26459}, {19092, 26465}, {22803, 45631}, {26400, 48517}, {26424, 48518}, {26518, 49084}, {26523, 49085}, {35868, 45642}, {35869, 45643}, {45528, 48770}, {45529, 48771}

X(49190) = reflection of X(i) in X(j) for these (i, j): (12924, 5), (22780, 49112), (49189, 83)
X(49190) = orthologic center (anti-outer-Yff, 2nd Neuberg)
X(49190) = X(83)-of-anti-outer-Yff triangle
X(49190) = X(12924)-of-Johnson triangle
X(49190) = X(13112)-of-anti-inner-Yff triangle
X(49190) = X(49189)-of-inner-Yff tangents triangle
X(49190) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (83, 7977, 10080), (83, 13112, 1)


X(49191) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO REFLECTION

Barycentrics    a^2*(a^11-(b+c)*a^10-2*(2*b^2-b*c+2*c^2)*a^9+4*(b^3+c^3)*a^8+(6*b^4+6*c^4-b*c*(4*b^2-13*b*c+4*c^2))*a^7-(b+c)*(6*b^4+6*c^4-b*c*(10*b^2-13*b*c+10*c^2))*a^6-(4*b^6+4*c^6+b^2*c^2*(9*b^2-2*b*c+9*c^2))*a^5+(b+c)*(4*b^6+4*c^6-(6*b^4+6*c^4-b*c*(9*b^2-8*b*c+9*c^2))*b*c)*a^4+(b^6+c^6+2*(3*b^4+3*c^4+b*c*(3*b^2+4*b*c+3*c^2))*b*c)*(b-c)^2*a^3-(b^6-c^6)*(b-c)*(b^2+4*b*c+c^2)*a^2-(b^4-c^4)*(b^2-c^2)*b*c*(b-2*c)*(2*b-c)*a+(b^2-c^2)^3*(b-c)*b*c*(2*b^2-b*c+2*c^2)) : :

The reciprocal orthologic center of these triangles is X(4).

X(49191) lies on these lines: {1, 54}, {5, 12936}, {195, 10680}, {539, 45700}, {1154, 11249}, {1209, 26363}, {2888, 10527}, {3574, 26332}, {6276, 26349}, {6277, 26342}, {6288, 26470}, {6689, 10198}, {6734, 12785}, {7691, 11012}, {8995, 45650}, {9920, 26308}, {9985, 26317}, {10267, 10610}, {10628, 49151}, {10943, 12889}, {11576, 26377}, {12116, 12254}, {12208, 26431}, {12307, 35252}, {12382, 43580}, {12480, 45625}, {12481, 45626}, {12797, 26452}, {12946, 26481}, {12956, 26475}, {12965, 45640}, {12971, 45641}, {12998, 45645}, {12999, 45644}, {13079, 26357}, {13986, 45651}, {18400, 48482}, {18544, 48675}, {18984, 26437}, {19049, 49257}, {19050, 49256}, {19095, 26458}, {19096, 26464}, {22804, 45630}, {24474, 32379}, {26399, 48521}, {26423, 48522}, {26517, 49088}, {26522, 49089}, {32214, 36966}, {44668, 45728}, {45526, 48774}, {45527, 48775}

X(49191) = reflection of X(i) in X(j) for these (i, j): (12341, 10610), (12936, 5), (49192, 54)
X(49191) = orthologic center (anti-inner-Yff, reflection)
X(49191) = X(54)-of-anti-inner-Yff triangle
X(49191) = X(12936)-of-Johnson triangle
X(49191) = X(13122)-of-anti-outer-Yff triangle
X(49191) = X(49192)-of-outer-Yff tangents triangle
X(49191) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (54, 7979, 10066), (54, 13121, 47378), (54, 13122, 1)


X(49192) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO REFLECTION

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

The reciprocal orthologic center of these triangles is X(4).

X(49192) lies on these lines: {1, 54}, {5, 12926}, {119, 6288}, {195, 10679}, {539, 45701}, {1154, 11248}, {1209, 26364}, {1470, 18984}, {1493, 37622}, {2077, 7691}, {2888, 5552}, {3574, 26333}, {6255, 15801}, {6256, 18400}, {6276, 26350}, {6277, 26343}, {6689, 10200}, {6735, 12785}, {8995, 45652}, {9920, 26309}, {9985, 26318}, {10269, 10610}, {10628, 49152}, {10942, 12890}, {11576, 26378}, {12115, 12254}, {12208, 26432}, {12307, 35251}, {12381, 43580}, {12480, 45627}, {12481, 45628}, {12797, 26453}, {12946, 26482}, {12956, 26476}, {12965, 45642}, {12971, 45643}, {12998, 45647}, {12999, 45646}, {13079, 26358}, {13986, 45653}, {18542, 48675}, {19047, 49257}, {19048, 49256}, {19095, 26459}, {19096, 26465}, {22804, 45631}, {26400, 48521}, {26424, 48522}, {26518, 49088}, {26523, 49089}, {32213, 36966}, {44668, 45729}, {45528, 48774}, {45529, 48775}

X(49192) = reflection of X(i) in X(j) for these (i, j): (12926, 5), (22781, 10610), (49191, 54)
X(49192) = orthologic center (anti-outer-Yff, reflection)
X(49192) = X(54)-of-anti-outer-Yff triangle
X(49192) = X(12926)-of-Johnson triangle
X(49192) = X(13121)-of-anti-inner-Yff triangle
X(49192) = X(49191)-of-inner-Yff tangents triangle
X(49192) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (54, 7979, 10082), (54, 13121, 1), (9905, 47378, 54)


X(49193) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 1st SCHIFFLER

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

The reciprocal orthologic center of these triangles is X(79).

X(49193) lies on these lines: {1, 5180}, {5, 12937}, {2475, 11571}, {3928, 12660}, {6734, 12786}, {6923, 49168}, {10267, 12342}, {10527, 12849}, {10680, 13126}, {10943, 12927}, {11012, 12556}, {11249, 22782}, {12116, 12255}, {12146, 26377}, {12209, 26431}, {12414, 26308}, {12482, 45625}, {12483, 45626}, {12504, 26317}, {12524, 33668}, {12535, 23016}, {12543, 45700}, {12600, 26332}, {12623, 13465}, {12639, 49183}, {12798, 26452}, {12807, 26342}, {12808, 26349}, {12917, 45654}, {12919, 26470}, {12947, 26481}, {12957, 26475}, {13000, 45645}, {13001, 45644}, {13080, 26357}, {13089, 26363}, {13919, 45650}, {13987, 45651}, {16116, 49176}, {18544, 48676}, {18985, 26437}, {19049, 49259}, {19050, 49258}, {19097, 26458}, {19098, 26464}, {22805, 45630}, {26399, 48523}, {26423, 48524}, {26517, 49090}, {26522, 49091}, {33859, 45638}, {35870, 45640}, {35871, 45641}, {45526, 48776}, {45527, 48777}

X(49193) = reflection of X(i) in X(j) for these (i, j): (12342, 49113), (12524, 33668), (12535, 23016), (12937, 5), (13465, 12623), (49194, 10266)
X(49193) = orthologic center (anti-inner-Yff, 1st Schiffler)
X(49193) = X(10266)-of-anti-inner-Yff triangle
X(49193) = X(12937)-of-Johnson triangle
X(49193) = X(13131)-of-anti-outer-Yff triangle
X(49193) = X(49194)-of-outer-Yff tangents triangle
X(49193) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (10266, 12913, 13129), (10266, 13100, 13128), (10266, 13131, 1), (10266, 14450, 13100), (12409, 18244, 10266)


X(49194) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 1st SCHIFFLER

Barycentrics    a^10-(5*b^2-8*b*c+5*c^2)*a^8-4*(b+c)*b*c*a^7+(10*b^4+10*c^4-b*c*(18*b^2-17*b*c+18*c^2))*a^6+2*(b+c)*(2*b^2+b*c+2*c^2)*b*c*a^5-2*(5*b^6+5*c^6-(7*b^4+7*c^4-(b-c)^2*b*c)*b*c)*a^4+2*(b+c)*(2*b^4+2*c^4-5*(b^2-b*c+c^2)*b*c)*b*c*a^3+(5*b^4+5*c^4-3*b*c*(2*b^2+b*c+2*c^2))*(b^2-c^2)^2*a^2-4*(b^2-c^2)^3*(b-c)*b*c*a-(b^2-c^2)^4*(b-c)^2 : :

The reciprocal orthologic center of these triangles is X(79).

X(49194) lies on these lines: {1, 5180}, {5, 12927}, {119, 12919}, {1470, 18985}, {2077, 12556}, {5552, 12849}, {6595, 39692}, {6735, 12786}, {10269, 22782}, {10679, 13126}, {10942, 12937}, {11248, 12342}, {12115, 12255}, {12146, 26378}, {12209, 26432}, {12414, 26309}, {12482, 45627}, {12483, 45628}, {12504, 26318}, {12524, 48695}, {12600, 26333}, {12639, 49171}, {12798, 26453}, {12807, 26343}, {12808, 26350}, {12917, 45655}, {12947, 26482}, {12957, 26476}, {13000, 45647}, {13001, 45646}, {13080, 26358}, {13089, 26364}, {13919, 45652}, {13987, 45653}, {18542, 48676}, {19047, 49259}, {19048, 49258}, {19097, 26459}, {19098, 26465}, {22805, 45631}, {26400, 48523}, {26424, 48524}, {26518, 49090}, {26523, 49091}, {33859, 45639}, {35870, 45642}, {35871, 45643}, {45528, 48776}, {45529, 48777}

X(49194) = reflection of X(i) in X(j) for these (i, j): (12927, 5), (22782, 49113), (49193, 10266)
X(49194) = orthologic center (anti-outer-Yff, 1st Schiffler)
X(49194) = X(10266)-of-anti-outer-Yff triangle
X(49194) = X(12927)-of-Johnson triangle
X(49194) = X(13130)-of-anti-inner-Yff triangle
X(49194) = X(49193)-of-inner-Yff tangents triangle
X(49194) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (10266, 13100, 13129), (10266, 13130, 1), (10266, 13131, 18244)


X(49195) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 1st TRI-SQUARES-CENTRAL

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

The reciprocal orthologic center of these triangles is X(13665).

X(49195) lies on these lines: {1, 1327}, {5, 13694}, {30, 49157}, {6734, 13688}, {10267, 13675}, {10527, 13678}, {10680, 13713}, {10943, 13693}, {11012, 13666}, {11240, 33456}, {11249, 22783}, {12116, 13674}, {13668, 26377}, {13672, 26431}, {13680, 26308}, {13682, 45625}, {13683, 45626}, {13685, 26317}, {13687, 26332}, {13689, 26452}, {13690, 26342}, {13691, 26349}, {13692, 26470}, {13695, 26481}, {13696, 26475}, {13697, 45645}, {13698, 45644}, {13699, 26357}, {13701, 26363}, {13920, 45650}, {13988, 45651}, {15682, 26517}, {18544, 48677}, {18986, 26437}, {19049, 49261}, {19050, 49260}, {19099, 26458}, {22541, 26464}, {22806, 45630}, {26399, 48525}, {26423, 48526}, {26522, 49093}, {35872, 45640}, {35873, 45641}, {45526, 48778}, {45527, 48780}, {45728, 49197}

X(49195) = reflection of X(i) in X(j) for these (i, j): (13675, 49114), (13694, 5), (49196, 1327)
X(49195) = orthologic center (anti-inner-Yff, 1st tri-squares-central)
X(49195) = X(1327)-of-anti-inner-Yff triangle
X(49195) = X(13694)-of-Johnson triangle
X(49195) = X(13717)-of-anti-outer-Yff triangle
X(49195) = X(49196)-of-outer-Yff tangents triangle
X(49195) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1327, 13702, 13714), (1327, 13717, 1)


X(49196) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 1st TRI-SQUARES-CENTRAL

Barycentrics    6*(a^4-2*(b^2+c^2)*a^2+2*(b+c)*b*c*a+b^4+c^4-2*(b^2+b*c+c^2)*b*c)*S*a^2+(a+b+c)*(4*a^7-4*(b+c)*a^6-(3*b^2-28*b*c+3*c^2)*a^5+(b+c)*(3*b^2-20*b*c+3*c^2)*a^4-2*(3*b^4+3*c^4+4*(b^2-4*b*c+c^2)*b*c)*a^3+2*(b^2-c^2)*(b-c)*(3*b^2+11*b*c+3*c^2)*a^2+5*(b^2-c^2)^2*(b^2-4*b*c+c^2)*a-5*(b^2-c^2)^3*(b-c)) : :

The reciprocal orthologic center of these triangles is X(13665).

X(49196) lies on these lines: {1, 1327}, {5, 13693}, {30, 49158}, {119, 13692}, {1470, 18986}, {2077, 13666}, {5552, 13678}, {6735, 13688}, {10269, 22783}, {10679, 13713}, {10942, 13694}, {11239, 33456}, {11248, 13675}, {12115, 13674}, {13668, 26378}, {13672, 26432}, {13680, 26309}, {13682, 45627}, {13683, 45628}, {13685, 26318}, {13687, 26333}, {13689, 26453}, {13690, 26343}, {13691, 26350}, {13695, 26482}, {13696, 26476}, {13697, 45647}, {13698, 45646}, {13699, 26358}, {13701, 26364}, {13920, 45652}, {13988, 45653}, {15682, 26518}, {18542, 48677}, {19047, 49261}, {19048, 49260}, {19099, 26459}, {22541, 26465}, {22806, 45631}, {26400, 48525}, {26424, 48526}, {26523, 49093}, {35872, 45642}, {35873, 45643}, {45528, 48778}, {45529, 48780}, {45729, 49198}

X(49196) = reflection of X(i) in X(j) for these (i, j): (13693, 5), (22783, 49114), (49195, 1327)
X(49196) = orthologic center (anti-outer-Yff, 1st tri-squares-central)
X(49196) = X(1327)-of-anti-outer-Yff triangle
X(49196) = X(13693)-of-Johnson triangle
X(49196) = X(13716)-of-anti-inner-Yff triangle
X(49196) = X(49195)-of-inner-Yff tangents triangle
X(49196) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1327, 13702, 13715), (1327, 13716, 1)


X(49197) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 2nd TRI-SQUARES-CENTRAL

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

The reciprocal orthologic center of these triangles is X(13785).

X(49197) lies on these lines: {1, 1328}, {5, 13814}, {30, 49155}, {6734, 13808}, {10267, 13795}, {10527, 13798}, {10680, 13836}, {10943, 13813}, {11012, 13786}, {11240, 33457}, {11249, 22784}, {12116, 13794}, {13788, 26377}, {13792, 26431}, {13800, 26308}, {13802, 45625}, {13803, 45626}, {13805, 26317}, {13807, 26332}, {13809, 26452}, {13810, 26342}, {13811, 26349}, {13812, 26470}, {13815, 26481}, {13816, 26475}, {13817, 45645}, {13818, 45644}, {13819, 26357}, {13821, 26363}, {13848, 45650}, {13849, 45651}, {15682, 26522}, {18544, 48678}, {18987, 26437}, {19049, 49263}, {19050, 49262}, {19100, 26464}, {19101, 26458}, {22807, 45630}, {26399, 48527}, {26423, 48528}, {26517, 49092}, {35874, 45640}, {35875, 45641}, {45526, 48781}, {45527, 48779}, {45728, 49195}

X(49197) = reflection of X(i) in X(j) for these (i, j): (13795, 49115), (13814, 5), (49198, 1328)
X(49197) = orthologic center (anti-inner-Yff, 2nd tri-squares-central)
X(49197) = X(1328)-of-anti-inner-Yff triangle
X(49197) = X(13814)-of-Johnson triangle
X(49197) = X(13840)-of-anti-outer-Yff triangle
X(49197) = X(49198)-of-outer-Yff tangents triangle
X(49197) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1328, 13822, 13837), (1328, 13840, 1)


X(49198) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    -6*(a^4-2*(b^2+c^2)*a^2+2*(b+c)*b*c*a+b^4+c^4-2*(b^2+b*c+c^2)*b*c)*S*a^2+(a+b+c)*(4*a^7-4*(b+c)*a^6-(3*b^2-28*b*c+3*c^2)*a^5+(b+c)*(3*b^2-20*b*c+3*c^2)*a^4-2*(3*b^4+3*c^4+4*(b^2-4*b*c+c^2)*b*c)*a^3+2*(b^2-c^2)*(b-c)*(3*b^2+11*b*c+3*c^2)*a^2+5*(b^2-c^2)^2*(b^2-4*b*c+c^2)*a-5*(b^2-c^2)^3*(b-c)) : :

The reciprocal orthologic center of these triangles is X(13785).

X(49198) lies on these lines: {1, 1328}, {5, 13813}, {30, 49156}, {119, 13812}, {1470, 18987}, {2077, 13786}, {5552, 13798}, {6735, 13808}, {10269, 22784}, {10679, 13836}, {10942, 13814}, {11239, 33457}, {11248, 13795}, {12115, 13794}, {13788, 26378}, {13792, 26432}, {13800, 26309}, {13802, 45627}, {13803, 45628}, {13805, 26318}, {13807, 26333}, {13809, 26453}, {13810, 26343}, {13811, 26350}, {13815, 26482}, {13816, 26476}, {13817, 45647}, {13818, 45646}, {13819, 26358}, {13821, 26364}, {13848, 45652}, {13849, 45653}, {15682, 26523}, {18542, 48678}, {19047, 49263}, {19048, 49262}, {19100, 26465}, {19101, 26459}, {22807, 45631}, {26400, 48527}, {26424, 48528}, {26518, 49092}, {35874, 45642}, {35875, 45643}, {45528, 48781}, {45529, 48779}, {45729, 49196}

X(49198) = reflection of X(i) in X(j) for these (i, j): (13813, 5), (22784, 49115), (49197, 1328)
X(49198) = orthologic center (anti-outer-Yff, 2nd tri-squares-central)
X(49198) = X(1328)-of-anti-outer-Yff triangle
X(49198) = X(13813)-of-Johnson triangle
X(49198) = X(13839)-of-anti-inner-Yff triangle
X(49198) = X(49197)-of-inner-Yff tangents triangle
X(49198) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1328, 13822, 13838), (1328, 13839, 1)


X(49199) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(49199) lies on these lines: {1, 67}, {5, 32288}, {511, 49159}, {518, 13214}, {542, 11249}, {1503, 49151}, {2781, 48482}, {6593, 26363}, {6698, 10198}, {6734, 32278}, {9970, 26470}, {10267, 32256}, {10527, 11061}, {10680, 32306}, {10943, 32287}, {11012, 32233}, {12116, 32247}, {14984, 49161}, {18544, 48679}, {19049, 49265}, {19050, 49264}, {26308, 32262}, {26317, 32268}, {26332, 32274}, {26342, 32280}, {26349, 32281}, {26357, 32297}, {26377, 32239}, {26399, 48529}, {26423, 48530}, {26431, 32242}, {26437, 32243}, {26452, 32279}, {26458, 32252}, {26464, 32253}, {26475, 32290}, {26481, 32289}, {26517, 49094}, {26522, 49095}, {32265, 45625}, {32266, 45626}, {32271, 45630}, {32295, 45645}, {32296, 45644}, {32303, 45650}, {32304, 45651}, {35876, 45640}, {35877, 45641}, {36201, 49185}, {45526, 48782}, {45527, 48783}

X(49199) = reflection of X(i) in X(j) for these (i, j): (32256, 49116), (32288, 5), (49200, 67)
X(49199) = orthologic center (anti-inner-Yff, Walsmith)
X(49199) = X(67)-of-anti-inner-Yff triangle
X(49199) = X(32288)-of-Johnson triangle
X(49199) = X(32310)-of-anti-outer-Yff triangle
X(49199) = X(49200)-of-outer-Yff tangents triangle
X(49199) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (67, 32298, 32307), (67, 32310, 1)


X(49200) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(49200) lies on these lines: {1, 67}, {5, 32287}, {119, 9970}, {511, 49160}, {542, 11248}, {1470, 32243}, {1503, 49152}, {2077, 32233}, {2781, 6256}, {5552, 11061}, {6593, 26364}, {6698, 10200}, {6735, 32278}, {10269, 32270}, {10679, 32306}, {10942, 32288}, {12115, 32247}, {14984, 49162}, {18542, 48679}, {19047, 49265}, {19048, 49264}, {26309, 32262}, {26318, 32268}, {26333, 32274}, {26343, 32280}, {26350, 32281}, {26358, 32297}, {26378, 32239}, {26400, 48529}, {26424, 48530}, {26432, 32242}, {26453, 32279}, {26459, 32252}, {26465, 32253}, {26476, 32290}, {26482, 32289}, {26518, 49094}, {26523, 49095}, {32265, 45627}, {32266, 45628}, {32271, 45631}, {32295, 45647}, {32296, 45646}, {32303, 45652}, {32304, 45653}, {35876, 45642}, {35877, 45643}, {36201, 49186}, {45528, 48782}, {45529, 48783}

X(49200) = reflection of X(i) in X(j) for these (i, j): (32270, 49116), (32287, 5), (49199, 67)
X(49200) = orthologic center (anti-outer-Yff, Walsmith)
X(49200) = X(67)-of-anti-outer-Yff triangle
X(49200) = X(32287)-of-Johnson triangle
X(49200) = X(32309)-of-anti-inner-Yff triangle
X(49200) = X(49199)-of-inner-Yff tangents triangle
X(49200) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (67, 32298, 32308), (67, 32309, 1)


X(49201) = PARALLELOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 1st ANTI-BROCARD

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

The reciprocal parallelogic center of these triangles is X(385).

X(49201) lies on the circumcircle of anti-inner-Yff triangle and these lines: {1, 99}, {5, 13181}, {98, 11012}, {114, 26332}, {115, 26363}, {148, 10527}, {542, 49151}, {543, 45700}, {620, 10198}, {690, 49203}, {2782, 11249}, {2783, 48694}, {2787, 48713}, {2794, 49153}, {2799, 49205}, {3023, 26357}, {3027, 26437}, {4027, 26431}, {5186, 26377}, {5969, 45728}, {6319, 26342}, {6320, 26349}, {6321, 26470}, {6734, 13178}, {7970, 37625}, {8591, 11240}, {8782, 26317}, {8997, 45650}, {10267, 13173}, {10529, 20094}, {10680, 13188}, {10902, 21166}, {10943, 13180}, {12116, 13172}, {12188, 35252}, {12190, 23235}, {13175, 26308}, {13176, 45625}, {13177, 45626}, {13179, 26452}, {13182, 26481}, {13183, 26475}, {13184, 45645}, {13185, 45644}, {13989, 45651}, {18544, 38733}, {19049, 49267}, {19050, 49266}, {19108, 26458}, {19109, 26464}, {22515, 45630}, {23698, 48482}, {24541, 38220}, {26399, 48531}, {26423, 48532}, {26517, 49096}, {26522, 49097}, {35878, 45640}, {35879, 45641}, {45526, 48784}, {45527, 48785}

X(49201) = reflection of X(i) in X(j) for these (i, j): (13173, 33813), (13181, 5), (49147, 11249), (49149, 45700), (49202, 99)
X(49201) = parallelogic center (anti-inner-Yff, T) for these triangles T: 1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard
X(49201) = X(99)-of-anti-inner-Yff triangle
X(49201) = X(13181)-of-Johnson triangle
X(49201) = X(13190)-of-anti-outer-Yff triangle
X(49201) = X(49202)-of-outer-Yff tangents triangle
X(49201) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (99, 7983, 10086), (99, 13190, 1)


X(49202) = PARALLELOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 1st ANTI-BROCARD

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

The reciprocal parallelogic center of these triangles is X(385).

X(49202) lies on the circumcircle of anti-outer-Yff triangle and these lines: {1, 99}, {5, 13180}, {98, 2077}, {114, 26333}, {115, 26364}, {119, 6321}, {148, 5552}, {542, 49152}, {543, 45701}, {620, 10200}, {690, 49204}, {1470, 3027}, {2782, 11248}, {2783, 48695}, {2787, 25438}, {2794, 49154}, {2798, 49207}, {2799, 49206}, {3023, 26358}, {4027, 26432}, {5186, 26378}, {5969, 45729}, {6256, 23698}, {6319, 26343}, {6320, 26350}, {6735, 13178}, {8591, 11239}, {8782, 26318}, {8997, 45652}, {10053, 38499}, {10269, 22514}, {10528, 20094}, {10679, 13188}, {10723, 41698}, {10769, 39692}, {10942, 13181}, {12115, 13172}, {12188, 35251}, {12189, 23235}, {13175, 26309}, {13176, 45627}, {13177, 45628}, {13179, 26453}, {13182, 26482}, {13183, 26476}, {13184, 45647}, {13185, 45646}, {13989, 45653}, {18542, 38733}, {19047, 49267}, {19048, 49266}, {19108, 26459}, {19109, 26465}, {21166, 37561}, {22515, 45631}, {26400, 48531}, {26424, 48532}, {26518, 49096}, {26523, 49097}, {35878, 45642}, {35879, 45643}, {45528, 48784}, {45529, 48785}

X(49202) = reflection of X(i) in X(j) for these (i, j): (13180, 5), (22514, 33813), (49148, 11248), (49150, 45701), (49201, 99)
X(49202) = parallelogic center (anti-outer-Yff, T) for these triangles T: 1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard
X(49202) = X(99)-of-anti-outer-Yff triangle
X(49202) = X(13180)-of-Johnson triangle
X(49202) = X(13189)-of-anti-inner-Yff triangle
X(49202) = X(49201)-of-inner-Yff tangents triangle
X(49202) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (99, 7983, 10089), (99, 13189, 1)


X(49203) = PARALLELOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO ANTI-ORTHOCENTROIDAL

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

The reciprocal parallelogic center of these triangles is X(323).

X(49203) lies on the circumcircle of anti-inner-Yff triangle and these lines: {1, 60}, {5, 13214}, {74, 11012}, {113, 26332}, {125, 26363}, {265, 26470}, {399, 10680}, {518, 32288}, {542, 45700}, {690, 49201}, {952, 12890}, {1112, 26377}, {1511, 10267}, {2771, 48694}, {2781, 49153}, {2854, 45728}, {2930, 12595}, {3024, 26357}, {3028, 26437}, {3448, 10527}, {5663, 11249}, {5972, 10198}, {6734, 13211}, {7732, 26342}, {7733, 26349}, {7978, 37625}, {8674, 48713}, {8998, 45650}, {9143, 11240}, {9517, 49205}, {10113, 45630}, {10529, 14683}, {10597, 20125}, {10620, 35252}, {10902, 15035}, {10943, 12889}, {11401, 19504}, {12116, 12383}, {12310, 26308}, {12375, 45640}, {12376, 45641}, {12382, 14094}, {12902, 18544}, {12903, 26481}, {12904, 26475}, {12906, 23236}, {13106, 37753}, {13107, 37752}, {13190, 15342}, {13193, 26431}, {13208, 45625}, {13209, 45626}, {13210, 26317}, {13212, 26452}, {13215, 45645}, {13216, 45644}, {13990, 45651}, {15034, 34486}, {16202, 32609}, {17702, 48482}, {19049, 49269}, {19050, 49268}, {19110, 26458}, {19111, 26464}, {26399, 48535}, {26423, 48536}, {26517, 49098}, {26522, 49099}, {43598, 43862}, {45526, 48786}, {45527, 48787}

X(49203) = reflection of X(i) in X(j) for these (i, j): (13204, 1511), (13214, 5), (49151, 11249), (49159, 10943), (49204, 110)
X(49203) = parallelogic center (anti-inner-Yff, T) for these triangles T: anti-orthocentroidal, orthocentroidal
X(49203) = X(110)-of-anti-inner-Yff triangle
X(49203) = X(13214)-of-Johnson triangle
X(49203) = X(13218)-of-anti-outer-Yff triangle
X(49203) = X(49204)-of-outer-Yff tangents triangle
X(49203) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (110, 7984, 10088), (110, 13218, 1)


X(49204) = PARALLELOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO ANTI-ORTHOCENTROIDAL

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

The reciprocal parallelogic center of these triangles is X(323).

X(49204) lies on the circumcircle of anti-outer-Yff triangle and these lines: {1, 60}, {5, 13213}, {74, 2077}, {113, 26333}, {119, 265}, {125, 26364}, {399, 10679}, {542, 45701}, {690, 49202}, {952, 12889}, {1112, 26378}, {1470, 3028}, {1511, 10269}, {2771, 34862}, {2781, 49154}, {2836, 10202}, {2842, 15035}, {2850, 49207}, {2854, 45729}, {2930, 12594}, {3024, 26358}, {3448, 5552}, {5609, 37622}, {5663, 11248}, {5972, 10200}, {6256, 17702}, {6735, 13211}, {7724, 12381}, {7732, 26343}, {7733, 26350}, {8674, 25438}, {8998, 45652}, {9143, 11239}, {9517, 49206}, {10065, 38508}, {10113, 45631}, {10528, 14683}, {10596, 20125}, {10620, 35251}, {10693, 41389}, {10733, 41698}, {10778, 39692}, {10942, 12890}, {11400, 19504}, {12115, 12383}, {12310, 26309}, {12375, 45642}, {12376, 45643}, {12778, 37562}, {12902, 18542}, {12903, 26482}, {12904, 26476}, {12905, 23236}, {13104, 37753}, {13105, 37752}, {13189, 15342}, {13193, 26432}, {13208, 45627}, {13209, 45628}, {13210, 26318}, {13212, 26453}, {13215, 45647}, {13216, 45646}, {13990, 45653}, {16203, 32609}, {19047, 49269}, {19048, 49268}, {19110, 26459}, {19111, 26465}, {26400, 48535}, {26424, 48536}, {26518, 49098}, {26523, 49099}, {43598, 43861}, {45528, 48786}, {45529, 48787}

X(49204) = reflection of X(i) in X(j) for these (i, j): (13213, 5), (22586, 1511), (49152, 11248), (49160, 10942), (49203, 110)
X(49204) = parallelogic center (anti-outer-Yff, T) for these triangles T: anti-orthocentroidal, orthocentroidal
X(49204) = X(110)-of-anti-outer-Yff triangle
X(49204) = X(13213)-of-Johnson triangle
X(49204) = X(13217)-of-anti-inner-Yff triangle
X(49204) = X(49203)-of-inner-Yff tangents triangle
X(49204) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (110, 7984, 10091), (110, 13217, 1)


X(49205) = PARALLELOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-YFF TO 1st ANTI-ORTHOSYMMEDIAL

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

The reciprocal parallelogic center of these triangles is X(10313).

X(49205) lies on the circumcircle of anti-inner-Yff triangle and these lines: {1, 112}, {5, 13295}, {127, 26363}, {132, 26332}, {1297, 11012}, {2781, 45728}, {2794, 48482}, {2799, 49201}, {2806, 48713}, {2831, 48694}, {3320, 26437}, {6020, 26357}, {6720, 10198}, {6734, 13280}, {9517, 49203}, {10267, 13206}, {10527, 13219}, {10680, 13310}, {10749, 26470}, {10902, 38699}, {10943, 13294}, {11249, 19159}, {11641, 26308}, {12116, 13200}, {13099, 37625}, {13115, 35252}, {13119, 38676}, {13166, 26377}, {13195, 26431}, {13229, 45625}, {13231, 45626}, {13236, 26317}, {13281, 26452}, {13282, 26342}, {13283, 26349}, {13296, 26481}, {13297, 26475}, {13298, 45645}, {13299, 45644}, {13923, 45650}, {13992, 45651}, {18544, 48681}, {19049, 49271}, {19050, 49270}, {19114, 26458}, {19115, 26464}, {19163, 45630}, {26399, 48537}, {26423, 48538}, {26517, 49100}, {26522, 49101}, {35880, 45640}, {35881, 45641}, {45526, 48788}, {45527, 48789}

X(49205) = reflection of X(i) in X(j) for these (i, j): (13206, 38608), (13295, 5), (49153, 11249), (49206, 112)
X(49205) = parallelogic center (anti-inner-Yff, T) for these triangles T: 1st anti-orthosymmedial, 1st orthosymmedial
X(49205) = X(112)-of-anti-inner-Yff triangle
X(49205) = X(13295)-of-Johnson triangle
X(49205) = X(13314)-of-anti-outer-Yff triangle
X(49205) = X(49206)-of-outer-Yff tangents triangle
X(49205) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (112, 10705, 13311), (112, 13314, 1)


X(49206) = PARALLELOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 1st ANTI-ORTHOSYMMEDIAL

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

The reciprocal parallelogic center of these triangles is X(10313).

X(49206) lies on the circumcircle of anti-outer-Yff triangle and these lines: {1, 112}, {5, 13294}, {119, 10749}, {127, 26364}, {132, 26333}, {1297, 2077}, {1470, 3320}, {2781, 45729}, {2794, 6256}, {2799, 49202}, {2806, 25438}, {2831, 48695}, {5552, 13219}, {6020, 26358}, {6720, 10200}, {6735, 13280}, {9517, 49204}, {10269, 19162}, {10679, 13310}, {10735, 41698}, {10780, 39692}, {10942, 13295}, {11248, 12340}, {11641, 26309}, {12115, 13200}, {13115, 35251}, {13116, 38510}, {13118, 38676}, {13166, 26378}, {13195, 26432}, {13229, 45627}, {13231, 45628}, {13236, 26318}, {13281, 26453}, {13282, 26343}, {13283, 26350}, {13296, 26482}, {13297, 26476}, {13298, 45647}, {13299, 45646}, {13923, 45652}, {13992, 45653}, {18542, 48681}, {19047, 49271}, {19048, 49270}, {19114, 26459}, {19115, 26465}, {19163, 45631}, {26400, 48537}, {26424, 48538}, {26518, 49100}, {26523, 49101}, {35880, 45642}, {35881, 45643}, {37561, 38699}, {45528, 48788}, {45529, 48789}

X(49206) = reflection of X(i) in X(j) for these (i, j): (13294, 5), (19162, 38608), (49154, 11248), (49205, 112)
X(49206) = parallelogic center (anti-outer-Yff, T) for these triangles T: 1st anti-orthosymmedial, 1st orthosymmedial
X(49206) = X(112)-of-anti-outer-Yff triangle
X(49206) = X(13294)-of-Johnson triangle
X(49206) = X(13313)-of-anti-inner-Yff triangle
X(49206) = X(49205)-of-inner-Yff tangents triangle
X(49206) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (112, 10705, 13312), (112, 13313, 1)


X(49207) = CYCLOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-YFF TO 1st CIRCUMPERP

Barycentrics    a*(a^12-(b+c)*a^11-3*(b^2-b*c+c^2)*a^10+3*(b+c)*(b^2+c^2)*a^9+(2*b^4+2*c^4-b*c*(7*b^2+2*b*c+7*c^2))*a^8-2*(b^4-3*b^2*c^2+c^4)*(b+c)*a^7+2*(b^4+c^4+3*b*c*(b+c)^2)*(b-c)^2*a^6-2*(b^2-c^2)*(b-c)*(b^4+c^4+b*c*(2*b^2+9*b*c+2*c^2))*a^5-(3*b^6+3*c^6-b^2*c^2*(15*b^2+32*b*c+15*c^2))*(b-c)^2*a^4+(b^2-c^2)*(b-c)*(3*b^6+3*c^6+(6*b^4+6*c^4+b*c*(3*b^2-16*b*c+3*c^2))*b*c)*a^3+(b^6+c^6-5*(b^4+c^4+b*c*(b-c)^2)*b*c)*(b^2-c^2)^2*a^2-(b^2-c^2)^3*(b-c)*(b^4+c^4+2*b*c*(b-c)^2)*a+(b^2-c^2)^4*(b-c)^2*b*c) : :

The reciprocal cyclologic center of these triangles is X(109).

X(49207) lies on the circumcircle of anti-outer-Yff triangle and these lines: {1, 102}, {3, 119}, {104, 13532}, {1295, 2077}, {1359, 1470}, {1633, 2950}, {2778, 37562}, {2791, 49148}, {2798, 49202}, {2804, 25438}, {2823, 3359}, {2834, 34813}, {2850, 49204}, {3295, 10271}, {3318, 26358}, {5552, 34188}, {6717, 10200}, {8185, 37414}, {9590, 10731}, {10269, 38606}, {10679, 38578}, {10776, 39692}, {12115, 37441}, {25640, 26333}, {35251, 38592}, {37561, 38696}

X(49207) = cyclologic center (anti-outer-Yff, 1st circumperp)
X(49207) = center of circle {{X(104), X(1295), X(15501)}}
X(49207) = X(15478)-of-1st circumperp triangle, when ABC is acute
X(49207) = X(108)-of-anti-outer-Yff triangle
X(49207) = circumperp conjugate of X(48695)

leftri

Centers related to 1st- and 2nd- Kenmotu-centers triangles: X(49208)-X(49271)

rightri

This preamble and centers X(49208)-X(49271) were contributed by César Eliud Lozada, May 20, 2022.

1st- and 2nd- Kenmotu-centers triangles were introduced in the preamble just before X(44582).


X(49208) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO 1st ALTINTAS-ISODYNAMIC

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

The reciprocal orthologic center of these triangles is X(4).

X(49208) lies on these lines: {6, 13}, {39, 48723}, {371, 35753}, {372, 6771}, {395, 6306}, {396, 6302}, {485, 5617}, {530, 32787}, {531, 49214}, {590, 618}, {615, 6669}, {616, 3068}, {619, 49267}, {1124, 10078}, {1151, 5473}, {1152, 21156}, {1335, 10062}, {1587, 6770}, {2066, 13076}, {2067, 18974}, {3070, 41022}, {3071, 5478}, {3311, 13103}, {3364, 46855}, {3390, 22511}, {5062, 48722}, {5412, 12142}, {5459, 13982}, {5463, 13846}, {6419, 16001}, {6420, 20415}, {6772, 33441}, {6779, 10668}, {7583, 49236}, {7584, 20252}, {7968, 11705}, {7975, 44635}, {8253, 36770}, {9115, 13646}, {9901, 18991}, {9916, 44598}, {9982, 44604}, {10611, 49239}, {10667, 36967}, {10671, 16962}, {12205, 44586}, {12337, 44590}, {12472, 44600}, {12473, 44602}, {12781, 13911}, {12793, 44610}, {12922, 44618}, {12932, 44620}, {12942, 31472}, {12952, 44623}, {12990, 44627}, {12991, 44629}, {13105, 44643}, {13107, 44645}, {13847, 22489}, {13916, 32553}, {19048, 49144}, {19050, 49143}, {22773, 44606}, {22846, 49237}, {23251, 36961}, {25185, 33471}, {33440, 41745}, {36765, 42265}, {41023, 49212}, {42216, 47610}, {44582, 48456}, {44584, 48457}, {44594, 49034}, {44596, 49035}

X(49208) = midpoint of X(371) and X(35753)
X(49208) = orthologic center (1st Kenmotu-centers, T) for these triangles T: 1st Altintas-isodynamic, Bankoff, 3rd Fermat-Dao, 7th Fermat-Dao, 11th Fermat-Dao, 15th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi, 1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi, 1st half-diamonds-central, 1st isodynamic-Dao, 3rd isodynamic-Dao, Largest-circumscribed-equilateral, 1st Lemoine-Dao, outer-Napoleon
X(49208) = X(13)-of-1st Kenmotu-centers triangle
X(49208) = X(6771)-of-1st Kenmotu-free-vertices triangle
X(49208) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 13, 49209), (6, 35822, 49210), (13, 19074, 6), (618, 13917, 590), (6302, 13705, 13876)


X(49209) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO 1st ALTINTAS-ISODYNAMIC

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

The reciprocal orthologic center of these triangles is X(4).

X(49209) lies on these lines: {6, 13}, {39, 48722}, {371, 6771}, {372, 35754}, {395, 6302}, {396, 6306}, {486, 5617}, {530, 32788}, {531, 49215}, {590, 6669}, {615, 618}, {616, 3069}, {619, 49266}, {1124, 10062}, {1151, 21156}, {1152, 5473}, {1335, 10078}, {1588, 6770}, {3070, 5478}, {3071, 41022}, {3312, 13103}, {3365, 46855}, {3389, 22511}, {5058, 48723}, {5413, 12142}, {5414, 13076}, {5459, 13917}, {5463, 13847}, {6419, 20415}, {6420, 16001}, {6502, 18974}, {6772, 33440}, {6779, 10672}, {7583, 20252}, {7584, 49237}, {7969, 11705}, {7975, 44636}, {8252, 36770}, {9115, 13765}, {9901, 18992}, {9916, 44599}, {9982, 44605}, {10611, 49238}, {10667, 16962}, {10671, 36967}, {12205, 44587}, {12337, 44591}, {12472, 44601}, {12473, 44603}, {12781, 13973}, {12793, 44611}, {12922, 44619}, {12932, 44621}, {12942, 44622}, {12952, 44624}, {12990, 44628}, {12991, 44630}, {13105, 44644}, {13107, 44646}, {13846, 22489}, {13981, 32553}, {19047, 49144}, {19049, 49143}, {22773, 44607}, {22846, 49236}, {23261, 36961}, {25186, 33473}, {33441, 41745}, {36765, 42262}, {41023, 49213}, {42215, 47610}, {44583, 48456}, {44585, 48457}, {44595, 49034}, {44597, 49035}

X(49209) = midpoint of X(372) and X(35754)
X(49209) = orthologic center (2nd Kenmotu-centers, T) for these triangles T: 1st Altintas-isodynamic, Bankoff, 3rd Fermat-Dao, 7th Fermat-Dao, 11th Fermat-Dao, 15th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi, 1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi, 1st half-diamonds-central, 1st isodynamic-Dao, 3rd isodynamic-Dao, Largest-circumscribed-equilateral, 1st Lemoine-Dao, outer-Napoleon
X(49209) = X(13)-of-2nd Kenmotu-centers triangle
X(49209) = X(6771)-of-2nd Kenmotu-free-vertices triangle
X(49209) = X(39787)-of-2nd Kenmotu diagonals triangle
X(49209) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 13, 49208), (6, 35823, 49211), (13, 19073, 6), (618, 13982, 615), (6306, 13825, 13929)


X(49210) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO 2nd ALTINTAS-ISODYNAMIC

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

The reciprocal orthologic center of these triangles is X(4).

X(49210) lies on these lines: {6, 13}, {39, 48725}, {371, 35846}, {372, 6774}, {395, 6303}, {396, 6307}, {485, 5613}, {530, 49214}, {531, 32787}, {590, 619}, {615, 6670}, {617, 3068}, {618, 49267}, {1124, 10077}, {1151, 5474}, {1152, 21157}, {1335, 10061}, {1587, 6773}, {2066, 13075}, {2067, 18975}, {3070, 41023}, {3071, 5479}, {3311, 13102}, {3365, 22510}, {3389, 46854}, {5062, 48724}, {5412, 12141}, {5460, 13981}, {5464, 13846}, {6419, 16002}, {6420, 20416}, {6775, 33443}, {6780, 10667}, {7583, 49238}, {7584, 20253}, {7968, 11706}, {7974, 44635}, {9117, 13645}, {9900, 18991}, {9915, 44598}, {9981, 44604}, {10612, 49237}, {10668, 36968}, {10672, 16963}, {12204, 44586}, {12336, 44590}, {12470, 44600}, {12471, 44602}, {12780, 13911}, {12792, 44610}, {12921, 44618}, {12931, 44620}, {12941, 31472}, {12951, 44623}, {12988, 44627}, {12989, 44629}, {13104, 44643}, {13106, 44645}, {13847, 22490}, {13917, 32552}, {19048, 49146}, {19050, 49145}, {22774, 44606}, {22891, 49239}, {23251, 36962}, {25189, 33470}, {33442, 41746}, {35742, 42253}, {41022, 49212}, {42216, 47611}, {44582, 48458}, {44584, 48459}, {44594, 49036}, {44596, 49037}

X(49210) = midpoint of X(371) and X(35850)
X(49210) = orthologic center (1st Kenmotu-centers, T) for these triangles T: 2nd Altintas-isodynamic, 4th Fermat-Dao, 8th Fermat-Dao, 12th Fermat-Dao, 16th Fermat-Dao, 1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi, 3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi, 2nd half-diamonds-central, 2nd isodynamic-Dao, 4th isodynamic-Dao, 2nd Lemoine-Dao, inner-Napoleon
X(49210) = X(14)-of-1st Kenmotu-centers triangle
X(49210) = X(6774)-of-1st Kenmotu-free-vertices triangle
X(49210) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 14, 49211), (6, 35822, 49208), (14, 19076, 6), (619, 13916, 590), (6303, 13703, 13875)


X(49211) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO 2nd ALTINTAS-ISODYNAMIC

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

The reciprocal orthologic center of these triangles is X(4).

X(49211) lies on these lines: {6, 13}, {39, 48724}, {371, 6774}, {372, 35849}, {395, 6307}, {396, 6303}, {486, 5613}, {530, 49215}, {531, 32788}, {590, 6670}, {615, 619}, {617, 3069}, {618, 49266}, {1124, 10061}, {1151, 21157}, {1152, 5474}, {1335, 10077}, {1588, 6773}, {3070, 5479}, {3071, 41023}, {3312, 13102}, {3364, 22510}, {3390, 46854}, {5058, 48725}, {5413, 12141}, {5414, 13075}, {5460, 13916}, {5464, 13847}, {6419, 20416}, {6420, 16002}, {6502, 18975}, {6775, 33442}, {6780, 10671}, {7583, 20253}, {7584, 49239}, {7969, 11706}, {7974, 44636}, {9117, 13764}, {9900, 18992}, {9915, 44599}, {9981, 44605}, {10612, 49236}, {10668, 16963}, {10672, 36968}, {12204, 44587}, {12336, 44591}, {12470, 44601}, {12471, 44603}, {12780, 13973}, {12792, 44611}, {12921, 44619}, {12931, 44621}, {12941, 44622}, {12951, 44624}, {12963, 35748}, {12988, 44628}, {12989, 44630}, {13104, 44644}, {13106, 44646}, {13846, 22490}, {13982, 32552}, {19047, 49146}, {19049, 49145}, {22774, 44607}, {22891, 49238}, {23261, 36962}, {25190, 33472}, {33443, 41746}, {35742, 42250}, {41022, 49213}, {42215, 47611}, {44583, 48458}, {44585, 48459}, {44595, 49036}, {44597, 49037}

X(49211) = midpoint of X(372) and X(35851)
X(49211) = orthologic center (2nd Kenmotu-centers, T) for these triangles T: 2nd Altintas-isodynamic, 4th Fermat-Dao, 8th Fermat-Dao, 12th Fermat-Dao, 16th Fermat-Dao, 1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi, 3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi, 2nd half-diamonds-central, 2nd isodynamic-Dao, 4th isodynamic-Dao, 2nd Lemoine-Dao, inner-Napoleon
X(49211) = X(14)-of-2nd Kenmotu-centers triangle
X(49211) = X(6774)-of-2nd Kenmotu-free-vertices triangle
X(49211) = X(39788)-of-2nd Kenmotu diagonals triangle
X(49211) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 14, 49210), (6, 35823, 49209), (14, 19075, 6), (619, 13981, 615), (6307, 13823, 13928)


X(49212) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO 1st ANTI-BROCARD

Barycentrics    (a^4-b^2*a^2-(b^2-c^2)*c^2)*(a^4-c^2*a^2+(b^2-c^2)*b^2)-2*S*a^2*(a^4-(b^2+c^2)*a^2+b^4-b^2*c^2+c^4) : :
X(49212) = 3*X(371)-X(35878) = 3*X(35824)+X(35878) = 2*X(35824)+X(49266) = 2*X(35878)-3*X(49266)

The reciprocal orthologic center of these triangles is X(5999).

X(49212) lies on the circumcircle of 1st Kenmotu-centers triangle and these lines: {3, 49267}, {5, 6230}, {6, 98}, {30, 49214}, {39, 48727}, {99, 1151}, {114, 590}, {115, 3071}, {147, 3068}, {148, 6459}, {371, 2782}, {372, 12042}, {485, 6033}, {486, 38224}, {542, 32787}, {543, 41945}, {615, 6036}, {690, 49216}, {1124, 10069}, {1152, 19108}, {1335, 10053}, {1587, 9862}, {1588, 14651}, {1668, 47366}, {1669, 47365}, {2066, 3027}, {2067, 3023}, {2783, 48714}, {2784, 13883}, {2787, 48700}, {2794, 3070}, {2799, 49218}, {3311, 12188}, {3564, 6231}, {3592, 19109}, {5062, 48726}, {5186, 11473}, {5412, 12131}, {5418, 15561}, {5420, 38739}, {5969, 8304}, {5984, 7585}, {6054, 13846}, {6055, 13967}, {6200, 33813}, {6221, 13188}, {6321, 6561}, {6409, 21166}, {6419, 35825}, {6425, 23235}, {6560, 38741}, {6564, 22505}, {6567, 48785}, {6721, 32789}, {6722, 42583}, {6811, 33430}, {7583, 49254}, {7968, 11710}, {7970, 44635}, {8976, 38743}, {8983, 21636}, {8997, 14981}, {9541, 13172}, {9616, 13174}, {9860, 18991}, {9861, 44598}, {9864, 13911}, {10577, 34127}, {10722, 23251}, {10723, 42263}, {11177, 19054}, {11632, 49215}, {11646, 33431}, {12176, 44586}, {12177, 19145}, {12178, 44590}, {12179, 44600}, {12180, 44602}, {12181, 44610}, {12182, 44618}, {12183, 44620}, {12184, 31472}, {12185, 44623}, {12186, 44627}, {12187, 44629}, {12189, 44643}, {12190, 44645}, {12239, 39846}, {13640, 45484}, {13665, 38744}, {13989, 38737}, {14061, 42262}, {14639, 23261}, {14849, 19051}, {15535, 49223}, {19048, 49148}, {19050, 49147}, {19060, 22265}, {20094, 43512}, {22504, 44606}, {22515, 35821}, {23514, 42270}, {23698, 42258}, {35823, 49102}, {36519, 42582}, {36709, 44647}, {38730, 42260}, {38740, 43880}, {38742, 42261}, {38745, 43879}, {38749, 42259}, {39809, 42271}, {39838, 42284}, {41022, 49210}, {41023, 49208}, {44582, 48462}, {44584, 48463}, {44594, 49040}, {44596, 49041}

X(49212) = midpoint of X(371) and X(35824)
X(49212) = reflection of X(i) in X(j) for these (i, j): (49213, 12829), (49266, 371)
X(49212) = inverse of X(35824) in Kenmotu circle
X(49212) = orthologic center (1st Kenmotu-centers, T) for these triangles T: 1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard
X(49212) = X(98)-of-1st Kenmotu-centers triangle
X(49212) = X(12042)-of-1st Kenmotu-free-vertices triangle
X(49212) = X(12829)-of-2nd anti-Kenmotu centers triangle
X(49212) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 98, 49213), (98, 19056, 6), (114, 8980, 590), (6200, 35879, 33813), (6231, 13670, 13873), (19108, 34473, 1152)


X(49213) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO 1st ANTI-BROCARD

Barycentrics    (a^4-b^2*a^2-(b^2-c^2)*c^2)*(a^4-c^2*a^2+(b^2-c^2)*b^2)+2*S*a^2*(a^4-(b^2+c^2)*a^2+b^4-b^2*c^2+c^4) : :
X(49213) = 3*X(372)-X(35879) = 3*X(35825)+X(35879) = 2*X(35825)+X(49267) = 2*X(35879)-3*X(49267)

The reciprocal orthologic center of these triangles is X(5999).

X(49213) lies on the circumcircle of 2nd Kenmotu-centers triangle and these lines: {3, 49266}, {5, 6231}, {6, 98}, {30, 49215}, {39, 48726}, {99, 1152}, {114, 615}, {115, 3070}, {147, 3069}, {148, 6460}, {371, 12042}, {372, 2782}, {485, 38224}, {486, 6033}, {542, 32788}, {543, 41946}, {590, 6036}, {690, 49217}, {1124, 10053}, {1151, 19109}, {1335, 10069}, {1587, 14651}, {1588, 9862}, {1668, 47365}, {1669, 47366}, {2783, 48715}, {2784, 13936}, {2787, 48701}, {2794, 3071}, {2799, 49219}, {3023, 6502}, {3027, 5414}, {3312, 12188}, {3564, 6230}, {3594, 19108}, {5058, 48727}, {5186, 11474}, {5413, 12131}, {5418, 38739}, {5420, 15561}, {5969, 8305}, {5984, 7586}, {6054, 13847}, {6055, 8980}, {6321, 6560}, {6396, 33813}, {6398, 13188}, {6410, 21166}, {6420, 35824}, {6426, 23235}, {6561, 38741}, {6565, 22505}, {6566, 48784}, {6721, 32790}, {6722, 42582}, {6813, 33431}, {7584, 49255}, {7969, 11710}, {7970, 44636}, {8997, 38737}, {9860, 18992}, {9861, 44599}, {9864, 13973}, {10576, 34127}, {10722, 23261}, {10723, 42264}, {11177, 19053}, {11632, 49214}, {11646, 33430}, {12176, 44587}, {12177, 19146}, {12178, 44591}, {12179, 44601}, {12180, 44603}, {12181, 44611}, {12182, 44619}, {12183, 44621}, {12184, 44622}, {12185, 44624}, {12186, 44628}, {12187, 44630}, {12189, 44644}, {12190, 44646}, {12240, 39846}, {13760, 45485}, {13785, 38744}, {13951, 38743}, {13971, 21636}, {13989, 14981}, {14061, 42265}, {14639, 23251}, {14849, 19052}, {15535, 49222}, {19047, 49148}, {19049, 49147}, {19059, 22265}, {20094, 43511}, {22504, 44607}, {22515, 35820}, {23514, 42273}, {23698, 42259}, {35822, 49102}, {36519, 42583}, {36714, 44648}, {38730, 42261}, {38740, 43879}, {38742, 42260}, {38745, 43880}, {38749, 42258}, {39809, 42272}, {39838, 42283}, {41022, 49211}, {41023, 49209}, {44583, 48462}, {44585, 48463}, {44595, 49040}, {44597, 49041}

X(49213) = midpoint of X(372) and X(35825)
X(49213) = reflection of X(i) in X(j) for these (i, j): (49212, 12829), (49267, 372)
X(49213) = orthologic center (2nd Kenmotu-centers, T) for these triangles T: 1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard
X(49213) = X(98)-of-2nd Kenmotu-centers triangle
X(49213) = X(1362)-of-2nd Kenmotu diagonals triangle
X(49213) = X(12042)-of-2nd Kenmotu-free-vertices triangle
X(49213) = X(12829)-of-1st anti-Kenmotu centers triangle
X(49213) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 98, 49212), (98, 19055, 6), (114, 13967, 615), (6230, 13790, 13926), (6396, 35878, 33813), (19109, 34473, 1151)


X(49214) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO ANTI-MCCAY

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

The reciprocal orthologic center of these triangles is X(9855).

X(49214) lies on these lines: {2, 49267}, {6, 598}, {30, 49212}, {39, 48729}, {99, 13846}, {115, 13823}, {148, 19054}, {371, 35698}, {372, 49102}, {485, 8724}, {530, 49210}, {531, 49208}, {542, 3070}, {543, 32787}, {590, 2482}, {615, 5461}, {1124, 10070}, {1151, 12117}, {1327, 6033}, {1335, 10054}, {1587, 12243}, {2066, 12354}, {2067, 18969}, {2782, 35822}, {2796, 13883}, {3068, 8591}, {3071, 9880}, {3311, 12355}, {5062, 48728}, {5412, 12132}, {5465, 49269}, {5969, 49252}, {6055, 41946}, {6419, 35699}, {6560, 14830}, {6564, 22566}, {7585, 8596}, {7968, 12258}, {8997, 15300}, {9166, 13847}, {9875, 18991}, {9876, 44598}, {9878, 44604}, {9881, 13911}, {9884, 44635}, {9892, 13676}, {10992, 31454}, {11632, 49213}, {12191, 44586}, {12326, 44590}, {12345, 44600}, {12346, 44602}, {12347, 44610}, {12348, 44618}, {12349, 44620}, {12350, 31472}, {12351, 44623}, {12352, 44627}, {12353, 44629}, {12356, 44643}, {12357, 44645}, {13665, 48657}, {13989, 14971}, {14692, 43342}, {15561, 42602}, {19048, 49150}, {19050, 49149}, {19053, 41135}, {22247, 32789}, {22565, 44606}, {23234, 42265}, {23698, 41945}, {37350, 44392}, {38740, 41964}, {38749, 43209}, {38750, 43254}, {44582, 48470}, {44584, 48471}, {44594, 49042}, {44596, 49043}

X(49214) = midpoint of X(371) and X(35698)
X(49214) = reflection of X(49266) in X(32787)
X(49214) = orthologic center (1st Kenmotu-centers, T) for these triangles T: anti-McCay, McCay, Moses-Steiner osculatory
X(49214) = X(671)-of-1st Kenmotu-centers triangle
X(49214) = X(43120)-of-anti-McCay triangle
X(49214) = X(49102)-of-1st Kenmotu-free-vertices triangle
X(49214) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 671, 49215), (671, 19058, 6), (2482, 13908, 590), (9166, 19108, 13847), (9892, 13676, 13874)


X(49215) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO ANTI-MCCAY

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

The reciprocal orthologic center of these triangles is X(9855).

X(49215) lies on these lines: {2, 49266}, {6, 598}, {30, 49213}, {39, 48728}, {99, 13847}, {115, 13703}, {148, 19053}, {371, 49102}, {372, 35699}, {486, 8724}, {530, 49211}, {531, 49209}, {542, 3071}, {543, 32788}, {590, 5461}, {615, 2482}, {1124, 10054}, {1152, 12117}, {1328, 6033}, {1335, 10070}, {1588, 12243}, {2782, 35823}, {2796, 13936}, {3069, 8591}, {3070, 9880}, {3312, 12355}, {5058, 48729}, {5413, 12132}, {5414, 12354}, {5465, 49268}, {5969, 49253}, {6055, 41945}, {6420, 35698}, {6502, 18969}, {6561, 14830}, {6565, 22566}, {7586, 8596}, {7969, 12258}, {8997, 14971}, {9166, 13846}, {9875, 18992}, {9876, 44599}, {9878, 44605}, {9881, 13973}, {9884, 44636}, {9894, 13796}, {11632, 49212}, {12191, 44587}, {12326, 44591}, {12345, 44601}, {12346, 44603}, {12347, 44611}, {12348, 44619}, {12349, 44621}, {12350, 44622}, {12351, 44624}, {12352, 44628}, {12353, 44630}, {12356, 44644}, {12357, 44646}, {13785, 48657}, {13989, 15300}, {14692, 43343}, {15561, 42603}, {19047, 49150}, {19049, 49149}, {19054, 41135}, {20398, 31454}, {22247, 32790}, {22565, 44607}, {23234, 42262}, {23698, 41946}, {37350, 44394}, {38740, 41963}, {38749, 43210}, {38750, 43255}, {44583, 48470}, {44585, 48471}, {44595, 49042}, {44597, 49043}

X(49215) = midpoint of X(372) and X(35699)
X(49215) = reflection of X(49267) in X(32788)
X(49215) = orthologic center (2nd Kenmotu-centers, T) for these triangles T: anti-McCay, McCay, Moses-Steiner osculatory
X(49215) = X(671)-of-2nd Kenmotu-centers triangle
X(49215) = X(43121)-of-anti-McCay triangle
X(49215) = X(49102)-of-2nd Kenmotu-free-vertices triangle
X(49215) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 671, 49214), (671, 19057, 6), (2482, 13968, 615), (9166, 19109, 13846), (9894, 13796, 13927)


X(49216) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*((a^4+(b^2-2*c^2)*a^2-(b^2-c^2)*(2*b^2+c^2))*(a^4-(2*b^2-c^2)*a^2+(b^2-c^2)*(b^2+2*c^2))-2*S*(a^6-(b^2+c^2)*a^4-(b^4-3*b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2))) : :
X(49216) = X(74)-3*X(47644) = 3*X(371)-X(12375) = X(12375)+3*X(35826) = 2*X(12375)-3*X(49268) = 2*X(35826)+X(49268)

The reciprocal orthologic center of these triangles is X(12112).

X(49216) lies on the circumcircle of 1st Kenmotu-centers triangle and these lines: {3, 10820}, {4, 44639}, {6, 74}, {30, 49222}, {39, 48731}, {110, 1151}, {113, 590}, {125, 3071}, {146, 3068}, {265, 6561}, {371, 5663}, {372, 12041}, {399, 6221}, {485, 7728}, {486, 15061}, {541, 32787}, {542, 41945}, {615, 6699}, {690, 49212}, {1112, 11473}, {1124, 10081}, {1152, 15055}, {1335, 10065}, {1503, 49264}, {1511, 6200}, {1539, 6564}, {1587, 12244}, {1702, 33535}, {2066, 3028}, {2067, 3024}, {2771, 31439}, {2777, 3070}, {2948, 9616}, {3311, 10620}, {3312, 15041}, {3448, 6459}, {3592, 15054}, {3594, 15021}, {5062, 48730}, {5412, 12133}, {5418, 14643}, {5420, 38728}, {5609, 6453}, {6409, 15035}, {6411, 15051}, {6419, 35827}, {6425, 14094}, {6438, 10818}, {6449, 32609}, {6455, 15040}, {6560, 19052}, {6565, 20304}, {6567, 48787}, {6723, 42583}, {7687, 42283}, {7968, 11709}, {7978, 44635}, {8674, 48700}, {8976, 38789}, {8991, 23315}, {8998, 15063}, {9517, 49218}, {9541, 12383}, {9647, 18968}, {9660, 12896}, {9675, 14901}, {9681, 23236}, {9904, 18991}, {9919, 44598}, {9970, 19145}, {9984, 44604}, {10113, 35821}, {10117, 19088}, {10264, 42215}, {10272, 35255}, {10577, 34128}, {10628, 49256}, {10706, 13846}, {10721, 23251}, {10733, 42263}, {10880, 12292}, {10897, 44573}, {12112, 44592}, {12121, 42260}, {12192, 44586}, {12239, 13417}, {12295, 42271}, {12327, 44590}, {12365, 44600}, {12366, 44602}, {12368, 13911}, {12369, 44610}, {12371, 44618}, {12372, 44620}, {12373, 31472}, {12374, 44623}, {12377, 44627}, {12378, 44629}, {12381, 44643}, {12382, 44645}, {12900, 32789}, {12970, 15647}, {13202, 42284}, {13287, 49250}, {13665, 38790}, {13969, 32788}, {13979, 35823}, {13990, 38727}, {14644, 23261}, {14677, 42216}, {14683, 43512}, {15059, 42262}, {15081, 23259}, {16111, 42259}, {16534, 41963}, {17702, 42258}, {17812, 44608}, {18762, 40685}, {19048, 49152}, {19050, 49151}, {19051, 20126}, {20125, 43509}, {20417, 46689}, {22583, 44606}, {23249, 44641}, {23515, 42270}, {32247, 39876}, {32292, 33851}, {34584, 35820}, {35834, 42266}, {36518, 42582}, {38729, 43880}, {38788, 42261}, {38791, 43879}, {42273, 46686}, {43806, 43826}, {44582, 48472}, {44584, 48473}, {44594, 49044}, {44596, 49045}

X(49216) = midpoint of X(i) and X(j) for these {i, j}: {371, 35826}, {13287, 49250}, {35834, 42266}
X(49216) = reflection of X(i) in X(j) for these (i, j): (3070, 46688), (49268, 371)
X(49216) = inverse of X(35826) in Kenmotu circle
X(49216) = orthologic center (1st Kenmotu-centers, T) for these triangles T: anti-orthocentroidal, orthocentroidal
X(49216) = X(74)-of-1st Kenmotu-centers triangle
X(49216) = X(3070)-of-anti-orthocentroidal triangle
X(49216) = X(12041)-of-1st Kenmotu-free-vertices triangle
X(49216) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 74, 49217), (74, 19060, 6), (113, 8994, 590), (399, 6221, 10819), (1539, 13915, 6564), (6200, 12376, 1511), (10264, 42215, 49223), (15055, 19110, 1152), (19052, 20127, 6560)


X(49217) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*((a^4+(b^2-2*c^2)*a^2-(b^2-c^2)*(2*b^2+c^2))*(a^4-(2*b^2-c^2)*a^2+(b^2-c^2)*(b^2+2*c^2))+2*S*(a^6-(b^2+c^2)*a^4-(b^4-3*b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2))) : :
X(49217) = 3*X(372)-X(12376) = X(12376)+3*X(35827) = 2*X(12376)-3*X(49269) = 2*X(35827)+X(49269)

The reciprocal orthologic center of these triangles is X(12112).

X(49217) lies on the circumcircle of 2nd Kenmotu-centers triangle and these lines: {3, 10819}, {4, 44640}, {6, 74}, {30, 49223}, {39, 48730}, {110, 1152}, {113, 615}, {125, 3070}, {146, 3069}, {265, 6560}, {371, 12041}, {372, 5663}, {399, 6398}, {485, 15061}, {486, 7728}, {541, 32788}, {542, 41946}, {590, 6699}, {690, 49213}, {1112, 11474}, {1124, 10065}, {1151, 15055}, {1335, 10081}, {1503, 49265}, {1511, 6396}, {1539, 6565}, {1588, 12244}, {1703, 33535}, {2771, 48715}, {2777, 3071}, {3024, 6502}, {3028, 5414}, {3311, 15041}, {3312, 10620}, {3448, 6460}, {3592, 15021}, {3594, 15054}, {5058, 48731}, {5413, 12133}, {5418, 38728}, {5420, 14643}, {5609, 6454}, {6410, 15035}, {6412, 15051}, {6420, 35826}, {6426, 14094}, {6437, 10817}, {6450, 32609}, {6456, 15040}, {6561, 19051}, {6564, 20304}, {6566, 48786}, {6723, 42582}, {7687, 42284}, {7969, 11709}, {7978, 44636}, {8674, 48701}, {8994, 32787}, {8998, 38727}, {9517, 49219}, {9904, 18992}, {9919, 44599}, {9970, 19146}, {9984, 44605}, {10113, 35820}, {10117, 19087}, {10264, 42216}, {10272, 35256}, {10576, 34128}, {10628, 49257}, {10706, 13847}, {10721, 23261}, {10733, 42264}, {10881, 12292}, {10898, 44573}, {12112, 44593}, {12121, 42261}, {12192, 44587}, {12240, 13417}, {12295, 42272}, {12327, 44591}, {12365, 44601}, {12366, 44603}, {12368, 13973}, {12369, 44611}, {12371, 44619}, {12372, 44621}, {12373, 44622}, {12374, 44624}, {12377, 44628}, {12378, 44630}, {12381, 44644}, {12382, 44646}, {12900, 32790}, {12964, 15647}, {13202, 42283}, {13288, 49251}, {13785, 38790}, {13915, 35822}, {13951, 38789}, {13980, 23315}, {13990, 15063}, {14644, 23251}, {14677, 42215}, {14683, 43511}, {15059, 42265}, {15081, 23249}, {16111, 42258}, {16534, 41964}, {17702, 42259}, {17812, 44609}, {18538, 40685}, {19047, 49152}, {19049, 49151}, {19052, 20126}, {20125, 43510}, {20417, 46688}, {22583, 44607}, {23259, 44642}, {23515, 42273}, {32247, 39875}, {32291, 33851}, {34584, 35821}, {35835, 42267}, {36518, 42583}, {38729, 43879}, {38788, 42260}, {38791, 43880}, {42270, 46686}, {43806, 43825}, {44583, 48472}, {44585, 48473}, {44595, 49044}, {44597, 49045}

X(49217) = midpoint of X(i) and X(j) for these {i, j}: {372, 35827}, {13288, 49251}, {35835, 42267}
X(49217) = reflection of X(i) in X(j) for these (i, j): (3071, 46689), (49269, 372)
X(49217) = orthologic center (2nd Kenmotu-centers, T) for these triangles T: anti-orthocentroidal, orthocentroidal
X(49217) = X(74)-of-2nd Kenmotu-centers triangle
X(49217) = X(1317)-of-2nd Kenmotu diagonals triangle
X(49217) = X(3071)-of-anti-orthocentroidal triangle
X(49217) = X(12041)-of-2nd Kenmotu-free-vertices triangle
X(49217) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 74, 49216), (74, 19059, 6), (113, 13969, 615), (399, 6398, 10820), (1539, 13979, 6565), (6396, 12375, 1511), (10264, 42216, 49222), (15055, 19111, 1151), (19051, 20127, 6561)


X(49218) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*((a^6-c^2*a^4+(b^4-c^4)*a^2-(b^2-c^2)*(2*b^4+b^2*c^2+c^4))*(a^6-b^2*a^4-(b^4-c^4)*a^2+(b^2-c^2)*(b^4+b^2*c^2+2*c^4))-2*S*(a^10-(b^2+c^2)*a^8+b^2*c^2*a^6-(b^6-c^6)*(b^2-c^2)*a^2+(b^8-c^8)*(b^2-c^2))) : :
X(49218) = 3*X(371)-X(35880) = 3*X(35828)+X(35880) = 2*X(35828)+X(49270) = 2*X(35880)-3*X(49270)

The reciprocal orthologic center of these triangles is X(19158).

X(49218) lies on the circumcircle of 1st Kenmotu-centers triangle and these lines: {3, 49271}, {6, 1297}, {39, 48733}, {112, 1151}, {127, 3071}, {132, 590}, {371, 35828}, {372, 38624}, {485, 12918}, {615, 34841}, {1124, 13117}, {1152, 19114}, {1335, 13116}, {1587, 12253}, {2066, 3320}, {2067, 6020}, {2781, 11241}, {2794, 42258}, {2799, 49212}, {2806, 48700}, {2831, 48714}, {3068, 12384}, {3311, 13115}, {3592, 19115}, {5062, 48732}, {5412, 12145}, {6200, 35881}, {6221, 13310}, {6409, 38699}, {6419, 35829}, {6425, 38676}, {6459, 13219}, {6561, 10749}, {6564, 19160}, {6567, 48789}, {7968, 12265}, {9517, 49216}, {9530, 32787}, {9541, 13200}, {9616, 13221}, {10735, 42263}, {11473, 13166}, {12207, 44586}, {12340, 44590}, {12408, 18991}, {12413, 44598}, {12478, 44600}, {12479, 44602}, {12503, 44604}, {12784, 13911}, {12796, 44610}, {12925, 44618}, {12935, 44620}, {12945, 31472}, {12955, 44623}, {12996, 44627}, {12997, 44629}, {13099, 44635}, {13118, 44643}, {13119, 44645}, {13665, 48658}, {13923, 31454}, {13985, 32788}, {19048, 49154}, {19050, 49153}, {19159, 44606}, {19163, 35821}, {23251, 44988}, {44582, 48474}, {44584, 48475}, {44594, 49046}, {44596, 49047}

X(49218) = midpoint of X(371) and X(35828)
X(49218) = reflection of X(49270) in X(371)
X(49218) = inverse of X(35828) in Kenmotu circle
X(49218) = orthologic center (1st Kenmotu-centers, T) for these triangles T: 1st anti-orthosymmedial, 1st orthosymmedial
X(49218) = X(1297)-of-1st Kenmotu-centers triangle
X(49218) = X(38624)-of-1st Kenmotu-free-vertices triangle
X(49218) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 1297, 49219), (132, 13918, 590), (1297, 19094, 6), (6200, 35881, 38608), (19114, 38717, 1152)


X(49219) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*((a^6-c^2*a^4+(b^4-c^4)*a^2-(b^2-c^2)*(2*b^4+b^2*c^2+c^4))*(a^6-b^2*a^4-(b^4-c^4)*a^2+(b^2-c^2)*(b^4+b^2*c^2+2*c^4))+2*S*(a^10-(b^2+c^2)*a^8+b^2*c^2*a^6-(b^6-c^6)*(b^2-c^2)*a^2+(b^8-c^8)*(b^2-c^2))) : :
X(49219) = 3*X(372)-X(35881) = 3*X(35829)+X(35881) = 2*X(35829)+X(49271) = 2*X(35881)-3*X(49271)

The reciprocal orthologic center of these triangles is X(19158).

X(49219) lies on the circumcircle of 2nd Kenmotu-centers triangle and these lines: {3, 49270}, {6, 1297}, {39, 48732}, {112, 1152}, {127, 3070}, {132, 615}, {371, 38624}, {372, 35829}, {486, 12918}, {590, 34841}, {1124, 13116}, {1151, 19115}, {1335, 13117}, {1588, 12253}, {2781, 11242}, {2794, 42259}, {2799, 49213}, {2806, 48701}, {2831, 48715}, {3069, 12384}, {3312, 13115}, {3320, 5414}, {3594, 19114}, {5058, 48733}, {5413, 12145}, {6020, 6502}, {6396, 35880}, {6398, 13310}, {6410, 38699}, {6420, 35828}, {6426, 38676}, {6460, 13219}, {6560, 10749}, {6565, 19160}, {6566, 48788}, {7969, 12265}, {9517, 49217}, {9530, 32788}, {10735, 42264}, {11474, 13166}, {12207, 44587}, {12340, 44591}, {12408, 18992}, {12413, 44599}, {12478, 44601}, {12479, 44603}, {12503, 44605}, {12784, 13973}, {12796, 44611}, {12925, 44619}, {12935, 44621}, {12945, 44622}, {12955, 44624}, {12996, 44628}, {12997, 44630}, {13099, 44636}, {13118, 44644}, {13119, 44646}, {13785, 48658}, {13918, 32787}, {19047, 49154}, {19049, 49153}, {19159, 44607}, {19163, 35820}, {23261, 44988}, {44583, 48474}, {44585, 48475}, {44595, 49046}, {44597, 49047}

X(49219) = midpoint of X(372) and X(35829)
X(49219) = reflection of X(49271) in X(372)
X(49219) = orthologic center (2nd Kenmotu-centers, T) for these triangles T: 1st anti-orthosymmedial, 1st orthosymmedial
X(49219) = X(1297)-of-2nd Kenmotu-centers triangle
X(49219) = X(3021)-of-2nd Kenmotu diagonals triangle
X(49219) = X(38624)-of-2nd Kenmotu-free-vertices triangle
X(49219) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 1297, 49218), (132, 13985, 615), (1297, 19093, 6), (6396, 35880, 38608), (19115, 38717, 1151)


X(49220) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO 3rd ANTI-TRI-SQUARES

Barycentrics    -2*((b^2+c^2)*a^2-(b^2-c^2)^2)*S+2*a^6-(b^2+c^2)*a^4+2*(b^2-c^2)^2*a^2+(b^2+c^2)*(b^2-c^2)^2 : :
X(49220) = X(486)+2*X(7583) = 4*X(5305)-X(44648) = 2*X(12963)+3*X(49262) = 2*X(13881)+X(44647) = X(49028)+2*X(49103)

The reciprocal orthologic center of these triangles is X(486).

X(49220) lies on these lines: {2, 494}, {4, 6424}, {5, 6}, {30, 12963}, {32, 3070}, {39, 590}, {53, 35764}, {115, 3071}, {141, 42060}, {187, 42259}, {230, 372}, {371, 5254}, {381, 32498}, {395, 6301}, {396, 6300}, {487, 3068}, {491, 7754}, {492, 7887}, {615, 640}, {638, 13758}, {639, 5028}, {641, 13989}, {732, 13931}, {1124, 10083}, {1151, 2549}, {1196, 8968}, {1285, 23269}, {1335, 10067}, {1504, 5309}, {1506, 42582}, {1570, 32435}, {1587, 6423}, {1692, 48466}, {2023, 3102}, {2066, 13081}, {2067, 18989}, {2275, 9661}, {2276, 9646}, {3053, 6560}, {3311, 12601}, {3364, 36762}, {3525, 45079}, {3815, 10576}, {3933, 45473}, {5013, 5418}, {5020, 8970}, {5023, 42261}, {5062, 7755}, {5306, 35822}, {5412, 12147}, {5420, 37637}, {5475, 42273}, {5523, 10880}, {6199, 22809}, {6229, 44394}, {6337, 13882}, {6410, 21843}, {6419, 35833}, {6459, 8375}, {6561, 44518}, {6564, 7745}, {6565, 45514}, {7581, 44595}, {7585, 12221}, {7612, 45101}, {7737, 23251}, {7738, 9540}, {7739, 13846}, {7747, 42284}, {7748, 9675}, {7765, 31454}, {7772, 31481}, {7968, 12268}, {7980, 44635}, {8253, 31401}, {8361, 45472}, {8576, 14715}, {8946, 41516}, {8960, 45512}, {8976, 9605}, {8981, 15048}, {8996, 44193}, {9593, 13893}, {9602, 9681}, {9607, 35812}, {9620, 12787}, {9674, 41963}, {9732, 39661}, {9755, 45407}, {9906, 18991}, {9921, 44598}, {9986, 44604}, {11648, 41945}, {12210, 44586}, {12343, 44590}, {12484, 44600}, {12485, 44602}, {12799, 44610}, {12928, 44618}, {12938, 44620}, {12948, 31472}, {12958, 16502}, {12968, 42216}, {12969, 13966}, {13002, 44627}, {13003, 44629}, {13132, 44643}, {13133, 44645}, {13665, 30435}, {13886, 31403}, {13905, 31459}, {13930, 24256}, {13932, 19054}, {13933, 32788}, {13939, 44597}, {13972, 23312}, {16583, 31583}, {19048, 49156}, {19050, 49155}, {22595, 44606}, {22617, 49261}, {23698, 43120}, {26463, 42561}, {31400, 32785}, {31455, 32789}, {32491, 35684}, {32492, 42215}, {33365, 49027}, {35820, 41410}, {36656, 40825}, {37348, 45411}, {39565, 42270}, {39660, 43119}, {42260, 44526}, {44582, 48478}, {44584, 48479}, {44594, 49048}, {45463, 49029}

X(49220) = midpoint of X(371) and X(35830)
X(49220) = complement of the isotomic conjugate of X(41516)
X(49220) = inverse of X(48467) in Kiepert circumhyperbola
X(49220) = orthologic center (1st Kenmotu-centers, T) for these triangles T: 3rd anti-tri-squares, 2nd half-squares, 4th tri-squares, inner-Vecten
X(49220) = X(486)-of-1st Kenmotu-centers triangle
X(49220) = X(49103)-of-1st Kenmotu-free-vertices triangle
X(49220) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 44596, 6424), (6, 486, 44648), (6, 3767, 49221), (6, 7583, 44647), (6, 13881, 486), (6, 42265, 2548), (115, 5058, 3071), (485, 486, 6290), (486, 13711, 13881), (486, 19105, 6), (590, 32494, 642), (642, 13921, 590), (1505, 7746, 615), (1587, 7735, 6423), (3068, 5286, 6422), (5305, 7583, 6), (5319, 31411, 6), (7738, 9540, 9600), (7748, 9675, 42258), (10576, 45513, 3815), (13711, 19105, 486), (13881, 19105, 44648)


X(49221) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO 4th ANTI-TRI-SQUARES

Barycentrics    2*((b^2+c^2)*a^2-(b^2-c^2)^2)*S+2*a^6-(b^2+c^2)*a^4+2*(b^2-c^2)^2*a^2+(b^2+c^2)*(b^2-c^2)^2 : :
X(49221) = X(485)+2*X(7584) = 4*X(5305)-X(44647) = 2*X(12968)+3*X(49261) = 2*X(13881)+X(44648) = X(49029)+2*X(49104)

The reciprocal orthologic center of these triangles is X(485).

X(49221) lies on these lines: {2, 493}, {4, 6423}, {5, 6}, {30, 12968}, {32, 3071}, {39, 615}, {53, 35765}, {115, 3070}, {141, 42009}, {187, 42258}, {230, 371}, {372, 5254}, {381, 32499}, {395, 6305}, {396, 6304}, {488, 3069}, {491, 7887}, {492, 7754}, {498, 31459}, {590, 639}, {631, 9600}, {637, 13638}, {640, 5028}, {642, 8997}, {732, 13878}, {1124, 10068}, {1152, 2549}, {1285, 23275}, {1335, 10084}, {1505, 5309}, {1506, 42583}, {1570, 32432}, {1588, 6424}, {1656, 31463}, {1692, 48467}, {2023, 3103}, {3053, 6561}, {3090, 31403}, {3167, 8970}, {3312, 12602}, {3525, 45078}, {3815, 10577}, {3933, 45472}, {5013, 5420}, {5023, 42260}, {5058, 7755}, {5070, 31465}, {5306, 35823}, {5413, 12148}, {5414, 13082}, {5418, 37637}, {5475, 42270}, {5523, 10881}, {6228, 44392}, {6337, 13934}, {6395, 22810}, {6409, 21843}, {6420, 35832}, {6460, 8376}, {6502, 18988}, {6560, 44518}, {6564, 45515}, {6565, 7745}, {7582, 44596}, {7586, 12222}, {7612, 45102}, {7737, 23261}, {7738, 13935}, {7739, 13847}, {7747, 42283}, {7748, 42259}, {7772, 43880}, {7969, 12269}, {7981, 44636}, {8252, 31401}, {8361, 45473}, {8375, 37689}, {8553, 9683}, {8577, 14715}, {8948, 41515}, {8981, 12962}, {9593, 13947}, {9605, 13951}, {9607, 35813}, {9620, 12788}, {9733, 39660}, {9755, 45406}, {9907, 18992}, {9922, 44599}, {9987, 44605}, {11648, 41946}, {12211, 44587}, {12344, 44591}, {12486, 44601}, {12487, 44603}, {12800, 44611}, {12929, 44619}, {12939, 44621}, {12949, 44622}, {12959, 16502}, {12963, 42215}, {13004, 44628}, {13005, 44630}, {13134, 44644}, {13135, 44646}, {13785, 30435}, {13850, 19053}, {13877, 24256}, {13879, 32787}, {13886, 44594}, {13910, 23311}, {13966, 15048}, {16583, 31582}, {19047, 49158}, {19049, 49157}, {22624, 44607}, {22646, 49262}, {23698, 43121}, {26363, 31464}, {26456, 31412}, {31400, 32786}, {31423, 31427}, {31455, 32790}, {31481, 42582}, {32490, 35685}, {32495, 42216}, {33364, 49026}, {35821, 41411}, {36655, 40825}, {37348, 45410}, {39565, 42273}, {39661, 43118}, {42261, 44526}, {44583, 48480}, {44585, 48481}, {44597, 49049}, {45462, 49028}

X(49221) = midpoint of X(372) and X(35831)
X(49221) = complement of the isotomic conjugate of X(41515)
X(49221) = inverse of X(48466) in Kiepert circumhyperbola
X(49221) = orthologic center (2nd Kenmotu-centers, T) for these triangles T: 4th anti-tri-squares, 1st half-squares, 3rd tri-squares, outer-Vecten
X(49221) = X(485)-of-2nd Kenmotu-centers triangle
X(49221) = X(39794)-of-2nd Kenmotu diagonals triangle
X(49221) = X(49104)-of-2nd Kenmotu-free-vertices triangle
X(49221) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 44595, 6423), (6, 485, 44647), (6, 3767, 49220), (6, 7584, 44648), (6, 13881, 485), (6, 42262, 2548), (6, 42265, 31411), (115, 5062, 3070), (485, 486, 6289), (485, 13834, 13881), (485, 19102, 6), (615, 32497, 641), (641, 13880, 615), (1504, 7746, 590), (1588, 7735, 6424), (3069, 5286, 6421), (5305, 7584, 6), (10577, 45512, 3815), (13834, 19102, 485), (13881, 19102, 44647), (31411, 43620, 42265)


X(49222) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO AAOA

Barycentrics    -2*S*a^2*(a^6-(b^2+c^2)*a^4-(b^4-3*b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2))+(-a^2+b^2+c^2)*((a^2-b^2+c^2)^2-c^2*a^2)*((a^2+b^2-c^2)^2-b^2*a^2) : :
X(49222) = X(12375)-3*X(35822) = X(35834)+2*X(46688)

The reciprocal orthologic center of these triangles is X(7574).

X(49222) lies on the circumcircle of 2nd outer-Vecten triangle and these lines: {2, 10820}, {5, 49269}, {6, 13}, {30, 49216}, {39, 48737}, {74, 6560}, {110, 485}, {125, 372}, {146, 23249}, {371, 12891}, {486, 14644}, {511, 49264}, {568, 44639}, {590, 1511}, {615, 20304}, {1124, 12904}, {1151, 12121}, {1152, 15061}, {1327, 10706}, {1335, 12903}, {1539, 42284}, {1587, 3448}, {1986, 44637}, {2066, 12896}, {2067, 18968}, {2771, 49240}, {2777, 35820}, {2931, 8939}, {3068, 10819}, {3069, 15081}, {3070, 5663}, {3071, 10113}, {3311, 12902}, {3312, 38724}, {3580, 32421}, {3581, 44592}, {3594, 15027}, {5062, 48736}, {5412, 12140}, {5418, 15035}, {5420, 15059}, {5504, 9676}, {5972, 10576}, {6200, 8994}, {6396, 6699}, {6409, 38723}, {6410, 38728}, {6419, 35835}, {6420, 36253}, {6454, 20397}, {6561, 10733}, {7583, 32423}, {7584, 11801}, {7728, 23251}, {7968, 12261}, {8253, 38794}, {8960, 8998}, {8976, 32609}, {8981, 34153}, {9140, 19059}, {10088, 31472}, {10091, 44623}, {10117, 35776}, {10264, 42216}, {10272, 18538}, {10577, 13990}, {10628, 49244}, {10721, 22644}, {10962, 12892}, {11562, 12239}, {11735, 35762}, {11804, 49257}, {12041, 42259}, {12201, 44586}, {12236, 44633}, {12295, 35821}, {12317, 23267}, {12334, 44590}, {12407, 18991}, {12412, 44598}, {12466, 44600}, {12467, 44602}, {12501, 44604}, {12778, 13911}, {12790, 44610}, {12889, 44618}, {12890, 44620}, {12893, 13909}, {12894, 44627}, {12895, 44629}, {12898, 44635}, {12905, 44643}, {12906, 44645}, {13211, 35774}, {13520, 45237}, {13979, 32788}, {14643, 42265}, {14677, 42226}, {15055, 42261}, {15088, 42583}, {15535, 49213}, {16003, 35827}, {16111, 42267}, {17835, 44608}, {19048, 49160}, {19050, 49159}, {19145, 32233}, {19457, 44588}, {19478, 44606}, {19484, 44625}, {20127, 42264}, {25320, 39875}, {32303, 33851}, {34584, 42272}, {35256, 40685}, {35764, 46682}, {35768, 46683}, {35786, 46686}, {35808, 46687}, {35840, 35876}, {44582, 48483}, {44584, 48484}, {44594, 49050}, {44596, 49051}

X(49222) = midpoint of X(i) and X(j) for these {i, j}: {371, 35834}, {35820, 35826}, {35840, 35876}
X(49222) = reflection of X(i) in X(j) for these (i, j): (371, 46688), (49268, 7583)
X(49222) = orthologic center (1st Kenmotu-centers, T) for these triangles T: antiAOA, AOA, 1st Hyacinth
X(49222) = X(125)-of-1st Kenmotu-free-vertices triangle
X(49222) = X(265)-of-1st Kenmotu-centers triangle
X(49222) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 265, 49223), (265, 19052, 6), (1511, 13915, 590), (3068, 12383, 10819), (6564, 12376, 113), (8994, 16163, 6200), (10264, 42216, 49217), (10733, 19060, 6561), (13990, 23515, 10577), (14644, 19110, 486)


X(49223) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO AAOA

Barycentrics    2*S*a^2*(a^6-(b^2+c^2)*a^4-(b^4-3*b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2))+(-a^2+b^2+c^2)*((a^2-b^2+c^2)^2-c^2*a^2)*((a^2+b^2-c^2)^2-b^2*a^2) : :
X(49223) = X(12376)-3*X(35823) = X(35835)+2*X(46689)

The reciprocal orthologic center of these triangles is X(7574).

X(49223) lies on the circumcircle of 2nd inner-Vecten triangle and these lines: {2, 10819}, {5, 49268}, {6, 13}, {30, 49217}, {39, 48736}, {74, 6561}, {110, 486}, {125, 371}, {146, 23259}, {372, 12892}, {485, 14644}, {511, 49265}, {568, 44640}, {590, 20304}, {615, 1511}, {1124, 12903}, {1151, 15061}, {1152, 12121}, {1328, 10706}, {1335, 12904}, {1539, 42283}, {1588, 3448}, {1986, 44638}, {2771, 49241}, {2777, 35821}, {2931, 8943}, {3068, 15081}, {3069, 10820}, {3070, 10113}, {3071, 5663}, {3311, 38724}, {3312, 12902}, {3580, 32419}, {3581, 44593}, {3592, 15027}, {5058, 48737}, {5413, 12140}, {5414, 12896}, {5418, 15059}, {5420, 15035}, {5972, 10577}, {6200, 6699}, {6396, 13969}, {6409, 38728}, {6410, 38723}, {6419, 36253}, {6420, 35834}, {6453, 20397}, {6502, 18968}, {6560, 10733}, {7583, 11801}, {7584, 32423}, {7728, 23261}, {7969, 12261}, {8252, 38794}, {8998, 10576}, {9140, 19060}, {9677, 13198}, {9681, 15057}, {10088, 44622}, {10091, 44624}, {10117, 35777}, {10264, 42215}, {10272, 18762}, {10628, 49245}, {10721, 22615}, {10960, 12891}, {11562, 12240}, {11735, 35763}, {11804, 49256}, {12041, 42258}, {12201, 44587}, {12236, 44634}, {12295, 35820}, {12317, 23273}, {12334, 44591}, {12407, 18992}, {12412, 44599}, {12466, 44601}, {12467, 44603}, {12501, 44605}, {12778, 13973}, {12790, 44611}, {12889, 44619}, {12890, 44621}, {12893, 13970}, {12894, 44628}, {12895, 44630}, {12898, 44636}, {12905, 44644}, {12906, 44646}, {13211, 35775}, {13521, 45237}, {13915, 32787}, {13951, 32609}, {13966, 34153}, {13990, 30714}, {14643, 42262}, {14677, 42225}, {15055, 42260}, {15088, 42582}, {15535, 49212}, {16003, 35826}, {16111, 42266}, {17835, 44609}, {19047, 49160}, {19049, 49159}, {19146, 32233}, {19457, 44589}, {19478, 44607}, {19485, 44626}, {20127, 42263}, {20396, 31454}, {25320, 39876}, {32304, 33851}, {34584, 42271}, {35255, 40685}, {35765, 46682}, {35769, 46683}, {35787, 46686}, {35809, 46687}, {35841, 35877}, {44583, 48483}, {44585, 48484}, {44595, 49050}, {44597, 49051}

X(49223) = midpoint of X(i) and X(j) for these {i, j}: {372, 35835}, {35821, 35827}, {35841, 35877}
X(49223) = reflection of X(i) in X(j) for these (i, j): (372, 46689), (49269, 7584)
X(49223) = orthologic center (2nd Kenmotu-centers, T) for these triangles T: antiAOA, AOA, 1st Hyacinth
X(49223) = X(125)-of-2nd Kenmotu-free-vertices triangle
X(49223) = X(265)-of-2nd Kenmotu-centers triangle
X(49223) = X(11570)-of-2nd Kenmotu diagonals triangle
X(49223) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 265, 49222), (265, 19051, 6), (1511, 13979, 615), (3069, 12383, 10820), (6565, 12375, 113), (8998, 23515, 10576), (10264, 42215, 49216), (10733, 19059, 6560), (13969, 16163, 6396), (14644, 19111, 485)


X(49224) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO ARIES

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

The reciprocal orthologic center of these triangles is X(9833).

X(49224) lies on these lines: {3, 26945}, {5, 6}, {30, 49250}, {39, 48739}, {52, 44637}, {343, 5408}, {371, 12424}, {372, 12359}, {539, 32787}, {590, 1147}, {615, 5449}, {1069, 44623}, {1124, 10071}, {1151, 12118}, {1154, 49244}, {1335, 10055}, {1585, 6515}, {1587, 11411}, {2066, 12428}, {2067, 18970}, {3068, 6193}, {3070, 13754}, {3071, 9927}, {3157, 31472}, {3167, 8976}, {3311, 12429}, {3547, 18924}, {3549, 19356}, {3580, 10881}, {5062, 48738}, {5412, 12134}, {5413, 41587}, {5418, 47391}, {5448, 42273}, {6146, 10897}, {6396, 44158}, {6419, 35837}, {6560, 12163}, {6561, 12293}, {6564, 22660}, {7689, 42259}, {7968, 12259}, {8939, 9937}, {9820, 10576}, {9896, 18991}, {9908, 44598}, {9923, 44604}, {9928, 13911}, {9933, 44635}, {10534, 13383}, {10880, 14516}, {10962, 12425}, {11417, 34224}, {12164, 13665}, {12193, 44586}, {12235, 44633}, {12328, 44590}, {12415, 44600}, {12416, 44602}, {12418, 44610}, {12422, 44618}, {12423, 44620}, {12426, 44627}, {12427, 44629}, {12430, 44643}, {12431, 44645}, {12891, 32384}, {13970, 32788}, {14984, 49264}, {17702, 42258}, {17834, 44608}, {18457, 44076}, {18939, 44625}, {19048, 49162}, {19050, 49161}, {22659, 44606}, {32789, 43839}, {41597, 43879}, {44582, 48485}, {44584, 48486}, {44594, 49052}, {44596, 49053}, {46085, 49269}

X(49224) = midpoint of X(371) and X(35836)
X(49224) = reflection of X(10665) in X(7583)
X(49224) = orthologic center (1st Kenmotu-centers, T) for these triangles T: Aries, 2nd Hyacinth
X(49224) = X(68)-of-1st Kenmotu-centers triangle
X(49224) = X(12359)-of-1st Kenmotu-free-vertices triangle
X(49224) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 68, 49225), (68, 19062, 6), (1147, 13909, 590), (3068, 6193, 8909)


X(49225) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO ARIES

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

The reciprocal orthologic center of these triangles is X(9833).

X(49225) lies on these lines: {2, 8909}, {3, 26873}, {5, 6}, {30, 49251}, {39, 48738}, {52, 44638}, {343, 5409}, {371, 12359}, {372, 12425}, {539, 32788}, {590, 5449}, {615, 1147}, {1069, 44624}, {1124, 10055}, {1152, 12118}, {1154, 49245}, {1335, 10071}, {1586, 6515}, {1588, 11411}, {3069, 6193}, {3070, 9927}, {3071, 13754}, {3157, 44622}, {3167, 13951}, {3312, 12429}, {3547, 18923}, {3549, 19355}, {3580, 10880}, {5058, 48739}, {5412, 41587}, {5413, 12134}, {5414, 12428}, {5420, 47391}, {5448, 42270}, {6146, 10898}, {6200, 44158}, {6420, 35836}, {6502, 18970}, {6560, 12293}, {6561, 12163}, {6565, 22660}, {7689, 42258}, {7969, 12259}, {8943, 9937}, {9820, 10577}, {9896, 18992}, {9908, 44599}, {9923, 44605}, {9928, 13973}, {9933, 44636}, {10533, 13383}, {10881, 14516}, {10960, 12424}, {11418, 34224}, {12164, 13785}, {12193, 44587}, {12235, 44634}, {12328, 44591}, {12415, 44601}, {12416, 44603}, {12418, 44611}, {12422, 44619}, {12423, 44621}, {12426, 44628}, {12427, 44630}, {12430, 44644}, {12431, 44646}, {12892, 32385}, {13909, 32787}, {14984, 49265}, {17702, 42259}, {17834, 44609}, {18459, 44076}, {18940, 44626}, {19047, 49162}, {19049, 49161}, {22659, 44607}, {32790, 43839}, {41597, 43880}, {44583, 48485}, {44585, 48486}, {44595, 49052}, {44597, 49053}, {46085, 49268}

X(49225) = midpoint of X(372) and X(35837)
X(49225) = reflection of X(10666) in X(7584)
X(49225) = orthologic center (2nd Kenmotu-centers, T) for these triangles T: Aries, 2nd Hyacinth
X(49225) = X(68)-of-2nd Kenmotu-centers triangle
X(49225) = X(1071)-of-2nd Kenmotu diagonals triangle
X(49225) = X(12359)-of-2nd Kenmotu-free-vertices triangle
X(49225) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 68, 49224), (68, 19061, 6), (1147, 13970, 615)


X(49226) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO BEVAN ANTIPODAL

Barycentrics    a*(-2*S*a+a^3+(b+c)*a^2-(b+c)^2*a-(b^2-c^2)*(b-c)) : :
X(49226) = 3*X(371)-X(35641) = X(7969)-4*X(31439) = X(7969)+2*X(35610) = 3*X(7969)-2*X(35641) = 2*X(31439)+X(35610) = 6*X(31439)-X(35641) = 3*X(35610)+X(35641)

The reciprocal orthologic center of these triangles is X(1).

X(49226) lies on these lines: {1, 1151}, {3, 7968}, {4, 13911}, {6, 40}, {8, 6459}, {10, 3071}, {20, 19066}, {37, 6212}, {39, 48741}, {44, 6213}, {46, 1124}, {55, 16232}, {57, 3297}, {65, 2066}, {145, 43512}, {165, 1152}, {355, 6561}, {371, 517}, {372, 3579}, {484, 3299}, {485, 12699}, {486, 26446}, {515, 42258}, {516, 3070}, {519, 41945}, {590, 946}, {615, 6684}, {942, 35808}, {944, 9541}, {962, 3068}, {997, 9679}, {1132, 46933}, {1155, 6502}, {1158, 49235}, {1317, 9649}, {1335, 5119}, {1376, 30556}, {1378, 12514}, {1385, 6200}, {1482, 6221}, {1537, 13922}, {1571, 6421}, {1572, 6422}, {1587, 6361}, {1588, 5657}, {1697, 3298}, {1698, 42262}, {1699, 13893}, {1706, 31438}, {1829, 11473}, {1836, 31472}, {1902, 5412}, {2067, 3057}, {2362, 19038}, {2771, 35826}, {2778, 13287}, {2800, 48714}, {2802, 48700}, {3056, 6252}, {3301, 11010}, {3311, 12702}, {3359, 19047}, {3474, 31408}, {3523, 13959}, {3576, 6409}, {3592, 7991}, {3594, 19003}, {3623, 9543}, {3634, 42583}, {3817, 42582}, {4301, 8983}, {4669, 42417}, {5062, 48740}, {5414, 37568}, {5415, 7957}, {5418, 5886}, {5584, 18999}, {5587, 23261}, {5603, 9540}, {5690, 42215}, {5691, 42263}, {5709, 19050}, {5731, 42638}, {5812, 44620}, {5818, 23259}, {5836, 31453}, {5840, 49240}, {5847, 49228}, {5901, 35255}, {6001, 49250}, {6204, 38487}, {6396, 31663}, {6407, 10247}, {6410, 35242}, {6411, 7987}, {6412, 16192}, {6419, 35611}, {6424, 9620}, {6425, 7982}, {6429, 16200}, {6431, 19004}, {6437, 11531}, {6445, 37624}, {6449, 10246}, {6453, 10222}, {6460, 9778}, {6468, 9618}, {6480, 33179}, {6564, 22793}, {6565, 9956}, {6567, 45716}, {7583, 28174}, {7585, 20070}, {7973, 17819}, {8227, 8253}, {8252, 31423}, {8414, 45398}, {8981, 22791}, {9575, 31427}, {9585, 16189}, {9588, 13947}, {9589, 31440}, {9600, 9619}, {9646, 12047}, {9647, 45287}, {9660, 10572}, {9661, 30384}, {9662, 37734}, {9681, 37727}, {9780, 42561}, {9812, 31412}, {9911, 44598}, {9955, 10576}, {9957, 35768}, {10164, 13971}, {10175, 42270}, {10253, 31539}, {10306, 44590}, {10533, 40658}, {10577, 11231}, {10595, 43509}, {11278, 35810}, {11362, 49233}, {12197, 44586}, {12458, 44600}, {12459, 44602}, {12497, 44604}, {12696, 44610}, {12700, 44618}, {12701, 44623}, {12703, 44643}, {12704, 44645}, {12970, 40660}, {13373, 35817}, {13464, 41963}, {13624, 35762}, {13665, 48661}, {13846, 31162}, {13936, 43174}, {13975, 32788}, {14121, 46835}, {15178, 35811}, {18480, 35788}, {18481, 42260}, {18483, 42273}, {18538, 40273}, {19048, 49163}, {19054, 34632}, {19925, 42283}, {22770, 44606}, {22841, 44627}, {22842, 44629}, {23251, 41869}, {24914, 44624}, {28146, 35820}, {28150, 42272}, {28160, 42266}, {28194, 32787}, {28198, 35822}, {28204, 35842}, {31447, 35813}, {31474, 36279}, {31673, 42271}, {31730, 42259}, {32612, 35785}, {32613, 35773}, {34339, 45643}, {34627, 43257}, {34638, 43209}, {35769, 37582}, {35787, 38140}, {37401, 49243}, {44582, 48487}, {44584, 48488}, {44594, 49054}, {44596, 49055}, {46684, 48701}

X(49226) = midpoint of X(i) and X(j) for these {i, j}: {371, 35610}, {42258, 49232}
X(49226) = reflection of X(i) in X(j) for these (i, j): (371, 31439), (3070, 13883), (7969, 371)
X(49226) = orthologic center (1st Kenmotu-centers, T) for these triangles T: Bevan antipodal, 3rd extouch
X(49226) = X(40)-of-1st Kenmotu-centers triangle
X(49226) = X(3579)-of-1st Kenmotu-free-vertices triangle
X(49226) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 9616, 1151), (3, 35775, 7968), (6, 40, 49227), (40, 1702, 6), (57, 31432, 3297), (165, 18992, 1152), (946, 13912, 590), (1572, 31437, 6422), (1588, 5657, 13973), (1699, 13893, 42265), (3311, 12702, 35774), (3576, 9582, 6409), (6200, 35642, 1385), (6409, 44636, 3576), (6425, 44635, 9583), (7982, 9583, 44635), (19038, 37567, 2362), (31439, 35610, 7969), (35788, 35821, 18480)


X(49227) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO BEVAN ANTIPODAL

Barycentrics    a*(2*S*a+a^3+(b+c)*a^2-(b+c)^2*a-(b^2-c^2)*(b-c)) : :
X(49227) = 3*X(372)-X(35642) = X(7968)+2*X(35611) = 3*X(7968)-2*X(35642) = 3*X(35611)+X(35642)

The reciprocal orthologic center of these triangles is X(1).

X(49227) lies on these lines: {1, 1152}, {3, 7969}, {4, 13973}, {6, 40}, {8, 6460}, {10, 3070}, {20, 19065}, {37, 6213}, {39, 48740}, {44, 6212}, {46, 1335}, {55, 2362}, {57, 3298}, {65, 5414}, {145, 43511}, {165, 1151}, {355, 6560}, {371, 3579}, {372, 517}, {484, 3301}, {485, 26446}, {486, 12699}, {515, 42259}, {516, 3071}, {519, 41946}, {590, 6684}, {615, 946}, {942, 35809}, {962, 3069}, {1124, 5119}, {1131, 46933}, {1155, 2067}, {1158, 49234}, {1376, 30557}, {1377, 12514}, {1385, 6396}, {1482, 6398}, {1537, 13991}, {1571, 6422}, {1572, 6421}, {1587, 5657}, {1588, 6361}, {1697, 3297}, {1698, 42265}, {1699, 13947}, {1829, 11474}, {1836, 44622}, {1902, 5413}, {2066, 37568}, {2771, 35827}, {2778, 13288}, {2800, 48715}, {2802, 48701}, {3056, 6404}, {3057, 6502}, {3299, 11010}, {3312, 12702}, {3359, 19048}, {3523, 13902}, {3576, 6410}, {3592, 9616}, {3594, 7991}, {3634, 42582}, {3817, 42583}, {4301, 13971}, {4640, 31453}, {4669, 42418}, {5058, 48741}, {5250, 31473}, {5416, 7957}, {5420, 5886}, {5584, 19000}, {5587, 23251}, {5603, 13935}, {5690, 42216}, {5691, 42264}, {5709, 19049}, {5731, 42637}, {5812, 44621}, {5818, 23249}, {5840, 49241}, {5847, 49229}, {5901, 35256}, {6001, 49251}, {6200, 31663}, {6408, 10247}, {6409, 9583}, {6411, 9615}, {6412, 7987}, {6419, 31439}, {6420, 35610}, {6423, 9620}, {6425, 9582}, {6426, 7982}, {6430, 16200}, {6432, 19003}, {6438, 11531}, {6446, 37624}, {6450, 10246}, {6454, 10222}, {6459, 9778}, {6481, 33179}, {6564, 9956}, {6565, 22793}, {6566, 45715}, {7090, 46835}, {7584, 28174}, {7586, 20070}, {7973, 17820}, {8227, 8252}, {8253, 31423}, {8406, 45399}, {8983, 10164}, {9588, 13893}, {9600, 31422}, {9780, 31412}, {9812, 42561}, {9911, 44599}, {9955, 10577}, {9957, 35769}, {10175, 42273}, {10252, 31538}, {10306, 44591}, {10534, 40658}, {10576, 11231}, {10595, 43510}, {11278, 35811}, {11362, 49232}, {12197, 44587}, {12458, 44601}, {12459, 44603}, {12497, 44605}, {12696, 44611}, {12700, 44619}, {12701, 44624}, {12703, 44644}, {12704, 44646}, {12964, 40660}, {13373, 35816}, {13389, 38487}, {13464, 41964}, {13624, 35763}, {13785, 48661}, {13847, 31162}, {13883, 43174}, {13912, 32787}, {13966, 22791}, {15178, 35810}, {16232, 19037}, {18480, 35789}, {18481, 42261}, {18483, 42270}, {18762, 40273}, {19047, 49163}, {19053, 34632}, {19925, 42284}, {22770, 44607}, {22841, 44628}, {22842, 44630}, {23261, 41869}, {24914, 44623}, {26066, 31484}, {28146, 35821}, {28150, 42271}, {28160, 42267}, {28194, 32788}, {28198, 35823}, {28204, 35843}, {31447, 35812}, {31673, 42272}, {31730, 42258}, {32612, 35784}, {32613, 35772}, {34339, 45642}, {34627, 43256}, {34638, 43210}, {35768, 37582}, {35786, 38140}, {37401, 49242}, {44583, 48487}, {44585, 48488}, {44595, 49054}, {44597, 49055}, {46684, 48700}

X(49227) = midpoint of X(i) and X(j) for these {i, j}: {372, 35611}, {42259, 49233}
X(49227) = reflection of X(i) in X(j) for these (i, j): (3071, 13936), (7968, 372)
X(49227) = orthologic center (2nd Kenmotu-centers, T) for these triangles T: Bevan antipodal, 3rd extouch
X(49227) = X(40)-of-2nd Kenmotu-centers triangle
X(49227) = X(3579)-of-2nd Kenmotu-free-vertices triangle
X(49227) = X(8422)-of-2nd Kenmotu diagonals triangle
X(49227) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 35774, 7969), (6, 40, 49226), (40, 1703, 6), (165, 18991, 1151), (946, 13975, 615), (1587, 5657, 13911), (1699, 13947, 42262), (3312, 12702, 35775), (6396, 35641, 1385), (6410, 44635, 3576), (9583, 35242, 6409), (9615, 16192, 6411), (9616, 19004, 3592), (19037, 37567, 16232), (35789, 35820, 18480)


X(49228) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO 9th BROCARD

Barycentrics    2*S*a^2*(a^2+b^2+c^2)+(-a^2+b^2+c^2)*(3*a^4+(b^2-c^2)^2) : :
X(49228) = 3*X(14853)-2*X(45862) = 3*X(14912)-X(45407) = X(42272)-4*X(44502)

The reciprocal orthologic center of these triangles is X(4).

X(49228) lies on these lines: {4, 6}, {30, 35840}, {39, 48743}, {69, 1151}, {141, 39387}, {182, 615}, {193, 490}, {230, 45511}, {371, 3564}, {372, 48906}, {485, 18440}, {486, 5050}, {487, 7789}, {511, 42258}, {524, 35949}, {542, 32787}, {590, 1352}, {1124, 39901}, {1152, 25406}, {1328, 14848}, {1335, 39900}, {1350, 35945}, {1351, 6561}, {1353, 35841}, {1504, 36709}, {1692, 48467}, {1843, 12239}, {1974, 30428}, {1975, 43134}, {2066, 39897}, {2067, 39873}, {3053, 12257}, {3068, 5921}, {3311, 39899}, {3589, 42583}, {3618, 42262}, {3815, 45510}, {3818, 42273}, {4048, 35938}, {5013, 12256}, {5062, 36714}, {5412, 39871}, {5420, 12017}, {5477, 45545}, {5847, 49226}, {5848, 48700}, {6200, 48876}, {6221, 11898}, {6409, 10519}, {6419, 39894}, {6564, 39884}, {6565, 18583}, {7968, 39870}, {8253, 40330}, {8414, 11292}, {8855, 45298}, {8994, 32275}, {9974, 31670}, {10011, 45555}, {10264, 35877}, {10516, 42582}, {10576, 18358}, {10577, 38110}, {11179, 19146}, {11180, 13846}, {12830, 33430}, {13354, 49253}, {13665, 48662}, {13910, 43879}, {13911, 39885}, {14561, 42270}, {14927, 42264}, {15069, 31454}, {15534, 42417}, {18991, 39878}, {19048, 49165}, {19050, 49164}, {19060, 32234}, {20080, 43512}, {21850, 35821}, {22615, 32495}, {24206, 32789}, {29012, 42272}, {31411, 36656}, {31472, 39891}, {32494, 43118}, {33878, 42260}, {34507, 41963}, {35787, 38136}, {35947, 44882}, {39660, 49087}, {39872, 44586}, {39877, 44590}, {39879, 44598}, {39880, 44600}, {39881, 44602}, {39882, 44604}, {39883, 44606}, {39886, 44610}, {39889, 44618}, {39890, 44620}, {39892, 44623}, {39895, 44627}, {39896, 44629}, {39898, 44635}, {39902, 44643}, {39903, 44645}, {41946, 43273}, {42259, 46264}, {44582, 48489}, {44584, 48490}, {44594, 49056}, {44596, 49057}

X(49228) = midpoint of X(i) and X(j) for these {i, j}: {193, 490}, {371, 39893}
X(49228) = reflection of X(3070) in X(6)
X(49228) = orthologic center (1st Kenmotu-centers, 9th Brocard)
X(49228) = X(6776)-of-1st Kenmotu-centers triangle
X(49228) = X(48906)-of-1st Kenmotu-free-vertices triangle
X(49228) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 6776, 49229), (6, 23261, 14853), (1352, 19145, 590), (1353, 42215, 35841), (1588, 14912, 6), (1588, 45407, 5254), (5254, 45407, 3070), (6776, 39876, 6)


X(49229) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO 9th BROCARD

Barycentrics    -2*S*a^2*(a^2+b^2+c^2)+(-a^2+b^2+c^2)*(3*a^4+(b^2-c^2)^2) : :
X(49229) = 3*X(14853)-2*X(45863) = 3*X(14912)-X(45406) = X(42271)-4*X(44501)

The reciprocal orthologic center of these triangles is X(4).

X(49229) lies on these lines: {4, 6}, {30, 35841}, {39, 48742}, {69, 1152}, {141, 39388}, {182, 590}, {193, 489}, {230, 45510}, {371, 48906}, {372, 3564}, {485, 5050}, {486, 18440}, {488, 7789}, {511, 42259}, {524, 35948}, {542, 32788}, {615, 1352}, {1124, 39900}, {1151, 25406}, {1327, 14848}, {1335, 39901}, {1350, 35944}, {1351, 6560}, {1353, 35840}, {1505, 36714}, {1692, 48466}, {1843, 12240}, {1974, 30427}, {1975, 43133}, {3053, 12256}, {3069, 5921}, {3312, 39899}, {3589, 42582}, {3618, 42265}, {3815, 45511}, {3818, 42270}, {4048, 35939}, {5013, 12257}, {5058, 36709}, {5413, 39871}, {5414, 39897}, {5418, 12017}, {5477, 45544}, {5847, 49227}, {5848, 48701}, {6396, 48876}, {6398, 11898}, {6410, 10519}, {6420, 39893}, {6502, 39873}, {6564, 18583}, {6565, 39884}, {7969, 39870}, {8252, 40330}, {8406, 11291}, {8854, 45298}, {9975, 31670}, {10011, 45554}, {10264, 35876}, {10516, 42583}, {10576, 38110}, {10577, 18358}, {11179, 19145}, {11180, 13847}, {12830, 33431}, {13354, 49252}, {13785, 48662}, {13969, 32275}, {13972, 43880}, {13973, 39885}, {14561, 42273}, {14927, 42263}, {15534, 42418}, {18992, 39878}, {19047, 49165}, {19049, 49164}, {19059, 32234}, {20080, 43511}, {21850, 35820}, {22644, 32492}, {24206, 32790}, {29012, 42271}, {32497, 43119}, {33878, 42261}, {34507, 41964}, {35786, 38136}, {35946, 44882}, {39661, 49086}, {39872, 44587}, {39877, 44591}, {39879, 44599}, {39880, 44601}, {39881, 44603}, {39882, 44605}, {39883, 44607}, {39886, 44611}, {39889, 44619}, {39890, 44621}, {39891, 44622}, {39892, 44624}, {39895, 44628}, {39896, 44630}, {39898, 44636}, {39902, 44644}, {39903, 44646}, {41945, 43273}, {42258, 46264}, {44583, 48489}, {44585, 48490}, {44595, 49056}, {44597, 49057}

X(49229) = midpoint of X(i) and X(j) for these {i, j}: {193, 489}, {372, 39894}
X(49229) = reflection of X(3071) in X(6)
X(49229) = orthologic center (2nd Kenmotu-centers, 9th Brocard)
X(49229) = X(6776)-of-2nd Kenmotu-centers triangle
X(49229) = X(8581)-of-2nd Kenmotu diagonals triangle
X(49229) = X(48906)-of-2nd Kenmotu-free-vertices triangle
X(49229) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 6776, 49228), (6, 23251, 14853), (1352, 19146, 615), (1353, 42216, 35840), (1587, 14912, 6), (1587, 45406, 5254), (5254, 45406, 3071), (6776, 39875, 6)


X(49230) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO 1st BROCARD-REFLECTED

Barycentrics    6*S*a^2*((b^2+c^2)*a^2+b^2*c^2)+((2*b^2+c^2)*a^2+b^2*c^2-c^4)*((b^2+2*c^2)*a^2-b^4+b^2*c^2) : :
X(49230) = X(3103)+2*X(7583) = 2*X(3103)+X(49252) = 4*X(7583)-X(49252)

The reciprocal orthologic center of these triangles is X(3).

X(49230) lies on these lines: {6, 98}, {39, 44647}, {371, 35838}, {372, 40108}, {485, 7697}, {511, 32787}, {590, 15819}, {732, 1991}, {1124, 22730}, {1151, 22676}, {1335, 22729}, {1587, 7709}, {2066, 22711}, {2067, 18971}, {2782, 35822}, {3068, 6194}, {3071, 22682}, {3094, 33435}, {3102, 19117}, {3103, 7583}, {3311, 22728}, {3564, 22725}, {3594, 7786}, {3934, 43879}, {5062, 48744}, {5188, 31454}, {5412, 22480}, {6419, 14881}, {6420, 11272}, {6564, 22681}, {7585, 44434}, {7968, 22475}, {8960, 49111}, {13330, 33434}, {13665, 48663}, {13846, 22712}, {13911, 22697}, {13983, 42582}, {18512, 32519}, {18991, 22650}, {19048, 49167}, {19050, 49166}, {19089, 42265}, {21163, 41946}, {21445, 44587}, {22521, 44586}, {22556, 44590}, {22655, 44598}, {22668, 44600}, {22672, 44602}, {22678, 44604}, {22680, 44606}, {22698, 44610}, {22703, 44618}, {22704, 44620}, {22705, 31472}, {22706, 44623}, {22709, 44627}, {22710, 44629}, {22713, 44635}, {22717, 22724}, {22721, 32788}, {22731, 44643}, {22732, 44645}, {44582, 48491}, {44584, 48492}, {44594, 49058}, {44596, 49059}

X(49230) = midpoint of X(371) and X(35838)
X(49230) = orthologic center (1st Kenmotu-centers, 1st Brocard-reflected)
X(49230) = X(262)-of-1st Kenmotu-centers triangle
X(49230) = X(40108)-of-1st Kenmotu-free-vertices triangle
X(49230) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 262, 49231), (262, 19064, 6), (3103, 7583, 49252), (15819, 22720, 590), (22717, 22726, 22724)


X(49231) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO 1st BROCARD-REFLECTED

Barycentrics    -6*S*a^2*((b^2+c^2)*a^2+b^2*c^2)+((2*b^2+c^2)*a^2+b^2*c^2-c^4)*((b^2+2*c^2)*a^2-b^4+b^2*c^2) : :
X(49231) = X(3102)+2*X(7584) = 2*X(3102)+X(49253) = 4*X(7584)-X(49253)

The reciprocal orthologic center of these triangles is X(3).

X(49231) lies on these lines: {6, 98}, {39, 44648}, {371, 40108}, {372, 35839}, {486, 7697}, {511, 32788}, {591, 732}, {615, 15819}, {1124, 22729}, {1152, 22676}, {1335, 22730}, {1588, 7709}, {2782, 35823}, {3069, 6194}, {3070, 22682}, {3094, 33434}, {3102, 7584}, {3103, 19116}, {3312, 22728}, {3564, 22724}, {3592, 7786}, {3934, 43880}, {5058, 48745}, {5413, 22480}, {5414, 22711}, {6419, 11272}, {6420, 14881}, {6502, 18971}, {6565, 22681}, {6683, 31454}, {7586, 44434}, {7969, 22475}, {8992, 42583}, {13330, 33435}, {13785, 48663}, {13847, 22712}, {13973, 22697}, {18510, 32519}, {18992, 22650}, {19047, 49167}, {19049, 49166}, {19090, 42262}, {21163, 41945}, {21445, 44586}, {22521, 44587}, {22556, 44591}, {22655, 44599}, {22668, 44601}, {22672, 44603}, {22678, 44605}, {22680, 44607}, {22698, 44611}, {22703, 44619}, {22704, 44621}, {22705, 44622}, {22706, 44624}, {22709, 44628}, {22710, 44630}, {22713, 44636}, {22719, 22725}, {22720, 32787}, {22731, 44644}, {22732, 44646}, {44583, 48491}, {44585, 48492}, {44595, 49058}, {44597, 49059}

X(49231) = midpoint of X(372) and X(35839)
X(49231) = orthologic center (2nd Kenmotu-centers, 1st Brocard-reflected)
X(49231) = X(262)-of-2nd Kenmotu-centers triangle
X(49231) = X(39792)-of-2nd Kenmotu diagonals triangle
X(49231) = X(40108)-of-2nd Kenmotu-free-vertices triangle
X(49231) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 262, 49230), (262, 19063, 6), (3102, 7584, 49253), (15819, 22721, 615), (22719, 22727, 22725)


X(49232) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO EXCENTERS-MIDPOINTS

Barycentrics    2*(-a+b+c)*S+a^2*(a+b+c) : :
X(49232) = 2*X(7969)-3*X(32787) = 4*X(13883)-3*X(32787) = 4*X(31439)-3*X(41945)

The reciprocal orthologic center of these triangles is X(10).

X(49232) lies on these lines: {1, 590}, {2, 44636}, {5, 35642}, {6, 8}, {10, 615}, {30, 35610}, {39, 48747}, {40, 42259}, {140, 35762}, {145, 3068}, {355, 3071}, {371, 952}, {372, 5690}, {485, 1482}, {486, 5790}, {515, 42258}, {516, 42272}, {517, 3070}, {518, 26300}, {519, 7969}, {758, 49242}, {944, 1151}, {946, 42273}, {958, 44591}, {962, 23251}, {1124, 10573}, {1125, 32789}, {1145, 48715}, {1152, 5657}, {1317, 13922}, {1335, 12647}, {1376, 44607}, {1377, 19047}, {1378, 19049}, {1483, 8981}, {1587, 12245}, {1698, 32790}, {1702, 5881}, {2066, 10950}, {2067, 10944}, {2098, 44623}, {2099, 31472}, {2362, 41687}, {2802, 49240}, {3069, 3617}, {3241, 13846}, {3244, 8983}, {3297, 18391}, {3299, 41684}, {3311, 12645}, {3416, 49079}, {3616, 8253}, {3621, 7585}, {3622, 32785}, {3623, 8972}, {3626, 13936}, {3632, 18991}, {3654, 41946}, {3679, 13973}, {3913, 44590}, {4415, 13386}, {4663, 26301}, {4668, 19003}, {4677, 19004}, {4678, 7586}, {5062, 48746}, {5252, 16232}, {5412, 12135}, {5416, 21677}, {5418, 10246}, {5554, 31473}, {5587, 42270}, {5599, 44603}, {5600, 44601}, {5603, 42265}, {5691, 42271}, {5727, 31432}, {5731, 6409}, {5818, 42262}, {5844, 7583}, {5882, 13912}, {5886, 42582}, {5901, 10576}, {6200, 34773}, {6221, 18526}, {6361, 42264}, {6419, 35843}, {6502, 40663}, {6560, 12702}, {6561, 18525}, {6564, 22791}, {6565, 18357}, {6914, 35773}, {6924, 35785}, {7584, 35789}, {7967, 9540}, {7981, 13882}, {8148, 13665}, {8252, 9780}, {8909, 9933}, {8960, 35810}, {8976, 10247}, {9956, 42583}, {10222, 43879}, {10577, 38042}, {10819, 12898}, {10912, 44618}, {11362, 49227}, {12019, 35803}, {12195, 44586}, {12410, 44598}, {12454, 44600}, {12455, 44602}, {12495, 44604}, {12513, 44606}, {12531, 19113}, {12626, 44610}, {12635, 44620}, {12636, 44627}, {12637, 44629}, {12648, 44643}, {12649, 44645}, {12699, 42284}, {12787, 32494}, {13461, 44416}, {13894, 16211}, {13901, 37734}, {13966, 38112}, {13975, 38127}, {13976, 38213}, {13977, 38128}, {14839, 49252}, {15863, 49241}, {16210, 44611}, {17334, 31547}, {18480, 42283}, {18493, 42277}, {19048, 49169}, {19050, 49168}, {19054, 31145}, {19079, 47033}, {19146, 38116}, {22644, 48661}, {28174, 35820}, {28186, 42266}, {28204, 31439}, {28208, 43210}, {31454, 37727}, {31499, 37525}, {31559, 31584}, {32786, 46933}, {35611, 42216}, {35786, 40273}, {35800, 39542}, {35808, 37730}, {37705, 42215}, {44392, 45444}, {44394, 45714}, {44582, 48493}, {44584, 48494}, {44594, 49060}, {44596, 49061}, {45476, 45719}

X(49232) = midpoint of X(371) and X(35842)
X(49232) = reflection of X(i) in X(j) for these (i, j): (7969, 13883), (35641, 7583), (42258, 49226)
X(49232) = orthologic center (1st Kenmotu-centers, T) for these triangles T: excenters-midpoints, Garcia-reflection, 2nd Schiffler
X(49232) = X(8)-of-1st Kenmotu-centers triangle
X(49232) = X(5690)-of-1st Kenmotu-free-vertices triangle
X(49232) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 13911, 590), (6, 8, 49233), (8, 19066, 6), (10, 7968, 615), (145, 3068, 44635), (355, 35775, 3071), (1483, 8981, 35763), (3679, 18992, 13973), (7969, 13883, 32787), (9780, 13959, 8252), (10576, 35811, 5901), (13973, 18992, 32788), (35642, 35788, 5)


X(49233) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO EXCENTERS-MIDPOINTS

Barycentrics    -2*(-a+b+c)*S+a^2*(a+b+c) : :
X(49233) = 2*X(7968)-3*X(32788) = 4*X(13936)-3*X(32788)

The reciprocal orthologic center of these triangles is X(10).

X(49233) lies on these lines: {1, 615}, {2, 44635}, {5, 35641}, {6, 8}, {10, 590}, {30, 35611}, {39, 48746}, {40, 42258}, {140, 35763}, {145, 3069}, {355, 3070}, {371, 5690}, {372, 952}, {484, 9647}, {485, 5790}, {486, 1482}, {515, 42259}, {516, 42271}, {517, 3071}, {518, 26301}, {519, 7968}, {758, 49243}, {944, 1152}, {946, 42270}, {958, 44590}, {962, 23261}, {1124, 12647}, {1125, 32790}, {1145, 48714}, {1151, 5657}, {1317, 13991}, {1335, 10573}, {1376, 44606}, {1377, 19050}, {1378, 19048}, {1478, 38235}, {1483, 13966}, {1588, 12245}, {1698, 32789}, {1703, 5881}, {2067, 40663}, {2098, 44624}, {2099, 44622}, {2362, 5252}, {2802, 49241}, {3068, 3617}, {3241, 13847}, {3244, 13971}, {3298, 18391}, {3301, 41684}, {3312, 12645}, {3416, 49078}, {3616, 8252}, {3621, 7586}, {3622, 32786}, {3623, 13941}, {3626, 13883}, {3632, 18992}, {3654, 41945}, {3679, 13911}, {3913, 44591}, {4415, 13387}, {4663, 26300}, {4668, 19004}, {4677, 19003}, {4678, 7585}, {5058, 48747}, {5413, 12135}, {5414, 10950}, {5415, 21677}, {5420, 10246}, {5554, 44643}, {5587, 42273}, {5599, 44602}, {5600, 44600}, {5603, 42262}, {5691, 42272}, {5731, 6410}, {5818, 42265}, {5844, 7584}, {5882, 13975}, {5886, 42583}, {5901, 10577}, {6361, 42263}, {6396, 34773}, {6398, 18526}, {6420, 35842}, {6502, 10944}, {6560, 18525}, {6561, 12702}, {6564, 18357}, {6565, 22791}, {6914, 35772}, {6924, 35784}, {7583, 35788}, {7967, 13935}, {7980, 13934}, {8148, 13785}, {8253, 9780}, {8981, 38112}, {8988, 38213}, {9583, 41963}, {9588, 9615}, {9660, 11010}, {9661, 18395}, {9956, 42582}, {10222, 43880}, {10247, 13951}, {10576, 38042}, {10820, 12898}, {10912, 44619}, {11362, 49226}, {12019, 35802}, {12195, 44587}, {12410, 44599}, {12454, 44601}, {12455, 44603}, {12495, 44605}, {12513, 44607}, {12531, 19112}, {12626, 44611}, {12635, 44621}, {12636, 44628}, {12637, 44630}, {12648, 44644}, {12649, 44646}, {12699, 42283}, {12788, 32497}, {13912, 38127}, {13913, 38128}, {13948, 16211}, {13958, 37734}, {14839, 49253}, {15863, 49240}, {16210, 44610}, {16232, 41687}, {17334, 31548}, {18480, 42284}, {18493, 42274}, {19047, 49169}, {19049, 49168}, {19053, 31145}, {19080, 47033}, {19145, 38116}, {22615, 48661}, {28174, 35821}, {28186, 42267}, {28204, 41946}, {28208, 43209}, {31473, 44645}, {31484, 44620}, {31560, 31585}, {32785, 46933}, {35610, 42215}, {35787, 40273}, {35801, 39542}, {35809, 37730}, {37705, 42216}, {44392, 45713}, {44394, 45445}, {44583, 48493}, {44585, 48494}, {44595, 49060}, {44597, 49061}, {45477, 45720}

X(49233) = midpoint of X(372) and X(35843)
X(49233) = reflection of X(i) in X(j) for these (i, j): (7968, 13936), (35642, 7584), (42259, 49227)
X(49233) = orthologic center (2nd Kenmotu-centers, T) for these triangles T: excenters-midpoints, Garcia-reflection, 2nd Schiffler
X(49233) = X(8)-of-2nd Kenmotu-centers triangle
X(49233) = X(5690)-of-2nd Kenmotu-free-vertices triangle
X(49233) = X(17641)-of-2nd Kenmotu diagonals triangle
X(49233) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 13973, 615), (6, 8, 49232), (8, 19065, 6), (10, 7969, 590), (145, 3069, 44636), (355, 35774, 3070), (1483, 13966, 35762), (3679, 18991, 13911), (7968, 13936, 32788), (9780, 13902, 8253), (10577, 35810, 5901), (13911, 18991, 32787), (35641, 35789, 5)


X(49234) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO EXTOUCH

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

The reciprocal orthologic center of these triangles is X(40).

X(49234) lies on these lines: {6, 84}, {39, 48749}, {371, 971}, {372, 34862}, {485, 6259}, {515, 42258}, {590, 6260}, {615, 6705}, {1124, 10085}, {1151, 1490}, {1158, 49227}, {1335, 1709}, {1587, 12246}, {1702, 10864}, {2066, 12680}, {2067, 12688}, {2829, 49240}, {3068, 6223}, {3071, 6245}, {3207, 32556}, {3298, 12705}, {3311, 12684}, {5062, 48748}, {5412, 12136}, {5658, 9540}, {5787, 6561}, {6001, 7969}, {6419, 35845}, {6459, 9799}, {6564, 22792}, {7968, 12114}, {7971, 44635}, {7992, 18991}, {9678, 12520}, {9841, 31438}, {9856, 35768}, {9910, 44598}, {9943, 31453}, {12196, 44586}, {12330, 44590}, {12456, 44600}, {12457, 44602}, {12496, 44604}, {12667, 13911}, {12668, 44610}, {12676, 44618}, {12677, 44620}, {12678, 31472}, {12679, 44623}, {12686, 44643}, {12687, 44645}, {13665, 48664}, {13973, 14647}, {13974, 32788}, {18237, 44606}, {18245, 44627}, {18246, 44629}, {19048, 49171}, {19050, 49170}, {44582, 48495}, {44584, 48496}, {44594, 49062}, {44596, 49063}

X(49234) = midpoint of X(371) and X(35844)
X(49234) = orthologic center (1st Kenmotu-centers, T) for these triangles T: extouch, 1st Zaniah
X(49234) = X(84)-of-1st Kenmotu-centers triangle
X(49234) = X(34862)-of-1st Kenmotu-free-vertices triangle
X(49234) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 84, 49235), (84, 19068, 6), (6260, 8987, 590)


X(49235) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO EXTOUCH

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

The reciprocal orthologic center of these triangles is X(40).

X(49235) lies on these lines: {6, 84}, {39, 48748}, {371, 34862}, {372, 971}, {486, 6259}, {515, 42259}, {590, 6705}, {615, 6260}, {1124, 1709}, {1152, 1490}, {1158, 49226}, {1335, 10085}, {1588, 12246}, {1703, 10864}, {2829, 49241}, {3069, 6223}, {3070, 6245}, {3207, 32555}, {3297, 12705}, {3312, 12684}, {5058, 48749}, {5413, 12136}, {5414, 12680}, {5658, 13935}, {5787, 6560}, {6001, 7968}, {6420, 35844}, {6460, 9799}, {6502, 12688}, {6565, 22792}, {7969, 12114}, {7971, 44636}, {7992, 18992}, {8987, 32787}, {9856, 35769}, {9910, 44599}, {12196, 44587}, {12330, 44591}, {12456, 44601}, {12457, 44603}, {12496, 44605}, {12667, 13973}, {12668, 44611}, {12676, 44619}, {12677, 44621}, {12678, 44622}, {12679, 44624}, {12686, 44644}, {12687, 44646}, {13785, 48664}, {13911, 14647}, {18237, 44607}, {18245, 44628}, {18246, 44630}, {19047, 49171}, {19049, 49170}, {44583, 48495}, {44585, 48496}, {44595, 49062}, {44597, 49063}

X(49235) = midpoint of X(372) and X(35845)
X(49235) = orthologic center (2nd Kenmotu-centers, T) for these triangles T: extouch, 1st Zaniah
X(49235) = X(84)-of-2nd Kenmotu-centers triangle
X(49235) = X(34862)-of-2nd Kenmotu-free-vertices triangle
X(49235) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 84, 49234), (84, 19067, 6), (6260, 13974, 615)


X(49236) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO INNER-FERMAT

Barycentrics    4*a^4+9*b^4-18*b^2*c^2+9*c^4-22*S*a^2-6*(b^2+c^2)*a^2+(3*a^4+(b^2+c^2)*a^2+(b^2-c^2)^2)*sqrt(3)-4*(b^2-c^2)^2 : :

The reciprocal orthologic center of these triangles is X(3).

X(49236) lies on these lines: {6, 17}, {39, 48751}, {371, 35846}, {372, 49105}, {395, 33394}, {485, 16627}, {533, 32787}, {590, 630}, {615, 6674}, {628, 3068}, {1124, 22885}, {1151, 22843}, {1335, 22884}, {1587, 22531}, {2066, 22865}, {2067, 18972}, {3070, 44667}, {3071, 22831}, {3311, 16628}, {5062, 48750}, {5412, 22481}, {5471, 42235}, {6419, 35849}, {6564, 22794}, {7583, 49208}, {7585, 22114}, {7968, 11740}, {10612, 49211}, {13665, 48665}, {13911, 22851}, {18991, 22651}, {19048, 49173}, {19050, 49172}, {22522, 44586}, {22557, 44590}, {22656, 44598}, {22669, 44600}, {22673, 44602}, {22745, 44604}, {22771, 44606}, {22846, 49209}, {22852, 44610}, {22857, 44618}, {22858, 44620}, {22859, 31472}, {22860, 44623}, {22863, 44627}, {22864, 44629}, {22867, 44635}, {22873, 22880}, {22877, 32788}, {22881, 33447}, {22886, 44643}, {22887, 44645}, {44582, 48497}, {44584, 48498}, {44594, 49064}, {44596, 49065}

X(49236) = midpoint of X(371) and X(35846)
X(49236) = orthologic center (1st Kenmotu-centers, T) for these triangles T: inner-Fermat, 1st half-diamonds
X(49236) = X(18)-of-1st Kenmotu-centers triangle
X(49236) = X(49105)-of-1st Kenmotu-free-vertices triangle
X(49236) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 18, 49237), (18, 19072, 6), (630, 22876, 590), (22873, 22882, 22880)


X(49237) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO INNER-FERMAT

Barycentrics    4*a^4+9*b^4-18*b^2*c^2+9*c^4+22*S*a^2-6*(b^2+c^2)*a^2-(3*a^4+(b^2+c^2)*a^2+(b^2-c^2)^2)*sqrt(3)-4*(b^2-c^2)^2 : :

The reciprocal orthologic center of these triangles is X(3).

X(49237) lies on these lines: {6, 17}, {39, 48750}, {371, 49105}, {372, 35849}, {395, 33392}, {486, 16627}, {533, 32788}, {590, 6674}, {615, 630}, {628, 3069}, {1124, 22884}, {1152, 22843}, {1335, 22885}, {1588, 22531}, {3070, 22831}, {3071, 44667}, {3312, 16628}, {5058, 48751}, {5413, 22481}, {5414, 22865}, {5471, 42237}, {6420, 35846}, {6502, 18972}, {6565, 22794}, {7584, 49209}, {7586, 22114}, {7969, 11740}, {10612, 49210}, {13785, 48665}, {13973, 22851}, {18992, 22651}, {19047, 49173}, {19049, 49172}, {22522, 44587}, {22557, 44591}, {22656, 44599}, {22669, 44601}, {22673, 44603}, {22745, 44605}, {22771, 44607}, {22846, 49208}, {22852, 44611}, {22857, 44619}, {22858, 44621}, {22859, 44622}, {22860, 44624}, {22863, 44628}, {22864, 44630}, {22867, 44636}, {22875, 22881}, {22876, 32787}, {22880, 33446}, {22886, 44644}, {22887, 44646}, {44583, 48497}, {44585, 48498}, {44595, 49064}, {44597, 49065}

X(49237) = midpoint of X(372) and X(35849)
X(49237) = orthologic center (2nd Kenmotu-centers, T) for these triangles T: inner-Fermat, 1st half-diamonds
X(49237) = X(18)-of-2nd Kenmotu-centers triangle
X(49237) = X(49105)-of-2nd Kenmotu-free-vertices triangle
X(49237) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 18, 49236), (18, 19069, 6), (630, 22877, 615), (22875, 22883, 22881)


X(49238) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO OUTER-FERMAT

Barycentrics    4*a^4+9*b^4-18*b^2*c^2+9*c^4-22*S*a^2-6*(b^2+c^2)*a^2-(3*a^4+(b^2+c^2)*a^2+(b^2-c^2)^2)*sqrt(3)-4*(b^2-c^2)^2 : :

The reciprocal orthologic center of these triangles is X(3).

X(49238) lies on these lines: {6, 17}, {39, 48753}, {371, 35753}, {372, 49106}, {396, 33393}, {485, 16626}, {532, 32787}, {590, 629}, {615, 6673}, {627, 3068}, {1124, 22930}, {1151, 22890}, {1335, 22929}, {1587, 22532}, {2066, 22910}, {2067, 18973}, {3070, 44666}, {3071, 22832}, {3311, 16629}, {5062, 48752}, {5412, 22482}, {5472, 42236}, {6419, 35847}, {6564, 22795}, {7583, 49210}, {7585, 22113}, {7968, 11739}, {10611, 49209}, {13665, 48666}, {13911, 22896}, {18991, 22652}, {19048, 49175}, {19050, 49174}, {19074, 36782}, {22523, 44586}, {22558, 44590}, {22657, 44598}, {22670, 44600}, {22674, 44602}, {22746, 44604}, {22772, 44606}, {22891, 49211}, {22897, 44610}, {22902, 44618}, {22903, 44620}, {22904, 31472}, {22905, 44623}, {22908, 44627}, {22909, 44629}, {22912, 44635}, {22918, 22925}, {22922, 32788}, {22926, 33445}, {22931, 44643}, {22932, 44645}, {44582, 48499}, {44584, 48500}, {44594, 49066}, {44596, 49067}

X(49238) = midpoint of X(371) and X(35848)
X(49238) = orthologic center (1st Kenmotu-centers, T) for these triangles T: outer-Fermat, 2nd half-diamonds
X(49238) = X(17)-of-1st Kenmotu-centers triangle
X(49238) = X(49106)-of-1st Kenmotu-free-vertices triangle
X(49238) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 17, 49239), (629, 22921, 590), (22918, 22927, 22925)


X(49239) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO OUTER-FERMAT

Barycentrics    4*a^4+9*b^4-18*b^2*c^2+9*c^4+22*S*a^2-6*(b^2+c^2)*a^2+(3*a^4+(b^2+c^2)*a^2+(b^2-c^2)^2)*sqrt(3)-4*(b^2-c^2)^2 : :

The reciprocal orthologic center of these triangles is X(3).

X(49239) lies on these lines: {6, 17}, {39, 48752}, {371, 49106}, {372, 35754}, {396, 33395}, {486, 16626}, {532, 32788}, {590, 6673}, {615, 629}, {627, 3069}, {1124, 22929}, {1152, 22890}, {1335, 22930}, {1588, 22532}, {3070, 22832}, {3071, 44666}, {3312, 16629}, {5058, 48753}, {5413, 22482}, {5414, 22910}, {5472, 42238}, {6420, 35848}, {6502, 18973}, {6565, 22795}, {7584, 49211}, {7586, 22113}, {7969, 11739}, {10611, 49208}, {13785, 48666}, {13973, 22896}, {18992, 22652}, {19047, 49175}, {19049, 49174}, {19073, 36782}, {22523, 44587}, {22558, 44591}, {22657, 44599}, {22670, 44601}, {22674, 44603}, {22746, 44605}, {22772, 44607}, {22891, 49210}, {22897, 44611}, {22902, 44619}, {22903, 44621}, {22904, 44622}, {22905, 44624}, {22908, 44628}, {22909, 44630}, {22912, 44636}, {22920, 22926}, {22921, 32787}, {22925, 33444}, {22931, 44644}, {22932, 44646}, {44583, 48499}, {44585, 48500}, {44595, 49066}, {44597, 49067}

X(49239) = midpoint of X(372) and X(35847)
X(49239) = orthologic center (2nd Kenmotu-centers, T) for these triangles T: outer-Fermat, 2nd half-diamonds
X(49239) = X(17)-of-2nd Kenmotu-centers triangle
X(49239) = X(49106)-of-2nd Kenmotu-free-vertices triangle
X(49239) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 17, 49238), (17, 19071, 6), (629, 22922, 615), (22920, 22928, 22926)


X(49240) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(49240) lies on these lines: {6, 80}, {10, 48715}, {11, 7968}, {39, 48755}, {100, 13911}, {149, 19066}, {214, 590}, {371, 35852}, {372, 12619}, {485, 6265}, {515, 48700}, {615, 6702}, {952, 7583}, {1124, 10073}, {1151, 12119}, {1335, 10057}, {1587, 12247}, {2066, 12743}, {2067, 18976}, {2771, 49222}, {2800, 3070}, {2802, 49232}, {2829, 49234}, {3068, 6224}, {3071, 6246}, {3311, 12747}, {5062, 48754}, {5412, 12137}, {5840, 49226}, {6419, 35853}, {6502, 20118}, {6560, 12515}, {6564, 12611}, {7585, 20085}, {7972, 44635}, {8983, 33337}, {9897, 18991}, {9912, 44598}, {10265, 48701}, {10577, 38182}, {10609, 13922}, {10738, 35775}, {12198, 44586}, {12331, 44590}, {12460, 44600}, {12461, 44602}, {12498, 44604}, {12729, 44610}, {12737, 44618}, {12738, 44620}, {12739, 31472}, {12740, 44623}, {12741, 44627}, {12742, 44629}, {12749, 44643}, {12750, 44645}, {12751, 19048}, {12773, 44606}, {13273, 16232}, {13665, 48667}, {13883, 48714}, {13893, 15015}, {13973, 19112}, {13976, 32788}, {13991, 34122}, {15863, 49233}, {16173, 44636}, {18992, 37718}, {19050, 49176}, {19914, 35774}, {23251, 34789}, {35788, 35883}, {38161, 42270}, {42259, 46684}, {44582, 48501}, {44584, 48502}, {44594, 49068}, {44596, 49069}

X(49240) = midpoint of X(371) and X(35852)
X(49240) = reflection of X(48714) in X(13883)
X(49240) = orthologic center (1st Kenmotu-centers, T) for these triangles T: Fuhrmann, K798i
X(49240) = X(80)-of-1st Kenmotu-centers triangle
X(49240) = X(12619)-of-1st Kenmotu-free-vertices triangle
X(49240) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 80, 49241), (80, 19078, 6), (214, 8988, 590)


X(49241) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(49241) lies on these lines: {6, 80}, {10, 48714}, {11, 7969}, {39, 48754}, {100, 13973}, {149, 19065}, {214, 615}, {371, 12619}, {372, 35853}, {486, 6265}, {515, 48701}, {590, 6702}, {952, 7584}, {1124, 10057}, {1152, 12119}, {1335, 10073}, {1588, 12247}, {2067, 20118}, {2362, 13273}, {2771, 49223}, {2800, 3071}, {2802, 49233}, {2829, 49235}, {3069, 6224}, {3070, 6246}, {3312, 12747}, {5058, 48755}, {5413, 12137}, {5414, 12743}, {5840, 49227}, {6420, 35852}, {6502, 18976}, {6561, 12515}, {6565, 12611}, {7586, 20085}, {7972, 44636}, {8988, 32787}, {9897, 18992}, {9912, 44599}, {10265, 48700}, {10576, 38182}, {10609, 13991}, {10738, 35774}, {12198, 44587}, {12331, 44591}, {12460, 44601}, {12461, 44603}, {12498, 44605}, {12729, 44611}, {12737, 44619}, {12738, 44621}, {12739, 44622}, {12740, 44624}, {12741, 44628}, {12742, 44630}, {12749, 44644}, {12750, 44646}, {12751, 19047}, {12773, 44607}, {13785, 48667}, {13911, 19113}, {13922, 34122}, {13936, 48715}, {13947, 15015}, {13971, 33337}, {15863, 49232}, {16173, 44635}, {18991, 37718}, {19049, 49176}, {19914, 35775}, {23261, 34789}, {35789, 35882}, {38161, 42273}, {42258, 46684}, {44583, 48501}, {44585, 48502}, {44595, 49068}, {44597, 49069}

X(49241) = midpoint of X(372) and X(35853)
X(49241) = reflection of X(48715) in X(13936)
X(49241) = orthologic center (2nd Kenmotu-centers, T) for these triangles T: Fuhrmann, K798i
X(49241) = X(80)-of-2nd Kenmotu-centers triangle
X(49241) = X(12619)-of-2nd Kenmotu-free-vertices triangle
X(49241) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 80, 49240), (80, 19077, 6), (214, 13976, 615)


X(49242) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO 2nd FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(49242) lies on these lines: {6, 79}, {30, 7969}, {39, 48757}, {191, 13893}, {371, 35854}, {372, 49107}, {485, 3652}, {590, 3647}, {615, 6701}, {758, 49232}, {1124, 16153}, {1151, 16113}, {1335, 16152}, {1587, 16116}, {2066, 16142}, {2067, 18977}, {2475, 19065}, {2771, 49222}, {3068, 3648}, {3071, 16125}, {3311, 16150}, {3649, 7968}, {5062, 48756}, {5412, 16114}, {5441, 44635}, {6175, 13973}, {6419, 35855}, {6564, 22798}, {7585, 20084}, {11263, 13971}, {11684, 13911}, {13665, 48668}, {13743, 44606}, {13902, 15677}, {16115, 44586}, {16117, 44590}, {16118, 18991}, {16119, 44598}, {16121, 44600}, {16122, 44602}, {16123, 44604}, {16129, 44610}, {16138, 44618}, {16139, 44620}, {16140, 31472}, {16141, 44623}, {16149, 32788}, {16154, 44643}, {16155, 44645}, {16161, 44627}, {16162, 44629}, {19048, 49178}, {19050, 49177}, {35774, 47032}, {37401, 49227}, {44582, 48503}, {44584, 48504}, {44594, 49070}, {44596, 49071}

X(49242) = midpoint of X(371) and X(35854)
X(49242) = orthologic center (1st Kenmotu-centers, T) for these triangles T: 2nd Fuhrmann, K798e
X(49242) = X(79)-of-1st Kenmotu-centers triangle
X(49242) = X(49107)-of-1st Kenmotu-free-vertices triangle
X(49242) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 79, 49243), (79, 19080, 6), (3647, 16148, 590)


X(49243) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO 2nd FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(49243) lies on these lines: {6, 79}, {30, 7968}, {39, 48756}, {191, 13947}, {371, 49107}, {372, 35855}, {486, 3652}, {590, 6701}, {615, 3647}, {758, 49233}, {1124, 16152}, {1152, 16113}, {1335, 16153}, {1588, 16116}, {2475, 19066}, {2771, 49223}, {3069, 3648}, {3070, 16125}, {3312, 16150}, {3649, 7969}, {5058, 48757}, {5413, 16114}, {5414, 16142}, {5441, 44636}, {6175, 13911}, {6420, 35854}, {6502, 18977}, {6565, 22798}, {7586, 20084}, {8983, 11263}, {11684, 13973}, {13743, 44607}, {13785, 48668}, {13959, 15677}, {16115, 44587}, {16117, 44591}, {16118, 18992}, {16119, 44599}, {16121, 44601}, {16122, 44603}, {16123, 44605}, {16129, 44611}, {16138, 44619}, {16139, 44621}, {16140, 44622}, {16141, 44624}, {16148, 32787}, {16154, 44644}, {16155, 44646}, {16161, 44628}, {16162, 44630}, {19047, 49178}, {19049, 49177}, {35775, 47032}, {37401, 49226}, {44583, 48503}, {44585, 48504}, {44595, 49070}, {44597, 49071}

X(49243) = midpoint of X(372) and X(35855)
X(49243) = orthologic center (2nd Kenmotu-centers, T) for these triangles T: 2nd Fuhrmann, K798e
X(49243) = X(79)-of-2nd Kenmotu-centers triangle
X(49243) = X(49107)-of-2nd Kenmotu-free-vertices triangle
X(49243) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 79, 49242), (79, 19079, 6), (3647, 16149, 615)


X(49244) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO HATZIPOLAKIS-MOSES

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

The reciprocal orthologic center of these triangles is X(6146).

X(49244) lies on these lines: {6, 3574}, {39, 48759}, {371, 18400}, {372, 49108}, {485, 32379}, {590, 32391}, {973, 44633}, {1124, 32404}, {1151, 32330}, {1154, 49224}, {1209, 10898}, {1335, 32403}, {1587, 32337}, {2066, 32390}, {2067, 32336}, {2917, 8939}, {3068, 32354}, {3071, 32369}, {3311, 32402}, {5062, 48758}, {5412, 32332}, {6146, 44612}, {6293, 44641}, {6419, 35859}, {6564, 32364}, {7968, 32331}, {10628, 49222}, {13665, 48669}, {13911, 32371}, {18991, 32356}, {19048, 49180}, {19050, 49179}, {31472, 32382}, {32335, 44586}, {32345, 44588}, {32347, 44590}, {32351, 49257}, {32357, 44598}, {32360, 44600}, {32361, 44602}, {32362, 44604}, {32363, 44606}, {32372, 44610}, {32380, 44618}, {32381, 44620}, {32383, 44623}, {32388, 44627}, {32389, 44629}, {32394, 44635}, {32400, 32788}, {32405, 44643}, {32406, 44645}, {44582, 48505}, {44584, 48506}, {44594, 49072}, {44596, 49073}

X(49244) = midpoint of X(371) and X(35858)
X(49244) = orthologic center (1st Kenmotu-centers, Hatzipolakis-Moses)
X(49244) = X(6145)-of-1st Kenmotu-centers triangle
X(49244) = X(49108)-of-1st Kenmotu-free-vertices triangle
X(49244) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 6145, 49245), (6145, 32343, 6), (32391, 32399, 590)


X(49245) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO HATZIPOLAKIS-MOSES

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

The reciprocal orthologic center of these triangles is X(6146).

X(49245) lies on these lines: {6, 3574}, {39, 48758}, {371, 49108}, {372, 18400}, {486, 32379}, {615, 32391}, {973, 44634}, {1124, 32403}, {1152, 32330}, {1154, 49225}, {1209, 10897}, {1335, 32404}, {1588, 32337}, {2917, 8943}, {3069, 32354}, {3070, 32369}, {3312, 32402}, {5058, 48759}, {5413, 32332}, {5414, 32390}, {6146, 44613}, {6293, 44642}, {6420, 35858}, {6502, 32336}, {6565, 32364}, {7969, 32331}, {10628, 49223}, {13785, 48669}, {13973, 32371}, {18992, 32356}, {19047, 49180}, {19049, 49179}, {32335, 44587}, {32345, 44589}, {32347, 44591}, {32351, 49256}, {32357, 44599}, {32360, 44601}, {32361, 44603}, {32362, 44605}, {32363, 44607}, {32372, 44611}, {32380, 44619}, {32381, 44621}, {32382, 44622}, {32383, 44624}, {32388, 44628}, {32389, 44630}, {32394, 44636}, {32399, 32787}, {32405, 44644}, {32406, 44646}, {44583, 48505}, {44585, 48506}, {44595, 49072}, {44597, 49073}

X(49245) = midpoint of X(372) and X(35859)
X(49245) = orthologic center (2nd Kenmotu-centers, Hatzipolakis-Moses)
X(49245) = X(6145)-of-2nd Kenmotu-centers triangle
X(49245) = X(39772)-of-2nd Kenmotu diagonals triangle
X(49245) = X(49108)-of-2nd Kenmotu-free-vertices triangle
X(49245) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 6145, 49244), (6145, 32342, 6), (32391, 32400, 615)


X(49246) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO 3rd HATZIPOLAKIS

Barycentrics    2*S*a^2*(a^12-2*(b^2+c^2)*a^10-((b^2-c^2)^2-9*b^2*c^2)*a^8+(b^2+c^2)*(4*b^4-13*b^2*c^2+4*c^4)*a^6-(b^8+c^8+b^2*c^2*(9*b^4-28*b^2*c^2+9*c^4))*a^4-(b^4-c^4)*(b^2-c^2)*(2*b^4-9*b^2*c^2+2*c^4)*a^2+(b^4-c^4)^2*(b^2-c^2)^2)+(a^8-(b^2+2*c^2)*a^6+4*b^2*c^2*a^4-(b^2-c^2)^2*(b^2-2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)^2)*(a^8-(2*b^2+c^2)*a^6+4*b^2*c^2*a^4+(2*b^2-c^2)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)^2) : :

The reciprocal orthologic center of these triangles is X(12241).

X(49246) lies on these lines: {6, 17837}, {39, 48811}, {371, 22960}, {372, 49109}, {485, 22955}, {590, 22966}, {1124, 22981}, {1151, 22951}, {1335, 22980}, {1587, 22533}, {2066, 22965}, {2067, 18978}, {2929, 8939}, {3068, 22647}, {3071, 22833}, {3311, 22979}, {5062, 48810}, {5412, 22483}, {6419, 35861}, {6564, 22800}, {7968, 22476}, {10962, 22961}, {12241, 44614}, {13665, 48670}, {13911, 22941}, {18991, 22653}, {19048, 49182}, {19050, 49181}, {22524, 44586}, {22530, 44633}, {22559, 44590}, {22658, 44598}, {22671, 44600}, {22675, 44602}, {22747, 44604}, {22776, 44606}, {22943, 44610}, {22956, 44618}, {22957, 44620}, {22958, 31472}, {22959, 44623}, {22963, 44627}, {22964, 44629}, {22969, 44635}, {22977, 32788}, {22982, 44643}, {22983, 44645}, {44582, 48507}, {44584, 48508}, {44594, 49074}, {44596, 49075}

X(49246) = midpoint of X(371) and X(35860)
X(49246) = orthologic center (1st Kenmotu-centers, 3rd Hatzipolakis)
X(49246) = X(22466)-of-1st Kenmotu-centers triangle
X(49246) = X(49109)-of-1st Kenmotu-free-vertices triangle
X(49246) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 22466, 49247), (19084, 22466, 6), (22966, 22976, 590)


X(49247) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO 3rd HATZIPOLAKIS

Barycentrics    -2*S*a^2*(a^12-2*(b^2+c^2)*a^10-((b^2-c^2)^2-9*b^2*c^2)*a^8+(b^2+c^2)*(4*b^4-13*b^2*c^2+4*c^4)*a^6-(b^8+c^8+b^2*c^2*(9*b^4-28*b^2*c^2+9*c^4))*a^4-(b^4-c^4)*(b^2-c^2)*(2*b^4-9*b^2*c^2+2*c^4)*a^2+(b^4-c^4)^2*(b^2-c^2)^2)+(a^8-(b^2+2*c^2)*a^6+4*b^2*c^2*a^4-(b^2-c^2)^2*(b^2-2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)^2)*(a^8-(2*b^2+c^2)*a^6+4*b^2*c^2*a^4+(2*b^2-c^2)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)^2) : :

The reciprocal orthologic center of these triangles is X(12241).

X(49247) lies on these lines: {6, 17837}, {39, 48810}, {371, 49109}, {372, 22961}, {486, 22955}, {615, 22966}, {1124, 22980}, {1152, 22951}, {1335, 22981}, {1588, 22533}, {2929, 8943}, {3069, 22647}, {3070, 22833}, {3312, 22979}, {5058, 48811}, {5413, 22483}, {5414, 22965}, {6420, 35860}, {6502, 18978}, {6565, 22800}, {7969, 22476}, {10960, 22960}, {12241, 44615}, {13785, 48670}, {13973, 22941}, {18992, 22653}, {19047, 49182}, {19049, 49181}, {22524, 44587}, {22530, 44634}, {22559, 44591}, {22658, 44599}, {22671, 44601}, {22675, 44603}, {22747, 44605}, {22776, 44607}, {22943, 44611}, {22956, 44619}, {22957, 44621}, {22958, 44622}, {22959, 44624}, {22963, 44628}, {22964, 44630}, {22969, 44636}, {22976, 32787}, {22982, 44644}, {22983, 44646}, {44583, 48507}, {44585, 48508}, {44595, 49074}, {44597, 49075}

X(49247) = midpoint of X(372) and X(35861)
X(49247) = orthologic center (2nd Kenmotu-centers, 3rd Hatzipolakis)
X(49247) = X(22466)-of-2nd Kenmotu-centers triangle
X(49247) = X(49109)-of-2nd Kenmotu-free-vertices triangle
X(49247) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 22466, 49246), (19083, 22466, 6), (22966, 22977, 615)


X(49248) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO HUTSON EXTOUCH

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

The reciprocal orthologic center of these triangles is X(40).

X(49248) lies on these lines: {6, 7160}, {39, 48813}, {371, 35862}, {372, 49110}, {485, 12856}, {590, 12864}, {1124, 10075}, {1151, 12120}, {1335, 10059}, {1587, 12249}, {2066, 12863}, {2067, 18979}, {3068, 9874}, {3071, 12599}, {3311, 12872}, {5062, 48812}, {5412, 12139}, {6419, 35863}, {6564, 22801}, {7968, 12260}, {8000, 44635}, {9898, 18991}, {12200, 44586}, {12333, 44590}, {12411, 44598}, {12464, 44600}, {12465, 44602}, {12500, 44604}, {12777, 13911}, {12789, 44610}, {12857, 44618}, {12858, 44620}, {12859, 31472}, {12860, 44623}, {12861, 44627}, {12862, 44629}, {12874, 44643}, {12875, 44645}, {13665, 48671}, {13978, 32788}, {19048, 49184}, {19050, 49183}, {22777, 44606}, {44582, 48509}, {44584, 48510}, {44594, 49076}, {44596, 49077}

X(49248) = midpoint of X(371) and X(35862)
X(49248) = orthologic center (1st Kenmotu-centers, Hutson extouch)
X(49248) = X(7160)-of-1st Kenmotu-centers triangle
X(49248) = X(49110)-of-1st Kenmotu-free-vertices triangle
X(49248) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 7160, 49249), (7160, 19086, 6), (12864, 13914, 590)


X(49249) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO HUTSON EXTOUCH

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

The reciprocal orthologic center of these triangles is X(40).

X(49249) lies on these lines: {6, 7160}, {39, 48812}, {371, 49110}, {372, 35863}, {486, 12856}, {615, 12864}, {1124, 10059}, {1152, 12120}, {1335, 10075}, {1588, 12249}, {3069, 9874}, {3070, 12599}, {3312, 12872}, {5058, 48813}, {5413, 12139}, {5414, 12863}, {6420, 35862}, {6502, 18979}, {6565, 22801}, {7969, 12260}, {8000, 44636}, {9898, 18992}, {12200, 44587}, {12333, 44591}, {12411, 44599}, {12464, 44601}, {12465, 44603}, {12500, 44605}, {12777, 13973}, {12789, 44611}, {12857, 44619}, {12858, 44621}, {12859, 44622}, {12860, 44624}, {12861, 44628}, {12862, 44630}, {12874, 44644}, {12875, 44646}, {13785, 48671}, {13914, 32787}, {19047, 49184}, {19049, 49183}, {22777, 44607}, {44583, 48509}, {44585, 48510}, {44595, 49076}, {44597, 49077}

X(49249) = midpoint of X(372) and X(35863)
X(49249) = orthologic center (2nd Kenmotu-centers, Hutson extouch)
X(49249) = X(7160)-of-2nd Kenmotu-centers triangle
X(49249) = X(49110)-of-2nd Kenmotu-free-vertices triangle
X(49249) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 7160, 49248), (7160, 19085, 6), (12864, 13978, 615)


X(49250) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO MIDHEIGHT

Barycentrics    a^2*(2*S*(-a^2+b^2+c^2)*(a^2-b^2+c^2)*(a^2+b^2-c^2)+(a^4+2*(b^2-c^2)*a^2-(b^2-c^2)*(3*b^2+c^2))*(a^4-2*(b^2-c^2)*a^2+(b^2-c^2)*(b^2+3*c^2))) : :
X(49250) = 4*X(371)-3*X(11241) = 3*X(11241)-2*X(12964) = 3*X(11241)+4*X(35864) = X(12964)+2*X(35864)

The reciprocal orthologic center of these triangles is X(4).

X(49250) lies on these lines: {3, 10534}, {4, 44633}, {6, 64}, {30, 49224}, {39, 48817}, {74, 10881}, {154, 6409}, {371, 6000}, {372, 3357}, {485, 5878}, {590, 2883}, {615, 6696}, {1124, 10076}, {1151, 1498}, {1152, 10606}, {1204, 5413}, {1335, 10060}, {1503, 26441}, {1587, 12250}, {1853, 23261}, {2066, 7355}, {2067, 6285}, {2777, 35820}, {3068, 6225}, {3070, 15311}, {3071, 6247}, {3092, 10605}, {3155, 26936}, {3156, 26918}, {3311, 13093}, {3312, 35450}, {3516, 19356}, {5062, 48816}, {5411, 34469}, {5412, 11381}, {5656, 9540}, {5663, 10665}, {5893, 42273}, {5894, 42259}, {5895, 23251}, {5925, 42264}, {6001, 49226}, {6200, 6759}, {6221, 12315}, {6241, 44612}, {6410, 8567}, {6411, 17821}, {6419, 35865}, {6425, 17819}, {6449, 32063}, {6455, 14530}, {6457, 17849}, {6459, 12324}, {6560, 20427}, {6561, 14216}, {6564, 22802}, {6565, 20299}, {7968, 12262}, {7973, 44635}, {9541, 34781}, {9833, 42260}, {9899, 18991}, {9914, 44598}, {10575, 10897}, {10577, 23329}, {10666, 12084}, {10880, 12290}, {10961, 44870}, {11206, 42638}, {11266, 32138}, {11417, 12279}, {11418, 11440}, {11438, 35765}, {11513, 46850}, {11598, 49269}, {12174, 19355}, {12202, 44586}, {12335, 44590}, {12376, 13293}, {12468, 44600}, {12469, 44602}, {12502, 44604}, {12779, 13911}, {12791, 44610}, {12920, 44618}, {12930, 44620}, {12940, 31472}, {12950, 44623}, {12984, 37497}, {12986, 44627}, {12987, 44629}, {13094, 44643}, {13095, 44645}, {13287, 49216}, {13474, 35764}, {13665, 48672}, {13937, 43903}, {13980, 32788}, {17812, 44592}, {18381, 35821}, {18400, 42266}, {19048, 49186}, {19050, 49185}, {22778, 44606}, {23325, 35787}, {23332, 42270}, {36201, 49264}, {40686, 42262}, {41362, 42271}, {44582, 48513}, {44584, 48514}, {44594, 49080}, {44596, 49081}

X(49250) = midpoint of X(371) and X(35864)
X(49250) = reflection of X(i) in X(j) for these (i, j): (12964, 371), (13287, 49216)
X(49250) = orthologic center (1st Kenmotu-centers, midheight)
X(49250) = X(64)-of-1st Kenmotu-centers triangle
X(49250) = X(3357)-of-1st Kenmotu-free-vertices triangle
X(49250) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 12970, 10534), (6, 64, 49251), (64, 19088, 6), (185, 11473, 6), (371, 12964, 11241), (1151, 1498, 10533), (2883, 8991, 590), (8567, 17820, 6410)


X(49251) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO MIDHEIGHT

Barycentrics    a^2*(-2*S*(-a^2+b^2+c^2)*(a^2-b^2+c^2)*(a^2+b^2-c^2)+(a^4+2*(b^2-c^2)*a^2-(b^2-c^2)*(3*b^2+c^2))*(a^4-2*(b^2-c^2)*a^2+(b^2-c^2)*(b^2+3*c^2))) : :
X(49251) = 4*X(372)-3*X(11242) = 3*X(11242)-2*X(12970) = 3*X(11242)+4*X(35865) = X(12970)+2*X(35865)

The reciprocal orthologic center of these triangles is X(4).

X(49251) lies on these lines: {3, 10533}, {4, 44634}, {6, 64}, {30, 49225}, {39, 48816}, {74, 10880}, {154, 6410}, {371, 3357}, {372, 6000}, {486, 5878}, {590, 6696}, {615, 2883}, {1124, 10060}, {1151, 10606}, {1152, 1498}, {1204, 5412}, {1335, 10076}, {1503, 8982}, {1588, 12250}, {1853, 23251}, {2777, 35821}, {3069, 6225}, {3070, 6247}, {3071, 15311}, {3093, 10605}, {3311, 35450}, {3312, 13093}, {3516, 19355}, {5058, 48817}, {5410, 34469}, {5413, 11381}, {5414, 7355}, {5656, 13935}, {5663, 10666}, {5893, 42270}, {5894, 42258}, {5895, 23261}, {5925, 42263}, {6001, 49227}, {6241, 44613}, {6285, 6502}, {6396, 6759}, {6398, 12315}, {6409, 8567}, {6412, 17821}, {6420, 35864}, {6426, 17820}, {6450, 32063}, {6456, 14530}, {6458, 17849}, {6460, 12324}, {6560, 14216}, {6561, 20427}, {6564, 20299}, {6565, 22802}, {7969, 12262}, {7973, 44636}, {8991, 32787}, {9833, 42261}, {9899, 18992}, {9914, 44599}, {10575, 10898}, {10576, 23329}, {10665, 12084}, {10881, 12290}, {10963, 44870}, {11206, 42637}, {11265, 32138}, {11417, 11440}, {11418, 12279}, {11438, 35764}, {11514, 46850}, {11598, 49268}, {12174, 19356}, {12202, 44587}, {12335, 44591}, {12375, 13293}, {12468, 44601}, {12469, 44603}, {12502, 44605}, {12779, 13973}, {12791, 44611}, {12920, 44619}, {12930, 44621}, {12940, 44622}, {12950, 44624}, {12985, 37497}, {12986, 44628}, {12987, 44630}, {13094, 44644}, {13095, 44646}, {13288, 49217}, {13474, 35765}, {13785, 48672}, {13884, 43903}, {17812, 44593}, {18381, 35820}, {18400, 42267}, {19047, 49186}, {19049, 49185}, {22778, 44607}, {23325, 35786}, {23332, 42273}, {36201, 49265}, {40686, 42265}, {41362, 42272}, {44583, 48513}, {44585, 48514}, {44595, 49080}, {44597, 49081}

X(49251) = midpoint of X(372) and X(35865)
X(49251) = reflection of X(i) in X(j) for these (i, j): (12970, 372), (13288, 49217)
X(49251) = orthologic center (2nd Kenmotu-centers, midheight)
X(49251) = X(64)-of-2nd Kenmotu-centers triangle
X(49251) = X(145)-of-2nd Kenmotu diagonals triangle
X(49251) = X(3357)-of-2nd Kenmotu-free-vertices triangle
X(49251) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 12964, 10533), (6, 64, 49250), (64, 19087, 6), (185, 11474, 6), (372, 12970, 11242), (1152, 1498, 10534), (2883, 13980, 615), (8567, 17819, 6409)


X(49252) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO 1st NEUBERG

Barycentrics    2*S*b^2*c^2+a^2*((b^2+c^2)*a^2+b^2*c^2) : :
X(49252) = 2*X(3103)-3*X(49230) = 4*X(7583)-3*X(49230)

The reciprocal orthologic center of these triangles is X(3).

X(49252) lies on these lines: {5, 3102}, {6, 76}, {39, 590}, {99, 13885}, {194, 3068}, {262, 42265}, {371, 2782}, {372, 49111}, {384, 44586}, {385, 44587}, {485, 3095}, {486, 7697}, {511, 3070}, {538, 32787}, {615, 3934}, {726, 13883}, {730, 7969}, {1124, 10079}, {1131, 44434}, {1151, 11257}, {1152, 22712}, {1335, 10063}, {1569, 8997}, {1587, 12251}, {2023, 13773}, {2066, 13077}, {2067, 18982}, {3069, 31276}, {3071, 6248}, {3094, 7389}, {3097, 13893}, {3103, 7583}, {3311, 13108}, {3366, 43539}, {3391, 43538}, {3734, 18994}, {4074, 45806}, {5062, 48818}, {5188, 42259}, {5412, 12143}, {5418, 11171}, {5969, 49214}, {5976, 49267}, {6194, 6460}, {6250, 22682}, {6318, 13707}, {6419, 35867}, {6560, 9821}, {6564, 14881}, {6683, 32789}, {6811, 33372}, {7585, 20081}, {7709, 9540}, {7751, 18993}, {7757, 13846}, {7786, 8253}, {7968, 12263}, {7976, 44635}, {8976, 32447}, {8981, 32448}, {9466, 13983}, {9902, 18991}, {9917, 44598}, {9983, 44604}, {10576, 11272}, {12338, 44590}, {12474, 44600}, {12475, 44602}, {12782, 13911}, {12794, 44610}, {12836, 44623}, {12837, 31472}, {12923, 44618}, {12933, 44620}, {12992, 44627}, {12993, 44629}, {13109, 44643}, {13110, 44645}, {13354, 49229}, {13665, 48673}, {13903, 32519}, {13910, 32449}, {14839, 49232}, {19048, 49188}, {19050, 49187}, {22681, 35787}, {22779, 44606}, {31239, 32790}, {32516, 35255}, {32521, 42216}, {33452, 41747}, {44582, 48515}, {44584, 48516}, {44594, 49082}, {44596, 49083}

X(49252) = midpoint of X(371) and X(35866)
X(49252) = reflection of X(3103) in X(7583)
X(49252) = orthologic center (1st Kenmotu-centers, 1st Neuberg)
X(49252) = X(76)-of-1st Kenmotu-centers triangle
X(49252) = X(49111)-of-1st Kenmotu-free-vertices triangle
X(49252) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 76, 49253), (39, 8992, 590), (76, 19090, 6), (3103, 7583, 49230), (5418, 32471, 11171), (6318, 13707, 13877)


X(49253) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO 1st NEUBERG

Barycentrics    -2*S*b^2*c^2+a^2*((b^2+c^2)*a^2+b^2*c^2) : :
X(49253) = 2*X(3102)-3*X(49231) = 4*X(7584)-3*X(49231)

The reciprocal orthologic center of these triangles is X(3).

X(49253) lies on these lines: {5, 3103}, {6, 76}, {39, 615}, {99, 13938}, {194, 3069}, {262, 42262}, {371, 49111}, {372, 2782}, {384, 44587}, {385, 44586}, {485, 7697}, {486, 3095}, {511, 3071}, {538, 32788}, {590, 3934}, {726, 13936}, {730, 7968}, {1124, 10063}, {1132, 44434}, {1151, 22712}, {1152, 11257}, {1335, 10079}, {1569, 13989}, {1588, 12251}, {2023, 13653}, {3068, 31276}, {3070, 6248}, {3094, 7388}, {3097, 13947}, {3102, 7584}, {3312, 13108}, {3367, 43539}, {3392, 43538}, {3734, 18993}, {4074, 45805}, {5058, 48819}, {5188, 42258}, {5413, 12143}, {5414, 13077}, {5420, 11171}, {5969, 49215}, {5976, 49266}, {6194, 6459}, {6251, 22682}, {6314, 13827}, {6420, 35866}, {6502, 18982}, {6561, 9821}, {6565, 14881}, {6683, 32790}, {6813, 33373}, {7586, 20081}, {7709, 13935}, {7751, 18994}, {7757, 13847}, {7786, 8252}, {7969, 12263}, {7976, 44636}, {8992, 9466}, {9902, 18992}, {9917, 44599}, {9983, 44605}, {10577, 11272}, {12338, 44591}, {12474, 44601}, {12475, 44603}, {12782, 13973}, {12794, 44611}, {12836, 44624}, {12837, 44622}, {12923, 44619}, {12933, 44621}, {12992, 44628}, {12993, 44630}, {13109, 44644}, {13110, 44646}, {13354, 49228}, {13785, 48673}, {13951, 32447}, {13961, 32519}, {13966, 32448}, {13972, 32449}, {14839, 49233}, {19047, 49188}, {19049, 49187}, {22681, 35786}, {22779, 44607}, {31239, 32789}, {32516, 35256}, {32521, 42215}, {33453, 41747}, {44583, 48515}, {44585, 48516}, {44595, 49082}, {44597, 49083}

X(49253) = midpoint of X(372) and X(35867)
X(49253) = reflection of X(3102) in X(7584)
X(49253) = orthologic center (2nd Kenmotu-centers, 1st Neuberg)
X(49253) = X(76)-of-2nd Kenmotu-centers triangle
X(49253) = X(39789)-of-2nd Kenmotu diagonals triangle
X(49253) = X(49111)-of-2nd Kenmotu-free-vertices triangle
X(49253) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 76, 49252), (39, 13983, 615), (76, 19089, 6), (3102, 7584, 49231), (5420, 32470, 11171), (6314, 13827, 13930)


X(49254) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO 2nd NEUBERG

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

The reciprocal orthologic center of these triangles is X(3).

X(49254) lies on these lines: {6, 76}, {39, 48771}, {371, 35838}, {372, 49112}, {485, 6287}, {590, 6292}, {615, 6704}, {754, 32787}, {1124, 10080}, {1151, 12122}, {1152, 9751}, {1335, 10064}, {1587, 12252}, {2066, 13078}, {2067, 18983}, {2896, 3068}, {3070, 29012}, {3071, 6249}, {3311, 13111}, {5058, 44647}, {5062, 48770}, {5412, 12144}, {6317, 13709}, {6419, 35869}, {6560, 8725}, {6564, 22803}, {7583, 49212}, {7585, 20088}, {7968, 12264}, {7977, 44635}, {8150, 18993}, {8253, 31268}, {8290, 49267}, {8992, 44772}, {9903, 18991}, {9918, 44598}, {12206, 44586}, {12339, 44590}, {12476, 44600}, {12477, 44602}, {12783, 13911}, {12795, 44610}, {12924, 44618}, {12934, 44620}, {12944, 31472}, {12954, 44623}, {12994, 44627}, {12995, 44629}, {13112, 44643}, {13113, 44645}, {13665, 48674}, {13846, 31168}, {13883, 17766}, {13984, 32788}, {19048, 49190}, {19050, 49189}, {22780, 44606}, {33454, 41749}, {44582, 48517}, {44584, 48518}, {44594, 49084}, {44596, 49085}

X(49254) = midpoint of X(371) and X(35868)
X(49254) = orthologic center (1st Kenmotu-centers, 2nd Neuberg)
X(49254) = X(83)-of-1st Kenmotu-centers triangle
X(49254) = X(49112)-of-1st Kenmotu-free-vertices triangle
X(49254) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 83, 49255), (83, 6275, 24273), (83, 19092, 6), (6292, 8993, 590), (6317, 13709, 13878)


X(49255) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO 2nd NEUBERG

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

The reciprocal orthologic center of these triangles is X(3).

X(49255) lies on these lines: {6, 76}, {39, 48770}, {371, 49112}, {372, 35839}, {486, 6287}, {590, 6704}, {615, 6292}, {754, 32788}, {1124, 10064}, {1151, 9751}, {1152, 12122}, {1335, 10080}, {1588, 12252}, {2896, 3069}, {3070, 6249}, {3071, 29012}, {3312, 13111}, {5058, 48771}, {5062, 44648}, {5413, 12144}, {5414, 13078}, {6313, 13829}, {6420, 35868}, {6502, 18983}, {6561, 8725}, {6565, 22803}, {7584, 49213}, {7586, 20088}, {7969, 12264}, {7977, 44636}, {8150, 18994}, {8252, 31268}, {8290, 49266}, {8993, 32787}, {9903, 18992}, {9918, 44599}, {12206, 44587}, {12339, 44591}, {12476, 44601}, {12477, 44603}, {12783, 13973}, {12795, 44611}, {12924, 44619}, {12934, 44621}, {12944, 44622}, {12954, 44624}, {12994, 44628}, {12995, 44630}, {13112, 44644}, {13113, 44646}, {13785, 48674}, {13847, 31168}, {13936, 17766}, {13983, 44772}, {19047, 49190}, {19049, 49189}, {22780, 44607}, {33455, 41749}, {44583, 48517}, {44585, 48518}, {44595, 49084}, {44597, 49085}

X(49255) = midpoint of X(372) and X(35869)
X(49255) = orthologic center (2nd Kenmotu-centers, 2nd Neuberg)
X(49255) = X(83)-of-2nd Kenmotu-centers triangle
X(49255) = X(39790)-of-2nd Kenmotu diagonals triangle
X(49255) = X(49112)-of-2nd Kenmotu-free-vertices triangle
X(49255) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 83, 49254), (83, 6274, 24273), (83, 19091, 6), (6292, 13984, 615), (6313, 13829, 13931)


X(49256) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO REFLECTION

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

The reciprocal orthologic center of these triangles is X(4).

X(49256) lies on these lines: {4, 44641}, {6, 24}, {39, 48775}, {195, 3311}, {371, 1154}, {372, 10610}, {389, 44612}, {485, 6288}, {539, 32787}, {590, 1209}, {615, 6689}, {1124, 10082}, {1151, 7691}, {1335, 10066}, {1493, 6419}, {1587, 12254}, {1588, 44639}, {2066, 13079}, {2067, 18984}, {2888, 3068}, {2914, 44592}, {2929, 32324}, {2965, 46621}, {3070, 18400}, {3071, 3574}, {3301, 47378}, {3592, 15801}, {5062, 48774}, {5412, 11576}, {6199, 12316}, {6221, 12307}, {6561, 15800}, {6564, 22804}, {7583, 32423}, {7584, 8254}, {7968, 12266}, {7979, 44635}, {8981, 21230}, {9905, 18991}, {9920, 44598}, {9977, 44656}, {9985, 44604}, {10576, 13565}, {10619, 21640}, {10628, 49216}, {10897, 12363}, {11597, 49269}, {11804, 49223}, {12208, 44586}, {12239, 32352}, {12242, 44633}, {12341, 44590}, {12480, 44600}, {12481, 44602}, {12606, 18457}, {12785, 13911}, {12797, 44610}, {12926, 44618}, {12936, 44620}, {12946, 31472}, {12956, 44623}, {12998, 44627}, {12999, 44629}, {13121, 44643}, {13122, 44645}, {13665, 48675}, {13986, 32788}, {17824, 44608}, {19048, 49192}, {19050, 49191}, {19060, 43580}, {19087, 32345}, {19117, 36966}, {20424, 42215}, {22781, 44606}, {32169, 35822}, {32340, 42284}, {32341, 44588}, {32351, 49245}, {32386, 44625}, {32396, 42583}, {41335, 46622}, {44582, 48521}, {44584, 48522}, {44594, 49088}, {44596, 49089}

X(49256) = midpoint of X(371) and X(12965)
X(49256) = orthologic center (1st Kenmotu-centers, reflection)
X(49256) = X(54)-of-1st Kenmotu-centers triangle
X(49256) = X(10610)-of-1st Kenmotu-free-vertices triangle
X(49256) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 54, 49257), (54, 19096, 6), (1209, 8995, 590)


X(49257) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO REFLECTION

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

The reciprocal orthologic center of these triangles is X(4).

X(49257) lies on these lines: {4, 44642}, {6, 24}, {39, 48774}, {195, 3312}, {371, 10610}, {372, 1154}, {389, 44613}, {486, 6288}, {539, 32788}, {590, 6689}, {615, 1209}, {1124, 10066}, {1152, 7691}, {1335, 10082}, {1493, 6420}, {1587, 44640}, {1588, 12254}, {2888, 3069}, {2914, 44593}, {2929, 32323}, {2965, 46622}, {3070, 3574}, {3071, 18400}, {3299, 47378}, {3594, 15801}, {5058, 48775}, {5413, 11576}, {5414, 13079}, {6395, 12316}, {6398, 12307}, {6502, 18984}, {6560, 15800}, {6565, 22804}, {7583, 8254}, {7584, 32423}, {7969, 12266}, {7979, 44636}, {8995, 32787}, {9905, 18992}, {9920, 44599}, {9977, 44657}, {9985, 44605}, {10577, 13565}, {10619, 21641}, {10628, 49217}, {10898, 12363}, {11597, 49268}, {11804, 49222}, {12208, 44587}, {12240, 32352}, {12242, 44634}, {12341, 44591}, {12480, 44601}, {12481, 44603}, {12606, 18459}, {12785, 13973}, {12797, 44611}, {12926, 44619}, {12936, 44621}, {12946, 44622}, {12956, 44624}, {12998, 44628}, {12999, 44630}, {13121, 44644}, {13122, 44646}, {13785, 48675}, {13966, 21230}, {17824, 44609}, {19047, 49192}, {19049, 49191}, {19059, 43580}, {19088, 32345}, {19116, 36966}, {20424, 42216}, {22781, 44607}, {32170, 35823}, {32340, 42283}, {32341, 44589}, {32351, 49244}, {32387, 44626}, {32396, 42582}, {41335, 46621}, {44583, 48521}, {44585, 48522}, {44595, 49088}, {44597, 49089}

X(49257) = midpoint of X(372) and X(12971)
X(49257) = orthologic center (2nd Kenmotu-centers, reflection)
X(49257) = X(54)-of-2nd Kenmotu-centers triangle
X(49257) = X(3649)-of-2nd Kenmotu diagonals triangle
X(49257) = X(10610)-of-2nd Kenmotu-free-vertices triangle
X(49257) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 54, 49256), (54, 19095, 6), (1209, 13986, 615)


X(49258) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO 1st SCHIFFLER

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

The reciprocal orthologic center of these triangles is X(79).

X(49258) lies on these lines: {6, 10266}, {39, 48777}, {371, 35870}, {372, 49113}, {485, 12919}, {590, 13089}, {1124, 13129}, {1151, 12556}, {1335, 13128}, {1587, 12255}, {2066, 13080}, {2067, 18985}, {3068, 12849}, {3071, 12600}, {3299, 18244}, {3311, 13126}, {5062, 48776}, {5412, 12146}, {6419, 35871}, {6564, 22805}, {7968, 12267}, {12209, 44586}, {12342, 44590}, {12409, 18991}, {12414, 44598}, {12482, 44600}, {12483, 44602}, {12504, 44604}, {12786, 13911}, {12798, 44610}, {12927, 44618}, {12937, 44620}, {12947, 31472}, {12957, 44623}, {13000, 44627}, {13001, 44629}, {13100, 44635}, {13130, 44643}, {13131, 44645}, {13665, 48676}, {13987, 32788}, {19048, 49194}, {19050, 49193}, {22782, 44606}, {44582, 48523}, {44584, 48524}, {44594, 49090}, {44596, 49091}

X(49258) = midpoint of X(371) and X(35870)
X(49258) = orthologic center (1st Kenmotu-centers, 1st Schiffler)
X(49258) = X(10266)-of-1st Kenmotu-centers triangle
X(49258) = X(49113)-of-1st Kenmotu-free-vertices triangle
X(49258) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 10266, 49259), (10266, 19098, 6), (13089, 13919, 590)


X(49259) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO 1st SCHIFFLER

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

The reciprocal orthologic center of these triangles is X(79).

X(49259) lies on these lines: {6, 10266}, {39, 48776}, {371, 49113}, {372, 35871}, {486, 12919}, {615, 13089}, {1124, 13128}, {1152, 12556}, {1335, 13129}, {1588, 12255}, {3069, 12849}, {3070, 12600}, {3301, 18244}, {3312, 13126}, {5058, 48777}, {5413, 12146}, {5414, 13080}, {6420, 35870}, {6502, 18985}, {6565, 22805}, {7969, 12267}, {12209, 44587}, {12342, 44591}, {12409, 18992}, {12414, 44599}, {12482, 44601}, {12483, 44603}, {12504, 44605}, {12786, 13973}, {12798, 44611}, {12927, 44619}, {12937, 44621}, {12947, 44622}, {12957, 44624}, {13000, 44628}, {13001, 44630}, {13100, 44636}, {13130, 44644}, {13131, 44646}, {13785, 48676}, {13919, 32787}, {19047, 49194}, {19049, 49193}, {22782, 44607}, {44583, 48523}, {44585, 48524}, {44595, 49090}, {44597, 49091}

X(49259) = midpoint of X(372) and X(35871)
X(49259) = orthologic center (2nd Kenmotu-centers, 1st Schiffler)
X(49259) = X(10266)-of-2nd Kenmotu-centers triangle
X(49259) = X(49113)-of-2nd Kenmotu-free-vertices triangle
X(49259) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 10266, 49258), (10266, 19097, 6), (13089, 13987, 615)


X(49260) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO 1st TRI-SQUARES-CENTRAL

Barycentrics    7*a^4+18*S*a^2+4*(b^2+c^2)*a^2-5*(b^2-c^2)^2 : :
X(49260) = 2*X(12962)-5*X(44647)

The reciprocal orthologic center of these triangles is X(13665).

X(49260) lies on these lines: {2, 8376}, {6, 1327}, {30, 12962}, {39, 48780}, {371, 35872}, {372, 49114}, {395, 22917}, {396, 22872}, {485, 13692}, {574, 42418}, {590, 13701}, {1124, 13715}, {1151, 13666}, {1335, 13714}, {1587, 13674}, {1991, 13669}, {2066, 13699}, {2067, 18986}, {3068, 13678}, {3070, 11648}, {3071, 13687}, {3311, 13713}, {5062, 48778}, {5306, 35822}, {5412, 13668}, {5471, 25189}, {5472, 25185}, {6419, 35873}, {6564, 22806}, {7746, 41952}, {7968, 13667}, {9600, 43256}, {9675, 32787}, {13662, 13712}, {13665, 48677}, {13672, 44586}, {13675, 44590}, {13679, 18991}, {13680, 44598}, {13682, 44600}, {13683, 44602}, {13685, 44604}, {13688, 13911}, {13689, 44610}, {13693, 44618}, {13694, 44620}, {13695, 31472}, {13696, 44623}, {13697, 44627}, {13698, 44629}, {13702, 44635}, {13716, 44643}, {13717, 44645}, {13848, 13908}, {13932, 19053}, {13988, 32788}, {14241, 44595}, {15682, 44594}, {19048, 49196}, {19050, 49195}, {19054, 33456}, {22783, 44606}, {36396, 43229}, {36400, 43228}, {43386, 44596}, {44582, 48525}, {44584, 48526}

X(49260) = midpoint of X(371) and X(35872)
X(49260) = orthologic center (1st Kenmotu-centers, 1st tri-squares-central)
X(49260) = X(1327)-of-1st Kenmotu-centers triangle
X(49260) = X(49114)-of-1st Kenmotu-free-vertices triangle
X(49260) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 1327, 49261), (1327, 22541, 6), (13662, 13712, 13846), (13701, 13920, 590)


X(49261) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO 1st TRI-SQUARES-CENTRAL

Barycentrics    a^4-6*S*a^2-2*(b^2+c^2)*a^2-5*(b^2-c^2)^2 : :
X(49261) = 2*X(12968)-5*X(49221)

The reciprocal orthologic center of these triangles is X(13665).

X(49261) lies on these lines: {2, 9600}, {6, 1327}, {30, 12968}, {39, 48778}, {115, 13703}, {187, 43210}, {371, 49114}, {372, 35873}, {395, 22872}, {396, 22917}, {486, 13692}, {590, 18362}, {615, 13701}, {1124, 13714}, {1152, 13666}, {1285, 43522}, {1335, 13715}, {1588, 13674}, {1991, 37350}, {2549, 13712}, {3069, 13678}, {3070, 13687}, {3071, 5309}, {3312, 13713}, {3543, 6423}, {3545, 6422}, {5013, 42603}, {5058, 48780}, {5072, 31465}, {5254, 35823}, {5413, 13668}, {5414, 13699}, {6420, 35872}, {6502, 18986}, {6565, 9300}, {7739, 36723}, {7748, 41946}, {7969, 13667}, {8376, 43256}, {9675, 42417}, {11648, 32788}, {13672, 44587}, {13675, 44591}, {13679, 18992}, {13680, 44599}, {13682, 44601}, {13683, 44603}, {13685, 44605}, {13688, 13973}, {13689, 44611}, {13693, 44619}, {13694, 44621}, {13695, 44622}, {13696, 44624}, {13697, 44628}, {13698, 44630}, {13702, 44636}, {13716, 44644}, {13717, 44646}, {13785, 48677}, {14241, 44594}, {14537, 42283}, {15682, 44595}, {15815, 43255}, {19047, 49196}, {19049, 49195}, {19053, 33456}, {19709, 31463}, {22617, 49220}, {22783, 44607}, {31403, 41106}, {36396, 43228}, {36400, 43229}, {43387, 44597}, {44583, 48525}, {44585, 48526}

X(49261) = midpoint of X(372) and X(35873)
X(49261) = orthologic center (2nd Kenmotu-centers, 1st tri-squares-central)
X(49261) = X(1327)-of-2nd Kenmotu-centers triangle
X(49261) = X(49114)-of-2nd Kenmotu-free-vertices triangle
X(49261) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 13831, 13932), (6, 1327, 49260), (1327, 19099, 6), (13701, 13988, 615)


X(49262) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    a^4+6*S*a^2-2*(b^2+c^2)*a^2-5*(b^2-c^2)^2 : :
X(49262) = 2*X(12963)-5*X(49220)

The reciprocal orthologic center of these triangles is X(13785).

X(49262) lies on these lines: {2, 13832}, {6, 1327}, {30, 12963}, {39, 48779}, {115, 13823}, {187, 43209}, {371, 35874}, {372, 49115}, {395, 22874}, {396, 22919}, {485, 13812}, {590, 13821}, {591, 37350}, {615, 18362}, {1124, 13838}, {1151, 13786}, {1285, 43521}, {1335, 13837}, {1587, 13794}, {2066, 13819}, {2067, 18987}, {2549, 13835}, {3068, 13798}, {3070, 5309}, {3071, 13807}, {3311, 13836}, {3543, 6424}, {3545, 6421}, {5013, 42602}, {5062, 48781}, {5254, 35822}, {5412, 13788}, {6419, 35875}, {6564, 9300}, {7739, 36726}, {7748, 41945}, {7968, 13787}, {8375, 43257}, {9675, 43210}, {11648, 32787}, {13665, 48678}, {13792, 44586}, {13795, 44590}, {13799, 18991}, {13800, 44598}, {13802, 44600}, {13803, 44602}, {13805, 44604}, {13808, 13911}, {13809, 44610}, {13813, 44618}, {13814, 44620}, {13815, 31472}, {13816, 44623}, {13817, 44627}, {13818, 44629}, {13822, 44635}, {13839, 44643}, {13840, 44645}, {14226, 44597}, {14241, 31403}, {14537, 42284}, {15682, 44596}, {15815, 43254}, {19048, 49198}, {19050, 49197}, {19054, 33457}, {22646, 49221}, {22784, 44606}, {31481, 41952}, {36397, 43228}, {36401, 43229}, {43386, 44594}, {44582, 48527}, {44584, 48528}

X(49262) = midpoint of X(371) and X(35874)
X(49262) = orthologic center (1st Kenmotu-centers, 2nd tri-squares-central)
X(49262) = X(1328)-of-1st Kenmotu-centers triangle
X(49262) = X(49115)-of-1st Kenmotu-free-vertices triangle
X(49262) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 13832, 13850), (6, 1328, 49263), (1328, 19100, 6), (13821, 13848, 590)


X(49263) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    7*a^4-18*S*a^2+4*(b^2+c^2)*a^2-5*(b^2-c^2)^2 : :
X(49263) = 2*X(12969)-5*X(44648)

The reciprocal orthologic center of these triangles is X(13785).

X(49263) lies on these lines: {2, 8375}, {6, 1327}, {30, 12969}, {39, 48781}, {371, 49115}, {372, 35875}, {395, 22919}, {396, 22874}, {486, 13812}, {574, 42417}, {591, 13789}, {615, 13821}, {1124, 13837}, {1152, 13786}, {1335, 13838}, {1588, 13794}, {3069, 13798}, {3070, 13807}, {3071, 11648}, {3312, 13836}, {5058, 48779}, {5306, 35823}, {5413, 13788}, {5414, 13819}, {5471, 25190}, {5472, 25186}, {6420, 35874}, {6502, 18987}, {6565, 22807}, {7746, 41951}, {7969, 13787}, {13782, 13835}, {13785, 48678}, {13792, 44587}, {13795, 44591}, {13799, 18992}, {13800, 44599}, {13802, 44601}, {13803, 44603}, {13805, 44605}, {13808, 13973}, {13809, 44611}, {13813, 44619}, {13814, 44621}, {13815, 44622}, {13816, 44624}, {13817, 44628}, {13818, 44630}, {13822, 44636}, {13839, 44644}, {13840, 44646}, {13848, 32787}, {13850, 19054}, {13968, 13988}, {14226, 44596}, {15682, 44597}, {19047, 49198}, {19049, 49197}, {19053, 33457}, {22784, 44607}, {36397, 43229}, {36401, 43228}, {43387, 44595}, {44583, 48527}, {44585, 48528}

X(49263) = midpoint of X(372) and X(35875)
X(49263) = orthologic center (2nd Kenmotu-centers, 2nd tri-squares-central)
X(49263) = X(1328)-of-2nd Kenmotu-centers triangle
X(49263) = X(49115)-of-2nd Kenmotu-free-vertices triangle
X(49263) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 1328, 49262), (1328, 19101, 6), (13782, 13835, 13847), (13821, 13849, 615)


X(49264) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(49264) lies on these lines: {6, 67}, {39, 48783}, {141, 49269}, {371, 542}, {372, 49116}, {485, 9970}, {511, 49222}, {590, 6593}, {615, 6698}, {1124, 32308}, {1151, 32233}, {1335, 32307}, {1503, 49216}, {1587, 32247}, {2066, 32297}, {2067, 32243}, {2781, 3070}, {2930, 8939}, {3068, 11061}, {3071, 32274}, {3311, 32306}, {5062, 48782}, {5181, 10962}, {5412, 32239}, {5418, 15462}, {6419, 35877}, {6564, 32271}, {7968, 32238}, {8976, 45016}, {9971, 44639}, {12367, 44592}, {13665, 48679}, {13846, 34319}, {13910, 25329}, {13911, 32278}, {14984, 49224}, {15061, 19146}, {18991, 32261}, {19048, 49200}, {19050, 49199}, {20301, 44501}, {31472, 32289}, {32242, 44586}, {32246, 44633}, {32256, 44590}, {32262, 44598}, {32265, 44600}, {32266, 44602}, {32268, 44604}, {32270, 44606}, {32279, 44610}, {32287, 44618}, {32288, 44620}, {32290, 44623}, {32295, 44627}, {32296, 44629}, {32298, 44635}, {32304, 32788}, {32309, 44643}, {32310, 44645}, {36201, 49250}, {40949, 44637}, {41731, 44656}, {44582, 48529}, {44584, 48530}, {44594, 49094}, {44596, 49095}

X(49264) = midpoint of X(371) and X(35876)
X(49264) = reflection of X(6) in X(46688)
X(49264) = inverse of X(49265) in Jerabek circumhyperbola
X(49264) = orthologic center (1st Kenmotu-centers, Walsmith)
X(49264) = X(67)-of-1st Kenmotu-centers triangle
X(49264) = X(49116)-of-1st Kenmotu-free-vertices triangle
X(49264) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 67, 49265), (67, 32253, 6), (6593, 32303, 590)


X(49265) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO WALSMITH

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

The reciprocal orthologic center of these triangles is X(125).

X(49265) lies on these lines: {6, 67}, {39, 48782}, {141, 49268}, {371, 49116}, {372, 542}, {486, 9970}, {511, 49223}, {590, 6698}, {615, 6593}, {1124, 32307}, {1152, 32233}, {1335, 32308}, {1503, 49217}, {1588, 32247}, {2781, 3071}, {2930, 8943}, {3069, 11061}, {3070, 32274}, {3312, 32306}, {5058, 48783}, {5181, 10960}, {5413, 32239}, {5414, 32297}, {5420, 15462}, {6420, 35876}, {6502, 32243}, {6565, 32271}, {7969, 32238}, {9971, 44640}, {12367, 44593}, {13654, 31463}, {13785, 48679}, {13847, 34319}, {13951, 45016}, {13972, 25329}, {13973, 32278}, {14984, 49225}, {15061, 19145}, {18992, 32261}, {19047, 49200}, {19049, 49199}, {20301, 44502}, {32242, 44587}, {32246, 44634}, {32256, 44591}, {32262, 44599}, {32265, 44601}, {32266, 44603}, {32268, 44605}, {32270, 44607}, {32279, 44611}, {32287, 44619}, {32288, 44621}, {32289, 44622}, {32290, 44624}, {32295, 44628}, {32296, 44630}, {32298, 44636}, {32303, 32787}, {32309, 44644}, {32310, 44646}, {36201, 49251}, {40949, 44638}, {41731, 44657}, {44583, 48529}, {44585, 48530}, {44595, 49094}, {44597, 49095}

X(49265) = midpoint of X(372) and X(35877)
X(49265) = reflection of X(6) in X(46689)
X(49265) = inverse of X(49264) in Jerabek circumhyperbola
X(49265) = orthologic center (2nd Kenmotu-centers, Walsmith)
X(49265) = X(67)-of-2nd Kenmotu-centers triangle
X(49265) = X(49116)-of-2nd Kenmotu-free-vertices triangle
X(49265) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 67, 49264), (67, 32252, 6), (6593, 32304, 615)


X(49266) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO 1st ANTI-BROCARD

Barycentrics    2*(a^2-c^2)*(a^2-b^2)*S+a^2*(a^4-(b^2+c^2)*a^2+b^4-b^2*c^2+c^4) : :
X(49266) = 3*X(371)-X(35824) = X(35824)+3*X(35878) = 2*X(35824)-3*X(49212) = 2*X(35878)+X(49212)

The reciprocal parallelogic center of these triangles is X(385).

X(49266) lies on the circumcircle of 1st Kenmotu-centers triangle and these lines: {2, 49215}, {3, 49213}, {6, 99}, {30, 44394}, {39, 48785}, {98, 1151}, {114, 3071}, {115, 590}, {147, 6459}, {148, 3068}, {371, 2782}, {372, 33813}, {485, 6321}, {486, 15561}, {542, 41945}, {543, 32787}, {615, 620}, {618, 49211}, {619, 49209}, {671, 13846}, {690, 49268}, {1124, 10089}, {1152, 19055}, {1335, 10086}, {1569, 5058}, {1587, 13172}, {2023, 8304}, {2066, 3023}, {2067, 3027}, {2482, 13989}, {2783, 48700}, {2787, 48714}, {2794, 42258}, {2799, 49270}, {3070, 23698}, {3311, 13188}, {3592, 19056}, {4027, 44586}, {5062, 48784}, {5186, 5412}, {5414, 15452}, {5418, 38224}, {5420, 38750}, {5976, 49253}, {5984, 43512}, {6033, 6561}, {6200, 12042}, {6221, 12188}, {6390, 44392}, {6409, 34473}, {6419, 35879}, {6425, 38664}, {6560, 38730}, {6564, 22515}, {6567, 48727}, {6721, 42583}, {6722, 32789}, {7585, 20094}, {7968, 11711}, {7983, 44635}, {8253, 14061}, {8290, 49255}, {8591, 19054}, {8782, 44604}, {8976, 38732}, {8980, 31454}, {8983, 11599}, {8998, 16278}, {9167, 13968}, {9540, 14651}, {9541, 9862}, {9616, 9860}, {10722, 42263}, {10723, 23251}, {10819, 18332}, {11473, 12131}, {11623, 41963}, {12239, 39817}, {12829, 12963}, {13173, 44590}, {13174, 18991}, {13175, 44598}, {13176, 44600}, {13177, 44602}, {13178, 13911}, {13179, 44610}, {13180, 44618}, {13181, 44620}, {13182, 31472}, {13183, 44623}, {13184, 44627}, {13185, 44629}, {13189, 44643}, {13190, 44645}, {13665, 38733}, {13847, 19057}, {13967, 38748}, {14639, 42265}, {14850, 19051}, {19048, 49202}, {19050, 49201}, {22505, 35821}, {22514, 44606}, {23514, 42582}, {31274, 32790}, {32135, 44501}, {33341, 44534}, {36519, 42270}, {38731, 42261}, {38734, 43879}, {38738, 42259}, {38741, 42260}, {38751, 43880}, {39652, 44587}, {39809, 42284}, {39838, 42271}, {41410, 41675}, {44582, 48531}, {44584, 48532}, {44594, 49096}, {44596, 49097}

X(49266) = midpoint of X(371) and X(35878)
X(49266) = reflection of X(i) in X(j) for these (i, j): (49212, 371), (49214, 32787)
X(49266) = inverse of X(35878) in Kenmotu circle
X(49266) = parallelogic center (1st Kenmotu-centers, T) for these triangles T: 1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard
X(49266) = X(99)-of-1st Kenmotu-centers triangle
X(49266) = X(33813)-of-1st Kenmotu-free-vertices triangle
X(49266) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 99, 49267), (99, 19109, 6), (115, 8997, 590), (6200, 35825, 12042), (10754, 44532, 49267), (19055, 21166, 1152), (19057, 41134, 13847)


X(49267) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO 1st ANTI-BROCARD

Barycentrics    -2*(a^2-c^2)*(a^2-b^2)*S+a^2*(a^4-(b^2+c^2)*a^2+b^4-b^2*c^2+c^4) : :
X(49267) = 3*X(372)-X(35825) = X(35825)+3*X(35879) = 2*X(35825)-3*X(49213) = 2*X(35879)+X(49213)

The reciprocal parallelogic center of these triangles is X(385).

X(49267) lies on the circumcircle of 2nd Kenmotu-centers triangle and these lines: {2, 49214}, {3, 49212}, {6, 99}, {30, 44392}, {39, 48784}, {98, 1152}, {114, 3070}, {115, 615}, {147, 6460}, {148, 3069}, {371, 33813}, {372, 2782}, {485, 15561}, {486, 6321}, {542, 41946}, {543, 32788}, {590, 620}, {618, 49210}, {619, 49208}, {671, 13847}, {690, 49269}, {1124, 10086}, {1151, 19056}, {1335, 10089}, {1569, 5062}, {1588, 13172}, {2023, 8305}, {2066, 15452}, {2482, 8997}, {2783, 48701}, {2787, 48715}, {2794, 42259}, {2799, 49271}, {3023, 5414}, {3027, 6502}, {3071, 23698}, {3312, 13188}, {3594, 19055}, {4027, 44587}, {5058, 48785}, {5186, 5413}, {5418, 38750}, {5420, 38224}, {5976, 49252}, {5984, 43511}, {6033, 6560}, {6390, 44394}, {6396, 12042}, {6398, 12188}, {6410, 34473}, {6420, 35878}, {6426, 38664}, {6561, 38730}, {6565, 22515}, {6566, 48726}, {6721, 42582}, {6722, 32790}, {7586, 20094}, {7969, 11711}, {7983, 44636}, {8252, 14061}, {8290, 49254}, {8591, 19053}, {8782, 44605}, {8980, 38748}, {9167, 13908}, {10722, 42264}, {10723, 23261}, {10820, 18332}, {11474, 12131}, {11599, 13971}, {11623, 41964}, {12240, 39817}, {12829, 12968}, {13173, 44591}, {13174, 18992}, {13175, 44599}, {13176, 44601}, {13177, 44603}, {13178, 13973}, {13179, 44611}, {13180, 44619}, {13181, 44621}, {13182, 44622}, {13183, 44624}, {13184, 44628}, {13185, 44630}, {13189, 44644}, {13190, 44646}, {13785, 38733}, {13846, 19058}, {13935, 14651}, {13951, 38732}, {13990, 16278}, {14639, 42262}, {14850, 19052}, {19047, 49202}, {19049, 49201}, {22505, 35820}, {22514, 44607}, {23514, 42583}, {31274, 32789}, {32135, 44502}, {33340, 44534}, {36519, 42273}, {38731, 42260}, {38734, 43880}, {38738, 42258}, {38741, 42261}, {38751, 43879}, {39652, 44586}, {39809, 42283}, {39838, 42272}, {41411, 41675}, {44583, 48531}, {44585, 48532}, {44595, 49096}, {44597, 49097}

X(49267) = midpoint of X(372) and X(35879)
X(49267) = reflection of X(i) in X(j) for these (i, j): (49213, 372), (49215, 32788)
X(49267) = parallelogic center (2nd Kenmotu-centers, T) for these triangles T: 1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard
X(49267) = X(99)-of-2nd Kenmotu-centers triangle
X(49267) = X(3022)-of-2nd Kenmotu diagonals triangle
X(49267) = X(33813)-of-2nd Kenmotu-free-vertices triangle
X(49267) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 99, 49266), (99, 19108, 6), (115, 13989, 615), (6396, 35824, 12042), (10754, 44532, 49266), (19056, 21166, 1151), (19058, 41134, 13846)


X(49268) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*(2*(a^2-c^2)*(a^2-b^2)*S+a^6-(b^2+c^2)*a^4-(b^4-3*b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2)) : :
X(49268) = 3*X(371)-X(35826) = 3*X(11241)-X(13287) = 3*X(12375)+X(35826) = 2*X(12375)+X(49216) = 3*X(32787)-2*X(46688) = 3*X(35822)-X(35834) = 2*X(35826)-3*X(49216)

The reciprocal parallelogic center of these triangles is X(323).

X(49268) lies on the circumcircle of 1st Kenmotu-centers triangle and these lines: {3, 10819}, {5, 49223}, {6, 110}, {39, 48787}, {74, 1151}, {113, 3071}, {125, 590}, {141, 49265}, {146, 6459}, {265, 485}, {371, 5663}, {372, 1511}, {399, 3311}, {486, 14643}, {541, 41945}, {542, 32787}, {615, 5972}, {690, 49266}, {1112, 5412}, {1124, 10091}, {1152, 15035}, {1335, 10088}, {1504, 14901}, {1539, 35821}, {1587, 12383}, {1986, 10880}, {2066, 3024}, {2067, 3028}, {2771, 48700}, {2777, 42258}, {2781, 11241}, {2948, 18991}, {3068, 3448}, {3070, 17702}, {3093, 15472}, {3312, 10820}, {3364, 36209}, {3389, 36208}, {3592, 14094}, {3594, 15034}, {5058, 46301}, {5062, 48786}, {5410, 19504}, {5418, 15061}, {5420, 38794}, {5465, 49215}, {5504, 8909}, {5609, 6419}, {5642, 13990}, {6199, 12308}, {6200, 12041}, {6221, 10620}, {6398, 15040}, {6409, 15055}, {6410, 15051}, {6412, 15036}, {6415, 8939}, {6425, 15054}, {6426, 15020}, {6428, 15039}, {6429, 10817}, {6449, 15041}, {6497, 15042}, {6560, 12121}, {6561, 7728}, {6564, 10113}, {6567, 48731}, {6723, 32789}, {7582, 20125}, {7583, 32423}, {7584, 10272}, {7585, 14683}, {7687, 42273}, {7723, 18457}, {7968, 11720}, {7984, 44635}, {8253, 15059}, {8674, 48714}, {8960, 13915}, {8976, 38724}, {8981, 10264}, {8983, 13605}, {8994, 16003}, {8997, 15357}, {9140, 13846}, {9143, 19054}, {9517, 49270}, {9541, 12244}, {9583, 33535}, {9616, 9904}, {9705, 43825}, {9976, 44656}, {10117, 17819}, {10533, 13288}, {10576, 20304}, {10577, 13979}, {10665, 12891}, {10721, 42263}, {10733, 23251}, {10897, 12358}, {11266, 20773}, {11473, 12133}, {11513, 13416}, {11579, 19145}, {11597, 49257}, {11598, 49251}, {11702, 12971}, {11801, 18538}, {11835, 35447}, {12006, 43867}, {12239, 21649}, {12240, 16223}, {12295, 42284}, {12310, 44598}, {12778, 35774}, {12900, 42583}, {12902, 13665}, {12903, 31472}, {12904, 44623}, {13193, 44586}, {13198, 19355}, {13202, 42271}, {13204, 44590}, {13208, 44600}, {13209, 44602}, {13210, 44604}, {13211, 13911}, {13212, 44610}, {13213, 44618}, {13214, 44620}, {13215, 44627}, {13216, 44629}, {13217, 44643}, {13218, 44645}, {13910, 25328}, {13969, 38793}, {14644, 42265}, {14984, 35840}, {15342, 19109}, {15462, 19146}, {16163, 42259}, {19048, 49204}, {19050, 49203}, {19052, 23236}, {19074, 37752}, {19076, 37753}, {20127, 42260}, {20379, 35812}, {20417, 41963}, {22586, 44606}, {23515, 42582}, {25556, 44501}, {34153, 42216}, {34584, 42266}, {35822, 35834}, {36253, 43879}, {36518, 42270}, {38723, 42261}, {38795, 43880}, {42283, 46686}, {43598, 43826}, {44582, 48535}, {44584, 48536}, {44594, 49098}, {44596, 49099}, {46085, 49225}

X(49268) = midpoint of X(i) and X(j) for these {i, j}: {6, 32291}, {371, 12375}, {10665, 12891}
X(49268) = reflection of X(i) in X(j) for these (i, j): (49216, 371), (49222, 7583)
X(49268) = inverse of X(12375) in Kenmotu circle
X(49268) = crosssum of X(3) and X(46688)
X(49268) = parallelogic center (1st Kenmotu-centers, T) for these triangles T: anti-orthocentroidal, orthocentroidal
X(49268) = X(110)-of-1st Kenmotu-centers triangle
X(49268) = X(1511)-of-1st Kenmotu-free-vertices triangle
X(49268) = X(32787)-of-anti-orthocentroidal triangle
X(49268) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 110, 49269), (110, 7732, 2930), (110, 19111, 6), (125, 8998, 590), (3312, 32609, 10820), (5972, 46689, 615), (6200, 35827, 12041), (6564, 35835, 10113), (10533, 13288, 15647), (14643, 19051, 486), (15035, 19059, 1152)


X(49269) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*(-2*(a^2-c^2)*(a^2-b^2)*S+a^6-(b^2+c^2)*a^4-(b^4-3*b^2*c^2+c^4)*a^2+(b^4-c^4)*(b^2-c^2)) : :
X(49269) = 3*X(372)-X(35827) = 3*X(11242)-X(13288) = 3*X(12376)+X(35827) = 2*X(12376)+X(49217) = 3*X(32788)-2*X(46689) = 3*X(35823)-X(35835) = 2*X(35827)-3*X(49217)

The reciprocal parallelogic center of these triangles is X(323).

X(49269) lies on the circumcircle of 2nd Kenmotu-centers triangle and these lines: {3, 10820}, {5, 49222}, {6, 110}, {39, 48786}, {74, 1152}, {113, 3070}, {125, 615}, {141, 49264}, {146, 6460}, {265, 486}, {371, 1511}, {372, 5663}, {399, 3312}, {485, 14643}, {541, 41946}, {542, 32788}, {590, 5972}, {690, 49267}, {1112, 5413}, {1124, 10088}, {1151, 15035}, {1335, 10091}, {1505, 14901}, {1539, 35820}, {1588, 12383}, {1986, 10881}, {2771, 48701}, {2777, 42259}, {2781, 11242}, {2948, 18992}, {3024, 5414}, {3028, 6502}, {3069, 3448}, {3071, 17702}, {3092, 15472}, {3311, 10819}, {3365, 36209}, {3390, 36208}, {3592, 15034}, {3594, 14094}, {5058, 48787}, {5062, 46301}, {5411, 19504}, {5418, 38794}, {5420, 15061}, {5465, 49214}, {5609, 6420}, {5642, 8998}, {6221, 15040}, {6395, 12308}, {6396, 12041}, {6398, 10620}, {6409, 15051}, {6410, 15055}, {6411, 15036}, {6416, 8943}, {6425, 15020}, {6426, 15054}, {6427, 15039}, {6430, 10818}, {6450, 15041}, {6496, 15042}, {6560, 7728}, {6561, 12121}, {6565, 10113}, {6566, 48730}, {6723, 32790}, {7581, 20125}, {7583, 10272}, {7584, 32423}, {7586, 14683}, {7687, 42270}, {7723, 18459}, {7969, 11720}, {7984, 44636}, {8252, 15059}, {8674, 48715}, {8994, 38793}, {9140, 13847}, {9143, 19053}, {9517, 49271}, {9705, 43826}, {9976, 44657}, {10117, 17820}, {10264, 13966}, {10534, 13287}, {10576, 13915}, {10577, 20304}, {10666, 12892}, {10721, 42264}, {10733, 23261}, {10898, 12358}, {11265, 20773}, {11474, 12133}, {11514, 13416}, {11579, 19146}, {11597, 49256}, {11598, 49250}, {11702, 12965}, {11801, 18762}, {11836, 35447}, {12006, 43868}, {12239, 16223}, {12240, 21649}, {12295, 42283}, {12310, 44599}, {12778, 35775}, {12900, 42582}, {12902, 13785}, {12903, 44622}, {12904, 44624}, {13193, 44587}, {13198, 19356}, {13202, 42272}, {13204, 44591}, {13208, 44601}, {13209, 44603}, {13210, 44605}, {13211, 13973}, {13212, 44611}, {13213, 44619}, {13214, 44621}, {13215, 44628}, {13216, 44630}, {13217, 44644}, {13218, 44646}, {13605, 13971}, {13951, 38724}, {13969, 16003}, {13972, 25328}, {13989, 15357}, {14644, 42262}, {14984, 35841}, {15342, 19108}, {15462, 19145}, {16163, 42258}, {19047, 49204}, {19049, 49203}, {19051, 23236}, {19073, 37752}, {19075, 37753}, {20127, 42261}, {20379, 35813}, {20417, 41964}, {22586, 44607}, {23515, 42583}, {25556, 44502}, {34153, 42215}, {34584, 42267}, {35823, 35835}, {36253, 43880}, {36518, 42273}, {38723, 42260}, {38795, 43879}, {42284, 46686}, {43598, 43825}, {44583, 48535}, {44585, 48536}, {44595, 49098}, {44597, 49099}, {46085, 49224}

X(49269) = midpoint of X(i) and X(j) for these {i, j}: {6, 32292}, {372, 12376}, {10666, 12892}
X(49269) = reflection of X(i) in X(j) for these (i, j): (49217, 372), (49223, 7584)
X(49269) = crosssum of X(3) and X(46689)
X(49269) = parallelogic center (2nd Kenmotu-centers, T) for these triangles T: anti-orthocentroidal, orthocentroidal
X(49269) = X(11)-of-2nd Kenmotu diagonals triangle
X(49269) = X(110)-of-2nd Kenmotu-centers triangle
X(49269) = X(1511)-of-2nd Kenmotu-free-vertices triangle
X(49269) = X(32788)-of-anti-orthocentroidal triangle
X(49269) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 110, 49268), (110, 7733, 2930), (110, 19110, 6), (125, 13990, 615), (3311, 32609, 10819), (5972, 46688, 590), (6396, 35826, 12041), (6565, 35834, 10113), (10534, 13287, 15647), (14643, 19052, 485), (15035, 19060, 1151)


X(49270) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-CENTERS TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*(2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^2-c^2)*(a^2-b^2)*S+a^10-(b^2+c^2)*a^8+b^2*c^2*a^6-(b^6-c^6)*(b^2-c^2)*a^2+(b^8-c^8)*(b^2-c^2)) : :
X(49270) = 3*X(371)-X(35828) = X(35828)+3*X(35880) = 2*X(35828)-3*X(49218) = 2*X(35880)+X(49218)

The reciprocal parallelogic center of these triangles is X(10313).

X(49270) lies on the circumcircle of 1st Kenmotu-centers triangle and these lines: {3, 49219}, {6, 74}, {39, 48789}, {127, 590}, {132, 3071}, {371, 35828}, {372, 38608}, {485, 10749}, {615, 6720}, {1124, 13312}, {1151, 1297}, {1152, 19093}, {1335, 13311}, {1587, 13200}, {2066, 6020}, {2067, 3320}, {2794, 3070}, {2799, 49266}, {2806, 48714}, {2831, 48700}, {3068, 13219}, {3311, 13310}, {3592, 19094}, {5062, 48788}, {5412, 13166}, {6200, 35829}, {6221, 13115}, {6409, 38717}, {6419, 35881}, {6425, 38689}, {6459, 12384}, {6561, 12918}, {6564, 19163}, {6567, 48733}, {7968, 11722}, {9517, 49268}, {9530, 41945}, {9541, 12253}, {9616, 12408}, {10705, 44635}, {10718, 13846}, {10735, 23251}, {11473, 12145}, {11641, 44598}, {12240, 16225}, {13195, 44586}, {13206, 44590}, {13221, 18991}, {13229, 44600}, {13231, 44602}, {13236, 44604}, {13280, 13911}, {13281, 44610}, {13294, 44618}, {13295, 44620}, {13296, 31472}, {13297, 44623}, {13298, 44627}, {13299, 44629}, {13313, 44643}, {13314, 44645}, {13665, 48681}, {13918, 31454}, {13992, 32788}, {14689, 42259}, {19048, 49206}, {19050, 49205}, {19160, 35821}, {19162, 44606}, {42263, 44988}, {44582, 48537}, {44584, 48538}, {44594, 49100}, {44596, 49101}

X(49270) = midpoint of X(371) and X(35880)
X(49270) = reflection of X(49218) in X(371)
X(49270) = inverse of X(35880) in Kenmotu circle
X(49270) = parallelogic center (1st Kenmotu-centers, T) for these triangles T: 1st anti-orthosymmedial, 1st orthosymmedial
X(49270) = X(112)-of-1st Kenmotu-centers triangle
X(49270) = X(38608)-of-1st Kenmotu-free-vertices triangle
X(49270) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 112, 49271), (112, 19115, 6), (127, 13923, 590), (6200, 35829, 38624), (19093, 38699, 1152)


X(49271) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-CENTERS TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*(-2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^2-c^2)*(a^2-b^2)*S+a^10-(b^2+c^2)*a^8+b^2*c^2*a^6-(b^6-c^6)*(b^2-c^2)*a^2+(b^8-c^8)*(b^2-c^2)) : :
X(49271) = 3*X(372)-X(35829) = X(35829)+3*X(35881) = 2*X(35829)-3*X(49219) = 2*X(35881)+X(49219)

The reciprocal parallelogic center of these triangles is X(10313).

X(49271) lies on the circumcircle of 2nd Kenmotu-centers triangle and these lines: {3, 49218}, {6, 74}, {39, 48788}, {127, 615}, {132, 3070}, {371, 38608}, {372, 35829}, {486, 10749}, {590, 6720}, {1124, 13311}, {1151, 19094}, {1152, 1297}, {1335, 13312}, {1588, 13200}, {2794, 3071}, {2799, 49267}, {2806, 48715}, {2831, 48701}, {3069, 13219}, {3312, 13310}, {3320, 6502}, {3594, 19093}, {5058, 48789}, {5413, 13166}, {5414, 6020}, {6396, 35828}, {6398, 13115}, {6410, 38717}, {6420, 35880}, {6426, 38689}, {6460, 12384}, {6560, 12918}, {6565, 19163}, {6566, 48732}, {7969, 11722}, {9517, 49269}, {9530, 41946}, {10705, 44636}, {10718, 13847}, {10735, 23261}, {11474, 12145}, {11641, 44599}, {12239, 16225}, {13195, 44587}, {13206, 44591}, {13221, 18992}, {13229, 44601}, {13231, 44603}, {13236, 44605}, {13280, 13973}, {13281, 44611}, {13294, 44619}, {13295, 44621}, {13296, 44622}, {13297, 44624}, {13298, 44628}, {13299, 44630}, {13313, 44644}, {13314, 44646}, {13785, 48681}, {13923, 32787}, {14676, 18994}, {14689, 42258}, {19047, 49206}, {19049, 49205}, {19160, 35820}, {19162, 44607}, {42264, 44988}, {44583, 48537}, {44585, 48538}, {44595, 49100}, {44597, 49101}

X(49271) = midpoint of X(372) and X(35881)
X(49271) = reflection of X(49219) in X(372)
X(49271) = parallelogic center (2nd Kenmotu-centers, T) for these triangles T: 1st anti-orthosymmedial, 1st orthosymmedial
X(49271) = X(112)-of-2nd Kenmotu-centers triangle
X(49271) = X(1358)-of-2nd Kenmotu diagonals triangle
X(49271) = X(38608)-of-2nd Kenmotu-free-vertices triangle
X(49271) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 112, 49270), (112, 19114, 6), (127, 13992, 615), (6396, 35828, 38624), (19094, 38699, 1151)

leftri

Points in a [[a,b,c], [a(b+c), b(c+a), c(a+b)]] coordinate system: X(49272)-X(49303)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1, L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1 is the line: a α + b β + c γ = 0.

L2 is the line a(b+c) α + b(c+a) β + c(a+b) γ = 0.

The origin is given by (0, 0) = X(693) = bc(b-c) : ca(c-a) : ab(a-b) .

Barycentrics u : v : w for a triangle center U = (x, y) in this system are given by

u : v : w = (b-c)(-bc + x - ay) : : ,

where, as functions of a, b, c, the coordinate x is antisymmetric and homogeneous of degree 2, and y is antisymmetric and homogeneous of degree 1.

The appearance of {x, y}, k in the following list means that (x, y) = X(k).

{-2 (a^2+b^2+c^2), -((2 (a^2+b^2+c^2))/(a+b+c))}, 47689}
{-2 (a^2+b^2+c^2), -((a^2+b^2+c^2)/(a+b+c))}, 47693
{-2 (a b+a c+b c), -a-b-c}, 26824
{-2 (a^2+b^2+c^2), 0}, 47662
{-2 (a b+a c+b c), 0}, 47675
{-((2 (a^3+b^3+c^3))/(a+b+c)), 0}, 47684
{-a^2-b^2-c^2, -2 (a+b+c)}, 44449
{-a^2-b^2-c^2, -((2 (a^2+b^2+c^2))/(a+b+c))}, 47687
{-a b-a c-b c, -2 (a+b+c)}, 48114
{-a b-a c-b c, -((2 (a^2+b^2+c^2))/(a+b+c))}, 48115
{-a b-a c-b c, -((2 (a b+a c+b c))/(a+b+c))}, 4804
{-a^2-b^2-c^2, -a-b-c}, 25259
{-a^2-b^2-c^2, -((a^2+b^2+c^2)/(a+b+c))}, 47690
{-a b-a c-b c, -a-b-c}, 4382
{-a b-a c-b c, -((a^2+b^2+c^2)/(a+b+c))}, 48119
{-a b-a c-b c, -((a b+a c+b c)/(a+b+c))}, 48120
{-a^2-b^2-c^2, 1/2 (-a-b-c)}, 48271
{-a b-a c-b c, 1/2 (-a-b-c)}, 48125
{-a b-a c-b c, -((a^2+b^2+c^2)/(2 (a+b+c)))}, 48126
{-a b-a c-b c, -((a b+a c+b c)/(2 (a+b+c)))}, 48127
{-a^2-b^2-c^2, 0}, 47660
{-a b-a c-b c, 0}, 47672
{-((a^3+b^3+c^3)/(a+b+c)), 0}, 47682
{-a b-a c-b c, 1/2 (a+b+c)}, 48133
{-a b-a c-b c, (a^2+b^2+c^2)/(2 (a+b+c))}, 48134
{-a b-a c-b c, (a b+a c+b c)/(2 (a+b+c))}, 48135
{-a^2-b^2-c^2, (a^2+b^2+c^2)/(a+b+c)}, 47696
{-a b-a c-b c, a+b+c}, 48141
{-a b-a c-b c, (a^2+b^2+c^2)/(a+b+c)}, 48142
{-a b-a c-b c, (a b+a c+b c)/(a+b+c)}, 48143
{-a b-a c-b c, 2 (a+b+c)}, 48147
{-a b-a c-b c, (2 (a^2+b^2+c^2))/(a+b+c)}, 48153
{-a b-a c-b c, (2 (a b+a c+b c))/(a+b+c)}, 48148
{1/2 (-a^2-b^2-c^2), -a-b-c}, 48269
{1/2 (-a b-a c-b c), -((a b+a c+b c)/(a+b+c))}, 48394
{1/2 (-a^2-b^2-c^2), 1/2 (-a-b-c)}, 3700
{1/2 (-a^2-b^2-c^2), -((a^2+b^2+c^2)/(2 (a+b+c)))}, 48396
{1/2 (-a^2-b^2-c^2), 0}, 6590
{1/2 (-a b-a c-b c), 0}, 48399
{1/2 (-a^2-b^2-c^2), 1/2 (a+b+c)}, 48276
{0, -2 (a+b+c)}, 48079
{0, -((2 (a^2+b^2+c^2))/(a+b+c))}, 47685
{0, -((2 (a b+a c+b c))/(a+b+c))}, 48080
{0, -a-b-c}, 20295
{0, -((a^2+b^2+c^2)/(a+b+c))}, 46403
{0, -((a b+a c+b c)/(a+b+c))}, 4010
{0, 1/2 (-a-b-c)}, 4106
{0, -((a^2+b^2+c^2)/(2 (a+b+c)))}, 48089
{0, -((a b+a c+b c)/(2 (a+b+c)))}, 48090
{0, 0}, 693
{0, 1/2 (a+b+c)}, 43067
{0, (a^2+b^2+c^2)/(2 (a+b+c))}, 7662
{0, (a b+a c+b c)/(2 (a+b+c))}, 48098
{0, a+b+c}, 7192
{0, (a^2+b^2+c^2)/(a+b+c)}, 47694
{0, (a b+a c+b c)/(a+b+c)}, 21146
{0, 2 (a+b+c)}, 48107
{0, (2 (a^2+b^2+c^2))/(a+b+c)}, 47697
{0, (2 (a b+a c+b c))/(a+b+c)}, 48108
{1/2 (a b+a c+b c), -2 (a+b+c)}, 48592
{1/2 (a b+a c+b c), -((2 (a^2+b^2+c^2))/(a+b+c))}, 48593
{1/2 (a b+a c+b c), -((2 (a b+a c+b c))/(a+b+c))}, 48037
{1/2 (a b+a c+b c), -a-b-c}, 48041
{1/2 (a b+a c+b c), -((a^2+b^2+c^2)/(a+b+c))}, 48042
{1/2 (a b+a c+b c), -((a b+a c+b c)/(a+b+c))}, 48043
{1/2 (a^2+b^2+c^2), 1/2 (-a-b-c)}, 23729
{1/2 (a b+a c+b c), 1/2 (-a-b-c)}, 48049
{1/2 (a b+a c+b c), -((a^2+b^2+c^2)/(2 (a+b+c)))}, 48050
{1/2 (a b+a c+b c), -((a b+a c+b c)/(2 (a+b+c)))}, 4806
{1/2 (a^2+b^2+c^2), 0}, 48398
{1/2 (a b+a c+b c), 0}, 3835
{1/2 (a^2+b^2+c^2), 1/2 (a+b+c)}, 21104
{1/2 (a^2+b^2+c^2), (a^2+b^2+c^2)/(2 (a+b+c))}, 23770
{1/2 (a b+a c+b c), 1/2 (a+b+c)}, 4369
{1/2 (a b+a c+b c), (a^2+b^2+c^2)/(2 (a+b+c))}, 3716
{1/2 (a b+a c+b c), (a b+a c+b c)/(2 (a+b+c))}, 3837
{1/2 (a^2+b^2+c^2), (a^2+b^2+c^2)/(a+b+c)}, 47123
{1/2 (a b+a c+b c), a+b+c}, 4932
{1/2 (a b+a c+b c), (a^2+b^2+c^2)/(a+b+c)}, 48063
{1/2 (a b+a c+b c), (a b+a c+b c)/(a+b+c)}, 24720
{1/2 (a b+a c+b c), 2 (a+b+c)}, 48071
{1/2 (a b+a c+b c), (2 (a^2+b^2+c^2))/(a+b+c)}, 48072
{1/2 (a b+a c+b c), (2 (a b+a c+b c))/(a+b+c)}, 48073
{a b+a c+b c, -2 (a+b+c)}, 48019
{a b+a c+b c, -((2 (a^2+b^2+c^2))/(a+b+c))}, 48020
{a b+a c+b c, -((2 (a b+a c+b c))/(a+b+c))}, 48021
{a^2+b^2+c^2, -((a^2+b^2+c^2)/(a+b+c))}, 47686
{a b+a c+b c, -a-b-c}, 4813
{a b+a c+b c, -((a^2+b^2+c^2)/(a+b+c))}, 48023
{a b+a c+b c, -((a b+a c+b c)/(a+b+c))}, 48024
{a b+a c+b c, 1/2 (-a-b-c)}, 48026
{a b+a c+b c, -((a^2+b^2+c^2)/(2 (a+b+c)))}, 48027
{a b+a c+b c, -((a b+a c+b c)/(2 (a+b+c)))}, 48028
{a^2+b^2+c^2, 0}, 47652
{a b+a c+b c, 0}, 661
{(a^3+b^3+c^3)/(a+b+c), 0}, 47680
{a b+a c+b c, 1/2 (a+b+c)}, 650
{a b+a c+b c, (a^2+b^2+c^2)/(2 (a+b+c))}, 48029
{a b+a c+b c, (a b+a c+b c)/(2 (a+b+c))}, 48030
{a^2+b^2+c^2, a+b+c}, 47676
{a^2+b^2+c^2, (a^2+b^2+c^2)/(a+b+c)}, 47691
{a b+a c+b c, a+b+c}, 649
{a b+a c+b c, (a^2+b^2+c^2)/(a+b+c)}, 4724
{a b+a c+b c, (a b+a c+b c)/(a+b+c)}, 1491
{a^2+b^2+c^2, (2 (a^2+b^2+c^2))/(a+b+c)}, 47695
{a b+a c+b c, 2 (a+b+c)}, 4979
{a b+a c+b c, (2 (a^2+b^2+c^2))/(a+b+c)}, 48032
{a b+a c+b c, (2 (a b+a c+b c))/(a+b+c)}, 2254
{2 (a b+a c+b c), -2 (a+b+c)}, 47939
{2 (a b+a c+b c), -((2 (a^2+b^2+c^2))/(a+b+c))}, 47940
{2 (a b+a c+b c), -((2 (a b+a c+b c))/(a+b+c))}, 47941
{2 (a b+a c+b c), -a-b-c}, 31290
{2 (a b+a c+b c), -((a^2+b^2+c^2)/(a+b+c))}, 47945
{2 (a b+a c+b c), -((a b+a c+b c)/(a+b+c))}, 47946
{2 (a b+a c+b c), 1/2 (-a-b-c)}, 47952
{2 (a b+a c+b c), -((a^2+b^2+c^2)/(2 (a+b+c)))}, 47953
{2 (a b+a c+b c), -((a b+a c+b c)/(2 (a+b+c)))}, 47954
{2 (a^2+b^2+c^2), 0}, 47651
{2 (a b+a c+b c), 0}, 47666
{2 (a b+a c+b c), 1/2 (a+b+c)}, 47962
{2 (a b+a c+b c), (a^2+b^2+c^2)/(2 (a+b+c))}, 47963
{2 (a b+a c+b c), (a b+a c+b c)/(2 (a+b+c))}, 47964
{2 (a^2+b^2+c^2), (a^2+b^2+c^2)/(a+b+c)}, 47688
{2 (a b+a c+b c), a+b+c}, 17494
{2 (a b+a c+b c), (a^2+b^2+c^2)/(a+b+c)}, 47969
{2 (a b+a c+b c), (a b+a c+b c)/(a+b+c)}, 4824
{2 (a^2+b^2+c^2), (2 (a^2+b^2+c^2))/(a+b+c)}, 47692
{2 (a b+a c+b c), 2 (a+b+c)}, 4380
{2 (a b+a c+b c), (2 (a^2+b^2+c^2))/(a+b+c)}, 47974
{2 (a b+a c+b c), (2 (a b+a c+b c))/(a+b+c)}, 47975
{-2*(a^2 + b^2 + c^2), -2*(a + b + c)}, 49272
{-2*(a^2 + b^2 + c^2), -a - b - c}, 49273
{(-2*(a^3 + b^3 + c^3))/(a + b + c), -a - b - c}, 49274
{-a^2 - b^2 - c^2, (-2*(a*b + a*c + b*c))/(a + b + c)}, 49275
{-((a^3 + b^3 + c^3)/(a + b + c)), (-2*(a*b + a*c + b*c))/(a + b + c)}, 49276
{-((a^3 + b^3 + c^3)/(a + b + c)), -a - b - c}, 49277
{-((a^3 + b^3 + c^3)/(a + b + c)), -((a^2 + b^2 + c^2)/(a + b + c))}, 49278
{-((a^3 + b^3 + c^3)/(a + b + c)), -((a*b + a*c + b*c)/(a + b + c))}, 49279
{-((a^3 + b^3 + c^3)/(a + b + c)), (-a - b - c)/2}, 49280
{-a^2 - b^2 - c^2, (a + b + c)/2}, 49281
{-a^2 - b^2 - c^2, a + b + c}, 49282
{-a^2 - b^2 - c^2, (2*(a*b + a*c + b*c))/(a + b + c)}, 49283
{(-a^2 - b^2 - c^2)/2, -2*(a + b + c)}, 49284
{(-a^2 - b^2 - c^2)/2, -((a^2 + b^2 + c^2)/(a + b + c))}, 49285
{(-a^2 - b^2 - c^2)/2, -((a*b + a*c + b*c)/(a + b + c))}, 49286
{(-(a*b) - a*c - b*c)/2, -a - b - c}, 49287
{-1/2*(a^3 + b^3 + c^3)/(a + b + c), -((a*b + a*c + b*c)/(a + b + c))}, 49288
{(-(a*b) - a*c - b*c)/2, (-a - b - c)/2}, 49289
{-1/2*(a^3 + b^3 + c^3)/(a + b + c), -1/2*(a*b + a*c + b*c)/(a + b + c)}, 49290
{(-(a*b) - a*c - b*c)/2, (a + b + c)/2}, 49291
{(-(a*b) - a*c - b*c)/2, (a^2 + b^2 + c^2)/(2*(a + b + c))}, 49292
{(-a^2 - b^2 - c^2)/2, a + b + c}, 49293
{(a^2 + b^2 + c^2)/2, -a - b - c}, 49294
{(a^2 + b^2 + c^2)/2, -((a*b + a*c + b*c)/(a + b + c))}, 49295
{(a^2 + b^2 + c^2)/2, a + b + c}, 49296
{a^2 + b^2 + c^2, -2*(a + b + c)}, 49297
{a^2 + b^2 + c^2, -a - b - c}, 49298
{a^2 + b^2 + c^2, (a + b + c)/2}, 49299
{(a^3 + b^3 + c^3)/(a + b + c), (a^2 + b^2 + c^2)/(a + b + c)}, 49300
{a^2 + b^2 + c^2, (2*(a*b + a*c + b*c))/(a + b + c)}, 49301
{2*(a^2 + b^2 + c^2), a + b + c}, 49302
{(2*(a^3 + b^3 + c^3))/(a + b + c), (a^2 + b^2 + c^2)/(a + b + c)}, 49303


X(49272) = X(513)X(47662)∩X(514)X(4838)

Barycentrics    (b - c)*(-2*a*b + 2*b^2 - 2*a*c + b*c + 2*c^2) : :
X(49272) = 4 X[4838] - 3 X[47655], 2 X[4838] - 3 X[47665], 5 X[4838] - 3 X[47670], X[4838] + 3 X[48112], 5 X[47655] - 4 X[47670], X[47655] + 4 X[48112], 5 X[47665] - 2 X[47670], X[47665] + 2 X[48112], X[47670] + 5 X[48112], 2 X[649] - 3 X[48557], 2 X[650] - 3 X[47772], 3 X[693] - 4 X[3700], 5 X[693] - 4 X[21104], 3 X[693] - 2 X[47676], 5 X[693] - 6 X[47790], 5 X[3700] - 3 X[21104], 2 X[3700] - 3 X[25259], 10 X[3700] - 9 X[47790], 2 X[21104] - 5 X[25259], 6 X[21104] - 5 X[47676], 2 X[21104] - 3 X[47790], 3 X[25259] - X[47676], 5 X[25259] - 3 X[47790], 5 X[47676] - 9 X[47790], and many others

X(49272) lies on these lines: {513, 47662}, {514, 4838}, {522, 47664}, {523, 47910}, {525, 4462}, {649, 48557}, {650, 47772}, {661, 30519}, {693, 918}, {812, 48117}, {824, 4988}, {900, 47663}, {2516, 31992}, {2527, 4897}, {2786, 4380}, {3004, 47769}, {3239, 4453}, {3667, 47700}, {3762, 20909}, {3776, 4120}, {3835, 47930}, {4024, 28851}, {4025, 4521}, {4122, 48108}, {4382, 28890}, {4391, 4707}, {4467, 4468}, {4728, 48421}, {4776, 16892}, {4784, 48236}, {4785, 48130}, {4790, 47773}, {4801, 7265}, {4806, 48174}, {4813, 28863}, {4820, 26824}, {4885, 48571}, {4931, 48399}, {4940, 48156}, {4944, 26985}, {4949, 20295}, {4979, 28906}, {6005, 47706}, {6008, 48124}, {7192, 48271}, {7659, 48208}, {14321, 44435}, {17161, 47962}, {17494, 28898}, {18004, 44429}, {21115, 48420}, {21116, 48417}, {22037, 48335}, {26853, 48095}, {27013, 47770}, {27138, 47754}, {28846, 47660}, {28855, 48275}, {28867, 48101}, {28871, 48141}, {28894, 31290}, {28910, 48397}, {29078, 48083}, {29148, 47684}, {29212, 47729}, {29280, 48265}, {29292, 48351}, {29294, 47970}, {29358, 47709}, {43067, 47870}, {45746, 48046}, {47652, 48269}, {47653, 48026}, {47656, 48437}, {47668, 47917}, {47671, 48430}, {47672, 48423}, {47673, 47996}, {47692, 48080}, {47702, 48037}, {47759, 47960}, {47762, 47971}, {47792, 48133}, {47916, 48041}, {47923, 48049}, {48013, 48567}, {48047, 48175}, {48404, 48428}

X(49272) = reflection of X(i) in X(j) for these {i,j}: {693, 25259}, {4380, 48094}, {4467, 4468}, {4801, 7265}, {7192, 48271}, {16892, 48270}, {17161, 47962}, {17494, 48087}, {26824, 4820}, {26853, 48095}, {45746, 48046}, {47651, 20295}, {47652, 48269}, {47653, 48026}, {47655, 47665}, {47657, 47666}, {47666, 48082}, {47668, 47917}, {47671, 48430}, {47673, 47996}, {47675, 4024}, {47676, 3700}, {47677, 661}, {47692, 48080}, {47702, 48037}, {47900, 48592}, {47916, 48041}, {47923, 48049}, {47930, 3835}, {47939, 48076}, {47974, 48078}, {48079, 44449}, {48107, 47660}, {48108, 4122}, {48335, 22037}, {48428, 48404}, {48434, 47769}, {48435, 45746}
X(49272) = barycentric product X(i)*X(j) for these {i,j}: {75, 48018}, {514, 17240}, {693, 4661}
X(49272) = barycentric quotient X(i)/X(j) for these {i,j}: {4661, 100}, {17240, 190}, {48018, 1}
X(49272) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3700, 47676, 693}, {3835, 47930, 48422}, {4025, 30565, 31209}, {4467, 4468, 31150}, {4931, 48399, 48424}, {16892, 48270, 4776}, {21104, 47790, 693}, {25259, 47676, 3700}, {45746, 48046, 48548}, {48435, 48548, 45746}


X(49273) = X(513)X(47662)∩X(514)X(4024)

Barycentrics    (b - c)*(a^2 - a*b + 2*b^2 - a*c + b*c + 2*c^2) : :
X(49273) = 9 X[2] - 8 X[21212], 3 X[16892] - 4 X[21212], 2 X[693] - 3 X[47870], 3 X[47870] - 4 X[48271], X[4608] + 4 X[48117], 3 X[20295] - 4 X[48269], 3 X[25259] - 2 X[48269], X[47659] + 2 X[48117], 2 X[649] - 3 X[47773], 8 X[650] - 9 X[31992], 4 X[650] - 3 X[47894], 2 X[650] - 3 X[48557], 9 X[31992] - 4 X[47677], 3 X[31992] - 2 X[47894], 3 X[31992] - 4 X[48557], 2 X[47677] - 3 X[47894], X[47677] - 3 X[48557], 2 X[661] - 3 X[47772], X[47653] - 3 X[47772], X[17161] - 4 X[48094], 3 X[17161] - 4 X[48277], 3 X[17494] - 2 X[48277], 3 X[48094] - X[48277], 3 X[7192] - 4 X[48276], and many others

X(49273) lies on these lines: {2, 16892}, {312, 693}, {321, 18071}, {513, 47662}, {514, 4024}, {522, 47663}, {523, 47969}, {649, 30519}, {650, 4850}, {661, 28863}, {768, 21225}, {812, 48130}, {824, 17147}, {826, 14318}, {918, 7192}, {1491, 48171}, {2254, 48208}, {2786, 26853}, {3004, 30565}, {3239, 27138}, {3309, 47706}, {3644, 4777}, {3700, 21297}, {3716, 48203}, {3776, 6548}, {3835, 47923}, {3885, 14077}, {4010, 47688}, {4025, 27013}, {4037, 18080}, {4106, 47651}, {4120, 26798}, {4122, 46403}, {4358, 29427}, {4359, 29404}, {4369, 47930}, {4380, 28898}, {4391, 27712}, {4467, 47776}, {4468, 45746}, {4500, 47869}, {4522, 47973}, {4762, 42044}, {4776, 47960}, {4785, 48138}, {4789, 21104}, {4802, 47946}, {4841, 47654}, {4874, 48241}, {4885, 48422}, {4897, 48567}, {4940, 47919}, {4976, 47892}, {6008, 48132}, {6546, 21196}, {6590, 47676}, {11068, 27486}, {14321, 48550}, {17166, 29354}, {17496, 48300}, {18004, 47968}, {21204, 48425}, {21222, 47682}, {21302, 47707}, {23885, 39179}, {27115, 47886}, {28840, 48112}, {28851, 48275}, {28859, 48076}, {28867, 48104}, {28871, 48147}, {28882, 48266}, {28890, 47672}, {28894, 47666}, {29037, 31291}, {29196, 48111}, {29328, 48140}, {29362, 48604}, {31150, 48435}, {31209, 47770}, {42325, 47710}, {45320, 48421}, {45343, 48418}, {46915, 47673}, {47657, 47962}, {47668, 47920}, {47675, 48397}, {47691, 48172}, {47699, 48040}, {47754, 48433}, {47759, 47958}, {47763, 47971}, {47769, 47995}, {47774, 48046}, {47790, 48398}, {47808, 48015}, {47824, 48405}, {47825, 48056}, {47834, 48326}, {47873, 48399}, {47879, 48426}, {47916, 48049}, {47924, 48043}, {47931, 48050}, {47975, 48088}, {48062, 48242}, {48063, 48239}, {48125, 48423}

X(49273) = midpoint of X(47664) and X(48436)
X(49273) = reflection of X(i) in X(j) for these {i,j}: {693, 48271}, {4380, 48095}, {4467, 47890}, {4608, 47659}, {7192, 47660}, {17161, 17494}, {17494, 48094}, {17496, 48300}, {20295, 25259}, {21222, 47682}, {21302, 47707}, {26824, 4024}, {26853, 48101}, {31290, 48082}, {45746, 4468}, {46403, 4122}, {47650, 48268}, {47651, 4106}, {47652, 3700}, {47653, 661}, {47654, 4841}, {47657, 47962}, {47666, 48087}, {47668, 47920}, {47673, 48000}, {47675, 48397}, {47676, 6590}, {47677, 650}, {47688, 4010}, {47699, 48040}, {47894, 48557}, {47907, 48041}, {47916, 48049}, {47919, 4940}, {47923, 3835}, {47924, 48043}, {47930, 4369}, {47931, 48050}, {47958, 48270}, {47968, 18004}, {47969, 48083}, {47973, 4522}, {47975, 48088}, {48428, 21196}, {48434, 47770}
X(49273) = anticomplement of X(16892)
X(49273) = anticomplement of the isogonal conjugate of X(4628)
X(49273) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {82, 150}, {83, 21293}, {100, 1369}, {101, 21289}, {213, 39346}, {251, 149}, {692, 2896}, {827, 75}, {4577, 17137}, {4593, 17138}, {4599, 17135}, {4628, 8}, {4630, 17147}, {18082, 21294}, {18098, 3448}, {32739, 21217}, {34072, 1}, {36081, 20553}, {42396, 20242}, {46288, 9263}, {46289, 4440}
X(49273) = crosspoint of X(i) and X(j) for these (i,j): {190, 10159}, {4577, 32014}
X(49273) = crosssum of X(i) and X(j) for these (i,j): {649, 5007}, {3005, 20970}
X(49273) = crossdifference of every pair of points on line {2308, 11205}
X(49273) = barycentric product X(i)*X(j) for these {i,j}: {1, 18072}, {514, 17285}
X(49273) = barycentric quotient X(i)/X(j) for these {i,j}: {17285, 190}, {18072, 75}
X(49273) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 47677, 47894}, {693, 48271, 47870}, {3239, 44435, 27138}, {3700, 47652, 21297}, {3776, 26985, 6548}, {3776, 47874, 26985}, {3835, 47923, 48156}, {4025, 47771, 27013}, {4369, 47930, 48571}, {4467, 47890, 47776}, {4468, 45746, 47775}, {4522, 47973, 48164}, {6546, 21196, 26777}, {6546, 48428, 21196}, {6590, 47676, 47780}, {47653, 47772, 661}, {47673, 48000, 46915}, {47677, 48557, 650}, {47894, 48557, 31992}, {47958, 48270, 47759}


X(49274) = X(2)X(4707)∩X(8)X(2785)

Barycentrics    (b - c)*(a^3 - 2*a^2*b - a*b^2 + 2*b^3 - 2*a^2*c - a*b*c + b^2*c - a*c^2 + b*c^2 + 2*c^3) : :
X(49274) = 3 X[3904] - 2 X[30725], 3 X[21222] - 4 X[30725], 2 X[4467] - 3 X[4560], 5 X[3616] - 4 X[4458], 5 X[3616] - 6 X[14432], 2 X[4458] - 3 X[14432], 7 X[3624] - 6 X[21181], 2 X[3676] - 3 X[6332], 8 X[3676] - 9 X[47796], 4 X[6332] - 3 X[47796], 2 X[3762] - 3 X[47772], 2 X[3801] - 3 X[47840], 4 X[3960] - 3 X[48571], 3 X[4391] - 2 X[43052], 2 X[4761] - 3 X[48208], 4 X[4794] - 3 X[48239], 7 X[9780] - 6 X[30574], 2 X[10015] - 3 X[30565], 4 X[18004] - 3 X[30709], 3 X[21297] - 2 X[47680]

X(49274) lies on these lines: {2, 4707}, {8, 2785}, {190, 644}, {448, 525}, {513, 47684}, {514, 4024}, {671, 35141}, {900, 9963}, {1639, 25529}, {2349, 2394}, {2786, 20094}, {3616, 4458}, {3624, 21181}, {3676, 6332}, {3738, 12532}, {3762, 4080}, {3801, 47840}, {3906, 48288}, {3960, 48571}, {4391, 18074}, {4761, 48208}, {4794, 48239}, {4822, 29116}, {4983, 29154}, {6370, 6740}, {7192, 47682}, {8045, 23755}, {9780, 30574}, {10015, 30565}, {14349, 29220}, {17161, 47683}, {17494, 23876}, {17496, 23875}, {18004, 30709}, {21297, 47680}, {21301, 29082}, {21302, 29304}, {28468, 48094}, {29102, 46403}, {29126, 44449}, {29130, 48081}, {29172, 48024}, {29224, 47688}, {29312, 47969}, {29332, 48123}

X(49274) = reflection of X(i) in X(j) for these {i,j}: {8, 4088}, {4608, 47681}, {7192, 47682}, {17161, 47683}, {21222, 3904}, {21302, 48272}, {23755, 8045}
X(49274) = anticomplement of X(4707)
X(49274) = anticomplement of the isotomic conjugate of X(47318)
X(49274) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {80, 21294}, {163, 6224}, {476, 21276}, {759, 150}, {1807, 13219}, {2161, 3448}, {2174, 14731}, {2222, 2893}, {2341, 33650}, {6187, 21221}, {9273, 17166}, {9274, 17161}, {14560, 17483}, {24624, 21293}, {32671, 1}, {32675, 2475}, {34079, 149}, {36069, 75}, {37140, 17135}, {47318, 6327}
X(49274) = X(47318)-Ceva conjugate of X(2)
X(49274) = X(11125)-Dao conjugate of X(14400)
X(49274) = crosspoint of X(i) and X(j) for these (i,j): {99, 20568}, {4554, 14616}
X(49274) = crosssum of X(i) and X(j) for these (i,j): {512, 2251}, {3063, 3724}, {20970, 42666}
X(49274) = crossdifference of every pair of points on line {2308, 3271}
X(49274) = {X(4458),X(14432)}-harmonic conjugate of X(3616)


X(49275) = X(513)X(4122)∩X(514)X(4170)

Barycentrics    (b - c)*(a^3 - a^2*b + a*b^2 + b^3 - a^2*c - a*b*c + 2*b^2*c + a*c^2 + 2*b*c^2 + c^3) : :
X(49275) = 2 X[649] - 3 X[48250], 4 X[676] - 3 X[48241], 2 X[1491] - 3 X[30565], 2 X[2254] - 3 X[47809], 4 X[2977] - 3 X[48242], 2 X[3004] - 3 X[47821], 4 X[3239] - 3 X[44429], 3 X[44429] - 2 X[48015], 4 X[3716] - 3 X[47797], 2 X[16892] - 3 X[47797], 2 X[3776] - 3 X[47832], 4 X[3835] - 3 X[48159], 2 X[47973] - 3 X[48159], 2 X[4025] - 3 X[47804], 3 X[4041] - 4 X[32212], 3 X[4120] - 2 X[48050], 3 X[4453] - 4 X[4874], 4 X[4522] - 3 X[31131], 3 X[4776] - 2 X[48007], and many others

X(49275) lies on these lines: {513, 4122}, {514, 4170}, {522, 47700}, {523, 47969}, {649, 48250}, {659, 4467}, {676, 48241}, {812, 48102}, {824, 4724}, {900, 48103}, {918, 47694}, {1491, 30565}, {2254, 47809}, {2977, 48242}, {3004, 47821}, {3239, 44429}, {3309, 47707}, {3667, 48106}, {3700, 46403}, {3716, 16892}, {3776, 47832}, {3835, 47973}, {4010, 47652}, {4025, 47804}, {4041, 32212}, {4106, 47686}, {4120, 48050}, {4453, 4874}, {4458, 47930}, {4468, 47975}, {4500, 48119}, {4522, 31131}, {4776, 48007}, {4777, 48614}, {4778, 4931}, {4784, 48567}, {4789, 21146}, {4806, 47968}, {4818, 4893}, {4824, 48048}, {4838, 47933}, {4913, 6546}, {4926, 48097}, {4976, 48240}, {4977, 20295}, {4988, 48001}, {6161, 29110}, {6590, 48108}, {7662, 47676}, {8045, 48151}, {17494, 48055}, {17496, 48299}, {21104, 47834}, {21192, 47817}, {21196, 47811}, {21222, 48290}, {23770, 48172}, {23879, 47970}, {24720, 47874}, {27013, 48231}, {27138, 48178}, {28851, 48142}, {28863, 47701}, {28882, 48139}, {28890, 47704}, {28894, 47699}, {29037, 48150}, {29062, 48111}, {29190, 47977}, {29212, 48324}, {29354, 48305}, {30519, 44433}, {30520, 47691}, {42325, 47711}, {45746, 48029}, {47653, 47998}, {47663, 48096}, {47665, 47974}, {47666, 48040}, {47667, 47963}, {47679, 48004}, {47698, 48087}, {47759, 47989}, {47769, 48027}, {47772, 48047}, {47790, 48089}, {47826, 48404}, {47870, 48396}, {47871, 48090}, {47943, 48049}, {47945, 48046}, {47951, 48543}, {47958, 48043}, {48023, 48270}, {48062, 48557}, {48069, 48236}, {48105, 48266}, {48112, 48153}, {48114, 48626}, {48252, 48405}

X(49275) = midpoint of X(i) and X(j) for these {i,j}: {4804, 48113}, {4838, 47933}, {47665, 47974}, {48105, 48266}, {48112, 48153}, {48114, 48626}
X(49275) = reflection of X(i) in X(j) for these {i,j}: {4467, 659}, {4824, 48048}, {4988, 48001}, {16892, 3716}, {17494, 48055}, {17496, 48299}, {21222, 48290}, {45746, 48029}, {46403, 3700}, {47652, 4010}, {47653, 47998}, {47663, 48096}, {47666, 48040}, {47667, 47963}, {47676, 7662}, {47679, 48004}, {47686, 4106}, {47687, 4122}, {47690, 48271}, {47698, 48087}, {47930, 4458}, {47938, 48037}, {47941, 48036}, {47943, 48049}, {47945, 48046}, {47958, 48043}, {47968, 4806}, {47973, 3835}, {47975, 4468}, {48015, 3239}, {48023, 48270}, {48108, 6590}, {48119, 4500}, {48151, 8045}, {48408, 48094}
X(49275) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3239, 48015, 44429}, {3716, 16892, 47797}, {3835, 47973, 48159}, {4806, 47968, 48550}


X(49276) = X(1)X(918)∩X(8)X(47772)

Barycentrics    (b - c)*(a^3 - 2*a^2*b + b^3 - 2*a^2*c - a*b*c + b^2*c + b*c^2 + c^3) : :
X(49276) = X[8] - 3 X[47772], 2 X[10] - 3 X[30565], 3 X[4822] - X[47902], 2 X[47979] - 3 X[48081], X[764] - 3 X[30605], 4 X[1125] - 3 X[4453], 6 X[1638] - 7 X[3624], 6 X[1639] - 5 X[1698], 5 X[3616] - 3 X[48571], 2 X[3960] - 3 X[14432], 3 X[4983] - 2 X[47990], 3 X[14349] - 2 X[48007], 13 X[34595] - 12 X[44902], 2 X[44314] - 3 X[45661], X[47925] - 3 X[48123]

X(49276) lies on these lines: {1, 918}, {8, 47772}, {10, 30565}, {191, 654}, {512, 48103}, {513, 47682}, {514, 4170}, {523, 48352}, {525, 4040}, {659, 690}, {663, 23875}, {667, 29200}, {764, 30605}, {826, 48336}, {891, 48083}, {926, 5904}, {1019, 48299}, {1125, 4453}, {1499, 47890}, {1638, 3624}, {1639, 1698}, {2785, 3762}, {2786, 5592}, {3309, 48272}, {3566, 4063}, {3616, 48571}, {3700, 47724}, {3716, 4707}, {3887, 4088}, {3910, 47970}, {3960, 14432}, {4010, 29102}, {4083, 48614}, {4122, 29188}, {4160, 48082}, {4367, 29252}, {4391, 29304}, {4467, 48284}, {4724, 23876}, {4730, 48056}, {4775, 47727}, {4879, 29354}, {4905, 6332}, {4983, 47990}, {6005, 48300}, {7265, 29051}, {14077, 48087}, {14349, 48007}, {21124, 48058}, {21132, 23884}, {21385, 48055}, {25259, 29066}, {29017, 48351}, {29021, 48367}, {29033, 48266}, {29047, 48338}, {29082, 48267}, {29094, 48265}, {29132, 47684}, {29148, 47728}, {29212, 47729}, {29220, 47708}, {29224, 48349}, {29288, 48337}, {29318, 47972}, {29350, 48094}, {34595, 44902}, {42325, 48278}, {44314, 45661}, {47676, 48295}, {47925, 48123}, {48290, 48320}

X(49276) = reflection of X(i) in X(j) for these {i,j}: {1019, 48299}, {4467, 48284}, {4707, 3716}, {4730, 48056}, {4905, 6332}, {21124, 48058}, {21385, 48055}, {47676, 48295}, {47680, 4010}, {47723, 4122}, {47724, 3700}, {47727, 4775}, {48320, 48290}


X(49277) = X(20)X(3667)∩X(512)X(48272)

Barycentrics    (b - c)*(-2*a^2*b - a*b^2 + b^3 - 2*a^2*c - a*b*c + b^2*c - a*c^2 + b*c^2 + c^3) : :
X(49277) = X[47907] - 3 X[48121], 2 X[47981] - 3 X[48085], 2 X[3004] - 3 X[14349], 3 X[1019] - 2 X[48013], 3 X[6332] - X[48013], 3 X[4063] - 4 X[11068], 3 X[4120] - 2 X[4791], 2 X[4142] - 3 X[47838], 2 X[20517] - 3 X[47840], X[47930] - 3 X[48131], X[47919] - 3 X[48128], X[48104] - 3 X[48300]

X(49277) lies on these lines: {20, 3667}, {512, 48272}, {513, 47682}, {514, 4024}, {522, 47683}, {525, 3004}, {661, 23876}, {690, 1491}, {826, 48123}, {918, 48335}, {1019, 6332}, {1734, 3566}, {2530, 29200}, {2786, 48321}, {2832, 48078}, {3762, 28468}, {3777, 29252}, {3835, 4707}, {3887, 48077}, {3904, 29148}, {3910, 47959}, {3960, 47971}, {4063, 11068}, {4088, 29350}, {4106, 47680}, {4120, 4791}, {4142, 47838}, {4170, 23877}, {4468, 21385}, {4522, 4761}, {4560, 29216}, {4705, 29284}, {4822, 29021}, {4823, 23755}, {4983, 29017}, {6005, 48278}, {10015, 14321}, {18118, 46487}, {20517, 47840}, {21124, 48054}, {21301, 29304}, {23875, 47930}, {23879, 47657}, {23887, 48080}, {24719, 29102}, {28481, 48111}, {28846, 48320}, {29078, 48288}, {29142, 48081}, {29202, 48093}, {29212, 48298}, {29256, 48053}, {29280, 48129}, {29312, 48024}, {29318, 47701}, {31042, 47786}, {47684, 48079}, {47919, 48128}, {48104, 48300}

X(49277) = midpoint of X(i) and X(j) for these {i,j}: {3904, 44449}, {47684, 48079}
X(49277) = reflection of X(i) in X(j) for these {i,j}: {1019, 6332}, {3762, 48270}, {4707, 3835}, {4761, 4522}, {10015, 14321}, {21124, 48054}, {21385, 4468}, {23755, 4823}, {25259, 22037}, {47680, 4106}, {47971, 3960}
X(49277) = crosssum of X(649) and X(2278)
X(49277) = crossdifference of every pair of points on line {2308, 44115}


X(49278) = X(1)X(522)∩X(8)X(48169)

Barycentrics    (b - c)*(-(a*b^2) + b^3 + a*b*c + b^2*c - a*c^2 + b*c^2 + c^3) : :
X(49278) = X[8] - 3 X[48169], 2 X[10] - 3 X[47808], 2 X[4088] - 3 X[48272], X[4088] - 3 X[48278], 2 X[47982] - 3 X[48086], 3 X[48122] - X[48598], 4 X[1125] - 3 X[47798], 5 X[1698] - 6 X[47806], 3 X[1734] - 4 X[4925], 5 X[3616] - 3 X[48239], 7 X[3624] - 6 X[47800], 3 X[4040] - 2 X[48014], 3 X[6332] - X[48014], 2 X[4142] - 3 X[47795], 2 X[4794] - 3 X[14432], 3 X[14349] - 2 X[47998], 4 X[19947] - 3 X[48227], 2 X[20517] - 3 X[47796], 2 X[21201] - 3 X[47832], X[47702] - 3 X[48131], X[48105] - 3 X[48300], 3 X[48616] - X[48617]

X(49278) lies on these lines: {1, 522}, {8, 48169}, {10, 47808}, {304, 20954}, {513, 47682}, {514, 4088}, {523, 48335}, {525, 4905}, {693, 23887}, {826, 3777}, {900, 48290}, {1125, 47798}, {1491, 29312}, {1577, 3810}, {1698, 47806}, {1734, 3910}, {1930, 3261}, {2254, 23876}, {2530, 29017}, {2826, 3700}, {2832, 48094}, {3616, 48239}, {3624, 47800}, {3762, 4522}, {3801, 23815}, {3904, 29066}, {3912, 47790}, {4040, 6332}, {4064, 4778}, {4142, 47795}, {4160, 48077}, {4560, 29190}, {4707, 24720}, {4761, 28468}, {4777, 47727}, {4790, 28541}, {4791, 21132}, {4794, 14432}, {4808, 29226}, {4823, 21118}, {4926, 48327}, {4951, 6550}, {4978, 23877}, {5904, 9000}, {8045, 28487}, {14349, 29142}, {16892, 29318}, {17023, 27486}, {17284, 47787}, {17496, 29062}, {19784, 48243}, {19836, 48173}, {19881, 48186}, {19947, 48227}, {20295, 29132}, {20517, 47796}, {21124, 48066}, {21130, 48182}, {21201, 29637}, {21222, 29212}, {21385, 48062}, {23765, 29354}, {23875, 48151}, {23879, 48410}, {23888, 48187}, {24719, 29029}, {29021, 47702}, {29047, 48334}, {29146, 48137}, {29160, 47652}, {29168, 48123}, {29192, 48298}, {29598, 47785}, {29633, 47828}, {47680, 48089}, {47684, 47685}, {47695, 48295}, {47725, 48398}, {48105, 48300}, {48111, 48299}, {48616, 48617}

X(49278) = midpoint of X(i) and X(j) for these {i,j}: {3904, 47687}, {47684, 47685}
X(49278) = reflection of X(i) in X(j) for these {i,j}: {3762, 4522}, {3801, 23815}, {4040, 6332}, {4707, 24720}, {21118, 4823}, {21124, 48066}, {21130, 48182}, {21132, 4791}, {21385, 48062}, {47680, 48089}, {47695, 48295}, {47725, 48398}, {47727, 48332}, {48111, 48299}, {48272, 48278}, {48324, 48290}
X(49278) = X(7236)-anticomplementary conjugate of X(149)
X(49278) = crossdifference of every pair of points on line {2183, 4290}
X(49278) = barycentric product X(514)*X(33089)
X(49278) = barycentric quotient X(33089)/X(190)


X(49279) = X(8)X(48171)∩X(10)X(48185)

Barycentrics    (b - c)*(a^3 - a^2*b + b^3 - a^2*c + b^2*c + b*c^2 + c^3) : :
X(49279) = X[8] - 3 X[48171], 2 X[10] - 3 X[48185], X[48106] - 3 X[48300], 3 X[4983] - 2 X[47983], 3 X[48123] - X[48599], 4 X[1125] - 3 X[48227], 5 X[1698] - 6 X[48199], 3 X[2530] - 2 X[48015], 3 X[6332] - X[48015], 4 X[3239] - 3 X[14431], 5 X[3616] - 3 X[48241], 7 X[3624] - 6 X[48215], 4 X[3798] - 3 X[30595], 2 X[4025] - 3 X[14419], 2 X[7178] - 3 X[47875], 3 X[14349] - 2 X[47999], 3 X[14413] - X[47930], 3 X[14432] - X[16892], 3 X[30580] - 2 X[48325], 3 X[30592] - 2 X[48398], X[47722] - 3 X[47790], X[47931] - 3 X[48131]

X(49279) lies on these lines: {8, 48171}, {10, 48185}, {512, 48106}, {513, 47682}, {514, 4010}, {522, 5592}, {523, 4775}, {525, 667}, {649, 690}, {659, 23876}, {663, 826}, {693, 29102}, {814, 7265}, {824, 48288}, {832, 4064}, {891, 48094}, {918, 4378}, {1019, 29200}, {1125, 48227}, {1577, 29082}, {1698, 48199}, {1960, 3906}, {2528, 8654}, {2530, 6332}, {2533, 29304}, {2787, 25259}, {3239, 14431}, {3566, 4834}, {3616, 48241}, {3624, 48215}, {3700, 29240}, {3798, 30595}, {3801, 29220}, {3900, 4808}, {4025, 14419}, {4040, 29017}, {4063, 29284}, {4083, 48097}, {4122, 29066}, {4170, 29025}, {4367, 23875}, {4391, 29094}, {4449, 29354}, {4707, 4874}, {4724, 29312}, {4730, 48062}, {4761, 48405}, {4794, 29318}, {4879, 29047}, {4895, 47700}, {4922, 29212}, {4990, 48403}, {6004, 48278}, {7178, 47875}, {7927, 48338}, {14077, 48088}, {14349, 47999}, {14413, 47930}, {14432, 16892}, {23877, 48305}, {28319, 48222}, {29021, 48336}, {29029, 47684}, {29110, 47729}, {29142, 48351}, {29144, 47726}, {29154, 47708}, {29160, 48349}, {29166, 47972}, {29168, 48367}, {29188, 47690}, {29202, 48331}, {29204, 47727}, {29208, 48337}, {29224, 47691}, {29246, 47715}, {29252, 48144}, {29280, 48330}, {29288, 48333}, {29298, 47707}, {29332, 47712}, {29340, 48266}, {29350, 48103}, {29358, 48294}, {29366, 47711}, {30519, 30580}, {30520, 48332}, {30592, 48398}, {47680, 48090}, {47722, 47790}, {47931, 48131}, {48295, 48326}

X(49279) = midpoint of X(i) and X(j) for these {i,j}: {4895, 47700}, {25259, 47728}, {47684, 48080}, {47726, 48352}
X(49279) = reflection of X(i) in X(j) for these {i,j}: {667, 48299}, {2530, 6332}, {4378, 48290}, {4707, 4874}, {4730, 48062}, {4761, 48405}, {47680, 48090}, {48326, 48295}, {48403, 4990}
X(49279) = barycentric product X(514)*X(33156)
X(49279) = barycentric quotient X(33156)/X(190)


X(49280) = X(72)X(521)∩X(304)X(15413)

Barycentrics    (b - c)*(-a + 2*b + 2*c)*(-a^2 + b^2 + c^2) : :
X(49280) = 3 X[905] - 2 X[4025], X[4025] - 3 X[6332], 2 X[47988] - 3 X[48091], 3 X[48128] - X[48605], 4 X[3239] - 3 X[45664], 2 X[10015] - 3 X[45664], X[4775] - 3 X[30605], X[4774] - 3 X[4951], 2 X[4791] - 3 X[4944], 3 X[4944] - X[43052], 2 X[7658] - 3 X[45683], X[47900] - 3 X[48121], X[47923] - 3 X[48131], X[48101] - 3 X[48300]

X(49280) lies on these lines: {72, 521}, {304, 15413}, {441, 525}, {513, 47682}, {514, 3700}, {650, 23876}, {826, 48136}, {891, 48088}, {1499, 48069}, {2401, 25242}, {2785, 4522}, {3239, 10015}, {3309, 48278}, {3669, 23875}, {3803, 48299}, {3900, 48272}, {3904, 25259}, {3910, 47965}, {4088, 14077}, {4130, 16601}, {4474, 28537}, {4693, 4775}, {4707, 4885}, {4774, 4951}, {4791, 4944}, {4802, 47681}, {4806, 29172}, {4926, 6161}, {4990, 21185}, {4992, 29332}, {5525, 48320}, {6051, 6129}, {6603, 28898}, {7265, 23880}, {7658, 45683}, {20295, 47684}, {22037, 29148}, {23813, 47680}, {28319, 48187}, {28475, 47728}, {29017, 48099}, {29102, 48089}, {29126, 48269}, {29312, 48029}, {29354, 48346}, {29358, 48348}, {29370, 48289}, {30520, 48335}, {47900, 48121}, {47923, 48131}, {48101, 48300}

X(49280) = midpoint of X(i) and X(j) for these {i,j}: {3904, 25259}, {20295, 47684}
X(49280) = reflection of X(i) in X(j) for these {i,j}: {905, 6332}, {3803, 48299}, {4707, 4885}, {10015, 3239}, {21185, 4990}, {43052, 4791}, {47680, 23813}
X(49280) = isotomic conjugate of the polar conjugate of X(4777)
X(49280) = X(30680)-Ceva conjugate of X(26932)
X(49280) = X(i)-isoconjugate of X(j) for these (i,j): {4, 34073}, {19, 4588}, {25, 4604}, {34, 5549}, {89, 8750}, {108, 2364}, {162, 28658}, {1783, 2163}, {1897, 28607}, {1973, 4597}, {2320, 32674}, {30588, 32676}
X(49280) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 4588), (125, 28658), (6337, 4597), (6505, 4604), (11517, 5549), (15526, 30588), (26932, 89), (34467, 28607), (35072, 2320), (36033, 34073), (36911, 1897), (38983, 2364), (39006, 2163), (40587, 1783), (40618, 39704), (40626, 30608)
X(49280) = crossdifference of every pair of points on line {25, 28658}
X(49280) = barycentric product X(i)*X(j) for these {i,j}: {45, 15413}, {63, 4791}, {69, 4777}, {304, 4893}, {305, 4775}, {306, 47683}, {337, 4800}, {345, 43052}, {348, 4944}, {525, 5235}, {693, 3940}, {905, 4671}, {1332, 4957}, {1565, 4767}, {2099, 35518}, {3267, 4273}, {3679, 4025}, {3977, 23598}, {4653, 14208}, {4720, 17094}, {4774, 7019}, {4814, 7182}, {4833, 20336}, {4931, 17206}, {5219, 6332}, {30605, 30786}
X(49280) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 4588}, {45, 1783}, {48, 34073}, {63, 4604}, {69, 4597}, {219, 5549}, {521, 2320}, {525, 30588}, {647, 28658}, {652, 2364}, {905, 89}, {1332, 5385}, {1405, 32674}, {1459, 2163}, {2099, 108}, {2177, 8750}, {3679, 1897}, {3940, 100}, {4025, 39704}, {4273, 112}, {4653, 162}, {4671, 6335}, {4720, 36797}, {4767, 15742}, {4770, 1824}, {4774, 7009}, {4775, 25}, {4777, 4}, {4791, 92}, {4800, 242}, {4814, 33}, {4833, 28}, {4867, 4242}, {4893, 19}, {4931, 1826}, {4944, 281}, {4957, 17924}, {5219, 653}, {5235, 648}, {6332, 30608}, {15413, 20569}, {22383, 28607}, {23352, 36125}, {23598, 6336}, {23884, 17923}, {30604, 407}, {30605, 468}, {36921, 1309}, {43052, 278}, {47683, 27}
X(49280) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3239, 10015, 45664}, {4944, 43052, 4791}


X(49281) = X(241)X(514)∩X(513)X(4122)

Barycentrics    (b - c)*(3*a^2 + a*b + 2*b^2 + a*c + 2*b*c + 2*c^2) : :
X(49281) = 3 X[650] - 2 X[48404], 3 X[3004] - 4 X[7658], 2 X[3004] - 3 X[47761], 2 X[3776] - 3 X[48563], 4 X[4369] - 3 X[47754], 2 X[4841] - 3 X[48560], 8 X[7658] - 9 X[47761], 4 X[11068] - 3 X[48560], 2 X[21104] - 3 X[43067], X[21104] - 3 X[48276], 4 X[31286] - 3 X[47880], 4 X[43061] - 3 X[47784], 3 X[47754] - 2 X[47960], X[47919] - 3 X[48563], 2 X[48402] - 3 X[48559], 5 X[25259] - 3 X[44449], X[25259] - 3 X[47660], 2 X[25259] - 3 X[48271], X[44449] - 5 X[47660], 2 X[44449] - 5 X[48271], 3 X[649] - X[47673], 2 X[661] - 3 X[47770], 4 X[2490] - 3 X[47783], 4 X[2516] - 3 X[47782], 4 X[2527] - 3 X[47785], 4 X[2529] - X[47653], 4 X[2529] - 3 X[47762], X[47653] - 3 X[47762], 2 X[3835] - 3 X[47881], 3 X[47881] - X[47950], and many others

X(49281) lies on these lines: {241, 514}, {513, 4122}, {523, 48060}, {649, 28894}, {661, 47770}, {693, 18074}, {812, 48397}, {824, 4790}, {900, 48067}, {2490, 47783}, {2516, 47782}, {2527, 47785}, {2529, 47653}, {3239, 47988}, {3835, 47881}, {3837, 47951}, {4024, 6008}, {4106, 6590}, {4120, 47937}, {4379, 47916}, {4380, 4777}, {4382, 48145}, {4394, 45746}, {4453, 7653}, {4468, 4977}, {4522, 4778}, {4608, 47664}, {4728, 47907}, {4762, 47671}, {4782, 4802}, {4785, 4820}, {4789, 23813}, {4874, 47961}, {4885, 47958}, {4926, 26853}, {4932, 28863}, {4940, 23731}, {4944, 48049}, {4979, 28898}, {7192, 30520}, {8045, 48128}, {14321, 47981}, {17069, 47768}, {20949, 30061}, {21146, 28195}, {23883, 48624}, {27486, 47654}, {28151, 47661}, {28165, 47658}, {28199, 47667}, {28209, 48038}, {28220, 31290}, {28840, 48087}, {28851, 48124}, {28859, 48026}, {28882, 48125}, {28910, 48117}, {31147, 47900}, {31148, 47923}, {45320, 48605}, {47651, 47780}, {47652, 47791}, {47657, 47776}, {47672, 48138}, {47677, 47763}, {47699, 48250}, {47702, 48578}, {47760, 47995}, {47772, 47939}, {47802, 47999}, {47812, 48598}, {47813, 47924}, {47832, 47902}, {47833, 48599}, {47870, 48079}, {47873, 48114}, {47925, 48253}, {47930, 48577}, {47931, 48579}, {47940, 48208}, {47945, 48236}, {47953, 48056}, {48130, 48141}, {48139, 48148}, {48142, 48146}

X(49281) = midpoint of X(i) and X(j) for these {i,j}: {4024, 48104}, {4380, 47659}, {4382, 48145}, {4608, 47664}, {7192, 47662}, {26853, 47665}, {47672, 48138}, {48101, 48275}, {48117, 48147}, {48130, 48141}, {48132, 48133}, {48139, 48148}, {48142, 48146}
X(49281) = reflection of X(i) in X(j) for these {i,j}: {4106, 6590}, {4841, 11068}, {23731, 4940}, {43067, 48276}, {45746, 4394}, {47919, 3776}, {47950, 3835}, {47951, 3837}, {47952, 4468}, {47953, 48056}, {47958, 4885}, {47960, 4369}, {47961, 4874}, {47962, 47890}, {47981, 14321}, {47988, 3239}, {48027, 48405}, {48128, 8045}, {48271, 47660}
X(49281) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4369, 47960, 47754}, {4841, 11068, 48560}, {4885, 47958, 48558}, {23731, 47874, 4940}, {45746, 48567, 4394}, {47881, 47950, 3835}, {47919, 48563, 3776}


X(49282) = X(2)X(47995)∩X(239)X(514)

Barycentrics    (b - c)*(2*a^2 + a*b + b^2 + a*c + b*c + c^2) : :
X(49282) = 3 X[649] - 2 X[21196], 4 X[649] - 3 X[27486], 7 X[649] - 6 X[45679], 4 X[3798] - 3 X[47894], 2 X[3798] - 3 X[48576], 2 X[4025] - 3 X[47763], 4 X[4765] - 3 X[46915], 4 X[4932] - 3 X[47755], 2 X[16892] - 3 X[47755], 8 X[21196] - 9 X[27486], 7 X[21196] - 9 X[45679], 4 X[21196] - 3 X[45746], 7 X[27486] - 8 X[45679], 3 X[27486] - 2 X[45746], 12 X[45679] - 7 X[45746], 2 X[45745] - 3 X[47776], X[47653] - 3 X[47763], X[47667] - 4 X[48060], X[47923] - 3 X[48577], 3 X[25259] - 2 X[44449], 3 X[25259] - 4 X[48271], X[44449] - 3 X[47660], 3 X[47660] - 2 X[48271], X[47659] + 2 X[48067], 4 X[650] - 3 X[47781], 2 X[650] - 3 X[48567], 2 X[661] - 3 X[47771], 3 X[693] - 2 X[23729], 2 X[693] - 3 X[47791], 4 X[23729] - 9 X[47791], and many others

X(49282) lies on these lines: {2, 47995}, {239, 514}, {513, 4122}, {522, 26853}, {523, 4380}, {650, 47781}, {659, 47699}, {661, 28859}, {665, 27648}, {693, 23729}, {812, 47656}, {824, 4979}, {900, 47665}, {918, 47662}, {1491, 2977}, {1635, 48404}, {2487, 3004}, {2526, 48252}, {2527, 47784}, {2529, 47761}, {3239, 47759}, {3676, 48156}, {3700, 48079}, {3716, 47938}, {3776, 31148}, {3835, 23731}, {4024, 4785}, {4106, 4789}, {4120, 48041}, {4369, 44435}, {4379, 47907}, {4394, 47782}, {4453, 47960}, {4458, 47924}, {4467, 4790}, {4468, 4778}, {4500, 48114}, {4581, 26652}, {4728, 47900}, {4762, 47674}, {4776, 47988}, {4777, 47658}, {4802, 47661}, {4813, 47769}, {4841, 31150}, {4874, 47944}, {4885, 47950}, {4897, 47677}, {4940, 47881}, {4976, 47657}, {6008, 48397}, {6084, 47675}, {6546, 25381}, {6590, 20295}, {7653, 47754}, {8045, 48121}, {8633, 47708}, {9508, 28195}, {10566, 43927}, {11068, 47775}, {14779, 28191}, {21104, 47651}, {21146, 47686}, {23879, 47976}, {24720, 47943}, {26798, 47787}, {26985, 47789}, {27013, 47768}, {27115, 43061}, {27138, 48554}, {28175, 47668}, {28209, 47939}, {28220, 47952}, {28225, 47772}, {28229, 47828}, {28481, 47718}, {28840, 48094}, {28851, 48130}, {28855, 48117}, {28863, 47971}, {28882, 47650}, {28886, 48112}, {28910, 48124}, {29270, 47678}, {30519, 48071}, {30565, 48026}, {30764, 47766}, {31209, 47767}, {43067, 47652}, {44429, 47989}, {47698, 48103}, {47701, 47798}, {47780, 48398}, {47792, 48268}, {47797, 47961}, {47804, 47998}, {47805, 48006}, {47809, 48027}, {47813, 47902}, {47821, 47983}, {47822, 47990}, {47823, 47999}, {47824, 48007}, {47870, 48269}, {47874, 47937}, {47891, 48421}, {47941, 48055}, {47945, 48062}, {47951, 48159}, {47982, 48164}, {48019, 48270}, {48029, 48250}, {48035, 48169}, {48039, 48208}, {48047, 48236}, {48402, 48565}, {48552, 48611}, {48563, 48605}, {48579, 48598}

X(49282) = midpoint of X(i) and X(j) for these {i,j}: {26853, 47659}, {47662, 48107}, {47672, 48145}, {48104, 48275}, {48130, 48147}, {48138, 48141}
X(49282) = reflection of X(i) in X(j) for these {i,j}: {693, 48276}, {4467, 4790}, {4988, 48008}, {16892, 4932}, {17494, 48060}, {20295, 6590}, {23731, 3835}, {25259, 47660}, {26853, 48067}, {31290, 4468}, {44449, 48271}, {45746, 649}, {47650, 47672}, {47651, 21104}, {47652, 43067}, {47653, 4025}, {47656, 48275}, {47657, 4976}, {47663, 48101}, {47666, 47890}, {47667, 17494}, {47676, 7192}, {47677, 4897}, {47679, 48011}, {47686, 21146}, {47698, 48103}, {47699, 659}, {47781, 48567}, {47894, 48576}, {47916, 3776}, {47924, 4458}, {47937, 48049}, {47938, 3716}, {47939, 48046}, {47941, 48055}, {47943, 24720}, {47944, 4874}, {47945, 48062}, {47950, 4885}, {47958, 4369}, {47981, 3239}, {48019, 48270}, {48079, 3700}, {48114, 4500}, {48121, 8045}
X(49282) = anticomplement of X(47995)
X(49282) = crossdifference of every pair of points on line {42, 2241}
X(49282) = barycentric product X(514)*X(17381)
X(49282) = barycentric quotient X(17381)/X(190)
X(49282) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 45746, 27486}, {693, 48276, 47791}, {3239, 47981, 47759}, {3835, 23731, 48543}, {4369, 47958, 44435}, {4885, 47950, 48550}, {4932, 16892, 47755}, {6590, 20295, 47790}, {31148, 47916, 3776}, {31290, 47773, 4468}, {43061, 47783, 27115}, {44449, 47660, 48271}, {44449, 48271, 25259}, {47653, 47763, 4025}, {47874, 47937, 48049}, {47939, 48557, 48046}


X(49283) = X(2)X(47998)∩X(422)X(2501)

Barycentrics    (b - c)*(a^3 + 3*a^2*b + a*b^2 + b^3 + 3*a^2*c + 3*a*b*c + 2*b^2*c + a*c^2 + 2*b*c^2 + c^3) : :
X(49283) = 2 X[659] - 3 X[48567], 2 X[661] - 3 X[47809], 4 X[676] - 3 X[48158], 2 X[1491] - 3 X[48252], 4 X[2977] - 3 X[47775], 2 X[3004] - 3 X[47824], 4 X[3676] - 3 X[48174], 2 X[3776] - 3 X[48579], X[47924] - 3 X[48579], 4 X[3837] - 3 X[48550], 2 X[47944] - 3 X[48550], 2 X[4010] - 3 X[4789], 4 X[4369] - 3 X[47797], 2 X[47701] - 3 X[47797], 2 X[4458] - 3 X[31148], 3 X[31148] - X[47702], 2 X[4468] - 3 X[48236], X[47941] - 3 X[48236], 2 X[4724] - 3 X[48250], and many others

X(49283) lies on these lines: {2, 47998}, {422, 2501}, {513, 4122}, {514, 1734}, {522, 4838}, {523, 4467}, {650, 47699}, {659, 48567}, {661, 47809}, {676, 48158}, {812, 47703}, {918, 47693}, {1491, 48252}, {2977, 47775}, {3004, 47824}, {3239, 47979}, {3676, 48174}, {3776, 47924}, {3800, 17166}, {3835, 47938}, {3837, 47944}, {4010, 4789}, {4088, 28840}, {4369, 47701}, {4458, 31148}, {4468, 47941}, {4522, 4813}, {4724, 48250}, {4776, 47983}, {4778, 47903}, {4802, 47654}, {4822, 8045}, {4841, 47825}, {4874, 48161}, {4913, 4988}, {4925, 48157}, {4963, 4977}, {6546, 48001}, {6590, 48080}, {7659, 28894}, {7662, 47791}, {9508, 47782}, {12073, 48291}, {15309, 47711}, {20295, 48396}, {21104, 47688}, {21146, 47652}, {23729, 48170}, {23731, 48050}, {23755, 29116}, {23770, 47780}, {24720, 47958}, {24721, 28859}, {28147, 47673}, {28209, 48083}, {28220, 48097}, {28225, 48078}, {28851, 48118}, {28882, 48119}, {29037, 48149}, {29062, 48110}, {29144, 47695}, {29190, 47976}, {30565, 48024}, {31290, 48047}, {36848, 47999}, {43067, 47691}, {44429, 47995}, {44433, 47972}, {44435, 47961}, {47650, 48126}, {47666, 48062}, {47689, 48107}, {47694, 48276}, {47700, 48147}, {47771, 48029}, {47773, 48055}, {47804, 48006}, {47808, 48027}, {47812, 47902}, {47828, 48404}, {47836, 48402}, {47871, 48098}, {47874, 48043}, {47890, 47969}, {47946, 48056}, {47989, 48164}, {48028, 48185}, {48030, 48235}, {48040, 48557}, {48046, 48171}, {48115, 48145}

X(49283) = midpoint of X(i) and X(j) for these {i,j}: {47689, 48107}, {47700, 48147}, {48115, 48145}, {48146, 48148}
X(49283) = reflection of X(i) in X(j) for these {i,j}: {4467, 4784}, {4813, 4522}, {4822, 8045}, {4988, 4913}, {20295, 48396}, {23731, 48050}, {31290, 48047}, {44449, 4122}, {47650, 48126}, {47652, 21146}, {47666, 48062}, {47688, 21104}, {47691, 43067}, {47694, 48276}, {47699, 650}, {47701, 4369}, {47702, 4458}, {47924, 3776}, {47938, 3835}, {47941, 4468}, {47944, 3837}, {47946, 48056}, {47958, 24720}, {47969, 47890}, {47973, 48073}, {47975, 48069}, {47979, 3239}, {48024, 48405}, {48080, 6590}, {48408, 48106}
X(49283) = anticomplement of X(47998)
X(49283) = crossdifference of every pair of points on line {2280, 20970}
X(49283) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3837, 47944, 48550}, {4369, 47701, 47797}, {24720, 47958, 48159}, {31148, 47702, 4458}, {31290, 48208, 48047}, {47924, 48579, 3776}, {47941, 48236, 4468}, {48024, 48405, 30565}


X(49284) = X(9)X(649)∩X(513)X(3700)

Barycentrics    (b - c)*(-3*a^2 - 4*a*b + b^2 - 4*a*c + 2*b*c + c^2) : :
X(49284) = 3 X[649] - 4 X[4521], 7 X[649] - 9 X[6544], 2 X[649] - 3 X[47765], 28 X[4521] - 27 X[6544], 8 X[4521] - 9 X[47765], 6 X[6544] - 7 X[47765], 4 X[3700] - 3 X[6590], 2 X[3700] - 3 X[48269], 5 X[3700] - 3 X[48276], 8 X[4949] - 3 X[6590], 4 X[4949] - 3 X[48269], 10 X[4949] - 3 X[48276], 5 X[6590] - 4 X[48276], 5 X[48269] - 2 X[48276], X[4838] + 3 X[48019], X[4838] - 3 X[48266], 3 X[4813] - X[4988], 2 X[650] - 3 X[47764], 3 X[661] - 2 X[4765], 4 X[661] - 3 X[47883], and many others

X(49284) lies on these lines: {9, 649}, {513, 3700}, {514, 4838}, {522, 4813}, {650, 28217}, {661, 3667}, {812, 48038}, {824, 47981}, {900, 45745}, {1635, 14351}, {1839, 3064}, {2527, 4790}, {2786, 47995}, {3239, 4979}, {3676, 4654}, {3798, 4776}, {3835, 5249}, {4024, 4778}, {4025, 28867}, {4369, 47786}, {4382, 28878}, {4468, 4785}, {4784, 47806}, {4786, 25666}, {4806, 47800}, {4820, 4977}, {4841, 4926}, {4885, 48574}, {4897, 4940}, {4932, 47787}, {4958, 28225}, {4962, 48277}, {5904, 29350}, {5905, 20295}, {6008, 48046}, {7659, 48545}, {11068, 26853}, {15599, 41853}, {21211, 30023}, {26798, 47755}, {28209, 48397}, {28292, 41869}, {28840, 48268}, {28898, 47988}, {28902, 48125}, {29078, 47983}, {30835, 41867}, {48060, 48270}

X(49284) = midpoint of X(i) and X(j) for these {i,j}: {44449, 48079}, {48019, 48266}, {48076, 48114}
X(49284) = reflection of X(i) in X(j) for these {i,j}: {3700, 4949}, {4025, 48049}, {4790, 14321}, {4897, 4940}, {4979, 3239}, {6590, 48269}, {26853, 11068}, {45745, 48026}, {47978, 48592}, {47995, 48041}, {48013, 3835}, {48014, 48037}, {48060, 48270}, {48398, 20295}
X(49284) = crossdifference of every pair of points on line {1149, 7373}
X(49284) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3239, 4979, 47768}, {3700, 4949, 48269}, {3835, 48013, 47758}, {4025, 48049, 48554}, {4790, 14321, 47766}, {4897, 4940, 47757}, {26853, 47769, 11068}


X(49285) = X(513)X(3700)∩X(514)X(4088)

Barycentrics    (b - c)*(-a^3 + a^2*b - a*b^2 + b^3 + a^2*c + 2*a*b*c + 3*b^2*c - a*c^2 + 3*b*c^2 + c^3) : :
X(49285) = 3 X[46403] - X[47686], 3 X[46403] + X[47693], X[47686] + 3 X[47690], 3 X[47690] - X[47693], 3 X[693] - X[47695], 2 X[3676] - 3 X[47812], 2 X[4458] - 3 X[21183], X[47123] + 2 X[47687], 3 X[47123] - 2 X[47695], 3 X[47687] + X[47695], 2 X[650] - 3 X[47806], 2 X[659] - 3 X[47766], 2 X[676] - 3 X[45320], 2 X[1491] - 3 X[48545], and many others

X(49285) lies on these lines: {513, 3700}, {514, 4088}, {522, 693}, {523, 2525}, {650, 47806}, {659, 47766}, {676, 45320}, {812, 48069}, {824, 48015}, {900, 7659}, {1491, 45745}, {2505, 28183}, {2517, 47136}, {2523, 6591}, {2786, 48073}, {2977, 48200}, {3239, 4724}, {3667, 4932}, {3669, 29278}, {3716, 47787}, {3798, 47824}, {3835, 48006}, {3837, 47757}, {3900, 48280}, {3904, 47721}, {4380, 48252}, {4394, 48232}, {4468, 4522}, {4521, 47811}, {4728, 47972}, {4765, 47828}, {4777, 23770}, {4778, 47660}, {4789, 6006}, {4823, 21175}, {4874, 47801}, {4885, 47800}, {4951, 48083}, {4962, 47834}, {4977, 48087}, {6332, 29051}, {11068, 47809}, {13246, 47779}, {17494, 47808}, {18004, 48040}, {23789, 29062}, {23815, 29086}, {24623, 47789}, {25380, 47785}, {26824, 48169}, {26985, 47798}, {28147, 47652}, {28155, 47688}, {28161, 47691}, {28169, 47692}, {28191, 47651}, {28221, 47132}, {28225, 47696}, {28229, 47662}, {28846, 48108}, {28878, 48148}, {29074, 48406}, {29362, 48062}, {30565, 47974}, {31131, 47975}, {45746, 48164}, {47661, 48175}, {47663, 48208}, {47672, 48077}, {47723, 48335}, {47764, 48024}, {47765, 48029}, {47786, 48043}, {47874, 48032}, {47883, 48182}, {47979, 48049}, {47995, 48050}, {47998, 48554}, {48020, 48275}, {48036, 48270}, {48094, 48115}, {48187, 48408}

X(49285) = midpoint of X(i) and X(j) for these {i,j}: {693, 47687}, {3904, 47721}, {4088, 48119}, {21301, 47719}, {46403, 47690}, {47652, 47689}, {47660, 47685}, {47672, 48077}, {47686, 47693}, {47703, 48023}, {47723, 48335}, {48020, 48275}, {48094, 48115}
X(49285) = reflection of X(i) in X(j) for these {i,j}: {4025, 24720}, {4468, 4522}, {4724, 3239}, {6590, 48396}, {21185, 4823}, {45745, 1491}, {47123, 693}, {47136, 2517}, {47883, 48182}, {47979, 48049}, {47982, 48042}, {47995, 48050}, {48006, 3835}, {48014, 3716}, {48036, 48270}, {48040, 18004}, {48398, 48089}
X(49285) = crossdifference of every pair of points on line {41, 16466}
X(49285) = barycentric product X(4327)*X(4391)
X(49285) = barycentric quotient X(4327)/X(651)
X(49285) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3239, 4724, 48546}, {45745, 48545, 1491}, {46403, 47693, 47686}, {47686, 47690, 47693}, {47787, 48014, 3716}


X(49286) = X(513)X(3700)∩X(514)X(4010)

Barycentrics    (b - c)*(a^3 - a^2*b + a*b^2 + b^3 - a^2*c + 3*b^2*c + a*c^2 + 3*b*c^2 + c^3) : :
X(49286) = X[2254] - 3 X[47874], X[2526] - 3 X[4944], 2 X[2977] - 3 X[47770], 2 X[3004] - 3 X[48555], 2 X[3676] - 3 X[47833], 2 X[3837] - 3 X[47787], 3 X[47787] - X[48015], 3 X[4120] - X[48023], X[4380] - 3 X[48250], 2 X[4394] - 3 X[48231], X[4467] - 3 X[47804], 4 X[4521] - 3 X[47827], 3 X[4728] - X[47973], 2 X[4765] - 3 X[48226], and many others

X(49286) lies on these lines: {513, 3700}, {514, 4010}, {522, 659}, {523, 4468}, {824, 3716}, {826, 21185}, {900, 48069}, {918, 7662}, {1491, 3239}, {2254, 47874}, {2526, 4944}, {2977, 47770}, {3004, 48555}, {3309, 48395}, {3676, 47833}, {3803, 29232}, {3835, 48007}, {3837, 47787}, {4024, 4724}, {4025, 4874}, {4106, 4977}, {4120, 48023}, {4380, 48250}, {4382, 48102}, {4394, 48231}, {4458, 30519}, {4467, 47804}, {4521, 47827}, {4728, 47973}, {4762, 48055}, {4765, 48226}, {4774, 28292}, {4777, 48056}, {4778, 24719}, {4789, 48108}, {4802, 48048}, {4804, 48094}, {4806, 47995}, {4818, 25666}, {4925, 48200}, {4926, 48247}, {4931, 48032}, {4940, 47989}, {4948, 45670}, {4988, 47826}, {4990, 48136}, {6084, 48096}, {7659, 47881}, {9508, 47766}, {14321, 48027}, {14837, 47872}, {16892, 47832}, {17069, 47803}, {18004, 48039}, {20295, 47696}, {21188, 47875}, {21201, 29318}, {21212, 47831}, {21297, 47686}, {23729, 28195}, {23770, 30520}, {23880, 48299}, {25259, 47694}, {25380, 47879}, {28147, 48349}, {28894, 47998}, {29078, 48248}, {29278, 48329}, {29328, 48060}, {29362, 48061}, {30565, 47975}, {31147, 47943}, {45745, 48546}, {45746, 47821}, {46403, 47790}, {47656, 47969}, {47659, 47699}, {47660, 48080}, {47671, 47927}, {47672, 48078}, {47676, 47834}, {47677, 47797}, {47690, 47870}, {47691, 48172}, {47698, 47772}, {47703, 47873}, {47704, 48117}, {47765, 48030}, {47769, 47945}, {47786, 47982}, {47811, 48277}, {47813, 47971}, {47887, 47930}, {47974, 48423}, {47999, 48554}, {48021, 48275}, {48082, 48142}, {48090, 48398}, {48119, 48416}, {48189, 48326}, {48264, 48300}, {48408, 48557}

X(49286) = midpoint of X(i) and X(j) for these {i,j}: {4024, 4724}, {4382, 48102}, {4804, 48094}, {20295, 47696}, {25259, 47694}, {47656, 47969}, {47659, 47699}, {47660, 48080}, {47671, 47927}, {47672, 48078}, {47704, 48117}, {48021, 48275}, {48061, 48268}, {48082, 48142}, {48083, 48120}, {48264, 48300}
X(49286) = reflection of X(i) in X(j) for these {i,j}: {1491, 3239}, {4025, 4874}, {4818, 25666}, {4948, 45670}, {47983, 48043}, {47989, 4940}, {47995, 4806}, {48007, 3835}, {48015, 3837}, {48027, 14321}, {48039, 18004}, {48069, 48405}, {48136, 4990}, {48398, 48090}
X(49286) = crossdifference of every pair of points on line {2275, 5021}
X(49286) = {X(47787),X(48015)}-harmonic conjugate of X(3837)


X(49287) = X(513)X(48394)∩X(514)X(4024)

Barycentrics    (b - c)*(-2*a^2 - a*b - a*c + 3*b*c) : :
X(49287) = 3 X[4382] + X[4813], 3 X[4382] - X[26824], 5 X[4382] + X[31290], 7 X[4382] + X[47908], 4 X[4382] + X[47984], 2 X[4382] + X[48041], X[4813] - 3 X[20295], 5 X[4813] - 3 X[31290], 7 X[4813] - 3 X[47908], 4 X[4813] - 3 X[47984], 2 X[4813] - 3 X[48041], 3 X[20295] + X[26824], 5 X[20295] - X[31290], and many others

X(49287) lies on these lines: {513, 48394}, {514, 4024}, {522, 4810}, {523, 47985}, {649, 21297}, {650, 812}, {659, 48547}, {661, 47664}, {693, 4785}, {802, 4526}, {824, 23729}, {900, 3776}, {2786, 48398}, {3667, 46403}, {3676, 24721}, {3700, 28882}, {3798, 21204}, {3837, 48575}, {3960, 23724}, {4010, 48063}, {4063, 28398}, {4120, 47663}, {4369, 6008}, {4379, 26853}, {4380, 4728}, {4394, 4928}, {4449, 28525}, {4762, 47996}, {4776, 47932}, {4782, 47831}, {4789, 48104}, {4800, 8689}, {4814, 21301}, {4820, 28863}, {4885, 45313}, {4893, 26798}, {4895, 28470}, {4897, 48415}, {4931, 47662}, {4940, 48000}, {4988, 48543}, {4992, 29238}, {6009, 14321}, {6084, 48270}, {7658, 45679}, {11068, 45661}, {17494, 31147}, {20979, 29738}, {21104, 28867}, {21118, 28515}, {24720, 29328}, {27673, 48011}, {28155, 47945}, {28161, 48023}, {28225, 48119}, {28840, 48125}, {28859, 48274}, {28906, 47676}, {29270, 30094}, {29340, 48325}, {29362, 48009}, {30519, 47652}, {30835, 47776}, {31182, 45684}, {31209, 45339}, {43067, 48071}, {47654, 47958}, {47665, 47916}, {47672, 48079}, {47675, 48019}, {47755, 48414}, {47759, 47926}, {47790, 48101}, {47791, 48418}, {47869, 48141}, {47870, 48138}, {47871, 47971}, {48017, 48050}, {48073, 48089}, {48276, 48417}, {48277, 48550}

X(49287) = midpoint of X(i) and X(j) for these {i,j}: {693, 48114}, {4382, 20295}, {4810, 24719}, {4813, 26824}, {23731, 47656}, {47650, 48082}, {47652, 48266}, {47659, 47907}, {47665, 47916}, {47672, 48079}, {47675, 48019}
X(49287) = reflection of X(i) in X(j) for these {i,j}: {3835, 4106}, {4369, 23813}, {4380, 31286}, {4897, 48415}, {4932, 693}, {47779, 21297}, {47984, 48041}, {47996, 48049}, {48000, 4940}, {48008, 3835}, {48009, 48043}, {48016, 4369}, {48017, 48050}, {48041, 20295}, {48042, 24719}, {48063, 4010}, {48071, 43067}, {48073, 48089}, {48276, 48417}
X(49287) = crossdifference of every pair of points on line {2308, 7296}
X(49287) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3835, 48008, 47778}, {4380, 4728, 31286}, {4382, 4813, 26824}, {20295, 26824, 4813}


X(49288) = X(1)X(25259)∩X(10)X(3239)

Barycentrics    (b - c)*(a^3 - 2*a^2*b + b^3 - 2*a^2*c + 2*b^2*c + 2*b*c^2 + c^3) : :
X(49288) = X[676] - 3 X[4990], 4 X[676] - 3 X[20517], 4 X[4990] - X[20517], X[4707] - 3 X[47832], X[4730] - 3 X[48185], X[4761] - 3 X[47874], 4 X[7658] - 5 X[19862], 3 X[14432] - X[48321], 3 X[19883] - 2 X[44551], X[21124] - 3 X[47838], X[47724] - 3 X[47790], 3 X[47772] + X[48304]

X(49288) lies on these lines: {1, 25259}, {10, 3239}, {512, 48405}, {514, 4010}, {522, 4794}, {525, 676}, {663, 7265}, {667, 29216}, {690, 4874}, {918, 48295}, {1125, 4025}, {1577, 29304}, {1960, 29078}, {2785, 4791}, {3700, 29066}, {3716, 23876}, {3743, 6589}, {3887, 4522}, {4040, 29190}, {4088, 48339}, {4122, 4775}, {4160, 48270}, {4170, 29158}, {4707, 47832}, {4730, 48185}, {4761, 47874}, {5592, 29033}, {6005, 8045}, {6332, 8714}, {7649, 44427}, {7658, 19862}, {11263, 46396}, {14432, 48321}, {17894, 42031}, {19883, 44551}, {21124, 47838}, {23879, 48099}, {29013, 48299}, {29037, 48294}, {29090, 48330}, {29102, 48090}, {29106, 48331}, {29132, 47682}, {29148, 48290}, {29220, 48403}, {47681, 47699}, {47690, 48352}, {47707, 48337}, {47711, 48338}, {47715, 48367}, {47724, 47790}, {47772, 48304}

X(49288) = midpoint of X(i) and X(j) for these {i,j}: {1, 25259}, {663, 7265}, {4088, 48339}, {4122, 4775}, {4170, 48300}, {47681, 47699}, {47682, 48080}, {47690, 48352}, {47707, 48337}, {47711, 48338}, {47715, 48367}
X(49288) = reflection of X(i) in X(j) for these {i,j}: {10, 3239}, {4025, 1125}


X(49289) = X(2)X(47932)∩X(513)X(48394)

Barycentrics    (b - c)*(-a^2 + 3*b*c) : :
X(49289) = 7 X[4106] - X[47914], 5 X[4106] - X[47952], 4 X[4106] - X[47991], 3 X[4106] - X[48026], 5 X[47914] - 7 X[47952], 4 X[47914] - 7 X[47991], 3 X[47914] - 7 X[48026], 2 X[47914] - 7 X[48049], X[47914] + 7 X[48125], 4 X[47952] - 5 X[47991], 3 X[47952] - 5 X[48026], 2 X[47952] - 5 X[48049], X[47952] + 5 X[48125], 3 X[47991] - 4 X[48026], and many others

X(49289) lies on these lines: {2, 47932}, {513, 48394}, {514, 3700}, {522, 3776}, {523, 47999}, {649, 693}, {650, 4928}, {661, 21297}, {814, 4504}, {824, 48268}, {1577, 18071}, {1635, 26985}, {1960, 29070}, {2254, 48170}, {2487, 45679}, {2516, 4763}, {2526, 28161}, {2786, 21104}, {3676, 48413}, {3716, 29362}, {3768, 20954}, {3835, 4762}, {3837, 4913}, {3887, 44319}, {3907, 21343}, {4024, 28863}, {4025, 48415}, {4394, 47779}, {4453, 48414}, {4467, 6545}, {4728, 17494}, {4750, 48412}, {4765, 47882}, {4775, 29051}, {4776, 47926}, {4778, 48126}, {4785, 43067}, {4789, 48101}, {4802, 47992}, {4804, 46403}, {4806, 48001}, {4810, 21146}, {4813, 47675}, {4820, 30519}, {4823, 29302}, {4830, 4874}, {4838, 47653}, {4893, 47664}, {4927, 4976}, {4932, 6008}, {4940, 47996}, {4949, 28910}, {4978, 6002}, {4979, 47780}, {4988, 48550}, {6590, 28882}, {7192, 48114}, {9404, 40166}, {11068, 47879}, {16892, 47871}, {17069, 21204}, {20295, 28840}, {24719, 48120}, {24924, 47776}, {25259, 28890}, {25380, 48184}, {26853, 31148}, {27013, 45663}, {28147, 48027}, {28191, 47953}, {28521, 48339}, {28851, 48269}, {28871, 44449}, {29033, 48295}, {29328, 48098}, {30592, 48288}, {30835, 31150}, {31147, 47666}, {31209, 45678}, {31286, 45320}, {44435, 48277}, {47650, 47790}, {47651, 48423}, {47656, 47958}, {47659, 47916}, {47660, 48416}, {47662, 47873}, {47663, 47874}, {47665, 47923}, {47673, 48156}, {47674, 48543}, {47676, 48266}, {47759, 47917}, {47791, 48104}, {47870, 48130}, {48032, 48172}, {48079, 48141}, {48080, 48119}

X(49289) = midpoint of X(i) and X(j) for these {i,j}: {661, 26824}, {693, 4382}, {4024, 47652}, {4106, 48125}, {4804, 46403}, {4810, 21146}, {4813, 47675}, {4838, 47653}, {7192, 48114}, {20295, 47672}, {23729, 48274}, {24719, 48120}, {47650, 48094}, {47656, 47958}, {47659, 47916}, {47665, 47923}, {47676, 48266}, {48079, 48141}, {48080, 48119}, {48268, 48398}
X(49289) = reflection of X(i) in X(j) for these {i,j}: {3716, 48090}, {3835, 23813}, {4025, 48415}, {4369, 693}, {4830, 4874}, {4913, 3837}, {4976, 21212}, {6590, 48417}, {17494, 25666}, {47991, 48049}, {47996, 4940}, {48000, 3835}, {48001, 4806}, {48008, 4885}, {48049, 4106}
X(49289) = complement of X(47932)
X(49289) = barycentric product X(i)*X(j) for these {i,j}: {514, 17117}, {693, 17123}
X(49289) = barycentric quotient X(i)/X(j) for these {i,j}: {17117, 190}, {17123, 100}
X(49289) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 4380, 4379}, {3835, 48000, 45315}, {4728, 17494, 25666}, {4885, 48008, 4763}, {4927, 4976, 21212}, {20295, 47869, 47672}, {21297, 26824, 661}, {47650, 47790, 48094}, {47662, 48424, 47873}, {48101, 48418, 4789}


X(49290) = X(1)X(4122)∩X(512)X(8045)

Barycentrics    (b - c)*(a^3 - a^2*b + b^3 - a^2*c + a*b*c + 2*b^2*c + 2*b*c^2 + c^3) : :
X(49290) = X[4024] + 3 X[14432], 3 X[14432] - X[48288], X[4467] - 3 X[14419], X[4707] - 3 X[47833], X[4730] - 3 X[47809], X[21124] - 3 X[47839], 3 X[30592] - X[47652], X[47728] + 3 X[47790], 3 X[47870] + X[48298], 3 X[48171] + X[48304]

X(49290) lies on these lines: {1, 4122}, {512, 8045}, {514, 4806}, {522, 1960}, {663, 29086}, {667, 29106}, {690, 4369}, {693, 29102}, {784, 6332}, {1577, 29094}, {2605, 23282}, {2787, 3700}, {3716, 29312}, {3743, 14838}, {3906, 4458}, {4010, 29029}, {4024, 14432}, {4064, 39547}, {4088, 48291}, {4142, 29256}, {4160, 18004}, {4367, 7265}, {4378, 25259}, {4467, 14419}, {4504, 29264}, {4707, 47833}, {4730, 47809}, {4775, 47690}, {4789, 30605}, {4823, 29082}, {4874, 23876}, {4879, 47711}, {4931, 30580}, {4990, 29142}, {6161, 47687}, {20517, 29202}, {21124, 47839}, {23770, 29224}, {29037, 48328}, {29062, 48330}, {29070, 48299}, {29074, 48294}, {29098, 48273}, {29154, 48403}, {29188, 48396}, {29190, 48331}, {29212, 48344}, {29298, 48395}, {29350, 48405}, {30592, 47652}, {47707, 48333}, {47715, 48336}, {47719, 48351}, {47726, 48349}, {47728, 47790}, {47870, 48298}, {48171, 48304}, {48271, 48332}, {48272, 48301}, {48278, 48305}

X(49290) = midpoint of X(i) and X(j) for these {i,j}: {1, 4122}, {2605, 23282}, {3700, 48290}, {4010, 47682}, {4024, 48288}, {4064, 39547}, {4088, 48291}, {4367, 7265}, {4378, 25259}, {4775, 47690}, {4789, 30605}, {4879, 47711}, {4931, 30580}, {6161, 47687}, {47707, 48333}, {47715, 48336}, {47719, 48351}, {47726, 48349}, {48271, 48332}, {48272, 48301}, {48273, 48300}, {48278, 48305}
X(49290) = {X(4024),X(14432)}-harmonic conjugate of X(48288)


X(49291) = X(241)X(514)∩X(513)X(48394)

Barycentrics    (b - c)*(a^2 + 2*a*b + 2*a*c + 3*b*c) : :
X(49291) = 2 X[650] - 3 X[4369], 8 X[650] - 9 X[4763], 5 X[650] - 6 X[31286], X[650] - 3 X[43067], 7 X[650] - 9 X[47761], 7 X[650] - 3 X[47920], 5 X[650] - 3 X[47962], 4 X[650] - 3 X[48000], X[650] + 3 X[48133], 11 X[650] - 9 X[48560], 5 X[650] - 9 X[48563], 4 X[4369] - 3 X[4763], 5 X[4369] - 4 X[31286], and many others

X(49291) lies on these lines: {2, 47917}, {241, 514}, {513, 48394}, {522, 48134}, {649, 47664}, {661, 4928}, {693, 4813}, {812, 4979}, {2786, 48274}, {3700, 28855}, {3716, 4977}, {3762, 18154}, {3835, 47991}, {3837, 47992}, {4379, 25666}, {4380, 48577}, {4382, 48107}, {4453, 4988}, {4467, 47671}, {4500, 28846}, {4507, 29226}, {4608, 47673}, {4728, 31290}, {4750, 47661}, {4762, 4932}, {4776, 47908}, {4778, 7662}, {4785, 48125}, {4789, 48082}, {4802, 4913}, {4820, 28906}, {4824, 25380}, {4842, 35519}, {4874, 28195}, {4885, 45315}, {4895, 17166}, {4940, 47984}, {4960, 4978}, {6008, 48071}, {6545, 27929}, {6590, 28851}, {7234, 48323}, {7653, 45313}, {7659, 28161}, {9508, 28175}, {16892, 47654}, {17161, 47670}, {17494, 31148}, {20295, 48147}, {21115, 47653}, {21116, 47652}, {21297, 48019}, {23731, 47871}, {23813, 48041}, {24666, 47929}, {24924, 47775}, {25259, 28871}, {26248, 48156}, {28229, 48029}, {28859, 48398}, {28863, 47676}, {28867, 48268}, {28878, 48270}, {28886, 48269}, {28890, 47660}, {29328, 48127}, {29362, 48135}, {30519, 48397}, {30835, 48548}, {31209, 45663}, {44429, 47909}, {44449, 48416}, {45320, 47952}, {47650, 48104}, {47656, 47971}, {47658, 48428}, {47659, 47930}, {47667, 47886}, {47669, 47894}, {47674, 47755}, {47694, 48148}, {47699, 47887}, {47759, 47903}, {47760, 47914}, {47762, 47926}, {47763, 47932}, {47790, 48076}, {47791, 48094}, {47802, 48608}, {47803, 48619}, {47804, 47927}, {47805, 47933}, {47812, 47945}, {47813, 47969}, {47821, 47904}, {47822, 47910}, {47823, 47928}, {47824, 47934}, {47832, 47941}, {47833, 47946}, {47834, 48021}, {47869, 48114}, {47870, 48112}, {47954, 48221}, {47974, 48578}, {47975, 48579}, {47995, 48415}, {48024, 48238}, {48050, 48098}, {48108, 48142}, {48164, 48583}, {48197, 48610}, {48216, 48620}, {48414, 48550}

X(49291) = midpoint of X(i) and X(j) for these {i,j}: {649, 47675}, {693, 48141}, {4382, 48107}, {4467, 47671}, {4608, 47673}, {4960, 4978}, {4979, 26824}, {7192, 47672}, {17161, 47670}, {20295, 48147}, {43067, 48133}, {47650, 48104}, {47656, 47971}, {47658, 48428}, {47659, 47930}, {47674, 48277}, {47676, 48275}, {47694, 48148}, {48108, 48142}
X(49291) = reflection of X(i) in X(j) for these {i,j}: {4369, 43067}, {4824, 25380}, {4841, 21212}, {4928, 47780}, {47666, 25666}, {47962, 31286}, {47984, 4940}, {47991, 3835}, {47992, 3837}, {47995, 48415}, {47996, 4885}, {48000, 4369}, {48001, 4874}, {48041, 23813}, {48049, 693}, {48050, 48098}, {48269, 48417}, {48404, 3676}
X(49291) = complement of X(47917)
X(49291) = barycentric product X(i)*X(j) for these {i,j}: {693, 4038}, {7192, 27798}, {16727, 24052}
X(49291) = barycentric quotient X(i)/X(j) for these {i,j}: {4038, 100}, {27798, 3952}
X(49291) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 47939, 31147}, {4369, 48000, 4763}, {4379, 47666, 25666}, {4608, 48571, 47673}, {4824, 48253, 25380}, {4841, 47891, 21212}, {4885, 47996, 45315}, {4979, 47672, 26824}, {7192, 26824, 4979}, {31286, 48563, 4369}, {43067, 47962, 48563}, {47674, 47755, 48277}, {47962, 48563, 31286}


X(49292) = X(2)X(47934)∩X(513)X(48394)

Barycentrics    (b - c)*(a^3 + a^2*b + 2*a*b^2 + a^2*c + 5*a*b*c + 3*b^2*c + 2*a*c^2 + 3*b*c^2) : :
X(49292) = 5 X[3716] - 2 X[47963], 3 X[3716] - 2 X[48029], X[3716] + 2 X[48134], 7 X[3716] - 2 X[48619], 5 X[7662] - X[47963], 4 X[7662] - X[48001], 3 X[7662] - X[48029], 7 X[7662] - X[48619], 4 X[47963] - 5 X[48001], 3 X[47963] - 5 X[48029], and many others

X(49292) lies on these lines: {2, 47934}, {513, 48394}, {514, 3716}, {522, 4897}, {523, 2487}, {650, 28147}, {661, 47834}, {693, 47940}, {812, 48120}, {1491, 48238}, {2254, 47780}, {3676, 4818}, {3835, 47992}, {3907, 17166}, {4010, 28840}, {4086, 18154}, {4088, 4789}, {4170, 4960}, {4379, 25380}, {4608, 26248}, {4724, 47675}, {4728, 47945}, {4762, 4830}, {4763, 28151}, {4776, 47909}, {4778, 23729}, {4800, 47946}, {4802, 4874}, {4804, 7192}, {4806, 47991}, {4815, 18155}, {4824, 25666}, {4885, 48010}, {4928, 48030}, {4948, 45663}, {4988, 47797}, {6002, 48393}, {17494, 47813}, {24924, 47825}, {26985, 47810}, {28155, 31286}, {28169, 48563}, {28191, 47962}, {28863, 48326}, {29051, 48324}, {29362, 48127}, {30835, 48549}, {45315, 48002}, {45328, 48017}, {45746, 47887}, {46403, 48153}, {47660, 47704}, {47666, 47832}, {47672, 47694}, {47673, 48241}, {47674, 47798}, {47691, 48275}, {47693, 47705}, {47695, 47703}, {47697, 48119}, {47698, 47874}, {47791, 48106}, {47804, 47926}, {47821, 47917}, {47822, 47928}, {47871, 47943}, {47964, 48202}, {48007, 48415}, {48020, 48170}, {48021, 48172}, {48024, 48189}, {48049, 48090}, {48080, 48141}, {48159, 48414}

X(49292) = midpoint of X(i) and X(j) for these {i,j}: {693, 48142}, {4170, 4960}, {4724, 47675}, {4804, 7192}, {7662, 48134}, {46403, 48153}, {47660, 47704}, {47672, 47694}, {47691, 48275}, {47693, 47705}, {47695, 47703}, {47697, 48119}, {48080, 48141}
X(49292) = reflection of X(i) in X(j) for these {i,j}: {3716, 7662}, {4818, 3676}, {4824, 25666}, {4913, 4369}, {4948, 45663}, {47975, 25380}, {47991, 4806}, {47992, 3835}, {48000, 4874}, {48001, 3716}, {48007, 48415}, {48010, 4885}, {48049, 48090}, {48050, 693}
X(49292) = complement of X(47934)
X(49292) = crossdifference of every pair of points on line {5217, 18755}
X(49292) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4379, 47975, 25380}, {4824, 47833, 25666}, {4874, 48000, 48562}, {47675, 48237, 4724}


X(49293) = X(239)X(514)∩X(513)X(3700)

Barycentrics    (b - c)*(3*a^2 + 2*a*b + b^2 + 2*a*c + 2*b*c + c^2) : :
X(49293) = 3 X[649] - 2 X[4765], 3 X[649] - X[4988], 9 X[649] - 8 X[14351], 11 X[649] - 9 X[14435], 2 X[649] - 3 X[48576], 2 X[3798] - 3 X[47763], 2 X[4025] - 3 X[48574], 3 X[4765] - 4 X[14351], 22 X[4765] - 27 X[14435], 4 X[4765] - 3 X[45745], and many others

X(49293) lies on these lines: {239, 514}, {513, 3700}, {522, 4838}, {523, 4790}, {650, 2523}, {661, 4521}, {812, 48067}, {824, 48013}, {900, 48397}, {1635, 28229}, {1638, 7653}, {2487, 47880}, {2490, 47777}, {2516, 47876}, {2529, 28220}, {2786, 48071}, {2977, 47953}, {3004, 47758}, {3064, 13401}, {3239, 4813}, {3667, 4024}, {3676, 31148}, {3716, 47979}, {3835, 47789}, {4369, 28859}, {4378, 8662}, {4379, 23731}, {4394, 4841}, {4406, 20952}, {4468, 28840}, {4728, 47937}, {4773, 28199}, {4785, 48268}, {4789, 48079}, {4802, 4976}, {4820, 28217}, {4874, 47983}, {4885, 47988}, {4893, 43061}, {4897, 28894}, {4940, 47788}, {4963, 47885}, {4984, 28155}, {6006, 48266}, {6008, 48274}, {6084, 48133}, {6545, 47907}, {6546, 47908}, {7649, 43925}, {11068, 47666}, {14321, 47881}, {14331, 21127}, {20295, 47791}, {26853, 47656}, {26985, 48543}, {27013, 47781}, {28147, 48277}, {28191, 47669}, {28209, 47765}, {28846, 47660}, {28878, 48094}, {28902, 48087}, {30565, 47939}, {31286, 47783}, {31290, 47771}, {42403, 44426}, {43067, 48398}, {47123, 48349}, {47672, 48104}, {47785, 48404}, {47786, 48041}, {47787, 47978}, {47800, 47998}, {47801, 48006}, {47806, 48027}, {47813, 47938}, {47874, 48019}, {47887, 47902}, {47940, 48252}, {47943, 48579}, {47950, 48563}, {47990, 48555}, {48023, 48545}, {48024, 48546}, {48034, 48270}

X(49293) = midpoint of X(i) and X(j) for these {i,j}: {4979, 48275}, {26853, 47656}, {47660, 48107}, {47672, 48104}, {48094, 48147}, {48101, 48141}
X(49293) = reflection of X(i) in X(j) for these {i,j}: {4025, 4932}, {4813, 3239}, {4841, 4394}, {4988, 4765}, {6590, 48276}, {7649, 43927}, {45745, 649}, {45746, 3798}, {47666, 11068}, {47953, 2977}, {47958, 3676}, {47978, 48049}, {47979, 3716}, {47981, 3835}, {47982, 24720}, {47983, 4874}, {47988, 4885}, {47995, 4369}, {48034, 48270}, {48269, 6590}, {48398, 43067}
X(49293) = crossdifference of every pair of points on line {42, 3295}
X(49293) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 4988, 4765}, {3239, 4813, 47764}, {4025, 4932, 48574}, {4369, 47995, 47757}, {4394, 4841, 47883}, {4765, 4988, 45745}, {4885, 47988, 48554}, {31148, 47958, 3676}, {45745, 48576, 649}, {45746, 47763, 3798}, {47666, 48567, 11068}, {47787, 47978, 48049}, {47789, 47981, 3835}


X(49294) = X(513)X(11934)∩X(514)X(4024)

Barycentrics    (b - c)*(3*a^2 + 2*a*b + b^2 + 2*a*c - 2*b*c + c^2) : :
X(49294) = X[21104] - 3 X[23729], 2 X[21104] - 3 X[48398], 3 X[4382] - X[47671], 3 X[20295] - X[25259], 3 X[23731] + X[47671], 2 X[25259] - 3 X[48269], X[47673] - 3 X[47958], and many others

X(49294) lies on these lines: {513, 11934}, {514, 4024}, {522, 47673}, {523, 47950}, {649, 7658}, {650, 48554}, {812, 45745}, {900, 47960}, {2527, 31250}, {3004, 6008}, {3239, 31147}, {3667, 16892}, {3676, 4979}, {3776, 48013}, {3798, 26853}, {3835, 47766}, {4025, 4785}, {4106, 6590}, {4120, 48138}, {4369, 48067}, {4380, 48550}, {4394, 47756}, {4468, 28882}, {4728, 48104}, {4762, 47988}, {4776, 11068}, {4778, 47672}, {4782, 48555}, {4786, 21212}, {4790, 47758}, {4806, 48546}, {4820, 48605}, {4885, 47768}, {4932, 21183}, {4940, 47765}, {4977, 48125}, {6006, 47971}, {6009, 47962}, {6084, 48026}, {14321, 48095}, {14837, 47935}, {17069, 48558}, {17494, 48543}, {21188, 47976}, {23813, 48276}, {26798, 47771}, {27013, 44432}, {28191, 47670}, {28209, 48133}, {28225, 48141}, {28840, 47978}, {28846, 47652}, {28851, 48034}, {28855, 48592}, {28878, 48019}, {29162, 48128}, {29328, 48007}, {29362, 47983}, {30835, 43061}, {42403, 46107}, {44449, 47651}, {47663, 47759}, {47783, 48008}, {47871, 48107}, {47874, 48145}, {47900, 48275}, {47916, 48266}, {48043, 48061}, {48050, 48069}, {48414, 48577}

X(49294) = midpoint of X(i) and X(j) for these {i,j}: {4024, 47907}, {4382, 23731}, {4820, 48605}, {31290, 47650}, {44449, 47651}, {47652, 48079}, {47672, 47937}, {47900, 48275}, {47916, 48266}, {47958, 48114}
X(49294) = reflection of X(i) in X(j) for these {i,j}: {4468, 48049}, {4979, 3676}, {6590, 4106}, {26853, 3798}, {45745, 47995}, {47890, 4940}, {47935, 14837}, {47976, 21188}, {48013, 3776}, {48016, 21212}, {48038, 48041}, {48060, 3835}, {48061, 48043}, {48067, 4369}, {48069, 48050}, {48095, 14321}, {48101, 3239}, {48269, 20295}, {48276, 23813}, {48398, 23729}
X(49294) = X(100)-anticomplementary conjugate of X(41927)
X(49294) = X(43733)-Ceva conjugate of X(1086)
X(49294) = crosspoint of X(190) and X(18841)
X(49294) = crosssum of X(649) and X(9605)
X(49294) = crossdifference of every pair of points on line {218, 2308}
X(49294) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3676, 4979, 48574}, {3835, 48060, 47766}, {4369, 48067, 48576}, {4468, 48049, 47764}, {4940, 47890, 47765}, {21212, 48016, 4786}, {26853, 44435, 3798}, {31147, 48101, 3239}, {48050, 48069, 48545}


X(49295) = X(513)X(11934)∩X(514)X(4010)

Barycentrics    (b - c)*(a^3 + 3*a^2*b + a*b^2 + b^3 + 3*a^2*c - b^2*c + a*c^2 - b*c^2 + c^3) : :
X(49295) = 2 X[650] - 3 X[48555], 2 X[2977] - 3 X[47760], 2 X[3798] - 3 X[48227], X[4088] - 3 X[31147], 3 X[4120] - X[48118], X[4380] - 3 X[47797], 2 X[4394] - 3 X[47799], X[4467] - 3 X[48174], 4 X[4521] - 3 X[47885], and many others

X(49295) lies on these lines: {513, 11934}, {514, 4010}, {522, 4810}, {523, 4106}, {650, 48555}, {900, 48015}, {2977, 47760}, {3239, 48103}, {3676, 4784}, {3700, 4802}, {3716, 28882}, {3798, 48227}, {3801, 28478}, {3835, 48062}, {3837, 48069}, {4024, 47924}, {4025, 29328}, {4088, 31147}, {4120, 48118}, {4122, 28147}, {4380, 47797}, {4382, 47701}, {4394, 47799}, {4458, 4785}, {4467, 48174}, {4468, 4806}, {4521, 47885}, {4728, 48106}, {4762, 47998}, {4776, 48408}, {4777, 47999}, {4778, 39547}, {4782, 47800}, {4804, 47958}, {4813, 47704}, {4834, 21188}, {4874, 48060}, {4940, 48047}, {4961, 21192}, {4977, 47979}, {4979, 47887}, {4992, 6332}, {6084, 48029}, {6362, 48616}, {6590, 48090}, {8712, 48400}, {9508, 47757}, {11068, 47822}, {14321, 48088}, {17069, 48192}, {18004, 47786}, {20295, 47691}, {21297, 47690}, {23731, 48142}, {23813, 48396}, {25259, 47688}, {26824, 47699}, {28175, 48271}, {28846, 48326}, {29114, 48348}, {29126, 48332}, {29162, 48136}, {29362, 48006}, {47650, 47969}, {47652, 48080}, {47663, 47821}, {47672, 47938}, {47693, 47790}, {47696, 48172}, {47698, 47759}, {47765, 48056}, {47787, 48405}, {47813, 48104}, {47832, 48101}, {47871, 48108}, {47874, 48146}, {47902, 48275}, {47945, 48543}, {47975, 48550}, {48030, 48554}, {48414, 48579}

X(49295) = midpoint of X(i) and X(j) for these {i,j}: {4024, 47924}, {4382, 47701}, {4804, 47958}, {4813, 47704}, {20295, 47691}, {23731, 48142}, {24719, 48349}, {25259, 47688}, {26824, 47699}, {47650, 47969}, {47652, 48080}, {47672, 47938}, {47902, 48275}, {47944, 48120}
X(49295) = reflection of X(i) in X(j) for these {i,j}: {4468, 4806}, {4784, 3676}, {4834, 21188}, {6332, 4992}, {6590, 48090}, {48040, 48043}, {48047, 4940}, {48060, 4874}, {48062, 3835}, {48069, 3837}, {48088, 14321}, {48103, 3239}, {48396, 23813}
X(49295) = crossdifference of every pair of points on line {218, 7296}


X(49296) = X(239)X(514)∩X(513)X(11934)

Barycentrics    (b - c)*(-a^2 - 2*a*b + b^2 - 2*a*c - 2*b*c + c^2) : :
X(49296) = 2 X[649] - 3 X[48574], 2 X[3798] - 3 X[47755], 3 X[4025] - 2 X[21196], 3 X[4750] - 2 X[4765], 3 X[4750] - X[47926], 3 X[4786] - 2 X[48008], 4 X[4932] - 3 X[48576], X[17494] - 3 X[47755], 4 X[21196] - 3 X[45745], and many others

X(49296) lies on these lines: {239, 514}, {513, 11934}, {522, 47672}, {523, 7659}, {647, 3669}, {650, 2487}, {661, 3676}, {693, 28846}, {812, 48013}, {900, 48125}, {918, 6590}, {2488, 6372}, {2786, 48268}, {3239, 4379}, {3667, 4382}, {3716, 48036}, {3776, 28840}, {3835, 21183}, {4088, 48579}, {4367, 8642}, {4369, 4468}, {4378, 8641}, {4406, 18071}, {4453, 47666}, {4458, 4778}, {4462, 24622}, {4467, 47675}, {4521, 24924}, {4724, 47801}, {4728, 48076}, {4762, 4897}, {4790, 6084}, {4801, 28478}, {4813, 6545}, {4874, 48040}, {4885, 28910}, {4893, 7658}, {4927, 4940}, {4963, 47877}, {4977, 47960}, {6006, 48114}, {6546, 43061}, {7178, 43932}, {7653, 47767}, {8645, 48343}, {8713, 48322}, {9029, 44319}, {11068, 47762}, {13246, 48009}, {14321, 45320}, {14837, 47918}, {17069, 47883}, {17161, 47674}, {20507, 29198}, {21188, 47959}, {21212, 47783}, {22388, 44408}, {23731, 28225}, {24720, 48039}, {25259, 47780}, {26853, 47650}, {26985, 47769}, {28147, 47673}, {28161, 47671}, {28169, 47670}, {28209, 47950}, {28871, 47787}, {28882, 48067}, {28886, 48034}, {28898, 48274}, {28902, 48026}, {30520, 48276}, {31147, 48414}, {31148, 48094}, {31290, 44435}, {47652, 48107}, {47654, 48434}, {47658, 48435}, {47698, 47824}, {47699, 48241}, {47754, 47952}, {47768, 47890}, {47785, 48000}, {47797, 47941}, {47800, 48029}, {47806, 48047}, {47813, 48078}, {47871, 48079}, {47874, 48112}, {47880, 47914}, {47886, 47917}, {47887, 48021}, {47930, 48275}, {47939, 48421}, {47946, 48227}, {48028, 48555}, {48087, 48563}

X(49296) = midpoint of X(i) and X(j) for these {i,j}: {4467, 47675}, {7192, 47676}, {16892, 48141}, {17161, 47674}, {23755, 48341}, {26853, 47650}, {47652, 48107}, {47658, 48435}, {47672, 47971}, {47930, 48275}, {47958, 48147}
X(49296) = reflection of X(i) in X(j) for these {i,j}: {661, 3676}, {4468, 4369}, {6590, 43067}, {17494, 3798}, {45745, 4025}, {47764, 21183}, {47765, 47891}, {47918, 14837}, {47926, 4765}, {47959, 21188}, {47962, 17069}, {47995, 3776}, {47996, 21212}, {48006, 4458}, {48009, 13246}, {48034, 48049}, {48036, 3716}, {48038, 3835}, {48039, 24720}, {48040, 4874}, {48046, 4885}, {48049, 48415}, {48060, 4932}, {48082, 3239}, {48268, 48399}, {48269, 693}, {48398, 21104}
X(49296) = X(3296)-Ceva conjugate of X(1086)
X(49296) = X(692)-isoconjugate of X(32022)
X(49296) = X(i)-Dao conjugate of X(j) for these (i, j): (1086, 32022), (4648, 30728)
X(49296) = crossdifference of every pair of points on line {42, 218}
X(49296) = barycentric product X(i)*X(j) for these {i,j}: {514, 4648}, {3261, 5021}, {4025, 4196}
X(49296) = barycentric quotient X(i)/X(j) for these {i,j}: {514, 32022}, {4196, 1897}, {4648, 190}, {5021, 101}
X(49296) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 3676, 47757}, {3835, 48038, 47764}, {4369, 4468, 47766}, {4379, 48082, 3239}, {4750, 47926, 4765}, {4874, 48040, 48546}, {4885, 48046, 47765}, {4932, 48060, 48576}, {17069, 47962, 47883}, {17494, 47755, 3798}, {21115, 48147, 47958}, {21183, 48038, 3835}, {21212, 47996, 47783}, {24720, 48039, 48545}, {47891, 48046, 4885}, {47939, 48421, 48550}


X(49297) = X(2)X(2527)∩X(513)X(41794)

Barycentrics    (b - c)*(3*a^2 + 2*a*b + b^2 + 2*a*c - b*c + c^2) : :
X(49297) = 9 X[2] - 8 X[2527], 3 X[47652] - 2 X[47676], 3 X[47695] - 4 X[48349], 4 X[4838] - 3 X[47658], X[4838] + 3 X[47900], X[4838] - 3 X[48114], X[47658] + 4 X[47900], X[47658] - 4 X[48114], 5 X[649] - 6 X[47882], 2 X[649] - 3 X[48550], and many others

X(49297) lies on these lines: {2, 2527}, {513, 41794}, {514, 4838}, {522, 47654}, {649, 47882}, {650, 48543}, {661, 47892}, {812, 4988}, {824, 47907}, {900, 47653}, {2786, 47916}, {3004, 26853}, {3667, 47677}, {3700, 20295}, {3835, 48104}, {4106, 4789}, {4380, 4765}, {4382, 28859}, {4453, 4979}, {4467, 4785}, {4521, 4776}, {4778, 4804}, {4784, 48159}, {4790, 44435}, {4806, 48250}, {4810, 4977}, {4813, 28882}, {4897, 48156}, {4940, 47771}, {4949, 25259}, {6008, 45746}, {6084, 31290}, {7192, 23729}, {14321, 47773}, {14351, 47785}, {17494, 47988}, {21297, 48276}, {23813, 47791}, {27013, 47756}, {27138, 47767}, {28195, 47674}, {28225, 48153}, {28846, 47651}, {28867, 47923}, {28898, 48605}, {29078, 48599}, {30565, 48049}, {31209, 48554}, {47662, 48269}, {47663, 48026}, {47666, 47981}, {47759, 47890}, {47762, 48067}, {47769, 48095}, {47886, 48016}, {47974, 47979}, {48013, 48422}, {48037, 48105}, {48041, 48094}, {48050, 48252}, {48107, 48398}, {48138, 48270}, {48415, 48577}

X(49297) = midpoint of X(47900) and X(48114)
X(49297) = reflection of X(i) in X(j) for these {i,j}: {4380, 47995}, {4467, 47958}, {7192, 23729}, {17494, 47988}, {26853, 3004}, {44449, 48079}, {45746, 47950}, {47660, 20295}, {47662, 48269}, {47663, 48026}, {47666, 47981}, {47939, 47978}, {47974, 47979}, {48076, 48592}, {48094, 48041}, {48101, 48049}, {48104, 3835}, {48105, 48037}, {48107, 48398}, {48138, 48270}
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3835, 48104, 48567}, {4380, 47995, 47782}, {7192, 23729, 47871}, {48049, 48101, 30565}


X(49298) = X(2)X(43061)∩X(513)X(41794)

Barycentrics    (b - c)*(2*a^2 + a*b + b^2 + a*c - b*c + c^2) : :
X(49298) = 9 X[2] - 8 X[43061], 4 X[43061] - 3 X[48060], 3 X[20295] - 2 X[48269], 2 X[23731] + X[47650], 3 X[25259] - 4 X[48269], X[47656] + 2 X[47907], 3 X[649] - 4 X[21212], 2 X[649] - 3 X[44435], 5 X[649] - 6 X[45674], 8 X[21212] - 9 X[44435], and many others

X(49298) lies on these lines: {2, 43061}, {513, 41794}, {514, 4024}, {522, 47653}, {523, 47940}, {649, 21212}, {650, 48550}, {661, 28882}, {693, 23729}, {812, 45746}, {824, 47916}, {900, 47677}, {918, 47651}, {2786, 47923}, {2978, 3808}, {3004, 4380}, {3239, 26798}, {3676, 47763}, {3700, 47662}, {3776, 4979}, {3835, 47771}, {4010, 47696}, {4025, 26853}, {4106, 47660}, {4369, 48104}, {4394, 48558}, {4453, 4790}, {4467, 6008}, {4468, 47759}, {4522, 48146}, {4728, 48145}, {4750, 48016}, {4762, 47667}, {4776, 47890}, {4777, 47654}, {4778, 48142}, {4782, 48552}, {4785, 16892}, {4789, 23813}, {4841, 6009}, {4885, 48567}, {4897, 48422}, {4932, 6545}, {4940, 30565}, {4977, 47675}, {6084, 47666}, {6548, 48576}, {6590, 21297}, {7192, 48398}, {11068, 48554}, {14321, 48557}, {17494, 47781}, {18004, 48140}, {21104, 48107}, {24719, 47690}, {26546, 30804}, {26777, 47783}, {27013, 47757}, {27138, 47766}, {28481, 47709}, {28840, 47937}, {28851, 48019}, {28859, 47672}, {28863, 48266}, {28867, 47930}, {28878, 47978}, {28890, 48076}, {28894, 48605}, {28898, 47919}, {29118, 48122}, {29158, 48086}, {29328, 47968}, {29362, 47699}, {30520, 44449}, {31147, 48138}, {31148, 48415}, {31209, 47756}, {43067, 47871}, {47769, 48049}, {47808, 48050}, {47891, 48420}, {47932, 48404}, {47969, 47983}, {47975, 47989}, {48013, 48571}, {48027, 48408}, {48043, 48102}, {48069, 48164}, {48130, 48270}

X(49298) = anticomplement of X(48060)
X(49298) = midpoint of X(i) and X(j) for these {i,j}: {4382, 47907}, {47651, 48079}, {47672, 47900}, {47916, 48114}
X(49298) = reflection of X(i) in X(j) for these {i,j}: {693, 23729}, {4380, 3004}, {4467, 47960}, {4979, 3776}, {7192, 48398}, {17494, 47995}, {25259, 20295}, {26853, 4025}, {31290, 47981}, {45746, 47958}, {47656, 4382}, {47659, 48268}, {47660, 4106}, {47662, 3700}, {47663, 661}, {47664, 4841}, {47666, 47988}, {47674, 26824}, {47676, 47652}, {47690, 24719}, {47696, 4010}, {47699, 47944}, {47932, 48404}, {47969, 47983}, {47975, 47989}, {48067, 3676}, {48082, 48041}, {48094, 48049}, {48095, 4940}, {48101, 3835}, {48102, 48043}, {48104, 4369}, {48106, 48050}, {48107, 21104}, {48130, 48270}, {48140, 18004}, {48146, 4522}, {48408, 48027}
X(49298) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {100, 41916}, {907, 75}, {18840, 21293}, {23051, 150}, {39951, 149}
X(49298) = crosspoint of X(190) and X(43527)
X(49298) = crosssum of X(i) and X(j) for these (i,j): {649, 7772}, {3804, 20970}
X(49298) = barycentric product X(514)*X(17380)
X(49298) = barycentric quotient X(17380)/X(190)
X(49298) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3004, 4380, 27486}, {3676, 48067, 47763}, {3776, 4979, 47755}, {3835, 48101, 47771}, {4106, 47660, 47790}, {4940, 48095, 30565}, {17494, 47995, 47781}, {26798, 47773, 3239}, {26853, 48156, 4025}, {47663, 48543, 661}, {48049, 48094, 47769}, {48050, 48106, 47808}


X(49299) = X(2)X(48421)∩X(241)X(514)

Barycentrics    (b - c)*(a^2 - a*b + 2*b^2 - a*c - 2*b*c + 2*c^2) : :
X(49299) = 3 X[2] - 5 X[48421], 3 X[650] - 4 X[21212], 2 X[650] - 3 X[47754], 5 X[650] - 6 X[47882], 3 X[1638] - 2 X[11068], 3 X[3676] - 2 X[43061], 4 X[3676] - 3 X[47761], 3 X[3776] - 2 X[21212], 4 X[3776] - 3 X[47754], 5 X[3776] - 3 X[47882], and many others

X(49299) lies on these lines: {2, 48421}, {241, 514}, {312, 693}, {513, 41794}, {523, 48015}, {649, 21115}, {661, 48558}, {676, 48061}, {824, 48125}, {918, 4106}, {1278, 4777}, {2516, 47892}, {3239, 4927}, {3309, 47716}, {3835, 28890}, {3837, 48088}, {3893, 14077}, {3900, 47720}, {4025, 6084}, {4379, 48130}, {4380, 48571}, {4382, 28898}, {4394, 4453}, {4411, 20892}, {4467, 47650}, {4468, 47760}, {4728, 48117}, {4762, 16892}, {4790, 28882}, {4802, 21146}, {4813, 28910}, {4820, 30519}, {4874, 48096}, {4885, 6545}, {4940, 48082}, {4977, 47961}, {6008, 47971}, {6546, 31287}, {7192, 47651}, {7653, 48567}, {11934, 23761}, {17161, 48434}, {17424, 17595}, {17490, 17494}, {21116, 48275}, {21196, 48426}, {21204, 31250}, {21438, 29739}, {23729, 28846}, {23813, 25259}, {26985, 30861}, {28151, 47654}, {28195, 47805}, {28220, 48158}, {28840, 47950}, {28851, 48026}, {28859, 48605}, {28863, 48397}, {28871, 48041}, {28878, 47988}, {28894, 47672}, {28902, 47981}, {29082, 48346}, {29102, 48332}, {31147, 48112}, {31148, 48138}, {31150, 48432}, {45320, 48124}, {47662, 47780}, {47664, 47894}, {47665, 47869}, {47666, 48156}, {47688, 48108}, {47698, 48159}, {47704, 47973}, {47802, 48056}, {47812, 48118}, {47813, 48139}, {47832, 48113}, {47833, 48604}, {47874, 48414}, {47886, 48425}, {47887, 48102}, {47907, 48147}, {47916, 48141}, {47924, 48148}, {47931, 48142}, {47952, 47995}, {47953, 47999}, {47974, 48203}, {48097, 48219}, {48140, 48253}, {48145, 48577}, {48146, 48579}, {48405, 48615}, {48578, 48626}

X(49299) = midpoint of X(i) and X(j) for these {i,j}: {4382, 47930}, {4467, 47650}, {7192, 47651}, {26824, 47677}, {47652, 47676}, {47653, 47675}, {47654, 47674}, {47672, 47923}, {47688, 48108}, {47704, 47973}, {47907, 48147}, {47916, 48141}, {47919, 48133}, {47924, 48148}, {47931, 48142}
X(49299) = reflection of X(i) in X(j) for these {i,j}: {650, 3776}, {4106, 48398}, {21196, 48426}, {25259, 23813}, {43067, 21104}, {47663, 4394}, {47770, 6545}, {47890, 3676}, {47920, 48404}, {47952, 47995}, {47953, 47999}, {47962, 3004}, {48061, 676}, {48082, 4940}, {48087, 3835}, {48088, 3837}, {48094, 4885}, {48095, 4369}, {48096, 4874}, {48271, 693}, {48397, 48399}, {48615, 48405}
X(49299) = X(30701)-Ceva conjugate of X(1086)
X(49299) = barycentric product X(i)*X(j) for these {i,j}: {514, 17282}, {693, 17597}
X(49299) = barycentric quotient X(i)/X(j) for these {i,j}: {17282, 190}, {17597, 100}
X(49299) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 3776, 47754}, {3676, 47890, 47761}, {4453, 47663, 4394}, {4885, 48094, 47770}, {6545, 48094, 4885}, {25259, 47871, 23813}, {47664, 48433, 47894}, {48420, 48557, 26985}


X(49300) = X(1)X(514)∩X(513)X(47680)

Barycentrics    (b - c)*(-(a*b^2) + b^3 - a*b*c - b^2*c - a*c^2 - b*c^2 + c^3) : :
X(49300) = 3 X[21118] - X[21132], 3 X[21118] + X[47704], X[47699] - 3 X[47708], 3 X[1577] - 2 X[4522], 4 X[4522] - 3 X[48272], 2 X[3960] - 3 X[47887], X[47684] - 3 X[48237], 3 X[47798] - 2 X[48284]

X(49300) lies on these lines: {1, 514}, {513, 47680}, {522, 4707}, {523, 10015}, {693, 23887}, {784, 3801}, {826, 48392}, {1577, 4522}, {1734, 7178}, {2785, 48339}, {2826, 21104}, {3011, 47771}, {3810, 4978}, {3904, 48295}, {3960, 47887}, {4024, 29318}, {4088, 4791}, {4379, 33140}, {4458, 48321}, {4560, 20517}, {4777, 47723}, {4802, 21111}, {4804, 23876}, {4823, 48278}, {4893, 29640}, {4905, 6362}, {5231, 21183}, {6005, 23755}, {6545, 29676}, {6546, 29675}, {6590, 47726}, {7192, 29132}, {7661, 21102}, {7662, 47682}, {10198, 47793}, {10916, 23789}, {11269, 47780}, {14077, 43052}, {14349, 48403}, {14794, 39476}, {21109, 21174}, {21112, 28151}, {21119, 28155}, {21179, 46385}, {23723, 45746}, {23770, 48335}, {23875, 48264}, {26228, 47773}, {26363, 47796}, {29017, 48393}, {29066, 47695}, {29082, 48305}, {29094, 48301}, {29160, 47660}, {29240, 48324}, {29312, 48120}, {29639, 44435}, {36152, 48387}, {47131, 47727}, {47132, 48290}, {47684, 48237}, {47729, 48286}, {47798, 48284}, {47959, 48400}

X(49300) = midpoint of X(21132) and X(47704)
X(49300) = reflection of X(i) in X(j) for these {i,j}: {1, 47123}, {1734, 7178}, {3904, 48295}, {4040, 21185}, {4088, 4791}, {4560, 20517}, {4724, 21201}, {14349, 48403}, {46385, 21179}, {47682, 7662}, {47726, 6590}, {47727, 47131}, {47729, 48286}, {47959, 48400}, {48272, 1577}, {48278, 4823}, {48290, 47132}, {48321, 4458}, {48335, 23770}
X(49300) = crossdifference of every pair of points on line {672, 2278}
X(49300) = barycentric product X(514)*X(33108)
X(49300) = barycentric quotient X(33108)/X(190)
X(49300) = {X(21118),X(47704)}-harmonic conjugate of X(21132)


X(49301) = X(2)X(48055)∩X(244)X(4965)

Barycentrics    (b - c)*(a^3 - a^2*b + a*b^2 + b^3 - a^2*c - 3*a*b*c + a*c^2 + c^3) : :
X(49301) = 2 X[659] - 3 X[4453], 2 X[661] - 3 X[48159], 4 X[3676] - 3 X[47804], 3 X[47804] - 2 X[48061], 2 X[3700] - 3 X[48170], 2 X[3716] - 3 X[6545], 4 X[3776] - 3 X[47797], 2 X[4724] - 3 X[47797], 4 X[3837] - 3 X[30565], and many others

X(49301) lies on these lines: {2, 48055}, {244, 4965}, {513, 41794}, {514, 1734}, {522, 47705}, {659, 3004}, {661, 48159}, {764, 3904}, {824, 48119}, {918, 20539}, {1635, 28229}, {2526, 47698}, {2832, 4707}, {3309, 47720}, {3676, 47804}, {3700, 48170}, {3716, 6545}, {3776, 4724}, {3835, 48078}, {3837, 30565}, {4010, 47871}, {4088, 28890}, {4142, 47936}, {4369, 48102}, {4458, 4778}, {4467, 29362}, {4468, 44429}, {4522, 48117}, {4750, 4830}, {4776, 48040}, {4789, 48098}, {4809, 28220}, {4818, 47926}, {5592, 14413}, {6546, 25380}, {9508, 28195}, {14430, 44314}, {17069, 48240}, {18004, 48167}, {20517, 47977}, {21104, 47694}, {21146, 47660}, {21188, 47815}, {21212, 47811}, {21222, 29240}, {23765, 29082}, {24719, 44449}, {24720, 47809}, {25259, 48089}, {27013, 48245}, {27138, 48166}, {28209, 47944}, {28213, 48244}, {28225, 47938}, {28840, 47943}, {28851, 48023}, {28859, 48598}, {28863, 47703}, {28878, 47982}, {30520, 47690}, {31148, 48626}, {31290, 47989}, {36848, 48056}, {42325, 47716}, {43067, 47696}, {44435, 48029}, {47656, 48126}, {47666, 48007}, {47699, 47960}, {47771, 48096}, {47781, 47963}, {47808, 48088}, {47812, 48113}, {47824, 47890}, {47832, 48415}, {47887, 48063}, {47927, 48404}, {47941, 47995}, {47946, 47999}, {47974, 48422}, {47998, 48156}, {48014, 48223}, {48024, 48550}, {48047, 48164}, {48050, 48082}, {48080, 48398}, {48097, 48235}, {48103, 48252}, {48139, 48579}, {48185, 48614}, {48405, 48604}

X(49301) = midpoint of X(i) and X(j) for these {i,j}: {47901, 48147}, {47930, 48115}, {47931, 48148}
X(49301) = reflection of X(i) in X(j) for these {i,j}: {3904, 764}, {4724, 3776}, {25259, 48089}, {31290, 47989}, {44433, 21115}, {44449, 24719}, {47656, 48126}, {47660, 21146}, {47666, 48007}, {47694, 21104}, {47695, 48326}, {47696, 43067}, {47698, 2526}, {47699, 47960}, {47926, 4818}, {47927, 48404}, {47936, 4142}, {47941, 47995}, {47946, 47999}, {47969, 3004}, {47975, 48015}, {47977, 20517}, {48032, 4458}, {48061, 3676}, {48078, 3835}, {48080, 48398}, {48082, 48050}, {48083, 3837}, {48094, 24720}, {48102, 4369}, {48106, 48073}, {48117, 4522}, {48408, 2254}, {48604, 48405}
X(49301) = anticomplement of X(48055)
X(49301) = crossdifference of every pair of points on line {1500, 2280}
X(49301) = barycentric product X(522)*X(24803)
X(49301) = barycentric quotient X(24803)/X(664)
X(49301) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3676, 48061, 47804}, {3776, 4724, 47797}, {3837, 48083, 30565}, {4369, 48102, 48250}, {4458, 48032, 44433}, {21115, 48032, 4458}, {24720, 48094, 47809}


X(49302) = X(2)X(3776)∩X(239)X(514)

Barycentrics    (b - c)*(a^2 - a*b + 2*b^2 - a*c - b*c + 2*c^2) : :
X(49302) = 3 X[2] - 4 X[3776], 2 X[649] - 3 X[48571], 4 X[4025] - 3 X[47776], 3 X[16892] - 2 X[21196], 4 X[16892] - 3 X[47894], 3 X[17494] - 4 X[21196], 2 X[17494] - 3 X[47894], 8 X[21196] - 9 X[47894], and many others

X(49302) lies on these lines: {2, 3776}, {239, 514}, {312, 693}, {321, 29739}, {513, 47651}, {522, 47650}, {650, 48422}, {659, 48241}, {661, 28890}, {764, 29224}, {812, 47930}, {824, 26824}, {918, 20295}, {2487, 4453}, {3004, 47775}, {3676, 47771}, {3700, 47871}, {3716, 48113}, {3835, 47772}, {3837, 48171}, {4024, 47869}, {4088, 48164}, {4122, 48170}, {4369, 21115}, {4382, 30519}, {4458, 47805}, {4467, 6084}, {4468, 44435}, {4608, 28894}, {4724, 48203}, {4762, 17161}, {4764, 4777}, {4776, 48087}, {4778, 47924}, {4802, 48108}, {4874, 48604}, {4885, 6548}, {6545, 26985}, {6546, 21212}, {17069, 47892}, {21104, 47660}, {21146, 47693}, {21297, 25259}, {21301, 29354}, {21302, 29288}, {23731, 28855}, {23738, 29116}, {23765, 29332}, {23770, 48172}, {24720, 48118}, {26777, 47886}, {26798, 48270}, {26853, 28882}, {27138, 30565}, {28840, 47916}, {28851, 31290}, {28863, 47659}, {28871, 48019}, {28886, 47937}, {28910, 47939}, {29102, 48298}, {31150, 48433}, {31209, 31233}, {42325, 47717}, {43067, 47662}, {44009, 47882}, {44429, 48088}, {45320, 48420}, {47664, 48434}, {47665, 48125}, {47666, 47960}, {47694, 48326}, {47698, 48007}, {47700, 48169}, {47759, 48082}, {47762, 48095}, {47774, 47995}, {47792, 48399}, {47797, 48055}, {47798, 48061}, {47804, 48096}, {47821, 48083}, {47822, 48614}, {47823, 48097}, {47824, 48103}, {47874, 48415}, {47941, 47961}, {47945, 47968}, {48029, 48174}, {48032, 48239}, {48038, 48543}, {48046, 48550}, {48047, 48159}, {48048, 48552}, {48049, 48112}, {48236, 48615}, {48242, 48408}, {48277, 48427}

X(49302) = reflection of X(i) in X(j) for these {i,j}: {4608, 47675}, {7192, 47676}, {17161, 47677}, {17494, 16892}, {20295, 47652}, {25259, 48398}, {26853, 47971}, {31290, 47958}, {44449, 23729}, {47653, 47923}, {47659, 47672}, {47660, 21104}, {47662, 43067}, {47663, 4025}, {47665, 48125}, {47666, 47960}, {47693, 21146}, {47694, 48326}, {47698, 48007}, {47773, 21115}, {47939, 47950}, {47941, 47961}, {47945, 47968}, {48094, 3776}, {48102, 4458}, {48112, 48049}, {48113, 3716}, {48117, 3835}, {48118, 24720}, {48124, 4885}, {48130, 4369}, {48138, 4932}, {48277, 48427}, {48604, 4874}
X(49302) = anticomplement of X(48094)
X(49302) = X(6012)-anticomplementary conjugate of X(69)
X(49302) = crosssum of X(213) and X(8654)
X(49302) = barycentric product X(514)*X(17283)
X(49302) = barycentric quotient X(17283)/X(190)
X(49302) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3776, 48094, 2}, {3835, 48117, 47772}, {4025, 47663, 47776}, {4369, 48130, 47773}, {4453, 47890, 27013}, {4458, 48102, 47805}, {4885, 48124, 48557}, {4885, 48421, 6548}, {6546, 21212, 27115}, {6546, 48425, 21212}, {16892, 17494, 47894}, {21104, 47660, 47780}, {21115, 48130, 4369}, {23729, 44449, 20295}, {24720, 48118, 48208}, {25259, 48398, 21297}, {31209, 48432, 47754}, {44449, 47652, 23729}, {48421, 48557, 4885}


X(49303) = X(1)X(514)∩X(8)X(523)

Barycentrics    (b - c)*(a^3 - a*b^2 + 2*b^3 - a*b*c - b^2*c - a*c^2 - b*c^2 + 2*c^3) : :
X(49303) = 3 X[21118] - X[48102], 3 X[47708] - 2 X[48006], 5 X[1698] - 6 X[4049], 4 X[7178] - 3 X[47836], 7 X[3622] - 6 X[30580], 2 X[4088] - 3 X[30709], 3 X[4391] - 2 X[48088], 4 X[4791] - 3 X[48171], and many others

X(49303) lies on these lines: {1, 514}, {8, 523}, {304, 693}, {513, 3868}, {522, 12625}, {977, 47844}, {1698, 4049}, {1788, 7178}, {3622, 30580}, {3737, 28082}, {3801, 4560}, {3904, 23770}, {4088, 30709}, {4391, 48088}, {4581, 23752}, {4705, 27690}, {4777, 47721}, {4789, 29579}, {4791, 48171}, {4802, 31359}, {6548, 19947}, {6550, 20042}, {7192, 20247}, {7199, 33930}, {7662, 47684}, {9508, 21145}, {10015, 48408}, {14779, 44010}, {16020, 47797}, {16816, 46915}, {16825, 47683}, {17230, 47792}, {19877, 28602}, {21129, 28191}, {21222, 48326}, {21301, 23877}, {23755, 29118}, {23887, 46403}, {24093, 28175}, {26824, 29312}, {29154, 48393}, {29160, 47693}, {29172, 48120}, {29240, 47695}, {29272, 48305}, {29332, 48392}, {29336, 31291}, {29674, 47726}, {47131, 47729}, {47682, 47834}, {47840, 48403}, {48203, 48288}, {48241, 48321}

X(49303) = reflection of X(i) in X(j) for these {i,j}: {3904, 23770}, {4560, 3801}, {4581, 23752}, {21222, 48326}, {46403, 47680}, {47684, 7662}, {47688, 47725}, {47728, 47123}, {47729, 47131}, {48298, 47691}, {48408, 10015}


X(49304) = X(109)X(42552)∩X(1411)X(10703)

Barycentrics    a (a-b) (a-c) (a^13-3 a^12 (b+c)+a^11 (b^2+13 b c+c^2)+a^10 (7 b^3-17 b^2 c-17 b c^2+7 c^3) -a^9 (11 b^4+5 b^3 c-47 b^2 c^2+5 b c^3+11 c^4) +a^8 (b^5+39 b^4 c-43 b^3 c^2-43 b^2 c^3+39 b c^4+c^5) +a^7 (14 b^6-44 b^5 c-16 b^4 c^2+93 b^3 c^3-16 b^2 c^4-44 b c^5+14 c^6) -a^6 (b-c)^2 (14 b^5+23 b^4 c-45 b^3 c^2-45 b^2 c^3+23 b c^4+14 c^5) -a^5 (b-c)^2 (b^6-36 b^5 c+3 b^4 c^2+56 b^3 c^3+3 b^2 c^4-36 b c^5+c^6) +a^4 (b-c)^2 (11 b^7-18 b^6 c-27 b^5 c^2+32 b^4 c^3+32 b^3 c^4-27 b^2 c^5-18 b c^6+11 c^7) -a^3 (b-c)^4 (7 b^6+17 b^5 c+b^4 c^2-13 b^3 c^3+b^2 c^4+17 b c^5+7 c^6) -a^2 (b-c)^4 (b^7-8 b^6 c-6 b^5 c^2+3 b^4 c^3+3 b^3 c^4-6 b^2 c^5-8 b c^6+c^7) +a (b-c)^6 (b+c)^2 (3 b^4-b^3 c+3 b^2 c^2-b c^3+3 c^4) -(b-c)^6 (b+c)^3 (b^4-b^3 c+2 b^2 c^2-b c^3+c^4)) : :

See Angel Montesdeoca euclid 5089.

X(49304) lies on these lines: {109,42552}, {1411,10703}, {4551,14887}

leftri

Centers related to 1st- and 2nd- anti-Kenmotu-centers triangles triangles: X(49305)-X(49372)

rightri

This preamble and centers X(49305)-X(49372) were contributed by César Eliud Lozada, May 21, 2022.

1st- and 2nd- anti-Kenmotu-centers triangles triangles were introduced in the preamble just before X(45345).


X(49305) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO 1st ALTINTAS-ISODYNAMIC

Barycentrics    4*a^2*S^2*sqrt(3)+2*(a^4+(b^2+c^2)*a^2-2*(b^2-c^2)^2)*S+4*a^6-4*(b^2+c^2)*a^4+2*(b^4+c^4)*a^2-2*(b^2+c^2)*(b^2-c^2)^2 : :
X(49305) = 3*X(13)-X(6270) = 3*X(6268)+X(6270) = 2*X(6268)+X(49306) = 2*X(6270)-3*X(49306)

The reciprocal orthologic center of these triangles is X(4).

X(49305) lies on these lines: {3, 48722}, {6, 13}, {30, 33440}, {492, 616}, {530, 591}, {531, 49311}, {618, 45472}, {2044, 6770}, {3102, 35754}, {3389, 45542}, {5318, 22601}, {5473, 12305}, {5478, 45440}, {5617, 6289}, {6771, 43119}, {7975, 45476}, {9733, 49335}, {9901, 45426}, {9916, 45428}, {9982, 45434}, {10062, 45490}, {10078, 45492}, {11705, 45398}, {12142, 45400}, {12205, 45402}, {12337, 45416}, {12472, 45430}, {12473, 45432}, {12781, 45444}, {12793, 45446}, {12922, 45454}, {12932, 45456}, {12942, 45458}, {12952, 45460}, {12990, 45467}, {12991, 45464}, {13076, 45470}, {13103, 45488}, {13105, 45494}, {13107, 45496}, {13748, 18586}, {13917, 45484}, {13982, 45487}, {18585, 33441}, {18974, 45404}, {22773, 45436}, {35753, 45462}, {36383, 36401}, {36439, 47610}, {41020, 42279}, {41023, 49309}, {45345, 48456}, {45347, 48457}, {45411, 48723}, {45412, 49373}, {45415, 49374}, {45421, 49035}, {45422, 49143}, {45424, 49144}

X(49305) = midpoint of X(i) and X(j) for these {i, j}: {13, 6268}, {616, 49034}
X(49305) = reflection of X(i) in X(j) for these (i, j): (3, 48722), (49306, 13)
X(49305) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: 1st Altintas-isodynamic, Bankoff, 3rd Fermat-Dao, 7th Fermat-Dao, 11th Fermat-Dao, 15th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi, 1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi, 1st half-diamonds-central, 1st isodynamic-Dao, 3rd isodynamic-Dao, Largest-circumscribed-equilateral, 1st Lemoine-Dao, outer-Napoleon
X(49305) = X(13)-of-1st anti-Kenmotu centers triangle
X(49305) = X(48722)-of-X3-ABC reflections triangle
X(49305) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (381, 45375, 49307), (381, 48655, 49306), (22796, 41042, 49306)


X(49306) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO 1st ALTINTAS-ISODYNAMIC

Barycentrics    -4*a^2*S^2*sqrt(3)-2*(a^4+(b^2+c^2)*a^2-2*(b^2-c^2)^2)*S+4*a^6-4*(b^2+c^2)*a^4+2*(b^4+c^4)*a^2-2*(b^2+c^2)*(b^2-c^2)^2 : :
X(49306) = 3*X(13)-X(6268) = X(6268)+3*X(6270) = 2*X(6268)-3*X(49305) = 2*X(6270)+X(49305)

The reciprocal orthologic center of these triangles is X(4).

X(49306) lies on these lines: {3, 48723}, {6, 13}, {30, 33441}, {491, 616}, {530, 1991}, {531, 49312}, {618, 45473}, {2043, 6770}, {3103, 35753}, {3390, 45543}, {5318, 22630}, {5473, 12306}, {5478, 45441}, {5617, 6290}, {6771, 43118}, {7975, 45477}, {9732, 49336}, {9901, 45427}, {9916, 45429}, {9982, 45435}, {10062, 45491}, {10078, 45493}, {11705, 45399}, {12142, 45401}, {12205, 45403}, {12337, 45417}, {12472, 45431}, {12473, 45433}, {12781, 45445}, {12793, 45447}, {12922, 45455}, {12932, 45457}, {12942, 45459}, {12952, 45461}, {12990, 45465}, {12991, 45466}, {13076, 45471}, {13103, 45489}, {13105, 45495}, {13107, 45497}, {13749, 18587}, {13917, 45486}, {13982, 45485}, {15765, 33440}, {18974, 45405}, {22773, 45437}, {35754, 45463}, {36383, 36400}, {36457, 47610}, {41020, 42278}, {41023, 49310}, {45346, 48457}, {45348, 48456}, {45410, 48722}, {45413, 49374}, {45414, 49373}, {45420, 49034}, {45423, 49143}, {45425, 49144}

X(49306) = midpoint of X(i) and X(j) for these {i, j}: {13, 6270}, {616, 49035}
X(49306) = reflection of X(i) in X(j) for these (i, j): (3, 48723), (49305, 13)
X(49306) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: 1st Altintas-isodynamic, Bankoff, 3rd Fermat-Dao, 7th Fermat-Dao, 11th Fermat-Dao, 15th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi, 1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi, 1st half-diamonds-central, 1st isodynamic-Dao, 3rd isodynamic-Dao, Largest-circumscribed-equilateral, 1st Lemoine-Dao, outer-Napoleon
X(49306) = X(13)-of-2nd anti-Kenmotu centers triangle
X(49306) = X(48723)-of-X3-ABC reflections triangle
X(49306) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (381, 45376, 49308), (381, 48655, 49305), (22796, 41042, 49305)


X(49307) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO 2nd ALTINTAS-ISODYNAMIC

Barycentrics    -4*a^2*S^2*sqrt(3)+2*(a^4+(b^2+c^2)*a^2-2*(b^2-c^2)^2)*S+4*a^6-4*(b^2+c^2)*a^4+2*(b^4+c^4)*a^2-2*(b^2+c^2)*(b^2-c^2)^2 : :
X(49307) = 3*X(14)-X(6271) = 3*X(6269)+X(6271) = 2*X(6269)+X(49308) = 2*X(6271)-3*X(49308) = 3*X(21157)-2*X(35748)

The reciprocal orthologic center of these triangles is X(4).

X(49307) lies on these lines: {3, 48724}, {6, 13}, {30, 33442}, {492, 617}, {530, 49311}, {531, 591}, {619, 45472}, {2043, 6773}, {3102, 35851}, {3364, 45542}, {5321, 22603}, {5474, 12305}, {5479, 45440}, {5613, 6289}, {6774, 43119}, {7974, 45476}, {9733, 49333}, {9900, 45426}, {9915, 45428}, {9981, 45434}, {10061, 45490}, {10077, 45492}, {11706, 45398}, {12141, 45400}, {12204, 45402}, {12336, 45416}, {12470, 45430}, {12471, 45432}, {12780, 45444}, {12792, 45446}, {12921, 45454}, {12931, 45456}, {12941, 45458}, {12951, 45460}, {12988, 45467}, {12989, 45464}, {13075, 45470}, {13102, 45488}, {13104, 45494}, {13106, 45496}, {13748, 18587}, {13916, 45484}, {13981, 45487}, {15765, 33443}, {18975, 45404}, {21157, 35748}, {22774, 45436}, {35759, 42279}, {35850, 45462}, {36382, 36397}, {36457, 47611}, {41021, 42278}, {41022, 49309}, {45345, 48458}, {45347, 48459}, {45411, 48725}, {45412, 49375}, {45415, 49376}, {45421, 49037}, {45422, 49145}, {45424, 49146}

X(49307) = midpoint of X(i) and X(j) for these {i, j}: {14, 6269}, {617, 49036}
X(49307) = reflection of X(i) in X(j) for these (i, j): (3, 48724), (49308, 14)
X(49307) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: 2nd Altintas-isodynamic, 4th Fermat-Dao, 8th Fermat-Dao, 12th Fermat-Dao, 16th Fermat-Dao, 1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi, 3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi, 2nd half-diamonds-central, 2nd isodynamic-Dao, 4th isodynamic-Dao, 2nd Lemoine-Dao, inner-Napoleon
X(49307) = X(14)-of-1st anti-Kenmotu centers triangle
X(49307) = X(48724)-of-X3-ABC reflections triangle
X(49307) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (381, 45375, 49305), (381, 48656, 49308), (22797, 41043, 49308)


X(49308) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO 2nd ALTINTAS-ISODYNAMIC

Barycentrics    4*a^2*S^2*sqrt(3)-2*(a^4+(b^2+c^2)*a^2-2*(b^2-c^2)^2)*S+4*a^6-4*(b^2+c^2)*a^4+2*(b^4+c^4)*a^2-2*(b^2+c^2)*(b^2-c^2)^2 : :
X(49308) = 3*X(14)-X(6269) = X(6269)+3*X(6271) = 2*X(6269)-3*X(49307) = 2*X(6271)+X(49307)

The reciprocal orthologic center of these triangles is X(4).

X(49308) lies on these lines: {3, 48725}, {6, 13}, {30, 33443}, {491, 617}, {530, 49312}, {531, 1991}, {619, 45473}, {2044, 6773}, {3103, 35850}, {3365, 45543}, {5321, 22632}, {5474, 12306}, {5479, 45441}, {5613, 6290}, {6774, 43118}, {7974, 45477}, {9732, 49334}, {9900, 45427}, {9915, 45429}, {9981, 45435}, {10061, 45491}, {10077, 45493}, {11706, 45399}, {12141, 45401}, {12204, 45403}, {12336, 45417}, {12470, 45431}, {12471, 45433}, {12780, 45445}, {12792, 45447}, {12921, 45455}, {12931, 45457}, {12941, 45459}, {12951, 45461}, {12988, 45465}, {12989, 45466}, {13075, 45471}, {13102, 45489}, {13104, 45495}, {13106, 45497}, {13749, 18586}, {13916, 45486}, {13981, 45485}, {18585, 33442}, {18975, 45405}, {22774, 45437}, {35851, 45463}, {36382, 36396}, {36439, 47611}, {41021, 42279}, {41022, 49310}, {45346, 48459}, {45348, 48458}, {45410, 48724}, {45413, 49376}, {45414, 49375}, {45420, 49036}, {45423, 49145}, {45425, 49146}

X(49308) = midpoint of X(i) and X(j) for these {i, j}: {14, 6271}, {617, 49037}
X(49308) = reflection of X(i) in X(j) for these (i, j): (3, 48725), (5474, 35748), (49307, 14)
X(49308) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: 2nd Altintas-isodynamic, 4th Fermat-Dao, 8th Fermat-Dao, 12th Fermat-Dao, 16th Fermat-Dao, 1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi, 3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi, 2nd half-diamonds-central, 2nd isodynamic-Dao, 4th isodynamic-Dao, 2nd Lemoine-Dao, inner-Napoleon
X(49308) = X(14)-of-2nd anti-Kenmotu centers triangle
X(49308) = X(48725)-of-X3-ABC reflections triangle
X(49308) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (381, 45376, 49306), (381, 48656, 49307), (22797, 41043, 49307)


X(49309) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO 1st ANTI-BROCARD

Barycentrics    2*(a^4-b^2*a^2-(b^2-c^2)*c^2)*(a^4-c^2*a^2+(b^2-c^2)*b^2)*S+3*(b^2+c^2)*a^8-4*(b^4+b^2*c^2+c^4)*a^6+3*(b^6+c^6)*a^4-2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*b^2*c^2 : :
X(49309) = 3*X(98)-X(6227) = 3*X(6226)+X(6227) = 2*X(6226)+X(49310) = 2*X(6227)-3*X(49310) = 3*X(11177)-X(49041)

The reciprocal orthologic center of these triangles is X(5999).

X(49309) lies on the circumcircle of 1st anti-Kenmotu centers triangle and these lines: {3, 48726}, {6, 98}, {30, 49311}, {99, 12305}, {114, 45472}, {115, 45440}, {147, 492}, {372, 2794}, {542, 591}, {690, 49313}, {1503, 33430}, {2782, 9733}, {2783, 48703}, {2784, 49347}, {2787, 48684}, {2799, 49315}, {3023, 45404}, {3027, 45470}, {3102, 35825}, {6033, 6231}, {7970, 45476}, {8980, 45484}, {9860, 45426}, {9861, 45428}, {9862, 45406}, {9864, 45444}, {10053, 45490}, {10069, 45492}, {11177, 45421}, {11710, 45398}, {12042, 43119}, {12131, 45400}, {12176, 45402}, {12178, 45416}, {12179, 45430}, {12180, 45432}, {12181, 45446}, {12182, 45454}, {12183, 45456}, {12184, 45458}, {12185, 45460}, {12186, 45467}, {12187, 45464}, {12188, 45488}, {12189, 45494}, {12190, 45496}, {13967, 45487}, {22504, 45436}, {22505, 45438}, {35824, 45462}, {36733, 48728}, {38744, 45375}, {41022, 49307}, {41023, 49305}, {45345, 48462}, {45347, 48463}, {45411, 48727}, {45412, 49379}, {45415, 49380}, {45422, 49147}, {45424, 49148}, {49353, 49355}

X(49309) = midpoint of X(i) and X(j) for these {i, j}: {98, 6226}, {147, 49040}
X(49309) = reflection of X(i) in X(j) for these (i, j): (3, 48726), (36733, 48728), (49310, 98), (49367, 9733)
X(49309) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: 1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard
X(49309) = X(98)-of-1st anti-Kenmotu centers triangle
X(49309) = X(48726)-of-X3-ABC reflections triangle
X(49309) = {X(98), X(10753)}-harmonic conjugate of X(49212)


X(49310) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO 1st ANTI-BROCARD

Barycentrics    -2*(a^4-b^2*a^2-(b^2-c^2)*c^2)*(a^4-c^2*a^2+(b^2-c^2)*b^2)*S+3*(b^2+c^2)*a^8-4*(b^4+b^2*c^2+c^4)*a^6+3*(b^6+c^6)*a^4-2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*b^2*c^2 : :
X(49310) = 3*X(98)-X(6226) = X(6226)+3*X(6227) = 2*X(6226)-3*X(49309) = 2*X(6227)+X(49309) = 3*X(11177)-X(49040)

The reciprocal orthologic center of these triangles is X(5999).

X(49310) lies on the circumcircle of 2nd anti-Kenmotu centers triangle and these lines: {3, 48727}, {6, 98}, {30, 49312}, {99, 12306}, {114, 45473}, {115, 45441}, {147, 491}, {371, 2794}, {542, 1991}, {690, 49314}, {1503, 33431}, {2782, 9732}, {2783, 48704}, {2784, 49348}, {2787, 48685}, {2799, 49316}, {3023, 45405}, {3027, 45471}, {3103, 35824}, {6033, 6230}, {7970, 45477}, {8980, 45486}, {9860, 45427}, {9861, 45429}, {9862, 45407}, {9864, 45445}, {10053, 45491}, {10069, 45493}, {11177, 45420}, {11710, 45399}, {12042, 43118}, {12131, 45401}, {12176, 45403}, {12178, 45417}, {12179, 45431}, {12180, 45433}, {12181, 45447}, {12182, 45455}, {12183, 45457}, {12184, 45459}, {12185, 45461}, {12186, 45465}, {12187, 45466}, {12188, 45489}, {12189, 45495}, {12190, 45497}, {13967, 45485}, {22504, 45437}, {22505, 45439}, {35825, 45463}, {36719, 48729}, {38744, 45376}, {41022, 49308}, {41023, 49306}, {45346, 48463}, {45348, 48462}, {45410, 48726}, {45413, 49380}, {45414, 49379}, {45423, 49147}, {45425, 49148}, {49354, 49356}

X(49310) = midpoint of X(i) and X(j) for these {i, j}: {98, 6227}, {147, 49041}
X(49310) = reflection of X(i) in X(j) for these (i, j): (3, 48727), (36719, 48729), (49309, 98), (49368, 9732)
X(49310) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: 1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard
X(49310) = X(98)-of-2nd anti-Kenmotu centers triangle
X(49310) = X(48727)-of-X3-ABC reflections triangle
X(49310) = {X(98), X(10753)}-harmonic conjugate of X(49213)


X(49311) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO ANTI-MCCAY

Barycentrics    2*(a^2-2*b^2+c^2)*(a^2+b^2-2*c^2)*S+4*a^6-3*(b^2+c^2)*a^4-(2*b^2-c^2)*(b^2-2*c^2)*(b^2+c^2) : :
X(49311) = 3*X(148)-X(49043) = 3*X(671)-X(9882) = X(9882)+3*X(9883) = 2*X(9882)-3*X(49312) = 2*X(9883)+X(49312)

The reciprocal orthologic center of these triangles is X(9855).

X(49311) lies on these lines: {3, 48728}, {6, 598}, {30, 49309}, {148, 45421}, {492, 8591}, {524, 33432}, {530, 49307}, {531, 49305}, {542, 13748}, {543, 591}, {590, 33343}, {1991, 6033}, {2482, 45472}, {2782, 49327}, {2796, 49347}, {3071, 33433}, {3102, 35699}, {5969, 49351}, {6289, 8724}, {6561, 9890}, {9766, 49368}, {9875, 45426}, {9876, 45428}, {9878, 45434}, {9880, 45440}, {9881, 45444}, {9884, 45476}, {10054, 45490}, {10070, 45492}, {12117, 12305}, {12132, 45400}, {12191, 45402}, {12243, 45406}, {12258, 45398}, {12326, 45416}, {12345, 45430}, {12346, 45432}, {12347, 45446}, {12348, 45454}, {12349, 45456}, {12350, 45458}, {12351, 45460}, {12352, 45467}, {12353, 45464}, {12354, 45470}, {12355, 45488}, {12356, 45494}, {12357, 45496}, {13677, 33342}, {13908, 45484}, {13968, 45487}, {18546, 35824}, {18969, 45404}, {22565, 45436}, {22566, 45438}, {35698, 45462}, {36656, 38745}, {43119, 49102}, {45345, 48470}, {45347, 48471}, {45375, 48657}, {45411, 48729}, {45412, 49381}, {45415, 49382}, {45422, 49149}, {45424, 49150}

X(49311) = midpoint of X(i) and X(j) for these {i, j}: {671, 9883}, {8591, 49042}
X(49311) = reflection of X(i) in X(j) for these (i, j): (3, 48728), (49312, 671), (49367, 591)
X(49311) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: anti-McCay, McCay, Moses-Steiner osculatory
X(49311) = X(671)-of-1st anti-Kenmotu centers triangle
X(49311) = X(9739)-of-anti-McCay triangle
X(49311) = X(48728)-of-X3-ABC reflections triangle
X(49311) = {X(671), X(8593)}-harmonic conjugate of X(49214)


X(49312) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO ANTI-MCCAY

Barycentrics    -2*(a^2-2*b^2+c^2)*(a^2+b^2-2*c^2)*S+4*a^6-3*(b^2+c^2)*a^4-(2*b^2-c^2)*(b^2-2*c^2)*(b^2+c^2) : :
X(49312) = 3*X(148)-X(49042) = 3*X(671)-X(9883) = 3*X(9882)+X(9883) = 2*X(9882)+X(49311) = 2*X(9883)-3*X(49311)

The reciprocal orthologic center of these triangles is X(9855).

X(49312) lies on these lines: {3, 48729}, {6, 598}, {30, 49310}, {148, 45420}, {491, 8591}, {524, 33433}, {530, 49308}, {531, 49306}, {542, 13749}, {543, 1991}, {591, 6033}, {615, 33342}, {2482, 45473}, {2782, 49328}, {2796, 49348}, {3070, 33432}, {3103, 35698}, {5969, 49352}, {6290, 8724}, {6560, 9890}, {9766, 49367}, {9875, 45427}, {9876, 45429}, {9878, 45435}, {9880, 45441}, {9881, 45445}, {9884, 45477}, {10054, 45491}, {10070, 45493}, {12117, 12306}, {12132, 45401}, {12191, 45403}, {12243, 45407}, {12258, 45399}, {12326, 45417}, {12345, 45431}, {12346, 45433}, {12347, 45447}, {12348, 45455}, {12349, 45457}, {12350, 45459}, {12351, 45461}, {12352, 45465}, {12353, 45466}, {12354, 45471}, {12355, 45489}, {12356, 45495}, {12357, 45497}, {13797, 33343}, {13908, 45486}, {13968, 45485}, {18546, 35825}, {18969, 45405}, {22565, 45437}, {22566, 45439}, {35699, 45463}, {36655, 38745}, {43118, 49102}, {45346, 48471}, {45348, 48470}, {45376, 48657}, {45410, 48728}, {45413, 49382}, {45414, 49381}, {45423, 49149}, {45425, 49150}

X(49312) = midpoint of X(i) and X(j) for these {i, j}: {671, 9882}, {8591, 49043}
X(49312) = reflection of X(i) in X(j) for these (i, j): (3, 48729), (49311, 671), (49368, 1991)
X(49312) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: anti-McCay, McCay, Moses-Steiner osculatory
X(49312) = X(671)-of-2nd anti-Kenmotu centers triangle
X(49312) = X(9738)-of-anti-McCay triangle
X(49312) = X(48729)-of-X3-ABC reflections triangle
X(49312) = {X(671), X(8593)}-harmonic conjugate of X(49215)


X(49313) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*(2*(a^4+(b^2-2*c^2)*a^2-(b^2-c^2)*(2*b^2+c^2))*(a^4-(2*b^2-c^2)*a^2+(b^2-c^2)*(b^2+2*c^2))*S+3*(b^2+c^2)*a^8-6*(b^4+c^4)*a^6+3*(b^2+c^2)*b^2*c^2*a^4+6*(b^6-c^6)*(b^2-c^2)*a^2+(b^4-c^4)*(b^2-c^2)*(-3*b^4-3*b^2*c^2-3*c^4)) : :
X(49313) = 3*X(74)-X(7725) = X(7725)+3*X(7726) = 2*X(7725)-3*X(49314) = 2*X(7726)+X(49314) = 3*X(15041)-2*X(48731)

The reciprocal orthologic center of these triangles is X(12112).

X(49313) lies on the circumcircle of 1st anti-Kenmotu centers triangle and these lines: {3, 48730}, {4, 45480}, {6, 74}, {30, 49319}, {110, 12305}, {113, 45472}, {125, 45440}, {146, 492}, {399, 44196}, {541, 591}, {542, 49367}, {690, 49309}, {1503, 49365}, {1539, 45438}, {2771, 48703}, {2777, 13748}, {3024, 45404}, {3028, 45470}, {3102, 35827}, {5663, 9733}, {6289, 7728}, {7687, 45474}, {7978, 45476}, {8674, 48684}, {8994, 45484}, {9517, 49315}, {9904, 45426}, {9919, 45428}, {9984, 45434}, {10065, 45490}, {10081, 45492}, {10620, 45488}, {10628, 49357}, {11709, 45398}, {12041, 43119}, {12112, 45418}, {12133, 45400}, {12192, 45402}, {12244, 45406}, {12327, 45416}, {12365, 45430}, {12366, 45432}, {12368, 45444}, {12369, 45446}, {12371, 45454}, {12372, 45456}, {12373, 45458}, {12374, 45460}, {12377, 45467}, {12378, 45464}, {12381, 45494}, {12382, 45496}, {13202, 45478}, {13969, 45487}, {15041, 45411}, {17702, 49321}, {17812, 45442}, {22583, 45436}, {35826, 45462}, {38790, 45375}, {45345, 48472}, {45347, 48473}, {45412, 49383}, {45415, 49384}, {45421, 49045}, {45422, 49151}, {45424, 49152}

X(49313) = midpoint of X(i) and X(j) for these {i, j}: {74, 7726}, {146, 49044}
X(49313) = reflection of X(i) in X(j) for these (i, j): (3, 48730), (49314, 74), (49369, 9733)
X(49313) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: anti-orthocentroidal, orthocentroidal
X(49313) = X(74)-of-1st anti-Kenmotu centers triangle
X(49313) = X(13748)-of-anti-orthocentroidal triangle
X(49313) = X(48730)-of-X3-ABC reflections triangle
X(49313) = {X(74), X(10752)}-harmonic conjugate of X(49216)


X(49314) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*(-2*(a^4+(b^2-2*c^2)*a^2-(b^2-c^2)*(2*b^2+c^2))*(a^4-(2*b^2-c^2)*a^2+(b^2-c^2)*(b^2+2*c^2))*S+3*(b^2+c^2)*a^8-6*(b^4+c^4)*a^6+3*(b^2+c^2)*b^2*c^2*a^4+6*(b^6-c^6)*(b^2-c^2)*a^2+(b^4-c^4)*(b^2-c^2)*(-3*b^4-3*b^2*c^2-3*c^4)) : :
X(49314) = 3*X(74)-X(7726) = 3*X(7725)+X(7726) = 2*X(7725)+X(49313) = 2*X(7726)-3*X(49313) = 3*X(15041)-2*X(48730)

The reciprocal orthologic center of these triangles is X(12112).

X(49314) lies on the circumcircle of 2nd anti-Kenmotu centers triangle and these lines: {3, 48731}, {4, 45481}, {6, 74}, {30, 49320}, {110, 12306}, {113, 45473}, {125, 45441}, {146, 491}, {399, 44199}, {541, 1991}, {542, 49368}, {690, 49310}, {1503, 49366}, {1539, 45439}, {2771, 48704}, {2777, 13749}, {3024, 45405}, {3028, 45471}, {3103, 35826}, {5663, 9732}, {6290, 7728}, {7687, 45475}, {7978, 45477}, {8674, 48685}, {8994, 45486}, {9517, 49316}, {9904, 45427}, {9919, 45429}, {9984, 45435}, {10065, 45491}, {10081, 45493}, {10620, 45489}, {10628, 49358}, {11709, 45399}, {12041, 43118}, {12112, 45419}, {12133, 45401}, {12192, 45403}, {12244, 45407}, {12327, 45417}, {12365, 45431}, {12366, 45433}, {12368, 45445}, {12369, 45447}, {12371, 45455}, {12372, 45457}, {12373, 45459}, {12374, 45461}, {12377, 45465}, {12378, 45466}, {12381, 45495}, {12382, 45497}, {13202, 45479}, {13969, 45485}, {15041, 45410}, {17702, 49322}, {17812, 45443}, {22583, 45437}, {35827, 45463}, {38790, 45376}, {45346, 48473}, {45348, 48472}, {45413, 49384}, {45414, 49383}, {45420, 49044}, {45423, 49151}, {45425, 49152}

X(49314) = midpoint of X(i) and X(j) for these {i, j}: {74, 7725}, {146, 49045}
X(49314) = reflection of X(i) in X(j) for these (i, j): (3, 48731), (49313, 74), (49370, 9732)
X(49314) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: anti-orthocentroidal, orthocentroidal
X(49314) = X(74)-of-2nd anti-Kenmotu centers triangle
X(49314) = X(13749)-of-anti-orthocentroidal triangle
X(49314) = X(48731)-of-X3-ABC reflections triangle
X(49314) = {X(74), X(10752)}-harmonic conjugate of X(49217)


X(49315) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*(2*(a^6-c^2*a^4+(b^4-c^4)*a^2-(b^2-c^2)*(2*b^4+b^2*c^2+c^4))*(a^6-b^2*a^4-(b^4-c^4)*a^2+(b^2-c^2)*(b^4+b^2*c^2+2*c^4))*S+3*(b^2+c^2)*a^12-4*(b^4+b^2*c^2+c^4)*a^10-(b^2+c^2)*(b^4-5*b^2*c^2+c^4)*a^8-4*(b^2-c^2)^2*b^2*c^2*a^6+(b^8-c^8)*a^4*(b^2-c^2)+4*(b^4-c^4)^2*(b^4+c^4)*a^2+(b^4-c^4)*(b^2-c^2)*(-3*b^8-3*c^8-b^2*c^2*(b^4+8*b^2*c^2+c^4))) : :
X(49315) = 3*X(1297)-X(12805) = X(12805)+3*X(12806) = 2*X(12805)-3*X(49316) = 2*X(12806)+X(49316)

The reciprocal orthologic center of these triangles is X(19158).

X(49315) lies on the circumcircle of 1st anti-Kenmotu centers triangle and these lines: {3, 48732}, {6, 1297}, {112, 12305}, {127, 45440}, {132, 45472}, {492, 12384}, {591, 9530}, {1160, 11641}, {2781, 49369}, {2794, 49367}, {2799, 49309}, {2806, 48684}, {2831, 48703}, {3102, 35829}, {3320, 45470}, {6020, 45404}, {6289, 12918}, {9517, 49313}, {9733, 49371}, {12145, 45400}, {12207, 45402}, {12253, 45406}, {12265, 45398}, {12340, 45416}, {12408, 45426}, {12413, 45428}, {12478, 45430}, {12479, 45432}, {12503, 45434}, {12784, 45444}, {12796, 45446}, {12925, 45454}, {12935, 45456}, {12945, 45458}, {12955, 45460}, {12996, 45467}, {12997, 45464}, {13099, 45476}, {13115, 45488}, {13116, 45490}, {13117, 45492}, {13118, 45494}, {13119, 45496}, {13918, 45484}, {13985, 45487}, {19159, 45436}, {19160, 45438}, {35828, 45462}, {38624, 43119}, {45345, 48474}, {45347, 48475}, {45375, 48658}, {45411, 48733}, {45412, 49385}, {45415, 49386}, {45421, 49047}, {45422, 49153}, {45424, 49154}

X(49315) = midpoint of X(i) and X(j) for these {i, j}: {1297, 12806}, {12384, 49046}
X(49315) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: 1st anti-orthosymmedial, 1st orthosymmedial
X(49315) = X(48732)-of-X3-ABC reflections triangle
X(49315) = X(1297)-of-1st anti-Kenmotu centers triangle
X(49315) = reflection of X(i) in X(j) for these (i, j): (3, 48732), (49316, 1297), (49371, 9733)


X(49316) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*(-2*(a^6-c^2*a^4+(b^4-c^4)*a^2-(b^2-c^2)*(2*b^4+b^2*c^2+c^4))*(a^6-b^2*a^4-(b^4-c^4)*a^2+(b^2-c^2)*(b^4+b^2*c^2+2*c^4))*S+3*(b^2+c^2)*a^12-4*(b^4+b^2*c^2+c^4)*a^10-(b^2+c^2)*(b^4-5*b^2*c^2+c^4)*a^8-4*(b^2-c^2)^2*b^2*c^2*a^6+(b^8-c^8)*a^4*(b^2-c^2)+4*(b^4-c^4)^2*(b^4+c^4)*a^2+(b^4-c^4)*(b^2-c^2)*(-3*b^8-3*c^8-b^2*c^2*(b^4+8*b^2*c^2+c^4))) : :
X(49316) = 3*X(1297)-X(12806) = 3*X(12805)+X(12806) = 2*X(12805)+X(49315) = 2*X(12806)-3*X(49315)

The reciprocal orthologic center of these triangles is X(19158).

X(49316) lies on the circumcircle of 2nd anti-Kenmotu centers triangle and these lines: {3, 48733}, {6, 1297}, {112, 12306}, {127, 45441}, {132, 45473}, {491, 12384}, {1161, 8996}, {1991, 9530}, {2781, 49370}, {2794, 49368}, {2799, 49310}, {2806, 48685}, {2831, 48704}, {3103, 35828}, {3320, 45471}, {6020, 45405}, {6290, 12918}, {9517, 49314}, {9732, 49372}, {12145, 45401}, {12207, 45403}, {12253, 45407}, {12265, 45399}, {12340, 45417}, {12408, 45427}, {12413, 45429}, {12478, 45431}, {12479, 45433}, {12503, 45435}, {12784, 45445}, {12796, 45447}, {12925, 45455}, {12935, 45457}, {12945, 45459}, {12955, 45461}, {12996, 45465}, {12997, 45466}, {13099, 45477}, {13115, 45489}, {13116, 45491}, {13117, 45493}, {13118, 45495}, {13119, 45497}, {13918, 45486}, {13985, 45485}, {19159, 45437}, {19160, 45439}, {35829, 45463}, {38624, 43118}, {45346, 48475}, {45348, 48474}, {45376, 48658}, {45410, 48732}, {45413, 49386}, {45414, 49385}, {45420, 49046}, {45423, 49153}, {45425, 49154}

X(49316) = midpoint of X(i) and X(j) for these {i, j}: {1297, 12805}, {12384, 49047}
X(49316) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: 1st anti-orthosymmedial, 1st orthosymmedial
X(49316) = X(48733)-of-X3-ABC reflections triangle
X(49316) = X(1297)-of-2nd anti-Kenmotu centers triangle
X(49316) = reflection of X(i) in X(j) for these (i, j): (3, 48733), (49315, 1297), (49372, 9732)


X(49317) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO 3rd ANTI-TRI-SQUARES

Barycentrics    2*S*((b^2+c^2)*a^2-(b^2-c^2)^2)+3*a^6-5*(b^2+c^2)*a^4+(3*b^4-2*b^2*c^2+3*c^4)*a^2-(b^2+c^2)*(b^2-c^2)^2 : :
X(49317) = 2*X(5)-3*X(486) = 2*X(5)+3*X(6280) = 4*X(5)-3*X(6290) = X(20)+3*X(12221) = X(20)-3*X(12256) = X(382)-3*X(12601) = 3*X(486)-X(6281) = 3*X(487)-5*X(631) = 4*X(548)-3*X(12123) = 3*X(591)-2*X(35684) = 5*X(631)+3*X(49048) = 5*X(631)-6*X(49103) = 6*X(642)-7*X(3526) = 7*X(3528)-3*X(12509) = 7*X(3832)-6*X(22596) = X(6278)-3*X(22591) = 3*X(6280)+X(6281) = 2*X(6280)+X(6290) = 2*X(6281)-3*X(6290) = X(49048)+2*X(49103)

The reciprocal orthologic center of these triangles is X(486).

X(49317) lies on these lines: {3, 591}, {4, 33456}, {5, 6}, {20, 6463}, {30, 22484}, {114, 45514}, {372, 49086}, {382, 12601}, {487, 492}, {542, 13927}, {548, 12123}, {575, 11313}, {576, 36656}, {637, 43118}, {639, 5050}, {640, 11898}, {642, 3526}, {1151, 48772}, {1351, 48466}, {3095, 49327}, {3102, 35833}, {3311, 45554}, {3398, 6229}, {3528, 12509}, {3832, 22596}, {3843, 6251}, {4309, 13081}, {4317, 18989}, {5070, 6119}, {5097, 45542}, {5881, 9906}, {6565, 49087}, {6811, 41624}, {7581, 26468}, {7980, 45476}, {8252, 48773}, {8414, 9680}, {8981, 13650}, {9714, 9921}, {9715, 12972}, {9732, 45510}, {9986, 45434}, {10067, 15888}, {10083, 37722}, {10133, 13428}, {11314, 34507}, {11362, 49347}, {12007, 23311}, {12147, 37122}, {12210, 45402}, {12268, 45398}, {12296, 33703}, {12343, 45416}, {12484, 45430}, {12485, 45432}, {12787, 45444}, {12799, 45446}, {12928, 45454}, {12938, 45456}, {12948, 37719}, {12958, 37720}, {13002, 45467}, {13003, 45464}, {13132, 45494}, {13133, 45496}, {13692, 22616}, {13812, 13847}, {13921, 45484}, {13932, 35822}, {13933, 45487}, {13934, 35813}, {13951, 45555}, {17800, 22809}, {20423, 36658}, {22595, 45436}, {23236, 49369}, {32455, 45861}, {32494, 39679}, {32788, 37342}, {32805, 49104}, {32811, 49115}, {33749, 44510}, {35830, 45462}, {35948, 45525}, {36349, 36437}, {36357, 36455}, {37726, 45422}, {37727, 45713}, {39899, 48467}, {42009, 43120}, {42060, 44485}, {45345, 48478}, {45347, 48479}, {45412, 49387}, {45415, 49388}, {45424, 49156}, {45544, 48660}

X(49317) = midpoint of X(i) and X(j) for these {i, j}: {486, 6280}, {487, 49048}, {12221, 12256}
X(49317) = reflection of X(i) in X(j) for these (i, j): (3, 48734), (487, 49103), (6281, 5), (6290, 486), (13692, 22616), (13812, 13847), (32811, 49115), (48659, 6251)
X(49317) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: 3rd anti-tri-squares, 2nd half-squares, 4th tri-squares, inner-Vecten
X(49317) = X(486)-of-1st anti-Kenmotu centers triangle
X(49317) = X(6281)-of-Johnson triangle
X(49317) = X(48734)-of-X3-ABC reflections triangle
X(49317) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5, 6281, 6290), (6, 49355, 6289), (486, 6281, 5), (486, 13770, 7584), (5874, 7584, 1352), (5874, 13770, 6290), (6214, 19116, 14561), (40693, 40694, 49221)


X(49318) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO 4th ANTI-TRI-SQUARES

Barycentrics    -2*S*((b^2+c^2)*a^2-(b^2-c^2)^2)+3*a^6-5*(b^2+c^2)*a^4+(3*b^4-2*b^2*c^2+3*c^4)*a^2-(b^2+c^2)*(b^2-c^2)^2 : :
X(49318) = 2*X(5)-3*X(485) = 2*X(5)+3*X(6279) = 4*X(5)-3*X(6289) = X(20)+3*X(12222) = X(20)-3*X(12257) = X(382)-3*X(12602) = 3*X(485)-X(6278) = 3*X(488)-5*X(631) = 4*X(548)-3*X(12124) = 5*X(631)+3*X(49049) = 5*X(631)-6*X(49104) = 6*X(641)-7*X(3526) = 3*X(1991)-2*X(35685) = 7*X(3528)-3*X(12510) = 7*X(3832)-6*X(22625) = X(6278)+3*X(6279) = 2*X(6278)-3*X(6289) = 2*X(6279)+X(6289) = X(6281)-3*X(22592) = X(49049)+2*X(49104)

The reciprocal orthologic center of these triangles is X(485).

X(49318) lies on these lines: {3, 1991}, {4, 33457}, {5, 6}, {20, 6462}, {30, 22485}, {114, 45515}, {371, 49087}, {382, 12602}, {488, 491}, {542, 13874}, {548, 12124}, {575, 11314}, {576, 36655}, {638, 43119}, {639, 11898}, {640, 5050}, {641, 3526}, {1152, 48773}, {1351, 48467}, {3095, 49328}, {3103, 35832}, {3312, 45555}, {3398, 6228}, {3528, 12510}, {3832, 22625}, {3843, 6250}, {4309, 13082}, {4317, 18988}, {5070, 6118}, {5097, 45543}, {5861, 21737}, {5881, 9907}, {6564, 49086}, {6813, 41624}, {7582, 26469}, {7981, 45477}, {8253, 48772}, {8976, 45554}, {9714, 9922}, {9715, 12973}, {9733, 45511}, {9987, 45435}, {10068, 15888}, {10084, 37722}, {10132, 13439}, {11313, 34507}, {11362, 49348}, {12007, 23312}, {12148, 37122}, {12211, 45403}, {12269, 45399}, {12297, 33703}, {12344, 45417}, {12486, 45431}, {12487, 45433}, {12788, 45445}, {12800, 45447}, {12929, 45455}, {12939, 45457}, {12949, 37719}, {12959, 37720}, {12961, 26875}, {13004, 45465}, {13005, 45466}, {13134, 45495}, {13135, 45497}, {13692, 13846}, {13771, 13966}, {13812, 22645}, {13850, 35823}, {13879, 45486}, {13880, 45485}, {13882, 35812}, {17800, 22810}, {20423, 36657}, {22624, 45437}, {23236, 49370}, {31454, 32497}, {32455, 45860}, {32787, 37343}, {32806, 49103}, {32810, 49114}, {33749, 44509}, {35744, 49334}, {35831, 45463}, {35949, 45524}, {36348, 36455}, {36356, 36437}, {37726, 45423}, {37727, 45714}, {39899, 48466}, {42009, 44486}, {42060, 43121}, {45346, 48481}, {45348, 48480}, {45413, 49390}, {45414, 49389}, {45425, 49158}, {45545, 48659}

X(49318) = midpoint of X(i) and X(j) for these {i, j}: {485, 6279}, {488, 49049}, {12222, 12257}
X(49318) = reflection of X(i) in X(j) for these (i, j): (3, 48735), (488, 49104), (6278, 5), (6289, 485), (13692, 13846), (13812, 22645), (32810, 49114), (48660, 6250)
X(49318) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: 4th anti-tri-squares, 1st half-squares, 3rd tri-squares, outer-Vecten
X(49318) = X(485)-of-2nd anti-Kenmotu centers triangle
X(49318) = X(6278)-of-Johnson triangle
X(49318) = X(48735)-of-X3-ABC reflections triangle
X(49318) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5, 6278, 6289), (6, 49356, 6290), (485, 6278, 5), (485, 13651, 7583), (5875, 7583, 1352), (5875, 13651, 6289), (6215, 19117, 14561), (40693, 40694, 49220)


X(49319) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO AAOA

Barycentrics    -2*(-a^2+b^2+c^2)*((a^2+b^2-c^2)^2-b^2*a^2)*((a^2-b^2+c^2)^2-c^2*a^2)*S+(2*a^6-2*(b^2+c^2)*a^4+(b^4+c^4)*a^2-(b^4-c^4)*(b^2-c^2))*(a^6-(b^2+c^2)*a^4-(b^4+c^4)*a^2+(b^4-c^4)*(b^2-c^2)) : :
X(49319) = 3*X(265)-X(12803) = X(12803)+3*X(12804) = 2*X(12803)-3*X(49320) = 2*X(12804)+X(49320) = 3*X(38724)-2*X(48737)

The reciprocal orthologic center of these triangles is X(7574).

X(49319) lies on these lines: {3, 48736}, {6, 13}, {30, 49313}, {110, 6289}, {125, 43119}, {492, 12383}, {511, 49365}, {568, 45480}, {1511, 45472}, {1986, 45478}, {2771, 49337}, {2777, 49349}, {2931, 44196}, {3102, 35835}, {3448, 45406}, {3581, 45418}, {5663, 13748}, {9733, 17702}, {10088, 45458}, {10091, 45460}, {10113, 45440}, {10628, 49341}, {10706, 49361}, {12121, 12305}, {12140, 45400}, {12201, 45402}, {12236, 45474}, {12261, 45398}, {12334, 45416}, {12407, 45426}, {12412, 45428}, {12466, 45430}, {12467, 45432}, {12501, 45434}, {12778, 45444}, {12790, 45446}, {12889, 45454}, {12890, 45456}, {12894, 45467}, {12895, 45464}, {12896, 45470}, {12898, 45476}, {12902, 45488}, {12903, 45490}, {12904, 45492}, {12905, 45494}, {12906, 45496}, {13915, 45484}, {13979, 45487}, {17835, 45442}, {18968, 45404}, {19457, 45408}, {19478, 45436}, {32423, 49355}, {35834, 45462}, {38724, 45411}, {45345, 48483}, {45347, 48484}, {45412, 49391}, {45415, 49392}, {45421, 49051}, {45422, 49159}, {45424, 49160}

X(49319) = midpoint of X(i) and X(j) for these {i, j}: {265, 12804}, {12383, 49050}
X(49319) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: AAOA, AOA, 1st Hyacinth
X(49319) = X(48736)-of-X3-ABC reflections triangle
X(49319) = X(265)-of-1st anti-Kenmotu centers triangle
X(49319) = reflection of X(i) in X(j) for these (i, j): (3, 48736), (49320, 265), (49369, 49355)


X(49320) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO AAOA

Barycentrics    2*(-a^2+b^2+c^2)*((a^2+b^2-c^2)^2-b^2*a^2)*((a^2-b^2+c^2)^2-c^2*a^2)*S+(2*a^6-2*(b^2+c^2)*a^4+(b^4+c^4)*a^2-(b^4-c^4)*(b^2-c^2))*(a^6-(b^2+c^2)*a^4-(b^4+c^4)*a^2+(b^4-c^4)*(b^2-c^2)) : :
X(49320) = 3*X(265)-X(12804) = 3*X(12803)+X(12804) = 2*X(12803)+X(49319) = 2*X(12804)-3*X(49319) = 3*X(38724)-2*X(48736)

The reciprocal orthologic center of these triangles is X(7574).

X(49320) lies on these lines: {3, 48737}, {6, 13}, {30, 49314}, {110, 6290}, {125, 43118}, {491, 12383}, {511, 49366}, {568, 45481}, {1511, 45473}, {1986, 45479}, {2771, 49338}, {2777, 49350}, {2931, 44199}, {3103, 35834}, {3448, 45407}, {3581, 45419}, {5663, 13749}, {9732, 17702}, {10088, 45459}, {10091, 45461}, {10113, 45441}, {10628, 49342}, {10706, 49364}, {12121, 12306}, {12140, 45401}, {12201, 45403}, {12236, 45475}, {12261, 45399}, {12334, 45417}, {12407, 45427}, {12412, 45429}, {12466, 45431}, {12467, 45433}, {12501, 45435}, {12778, 45445}, {12790, 45447}, {12889, 45455}, {12890, 45457}, {12894, 45465}, {12895, 45466}, {12896, 45471}, {12898, 45477}, {12902, 45489}, {12903, 45491}, {12904, 45493}, {12905, 45495}, {12906, 45497}, {13915, 45486}, {13979, 45485}, {17835, 45443}, {18968, 45405}, {19457, 45409}, {19478, 45437}, {32423, 49356}, {35835, 45463}, {38724, 45410}, {45346, 48484}, {45348, 48483}, {45413, 49392}, {45414, 49391}, {45420, 49050}, {45423, 49159}, {45425, 49160}

X(49320) = midpoint of X(i) and X(j) for these {i, j}: {265, 12803}, {12383, 49051}
X(49320) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: AAOA, AOA, 1st Hyacinth
X(49320) = X(48737)-of-X3-ABC reflections triangle
X(49320) = X(265)-of-2nd anti-Kenmotu centers triangle
X(49320) = reflection of X(i) in X(j) for these (i, j): (3, 48737), (49319, 265), (49370, 49356)


X(49321) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO ARIES

Barycentrics    (2*(a^4-2*b^2*a^2+(b^2-c^2)^2)*(a^4-2*c^2*a^2+(b^2-c^2)^2)*S+(2*a^4-(b^2+c^2)*a^2+(b^2-c^2)^2)*(a^6-(b^2+c^2)*a^4-(b^2+c^2)^2*a^2+(b^4-c^4)*(b^2-c^2)))*(-a^2+b^2+c^2) : :
X(49321) = 3*X(68)-X(9929) = X(9929)+3*X(9930) = 2*X(9929)-3*X(49322) = 2*X(9930)+X(49322)

The reciprocal orthologic center of these triangles is X(9833).

X(49321) lies on these lines: {3, 45408}, {5, 6}, {30, 49349}, {52, 45478}, {343, 10132}, {492, 6193}, {539, 591}, {1069, 45460}, {1147, 45472}, {1154, 49341}, {3102, 35837}, {3157, 45458}, {5200, 6515}, {6146, 45452}, {9733, 44665}, {9896, 45426}, {9908, 45428}, {9923, 45434}, {9927, 45440}, {9928, 45444}, {9933, 45476}, {9937, 44196}, {10055, 45490}, {10071, 45492}, {11411, 45406}, {12118, 12305}, {12134, 45400}, {12164, 45375}, {12193, 45402}, {12235, 45474}, {12259, 45398}, {12328, 45416}, {12359, 43119}, {12415, 45430}, {12416, 45432}, {12418, 45446}, {12422, 45454}, {12423, 45456}, {12426, 45467}, {12427, 45464}, {12428, 45470}, {12429, 45488}, {12430, 45494}, {12431, 45496}, {13748, 13754}, {13909, 45484}, {13970, 45487}, {14984, 49365}, {17702, 49313}, {17834, 45442}, {18474, 49087}, {18970, 45404}, {22659, 45436}, {22660, 45438}, {35836, 45462}, {37476, 48772}, {45345, 48485}, {45347, 48486}, {45411, 48739}, {45412, 49393}, {45415, 49394}, {45421, 49053}, {45422, 49161}, {45424, 49162}

X(49321) = midpoint of X(i) and X(j) for these {i, j}: {68, 9930}, {6193, 49052}
X(49321) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: Aries, 2nd Hyacinth
X(49321) = X(48738)-of-X3-ABC reflections triangle
X(49321) = X(68)-of-1st anti-Kenmotu centers triangle
X(49321) = reflection of X(i) in X(j) for these (i, j): (3, 48738), (49322, 68)


X(49322) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO ARIES

Barycentrics    (-2*(a^4-2*b^2*a^2+(b^2-c^2)^2)*(a^4-2*c^2*a^2+(b^2-c^2)^2)*S+(2*a^4-(b^2+c^2)*a^2+(b^2-c^2)^2)*(a^6-(b^2+c^2)*a^4-(b^2+c^2)^2*a^2+(b^4-c^4)*(b^2-c^2)))*(-a^2+b^2+c^2) : :
X(49322) = 3*X(68)-X(9930) = 3*X(9929)+X(9930) = 2*X(9929)+X(49321) = 2*X(9930)-3*X(49321)

The reciprocal orthologic center of these triangles is X(9833).

X(49322) lies on these lines: {3, 45409}, {5, 6}, {30, 49350}, {52, 45479}, {343, 10133}, {491, 6193}, {539, 1991}, {1069, 45461}, {1147, 45473}, {1154, 49342}, {3103, 35836}, {3157, 45459}, {6146, 45453}, {8996, 37488}, {9732, 44665}, {9896, 45427}, {9908, 45429}, {9923, 45435}, {9927, 45441}, {9928, 45445}, {9933, 45477}, {9937, 44199}, {10055, 45491}, {10071, 45493}, {11411, 45407}, {12118, 12306}, {12134, 45401}, {12164, 45376}, {12193, 45403}, {12235, 45475}, {12259, 45399}, {12328, 45417}, {12359, 43118}, {12415, 45431}, {12416, 45433}, {12418, 45447}, {12422, 45455}, {12423, 45457}, {12426, 45465}, {12427, 45466}, {12428, 45471}, {12429, 45489}, {12430, 45495}, {12431, 45497}, {13749, 13754}, {13909, 45486}, {13970, 45485}, {14984, 49366}, {17702, 49314}, {17834, 45443}, {18474, 49086}, {18970, 45405}, {22659, 45437}, {22660, 45439}, {35837, 45463}, {37476, 48773}, {45346, 48486}, {45348, 48485}, {45410, 48738}, {45413, 49394}, {45414, 49393}, {45420, 49052}, {45423, 49161}, {45425, 49162}

X(49322) = midpoint of X(i) and X(j) for these {i, j}: {68, 9929}, {6193, 49053}
X(49322) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: Aries, 2nd Hyacinth
X(49322) = X(48739)-of-X3-ABC reflections triangle
X(49322) = X(68)-of-2nd anti-Kenmotu centers triangle
X(49322) = reflection of X(i) in X(j) for these (i, j): (3, 48739), (49321, 68)


X(49323) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO BEVAN ANTIPODAL

Barycentrics    a*(2*(a^3+(b+c)*a^2-(b+c)^2*a-(b^2-c^2)*(b-c))*S+(b+c)*a^4+2*(b^2-b*c+c^2)*a^3+2*(b+c)*b*c*a^2-2*(b+c)^2*(b^2-b*c+c^2)*a-(b^2-c^2)*(b-c)*(b^2+c^2)) : :
X(49323) = 3*X(40)-X(12697) = X(12697)+3*X(12698) = 2*X(12697)-3*X(49324) = 2*X(12698)+X(49324) = 3*X(34632)-X(49055)

The reciprocal orthologic center of these triangles is X(1).

X(49323) lies on these lines: {1, 12305}, {3, 45398}, {4, 45444}, {6, 40}, {10, 45440}, {46, 45492}, {65, 45470}, {492, 962}, {515, 49329}, {516, 13748}, {517, 9733}, {591, 28194}, {946, 45472}, {1836, 45458}, {1902, 45400}, {2800, 48703}, {2802, 48684}, {3057, 45404}, {3102, 35611}, {3579, 43119}, {5119, 45490}, {5709, 45422}, {5812, 45456}, {5840, 49337}, {5847, 49325}, {6001, 49349}, {6289, 12699}, {6361, 45406}, {7982, 45476}, {7991, 45426}, {9911, 45428}, {10306, 45416}, {12197, 45402}, {12458, 45430}, {12459, 45432}, {12497, 45434}, {12696, 45446}, {12700, 45454}, {12701, 45460}, {12702, 45488}, {12703, 45494}, {12704, 45496}, {13912, 45484}, {13975, 45487}, {22770, 45436}, {22793, 45438}, {22841, 45467}, {22842, 45464}, {28174, 49355}, {34632, 45421}, {35610, 45462}, {36656, 45546}, {45345, 48487}, {45347, 48488}, {45375, 48661}, {45411, 48741}, {45412, 49395}, {45415, 49396}, {45424, 49163}

X(49323) = midpoint of X(i) and X(j) for these {i, j}: {40, 12698}, {962, 49054}
X(49323) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: Bevan antipodal, 3rd extouch
X(49323) = X(48740)-of-X3-ABC reflections triangle
X(49323) = X(40)-of-1st anti-Kenmotu centers triangle
X(49323) = reflection of X(i) in X(j) for these (i, j): (3, 48740), (13748, 49347), (45713, 9733), (49324, 40)


X(49324) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO BEVAN ANTIPODAL

Barycentrics    a*(-2*(a^3+(b+c)*a^2-(b+c)^2*a-(b^2-c^2)*(b-c))*S+(b+c)*a^4+2*(b^2-b*c+c^2)*a^3+2*(b+c)*b*c*a^2-2*(b+c)^2*(b^2-b*c+c^2)*a-(b^2-c^2)*(b-c)*(b^2+c^2)) : :
X(49324) = 3*X(40)-X(12698) = 3*X(12697)+X(12698) = 2*X(12697)+X(49323) = 2*X(12698)-3*X(49323) = 3*X(34632)-X(49054)

The reciprocal orthologic center of these triangles is X(1).

X(49324) lies on these lines: {1, 12306}, {3, 45399}, {4, 45445}, {6, 40}, {10, 45441}, {46, 45493}, {65, 45471}, {491, 962}, {515, 49330}, {516, 13749}, {517, 9732}, {946, 45473}, {1836, 45459}, {1902, 45401}, {1991, 28194}, {2800, 48704}, {2802, 48685}, {3057, 45405}, {3103, 35610}, {3579, 43118}, {5119, 45491}, {5709, 45423}, {5812, 45457}, {5840, 49338}, {5847, 49326}, {6001, 49350}, {6290, 12699}, {6361, 45407}, {7982, 45477}, {7991, 45427}, {9911, 45429}, {10306, 45417}, {12197, 45403}, {12458, 45431}, {12459, 45433}, {12497, 45435}, {12696, 45447}, {12700, 45455}, {12701, 45461}, {12702, 45489}, {12703, 45495}, {12704, 45497}, {13912, 45486}, {13975, 45485}, {22770, 45437}, {22793, 45439}, {22841, 45465}, {22842, 45466}, {28174, 49356}, {34632, 45420}, {35611, 45463}, {36655, 45547}, {45346, 48488}, {45348, 48487}, {45376, 48661}, {45410, 48740}, {45413, 49396}, {45414, 49395}, {45425, 49163}

X(49324) = midpoint of X(i) and X(j) for these {i, j}: {40, 12697}, {962, 49055}
X(49324) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: Bevan antipodal, 3rd extouch
X(49324) = X(48741)-of-X3-ABC reflections triangle
X(49324) = X(40)-of-2nd anti-Kenmotu centers triangle
X(49324) = reflection of X(i) in X(j) for these (i, j): (3, 48741), (13749, 49348), (45714, 9732), (49323, 40)


X(49325) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO 9th BROCARD

Barycentrics    -2*(-a^2+b^2+c^2)*(3*a^4+(b^2-c^2)^2)*S+(a^2+b^2+c^2)*(2*a^6-(b^2+c^2)*a^4-(b^4-c^4)*(b^2-c^2)) : :
X(49325) = 3*X(5050)-2*X(48466) = X(5870)-3*X(14912) = 3*X(6776)-X(39887) = 2*X(14233)-3*X(14853) = X(39887)+3*X(39888) = 2*X(39887)-3*X(49326) = 2*X(39888)+X(49326)

The reciprocal orthologic center of these triangles is X(4).

X(49325) lies on these lines: {3, 48742}, {4, 6}, {69, 12305}, {492, 5921}, {542, 591}, {1350, 35947}, {1352, 45472}, {2456, 6290}, {2794, 35841}, {3102, 39894}, {3564, 9733}, {3818, 44510}, {5050, 48466}, {5085, 39387}, {5847, 49323}, {5848, 48684}, {6289, 18440}, {7710, 13758}, {8414, 21736}, {8721, 39679}, {9756, 45511}, {19145, 45484}, {19146, 45487}, {29012, 44654}, {35945, 44882}, {35949, 43273}, {39870, 45398}, {39871, 45400}, {39872, 45402}, {39873, 45404}, {39877, 45416}, {39878, 45426}, {39879, 45428}, {39880, 45430}, {39881, 45432}, {39882, 45434}, {39883, 45436}, {39884, 45438}, {39885, 45444}, {39886, 45446}, {39889, 45454}, {39890, 45456}, {39891, 45458}, {39892, 45460}, {39893, 45462}, {39895, 45467}, {39896, 45464}, {39897, 45470}, {39898, 45476}, {39899, 45488}, {39900, 45490}, {39901, 45492}, {39902, 45494}, {39903, 45496}, {43119, 48906}, {45345, 48489}, {45347, 48490}, {45375, 48662}, {45411, 48743}, {45412, 49397}, {45415, 49398}, {45421, 49057}, {45422, 49164}, {45424, 49165}

X(49325) = midpoint of X(i) and X(j) for these {i, j}: {5871, 39874}, {5921, 49056}, {6776, 39888}
X(49325) = reflection of X(i) in X(j) for these (i, j): (3, 48742), (13748, 6), (18440, 48467), (49326, 6776)
X(49325) = orthologic center (1st anti-Kenmotu centers, 9th Brocard)
X(49325) = X(6776)-of-1st anti-Kenmotu centers triangle
X(49325) = X(48742)-of-X3-ABC reflections triangle
X(49325) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 6776, 49228), (6776, 39875, 8550)


X(49326) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO 9th BROCARD

Barycentrics    2*(-a^2+b^2+c^2)*(3*a^4+(b^2-c^2)^2)*S+(a^2+b^2+c^2)*(2*a^6-(b^2+c^2)*a^4-(b^4-c^4)*(b^2-c^2)) : :
X(49326) = 3*X(5050)-2*X(48467) = X(5871)-3*X(14912) = 3*X(6776)-X(39888) = 2*X(14230)-3*X(14853) = 3*X(39887)+X(39888) = 2*X(39887)+X(49325) = 2*X(39888)-3*X(49325)

The reciprocal orthologic center of these triangles is X(4).

X(49326) lies on these lines: {3, 48743}, {4, 6}, {69, 12306}, {491, 5921}, {542, 1991}, {1350, 35946}, {1352, 45473}, {2456, 6289}, {2794, 35840}, {3103, 39893}, {3564, 9732}, {3818, 44509}, {5050, 48467}, {5085, 39388}, {5847, 49324}, {5848, 48685}, {6290, 18440}, {7710, 13638}, {8721, 39648}, {9756, 45510}, {19145, 45486}, {19146, 45485}, {29012, 44655}, {35944, 44882}, {35948, 43273}, {39870, 45399}, {39871, 45401}, {39872, 45403}, {39873, 45405}, {39877, 45417}, {39878, 45427}, {39879, 45429}, {39880, 45431}, {39881, 45433}, {39882, 45435}, {39883, 45437}, {39884, 45439}, {39885, 45445}, {39886, 45447}, {39889, 45455}, {39890, 45457}, {39891, 45459}, {39892, 45461}, {39894, 45463}, {39895, 45465}, {39896, 45466}, {39897, 45471}, {39898, 45477}, {39899, 45489}, {39900, 45491}, {39901, 45493}, {39902, 45495}, {39903, 45497}, {43118, 48906}, {45346, 48490}, {45348, 48489}, {45376, 48662}, {45410, 48742}, {45413, 49398}, {45414, 49397}, {45420, 49056}, {45423, 49164}, {45425, 49165}

X(49326) = midpoint of X(i) and X(j) for these {i, j}: {5870, 39874}, {5921, 49057}, {6776, 39887}
X(49326) = reflection of X(i) in X(j) for these (i, j): (3, 48743), (13749, 6), (18440, 48466), (49325, 6776)
X(49326) = orthologic center (2nd anti-Kenmotu centers, 9th Brocard)
X(49326) = X(6776)-of-2nd anti-Kenmotu centers triangle
X(49326) = X(48743)-of-X3-ABC reflections triangle
X(49326) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 6776, 49229), (6776, 39876, 8550)


X(49327) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO 1st BROCARD-REFLECTED

Barycentrics    2*((2*b^2+c^2)*a^2+b^2*c^2-c^4)*((b^2+2*c^2)*a^2-b^4+b^2*c^2)*S+3*(b^2+c^2)*a^8-4*(b^4+b^2*c^2+c^4)*a^6+3*(b^6+c^6)*a^4-2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*b^2*c^2 : :
X(49327) = 3*X(262)-X(22699) = 2*X(3102)+X(13748) = X(22699)+3*X(22700) = 2*X(22699)-3*X(49328) = 2*X(22700)+X(49328) = X(49351)-4*X(49355)

The reciprocal orthologic center of these triangles is X(3).

X(49327) lies on these lines: {3, 48744}, {6, 98}, {492, 6194}, {511, 591}, {2782, 49311}, {3095, 49317}, {3102, 13748}, {6228, 6289}, {7709, 45406}, {9733, 49353}, {11842, 48726}, {12305, 22676}, {15819, 45472}, {18971, 45404}, {22475, 45398}, {22480, 45400}, {22521, 45402}, {22556, 45416}, {22650, 45426}, {22655, 45428}, {22668, 45430}, {22672, 45432}, {22678, 45434}, {22680, 45436}, {22681, 45438}, {22682, 45440}, {22697, 45444}, {22698, 45446}, {22703, 45454}, {22704, 45456}, {22705, 45458}, {22706, 45460}, {22709, 45467}, {22710, 45464}, {22711, 45470}, {22713, 45476}, {22720, 45484}, {22721, 45487}, {22728, 45488}, {22729, 45490}, {22730, 45492}, {22731, 45494}, {22732, 45496}, {32515, 49351}, {33435, 44392}, {35838, 45462}, {40108, 43119}, {45345, 48491}, {45347, 48492}, {45375, 48663}, {45411, 48745}, {45412, 49399}, {45415, 49400}, {45421, 49059}, {45422, 49166}, {45424, 49167}

X(49327) = midpoint of X(i) and X(j) for these {i, j}: {262, 22700}, {6194, 49058}
X(49327) = orthologic center (1st anti-Kenmotu centers, 1st Brocard-reflected)
X(49327) = X(48744)-of-X3-ABC reflections triangle
X(49327) = X(262)-of-1st anti-Kenmotu centers triangle
X(49327) = reflection of X(i) in X(j) for these (i, j): (3, 48744), (49328, 262)


X(49328) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO 1st BROCARD-REFLECTED

Barycentrics    -2*((2*b^2+c^2)*a^2+b^2*c^2-c^4)*((b^2+2*c^2)*a^2-b^4+b^2*c^2)*S+3*(b^2+c^2)*a^8-4*(b^4+b^2*c^2+c^4)*a^6+3*(b^6+c^6)*a^4-2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*b^2*c^2 : :
X(49328) = 3*X(262)-X(22700) = 2*X(3103)+X(13749) = 3*X(22699)+X(22700) = 2*X(22699)+X(49327) = 2*X(22700)-3*X(49327) = X(49352)-4*X(49356)

The reciprocal orthologic center of these triangles is X(3).

X(49328) lies on these lines: {3, 48745}, {6, 98}, {491, 6194}, {511, 1991}, {2782, 49312}, {3095, 49318}, {3103, 13749}, {6229, 6290}, {7709, 45407}, {9732, 49354}, {11842, 48727}, {12306, 22676}, {15819, 45473}, {18971, 45405}, {22475, 45399}, {22480, 45401}, {22521, 45403}, {22556, 45417}, {22650, 45427}, {22655, 45429}, {22668, 45431}, {22672, 45433}, {22678, 45435}, {22680, 45437}, {22681, 45439}, {22682, 45441}, {22697, 45445}, {22698, 45447}, {22703, 45455}, {22704, 45457}, {22705, 45459}, {22706, 45461}, {22709, 45465}, {22710, 45466}, {22711, 45471}, {22713, 45477}, {22720, 45486}, {22721, 45485}, {22728, 45489}, {22729, 45491}, {22730, 45493}, {22731, 45495}, {22732, 45497}, {32515, 49352}, {33434, 44394}, {35839, 45463}, {40108, 43118}, {45346, 48492}, {45348, 48491}, {45376, 48663}, {45410, 48744}, {45413, 49400}, {45414, 49399}, {45420, 49058}, {45423, 49166}, {45425, 49167}

X(49328) = midpoint of X(i) and X(j) for these {i, j}: {262, 22699}, {6194, 49059}
X(49328) = orthologic center (2nd anti-Kenmotu centers, 1st Brocard-reflected)
X(49328) = X(48745)-of-X3-ABC reflections triangle
X(49328) = X(262)-of-2nd anti-Kenmotu centers triangle
X(49328) = reflection of X(i) in X(j) for these (i, j): (3, 48745), (49327, 262)


X(49329) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO EXCENTERS-MIDPOINTS

Barycentrics    -2*(-a+b+c)*S+2*a^3+(b^2+c^2)*a-(b+c)*(b^2+c^2) : :
X(49329) = 3*X(8)-X(12627) = 3*X(591)-2*X(45713) = 3*X(591)-4*X(49347) = X(12627)+3*X(12628) = 2*X(12627)-3*X(49330) = 2*X(12628)+X(49330) = 3*X(31145)-X(49061)

The reciprocal orthologic center of these triangles is X(10).

X(49329) lies on these lines: {1, 45444}, {3, 48746}, {6, 8}, {10, 45398}, {145, 492}, {325, 45477}, {355, 45440}, {515, 49323}, {517, 13748}, {518, 49078}, {519, 591}, {758, 49339}, {944, 12305}, {952, 9733}, {1482, 6289}, {2098, 45460}, {2099, 45458}, {2802, 49337}, {3102, 35843}, {3632, 45426}, {3913, 45416}, {4884, 46422}, {5688, 15835}, {5690, 43119}, {5844, 49355}, {8148, 45375}, {9766, 45720}, {10573, 45492}, {10912, 45454}, {10944, 45404}, {10950, 45470}, {12135, 45400}, {12195, 45402}, {12245, 45406}, {12410, 45428}, {12454, 45430}, {12455, 45432}, {12495, 45434}, {12513, 45436}, {12626, 45446}, {12635, 45456}, {12636, 45467}, {12637, 45464}, {12645, 45488}, {12647, 45490}, {12648, 45494}, {12649, 45496}, {13911, 45484}, {13973, 45487}, {14839, 49351}, {22791, 45438}, {28538, 49079}, {31145, 45421}, {35842, 45462}, {45345, 48493}, {45347, 48494}, {45411, 48747}, {45412, 49401}, {45415, 49402}, {45422, 49168}, {45424, 49169}

X(49329) = midpoint of X(i) and X(j) for these {i, j}: {8, 12628}, {145, 49060}
X(49329) = reflection of X(i) in X(j) for these (i, j): (3, 48746), (45713, 49347), (49330, 8)
X(49329) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: excenters-midpoints, Garcia-reflection, 2nd Schiffler
X(49329) = X(8)-of-1st anti-Kenmotu centers triangle
X(49329) = X(48746)-of-X3-ABC reflections triangle
X(49329) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 45444, 45472), (145, 492, 45476), (45713, 49347, 591)


X(49330) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO EXCENTERS-MIDPOINTS

Barycentrics    2*(-a+b+c)*S+2*a^3+(b^2+c^2)*a-(b+c)*(b^2+c^2) : :
X(49330) = 3*X(8)-X(12628) = 3*X(1991)-2*X(45714) = 3*X(1991)-4*X(49348) = 3*X(12627)+X(12628) = 2*X(12627)+X(49329) = 2*X(12628)-3*X(49329) = 3*X(31145)-X(49060)

The reciprocal orthologic center of these triangles is X(10).

X(49330) lies on these lines: {1, 45445}, {3, 48747}, {6, 8}, {10, 45399}, {145, 491}, {325, 45476}, {355, 45441}, {515, 49324}, {517, 13749}, {518, 49079}, {519, 1991}, {758, 49340}, {944, 12306}, {952, 9732}, {1482, 6290}, {2098, 45461}, {2099, 45459}, {2802, 49338}, {3052, 13461}, {3103, 35842}, {3632, 45427}, {3913, 45417}, {4884, 46421}, {5689, 15834}, {5690, 43118}, {5844, 49356}, {8148, 45376}, {9766, 45719}, {10573, 45493}, {10912, 45455}, {10944, 45405}, {10950, 45471}, {12135, 45401}, {12195, 45403}, {12245, 45407}, {12410, 45429}, {12454, 45431}, {12455, 45433}, {12495, 45435}, {12513, 45437}, {12626, 45447}, {12635, 45457}, {12636, 45465}, {12637, 45466}, {12645, 45489}, {12647, 45491}, {12648, 45495}, {12649, 45497}, {13911, 45486}, {13973, 45485}, {14839, 49352}, {22791, 45439}, {28538, 49078}, {31145, 45420}, {35843, 45463}, {45346, 48494}, {45348, 48493}, {45410, 48746}, {45413, 49402}, {45414, 49401}, {45423, 49168}, {45425, 49169}

X(49330) = midpoint of X(i) and X(j) for these {i, j}: {8, 12627}, {145, 49061}
X(49330) = reflection of X(i) in X(j) for these (i, j): (3, 48747), (45714, 49348), (49329, 8)
X(49330) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: excenters-midpoints, Garcia-reflection, 2nd Schiffler
X(49330) = X(8)-of-2nd anti-Kenmotu centers triangle
X(49330) = X(48747)-of-X3-ABC reflections triangle
X(49330) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 45445, 45473), (145, 491, 45477), (45714, 49348, 1991)


X(49331) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO EXTOUCH

Barycentrics    a*(2*(a^3+(b-c)*a^2-(b-c)^2*a-(b+c)*(b^2-c^2))*(a^3-(b-c)*a^2-(b-c)^2*a+(b+c)*(b^2-c^2))*S+(b+c)*a^7+(b^2+4*b*c+c^2)*a^6-(b+c)*(3*b^2-2*b*c+3*c^2)*a^5-3*(b^2+c^2)*(b-c)^2*a^4+(b^2-c^2)*(b-c)*(3*b^2+2*b*c+3*c^2)*a^3+(3*b^2+4*b*c+3*c^2)*(b-c)^4*a^2-(b^2-c^2)^3*(b-c)*a-(b^2-c^2)^2*(b+c)^2*(b^2+c^2)) : :
X(49331) = 3*X(84)-X(6258) = 3*X(6257)+X(6258) = 2*X(6257)+X(49332) = 2*X(6258)-3*X(49332)

The reciprocal orthologic center of these triangles is X(40).

X(49331) lies on these lines: {3, 48748}, {6, 84}, {492, 6223}, {515, 49323}, {971, 9733}, {1490, 12305}, {1709, 45490}, {2829, 49337}, {3102, 35845}, {6001, 45713}, {6245, 45440}, {6259, 6289}, {6260, 45472}, {7971, 45476}, {7992, 45426}, {8987, 45484}, {9910, 45428}, {10085, 45492}, {12114, 45398}, {12136, 45400}, {12196, 45402}, {12246, 45406}, {12330, 45416}, {12456, 45430}, {12457, 45432}, {12496, 45434}, {12667, 45444}, {12668, 45446}, {12676, 45454}, {12677, 45456}, {12678, 45458}, {12679, 45460}, {12680, 45470}, {12684, 45488}, {12686, 45494}, {12687, 45496}, {12688, 45404}, {13974, 45487}, {18237, 45436}, {18245, 45467}, {18246, 45464}, {22792, 45438}, {34862, 43119}, {35844, 45462}, {45345, 48495}, {45347, 48496}, {45375, 48664}, {45411, 48749}, {45412, 49403}, {45415, 49404}, {45421, 49063}, {45422, 49170}, {45424, 49171}

X(49331) = midpoint of X(i) and X(j) for these {i, j}: {84, 6257}, {6223, 49062}
X(49331) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: extouch, 1st Zaniah
X(49331) = X(48748)-of-X3-ABC reflections triangle
X(49331) = X(84)-of-1st anti-Kenmotu centers triangle
X(49331) = reflection of X(i) in X(j) for these (i, j): (3, 48748), (49332, 84)


X(49332) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO EXTOUCH

Barycentrics    a*(-2*(a^3+(b-c)*a^2-(b-c)^2*a-(b+c)*(b^2-c^2))*(a^3-(b-c)*a^2-(b-c)^2*a+(b+c)*(b^2-c^2))*S+(b+c)*a^7+(b^2+4*b*c+c^2)*a^6-(b+c)*(3*b^2-2*b*c+3*c^2)*a^5-3*(b^2+c^2)*(b-c)^2*a^4+(b^2-c^2)*(b-c)*(3*b^2+2*b*c+3*c^2)*a^3+(3*b^2+4*b*c+3*c^2)*(b-c)^4*a^2-(b^2-c^2)^3*(b-c)*a-(b^2-c^2)^2*(b+c)^2*(b^2+c^2)) : :
X(49332) = 3*X(84)-X(6257) = X(6257)+3*X(6258) = 2*X(6257)-3*X(49331) = 2*X(6258)+X(49331)

The reciprocal orthologic center of these triangles is X(40).

X(49332) lies on these lines: {3, 48749}, {6, 84}, {491, 6223}, {515, 49324}, {971, 9732}, {1490, 12306}, {1709, 45491}, {2829, 49338}, {3103, 35844}, {6001, 45714}, {6245, 45441}, {6259, 6290}, {6260, 45473}, {7971, 45477}, {7992, 45427}, {8987, 45486}, {9910, 45429}, {10085, 45493}, {12114, 45399}, {12136, 45401}, {12196, 45403}, {12246, 45407}, {12330, 45417}, {12456, 45431}, {12457, 45433}, {12496, 45435}, {12667, 45445}, {12668, 45447}, {12676, 45455}, {12677, 45457}, {12678, 45459}, {12679, 45461}, {12680, 45471}, {12684, 45489}, {12686, 45495}, {12687, 45497}, {12688, 45405}, {13974, 45485}, {18237, 45437}, {18245, 45465}, {18246, 45466}, {22792, 45439}, {34862, 43118}, {35845, 45463}, {45346, 48496}, {45348, 48495}, {45376, 48664}, {45410, 48748}, {45413, 49404}, {45414, 49403}, {45420, 49062}, {45423, 49170}, {45425, 49171}

X(49332) = midpoint of X(i) and X(j) for these {i, j}: {84, 6258}, {6223, 49063}
X(49332) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: extouch, 1st Zaniah
X(49332) = X(48749)-of-X3-ABC reflections triangle
X(49332) = X(84)-of-2nd anti-Kenmotu centers triangle
X(49332) = reflection of X(i) in X(j) for these (i, j): (3, 48749), (49331, 84)


X(49333) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO INNER-FERMAT

Barycentrics    -2*a^2*S^2*sqrt(3)-(a^4-3*(b^2+c^2)*a^2+2*(b^2-c^2)^2)*S+2*a^6-4*(b^2+c^2)*a^4+3*(b^4+c^4)*a^2-(b^2+c^2)*(b^2-c^2)^2 : :
X(49333) = 3*X(18)-X(22853) = X(22853)+3*X(22854) = 2*X(22853)-3*X(49334) = 2*X(22854)+X(49334)

The reciprocal orthologic center of these triangles is X(3).

X(49333) lies on these lines: {3, 48750}, {6, 17}, {492, 628}, {533, 591}, {630, 45472}, {3102, 35849}, {6289, 16627}, {9733, 49307}, {11740, 45398}, {12305, 22843}, {13748, 44667}, {16628, 45488}, {18585, 33441}, {18972, 45404}, {22114, 42282}, {22481, 45400}, {22522, 45402}, {22531, 45406}, {22557, 45416}, {22651, 45426}, {22656, 45428}, {22669, 45430}, {22673, 45432}, {22745, 45434}, {22771, 45436}, {22794, 45438}, {22831, 45440}, {22851, 45444}, {22852, 45446}, {22857, 45454}, {22858, 45456}, {22859, 45458}, {22860, 45460}, {22863, 45467}, {22864, 45464}, {22865, 45470}, {22867, 45476}, {22876, 45484}, {22877, 45487}, {22884, 45490}, {22885, 45492}, {22886, 45494}, {22887, 45496}, {35846, 45462}, {43119, 49105}, {45345, 48497}, {45347, 48498}, {45375, 48665}, {45411, 48751}, {45412, 49405}, {45415, 49406}, {45421, 49065}, {45422, 49172}, {45424, 49173}

X(49333) = midpoint of X(i) and X(j) for these {i, j}: {18, 22854}, {628, 49064}
X(49333) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: inner-Fermat, 1st half-diamonds
X(49333) = X(48750)-of-X3-ABC reflections triangle
X(49333) = X(18)-of-1st anti-Kenmotu centers triangle
X(49333) = reflection of X(i) in X(j) for these (i, j): (3, 48750), (49334, 18)


X(49334) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO INNER-FERMAT

Barycentrics    2*a^2*S^2*sqrt(3)+(a^4-3*(b^2+c^2)*a^2+2*(b^2-c^2)^2)*S+2*a^6-4*(b^2+c^2)*a^4+3*(b^4+c^4)*a^2-(b^2+c^2)*(b^2-c^2)^2 : :
X(49334) = 3*X(18)-X(22854) = 3*X(22853)+X(22854) = 2*X(22853)+X(49333) = 2*X(22854)-3*X(49333)

The reciprocal orthologic center of these triangles is X(3).

X(49334) lies on these lines: {3, 48751}, {6, 17}, {491, 628}, {533, 1991}, {630, 45473}, {3103, 35846}, {6290, 16627}, {9732, 49308}, {11740, 45399}, {12306, 22843}, {13749, 44667}, {15765, 33440}, {16628, 45489}, {18972, 45405}, {22114, 35732}, {22481, 45401}, {22522, 45403}, {22531, 45407}, {22557, 45417}, {22651, 45427}, {22656, 45429}, {22669, 45431}, {22673, 45433}, {22745, 45435}, {22771, 45437}, {22794, 45439}, {22831, 45441}, {22851, 45445}, {22852, 45447}, {22857, 45455}, {22858, 45457}, {22859, 45459}, {22860, 45461}, {22863, 45465}, {22864, 45466}, {22865, 45471}, {22867, 45477}, {22876, 45486}, {22877, 45485}, {22884, 45491}, {22885, 45493}, {22886, 45495}, {22887, 45497}, {35744, 49318}, {35849, 45463}, {43118, 49105}, {45346, 48498}, {45348, 48497}, {45376, 48665}, {45410, 48750}, {45413, 49406}, {45414, 49405}, {45420, 49064}, {45423, 49172}, {45425, 49173}

X(49334) = midpoint of X(i) and X(j) for these {i, j}: {18, 22853}, {628, 49065}
X(49334) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: inner-Fermat, 1st half-diamonds
X(49334) = X(48751)-of-X3-ABC reflections triangle
X(49334) = X(18)-of-2nd anti-Kenmotu centers triangle
X(49334) = reflection of X(i) in X(j) for these (i, j): (3, 48751), (49333, 18)


X(49335) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO OUTER-FERMAT

Barycentrics    2*a^2*S^2*sqrt(3)-(a^4-3*(b^2+c^2)*a^2+2*(b^2-c^2)^2)*S+2*a^6-4*(b^2+c^2)*a^4+3*(b^4+c^4)*a^2-(b^2+c^2)*(b^2-c^2)^2 : :
X(49335) = 3*X(17)-X(22898) = X(22898)+3*X(22899) = 2*X(22898)-3*X(49336) = 2*X(22899)+X(49336)

The reciprocal orthologic center of these triangles is X(3).

X(49335) lies on these lines: {3, 48752}, {6, 17}, {492, 627}, {532, 591}, {629, 45472}, {3102, 35847}, {6289, 16626}, {9733, 49305}, {11739, 45398}, {12305, 22890}, {13748, 44666}, {15765, 33443}, {16629, 45488}, {18973, 45404}, {22113, 35732}, {22482, 45400}, {22523, 45402}, {22532, 45406}, {22558, 45416}, {22652, 45426}, {22657, 45428}, {22670, 45430}, {22674, 45432}, {22746, 45434}, {22772, 45436}, {22795, 45438}, {22832, 45440}, {22896, 45444}, {22897, 45446}, {22902, 45454}, {22903, 45456}, {22904, 45458}, {22905, 45460}, {22908, 45467}, {22909, 45464}, {22910, 45470}, {22912, 45476}, {22921, 45484}, {22922, 45487}, {22929, 45490}, {22930, 45492}, {22931, 45494}, {22932, 45496}, {35848, 45462}, {43119, 49106}, {45345, 48499}, {45347, 48500}, {45375, 48666}, {45411, 48753}, {45412, 49407}, {45415, 49408}, {45421, 49067}, {45422, 49174}, {45424, 49175}

X(49335) = midpoint of X(i) and X(j) for these {i, j}: {17, 22899}, {627, 49066}
X(49335) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: outer-Fermat, 2nd half-diamonds
X(49335) = X(48752)-of-X3-ABC reflections triangle
X(49335) = X(17)-of-1st anti-Kenmotu centers triangle
X(49335) = reflection of X(i) in X(j) for these (i, j): (3, 48752), (49336, 17)


X(49336) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO OUTER-FERMAT

Barycentrics    -2*a^2*S^2*sqrt(3)+(a^4-3*(b^2+c^2)*a^2+2*(b^2-c^2)^2)*S+2*a^6-4*(b^2+c^2)*a^4+3*(b^4+c^4)*a^2-(b^2+c^2)*(b^2-c^2)^2 : :
X(49336) = 3*X(17)-X(22899) = 3*X(22898)+X(22899) = 2*X(22898)+X(49335) = 2*X(22899)-3*X(49335)

The reciprocal orthologic center of these triangles is X(3).

X(49336) lies on these lines: {3, 48753}, {6, 17}, {491, 627}, {532, 1991}, {629, 45473}, {3103, 35848}, {6290, 16626}, {9732, 49306}, {11739, 45399}, {12306, 22890}, {13749, 44666}, {16629, 45489}, {18585, 33442}, {18973, 45405}, {22113, 42282}, {22482, 45401}, {22523, 45403}, {22532, 45407}, {22558, 45417}, {22652, 45427}, {22657, 45429}, {22670, 45431}, {22674, 45433}, {22746, 45435}, {22772, 45437}, {22795, 45439}, {22832, 45441}, {22896, 45445}, {22897, 45447}, {22902, 45455}, {22903, 45457}, {22904, 45459}, {22905, 45461}, {22908, 45465}, {22909, 45466}, {22910, 45471}, {22912, 45477}, {22921, 45486}, {22922, 45485}, {22929, 45491}, {22930, 45493}, {22931, 45495}, {22932, 45497}, {35847, 45463}, {43118, 49106}, {45346, 48500}, {45348, 48499}, {45376, 48666}, {45410, 48752}, {45413, 49408}, {45414, 49407}, {45420, 49066}, {45423, 49174}, {45425, 49175}

X(49336) = midpoint of X(i) and X(j) for these {i, j}: {17, 22898}, {627, 49067}
X(49336) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: outer-Fermat, 2nd half-diamonds
X(49336) = X(48753)-of-X3-ABC reflections triangle
X(49336) = X(17)-of-2nd anti-Kenmotu centers triangle
X(49336) = reflection of X(i) in X(j) for these (i, j): (3, 48753), (49335, 17)


X(49337) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO FUHRMANN

Barycentrics    2*(a^2-b*a+b^2-c^2)*(a^2-c*a-b^2+c^2)*S+2*a^6-(b+c)*a^5-(b-c)^2*a^4-(b+c)*b*c*a^3+(b^2+c^2)*b*c*a^2+(b^4-c^4)*(b-c)*a-(b^4-c^4)*(b^2-c^2) : :
X(49337) = 3*X(80)-X(6263) = 3*X(6262)+X(6263) = 2*X(6262)+X(49338) = 2*X(6263)-3*X(49338)

The reciprocal orthologic center of these triangles is X(3).

X(49337) lies on these lines: {3, 48754}, {6, 80}, {11, 45398}, {100, 45444}, {214, 45472}, {492, 6224}, {515, 48684}, {952, 45713}, {2771, 49319}, {2800, 13748}, {2802, 49329}, {2829, 49331}, {3102, 35853}, {5840, 49323}, {6246, 45440}, {6265, 6289}, {7972, 45476}, {8988, 45484}, {9897, 45426}, {9912, 45428}, {10057, 45490}, {10073, 45492}, {12119, 12305}, {12137, 45400}, {12198, 45402}, {12247, 45406}, {12331, 45416}, {12460, 45430}, {12461, 45432}, {12498, 45434}, {12611, 45438}, {12619, 43119}, {12729, 45446}, {12737, 45454}, {12738, 45456}, {12739, 45458}, {12740, 45460}, {12741, 45467}, {12742, 45464}, {12743, 45470}, {12747, 45488}, {12749, 45494}, {12750, 45496}, {12751, 45424}, {12773, 45436}, {13976, 45487}, {18976, 45404}, {35852, 45462}, {45345, 48501}, {45347, 48502}, {45375, 48667}, {45411, 48755}, {45412, 49409}, {45415, 49410}, {45421, 49069}, {45422, 49176}, {48703, 49347}

X(49337) = midpoint of X(i) and X(j) for these {i, j}: {80, 6262}, {6224, 49068}
X(49337) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: Fuhrmann, K798i
X(49337) = X(48754)-of-X3-ABC reflections triangle
X(49337) = X(80)-of-1st anti-Kenmotu centers triangle
X(49337) = reflection of X(i) in X(j) for these (i, j): (3, 48754), (48703, 49347), (49338, 80)


X(49338) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO FUHRMANN

Barycentrics    -2*(a^2-b*a+b^2-c^2)*(a^2-c*a-b^2+c^2)*S+2*a^6-(b+c)*a^5-(b-c)^2*a^4-(b+c)*b*c*a^3+(b^2+c^2)*b*c*a^2+(b^4-c^4)*(b-c)*a-(b^4-c^4)*(b^2-c^2) : :
X(49338) = 3*X(80)-X(6262) = X(6262)+3*X(6263) = 2*X(6262)-3*X(49337) = 2*X(6263)+X(49337)

The reciprocal orthologic center of these triangles is X(3).

X(49338) lies on these lines: {3, 48755}, {6, 80}, {11, 45399}, {100, 45445}, {214, 45473}, {491, 6224}, {515, 48685}, {952, 45714}, {2771, 49320}, {2800, 13749}, {2802, 49330}, {2829, 49332}, {3103, 35852}, {5840, 49324}, {6246, 45441}, {6265, 6290}, {7972, 45477}, {8988, 45486}, {9897, 45427}, {9912, 45429}, {10057, 45491}, {10073, 45493}, {12119, 12306}, {12137, 45401}, {12198, 45403}, {12247, 45407}, {12331, 45417}, {12460, 45431}, {12461, 45433}, {12498, 45435}, {12611, 45439}, {12619, 43118}, {12729, 45447}, {12737, 45455}, {12738, 45457}, {12739, 45459}, {12740, 45461}, {12741, 45465}, {12742, 45466}, {12743, 45471}, {12747, 45489}, {12749, 45495}, {12750, 45497}, {12751, 45425}, {12773, 45437}, {13976, 45485}, {18976, 45405}, {35853, 45463}, {45346, 48502}, {45348, 48501}, {45376, 48667}, {45410, 48754}, {45413, 49410}, {45414, 49409}, {45420, 49068}, {45423, 49176}, {48704, 49348}

X(49338) = midpoint of X(i) and X(j) for these {i, j}: {80, 6263}, {6224, 49069}
X(49338) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: Fuhrmann, K798i
X(49338) = X(48755)-of-X3-ABC reflections triangle
X(49338) = X(80)-of-2nd anti-Kenmotu centers triangle
X(49338) = reflection of X(i) in X(j) for these (i, j): (3, 48755), (48704, 49348), (49337, 80)


X(49339) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO 2nd FUHRMANN

Barycentrics    2*(a^2+b*a-c^2+b^2)*(a^2+c*a-b^2+c^2)*S+2*a^6+(b+c)*a^5-(b+c)^2*a^4-(b+c)*b*c*a^3+(b^2+c^2)*b*c*a^2-(b^4-c^4)*(b-c)*a-(b^4-c^4)*(b^2-c^2) : :
X(49339) = 3*X(79)-X(16130) = X(16130)+3*X(16131) = 2*X(16130)-3*X(49340) = 2*X(16131)+X(49340)

The reciprocal orthologic center of these triangles is X(3).

X(49339) lies on these lines: {3, 48756}, {6, 79}, {30, 45713}, {492, 3648}, {758, 49329}, {2771, 49319}, {3102, 35855}, {3647, 45472}, {3649, 45398}, {3652, 6289}, {5441, 45476}, {11684, 45444}, {12305, 16113}, {13743, 45436}, {16114, 45400}, {16115, 45402}, {16116, 45406}, {16117, 45416}, {16118, 45426}, {16119, 45428}, {16121, 45430}, {16122, 45432}, {16123, 45434}, {16125, 45440}, {16129, 45446}, {16138, 45454}, {16139, 45456}, {16140, 45458}, {16141, 45460}, {16142, 45470}, {16148, 45484}, {16149, 45487}, {16150, 45488}, {16152, 45490}, {16153, 45492}, {16154, 45494}, {16155, 45496}, {16161, 45467}, {16162, 45464}, {18977, 45404}, {22798, 45438}, {35854, 45462}, {43119, 49107}, {45345, 48503}, {45347, 48504}, {45375, 48668}, {45411, 48757}, {45412, 49411}, {45415, 49412}, {45421, 49071}, {45422, 49177}, {45424, 49178}

X(49339) = midpoint of X(i) and X(j) for these {i, j}: {79, 16131}, {3648, 49070}
X(49339) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: 2nd Fuhrmann, K798e
X(49339) = X(48756)-of-X3-ABC reflections triangle
X(49339) = X(79)-of-1st anti-Kenmotu centers triangle
X(49339) = reflection of X(i) in X(j) for these (i, j): (3, 48756), (49340, 79)


X(49340) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO 2nd FUHRMANN

Barycentrics    -2*(a^2+b*a-c^2+b^2)*(a^2+c*a-b^2+c^2)*S+2*a^6+(b+c)*a^5-(b+c)^2*a^4-(b+c)*b*c*a^3+(b^2+c^2)*b*c*a^2-(b^4-c^4)*(b-c)*a-(b^4-c^4)*(b^2-c^2) : :
X(49340) = 3*X(79)-X(16131) = 3*X(16130)+X(16131) = 2*X(16130)+X(49339) = 2*X(16131)-3*X(49339)

The reciprocal orthologic center of these triangles is X(3).

X(49340) lies on these lines: {3, 48757}, {6, 79}, {30, 45714}, {491, 3648}, {758, 49330}, {2771, 49320}, {3103, 35854}, {3647, 45473}, {3649, 45399}, {3652, 6290}, {5441, 45477}, {11684, 45445}, {12306, 16113}, {13743, 45437}, {16114, 45401}, {16115, 45403}, {16116, 45407}, {16117, 45417}, {16118, 45427}, {16119, 45429}, {16121, 45431}, {16122, 45433}, {16123, 45435}, {16125, 45441}, {16129, 45447}, {16138, 45455}, {16139, 45457}, {16140, 45459}, {16141, 45461}, {16142, 45471}, {16148, 45486}, {16149, 45485}, {16150, 45489}, {16152, 45491}, {16153, 45493}, {16154, 45495}, {16155, 45497}, {16161, 45465}, {16162, 45466}, {18977, 45405}, {22798, 45439}, {35855, 45463}, {43118, 49107}, {45346, 48504}, {45348, 48503}, {45376, 48668}, {45410, 48756}, {45413, 49412}, {45414, 49411}, {45420, 49070}, {45423, 49177}, {45425, 49178}

X(49340) = midpoint of X(i) and X(j) for these {i, j}: {79, 16130}, {3648, 49071}
X(49340) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: 2nd Fuhrmann, K798e
X(49340) = X(48757)-of-X3-ABC reflections triangle
X(49340) = X(79)-of-2nd anti-Kenmotu centers triangle
X(49340) = reflection of X(i) in X(j) for these (i, j): (3, 48757), (49339, 79)


X(49341) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO HATZIPOLAKIS-MOSES

Barycentrics    2*(a^8-(2*b^2+c^2)*a^6+(b^2-c^2)*(2*b^4+b^2*c^2+c^4)*a^2-(b^4-c^4)*(b^2-c^2)^2)*(a^8-(b^2+2*c^2)*a^6-(b^2-c^2)*(b^4+b^2*c^2+2*c^4)*a^2+(b^4-c^4)*(b^2-c^2)^2)*S+(a^6-(b^2+c^2)*a^4-(b^2+c^2)^2*a^2+(b^4-c^4)*(b^2-c^2))*(2*a^12-4*(b^2+c^2)*a^10+(b^4+4*b^2*c^2+c^4)*a^8+2*(b^4-c^4)*(b^2-c^2)*a^6-2*(b^6-c^6)*(b^2-c^2)*a^4+2*(b^8-c^8)*a^2*(b^2-c^2)-(b^4-c^4)^2*(b^2-c^2)^2) : :
X(49341) = 3*X(6145)-X(32373) = X(32373)+3*X(32374) = 2*X(32373)-3*X(49342) = 2*X(32374)+X(49342)

The reciprocal orthologic center of these triangles is X(6146).

X(49341) lies on these lines: {3, 48758}, {6, 3574}, {492, 32354}, {973, 45474}, {1154, 49321}, {2917, 44196}, {3102, 35859}, {6146, 45450}, {6289, 32379}, {6293, 45482}, {9733, 18400}, {10628, 49319}, {12305, 32330}, {32331, 45398}, {32332, 45400}, {32335, 45402}, {32336, 45404}, {32337, 45406}, {32345, 45408}, {32347, 45416}, {32356, 45426}, {32357, 45428}, {32360, 45430}, {32361, 45432}, {32362, 45434}, {32363, 45436}, {32364, 45438}, {32369, 45440}, {32371, 45444}, {32372, 45446}, {32380, 45454}, {32381, 45456}, {32382, 45458}, {32383, 45460}, {32388, 45467}, {32389, 45464}, {32390, 45470}, {32391, 45472}, {32394, 45476}, {32399, 45484}, {32400, 45487}, {32402, 45488}, {32403, 45490}, {32404, 45492}, {32405, 45494}, {32406, 45496}, {35858, 45462}, {43119, 49108}, {45345, 48505}, {45347, 48506}, {45375, 48669}, {45411, 48759}, {45412, 49413}, {45415, 49414}, {45421, 49073}, {45422, 49179}, {45424, 49180}

X(49341) = midpoint of X(i) and X(j) for these {i, j}: {6145, 32374}, {32354, 49072}
X(49341) = orthologic center (1st anti-Kenmotu centers, Hatzipolakis-Moses)
X(49341) = X(48758)-of-X3-ABC reflections triangle
X(49341) = X(6145)-of-1st anti-Kenmotu centers triangle
X(49341) = reflection of X(i) in X(j) for these (i, j): (3, 48758), (49342, 6145)


X(49342) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO HATZIPOLAKIS-MOSES

Barycentrics    -2*(a^8-(2*b^2+c^2)*a^6+(b^2-c^2)*(2*b^4+b^2*c^2+c^4)*a^2-(b^4-c^4)*(b^2-c^2)^2)*(a^8-(b^2+2*c^2)*a^6-(b^2-c^2)*(b^4+b^2*c^2+2*c^4)*a^2+(b^4-c^4)*(b^2-c^2)^2)*S+(a^6-(b^2+c^2)*a^4-(b^2+c^2)^2*a^2+(b^4-c^4)*(b^2-c^2))*(2*a^12-4*(b^2+c^2)*a^10+(b^4+4*b^2*c^2+c^4)*a^8+2*(b^4-c^4)*(b^2-c^2)*a^6-2*(b^6-c^6)*(b^2-c^2)*a^4+2*(b^8-c^8)*a^2*(b^2-c^2)-(b^4-c^4)^2*(b^2-c^2)^2) : :
X(49342) = 3*X(6145)-X(32374) = 3*X(32373)+X(32374) = 2*X(32373)+X(49341) = 2*X(32374)-3*X(49341)

The reciprocal orthologic center of these triangles is X(6146).

X(49342) lies on these lines: {3, 48759}, {6, 3574}, {491, 32354}, {973, 45475}, {1154, 49322}, {2917, 44199}, {3103, 35858}, {6146, 45451}, {6290, 32379}, {6293, 45483}, {9732, 18400}, {10628, 49320}, {12306, 32330}, {32331, 45399}, {32332, 45401}, {32335, 45403}, {32336, 45405}, {32337, 45407}, {32345, 45409}, {32347, 45417}, {32356, 45427}, {32357, 45429}, {32360, 45431}, {32361, 45433}, {32362, 45435}, {32363, 45437}, {32364, 45439}, {32369, 45441}, {32371, 45445}, {32372, 45447}, {32380, 45455}, {32381, 45457}, {32382, 45459}, {32383, 45461}, {32388, 45465}, {32389, 45466}, {32390, 45471}, {32391, 45473}, {32394, 45477}, {32399, 45486}, {32400, 45485}, {32402, 45489}, {32403, 45491}, {32404, 45493}, {32405, 45495}, {32406, 45497}, {35859, 45463}, {43118, 49108}, {45346, 48506}, {45348, 48505}, {45376, 48669}, {45410, 48758}, {45413, 49414}, {45414, 49413}, {45420, 49072}, {45423, 49179}, {45425, 49180}

X(49342) = midpoint of X(i) and X(j) for these {i, j}: {6145, 32373}, {32354, 49073}
X(49342) = orthologic center (2nd anti-Kenmotu centers, Hatzipolakis-Moses)
X(49342) = X(48759)-of-X3-ABC reflections triangle
X(49342) = X(6145)-of-2nd anti-Kenmotu centers triangle
X(49342) = reflection of X(i) in X(j) for these (i, j): (3, 48759), (49341, 6145)


X(49343) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO 3rd HATZIPOLAKIS

Barycentrics    -2*(a^8-(2*b^2+c^2)*a^6+4*b^2*c^2*a^4+(2*b^2-c^2)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)^2)*(a^8-(b^2+2*c^2)*a^6+4*b^2*c^2*a^4-(b^2-c^2)^2*(b^2-2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)^2)*S+(a^2+b^2-c^2)*(-a^2+b^2+c^2)*(a^2-b^2+c^2)*(2*a^12-4*(b^2+c^2)*a^10+(b^4+12*b^2*c^2+c^4)*a^8+2*(b^2+c^2)*(b^4-4*b^2*c^2+c^4)*a^6-2*(b^6-c^6)*(b^2-c^2)*a^4+2*(b^4-c^4)*(b^2-c^2)^3*a^2-(b^4-c^4)^2*(b^2-c^2)^2) : :
X(49343) = 3*X(22466)-X(22945) = X(22945)+3*X(22947) = 2*X(22945)-3*X(49344) = 2*X(22947)+X(49344)

The reciprocal orthologic center of these triangles is X(12241).

X(49343) lies on these lines: {3, 48810}, {6, 17837}, {492, 22647}, {2929, 44196}, {3102, 35861}, {6289, 22955}, {12241, 45448}, {12305, 22951}, {18978, 45404}, {22476, 45398}, {22483, 45400}, {22524, 45402}, {22530, 45474}, {22533, 45406}, {22559, 45416}, {22653, 45426}, {22658, 45428}, {22671, 45430}, {22675, 45432}, {22747, 45434}, {22776, 45436}, {22800, 45438}, {22833, 45440}, {22941, 45444}, {22943, 45446}, {22956, 45454}, {22957, 45456}, {22958, 45458}, {22959, 45460}, {22963, 45467}, {22964, 45464}, {22965, 45470}, {22966, 45472}, {22969, 45476}, {22976, 45484}, {22977, 45487}, {22979, 45488}, {22980, 45490}, {22981, 45492}, {22982, 45494}, {22983, 45496}, {35860, 45462}, {43119, 49109}, {45345, 48507}, {45347, 48508}, {45375, 48670}, {45411, 48811}, {45412, 49415}, {45415, 49416}, {45421, 49075}, {45422, 49181}, {45424, 49182}

X(49343) = midpoint of X(i) and X(j) for these {i, j}: {22466, 22947}, {22647, 49074}
X(49343) = orthologic center (1st anti-Kenmotu centers, 3rd Hatzipolakis)
X(49343) = X(48810)-of-X3-ABC reflections triangle
X(49343) = X(22466)-of-1st anti-Kenmotu centers triangle
X(49343) = reflection of X(i) in X(j) for these (i, j): (3, 48810), (49344, 22466)


X(49344) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO 3rd HATZIPOLAKIS

Barycentrics    2*(a^8-(2*b^2+c^2)*a^6+4*b^2*c^2*a^4+(2*b^2-c^2)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)^2)*(a^8-(b^2+2*c^2)*a^6+4*b^2*c^2*a^4-(b^2-c^2)^2*(b^2-2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)^2)*S+(a^2+b^2-c^2)*(-a^2+b^2+c^2)*(a^2-b^2+c^2)*(2*a^12-4*(b^2+c^2)*a^10+(b^4+12*b^2*c^2+c^4)*a^8+2*(b^2+c^2)*(b^4-4*b^2*c^2+c^4)*a^6-2*(b^6-c^6)*(b^2-c^2)*a^4+2*(b^4-c^4)*(b^2-c^2)^3*a^2-(b^4-c^4)^2*(b^2-c^2)^2) : :
X(49344) = 3*X(22466)-X(22947) = 3*X(22945)+X(22947) = 2*X(22945)+X(49343) = 2*X(22947)-3*X(49343)

The reciprocal orthologic center of these triangles is X(12241).

X(49344) lies on these lines: {3, 48811}, {6, 17837}, {491, 22647}, {2929, 44199}, {3103, 35860}, {6290, 22955}, {12241, 45449}, {12306, 22951}, {18978, 45405}, {22476, 45399}, {22483, 45401}, {22524, 45403}, {22530, 45475}, {22533, 45407}, {22559, 45417}, {22653, 45427}, {22658, 45429}, {22671, 45431}, {22675, 45433}, {22747, 45435}, {22776, 45437}, {22800, 45439}, {22833, 45441}, {22941, 45445}, {22943, 45447}, {22956, 45455}, {22957, 45457}, {22958, 45459}, {22959, 45461}, {22963, 45465}, {22964, 45466}, {22965, 45471}, {22966, 45473}, {22969, 45477}, {22976, 45486}, {22977, 45485}, {22979, 45489}, {22980, 45491}, {22981, 45493}, {22982, 45495}, {22983, 45497}, {35861, 45463}, {43118, 49109}, {45346, 48508}, {45348, 48507}, {45376, 48670}, {45410, 48810}, {45413, 49416}, {45414, 49415}, {45420, 49074}, {45423, 49181}, {45425, 49182}

X(49344) = midpoint of X(i) and X(j) for these {i, j}: {22466, 22945}, {22647, 49075}
X(49344) = orthologic center (2nd anti-Kenmotu centers, 3rd Hatzipolakis)
X(49344) = X(48811)-of-X3-ABC reflections triangle
X(49344) = X(22466)-of-2nd anti-Kenmotu centers triangle
X(49344) = reflection of X(i) in X(j) for these (i, j): (3, 48811), (49343, 22466)


X(49345) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO HUTSON EXTOUCH

Barycentrics    a*(2*(a^3-(b-c)*a^2-(b^2+6*b*c+c^2)*a+(b+c)*(b^2-c^2))*(a^3+(b-c)*a^2-(b^2+6*b*c+c^2)*a-(b+c)*(b^2-c^2))*S+(b+c)*a^7+(b^2+4*b*c+c^2)*a^6-(b+c)*(3*b^2-2*b*c+3*c^2)*a^5-(b^2+c^2)*(3*b^2+26*b*c+3*c^2)*a^4+(b+c)*(3*b^4+3*c^4-2*b*c*(2*b^2+15*b*c+2*c^2))*a^3+(b^2+6*b*c+c^2)*(3*b^4+3*c^4+2*b*c*(3*b^2-b*c+3*c^2))*a^2-(b^2-c^2)^3*(b-c)*a-(b^2-c^2)^2*(b+c)^2*(b^2+c^2)) : :
X(49345) = 3*X(7160)-X(12801) = X(12801)+3*X(12802) = 2*X(12801)-3*X(49346) = 2*X(12802)+X(49346)

The reciprocal orthologic center of these triangles is X(40).

X(49345) lies on these lines: {3, 48812}, {6, 7160}, {492, 9874}, {3102, 35863}, {6289, 12856}, {8000, 45476}, {9898, 45426}, {10059, 45490}, {10075, 45492}, {12120, 12305}, {12139, 45400}, {12200, 45402}, {12249, 45406}, {12260, 45398}, {12333, 45416}, {12411, 45428}, {12464, 45430}, {12465, 45432}, {12500, 45434}, {12599, 45440}, {12777, 45444}, {12789, 45446}, {12857, 45454}, {12858, 45456}, {12859, 45458}, {12860, 45460}, {12861, 45467}, {12862, 45464}, {12863, 45470}, {12864, 45472}, {12872, 45488}, {12874, 45494}, {12875, 45496}, {13914, 45484}, {13978, 45487}, {18979, 45404}, {22777, 45436}, {22801, 45438}, {35862, 45462}, {43119, 49110}, {45345, 48509}, {45347, 48510}, {45375, 48671}, {45411, 48813}, {45412, 49417}, {45415, 49418}, {45421, 49077}, {45422, 49183}, {45424, 49184}

X(49345) = midpoint of X(i) and X(j) for these {i, j}: {7160, 12802}, {9874, 49076}
X(49345) = orthologic center (1st anti-Kenmotu centers, Hutson extouch)
X(49345) = X(48812)-of-X3-ABC reflections triangle
X(49345) = X(7160)-of-1st anti-Kenmotu centers triangle
X(49345) = reflection of X(i) in X(j) for these (i, j): (3, 48812), (49346, 7160)


X(49346) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO HUTSON EXTOUCH

Barycentrics    a*(-2*(a^3-(b-c)*a^2-(b^2+6*b*c+c^2)*a+(b+c)*(b^2-c^2))*(a^3+(b-c)*a^2-(b^2+6*b*c+c^2)*a-(b+c)*(b^2-c^2))*S+(b+c)*a^7+(b^2+4*b*c+c^2)*a^6-(b+c)*(3*b^2-2*b*c+3*c^2)*a^5-(b^2+c^2)*(3*b^2+26*b*c+3*c^2)*a^4+(b+c)*(3*b^4+3*c^4-2*b*c*(2*b^2+15*b*c+2*c^2))*a^3+(b^2+6*b*c+c^2)*(3*b^4+3*c^4+2*b*c*(3*b^2-b*c+3*c^2))*a^2-(b^2-c^2)^3*(b-c)*a-(b^2-c^2)^2*(b+c)^2*(b^2+c^2)) : :
X(49346) = 3*X(7160)-X(12802) = 3*X(12801)+X(12802) = 2*X(12801)+X(49345) = 2*X(12802)-3*X(49345)

The reciprocal orthologic center of these triangles is X(40).

X(49346) lies on these lines: {3, 48813}, {6, 7160}, {491, 9874}, {3103, 35862}, {6290, 12856}, {8000, 45477}, {9898, 45427}, {10059, 45491}, {10075, 45493}, {12120, 12306}, {12139, 45401}, {12200, 45403}, {12249, 45407}, {12260, 45399}, {12333, 45417}, {12411, 45429}, {12464, 45431}, {12465, 45433}, {12500, 45435}, {12599, 45441}, {12777, 45445}, {12789, 45447}, {12857, 45455}, {12858, 45457}, {12859, 45459}, {12860, 45461}, {12861, 45465}, {12862, 45466}, {12863, 45471}, {12864, 45473}, {12872, 45489}, {12874, 45495}, {12875, 45497}, {13914, 45486}, {13978, 45485}, {18979, 45405}, {22777, 45437}, {22801, 45439}, {35863, 45463}, {43118, 49110}, {45346, 48510}, {45348, 48509}, {45376, 48671}, {45410, 48812}, {45413, 49418}, {45414, 49417}, {45420, 49076}, {45423, 49183}, {45425, 49184}

X(49346) = midpoint of X(i) and X(j) for these {i, j}: {7160, 12801}, {9874, 49077}
X(49346) = orthologic center (2nd anti-Kenmotu centers, Hutson extouch)
X(49346) = X(48813)-of-X3-ABC reflections triangle
X(49346) = X(7160)-of-2nd anti-Kenmotu centers triangle
X(49346) = reflection of X(i) in X(j) for these (i, j): (3, 48813), (49345, 7160)


X(49347) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO 1st JENKINS

Barycentrics    -2*S*(b+c)+2*a^3+(b+c)*a^2-(b+c)*(b^2+c^2) : :
X(49347) = 3*X(591)-X(45713) = 3*X(591)+X(49329) = 3*X(3679)-X(49079) = 3*X(26446)-2*X(48815)

The reciprocal orthologic center of these triangles is X(10).

X(49347) lies on these lines: {1, 492}, {3, 48814}, {6, 10}, {8, 45426}, {40, 45406}, {226, 45458}, {355, 45488}, {371, 45546}, {515, 9733}, {516, 13748}, {517, 49355}, {519, 591}, {639, 45500}, {726, 49351}, {730, 3102}, {946, 6289}, {950, 45470}, {1125, 45398}, {1210, 45492}, {1505, 4769}, {2784, 49309}, {2796, 49311}, {3244, 45476}, {3679, 45421}, {3846, 5405}, {4078, 31595}, {4297, 12305}, {6684, 43119}, {7774, 45427}, {7968, 44392}, {8666, 45436}, {8715, 45416}, {10106, 45404}, {10915, 45424}, {10916, 45422}, {11362, 49317}, {12053, 45460}, {12699, 45375}, {12788, 35775}, {13758, 13947}, {13975, 39679}, {17766, 49353}, {18483, 45438}, {19066, 26444}, {19925, 45440}, {21077, 45456}, {26446, 45411}, {31397, 45490}, {45345, 48511}, {45347, 48512}, {45412, 49419}, {45415, 49420}, {48703, 49337}

X(49347) = midpoint of X(i) and X(j) for these {i, j}: {1, 49078}, {13748, 49323}, {45713, 49329}, {48703, 49337}
X(49347) = reflection of X(i) in X(j) for these (i, j): (3, 48814), (49348, 10)
X(49347) = X(8)-beth conjugate of-X(49348)
X(49347) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: 1st Jenkins, 1st Savin
X(49347) = X(10)-of-1st anti-Kenmotu centers triangle
X(49347) = X(48814)-of-X3-ABC reflections triangle
X(49347) = X(49078)-of-anti-Aquila triangle
X(49347) = X(49348)-of-outer-Garcia triangle
X(49347) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 45444, 10), (591, 49329, 45713), (3416, 13973, 10), (5688, 13936, 10), (45398, 45472, 1125)


X(49348) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO 1st JENKINS

Barycentrics    2*S*(b+c)+2*a^3+(b+c)*a^2-(b+c)*(b^2+c^2) : :
X(49348) = 3*X(1991)-X(45714) = 3*X(1991)+X(49330) = 3*X(3679)-X(49078) = 3*X(26446)-2*X(48814)

The reciprocal orthologic center of these triangles is X(10).

X(49348) lies on these lines: {1, 491}, {3, 48815}, {6, 10}, {8, 45427}, {40, 45407}, {226, 45459}, {355, 45489}, {372, 45547}, {515, 9732}, {516, 13749}, {517, 49356}, {519, 1991}, {640, 45501}, {726, 49352}, {730, 3103}, {946, 6290}, {950, 45471}, {1125, 45399}, {1210, 45493}, {1504, 4769}, {2784, 49310}, {2796, 49312}, {3244, 45477}, {3679, 45420}, {3846, 5393}, {4078, 31594}, {4297, 12306}, {6684, 43118}, {7774, 45426}, {7969, 44394}, {8666, 45437}, {8715, 45417}, {10106, 45405}, {10915, 45425}, {10916, 45423}, {11362, 49318}, {12053, 45461}, {12699, 45376}, {12787, 35774}, {13638, 13893}, {13912, 39648}, {17766, 49354}, {18483, 45439}, {19065, 26445}, {19925, 45441}, {21077, 45457}, {26446, 45410}, {31397, 45491}, {45346, 48512}, {45348, 48511}, {45413, 49420}, {45414, 49419}, {48704, 49338}

X(49348) = midpoint of X(i) and X(j) for these {i, j}: {1, 49079}, {13749, 49324}, {45714, 49330}, {48704, 49338}
X(49348) = reflection of X(i) in X(j) for these (i, j): (3, 48815), (49347, 10)
X(49348) = X(8)-beth conjugate of-X(49347)
X(49348) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: 1st Jenkins, 1st Savin
X(49348) = X(10)-of-2nd anti-Kenmotu centers triangle
X(49348) = X(48815)-of-X3-ABC reflections triangle
X(49348) = X(49079)-of-anti-Aquila triangle
X(49348) = X(49347)-of-outer-Garcia triangle
X(49348) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 45445, 10), (1991, 49330, 45714), (3416, 13911, 10), (5689, 13883, 10), (45399, 45473, 1125)


X(49349) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO MIDHEIGHT

Barycentrics    a^2*((a^4-2*(b^2-c^2)*a^2+(b^2-c^2)*(b^2+3*c^2))*(a^4+2*(b^2-c^2)*a^2-(b^2-c^2)*(3*b^2+c^2))*S+2*(b^2+c^2)*a^8-4*(b^4-b^2*c^2+c^4)*a^6+4*(b^6-c^6)*(b^2-c^2)*a^2-2*(b^4-c^4)^2*(b^2+c^2)) : :
X(49349) = 3*X(64)-X(6267) = 3*X(6266)+X(6267) = 2*X(6266)+X(49350) = 2*X(6267)-3*X(49350) = 3*X(35450)-2*X(48817)

The reciprocal orthologic center of these triangles is X(4).

X(49349) lies on these lines: {3, 48816}, {4, 45474}, {6, 64}, {30, 49321}, {492, 6225}, {1498, 12305}, {1503, 49038}, {2777, 49319}, {2883, 45472}, {3102, 35865}, {3357, 43119}, {5878, 6289}, {5895, 45478}, {6000, 9733}, {6001, 49323}, {6241, 45450}, {6247, 45440}, {6285, 45404}, {7355, 45470}, {7973, 45476}, {8991, 45484}, {9899, 45426}, {9914, 45428}, {10060, 45490}, {10076, 45492}, {11381, 45400}, {12202, 45402}, {12250, 45406}, {12262, 45398}, {12335, 45416}, {12468, 45430}, {12469, 45432}, {12502, 45434}, {12779, 45444}, {12791, 45446}, {12920, 45454}, {12930, 45456}, {12940, 45458}, {12950, 45460}, {12986, 45467}, {12987, 45464}, {13093, 45488}, {13094, 45494}, {13095, 45496}, {13748, 15311}, {13980, 45487}, {17812, 45418}, {22778, 45436}, {22802, 45438}, {35450, 45411}, {35864, 45462}, {36201, 49365}, {45345, 48513}, {45347, 48514}, {45375, 48672}, {45412, 49421}, {45415, 49422}, {45421, 49081}, {45422, 49185}, {45424, 49186}

X(49349) = midpoint of X(i) and X(j) for these {i, j}: {64, 6266}, {6225, 49080}
X(49349) = orthologic center (1st anti-Kenmotu centers, midheight)
X(49349) = X(48816)-of-X3-ABC reflections triangle
X(49349) = X(64)-of-1st anti-Kenmotu centers triangle
X(49349) = reflection of X(i) in X(j) for these (i, j): (3, 48816), (49350, 64)


X(49350) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO MIDHEIGHT

Barycentrics    a^2*(-(a^4-2*(b^2-c^2)*a^2+(b^2-c^2)*(b^2+3*c^2))*(a^4+2*(b^2-c^2)*a^2-(b^2-c^2)*(3*b^2+c^2))*S+2*(b^2+c^2)*a^8-4*(b^4-b^2*c^2+c^4)*a^6+4*(b^6-c^6)*(b^2-c^2)*a^2-2*(b^4-c^4)^2*(b^2+c^2)) : :
X(49350) = 3*X(64)-X(6266) = X(6266)+3*X(6267) = 2*X(6266)-3*X(49349) = 2*X(6267)+X(49349) = 3*X(35450)-2*X(48816)

The reciprocal orthologic center of these triangles is X(4).

X(49350) lies on these lines: {3, 48817}, {4, 45475}, {6, 64}, {30, 49322}, {491, 6225}, {1498, 12306}, {1503, 49039}, {2777, 49320}, {2883, 45473}, {3103, 35864}, {3357, 43118}, {5878, 6290}, {5895, 45479}, {6000, 9732}, {6001, 49324}, {6241, 45451}, {6247, 45441}, {6285, 45405}, {7355, 45471}, {7973, 45477}, {8991, 45486}, {9899, 45427}, {9914, 45429}, {10060, 45491}, {10076, 45493}, {11381, 45401}, {12202, 45403}, {12250, 45407}, {12262, 45399}, {12335, 45417}, {12468, 45431}, {12469, 45433}, {12502, 45435}, {12779, 45445}, {12791, 45447}, {12920, 45455}, {12930, 45457}, {12940, 45459}, {12950, 45461}, {12986, 45465}, {12987, 45466}, {13093, 45489}, {13094, 45495}, {13095, 45497}, {13749, 15311}, {13980, 45485}, {17812, 45419}, {22778, 45437}, {22802, 45439}, {35450, 45410}, {35865, 45463}, {36201, 49366}, {45346, 48514}, {45348, 48513}, {45376, 48672}, {45413, 49422}, {45414, 49421}, {45420, 49080}, {45423, 49185}, {45425, 49186}

X(49350) = midpoint of X(i) and X(j) for these {i, j}: {64, 6267}, {6225, 49081}
X(49350) = orthologic center (2nd anti-Kenmotu centers, midheight)
X(49350) = X(48817)-of-X3-ABC reflections triangle
X(49350) = X(64)-of-2nd anti-Kenmotu centers triangle
X(49350) = reflection of X(i) in X(j) for these (i, j): (3, 48817), (49349, 64)


X(49351) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO 1st NEUBERG

Barycentrics    -2*S*b^2*c^2+(b^2+c^2)*(a^4-b^2*c^2) : :
X(49351) = 3*X(76)-X(6273) = 3*X(591)-2*X(3102) = 3*X(6272)+X(6273) = 2*X(6272)+X(49352) = 2*X(6273)-3*X(49352) = 3*X(49327)-4*X(49355)

The reciprocal orthologic center of these triangles is X(3).

X(49351) lies on these lines: {3, 48818}, {6, 76}, {39, 45472}, {194, 492}, {371, 8149}, {372, 736}, {384, 45402}, {486, 31981}, {511, 13748}, {538, 591}, {698, 3071}, {726, 49347}, {730, 45713}, {1505, 37004}, {1613, 45805}, {2782, 9733}, {3095, 6289}, {5969, 49311}, {5976, 12963}, {6248, 45440}, {7976, 45476}, {8304, 49368}, {8992, 45484}, {9902, 45426}, {9917, 45428}, {9983, 45434}, {10063, 45490}, {10079, 45492}, {10577, 32189}, {11257, 12305}, {12143, 45400}, {12251, 45406}, {12263, 45398}, {12338, 45416}, {12474, 45430}, {12475, 45432}, {12782, 45444}, {12794, 45446}, {12836, 45460}, {12837, 45458}, {12923, 45454}, {12933, 45456}, {12992, 45467}, {12993, 45464}, {13077, 45470}, {13108, 45488}, {13109, 45494}, {13110, 45496}, {13983, 45487}, {14839, 49329}, {14881, 45438}, {18982, 45404}, {22779, 45436}, {32470, 34511}, {32515, 49327}, {35866, 45462}, {43119, 49111}, {45345, 48515}, {45347, 48516}, {45375, 48673}, {45411, 48819}, {45412, 49423}, {45415, 49424}, {45421, 49083}, {45422, 49187}, {45424, 49188}

X(49351) = midpoint of X(i) and X(j) for these {i, j}: {76, 6272}, {194, 49082}
X(49351) = reflection of X(i) in X(j) for these (i, j): (3, 48818), (49352, 76)
X(49351) = orthologic center (1st anti-Kenmotu centers, 1st Neuberg)
X(49351) = X(76)-of-1st anti-Kenmotu centers triangle
X(49351) = X(8149)-of-2nd Kenmotu-free-vertices triangle
X(49351) = X(48818)-of-X3-ABC reflections triangle
X(49351) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (76, 19089, 24256), (76, 32451, 49252)


X(49352) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO 1st NEUBERG

Barycentrics    2*S*b^2*c^2+(b^2+c^2)*(a^4-b^2*c^2) : :
X(49352) = 3*X(76)-X(6272) = 3*X(1991)-2*X(3103) = X(6272)+3*X(6273) = 2*X(6272)-3*X(49351) = 2*X(6273)+X(49351) = 3*X(49328)-4*X(49356)

The reciprocal orthologic center of these triangles is X(3).

X(49352) lies on these lines: {3, 48819}, {6, 76}, {39, 45473}, {194, 491}, {371, 736}, {372, 8149}, {384, 45403}, {485, 31981}, {511, 13749}, {538, 1991}, {698, 3070}, {726, 49348}, {730, 45714}, {1504, 37004}, {1613, 45806}, {2782, 9732}, {3095, 6290}, {5969, 49312}, {5976, 12968}, {6248, 45441}, {7976, 45477}, {8305, 49367}, {8992, 45486}, {9902, 45427}, {9917, 45429}, {9983, 45435}, {10063, 45491}, {10079, 45493}, {10576, 32189}, {11257, 12306}, {12143, 45401}, {12251, 45407}, {12263, 45399}, {12338, 45417}, {12474, 45431}, {12475, 45433}, {12782, 45445}, {12794, 45447}, {12836, 45461}, {12837, 45459}, {12923, 45455}, {12933, 45457}, {12992, 45465}, {12993, 45466}, {13077, 45471}, {13108, 45489}, {13109, 45495}, {13110, 45497}, {13983, 45485}, {14839, 49330}, {14881, 45439}, {18982, 45405}, {22779, 45437}, {32471, 34511}, {32515, 49328}, {35867, 45463}, {43118, 49111}, {45346, 48516}, {45348, 48515}, {45376, 48673}, {45410, 48818}, {45413, 49424}, {45414, 49423}, {45420, 49082}, {45423, 49187}, {45425, 49188}

X(49352) = midpoint of X(i) and X(j) for these {i, j}: {76, 6273}, {194, 49083}
X(49352) = reflection of X(i) in X(j) for these (i, j): (3, 48819), (49351, 76)
X(49352) = orthologic center (2nd anti-Kenmotu centers, 1st Neuberg)
X(49352) = X(76)-of-2nd anti-Kenmotu centers triangle
X(49352) = X(8149)-of-1st Kenmotu-free-vertices triangle
X(49352) = X(48819)-of-X3-ABC reflections triangle
X(49352) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (76, 19090, 24256), (76, 32451, 49253)


X(49353) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO 2nd NEUBERG

Barycentrics    -2*(a^2+c^2)*(a^2+b^2)*S+(b^2+c^2)*(a^4-b^2*c^2) : :
X(49353) = 3*X(83)-X(6275) = 3*X(6274)+X(6275) = 2*X(6274)+X(49354) = 2*X(6275)-3*X(49354)

The reciprocal orthologic center of these triangles is X(3).

X(49353) lies on these lines: {3, 48770}, {6, 76}, {372, 591}, {492, 2896}, {3071, 33433}, {3102, 35869}, {5058, 13877}, {5420, 13086}, {6249, 45440}, {6287, 6289}, {6292, 13931}, {6308, 39679}, {7977, 45476}, {8993, 45484}, {9733, 49327}, {9903, 45426}, {9918, 45428}, {10064, 45490}, {10080, 45492}, {12122, 12305}, {12144, 45400}, {12206, 45402}, {12252, 45406}, {12264, 45398}, {12339, 45416}, {12476, 45430}, {12477, 45432}, {12783, 45444}, {12795, 45446}, {12924, 45454}, {12934, 45456}, {12944, 45458}, {12954, 45460}, {12994, 45467}, {12995, 45464}, {13078, 45470}, {13111, 45488}, {13112, 45494}, {13113, 45496}, {13748, 29012}, {13984, 45487}, {17766, 49347}, {18548, 35868}, {18983, 45404}, {22780, 45436}, {22803, 45438}, {43119, 49112}, {45345, 48517}, {45347, 48518}, {45375, 48674}, {45411, 48771}, {45412, 49425}, {45415, 49426}, {45421, 49085}, {45422, 49189}, {45424, 49190}, {49309, 49355}

X(49353) = midpoint of X(i) and X(j) for these {i, j}: {83, 6274}, {2896, 49084}
X(49353) = reflection of X(i) in X(j) for these (i, j): (3, 48770), (49354, 83)
X(49353) = orthologic center (1st anti-Kenmotu centers, 2nd Neuberg)
X(49353) = X(83)-of-1st anti-Kenmotu centers triangle
X(49353) = X(35701)-of-2nd Kenmotu-centers triangle
X(49353) = X(48770)-of-X3-ABC reflections triangle
X(49353) = {X(6), X(35701)}-harmonic conjugate of X(49354)


X(49354) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO 2nd NEUBERG

Barycentrics    2*(a^2+c^2)*(a^2+b^2)*S+(b^2+c^2)*(a^4-b^2*c^2) : :
X(49354) = 3*X(83)-X(6274) = X(6274)+3*X(6275) = 2*X(6274)-3*X(49353) = 2*X(6275)+X(49353)

The reciprocal orthologic center of these triangles is X(3).

X(49354) lies on these lines: {3, 48771}, {6, 76}, {371, 754}, {491, 2896}, {3070, 33432}, {3103, 35868}, {5062, 13930}, {5418, 13086}, {6249, 45441}, {6287, 6290}, {6292, 13878}, {6308, 39648}, {7977, 45477}, {8993, 45486}, {9732, 49328}, {9903, 45427}, {9918, 45429}, {10064, 45491}, {10080, 45493}, {12122, 12306}, {12144, 45401}, {12206, 45403}, {12252, 45407}, {12264, 45399}, {12339, 45417}, {12476, 45431}, {12477, 45433}, {12783, 45445}, {12795, 45447}, {12924, 45455}, {12934, 45457}, {12944, 45459}, {12954, 45461}, {12994, 45465}, {12995, 45466}, {13078, 45471}, {13111, 45489}, {13112, 45495}, {13113, 45497}, {13749, 29012}, {13984, 45485}, {17766, 49348}, {18548, 35869}, {18983, 45405}, {22780, 45437}, {22803, 45439}, {43118, 49112}, {45346, 48518}, {45348, 48517}, {45376, 48674}, {45410, 48770}, {45413, 49426}, {45414, 49425}, {45420, 49084}, {45423, 49189}, {45425, 49190}, {49310, 49356}

X(49354) = midpoint of X(i) and X(j) for these {i, j}: {83, 6275}, {2896, 49085}
X(49354) = reflection of X(i) in X(j) for these (i, j): (3, 48771), (49353, 83)
X(49354) = orthologic center (2nd anti-Kenmotu centers, 2nd Neuberg)
X(49354) = X(83)-of-2nd anti-Kenmotu centers triangle
X(49354) = X(35701)-of-1st Kenmotu-centers triangle
X(49354) = X(48771)-of-X3-ABC reflections triangle
X(49354) = {X(6), X(35701)}-harmonic conjugate of X(49353)


X(49355) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO ORTHIC AXES

Barycentrics    -2*((b^2+c^2)*a^2-(b^2-c^2)^2)*S+(-a^2+b^2+c^2)*(2*a^4-(b^2+c^2)*a^2+(b^2-c^2)^2) : :
X(49355) = 3*X(5)-X(5875) = 3*X(381)-X(49087) = 3*X(591)-X(9733) = 3*X(591)+X(13748) = 3*X(5874)+X(5875) = 2*X(5874)+X(49356) = 2*X(5875)-3*X(49356) = 3*X(41490)-2*X(43141) = 2*X(48772)+X(49086) = 3*X(49327)+X(49351)

The reciprocal orthologic center of these triangles is X(4).

X(49355) lies on these lines: {2, 45411}, {3, 489}, {4, 43133}, {5, 6}, {26, 45428}, {30, 591}, {76, 14234}, {98, 8825}, {114, 5058}, {140, 43119}, {182, 639}, {355, 45426}, {371, 45554}, {372, 44392}, {381, 45421}, {389, 48738}, {487, 32829}, {488, 32815}, {495, 45458}, {496, 45460}, {511, 48466}, {517, 49347}, {524, 44654}, {542, 44476}, {546, 45438}, {550, 12305}, {576, 45542}, {615, 10104}, {620, 641}, {640, 34507}, {671, 14231}, {952, 45713}, {1351, 36656}, {1483, 45476}, {1587, 26468}, {1588, 37343}, {1591, 11245}, {2782, 3071}, {3069, 37342}, {3070, 45462}, {3095, 13766}, {3155, 13428}, {3629, 45861}, {5050, 11313}, {5690, 45444}, {5844, 49329}, {5901, 45398}, {6229, 44390}, {6421, 37242}, {6424, 37466}, {6756, 45400}, {6811, 7774}, {7389, 45410}, {8414, 35255}, {8550, 23311}, {8703, 49363}, {8968, 34986}, {9738, 32419}, {10577, 45555}, {10942, 45424}, {10943, 45422}, {11272, 22719}, {12221, 21736}, {12256, 12322}, {12257, 32805}, {12314, 48660}, {12963, 37459}, {13088, 13830}, {13758, 13951}, {13794, 32810}, {13925, 45484}, {13966, 39679}, {13993, 45487}, {15171, 45470}, {15234, 45968}, {15236, 45298}, {15687, 49361}, {15765, 33443}, {18440, 36655}, {18546, 32421}, {18585, 33441}, {18990, 45404}, {21243, 48739}, {21850, 36658}, {22625, 45862}, {26346, 36712}, {28174, 49323}, {32134, 45402}, {32141, 45416}, {32146, 45430}, {32147, 45432}, {32151, 45434}, {32153, 45436}, {32162, 45446}, {32177, 45467}, {32178, 45464}, {32213, 45494}, {32214, 45496}, {32423, 49319}, {32450, 45545}, {32515, 49327}, {36657, 39884}, {39661, 42216}, {41490, 43141}, {43121, 48734}, {43126, 48781}, {43134, 45579}, {43143, 48778}, {44380, 44509}, {45345, 48519}, {45347, 48520}, {45412, 49427}, {45415, 49428}, {49309, 49353}

X(49355) = midpoint of X(i) and X(j) for these {i, j}: {3, 49086}, {5, 5874}, {9733, 13748}, {49319, 49369}
X(49355) = reflection of X(i) in X(j) for these (i, j): (3, 48772), (49356, 5)
X(49355) = anticomplement of X(48773)
X(49355) = orthologic center (1st anti-Kenmotu centers, T) for these triangles T: orthic axes, Yiu tangents
X(49355) = center of circle {{X(3), X(18348), X(49086)}}
X(49355) = X(5)-of-1st anti-Kenmotu centers triangle
X(49355) = X(48772)-of-X3-ABC reflections triangle
X(49355) = X(49086)-of-anti-X3-ABC reflections triangle
X(49355) = X(49087)-of-Ehrmann-mid triangle
X(49355) = X(49356)-of-Johnson triangle
X(49355) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5, 1353, 7583), (5, 19116, 18583), (6, 6289, 5), (486, 1352, 5), (486, 6278, 1352), (492, 45406, 3), (591, 13748, 9733), (637, 45510, 3), (6214, 7584, 5), (6215, 18762, 5), (6289, 49317, 6), (6290, 42262, 5), (10515, 14561, 5), (26441, 45508, 3), (42783, 42784, 49221), (43119, 45472, 140), (45375, 45488, 4), (45377, 45489, 6811), (45438, 45440, 546), (45458, 45490, 495), (45460, 45492, 496)


X(49356) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO ORTHIC AXES

Barycentrics    2*((b^2+c^2)*a^2-(b^2-c^2)^2)*S+(-a^2+b^2+c^2)*(2*a^4-(b^2+c^2)*a^2+(b^2-c^2)^2) : :
X(49356) = 3*X(5)-X(5874) = 3*X(381)-X(49086) = 3*X(1991)-X(9732) = 3*X(1991)+X(13749) = X(5874)+3*X(5875) = 2*X(5874)-3*X(49355) = 2*X(5875)+X(49355) = 3*X(41491)-2*X(43144) = 2*X(48773)+X(49087) = 3*X(49328)+X(49352)

The reciprocal orthologic center of these triangles is X(4).

X(49356) lies on these lines: {2, 45410}, {3, 490}, {4, 43134}, {5, 6}, {26, 45429}, {30, 1991}, {76, 14238}, {114, 5062}, {140, 43118}, {182, 640}, {355, 45427}, {371, 44394}, {372, 45555}, {381, 45420}, {389, 48739}, {487, 32815}, {488, 32829}, {495, 45459}, {496, 45461}, {511, 48467}, {517, 49348}, {524, 44655}, {542, 44475}, {546, 45439}, {550, 12306}, {576, 45543}, {590, 10104}, {620, 642}, {639, 34507}, {671, 14245}, {952, 45714}, {1271, 21737}, {1351, 36655}, {1483, 45477}, {1587, 37342}, {1588, 26469}, {1592, 11245}, {2782, 3070}, {3068, 37343}, {3071, 45463}, {3095, 13647}, {3156, 13439}, {3629, 45860}, {5050, 11314}, {5690, 45445}, {5844, 49330}, {5901, 45399}, {6228, 44391}, {6422, 37242}, {6423, 37466}, {6756, 45401}, {6813, 7774}, {7388, 45411}, {8406, 35256}, {8550, 23312}, {8703, 49362}, {8968, 21243}, {8976, 13638}, {8981, 39648}, {9739, 32421}, {10576, 45554}, {10942, 45425}, {10943, 45423}, {11272, 22717}, {12256, 32806}, {12257, 12323}, {12313, 48659}, {12968, 37459}, {13087, 13710}, {13674, 32811}, {13925, 45486}, {13993, 45485}, {15171, 45471}, {15233, 45968}, {15235, 45298}, {15687, 49364}, {15765, 33440}, {18440, 36656}, {18546, 32419}, {18585, 33442}, {18990, 45405}, {21850, 36657}, {22596, 45863}, {26336, 36711}, {28174, 49324}, {32134, 45403}, {32141, 45417}, {32146, 45431}, {32147, 45433}, {32151, 45435}, {32153, 45437}, {32162, 45447}, {32177, 45465}, {32178, 45466}, {32213, 45495}, {32214, 45497}, {32423, 49320}, {32450, 45544}, {32515, 49328}, {36658, 39884}, {39660, 42215}, {41491, 43144}, {43120, 48735}, {43127, 48780}, {43133, 45578}, {43145, 48779}, {44380, 44510}, {45346, 48520}, {45348, 48519}, {45413, 49428}, {45414, 49427}, {49310, 49354}

X(49356) = midpoint of X(i) and X(j) for these {i, j}: {3, 49087}, {5, 5875}, {9732, 13749}, {49320, 49370}
X(49356) = reflection of X(i) in X(j) for these (i, j): (3, 48773), (49355, 5)
X(49356) = anticomplement of X(48772)
X(49356) = orthologic center (2nd anti-Kenmotu centers, T) for these triangles T: orthic axes, Yiu tangents
X(49356) = center of circle {{X(3), X(18348), X(49087)}}
X(49356) = X(5)-of-2nd anti-Kenmotu centers triangle
X(49356) = X(48773)-of-X3-ABC reflections triangle
X(49356) = X(49086)-of-Ehrmann-mid triangle
X(49356) = X(49087)-of-anti-X3-ABC reflections triangle
X(49356) = X(49355)-of-Johnson triangle
X(49356) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5, 1353, 7584), (5, 19117, 18583), (6, 6290, 5), (485, 1352, 5), (485, 6281, 1352), (485, 31411, 7583), (491, 45407, 3), (638, 45511, 3), (1991, 13749, 9732), (6214, 18538, 5), (6215, 7583, 5), (6289, 42265, 5), (6290, 49318, 6), (8982, 45509, 3), (10514, 14561, 5), (15069, 42265, 6289), (42783, 42784, 49220), (43118, 45473, 140), (45376, 45489, 4), (45378, 45488, 6813), (45439, 45441, 546), (45459, 45491, 495), (45461, 45493, 496)


X(49357) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO REFLECTION

Barycentrics    a^2*(2*(a^4-(b^2+2*c^2)*a^2-(b^2-c^2)*c^2)*(a^4-(2*b^2+c^2)*a^2+(b^2-c^2)*b^2)*S+(b^2+c^2)*a^8-2*(b^2+c^2)^2*a^6+3*(b^2+c^2)*b^2*c^2*a^4+2*(b^6-c^6)*(b^2-c^2)*a^2-(b^6+c^6)*(b^2-c^2)^2) : :
X(49357) = 3*X(54)-X(6277) = 3*X(6276)+X(6277) = 2*X(6276)+X(49358) = 2*X(6277)-3*X(49358)

The reciprocal orthologic center of these triangles is X(4).

X(49357) lies on these lines: {3, 48774}, {4, 45482}, {6, 24}, {195, 44196}, {389, 45450}, {492, 2888}, {539, 591}, {1154, 9733}, {1209, 45472}, {2914, 45418}, {3102, 12971}, {3574, 45440}, {6288, 6289}, {7691, 12305}, {7979, 45476}, {8995, 45484}, {9905, 45426}, {9920, 45428}, {9977, 44510}, {9985, 45434}, {10066, 45490}, {10082, 45492}, {10610, 43119}, {10628, 49313}, {11576, 45400}, {12208, 45402}, {12242, 45474}, {12254, 45406}, {12266, 45398}, {12341, 45416}, {12480, 45430}, {12481, 45432}, {12785, 45444}, {12797, 45446}, {12926, 45454}, {12936, 45456}, {12946, 45458}, {12956, 45460}, {12965, 45462}, {12998, 45467}, {12999, 45464}, {13079, 45470}, {13121, 45494}, {13122, 45496}, {13748, 18400}, {13986, 45487}, {17824, 45442}, {18984, 45404}, {22781, 45436}, {22804, 45438}, {32341, 45408}, {32423, 49319}, {45345, 48521}, {45347, 48522}, {45375, 48675}, {45411, 48775}, {45412, 49429}, {45415, 49430}, {45421, 49089}, {45422, 49191}, {45424, 49192}

X(49357) = midpoint of X(i) and X(j) for these {i, j}: {54, 6276}, {2888, 49088}
X(49357) = orthologic center (1st anti-Kenmotu centers, reflection)
X(49357) = X(48774)-of-X3-ABC reflections triangle
X(49357) = X(54)-of-1st anti-Kenmotu centers triangle
X(49357) = reflection of X(i) in X(j) for these (i, j): (3, 48774), (49358, 54)


X(49358) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO REFLECTION

Barycentrics    a^2*(-2*(a^4-(b^2+2*c^2)*a^2-(b^2-c^2)*c^2)*(a^4-(2*b^2+c^2)*a^2+(b^2-c^2)*b^2)*S+(b^2+c^2)*a^8-2*(b^2+c^2)^2*a^6+3*(b^2+c^2)*b^2*c^2*a^4+2*(b^6-c^6)*(b^2-c^2)*a^2-(b^6+c^6)*(b^2-c^2)^2) : :
X(49358) = 3*X(54)-X(6276) = X(6276)+3*X(6277) = 2*X(6276)-3*X(49357) = 2*X(6277)+X(49357)

The reciprocal orthologic center of these triangles is X(4).

X(49358) lies on these lines: {3, 48775}, {4, 45483}, {6, 24}, {195, 44199}, {389, 45451}, {491, 2888}, {539, 1991}, {1154, 9732}, {1209, 45473}, {2914, 45419}, {3103, 12965}, {3574, 45441}, {6288, 6290}, {7691, 12306}, {7979, 45477}, {8995, 45486}, {9905, 45427}, {9920, 45429}, {9977, 44509}, {9985, 45435}, {10066, 45491}, {10082, 45493}, {10610, 43118}, {10628, 49314}, {11576, 45401}, {12208, 45403}, {12242, 45475}, {12254, 45407}, {12266, 45399}, {12341, 45417}, {12480, 45431}, {12481, 45433}, {12785, 45445}, {12797, 45447}, {12926, 45455}, {12936, 45457}, {12946, 45459}, {12956, 45461}, {12971, 45463}, {12998, 45465}, {12999, 45466}, {13079, 45471}, {13121, 45495}, {13122, 45497}, {13749, 18400}, {13986, 45485}, {17824, 45443}, {18984, 45405}, {22781, 45437}, {22804, 45439}, {32341, 45409}, {32423, 49320}, {45346, 48522}, {45348, 48521}, {45376, 48675}, {45410, 48774}, {45413, 49430}, {45414, 49429}, {45420, 49088}, {45423, 49191}, {45425, 49192}

X(49358) = midpoint of X(i) and X(j) for these {i, j}: {54, 6277}, {2888, 49089}
X(49358) = orthologic center (2nd anti-Kenmotu centers, reflection)
X(49358) = X(48775)-of-X3-ABC reflections triangle
X(49358) = X(54)-of-2nd anti-Kenmotu centers triangle
X(49358) = reflection of X(i) in X(j) for these (i, j): (3, 48775), (49357, 54)


X(49359) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO 1st SCHIFFLER

Barycentrics    -2*(-a+b+c)*(a^3-(b-3*c)*a^2-(b^2+b*c-3*c^2)*a+(b^2-c^2)*(b-c))*(a^3+(3*b-c)*a^2+(3*b^2-b*c-c^2)*a+(b^2-c^2)*(b-c))*S+2*a^9-5*(b^2+c^2)*a^7+(b+c)*(b^2+c^2)*a^6+(3*b^4+3*c^4+8*b*c*(b^2+c^2))*a^5-(b^2-c^2)*(b-c)*(3*b^2+4*b*c+3*c^2)*a^4+(b^6+c^6-8*b*c*(b^4+c^4))*a^3+(b+c)*(b^2+c^2)*(3*b^4+3*c^4-b*c*(4*b^2-b*c+4*c^2))*a^2-(b^4-c^4)^2*a-(b^4-c^4)*(b^2-c^2)^2*(b-c) : :
X(49359) = 3*X(10266)-X(12807) = X(12807)+3*X(12808) = 2*X(12807)-3*X(49360) = 2*X(12808)+X(49360)

The reciprocal orthologic center of these triangles is X(79).

X(49359) lies on these lines: {3, 48776}, {6, 10266}, {492, 12849}, {3102, 35871}, {6289, 12919}, {12146, 45400}, {12209, 45402}, {12255, 45406}, {12267, 45398}, {12305, 12556}, {12342, 45416}, {12409, 45426}, {12414, 45428}, {12482, 45430}, {12483, 45432}, {12504, 45434}, {12600, 45440}, {12786, 45444}, {12798, 45446}, {12927, 45454}, {12937, 45456}, {12947, 45458}, {12957, 45460}, {13000, 45467}, {13001, 45464}, {13080, 45470}, {13089, 45472}, {13100, 45476}, {13126, 45488}, {13128, 45490}, {13129, 45492}, {13130, 45494}, {13131, 45496}, {13919, 45484}, {13987, 45487}, {18985, 45404}, {22782, 45436}, {22805, 45438}, {35870, 45462}, {43119, 49113}, {45345, 48523}, {45347, 48524}, {45375, 48676}, {45411, 48777}, {45412, 49431}, {45415, 49432}, {45421, 49091}, {45422, 49193}, {45424, 49194}

X(49359) = midpoint of X(i) and X(j) for these {i, j}: {10266, 12808}, {12849, 49090}
X(49359) = orthologic center (1st anti-Kenmotu centers, 1st Schiffler)
X(49359) = X(48776)-of-X3-ABC reflections triangle
X(49359) = X(10266)-of-1st anti-Kenmotu centers triangle
X(49359) = reflection of X(i) in X(j) for these (i, j): (3, 48776), (49360, 10266)


X(49360) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO 1st SCHIFFLER

Barycentrics    2*(-a+b+c)*(a^3-(b-3*c)*a^2-(b^2+b*c-3*c^2)*a+(b^2-c^2)*(b-c))*(a^3+(3*b-c)*a^2+(3*b^2-b*c-c^2)*a+(b^2-c^2)*(b-c))*S+2*a^9-5*(b^2+c^2)*a^7+(b+c)*(b^2+c^2)*a^6+(3*b^4+3*c^4+8*b*c*(b^2+c^2))*a^5-(b^2-c^2)*(b-c)*(3*b^2+4*b*c+3*c^2)*a^4+(b^6+c^6-8*b*c*(b^4+c^4))*a^3+(b+c)*(b^2+c^2)*(3*b^4+3*c^4-b*c*(4*b^2-b*c+4*c^2))*a^2-(b^4-c^4)^2*a-(b^4-c^4)*(b^2-c^2)^2*(b-c) : :
X(49360) = 3*X(10266)-X(12808) = 3*X(12807)+X(12808) = 2*X(12807)+X(49359) = 2*X(12808)-3*X(49359)

The reciprocal orthologic center of these triangles is X(79).

X(49360) lies on these lines: {3, 48777}, {6, 10266}, {491, 12849}, {3103, 35870}, {6290, 12919}, {12146, 45401}, {12209, 45403}, {12255, 45407}, {12267, 45399}, {12306, 12556}, {12342, 45417}, {12409, 45427}, {12414, 45429}, {12482, 45431}, {12483, 45433}, {12504, 45435}, {12600, 45441}, {12786, 45445}, {12798, 45447}, {12927, 45455}, {12937, 45457}, {12947, 45459}, {12957, 45461}, {13000, 45465}, {13001, 45466}, {13080, 45471}, {13089, 45473}, {13100, 45477}, {13126, 45489}, {13128, 45491}, {13129, 45493}, {13130, 45495}, {13131, 45497}, {13919, 45486}, {13987, 45485}, {18985, 45405}, {22782, 45437}, {22805, 45439}, {35871, 45463}, {43118, 49113}, {45346, 48524}, {45348, 48523}, {45376, 48676}, {45410, 48776}, {45413, 49432}, {45414, 49431}, {45420, 49090}, {45423, 49193}, {45425, 49194}

X(49360) = midpoint of X(i) and X(j) for these {i, j}: {10266, 12807}, {12849, 49091}
X(49360) = orthologic center (2nd anti-Kenmotu centers, 1st Schiffler)
X(49360) = X(48777)-of-X3-ABC reflections triangle
X(49360) = X(10266)-of-2nd anti-Kenmotu centers triangle
X(49360) = reflection of X(i) in X(j) for these (i, j): (3, 48777), (49359, 10266)


X(49361) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO 1st TRI-SQUARES-CENTRAL

Barycentrics    7*a^6-(b^2+c^2)*a^4-(b^2-2*b*c-c^2)*(b^2+2*b*c-c^2)*a^2+2*(4*a^4+(b^2+c^2)*a^2-5*(b^2-c^2)^2)*S-5*(b^2+c^2)*(b^2-c^2)^2 : :
X(49361) = 3*X(4)-X(33456) = 9*X(4)-X(49093) = 5*X(381)-2*X(48780) = 3*X(1327)-X(13690) = 3*X(3545)-2*X(49114) = 3*X(3839)-X(13674) = 6*X(3845)-X(13690) = 2*X(3845)+X(13691) = 4*X(3845)-X(49362) = 5*X(6289)-2*X(12305) = 2*X(13666)-5*X(13692) = 3*X(13666)-5*X(13712) = 2*X(13687)-3*X(14269) = X(13690)+3*X(13691) = 2*X(13690)-3*X(49362) = 2*X(13691)+X(49362) = 3*X(13692)-2*X(13712) = X(13713)-3*X(38335) = 3*X(33456)-X(49093)

The reciprocal orthologic center of these triangles is X(13665).

X(49361) lies on these lines: {2, 22806}, {3, 48778}, {4, 33456}, {6, 1327}, {30, 6289}, {114, 45499}, {381, 13748}, {492, 13678}, {591, 3830}, {1991, 6033}, {3102, 35873}, {3534, 13701}, {3543, 9733}, {3545, 43119}, {3839, 13674}, {6560, 22616}, {6565, 13932}, {8414, 42602}, {9766, 18539}, {10706, 49319}, {13667, 45398}, {13668, 45400}, {13672, 45402}, {13675, 45416}, {13679, 45426}, {13680, 45428}, {13682, 45430}, {13683, 45432}, {13685, 45434}, {13687, 14269}, {13688, 28198}, {13693, 45454}, {13694, 45456}, {13695, 45458}, {13696, 45460}, {13697, 45467}, {13698, 45464}, {13699, 45470}, {13702, 45476}, {13713, 38335}, {13714, 45490}, {13715, 45492}, {13716, 45494}, {13717, 45496}, {13850, 13908}, {13920, 45484}, {13988, 45487}, {14232, 36726}, {15687, 49355}, {18986, 45404}, {21850, 22484}, {22783, 45436}, {22872, 36466}, {22917, 36448}, {32419, 48660}, {35872, 45462}, {45345, 48525}, {45347, 48526}, {45412, 49433}, {45415, 49434}, {45422, 49195}, {45424, 49196}

X(49361) = midpoint of X(i) and X(j) for these {i, j}: {1327, 13691}, {3830, 48677}, {13678, 15682}
X(49361) = reflection of X(i) in X(j) for these (i, j): (2, 22806), (3, 48778), (1327, 3845), (3534, 13701), (49362, 1327)
X(49361) = orthologic center (1st anti-Kenmotu centers, 1st tri-squares-central)
X(49361) = X(1327)-of-1st anti-Kenmotu centers triangle
X(49361) = X(48778)-of-X3-ABC reflections triangle
X(49361) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1327, 1328, 49261), (3830, 45375, 591), (3845, 13691, 49362)


X(49362) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO 1st TRI-SQUARES-CENTRAL

Barycentrics    13*a^6-13*(b^2+c^2)*a^4+(5*b^4-6*b^2*c^2+5*c^4)*a^2-2*(4*a^4+(b^2+c^2)*a^2-5*(b^2-c^2)^2)*S-5*(b^2+c^2)*(b^2-c^2)^2 : :
X(49362) = X(2)-3*X(13674) = 4*X(2)-3*X(13692) = 5*X(2)-6*X(49114) = 3*X(1327)-2*X(3845) = 3*X(1327)-X(13691) = 2*X(3845)+3*X(13690) = 4*X(3845)-3*X(49361) = 4*X(12100)-3*X(13712) = 3*X(13666)-4*X(15690) = 4*X(13674)-X(13692) = 5*X(13674)-2*X(49114) = 3*X(13678)-5*X(19708) = 3*X(13690)+X(13691) = 2*X(13690)+X(49361) = 2*X(13691)-3*X(49361) = 5*X(13692)-8*X(49114) = 6*X(13701)-7*X(15701) = X(15682)-3*X(33456) = 5*X(19708)+3*X(49093) = 5*X(19709)-3*X(48677)

The reciprocal orthologic center of these triangles is X(13665).

X(49362) lies on these lines: {2, 6290}, {3, 48780}, {6, 1327}, {30, 22485}, {491, 13678}, {1991, 3534}, {3103, 35872}, {3830, 13749}, {8703, 49356}, {9732, 11001}, {12100, 13712}, {12306, 13666}, {13667, 45399}, {13668, 45401}, {13672, 45403}, {13675, 45417}, {13679, 45427}, {13680, 45429}, {13682, 45431}, {13683, 45433}, {13685, 45435}, {13687, 45441}, {13688, 45445}, {13689, 45447}, {13693, 45455}, {13694, 45457}, {13695, 45459}, {13696, 45461}, {13697, 45465}, {13698, 45466}, {13699, 45471}, {13701, 15701}, {13702, 45477}, {13713, 45489}, {13714, 45491}, {13715, 45493}, {13716, 45495}, {13717, 45497}, {13920, 45486}, {13988, 45485}, {15682, 33456}, {18986, 45405}, {19709, 45376}, {22783, 45437}, {22806, 41106}, {35873, 45463}, {36382, 36396}, {36383, 36400}, {45346, 48526}, {45348, 48525}, {45410, 48778}, {45413, 49434}, {45414, 49433}, {45423, 49195}, {45425, 49196}

X(49362) = midpoint of X(i) and X(j) for these {i, j}: {1327, 13690}, {13678, 49093}
X(49362) = reflection of X(i) in X(j) for these (i, j): (3, 48780), (13691, 3845), (49361, 1327)
X(49362) = orthologic center (2nd anti-Kenmotu centers, 1st tri-squares-central)
X(49362) = X(1327)-of-2nd anti-Kenmotu centers triangle
X(49362) = X(48780)-of-X3-ABC reflections triangle
X(49362) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1327, 13691, 3845), (3845, 13691, 49361), (41112, 41113, 49262)


X(49363) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    13*a^6-13*(b^2+c^2)*a^4+(5*b^4-6*b^2*c^2+5*c^4)*a^2+2*(4*a^4+(b^2+c^2)*a^2-5*(b^2-c^2)^2)*S-5*(b^2+c^2)*(b^2-c^2)^2 : :
X(49363) = X(2)-3*X(13794) = 4*X(2)-3*X(13812) = 5*X(2)-6*X(49115) = 3*X(1328)-2*X(3845) = 3*X(1328)-X(13810) = 2*X(3845)+3*X(13811) = 4*X(3845)-3*X(49364) = 4*X(12100)-3*X(13835) = 3*X(13786)-4*X(15690) = 4*X(13794)-X(13812) = 5*X(13794)-2*X(49115) = 3*X(13798)-5*X(19708) = X(13810)+3*X(13811) = 2*X(13810)-3*X(49364) = 2*X(13811)+X(49364) = 5*X(13812)-8*X(49115) = 6*X(13821)-7*X(15701) = X(15682)-3*X(33457) = 5*X(19708)+3*X(49092) = 5*X(19709)-3*X(48678)

The reciprocal orthologic center of these triangles is X(13785).

X(49363) lies on these lines: {2, 6222}, {3, 48781}, {6, 1327}, {30, 22484}, {492, 13798}, {591, 3534}, {3102, 35875}, {3830, 13748}, {8703, 49355}, {12100, 13835}, {12305, 13786}, {13787, 45398}, {13788, 45400}, {13792, 45402}, {13795, 45416}, {13799, 45426}, {13800, 45428}, {13802, 45430}, {13803, 45432}, {13805, 45434}, {13807, 45440}, {13808, 45444}, {13809, 45446}, {13813, 45454}, {13814, 45456}, {13815, 45458}, {13816, 45460}, {13817, 45467}, {13818, 45464}, {13819, 45470}, {13821, 15701}, {13822, 45476}, {13836, 45488}, {13837, 45490}, {13838, 45492}, {13839, 45494}, {13840, 45496}, {13848, 45484}, {13849, 45487}, {15682, 33457}, {18987, 45404}, {19709, 45375}, {22784, 45436}, {22807, 41106}, {35874, 45462}, {36382, 36397}, {36383, 36401}, {45345, 48527}, {45347, 48528}, {45411, 48779}, {45412, 49435}, {45415, 49436}, {45422, 49197}, {45424, 49198}

X(49363) = midpoint of X(i) and X(j) for these {i, j}: {1328, 13811}, {13798, 49092}
X(49363) = reflection of X(i) in X(j) for these (i, j): (3, 48781), (13810, 3845), (49364, 1328)
X(49363) = orthologic center (1st anti-Kenmotu centers, 2nd tri-squares-central)
X(49363) = X(1328)-of-1st anti-Kenmotu centers triangle
X(49363) = X(48781)-of-X3-ABC reflections triangle
X(49363) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1328, 13810, 3845), (3845, 13810, 49364), (41112, 41113, 49261)


X(49364) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    7*a^6-(b^2+c^2)*a^4-(b^2-2*b*c-c^2)*(b^2+2*b*c-c^2)*a^2-2*(4*a^4+(b^2+c^2)*a^2-5*(b^2-c^2)^2)*S-5*(b^2+c^2)*(b^2-c^2)^2 : :
X(49364) = 3*X(4)-X(33457) = 9*X(4)-X(49092) = 5*X(381)-2*X(48781) = 3*X(1328)-X(13811) = 3*X(3545)-2*X(49115) = 3*X(3839)-X(13794) = 2*X(3845)+X(13810) = 6*X(3845)-X(13811) = 4*X(3845)-X(49363) = 5*X(6290)-2*X(12306) = 2*X(13786)-5*X(13812) = 3*X(13786)-5*X(13835) = 2*X(13807)-3*X(14269) = 3*X(13810)+X(13811) = 2*X(13810)+X(49363) = 2*X(13811)-3*X(49363) = 3*X(13812)-2*X(13835) = X(13836)-3*X(38335) = 3*X(33457)-X(49092)

The reciprocal orthologic center of these triangles is X(13785).

X(49364) lies on these lines: {2, 22807}, {3, 48779}, {4, 33457}, {6, 1327}, {30, 6290}, {114, 45498}, {381, 13749}, {491, 13798}, {591, 6033}, {1991, 3830}, {3103, 35874}, {3534, 13821}, {3543, 9732}, {3545, 43118}, {3839, 13794}, {6561, 22645}, {6564, 13850}, {8406, 42603}, {9766, 26438}, {10706, 49320}, {13787, 45399}, {13788, 45401}, {13792, 45403}, {13795, 45417}, {13799, 45427}, {13800, 45429}, {13802, 45431}, {13803, 45433}, {13805, 45435}, {13807, 14269}, {13808, 28198}, {13813, 45455}, {13814, 45457}, {13815, 45459}, {13816, 45461}, {13817, 45465}, {13818, 45466}, {13819, 45471}, {13822, 45477}, {13836, 38335}, {13837, 45491}, {13838, 45493}, {13839, 45495}, {13840, 45497}, {13848, 45486}, {13849, 45485}, {13932, 13968}, {14237, 36723}, {15687, 49356}, {18987, 45405}, {21850, 22485}, {22784, 45437}, {22874, 36448}, {22919, 36466}, {32421, 48659}, {35875, 45463}, {45346, 48528}, {45348, 48527}, {45413, 49436}, {45414, 49435}, {45423, 49197}, {45425, 49198}

X(49364) = midpoint of X(i) and X(j) for these {i, j}: {1328, 13810}, {3830, 48678}, {13798, 15682}
X(49364) = reflection of X(i) in X(j) for these (i, j): (2, 22807), (3, 48779), (1328, 3845), (3534, 13821), (49363, 1328)
X(49364) = orthologic center (2nd anti-Kenmotu centers, 2nd tri-squares-central)
X(49364) = X(1328)-of-2nd anti-Kenmotu centers triangle
X(49364) = X(48779)-of-X3-ABC reflections triangle
X(49364) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1327, 1328, 49262), (3830, 45376, 1991), (3845, 13810, 49363)


X(49365) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO WALSMITH

Barycentrics    2*(a^4-c^2*a^2+c^4-b^4)*(a^4-b^2*a^2+b^4-c^4)*S+(a^2+b^2+c^2)*(2*a^8-2*(b^2+c^2)*a^6-(b^4-4*b^2*c^2+c^4)*a^4+2*(b^4-c^4)*(b^2-c^2)*a^2-(b^4-c^4)^2) : :
X(49365) = 3*X(67)-X(32280) = X(32280)+3*X(32281) = 2*X(32280)-3*X(49366) = 2*X(32281)+X(49366)

The reciprocal orthologic center of these triangles is X(125).

X(49365) lies on these lines: {3, 48782}, {6, 67}, {492, 11061}, {511, 49319}, {542, 9733}, {1503, 49313}, {2781, 13748}, {2930, 44196}, {3102, 35877}, {6289, 9970}, {6593, 45472}, {9971, 45480}, {12305, 32233}, {12367, 45418}, {13774, 32304}, {14984, 49321}, {32238, 45398}, {32239, 45400}, {32242, 45402}, {32243, 45404}, {32246, 45474}, {32247, 45406}, {32256, 45416}, {32261, 45426}, {32262, 45428}, {32265, 45430}, {32266, 45432}, {32268, 45434}, {32270, 45436}, {32271, 45438}, {32274, 45440}, {32278, 45444}, {32279, 45446}, {32287, 45454}, {32288, 45456}, {32289, 45458}, {32290, 45460}, {32295, 45467}, {32296, 45464}, {32297, 45470}, {32298, 45476}, {32303, 45484}, {32306, 45488}, {32307, 45490}, {32308, 45492}, {32309, 45494}, {32310, 45496}, {35876, 45462}, {36201, 49349}, {40949, 45478}, {41731, 44510}, {43119, 49116}, {45345, 48529}, {45347, 48530}, {45375, 48679}, {45411, 48783}, {45412, 49437}, {45415, 49438}, {45421, 49095}, {45422, 49199}, {45424, 49200}

X(49365) = midpoint of X(i) and X(j) for these {i, j}: {67, 32281}, {11061, 49094}
X(49365) = reflection of X(i) in X(j) for these (i, j): (3, 48782), (49366, 67)
X(49365) = orthologic center (1st anti-Kenmotu centers, Walsmith)
X(49365) = X(67)-of-1st anti-Kenmotu centers triangle
X(49365) = X(48782)-of-X3-ABC reflections triangle
X(49365) = {X(67), X(32252)}-harmonic conjugate of X(125)


X(49366) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO WALSMITH

Barycentrics    -2*(a^4-c^2*a^2+c^4-b^4)*(a^4-b^2*a^2+b^4-c^4)*S+(a^2+b^2+c^2)*(2*a^8-2*(b^2+c^2)*a^6-(b^4-4*b^2*c^2+c^4)*a^4+2*(b^4-c^4)*(b^2-c^2)*a^2-(b^4-c^4)^2) : :
X(49366) = 3*X(67)-X(32281) = 3*X(32280)+X(32281) = 2*X(32280)+X(49365) = 2*X(32281)-3*X(49365)

The reciprocal orthologic center of these triangles is X(125).

X(49366) lies on these lines: {3, 48783}, {6, 67}, {491, 11061}, {511, 49320}, {542, 9732}, {1503, 49314}, {2781, 13749}, {2930, 44199}, {3103, 35876}, {6290, 9970}, {6593, 45473}, {9971, 45481}, {12306, 32233}, {12367, 45419}, {13654, 32303}, {14984, 49322}, {32238, 45399}, {32239, 45401}, {32242, 45403}, {32243, 45405}, {32246, 45475}, {32247, 45407}, {32256, 45417}, {32261, 45427}, {32262, 45429}, {32265, 45431}, {32266, 45433}, {32268, 45435}, {32270, 45437}, {32271, 45439}, {32274, 45441}, {32278, 45445}, {32279, 45447}, {32287, 45455}, {32288, 45457}, {32289, 45459}, {32290, 45461}, {32295, 45465}, {32296, 45466}, {32297, 45471}, {32298, 45477}, {32304, 45485}, {32306, 45489}, {32307, 45491}, {32308, 45493}, {32309, 45495}, {32310, 45497}, {35877, 45463}, {36201, 49350}, {40949, 45479}, {41731, 44509}, {43118, 49116}, {45346, 48530}, {45348, 48529}, {45376, 48679}, {45410, 48782}, {45413, 49438}, {45414, 49437}, {45420, 49094}, {45423, 49199}, {45425, 49200}

X(49366) = midpoint of X(i) and X(j) for these {i, j}: {67, 32280}, {11061, 49095}
X(49366) = reflection of X(i) in X(j) for these (i, j): (3, 48783), (49365, 67)
X(49366) = orthologic center (2nd anti-Kenmotu centers, Walsmith)
X(49366) = X(67)-of-2nd anti-Kenmotu centers triangle
X(49366) = X(48783)-of-X3-ABC reflections triangle
X(49366) = {X(67), X(32253)}-harmonic conjugate of X(125)


X(49367) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO 1st ANTI-BROCARD

Barycentrics    2*(a^2-c^2)*(a^2-b^2)*S+(b^2+c^2)*a^4-2*(b^4+c^4)*a^2+b^2*c^2*(b^2+c^2) : :
X(49367) = 3*X(99)-X(6319) = X(6319)+3*X(6320) = 2*X(6319)-3*X(49368) = 2*X(6320)+X(49368) = 3*X(8591)-X(49097)

The reciprocal parallelogic center of these triangles is X(385).

X(49367) lies on the circumcircle of 1st anti-Kenmotu centers triangle and these lines: {3, 48784}, {6, 99}, {98, 12305}, {114, 45440}, {115, 45472}, {148, 492}, {538, 35825}, {542, 49313}, {543, 591}, {690, 49369}, {1991, 9894}, {2782, 9733}, {2783, 48684}, {2787, 48703}, {2794, 49315}, {2799, 49371}, {3023, 45470}, {3027, 45404}, {3070, 33341}, {3102, 35869}, {4027, 45402}, {5149, 45513}, {5186, 45400}, {6289, 6321}, {7778, 13773}, {7781, 35878}, {7983, 45476}, {8178, 35824}, {8305, 49352}, {8591, 45421}, {8782, 45434}, {8997, 45484}, {9766, 49312}, {10086, 45490}, {10089, 45492}, {11711, 45398}, {12968, 36849}, {13172, 45406}, {13173, 45416}, {13174, 45426}, {13175, 45428}, {13176, 45430}, {13177, 45432}, {13178, 45444}, {13179, 45446}, {13180, 45454}, {13181, 45456}, {13182, 45458}, {13183, 45460}, {13184, 45467}, {13185, 45464}, {13188, 45488}, {13189, 45494}, {13190, 45496}, {13748, 23698}, {13989, 45487}, {22514, 45436}, {22515, 45438}, {33813, 43119}, {38733, 45375}, {45345, 48531}, {45347, 48532}, {45411, 48785}, {45412, 49439}, {45415, 49440}, {45422, 49201}, {45424, 49202}

X(49367) = midpoint of X(i) and X(j) for these {i, j}: {99, 6320}, {148, 49096}
X(49367) = reflection of X(i) in X(j) for these (i, j): (3, 48784), (1991, 9894), (49309, 9733), (49311, 591), (49368, 99)
X(49367) = parallelogic center (1st anti-Kenmotu centers, T) for these triangles T: 1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard
X(49367) = X(99)-of-1st anti-Kenmotu centers triangle
X(49367) = X(48784)-of-X3-ABC reflections triangle
X(49367) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (99, 10754, 49266), (99, 19108, 5026)


X(49368) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO 1st ANTI-BROCARD

Barycentrics    -2*(a^2-c^2)*(a^2-b^2)*S+(b^2+c^2)*a^4-2*(b^4+c^4)*a^2+b^2*c^2*(b^2+c^2) : :
X(49368) = 3*X(99)-X(6320) = 3*X(6319)+X(6320) = 2*X(6319)+X(49367) = 2*X(6320)-3*X(49367) = 3*X(8591)-X(49096)

The reciprocal parallelogic center of these triangles is X(385).

X(49368) lies on the circumcircle of 2nd anti-Kenmotu centers triangle and these lines: {3, 48785}, {6, 99}, {98, 12306}, {114, 45441}, {115, 45473}, {148, 491}, {538, 35824}, {542, 49314}, {543, 1991}, {591, 9892}, {690, 49370}, {2782, 9732}, {2783, 48685}, {2787, 48704}, {2794, 49316}, {2799, 49372}, {3023, 45471}, {3027, 45405}, {3071, 33340}, {3103, 35868}, {4027, 45403}, {5149, 45512}, {5186, 45401}, {6290, 6321}, {7778, 13653}, {7781, 35879}, {7983, 45477}, {8178, 35825}, {8304, 49351}, {8591, 45420}, {8782, 45435}, {8997, 45486}, {9766, 49311}, {10086, 45491}, {10089, 45493}, {11711, 45399}, {12963, 36849}, {13172, 45407}, {13173, 45417}, {13174, 45427}, {13175, 45429}, {13176, 45431}, {13177, 45433}, {13178, 45445}, {13179, 45447}, {13180, 45455}, {13181, 45457}, {13182, 45459}, {13183, 45461}, {13184, 45465}, {13185, 45466}, {13188, 45489}, {13189, 45495}, {13190, 45497}, {13749, 23698}, {13989, 45485}, {22514, 45437}, {22515, 45439}, {33813, 43118}, {38733, 45376}, {45346, 48532}, {45348, 48531}, {45410, 48784}, {45413, 49440}, {45414, 49439}, {45423, 49201}, {45425, 49202}

X(49368) = midpoint of X(i) and X(j) for these {i, j}: {99, 6319}, {148, 49097}
X(49368) = reflection of X(i) in X(j) for these (i, j): (3, 48785), (591, 9892), (49310, 9732), (49312, 1991), (49367, 99)
X(49368) = parallelogic center (2nd anti-Kenmotu centers, T) for these triangles T: 1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard
X(49368) = X(99)-of-2nd anti-Kenmotu centers triangle
X(49368) = X(48785)-of-X3-ABC reflections triangle
X(49368) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (99, 10754, 49267), (99, 19109, 5026)


X(49369) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*(2*(a^2-c^2)*(a^2-b^2)*S+(b^2+c^2)*a^4-4*b^2*c^2*a^2-(b^4-3*b^2*c^2+c^4)*(b^2+c^2)) : :
X(49369) = 3*X(110)-X(7732) = X(7732)+3*X(7733) = 2*X(7732)-3*X(49370) = 2*X(7733)+X(49370) = 3*X(9143)-X(49099) = 3*X(32609)-2*X(48787)

The reciprocal parallelogic center of these triangles is X(323).

X(49369) lies on the circumcircle of 1st anti-Kenmotu centers triangle and these lines: {3, 48786}, {6, 110}, {74, 12287}, {113, 45440}, {125, 45472}, {265, 6289}, {399, 45488}, {492, 3448}, {542, 591}, {690, 49367}, {1112, 45400}, {1511, 43119}, {2771, 48684}, {2781, 49315}, {2948, 45426}, {3024, 45470}, {3028, 45404}, {3102, 12376}, {5663, 9733}, {7778, 13774}, {7984, 45476}, {8674, 48703}, {8998, 45484}, {9143, 45421}, {9517, 49371}, {9976, 44510}, {10088, 45490}, {10091, 45492}, {10113, 45438}, {10820, 39679}, {11720, 45398}, {12310, 45428}, {12375, 45462}, {12383, 45406}, {12902, 45375}, {12903, 45458}, {12904, 45460}, {13193, 45402}, {13204, 45416}, {13208, 45430}, {13209, 45432}, {13210, 45434}, {13211, 45444}, {13212, 45446}, {13213, 45454}, {13214, 45456}, {13215, 45467}, {13216, 45464}, {13217, 45494}, {13218, 45496}, {13748, 17702}, {13990, 45487}, {22586, 45436}, {23236, 49317}, {32423, 49319}, {32609, 45411}, {45345, 48535}, {45347, 48536}, {45412, 49441}, {45415, 49442}, {45422, 49203}, {45424, 49204}

X(49369) = midpoint of X(i) and X(j) for these {i, j}: {110, 7733}, {3448, 49098}
X(49369) = reflection of X(i) in X(j) for these (i, j): (3, 48786), (49313, 9733), (49319, 49355), (49370, 110)
X(49369) = inverse of X(49268) in MacBeath circumconic
X(49369) = crossdifference of every pair of points on line {X(690), X(46688)}
X(49369) = parallelogic center (1st anti-Kenmotu centers, T) for these triangles T: anti-orthocentroidal, orthocentroidal
X(49369) = X(110)-of-1st anti-Kenmotu centers triangle
X(49369) = X(591)-of-anti-orthocentroidal triangle
X(49369) = X(48786)-of-X3-ABC reflections triangle
X(49369) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (110, 895, 49268), (110, 19110, 6593)


X(49370) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*(-2*(a^2-c^2)*(a^2-b^2)*S+(b^2+c^2)*a^4-4*b^2*c^2*a^2-(b^4-3*b^2*c^2+c^4)*(b^2+c^2)) : :
X(49370) = 3*X(110)-X(7733) = 3*X(7732)+X(7733) = 2*X(7732)+X(49369) = 2*X(7733)-3*X(49369) = 3*X(9143)-X(49098) = 3*X(32609)-2*X(48786)

The reciprocal parallelogic center of these triangles is X(323).

X(49370) lies on the circumcircle of 2nd anti-Kenmotu centers triangle and these lines: {3, 48787}, {6, 110}, {74, 12288}, {113, 45441}, {125, 45473}, {265, 6290}, {399, 45489}, {491, 3448}, {542, 1991}, {690, 49368}, {1112, 45401}, {1511, 43118}, {2771, 48685}, {2781, 49316}, {2948, 45427}, {3024, 45471}, {3028, 45405}, {3103, 12375}, {5663, 9732}, {7778, 13654}, {7984, 45477}, {8674, 48704}, {8998, 45486}, {9143, 45420}, {9517, 49372}, {9976, 44509}, {10088, 45491}, {10091, 45493}, {10113, 45439}, {10819, 39648}, {11720, 45399}, {12310, 45429}, {12376, 45463}, {12383, 45407}, {12902, 45376}, {12903, 45459}, {12904, 45461}, {13193, 45403}, {13204, 45417}, {13208, 45431}, {13209, 45433}, {13210, 45435}, {13211, 45445}, {13212, 45447}, {13213, 45455}, {13214, 45457}, {13215, 45465}, {13216, 45466}, {13217, 45495}, {13218, 45497}, {13749, 17702}, {13990, 45485}, {22586, 45437}, {23236, 49318}, {32423, 49320}, {32609, 45410}, {45346, 48536}, {45348, 48535}, {45413, 49442}, {45414, 49441}, {45423, 49203}, {45425, 49204}

X(49370) = midpoint of X(i) and X(j) for these {i, j}: {110, 7732}, {3448, 49099}
X(49370) = reflection of X(i) in X(j) for these (i, j): (3, 48787), (49314, 9732), (49320, 49356), (49369, 110)
X(49370) = inverse of X(49269) in MacBeath circumconic
X(49370) = crossdifference of every pair of points on line {X(690), X(46689)}
X(49370) = parallelogic center (2nd anti-Kenmotu centers, T) for these triangles T: anti-orthocentroidal, orthocentroidal
X(49370) = X(110)-of-2nd anti-Kenmotu centers triangle
X(49370) = X(1991)-of-anti-orthocentroidal triangle
X(49370) = X(48787)-of-X3-ABC reflections triangle
X(49370) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (110, 895, 49269), (110, 19111, 6593)


X(49371) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ANTI-KENMOTU-CENTERS TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*(2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^2-c^2)*(a^2-b^2)*S+(b^2+c^2)*a^8-2*(b^4+c^4)*a^6+(b^2+c^2)*b^2*c^2*a^4+2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*(b^4+b^2*c^2+c^4)) : :
X(49371) = 3*X(112)-X(13282) = X(13282)+3*X(13283) = 2*X(13282)-3*X(49372) = 2*X(13283)+X(49372)

The reciprocal parallelogic center of these triangles is X(10313).

X(49371) lies on the circumcircle of 1st anti-Kenmotu centers triangle and these lines: {3, 48788}, {6, 74}, {127, 45472}, {132, 11474}, {372, 2794}, {492, 13219}, {1152, 19165}, {1297, 12305}, {2799, 49367}, {2806, 48703}, {2831, 48684}, {3102, 35881}, {3320, 45404}, {6020, 45470}, {6289, 10749}, {6396, 34217}, {6398, 11641}, {6454, 15562}, {9517, 49369}, {9733, 49315}, {10705, 45476}, {10735, 10881}, {10898, 14689}, {11610, 12968}, {11722, 45398}, {13166, 45400}, {13195, 45402}, {13200, 45406}, {13206, 45416}, {13221, 45426}, {13229, 45430}, {13231, 45432}, {13236, 45434}, {13280, 45444}, {13281, 45446}, {13294, 45454}, {13295, 45456}, {13296, 45458}, {13297, 45460}, {13298, 45467}, {13299, 45464}, {13310, 45488}, {13311, 45490}, {13312, 45492}, {13313, 45494}, {13314, 45496}, {13923, 45484}, {13992, 45487}, {19162, 45436}, {19163, 45438}, {35880, 45462}, {38608, 43119}, {45345, 48537}, {45347, 48538}, {45375, 48681}, {45411, 48789}, {45412, 49443}, {45415, 49444}, {45421, 49101}, {45422, 49205}, {45424, 49206}

X(49371) = midpoint of X(i) and X(j) for these {i, j}: {112, 13283}, {13219, 49100}
X(49371) = reflection of X(i) in X(j) for these (i, j): (3, 48788), (49315, 9733), (49372, 112)
X(49371) = crossdifference of every pair of points on line {X(9033), X(46688)}
X(49371) = parallelogic center (1st anti-Kenmotu centers, T) for these triangles T: 1st anti-orthosymmedial, 1st orthosymmedial
X(49371) = center of circle {{X(112), X(13283), X(39383)}}
X(49371) = X(112)-of-1st anti-Kenmotu centers triangle
X(49371) = X(10699)-of-2nd Kenmotu diagonals triangle
X(49371) = X(42215)-of-1st anti-orthosymmedial triangle
X(49371) = X(48788)-of-X3-ABC reflections triangle
X(49371) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (112, 10766, 49270), (112, 19114, 28343)


X(49372) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ANTI-KENMOTU-CENTERS TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*(-2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^2-c^2)*(a^2-b^2)*S+(b^2+c^2)*a^8-2*(b^4+c^4)*a^6+(b^2+c^2)*b^2*c^2*a^4+2*(b^6-c^6)*(b^2-c^2)*a^2-(b^4-c^4)*(b^2-c^2)*(b^4+b^2*c^2+c^4)) : :
X(49372) = 3*X(112)-X(13283) = 3*X(13282)+X(13283) = 2*X(13282)+X(49371) = 2*X(13283)-3*X(49371)

The reciprocal parallelogic center of these triangles is X(10313).

X(49372) lies on the circumcircle of 2nd anti-Kenmotu centers triangle and these lines: {3, 48789}, {6, 74}, {127, 45473}, {132, 11473}, {371, 2794}, {491, 13219}, {1151, 19165}, {1297, 12306}, {2799, 49368}, {2806, 48704}, {2831, 48685}, {3103, 35880}, {3320, 45405}, {6020, 45471}, {6200, 34217}, {6221, 11641}, {6290, 10749}, {6453, 15562}, {9517, 49370}, {9530, 26875}, {9732, 49316}, {10705, 45477}, {10735, 10880}, {10897, 14689}, {11610, 12963}, {11722, 45399}, {13166, 45401}, {13195, 45403}, {13200, 45407}, {13206, 45417}, {13221, 45427}, {13229, 45431}, {13231, 45433}, {13236, 45435}, {13280, 45445}, {13281, 45447}, {13294, 45455}, {13295, 45457}, {13296, 45459}, {13297, 45461}, {13298, 45465}, {13299, 45466}, {13310, 45489}, {13311, 45491}, {13312, 45493}, {13313, 45495}, {13314, 45497}, {13923, 45486}, {13992, 45485}, {19162, 45437}, {19163, 45439}, {35881, 45463}, {38608, 43118}, {45346, 48538}, {45348, 48537}, {45376, 48681}, {45410, 48788}, {45413, 49444}, {45414, 49443}, {45420, 49100}, {45423, 49205}, {45425, 49206}

X(49372) = midpoint of X(i) and X(j) for these {i, j}: {112, 13282}, {13219, 49101}
X(49372) = reflection of X(i) in X(j) for these (i, j): (3, 48789), (49316, 9732), (49371, 112)
X(49372) = crossdifference of every pair of points on line {X(9033), X(46689)}
X(49372) = parallelogic center (2nd anti-Kenmotu centers, T) for these triangles T: 1st anti-orthosymmedial, 1st orthosymmedial
X(49372) = center of circle {{X(112), X(13282), X(39384)}}
X(49372) = X(112)-of-2nd anti-Kenmotu centers triangle
X(49372) = X(42216)-of-1st anti-orthosymmedial triangle
X(49372) = X(48789)-of-X3-ABC reflections triangle
X(49372) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (112, 10766, 49271), (112, 19115, 28343)

leftri

Centers related to anti-Lucas(±1)-homothetic triangles: X(49373)-X(49444)

rightri

This preamble and centers X(49373)-X(49444) were contributed by César Eliud Lozada, May 21, 2022.

Anti-Lucas(±1)-homothetic triangles were introduced in the preamble just before X(45345).


X(49373) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 1st ALTINTAS-ISODYNAMIC

Barycentrics    -2*S*a^2*(4*b^2*c^2*(b^2+c^2)-S*(a^4-2*(b^2+c^2)*a^2+5*b^4+2*b^2*c^2+5*c^4))*sqrt(3)+(a^8-17*(b^2+c^2)*a^6+17*(b^2+c^2)^2*a^4+((b^2-c^2)^2-4*b^2*c^2)*(b^2+c^2)*a^2-2*((b^2-c^2)^2-4*b^2*c^2)*(b^2-c^2)^2)*S+2*(-a^2+b^2+c^2)*(2*a^8-4*(b^2+c^2)*a^6+3*(b^4-4*b^2*c^2+c^4)*a^4-2*(b^4-c^4)*(b^2-c^2)*a^2+(b^2-c^2)^4) : :

The reciprocal orthologic center of these triangles is X(4).

X(49373) lies on these lines: {13, 494}, {530, 45698}, {531, 49381}, {542, 45726}, {616, 26503}, {618, 5491}, {5473, 26293}, {5478, 26329}, {5617, 26467}, {6268, 26338}, {6270, 45594}, {6464, 49374}, {6770, 26440}, {6771, 26507}, {7975, 26504}, {9901, 26299}, {9916, 26305}, {9982, 26313}, {10062, 45611}, {10078, 45613}, {11705, 26368}, {12142, 26374}, {12205, 26428}, {12337, 26502}, {12472, 45588}, {12473, 45590}, {12781, 26443}, {12793, 26448}, {12922, 26489}, {12932, 26484}, {12942, 26478}, {12952, 26472}, {12990, 45604}, {13076, 26354}, {13103, 45609}, {13105, 26511}, {13107, 26510}, {13917, 45605}, {13982, 45608}, {18523, 48655}, {18974, 26434}, {19073, 26455}, {19074, 26461}, {22773, 26323}, {22796, 45592}, {26392, 48456}, {26416, 48457}, {26505, 49034}, {26506, 49035}, {26508, 49143}, {26509, 49144}, {35753, 45599}, {35754, 45602}, {41022, 48469}, {41023, 49379}, {45412, 49305}, {45414, 49306}, {45516, 48722}, {45518, 48723}, {45595, 49208}, {45598, 49209}, {49377, 49407}, {49405, 49427}

X(49373) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: 1st Altintas-isodynamic, Bankoff, 3rd Fermat-Dao, 7th Fermat-Dao, 11th Fermat-Dao, 15th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi, 1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi, 1st half-diamonds-central, 1st isodynamic-Dao, 3rd isodynamic-Dao, Largest-circumscribed-equilateral, 1st Lemoine-Dao, outer-Napoleon
X(49373) = X(13)-of-anti-Lucas(-1) homothetic triangle


X(49374) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 1st ALTINTAS-ISODYNAMIC

Barycentrics    -2*S*a^2*(4*b^2*c^2*(b^2+c^2)+S*(a^4-2*(b^2+c^2)*a^2+5*b^4+2*b^2*c^2+5*c^4))*sqrt(3)-(a^8-17*(b^2+c^2)*a^6+17*(b^2+c^2)^2*a^4+((b^2-c^2)^2-4*b^2*c^2)*(b^2+c^2)*a^2-2*((b^2-c^2)^2-4*b^2*c^2)*(b^2-c^2)^2)*S+2*(-a^2+b^2+c^2)*(2*a^8-4*(b^2+c^2)*a^6+3*(b^4-4*b^2*c^2+c^4)*a^4-2*(b^4-c^4)*(b^2-c^2)*a^2+(b^2-c^2)^4) : :

The reciprocal orthologic center of these triangles is X(4).

X(49374) lies on these lines: {13, 493}, {530, 45699}, {531, 49382}, {542, 45727}, {616, 26494}, {618, 5490}, {5473, 26292}, {5478, 26328}, {5617, 26466}, {6268, 26347}, {6270, 26337}, {6464, 49373}, {6770, 26439}, {6771, 26498}, {7975, 26495}, {9901, 26298}, {9916, 26304}, {9982, 26312}, {10062, 45612}, {10078, 45614}, {11705, 26367}, {12142, 26373}, {12205, 26427}, {12337, 26493}, {12472, 45589}, {12473, 45591}, {12781, 26442}, {12793, 26447}, {12922, 26488}, {12932, 26483}, {12942, 26477}, {12952, 26471}, {12991, 45603}, {13076, 26353}, {13103, 45610}, {13105, 45615}, {13107, 26501}, {13917, 45607}, {13982, 45606}, {18521, 48655}, {18974, 26433}, {19073, 26454}, {19074, 26460}, {22773, 26322}, {22796, 45593}, {26391, 48456}, {26415, 48457}, {26496, 49034}, {26497, 49035}, {26499, 49143}, {26500, 49144}, {35753, 45601}, {35754, 45600}, {41022, 48468}, {41023, 49380}, {45413, 49306}, {45415, 49305}, {45517, 48723}, {45519, 48722}, {45596, 49209}, {45597, 49208}, {49378, 49408}, {49406, 49428}

X(49374) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: 1st Altintas-isodynamic, Bankoff, 3rd Fermat-Dao, 7th Fermat-Dao, 11th Fermat-Dao, 15th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi, 1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi, 1st half-diamonds-central, 1st isodynamic-Dao, 3rd isodynamic-Dao, Largest-circumscribed-equilateral, 1st Lemoine-Dao, outer-Napoleon
X(49374) = X(13)-of-anti-Lucas(+1) homothetic triangle


X(49375) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 2nd ALTINTAS-ISODYNAMIC

Barycentrics    2*S*a^2*(4*b^2*c^2*(b^2+c^2)-S*(a^4-2*(b^2+c^2)*a^2+5*b^4+2*b^2*c^2+5*c^4))*sqrt(3)+(a^8-17*(b^2+c^2)*a^6+17*(b^2+c^2)^2*a^4+((b^2-c^2)^2-4*b^2*c^2)*(b^2+c^2)*a^2-2*((b^2-c^2)^2-4*b^2*c^2)*(b^2-c^2)^2)*S+2*(-a^2+b^2+c^2)*(2*a^8-4*(b^2+c^2)*a^6+3*(b^4-4*b^2*c^2+c^4)*a^4-2*(b^4-c^4)*(b^2-c^2)*a^2+(b^2-c^2)^4) : :

The reciprocal orthologic center of these triangles is X(4).

X(49375) lies on these lines: {14, 494}, {530, 49381}, {531, 45698}, {542, 45726}, {617, 26503}, {619, 5491}, {5474, 26293}, {5479, 26329}, {5613, 26467}, {6269, 26338}, {6271, 45594}, {6464, 49376}, {6773, 26440}, {6774, 26507}, {7974, 26504}, {9900, 26299}, {9915, 26305}, {9981, 26313}, {10061, 45611}, {10077, 45613}, {11706, 26368}, {12141, 26374}, {12204, 26428}, {12336, 26502}, {12470, 45588}, {12471, 45590}, {12780, 26443}, {12792, 26448}, {12921, 26489}, {12931, 26484}, {12941, 26478}, {12951, 26472}, {12988, 45604}, {13075, 26354}, {13102, 45609}, {13104, 26511}, {13106, 26510}, {13916, 45605}, {13981, 45608}, {18523, 48656}, {18975, 26434}, {19075, 26455}, {19076, 26461}, {22774, 26323}, {22797, 45592}, {26392, 48458}, {26416, 48459}, {26505, 49036}, {26506, 49037}, {26508, 49145}, {26509, 49146}, {35850, 45599}, {35851, 45602}, {41022, 49379}, {41023, 48469}, {45412, 49307}, {45414, 49308}, {45516, 48724}, {45518, 48725}, {45595, 49210}, {45598, 49211}, {49377, 49405}, {49407, 49427}

X(49375) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: 2nd Altintas-isodynamic, 4th Fermat-Dao, 8th Fermat-Dao, 12th Fermat-Dao, 16th Fermat-Dao, 1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi, 3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi, 2nd half-diamonds-central, 2nd isodynamic-Dao, 4th isodynamic-Dao, 2nd Lemoine-Dao, inner-Napoleon
X(49375) = X(14)-of-anti-Lucas(-1) homothetic triangle


X(49376) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 2nd ALTINTAS-ISODYNAMIC

Barycentrics    2*S*a^2*(4*b^2*c^2*(b^2+c^2)+S*(a^4-2*(b^2+c^2)*a^2+5*b^4+2*b^2*c^2+5*c^4))*sqrt(3)-(a^8-17*(b^2+c^2)*a^6+17*(b^2+c^2)^2*a^4+((b^2-c^2)^2-4*b^2*c^2)*(b^2+c^2)*a^2-2*((b^2-c^2)^2-4*b^2*c^2)*(b^2-c^2)^2)*S+2*(-a^2+b^2+c^2)*(2*a^8-4*(b^2+c^2)*a^6+3*(b^4-4*b^2*c^2+c^4)*a^4-2*(b^4-c^4)*(b^2-c^2)*a^2+(b^2-c^2)^4) : :

The reciprocal orthologic center of these triangles is X(4).

X(49376) lies on these lines: {14, 493}, {530, 49382}, {531, 45699}, {542, 45727}, {617, 26494}, {619, 5490}, {5474, 26292}, {5479, 26328}, {5613, 26466}, {6269, 26347}, {6271, 26337}, {6464, 49375}, {6773, 26439}, {6774, 26498}, {7974, 26495}, {9900, 26298}, {9915, 26304}, {9981, 26312}, {10061, 45612}, {10077, 45614}, {11706, 26367}, {12141, 26373}, {12204, 26427}, {12336, 26493}, {12470, 45589}, {12471, 45591}, {12780, 26442}, {12792, 26447}, {12921, 26488}, {12931, 26483}, {12941, 26477}, {12951, 26471}, {12989, 45603}, {13075, 26353}, {13102, 45610}, {13104, 45615}, {13106, 26501}, {13916, 45607}, {13981, 45606}, {18521, 48656}, {18975, 26433}, {19075, 26454}, {19076, 26460}, {22774, 26322}, {22797, 45593}, {26391, 48458}, {26415, 48459}, {26496, 49036}, {26497, 49037}, {26499, 49145}, {26500, 49146}, {35850, 45601}, {35851, 45600}, {41022, 49380}, {41023, 48468}, {45413, 49308}, {45415, 49307}, {45517, 48725}, {45519, 48724}, {45596, 49211}, {45597, 49210}, {49378, 49406}, {49408, 49428}

X(49376) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: 2nd Altintas-isodynamic, 4th Fermat-Dao, 8th Fermat-Dao, 12th Fermat-Dao, 16th Fermat-Dao, 1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi, 3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi, 2nd half-diamonds-central, 2nd isodynamic-Dao, 4th isodynamic-Dao, 2nd Lemoine-Dao, inner-Napoleon
X(49376) = X(14)-of-anti-Lucas(+1) homothetic triangle


X(49377) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO ANTI-ASCELLA

Barycentrics    a^2*(-(a^2+b^2+c^2)*(a^4-4*(b^2+c^2)*a^2+3*b^4-2*b^2*c^2+3*c^4)*S+2*(b^2+c^2)*a^6-2*(3*b^4+4*b^2*c^2+3*c^4)*a^4+2*(b^2+c^2)*(3*b^4-4*b^2*c^2+3*c^4)*a^2-2*(b^2-c^2)^4) : :
X(49377) = 3*X(45698)-X(48469) = 3*X(45698)-2*X(49427)

The reciprocal orthologic center of these triangles is X(1593).

X(49377) lies on these lines: {1, 26354}, {3, 494}, {4, 26374}, {5, 5491}, {6, 12229}, {20, 26440}, {30, 45698}, {40, 26299}, {55, 45611}, {56, 45613}, {68, 12601}, {155, 1351}, {355, 26443}, {371, 45595}, {372, 45598}, {382, 18523}, {511, 45726}, {515, 49419}, {517, 45717}, {542, 49437}, {952, 48689}, {971, 49403}, {1154, 49429}, {1160, 26338}, {1161, 45594}, {1385, 26368}, {1478, 26478}, {1479, 26472}, {1482, 26504}, {2782, 49379}, {3311, 26461}, {3312, 26455}, {3398, 26428}, {3527, 45489}, {3564, 49397}, {5663, 49383}, {6000, 49421}, {7387, 26305}, {8981, 45605}, {9732, 18981}, {9733, 45412}, {9738, 45518}, {9739, 45516}, {9821, 26313}, {10318, 26498}, {10525, 26489}, {10526, 26484}, {10669, 45604}, {10679, 26511}, {10680, 26510}, {11248, 26502}, {11249, 26323}, {11251, 26448}, {11252, 45588}, {11253, 45590}, {13966, 45608}, {17702, 49391}, {18400, 49413}, {24243, 49029}, {26392, 48460}, {26416, 48461}, {26505, 49038}, {26506, 49039}, {44665, 49393}, {49373, 49407}, {49375, 49405}, {49385, 49443}, {49399, 49425}

X(49377) = midpoint of X(i) and X(j) for these {i, j}: {45717, 49395}, {48689, 48708}, {49379, 49439}, {49383, 49441}, {49385, 49443}
X(49377) = reflection of X(48469) in X(49427)
X(49377) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: anti-Ascella, anti-Atik, 1st anti-circumperp, anti-Conway, 2nd anti-Conway, 3rd anti-Euler, 4th anti-Euler, anti-excenters-reflections, 2nd anti-extouch, anti-Honsberger, anti-Hutson intouch, anti-incircle-circles, anti-inverse-in-incircle, 6th anti-mixtilinear, 1st anti-Sharygin, anti-tangential-midarc, anti-Ursa minor, anti-Wasat, circumorthic, Ehrmann-side, Ehrmann-vertex, 2nd Ehrmann, 2nd Euler, 1st excosine, extangents, intangents, 1st Kenmotu diagonals, 2nd Kenmotu diagonals, Kosnita, Lucas antipodal tangents, Lucas(-1) antipodal tangents, orthic, submedial, tangential, inner tri-equilateral, outer tri-equilateral, Trinh
X(49377) = center of circle {{X(48689), X(48708), X(49379)}}
X(49377) = X(3)-of-anti-Lucas(-1) homothetic triangle
X(49377) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 494, 26507), (3, 45609, 494), (4, 26467, 45592), (4, 26503, 26467), (371, 45599, 45595), (372, 45602, 45598), (494, 26293, 3), (1351, 5446, 49378), (5491, 26329, 5), (26293, 45609, 26507), (26354, 26434, 1), (45698, 48469, 49427)


X(49378) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO ANTI-ASCELLA

Barycentrics    a^2*((a^2+b^2+c^2)*(a^4-4*(b^2+c^2)*a^2+3*b^4-2*b^2*c^2+3*c^4)*S+2*(b^2+c^2)*a^6-2*(3*b^4+4*b^2*c^2+3*c^4)*a^4+2*(b^2+c^2)*(3*b^4-4*b^2*c^2+3*c^4)*a^2-2*(b^2-c^2)^4) : :
X(49378) = 3*X(45699)-X(48468) = 3*X(45699)-2*X(49428)

The reciprocal orthologic center of these triangles is X(1593).

X(49378) lies on these lines: {1, 26353}, {3, 493}, {4, 26373}, {5, 5490}, {6, 12230}, {20, 26439}, {30, 45699}, {40, 26298}, {55, 45612}, {56, 45614}, {68, 12602}, {155, 1351}, {355, 26442}, {371, 45597}, {372, 45596}, {382, 18521}, {511, 45727}, {515, 49420}, {517, 45718}, {542, 49438}, {952, 48688}, {971, 49404}, {1154, 49430}, {1160, 26347}, {1161, 26337}, {1385, 26367}, {1478, 26477}, {1479, 26471}, {1482, 26495}, {2782, 49380}, {3311, 26460}, {3312, 26454}, {3398, 26427}, {3527, 45488}, {3564, 49398}, {5093, 8950}, {5663, 49384}, {6000, 49422}, {7387, 26304}, {8981, 45607}, {9732, 45413}, {9733, 18980}, {9738, 45517}, {9739, 45519}, {9821, 26312}, {10318, 26507}, {10525, 26488}, {10526, 26483}, {10673, 45603}, {10679, 45615}, {10680, 26501}, {11248, 26493}, {11249, 26322}, {11251, 26447}, {11252, 45589}, {11253, 45591}, {13966, 45606}, {17702, 49392}, {18400, 49414}, {24244, 49028}, {26391, 48460}, {26415, 48461}, {26496, 49038}, {26497, 49039}, {44665, 49394}, {49374, 49408}, {49376, 49406}, {49386, 49444}, {49400, 49426}

X(49378) = midpoint of X(i) and X(j) for these {i, j}: {45718, 49396}, {48688, 48707}, {49380, 49440}, {49384, 49442}, {49386, 49444}
X(49378) = reflection of X(48468) in X(49428)
X(49378) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: anti-Ascella, anti-Atik, 1st anti-circumperp, anti-Conway, 2nd anti-Conway, 3rd anti-Euler, 4th anti-Euler, anti-excenters-reflections, 2nd anti-extouch, anti-Honsberger, anti-Hutson intouch, anti-incircle-circles, anti-inverse-in-incircle, 6th anti-mixtilinear, 1st anti-Sharygin, anti-tangential-midarc, anti-Ursa minor, anti-Wasat, circumorthic, Ehrmann-side, Ehrmann-vertex, 2nd Ehrmann, 2nd Euler, 1st excosine, extangents, intangents, 1st Kenmotu diagonals, 2nd Kenmotu diagonals, Kosnita, Lucas antipodal tangents, Lucas(-1) antipodal tangents, orthic, submedial, tangential, inner tri-equilateral, outer tri-equilateral, Trinh
X(49378) = center of circle {{X(48688), X(48707), X(49380)}}
X(49378) = X(3)-of-anti-Lucas(+1) homothetic triangle
X(49378) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 493, 26498), (3, 45610, 493), (4, 26466, 45593), (4, 26494, 26466), (371, 45601, 45597), (372, 45600, 45596), (493, 26292, 3), (1351, 5446, 49377), (5490, 26328, 5), (26292, 45610, 26498), (26353, 26433, 1), (45699, 48468, 49428)


X(49379) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 1st ANTI-BROCARD

Barycentrics    (a^12-3*(b^2+c^2)*a^10-(4*b^4+19*b^2*c^2+4*c^4)*a^8+2*(b^2+c^2)*(4*b^4+9*b^2*c^2+4*c^4)*a^6-(b^4+4*b^2*c^2+c^4)*(5*b^4-4*b^2*c^2+5*c^4)*a^4+(b^4-c^4)*(b^2-c^2)*(3*b^4+8*b^2*c^2+3*c^4)*a^2-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2*b^2*c^2)*S-3*(b^2+c^2)*a^12+2*(5*b^4+8*b^2*c^2+5*c^4)*a^10-(b^2+c^2)*(14*b^4-9*b^2*c^2+14*c^4)*a^8+4*(3*b^8+3*c^8-(3*b^4+2*b^2*c^2+3*c^4)*b^2*c^2)*a^6-(b^2+c^2)*(7*b^8+7*c^8-22*(b^4-b^2*c^2+c^4)*b^2*c^2)*a^4+2*(b^2-c^2)^2*(b^8+c^8-2*(2*b^4+b^2*c^2+2*c^4)*b^2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)^3*b^2*c^2 : :

The reciprocal orthologic center of these triangles is X(5999).

X(49379) lies on the circumcircle of anti-Lucas(-1) homothetic triangle and these lines: {30, 49381}, {98, 494}, {99, 26293}, {114, 5491}, {115, 26329}, {147, 26503}, {542, 45698}, {690, 49383}, {2782, 49377}, {2783, 48708}, {2784, 49419}, {2787, 48689}, {2794, 48469}, {2799, 49385}, {3023, 26434}, {3027, 26354}, {6033, 26467}, {6226, 26338}, {6227, 45594}, {6464, 49380}, {7970, 26504}, {8980, 45605}, {9860, 26299}, {9861, 26305}, {9862, 26313}, {9864, 26443}, {10053, 45611}, {10069, 45613}, {11710, 26368}, {12042, 26507}, {12131, 26374}, {12176, 26428}, {12178, 26502}, {12179, 45588}, {12180, 45590}, {12181, 26448}, {12182, 26489}, {12183, 26484}, {12184, 26478}, {12185, 26472}, {12186, 45604}, {12188, 45609}, {12189, 26511}, {12190, 26510}, {13967, 45608}, {18523, 38744}, {19055, 26455}, {19056, 26461}, {22504, 26323}, {22505, 45592}, {26392, 48462}, {26416, 48463}, {26505, 49040}, {26506, 49041}, {26508, 49147}, {26509, 49148}, {35824, 45599}, {35825, 45602}, {41022, 49375}, {41023, 49373}, {45412, 49309}, {45414, 49310}, {45516, 48726}, {45518, 48727}, {45595, 49212}, {45598, 49213}, {45726, 49399}, {49425, 49427}

X(49379) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: 1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard
X(49379) = X(98)-of-anti-Lucas(-1) homothetic triangle
X(49379) = reflection of X(49439) in X(49377)


X(49380) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 1st ANTI-BROCARD

Barycentrics    -(a^12-3*(b^2+c^2)*a^10-(4*b^4+19*b^2*c^2+4*c^4)*a^8+2*(b^2+c^2)*(4*b^4+9*b^2*c^2+4*c^4)*a^6-(b^4+4*b^2*c^2+c^4)*(5*b^4-4*b^2*c^2+5*c^4)*a^4+(b^4-c^4)*(b^2-c^2)*(3*b^4+8*b^2*c^2+3*c^4)*a^2-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2*b^2*c^2)*S-3*(b^2+c^2)*a^12+2*(5*b^4+8*b^2*c^2+5*c^4)*a^10-(b^2+c^2)*(14*b^4-9*b^2*c^2+14*c^4)*a^8+4*(3*b^8+3*c^8-(3*b^4+2*b^2*c^2+3*c^4)*b^2*c^2)*a^6-(b^2+c^2)*(7*b^8+7*c^8-22*(b^4-b^2*c^2+c^4)*b^2*c^2)*a^4+2*(b^2-c^2)^2*(b^8+c^8-2*(2*b^4+b^2*c^2+2*c^4)*b^2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)^3*b^2*c^2 : :

The reciprocal orthologic center of these triangles is X(5999).

X(49380) lies on the circumcircle of anti-Lucas(+1) homothetic triangle and these lines: {30, 49382}, {98, 493}, {99, 26292}, {114, 5490}, {115, 26328}, {147, 26494}, {542, 45699}, {690, 49384}, {2782, 49378}, {2783, 48707}, {2784, 49420}, {2787, 48688}, {2794, 48468}, {2799, 49386}, {3023, 26433}, {3027, 26353}, {6033, 26466}, {6226, 26347}, {6227, 26337}, {6464, 49379}, {7970, 26495}, {8980, 45607}, {9860, 26298}, {9861, 26304}, {9862, 26312}, {10053, 45612}, {10069, 45614}, {11710, 26367}, {12042, 26498}, {12131, 26373}, {12176, 26427}, {12178, 26493}, {12179, 45589}, {12180, 45591}, {12181, 26447}, {12182, 26488}, {12183, 26483}, {12184, 26477}, {12185, 26471}, {12187, 45603}, {12188, 45610}, {12189, 45615}, {12190, 26501}, {13967, 45606}, {18521, 38744}, {19055, 26454}, {19056, 26460}, {22504, 26322}, {22505, 45593}, {26391, 48462}, {26415, 48463}, {26496, 49040}, {26497, 49041}, {26499, 49147}, {26500, 49148}, {35824, 45601}, {35825, 45600}, {41022, 49376}, {41023, 49374}, {45413, 49310}, {45415, 49309}, {45517, 48727}, {45519, 48726}, {45596, 49213}, {45597, 49212}, {45727, 49400}, {49426, 49428}

X(49380) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: 1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard
X(49380) = X(98)-of-anti-Lucas(+1) homothetic triangle
X(49380) = reflection of X(49440) in X(49378)


X(49381) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO ANTI-MCCAY

Barycentrics    -(a^8-19*(b^2+c^2)*a^6+(17*b^4+35*b^2*c^2+17*c^4)*a^4-(b^2+c^2)*(b^4+12*b^2*c^2+c^4)*a^2-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-2*c^2)*(2*b^2-c^2))*S+4*a^10-11*(b^2+c^2)*a^8+2*(5*b^4-6*b^2*c^2+5*c^4)*a^6-(b^2+c^2)*(5*b^4-27*b^2*c^2+5*c^4)*a^4+2*(2*b^4-7*b^2*c^2+2*c^4)*(b^2+c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)*(b^2-2*c^2)*(2*b^2-c^2) : :

The reciprocal orthologic center of these triangles is X(9855).

X(49381) lies on these lines: {30, 49379}, {494, 671}, {530, 49375}, {531, 49373}, {542, 48469}, {543, 45698}, {2482, 5491}, {2782, 49399}, {2796, 49419}, {5969, 49423}, {6464, 49382}, {8591, 26503}, {8724, 26467}, {9830, 45726}, {9875, 26299}, {9876, 26305}, {9878, 26313}, {9880, 26329}, {9881, 26443}, {9882, 45594}, {9883, 26338}, {9884, 26504}, {10054, 45611}, {10070, 45613}, {12117, 26293}, {12132, 26374}, {12191, 26428}, {12243, 26440}, {12258, 26368}, {12326, 26502}, {12345, 45588}, {12346, 45590}, {12347, 26448}, {12348, 26489}, {12349, 26484}, {12350, 26478}, {12351, 26472}, {12352, 45604}, {12354, 26354}, {12355, 45609}, {12356, 26511}, {12357, 26510}, {13908, 45605}, {13968, 45608}, {18523, 48657}, {18969, 26434}, {19057, 26455}, {19058, 26461}, {22565, 26323}, {22566, 45592}, {26392, 48470}, {26416, 48471}, {26505, 49042}, {26506, 49043}, {26507, 49102}, {26508, 49149}, {26509, 49150}, {35698, 45599}, {35699, 45602}, {45412, 49311}, {45414, 49312}, {45516, 48728}, {45518, 48729}, {45595, 49214}, {45598, 49215}

X(49381) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: anti-McCay, McCay, Moses-Steiner osculatory
X(49381) = X(671)-of-anti-Lucas(-1) homothetic triangle
X(49381) = reflection of X(49439) in X(45698)


X(49382) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO ANTI-MCCAY

Barycentrics    (a^8-19*(b^2+c^2)*a^6+(17*b^4+35*b^2*c^2+17*c^4)*a^4-(b^2+c^2)*(b^4+12*b^2*c^2+c^4)*a^2-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-2*c^2)*(2*b^2-c^2))*S+4*a^10-11*(b^2+c^2)*a^8+2*(5*b^4-6*b^2*c^2+5*c^4)*a^6-(b^2+c^2)*(5*b^4-27*b^2*c^2+5*c^4)*a^4+2*(2*b^4-7*b^2*c^2+2*c^4)*(b^2+c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)*(b^2-2*c^2)*(2*b^2-c^2) : :

The reciprocal orthologic center of these triangles is X(9855).

X(49382) lies on these lines: {30, 49380}, {493, 671}, {530, 49376}, {531, 49374}, {542, 48468}, {543, 45699}, {2482, 5490}, {2782, 49400}, {2796, 49420}, {5969, 49424}, {6464, 49381}, {8591, 26494}, {8724, 26466}, {9830, 45727}, {9875, 26298}, {9876, 26304}, {9878, 26312}, {9880, 26328}, {9881, 26442}, {9882, 26337}, {9883, 26347}, {9884, 26495}, {10054, 45612}, {10070, 45614}, {12117, 26292}, {12132, 26373}, {12191, 26427}, {12243, 26439}, {12258, 26367}, {12326, 26493}, {12345, 45589}, {12346, 45591}, {12347, 26447}, {12348, 26488}, {12349, 26483}, {12350, 26477}, {12351, 26471}, {12353, 45603}, {12354, 26353}, {12355, 45610}, {12356, 45615}, {12357, 26501}, {13908, 45607}, {13968, 45606}, {18521, 48657}, {18969, 26433}, {19057, 26454}, {19058, 26460}, {22565, 26322}, {22566, 45593}, {26391, 48470}, {26415, 48471}, {26496, 49042}, {26497, 49043}, {26498, 49102}, {26499, 49149}, {26500, 49150}, {35698, 45601}, {35699, 45600}, {45413, 49312}, {45415, 49311}, {45517, 48729}, {45519, 48728}, {45596, 49215}, {45597, 49214}

X(49382) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: anti-McCay, McCay, Moses-Steiner osculatory
X(49382) = X(671)-of-anti-Lucas(+1) homothetic triangle
X(49382) = reflection of X(49440) in X(45699)


X(49383) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*(-(a^12-3*(b^2+c^2)*a^10-(8*b^4+11*b^2*c^2+8*c^4)*a^8+2*(b^2+c^2)*(15*b^4-13*b^2*c^2+15*c^4)*a^6-(27*b^8+27*c^8-2*b^2*c^2*(8*b^4-7*b^2*c^2+8*c^4))*a^4+(b^4-c^4)*(b^2-c^2)*(5*b^4-4*b^2*c^2+5*c^4)*a^2+(2*b^8+2*c^8+b^2*c^2*(7*b^4+18*b^2*c^2+7*c^4))*(b^2-c^2)^2)*S+3*(b^2+c^2)*a^12-12*(b^4+b^2*c^2+c^4)*a^10+(b^2+c^2)*(15*b^4-11*b^2*c^2+15*c^4)*a^8+4*(5*b^4-8*b^2*c^2+5*c^4)*b^2*c^2*a^6-(b^2+c^2)*(15*b^8+15*c^8-2*b^2*c^2*(3*b^4+5*b^2*c^2+3*c^4))*a^4+4*(b^2-c^2)^2*(3*b^8+3*c^8+2*b^2*c^2*(b^4+5*b^2*c^2+c^4))*a^2-(b^4-c^4)*(b^2-c^2)^3*(3*b^4-b^2*c^2+3*c^4)) : :

The reciprocal orthologic center of these triangles is X(12112).

X(49383) lies on the circumcircle of anti-Lucas(-1) homothetic triangle and these lines: {30, 49391}, {74, 494}, {110, 26293}, {113, 5491}, {125, 26329}, {146, 26503}, {541, 45698}, {542, 49439}, {690, 49379}, {1503, 49437}, {1539, 45592}, {2771, 48708}, {2777, 48469}, {2781, 45726}, {3024, 26434}, {3028, 26354}, {5663, 49377}, {6464, 49384}, {7725, 45594}, {7726, 26338}, {7728, 26467}, {7978, 26504}, {8674, 48689}, {8994, 45605}, {9517, 49385}, {9904, 26299}, {9919, 26305}, {9984, 26313}, {10065, 45611}, {10081, 45613}, {10620, 45609}, {10628, 49429}, {11709, 26368}, {12041, 26507}, {12133, 26374}, {12192, 26428}, {12244, 26440}, {12327, 26502}, {12365, 45588}, {12366, 45590}, {12368, 26443}, {12369, 26448}, {12371, 26489}, {12372, 26484}, {12373, 26478}, {12374, 26472}, {12377, 45604}, {12381, 26511}, {12382, 26510}, {13969, 45608}, {17702, 49393}, {18523, 38790}, {19059, 26455}, {19060, 26461}, {22583, 26323}, {26392, 48472}, {26416, 48473}, {26505, 49044}, {26506, 49045}, {26508, 49151}, {26509, 49152}, {35826, 45599}, {35827, 45602}, {45412, 49313}, {45414, 49314}, {45516, 48730}, {45518, 48731}, {45595, 49216}, {45598, 49217}

X(49383) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: anti-orthocentroidal, orthocentroidal
X(49383) = X(74)-of-anti-Lucas(-1) homothetic triangle
X(49383) = reflection of X(49441) in X(49377)


X(49384) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO ANTI-ORTHOCENTROIDAL

Barycentrics    a^2*((a^12-3*(b^2+c^2)*a^10-(8*b^4+11*b^2*c^2+8*c^4)*a^8+2*(b^2+c^2)*(15*b^4-13*b^2*c^2+15*c^4)*a^6-(27*b^8+27*c^8-2*b^2*c^2*(8*b^4-7*b^2*c^2+8*c^4))*a^4+(b^4-c^4)*(b^2-c^2)*(5*b^4-4*b^2*c^2+5*c^4)*a^2+(2*b^8+2*c^8+b^2*c^2*(7*b^4+18*b^2*c^2+7*c^4))*(b^2-c^2)^2)*S+3*(b^2+c^2)*a^12-12*(b^4+b^2*c^2+c^4)*a^10+(b^2+c^2)*(15*b^4-11*b^2*c^2+15*c^4)*a^8+4*(5*b^4-8*b^2*c^2+5*c^4)*b^2*c^2*a^6-(b^2+c^2)*(15*b^8+15*c^8-2*b^2*c^2*(3*b^4+5*b^2*c^2+3*c^4))*a^4+4*(b^2-c^2)^2*(3*b^8+3*c^8+2*b^2*c^2*(b^4+5*b^2*c^2+c^4))*a^2-(b^4-c^4)*(b^2-c^2)^3*(3*b^4-b^2*c^2+3*c^4)) : :

The reciprocal orthologic center of these triangles is X(12112).

X(49384) lies on the circumcircle of anti-Lucas(+1) homothetic triangle and these lines: {30, 49392}, {74, 493}, {110, 26292}, {113, 5490}, {125, 26328}, {146, 26494}, {541, 45699}, {542, 49440}, {690, 49380}, {1503, 49438}, {1539, 45593}, {2771, 48707}, {2777, 48468}, {2781, 45727}, {3024, 26433}, {3028, 26353}, {5663, 49378}, {6464, 49383}, {7725, 26337}, {7726, 26347}, {7728, 26466}, {7978, 26495}, {8674, 48688}, {8994, 45607}, {9517, 49386}, {9904, 26298}, {9919, 26304}, {9984, 26312}, {10065, 45612}, {10081, 45614}, {10620, 45610}, {10628, 49430}, {11709, 26367}, {12041, 26498}, {12133, 26373}, {12192, 26427}, {12244, 26439}, {12327, 26493}, {12365, 45589}, {12366, 45591}, {12368, 26442}, {12369, 26447}, {12371, 26488}, {12372, 26483}, {12373, 26477}, {12374, 26471}, {12378, 45603}, {12381, 45615}, {12382, 26501}, {13969, 45606}, {17702, 49394}, {18521, 38790}, {19059, 26454}, {19060, 26460}, {22583, 26322}, {26391, 48472}, {26415, 48473}, {26496, 49044}, {26497, 49045}, {26499, 49151}, {26500, 49152}, {35826, 45601}, {35827, 45600}, {45413, 49314}, {45415, 49313}, {45517, 48731}, {45519, 48730}, {45596, 49217}, {45597, 49216}

X(49384) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: anti-orthocentroidal, orthocentroidal
X(49384) = X(74)-of-anti-Lucas(+1) homothetic triangle
X(49384) = reflection of X(49442) in X(49378)


X(49385) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*(-(a^16-3*(b^2+c^2)*a^14-(5*b^4+17*b^2*c^2+5*c^4)*a^12+(b^2+c^2)*(9*b^4+16*b^2*c^2+9*c^4)*a^10+9*(b^4-3*b^2*c^2+c^4)*(b^2+c^2)^2*a^8-(b^4-c^4)*(b^2-c^2)*(9*b^4-14*b^2*c^2+9*c^4)*a^6-(b^2-c^2)^2*(7*b^8+7*c^8+b^2*c^2*(25*b^4+24*b^2*c^2+25*c^4))*a^4+(b^4-c^4)*(b^2-c^2)^3*(3*b^4-4*b^2*c^2+3*c^4)*a^2+(2*b^12+2*c^12+3*(3*b^8+3*c^8+2*b^2*c^2*(b^4+5*b^2*c^2+c^4))*b^2*c^2)*(b^2-c^2)^2)*S+3*(b^2+c^2)*a^16-2*(5*b^4+8*b^2*c^2+5*c^4)*a^14+(b^2+c^2)*(10*b^4-b^2*c^2+10*c^4)*a^12-2*(b^8+c^8-3*b^2*c^2*(b^4+c^4))*a^10+(b^2+c^2)*(17*b^4-42*b^2*c^2+17*c^4)*b^2*c^2*a^8+2*(b^2-c^2)^6*a^6-(b^4-c^4)*(b^2-c^2)*(10*b^8+10*c^8+b^2*c^2*(19*b^4+22*b^2*c^2+19*c^4))*a^4+2*(b^4-c^4)^2*(5*b^8+5*c^8-b^2*c^2*(5*b^4-16*b^2*c^2+5*c^4))*a^2-(b^4-c^4)*(b^2-c^2)^3*(3*b^8+3*c^8-b^2*c^2*(3*b^4-8*b^2*c^2+3*c^4))) : :

The reciprocal orthologic center of these triangles is X(19158).

X(49385) lies on the circumcircle of anti-Lucas(-1) homothetic triangle and these lines: {112, 26293}, {127, 26329}, {132, 5491}, {494, 1297}, {2781, 49441}, {2794, 49439}, {2799, 49379}, {2806, 48689}, {2831, 48708}, {3320, 26354}, {6020, 26434}, {6464, 49386}, {9517, 49383}, {9530, 45698}, {12145, 26374}, {12207, 26428}, {12253, 26440}, {12265, 26368}, {12340, 26502}, {12384, 26503}, {12408, 26299}, {12413, 26305}, {12478, 45588}, {12479, 45590}, {12503, 26313}, {12784, 26443}, {12796, 26448}, {12805, 45594}, {12806, 26338}, {12918, 26467}, {12925, 26489}, {12935, 26484}, {12945, 26478}, {12955, 26472}, {12996, 45604}, {13099, 26504}, {13115, 45609}, {13116, 45611}, {13117, 45613}, {13118, 26511}, {13119, 26510}, {13918, 45605}, {13985, 45608}, {18523, 48658}, {19093, 26455}, {19094, 26461}, {19159, 26323}, {19160, 45592}, {26392, 48474}, {26416, 48475}, {26505, 49046}, {26506, 49047}, {26507, 38624}, {26508, 49153}, {26509, 49154}, {35828, 45599}, {35829, 45602}, {45412, 49315}, {45414, 49316}, {45516, 48732}, {45518, 48733}, {45595, 49218}, {45598, 49219}, {49377, 49443}

X(49385) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: 1st anti-orthosymmedial, 1st orthosymmedial
X(49385) = X(1297)-of-anti-Lucas(-1) homothetic triangle
X(49385) = reflection of X(49443) in X(49377)


X(49386) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 1st ANTI-ORTHOSYMMEDIAL

Barycentrics    a^2*((a^16-3*(b^2+c^2)*a^14-(5*b^4+17*b^2*c^2+5*c^4)*a^12+(b^2+c^2)*(9*b^4+16*b^2*c^2+9*c^4)*a^10+9*(b^4-3*b^2*c^2+c^4)*(b^2+c^2)^2*a^8-(b^4-c^4)*(b^2-c^2)*(9*b^4-14*b^2*c^2+9*c^4)*a^6-(b^2-c^2)^2*(7*b^8+7*c^8+b^2*c^2*(25*b^4+24*b^2*c^2+25*c^4))*a^4+(b^4-c^4)*(b^2-c^2)^3*(3*b^4-4*b^2*c^2+3*c^4)*a^2+(2*b^12+2*c^12+3*(3*b^8+3*c^8+2*b^2*c^2*(b^4+5*b^2*c^2+c^4))*b^2*c^2)*(b^2-c^2)^2)*S+3*(b^2+c^2)*a^16-2*(5*b^4+8*b^2*c^2+5*c^4)*a^14+(b^2+c^2)*(10*b^4-b^2*c^2+10*c^4)*a^12-2*(b^8+c^8-3*b^2*c^2*(b^4+c^4))*a^10+(b^2+c^2)*(17*b^4-42*b^2*c^2+17*c^4)*b^2*c^2*a^8+2*(b^2-c^2)^6*a^6-(b^4-c^4)*(b^2-c^2)*(10*b^8+10*c^8+b^2*c^2*(19*b^4+22*b^2*c^2+19*c^4))*a^4+2*(b^4-c^4)^2*(5*b^8+5*c^8-b^2*c^2*(5*b^4-16*b^2*c^2+5*c^4))*a^2-(b^4-c^4)*(b^2-c^2)^3*(3*b^8+3*c^8-b^2*c^2*(3*b^4-8*b^2*c^2+3*c^4))) : :

The reciprocal orthologic center of these triangles is X(19158).

X(49386) lies on the circumcircle of anti-Lucas(+1) homothetic triangle and these lines: {112, 26292}, {127, 26328}, {132, 5490}, {493, 1297}, {2781, 49442}, {2794, 49440}, {2799, 49380}, {2806, 48688}, {2831, 48707}, {3320, 26353}, {6020, 26433}, {6464, 49385}, {9517, 49384}, {9530, 45699}, {12145, 26373}, {12207, 26427}, {12253, 26439}, {12265, 26367}, {12340, 26493}, {12384, 26494}, {12408, 26298}, {12413, 26304}, {12478, 45589}, {12479, 45591}, {12503, 26312}, {12784, 26442}, {12796, 26447}, {12805, 26337}, {12806, 26347}, {12918, 26466}, {12925, 26488}, {12935, 26483}, {12945, 26477}, {12955, 26471}, {12997, 45603}, {13099, 26495}, {13115, 45610}, {13116, 45612}, {13117, 45614}, {13118, 45615}, {13119, 26501}, {13918, 45607}, {13985, 45606}, {18521, 48658}, {19093, 26454}, {19094, 26460}, {19159, 26322}, {19160, 45593}, {26391, 48474}, {26415, 48475}, {26496, 49046}, {26497, 49047}, {26498, 38624}, {26499, 49153}, {26500, 49154}, {35828, 45601}, {35829, 45600}, {45413, 49316}, {45415, 49315}, {45517, 48733}, {45519, 48732}, {45596, 49219}, {45597, 49218}, {49378, 49444}

X(49386) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: 1st anti-orthosymmedial, 1st orthosymmedial
X(49386) = X(1297)-of-anti-Lucas(+1) homothetic triangle
X(49386) = reflection of X(49444) in X(49378)


X(49387) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 3rd ANTI-TRI-SQUARES

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

The reciprocal orthologic center of these triangles is X(486).

X(49387) lies on these lines: {4, 26506}, {30, 49435}, {372, 24243}, {485, 642}, {486, 494}, {487, 26503}, {3564, 45726}, {6251, 26329}, {6280, 26338}, {6281, 45594}, {6290, 26467}, {6464, 49388}, {6560, 8946}, {7980, 26504}, {9906, 26299}, {9921, 26305}, {9986, 26313}, {10067, 45611}, {10083, 45613}, {12123, 26293}, {12147, 26374}, {12210, 26428}, {12256, 26440}, {12268, 26368}, {12343, 26502}, {12484, 45588}, {12485, 45590}, {12601, 45609}, {12787, 26443}, {12799, 26448}, {12928, 26489}, {12938, 26484}, {12948, 26478}, {12958, 26472}, {13002, 45604}, {13081, 26354}, {13132, 26511}, {13133, 26510}, {13921, 45605}, {13933, 45608}, {18523, 48659}, {18989, 26434}, {19104, 26455}, {19105, 26461}, {22595, 26323}, {22596, 45592}, {26392, 48478}, {26416, 48479}, {26505, 49048}, {26507, 49103}, {26508, 49155}, {26509, 49156}, {32419, 45698}, {35830, 45599}, {35833, 45602}, {44648, 45598}, {45412, 49317}, {45516, 48734}, {45595, 49220}

X(49387) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: 3rd anti-tri-squares, 2nd half-squares, 4th tri-squares, inner-Vecten
X(49387) = X(486)-of-anti-Lucas(-1) homothetic triangle
X(49387) = {X(45726), X(49427)}-harmonic conjugate of X(49389)


X(49388) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 3rd ANTI-TRI-SQUARES

Barycentrics    5*a^10-18*(b^2+c^2)*a^8+2*(15*b^4+4*b^2*c^2+15*c^4)*a^6-4*(b^2+c^2)*(7*b^4-10*b^2*c^2+7*c^4)*a^4+(b^2-c^2)^2*(13*b^4+2*b^2*c^2+13*c^4)*a^2-2*(7*(b^2+c^2)*a^6-(9*b^4+22*b^2*c^2+9*c^4)*a^4+(b^2+c^2)*(b^4+10*b^2*c^2+c^4)*a^2+(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2)*S-2*(b^2+c^2)*(b^2-c^2)^4 : :

The reciprocal orthologic center of these triangles is X(486).

X(49388) lies on these lines: {4, 26497}, {30, 49436}, {486, 493}, {487, 26494}, {642, 5490}, {3564, 45727}, {6251, 26328}, {6280, 26347}, {6281, 26337}, {6290, 26466}, {6464, 49387}, {7980, 26495}, {9906, 26298}, {9921, 26304}, {9986, 26312}, {10067, 45612}, {10083, 45614}, {12123, 26292}, {12147, 26373}, {12210, 26427}, {12256, 26439}, {12268, 26367}, {12343, 26493}, {12484, 45589}, {12485, 45591}, {12601, 45610}, {12787, 26442}, {12799, 26447}, {12928, 26488}, {12938, 26483}, {12948, 26477}, {12958, 26471}, {13003, 45603}, {13081, 26353}, {13132, 45615}, {13133, 26501}, {13921, 45607}, {13933, 45606}, {18521, 48659}, {18989, 26433}, {19104, 26454}, {19105, 26460}, {22595, 26322}, {22596, 45593}, {26391, 48478}, {26415, 48479}, {26496, 49048}, {26498, 49103}, {26499, 49155}, {26500, 49156}, {32419, 45699}, {35830, 45601}, {35833, 45600}, {44648, 45596}, {45415, 49317}, {45519, 48734}, {45597, 49220}

X(49388) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: 3rd anti-tri-squares, 2nd half-squares, 4th tri-squares, inner-Vecten
X(49388) = X(486)-of-anti-Lucas(+1) homothetic triangle
X(49388) = {X(45727), X(49428)}-harmonic conjugate of X(49390)


X(49389) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 4th ANTI-TRI-SQUARES

Barycentrics    5*a^10-18*(b^2+c^2)*a^8+2*(15*b^4+4*b^2*c^2+15*c^4)*a^6-4*(b^2+c^2)*(7*b^4-10*b^2*c^2+7*c^4)*a^4+(b^2-c^2)^2*(13*b^4+2*b^2*c^2+13*c^4)*a^2+2*(7*(b^2+c^2)*a^6-(9*b^4+22*b^2*c^2+9*c^4)*a^4+(b^2+c^2)*(b^4+10*b^2*c^2+c^4)*a^2+(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2)*S-2*(b^2+c^2)*(b^2-c^2)^4 : :

The reciprocal orthologic center of these triangles is X(485).

X(49389) lies on these lines: {4, 26505}, {30, 49433}, {485, 494}, {488, 26503}, {641, 5491}, {3564, 45726}, {6250, 26329}, {6278, 26338}, {6279, 45594}, {6289, 26467}, {6464, 49390}, {7981, 26504}, {9907, 26299}, {9922, 26305}, {9987, 26313}, {10068, 45611}, {10084, 45613}, {12124, 26293}, {12148, 26374}, {12211, 26428}, {12257, 26440}, {12269, 26368}, {12344, 26502}, {12486, 45588}, {12487, 45590}, {12602, 45609}, {12788, 26443}, {12800, 26448}, {12929, 26489}, {12939, 26484}, {12949, 26478}, {12959, 26472}, {13004, 45604}, {13082, 26354}, {13134, 26511}, {13135, 26510}, {13879, 45605}, {13880, 45608}, {18523, 48660}, {18988, 26434}, {19102, 26455}, {19103, 26461}, {22624, 26323}, {22625, 45592}, {26392, 48480}, {26416, 48481}, {26506, 49049}, {26507, 49104}, {26508, 49157}, {26509, 49158}, {32421, 45698}, {35831, 45602}, {35832, 45599}, {44647, 45595}, {45414, 49318}, {45518, 48735}, {45598, 49221}

X(49389) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: 4th anti-tri-squares, 1st half-squares, 3rd tri-squares, outer-Vecten
X(49389) = X(485)-of-anti-Lucas(-1) homothetic triangle
X(49389) = {X(45726), X(49427)}-harmonic conjugate of X(49387)


X(49390) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 4th ANTI-TRI-SQUARES

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

The reciprocal orthologic center of these triangles is X(485).

X(49390) lies on these lines: {4, 26496}, {30, 49434}, {371, 24244}, {485, 493}, {486, 641}, {488, 26494}, {3564, 45727}, {6250, 26328}, {6278, 26347}, {6279, 26337}, {6289, 26466}, {6464, 49389}, {6561, 8948}, {7981, 26495}, {9907, 26298}, {9922, 26304}, {9987, 26312}, {10068, 45612}, {10084, 45614}, {12124, 26292}, {12148, 26373}, {12211, 26427}, {12257, 26439}, {12269, 26367}, {12344, 26493}, {12486, 45589}, {12487, 45591}, {12602, 45610}, {12788, 26442}, {12800, 26447}, {12929, 26488}, {12939, 26483}, {12949, 26477}, {12959, 26471}, {13005, 45603}, {13082, 26353}, {13134, 45615}, {13135, 26501}, {13879, 45607}, {13880, 45606}, {18521, 48660}, {18988, 26433}, {19102, 26454}, {19103, 26460}, {22624, 26322}, {22625, 45593}, {26391, 48480}, {26415, 48481}, {26497, 49049}, {26498, 49104}, {26499, 49157}, {26500, 49158}, {32421, 45699}, {35831, 45600}, {35832, 45601}, {44647, 45597}, {45413, 49318}, {45517, 48735}, {45596, 49221}

X(49390) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: 4th anti-tri-squares, 1st half-squares, 3rd tri-squares, outer-Vecten
X(49390) = X(485)-of-anti-Lucas(+1) homothetic triangle
X(49390) = {X(45727), X(49428)}-harmonic conjugate of X(49388)


X(49391) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO AAOA

Barycentrics    -(a^14-12*(b^2+c^2)*a^12+(26*b^4+45*b^2*c^2+26*c^4)*a^10-(b^2+c^2)*(17*b^4+25*b^2*c^2+17*c^4)*a^8+(b^4+c^4+b*c*(b^2+4*b*c-c^2))*(b^4+c^4-b*c*(b^2-4*b*c-c^2))*a^6-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2+c^2)*(2*b^4-3*b^2*c^2+2*c^4)*a^4+4*(b^2-c^2)^2*(b^8+c^8-3*b^2*c^2*(b^4+c^4))*a^2-(-4*b^2*c^2+(b^2-c^2)^2)*(b^4-c^4)*(b^2-c^2)^3)*S+2*a^16-8*(b^2+c^2)*a^14+(11*b^4+8*b^2*c^2+11*c^4)*a^12-2*(b^2+c^2)*(2*b^4-9*b^2*c^2+2*c^4)*a^10-(5*b^8+5*c^8+2*b^2*c^2*(7*b^4+19*b^2*c^2+7*c^4))*a^8+2*(b^2+c^2)*(4*b^8+4*c^8-b^2*c^2*(7*b^4-16*b^2*c^2+7*c^4))*a^6-(7*b^8+7*c^8+2*b^2*c^2*(2*b^4+b^2*c^2+2*c^4))*(b^2-c^2)^2*a^4+4*(b^6-c^6)*(b^2-c^2)^2*(b^4-c^4)*a^2-(b^2+c^2)^2*(b^2-c^2)^6 : :

The reciprocal orthologic center of these triangles is X(7574).

X(49391) lies on these lines: {30, 49383}, {110, 26467}, {113, 45592}, {125, 26507}, {265, 494}, {399, 18523}, {511, 49437}, {542, 45726}, {1511, 5491}, {2771, 49409}, {2777, 49421}, {3448, 26440}, {5663, 48469}, {6464, 49392}, {10088, 26478}, {10091, 26472}, {10113, 26329}, {10628, 49413}, {12121, 26293}, {12140, 26374}, {12201, 26428}, {12261, 26368}, {12334, 26502}, {12383, 26503}, {12407, 26299}, {12412, 26305}, {12466, 45588}, {12467, 45590}, {12501, 26313}, {12778, 26443}, {12790, 26448}, {12803, 45594}, {12804, 26338}, {12889, 26489}, {12890, 26484}, {12894, 45604}, {12896, 26354}, {12898, 26504}, {12902, 45609}, {12903, 45611}, {12904, 45613}, {12905, 26511}, {12906, 26510}, {13915, 45605}, {13979, 45608}, {17702, 49377}, {18968, 26434}, {19051, 26455}, {19052, 26461}, {19478, 26323}, {26392, 48483}, {26416, 48484}, {26505, 49050}, {26506, 49051}, {26508, 49159}, {26509, 49160}, {32423, 49427}, {35834, 45599}, {35835, 45602}, {45412, 49319}, {45414, 49320}, {45516, 48736}, {45518, 48737}, {45595, 49222}, {45598, 49223}

X(49391) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: AAOA, AOA, 1st Hyacinth
X(49391) = X(265)-of-anti-Lucas(-1) homothetic triangle
X(49391) = reflection of X(49441) in X(49427)


X(49392) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO AAOA

Barycentrics    (a^14-12*(b^2+c^2)*a^12+(26*b^4+45*b^2*c^2+26*c^4)*a^10-(b^2+c^2)*(17*b^4+25*b^2*c^2+17*c^4)*a^8+(b^4+c^4+b*c*(b^2+4*b*c-c^2))*(b^4+c^4-b*c*(b^2-4*b*c-c^2))*a^6-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2+c^2)*(2*b^4-3*b^2*c^2+2*c^4)*a^4+4*(b^2-c^2)^2*(b^8+c^8-3*b^2*c^2*(b^4+c^4))*a^2-(-4*b^2*c^2+(b^2-c^2)^2)*(b^4-c^4)*(b^2-c^2)^3)*S+2*a^16-8*(b^2+c^2)*a^14+(11*b^4+8*b^2*c^2+11*c^4)*a^12-2*(b^2+c^2)*(2*b^4-9*b^2*c^2+2*c^4)*a^10-(5*b^8+5*c^8+2*b^2*c^2*(7*b^4+19*b^2*c^2+7*c^4))*a^8+2*(b^2+c^2)*(4*b^8+4*c^8-b^2*c^2*(7*b^4-16*b^2*c^2+7*c^4))*a^6-(7*b^8+7*c^8+2*b^2*c^2*(2*b^4+b^2*c^2+2*c^4))*(b^2-c^2)^2*a^4+4*(b^6-c^6)*(b^2-c^2)^2*(b^4-c^4)*a^2-(b^2+c^2)^2*(b^2-c^2)^6 : :

The reciprocal orthologic center of these triangles is X(7574).

X(49392) lies on these lines: {30, 49384}, {110, 26466}, {113, 45593}, {125, 26498}, {265, 493}, {399, 18521}, {511, 49438}, {542, 45727}, {1511, 5490}, {2771, 49410}, {2777, 49422}, {3448, 26439}, {5663, 48468}, {6464, 49391}, {10088, 26477}, {10091, 26471}, {10113, 26328}, {10628, 49414}, {12121, 26292}, {12140, 26373}, {12201, 26427}, {12261, 26367}, {12334, 26493}, {12383, 26494}, {12407, 26298}, {12412, 26304}, {12466, 45589}, {12467, 45591}, {12501, 26312}, {12778, 26442}, {12790, 26447}, {12803, 26337}, {12804, 26347}, {12889, 26488}, {12890, 26483}, {12895, 45603}, {12896, 26353}, {12898, 26495}, {12902, 45610}, {12903, 45612}, {12904, 45614}, {12905, 45615}, {12906, 26501}, {13915, 45607}, {13979, 45606}, {17702, 49378}, {18968, 26433}, {19051, 26454}, {19052, 26460}, {19478, 26322}, {26391, 48483}, {26415, 48484}, {26496, 49050}, {26497, 49051}, {26499, 49159}, {26500, 49160}, {32423, 49428}, {35834, 45601}, {35835, 45600}, {45413, 49320}, {45415, 49319}, {45517, 48737}, {45519, 48736}, {45596, 49223}, {45597, 49222}

X(49392) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: AAOA, AOA, 1st Hyacinth
X(49392) = X(265)-of-anti-Lucas(+1) homothetic triangle
X(49392) = reflection of X(49442) in X(49428)


X(49393) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO ARIES

Barycentrics    ((a^12-12*(b^2+c^2)*a^10+(23*b^4+34*b^2*c^2+23*c^4)*a^8-16*(b^6+c^6)*a^6+(7*b^8+7*c^8-2*b^2*c^2*(8*b^4-b^2*c^2+8*c^4))*a^4-4*(b^4-c^4)*(b^2-c^2)*(b^4-4*b^2*c^2+c^4)*a^2+(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^4)*S-2*a^14+7*(b^2+c^2)*a^12-4*(2*b^4-b^2*c^2+2*c^4)*a^10+(b^2+c^2)*(b^4-30*b^2*c^2+c^4)*a^8+2*(3*b^4-2*b^2*c^2+3*c^4)*(b^4+4*b^2*c^2+c^4)*a^6-(b^4-c^4)*(b^2-c^2)*(7*b^4+6*b^2*c^2+7*c^4)*a^4+4*(b^4-c^4)^2*(b^2-c^2)^2*a^2-(b^2+c^2)*(b^2-c^2)^6)*(-a^2+b^2+c^2) : :

The reciprocal orthologic center of these triangles is X(9833).

X(49393) lies on these lines: {30, 49421}, {68, 494}, {155, 26467}, {539, 45698}, {1069, 26472}, {1147, 5491}, {1154, 49413}, {3157, 26478}, {3564, 45726}, {6193, 26503}, {6464, 49394}, {9896, 26299}, {9908, 26305}, {9923, 26313}, {9927, 26329}, {9928, 26443}, {9929, 45594}, {9930, 26338}, {9933, 26504}, {10055, 45611}, {10071, 45613}, {11411, 26440}, {12118, 26293}, {12134, 26374}, {12164, 18523}, {12193, 26428}, {12259, 26368}, {12328, 26502}, {12359, 26507}, {12415, 45588}, {12416, 45590}, {12418, 26448}, {12422, 26489}, {12423, 26484}, {12426, 45604}, {12428, 26354}, {12429, 45609}, {12430, 26511}, {12431, 26510}, {13754, 48469}, {13909, 45605}, {13970, 45608}, {14984, 49437}, {17702, 49383}, {18970, 26434}, {19061, 26455}, {19062, 26461}, {22659, 26323}, {22660, 45592}, {26392, 48485}, {26416, 48486}, {26505, 49052}, {26506, 49053}, {26508, 49161}, {26509, 49162}, {35836, 45599}, {35837, 45602}, {44665, 49377}, {45412, 49321}, {45414, 49322}, {45516, 48738}, {45518, 48739}, {45595, 49224}, {45598, 49225}

X(49393) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: Aries, 2nd Hyacinth
X(49393) = X(68)-of-anti-Lucas(-1) homothetic triangle


X(49394) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO ARIES

Barycentrics    (-(a^12-12*(b^2+c^2)*a^10+(23*b^4+34*b^2*c^2+23*c^4)*a^8-16*(b^6+c^6)*a^6+(7*b^8+7*c^8-2*b^2*c^2*(8*b^4-b^2*c^2+8*c^4))*a^4-4*(b^4-c^4)*(b^2-c^2)*(b^4-4*b^2*c^2+c^4)*a^2+(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^4)*S-2*a^14+7*(b^2+c^2)*a^12-4*(2*b^4-b^2*c^2+2*c^4)*a^10+(b^2+c^2)*(b^4-30*b^2*c^2+c^4)*a^8+2*(3*b^4-2*b^2*c^2+3*c^4)*(b^4+4*b^2*c^2+c^4)*a^6-(b^4-c^4)*(b^2-c^2)*(7*b^4+6*b^2*c^2+7*c^4)*a^4+4*(b^4-c^4)^2*(b^2-c^2)^2*a^2-(b^2+c^2)*(b^2-c^2)^6)*(-a^2+b^2+c^2) : :

The reciprocal orthologic center of these triangles is X(9833).

X(49394) lies on these lines: {30, 49422}, {68, 493}, {155, 26466}, {539, 45699}, {1069, 26471}, {1147, 5490}, {1154, 49414}, {3157, 26477}, {3564, 45727}, {6193, 26494}, {6464, 49393}, {9896, 26298}, {9908, 26304}, {9923, 26312}, {9927, 26328}, {9928, 26442}, {9929, 26337}, {9930, 26347}, {9933, 26495}, {10055, 45612}, {10071, 45614}, {11411, 26439}, {12118, 26292}, {12134, 26373}, {12164, 18521}, {12193, 26427}, {12259, 26367}, {12328, 26493}, {12359, 26498}, {12415, 45589}, {12416, 45591}, {12418, 26447}, {12422, 26488}, {12423, 26483}, {12427, 45603}, {12428, 26353}, {12429, 45610}, {12430, 45615}, {12431, 26501}, {13754, 48468}, {13909, 45607}, {13970, 45606}, {14984, 49438}, {17702, 49384}, {18970, 26433}, {19061, 26454}, {19062, 26460}, {22659, 26322}, {22660, 45593}, {26391, 48485}, {26415, 48486}, {26496, 49052}, {26497, 49053}, {26499, 49161}, {26500, 49162}, {35836, 45601}, {35837, 45600}, {44665, 49378}, {45413, 49322}, {45415, 49321}, {45517, 48739}, {45519, 48738}, {45596, 49225}, {45597, 49224}

X(49394) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: Aries, 2nd Hyacinth
X(49394) = X(68)-of-anti-Lucas(+1) homothetic triangle


X(49395) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO BEVAN ANTIPODAL

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

The reciprocal orthologic center of these triangles is X(1).

X(49395) lies on these lines: {1, 26293}, {3, 26368}, {4, 26443}, {10, 26329}, {40, 494}, {46, 45613}, {65, 26354}, {515, 49401}, {516, 48469}, {517, 45717}, {946, 5491}, {962, 26503}, {1702, 26461}, {1703, 26455}, {1836, 26478}, {1902, 26374}, {2800, 48708}, {2802, 48689}, {3057, 26434}, {3579, 26507}, {5119, 45611}, {5709, 26508}, {5812, 26484}, {5840, 49409}, {5847, 49397}, {6001, 49421}, {6361, 26440}, {6464, 49396}, {7982, 26504}, {7991, 26299}, {9911, 26305}, {10306, 26502}, {12197, 26428}, {12458, 45588}, {12459, 45590}, {12497, 26313}, {12696, 26448}, {12697, 45594}, {12698, 26338}, {12699, 26467}, {12700, 26489}, {12701, 26472}, {12702, 45609}, {12703, 26511}, {12704, 26510}, {13912, 45605}, {13975, 45608}, {18523, 48661}, {22770, 26323}, {22793, 45592}, {22841, 45604}, {26392, 48487}, {26416, 48488}, {26505, 49054}, {26506, 49055}, {26509, 49163}, {28174, 49427}, {28194, 45698}, {35610, 45599}, {35611, 45602}, {45412, 49323}, {45414, 49324}, {45516, 48740}, {45518, 48741}, {45595, 49226}, {45598, 49227}

X(49395) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: Bevan antipodal, 3rd extouch
X(49395) = X(40)-of-anti-Lucas(-1) homothetic triangle
X(49395) = reflection of X(i) in X(j) for these (i, j): (45717, 49377), (48469, 49419)


X(49396) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO BEVAN ANTIPODAL

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

The reciprocal orthologic center of these triangles is X(1).

X(49396) lies on these lines: {1, 26292}, {3, 26367}, {4, 26442}, {10, 26328}, {40, 493}, {46, 45614}, {65, 26353}, {515, 49402}, {516, 48468}, {517, 45718}, {946, 5490}, {962, 26494}, {1702, 26460}, {1703, 26454}, {1836, 26477}, {1902, 26373}, {2800, 48707}, {2802, 48688}, {3057, 26433}, {3579, 26498}, {5119, 45612}, {5709, 26499}, {5812, 26483}, {5840, 49410}, {5847, 49398}, {6001, 49422}, {6361, 26439}, {6464, 49395}, {7982, 26495}, {7991, 26298}, {9911, 26304}, {10306, 26493}, {12197, 26427}, {12458, 45589}, {12459, 45591}, {12497, 26312}, {12696, 26447}, {12697, 26337}, {12698, 26347}, {12699, 26466}, {12700, 26488}, {12701, 26471}, {12702, 45610}, {12703, 45615}, {12704, 26501}, {13912, 45607}, {13975, 45606}, {18521, 48661}, {22770, 26322}, {22793, 45593}, {22842, 45603}, {26391, 48487}, {26415, 48488}, {26496, 49054}, {26497, 49055}, {26500, 49163}, {28174, 49428}, {28194, 45699}, {35610, 45601}, {35611, 45600}, {45413, 49324}, {45415, 49323}, {45517, 48741}, {45519, 48740}, {45596, 49227}, {45597, 49226}

X(49396) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: Bevan antipodal, 3rd extouch
X(49396) = X(40)-of-anti-Lucas(+1) homothetic triangle
X(49396) = reflection of X(i) in X(j) for these (i, j): (45718, 49378), (48468, 49420)


X(49397) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 9th BROCARD

Barycentrics    -(3*a^10-17*(b^2+c^2)*a^8+2*(9*b^4+4*b^2*c^2+9*c^4)*a^6-2*(b^2+c^2)*(7*b^4-4*b^2*c^2+7*c^4)*a^4+(11*b^4+14*b^2*c^2+11*c^4)*(b^2-c^2)^2*a^2-(-4*b^2*c^2+(b^2-c^2)^2)*(b^4-c^4)*(b^2-c^2))*S+2*a^12-3*(b^2+c^2)*a^10-(b^4+18*b^2*c^2+c^4)*a^8+2*(b^2+c^2)*(b^4+6*b^2*c^2+c^4)*a^6-8*(b^2+c^2)^2*b^2*c^2*a^4+(b^4-c^4)*(b^2-c^2)*(b^4+14*b^2*c^2+c^4)*a^2-(b^4-c^4)^2*(b^2-c^2)^2 : :

The reciprocal orthologic center of these triangles is X(4).

X(49397) lies on these lines: {6, 26329}, {69, 26293}, {494, 6776}, {542, 45698}, {1352, 5491}, {1503, 45726}, {3564, 49377}, {5847, 49395}, {5848, 48689}, {5921, 26503}, {6464, 49398}, {18440, 26467}, {18523, 48662}, {19145, 45605}, {19146, 45608}, {26299, 39878}, {26305, 39879}, {26313, 39882}, {26323, 39883}, {26338, 39888}, {26354, 39897}, {26368, 39870}, {26374, 39871}, {26392, 48489}, {26416, 48490}, {26428, 39872}, {26434, 39873}, {26440, 39874}, {26443, 39885}, {26448, 39886}, {26455, 39875}, {26461, 39876}, {26472, 39892}, {26478, 39891}, {26484, 39890}, {26489, 39889}, {26502, 39877}, {26504, 39898}, {26505, 49056}, {26506, 49057}, {26507, 48906}, {26508, 49164}, {26509, 49165}, {26510, 39903}, {26511, 39902}, {39880, 45588}, {39881, 45590}, {39884, 45592}, {39887, 45594}, {39893, 45599}, {39894, 45602}, {39895, 45604}, {39899, 45609}, {39900, 45611}, {39901, 45613}, {45412, 49325}, {45414, 49326}, {45516, 48742}, {45518, 48743}, {45595, 49228}, {45598, 49229}

X(49397) = orthologic center (anti-Lucas(-1) homothetic, 9th Brocard)
X(49397) = X(6776)-of-anti-Lucas(-1) homothetic triangle
X(49397) = reflection of X(48469) in X(45726)


X(49398) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 9th BROCARD

Barycentrics    (3*a^10-17*(b^2+c^2)*a^8+2*(9*b^4+4*b^2*c^2+9*c^4)*a^6-2*(b^2+c^2)*(7*b^4-4*b^2*c^2+7*c^4)*a^4+(11*b^4+14*b^2*c^2+11*c^4)*(b^2-c^2)^2*a^2-(-4*b^2*c^2+(b^2-c^2)^2)*(b^4-c^4)*(b^2-c^2))*S+2*a^12-3*(b^2+c^2)*a^10-(b^4+18*b^2*c^2+c^4)*a^8+2*(b^2+c^2)*(b^4+6*b^2*c^2+c^4)*a^6-8*(b^2+c^2)^2*b^2*c^2*a^4+(b^4-c^4)*(b^2-c^2)*(b^4+14*b^2*c^2+c^4)*a^2-(b^4-c^4)^2*(b^2-c^2)^2 : :

The reciprocal orthologic center of these triangles is X(4).

X(49398) lies on these lines: {6, 26328}, {69, 26292}, {493, 6776}, {542, 45699}, {1352, 5490}, {1503, 45727}, {3564, 49378}, {5847, 49396}, {5848, 48688}, {5921, 26494}, {6464, 49397}, {18440, 26466}, {18521, 48662}, {19145, 45607}, {19146, 45606}, {26298, 39878}, {26304, 39879}, {26312, 39882}, {26322, 39883}, {26337, 39887}, {26347, 39888}, {26353, 39897}, {26367, 39870}, {26373, 39871}, {26391, 48489}, {26415, 48490}, {26427, 39872}, {26433, 39873}, {26439, 39874}, {26442, 39885}, {26447, 39886}, {26454, 39875}, {26460, 39876}, {26471, 39892}, {26477, 39891}, {26483, 39890}, {26488, 39889}, {26493, 39877}, {26495, 39898}, {26496, 49056}, {26497, 49057}, {26498, 48906}, {26499, 49164}, {26500, 49165}, {26501, 39903}, {39880, 45589}, {39881, 45591}, {39884, 45593}, {39893, 45601}, {39894, 45600}, {39896, 45603}, {39899, 45610}, {39900, 45612}, {39901, 45614}, {39902, 45615}, {45413, 49326}, {45415, 49325}, {45517, 48743}, {45519, 48742}, {45596, 49229}, {45597, 49228}

X(49398) = orthologic center (anti-Lucas(+1) homothetic, 9th Brocard)
X(49398) = X(6776)-of-anti-Lucas(+1) homothetic triangle
X(49398) = reflection of X(48468) in X(45727)


X(49399) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 1st BROCARD-REFLECTED

Barycentrics    ((10*b^4+19*b^2*c^2+10*c^4)*a^8-10*(b^4+b^2*c^2+c^4)*(b^2+c^2)*a^6-2*(b^8+c^8+4*b^2*c^2*(2*b^4+3*b^2*c^2+2*c^4))*a^4+2*(b^4-c^4)*(b^2-c^2)*(b^4-3*b^2*c^2+c^4)*a^2+(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2*b^2*c^2)*S+3*(b^2+c^2)*a^12-2*(5*b^4+8*b^2*c^2+5*c^4)*a^10+(b^2+c^2)*(14*b^4-13*b^2*c^2+14*c^4)*a^8-4*(3*b^8+3*c^8-4*(b^4+b^2*c^2+c^4)*b^2*c^2)*a^6+(b^2+c^2)*(7*b^8+7*c^8-2*b^2*c^2*(9*b^4-23*b^2*c^2+9*c^4))*a^4-2*(b^2-c^2)^4*(b^4+c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3*b^2*c^2 : :
X(49399) = X(49423)-4*X(49427)

The reciprocal orthologic center of these triangles is X(3).

X(49399) lies on these lines: {262, 494}, {511, 45698}, {2782, 49381}, {5491, 15819}, {6194, 26503}, {6464, 49400}, {7697, 26467}, {7709, 26440}, {18523, 48663}, {18971, 26434}, {19063, 26455}, {19064, 26461}, {22475, 26368}, {22480, 26374}, {22521, 26428}, {22556, 26502}, {22650, 26299}, {22655, 26305}, {22668, 45588}, {22672, 45590}, {22676, 26293}, {22678, 26313}, {22680, 26323}, {22681, 45592}, {22682, 26329}, {22697, 26443}, {22698, 26448}, {22699, 45594}, {22700, 26338}, {22703, 26489}, {22704, 26484}, {22705, 26478}, {22706, 26472}, {22709, 45604}, {22711, 26354}, {22713, 26504}, {22720, 45605}, {22721, 45608}, {22728, 45609}, {22729, 45611}, {22730, 45613}, {22731, 26511}, {22732, 26510}, {26392, 48491}, {26416, 48492}, {26505, 49058}, {26506, 49059}, {26507, 40108}, {26508, 49166}, {26509, 49167}, {32515, 49423}, {35838, 45599}, {35839, 45602}, {45412, 49327}, {45414, 49328}, {45516, 48744}, {45518, 48745}, {45595, 49230}, {45598, 49231}, {45726, 49379}, {49377, 49425}

X(49399) = orthologic center (anti-Lucas(-1) homothetic, 1st Brocard-reflected)
X(49399) = X(262)-of-anti-Lucas(-1) homothetic triangle


X(49400) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 1st BROCARD-REFLECTED

Barycentrics    -((10*b^4+19*b^2*c^2+10*c^4)*a^8-10*(b^4+b^2*c^2+c^4)*(b^2+c^2)*a^6-2*(b^8+c^8+4*b^2*c^2*(2*b^4+3*b^2*c^2+2*c^4))*a^4+2*(b^4-c^4)*(b^2-c^2)*(b^4-3*b^2*c^2+c^4)*a^2+(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2*b^2*c^2)*S+3*(b^2+c^2)*a^12-2*(5*b^4+8*b^2*c^2+5*c^4)*a^10+(b^2+c^2)*(14*b^4-13*b^2*c^2+14*c^4)*a^8-4*(3*b^8+3*c^8-4*(b^4+b^2*c^2+c^4)*b^2*c^2)*a^6+(b^2+c^2)*(7*b^8+7*c^8-2*b^2*c^2*(9*b^4-23*b^2*c^2+9*c^4))*a^4-2*(b^2-c^2)^4*(b^4+c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3*b^2*c^2 : :
X(49400) = X(49424)-4*X(49428)

The reciprocal orthologic center of these triangles is X(3).

X(49400) lies on these lines: {262, 493}, {511, 45699}, {2782, 49382}, {5490, 15819}, {6194, 26494}, {6464, 49399}, {7697, 26466}, {7709, 26439}, {18521, 48663}, {18971, 26433}, {19063, 26454}, {19064, 26460}, {22475, 26367}, {22480, 26373}, {22521, 26427}, {22556, 26493}, {22650, 26298}, {22655, 26304}, {22668, 45589}, {22672, 45591}, {22676, 26292}, {22678, 26312}, {22680, 26322}, {22681, 45593}, {22682, 26328}, {22697, 26442}, {22698, 26447}, {22699, 26337}, {22700, 26347}, {22703, 26488}, {22704, 26483}, {22705, 26477}, {22706, 26471}, {22710, 45603}, {22711, 26353}, {22713, 26495}, {22720, 45607}, {22721, 45606}, {22728, 45610}, {22729, 45612}, {22730, 45614}, {22731, 45615}, {22732, 26501}, {26391, 48491}, {26415, 48492}, {26496, 49058}, {26497, 49059}, {26498, 40108}, {26499, 49166}, {26500, 49167}, {32515, 49424}, {35838, 45601}, {35839, 45600}, {45413, 49328}, {45415, 49327}, {45517, 48745}, {45519, 48744}, {45596, 49231}, {45597, 49230}, {45727, 49380}, {49378, 49426}

X(49400) = orthologic center (anti-Lucas(+1) homothetic, 1st Brocard-reflected)
X(49400) = X(262)-of-anti-Lucas(+1) homothetic triangle


X(49401) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO EXCENTERS-MIDPOINTS

Barycentrics    -(a^5-(b+c)*a^4-10*(b^2+c^2)*a^3+2*(b+c)*(b^2+c^2)*a^2+(-4*b^2*c^2+(b^2-c^2)^2)*a-(-4*b^2*c^2+(b^2-c^2)^2)*(b+c))*S+2*a^7-3*(b^2+c^2)*a^5-(b+c)*(b^2+c^2)*a^4-16*b^2*c^2*a^3+2*(b+c)*(b^2+c^2)^2*a^2+(b^4-c^4)*(b^2-c^2)*a-(b^4-c^4)*(b^2-c^2)*(b+c) : :
X(49401) = 3*X(45698)-2*X(45717) = 3*X(45698)-4*X(49419)

The reciprocal orthologic center of these triangles is X(10).

X(49401) lies on these lines: {1, 5491}, {8, 494}, {10, 26368}, {145, 26503}, {355, 26329}, {515, 49395}, {517, 48469}, {519, 45698}, {758, 49411}, {944, 26293}, {952, 48689}, {1482, 26467}, {2098, 26472}, {2099, 26478}, {2802, 49409}, {3632, 26299}, {3913, 26502}, {5690, 26507}, {5844, 49427}, {5846, 45726}, {6464, 49402}, {7718, 8946}, {8148, 18523}, {10573, 45613}, {10912, 26489}, {10944, 26434}, {10950, 26354}, {12135, 26374}, {12195, 26428}, {12245, 26440}, {12410, 26305}, {12454, 45588}, {12455, 45590}, {12495, 26313}, {12513, 26323}, {12626, 26448}, {12627, 45594}, {12628, 26338}, {12635, 26484}, {12636, 45604}, {12645, 45609}, {12647, 45611}, {12648, 26511}, {12649, 26510}, {13911, 45605}, {13973, 45608}, {14839, 49423}, {19065, 26455}, {19066, 26461}, {22791, 45592}, {26392, 48493}, {26416, 48494}, {26505, 49060}, {26506, 49061}, {26508, 49168}, {26509, 49169}, {35842, 45599}, {35843, 45602}, {45412, 49329}, {45414, 49330}, {45516, 48746}, {45518, 48747}, {45595, 49232}, {45598, 49233}

X(49401) = reflection of X(45717) in X(49419)
X(49401) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: excenters-midpoints, Garcia-reflection, 2nd Schiffler
X(49401) = X(8)-of-anti-Lucas(-1) homothetic triangle
X(49401) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 26443, 5491), (145, 26503, 26504), (45717, 49419, 45698)


X(49402) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO EXCENTERS-MIDPOINTS

Barycentrics    (a^5-(b+c)*a^4-10*(b^2+c^2)*a^3+2*(b+c)*(b^2+c^2)*a^2+(-4*b^2*c^2+(b^2-c^2)^2)*a-(-4*b^2*c^2+(b^2-c^2)^2)*(b+c))*S+2*a^7-3*(b^2+c^2)*a^5-(b+c)*(b^2+c^2)*a^4-16*b^2*c^2*a^3+2*(b+c)*(b^2+c^2)^2*a^2+(b^4-c^4)*(b^2-c^2)*a-(b^4-c^4)*(b^2-c^2)*(b+c) : :
X(49402) = 3*X(45699)-2*X(45718) = 3*X(45699)-4*X(49420)

The reciprocal orthologic center of these triangles is X(10).

X(49402) lies on these lines: {1, 5490}, {8, 493}, {10, 26367}, {145, 26494}, {355, 26328}, {515, 49396}, {517, 48468}, {519, 45699}, {758, 49412}, {944, 26292}, {952, 48688}, {1482, 26466}, {2098, 26471}, {2099, 26477}, {2802, 49410}, {3632, 26298}, {3913, 26493}, {5690, 26498}, {5844, 49428}, {5846, 45727}, {6464, 49401}, {7718, 8948}, {8148, 18521}, {10573, 45614}, {10912, 26488}, {10944, 26433}, {10950, 26353}, {12135, 26373}, {12195, 26427}, {12245, 26439}, {12410, 26304}, {12454, 45589}, {12455, 45591}, {12495, 26312}, {12513, 26322}, {12626, 26447}, {12627, 26337}, {12628, 26347}, {12635, 26483}, {12637, 45603}, {12645, 45610}, {12647, 45612}, {12648, 45615}, {12649, 26501}, {13911, 45607}, {13973, 45606}, {14839, 49424}, {19065, 26454}, {19066, 26460}, {22791, 45593}, {26391, 48493}, {26415, 48494}, {26496, 49060}, {26497, 49061}, {26499, 49168}, {26500, 49169}, {35842, 45601}, {35843, 45600}, {45413, 49330}, {45415, 49329}, {45517, 48747}, {45519, 48746}, {45596, 49233}, {45597, 49232}

X(49402) = reflection of X(45718) in X(49420)
X(49402) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: excenters-midpoints, Garcia-reflection, 2nd Schiffler
X(49402) = X(8)-of-anti-Lucas(+1) homothetic triangle
X(49402) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 26442, 5490), (145, 26494, 26495), (45718, 49420, 45699)


X(49403) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO EXTOUCH

Barycentrics    a*(-(a^10-(5*b^2-6*b*c+5*c^2)*a^8-4*(b+c)*(b^2+c^2)*a^7+2*(5*b^4+5*c^4-4*b*c*(4*b^2-b*c+4*c^2))*a^6+4*(b+c)*(b^2+c^2)*(3*b^2-2*b*c+3*c^2)*a^5-2*(5*b^4+5*c^4+4*b*c*(b^2+c^2))*(b-c)^2*a^4-4*(b^4-c^4)*(b-c)*(3*b^2+2*b*c+3*c^2)*a^3+(5*b^6+5*c^6+(26*b^4+26*c^4+b*c*(31*b^2+36*b*c+31*c^2))*b*c)*(b-c)^2*a^2+4*(b^4-c^4)*(b^2-c^2)^2*(b-c)*a+(b^2-c^2)^2*(b+c)^2*(4*b^2*c^2-(b^2-c^2)^2))*S+(b+c)*a^11+(b^2+4*b*c+c^2)*a^10-(b+c)*(5*b^2-2*b*c+5*c^2)*a^9-(5*b^2+2*b*c+5*c^2)*(b^2+c^2)*a^8+2*(b+c)*(5*b^4+5*c^4-4*b*c*(b^2-b*c+c^2))*a^7+2*(5*b^6+5*c^6-(8*b^4+8*c^4-b*c*(11*b^2-24*b*c+11*c^2))*b*c)*a^6-2*(b+c)*(5*b^6+5*c^6-3*(2*b^4+2*c^4+b*c*(b^2+c^2))*b*c)*a^5-2*(b^2+c^2)*(5*b^4-2*b^2*c^2+5*c^4)*(b-c)^2*a^4+(b^2-c^2)*(b-c)*(5*b^6+5*c^6+(2*b^4+2*c^4-b*c*(17*b^2+12*b*c+17*c^2))*b*c)*a^3+(b^2-c^2)^2*(5*b^6+5*c^6-(4*b^4+4*c^4-b*c*(11*b^2+24*b*c+11*c^2))*b*c)*a^2-(b^2-c^2)^3*(b-c)*a*(b^2-2*b*c-c^2)*(b^2+2*b*c-c^2)-(b^2-c^2)^4*(b+c)^2*(b^2+c^2)) : :

The reciprocal orthologic center of these triangles is X(40).

X(49403) lies on these lines: {84, 494}, {515, 49395}, {971, 49377}, {1490, 26293}, {1709, 45611}, {2829, 49409}, {5491, 6260}, {6001, 45717}, {6223, 26503}, {6245, 26329}, {6257, 26338}, {6258, 45594}, {6259, 26467}, {6464, 49404}, {7971, 26504}, {7992, 26299}, {8987, 45605}, {9910, 26305}, {10085, 45613}, {12114, 26368}, {12136, 26374}, {12196, 26428}, {12246, 26440}, {12330, 26502}, {12456, 45588}, {12457, 45590}, {12496, 26313}, {12667, 26443}, {12668, 26448}, {12676, 26489}, {12677, 26484}, {12678, 26478}, {12679, 26472}, {12680, 26354}, {12684, 45609}, {12686, 26511}, {12687, 26510}, {12688, 26434}, {13974, 45608}, {18237, 26323}, {18245, 45604}, {18523, 48664}, {19067, 26455}, {19068, 26461}, {22792, 45592}, {26392, 48495}, {26416, 48496}, {26505, 49062}, {26506, 49063}, {26507, 34862}, {26508, 49170}, {26509, 49171}, {35844, 45599}, {35845, 45602}, {45412, 49331}, {45414, 49332}, {45516, 48748}, {45518, 48749}, {45595, 49234}, {45598, 49235}

X(49403) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: extouch, 1st Zaniah
X(49403) = X(84)-of-anti-Lucas(-1) homothetic triangle


X(49404) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO EXTOUCH

Barycentrics    a*((a^10-(5*b^2-6*b*c+5*c^2)*a^8-4*(b+c)*(b^2+c^2)*a^7+2*(5*b^4+5*c^4-4*b*c*(4*b^2-b*c+4*c^2))*a^6+4*(b+c)*(b^2+c^2)*(3*b^2-2*b*c+3*c^2)*a^5-2*(5*b^4+5*c^4+4*b*c*(b^2+c^2))*(b-c)^2*a^4-4*(b^4-c^4)*(b-c)*(3*b^2+2*b*c+3*c^2)*a^3+(5*b^6+5*c^6+(26*b^4+26*c^4+b*c*(31*b^2+36*b*c+31*c^2))*b*c)*(b-c)^2*a^2+4*(b^4-c^4)*(b^2-c^2)^2*(b-c)*a+(b^2-c^2)^2*(b+c)^2*(4*b^2*c^2-(b^2-c^2)^2))*S+(b+c)*a^11+(b^2+4*b*c+c^2)*a^10-(b+c)*(5*b^2-2*b*c+5*c^2)*a^9-(5*b^2+2*b*c+5*c^2)*(b^2+c^2)*a^8+2*(b+c)*(5*b^4+5*c^4-4*b*c*(b^2-b*c+c^2))*a^7+2*(5*b^6+5*c^6-(8*b^4+8*c^4-b*c*(11*b^2-24*b*c+11*c^2))*b*c)*a^6-2*(b+c)*(5*b^6+5*c^6-3*(2*b^4+2*c^4+b*c*(b^2+c^2))*b*c)*a^5-2*(b^2+c^2)*(5*b^4-2*b^2*c^2+5*c^4)*(b-c)^2*a^4+(b^2-c^2)*(b-c)*(5*b^6+5*c^6+(2*b^4+2*c^4-b*c*(17*b^2+12*b*c+17*c^2))*b*c)*a^3+(b^2-c^2)^2*(5*b^6+5*c^6-(4*b^4+4*c^4-b*c*(11*b^2+24*b*c+11*c^2))*b*c)*a^2-(b^2-c^2)^3*(b-c)*a*(b^2-2*b*c-c^2)*(b^2+2*b*c-c^2)-(b^2-c^2)^4*(b+c)^2*(b^2+c^2)) : :

The reciprocal orthologic center of these triangles is X(40).

X(49404) lies on these lines: {84, 493}, {515, 49396}, {971, 49378}, {1490, 26292}, {1709, 45612}, {2829, 49410}, {5490, 6260}, {6001, 45718}, {6223, 26494}, {6245, 26328}, {6257, 26347}, {6258, 26337}, {6259, 26466}, {6464, 49403}, {7971, 26495}, {7992, 26298}, {8987, 45607}, {9910, 26304}, {10085, 45614}, {12114, 26367}, {12136, 26373}, {12196, 26427}, {12246, 26439}, {12330, 26493}, {12456, 45589}, {12457, 45591}, {12496, 26312}, {12667, 26442}, {12668, 26447}, {12676, 26488}, {12677, 26483}, {12678, 26477}, {12679, 26471}, {12680, 26353}, {12684, 45610}, {12686, 45615}, {12687, 26501}, {12688, 26433}, {13974, 45606}, {18237, 26322}, {18246, 45603}, {18521, 48664}, {19067, 26454}, {19068, 26460}, {22792, 45593}, {26391, 48495}, {26415, 48496}, {26496, 49062}, {26497, 49063}, {26498, 34862}, {26499, 49170}, {26500, 49171}, {35844, 45601}, {35845, 45600}, {45413, 49332}, {45415, 49331}, {45517, 48749}, {45519, 48748}, {45596, 49235}, {45597, 49234}

X(49404) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: extouch, 1st Zaniah
X(49404) = X(84)-of-anti-Lucas(+1) homothetic triangle


X(49405) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO INNER-FERMAT

Barycentrics    -2*a^2*S*(4*b^2*c^2*(b^2+c^2)-S*(a^4-2*(b^2+c^2)*a^2+5*b^4+2*b^2*c^2+5*c^4))*sqrt(3)+(a^8+11*(b^2+c^2)*a^6-(19*b^4+54*b^2*c^2+19*c^4)*a^4+(b^2+c^2)*(5*b^4+2*b^2*c^2+5*c^4)*a^2+2*(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2)*S+4*a^10-16*(b^2+c^2)*a^8+2*(13*b^4+4*b^2*c^2+13*c^4)*a^6-2*(b^2+c^2)*(11*b^4-24*b^2*c^2+11*c^4)*a^4+2*(b^2-c^2)^2*(5*b^4-2*b^2*c^2+5*c^4)*a^2-2*(b^4-c^4)*(b^2-c^2)^3 : :

The reciprocal orthologic center of these triangles is X(3).

X(49405) lies on these lines: {18, 494}, {533, 45698}, {628, 26503}, {630, 5491}, {5965, 45726}, {6464, 49406}, {11740, 26368}, {16627, 26467}, {16628, 45609}, {18523, 48665}, {18972, 26434}, {19069, 26455}, {19072, 26461}, {22481, 26374}, {22522, 26428}, {22531, 26440}, {22557, 26502}, {22651, 26299}, {22656, 26305}, {22669, 45588}, {22673, 45590}, {22745, 26313}, {22771, 26323}, {22794, 45592}, {22831, 26329}, {22843, 26293}, {22851, 26443}, {22852, 26448}, {22853, 45594}, {22854, 26338}, {22857, 26489}, {22858, 26484}, {22859, 26478}, {22860, 26472}, {22863, 45604}, {22865, 26354}, {22867, 26504}, {22876, 45605}, {22877, 45608}, {22884, 45611}, {22885, 45613}, {22886, 26511}, {22887, 26510}, {26392, 48497}, {26416, 48498}, {26505, 49064}, {26506, 49065}, {26507, 49105}, {26508, 49172}, {26509, 49173}, {35846, 45599}, {35849, 45602}, {44667, 48469}, {45412, 49333}, {45414, 49334}, {45516, 48750}, {45518, 48751}, {45595, 49236}, {45598, 49237}, {49373, 49427}, {49375, 49377}

X(49405) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: inner-Fermat, 1st half-diamonds
X(49405) = X(18)-of-anti-Lucas(-1) homothetic triangle


X(49406) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO INNER-FERMAT

Barycentrics    -2*a^2*S*(4*b^2*c^2*(b^2+c^2)+S*(a^4-2*(b^2+c^2)*a^2+5*b^4+2*b^2*c^2+5*c^4))*sqrt(3)-(a^8+11*(b^2+c^2)*a^6-(19*b^4+54*b^2*c^2+19*c^4)*a^4+(b^2+c^2)*(5*b^4+2*b^2*c^2+5*c^4)*a^2+2*(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2)*S+4*a^10-16*(b^2+c^2)*a^8+2*(13*b^4+4*b^2*c^2+13*c^4)*a^6-2*(b^2+c^2)*(11*b^4-24*b^2*c^2+11*c^4)*a^4+2*(b^2-c^2)^2*(5*b^4-2*b^2*c^2+5*c^4)*a^2-2*(b^4-c^4)*(b^2-c^2)^3 : :

The reciprocal orthologic center of these triangles is X(3).

X(49406) lies on these lines: {18, 493}, {533, 45699}, {628, 26494}, {630, 5490}, {5965, 45727}, {6464, 49405}, {11740, 26367}, {16627, 26466}, {16628, 45610}, {18521, 48665}, {18972, 26433}, {19069, 26454}, {19072, 26460}, {22481, 26373}, {22522, 26427}, {22531, 26439}, {22557, 26493}, {22651, 26298}, {22656, 26304}, {22669, 45589}, {22673, 45591}, {22745, 26312}, {22771, 26322}, {22794, 45593}, {22831, 26328}, {22843, 26292}, {22851, 26442}, {22852, 26447}, {22853, 26337}, {22854, 26347}, {22857, 26488}, {22858, 26483}, {22859, 26477}, {22860, 26471}, {22864, 45603}, {22865, 26353}, {22867, 26495}, {22876, 45607}, {22877, 45606}, {22884, 45612}, {22885, 45614}, {22886, 45615}, {22887, 26501}, {26391, 48497}, {26415, 48498}, {26496, 49064}, {26497, 49065}, {26498, 49105}, {26499, 49172}, {26500, 49173}, {35846, 45601}, {35849, 45600}, {44667, 48468}, {45413, 49334}, {45415, 49333}, {45517, 48751}, {45519, 48750}, {45596, 49237}, {45597, 49236}, {49374, 49428}, {49376, 49378}

X(49406) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: inner-Fermat, 1st half-diamonds
X(49406) = X(18)-of-anti-Lucas(+1) homothetic triangle


X(49407) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO OUTER-FERMAT

Barycentrics    2*a^2*S*(4*b^2*c^2*(b^2+c^2)-S*(a^4-2*(b^2+c^2)*a^2+5*b^4+2*b^2*c^2+5*c^4))*sqrt(3)+(a^8+11*(b^2+c^2)*a^6-(19*b^4+54*b^2*c^2+19*c^4)*a^4+(b^2+c^2)*(5*b^4+2*b^2*c^2+5*c^4)*a^2+2*(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2)*S+4*a^10-16*(b^2+c^2)*a^8+2*(13*b^4+4*b^2*c^2+13*c^4)*a^6-2*(b^2+c^2)*(11*b^4-24*b^2*c^2+11*c^4)*a^4+2*(b^2-c^2)^2*(5*b^4-2*b^2*c^2+5*c^4)*a^2-2*(b^4-c^4)*(b^2-c^2)^3 : :

The reciprocal orthologic center of these triangles is X(3).

X(49407) lies on these lines: {17, 494}, {532, 45698}, {627, 26503}, {629, 5491}, {5965, 45726}, {6464, 49408}, {11739, 26368}, {16626, 26467}, {16629, 45609}, {18523, 48666}, {18973, 26434}, {19070, 26461}, {19071, 26455}, {22482, 26374}, {22523, 26428}, {22532, 26440}, {22558, 26502}, {22652, 26299}, {22657, 26305}, {22670, 45588}, {22674, 45590}, {22746, 26313}, {22772, 26323}, {22795, 45592}, {22832, 26329}, {22890, 26293}, {22896, 26443}, {22897, 26448}, {22898, 45594}, {22899, 26338}, {22902, 26489}, {22903, 26484}, {22904, 26478}, {22905, 26472}, {22908, 45604}, {22910, 26354}, {22912, 26504}, {22921, 45605}, {22922, 45608}, {22929, 45611}, {22930, 45613}, {22931, 26511}, {22932, 26510}, {26392, 48499}, {26416, 48500}, {26505, 49066}, {26506, 49067}, {26507, 49106}, {26508, 49174}, {26509, 49175}, {35847, 45602}, {35848, 45599}, {44666, 48469}, {45412, 49335}, {45414, 49336}, {45516, 48752}, {45518, 48753}, {45595, 49238}, {45598, 49239}, {49373, 49377}, {49375, 49427}

X(49407) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: outer-Fermat, 2nd half-diamonds
X(49407) = X(17)-of-anti-Lucas(-1) homothetic triangle


X(49408) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO OUTER-FERMAT

Barycentrics    2*a^2*S*(4*b^2*c^2*(b^2+c^2)+S*(a^4-2*(b^2+c^2)*a^2+5*b^4+2*b^2*c^2+5*c^4))*sqrt(3)-(a^8+11*(b^2+c^2)*a^6-(19*b^4+54*b^2*c^2+19*c^4)*a^4+(b^2+c^2)*(5*b^4+2*b^2*c^2+5*c^4)*a^2+2*(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2)*S+4*a^10-16*(b^2+c^2)*a^8+2*(13*b^4+4*b^2*c^2+13*c^4)*a^6-2*(b^2+c^2)*(11*b^4-24*b^2*c^2+11*c^4)*a^4+2*(b^2-c^2)^2*(5*b^4-2*b^2*c^2+5*c^4)*a^2-2*(b^4-c^4)*(b^2-c^2)^3 : :

The reciprocal orthologic center of these triangles is X(3).

X(49408) lies on these lines: {17, 493}, {532, 45699}, {627, 26494}, {629, 5490}, {5965, 45727}, {6464, 49407}, {11739, 26367}, {16626, 26466}, {16629, 45610}, {18521, 48666}, {18973, 26433}, {19070, 26460}, {19071, 26454}, {22482, 26373}, {22523, 26427}, {22532, 26439}, {22558, 26493}, {22652, 26298}, {22657, 26304}, {22670, 45589}, {22674, 45591}, {22746, 26312}, {22772, 26322}, {22795, 45593}, {22832, 26328}, {22890, 26292}, {22896, 26442}, {22897, 26447}, {22898, 26337}, {22899, 26347}, {22902, 26488}, {22903, 26483}, {22904, 26477}, {22905, 26471}, {22909, 45603}, {22910, 26353}, {22912, 26495}, {22921, 45607}, {22922, 45606}, {22929, 45612}, {22930, 45614}, {22931, 45615}, {22932, 26501}, {26391, 48499}, {26415, 48500}, {26496, 49066}, {26497, 49067}, {26498, 49106}, {26499, 49174}, {26500, 49175}, {35847, 45600}, {35848, 45601}, {44666, 48468}, {45413, 49336}, {45415, 49335}, {45517, 48753}, {45519, 48752}, {45596, 49239}, {45597, 49238}, {49374, 49378}, {49376, 49428}

X(49408) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: outer-Fermat, 2nd half-diamonds
X(49408) = X(17)-of-anti-Lucas(+1) homothetic triangle


X(49409) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(49409) lies on these lines: {11, 26368}, {80, 494}, {100, 26443}, {214, 5491}, {515, 48689}, {952, 45717}, {2771, 49391}, {2800, 48469}, {2802, 49401}, {2829, 49403}, {5840, 49395}, {6224, 26503}, {6246, 26329}, {6262, 26338}, {6263, 45594}, {6265, 26467}, {6464, 49410}, {7972, 26504}, {8988, 45605}, {9897, 26299}, {9912, 26305}, {10057, 45611}, {10073, 45613}, {12119, 26293}, {12137, 26374}, {12198, 26428}, {12247, 26440}, {12331, 26502}, {12460, 45588}, {12461, 45590}, {12498, 26313}, {12611, 45592}, {12619, 26507}, {12729, 26448}, {12737, 26489}, {12738, 26484}, {12739, 26478}, {12740, 26472}, {12741, 45604}, {12743, 26354}, {12747, 45609}, {12749, 26511}, {12750, 26510}, {12751, 26509}, {12773, 26323}, {13976, 45608}, {18523, 48667}, {18976, 26434}, {19077, 26455}, {19078, 26461}, {26392, 48501}, {26416, 48502}, {26505, 49068}, {26506, 49069}, {26508, 49176}, {35852, 45599}, {35853, 45602}, {45412, 49337}, {45414, 49338}, {45516, 48754}, {45518, 48755}, {45595, 49240}, {45598, 49241}, {48708, 49419}

X(49409) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: Fuhrmann, K798i
X(49409) = X(80)-of-anti-Lucas(-1) homothetic triangle
X(49409) = reflection of X(48708) in X(49419)


X(49410) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(49410) lies on these lines: {11, 26367}, {80, 493}, {100, 26442}, {214, 5490}, {515, 48688}, {952, 45718}, {2771, 49392}, {2800, 48468}, {2802, 49402}, {2829, 49404}, {5840, 49396}, {6224, 26494}, {6246, 26328}, {6262, 26347}, {6263, 26337}, {6265, 26466}, {6464, 49409}, {7972, 26495}, {8988, 45607}, {9897, 26298}, {9912, 26304}, {10057, 45612}, {10073, 45614}, {12119, 26292}, {12137, 26373}, {12198, 26427}, {12247, 26439}, {12331, 26493}, {12460, 45589}, {12461, 45591}, {12498, 26312}, {12611, 45593}, {12619, 26498}, {12729, 26447}, {12737, 26488}, {12738, 26483}, {12739, 26477}, {12740, 26471}, {12742, 45603}, {12743, 26353}, {12747, 45610}, {12749, 45615}, {12750, 26501}, {12751, 26500}, {12773, 26322}, {13976, 45606}, {18521, 48667}, {18976, 26433}, {19077, 26454}, {19078, 26460}, {26391, 48501}, {26415, 48502}, {26496, 49068}, {26497, 49069}, {26499, 49176}, {35852, 45601}, {35853, 45600}, {45413, 49338}, {45415, 49337}, {45517, 48755}, {45519, 48754}, {45596, 49241}, {45597, 49240}, {48707, 49420}

X(49410) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: Fuhrmann, K798i
X(49410) = X(80)-of-anti-Lucas(+1) homothetic triangle
X(49410) = reflection of X(48707) in X(49420)


X(49411) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 2nd FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(49411) lies on these lines: {30, 45717}, {79, 494}, {758, 49401}, {2771, 49391}, {3647, 5491}, {3648, 26503}, {3649, 26368}, {3652, 26467}, {5441, 26504}, {6464, 49412}, {11684, 26443}, {13743, 26323}, {16113, 26293}, {16114, 26374}, {16115, 26428}, {16116, 26440}, {16117, 26502}, {16118, 26299}, {16119, 26305}, {16121, 45588}, {16122, 45590}, {16123, 26313}, {16125, 26329}, {16129, 26448}, {16130, 45594}, {16131, 26338}, {16138, 26489}, {16139, 26484}, {16140, 26478}, {16141, 26472}, {16142, 26354}, {16148, 45605}, {16149, 45608}, {16150, 45609}, {16152, 45611}, {16153, 45613}, {16154, 26511}, {16155, 26510}, {16161, 45604}, {18523, 48668}, {18977, 26434}, {19079, 26455}, {19080, 26461}, {22798, 45592}, {26392, 48503}, {26416, 48504}, {26505, 49070}, {26506, 49071}, {26507, 49107}, {26508, 49177}, {26509, 49178}, {35854, 45599}, {35855, 45602}, {45412, 49339}, {45414, 49340}, {45516, 48756}, {45518, 48757}, {45595, 49242}, {45598, 49243}

X(49411) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: 2nd Fuhrmann, K798e
X(49411) = X(79)-of-anti-Lucas(-1) homothetic triangle


X(49412) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 2nd FUHRMANN

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

The reciprocal orthologic center of these triangles is X(3).

X(49412) lies on these lines: {30, 45718}, {79, 493}, {758, 49402}, {2771, 49392}, {3647, 5490}, {3648, 26494}, {3649, 26367}, {3652, 26466}, {5441, 26495}, {6464, 49411}, {11684, 26442}, {13743, 26322}, {16113, 26292}, {16114, 26373}, {16115, 26427}, {16116, 26439}, {16117, 26493}, {16118, 26298}, {16119, 26304}, {16121, 45589}, {16122, 45591}, {16123, 26312}, {16125, 26328}, {16129, 26447}, {16130, 26337}, {16131, 26347}, {16138, 26488}, {16139, 26483}, {16140, 26477}, {16141, 26471}, {16142, 26353}, {16148, 45607}, {16149, 45606}, {16150, 45610}, {16152, 45612}, {16153, 45614}, {16154, 45615}, {16155, 26501}, {16162, 45603}, {18521, 48668}, {18977, 26433}, {19079, 26454}, {19080, 26460}, {22798, 45593}, {26391, 48503}, {26415, 48504}, {26496, 49070}, {26497, 49071}, {26498, 49107}, {26499, 49177}, {26500, 49178}, {35854, 45601}, {35855, 45600}, {45413, 49340}, {45415, 49339}, {45517, 48757}, {45519, 48756}, {45596, 49243}, {45597, 49242}

X(49412) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: 2nd Fuhrmann, K798e
X(49412) = X(79)-of-anti-Lucas(+1) homothetic triangle


X(49413) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO HATZIPOLAKIS-MOSES

Barycentrics    -(a^20-13*(b^2+c^2)*a^18+(37*b^4+67*b^2*c^2+37*c^4)*a^16-10*(b^2+c^2)*(3*b^4+5*b^2*c^2+3*c^4)*a^14-(20*b^4-27*b^2*c^2+20*c^4)*(b^2+c^2)^2*a^12+8*(b^2+c^2)*(5*b^8+5*c^8+2*b^2*c^2*(b^4-b^2*c^2+c^4))*a^10-3*(b^2-c^2)^2*(4*b^8+4*c^8+3*b^2*c^2*(5*b^4+6*b^2*c^2+5*c^4))*a^8-2*(b^6-c^6)*(b^2-c^2)^2*(b^4-c^4)*a^6-(b^2-c^2)^2*(5*b^12+5*c^12-(11*b^8+11*c^8+13*b^2*c^2*(b^2+c^2)^2)*b^2*c^2)*a^4+(b^4-c^4)*(b^2-c^2)^3*(5*b^8+5*c^8-2*b^2*c^2*(8*b^4+5*b^2*c^2+8*c^4))*a^2-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^6*(b^2+c^2)^2)*S+2*a^22-10*(b^2+c^2)*a^20+(17*b^4+20*b^2*c^2+17*c^4)*a^18-5*(b^2+c^2)*(b^4-4*b^2*c^2+c^4)*a^16-2*(10*b^8+10*c^8+b^2*c^2*(23*b^4+38*b^2*c^2+23*c^4))*a^14+2*(b^2+c^2)*(b^4+c^4)*(14*b^4-17*b^2*c^2+14*c^4)*a^12-2*(7*b^12+7*c^12-(25*b^8+25*c^8+b^2*c^2*(11*b^4-10*b^2*c^2+11*c^4))*b^2*c^2)*a^10-2*(b^6-c^6)*(b^4-c^4)*(b^4+10*b^2*c^2+c^4)*a^8+2*(b^4-c^4)^2*(5*b^8+5*c^8-b^2*c^2*(5*b^4-12*b^2*c^2+5*c^4))*a^6-2*(b^8-c^8)*a^4*(b^2-c^2)^3*(5*b^4+7*b^2*c^2+5*c^4)+(5*b^4+6*b^2*c^2+5*c^4)*(b^2+c^2)^2*(b^2-c^2)^6*a^2-(b^2+c^2)^3*(b^2-c^2)^8 : :

The reciprocal orthologic center of these triangles is X(6146).

X(49413) lies on these lines: {494, 6145}, {1154, 49393}, {5491, 32391}, {6464, 49414}, {10628, 49391}, {18400, 49377}, {18523, 48669}, {26293, 32330}, {26299, 32356}, {26305, 32357}, {26313, 32362}, {26323, 32363}, {26329, 32369}, {26338, 32374}, {26354, 32390}, {26368, 32331}, {26374, 32332}, {26392, 48505}, {26416, 48506}, {26428, 32335}, {26434, 32336}, {26440, 32337}, {26443, 32371}, {26448, 32372}, {26455, 32342}, {26461, 32343}, {26467, 32379}, {26472, 32383}, {26478, 32382}, {26484, 32381}, {26489, 32380}, {26502, 32347}, {26503, 32354}, {26504, 32394}, {26505, 49072}, {26506, 49073}, {26507, 49108}, {26508, 49179}, {26509, 49180}, {26510, 32406}, {26511, 32405}, {32360, 45588}, {32361, 45590}, {32364, 45592}, {32373, 45594}, {32388, 45604}, {32399, 45605}, {32400, 45608}, {32402, 45609}, {32403, 45611}, {32404, 45613}, {35858, 45599}, {35859, 45602}, {45412, 49341}, {45414, 49342}, {45516, 48758}, {45518, 48759}, {45595, 49244}, {45598, 49245}

X(49413) = orthologic center (anti-Lucas(-1) homothetic, Hatzipolakis-Moses)
X(49413) = X(6145)-of-anti-Lucas(-1) homothetic triangle


X(49414) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO HATZIPOLAKIS-MOSES

Barycentrics    (a^20-13*(b^2+c^2)*a^18+(37*b^4+67*b^2*c^2+37*c^4)*a^16-10*(b^2+c^2)*(3*b^4+5*b^2*c^2+3*c^4)*a^14-(20*b^4-27*b^2*c^2+20*c^4)*(b^2+c^2)^2*a^12+8*(b^2+c^2)*(5*b^8+5*c^8+2*b^2*c^2*(b^4-b^2*c^2+c^4))*a^10-3*(b^2-c^2)^2*(4*b^8+4*c^8+3*b^2*c^2*(5*b^4+6*b^2*c^2+5*c^4))*a^8-2*(b^6-c^6)*(b^2-c^2)^2*(b^4-c^4)*a^6-(b^2-c^2)^2*(5*b^12+5*c^12-(11*b^8+11*c^8+13*b^2*c^2*(b^2+c^2)^2)*b^2*c^2)*a^4+(b^4-c^4)*(b^2-c^2)^3*(5*b^8+5*c^8-2*b^2*c^2*(8*b^4+5*b^2*c^2+8*c^4))*a^2-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^6*(b^2+c^2)^2)*S+2*a^22-10*(b^2+c^2)*a^20+(17*b^4+20*b^2*c^2+17*c^4)*a^18-5*(b^2+c^2)*(b^4-4*b^2*c^2+c^4)*a^16-2*(10*b^8+10*c^8+b^2*c^2*(23*b^4+38*b^2*c^2+23*c^4))*a^14+2*(b^2+c^2)*(b^4+c^4)*(14*b^4-17*b^2*c^2+14*c^4)*a^12-2*(7*b^12+7*c^12-(25*b^8+25*c^8+b^2*c^2*(11*b^4-10*b^2*c^2+11*c^4))*b^2*c^2)*a^10-2*(b^6-c^6)*(b^4-c^4)*(b^4+10*b^2*c^2+c^4)*a^8+2*(b^4-c^4)^2*(5*b^8+5*c^8-b^2*c^2*(5*b^4-12*b^2*c^2+5*c^4))*a^6-2*(b^8-c^8)*a^4*(b^2-c^2)^3*(5*b^4+7*b^2*c^2+5*c^4)+(5*b^4+6*b^2*c^2+5*c^4)*(b^2+c^2)^2*(b^2-c^2)^6*a^2-(b^2+c^2)^3*(b^2-c^2)^8 : :

The reciprocal orthologic center of these triangles is X(6146).

X(49414) lies on these lines: {493, 6145}, {1154, 49394}, {5490, 32391}, {6464, 49413}, {10628, 49392}, {18400, 49378}, {18521, 48669}, {26292, 32330}, {26298, 32356}, {26304, 32357}, {26312, 32362}, {26322, 32363}, {26328, 32369}, {26337, 32373}, {26347, 32374}, {26353, 32390}, {26367, 32331}, {26373, 32332}, {26391, 48505}, {26415, 48506}, {26427, 32335}, {26433, 32336}, {26439, 32337}, {26442, 32371}, {26447, 32372}, {26454, 32342}, {26460, 32343}, {26466, 32379}, {26471, 32383}, {26477, 32382}, {26483, 32381}, {26488, 32380}, {26493, 32347}, {26494, 32354}, {26495, 32394}, {26496, 49072}, {26497, 49073}, {26498, 49108}, {26499, 49179}, {26500, 49180}, {26501, 32406}, {32360, 45589}, {32361, 45591}, {32364, 45593}, {32389, 45603}, {32399, 45607}, {32400, 45606}, {32402, 45610}, {32403, 45612}, {32404, 45614}, {32405, 45615}, {35858, 45601}, {35859, 45600}, {45413, 49342}, {45415, 49341}, {45517, 48759}, {45519, 48758}, {45596, 49245}, {45597, 49244}

X(49414) = orthologic center (anti-Lucas(+1) homothetic, Hatzipolakis-Moses)
X(49414) = X(6145)-of-anti-Lucas(+1) homothetic triangle


X(49415) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 3rd HATZIPOLAKIS

Barycentrics    -(a^20-13*(b^2+c^2)*a^18+(37*b^4+75*b^2*c^2+37*c^4)*a^16-2*(b^2+c^2)*(15*b^4+71*b^2*c^2+15*c^4)*a^14-(20*b^8+20*c^8-b^2*c^2*(159*b^4+326*b^2*c^2+159*c^4))*a^12+8*(b^2+c^2)*(5*b^8+5*c^8-4*b^2*c^2*(b^4+8*b^2*c^2+c^4))*a^10-(12*b^12+12*c^12+(101*b^8+101*c^8-2*b^2*c^2*(52*b^4+105*b^2*c^2+52*c^4))*b^2*c^2)*a^8-2*(b^4-c^4)*(b^2-c^2)*(b^8+c^8-b^2*c^2*(11*b^4+36*b^2*c^2+11*c^4))*a^6-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^4*(5*b^4+b^2*c^2+5*c^4)*a^4+(b^2-c^2)^6*(b^2+c^2)*(5*b^4-14*b^2*c^2+5*c^4)*a^2-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^6*(b^2+c^2)^2)*S+2*a^22-10*(b^2+c^2)*a^20+(17*b^4+36*b^2*c^2+17*c^4)*a^18-5*(b^2+c^2)*(b^4+8*b^2*c^2+c^4)*a^16-2*(10*b^8+10*c^8-b^2*c^2*(13*b^4-10*b^2*c^2+13*c^4))*a^14+2*(b^2+c^2)*(14*b^8+14*c^8-b^2*c^2*(23*b^4-72*b^2*c^2+23*c^4))*a^12-2*(7*b^12+7*c^12-(5*b^8+5*c^8+b^2*c^2*(11*b^4-146*b^2*c^2+11*c^4))*b^2*c^2)*a^10-2*(b^2+c^2)*(b^12+c^12-(13*b^8+13*c^8-b^2*c^2*(87*b^4-182*b^2*c^2+87*c^4))*b^2*c^2)*a^8+2*(b^2-c^2)^2*(5*b^12+5*c^12-(15*b^8+15*c^8-b^2*c^2*(19*b^4+46*b^2*c^2+19*c^4))*b^2*c^2)*a^6-2*(b^6-c^6)*(b^2-c^2)^2*(b^4-c^4)*(5*b^4-12*b^2*c^2+5*c^4)*a^4+(5*b^4-2*b^2*c^2+5*c^4)*(b^2+c^2)^2*(b^2-c^2)^6*a^2-(b^2+c^2)^3*(b^2-c^2)^8 : :

The reciprocal orthologic center of these triangles is X(12241).

X(49415) lies on these lines: {494, 22466}, {5491, 22966}, {6464, 49416}, {18523, 48670}, {18978, 26434}, {19083, 26455}, {19084, 26461}, {22476, 26368}, {22483, 26374}, {22524, 26428}, {22533, 26440}, {22559, 26502}, {22647, 26503}, {22653, 26299}, {22658, 26305}, {22671, 45588}, {22675, 45590}, {22747, 26313}, {22776, 26323}, {22800, 45592}, {22833, 26329}, {22941, 26443}, {22943, 26448}, {22945, 45594}, {22947, 26338}, {22951, 26293}, {22955, 26467}, {22956, 26489}, {22957, 26484}, {22958, 26478}, {22959, 26472}, {22963, 45604}, {22965, 26354}, {22969, 26504}, {22976, 45605}, {22977, 45608}, {22979, 45609}, {22980, 45611}, {22981, 45613}, {22982, 26511}, {22983, 26510}, {26392, 48507}, {26416, 48508}, {26505, 49074}, {26506, 49075}, {26507, 49109}, {26508, 49181}, {26509, 49182}, {35860, 45599}, {35861, 45602}, {45412, 49343}, {45414, 49344}, {45516, 48810}, {45518, 48811}, {45595, 49246}, {45598, 49247}

X(49415) = orthologic center (anti-Lucas(-1) homothetic, 3rd Hatzipolakis)
X(49415) = X(22466)-of-anti-Lucas(-1) homothetic triangle


X(49416) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 3rd HATZIPOLAKIS

Barycentrics    (a^20-13*(b^2+c^2)*a^18+(37*b^4+75*b^2*c^2+37*c^4)*a^16-2*(b^2+c^2)*(15*b^4+71*b^2*c^2+15*c^4)*a^14-(20*b^8+20*c^8-b^2*c^2*(159*b^4+326*b^2*c^2+159*c^4))*a^12+8*(b^2+c^2)*(5*b^8+5*c^8-4*b^2*c^2*(b^4+8*b^2*c^2+c^4))*a^10-(12*b^12+12*c^12+(101*b^8+101*c^8-2*b^2*c^2*(52*b^4+105*b^2*c^2+52*c^4))*b^2*c^2)*a^8-2*(b^4-c^4)*(b^2-c^2)*(b^8+c^8-b^2*c^2*(11*b^4+36*b^2*c^2+11*c^4))*a^6-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^4*(5*b^4+b^2*c^2+5*c^4)*a^4+(b^2-c^2)^6*(b^2+c^2)*(5*b^4-14*b^2*c^2+5*c^4)*a^2-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^6*(b^2+c^2)^2)*S+2*a^22-10*(b^2+c^2)*a^20+(17*b^4+36*b^2*c^2+17*c^4)*a^18-5*(b^2+c^2)*(b^4+8*b^2*c^2+c^4)*a^16-2*(10*b^8+10*c^8-b^2*c^2*(13*b^4-10*b^2*c^2+13*c^4))*a^14+2*(b^2+c^2)*(14*b^8+14*c^8-b^2*c^2*(23*b^4-72*b^2*c^2+23*c^4))*a^12-2*(7*b^12+7*c^12-(5*b^8+5*c^8+b^2*c^2*(11*b^4-146*b^2*c^2+11*c^4))*b^2*c^2)*a^10-2*(b^2+c^2)*(b^12+c^12-(13*b^8+13*c^8-b^2*c^2*(87*b^4-182*b^2*c^2+87*c^4))*b^2*c^2)*a^8+2*(b^2-c^2)^2*(5*b^12+5*c^12-(15*b^8+15*c^8-b^2*c^2*(19*b^4+46*b^2*c^2+19*c^4))*b^2*c^2)*a^6-2*(b^6-c^6)*(b^2-c^2)^2*(b^4-c^4)*(5*b^4-12*b^2*c^2+5*c^4)*a^4+(5*b^4-2*b^2*c^2+5*c^4)*(b^2+c^2)^2*(b^2-c^2)^6*a^2-(b^2+c^2)^3*(b^2-c^2)^8 : :

The reciprocal orthologic center of these triangles is X(12241).

X(49416) lies on these lines: {493, 22466}, {5490, 22966}, {6464, 49415}, {18521, 48670}, {18978, 26433}, {19083, 26454}, {19084, 26460}, {22476, 26367}, {22483, 26373}, {22524, 26427}, {22533, 26439}, {22559, 26493}, {22647, 26494}, {22653, 26298}, {22658, 26304}, {22671, 45589}, {22675, 45591}, {22747, 26312}, {22776, 26322}, {22800, 45593}, {22833, 26328}, {22941, 26442}, {22943, 26447}, {22945, 26337}, {22947, 26347}, {22951, 26292}, {22955, 26466}, {22956, 26488}, {22957, 26483}, {22958, 26477}, {22959, 26471}, {22964, 45603}, {22965, 26353}, {22969, 26495}, {22976, 45607}, {22977, 45606}, {22979, 45610}, {22980, 45612}, {22981, 45614}, {22982, 45615}, {22983, 26501}, {26391, 48507}, {26415, 48508}, {26496, 49074}, {26497, 49075}, {26498, 49109}, {26499, 49181}, {26500, 49182}, {35860, 45601}, {35861, 45600}, {45413, 49344}, {45415, 49343}, {45517, 48811}, {45519, 48810}, {45596, 49247}, {45597, 49246}

X(49416) = orthologic center (anti-Lucas(+1) homothetic, 3rd Hatzipolakis)
X(49416) = X(22466)-of-anti-Lucas(+1) homothetic triangle


X(49417) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO HUTSON EXTOUCH

Barycentrics    a*(-(a^10-5*(b+c)^2*a^8-4*(b+c)*(b^2+c^2)*a^7+2*(5*b^4+5*c^4+4*b*c*(b+2*c)*(2*b+c))*a^6+4*(b+c)*(b^2+c^2)*(3*b^2-2*b*c+3*c^2)*a^5-2*(5*b^6+5*c^6-(14*b^4+14*c^4-b*c*(29*b^2-72*b*c+29*c^2))*b*c)*a^4-4*(b+c)*(b^2+c^2)*(3*b^4+3*c^4-2*b*c*(2*b^2+15*b*c+2*c^2))*a^3+(5*b^8+5*c^8-2*(16*b^6+16*c^6-(8*b^4+8*c^4-b*c*(8*b^2+101*b*c+8*c^2))*b*c)*b*c)*a^2+4*(b^4-c^4)*(b^2-c^2)^2*(b-c)*a+(b^2-c^2)^2*(b+c)^2*(4*b^2*c^2-(b^2-c^2)^2))*S+(b+c)*a^11+(b^2+4*b*c+c^2)*a^10-(b+c)*(5*b^2-2*b*c+5*c^2)*a^9-(b^2+c^2)*(5*b^2+34*b*c+5*c^2)*a^8+2*(b+c)*(5*b^4+5*c^4-4*b*c*(b^2+3*b*c+c^2))*a^7+2*(5*b^6+5*c^6+(40*b^4+40*c^4+b*c*(27*b^2+40*b*c+27*c^2))*b*c)*a^6-2*(b+c)*(5*b^6+5*c^6-(6*b^4+6*c^4+35*b*c*(b^2+c^2))*b*c)*a^5-2*(5*b^6+5*c^6+(38*b^4+38*c^4+5*b*c*(7*b^2-12*b*c+7*c^2))*b*c)*(b^2+c^2)*a^4+(b+c)*(5*b^8+5*c^8-2*(4*b^6+4*c^6+(24*b^4+24*c^4-b*c*(12*b^2+91*b*c+12*c^2))*b*c)*b*c)*a^3+(b^2-c^2)^2*(5*b^6+5*c^6+(28*b^4+28*c^4+b*c*(43*b^2-40*b*c+43*c^2))*b*c)*a^2-(b^2-c^2)^3*(b-c)*a*(b^2-2*b*c-c^2)*(b^2+2*b*c-c^2)-(b^2-c^2)^4*(b+c)^2*(b^2+c^2)) : :

The reciprocal orthologic center of these triangles is X(40).

X(49417) lies on these lines: {494, 7160}, {5491, 12864}, {6464, 49418}, {8000, 26504}, {9874, 26503}, {9898, 26299}, {10059, 45611}, {10075, 45613}, {12120, 26293}, {12139, 26374}, {12200, 26428}, {12249, 26440}, {12260, 26368}, {12333, 26502}, {12411, 26305}, {12464, 45588}, {12465, 45590}, {12500, 26313}, {12599, 26329}, {12777, 26443}, {12789, 26448}, {12801, 45594}, {12802, 26338}, {12856, 26467}, {12857, 26489}, {12858, 26484}, {12859, 26478}, {12860, 26472}, {12861, 45604}, {12863, 26354}, {12872, 45609}, {12874, 26511}, {12875, 26510}, {13914, 45605}, {13978, 45608}, {18523, 48671}, {18979, 26434}, {19085, 26455}, {19086, 26461}, {22777, 26323}, {22801, 45592}, {26392, 48509}, {26416, 48510}, {26505, 49076}, {26506, 49077}, {26507, 49110}, {26508, 49183}, {26509, 49184}, {35862, 45599}, {35863, 45602}, {45412, 49345}, {45414, 49346}, {45516, 48812}, {45518, 48813}, {45595, 49248}, {45598, 49249}

X(49417) = orthologic center (anti-Lucas(-1) homothetic, Hutson extouch)
X(49417) = X(7160)-of-anti-Lucas(-1) homothetic triangle


X(49418) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO HUTSON EXTOUCH

Barycentrics    a*((a^10-5*(b+c)^2*a^8-4*(b+c)*(b^2+c^2)*a^7+2*(5*b^4+5*c^4+4*b*c*(b+2*c)*(2*b+c))*a^6+4*(b+c)*(b^2+c^2)*(3*b^2-2*b*c+3*c^2)*a^5-2*(5*b^6+5*c^6-(14*b^4+14*c^4-b*c*(29*b^2-72*b*c+29*c^2))*b*c)*a^4-4*(b+c)*(b^2+c^2)*(3*b^4+3*c^4-2*b*c*(2*b^2+15*b*c+2*c^2))*a^3+(5*b^8+5*c^8-2*(16*b^6+16*c^6-(8*b^4+8*c^4-b*c*(8*b^2+101*b*c+8*c^2))*b*c)*b*c)*a^2+4*(b^4-c^4)*(b^2-c^2)^2*(b-c)*a+(b^2-c^2)^2*(b+c)^2*(4*b^2*c^2-(b^2-c^2)^2))*S+(b+c)*a^11+(b^2+4*b*c+c^2)*a^10-(b+c)*(5*b^2-2*b*c+5*c^2)*a^9-(b^2+c^2)*(5*b^2+34*b*c+5*c^2)*a^8+2*(b+c)*(5*b^4+5*c^4-4*b*c*(b^2+3*b*c+c^2))*a^7+2*(5*b^6+5*c^6+(40*b^4+40*c^4+b*c*(27*b^2+40*b*c+27*c^2))*b*c)*a^6-2*(b+c)*(5*b^6+5*c^6-(6*b^4+6*c^4+35*b*c*(b^2+c^2))*b*c)*a^5-2*(5*b^6+5*c^6+(38*b^4+38*c^4+5*b*c*(7*b^2-12*b*c+7*c^2))*b*c)*(b^2+c^2)*a^4+(b+c)*(5*b^8+5*c^8-2*(4*b^6+4*c^6+(24*b^4+24*c^4-b*c*(12*b^2+91*b*c+12*c^2))*b*c)*b*c)*a^3+(b^2-c^2)^2*(5*b^6+5*c^6+(28*b^4+28*c^4+b*c*(43*b^2-40*b*c+43*c^2))*b*c)*a^2-(b^2-c^2)^3*(b-c)*a*(b^2-2*b*c-c^2)*(b^2+2*b*c-c^2)-(b^2-c^2)^4*(b+c)^2*(b^2+c^2)) : :

The reciprocal orthologic center of these triangles is X(40).

X(49418) lies on these lines: {493, 7160}, {5490, 12864}, {6464, 49417}, {8000, 26495}, {9874, 26494}, {9898, 26298}, {10059, 45612}, {10075, 45614}, {12120, 26292}, {12139, 26373}, {12200, 26427}, {12249, 26439}, {12260, 26367}, {12333, 26493}, {12411, 26304}, {12464, 45589}, {12465, 45591}, {12500, 26312}, {12599, 26328}, {12777, 26442}, {12789, 26447}, {12801, 26337}, {12802, 26347}, {12856, 26466}, {12857, 26488}, {12858, 26483}, {12859, 26477}, {12860, 26471}, {12862, 45603}, {12863, 26353}, {12872, 45610}, {12874, 45615}, {12875, 26501}, {13914, 45607}, {13978, 45606}, {18521, 48671}, {18979, 26433}, {19085, 26454}, {19086, 26460}, {22777, 26322}, {22801, 45593}, {26391, 48509}, {26415, 48510}, {26496, 49076}, {26497, 49077}, {26498, 49110}, {26499, 49183}, {26500, 49184}, {35862, 45601}, {35863, 45600}, {45413, 49346}, {45415, 49345}, {45517, 48813}, {45519, 48812}, {45596, 49249}, {45597, 49248}

X(49418) = orthologic center (anti-Lucas(+1) homothetic, Hutson extouch)
X(49418) = X(7160)-of-anti-Lucas(+1) homothetic triangle


X(49419) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 1st JENKINS

Barycentrics    ((b+c)*a^4+8*(b^2+c^2)*a^3+2*(b+c)*(b^2+c^2)*a^2+(-4*b^2*c^2+(b^2-c^2)^2)*(b+c))*S+2*a^7+(b+c)*a^6-4*(b^2+c^2)*a^5-3*(b+c)*(b^2+c^2)*a^4+2*(-4*b^2*c^2+(b^2-c^2)^2)*a^3+(b+c)*(3*b^4-2*b^2*c^2+3*c^4)*a^2-(b^4-c^4)*(b^2-c^2)*(b+c) : :
X(49419) = 3*X(45698)-X(45717) = 3*X(45698)+X(49401)

The reciprocal orthologic center of these triangles is X(10).

X(49419) lies on these lines: {1, 26503}, {8, 26299}, {10, 494}, {40, 26440}, {226, 26478}, {355, 45609}, {515, 49377}, {516, 48469}, {517, 49427}, {519, 45698}, {726, 49423}, {946, 26467}, {950, 26354}, {1125, 5491}, {1210, 45613}, {2784, 49379}, {2796, 49381}, {3244, 26504}, {4297, 26293}, {5847, 45726}, {6464, 49420}, {6684, 26507}, {8666, 26323}, {8715, 26502}, {10106, 26434}, {10915, 26509}, {10916, 26508}, {12053, 26472}, {12699, 18523}, {13883, 45595}, {13936, 45598}, {17766, 49425}, {18483, 45592}, {19925, 26329}, {21077, 26484}, {26392, 48511}, {26416, 48512}, {26505, 49078}, {26506, 49079}, {31397, 45611}, {45412, 49347}, {45414, 49348}, {45516, 48814}, {45518, 48815}, {48708, 49409}

X(49419) = midpoint of X(i) and X(j) for these {i, j}: {45717, 49401}, {48469, 49395}, {48708, 49409}
X(49419) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: 1st Jenkins, 1st Savin
X(49419) = X(10)-of-anti-Lucas(-1) homothetic triangle
X(49419) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (494, 26443, 10), (5491, 26368, 1125), (45698, 49401, 45717)


X(49420) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 1st JENKINS

Barycentrics    -((b+c)*a^4+8*(b^2+c^2)*a^3+2*(b+c)*(b^2+c^2)*a^2+((b^2-c^2)^2-4*b^2*c^2)*(b+c))*S+2*a^7+(b+c)*a^6-4*(b^2+c^2)*a^5-3*(b+c)*(b^2+c^2)*a^4+2*((b^2-c^2)^2-4*b^2*c^2)*a^3+(b+c)*(3*b^4-2*b^2*c^2+3*c^4)*a^2-(b^4-c^4)*(b^2-c^2)*(b+c) : :
X(49420) = 3*X(45699)-X(45718) = 3*X(45699)+X(49402)

The reciprocal orthologic center of these triangles is X(10).

X(49420) lies on these lines: {1, 26494}, {8, 26298}, {10, 493}, {40, 26439}, {226, 26477}, {355, 45610}, {515, 49378}, {516, 48468}, {517, 49428}, {519, 45699}, {726, 49424}, {946, 26466}, {950, 26353}, {1125, 5490}, {1210, 45614}, {2784, 49380}, {2796, 49382}, {3244, 26495}, {4297, 26292}, {5847, 45727}, {6464, 49419}, {6684, 26498}, {8666, 26322}, {8715, 26493}, {10106, 26433}, {10915, 26500}, {10916, 26499}, {12053, 26471}, {12699, 18521}, {13883, 45597}, {13936, 45596}, {17766, 49426}, {18483, 45593}, {19925, 26328}, {21077, 26483}, {26391, 48511}, {26415, 48512}, {26496, 49078}, {26497, 49079}, {31397, 45612}, {45413, 49348}, {45415, 49347}, {45517, 48815}, {45519, 48814}, {48707, 49410}

X(49420) = midpoint of X(i) and X(j) for these {i, j}: {45718, 49402}, {48468, 49396}, {48707, 49410}
X(49420) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: 1st Jenkins, 1st Savin
X(49420) = X(10)-of-anti-Lucas(+1) homothetic triangle
X(49420) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (493, 26442, 10), (5490, 26367, 1125), (45699, 49402, 45718)


X(49421) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO MIDHEIGHT

Barycentrics    a^2*(-(a^12-2*(b^2+c^2)*a^10-(17*b^4+18*b^2*c^2+17*c^4)*a^8+4*(b^2+c^2)*(13*b^4-18*b^2*c^2+13*c^4)*a^6-(b^2-c^2)^2*(49*b^4+54*b^2*c^2+49*c^4)*a^4+2*(b^4-c^4)*(b^2-c^2)*(7*b^4+2*b^2*c^2+7*c^4)*a^2+(b^2-c^2)^2*(b^4+c^4+2*(b^2+3*b*c-c^2)*b*c)*(b^4+c^4-2*(b^2-3*b*c-c^2)*b*c))*S+4*(b^2+c^2)*a^12-8*(2*b^4+b^2*c^2+2*c^4)*a^10+4*(b^2+c^2)*(5*b^4-9*b^2*c^2+5*c^4)*a^8+16*(3*b^4-4*b^2*c^2+3*c^4)*b^2*c^2*a^6-4*(b^4-c^4)*(b^2-c^2)*(5*b^4+12*b^2*c^2+5*c^4)*a^4+8*(b^2-c^2)^2*(2*b^8+2*c^8+b^2*c^2*(3*b^2+c^2)*(b^2+3*c^2))*a^2-(b^4-c^4)*(b^2-c^2)^3*(4*b^4+4*b^2*c^2+4*c^4)) : :

The reciprocal orthologic center of these triangles is X(4).

X(49421) lies on these lines: {30, 49393}, {64, 494}, {1498, 26293}, {2777, 49391}, {2883, 5491}, {3357, 26507}, {5878, 26467}, {6000, 49377}, {6001, 49395}, {6225, 26503}, {6247, 26329}, {6266, 26338}, {6267, 45594}, {6285, 26434}, {6464, 49422}, {7355, 26354}, {7973, 26504}, {8946, 15811}, {8991, 45605}, {9899, 26299}, {9914, 26305}, {10060, 45611}, {10076, 45613}, {11381, 26374}, {12202, 26428}, {12250, 26440}, {12262, 26368}, {12335, 26502}, {12468, 45588}, {12469, 45590}, {12502, 26313}, {12779, 26443}, {12791, 26448}, {12920, 26489}, {12930, 26484}, {12940, 26478}, {12950, 26472}, {12986, 45604}, {13093, 45609}, {13094, 26511}, {13095, 26510}, {13980, 45608}, {15311, 48469}, {18523, 48672}, {19087, 26455}, {19088, 26461}, {22778, 26323}, {22802, 45592}, {26392, 48513}, {26416, 48514}, {26505, 49080}, {26506, 49081}, {26508, 49185}, {26509, 49186}, {34146, 45726}, {35864, 45599}, {35865, 45602}, {36201, 49437}, {45412, 49349}, {45414, 49350}, {45516, 48816}, {45518, 48817}, {45595, 49250}, {45598, 49251}

X(49421) = orthologic center (anti-Lucas(-1) homothetic, midheight)
X(49421) = X(64)-of-anti-Lucas(-1) homothetic triangle


X(49422) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO MIDHEIGHT

Barycentrics    a^2*((a^12-2*(b^2+c^2)*a^10-(17*b^4+18*b^2*c^2+17*c^4)*a^8+4*(b^2+c^2)*(13*b^4-18*b^2*c^2+13*c^4)*a^6-(b^2-c^2)^2*(49*b^4+54*b^2*c^2+49*c^4)*a^4+2*(b^4-c^4)*(b^2-c^2)*(7*b^4+2*b^2*c^2+7*c^4)*a^2+(b^2-c^2)^2*(b^4+c^4+2*(b^2+3*b*c-c^2)*b*c)*(b^4+c^4-2*(b^2-3*b*c-c^2)*b*c))*S+4*(b^2+c^2)*a^12-8*(2*b^4+b^2*c^2+2*c^4)*a^10+4*(b^2+c^2)*(5*b^4-9*b^2*c^2+5*c^4)*a^8+16*(3*b^4-4*b^2*c^2+3*c^4)*b^2*c^2*a^6-4*(b^4-c^4)*(b^2-c^2)*(5*b^4+12*b^2*c^2+5*c^4)*a^4+8*(b^2-c^2)^2*(2*b^8+2*c^8+b^2*c^2*(3*b^2+c^2)*(b^2+3*c^2))*a^2-(b^4-c^4)*(b^2-c^2)^3*(4*b^4+4*b^2*c^2+4*c^4)) : :

The reciprocal orthologic center of these triangles is X(4).

X(49422) lies on these lines: {30, 49394}, {64, 493}, {1498, 26292}, {2777, 49392}, {2883, 5490}, {3357, 26498}, {5878, 26466}, {6000, 49378}, {6001, 49396}, {6225, 26494}, {6247, 26328}, {6266, 26347}, {6267, 26337}, {6285, 26433}, {6464, 49421}, {7355, 26353}, {7973, 26495}, {8948, 15811}, {8991, 45607}, {9899, 26298}, {9914, 26304}, {10060, 45612}, {10076, 45614}, {11381, 26373}, {12202, 26427}, {12250, 26439}, {12262, 26367}, {12335, 26493}, {12468, 45589}, {12469, 45591}, {12502, 26312}, {12779, 26442}, {12791, 26447}, {12920, 26488}, {12930, 26483}, {12940, 26477}, {12950, 26471}, {12987, 45603}, {13093, 45610}, {13094, 45615}, {13095, 26501}, {13980, 45606}, {15311, 48468}, {18521, 48672}, {19087, 26454}, {19088, 26460}, {22778, 26322}, {22802, 45593}, {26391, 48513}, {26415, 48514}, {26496, 49080}, {26497, 49081}, {26499, 49185}, {26500, 49186}, {34146, 45727}, {35864, 45601}, {35865, 45600}, {36201, 49438}, {45413, 49350}, {45415, 49349}, {45517, 48817}, {45519, 48816}, {45596, 49251}, {45597, 49250}

X(49422) = orthologic center (anti-Lucas(+1) homothetic, midheight)
X(49422) = X(64)-of-anti-Lucas(+1) homothetic triangle


X(49423) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 1st NEUBERG

Barycentrics    ((4*b^4+9*b^2*c^2+4*c^4)*a^4-2*(b^2+c^2)*b^2*c^2*a^2+((b^2-c^2)^2-4*b^2*c^2)*b^2*c^2)*S+(b^2+c^2)*(a^8-2*(b^2+c^2)*a^6+(b^2+3*b*c+c^2)*(b^2-3*b*c+c^2)*a^4+2*(b^2+c^2)*b^2*c^2*a^2-(b^2-c^2)^2*b^2*c^2) : :
X(49423) = 3*X(49399)-4*X(49427)

The reciprocal orthologic center of these triangles is X(3).

X(49423) lies on these lines: {39, 5491}, {76, 494}, {194, 26503}, {384, 26428}, {511, 48469}, {538, 45698}, {726, 49419}, {730, 45717}, {732, 45726}, {2782, 49377}, {3095, 26467}, {5969, 49381}, {6248, 26329}, {6272, 26338}, {6273, 45594}, {6464, 49424}, {7976, 26504}, {8992, 45605}, {9902, 26299}, {9917, 26305}, {9983, 26313}, {10063, 45611}, {10079, 45613}, {11257, 26293}, {12143, 26374}, {12251, 26440}, {12263, 26368}, {12338, 26502}, {12474, 45588}, {12475, 45590}, {12782, 26443}, {12794, 26448}, {12836, 26472}, {12837, 26478}, {12923, 26489}, {12933, 26484}, {12992, 45604}, {13077, 26354}, {13108, 45609}, {13109, 26511}, {13110, 26510}, {13983, 45608}, {14839, 49401}, {14881, 45592}, {18523, 48673}, {18982, 26434}, {19089, 26455}, {19090, 26461}, {22779, 26323}, {26392, 48515}, {26416, 48516}, {26505, 49082}, {26506, 49083}, {26507, 49111}, {26508, 49187}, {26509, 49188}, {32515, 49399}, {35866, 45599}, {35867, 45602}, {45412, 49351}, {45414, 49352}, {45516, 48818}, {45518, 48819}, {45595, 49252}, {45598, 49253}

X(49423) = orthologic center (anti-Lucas(-1) homothetic, 1st Neuberg)
X(49423) = X(76)-of-anti-Lucas(-1) homothetic triangle


X(49424) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 1st NEUBERG

Barycentrics    -((4*b^4+9*b^2*c^2+4*c^4)*a^4-2*(b^2+c^2)*b^2*c^2*a^2+((b^2-c^2)^2-4*b^2*c^2)*b^2*c^2)*S+(b^2+c^2)*(a^8-2*(b^2+c^2)*a^6+(b^2+3*b*c+c^2)*(b^2-3*b*c+c^2)*a^4+2*(b^2+c^2)*b^2*c^2*a^2-(b^2-c^2)^2*b^2*c^2) : :
X(49424) = 3*X(49400)-4*X(49428)

The reciprocal orthologic center of these triangles is X(3).

X(49424) lies on these lines: {39, 5490}, {76, 493}, {194, 26494}, {384, 26427}, {511, 48468}, {538, 45699}, {726, 49420}, {730, 45718}, {732, 45727}, {2782, 49378}, {3095, 26466}, {5969, 49382}, {6248, 26328}, {6272, 26347}, {6273, 26337}, {6464, 49423}, {7976, 26495}, {8992, 45607}, {9902, 26298}, {9917, 26304}, {9983, 26312}, {10063, 45612}, {10079, 45614}, {11257, 26292}, {12143, 26373}, {12251, 26439}, {12263, 26367}, {12338, 26493}, {12474, 45589}, {12475, 45591}, {12782, 26442}, {12794, 26447}, {12836, 26471}, {12837, 26477}, {12923, 26488}, {12933, 26483}, {12993, 45603}, {13077, 26353}, {13108, 45610}, {13109, 45615}, {13110, 26501}, {13983, 45606}, {14839, 49402}, {14881, 45593}, {18521, 48673}, {18982, 26433}, {19089, 26454}, {19090, 26460}, {22779, 26322}, {26391, 48515}, {26415, 48516}, {26496, 49082}, {26497, 49083}, {26498, 49111}, {26499, 49187}, {26500, 49188}, {32515, 49400}, {35866, 45601}, {35867, 45600}, {45413, 49352}, {45415, 49351}, {45517, 48819}, {45519, 48818}, {45596, 49253}, {45597, 49252}

X(49424) = orthologic center (anti-Lucas(+1) homothetic, 1st Neuberg)
X(49424) = X(76)-of-anti-Lucas(+1) homothetic triangle


X(49425) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 2nd NEUBERG

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

The reciprocal orthologic center of these triangles is X(3).

X(49425) lies on these lines: {83, 494}, {732, 45726}, {754, 45698}, {2896, 26313}, {5491, 6292}, {6249, 26329}, {6274, 26338}, {6275, 45594}, {6287, 26467}, {6464, 49426}, {7977, 26504}, {8993, 45605}, {9903, 26299}, {9918, 26305}, {10064, 45611}, {10080, 45613}, {12122, 26293}, {12144, 26374}, {12206, 26428}, {12252, 26440}, {12264, 26368}, {12339, 26502}, {12476, 45588}, {12477, 45590}, {12783, 26443}, {12795, 26448}, {12924, 26489}, {12934, 26484}, {12944, 26478}, {12954, 26472}, {12994, 45604}, {13078, 26354}, {13111, 45609}, {13112, 26511}, {13113, 26510}, {13984, 45608}, {17766, 49419}, {18523, 48674}, {18983, 26434}, {19091, 26455}, {19092, 26461}, {22780, 26323}, {22803, 45592}, {26392, 48517}, {26416, 48518}, {26505, 49084}, {26506, 49085}, {26507, 49112}, {26508, 49189}, {26509, 49190}, {29012, 48469}, {35868, 45599}, {35869, 45602}, {45412, 49353}, {45414, 49354}, {45516, 48770}, {45518, 48771}, {45595, 49254}, {45598, 49255}, {49377, 49399}, {49379, 49427}

X(49425) = orthologic center (anti-Lucas(-1) homothetic, 2nd Neuberg)
X(49425) = X(83)-of-anti-Lucas(-1) homothetic triangle


X(49426) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 2nd NEUBERG

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

The reciprocal orthologic center of these triangles is X(3).

X(49426) lies on these lines: {83, 493}, {732, 45727}, {754, 45699}, {2896, 26312}, {5490, 6292}, {6249, 26328}, {6274, 26347}, {6275, 26337}, {6287, 26466}, {6464, 49425}, {7977, 26495}, {8993, 45607}, {9903, 26298}, {9918, 26304}, {10064, 45612}, {10080, 45614}, {12122, 26292}, {12144, 26373}, {12206, 26427}, {12252, 26439}, {12264, 26367}, {12339, 26493}, {12476, 45589}, {12477, 45591}, {12783, 26442}, {12795, 26447}, {12924, 26488}, {12934, 26483}, {12944, 26477}, {12954, 26471}, {12995, 45603}, {13078, 26353}, {13111, 45610}, {13112, 45615}, {13113, 26501}, {13984, 45606}, {17766, 49420}, {18521, 48674}, {18983, 26433}, {19091, 26454}, {19092, 26460}, {22780, 26322}, {22803, 45593}, {26391, 48517}, {26415, 48518}, {26496, 49084}, {26497, 49085}, {26498, 49112}, {26499, 49189}, {26500, 49190}, {29012, 48468}, {35868, 45601}, {35869, 45600}, {45413, 49354}, {45415, 49353}, {45517, 48771}, {45519, 48770}, {45596, 49255}, {45597, 49254}, {49378, 49400}, {49380, 49428}

X(49426) = orthologic center (anti-Lucas(+1) homothetic, 2nd Neuberg)
X(49426) = X(83)-of-anti-Lucas(+1) homothetic triangle


X(49427) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO ORTHIC AXES

Barycentrics    (7*(b^2+c^2)*a^6-(9*b^4+22*b^2*c^2+9*c^4)*a^4+(b^2+c^2)^3*a^2+((b^2-c^2)^2-4*b^2*c^2)*(b^2-c^2)^2)*S+2*a^10-7*(b^2+c^2)*a^8+10*(b^4+c^4)*a^6-4*(2*b^2-c^2)*(b^2-2*c^2)*(b^2+c^2)*a^4+4*(b^2-c^2)^2*(b^4+c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(49427) = 3*X(45698)+X(48469) = 3*X(45698)-X(49377) = 3*X(49399)+X(49423)

The reciprocal orthologic center of these triangles is X(4).

X(49427) lies on these lines: {3, 26440}, {4, 18523}, {5, 494}, {26, 26305}, {30, 45698}, {140, 5491}, {355, 26299}, {495, 26478}, {496, 26472}, {517, 49419}, {546, 26329}, {550, 26293}, {952, 45717}, {1483, 26504}, {3070, 45599}, {3071, 45602}, {3564, 45726}, {5690, 26443}, {5844, 49401}, {5874, 26338}, {5875, 45594}, {5901, 26368}, {6464, 49428}, {6756, 26374}, {7583, 45595}, {7584, 45598}, {7715, 8946}, {10942, 26484}, {10943, 26489}, {13925, 45605}, {13993, 45608}, {15171, 26354}, {18990, 26434}, {19116, 26455}, {19117, 26461}, {26313, 32151}, {26323, 32153}, {26392, 48519}, {26416, 48520}, {26428, 32134}, {26448, 32162}, {26502, 32141}, {26505, 49086}, {26506, 49087}, {26510, 32214}, {26511, 32213}, {28174, 49395}, {32146, 45588}, {32147, 45590}, {32177, 45604}, {32423, 49391}, {32515, 49399}, {45412, 49355}, {45414, 49356}, {45516, 48772}, {45518, 48773}, {49373, 49405}, {49375, 49407}, {49379, 49425}

X(49427) = midpoint of X(i) and X(j) for these {i, j}: {48469, 49377}, {49391, 49441}
X(49427) = orthologic center (anti-Lucas(-1) homothetic, T) for these triangles T: orthic axes, Yiu tangents
X(49427) = X(5)-of-anti-Lucas(-1) homothetic triangle
X(49427) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (494, 26467, 5), (5491, 26507, 140), (18523, 45609, 4), (26329, 45592, 546), (26440, 26503, 3), (26472, 45613, 496), (26478, 45611, 495), (45698, 48469, 49377), (49387, 49389, 45726)


X(49428) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO ORTHIC AXES

Barycentrics    -(7*(b^2+c^2)*a^6-(9*b^4+22*b^2*c^2+9*c^4)*a^4+(b^2+c^2)^3*a^2+((b^2-c^2)^2-4*b^2*c^2)*(b^2-c^2)^2)*S+2*a^10-7*(b^2+c^2)*a^8+10*(b^4+c^4)*a^6-4*(2*b^2-c^2)*(b^2-2*c^2)*(b^2+c^2)*a^4+4*(b^2-c^2)^2*(b^4+c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(49428) = 3*X(45699)+X(48468) = 3*X(45699)-X(49378) = 3*X(49400)+X(49424)

The reciprocal orthologic center of these triangles is X(4).

X(49428) lies on these lines: {3, 26439}, {4, 18521}, {5, 493}, {26, 26304}, {30, 45699}, {140, 5490}, {355, 26298}, {495, 26477}, {496, 26471}, {517, 49420}, {546, 26328}, {550, 26292}, {952, 45718}, {1483, 26495}, {3070, 45601}, {3071, 45600}, {3564, 45727}, {5690, 26442}, {5844, 49402}, {5874, 26347}, {5875, 26337}, {5901, 26367}, {6464, 49427}, {6756, 26373}, {7583, 45597}, {7584, 45596}, {7715, 8948}, {10942, 26483}, {10943, 26488}, {13925, 45607}, {13993, 45606}, {15171, 26353}, {18990, 26433}, {19116, 26454}, {19117, 26460}, {26312, 32151}, {26322, 32153}, {26391, 48519}, {26415, 48520}, {26427, 32134}, {26447, 32162}, {26493, 32141}, {26496, 49086}, {26497, 49087}, {26501, 32214}, {28174, 49396}, {32146, 45589}, {32147, 45591}, {32178, 45603}, {32213, 45615}, {32423, 49392}, {32515, 49400}, {45413, 49356}, {45415, 49355}, {45517, 48773}, {45519, 48772}, {49374, 49406}, {49376, 49408}, {49380, 49426}

X(49428) = midpoint of X(i) and X(j) for these {i, j}: {48468, 49378}, {49392, 49442}
X(49428) = orthologic center (anti-Lucas(+1) homothetic, T) for these triangles T: orthic axes, Yiu tangents
X(49428) = X(5)-of-anti-Lucas(+1) homothetic triangle
X(49428) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (493, 26466, 5), (5490, 26498, 140), (18521, 45610, 4), (26328, 45593, 546), (26439, 26494, 3), (26471, 45614, 496), (26477, 45612, 495), (45699, 48468, 49378), (49388, 49390, 45727)


X(49429) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO REFLECTION

Barycentrics    a^2*(-(a^12-5*(b^2+c^2)*a^10+(10*b^4+9*b^2*c^2+10*c^4)*a^8-2*(b^2+c^2)*(7*b^4-3*b^2*c^2+7*c^4)*a^6+(17*b^8+17*c^8+2*b^2*c^2*(4*b^4+5*b^2*c^2+4*c^4))*a^4-(b^4-c^4)*(b^2-c^2)*(13*b^4+8*b^2*c^2+13*c^4)*a^2+(4*b^8+4*c^8-b^2*c^2*(b^2+c^2)^2)*(b^2-c^2)^2)*S+(b^2+c^2)*a^12-4*(b^2+c^2)^2*a^10+(b^2+c^2)*(5*b^4+9*b^2*c^2+5*c^4)*a^8-4*(3*b^4+4*b^2*c^2+3*c^4)*b^2*c^2*a^6-(b^2+c^2)*(b^4+c^4)*(5*b^4-22*b^2*c^2+5*c^4)*a^4+4*(b^2-c^2)^2*(b^8+c^8-b^2*c^2*(3*b^4+4*b^2*c^2+3*c^4))*a^2-(b^4-c^4)*(b^2-c^2)^3*(b^4-5*b^2*c^2+c^4)) : :

The reciprocal orthologic center of these triangles is X(4).

X(49429) lies on these lines: {54, 494}, {195, 45609}, {539, 45698}, {1154, 49377}, {1209, 5491}, {2888, 26503}, {3574, 26329}, {6276, 26338}, {6277, 45594}, {6288, 26467}, {6464, 49430}, {7691, 26293}, {7979, 26504}, {8995, 45605}, {9905, 26299}, {9920, 26305}, {9985, 26313}, {10066, 45611}, {10082, 45613}, {10610, 26507}, {10628, 49383}, {11576, 26374}, {12208, 26428}, {12254, 26440}, {12266, 26368}, {12341, 26502}, {12480, 45588}, {12481, 45590}, {12785, 26443}, {12797, 26448}, {12926, 26489}, {12936, 26484}, {12946, 26478}, {12956, 26472}, {12965, 45599}, {12971, 45602}, {12998, 45604}, {13079, 26354}, {13121, 26511}, {13122, 26510}, {13986, 45608}, {18400, 48469}, {18523, 48675}, {18984, 26434}, {19095, 26455}, {19096, 26461}, {22781, 26323}, {22804, 45592}, {26392, 48521}, {26416, 48522}, {26505, 49088}, {26506, 49089}, {26508, 49191}, {26509, 49192}, {32423, 49391}, {44668, 45726}, {45412, 49357}, {45414, 49358}, {45516, 48774}, {45518, 48775}, {45595, 49256}, {45598, 49257}

X(49429) = orthologic center (anti-Lucas(-1) homothetic, reflection)
X(49429) = X(54)-of-anti-Lucas(-1) homothetic triangle


X(49430) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO REFLECTION

Barycentrics    a^2*((a^12-5*(b^2+c^2)*a^10+(10*b^4+9*b^2*c^2+10*c^4)*a^8-2*(b^2+c^2)*(7*b^4-3*b^2*c^2+7*c^4)*a^6+(17*b^8+17*c^8+2*b^2*c^2*(4*b^4+5*b^2*c^2+4*c^4))*a^4-(b^4-c^4)*(b^2-c^2)*(13*b^4+8*b^2*c^2+13*c^4)*a^2+(4*b^8+4*c^8-b^2*c^2*(b^2+c^2)^2)*(b^2-c^2)^2)*S+(b^2+c^2)*a^12-4*(b^2+c^2)^2*a^10+(b^2+c^2)*(5*b^4+9*b^2*c^2+5*c^4)*a^8-4*(3*b^4+4*b^2*c^2+3*c^4)*b^2*c^2*a^6-(b^2+c^2)*(b^4+c^4)*(5*b^4-22*b^2*c^2+5*c^4)*a^4+4*(b^2-c^2)^2*(b^8+c^8-b^2*c^2*(3*b^4+4*b^2*c^2+3*c^4))*a^2-(b^4-c^4)*(b^2-c^2)^3*(b^4-5*b^2*c^2+c^4)) : :

The reciprocal orthologic center of these triangles is X(4).

X(49430) lies on these lines: {54, 493}, {195, 45610}, {539, 45699}, {1154, 49378}, {1209, 5490}, {2888, 26494}, {3574, 26328}, {6276, 26347}, {6277, 26337}, {6288, 26466}, {6464, 49429}, {7691, 26292}, {7979, 26495}, {8995, 45607}, {9905, 26298}, {9920, 26304}, {9985, 26312}, {10066, 45612}, {10082, 45614}, {10610, 26498}, {10628, 49384}, {11576, 26373}, {12208, 26427}, {12254, 26439}, {12266, 26367}, {12341, 26493}, {12480, 45589}, {12481, 45591}, {12785, 26442}, {12797, 26447}, {12926, 26488}, {12936, 26483}, {12946, 26477}, {12956, 26471}, {12965, 45601}, {12971, 45600}, {12999, 45603}, {13079, 26353}, {13121, 45615}, {13122, 26501}, {13986, 45606}, {18400, 48468}, {18521, 48675}, {18984, 26433}, {19095, 26454}, {19096, 26460}, {22781, 26322}, {22804, 45593}, {26391, 48521}, {26415, 48522}, {26496, 49088}, {26497, 49089}, {26499, 49191}, {26500, 49192}, {32423, 49392}, {44668, 45727}, {45413, 49358}, {45415, 49357}, {45517, 48775}, {45519, 48774}, {45596, 49257}, {45597, 49256}

X(49430) = orthologic center (anti-Lucas(+1) homothetic, reflection)
X(49430) = X(54)-of-anti-Lucas(+1) homothetic triangle


X(49431) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 1st SCHIFFLER

Barycentrics    -(a^11+(b+c)*a^10-(13*b^2-4*b*c+13*c^2)*a^9-(b+c)*(5*b^2-2*b*c+5*c^2)*a^8+(34*b^4+34*c^4-(12*b^2-49*b*c+12*c^2)*b*c)*a^7+(b+c)*(10*b^4+10*c^4-(8*b^2-7*b*c+8*c^2)*b*c)*a^6-2*(17*b^6+17*c^6+2*(b^4+c^4+(7*b^2+10*b*c+7*c^2)*b*c)*b*c)*a^5-2*(b+c)*(5*b^6+5*c^6-6*(b^4+c^4-2*b*c*(b^2+c^2))*b*c)*a^4+(13*b^8+13*c^8+(12*b^6+12*c^6-(23*b^4+23*c^4-4*(b^2+4*b*c+c^2)*b*c)*b*c)*b*c)*a^3+(b+c)*(5*b^8+5*c^8-(8*b^6+8*c^6+(17*b^4+17*c^4-4*b*c*(6*b^2-b*c+6*c^2))*b*c)*b*c)*a^2-((b^2-c^2)^2-4*b^2*c^2)*(b^2-c^2)*(b^4-c^4)*a+(b^2-c^2)^3*(b-c)*(-(b^2-c^2)^2+4*b^2*c^2))*S+2*a^13-9*(b^2+c^2)*a^11+(b+c)*(b^2+c^2)*a^10+(15*b^4+15*c^4+8*b*c*(b^2+b*c+c^2))*a^9-(b+c)*(5*b^4+5*c^4-2*b*c*(b^2-b*c+c^2))*a^8-(10*b^6+10*c^6+(24*b^4+24*c^4-b*c*(23*b^2-32*b*c+23*c^2))*b*c)*a^7+(b+c)*(b^2+c^2)*(10*b^4+10*c^4-b*c*(8*b^2+5*b*c+8*c^2))*a^6+8*(3*b^6+3*c^6-(4*b^4+4*c^4+b*c*(b+c)^2)*b*c)*b*c*a^5-2*(b+c)*(5*b^8+5*c^8-(6*b^6+6*c^6-(3*b^4+3*c^4-2*b*c*(5*b^2-14*b*c+5*c^2))*b*c)*b*c)*a^4+(b^2-c^2)^2*(3*b^6+3*c^6-2*(4*b^4+4*c^4-b*c*(7*b^2+8*b*c+7*c^2))*b*c)*a^3+(b^4-c^4)*(b^2-c^2)*(b+c)*(5*b^4+5*c^4-b*c*(8*b^2-5*b*c+8*c^2))*a^2-(b^4-c^4)^2*(b^2-c^2)^2*a-(b^2-c^2)^5*(b-c)*(b^2+c^2) : :

The reciprocal orthologic center of these triangles is X(79).

X(49431) lies on these lines: {494, 10266}, {5491, 13089}, {6464, 49432}, {12146, 26374}, {12209, 26428}, {12255, 26440}, {12267, 26368}, {12342, 26502}, {12409, 26299}, {12414, 26305}, {12482, 45588}, {12483, 45590}, {12504, 26313}, {12556, 26293}, {12600, 26329}, {12786, 26443}, {12798, 26448}, {12807, 45594}, {12808, 26338}, {12849, 26503}, {12919, 26467}, {12927, 26489}, {12937, 26484}, {12947, 26478}, {12957, 26472}, {13000, 45604}, {13080, 26354}, {13100, 26504}, {13126, 45609}, {13128, 45611}, {13129, 45613}, {13130, 26511}, {13131, 26510}, {13919, 45605}, {13987, 45608}, {18523, 48676}, {18985, 26434}, {19097, 26455}, {19098, 26461}, {22782, 26323}, {22805, 45592}, {26392, 48523}, {26416, 48524}, {26505, 49090}, {26506, 49091}, {26507, 49113}, {26508, 49193}, {26509, 49194}, {35870, 45599}, {35871, 45602}, {45412, 49359}, {45414, 49360}, {45516, 48776}, {45518, 48777}, {45595, 49258}, {45598, 49259}

X(49431) = orthologic center (anti-Lucas(-1) homothetic, 1st Schiffler)
X(49431) = X(10266)-of-anti-Lucas(-1) homothetic triangle


X(49432) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 1st SCHIFFLER

Barycentrics    (a^11+(b+c)*a^10-(13*b^2-4*b*c+13*c^2)*a^9-(b+c)*(5*b^2-2*b*c+5*c^2)*a^8+(34*b^4+34*c^4-(12*b^2-49*b*c+12*c^2)*b*c)*a^7+(b+c)*(10*b^4+10*c^4-(8*b^2-7*b*c+8*c^2)*b*c)*a^6-2*(17*b^6+17*c^6+2*(b^4+c^4+(7*b^2+10*b*c+7*c^2)*b*c)*b*c)*a^5-2*(b+c)*(5*b^6+5*c^6-6*(b^4+c^4-2*b*c*(b^2+c^2))*b*c)*a^4+(13*b^8+13*c^8+(12*b^6+12*c^6-(23*b^4+23*c^4-4*(b^2+4*b*c+c^2)*b*c)*b*c)*b*c)*a^3+(b+c)*(5*b^8+5*c^8-(8*b^6+8*c^6+(17*b^4+17*c^4-4*b*c*(6*b^2-b*c+6*c^2))*b*c)*b*c)*a^2-((b^2-c^2)^2-4*b^2*c^2)*(b^2-c^2)*(b^4-c^4)*a+(b^2-c^2)^3*(b-c)*(-(b^2-c^2)^2+4*b^2*c^2))*S+2*a^13-9*(b^2+c^2)*a^11+(b+c)*(b^2+c^2)*a^10+(15*b^4+15*c^4+8*b*c*(b^2+b*c+c^2))*a^9-(b+c)*(5*b^4+5*c^4-2*b*c*(b^2-b*c+c^2))*a^8-(10*b^6+10*c^6+(24*b^4+24*c^4-b*c*(23*b^2-32*b*c+23*c^2))*b*c)*a^7+(b+c)*(b^2+c^2)*(10*b^4+10*c^4-b*c*(8*b^2+5*b*c+8*c^2))*a^6+8*(3*b^6+3*c^6-(4*b^4+4*c^4+b*c*(b+c)^2)*b*c)*b*c*a^5-2*(b+c)*(5*b^8+5*c^8-(6*b^6+6*c^6-(3*b^4+3*c^4-2*b*c*(5*b^2-14*b*c+5*c^2))*b*c)*b*c)*a^4+(b^2-c^2)^2*(3*b^6+3*c^6-2*(4*b^4+4*c^4-b*c*(7*b^2+8*b*c+7*c^2))*b*c)*a^3+(b^4-c^4)*(b^2-c^2)*(b+c)*(5*b^4+5*c^4-b*c*(8*b^2-5*b*c+8*c^2))*a^2-(b^4-c^4)^2*(b^2-c^2)^2*a-(b^2-c^2)^5*(b-c)*(b^2+c^2) : :

The reciprocal orthologic center of these triangles is X(79).

X(49432) lies on these lines: {493, 10266}, {5490, 13089}, {6464, 49431}, {12146, 26373}, {12209, 26427}, {12255, 26439}, {12267, 26367}, {12342, 26493}, {12409, 26298}, {12414, 26304}, {12482, 45589}, {12483, 45591}, {12504, 26312}, {12556, 26292}, {12600, 26328}, {12786, 26442}, {12798, 26447}, {12807, 26337}, {12808, 26347}, {12849, 26494}, {12919, 26466}, {12927, 26488}, {12937, 26483}, {12947, 26477}, {12957, 26471}, {13001, 45603}, {13080, 26353}, {13100, 26495}, {13126, 45610}, {13128, 45612}, {13129, 45614}, {13130, 45615}, {13131, 26501}, {13919, 45607}, {13987, 45606}, {18521, 48676}, {18985, 26433}, {19097, 26454}, {19098, 26460}, {22782, 26322}, {22805, 45593}, {26391, 48523}, {26415, 48524}, {26496, 49090}, {26497, 49091}, {26498, 49113}, {26499, 49193}, {26500, 49194}, {35870, 45601}, {35871, 45600}, {45413, 49360}, {45415, 49359}, {45517, 48777}, {45519, 48776}, {45596, 49259}, {45597, 49258}

X(49432) = orthologic center (anti-Lucas(+1) homothetic, 1st Schiffler)
X(49432) = X(10266)-of-anti-Lucas(+1) homothetic triangle


X(49433) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 1st TRI-SQUARES-CENTRAL

Barycentrics    23*a^10-66*(b^2+c^2)*a^8+2*(41*b^4-20*b^2*c^2+41*c^4)*a^6-68*(b^2-c^2)^2*(b^2+c^2)*a^4+(b^2-c^2)^2*(39*b^4+38*b^2*c^2+39*c^4)*a^2-2*(4*a^8-47*(b^2+c^2)*a^6+(41*b^4+70*b^2*c^2+41*c^4)*a^4+7*(-4*b^2*c^2+(b^2-c^2)^2)*(b^2+c^2)*a^2-5*(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2)*S-10*(b^2+c^2)*(b^2-c^2)^4 : :

The reciprocal orthologic center of these triangles is X(13665).

X(49433) lies on these lines: {30, 49389}, {494, 1327}, {5491, 13701}, {6464, 49434}, {13666, 26293}, {13667, 26368}, {13668, 26374}, {13672, 26428}, {13674, 26440}, {13675, 26502}, {13678, 26503}, {13679, 26299}, {13680, 26305}, {13682, 45588}, {13683, 45590}, {13685, 26313}, {13687, 26329}, {13688, 26443}, {13689, 26448}, {13690, 45594}, {13691, 26338}, {13692, 26467}, {13693, 26489}, {13694, 26484}, {13695, 26478}, {13696, 26472}, {13697, 45604}, {13699, 26354}, {13702, 26504}, {13713, 45609}, {13714, 45611}, {13715, 45613}, {13716, 26511}, {13717, 26510}, {13920, 45605}, {13988, 45608}, {15682, 26505}, {18523, 48677}, {18986, 26434}, {19099, 26455}, {22541, 26461}, {22783, 26323}, {22806, 45592}, {26392, 48525}, {26416, 48526}, {26506, 49093}, {26507, 49114}, {26508, 49195}, {26509, 49196}, {35872, 45599}, {35873, 45602}, {45412, 49361}, {45414, 49362}, {45516, 48778}, {45518, 48780}, {45595, 49260}, {45598, 49261}, {45726, 49435}

X(49433) = orthologic center (anti-Lucas(-1) homothetic, 1st tri-squares-central)
X(49433) = X(1327)-of-anti-Lucas(-1) homothetic triangle


X(49434) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 1st TRI-SQUARES-CENTRAL

Barycentrics    17*a^10-42*(b^2+c^2)*a^8+22*(b^4-4*b^2*c^2+c^4)*a^6+4*(b^2+c^2)*(b^4+34*b^2*c^2+c^4)*a^4+(9*b^4+26*b^2*c^2+9*c^4)*(b^2-c^2)^2*a^2+2*(4*a^8-47*(b^2+c^2)*a^6+(41*b^4+70*b^2*c^2+41*c^4)*a^4+(b^2+c^2)*(7*b^4+6*b^2*c^2+7*c^4)*a^2-5*(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2)*S-10*(b^2+c^2)*(b^2-c^2)^4 : :

The reciprocal orthologic center of these triangles is X(13665).

X(49434) lies on these lines: {30, 49390}, {493, 1327}, {5490, 13701}, {6464, 49433}, {13666, 26292}, {13667, 26367}, {13668, 26373}, {13672, 26427}, {13674, 26439}, {13675, 26493}, {13678, 26494}, {13679, 26298}, {13680, 26304}, {13682, 45589}, {13683, 45591}, {13685, 26312}, {13687, 26328}, {13688, 26442}, {13689, 26447}, {13690, 26337}, {13691, 26347}, {13692, 26466}, {13693, 26488}, {13694, 26483}, {13695, 26477}, {13696, 26471}, {13698, 45603}, {13699, 26353}, {13702, 26495}, {13713, 45610}, {13714, 45612}, {13715, 45614}, {13716, 45615}, {13717, 26501}, {13920, 45607}, {13988, 45606}, {15682, 26496}, {18521, 48677}, {18986, 26433}, {19099, 26454}, {22541, 26460}, {22783, 26322}, {22806, 45593}, {26391, 48525}, {26415, 48526}, {26497, 49093}, {26498, 49114}, {26499, 49195}, {26500, 49196}, {35872, 45601}, {35873, 45600}, {45413, 49362}, {45415, 49361}, {45517, 48780}, {45519, 48778}, {45596, 49261}, {45597, 49260}, {45727, 49436}

X(49434) = orthologic center (anti-Lucas(+1) homothetic, 1st tri-squares-central)
X(49434) = X(1327)-of-anti-Lucas(+1) homothetic triangle


X(49435) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    17*a^10-42*(b^2+c^2)*a^8+22*(b^4-4*b^2*c^2+c^4)*a^6+4*(b^2+c^2)*(b^4+34*b^2*c^2+c^4)*a^4+(9*b^4+26*b^2*c^2+9*c^4)*(b^2-c^2)^2*a^2-2*(4*a^8-47*(b^2+c^2)*a^6+(41*b^4+70*b^2*c^2+41*c^4)*a^4+(b^2+c^2)*(7*b^4+6*b^2*c^2+7*c^4)*a^2-5*(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2)*S-10*(b^2+c^2)*(b^2-c^2)^4 : :

The reciprocal orthologic center of these triangles is X(13785).

X(49435) lies on these lines: {30, 49387}, {494, 1328}, {5491, 13821}, {6464, 49436}, {13786, 26293}, {13787, 26368}, {13788, 26374}, {13792, 26428}, {13794, 26440}, {13795, 26502}, {13798, 26503}, {13799, 26299}, {13800, 26305}, {13802, 45588}, {13803, 45590}, {13805, 26313}, {13807, 26329}, {13808, 26443}, {13809, 26448}, {13810, 45594}, {13811, 26338}, {13812, 26467}, {13813, 26489}, {13814, 26484}, {13815, 26478}, {13816, 26472}, {13817, 45604}, {13819, 26354}, {13822, 26504}, {13836, 45609}, {13837, 45611}, {13838, 45613}, {13839, 26511}, {13840, 26510}, {13848, 45605}, {13849, 45608}, {15682, 26506}, {18523, 48678}, {18987, 26434}, {19100, 26461}, {19101, 26455}, {22784, 26323}, {22807, 45592}, {26392, 48527}, {26416, 48528}, {26505, 49092}, {26507, 49115}, {26508, 49197}, {26509, 49198}, {35874, 45599}, {35875, 45602}, {45412, 49363}, {45414, 49364}, {45516, 48781}, {45518, 48779}, {45595, 49262}, {45598, 49263}, {45726, 49433}

X(49435) = orthologic center (anti-Lucas(-1) homothetic, 2nd tri-squares-central)


X(49436) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    23*a^10-66*(b^2+c^2)*a^8+2*(41*b^4-20*b^2*c^2+41*c^4)*a^6-68*(b^2-c^2)^2*(b^2+c^2)*a^4+(b^2-c^2)^2*(39*b^4+38*b^2*c^2+39*c^4)*a^2+2*(4*a^8-47*(b^2+c^2)*a^6+(41*b^4+70*b^2*c^2+41*c^4)*a^4+7*(-4*b^2*c^2+(b^2-c^2)^2)*(b^2+c^2)*a^2-5*(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2)*S-10*(b^2+c^2)*(b^2-c^2)^4 : :

The reciprocal orthologic center of these triangles is X(13785).

X(49436) lies on these lines: {30, 49388}, {493, 1328}, {5490, 13821}, {6464, 49435}, {13786, 26292}, {13787, 26367}, {13788, 26373}, {13792, 26427}, {13794, 26439}, {13795, 26493}, {13798, 26494}, {13799, 26298}, {13800, 26304}, {13802, 45589}, {13803, 45591}, {13805, 26312}, {13807, 26328}, {13808, 26442}, {13809, 26447}, {13810, 26337}, {13811, 26347}, {13812, 26466}, {13813, 26488}, {13814, 26483}, {13815, 26477}, {13816, 26471}, {13818, 45603}, {13819, 26353}, {13822, 26495}, {13836, 45610}, {13837, 45612}, {13838, 45614}, {13839, 45615}, {13840, 26501}, {13848, 45607}, {13849, 45606}, {15682, 26497}, {18521, 48678}, {18987, 26433}, {19100, 26460}, {19101, 26454}, {22784, 26322}, {22807, 45593}, {26391, 48527}, {26415, 48528}, {26496, 49092}, {26498, 49115}, {26499, 49197}, {26500, 49198}, {35874, 45601}, {35875, 45600}, {45413, 49364}, {45415, 49363}, {45517, 48779}, {45519, 48781}, {45596, 49263}, {45597, 49262}, {45727, 49434}

X(49436) = orthologic center (anti-Lucas(+1) homothetic, 2nd tri-squares-central)
X(49436) = X(1328)-of-anti-Lucas(+1) homothetic triangle


X(49437) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO WALSMITH

Barycentrics    -(a^12-11*(b^2+c^2)*a^10+7*(b^4+b^2*c^2+c^4)*a^8+2*(b^2+c^2)*(4*b^4-3*b^2*c^2+4*c^4)*a^6-(7*b^8+7*c^8+3*b^2*c^2*(b^4+c^4))*a^4+(b^4-c^4)*(b^2-c^2)*(3*b^4-2*b^2*c^2+3*c^4)*a^2-(-4*b^2*c^2+(b^2-c^2)^2)*(b^4-c^4)^2)*S+2*a^14-4*(b^2+c^2)*a^12-(b^4+12*b^2*c^2+c^4)*a^10+(b^2+c^2)*(7*b^4+4*b^2*c^2+7*c^4)*a^8-2*(2*b^8+2*c^8-5*(b^2-c^2)^2*b^2*c^2)*a^6-2*(b^2+c^2)*(b^8+c^8+3*(b^2-c^2)^2*b^2*c^2)*a^4+(b^4-c^4)^2*(3*b^4+2*b^2*c^2+3*c^4)*a^2-(b^4-c^4)^3*(b^2-c^2) : :

The reciprocal orthologic center of these triangles is X(125).

X(49437) lies on these lines: {67, 494}, {511, 49391}, {542, 49377}, {1503, 49383}, {2781, 48469}, {5491, 6593}, {6464, 49438}, {9970, 26467}, {11061, 26503}, {14984, 49393}, {18523, 48679}, {26293, 32233}, {26299, 32261}, {26305, 32262}, {26313, 32268}, {26323, 32270}, {26329, 32274}, {26338, 32281}, {26354, 32297}, {26368, 32238}, {26374, 32239}, {26392, 48529}, {26416, 48530}, {26428, 32242}, {26434, 32243}, {26440, 32247}, {26443, 32278}, {26448, 32279}, {26455, 32252}, {26461, 32253}, {26472, 32290}, {26478, 32289}, {26484, 32288}, {26489, 32287}, {26502, 32256}, {26504, 32298}, {26505, 49094}, {26506, 49095}, {26507, 49116}, {26508, 49199}, {26509, 49200}, {26510, 32310}, {26511, 32309}, {32265, 45588}, {32266, 45590}, {32271, 45592}, {32280, 45594}, {32295, 45604}, {32303, 45605}, {32304, 45608}, {32306, 45609}, {32307, 45611}, {32308, 45613}, {35876, 45599}, {35877, 45602}, {36201, 49421}, {45412, 49365}, {45414, 49366}, {45516, 48782}, {45518, 48783}, {45595, 49264}, {45598, 49265}

X(49437) = orthologic center (anti-Lucas(-1) homothetic, Walsmith)
X(49437) = X(67)-of-anti-Lucas(-1) homothetic triangle


X(49438) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO WALSMITH

Barycentrics    (a^12-11*(b^2+c^2)*a^10+7*(b^4+b^2*c^2+c^4)*a^8+2*(b^2+c^2)*(4*b^4-3*b^2*c^2+4*c^4)*a^6-(7*b^8+7*c^8+3*b^2*c^2*(b^4+c^4))*a^4+(b^4-c^4)*(b^2-c^2)*(3*b^4-2*b^2*c^2+3*c^4)*a^2-(-4*b^2*c^2+(b^2-c^2)^2)*(b^4-c^4)^2)*S+2*a^14-4*(b^2+c^2)*a^12-(b^4+12*b^2*c^2+c^4)*a^10+(b^2+c^2)*(7*b^4+4*b^2*c^2+7*c^4)*a^8-2*(2*b^8+2*c^8-5*(b^2-c^2)^2*b^2*c^2)*a^6-2*(b^2+c^2)*(b^8+c^8+3*(b^2-c^2)^2*b^2*c^2)*a^4+(b^4-c^4)^2*(3*b^4+2*b^2*c^2+3*c^4)*a^2-(b^4-c^4)^3*(b^2-c^2) : :

The reciprocal orthologic center of these triangles is X(125).

X(49438) lies on these lines: {67, 493}, {511, 49392}, {542, 49378}, {1503, 49384}, {2781, 48468}, {5490, 6593}, {6464, 49437}, {9970, 26466}, {11061, 26494}, {14984, 49394}, {18521, 48679}, {26292, 32233}, {26298, 32261}, {26304, 32262}, {26312, 32268}, {26322, 32270}, {26328, 32274}, {26337, 32280}, {26347, 32281}, {26353, 32297}, {26367, 32238}, {26373, 32239}, {26391, 48529}, {26415, 48530}, {26427, 32242}, {26433, 32243}, {26439, 32247}, {26442, 32278}, {26447, 32279}, {26454, 32252}, {26460, 32253}, {26471, 32290}, {26477, 32289}, {26483, 32288}, {26488, 32287}, {26493, 32256}, {26495, 32298}, {26496, 49094}, {26497, 49095}, {26498, 49116}, {26499, 49199}, {26500, 49200}, {26501, 32310}, {32265, 45589}, {32266, 45591}, {32271, 45593}, {32296, 45603}, {32303, 45607}, {32304, 45606}, {32306, 45610}, {32307, 45612}, {32308, 45614}, {32309, 45615}, {35876, 45601}, {35877, 45600}, {36201, 49422}, {45413, 49366}, {45415, 49365}, {45517, 48783}, {45519, 48782}, {45596, 49265}, {45597, 49264}

X(49438) = orthologic center (anti-Lucas(+1) homothetic, Walsmith)
X(49438) = X(67)-of-anti-Lucas(+1) homothetic triangle


X(49439) = PARALLELOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 1st ANTI-BROCARD

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

The reciprocal parallelogic center of these triangles is X(385).

X(49439) lies on the circumcircle of anti-Lucas(-1) homothetic triangle and these lines: {98, 26293}, {99, 494}, {114, 26329}, {115, 5491}, {148, 26503}, {542, 49383}, {543, 45698}, {690, 49441}, {2782, 49377}, {2783, 48689}, {2787, 48708}, {2794, 49385}, {2799, 49443}, {3023, 26354}, {3027, 26434}, {4027, 26428}, {5186, 26374}, {5969, 45726}, {6319, 45594}, {6320, 26338}, {6321, 26467}, {6464, 49440}, {7983, 26504}, {8782, 26313}, {8997, 45605}, {10086, 45611}, {10089, 45613}, {11711, 26368}, {13172, 26440}, {13173, 26502}, {13174, 26299}, {13175, 26305}, {13176, 45588}, {13177, 45590}, {13178, 26443}, {13179, 26448}, {13180, 26489}, {13181, 26484}, {13182, 26478}, {13183, 26472}, {13184, 45604}, {13188, 45609}, {13189, 26511}, {13190, 26510}, {13989, 45608}, {18523, 38733}, {19108, 26455}, {19109, 26461}, {22514, 26323}, {22515, 45592}, {23698, 48469}, {26392, 48531}, {26416, 48532}, {26505, 49096}, {26506, 49097}, {26507, 33813}, {26508, 49201}, {26509, 49202}, {35878, 45599}, {35879, 45602}, {45412, 49367}, {45414, 49368}, {45516, 48784}, {45518, 48785}, {45595, 49266}, {45598, 49267}

X(49439) = parallelogic center (anti-Lucas(-1) homothetic, T) for these triangles T: 1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard
X(49439) = X(99)-of-anti-Lucas(-1) homothetic triangle
X(49439) = reflection of X(i) in X(j) for these (i, j): (49379, 49377), (49381, 45698)


X(49440) = PARALLELOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 1st ANTI-BROCARD

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

The reciprocal parallelogic center of these triangles is X(385).

X(49440) lies on the circumcircle of anti-Lucas(+1) homothetic triangle and these lines: {98, 26292}, {99, 493}, {114, 26328}, {115, 5490}, {148, 26494}, {542, 49384}, {543, 45699}, {690, 49442}, {2782, 49378}, {2783, 48688}, {2787, 48707}, {2794, 49386}, {2799, 49444}, {3023, 26353}, {3027, 26433}, {4027, 26427}, {5186, 26373}, {5969, 45727}, {6319, 26337}, {6320, 26347}, {6321, 26466}, {6464, 49439}, {7983, 26495}, {8782, 26312}, {8997, 45607}, {10086, 45612}, {10089, 45614}, {11711, 26367}, {13172, 26439}, {13173, 26493}, {13174, 26298}, {13175, 26304}, {13176, 45589}, {13177, 45591}, {13178, 26442}, {13179, 26447}, {13180, 26488}, {13181, 26483}, {13182, 26477}, {13183, 26471}, {13185, 45603}, {13188, 45610}, {13189, 45615}, {13190, 26501}, {13989, 45606}, {18521, 38733}, {19108, 26454}, {19109, 26460}, {22514, 26322}, {22515, 45593}, {23698, 48468}, {26391, 48531}, {26415, 48532}, {26496, 49096}, {26497, 49097}, {26498, 33813}, {26499, 49201}, {26500, 49202}, {35878, 45601}, {35879, 45600}, {45413, 49368}, {45415, 49367}, {45517, 48785}, {45519, 48784}, {45596, 49267}, {45597, 49266}

X(49440) = parallelogic center (anti-Lucas(+1) homothetic, T) for these triangles T: 1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard
X(49440) = X(99)-of-anti-Lucas(+1) homothetic triangle
X(49440) = reflection of X(i) in X(j) for these (i, j): (49380, 49378), (49382, 45699)


X(49441) = PARALLELOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO ANTI-ORTHOCENTROIDAL

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

The reciprocal parallelogic center of these triangles is X(323).

X(49441) lies on the circumcircle of anti-Lucas(-1) homothetic triangle and these lines: {74, 26293}, {110, 494}, {113, 26329}, {125, 5491}, {265, 26467}, {399, 45609}, {542, 45698}, {690, 49439}, {1112, 26374}, {1511, 26507}, {2771, 48689}, {2781, 49385}, {2854, 45726}, {2948, 26299}, {3024, 26354}, {3028, 26434}, {3448, 26503}, {5663, 49377}, {6464, 49442}, {7732, 45594}, {7733, 26338}, {7984, 26504}, {8674, 48708}, {8998, 45605}, {9517, 49443}, {10088, 45611}, {10091, 45613}, {10113, 45592}, {11720, 26368}, {12310, 26305}, {12375, 45599}, {12376, 45602}, {12383, 26440}, {12902, 18523}, {12903, 26478}, {12904, 26472}, {13193, 26428}, {13204, 26502}, {13208, 45588}, {13209, 45590}, {13210, 26313}, {13211, 26443}, {13212, 26448}, {13213, 26489}, {13214, 26484}, {13215, 45604}, {13217, 26511}, {13218, 26510}, {13990, 45608}, {17702, 48469}, {19110, 26455}, {19111, 26461}, {22586, 26323}, {26392, 48535}, {26416, 48536}, {26505, 49098}, {26506, 49099}, {26508, 49203}, {26509, 49204}, {32423, 49391}, {45412, 49369}, {45414, 49370}, {45516, 48786}, {45518, 48787}, {45595, 49268}, {45598, 49269}

X(49441) = parallelogic center (anti-Lucas(-1) homothetic, T) for these triangles T: anti-orthocentroidal, orthocentroidal
X(49441) = X(110)-of-anti-Lucas(-1) homothetic triangle
X(49441) = reflection of X(i) in X(j) for these (i, j): (49383, 49377), (49391, 49427)


X(49442) = PARALLELOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO ANTI-ORTHOCENTROIDAL

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

The reciprocal parallelogic center of these triangles is X(323).

X(49442) lies on the circumcircle of anti-Lucas(+1) homothetic triangle and these lines: {74, 26292}, {110, 493}, {113, 26328}, {125, 5490}, {265, 26466}, {399, 45610}, {542, 45699}, {690, 49440}, {1112, 26373}, {1511, 26498}, {2771, 48688}, {2781, 49386}, {2854, 45727}, {2948, 26298}, {3024, 26353}, {3028, 26433}, {3448, 26494}, {5663, 49378}, {6464, 49441}, {7732, 26337}, {7733, 26347}, {7984, 26495}, {8674, 48707}, {8998, 45607}, {9517, 49444}, {10088, 45612}, {10091, 45614}, {10113, 45593}, {11720, 26367}, {12310, 26304}, {12375, 45601}, {12376, 45600}, {12383, 26439}, {12902, 18521}, {12903, 26477}, {12904, 26471}, {13193, 26427}, {13204, 26493}, {13208, 45589}, {13209, 45591}, {13210, 26312}, {13211, 26442}, {13212, 26447}, {13213, 26488}, {13214, 26483}, {13216, 45603}, {13217, 45615}, {13218, 26501}, {13990, 45606}, {17702, 48468}, {19110, 26454}, {19111, 26460}, {22586, 26322}, {26391, 48535}, {26415, 48536}, {26496, 49098}, {26497, 49099}, {26499, 49203}, {26500, 49204}, {32423, 49392}, {45413, 49370}, {45415, 49369}, {45517, 48787}, {45519, 48786}, {45596, 49269}, {45597, 49268}

X(49442) = parallelogic center (anti-Lucas(+1) homothetic, T) for these triangles T: anti-orthocentroidal, orthocentroidal
X(49442) = X(110)-of-anti-Lucas(+1) homothetic triangle
X(49442) = reflection of X(i) in X(j) for these (i, j): (49384, 49378), (49392, 49428)


X(49443) = PARALLELOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(-1) HOMOTHETIC TO 1st ANTI-ORTHOSYMMEDIAL

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

The reciprocal parallelogic center of these triangles is X(10313).

X(49443) lies on the circumcircle of anti-Lucas(-1) homothetic triangle and these lines: {112, 494}, {127, 5491}, {132, 26329}, {1297, 26293}, {2781, 45726}, {2794, 48469}, {2799, 49439}, {2806, 48708}, {2831, 48689}, {3320, 26434}, {6020, 26354}, {6464, 49444}, {9517, 49441}, {10705, 26504}, {10749, 26467}, {11641, 26305}, {11722, 26368}, {13166, 26374}, {13195, 26428}, {13200, 26440}, {13206, 26502}, {13219, 26503}, {13221, 26299}, {13229, 45588}, {13231, 45590}, {13236, 26313}, {13280, 26443}, {13281, 26448}, {13282, 45594}, {13283, 26338}, {13294, 26489}, {13295, 26484}, {13296, 26478}, {13297, 26472}, {13298, 45604}, {13310, 45609}, {13311, 45611}, {13312, 45613}, {13313, 26511}, {13314, 26510}, {13923, 45605}, {13992, 45608}, {18523, 48681}, {19114, 26455}, {19115, 26461}, {19162, 26323}, {19163, 45592}, {26392, 48537}, {26416, 48538}, {26505, 49100}, {26506, 49101}, {26507, 38608}, {26508, 49205}, {26509, 49206}, {35880, 45599}, {35881, 45602}, {45412, 49371}, {45414, 49372}, {45516, 48788}, {45518, 48789}, {45595, 49270}, {45598, 49271}, {49377, 49385}

X(49443) = parallelogic center (anti-Lucas(-1) homothetic, T) for these triangles T: 1st anti-orthosymmedial, 1st orthosymmedial
X(49443) = X(112)-of-anti-Lucas(-1) homothetic triangle
X(49443) = reflection of X(49385) in X(49377)


X(49444) = PARALLELOGIC CENTER OF THESE TRIANGLES: ANTI-LUCAS(+1) HOMOTHETIC TO 1st ANTI-ORTHOSYMMEDIAL

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

The reciprocal parallelogic center of these triangles is X(10313).

X(49444) lies on the circumcircle of anti-Lucas(+1) homothetic triangle and these lines: {112, 493}, {127, 5490}, {132, 26328}, {1297, 26292}, {2781, 45727}, {2794, 48468}, {2799, 49440}, {2806, 48707}, {2831, 48688}, {3320, 26433}, {6020, 26353}, {6464, 49443}, {9517, 49442}, {10705, 26495}, {10749, 26466}, {11641, 26304}, {11722, 26367}, {13166, 26373}, {13195, 26427}, {13200, 26439}, {13206, 26493}, {13219, 26494}, {13221, 26298}, {13229, 45589}, {13231, 45591}, {13236, 26312}, {13280, 26442}, {13281, 26447}, {13282, 26337}, {13283, 26347}, {13294, 26488}, {13295, 26483}, {13296, 26477}, {13297, 26471}, {13299, 45603}, {13310, 45610}, {13311, 45612}, {13312, 45614}, {13313, 45615}, {13314, 26501}, {13923, 45607}, {13992, 45606}, {18521, 48681}, {19114, 26454}, {19115, 26460}, {19162, 26322}, {19163, 45593}, {26391, 48537}, {26415, 48538}, {26496, 49100}, {26497, 49101}, {26498, 38608}, {26499, 49205}, {26500, 49206}, {35880, 45601}, {35881, 45600}, {45413, 49372}, {45415, 49371}, {45517, 48789}, {45519, 48788}, {45596, 49271}, {45597, 49270}, {49378, 49386}

X(49444) = parallelogic center (anti-Lucas(+1) homothetic, T) for these triangles T: 1st anti-orthosymmedial, 1st orthosymmedial
X(49444) = X(112)-of-anti-Lucas(+1) homothetic triangle
X(49444) = reflection of X(49386) in X(49378)

leftri

Points in a [[bc(b-c),ca(c-a),ab(a-b)], [a(b^2-c^2),b(c^2-a^2),c(a^2-b^2)]] coordinate system: X(49445)-X(49500)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1, L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1 is the line: bc(b-c) α + ca(c-a) β + ab(a-b) γ = 0.

L2 is the line a(b^2-c^2) α + b(c^2-a^2) β + c(a^2-b^2) γ = 0.

The origin is given by (0, 0) = X(1) = a : b : c .

Barycentrics u : v : w for a triangle center U = (x, y) in this system are given by

u : v : w = -a(a+b)(a+c)(b-c)(ab+ac+bc) - a(ab+ac-b^2-c^2)x + (b+c)(a^2-bc)y : : ,

where, as functions of a, b, c, the coordinate x is antisymmetric and homogeneous of degree 3, and y is antisymmetric and homogeneous of degree 3.

The appearance of {x, y}, k in the following list means that (x, y) = X(k).

{-((2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)), 0}, 16496
{-2 (a-b) (a-c) (b-c), 2 (a-b) (a-c) (b-c)}, 3632
{-((a-b) (a-c) (b-c)), -((a-b) (a-c) (b-c))}, 192
{-((a (a-b) b (a-c) (b-c) c)/(a^3+b^3+c^3)), -(((a-b) (a+b) (a-c) (b-c) (a+c) (b+c))/(a^3+b^3+c^3))}, 3891
{-((a-b) (a-c) (b-c)), 0}, 984
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)), 0}, 3242
{-((a-b) (a-c) (b-c)), (a-b) (a-c) (b-c)}, 8
{-((a (a-b) b (a-c) (b-c) c)/(a^3+b^3+c^3)), (a (a-b) b (a-c) (b-c) c)/(a^3+b^3+c^3)}, 3938
{-(1/2) (a-b) (a-c) (b-c), -(1/2) (a-b) (a-c) (b-c)}, 3993
{-(1/2) (a-b) (a-c) (b-c), 0}, 37
{-(1/2) (a-b) (a-c) (b-c), 1/2 (a-b) (a-c) (b-c)}, 10
{-(1/2) (a-b) (a-c) (b-c), (a-b) (a-c) (b-c)}, 3696
{0, -((2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2))}, 3875
{0, -(((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2))}, 32921
{0, 0}, 1
{0, 1/2 (a-b) (a-c) (b-c)}, 24325
{0, (a-b) (a-c) (b-c)}, 75
{0, ((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)}, 32941
{0, (2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)}, 3886
{((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a^2+b^2+c^2)), -(((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2))}, 4852
{1/2 (a-b) (a-c) (b-c), -(1/2) (a-b) (a-c) (b-c)}, 3244
{((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a^2+b^2+c^2)), 0}, 1386
{1/2 (a-b) (a-c) (b-c), 2 (a-b) (a-c) (b-c)}, 4686
{(a-b) (a-c) (b-c), -((a-b) (a-c) (b-c))}, 145
{((a-b) (a+b) (a-c) (b-c) (a+c) (b+c))/(a^3+b^3+c^3), -(((a-b) (a+b) (a-c) (b-c) (a+c) (b+c))/(a^3+b^3+c^3))}, 3187
{((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2), 0}, 6
{((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2), ((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a^2+b^2+c^2))}, 4672
{(a-b) (a-c) (b-c), (a-b) (a-c) (b-c)}, 24349
{((a-b) (a+b) (a-c) (b-c) (a+c) (b+c))/(a^3+b^3+c^3), (a (a-b) b (a-c) (b-c) c)/(a^3+b^3+c^3)}, 31
{((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2), ((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)}, 3923
{((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2), (2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)}, 5695
{2 (a-b) (a-c) (b-c), -2 (a-b) (a-c) (b-c)}, 3633
{(2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2), 0}, 3751
{(2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2), ((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)}, 32935
{(2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2), (2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)}, 3729
{-2*(a - b)*(a - c)*(b - c), -2*(a - b)*(a - c)*(b - c)}, 49445
{(-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), (-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49446
{-2*(a - b)*(a - c)*(b - c), -((a - b)*(a - c)*(b - c))}, 49447
{-2*(a - b)*(a - c)*(b - c), 0}, 49448
{-2*(a - b)*(a - c)*(b - c), ((a - b)*(a - c)*(b - c))/2}, 49449
{-2*(a - b)*(a - c)*(b - c), (a - b)*(a - c)*(b - c)}, 49450
{(-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), (2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49451
{-((a - b)*(a - c)*(b - c)), -2*(a - b)*(a - c)*(b - c)}, 49452
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)), (-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49453
{-(((a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c))/(a^3 + b^3 + c^3)), -((a*(a - b)*b*(a - c)*(b - c)*c)/(a^3 + b^3 + c^3))}, 49454
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)), -(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2))}, 49455
{-((a - b)*(a - c)*(b - c)), -1/2*((a - b)*(a - c)*(b - c))}, 49456
{-((a - b)*(a - c)*(b - c)), ((a - b)*(a - c)*(b - c))/2}, 49457
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)), ((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49458
{-((a - b)*(a - c)*(b - c)), 2*(a - b)*(a - c)*(b - c)}, 49459
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)), (2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49460
{-1/2*((a - b)*(a - c)*(b - c)), -2*(a - b)*(a - c)*(b - c)}, 49461
{-1/2*((a - b)*(a - c)*(b - c)), -((a - b)*(a - c)*(b - c))}, 49462
{-1/2*((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), -(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2))}, 49463
{-1/2*((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), -1/2*((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49464
{-1/2*((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), 0}, 49465
{-1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c), ((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(2*(a*b + a*c + b*c))}, 49466
{-1/2*((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), ((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49467
{-1/2*((a - b)*(a - c)*(b - c)), 2*(a - b)*(a - c)*(b - c)}, 49468
{0, -2*(a - b)*(a - c)*(b - c)}, 49469
{0, -((a - b)*(a - c)*(b - c))}, 49470
{0, -1/2*((a - b)*(a - c)*(b - c))}, 49471
{0, -1/2*((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49472
{0, ((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(2*(a^2 + b^2 + c^2))}, 49473
{0, 2*(a - b)*(a - c)*(b - c)}, 49474
{((a - b)*(a - c)*(b - c))/2, -((a - b)*(a - c)*(b - c))}, 49475
{((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(2*(a*b + a*c + b*c)), -1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c)}, 49476
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(2*(a^2 + b^2 + c^2)), -1/2*((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49477
{((a - b)*(a - c)*(b - c))/2, 0}, 49478
{((a - b)*(a - c)*(b - c))/2, ((a - b)*(a - c)*(b - c))/2}, 49479
{((a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c))/(2*(a^3 + b^3 + c^3)), (a*(a - b)*b*(a - c)*(b - c)*c)/(2*(a^3 + b^3 + c^3))}, 49480
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(2*(a^2 + b^2 + c^2)), ((a - b)*(a - c)*(b - c))/2}, 49481
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(2*(a^2 + b^2 + c^2)), ((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(2*(a^2 + b^2 + c^2))}, 49482
{((a - b)*(a - c)*(b - c))/2, (a - b)*(a - c)*(b - c)}, 49483
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(2*(a^2 + b^2 + c^2)), ((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49484
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(2*(a^2 + b^2 + c^2)), (2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49485
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), (-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49486
{(a*(a - b)*b*(a - c)*(b - c)*c)/(a^3 + b^3 + c^3), -((a*(a - b)*b*(a - c)*(b - c)*c)/(a^3 + b^3 + c^3))}, 49487
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), -(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2))}, 49488
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), -1/2*((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49489
{(a - b)*(a - c)*(b - c), 0}, 49490
{(a - b)*(a - c)*(b - c), ((a - b)*(a - c)*(b - c))/2}, 49491
{(a*(a - b)*b*(a - c)*(b - c)*c)/(a^3 + b^3 + c^3), ((a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c))/(a^3 + b^3 + c^3)}, 49492
{(a - b)*(a - c)*(b - c), 2*(a - b)*(a - c)*(b - c)}, 49493
{(2*a*(a - b)*b*(a - c)*(b - c)*c)/(a^3 + b^3 + c^3), (-2*a*(a - b)*b*(a - c)*(b - c)*c)/(a^3 + b^3 + c^3)}, 49494
{(2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), (-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49495
{(2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), -((a - b)*(a - c)*(b - c))}, 49496
{(2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), -(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2))}, 49497
{2*(a - b)*(a - c)*(b - c), 0}, 49498
{2*(a - b)*(a - c)*(b - c), (a - b)*(a - c)*(b - c)}, 49499
{(2*(a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c))/(a^3 + b^3 + c^3), (2*a*(a - b)*b*(a - c)*(b - c)*c)/(a^3 + b^3 + c^3)}, 49500


X(49445) = X(1)X(87)∩X(2)X(4135)

Barycentrics    a^2*b + 2*a*b^2 + a^2*c + a*b*c - 2*b^2*c + 2*a*c^2 - 2*b*c^2 : :
X(49445) = 3 X[1] - 4 X[3993], 3 X[1] - 2 X[24349], 3 X[192] - 2 X[3993], 3 X[192] - X[24349], 8 X[37] - 7 X[3624], 6 X[37] - 5 X[40328], 21 X[3624] - 20 X[40328], 4 X[75] - 5 X[1698], 3 X[75] - 4 X[3842], 15 X[1698] - 16 X[3842], X[3633] - 8 X[4718], 4 X[984] - 3 X[3679], 3 X[984] - 2 X[3696], 9 X[3679] - 8 X[3696], X[3632] + 4 X[3644], 4 X[1125] - 5 X[4704], 3 X[1699] - 4 X[20430], 8 X[3634] - 7 X[4772], 16 X[3739] - 17 X[19872], 3 X[4664] - 2 X[24325], 4 X[4664] - 3 X[25055], 8 X[24325] - 9 X[25055], 5 X[4668] - 4 X[4709], 2 X[4740] - 3 X[19875], 5 X[4821] - 7 X[9780], 4 X[15569] - 3 X[31178], 14 X[27268] - 13 X[34595]

X(49445) lies on these lines: {1, 87}, {2, 4135}, {8, 4788}, {10, 1278}, {37, 3624}, {38, 42044}, {43, 3952}, {75, 1089}, {190, 16468}, {238, 17262}, {312, 17591}, {335, 29573}, {345, 33152}, {346, 29637}, {350, 3097}, {518, 3633}, {519, 31302}, {536, 984}, {740, 3632}, {978, 3159}, {982, 3175}, {1125, 4704}, {1266, 4078}, {1699, 20430}, {1757, 3875}, {2275, 20688}, {3210, 3971}, {3242, 4693}, {3293, 21080}, {3550, 32926}, {3634, 4772}, {3662, 6541}, {3663, 29674}, {3672, 29633}, {3703, 33154}, {3712, 17725}, {3739, 19872}, {3751, 9055}, {3773, 4389}, {3782, 33092}, {3790, 3821}, {3797, 17284}, {3836, 4398}, {3891, 8616}, {3932, 33149}, {3943, 33087}, {3950, 24231}, {3977, 29658}, {3989, 28605}, {3994, 4850}, {3995, 17155}, {4032, 4355}, {4054, 29657}, {4065, 25295}, {4090, 4734}, {4334, 4552}, {4353, 29660}, {4360, 32935}, {4363, 43997}, {4365, 7226}, {4384, 27481}, {4387, 17598}, {4392, 31137}, {4415, 32855}, {4419, 33082}, {4429, 4439}, {4441, 40774}, {4535, 17228}, {4649, 17318}, {4659, 24342}, {4664, 24325}, {4668, 4709}, {4671, 29827}, {4716, 5220}, {4740, 19875}, {4780, 4899}, {4816, 28484}, {4821, 9780}, {4854, 33169}, {4884, 33141}, {4903, 6686}, {4970, 32937}, {4974, 17336}, {5691, 29010}, {5852, 17388}, {6057, 33174}, {6682, 42034}, {8026, 34020}, {9589, 29054}, {15485, 32922}, {15569, 31178}, {16557, 20375}, {16825, 17261}, {16826, 27494}, {16834, 33888}, {17063, 35652}, {17165, 42042}, {17246, 32784}, {17276, 32846}, {17301, 33159}, {17347, 17772}, {17355, 29646}, {17359, 25539}, {17377, 17771}, {17776, 33147}, {19785, 33164}, {19847, 27291}, {22220, 24046}, {24165, 25502}, {24248, 32847}, {24427, 42720}, {26128, 42033}, {27268, 34595}, {27538, 36634}, {29664, 48642}, {29856, 33155}, {29858, 32849}, {30699, 33138}, {32848, 33151}, {32854, 33100}, {32862, 33145}, {32928, 32933}, {32939, 37604}, {33088, 33099}, {33093, 33098}

X(49445) = midpoint of X(8) and X(4788)
X(49445) = reflection of X(i) in X(j) for these {i,j}: {1, 192}, {1278, 10}, {24349, 3993}, {25295, 4065}
X(49445) = crossdifference of every pair of points on line {20979, 39521}
X(49445) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {190, 32921, 16468}, {192, 24349, 3993}, {3210, 3971, 16569}, {3891, 32936, 8616}, {3993, 24349, 1}, {3995, 17155, 26102}, {4671, 46901, 29827}, {4970, 32937, 42043}, {17147, 32925, 43}, {24165, 41839, 25502}, {32849, 33143, 29858}, {32926, 32934, 3550}, {33155, 33161, 29856}


X(49446) = X(1)X(87)∩X(2)X(4082)

Barycentrics    a^3 + 3*a*b^2 - 2*b^2*c + 3*a*c^2 - 2*b*c^2 : :
X(49446) = 3 X[1] - 2 X[3923], 3 X[3729] - 4 X[3923], 3 X[2] - 4 X[4353], 4 X[10] - 5 X[17304], 2 X[3751] - 3 X[16834], 3 X[16834] - 4 X[32921], 3 X[3241] - X[24280], 2 X[3416] - 3 X[17274], 5 X[3616] - 4 X[17355], 3 X[3679] - 4 X[3821], 3 X[3873] - 2 X[32118], 4 X[4672] - 5 X[16491], 3 X[16475] - 2 X[32935], 2 X[17351] - 3 X[38315], 8 X[24295] - 9 X[25055]

X(49446) lies on these lines: {1, 87}, {2, 4082}, {6, 28582}, {8, 3663}, {9, 32922}, {10, 17304}, {38, 11679}, {43, 17794}, {57, 14594}, {63, 3891}, {75, 7174}, {145, 516}, {190, 7290}, {193, 5850}, {200, 3210}, {238, 25728}, {239, 5223}, {312, 3677}, {518, 3875}, {519, 11160}, {536, 3242}, {537, 3751}, {596, 975}, {612, 17155}, {614, 30568}, {740, 16496}, {968, 32923}, {982, 30567}, {984, 4384}, {990, 3870}, {1266, 2550}, {1279, 17262}, {1469, 14839}, {1699, 29840}, {1999, 35621}, {2999, 32937}, {3008, 27549}, {3175, 17597}, {3187, 20068}, {3241, 17132}, {3243, 24841}, {3244, 28526}, {3339, 41261}, {3416, 17274}, {3616, 16673}, {3632, 4660}, {3633, 17766}, {3679, 3821}, {3703, 25527}, {3711, 4706}, {3717, 4000}, {3731, 16823}, {3749, 32934}, {3769, 3928}, {3772, 4884}, {3790, 17284}, {3868, 10444}, {3871, 24309}, {3873, 32118}, {3883, 4419}, {3912, 4310}, {3932, 17282}, {3971, 5272}, {3977, 26228}, {3995, 4666}, {4008, 20881}, {4135, 29668}, {4283, 29561}, {4298, 20009}, {4312, 4440}, {4344, 4454}, {4398, 32850}, {4402, 5686}, {4429, 4901}, {4645, 4862}, {4649, 20162}, {4654, 33073}, {4655, 17769}, {4659, 5263}, {4672, 16491}, {4684, 17314}, {4712, 24600}, {4718, 4864}, {4847, 30699}, {4968, 24547}, {5231, 37759}, {5234, 19851}, {5256, 17165}, {5268, 24165}, {5269, 32939}, {5271, 7226}, {5287, 17140}, {5542, 17316}, {5573, 18743}, {5695, 28555}, {5846, 17276}, {6738, 11851}, {7322, 19804}, {7982, 29057}, {7991, 24728}, {8580, 17490}, {8581, 9312}, {9315, 16557}, {9797, 9801}, {10582, 41839}, {11038, 15590}, {12618, 26015}, {12723, 34791}, {15601, 17336}, {16020, 25101}, {16468, 24821}, {16469, 17350}, {16475, 32935}, {16487, 25269}, {16830, 25590}, {16831, 24325}, {17127, 25734}, {17298, 24231}, {17299, 28472}, {17351, 38315}, {17389, 41842}, {17489, 30625}, {17594, 32920}, {18193, 29649}, {19789, 25006}, {19861, 25243}, {20045, 35258}, {23052, 46108}, {23511, 27538}, {23681, 29641}, {24259, 42042}, {24260, 42043}, {24295, 25055}, {24342, 48854}, {25099, 37592}, {28516, 32941}, {28562, 34747}, {28609, 33071}, {29054, 41863}, {29575, 38024}, {29597, 31178}, {29828, 46901}, {29855, 33161}, {29857, 33143}, {31164, 33070}, {31995, 39587}, {38052, 48627}

X(49446) = reflection of X(i) in X(j) for these {i,j}: {8, 3663}, {3632, 4660}, {3729, 1}, {3751, 32921}, {3886, 3242}, {7991, 24728}, {12723, 34791}
X(49446) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {239, 31302, 5223}, {614, 32925, 30568}, {3751, 32921, 16834}


X(49447) = X(1)X(190)∩X(10)X(75)

Barycentrics    2*a*b^2 + a*b*c - b^2*c + 2*a*c^2 - b*c^2 : :
X(49447) = 2 X[1] - 3 X[4664], 4 X[10] - 3 X[75], 2 X[10] - 3 X[984], 6 X[37] - 5 X[3616], 5 X[3616] - 3 X[24349], X[145] - 3 X[192], X[145] + 3 X[31302], 8 X[25557] - 9 X[27475], 2 X[3632] + 3 X[3644], 4 X[1125] - 3 X[31178], 3 X[1278] - 7 X[4678], 6 X[3696] - 7 X[4678], 5 X[3617] - 3 X[4740], 14 X[3624] - 15 X[4687], 7 X[3624] - 6 X[24325], 5 X[4687] - 4 X[24325], 2 X[3635] - 3 X[3993], 12 X[3739] - 13 X[19877], 8 X[3842] - 7 X[4751], 10 X[4668] - 3 X[4764], 12 X[4681] - 7 X[20057], 6 X[4688] - 7 X[9780], 15 X[4699] - 17 X[46932], 5 X[4704] - 4 X[15569], 3 X[4709] - 4 X[4746], 6 X[4718] + X[20053], 12 X[4755] - 11 X[5550], 3 X[4788] + 5 X[20052], 2 X[18481] - 3 X[30273], 16 X[19878] - 15 X[40328], 3 X[20430] - 2 X[22791]

X(49447) lies on these lines: {1, 190}, {2, 3967}, {8, 536}, {9, 32922}, {10, 75}, {37, 2275}, {38, 312}, {43, 42054}, {45, 16823}, {63, 3769}, {141, 3790}, {144, 145}, {210, 3210}, {238, 17336}, {239, 5220}, {244, 30829}, {291, 30963}, {321, 7226}, {329, 33071}, {335, 16593}, {344, 4310}, {345, 33126}, {354, 41839}, {612, 32939}, {714, 2292}, {740, 3632}, {756, 17155}, {846, 32920}, {982, 3971}, {1001, 17261}, {1125, 17354}, {1215, 29825}, {1278, 3696}, {1386, 17350}, {1633, 3871}, {1698, 17305}, {1757, 3759}, {2276, 17794}, {3006, 33151}, {3097, 17793}, {3175, 10453}, {3219, 3891}, {3242, 3685}, {3416, 6646}, {3617, 4740}, {3624, 4687}, {3635, 3993}, {3662, 3932}, {3666, 32937}, {3670, 46937}, {3677, 30568}, {3679, 28554}, {3681, 17147}, {3703, 27184}, {3705, 4415}, {3729, 5263}, {3739, 19877}, {3740, 17490}, {3741, 42034}, {3751, 4360}, {3752, 27538}, {3755, 4899}, {3773, 17228}, {3775, 48630}, {3782, 29641}, {3789, 17759}, {3797, 17230}, {3826, 48627}, {3836, 48629}, {3840, 20942}, {3842, 4751}, {3844, 17236}, {3868, 22299}, {3873, 3995}, {3875, 5223}, {3879, 5850}, {3896, 4661}, {3920, 32933}, {3938, 32936}, {3950, 4684}, {3952, 4850}, {3961, 32934}, {3989, 32771}, {3999, 30947}, {4000, 27549}, {4011, 17598}, {4026, 17247}, {4075, 24046}, {4078, 17234}, {4080, 10129}, {4096, 16569}, {4283, 18046}, {4344, 4488}, {4346, 39570}, {4353, 17353}, {4358, 4392}, {4363, 16830}, {4373, 40333}, {4393, 4663}, {4414, 32927}, {4424, 4737}, {4425, 33169}, {4438, 33152}, {4439, 17227}, {4440, 5880}, {4452, 5686}, {4454, 39587}, {4642, 44720}, {4645, 17276}, {4649, 17393}, {4655, 32847}, {4668, 4764}, {4671, 46909}, {4679, 5211}, {4681, 20057}, {4683, 32854}, {4688, 9780}, {4699, 46932}, {4701, 28522}, {4703, 32866}, {4704, 15569}, {4709, 4746}, {4718, 20053}, {4734, 4849}, {4755, 5550}, {4788, 20052}, {4865, 33099}, {4946, 4970}, {4966, 17242}, {4968, 31359}, {4981, 28605}, {5014, 33100}, {5057, 29832}, {5205, 17595}, {5302, 19851}, {5311, 32940}, {5846, 17334}, {5847, 17347}, {5852, 17364}, {5905, 33073}, {6541, 17240}, {7290, 25728}, {9330, 24589}, {9369, 37614}, {9371, 24499}, {10327, 33068}, {15481, 17349}, {16825, 17335}, {17017, 32938}, {17025, 41241}, {17135, 42044}, {17154, 31035}, {17165, 28606}, {17184, 32862}, {17302, 38047}, {17329, 33082}, {17333, 28503}, {17342, 29637}, {17357, 26150}, {17361, 32846}, {17362, 28472}, {17367, 31349}, {17370, 33159}, {17377, 34379}, {17384, 26083}, {17399, 29633}, {17484, 33070}, {17599, 27064}, {17717, 21093}, {17721, 17777}, {17763, 36263}, {17776, 33124}, {18157, 33947}, {18481, 30273}, {18525, 29010}, {19586, 20694}, {19785, 33118}, {19786, 33163}, {19812, 32780}, {19830, 33132}, {19878, 40328}, {20020, 44447}, {20037, 31165}, {20173, 26015}, {20284, 21902}, {20359, 41835}, {20430, 22791}, {21342, 35652}, {24003, 31233}, {24248, 32850}, {24397, 36801}, {24703, 29840}, {25502, 42053}, {26037, 42041}, {26102, 42055}, {26128, 33164}, {26580, 33089}, {27494, 31322}, {27496, 42027}, {29054, 41869}, {29614, 31317}, {29621, 30340}, {29634, 44416}, {29643, 32856}, {29653, 33103}, {29671, 33101}, {29673, 33154}, {30957, 42038}, {31330, 42029}, {32774, 33166}, {32775, 33161}, {32776, 33162}, {32848, 33065}, {32849, 33122}, {32859, 33093}, {32912, 32928}, {32931, 46901}, {32950, 33091}, {33064, 33092}, {33066, 33088}, {33072, 33098}, {33113, 33153}, {33114, 33155}, {33115, 33143}, {33116, 33144}, {33117, 33145}, {33171, 42033}

X(49447) = midpoint of X(192) and X(31302)
X(49447) = reflection of X(i) in X(j) for these {i,j}: {75, 984}, {1278, 3696}, {24349, 37}
X(49447) = X(667)-isoconjugate of X(9067)
X(49447) = X(i)-Dao conjugate of X(j) for these (i, j): (6631, 9067), (17756, 16833)
X(49447) = crossdifference of every pair of points on line {1919, 3768}
X(49447) = barycentric product X(i)*X(j) for these {i,j}: {75, 17756}, {190, 44429}, {1978, 9010}
X(49447) = barycentric quotient X(i)/X(j) for these {i,j}: {190, 9067}, {9010, 649}, {17756, 1}, {44429, 514}
X(49447) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 190, 4676}, {1, 24821, 32935}, {1, 32935, 3758}, {8, 4419, 24723}, {38, 3994, 30942}, {38, 32925, 312}, {63, 32926, 3769}, {145, 20073, 5698}, {756, 17155, 19804}, {982, 3971, 18743}, {1757, 32921, 3759}, {3242, 17262, 3685}, {3663, 3717, 4429}, {3729, 7174, 5263}, {3994, 30942, 312}, {3995, 20068, 3873}, {4003, 4009, 2}, {4078, 24231, 17234}, {4415, 4884, 3705}, {6541, 33087, 17240}, {30942, 32925, 3994}


X(49448) = X(1)X(6)∩X(2)X(4090)

Barycentrics    a*(a*b - 2*b^2 + a*c - b*c - 2*c^2) : :
X(49448) = 3 X[1] - 4 X[37], 7 X[1] - 8 X[15569], 2 X[37] - 3 X[984], 7 X[37] - 6 X[15569], 7 X[984] - 4 X[15569], 3 X[8] - X[1278], 3 X[8] - 2 X[4709], X[1278] + 3 X[31302], 2 X[4709] + 3 X[31302], 6 X[10] - 5 X[4699], 5 X[4699] - 3 X[24349], 2 X[75] - 3 X[3679], 3 X[75] - 4 X[4732], 9 X[3679] - 8 X[4732], 6 X[551] - 7 X[27268], 3 X[3632] + 2 X[3644], 15 X[1698] - 14 X[4751], 5 X[1698] - 4 X[24325], 7 X[4751] - 6 X[24325], 3 X[3241] - 5 X[4704], 7 X[3624] - 8 X[3842], 4 X[3696] - 5 X[4668], 3 X[3696] - 2 X[4726], 15 X[4668] - 8 X[4726], 8 X[3739] - 9 X[19875], 4 X[3739] - 3 X[31178], 3 X[19875] - 2 X[31178], 8 X[4681] - 3 X[34747], 10 X[4687] - 9 X[25055], X[4788] + 3 X[31145], 21 X[19876] - 20 X[31238]

X(49448) lies on these lines: {1, 6}, {2, 4090}, {8, 726}, {10, 3662}, {35, 20805}, {36, 34247}, {38, 43}, {42, 4661}, {55, 22149}, {63, 3099}, {69, 32847}, {75, 537}, {100, 28563}, {141, 33165}, {145, 3993}, {190, 32941}, {192, 519}, {200, 17596}, {210, 982}, {291, 3789}, {312, 42054}, {329, 33106}, {333, 32920}, {335, 4384}, {354, 25502}, {528, 17334}, {536, 4677}, {551, 27268}, {612, 32913}, {740, 3632}, {752, 17347}, {756, 3873}, {758, 3728}, {846, 3870}, {872, 5313}, {894, 36480}, {899, 4392}, {908, 29676}, {968, 3979}, {978, 3678}, {986, 34790}, {995, 4134}, {1125, 17338}, {1150, 32927}, {1211, 33169}, {1698, 4751}, {1738, 24393}, {1742, 2801}, {1929, 39959}, {2108, 4712}, {2275, 21830}, {2293, 40269}, {2308, 29815}, {2550, 32857}, {2810, 3688}, {2886, 33101}, {2895, 32854}, {3006, 33065}, {3008, 27484}, {3097, 3783}, {3210, 4685}, {3216, 29492}, {3219, 3938}, {3240, 46901}, {3241, 4704}, {3305, 29820}, {3315, 17125}, {3434, 33099}, {3501, 9941}, {3617, 7613}, {3624, 3842}, {3625, 28522}, {3661, 33888}, {3666, 21870}, {3670, 6048}, {3683, 17715}, {3689, 17601}, {3696, 4668}, {3697, 24174}, {3703, 33084}, {3711, 17595}, {3715, 17123}, {3717, 29674}, {3720, 4430}, {3729, 24821}, {3739, 19875}, {3740, 17063}, {3741, 32937}, {3744, 7262}, {3749, 3929}, {3750, 41711}, {3752, 36634}, {3759, 4753}, {3782, 32865}, {3786, 18792}, {3797, 17294}, {3811, 37574}, {3840, 27538}, {3876, 21214}, {3877, 17460}, {3891, 32864}, {3901, 29382}, {3920, 32912}, {3925, 33103}, {3927, 5255}, {3932, 33087}, {3935, 4414}, {3940, 37617}, {3944, 4847}, {3952, 30942}, {3971, 10453}, {3976, 5044}, {3989, 17018}, {3992, 20923}, {3996, 32934}, {4015, 24046}, {4078, 4684}, {4085, 4389}, {4096, 18743}, {4113, 42051}, {4310, 5686}, {4334, 17092}, {4335, 34784}, {4356, 4924}, {4357, 29659}, {4358, 31137}, {4383, 17598}, {4407, 5224}, {4413, 18201}, {4415, 33141}, {4432, 17336}, {4438, 33126}, {4439, 17233}, {4469, 18206}, {4514, 4703}, {4641, 17716}, {4643, 9055}, {4651, 17155}, {4655, 32850}, {4657, 47359}, {4662, 24440}, {4669, 4740}, {4671, 31136}, {4681, 34747}, {4683, 5014}, {4687, 25055}, {4693, 17262}, {4723, 20892}, {4764, 28554}, {4777, 23838}, {4788, 31145}, {4816, 28516}, {4863, 33095}, {4865, 33066}, {4884, 32855}, {4970, 20012}, {4981, 32771}, {5010, 15624}, {5235, 18173}, {5263, 32935}, {5278, 32923}, {5293, 37608}, {5316, 24216}, {5691, 29054}, {5739, 32866}, {5881, 29010}, {5905, 33109}, {6542, 27481}, {6763, 37603}, {7201, 18421}, {7232, 31151}, {7321, 24693}, {7982, 20430}, {8580, 18193}, {9041, 17332}, {9330, 30950}, {9819, 11997}, {10009, 25280}, {10176, 21330}, {10327, 33085}, {10436, 36531}, {16571, 24464}, {16830, 43997}, {16831, 31323}, {17038, 30116}, {17135, 32925}, {17140, 26037}, {17145, 31035}, {17165, 31025}, {17184, 33117}, {17255, 48829}, {17256, 36494}, {17257, 36479}, {17260, 24331}, {17276, 24715}, {17277, 24841}, {17279, 47358}, {17284, 17755}, {17306, 36478}, {17308, 27495}, {17350, 36534}, {17353, 29660}, {17362, 28503}, {17397, 31314}, {17484, 33104}, {17725, 35466}, {17889, 25006}, {19586, 20683}, {19804, 42055}, {19876, 31238}, {21060, 24239}, {21226, 32453}, {21578, 27472}, {21806, 28606}, {22271, 31855}, {23653, 25061}, {24462, 42341}, {24552, 32938}, {24892, 33153}, {24943, 33166}, {25351, 48629}, {25352, 27147}, {26128, 33118}, {26580, 33120}, {27064, 29652}, {27184, 29673}, {28604, 48809}, {29641, 33064}, {29670, 38000}, {29690, 31053}, {29816, 37685}, {29825, 46897}, {29827, 32931}, {29832, 32843}, {29856, 32775}, {29858, 33115}, {30615, 33079}, {30829, 42056}, {32782, 33162}, {32783, 33163}, {32853, 32926}, {32856, 33108}, {32859, 33072}, {32862, 33081}, {32933, 32945}, {33080, 33091}, {33098, 33110}, {33136, 33151}, {33137, 33152}, {33138, 33144}, {33139, 33143}, {33161, 33175}, {33164, 33171}, {38302, 44671}, {41839, 42057}

X(49448) = midpoint of X(8) and X(31302)
X(49448) = reflection of X(i) in X(j) for these {i,j}: {1, 984}, {145, 3993}, {1278, 4709}, {4740, 4669}, {7982, 20430}, {24349, 10}
X(49448) = X(514)-isoconjugate of X(30554)
X(49448) = crossdifference of every pair of points on line {513, 23472}
X(49448) = barycentric product X(i)*X(j) for these {i,j}: {1, 17230}, {72, 31916}, {100, 30519}
X(49448) = barycentric quotient X(i)/X(j) for these {i,j}: {692, 30554}, {9461, 1635}, {17230, 75}, {30519, 693}, {31916, 286}
X(49448) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 9, 15485}, {1, 1757, 16468}, {1, 5223, 1757}, {8, 1278, 4709}, {8, 6646, 4660}, {9, 16496, 1}, {9, 16973, 16779}, {38, 43, 17591}, {38, 3681, 43}, {38, 21805, 4850}, {45, 42871, 16484}, {63, 3961, 3550}, {210, 982, 16569}, {238, 3242, 1}, {612, 32913, 37604}, {756, 3873, 26102}, {3219, 3938, 8616}, {3242, 5220, 238}, {3681, 4850, 21805}, {3715, 17597, 17123}, {3740, 21342, 17063}, {3751, 7174, 1}, {3751, 16496, 16973}, {4651, 20068, 17155}, {4661, 7226, 42}, {4850, 21805, 43}, {4867, 16499, 1}, {16484, 42871, 1}, {27495, 31317, 17308}, {32775, 33114, 29856}, {32931, 46909, 29827}, {33115, 33122, 29858}


X(49449) = X(1)X(4753)∩X(8)X(537)

Barycentrics    3*a^2*b - 4*a*b^2 + 3*a^2*c - 2*a*b*c - b^2*c - 4*a*c^2 - b*c^2 : :
X(49449) = 7 X[8] - 3 X[4740], 7 X[10] - 6 X[3739], 4 X[10] - 3 X[24325], 8 X[3739] - 7 X[24325], 3 X[37] - 2 X[3635], 3 X[75] - 5 X[4668], X[145] - 3 X[984], 7 X[145] - 15 X[4704], 7 X[984] - 5 X[4704], 3 X[192] + X[20053], 7 X[3632] + 3 X[3644], 5 X[3616] - 6 X[3842], 5 X[3617] - 3 X[31178], X[3633] - 3 X[4664], 3 X[3696] - 4 X[4746], 7 X[4678] - 6 X[4732], 7 X[4678] - 3 X[24349], 3 X[4688] - 4 X[4691], 5 X[20052] + 3 X[31302], 15 X[40328] - 17 X[46932]

X(49449) lies on these lines: {1, 4753}, {8, 537}, {10, 141}, {37, 3635}, {38, 19998}, {75, 4668}, {145, 984}, {192, 20053}, {210, 4871}, {536, 3625}, {726, 4701}, {740, 3632}, {1215, 4661}, {3242, 4974}, {3616, 3842}, {3617, 31178}, {3633, 4664}, {3666, 4946}, {3681, 30942}, {3696, 4746}, {3773, 4899}, {3994, 17135}, {4096, 10453}, {4113, 24165}, {4416, 17765}, {4432, 5220}, {4457, 17155}, {4651, 42055}, {4677, 28554}, {4678, 4732}, {4685, 4706}, {4688, 4691}, {4709, 28582}, {5223, 32941}, {7226, 20048}, {17230, 17755}, {17347, 28494}, {18525, 29054}, {20011, 42039}, {20052, 28516}, {27495, 29614}, {29824, 42056}, {40328, 46932}

X(49449) = reflection of X(24349) in X(4732)


X(49450) = X(1)X(872)∩X(7)X(8)

Barycentrics    2*a^2*b - 2*a*b^2 + 2*a^2*c - a*b*c - b^2*c - 2*a*c^2 - b*c^2 : :
X(49450) = 3 X[1] - 4 X[3842], 4 X[1] - 5 X[4687], 16 X[3842] - 15 X[4687], 3 X[8] - 2 X[3696], 3 X[8] - X[24349], 3 X[75] - 4 X[3696], 3 X[75] - 2 X[24349], 8 X[10] - 7 X[4751], 6 X[10] - 5 X[40328], 21 X[4751] - 20 X[40328], 3 X[984] - 2 X[3993], 4 X[984] - 3 X[4664], 2 X[3883] - 3 X[17346], 8 X[3993] - 9 X[4664], 3 X[31145] + X[31302], 8 X[3625] - X[4764], 4 X[3632] + X[3644], X[1278] - 5 X[20052], 3 X[3241] - 4 X[15569], 2 X[3243] - 3 X[27475], 5 X[3617] - 4 X[3739], 7 X[3622] - 8 X[4698], 5 X[3623] - 7 X[27268], 3 X[3679] - 2 X[24325], 5 X[4668] - 4 X[4732], 7 X[4678] - 5 X[4699], 4 X[4681] + X[20054], 5 X[4704] - X[20014], 10 X[31238] - 11 X[46933]

X(49450) lies on these lines: {1, 872}, {2, 4849}, {7, 8}, {10, 4684}, {37, 145}, {63, 3996}, {72, 4043}, {190, 3886}, {192, 3621}, {200, 14829}, {210, 10453}, {239, 3242}, {312, 3681}, {321, 4661}, {333, 3870}, {335, 9041}, {341, 10449}, {344, 5686}, {354, 4113}, {516, 17347}, {517, 48878}, {519, 751}, {536, 31145}, {537, 4677}, {668, 21615}, {726, 3625}, {740, 3632}, {899, 31233}, {952, 30273}, {982, 4685}, {1001, 17335}, {1150, 3935}, {1278, 20052}, {1279, 17349}, {1386, 36534}, {1738, 48629}, {1757, 4676}, {1992, 4344}, {2275, 21897}, {2321, 4899}, {2895, 5014}, {2975, 15624}, {3240, 46909}, {3241, 15569}, {3243, 4384}, {3434, 33066}, {3555, 9534}, {3617, 3739}, {3622, 4698}, {3623, 27268}, {3666, 20012}, {3679, 17297}, {3685, 5220}, {3699, 27489}, {3706, 32937}, {3711, 5205}, {3717, 17233}, {3742, 26038}, {3744, 37652}, {3751, 3758}, {3755, 4389}, {3757, 4042}, {3769, 3961}, {3774, 16975}, {3775, 29659}, {3786, 30939}, {3789, 30963}, {3797, 20055}, {3823, 17232}, {3844, 48639}, {3869, 20248}, {3873, 4651}, {3894, 4714}, {3896, 7226}, {3912, 24393}, {3932, 17240}, {3938, 32864}, {3957, 5278}, {3999, 24620}, {4005, 19582}, {4026, 17250}, {4032, 37709}, {4051, 20593}, {4310, 37756}, {4359, 4430}, {4360, 7174}, {4388, 4863}, {4393, 27495}, {4416, 5853}, {4417, 4847}, {4429, 17227}, {4431, 4923}, {4457, 42055}, {4479, 17794}, {4514, 5739}, {4531, 17144}, {4649, 36480}, {4668, 4732}, {4669, 31178}, {4678, 4699}, {4681, 20054}, {4690, 24357}, {4701, 4709}, {4702, 15481}, {4704, 20014}, {4753, 16468}, {4850, 19998}, {4864, 17348}, {4901, 17294}, {4952, 20056}, {4966, 17241}, {4981, 17018}, {5057, 21283}, {5233, 26015}, {5269, 41629}, {5743, 29843}, {5844, 20430}, {5846, 17363}, {5881, 29054}, {6682, 42043}, {9053, 17362}, {9451, 24586}, {10005, 27484}, {12513, 34247}, {12645, 29010}, {14552, 20015}, {14555, 36845}, {14923, 20718}, {16496, 32922}, {16823, 42871}, {16826, 20156}, {16830, 17394}, {17121, 38315}, {17156, 32926}, {17165, 42029}, {17263, 38057}, {17264, 27549}, {17298, 38200}, {17329, 24723}, {17371, 38047}, {17381, 19868}, {17389, 31323}, {17490, 21342}, {17751, 20923}, {18134, 25006}, {18157, 33297}, {20011, 28606}, {20942, 27538}, {21085, 33169}, {21384, 39258}, {21805, 30942}, {24003, 31137}, {27291, 45219}, {29615, 31317}, {29673, 33084}, {29824, 30829}, {31136, 32931}, {31238, 46933}, {32859, 33110}, {32865, 33064}, {32912, 32945}, {33065, 33136}, {33081, 33117}, {33114, 33175}, {33118, 33171}, {33122, 33139}, {33126, 33137}

X(49450) = midpoint of X(192) and X(3621)
X(49450) = reflection of X(i) in X(j) for these {i,j}: {75, 8}, {145, 37}, {4709, 4701}, {24349, 3696}, {24357, 4690}, {31178, 4669}
X(49450) = barycentric product X(8)*X(31225)
X(49450) = barycentric quotient X(31225)/X(7)
X(49450) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 69, 32850}, {8, 24349, 3696}, {10, 4684, 17234}, {75, 16284, 20448}, {210, 10453, 18743}, {1757, 32941, 4676}, {3681, 17135, 312}, {3685, 5220, 17336}, {3696, 24349, 75}, {3706, 32937, 42034}, {3751, 5263, 3758}, {3873, 4651, 19804}, {3886, 5223, 190}, {3961, 32853, 3769}, {4042, 41711, 3757}, {10449, 34790, 341}


X(49451) = X(1)X(2)∩X(57)X(3996)

Barycentrics    a^3 - 4*a^2*b + 3*a*b^2 - 4*a^2*c + 2*b^2*c + 3*a*c^2 + 2*b*c^2 : :
X(49451) = 4 X[1] - 3 X[16834], 2 X[8] - 3 X[17294], 5 X[3617] - 6 X[29594], 3 X[3729] - 4 X[5695], 3 X[3886] - 2 X[5695], 3 X[3751] - 4 X[4672], 2 X[4672] - 3 X[32941], 4 X[3755] - 5 X[17304], 2 X[4663] - 3 X[48805]

X(49451) lies on these lines: {1, 2}, {57, 3996}, {69, 5853}, {75, 3243}, {85, 3340}, {213, 37542}, {333, 10389}, {344, 24393}, {346, 4899}, {390, 4416}, {391, 8236}, {518, 3729}, {728, 21384}, {740, 16496}, {1043, 6762}, {1222, 2279}, {1441, 11526}, {2136, 37555}, {2223, 12513}, {2481, 3680}, {2550, 4684}, {2809, 3869}, {3158, 14829}, {3242, 3875}, {3681, 30568}, {3685, 5223}, {3696, 42871}, {3706, 41711}, {3748, 4042}, {3749, 32853}, {3751, 4672}, {3755, 17304}, {3893, 20358}, {3913, 37575}, {4001, 20075}, {4050, 24578}, {4113, 4423}, {4361, 4864}, {4417, 24392}, {4663, 48805}, {4673, 11523}, {4702, 5220}, {4779, 6172}, {4901, 17233}, {4923, 42696}, {4924, 17355}, {5686, 25101}, {5839, 16970}, {5850, 24280}, {6604, 10106}, {7176, 32003}, {7406, 43170}, {9053, 16973}, {9580, 33066}, {11038, 24199}, {11520, 20880}, {11531, 41792}, {11682, 30807}, {12630, 32099}, {15829, 30854}, {16517, 17314}, {17234, 38200}, {17277, 38316}, {17296, 32850}, {19804, 44841}, {28566, 40341}, {43166, 48878}

X(49451) = reflection of X(i) in X(j) for these {i,j}: {3729, 3886}, {3751, 32941}, {3875, 3242}, {4924, 17355}
X(49451) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 8, 4384}, {1, 16830, 29597}, {8, 29627, 3617}, {200, 10453, 30567}, {2550, 4684, 17298}, {3241, 16830, 1}, {3244, 36480, 1}, {3621, 29616, 8}, {3623, 16826, 1}, {3685, 5223, 25728}, {3870, 17135, 11679}, {16284, 17144, 2481}


X(49452) = X(1)X(536)∩X(8)X(192)

Barycentrics    2*a^2*b + a*b^2 + 2*a^2*c + a*b*c - 2*b^2*c + a*c^2 - 2*b*c^2 : :
X(49452) = 4 X[1] - 3 X[31178], X[8] - 3 X[192], 2 X[8] - 3 X[984], 2 X[10] - 3 X[4664], 6 X[37] - 5 X[1698], 3 X[75] - 4 X[1125], 4 X[75] - 5 X[40328], 2 X[1125] - 3 X[3993], 16 X[1125] - 15 X[40328], 8 X[3993] - 5 X[40328], X[3633] + 6 X[4718], 2 X[3244] + 3 X[3644], 3 X[1278] - 7 X[3622], 7 X[3622] - 6 X[24325], 5 X[3616] - 3 X[4740], 5 X[3623] + 3 X[4788], 5 X[3623] - 3 X[24349], 7 X[3624] - 6 X[4688], 12 X[3739] - 13 X[34595], 4 X[3842] - 5 X[4704], 12 X[3842] - 11 X[46933], 15 X[4704] - 11 X[46933], 4 X[4691] - 3 X[4709], 2 X[18480] - 3 X[20430], X[20014] + 3 X[31302], 3 X[30273] - 2 X[31730]

X(49452) lies on these lines: {1, 536}, {8, 192}, {9, 4716}, {10, 4664}, {37, 1698}, {42, 42044}, {43, 3175}, {75, 1125}, {145, 537}, {238, 3875}, {306, 33154}, {312, 4970}, {320, 33869}, {321, 17592}, {335, 39720}, {345, 33135}, {346, 33159}, {350, 3795}, {518, 3633}, {726, 3244}, {982, 17147}, {986, 2901}, {1278, 3622}, {1738, 3950}, {1757, 17262}, {1962, 28605}, {1999, 4650}, {2321, 32784}, {3187, 7262}, {3210, 17063}, {3240, 3994}, {3241, 28554}, {3616, 4740}, {3623, 4788}, {3624, 4688}, {3661, 4527}, {3663, 33087}, {3666, 4519}, {3685, 32921}, {3696, 4681}, {3712, 29658}, {3717, 4780}, {3723, 43997}, {3729, 4649}, {3739, 34595}, {3755, 33165}, {3775, 17247}, {3790, 4085}, {3797, 17367}, {3821, 17233}, {3836, 17242}, {3842, 4704}, {3879, 28526}, {3891, 17715}, {3896, 32925}, {3912, 33149}, {3914, 33092}, {3923, 4360}, {3943, 29674}, {3967, 42043}, {3969, 32776}, {3980, 34064}, {3995, 32860}, {4003, 31137}, {4028, 33101}, {4062, 33151}, {4133, 4357}, {4169, 20006}, {4312, 4898}, {4365, 28606}, {4387, 29821}, {4393, 4672}, {4429, 6541}, {4439, 4743}, {4442, 29643}, {4655, 6542}, {4671, 46904}, {4683, 20017}, {4686, 15569}, {4691, 4709}, {4777, 6161}, {4851, 32857}, {4852, 16468}, {4854, 32778}, {5904, 44671}, {6685, 42034}, {6686, 20942}, {6745, 20173}, {7201, 10404}, {11997, 41864}, {12699, 29010}, {16477, 16834}, {16569, 35652}, {16777, 24342}, {16825, 17160}, {17281, 29633}, {17292, 27474}, {17299, 33082}, {17301, 29637}, {17302, 25539}, {17314, 24248}, {17364, 17767}, {17365, 28556}, {17377, 17770}, {17380, 24295}, {17388, 17768}, {17389, 28542}, {17393, 33682}, {17395, 29646}, {17601, 17763}, {17716, 32928}, {17755, 27480}, {17776, 33132}, {18480, 20430}, {19785, 33158}, {19796, 29642}, {19856, 41312}, {20012, 42054}, {20014, 31302}, {20171, 27385}, {24210, 32855}, {25453, 42033}, {26102, 42051}, {27804, 32771}, {30273, 31730}, {30699, 33130}, {32848, 33134}, {32849, 33128}, {32852, 33100}, {32858, 33145}, {33088, 33095}, {33093, 33094}, {33155, 33156}, {42029, 43223}

X(49452) = midpoint of X(4788) and X(24349)
X(49452) = reflection of X(i) in X(j) for these {i,j}: {75, 3993}, {984, 192}, {1278, 24325}, {3696, 4681}, {4686, 15569}
X(49452) = crossdifference of every pair of points on line {20981, 39521}
X(49452) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1999, 32934, 4650}, {3187, 32936, 7262}, {3666, 4519, 29827}, {5695, 17318, 1}, {17147, 32915, 982}, {17314, 24248, 32846}, {32928, 32929, 17716}


X(49453) = X(1)X(536)∩X(2)X(6057)

Barycentrics    a^3 + a^2*b + 2*a*b^2 + a^2*c - 2*b^2*c + 2*a*c^2 - 2*b*c^2 : :
X(49453) = 4 X[1] - 3 X[48805], 2 X[5695] - 3 X[48805], 7 X[6] - 8 X[4991], 3 X[6] - 2 X[32935], 4 X[4991] - 7 X[32921], 12 X[4991] - 7 X[32935], 3 X[32921] - X[32935], 2 X[8] - 3 X[48829], 2 X[10] - 3 X[17301], 4 X[1125] - 3 X[17281], 5 X[1698] - 6 X[17382], 5 X[3617] - 6 X[48821], 7 X[3622] - 6 X[48810], 7 X[3624] - 6 X[17359], 5 X[3763] - 4 X[3773], 4 X[3844] - 5 X[17304], 2 X[3923] - 3 X[38315], 4 X[3946] - 3 X[38047], 2 X[4663] - 3 X[16834], 3 X[16475] - 2 X[17351]

X(49453) lies on these lines: {1, 536}, {2, 6057}, {6, 726}, {8, 4389}, {10, 17119}, {45, 16825}, {55, 3891}, {56, 4552}, {75, 16830}, {141, 28472}, {145, 528}, {192, 1001}, {193, 5852}, {238, 17262}, {239, 5220}, {321, 17599}, {345, 17061}, {518, 3875}, {519, 4655}, {545, 24695}, {612, 42051}, {614, 3175}, {740, 3242}, {940, 17155}, {984, 4361}, {1125, 4029}, {1266, 5880}, {1278, 5263}, {1279, 4718}, {1376, 3210}, {1386, 3729}, {1482, 2783}, {1698, 17382}, {2321, 4353}, {2550, 4452}, {2886, 30699}, {2999, 3967}, {3052, 32934}, {3058, 19993}, {3216, 4069}, {3244, 28580}, {3416, 3663}, {3555, 44670}, {3617, 48821}, {3622, 48810}, {3624, 17359}, {3644, 3685}, {3666, 29828}, {3672, 4026}, {3696, 7174}, {3703, 19785}, {3712, 26228}, {3751, 4852}, {3763, 3773}, {3782, 33088}, {3790, 16706}, {3844, 17304}, {3886, 28484}, {3896, 41711}, {3923, 28516}, {3925, 19789}, {3932, 4000}, {3946, 38047}, {3971, 37679}, {3989, 19732}, {3995, 4423}, {4042, 7226}, {4054, 17723}, {4078, 17278}, {4259, 14839}, {4310, 4966}, {4360, 24349}, {4383, 32924}, {4387, 7191}, {4398, 4645}, {4402, 38057}, {4413, 17495}, {4419, 17224}, {4436, 37590}, {4442, 29832}, {4660, 17769}, {4663, 16834}, {4664, 16823}, {4672, 28554}, {4688, 39586}, {4733, 32087}, {4756, 14997}, {4851, 24231}, {4884, 33137}, {4942, 27064}, {4970, 32920}, {4974, 16885}, {5272, 35652}, {5846, 24248}, {5847, 17276}, {6144, 17771}, {6541, 17267}, {7232, 32846}, {7976, 38499}, {8167, 41839}, {11235, 29840}, {12513, 44352}, {16466, 43993}, {16475, 17351}, {16496, 28581}, {16777, 24325}, {17025, 41242}, {17070, 30741}, {17133, 47358}, {17150, 32933}, {17255, 33082}, {17269, 29637}, {17285, 26150}, {17290, 29674}, {17309, 33087}, {17316, 25557}, {17323, 32784}, {17595, 17763}, {17597, 32915}, {17602, 17740}, {17772, 40341}, {19796, 29641}, {19899, 23869}, {20020, 34612}, {20132, 27494}, {20135, 27478}, {20154, 27481}, {20182, 32771}, {21342, 39594}, {24165, 37674}, {24180, 34261}, {24280, 28556}, {24441, 24697}, {27480, 32029}, {28522, 32941}, {29113, 48661}, {30811, 32848}, {32842, 33151}, {32845, 37540}, {32847, 33149}, {32854, 33145}, {32855, 33152}, {32862, 33150}, {32866, 33154}, {33089, 33155}, {33092, 33147}, {33093, 33146}, {37660, 46901}, {39567, 47357}

X(49453) = reflection of X(i) in X(j) for these {i,j}: {6, 32921}, {2321, 4353}, {3416, 3663}, {3729, 1386}, {3751, 4852}, {5695, 1}
X(49453) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5695, 48805}, {192, 32922, 1001}, {3210, 32926, 1376}, {3891, 17147, 55}, {4310, 17314, 4966}, {4442, 29832, 31140}, {7174, 17151, 3696}, {7191, 42044, 4387}, {17155, 32928, 940}, {32848, 33143, 30811}, {32924, 32925, 4383}


X(49454) = X(1)X(21)∩X(8)X(2887)

Barycentrics    a*(a^3 - a^2*b + 2*b^3 - a^2*c + 2*c^3) : :
X(49454) = 4 X[10] - 5 X[31237], 2 X[4680] - 3 X[31134], 5 X[3616] - 4 X[6679], 5 X[3623] - X[20064], 3 X[10283] - 2 X[20575], 3 X[33143] - 4 X[39544]

X(49454) lies on these lines: {1, 21}, {8, 2887}, {10, 31237}, {30, 33098}, {37, 44840}, {41, 3721}, {65, 976}, {72, 3924}, {75, 7257}, {78, 24443}, {145, 6327}, {200, 4695}, {209, 4517}, {244, 997}, {386, 41696}, {517, 3938}, {518, 36267}, {519, 3891}, {612, 11529}, {674, 1469}, {734, 7976}, {740, 37003}, {748, 5692}, {750, 5902}, {752, 3241}, {899, 3940}, {960, 28082}, {982, 4511}, {986, 34772}, {995, 4867}, {999, 17449}, {1104, 3962}, {1149, 5289}, {1193, 12635}, {1201, 5730}, {1279, 31165}, {1319, 21342}, {1320, 3551}, {1478, 32856}, {1722, 3984}, {1724, 4067}, {1739, 9350}, {1854, 2098}, {2170, 16973}, {2177, 4424}, {2251, 36283}, {2280, 3735}, {2835, 4319}, {3120, 3419}, {3340, 28039}, {3476, 4331}, {3616, 6679}, {3623, 20064}, {3670, 22836}, {3720, 15934}, {3722, 5119}, {3744, 44663}, {3782, 44669}, {3811, 4642}, {3872, 16496}, {3905, 17137}, {3930, 9620}, {3953, 30144}, {4018, 5266}, {4084, 5264}, {4168, 26085}, {4257, 4880}, {4332, 12709}, {4343, 42871}, {4392, 37617}, {4414, 24929}, {4420, 24440}, {4864, 5919}, {4920, 21285}, {5080, 33101}, {5255, 36565}, {5425, 30116}, {5719, 29678}, {5837, 28027}, {5883, 17124}, {6737, 23536}, {9364, 18419}, {10176, 17125}, {10283, 20575}, {10459, 28388}, {10544, 23154}, {11114, 33099}, {13161, 41575}, {15829, 28011}, {16086, 25957}, {16483, 29818}, {17054, 27627}, {17142, 32941}, {17579, 32857}, {17721, 34647}, {18193, 35262}, {19860, 25894}, {19869, 26061}, {21935, 49168}, {25681, 28096}, {30105, 46899}, {31053, 37717}, {31272, 31520}, {32853, 39766}, {32859, 38456}, {33104, 39542}, {33143, 39544}, {33145, 48837}, {33153, 37716}

X(49454) = midpoint of X(145) and X(6327)
X(49454) = reflection of X(i) in X(j) for these {i,j}: {8, 2887}, {31, 1}
X(49454) = crosssum of X(1) and X(37817)
X(49454) = barycentric product X(1)*X(30811)
X(49454) = barycentric quotient X(30811)/X(75)
X(49454) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3868, 1468}, {1, 3869, 3915}, {1, 3899, 40091}, {1, 3901, 58}, {1, 12559, 2650}, {3953, 30144, 32577}, {5289, 17597, 1149}, {5692, 30117, 748}, {5902, 30115, 750}, {12635, 37549, 1193}


X(49455) = X(1)X(87)∩X(6)X(537)

Barycentrics    a^3 + 2*a*b^2 - b^2*c + 2*a*c^2 - b*c^2 : :
X(49455) = 3 X[1] - X[3729], 2 X[3729] - 3 X[3923], 2 X[4852] - 3 X[32921], 3 X[551] - 2 X[17355], 5 X[3616] - 4 X[24295], 5 X[3623] - X[24280], 3 X[3679] - 5 X[17304], 2 X[4085] - 3 X[17301], 2 X[4672] - 3 X[38315], X[17299] - 3 X[47358]

X(49455) lies on these lines: {1, 87}, {6, 537}, {8, 3821}, {10, 4000}, {37, 24331}, {38, 1150}, {42, 24260}, {69, 519}, {75, 4495}, {86, 31178}, {141, 28503}, {145, 17766}, {238, 17336}, {312, 17598}, {321, 29652}, {344, 1125}, {345, 29656}, {386, 8865}, {516, 944}, {517, 24728}, {518, 4523}, {536, 32941}, {551, 3247}, {596, 30142}, {612, 24165}, {614, 3971}, {740, 3242}, {752, 17276}, {940, 42055}, {982, 29649}, {984, 16825}, {988, 8669}, {1215, 17599}, {1278, 36534}, {1386, 28582}, {1482, 29057}, {1757, 31302}, {2784, 39898}, {2796, 3241}, {2999, 4090}, {3006, 33143}, {3120, 29832}, {3159, 30148}, {3210, 3961}, {3416, 17769}, {3555, 12721}, {3616, 24295}, {3623, 24280}, {3635, 28526}, {3644, 4693}, {3662, 32847}, {3666, 29670}, {3672, 36479}, {3677, 3840}, {3679, 17117}, {3681, 32924}, {3703, 26128}, {3705, 33152}, {3744, 32934}, {3782, 4865}, {3790, 29637}, {3870, 4970}, {3873, 32928}, {3874, 10441}, {3879, 33869}, {3881, 32118}, {3886, 28522}, {3920, 3980}, {3938, 17147}, {3944, 29840}, {4011, 7191}, {4085, 17301}, {4096, 37679}, {4256, 18048}, {4310, 4869}, {4360, 24841}, {4383, 42054}, {4389, 33076}, {4392, 17763}, {4393, 17738}, {4398, 24715}, {4407, 17275}, {4414, 20045}, {4418, 29815}, {4432, 17262}, {4434, 17595}, {4438, 4884}, {4439, 17279}, {4514, 33154}, {4655, 5846}, {4664, 16484}, {4672, 38315}, {4681, 42819}, {4699, 36531}, {4702, 4718}, {4709, 17151}, {4732, 17119}, {4759, 25728}, {4850, 32927}, {4862, 24692}, {4906, 35652}, {4967, 48809}, {4974, 5220}, {5014, 33145}, {5278, 42039}, {5311, 17140}, {5695, 28516}, {5904, 43993}, {6534, 48866}, {7033, 34020}, {7081, 17591}, {7226, 32914}, {7263, 24693}, {8720, 37552}, {10327, 24169}, {13735, 16498}, {14976, 28562}, {15485, 17261}, {15668, 24325}, {16706, 33165}, {17017, 17165}, {17018, 24259}, {17024, 32930}, {17150, 20068}, {17184, 32854}, {17280, 29660}, {17299, 47358}, {17302, 29659}, {17318, 42871}, {17345, 28538}, {17350, 24821}, {17383, 36478}, {17469, 32933}, {17716, 32939}, {17725, 32851}, {17776, 29672}, {19785, 29673}, {19786, 33169}, {19796, 32865}, {20145, 29584}, {24210, 29844}, {24309, 25439}, {25354, 39581}, {25590, 48854}, {26223, 29819}, {26227, 46901}, {26230, 33161}, {27184, 32866}, {28554, 48805}, {28606, 29651}, {29588, 41842}, {29634, 33167}, {29636, 33170}, {29638, 32849}, {29641, 33147}, {29643, 33148}, {29644, 32771}, {29654, 33163}, {29671, 30828}, {29676, 37759}, {29820, 41839}, {29821, 32937}, {29848, 33168}, {29849, 33153}, {29852, 33166}, {31151, 48629}, {31995, 48856}, {32087, 48802}, {32774, 33162}, {32775, 33089}, {32776, 33090}, {32842, 33065}, {32844, 33151}, {32848, 33122}, {32850, 33149}, {32855, 33126}, {32856, 33070}, {32862, 33123}, {32943, 42044}, {33064, 33088}, {33069, 33093}, {33071, 33101}, {33072, 33146}, {33073, 33103}, {33091, 33125}, {33092, 33124}, {33117, 33150}, {33120, 33155}, {37674, 42053}

X(49455) = midpoint of X(i) and X(j) for these {i,j}: {145, 24248}, {3555, 12721}, {3875, 16496}
X(49455) = reflection of X(i) in X(j) for these {i,j}: {8, 3821}, {10, 4353}, {3923, 1}, {4660, 3663}, {32118, 3881}, {32935, 1386}
X(49455) = crossdifference of every pair of points on line {20979, 47330}
X(49455) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {38, 3891, 4362}, {312, 17598, 29668}, {982, 32926, 29649}, {984, 32922, 16825}, {1215, 17599, 29650}, {3666, 32920, 29670}, {3920, 17155, 3980}, {4884, 17061, 4438}, {7191, 32925, 4011}, {17150, 20068, 32912}, {28606, 32923, 29651}


X(49456) = X(1)X(190)∩X(2)X(3994)

Barycentrics    a^2*b + 2*a*b^2 + a^2*c + 2*a*b*c - b^2*c + 2*a*c^2 - b*c^2 : :
X(49456) = X[1] - 3 X[4664], X[8] + 3 X[192], X[8] - 3 X[984], 3 X[37] - 2 X[1125], 4 X[1125] - 3 X[24325], 3 X[75] - 5 X[1698], 5 X[1698] - 6 X[3842], X[3244] - 3 X[3993], X[3244] - 6 X[4681], 3 X[1278] - 11 X[46933], 5 X[3616] - 3 X[31178], 7 X[3622] - 15 X[4704], 7 X[3622] - 3 X[24349], 5 X[4704] - X[24349], 5 X[3623] + 3 X[31302], 4 X[3634] - 3 X[4688], X[3644] + 2 X[4732], 3 X[3696] - 4 X[4691], 4 X[4691] + 3 X[4718], 15 X[4687] - 13 X[34595], 3 X[4740] - 7 X[9780], 6 X[4755] - 5 X[19862], 21 X[4772] - 29 X[46930], X[12699] - 3 X[20430], 7 X[27268] - 5 X[40328]

X(49456) lies on these lines: {1, 190}, {2, 3994}, {8, 192}, {9, 4974}, {10, 536}, {37, 39}, {38, 3995}, {42, 42054}, {43, 4096}, {45, 16825}, {75, 1089}, {141, 6541}, {210, 4970}, {238, 17261}, {244, 31035}, {312, 6682}, {321, 3989}, {335, 29569}, {350, 40774}, {518, 3244}, {612, 32934}, {714, 3743}, {756, 17147}, {846, 32926}, {899, 42056}, {968, 32920}, {982, 30947}, {1215, 28606}, {1278, 46933}, {1757, 4360}, {1961, 32939}, {1962, 17165}, {2276, 17793}, {2321, 3775}, {3097, 30963}, {3175, 3741}, {3219, 3791}, {3616, 31178}, {3622, 4704}, {3623, 31302}, {3634, 4688}, {3644, 4732}, {3661, 4535}, {3663, 3836}, {3666, 3971}, {3696, 4691}, {3703, 4425}, {3717, 4085}, {3720, 42055}, {3739, 28555}, {3773, 4357}, {3782, 29653}, {3790, 17247}, {3797, 17292}, {3821, 3932}, {3840, 35652}, {3846, 4656}, {3879, 17771}, {3883, 17769}, {3920, 32936}, {3923, 17262}, {3952, 46904}, {3967, 6685}, {3985, 41269}, {4003, 4871}, {4011, 17599}, {4032, 10404}, {4065, 44671}, {4098, 5542}, {4122, 4913}, {4135, 44417}, {4358, 46901}, {4365, 4981}, {4387, 29652}, {4389, 29674}, {4407, 4527}, {4414, 4434}, {4415, 29671}, {4416, 17772}, {4419, 4655}, {4505, 6376}, {4649, 17319}, {4651, 42041}, {4659, 39586}, {4683, 33093}, {4687, 34595}, {4697, 5311}, {4703, 33088}, {4709, 28484}, {4740, 9780}, {4753, 5220}, {4755, 19862}, {4772, 46930}, {4780, 24393}, {4850, 24003}, {4852, 15481}, {4854, 29673}, {4884, 29655}, {4892, 29643}, {4991, 16669}, {5205, 17593}, {5231, 20173}, {5297, 32845}, {5625, 16777}, {5695, 36480}, {5718, 21093}, {5852, 17390}, {5880, 24404}, {6646, 32846}, {7174, 32941}, {7226, 32915}, {10180, 32771}, {12699, 20430}, {15569, 28582}, {16468, 17336}, {16475, 25728}, {17011, 32938}, {17019, 32940}, {17135, 42039}, {17154, 17450}, {17242, 33087}, {17258, 33082}, {17264, 29637}, {17302, 33159}, {17320, 29633}, {17334, 17770}, {17351, 33682}, {17354, 29646}, {17358, 25539}, {17367, 17755}, {17591, 18743}, {17592, 32937}, {17600, 27064}, {17722, 17777}, {17776, 26128}, {18480, 29010}, {19786, 33164}, {20073, 24695}, {21801, 24484}, {23689, 28974}, {24165, 44307}, {24723, 32847}, {24850, 30142}, {25101, 31289}, {25124, 31320}, {25351, 33149}, {26102, 42053}, {26580, 32848}, {27065, 32924}, {27184, 33092}, {27268, 40328}, {27269, 46032}, {27494, 31336}, {27798, 28605}, {28595, 32776}, {29057, 31395}, {29606, 43180}, {29641, 33154}, {29645, 44416}, {29822, 31161}, {29854, 33146}, {31330, 42044}, {32775, 32849}, {32783, 42033}, {32913, 34064}, {32914, 33761}, {33072, 33100}, {33073, 33099}, {33115, 33155}, {33116, 33152}

X(49456) = midpoint of X(i) and X(j) for these {i,j}: {192, 984}, {3696, 4718}
X(49456) = reflection of X(i) in X(j) for these {i,j}: {75, 3842}, {3993, 4681}, {24325, 37}
X(49456) = crossdifference of every pair of points on line {3768, 4057}
X(49456) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 190, 4672}, {9, 32921, 4974}, {3097, 30963, 40533}, {3219, 32928, 3791}, {3663, 4078, 3836}, {3790, 17247, 32784}, {3932, 17246, 3821}, {5311, 32933, 4697}, {28606, 32925, 1215}, {29643, 33151, 4892}, {32776, 32862, 28595}


X(49457) = X(1)X(872)∩X(2)X(17145)

Barycentrics    a^2*b - 2*a*b^2 + a^2*c - 2*a*b*c - b^2*c - 2*a*c^2 - b*c^2 : :
X(49457) = 3 X[1] - 5 X[4687], 6 X[3842] - 5 X[4687], 3 X[8] + X[192], X[192] - 3 X[984], 3 X[10] - 2 X[3739], 4 X[3739] - 3 X[24325], 3 X[5883] - 2 X[13476], X[75] - 3 X[3679], 3 X[3679] - 2 X[4732], 3 X[4669] - X[4709], 3 X[551] - 4 X[4698], 6 X[3626] - X[4686], 3 X[3696] - X[4686], 3 X[3241] - 7 X[27268], 15 X[3617] - 7 X[4772], 5 X[3617] - X[24349], 7 X[4772] - 3 X[24349], 6 X[3828] - 5 X[31238], 15 X[4668] - X[4764], 21 X[4678] - 5 X[4821], 7 X[4678] + X[31302], 5 X[4821] + 3 X[31302], 2 X[4681] + 3 X[34641], 5 X[4699] - 3 X[31178], 5 X[4704] + 3 X[31145], 4 X[4739] - 9 X[38098], 7 X[4751] - 9 X[19875], 7 X[9780] - 5 X[40328], 3 X[10176] - 4 X[40607], 3 X[17251] - X[24357]

X(49457) lies on these lines: {1, 872}, {2, 17145}, {6, 4753}, {7, 24693}, {8, 192}, {9, 4432}, {10, 141}, {37, 519}, {38, 4651}, {39, 21897}, {42, 4981}, {43, 6682}, {75, 537}, {86, 36531}, {200, 32916}, {210, 3741}, {214, 27473}, {239, 27495}, {312, 4096}, {319, 32847}, {321, 42054}, {333, 3961}, {355, 29054}, {517, 45305}, {524, 25384}, {528, 17332}, {536, 4669}, {551, 4698}, {612, 32853}, {678, 30564}, {726, 3626}, {742, 4690}, {752, 4416}, {756, 17135}, {846, 3996}, {899, 46909}, {908, 21242}, {956, 34247}, {966, 36479}, {982, 24620}, {993, 15624}, {1107, 3774}, {1125, 17337}, {1150, 4434}, {1211, 29673}, {1215, 3681}, {1278, 28554}, {1449, 48854}, {1698, 17283}, {1757, 4672}, {1921, 25280}, {1962, 20011}, {2321, 4439}, {2345, 48802}, {2550, 4655}, {2796, 17334}, {2887, 25006}, {2895, 33072}, {3219, 32945}, {3241, 27268}, {3242, 16825}, {3244, 15569}, {3252, 38980}, {3434, 4703}, {3617, 4772}, {3625, 3993}, {3636, 4989}, {3661, 17755}, {3662, 25351}, {3666, 4113}, {3697, 3831}, {3703, 21085}, {3706, 3971}, {3711, 37660}, {3715, 4011}, {3717, 3773}, {3740, 3840}, {3789, 17793}, {3790, 4535}, {3791, 3920}, {3797, 29615}, {3828, 31238}, {3846, 4104}, {3873, 26037}, {3883, 17765}, {3896, 3989}, {3902, 22016}, {3923, 5220}, {3925, 33064}, {3935, 32917}, {3938, 5278}, {3992, 18137}, {3995, 42041}, {4032, 5252}, {4042, 4362}, {4085, 4357}, {4090, 44417}, {4133, 4923}, {4358, 31136}, {4359, 42055}, {4383, 29652}, {4384, 16496}, {4399, 28503}, {4457, 7226}, {4643, 4660}, {4649, 16830}, {4661, 27798}, {4663, 33682}, {4664, 4677}, {4668, 4764}, {4678, 4821}, {4681, 34641}, {4683, 33110}, {4688, 4745}, {4693, 17261}, {4697, 32912}, {4699, 31178}, {4702, 16814}, {4704, 31145}, {4723, 20891}, {4739, 38098}, {4746, 28522}, {4751, 19875}, {4759, 15492}, {4771, 41269}, {4849, 6685}, {4865, 5739}, {4883, 25501}, {4886, 32866}, {4892, 33065}, {4969, 36409}, {5223, 32935}, {5224, 29659}, {5233, 29676}, {5271, 32920}, {5297, 32919}, {5737, 29670}, {5741, 29690}, {5743, 29655}, {5881, 30273}, {6542, 31323}, {6646, 24715}, {7174, 32921}, {7322, 39594}, {9780, 40328}, {10176, 34587}, {10180, 17018}, {15485, 17335}, {16484, 17260}, {16552, 39258}, {16569, 31233}, {16826, 20138}, {16831, 31322}, {16832, 27475}, {16885, 48805}, {17063, 26038}, {17147, 42039}, {17165, 21020}, {17245, 25352}, {17251, 24357}, {17253, 48829}, {17259, 24331}, {17278, 47358}, {17288, 31151}, {17303, 47359}, {17307, 36478}, {17345, 24692}, {17347, 28558}, {17349, 36534}, {17352, 29660}, {17449, 24589}, {17469, 19742}, {17592, 20012}, {17716, 37652}, {19732, 29651}, {19804, 42053}, {19853, 41876}, {19998, 46904}, {21026, 31017}, {24003, 30942}, {24987, 26530}, {25146, 48639}, {26580, 33136}, {27065, 32943}, {27184, 32865}, {27317, 36546}, {27484, 29611}, {28595, 32782}, {28599, 43990}, {29570, 31336}, {29593, 31317}, {29641, 33084}, {29668, 37679}, {29685, 41809}, {29861, 30832}, {30271, 43174}, {30829, 31137}, {30970, 46897}, {31025, 31161}, {32775, 33139}, {32783, 33118}, {32844, 37656}, {32850, 33082}, {33066, 33109}, {33079, 37653}, {33115, 33175}, {33126, 33138}, {42057, 44307}

X(49457) = midpoint of X(i) and X(j) for these {i,j}: {8, 984}, {3625, 3993}, {4664, 4677}, {5881, 30273}
X(49457) = reflection of X(i) in X(j) for these {i,j}: {1, 3842}, {75, 4732}, {3244, 15569}, {3696, 3626}, {4688, 4745}, {24325, 10}, {30271, 43174}
X(49457) = X(28852)-complementary conjugate of X(514)
X(49457) = crossdifference of every pair of points on line {20981, 21007}
X(49457) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17145, 17450}, {8, 1654, 33076}, {9, 32941, 4432}, {75, 3679, 4732}, {1757, 5263, 4672}, {3666, 4113, 4685}, {3681, 31330, 1215}, {3920, 32864, 3791}, {4085, 4407, 4357}, {4104, 4847, 3846}, {17259, 42871, 24331}, {19732, 41711, 29651}, {32782, 33117, 28595}, {33065, 33108, 4892}


X(49458) = X(1)X(2)∩X(69)X(17766)

Barycentrics    a^3 - 2*a^2*b + 2*a*b^2 - 2*a^2*c + b^2*c + 2*a*c^2 + b*c^2 : :
X(49458) = 5 X[1] - 3 X[16834], 2 X[3626] - 3 X[29594], X[3632] - 3 X[17294], 5 X[3923] - 4 X[17351], 3 X[3923] - 2 X[32935], 6 X[17351] - 5 X[32935], 2 X[17351] - 5 X[32941], X[32935] - 3 X[32941], 2 X[4672] - 3 X[48805], 2 X[4743] - 3 X[17301], 4 X[4991] - 5 X[16491]

X(49458) lies on these lines: {1, 2}, {69, 17766}, {149, 33065}, {333, 17715}, {516, 39898}, {518, 3923}, {528, 4655}, {537, 5695}, {726, 3886}, {740, 3242}, {944, 2784}, {982, 3996}, {1107, 3991}, {1150, 3722}, {1215, 41711}, {2177, 46909}, {2223, 8666}, {2321, 16973}, {2809, 3878}, {2887, 4863}, {3058, 4703}, {3120, 21283}, {3416, 17765}, {3434, 33064}, {3673, 17144}, {3681, 4011}, {3696, 4864}, {3706, 32920}, {3711, 24003}, {3739, 15570}, {3744, 32853}, {3873, 3980}, {3950, 16517}, {3993, 7174}, {4353, 4780}, {4387, 42054}, {4418, 4430}, {4432, 5220}, {4514, 33084}, {4515, 17448}, {4660, 5853}, {4661, 32930}, {4672, 48805}, {4683, 34611}, {4743, 17301}, {4892, 31140}, {4991, 16491}, {5014, 33081}, {5150, 43146}, {5258, 23407}, {7982, 12251}, {8715, 37575}, {10914, 20358}, {12513, 37590}, {17143, 33930}, {17276, 17764}, {17299, 17769}, {17718, 21242}, {20504, 29304}, {21132, 48339}, {24253, 43149}, {24325, 42871}, {24693, 25557}, {27474, 32029}, {28498, 40341}, {28581, 32921}, {32850, 33087}, {32865, 33124}, {33069, 33110}, {33122, 33136}, {33126, 33141}

X(49458) = midpoint of X(3886) and X(16496)
X(49458) = reflection of X(i) in X(j) for these {i,j}: {3923, 32941}, {4780, 4353}
X(49458) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 8, 16825}, {1, 10, 24331}, {1, 3632, 239}, {1, 3679, 16823}, {1, 16831, 3636}, {1, 36531, 3616}, {1, 39586, 551}, {42, 29652, 29650}, {145, 36534, 1}, {3681, 32943, 4011}, {3741, 3870, 29670}, {3873, 32945, 3980}, {3938, 17135, 4362}, {3957, 31330, 29651}, {3961, 10453, 29649}, {20057, 29570, 1}, {39581, 48802, 10}


X(49459) = X(1)X(3696)∩X(2)X(4732)

Barycentrics    2*a^2*b - a*b^2 + 2*a^2*c - a*b*c - 2*b^2*c - a*c^2 - 2*b*c^2 : :
X(49459) = 3 X[1] - 4 X[3739], 4 X[1] - 5 X[40328], 3 X[3696] - 2 X[3739], 8 X[3696] - 5 X[40328], 16 X[3739] - 15 X[40328], 3 X[2] - 4 X[4732], 3 X[8] - X[192], 2 X[192] - 3 X[984], 6 X[10] - 5 X[4687], 2 X[37] - 3 X[3679], 4 X[75] - 3 X[31178], 8 X[4709] - 3 X[31178], 2 X[17378] - 3 X[24452], 3 X[145] - 7 X[4772], 7 X[4772] - 6 X[24325], 3 X[27474] - 2 X[32941], 3 X[3632] + 2 X[4686], X[1278] + 3 X[31145], 6 X[551] - 7 X[4751], 6 X[3625] + X[4764], 5 X[1698] - 4 X[15569], 3 X[3241] - 5 X[4699], 5 X[3617] - 4 X[3842], 3 X[3621] + 5 X[4821], 5 X[4821] - 3 X[24349], X[3644] - 6 X[34641], 8 X[4698] - 9 X[19875], 8 X[4739] - 3 X[34747], 3 X[5692] - 4 X[22271], 5 X[20052] - X[31302], 9 X[25055] - 10 X[31238]

X(49459) lies on these lines: {1, 3696}, {2, 4732}, {8, 192}, {9, 4693}, {10, 4687}, {37, 3679}, {43, 3706}, {69, 24715}, {75, 519}, {145, 4772}, {171, 17156}, {238, 3886}, {239, 27474}, {306, 32865}, {312, 4685}, {319, 4660}, {335, 20055}, {495, 21926}, {518, 3632}, {528, 17362}, {536, 4677}, {537, 1278}, {551, 4751}, {594, 29659}, {726, 3625}, {752, 17363}, {846, 4042}, {982, 17135}, {1150, 17601}, {1215, 20012}, {1320, 27488}, {1698, 15569}, {1738, 21255}, {1757, 5695}, {1921, 17144}, {2321, 33165}, {2550, 32846}, {2667, 30116}, {2796, 17347}, {2805, 9897}, {2895, 33094}, {3175, 4113}, {3187, 17716}, {3241, 4699}, {3434, 32861}, {3596, 4783}, {3617, 3842}, {3621, 4821}, {3626, 3993}, {3644, 34641}, {3661, 4085}, {3681, 4365}, {3687, 33141}, {3717, 4133}, {3750, 5271}, {3755, 4923}, {3775, 4743}, {3790, 4527}, {3797, 29617}, {3840, 31233}, {3896, 17592}, {3902, 20891}, {3914, 33084}, {3969, 33117}, {3996, 4362}, {4028, 33111}, {4046, 32778}, {4061, 24210}, {4062, 33108}, {4090, 42034}, {4357, 4780}, {4360, 36480}, {4384, 16484}, {4407, 17247}, {4416, 28580}, {4432, 17349}, {4442, 33065}, {4445, 48829}, {4460, 48856}, {4650, 32853}, {4651, 31035}, {4664, 4669}, {4671, 21805}, {4695, 21330}, {4698, 19875}, {4701, 28522}, {4702, 15485}, {4723, 22016}, {4734, 6682}, {4739, 34747}, {4742, 29982}, {4753, 17350}, {4816, 28484}, {4819, 5718}, {4847, 32855}, {4850, 31136}, {4863, 32866}, {4867, 27471}, {4891, 25502}, {4971, 24357}, {5252, 7201}, {5692, 22271}, {5727, 11997}, {5739, 33095}, {5904, 20718}, {7262, 32864}, {10449, 24440}, {10453, 17063}, {11362, 30273}, {12245, 29054}, {14459, 33070}, {15624, 48696}, {16496, 17151}, {16610, 31137}, {16777, 36531}, {16831, 31342}, {17018, 21020}, {17119, 42871}, {17122, 39594}, {17163, 20011}, {17232, 25351}, {17293, 36478}, {17296, 31151}, {17299, 32847}, {17300, 24693}, {17321, 48802}, {17322, 48809}, {17361, 24692}, {17366, 29660}, {17715, 32914}, {18137, 34587}, {18617, 37546}, {19804, 42057}, {19998, 32931}, {20016, 31317}, {20017, 33072}, {20052, 28516}, {20363, 21868}, {21085, 32773}, {21283, 32844}, {24437, 24464}, {25006, 33092}, {25055, 31238}, {27483, 29570}, {28653, 48822}, {31993, 42042}, {32852, 33110}, {33077, 33136}, {33081, 33131}, {33128, 33175}, {33132, 33171}, {33137, 33160}, {33139, 33156}, {36479, 42696}, {42043, 44417}, {48635, 48821}

X(49459) = midpoint of X(3621) and X(24349)
X(49459) = reflection of X(i) in X(j) for these {i,j}: {1, 3696}, {75, 4709}, {145, 24325}, {984, 8}, {3993, 3626}, {4664, 4669}, {30273, 11362}
X(49459) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3187, 32945, 17716}, {3896, 31330, 17592}, {4702, 17348, 15485}, {17135, 32860, 982}, {17163, 20011, 32771}, {32853, 32932, 4650}, {32864, 32929, 7262}


X(49460) = X(1)X(3696)∩X(6)X(519)

Barycentrics    a^3 - 3*a^2*b + 2*a*b^2 - 3*a^2*c + 2*b^2*c + 2*a*c^2 + 2*b*c^2 : :
X(49460) = 3 X[1] - 2 X[4852], 2 X[6] - 3 X[48805], 4 X[17355] - 3 X[47359], 4 X[32941] - 3 X[48805], 3 X[48832] - 4 X[48863], 4 X[141] - 3 X[48829], X[3729] - 3 X[3886], 2 X[3729] - 3 X[5695], 3 X[599] - 2 X[4660], 5 X[3618] - 6 X[48810], 7 X[3619] - 6 X[48821], 2 X[3663] - 3 X[47358], 3 X[3679] - 4 X[17229], 5 X[3763] - 4 X[4085], 2 X[4780] - 3 X[17301], 3 X[48801] - 2 X[48837], 3 X[48803] - 2 X[48847]

X(49460) lies on these lines: {1, 3696}, {6, 519}, {8, 344}, {9, 4702}, {10, 17267}, {55, 1150}, {56, 29746}, {69, 528}, {75, 42871}, {86, 3241}, {141, 48829}, {145, 5263}, {238, 3632}, {306, 4863}, {321, 41711}, {333, 4428}, {391, 47357}, {518, 3729}, {536, 16496}, {594, 36479}, {599, 4660}, {673, 29616}, {740, 3242}, {752, 40341}, {940, 32945}, {956, 8053}, {964, 2334}, {1043, 3286}, {1213, 48802}, {1278, 24841}, {1376, 3996}, {1441, 2099}, {1621, 4042}, {2163, 16401}, {2177, 31136}, {2550, 4869}, {2886, 30828}, {2895, 34611}, {3052, 32853}, {3058, 5739}, {3158, 35613}, {3305, 4113}, {3416, 5853}, {3618, 48810}, {3619, 48821}, {3633, 4649}, {3661, 20162}, {3663, 47358}, {3679, 16484}, {3681, 4387}, {3685, 5220}, {3686, 30331}, {3706, 3870}, {3711, 4358}, {3714, 6765}, {3723, 48854}, {3744, 17156}, {3748, 5271}, {3750, 5737}, {3763, 4085}, {3896, 17599}, {3913, 5132}, {3936, 21283}, {3974, 20015}, {4007, 16503}, {4101, 12701}, {4360, 36534}, {4366, 20055}, {4383, 32943}, {4384, 42819}, {4413, 29824}, {4417, 11235}, {4421, 14829}, {4423, 4651}, {4432, 16885}, {4445, 33076}, {4673, 12635}, {4677, 15485}, {4684, 5880}, {4685, 37679}, {4693, 17262}, {4709, 17119}, {4732, 24331}, {4733, 28635}, {4780, 17301}, {4851, 20181}, {4891, 5268}, {5687, 20470}, {5741, 11238}, {5774, 25439}, {5852, 24280}, {6542, 20172}, {7232, 24715}, {8692, 17349}, {10385, 14552}, {15533, 28562}, {15571, 34247}, {16394, 16474}, {16777, 36480}, {16833, 35227}, {17269, 33165}, {17276, 28580}, {17293, 29659}, {17309, 32847}, {17389, 20131}, {17398, 48830}, {17597, 32860}, {20011, 24552}, {20012, 32942}, {20049, 37677}, {20135, 29574}, {20150, 48858}, {20154, 29617}, {30811, 33136}, {32919, 37540}, {34607, 37655}, {35272, 47626}, {37474, 37727}, {37674, 42057}, {48801, 48837}, {48803, 48847}

X(49460) = reflection of X(i) in X(j) for these {i,j}: {6, 32941}, {5695, 3886}
X(49460) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 32941, 48805}, {2177, 31136, 37660}, {3679, 16484, 17259}, {3936, 21283, 31140}, {3996, 10453, 1376}


X(49461) = X(1)X(4686)∩X(10)X(37)

Barycentrics    (b + c)*(-5*a^2 - a*b - a*c + 4*b*c) : :
X(49461) = 4 X[10] - 5 X[37], 6 X[10] - 5 X[3696], 9 X[10] - 10 X[3842], 3 X[10] - 5 X[3993], 7 X[10] - 5 X[4709], 11 X[10] - 10 X[4732], 3 X[37] - 2 X[3696], 9 X[37] - 8 X[3842], 3 X[37] - 4 X[3993], 7 X[37] - 4 X[4709], 11 X[37] - 8 X[4732], 3 X[3696] - 4 X[3842], 7 X[3696] - 6 X[4709], 11 X[3696] - 12 X[4732], 2 X[3842] - 3 X[3993], 14 X[3842] - 9 X[4709], 11 X[3842] - 9 X[4732], 7 X[3993] - 3 X[4709], 11 X[3993] - 6 X[4732], 11 X[4709] - 14 X[4732], 5 X[75] - 7 X[3622], 5 X[192] - X[3621], 2 X[3633] + 5 X[4718], 9 X[3241] - 5 X[24349], 5 X[984] - 3 X[4677], 5 X[3616] - 4 X[4739], 10 X[3739] - 11 X[5550], 25 X[4687] - 23 X[46931], 3 X[4688] - 4 X[15569], 5 X[4688] - 6 X[25055], 9 X[4688] - 10 X[40328], 10 X[15569] - 9 X[25055], 6 X[15569] - 5 X[40328], 27 X[25055] - 25 X[40328], 25 X[31238] - 26 X[34595]

X(49461) lies on these lines: {1, 4686}, {8, 4681}, {10, 37}, {42, 22034}, {75, 3622}, {145, 3644}, {192, 3621}, {516, 17388}, {518, 3633}, {536, 3241}, {984, 4677}, {1100, 5695}, {1279, 3875}, {1386, 4693}, {2805, 9963}, {3175, 3896}, {3210, 4891}, {3244, 28516}, {3416, 4727}, {3616, 4739}, {3685, 4852}, {3739, 5550}, {3752, 30957}, {3823, 17242}, {3879, 28530}, {3883, 4971}, {3886, 17318}, {3923, 16666}, {3994, 21870}, {4365, 37593}, {4519, 46904}, {4687, 46931}, {4688, 15569}, {4690, 9791}, {4702, 32921}, {4706, 31197}, {4716, 15254}, {17147, 21342}, {17164, 31503}, {17365, 28557}, {17372, 24723}, {17374, 24248}, {17377, 28570}, {27804, 31993}, {31238, 34595}

X(49461) = midpoint of X(145) and X(3644)
X(49461) = reflection of X(i) in X(j) for these {i,j}: {8, 4681}, {3696, 3993}, {4686, 1}
X(49461) = crossdifference of every pair of points on line {3733, 39521}
X(49461) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3175, 3896, 4849}, {3696, 3993, 37}


X(49462) = X(1)X(536)∩X(10)X(37)

Barycentrics    (b + c)*(-3*a^2 - a*b - a*c + 2*b*c) : :
X(49462) = 5 X[1] - 3 X[31178], X[8] - 3 X[4664], 2 X[10] - 3 X[37], 4 X[10] - 3 X[3696], 5 X[10] - 6 X[3842], X[10] - 3 X[3993], 5 X[10] - 3 X[4709], 7 X[10] - 6 X[4732], 5 X[37] - 4 X[3842], 5 X[37] - 2 X[4709], 7 X[37] - 4 X[4732], 5 X[3696] - 8 X[3842], X[3696] - 4 X[3993], 5 X[3696] - 4 X[4709], 7 X[3696] - 8 X[4732], 2 X[3842] - 5 X[3993], 7 X[3842] - 5 X[4732], 5 X[3993] - X[4709], 7 X[3993] - 2 X[4732], 7 X[4709] - 10 X[4732], 3 X[75] - 5 X[3616], 5 X[3616] - 6 X[15569], X[145] + 3 X[192], 5 X[145] + 3 X[31302], 5 X[192] - X[31302], 4 X[3635] + 3 X[4718], 3 X[984] - X[3632], X[3632] - 6 X[4681], 4 X[1125] - 3 X[4688], 5 X[1698] - 6 X[4755], 7 X[3622] - 3 X[4740], 7 X[3624] - 6 X[3739], 8 X[3636] - 3 X[4686], 4 X[3636] - 3 X[24325], 3 X[3644] + 7 X[20057], 7 X[20057] - 3 X[24349], 7 X[4533] - 6 X[22271], 7 X[4678] - 15 X[4704], 15 X[4687] - 13 X[19877], 4 X[4739] - 5 X[40328], X[6361] - 3 X[30273], X[18525] - 3 X[20430], 16 X[19878] - 15 X[31238], 21 X[27268] - 17 X[46932]

X(49462) lies on these lines: {1, 536}, {2, 4519}, {8, 4664}, {10, 37}, {42, 3175}, {43, 35652}, {65, 4552}, {72, 44671}, {75, 3616}, {144, 145}, {190, 4663}, {210, 3896}, {238, 4852}, {239, 15254}, {306, 4854}, {319, 9791}, {321, 27804}, {335, 29619}, {346, 38047}, {354, 17147}, {537, 3244}, {726, 3635}, {982, 4891}, {984, 3632}, {1001, 3875}, {1100, 3923}, {1125, 4688}, {1215, 22034}, {1266, 25557}, {1279, 32921}, {1386, 3685}, {1698, 4755}, {1738, 17243}, {1962, 4365}, {1999, 4640}, {2667, 40935}, {3187, 3683}, {3210, 3742}, {3240, 4009}, {3293, 4069}, {3416, 17314}, {3622, 4740}, {3624, 3739}, {3636, 4686}, {3644, 20057}, {3663, 4966}, {3664, 28557}, {3666, 30942}, {3681, 20048}, {3706, 28606}, {3720, 42051}, {3740, 41839}, {3744, 32928}, {3745, 32929}, {3748, 3891}, {3751, 17262}, {3752, 4871}, {3795, 20530}, {3821, 17231}, {3834, 33149}, {3844, 17233}, {3848, 17490}, {3879, 17768}, {3952, 21870}, {3971, 4849}, {4003, 29824}, {4018, 20718}, {4028, 4415}, {4368, 21904}, {4387, 5256}, {4393, 4676}, {4418, 37595}, {4429, 17242}, {4436, 37609}, {4442, 19791}, {4452, 38053}, {4533, 22271}, {4641, 32936}, {4645, 17315}, {4649, 17351}, {4655, 17374}, {4672, 16666}, {4678, 4704}, {4682, 32932}, {4687, 19877}, {4689, 17763}, {4690, 24697}, {4716, 17348}, {4734, 18743}, {4739, 40328}, {4851, 24248}, {4883, 17155}, {4889, 28570}, {5263, 17319}, {5847, 17388}, {5880, 17316}, {6361, 30273}, {6542, 24723}, {7283, 41813}, {15481, 17261}, {15571, 37575}, {16672, 39586}, {16823, 17160}, {17018, 42044}, {17229, 32784}, {17235, 33087}, {17334, 34379}, {17359, 29633}, {17365, 28526}, {17372, 33082}, {17376, 32857}, {17382, 29637}, {17389, 28534}, {17390, 28530}, {17592, 29825}, {17759, 28600}, {18525, 20430}, {19878, 31238}, {20694, 27809}, {21342, 42057}, {21345, 21883}, {21949, 29653}, {22791, 29010}, {24342, 28639}, {27268, 46932}, {28898, 30573}, {30818, 46904}, {31503, 42027}, {32845, 37520}, {32860, 44307}, {32922, 42819}, {34772, 38336}

X(49462) = midpoint of X(3644) and X(24349)
X(49462) = reflection of X(i) in X(j) for these {i,j}: {37, 3993}, {75, 15569}, {984, 4681}, {3696, 37}, {4686, 24325}, {4709, 3842}
X(49462) = X(1019)-isoconjugate of X(6016)
X(49462) = crossdifference of every pair of points on line {3733, 20980}
X(49462) = barycentric product X(i)*X(j) for these {i,j}: {10, 16834}, {3952, 6008}, {8657, 27808}
X(49462) = barycentric quotient X(i)/X(j) for these {i,j}: {4557, 6016}, {6008, 7192}, {8657, 3733}, {16834, 86}
X(49462) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {42, 3175, 3967}, {321, 27804, 37593}, {1962, 4365, 31993}, {2321, 4356, 4026}, {2901, 3931, 3714}, {2901, 4065, 3931}, {3685, 4360, 1386}, {3755, 3950, 3932}, {3774, 20688, 37}, {3896, 3995, 210}, {32932, 34064, 4682}


X(49463) = X(1)X(536)∩X(6)X(28582)

Barycentrics    2*a^3 + a^2*b + 3*a*b^2 + a^2*c - 2*b^2*c + 3*a*c^2 - 2*b*c^2 : :
X(49463) = 3 X[1] - X[5695], 5 X[1] - 3 X[48805], 5 X[5695] - 9 X[48805], X[8] - 3 X[17301], 2 X[10] - 3 X[17382], 3 X[1386] - 2 X[4672], 4 X[4672] - 3 X[17351], 4 X[1125] - 3 X[17359], 5 X[3616] - 3 X[17281], 2 X[3626] - 3 X[48821], X[3632] - 3 X[48829], 4 X[3636] - 3 X[48810], X[3729] - 3 X[38315]

X(49463) lies on these lines: {1, 536}, {6, 28582}, {8, 17237}, {10, 4395}, {37, 16823}, {72, 43993}, {141, 4353}, {145, 320}, {192, 1279}, {210, 32924}, {321, 29823}, {354, 32928}, {518, 4523}, {519, 4743}, {528, 3244}, {537, 4663}, {596, 37594}, {614, 35652}, {726, 1386}, {984, 17348}, {1001, 4681}, {1100, 24349}, {1125, 17359}, {1999, 21342}, {2321, 28472}, {2783, 10222}, {3175, 7191}, {3241, 15590}, {3242, 3875}, {3416, 17235}, {3616, 17281}, {3626, 48821}, {3629, 5850}, {3632, 48829}, {3635, 28580}, {3636, 48810}, {3663, 5846}, {3666, 3891}, {3685, 4718}, {3703, 30768}, {3717, 17366}, {3729, 38315}, {3739, 39586}, {3744, 17147}, {3745, 17155}, {3752, 5205}, {3755, 9053}, {3759, 31302}, {3772, 30741}, {3790, 17357}, {3821, 17769}, {3823, 4000}, {3883, 17246}, {3920, 42051}, {3923, 28555}, {3932, 17356}, {3967, 29821}, {3993, 42819}, {4003, 17763}, {4054, 17726}, {4310, 4851}, {4349, 7228}, {4361, 7174}, {4641, 17150}, {4655, 28538}, {4665, 19868}, {4682, 24165}, {4684, 17388}, {4686, 5263}, {4688, 16830}, {4689, 20045}, {4884, 40940}, {4891, 17597}, {4912, 24695}, {4914, 32776}, {4974, 15481}, {5542, 17390}, {5847, 17345}, {7290, 17262}, {16020, 41313}, {16477, 24821}, {17024, 42044}, {17140, 37595}, {17276, 28570}, {17376, 24231}, {17599, 29826}, {17794, 21904}, {19785, 31091}, {19796, 21949}, {22034, 32942}, {24248, 28566}, {24325, 28639}, {28329, 47358}, {28484, 32941}, {32923, 37593}, {34791, 44670}, {39581, 41312}

X(49463) = midpoint of X(3242) and X(3875)
X(49463) = reflection of X(i) in X(j) for these {i,j}: {141, 4353}, {3416, 17235}, {4852, 32921}, {17351, 1386}


X(49464) = X(1)X(87)∩X(10)X(10159)

Barycentrics    2*a^3 + 3*a*b^2 - b^2*c + 3*a*c^2 - b*c^2 : :
X(49464) = 5 X[1] - X[3729], 3 X[1] - X[3923], 3 X[3729] - 5 X[3923], 3 X[551] - 2 X[24295], 3 X[3241] + X[24248], X[3632] - 5 X[17304], 3 X[3892] - X[32118], X[32935] - 3 X[38315]

X(49464) lies on these lines: {1, 87}, {10, 10159}, {141, 17769}, {145, 4660}, {320, 3244}, {516, 1482}, {519, 599}, {537, 1386}, {551, 17264}, {984, 17335}, {1125, 4078}, {2308, 20068}, {2796, 7983}, {3241, 24248}, {3623, 28550}, {3625, 4716}, {3626, 4361}, {3632, 17287}, {3636, 4029}, {3677, 29649}, {3741, 3891}, {3745, 42055}, {3751, 4991}, {3773, 28503}, {3790, 29660}, {3840, 17598}, {3881, 35631}, {3892, 32118}, {3920, 24165}, {3938, 4970}, {3971, 7191}, {3995, 29818}, {4003, 4434}, {4085, 9053}, {4090, 29821}, {4135, 32942}, {4527, 28472}, {4649, 24841}, {4655, 28512}, {4672, 28582}, {4682, 42053}, {4685, 32924}, {4759, 7290}, {4795, 17132}, {4884, 6679}, {5266, 8720}, {6685, 17599}, {7174, 16825}, {7982, 24728}, {8669, 37592}, {10222, 29057}, {16468, 31302}, {17024, 32925}, {17140, 29816}, {17155, 29815}, {17165, 29819}, {17276, 28508}, {17345, 28498}, {17738, 29584}, {20045, 46901}, {21241, 29832}, {24260, 42042}, {28522, 32941}, {29831, 33161}, {29834, 33170}, {29836, 32849}, {29838, 33167}, {29840, 33152}, {32923, 43223}, {32928, 42057}, {32935, 38315}

X(49464) = midpoint of X(i) and X(j) for these {i,j}: {145, 4660}, {3242, 32921}, {3244, 3663}, {7982, 24728}
X(49464) = reflection of X(i) in X(j) for these {i,j}: {3751, 4991}, {3821, 4353}, {17355, 3636}
X(49464) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 24349, 33682}, {17598, 32926, 3840}, {17599, 32920, 6685}, {29832, 33143, 21241}


X(49465) = X(1)X(6)∩X(2)X(4906)

Barycentrics    a*(2*a^2 - a*b + 3*b^2 - a*c + 3*c^2) : :
X(49465) = 3 X[1] - X[6], 5 X[1] - X[3751], 4 X[1] - X[4663], 7 X[1] - 3 X[16475], 9 X[1] - 5 X[16491], 3 X[1] + X[16496], 5 X[1] - 3 X[38315], 2 X[6] - 3 X[1386], X[6] + 3 X[3242], 5 X[6] - 3 X[3751], 4 X[6] - 3 X[4663], 7 X[6] - 9 X[16475], 3 X[6] - 5 X[16491], 5 X[6] - 9 X[38315], X[1386] + 2 X[3242], 5 X[1386] - 2 X[3751], 7 X[1386] - 6 X[16475], 9 X[1386] - 10 X[16491], 3 X[1386] + 2 X[16496], 5 X[1386] - 6 X[38315], 5 X[3242] + X[3751], 4 X[3242] + X[4663], 7 X[3242] + 3 X[16475], 9 X[3242] + 5 X[16491], 3 X[3242] - X[16496], 5 X[3242] + 3 X[38315], 4 X[3751] - 5 X[4663], 7 X[3751] - 15 X[16475], 9 X[3751] - 25 X[16491], 3 X[3751] + 5 X[16496], X[3751] - 3 X[38315], 7 X[4663] - 12 X[16475], 9 X[4663] - 20 X[16491], 3 X[4663] + 4 X[16496], 5 X[4663] - 12 X[38315], 27 X[16475] - 35 X[16491], 9 X[16475] + 7 X[16496], 5 X[16475] - 7 X[38315], 5 X[16491] + 3 X[16496], 25 X[16491] - 27 X[38315], 5 X[16496] + 9 X[38315], 3 X[8] - 7 X[3619], 7 X[3619] - 6 X[3844], 3 X[10] - 4 X[34573], X[69] + 3 X[3241], X[69] - 3 X[47358], 2 X[4085] - 3 X[17382], 3 X[48820] - X[48847], 3 X[145] + 5 X[3620], 3 X[3416] - 5 X[3620], 3 X[551] - 2 X[3589], 5 X[551] - 3 X[38089], 10 X[3589] - 9 X[38089], 3 X[1385] - 2 X[5092], 3 X[1482] + X[33878], 3 X[3244] + 2 X[3631], 5 X[3616] - 3 X[38047], 5 X[3618] - 9 X[38314], 5 X[3618] - 3 X[47359], 3 X[38314] - X[47359], 15 X[3623] + X[20080], X[3630] + 6 X[3635], 3 X[3655] - X[46264], 3 X[3656] - X[31670], 3 X[3679] - 5 X[3763], X[3729] - 3 X[48805], X[4677] - 3 X[21358], X[5881] - 3 X[10516], 9 X[7967] - X[39874], 3 X[7967] + X[39898], X[39874] + 3 X[39898], X[7991] - 3 X[31884], 5 X[8227] - 3 X[38144], 6 X[9956] - 7 X[42786], 9 X[10246] - 5 X[12017], 9 X[10247] - X[44456], 5 X[10595] - 3 X[38035], X[11008] - 21 X[20057], 3 X[12699] - X[43621], 5 X[17304] - 3 X[48829], 2 X[17355] - 3 X[48810], 5 X[19862] - 3 X[38191], 3 X[21167] - 2 X[43174], 9 X[25055] - 7 X[47355], 3 X[31162] - X[48910], 6 X[33179] - X[37517], 5 X[37624] - 3 X[38029], X[47279] - 3 X[47477], 3 X[47321] - 5 X[47452], 5 X[47456] - 3 X[47506], 3 X[48819] - X[48837]

X(49465) lies on these lines: {1, 6}, {2, 4906}, {8, 3619}, {10, 9053}, {38, 902}, {55, 7293}, {65, 33844}, {69, 3241}, {75, 36534}, {100, 4003}, {106, 30115}, {141, 519}, {145, 3416}, {171, 21342}, {182, 15178}, {192, 4702}, {193, 17488}, {210, 7191}, {347, 3476}, {354, 3920}, {511, 10222}, {517, 3098}, {528, 3663}, {536, 32941}, {537, 17351}, {551, 3589}, {612, 3742}, {614, 3740}, {750, 3999}, {752, 17345}, {756, 29818}, {760, 41413}, {894, 24841}, {942, 30145}, {952, 18358}, {999, 12329}, {1155, 4392}, {1280, 1390}, {1350, 7982}, {1352, 37727}, {1376, 3677}, {1385, 5092}, {1442, 14151}, {1469, 9047}, {1480, 6001}, {1482, 33878}, {1503, 5882}, {1837, 36579}, {2099, 7190}, {2177, 3666}, {2321, 28503}, {2646, 36565}, {2836, 5919}, {3056, 5048}, {3057, 3100}, {3175, 32943}, {3244, 3631}, {3295, 22769}, {3303, 36740}, {3304, 36741}, {3315, 5297}, {3616, 17263}, {3618, 38314}, {3623, 20080}, {3630, 3635}, {3655, 46264}, {3656, 31670}, {3672, 47595}, {3679, 3763}, {3681, 14997}, {3683, 7226}, {3689, 4850}, {3696, 17117}, {3706, 3891}, {3722, 4689}, {3729, 48805}, {3739, 36480}, {3745, 3873}, {3746, 4265}, {3748, 28606}, {3752, 3961}, {3779, 44840}, {3811, 4719}, {3813, 34937}, {3818, 28204}, {3821, 17765}, {3827, 9957}, {3838, 33144}, {3848, 5268}, {3870, 17599}, {3878, 9021}, {3881, 37594}, {3884, 34378}, {3886, 28484}, {3923, 28582}, {3957, 37593}, {3966, 19993}, {3967, 32942}, {3979, 17600}, {4133, 28472}, {4256, 37592}, {4257, 5266}, {4260, 9049}, {4296, 9850}, {4301, 29181}, {4310, 5880}, {4318, 8581}, {4353, 5853}, {4424, 18183}, {4437, 17023}, {4641, 17469}, {4648, 48856}, {4655, 28566}, {4657, 36479}, {4660, 17235}, {4669, 20582}, {4670, 9055}, {4676, 31302}, {4677, 21358}, {4693, 4718}, {4698, 24331}, {4847, 17061}, {4849, 29821}, {4863, 19785}, {4883, 5311}, {4914, 32782}, {5044, 30148}, {5045, 30142}, {5087, 17721}, {5096, 5563}, {5252, 37800}, {5256, 41711}, {5263, 17116}, {5308, 38186}, {5480, 13464}, {5695, 28555}, {5836, 37549}, {5845, 30331}, {5848, 12735}, {5881, 10516}, {7289, 31393}, {7322, 8167}, {7962, 10387}, {7967, 39874}, {7991, 31884}, {8227, 38144}, {9015, 48285}, {9029, 48287}, {9040, 48347}, {9507, 37675}, {9589, 48872}, {9956, 42786}, {10106, 16888}, {10246, 12017}, {10247, 44456}, {10459, 28403}, {10595, 38035}, {11008, 20057}, {11363, 44091}, {11366, 12453}, {11367, 12452}, {12587, 37739}, {12588, 37738}, {12589, 37740}, {12699, 43621}, {15668, 48854}, {16826, 32029}, {17012, 21870}, {17231, 32847}, {17237, 33076}, {17276, 28534}, {17304, 48829}, {17327, 48851}, {17355, 48810}, {17357, 29660}, {17384, 29659}, {17445, 17792}, {17449, 37520}, {17602, 26015}, {17605, 33153}, {17724, 29639}, {17725, 29676}, {19860, 25929}, {19862, 38191}, {20045, 46909}, {21167, 43174}, {21949, 33147}, {25055, 47355}, {28194, 48881}, {28198, 48880}, {28202, 48879}, {28208, 48884}, {28581, 32921}, {28633, 48809}, {28634, 48802}, {29630, 32108}, {29652, 32920}, {29686, 33162}, {29816, 37595}, {29823, 46897}, {29831, 33114}, {29832, 33122}, {29836, 33115}, {29838, 33121}, {29840, 33126}, {30818, 32927}, {31162, 48910}, {31238, 36531}, {31792, 34381}, {31993, 32923}, {32945, 42051}, {33179, 37517}, {37624, 38029}, {38053, 39587}, {43149, 47373}, {47279, 47477}, {47321, 47452}, {47456, 47506}, {48819, 48837}

X(49465) = midpoint of X(i) and X(j) for these {i,j}: {1, 3242}, {6, 16496}, {145, 3416}, {1350, 7982}, {1352, 37727}, {3057, 24476}, {3241, 47358}, {9589, 48872}
X(49465) = reflection of X(i) in X(j) for these {i,j}: {8, 3844}, {182, 15178}, {1386, 1}, {4660, 17235}, {4663, 1386}, {4669, 20582}, {5480, 13464}
X(49465) = barycentric product X(1)*X(29596)
X(49465) = barycentric quotient X(29596)/X(75)
X(49465) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 37, 42819}, {1, 984, 1279}, {1, 3640, 45399}, {1, 3641, 45398}, {1, 3731, 35227}, {1, 3751, 38315}, {1, 4864, 15570}, {1, 7174, 1001}, {1, 16496, 6}, {6, 3242, 16496}, {9, 16487, 8692}, {38, 3744, 4640}, {354, 3920, 4682}, {612, 17597, 3742}, {984, 1279, 15254}, {984, 15485, 16814}, {1279, 16814, 15485}, {3722, 46901, 4689}, {3731, 35227, 1001}, {3873, 29815, 3745}, {3961, 17598, 3752}, {7174, 35227, 3731}, {8692, 16487, 3246}, {15485, 16814, 15254}, {16521, 16777, 37}, {29652, 32920, 44417}, {29660, 33165, 17357}


X(49466) = X(1)X(2)∩X(9)X(4899)

Barycentrics    2*a^3 - 3*a^2*b + 2*a*b^2 - b^3 - 3*a^2*c - 2*a*b*c - b^2*c + 2*a*c^2 - b*c^2 - c^3 : :
X(49466) = 4 X[1] - 3 X[29574], X[3621] - 3 X[29617], 5 X[3623] - 3 X[17389]

X(49466) lies on these lines: {1, 2}, {9, 4899}, {37, 9053}, {69, 3243}, {72, 22048}, {75, 5853}, {85, 10106}, {141, 4864}, {142, 32850}, {149, 4054}, {226, 4514}, {344, 4901}, {345, 10389}, {346, 8236}, {354, 4030}, {390, 3729}, {516, 24349}, {517, 49131}, {518, 3883}, {728, 37556}, {730, 41794}, {1001, 3717}, {1219, 4313}, {1222, 1438}, {1279, 17353}, {1909, 2481}, {2321, 16503}, {2550, 24199}, {2975, 40910}, {3057, 14839}, {3242, 4357}, {3340, 3674}, {3416, 4684}, {3685, 30331}, {3699, 5316}, {3703, 3748}, {3731, 4929}, {3755, 32922}, {3790, 43179}, {3879, 5846}, {3886, 4431}, {3914, 32923}, {3932, 42819}, {3966, 41711}, {3997, 5299}, {4001, 4430}, {4078, 16484}, {4346, 15590}, {4423, 30615}, {4454, 30332}, {4480, 5698}, {4645, 5542}, {4660, 24231}, {4894, 13407}, {4923, 5564}, {4966, 15570}, {5014, 5249}, {5015, 21620}, {5048, 24250}, {5795, 30854}, {8666, 37576}, {10005, 18230}, {11038, 17298}, {12513, 37580}, {12630, 32087}, {12640, 19589}, {16284, 33944}, {16502, 37542}, {16779, 17355}, {17277, 24393}, {17365, 28566}, {17715, 33169}, {17765, 24325}, {18141, 44841}, {18689, 20880}, {21342, 44419}, {24210, 32920}, {24723, 24841}, {25719, 39775}, {32937, 40998}, {33159, 38191}, {33170, 35263}

X(49466) = reflection of X(4416) in X(3883)
X(49466) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 8, 3912}, {1, 29598, 3622}, {1, 29633, 551}, {1, 29646, 3636}, {1, 29659, 1125}, {8, 3616, 39570}, {8, 16823, 10}, {8, 28058, 6736}, {1001, 3717, 25101}, {3416, 42871, 4684}, {3623, 26626, 1}, {3957, 33090, 306}, {3979, 32866, 4028}, {4901, 38316, 344}, {7172, 10580, 30567}, {29670, 29844, 24239}


X(49467) = X(1)X(3696)∩X(8)X(1279)

Barycentrics    2*a^3 - 3*a^2*b + 3*a*b^2 - 3*a^2*c + 2*b^2*c + 3*a*c^2 + 2*b*c^2 : :
X(49467) = 4 X[3923] - 3 X[17351], 5 X[3923] - 3 X[32935], X[3923] - 3 X[32941], 5 X[17351] - 4 X[32935], X[17351] - 4 X[32941], X[32935] - 5 X[32941], 5 X[1386] - 4 X[4991], X[3751] - 3 X[48805], 2 X[3755] - 3 X[17382], X[24248] - 3 X[47358]

X(49467) lies on these lines: {1, 3696}, {8, 1279}, {10, 42819}, {69, 28566}, {75, 4864}, {141, 5853}, {145, 1100}, {210, 32943}, {354, 32945}, {390, 4643}, {516, 17345}, {518, 3923}, {519, 597}, {536, 3242}, {612, 4891}, {748, 4113}, {952, 12618}, {966, 8236}, {984, 4702}, {1043, 16696}, {2321, 9053}, {2550, 3834}, {2805, 12721}, {3241, 28329}, {3243, 4363}, {3621, 3759}, {3623, 17394}, {3625, 4974}, {3689, 30942}, {3706, 3938}, {3722, 31136}, {3744, 17135}, {3748, 31330}, {3751, 48805}, {3752, 3996}, {3755, 17382}, {3870, 44417}, {3883, 4690}, {3935, 30818}, {3941, 12513}, {3957, 31993}, {3974, 4952}, {4133, 28503}, {4371, 39567}, {4399, 4923}, {4422, 24393}, {4432, 15481}, {4519, 32927}, {4670, 5263}, {4681, 7174}, {4682, 42057}, {4684, 17376}, {4689, 46909}, {4849, 32942}, {4863, 33171}, {4873, 4929}, {4899, 17340}, {4901, 17269}, {4912, 24280}, {5695, 16496}, {5737, 10389}, {5772, 20050}, {5846, 17372}, {12630, 29611}, {15569, 36480}, {15570, 24325}, {17231, 32850}, {17259, 38316}, {17265, 38200}, {19868, 25498}, {21283, 33122}, {21342, 32932}, {21870, 32944}, {21949, 33124}, {24248, 47358}, {24357, 36534}, {28633, 39581}

X(49467) = midpoint of X(i) and X(j) for these {i,j}: {145, 17299}, {3242, 3886}, {5695, 16496}
X(49467) = reflection of X(i) in X(j) for these {i,j}: {8, 17229}, {4852, 1}
X(49467) = {X(8),X(1279)}-harmonic conjugate of X(17348)


X(49468) = X(1)X(4688)∩X(10)X(37)

Barycentrics    (b + c)*(-3*a^2 + a*b + a*c + 4*b*c) : :
X(49468) = 2 X[1] - 3 X[4688], 4 X[10] - 3 X[37], 2 X[10] - 3 X[3696], 7 X[10] - 6 X[3842], 5 X[10] - 3 X[3993], X[10] - 3 X[4709], 5 X[10] - 6 X[4732], 7 X[37] - 8 X[3842], 5 X[37] - 4 X[3993], X[37] - 4 X[4709], 5 X[37] - 8 X[4732], 7 X[3696] - 4 X[3842], 5 X[3696] - 2 X[3993], 5 X[3696] - 4 X[4732], 10 X[3842] - 7 X[3993], 2 X[3842] - 7 X[4709], 5 X[3842] - 7 X[4732], X[3993] - 5 X[4709], 5 X[4709] - 2 X[4732], 3 X[75] - X[145], 3 X[192] - 7 X[4678], 2 X[3632] + 3 X[4686], 3 X[984] - 5 X[4668], 10 X[4668] - 3 X[4718], 3 X[1278] + 5 X[20052], 5 X[3616] - 6 X[3739], 5 X[3617] - 3 X[4664], X[3621] + 3 X[4740], 7 X[3624] - 6 X[15569], 14 X[3624] - 15 X[31238], 4 X[15569] - 5 X[31238], X[3633] - 3 X[31178], 2 X[3635] - 3 X[24325], 5 X[4005] - 6 X[22271], 15 X[4687] - 17 X[46932], 12 X[4698] - 13 X[19877], 6 X[4726] + X[20053], X[20053] + 3 X[24349], 12 X[4739] - 7 X[20057], 6 X[4755] - 7 X[9780], 2 X[18481] - 3 X[30271]

X(49468) lies on these lines: {1, 4688}, {8, 536}, {10, 37}, {44, 5695}, {65, 44671}, {72, 21889}, {75, 145}, {192, 4678}, {210, 3994}, {306, 21949}, {321, 4849}, {390, 4371}, {516, 17362}, {518, 3632}, {537, 3625}, {726, 4701}, {899, 4519}, {984, 4668}, {1043, 25536}, {1215, 4946}, {1278, 20052}, {1279, 3886}, {1386, 4716}, {1738, 17231}, {2550, 17299}, {3175, 4651}, {3242, 17151}, {3616, 3739}, {3617, 4664}, {3621, 4740}, {3624, 15569}, {3633, 31178}, {3635, 24325}, {3663, 4923}, {3685, 17348}, {3706, 3752}, {3823, 17233}, {3883, 4399}, {3896, 17163}, {3914, 4046}, {3923, 16669}, {3962, 20718}, {3967, 4685}, {3971, 4457}, {4003, 31136}, {4005, 22271}, {4061, 4415}, {4113, 32925}, {4416, 28530}, {4429, 17229}, {4645, 17372}, {4673, 45219}, {4684, 7263}, {4687, 46932}, {4693, 15254}, {4698, 19877}, {4702, 16825}, {4726, 20053}, {4739, 20057}, {4746, 28522}, {4755, 9780}, {4764, 31302}, {4852, 5263}, {4871, 16602}, {4891, 19804}, {4980, 20011}, {5880, 17374}, {17135, 21342}, {17311, 38052}, {17334, 28557}, {17344, 24248}, {17363, 28570}, {17395, 19868}, {17751, 41683}, {18481, 30271}, {20012, 42029}, {20048, 28605}, {21020, 37593}, {28554, 34641}

X(49468) = midpoint of X(4764) and X(31302)
X(49468) = reflection of X(i) in X(j) for these {i,j}: {37, 3696}, {3696, 4709}, {3883, 4399}, {3993, 4732}, {4718, 984}, {24349, 4726}
X(49468) = barycentric product X(i)*X(j) for these {i,j}: {10, 16833}, {4033, 48572}
X(49468) = barycentric quotient X(i)/X(j) for these {i,j}: {16833, 86}, {48572, 1019}
X(49468) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 24723, 4690}, {210, 4365, 22034}, {3706, 4706, 30942}, {3706, 32860, 3752}, {3886, 4361, 1279}, {3896, 17163, 31993}, {4706, 30942, 3752}, {17135, 42051, 21342}, {30942, 32860, 4706}


X(49469) = X(1)X(75)∩X(2)X(4709)

Barycentrics    3*a^2*b + 3*a^2*c + a*b*c - 2*b^2*c - 2*b*c^2 : :
X(49469) = 3 X[1] - 2 X[75], 5 X[1] - 4 X[24325], 5 X[75] - 6 X[24325], 3 X[8] - 5 X[4704], 6 X[3993] - 5 X[4704], 6 X[10] - 7 X[27268], 4 X[37] - 3 X[3679], 3 X[145] + X[4788], 3 X[3633] + 4 X[4718], 2 X[3644] + 3 X[34747], 6 X[551] - 5 X[4699], 3 X[984] - 4 X[4681], 3 X[3632] - 8 X[4681], X[1278] - 3 X[3241], 5 X[1698] - 4 X[3696], 15 X[1698] - 16 X[4698], 3 X[3696] - 4 X[4698], 7 X[3624] - 8 X[15569], 21 X[3624] - 20 X[31238], 6 X[15569] - 5 X[31238], 8 X[3739] - 9 X[25055], 2 X[4780] - 3 X[27480], 2 X[4686] - 3 X[31178], 5 X[4687] - 4 X[4732], 10 X[4687] - 9 X[19875], 8 X[4732] - 9 X[19875], 7 X[4772] - 9 X[38314], 2 X[4793] - 3 X[30116]

X(49469) lies on these lines: {1, 75}, {2, 4709}, {6, 4693}, {8, 3993}, {10, 17242}, {37, 3679}, {42, 4671}, {43, 3896}, {145, 726}, {192, 519}, {239, 15485}, {312, 42043}, {321, 42042}, {335, 29605}, {495, 21927}, {518, 3633}, {528, 17388}, {537, 3644}, {551, 4699}, {742, 16496}, {752, 17377}, {846, 17156}, {978, 29982}, {984, 3632}, {1001, 4716}, {1278, 3241}, {1698, 3696}, {1757, 25728}, {1999, 3550}, {2321, 29659}, {2796, 17364}, {2901, 22016}, {3187, 8616}, {3210, 42057}, {3244, 24349}, {3247, 36531}, {3624, 15569}, {3685, 16468}, {3706, 17592}, {3739, 25055}, {3755, 29674}, {3759, 4432}, {3797, 16834}, {3821, 48633}, {3840, 4734}, {3879, 28580}, {3899, 44671}, {3901, 20718}, {3912, 4780}, {3923, 17120}, {3943, 33165}, {3944, 4028}, {3946, 29660}, {3971, 20012}, {4026, 48636}, {4032, 18421}, {4062, 33134}, {4085, 17233}, {4361, 16484}, {4365, 17018}, {4429, 4743}, {4649, 5695}, {4660, 6542}, {4664, 4677}, {4685, 41839}, {4686, 31178}, {4687, 4732}, {4702, 4852}, {4742, 20892}, {4753, 17336}, {4772, 38314}, {4793, 30116}, {4850, 31137}, {4851, 24715}, {4854, 33084}, {4891, 17063}, {4966, 33149}, {4970, 10453}, {4975, 20923}, {5881, 20430}, {7982, 29010}, {7991, 30273}, {11531, 29054}, {16569, 30829}, {17038, 42285}, {17117, 24331}, {17145, 17147}, {17146, 17155}, {17241, 25351}, {17286, 36478}, {17299, 33076}, {17309, 48829}, {17311, 31151}, {17314, 32847}, {17317, 24693}, {17319, 36480}, {17375, 24692}, {17596, 39594}, {17733, 37574}, {18743, 36634}, {19823, 33171}, {19824, 33147}, {19828, 33124}, {19829, 26128}, {20011, 32925}, {20016, 27481}, {20017, 32947}, {20050, 31302}, {21214, 30044}, {21296, 24248}, {24589, 26102}, {25399, 25698}, {27474, 29598}, {27478, 29585}, {27804, 31330}, {28604, 48822}, {29576, 31308}, {29602, 31342}, {29609, 31329}, {29827, 46904}, {29856, 33156}, {29858, 33128}, {32099, 33082}, {32784, 48635}, {32932, 37604}, {33087, 48632}, {34247, 48696}, {39697, 39742}

X(49469) = midpoint of X(20050) and X(31302)
X(49469) = reflection of X(i) in X(j) for these {i,j}: {8, 3993}, {3632, 984}, {4677, 4664}, {5881, 20430}, {7991, 30273}, {24349, 3244}
X(49469) = anticomplement of X(4709)
X(49469) = crossdifference of every pair of points on line {798, 39521}
X(49469) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3896, 32915, 43}, {4360, 32941, 1}, {4687, 4732, 19875}, {4970, 10453, 17591}


X(49470) = X(1)X(75)∩X(8)X(37)

Barycentrics    2*a^2*b + 2*a^2*c + a*b*c - b^2*c - b*c^2 : :
X(49470) = 3 X[1] - 2 X[24325], 3 X[75] - 4 X[24325], 3 X[2] - 4 X[15569], 4 X[10] - 5 X[4687], 3 X[145] + X[31302], 3 X[192] - X[31302], 2 X[984] - 3 X[4664], 4 X[3993] - 3 X[4664], 3 X[3241] - X[24349], 6 X[551] - 5 X[40328], 4 X[3244] + X[3644], 8 X[1125] - 7 X[4751], 4 X[4709] - 7 X[4751], X[1278] - 5 X[3623], 5 X[1698] - 4 X[4732], 2 X[2550] - 3 X[27475], 5 X[3616] - 4 X[3739], 5 X[3617] - 7 X[27268], X[3621] - 5 X[4704], 7 X[3622] - 5 X[4699], 8 X[3635] - X[4764], 3 X[3679] - 4 X[3842], 5 X[3876] - 4 X[22271], 5 X[3889] - 4 X[13476], 4 X[4681] + X[20050], 2 X[4686] - 7 X[20057], 2 X[4688] - 3 X[38314], 8 X[4698] - 7 X[9780], 3 X[4828] - 4 X[48295], 11 X[5550] - 10 X[31238], 3 X[5731] - 2 X[30271]

X(49470) lies on these lines: {1, 75}, {2, 3696}, {6, 3685}, {8, 37}, {10, 4687}, {31, 643}, {33, 92}, {42, 312}, {43, 18743}, {55, 1999}, {65, 24523}, {69, 24723}, {81, 32929}, {85, 42289}, {144, 145}, {149, 27491}, {190, 3751}, {210, 20012}, {238, 3759}, {239, 1001}, {306, 32773}, {320, 24248}, {321, 17018}, {333, 968}, {335, 528}, {341, 872}, {345, 33121}, {350, 21615}, {354, 3210}, {386, 18137}, {497, 33071}, {516, 3879}, {517, 30273}, {519, 751}, {536, 3241}, {551, 40328}, {596, 39739}, {612, 3996}, {664, 2263}, {726, 3244}, {742, 3242}, {757, 11104}, {846, 32853}, {894, 5695}, {899, 30829}, {940, 32932}, {952, 20430}, {960, 20018}, {982, 4970}, {986, 4022}, {988, 39584}, {994, 2802}, {1125, 4709}, {1155, 37684}, {1193, 20923}, {1201, 30090}, {1215, 42034}, {1266, 5542}, {1278, 3623}, {1279, 4852}, {1386, 3797}, {1458, 39126}, {1482, 29010}, {1621, 3187}, {1698, 4732}, {1707, 41629}, {1738, 4780}, {1757, 17336}, {1836, 17778}, {1839, 1891}, {1962, 31330}, {2177, 17763}, {2550, 17316}, {2650, 17157}, {2805, 6224}, {2901, 4043}, {3175, 32937}, {3189, 20009}, {3208, 39258}, {3240, 4358}, {3243, 24841}, {3293, 46937}, {3340, 4032}, {3416, 6542}, {3434, 19791}, {3475, 30699}, {3616, 3739}, {3617, 27268}, {3621, 4704}, {3622, 4699}, {3635, 4764}, {3661, 4026}, {3662, 4966}, {3663, 4684}, {3666, 10453}, {3673, 20448}, {3679, 3842}, {3681, 3995}, {3683, 37652}, {3702, 19767}, {3717, 3950}, {3720, 19804}, {3741, 17592}, {3742, 17490}, {3750, 4362}, {3752, 4734}, {3755, 3912}, {3758, 3923}, {3771, 33135}, {3772, 29839}, {3773, 29659}, {3775, 17250}, {3783, 30963}, {3790, 3943}, {3791, 8616}, {3821, 17227}, {3826, 17244}, {3836, 4743}, {3844, 17230}, {3868, 20718}, {3871, 15624}, {3873, 17147}, {3876, 22271}, {3877, 44671}, {3889, 13476}, {3890, 20040}, {3891, 3957}, {3913, 34247}, {3914, 18134}, {3931, 10449}, {3932, 17242}, {3936, 33134}, {3938, 32928}, {3969, 29667}, {3979, 32920}, {3980, 4038}, {4009, 21870}, {4023, 4819}, {4028, 4417}, {4029, 24393}, {4062, 25760}, {4085, 17240}, {4356, 4357}, {4359, 29814}, {4361, 16823}, {4365, 32771}, {4373, 30340}, {4387, 27064}, {4398, 24231}, {4414, 32919}, {4425, 33084}, {4432, 16468}, {4442, 31019}, {4452, 11038}, {4460, 8236}, {4464, 30331}, {4514, 33088}, {4552, 7672}, {4640, 37683}, {4642, 21330}, {4643, 9791}, {4644, 24280}, {4645, 4851}, {4655, 17361}, {4660, 17386}, {4663, 17350}, {4671, 46897}, {4681, 20050}, {4686, 20057}, {4688, 38314}, {4696, 22016}, {4698, 9780}, {4706, 24620}, {4716, 16484}, {4718, 28582}, {4733, 29576}, {4777, 47729}, {4788, 28555}, {4812, 36565}, {4828, 48295}, {4849, 27538}, {4850, 29824}, {4854, 27184}, {4871, 31233}, {4883, 42051}, {4889, 28566}, {4923, 5257}, {4956, 31179}, {4972, 32858}, {4974, 15485}, {4975, 5313}, {5014, 33093}, {5057, 31034}, {5132, 15571}, {5212, 5316}, {5220, 17261}, {5256, 32942}, {5311, 32945}, {5550, 31238}, {5731, 30271}, {5846, 17388}, {5847, 17377}, {5880, 17300}, {5919, 20037}, {6051, 9534}, {6541, 33165}, {7201, 10106}, {7290, 16834}, {7982, 29054}, {8299, 17027}, {9312, 12560}, {10371, 26117}, {10465, 31779}, {10501, 16018}, {11269, 32851}, {11679, 37553}, {14829, 17594}, {14839, 32453}, {15254, 17349}, {15888, 21927}, {16602, 26103}, {16610, 30947}, {16777, 16830}, {17011, 24552}, {17017, 32943}, {17023, 27474}, {17064, 41878}, {17135, 27804}, {17165, 42044}, {17228, 32784}, {17280, 38047}, {17281, 36409}, {17310, 48829}, {17315, 32850}, {17328, 24697}, {17342, 33159}, {17347, 34379}, {17359, 26083}, {17360, 33082}, {17364, 17768}, {17365, 28530}, {17370, 29637}, {17371, 29633}, {17378, 28580}, {17382, 26150}, {17387, 24715}, {17600, 29652}, {17718, 37759}, {17733, 37573}, {17776, 33118}, {18139, 33131}, {19785, 33124}, {19786, 33171}, {19812, 32783}, {19830, 33147}, {19998, 31035}, {20017, 33075}, {20055, 27495}, {20171, 34772}, {20363, 20691}, {20942, 42043}, {21242, 29657}, {21746, 35104}, {21902, 24528}, {21926, 25466}, {24357, 36534}, {24627, 38473}, {25453, 33158}, {25557, 48627}, {27483, 29612}, {28370, 30044}, {29327, 48908}, {29577, 48821}, {29584, 31317}, {29610, 31319}, {29617, 31323}, {29621, 40333}, {29631, 33156}, {29632, 33128}, {29635, 33160}, {29642, 33132}, {29643, 33136}, {29653, 32865}, {29655, 32855}, {29671, 33141}, {29673, 33092}, {29829, 32779}, {29830, 33129}, {29835, 33089}, {30942, 46904}, {31308, 31322}, {32774, 33173}, {32776, 33081}, {32848, 33120}, {32849, 33114}, {32852, 32947}, {32859, 33100}, {32863, 32950}, {32912, 32936}, {32913, 32934}, {32946, 33095}, {32949, 33094}, {33064, 33154}, {33069, 33145}, {33113, 33142}, {33116, 33137}, {33122, 33155}, {33149, 48629}, {33163, 42033}, {36815, 47318}, {37580, 41251}, {39581, 42696}, {39702, 39742}

X(49470) = midpoint of X(145) and X(192)
X(49470) = reflection of X(i) in X(j) for these {i,j}: {8, 37}, {75, 1}, {984, 3993}, {3696, 15569}, {3797, 4702}, {4709, 1125}
X(49470) = anticomplement of X(3696)
X(49470) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1002, 1330}, {1333, 27484}, {2279, 2895}, {27475, 21287}, {42290, 2893}, {42302, 69}
X(49470) = X(i)-isoconjugate of X(j) for these (i,j): {6, 39981}, {32, 40030}
X(49470) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 39981), (6376, 40030)
X(49470) = crosspoint of X(7035) and X(32041)
X(49470) = crossdifference of every pair of points on line {798, 20980}
X(49470) = barycentric product X(i)*X(j) for these {i,j}: {1, 30830}, {75, 37657}, {190, 48080}
X(49470) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 39981}, {75, 40030}, {30830, 75}, {37657, 1}, {48080, 514}
X(49470) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1045, 2274}, {1, 3875, 32922}, {1, 3886, 5263}, {1, 43997, 5625}, {6, 3685, 4676}, {42, 32915, 312}, {55, 1999, 3769}, {75, 18156, 18157}, {968, 17156, 333}, {984, 3993, 4664}, {3696, 15569, 2}, {3706, 37593, 2}, {3720, 32860, 19804}, {3755, 3912, 4429}, {3821, 33087, 17227}, {3923, 4649, 3758}, {3995, 20011, 3681}, {3996, 34064, 612}, {4028, 24210, 4417}, {4365, 32771, 42029}, {4649, 4693, 3923}, {4716, 16484, 16825}, {4849, 35652, 27538}, {4970, 42057, 982}, {17135, 27804, 28606}, {17594, 39594, 14829}, {20012, 41839, 210}, {27480, 31342, 27475}


X(49471) = X(1)X(75)∩X(37)X(519)

Barycentrics    3*a^2*b + 3*a^2*c + 2*a*b*c - b^2*c - b*c^2 : :
X(49471) = 3 X[1] - X[75], 2 X[75] - 3 X[24325], 3 X[8] - 7 X[27268], 6 X[3842] - 7 X[27268], 3 X[10] - 4 X[4698], 2 X[4698] - 3 X[15569], 3 X[145] + 5 X[4704], 3 X[984] - 5 X[4704], X[192] + 3 X[3241], 3 X[3244] + 2 X[4681], 3 X[3993] - 2 X[4681], 3 X[551] - 2 X[3739], 3 X[551] - X[4709], 6 X[3635] + X[4718], 6 X[1125] - 5 X[31238], 3 X[3696] - 5 X[31238], X[1278] - 3 X[31178], 7 X[3622] - 5 X[40328], 15 X[3623] + X[4788], 5 X[3623] - X[24349], X[4788] + 3 X[24349], 3 X[3679] - 5 X[4687], 3 X[3892] - 2 X[13476], 5 X[4699] - 9 X[38314], 7 X[4751] - 9 X[25055], 3 X[10176] - 2 X[22271]

X(49471) lies on these lines: {1, 75}, {2, 4732}, {6, 4432}, {8, 3842}, {9, 4753}, {10, 4698}, {37, 519}, {38, 17145}, {42, 4358}, {43, 30829}, {142, 4780}, {145, 984}, {192, 537}, {238, 17121}, {239, 16484}, {312, 42042}, {335, 29588}, {354, 4970}, {518, 3244}, {528, 17390}, {551, 3739}, {726, 3635}, {752, 3879}, {756, 20011}, {872, 4738}, {894, 4693}, {968, 32853}, {1001, 4974}, {1100, 4702}, {1125, 3696}, {1193, 29982}, {1201, 30044}, {1215, 4671}, {1278, 31178}, {1482, 29054}, {1621, 3791}, {1738, 4743}, {1953, 5819}, {1961, 3996}, {1962, 17135}, {1999, 3750}, {2099, 4032}, {2177, 4434}, {2345, 48830}, {2796, 17365}, {2805, 33337}, {3210, 42053}, {3240, 24003}, {3476, 7201}, {3622, 40328}, {3623, 4788}, {3644, 28554}, {3664, 28580}, {3666, 42057}, {3679, 4687}, {3685, 4649}, {3706, 43223}, {3720, 3896}, {3741, 37593}, {3751, 25728}, {3755, 3836}, {3759, 15485}, {3774, 20363}, {3795, 40533}, {3797, 29584}, {3821, 4966}, {3840, 4891}, {3846, 4028}, {3874, 4065}, {3883, 17772}, {3892, 13476}, {3898, 44671}, {3912, 4085}, {3931, 35633}, {3943, 36409}, {3950, 4439}, {3957, 32928}, {3961, 34064}, {3969, 29685}, {3970, 20593}, {3979, 32926}, {3995, 42054}, {4007, 48851}, {4022, 4424}, {4026, 48635}, {4038, 32932}, {4043, 4692}, {4090, 35652}, {4094, 20985}, {4096, 41839}, {4297, 31779}, {4361, 24331}, {4393, 17755}, {4457, 26037}, {4648, 24693}, {4655, 21296}, {4660, 4851}, {4669, 4755}, {4685, 44307}, {4697, 32929}, {4699, 38314}, {4716, 16823}, {4734, 17063}, {4742, 20891}, {4751, 25055}, {4759, 16669}, {4777, 48285}, {4793, 22316}, {4819, 5241}, {4852, 42819}, {4854, 33064}, {4883, 24165}, {4889, 28538}, {4892, 33134}, {4971, 25384}, {4975, 18137}, {5312, 25079}, {5313, 25106}, {6542, 33076}, {6682, 10453}, {7264, 20448}, {7982, 30273}, {9330, 20048}, {10176, 22271}, {10180, 31330}, {10222, 29010}, {15624, 25439}, {16777, 36480}, {16884, 48805}, {17011, 32943}, {17019, 32945}, {17146, 17147}, {17233, 29659}, {17234, 25351}, {17242, 33165}, {17285, 36478}, {17300, 24715}, {17303, 48822}, {17311, 48829}, {17312, 31151}, {17314, 36479}, {17315, 32847}, {17318, 42871}, {17364, 28558}, {17376, 24692}, {17380, 29660}, {17450, 17495}, {17601, 37684}, {17778, 33095}, {17779, 25531}, {18743, 42043}, {19823, 26128}, {19828, 33147}, {19829, 33124}, {19832, 32783}, {20016, 31308}, {20182, 29652}, {20430, 37727}, {21805, 31035}, {21883, 22199}, {26103, 31228}, {26626, 27474}, {27401, 34772}, {27475, 29602}, {27480, 29585}, {27483, 29592}, {28595, 32858}, {29576, 31336}, {29593, 31319}, {29814, 32860}, {29817, 32924}, {29824, 46904}, {29829, 33156}, {29830, 33128}, {29835, 32848}, {29837, 33160}, {29839, 33135}, {29843, 32855}, {32784, 48634}, {32916, 37553}, {33087, 48633}, {35104, 39543}

X(49471) = midpoint of X(i) and X(j) for these {i,j}: {145, 984}, {3244, 3993}, {7982, 30273}, {20430, 37727}
X(49471) = reflection of X(i) in X(j) for these {i,j}: {8, 3842}, {10, 15569}, {3696, 1125}, {4669, 4755}, {4709, 3739}, {24325, 1}
X(49471) = anticomplement of X(4732)
X(49471) = crossdifference of every pair of points on line {798, 23650}
X(49471) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {551, 4709, 3739}, {3685, 4649, 4672}, {10453, 17592, 6682}, {17018, 32915, 1215}, {20016, 31308, 31323}, {21805, 31035, 42056}, {37553, 39594, 32916}


X(49472) = X(1)X(75)∩X(6)X(537)

Barycentrics    2*a^3 + a^2*b + 2*a*b^2 + a^2*c - b^2*c + 2*a*c^2 - b*c^2 : :
X(49472) = 3 X[1] + X[3875], 5 X[1] - X[3886], 3 X[1] - X[32941], 5 X[3875] + 3 X[3886], X[3875] - 3 X[32921], X[3886] + 5 X[32921], 3 X[3886] - 5 X[32941], 3 X[32921] + X[32941], 3 X[551] - X[2321], 3 X[1386] - X[17351], 3 X[4672] - 2 X[17351], 5 X[3616] - 2 X[4535], 2 X[3635] + X[4743], 4 X[3636] - X[4527], X[3729] - 5 X[16491], X[3923] - 3 X[38315], X[4660] - 3 X[17301], 3 X[16475] - X[32935], X[16496] + 3 X[16834], 5 X[17286] - 9 X[25055]

X(49472) lies on these lines: {1, 75}, {6, 537}, {8, 17383}, {10, 17366}, {38, 3791}, {42, 30982}, {81, 42055}, {141, 519}, {145, 32846}, {192, 4432}, {238, 17261}, {239, 27495}, {321, 29819}, {335, 4393}, {551, 2321}, {726, 1386}, {752, 3663}, {940, 42053}, {982, 37684}, {984, 4974}, {1120, 7194}, {1125, 3773}, {1215, 3891}, {1279, 3993}, {1482, 24257}, {1999, 17598}, {3210, 17716}, {3241, 17300}, {3244, 3755}, {3246, 4681}, {3555, 4523}, {3589, 28503}, {3616, 4535}, {3635, 4743}, {3636, 4527}, {3679, 17307}, {3686, 4407}, {3699, 17779}, {3703, 29654}, {3729, 16491}, {3744, 4970}, {3745, 24165}, {3757, 17600}, {3759, 4753}, {3769, 17591}, {3821, 5846}, {3842, 16825}, {3874, 18178}, {3881, 44661}, {3920, 32924}, {3923, 28516}, {3969, 29686}, {4000, 25351}, {4078, 31289}, {4096, 4383}, {4307, 4373}, {4353, 5847}, {4359, 29816}, {4361, 4732}, {4362, 6682}, {4371, 48802}, {4402, 48856}, {4434, 4850}, {4439, 17353}, {4649, 20180}, {4655, 28498}, {4660, 17301}, {4663, 4991}, {4664, 15485}, {4697, 17155}, {4719, 8669}, {4722, 20068}, {4780, 17392}, {4865, 19785}, {4892, 33070}, {5235, 32914}, {5256, 32920}, {7191, 32928}, {10222, 48934}, {16475, 32935}, {16484, 17000}, {16496, 16834}, {16706, 32847}, {16777, 24331}, {17011, 32923}, {17012, 32927}, {17024, 32915}, {17025, 32931}, {17061, 29671}, {17140, 26860}, {17147, 17469}, {17233, 29660}, {17235, 28538}, {17276, 28558}, {17286, 25055}, {17302, 33076}, {17318, 24358}, {17367, 33165}, {17379, 31178}, {17380, 29659}, {17722, 37759}, {17726, 25385}, {19742, 42039}, {19786, 32866}, {19796, 33109}, {20045, 46904}, {20132, 29584}, {20182, 29651}, {22791, 29040}, {24248, 28494}, {24349, 37677}, {26128, 33088}, {26230, 32848}, {27474, 29570}, {28595, 32774}, {28634, 48809}, {29634, 32855}, {29636, 33089}, {29815, 32860}, {29820, 34064}, {29821, 32926}, {29831, 33156}, {29832, 33128}, {29834, 32779}, {29838, 33160}, {29840, 33135}, {29852, 32862}, {32775, 32842}, {32844, 33155}, {32911, 42054}, {33071, 33152}, {33072, 33150}, {33073, 33147}, {33093, 33123}, {37639, 42038}, {37680, 42056}

X(49472) = midpoint of X(i) and X(j) for these {i,j}: {1, 32921}, {1482, 24257}, {3244, 3755}, {3555, 4523}, {3875, 32941}
X(49472) = reflection of X(i) in X(j) for these {i,j}: {3773, 1125}, {4085, 3946}, {4663, 4991}, {4672, 1386}
X(49472) = crossdifference of every pair of points on line {798, 47330}
X(49472) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3875, 32941}, {1, 32922, 24325}, {38, 17150, 3791}, {3891, 17017, 1215}, {4361, 36480, 4732}, {4362, 17599, 6682}, {32774, 32854, 28595}, {32921, 32941, 3875}, {33070, 33143, 4892}


X(49473) = X(1)X(75)∩X(2)X(3722)

Barycentrics    2*a^3 - a^2*b + 2*a*b^2 - a^2*c + b^2*c + 2*a*c^2 + b*c^2 : :
X(49473) = 5 X[1] - X[3875], 3 X[1] + X[3886], 3 X[1] - X[32921], 3 X[3875] + 5 X[3886], 3 X[3875] - 5 X[32921], X[3875] + 5 X[32941], X[3886] - 3 X[32941], X[32921] + 3 X[32941], X[145] + 2 X[4535], 3 X[392] - X[4523], 3 X[1386] - 2 X[4991], 2 X[24295] - 3 X[48810], X[3242] + 3 X[48805], X[3923] - 3 X[48805], 3 X[551] - X[3755], X[3632] - 5 X[17286], 2 X[3635] + X[4527], 4 X[3636] - X[4743], 3 X[10246] - X[24257]

X(49473) lies on these lines: {1, 75}, {2, 3722}, {8, 4974}, {10, 1279}, {38, 4427}, {55, 6682}, {69, 28498}, {141, 17766}, {145, 4535}, {149, 32775}, {392, 4523}, {516, 48881}, {518, 4672}, {519, 597}, {528, 3821}, {537, 3242}, {551, 3755}, {902, 46909}, {984, 4432}, {996, 34893}, {1001, 3842}, {1100, 2321}, {1125, 3813}, {1215, 3938}, {1376, 29668}, {2550, 25351}, {2607, 5330}, {2886, 29656}, {3011, 21242}, {3058, 4425}, {3434, 26128}, {3626, 17348}, {3632, 3759}, {3635, 4527}, {3636, 3946}, {3663, 17764}, {3699, 3961}, {3741, 3744}, {3745, 42057}, {3748, 43223}, {3749, 32916}, {3775, 3883}, {3791, 17135}, {3870, 25496}, {3873, 4697}, {3884, 44661}, {3896, 29819}, {3920, 32943}, {3925, 29672}, {3935, 32944}, {3941, 8666}, {3957, 32772}, {3980, 17597}, {3993, 4702}, {3996, 29821}, {4011, 4096}, {4307, 32093}, {4353, 28580}, {4359, 29818}, {4393, 27474}, {4418, 42055}, {4429, 29660}, {4434, 30942}, {4514, 32783}, {4655, 28494}, {4670, 15570}, {4732, 16825}, {4753, 16468}, {4756, 32930}, {4759, 15481}, {4847, 6679}, {4863, 25453}, {4865, 33171}, {4892, 33104}, {4972, 29686}, {5014, 24943}, {5695, 28516}, {5783, 21769}, {7191, 32945}, {10022, 17133}, {10246, 24257}, {10453, 17716}, {11680, 29848}, {16484, 16830}, {16496, 32935}, {16826, 20153}, {17024, 32860}, {17276, 28546}, {17345, 28508}, {17598, 32932}, {17614, 24659}, {17724, 25385}, {19284, 46190}, {21283, 29831}, {24169, 34612}, {26230, 33136}, {28558, 47358}, {29040, 34773}, {29634, 33141}, {29637, 32850}, {29638, 33108}, {29815, 32915}, {29823, 46904}, {29832, 33156}, {29836, 33129}, {29838, 33135}, {29840, 33160}, {32776, 34611}, {32844, 33175}, {33072, 33173}, {33106, 33126}, {33109, 33124}, {33110, 33123}, {38316, 39586}

X(49473) = midpoint of X(i) and X(j) for these {i,j}: {1, 32941}, {2321, 3244}, {3242, 3923}, {3886, 32921}, {16496, 32935}
X(49473) = reflection of X(i) in X(j) for these {i,j}: {3946, 3636}, {4085, 1125}, {4743, 3946}
X(49473) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3886, 32921}, {1, 5263, 24325}, {55, 29652, 6682}, {1001, 36480, 3842}, {3242, 48805, 3923}, {3938, 24552, 1215}, {3980, 17597, 42053}, {5014, 24943, 28595}, {17135, 17469, 3791}, {21283, 29831, 33128}, {32921, 32941, 3886}, {33104, 33122, 4892}


X(49474) = X(1)X(75)∩X(8)X(726)

Barycentrics    a^2*b + a^2*c - a*b*c - 2*b^2*c - 2*b*c^2 : :
X(49474) = 3 X[1] - 4 X[24325], 3 X[75] - 2 X[24325], 3 X[8] - X[31302], X[1278] + 2 X[4709], 3 X[1278] + X[31302], 6 X[4709] - X[31302], 4 X[37] - 5 X[1698], X[145] - 5 X[4821], 3 X[165] - 2 X[30273], X[3632] + 4 X[4686], 3 X[4740] - X[24349], 2 X[984] - 3 X[3679], 3 X[3679] - 4 X[3696], 4 X[1125] - 5 X[4699], 3 X[3097] - 2 X[32453], 5 X[3616] - 7 X[4772], 5 X[3617] - X[4788], 7 X[3624] - 8 X[3739], X[3633] - 8 X[4726], 8 X[3634] - 7 X[27268], X[3644] - 4 X[4732], 4 X[3842] - 3 X[4664], 8 X[3842] - 9 X[19875], 2 X[4664] - 3 X[19875], 5 X[4668] + 2 X[4764], 3 X[4688] - 2 X[15569], 4 X[4688] - 3 X[25055], 6 X[4688] - 5 X[40328], 8 X[15569] - 9 X[25055], 4 X[15569] - 5 X[40328], 9 X[25055] - 10 X[40328], 16 X[4698] - 17 X[19872], 5 X[4704] - 7 X[9780], 14 X[4751] - 13 X[34595], 3 X[5587] - 2 X[20430]

X(49474) lies on these lines: {1, 75}, {2, 3993}, {5, 21927}, {6, 4716}, {8, 726}, {10, 192}, {37, 1698}, {40, 29010}, {42, 28605}, {43, 321}, {63, 13174}, {69, 32857}, {76, 4710}, {141, 33149}, {145, 4821}, {165, 30273}, {200, 17890}, {238, 4361}, {239, 3923}, {244, 31137}, {306, 17889}, {312, 16569}, {319, 4655}, {333, 32934}, {335, 17294}, {345, 33138}, {350, 10009}, {386, 42031}, {518, 3632}, {519, 4740}, {536, 984}, {537, 4677}, {573, 29347}, {594, 32784}, {596, 39742}, {742, 3751}, {756, 42044}, {758, 37003}, {846, 5271}, {899, 4671}, {936, 20171}, {978, 20891}, {982, 3706}, {986, 5295}, {995, 4717}, {1001, 4693}, {1086, 33087}, {1089, 6048}, {1125, 4699}, {1150, 32845}, {1211, 33154}, {1215, 42029}, {1423, 7235}, {1574, 20688}, {1738, 2321}, {1742, 29016}, {1757, 3729}, {1836, 32861}, {1921, 3760}, {1999, 3980}, {2108, 17026}, {2345, 29633}, {2550, 32847}, {2783, 6210}, {2796, 29617}, {2886, 32855}, {2895, 33098}, {2901, 28612}, {2960, 6763}, {3097, 17759}, {3120, 33077}, {3187, 4418}, {3210, 3741}, {3223, 18793}, {3293, 22316}, {3339, 4032}, {3416, 9055}, {3434, 32866}, {3501, 24269}, {3550, 4362}, {3616, 4772}, {3617, 4788}, {3624, 3739}, {3633, 4726}, {3634, 27268}, {3644, 4732}, {3661, 3821}, {3685, 15485}, {3686, 28557}, {3687, 3944}, {3702, 20892}, {3703, 32865}, {3705, 5988}, {3714, 24440}, {3740, 22034}, {3755, 29659}, {3759, 4672}, {3772, 33160}, {3773, 4429}, {3775, 4389}, {3782, 4046}, {3783, 4441}, {3795, 21264}, {3797, 4384}, {3826, 3943}, {3836, 4527}, {3840, 17490}, {3842, 4664}, {3883, 28580}, {3891, 32945}, {3894, 44671}, {3896, 4980}, {3912, 4133}, {3914, 32778}, {3925, 33092}, {3946, 29646}, {3966, 33095}, {3969, 25957}, {3995, 26037}, {3996, 32920}, {4000, 29637}, {4026, 4665}, {4062, 31019}, {4135, 27538}, {4359, 26102}, {4363, 4649}, {4364, 4733}, {4371, 5698}, {4387, 17123}, {4392, 31136}, {4393, 33682}, {4399, 28530}, {4416, 28526}, {4417, 48643}, {4442, 25760}, {4457, 42054}, {4479, 17793}, {4519, 16610}, {4643, 42334}, {4651, 32925}, {4668, 4764}, {4676, 4974}, {4685, 32937}, {4688, 15569}, {4698, 19872}, {4703, 4886}, {4704, 9780}, {4706, 30818}, {4734, 6685}, {4751, 34595}, {4777, 47724}, {4812, 5293}, {4816, 28582}, {4850, 29827}, {4871, 24620}, {4966, 7263}, {5223, 24821}, {5278, 32936}, {5290, 7201}, {5564, 24723}, {5587, 20430}, {5739, 33099}, {5814, 24851}, {5839, 24695}, {5880, 17299}, {6535, 29679}, {7613, 29616}, {7991, 29054}, {8580, 20173}, {8616, 32914}, {9791, 27481}, {10449, 42027}, {10453, 24165}, {11679, 17596}, {13476, 39711}, {14459, 31034}, {15523, 33131}, {16833, 17755}, {16834, 31317}, {17023, 27480}, {17135, 17154}, {17147, 17163}, {17156, 32913}, {17225, 47359}, {17267, 31252}, {17275, 24697}, {17281, 33159}, {17284, 27474}, {17316, 27478}, {17321, 19856}, {17334, 28556}, {17346, 28542}, {17347, 17767}, {17362, 17768}, {17363, 17770}, {17367, 24295}, {17382, 25539}, {17495, 30942}, {17592, 31993}, {17593, 37660}, {17733, 37608}, {17740, 33140}, {18193, 35613}, {19785, 32783}, {19789, 33147}, {19796, 26128}, {19804, 25502}, {19820, 33124}, {20017, 32949}, {20055, 24692}, {20292, 32852}, {20895, 23690}, {21020, 28606}, {21085, 27184}, {21330, 24046}, {22167, 24443}, {24357, 36531}, {24552, 32924}, {24693, 36494}, {24789, 33158}, {24892, 33168}, {24943, 33150}, {25354, 29576}, {25492, 27343}, {29610, 31329}, {29612, 31308}, {29825, 46904}, {29856, 32779}, {29858, 33129}, {30699, 33152}, {31053, 48642}, {32777, 33132}, {32782, 33145}, {32842, 33104}, {32848, 33108}, {32853, 32939}, {32854, 33110}, {32864, 32933}, {33075, 33094}, {33080, 33102}, {33081, 33146}, {33088, 33109}, {33089, 33136}, {33137, 33167}, {33139, 33161}, {33143, 33175}, {33155, 46918}, {36634, 42034}

X(49474) = anticomplement of X(3993)
X(49474) = midpoint of X(8) and X(1278)
X(49474) = reflection of X(i) in X(j) for these {i,j}: {1, 75}, {8, 4709}, {192, 10}, {984, 3696}
X(49474) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {27494, 21287}, {40735, 1654}
X(49474) = X(i)-isoconjugate of X(j) for these (i,j): {6, 39952}, {32, 40031}
X(49474) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 39952), (6376, 40031)
X(49474) = crossdifference of every pair of points on line {798, 23472}
X(49474) = barycentric product X(i)*X(j) for these {i,j}: {1, 31060}, {75, 37673}, {190, 48090}
X(49474) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 39952}, {75, 40031}, {31060, 75}, {37673, 1}, {48090, 514}
X(49474) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 16571, 18792}, {1, 24342, 43997}, {8, 24248, 33082}, {239, 3923, 16468}, {321, 32860, 43}, {984, 3696, 3679}, {1738, 2321, 29674}, {1999, 3980, 37604}, {3210, 3741, 17591}, {3685, 16825, 15485}, {3685, 17117, 16825}, {3706, 42051, 982}, {3782, 4046, 33084}, {3836, 4527, 17233}, {3896, 4980, 32771}, {3896, 32771, 42042}, {4359, 32915, 26102}, {4361, 5695, 238}, {4362, 32932, 3550}, {4688, 15569, 40328}, {5263, 17160, 32921}, {5263, 32921, 1}, {5880, 17299, 32846}, {15569, 40328, 25055}, {17147, 17163, 31330}, {19789, 33171, 33147}, {32779, 33128, 29856}, {32914, 32929, 8616}, {32922, 32941, 1}, {33129, 33156, 29858}


X(49475) = X(1)X(3696)∩X(37)X(519)

Barycentrics    5*a^2*b - a*b^2 + 5*a^2*c + 2*a*b*c - 2*b^2*c - a*c^2 - 2*b*c^2 : :
X(49475) = 3 X[1] - 2 X[3739], 7 X[1] - 5 X[40328], 3 X[3696] - 4 X[3739], 7 X[3696] - 10 X[40328], 14 X[3739] - 15 X[40328], 3 X[8] - 5 X[4687], 5 X[4687] - 6 X[15569], X[75] - 3 X[3241], 3 X[145] + X[192], 7 X[145] + X[31302], 7 X[192] - 3 X[31302], 3 X[392] - 2 X[22271], 3 X[551] - 2 X[4732], 6 X[551] - 5 X[31238], 4 X[4732] - 5 X[31238], 6 X[3244] - X[4686], 15 X[3623] - 7 X[4772], 3 X[3679] - 4 X[4698], 2 X[4681] + 3 X[34747], 3 X[4688] - 2 X[4709], 5 X[4704] + 3 X[20049], 2 X[4726] - 3 X[31178], 7 X[4751] - 9 X[38314], X[4764] - 3 X[24349], 7 X[27268] - 3 X[31145]

X(49475) lies on these lines: {1, 3696}, {6, 4702}, {8, 4687}, {37, 519}, {42, 30818}, {43, 4891}, {75, 3241}, {144, 145}, {210, 20011}, {239, 31342}, {346, 47359}, {354, 3896}, {392, 22271}, {528, 3879}, {537, 4718}, {551, 4732}, {740, 3244}, {984, 3633}, {1086, 4780}, {1100, 32941}, {1449, 48805}, {2805, 7972}, {3187, 3748}, {3246, 3759}, {3555, 20718}, {3623, 4772}, {3625, 3842}, {3635, 24325}, {3672, 47358}, {3679, 4698}, {3685, 4663}, {3706, 17018}, {3723, 36480}, {3740, 20012}, {3742, 24620}, {3752, 42057}, {3755, 4966}, {3875, 42871}, {3967, 32915}, {3996, 4682}, {4085, 17231}, {4255, 39584}, {4358, 21870}, {4432, 16669}, {4457, 25501}, {4519, 46897}, {4646, 35633}, {4660, 17374}, {4677, 4755}, {4681, 34747}, {4688, 4709}, {4689, 32919}, {4693, 17351}, {4704, 20049}, {4726, 31178}, {4727, 36409}, {4733, 4923}, {4742, 18137}, {4751, 38314}, {4753, 15492}, {4764, 24349}, {4864, 32921}, {4883, 32860}, {4914, 20017}, {4946, 24003}, {4970, 21342}, {5882, 30271}, {15570, 32922}, {16484, 17348}, {16496, 17318}, {17135, 37593}, {17229, 29659}, {17296, 48829}, {17299, 36479}, {17303, 48830}, {17364, 28534}, {17365, 28580}, {17372, 33076}, {17376, 24715}, {17377, 28538}, {17393, 36534}, {21806, 31136}, {25384, 28329}, {27268, 31145}, {32945, 37595}, {42042, 44417}

X(49475) = midpoint of X(984) and X(3633)
X(49475) = reflection of X(i) in X(j) for these {i,j}: {8, 15569}, {3625, 3842}, {3696, 1}, {4677, 4755}, {24325, 3635}, {30271, 5882}
X(49475) = {X(551),X(4732)}-harmonic conjugate of X(31238)


X(49476) = X(1)X(2)∩X(6)X(3717)

Barycentrics    2*a^3 + a^2*b + 2*a*b^2 - b^3 + a^2*c + 2*a*b*c - b^2*c + 2*a*c^2 - b*c^2 - c^3 : :
X(49476) = 2 X[1] - 3 X[29574], X[145] - 3 X[17389], 5 X[3617] - 3 X[29617], 15 X[29622] - 13 X[46934]

X(49476) lies on these lines: {1, 2}, {6, 3717}, {37, 3883}, {55, 21982}, {65, 7198}, {69, 7174}, {142, 32922}, {192, 516}, {193, 5223}, {226, 32926}, {238, 4078}, {304, 33941}, {344, 7290}, {345, 5269}, {346, 4344}, {388, 3674}, {517, 49132}, {518, 3688}, {730, 17760}, {894, 4349}, {908, 33070}, {984, 4416}, {1266, 5880}, {1279, 17243}, {1386, 3932}, {1429, 4848}, {1449, 4901}, {1573, 4875}, {1697, 3496}, {1738, 32921}, {1743, 27549}, {1891, 17442}, {1897, 30687}, {1930, 4968}, {2321, 5263}, {2325, 4676}, {2329, 5837}, {2550, 3875}, {2901, 22048}, {3057, 20715}, {3061, 5795}, {3177, 12527}, {3242, 4684}, {3416, 4357}, {3452, 33071}, {3644, 28557}, {3662, 4353}, {3663, 4645}, {3664, 24349}, {3677, 18141}, {3685, 3950}, {3703, 3745}, {3710, 3997}, {3729, 4307}, {3751, 4899}, {3755, 4360}, {3769, 5745}, {3780, 16782}, {3790, 17355}, {3823, 17366}, {3871, 40910}, {3886, 17314}, {3891, 5249}, {3895, 5011}, {3905, 5794}, {3913, 37580}, {3914, 32928}, {3946, 4429}, {3977, 17126}, {3993, 17766}, {4001, 7226}, {4030, 37593}, {4035, 33126}, {4054, 33112}, {4082, 27064}, {4104, 32861}, {4138, 33152}, {4297, 18788}, {4310, 17298}, {4356, 17319}, {4385, 5717}, {4388, 4656}, {4402, 40333}, {4439, 4672}, {4440, 30424}, {4447, 37575}, {4480, 24695}, {4513, 5710}, {4514, 34064}, {4681, 28566}, {4686, 28472}, {4718, 28530}, {4856, 16779}, {4865, 24210}, {4989, 17352}, {5100, 41813}, {5250, 17742}, {5294, 32862}, {5542, 17300}, {5603, 36683}, {5850, 17364}, {6211, 39870}, {7146, 10106}, {7322, 14555}, {8715, 37576}, {9053, 17390}, {9347, 33089}, {12194, 37588}, {12437, 19589}, {12526, 20111}, {12577, 17480}, {12640, 19557}, {14548, 39959}, {15590, 30340}, {16469, 26685}, {16503, 24393}, {17279, 38315}, {17315, 20179}, {17318, 24699}, {17334, 28570}, {17365, 28582}, {17388, 28581}, {17600, 33079}, {17716, 33092}, {17726, 30818}, {17769, 24325}, {18156, 33938}, {25264, 39350}, {30701, 39958}, {32849, 35263}, {32925, 41011}, {33159, 38049}, {38046, 42871}, {40998, 41839}, {48806, 48828}

X(49476) = midpoint of X(17364) and X(31302)
X(49476) = reflection of X(i) in X(j) for these {i,j}: {3883, 37}, {4416, 984}, {24349, 3664}
X(49476) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 10, 17023}, {1, 3632, 36479}, {1, 17284, 3616}, {1, 29637, 551}, {1, 29660, 3636}, {1, 29674, 1125}, {1, 32847, 10}, {8, 16830, 10}, {145, 17316, 1}, {145, 29621, 39567}, {238, 4078, 25101}, {612, 33088, 3687}, {1125, 29674, 29596}, {1386, 3932, 17353}, {3242, 4851, 4684}, {3617, 29610, 10}, {3679, 19856, 10}, {3920, 33093, 306}, {4360, 32850, 3755}, {29621, 39567, 3616}, {32926, 33073, 226}, {32928, 33072, 3914}


X(49477) = X(1)X(2)∩X(6)X(726)

Barycentrics    2*a^3 + 2*a^2*b + a*b^2 + 2*a^2*c - b^2*c + a*c^2 - b*c^2 : :
X(49477) = X[1] + 3 X[16834], 7 X[3624] - 3 X[17294], 5 X[19862] - 3 X[29594], 3 X[6] - X[32935], 2 X[4991] + X[32921], 6 X[4991] - X[32935], 3 X[32921] + X[32935], X[2321] - 3 X[38049], 2 X[24295] - 3 X[38049], X[3875] + 3 X[16475], X[3923] - 3 X[16475], X[3886] - 5 X[16491], 2 X[4535] - 3 X[17359], X[4655] - 3 X[17301], X[32941] - 3 X[38315]

X(49477) lies on these lines: {1, 2}, {3, 20475}, {6, 726}, {31, 4970}, {37, 4974}, {58, 99}, {75, 33682}, {81, 24165}, {83, 34475}, {141, 17772}, {190, 16477}, {192, 16468}, {213, 3159}, {238, 3993}, {330, 40753}, {333, 17600}, {514, 24286}, {515, 36685}, {516, 24257}, {528, 4743}, {536, 4672}, {537, 4663}, {596, 20963}, {740, 1386}, {870, 20888}, {946, 2784}, {984, 3759}, {1100, 24325}, {1757, 17121}, {2271, 41656}, {2308, 17147}, {2321, 24295}, {2809, 3881}, {3227, 35180}, {3550, 4734}, {3555, 20715}, {3589, 3773}, {3629, 17771}, {3663, 17770}, {3666, 3791}, {3707, 16521}, {3736, 18170}, {3747, 4065}, {3755, 17766}, {3775, 17362}, {3821, 3946}, {3836, 17366}, {3842, 17348}, {3874, 20358}, {3875, 3923}, {3886, 16491}, {3896, 17469}, {3971, 32911}, {3989, 19742}, {3994, 41241}, {4085, 5846}, {4090, 32926}, {4135, 27064}, {4353, 4856}, {4427, 21747}, {4527, 4971}, {4535, 17359}, {4649, 20179}, {4655, 17301}, {4660, 28512}, {4697, 42051}, {4699, 43997}, {4709, 4716}, {4759, 17318}, {5145, 18194}, {5852, 32455}, {6329, 28472}, {6541, 17353}, {8691, 9082}, {8715, 37590}, {12263, 20970}, {12609, 20257}, {16704, 46901}, {16706, 32846}, {16972, 17355}, {17117, 24342}, {17123, 34064}, {17143, 42031}, {17144, 33941}, {17155, 37685}, {17228, 25539}, {17243, 31289}, {17302, 33082}, {17320, 24697}, {17351, 28516}, {17373, 26150}, {17377, 33087}, {17380, 32784}, {17394, 40328}, {17448, 37592}, {17490, 37604}, {17591, 37683}, {17599, 32853}, {17726, 21242}, {17778, 33147}, {17793, 21904}, {19133, 24253}, {19785, 32946}, {19786, 32861}, {19796, 33097}, {20132, 27478}, {20158, 27481}, {21010, 25440}, {21241, 33070}, {21443, 30940}, {21877, 23533}, {24074, 25264}, {24248, 28508}, {24692, 33149}, {31034, 33143}, {31997, 33936}, {32774, 32852}, {32843, 33155}, {32941, 38315}, {32949, 33150}, {33071, 33135}, {33073, 33132}, {34063, 37607}, {35148, 35172}, {37023, 37575}

X(49477) = midpoint of X(i) and X(j) for these {i,j}: {6, 32921}, {1386, 4852}, {3875, 3923}, {4353, 4856}
X(49477) = reflection of X(i) in X(j) for these {i,j}: {6, 4991}, {2321, 24295}, {3773, 3589}, {3821, 3946}
X(49477) = X(29079)-complementary conjugate of X(513)
X(49477) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 239, 10}, {1, 3216, 3009}, {1, 3624, 29570}, {1, 3632, 36534}, {1, 16823, 551}, {1, 16825, 1125}, {1, 16833, 39586}, {1, 24331, 3636}, {8, 29633, 10}, {81, 32924, 24165}, {238, 4360, 3993}, {239, 29614, 16816}, {551, 39580, 1125}, {1999, 29821, 3840}, {2321, 38049, 24295}, {2999, 29649, 6686}, {3187, 17017, 3741}, {3875, 16475, 3923}, {4362, 5256, 6685}, {4716, 5263, 4709}, {14459, 29834, 33175}, {16823, 29584, 1}, {17011, 32914, 43223}, {17150, 45222, 42}, {17162, 29823, 31136}, {32911, 32928, 3971}, {33070, 33128, 21241}


X(49478) = X(1)X(6)∩X(2)X(4849)

Barycentrics    a*(3*a*b - b^2 + 3*a*c + 2*b*c - c^2) : :
X(49478) = 3 X[1] - X[984], 3 X[1] - 2 X[15569], 3 X[37] - 2 X[984], 3 X[37] - 4 X[15569], 4 X[10] - 5 X[31238], X[192] - 5 X[3623], 2 X[3696] - 3 X[4688], 3 X[4688] - 4 X[24325], 3 X[3241] + X[24349], 3 X[551] - 2 X[3842], 8 X[3635] - X[4718], 4 X[3244] + X[4686], 5 X[3616] - 4 X[4698], 5 X[3617] - 7 X[4751], X[3621] - 5 X[4699], 7 X[3622] - 5 X[4687], 3 X[3679] - 5 X[40328], 3 X[4664] - X[31302], 2 X[4681] - 7 X[20057], 4 X[4739] + X[20050], 2 X[4755] - 3 X[38314], 7 X[4772] + X[20014], 3 X[7967] - X[30273], 3 X[10247] - X[20430], 5 X[25917] - 4 X[40607]

X(49478) lies on these lines: {1, 6}, {2, 4849}, {8, 3739}, {10, 4966}, {31, 3748}, {38, 37593}, {42, 244}, {43, 3742}, {55, 22060}, {56, 15624}, {57, 42314}, {65, 1418}, {75, 145}, {77, 11526}, {81, 643}, {100, 37520}, {141, 4684}, {171, 3979}, {192, 3623}, {200, 37674}, {210, 3720}, {241, 7672}, {269, 3340}, {312, 4891}, {335, 29584}, {386, 5045}, {390, 4644}, {516, 17365}, {517, 991}, {519, 3696}, {524, 3883}, {536, 3241}, {537, 3993}, {551, 3842}, {612, 41711}, {726, 3635}, {740, 3244}, {750, 3689}, {872, 1201}, {899, 17450}, {940, 3870}, {942, 4646}, {944, 3332}, {982, 42042}, {995, 5049}, {1002, 2276}, {1015, 3774}, {1086, 3755}, {1125, 17337}, {1155, 2177}, {1193, 17609}, {1215, 42057}, {1253, 2646}, {1317, 33966}, {1319, 1471}, {1320, 2805}, {1385, 13329}, {1419, 7201}, {1427, 5173}, {1456, 11011}, {1462, 14151}, {1468, 21059}, {1475, 39258}, {1483, 29010}, {1621, 4641}, {1707, 4428}, {1738, 25557}, {1834, 21620}, {2098, 11997}, {2099, 2263}, {2191, 2334}, {2293, 2650}, {2550, 4675}, {2810, 39543}, {2999, 44841}, {3011, 37703}, {3052, 10389}, {3058, 41011}, {3175, 17165}, {3218, 4689}, {3240, 16610}, {3293, 5439}, {3303, 21002}, {3304, 34247}, {3315, 17012}, {3333, 4255}, {3416, 17374}, {3475, 3772}, {3616, 4698}, {3617, 4751}, {3621, 4699}, {3622, 4687}, {3625, 4732}, {3661, 31306}, {3664, 5853}, {3666, 3873}, {3679, 40328}, {3681, 9330}, {3683, 32912}, {3685, 17351}, {3688, 9049}, {3706, 32771}, {3714, 35633}, {3717, 17243}, {3736, 16726}, {3740, 26102}, {3745, 3938}, {3750, 4640}, {3783, 28600}, {3797, 29588}, {3812, 21896}, {3823, 17234}, {3834, 4429}, {3838, 33141}, {3844, 29659}, {3848, 16569}, {3868, 37548}, {3874, 3931}, {3879, 5846}, {3881, 37592}, {3886, 4363}, {3889, 19767}, {3896, 17140}, {3920, 37595}, {3923, 4702}, {3935, 37633}, {3936, 29835}, {3961, 4038}, {3976, 4719}, {3999, 4850}, {4000, 11038}, {4003, 17449}, {4026, 17237}, {4113, 26037}, {4265, 40910}, {4310, 17301}, {4353, 17395}, {4356, 17246}, {4359, 20011}, {4383, 4666}, {4407, 25354}, {4417, 29843}, {4424, 24473}, {4430, 28606}, {4514, 17778}, {4515, 17750}, {4645, 17376}, {4664, 31302}, {4670, 5263}, {4681, 20057}, {4696, 18137}, {4739, 20050}, {4755, 38314}, {4772, 20014}, {4777, 30573}, {4847, 17056}, {4852, 32922}, {4901, 29573}, {4906, 29821}, {4914, 32852}, {4924, 24393}, {4929, 29602}, {4970, 42055}, {5087, 24217}, {5121, 17051}, {5222, 27475}, {5249, 21949}, {5256, 17597}, {5573, 30350}, {5712, 36845}, {5718, 26015}, {5727, 27471}, {5733, 37727}, {5850, 17334}, {5882, 29054}, {6769, 37501}, {7071, 42856}, {7190, 30318}, {7277, 30331}, {7373, 15287}, {7967, 30273}, {8580, 37682}, {8581, 42289}, {8679, 21746}, {9041, 17755}, {9053, 17390}, {10005, 29621}, {10247, 20430}, {10453, 44417}, {10459, 28350}, {10578, 37642}, {10582, 37679}, {10695, 44858}, {11019, 37662}, {11269, 17718}, {11520, 37614}, {12675, 37529}, {13374, 37699}, {13405, 37646}, {14547, 17642}, {16604, 21897}, {16823, 17348}, {16830, 28639}, {17063, 42043}, {17135, 31993}, {17145, 29822}, {17275, 39581}, {17278, 38053}, {17300, 32850}, {17345, 24723}, {17357, 38047}, {17364, 28570}, {17389, 31317}, {17398, 19868}, {18613, 20967}, {19624, 24929}, {19804, 20012}, {19860, 25878}, {19998, 24589}, {21805, 30950}, {21806, 46901}, {22034, 32915}, {22769, 37580}, {24512, 44798}, {25384, 36534}, {25917, 40607}, {27474, 29605}, {27484, 29624}, {27495, 29586}, {27549, 41313}, {27827, 39739}, {29580, 31323}, {29651, 32853}, {29685, 33081}, {29817, 32911}, {29824, 30818}, {29829, 33122}, {29830, 33114}, {29837, 33126}, {29839, 33121}, {31138, 48829}, {32937, 35652}, {33771, 37582}, {34195, 44302}, {41310, 47359}, {41311, 47358}

X(49478) = midpoint of X(i) and X(j) for these {i,j}: {75, 145}, {2650, 2667}
X(49478) = reflection of X(i) in X(j) for these {i,j}: {8, 3739}, {37, 1}, {65, 13476}, {984, 15569}, {3625, 4732}, {3696, 24325}
X(49478) = X(37138)-Ceva conjugate of X(513)
X(49478) = X(i)-Dao conjugate of X(j) for these (i, j): (24393, 10005), (29571, 4441)
X(49478) = crosspoint of X(1) and X(1002)
X(49478) = crosssum of X(1) and X(1001)
X(49478) = barycentric product X(i)*X(j) for these {i,j}: {1, 29571}, {57, 24393}, {72, 31922}, {4924, 8056}
X(49478) = barycentric quotient X(i)/X(j) for these {i,j}: {4924, 18743}, {24393, 312}, {29571, 75}, {31922, 286}
X(49478) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 6, 1279}, {1, 238, 42819}, {1, 984, 15569}, {1, 1449, 38315}, {1, 1743, 38316}, {1, 1757, 16484}, {1, 3243, 3242}, {1, 3751, 1001}, {1, 4649, 1386}, {1, 5904, 6051}, {1, 7174, 16777}, {1, 16469, 35227}, {1, 42871, 4864}, {6, 16777, 16970}, {10, 4966, 17231}, {42, 354, 3752}, {43, 3742, 16602}, {65, 1458, 1418}, {81, 3957, 3744}, {238, 4663, 16669}, {984, 15569, 37}, {1001, 3751, 44}, {1100, 4864, 1}, {1386, 4649, 16666}, {1386, 15570, 1}, {1757, 15254, 15492}, {1757, 16484, 15254}, {3666, 3873, 21342}, {3681, 29814, 44307}, {3696, 24325, 4688}, {3750, 32913, 4640}, {3755, 5542, 1086}, {3797, 29588, 31342}, {3873, 17018, 3666}, {3896, 17140, 42051}, {3961, 4038, 4682}, {4663, 42819, 238}, {4924, 29571, 24393}, {17145, 29822, 46909}, {17449, 46904, 4003}, {17450, 21870, 31197}, {29588, 31314, 3797}, {29659, 33087, 3844}, {29824, 46897, 30818}, {47358, 48830, 41311}


X(49479) = X(1)X(87)∩X(10)X(141)

Barycentrics    2*a^2*b - a*b^2 + 2*a^2*c + 2*a*b*c + b^2*c - a*c^2 + b*c^2 : :
X(49479) = 3 X[1] - X[192], 2 X[192] - 3 X[3993], X[192] + 3 X[24349], X[3993] + 2 X[24349], 3 X[8] - 7 X[4772], 3 X[10] - 4 X[3739], 2 X[3739] - 3 X[24325], 2 X[37] - 3 X[551], X[75] - 3 X[31178], X[4709] - 6 X[31178], 3 X[145] + 5 X[4821], 3 X[3244] + 2 X[4686], 3 X[984] - 5 X[4687], 6 X[1125] - 5 X[4687], X[1278] + 3 X[3241], 5 X[3616] - X[31302], 4 X[3634] - 5 X[40328], 6 X[3635] + X[4764], 3 X[3679] - 5 X[4699], 6 X[3828] - 7 X[4751], 4 X[3842] - 5 X[19862], 3 X[4669] - 4 X[4732], 3 X[4688] - 2 X[4732], 8 X[4698] - 9 X[19883], 5 X[4704] - 9 X[38314], 8 X[4739] - 3 X[34641], 9 X[25055] - 7 X[27268]

X(49479) lies on these lines: {1, 87}, {2, 4090}, {7, 4660}, {8, 4772}, {9, 24331}, {10, 141}, {37, 537}, {38, 43223}, {42, 17140}, {43, 24620}, {57, 29670}, {63, 29651}, {75, 519}, {81, 32923}, {86, 24841}, {145, 4821}, {190, 16484}, {226, 29655}, {239, 27478}, {244, 46897}, {320, 33076}, {321, 42057}, {335, 17023}, {354, 1215}, {527, 24357}, {528, 7228}, {553, 18957}, {740, 3244}, {742, 4667}, {749, 984}, {752, 17365}, {756, 25501}, {758, 25124}, {940, 32920}, {982, 6685}, {1001, 32935}, {1086, 4085}, {1213, 4407}, {1278, 3241}, {1279, 4672}, {1621, 32940}, {1757, 16823}, {1909, 21443}, {2801, 45305}, {2810, 17049}, {3023, 34194}, {3120, 29835}, {3210, 42042}, {3315, 32944}, {3475, 3771}, {3616, 31302}, {3625, 3696}, {3634, 40328}, {3635, 4764}, {3662, 29659}, {3666, 42055}, {3672, 48830}, {3677, 29650}, {3679, 4699}, {3720, 3971}, {3741, 3873}, {3744, 4697}, {3750, 32939}, {3751, 16825}, {3752, 42053}, {3753, 24182}, {3757, 32913}, {3758, 36494}, {3773, 4966}, {3797, 29574}, {3821, 24231}, {3828, 4751}, {3831, 18398}, {3833, 25106}, {3842, 19862}, {3870, 3980}, {3883, 17770}, {3912, 31317}, {3944, 29843}, {3952, 30950}, {3957, 4418}, {3979, 32932}, {3989, 20068}, {3992, 29982}, {4011, 4666}, {4032, 4315}, {4038, 32926}, {4125, 18137}, {4135, 4883}, {4297, 29054}, {4342, 11997}, {4358, 17450}, {4359, 4685}, {4363, 32941}, {4430, 31330}, {4432, 17351}, {4434, 37520}, {4439, 17243}, {4514, 33097}, {4649, 20179}, {4661, 26037}, {4663, 4974}, {4669, 4688}, {4670, 9055}, {4692, 20891}, {4694, 21330}, {4698, 19883}, {4704, 38314}, {4718, 28554}, {4723, 30044}, {4737, 30090}, {4739, 34641}, {4753, 17348}, {4759, 15485}, {4867, 27492}, {4871, 32931}, {4970, 17018}, {4975, 22016}, {5249, 29673}, {5284, 32938}, {5294, 29672}, {5493, 30271}, {5882, 29010}, {6682, 21342}, {6686, 17063}, {7321, 24715}, {8025, 29816}, {8669, 37607}, {8720, 37573}, {10009, 24524}, {10436, 16496}, {13464, 20430}, {15569, 28582}, {16604, 21830}, {16826, 33888}, {16832, 27484}, {17141, 25302}, {17145, 31025}, {17154, 29822}, {17184, 29685}, {17234, 33165}, {17261, 24821}, {17272, 48851}, {17278, 47359}, {17291, 36478}, {17300, 32847}, {17303, 47358}, {17321, 48822}, {17368, 29660}, {17390, 28503}, {17483, 32947}, {17490, 42043}, {17597, 25496}, {17755, 29571}, {17778, 32866}, {17793, 28600}, {18134, 33169}, {18139, 33162}, {19717, 29819}, {21101, 24512}, {21211, 29350}, {21241, 31019}, {21296, 48849}, {21805, 24589}, {22220, 46190}, {25055, 27268}, {25385, 26015}, {25502, 27538}, {26034, 29669}, {26098, 29844}, {26102, 32937}, {26842, 32948}, {27064, 29820}, {27186, 33117}, {27254, 36542}, {27481, 29570}, {29631, 33148}, {29632, 33170}, {29635, 33144}, {29642, 33163}, {29667, 33069}, {29814, 32925}, {29817, 32930}, {29829, 33143}, {29830, 33161}, {29837, 33152}, {29839, 33167}, {29845, 33153}, {29851, 33166}, {31312, 39586}, {32773, 33103}, {32780, 33124}, {32927, 37633}, {32949, 33090}, {33121, 33130}, {42054, 44307}, {48631, 48821}

X(49479) = midpoint of X(1) and X(24349)
X(49479) = reflection of X(i) in X(j) for these {i,j}: {10, 24325}, {984, 1125}, {3625, 3696}, {3993, 1}, {4669, 4688}, {4709, 75}, {5493, 30271}, {20430, 13464}
X(49479) = X(30554)-complementary conjugate of X(514)
X(49479) = crossdifference of every pair of points on line {4491, 20979}
X(49479) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17146, 17449}, {7, 4660, 24692}, {7, 36479, 4660}, {42, 17140, 24165}, {354, 1215, 3840}, {3720, 17165, 3971}, {3873, 32771, 3741}, {4363, 42871, 32941}, {10436, 16496, 36480}, {15485, 17350, 4759}, {17018, 17155, 4970}, {17145, 31025, 31136}, {17154, 29822, 46901}, {17351, 42819, 4432}, {17450, 31161, 4358}, {31019, 33120, 21241}


X(49480) = X(1)X(21)∩X(2)X(4680)

Barycentrics    a*(2*a^3 + a^2*b + b^3 + a^2*c + c^3) : :
X(49480) = 3 X[3576] - X[30269], 5 X[3616] - X[6327], 7 X[3622] + X[20064], 7 X[3624] - 5 X[31237], 3 X[25055] - X[31134], 3 X[38314] + X[42058]

X(49480) lies on these lines: {1, 21}, {2, 4680}, {6, 4574}, {10, 1104}, {30, 17061}, {32, 16600}, {35, 5262}, {36, 5310}, {44, 4134}, {55, 4868}, {56, 2922}, {82, 759}, {106, 7194}, {171, 5883}, {209, 37080}, {214, 995}, {238, 10176}, {295, 11712}, {315, 25598}, {384, 30168}, {386, 16478}, {405, 30142}, {519, 3703}, {540, 33064}, {551, 752}, {609, 26242}, {674, 1386}, {712, 4797}, {734, 12263}, {740, 18805}, {744, 24325}, {750, 3833}, {754, 25345}, {859, 16687}, {902, 4424}, {952, 20575}, {958, 30145}, {976, 1724}, {982, 4257}, {997, 7290}, {999, 1486}, {1089, 11319}, {1125, 2887}, {1149, 40148}, {1191, 30144}, {1193, 27658}, {1203, 34772}, {1215, 48866}, {1319, 1401}, {1451, 12432}, {1453, 3811}, {1455, 4315}, {1478, 26228}, {2243, 46902}, {2251, 46907}, {2363, 37816}, {2390, 24928}, {2802, 37610}, {3011, 3822}, {3073, 31803}, {3271, 15049}, {3576, 30269}, {3583, 33133}, {3616, 6327}, {3622, 20064}, {3624, 31237}, {3735, 21793}, {3746, 17016}, {3749, 25439}, {3752, 37589}, {3754, 3924}, {3920, 5251}, {3957, 16474}, {4234, 32922}, {4245, 20990}, {4253, 16787}, {4256, 29821}, {4302, 19785}, {4362, 48863}, {4372, 25497}, {4386, 16611}, {4426, 28594}, {4511, 5315}, {4692, 20045}, {4694, 29818}, {4766, 30886}, {4850, 5010}, {5259, 27784}, {5267, 37592}, {5269, 16485}, {5300, 19846}, {5692, 17127}, {5710, 30147}, {5711, 30143}, {5716, 10198}, {5725, 10197}, {5902, 17126}, {5904, 36565}, {6284, 36250}, {6533, 19284}, {7807, 30170}, {7831, 16706}, {7892, 30169}, {7951, 29665}, {8069, 24025}, {11019, 46974}, {11113, 17602}, {13735, 32926}, {15228, 33102}, {15955, 37588}, {16060, 30126}, {16370, 17599}, {16466, 22836}, {16470, 25078}, {16684, 19259}, {16884, 31449}, {16905, 30149}, {16916, 30138}, {17064, 48827}, {17550, 30118}, {17684, 30134}, {17716, 30116}, {17717, 38062}, {17734, 37717}, {17768, 39544}, {19851, 28612}, {20267, 26099}, {22837, 37542}, {24046, 37603}, {24167, 37582}, {24586, 30105}, {25055, 31134}, {25440, 37552}, {26128, 48835}, {26725, 33112}, {28082, 37522}, {29645, 40984}, {29654, 48843}, {29656, 38456}, {30130, 33821}, {30167, 33816}, {33107, 37701}, {38314, 42058}

X(49480) = midpoint of X(1) and X(31)
X(49480) = reflection of X(i) in X(j) for these {i,j}: {10, 6679}, {2887, 1125}
X(49480) = complement of X(4680)
X(49480) = complement of the isogonal conjugate of X(22453)
X(49480) = X(22453)-complementary conjugate of X(10)
X(49480) = crosspoint of X(765) and X(9070)
X(49480) = crosssum of X(244) and X(9013)
X(49480) = barycentric product X(31)*X(30893)
X(49480) = barycentric quotient X(30893)/X(561)
X(49480) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 58, 3874}, {1, 595, 3878}, {1, 1468, 3881}, {1, 3915, 3884}, {1, 5248, 3743}, {1, 37817, 993}, {1, 40091, 3898}, {32, 16974, 16600}, {171, 30117, 5883}, {238, 30115, 10176}, {976, 1724, 3678}, {982, 4257, 4973}, {1104, 5266, 10}, {3924, 5264, 3754}


X(49481) = X(6)X(75)∩X(10)X(141)

Barycentrics    a^3*b + a^3*c + 2*a^2*b*c + b^3*c + b*c^3 : :
X(49481) = X[69] - 5 X[4699], X[192] - 5 X[3618], X[193] + 7 X[4772], X[984] - 3 X[38047], X[3629] + 4 X[4739], 5 X[3763] - 7 X[4751], X[3993] - 3 X[38049], X[4664] - 3 X[47352], X[4686] + 4 X[6329], 5 X[4687] - 7 X[47355], 2 X[4755] - 3 X[48310], 3 X[5085] - X[30273], 3 X[13331] - X[32453], 3 X[14561] - X[20430], X[17299] - 3 X[27474], 5 X[31238] - 4 X[34573]

X(49481) lies on these lines: {1, 25497}, {2, 3726}, {6, 75}, {7, 24699}, {9, 24357}, {10, 141}, {37, 3589}, {69, 4699}, {86, 32029}, {182, 29010}, {192, 3618}, {193, 4772}, {335, 16706}, {354, 30748}, {519, 24254}, {524, 4688}, {536, 597}, {537, 17382}, {672, 24326}, {674, 18805}, {726, 3946}, {732, 21443}, {740, 1386}, {966, 27484}, {984, 4657}, {1215, 21264}, {1441, 34253}, {1468, 4372}, {1475, 16720}, {1575, 24631}, {1914, 4797}, {1930, 20963}, {2176, 39731}, {2238, 26234}, {2242, 30108}, {2280, 4376}, {2876, 17049}, {3230, 46899}, {3242, 15668}, {3263, 24512}, {3416, 28634}, {3629, 4739}, {3696, 4399}, {3721, 17141}, {3729, 36404}, {3763, 4751}, {3778, 38995}, {3780, 20911}, {3797, 4360}, {3842, 25498}, {3862, 40093}, {3873, 30945}, {3875, 16972}, {3954, 16818}, {3993, 38049}, {4000, 24349}, {4359, 37676}, {4411, 9015}, {4437, 17245}, {4664, 47352}, {4686, 6329}, {4687, 29614}, {4721, 7264}, {4754, 20880}, {4755, 48310}, {4805, 7272}, {4851, 32847}, {4950, 36500}, {5085, 30273}, {5750, 25384}, {5845, 7228}, {9002, 21211}, {9016, 17792}, {9053, 17390}, {10436, 16973}, {13331, 32453}, {14210, 16971}, {14561, 20430}, {16496, 36531}, {16503, 24358}, {17027, 33931}, {17034, 33941}, {17265, 27475}, {17279, 38186}, {17299, 27474}, {17300, 27487}, {17302, 33888}, {17306, 36478}, {17307, 27495}, {17320, 31349}, {17322, 31323}, {17352, 36494}, {17396, 27481}, {17398, 31306}, {17499, 33940}, {17750, 33937}, {18157, 18166}, {18162, 19557}, {19120, 32115}, {19856, 40328}, {20271, 27299}, {20541, 29673}, {20891, 41233}, {20892, 28369}, {20923, 33938}, {23536, 24366}, {27476, 31034}, {27491, 30811}, {29181, 30271}, {30941, 31077}, {31178, 47359}, {31238, 34573}, {33891, 37678}

X(49481) = midpoint of X(i) and X(j) for these {i,j}: {6, 75}, {31178, 47359}
X(49481) = reflection of X(i) in X(j) for these {i,j}: {37, 3589}, {141, 3739}
X(49481) = crossdifference of every pair of points on line {788, 21003}
X(49481) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {239, 894, 20179}, {4361, 4363, 20181}, {17141, 26965, 3721}


X(49482) = X(1)X(87)∩X(6)X(519)

Barycentrics    2*a^3 + a*b^2 + b^2*c + a*c^2 + b*c^2 : :
X(49482) = 3 X[1] + X[3729], X[3729] - 3 X[3923], X[6] + 3 X[48805], X[996] - 3 X[48826], X[32941] - 3 X[48805], 3 X[48811] - X[48863], 3 X[551] - X[3663], X[141] - 3 X[48810], 3 X[392] + X[12723], 3 X[1386] - X[4852], 3 X[3576] - X[24728], 5 X[3616] - X[24248], 7 X[3622] + X[24280], X[3755] - 3 X[38049], X[3875] - 5 X[16491], X[3886] + 2 X[4991], X[3886] + 3 X[16475], 2 X[4991] - 3 X[16475], X[5695] + 3 X[38315], X[32921] - 3 X[38315], 5 X[17304] - 9 X[25055], X[24257] - 3 X[38029], 7 X[47355] - 3 X[48829]

X(49482) lies on these lines: {1, 87}, {2, 902}, {3, 142}, {6, 519}, {8, 16468}, {9, 4759}, {10, 82}, {31, 1150}, {37, 4432}, {55, 6685}, {57, 29668}, {63, 29652}, {81, 32943}, {86, 99}, {100, 32944}, {141, 752}, {149, 29631}, {171, 3840}, {226, 29656}, {239, 4709}, {312, 17716}, {321, 17469}, {354, 4697}, {391, 48802}, {392, 12723}, {497, 29635}, {518, 4672}, {528, 3589}, {537, 17351}, {612, 4011}, {614, 3980}, {673, 31191}, {730, 36232}, {740, 1386}, {750, 4871}, {896, 46909}, {956, 36635}, {960, 12722}, {964, 3915}, {966, 48809}, {968, 29644}, {984, 4676}, {993, 20992}, {995, 1740}, {1100, 4702}, {1201, 11115}, {1215, 3744}, {1220, 37588}, {1279, 24325}, {1376, 6686}, {1385, 29057}, {1428, 24253}, {1621, 4203}, {1836, 26128}, {1966, 21443}, {2209, 37610}, {2295, 23660}, {2308, 17135}, {2330, 5150}, {2702, 2726}, {2784, 12177}, {2886, 6679}, {3008, 20172}, {3011, 25385}, {3052, 32916}, {3120, 26230}, {3161, 48856}, {3241, 37677}, {3242, 32935}, {3244, 4649}, {3246, 3739}, {3416, 28512}, {3434, 25453}, {3576, 24728}, {3616, 24248}, {3622, 24280}, {3625, 16477}, {3636, 4353}, {3662, 24692}, {3679, 17349}, {3696, 4974}, {3706, 3791}, {3712, 17726}, {3720, 24259}, {3722, 46897}, {3731, 48854}, {3749, 29670}, {3755, 38049}, {3771, 26098}, {3773, 5846}, {3826, 31289}, {3828, 8692}, {3831, 5264}, {3833, 9519}, {3842, 15254}, {3844, 28566}, {3875, 16491}, {3878, 32118}, {3886, 4991}, {3912, 14621}, {3914, 29654}, {3920, 3971}, {3938, 26223}, {3944, 29634}, {3946, 28580}, {3961, 4090}, {3995, 29816}, {4135, 32926}, {4307, 4869}, {4315, 7175}, {4357, 36537}, {4360, 4693}, {4365, 17150}, {4366, 17023}, {4388, 32783}, {4407, 17332}, {4418, 7191}, {4427, 29823}, {4434, 30818}, {4439, 17340}, {4450, 32781}, {4514, 32780}, {4640, 6682}, {4645, 29637}, {4655, 28508}, {4670, 42819}, {4685, 32911}, {4732, 17348}, {4753, 16669}, {4797, 25368}, {4857, 25441}, {4865, 32777}, {4906, 42053}, {4970, 17017}, {5014, 26061}, {5057, 32775}, {5132, 20108}, {5249, 29672}, {5266, 8669}, {5269, 29649}, {5284, 25501}, {5294, 29673}, {5315, 27644}, {5603, 24669}, {5695, 28522}, {5749, 16779}, {5988, 22498}, {6327, 24943}, {6666, 25352}, {6693, 24387}, {7290, 16825}, {8258, 10916}, {8299, 40718}, {8666, 37507}, {8715, 37502}, {8720, 24850}, {10436, 24331}, {10459, 11319}, {10582, 24283}, {11362, 37510}, {15571, 16679}, {16394, 16483}, {16487, 25590}, {16503, 30331}, {16549, 20459}, {16704, 21747}, {16706, 24715}, {16801, 17000}, {16823, 24342}, {16826, 17738}, {17024, 17155}, {17050, 25497}, {17061, 48643}, {17126, 30942}, {17127, 31330}, {17140, 29818}, {17147, 29819}, {17184, 29686}, {17200, 30940}, {17229, 28538}, {17235, 28534}, {17260, 36531}, {17278, 24693}, {17280, 32847}, {17283, 31151}, {17304, 25055}, {17321, 33869}, {17345, 28558}, {17350, 36534}, {17354, 33165}, {17356, 25351}, {17368, 29659}, {17389, 20145}, {17594, 29650}, {17598, 32939}, {17599, 32934}, {17688, 30038}, {17722, 32851}, {18794, 40790}, {19284, 28352}, {19312, 25354}, {19689, 30180}, {19786, 33095}, {20064, 33080}, {20101, 33085}, {20132, 29574}, {20158, 29617}, {20292, 33123}, {21242, 35466}, {21345, 23533}, {21805, 41241}, {24210, 29645}, {24257, 38029}, {24260, 26102}, {24725, 33122}, {26825, 27097}, {27186, 29853}, {27254, 36541}, {27273, 30104}, {29586, 41842}, {29632, 33112}, {29636, 33134}, {29638, 31019}, {29639, 35263}, {29648, 32776}, {29666, 33125}, {29815, 32925}, {29821, 32932}, {29826, 35258}, {29831, 33143}, {29832, 33161}, {29834, 33155}, {29836, 33148}, {29838, 33152}, {29840, 33167}, {29846, 33107}, {29848, 31053}, {29850, 33110}, {29852, 33131}, {30030, 33816}, {30063, 33817}, {31137, 37684}, {32774, 33094}, {32779, 32844}, {32843, 33175}, {32927, 41242}, {32946, 33171}, {32949, 33173}, {33064, 41011}, {33070, 33156}, {33071, 33160}, {33072, 33157}, {33073, 33158}, {33096, 33126}, {33097, 33124}, {34445, 43531}, {47355, 48829}, {47357, 48822}

X(49482) = midpoint of X(i) and X(j) for these {i,j}: {1, 3923}, {6, 32941}, {960, 12722}, {3242, 32935}, {3878, 32118}, {5695, 32921}
X(49482) = reflection of X(i) in X(j) for these {i,j}: {10, 24295}, {3821, 1125}, {4085, 3589}, {4353, 3636}
X(49482) = complement of X(4660)
X(49482) = crossdifference of every pair of points on line {6586, 9002}
X(49482) = barycentric product X(190)*X(48248)
X(49482) = barycentric quotient X(48248)/X(514)
X(49482) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3685, 3993}, {2, 33104, 21241}, {6, 48805, 32941}, {31, 24552, 3741}, {55, 25496, 6685}, {81, 32943, 42057}, {86, 16484, 551}, {171, 32942, 3840}, {238, 5255, 4279}, {238, 5263, 10}, {1621, 32772, 43223}, {3920, 32930, 3971}, {3961, 27064, 4090}, {4418, 7191, 24165}, {4427, 29823, 46901}, {5255, 13740, 10}, {5695, 38315, 32921}, {17017, 32929, 4970}, {17289, 33076, 10}, {21747, 31136, 16704}, {24850, 37592, 8720}, {32850, 33159, 10}, {32911, 32945, 4685}


X(49483) = X(7)X(8)∩X(37)X(39)

Barycentrics    a^2*b - a*b^2 + a^2*c + 2*a*b*c + 2*b^2*c - a*c^2 + 2*b*c^2 : :
X(49483) = X[1] - 3 X[31178], X[8] - 3 X[75], 2 X[8] - 3 X[3696], X[8] + 3 X[24349], X[3696] + 2 X[24349], 2 X[10] - 3 X[4688], 3 X[37] - 4 X[1125], 2 X[1125] - 3 X[24325], X[145] + 3 X[4740], 3 X[192] - 7 X[3622], 7 X[3622] - 6 X[15569], 2 X[3244] + 3 X[4686], 3 X[984] - 5 X[1698], 5 X[1698] - 6 X[3739], 3 X[1278] + 5 X[3623], 5 X[3616] - 3 X[4664], 7 X[3624] - 6 X[4755], X[3633] + 6 X[4726], 4 X[3842] - 5 X[31238], 12 X[4698] - 13 X[34595], 4 X[4698] - 5 X[40328], 13 X[34595] - 15 X[40328], 5 X[4699] - X[31302], 15 X[4699] - 11 X[46933], 3 X[31302] - 11 X[46933], 15 X[4821] + X[20014], 5 X[18493] - 3 X[20430], 3 X[30271] - 2 X[31730]

X(49483) lies on these lines: {1, 536}, {2, 3967}, {7, 8}, {10, 537}, {11, 4054}, {37, 39}, {38, 30970}, {42, 42051}, {44, 16825}, {141, 24231}, {142, 3932}, {145, 4740}, {190, 15254}, {192, 3622}, {210, 4359}, {238, 17351}, {239, 4663}, {244, 30818}, {291, 21264}, {312, 3742}, {321, 354}, {335, 17292}, {346, 38053}, {350, 28600}, {551, 28554}, {740, 3244}, {894, 1386}, {899, 31161}, {942, 3714}, {982, 29827}, {984, 1698}, {1001, 3729}, {1089, 5439}, {1100, 32921}, {1155, 26227}, {1215, 3752}, {1278, 3623}, {1279, 3923}, {1456, 28968}, {1738, 7263}, {1757, 17348}, {2321, 4966}, {2345, 4310}, {3057, 4459}, {3175, 3720}, {3240, 4706}, {3242, 17118}, {3246, 4676}, {3555, 4647}, {3616, 4664}, {3624, 4755}, {3633, 4726}, {3662, 3844}, {3663, 4026}, {3666, 17155}, {3683, 32933}, {3685, 42819}, {3686, 5850}, {3697, 28611}, {3698, 4696}, {3702, 17609}, {3703, 5249}, {3704, 21620}, {3705, 3838}, {3706, 3873}, {3717, 3826}, {3740, 19804}, {3741, 21342}, {3744, 4418}, {3745, 3891}, {3748, 32929}, {3751, 4361}, {3753, 4692}, {3757, 4640}, {3773, 17231}, {3790, 17234}, {3797, 29569}, {3812, 4385}, {3823, 33165}, {3824, 30172}, {3833, 4125}, {3834, 29674}, {3840, 42053}, {3842, 31238}, {3848, 18743}, {3874, 5295}, {3881, 42031}, {3883, 17768}, {3886, 42871}, {3892, 4717}, {3912, 25557}, {3952, 24589}, {3966, 5905}, {3974, 9776}, {3980, 32920}, {3993, 4718}, {3994, 30950}, {3999, 30942}, {4000, 38047}, {4078, 17245}, {4113, 4661}, {4307, 7222}, {4384, 5220}, {4387, 4666}, {4411, 23100}, {4416, 5852}, {4419, 39581}, {4429, 48627}, {4431, 4684}, {4440, 24723}, {4442, 29835}, {4454, 5698}, {4461, 11038}, {4641, 32914}, {4649, 4852}, {4682, 32926}, {4689, 32845}, {4690, 24699}, {4698, 34595}, {4699, 31302}, {4723, 4731}, {4756, 35595}, {4821, 20014}, {4864, 32941}, {4883, 32915}, {4901, 38052}, {4906, 32942}, {4914, 6327}, {4942, 8167}, {4974, 16669}, {4980, 17135}, {4981, 20068}, {5263, 17116}, {5302, 16817}, {5312, 39711}, {5625, 46845}, {5846, 7228}, {5847, 17365}, {6358, 17625}, {7174, 25590}, {7292, 41242}, {10453, 42029}, {15481, 17277}, {16610, 32931}, {16815, 31349}, {17147, 37593}, {17154, 31025}, {17229, 33087}, {17235, 32784}, {17345, 33082}, {17356, 33159}, {17359, 29637}, {17362, 34379}, {17367, 31317}, {17370, 26083}, {17371, 26150}, {17376, 32846}, {17382, 29633}, {17390, 28472}, {17483, 33075}, {17495, 46897}, {17595, 29828}, {17718, 17740}, {17755, 27478}, {17763, 37520}, {17781, 41002}, {17889, 33169}, {18493, 20430}, {19791, 29833}, {20292, 33090}, {20716, 26234}, {20942, 26103}, {21101, 44798}, {21923, 23636}, {21949, 29673}, {24003, 31197}, {24171, 25914}, {24789, 33163}, {25102, 46032}, {26102, 35652}, {26263, 37762}, {26724, 33166}, {26842, 33078}, {27186, 32862}, {27494, 31306}, {27499, 42027}, {28612, 34790}, {29010, 34773}, {29054, 30271}, {29616, 30340}, {29651, 32934}, {29655, 48643}, {29659, 33149}, {29667, 33146}, {29685, 33145}, {29814, 42044}, {31019, 33089}, {31241, 42038}, {32778, 33103}, {32779, 33148}, {32780, 33147}, {32857, 33076}, {32866, 33097}, {32925, 44307}, {32928, 37595}, {33129, 33170}, {33130, 33167}

X(49483) = midpoint of X(75) and X(24349)
X(49483) = reflection of X(i) in X(j) for these {i,j}: {37, 24325}, {192, 15569}, {984, 3739}, {3696, 75}, {4718, 3993}
X(49483) = X(9067)-complementary conjugate of X(21260)
X(49483) = crossdifference of every pair of points on line {3063, 4057}
X(49483) = barycentric product X(190)*X(47812)
X(49483) = barycentric quotient X(47812)/X(514)
X(49483) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4659, 5695}, {1, 5695, 4702}, {8, 42697, 5880}, {190, 16823, 15254}, {321, 17140, 354}, {321, 29824, 4519}, {354, 4519, 29824}, {894, 32922, 1386}, {1215, 24165, 3752}, {2321, 5542, 4966}, {3717, 24199, 3826}, {3741, 42055, 21342}, {3757, 32939, 4640}, {3873, 28605, 3706}, {4359, 17165, 210}, {4418, 32923, 3744}, {4942, 8167, 30568}, {16825, 32935, 44}, {17154, 31025, 46909}, {17155, 32771, 3666}, {19804, 32937, 3740}, {32914, 32940, 4641}


X(49484) = X(1)X(536)∩X(8)X(44)

Barycentrics    2*a^3 - a^2*b + a*b^2 - a^2*c + 2*b^2*c + a*c^2 + 2*b*c^2 : :
X(49484) = X[1] - 3 X[48805], X[5695] + 3 X[48805], X[8] - 3 X[17281], 2 X[10] - 3 X[17359], 3 X[3923] - X[32935], 3 X[17351] - 2 X[32935], X[17351] + 2 X[32941], X[32935] + 3 X[32941], 4 X[1125] - 3 X[17382], 2 X[1125] - 3 X[48810], 5 X[1698] - 3 X[48829], 5 X[3616] - 3 X[17301], 4 X[3634] - 3 X[48821], X[3875] - 3 X[38315], X[4780] - 3 X[38049]

X(49484) lies on these lines: {1, 536}, {2, 4689}, {6, 3886}, {8, 44}, {10, 528}, {31, 3706}, {37, 3685}, {55, 29828}, {69, 28570}, {75, 1279}, {100, 30818}, {105, 30748}, {141, 516}, {145, 3758}, {149, 32779}, {210, 32930}, {238, 3696}, {321, 3744}, {354, 4418}, {390, 2345}, {392, 2805}, {517, 48863}, {518, 3923}, {519, 4527}, {594, 3883}, {595, 5295}, {612, 4387}, {740, 1386}, {896, 31136}, {940, 4891}, {950, 5835}, {960, 44670}, {964, 37548}, {1001, 3739}, {1010, 16745}, {1125, 17067}, {1155, 30942}, {1201, 2234}, {1385, 2783}, {1621, 31993}, {1697, 5793}, {1698, 48829}, {1738, 17356}, {1836, 33171}, {2321, 5846}, {2550, 3823}, {2831, 5887}, {3052, 11679}, {3057, 43135}, {3175, 3920}, {3242, 3729}, {3244, 28503}, {3246, 16825}, {3416, 17229}, {3434, 32777}, {3454, 22793}, {3589, 3755}, {3616, 17301}, {3617, 17335}, {3622, 41847}, {3625, 4753}, {3626, 4759}, {3634, 48821}, {3663, 28530}, {3666, 24552}, {3683, 31330}, {3689, 32931}, {3702, 37539}, {3712, 29639}, {3714, 5255}, {3717, 17340}, {3740, 4011}, {3741, 4640}, {3742, 3980}, {3745, 32915}, {3748, 32771}, {3752, 32932}, {3771, 3838}, {3773, 17766}, {3821, 17764}, {3834, 5880}, {3844, 4660}, {3875, 38315}, {3935, 41242}, {3961, 3967}, {3996, 4849}, {4003, 32845}, {4026, 17385}, {4050, 36406}, {4054, 17724}, {4085, 24295}, {4195, 4673}, {4307, 4851}, {4312, 7232}, {4344, 17314}, {4349, 17390}, {4353, 28557}, {4356, 17045}, {4361, 7290}, {4364, 19868}, {4365, 17469}, {4427, 46909}, {4429, 17357}, {4436, 37575}, {4442, 26230}, {4512, 5737}, {4519, 17763}, {4641, 17135}, {4643, 5698}, {4645, 17231}, {4646, 13740}, {4655, 28534}, {4667, 17224}, {4684, 17365}, {4686, 32922}, {4688, 16823}, {4697, 42057}, {4709, 4974}, {4715, 24695}, {4755, 39586}, {4780, 38049}, {4847, 44416}, {4863, 33163}, {4864, 24349}, {4906, 24165}, {4912, 47358}, {4966, 17376}, {5057, 33175}, {5542, 7228}, {5701, 25066}, {5743, 40998}, {5784, 24410}, {5847, 17372}, {5853, 17355}, {7174, 17262}, {7191, 42051}, {7222, 11038}, {7227, 30331}, {7229, 8236}, {7238, 30424}, {7761, 28897}, {8299, 21264}, {9746, 15271}, {10129, 30823}, {11104, 16702}, {11115, 30939}, {12263, 36219}, {13735, 16821}, {14942, 44798}, {15569, 28639}, {15571, 37609}, {16484, 24342}, {17235, 24248}, {17237, 24723}, {17265, 38052}, {17276, 24280}, {17280, 32850}, {17345, 17768}, {17601, 29827}, {17605, 29846}, {17721, 17740}, {19998, 41241}, {20132, 31342}, {20292, 33173}, {21282, 48647}, {21283, 33114}, {21342, 32939}, {22034, 32926}, {24325, 42819}, {24697, 24711}, {24715, 29637}, {24943, 33094}, {25531, 31197}, {25590, 38316}, {28146, 48835}, {28194, 48859}, {28484, 32921}, {28599, 48648}, {29611, 30332}, {29652, 32934}, {29656, 48643}, {29660, 33149}, {29667, 34611}, {29686, 33145}, {29815, 42044}, {29824, 37520}, {29857, 31140}, {32772, 37593}, {32783, 33095}, {33104, 33156}, {33106, 33160}, {33109, 33158}, {33110, 33157}, {35258, 37660}, {35263, 35466}, {39581, 47357}

X(49484) = midpoint of X(i) and X(j) for these {i,j}: {1, 5695}, {6, 3886}, {3242, 3729}, {3923, 32941}, {17276, 24280}
X(49484) = reflection of X(i) in X(j) for these {i,j}: {3416, 17229}, {3755, 3589}, {4085, 24295}, {4660, 3844}, {4663, 4672}, {4852, 1386}, {17351, 3923}, {17382, 48810}, {24248, 17235}
X(49484) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 4676, 44}, {10, 4432, 15254}, {238, 3696, 17348}, {612, 4387, 35652}, {2550, 17279, 3823}, {3685, 5263, 37}, {3996, 27064, 4849}, {4418, 32943, 354}, {5695, 48805, 1}, {24552, 32929, 3666}, {32930, 32945, 210}, {32932, 32942, 3752}


X(49485) = X(1)X(4686)∩X(8)X(15481)

Barycentrics    2*a^3 - 3*a^2*b + a*b^2 - 3*a^2*c + 4*b^2*c + a*c^2 + 4*b*c^2 : :
X(49485) = X[3729] + 3 X[3886], X[3729] - 3 X[5695], 3 X[1386] - 2 X[4852], X[3875] - 3 X[48805], 2 X[3946] - 3 X[48810], 2 X[4085] - 3 X[17359], 5 X[17286] - 3 X[48829]

X(49485) lies on these lines: {1, 4686}, {8, 15481}, {37, 4693}, {69, 28534}, {75, 4702}, {100, 4519}, {141, 28580}, {518, 3729}, {519, 3629}, {528, 2321}, {536, 32941}, {740, 1386}, {752, 17372}, {1150, 3706}, {2796, 17345}, {3175, 32945}, {3242, 28555}, {3244, 28472}, {3246, 4361}, {3589, 4780}, {3644, 36534}, {3679, 16814}, {3685, 3696}, {3689, 4671}, {3740, 4387}, {3744, 4365}, {3748, 28605}, {3838, 30828}, {3875, 48805}, {3923, 4663}, {3946, 48810}, {3961, 22034}, {3967, 3996}, {3980, 4891}, {4085, 17359}, {4133, 5846}, {4307, 4916}, {4432, 4709}, {4527, 17766}, {4659, 42871}, {4660, 17229}, {4673, 11260}, {4681, 36480}, {4682, 32915}, {4688, 16484}, {4717, 24929}, {4720, 31165}, {4739, 24331}, {4743, 24295}, {4869, 5880}, {4906, 32943}, {4914, 34611}, {5263, 17319}, {8692, 16833}, {15569, 15668}, {17231, 24715}, {17286, 48829}, {17299, 28538}, {21081, 22793}, {21870, 41242}, {21949, 33158}, {32087, 47357}

X(49485) = midpoint of X(3886) and X(5695)
X(49485) = reflection of X(i) in X(j) for these {i,j}: {4660, 17229}, {4663, 3923}, {4743, 24295}, {4780, 3589}
X(49485) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 4702, 42819}, {3685, 3696, 15254}, {3706, 32929, 4640}, {4432, 4709, 17348}, {32943, 42051, 4906}


X(49486) = X(1)X(3696)∩X(2)X(4046)

Barycentrics    a^3 + 3*a^2*b + 3*a^2*c - 2*b^2*c - 2*b*c^2 : :
X(49486) = 3 X[6] - 2 X[3923], 5 X[6] - 4 X[4672], 5 X[3923] - 6 X[4672], 4 X[3923] - 3 X[5695], 8 X[4672] - 5 X[5695], 3 X[599] - 4 X[3821], 2 X[3416] - 3 X[48829], 4 X[3755] - 3 X[48829], 4 X[4353] - 3 X[47358], 2 X[1386] - 3 X[16834], 4 X[1386] - 3 X[48805], X[3886] - 3 X[16834], 2 X[3886] - 3 X[48805], 5 X[1698] - 4 X[17229], 3 X[1992] - X[24280], 2 X[2321] - 3 X[38047], 4 X[3844] - 3 X[17294], 2 X[4133] - 3 X[17281], 8 X[24295] - 9 X[47352], 2 X[32941] - 3 X[38315]

X(49486) lies on these lines: {1, 3696}, {2, 4046}, {6, 740}, {8, 4026}, {10, 4060}, {42, 21730}, {45, 3993}, {55, 3187}, {145, 2550}, {192, 5220}, {193, 17768}, {239, 1001}, {382, 29093}, {387, 3704}, {405, 4068}, {497, 20043}, {518, 3875}, {519, 599}, {524, 24248}, {528, 32029}, {536, 3751}, {940, 32860}, {984, 17318}, {986, 24437}, {1150, 17162}, {1281, 14614}, {1350, 24257}, {1351, 2783}, {1376, 1999}, {1386, 3886}, {1698, 17229}, {1738, 4851}, {1757, 17262}, {1834, 34528}, {1962, 19732}, {1992, 24280}, {2098, 20040}, {2321, 38047}, {2334, 4968}, {2784, 36990}, {2795, 22253}, {2796, 15534}, {3052, 3791}, {3295, 16684}, {3306, 4706}, {3629, 24695}, {3666, 17156}, {3679, 28329}, {3685, 3759}, {3686, 4356}, {3706, 5256}, {3711, 19998}, {3712, 24597}, {3715, 3995}, {3723, 39586}, {3729, 4663}, {3752, 39594}, {3769, 4421}, {3772, 4028}, {3775, 17325}, {3826, 17316}, {3836, 17311}, {3842, 16672}, {3844, 17294}, {3879, 5880}, {3891, 13576}, {3932, 17314}, {4000, 4966}, {4042, 28606}, {4062, 30811}, {4133, 17281}, {4255, 17733}, {4259, 35104}, {4363, 4649}, {4371, 39581}, {4383, 32915}, {4384, 15569}, {4387, 32911}, {4393, 5263}, {4402, 38053}, {4429, 6542}, {4436, 37507}, {4442, 31034}, {4445, 32784}, {4552, 41712}, {4645, 17377}, {4655, 40341}, {4660, 4743}, {4676, 17121}, {4693, 16468}, {4702, 7290}, {4709, 16884}, {4734, 14829}, {4780, 5847}, {4819, 17602}, {4854, 5739}, {4860, 17495}, {4868, 5774}, {4891, 5272}, {4923, 19868}, {4970, 32853}, {4972, 20017}, {5271, 37593}, {5278, 27804}, {5687, 20990}, {5699, 11485}, {5700, 11486}, {5737, 17592}, {5800, 44669}, {5988, 9766}, {5992, 7837}, {6007, 37516}, {6144, 17770}, {7232, 33149}, {9534, 41813}, {9791, 17346}, {10180, 19744}, {10477, 44671}, {11235, 33071}, {11477, 29057}, {12635, 20018}, {14459, 25760}, {16830, 17393}, {17054, 35633}, {17070, 30828}, {17119, 24325}, {17133, 47359}, {17135, 17599}, {17148, 37567}, {17160, 24349}, {17163, 19684}, {17251, 42334}, {17269, 33159}, {17276, 34379}, {17290, 33087}, {17293, 29633}, {17309, 29674}, {17363, 24723}, {17595, 32919}, {17597, 32924}, {19701, 21020}, {19765, 27368}, {20012, 32926}, {20182, 31330}, {24295, 47352}, {24394, 32118}, {24552, 45222}, {28522, 32935}, {29040, 48910}, {29097, 39899}, {29301, 44456}, {31140, 33070}, {32941, 38315}, {37660, 46904}

X(49486) = reflection of X(i) in X(j) for these {i,j}: {1, 4852}, {1350, 24257}, {3242, 32921}, {3416, 3755}, {3729, 4663}, {3886, 1386}, {4660, 4743}, {5695, 6}, {17299, 10}, {24695, 3629}, {40341, 4655}, {48805, 16834}
X(49486) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4716, 4361}, {145, 32922, 42871}, {1386, 3886, 48805}, {3187, 3896, 55}, {3416, 3755, 48829}, {3886, 16834, 1386}, {3891, 20011, 41711}, {4062, 33128, 30811}


X(49487) = X(1)X(2)∩X(3)X(4642)

Barycentrics    a*(a^3 + b^3 + 2*a*b*c - b^2*c - b*c^2 + c^3) : :
X(49487) = 5 X[3616] - 4 X[29656]

X(49487) lies on these lines: {1, 2}, {3, 4642}, {6, 1411}, {21, 37598}, {30, 33094}, {31, 517}, {37, 4390}, {38, 956}, {41, 41015}, {44, 31165}, {56, 2933}, {58, 5903}, {65, 603}, {68, 1245}, {172, 3959}, {212, 1104}, {219, 40977}, {238, 3877}, {244, 999}, {355, 21935}, {392, 748}, {404, 24440}, {484, 4257}, {495, 33127}, {515, 3914}, {518, 36267}, {529, 3782}, {595, 5697}, {601, 37562}, {609, 5011}, {672, 9620}, {750, 3753}, {756, 9708}, {758, 4137}, {902, 5119}, {952, 30448}, {958, 2292}, {977, 1222}, {983, 1320}, {986, 2975}, {993, 4414}, {996, 4692}, {1042, 21147}, {1086, 5434}, {1191, 2098}, {1203, 11009}, {1279, 5919}, {1317, 17366}, {1319, 3752}, {1334, 16968}, {1376, 4695}, {1393, 26437}, {1453, 7982}, {1457, 38008}, {1459, 30573}, {1478, 3120}, {1482, 16466}, {1572, 21764}, {1724, 3878}, {1834, 10950}, {1837, 33177}, {1951, 10315}, {2177, 24929}, {2181, 7497}, {2242, 3125}, {2269, 5336}, {2274, 7235}, {2308, 25415}, {2646, 4646}, {2650, 3157}, {2802, 37610}, {2886, 5724}, {3304, 17054}, {3340, 4332}, {3419, 33136}, {3476, 4000}, {3670, 8666}, {3725, 12081}, {3727, 4426}, {3735, 5282}, {3744, 3880}, {3749, 3895}, {3751, 21829}, {3754, 37522}, {3772, 5252}, {3869, 5247}, {3885, 37588}, {3902, 32941}, {3931, 10448}, {3940, 21805}, {3944, 5080}, {3987, 25440}, {4216, 5143}, {4252, 37567}, {4255, 34471}, {4256, 37525}, {4315, 24177}, {4318, 23579}, {4320, 34039}, {4322, 34489}, {4376, 35101}, {4383, 5289}, {4415, 34606}, {4432, 11346}, {4441, 24291}, {4446, 7170}, {4475, 5902}, {4641, 44663}, {4653, 25060}, {4737, 32927}, {4850, 37617}, {5115, 21863}, {5176, 33133}, {5253, 24174}, {5255, 14923}, {5266, 10914}, {5425, 16474}, {5429, 17126}, {5563, 24046}, {5725, 33105}, {5727, 45272}, {5836, 37539}, {6187, 11334}, {6327, 38456}, {7194, 20098}, {7290, 7962}, {7373, 46190}, {7986, 18519}, {8069, 24028}, {8074, 40128}, {8578, 21105}, {9028, 42289}, {9310, 16583}, {10106, 23536}, {10441, 34281}, {10457, 18180}, {10912, 37542}, {11114, 33095}, {11194, 17595}, {11224, 16469}, {11680, 37717}, {12513, 37549}, {15898, 40172}, {15950, 37662}, {16483, 23112}, {16485, 31393}, {17061, 38455}, {17549, 17601}, {17579, 24715}, {18676, 37168}, {20067, 33102}, {21740, 37699}, {23537, 45287}, {23659, 31394}, {24160, 37719}, {24725, 39542}, {24928, 32577}, {33146, 34605}, {33771, 37571}, {37646, 40663}, {37728, 48847}, {37732, 40257}

X(49487) = reflection of X(i) in X(j) for these {i,j}: {8, 29673}, {3938, 1}
X(49487) = crosspoint of X(1) and X(998)
X(49487) = crosssum of X(1) and X(997)
X(49487) = crossdifference of every pair of points on line {649, 3738}
X(49487) = barycentric product X(1)*X(17720)
X(49487) = barycentric quotient X(17720)/X(75)
X(49487) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 8, 976}, {1, 43, 4511}, {1, 614, 1149}, {1, 1722, 19861}, {1, 3216, 30144}, {1, 3293, 22836}, {1, 3679, 30115}, {1, 3924, 28082}, {1, 9623, 612}, {1, 29820, 38314}, {1, 30116, 5311}, {8, 39766, 4362}, {42, 1201, 22350}, {65, 1455, 9316}, {958, 37614, 2292}, {993, 4424, 4414}, {1104, 3057, 3915}, {1722, 19861, 27627}, {3735, 5291, 5282}, {4861, 5262, 1}, {5119, 37817, 902}, {5176, 33133, 37716}, {7191, 38460, 1}


X(49488) = X(1)X(2)∩X(4)X(2784)

Barycentrics    a^3 + 2*a^2*b + 2*a^2*c - b^2*c - b*c^2 : :
X(49488) = X[1] - 3 X[16834], 5 X[1698] - 3 X[17294], 4 X[3634] - 3 X[29594], 3 X[6] - 2 X[4672], 3 X[6] - X[5695], 3 X[3923] - 4 X[4672], 3 X[3923] - 2 X[5695], X[4780] + 2 X[4856], 3 X[1992] - X[24695], 5 X[3618] - 4 X[24295], 2 X[3773] - 3 X[38047], X[17299] - 3 X[38047], X[3886] - 4 X[4991], X[3886] - 3 X[16475], 4 X[4991] - 3 X[16475], 2 X[4527] - 3 X[17281]

X(49488) lies on these lines: {1, 2}, {4, 2784}, {6, 740}, {9, 3993}, {31, 3896}, {32, 32115}, {40, 7709}, {55, 3791}, {58, 11104}, {61, 5699}, {62, 5700}, {63, 4970}, {69, 3821}, {75, 4649}, {81, 3980}, {192, 1757}, {193, 17770}, {194, 1046}, {213, 2901}, {238, 3759}, {274, 4658}, {295, 2809}, {319, 32784}, {320, 33149}, {333, 17592}, {511, 24257}, {516, 4780}, {517, 49129}, {518, 4523}, {524, 4655}, {536, 4663}, {576, 2783}, {595, 3802}, {726, 3751}, {752, 4743}, {758, 24268}, {846, 37652}, {870, 1126}, {946, 36675}, {966, 25354}, {984, 4360}, {986, 17206}, {1001, 4974}, {1009, 4433}, {1045, 5145}, {1054, 37684}, {1100, 3696}, {1107, 3931}, {1150, 46904}, {1281, 7766}, {1330, 20536}, {1351, 29057}, {1386, 28581}, {1449, 4709}, {1724, 3747}, {1738, 3879}, {1834, 10026}, {1962, 5278}, {1992, 2796}, {2176, 4574}, {2223, 8715}, {2308, 32929}, {2321, 16972}, {2344, 4251}, {2795, 7798}, {2895, 32776}, {3120, 31034}, {3210, 32913}, {3339, 7176}, {3416, 4085}, {3555, 20358}, {3618, 24295}, {3629, 17768}, {3663, 34379}, {3666, 32853}, {3681, 32928}, {3685, 16468}, {3695, 16974}, {3706, 25496}, {3717, 4464}, {3729, 28522}, {3730, 39252}, {3743, 5283}, {3746, 23407}, {3755, 4660}, {3773, 17299}, {3775, 4657}, {3780, 17475}, {3795, 37686}, {3823, 4889}, {3826, 17390}, {3836, 4851}, {3842, 16777}, {3844, 17372}, {3873, 32924}, {3886, 4991}, {3913, 37590}, {3914, 32946}, {3932, 17388}, {3936, 33128}, {3950, 16970}, {3969, 26061}, {3996, 17716}, {4011, 32911}, {4026, 17362}, {4038, 19804}, {4042, 20182}, {4065, 16552}, {4133, 17355}, {4253, 24578}, {4260, 35104}, {4356, 16517}, {4361, 24325}, {4365, 26223}, {4368, 37657}, {4385, 17144}, {4395, 25557}, {4414, 16704}, {4417, 33135}, {4418, 37685}, {4425, 5739}, {4429, 17377}, {4442, 24725}, {4527, 17281}, {4641, 32934}, {4642, 24464}, {4646, 17448}, {4650, 41629}, {4676, 4693}, {4681, 15481}, {4703, 4854}, {4706, 37520}, {4722, 32933}, {4732, 16884}, {4733, 17398}, {4734, 17596}, {4753, 5220}, {4771, 5275}, {4850, 32919}, {4868, 16975}, {4966, 17366}, {4972, 32852}, {5138, 24253}, {5224, 42334}, {5264, 20985}, {5587, 36677}, {5625, 15668}, {5687, 21010}, {5814, 16519}, {5988, 7774}, {6541, 17314}, {6651, 20158}, {7839, 32117}, {8666, 37575}, {8682, 24293}, {9345, 24589}, {10180, 19732}, {12514, 21384}, {15534, 28558}, {15569, 17348}, {16706, 33087}, {17147, 32912}, {17163, 19717}, {17233, 33159}, {17241, 31252}, {17276, 17771}, {17346, 24697}, {17351, 28484}, {17363, 33082}, {17364, 32857}, {17379, 24342}, {17723, 21242}, {17738, 27480}, {17778, 17889}, {18134, 33132}, {18206, 35915}, {19684, 21020}, {19701, 27798}, {19740, 27812}, {19742, 27804}, {19785, 33064}, {19786, 33084}, {19796, 33103}, {20086, 33102}, {20257, 21620}, {20546, 27556}, {21105, 48321}, {21877, 23543}, {23888, 24097}, {24260, 37676}, {24362, 32922}, {24440, 34063}, {25426, 43531}, {25440, 37609}, {28337, 48821}, {28530, 32455}, {28606, 32864}, {29040, 31670}, {29093, 48901}, {29301, 37517}, {32773, 32861}, {32774, 33081}, {32843, 33134}, {32848, 33114}, {32855, 33121}, {32859, 33145}, {32863, 33125}, {32865, 33073}, {32938, 42044}, {32949, 33131}, {33065, 33155}, {33066, 33154}, {33069, 33150}, {33070, 33136}, {33071, 33141}, {33092, 33118}, {38456, 48837}, {40925, 43174}, {41656, 48932}

X(49488) = midpoint of X(i) and X(j) for these {i,j}: {193, 24248}, {3751, 3875}
X(49488) = reflection of X(i) in X(j) for these {i,j}: {69, 3821}, {3416, 4085}, {3923, 6}, {4133, 17355}, {4660, 3755}, {5695, 4672}, {17299, 3773}, {17372, 3844}, {24728, 24257}, {32921, 4852}, {32935, 4663}, {32941, 1386}
X(49488) = psi-transform of X(48443)
X(49488) = X(513)-isoconjugate of X(29329)
X(49488) = X(39026)-Dao conjugate of X(29329)
X(49488) = barycentric product X(190)*X(29328)
X(49488) = barycentric quotient X(i)/X(j) for these {i,j}: {101, 29329}, {29328, 514}
X(49488) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 8, 36480}, {1, 239, 16825}, {1, 1698, 16826}, {1, 3293, 869}, {1, 3679, 16830}, {1, 4384, 1125}, {1, 16825, 24331}, {6, 5695, 4672}, {8, 4393, 1}, {42, 3187, 4362}, {42, 4362, 29670}, {43, 1999, 29649}, {81, 32860, 3980}, {1834, 10026, 37159}, {2999, 39594, 3840}, {3685, 17121, 16468}, {3741, 5256, 29650}, {4028, 40940, 3771}, {4429, 17377, 32846}, {4649, 4716, 75}, {4672, 5695, 3923}, {4693, 16477, 4676}, {4734, 37683, 17596}, {5256, 17156, 3741}, {10453, 29821, 29668}, {14459, 29631, 33077}, {16830, 29584, 1}, {17011, 31330, 29644}, {17017, 17135, 29652}, {17018, 32914, 29651}, {17135, 45222, 17017}, {17150, 20011, 3938}, {17299, 38047, 3773}, {32911, 32915, 4011}


X(49489) = X(1)X(872)∩X(2)X(5625)

Barycentrics    2*a^3 + 3*a^2*b + 3*a^2*c - b^2*c - b*c^2 : :
X(49489) = 3 X[6] - X[3923], 5 X[6] - X[5695], 2 X[3923] - 3 X[4672], 5 X[3923] - 3 X[5695], 5 X[4672] - 2 X[5695], 3 X[597] - 2 X[24295], X[3751] + 3 X[16834], 3 X[16834] - X[32921], 3 X[1992] + X[24248], X[4085] + 2 X[4856], 9 X[5032] - X[24280], 3 X[16475] - X[32941]

X(49489) lies on these lines: {1, 872}, {2, 5625}, {6, 740}, {10, 1100}, {38, 45222}, {42, 3791}, {43, 40533}, {44, 3993}, {193, 4655}, {238, 17121}, {239, 4649}, {319, 29633}, {516, 4743}, {519, 597}, {524, 3821}, {537, 3751}, {576, 29057}, {726, 4663}, {752, 3755}, {894, 4716}, {984, 4393}, {1125, 17348}, {1215, 3187}, {1279, 3244}, {1351, 24257}, {1353, 2792}, {1449, 4732}, {1698, 17394}, {1757, 4360}, {1962, 19742}, {1964, 3293}, {1992, 24248}, {2308, 3896}, {2783, 5097}, {2784, 5480}, {2796, 8584}, {3216, 29559}, {3240, 4434}, {3629, 17770}, {3634, 28639}, {3635, 42819}, {3663, 17771}, {3685, 16477}, {3689, 4946}, {3696, 16666}, {3745, 4685}, {3769, 42043}, {3775, 17023}, {3836, 3879}, {3844, 4725}, {3875, 28516}, {3941, 8715}, {3946, 34379}, {4026, 4969}, {4028, 6679}, {4042, 29644}, {4085, 4856}, {4432, 16468}, {4527, 17355}, {4535, 17299}, {4641, 4970}, {4650, 4734}, {4660, 28498}, {4697, 32860}, {4709, 16668}, {4722, 17147}, {4780, 17764}, {4892, 31034}, {4938, 31017}, {5032, 24280}, {5256, 6682}, {5278, 10180}, {5988, 41624}, {6048, 24661}, {6541, 17388}, {6542, 33159}, {11477, 24728}, {12212, 32115}, {12618, 28870}, {14459, 32779}, {16475, 32941}, {16704, 46904}, {16709, 28611}, {16816, 40328}, {17011, 32864}, {17012, 32919}, {17027, 17793}, {17150, 43534}, {17156, 25496}, {17163, 19743}, {17312, 31252}, {17330, 25354}, {17351, 28522}, {17363, 32784}, {17364, 33149}, {17367, 33087}, {17377, 29674}, {17469, 20011}, {17592, 37652}, {17596, 41629}, {17716, 20012}, {17768, 32455}, {17778, 33132}, {19684, 27798}, {19717, 21020}, {19741, 27812}, {20017, 26061}, {20055, 26083}, {20086, 33067}, {21850, 29040}, {24342, 46922}, {24695, 28546}, {28595, 32852}, {31313, 46932}, {32924, 42055}, {32928, 42054}, {38456, 48847}

X(49489) = midpoint of X(i) and X(j) for these {i,j}: {193, 4655}, {1351, 24257}, {3751, 32921}, {3875, 32935}, {4663, 4852}, {11477, 24728}
X(49489) = reflection of X(i) in X(j) for these {i,j}: {1386, 4991}, {4527, 17355}, {4672, 6}, {17299, 4535}
X(49489) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3759, 4974}, {239, 4649, 24325}, {3696, 16666, 33682}, {3751, 16834, 32921}, {5256, 32853, 6682}, {31034, 33128, 4892}, {32860, 37685, 4697}


X(49490) = X(1)X(6)∩X(2)X(17145)

Barycentrics    a*(2*a*b - b^2 + 2*a*c + b*c - c^2) : :
X(49490) = 3 X[1] - 2 X[37], 5 X[1] - 4 X[15569], 4 X[37] - 3 X[984], 5 X[37] - 6 X[15569], 5 X[984] - 8 X[15569], 3 X[8] - 5 X[4699], 3 X[8] - 4 X[4732], 5 X[4699] - 4 X[4732], 5 X[4699] - 6 X[24325], 2 X[4732] - 3 X[24325], 6 X[10] - 7 X[4751], 4 X[10] - 5 X[40328], 14 X[4751] - 15 X[40328], 3 X[75] - 2 X[4709], 2 X[75] - 3 X[31178], 4 X[4709] - 9 X[31178], 3 X[145] + X[1278], X[1278] - 3 X[24349], X[192] - 3 X[3241], 6 X[551] - 5 X[4687], 6 X[3244] - X[3644], 5 X[3616] - 4 X[3842], 5 X[3623] - X[31302], 3 X[3632] - 8 X[4739], 3 X[3696] - 4 X[4739], 3 X[3633] + 4 X[4726], 3 X[3679] - 4 X[3739], 3 X[5902] - 4 X[13476], 2 X[4686] + 3 X[34747], 8 X[4698] - 9 X[25055], 7 X[4772] - 3 X[31145], 5 X[4821] + 3 X[20049], 9 X[19875] - 10 X[31238], 7 X[27268] - 9 X[38314]

X(49490) lies on these lines: {1, 6}, {2, 17145}, {7, 24715}, {8, 4699}, {10, 4684}, {31, 3957}, {36, 4497}, {38, 4430}, {42, 982}, {43, 354}, {55, 3979}, {63, 3750}, {65, 4334}, {69, 33076}, {75, 519}, {80, 27471}, {81, 3938}, {86, 36480}, {89, 678}, {141, 29659}, {145, 740}, {149, 24725}, {171, 3870}, {192, 537}, {200, 17122}, {210, 4883}, {226, 33141}, {244, 3240}, {291, 1002}, {306, 33169}, {312, 42057}, {320, 4660}, {333, 29651}, {335, 4393}, {386, 3881}, {390, 24695}, {497, 33096}, {517, 1742}, {524, 24357}, {528, 17365}, {551, 4687}, {612, 4038}, {726, 3244}, {748, 29817}, {750, 3935}, {752, 17364}, {756, 4661}, {758, 2667}, {872, 995}, {894, 32941}, {908, 24217}, {940, 3961}, {942, 24440}, {944, 29054}, {978, 5045}, {985, 1280}, {986, 3874}, {999, 34247}, {1046, 3295}, {1054, 4860}, {1125, 17352}, {1193, 3889}, {1215, 10453}, {1253, 30284}, {1266, 4780}, {1458, 7672}, {1486, 24436}, {1621, 7262}, {1647, 37651}, {1698, 17265}, {1707, 10389}, {1738, 5542}, {1921, 24524}, {1962, 7226}, {1999, 32920}, {2099, 6180}, {2177, 3218}, {2263, 11526}, {2275, 3774}, {2310, 40269}, {2334, 7194}, {2805, 12653}, {2810, 21746}, {3008, 27475}, {3187, 32923}, {3210, 42055}, {3293, 18398}, {3434, 33097}, {3475, 33130}, {3476, 4032}, {3589, 29660}, {3616, 3842}, {3623, 31302}, {3632, 3696}, {3633, 4726}, {3635, 3993}, {3662, 4085}, {3666, 42042}, {3679, 3739}, {3681, 3720}, {3685, 32935}, {3689, 37520}, {3722, 17126}, {3729, 4693}, {3740, 25502}, {3742, 4849}, {3748, 4641}, {3752, 42043}, {3755, 24231}, {3757, 32853}, {3763, 36478}, {3771, 33121}, {3779, 3792}, {3797, 17389}, {3811, 37607}, {3846, 29843}, {3868, 37598}, {3883, 34379}, {3894, 4424}, {3896, 17155}, {3912, 33165}, {3914, 33103}, {3936, 33120}, {3953, 5312}, {3967, 4891}, {3980, 3996}, {4028, 32855}, {4062, 33089}, {4078, 4899}, {4090, 18743}, {4253, 39258}, {4327, 30318}, {4360, 24841}, {4383, 29820}, {4385, 35633}, {4392, 46904}, {4407, 17248}, {4413, 5524}, {4417, 29655}, {4432, 17350}, {4434, 37684}, {4438, 29839}, {4439, 17242}, {4487, 30044}, {4514, 32946}, {4657, 47358}, {4658, 30145}, {4666, 17123}, {4671, 31161}, {4674, 5902}, {4677, 4688}, {4685, 19804}, {4686, 34747}, {4694, 5313}, {4698, 25055}, {4702, 17351}, {4722, 17127}, {4723, 29982}, {4737, 20923}, {4742, 22016}, {4753, 17349}, {4772, 31145}, {4788, 28554}, {4821, 20049}, {4847, 33111}, {4851, 32847}, {4863, 33109}, {4865, 17778}, {4941, 24399}, {4966, 29674}, {4972, 33069}, {5014, 32949}, {5249, 32865}, {5256, 17598}, {5272, 44841}, {5297, 9345}, {5308, 27484}, {5439, 6048}, {5697, 20718}, {5718, 29676}, {5882, 30273}, {5905, 33095}, {6542, 27474}, {7146, 34253}, {7232, 48829}, {7271, 18421}, {7613, 30340}, {7962, 11997}, {7982, 12652}, {7991, 30271}, {8298, 9451}, {9041, 17390}, {10222, 20430}, {11269, 17719}, {14829, 29670}, {15668, 36531}, {16602, 36634}, {16704, 18174}, {17135, 31025}, {17140, 20011}, {17146, 17495}, {17165, 32915}, {17262, 24821}, {17270, 48851}, {17277, 24331}, {17279, 47359}, {17298, 31151}, {17308, 31306}, {17316, 17755}, {17321, 48830}, {17322, 48822}, {17379, 36534}, {17387, 27487}, {17388, 28503}, {17397, 27495}, {17469, 37685}, {17483, 33094}, {17490, 42053}, {17591, 21342}, {17597, 29821}, {17609, 21214}, {17717, 26015}, {17718, 33140}, {17724, 29658}, {17725, 27491}, {17738, 20162}, {18134, 29673}, {18139, 33117}, {18157, 33937}, {19860, 26657}, {19875, 31238}, {20068, 27804}, {21143, 29350}, {22769, 37576}, {23344, 37525}, {23511, 30350}, {24003, 30947}, {24210, 33101}, {24362, 32922}, {24693, 26806}, {25415, 44670}, {25453, 33124}, {25539, 29633}, {25760, 29835}, {26061, 33173}, {26098, 36845}, {26223, 32943}, {26227, 32919}, {26815, 27285}, {27268, 38314}, {27479, 33104}, {28653, 48809}, {29010, 37727}, {29570, 31323}, {29588, 33888}, {29631, 33122}, {29632, 33114}, {29635, 33126}, {29637, 38047}, {29642, 33118}, {29667, 33081}, {29675, 35466}, {29685, 32782}, {29824, 32931}, {29829, 32775}, {29830, 33115}, {29844, 33071}, {29861, 30811}, {30329, 42079}, {30818, 31137}, {30942, 46897}, {31006, 31330}, {31019, 33136}, {31034, 32844}, {32099, 48849}, {32773, 33064}, {32780, 33171}, {32852, 33090}, {32856, 33134}, {32858, 33162}, {32859, 32947}, {32863, 33074}, {32929, 32940}, {33127, 33142}, {33128, 33148}, {33135, 33144}, {33156, 33170}, {33158, 33163}, {36275, 42084}, {41839, 42054}, {48632, 48821}

X(49490) = midpoint of X(145) and X(24349)
X(49490) = reflection of X(i) in X(j) for these {i,j}: {8, 24325}, {984, 1}, {3632, 3696}, {3993, 3635}, {4677, 4688}, {7991, 30271}, {20430, 10222}, {30273, 5882}
X(49490) = X(514)-isoconjugate of X(28852)
X(49490) = X(17244)-Dao conjugate of X(4479)
X(49490) = crosssum of X(1) and X(15485)
X(49490) = crossdifference of every pair of points on line {513, 23650}
X(49490) = barycentric product X(i)*X(j) for these {i,j}: {1, 17244}, {100, 28851}
X(49490) = barycentric quotient X(i)/X(j) for these {i,j}: {692, 28852}, {17244, 75}, {28851, 693}
X(49490) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 9, 16484}, {1, 1757, 1001}, {1, 3751, 238}, {1, 15485, 42819}, {1, 16468, 1279}, {1, 16667, 16491}, {1, 45751, 16497}, {6, 42871, 1}, {8, 4699, 4732}, {10, 4684, 33087}, {31, 3957, 17715}, {38, 17018, 17592}, {42, 3873, 982}, {42, 17449, 4850}, {43, 354, 17063}, {44, 42819, 15485}, {55, 32913, 4650}, {69, 36479, 33076}, {81, 3938, 17716}, {210, 4883, 26102}, {354, 21870, 16610}, {386, 3881, 3976}, {940, 41711, 3961}, {1279, 4663, 16468}, {1279, 15570, 1}, {1386, 4864, 1}, {1621, 32912, 7262}, {2177, 3218, 17601}, {3293, 18398, 24174}, {3475, 33137, 33130}, {3742, 4849, 16569}, {3748, 4641, 8616}, {3755, 24231, 33149}, {3873, 4850, 17449}, {3979, 32913, 55}, {4430, 17018, 38}, {4661, 29814, 756}, {4663, 15570, 1279}, {4732, 24325, 4699}, {4850, 17449, 982}, {4867, 16490, 1}, {6542, 31314, 31317}, {6542, 31317, 27474}, {16610, 21870, 43}, {17140, 20011, 32860}, {17450, 21805, 2}, {35466, 37703, 29675}


X(49491) = X(1)X(190)∩X(10)X(141)

Barycentrics    3*a^2*b - 2*a*b^2 + 3*a^2*c + 2*a*b*c + b^2*c - 2*a*c^2 + b*c^2 : :
X(49491) = 5 X[1] - 3 X[4664], X[8] - 3 X[31178], 5 X[10] - 6 X[3739], 2 X[10] - 3 X[24325], 4 X[3739] - 5 X[24325], 3 X[37] - 4 X[3636], 3 X[75] - X[3632], 5 X[145] + 3 X[1278], X[145] + 3 X[24349], X[1278] - 5 X[24349], 3 X[192] - 7 X[20057], 10 X[3635] - 3 X[4718], 3 X[984] - 5 X[3616], 5 X[984] - 7 X[27268], 25 X[3616] - 21 X[27268], 7 X[3624] - 6 X[3842], 2 X[3626] - 3 X[4688], 3 X[3696] - 2 X[4701], 5 X[4668] - 6 X[4732], 3 X[4740] + X[20050], 6 X[4755] - 7 X[15808], 13 X[19877] - 15 X[40328]

X(49491) lies on these lines: {1, 190}, {8, 24693}, {10, 141}, {37, 3636}, {38, 29822}, {42, 42055}, {43, 42053}, {75, 3632}, {145, 740}, {192, 20057}, {244, 17146}, {335, 31314}, {354, 4871}, {536, 3244}, {726, 3635}, {984, 3616}, {1215, 3873}, {1266, 4743}, {1962, 20068}, {3241, 28554}, {3243, 32941}, {3475, 4438}, {3624, 3842}, {3626, 4688}, {3696, 4701}, {3720, 42054}, {3742, 4090}, {3751, 4974}, {3773, 4684}, {3791, 32923}, {3797, 29619}, {3879, 17769}, {3883, 17771}, {3923, 42871}, {3938, 4697}, {3952, 17450}, {3957, 32940}, {3971, 4883}, {3979, 32939}, {3980, 41711}, {3993, 28582}, {3994, 17165}, {4085, 24231}, {4096, 26102}, {4135, 4891}, {4430, 32771}, {4649, 20180}, {4655, 36479}, {4668, 4732}, {4706, 4946}, {4740, 20050}, {4753, 16825}, {4755, 15808}, {4892, 33120}, {5220, 24331}, {6682, 29825}, {6685, 21342}, {7226, 10180}, {11814, 17051}, {15570, 17351}, {17140, 19998}, {17154, 46904}, {17230, 31317}, {17244, 17755}, {17364, 28498}, {17365, 17766}, {17449, 46897}, {18481, 29054}, {19877, 40328}, {20048, 32860}, {28595, 33069}, {29569, 31349}, {29817, 32938}, {29824, 31161}, {29835, 32856}, {29843, 33101}, {30950, 42056}

X(49491) = crossdifference of every pair of points on line {3768, 21007}
X(49491) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 32935, 4432}, {4946, 24165, 4706}


X(49492) = X(1)X(321)∩X(8)X(21)

Barycentrics    (a - b - c)*(a^3 - a*b^2 - b^2*c - a*c^2 - b*c^2) : :
X(49492) = 5 X[3616] - 4 X[17061]

X(49492) lies on these lines: {1, 321}, {2, 37715}, {3, 17751}, {8, 21}, {10, 10448}, {30, 6327}, {31, 519}, {56, 35999}, {78, 3701}, {100, 4216}, {145, 4195}, {171, 16393}, {200, 4723}, {218, 26770}, {219, 346}, {238, 11346}, {306, 515}, {312, 4511}, {332, 11103}, {341, 4420}, {517, 32929}, {750, 19336}, {758, 32933}, {944, 37399}, {952, 49128}, {956, 1011}, {993, 1150}, {997, 4358}, {999, 16405}, {1089, 22836}, {1193, 5192}, {1220, 19767}, {1222, 20050}, {1320, 7155}, {1478, 3936}, {1975, 17137}, {2099, 5695}, {2268, 2321}, {2298, 17314}, {2309, 32941}, {2364, 4873}, {2646, 3714}, {2975, 10449}, {3006, 3419}, {3241, 28503}, {3421, 30943}, {3488, 47511}, {3596, 6740}, {3616, 17061}, {3679, 32917}, {3685, 3877}, {3695, 13733}, {3710, 6737}, {3811, 4696}, {3822, 30834}, {3833, 24594}, {3869, 7283}, {3872, 3886}, {3933, 21285}, {3935, 4737}, {3940, 3952}, {4101, 12527}, {4203, 10453}, {4224, 10327}, {4234, 17126}, {4255, 26030}, {4302, 4450}, {4385, 34772}, {4387, 5289}, {4388, 11114}, {4417, 5080}, {4645, 17579}, {4647, 30147}, {4651, 9708}, {4673, 4861}, {4702, 5919}, {4942, 12635}, {4966, 5434}, {4972, 48837}, {5016, 10572}, {5251, 5278}, {5260, 9534}, {5264, 10457}, {5687, 28348}, {5711, 11115}, {5730, 25253}, {5731, 34255}, {5774, 16370}, {5793, 19765}, {6224, 17233}, {7080, 26091}, {7270, 19840}, {7841, 31023}, {9310, 21071}, {10458, 30116}, {11319, 16466}, {12746, 21278}, {13735, 17127}, {14012, 33093}, {15934, 17140}, {16086, 32862}, {17033, 33819}, {17677, 25958}, {17678, 25959}, {17679, 25957}, {17682, 29986}, {17683, 29966}, {17697, 20036}, {17740, 18391}, {17757, 37354}, {18525, 27558}, {18761, 48877}, {19869, 32774}, {20067, 32863}, {24596, 30109}, {24929, 26227}, {29616, 37416}, {29785, 40006}, {29846, 37716}, {29849, 37717}, {30172, 47033}, {30567, 35262}, {30942, 37617}, {32852, 38456}, {33083, 37038}, {35250, 48935}

X(49492) = reflection of X(i) in X(j) for these {i,j}: {8, 3703}, {3891, 1}
X(49492) = X(i)-isoconjugate of X(j) for these (i,j): {56, 994}, {57, 46018}, {1408, 45095}
X(49492) = X(i)-Dao conjugate of X(j) for these (i, j): (1, 994), (5452, 46018)
X(49492) = barycentric product X(i)*X(j) for these {i,j}: {8, 1150}, {312, 993}, {345, 5136}, {2278, 3596}, {3699, 48321}
X(49492) = barycentric quotient X(i)/X(j) for these {i,j}: {9, 994}, {55, 46018}, {993, 57}, {1150, 7}, {2278, 56}, {2321, 45095}, {5136, 278}, {48321, 3676}
X(49492) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 48863, 24552}, {10, 10448, 16342}, {3704, 10950, 8}, {3872, 3886, 3902}, {5793, 19765, 26115}, {11319, 20040, 16466}


X(49493) = X(1)X(536)∩X(10)X(75)

Barycentrics    a*b^2 - a*b*c - 2*b^2*c + a*c^2 - 2*b*c^2 : :
X(49493) = 2 X[1] - 3 X[31178], X[8] - 3 X[4740], 2 X[10] - 3 X[75], 4 X[10] - 3 X[984], 6 X[37] - 7 X[3624], 4 X[37] - 5 X[40328], 14 X[3624] - 15 X[40328], X[145] + 3 X[1278], X[145] - 3 X[24349], 3 X[192] - 5 X[3616], 5 X[3616] - 6 X[24325], 8 X[4535] - 9 X[27474], X[3632] - 6 X[4686], 4 X[1125] - 3 X[4664], 5 X[1698] - 6 X[4688], 4 X[3635] + 3 X[4764], 8 X[3636] - 3 X[3644], 4 X[3636] - 3 X[3993], 6 X[3696] - 5 X[4668], 5 X[4668] - 12 X[4726], 4 X[3842] - 5 X[4699], 12 X[3842] - 13 X[19877], 15 X[4699] - 13 X[19877], 7 X[4678] - 15 X[4821], 7 X[4678] - 3 X[31302], 5 X[4821] - X[31302], 15 X[4687] - 16 X[19878], 2 X[4701] - 3 X[4709], 21 X[4751] - 20 X[31253], 12 X[4755] - 13 X[34595], 21 X[4772] - 17 X[46932], 4 X[9955] - 3 X[20430]

X(49493) lies on these lines: {1, 536}, {2, 3994}, {7, 32846}, {8, 537}, {10, 75}, {37, 3624}, {38, 28605}, {43, 4706}, {145, 740}, {190, 16825}, {192, 3616}, {226, 32855}, {238, 3729}, {239, 32935}, {244, 4671}, {291, 4441}, {306, 33103}, {312, 4871}, {321, 982}, {335, 4535}, {345, 33130}, {518, 3632}, {596, 3976}, {714, 4647}, {764, 4777}, {894, 32921}, {1086, 29674}, {1089, 24174}, {1125, 4664}, {1215, 3210}, {1698, 4688}, {1757, 4361}, {1836, 32866}, {2321, 24231}, {3097, 21264}, {3120, 33089}, {3175, 26102}, {3187, 32940}, {3240, 31161}, {3416, 32857}, {3635, 4764}, {3636, 3644}, {3649, 7201}, {3662, 3773}, {3666, 29825}, {3687, 33101}, {3696, 4668}, {3703, 17889}, {3705, 48643}, {3712, 29675}, {3720, 42044}, {3739, 25503}, {3741, 42029}, {3742, 22034}, {3751, 4716}, {3757, 32934}, {3772, 33167}, {3775, 48628}, {3782, 32778}, {3790, 3836}, {3795, 17759}, {3797, 17244}, {3813, 4953}, {3840, 42034}, {3842, 4699}, {3873, 4365}, {3875, 4649}, {3883, 28526}, {3891, 4418}, {3914, 33169}, {3923, 32922}, {3932, 7263}, {3943, 25557}, {3966, 33099}, {3967, 16569}, {3969, 33069}, {3971, 19804}, {3980, 32926}, {3999, 4519}, {4000, 33159}, {4003, 29827}, {4054, 17717}, {4066, 24046}, {4078, 24199}, {4096, 26038}, {4133, 4684}, {4135, 18743}, {4310, 4461}, {4359, 32925}, {4362, 4650}, {4387, 29820}, {4419, 24697}, {4442, 33120}, {4444, 4804}, {4454, 24695}, {4678, 4821}, {4687, 19878}, {4701, 4709}, {4718, 15569}, {4751, 31253}, {4755, 34595}, {4772, 46932}, {4859, 31252}, {4942, 37679}, {4968, 37598}, {4974, 17350}, {4980, 31330}, {5145, 17445}, {5220, 17119}, {5233, 21093}, {5249, 33092}, {5852, 17362}, {5880, 32847}, {5904, 22300}, {5905, 32861}, {6057, 40688}, {6361, 29054}, {6535, 33172}, {6541, 17234}, {6763, 16548}, {7226, 21020}, {7228, 28472}, {7262, 32914}, {9955, 20430}, {10129, 27479}, {10453, 42055}, {11680, 48642}, {15523, 33146}, {16468, 17351}, {16816, 31349}, {17118, 24342}, {17140, 32915}, {17147, 17592}, {17163, 20068}, {17165, 19998}, {17276, 33082}, {17281, 29637}, {17289, 25539}, {17301, 29633}, {17339, 31289}, {17363, 17771}, {17364, 17772}, {17369, 29646}, {17483, 32852}, {17495, 32931}, {17591, 44417}, {17593, 29828}, {17601, 26227}, {17715, 32923}, {17719, 17740}, {18481, 29010}, {19785, 32780}, {19789, 33132}, {19796, 25453}, {19820, 33118}, {20292, 32854}, {24003, 24620}, {24248, 33076}, {24725, 32842}, {24789, 33164}, {25502, 35652}, {26061, 33150}, {26223, 32924}, {29642, 42033}, {29667, 33145}, {30699, 33135}, {30998, 40533}, {31019, 32848}, {32777, 33147}, {32779, 33143}, {32856, 33077}, {32920, 32932}, {33074, 33102}, {33075, 33098}, {33088, 33097}, {33090, 33094}, {33127, 33168}, {33128, 33170}, {33129, 33161}, {33131, 33162}, {33144, 33160}, {33148, 33156}, {34860, 42027}, {38499, 38511}, {42334, 42696}

X(49493) = midpoint of X(1278) and X(24349)
X(49493) = reflection of X(i) in X(j) for these {i,j}: {192, 24325}, {984, 75}, {3644, 3993}, {3696, 4726}, {4718, 15569}
X(49493) = barycentric product X(190)*X(48184)
X(49493) = barycentric quotient X(48184)/X(514)
X(49493) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 4440, 4655}, {10, 1266, 33149}, {312, 24165, 17063}, {321, 17155, 982}, {2321, 24231, 33087}, {3751, 17151, 4716}, {3790, 48627, 3836}, {3891, 4418, 17716}, {3999, 4519, 31137}, {4362, 32939, 4650}, {17147, 32771, 17592}, {19789, 33163, 33132}, {26227, 32845, 17601}, {32914, 32933, 7262}, {32923, 32929, 17715}


X(49494) = X(1)X(2)∩X(31)X(2802)

Barycentrics    a*(a^3 + b^3 + 4*a*b*c - 2*b^2*c - 2*b*c^2 + c^3) : :
X(49494) = 3 X[1] - 2 X[3938], 3 X[3679] - 4 X[29673], 9 X[25055] - 8 X[29656], 2 X[20896] - 3 X[46895]

X(49494) lies on these lines: {1, 2}, {31, 2802}, {56, 3987}, {57, 1417}, {58, 14923}, {80, 33141}, {321, 996}, {517, 4641}, {535, 33094}, {595, 3885}, {748, 3898}, {940, 40587}, {956, 4424}, {986, 5288}, {999, 1739}, {1054, 37587}, {1145, 37646}, {1320, 32911}, {1387, 37663}, {1453, 3680}, {1724, 3057}, {1757, 3899}, {2093, 26934}, {2099, 34048}, {3219, 17461}, {3245, 4650}, {3550, 5541}, {3666, 16499}, {3670, 12513}, {3751, 25415}, {3772, 24222}, {3880, 37610}, {3893, 5266}, {3895, 37817}, {3897, 33771}, {3902, 48863}, {3959, 17736}, {3968, 17124}, {4051, 5280}, {4642, 8666}, {5119, 18163}, {5247, 5697}, {5258, 37598}, {5264, 10914}, {5269, 11525}, {5315, 41702}, {5348, 17636}, {5563, 24440}, {5836, 37522}, {6205, 21888}, {9620, 45751}, {9896, 18506}, {10912, 16466}, {11014, 37699}, {12653, 16468}, {17063, 37602}, {17614, 21896}, {20896, 46895}, {24806, 47057}, {26688, 34587}, {26741, 41554}

X(49494) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4668, 5293}, {1, 4677, 3961}, {1, 31855, 997}, {8, 15955, 1}, {386, 4861, 1}, {995, 38460, 1}, {1193, 22837, 1}, {3241, 30117, 1}, {3244, 3924, 1}, {3635, 28082, 1}, {17015, 30116, 1}


X(49495) = X(1)X(2)∩X(6)X(3886)

Barycentrics    a^3 + 4*a^2*b - a*b^2 + 4*a^2*c - 2*b^2*c - a*c^2 - 2*b*c^2 : :
X(49495) = 2 X[1] - 3 X[16834], 4 X[10] - 3 X[17294], 7 X[9780] - 6 X[29594], 3 X[3729] - 4 X[32935], 3 X[3751] - 2 X[32935], 3 X[16475] - 2 X[32941], 5 X[17286] - 6 X[38047]

X(49495) lies on these lines: {1, 2}, {6, 3886}, {40, 4229}, {63, 3896}, {65, 7223}, {69, 3755}, {148, 152}, {165, 37683}, {192, 5223}, {193, 516}, {194, 7991}, {213, 4513}, {333, 37553}, {385, 9746}, {517, 49130}, {518, 3875}, {740, 3729}, {968, 32864}, {980, 4646}, {1449, 5263}, {1697, 21384}, {1738, 17298}, {1743, 3685}, {1757, 25728}, {2136, 24578}, {2223, 3913}, {2279, 3501}, {2481, 17158}, {2550, 3879}, {2665, 39969}, {2809, 3868}, {3158, 3769}, {3177, 12526}, {3208, 39252}, {3242, 4852}, {3243, 32922}, {3696, 10436}, {3717, 16970}, {3749, 3791}, {3759, 7290}, {3779, 35104}, {3823, 17311}, {3883, 5839}, {3895, 45751}, {3950, 27549}, {3951, 25237}, {3996, 5269}, {4000, 4684}, {4026, 17270}, {4042, 37593}, {4312, 17364}, {4356, 17257}, {4360, 7174}, {4402, 11038}, {4429, 17296}, {4442, 31164}, {4512, 37652}, {4655, 4743}, {4663, 5695}, {4676, 16670}, {4706, 4860}, {4780, 24248}, {4875, 5283}, {4891, 37679}, {4923, 5750}, {4938, 31134}, {4966, 17282}, {4968, 32104}, {5250, 16552}, {5687, 37609}, {5710, 20963}, {5846, 16973}, {6144, 28570}, {6629, 35915}, {6762, 37555}, {7176, 25718}, {7322, 34064}, {10444, 29311}, {10980, 17490}, {12513, 37575}, {12527, 20111}, {16048, 45765}, {16469, 17121}, {16475, 32941}, {16476, 37588}, {16496, 32921}, {16704, 35258}, {16968, 21711}, {16972, 17299}, {17151, 24349}, {17286, 38047}, {17300, 38052}, {17377, 32850}, {17594, 32853}, {20154, 31342}, {24392, 33071}, {24695, 28580}, {30568, 32915}, {32092, 33936}

X(49495) = reflection of X(i) in X(j) for these {i,j}: {69, 3755}, {3242, 4852}, {3729, 3751}, {3886, 6}, {4655, 4743}, {5695, 4663}, {16496, 32921}, {24248, 4780}
X(49495) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 10, 16831}, {1, 3679, 39586}, {1, 4668, 36531}, {1, 16832, 3616}, {1, 16833, 16823}, {1, 39586, 29597}, {8, 3241, 39587}, {42, 17156, 11679}, {43, 39594, 30567}, {145, 239, 1}, {145, 39567, 3241}, {1999, 20012, 200}, {3187, 20011, 3870}, {3241, 16823, 1}, {3244, 16825, 1}, {3635, 24331, 1}


X(49496) = X(6)X(75)∩X(37)X(69)

Barycentrics    2*a^3*b + 2*a^3*c + a^2*b*c - b^3*c - b*c^3 : :
X(49496) = 4 X[141] - 5 X[4687], 8 X[3589] - 7 X[4751], 5 X[3618] - 4 X[3739], 7 X[3619] - 8 X[4698], 5 X[3620] - 7 X[27268], 4 X[3629] + X[3644], 4 X[4681] + X[11008], 5 X[4704] - X[20080], X[4740] - 3 X[5032], 4 X[4755] - 3 X[21356], X[4764] - 8 X[32455], 3 X[16475] - 2 X[24325], 3 X[27475] - 2 X[47595], 4 X[17355] - 3 X[27474], 3 X[25406] - 2 X[30271], 6 X[38049] - 5 X[40328]

X(49496) lies on these lines: {6, 75}, {37, 69}, {65, 21216}, {85, 17033}, {86, 16972}, {141, 4687}, {144, 145}, {213, 304}, {312, 24514}, {335, 5845}, {354, 26274}, {385, 3769}, {511, 30273}, {524, 4664}, {536, 1992}, {599, 29575}, {726, 32451}, {740, 3729}, {746, 5028}, {872, 4019}, {966, 31322}, {984, 4416}, {1100, 24357}, {1193, 25918}, {1351, 29010}, {1386, 17379}, {1423, 39775}, {1469, 19565}, {1654, 3416}, {1743, 17755}, {1814, 2995}, {1999, 10025}, {2176, 18156}, {2238, 30758}, {3242, 17319}, {3263, 37657}, {3290, 30962}, {3564, 20430}, {3589, 4751}, {3618, 3739}, {3619, 4698}, {3620, 27268}, {3629, 3644}, {3631, 29623}, {3673, 17034}, {3681, 31087}, {3763, 29626}, {3779, 25050}, {3797, 17350}, {3868, 17489}, {3875, 32029}, {3876, 25263}, {3993, 34379}, {3997, 33936}, {4032, 9312}, {4360, 16973}, {4385, 17499}, {4437, 17242}, {4657, 36409}, {4681, 11008}, {4699, 24599}, {4704, 20080}, {4740, 5032}, {4755, 21356}, {4764, 32455}, {4849, 40883}, {5846, 17363}, {5905, 19791}, {7774, 33071}, {8584, 17225}, {14210, 35274}, {16284, 17752}, {16475, 24325}, {17007, 33078}, {17275, 25384}, {17277, 36404}, {17300, 27475}, {17331, 31323}, {17343, 27495}, {17352, 27487}, {17355, 27474}, {18157, 27644}, {19860, 25898}, {20018, 25242}, {20036, 27340}, {20963, 39731}, {21281, 41015}, {22370, 39258}, {23151, 41251}, {24690, 41269}, {25406, 30271}, {26242, 30941}, {27491, 31034}, {28604, 38047}, {29619, 40341}, {30945, 46907}, {34253, 39126}, {38049, 40328}, {39774, 44421}

X(49496) = midpoint of X(192) and X(193)
X(49496) = reflection of X(i) in X(j) for these {i,j}: {69, 37}, {75, 6}, {33936, 3997}
X(49496) = crossdifference of every pair of points on line {788, 20980}


X(49497) = X(1)X(872)∩X(6)X(519)

Barycentrics    a^3 + 3*a^2*b - a*b^2 + 3*a^2*c - b^2*c - a*c^2 - b*c^2 : :
X(49497) = 5 X[6] - 3 X[48805], X[17299] - 3 X[47359], 5 X[32941] - 6 X[48805], 4 X[4852] - 3 X[32921], X[3729] - 3 X[3751], 2 X[3729] - 3 X[32935], 2 X[3631] - 3 X[48821], 4 X[4991] - 3 X[38315], 4 X[6329] - 3 X[48810], X[16496] - 3 X[16834], X[40341] - 3 X[48829]

X(49497) lies on these lines: {1, 872}, {6, 519}, {8, 4649}, {9, 4753}, {10, 4445}, {31, 20011}, {42, 1150}, {69, 4085}, {86, 3679}, {145, 238}, {171, 20012}, {193, 752}, {319, 29659}, {333, 42042}, {516, 11477}, {518, 4523}, {524, 4660}, {527, 4780}, {528, 3629}, {537, 3875}, {551, 17259}, {740, 3729}, {750, 19998}, {940, 4685}, {966, 48830}, {984, 17319}, {1001, 3244}, {1100, 36480}, {1213, 48822}, {1215, 17156}, {1698, 17241}, {1743, 4432}, {1757, 17336}, {2177, 16704}, {2274, 3293}, {3187, 32920}, {3240, 32919}, {3241, 16484}, {3286, 8715}, {3550, 41629}, {3625, 33682}, {3631, 48821}, {3632, 5263}, {3633, 16468}, {3644, 24821}, {3664, 24693}, {3750, 37652}, {3755, 4655}, {3780, 40728}, {3791, 3870}, {3836, 4869}, {3886, 4672}, {3896, 32912}, {3913, 37507}, {3923, 4663}, {3993, 5220}, {4028, 4438}, {4034, 48851}, {4042, 43223}, {4062, 33114}, {4113, 37595}, {4363, 4709}, {4383, 42057}, {4407, 17321}, {4430, 32924}, {4439, 17314}, {4661, 32928}, {4668, 43997}, {4677, 46922}, {4693, 17350}, {4702, 16669}, {4716, 24349}, {4722, 32929}, {4732, 10436}, {4743, 17771}, {4849, 29649}, {4991, 38315}, {5132, 8666}, {5156, 20018}, {5625, 39586}, {5839, 36479}, {6329, 48810}, {6542, 33165}, {8053, 25439}, {11239, 27317}, {11362, 37474}, {12513, 37502}, {14459, 33089}, {14621, 20016}, {14829, 42043}, {15534, 28562}, {16477, 20050}, {16496, 16834}, {16801, 17315}, {16829, 20140}, {17018, 32864}, {17117, 31178}, {17126, 20048}, {17135, 25496}, {17228, 36478}, {17298, 25351}, {17348, 24331}, {17363, 33076}, {17364, 24715}, {17375, 31151}, {17377, 32847}, {17389, 20142}, {17394, 36531}, {17398, 48809}, {17764, 24695}, {17778, 32865}, {20017, 33162}, {20132, 29617}, {20150, 48852}, {20154, 29574}, {24524, 30940}, {30828, 33137}, {31034, 33136}, {31145, 37677}, {32945, 37685}, {37510, 37727}, {40341, 48829}

X(49497) = reflection of X(i) in X(j) for these {i,j}: {69, 4085}, {3886, 4672}, {3923, 4663}, {4655, 3755}, {24248, 4743}, {32935, 3751}, {32941, 6}
X(49497) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {42, 32853, 32916}, {3241, 17349, 16484}, {3896, 32912, 32934}


X(49498) = X(1)X(6)∩X(8)X(4772)

Barycentrics    a*(3*a*b - 2*b^2 + 3*a*c + b*c - 2*c^2) : :
X(49498) = 5 X[1] - 4 X[37], 3 X[1] - 2 X[984], 9 X[1] - 8 X[15569], 6 X[37] - 5 X[984], 9 X[37] - 10 X[15569], 3 X[984] - 4 X[15569], 5 X[8] - 7 X[4772], 5 X[145] - X[4788], 3 X[4740] - 5 X[24349], 5 X[3633] + 2 X[4764], 3 X[3241] - 2 X[3993], 3 X[3241] - X[31302], 4 X[3626] - 5 X[4699], 8 X[3636] - 7 X[27268], 3 X[3679] - 4 X[24325], 4 X[3696] - 3 X[4677], 2 X[3696] - 3 X[31178], 8 X[3842] - 9 X[25055], 5 X[4704] - 7 X[20057], 5 X[4821] - X[20054], 3 X[16200] - 2 X[20430], 9 X[19875] - 10 X[40328]

X(49498) lies on these lines: {1, 6}, {8, 4772}, {10, 17232}, {38, 42042}, {42, 4392}, {43, 244}, {63, 3979}, {75, 3632}, {145, 726}, {171, 41711}, {192, 3244}, {210, 25502}, {335, 16834}, {354, 16569}, {519, 4740}, {536, 34747}, {740, 3633}, {978, 3881}, {982, 42043}, {1002, 3783}, {1278, 20050}, {1280, 8300}, {1471, 14151}, {1698, 17283}, {3216, 29439}, {3240, 17449}, {3241, 3993}, {3293, 29749}, {3306, 5524}, {3475, 33138}, {3550, 3870}, {3621, 4709}, {3626, 4699}, {3636, 27268}, {3661, 31314}, {3679, 17297}, {3681, 26102}, {3696, 4677}, {3720, 4661}, {3748, 7262}, {3797, 29605}, {3811, 37608}, {3842, 25055}, {3889, 21214}, {3957, 8616}, {3961, 37604}, {3999, 21870}, {4334, 7672}, {4398, 4743}, {4641, 17715}, {4684, 29674}, {4704, 20057}, {4777, 14812}, {4821, 20054}, {4849, 17063}, {4863, 33097}, {4924, 5542}, {4966, 33165}, {5563, 34247}, {6048, 18398}, {7280, 15624}, {9263, 32453}, {16200, 20430}, {17145, 30942}, {17146, 19998}, {17155, 20011}, {17294, 31317}, {17364, 17766}, {17377, 17769}, {17389, 33888}, {17755, 29573}, {19875, 40328}, {20012, 24165}, {22045, 32925}, {24841, 32921}, {27475, 31183}, {27481, 29588}, {27484, 29571}, {27495, 29603}, {29597, 31323}, {29669, 37653}, {29825, 46909}, {29827, 46897}, {29835, 33065}, {29856, 33122}, {29858, 33114}, {31137, 32931}, {32937, 42057}, {33082, 36479}, {33106, 36845}, {33159, 47359}, {33682, 36534}, {36480, 43997}

X(49498) = midpoint of X(1278) and X(20050)
X(49498) = reflection of X(i) in X(j) for these {i,j}: {192, 3244}, {3621, 4709}, {3632, 75}, {4677, 31178}, {31302, 3993}
X(49498) = barycentric product X(i)*X(j) for these {i,j}: {1, 29572}, {72, 31929}
X(49498) = barycentric quotient X(i)/X(j) for these {i,j}: {29572, 75}, {31929, 286}
X(49498) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1757, 15485}, {1, 3751, 16468}, {238, 42871, 1}, {3241, 31302, 3993}, {3242, 4649, 1}, {3243, 3751, 1}, {3243, 16670, 15600}, {3870, 32913, 3550}, {3957, 32912, 8616}, {4849, 17063, 36634}


X(49499) = X(1)X(190)∩X(7)X(8)

Barycentrics    2*a^2*b - 2*a*b^2 + 2*a^2*c + a*b*c + b^2*c - 2*a*c^2 + b*c^2 : :
X(49499) = 4 X[1] - 3 X[4664], 2 X[8] - 3 X[75], 5 X[8] - 6 X[3696], X[8] - 3 X[24349], 5 X[75] - 4 X[3696], 2 X[3696] - 5 X[24349], 2 X[10] - 3 X[31178], 6 X[37] - 7 X[3622], 7 X[3622] - 3 X[31302], 3 X[192] - 5 X[3623], 8 X[3244] - 3 X[3644], 4 X[3633] + 3 X[4764], 3 X[984] - 4 X[1125], 4 X[984] - 5 X[4687], 16 X[1125] - 15 X[4687], 3 X[1278] + X[20014], 20 X[1698] - 21 X[4751], 5 X[1698] - 6 X[24325], 7 X[4751] - 8 X[24325], 5 X[3617] - 6 X[4688], X[3621] - 3 X[4740], 12 X[3739] - 11 X[46933], 12 X[3842] - 13 X[34595], 6 X[4686] - X[20054], 12 X[4755] - 13 X[46934], 3 X[30273] - 4 X[34773], 30 X[31238] - 29 X[46930]

X(49499) lies on these lines: {1, 190}, {2, 3999}, {7, 8}, {10, 17227}, {37, 3622}, {43, 42055}, {86, 7174}, {142, 4899}, {145, 536}, {192, 3623}, {244, 31233}, {312, 3873}, {321, 4430}, {335, 17367}, {341, 942}, {344, 11038}, {350, 1002}, {354, 4009}, {714, 2650}, {726, 3244}, {740, 3633}, {749, 984}, {894, 3242}, {1001, 17336}, {1043, 41863}, {1193, 34860}, {1215, 29827}, {1222, 3340}, {1265, 11037}, {1278, 20014}, {1279, 17350}, {1698, 4751}, {1897, 42856}, {3243, 3729}, {3306, 3699}, {3475, 33116}, {3555, 4673}, {3617, 4688}, {3619, 5772}, {3621, 4740}, {3681, 17140}, {3685, 42871}, {3717, 5542}, {3739, 46933}, {3742, 27538}, {3751, 3759}, {3755, 4398}, {3769, 32913}, {3786, 16709}, {3790, 4966}, {3842, 34595}, {3844, 48638}, {3870, 32939}, {3874, 4385}, {3883, 5850}, {3894, 4692}, {3932, 17241}, {3938, 32940}, {3952, 17146}, {3957, 32933}, {3967, 20942}, {3979, 32934}, {4026, 17249}, {4090, 17063}, {4096, 25502}, {4260, 18143}, {4310, 16706}, {4353, 17380}, {4359, 4661}, {4392, 46897}, {4415, 29843}, {4429, 24231}, {4488, 8236}, {4514, 5905}, {4519, 10453}, {4578, 5253}, {4684, 17233}, {4686, 20054}, {4737, 5902}, {4755, 46934}, {4849, 17490}, {4850, 17154}, {4860, 5205}, {4864, 17351}, {4883, 41839}, {4888, 4929}, {4901, 17298}, {5014, 17483}, {5220, 16823}, {5222, 15590}, {5223, 17277}, {5263, 16496}, {5846, 17364}, {9053, 17365}, {10385, 44446}, {13476, 20923}, {16569, 42053}, {16830, 41847}, {17120, 38315}, {17135, 42029}, {17164, 44671}, {17244, 31349}, {17256, 39581}, {17263, 27549}, {17292, 31317}, {17370, 38047}, {17449, 32931}, {17597, 27064}, {17609, 19582}, {17755, 27475}, {17794, 30963}, {18398, 46937}, {18412, 20927}, {18526, 29010}, {20012, 42051}, {20068, 28606}, {20718, 25295}, {21093, 24217}, {24199, 24393}, {24723, 36479}, {25728, 38316}, {26102, 42054}, {27491, 27757}, {27792, 40952}, {29569, 33888}, {29655, 33101}, {29673, 33103}, {29835, 33151}, {29844, 33096}, {30273, 34773}, {30340, 39570}, {30568, 44841}, {30942, 31161}, {30970, 32771}, {31238, 46930}, {32856, 33120}, {32859, 33090}, {32912, 32923}, {32932, 41711}, {33064, 33169}, {33069, 33162}, {33114, 33148}, {33121, 33144}, {33122, 33170}, {33124, 33163}

X(49499) = reflection of X(i) in X(j) for these {i,j}: {75, 24349}, {17347, 3883}, {31302, 37}
X(49499) = crossdifference of every pair of points on line {3063, 3768}
X(49499) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 32935, 4676}, {354, 4009, 30947}, {354, 32937, 18743}, {3681, 17140, 19804}, {3717, 5542, 17234}, {3751, 32922, 3759}, {3790, 4966, 17240}, {3873, 17165, 312}, {4009, 30947, 18743}, {4429, 24231, 48629}, {5220, 16823, 17335}, {27549, 38053, 17263}, {30947, 32937, 4009}, {32913, 32920, 3769}


X(49500) = X(1)X(21)∩X(6)X(4424)

Barycentrics    a*(a^3 + 2*a^2*b - b^3 + 2*a^2*c - c^3) : :
X(49500) = 3 X[165] - 2 X[30269], 3 X[3679] - 2 X[4680], 5 X[1698] - 4 X[2887], 7 X[3624] - 8 X[6679], 3 X[5886] - 4 X[20575], 3 X[19875] - 2 X[31134]

X(49500) lies on these lines: {1, 21}, {6, 4424}, {8, 20064}, {10, 6327}, {19, 1743}, {36, 3185}, {40, 209}, {43, 484}, {44, 3753}, {46, 2390}, {56, 23169}, {65, 1724}, {72, 5264}, {165, 30269}, {171, 5692}, {213, 1759}, {221, 16471}, {238, 5902}, {517, 4641}, {518, 37610}, {519, 32912}, {560, 4736}, {601, 31806}, {602, 5884}, {674, 3751}, {734, 9902}, {748, 5883}, {750, 10176}, {752, 1757}, {960, 37522}, {976, 4067}, {978, 3336}, {982, 4880}, {986, 1203}, {995, 3218}, {1104, 4018}, {1191, 3953}, {1279, 24473}, {1478, 24695}, {1572, 45751}, {1575, 6205}, {1698, 2887}, {1714, 4295}, {1739, 4383}, {1740, 2948}, {1754, 6001}, {1788, 34029}, {1877, 4848}, {2176, 17736}, {2258, 5313}, {3017, 33134}, {3072, 5693}, {3073, 37625}, {3219, 30116}, {3337, 21214}, {3624, 6679}, {3670, 16466}, {3822, 24725}, {3833, 17125}, {3924, 4084}, {3927, 5710}, {3940, 37540}, {3962, 5266}, {3970, 14974}, {3987, 37567}, {3997, 5282}, {4252, 5730}, {4257, 4511}, {4386, 21839}, {4692, 32935}, {4694, 16483}, {5011, 37657}, {5180, 33142}, {5247, 5903}, {5251, 7262}, {5255, 5904}, {5271, 46895}, {5292, 11415}, {5398, 14988}, {5886, 20575}, {5887, 37530}, {7098, 10571}, {7951, 33096}, {10974, 42448}, {11552, 17889}, {11813, 29662}, {15071, 37570}, {16086, 20101}, {16670, 21380}, {17015, 17461}, {17126, 30115}, {17127, 30117}, {17734, 31053}, {18393, 33140}, {19867, 26034}, {19875, 31134}, {24586, 46899}, {25526, 31359}, {26066, 37693}, {32950, 48843}, {35466, 39542}, {36283, 46907}, {37587, 47623}, {44447, 48837}

X(49500) = midpoint of X(8) and X(20064)
X(49500) = reflection of X(i) in X(j) for these {i,j}: {1, 31}, {6327, 10}
X(49500) = X(994)-Ceva conjugate of X(1)
X(49500) = barycentric product X(1)*X(31034)
X(49500) = barycentric quotient X(31034)/X(75)
X(49500) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {58, 3869, 1}, {595, 3868, 1}, {1468, 3878, 1}, {2650, 5248, 1}, {3873, 40091, 1}, {3874, 3915, 1}, {4383, 36279, 1739}, {4880, 5315, 982}

leftri

Points in a [[bc(b-c),ca(c-a),ab(a-b)], [a^2(b-c),b^2(c-a), c^2(a-b))]] coordinate system: X(49501)-X(49536)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1, L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1 is the line: bc(b-c) α + ca(c-a) β + ab(a-b) γ = 0.

L2 is the line a^2(b-c) α + b^2(c-a) β + c^2(a-b) γ = 0.

The origin is given by (0, 0) = X(984) = a(b-c) : b(c-a) : c(a-b) .

Barycentrics u : v : w for a triangle center U = (x, y) in this system are given by

u : v : w = -a(a+b)(a+c)(b-c)(b^2+bc+c^2) - a(ab+ac-b^2-c^2)x + (ab^2+ac^2-b^2c-bc^2)y : : ,

where, as functions of a, b, c, the coordinate x is antisymmetric and homogeneous of degree 3, and y is antisymmetric and homogeneous of degree 3.

The appearance of {x, y}, k in the following list means that (x, y) = X(k).

{-2 (a-b) (a-c) (b-c), (a-b) (a-c) (b-c)}, 49450
{-2 (a-b) (a-c) (b-c), 2 (a-b) (a-c) (b-c)}, 49459
{-((a-b) (a-c) (b-c)), -((a-b) (a-c) (b-c))}, 31302
{-((a-b) (a-c) (b-c)), 0}, 49448
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c)), ((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a b+a c+b c))}, 3883
{-((a-b) (a-c) (b-c)), (a-b) (a-c) (b-c)}, 8
{-((a-b) (a-c) (b-c)), 2 (a-b) (a-c) (b-c)}, 49474
{-(1/2) (a-b) (a-c) (b-c), 1/2 (a-b) (a-c) (b-c)}, 49457
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a^2+b^2+c^2))), 1/2 (a-b) (a-c) (b-c)}, 141
{-(1/2) (a-b) (a-c) (b-c), (a-b) (a-c) (b-c)}, 3696
{-(1/2) (a-b) (a-c) (b-c), 2 (a-b) (a-c) (b-c)}, 4686
{0, -((a-b) (a-c) (b-c))}, 49447
{0, 0}, 984
{0, 1/2 (a-b) (a-c) (b-c)}, 10
{0, (a-b) (a-c) (b-c)}, 75
{0, 2 (a-b) (a-c) (b-c)}, 49493
{1/2 (a-b) (a-c) (b-c), -(1/2) (a-b) (a-c) (b-c)}, 49456
{1/2 (a-b) (a-c) (b-c), 0}, 37
{1/2 (a-b) (a-c) (b-c), 1/2 (a-b) (a-c) (b-c)}, 24325
{1/2 (a-b) (a-c) (b-c), (a-b) (a-c) (b-c)}, 49483
{(a-b) (a-c) (b-c), -2 (a-b) (a-c) (b-c)}, 49445
{(a-b) (a-c) (b-c), -((2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2))}, 49446
{(a-b) (a-c) (b-c), -((a-b) (a-c) (b-c))}, 192
{(a-b) (a-c) (b-c), -(((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2))}, 49455
{(a-b) (a-c) (b-c), -(1/2) (a-b) (a-c) (b-c)}, 3993
{(a-b) (a-c) (b-c), -(((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a^2+b^2+c^2)))}, 49464
{(a-b) (a-c) (b-c), 0}, 1
{(a-b) (a-c) (b-c), 1/2 (a-b) (a-c) (b-c)}, 49479
{(a-b) (a-c) (b-c), ((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a^2+b^2+c^2))}, 49482
{(a-b) (a-c) (b-c), (a-b) (a-c) (b-c)}, 24349
{(a-b) (a-c) (b-c), ((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)}, 3923
{(a-b) (a-c) (b-c), (2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)}, 3729
{2 (a-b) (a-c) (b-c), -2 (a-b) (a-c) (b-c)}, 49452
{2 (a-b) (a-c) (b-c), -((a-b) (a-c) (b-c))}, 49470
{2 (a-b) (a-c) (b-c), -(1/2) (a-b) (a-c) (b-c)}, 3244
{2 (a-b) (a-c) (b-c), 0}, 49490
{2 (a-b) (a-c) (b-c), (a-b) (a-c) (b-c)}, 49499
{-2*(a - b)*(a - c)*(b - c), -((a - b)*(a - c)*(b - c))}, 49501
{(-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), -((a - b)*(a - c)*(b - c))}, 49502
{-2*(a - b)*(a - c)*(b - c), 0}, 49503
{-2*(a - b)*(a - c)*(b - c), ((a - b)*(a - c)*(b - c))/2}, 49504
{(-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), ((a - b)*(a - c)*(b - c))/2}, 49505
{(-2*(a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c), ((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c)}, 49506
{(-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), (2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49507
{-((a - b)*(a - c)*(b - c)), -1/2*((a - b)*(a - c)*(b - c))}, 49508
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)), 0}, 49509
{-((a - b)*(a - c)*(b - c)), ((a - b)*(a - c)*(b - c))/2}, 49510
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)), ((a - b)*(a - c)*(b - c))/2}, 49511
{-(((a - b)*(a - c)*(b - c)*(a^3 + b^3 + c^3))/((a + b)*(a + c)*(b + c))), ((a - b)*(a - c)*(b - c)*(a^3 + b^3 + c^3))/((a + b)*(a + c)*(b + c))}, 49512
{-1/2*((a - b)*(a - c)*(b - c)), -((a - b)*(a - c)*(b - c))}, 49513
{-1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c), -((a - b)*(a - c)*(b - c))}, 49514
{-1/2*((a - b)*(a - c)*(b - c)), 0}, 49515
{-1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c), ((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(2*(a*b + a*c + b*c))}, 49516
{0, -2*(a - b)*(a - c)*(b - c)}, 49517
{0, (-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49518
{0, -(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2))}, 49519
{0, -1/2*((a - b)*(a - c)*(b - c))}, 49520
{0, -1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c)}, 49521
{((a - b)*(a - c)*(b - c))/2, -2*(a - b)*(a - c)*(b - c)}, 49522
{((a - b)*(a - c)*(b - c))/2, -((a - b)*(a - c)*(b - c))}, 49523
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(2*(a^2 + b^2 + c^2)), ((a - b)*(a - c)*(b - c))/2}, 49524
{((a - b)*(a - c)*(b - c))/2, 2*(a - b)*(a - c)*(b - c)}, 49525
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), -(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2))}, 49526
{((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c), -1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c)}, 49527
{(a - b)*(a - c)*(b - c), ((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(2*(a*b + a*c + b*c))}, 49528
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), ((a - b)*(a - c)*(b - c))/2}, 49529
{(a - b)*(a - c)*(b - c), (a*(a - b)*b*(a - c)*(b - c)*c)/(a^3 + b^3 + c^3)}, 49530
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), (a - b)*(a - c)*(b - c)}, 49531
{(a - b)*(a - c)*(b - c), 2*(a - b)*(a - c)*(b - c)}, 49532
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), 2*(a - b)*(a - c)*(b - c)}, 49533
{(2*(a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c), -(((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c))}, 49534
{2*(a - b)*(a - c)*(b - c), ((a - b)*(a - c)*(b - c))/2}, 49535
{(2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), ((a - b)*(a - c)*(b - c))/2}, 49536


X(49501) = X(1)X(17336)∩X(144)X(145)

Barycentrics    2*a^2*b - 4*a*b^2 + 2*a^2*c - a*b*c + b^2*c - 4*a*c^2 + b*c^2 : :
X(49501) = 3 X[8] - 2 X[4686], 10 X[37] - 9 X[38314], 5 X[75] - 6 X[3679], 7 X[75] - 8 X[4732], 3 X[75] - 4 X[49457], 21 X[3679] - 20 X[4732], 3 X[3679] - 5 X[49448], 9 X[3679] - 10 X[49457], 4 X[4732] - 7 X[49448], 6 X[4732] - 7 X[49457], 3 X[49448] - 2 X[49457], 3 X[145] - 5 X[192], X[145] - 5 X[31302], 2 X[145] - 5 X[49447], 7 X[145] - 10 X[49462], 4 X[145] - 5 X[49470], 9 X[145] - 10 X[49475], X[192] - 3 X[31302], 2 X[192] - 3 X[49447], 7 X[192] - 6 X[49462], 4 X[192] - 3 X[49470], 3 X[192] - 2 X[49475], 7 X[31302] - 2 X[49462], 4 X[31302] - X[49470], 9 X[31302] - 2 X[49475], 7 X[49447] - 4 X[49462], 9 X[49447] - 4 X[49475], 8 X[49462] - 7 X[49470], 9 X[49462] - 7 X[49475], 9 X[49470] - 8 X[49475], 12 X[3625] - 5 X[4764], 4 X[3625] - 5 X[49450], 6 X[3625] - 5 X[49459], X[4764] - 3 X[49450], 3 X[49450] - 2 X[49459], 5 X[984] - 4 X[1125], 6 X[984] - 5 X[4687], 3 X[984] - 2 X[49479], 24 X[1125] - 25 X[4687], 6 X[1125] - 5 X[49479], 8 X[1125] - 5 X[49499], 5 X[4687] - 4 X[49479], 5 X[4687] - 3 X[49499], 4 X[49479] - 3 X[49499], 3 X[3241] - 4 X[4681], 6 X[3696] - 5 X[4821], 20 X[3739] - 21 X[9780], 4 X[3739] - 3 X[24349], 7 X[9780] - 5 X[24349], 3 X[4664] - 2 X[49490], 8 X[4746] - 5 X[49493], 7 X[4751] - 6 X[31178], 7 X[4772] - 6 X[49483]

X(49501) lies on these lines: {1, 17336}, {8, 4686}, {9, 24841}, {10, 48629}, {37, 38314}, {75, 537}, {144, 145}, {190, 16496}, {210, 24620}, {335, 29628}, {519, 3644}, {726, 3625}, {749, 984}, {982, 31233}, {3241, 4681}, {3242, 4676}, {3621, 28484}, {3632, 28516}, {3681, 17495}, {3696, 4821}, {3717, 21255}, {3739, 5772}, {3759, 49455}, {3873, 31035}, {3876, 34860}, {4429, 4899}, {4439, 17240}, {4664, 49490}, {4702, 25269}, {4746, 49493}, {4751, 31178}, {4772, 49483}, {5223, 32922}, {9041, 17334}, {17227, 33165}, {17249, 29659}, {17258, 36479}, {17261, 42871}, {17280, 47358}, {17302, 47359}, {17329, 33076}, {17350, 49465}, {17351, 36534}, {17361, 32847}, {17363, 28503}, {17449, 30829}, {18743, 42054}, {20050, 49461}, {21342, 27538}, {24821, 32941}, {26840, 30615}, {29587, 33888}, {30818, 32937}, {49449, 49474}, {49456, 49498}

X(49501) = reflection of X(i) in X(j) for these {i,j}: {75, 49448}, {4764, 49459}, {20050, 49461}, {49447, 31302}, {49470, 49447}, {49474, 49449}, {49498, 49456}, {49499, 984}
X(49501) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {984, 49479, 4687}, {4687, 49499, 49479}, {4764, 49450, 49459}


X(49502) = X(75)X(141)∩X(144)X(145)

Barycentrics    -2*a*b^3 + 3*a^2*b*c - 2*a*b^2*c + b^3*c - 2*a*b*c^2 - 2*a*c^3 + b*c^3 : :
X(49502) = 2 X[6] - 3 X[4664], 6 X[37] - 5 X[3618], 3 X[75] - 4 X[141], 3 X[192] - X[193], 2 X[193] - 3 X[49496], 3 X[3644] + 2 X[40341], 7 X[3619] - 6 X[4688], 5 X[3620] - 3 X[4740], 15 X[4687] - 14 X[47355], 5 X[4687] - 4 X[49481], 7 X[47355] - 6 X[49481], 3 X[20430] - 2 X[21850], 3 X[30273] - 2 X[46264], 3 X[32453] - 2 X[41622]

X(49502) lies on these lines: {6, 4664}, {9, 32029}, {37, 3618}, {69, 536}, {75, 141}, {144, 145}, {190, 16973}, {210, 26274}, {537, 3729}, {726, 4133}, {742, 3644}, {894, 3242}, {984, 4899}, {1278, 45789}, {3619, 4688}, {3620, 4373}, {3630, 17225}, {3726, 30758}, {3751, 49456}, {3868, 28598}, {3873, 31087}, {3889, 25263}, {3954, 39731}, {4431, 49493}, {4440, 47595}, {4687, 29614}, {5847, 49452}, {7229, 24349}, {9041, 17333}, {9053, 17363}, {16284, 33890}, {17339, 31349}, {17379, 49465}, {18440, 29010}, {20430, 21850}, {21342, 40883}, {30273, 46264}, {30946, 41794}, {31322, 36494}, {32453, 41622}, {39721, 42696}

X(49502) = reflection of X(i) in X(j) for these {i,j}: {3751, 49456}, {49496, 192}, {49499, 3242}


X(49503) = X(1)X(6)∩X(8)X(537)

Barycentrics    a*(2*a*b - 3*b^2 + 2*a*c - b*c - 3*c^2) : :
X(49503) = 5 X[1] - 6 X[37], 2 X[1] - 3 X[984], 11 X[1] - 12 X[15569], X[1] - 3 X[49448], 7 X[1] - 6 X[49478], 4 X[1] - 3 X[49490], 5 X[1] - 3 X[49498], 4 X[37] - 5 X[984], 11 X[37] - 10 X[15569], 2 X[37] - 5 X[49448], 7 X[37] - 5 X[49478], 8 X[37] - 5 X[49490], 11 X[984] - 8 X[15569], 7 X[984] - 4 X[49478], 5 X[984] - 2 X[49498], 4 X[15569] - 11 X[49448], 14 X[15569] - 11 X[49478], 16 X[15569] - 11 X[49490], 20 X[15569] - 11 X[49498], 7 X[49448] - 2 X[49478], 4 X[49448] - X[49490], 5 X[49448] - X[49498], 8 X[49478] - 7 X[49490], 10 X[49478] - 7 X[49498], 5 X[49490] - 4 X[49498], 5 X[8] - 3 X[4740], 3 X[4740] - 10 X[49449], 6 X[4740] - 5 X[49493], 4 X[49449] - X[49493], 4 X[10] - 3 X[31178], 3 X[31178] - 2 X[49499], 3 X[75] - 4 X[3626], 3 X[192] - X[20050], 10 X[3625] - 3 X[4764], 2 X[3625] - 3 X[49450], 4 X[3625] - 3 X[49459], X[4764] - 5 X[49450], 2 X[4764] - 5 X[49459], 5 X[3621] + 3 X[4788], X[3621] + 3 X[31302], X[4788] - 5 X[31302], 2 X[3244] - 3 X[4664], 25 X[3617] - 21 X[4772], 5 X[3617] - 3 X[24349], 5 X[3617] - 6 X[49457], 7 X[4772] - 5 X[24349], 7 X[4772] - 10 X[49457], 16 X[3634] - 15 X[40328], 4 X[3634] - 3 X[49479], 5 X[40328] - 4 X[49479], 3 X[3679] - 2 X[49483], 12 X[3842] - 11 X[5550], 3 X[4677] - 2 X[49468], 15 X[4687] - 14 X[15808], 5 X[4816] - 3 X[49474], 7 X[9780] - 6 X[24325], 2 X[11278] - 3 X[20430]

X(49503) lies on these lines: {1, 6}, {2, 49491}, {8, 537}, {10, 17227}, {38, 3240}, {43, 4003}, {75, 3626}, {145, 49456}, {190, 49458}, {192, 20050}, {210, 3999}, {319, 33869}, {335, 16816}, {519, 49447}, {536, 3632}, {726, 3625}, {740, 3621}, {756, 4430}, {846, 41711}, {899, 982}, {1054, 3711}, {3219, 17715}, {3244, 4664}, {3617, 4772}, {3633, 49462}, {3634, 40328}, {3678, 3976}, {3679, 49483}, {3715, 29820}, {3717, 33087}, {3759, 49464}, {3842, 5550}, {3873, 30950}, {3878, 42083}, {3935, 17601}, {3938, 7262}, {3951, 37588}, {3961, 4650}, {4005, 21214}, {4009, 31137}, {4392, 21805}, {4672, 36534}, {4677, 49468}, {4687, 15808}, {4693, 49451}, {4716, 49446}, {4722, 29815}, {4816, 28582}, {4847, 33101}, {4849, 17591}, {4863, 33099}, {4899, 33165}, {5217, 23085}, {5524, 17595}, {5695, 24821}, {7226, 17592}, {9330, 17450}, {9780, 24325}, {10453, 42054}, {11278, 20430}, {16569, 21342}, {16825, 24841}, {17018, 42039}, {17230, 31349}, {17347, 17766}, {17350, 49473}, {17363, 17769}, {17716, 32912}, {17755, 29579}, {20068, 32860}, {24231, 24393}, {24440, 34790}, {24697, 36479}, {25006, 33103}, {25539, 38047}, {26038, 42053}, {27474, 33888}, {27495, 29608}, {27538, 30948}, {28554, 31145}, {28581, 49445}, {29591, 31317}, {29595, 31323}, {29633, 47359}, {29637, 47358}, {29814, 42041}, {30615, 33085}, {30947, 42056}

X(49503) = reflection of X(i) in X(j) for these {i,j}: {8, 49449}, {145, 49456}, {984, 49448}, {3633, 49462}, {24349, 49457}, {49452, 49447}, {49459, 49450}, {49490, 984}, {49493, 8}, {49498, 37}, {49499, 10}
X(49503) = anticomplement of X(49491)
X(49503) = barycentric product X(1)*X(29577)
X(49503) = barycentric quotient X(29577)/X(75)
X(49503) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 49499, 31178}, {3935, 36263, 17601}, {4864, 15481, 15485}, {5223, 16496, 238}


X(49504) = X(8)X(4821)∩X(10)X(141)

Barycentrics    4*a^2*b - 5*a*b^2 + 4*a^2*c - 2*a*b*c - b^2*c - 5*a*c^2 - b*c^2 : :
X(49504) = 9 X[8] - 5 X[4821], 9 X[10] - 8 X[3739], 5 X[10] - 4 X[24325], X[10] - 4 X[49449], 3 X[10] - 4 X[49457], 3 X[10] - 2 X[49479], 7 X[10] - 4 X[49491], 10 X[3739] - 9 X[24325], 2 X[3739] - 9 X[49449], 2 X[3739] - 3 X[49457], 4 X[3739] - 3 X[49479], 14 X[3739] - 9 X[49491], X[24325] - 5 X[49449], 3 X[24325] - 5 X[49457], 6 X[24325] - 5 X[49479], 7 X[24325] - 5 X[49491], 3 X[49449] - X[49457], 6 X[49449] - X[49479], 7 X[49449] - X[49491], 7 X[49457] - 3 X[49491], 7 X[49479] - 6 X[49491], 2 X[75] - 3 X[4669], X[192] - 3 X[49448], 5 X[192] - 3 X[49469], 5 X[49448] - X[49469], 2 X[4686] - 3 X[4709], 4 X[4686] - 9 X[34641], 2 X[4709] - 3 X[34641], 9 X[551] - 10 X[4687], 3 X[551] - 2 X[49490], 5 X[4687] - 3 X[49490], 9 X[3625] - 2 X[4764], 3 X[3625] - 2 X[49459], X[4764] - 9 X[49450], X[4764] - 3 X[49459], 3 X[49450] - X[49459], X[1278] - 3 X[4677], 9 X[3679] - 7 X[4772], 8 X[3842] - 7 X[15808], 3 X[3993] - 2 X[49475], 5 X[4699] - 6 X[4745], 2 X[31178] - 3 X[38098]

X(49504) lies on these lines: {8, 4821}, {10, 141}, {75, 4669}, {192, 519}, {537, 4686}, {551, 4687}, {726, 3625}, {984, 3244}, {1125, 49498}, {1278, 4677}, {3621, 49445}, {3626, 24349}, {3632, 28522}, {3679, 4772}, {3681, 3840}, {3741, 4661}, {3842, 15808}, {3993, 49475}, {4090, 30818}, {4113, 42055}, {4134, 34587}, {4135, 17135}, {4685, 17495}, {4699, 4745}, {4701, 49474}, {4738, 20892}, {4753, 49465}, {4946, 46901}, {5223, 49458}, {17347, 28562}, {31035, 42057}, {31178, 38098}

X(49504) = midpoint of X(i) and X(j) for these {i,j}: {3621, 49445}, {3632, 31302}
X(49504) = reflection of X(i) in X(j) for these {i,j}: {3244, 984}, {3625, 49450}, {24349, 3626}, {49474, 4701}, {49479, 49457}, {49498, 1125}
X(49504) = {X(49457),X(49479)}-harmonic conjugate of X(10)


X(49505) = X(1)X(193)∩X(6)X(551)

Barycentrics    3*a^2*b - 4*a*b^2 - b^3 + 3*a^2*c - b^2*c - 4*a*c^2 - b*c^2 - c^3 : :
X(49505) = 3 X[1] - X[193], 2 X[6] - 3 X[551], 7 X[6] - 9 X[38023], X[6] - 3 X[47358], 7 X[551] - 6 X[38023], 3 X[38023] - 7 X[47358], 3 X[10] - 4 X[141], 7 X[10] - 8 X[3844], 7 X[10] - 6 X[38191], 7 X[141] - 6 X[3844], 14 X[141] - 9 X[38191], 4 X[3844] - 3 X[38191], 3 X[946] - 2 X[21850], 6 X[1125] - 5 X[3618], 5 X[3618] - 3 X[3751], 3 X[1386] - 2 X[32455], 3 X[1992] - 5 X[16491], 3 X[3241] + X[20080], 3 X[3242] + X[40341], 3 X[3244] + 2 X[40341], 8 X[3589] - 9 X[19883], 7 X[3619] - 6 X[3828], 5 X[3620] - 3 X[3679], 8 X[3631] - 3 X[34641], 4 X[3636] - 3 X[16475], 3 X[3655] - X[39899], 3 X[3656] - X[44456], 5 X[3763] - 3 X[47359], 9 X[3817] - 8 X[19130], 4 X[3818] - 3 X[34648], 3 X[4297] - 2 X[46264], 3 X[4663] - 4 X[6329], 4 X[4663] - 7 X[15808], 2 X[4663] - 3 X[38049], 16 X[6329] - 21 X[15808], 8 X[6329] - 9 X[38049], 7 X[15808] - 6 X[38049], 2 X[4745] - 3 X[21356], 3 X[5731] - X[39878], 3 X[10519] - 2 X[43174], 15 X[19862] - 14 X[47355], 3 X[34638] - 4 X[48881], X[47281] - 3 X[47593]

X(49505) lies on these lines: {1, 193}, {6, 551}, {8, 7613}, {10, 141}, {38, 4028}, {69, 519}, {226, 21242}, {319, 24841}, {354, 4104}, {511, 4301}, {515, 18440}, {516, 39898}, {524, 49465}, {527, 32941}, {528, 17345}, {537, 2321}, {545, 49485}, {599, 4669}, {726, 4133}, {946, 21850}, {984, 4684}, {1125, 3618}, {1266, 49459}, {1350, 5493}, {1351, 13464}, {1353, 15178}, {1386, 32455}, {1469, 3671}, {1738, 48629}, {1992, 16491}, {2801, 21629}, {3056, 4342}, {3241, 17247}, {3242, 3244}, {3416, 3625}, {3564, 5882}, {3589, 19883}, {3619, 3828}, {3620, 3679}, {3630, 28538}, {3631, 9041}, {3636, 16475}, {3655, 39899}, {3656, 44456}, {3664, 36480}, {3717, 33087}, {3763, 47359}, {3817, 19130}, {3818, 34648}, {3840, 21060}, {3878, 34381}, {3886, 28526}, {3912, 49448}, {3923, 5850}, {3938, 4001}, {3945, 48854}, {3946, 49497}, {3999, 4023}, {4054, 31136}, {4061, 24165}, {4067, 34378}, {4078, 4966}, {4084, 24476}, {4113, 40688}, {4138, 4847}, {4297, 46264}, {4310, 4402}, {4353, 49488}, {4357, 49490}, {4407, 5257}, {4429, 48637}, {4643, 42871}, {4655, 5853}, {4656, 42057}, {4663, 6329}, {4685, 24177}, {4702, 17334}, {4745, 21356}, {4899, 29674}, {4967, 31178}, {5224, 48853}, {5232, 48851}, {5233, 24216}, {5267, 22769}, {5731, 39878}, {5848, 33337}, {5852, 49484}, {9029, 23789}, {10222, 34380}, {10519, 43174}, {11362, 48876}, {11898, 37727}, {17145, 26580}, {17246, 49475}, {17272, 36479}, {17276, 28580}, {17332, 42819}, {17364, 36534}, {17372, 28503}, {17768, 49467}, {17771, 49473}, {17781, 32943}, {19862, 47355}, {24248, 49451}, {24349, 48628}, {24692, 47595}, {25006, 33069}, {25590, 48802}, {26015, 33065}, {28194, 33878}, {28236, 39885}, {31229, 33122}, {33082, 49466}, {34638, 48881}, {47281, 47593}, {48630, 49499}

X(49505) = midpoint of X(i) and X(j) for these {i,j}: {69, 16496}, {11898, 37727}, {17276, 49460}, {24248, 49451}
X(49505) = reflection of X(i) in X(j) for these {i,j}: {551, 47358}, {1351, 13464}, {1353, 15178}, {3244, 3242}, {3625, 3416}, {3751, 1125}, {4084, 24476}, {4669, 599}, {4780, 3663}, {5493, 1350}, {11362, 48876}, {49488, 4353}, {49497, 3946}
X(49505) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {142, 49457, 10}, {3836, 24393, 10}, {3836, 49449, 24393}, {3844, 38191, 10}, {4847, 33064, 4138}


X(49506) = X(1)X(141)∩X(8)X(238)

Barycentrics    2*a^3 - a^2*b + a*b^2 - b^3 - a^2*c - a*b*c - b^2*c + a*c^2 - b*c^2 - c^3 : :
X(49506) = 5 X[1] - 4 X[17390]

X(49506) lies on these lines: {1, 141}, {8, 238}, {9, 3632}, {10, 17352}, {31, 33090}, {43, 4030}, {55, 32855}, {75, 17766}, {145, 17343}, {192, 17769}, {306, 17715}, {319, 49458}, {390, 4693}, {516, 49493}, {519, 751}, {524, 49498}, {528, 49474}, {551, 25539}, {614, 33079}, {748, 33091}, {752, 24349}, {902, 33089}, {952, 6210}, {956, 7295}, {1001, 32847}, {1278, 17764}, {1279, 29674}, {1386, 29659}, {1423, 10944}, {1621, 32854}, {1756, 37707}, {2177, 32842}, {3052, 33167}, {3220, 5288}, {3242, 33082}, {3244, 4357}, {3625, 3717}, {3626, 17353}, {3633, 7174}, {3661, 49473}, {3679, 7290}, {3703, 8616}, {3722, 33077}, {3744, 4914}, {3749, 33160}, {3750, 33088}, {3757, 4865}, {3769, 29655}, {3775, 36534}, {3790, 4432}, {3844, 29660}, {3870, 32861}, {3891, 32947}, {3932, 15485}, {3938, 33075}, {3957, 32852}, {3961, 3966}, {4034, 16970}, {4344, 48849}, {4362, 4514}, {4365, 34611}, {4388, 32920}, {4389, 49464}, {4450, 17155}, {4649, 36479}, {4660, 32922}, {4677, 4901}, {4816, 15601}, {5014, 32865}, {5847, 49466}, {5853, 49459}, {5904, 9049}, {6327, 32923}, {7191, 33074}, {9053, 49448}, {10327, 17123}, {14829, 29844}, {15570, 17374}, {16020, 31252}, {16498, 19869}, {16825, 32850}, {17024, 32781}, {17127, 33162}, {17257, 20050}, {17364, 28498}, {17469, 29667}, {17591, 44419}, {17597, 33085}, {17598, 19993}, {17717, 26227}, {17722, 29828}, {17725, 20045}, {17726, 29825}, {17755, 29617}, {17763, 24217}, {17770, 49499}, {20064, 32940}, {24723, 49455}, {25957, 28599}, {27549, 31145}, {28337, 34747}, {28503, 49445}, {28512, 49479}, {28538, 49478}, {28566, 49483}, {29633, 38315}, {29638, 48647}, {29651, 33073}, {29670, 33071}, {29818, 33172}, {29832, 32917}, {29840, 32916}, {31134, 33148}

X(49506) = reflection of X(i) in X(j) for these {i,j}: {984, 3883}, {3632, 17362}, {17364, 49491}, {17377, 3244}, {49490, 49466}
X(49506) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3416, 33087}, {1, 33076, 32784}, {8, 238, 33165}, {31, 33090, 33169}, {55, 32866, 32855}, {1621, 32854, 33092}, {3679, 7290, 33159}, {3744, 4914, 32778}, {3757, 4865, 33111}, {3891, 32947, 33154}, {3938, 33075, 33084}, {4362, 4514, 33141}, {4388, 32920, 33101}, {4660, 32922, 33149}, {5014, 32914, 32865}, {6327, 32923, 33103}, {7191, 33074, 33174}, {19993, 26034, 17598}, {20045, 25760, 17725}, {26227, 32844, 17717}


X(49507) = X(8)X(192)∩X(75)X(142)

Barycentrics    a^2*b^2 - a*b^3 + 3*a^2*b*c - 2*a*b^2*c + a^2*c^2 - 2*a*b*c^2 - 2*b^2*c^2 - a*c^3 : :
X(49507) = 2 X[75] - 3 X[27474], 4 X[2321] - 3 X[27474], 4 X[3739] - 5 X[17286], 4 X[3946] - 5 X[4687], 4 X[4527] - X[49493], 5 X[4704] - 3 X[27480], 3 X[17281] - 2 X[49481}

X(49507) lies on these lines: {8, 192}, {37, 3875}, {75, 142}, {85, 7201}, {335, 1278}, {346, 17755}, {518, 3729}, {519, 49496}, {536, 599}, {594, 24357}, {726, 4133}, {742, 17299}, {894, 32941}, {982, 17759}, {1921, 4110}, {3061, 17144}, {3161, 27484}, {3687, 20173}, {3693, 17026}, {3722, 17002}, {3739, 17267}, {3760, 4006}, {3773, 48628}, {3913, 17739}, {3930, 4441}, {3936, 27479}, {3946, 4687}, {3970, 32104}, {3986, 31322}, {4032, 6604}, {4054, 27491}, {4085, 17248}, {4416, 5853}, {4461, 24349}, {4527, 49493}, {4664, 17133}, {4673, 17760}, {4699, 29627}, {4704, 27480}, {4713, 20693}, {4898, 31342}, {16777, 25384}, {16823, 17319}, {16998, 17715}, {17135, 25249}, {17158, 30038}, {17247, 27495}, {17281, 49481}, {17363, 17765}, {17379, 49473}, {20073, 49449}, {21070, 33937}, {28604, 40328}, {31087, 32915}, {49466, 49470}

X(49507) = reflection of X(i) in X(j) for these {i,j}: {75, 2321}, {3875, 37}, {49490, 32941}
X(49507) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 2321, 27474}, {75, 17240, 27487}, {75, 27475, 24199}


X(49508) = X(8)X(726)∩X(10)X(537)

Barycentrics    2*a^2*b - 5*a*b^2 + 2*a^2*c - 2*a*b*c + b^2*c - 5*a*c^2 + b*c^2 : :
X(49508) = 7 X[8] - 3 X[1278], 4 X[8] - 3 X[4709], X[8] + 3 X[31302], X[8] - 3 X[49448], 5 X[8] - 3 X[49474], 4 X[1278] - 7 X[4709], X[1278] + 7 X[31302], X[1278] - 7 X[49448], 5 X[1278] - 7 X[49474], X[4709] + 4 X[31302], X[4709] - 4 X[49448], 5 X[4709] - 4 X[49474], 5 X[31302] + X[49474], 5 X[49448] - X[49474], 7 X[10] - 6 X[4688], 3 X[10] - 2 X[49483], 9 X[4688] - 7 X[49483], 3 X[75] - 4 X[4691], 3 X[192] - X[3633], 2 X[3244] - 3 X[3993], 7 X[3244] - 12 X[4681], 5 X[3244] - 6 X[49471], 7 X[3993] - 8 X[4681], 3 X[3993] - 4 X[49456], 5 X[3993] - 4 X[49471], 6 X[4681] - 7 X[49456], 10 X[4681] - 7 X[49471], 5 X[49456] - 3 X[49471], 3 X[49447] - X[49452], 3 X[551] - 2 X[49491], 3 X[984] - 2 X[1125], 7 X[984] - 5 X[4687], 3 X[984] - X[49499], 14 X[1125] - 15 X[4687], 4 X[1125] - 3 X[49479], 10 X[4687] - 7 X[49479], 15 X[4687] - 7 X[49499], 3 X[49479] - 2 X[49499], 5 X[1698] - 3 X[24349], 5 X[3623] - 3 X[49498], 4 X[3634] - 3 X[31178], 2 X[3635] - 3 X[4664], 5 X[4668] - 3 X[4740], X[20014] - 3 X[49469], 3 X[34641] - 2 X[49468]

X(49508) lies on these lines: {1, 4759}, {8, 726}, {10, 537}, {37, 15828}, {38, 4090}, {75, 4691}, {192, 3633}, {518, 3244}, {519, 49447}, {536, 3625}, {551, 49491}, {749, 984}, {1698, 17291}, {1757, 49464}, {3623, 49498}, {3626, 49493}, {3634, 31178}, {3635, 4664}, {3821, 4899}, {3840, 4009}, {3971, 29824}, {3999, 42056}, {4096, 21342}, {4135, 4519}, {4661, 4970}, {4668, 4740}, {4753, 49463}, {5223, 49455}, {7174, 33682}, {17165, 30970}, {17292, 33888}, {17334, 17765}, {17347, 28512}, {20014, 49469}, {20068, 24165}, {25501, 42041}, {28522, 49450}, {28554, 34641}, {28582, 49457}, {29596, 31349}, {29827, 32937}, {42039, 43223}

X(49508) = midpoint of X(31302) and X(49448)
X(49508) = reflection of X(i) in X(j) for these {i,j}: {3244, 49456}, {3625, 49449}, {49479, 984}, {49493, 3626}, {49499, 1125}
X(49508) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {984, 49499, 1125}, {1125, 49499, 49479}, {3244, 49456, 3993}


X(49509) = X(1)X(6)∩X(2)X(3726)

Barycentrics    a*(-b^3 + a*b*c - b^2*c - b*c^2 - c^3) : :
X(49509) = 4 X[15569] - 3 X[38315], X[193] - 5 X[4704], 3 X[4664] - X[49496], X[1278] - 5 X[3620], X[3779] - 3 X[19586], 4 X[3589] - 5 X[4687], 5 X[3618] - 7 X[27268], 7 X[3619] - 5 X[4699], 4 X[3631] + X[3644], 4 X[3739] - 5 X[3763], 4 X[3842] - 3 X[38047], 4 X[4681] + X[40341], 2 X[4688] - 3 X[21358], 8 X[4698] - 7 X[47355], X[4740] - 3 X[21356], 7 X[4751] - 8 X[34573], 4 X[4755] - 3 X[47352], 4 X[17229] - 3 X[27474], 2 X[30271] - 3 X[31884]

X(49509) lies on these lines: {1, 6}, {2, 3726}, {8, 3721}, {10, 20271}, {38, 2276}, {42, 41269}, {43, 20693}, {63, 17735}, {69, 192}, {75, 141}, {78, 21008}, {86, 4469}, {145, 3727}, {172, 976}, {193, 4704}, {210, 3290}, {257, 24524}, {321, 4485}, {341, 21025}, {346, 31302}, {511, 20430}, {519, 3735}, {524, 4664}, {536, 599}, {537, 17281}, {612, 40750}, {674, 21829}, {698, 17762}, {712, 33936}, {726, 2321}, {732, 32453}, {740, 3416}, {762, 1698}, {982, 1575}, {986, 20691}, {997, 9259}, {1030, 2870}, {1278, 3620}, {1352, 29010}, {1469, 2171}, {1503, 30273}, {1574, 24046}, {1761, 2076}, {1914, 3938}, {1921, 30473}, {1953, 20706}, {2160, 41454}, {2178, 12329}, {2238, 3681}, {2242, 30115}, {2275, 33299}, {2277, 3949}, {2294, 3728}, {2295, 3868}, {2310, 3056}, {2345, 24349}, {2876, 3688}, {2887, 4119}, {3125, 3679}, {3263, 30945}, {3509, 3961}, {3589, 4687}, {3617, 21951}, {3618, 27268}, {3619, 4699}, {3631, 3644}, {3670, 4006}, {3722, 10987}, {3739, 3763}, {3741, 21101}, {3744, 21793}, {3774, 4261}, {3782, 21956}, {3797, 17233}, {3811, 18755}, {3842, 38047}, {3863, 4451}, {3873, 24512}, {3874, 17750}, {3927, 14974}, {3943, 49447}, {3976, 16604}, {3985, 42054}, {3993, 5847}, {4007, 49474}, {4037, 32925}, {4043, 24077}, {4060, 4709}, {4071, 33064}, {4331, 12588}, {4357, 24357}, {4385, 21024}, {4390, 49454}, {4392, 17756}, {4415, 20173}, {4445, 18179}, {4517, 17464}, {4526, 47329}, {4652, 39255}, {4661, 37657}, {4662, 16605}, {4681, 29605}, {4688, 21358}, {4698, 29603}, {4727, 49452}, {4740, 21356}, {4751, 29608}, {4755, 47352}, {4799, 20553}, {4967, 27478}, {5011, 36283}, {5096, 21773}, {5224, 27495}, {5277, 17736}, {5718, 27491}, {5750, 49479}, {5845, 17334}, {5846, 17388}, {7064, 20455}, {7077, 7237}, {7201, 24471}, {8193, 21771}, {8558, 16283}, {9041, 17330}, {9053, 17362}, {10387, 11997}, {10436, 25384}, {12607, 21965}, {16583, 34790}, {17053, 21830}, {17137, 28598}, {17225, 22165}, {17229, 27474}, {17232, 27487}, {17242, 27481}, {17245, 27475}, {17275, 49457}, {17276, 33869}, {17277, 32029}, {17279, 17755}, {17280, 33888}, {17289, 31317}, {17303, 24325}, {17342, 31349}, {17369, 49499}, {17456, 32854}, {17737, 33153}, {17792, 24341}, {18055, 26801}, {18189, 33297}, {18208, 19584}, {20275, 25748}, {20483, 25957}, {20692, 37555}, {20947, 31028}, {20955, 33890}, {21070, 24068}, {21240, 33937}, {21342, 44798}, {21853, 24476}, {21868, 24440}, {22230, 24528}, {24575, 41531}, {25129, 25504}, {27476, 31017}, {27484, 37650}, {28606, 37676}, {30271, 31884}, {30412, 36491}, {30413, 36492}, {30941, 31087}, {31027, 33931}, {36263, 41423}, {47359, 48822}

X(49509) = midpoint of X(i) and X(j) for these {i,j}: {69, 192}, {16496, 49448}
X(49509) = reflection of X(i) in X(j) for these {i,j}: {6, 37}, {75, 141}, {49490, 49465}
X(49509) = anticomplement of X(49481)
X(49509) = Moses-circle-inverse of X(1925)
X(49509) = X(30965)-Ceva conjugate of X(29674)
X(49509) = crosspoint of X(29674) and X(36482)
X(49509) = crosssum of X(6) and X(37590)
X(49509) = barycentric product X(i)*X(j) for these {i,j}: {1, 29674}, {9, 36482}, {37, 30965}
X(49509) = barycentric quotient X(i)/X(j) for these {i,j}: {29674, 75}, {30965, 274}, {36482, 85}
X(49509) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 3721, 3959}, {9, 16496, 16973}, {9, 16973, 6}, {38, 3930, 2276}, {210, 3290, 37673}, {3247, 3751, 16972}, {3509, 3961, 4386}, {3681, 26242, 2238}, {3751, 16972, 6}, {3874, 28594, 17750}, {3938, 5282, 1914}


X(49510) = X(8)X(726)∩X(10)X(141)

Barycentrics    2*a^2*b - 3*a*b^2 + 2*a^2*c - 2*a*b*c - b^2*c - 3*a*c^2 - b*c^2 : :
X(49510) = 5 X[1] - 7 X[27268], 5 X[8] - X[1278], 3 X[8] + X[31302], 3 X[8] - X[49474], 2 X[1278] - 5 X[4709], 3 X[1278] + 5 X[31302], X[1278] + 5 X[49448], 3 X[1278] - 5 X[49474], 3 X[4709] + 2 X[31302], X[4709] + 2 X[49448], 3 X[4709] - 2 X[49474], X[31302] - 3 X[49448], 3 X[49448] + X[49474], 5 X[10] - 4 X[3739], 3 X[10] - 2 X[24325], X[10] + 2 X[49449], 5 X[10] - 2 X[49491], 6 X[3739] - 5 X[24325], 2 X[3739] + 5 X[49449], 2 X[3739] - 5 X[49457], 8 X[3739] - 5 X[49479], X[24325] + 3 X[49449], X[24325] - 3 X[49457], 4 X[24325] - 3 X[49479], 5 X[24325] - 3 X[49491], 3 X[38191] - 2 X[49481], 4 X[49449] + X[49479], 5 X[49449] + X[49491], 4 X[49457] - X[49479], 5 X[49457] - X[49491], 5 X[49479] - 4 X[49491], 5 X[984] - 3 X[4664], 3 X[984] - X[49470], 5 X[3993] - 6 X[4664], X[3993] + 2 X[49450], 3 X[3993] - 2 X[49470], 3 X[4664] + 5 X[49450], 9 X[4664] - 5 X[49470], 3 X[49450] + X[49470], 2 X[3696] - 3 X[4669], 3 X[551] - 4 X[3842], 3 X[551] - 2 X[49478], 5 X[3625] + 2 X[4718], 4 X[3636] - 5 X[4687], 3 X[3679] - X[24349], 6 X[3828] - 5 X[40328], 3 X[4677] + X[49445], 2 X[4688] - 3 X[38098], 4 X[4691] - X[49499], 8 X[4698] - 7 X[15808], 2 X[4701] + X[49447], 5 X[4704] - X[20050], 4 X[4746] - X[49493]

X(49510) lies on these lines: {1, 4991}, {2, 49498}, {8, 726}, {9, 49458}, {10, 141}, {37, 3244}, {38, 4685}, {44, 49473}, {75, 3626}, {192, 3632}, {210, 3840}, {239, 49464}, {519, 751}, {536, 34641}, {537, 3696}, {551, 3842}, {668, 21443}, {740, 3625}, {756, 42057}, {1125, 17352}, {1386, 4753}, {1757, 49482}, {2550, 24692}, {3243, 24331}, {3621, 49469}, {3636, 4687}, {3679, 24349}, {3681, 3741}, {3706, 4135}, {3751, 33682}, {3828, 40328}, {3896, 42039}, {3923, 5223}, {3952, 31136}, {3971, 17135}, {3989, 20011}, {4015, 46827}, {4026, 4407}, {4042, 32920}, {4104, 29655}, {4416, 17766}, {4430, 26037}, {4432, 15481}, {4457, 42051}, {4533, 25079}, {4651, 17154}, {4661, 31330}, {4667, 25384}, {4677, 49445}, {4688, 38098}, {4690, 9055}, {4691, 49499}, {4698, 15808}, {4701, 28522}, {4703, 4863}, {4704, 20050}, {4732, 49483}, {4743, 17246}, {4745, 31178}, {4746, 49493}, {4849, 6682}, {4924, 25354}, {4946, 46904}, {4970, 7226}, {4974, 49465}, {4981, 43223}, {5220, 32941}, {5267, 15624}, {5524, 24627}, {7174, 49488}, {8666, 34247}, {14555, 29844}, {16468, 36534}, {16496, 16825}, {17023, 27495}, {17145, 30950}, {17284, 27484}, {17334, 17764}, {17347, 28508}, {17362, 17769}, {17448, 21830}, {17755, 29594}, {19998, 46901}, {20055, 27481}, {20430, 28234}, {21241, 33065}, {21805, 46909}, {25006, 33064}, {27475, 31211}, {28236, 30273}, {28516, 49468}, {28581, 49456}, {29010, 47745}, {29574, 31323}, {29610, 31314}, {29615, 33888}

X(49510) = midpoint of X(i) and X(j) for these {i,j}: {8, 49448}, {192, 3632}, {984, 49450}, {3621, 49469}, {31302, 49474}, {49447, 49459}, {49449, 49457}
X(49510) = reflection of X(i) in X(j) for these {i,j}: {10, 49457}, {75, 3626}, {3244, 37}, {3993, 984}, {4667, 25384}, {4709, 8}, {31178, 4745}, {49459, 4701}, {49478, 3842}, {49479, 10}, {49483, 4732}, {49490, 1125}, {49491, 3739}
X(49510) = complement of X(49498)
X(49510) = crossdifference of every pair of points on line {21007, 23472}
X(49510) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 31302, 49474}, {3681, 3741, 4090}, {3706, 42054, 4135}, {3751, 36480, 33682}, {3842, 49478, 551}, {15481, 49467, 4432}, {21255, 38210, 10}, {49448, 49474, 31302}


X(49511) = X(1)X(69)∩X(10)X(141)

Barycentrics    a^2*b - 2*a*b^2 - b^3 + a^2*c - b^2*c - 2*a*c^2 - b*c^2 - c^3 : :
X(49511) = 4 X[2] - 3 X[38089], 4 X[3751] - 9 X[38089], 4 X[5] - 3 X[38146], 2 X[6] - 3 X[38049], 4 X[1125] - 3 X[38049], X[8] - 5 X[3620], 5 X[3620] + X[16496], 3 X[10] - 4 X[3844], 4 X[10] - 3 X[38191], 3 X[141] - 2 X[3844], 8 X[141] - 3 X[38191], 4 X[142] - 3 X[38187], 16 X[3844] - 9 X[38191], X[40] - 3 X[10519], 3 X[10519] + X[39898], 4 X[140] - 3 X[38118], 2 X[182] - 3 X[10165], X[193] - 5 X[3616], X[193] - 3 X[16475], 5 X[3616] - 3 X[16475], 3 X[599] + X[3242], 3 X[599] - X[3416], X[3242] - 3 X[47358], X[3416] + 3 X[47358], 3 X[17301] - X[49486], 3 X[551] - 2 X[1386], 2 X[3773] - 3 X[29594], 2 X[597] - 3 X[19883], X[1351] - 3 X[5886], X[1353] - 3 X[38028], 5 X[1698] - 7 X[3619], X[1992] - 3 X[25055], X[3244] + 4 X[3631], 2 X[3631] + X[49465], 3 X[3576] - X[6776], 4 X[3589] - 5 X[19862], 2 X[4663] - 5 X[19862], 5 X[3618] - 7 X[3624], 7 X[3622] - 5 X[16491], 7 X[3622] + X[20080], 5 X[16491] + X[20080], 4 X[3628] - 3 X[38167], 2 X[3629] - 7 X[15808], 4 X[3634] - 5 X[3763], 4 X[3634] - 3 X[38047], 5 X[3763] - 3 X[38047], 4 X[3636] - 3 X[38315], 4 X[3636] + X[40341], 3 X[38315] + X[40341], X[3679] - 3 X[21356], 3 X[3817] - 2 X[5480], 2 X[3828] - 3 X[21358], 3 X[21358] - X[47359], X[3886] + 3 X[17274], 3 X[17274] - X[24248], X[4780] - 4 X[17235], 3 X[5587] - 5 X[40330], 3 X[5731] + X[5921], X[5882] + 2 X[34507], 4 X[6666] - 3 X[38194], 4 X[6667] - 3 X[38197], 4 X[6668] - 3 X[38198], 5 X[7987] - 3 X[25406], 5 X[7987] - X[39878], 3 X[25406] - X[39878], 5 X[8227] - 3 X[14853], 3 X[10175] - 4 X[24206], 3 X[10246] + X[11898], 3 X[10516] - 2 X[19925], X[10754] - 3 X[38220], X[10755] - 3 X[16173], X[11160] + 3 X[38314], 3 X[11230] - 2 X[18583], X[11362] - 4 X[40107], X[11477] - 3 X[38035], 2 X[12512] - 3 X[31884], X[15534] - 3 X[38023], 3 X[17294] + X[49446], 5 X[17304] - X[49495], 5 X[18493] - X[44456], 8 X[19878] - 7 X[47355]

X(49511) lies on these lines: {1, 69}, {2, 3751}, {3, 39877}, {4, 39553}, {5, 38146}, {6, 1125}, {8, 1738}, {10, 141}, {31, 4001}, {37, 4966}, {38, 306}, {40, 10519}, {46, 29747}, {63, 33171}, {72, 34378}, {75, 24231}, {140, 38118}, {145, 17236}, {182, 10165}, {193, 3616}, {210, 20455}, {214, 5848}, {226, 1469}, {238, 4416}, {307, 1458}, {319, 32922}, {320, 5263}, {333, 33124}, {354, 1211}, {391, 16020}, {511, 946}, {515, 1352}, {516, 1350}, {517, 48876}, {519, 599}, {524, 551}, {527, 3923}, {528, 49467}, {536, 4133}, {537, 3773}, {542, 11709}, {553, 3980}, {579, 5227}, {594, 49483}, {597, 19883}, {611, 13411}, {613, 44675}, {614, 5739}, {726, 2321}, {730, 14994}, {740, 3663}, {742, 3993}, {752, 49473}, {758, 24476}, {896, 35263}, {908, 30942}, {944, 39885}, {950, 12589}, {960, 34381}, {966, 38053}, {971, 21629}, {982, 3687}, {984, 3912}, {990, 28849}, {993, 9028}, {1001, 4643}, {1086, 3696}, {1150, 3011}, {1193, 4101}, {1201, 15983}, {1213, 39580}, {1266, 49474}, {1279, 17344}, {1319, 39897}, {1351, 5886}, {1353, 38028}, {1385, 3564}, {1503, 4297}, {1654, 16823}, {1698, 3619}, {1757, 17353}, {1829, 41584}, {1992, 25055}, {2092, 37592}, {2308, 29686}, {2646, 39873}, {2801, 12618}, {2809, 4523}, {2810, 3038}, {2854, 13605}, {2886, 4138}, {2887, 4847}, {2895, 7191}, {3006, 31017}, {3056, 12053}, {3098, 31730}, {3120, 31136}, {3218, 33175}, {3219, 33173}, {3243, 36479}, {3244, 3631}, {3315, 31143}, {3454, 10916}, {3576, 6776}, {3589, 4663}, {3612, 39900}, {3618, 3624}, {3622, 16491}, {3625, 9053}, {3628, 38167}, {3629, 15808}, {3634, 3763}, {3636, 38315}, {3661, 24349}, {3664, 19868}, {3666, 4028}, {3671, 24471}, {3679, 21356}, {3681, 33172}, {3685, 6646}, {3686, 16825}, {3706, 3782}, {3717, 29674}, {3736, 16887}, {3742, 5743}, {3757, 37653}, {3771, 5745}, {3786, 30965}, {3789, 30945}, {3790, 17230}, {3817, 5480}, {3818, 31673}, {3827, 3878}, {3828, 21358}, {3831, 21075}, {3837, 9032}, {3842, 4407}, {3846, 11019}, {3870, 26034}, {3873, 32782}, {3886, 17274}, {3914, 17135}, {3920, 32863}, {3932, 17231}, {3935, 33086}, {3936, 29639}, {3938, 33080}, {3946, 49488}, {3950, 49456}, {3957, 33083}, {3961, 33085}, {3966, 17597}, {3976, 17065}, {3977, 33156}, {3996, 33068}, {4023, 16610}, {4026, 17237}, {4035, 29671}, {4042, 24789}, {4046, 42051}, {4054, 32856}, {4061, 24177}, {4062, 46901}, {4067, 9021}, {4082, 42054}, {4129, 9040}, {4259, 12609}, {4301, 31779}, {4307, 21296}, {4334, 9436}, {4356, 49471}, {4364, 15569}, {4389, 49470}, {4392, 33077}, {4417, 24239}, {4422, 15481}, {4425, 42057}, {4429, 17227}, {4430, 29667}, {4431, 49493}, {4432, 5845}, {4438, 20106}, {4441, 40030}, {4527, 28516}, {4645, 17288}, {4648, 39586}, {4649, 17023}, {4660, 5853}, {4661, 29679}, {4667, 33682}, {4669, 9041}, {4672, 17771}, {4676, 17347}, {4683, 32943}, {4685, 24169}, {4688, 4733}, {4690, 25357}, {4700, 4989}, {4703, 40998}, {4709, 4923}, {4715, 48810}, {4753, 31191}, {4780, 17235}, {4871, 5316}, {4892, 21242}, {4899, 33165}, {4981, 18139}, {5121, 5233}, {5220, 17279}, {5223, 17284}, {5232, 11038}, {5248, 36740}, {5249, 31330}, {5268, 18141}, {5272, 14555}, {5294, 24943}, {5361, 29681}, {5372, 29665}, {5552, 27305}, {5587, 40330}, {5695, 17276}, {5708, 5955}, {5731, 5921}, {5850, 17355}, {5852, 17351}, {5880, 7232}, {5882, 34507}, {5901, 34380}, {5965, 12266}, {5969, 11599}, {6173, 48802}, {6666, 38194}, {6667, 38197}, {6668, 38198}, {6789, 16504}, {7174, 17296}, {7226, 32858}, {7289, 12514}, {7292, 37656}, {7987, 25406}, {8227, 14853}, {8263, 44662}, {8299, 24690}, {8679, 21616}, {8896, 40959}, {9001, 48295}, {9004, 10176}, {9015, 48284}, {9024, 21630}, {9037, 11813}, {9052, 17792}, {9534, 24178}, {9583, 39876}, {9780, 27147}, {9791, 17254}, {9955, 21850}, {10106, 12588}, {10175, 24206}, {10246, 11898}, {10371, 37549}, {10387, 12575}, {10449, 13161}, {10453, 24210}, {10479, 13407}, {10516, 19925}, {10754, 38220}, {10755, 16173}, {11160, 38314}, {11230, 18583}, {11362, 40107}, {11365, 37491}, {11477, 38035}, {11679, 33144}, {11725, 14645}, {12259, 34382}, {12261, 14984}, {12329, 25440}, {12512, 31884}, {12586, 17647}, {12610, 29311}, {12699, 33878}, {13405, 32916}, {13624, 48906}, {14829, 33126}, {15254, 17332}, {15534, 38023}, {15585, 40660}, {15988, 24541}, {16468, 29660}, {16484, 24697}, {16704, 26230}, {16830, 17300}, {17030, 20139}, {17064, 26132}, {17145, 29835}, {17156, 19785}, {17228, 49499}, {17229, 28582}, {17233, 49447}, {17246, 49462}, {17273, 24723}, {17294, 49446}, {17299, 49453}, {17304, 49495}, {17345, 17768}, {17367, 26150}, {17372, 49463}, {17421, 17441}, {17448, 18904}, {17598, 32861}, {17625, 26942}, {17718, 37660}, {17733, 34937}, {17770, 49482}, {17772, 49472}, {17781, 32930}, {17794, 31027}, {18183, 21081}, {18358, 18480}, {18417, 41718}, {18440, 18481}, {18483, 31670}, {18493, 44456}, {19843, 25521}, {19861, 25023}, {19878, 47355}, {20456, 28288}, {21085, 24165}, {22165, 28538}, {22174, 46190}, {24552, 32859}, {24597, 29855}, {24603, 40328}, {25006, 25957}, {25527, 33137}, {25697, 33337}, {25760, 26015}, {26083, 29613}, {26128, 32853}, {26580, 29824}, {26723, 32864}, {26840, 32932}, {27549, 29579}, {28146, 48874}, {28150, 48873}, {28158, 48872}, {28160, 39884}, {28164, 36990}, {28530, 49485}, {29596, 33159}, {29634, 37683}, {29648, 37685}, {29652, 32946}, {29659, 49498}, {29831, 31303}, {29839, 38000}, {30768, 33114}, {31211, 38186}, {32029, 42334}, {32331, 44668}, {32775, 32919}, {32783, 32913}, {32784, 49490}, {32846, 49476}, {32942, 33066}, {32945, 33067}, {33076, 49466}, {33149, 49459}, {33169, 39597}, {34648, 47354}, {37618, 39901}, {37676, 43223}, {47551, 47593}

X(49511) = midpoint of X(i) and X(j) for these {i,j}: {1, 69}, {8, 16496}, {40, 39898}, {599, 47358}, {944, 39885}, {1469, 10477}, {3242, 3416}, {3886, 24248}, {4655, 32941}, {4660, 49458}, {5695, 17276}, {12699, 33878}, {17299, 49453}, {17345, 49484}, {17372, 49463}, {18440, 18481}, {47551, 47593}
X(49511) = reflection of X(i) in X(j) for these {i,j}: {6, 1125}, {10, 141}, {3244, 49465}, {3755, 3821}, {4663, 3589}, {13605, 32238}, {18480, 18358}, {21850, 9955}, {31670, 18483}, {31673, 3818}, {31730, 3098}, {32921, 4353}, {32935, 17355}, {34648, 47354}, {39870, 1385}, {40660, 15585}, {47359, 3828}, {48906, 13624}, {49488, 3946}
X(49511) = complement of X(3751)
X(49511) = complement of the isogonal conjugate of X(39954)
X(49511) = complement of the isotomic conjugate of X(40028)
X(49511) = X(i)-complementary conjugate of X(j) for these (i,j): {28847, 514}, {39721, 141}, {39954, 10}, {40028, 2887}
X(49511) = crosspoint of X(2) and X(40028)
X(49511) = crossdifference of every pair of points on line {2484, 21007}
X(49511) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 33082, 3883}, {6, 1125, 38049}, {8, 3662, 1738}, {10, 5542, 24325}, {10, 21255, 3836}, {38, 33081, 306}, {193, 3616, 16475}, {599, 3242, 3416}, {982, 33084, 3687}, {984, 3912, 4078}, {984, 33087, 3912}, {1150, 33122, 3011}, {1757, 29637, 17353}, {3416, 47358, 3242}, {3741, 33064, 226}, {3763, 38047, 3634}, {3775, 24325, 10}, {3836, 49457, 10}, {3886, 17274, 24248}, {3936, 46909, 29639}, {4357, 4684, 1}, {5232, 11038, 39581}, {7987, 39878, 25406}, {10453, 27184, 24210}, {10519, 39898, 40}, {17135, 17184, 3914}, {17227, 49450, 4429}, {17230, 31302, 3790}, {17237, 49478, 4026}, {21358, 47359, 3828}, {24552, 32859, 41011}, {24943, 32912, 5294}, {26128, 32853, 40940}, {29674, 49448, 3717}, {30942, 33065, 908}, {31330, 33069, 5249}, {32864, 33123, 26723}, {33156, 36263, 3977}


X(49512) = X(8)X(192)∩X(21)X(75)

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

X(49512) lies on these lines: {8, 192}, {21, 75}, {37, 5051}, {92, 11688}, {306, 3993}, {321, 4199}, {846, 5271}, {1001, 35550}, {1281, 1283}, {1284, 1441}, {1621, 20896}, {1962, 29839}, {2294, 4645}, {3145, 4812}, {3685, 18697}, {3705, 25080}, {3923, 11320}, {4016, 24723}, {4137, 32947}, {4195, 32117}, {4220, 30273}, {4359, 8731}, {4647, 5251}, {6872, 17164}, {8680, 24349}, {9840, 29010}, {11533, 49469}, {12579, 28522}, {16823, 18698}, {21020, 33115}, {23689, 26237}


X(49513) = X(8)X(4764)∩X(144)X(145)

Barycentrics    a^2*b - 5*a*b^2 + a^2*c - 2*a*b*c + 2*b^2*c - 5*a*c^2 + 2*b*c^2 : :
X(49513) = 3 X[8] - X[4764], 7 X[37] - 6 X[551], 3 X[37] - 2 X[49479], 9 X[551] - 7 X[49479], 3 X[145] - 7 X[192], X[145] + 7 X[31302], X[145] - 7 X[49447], 4 X[145] - 7 X[49462], 5 X[145] - 7 X[49470], 6 X[145] - 7 X[49475], X[192] + 3 X[31302], X[192] - 3 X[49447], 4 X[192] - 3 X[49462], 5 X[192] - 3 X[49470], 4 X[31302] + X[49462], 5 X[31302] + X[49470], 6 X[31302] + X[49475], 4 X[49447] - X[49462], 5 X[49447] - X[49470], 6 X[49447] - X[49475], 5 X[49462] - 4 X[49470], 3 X[49462] - 2 X[49475], 6 X[49470] - 5 X[49475], 3 X[4677] - 7 X[49448], 9 X[4677] - 7 X[49459], 3 X[49448] - X[49459], 8 X[3626] - 7 X[3696], 12 X[3626] - 7 X[4686], 6 X[3626] - 7 X[49457], 3 X[3696] - 2 X[4686], 3 X[3696] - 4 X[49457], 7 X[984] - 5 X[1698], 3 X[984] - 2 X[3739], 15 X[1698] - 14 X[3739], 10 X[1698] - 7 X[49483], 4 X[3739] - 3 X[49483], 3 X[3679] - 2 X[4726], 35 X[4687] - 33 X[5550], 5 X[4687] - 3 X[24349], 11 X[5550] - 7 X[24349], 4 X[4698] - 3 X[31178], 8 X[19878] - 7 X[24325]

X(49513) lies on these lines: {8, 4764}, {37, 537}, {38, 3967}, {44, 49455}, {75, 4723}, {144, 145}, {190, 49465}, {210, 17495}, {335, 29626}, {346, 47358}, {354, 20068}, {519, 4718}, {536, 4677}, {726, 3626}, {984, 1698}, {1757, 49463}, {3246, 17336}, {3672, 47359}, {3679, 4726}, {3714, 24068}, {3740, 24620}, {3752, 42054}, {3932, 21255}, {3952, 4003}, {3971, 21342}, {4009, 4392}, {4096, 16602}, {4416, 28503}, {4439, 17231}, {4681, 49490}, {4687, 5550}, {4698, 31178}, {4702, 16496}, {4709, 28554}, {5220, 49446}, {5223, 49453}, {5852, 49476}, {15481, 32922}, {15569, 49499}, {16669, 49472}, {17235, 33165}, {17261, 24841}, {17345, 32847}, {17347, 28538}, {17351, 24821}, {19878, 24325}, {27481, 29623}, {27538, 31233}, {28484, 49450}, {28516, 49468}, {28522, 49449}, {28581, 49445}, {31197, 42056}, {31993, 42039}, {49456, 49478}

X(49513) = midpoint of X(31302) and X(49447)
X(49513) = reflection of X(i) in X(j) for these {i,j}: {4686, 49457}, {49475, 192}, {49478, 49456}, {49483, 984}, {49490, 4681}, {49499, 15569}
X(49513) = crossdifference of every pair of points on line {4491, 20980}
X(49513) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {192, 49475, 49462}, {4686, 49457, 3696}, {16496, 17262, 4702}, {17261, 24841, 42819}


X(49514) = X(37)X(86)∩X(144)X(145)

Barycentrics    a^3*b - 2*a^2*b^2 - a*b^3 + a^3*c - 2*a^2*b*c - a*b^2*c - 2*a^2*c^2 - a*b*c^2 + 2*b^2*c^2 - a*c^3 : :
X(49514) = 2 X[3879] - 3 X[31342]

X(49514) lies on these lines: {9, 20154}, {10, 47286}, {37, 86}, {65, 1655}, {72, 25264}, {75, 966}, {144, 145}, {194, 960}, {210, 17759}, {385, 4640}, {536, 17333}, {740, 4416}, {742, 17334}, {984, 3729}, {986, 25994}, {997, 31859}, {1155, 16997}, {1654, 3696}, {3219, 19791}, {3663, 17755}, {3666, 24514}, {3683, 16998}, {3739, 4389}, {3797, 6646}, {3812, 27269}, {3879, 31342}, {3931, 17499}, {4037, 24690}, {4373, 4699}, {4431, 49457}, {4452, 27484}, {4480, 49456}, {4676, 15569}, {4698, 17354}, {5087, 7777}, {5836, 41838}, {5919, 9263}, {7754, 12514}, {7774, 24703}, {9593, 26687}, {15254, 17000}, {16517, 20172}, {17007, 32950}, {17116, 31323}, {17246, 49481}, {17247, 31317}, {17272, 27474}, {17305, 31238}, {17316, 41325}, {17319, 49478}, {17321, 31306}, {17363, 28581}, {17752, 21872}, {17792, 20694}, {18600, 26689}, {19582, 25918}, {20356, 22343}, {21874, 33296}, {25248, 26563}, {37593, 40721}

X(49514) = crossdifference of every pair of points on line {4455, 20980}
X(49514) = barycentric product X(190)*X(30765)
X(49514) = barycentric quotient X(30765)/X(514)
X(49514) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {144, 192, 49496}, {192, 193, 49470}, {335, 17261, 37}


X(49515) = X(1)X(6)∩X(38)X(210)

Barycentrics    a*(a*b - 3*b^2 + a*c - 2*b*c - 3*c^2) : :
X(49515) = 2 X[1] - 3 X[37], X[1] - 3 X[984], 5 X[1] - 6 X[15569], X[1] + 3 X[49448], 4 X[1] - 3 X[49478], 5 X[1] - 3 X[49490], 7 X[1] - 3 X[49498], 5 X[37] - 4 X[15569], X[37] + 2 X[49448], 5 X[37] - 2 X[49490], 7 X[37] - 2 X[49498], 5 X[984] - 2 X[15569], 4 X[984] - X[49478], 5 X[984] - X[49490], 7 X[984] - X[49498], 2 X[15569] + 5 X[49448], 8 X[15569] - 5 X[49478], 14 X[15569] - 5 X[49498], 4 X[49448] + X[49478], 5 X[49448] + X[49490], 7 X[49448] + X[49498], 5 X[49478] - 4 X[49490], 7 X[49478] - 4 X[49498], 7 X[49490] - 5 X[49498], 2 X[49447] + X[49468], 4 X[10] - 3 X[4688], 3 X[4688] - 2 X[49483], 3 X[75] - 5 X[3617], 5 X[3617] + 3 X[31302], X[145] - 3 X[4664], 3 X[192] + X[3621], X[3621] - 3 X[49450], 2 X[3621] + 3 X[49461], 2 X[49450] + X[49461], 2 X[49449] + X[49462], 4 X[3626] - 3 X[3696], 8 X[3626] - 3 X[4686], 2 X[3626] - 3 X[49457], X[4686] - 4 X[49457], 4 X[3625] + 3 X[4718], 5 X[1698] - 3 X[31178], 4 X[3579] - 3 X[30271], 5 X[3616] - 6 X[4755], 4 X[3634] - 3 X[24325], 16 X[3634] - 15 X[31238], 4 X[24325] - 5 X[31238], 3 X[3679] - X[49493], 6 X[3739] - 7 X[9780], 7 X[9780] - 3 X[24349], 6 X[3842] - 5 X[19862], 5 X[19862] - 3 X[49479], 7 X[4678] - 3 X[4740], 6 X[4681] - X[20050], X[20050] - 3 X[49470], 15 X[4687] - 13 X[46934], 12 X[4698] - 11 X[5550], 21 X[4751] - 23 X[46931], 5 X[4816] + 3 X[49445], 5 X[4816] - 3 X[49459], X[8148] - 3 X[20430], 17 X[19872] - 15 X[40328]

X(49515) lies on these lines: {1, 6}, {2, 3999}, {8, 536}, {10, 537}, {38, 210}, {42, 42039}, {63, 37540}, {75, 3617}, {141, 3717}, {145, 4664}, {190, 49484}, {192, 3621}, {239, 49463}, {244, 31197}, {335, 16815}, {354, 756}, {516, 17334}, {519, 49449}, {524, 49476}, {614, 3715}, {726, 3626}, {740, 3625}, {968, 41711}, {982, 3740}, {986, 4662}, {1125, 49491}, {1155, 36263}, {1193, 4005}, {1418, 8581}, {1575, 3789}, {1698, 31178}, {1739, 3921}, {2292, 44671}, {2310, 3057}, {2550, 17276}, {3052, 3929}, {3175, 17135}, {3214, 22271}, {3216, 4533}, {3219, 3744}, {3240, 3666}, {3305, 17597}, {3315, 35595}, {3416, 17344}, {3579, 30271}, {3616, 4755}, {3632, 49452}, {3634, 24325}, {3662, 3823}, {3663, 24393}, {3670, 3697}, {3677, 37679}, {3678, 37592}, {3679, 49493}, {3683, 3938}, {3685, 49467}, {3687, 4884}, {3688, 8679}, {3689, 4414}, {3699, 24627}, {3706, 22034}, {3720, 42041}, {3728, 20718}, {3739, 5772}, {3741, 3967}, {3745, 32912}, {3755, 17246}, {3756, 5316}, {3782, 21949}, {3786, 16696}, {3790, 17229}, {3826, 24231}, {3838, 33101}, {3840, 4096}, {3842, 19862}, {3844, 33165}, {3873, 44307}, {3883, 9053}, {3886, 17262}, {3920, 4641}, {3932, 17231}, {3935, 4689}, {3951, 5710}, {3952, 30818}, {3957, 33761}, {3961, 4640}, {3962, 10459}, {3983, 24443}, {3989, 37593}, {3993, 49475}, {3994, 4519}, {4000, 5686}, {4009, 30942}, {4022, 28352}, {4078, 4966}, {4090, 6682}, {4113, 32860}, {4310, 17278}, {4327, 41712}, {4331, 5252}, {4349, 7277}, {4353, 17366}, {4357, 4899}, {4359, 20068}, {4361, 49446}, {4392, 16610}, {4415, 4847}, {4416, 5846}, {4429, 17235}, {4430, 4883}, {4469, 16728}, {4557, 37575}, {4644, 39587}, {4645, 17345}, {4646, 34790}, {4651, 42051}, {4661, 28606}, {4669, 28554}, {4670, 16830}, {4676, 36534}, {4678, 4740}, {4681, 20050}, {4682, 32913}, {4684, 17243}, {4687, 46934}, {4698, 5550}, {4702, 49458}, {4709, 28516}, {4712, 20331}, {4722, 29816}, {4751, 46931}, {4753, 49477}, {4777, 21132}, {4816, 28484}, {4862, 38200}, {4871, 42056}, {4891, 41839}, {4901, 17272}, {4906, 17123}, {4974, 49464}, {4981, 17165}, {5087, 29676}, {5204, 34247}, {5217, 15624}, {5221, 28017}, {5263, 17351}, {5295, 24068}, {5297, 37520}, {5524, 17593}, {5542, 17245}, {5573, 30393}, {5756, 31794}, {5836, 24341}, {5850, 17365}, {6646, 32850}, {7069, 17642}, {7322, 37674}, {8148, 20430}, {9041, 49466}, {9049, 21746}, {10453, 35652}, {10980, 37682}, {12652, 16112}, {12721, 21867}, {12782, 21868}, {13476, 14626}, {14872, 15852}, {16823, 24841}, {17154, 24589}, {17279, 27549}, {17292, 31349}, {17318, 49495}, {17347, 28570}, {17348, 32922}, {17369, 19868}, {17384, 38047}, {17605, 29690}, {17721, 31018}, {17755, 29596}, {17794, 21264}, {18743, 30948}, {19872, 40328}, {21060, 37662}, {21093, 21242}, {21805, 46901}, {21870, 46904}, {26034, 30615}, {27495, 29591}, {27627, 40607}, {28555, 49474}, {29010, 37705}, {29054, 31673}, {29578, 31323}, {29608, 31317}, {29823, 41241}, {30970, 31161}, {32636, 36508}, {32935, 36480}, {32937, 44417}, {41310, 47358}, {41311, 47359}

X(49515) = midpoint of X(i) and X(j) for these {i,j}: {8, 49447}, {75, 31302}, {192, 49450}, {984, 49448}, {3632, 49452}, {49445, 49459}, {49449, 49456}
X(49515) = reflection of X(i) in X(j) for these {i,j}: {37, 984}, {3696, 49457}, {3883, 17332}, {4686, 3696}, {24349, 3739}, {49461, 192}, {49462, 49456}, {49468, 8}, {49470, 4681}, {49475, 3993}, {49478, 37}, {49479, 3842}, {49483, 10}, {49490, 15569}, {49491, 1125}
X(49515) = complement of X(49499)
X(49515) = crossdifference of every pair of points on line {513, 16786}
X(49515) = X(1)-lineconjugate of X(16786)
X(49515) = barycentric product X(1)*X(29594)
X(49515) = barycentric quotient X(29594)/X(75)
X(49515) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1757, 16477}, {1, 4663, 16666}, {1, 5220, 44}, {1, 16477, 1386}, {9, 3242, 1279}, {10, 49483, 4688}, {38, 210, 3752}, {38, 899, 4003}, {210, 4003, 899}, {238, 15481, 15492}, {899, 4003, 3752}, {982, 3740, 16602}, {986, 4662, 21896}, {1001, 16496, 4864}, {1386, 1757, 16669}, {3666, 3681, 4849}, {3681, 7226, 3666}, {3706, 32925, 22034}, {3741, 42054, 3967}, {3782, 25006, 21949}, {3952, 46909, 30818}, {3994, 31136, 4519}, {4310, 38057, 17278}, {4864, 16814, 1001}, {4981, 17165, 31993}, {5223, 7174, 6}, {15481, 49465, 238}


X(49516) = X(8)X(192)∩X(9)X(75)

Barycentrics    a^3*b - a^2*b^2 + a^3*c - 2*a^2*b*c - a*b^2*c - b^3*c - a^2*c^2 - a*b*c^2 - b*c^3 : :
X(49516) = X[17347] + 3 X[36494]

X(49516) lies on these lines: {1, 49496}, {6, 24357}, {8, 192}, {9, 75}, {10, 25994}, {37, 141}, {38, 24513}, {44, 49481}, {85, 1221}, {144, 24349}, {193, 49490}, {220, 16822}, {238, 894}, {325, 25353}, {335, 6646}, {346, 27474}, {518, 3883}, {536, 17330}, {537, 17333}, {672, 24631}, {756, 31087}, {960, 17760}, {982, 26274}, {1212, 30038}, {1213, 25384}, {1215, 24514}, {1334, 20911}, {1921, 17787}, {1930, 3294}, {2238, 24326}, {2650, 20109}, {3696, 3717}, {3726, 24690}, {3730, 33945}, {3739, 6687}, {3740, 40883}, {3757, 10025}, {3797, 17261}, {3842, 4019}, {3875, 16517}, {3985, 33931}, {4071, 37664}, {4095, 6376}, {4110, 4505}, {4434, 16997}, {4461, 27549}, {4480, 49483}, {4568, 10176}, {4664, 17271}, {4687, 17283}, {4699, 7229}, {4704, 29616}, {4732, 33165}, {6210, 29054}, {6604, 7201}, {7174, 49451}, {7205, 40864}, {7264, 29433}, {8424, 20678}, {9055, 17332}, {9318, 37670}, {10436, 16970}, {11679, 20173}, {14829, 36540}, {16601, 29960}, {16991, 28595}, {16992, 24333}, {17007, 33074}, {17045, 36409}, {17116, 20138}, {17137, 218 08}, {17152, 17451}, {17252, 27495}, {17263, 27487}, {17298, 27475}, {17319, 49471}, {17347, 36494}, {17350, 31317}, {17751, 25261}, {20072, 49491}, {20073, 49493}, {20435, 25001}, {20880, 28287}, {21214, 25918}, {21232, 33934}, {21384, 39731}, {21802, 25499}, {24586, 40131}, {25066, 29991}, {25342, 37688}, {25935, 26530}, {26279, 32918}, {27268, 29627}, {28604, 33159}

X(49516) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 75, 17755}, {192, 17257, 984}, {672, 26234, 24631}, {984, 33076, 49457}


X(49517) = X(1)X(4681)∩X(10)X(75)

Barycentrics    3*a*b^2 + a*b*c - 2*b^2*c + 3*a*c^2 - 2*b*c^2 : :
X(49517) = 3 X[1] - 4 X[4681], 6 X[10] - 5 X[75], 4 X[10] - 5 X[984], 2 X[10] - 5 X[49447], 8 X[10] - 5 X[49493], 2 X[75] - 3 X[984], X[75] - 3 X[49447], 4 X[75] - 3 X[49493], 4 X[49447] - X[49493], 10 X[37] - 9 X[25055], 4 X[37] - 3 X[31178], 6 X[25055] - 5 X[31178], 5 X[192] - 3 X[3241], 3 X[192] - 2 X[49471], 9 X[3241] - 10 X[49471], 6 X[3241] - 5 X[49490], 4 X[49471] - 3 X[49490], 3 X[3633] - 10 X[4718], X[3633] - 5 X[49445], 2 X[3633] - 5 X[49452], 3 X[3633] - 5 X[49469], 2 X[4718] - 3 X[49445], 4 X[4718] - 3 X[49452], 5 X[4718] - 3 X[49461], 5 X[49445] - 2 X[49461], 3 X[49445] - X[49469], 5 X[49452] - 4 X[49461], 3 X[49452] - 2 X[49469], 6 X[49461] - 5 X[49469], 3 X[4677] - 5 X[49448], 6 X[4677] - 5 X[49459], 3 X[3621] + 5 X[4788], X[3621] - 5 X[31302], X[4788] + 3 X[31302], 21 X[3622] - 25 X[4704], 7 X[3622] - 5 X[24349], 7 X[3622] - 10 X[49456], 5 X[4704] - 3 X[24349], 5 X[4704] - 6 X[49456], 3 X[3679] - 2 X[4686], 20 X[3739] - 21 X[19876], 3 X[4664] - 2 X[49479], 40 X[4698] - 39 X[34595], 16 X[4698] - 15 X[40328], 4 X[4698] - 3 X[49483], 26 X[34595] - 25 X[40328], 13 X[34595] - 10 X[49483], 5 X[40328] - 4 X[49483], 4 X[4732] - 3 X[4740], 8 X[4739] - 9 X[19875], 11 X[5550] - 10 X[24325], 33 X[5550] - 35 X[27268], 6 X[24325] - 7 X[27268], 51 X[19872] - 50 X[31238]

X(49517) lies on these lines: {1, 4681}, {6, 24821}, {8, 28516}, {10, 75}, {37, 25055}, {38, 4671}, {190, 49455}, {192, 537}, {238, 25728}, {335, 29572}, {518, 3633}, {519, 3644}, {536, 4677}, {740, 3621}, {982, 4358}, {1278, 28554}, {1757, 49453}, {3159, 3976}, {3210, 42054}, {3622, 4704}, {3632, 28484}, {3662, 4439}, {3679, 4686}, {3739, 19876}, {3773, 48634}, {3790, 48633}, {3795, 17794}, {3797, 29577}, {3891, 7262}, {3932, 48631}, {3944, 4884}, {3967, 17591}, {3971, 17063}, {3977, 17725}, {3993, 49499}, {3994, 4392}, {3995, 17146}, {4096, 17490}, {4407, 48628}, {4419, 33076}, {4432, 25269}, {4650, 32926}, {4664, 49479}, {4676, 49464}, {4693, 16496}, {4698, 34595}, {4709, 4764}, {4716, 5223}, {4732, 4740}, {4739, 19875}, {4862, 31151}, {5550, 24325}, {5902, 22306}, {6534, 42285}, {16468, 49463}, {17118, 36531}, {17120, 32935}, {17121, 32921}, {17145, 20068}, {17155, 24589}, {17165, 17592}, {17246, 29659}, {17276, 32847}, {17323, 36478}, {17334, 28503}, {17340, 29660}, {17350, 49472}, {17601, 32927}, {17715, 32936}, {17716, 32933}, {19823, 33163}, {19824, 33132}, {19828, 33118}, {19829, 25453}, {19872, 31238}, {21296, 32846}, {24620, 42056}, {24816, 41777}, {27481, 29581}, {27494, 31323}, {28522, 49450}, {28555, 49474}, {28605, 42039}, {29674, 48632}, {41839, 42055}, {42040, 46938}, {49462, 49498}

X(49517) = reflection of X(i) in X(j) for these {i,j}: {984, 49447}, {1278, 49457}, {3633, 49461}, {4764, 4709}, {24349, 49456}, {49452, 49445}, {49459, 49448}, {49469, 4718}, {49490, 192}, {49493, 984}, {49498, 49462}, {49499, 3993}
X(49517) = crossdifference of every pair of points on line {1919, 23650}
X(49517) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4718, 49469, 49452}, {49445, 49469, 4718}


X(49518) = X(7)X(192)∩X(10)X(75)

Barycentrics    a^2*b^2 + a*b^3 + a^2*b*c + a^2*c^2 - 2*b^2*c^2 + a*c^3 : :
X(49518) = 4 X[141] - 3 X[27474], X[193] - 3 X[27480], 4 X[3739] - 5 X[17304], 5 X[4687] - 4 X[17355], 3 X[17301] - 2 X[49481], 2 X[24254] - 3 X[48840], X[24282] - 3 X[48838]

X(49518) lies on these lines: {1, 1975}, {2, 3985}, {6, 17738}, {7, 192}, {9, 20154}, {10, 75}, {37, 980}, {38, 4441}, {63, 19791}, {69, 740}, {86, 3923}, {141, 27474}, {183, 17596}, {193, 27480}, {194, 3061}, {257, 20081}, {304, 24214}, {307, 20171}, {314, 40874}, {315, 24851}, {319, 4660}, {320, 33869}, {325, 3944}, {350, 982}, {516, 3879}, {518, 3875}, {527, 49496}, {536, 599}, {538, 3735}, {742, 17276}, {846, 16992}, {1071, 10441}, {1909, 37598}, {2292, 34284}, {2796, 17378}, {3159, 33942}, {3210, 30946}, {3263, 32925}, {3496, 7754}, {3662, 3797}, {3664, 3993}, {3670, 3760}, {3672, 24349}, {3696, 17270}, {3739, 17304}, {3761, 4424}, {3945, 24280}, {3971, 30758}, {4000, 17755}, {4021, 49479}, {4037, 30945}, {4051, 21226}, {4087, 17149}, {4360, 24841}, {4402, 27484}, {4414, 37670}, {4452, 31302}, {4664, 17132}, {4687, 17355}, {4699, 31323}, {4788, 45789}, {4862, 49445}, {7032, 20356}, {7204, 30545}, {7262, 33295}, {7283, 24549}, {7757, 18061}, {9312, 12709}, {9436, 20173}, {10446, 29057}, {10889, 11997}, {11185, 37717}, {14377, 30130}, {17063, 30963}, {17118, 25384}, {17147, 20347}, {17151, 49448}, {17155, 26234}, {17175, 27785}, {17206, 17733}, {17246, 24357}, {17272, 49474}, {17301, 49481}, {17302, 31317}, {17320, 31178}, {17321, 24325}, {17322, 40328}, {17377, 17766}, {17393, 49464}, {17394, 49482}, {17592, 24259}, {17889, 37664}, {18034, 40155}, {18135, 24443}, {18140, 24174}, {18156, 24215}, {18600, 25253}, {20553, 33094}, {24045, 30170}, {24254, 48840}, {24260, 37678}, {24282, 48838}, {24330, 41269}, {25503, 31238}, {25591, 27162}, {26247, 41423}, {27481, 48627}, {27487, 48629}, {27495, 48628}, {30941, 32915}, {42696, 49457}, {42697, 49456}

X(49518) = reflection of X(i) in X(j) for these {i,j}: {75, 3663}, {3729, 37}, {49459, 4660}, {49490, 49455}


X(49519) = X(1)X(335)∩X(10)X(75)

Barycentrics    a^3*b^2 + a^2*b^3 + a*b^4 + a^3*b*c + a^2*b^2*c + a*b^3*c + a^3*c^2 + a^2*b*c^2 - b^3*c^2 + a^2*c^3 + a*b*c^3 - b^2*c^3 + a*c^4 : :
X(49519) = 5 X[4687] - 4 X[24295], 5 X[4704] - X[24280]

X(49519) lies on these lines: {1, 335}, {4, 46507}, {8, 33832}, {10, 75}, {37, 3923}, {192, 4645}, {257, 9902}, {516, 3993}, {518, 4523}, {537, 17301}, {712, 24293}, {730, 3735}, {740, 3416}, {742, 4655}, {1698, 31323}, {2276, 43534}, {2796, 4664}, {3097, 4518}, {3666, 24260}, {3729, 24342}, {3797, 29674}, {3842, 17303}, {4353, 49479}, {4362, 19791}, {4368, 26242}, {4657, 24325}, {4687, 24295}, {4704, 24280}, {5880, 24404}, {9943, 24728}, {17302, 24349}, {17399, 31178}, {17400, 40328}, {17766, 49470}, {17770, 49496}, {19834, 25453}, {20430, 29057}, {24259, 28606}, {29633, 31317}, {30142, 33731}, {40718, 41269}, {49446, 49448}, {49464, 49490}

X(49519) = midpoint of X(i) and X(j) for these {i,j}: {192, 24248}, {49446, 49448}
X(49519) = reflection of X(i) in X(j) for these {i,j}: {75, 3821}, {3923, 37}, {49479, 4353}, {49490, 49464}


X(49520) = X(1)X(4704)∩X(10)X(75)

Barycentrics    3*a*b^2 + 2*a*b*c - b^2*c + 3*a*c^2 - b*c^2 : :
X(49520) = 3 X[1] - 5 X[4704], 5 X[4704] + 3 X[31302], 3 X[8] + X[4788], X[4788] - 3 X[49445], 3 X[10] - 2 X[75], X[10] + 2 X[49447], 5 X[10] - 2 X[49493], X[75] - 3 X[984], X[75] + 3 X[49447], 5 X[75] - 3 X[49493], 5 X[984] - X[49493], 5 X[49447] + X[49493], 4 X[37] - 3 X[551], 3 X[551] - 2 X[49479], 3 X[192] - X[49469], 3 X[49448] + X[49469], 3 X[3244] - 8 X[4681], X[3244] - 4 X[49456], 3 X[3244] - 4 X[49471], 3 X[3993] - 4 X[4681], 3 X[3993] - 2 X[49471], 2 X[4681] - 3 X[49456], 3 X[49456] - X[49471], 3 X[4669] - 2 X[4709], 3 X[4669] - 4 X[49457], 3 X[3625] + 4 X[4718], 6 X[1125] - 7 X[27268], 3 X[24349] - 7 X[27268], X[1278] - 3 X[3679], 2 X[3644] + 3 X[34641], 3 X[34641] - 2 X[49459], 6 X[3828] - 5 X[4699], 6 X[3842] - 5 X[31238], 5 X[31238] - 3 X[49483], 3 X[4664] - X[49490], 4 X[4686] - 9 X[38098], 8 X[4732] - 9 X[38098], 10 X[4687] - 9 X[19883], 5 X[4687] - 3 X[31178], 3 X[19883] - 2 X[31178], 16 X[4698] - 15 X[19862], 4 X[4698] - 3 X[24325], 5 X[19862] - 4 X[24325], 7 X[4772] - 9 X[19875]

X(49520) lies on these lines: {1, 4704}, {8, 4788}, {9, 49455}, {10, 75}, {37, 537}, {38, 3840}, {44, 49472}, {141, 4439}, {190, 49482}, {192, 519}, {238, 49464}, {321, 42039}, {335, 29571}, {518, 3244}, {536, 4669}, {594, 4407}, {740, 3625}, {752, 17334}, {756, 24165}, {894, 24821}, {982, 30829}, {1125, 17368}, {1278, 3679}, {1757, 17121}, {3159, 22016}, {3626, 49474}, {3635, 49498}, {3644, 34641}, {3666, 4090}, {3670, 30044}, {3681, 4970}, {3696, 28516}, {3699, 17593}, {3720, 17146}, {3728, 4793}, {3729, 36480}, {3731, 24331}, {3741, 4135}, {3752, 4096}, {3773, 48635}, {3775, 48636}, {3790, 48634}, {3797, 29594}, {3828, 4699}, {3836, 48631}, {3842, 31238}, {3846, 4884}, {3912, 27481}, {3923, 7174}, {3932, 48632}, {3952, 46901}, {3953, 22220}, {3967, 6682}, {3989, 17165}, {3992, 20892}, {3994, 46909}, {3995, 17145}, {4003, 24003}, {4075, 29982}, {4085, 17246}, {4125, 20891}, {4301, 20430}, {4359, 42041}, {4392, 4871}, {4419, 4660}, {4424, 4738}, {4432, 49465}, {4461, 48802}, {4488, 48856}, {4656, 29655}, {4664, 49490}, {4685, 17147}, {4686, 4732}, {4687, 19883}, {4698, 19862}, {4740, 4745}, {4753, 4852}, {4756, 32944}, {4759, 17336}, {4772, 19875}, {4974, 15481}, {5220, 32921}, {5223, 49488}, {5293, 8720}, {6646, 32847}, {6685, 32937}, {6686, 17591}, {9369, 11533}, {15569, 49491}, {16484, 24841}, {16610, 42056}, {16825, 49446}, {17023, 33888}, {17116, 36531}, {17140, 25501}, {17154, 30950}, {17247, 29659}, {17258, 33076}, {17262, 32941}, {17276, 24692}, {17318, 49497}, {17324, 36478}, {17332, 28503}, {17339, 29660}, {17448, 20688}, {17449, 31035}, {17755, 31191}, {17770, 49476}, {17794, 40774}, {19823, 25453}, {19828, 33132}, {19829, 33118}, {19832, 32780}, {21093, 29639}, {21241, 33151}, {24199, 25352}, {25269, 36534}, {25391, 25399}, {25601, 36541}, {26065, 29842}, {27478, 31323}, {27494, 29576}, {28581, 49449}, {29668, 30568}, {29674, 48633}, {30358, 31397}, {32923, 33761}, {32935, 33682}, {42027, 42285}, {42055, 44307}, {49450, 49452}

X(49520) = midpoint of X(i) and X(j) for these {i,j}: {1, 31302}, {8, 49445}, {192, 49448}, {984, 49447}, {3644, 49459}, {49450, 49452}
X(49520) = reflection of X(i) in X(j) for these {i,j}: {10, 984}, {3244, 3993}, {3993, 49456}, {4301, 20430}, {4686, 4732}, {4709, 49457}, {4740, 4745}, {24349, 1125}, {49471, 4681}, {49474, 3626}, {49479, 37}, {49483, 3842}, {49491, 15569}, {49498, 3635}
X(49520) = crossdifference of every pair of points on line {1919, 4491}
X(49520) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 49479, 551}, {38, 3971, 3840}, {3666, 42054, 4090}, {3717, 3821, 10}, {3741, 32925, 4135}, {3989, 17165, 43223}, {4681, 49471, 3993}, {4709, 49457, 4669}, {7226, 32925, 3741}, {15481, 49463, 4974}, {17591, 27538, 6686}, {49456, 49471, 4681}


X(49521) = X(9)X(192)∩X(10)X(75)

Barycentrics    a^2*b^2 + a*b^3 + 2*a*b^2*c - b^3*c + a^2*c^2 + 2*a*b*c^2 + a*c^3 - b*c^3 : :
X(49521) = X[192] - 3 X[27481], 4 X[3739] - 3 X[27478], 5 X[4687] - 3 X[36494], 7 X[4772] - 3 X[27494]

X(49521) lies on these lines: {2, 21101}, {7, 31302}, {9, 192}, {10, 75}, {37, 3589}, {38, 3263}, {69, 32847}, {86, 24841}, {142, 335}, {190, 20179}, {238, 3993}, {256, 40844}, {350, 3971}, {518, 3688}, {522, 27855}, {536, 17330}, {672, 31087}, {712, 1573}, {740, 3883}, {742, 4416}, {756, 26234}, {894, 33888}, {958, 3905}, {982, 30758}, {1107, 17760}, {1278, 17257}, {1334, 28598}, {1475, 25263}, {2321, 3797}, {3634, 24166}, {3672, 27549}, {3691, 17489}, {3721, 30030}, {3728, 18697}, {3729, 16517}, {3739, 27478}, {3741, 33931}, {3831, 33932}, {3840, 20947}, {3954, 29960}, {4090, 37678}, {4119, 26590}, {4136, 26558}, {4424, 4986}, {4441, 32925}, {4464, 30331}, {4561, 37617}, {4687, 36494}, {4699, 17306}, {4704, 26685}, {4709, 5564}, {4772, 5936}, {4901, 17270}, {5257, 31323}, {5750, 31317}, {7174, 10436}, {7226, 31130}, {16503, 32029}, {16992, 32920}, {17151, 49445}, {17276, 24699}, {17321, 29633}, {17322, 33159}, {18140, 24172}, {20271, 30063}, {20895, 44694}, {21255, 27487}, {21830, 27633}, {24173, 40093}, {24214, 33933}, {24215, 33943}, {24547, 25024}, {25590, 36531}, {27268, 29614}, {27626, 41240}, {28287, 41233}, {32927, 37670}, {33890, 41838}, {39717, 42027}, {42696, 49474}

X(49521) = crossdifference of every pair of points on line {1919, 21003}
X(49521) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 17755, 17353}, {37, 49481, 17023}, {75, 313, 21443}, {75, 984, 4357}


X(49522) = X(8)X(536)∩X(37)X(39)

Barycentrics    a^2*b + 5*a*b^2 + a^2*c + 2*a*b*c - 4*b^2*c + 5*a*c^2 - 4*b*c^2 : :
X(49522) = X[8] - 3 X[49447], 4 X[8] - 3 X[49468], 4 X[49447] - X[49468], 9 X[37] - 8 X[1125], 5 X[37] - 4 X[24325], 3 X[37] - 4 X[49456], 3 X[37] - 2 X[49483], 10 X[1125] - 9 X[24325], 2 X[1125] - 3 X[49456], 4 X[1125] - 3 X[49483], 3 X[24325] - 5 X[49456], 6 X[24325] - 5 X[49483], 9 X[75] - 11 X[46933], 9 X[192] - 5 X[3623], 3 X[192] - X[49499], 10 X[3623] - 9 X[49478], 5 X[3623] - 3 X[49499], 3 X[49478] - 2 X[49499], 2 X[3633] - 9 X[4718], X[3633] - 9 X[49445], X[3633] - 3 X[49452], 4 X[3633] - 9 X[49461], 5 X[3633] - 9 X[49469], 3 X[4718] - 2 X[49452], 5 X[4718] - 2 X[49469], 3 X[49445] - X[49452], 4 X[49445] - X[49461], 5 X[49445] - X[49469], 4 X[49452] - 3 X[49461], 5 X[49452] - 3 X[49469], 5 X[49461] - 4 X[49469], 2 X[3244] - 3 X[49462], 10 X[1698] - 9 X[4688], 5 X[1698] - 3 X[49493], 3 X[4688] - 2 X[49493], 7 X[3622] - 9 X[4664], 9 X[3644] + X[20054], X[20054] - 9 X[31302]

X(49522) lies on these lines: {8, 536}, {10, 28554}, {37, 39}, {38, 4519}, {44, 49453}, {75, 46933}, {190, 49463}, {192, 3623}, {518, 3633}, {537, 3244}, {545, 49476}, {984, 3987}, {1201, 42083}, {1279, 17262}, {1698, 4688}, {3175, 21342}, {3622, 4664}, {3644, 20054}, {3696, 28516}, {3752, 4009}, {3790, 17235}, {3823, 4398}, {3971, 16602}, {3994, 4003}, {4409, 30424}, {4416, 28472}, {4646, 24068}, {4663, 24821}, {4681, 24349}, {4788, 49450}, {4849, 17147}, {5850, 17388}, {15593, 32087}, {16666, 32935}, {16669, 32921}, {28484, 49448}, {30947, 35652}

X(49522) = midpoint of X(i) and X(j) for these {i,j}: {3644, 31302}, {4788, 49450}
X(49522) = reflection of X(i) in X(j) for these {i,j}: {4686, 984}, {4718, 49445}, {24349, 4681}, {49461, 4718}, {49478, 192}, {49483, 49456}
X(49522) = crossdifference of every pair of points on line {4057, 39521}
X(49522) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {17262, 49446, 1279}, {49456, 49483, 37}


X(49523) = X(1)X(4681)∩X(37)X(39)

Barycentrics    a^2*b + 3*a*b^2 + a^2*c + 2*a*b*c - 2*b^2*c + 3*a*c^2 - 2*b*c^2 : :
X(49523) = 5 X[37] - 4 X[1125], 3 X[37] - 2 X[24325], 6 X[1125] - 5 X[24325], 2 X[1125] - 5 X[49456], 8 X[1125] - 5 X[49483], X[24325] - 3 X[49456], 4 X[24325] - 3 X[49483], 4 X[49456] - X[49483], 5 X[75] - 7 X[9780], X[145] - 5 X[192], 3 X[145] + 5 X[31302], X[145] + 5 X[49447], 2 X[145] - 5 X[49462], 3 X[145] - 5 X[49470], 4 X[145] - 5 X[49475], 3 X[192] + X[31302], 3 X[192] - X[49470], 4 X[192] - X[49475], X[31302] - 3 X[49447], 2 X[31302] + 3 X[49462], 4 X[31302] + 3 X[49475], 2 X[49447] + X[49462], 3 X[49447] + X[49470], 4 X[49447] + X[49475], 3 X[49462] - 2 X[49470], 4 X[49470] - 3 X[49475], 5 X[984] - 3 X[3679], 3 X[984] - X[49474], 6 X[3679] - 5 X[3696], 3 X[3679] + 5 X[49445], 9 X[3679] - 5 X[49474], X[3696] + 2 X[49445], 3 X[3696] - 2 X[49474], 3 X[49445] + X[49474], 2 X[3625] + 5 X[4718], 5 X[1698] - 4 X[4739], 4 X[3842] - 3 X[4688], 3 X[4664] - 2 X[15569], 3 X[4664] - X[24349], 5 X[4664] - 3 X[38314], 10 X[15569] - 9 X[38314], 5 X[24349] - 9 X[38314], 25 X[4699] - 29 X[46930], 4 X[4746] - 5 X[49457], 8 X[4746] - 5 X[49468], 6 X[4755] - 5 X[40328]

X(49523) lies on these lines: {1, 4681}, {8, 3644}, {9, 49453}, {10, 4686}, {37, 39}, {38, 3175}, {44, 32921}, {75, 3701}, {144, 145}, {190, 1386}, {210, 17147}, {238, 49463}, {239, 15481}, {335, 29575}, {354, 3995}, {519, 49461}, {536, 984}, {537, 3993}, {740, 3625}, {756, 42051}, {982, 35652}, {1001, 49446}, {1086, 4078}, {1100, 32935}, {1266, 3826}, {1279, 49455}, {1698, 4739}, {1757, 4852}, {3097, 20530}, {3210, 3740}, {3242, 4702}, {3416, 4419}, {3663, 3932}, {3666, 3967}, {3672, 38047}, {3683, 3891}, {3685, 49465}, {3706, 7226}, {3739, 25503}, {3741, 22034}, {3742, 41839}, {3744, 32936}, {3745, 32933}, {3751, 17318}, {3752, 3971}, {3773, 17237}, {3790, 3844}, {3797, 29587}, {3821, 4439}, {3823, 33149}, {3842, 4688}, {3875, 5220}, {3879, 5852}, {3883, 28503}, {3931, 24068}, {3950, 4966}, {3977, 17602}, {3989, 31993}, {3994, 30818}, {4003, 4358}, {4009, 4850}, {4029, 5542}, {4135, 6682}, {4360, 4663}, {4365, 42039}, {4432, 49464}, {4452, 38057}, {4519, 46909}, {4552, 8581}, {4640, 32926}, {4641, 32928}, {4649, 24821}, {4664, 15569}, {4676, 25269}, {4682, 32939}, {4689, 32927}, {4693, 49467}, {4699, 46930}, {4746, 28522}, {4755, 40328}, {4756, 17012}, {4849, 4970}, {4884, 24210}, {4974, 15492}, {5223, 49486}, {5625, 39260}, {5695, 7174}, {5847, 17334}, {6541, 17231}, {15254, 17261}, {15570, 24841}, {16669, 49477}, {16814, 16825}, {17118, 39586}, {17155, 44307}, {17165, 37593}, {17235, 29674}, {17243, 24231}, {17332, 28472}, {17342, 26150}, {17345, 32846}, {17382, 33159}, {17388, 34379}, {17399, 26083}, {17459, 21902}, {17768, 49476}, {21264, 40774}, {27481, 29628}, {28581, 49448}, {28898, 48278}, {32940, 37595}

X(49523) = midpoint of X(i) and X(j) for these {i,j}: {8, 3644}, {192, 49447}, {984, 49445}, {31302, 49470}, {49448, 49452}
X(49523) = reflection of X(i) in X(j) for these {i,j}: {1, 4681}, {37, 49456}, {3696, 984}, {4686, 10}, {24349, 15569}, {49462, 192}, {49468, 49457}, {49475, 49462}, {49478, 3993}, {49483, 37}, {49493, 3739}
X(49523) = crossdifference of every pair of points on line {4057, 20980}
X(49523) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {192, 31302, 49470}, {3666, 32925, 3967}, {3790, 4389, 3844}, {3994, 46901, 30818}, {4664, 24349, 15569}, {4970, 42054, 4849}, {7226, 42044, 3706}, {17261, 32922, 15254}, {49447, 49470, 31302}


X(49524) = X(6)X(8)∩X(10)X(141)

Barycentrics    2*a^2*b - a*b^2 + b^3 + 2*a^2*c + b^2*c - a*c^2 + b*c^2 + c^3 : :
X(49524) = X[1] - 3 X[38047], 2 X[3589] - 3 X[38047], X[2] - 3 X[38087], X[3242] - 9 X[38087], X[3] - 3 X[38116], X[4] - 3 X[38144], X[5] - 3 X[38165], X[7] - 3 X[38185], X[9] - 3 X[38190], 3 X[10] - 2 X[3844], X[10] - 3 X[38191], 3 X[141] - 4 X[3844], X[141] - 6 X[38191], 2 X[3844] - 9 X[38191], X[11] - 3 X[38192], X[12] - 3 X[38193], X[69] - 5 X[3617], X[145] - 5 X[3618], X[145] - 3 X[38315], 5 X[3618] - 3 X[38315], X[193] + 7 X[4678], 3 X[597] - 2 X[1386], 3 X[17359] - X[49467], 4 X[24295] - 3 X[48810], 3 X[48810] - 2 X[49473], X[3416] - 3 X[3679], X[3416] + 3 X[47359], 3 X[3679] + X[3751], X[3751] - 3 X[47359], 2 X[3821] - 3 X[48821], X[24248] - 3 X[48829], 2 X[551] - 3 X[48310], X[944] - 3 X[5085], X[1350] - 3 X[5657], X[1352] - 3 X[5790], X[1482] - 3 X[14561], X[1483] - 3 X[38110], 5 X[1698] - X[16496], 5 X[1698] - 4 X[34573], X[16496] - 4 X[34573], X[3241] - 3 X[47352], X[3243] - 3 X[38186], X[3244] - 3 X[38049], 5 X[3616] - 7 X[47355], 7 X[3619] - 11 X[46933], 4 X[3626] + X[3629], 2 X[3626] + X[4663], X[3630] - 8 X[4691], X[3632] + 4 X[6329], X[3632] + 3 X[16475], 4 X[6329] - 3 X[16475], X[3633] - 5 X[16491], 3 X[3753] - X[24476], 5 X[3763] - 7 X[9780], X[3886] - 3 X[17281], X[4301] - 3 X[38146], 2 X[4353] - 3 X[17382], 5 X[4668] + 2 X[32455], 2 X[4669] + X[8584], 4 X[4745] - X[22165], X[4924] + 3 X[29594], 3 X[5050] + X[12645], 5 X[5818] - 3 X[10516], 5 X[5818] - X[39898], 3 X[10516] - X[39898], X[5882] - 3 X[38118], 2 X[5901] - 3 X[38317], 3 X[6034] - X[7983], 4 X[6684] - 3 X[21167], X[7976] - 3 X[13331], X[7982] - 3 X[38035], 3 X[9778] - X[48872], X[10222] - 3 X[38167], 5 X[12017] - X[18526], X[12245] + 3 X[14853], X[12583] - 3 X[16210], X[12898] - 3 X[15462], X[15826] + 2 X[47492], 5 X[17286] - X[49451], 3 X[17301] - X[49446], 3 X[19875] - 2 X[20582], 3 X[19875] - X[47358], 2 X[24206] - 3 X[38042], X[25416] - 3 X[38050], 4 X[25555] - 3 X[38040], 3 X[38200] - X[47595], X[30331] - 3 X[38194], X[37727] - 3 X[38029], 3 X[38074] - X[47353], 3 X[38112] - X[48876], 3 X[38138] - X[39884], 3 X[38145] - X[43166]

X(49524) lies on these lines: {1, 3589}, {2, 1280}, {3, 38116}, {4, 38144}, {5, 38165}, {6, 8}, {7, 38185}, {9, 38190}, {10, 141}, {11, 32931}, {12, 28109}, {31, 4030}, {37, 3717}, {40, 29181}, {42, 3703}, {43, 33169}, {44, 3883}, {45, 27549}, {55, 33163}, {63, 44419}, {65, 9021}, {69, 3617}, {81, 33091}, {100, 4265}, {145, 3618}, {149, 41242}, {182, 952}, {193, 4678}, {210, 5743}, {291, 25350}, {313, 4696}, {355, 1503}, {388, 28079}, {511, 5690}, {515, 44882}, {516, 17351}, {517, 5480}, {519, 597}, {524, 3416}, {528, 3923}, {536, 3755}, {537, 3821}, {545, 24248}, {551, 48310}, {611, 10573}, {612, 6703}, {613, 12647}, {698, 12782}, {726, 4085}, {730, 32449}, {742, 3696}, {756, 4126}, {894, 32850}, {940, 10327}, {944, 5085}, {956, 36741}, {958, 12329}, {966, 5686}, {984, 4026}, {1001, 4422}, {1002, 30945}, {1086, 4429}, {1100, 49476}, {1125, 49465}, {1145, 9024}, {1211, 3681}, {1215, 2886}, {1279, 17353}, {1350, 5657}, {1352, 5790}, {1376, 22769}, {1428, 10944}, {1469, 40663}, {1482, 14561}, {1483, 38110}, {1621, 33166}, {1691, 12195}, {1698, 16496}, {1706, 7289}, {1738, 7263}, {1757, 33076}, {1829, 3867}, {1834, 4385}, {1974, 12135}, {2177, 3712}, {2321, 28581}, {2330, 10950}, {2550, 4363}, {2809, 24254}, {2885, 8582}, {2975, 5096}, {3006, 5718}, {3036, 5848}, {3052, 26065}, {3058, 32930}, {3120, 31161}, {3240, 33089}, {3241, 47352}, {3243, 17284}, {3244, 38049}, {3313, 16980}, {3421, 5800}, {3579, 48881}, {3616, 47355}, {3619, 46933}, {3626, 3629}, {3630, 4691}, {3632, 6329}, {3633, 16491}, {3661, 49450}, {3662, 49499}, {3663, 28582}, {3666, 4884}, {3685, 17340}, {3687, 4849}, {3705, 37662}, {3710, 37548}, {3729, 28530}, {3744, 5294}, {3750, 33164}, {3753, 24476}, {3754, 34378}, {3757, 33118}, {3763, 9780}, {3779, 15985}, {3782, 4972}, {3790, 3943}, {3816, 11814}, {3818, 18357}, {3827, 5836}, {3846, 4090}, {3870, 32777}, {3873, 29679}, {3875, 28472}, {3886, 17281}, {3912, 49478}, {3925, 32771}, {3935, 32779}, {3936, 31079}, {3938, 26061}, {3946, 49463}, {3957, 33157}, {3961, 32780}, {3967, 24210}, {3969, 20011}, {3976, 25914}, {3977, 4689}, {3979, 33158}, {3993, 4439}, {4023, 21805}, {4058, 4923}, {4078, 15569}, {4082, 35652}, {4147, 9029}, {4301, 38146}, {4310, 17290}, {4353, 17382}, {4356, 4681}, {4357, 4899}, {4358, 29835}, {4389, 31302}, {4415, 32773}, {4418, 34612}, {4425, 42054}, {4430, 33172}, {4431, 49468}, {4438, 6690}, {4514, 27064}, {4643, 5223}, {4645, 17365}, {4648, 39570}, {4649, 32847}, {4651, 37676}, {4655, 5852}, {4657, 7174}, {4660, 17768}, {4661, 32782}, {4668, 32455}, {4669, 8584}, {4672, 17766}, {4684, 17231}, {4712, 24326}, {4743, 28522}, {4745, 22165}, {4780, 28484}, {4847, 44417}, {4848, 24471}, {4854, 32925}, {4864, 17357}, {4871, 17051}, {4924, 29594}, {4929, 29598}, {4966, 29674}, {4971, 49486}, {5014, 26223}, {5050, 12645}, {5092, 34773}, {5192, 16794}, {5220, 17332}, {5252, 16799}, {5432, 33119}, {5554, 12594}, {5599, 12453}, {5600, 12452}, {5687, 36740}, {5818, 10516}, {5844, 18583}, {5850, 17345}, {5853, 17355}, {5880, 7228}, {5882, 38118}, {5901, 38317}, {6034, 7983}, {6057, 32915}, {6361, 48910}, {6536, 42041}, {6541, 49471}, {6684, 21167}, {6707, 39586}, {7081, 33121}, {7172, 37642}, {7968, 13972}, {7969, 13910}, {7976, 13331}, {7982, 38035}, {8256, 8679}, {8705, 47321}, {9025, 25382}, {9054, 10477}, {9284, 21893}, {9778, 48872}, {9969, 23841}, {10222, 38167}, {10791, 42421}, {11246, 32940}, {12017, 18526}, {12245, 14853}, {12583, 16210}, {12702, 31670}, {12898, 15462}, {13211, 32278}, {13576, 24330}, {14839, 24256}, {15621, 18235}, {15826, 47492}, {16587, 22199}, {16790, 36500}, {16823, 17337}, {16830, 17398}, {16972, 17299}, {16973, 17303}, {17018, 32862}, {17056, 29641}, {17061, 25453}, {17140, 40688}, {17246, 49447}, {17259, 38057}, {17265, 38053}, {17280, 20180}, {17286, 49451}, {17301, 49446}, {17334, 24723}, {17366, 32922}, {17385, 19868}, {17602, 29631}, {17718, 29857}, {17719, 29861}, {17725, 29856}, {17726, 29832}, {17765, 49482}, {17769, 49477}, {18183, 24443}, {18253, 41454}, {18525, 46264}, {18743, 29843}, {19130, 22791}, {19875, 20582}, {20423, 34718}, {21699, 27714}, {23638, 38992}, {23970, 28130}, {24169, 42055}, {24206, 38042}, {24231, 48631}, {24987, 25966}, {25006, 31993}, {25416, 38050}, {25555, 38040}, {25590, 38200}, {25591, 37722}, {25992, 28082}, {26015, 30818}, {26083, 36534}, {26227, 33114}, {26251, 46909}, {26582, 31317}, {28174, 48901}, {28178, 48904}, {28186, 48898}, {28190, 48896}, {28503, 32921}, {28595, 33064}, {29632, 37703}, {29690, 31264}, {29850, 32923}, {30331, 38194}, {32784, 49448}, {32855, 42043}, {32911, 33090}, {32912, 33074}, {32913, 33079}, {32938, 32947}, {33087, 49498}, {33092, 42042}, {33171, 41711}, {34627, 43273}, {35026, 35041}, {37705, 48906}, {37727, 38029}, {38074, 47353}, {38112, 48876}, {38138, 39884}, {38145, 43166}, {39870, 47745}, {44669, 47373}, {48628, 49496}, {48800, 48870}, {48804, 48857}, {48806, 48842}

X(49524) = midpoint of X(i) and X(j) for these {i,j}: {6, 8}, {3313, 16980}, {3416, 3751}, {3679, 47359}, {4660, 32935}, {5252, 16799}, {6361, 48910}, {12702, 31670}, {13211, 32278}, {17299, 49495}, {18525, 46264}, {20423, 34718}, {34627, 43273}, {37705, 48906}, {39870, 47745}, {48800, 48870}, {48804, 48857}, {48806, 48842}
X(49524) = reflection of X(i) in X(j) for these {i,j}: {1, 3589}, {141, 10}, {3629, 4663}, {3818, 18357}, {9969, 23841}, {22791, 19130}, {34773, 5092}, {47358, 20582}, {48881, 3579}, {49463, 3946}, {49465, 1125}, {49473, 24295}, {49484, 17355}
X(49524) = complement of X(3242)
X(49524) = X(30555)-complementary conjugate of X(514)
X(49524) = crossdifference of every pair of points on line {6371, 8659}
X(49524) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3932, 17243}, {1, 33165, 3932}, {1, 38047, 3589}, {8, 5772, 2345}, {8, 19065, 49329}, {8, 19066, 49330}, {10, 142, 3823}, {10, 24325, 3826}, {10, 49479, 3836}, {42, 33162, 3703}, {55, 33163, 44416}, {145, 3618, 38315}, {984, 4026, 4364}, {984, 29659, 4026}, {1215, 29673, 2886}, {1738, 49483, 7263}, {2177, 33161, 3712}, {3006, 46897, 5718}, {3416, 47359, 3751}, {3679, 3751, 3416}, {3681, 29667, 1211}, {3790, 49470, 3943}, {3826, 24325, 34824}, {3836, 49479, 25557}, {4429, 24349, 1086}, {4438, 29670, 6690}, {4972, 17165, 3782}, {5818, 39898, 10516}, {7081, 33121, 37646}, {17353, 49466, 1279}, {19875, 47358, 20582}, {24295, 49473, 48810}, {25453, 32920, 17061}, {26227, 33114, 35466}, {29631, 32927, 17602}, {29674, 49490, 4966}, {32771, 33117, 3925}, {32773, 32937, 4415}, {32931, 33120, 11}, {32940, 32948, 11246}, {38057, 39581, 17259}


X(49525) = X(1)X(4718)∩X(37)X(39)

Barycentrics    a^2*b - 3*a*b^2 + a^2*c + 2*a*b*c + 4*b^2*c - 3*a*c^2 + 4*b*c^2 : :
X(49525) = 7 X[37] - 8 X[1125], 3 X[37] - 4 X[24325], 5 X[37] - 4 X[49456], 6 X[1125] - 7 X[24325], 10 X[1125] - 7 X[49456], 4 X[1125] - 7 X[49483], 5 X[24325] - 3 X[49456], 2 X[24325] - 3 X[49483], 2 X[49456] - 5 X[49483], 7 X[75] - 5 X[3617], 3 X[75] - X[31302], 15 X[3617] - 7 X[31302], 2 X[3632] - 7 X[4686], 5 X[3632] - 7 X[49459], 4 X[3632] - 7 X[49468], 3 X[3632] - 7 X[49474], X[3632] - 7 X[49493], 5 X[4686] - 2 X[49459], 3 X[4686] - 2 X[49474], 4 X[49459] - 5 X[49468], 3 X[49459] - 5 X[49474], X[49459] - 5 X[49493], 3 X[49468] - 4 X[49474], X[49468] - 4 X[49493], X[49474] - 3 X[49493], 3 X[3241] - 7 X[24349], 12 X[3241] - 7 X[49461], 9 X[3241] - 7 X[49470], 6 X[3241] - 7 X[49478], 4 X[24349] - X[49461], 3 X[24349] - X[49470], 3 X[49461] - 4 X[49470], 2 X[49470] - 3 X[49478], 7 X[3696] - 6 X[4669], 2 X[984] - 3 X[4688], 7 X[984] - 9 X[19875], 7 X[4688] - 6 X[19875], 7 X[1278] + X[20014], X[20014] - 7 X[49499], 14 X[3739] - 13 X[19877], 13 X[19877] - 7 X[49447], 3 X[4740] - X[49450], 2 X[15569] - 3 X[31178], 3 X[31178] - X[49445], 34 X[19872] - 35 X[31238]

X(49525) lies on these lines: {1, 4718}, {8, 4726}, {37, 39}, {75, 3617}, {145, 4764}, {321, 17154}, {354, 22034}, {518, 3632}, {536, 3241}, {537, 3696}, {545, 3883}, {894, 49463}, {984, 1739}, {1100, 49453}, {1278, 20014}, {1279, 3729}, {3175, 17140}, {3242, 4659}, {3717, 7263}, {3739, 19877}, {3752, 17155}, {3790, 3834}, {3797, 29589}, {3823, 48627}, {3879, 28472}, {3943, 5542}, {3967, 16602}, {3993, 28554}, {3999, 4671}, {4009, 31197}, {4135, 42053}, {4310, 17281}, {4363, 49446}, {4519, 17449}, {4693, 15570}, {4740, 49450}, {4849, 17165}, {4864, 5695}, {4883, 42044}, {4914, 33098}, {4942, 5272}, {4980, 20068}, {5223, 17119}, {5850, 17362}, {7174, 17118}, {7228, 49476}, {15481, 24821}, {15492, 16825}, {15569, 31178}, {16666, 32921}, {16669, 32935}, {17231, 24231}, {17351, 32922}, {19872, 31238}, {24841, 49467}, {28484, 49490}, {28516, 49462}, {28522, 49475}, {28530, 49466}

X(49525) = midpoint of X(i) and X(j) for these {i,j}: {145, 4764}, {1278, 49499}
X(49525) = reflection of X(i) in X(j) for these {i,j}: {8, 4726}, {37, 49483}, {4686, 49493}, {4718, 1}, {49445, 15569}, {49447, 3739}, {49461, 49478}, {49462, 49479}, {49468, 4686}, {49475, 49491}, {49476, 7228}, {49478, 24349}
X(49525) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3967, 24165, 16602}, {17165, 42051, 4849}, {31178, 49445, 15569}


X(49526) = X(1)X(20159)∩X(8)X(192)

Barycentrics    2*a^3*b^2 + a*b^4 + 3*a^3*b*c + a^2*b^2*c + 2*a^3*c^2 + a^2*b*c^2 - b^3*c^2 - b^2*c^3 + a*c^4 : :
X(49526) = 2 X[4743] + X[49447]

X(49526) lies on these lines: {1, 20159}, {8, 192}, {37, 4702}, {75, 4085}, {335, 4393}, {344, 3842}, {518, 4523}, {519, 3735}, {726, 3755}, {742, 4660}, {752, 49496}, {1953, 5819}, {3773, 48630}, {3795, 4518}, {3797, 33165}, {3875, 49448}, {3946, 49479}, {3993, 5853}, {4000, 24325}, {4743, 49447}, {9941, 17034}, {15590, 49491}, {17765, 49470}, {17769, 49450}, {19791, 32920}, {20016, 27480}, {27474, 29593}

X(49526) = midpoint of X(3875) and X(49448)
X(49526) = reflection of X(i) in X(j) for these {i,j}: {75, 4085}, {32941, 37}, {49479, 3946}, {49490, 49472}


X(49527) = X(1)X(344)∩X(9)X(145)

Barycentrics    2*a^3 - a^2*b + 4*a*b^2 - b^3 - a^2*c + 2*a*b*c - b^2*c + 4*a*c^2 - b*c^2 - c^3 : :
X(49527) = 3 X[29574] - 2 X[49478]

X(49527) lies on these lines: {1, 344}, {2, 4901}, {6, 4899}, {8, 3672}, {9, 145}, {10, 10159}, {37, 9053}, {63, 20020}, {192, 5853}, {238, 3244}, {239, 24393}, {516, 49447}, {518, 3688}, {519, 751}, {527, 31302}, {551, 33159}, {908, 29832}, {1125, 17341}, {1266, 2550}, {1279, 25101}, {1738, 49455}, {3220, 3871}, {3241, 7290}, {3242, 3912}, {3243, 17316}, {3305, 19993}, {3452, 29840}, {3617, 4402}, {3621, 17257}, {3623, 26685}, {3625, 33076}, {3626, 32784}, {3663, 32850}, {3664, 49499}, {3696, 28503}, {3711, 5212}, {3790, 36534}, {3828, 25539}, {3891, 25006}, {3920, 33170}, {3932, 49465}, {3943, 49467}, {4082, 32942}, {4104, 32866}, {4353, 4429}, {4416, 5846}, {4439, 49473}, {4464, 49495}, {4514, 4656}, {4666, 30614}, {4684, 16496}, {4847, 32926}, {4864, 17243}, {5211, 5316}, {5222, 10005}, {5294, 29815}, {5542, 24841}, {5847, 49448}, {5882, 6211}, {6210, 28234}, {6762, 20009}, {7295, 25439}, {9041, 17755}, {10436, 39587}, {12648, 40880}, {16517, 17314}, {17282, 39570}, {17334, 28566}, {17599, 30615}, {17765, 49456}, {17769, 49457}, {17772, 49449}, {18230, 39567}, {20056, 38000}, {21060, 33071}, {24391, 41261}, {24620, 46916}, {28472, 49468}, {28580, 49445}, {29633, 38191}, {29639, 32927}

X(49527) = reflection of X(i) in X(j) for these {i,j}: {3879, 49476}, {3883, 984}, {49466, 37}, {49499, 3664}
X(49527) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3717, 17353}, {8, 7174, 4357}, {2550, 49446, 1266}, {3241, 27549, 7290}


X(49528) = X(1)X(87)∩X(75)X(142)

Barycentrics    a^2*b^2 - a*b^3 + 4*a^2*b*c + b^3*c + a^2*c^2 - a*c^3 + b*c^3 : :
X(49528) = 2 X[75] - 3 X[27478], X[75] - 3 X[36494], 5 X[4704] - 3 X[27481], X[4788] + 3 X[27494]

X(49528) lies on these lines: {1, 87}, {37, 3589}, {38, 23462}, {43, 26274}, {75, 142}, {190, 16503}, {193, 49498}, {335, 3663}, {350, 21101}, {518, 3883}, {536, 17392}, {551, 4568}, {740, 49476}, {742, 3879}, {984, 4899}, {1278, 17316}, {1334, 17141}, {3161, 4704}, {3674, 7201}, {3693, 24631}, {3720, 31087}, {3726, 24326}, {3739, 29596}, {3742, 40883}, {3797, 3950}, {3930, 26234}, {3963, 21443}, {3970, 29960}, {3986, 31323}, {4110, 10009}, {4119, 37664}, {4357, 24357}, {4360, 20179}, {4480, 49499}, {4686, 29601}, {4699, 17284}, {4709, 32847}, {4740, 29573}, {4772, 29579}, {4788, 27494}, {4821, 29583}, {7146, 39126}, {7774, 29844}, {14951, 24524}, {16779, 17350}, {17120, 31314}, {17248, 29659}, {17257, 36479}, {17261, 33888}, {17355, 31317}, {17759, 24165}, {17761, 22017}, {21071, 33941}, {21808, 30030}, {21830, 28366}, {24172, 27020}, {25255, 25295}, {27268, 29598}, {28604, 29637}, {29674, 48628}, {29968, 33937}, {30038, 39731}, {30821, 31077}, {49490, 49496}

X(49528) = reflection of X(27478) in X(36494)
X(49528) = crossdifference of every pair of points on line {20979, 21003}
X(49528) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 17755, 25101}, {37, 49481, 17353}, {192, 17319, 3993}, {192, 24349, 3729}, {3993, 49479, 49482}


X(49529) = X(1)X(344)∩X(10)X(141)

Barycentrics    3*a^2*b - 2*a*b^2 + b^3 + 3*a^2*c + b^2*c - 2*a*c^2 + b*c^2 + c^3 : :
X(49529) = 3 X[1] - 5 X[3618], 2 X[1] - 3 X[38049], 10 X[3618] - 9 X[38049], X[6] - 3 X[47359], 3 X[17281] - X[49460], 3 X[8] + X[193], X[193] - 3 X[3751], 3 X[10] - 2 X[141], 5 X[10] - 4 X[3844], 2 X[10] - 3 X[38191], 5 X[141] - 6 X[3844], 4 X[141] - 9 X[38191], 8 X[3844] - 15 X[38191], 2 X[5542] - 3 X[38187], X[69] - 3 X[3679], X[145] - 3 X[16475], 3 X[355] - X[18440], 3 X[551] - 4 X[3589], 2 X[551] - 3 X[38089], 3 X[551] - 2 X[49465], 8 X[3589] - 9 X[38089], 9 X[38089] - 4 X[49465], 3 X[946] - 4 X[19130], 2 X[946] - 3 X[38146], 8 X[19130] - 9 X[38146], 2 X[1001] - 3 X[38194], and many others

X(49529) lies on these lines: {1, 344}, {2, 16496}, {6, 519}, {8, 193}, {9, 36479}, {10, 141}, {65, 34378}, {69, 3679}, {145, 3790}, {182, 5882}, {210, 5241}, {226, 21241}, {238, 49466}, {306, 33162}, {355, 18440}, {391, 48849}, {392, 7064}, {511, 11362}, {515, 46264}, {516, 32935}, {517, 21629}, {524, 4669}, {527, 4660}, {528, 17351}, {536, 4780}, {537, 3663}, {551, 3589}, {599, 4745}, {726, 3755}, {730, 41622}, {742, 4709}, {908, 33120}, {940, 30615}, {946, 19130}, {952, 39870}, {966, 48851}, {984, 4899}, {993, 12329}, {1001, 38194}, {1125, 3242}, {1213, 48853}, {1215, 4847}, {1350, 43174}, {1385, 38118}, {1386, 3244}, {1387, 38197}, {1469, 4848}, {1738, 24349}, {1757, 3883}, {1992, 4677}, {2177, 3977}, {2325, 36404}, {2550, 7222}, {2810, 17792}, {3011, 31229}, {3241, 16491}, {3247, 48830}, {3416, 3626}, {3452, 4090}, {3596, 4737}, {3617, 26806}, {3619, 19875}, {3625, 4663}, {3629, 28538}, {3631, 38098}, {3635, 38315}, {3654, 33878}, {3655, 12017}, {3681, 4104}, {3687, 33169}, {3703, 4028}, {3722, 35263}, {3729, 28580}, {3749, 26065}, {3754, 24476}, {3763, 3828}, {3773, 4924}, {3846, 21060}, {3870, 33163}, {3879, 32847}, {3912, 33165}, {3913, 37492}, {3914, 17165}, {3923, 5853}, {3932, 49478}, {3935, 33170}, {3938, 5294}, {3943, 49475}, {3946, 49455}, {3950, 4439}, {3952, 29835}, {3957, 33166}, {3974, 39594}, {3979, 33164}, {4001, 33074}, {4030, 4641}, {4054, 31161}, {4084, 9021}, {4126, 44307}, {4133, 28581}, {4301, 5480}, {4356, 49456}, {4357, 29659}, {4416, 33076}, {4422, 42819}, {4429, 24231}, {4430, 29679}, {4431, 49459}, {4432, 30331}, {4437, 29571}, {4438, 13405}, {4649, 49476}, {4655, 5850}, {4656, 42054}, {4661, 29667}, {4672, 17765}, {4684, 29674}, {4685, 37676}, {4702, 17340}, {4743, 28516}, {4807, 9040}, {4852, 28503}, {5014, 41011}, {5050, 37727}, {5138, 12437}, {5249, 33117}, {5493, 29181}, {5587, 39898}, {5686, 39581}, {5745, 29670}, {5750, 16973}, {5836, 34381}, {5837, 9052}, {5848, 15863}, {5881, 6776}, {5901, 38167}, {6666, 24331}, {6684, 38116}, {6702, 38192}, {7982, 14853}, {8666, 36741}, {8715, 36740}, {9956, 38165}, {10222, 18583}, {13464, 14561}, {13607, 38029}, {15178, 38110}, {16484, 25101}, {16706, 24841}, {17023, 32029}, {17235, 48821}, {17276, 48829}, {17279, 42871}, {17368, 36534}, {17766, 41749}, {17769, 49489}, {17781, 32947}, {19586, 20340}, {19925, 38144}, {22769, 25440}, {24175, 42053}, {24177, 42055}, {24199, 31178}, {24206, 31399}, {24210, 32937}, {24693, 47595}, {25006, 32771}, {25881, 46190}, {26015, 32931}, {26723, 32923}, {27538, 29843}, {28194, 31670}, {28204, 48906}, {29639, 46897}, {30768, 33122}, {31673, 48884}, {31730, 48880}, {32777, 41711}, {32920, 40940}, {33084, 39597}, {33179, 38040}, {34627, 39874}, {34718, 44456}, {37708, 39901}, {37711, 39900}, {37712, 39878}, {37737, 38198}, {38048, 43179}, {47277, 47490}, {47279, 47488}, {47281, 47494}, {47449, 47496}, {47454, 47495}, {47456, 47472}, {47457, 47491}, {47459, 47489}, {47460, 47537}, {47461, 47536}, {47463, 47533}, {47464, 47564}, {48630, 49450}

X(49529) = midpoint of X(i) and X(j) for these {i,j}: {8, 3751}, {1992, 4677}, {5881, 6776}, {47277, 47490}, {49459, 49496}
X(49529) = reflection of X(i) in X(j) for these {i,j}: {599, 4745}, {1350, 43174}, {3242, 1125}, {3244, 1386}, {3416, 3626}, {3663, 4085}, {4301, 5480}, {5882, 182}, {10222, 18583}, {24476, 3754}, {32941, 17355}, {47358, 3828}, {47491, 47457}, {49455, 3946}, {49465, 3589}, {49479, 49481}
X(49529) = complement of X(16496)
X(49529) = crossdifference of every pair of points on line {9002, 21007}
X(49529) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3717, 4078}, {10, 5542, 3836}, {10, 49479, 142}, {3242, 38047, 1125}, {3589, 49465, 551}, {3836, 49491, 5542}, {4090, 29655, 3452}, {4429, 49499, 24231}, {4439, 49471, 3950}, {29659, 49448, 4357}, {29674, 49498, 4684}, {31161, 33136, 4054}, {33165, 49490, 3912}, {38087, 47358, 3828}


X(49530) = X(1)X(87)∩X(37)X(48)

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

X(49530) lies on these lines: {1, 87}, {21, 976}, {31, 518}, {37, 48}, {38, 1011}, {42, 345}, {56, 21330}, {75, 3924}, {244, 16405}, {612, 7675}, {698, 4376}, {740, 49487}, {958, 3728}, {964, 4812}, {982, 4203}, {1193, 17526}, {1582, 17522}, {2293, 3486}, {3242, 20992}, {3720, 33143}, {3747, 35628}, {3842, 16342}, {5311, 10458}, {7770, 30028}, {15955, 49469}, {21775, 22230}, {28348, 34247}, {31302, 36565}

X(49530) = crossdifference of every pair of points on line {20979, 21189}


X(49531) = X(6)X(740)∩X(7)X(8)

Barycentrics    a^3*b^2 - a^2*b^3 + 3*a^3*b*c + a^2*b^2*c + b^4*c + a^3*c^2 + a^2*b*c^2 + b^3*c^2 - a^2*c^3 + b^2*c^3 + b*c^4 : :
X(49531) = 2 X[37] - 3 X[38047], 3 X[16475] - X[49469], 3 X[38315] - 2 X[49471]

X(49531) lies on these lines: {1, 25497}, {2, 9507}, {6, 740}, {7, 8}, {10, 20271}, {37, 38047}, {141, 4733}, {335, 4429}, {536, 47359}, {537, 48829}, {726, 3755}, {742, 3751}, {984, 4026}, {1001, 17755}, {1002, 31130}, {1386, 3797}, {2325, 3993}, {3242, 24325}, {3789, 26234}, {3826, 4437}, {3844, 29593}, {3967, 20173}, {4663, 49496}, {4688, 47358}, {4709, 5847}, {5263, 31317}, {5846, 49459}, {9041, 31178}, {9053, 49490}, {13576, 17165}, {15569, 26626}, {16475, 49469}, {20716, 32937}, {28600, 30758}, {32860, 37676}, {38315, 49471}

X(49531) = midpoint of X(3751) and X(49474)
X(49531) = reflection of X(i) in X(j) for these {i,j}: {1, 49481}, {3242, 24325}, {3416, 3696}, {47358, 4688}, {49470, 1386}, {49496, 4663}


X(49532) = X(1)X(87)∩X(7)X(32847)

Barycentrics    a^2*b - 2*a*b^2 + a^2*c + a*b*c + 2*b^2*c - 2*a*c^2 + 2*b*c^2 : :
X(49532) = 3 X[1] - 2 X[192], 5 X[1] - 4 X[3993], 3 X[1] - 4 X[49479], 5 X[192] - 6 X[3993], X[192] - 3 X[24349], 4 X[192] - 3 X[49445], 2 X[3993] - 5 X[24349], 8 X[3993] - 5 X[49445], 3 X[3993] - 5 X[49479], 4 X[24349] - X[49445], 3 X[24349] - 2 X[49479], 3 X[49445] - 8 X[49479], 3 X[8] - 5 X[4821], 6 X[10] - 7 X[4772], 7 X[4772] - 3 X[31302], 8 X[37] - 9 X[25055], 2 X[37] - 3 X[31178], 3 X[25055] - 4 X[31178], 4 X[75] - 3 X[3679], 5 X[75] - 4 X[4732], 3 X[75] - 2 X[49457], 15 X[3679] - 16 X[4732], 3 X[3679] - 2 X[49448], 9 X[3679] - 8 X[49457], 8 X[4732] - 5 X[49448], 6 X[4732] - 5 X[49457], 3 X[49448] - 4 X[49457], 3 X[3632] - 8 X[4686], 3 X[3632] - 4 X[49459], 5 X[3632] - 8 X[49468], X[3632] - 4 X[49493], 5 X[4686] - 3 X[49468], 4 X[4686] - 3 X[49474], 2 X[4686] - 3 X[49493], 5 X[49459] - 6 X[49468], 2 X[49459] - 3 X[49474], X[49459] - 3 X[49493], 4 X[49468] - 5 X[49474], 2 X[49468] - 5 X[49493], 3 X[49469] - 4 X[49475], 2 X[49475] - 3 X[49490], 6 X[551] - 5 X[4704], 3 X[3633] + 4 X[4764], X[3633] - 4 X[49499], 2 X[4764] + 3 X[49498], X[4764] + 3 X[49499], 4 X[984] - 5 X[1698], 3 X[984] - 4 X[3739], 15 X[1698] - 16 X[3739], 5 X[1698] - 8 X[49483], 2 X[3739] - 3 X[49483], 3 X[3241] - X[4788], 21 X[3624] - 20 X[4687], 7 X[3624] - 8 X[24325], 7 X[3624] - 4 X[49447], 5 X[4687] - 6 X[24325], 5 X[4687] - 3 X[49447], 2 X[3728] - 3 X[46895], 16 X[3842] - 17 X[19872], 3 X[4677] - 4 X[4709], 2 X[4709] - 3 X[4740], 10 X[4699] - 9 X[19875], 5 X[4816] - 4 X[49450], 5 X[11522] - 4 X[20430]

X(49532) lies on these lines: {1, 87}, {7, 32847}, {8, 4821}, {9, 24821}, {10, 4772}, {37, 25055}, {43, 17155}, {75, 537}, {145, 28522}, {190, 15485}, {239, 27494}, {312, 42055}, {335, 17284}, {518, 3632}, {519, 1278}, {536, 49469}, {551, 4704}, {596, 978}, {740, 3633}, {982, 30818}, {984, 1698}, {1086, 33165}, {1125, 17339}, {1215, 17591}, {3210, 42043}, {3241, 4788}, {3550, 32920}, {3624, 4687}, {3644, 28554}, {3663, 29659}, {3703, 33103}, {3728, 46895}, {3758, 49472}, {3782, 33169}, {3797, 29573}, {3842, 19872}, {3891, 32940}, {3967, 17063}, {3971, 25502}, {3977, 29675}, {3992, 30090}, {4054, 29676}, {4085, 4398}, {4090, 17490}, {4310, 29637}, {4353, 29646}, {4365, 4430}, {4384, 33888}, {4392, 29827}, {4439, 17234}, {4440, 4660}, {4649, 49453}, {4659, 9055}, {4671, 17449}, {4677, 4709}, {4693, 42871}, {4699, 19875}, {4756, 17125}, {4777, 23345}, {4816, 49450}, {4850, 31161}, {4884, 33111}, {5905, 32866}, {6763, 16551}, {7174, 24342}, {8616, 32923}, {9336, 20363}, {11522, 20430}, {16468, 32922}, {16484, 17262}, {16569, 24165}, {16831, 27481}, {16832, 27478}, {17116, 36480}, {17140, 26102}, {17147, 42042}, {17154, 30942}, {17160, 49497}, {17261, 24331}, {17276, 33076}, {17304, 36478}, {17355, 29660}, {17365, 28503}, {17483, 32854}, {17755, 31183}, {18743, 42053}, {19804, 42054}, {20068, 31330}, {20891, 39742}, {21255, 24231}, {24841, 32941}, {25590, 36531}, {28516, 49470}, {28526, 49466}, {28555, 49452}, {29598, 31317}, {29825, 46901}, {29856, 33143}, {29858, 33148}, {32856, 33089}, {32926, 37604}, {33090, 33098}, {33144, 33167}, {33146, 33162}, {33147, 33163}

X(49532) = reflection of X(i) in X(j) for these {i,j}: {1, 24349}, {192, 49479}, {984, 49483}, {3632, 49474}, {3633, 49498}, {3644, 49471}, {4677, 4740}, {31302, 10}, {49445, 1}, {49447, 24325}, {49448, 75}, {49452, 49478}, {49459, 4686}, {49469, 49490}, {49470, 49491}, {49474, 49493}, {49498, 49499}
X(49532) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 49448, 3679}, {192, 24349, 49479}, {192, 49479, 1}, {894, 49455, 1}, {4090, 17490, 36634}, {4671, 17449, 31137}, {4686, 49459, 49474}, {17140, 32925, 26102}, {17155, 17165, 43}, {24165, 32937, 16569}, {32920, 32939, 3550}, {32922, 32935, 16468}, {32923, 32933, 8616}, {33143, 33170, 29856}, {33148, 33161, 29858}, {49459, 49493, 4686}


X(49533) = X(6)X(536)∩X(75)X(141)

Barycentrics    -(a*b^3) + 3*a^2*b*c - a*b^2*c + 2*b^3*c - a*b*c^2 - a*c^3 + 2*b*c^3 : :
X(49533) = 6 X[37] - 7 X[47355], X[69] - 3 X[4740], 3 X[75] - 2 X[141], 3 X[192] - 5 X[3618], 5 X[3618] - 6 X[49481], X[193] + 3 X[1278], 6 X[4686] - X[40341], 4 X[3589] - 3 X[4664], 3 X[3644] - 8 X[6329], 5 X[3763] - 6 X[4688], 3 X[4764] + 4 X[32455], 4 X[32455] - 3 X[49496], 4 X[19130] - 3 X[20430], 3 X[31178] - 2 X[49465], 3 X[38047] - 2 X[49456], 3 X[38315] - 2 X[49462]

X(49533) lies on these lines: {6, 536}, {37, 29598}, {69, 4740}, {75, 141}, {192, 3618}, {193, 742}, {518, 3632}, {537, 4660}, {726, 3755}, {1386, 49452}, {3242, 17118}, {3589, 4664}, {3629, 17225}, {3631, 39707}, {3644, 6329}, {3726, 31130}, {3763, 4688}, {4371, 5819}, {4659, 16973}, {4713, 41794}, {4737, 21138}, {4764, 32455}, {7222, 24349}, {9053, 17365}, {17246, 49447}, {17336, 31349}, {19130, 20430}, {20271, 33937}, {28554, 47359}, {29010, 46264}, {31178, 49465}, {38047, 49456}, {38315, 49462}

X(49533) = midpoint of X(4764) and X(49496)
X(49533) = reflection of X(i) in X(j) for these {i,j}: {192, 49481}, {3242, 49483}, {49452, 1386}


X(49534) = X(1)X(3589)∩X(145)X(238)

Barycentrics    2*a^3 - a^2*b + 3*a*b^2 - b^3 - a^2*c + a*b*c - b^2*c + 3*a*c^2 - b*c^2 - c^3 : :
X(49534) = 3 X[984] - 2 X[3883], 4 X[4399] - 5 X[4668]

X(49534) lies on these lines: {1, 3589}, {8, 3775}, {9, 3633}, {10, 17370}, {145, 238}, {171, 20020}, {192, 17765}, {519, 751}, {528, 49445}, {752, 31302}, {3006, 17725}, {3242, 32847}, {3244, 3717}, {3550, 4884}, {3625, 4357}, {3632, 7174}, {3635, 17353}, {3751, 4929}, {3773, 36534}, {3790, 49473}, {3891, 32865}, {3920, 33169}, {3938, 33092}, {3961, 32855}, {4310, 31151}, {4399, 4668}, {4429, 49464}, {4865, 33101}, {5014, 33154}, {5844, 6210}, {5846, 49448}, {5853, 49452}, {6211, 37727}, {9041, 49498}, {10327, 17598}, {16496, 32846}, {17123, 19993}, {17257, 20053}, {17347, 28512}, {17363, 49449}, {17389, 17755}, {17717, 29832}, {17766, 49447}, {20056, 32916}, {24715, 49446}, {28503, 49474}, {29674, 49465}, {29815, 33162}, {29821, 30615}, {31252, 39570}, {32850, 33149}, {32854, 33084}, {32920, 33111}, {32926, 33141}, {33072, 33103}, {33091, 33174}, {49476, 49490}

X(49534) = reflection of X(i) in X(j) for these {i,j}: {3633, 17388}, {17363, 49449}, {49490, 49476}
X(49534) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4901, 33159}, {3242, 32847, 33087}, {3632, 7174, 33076}, {4901, 33159, 33165}, {29832, 32927, 17717}, {32850, 49455, 33149}


X(49535) = X(1)X(4704)∩X(10)X(141)

Barycentrics    4*a^2*b - 3*a*b^2 + 4*a^2*c + 2*a*b*c + b^2*c - 3*a*c^2 + b*c^2 : :
X(49534) = 7 X[1] - 5 X[4704], 3 X[1] - X[31302], 15 X[4704] - 7 X[31302], 7 X[10] - 8 X[3739], 3 X[10] - 4 X[24325], 7 X[10] - 4 X[49449], 5 X[10] - 4 X[49457], X[10] - 4 X[49491], 6 X[3739] - 7 X[24325], 10 X[3739] - 7 X[49457], 4 X[3739] - 7 X[49479], 2 X[3739] - 7 X[49491], 7 X[24325] - 3 X[49449], 5 X[24325] - 3 X[49457], 2 X[24325] - 3 X[49479], X[24325] - 3 X[49491], 5 X[49449] - 7 X[49457], 2 X[49449] - 7 X[49479], X[49449] - 7 X[49491], 2 X[49457] - 5 X[49479], X[49457] - 5 X[49491], 3 X[4740] - 7 X[24349], 9 X[4740] - 7 X[49474], 3 X[4740] + 7 X[49498], 3 X[24349] - X[49474], X[49474] + 3 X[49498], 3 X[551] - 2 X[984], 7 X[3244] - 2 X[3644], 5 X[3244] - 2 X[49452], 3 X[3244] - 2 X[49470], X[3244] + 2 X[49499], 5 X[3644] - 7 X[49452], 3 X[3644] - 7 X[49470], X[3644] - 7 X[49490], X[3644] + 7 X[49499], 3 X[49452] - 5 X[49470], X[49452] - 5 X[49490], X[49452] + 5 X[49499], X[49470] - 3 X[49490], X[49470] + 3 X[49499], 3 X[3241] - X[49445], 4 X[3696] - 3 X[34641], 8 X[3842] - 9 X[19883], 5 X[4668] - 7 X[4772], 3 X[4669] - 2 X[49450], 3 X[31178] - X[49450], 4 X[4691] - 5 X[4699], 5 X[4821] - X[20053], 19 X[22266] - 20 X[31238]

X(49535) lies on these lines: {1, 4704}, {10, 141}, {37, 15828}, {42, 17154}, {75, 3625}, {145, 28522}, {192, 3635}, {354, 4090}, {519, 4740}, {537, 3993}, {551, 984}, {726, 3244}, {899, 17146}, {1125, 17338}, {1278, 3633}, {3241, 49445}, {3242, 33682}, {3243, 3923}, {3696, 34641}, {3741, 4430}, {3840, 3873}, {3842, 19883}, {4135, 17165}, {4432, 15570}, {4649, 24841}, {4667, 9055}, {4668, 4772}, {4669, 31178}, {4672, 4864}, {4685, 17140}, {4691, 4699}, {4709, 49483}, {4821, 20053}, {4849, 42053}, {4883, 42054}, {4946, 17495}, {5223, 24331}, {17023, 31314}, {17364, 28512}, {17365, 17765}, {17755, 29600}, {17770, 49466}, {22266, 31238}, {24182, 33815}, {27484, 31211}, {28516, 49475}, {28554, 49461}, {28582, 49471}, {29574, 33888}, {29594, 31317}, {32935, 42871}

X(49535) = midpoint of X(i) and X(j) for these {i,j}: {1278, 3633}, {24349, 49498}, {49490, 49499}
X(49535) = reflection of X(i) in X(j) for these {i,j}: {10, 49479}, {192, 3635}, {3244, 49490}, {3625, 75}, {3993, 49478}, {4669, 31178}, {4709, 49483}, {49448, 1125}, {49449, 3739}, {49479, 49491}
X(49535) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4649, 24841, 49464}, {17165, 42057, 4135}


X(49536) = X(1)X(4899)∩X(10)X(141)

Barycentrics    5*a^2*b - 4*a*b^2 + b^3 + 5*a^2*c + b^2*c - 4*a*c^2 + b*c^2 + c^3 : :
X(49536) = 5 X[8] - X[20080], 5 X[10] - 4 X[141], 9 X[10] - 8 X[3844], 5 X[10] - 6 X[38191], 9 X[141] - 10 X[3844], 2 X[141] - 3 X[38191], 20 X[3844] - 27 X[38191], 3 X[1992] - 5 X[3751], X[4133] + 2 X[4924], 3 X[551] - 2 X[3242], 5 X[551] - 6 X[47352], 5 X[3242] - 9 X[47352], X[3242] - 3 X[47359], 3 X[47352] - 5 X[47359], 2 X[599] - 3 X[38098], 5 X[946] - 6 X[38136], 2 X[1352] - 3 X[38155], 2 X[3416] - 3 X[4669], 5 X[3416] - 3 X[15533], 5 X[4669] - 2 X[15533], 8 X[3589] - 7 X[15808], 5 X[3618] - 4 X[3636], 5 X[3625] + 2 X[6144], 2 X[3635] - 3 X[16475], 3 X[3919] - 2 X[24476], 3 X[5032] - X[34747], 3 X[5050] - 2 X[13607], X[5921] - 3 X[37712], 5 X[19862] - 6 X[38047], 5 X[31399] - 6 X[38165], 3 X[38049] - 2 X[49465], 3 X[38127] - 2 X[48876], 3 X[38201] - 2 X[47595]

X(49536) lies on these lines: {1, 4899}, {6, 2325}, {8, 17116}, {10, 141}, {69, 3626}, {193, 3632}, {519, 1992}, {524, 34641}, {537, 3755}, {551, 3242}, {599, 38098}, {726, 4780}, {946, 38136}, {1125, 16496}, {1210, 27422}, {1351, 28234}, {1352, 38155}, {1386, 9041}, {1738, 49499}, {1757, 49466}, {3416, 4669}, {3564, 47745}, {3589, 15808}, {3618, 3636}, {3625, 5847}, {3635, 16475}, {3717, 49490}, {3912, 49498}, {3919, 24476}, {4028, 32848}, {4078, 49478}, {4082, 42057}, {4084, 34378}, {4090, 11019}, {4126, 4883}, {4138, 29673}, {4422, 15570}, {4437, 29600}, {4660, 5850}, {4663, 9053}, {4684, 33165}, {4847, 25385}, {5032, 34747}, {5050, 13607}, {5223, 36479}, {5267, 12329}, {5853, 32935}, {5921, 37712}, {6776, 28236}, {17355, 49458}, {19862, 38047}, {19925, 39898}, {21060, 29655}, {25439, 37492}, {31399, 38165}, {32029, 49464}, {38049, 49465}, {38127, 48876}, {38201, 47595}

X(49536) = midpoint of X(193) and X(3632)
X(49536) = reflection of X(i) in X(j) for these {i,j}: {69, 3626}, {551, 47359}, {3244, 6}, {16496, 1125}, {39898, 19925}, {49458, 17355}
X(49536) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {141, 38191, 10}, {24325, 24393, 10}

leftri

Centers related to 1st- and 2nd- Savin triangles: X(49537)-X(49633)

rightri

This preamble and centers X(49537)-X(49633) were contributed by César Eliud Lozada, May 22, 2022.

1st- and 2nd- Savin triangles were introduced in the preamble just before X(44301).


X(49537) = PERSPECTOR OF THESE TRIANGLES: 1st SAVIN AND URSA MINOR

Barycentrics    a*((b-c)^2*a^2-(b^3+c^3)*a+b*c*(b-c)^2) : :
X(49537) = 3*X(210)-2*X(4416) = 3*X(354)-4*X(3664) = 3*X(354)-2*X(21746) = 6*X(3740)-5*X(17331) = 5*X(17609)-4*X(39543)

X(49537) lies on these lines: {1, 1463}, {2, 9309}, {7, 3056}, {11, 45305}, {37, 513}, {46, 48875}, {55, 1742}, {56, 6210}, {65, 511}, {72, 17770}, {75, 9025}, {87, 41886}, {142, 3271}, {144, 4517}, {175, 6283}, {176, 6405}, {210, 4416}, {226, 20359}, {256, 7184}, {291, 7240}, {354, 1122}, {516, 3057}, {518, 17364}, {527, 3688}, {573, 1155}, {651, 2330}, {674, 17365}, {894, 3888}, {991, 1456}, {1042, 8240}, {1214, 17611}, {1319, 31394}, {1423, 21010}, {1441, 4459}, {1469, 4307}, {1716, 28365}, {1756, 37609}, {1836, 10401}, {1837, 48878}, {2227, 16606}, {2234, 21857}, {2269, 3000}, {2309, 20731}, {3663, 4014}, {3671, 10544}, {3677, 19604}, {3706, 34282}, {3740, 17331}, {3752, 23659}, {3779, 4644}, {3781, 24695}, {3784, 26098}, {3878, 28508}, {3879, 6007}, {3917, 41011}, {3931, 49557}, {3937, 29639}, {3942, 17447}, {4110, 24451}, {4124, 20905}, {4252, 28275}, {4499, 17261}, {4553, 17351}, {5880, 37516}, {5919, 29349}, {6004, 36226}, {7032, 28358}, {7155, 20917}, {7175, 17798}, {7186, 33097}, {7196, 30547}, {7228, 9024}, {7277, 22277}, {7321, 25048}, {9579, 10480}, {9957, 29229}, {11997, 15726}, {12047, 48934}, {14100, 39775}, {17263, 24482}, {17338, 25108}, {17350, 25279}, {17368, 25144}, {17605, 24220}, {17606, 48888}, {17609, 39543}, {17668, 40965}, {19951, 25995}, {20258, 20486}, {20343, 34832}, {20715, 43216}, {20978, 28351}, {21138, 23677}, {21321, 22053}, {24456, 24661}, {24655, 27254}, {24752, 27334}, {26910, 29680}, {27626, 36635}, {37600, 48929}

X(49537) = reflection of X(21746) in X(3664)
X(49537) = barycentric product X(i)*X(j) for these {i, j}: {87, 20528}, {331, 20781}, {932, 23756}
X(49537) = trilinear product X(i)*X(j) for these {i, j}: {85, 23522}, {273, 20781}, {330, 20667}, {1434, 22205}
X(49537) = X(7)-daleth conjugate of-X(20358)
X(49537) = perspector (1st Savin, Ursa-minor)
X(49537) = X(264)-of-Ursa-minor triangle, when ABC is acute
X(49537) = X(1742)-of-Mandart-incircle triangle
X(49537) = X(3164)-of-intouch triangle, when ABC is acute
X(49537) = X(6210)-of-2nd anti-circumperp-tangential triangle
X(49537) = X(40896)-of-inverse-in-incircle triangle, when ABC is acute
X(49537) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 3551, 4941), (7, 3056, 20358), (256, 7184, 37596), (894, 3888, 17792), (3057, 31391, 17635), (3664, 21746, 354), (7155, 26135, 20917), (24451, 25311, 4110)


X(49538) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st SAVIN TO 1st ALTINTAS-ISODYNAMIC

Barycentrics    2*(2*a^6-(b+c)*a^5+2*b*c*a^4-(b+c)*(2*b^2+3*b*c+2*c^2)*a^3-(4*b^4+4*c^4-b*c*(7*b^2-10*b*c+7*c^2))*a^2+(b+c)*(2*b^4+2*c^4-b*c*(3*b^2-b*c+3*c^2))*a+(b^4+c^4+b*c*(b^2-b*c+c^2))*(b-c)^2)*sqrt(3)*S+(-a+b+c)*(a+b-c)*(a-b+c)*(2*a^5-(b+c)*a^4-11*(b^2+c^2)*a^3-(b+c)*(5*b^2-3*b*c+5*c^2)*a^2-(b^4+14*b^2*c^2+c^4)*a-(b+c)*(b^4+c^4-b*c*(3*b^2-5*b*c+3*c^2))) : :
X(49538) = 4*X(6669)-3*X(49569) = 3*X(21359)-X(49575)

The reciprocal orthologic center of these triangles is X(49539).

X(49538) lies on these lines: {1, 616}, {2, 49571}, {10, 40707}, {13, 226}, {81, 41639}, {86, 99}, {298, 519}, {299, 49611}, {530, 37631}, {532, 49594}, {618, 3666}, {1125, 30471}, {1319, 3638}, {3180, 41638}, {3649, 11705}, {4357, 11129}, {5243, 22892}, {5530, 49634}, {5978, 5988}, {6669, 36668}, {11299, 49604}, {13442, 41022}, {14904, 29574}, {21359, 49575}, {37833, 44431}

X(49538) = reflection of X(i) in X(j) for these (i, j): (3180, 41638), (49540, 15903)
X(49538) = anticomplement of X(49571)
X(49538) = orthologic center (1st Savin, T) for these triangles T: 1st Altintas-isodynamic, Bankoff, 3rd Fermat-Dao, 7th Fermat-Dao, 11th Fermat-Dao, 15th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi, 1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi, 1st half-diamonds-central, 1st isodynamic-Dao, 3rd isodynamic-Dao, Largest-circumscribed-equilateral, 1st Lemoine-Dao, outer-Napoleon
X(49538) = X(13)-of-1st Savin triangle
X(49538) = X(3165)-of-intouch triangle, when ABC is acute
X(49538) = {X(551), X(3663)}-harmonic conjugate of X(49540)


X(49539) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ALTINTAS-ISODYNAMIC TO 1st SAVIN

Barycentrics    2*(2*a^4-(b+c)*a^3+(b+c)^2*a^2+(b^2-c^2)*(b-c)*a-3*(b^2-c^2)^2)*sqrt(3)*S+6*a^6+(b+c)*a^5-(b+c)^2*a^4-2*(b+c)*(b^2+c^2)*a^3+4*(b+c)^2*b*c*a^2+(b^2-c^2)^2*(b+c)*a-(5*b^2+2*b*c+5*c^2)*(b^2-c^2)^2 : :
X(49539) = X(41020)-3*X(49569) = 3*X(41024)+X(49575) = 3*X(41036)-X(49594)

The reciprocal orthologic center of these triangles is X(49538).

X(49539) lies on these lines: {4, 49573}, {115, 118}, {519, 41016}, {1503, 49596}, {2796, 41060}, {7684, 41638}, {41018, 49559}, {41019, 49603}, {41020, 49569}, {41022, 49571}, {41024, 49575}, {41026, 49579}, {41028, 49580}, {41030, 49581}, {41032, 49582}, {41034, 49588}, {41036, 49594}, {41038, 49604}, {41040, 49611}

X(49539) = orthologic center (1st Altintas-isodynamic, T) for these triangles T: 1st Jenkins, 1st Savin
X(49539) = reflection of X(41638) in X(7684)


X(49540) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st SAVIN TO 2nd ALTINTAS-ISODYNAMIC

Barycentrics    -2*(2*a^6-(b+c)*a^5+2*b*c*a^4-(b+c)*(2*b^2+3*b*c+2*c^2)*a^3-(4*b^4+4*c^4-b*c*(7*b^2-10*b*c+7*c^2))*a^2+(b+c)*(2*b^4+2*c^4-b*c*(3*b^2-b*c+3*c^2))*a+(b^4+c^4+b*c*(b^2-b*c+c^2))*(b-c)^2)*sqrt(3)*S+(-a+b+c)*(a+b-c)*(a-b+c)*(2*a^5-(b+c)*a^4-11*(b^2+c^2)*a^3-(b+c)*(5*b^2-3*b*c+5*c^2)*a^2-(b^4+14*b^2*c^2+c^4)*a-(b+c)*(b^4+c^4-b*c*(3*b^2-5*b*c+3*c^2))) : :
X(49540) = 4*X(6670)-3*X(49570) = 3*X(21360)-X(49576)

The reciprocal orthologic center of these triangles is X(49541).

X(49540) lies on these lines: {1, 617}, {2, 49572}, {10, 40706}, {14, 226}, {81, 41649}, {86, 99}, {298, 49610}, {299, 519}, {531, 37631}, {533, 49595}, {619, 3666}, {1125, 30472}, {1319, 3639}, {3181, 41648}, {3649, 11706}, {4357, 11128}, {5242, 22848}, {5530, 49635}, {5979, 5988}, {6670, 36669}, {11300, 49605}, {13442, 41023}, {14905, 29574}, {21360, 49576}, {37830, 44431}

X(49540) = reflection of X(i) in X(j) for these (i, j): (3181, 41648), (49538, 15903)
X(49540) = anticomplement of X(49572)
X(49540) = orthologic center (1st Savin, T) for these triangles T: 2nd Altintas-isodynamic, 4th Fermat-Dao, 8th Fermat-Dao, 12th Fermat-Dao, 16th Fermat-Dao, 1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi, 3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi, 2nd half-diamonds-central, 2nd isodynamic-Dao, 4th isodynamic-Dao, 2nd Lemoine-Dao, inner-Napoleon
X(49540) = X(14)-of-1st Savin triangle
X(49540) = X(3166)-of-intouch triangle, when ABC is acute
X(49540) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (551, 3663, 49538), (17320, 37617, 49538)


X(49541) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ALTINTAS-ISODYNAMIC TO 1st SAVIN

Barycentrics    -2*(2*a^4-(b+c)*a^3+(b+c)^2*a^2+(b^2-c^2)*(b-c)*a-3*(b^2-c^2)^2)*sqrt(3)*S+6*a^6+(b+c)*a^5-(b+c)^2*a^4-2*(b+c)*(b^2+c^2)*a^3+4*(b+c)^2*b*c*a^2+(b^2-c^2)^2*(b+c)*a-(5*b^2+2*b*c+5*c^2)*(b^2-c^2)^2 : :
X(49541) = X(41021)-3*X(49570) = 3*X(41025)+X(49576) = 3*X(41037)-X(49595)

The reciprocal orthologic center of these triangles is X(49540).

X(49541) lies on these lines: {4, 49574}, {115, 118}, {519, 41017}, {1503, 49597}, {2796, 41061}, {7685, 41648}, {41021, 49570}, {41023, 49572}, {41025, 49576}, {41027, 49583}, {41029, 49584}, {41031, 49577}, {41033, 49578}, {41035, 49589}, {41037, 49595}, {41039, 49605}, {41041, 49610}

X(49541) = orthologic center (2nd Altintas-isodynamic, T) for these triangles T: 1st Jenkins, 1st Savin
X(49541) = reflection of X(41648) in X(7685)


X(49542) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-ARA TO 1st SAVIN

Barycentrics    (a^2+b^2-c^2)*(a^2-b^2+c^2)*(2*a^3+(b+c)*a^2+(b+c)*(b^2+c^2)) : :
X(49542) = 3*X(428)-X(1829) = 3*X(428)+X(12135)

The reciprocal orthologic center of these triangles is X(1).

X(49542) lies on these lines: {1, 4}, {2, 34712}, {8, 6995}, {10, 25}, {19, 2321}, {24, 6684}, {27, 3912}, {28, 1861}, {30, 37613}, {40, 7487}, {145, 7408}, {235, 19925}, {355, 1598}, {406, 19784}, {427, 1125}, {428, 519}, {444, 3831}, {468, 3634}, {469, 17023}, {475, 19836}, {516, 1902}, {517, 6756}, {551, 5064}, {726, 12143}, {860, 19869}, {936, 37394}, {996, 4186}, {1041, 1448}, {1063, 45132}, {1076, 36496}, {1172, 5280}, {1210, 11399}, {1385, 1595}, {1386, 3867}, {1395, 5264}, {1398, 4315}, {1452, 4848}, {1474, 5750}, {1503, 44547}, {1593, 4297}, {1596, 18480}, {1597, 18481}, {1698, 6353}, {1724, 2212}, {1737, 4231}, {1753, 37395}, {1824, 2901}, {1826, 1973}, {1839, 3970}, {1842, 41013}, {1843, 5847}, {1844, 29040}, {1862, 1900}, {1872, 7511}, {1876, 4298}, {1883, 40985}, {1885, 28164}, {1890, 5853}, {1892, 3671}, {2172, 40942}, {2354, 21061}, {2784, 5185}, {2796, 12132}, {3087, 9575}, {3088, 3576}, {3089, 5587}, {3244, 11396}, {3293, 40976}, {3416, 7716}, {3515, 10164}, {3517, 26446}, {3541, 10165}, {3542, 10175}, {3579, 37458}, {3616, 7378}, {3622, 7409}, {3624, 8889}, {3626, 10301}, {3674, 7282}, {3678, 41609}, {3679, 7714}, {3686, 44103}, {3817, 7507}, {3830, 34643}, {4185, 5101}, {4212, 29637}, {4213, 29633}, {4222, 5795}, {4232, 9780}, {4292, 32118}, {4314, 7071}, {5089, 28594}, {5094, 19862}, {5155, 17516}, {5174, 37390}, {5223, 7717}, {5342, 49466}, {5410, 49548}, {5411, 49547}, {5412, 13883}, {5413, 13936}, {5690, 7715}, {5745, 14017}, {5901, 16198}, {6001, 16621}, {6240, 28150}, {6622, 7989}, {6623, 18492}, {6700, 37432}, {6734, 7466}, {6994, 17316}, {7102, 28076}, {7403, 24301}, {7490, 17284}, {7505, 10172}, {7576, 28194}, {8666, 22479}, {8715, 11383}, {8946, 26443}, {8948, 26442}, {9028, 14054}, {9956, 21841}, {10594, 37546}, {10915, 26378}, {10916, 26377}, {11334, 34851}, {11362, 37122}, {11380, 49545}, {11384, 49555}, {11385, 49556}, {11386, 49561}, {11388, 49586}, {11389, 49587}, {11390, 49600}, {11391, 21077}, {11394, 49606}, {11395, 49607}, {11398, 31397}, {11400, 49626}, {11401, 49627}, {11832, 49585}, {12144, 17766}, {12233, 40658}, {12432, 29043}, {12571, 23047}, {12699, 18494}, {12779, 15811}, {13411, 37362}, {13488, 28160}, {13730, 34823}, {13884, 49618}, {13937, 49619}, {14953, 26158}, {16228, 48327}, {16472, 39588}, {18525, 18535}, {18533, 31730}, {18560, 28172}, {19867, 37168}, {24982, 35973}, {26208, 31014}, {26371, 48511}, {26372, 48512}, {26373, 49420}, {26374, 49419}, {26375, 49078}, {26376, 49079}, {28234, 41722}, {31757, 47328}, {34790, 41611}, {34822, 37034}, {35242, 37460}, {35764, 49601}, {35765, 49602}, {38140, 44960}, {44426, 48324}, {45400, 49347}, {45401, 49348}, {45502, 48814}, {45503, 48815}

X(49542) = midpoint of X(i) and X(j) for these {i, j}: {1829, 12135}, {1862, 12137}, {1902, 3575}
X(49542) = polar conjugate of the isotomic conjugate of X(5294)
X(49542) = barycentric product X(i)*X(j) for these {i, j}: {4, 5294}, {92, 5266}
X(49542) = trilinear product X(i)*X(j) for these {i, j}: {4, 5266}, {19, 5294}
X(49542) = Zosma transform of X(3670)
X(49542) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(5266)}} and {{A, B, C, X(80), X(13161)}}
X(49542) = orthologic center (anti-Ara, T) for these triangles T: 1st Jenkins, 1st Savin
X(49542) = X(10)-of-anti-Ara triangle
X(49542) = X(5571)-of-orthic triangle, when ABC is acute
X(49542) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 33, 39579), (4, 6198, 1848), (4, 7009, 1838), (4, 7718, 1), (8, 6995, 7713), (25, 5090, 10), (427, 11363, 1125), (428, 12135, 1829), (7102, 28076, 39585)


X(49543) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-ARTZT TO 1st SAVIN

Barycentrics    8*a^2+3*(b+c)*a-b^2-6*b*c-c^2 : :
X(49543) = X(2)-3*X(16834) = 5*X(2)-3*X(17294) = 4*X(2)-3*X(29594) = 5*X(16834)-X(17294) = 4*X(16834)-X(29594) = 4*X(17294)-5*X(29594) = 3*X(19883)-2*X(49560)

The reciprocal orthologic center of these triangles is X(2).

X(49543) lies on these lines: {1, 2}, {6, 17133}, {99, 17222}, {524, 3663}, {527, 15534}, {536, 8584}, {545, 41149}, {553, 7223}, {597, 2321}, {598, 4052}, {599, 3946}, {726, 22486}, {1743, 4460}, {1992, 3875}, {2796, 8593}, {3175, 4115}, {3629, 4912}, {3686, 41312}, {3729, 5032}, {3755, 28538}, {3759, 3950}, {3773, 38089}, {3879, 37756}, {3913, 21539}, {3928, 41319}, {3986, 17393}, {4021, 5839}, {4098, 17349}, {4133, 4991}, {4349, 4716}, {4363, 4982}, {4545, 17327}, {4700, 17318}, {4725, 22165}, {4780, 28562}, {4898, 37681}, {4910, 41313}, {4924, 9041}, {5847, 49630}, {8666, 16436}, {8715, 16431}, {12513, 21509}, {13637, 49620}, {13757, 49621}, {15533, 17301}, {17151, 35578}, {17229, 48310}, {17299, 47352}, {17351, 20583}, {17362, 41311}, {17372, 20582}, {17377, 21255}, {17382, 28337}, {17388, 41310}, {47356, 49486}

X(49543) = midpoint of X(i) and X(j) for these {i, j}: {1992, 3875}, {3241, 49495}, {47356, 49486}
X(49543) = reflection of X(i) in X(j) for these (i, j): (551, 49477), (599, 3946), (1992, 4856), (2321, 597), (17351, 20583), (17372, 20582)
X(49543) = intersection, other than A, B, C, of circumconics {{A, B, C, X(42), X(17222)}} and {{A, B, C, X(145), X(598)}}
X(49543) = orthologic center (anti-Artzt, T) for these triangles T: 1st Jenkins, 1st Savin
X(49543) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (239, 3244, 29571), (3632, 17014, 29604), (3759, 4464, 3950), (16834, 29584, 49477), (16834, 49495, 16833), (17023, 20016, 3625), (17389, 41140, 29600), (29588, 29620, 29574)


X(49544) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ANTI-BROCARD TO 1st SAVIN

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

The reciprocal orthologic center of these triangles is X(5988).

X(49544) lies on these lines: {1, 2}, {3, 49562}, {147, 516}, {291, 4071}, {325, 740}, {518, 10026}, {726, 1916}, {1281, 7779}, {1738, 20541}, {2784, 5999}, {2795, 7813}, {2796, 7840}, {3314, 3821}, {3329, 24295}, {3923, 7774}, {4027, 49546}, {4425, 31089}, {4518, 6541}, {4655, 7788}, {4672, 41624}, {5015, 35916}, {5695, 9766}, {5846, 44379}, {5847, 17731}, {7179, 49474}, {7778, 49486}, {7792, 49489}, {7906, 32117}, {8290, 17766}, {8592, 28562}, {9053, 44399}, {9772, 21636}, {13161, 37159}, {20536, 34379}, {21076, 24437}, {24248, 37668}, {25354, 31090}, {25385, 31120}, {26244, 42334}

X(49544) = midpoint of X(1281) and X(7779)
X(49544) = reflection of X(i) in X(j) for these (i, j): (5988, 325), (49550, 551)
X(49544) = orthologic center (1st anti-Brocard, T) for these triangles T: 1st Jenkins, 1st Savin
X(49544) = X(11599)-of-1st anti-Brocard triangle
X(49544) = {X(3705), X(29840)}-harmonic conjugate of X(29655)


X(49545) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 5th ANTI-BROCARD TO 1st SAVIN

Barycentrics    2*a^5+2*(b+c)*a^4+(b+c)*(b^2+c^2)*a^2+b^2*c^2*(b+c) : :
X(49545) = 3*X(12150)-X(12194) = 3*X(12150)+X(12195)

The reciprocal orthologic center of these triangles is X(1).

X(49545) lies on these lines: {1, 7787}, {2, 34714}, {8, 10789}, {10, 32}, {40, 10788}, {83, 1125}, {98, 19925}, {182, 4297}, {226, 10797}, {355, 11842}, {384, 726}, {515, 3398}, {516, 12110}, {517, 32134}, {518, 42421}, {519, 12150}, {727, 5255}, {730, 5007}, {946, 10796}, {950, 10799}, {1010, 34476}, {1078, 3634}, {1210, 10802}, {1698, 7793}, {2080, 6684}, {2784, 12176}, {2796, 12191}, {3029, 20970}, {3097, 3552}, {3099, 10346}, {3244, 10800}, {3576, 10359}, {3817, 10358}, {3971, 11320}, {3972, 12782}, {4279, 5247}, {5171, 10164}, {5847, 12212}, {6685, 41258}, {7766, 9902}, {7804, 12263}, {7808, 19862}, {8666, 22520}, {8669, 37100}, {8715, 11490}, {9941, 10348}, {10104, 10175}, {10106, 12835}, {10790, 49553}, {10792, 49586}, {10793, 49587}, {10794, 49600}, {10795, 21077}, {10798, 12053}, {10801, 31397}, {10803, 49626}, {10804, 49627}, {10915, 26432}, {10916, 26431}, {11380, 49542}, {11837, 49555}, {11838, 49556}, {11839, 49585}, {11840, 49606}, {11841, 49607}, {12198, 13194}, {12203, 28164}, {12206, 17766}, {12699, 18501}, {13883, 44586}, {13885, 49618}, {13936, 44587}, {13938, 49619}, {14880, 31673}, {17692, 40774}, {18483, 18502}, {18993, 49547}, {18994, 49548}, {26379, 48511}, {26403, 48512}, {26427, 49420}, {26428, 49419}, {26429, 49078}, {26430, 49079}, {33682, 41239}, {35766, 49601}, {35767, 49602}, {45402, 49347}, {45403, 49348}, {45504, 48814}, {45505, 48815}

X(49545) = midpoint of X(i) and X(j) for these {i, j}: {12110, 12197}, {12194, 12195}, {12198, 13194}
X(49545) = orthologic center (5th anti-Brocard, T) for these triangles T: 1st Jenkins, 1st Savin
X(49545) = X(10)-of-5th anti-Brocard triangle
X(49545) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (32, 10791, 10), (83, 11364, 1125), (12150, 12195, 12194)


X(49546) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 6th ANTI-BROCARD TO 1st SAVIN

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

The reciprocal orthologic center of these triangles is X(5988).

X(49546) lies on these lines: {6, 726}, {182, 49560}, {516, 12177}, {519, 5182}, {740, 13196}, {2456, 2784}, {2796, 12151}, {4027, 49544}, {5038, 24295}, {10131, 49562}, {17770, 32115}, {39141, 49488}

X(49546) = orthologic center (6th anti-Brocard, T) for these triangles T: 1st Jenkins, 1st Savin
X(49546) = X(11599)-of-6th anti-Brocard triangle


X(49547) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-INNER-GREBE TO 1st SAVIN

Barycentrics    -(b+c)*S+2*a^2*(a+b+c) : :
X(49547) = X(18992)-3*X(19053) = 3*X(19053)+X(19065)

The reciprocal orthologic center of these triangles is X(1).

X(49547) lies on these lines: {1, 7586}, {2, 13888}, {6, 10}, {8, 19003}, {40, 7582}, {226, 19027}, {355, 6418}, {371, 10164}, {372, 4297}, {486, 3817}, {515, 3312}, {516, 1588}, {517, 19116}, {519, 18992}, {551, 7969}, {615, 8983}, {726, 19089}, {946, 7584}, {950, 19037}, {1125, 3069}, {1210, 3301}, {1335, 11019}, {1449, 7090}, {1504, 31396}, {1587, 19925}, {1698, 7585}, {1702, 43174}, {1743, 31594}, {2362, 3671}, {2784, 19055}, {2796, 19057}, {3068, 3634}, {3244, 7968}, {3298, 21625}, {3299, 31397}, {3311, 6684}, {3616, 13942}, {3624, 13941}, {3625, 49233}, {3626, 19066}, {3636, 13959}, {3828, 13893}, {3911, 18996}, {3947, 44622}, {4301, 35774}, {4314, 5414}, {4315, 6502}, {4669, 49232}, {4856, 49593}, {5248, 19000}, {5411, 49542}, {5493, 49227}, {5587, 7581}, {5731, 42523}, {5790, 6501}, {6347, 37685}, {6395, 18481}, {6417, 26446}, {6419, 13912}, {6420, 49602}, {6459, 12512}, {6460, 28164}, {7583, 10175}, {8227, 13939}, {8666, 19013}, {8715, 18999}, {8976, 10172}, {9583, 13935}, {9956, 19117}, {10106, 18995}, {10165, 13966}, {10915, 26459}, {10916, 26458}, {11230, 13993}, {11263, 16149}, {12053, 19029}, {12571, 42561}, {12699, 18510}, {13411, 13963}, {13605, 46689}, {13785, 18483}, {13847, 19883}, {13962, 44675}, {13972, 38049}, {14121, 16670}, {16192, 43512}, {17355, 49592}, {17766, 19091}, {18249, 31438}, {18492, 23267}, {18993, 49545}, {19005, 49553}, {19007, 49555}, {19009, 49556}, {19011, 49561}, {19017, 49585}, {19023, 49600}, {19025, 21077}, {19031, 49606}, {19033, 49607}, {19047, 49626}, {19049, 49627}, {19077, 19112}, {19878, 32786}, {23273, 41869}, {25352, 36553}, {26384, 48511}, {26408, 48512}, {26454, 49420}, {26455, 49419}, {26456, 49078}, {26457, 49079}, {30331, 35809}, {31253, 32785}, {31673, 42216}, {31730, 42215}, {35770, 38155}, {35822, 38076}, {45512, 48814}, {45514, 48815}, {49617, 49620}, {49621, 49624}

X(49547) = midpoint of X(i) and X(j) for these {i, j}: {1588, 1703}, {18992, 19065}, {19077, 19112}
X(49547) = orthologic center (anti-inner-Grebe, T) for these triangles T: 1st Jenkins, 1st Savin
X(49547) = X(10)-of-anti-inner-Grebe triangle
X(49547) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 10, 49548), (6, 13936, 10), (6, 13973, 13883), (371, 13975, 10164), (615, 8983, 19862), (1698, 7585, 49618), (3068, 13947, 3634), (3069, 18991, 1125), (5688, 38047, 10), (7969, 13971, 551), (7969, 32788, 13971), (13883, 13936, 13973), (13883, 13973, 10), (19053, 19065, 18992)


X(49548) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-OUTER-GREBE TO 1st SAVIN

Barycentrics    (b+c)*S+2*a^2*(a+b+c) : :
X(49548) = X(18991)-3*X(19054) = 3*X(19054)+X(19066)

The reciprocal orthologic center of these triangles is X(1).

X(49548) lies on these lines: {1, 7585}, {2, 13942}, {6, 10}, {8, 19004}, {40, 7581}, {226, 19028}, {355, 6417}, {371, 4297}, {372, 10164}, {485, 3817}, {515, 3311}, {516, 1587}, {517, 19117}, {519, 18991}, {551, 7968}, {590, 13971}, {726, 19090}, {946, 7583}, {950, 19038}, {1124, 11019}, {1125, 3068}, {1210, 3299}, {1449, 14121}, {1505, 31396}, {1588, 19925}, {1698, 7586}, {1703, 43174}, {1743, 31595}, {2066, 4314}, {2067, 4315}, {2784, 19056}, {2796, 19058}, {3069, 3634}, {3244, 7969}, {3297, 21625}, {3301, 31397}, {3312, 6684}, {3616, 13888}, {3624, 8972}, {3625, 49232}, {3626, 19065}, {3636, 13902}, {3671, 16232}, {3828, 13947}, {3911, 18995}, {3947, 31472}, {4298, 31408}, {4301, 35775}, {4669, 49233}, {4856, 49592}, {5248, 18999}, {5410, 49542}, {5493, 49226}, {5587, 7582}, {5731, 42522}, {5790, 6500}, {6199, 18481}, {6348, 37685}, {6418, 26446}, {6419, 49601}, {6420, 13975}, {6459, 28164}, {6460, 9616}, {7090, 16670}, {7584, 10175}, {8227, 13886}, {8666, 19014}, {8715, 19000}, {8981, 10165}, {9956, 19116}, {10106, 18996}, {10172, 13951}, {10915, 26465}, {10916, 26464}, {11230, 13925}, {11263, 16148}, {12053, 19030}, {12571, 31412}, {12575, 31432}, {12699, 18512}, {13411, 13905}, {13605, 46688}, {13665, 18483}, {13846, 19883}, {13904, 44675}, {13910, 38049}, {16192, 43511}, {17355, 49593}, {17766, 19092}, {18250, 31438}, {18492, 23273}, {18994, 49545}, {19006, 49553}, {19008, 49555}, {19010, 49556}, {19012, 49561}, {19018, 49585}, {19024, 49600}, {19026, 21077}, {19032, 49606}, {19034, 49607}, {19048, 49626}, {19050, 49627}, {19078, 19113}, {19878, 32785}, {23267, 41869}, {25352, 36552}, {26385, 48511}, {26409, 48512}, {26460, 49420}, {26461, 49419}, {26462, 49078}, {26463, 49079}, {30331, 35808}, {31253, 32786}, {31439, 31730}, {31673, 42215}, {35771, 38155}, {35823, 38076}, {45513, 48815}, {45515, 48814}, {49615, 49621}, {49620, 49625}

X(49548) = midpoint of X(i) and X(j) for these {i, j}: {1587, 1702}, {18991, 19066}, {19078, 19113}
X(49548) = orthologic center (anti-outer-Grebe, T) for these triangles T: 1st Jenkins, 1st Savin
X(49548) = X(10)-of-anti-outer-Grebe triangle
X(49548) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 10, 49547), (6, 13883, 10), (6, 13911, 13936), (372, 13912, 10164), (590, 13971, 19862), (1698, 7586, 49619), (3068, 18992, 1125), (3069, 13893, 3634), (5689, 38047, 10), (6460, 9616, 12512), (7968, 8983, 551), (7968, 32787, 8983), (13883, 13936, 13911), (13911, 13936, 10), (19054, 19066, 18991), (31439, 42216, 31730)


X(49549) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st SAVIN TO ANTI-MCCAY

Barycentrics    4*a^4-3*(b+c)*a^3-2*(2*b^2-3*b*c+2*c^2)*a^2+3*(b+c)*(2*b^2-3*b*c+2*c^2)*a+(b^2+c^2)*(b^2-3*b*c+c^2) : :
X(49549) = X(1281)-3*X(38314)

The reciprocal orthologic center of these triangles is X(49550).

X(49549) lies on these lines: {1, 2796}, {2, 15903}, {10, 42010}, {99, 17223}, {226, 664}, {519, 5988}, {524, 49550}, {542, 13442}, {543, 37631}, {551, 49563}, {1015, 2482}, {1281, 38314}, {2784, 3241}, {2789, 47871}, {2799, 45341}, {3912, 5461}, {5530, 49638}, {8596, 41825}, {14210, 20912}, {17197, 33296}, {27295, 29573}

X(49549) = orthologic center (1st Savin, T) for these triangles T: anti-McCay, McCay, Moses-Steiner osculatory
X(49549) = reflection of X(2) in X(15903)


X(49550) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-MCCAY TO 1st SAVIN

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

The reciprocal orthologic center of these triangles is X(49549).

X(49550) lies on these lines: {1, 2}, {524, 49549}, {726, 11152}, {2796, 9855}, {7840, 15903}, {8587, 34899}, {8591, 17132}, {17133, 37792}, {33274, 49609}

X(49550) = orthologic center (anti-McCay, T) for these triangles T: 1st Jenkins, 1st Savin
X(49550) = reflection of X(i) in X(j) for these (i, j): (7840, 15903), (49544, 551)


X(49551) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ANTI-TRI-SQUARES TO 1st SAVIN

Barycentrics    6*a^6+(b+c)*a^5-(21*b^2+2*b*c+21*c^2)*a^4-2*(b+c)*(2*b^2+b*c+2*c^2)*a^3+2*(7*b^4+7*c^4+b*c*(5*b^2-8*b*c+5*c^2))*a^2+(b^2-c^2)*(b-c)*(3*b^2+4*b*c+3*c^2)*a+(b^2-4*b*c+c^2)*(b^2-c^2)^2+2*S*(8*a^4+3*(b+c)*a^3+(5*b^2-6*b*c+5*c^2)*a^2-(b+c)*(b^2-4*b*c+c^2)*a-(7*b^2-12*b*c+7*c^2)*(b+c)^2) : :
X(49551) = 3*X(486)-2*X(49623)

The reciprocal orthologic center of these triangles is X(31583).

X(49551) lies on these lines: {10, 486}, {487, 41930}, {519, 1328}, {5905, 12221}, {6561, 49624}, {6565, 49593}, {13808, 49619}, {18483, 49552}, {22591, 28526}, {31583, 32419}

X(49551) = orthologic center (3rd anti-tri-squares, T) for these triangles T: 1st Jenkins, 1st Savin


X(49552) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ANTI-TRI-SQUARES TO 1st SAVIN

Barycentrics    6*a^6+(b+c)*a^5-(21*b^2+2*b*c+21*c^2)*a^4-2*(b+c)*(2*b^2+b*c+2*c^2)*a^3+2*(7*b^4+7*c^4+b*c*(5*b^2-8*b*c+5*c^2))*a^2+(b^2-c^2)*(b-c)*(3*b^2+4*b*c+3*c^2)*a+(b^2-4*b*c+c^2)*(b^2-c^2)^2-2*S*(8*a^4+3*(b+c)*a^3+(5*b^2-6*b*c+5*c^2)*a^2-(b+c)*(b^2-4*b*c+c^2)*a-(7*b^2-12*b*c+7*c^2)*(b+c)^2) : :
X(49552) = 3*X(485)-2*X(49622)

The reciprocal orthologic center of these triangles is X(31582).

X(49552) lies on these lines: {10, 485}, {488, 41930}, {519, 1327}, {5905, 12222}, {6560, 49625}, {6564, 49592}, {13688, 49618}, {18483, 49551}, {22592, 28526}, {31582, 32421}

X(49552) = orthologic center (4th anti-tri-squares, T) for these triangles T: 1st Jenkins, 1st Savin


X(49553) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ARA TO 1st SAVIN

Barycentrics    a^2*(a^5+(b+c)*a^4-(b^2-c^2)^2*a-(b+c)*(b^4+c^4)) : :
X(49553) = X(9798)-3*X(9909) = 3*X(9909)+X(12410)

The reciprocal orthologic center of these triangles is X(1).

X(49553) lies on these lines: {1, 22}, {2, 34657}, {3, 142}, {4, 15177}, {6, 31757}, {8, 23}, {10, 25}, {24, 40}, {26, 517}, {35, 968}, {55, 2915}, {56, 2922}, {58, 7295}, {145, 37913}, {159, 5847}, {165, 17928}, {186, 6361}, {197, 8715}, {226, 10831}, {355, 7517}, {378, 41869}, {386, 37576}, {394, 31737}, {405, 20988}, {498, 35996}, {499, 37449}, {515, 7387}, {519, 9798}, {595, 5329}, {674, 42463}, {692, 5752}, {726, 9917}, {758, 3556}, {944, 12088}, {950, 10833}, {952, 17714}, {958, 20831}, {960, 9712}, {962, 7488}, {993, 13730}, {1181, 31732}, {1210, 10046}, {1324, 8669}, {1479, 37231}, {1482, 2937}, {1598, 19925}, {1658, 28174}, {1698, 1995}, {1699, 7503}, {1836, 9659}, {1837, 9673}, {1973, 4456}, {2070, 12702}, {2175, 10974}, {2392, 3157}, {2550, 17562}, {2784, 9861}, {2796, 9876}, {2807, 46730}, {2916, 38315}, {3053, 32758}, {3060, 16473}, {3085, 35988}, {3244, 8192}, {3338, 7293}, {3416, 20987}, {3437, 20877}, {3515, 5493}, {3517, 43174}, {3518, 5657}, {3576, 10323}, {3579, 6644}, {3616, 6636}, {3622, 7492}, {3624, 7485}, {3626, 20850}, {3634, 5020}, {3678, 12329}, {3811, 40910}, {3817, 7395}, {3841, 7535}, {3881, 22769}, {4026, 37317}, {4220, 10198}, {4224, 26363}, {4228, 19854}, {4278, 16876}, {4294, 7520}, {4297, 11414}, {4299, 35998}, {4301, 9715}, {4302, 16049}, {4354, 20243}, {5012, 16472}, {5252, 9658}, {5285, 12514}, {5347, 16466}, {5358, 33137}, {5550, 15246}, {5587, 10594}, {5594, 49587}, {5595, 49586}, {5603, 7512}, {5687, 20989}, {5690, 37440}, {5790, 18378}, {5818, 34484}, {5836, 9713}, {5899, 18525}, {5901, 7525}, {6642, 6684}, {7484, 19862}, {7502, 22791}, {7506, 26446}, {7509, 8227}, {7514, 9955}, {7516, 11230}, {7521, 11677}, {7526, 22793}, {7529, 10175}, {7530, 18480}, {7982, 9626}, {7991, 9590}, {8190, 49555}, {8191, 49556}, {8194, 49606}, {8195, 49607}, {8276, 13912}, {8277, 13975}, {8666, 22654}, {9589, 38444}, {9672, 12701}, {9714, 11362}, {9778, 22467}, {9780, 13595}, {9812, 14118}, {9818, 18483}, {9912, 13222}, {9918, 17766}, {9956, 13861}, {10037, 31397}, {10106, 18954}, {10200, 19649}, {10246, 13564}, {10790, 49545}, {10828, 49561}, {10829, 49600}, {10830, 21077}, {10832, 12053}, {10834, 49626}, {10835, 49627}, {10915, 26309}, {10916, 26308}, {11102, 32773}, {11250, 28178}, {11329, 30110}, {11340, 16831}, {11350, 29571}, {11363, 21213}, {11479, 12571}, {11517, 15494}, {11599, 39832}, {11853, 49585}, {12083, 18481}, {12084, 28146}, {12085, 28150}, {12107, 28212}, {12575, 16541}, {13171, 13605}, {13205, 35221}, {13883, 44598}, {13889, 49618}, {13936, 44599}, {13943, 49619}, {14002, 46933}, {14070, 28194}, {14953, 28410}, {15331, 28216}, {15654, 49613}, {16064, 24331}, {16195, 28228}, {16419, 19878}, {17798, 19762}, {17814, 31752}, {18324, 28198}, {18534, 31673}, {18616, 20875}, {19005, 49547}, {19006, 49548}, {19310, 19858}, {19763, 23868}, {19784, 37325}, {19843, 37254}, {19844, 26241}, {20918, 23843}, {21636, 39803}, {23398, 23849}, {23850, 23853}, {25440, 37034}, {26302, 48511}, {26303, 48512}, {26304, 49420}, {26305, 49419}, {26306, 49078}, {26307, 49079}, {26364, 33849}, {28164, 39568}, {28383, 34868}, {31162, 44837}, {31728, 37489}, {31738, 37486}, {34379, 37491}, {34595, 40916}, {34632, 37940}, {34656, 37904}, {34668, 47313}, {34718, 37956}, {35776, 49601}, {35777, 49602}, {36152, 37311}, {37250, 40292}, {37285, 39578}, {37705, 37947}, {45428, 49347}, {45429, 49348}, {45532, 48814}, {45533, 48815}

X(49553) = midpoint of X(i) and X(j) for these {i, j}: {3, 9911}, {3556, 37547}, {9798, 12410}, {9912, 13222}
X(49553) = Cevapoint of X(6) and X(39700)
X(49553) = crosssum of X(6) and X(5301)
X(49553) = orthologic center (Ara, T) for these triangles T: 1st Jenkins, 1st Savin
X(49553) = X(10)-of-Ara triangle
X(49553) = X(4347)-of-2nd circumperp tangential triangle
X(49553) = X(9911)-of-anti-X3-ABC reflections triangle
X(49553) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 9591, 22), (3, 1486, 5248), (3, 11365, 1125), (8, 23, 8185), (25, 8193, 10), (40, 9625, 24), (55, 2915, 39582), (55, 27802, 30142), (8185, 37546, 8), (9909, 12410, 9798), (20872, 36641, 39475), (37034, 37577, 25440)


X(49554) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ARTZT TO 1st SAVIN

Barycentrics    (b+c)*a^2+4*(b^2-b*c+c^2)*a-(b+c)*(3*b^2-4*b*c+3*c^2) : :
X(49554) = X(10)+2*X(49613) = 2*X(8669)-5*X(19862) = 3*X(19883)-2*X(49608)

The reciprocal orthologic center of these triangles is X(2).

X(49554) lies on these lines: {1, 2}, {11, 3175}, {226, 42055}, {262, 726}, {325, 3663}, {516, 7710}, {527, 9766}, {536, 3829}, {740, 24386}, {982, 4138}, {988, 48813}, {1007, 3875}, {1699, 9742}, {2321, 3815}, {2784, 22664}, {2796, 6054}, {3452, 4096}, {3816, 4078}, {3911, 4865}, {3928, 6210}, {3946, 7778}, {4133, 32855}, {4231, 48713}, {4301, 49609}, {4719, 48845}, {4725, 13468}, {4780, 33141}, {4852, 44377}, {4856, 7735}, {4884, 5087}, {5847, 49631}, {7736, 17355}, {8666, 19544}, {8715, 16434}, {9751, 10164}, {9770, 17132}, {9771, 28329}, {9774, 28562}, {9909, 15654}, {11184, 17133}, {11235, 28580}, {13638, 49620}, {13758, 49621}, {15491, 17229}, {16052, 37592}, {17299, 31489}, {17723, 19722}, {18134, 24216}, {20498, 42054}, {20545, 35652}, {21241, 24177}, {21636, 34899}, {24387, 37360}, {24477, 34379}, {33071, 41629}

X(49554) = midpoint of X(21636) and X(34899)
X(49554) = orthologic center (Artzt, T) for these triangles T: 1st Jenkins, 1st Savin
X(49554) = X(32319)-of-3rd Euler triangle, when ABC is acute
X(49554) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3705, 24239, 10), (26015, 29849, 4028)


X(49555) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st AURIGA TO 1st SAVIN

Barycentrics    -2*(2*a-b-c)*S*sqrt(R*(4*R+r))+a^2*(-a+b+c)*(a+b+c) : :
X(49555) = X(55)-3*X(11207) = 5*X(55)-3*X(11208) = 3*X(55)-X(12455) = 5*X(11207)-X(11208) = 3*X(11207)+X(12454) = 9*X(11207)-X(12455) = 6*X(11207)-X(49556) = 3*X(11208)+5*X(12454) = 9*X(11208)-5*X(12455) = 6*X(11208)-5*X(49556) = 3*X(12454)+X(12455) = 2*X(12454)+X(49556) = 2*X(12455)-3*X(49556)

The reciprocal orthologic center of these triangles is X(1).

X(49555) lies on these lines: {1, 5601}, {8, 8186}, {10, 5597}, {40, 11843}, {55, 519}, {145, 8187}, {226, 11869}, {355, 11875}, {515, 11252}, {516, 9834}, {517, 32146}, {726, 12474}, {946, 8200}, {950, 11873}, {1125, 5599}, {1210, 11879}, {2784, 12179}, {2796, 12345}, {3244, 5598}, {3625, 8204}, {3626, 5600}, {3632, 5602}, {3635, 11367}, {4297, 11822}, {5847, 12452}, {6684, 45620}, {8190, 49553}, {8196, 19925}, {8198, 49586}, {8199, 49587}, {8201, 49606}, {8202, 49607}, {8207, 47745}, {8666, 11493}, {8715, 11492}, {9835, 28236}, {10106, 18955}, {10915, 45627}, {10916, 45625}, {11253, 28234}, {11384, 49542}, {11837, 49545}, {11861, 49561}, {11863, 49585}, {11865, 49600}, {11867, 21077}, {11871, 12053}, {11877, 31397}, {11881, 49626}, {11883, 49627}, {12460, 13228}, {12476, 17766}, {12699, 45379}, {13607, 45621}, {13883, 44600}, {13890, 49618}, {13936, 44601}, {13944, 49619}, {18483, 18495}, {19007, 49547}, {19008, 49548}, {22836, 26351}, {22837, 26352}, {35778, 49601}, {35781, 49602}, {45353, 48512}, {45430, 49347}, {45431, 49348}, {45534, 48814}, {45535, 48815}, {45588, 49419}, {45589, 49420}, {49012, 49078}, {49013, 49079}

X(49555) = midpoint of X(i) and X(j) for these {i, j}: {55, 12454}, {9834, 12458}, {12460, 13228}
X(49555) = reflection of X(49556) in X(55)
X(49555) = orthologic center (1st Auriga, T) for these triangles T: 1st Jenkins, 1st Savin
X(49555) = X(10)-of-1st Auriga triangle
X(49555) = X(3244)-of-2nd Auriga triangle
X(49555) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5597, 8197, 10), (5599, 11366, 1125), (11207, 12454, 55)


X(49556) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd AURIGA TO 1st SAVIN

Barycentrics    2*(2*a-b-c)*S*sqrt(R*(4*R+r))+a^2*(-a+b+c)*(a+b+c) : :
X(49556) = 5*X(55)-3*X(11207) = X(55)-3*X(11208) = 3*X(55)-X(12454) = X(11207)-5*X(11208) = 9*X(11207)-5*X(12454) = 3*X(11207)+5*X(12455) = 6*X(11207)-5*X(49555) = 9*X(11208)-X(12454) = 3*X(11208)+X(12455) = 6*X(11208)-X(49555) = X(12454)+3*X(12455) = 2*X(12454)-3*X(49555) = 2*X(12455)+X(49555)

The reciprocal orthologic center of these triangles is X(1).

X(49556) lies on these lines: {1, 5602}, {8, 8187}, {10, 5598}, {40, 11844}, {55, 519}, {145, 8186}, {226, 11870}, {355, 11876}, {515, 11253}, {516, 9835}, {517, 32147}, {726, 12475}, {946, 8207}, {950, 11874}, {1125, 5600}, {1210, 11880}, {2784, 12180}, {2796, 12346}, {3244, 5597}, {3625, 8197}, {3626, 5599}, {3632, 5601}, {3635, 11366}, {4297, 11823}, {5847, 12453}, {6684, 45621}, {8191, 49553}, {8200, 47745}, {8203, 19925}, {8205, 49586}, {8206, 49587}, {8208, 49606}, {8209, 49607}, {8666, 11492}, {8715, 11493}, {9834, 28236}, {10106, 18956}, {10915, 45628}, {10916, 45626}, {11252, 28234}, {11385, 49542}, {11838, 49545}, {11862, 49561}, {11864, 49585}, {11866, 49600}, {11868, 21077}, {11872, 12053}, {11878, 31397}, {11882, 49626}, {11884, 49627}, {12461, 13230}, {12477, 17766}, {12699, 45380}, {13607, 45620}, {13883, 44602}, {13891, 49618}, {13936, 44603}, {13945, 49619}, {18483, 18497}, {19009, 49547}, {19010, 49548}, {22836, 26352}, {22837, 26351}, {35779, 49602}, {35780, 49601}, {45354, 48511}, {45432, 49347}, {45433, 49348}, {45536, 48814}, {45537, 48815}, {45590, 49419}, {45591, 49420}, {49014, 49078}, {49015, 49079}

X(49556) = midpoint of X(i) and X(j) for these {i, j}: {55, 12455}, {9835, 12459}, {12461, 13230}
X(49556) = reflection of X(49555) in X(55)
X(49556) = orthologic center (2nd Auriga, T) for these triangles T: 1st Jenkins, 1st Savin
X(49556) = X(10)-of-2nd Auriga triangle
X(49556) = X(3244)-of-1st Auriga triangle
X(49556) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5598, 8204, 10), (5600, 11367, 1125), (11208, 12455, 55)


X(49557) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st SAVIN TO AYME

Barycentrics    a*((b-c)^2*a^4+(b+c)*(b^2-4*b*c+c^2)*a^3-(b^4+c^4+b*c*(3*b^2+8*b*c+3*c^2))*a^2-(b+c)*(b^4+4*b^2*c^2+c^4)*a+(b^2-c^2)^2*b*c) : :
X(49557) = X(3555)-3*X(42045) = 3*X(3578)-5*X(3697) = 2*X(5045)-3*X(37631)

The reciprocal orthologic center of these triangles is X(49558).

X(49557) lies on these lines: {1, 10108}, {30, 9957}, {55, 48926}, {57, 48928}, {73, 500}, {226, 48933}, {511, 942}, {513, 3743}, {524, 34790}, {540, 960}, {999, 48883}, {3295, 6180}, {3555, 42045}, {3578, 3697}, {3918, 46187}, {3931, 49537}, {4340, 5752}, {5045, 37631}, {5122, 35203}, {5126, 48930}, {5482, 5718}, {5530, 35059}, {5712, 37482}, {5722, 48877}, {9840, 24928}, {13411, 15368}, {15447, 31663}, {17220, 48941}, {18180, 26131}, {23061, 46441}, {25405, 48894}, {34466, 37522}, {37582, 48882}

X(49557) = reflection of X(i) in X(j) for these (i, j): (1, 10108), (500, 10105)
X(49557) = orthologic center (1st Savin, T) for these triangles T: Ayme, incentral
X(49557) = X(10108)-of-Aquila triangle
X(49557) = X(48926)-of-Mandart-incircle triangle
X(49557) = {X(5717), X(11573)}-harmonic conjugate of X(942)


X(49558) = ORTHOLOGIC CENTER OF THESE TRIANGLES: AYME TO 1st SAVIN

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

The reciprocal orthologic center of these triangles is X(49557).

X(49558) lies on these lines: {10, 321}, {19, 596}, {612, 4065}, {758, 44545}, {1125, 40941}, {24176, 40940}

X(49558) = orthologic center (Ayme, T) for these triangles T: 1st Jenkins, 1st Savin
X(49558) = {X(4647), X(40973)}-harmonic conjugate of X(10)


X(49559) = ORTHOLOGIC CENTER OF THESE TRIANGLES: BANKOFF TO 1st SAVIN

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

The reciprocal orthologic center of these triangles is X(49538).

X(49559) lies on these lines: {3, 49611}, {519, 34551}, {1151, 49604}, {2796, 35748}, {3390, 41638}, {35730, 49569}, {35731, 49571}, {35732, 49573}, {35733, 49575}, {35734, 49579}, {35735, 49580}, {35736, 49581}, {35737, 49582}, {35738, 49588}, {35739, 49594}, {35740, 49596}, {36762, 49603}, {41018, 49539}

X(49559) = orthologic center (Bankoff, T) for these triangles T: 1st Jenkins, 1st Savin


X(49560) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st BROCARD TO 1st SAVIN

Barycentrics    (b+c)*a^2-(b^2+c^2)*a-(b+c)*(b^2+b*c+c^2) : :
X(49560) = X(1)+3*X(17294) = X(10)-3*X(29594) = 5*X(1698)-X(49495) = 7*X(3624)-3*X(16834) = 3*X(3679)+X(49451) = 3*X(19883)-X(49543)

The reciprocal orthologic center of these triangles is X(5988).

X(49560) lies on these lines: {1, 2}, {3, 2784}, {6, 24295}, {37, 3775}, {38, 3969}, {58, 17731}, {69, 3923}, {75, 33087}, {76, 4485}, {141, 740}, {182, 49546}, {238, 319}, {312, 33084}, {321, 32856}, {333, 33158}, {334, 17143}, {384, 49562}, {515, 49129}, {516, 1352}, {518, 3773}, {524, 4672}, {536, 4527}, {537, 4535}, {594, 4966}, {595, 41822}, {599, 2796}, {726, 2321}, {752, 49484}, {846, 37653}, {946, 7697}, {984, 6541}, {1001, 4445}, {1043, 35916}, {1078, 32115}, {1150, 33156}, {1386, 17372}, {1738, 4709}, {1757, 17280}, {2783, 40107}, {2792, 34507}, {2809, 3678}, {2887, 3706}, {2895, 32930}, {2896, 13174}, {3098, 29040}, {3120, 31017}, {3159, 3954}, {3314, 5988}, {3416, 17766}, {3454, 37159}, {3589, 49489}, {3620, 24248}, {3631, 17768}, {3662, 49474}, {3663, 4133}, {3685, 17287}, {3696, 3836}, {3704, 49609}, {3751, 17286}, {3763, 49486}, {3790, 49448}, {3817, 36677}, {3826, 4732}, {3842, 17243}, {3844, 4085}, {3879, 33682}, {3886, 4660}, {3896, 32781}, {3932, 49457}, {3936, 25385}, {3943, 49456}, {3976, 46032}, {3993, 4357}, {3996, 33079}, {4011, 5739}, {4023, 24003}, {4026, 48635}, {4038, 19808}, {4058, 5542}, {4283, 24437}, {4365, 17184}, {4387, 4703}, {4389, 49452}, {4418, 32863}, {4425, 32782}, {4429, 49459}, {4431, 24231}, {4647, 20913}, {4649, 17289}, {4663, 17359}, {4665, 25557}, {4671, 21093}, {4676, 17360}, {4684, 49479}, {4690, 15254}, {4693, 24723}, {4710, 20891}, {4716, 16706}, {4733, 17245}, {4886, 17123}, {4974, 17362}, {4991, 38049}, {5220, 17269}, {5224, 25354}, {5233, 11814}, {5263, 17295}, {5625, 17398}, {5846, 49473}, {5847, 49482}, {6057, 42054}, {6535, 17165}, {10000, 49561}, {10008, 28526}, {10026, 21024}, {10519, 24728}, {14810, 29093}, {14829, 33160}, {15569, 17239}, {16468, 17363}, {16589, 27784}, {17227, 33149}, {17228, 32784}, {17235, 28484}, {17237, 49462}, {17271, 24697}, {17277, 42334}, {17281, 32935}, {17285, 33159}, {17288, 32857}, {17299, 32921}, {17300, 24342}, {17345, 17767}, {17348, 31289}, {17351, 17771}, {17355, 34379}, {17380, 25539}, {17391, 43997}, {17499, 20536}, {17764, 49485}, {17765, 49467}, {17769, 49465}, {17798, 25440}, {18139, 21020}, {18553, 29032}, {18697, 44153}, {18891, 33778}, {19925, 36675}, {20486, 24390}, {20544, 24387}, {20546, 34528}, {20691, 37592}, {20888, 33930}, {22165, 28558}, {23888, 24093}, {24169, 32860}, {24552, 32852}, {28605, 33069}, {29057, 48876}, {29097, 43150}, {32777, 32853}, {32779, 32919}, {32848, 46909}, {32861, 32942}, {32864, 33157}, {32929, 33080}, {32932, 33085}, {32943, 33075}, {32945, 33078}, {33101, 42034}, {33103, 42029}, {33136, 48647}, {33162, 48648}, {33165, 49450}, {38047, 49497}, {38456, 48863}, {43531, 49564}, {47681, 49303}, {48634, 49469}

X(49560) = midpoint of X(i) and X(j) for these {i, j}: {8, 49458}, {69, 3923}, {1386, 17372}, {3416, 32941}, {3663, 4133}, {3886, 4660}, {4655, 5695}, {17299, 32921}
X(49560) = reflection of X(i) in X(j) for these (i, j): (6, 24295), (3773, 17229), (3821, 141), (4085, 3844), (49477, 1125), (49489, 3589)
X(49560) = complement of X(49488)
X(49560) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(18032)}} and {{A, B, C, X(42), X(11599)}}
X(49560) = orthologic center (1st Brocard, T) for these triangles T: 1st Jenkins, 1st Savin
X(49560) = X(11599)-of-1st Brocard triangle
X(49560) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 3624, 29586), (1, 3661, 10), (8, 17230, 29674), (8, 29674, 10), (10, 19862, 24603), (10, 29571, 3634), (306, 3741, 29671), (321, 33081, 33064), (594, 4966, 24325), (599, 5695, 4655), (984, 17233, 6541), (1999, 32783, 29645), (3187, 24943, 29654), (3616, 29588, 1), (3661, 17244, 29591), (3685, 17287, 33082), (3696, 17231, 3836), (4362, 33171, 29656), (4671, 33065, 21093), (5263, 17295, 32846), (10453, 32778, 29655), (15523, 17135, 29673), (31330, 32858, 29653), (32782, 32915, 4425), (32914, 33173, 29672), (49610, 49611, 49608), (49624, 49625, 8669)


X(49561) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 5th BROCARD TO 1st SAVIN

Barycentrics    2*a^5+(b+c)*a^4-(b+c)*(b^2+c^2)*a^2-(b^3+c^3)*(b^2+b*c+c^2) : :
X(49561) = 3*X(7811)-X(9941) = 3*X(7811)+X(12495)

The reciprocal orthologic center of these triangles is X(1).

X(49561) lies on these lines: {1, 2896}, {2, 34674}, {8, 3099}, {10, 32}, {40, 2784}, {226, 10873}, {355, 9301}, {515, 9821}, {516, 9873}, {517, 32151}, {519, 7811}, {551, 7865}, {560, 21083}, {726, 9983}, {730, 46283}, {946, 9996}, {950, 10877}, {1125, 3096}, {1210, 10047}, {1698, 10583}, {2076, 3416}, {2796, 9878}, {3094, 5847}, {3098, 4297}, {3244, 9997}, {3550, 3661}, {3576, 10357}, {3634, 7846}, {3817, 10356}, {6541, 17742}, {6684, 26316}, {7914, 19862}, {8666, 22744}, {8715, 11494}, {8782, 9902}, {9993, 19925}, {9994, 49586}, {9995, 49587}, {10000, 49560}, {10038, 31397}, {10106, 18957}, {10346, 10789}, {10347, 12194}, {10828, 49553}, {10871, 49600}, {10872, 21077}, {10874, 12053}, {10875, 49606}, {10876, 49607}, {10878, 49626}, {10879, 49627}, {10915, 26318}, {10916, 26317}, {11386, 49542}, {11599, 43449}, {11861, 49555}, {11862, 49556}, {11885, 49585}, {12195, 12783}, {12498, 13235}, {12699, 18503}, {13624, 42787}, {13883, 44604}, {13892, 49618}, {13936, 44605}, {13946, 49619}, {18483, 18500}, {19011, 49547}, {19012, 49548}, {26310, 48511}, {26311, 48512}, {26312, 49420}, {26313, 49419}, {26314, 49078}, {26315, 49079}, {35782, 49601}, {35783, 49602}, {45434, 49347}, {45435, 49348}, {45538, 48814}, {45539, 48815}, {48807, 48822}

X(49561) = midpoint of X(i) and X(j) for these {i, j}: {9873, 12497}, {9941, 12495}, {12498, 13235}
X(49561) = orthologic center (5th Brocard, T) for these triangles T: 1st Jenkins, 1st Savin
X(49561) = X(10)-of-5th Brocard triangle
X(49561) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (32, 9857, 10), (3096, 11368, 1125), (7811, 12495, 9941)


X(49562) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 6th BROCARD TO 1st SAVIN

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

The reciprocal orthologic center of these triangles is X(5988).

X(49562) lies on these lines: {1, 2896}, {3, 49544}, {10, 17688}, {20, 2784}, {315, 5988}, {384, 49560}, {516, 9863}, {519, 7833}, {740, 7750}, {2795, 7826}, {2796, 9939}, {3923, 20065}, {7787, 24295}, {7791, 49488}, {7893, 17770}, {10131, 49546}, {16458, 19761}

X(49562) = orthologic center (6th Brocard, T) for these triangles T: 1st Jenkins, 1st Savin
X(49562) = X(11599)-of-6th Brocard triangle
X(49562) = midpoint of X(7893) and X(32117)


X(49563) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st SAVIN TO 1st BROCARD-REFLECTED

Barycentrics    3*(b^2+c^2)*a^3+(b+c)*(2*b^2-b*c+2*c^2)*a^2+(b^4+4*b^2*c^2+c^4)*a-(b^2-c^2)*(b-c)*b*c : :
X(49563) = 4*X(1125)-X(17760) = 5*X(3616)-X(7985) = 5*X(3616)+X(33890)

The reciprocal orthologic center of these triangles is X(49564).

X(49563) lies on these lines: {1, 1447}, {2, 726}, {10, 33891}, {39, 3290}, {76, 37039}, {183, 32921}, {226, 262}, {256, 10854}, {354, 511}, {385, 49477}, {551, 49549}, {614, 5145}, {986, 44430}, {988, 7709}, {1125, 10335}, {1281, 49482}, {3011, 25094}, {3616, 7985}, {3663, 5988}, {3666, 5432}, {3753, 14839}, {3864, 29571}, {4003, 37691}, {4991, 7766}, {5483, 7191}, {5530, 22729}, {5852, 9300}, {7697, 13161}, {9865, 25354}, {9902, 39581}, {11174, 32935}, {12263, 49598}, {12782, 24174}, {14949, 16823}, {15271, 49453}, {17592, 22712}, {17771, 41624}, {17772, 37671}, {21443, 23689}, {22706, 24210}, {24248, 44431}, {26243, 32924}, {26274, 32453}, {30519, 47800}, {32515, 37592}, {41825, 44434}

X(49563) = midpoint of X(7985) and X(33890)
X(49563) = orthologic center (1st Savin, 1st Brocard-reflected)
X(49563) = complement of the isotomic conjugate of X(47647)


X(49564) = X(3)-OF-1st SAVIN TRIANGLE

Barycentrics    2*a^4+5*(b+c)*a^3+2*(b+2*c)*(2*b+c)*a^2+3*(b+c)*b*c*a-(b^3+c^3)*(b+c) : :
X(49564) = X(2292)+3*X(42045) = X(4647)-3*X(23812) = 3*X(37631)-X(49598)

X(49564) lies on these lines: {1, 1330}, {10, 86}, {81, 3178}, {316, 13161}, {519, 37631}, {540, 12579}, {940, 17748}, {986, 17378}, {1046, 20090}, {1125, 1211}, {1317, 1365}, {2292, 42045}, {2796, 4065}, {3664, 39774}, {3743, 17770}, {4205, 5625}, {4647, 23812}, {4987, 6155}, {5712, 17733}, {5717, 35633}, {8025, 20653}, {8728, 49489}, {16704, 27577}, {21085, 25526}, {26860, 27558}, {27368, 37635}, {28612, 34282}, {33097, 41813}, {43531, 49560}

X(49564) = perspector of the circumconic {{A, B, C, X(4632), X(8052)}}
X(49564) = X(3)-of-1st Savin triangle
X(49564) = X(23719)-of-intouch triangle, when ABC is acute
X(49564) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (81, 3178, 8258), (14007, 42334, 10)


X(49565) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st SAVIN TO INNER-FERMAT

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

The reciprocal orthologic center of these triangles is X(49566).

X(49565) lies on these lines: {1, 628}, {10, 40706}, {12, 3638}, {18, 226}, {44, 8260}, {299, 49566}, {303, 49590}, {533, 37631}, {630, 3666}, {1125, 30471}, {3634, 44032}, {3663, 17322}, {4357, 11133}, {5530, 49643}, {5983, 5988}, {6674, 37691}, {13442, 44667}, {22114, 41825}, {33396, 42677}

X(49565) = orthologic center (1st Savin, T) for these triangles T: inner-Fermat, 1st half-diamonds
X(49565) = X(41090)-of-intouch triangle, when ABC is acute
X(49565) = {X(3663), X(19862)}-harmonic conjugate of X(49567)


X(49566) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-FERMAT TO 1st SAVIN

Barycentrics    -2*(2*a+b+c)*S+sqrt(3)*(2*a-b-c)*(a+b+c)^2 : :
X(49566) = 2*X(1125)-3*X(49610) = 4*X(1125)-3*X(49611) = 5*X(1698)-6*X(49588) = 3*X(19875)-X(49577)

The reciprocal orthologic center of these triangles is X(49565).

X(49566) lies on these lines: {1, 2}, {14, 36930}, {299, 49565}, {530, 46976}, {726, 3104}, {946, 16626}, {2321, 41648}, {12699, 48655}, {18480, 49573}, {22651, 33412}

X(49566) = midpoint of X(i) and X(j) for these {i, j}: {3241, 49581}, {3679, 49578}
X(49566) = reflection of X(i) in X(j) for these (i, j): (10, 49591), (49568, 1125), (49579, 551), (49584, 3828), (49611, 49610)
X(49566) = anticomplement of X(49590)
X(49566) = orthologic center (inner-Fermat, T) for these triangles T: 1st Jenkins, 1st Savin
X(49566) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 40714, 10), (8, 17733, 49568), (1125, 49568, 49611), (49568, 49610, 1125), (49624, 49625, 49610)


X(49567) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st SAVIN TO OUTER-FERMAT

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

The reciprocal orthologic center of these triangles is X(49568).

X(49567) lies on these lines: {1, 627}, {10, 40707}, {12, 3639}, {17, 226}, {44, 8259}, {298, 49568}, {302, 49591}, {532, 37631}, {629, 3666}, {1125, 30472}, {3634, 44030}, {3663, 17322}, {4357, 11132}, {5530, 49644}, {5982, 5988}, {6673, 37691}, {13442, 44666}, {22113, 41825}, {33397, 42680}

X(49567) = orthologic center (1st Savin, T) for these triangles T: outer-Fermat, 2nd half-diamonds
X(49567) = X(41089)-of-intouch triangle, when ABC is acute
X(49567) = {X(3663), X(19862)}-harmonic conjugate of X(49565)


X(49568) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-FERMAT TO 1st SAVIN

Barycentrics    2*(2*a+b+c)*S+sqrt(3)*(2*a-b-c)*(a+b+c)^2 : :
X(49568) = 4*X(1125)-3*X(49610) = 2*X(1125)-3*X(49611) = 5*X(1698)-6*X(49589) = 3*X(19875)-X(49581)

The reciprocal orthologic center of these triangles is X(49567).

X(49568) lies on these lines: {1, 2}, {13, 36931}, {298, 49567}, {531, 46976}, {726, 3105}, {946, 16627}, {2321, 41638}, {12699, 48656}, {18480, 49574}, {22652, 33413}

X(49568) = midpoint of X(i) and X(j) for these {i, j}: {3241, 49577}, {3679, 49582}
X(49568) = reflection of X(i) in X(j) for these (i, j): (10, 49590), (49566, 1125), (49580, 3828), (49583, 551), (49610, 49611)
X(49568) = anticomplement of X(49591)
X(49568) = orthologic center (outer-Fermat, T) for these triangles T: 1st Jenkins, 1st Savin
X(49568) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 40713, 10), (8, 17733, 49566), (1125, 49566, 49610), (49566, 49611, 1125), (49624, 49625, 49611)


X(49569) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd FERMAT-DAO TO 1st SAVIN

Barycentrics    (2*a^6-5*(b^2+c^2)*a^4+(b+c)*(b^2+b*c+c^2)*a^3+(b^4+c^4-3*b*c*(b^2+4*b*c+c^2))*a^2-(b^3-c^3)*(b^2-c^2)*a+(2*b^2+b*c+2*c^2)*(b^2-c^2)^2)*sqrt(3)-2*S*(2*a^4-2*(b+c)*a^3+(7*b^2+4*b*c+7*c^2)*a^2+(b+c)*(b^2-3*b*c+c^2)*a-(4*b^2-9*b*c+4*c^2)*(b+c)^2) : :
X(49569) = X(13)+2*X(49571) = X(15)+2*X(49596) = 4*X(6669)-X(49538) = 4*X(11542)-X(49594) = 5*X(16960)-2*X(41638) = 5*X(16960)+X(49575) = X(41020)+2*X(49539) = 2*X(41638)+X(49575)

The reciprocal orthologic center of these triangles is X(49538).

X(49569) lies on these lines: {2, 11789}, {10, 13}, {15, 49596}, {17, 49611}, {61, 49573}, {62, 49588}, {214, 5243}, {516, 41036}, {519, 16267}, {2792, 10175}, {2796, 5470}, {3634, 11790}, {6669, 36668}, {11542, 49594}, {16808, 49604}, {16960, 41638}, {22846, 49589}, {35730, 49559}, {36763, 49603}, {41020, 49539}, {42506, 49580}

X(49569) = orthologic center (3rd Fermat-Dao, T) for these triangles T: 1st Jenkins, 1st Savin
X(49569) = {X(16960), X(49575)}-harmonic conjugate of X(41638)


X(49570) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th FERMAT-DAO TO 1st SAVIN

Barycentrics    (2*a^6-5*(b^2+c^2)*a^4+(b+c)*(b^2+b*c+c^2)*a^3+(b^4+c^4-3*b*c*(b^2+4*b*c+c^2))*a^2-(b^3-c^3)*(b^2-c^2)*a+(2*b^2+b*c+2*c^2)*(b^2-c^2)^2)*sqrt(3)+2*S*(2*a^4-2*(b+c)*a^3+(7*b^2+4*b*c+7*c^2)*a^2+(b+c)*(b^2-3*b*c+c^2)*a-(4*b^2-9*b*c+4*c^2)*(b+c)^2) : :
X(49570) = X(14)+2*X(49572) = X(16)+2*X(49597) = 4*X(6670)-X(49540) = 4*X(11543)-X(49595) = 5*X(16961)-2*X(41648) = 5*X(16961)+X(49576) = X(41021)+2*X(49541) = 2*X(41648)+X(49576)

The reciprocal orthologic center of these triangles is X(49540).

X(49570) lies on these lines: {2, 11752}, {10, 14}, {16, 49597}, {18, 49610}, {61, 49589}, {62, 49574}, {214, 5242}, {516, 41037}, {519, 16268}, {2792, 10175}, {2796, 5469}, {3634, 11791}, {6670, 36669}, {11543, 49595}, {16809, 49605}, {16961, 41648}, {22891, 49588}, {41021, 49541}, {42507, 49584}

X(49570) = orthologic center (4th Fermat-Dao, T) for these triangles T: 1st Jenkins, 1st Savin
X(49570) = {X(16961), X(49576)}-harmonic conjugate of X(41648)


X(49571) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 7th FERMAT-DAO TO 1st SAVIN

Barycentrics    (a+b+c)*(2*a^2-(b+c)*a+(b+c)^2)*sqrt(3)+2*S*(2*a+5*c+5*b) : :
X(49571) = X(13)-3*X(49569) = 3*X(16267)-X(49594) = 3*X(16962)+X(49575)

The reciprocal orthologic center of these triangles is X(49538).

X(49571) lies on these lines: {2, 49538}, {10, 13}, {30, 49596}, {115, 121}, {333, 41639}, {381, 49604}, {395, 8258}, {396, 519}, {516, 41016}, {618, 5745}, {1125, 22892}, {3634, 22847}, {3923, 16635}, {6669, 44417}, {10654, 49573}, {13876, 49622}, {13929, 49623}, {16267, 49594}, {16644, 49611}, {16962, 49575}, {35731, 49559}, {36764, 49603}, {41022, 49539}

X(49571) = reflection of X(41638) in X(396)
X(49571) = orthologic center (7th Fermat-Dao, T) for these triangles T: 1st Jenkins, 1st Savin
X(49571) = X(3165)-of-2nd Zaniah triangle, when ABC is acute
X(49571) = complement of X(49538)


X(49572) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 8th FERMAT-DAO TO 1st SAVIN

Barycentrics    (a+b+c)*(2*a^2-(b+c)*a+(b+c)^2)*sqrt(3)-2*S*(2*a+5*c+5*b) : :
X(49572) = X(14)-3*X(49570) = 3*X(16268)-X(49595) = 3*X(16963)+X(49576)

The reciprocal orthologic center of these triangles is X(49540).

X(49572) lies on these lines: {2, 49540}, {10, 14}, {30, 49597}, {115, 121}, {333, 41649}, {381, 49605}, {395, 519}, {396, 8258}, {516, 41017}, {619, 5745}, {1125, 22848}, {3634, 22893}, {3923, 16634}, {6670, 44417}, {10653, 49574}, {13875, 49622}, {13928, 49623}, {16268, 49595}, {16645, 49610}, {16963, 49576}, {41023, 49541}

X(49572) = reflection of X(41648) in X(395)
X(49572) = complement of X(49540)
X(49572) = orthologic center (8th Fermat-Dao, T) for these triangles T: 1st Jenkins, 1st Savin
X(49572) = X(3166)-of-2nd Zaniah triangle, when ABC is acute
X(49572) = {X(3828), X(17355)}-harmonic conjugate of X(49571)


X(49573) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 11th FERMAT-DAO TO 1st SAVIN

Barycentrics    (2*a^4-(b+c)*a^3+(b+c)^2*a^2+(b^2-c^2)*(b-c)*a-3*(b^2-c^2)^2)*sqrt(3)-2*S*(a+b+c)*(2*a-b-c) : :
X(49573) = 2*X(3845)+X(49580) = 4*X(5066)-X(49579) = 3*X(10175)-2*X(49589) = 2*X(18480)+X(49566) = X(31673)+2*X(49591) = 3*X(36765)-X(49603) = 5*X(41099)+X(49581) = 7*X(41106)-X(49582)

The reciprocal orthologic center of these triangles is X(49538).

X(49573) lies on these lines: {3, 49588}, {4, 49539}, {5, 49611}, {6, 49596}, {10, 14}, {61, 49569}, {355, 381}, {515, 49610}, {516, 41038}, {2321, 49597}, {2796, 25164}, {3178, 11096}, {3845, 49580}, {5066, 49579}, {5321, 49604}, {7354, 36669}, {10175, 49589}, {10654, 49571}, {16628, 49609}, {16634, 49488}, {16808, 49594}, {16809, 49575}, {17606, 36668}, {18480, 49566}, {18582, 41638}, {31673, 49591}, {35732, 49559}, {36765, 49603}, {41099, 49581}, {41106, 49582}

X(49573) = orthologic center (11th Fermat-Dao, T) for these triangles T: 1st Jenkins, 1st Savin
X(49573) = X(49611)-of-Johnson triangle
X(49573) = X(49588)-of-X3-ABC reflections triangle
X(49573) = reflection of X(i) in X(j) for these (i, j): (3, 49588), (49574, 19925), (49611, 5)


X(49574) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 12th FERMAT-DAO TO 1st SAVIN

Barycentrics    (2*a^4-(b+c)*a^3+(b+c)^2*a^2+(b^2-c^2)*(b-c)*a-3*(b^2-c^2)^2)*sqrt(3)+2*S*(a+b+c)*(2*a-b-c) : :
X(49574) = 2*X(3845)+X(49584) = 4*X(5066)-X(49583) = 3*X(10175)-2*X(49588) = 2*X(18480)+X(49568) = X(31673)+2*X(49590) = 5*X(41099)+X(49577) = 7*X(41106)-X(49578)

The reciprocal orthologic center of these triangles is X(49540).

X(49574) lies on these lines: {3, 49589}, {4, 49541}, {5, 49610}, {6, 49597}, {10, 13}, {62, 49570}, {355, 381}, {515, 49611}, {516, 41039}, {2321, 49596}, {2796, 25154}, {3178, 11095}, {3845, 49584}, {5066, 49583}, {5318, 49605}, {7354, 36668}, {10175, 49588}, {10653, 49572}, {16629, 49609}, {16635, 49488}, {16808, 49576}, {16809, 49595}, {17606, 36669}, {18480, 49568}, {18581, 41648}, {31673, 49590}, {41099, 49577}, {41106, 49578}

X(49574) = orthologic center (12th Fermat-Dao, T) for these triangles T: 1st Jenkins, 1st Savin
X(49574) = X(49610)-of-Johnson triangle
X(49574) = X(49589)-of-X3-ABC reflections triangle
X(49574) = reflection of X(i) in X(j) for these (i, j): (3, 49589), (49573, 19925), (49610, 5)


X(49575) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 15th FERMAT-DAO TO 1st SAVIN

Barycentrics    (a^4-(b+c)*a^3+2*b*c*a^2+(b^2-c^2)*(b-c)*a-(b^2-c^2)^2)*sqrt(3)-2*(a^2+(b+c)*a-(b+c)^2)*S : :
X(49575) = 3*X(13)-2*X(49594) = 3*X(13)-4*X(49596) = 5*X(16960)-4*X(41638) = 5*X(16960)-6*X(49569) = 3*X(16962)-4*X(49571) = 3*X(21359)-2*X(49538) = 3*X(41024)-4*X(49539) = 2*X(41638)-3*X(49569)

The reciprocal orthologic center of these triangles is X(49538).

X(49575) lies on these lines: {10, 18}, {13, 519}, {355, 4053}, {1277, 5541}, {2796, 25166}, {3679, 37831}, {5741, 40713}, {6777, 12781}, {16809, 49573}, {16960, 41638}, {16962, 49571}, {16964, 49604}, {16966, 49611}, {17766, 49605}, {21359, 49538}, {33416, 49588}, {35733, 49559}, {36766, 49603}, {41024, 49539}, {41100, 49580}, {41107, 49581}, {41121, 49582}

X(49575) = reflection of X(49594) in X(49596)
X(49575) = orthologic center (15th Fermat-Dao, T) for these triangles T: 1st Jenkins, 1st Savin
X(49575) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (355, 17299, 49576), (41638, 49569, 16960), (49594, 49596, 13)


X(49576) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 16th FERMAT-DAO TO 1st SAVIN

Barycentrics    (a^4-(b+c)*a^3+2*b*c*a^2+(b^2-c^2)*(b-c)*a-(b^2-c^2)^2)*sqrt(3)+2*(a^2+(b+c)*a-(b+c)^2)*S : :
X(49576) = 3*X(14)-2*X(49595) = 3*X(14)-4*X(49597) = 5*X(16961)-4*X(41648) = 5*X(16961)-6*X(49570) = 3*X(16963)-4*X(49572) = 3*X(21360)-2*X(49540) = 3*X(41025)-4*X(49541) = 2*X(41648)-3*X(49570)

The reciprocal orthologic center of these triangles is X(49540).

X(49576) lies on these lines: {10, 17}, {14, 519}, {355, 4053}, {1276, 5541}, {2796, 25156}, {3679, 37834}, {5741, 40714}, {6778, 12780}, {16808, 49574}, {16961, 41648}, {16963, 49572}, {16965, 49605}, {16967, 49610}, {17766, 49604}, {21360, 49540}, {33417, 49589}, {41025, 49541}, {41101, 49584}, {41108, 49577}, {41122, 49578}

X(49576) = reflection of X(49595) in X(49597)
X(49576) = orthologic center (16th Fermat-Dao, T) for these triangles T: 1st Jenkins, 1st Savin
X(49576) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (355, 17299, 49575), (41648, 49570, 16961), (49595, 49597, 14)


X(49577) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI TO 1st SAVIN

Barycentrics    3*(2*a-c-b)*(a+b+c)^2*sqrt(3)-2*S*(4*a-5*c-5*b) : :
X(49577) = 11*X(2)-12*X(49589) = 7*X(2)-6*X(49610) = 3*X(3679)-2*X(49580) = 3*X(19875)-2*X(49566) = 3*X(25055)-4*X(49590)

The reciprocal orthologic center of these triangles is X(49540).

X(49577) lies on these lines: {1, 2}, {2796, 35749}, {41031, 49541}, {41099, 49574}, {41108, 49576}, {41120, 49595}

X(49577) = reflection of X(i) in X(j) for these (i, j): (2, 49584), (3241, 49568), (49578, 2), (49581, 4669)
X(49577) = orthologic center (1st inner-Fermat-Dao-Nhi, T) for these triangles T: 1st Jenkins, 1st Savin
X(49577) = anticomplement of X(49583)


X(49578) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI TO 1st SAVIN

Barycentrics    3*(2*a-c-b)*(a+b+c)^2*sqrt(3)-2*S*(8*a-c-b) : :
X(49578) = 3*X(1)-2*X(49579) = 13*X(2)-12*X(49589) = 5*X(2)-6*X(49610)

The reciprocal orthologic center of these triangles is X(49540).

X(49578) lies on these lines: {1, 2}, {2796, 35750}, {41033, 49541}, {41106, 49574}, {41113, 49595}, {41122, 49576}

X(49578) = reflection of X(i) in X(j) for these (i, j): (2, 49583), (3679, 49566), (4677, 49580), (49577, 2)
X(49578) = orthologic center (2nd inner-Fermat-Dao-Nhi, T) for these triangles T: 1st Jenkins, 1st Savin
X(49578) = anticomplement of X(49584)


X(49579) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI TO 1st SAVIN

Barycentrics    3*(2*a-c-b)*(a+b+c)^2*sqrt(3)+2*S*(10*a+b+c) : :
X(49579) = 3*X(1)-X(49578) = 7*X(2)-6*X(49588) = 2*X(2)-3*X(49611) = 3*X(19883)-2*X(49591)

The reciprocal orthologic center of these triangles is X(49538).

X(49579) lies on these lines: {1, 2}, {2796, 36329}, {5066, 49573}, {35734, 49559}, {35751, 49603}, {41026, 49539}, {41101, 49604}, {41107, 49594}, {41119, 49596}

X(49579) = midpoint of X(2) and X(49582)
X(49579) = reflection of X(i) in X(j) for these (i, j): (3679, 49590), (49566, 551), (49580, 2)
X(49579) = complement of X(49581)
X(49579) = orthologic center (3rd inner-Fermat-Dao-Nhi, T) for these triangles T: 1st Jenkins, 1st Savin
X(49579) = {X(49580), X(49611)}-harmonic conjugate of X(2)


X(49580) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI TO 1st SAVIN

Barycentrics    3*(2*a-c-b)*(a+b+c)^2*sqrt(3)+2*S*(2*a-7*c-7*b) : :
X(49580) = 5*X(2)-6*X(49588) = 4*X(2)-3*X(49611) = 3*X(3679)-X(49577) = 3*X(19875)-2*X(49590)

The reciprocal orthologic center of these triangles is X(49538).

X(49580) lies on these lines: {1, 2}, {2796, 36330}, {3845, 49573}, {35735, 49559}, {36767, 49603}, {41028, 49539}, {41100, 49575}, {41108, 49604}, {41112, 49596}, {41121, 49594}, {42506, 49569}

X(49580) = midpoint of X(i) and X(j) for these {i, j}: {2, 49581}, {4677, 49578}
X(49580) = reflection of X(i) in X(j) for these (i, j): (551, 49591), (49568, 3828), (49579, 2), (49584, 4745)
X(49580) = complement of X(49582)
X(49580) = orthologic center (4th inner-Fermat-Dao-Nhi, T) for these triangles T: 1st Jenkins, 1st Savin
X(49580) = {X(2), X(49579)}-harmonic conjugate of X(49611)


X(49581) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI TO 1st SAVIN

Barycentrics    3*(2*a-c-b)*(a+b+c)^2*sqrt(3)+2*S*(4*a-5*c-5*b) : :
X(49581) = 11*X(2)-12*X(49588) = 7*X(2)-6*X(49611) = 3*X(3679)-2*X(49584) = 3*X(19875)-2*X(49568) = 3*X(25055)-4*X(49591)

The reciprocal orthologic center of these triangles is X(49538).

X(49581) lies on these lines: {1, 2}, {2796, 36327}, {35736, 49559}, {36768, 49603}, {41030, 49539}, {41099, 49573}, {41107, 49575}, {41119, 49594}

X(49581) = reflection of X(i) in X(j) for these (i, j): (2, 49580), (3241, 49566), (49577, 4669), (49582, 2)
X(49581) = orthologic center (1st outer-Fermat-Dao-Nhi, T) for these triangles T: 1st Jenkins, 1st Savin
X(49581) = anticomplement of X(49579)


X(49582) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI TO 1st SAVIN

Barycentrics    3*(2*a-c-b)*(a+b+c)^2*sqrt(3)+2*S*(8*a-c-b) : :
X(49582) = 3*X(1)-2*X(49583) = 13*X(2)-12*X(49588) = 5*X(2)-6*X(49611)

The reciprocal orthologic center of these triangles is X(49538).

X(49582) lies on these lines: {1, 2}, {2796, 36331}, {35737, 49559}, {36769, 49603}, {41032, 49539}, {41106, 49573}, {41112, 49594}, {41121, 49575}

X(49582) = reflection of X(i) in X(j) for these (i, j): (2, 49579), (3679, 49568), (4677, 49584), (49581, 2)
X(49582) = orthologic center (2nd outer-Fermat-Dao-Nhi, T) for these triangles T: 1st Jenkins, 1st Savin
X(49582) = anticomplement of X(49580)


X(49583) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI TO 1st SAVIN

Barycentrics    -2*(10*a+b+c)*S+3*(2*a-b-c)*(a+b+c)^2*sqrt(3) : :
X(49583) = 3*X(1)-X(49582) = 7*X(2)-6*X(49589) = 2*X(2)-3*X(49610) = 3*X(19883)-2*X(49590)

The reciprocal orthologic center of these triangles is X(49540).

X(49583) lies on these lines: {1, 2}, {2796, 35751}, {5066, 49574}, {41027, 49541}, {41100, 49605}, {41108, 49595}, {41120, 49597}

X(49583) = midpoint of X(2) and X(49578)
X(49583) = reflection of X(i) in X(j) for these (i, j): (3679, 49591), (49568, 551), (49584, 2)
X(49583) = complement of X(49577)
X(49583) = orthologic center (3rd outer-Fermat-Dao-Nhi, T) for these triangles T: 1st Jenkins, 1st Savin
X(49583) = {X(49584), X(49610)}-harmonic conjugate of X(2)


X(49584) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI TO 1st SAVIN

Barycentrics    -2*(2*a-7*b-7*c)*S+3*(2*a-b-c)*(a+b+c)^2*sqrt(3) : :
X(49584) = 5*X(2)-6*X(49589) = 4*X(2)-3*X(49610) = 3*X(3679)-X(49581) = 3*X(19875)-2*X(49591)

The reciprocal orthologic center of these triangles is X(49540).

X(49584) lies on these lines: {1, 2}, {2796, 35752}, {3845, 49574}, {41029, 49541}, {41101, 49576}, {41107, 49605}, {41113, 49597}, {41122, 49595}, {42507, 49570}

X(49584) = midpoint of X(i) and X(j) for these {i, j}: {2, 49577}, {4677, 49582}
X(49584) = reflection of X(i) in X(j) for these (i, j): (551, 49590), (49566, 3828), (49580, 4745), (49583, 2)
X(49584) = complement of X(49578)
X(49584) = orthologic center (4th outer-Fermat-Dao-Nhi, T) for these triangles T: 1st Jenkins, 1st Savin
X(49584) = {X(2), X(49583)}-harmonic conjugate of X(49610)


X(49585) = ORTHOLOGIC CENTER OF THESE TRIANGLES: GOSSARD TO 1st SAVIN

Barycentrics    (2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)*(2*a^9+(b+c)*a^8-2*(b^2+c^2)*a^7-(b+c)*(b^2+c^2)*a^6-2*(2*b^2-c^2)*(b^2-2*c^2)*a^5-(b^4-3*b^2*c^2+c^4)*(b+c)*a^4+6*(b^4-c^4)*(b^2-c^2)*a^3+(b^4-c^4)*(b^2-c^2)*(b+c)*a^2-2*(b^2-c^2)^2*(b^4+3*b^2*c^2+c^4)*a-(b^2-c^2)^2*(b+c)*b^2*c^2) : :
X(49585) = X(1)-3*X(16212) = X(8)-3*X(11852) = X(40)-3*X(11845) = X(355)-3*X(11911) = 2*X(1125)-3*X(11831) = X(1650)-3*X(11831) = 3*X(1651)-X(12438) = 3*X(1651)+X(12626) = 5*X(3616)-X(45289) = 2*X(3626)-3*X(16210) = 4*X(3634)-5*X(15183) = 2*X(3635)-3*X(16211) = X(4240)+3*X(16212) = X(4301)+2*X(15774) = 2*X(6684)-3*X(26451) = 2*X(11049)-3*X(19883) = X(11050)-3*X(25055) = 3*X(11897)-2*X(19925) = 2*X(12512)-3*X(16190) = 4*X(15184)-5*X(19862)

The reciprocal orthologic center of these triangles is X(1).

X(49585) lies on these lines: {1, 4240}, {8, 11852}, {10, 402}, {30, 551}, {40, 11845}, {226, 11905}, {355, 11911}, {515, 11251}, {516, 12113}, {517, 32162}, {519, 1651}, {726, 12794}, {950, 11909}, {1125, 1650}, {1210, 11913}, {2784, 12181}, {2796, 12347}, {3244, 11910}, {3616, 45289}, {3626, 16210}, {3634, 15183}, {3635, 16211}, {3656, 20128}, {4301, 15774}, {5847, 12583}, {6684, 26451}, {8666, 22755}, {8715, 11848}, {9033, 11718}, {10106, 18958}, {10915, 26453}, {10916, 26452}, {11049, 19883}, {11050, 25055}, {11832, 49542}, {11839, 49545}, {11853, 49553}, {11863, 49555}, {11864, 49556}, {11885, 49561}, {11897, 19925}, {11901, 49586}, {11902, 49587}, {11903, 49600}, {11904, 21077}, {11906, 12053}, {11907, 49606}, {11908, 49607}, {11912, 31397}, {11914, 49626}, {11915, 49627}, {12512, 16190}, {12699, 18508}, {12729, 13268}, {12795, 17766}, {13883, 44610}, {13894, 49618}, {13936, 44611}, {13948, 49619}, {15184, 19862}, {18483, 18507}, {19017, 49547}, {19018, 49548}, {26383, 48511}, {26407, 48512}, {26447, 49420}, {26448, 49419}, {26449, 49078}, {26450, 49079}, {35790, 49601}, {35791, 49602}, {45446, 49347}, {45447, 49348}, {45548, 48814}, {45549, 48815}

X(49585) = midpoint of X(i) and X(j) for these {i, j}: {1, 4240}, {3656, 20128}, {12113, 12696}, {12438, 12626}, {12699, 18508}, {12729, 13268}
X(49585) = reflection of X(i) in X(j) for these (i, j): (10, 402), (1650, 1125), (18507, 18483)
X(49585) = orthologic center (Gossard, T) for these triangles T: 1st Jenkins, 1st Savin
X(49585) = center of circle {{X(1), X(3109), X(4240)}}
X(49585) = X(10)-of-Gossard triangle
X(49585) = X(4240)-of-anti-Aquila triangle
X(49585) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1650, 11831, 1125), (1651, 12626, 12438), (4240, 16212, 1)


X(49586) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-GREBE TO 1st SAVIN

Barycentrics    S*(b+c)+2*a^3+(b+c)*a^2-(b+c)*(b^2+c^2) : :
X(49586) = 3*X(10)-2*X(49347) = X(3641)-3*X(5861) = 3*X(5861)+X(12627) = 3*X(10164)-4*X(48815) = X(49347)-3*X(49348) = 4*X(49347)-3*X(49587) = 4*X(49348)-X(49587)

The reciprocal orthologic center of these triangles is X(1).

X(49586) lies on these lines: {1, 1271}, {6, 10}, {8, 5589}, {40, 10783}, {226, 10923}, {355, 11916}, {515, 1161}, {516, 5871}, {517, 5875}, {519, 3641}, {726, 6273}, {946, 6215}, {950, 10927}, {1125, 5591}, {1210, 10048}, {2784, 6227}, {2796, 9882}, {3244, 5605}, {3576, 10517}, {3626, 26339}, {3817, 10514}, {4297, 11824}, {4301, 6281}, {5595, 49553}, {6202, 19925}, {6263, 13269}, {6275, 17766}, {6684, 26341}, {8198, 49555}, {8205, 49556}, {8216, 49606}, {8217, 49607}, {8666, 22756}, {8715, 11497}, {8974, 49618}, {9994, 49561}, {10040, 31397}, {10106, 18959}, {10164, 45552}, {10792, 49545}, {10915, 26343}, {10916, 26342}, {10919, 49600}, {10921, 21077}, {10925, 12053}, {10929, 49626}, {10931, 49627}, {11388, 49542}, {11901, 49585}, {12699, 26336}, {13949, 49619}, {13975, 45547}, {15834, 45399}, {18483, 18509}, {26334, 48511}, {26335, 48512}, {26337, 49420}, {35792, 49601}, {35795, 49602}, {45550, 48814}, {45594, 49419}

X(49586) = midpoint of X(i) and X(j) for these {i, j}: {3641, 12627}, {5871, 12697}, {6263, 13269}
X(49586) = reflection of X(i) in X(j) for these (i, j): (10, 49348), (49078, 3626), (49587, 10)
X(49586) = X(8)-beth conjugate of-X(49587)
X(49586) = orthologic center (inner-Grebe, T) for these triangles T: 1st Jenkins, 1st Savin
X(49586) = X(10)-of-inner-Grebe triangle
X(49586) = X(5689)-of-2nd anti-Kenmotu centers triangle
X(49586) = X(49587)-of-outer-Garcia triangle
X(49586) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 5689, 10), (3416, 13883, 10), (5591, 11370, 1125), (5688, 13911, 10), (5861, 12627, 3641), (13936, 45445, 10)


X(49587) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-GREBE TO 1st SAVIN

Barycentrics    -S*(b+c)+2*a^3+(b+c)*a^2-(b+c)*(b^2+c^2) : :
X(49587) = 3*X(10)-2*X(49348) = X(3640)-3*X(5860) = 3*X(5860)+X(12628) = 3*X(10164)-4*X(48814) = 3*X(49347)-X(49348) = 4*X(49347)-X(49586) = 4*X(49348)-3*X(49586)

The reciprocal orthologic center of these triangles is X(1).

X(49587) lies on these lines: {1, 1270}, {6, 10}, {8, 5588}, {40, 10784}, {226, 10924}, {355, 11917}, {515, 1160}, {516, 5870}, {517, 5874}, {519, 3640}, {726, 6272}, {946, 6214}, {950, 10928}, {1125, 5590}, {1210, 10049}, {2784, 6226}, {2796, 9883}, {3244, 5604}, {3576, 10518}, {3626, 26340}, {3817, 10515}, {4297, 11825}, {4301, 6278}, {5594, 49553}, {6201, 19925}, {6262, 13270}, {6274, 17766}, {6684, 26348}, {8199, 49555}, {8206, 49556}, {8218, 49606}, {8219, 49607}, {8666, 22757}, {8715, 11498}, {8975, 49618}, {9995, 49561}, {10041, 31397}, {10106, 18960}, {10164, 45553}, {10793, 49545}, {10915, 26350}, {10916, 26349}, {10920, 49600}, {10922, 21077}, {10926, 12053}, {10930, 49626}, {10932, 49627}, {11389, 49542}, {11902, 49585}, {12699, 26346}, {13912, 45546}, {13950, 49619}, {15835, 45398}, {18483, 18511}, {26338, 49419}, {26344, 48511}, {26345, 48512}, {26347, 49420}, {35793, 49602}, {35794, 49601}, {45551, 48815}

X(49587) = midpoint of X(i) and X(j) for these {i, j}: {3640, 12628}, {5870, 12698}, {6262, 13270}
X(49587) = reflection of X(i) in X(j) for these (i, j): (10, 49347), (49079, 3626), (49586, 10)
X(49587) = X(8)-beth conjugate of-X(49586)
X(49587) = orthologic center (outer-Grebe, T) for these triangles T: 1st Jenkins, 1st Savin
X(49587) = X(10)-of-outer-Grebe triangle
X(49587) = X(5688)-of-1st anti-Kenmotu centers triangle
X(49587) = X(49586)-of-outer-Garcia triangle
X(49587) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 5688, 10), (3416, 13936, 10), (5590, 11371, 1125), (5689, 13973, 10), (5860, 12628, 3640), (13883, 45444, 10)


X(49588) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS-CENTRAL TO 1st SAVIN

Barycentrics    -2*sqrt(3)*(2*a+3*b+3*c)*S+(2*a-b-c)*(a+b+c)^2 : :
X(49588) = 7*X(2)-X(49579) = 5*X(2)+X(49580) = 11*X(2)+X(49581) = 13*X(2)-X(49582) = 5*X(1698)+X(49566) = 4*X(3634)-X(49590) = 2*X(3634)+X(49591)

The reciprocal orthologic center of these triangles is X(49538).

X(49588) lies on these lines: {1, 2}, {3, 49573}, {12, 36669}, {16, 49596}, {62, 49569}, {395, 8258}, {2796, 5460}, {6684, 6774}, {10175, 49574}, {16966, 49594}, {18581, 49604}, {21077, 33429}, {22891, 49570}, {23302, 41638}, {33416, 49575}, {35738, 49559}, {36770, 49603}, {41034, 49539}

X(49588) = midpoint of X(i) and X(j) for these {i, j}: {3, 49573}, {10, 49610}, {49589, 49591}
X(49588) = reflection of X(i) in X(j) for these (i, j): (49589, 3634), (49590, 49589)
X(49588) = complement of X(49611)
X(49588) = orthologic center (1st half-diamonds-central, T) for these triangles T: 1st Jenkins, 1st Savin
X(49588) = X(49573)-of-anti-X3-ABC reflections triangle
X(49588) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 17748, 49589), (3634, 49591, 49590)


X(49589) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS-CENTRAL TO 1st SAVIN

Barycentrics    2*sqrt(3)*(2*a+3*b+3*c)*S+(2*a-b-c)*(a+b+c)^2 : :
X(49589) = 11*X(2)+X(49577) = 13*X(2)-X(49578) = 7*X(2)-X(49583) = 5*X(2)+X(49584) = 5*X(1698)+X(49568) = 2*X(3634)+X(49590) = 4*X(3634)-X(49591)

The reciprocal orthologic center of these triangles is X(49540).

X(49589) lies on these lines: {1, 2}, {3, 49574}, {12, 36668}, {15, 49597}, {61, 49570}, {396, 8258}, {2796, 5459}, {6684, 6771}, {10175, 49573}, {16967, 49595}, {18582, 49605}, {21077, 33428}, {22846, 49569}, {23303, 41648}, {33417, 49576}, {41035, 49541}

X(49589) = midpoint of X(i) and X(j) for these {i, j}: {3, 49574}, {10, 49611}, {49588, 49590}
X(49589) = reflection of X(i) in X(j) for these (i, j): (49588, 3634), (49591, 49588)
X(49589) = complement of X(49610)
X(49589) = orthologic center (2nd half-diamonds-central, T) for these triangles T: 1st Jenkins, 1st Savin
X(49589) = X(49574)-of-anti-X3-ABC reflections triangle
X(49589) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 17748, 49588), (3634, 49590, 49591)


X(49590) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-DIAMONDS TO 1st SAVIN

Barycentrics    2*(2*a+3*b+3*c)*S+(2*a-b-c)*(a+b+c)^2*sqrt(3) : :
X(49590) = X(1)-3*X(49611) = 4*X(3634)-3*X(49588) = 2*X(3634)-3*X(49589) = 5*X(19862)-3*X(49610) = 3*X(19875)-X(49580) = 3*X(19883)-X(49583) = 3*X(25055)+X(49577)

The reciprocal orthologic center of these triangles is X(49565).

X(49590) lies on these lines: {1, 2}, {303, 49565}, {3579, 47610}, {6684, 49106}, {8258, 41638}, {17770, 42680}, {18483, 22797}, {21077, 33397}, {28526, 49605}, {31673, 49574}, {32636, 36668}

X(49590) = midpoint of X(i) and X(j) for these {i, j}: {10, 49568}, {551, 49584}, {3679, 49579}
X(49590) = reflection of X(i) in X(j) for these (i, j): (49588, 49589), (49591, 3634)
X(49590) = complement of X(49566)
X(49590) = orthologic center (1st half-diamonds, T) for these triangles T: 1st Jenkins, 1st Savin
X(49590) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 17748, 49591), (3634, 49591, 49588), (49589, 49591, 3634)


X(49591) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-DIAMONDS TO 1st SAVIN

Barycentrics    -2*(2*a+3*b+3*c)*S+(2*a-b-c)*(a+b+c)^2*sqrt(3) : :
X(49591) = X(1)-3*X(49610) = 2*X(3634)-3*X(49588) = 4*X(3634)-3*X(49589) = 5*X(19862)-3*X(49611) = 3*X(19875)-X(49584) = 3*X(19883)-X(49579) = 3*X(25055)+X(49581)

The reciprocal orthologic center of these triangles is X(49567).

X(49591) lies on these lines: {1, 2}, {302, 49567}, {3579, 47611}, {6684, 49105}, {8258, 41648}, {17770, 42677}, {18483, 22796}, {21077, 33396}, {28526, 49604}, {31673, 49573}, {32636, 36669}

X(49591) = midpoint of X(i) and X(j) for these {i, j}: {10, 49566}, {551, 49580}, {3679, 49583}
X(49591) = reflection of X(i) in X(j) for these (i, j): (49589, 49588), (49590, 3634)
X(49591) = complement of X(49568)
X(49591) = orthologic center (2nd half-diamonds, T) for these triangles T: 1st Jenkins, 1st Savin
X(49591) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 17748, 49590), (3634, 49590, 49589), (49588, 49590, 3634)


X(49592) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st HALF-SQUARES TO 1st SAVIN

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

The reciprocal orthologic center of these triangles is X(31582).

X(49592) lies on these lines: {1, 2}, {4, 49078}, {40, 12256}, {492, 31582}, {516, 5870}, {740, 49347}, {2321, 13936}, {3068, 49622}, {3704, 7968}, {3714, 49233}, {3755, 5688}, {3950, 31595}, {4385, 26301}, {4856, 49548}, {5839, 14121}, {6564, 49552}, {7090, 17314}, {10911, 42051}, {12221, 28526}, {13947, 49623}, {13973, 17299}, {17355, 49547}, {17772, 49348}, {33364, 45719}, {45444, 49486}, {49618, 49620}

X(49592) = reflection of X(i) in X(j) for these (i, j): (1, 49624), (49593, 10)
X(49592) = anticomplement of X(49625)
X(49592) = orthologic center (1st half-squares, T) for these triangles T: 1st Jenkins, 1st Savin
X(49592) = X(49624)-of-Aquila triangle
X(49592) = X(49622)-of-3rd anti-tri-squares-central triangle
X(49592) = X(49593)-of-outer-Garcia triangle
X(49592) = X(8)-beth conjugate of-X(49593)


X(49593) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd HALF-SQUARES TO 1st SAVIN

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

The reciprocal orthologic center of these triangles is X(31583).

X(49593) lies on these lines: {1, 2}, {4, 49079}, {40, 12257}, {491, 31583}, {516, 5871}, {518, 9808}, {740, 49348}, {2321, 13883}, {3069, 49623}, {3704, 7969}, {3714, 49232}, {3755, 5689}, {3950, 31594}, {4385, 26300}, {4856, 49547}, {5839, 7090}, {6565, 49551}, {10910, 42051}, {12222, 28526}, {13893, 49622}, {13911, 17299}, {14121, 17314}, {17355, 49548}, {17772, 49347}, {31438, 31595}, {33365, 45720}, {45445, 49486}, {49619, 49621}

X(49593) = reflection of X(i) in X(j) for these (i, j): (1, 49625), (49592, 10)
X(49593) = anticomplement of X(49624)
X(49593) = orthologic center (2nd half-squares, T) for these triangles T: 1st Jenkins, 1st Savin
X(49593) = X(49625)-of-Aquila triangle
X(49593) = X(49592)-of-outer-Garcia triangle
X(49593) = X(8)-beth conjugate of-X(49592)


X(49594) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ISODYNAMIC-DAO TO 1st SAVIN

Barycentrics    -2*(4*a^2+(b+c)*a-(b+c)^2)*S-((b+c)*a^3+(b-c)^2*a^2-(b^2-c^2)*(b-c)*a-(b^2-c^2)^2)*sqrt(3) : :
X(49594) = 3*X(13)-X(49575) = 3*X(13)-2*X(49596) = 4*X(11542)-3*X(49569) = 3*X(16267)-2*X(49571) = 3*X(41036)-2*X(49539)

The reciprocal orthologic center of these triangles is X(49538).

X(49594) lies on these lines: {10, 17}, {13, 519}, {15, 41638}, {16, 49611}, {61, 49604}, {239, 33396}, {516, 41020}, {532, 49538}, {551, 37831}, {726, 3105}, {946, 32431}, {1277, 3218}, {2796, 22997}, {3879, 33397}, {11542, 49569}, {16267, 49571}, {16808, 49573}, {16966, 49588}, {17300, 33428}, {23006, 49603}, {35739, 49559}, {41036, 49539}, {41107, 49579}, {41112, 49582}, {41119, 49581}, {41121, 49580}

X(49594) = reflection of X(i) in X(j) for these (i, j): (15, 41638), (49575, 49596)
X(49594) = orthologic center (1st isodynamic-Dao, T) for these triangles T: 1st Jenkins, 1st Savin
X(49594) = {X(13), X(49575)}-harmonic conjugate of X(49596)


X(49595) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ISODYNAMIC-DAO TO 1st SAVIN

Barycentrics    2*(4*a^2+(b+c)*a-(b+c)^2)*S-((b+c)*a^3+(b-c)^2*a^2-(b^2-c^2)*(b-c)*a-(b^2-c^2)^2)*sqrt(3) : :
X(49595) = 3*X(14)-X(49576) = 3*X(14)-2*X(49597) = 4*X(11543)-3*X(49570) = 3*X(16268)-2*X(49572) = 3*X(41037)-2*X(49541)

The reciprocal orthologic center of these triangles is X(49540).

X(49595) lies on these lines: {10, 18}, {14, 519}, {15, 49610}, {16, 41648}, {62, 49605}, {239, 33397}, {516, 41021}, {533, 49540}, {551, 37834}, {726, 3104}, {946, 32431}, {1276, 3218}, {2796, 22998}, {3879, 33396}, {11543, 49570}, {16268, 49572}, {16809, 49574}, {16967, 49589}, {17300, 33429}, {41037, 49541}, {41108, 49583}, {41113, 49578}, {41120, 49577}, {41122, 49584}

X(49595) = reflection of X(i) in X(j) for these (i, j): (16, 41648), (49576, 49597)
X(49595) = orthologic center (2nd isodynamic-Dao, T) for these triangles T: 1st Jenkins, 1st Savin
X(49595) = {X(14), X(49576)}-harmonic conjugate of X(49597)


X(49596) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd ISODYNAMIC-DAO TO 1st SAVIN

Barycentrics    2*(2*a^2-(b+c)*a+(b+c)^2)*S+(2*a^4-(b+c)*a^3+(b+c)^2*a^2+(b^2-c^2)*(b-c)*a-3*(b^2-c^2)^2)*sqrt(3) : :
X(49596) = 3*X(13)+X(49575) = 3*X(13)-X(49594) = X(15)-3*X(49569)

The reciprocal orthologic center of these triangles is X(49538).

X(49596) lies on these lines: {4, 9}, {6, 49573}, {13, 519}, {15, 49569}, {16, 49588}, {30, 49571}, {1503, 49539}, {2321, 49574}, {2796, 31709}, {3828, 37831}, {11542, 41638}, {18582, 49611}, {35740, 49559}, {36771, 49603}, {41112, 49580}, {41119, 49579}

X(49596) = midpoint of X(49575) and X(49594)
X(49596) = reflection of X(41638) in X(11542)
X(49596) = orthologic center (3rd isodynamic-Dao, T) for these triangles T: 1st Jenkins, 1st Savin
X(49596) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (10, 32431, 49597), (13, 49575, 49594), (17355, 19925, 49597)


X(49597) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th ISODYNAMIC-DAO TO 1st SAVIN

Barycentrics    -2*(2*a^2-(b+c)*a+(b+c)^2)*S+(2*a^4-(b+c)*a^3+(b+c)^2*a^2+(b^2-c^2)*(b-c)*a-3*(b^2-c^2)^2)*sqrt(3) : :
X(49597) = 3*X(14)+X(49576) = 3*X(14)-X(49595) = X(16)-3*X(49570)

The reciprocal orthologic center of these triangles is X(49540).

X(49597) lies on these lines: {4, 9}, {6, 49574}, {14, 519}, {15, 49589}, {16, 49570}, {30, 49572}, {1503, 49541}, {2321, 49573}, {2796, 31710}, {3828, 37834}, {11543, 41648}, {18581, 49610}, {41113, 49584}, {41120, 49583}

X(49597) = midpoint of X(49576) and X(49595)
X(49597) = reflection of X(41648) in X(11543)
X(49597) = orthologic center (4th isodynamic-Dao, T) for these triangles T: 1st Jenkins, 1st Savin
X(49597) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (10, 32431, 49596), (14, 49576, 49595), (17355, 19925, 49596)


X(49598) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st SAVIN TO 1st JENKINS

Barycentrics    (b+c)*(a^3+(b+c)*a^2+b*c*(b+c+3*a)) : :
X(49598) = X(1)+3*X(46895) = 3*X(2)+X(17164) = X(8)-3*X(21020) = 2*X(10)-3*X(27798) = X(145)+3*X(17163) = 3*X(551)-X(4065) = 4*X(1125)-3*X(10180) = 3*X(1962)-5*X(3616) = X(2650)+3*X(21020) = 5*X(3617)-9*X(27812) = 7*X(3622)-3*X(27804) = 2*X(3743)-3*X(10180) = X(4647)-3*X(46895) = 2*X(12579)-3*X(13745) = 3*X(37631)-2*X(49564)

The reciprocal orthologic center of these triangles is X(49599).

X(49598) lies on these lines: {1, 75}, {2, 986}, {3, 3980}, {5, 25385}, {8, 2650}, {10, 12}, {21, 4418}, {37, 43224}, {40, 7413}, {46, 32916}, {58, 4697}, {81, 27368}, {145, 17163}, {238, 16817}, {333, 1046}, {386, 28612}, {392, 24182}, {404, 3724}, {405, 3923}, {474, 1403}, {512, 48050}, {516, 13442}, {517, 15973}, {519, 37631}, {523, 24099}, {551, 4065}, {690, 3716}, {714, 49483}, {744, 1104}, {756, 19874}, {846, 11110}, {894, 5247}, {940, 17733}, {942, 3741}, {946, 30778}, {958, 4363}, {960, 3739}, {962, 7379}, {964, 3924}, {966, 3958}, {978, 3725}, {984, 19853}, {993, 37227}, {996, 6757}, {1042, 1441}, {1125, 3666}, {1193, 4359}, {1203, 4974}, {1213, 21879}, {1220, 17789}, {1224, 17946}, {1245, 40718}, {1281, 19312}, {1284, 27697}, {1330, 33097}, {1503, 35099}, {1724, 4672}, {1909, 35544}, {1962, 3210}, {2294, 2345}, {2329, 42669}, {2550, 18673}, {2771, 48887}, {2783, 48894}, {2785, 24353}, {2796, 12579}, {2901, 42031}, {2944, 6996}, {3120, 5051}, {3178, 3704}, {3214, 46897}, {3216, 28611}, {3293, 4714}, {3295, 29651}, {3339, 18229}, {3555, 49479}, {3617, 27812}, {3622, 27804}, {3624, 31326}, {3634, 24003}, {3670, 6682}, {3695, 29653}, {3702, 3720}, {3706, 35633}, {3728, 24349}, {3747, 16823}, {3757, 5255}, {3775, 11551}, {3812, 3831}, {3821, 13728}, {3840, 5439}, {3842, 16828}, {3846, 12047}, {3868, 30984}, {3869, 31339}, {3872, 17874}, {3876, 26037}, {3878, 47515}, {3931, 43223}, {3936, 20653}, {3953, 42053}, {3985, 16589}, {4011, 11108}, {4016, 17303}, {4096, 19870}, {4151, 48280}, {4195, 32117}, {4205, 4425}, {4300, 28850}, {4362, 5711}, {4413, 38286}, {4414, 16342}, {4427, 17588}, {4432, 5259}, {4438, 19854}, {4459, 8240}, {4511, 31880}, {4642, 26115}, {4683, 14450}, {4754, 35102}, {4771, 20970}, {4772, 20036}, {4968, 10459}, {5015, 33109}, {5047, 32930}, {5082, 36479}, {5221, 37660}, {5235, 11684}, {5262, 32772}, {5302, 17351}, {5329, 19844}, {5436, 25375}, {5496, 30144}, {5530, 49599}, {5687, 29670}, {5692, 25106}, {5718, 17748}, {5749, 40977}, {5814, 32946}, {5835, 25466}, {5902, 10479}, {5904, 49457}, {5955, 11374}, {5977, 5988}, {6147, 33064}, {6358, 37558}, {6651, 16912}, {6998, 8235}, {7229, 25242}, {8258, 35466}, {8424, 20836}, {9780, 32931}, {9785, 42446}, {9840, 29057}, {10176, 25444}, {10916, 21242}, {11321, 16822}, {11533, 14007}, {11688, 37442}, {11814, 17575}, {12263, 49563}, {12514, 24310}, {12688, 45305}, {13725, 24248}, {13736, 24280}, {14949, 17116}, {16062, 17889}, {16466, 16825}, {16478, 19851}, {16601, 17355}, {16819, 17755}, {16821, 44352}, {16850, 24259}, {16851, 24283}, {16917, 27954}, {17030, 24631}, {17048, 21264}, {17451, 26035}, {17514, 25354}, {17596, 19270}, {17751, 31025}, {17754, 40978}, {17793, 19856}, {18235, 28258}, {19767, 32860}, {19867, 25351}, {20360, 28604}, {20896, 49487}, {21085, 41014}, {21147, 23555}, {21232, 25132}, {21627, 24394}, {21921, 27040}, {22011, 28594}, {24159, 26128}, {24165, 37592}, {24178, 24199}, {24333, 42461}, {24390, 29655}, {24541, 25094}, {24552, 28082}, {24589, 27627}, {24851, 26117}, {24897, 27785}, {24987, 25984}, {25080, 25083}, {25088, 25095}, {25380, 42666}, {25645, 26725}, {25650, 33160}, {26030, 31264}, {26363, 37591}, {27811, 46934}, {29301, 48939}, {29673, 31419}, {30143, 48863}, {30818, 46827}, {30824, 31246}, {31435, 37555}, {31794, 39564}, {31803, 48888}, {32932, 37573}, {32935, 41229}, {33108, 36568}, {34791, 44671}

X(49598) = midpoint of X(i) and X(j) for these {i, j}: {1, 4647}, {8, 2650}, {2292, 17164}, {3728, 24349}, {3872, 17874}, {4968, 10459}, {20896, 49487}
X(49598) = reflection of X(i) in X(j) for these (i, j): (3743, 1125), (25124, 24325), (42666, 25380)
X(49598) = complement of X(2292)
X(49598) = complementary conjugate of the complement of X(2363)
X(49598) = barycentric product X(321)*X(37607)
X(49598) = barycentric quotient X(i)/X(j) for these (i, j): (37, 43073), (65, 43071), (71, 43072), (1284, 43075), (1400, 43070)
X(49598) = trilinear product X(10)*X(37607)
X(49598) = trilinear quotient X(i)/X(j) for these (i, j): (10, 43073), (12, 43074), (65, 43070), (72, 43072), (226, 43071)
X(49598) = perspector of the circumconic {{A, B, C, X(799), X(4552)}}
X(49598) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(181)}} and {{A, B, C, X(10), X(314)}}
X(49598) = X(i)-complementary conjugate of-X(j) for these (i, j): (961, 442), (1169, 2)
X(49598) = X(10)-Dao conjugate of X(43073)
X(49598) = X(i)-isoconjugate-of-X(j) for these {i, j}: {21, 43070}, {28, 43072}, {58, 43073}, {60, 43074}
X(49598) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (37, 43073), (65, 43071), (71, 43072)
X(49598) = orthologic center (1st Savin, 1st Jenkins)
X(49598) = X(4)-of-1st Savin triangle
X(49598) = X(4647)-of-anti-Aquila triangle
X(49598) = X(35717)-of-Wasat triangle, when ABC is acute
X(49598) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 24342, 1010), (1, 28619, 5625), (1, 41812, 25526), (1, 46895, 4647), (2, 17164, 2292), (10, 4090, 3697), (10, 11263, 3454), (10, 12609, 2887), (21, 4418, 24850), (65, 31993, 10), (75, 86, 39774), (894, 16824, 5247), (1125, 3743, 10180), (1215, 27798, 25123), (2650, 21020, 8), (3120, 27714, 5051), (3454, 11263, 4892), (3670, 19863, 6682), (3704, 17056, 3178), (3812, 44417, 3831), (14450, 26064, 4683)


X(49599) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JENKINS TO 1st SAVIN

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

The reciprocal orthologic center of these triangles is X(49598).

X(49599) lies on these lines: {10, 37}, {714, 12607}, {758, 970}, {3597, 43677}, {4362, 31496}, {5530, 49598}, {9565, 29671}, {25059, 31339}, {35203, 38456}

X(49599) = orthologic center (1st Jenkins, 1st Savin)
X(49599) = X(4)-of-1st Jenkins triangle


X(49600) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-JOHNSON TO 1st SAVIN

Barycentrics    (b+c)*a^3+(b^2-6*b*c+c^2)*a^2-(b+c)*(b^2-4*b*c+c^2)*a-(b^2-c^2)^2 : :
X(49600) = X(40)-3*X(45700) = X(355)-3*X(11235) = 5*X(355)-3*X(34717) = 3*X(355)+X(47746) = 3*X(381)-X(32049) = 5*X(962)+3*X(28610) = X(962)+3*X(34625) = X(1482)-3*X(34640) = 3*X(1699)+X(12629) = X(2136)-5*X(8227) = X(2136)-3*X(45701) = 3*X(3656)-X(12635) = X(10912)+3*X(11235) = 5*X(10912)+3*X(34717) = 3*X(10912)-X(47746) = X(10916)+2*X(13463) = 5*X(11235)-X(34717) = 9*X(11235)+X(47746) = X(21077)+2*X(21627) = X(28610)-5*X(34625) = 9*X(34717)+5*X(47746)

The reciprocal orthologic center of these triangles is X(1).

X(49600) lies on these lines: {1, 224}, {5, 3880}, {8, 5187}, {10, 11}, {12, 49626}, {30, 11260}, {35, 48713}, {40, 10785}, {46, 10529}, {65, 10949}, {145, 12047}, {149, 4861}, {226, 3244}, {355, 381}, {442, 5919}, {496, 5836}, {498, 3895}, {515, 10525}, {516, 8666}, {517, 3813}, {518, 21850}, {528, 1385}, {529, 22793}, {551, 17614}, {726, 12923}, {758, 4301}, {908, 3632}, {950, 10947}, {952, 12608}, {956, 12701}, {962, 1709}, {993, 10624}, {997, 5082}, {1125, 1376}, {1210, 10948}, {1320, 5086}, {1329, 7743}, {1478, 36846}, {1479, 3872}, {1519, 5881}, {1537, 14872}, {1697, 26363}, {1698, 10584}, {1699, 12629}, {1706, 10200}, {1737, 14923}, {1739, 28018}, {2098, 3419}, {2136, 8227}, {2170, 21073}, {2321, 17444}, {2784, 12182}, {2796, 12348}, {2886, 9957}, {3086, 26062}, {3158, 9624}, {3189, 10595}, {3241, 13407}, {3338, 11240}, {3452, 3626}, {3612, 20075}, {3625, 11813}, {3633, 18393}, {3634, 31493}, {3635, 21620}, {3671, 3881}, {3678, 17658}, {3679, 41012}, {3680, 5587}, {3746, 24541}, {3753, 37722}, {3754, 11019}, {3811, 5603}, {3814, 6736}, {3817, 17648}, {3829, 9956}, {3878, 4847}, {3885, 10039}, {3889, 11551}, {3892, 17616}, {3893, 17757}, {3897, 34611}, {3913, 5886}, {3918, 9843}, {4015, 18236}, {4051, 5179}, {4297, 11826}, {4512, 31458}, {4731, 17575}, {4853, 9614}, {4863, 5730}, {5119, 10527}, {5123, 10593}, {5178, 5330}, {5248, 12575}, {5450, 40255}, {5493, 17613}, {5533, 39776}, {5542, 17624}, {5552, 23708}, {5687, 10965}, {5690, 27870}, {5697, 6734}, {5705, 9819}, {5847, 12586}, {5850, 16112}, {5853, 13464}, {5855, 11278}, {5880, 7373}, {5882, 12737}, {5903, 26015}, {5927, 13865}, {6260, 28236}, {6684, 26492}, {6735, 7741}, {6762, 31162}, {6765, 11522}, {6767, 28628}, {6833, 12703}, {6911, 8668}, {7680, 13600}, {7982, 24392}, {8728, 10179}, {9785, 19843}, {9955, 12607}, {10106, 18961}, {10165, 13205}, {10175, 12640}, {10198, 31393}, {10222, 33592}, {10523, 25639}, {10524, 10827}, {10528, 37692}, {10742, 11256}, {10794, 49545}, {10829, 49553}, {10871, 49561}, {10919, 49586}, {10920, 49587}, {10945, 49606}, {10946, 49607}, {11009, 41575}, {11112, 20323}, {11231, 32157}, {11362, 24386}, {11390, 49542}, {11508, 25440}, {11865, 49555}, {11866, 49556}, {11903, 49585}, {12513, 12699}, {12514, 30305}, {12541, 34619}, {12559, 36845}, {12610, 12924}, {12617, 45776}, {12625, 16200}, {12649, 25415}, {12670, 17655}, {13411, 25439}, {13883, 44618}, {13895, 49618}, {13936, 44619}, {13952, 49619}, {16173, 25438}, {16207, 37712}, {17626, 21625}, {18357, 32537}, {18480, 38455}, {18483, 18516}, {19023, 49547}, {19024, 49548}, {20050, 31053}, {20057, 31019}, {20257, 34847}, {21090, 41006}, {21621, 29844}, {23340, 26470}, {24982, 37720}, {25466, 31792}, {26488, 49420}, {26489, 49419}, {26490, 49078}, {26491, 49079}, {27385, 37735}, {32214, 34339}, {32426, 38140}, {33956, 37705}, {34719, 37571}, {34791, 39542}, {35239, 42842}, {35796, 49601}, {35797, 49602}, {37562, 37726}, {37710, 41702}, {38460, 45287}, {45454, 49347}, {45455, 49348}, {45556, 48814}, {45557, 48815}

X(49600) = midpoint of X(i) and X(j) for these {i, j}: {355, 10912}, {946, 21627}, {3680, 49169}, {3813, 13463}, {7982, 49168}, {10742, 11256}, {12114, 12700}, {12513, 12699}, {12737, 13271}
X(49600) = reflection of X(i) in X(j) for these (i, j): (10, 24387), (8715, 1125), (10915, 5), (10916, 3813), (12607, 9955), (12616, 10943), (21077, 946), (22836, 13464), (32537, 18357)
X(49600) = orthologic center (inner-Johnson, T) for these triangles T: 1st Jenkins, 1st Savin
X(49600) = X(10)-of-inner-Johnson triangle
X(49600) = X(1498)-of-K798i triangle, when ABC is acute
X(49600) = X(3357)-of-Wasat triangle, when ABC is acute
X(49600) = X(5878)-of-3rd Euler triangle, when ABC is acute
X(49600) = X(10915)-of-Johnson triangle
X(49600) = X(20299)-of-Ursa-major triangle, when ABC is acute
X(49600) = X(20427)-of-4th Euler triangle, when ABC is acute
X(49600) = X(32049)-of-Ehrmann-mid triangle
X(49600) = X(49626)-of-outer-Johnson triangle
X(49600) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 3434, 17647), (8, 30384, 21616), (10, 4342, 3884), (10, 21630, 12053), (11, 10914, 10), (149, 4861, 10572), (355, 10893, 19925), (1145, 17606, 10), (1376, 11373, 1125), (1706, 37704, 10200), (2136, 8227, 45701), (3057, 24390, 10), (3625, 11813, 21075), (3680, 5587, 49169), (3885, 11680, 10039), (7982, 24392, 49168), (10826, 30323, 10043), (10912, 11235, 355), (34122, 37829, 10), (37735, 48696, 27385)


X(49601) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st KENMOTU-FREE-VERTICES TO 1st SAVIN

Barycentrics    2*S*a^2+a^4-(b+c)*a^3+2*b*c*a^2+(b^2-c^2)*(b-c)*a-(b^2-c^2)^2 : :
X(49601) = X(35641)-3*X(35822) = 3*X(35822)+X(35842)

The reciprocal orthologic center of these triangles is X(1).

X(49601) lies on these lines: {1, 485}, {3, 13911}, {4, 19066}, {5, 7968}, {6, 355}, {8, 1587}, {10, 372}, {30, 49226}, {40, 6560}, {80, 3299}, {165, 42261}, {226, 35800}, {371, 515}, {486, 5587}, {516, 35610}, {517, 3070}, {519, 35641}, {590, 1385}, {615, 9956}, {726, 35866}, {730, 3103}, {912, 49224}, {944, 3068}, {946, 6564}, {950, 35808}, {952, 7583}, {962, 23249}, {1124, 1837}, {1125, 10576}, {1151, 18481}, {1152, 26446}, {1210, 35769}, {1319, 9661}, {1327, 31162}, {1335, 5252}, {1378, 5794}, {1388, 13898}, {1478, 16232}, {1482, 13665}, {1698, 5420}, {1699, 42269}, {1702, 5691}, {1703, 3679}, {1737, 6502}, {2066, 10572}, {2067, 45287}, {2362, 10573}, {2646, 9646}, {2784, 35824}, {2796, 35698}, {3069, 5818}, {3071, 18480}, {3090, 13959}, {3093, 5090}, {3097, 32471}, {3244, 35810}, {3297, 5722}, {3301, 37710}, {3311, 18525}, {3312, 5790}, {3560, 44591}, {3576, 5418}, {3579, 42259}, {3586, 31432}, {3655, 13846}, {4297, 6200}, {5414, 10039}, {5603, 31412}, {5657, 6460}, {5690, 42216}, {5731, 9540}, {5847, 35840}, {5881, 18991}, {5882, 8960}, {5886, 42265}, {5901, 18538}, {6396, 6684}, {6419, 49548}, {6420, 13936}, {6565, 19925}, {6911, 44607}, {7581, 19065}, {7584, 18357}, {7967, 13886}, {7989, 42274}, {8227, 42277}, {8666, 35784}, {8715, 35772}, {8953, 31533}, {8976, 10246}, {8981, 34773}, {8988, 11715}, {9616, 42260}, {9619, 31463}, {9681, 31440}, {9778, 43407}, {9780, 13935}, {9812, 23253}, {9948, 35845}, {9955, 42273}, {10106, 35768}, {10175, 10577}, {10194, 30315}, {10265, 35857}, {10826, 44624}, {10827, 44622}, {10915, 45642}, {10916, 45640}, {10944, 19030}, {10950, 19028}, {11230, 42582}, {11362, 35611}, {12053, 35802}, {12245, 23267}, {12619, 48701}, {12645, 18512}, {12699, 23251}, {12751, 19078}, {12929, 45460}, {12939, 45458}, {13464, 35811}, {13888, 43430}, {13897, 34471}, {13966, 38042}, {13977, 34122}, {15178, 43879}, {17766, 35868}, {18391, 31408}, {18483, 35786}, {18492, 42268}, {19003, 37714}, {19004, 37712}, {19053, 38074}, {19054, 34627}, {19116, 38138}, {19117, 37705}, {19146, 38047}, {19876, 43255}, {21077, 35798}, {22644, 41869}, {22793, 42284}, {25055, 42602}, {28146, 42272}, {28160, 31439}, {28164, 42266}, {28204, 32787}, {28208, 41945}, {31397, 35809}, {31399, 35813}, {31475, 37721}, {31499, 37600}, {31673, 35821}, {31730, 42267}, {33697, 42271}, {33899, 49235}, {35764, 49542}, {35766, 49545}, {35770, 38155}, {35776, 49553}, {35778, 49555}, {35780, 49556}, {35782, 49561}, {35790, 49585}, {35792, 49586}, {35794, 49587}, {35796, 49600}, {35804, 49606}, {35806, 49607}, {35812, 49618}, {35814, 49619}, {35816, 49626}, {35818, 49627}, {35843, 47745}, {35852, 35882}, {37624, 45384}, {37700, 44620}, {37727, 44635}, {38140, 42270}, {38235, 41687}, {39661, 49079}, {45357, 48511}, {45359, 48512}, {45462, 49347}, {45564, 48815}, {45599, 49419}, {45601, 49420}, {49018, 49078}

X(49601) = midpoint of X(i) and X(j) for these {i, j}: {3070, 49232}, {35610, 35820}, {35641, 35842}, {35852, 35882}
X(49601) = reflection of X(i) in X(j) for these (i, j): (371, 13883), (7969, 7583), (42258, 31439)
X(49601) = orthologic center (1st Kenmotu-free-vertices, T) for these triangles T: 1st Jenkins, 1st Savin
X(49601) = X(10)-of-1st Kenmotu-free-vertices triangle
X(49601) = X(355)-of-1st Kenmotu-centers triangle
X(49601) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 19066, 35775), (6, 355, 49602), (8, 1587, 35774), (372, 35788, 10), (1702, 5691, 6561), (3312, 5790, 13973), (3576, 13893, 5418), (4297, 13912, 6200), (5587, 18992, 486), (5690, 42216, 49227), (5882, 8983, 35763), (6420, 35789, 13936), (6564, 35642, 946), (7967, 13886, 13902), (8960, 35763, 8983), (10175, 13971, 10577), (10576, 35762, 1125), (35822, 35842, 35641), (42265, 44636, 5886)


X(49602) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd KENMOTU-FREE-VERTICES TO 1st SAVIN

Barycentrics    -2*S*a^2+a^4-(b+c)*a^3+2*b*c*a^2+(b^2-c^2)*(b-c)*a-(b^2-c^2)^2 : :
X(49602) = X(35642)-3*X(35823) = 3*X(35823)+X(35843)

The reciprocal orthologic center of these triangles is X(1).

X(49602) lies on these lines: {1, 486}, {3, 13973}, {4, 19065}, {5, 7969}, {6, 355}, {8, 1588}, {10, 371}, {30, 49227}, {40, 6561}, {80, 3301}, {165, 42260}, {226, 35801}, {372, 515}, {485, 5587}, {516, 35611}, {517, 3071}, {519, 35642}, {590, 9956}, {615, 1385}, {726, 35867}, {730, 3102}, {912, 49225}, {944, 3069}, {946, 6565}, {950, 35809}, {952, 7584}, {962, 23259}, {1124, 5252}, {1125, 10577}, {1151, 26446}, {1152, 18481}, {1155, 9647}, {1210, 35768}, {1328, 31162}, {1335, 1837}, {1377, 5794}, {1388, 13955}, {1478, 2362}, {1482, 13785}, {1698, 5418}, {1699, 42268}, {1702, 3679}, {1703, 5691}, {1737, 2067}, {1836, 38235}, {2066, 10039}, {2784, 35825}, {2796, 35699}, {3068, 5818}, {3070, 18480}, {3090, 13902}, {3092, 5090}, {3097, 32470}, {3244, 35811}, {3298, 5722}, {3299, 37710}, {3311, 5790}, {3312, 18525}, {3560, 44590}, {3576, 5420}, {3579, 42258}, {3655, 13847}, {4297, 6396}, {5414, 10572}, {5603, 42561}, {5657, 6459}, {5690, 42215}, {5731, 13935}, {5847, 35841}, {5881, 18992}, {5882, 13971}, {5886, 42262}, {5901, 18762}, {6200, 6684}, {6419, 13883}, {6420, 49547}, {6502, 45287}, {6564, 19925}, {6911, 44606}, {7582, 19066}, {7583, 18357}, {7967, 13939}, {7989, 42277}, {8227, 42274}, {8666, 35785}, {8715, 35773}, {8978, 31533}, {8981, 38042}, {8983, 10175}, {9540, 9780}, {9582, 9588}, {9615, 31423}, {9660, 37568}, {9661, 17606}, {9678, 26066}, {9679, 37828}, {9683, 37557}, {9778, 43408}, {9812, 23263}, {9948, 35844}, {9955, 42270}, {10106, 35769}, {10195, 30315}, {10246, 13951}, {10265, 35856}, {10573, 16232}, {10826, 44623}, {10827, 31472}, {10915, 45643}, {10916, 45641}, {10944, 19029}, {10950, 19027}, {11230, 42583}, {11362, 35610}, {11715, 13976}, {12053, 35803}, {12245, 23273}, {12619, 48700}, {12645, 18510}, {12699, 23261}, {12751, 19077}, {12928, 45461}, {12938, 45459}, {13464, 35810}, {13913, 34122}, {13942, 43431}, {13954, 34471}, {13966, 34773}, {15178, 43880}, {17766, 35869}, {18483, 35787}, {18492, 42269}, {19003, 37712}, {19004, 37714}, {19053, 34627}, {19054, 38074}, {19116, 37705}, {19117, 38138}, {19145, 38047}, {19876, 43254}, {21077, 35799}, {22615, 41869}, {22793, 42283}, {25055, 42603}, {28146, 42271}, {28160, 42259}, {28164, 42267}, {28204, 32788}, {28208, 41946}, {31397, 35808}, {31399, 35812}, {31673, 35820}, {31730, 42266}, {33697, 42272}, {33899, 49234}, {35765, 49542}, {35767, 49545}, {35771, 38155}, {35777, 49553}, {35779, 49556}, {35781, 49555}, {35783, 49561}, {35791, 49585}, {35793, 49587}, {35795, 49586}, {35797, 49600}, {35805, 49607}, {35807, 49606}, {35813, 49619}, {35815, 49618}, {35817, 49626}, {35819, 49627}, {35842, 47745}, {35853, 35883}, {37624, 45385}, {37700, 44621}, {37727, 44636}, {38140, 42273}, {39660, 49078}, {45358, 48512}, {45360, 48511}, {45463, 49348}, {45565, 48814}, {45600, 49420}, {45602, 49419}, {49019, 49079}

X(49602) = midpoint of X(i) and X(j) for these {i, j}: {3071, 49233}, {35611, 35821}, {35642, 35843}, {35853, 35883}
X(49602) = reflection of X(i) in X(j) for these (i, j): (372, 13936), (7968, 7584)
X(49602) = orthologic center (2nd Kenmotu-free-vertices, T) for these triangles T: 1st Jenkins, 1st Savin
X(49602) = X(10)-of-2nd Kenmotu-free-vertices triangle
X(49602) = X(355)-of-2nd Kenmotu-centers triangle
X(49602) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 19065, 35774), (6, 355, 49601), (8, 1588, 35775), (371, 35789, 10), (1698, 9583, 5418), (1703, 5691, 6560), (3311, 5790, 13911), (3576, 13947, 5420), (4297, 13975, 6396), (5587, 18991, 485), (5690, 42215, 49226), (5882, 13971, 35762), (6419, 35788, 13883), (6565, 35641, 946), (7967, 13939, 13959), (8983, 10175, 10576), (10577, 35763, 1125), (35823, 35843, 35642), (42262, 44635, 5886)


X(49603) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LARGEST-CIRCUMSCRIBED-EQUILATERAL TO 1st SAVIN

Barycentrics    -2*sqrt(3)*(a^3+(b+c)*a^2-(b+c)*b*c+(b^2+c^2)*a)*S+(a+b+c)*(3*a^4-2*(b+c)*a^3-4*(b^2-b*c+c^2)*a^2+(b+c)^2*b*c+(b+c)*(b^2-3*b*c+c^2)*a) : :
X(49603) = X(35751)+2*X(49579) = 3*X(36765)-2*X(49573) = 5*X(36767)-2*X(49580) = 4*X(36768)-X(49581) = 2*X(36769)+X(49582) = 5*X(36770)-4*X(49588)

The reciprocal orthologic center of these triangles is X(49538).

X(49603) lies on these lines: {13, 49611}, {516, 36761}, {519, 5463}, {551, 36775}, {726, 32465}, {2796, 9114}, {4297, 5473}, {9112, 41638}, {11711, 32921}, {21636, 36776}, {23006, 49594}, {23870, 30580}, {35751, 49579}, {36762, 49559}, {36763, 49569}, {36764, 49571}, {36765, 49573}, {36766, 49575}, {36767, 49580}, {36768, 49581}, {36769, 49582}, {36770, 49588}, {36771, 49596}, {36772, 49604}, {36782, 49610}, {41019, 49539}

X(49603) = orthologic center (Largest-circumscribed-equilateral, T) for these triangles T: 1st Jenkins, 1st Savin
X(49603) = reflection of X(13) in X(49611)


X(49604) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st LEMOINE-DAO TO 1st SAVIN

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

The reciprocal orthologic center of these triangles is X(49538).

X(49604) lies on these lines: {4, 9}, {14, 2796}, {15, 49611}, {61, 49594}, {381, 49571}, {519, 10654}, {726, 3104}, {1151, 49559}, {2321, 22512}, {3729, 40714}, {3821, 42677}, {5321, 49573}, {11299, 49538}, {11485, 41638}, {16808, 49569}, {16964, 49575}, {17766, 49576}, {18581, 49588}, {28526, 49591}, {36772, 49603}, {41038, 49539}, {41101, 49579}, {41108, 49580}

X(49604) = reflection of X(49605) in X(17355)
X(49604) = orthologic center (1st Lemoine-Dao, T) for these triangles T: 1st Jenkins, 1st Savin
X(49604) = {X(1766), X(4660)}-harmonic conjugate of X(49605)


X(49605) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd LEMOINE-DAO TO 1st SAVIN

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

The reciprocal orthologic center of these triangles is X(49540).

X(49605) lies on these lines: {4, 9}, {13, 2796}, {16, 49610}, {62, 49595}, {381, 49572}, {519, 10653}, {726, 3105}, {2321, 22513}, {3729, 40713}, {3821, 42680}, {5318, 49574}, {11300, 49540}, {11486, 41648}, {16809, 49570}, {16965, 49576}, {17766, 49575}, {18582, 49589}, {28526, 49590}, {41039, 49541}, {41100, 49583}, {41107, 49584}

X(49605) = reflection of X(49604) in X(17355)
X(49605) = orthologic center (2nd Lemoine-Dao, T) for these triangles T: 1st Jenkins, 1st Savin
X(49605) = {X(1766), X(4660)}-harmonic conjugate of X(49604)


X(49606) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS(+1) HOMOTHETIC TO 1st SAVIN

Barycentrics    2*(a^5+(b+c)*a^4-2*(b^2+c^2)*a^3-2*(b+c)*(b^2+c^2)*a^2+(-4*b^2*c^2+(b^2-c^2)^2)*a+(b^2-c^2)^2*(b+c))*a^2+((b+c)*a^4-8*(b^2+c^2)*a^3-6*(b+c)*(b^2+c^2)*a^2+(b+c)*(b^2+c^2)^2)*S : :
X(49606) = 3*X(12152)-X(12440) = 3*X(12152)+X(12636)

The reciprocal orthologic center of these triangles is X(1).

X(49606) lies on these lines: {1, 6462}, {8, 8188}, {10, 493}, {40, 11846}, {226, 11930}, {355, 11949}, {515, 10669}, {516, 9838}, {517, 32177}, {519, 12152}, {726, 12992}, {946, 8220}, {950, 11947}, {1125, 8222}, {1210, 11953}, {2784, 12186}, {2796, 12352}, {3244, 8210}, {4297, 11828}, {5847, 12590}, {6461, 49607}, {6684, 45623}, {8194, 49553}, {8201, 49555}, {8208, 49556}, {8212, 19925}, {8216, 49586}, {8218, 49587}, {8666, 22761}, {8715, 11503}, {10106, 18963}, {10875, 49561}, {10915, 45647}, {10916, 45645}, {10945, 49600}, {10951, 21077}, {11394, 49542}, {11840, 49545}, {11907, 49585}, {11932, 12053}, {11951, 31397}, {11955, 49626}, {11957, 49627}, {12699, 45381}, {12741, 13275}, {12994, 17766}, {13883, 44627}, {13899, 49618}, {13936, 44628}, {13956, 49619}, {18483, 18520}, {19031, 49547}, {19032, 49548}, {35804, 49601}, {35807, 49602}, {45362, 48511}, {45364, 48512}, {45465, 49348}, {45467, 49347}, {45567, 48815}, {45569, 48814}, {45604, 49419}, {49020, 49078}, {49021, 49079}

X(49606) = midpoint of X(i) and X(j) for these {i, j}: {9838, 22841}, {12440, 12636}, {12741, 13275}
X(49606) = orthologic center (Lucas(+1) homothetic, T) for these triangles T: 1st Jenkins, 1st Savin
X(49606) = X(10)-of-Lucas(+1) homothetic triangle
X(49606) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (493, 8214, 10), (8222, 11377, 1125), (12152, 12636, 12440)


X(49607) = ORTHOLOGIC CENTER OF THESE TRIANGLES: LUCAS(-1) HOMOTHETIC TO 1st SAVIN

Barycentrics    2*(a^5+(b+c)*a^4-2*(b^2+c^2)*a^3-2*(b+c)*(b^2+c^2)*a^2+(-4*b^2*c^2+(b^2-c^2)^2)*a+(b^2-c^2)^2*(b+c))*a^2-((b+c)*a^4-8*(b^2+c^2)*a^3-6*(b+c)*(b^2+c^2)*a^2+(b+c)*(b^2+c^2)^2)*S : :
X(49607) = 3*X(12153)-X(12441) = 3*X(12153)+X(12637)

The reciprocal orthologic center of these triangles is X(1).

X(49607) lies on these lines: {1, 6463}, {8, 8189}, {10, 494}, {40, 11847}, {226, 11931}, {355, 11950}, {515, 10673}, {516, 9839}, {517, 32178}, {519, 12153}, {726, 12993}, {946, 8221}, {950, 11948}, {1125, 8223}, {1210, 11954}, {2784, 12187}, {2796, 12353}, {3244, 8211}, {4297, 11829}, {5847, 12591}, {6461, 49606}, {6684, 45624}, {8195, 49553}, {8202, 49555}, {8209, 49556}, {8213, 19925}, {8217, 49586}, {8219, 49587}, {8666, 22762}, {8715, 11504}, {10106, 18964}, {10876, 49561}, {10915, 45646}, {10916, 45644}, {10946, 49600}, {10952, 21077}, {11395, 49542}, {11841, 49545}, {11908, 49585}, {11933, 12053}, {11952, 31397}, {11956, 49626}, {11958, 49627}, {12699, 45382}, {12742, 13276}, {12995, 17766}, {13883, 44629}, {13900, 49618}, {13936, 44630}, {13957, 49619}, {18483, 18522}, {19033, 49547}, {19034, 49548}, {35805, 49602}, {35806, 49601}, {45361, 48511}, {45363, 48512}, {45464, 49347}, {45466, 49348}, {45566, 48814}, {45568, 48815}, {45603, 49420}, {49022, 49078}, {49023, 49079}

X(49607) = midpoint of X(i) and X(j) for these {i, j}: {9839, 22842}, {12441, 12637}, {12742, 13276}
X(49607) = orthologic center (Lucas(-1) homothetic, T) for these triangles T: 1st Jenkins, 1st Savin
X(49607) = X(10)-of-Lucas(-1) homothetic triangle
X(49607) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (494, 8215, 10), (8223, 11378, 1125), (12153, 12637, 12441)


X(49608) = ORTHOLOGIC CENTER OF THESE TRIANGLES: MCCAY TO 1st SAVIN

Barycentrics    4*a^4-(b+c)*a^3-2*(2*b^2-b*c+2*c^2)*a^2+(b+c)*(2*b^2-3*b*c+2*c^2)*a+(b^2-3*b*c+c^2)*(b+c)^2 : :
X(49608) = 2*X(1125)+X(8669) = 4*X(1125)-X(49613) = 2*X(8669)+X(49613) = 3*X(19883)-X(49554)

The reciprocal orthologic center of these triangles is X(49549).

X(49608) lies on these lines: {1, 2}, {3, 2796}, {58, 37792}, {140, 49609}, {183, 15903}, {524, 24317}, {726, 10165}, {946, 28562}, {4434, 15950}, {5298, 42055}, {5886, 17766}, {7270, 27759}, {7607, 34899}, {7618, 8720}, {28580, 48932}, {31157, 42054}, {34506, 35103}

X(49608) = orthologic center (McCay, T) for these triangles T: 1st Jenkins, 1st Savin
X(49608) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1125, 8669, 49613), (49610, 49611, 49560)


X(49609) = ORTHOLOGIC CENTER OF THESE TRIANGLES: MOSES-STEINER OSCULATORY TO 1st SAVIN

Barycentrics    (b+c)*a^3-2*(b^2+b*c+c^2)*a^2-(b+c)*(2*b^2-3*b*c+2*c^2)*a+(b^3+c^3)*(b+c) : :
X(49609) = 4*X(140)-3*X(49608) = X(4301)-3*X(49554)

The reciprocal orthologic center of these triangles is X(49549).

X(49609) lies on these lines: {2, 11533}, {3, 519}, {4, 2796}, {8, 17596}, {10, 75}, {40, 12252}, {65, 29671}, {140, 49608}, {515, 8720}, {517, 49613}, {537, 12607}, {758, 970}, {1043, 34882}, {1125, 17054}, {1403, 4848}, {1572, 41662}, {1697, 29844}, {1788, 29649}, {1837, 32934}, {3178, 5902}, {3679, 4201}, {3704, 49560}, {3971, 24982}, {4096, 9711}, {4301, 49554}, {4642, 29673}, {4685, 37467}, {4745, 11359}, {4865, 37567}, {4884, 8256}, {5086, 32845}, {5493, 28562}, {5835, 6682}, {6337, 49488}, {6684, 8669}, {7763, 15903}, {7764, 35103}, {9053, 32157}, {11681, 21093}, {11814, 19582}, {15888, 42055}, {16628, 49573}, {16629, 49574}, {17132, 34505}, {17164, 25385}, {17674, 24443}, {17770, 48875}, {19925, 28526}, {21031, 42054}, {21712, 31017}, {24165, 24987}, {25005, 32925}, {25650, 34895}, {28850, 33899}, {29655, 37598}, {29656, 37549}, {33274, 49550}

X(49609) = reflection of X(8669) in X(6684)
X(49609) = orthologic center (Moses-Steiner osculatory, T) for these triangles T: 1st Jenkins, 1st Savin
X(49609) = {X(10), X(986)}-harmonic conjugate of X(3821)


X(49610) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-NAPOLEON TO 1st SAVIN

Barycentrics    -2*sqrt(3)*(2*a+b+c)*S+(2*a-b-c)*(a+b+c)^2 : :
X(49610) = X(1)+2*X(49591) = 7*X(2)-X(49577) = 5*X(2)+X(49578) = 2*X(2)+X(49583) = 4*X(2)-X(49584) = 2*X(1125)+X(49566) = 4*X(1125)-X(49568) = 5*X(19862)-2*X(49590)

The reciprocal orthologic center of these triangles is X(49540).

X(49610) lies on these lines: {1, 2}, {5, 49574}, {6, 41648}, {15, 49595}, {16, 49605}, {18, 49570}, {65, 36669}, {298, 49540}, {515, 49573}, {530, 38330}, {618, 15349}, {726, 3106}, {946, 5617}, {2784, 9749}, {2796, 5463}, {5433, 36668}, {8720, 14145}, {16645, 49572}, {16967, 49576}, {18581, 49597}, {36782, 49603}, {37144, 38456}, {41041, 49541}

X(49610) = midpoint of X(49566) and X(49611)
X(49610) = reflection of X(i) in X(j) for these (i, j): (10, 49588), (49568, 49611), (49574, 5), (49611, 1125)
X(49610) = anticomplement of X(49589)
X(49610) = orthologic center (inner-Napoleon, T) for these triangles T: 1st Jenkins, 1st Savin
X(49610) = X(49574)-of-Johnson triangle
X(49610) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 17733, 49611), (2, 49583, 49584), (1125, 49566, 49568), (16825, 45700, 49611), (49560, 49608, 49611), (49624, 49625, 49566)


X(49611) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-NAPOLEON TO 1st SAVIN

Barycentrics    2*sqrt(3)*(2*a+b+c)*S+(2*a-b-c)*(a+b+c)^2 : :
X(49611) = X(1)+2*X(49590) = 2*X(2)+X(49579) = 4*X(2)-X(49580) = 7*X(2)-X(49581) = 5*X(2)+X(49582) = 4*X(1125)-X(49566) = 2*X(1125)+X(49568) = 5*X(19862)-2*X(49591)

The reciprocal orthologic center of these triangles is X(49538).

X(49611) lies on these lines: {1, 2}, {3, 49559}, {5, 49573}, {6, 41638}, {13, 49603}, {15, 49604}, {16, 49594}, {17, 49569}, {65, 36668}, {299, 49538}, {515, 49574}, {531, 38330}, {619, 15349}, {726, 3107}, {946, 5613}, {2784, 9750}, {2796, 5464}, {5433, 36669}, {8720, 14144}, {16644, 49571}, {16966, 49575}, {18582, 49596}, {37145, 38456}, {41040, 49539}

X(49611) = midpoint of X(i) and X(j) for these {i, j}: {13, 49603}, {49568, 49610}
X(49611) = reflection of X(i) in X(j) for these (i, j): (10, 49589), (49566, 49610), (49573, 5), (49610, 1125)
X(49611) = anticomplement of X(49588)
X(49611) = orthologic center (outer-Napoleon, T) for these triangles T: 1st Jenkins, 1st Savin
X(49611) = X(49573)-of-Johnson triangle
X(49611) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 17733, 49610), (2, 49579, 49580), (1125, 49568, 49566), (16825, 45700, 49610), (49560, 49608, 49610), (49624, 49625, 49568)


X(49612) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st SAVIN TO 2nd NEUBERG

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

The reciprocal orthologic center of these triangles is X(49613).

X(49612) lies on these lines: {1, 2896}, {2, 17741}, {10, 33891}, {81, 41663}, {83, 226}, {732, 1107}, {754, 37631}, {1125, 5988}, {1500, 3666}, {1580, 29654}, {2329, 16706}, {3061, 4389}, {3314, 49613}, {3616, 44431}, {3663, 17760}, {3905, 17301}, {4000, 16822}, {4391, 27951}, {4657, 24273}, {5483, 26639}, {5530, 49646}, {6704, 37691}, {7779, 41662}, {7977, 49466}, {9478, 17062}, {9575, 17274}, {12783, 49476}, {13442, 29012}, {14949, 17324}, {16887, 40432}, {17193, 26843}, {17284, 31326}, {17326, 19879}, {20088, 26626}, {20917, 39731}, {24169, 40790}, {24178, 24199}, {24211, 26959}, {29574, 31168}, {29596, 31268}, {33953, 38814}

X(49612) = complement of X(17741)
X(49612) = Cevapoint of X(514) and X(18047)
X(49612) = orthologic center (1st Savin, 2nd Neuberg)
X(49612) = {X(1429), X(19786)}-harmonic conjugate of X(17023)


X(49613) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd NEUBERG TO 1st SAVIN

Barycentrics    (b+c)*a^3+2*(b^2-b*c+c^2)*a^2+(b+c)*b*c*a-(b^3+c^3)*(b+c) : :
X(49613) = X(10)-3*X(49554) = 4*X(1125)-3*X(49608) = 2*X(8669)-3*X(49608) = X(17733)-3*X(45700)

The reciprocal orthologic center of these triangles is X(49612).

X(49613) lies on these lines: {1, 2}, {3, 17766}, {6, 41662}, {56, 4865}, {496, 20545}, {516, 8720}, {517, 49609}, {540, 48939}, {726, 946}, {740, 3813}, {988, 4660}, {1191, 4438}, {1220, 17722}, {2275, 4071}, {2796, 12699}, {2975, 30366}, {3314, 49612}, {3649, 42055}, {3815, 4095}, {3821, 37592}, {3905, 15903}, {3971, 41012}, {3976, 41886}, {4085, 4719}, {4109, 16975}, {4434, 5433}, {4673, 32855}, {4968, 25385}, {5015, 37617}, {5253, 33072}, {5847, 43149}, {6210, 17770}, {8666, 38456}, {9022, 24317}, {11375, 32920}, {11813, 24068}, {11814, 46937}, {12701, 32934}, {15654, 49553}, {18139, 46190}, {20487, 37722}, {20498, 21616}, {21241, 23536}, {25135, 34791}, {25440, 41346}, {28562, 31730}, {32851, 37588}, {33103, 34860}, {34937, 49464}

X(49613) = reflection of X(8669) in X(1125)
X(49613) = orthologic center (2nd Neuberg, T) for these triangles T: 1st Jenkins, 1st Savin
X(49613) = X(29671)-of-anti-inner-Yff triangle
X(49613) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 3624, 29838), (1, 3705, 10), (1125, 8669, 49608), (49624, 49625, 49477)


X(49614) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st SAVIN TO 1st TRI-SQUARES-CENTRAL

Barycentrics    6*((b+c)*a+(b-c)^2)*S+(-a+b+c)*(10*a+b+c)*(a+b-c)*(a-b+c) : :

The reciprocal orthologic center of these triangles is X(49615).

X(49614) lies on these lines: {1, 13678}, {226, 1327}, {519, 31582}, {551, 31583}, {3663, 49616}, {3666, 13701}, {5393, 37691}, {5530, 49647}

X(49614) = orthologic center (1st Savin, 1st tri-squares-central)


X(49615) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st TRI-SQUARES-CENTRAL TO 1st SAVIN

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

The reciprocal orthologic center of these triangles is X(49614).

X(49615) lies on these lines: {519, 3068}, {966, 3828}, {1125, 14121}, {13883, 49622}, {49548, 49621}, {49618, 49625}

X(49615) = orthologic center (1st tri-squares-central, T) for these triangles T: 1st Jenkins, 1st Savin
X(49615) = {X(13883), X(49622)}-harmonic conjugate of X(49624)


X(49616) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st SAVIN TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    -6*((b+c)*a+(b-c)^2)*S+(-a+b+c)*(10*a+b+c)*(a+b-c)*(a-b+c) : :

The reciprocal orthologic center of these triangles is X(49617).

X(49616) lies on these lines: {1, 13798}, {226, 1328}, {519, 31583}, {551, 31582}, {3663, 49614}, {3666, 13821}, {5405, 37691}, {5530, 49648}

X(49616) = orthologic center (1st Savin, 2nd tri-squares-central)


X(49617) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd TRI-SQUARES-CENTRAL TO 1st SAVIN

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

The reciprocal orthologic center of these triangles is X(49616).

X(49617) lies on these lines: {519, 3069}, {966, 3828}, {1125, 7090}, {13936, 49623}, {49547, 49620}, {49619, 49624}

X(49617) = orthologic center (2nd tri-squares-central, T) for these triangles T: 1st Jenkins, 1st Savin
X(49617) = {X(13936), X(49623)}-harmonic conjugate of X(49625)


X(49618) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd TRI-SQUARES-CENTRAL TO 1st SAVIN

Barycentrics    (2*a+3*b+3*c)*S+2*a^2*(a+b+c) : :
X(49618) = X(8983)-3*X(13846) = 3*X(8983)-X(44635) = 3*X(13846)+X(13911) = 9*X(13846)-X(44635) = 3*X(13911)+X(44635)

The reciprocal orthologic center of these triangles is X(1).

X(49618) lies on these lines: {1, 8972}, {2, 13942}, {6, 3634}, {8, 13888}, {10, 3068}, {40, 13886}, {226, 13897}, {355, 13903}, {371, 19925}, {485, 516}, {515, 8981}, {517, 13925}, {519, 8983}, {551, 19066}, {590, 1125}, {615, 31253}, {726, 8992}, {946, 8976}, {950, 13901}, {1151, 28164}, {1210, 13905}, {1587, 10164}, {1698, 7585}, {1702, 3817}, {2784, 8980}, {2796, 13908}, {3070, 12512}, {3244, 13902}, {3311, 10175}, {3316, 8227}, {3626, 7969}, {3635, 49232}, {3828, 13936}, {3911, 19028}, {4297, 9540}, {4298, 31472}, {4745, 49233}, {5393, 31594}, {5691, 9585}, {5847, 13910}, {6221, 31673}, {6684, 7583}, {7581, 31423}, {7584, 10172}, {8253, 13971}, {8666, 22763}, {8715, 13887}, {8960, 35611}, {8974, 49586}, {8975, 49587}, {8988, 13922}, {8993, 17766}, {9582, 23249}, {9616, 31412}, {9646, 13405}, {9780, 19004}, {10106, 18965}, {10171, 10576}, {10915, 45652}, {10916, 45650}, {11231, 19117}, {12053, 13898}, {12571, 42265}, {12575, 44623}, {12699, 45384}, {13665, 31730}, {13688, 49552}, {13884, 49542}, {13885, 49545}, {13889, 49553}, {13890, 49555}, {13891, 49556}, {13892, 49561}, {13894, 49585}, {13895, 49600}, {13896, 21077}, {13899, 49606}, {13900, 49607}, {13904, 31397}, {13906, 49626}, {13907, 49627}, {13941, 19872}, {13947, 19054}, {13959, 19883}, {18483, 18538}, {18992, 19862}, {23251, 28158}, {23267, 35242}, {25352, 36492}, {31399, 31487}, {35774, 43430}, {35812, 49601}, {35815, 49602}, {43879, 49226}, {45365, 48511}, {45368, 48512}, {45484, 49347}, {45486, 49348}, {45574, 48814}, {45576, 48815}, {45605, 49419}, {45607, 49420}, {49027, 49079}, {49592, 49620}, {49615, 49625}

X(49618) = midpoint of X(i) and X(j) for these {i, j}: {485, 13912}, {8983, 13911}, {8988, 13922}
X(49618) = orthologic center (3rd tri-squares-central, T) for these triangles T: 1st Jenkins, 1st Savin
X(49618) = X(10)-of-3rd tri-squares-central triangle
X(49618) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 3634, 49619), (590, 13883, 1125), (1698, 7585, 49547), (3068, 13893, 10), (8253, 13971, 19878), (13846, 13911, 8983), (18538, 31439, 18483), (18992, 32785, 19862)


X(49619) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th TRI-SQUARES-CENTRAL TO 1st SAVIN

Barycentrics    -(2*a+3*b+3*c)*S+2*a^2*(a+b+c) : :
X(49619) = 3*X(13847)-X(13971) = 3*X(13847)+X(13973) = 9*X(13847)-X(44636) = 3*X(13971)-X(44636) = 3*X(13973)+X(44636)

The reciprocal orthologic center of these triangles is X(1).

X(49619) lies on these lines: {1, 13941}, {2, 13888}, {6, 3634}, {8, 13942}, {10, 3069}, {40, 13939}, {226, 13954}, {355, 13961}, {372, 19925}, {486, 516}, {515, 13966}, {517, 13993}, {519, 13847}, {551, 19065}, {590, 31253}, {615, 1125}, {726, 13983}, {946, 13951}, {950, 13958}, {1152, 28164}, {1210, 13963}, {1588, 9582}, {1698, 7586}, {1703, 3817}, {2784, 13967}, {2796, 13968}, {3071, 12512}, {3244, 13959}, {3312, 10175}, {3317, 8227}, {3626, 7968}, {3635, 49233}, {3828, 13883}, {3911, 19027}, {4297, 13935}, {4298, 44622}, {4745, 49232}, {5405, 31595}, {5847, 13972}, {6398, 31673}, {6684, 7584}, {7582, 31423}, {7583, 10172}, {8252, 8983}, {8666, 22764}, {8715, 13940}, {8972, 19872}, {9780, 19003}, {10106, 18966}, {10171, 10577}, {10915, 45653}, {10916, 45651}, {11231, 19116}, {12053, 13955}, {12571, 42262}, {12575, 44624}, {12699, 45385}, {13785, 31730}, {13808, 49551}, {13893, 19053}, {13902, 19883}, {13937, 49542}, {13938, 49545}, {13943, 49553}, {13944, 49555}, {13945, 49556}, {13946, 49561}, {13948, 49585}, {13949, 49586}, {13950, 49587}, {13952, 49600}, {13953, 21077}, {13956, 49606}, {13957, 49607}, {13962, 31397}, {13964, 49626}, {13965, 49627}, {13976, 13991}, {13984, 17766}, {18483, 18762}, {18991, 19862}, {23261, 28158}, {23273, 35242}, {25352, 36491}, {35610, 43174}, {35775, 43431}, {35813, 49602}, {35814, 49601}, {43880, 49227}, {45366, 48511}, {45367, 48512}, {45485, 49348}, {45487, 49347}, {45575, 48815}, {45577, 48814}, {45606, 49420}, {45608, 49419}, {49026, 49078}, {49593, 49621}, {49617, 49624}

X(49619) = midpoint of X(i) and X(j) for these {i, j}: {486, 13975}, {13971, 13973}, {13976, 13991}
X(49619) = orthologic center (4th tri-squares-central, T) for these triangles T: 1st Jenkins, 1st Savin
X(49619) = X(10)-of-4th tri-squares-central triangle
X(49619) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 3634, 49618), (615, 13936, 1125), (1698, 7586, 49548), (3069, 13947, 10), (8252, 8983, 19878), (13847, 13973, 13971), (18991, 32786, 19862)


X(49620) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st TRI-SQUARES TO 1st SAVIN

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

The reciprocal orthologic center of these triangles is X(2).

X(49620) lies on these lines: {2, 4856}, {519, 3068}, {726, 22722}, {1991, 3946}, {2321, 32787}, {2796, 13640}, {3635, 6352}, {4725, 45871}, {5847, 49632}, {7585, 17355}, {13637, 49543}, {13638, 49554}, {13639, 17132}, {13664, 28329}, {49489, 49633}, {49547, 49617}, {49548, 49625}, {49592, 49618}

X(49620) = orthologic center (1st tri-squares, T) for these triangles T: 1st Jenkins, 1st Savin
X(49620) = {X(2), X(4856)}-harmonic conjugate of X(49621)


X(49621) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd TRI-SQUARES TO 1st SAVIN

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

The reciprocal orthologic center of these triangles is X(2).

X(49621) lies on these lines: {2, 4856}, {519, 3069}, {591, 3946}, {726, 22723}, {2321, 32788}, {2796, 13760}, {3635, 6351}, {4725, 45872}, {5847, 49633}, {7586, 17355}, {13757, 49543}, {13758, 49554}, {13759, 17132}, {13784, 28329}, {49489, 49632}, {49547, 49624}, {49548, 49615}, {49593, 49619}

X(49621) = orthologic center (2nd tri-squares, T) for these triangles T: 1st Jenkins, 1st Savin
X(49621) = {X(2), X(4856)}-harmonic conjugate of X(49620)


X(49622) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 3rd TRI-SQUARES TO 1st SAVIN

Barycentrics    2*(2*a+3*b+3*c)*S+(a+b+c)*(2*a^2-(b+c)*a+(b+c)^2) : :
X(49622) = 3*X(485)-X(49552)

The reciprocal orthologic center of these triangles is X(31582).

X(49622) lies on these lines: {2, 31582}, {10, 485}, {45, 3634}, {516, 36656}, {519, 8983}, {590, 49625}, {641, 5745}, {1125, 13882}, {1329, 31558}, {3068, 49592}, {3664, 42009}, {3686, 44647}, {3828, 13850}, {5490, 10436}, {5750, 49221}, {6118, 44417}, {6222, 48932}, {13875, 49572}, {13876, 49571}, {13883, 49615}, {13893, 49593}, {14121, 30478}

X(49622) = complement of X(31582)
X(49622) = orthologic center (3rd tri-squares, T) for these triangles T: 1st Jenkins, 1st Savin
X(49622) = X(49592)-of-3rd tri-squares-central triangle
X(49622) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3634, 17355, 49623), (49615, 49624, 13883)


X(49623) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 4th TRI-SQUARES TO 1st SAVIN

Barycentrics    -2*(2*a+3*b+3*c)*S+(a+b+c)*(2*a^2-(b+c)*a+(b+c)^2) : :
X(49623) = 3*X(486)-X(49551)

The reciprocal orthologic center of these triangles is X(31583).

X(49623) lies on these lines: {2, 31583}, {10, 486}, {45, 3634}, {516, 36655}, {519, 13847}, {615, 49624}, {642, 5745}, {1125, 13934}, {1329, 31557}, {3069, 49593}, {3664, 42060}, {3686, 44648}, {3828, 13932}, {5491, 10436}, {5750, 49220}, {6119, 44417}, {6399, 48932}, {7090, 30478}, {13928, 49572}, {13929, 49571}, {13936, 49617}, {13947, 49592}, {18234, 26066}

X(49623) = complement of X(31583)
X(49623) = orthologic center (4th tri-squares, T) for these triangles T: 1st Jenkins, 1st Savin
X(49623) = X(49593)-of-4th tri-squares-central triangle
X(49623) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3634, 17355, 49622), (49617, 49625, 13936)


X(49624) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-VECTEN TO 1st SAVIN

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

The reciprocal orthologic center of these triangles is X(31583).

X(49624) lies on these lines: {1, 2}, {69, 31583}, {488, 28526}, {615, 49623}, {726, 3102}, {946, 6289}, {2321, 13971}, {3875, 31582}, {4361, 31534}, {4851, 31535}, {6561, 49551}, {12699, 48677}, {13883, 49615}, {49547, 49621}, {49617, 49619}

X(49624) = midpoint of X(1) and X(49592)
X(49624) = reflection of X(49625) in X(1125)
X(49624) = complement of X(49593)
X(49624) = orthologic center (inner-Vecten, T) for these triangles T: 1st Jenkins, 1st Savin
X(49624) = X(49592)-of-anti-Aquila triangle
X(49624) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (10, 17733, 49625), (8669, 49560, 49625), (13883, 49622, 49615), (49477, 49613, 49625), (49566, 49610, 49625), (49568, 49611, 49625)


X(49625) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-VECTEN TO 1st SAVIN

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

The reciprocal orthologic center of these triangles is X(31582).

X(49625) lies on these lines: {1, 2}, {69, 31582}, {487, 28526}, {590, 49622}, {726, 3103}, {946, 6290}, {2321, 8983}, {3875, 31583}, {4361, 31535}, {4851, 31534}, {6560, 49552}, {12699, 48678}, {13936, 49617}, {31453, 31595}, {49548, 49620}, {49615, 49618}

X(49625) = midpoint of X(1) and X(49593)
X(49625) = reflection of X(49624) in X(1125)
X(49625) = complement of X(49592)
X(49625) = orthologic center (outer-Vecten, T) for these triangles T: 1st Jenkins, 1st Savin
X(49625) = X(49593)-of-anti-Aquila triangle
X(49625) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (10, 17733, 49624), (8669, 49560, 49624), (13936, 49623, 49617), (49477, 49613, 49624), (49566, 49610, 49624), (49568, 49611, 49624)


X(49626) = ORTHOLOGIC CENTER OF THESE TRIANGLES: INNER-YFF TANGENTS TO 1st SAVIN

Barycentrics    (b+c)*a^3-(b^2+10*b*c+c^2)*a^2-(b+c)*(b^2-4*b*c+c^2)*a+(b^2-c^2)^2 : :
X(49626) = X(1)-3*X(11239) = 3*X(10)-2*X(4847) = 3*X(551)-4*X(13405) = 2*X(1125)-3*X(10056) = X(3872)-3*X(10056) = X(4847)-3*X(31397) = 6*X(10197)-5*X(19862) = 3*X(11239)+X(12648)

The reciprocal orthologic center of these triangles is X(1).

X(49626) lies on these lines: {1, 2}, {12, 49600}, {40, 10805}, {72, 45081}, {119, 3817}, {226, 2802}, {354, 1145}, {355, 12000}, {442, 3893}, {495, 3838}, {515, 10679}, {516, 12115}, {517, 32213}, {726, 13109}, {946, 10942}, {950, 10965}, {1000, 25568}, {1329, 31792}, {1470, 4315}, {1478, 3895}, {1512, 16200}, {2784, 12189}, {2796, 12356}, {3057, 10955}, {3256, 25438}, {3295, 32049}, {3452, 3898}, {3612, 36977}, {3663, 20930}, {3820, 10179}, {3871, 45287}, {3874, 11362}, {3881, 4848}, {3884, 21075}, {3885, 12047}, {3913, 17647}, {3914, 24222}, {3919, 5542}, {3947, 26482}, {3987, 23675}, {4084, 37562}, {4297, 11248}, {4301, 12608}, {4314, 26358}, {4342, 11813}, {5045, 8256}, {5119, 44447}, {5493, 49163}, {5559, 41696}, {5587, 10596}, {5690, 13373}, {5847, 12594}, {5853, 42885}, {5881, 12617}, {5919, 17757}, {6245, 33596}, {6256, 49184}, {6684, 16203}, {7373, 37828}, {7682, 37713}, {8666, 22768}, {8715, 10106}, {9957, 12607}, {10164, 10269}, {10531, 19925}, {10803, 49545}, {10834, 49553}, {10878, 49561}, {10912, 11374}, {10914, 12609}, {10929, 49586}, {10930, 49587}, {10958, 12053}, {11400, 49542}, {11525, 25525}, {11881, 49555}, {11882, 49556}, {11914, 49585}, {11955, 49606}, {11956, 49607}, {12245, 12559}, {12541, 31418}, {12616, 37727}, {12640, 21620}, {12699, 18545}, {12749, 13278}, {13112, 17766}, {13407, 14923}, {13600, 18242}, {13883, 44643}, {13906, 49618}, {13936, 44644}, {13964, 49619}, {18483, 18542}, {19047, 49547}, {19048, 49548}, {21060, 41389}, {21627, 25639}, {24929, 38455}, {26402, 48511}, {26426, 48512}, {26511, 49419}, {26520, 49078}, {26525, 49079}, {30331, 42843}, {30513, 40998}, {32157, 37582}, {32537, 37730}, {33337, 41553}, {33895, 37737}, {33956, 37728}, {35816, 49601}, {35817, 49602}, {37701, 41702}, {44784, 44840}, {45494, 49347}, {45495, 49348}, {45584, 48814}, {45585, 48815}, {45615, 49420}

X(49626) = midpoint of X(i) and X(j) for these {i, j}: {1, 12648}, {1478, 3895}, {3870, 12647}, {12115, 12703}, {12749, 13278}
X(49626) = reflection of X(i) in X(j) for these (i, j): (10, 31397), (3872, 1125), (33337, 41553)
X(49626) = orthologic center (inner-Yff tangents, T) for these triangles T: 1st Jenkins, 1st Savin
X(49626) = X(10)-of-inner-Yff tangents triangle
X(49626) = X(10915)-of-inner-Yff triangle
X(49626) = X(12648)-of-anti-Aquila triangle
X(49626) = X(31397)-of-anti-outer-Yff triangle
X(49626) = X(49600)-of-1st Johnson-Yff triangle
X(49626) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 1698, 10586), (1, 5552, 1125), (1, 10915, 10), (10, 3244, 49627), (145, 10039, 10916), (1125, 6736, 10), (3872, 10056, 1125), (9957, 12607, 21616), (10039, 10916, 10), (10914, 15888, 12609), (11239, 12648, 1), (12608, 23340, 4301)


X(49627) = ORTHOLOGIC CENTER OF THESE TRIANGLES: OUTER-YFF TANGENTS TO 1st SAVIN

Barycentrics    (b+c)*a^3-(b^2-6*b*c+c^2)*a^2-(b+c)*(b^2+c^2)*a+(b^2-c^2)^2 : :
X(49627) = X(1)-3*X(11240) = 3*X(10)-2*X(6736) = X(78)-3*X(10072) = 3*X(551)-2*X(30144) = 2*X(1125)-3*X(10072) = 3*X(1210)-X(6736) = 5*X(3616)-X(20013) = 2*X(6700)-3*X(10199) = 4*X(6700)-5*X(19862) = 6*X(10199)-5*X(19862) = 3*X(11240)+X(12649)

The reciprocal orthologic center of these triangles is X(1).

X(49627) lies on these lines: {1, 2}, {5, 34791}, {11, 3555}, {40, 10806}, {56, 41565}, {65, 10949}, {72, 37722}, {149, 1770}, {214, 12437}, {225, 39697}, {226, 3881}, {354, 12609}, {355, 12001}, {442, 17609}, {474, 4863}, {496, 518}, {515, 10680}, {516, 12116}, {517, 32214}, {528, 37582}, {726, 13110}, {758, 10959}, {908, 37720}, {912, 946}, {942, 3813}, {950, 8666}, {999, 17647}, {1058, 12514}, {1069, 45728}, {1475, 21073}, {1482, 12616}, {1861, 38295}, {2784, 12190}, {2796, 12357}, {2800, 4084}, {2801, 41560}, {2802, 4848}, {2886, 3824}, {3058, 3916}, {3243, 8227}, {3254, 10308}, {3304, 3419}, {3333, 24392}, {3338, 3434}, {3689, 13747}, {3710, 4975}, {3742, 16216}, {3748, 7483}, {3816, 34790}, {3817, 26470}, {3825, 21075}, {3868, 30384}, {3873, 12047}, {3878, 24391}, {3879, 24202}, {3889, 11680}, {3892, 21620}, {3898, 5837}, {3911, 8715}, {3914, 3953}, {3947, 26481}, {3950, 8609}, {3976, 23537}, {3983, 17575}, {4015, 5316}, {4292, 7284}, {4297, 11249}, {4309, 4652}, {4311, 10074}, {4314, 5267}, {4315, 26437}, {4640, 15172}, {4662, 17527}, {4694, 23536}, {4780, 37565}, {4852, 17043}, {4856, 20262}, {4973, 31730}, {5049, 25466}, {5083, 41537}, {5436, 31458}, {5493, 5709}, {5542, 11263}, {5587, 10597}, {5603, 12559}, {5687, 17728}, {5722, 12513}, {5745, 40270}, {5794, 7373}, {5847, 12595}, {5853, 25440}, {5904, 41012}, {5905, 36599}, {6598, 15179}, {6675, 42819}, {6684, 16202}, {6767, 26066}, {9710, 17051}, {10106, 18967}, {10164, 10267}, {10395, 11376}, {10532, 19925}, {10785, 37569}, {10804, 49545}, {10835, 49553}, {10879, 49561}, {10931, 49586}, {10932, 49587}, {11037, 31418}, {11260, 37730}, {11373, 12635}, {11374, 42871}, {11401, 49542}, {11523, 37704}, {11545, 32537}, {11813, 14054}, {11883, 49555}, {11884, 49556}, {11915, 49585}, {11957, 49606}, {11958, 49607}, {12618, 49455}, {12699, 18543}, {12776, 49176}, {13113, 17766}, {13883, 44645}, {13907, 49618}, {13936, 44646}, {13965, 49619}, {15296, 18233}, {16173, 41696}, {18483, 18544}, {19049, 49547}, {19050, 49548}, {20118, 25416}, {21096, 24036}, {23789, 47123}, {24046, 24216}, {24388, 32921}, {24928, 44669}, {25568, 47743}, {26401, 48511}, {26425, 48512}, {26501, 49420}, {26510, 49419}, {26519, 49078}, {26524, 49079}, {30331, 42842}, {33337, 41554}, {34719, 37572}, {35818, 49601}, {35819, 49602}, {36977, 37711}, {37566, 41556}, {37583, 48713}, {37602, 47033}, {45496, 49347}, {45497, 49348}, {45586, 48814}, {45587, 48815}, {48482, 49170}

X(49627) = midpoint of X(i) and X(j) for these {i, j}: {1, 12649}, {10573, 36846}, {12116, 12704}, {12750, 13279}, {12776, 49176}, {36977, 37711}
X(49627) = reflection of X(i) in X(j) for these (i, j): (10, 1210), (78, 1125), (21075, 3825), (21616, 496), (33337, 41554)
X(49627) = intersection, other than A, B, C, of circumconics {{A, B, C, X(78), X(39697)}} and {{A, B, C, X(225), X(31855)}}
X(49627) = orthologic center (outer-Yff tangents, T) for these triangles T: 1st Jenkins, 1st Savin
X(49627) = X(10)-of-outer-Yff tangents triangle
X(49627) = X(1210)-of-anti-inner-Yff triangle
X(49627) = X(10916)-of-outer-Yff triangle
X(49627) = X(11457)-of-Wasat triangle, when ABC is acute
X(49627) = X(12649)-of-anti-Aquila triangle
X(49627) = X(21077)-of-2nd Johnson-Yff triangle
X(49627) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 1698, 10587), (1, 5231, 10198), (1, 10527, 1125), (1, 10916, 10), (1, 26015, 10916), (10, 3244, 49626), (10, 21625, 551), (11, 3555, 21077), (78, 10072, 1125), (145, 1737, 10915), (354, 24390, 12609), (1058, 24477, 12514), (1125, 4847, 10), (1737, 10915, 10), (3086, 36845, 3811), (3626, 8582, 10), (3881, 24387, 226), (3889, 11680, 13407), (3892, 25639, 21620), (3976, 33141, 23537), (4084, 21630, 4301), (4666, 19854, 1125), (5704, 9797, 34619), (6700, 10199, 19862), (11240, 12649, 1), (11240, 26015, 1210), (21620, 24386, 25639)


X(49628) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st PARRY TO 1st SAVIN

Barycentrics    (b-c)*(a^5-5*(b+c)*a^4-(b^2+c^2)*a^3+3*(b+c)*(b^2+c^2)*a^2+(b^4-b^2*c^2+c^4)*a-(b+c)*(b^4-b^2*c^2+c^4)) : :
X(49628) = 3*X(9123)-X(9810) = 3*X(9123)+X(13250)

The reciprocal parallelogic center of these triangles is X(1).

X(49628) lies on these lines: {110, 48970}, {351, 522}, {513, 14610}, {514, 9131}, {2786, 9147}, {2789, 9485}, {3667, 9123}, {4777, 32193}, {4785, 22733}, {4962, 13251}, {5075, 47694}, {9135, 28478}, {9215, 49002}, {9978, 13263}, {9979, 28161}, {13306, 28470}, {13308, 28487}

X(49628) = midpoint of X(i) and X(j) for these {i, j}: {9131, 9811}, {9810, 13250}, {9978, 13263}
X(49628) = reflection of X(49629) in X(351)
X(49628) = parallelogic center (1st Parry, T) for these triangles T: 1st Jenkins, 1st Savin
X(49628) = X(10)-of-1st Parry triangle
X(49628) = X(4297)-of-2nd Parry triangle
X(49628) = {X(9123), X(13250)}-harmonic conjugate of X(9810)


X(49629) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd PARRY TO 1st SAVIN

Barycentrics    (b-c)*(a^5+3*(b+c)*a^4-(b^2+c^2)*a^3-(b+c)*(b^2+c^2)*a^2+(b^4-b^2*c^2+c^4)*a-(b+c)*(b^4-b^2*c^2+c^4)) : :
X(49629) = 3*X(9185)-X(9811) = 3*X(9185)+X(13251)

The reciprocal parallelogic center of these triangles is X(1).

X(49629) lies on these lines: {2, 2786}, {111, 49002}, {351, 522}, {513, 32193}, {514, 9810}, {2789, 5466}, {3124, 24195}, {3569, 28478}, {3667, 9185}, {4024, 4560}, {4129, 27710}, {4777, 14610}, {4785, 22734}, {4962, 13250}, {9131, 28161}, {9216, 48970}, {9980, 13264}, {13307, 28470}, {13309, 28487}, {18004, 24353}, {23755, 31290}

X(49629) = midpoint of X(i) and X(j) for these {i, j}: {9810, 9979}, {9811, 13251}, {9980, 13264}
X(49629) = reflection of X(49628) in X(351)
X(49629) = parallelogic center (2nd Parry, T) for these triangles T: 1st Jenkins, 1st Savin
X(49629) = X(4297)-of-1st Parry triangle
X(49629) = X(10)-of-2nd Parry triangle
X(49629) = perspector of the circumconic {{A, B, C, X(18812), X(35153)}}


X(49630) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ANTI-ARTZT TO 2nd SAVIN

Barycentrics    4*a^3-5*(b+c)*a^2-2*(b^2+c^2)*a-(b+c)*(5*b^2-6*b*c+5*c^2) : :
X(49630) = X(3663)+2*X(4660) = 5*X(3663)-2*X(49455) = X(3886)-3*X(21356) = 5*X(4660)+X(49455) = 2*X(4672)-3*X(38089) = 5*X(17304)-3*X(38314) = 2*X(17355)-3*X(19875) = 3*X(19883)-2*X(49482) = X(47359)-3*X(48829)

The reciprocal orthologic center of these triangles is X(2).

X(49630) lies on these lines: {2, 165}, {10, 190}, {69, 519}, {392, 9519}, {524, 3755}, {527, 47359}, {551, 3821}, {726, 4669}, {2784, 11161}, {3241, 4353}, {3416, 17133}, {3662, 30331}, {3664, 48830}, {3679, 10005}, {3828, 3923}, {3883, 37756}, {3886, 21356}, {3946, 47356}, {4061, 31143}, {4082, 33100}, {4085, 28558}, {4201, 4301}, {4234, 34638}, {4312, 35578}, {4356, 4645}, {4656, 32948}, {4672, 38089}, {4745, 28526}, {4847, 32950}, {4887, 36479}, {4896, 24692}, {4956, 33086}, {5493, 16062}, {5847, 49543}, {5853, 47358}, {8584, 28570}, {10445, 17532}, {11019, 33068}, {11160, 49495}, {11359, 28194}, {13637, 49632}, {13757, 49633}, {16370, 24309}, {17304, 38314}, {17355, 19875}, {17767, 38191}, {18252, 44663}, {19883, 49482}, {20582, 49484}, {21937, 48932}, {22165, 28581}, {24177, 32947}, {28198, 48815}, {28494, 38049}, {28534, 48821}, {28580, 29594}, {29600, 31151}, {31145, 49446}, {33869, 48851}

X(49630) = midpoint of X(i) and X(j) for these {i, j}: {3679, 24248}, {11160, 49495}, {31145, 49446}
X(49630) = orthologic center (anti-Artzt, 2nd Savin)
X(49630) = reflection of X(i) in X(j) for these (i, j): (551, 3821), (3241, 4353), (3923, 3828), (47356, 3946), (49484, 20582)


X(49631) = ORTHOLOGIC CENTER OF THESE TRIANGLES: ARTZT TO 2nd SAVIN

Barycentrics    4*a^5+(b+c)*a^4-2*(b^2+c^2)*a^3-2*(b+c)*(3*b^2-b*c+3*c^2)*a^2+2*(b^2-c^2)^2*a+(b^2-c^2)*(b-c)*(b^2+4*b*c+c^2) : :
X(49631) = 5*X(2)-X(44431) = X(10)+2*X(48932) = 2*X(6684)+X(48900) = 5*X(9746)+X(44431)

The reciprocal orthologic center of these triangles is X(2).

X(49631) lies on these lines: {2, 165}, {3, 39580}, {5, 28897}, {10, 98}, {40, 7410}, {140, 6714}, {230, 3755}, {511, 28600}, {515, 48853}, {551, 22712}, {946, 28862}, {1447, 5542}, {3598, 43180}, {3886, 34229}, {4061, 26243}, {4349, 24239}, {5493, 39605}, {5847, 49554}, {6684, 28881}, {7179, 30424}, {7390, 19925}, {10165, 28850}, {10175, 28845}, {13468, 28581}, {13638, 49632}, {13758, 49633}, {21554, 48925}, {26446, 28849}, {28236, 48851}, {28854, 38068}, {28870, 38127}, {28901, 38042}, {37667, 49495}, {39586, 43174}

X(49631) = orthologic center (Artzt, 2nd Savin)
X(49631) = midpoint of X(2) and X(9746)


X(49632) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st TRI-SQUARES TO 2nd SAVIN

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

The reciprocal orthologic center of these triangles is X(2).

X(49632) lies on these lines: {1, 2}, {516, 3068}, {590, 3755}, {2784, 13653}, {5847, 49620}, {8959, 13912}, {8974, 9746}, {13637, 49630}, {13638, 49631}, {28581, 45871}, {49489, 49621}

X(49632) = orthologic center (1st tri-squares, 2nd Savin)


X(49633) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd TRI-SQUARES TO 2nd SAVIN

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

The reciprocal orthologic center of these triangles is X(2).

X(49633) lies on these lines: {1, 2}, {516, 3069}, {615, 3755}, {2784, 13773}, {5847, 49621}, {9746, 13950}, {13757, 49630}, {13758, 49631}, {28581, 45872}, {49489, 49620}

X(49633) = orthologic center (2nd tri-squares, 2nd Savin)

leftri

Centers related to Jenkins triangles: X(49634)-X(49668)

rightri

This preamble and centers X(49634)-X(49668) were contributed by César Eliud Lozada, May 22, 2022.

1st- and 2nd- Jenkin triangles were introduced in "Hechos Geométricos en el Triángulo", by Angel Montesdeoca. These two triangles, and three other related Jenkins triangles are defined in the Index of triangles referenced in ETC.


X(49634) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JENKINS TO 1st ALTINTAS-ISODYNAMIC

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

The reciprocal orthologic center of these triangles is X(49539).

X(49634) lies on these lines: {10, 13}, {2796, 49635}, {5530, 49538}, {17748, 49644}

X(49634) = orthologic center (1st Jenkins, T) for these triangles T: 1st Altintas-isodynamic, Bankoff, 3rd Fermat-Dao, 7th Fermat-Dao, 11th Fermat-Dao, 15th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi, 1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi, 1st half-diamonds-central, 1st isodynamic-Dao, 3rd isodynamic-Dao, Largest-circumscribed-equilateral, 1st Lemoine-Dao, outer-Napoleon
X(49634) = X(13)-of-1st Jenkins triangle


X(49635) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JENKINS TO 2nd ALTINTAS-ISODYNAMIC

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

The reciprocal orthologic center of these triangles is X(49541).

X(49635) lies on these lines: {10, 14}, {2796, 49634}, {5530, 49540}, {17748, 49643}

X(49635) = orthologic center (1st Jenkins, T) for these triangles T: 2nd Altintas-isodynamic, 4th Fermat-Dao, 8th Fermat-Dao, 12th Fermat-Dao, 16th Fermat-Dao, 1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi, 3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi, 2nd half-diamonds-central, 2nd isodynamic-Dao, 4th isodynamic-Dao, 2nd Lemoine-Dao, inner-Napoleon
X(49635) = X(14)-of-1st Jenkins triangle


X(49636) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JENKINS TO ANTI-ARTZT

Barycentrics    (b+c)*a^3+(5*b^2+6*b*c+5*c^2)*a^2+(b^2-4*b*c+c^2)*(b+c)*a-(3*b^2-4*b*c+3*c^2)*(b+c)^2 : :
X(49636) = X(10)+2*X(17748) = 4*X(3634)-X(17733)

The reciprocal orthologic center of these triangles is X(49543).

X(49636) lies on these lines: {1, 2}, {12, 42051}, {181, 24473}, {381, 28580}, {726, 49642}, {740, 10175}, {758, 10440}, {970, 44663}, {1329, 35652}, {2092, 16052}, {2796, 10445}, {3597, 4052}, {3820, 4078}, {3928, 9548}, {4930, 9567}, {5050, 5847}, {5725, 19276}, {5827, 19279}, {5955, 19277}, {8715, 37415}, {10164, 38456}, {11236, 39566}, {11681, 42044}, {21075, 42054}, {21620, 42053}, {28609, 39591}, {39573, 42049}

X(49636) = orthologic center (1st Jenkins, T) for these triangles T: anti-Artzt, Artzt, 1st tri-squares, 2nd tri-squares
X(49636) = {X(29641), X(38471)}-harmonic conjugate of X(10)


X(49637) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JENKINS TO 1st ANTI-BROCARD

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

The reciprocal orthologic center of these triangles is X(49544).

X(49637) lies on the circumcircle of 2nd Jenkins triangle and these lines: {10, 98}, {114, 5517}, {115, 119}, {147, 18596}, {355, 18755}, {519, 49638}, {573, 1761}, {2051, 11611}, {2782, 39566}, {2796, 10445}, {3029, 39591}, {3597, 11599}, {3687, 34454}, {5530, 5988}, {9860, 32778}, {10692, 49148}, {17748, 49645}, {21636, 29671}

X(49637) = orthologic center (1st Jenkins, T) for these triangles T: 1st anti-Brocard, 6th anti-Brocard, 1st Brocard, 6th Brocard
X(49637) = cyclologic center (2nd Jenkins, 1st Jenkins)
X(49637) = X(12610)-of-1st anti-Brocard triangle
X(49637) = inverse of X(101) in radical circle of excircles


X(49638) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JENKINS TO ANTI-MCCAY

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

The reciprocal orthologic center of these triangles is X(49550).

X(49638) lies on these lines: {10, 190}, {519, 49637}, {3597, 34899}, {5530, 49549}

X(49638) = orthologic center (1st Jenkins, T) for these triangles T: anti-McCay, McCay, Moses-Steiner osculatory


X(49639) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JENKINS TO 3rd ANTI-TRI-SQUARES

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

The reciprocal orthologic center of these triangles is X(49551).

X(49639) lies on these lines: {10, 486}, {519, 49648}, {5530, 31583}, {12963, 13973}, {28526, 49640}

X(49639) = orthologic center (1st Jenkins, T) for these triangles T: 3rd anti-tri-squares, 2nd half-squares, 4th tri-squares, inner-Vecten


X(49640) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JENKINS TO 4th ANTI-TRI-SQUARES

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

The reciprocal orthologic center of these triangles is X(49552).

X(49640) lies on these lines: {10, 485}, {519, 49647}, {5530, 31582}, {12968, 13911}, {28526, 49639}

X(49640) = orthologic center (1st Jenkins, T) for these triangles T: 4th anti-tri-squares, 1st half-squares, 3rd tri-squares, outer-Vecten


X(49641) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JENKINS TO AYME

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

The reciprocal orthologic center of these triangles is X(49558).

X(49641) lies on these lines: {3, 18169}, {43, 48907}, {511, 6684}, {517, 3743}, {549, 970}, {573, 37536}, {5530, 35059}, {9548, 48928}, {9566, 37521}, {15310, 48887}, {35631, 48917}

X(49641) = orthologic center (1st Jenkins, T) for these triangles T: Ayme, incentral
X(49641) = midpoint of X(35631) and X(48917)


X(49642) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JENKINS TO 1st BROCARD-REFLECTED

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

The reciprocal orthologic center of these triangles is X(49564).

X(49642) lies on these lines: {10, 262}, {43, 22650}, {511, 26446}, {726, 49636}, {3597, 34475}, {5530, 22729}, {11681, 20632}, {17748, 49646}, {19763, 22556}, {22475, 30116}

X(49642) = orthologic center (1st Jenkins, 1st Brocard-reflected)


X(49643) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JENKINS TO INNER-FERMAT

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

The reciprocal orthologic center of these triangles is X(49566).

X(49643) lies on these lines: {10, 18}, {5530, 49565}, {17748, 49635}

X(49643) = orthologic center (1st Jenkins, T) for these triangles T: inner-Fermat, 1st half-diamonds


X(49644) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JENKINS TO OUTER-FERMAT

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

The reciprocal orthologic center of these triangles is X(49568).

X(49644) lies on these lines: {10, 17}, {5530, 49567}, {17748, 49634}

X(49644) = orthologic center (1st Jenkins, T) for these triangles T: outer-Fermat, 2nd half-diamonds


X(49645) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JENKINS TO 1st NEUBERG

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

The reciprocal orthologic center of these triangles is X(8669).

X(49645) lies on these lines: {3, 730}, {10, 75}, {5530, 17760}, {7146, 29671}, {8850, 28386}, {9902, 17596}, {17748, 49637}

X(49645) = orthologic center (1st Jenkins, 1st Neuberg)


X(49646) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JENKINS TO 2nd NEUBERG

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

The reciprocal orthologic center of these triangles is X(49613).

X(49646) lies on these lines: {10, 82}, {5530, 49612}, {17748, 49642}

X(49646) = orthologic center (1st Jenkins, 2nd Neuberg)


X(49647) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JENKINS TO 1st TRI-SQUARES-CENTRAL

Barycentrics    3*(b+c)*a^5+6*(b^2+b*c+c^2)*a^4-3*(b+c)*(b^2+b*c+c^2)*a^3-3*(b^2-c^2)*(b-c)*b*c*a-3*(b^2-3*b*c+c^2)*(b+c)^2*a^2-2*(4*(b+c)*a^3-(7*b^2+12*b*c+7*c^2)*a^2-(b+c)*(5*b^2-11*b*c+5*c^2)*a+(6*b^2-11*b*c+6*c^2)*(b+c)^2)*S-3*(b^2-c^2)^2*(b^2+b*c+c^2) : :

The reciprocal orthologic center of these triangles is X(49615).

X(49647) lies on these lines: {10, 1327}, {519, 49640}, {5530, 49614}

X(49647) = orthologic center (1st Jenkins, 1st tri-squares-central)


X(49648) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st JENKINS TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    3*(b+c)*a^5+6*(b^2+b*c+c^2)*a^4-3*(b+c)*(b^2+b*c+c^2)*a^3-3*(b^2-c^2)*(b-c)*b*c*a-3*(b^2-3*b*c+c^2)*(b+c)^2*a^2+2*(4*(b+c)*a^3-(7*b^2+12*b*c+7*c^2)*a^2-(b+c)*(5*b^2-11*b*c+5*c^2)*a+(6*b^2-11*b*c+6*c^2)*(b+c)^2)*S-3*(b^2-c^2)^2*(b^2+b*c+c^2) : :

The reciprocal orthologic center of these triangles is X(49617).

X(49648) lies on these lines: {10, 1328}, {519, 49639}, {5530, 49616}

X(49648) = orthologic center (1st Jenkins, 2nd tri-squares-central)


X(49649) = PERSPECTOR OF THESE TRIANGLES: OUTER-GARCIA AND 1st JENKINS

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

X(49649) lies on these lines: {515, 45048}, {3679, 10434}, {3944, 4424}

X(49649) = perspector (outer-Garcia, 1st Jenkins)


X(49650) = CYCLOLOGIC CENTER OF THESE TRIANGLES: 1st JENKINS TO 2nd JENKINS

Barycentrics    (b+c)*((b+c)*a^6+(b^2+3*b*c+c^2)*a^5-3*(b^3+c^3)*a^4-(4*b^4+4*c^4+b*c*(3*b^2-4*b*c+3*c^2))*a^3-(b+c)*(b^4-5*b^2*c^2+c^4)*a^2+(b^4+c^4+b*c*(b^2+b*c+c^2))*b*c*a-b^3*c^3*(b+c)) : :
X(49650) = 5*X(1698)-X(38477)

The reciprocal cyclologic center of these triangles is X(49637).

X(49650) lies on the circumcircle of 1st Jenkins triangle and these lines: {10, 115}, {43, 741}, {1698, 38477}, {3035, 6685}, {5539, 6048}, {6010, 9548}

X(49650) = midpoint of X(10) and X(5213)
X(49650) = cyclologic center (1st Jenkins, 2nd Jenkins)
X(49650) = inverse of X(11599) in radical circle of excircles


X(49651) = PERSPECTOR OF THESE TRIANGLES: JENKINS-TANGENTIAL AND 2nd JENKINS

Barycentrics    (b+c)*((b+c)^2*a^8+2*(b+c)*(b^2-6*b*c+c^2)*a^7-(b^4+c^4+5*b*c*(2*b^2-b*c+2*c^2))*a^6-2*(b+c)*(2*b^4+2*c^4-3*b*c*(3*b^2-2*b*c+3*c^2))*a^5-(b^6+c^6-2*b*c*(3*b^2+b*c+3*c^2)*(b^2-b*c+c^2))*a^4+2*(b+c)*(b^6+c^6-(4*b^4+4*c^4-b*c*(11*b^2-20*b*c+11*c^2))*b*c)*a^3+(b^3-c^3)*(b-c)*(b^4+c^4+b*c*(3*b^2+8*b*c+3*c^2))*a^2+2*(b^4-c^4)*(b^2+c^2)*b*c*(b-c)*a+(b^2-c^2)^2*(b-c)^2*b^2*c^2) : :

X(49651) lies on these lines: {226, 2092}

X(49651) = perspector (Jenkins-tangential, 2nd Jenkins)


X(49652) = PERSPECTOR OF THESE TRIANGLES: 2nd JENKINS AND 2nd ZANIAH

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

X(49652) lies on these lines: {9, 38408}, {10, 58}, {960, 1682}, {1158, 9548}, {5233, 17748}, {5777, 39591}

X(49652) = perspector (2nd Jenkins, 2nd Zaniah)


X(49653) = CYCLOLOGIC CENTER OF THESE TRIANGLES: 2nd JENKINS TO JENKINS-CONTACT

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

The reciprocal cyclologic center of these triangles is X(10).

X(49653) lies on these lines: {4, 9}, {304, 309}, {514, 2517}, {515, 6518}, {1214, 1368}, {3687, 27474}, {5088, 19853}, {7396, 29641}, {17860, 21062}, {20205, 20368}, {29057, 40880}, {39605, 40937}

X(49653) = orthoassociate of X(7713)
X(49653) = inverse of X(40) in radical circle of excircles
X(49653) = inverse of X(7713) in polar circle
X(49653) = cyclologic center (2nd Jenkins, Jenkins-contact)
X(49653) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(44190)}} and {{A, B, C, X(19), X(309)}}


X(49654) = PERSPECTOR OF THESE TRIANGLES: APOLLONIUS AND 3rd JENKINS

Barycentrics    a*(b+c)*((b+c)*(3*b^2+8*b*c+3*c^2)*a^8+3*(3*b^2+4*b*c+3*c^2)*(b+c)^2*a^7+3*(b+c)*(2*b^4+2*c^4+b*c*(8*b^2+21*b*c+8*c^2))*a^6-(6*b^6+6*c^6-(12*b^4+12*c^4+b*c*(87*b^2+122*b*c+87*c^2))*b*c)*a^5-(b+c)*(9*b^6+9*c^6-b^2*c^2*(31*b^2+104*b*c+31*c^2))*a^4-(3*b^8+3*c^8+2*(9*b^6+9*c^6-(b^4+c^4+b*c*(47*b^2+59*b*c+47*c^2))*b*c)*b*c)*a^3-(b+c)*(8*b^6+8*c^6-(7*b^4+7*c^4+6*b*c*(4*b^2+13*b*c+4*c^2))*b*c)*b*c*a^2-(3*b^4+3*c^4-2*b*c*(8*b^2+5*b*c+8*c^2))*(b+c)^2*b^2*c^2*a+4*b^4*c^4*(b+c)^3) : :

X(49654) lies on these lines: {10, 49658}, {181, 37868}, {573, 49655}, {970, 49656}, {1682, 49659}, {10822, 49657}, {10823, 49660}, {10824, 49661}, {11758, 49663}, {11767, 49664}, {11776, 49665}, {11785, 49666}, {11989, 49662}, {44845, 44850}

X(49654) = perspector (Apollonius, 3rd Jenkins)


X(49655) = PERSPECTOR OF THESE TRIANGLES: APUS AND 3rd JENKINS

Barycentrics    a*((b+c)*(3*b^2+8*b*c+3*c^2)*a^8+(12*b^4+12*c^4+b*c*(45*b^2+64*b*c+45*c^2))*a^7+(b+c)*(18*b^4+18*c^4+b*c*(66*b^2+103*b*c+66*c^2))*a^6+(12*b^6+12*c^6+(92*b^4+92*c^4+b*c*(240*b^2+317*b*c+240*c^2))*b*c)*a^5+(b+c)*(3*b^6+3*c^6+(54*b^4+54*c^4+b*c*(147*b^2+218*b*c+147*c^2))*b*c)*a^4+(b^2+4*b*c+c^2)*(15*b^2+14*b*c+15*c^2)*(b+c)^2*b*c*a^3+3*(b+c)*(9*b^4+9*c^4+2*b*c*(11*b^2+19*b*c+11*c^2))*b^2*c^2*a^2+(19*b^2+14*b*c+19*c^2)*(b+c)^2*b^3*c^3*a+4*b^4*c^4*(b+c)^3)*(-a+b+c) : :

X(49655) lies on these lines: {3, 49656}, {4, 49658}, {55, 37868}, {56, 49659}, {573, 49654}, {5584, 49657}, {8273, 49660}, {11759, 49663}, {11768, 49664}, {11777, 49665}, {11786, 49666}, {11990, 49662}, {44846, 44850}

X(49655) = perspector (Apus, 3rd Jenkins)


X(49656) = PERSPECTOR OF THESE TRIANGLES: EXCENTRAL AND 3rd JENKINS

Barycentrics    (b+c)*(b^2+4*b*c+c^2)*a^7+(5*b^2+8*b*c+5*c^2)*(b^2+3*b*c+c^2)*a^6+(b+c)*(9*b^4+9*c^4+b*c*(31*b^2+45*b*c+31*c^2))*a^5+(7*b^6+7*c^6+(39*b^4+39*c^4+b*c*(104*b^2+141*b*c+104*c^2))*b*c)*a^4+(b+c)*(2*b^6+2*c^6+(23*b^4+23*c^4+b*c*(61*b^2+75*b*c+61*c^2))*b*c)*a^3+(8*b^4+8*c^4+b*c*(19*b^2+39*b*c+19*c^2))*(b+c)^2*b*c*a^2+(8*b^2+5*b*c+8*c^2)*(b+c)^3*b^2*c^2*a+2*b^3*c^3*(b+c)^4 : :

X(49656) lies on these lines: {1, 37868}, {3, 49655}, {5, 49658}, {10, 49667}, {40, 49657}, {165, 49661}, {970, 49654}, {5750, 38409}, {6043, 49662}, {7991, 44850}, {11754, 49663}, {11763, 49664}, {11772, 49665}, {11781, 49666}

X(49656) = perspector (excentral, 3rd Jenkins)
X(49656) = {X(37868), X(49659)}-harmonic conjugate of X(1)


X(49657) = PERSPECTOR OF THESE TRIANGLES: EXTANGENTS AND 3rd JENKINS

Barycentrics    (b+c)*((b+c)^2*a^9+(b+c)*(3*b^2+4*b*c+3*c^2)*a^8+(3*b^4+3*c^4+b*c*(13*b^2+22*b*c+13*c^2))*a^7+(b+c)*(12*b^2+23*b*c+12*c^2)*b*c*a^6-(3*b^6+3*c^6-(4*b^4+4*c^4+b*c*(37*b^2+58*b*c+37*c^2))*b*c)*a^5-(b+c)*(3*b^6+3*c^6-b^2*c^2*(19*b^2+43*b*c+19*c^2))*a^4-(b^2+b*c+c^2)*(b^6+c^6+(6*b^4+6*c^4-b*c*(9*b^2+40*b*c+9*c^2))*b*c)*a^3-(b+c)*(4*b^6+4*c^6-(b^4+c^4+6*b*c*(b^2+5*b*c+c^2))*b*c)*b*c*a^2-2*(2*b^4+2*c^4-3*b*c*(b^2+c^2))*(b+c)^2*b^2*c^2*a-(b^2-c^2)^2*(b+c)*b^3*c^3) : :

X(49657) lies on these lines: {40, 49656}, {55, 49659}, {65, 37868}, {3925, 49658}, {5183, 44850}, {5584, 49655}, {7957, 49660}, {7964, 49661}, {10822, 49654}, {11756, 49663}, {11765, 49664}, {11774, 49665}, {11783, 49666}, {11991, 49662}

X(49657) = perspector (extangents, 3rd Jenkins)


X(49658) = PERSPECTOR OF THESE TRIANGLES: FEUERBACH AND 3rd JENKINS

Barycentrics    (b+c)*((3*b^2+4*b*c+3*c^2)*(b+c)^2*a^7+(b+c)*(6*b^4+6*c^4+b*c*(13*b^2+28*b*c+13*c^2))*a^6+(16*b^4+16*c^4+b*c*(67*b^2+86*b*c+67*c^2))*b*c*a^5-(b+c)*(6*b^6+6*c^6-(10*b^4+10*c^4+7*b*c*(4*b^2+11*b*c+4*c^2))*b*c)*a^4-(3*b^8+3*c^8+2*(7*b^6+7*c^6-b^2*c^2*(37*b^2+45*b*c+37*c^2))*b*c)*a^3-(b+c)*(11*b^6+11*c^6-(2*b^4+2*c^4+b*c*(b^2+60*b*c+c^2))*b*c)*b*c*a^2-(11*b^4+11*c^4-2*b*c*(8*b^2-3*b*c+8*c^2))*(b+c)^2*b^2*c^2*a-3*(b^2-c^2)^2*(b+c)*b^3*c^3) : :

X(49658) lies on these lines: {4, 49655}, {5, 49656}, {10, 49654}, {11, 49659}, {12, 37868}, {3925, 49657}, {7958, 49660}, {7965, 49661}, {11755, 49663}, {11764, 49664}, {11773, 49665}, {11782, 49666}, {11992, 49662}, {44847, 44850}

X(49658) = perspector (Feuerbach, 3rd Jenkins)


X(49659) = PERSPECTOR OF THESE TRIANGLES: INCENTRAL AND 3rd JENKINS

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

X(49659) lies on these lines: {1, 37868}, {11, 49658}, {15, 49663}, {16, 49665}, {55, 49657}, {56, 49655}, {57, 49661}, {1682, 49654}, {3795, 6685}, {7962, 44850}, {11993, 49662}

X(49659) = perspector (incentral, 3rd Jenkins)
X(49659) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 49656, 37868), (49663, 49664, 15), (49665, 49666, 16)


X(49660) = PERSPECTOR OF THESE TRIANGLES: 3rd JENKINS AND 2nd MIXTILINEAR

Barycentrics    (b+c)^3*a^10+(b^2-c^2)^2*a^9-3*((b^2-c^2)^2-4*b^2*c^2)*(b+c)*a^8-(3*b^6+3*c^6-(18*b^4+18*c^4+b*c*(79*b^2+108*b*c+79*c^2))*b*c)*a^7+(b+c)*(3*b^6+3*c^6+(34*b^4+34*c^4+b*c*(113*b^2+193*b*c+113*c^2))*b*c)*a^6+(3*b^8+3*c^8+2*(16*b^6+16*c^6+(90*b^4+90*c^4+b*c*(218*b^2+279*b*c+218*c^2))*b*c)*b*c)*a^5-(b+c)*(b^8+c^8-(16*b^6+16*c^6+(100*b^4+100*c^4+3*b*c*(83*b^2+116*b*c+83*c^2))*b*c)*b*c)*a^4-(b^8+c^8-2*(14*b^4+14*c^4+b*c*(54*b^2+67*b*c+54*c^2))*b^2*c^2)*(b+c)^2*a^3-(4*b^6+4*c^6-(8*b^4+8*c^4+5*b*c*(b+3*c)*(3*b+c))*b*c)*(b+c)^3*b*c*a^2-4*(b^4+c^4-2*b*c*(b^2+c^2))*(b+c)^4*b^2*c^2*a-(b^2-c^2)^2*(b+c)^3*b^3*c^3 : :

X(49660) lies on these lines: {1, 37868}, {3, 49661}, {7957, 49657}, {7958, 49658}, {8158, 44850}, {8273, 49655}, {10823, 49654}, {11757, 49663}, {11766, 49664}, {11775, 49665}, {11784, 49666}, {11994, 49662}

X(49660) = perspector (3rd Jenkins, 2nd mixtilinear)


X(49661) = PERSPECTOR OF THESE TRIANGLES: 3rd JENKINS AND 4th MIXTILINEAR

Barycentrics    ((b+c)*(5*b^2+14*b*c+5*c^2)*a^8+(17*b^4+17*c^4+2*(31*b^2+43*b*c+31*c^2)*b*c)*a^7+2*(b+c)*(10*b^4+10*c^4+(35*b^2+57*b*c+35*c^2)*b*c)*a^6+2*(4*b^6+4*c^6+(39*b^4+39*c^4+b*c*(107*b^2+141*b*c+107*c^2))*b*c)*a^5-(b+c)*(b^6+c^6-(36*b^4+36*c^4+b*c*(99*b^2+157*b*c+99*c^2))*b*c)*a^4-(b^6+c^6-(2*b^4+2*c^4+b*c*(43*b^2+46*b*c+43*c^2))*b*c)*(b+c)^2*a^3-4*(b+c)*(b^6+c^6-(2*b^4+2*c^4+b*c*(5*b^2+13*b*c+5*c^2))*b*c)*b*c*a^2-4*(b^4+c^4-2*b*c*(b^2+c^2))*(b+c)^2*b^2*c^2*a-(b^2-c^2)^2*(b+c)*b^3*c^3)*(-a+b+c) : :

X(49661) lies on these lines: {3, 49660}, {55, 37868}, {57, 49659}, {165, 49656}, {6244, 44850}, {7964, 49657}, {7965, 49658}, {10824, 49654}, {11760, 49663}, {11769, 49664}, {11778, 49665}, {11787, 49666}, {11995, 49662}

X(49661) = perspector (3rd Jenkins, 4th mixtilinear)


X(49662) = PERSPECTOR OF THESE TRIANGLES: 3rd JENKINS AND MONTESDEOCA-HUNG

Barycentrics    (b+c)*(2*(b+c)^2*a^13+8*(b+c)*(b^2+b*c+c^2)*a^12+4*(3*b^4+3*c^4+(9*b^2+14*b*c+9*c^2)*b*c)*a^11+4*(b+c)*(2*b^4+2*c^4+(11*b^2+12*b*c+11*c^2)*b*c)*a^10-(b^6+c^6-(16*b^4+16*c^4+27*(b+c)^2*b*c)*b*c)*a^9-(b+c)*(15*b^6+15*c^6+(85*b^4+85*c^4+(167*b^2+228*b*c+167*c^2)*b*c)*b*c)*a^8-(32*b^8+32*c^8+(231*b^6+231*c^6+(697*b^4+697*c^4+5*(259*b^2+310*b*c+259*c^2)*b*c)*b*c)*b*c)*a^7-(b+c)*(38*b^8+38*c^8+(242*b^6+242*c^6+(747*b^4+747*c^4+b*c*(1357*b^2+1668*b*c+1357*c^2))*b*c)*b*c)*a^6-(27*b^10+27*c^10+(222*b^8+222*c^8+(895*b^6+895*c^6+(2187*b^4+2187*c^4+2*b*c*(1813*b^2+2130*b*c+1813*c^2))*b*c)*b*c)*b*c)*a^5-(b+c)*(11*b^10+11*c^10+(109*b^8+109*c^8+(443*b^6+443*c^6+6*(179*b^4+179*c^4+3*b*c*(99*b^2+118*b*c+99*c^2))*b*c)*b*c)*b*c)*a^4-(2*b^10+2*c^10+(39*b^8+39*c^8+(149*b^6+149*c^6+(370*b^4+370*c^4+b*c*(625*b^2+718*b*c+625*c^2))*b*c)*b*c)*b*c)*(b+c)^2*a^3-(8*b^8+8*c^8+(35*b^6+35*c^6+(93*b^4+93*c^4+b*c*(133*b^2+174*b*c+133*c^2))*b*c)*b*c)*(b+c)^3*b*c*a^2-(8*b^6+8*c^6+(9*b^4+9*c^4+8*b*c*(3*b^2+2*b*c+3*c^2))*b*c)*(b+c)^4*b^2*c^2*a-2*(b^4+b^2*c^2+c^4)*(b+c)^5*b^3*c^3) : :

X(49662) lies on these lines: {6042, 37868}, {6043, 49656}, {11761, 49663}, {11770, 49664}, {11779, 49665}, {11788, 49666}, {11989, 49654}, {11990, 49655}, {11991, 49657}, {11992, 49658}, {11993, 49659}, {11994, 49660}, {11995, 49661}, {44850, 44852}

X(49662) = perspector (3rd Jenkins, Montesdeoca-Hung)


X(49663) = PERSPECTOR OF THESE TRIANGLES: 3rd JENKINS AND 1st PRZYBYŁOWSKI-BOLLIN

Barycentrics    4*sqrt(3)*S*(a+b+c)*(2*(b+c)*a^4+(3*b^2+4*b*c+3*c^2)*a^3+(b+c)*(b^2+5*b*c+c^2)*a^2+3*(b^2+b*c+c^2)*b*c*a+(b+c)*b^2*c^2)*((b^2+3*b*c+c^2)*a^2+(b+c)*(b^2+c^2)*a+(b+c)^2*b*c)*sqrt(SW+sqrt(3)*S)+sqrt(3)*(2*S+(-a^2+b^2+c^2)*sqrt(3))*((b+c)*a^2+(b^2+b*c+c^2)*a+b*c*(b+c))*((3*b^2+8*b*c+3*c^2)*a^4+2*(b+c)*(3*b^2+4*b*c+3*c^2)*a^3+(3*b^4+3*c^4+b*c*(14*b^2+25*b*c+14*c^2))*a^2+2*(b+c)*(4*b^2+3*b*c+4*c^2)*b*c*a+3*b^2*c^2*(b+c)^2)*a^2 : :

X(49663) lies on these lines: {15, 49659}, {1379, 49666}, {1380, 49665}, {11753, 37868}, {11754, 49656}, {11755, 49658}, {11756, 49657}, {11757, 49660}, {11758, 49654}, {11759, 49655}, {11760, 49661}, {11761, 49662}, {44850, 44853}

X(49663) = perspector (3rd Jenkins, 1st Przybyłowski-Bollin)
X(49663) = {X(15), X(49659)}-harmonic conjugate of X(49664)


X(49664) = PERSPECTOR OF THESE TRIANGLES: 3rd JENKINS AND 2nd PRZYBYŁOWSKI-BOLLIN

Barycentrics    -4*sqrt(3)*S*(a+b+c)*(2*(b+c)*a^4+(3*b^2+4*b*c+3*c^2)*a^3+(b+c)*(b^2+5*b*c+c^2)*a^2+3*(b^2+b*c+c^2)*b*c*a+(b+c)*b^2*c^2)*((b^2+3*b*c+c^2)*a^2+(b+c)*(b^2+c^2)*a+(b+c)^2*b*c)*sqrt(SW+sqrt(3)*S)+sqrt(3)*(2*S+(-a^2+b^2+c^2)*sqrt(3))*((b+c)*a^2+(b^2+b*c+c^2)*a+b*c*(b+c))*((3*b^2+8*b*c+3*c^2)*a^4+2*(b+c)*(3*b^2+4*b*c+3*c^2)*a^3+(3*b^4+3*c^4+b*c*(14*b^2+25*b*c+14*c^2))*a^2+2*(b+c)*(4*b^2+3*b*c+4*c^2)*b*c*a+3*b^2*c^2*(b+c)^2)*a^2 : :

X(49664) lies on these lines: {15, 49659}, {1379, 49665}, {1380, 49666}, {11762, 37868}, {11763, 49656}, {11764, 49658}, {11765, 49657}, {11766, 49660}, {11767, 49654}, {11768, 49655}, {11769, 49661}, {11770, 49662}, {44850, 44854}

X(49664) = perspector (3rd Jenkins, 2nd Przybyłowski-Bollin)
X(49664) = {X(15), X(49659)}-harmonic conjugate of X(49663)


X(49665) = PERSPECTOR OF THESE TRIANGLES: 3rd JENKINS AND 3rd PRZYBYŁOWSKI-BOLLIN

Barycentrics    -4*sqrt(3)*S*(a+b+c)*(2*(b+c)*a^4+(3*b^2+4*b*c+3*c^2)*a^3+(b+c)*(b^2+5*b*c+c^2)*a^2+3*(b^2+b*c+c^2)*b*c*a+(b+c)*b^2*c^2)*((b^2+3*b*c+c^2)*a^2+(b+c)*(b^2+c^2)*a+(b+c)^2*b*c)*sqrt(SW-sqrt(3)*S)-sqrt(3)*(2*S-(-a^2+b^2+c^2)*sqrt(3))*((b+c)*a^2+(b^2+b*c+c^2)*a+b*c*(b+c))*((3*b^2+8*b*c+3*c^2)*a^4+2*(b+c)*(3*b^2+4*b*c+3*c^2)*a^3+(3*b^4+3*c^4+b*c*(14*b^2+25*b*c+14*c^2))*a^2+2*(b+c)*(4*b^2+3*b*c+4*c^2)*b*c*a+3*b^2*c^2*(b+c)^2)*a^2 : :

X(49665) lies on these lines: {16, 49659}, {1379, 49664}, {1380, 49663}, {11771, 37868}, {11772, 49656}, {11773, 49658}, {11774, 49657}, {11775, 49660}, {11776, 49654}, {11777, 49655}, {11778, 49661}, {11779, 49662}, {44850, 44855}

X(49665) = perspector (3rd Jenkins, 3rd Przybyłowski-Bollin)
X(49665) = {X(16), X(49659)}-harmonic conjugate of X(49666)


X(49666) = PERSPECTOR OF THESE TRIANGLES: 3rd JENKINS AND 4th PRZYBYŁOWSKI-BOLLIN

Barycentrics    4*sqrt(3)*S*(a+b+c)*(2*(b+c)*a^4+(3*b^2+4*b*c+3*c^2)*a^3+(b+c)*(b^2+5*b*c+c^2)*a^2+3*(b^2+b*c+c^2)*b*c*a+(b+c)*b^2*c^2)*((b^2+3*b*c+c^2)*a^2+(b+c)*(b^2+c^2)*a+(b+c)^2*b*c)*sqrt(SW-sqrt(3)*S)-sqrt(3)*(2*S-(-a^2+b^2+c^2)*sqrt(3))*((b+c)*a^2+(b^2+b*c+c^2)*a+b*c*(b+c))*((3*b^2+8*b*c+3*c^2)*a^4+2*(b+c)*(3*b^2+4*b*c+3*c^2)*a^3+(3*b^4+3*c^4+b*c*(14*b^2+25*b*c+14*c^2))*a^2+2*(b+c)*(4*b^2+3*b*c+4*c^2)*b*c*a+3*b^2*c^2*(b+c)^2)*a^2 : :

X(49666) lies on these lines: {16, 49659}, {1379, 49663}, {1380, 49664}, {11780, 37868}, {11781, 49656}, {11782, 49658}, {11783, 49657}, {11784, 49660}, {11785, 49654}, {11786, 49655}, {11787, 49661}, {11788, 49662}, {44850, 44856}

X(49666) = perspector (3rd Jenkins, 4th Przybyłowski-Bollin)
X(49666) = {X(16), X(49659)}-harmonic conjugate of X(49665)


X(49667) = PERSPECTOR OF THESE TRIANGLES: 3rd JENKINS AND 2nd ZANIAH

Barycentrics    (-a+b+c)*((b^2+4*b*c+c^2)*(b+c)^2*a^8+(b+c)*(4*b^4+4*c^4+b*c*(19*b^2+28*b*c+19*c^2))*a^7+2*(3*b^6+3*c^6+(20*b^4+20*c^4+b*c*(57*b^2+79*b*c+57*c^2))*b*c)*a^6+(b+c)*(4*b^6+4*c^6+(38*b^4+38*c^4+b*c*(114*b^2+145*b*c+114*c^2))*b*c)*a^5+(b^8+c^8+(26*b^6+26*c^6+(114*b^4+114*c^4+b*c*(260*b^2+339*b*c+260*c^2))*b*c)*b*c)*a^4+(b+c)*(7*b^6+7*c^6+(46*b^4+46*c^4+b*c*(113*b^2+128*b*c+113*c^2))*b*c)*b*c*a^3+2*(7*b^4+7*c^4+b*c*(10*b^2+23*b*c+10*c^2))*(b+c)^2*b^2*c^2*a^2+(7*b^2+2*b*c+7*c^2)*(b+c)^3*b^3*c^3*a+b^4*c^4*(b+c)^4) : :

X(49667) lies on these lines: {9, 38409}, {10, 49656}, {960, 37868}

X(49667) = perspector (3rd Jenkins, 2nd Zaniah)


X(49668) = PERSPECTOR OF THESE TRIANGLES: JENKINS-TANGENTIAL AND MEDIAL

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

X(49668) lies on these lines: {2, 38407}, {3452, 34258}, {17793, 19803}

X(49668) = perspector (Jenkins-tangential, medial)


X(49669) = EULER LINE INTERCEPT OF X(182)X(1177)

Barycentrics    3*a^10-5*(b^2+c^2)*a^8-2*(-4*b^2*c^2+(b^2-c^2)^2)*a^6+2*(b^2+c^2)*(3*b^4-4*b^2*c^2+3*c^4)*a^4-(b^2-c^2)^2*(b^4+10*b^2*c^2+c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(49669) = 2*X(5)-3*X(9818), 4*X(5)-3*X(18420), 3*X(376)-2*X(33532), X(382)-3*X(1597), 4*X(548)-3*X(35243), 5*X(631)-6*X(7514)

See Antreas Hatzipolakis and César Lozada, euclid 5093.

X(49669) lies on these lines: {2, 3}, {68, 13403}, {74, 18911}, {113, 39242}, {141, 32620}, {146, 11003}, {182, 1177}, {184, 15063}, {511, 4549}, {541, 9970}, {542, 5486}, {1350, 35254}, {1352, 4550}, {1503, 8547}, {1514, 13394}, {1533, 35268}, {1899, 16003}, {2549, 3018}, {3003, 7737}, {4293, 37729}, {4299, 37696}, {4302, 37697}, {4316, 9817}, {4324, 19372}, {5480, 40909}, {5651, 16163}, {5654, 11430}, {5663, 6776}, {5876, 6193}, {5895, 37476}, {5907, 12118}, {5921, 32423}, {5925, 37514}, {6000, 44479}, {6781, 10314}, {6800, 32111}, {7689, 39571}, {7706, 14561}, {7728, 14805}, {9813, 19924}, {9822, 48880}, {9826, 20127}, {10293, 43697}, {10519, 33533}, {10627, 11821}, {11271, 41726}, {11411, 12370}, {11425, 22660}, {11440, 18912}, {11457, 15062}, {12022, 18917}, {12162, 19467}, {12163, 12241}, {12164, 43595}, {12244, 14708}, {12250, 13491}, {12289, 43613}, {13754, 32284}, {14457, 43689}, {14826, 15060}, {14915, 46264}, {15057, 26913}, {15069, 44665}, {15311, 34117}, {16111, 37470}, {16194, 31383}, {16511, 36201}, {16657, 37489}, {18435, 23236}, {18913, 18952}, {18925, 32139}, {18945, 32140}, {19137, 48892}, {20379, 23291}, {20427, 40647}, {32815, 44135}, {34545, 34796}, {34785, 44870}, {35237, 44882}, {35260, 46817}, {40441, 43695}, {41719, 48906}, {44413, 44492}

X(49669) = reflection of X(i) in X(j) for these (i, j): (4, 31861), (1350, 35254), (1352, 4550), (4846, 182), (18420, 9818), (35237, 44882), (40909, 5480)
X(49669) = intersection, other than A, B, C, of circumconics {{A, B, C, X(23), X(18850)}} and {{A, B, C, X(68), X(38323)}}
X(49669) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 35485, 3), (3, 381, 468), (3, 34622, 550), (4, 376, 23), (4, 14118, 3549), (5, 18580, 2), (5, 47335, 6644), (23, 37077, 4), (376, 18537, 6644), (376, 46336, 3), (381, 18323, 4), (468, 44285, 3), (5169, 10296, 4), (7527, 10296, 5169), (7575, 44275, 4232), (10297, 44218, 5094), (14130, 18404, 3541), (18324, 46030, 6353), (18537, 40132, 5), (35921, 37929, 3), (37911, 44920, 5), (37981, 44438, 4)


X(49670) = EULER LINE INTERCEPT OF X(393)X(43619)

Barycentrics    (11*a^6-17*(b^2+c^2)*a^4+(b^4+30*b^2*c^2+c^4)*a^2+5*(b^4-c^4)*(b^2-c^2))*(a^2-b^2+c^2)*(a^2+b^2-c^2) : :
X(49670) = 5*X(4)-6*X(1597), 7*X(4)-6*X(18494), 4*X(550)-3*X(35513)

See Antreas Hatzipolakis and César Lozada, euclid 5093.

X(49670) lies on these lines: {2, 3}, {393, 43619}, {541, 32234}, {1514, 35260}, {1899, 10990}, {1990, 44526}, {2549, 40138}, {2777, 5095}, {3087, 43618}, {3092, 42414}, {3093, 42413}, {5486, 36201}, {5702, 15048}, {5895, 18925}, {5921, 17702}, {5925, 18909}, {6000, 15073}, {6103, 43448}, {7737, 40135}, {8717, 19128}, {10606, 18918}, {11003, 15472}, {11180, 32250}, {11469, 12134}, {12250, 21659}, {15471, 43273}, {17983, 18850}, {18387, 44795}, {18914, 32601}, {18945, 20427}, {20417, 23291}, {32815, 44134}, {38788, 41467}, {43576, 44080}

X(49670) = inverse of X(47310) in polar circle
X(49670) = orthoassociate of X(47310)
X(49670) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 376, 468), (4, 35485, 2), (4, 37118, 3091), (4, 37460, 3089), (20, 3543, 23), (468, 44438, 4), (1885, 37196, 4), (3088, 34621, 3089), (35480, 35484, 4), (35490, 37118, 4)


X(49671) = EULER LINE INTERCEPT OF X(182)X(4550)

Barycentrics    a^2*(a^8-2*(b^2+c^2)*a^6+2*b^2*c^2*a^4+(b^2+c^2)*(2*b^4+b^2*c^2+2*c^4)*a^2-(b^2-c^2)^2*(b^4+5*b^2*c^2+c^4)) : :
X(49671) = 5*X(3)+3*X(1597), X(3)-3*X(7514), X(3)+3*X(9818), 3*X(3)-X(33532), 7*X(3)-3*X(35243)

See Antreas Hatzipolakis and César Lozada, euclid 5093.

X(49671) lies on these lines: {2, 3}, {6, 32599}, {49, 15056}, {68, 43575}, {74, 40280}, {110, 14805}, {182, 4550}, {184, 5609}, {373, 32110}, {399, 11003}, {511, 12039}, {541, 10168}, {542, 8546}, {567, 11422}, {568, 15019}, {569, 5876}, {574, 2493}, {575, 13754}, {576, 1154}, {578, 11591}, {1147, 14128}, {1352, 2930}, {1495, 34513}, {1499, 44821}, {1511, 5651}, {2777, 15578}, {2781, 32154}, {2782, 13233}, {2917, 20584}, {3098, 16776}, {3292, 5891}, {3431, 14926}, {3455, 22566}, {3581, 5640}, {3818, 35707}, {4549, 14561}, {4846, 34437}, {5012, 14094}, {5063, 44468}, {5085, 11472}, {5092, 14915}, {5158, 47228}, {5476, 37827}, {5480, 35254}, {5613, 13858}, {5617, 13859}, {5621, 38064}, {5650, 10564}, {5907, 32046}, {6000, 15579}, {6101, 11424}, {6241, 37471}, {6759, 45958}, {7689, 12006}, {7706, 38317}, {7737, 11063}, {7761, 34827}, {7998, 37477}, {7999, 37495}, {8542, 14984}, {8717, 17508}, {9659, 10593}, {9672, 10592}, {9729, 32138}, {9734, 14662}, {9775, 10870}, {10095, 46730}, {10170, 11430}, {10264, 18911}, {10272, 19457}, {10539, 10610}, {10982, 14449}, {11178, 12584}, {11179, 16010}, {11180, 32254}, {11411, 32165}, {11438, 13363}, {11444, 37472}, {11477, 39522}, {12041, 22112}, {12111, 13353}, {12161, 31834}, {12893, 15088}, {13336, 13491}, {13339, 15072}, {13346, 32142}, {13352, 15067}, {13394, 46817}, {13434, 18436}, {14687, 15922}, {15027, 23293}, {15030, 37513}, {15033, 23039}, {15048, 16310}, {15068, 37506}, {15080, 16261}, {15083, 32136}, {15092, 39825}, {15109, 43619}, {15177, 38034}, {15462, 19151}, {15582, 18400}, {16194, 22352}, {17702, 24206}, {19139, 34801}, {21243, 36253}, {22791, 37546}, {25711, 43650}, {32139, 37476}, {32424, 34010}, {32515, 40879}, {33884, 37496}, {34783, 43651}, {40247, 41597}, {41462, 43576}, {43620, 44533}, {43697, 45016}, {47558, 48876}

X(49671) = midpoint of X(i) and X(j) for these {i, j}: {3, 31861}, {182, 4550}, {5480, 35254}, {7514, 9818}, {19139, 34801}
X(49671) = circumperp conjugate of the anticomplement of X(44266)
X(49671) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 18580, 140), (3, 381, 23), (3, 5072, 3518), (3, 11284, 6644), (3, 12106, 1658), (3, 35001, 376), (3, 40916, 549), (4, 14787, 5), (5, 549, 468), (5, 7575, 1995), (5, 18572, 381), (23, 35921, 3), (26, 11479, 3850), (140, 44235, 3549), (378, 40916, 3), (549, 37950, 3), (1593, 7516, 548), (7393, 12084, 3530), (7395, 7526, 140), (7464, 7496, 3), (7514, 31861, 3), (7527, 7550, 3), (10297, 37454, 5), (10303, 35475, 3), (13596, 15246, 3534), (15331, 35018, 6642)


X(49672) = EULER LINE INTERCEPT OF X(599)X(5622)

Barycentrics    5*a^10-12*(b^2+c^2)*a^8+2*(2*b^4+17*b^2*c^2+2*c^4)*a^6+2*(b^2+c^2)*(5*b^4-18*b^2*c^2+5*c^4)*a^4-(b^2-c^2)^2*(9*b^4+8*b^2*c^2+9*c^4)*a^2+2*(b^4-c^4)*(b^2-c^2)^3 : :
X(49672) = 4*X(3)+5*X(31282), 8*X(3)+X(35490), X(24)-10*X(631), X(24)+8*X(16196), 8*X(140)+X(11413), 2*X(235)-11*X(3525), 4*X(549)-X(15078), 8*X(549)+X(31180), 5*X(631)+4*X(16196), 10*X(632)-X(31725)

See Antreas Hatzipolakis and César Lozada, euclid 5093.

X(49672) lies on these lines: {2, 3}, {599, 5622}, {5642, 11456}, {6699, 15066}, {6800, 38793}, {10168, 44493}, {10249, 21358}, {11438, 13857}, {11464, 43273}, {15068, 20126}, {15080, 20771}, {15360, 37483}, {15361, 37494}, {20191, 44752}, {32225, 37480}, {34507, 38729}

X(49672) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 376, 403), (2, 2071, 381), (2, 37077, 5055), (140, 44218, 2), (549, 10257, 2), (549, 43957, 3524), (631, 16196, 24), (9818, 15694, 2), (44273, 47097, 4)


X(49673) = EULER LINE INTERCEPT OF X(6)X(22051)

Barycentrics    (b^2+c^2)*a^8-2*(b^4+b^2*c^2+c^4)*a^6+3*(b^2+c^2)*b^2*c^2*a^4+(2*b^4-b^2*c^2+2*c^4)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(49673) = 3*X(2)+X(18404), 9*X(2)-X(35471), X(3)-5*X(31282), 3*X(3)+X(35490), 3*X(5)-X(235), X(24)-5*X(1656), X(235)+3*X(11585), 2*X(235)-3*X(44235), 3*X(381)+X(11413), 3*X(381)-X(44271), 3*X(547)-X(44232), 3*X(549)-X(44240)

See Antreas Hatzipolakis and César Lozada, euclid 5093.

X(49673) lies on these lines: {2, 3}, {6, 22051}, {110, 45731}, {113, 13491}, {125, 5876}, {156, 10272}, {1147, 45970}, {1511, 21659}, {1531, 34798}, {1568, 6102}, {1614, 14643}, {2888, 11804}, {3567, 20424}, {3574, 15026}, {5448, 13630}, {5449, 11591}, {5654, 18952}, {5891, 34826}, {5907, 13561}, {5944, 20771}, {5972, 32171}, {6699, 32210}, {6723, 20191}, {7699, 15028}, {8571, 40805}, {9703, 36966}, {9927, 11801}, {10264, 12111}, {10282, 13470}, {11064, 12370}, {11264, 41597}, {11440, 15061}, {11444, 11704}, {11793, 45780}, {12006, 18388}, {12161, 45969}, {12359, 31834}, {13403, 14156}, {13565, 24206}, {14128, 21243}, {14852, 44752}, {15067, 23515}, {15068, 18356}, {15087, 43816}, {15088, 15465}, {15806, 32046}, {18350, 25739}, {18358, 20300}, {18383, 43586}, {18390, 46114}, {18435, 23294}, {18436, 26917}, {18912, 32165}, {20299, 45959}, {22802, 23315}, {23293, 45622}, {26913, 34783}, {32136, 43573}, {34148, 43821}, {40111, 44076}

X(49673) = midpoint of X(i) and X(j) for these {i, j}: {5, 11585}, {11413, 44271}, {18404, 37814}, {31180, 44270}, {37440, 37444}
X(49673) = reflection of X(i) in X(j) for these (i, j): (16238, 3628), (43615, 140), (44226, 3850), (44235, 5), (44247, 3530), (45179, 13413)
X(49673) = complement of X(37814)
X(49673) = inverse of X(34152) in: MacBeath inconic, nine-point circle
X(49673) = inverse of X(43809) in: orthocentroidal circle, Yff hyperbola
X(49673) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 10255, 5), (5, 427, 3850), (5, 550, 403), (5, 13371, 546), (5, 33332, 3091), (5, 37938, 4), (403, 37452, 550), (1368, 15761, 548), (1656, 7577, 5), (6640, 18570, 5498), (13413, 35018, 5), (16868, 35490, 235), (18564, 21844, 550), (23335, 46030, 3853), (31101, 44958, 1657)


X(49674) = EULER LINE INTERCEPT OF X(373)X(10628)

Barycentrics    a^10-6*(b^2+c^2)*a^8+(8*b^4+5*b^2*c^2+8*c^4)*a^6+2*(b^2+c^2)*(b^4+c^4)*a^4-(b^2-c^2)^2*(9*b^4+7*b^2*c^2+9*c^4)*a^2+4*(b^4-c^4)*(b^2-c^2)^3 : :
X(49674) = 8*X(5)+X(3520), 5*X(631)+4*X(23047)

See Antreas Hatzipolakis and César Lozada, euclid 5093.

X(49674) lies on these lines: {2, 3}, {373, 10628}, {5642, 41171}, {7703, 12112}, {9140, 15032}, {11178, 22151}, {11693, 43839}, {14389, 15081}, {15018, 20304}, {15462, 25561}, {24206, 41721}, {34155, 41720}

X(49674) = reflection of X(26644) in X(44879)
X(49674) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 381, 186), (2, 3153, 549), (547, 2072, 2), (7514, 15703, 2), (13413, 44282, 381)

leftri

Points in a [[bc(b-c),ca(c-a),ab(a-b), [(b-c)^3, (c-a)^3,(a-b)^3]] coordinate system: X(49675)-X(497156)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1, L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1 is the line: bc(b-c) \alpha + ca(v-a) β ab(a-b) γ = 0.

L2 is the line (b-c)^3 α + (c-a)^3 β + (a-b)^3 γ = 0.

The origin is given by (0, 0) = X(238) = a^2 - b c : : .

Barycentrics u : v : w for a triangle center U = (x, y) in this system are given by

u : v : w = -a(a-b)(a-c)(b-c)(a^2 - b c) - a (a b + a c - b^2 - c^2) x + (2a - b - c)(a^2 + b^2 + c^2 - a b - a c - b c) y : : ,

where, as functions of a, b, c, the coordinate x is antisymmetric of degree 3, and y is antisymmetric of degree 3.

The appearance of {x, y}, k in the following list means that (x, y) = X(k).

{-2 (a-b) (a-c) (b-c), (a-b) (a-c) (b-c)}, 32850
{-((a-b) (a-c) (b-c)), -2 (a-b) (a-c) (b-c)}, 3633
{-((a-b) (a-c) (b-c)), -((2 a (a-b) b (a-c) (b-c) c)/(a^3+b^3+c^3))}, 49494
{-((a-b) (a-c) (b-c)), -((2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2))}, 49495
{-((a-b) (a-c) (b-c)), -((a-b) (a-c) (b-c))}, 145
{-((a-b) (a-c) (b-c)), -((a (a-b) b (a-c) (b-c) c)/(a^3+b^3+c^3))}, 49487
{-((a-b) (a-c) (b-c)), -(((a-b) (a+b) (a-c) (b-c) (a+c) (b+c))/(a^3+b^3+c^3))}, 3187
{-((a-b) (a-c) (b-c)), -(((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2))}, 49488
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c)), -((a-b) (a-c) (b-c))}, 49470
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c)), -(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c))}, 49534
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)), -(((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2))}, 49497
{-((a-b) (a-c) (b-c)), -(1/2) (a-b) (a-c) (b-c)}, 3244
{-((a-b) (a-c) (b-c)), -(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a b+a c+b c)))}, 49476
{-((a-b) (a-c) (b-c)), -(((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a^2+b^2+c^2)))}, 49477
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c)), -(1/2) (a-b) (a-c) (b-c)}, 3993
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c)), -(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a b+a c+b c)))}, 49527
{-((a-b) (a-c) (b-c)), 0}, 1
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c)), 0}, 984
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)), 0}, 6
{-((a-b) (a-c) (b-c)), 1/2 (a-b) (a-c) (b-c)}, 10
{-((a-b) (a-c) (b-c)), ((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a b+a c+b c))}, 49466
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c)), 1/2 (a-b) (a-c) (b-c)}, 49510
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c)), ((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a b+a c+b c))}, 3883
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)), 1/2 (a-b) (a-c) (b-c)}, 49529
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)), ((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a^2+b^2+c^2))}, 49482
{-((a-b) (a-c) (b-c)), (a-b) (a-c) (b-c)}, 8
{-((a-b) (a-c) (b-c)), (a (a-b) b (a-c) (b-c) c)/(a^3+b^3+c^3)}, 3938
{-((a-b) (a-c) (b-c)), ((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)}, 49458
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c)), (a-b) (a-c) (b-c)}, 49450
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c)), ((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c)}, 49506
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)), ((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)}, 32941
{-((a-b) (a-c) (b-c)), 2 (a-b) (a-c) (b-c)}, 3632
{-((a-b) (a-c) (b-c)), (2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)}, 49451
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)), (2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)}, 49460
{-(1/2) (a-b) (a-c) (b-c), 0}, 1279
{0, 0}, 238
{1/2 (a-b) (a-c) (b-c), 0}, 44
{(a-b) (a-c) (b-c), 0}, 1757
{-2*(a - b)*(a - c)*(b - c), 0}, 49675
{-2*(a - b)*(a - c)*(b - c), ((a - b)*(a - c)*(b - c))/2}, 49676
{-2*(a - b)*(a - c)*(b - c), 2*(a - b)*(a - c)*(b - c)}, 49677
{-(((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c)), -2*(a - b)*(a - c)*(b - c)}, 49678
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)), -2*(a - b)*(a - c)*(b - c)}, 49679
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)), (-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49680
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)), -((a - b)*(a - c)*(b - c))}, 49681
{-((a - b)*(a - c)*(b - c)), -1/2*(a*(a - b)*b*(a - c)*(b - c)*c)/(a^3 + b^3 + c^3)}, 49682
{-((a - b)*(a - c)*(b - c)), -1/2*((a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c))/(a^3 + b^3 + c^3)}, 49683
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)), -1/2*((a - b)*(a - c)*(b - c))}, 49684
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)), -1/2*((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)}, 49685
{-((a - b)*(a - c)*(b - c)), (a*(a - b)*b*(a - c)*(b - c)*c)/(2*(a^3 + b^3 + c^3))}, 49686
{-((a - b)*(a - c)*(b - c)), ((a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c))/(a^3 + b^3 + c^3)}, 49687
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)), (a - b)*(a - c)*(b - c)}, 49688
{-(((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c)), 2*(a - b)*(a - c)*(b - c)}, 49689
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)), 2*(a - b)*(a - c)*(b - c)}, 49690
{-1/2*((a - b)*(a - c)*(b - c)), -1/2*((a - b)*(a - c)*(b - c))}, 49691
{-1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c), 0}, 49692
{-1/2*((a - b)*(a - c)*(b - c)), ((a - b)*(a - c)*(b - c))/2}, 49693
{-1/2*((a - b)*(a - c)*(b - c)), (a - b)*(a - c)*(b - c)}, 49694
{0, -((a - b)*(a - c)*(b - c))}, 49695
{0, -1/2*((a - b)*(a - c)*(b - c))}, 49696
{0, ((a - b)*(a - c)*(b - c))/2}, 49697
{0, (a - b)*(a - c)*(b - c)}, 49698
{((a - b)*(a - c)*(b - c))/2, -((a - b)*(a - c)*(b - c))}, 49699
{((a - b)*(a - c)*(b - c))/2, -1/2*((a - b)*(a - c)*(b - c))}, 49700
{((a - b)*(a - c)*(b - c))/2, ((a - b)*(a - c)*(b - c))/2}, 49701
{((a - b)*(a - c)*(b - c))/2, (a - b)*(a - c)*(b - c)}, 49702
{((a - b)*(a - c)*(b - c))/2, 2*(a - b)*(a - c)*(b - c)}, 49703
{(a - b)*(a - c)*(b - c), -((a - b)*(a - c)*(b - c))}, 49704
{(a - b)*(a - c)*(b - c), -1/2*((a - b)*(a - c)*(b - c))}, 49705
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), 0}, 49706
{(a - b)*(a - c)*(b - c), (a - b)*(a - c)*(b - c)}, 49707
{2*(a - b)*(a - c)*(b - c), -2*(a - b)*(a - c)*(b - c)}, 49708
{2*(a - b)*(a - c)*(b - c), -((a - b)*(a - c)*(b - c))}, 49709
{2*(a - b)*(a - c)*(b - c), -1/2*((a - b)*(a - c)*(b - c))}, 49710
{(2*(a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c), -1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c)}, 49711
{2*(a - b)*(a - c)*(b - c), 0}, 49712
{2*(a - b)*(a - c)*(b - c), ((a - b)*(a - c)*(b - c))/2}, 49713
{2*(a - b)*(a - c)*(b - c), (a - b)*(a - c)*(b - c)}, 49714
{(2*(a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c), (a - b)*(a - c)*(b - c)}, 49715


X(49675) = X(1)X(6)∩X(8)X(3836)

Barycentrics    a*(a^2 - 2*a*b + 2*b^2 - 2*a*c - b*c + 2*c^2) : :
X(49675) = 5 X[1] - 2 X[44], 3 X[1] - 2 X[1279], 3 X[1] - X[1757], 7 X[1] - 4 X[3246], 4 X[44] - 5 X[238], 3 X[44] - 5 X[1279], 6 X[44] - 5 X[1757], 7 X[44] - 10 X[3246], X[44] - 5 X[4864], 3 X[238] - 4 X[1279], 3 X[238] - 2 X[1757], 7 X[238] - 8 X[3246], X[238] - 4 X[4864], 7 X[1279] - 6 X[3246], X[1279] - 3 X[4864], 7 X[1757] - 12 X[3246], X[1757] - 6 X[4864], 2 X[3246] - 7 X[4864], 4 X[10] - 5 X[31252], X[320] + 2 X[3244], 3 X[31151] - 2 X[32850], X[4693] + 2 X[24841], 5 X[3616] - 4 X[31289], X[3632] - 4 X[3834], 3 X[3679] - 4 X[3823], 7 X[20057] - X[20072], 2 X[31138] + X[34747]

X(49675) lies on these lines: {1, 6}, {8, 3836}, {10, 17283}, {31, 4430}, {38, 3750}, {42, 17598}, {43, 17597}, {63, 17715}, {69, 49506}, {75, 49458}, {100, 17449}, {145, 4310}, {149, 32856}, {171, 3873}, {200, 17063}, {210, 29820}, {244, 3935}, {291, 1280}, {320, 3244}, {354, 3961}, {497, 33101}, {513, 48282}, {519, 1738}, {528, 32857}, {537, 3685}, {726, 4693}, {748, 4661}, {752, 3241}, {756, 29817}, {846, 3748}, {894, 49473}, {899, 3315}, {976, 3889}, {982, 3870}, {1054, 3689}, {1458, 14151}, {1463, 2099}, {1482, 15310}, {1721, 7982}, {1961, 4883}, {2177, 4392}, {2239, 17018}, {2263, 30318}, {2650, 28026}, {3058, 33099}, {3158, 18193}, {3218, 3722}, {3434, 33103}, {3475, 33111}, {3616, 31289}, {3623, 17771}, {3632, 3834}, {3633, 49486}, {3635, 17770}, {3636, 25072}, {3666, 3979}, {3679, 3823}, {3681, 17123}, {3684, 3726}, {3699, 4871}, {3744, 32913}, {3749, 4650}, {3792, 9052}, {3811, 3976}, {3868, 37588}, {3874, 5255}, {3881, 37607}, {3883, 49505}, {3886, 49493}, {3892, 30115}, {3894, 37610}, {3912, 32029}, {3920, 4038}, {3923, 49499}, {3932, 9041}, {3996, 24165}, {4030, 33085}, {4327, 11526}, {4417, 29844}, {4440, 17764}, {4449, 37998}, {4514, 33064}, {4702, 28582}, {4847, 33130}, {4849, 4906}, {4863, 17889}, {4966, 9053}, {5014, 33069}, {5045, 5293}, {5083, 9364}, {5263, 49479}, {5268, 44841}, {5297, 17450}, {5524, 16610}, {5563, 20990}, {5695, 49532}, {5853, 24231}, {6165, 48296}, {6542, 17769}, {6745, 24216}, {6765, 24440}, {7292, 21805}, {9335, 9350}, {9337, 9352}, {10453, 32920}, {11269, 17725}, {16823, 49457}, {16825, 49450}, {17135, 30969}, {17140, 32945}, {17145, 20045}, {17154, 32845}, {17165, 32943}, {17277, 49510}, {17353, 49536}, {17596, 21342}, {17599, 42042}, {17718, 29676}, {17719, 26015}, {17724, 33140}, {17779, 21870}, {18208, 19589}, {20011, 32924}, {20057, 20072}, {20068, 32936}, {24349, 32941}, {29596, 38191}, {29637, 49524}, {29638, 33114}, {29640, 37703}, {29655, 33126}, {29656, 33121}, {29660, 38047}, {29672, 33118}, {29673, 33124}, {29818, 32911}, {29824, 32927}, {29835, 32775}, {30614, 33088}, {31138, 34747}, {32784, 36479}, {32926, 42057}, {32932, 42055}, {33076, 49466}, {33081, 33090}, {33098, 34611}, {33120, 33122}, {33136, 33148}, {33141, 33144}, {33159, 49529}, {33162, 33173}, {33169, 33171}, {39344, 41339}, {49446, 49452}, {49451, 49459}, {49453, 49469}, {49455, 49470}, {49460, 49474}, {49463, 49475}, {49467, 49483}, {49482, 49535}, {49485, 49525}

X(49675) = midpoint of X(145) and X(4645)
X(49675) = reflection of X(i) in X(j) for these {i,j}: {1, 4864}, {8, 3836}, {238, 1}, {1757, 1279}, {4716, 32922}, {24715, 24231}, {32846, 4684}, {32847, 4966}
X(49675) = X(514)-isoconjugate of X(28891)
X(49675) = crossdifference of every pair of points on line {513, 16669}
X(49675) = X(i)-lineconjugate of X(j) for these (i,j): {1, 16669}, {48282, 513}
X(49675) = barycentric product X(i)*X(j) for these {i,j}: {1, 17266}, {72, 31921}, {100, 28890}
X(49675) = barycentric quotient X(i)/X(j) for these {i,j}: {692, 28891}, {17266, 75}, {28890, 693}, {31921, 286}
X(49675) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 984, 16484}, {1, 1757, 1279}, {1, 3243, 49490}, {1, 16496, 984}, {1, 49448, 1001}, {1, 49490, 4649}, {1, 49498, 6}, {9, 15600, 1}, {37, 15570, 1}, {38, 3957, 3750}, {100, 17449, 18201}, {354, 3961, 17122}, {1279, 1757, 238}, {2177, 4392, 17593}, {3242, 42871, 1}, {3244, 49464, 4360}, {3689, 3999, 1054}, {3873, 3938, 171}, {17145, 20045, 32919}, {17597, 41711, 43}, {33144, 36845, 33141}, {49465, 49478, 1}, {49466, 49511, 33076}, {49473, 49491, 894}


X(49676) = X(1)X(2896)∩X(10)X(141)

Barycentrics    a^2*b - a*b^2 - b^3 + a^2*c + 2*a*b*c - a*c^2 - c^3 : :
X(49676) = 3 X[10] - 4 X[3823], X[10] - 4 X[3834], X[3823] - 3 X[3834], 2 X[3823] - 3 X[3836], 2 X[44] - 5 X[19862], 5 X[19862] - 4 X[31289], X[320] + 2 X[1125], X[6541] + 2 X[24231], X[4716] - 3 X[37756], 3 X[17297] - X[32846], 3 X[17297] + X[32922], 3 X[31151] - X[32850], 3 X[551] - 2 X[1279], X[551] + 2 X[31138], X[1279] + 3 X[31138], 4 X[3246] - 7 X[15808], 7 X[3624] - X[20072], 4 X[3634] - 5 X[31252], X[4432] + 2 X[7238], X[4753] - 4 X[40480]

X(49676) lies on these lines: {1, 2896}, {2, 1757}, {7, 3923}, {10, 141}, {11, 4892}, {31, 29672}, {38, 18139}, {42, 24169}, {44, 5257}, {57, 3771}, {58, 86}, {63, 29642}, {69, 16825}, {75, 33087}, {81, 29654}, {171, 29656}, {226, 1401}, {244, 3936}, {295, 9470}, {306, 24165}, {312, 33103}, {335, 726}, {350, 9505}, {354, 2887}, {386, 25470}, {498, 27305}, {513, 11813}, {516, 24692}, {519, 1738}, {524, 4974}, {527, 24358}, {537, 3932}, {551, 752}, {614, 32946}, {740, 1086}, {748, 32859}, {750, 33122}, {846, 26840}, {894, 24295}, {896, 24542}, {908, 4871}, {940, 26128}, {946, 15310}, {982, 18134}, {984, 17234}, {1001, 4655}, {1015, 18904}, {1266, 28522}, {1386, 17376}, {1621, 33067}, {1647, 31029}, {1698, 27147}, {1914, 4987}, {1999, 33147}, {2239, 43223}, {2550, 49458}, {2796, 3685}, {3006, 17449}, {3008, 34379}, {3120, 29824}, {3178, 3670}, {3218, 29632}, {3219, 29851}, {3244, 3755}, {3246, 15808}, {3315, 32844}, {3337, 25645}, {3475, 29670}, {3616, 17236}, {3624, 17248}, {3634, 17307}, {3663, 3993}, {3681, 25961}, {3703, 42055}, {3720, 4425}, {3726, 4071}, {3741, 5208}, {3742, 3846}, {3750, 33068}, {3751, 17282}, {3757, 33085}, {3773, 17231}, {3778, 3953}, {3790, 49532}, {3831, 13407}, {3837, 6165}, {3842, 17245}, {3873, 25957}, {3879, 49477}, {3914, 42057}, {3943, 28516}, {3957, 32948}, {3976, 41886}, {3980, 33171}, {4000, 49488}, {4011, 5905}, {4026, 48632}, {4028, 24177}, {4038, 19786}, {4062, 17495}, {4078, 49520}, {4085, 49478}, {4138, 11019}, {4310, 4869}, {4358, 21093}, {4359, 21085}, {4368, 20347}, {4388, 29820}, {4392, 29643}, {4398, 49452}, {4414, 29830}, {4416, 17000}, {4417, 17063}, {4418, 26842}, {4422, 5852}, {4423, 4703}, {4429, 49490}, {4430, 33117}, {4432, 7238}, {4434, 17724}, {4439, 28582}, {4519, 48641}, {4527, 4686}, {4649, 16706}, {4663, 17356}, {4667, 38049}, {4672, 17365}, {4683, 5284}, {4702, 17764}, {4710, 20892}, {4715, 19883}, {4743, 49475}, {4753, 40480}, {4851, 32921}, {4860, 30811}, {4865, 17597}, {4887, 28526}, {5220, 17265}, {5224, 40328}, {5524, 26073}, {5625, 17045}, {5712, 29650}, {5880, 32941}, {6682, 17056}, {7191, 32949}, {7226, 29854}, {7292, 32843}, {10453, 17889}, {11038, 36479}, {12053, 33551}, {14829, 33130}, {14996, 29636}, {15254, 17345}, {15523, 17140}, {15569, 17235}, {16020, 21296}, {16468, 17364}, {16484, 24723}, {16597, 34587}, {16823, 17288}, {17018, 33125}, {17023, 20132}, {17031, 30941}, {17122, 33126}, {17123, 33066}, {17126, 29638}, {17127, 29853}, {17146, 31079}, {17155, 32858}, {17165, 29687}, {17227, 32784}, {17232, 24349}, {17233, 49493}, {17241, 49447}, {17242, 49445}, {17243, 49456}, {17279, 32935}, {17283, 33159}, {17291, 29633}, {17311, 49453}, {17355, 43180}, {17366, 49489}, {17374, 17772}, {17379, 26150}, {17381, 25539}, {17483, 32930}, {17596, 29839}, {17598, 33073}, {17733, 24159}, {17748, 24046}, {17763, 33148}, {17778, 29821}, {18141, 29649}, {18201, 32851}, {18743, 33101}, {19717, 29684}, {19804, 33084}, {19878, 31311}, {20292, 32943}, {20337, 20546}, {20363, 36217}, {21077, 46827}, {21081, 24176}, {21241, 26015}, {21629, 43177}, {21805, 24988}, {23537, 35633}, {23681, 39594}, {23812, 32772}, {23958, 29866}, {24241, 30962}, {24331, 38053}, {24342, 26806}, {24470, 24850}, {24627, 29640}, {24628, 26629}, {24691, 25353}, {24789, 32853}, {25385, 30942}, {25521, 26363}, {25527, 29635}, {25959, 33120}, {26034, 29651}, {26098, 29668}, {26102, 27184}, {26223, 29677}, {26580, 30950}, {26724, 32864}, {27003, 29846}, {27186, 31330}, {28288, 29964}, {28403, 30034}, {29634, 37604}, {29658, 37684}, {29814, 32776}, {29817, 32947}, {29852, 37685}, {30109, 40857}, {30117, 38456}, {30957, 31053}, {32771, 33172}, {32775, 37633}, {32863, 32914}, {32915, 33146}, {32919, 33129}, {32923, 33078}, {32939, 33158}, {32940, 33157}, {32942, 33097}, {33149, 48629}, {33165, 49499}, {38024, 48851}, {38989, 46842}, {48627, 49474}, {48631, 49471}, {49464, 49476}

X(49676) = complement of X(1757)
X(49676) = midpoint of X(i) and X(j) for these {i,j}: {1, 4645}, {238, 320}, {1086, 4966}, {1738, 4684}, {3685, 32857}, {3912, 24231}, {32846, 32922}
X(49676) = reflection of X(i) in X(j) for these {i,j}: {10, 3836}, {44, 31289}, {238, 1125}, {3244, 4864}, {3836, 3834}, {6541, 3912}
X(49676) = complement of the isogonal conjugate of X(1929)
X(49676) = complement of the isotomic conjugate of X(18032)
X(49676) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 6651}, {81, 20529}, {86, 20339}, {274, 20548}, {512, 41180}, {514, 46668}, {649, 35080}, {1929, 10}, {2054, 1213}, {2702, 514}, {6650, 141}, {9278, 1211}, {9505, 3836}, {9506, 3912}, {11599, 3454}, {17930, 512}, {17940, 523}, {17962, 2}, {17972, 3}, {17982, 5}, {18001, 115}, {18014, 125}, {18032, 2887}, {35148, 3835}, {37135, 513}, {40725, 20333}, {40767, 17793}
X(49676) = X(4589)-Ceva conjugate of X(514)
X(49676) = crosspoint of X(i) and X(j) for these (i,j): {2, 18032}, {86, 335}
X(49676) = crosssum of X(i) and X(j) for these (i,j): {6, 18266}, {42, 1914}
X(49676) = crossdifference of every pair of points on line {4079, 21007}
X(49676) = barycentric product X(1509)*X(21718)
X(49676) = barycentric quotient X(21718)/X(594)
X(49676) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3662, 3821}, {2, 33069, 33064}, {10, 5542, 49479}, {10, 49504, 24393}, {10, 49505, 49510}, {10, 49535, 49529}, {38, 18139, 29653}, {81, 33123, 29654}, {141, 24325, 10}, {141, 25557, 24325}, {142, 49511, 10}, {171, 33124, 29656}, {354, 2887, 29655}, {894, 29637, 24295}, {908, 4871, 11814}, {940, 26128, 29645}, {982, 18134, 29671}, {1001, 7232, 4655}, {1125, 3664, 33682}, {1125, 4357, 25354}, {3720, 17184, 4425}, {3739, 3775, 10}, {3826, 49457, 10}, {3873, 25957, 29673}, {4358, 32856, 21093}, {4359, 33081, 21085}, {5542, 21255, 10}, {16823, 17288, 33082}, {17231, 49483, 3773}, {17232, 24349, 29674}, {17297, 32922, 32846}, {17379, 26150, 29646}, {18141, 33144, 29649}, {26842, 33173, 4418}, {30942, 31019, 25385}, {48629, 49470, 33149}


X(49677) = X(1)X(3823)∩X(8)X(238)

Barycentrics    3*a^3 - 4*a^2*b + 4*a*b^2 - 2*b^3 - 4*a^2*c + a*b*c + 4*a*c^2 - 2*c^3 : :
X(49677) = 3 X[1] - 4 X[3823], 4 X[1] - 5 X[31252], 16 X[3823] - 15 X[31252], 2 X[44] - 5 X[4816], 3 X[31151] - 4 X[32850], 2 X[1279] - 3 X[3679], X[1757] - 3 X[4677], 5 X[3617] - 4 X[31289]

X(49677) lies on these lines: {1, 3823}, {8, 238}, {44, 4007}, {145, 3836}, {518, 3632}, {519, 1738}, {594, 16786}, {752, 31145}, {1279, 3679}, {1757, 4677}, {3617, 31289}, {3621, 4645}, {3625, 17766}, {3633, 4864}, {3944, 4952}, {4693, 5853}, {4929, 49517}, {5014, 33065}, {9041, 32857}, {12645, 15310}, {20011, 30969}

X(49677) = midpoint of X(3621) and X(4645)
vreflection of X(i) in X(j) for these {i,j}: {145, 3836}, {238, 8}, {3633, 4864}


X(49678) = X(1)X(3696)∩X(2)X(4457)

Barycentrics    4*a^2*b - a*b^2 + 4*a^2*c + a*b*c - 2*b^2*c - a*c^2 - 2*b*c^2 : :
X(49678) = 3 X[1] - 2 X[3696], 5 X[1] - 4 X[3739], 6 X[1] - 5 X[40328], 5 X[3696] - 6 X[3739], 4 X[3696] - 5 X[40328], 4 X[3696] - 3 X[49459], X[3696] - 3 X[49475], 24 X[3739] - 25 X[40328], 8 X[3739] - 5 X[49459], 2 X[3739] - 5 X[49475], 5 X[40328] - 3 X[49459], 5 X[40328] - 12 X[49475], X[49459] - 4 X[49475], 3 X[8] - 4 X[3842], 5 X[8] - 7 X[27268], 20 X[3842] - 21 X[27268], 2 X[3842] - 3 X[49471], 7 X[27268] - 10 X[49471], 5 X[145] - X[1278], 3 X[145] - X[24349], 5 X[145] - 2 X[49491], 4 X[145] - X[49493], 3 X[1278] - 5 X[24349], 2 X[1278] - 5 X[49490], 4 X[1278] - 5 X[49493], 2 X[24349] - 3 X[49490], 5 X[24349] - 6 X[49491], 4 X[24349] - 3 X[49493], 5 X[49490] - 4 X[49491], 8 X[49491] - 5 X[49493], 2 X[20050] + X[49503], 5 X[3633] + 2 X[4718], 3 X[3633] + X[49445], 2 X[3633] + X[49452], 3 X[3633] + 2 X[49461], 4 X[3633] + X[49517], 7 X[3633] + 2 X[49522], 6 X[4718] - 5 X[49445], 4 X[4718] - 5 X[49452], 3 X[4718] - 5 X[49461], 2 X[4718] - 5 X[49469], 8 X[4718] - 5 X[49517], 7 X[4718] - 5 X[49522], 2 X[49445] - 3 X[49452], X[49445] - 3 X[49469], 4 X[49445] - 3 X[49517], 7 X[49445] - 6 X[49522], 3 X[49452] - 4 X[49461], 7 X[49452] - 4 X[49522], 2 X[49461] - 3 X[49469], 8 X[49461] - 3 X[49517], 7 X[49461] - 3 X[49522], 4 X[49469] - X[49517], 7 X[49469] - 2 X[49522], 7 X[49517] - 8 X[49522], 3 X[984] - 4 X[3993], 5 X[984] - 6 X[4664], 3 X[984] - 2 X[49450], 5 X[984] - 4 X[49510], 10 X[3993] - 9 X[4664], 2 X[3993] - 3 X[49470], 5 X[3993] - 3 X[49510], 9 X[4664] - 5 X[49450], 3 X[4664] - 5 X[49470], 3 X[4664] - 2 X[49510], X[49450] - 3 X[49470], 5 X[49450] - 6 X[49510], 5 X[49470] - 2 X[49510], 3 X[34747] - X[49498], 3 X[3241] - 2 X[24325], 5 X[3616] - 4 X[4732], 4 X[3626] - 5 X[4687], 8 X[3636] - 7 X[4751], 3 X[3679] - 4 X[15569], 3 X[27474] - 4 X[49473], 5 X[4699] - 7 X[20057], 5 X[4704] - X[20054], X[20014] + 2 X[49456], 3 X[20049] + X[31302], 3 X[31178] - 2 X[49474], 3 X[31178] - 4 X[49478]

X(49678) lies on these lines: {1, 3696}, {2, 4457}, {8, 3842}, {10, 17240}, {37, 3632}, {75, 3244}, {145, 740}, {192, 20050}, {238, 49495}, {518, 3633}, {519, 751}, {536, 34747}, {982, 3896}, {3187, 17715}, {3241, 24325}, {3616, 4732}, {3621, 49457}, {3626, 4687}, {3635, 4709}, {3636, 4751}, {3662, 4743}, {3679, 15569}, {3685, 49497}, {3706, 42042}, {3750, 17156}, {3751, 4693}, {3755, 33087}, {3886, 4649}, {3952, 20011}, {4028, 33141}, {4360, 49458}, {4384, 31342}, {4393, 27474}, {4684, 4780}, {4699, 20057}, {4702, 16468}, {4704, 20054}, {4891, 16569}, {4910, 49481}, {7201, 10944}, {17063, 42057}, {17135, 17592}, {17364, 17764}, {17377, 17766}, {17601, 32919}, {17769, 49507}, {20014, 49456}, {20048, 21805}, {20049, 31302}, {24440, 35633}, {28234, 30273}, {28484, 49532}, {28522, 49499}, {29649, 43290}, {31178, 49474}, {49448, 49462}

X(49678) = midpoint of X(i) and X(j) for these {i,j}: {192, 20050}, {3633, 49469}
X(49678) = reflection of X(i) in X(j) for these {i,j}: {1, 49475}, {8, 49471}, {75, 3244}, {984, 49470}, {1278, 49491}, {3621, 49457}, {3632, 37}, {4709, 3635}, {49445, 49461}, {49448, 49462}, {49450, 3993}, {49452, 49469}, {49459, 1}, {49474, 49478}, {49490, 145}, {49493, 49490}, {49503, 192}, {49517, 49452}
X(49678) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3696, 40328}, {3993, 49450, 984}, {4664, 49510, 984}, {4684, 4780, 33149}, {40328, 49459, 3696}, {49445, 49461, 49452}, {49445, 49469, 49461}, {49450, 49470, 3993}, {49474, 49478, 31178}


X(49679) = X(6)X(519)∩X(69)X(145)

Barycentrics    5*a^3 - a^2*b + 4*a*b^2 - 2*b^3 - a^2*c - 2*b^2*c + 4*a*c^2 - 2*b*c^2 - 2*c^3 : :
X(49679) = 6 X[1] - 5 X[3763], 5 X[1] - 4 X[3844], 25 X[3763] - 24 X[3844], 7 X[6] - 6 X[47359], 5 X[6] - 4 X[49529], 15 X[47359] - 14 X[49529], 3 X[48804] - 4 X[48866], 3 X[8] - 4 X[3589], 2 X[8] - 3 X[38315], 8 X[3589] - 9 X[38315], X[69] - 3 X[145], 2 X[69] - 3 X[3242], 2 X[141] - 3 X[3241], X[193] + 3 X[20049], 6 X[3633] + X[6144], 3 X[599] - 4 X[49465], 3 X[944] - 2 X[48881], 3 X[1482] - 2 X[3818], 5 X[3618] - 3 X[31145], 10 X[3618] - 9 X[38087], 2 X[31145] - 3 X[38087], 2 X[3625] - 3 X[38047], 2 X[3629] + 3 X[20050], 6 X[3679] - 7 X[47355], 3 X[4677] - 5 X[16491], 2 X[4677] - 3 X[47352], 10 X[16491] - 9 X[47352], 2 X[4701] - 3 X[38049], 4 X[5092] - 3 X[34718], 4 X[5882] - 3 X[31884], 4 X[10222] - 3 X[10516], 2 X[12645] - 3 X[38144], 3 X[12702] - 4 X[48892], 3 X[15533] - 4 X[49505], X[16496] - 3 X[34747], 6 X[34747] - X[40341], 3 X[18525] - 4 X[48895], X[33878] - 3 X[34748], 8 X[34573] - 9 X[38314], 2 X[34641] - 3 X[38023], 3 X[38035] - 2 X[47745], X[47276] - 4 X[47537], X[47279] - 3 X[47535], 2 X[47449] - 3 X[47493], 3 X[47450] - 4 X[47491], 5 X[47452] - 6 X[47472], 5 X[47453] - 4 X[47492], 4 X[47454] - 3 X[47494], 3 X[47455] - 2 X[47490], 5 X[47456] - 3 X[47531], 3 X[48800] - 4 X[48843], 3 X[48829] - 4 X[49472]

X(49679) lies on these lines: {1, 3763}, {6, 519}, {8, 3589}, {69, 145}, {141, 3241}, {193, 9041}, {517, 48905}, {518, 3633}, {599, 49465}, {944, 48881}, {952, 31670}, {1213, 48856}, {1350, 37727}, {1386, 3632}, {1482, 3818}, {2916, 37546}, {3052, 3977}, {3244, 3416}, {3618, 31145}, {3621, 49524}, {3625, 38047}, {3629, 9053}, {3679, 47355}, {3891, 21282}, {3913, 5096}, {4265, 12513}, {4445, 36534}, {4677, 16491}, {4701, 38049}, {5092, 34718}, {5220, 49534}, {5695, 17769}, {5844, 48906}, {5882, 31884}, {7982, 36990}, {10222, 10516}, {10387, 37740}, {12595, 41575}, {12645, 38144}, {12702, 48892}, {14839, 41747}, {15533, 49505}, {16487, 41310}, {16496, 28538}, {16884, 36479}, {17267, 32847}, {17325, 33076}, {17398, 48849}, {17765, 49486}, {17766, 49453}, {18525, 48895}, {20045, 30834}, {28204, 48910}, {28566, 49446}, {32113, 47489}, {33878, 34748}, {34573, 38314}, {34641, 38023}, {38035, 47745}, {47276, 47537}, {47279, 47535}, {47449, 47493}, {47450, 47491}, {47452, 47472}, {47453, 47492}, {47454, 47494}, {47455, 47490}, {47456, 47531}, {47457, 47533}, {48800, 48843}, {48829, 49472}, {49475, 49509}

X(49679) = reflection of X(i) in X(j) for these {i,j}: {1350, 37727}, {3242, 145}, {3416, 3244}, {3621, 49524}, {3632, 1386}, {32113, 47489}, {36990, 7982}, {40341, 16496}, {47533, 47457}, {49509, 49475}
X(49679) = crossdifference of every pair of points on line {9002, 39521}


X(49680) = X(6)X(519)∩X(8)X(86)

Barycentrics    a^3 + 5*a^2*b - 2*a*b^2 + 5*a^2*c - 2*b^2*c - 2*a*c^2 - 2*b*c^2 : :
X(49680) = 3 X[6] - 2 X[32941], 4 X[6] - 3 X[48805], 5 X[6] - 4 X[49482], 2 X[2321] - 3 X[47359], 8 X[32941] - 9 X[48805], 4 X[32941] - 3 X[49460], 5 X[32941] - 6 X[49482], X[32941] - 3 X[49497], 3 X[48805] - 2 X[49460], 15 X[48805] - 16 X[49482], 3 X[48805] - 8 X[49497], 5 X[49460] - 8 X[49482], X[49460] - 4 X[49497], 2 X[49482] - 5 X[49497], 2 X[69] - 3 X[48829], 5 X[3875] - 3 X[49446], 4 X[3875] - 3 X[49453], 2 X[3875] - 3 X[49486], X[3875] - 3 X[49495], 4 X[49446] - 5 X[49453], 2 X[49446] - 5 X[49486], X[49446] - 5 X[49495], X[49453] - 4 X[49495], 3 X[599] - 4 X[4085], 3 X[3242] - 4 X[49472], 2 X[49472] - 3 X[49488], 5 X[3620] - 6 X[48821], 3 X[3679] - 2 X[17372], 3 X[3751] - 2 X[17351], 3 X[5695] - 4 X[17351], 4 X[3946] - 3 X[47358], 3 X[16475] - 2 X[49467], 3 X[16834] - 2 X[49465], 3 X[17301] - 2 X[49505], 3 X[38315] - 2 X[49458], 3 X[38315] - 4 X[49489], 3 X[48801] - 4 X[48847]

X(49680) lies on these lines: {1, 4698}, {6, 519}, {8, 86}, {9, 49475}, {10, 17311}, {42, 37660}, {45, 49471}, {55, 16704}, {69, 48829}, {100, 20048}, {145, 1001}, {193, 528}, {238, 3633}, {239, 27475}, {518, 3875}, {599, 4085}, {752, 6144}, {1120, 20037}, {1213, 48830}, {1376, 20012}, {1386, 49451}, {1743, 4702}, {2110, 19994}, {3187, 41711}, {3241, 17277}, {3242, 49472}, {3286, 3913}, {3620, 48821}, {3621, 5263}, {3632, 4649}, {3679, 15668}, {3696, 25590}, {3751, 5695}, {3886, 4663}, {3946, 47358}, {4026, 5232}, {4042, 5235}, {4113, 5287}, {4361, 49490}, {4363, 49459}, {4413, 19998}, {4421, 37683}, {4428, 37652}, {4445, 29659}, {4660, 40341}, {4685, 37674}, {4700, 30331}, {4709, 17118}, {4716, 49498}, {4753, 16885}, {4780, 17276}, {4816, 43997}, {4819, 17740}, {4849, 39594}, {4852, 16496}, {5132, 12513}, {5220, 17261}, {5223, 49462}, {5737, 42042}, {15485, 34747}, {16475, 49467}, {16777, 49457}, {16834, 49465}, {16884, 36480}, {17119, 49479}, {17262, 49469}, {17301, 49505}, {17309, 33165}, {17318, 49448}, {17362, 36479}, {17379, 31145}, {17389, 20154}, {17393, 49450}, {17398, 48802}, {20016, 20172}, {20131, 29617}, {20150, 48850}, {20156, 29574}, {31034, 31140}, {37679, 42057}, {38315, 49458}, {48801, 48847}

X(49680) = reflection of X(i) in X(j) for these {i,j}: {6, 49497}, {3242, 49488}, {3886, 4663}, {5695, 3751}, {16496, 4852}, {17276, 4780}, {17299, 49529}, {40341, 4660}, {49451, 1386}, {49453, 49486}, {49458, 49489}, {49460, 6}, {49486, 49495}
X(49680) = crossdifference of every pair of points on line {4832, 9002}
X(49680) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 49460, 48805}, {49458, 49489, 38315}


X(49681) = X(1)X(141)∩X(6)X(519)

Barycentrics    3*a^3 + 2*a*b^2 - b^3 - b^2*c + 2*a*c^2 - b*c^2 - c^3 : :
X(49681) = 3 X[1] - 2 X[141], 4 X[141] - 3 X[3416], 4 X[6] - 3 X[47359], 3 X[6] - 2 X[49529], 2 X[2321] - 3 X[48805], 3 X[17281] - 4 X[49482], 9 X[47359] - 8 X[49529], 3 X[48824] - 2 X[48863], 3 X[8] - 5 X[3618], 2 X[8] - 3 X[38047], 6 X[1386] - 5 X[3618], 4 X[1386] - 3 X[38047], 10 X[3618] - 9 X[38047], 2 X[10] - 3 X[38315], 6 X[10] - 7 X[47355], 9 X[38315] - 7 X[47355], X[69] - 3 X[3241], 2 X[69] - 3 X[47358], 3 X[3241] - 2 X[49465], 3 X[47358] - 4 X[49465], 3 X[145] + X[193], 3 X[49470] - X[49502], 3 X[355] - 4 X[19130], 2 X[355] - 3 X[38035], 8 X[19130] - 9 X[38035], 6 X[551] - 5 X[3763], 3 X[1482] - X[18440], 2 X[2550] - 3 X[38046], 2 X[3036] - 3 X[38050], 2 X[3098] - 3 X[3655], 3 X[3242] - X[40341], 3 X[3242] - 2 X[49505], 6 X[3244] - X[40341], 3 X[3244] - X[49505], 4 X[3589] - 3 X[3679], 4 X[3589] - 5 X[16491], 8 X[3589] - 9 X[38023], 3 X[3679] - 5 X[16491], 2 X[3679] - 3 X[38023], 10 X[16491] - 9 X[38023], 5 X[3616] - 4 X[3844], 7 X[3619] - 9 X[38314], 2 X[3626] - 3 X[38049], 2 X[3629] + 3 X[34747], 3 X[3632] - 8 X[6329], X[3632] - 3 X[16475], 8 X[6329] - 9 X[16475], 4 X[6329] - 3 X[49524], 3 X[16475] - 2 X[49524], 3 X[3633] + 4 X[32455], 3 X[3751] - 4 X[32455], 3 X[3654] - 4 X[5092], 3 X[3656] - 2 X[3818], 4 X[3946] - 3 X[48829], 2 X[4660] - 3 X[17301], 3 X[17301] - 4 X[49472], 2 X[4663] + X[20050], 2 X[4669] - 3 X[47352], 2 X[4701] - 3 X[38191], 3 X[5085] - 2 X[11362], 2 X[5690] - 3 X[38029], 3 X[10516] - 4 X[13464], 5 X[12017] - 3 X[34718], 3 X[12699] - 2 X[48884], 3 X[16200] - X[39885], 5 X[17286] - 6 X[48810], 3 X[18481] - 2 X[48880], 6 X[21167] - 7 X[30389], 2 X[24393] - 3 X[38048], 9 X[25055] - 8 X[34573], 3 X[34631] + X[39874], 2 X[34641] - 3 X[38087], 3 X[34748] + X[44456], 3 X[38144] - 2 X[47745], X[47279] - 3 X[47493], X[47280] + 2 X[47537], X[47281] + 3 X[47535], 2 X[47449] - 3 X[47472], 5 X[47452] - 6 X[47495], 4 X[47454] - 3 X[47488], 3 X[47455] - 2 X[47492], 5 X[47456] - 3 X[47494], 5 X[47458] - 2 X[47564], 3 X[47459] - X[47533], 3 X[48819] - 2 X[48835]

X(49681) lies on these lines: {1, 141}, {2, 4914}, {6, 519}, {8, 1386}, {10, 4989}, {69, 3241}, {144, 145}, {210, 20020}, {239, 38186}, {319, 36534}, {344, 3246}, {354, 19993}, {355, 19130}, {511, 37727}, {515, 48910}, {516, 49453}, {517, 46264}, {524, 16496}, {528, 3875}, {551, 3763}, {597, 4677}, {612, 5241}, {740, 49533}, {742, 49490}, {752, 17276}, {952, 21850}, {966, 48856}, {1001, 49476}, {1100, 36479}, {1213, 48854}, {1350, 5882}, {1352, 10222}, {1428, 41687}, {1469, 37738}, {1482, 18440}, {1503, 7982}, {1707, 4884}, {1757, 49534}, {1836, 3891}, {2550, 4402}, {3006, 31229}, {3036, 38050}, {3098, 3655}, {3187, 4863}, {3242, 3244}, {3476, 24471}, {3555, 3827}, {3589, 3679}, {3616, 3844}, {3619, 38314}, {3626, 38049}, {3629, 9041}, {3632, 6329}, {3633, 3751}, {3635, 49511}, {3654, 5092}, {3656, 3818}, {3696, 4371}, {3729, 28503}, {3744, 33088}, {3769, 29840}, {3772, 4865}, {3879, 42871}, {3913, 36741}, {3920, 3966}, {3923, 17769}, {3932, 7290}, {3946, 48829}, {4030, 5256}, {4265, 8666}, {4301, 36990}, {4307, 7222}, {4344, 7229}, {4362, 21242}, {4437, 29605}, {4645, 48629}, {4655, 28512}, {4660, 17301}, {4663, 20050}, {4669, 47352}, {4701, 38191}, {4702, 17314}, {4901, 16469}, {4906, 18141}, {4969, 36404}, {5014, 17150}, {5048, 12589}, {5085, 11362}, {5090, 46026}, {5096, 8715}, {5220, 49527}, {5227, 31393}, {5263, 48628}, {5480, 5881}, {5690, 38029}, {5814, 30145}, {5820, 33895}, {5848, 25416}, {5853, 49486}, {5880, 32922}, {7972, 9024}, {7991, 44882}, {8692, 25101}, {9055, 49469}, {10516, 13464}, {11011, 12588}, {12017, 34718}, {12513, 36740}, {12699, 48884}, {14839, 41622}, {15485, 41313}, {16200, 39885}, {16972, 17362}, {17024, 33078}, {17275, 36480}, {17279, 32847}, {17286, 48810}, {17316, 42819}, {17364, 24841}, {17398, 48851}, {17469, 32777}, {17716, 32866}, {17718, 20045}, {17720, 32844}, {17721, 17763}, {17723, 26227}, {17726, 29828}, {17765, 49488}, {17766, 32921}, {17768, 49446}, {17772, 49458}, {17792, 20037}, {18481, 48880}, {19586, 20044}, {21167, 30389}, {24248, 28566}, {24280, 28555}, {24393, 38048}, {24476, 34791}, {24695, 28582}, {24703, 32926}, {24789, 33072}, {25055, 34573}, {28194, 48905}, {28204, 31670}, {28208, 43621}, {28234, 39870}, {28581, 49531}, {28599, 32774}, {29573, 35227}, {29815, 33075}, {29819, 33074}, {29831, 48647}, {30615, 32911}, {32113, 47491}, {34631, 39874}, {34641, 38087}, {34748, 44456}, {38053, 39567}, {38144, 47745}, {41575, 45728}, {47277, 47536}, {47279, 47493}, {47280, 47537}, {47281, 47535}, {47449, 47472}, {47452, 47495}, {47454, 47488}, {47455, 47492}, {47456, 47494}, {47457, 47490}, {47458, 47564}, {47459, 47533}, {48819, 48835}, {49459, 49481}, {49471, 49509}

X(49681) = midpoint of X(i) and X(j) for these {i,j}: {3633, 3751}, {47277, 47536}
X(49681) = reflection of X(i) in X(j) for these {i,j}: {8, 1386}, {69, 49465}, {1350, 5882}, {1352, 10222}, {3242, 3244}, {3416, 1}, {3632, 49524}, {4655, 49464}, {4660, 49472}, {4677, 597}, {5881, 5480}, {7991, 44882}, {17276, 49455}, {17299, 32941}, {24248, 49463}, {24476, 34791}, {32113, 47491}, {36990, 4301}, {40341, 49505}, {47358, 3241}, {47490, 47457}, {47595, 42871}, {49459, 49481}, {49509, 49471}, {49511, 3635}
X(49681) = crossdifference of every pair of points on line {2483, 9002}
X(49681) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 33076, 4657}, {8, 1386, 38047}, {69, 3241, 49465}, {69, 49465, 47358}, {3242, 40341, 49505}, {3589, 16491, 38023}, {3632, 16475, 49524}, {3679, 16491, 3589}, {4660, 49472, 17301}, {17469, 32854, 32777}, {20045, 33070, 17718}


X(49682) = X(1)X(2)∩X(56)X(24167)

Barycentrics    a*(2*a^3 + 2*b^3 + 2*a*b*c - b^2*c - b*c^2 + 2*c^3) : :
X(49682) = 3 X[1] - X[3938], 3 X[1] + X[49494], 3 X[551] - 2 X[29656], X[3938] + 3 X[49487], 3 X[49487] - X[49494]

X(49682) lies on these lines: {1, 2}, {56, 24167}, {58, 4084}, {80, 33133}, {81, 759}, {171, 3919}, {214, 3752}, {226, 1411}, {517, 49480}, {529, 39544}, {535, 3782}, {758, 4641}, {952, 17061}, {986, 5267}, {996, 32920}, {999, 1324}, {1104, 3878}, {1168, 47056}, {1279, 3898}, {1757, 4525}, {2163, 23958}, {2802, 3744}, {3295, 34868}, {3315, 37602}, {3754, 37539}, {3822, 5724}, {3899, 17127}, {3931, 35016}, {4067, 5247}, {4316, 33102}, {4717, 48863}, {4744, 5429}, {4793, 32945}, {4797, 35103}, {4850, 37525}, {4867, 32911}, {4868, 24929}, {5248, 37614}, {5251, 33761}, {6211, 16200}, {6224, 33150}, {7373, 38903}, {8616, 17461}, {8666, 37549}, {10544, 31737}, {10572, 36250}, {11529, 26934}, {12053, 33177}, {28522, 49530}, {33815, 37522}

X(49682) = midpoint of X(i) and X(j) for these {i,j}: {1, 49487}, {3938, 49494}
X(49682) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3632, 36565}, {1, 3924, 1125}, {1, 15955, 3244}, {1, 19860, 30142}, {1, 28082, 3636}, {1, 30117, 551}, {1, 49494, 3938}, {3938, 29820, 29656}, {3938, 49487, 49494}


X(49683) = X(1)X(2)∩X(19)X(39697)

Barycentrics    2*a^4 + 2*a^3*b + a^2*b^2 + a*b^3 + 2*a^3*c + 2*a^2*b*c - a*b^2*c - b^3*c + a^2*c^2 - a*b*c^2 - 2*b^2*c^2 + a*c^3 - b*c^3 : :
X(49683) = 5 X[3616] - X[20017], 7 X[3622] + X[20046], 5 X[19862] - 4 X[20106], X[4680] - 3 X[33128]

X(49683) lies on these lines: {1, 2}, {19, 39697}, {36, 32924}, {58, 32939}, {321, 48866}, {524, 39544}, {540, 3782}, {596, 1468}, {740, 18805}, {758, 3791}, {993, 32921}, {1104, 2901}, {1386, 9022}, {1724, 3159}, {2975, 43993}, {3210, 4257}, {3759, 18061}, {3875, 37817}, {3879, 26728}, {4065, 5248}, {4234, 17160}, {4360, 4653}, {4574, 16685}, {4680, 33128}, {4717, 49482}, {4852, 24929}, {4974, 10176}, {5247, 24068}, {5251, 32928}, {9895, 34791}, {11357, 16672}, {16418, 17318}, {16474, 32923}, {16974, 21070}, {17119, 19276}, {17200, 33935}, {19785, 48835}, {24176, 37522}

X(49683) = midpoint of X(1) and X(3187)
X(49683) = reflection of X(i) in X(j) for these {i,j}: {10, 40940}, {306, 1125}
X(49683) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 20083, 10}, {17150, 39766, 1}


X(49684) = X(1)X(69)∩X(6)X(519)

Barycentrics    4*a^3 + a^2*b + 2*a*b^2 - b^3 + a^2*c - b^2*c + 2*a*c^2 - b*c^2 - c^3 : :
X(49684) = 3 X[1] - X[69], 2 X[69] - 3 X[49511], 3 X[2] - 5 X[16491], 5 X[6] - 3 X[47359], X[17299] - 3 X[48805], 6 X[47359] - 5 X[49529], X[8] - 3 X[16475], 2 X[8] - 3 X[38191], 3 X[10] - 4 X[3589], 2 X[10] - 3 X[38049], 3 X[1386] - 2 X[3589], 4 X[1386] - 3 X[38049], 8 X[3589] - 9 X[38049], 2 X[141] - 3 X[551], X[193] + 3 X[3241], 3 X[3241] - X[16496], 2 X[355] - 3 X[38146], 3 X[39870] - 2 X[48906], 3 X[3244] + 2 X[3629], 3 X[946] - 2 X[3818], 6 X[1125] - 5 X[3763], 2 X[1125] - 3 X[38315], 3 X[3416] - 5 X[3763], X[3416] - 3 X[38315], 5 X[3763] - 9 X[38315], 3 X[1482] + X[39899], 2 X[2550] - 3 X[38187], 2 X[3036] - 3 X[38197], 3 X[3242] + X[6144], 6 X[3635] + X[6144], 5 X[3618] - 3 X[3679], 10 X[3618] - 9 X[38089], 2 X[3679] - 3 X[38089], 7 X[3619] - 9 X[25055], 5 X[3620] - 9 X[38314], 2 X[3626] - 3 X[38047], 3 X[3654] - 5 X[12017], 3 X[3655] - X[33878], 3 X[3656] - X[18440], 2 X[3828] - 3 X[38023], 6 X[3828] - 7 X[47355], 9 X[38023] - 7 X[47355], 4 X[3844] - 5 X[19862], 3 X[4297] - 2 X[48881], 2 X[4745] - 3 X[47352], 3 X[5085] - 2 X[43174], 3 X[5603] - X[39885], 2 X[5690] - 3 X[38118], 5 X[5734] - X[5921], X[5881] - 3 X[14853], 8 X[6329] - 3 X[34641], 2 X[6684] - 3 X[38029], 2 X[6702] - 3 X[38050], 3 X[7983] + X[45018], X[7991] - 3 X[25406], 7 X[9624] - 5 X[40330], 2 X[9956] - 3 X[38040], 3 X[11224] + X[39878], 3 X[16200] - X[39898], 2 X[17229] - 3 X[48810], 9 X[19883] - 8 X[34573], 2 X[19925] - 3 X[38035], 2 X[24393] - 3 X[38194], 5 X[31399] - 6 X[38317], 3 X[31673] - 4 X[48895], 3 X[31730] - 4 X[48892], X[40341] - 3 X[47358], X[47279] - 3 X[47472], X[47281] + 3 X[47493], 2 X[47449] - 3 X[47495], 4 X[47454] - 3 X[47496], 5 X[47456] - 3 X[47488], 3 X[47459] - X[47490], 4 X[47460] - X[47564], 5 X[47461] - X[47533], 3 X[47463] + X[47536], 2 X[47464] + X[47537]

X(49684) lies on these lines: {1, 69}, {2, 16491}, {6, 519}, {8, 16475}, {10, 1386}, {31, 3977}, {141, 551}, {145, 3685}, {182, 11362}, {193, 3241}, {238, 4078}, {306, 17469}, {355, 38146}, {391, 48856}, {511, 5882}, {515, 31670}, {516, 32921}, {517, 39870}, {518, 3244}, {524, 49465}, {527, 49455}, {528, 4780}, {597, 4669}, {726, 41747}, {742, 4667}, {752, 3663}, {946, 3818}, {966, 48854}, {1125, 3416}, {1351, 37727}, {1352, 13464}, {1428, 4848}, {1449, 36479}, {1482, 39899}, {1503, 4301}, {1757, 49527}, {1770, 43993}, {2550, 38187}, {3011, 30834}, {3036, 38197}, {3187, 21283}, {3242, 3635}, {3246, 17243}, {3555, 34378}, {3564, 10222}, {3616, 17312}, {3618, 3679}, {3619, 25055}, {3620, 38314}, {3625, 49524}, {3626, 38047}, {3654, 12017}, {3655, 33878}, {3656, 18440}, {3686, 16972}, {3687, 17716}, {3717, 16468}, {3744, 4028}, {3755, 17766}, {3769, 24239}, {3791, 4847}, {3821, 28512}, {3827, 3874}, {3828, 38023}, {3844, 19862}, {3875, 28580}, {3881, 24476}, {3891, 41011}, {3914, 17150}, {3920, 4104}, {3946, 4660}, {3950, 4432}, {4034, 48802}, {4035, 29656}, {4133, 49484}, {4138, 17061}, {4260, 12437}, {4297, 48881}, {4307, 31995}, {4315, 24471}, {4344, 32087}, {4349, 24325}, {4353, 4655}, {4464, 49469}, {4480, 49517}, {4649, 49466}, {4663, 9053}, {4672, 17769}, {4700, 36404}, {4702, 17388}, {4709, 49481}, {4745, 47352}, {4865, 40940}, {4899, 49534}, {4971, 49485}, {5048, 39873}, {5085, 43174}, {5138, 24391}, {5263, 5564}, {5294, 32854}, {5493, 44882}, {5603, 39885}, {5690, 38118}, {5734, 5921}, {5853, 49488}, {5881, 14853}, {6329, 34641}, {6684, 38029}, {6702, 38050}, {6776, 7982}, {7321, 32922}, {7972, 10755}, {7983, 45018}, {7991, 25406}, {8666, 36740}, {8692, 41313}, {8715, 36741}, {9001, 48285}, {9024, 33337}, {9041, 32455}, {9589, 14927}, {9624, 40330}, {9956, 38040}, {11011, 39897}, {11224, 39878}, {12329, 25439}, {12513, 37492}, {15178, 48876}, {15953, 18170}, {16200, 39898}, {16484, 29574}, {16487, 29573}, {17023, 33076}, {17229, 48810}, {17351, 28503}, {17353, 32847}, {17363, 36534}, {17390, 42819}, {17398, 48853}, {17765, 49489}, {17768, 49463}, {17770, 49464}, {17772, 49473}, {19883, 34573}, {19925, 38035}, {21850, 28204}, {24216, 37684}, {24393, 38194}, {24695, 49446}, {25415, 39901}, {26723, 33072}, {28194, 46264}, {28526, 49453}, {30323, 39900}, {31399, 38317}, {31673, 48895}, {31730, 48892}, {32848, 35263}, {34381, 34791}, {37676, 42057}, {40341, 47358}, {47277, 47489}, {47279, 47472}, {47281, 47493}, {47449, 47495}, {47454, 47496}, {47456, 47488}, {47457, 47492}, {47459, 47490}, {47460, 47564}, {47461, 47533}, {47463, 47536}, {47464, 47537}, {49490, 49496}

X(49684) = midpoint of X(i) and X(j) for these {i,j}: {145, 3751}, {193, 16496}, {1351, 37727}, {6776, 7982}, {7972, 10755}, {9589, 14927}, {24695, 49446}, {47277, 47489}, {49490, 49496}
X(49684) = reflection of X(i) in X(j) for these {i,j}: {10, 1386}, {1352, 13464}, {2321, 49482}, {3242, 3635}, {3416, 1125}, {3625, 49524}, {3663, 49472}, {3755, 49477}, {4133, 49484}, {4655, 4353}, {4660, 3946}, {4669, 597}, {4709, 49481}, {4780, 4852}, {5493, 44882}, {11362, 182}, {24476, 3881}, {38191, 16475}, {47492, 47457}, {48876, 15178}, {49497, 4856}, {49505, 49465}, {49511, 1}, {49529, 6}, {49536, 4663}
X(49684) = crossdifference of every pair of points on line {2484, 9002}
X(49684) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 1386, 38049}, {193, 3241, 16496}, {238, 49476, 4078}, {3244, 30331, 49471}, {3416, 38315, 1125}


X(49685) = X(6)X(519)∩X(10)X(86)

Barycentrics    2*a^3 + 4*a^2*b - a*b^2 + 4*a^2*c - b^2*c - a*c^2 - b*c^2 : :
X(49685) = 3 X[6] - X[32941], 7 X[6] - 3 X[48805], 5 X[6] - X[49460], 7 X[32941] - 9 X[48805], 5 X[32941] - 3 X[49460], 2 X[32941] - 3 X[49482], X[32941] + 3 X[49497], 15 X[48805] - 7 X[49460], 6 X[48805] - 7 X[49482], 3 X[48805] + 7 X[49497], 2 X[49460] - 5 X[49482], X[49460] + 5 X[49497], X[49482] + 2 X[49497], 3 X[49464] - 4 X[49472], X[49464] - 4 X[49489], 2 X[49472] - 3 X[49477], X[49472] - 3 X[49489], 3 X[3751] + X[3875], X[3875] - 3 X[49488], 3 X[4663] - X[17351], X[3630] - 3 X[48821], X[6144] + 3 X[48829], 3 X[16475] - X[49458], 3 X[16834] - X[49455]

X(49685) lies on these lines: {1, 4991}, {6, 519}, {8, 33682}, {10, 86}, {37, 4753}, {42, 16704}, {43, 37684}, {44, 49471}, {81, 4685}, {100, 4946}, {145, 16468}, {193, 4660}, {238, 3244}, {239, 27478}, {391, 48830}, {516, 1351}, {518, 49464}, {524, 4085}, {528, 32455}, {537, 4852}, {551, 17277}, {726, 3751}, {740, 4663}, {752, 3629}, {894, 4709}, {966, 48822}, {984, 17393}, {1001, 3635}, {1100, 49457}, {1125, 17259}, {1449, 36480}, {1698, 17312}, {1743, 4759}, {1757, 3993}, {1992, 28562}, {1999, 4090}, {2308, 20011}, {2796, 4780}, {3214, 18792}, {3241, 15485}, {3617, 43997}, {3625, 5263}, {3630, 48821}, {3679, 17379}, {3755, 17770}, {3758, 49459}, {3759, 49490}, {3780, 21760}, {3821, 34379}, {3828, 15668}, {3896, 4722}, {3923, 49495}, {4360, 49520}, {4393, 49448}, {4407, 17045}, {4432, 16669}, {4434, 21870}, {4439, 17388}, {4651, 26860}, {4669, 46922}, {4670, 4732}, {4672, 28581}, {4702, 16671}, {4743, 17768}, {4938, 48647}, {4970, 32912}, {4974, 49478}, {5235, 32864}, {5882, 37510}, {6144, 48829}, {6685, 32853}, {8666, 37502}, {8715, 37507}, {10056, 27317}, {10164, 46822}, {14459, 33170}, {16475, 49458}, {16801, 25101}, {16834, 49455}, {17287, 36478}, {17350, 49469}, {17363, 29659}, {17364, 24692}, {17376, 25351}, {17377, 33165}, {17389, 20158}, {17772, 49524}, {20086, 32948}, {20142, 29574}, {20145, 29617}, {20992, 25439}, {21241, 31034}, {24695, 28550}, {25390, 25694}, {28522, 32935}, {32911, 42057}, {32922, 49535}, {36598, 39969}, {37474, 43174}, {37652, 42042}, {37683, 42043}

X(49685) = midpoint of X(i) and X(j) for these {i,j}: {6, 49497}, {193, 4660}, {3244, 4924}, {3751, 49488}, {3923, 49495}, {32935, 49486}
X(49685) = reflection of X(i) in X(j) for these {i,j}: {1, 4991}, {49464, 49477}, {49477, 49489}, {49482, 6}
X(49685) = {X(16669),X(49475)}-harmonic conjugate of X(4432)


X(49686) = X(1)X(2)∩X(238)X(4134)

Barycentrics    a*(2*a^3 + 2*b^3 - 2*a*b*c + b^2*c + b*c^2 + 2*c^3) : :
X(49686) = 3 X[1] - X[49487], 5 X[1] - X[49494], 3 X[3938] + X[49487], 5 X[3938] + X[49494], 5 X[49487] - 3 X[49494], X[4680] - 3 X[33122]

X(49686) lies on these lines: {1, 2}, {238, 4134}, {518, 49480}, {528, 39544}, {595, 4067}, {758, 3744}, {993, 3242}, {1279, 10176}, {1376, 24168}, {3295, 23850}, {3583, 33153}, {3722, 4424}, {3822, 17724}, {3874, 5266}, {3881, 37539}, {3892, 4864}, {3894, 17126}, {4084, 5255}, {4125, 32927}, {4234, 24841}, {4256, 17598}, {4342, 45272}, {4392, 5010}, {4680, 33122}, {4717, 32941}, {4973, 21342}, {8715, 37549}, {16496, 37817}, {22012, 49482}, {24167, 25440}, {24929, 49465}, {32920, 48863}, {33095, 34649}, {37610, 49454}

X(49686) = midpoint of X(i) and X(j) for these {i,j}: {1, 3938}, {37610, 49454}
X(49686) = reflection of X(i) in X(j) for these {i,j}: {10, 29656}, {29673, 1125}
X(49686) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 78, 30148}, {1, 976, 1125}, {1, 3961, 30117}, {1, 5313, 17024}, {1, 30115, 551}, {3961, 30117, 10}, {21342, 37589, 4973}


X(49687) = X(1)X(2)∩X(30)X(32859)

Barycentrics    a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3 - 2*a^3*c - 2*a^2*b*c + a*b^2*c + b^3*c - a^2*c^2 + a*b*c^2 + 2*b^2*c^2 + 2*a*c^3 + b*c^3 : :
X(49687) = 5 X[3616] - 4 X[40940], 5 X[3623] - X[20046], 7 X[9780] - 8 X[20106]

X(49687) lies on these lines: {1, 2}, {30, 32859}, {44, 11346}, {75, 4720}, {320, 17579}, {322, 1320}, {518, 49492}, {740, 37003}, {758, 32929}, {950, 4101}, {1043, 3868}, {1150, 24929}, {1441, 2099}, {2897, 6224}, {3242, 9022}, {3419, 3936}, {3488, 5739}, {3696, 44840}, {3702, 12635}, {3940, 4358}, {4001, 4304}, {4359, 15934}, {4702, 31165}, {4742, 5289}, {5016, 41014}, {5722, 5741}, {9317, 17296}, {9963, 17361}, {11114, 33066}, {12559, 17164}, {16371, 24593}, {16704, 37817}, {16861, 17335}, {17184, 48837}, {18655, 21296}, {19336, 37520}, {20896, 34195}, {26223, 48863}, {32774, 48847}, {49470, 49512}

X(49687) = midpoint of X(145) and X(20017)
X(49687) = reflection of X(i) in X(j) for these {i,j}: {8, 306}, {3187, 1}
X(49687) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17156, 39766}, {2099, 49460, 3902}


X(49688) = X(6)X(519)∩X(7)X(8)

Barycentrics    a^3 - 2*a^2*b + 2*a*b^2 - b^3 - 2*a^2*c - b^2*c + 2*a*c^2 - b*c^2 - c^3 : :
X(49688) = 3 X[1] - 4 X[3589], 2 X[1] - 3 X[38047], 8 X[3589] - 9 X[38047], 2 X[3589] - 3 X[49524], 3 X[38047] - 4 X[49524], 2 X[6] - 3 X[47359], 3 X[17281] - 2 X[32941], 4 X[17355] - 3 X[48805], 3 X[47359] - 4 X[49529], 3 X[48824] - 4 X[48866], 3 X[8] - X[69], 2 X[69] - 3 X[3416], 6 X[10] - 5 X[3763], 3 X[3242] - 5 X[3763], 3 X[40] - 2 X[48881], 2 X[141] - 3 X[3679], 4 X[141] - 3 X[47358], 3 X[3679] - X[16496], 2 X[16496] - 3 X[47358], X[193] + 3 X[31145], 3 X[355] - 2 X[3818], 2 X[551] - 3 X[38087], 6 X[551] - 7 X[47355], 9 X[38087] - 7 X[47355], 6 X[597] - 5 X[16491], 3 X[599] - 2 X[49505], 3 X[4669] - X[49505], 2 X[946] - 3 X[38144], 2 X[1001] - 3 X[38190], 2 X[1125] - 3 X[38191], 2 X[1385] - 3 X[38116], 2 X[1387] - 3 X[38192], 2 X[1482] - 3 X[38035], 2 X[1483] - 3 X[38029], 2 X[3098] - 3 X[3654], 3 X[3241] - 5 X[3618], 2 X[3241] - 3 X[38023], 10 X[3618] - 9 X[38023], 2 X[3243] - 3 X[38046], 2 X[3244] - 3 X[38315], 5 X[3617] - 4 X[3844], X[3621] + 2 X[4663], 6 X[3625] + X[6144], X[6144] - 6 X[49536], 2 X[3629] + 3 X[3632], 2 X[3629] - 3 X[3751], X[3633] - 3 X[16475], 2 X[3635] - 3 X[38049], 3 X[3655] - 4 X[5092], 3 X[3656] - 4 X[19130], 2 X[3663] - 3 X[48829], 3 X[38186] - 2 X[42871], 4 X[4085] - 3 X[17301], 3 X[17301] - 2 X[49455], 4 X[4745] - 3 X[21358], 3 X[5085] - 2 X[5882], 2 X[5542] - 3 X[38185], 2 X[5901] - 3 X[38165], 8 X[6329] - 3 X[34747], 7 X[9588] - 6 X[21167], 2 X[10222] - 3 X[14561], 3 X[12645] + X[39899], 3 X[12699] - 4 X[48895], 2 X[13607] - 3 X[38118], 5 X[17304] - 6 X[48821], 3 X[18481] - 4 X[48892], 9 X[19875] - 8 X[34573], 3 X[31884] - 4 X[43174], 2 X[33179] - 3 X[38167], X[33878] - 3 X[34718], 6 X[34641] - X[40341], 2 X[37737] - 3 X[38193], 3 X[38194] - 2 X[43179], X[47279] - 3 X[47494], X[47280] + 2 X[47564], X[47281] + 3 X[47531], 2 X[47449] - 3 X[47488], 5 X[47452] - 6 X[47496], 4 X[47454] - 3 X[47472], 3 X[47455] - 2 X[47491], 5 X[47456] - 3 X[47493], 5 X[47458] - 2 X[47537], 3 X[47459] - X[47536], 3 X[48819] - 4 X[48843]

X(49688) lies on these lines: {1, 3589}, {2, 4906}, {6, 519}, {7, 8}, {10, 3242}, {37, 36479}, {40, 48881}, {55, 3977}, {63, 4030}, {72, 43726}, {141, 3679}, {145, 1386}, {182, 37727}, {193, 28538}, {306, 41711}, {321, 4863}, {344, 42819}, {346, 4702}, {354, 10327}, {355, 3818}, {497, 3967}, {515, 48905}, {517, 31670}, {524, 4677}, {528, 3729}, {537, 4660}, {551, 38087}, {594, 16973}, {597, 16491}, {599, 4669}, {730, 41747}, {742, 49459}, {946, 38144}, {952, 16799}, {956, 12329}, {966, 48849}, {1001, 3717}, {1125, 38191}, {1213, 48851}, {1350, 11362}, {1385, 38116}, {1387, 38192}, {1411, 3872}, {1428, 37738}, {1482, 38035}, {1483, 38029}, {1503, 5881}, {1654, 49502}, {1757, 49506}, {1836, 5014}, {1837, 4696}, {2325, 30331}, {2330, 37740}, {3006, 17718}, {3056, 28597}, {3098, 3654}, {3161, 47357}, {3241, 3618}, {3243, 4966}, {3244, 38315}, {3246, 26685}, {3303, 3710}, {3305, 4126}, {3419, 4692}, {3616, 17341}, {3617, 3844}, {3621, 4663}, {3625, 5847}, {3626, 49511}, {3629, 3632}, {3633, 16475}, {3635, 38049}, {3655, 5092}, {3656, 19130}, {3661, 32029}, {3662, 24841}, {3663, 48829}, {3681, 3966}, {3689, 17740}, {3703, 3870}, {3704, 6765}, {3722, 33161}, {3723, 48830}, {3744, 33163}, {3745, 20020}, {3748, 17776}, {3749, 44416}, {3755, 49453}, {3769, 20056}, {3772, 29673}, {3773, 49458}, {3827, 10914}, {3873, 33091}, {3875, 28503}, {3883, 4899}, {3912, 38186}, {3913, 36740}, {3923, 17765}, {3935, 33089}, {3938, 32777}, {3943, 36404}, {3952, 4679}, {3957, 32862}, {3961, 4952}, {3974, 36845}, {3979, 33092}, {4026, 4929}, {4054, 31140}, {4085, 17301}, {4265, 8715}, {4384, 4437}, {4419, 49513}, {4430, 33078}, {4514, 24703}, {4643, 9055}, {4657, 29659}, {4659, 5845}, {4661, 33075}, {4675, 49479}, {4701, 34379}, {4720, 41610}, {4737, 21290}, {4745, 21358}, {4847, 37695}, {4851, 32847}, {4884, 17594}, {4914, 5739}, {5085, 5882}, {5096, 8666}, {5423, 26105}, {5480, 7982}, {5493, 48872}, {5542, 38185}, {5687, 22769}, {5695, 5853}, {5901, 38165}, {5903, 9021}, {6329, 34747}, {6646, 49501}, {7046, 37790}, {7172, 24477}, {7991, 29181}, {8197, 12453}, {8204, 12452}, {9037, 25304}, {9049, 10477}, {9588, 21167}, {10005, 38057}, {10222, 14561}, {12513, 36741}, {12645, 39899}, {12699, 48895}, {13607, 38118}, {15254, 27549}, {16484, 41313}, {16972, 17388}, {17264, 38088}, {17275, 49457}, {17289, 36534}, {17303, 36480}, {17304, 48821}, {17314, 49475}, {17398, 48854}, {17715, 33164}, {17720, 32927}, {17721, 32931}, {17723, 29832}, {17724, 29857}, {17725, 29861}, {17766, 32935}, {17769, 49488}, {18481, 48892}, {19133, 49492}, {19586, 20352}, {19875, 34573}, {20045, 33114}, {20068, 32950}, {24248, 28582}, {24695, 28566}, {24715, 49532}, {24723, 31302}, {24789, 32923}, {26300, 49330}, {26301, 49329}, {28194, 48910}, {28198, 43621}, {28204, 46264}, {28599, 32859}, {31079, 33122}, {31161, 33104}, {31395, 35552}, {31884, 43174}, {32113, 47492}, {32846, 49498}, {33082, 49503}, {33179, 38167}, {33878, 34718}, {34641, 40341}, {37737, 38193}, {38053, 39570}, {38194, 43179}, {47277, 47533}, {47279, 47494}, {47280, 47564}, {47281, 47531}, {47449, 47488}, {47452, 47496}, {47454, 47472}, {47455, 47491}, {47456, 47493}, {47457, 47489}, {47458, 47537}, {47459, 47536}, {48819, 48843}

X(49688) = midpoint of X(i) and X(j) for these {i,j}: {3625, 49536}, {3632, 3751}, {47277, 47533}
X(49688) = reflection of X(i) in X(j) for these {i,j}: {1, 49524}, {6, 49529}, {145, 1386}, {599, 4669}, {1350, 11362}, {3242, 10}, {3416, 8}, {7982, 5480}, {16496, 141}, {17276, 4660}, {24476, 5836}, {32113, 47492}, {37727, 182}, {47358, 3679}, {47489, 47457}, {48872, 5493}, {49453, 3755}, {49455, 4085}, {49458, 3773}, {49460, 2321}, {49490, 49481}, {49509, 49457}, {49511, 3626}
X(49688) = anticomplement of X(49465)
X(49688) = crossdifference of every pair of points on line {3063, 9002}
X(49688) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4901, 3932}, {1, 33165, 17279}, {1, 49524, 38047}, {6, 49529, 47359}, {8, 24349, 32850}, {141, 16496, 47358}, {3679, 16496, 141}, {3681, 33090, 3966}, {3717, 49466, 1001}, {3883, 4899, 5220}, {3938, 33162, 32777}, {4085, 49455, 17301}, {4514, 32937, 24703}, {4696, 36500, 1837}, {5014, 17165, 1836}, {24349, 32850, 5880}, {29673, 32920, 3772}, {29832, 46897, 17723}, {32847, 49490, 4851}, {32923, 33117, 24789}, {32927, 33120, 17720}, {33076, 49448, 4643}


X(49689) = X(1)X(4698)∩X(8)X(4699)

Barycentrics    4*a^2*b - 3*a*b^2 + 4*a^2*c - a*b*c - 2*b^2*c - 3*a*c^2 - 2*b*c^2 : :
X(49689) = 7 X[1] - 8 X[4698], 7 X[8] - 5 X[4699], 5 X[8] - 4 X[4732], 3 X[8] - 2 X[24325], 25 X[4699] - 28 X[4732], 15 X[4699] - 14 X[24325], 10 X[4699] - 7 X[49490], 6 X[4732] - 5 X[24325], 8 X[4732] - 5 X[49490], 4 X[24325] - 3 X[49490], 3 X[75] - 2 X[49535], 3 X[3625] - X[49535], X[20053] + 2 X[49449], 7 X[3632] - 2 X[4686], 5 X[3632] - 2 X[49468], 3 X[3632] - X[49474], 4 X[3632] - X[49493], 9 X[3632] - 2 X[49525], 5 X[3632] - X[49532], 4 X[4686] - 7 X[49459], 5 X[4686] - 7 X[49468], 6 X[4686] - 7 X[49474], 8 X[4686] - 7 X[49493], 9 X[4686] - 7 X[49525], 10 X[4686] - 7 X[49532], 5 X[49459] - 4 X[49468], 3 X[49459] - 2 X[49474], 9 X[49459] - 4 X[49525], 5 X[49459] - 2 X[49532], 6 X[49468] - 5 X[49474], 8 X[49468] - 5 X[49493], 9 X[49468] - 5 X[49525], 4 X[49474] - 3 X[49493], 3 X[49474] - 2 X[49525], 5 X[49474] - 3 X[49532], 9 X[49493] - 8 X[49525], 5 X[49493] - 4 X[49532], 10 X[49525] - 9 X[49532], 5 X[984] - 4 X[3993], 7 X[984] - 6 X[4664], 3 X[984] - 2 X[49470], 3 X[984] - 4 X[49510], 14 X[3993] - 15 X[4664], 2 X[3993] - 5 X[49450], 6 X[3993] - 5 X[49470], 3 X[3993] - 5 X[49510], 3 X[4664] - 7 X[49450], 9 X[4664] - 7 X[49470], 9 X[4664] - 14 X[49510], 3 X[49450] - X[49470], 3 X[49450] - 2 X[49510], 7 X[3621] + X[4788], 3 X[3621] + X[31302], 2 X[3621] + X[49503], 4 X[3621] + X[49517], 3 X[4788] - 7 X[31302], 2 X[4788] - 7 X[49503], 4 X[4788] - 7 X[49517], 2 X[31302] - 3 X[49503], 4 X[31302] - 3 X[49517], 3 X[3241] - 4 X[3842], 4 X[3635] - 5 X[4687], 6 X[3679] - 5 X[40328], 3 X[3679] - 2 X[49478], 5 X[40328] - 4 X[49478], 2 X[3696] - 3 X[4677], 4 X[3696] - 3 X[31178], 3 X[4677] - X[49498], 3 X[31178] - 2 X[49498], 4 X[3739] - 5 X[4668], 8 X[4691] - 7 X[4751], 5 X[20052] - 2 X[49491], X[20054] + 2 X[49456], X[24349] - 3 X[31145], 3 X[49448] - 2 X[49523], 3 X[49452] - 4 X[49523]

X(49689) lies on these lines: {1, 4698}, {8, 4699}, {10, 17241}, {37, 3633}, {75, 3625}, {145, 49457}, {192, 20053}, {238, 49451}, {518, 3632}, {519, 751}, {740, 3621}, {1757, 49460}, {3241, 3842}, {3635, 4687}, {3644, 49508}, {3679, 40328}, {3696, 4677}, {3739, 4668}, {3979, 4042}, {3996, 4650}, {4113, 26102}, {4685, 17063}, {4691, 4751}, {4693, 5223}, {4701, 49479}, {4709, 49499}, {4716, 16496}, {5288, 15624}, {10453, 24003}, {16468, 49467}, {17135, 32931}, {17154, 32860}, {17363, 17765}, {17592, 20011}, {17715, 32864}, {20048, 46904}, {20050, 49471}, {20052, 49491}, {20054, 49456}, {20055, 27474}, {21870, 29827}, {24349, 31145}, {28522, 49501}, {28581, 49448}, {33149, 49505}, {36479, 42334}, {36534, 49489}, {49447, 49504}, {49469, 49515}

X(49689) = midpoint of X(192) and X(20053)
X(49689) = reflection of X(i) in X(j) for these {i,j}: {75, 3625}, {145, 49457}, {192, 49449}, {984, 49450}, {3633, 37}, {3644, 49508}, {20050, 49471}, {31178, 4677}, {49447, 49504}, {49452, 49448}, {49459, 3632}, {49469, 49515}, {49470, 49510}, {49479, 4701}, {49490, 8}, {49493, 49459}, {49498, 3696}, {49499, 4709}, {49517, 49503}, {49532, 49468}
X(49689) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3679, 49478, 40328}, {3696, 49498, 31178}, {4677, 49498, 3696}, {49450, 49470, 49510}, {49470, 49510, 984}


X(49690) = X(6)X(519)∩X(8)X(141)

Barycentrics    3*a^3 - 3*a^2*b + 4*a*b^2 - 2*b^3 - 3*a^2*c - 2*b^2*c + 4*a*c^2 - 2*b*c^2 - 2*c^3 : :
X(49690) = 6 X[1] - 7 X[47355], 5 X[6] - 6 X[47359], 3 X[6] - 4 X[49529], 9 X[47359] - 10 X[49529], 3 X[48804] - 2 X[48863], 3 X[8] - 2 X[141], 4 X[141] - 3 X[3242], X[69] - 3 X[31145], 3 X[145] - 5 X[3618], 2 X[145] - 3 X[38315], 10 X[3618] - 9 X[38315], 5 X[3618] - 6 X[49524], 3 X[38315] - 4 X[49524], X[193] + 3 X[3621], 6 X[3632] - X[40341], 3 X[599] - 2 X[16496], 3 X[4677] - X[16496], 3 X[1482] - 4 X[19130], 2 X[1482] - 3 X[38144], 8 X[19130] - 9 X[38144], 2 X[1483] - 3 X[38116], 2 X[3098] - 3 X[34718], 3 X[3241] - 4 X[3589], 2 X[3241] - 3 X[38087], 8 X[3589] - 9 X[38087], 2 X[3243] - 3 X[38185], 2 X[3244] - 3 X[38047], 3 X[3416] - 2 X[49505], 3 X[3625] - X[49505], 2 X[3635] - 3 X[38191], 6 X[3679] - 5 X[3763], 3 X[3679] - 2 X[49465], 5 X[3763] - 4 X[49465], 4 X[3844] - 5 X[4668], 4 X[4669] - 3 X[21358], 3 X[5085] - 2 X[37727], 8 X[6329] - 3 X[20050], 4 X[11362] - 3 X[31884], 5 X[12017] - 3 X[34748], 3 X[12645] - X[18440], 3 X[12702] - 2 X[48880], 5 X[16491] - 3 X[34747], 3 X[18525] - 2 X[48884], 3 X[20053] + 4 X[32455], X[47276] - 4 X[47564], X[47279] - 3 X[47531], 2 X[47449] - 3 X[47494], 3 X[47450] - 4 X[47492], 5 X[47452] - 6 X[47488], 5 X[47453] - 4 X[47491], 4 X[47454] - 3 X[47493], 3 X[47455] - 2 X[47489], 5 X[47456] - 3 X[47535], 3 X[48661] - 4 X[48943], 3 X[48800] - 2 X[48835], 3 X[48829] - 2 X[49455], 3 X[49450] - X[49502]

X(49690) lies on these lines: {1, 17267}, {6, 519}, {8, 141}, {69, 903}, {145, 3618}, {193, 3621}, {517, 48910}, {518, 3632}, {599, 4677}, {952, 46264}, {1213, 48849}, {1279, 4901}, {1386, 3633}, {1482, 19130}, {1483, 38116}, {3098, 34718}, {3241, 3589}, {3243, 38185}, {3244, 38047}, {3416, 3625}, {3635, 38191}, {3679, 3763}, {3687, 4952}, {3827, 3893}, {3844, 4668}, {3913, 4265}, {4669, 21358}, {4701, 49511}, {4727, 36404}, {4863, 5101}, {4929, 49515}, {5085, 37727}, {5096, 12513}, {5220, 49506}, {5695, 17765}, {5844, 21850}, {5881, 36990}, {6144, 28538}, {6329, 20050}, {7232, 24841}, {7991, 48872}, {9021, 14923}, {11362, 31884}, {11396, 46026}, {12017, 34748}, {12645, 18440}, {12702, 48880}, {16491, 34747}, {16777, 36479}, {17253, 33076}, {17293, 36534}, {17311, 32847}, {17398, 48856}, {17597, 33091}, {17724, 31091}, {17769, 49486}, {18525, 48884}, {20045, 31229}, {20053, 32455}, {20055, 32029}, {21241, 32920}, {28204, 48905}, {28581, 49507}, {30615, 37679}, {32113, 47490}, {32850, 48627}, {32854, 41711}, {34641, 47358}, {35227, 41310}, {47276, 47564}, {47279, 47531}, {47449, 47494}, {47450, 47492}, {47452, 47488}, {47453, 47491}, {47454, 47493}, {47455, 47489}, {47456, 47535}, {47457, 47536}, {48661, 48943}, {48800, 48835}, {48829, 49455}, {49450, 49502}

X(49690) = reflection of X(i) in X(j) for these {i,j}: {145, 49524}, {599, 4677}, {3242, 8}, {3416, 3625}, {3633, 1386}, {32113, 47490}, {36990, 5881}, {47358, 34641}, {47536, 47457}, {48872, 7991}, {49511, 4701}
X(49690) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {145, 49524, 38315}, {3679, 49465, 3763}, {32847, 42871, 17311}


X(49691) = X(1)X(3836)∩X(145)X(238)

Barycentrics    4*a^3 - 4*a^2*b + 4*a*b^2 - b^3 - 4*a^2*c - 2*a*b*c + 4*a*c^2 - c^3 : :
X(49691) = 3 X[1] - X[32850], 3 X[3836] - 2 X[32850], 3 X[551] - 2 X[3823], 7 X[3622] - 5 X[31252], 5 X[3623] - X[4645]

X(49691) lies on these lines: {1, 3836}, {8, 31289}, {44, 4856}, {145, 238}, {518, 3244}, {519, 1279}, {551, 3823}, {752, 3241}, {1317, 1463}, {1483, 15310}, {3622, 31252}, {3623, 4645}, {3635, 4353}, {3846, 3938}, {4439, 9053}, {16786, 17314}, {17767, 24841}, {20041, 28375}, {30614, 32934}, {49466, 49473}

X(49691) = midpoint of X(145) and X(238)
X(49691) = reflection of X(i) in X(j) for these {i,j}: {8, 31289}, {3836, 1}, {4864, 3635}


X(49692) = X(1)X(6)∩X(10)X(25994)

Barycentrics    a*(a^3*b + a^2*b^2 - a*b^3 + b^4 + a^3*c + 2*a^2*b*c - 3*a*b^2*c + a^2*c^2 - 3*a*b*c^2 - a*c^3 + c^4) : :
X(49692) = 2 X[3246] + X[49515], 4 X[6687] - X[49483]

X(49692) lies on these lines: {1, 6}, {10, 25994}, {192, 27549}, {241, 1463}, {291, 3290}, {513, 24462}, {726, 3008}, {740, 3717}, {742, 3932}, {756, 2239}, {2340, 44694}, {2348, 8300}, {2664, 25083}, {3085, 26068}, {3097, 3752}, {3666, 40774}, {3693, 3783}, {3696, 33165}, {3739, 33159}, {3823, 4708}, {3836, 3842}, {3883, 17765}, {4645, 17257}, {4901, 49459}, {6184, 21830}, {6211, 9441}, {6687, 49483}, {7295, 15624}, {12782, 16583}, {16020, 24349}, {16605, 46032}, {16728, 18792}, {17122, 36540}, {17256, 32850}, {17306, 31252}, {17353, 24325}, {19791, 32925}, {20173, 33137}, {24320, 34247}, {24357, 38047}, {24744, 28023}, {49456, 49521}, {49471, 49527}, {49475, 49534}, {49514, 49519}

X(49692) = midpoint of X(238) and X(984)
X(49692) = reflection of X(i) in X(j) for these {i,j}: {3836, 3842}, {4864, 15569}, {24325, 31289}
X(49692) = X(24462)-lineconjugate of X(513)


X(49693) = X(8)X(238)∩X(10)X(141)

Barycentrics    2*a^2*b - 2*a*b^2 + b^3 + 2*a^2*c - 2*a*b*c - 2*a*c^2 + c^3 : :
X(49693) = 3 X[10] - 2 X[3823], 5 X[10] - 2 X[3834], 5 X[3823] - 3 X[3834], 4 X[3823] - 3 X[3836], 4 X[3834] - 5 X[3836], X[44] + 2 X[3626], X[1757] + 3 X[3679], 3 X[3679] - X[32850], X[3244] - 4 X[6687], 2 X[3246] + X[3625], 5 X[3617] - X[4645], 7 X[9780] - 5 X[31252]

X(49693) lies on these lines: {1, 17263}, {8, 238}, {10, 141}, {44, 594}, {190, 17764}, {192, 4743}, {200, 4438}, {210, 3846}, {239, 17769}, {320, 17270}, {513, 4807}, {519, 1279}, {537, 1738}, {740, 3717}, {752, 1757}, {765, 41684}, {984, 4085}, {1125, 4864}, {1215, 25006}, {1463, 40663}, {1914, 4541}, {2238, 4119}, {2239, 4651}, {2550, 32935}, {2886, 4090}, {2887, 3681}, {3006, 21805}, {3008, 4437}, {3244, 6687}, {3246, 3625}, {3617, 4645}, {3632, 17233}, {3635, 4989}, {3662, 49503}, {3699, 33140}, {3703, 4685}, {3740, 29655}, {3755, 49456}, {3790, 4527}, {3821, 49515}, {3914, 42054}, {3935, 33115}, {3952, 33136}, {3961, 6679}, {3971, 4126}, {3996, 33164}, {4011, 4863}, {4078, 49471}, {4096, 24210}, {4113, 21085}, {4147, 37998}, {4362, 30615}, {4407, 32784}, {4429, 49448}, {4430, 25961}, {4432, 5853}, {4480, 28546}, {4655, 5223}, {4660, 5220}, {4661, 25957}, {4691, 4733}, {4715, 38098}, {4753, 5847}, {4849, 29671}, {4910, 49488}, {4916, 49497}, {5524, 32851}, {5554, 25903}, {5690, 15310}, {5839, 16786}, {5852, 24692}, {6541, 28581}, {7229, 20072}, {9780, 31252}, {10005, 32921}, {10327, 32853}, {11362, 21629}, {17234, 49498}, {17279, 49458}, {17353, 49473}, {17366, 49464}, {17449, 24988}, {17767, 24715}, {17772, 32847}, {17793, 40609}, {18201, 26073}, {19732, 29669}, {19998, 32848}, {20012, 33092}, {21242, 32931}, {24003, 26015}, {24231, 25351}, {24693, 38200}, {27538, 33141}, {29642, 41711}, {29674, 49450}, {29844, 37679}, {31302, 33149}, {32864, 33091}, {32865, 32937}, {32927, 33139}, {32938, 33110}, {32945, 33166}, {33084, 48651}, {33101, 48649}, {36479, 38057}, {36480, 38047}, {38087, 48809}, {38097, 48851}, {49472, 49527}, {49476, 49489}

X(49693) = midpoint of X(i) and X(j) for these {i,j}: {8, 238}, {765, 41684}, {1738, 4899}, {1757, 32850}
X(49693) = reflection of X(i) in X(j) for these {i,j}: {1, 31289}, {3836, 10}, {4439, 3717}, {4864, 1125}, {24231, 25351}
X(49693) = X(28891)-complementary conjugate of X(514)
X(49693) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 17349, 49506}, {8, 33165, 3773}, {10, 24393, 49457}, {10, 49457, 3775}, {10, 49479, 3826}, {10, 49510, 141}, {10, 49529, 24325}, {10, 49536, 142}, {142, 49536, 49491}, {210, 29673, 3846}, {1757, 3679, 32850}, {3681, 33117, 2887}, {3790, 49459, 4527}, {3961, 33118, 6679}, {32865, 32937, 48643}


X(49694) = X(7)X(8)∩X(10)X(4864)

Barycentrics    2*a^3 - 5*a^2*b + 5*a*b^2 - 2*b^3 - 5*a^2*c + 2*a*b*c + 5*a*c^2 - 2*c^3 : :
X(49694) = 7 X[8] - X[320], 5 X[8] - X[4645], 3 X[8] - X[32850], 5 X[320] - 7 X[4645], 3 X[320] - 7 X[32850], 3 X[4645] - 5 X[32850], X[44] + 2 X[3625], X[1757] + 3 X[4677], 2 X[3246] + X[3621], X[3633] - 4 X[6687], 3 X[3679] - 2 X[3823], 2 X[3834] - 5 X[4668], 8 X[4691] - 5 X[31243]

X(49694) lies on these lines: {7, 8}, {10, 4864}, {44, 2321}, {238, 3632}, {519, 1279}, {528, 4899}, {752, 34641}, {910, 4541}, {1738, 9041}, {1757, 4677}, {3244, 31289}, {3246, 3621}, {3626, 3836}, {3633, 6687}, {3679, 3823}, {3717, 4702}, {3834, 4445}, {3967, 4863}, {4113, 33090}, {4691, 31243}, {4701, 17766}, {4816, 28566}, {4852, 49534}, {4929, 49453}, {4952, 33137}, {17344, 49449}, {21870, 29832}, {33165, 49467}

X(49694) = midpoint of X(238) and X(3632)
X(49694) = reflection of X(i) in X(j) for these {i,j}: {3244, 31289}, {3836, 3626}, {4702, 3717}, {4864, 10}
X(49694) = {X(3632),X(4901)}-harmonic conjugate of X(49460)


X(49695) = X(1)X(3836)∩X(144)X(145)

Barycentrics    3*a^3 - 3*a^2*b + 3*a*b^2 - b^3 - 3*a^2*c - a*b*c + 3*a*c^2 - c^3 : :
X(49695) = 3 X[1] - 2 X[3836], 4 X[3836] - 3 X[32850], 5 X[8] - 8 X[6687], 5 X[1279] - 4 X[6687], 2 X[44] + X[20050], 5 X[145] + X[20072], X[320] - 4 X[3244], 6 X[551] - 5 X[31252], 3 X[3241] - X[4645], 3 X[3241] - 2 X[4864], 5 X[3241] - 2 X[31138], 5 X[4645] - 6 X[31138], 5 X[4864] - 3 X[31138], 4 X[3246] - X[3621], 5 X[3616] - 4 X[3823], 3 X[3679] - 4 X[31289], 4 X[3834] - 7 X[20057]

X(49695) lies on these lines: {1, 3836}, {8, 1279}, {44, 3161}, {144, 145}, {238, 519}, {239, 16593}, {319, 49458}, {320, 3244}, {516, 24841}, {551, 31252}, {1463, 37738}, {1757, 3633}, {2321, 16786}, {3241, 4645}, {3242, 17255}, {3246, 3621}, {3616, 3823}, {3626, 17285}, {3632, 17233}, {3679, 31289}, {3685, 9053}, {3689, 5211}, {3722, 32851}, {3744, 33121}, {3769, 36845}, {3834, 20057}, {3870, 33071}, {3890, 20035}, {3938, 4514}, {3957, 33073}, {4952, 27538}, {5014, 25959}, {5121, 43290}, {5263, 49466}, {5853, 32922}, {15310, 37727}, {15570, 17300}, {15600, 17298}, {17289, 49473}, {17389, 20162}, {17715, 33116}, {20075, 30614}, {30331, 49527}

X(49695) = midpoint of X(1757) and X(3633)
X(49695) = reflection of X(i) in X(j) for these {i,j}: {8, 1279}, {4645, 4864}, {32850, 1}
X(49695) = crossdifference of every pair of points on line {20980, 21143}
X(49695) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3241, 4645, 4864}, {3938, 4514, 33126}, {49458, 49506, 319}


X(49696) = X(1)X(2896)∩X(238)X(519)

Barycentrics    4*a^3 - 3*a^2*b + 3*a*b^2 - b^3 - 3*a^2*c - 2*a*b*c + 3*a*c^2 - c^3 : :
X(49696) = 3 X[1] - X[4645], 3 X[10] - 4 X[31289], 3 X[1279] - 2 X[31289], 3 X[551] - 2 X[3836], 6 X[1125] - 5 X[31252], 5 X[31252] - 3 X[32850], 4 X[3246] - X[3625], 4 X[3823] - 5 X[19862]

X(49696) lies on these lines: {1, 2896}, {10, 1279}, {44, 3950}, {145, 1757}, {238, 519}, {320, 4021}, {390, 49455}, {516, 24813}, {518, 3244}, {551, 3836}, {752, 4356}, {1125, 31252}, {2239, 42057}, {3246, 3625}, {3635, 17770}, {3744, 29655}, {3749, 29844}, {3823, 19862}, {4432, 9053}, {4514, 29656}, {4684, 28512}, {4702, 17769}, {4759, 4899}, {5014, 29672}, {5882, 15310}, {6687, 48636}, {16786, 17355}, {17715, 29671}, {24169, 29818}, {24231, 28562}, {49466, 49482}

X(49696) = midpoint of X(145) and X(1757)
X(49696) = reflection of X(i) in X(j) for these {i,j}: {10, 1279}, {4899, 4759}, {32850, 1125}
X(49696) = {X(3244),X(30331)}-harmonic conjugate of X(3993)


X(49697) = X(10)X(141)∩X(238)X(519)

Barycentrics    3*a^2*b - 3*a*b^2 + b^3 + 3*a^2*c - 2*a*b*c - 3*a*c^2 + c^3 : :
X(49697) = 5 X[10] - 4 X[3823], 7 X[10] - 4 X[3834], 3 X[10] - 2 X[3836], 7 X[3823] - 5 X[3834], 6 X[3823] - 5 X[3836], 6 X[3834] - 7 X[3836], 2 X[44] + X[3625], X[320] - 4 X[4691], 3 X[551] - 2 X[4864], 3 X[551] - 4 X[31289], 3 X[3679] - X[4645], 6 X[3828] - 5 X[31252], 5 X[4668] + X[20072]

X(49697) lies on these lines: {1, 17338}, {8, 1757}, {10, 141}, {44, 2321}, {210, 29655}, {238, 519}, {320, 4691}, {551, 4864}, {726, 4899}, {752, 4669}, {1279, 3244}, {1463, 4848}, {2239, 4685}, {3008, 32029}, {3626, 17770}, {3632, 3790}, {3633, 17242}, {3635, 31333}, {3663, 49508}, {3679, 4645}, {3681, 25760}, {3755, 49520}, {3759, 49534}, {3821, 49448}, {3828, 31252}, {3884, 7064}, {4085, 49515}, {4090, 4847}, {4429, 49503}, {4439, 28581}, {4480, 28550}, {4660, 5223}, {4661, 25959}, {4668, 20072}, {4743, 49523}, {4745, 31151}, {4753, 5846}, {4856, 16786}, {4923, 34641}, {4974, 9053}, {5686, 36479}, {5772, 48802}, {5850, 24692}, {11362, 15310}, {11814, 26015}, {17154, 24200}, {20180, 25101}, {20496, 25298}, {21085, 33162}, {21093, 33136}, {24331, 38057}, {29656, 33118}, {30615, 32853}, {33149, 49501}, {33165, 49450}, {49477, 49527}

X(49697) = midpoint of X(8) and X(1757)
X(49697) = reflection of X(i) in X(j) for these {i,j}: {3244, 1279}, {4864, 31289}, {6541, 3717}, {31151, 4745}, {32850, 3626}
X(49697) = crossdifference of every pair of points on line {21007, 21143}
X(49697) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 49504, 49511}, {10, 49535, 142}, {10, 49536, 49479}, {4661, 33117, 33064}, {4864, 31289, 551}, {24393, 49529, 10}, {49457, 49524, 10}


X(49698) = X(7)X(8)∩X(238)X(519)

Barycentrics    a^3 - 3*a^2*b + 3*a*b^2 - b^3 - 3*a^2*c + a*b*c + 3*a*c^2 - c^3 : :
X(49698) = 3 X[1] - 4 X[31289], 4 X[8] - X[320], 3 X[8] - X[4645], 3 X[320] - 4 X[4645], 2 X[4645] - 3 X[32850], 6 X[10] - 5 X[31252], 2 X[44] + X[3621], 4 X[3717] - 3 X[17264], 4 X[3246] - X[20050], 5 X[3617] - 4 X[3823], 5 X[3623] - 8 X[6687], 3 X[3679] - 2 X[3836], 4 X[3834] - 7 X[4678], 5 X[20052] + X[20072]

X(49698) lies on these lines: {1, 17263}, {2, 4864}, {7, 8}, {10, 17283}, {44, 346}, {145, 344}, {190, 4899}, {238, 519}, {239, 4437}, {345, 20015}, {390, 17336}, {752, 4677}, {1222, 6737}, {1265, 6764}, {1738, 24841}, {1757, 3632}, {1997, 6555}, {3008, 36807}, {3161, 12630}, {3187, 19815}, {3242, 16706}, {3243, 17234}, {3246, 20050}, {3509, 4541}, {3617, 3823}, {3623, 6687}, {3625, 17766}, {3679, 3836}, {3681, 4514}, {3699, 26015}, {3790, 49460}, {3834, 4678}, {3870, 33116}, {3875, 4929}, {3879, 4924}, {3888, 9026}, {3911, 43290}, {3935, 32851}, {3938, 33118}, {3961, 33121}, {3999, 26073}, {4360, 49527}, {4429, 16496}, {4461, 20052}, {4487, 37788}, {4660, 49503}, {4661, 5014}, {4669, 31151}, {4701, 17770}, {4816, 17771}, {4849, 29840}, {4863, 32937}, {4886, 33090}, {4901, 17233}, {4935, 28974}, {5100, 5904}, {5263, 49529}, {5423, 20942}, {5686, 17335}, {7174, 17320}, {9041, 37756}, {10453, 30615}, {12649, 20946}, {17241, 39570}, {17258, 49515}, {17277, 24393}, {17280, 49467}, {17289, 49524}, {17317, 49478}, {17394, 39587}, {17764, 24821}, {17774, 30852}, {18743, 36845}, {24248, 49501}, {24723, 49448}, {29641, 41711}, {29673, 33126}, {33076, 49510}, {33082, 49449}, {33117, 33124}, {33165, 49458}, {36534, 38047}, {49488, 49534}
774

X(49698) = midpoint of X(1757) and X(3632)
X(49698) = reflection of X(i) in X(j) for these {i,j}: {145, 1279}, {190, 4899}, {320, 32850}, {24841, 1738}, {31151, 4669}, {32850, 8}
X(49698) = anticomplement of X(4864)
X(49698) = crossdifference of every pair of points on line {3063, 21143}
X(49698) = barycentric quotient X(38371)/X(6084)
X(49698) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 49450, 319}, {145, 10005, 344}, {2550, 49499, 7321}, {3699, 26015, 37758}, {4661, 5014, 33066}, {4901, 49451, 17233}, {24393, 49466, 17277}


X(49699) = X(1)X(3834)∩X(44)X(519)

Barycentrics    (2*a - b - c)*(3*a^2 - a*b + 2*b^2 - a*c - 2*b*c + 2*c^2) : :
X(49699) = 3 X[1] - 2 X[3834], 5 X[1] - 3 X[31151], 10 X[3834] - 9 X[31151], 2 X[10] - 3 X[1279], 5 X[10] - 6 X[31289], 5 X[1279] - 4 X[31289], 2 X[3943] - 3 X[4702], 3 X[145] + X[20072], 3 X[238] - X[3632], X[320] - 3 X[3241], 6 X[551] - 5 X[31243], 5 X[3616] - 3 X[32850], 7 X[3624] - 6 X[3823], 4 X[3635] - 3 X[4864], 4 X[3636] - 3 X[3836], 3 X[3679] - 4 X[6687], 3 X[4645] - 7 X[20057]

X(49699) lies on these lines: {1, 3834}, {8, 3246}, {10, 1279}, {44, 519}, {144, 145}, {238, 3632}, {320, 3241}, {528, 1266}, {551, 31243}, {752, 3244}, {3616, 17370}, {3624, 3823}, {3635, 4353}, {3636, 3836}, {3679, 6687}, {3744, 33120}, {4029, 30331}, {4389, 49465}, {4430, 20093}, {4645, 20057}, {4677, 17269}, {4715, 17318}, {16786, 48805}, {16796, 37542}, {17160, 43287}, {17244, 42819}, {17250, 36534}, {17395, 31138}, {24841, 28534}, {49467, 49506}

X(49699) = reflection of X(8) in X(3246)
X(49699) = crossdifference of every pair of points on line {20980, 23345}


X(49700) = X(8)X(238)∩X(44)X(519)

Barycentrics    (2*a - b - c)*(2*a^2 + b^2 - b*c + c^2) : :
X(49700) = 3 X[1] - X[320], X[8] - 3 X[238], 3 X[10] - 4 X[6687], 3 X[3246] - 2 X[6687], 2 X[2325] - 3 X[4432], 4 X[2325] - 3 X[4439], 3 X[4702] - X[4727], 3 X[551] - 2 X[3834], 2 X[1125] - 3 X[1279], 4 X[1125] - 3 X[3836], 6 X[1125] - 5 X[31243], 9 X[1279] - 5 X[31243], 9 X[3836] - 10 X[31243], 5 X[1698] - 6 X[31289], 5 X[1698] - 3 X[32850], 3 X[1757] + X[3633], 3 X[3241] + X[20072], 5 X[3616] - 3 X[31151], 7 X[3622] - 3 X[4645]

X(49700) lies on these lines: {1, 320}, {8, 238}, {10, 3246}, {44, 519}, {390, 32921}, {513, 48285}, {518, 3244}, {528, 4395}, {535, 14190}, {537, 4480}, {551, 3834}, {1086, 28562}, {1125, 1279}, {1698, 4894}, {1757, 3633}, {1914, 4070}, {2239, 29824}, {2887, 29638}, {3052, 29844}, {3241, 20072}, {3616, 31151}, {3622, 4645}, {3623, 17771}, {3685, 17769}, {3707, 49457}, {3744, 3846}, {3775, 3883}, {4085, 17367}, {4405, 4709}, {4407, 36534}, {4450, 29818}, {4514, 6679}, {4660, 17290}, {4672, 49466}, {4684, 28498}, {4864, 17770}, {4966, 28512}, {4974, 5853}, {5263, 16801}, {15310, 34773}, {16484, 29569}, {16786, 36479}, {17292, 33076}, {17369, 49482}, {17469, 29833}, {17764, 32922}, {19993, 32934}, {23634, 49490}, {24231, 28494}, {27757, 32844}, {28882, 48349}, {29676, 30608}, {30578, 32927}

X(49700) = reflection of X(i) in X(j) for these {i,j}: {10, 3246}, {3836, 1279}, {4439, 4432}, {32850, 31289}
X(49700) = X(1022)-isoconjugate of X(28883)
X(49700) = barycentric product X(i)*X(j) for these {i,j}: {519, 17367}, {3264, 5332}, {4085, 16704}, {17780, 28882}, {30939, 46907}
X(49700) = barycentric quotient X(i)/X(j) for these {i,j}: {4085, 4080}, {5332, 106}, {17367, 903}, {23344, 28883}, {28882, 6548}, {46907, 4674}, {48349, 4049}
X(49700) = {X(3883),X(49473)}-harmonic conjugate of X(3775)


X(49701) = X(10)X(141)∩X(44)X(519)

Barycentrics    (2*a - b - c)*(2*a*b - b^2 + 2*a*c + b*c - c^2) : :
X(49701) = 3 X[8] + X[20072], 7 X[10] - 6 X[3823], 3 X[10] - 2 X[3834], 4 X[10] - 3 X[3836], 9 X[3823] - 7 X[3834], 8 X[3823] - 7 X[3836], 8 X[3834] - 9 X[3836], 2 X[3943] - 3 X[4439], 2 X[4700] - 3 X[4753], X[145] - 3 X[238], X[320] - 3 X[3679], 3 X[551] - 4 X[6687], 3 X[1279] - 2 X[3635], 3 X[1757] + X[3632], 5 X[3616] - 6 X[31289], 5 X[3617] - 3 X[31151], 4 X[3636] - 3 X[4864], 6 X[3828] - 5 X[31243], 3 X[4645] - 7 X[4678], 5 X[4668] - 3 X[32850], 15 X[31252] - 17 X[46932]

X(49701) lies on these lines: {8, 752}, {10, 141}, {44, 519}, {145, 238}, {320, 3679}, {537, 1266}, {551, 6687}, {740, 4899}, {1279, 3635}, {1757, 3632}, {2239, 19998}, {2887, 4661}, {3244, 3246}, {3264, 4738}, {3616, 31289}, {3617, 31151}, {3636, 4864}, {3681, 3846}, {3773, 49450}, {3828, 31243}, {4029, 49471}, {4078, 4924}, {4080, 33136}, {4085, 4389}, {4119, 4144}, {4126, 42057}, {4407, 17250}, {4487, 4783}, {4645, 4678}, {4665, 4669}, {4668, 17771}, {4701, 17766}, {4743, 49447}, {4745, 31138}, {4746, 17770}, {9326, 36593}, {17230, 33165}, {17244, 49490}, {17449, 24183}, {24821, 28542}, {26137, 33111}, {29860, 33118}, {31252, 46932}, {36480, 47359}, {49489, 49527}

X(49701) = reflection of X(i) in X(j) for these {i,j}: {3244, 3246}, {31138, 4745}
X(49701) = X(1022)-isoconjugate of X(28852)
X(49701) = crossdifference of every pair of points on line {21007, 23345}
X(49701) = barycentric product X(i)*X(j) for these {i,j}: {519, 17244}, {4358, 49490}, {17780, 28851}
X(49701) = barycentric quotient X(i)/X(j) for these {i,j}: {17244, 903}, {23344, 28852}, {28851, 6548}, {49490, 88}
X(49701) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 49479, 34824}, {24393, 49536, 24325}, {49510, 49524, 3775}


X(49702) = X(7)X(8)∩X(44)X(519)

Barycentrics    (2*a - b - c)*(a^2 - 3*a*b + 2*b^2 - 3*a*c - 2*b*c + 2*c^2) : :
X(49702) = 3 X[1] - 4 X[6687], 3 X[8] - X[320], 7 X[8] - 3 X[4645], 5 X[8] - 3 X[32850], 7 X[320] - 9 X[4645], 5 X[320] - 9 X[32850], 5 X[4645] - 7 X[32850], 6 X[10] - 5 X[31243], 4 X[2325] - 3 X[4702], 3 X[238] - X[3633], 4 X[1125] - 3 X[4864], 3 X[1279] - 2 X[3244], 3 X[3679] - 2 X[3834], 3 X[3836] - 4 X[4691], 5 X[4668] - 3 X[31151], X[20072] + 3 X[31145]

X(49702) lies on these lines: {1, 6687}, {7, 8}, {10, 31243}, {44, 519}, {145, 3246}, {238, 3633}, {528, 4480}, {679, 36593}, {752, 3625}, {1125, 4864}, {1279, 3244}, {3632, 5695}, {3679, 3834}, {3836, 4691}, {4133, 17765}, {4395, 9041}, {4659, 4677}, {4668, 31151}, {4669, 31138}, {4738, 36919}, {4847, 36914}, {4873, 49460}, {4929, 49486}, {16496, 17290}, {17344, 49504}, {17367, 49465}, {17369, 49529}, {20072, 31145}, {31722, 47357}

X(49702) = reflection of X(i) in X(j) for these {i,j}: {145, 3246}, {31138, 4669}
X(49702) = crossdifference of every pair of points on line {3063, 23345}
X(49702) = barycentric product X(4358)*X(42871)
X(49702) = barycentric quotient X(42871)/X(88)


X(49703) = X(8)X(3834)∩X(44)X(519)

Barycentrics    (2*a - b - c)*(3*a^2 - 5*a*b + 4*b^2 - 5*a*c - 4*b*c + 4*c^2) : :
X(49703) = 3 X[8] - 2 X[3834], 4 X[10] - 3 X[4864], 2 X[145] - 3 X[1279], X[320] - 3 X[31145], 3 X[3241] - 4 X[6687], 3 X[3621] + X[20072], 6 X[3679] - 5 X[31243], 6 X[3823] - 7 X[4678], 3 X[3836] - 4 X[4746], 5 X[4816] - 3 X[31151], 5 X[20052] - 3 X[32850]

X(49703) lies on these lines: {8, 3834}, {10, 4864}, {44, 519}, {145, 344}, {320, 31145}, {518, 3632}, {1266, 9041}, {3241, 6687}, {3246, 3633}, {3621, 20072}, {3635, 4989}, {3679, 31243}, {3823, 4678}, {3836, 4746}, {4677, 17119}, {4816, 31151}, {4929, 49461}, {20052, 32850}

X(49703) = reflection of X(i) in X(j) for these {i,j}: {3633, 3246}, {31138, 4677}


X(49704) = X(1)X(2896)∩X(8)X(238)

Barycentrics    3*a^3 - 2*a^2*b + 2*a*b^2 - b^3 - 2*a^2*c - a*b*c + 2*a*c^2 - c^3 : :
X(49704) = 3 X[2] - 4 X[1279], 9 X[2] - 8 X[3823], 3 X[1279] - 2 X[3823], 4 X[3823] - 3 X[32850], 4 X[44] - X[3621], 2 X[145] + X[20072], 2 X[320] - 5 X[3623], 5 X[3623] - 4 X[4864], 8 X[3246] - 5 X[3617], 5 X[3616] - 4 X[3836], 4 X[3717] - 5 X[4473], 11 X[5550] - 10 X[31252], 7 X[9780] - 8 X[31289], 2 X[31151] - 3 X[38314]

X(49704) lies on these lines: {1, 2896}, {2, 1279}, {8, 238}, {11, 37764}, {20, 12390}, {44, 346}, {55, 29840}, {100, 5211}, {144, 145}, {149, 20045}, {190, 9053}, {239, 5853}, {312, 20056}, {319, 49467}, {320, 3623}, {385, 14942}, {513, 20039}, {516, 4440}, {519, 1757}, {528, 32922}, {643, 16704}, {740, 21295}, {752, 3241}, {894, 49466}, {944, 15310}, {962, 17481}, {1280, 40868}, {1463, 3476}, {1654, 3883}, {2239, 10453}, {3058, 32926}, {3100, 38460}, {3189, 20036}, {3210, 19993}, {3242, 6646}, {3243, 17364}, {3244, 17770}, {3246, 3617}, {3434, 26032}, {3550, 29844}, {3555, 20077}, {3616, 3836}, {3622, 17383}, {3632, 3790}, {3705, 3749}, {3717, 4473}, {3722, 32844}, {3748, 33073}, {3797, 20016}, {3873, 20101}, {3891, 34611}, {3903, 17493}, {3938, 4388}, {3957, 17778}, {4030, 32942}, {4319, 36846}, {4339, 28026}, {4344, 17379}, {4366, 4437}, {4430, 20064}, {4450, 26840}, {4678, 48630}, {4693, 17769}, {4779, 20014}, {4865, 17715}, {4901, 17339}, {4929, 25728}, {5082, 19851}, {5205, 26139}, {5263, 17000}, {5269, 29843}, {5550, 31252}, {5749, 16786}, {6163, 38455}, {7292, 26073}, {8236, 17316}, {9780, 31289}, {11851, 20070}, {12648, 23693}, {16086, 40091}, {17244, 38316}, {17261, 49527}, {17363, 49451}, {17490, 17784}, {17495, 20095}, {17716, 29837}, {17768, 24841}, {17777, 32927}, {20020, 41839}, {20042, 47045}, {20090, 49478}, {21282, 33148}, {24723, 49465}, {27268, 39587}, {28562, 32857}, {28599, 33173}, {29628, 38200}, {29818, 32948}, {29838, 32773}, {30331, 49476}, {30614, 44447}, {31151, 38314}, {31300, 49499}, {33076, 49473}, {36845, 37683}

X(49704) = reflection of X(i) in X(j) for these {i,j}: {8, 238}, {320, 4864}, {4645, 1}, {16086, 40091}, {32850, 1279}
X(49704) = anticomplement of X(32850)
X(49704) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {145, 390, 192}, {149, 20045, 37759}, {1279, 32850, 2}, {3744, 4514, 2}, {4865, 17715, 29839}, {19993, 20075, 3210}, {32941, 49506, 8}


X(49705) = X(1)X(6646)∩X(10)X(82)

Barycentrics    4*a^3 - a^2*b + a*b^2 - b^3 - a^2*c - 2*a*b*c + a*c^2 - c^3 : :
X(49705) = 3 X[10] - 2 X[32850], 3 X[238] - X[32850], 4 X[44] - X[3625], 3 X[551] - 4 X[1279], 7 X[551] - 4 X[31138], 7 X[1279] - 3 X[31138], 8 X[3246] - 5 X[19862], 4 X[3836] - 5 X[19862], 2 X[3635] + X[20072], 3 X[19883] - 2 X[31151]

X(49705) lies on these lines: {1, 6646}, {10, 82}, {31, 29655}, {44, 2321}, {390, 49488}, {518, 3244}, {519, 1757}, {528, 4974}, {551, 752}, {1086, 28494}, {1125, 4645}, {1266, 28550}, {1463, 4315}, {1707, 29844}, {1738, 28562}, {2239, 3840}, {2796, 32922}, {3058, 3791}, {3246, 3836}, {3633, 25728}, {3635, 17319}, {3717, 4759}, {3912, 28512}, {4297, 15310}, {4307, 24331}, {4388, 29656}, {4425, 17469}, {4432, 5846}, {4434, 11814}, {4450, 24169}, {4660, 7290}, {4676, 49506}, {4702, 17772}, {4864, 17771}, {4966, 28498}, {5698, 49455}, {6327, 29672}, {8616, 29671}, {17127, 29673}, {17336, 49534}, {19883, 31151}, {20045, 21093}, {20101, 29820}, {21747, 29835}, {24231, 28508}, {28256, 46827}, {29654, 32947}, {30653, 33120}, {38456, 40091}, {49528, 49535}

X(49705) = reflection of X(i) in X(j) for these {i,j}: {10, 238}, {3717, 4759}, {3836, 3246}, {4645, 1125}, {6541, 4432}
X(49705) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3883, 49482, 10}, {24295, 33076, 10}


X(49706) = X(1)X(6)∩X(55)X(2239)

Barycentrics    a*(a^4 + 2*a^2*b^2 - a*b^3 + a^2*b*c - 2*b^3*c + 2*a^2*c^2 - a*c^3 - 2*b*c^3) : :
X(49706) = 4 X[1279] - 3 X[38315], 5 X[3763] - 4 X[3836], 3 X[21358] - 2 X[31151], 8 X[31289] - 7 X[47355]

X(49706) lies on these lines: {1, 6}, {55, 2239}, {105, 2238}, {141, 4645}, {519, 24294}, {599, 752}, {673, 9453}, {742, 3685}, {1350, 15310}, {1621, 37676}, {1634, 3286}, {2110, 5096}, {3416, 17766}, {3661, 20172}, {3763, 3836}, {3783, 8301}, {3823, 17308}, {3862, 9470}, {4265, 8053}, {4366, 4437}, {7677, 34253}, {8299, 17735}, {9055, 32922}, {12329, 28256}, {16823, 49481}, {16825, 49531}, {17277, 49524}, {17765, 49460}, {17770, 49482}, {20142, 32029}, {20718, 46149}, {20992, 22769}, {21358, 31151}, {31289, 47355}, {38087, 48851}, {47352, 48822}

X(49706) = reflection of X(i) in X(j) for these {i,j}: {6, 238}, {4645, 141}
X(49706) = {X(1),X(49509)}-harmonic conjugate of X(3242)


X(49707) = X(7)X(8)∩X(145)X(238)

Barycentrics    a^3 - 4*a^2*b + 4*a*b^2 - b^3 - 4*a^2*c + a*b*c + 4*a*c^2 - c^3 : :
X(49707) = 5 X[8] - 2 X[320], 3 X[8] - 2 X[32850], 4 X[320] - 5 X[4645], 3 X[320] - 5 X[32850], 3 X[4645] - 4 X[32850], 4 X[44] - X[20050], 4 X[1279] - 3 X[3241], 5 X[3616] - 4 X[4864], 5 X[3617] - 4 X[3836], 7 X[3622] - 8 X[31289], 2 X[3632] + X[20072], 10 X[31252] - 11 X[46933]

X(49707) lies on these lines: {1, 17338}, {7, 8}, {44, 3161}, {145, 238}, {519, 1757}, {752, 31145}, {894, 49536}, {1279, 3241}, {1654, 49510}, {2239, 20012}, {3244, 17121}, {3616, 4864}, {3617, 3836}, {3621, 17765}, {3622, 31289}, {3625, 17770}, {3626, 17287}, {3632, 3729}, {3769, 4952}, {3790, 49451}, {4388, 4661}, {4924, 49476}, {4929, 49495}, {5211, 21805}, {5844, 6163}, {6542, 17755}, {6646, 49503}, {9041, 32922}, {9791, 49515}, {12245, 15310}, {15570, 17263}, {16823, 24393}, {17280, 49458}, {17292, 38191}, {17300, 49498}, {17449, 26073}, {17769, 20016}, {17771, 20052}, {20036, 28256}, {20056, 32853}, {26806, 49491}, {27538, 36845}, {29590, 32108}, {29839, 41711}, {31252, 46933}, {33076, 49449}, {33082, 49504}

X(49707) = reflection of X(i) in X(j) for these {i,j}: {145, 238}, {3685, 4899}, {4645, 8}
X(49707) = X(28891)-anticomplementary conjugate of X(514)
X(49707) = {X(49497),X(49534)}-harmonic conjugate of X(145)


X(49708) = X(1)X(3834)∩X(8)X(238)

Barycentrics    5*a^3 - 4*a^2*b + 4*a*b^2 - 2*b^3 - 4*a^2*c - a*b*c + 4*a*c^2 - 2*c^3 : :
X(49708) = 5 X[1] - 4 X[3834], 4 X[1] - 3 X[31151], 16 X[3834] - 15 X[31151], 2 X[8] - 3 X[238], 16 X[1125] - 15 X[31252], 4 X[1125] - 3 X[32850], 5 X[31252] - 4 X[32850], 6 X[1279] - 5 X[1698], 4 X[3246] - 3 X[3679], 7 X[3622] - 6 X[3836], 5 X[3623] - 3 X[4645], 12 X[3823] - 13 X[34595], 12 X[31289] - 11 X[46933]

X(49708) lies on these lines: {1, 3834}, {8, 238}, {44, 3632}, {145, 752}, {190, 519}, {320, 3244}, {390, 49534}, {518, 3633}, {1125, 31252}, {1279, 1698}, {3246, 3679}, {3622, 3836}, {3623, 4645}, {3722, 27757}, {3744, 29861}, {3823, 34595}, {4715, 34747}, {4716, 5853}, {5014, 29638}, {6687, 17293}, {15310, 18526}, {16786, 17369}, {17292, 49473}, {17360, 49458}, {20050, 20072}, {24841, 28562}, {31289, 46933}

X(49708) = midpoint of X(20050) and X(20072)
X(49708) = reflection of X(i) in X(j) for these {i,j}: {320, 3244}, {3632, 44}


X(49709) = X(1)X(320)∩X(8)X(44)

Barycentrics    3*a^3 - a^2*b + a*b^2 - b^3 - a^2*c - a*b*c + a*c^2 - c^3 : :
X(49709) = 3 X[2] - 4 X[3246], 2 X[10] - 3 X[238], 4 X[10] - 3 X[32850], 2 X[1266] - 3 X[32922], 4 X[1125] - 3 X[31151], 6 X[1279] - 5 X[3616], 3 X[1279] - 2 X[3834], 5 X[3616] - 4 X[3834], 5 X[3616] - 3 X[4645], 4 X[3834] - 3 X[4645], 3 X[1757] - X[3632], 7 X[3624] - 6 X[3836], 3 X[3685] - 2 X[3943], 12 X[3823] - 13 X[19877], 4 X[4432] - 3 X[17264], 3 X[17264] - 2 X[32847], 6 X[4864] - 7 X[20057], 11 X[5550] - 10 X[31243], 8 X[6687] - 7 X[9780], 16 X[19878] - 15 X[31252], 2 X[24715] - 3 X[37756], 2 X[31138] - 3 X[38314]

X(49709) lies on these lines: {1, 320}, {2, 3246}, {8, 44}, {10, 82}, {31, 4514}, {55, 33071}, {144, 145}, {190, 519}, {239, 528}, {319, 32941}, {354, 20101}, {497, 3769}, {513, 4922}, {516, 1266}, {517, 25048}, {527, 24841}, {551, 17305}, {902, 32844}, {1001, 17244}, {1125, 31151}, {1155, 5211}, {1279, 3616}, {1621, 33073}, {1724, 5100}, {1757, 3632}, {1914, 4144}, {1936, 2342}, {1999, 3058}, {2239, 30942}, {2887, 29860}, {3011, 25529}, {3021, 4831}, {3052, 3705}, {3187, 34611}, {3241, 4419}, {3416, 17230}, {3624, 3836}, {3635, 17770}, {3661, 48805}, {3679, 17354}, {3685, 3943}, {3722, 32843}, {3744, 4388}, {3748, 17778}, {3749, 4417}, {3758, 36479}, {3823, 19877}, {3873, 20064}, {3879, 30331}, {3915, 7270}, {3923, 49506}, {3938, 33066}, {3967, 20056}, {4026, 29614}, {4029, 49476}, {4030, 27064}, {4080, 5057}, {4318, 41804}, {4429, 7290}, {4432, 17264}, {4434, 37758}, {4440, 28534}, {4450, 7191}, {4640, 29840}, {4643, 36534}, {4650, 29844}, {4660, 16706}, {4700, 5853}, {4702, 6542}, {4741, 47358}, {4863, 37652}, {4864, 20057}, {4865, 8616}, {4886, 32945}, {5014, 17127}, {5081, 8750}, {5087, 26136}, {5121, 31227}, {5205, 16594}, {5550, 31243}, {6327, 33124}, {6646, 49465}, {6687, 9780}, {7292, 24183}, {8692, 17338}, {15310, 18481}, {15485, 17263}, {16484, 17317}, {16487, 17282}, {16491, 17380}, {16496, 17347}, {16823, 34824}, {17024, 32950}, {17160, 28580}, {17256, 36480}, {17292, 48810}, {17298, 35227}, {17300, 42819}, {17316, 47357}, {17363, 49460}, {17364, 42871}, {17367, 48829}, {17469, 19786}, {17715, 32946}, {19796, 33094}, {19878, 31252}, {19993, 44447}, {20077, 34791}, {20078, 30614}, {20092, 20097}, {21282, 33129}, {24564, 25903}, {24695, 49499}, {24715, 28562}, {28494, 32857}, {28512, 32846}, {28599, 33157}, {29630, 48821}, {29638, 31134}, {29818, 33067}, {30588, 33112}, {30653, 33114}, {30991, 33122}, {31138, 38314}, {32854, 42033}, {33082, 49473}

X(49709) = midpoint of X(145) and X(20072)
X(49709) = reflection of X(i) in X(j) for these {i,j}: {8, 44}, {320, 1}, {4645, 1279}, {5057, 14190}, {6542, 4702}, {32847, 4432}, {32850, 238}
X(49709) = crossdifference of every pair of points on line {20980, 21123}
X(49709) = barycentric product X(190)*X(44433)
X(49709) = barycentric quotient X(44433)/X(514)
X(49709) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {31, 4514, 33121}, {145, 5698, 49447}, {902, 32844, 32851}, {1279, 3834, 3616}, {3616, 4645, 3834}, {3744, 4388, 33126}, {4432, 32847, 17264}, {4450, 7191, 33068}, {4865, 8616, 33116}, {5014, 17127, 33118}, {17469, 32947, 19786}, {33076, 49482, 17289}


X(49710) = X(10)X(44)∩X(58)X(86)

Barycentrics    4*a^3 + a^2*b - a*b^2 - b^3 + a^2*c - 2*a*b*c - a*c^2 - c^3 : :
X(49710) = X[8] - 3 X[1757], 3 X[238] - X[320], 3 X[238] - 2 X[1125], 3 X[551] - 4 X[3246], 5 X[1698] - 3 X[4645], 4 X[2325] - 3 X[6541], 4 X[3634] - 3 X[31151], 4 X[3834] - 5 X[19862], 3 X[3836] - 4 X[6687], 2 X[4395] - 3 X[4974], 4 X[4691] - 3 X[32850], 3 X[19883] - 2 X[31138], 5 X[31243] - 6 X[31289]

X(49710) lies on these lines: {1, 17333}, {8, 1757}, {10, 44}, {58, 86}, {144, 49455}, {190, 519}, {239, 2796}, {513, 23795}, {518, 3244}, {524, 4432}, {528, 4753}, {551, 3246}, {726, 4480}, {740, 4969}, {758, 3271}, {970, 15310}, {1086, 28558}, {1279, 17771}, {1698, 4645}, {1738, 28508}, {1743, 4660}, {2308, 4425}, {2325, 5847}, {2651, 5057}, {3008, 24692}, {3634, 31151}, {3717, 28512}, {3821, 16468}, {3834, 19862}, {3836, 6687}, {3912, 4759}, {3932, 28498}, {4085, 16669}, {4133, 17765}, {4368, 29824}, {4388, 29861}, {4395, 4974}, {4416, 49482}, {4439, 28538}, {4641, 29655}, {4644, 24331}, {4655, 17290}, {4676, 17360}, {4683, 29654}, {4691, 32850}, {4697, 41002}, {4700, 28580}, {4703, 29645}, {4727, 17772}, {4741, 29660}, {5698, 49488}, {7262, 29671}, {11813, 17197}, {15485, 17364}, {16477, 24723}, {16825, 24695}, {17127, 29638}, {17292, 24295}, {17334, 49472}, {17335, 25352}, {17717, 30608}, {17763, 30578}, {17960, 24200}, {19883, 31138}, {21747, 26580}, {24593, 25377}, {27757, 32843}, {29656, 33066}, {29672, 32859}, {30653, 33065}, {31243, 31289}, {49479, 49516}

X(49710) = midpoint of X(i) and X(j) for these {i,j}: {1, 20072}, {17960, 31301}
X(49710) = reflection of X(i) in X(j) for these {i,j}: {10, 44}, {320, 1125}, {3912, 4759}, {24692, 3008}
X(49710) = {X(238),X(320)}-harmonic conjugate of X(1125)


X(49711) = X(44)X(141)∩X(58)X(86)

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

X(49711) lies on these lines: {9, 17244}, {10, 7768}, {44, 141}, {58, 86}, {69, 1757}, {75, 17766}, {109, 2862}, {142, 17000}, {335, 527}, {513, 23785}, {516, 1266}, {518, 3688}, {519, 43287}, {524, 17755}, {752, 3883}, {984, 17378}, {2114, 17950}, {3717, 32846}, {3834, 17398}, {3912, 24358}, {4001, 30965}, {4438, 7788}, {4645, 10436}, {4667, 20132}, {4715, 4755}, {4887, 28508}, {4967, 32850}, {7290, 17274}, {17257, 29595}, {17271, 33159}, {17297, 41141}, {17360, 33165}, {17365, 49516}, {20924, 38456}, {32784, 41847}

X(49711) = midpoint of X(17364) and X(20072)
X(49711) = reflection of X(i) in X(j) for these {i,j}: {320, 3664}, {4416, 44}
X(49711) = {X(238),X(320)}-harmonic conjugate of X(4357)


X(49712) = X(1)X(6)∩X(10)X(320)

Barycentrics    a*(a^2 + 2*a*b - 2*b^2 + 2*a*c - b*c - 2*c^2) : :
X(49712) = 2 X[1] - 3 X[238], 5 X[1] - 6 X[1279], X[1] - 3 X[1757], 3 X[1] - 4 X[3246], 7 X[1] - 6 X[4864], 4 X[44] - 3 X[238], 5 X[44] - 3 X[1279], 2 X[44] - 3 X[1757], 3 X[44] - 2 X[3246], 7 X[44] - 3 X[4864], 5 X[238] - 4 X[1279], 9 X[238] - 8 X[3246], 7 X[238] - 4 X[4864], 2 X[1279] - 5 X[1757], 9 X[1279] - 10 X[3246], 7 X[1279] - 5 X[4864], 9 X[1757] - 4 X[3246], 7 X[1757] - 2 X[4864], 14 X[3246] - 9 X[4864], 4 X[10] - 3 X[31151], 2 X[320] - 3 X[31151], 3 X[4716] - 2 X[17160], 5 X[1698] - 4 X[3834], 3 X[1738] - 2 X[4887], 5 X[3617] - 3 X[4645], 7 X[3624] - 8 X[6687], 4 X[3626] - 3 X[32850], 16 X[3634] - 15 X[31252], 6 X[3836] - 7 X[9780], 11 X[5550] - 12 X[31289], 4 X[17067] - 3 X[24231], 3 X[19875] - 2 X[31138]

X(49712) lies on these lines: {1, 6}, {2, 4407}, {8, 752}, {10, 320}, {31, 4661}, {36, 4557}, {38, 17012}, {43, 17595}, {63, 17601}, {69, 33165}, {88, 291}, {89, 750}, {171, 3681}, {190, 519}, {192, 49497}, {200, 4650}, {210, 17122}, {239, 537}, {329, 33141}, {513, 3245}, {517, 9355}, {524, 32847}, {527, 24715}, {536, 24821}, {668, 4495}, {678, 896}, {726, 4716}, {748, 4430}, {756, 4038}, {758, 2643}, {765, 5385}, {894, 49457}, {1046, 34790}, {1155, 1282}, {1253, 40269}, {1463, 5221}, {1698, 3834}, {1738, 4887}, {1999, 42054}, {2239, 3240}, {2243, 3684}, {2801, 9441}, {2810, 3792}, {2895, 33162}, {3000, 8285}, {3099, 20693}, {3158, 16570}, {3218, 21805}, {3219, 3750}, {3257, 4792}, {3617, 4645}, {3621, 17765}, {3624, 6687}, {3625, 17766}, {3626, 17770}, {3632, 5695}, {3634, 17307}, {3678, 37607}, {3679, 4363}, {3683, 3979}, {3715, 26102}, {3717, 32846}, {3729, 49459}, {3758, 36480}, {3759, 49455}, {3775, 29591}, {3783, 20331}, {3836, 9780}, {3842, 29578}, {3870, 7262}, {3873, 17123}, {3875, 49517}, {3883, 49536}, {3920, 4722}, {3923, 49450}, {3951, 37598}, {3952, 32919}, {3961, 4641}, {4001, 33079}, {4003, 17779}, {4078, 29601}, {4085, 6646}, {4090, 14829}, {4127, 15955}, {4334, 41712}, {4346, 33149}, {4360, 49520}, {4361, 49532}, {4384, 31178}, {4416, 33076}, {4436, 48696}, {4439, 6542}, {4480, 28580}, {4643, 29659}, {4651, 32940}, {4660, 17347}, {4670, 36531}, {4672, 49449}, {4676, 49458}, {4685, 32939}, {4724, 13266}, {4732, 17116}, {4783, 40875}, {4816, 28566}, {4847, 33096}, {4849, 17596}, {4852, 49513}, {4880, 22323}, {4899, 5847}, {4969, 28503}, {5263, 49510}, {5550, 31289}, {5739, 33169}, {5852, 32857}, {5905, 32865}, {7226, 17013}, {8616, 41711}, {8679, 18735}, {9330, 9345}, {9332, 9347}, {9350, 23958}, {9458, 24593}, {12526, 41772}, {12702, 15310}, {16704, 32927}, {16815, 24325}, {16816, 24349}, {16823, 49491}, {16825, 49499}, {17011, 42039}, {17019, 42041}, {17020, 42038}, {17029, 17794}, {17067, 24231}, {17121, 49472}, {17135, 32938}, {17165, 32864}, {17237, 36478}, {17261, 49471}, {17262, 49469}, {17277, 49479}, {17310, 27949}, {17335, 24331}, {17350, 32941}, {17353, 49505}, {17449, 37680}, {17450, 35595}, {17484, 33136}, {17598, 32911}, {17725, 24597}, {17749, 29552}, {17781, 33095}, {17799, 19589}, {18198, 18792}, {19742, 32923}, {19875, 31138}, {19998, 30579}, {20011, 32936}, {20012, 32934}, {20068, 32924}, {24217, 31018}, {24436, 40910}, {25006, 33097}, {25286, 33764}, {27549, 29583}, {29579, 33087}, {29596, 33159}, {29660, 47358}, {29673, 33066}, {30564, 32917}, {31136, 41242}, {31302, 32921}, {32853, 32937}, {32856, 33139}, {32859, 33117}, {32920, 37652}, {33064, 33118}, {33065, 33114}, {33081, 33166}, {33082, 49524}, {33084, 33163}, {33101, 33137}, {33140, 37691}, {36279, 46032}, {37131, 37138}, {49445, 49486}, {49447, 49488}, {49452, 49495}, {49477, 49508}, {49482, 49504}

X(49712) = midpoint of X(8) and X(20072)
X(49712) = reflection of X(i) in X(j) for these {i,j}: {1, 44}, {238, 1757}, {239, 4753}, {320, 10}, {3792, 20683}, {4693, 190}, {6542, 4439}, {32846, 3717}
X(49712) = X(514)-isoconjugate of X(28875)
X(49712) = crossdifference of every pair of points on line {513, 16666}
X(49712) = X(i)-lineconjugate of X(j) for these (i,j): {1, 16666}, {3245, 513}
X(49712) = barycentric product X(i)*X(j) for these {i,j}: {1, 17310}, {190, 48244}, {291, 27949}
X(49712) = barycentric quotient X(i)/X(j) for these {i,j}: {692, 28875}, {17310, 75}, {27949, 350}, {48244, 514}
X(49712) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 44, 238}, {1, 1757, 44}, {9, 49490, 16484}, {10, 320, 31151}, {210, 32913, 17122}, {984, 3751, 4649}, {3240, 36263, 17593}, {3681, 32912, 171}, {3751, 5223, 984}, {3759, 49501, 49455}, {4416, 49529, 33076}, {4643, 47359, 29659}, {4663, 49515, 1}, {16885, 42871, 15485}


X(49713) = X(10)X(141)∩X(190)X(519)

Barycentrics    7*a^2*b - 7*a*b^2 + b^3 + 7*a^2*c - 2*a*b*c - 7*a*c^2 + c^3 : :
X(49713) = 13 X[10] - 12 X[3823], 5 X[10] - 4 X[3834], 7 X[10] - 6 X[3836], 15 X[3823] - 13 X[3834], 14 X[3823] - 13 X[3836], 14 X[3834] - 15 X[3836], X[145] - 3 X[1757], 3 X[238] - 2 X[3635], 3 X[4645] - 5 X[4668], 4 X[4691] - 3 X[31151], 4 X[4746] - 3 X[32850], 8 X[6687] - 7 X[15808], 2 X[31138] - 3 X[38098]}

X(49713) lies on these lines: {10, 141}, {44, 3244}, {145, 1757}, {190, 519}, {238, 3635}, {320, 3626}, {752, 3625}, {2239, 4946}, {3632, 3729}, {3636, 25072}, {3993, 4924}, {4389, 49503}, {4645, 4668}, {4661, 33120}, {4691, 31151}, {4701, 17770}, {4715, 34641}, {4746, 32850}, {4753, 9041}, {4899, 6541}, {4910, 49497}, {5524, 30577}, {6687, 15808}, {17244, 49498}, {17247, 49448}, {31138, 38098}

X(49713) = midpoint of X(3632) and X(20072)
X(49713) = reflection of X(i) in X(j) for these {i,j}: {320, 3626}, {3244, 44}, {6541, 4899}


X(49714) = X(7)X(8)∩X(44)X(145)

Barycentrics    a^3 - 5*a^2*b + 5*a*b^2 - b^3 - 5*a^2*c + a*b*c + 5*a*c^2 - c^3 : :
X(49714) = 5 X[8] - 3 X[4645], 4 X[8] - 3 X[32850], 5 X[320] - 6 X[4645], 2 X[320] - 3 X[32850], 4 X[4645] - 5 X[32850], 3 X[238] - 2 X[3244], 6 X[1279] - 5 X[3623], 3 X[1757] - X[3633], 2 X[2325] - 3 X[4899], 3 X[3241] - 4 X[3246], 5 X[3617] - 4 X[3834], 7 X[3622] - 6 X[4864], 7 X[3622] - 8 X[6687], 3 X[4864] - 4 X[6687], 4 X[3626] - 3 X[31151], 2 X[24841] - 3 X[37756], 10 X[31243] - 11 X[46933]

X(49714) lies on these lines: {7, 8}, {44, 145}, {190, 519}, {238, 3244}, {239, 9041}, {752, 3632}, {1279, 3623}, {1477, 6079}, {1757, 3633}, {2325, 4899}, {3241, 3246}, {3242, 17367}, {3257, 28234}, {3617, 3834}, {3621, 20072}, {3622, 4864}, {3626, 31151}, {3707, 49466}, {3888, 9039}, {4152, 5205}, {4454, 4715}, {4480, 5853}, {4514, 4661}, {4779, 20014}, {4873, 49451}, {4952, 37683}, {4969, 9053}, {4982, 16786}, {4997, 26015}, {5263, 49536}, {8236, 31722}, {16496, 16706}, {17256, 36479}, {17258, 49448}, {17263, 42871}, {17289, 49529}, {17292, 49524}, {17317, 49490}, {24723, 49503}, {24841, 37756}, {29569, 49478}, {29613, 38087}, {29638, 33118}, {29861, 33126}, {31243, 46933}, {33076, 49504}, {33116, 41711}, {36534, 47359}

X(49714) = midpoint of X(3621) and X(20072)
X(49714) = reflection of X(i) in X(j) for these {i,j}: {145, 44}, {320, 8}
X(49714) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 320, 32850}, {4864, 6687, 3622}


X(49715) = X(7)X(8)∩X(44)X(192)

Barycentrics    a^3*b - a*b^3 + a^3*c + 3*a^2*b*c - 2*a*b^2*c + b^3*c - 2*a*b*c^2 - b^2*c^2 - a*c^3 + b*c^3 : :
X(49715) = 4 X[3696] - 3 X[32850], 3 X[238] - 2 X[3993], 2 X[335] - 3 X[37756], 3 X[1757] - X[49445], 4 X[3834] - 5 X[4699], 8 X[6687] - 7 X[27268], 3 X[17264] - 4 X[17755]

X(49715) lies on these lines: {7, 8}, {44, 192}, {238, 3993}, {239, 9055}, {335, 37756}, {350, 3952}, {519, 43287}, {536, 17487}, {726, 4716}, {752, 49474}, {984, 17320}, {1268, 31252}, {1278, 5839}, {1279, 17393}, {1757, 3875}, {3263, 41851}, {3555, 33943}, {3711, 26240}, {3739, 29591}, {3834, 4699}, {3842, 17322}, {4085, 4389}, {4384, 36494}, {4479, 32937}, {4670, 31314}, {4715, 4740}, {4864, 17394}, {6687, 27268}, {16706, 49509}, {17256, 24357}, {17264, 17755}, {17271, 49510}, {17277, 49528}, {17289, 49481}, {17318, 27481}, {17335, 27484}, {17378, 49498}, {20247, 25280}, {20693, 33891}, {28653, 40328}, {33944, 34790}, {34791, 41875}

X(49715) = midpoint of X(1278) and X(20072)
X(49715) = reflection of X(i) in X(j) for these {i,j}: {192, 44}, {320, 75}
X(49715) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 17791, 20435}, {320, 5564, 32850}

leftri

Points in a [[b^2 - c^2, c^2 - a^2, a^2 - b^2], [(b^2 - c^2)(a^2 - b^2 - c^2), (c^2 - a^2)(b^2 - c^2 - a^2), (a^2 - b^2)(c^2 - a^2 - b^2) ]] coordinate system: X(49716)-X(49749)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1, L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1 is the line: (b^2 - c^2) α + (c^2 - a^2) β (a^2 - b^2) γ = 0.

L2 is the line (b^2 - c^2)(a^2 - b^2 - c^2) α + (c^2 - a^2)(b^2 - c^2 - a^2) β + (a^2 - b^2)(c^2 - a^2 - b^2) γ = 0 (Euler line).

The origin is given by (0,0) = X(2) = 1 : 1 : 1 .

Barycentrics u : v : w for a triangle center U = (x, y) in this system are given by

u : v : w = -2(a^2 - b^2)(a^2 - c^2)(b^2 - c^2) + (-2a^2 + b^2 + c^2) x + (-2a^4 + b^4 + c^4 + a^2 b^2 + a^2 c^2 - 2 b^2 c^2 ) y : : ,

where, as functions of a, b, c, the coordinate x is symmetric of degree 4, and y is antisymmetric of degree 2.

The appearance of {x, y}, k in the following list means that (x, y) = X(k).

{-2 (a-b) (a-c) (b-c) (a+b+c), 0}, 3578
{-((2 (a-b) (a+b) (a-c) (b-c) (a+c) (b+c))/(a^2+b^2+c^2)), 0}, 599
{-((2 (a-b) (a+b) (a-c) (b-c) (a+c) (b+c))/(a b+a c+b c)), 0}, 17346
{-2 (a-b) (a-c) (b-c) (a+b+c), (2 (a-b) (a-c) (b-c))/(a+b+c)}, 8
{-(((a-b) (a+b) (a-c) (b-c) (a+c) (b+c))/(a^2+b^2+c^2)), 0}, 141
{-(((a-b) (a+b) (a-c) (b-c) (a+c) (b+c))/(a b+a c+b c)), 0}, 17330
{-((a-b) (a-c) (b-c) (a+b+c)), ((a-b) (a-c) (b-c))/(a+b+c)}, 3679
{-((a-b) (a-c) (b-c) (a+b+c)), ((a-b) (a-c) (b-c) (a b+a c+b c))/(a b c)}, 34612
{-(((a-b) (a+b) (a-c) (b-c) (a+c) (b+c))/(2 (a^2+b^2+c^2))), 0}, 20582
{-(1/2) (a-b) (a-c) (b-c) (a+b+c), ((a-b) (a-c) (b-c))/(2 (a+b+c))}, 10
{0, -(((a-b) (a-c) (b-c))/(a+b+c))}, 13745
{0, 0}, 2
{1/2 (a-b) (a-c) (b-c) (a+b+c), -(((a-b) (a-c) (b-c))/(2 (a+b+c)))}, 551
{((a-b) (a+b) (a-c) (b-c) (a+c) (b+c))/(2 (a^2+b^2+c^2)), 0}, 3589
{(a-b) (a-c) (b-c) (a+b+c), -(((a-b) (a-c) (b-c))/(a+b+c))}, 1
{(a-b) (a-c) (b-c) (a+b+c), -(((a-b) (a-c) (b-c) (a b+a c+b c))/(a b c))}, 3058
{(a-b) (a-c) (b-c) (a+b+c), 0}, 37631
{((a-b) (a+b) (a-c) (b-c) (a+c) (b+c))/(a^2+b^2+c^2), 0}, 597
{((a-b) (a+b) (a-c) (b-c) (a+c) (b+c))/(a b+a c+b c), 0}, 17392
{2 (a-b) (a-c) (b-c) (a+b+c), -((2 (a-b) (a-c) (b-c))/(a+b+c))}, 3241
{2 (a-b) (a-c) (b-c) (a+b+c), -((2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a b c))}, 34611
{2 (a-b) (a-c) (b-c) (a+b+c), 0}, 42045
{(2 (a-b) (a+b) (a-c) (b-c) (a+c) (b+c))/(a^2+b^2+c^2), 0}, 6
{(2 (a-b) (a+b) (a-c) (b-c) (a+c) (b+c))/(a b+a c+b c), 0}, 17378
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), -(((a - b)*(a - c)*(b - c))/(a + b + c))}, 49716
{(-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c), 0}, 49717
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), ((a - b)*(a - c)*(b - c))/(2*(a + b + c))}, 49718
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), (2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a*b*c)}, 49719
{(-2*a*(a - b)*b*(a - c)*(b - c)*c)/(a*b + a*c + b*c), (2*(a - b)*(a - c)*(b - c))/(a + b + c)}, 49720
{(-2*(a - b)*(a - c)*(b - c)*(a^3 + b^3 + c^3))/(a^2 + b^2 + c^2), (2*(a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2)}, 49721
{(-2*(a - b)*(a - c)*(b - c)*(a^3 + b^3 + c^3))/(a*b + a*c + b*c), (2*(a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c)}, 49722
{-((a - b)*(a - c)*(b - c)*(a + b + c)), -(((a - b)*(a - c)*(b - c))/(a + b + c))}, 49723
{-((a - b)*(a - c)*(b - c)*(a + b + c)), 0}, 49724
{-((a*(a - b)*b*(a - c)*(b - c)*c)/(a*b + a*c + b*c)), ((a - b)*(a - c)*(b - c))/(a + b + c)}, 49725
{-(((a - b)*(a - c)*(b - c)*(a^3 + b^3 + c^3))/(a^2 + b^2 + c^2)), ((a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2)}, 49726
{-(((a - b)*(a - c)*(b - c)*(a^3 + b^3 + c^3))/(a*b + a*c + b*c)), ((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c)}, 49727
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), -(((a - b)*(a - c)*(b - c))/(a + b + c))}, 49728
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), -1/2*((a - b)*(a - c)*(b - c))/(a + b + c)}, 49729
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), 0}, 49730
{-1/2*((a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c))/(a*b + a*c + b*c), 0}, 49731
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), ((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(2*a*b*c)}, 49732
{-1/2*((a - b)*(a - c)*(b - c)*(a^3 + b^3 + c^3))/(a*b + a*c + b*c), ((a - b)*(a - c)*(b - c)*(a + b + c))/(2*(a*b + a*c + b*c))}, 49733
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), (2*(a - b)*(a - c)*(b - c))/(a + b + c)}, 49734
{0, (-2*(a - b)*(a - c)*(b - c))/(a + b + c)}, 49735
{((a - b)*(a - c)*(b - c)*(a + b + c))/2, -1/2*((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a*b*c)}, 49736
{((a - b)*(a - c)*(b - c)*(a^3 + b^3 + c^3))/(2*(a*b + a*c + b*c)), -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c)}, 49737
{((a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c))/(2*(a*b + a*c + b*c)), 0}, 49738
{(a - b)*(a - c)*(b - c)*(a + b + c), (-2*(a - b)*(a - c)*(b - c))/(a + b + c)}, 49739
{(a*(a - b)*b*(a - c)*(b - c)*c)/(a*b + a*c + b*c), -(((a - b)*(a - c)*(b - c))/(a + b + c))}, 49740
{((a - b)*(a - c)*(b - c)*(a^3 + b^3 + c^3))/(a^2 + b^2 + c^2), -(((a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2))}, 49741
{((a - b)*(a - c)*(b - c)*(a^3 + b^3 + c^3))/(a*b + a*c + b*c), -(((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c))}, 49742
{(a - b)*(a - c)*(b - c)*(a + b + c), ((a - b)*(a - c)*(b - c))/(2*(a + b + c))}, 49743
{(a - b)*(a - c)*(b - c)*(a + b + c), ((a - b)*(a - c)*(b - c))/(a + b + c)}, 49744
{(a - b)*(a - c)*(b - c)*(a + b + c), (2*(a - b)*(a - c)*(b - c))/(a + b + c)}, 49745
{(2*a*(a - b)*b*(a - c)*(b - c)*c)/(a*b + a*c + b*c), (-2*(a - b)*(a - c)*(b - c))/(a + b + c)}, 49746
{(2*(a - b)*(a - c)*(b - c)*(a^3 + b^3 + c^3))/(a^2 + b^2 + c^2), (-2*(a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2)}, 49747
{(2*(a - b)*(a - c)*(b - c)*(a^3 + b^3 + c^3))/(a*b + a*c + b*c), (-2*(a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c)}, 49748
{(2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c), 0}, 49749


X(49716) = X(1)X(524)∩X(8)X(30)

Barycentrics    2*a^4 + 2*a^3*b - a^2*b^2 - 2*a*b^3 - b^4 + 2*a^3*c - 4*a*b^2*c - 2*b^3*c - a^2*c^2 - 4*a*b*c^2 - 2*b^2*c^2 - 2*a*c^3 - 2*b*c^3 - c^4 : :
X(49716) = 2 X[1] - 3 X[13745], X[8] - 3 X[3578], 4 X[1125] - 3 X[37631], 5 X[3616] - 3 X[42045], 3 X[10180] - 2 X[49564]

X(49716) lies on these lines: {1, 524}, {3, 5739}, {4, 14552}, {5, 1150}, {6, 13728}, {8, 30}, {10, 540}, {21, 2895}, {58, 1211}, {63, 5814}, {69, 405}, {72, 511}, {78, 500}, {81, 4205}, {86, 17514}, {140, 5741}, {141, 1724}, {191, 3704}, {193, 13725}, {200, 48897}, {213, 15989}, {218, 15984}, {283, 33305}, {306, 31445}, {318, 46467}, {319, 7283}, {320, 16817}, {325, 34016}, {329, 48941}, {333, 442}, {385, 46707}, {391, 443}, {404, 37656}, {474, 14555}, {542, 48939}, {896, 20653}, {908, 48931}, {942, 4001}, {956, 3564}, {966, 4340}, {1008, 7762}, {1009, 7767}, {1010, 1654}, {1104, 17344}, {1125, 37631}, {1213, 25526}, {1375, 24632}, {1453, 17272}, {1503, 48883}, {1770, 3696}, {1792, 37286}, {1935, 26942}, {1992, 19766}, {2287, 18641}, {2476, 5361}, {2975, 48930}, {3219, 3695}, {3293, 44419}, {3416, 41229}, {3419, 48937}, {3421, 15971}, {3436, 5774}, {3454, 35466}, {3555, 3883}, {3616, 42045}, {3620, 13742}, {3647, 3712}, {3686, 4292}, {3687, 3916}, {3872, 48903}, {3933, 13723}, {3936, 6675}, {3940, 48907}, {4023, 15447}, {4046, 41814}, {4061, 31730}, {4101, 24929}, {4187, 14829}, {4193, 5372}, {4195, 7893}, {4201, 7839}, {4202, 19742}, {4309, 49460}, {4359, 24470}, {4388, 24390}, {4417, 7483}, {4420, 48927}, {4511, 5453}, {4647, 17768}, {4670, 19857}, {4683, 27368}, {4703, 17733}, {4720, 15680}, {4741, 19851}, {4869, 17552}, {4899, 29317}, {4921, 16052}, {4966, 5259}, {5044, 49557}, {5047, 32863}, {5051, 16704}, {5084, 37655}, {5165, 17330}, {5223, 29181}, {5232, 37037}, {5233, 13747}, {5235, 26131}, {5247, 15985}, {5278, 8728}, {5305, 37025}, {5323, 16429}, {5440, 48893}, {5687, 37425}, {5712, 16343}, {5730, 34380}, {5738, 16416}, {5743, 37522}, {5835, 49500}, {5965, 48894}, {6147, 32859}, {6327, 31419}, {6390, 37023}, {6515, 37228}, {6734, 13408}, {7046, 46468}, {7758, 19758}, {7774, 37053}, {7779, 19312}, {9534, 11112}, {9791, 41813}, {10180, 49564}, {10371, 12514}, {10381, 18180}, {10432, 40995}, {10449, 11113}, {11110, 17778}, {11115, 43990}, {11245, 47521}, {11246, 28612}, {11433, 19520}, {11544, 17491}, {11679, 48899}, {13730, 37491}, {13732, 48876}, {13736, 20080}, {13740, 37653}, {13869, 36223}, {14007, 26044}, {14023, 19761}, {15171, 17135}, {15670, 25650}, {15823, 45206}, {15973, 17757}, {16062, 37652}, {16342, 31034}, {16466, 28369}, {16842, 18141}, {16948, 31143}, {17206, 19329}, {17234, 17590}, {17238, 37036}, {17277, 17529}, {17300, 37035}, {17349, 33833}, {17379, 37039}, {17557, 37635}, {17676, 48847}, {17698, 32782}, {17770, 49598}, {18928, 19521}, {19309, 45962}, {19723, 48834}, {20018, 37038}, {21085, 24850}, {21677, 36974}, {25963, 37636}

X(49716) = midpoint of X(48877) and X(48935)
X(49716) = reflection of X(i) in X(j) for these {i,j}: {13408, 48887}, {49557, 5044}
X(49716) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21, 2895, 41014}, {81, 26064, 4205}, {333, 1330, 442}, {966, 4340, 16458}, {1654, 20077, 1010}, {3647, 21081, 3712}


X(49717) = X(2)X(6)∩X(10)X(4754)

Barycentrics    a^3*b - 2*a^2*b^2 - 2*a*b^3 + a^3*c - 2*a^2*b*c - 5*a*b^2*c - 2*b^3*c - 2*a^2*c^2 - 5*a*b*c^2 - 2*b^2*c^2 - 2*a*c^3 - 2*b*c^3 : :
X(49717) = 4 X[10] - X[4754]

X(49717) lies on these lines: {2, 6}, {10, 4754}, {30, 48802}, {42, 4690}, {256, 4496}, {350, 17252}, {511, 3789}, {536, 3728}, {538, 3679}, {540, 48809}, {672, 17239}, {742, 4981}, {1836, 4643}, {2227, 36856}, {2276, 17270}, {3720, 4708}, {3741, 4465}, {3775, 8299}, {4364, 17135}, {4441, 17253}, {4651, 25349}, {4670, 4722}, {4748, 10453}, {16552, 48860}, {17027, 17250}, {17032, 17360}, {17210, 20970}, {17237, 24592}, {17256, 31027}, {17328, 24514}, {17759, 32025}, {24326, 49457}, {24691, 26037}

X(49717) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1654, 30966, 2238}, {4643, 31330, 24330}


X(49718) = X(8)X(30)∩X(10)X(524)

Barycentrics    2*a^4 + 4*a^3*b - a^2*b^2 - 4*a*b^3 - b^4 + 4*a^3*c - 8*a*b^2*c - 4*b^3*c - a^2*c^2 - 8*a*b*c^2 - 6*b^2*c^2 - 4*a*c^3 - 4*b*c^3 - c^4 : :
X(49718) = X[8] + 3 X[3578], X[145] - 3 X[13745], 5 X[1698] - 3 X[37631], 7 X[9780] - 3 X[42045]

X(49718) lies on these lines: {3, 14552}, {5, 5739}, {8, 30}, {10, 524}, {63, 48924}, {69, 8728}, {78, 5453}, {140, 1150}, {145, 13745}, {191, 4046}, {193, 2049}, {200, 500}, {319, 3695}, {333, 6675}, {391, 11108}, {442, 2895}, {511, 34790}, {540, 3626}, {942, 3686}, {956, 48930}, {1046, 42334}, {1211, 25441}, {1213, 4658}, {1654, 4205}, {1698, 37631}, {2287, 22136}, {2901, 17332}, {3421, 46704}, {3564, 5814}, {3579, 4061}, {3628, 5741}, {3629, 43531}, {3704, 41814}, {3932, 41822}, {3940, 48909}, {3945, 16456}, {4001, 24470}, {4023, 47742}, {4042, 31419}, {4101, 5719}, {4187, 37656}, {4416, 5295}, {4847, 48887}, {4853, 48903}, {4882, 48897}, {4938, 27577}, {5051, 43990}, {5271, 6147}, {5361, 7483}, {5372, 13747}, {5774, 15973}, {5783, 15992}, {5815, 48941}, {6390, 34016}, {6515, 47510}, {6907, 11411}, {7046, 46467}, {9780, 42045}, {10449, 17346}, {11036, 30711}, {14005, 20086}, {14007, 20090}, {14555, 17527}, {15172, 17135}, {16062, 17343}, {16408, 37655}, {16454, 31303}, {17344, 23537}, {17529, 32863}, {17551, 41819}, {17698, 37652}, {18253, 21081}, {20080, 37153}, {21075, 48931}, {24883, 31143}, {25669, 35466}, {45794, 47516}, {46707, 47286}

X(49718) = {X(333),X(41014)}-harmonic conjugate of X(6675)


X(49719) = X(2)X(11)∩X(8)X(30)

Barycentrics    2*a^3 - 2*a^2*b + a*b^2 - b^3 - 2*a^2*c + a*b*c + b^2*c + a*c^2 + b*c^2 - c^3 : :
X(49719) = 4 X[3058] - 3 X[34611], X[3058] - 3 X[34612], X[34611] - 4 X[34612], 3 X[3681] - 2 X[17781], 7 X[17579] - 4 X[34637], 5 X[17579] - 2 X[34690], 7 X[34605] - 8 X[34637], 5 X[34605] - 4 X[34690], 10 X[34637] - 7 X[34690], 4 X[553] - 3 X[3873], 5 X[3616] - 4 X[15170], 5 X[3617] - 2 X[6284], X[3621] + 2 X[7354], 2 X[3625] + X[10483], X[3885] - 4 X[17647], 7 X[4002] - 4 X[31795], 11 X[5550] - 8 X[15172], 3 X[5640] - 4 X[22278], 3 X[5657] - 2 X[28459], 5 X[5734] - 8 X[37281], 2 X[6253] + X[20070], 7 X[9780] - 4 X[15171], 4 X[18990] - X[20050]

X(49719) lies on these lines: {2, 11}, {8, 30}, {10, 41872}, {40, 5178}, {72, 28198}, {78, 31162}, {145, 5434}, {200, 5057}, {321, 14458}, {376, 2975}, {381, 5687}, {404, 10072}, {516, 3681}, {517, 11459}, {519, 3868}, {524, 25304}, {527, 25722}, {529, 31145}, {535, 4677}, {549, 24390}, {551, 34719}, {553, 3873}, {902, 32865}, {944, 28458}, {956, 3534}, {958, 15677}, {1325, 37546}, {1478, 15679}, {1836, 3935}, {2177, 33109}, {2475, 3913}, {2476, 3584}, {3017, 5264}, {3052, 33139}, {3189, 34195}, {3218, 4863}, {3241, 11037}, {3242, 33102}, {3295, 44217}, {3419, 3654}, {3421, 15682}, {3436, 3543}, {3524, 10527}, {3545, 5552}, {3550, 33136}, {3582, 25440}, {3616, 15170}, {3617, 6284}, {3621, 7354}, {3625, 10483}, {3655, 4861}, {3656, 4511}, {3679, 5086}, {3689, 31053}, {3711, 26792}, {3722, 17889}, {3744, 33131}, {3746, 4197}, {3748, 27186}, {3749, 33129}, {3813, 4188}, {3828, 34649}, {3830, 5080}, {3839, 7080}, {3845, 17757}, {3869, 28194}, {3870, 4654}, {3871, 6175}, {3885, 17647}, {3886, 33078}, {3938, 24715}, {3940, 5180}, {3957, 5880}, {3961, 33094}, {3984, 9589}, {3996, 6327}, {4002, 31795}, {4030, 28605}, {4294, 5260}, {4302, 15678}, {4309, 5047}, {4417, 21282}, {4420, 12699}, {4430, 11246}, {4441, 37671}, {4660, 32782}, {4661, 17768}, {4685, 25306}, {4689, 29664}, {4853, 34628}, {4855, 25055}, {4917, 5290}, {5014, 32932}, {5055, 27529}, {5175, 11113}, {5262, 48824}, {5303, 10304}, {5306, 21956}, {5325, 25006}, {5550, 15172}, {5640, 22278}, {5657, 28459}, {5695, 33091}, {5710, 48842}, {5734, 37281}, {6253, 20070}, {6736, 34648}, {6901, 37622}, {6923, 38665}, {6948, 38669}, {6950, 10993}, {7753, 34735}, {7788, 20553}, {7811, 17143}, {7837, 17759}, {8168, 12943}, {9300, 17756}, {9352, 26015}, {9670, 37162}, {9710, 16865}, {9780, 15171}, {10327, 42032}, {10691, 34665}, {10914, 28204}, {11194, 36004}, {12513, 37256}, {12632, 37435}, {13199, 22758}, {13587, 36152}, {14614, 37857}, {14829, 21283}, {15670, 31419}, {15671, 19854}, {15683, 34630}, {16370, 34707}, {16371, 38901}, {17018, 37631}, {17155, 17765}, {17483, 41711}, {17566, 24387}, {17572, 37722}, {17574, 31458}, {17577, 45701}, {17601, 29690}, {17764, 32925}, {17766, 32860}, {17782, 29640}, {18990, 20050}, {20049, 34749}, {20086, 49680}, {21949, 29681}, {25278, 32819}, {25351, 29853}, {26842, 42871}, {28202, 34790}, {28580, 42044}, {29679, 49484}, {30308, 30852}, {31141, 34706}, {32850, 32862}, {32863, 49460}, {32941, 32948}, {33067, 49458}, {33106, 37651}, {33125, 49473}, {33142, 37540}, {34626, 37299}, {42025, 48830}

X(49719) = reflection of X(i) in X(j) for these {i,j}: {2, 34612}, {145, 5434}, {944, 28458}, {3241, 11112}, {3543, 34746}, {4430, 11246}, {11114, 3679}, {15683, 34630}, {20049, 34749}, {31145, 34720}, {34605, 17579}, {34611, 2}, {34629, 381}, {34649, 3828}, {34665, 10691}, {34708, 3829}, {34719, 551}, {34735, 7753}, {34745, 549}
X(49719) = anticomplement of X(3058)
X(49719) = anticomplement of the isogonal conjugate of X(41431)
X(49719) = X(41431)-anticomplementary conjugate of X(8)
X(49719) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 149, 11238}, {2, 10385, 1621}, {2, 20075, 10385}, {8, 6361, 11684}, {55, 33110, 33108}, {100, 3434, 11680}, {1376, 11238, 2}, {2550, 10385, 2}, {2550, 20075, 1621}, {2886, 4995, 2}, {3434, 17784, 100}, {3829, 6174, 2}, {3871, 6175, 10056}, {3938, 24715, 33146}, {3961, 33094, 33151}, {4421, 31140, 2}, {4660, 32945, 32782}, {5014, 32932, 33089}, {20095, 33110, 55}, {32850, 32929, 32862}, {32941, 32948, 33172}


X(49720) = X(2)X(11)∩X(8)X(524)

Barycentrics    2*a^3 - a^2*b + 2*a*b^2 - b^3 - a^2*c + 3*a*b*c + 2*b^2*c + 2*a*c^2 + 2*b*c^2 - c^3 : :
X(49720) = X[17377] + 2 X[49459], 3 X[24452] - X[31178], 4 X[15569] - 5 X[29622], X[17347] - 4 X[49457], 5 X[17391] - 2 X[49475]

X(49720) lies on these lines: {1, 4743}, {2, 11}, {8, 524}, {10, 598}, {75, 519}, {86, 48830}, {551, 1738}, {599, 4645}, {740, 36494}, {752, 1757}, {894, 47359}, {984, 2796}, {1086, 36534}, {1992, 4307}, {2345, 16885}, {3241, 17392}, {3246, 29628}, {3416, 29615}, {3685, 41313}, {3696, 28538}, {3886, 29573}, {3913, 26051}, {4000, 38314}, {4042, 20101}, {4085, 17381}, {4195, 9710}, {4309, 37035}, {4357, 49630}, {4384, 49709}, {4389, 24715}, {4417, 33109}, {4660, 5224}, {4664, 28580}, {4702, 17244}, {4740, 28503}, {4780, 17393}, {4912, 49515}, {4933, 29643}, {4956, 5297}, {5233, 33104}, {5252, 40862}, {5880, 47358}, {6327, 31143}, {7321, 16496}, {9041, 24349}, {11116, 37546}, {13745, 19853}, {15569, 29622}, {15953, 36289}, {16706, 25055}, {16830, 41312}, {17116, 49688}, {17117, 49681}, {17132, 49447}, {17133, 49476}, {17234, 32941}, {17242, 49485}, {17271, 48802}, {17289, 19875}, {17300, 49460}, {17313, 20181}, {17320, 48854}, {17333, 28534}, {17347, 28558}, {17352, 49482}, {17370, 19883}, {17391, 49475}, {18134, 32945}, {20090, 49680}, {21283, 37633}, {21949, 29634}, {24841, 42697}, {25351, 29660}, {25385, 27777}, {26806, 42871}, {27147, 42819}, {28329, 49468}, {29574, 49470}, {31177, 33065}, {31179, 33112}, {35043, 40875}, {41310, 49484}, {48627, 49465}

X(49720) = reflection of X(i) in X(j) for these {i,j}: {3241, 17392}, {17346, 3679}, {29617, 3696}, {49470, 29574}
X(49720) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2550, 5263, 4429}, {24715, 36480, 4389}


X(49721) = X(2)X(45)∩X(6)X(536)

Barycentrics    3*a^2 - 2*a*b - 2*a*c + 4*b*c : :
X(49721) = X[6] + 2 X[3729], 5 X[6] - 2 X[3875], 7 X[6] - 4 X[4852], 3 X[6] - 2 X[16834], X[6] - 4 X[17351], 5 X[3729] + X[3875], 7 X[3729] + 2 X[4852], 3 X[3729] + X[16834], X[3729] + 2 X[17351], 7 X[3875] - 10 X[4852], 3 X[3875] - 5 X[16834], X[3875] - 10 X[17351], 6 X[4852] - 7 X[16834], X[4852] - 7 X[17351], X[16834] - 6 X[17351], X[5695] + 2 X[32935], 3 X[599] - 4 X[29594], 3 X[17281] - 2 X[29594], X[3242] - 4 X[3923], 5 X[3242] - 8 X[49473], 5 X[3923] - 2 X[49473], 5 X[48805] - 4 X[49473], 4 X[2321] - X[40341], 3 X[38087] - 2 X[48829], 4 X[3663] - 7 X[47355], 5 X[3763] - 2 X[17276], 5 X[3763] - 8 X[17355], X[17276] - 4 X[17355], 4 X[4672] - X[49453], 2 X[17274] - 3 X[21358], 4 X[17359] - 3 X[21358], X[6144] + 2 X[17299], 2 X[17301] - 3 X[47352], 5 X[17286] - 2 X[17345], X[24280] + 2 X[49524]

X(49721) lies on these lines: {1, 49522}, {2, 45}, {6, 536}, {7, 17267}, {9, 4688}, {44, 4659}, {55, 31161}, {69, 28333}, {75, 16885}, {86, 16674}, {144, 594}, {171, 4942}, {192, 16884}, {193, 28337}, {320, 17269}, {344, 7228}, {346, 17311}, {519, 5695}, {527, 599}, {537, 3242}, {597, 28297}, {726, 38315}, {750, 4937}, {894, 4664}, {1001, 31178}, {1213, 7229}, {1376, 23343}, {1449, 4718}, {1743, 4686}, {1992, 4971}, {2321, 40341}, {2325, 4675}, {2345, 4488}, {2796, 38087}, {3161, 7222}, {3230, 36871}, {3245, 3679}, {3285, 16046}, {3644, 17120}, {3663, 47355}, {3739, 25728}, {3758, 17318}, {3763, 17276}, {3943, 4644}, {3980, 42056}, {4054, 31187}, {4361, 4740}, {4387, 32940}, {4421, 4436}, {4445, 17347}, {4461, 17362}, {4480, 4643}, {4670, 16672}, {4672, 28554}, {4677, 49712}, {4715, 15533}, {4755, 10436}, {4764, 17121}, {4767, 24344}, {4795, 29574}, {4862, 17357}, {4873, 17374}, {4908, 29573}, {4912, 17274}, {4980, 19723}, {5698, 48849}, {5749, 17246}, {5819, 6172}, {6068, 28118}, {6144, 17299}, {6173, 41310}, {6646, 17293}, {7227, 17257}, {7232, 17280}, {7238, 29579}, {7263, 26685}, {7277, 17314}, {7290, 49525}, {7321, 17265}, {8584, 28309}, {15590, 38314}, {15668, 16677}, {16475, 28555}, {16669, 17151}, {16814, 25590}, {17116, 17259}, {17132, 17301}, {17233, 31300}, {17251, 17333}, {17255, 17289}, {17258, 17327}, {17264, 17313}, {17286, 17345}, {17309, 17364}, {17323, 17368}, {17337, 31995}, {17382, 28322}, {17392, 35578}, {17735, 47037}, {17754, 41144}, {20172, 31349}, {22758, 38531}, {24248, 48821}, {24280, 49524}, {24409, 32930}, {24425, 42055}, {24514, 41142}, {25734, 31993}, {28526, 38047}, {28580, 47359}, {29575, 39704}, {30568, 37682}, {44419, 44446}, {44663, 48812}

X(49721) = reflection of X(i) in X(j) for these {i,j}: {599, 17281}, {3242, 48805}, {15533, 17294}, {17274, 17359}, {24248, 48821}, {48805, 3923}
X(49721) = crossdifference of every pair of points on line {1960, 9010}
X(49721) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 17340, 17267}, {44, 4659, 17119}, {190, 4363, 45}, {346, 17365, 17311}, {894, 17262, 16777}, {2345, 4488, 17334}, {2345, 17334, 17253}, {3161, 7222, 17245}, {3729, 17351, 6}, {4419, 17369, 17325}, {4440, 17354, 17290}, {7321, 17339, 17265}, {15668, 17261, 16677}, {17116, 17336, 17259}, {17274, 17359, 21358}, {17276, 17355, 3763}


X(49722) = X(1)X(28542)∩X(2)X(45)

Barycentrics    2*a^2 - a*b - b^2 - a*c + 5*b*c - c^2 : :
X(49722) = 7 X[75] - 4 X[3686], 5 X[75] - 2 X[4416], 4 X[75] - X[17347], 10 X[3686] - 7 X[4416], 8 X[3686] - 7 X[17346], 16 X[3686] - 7 X[17347], 4 X[4416] - 5 X[17346], 8 X[4416] - 5 X[17347], X[192] - 4 X[7228], 3 X[17378] - 2 X[17389], X[1278] + 2 X[17365], 2 X[1278] + X[17377], 4 X[17365] - X[17377], X[3644] - 4 X[3664], 2 X[3879] + X[4764], 2 X[4686] + X[17364], 5 X[4699] - 2 X[17334], 2 X[4718] - 5 X[17391], 4 X[4726] - X[17363], 8 X[4739] - 5 X[17331], 7 X[4772] - 4 X[17332], X[4788] - 4 X[17390], 5 X[4821] - 2 X[17362], 2 X[29574] - 3 X[39704]

X(49722) lies on these lines: {1, 28542}, {2, 45}, {7, 17233}, {37, 28322}, {75, 527}, {86, 7222}, {192, 7228}, {320, 4659}, {519, 49493}, {524, 4740}, {528, 24349}, {536, 17378}, {553, 42034}, {894, 4398}, {1150, 35596}, {1266, 3758}, {1278, 4971}, {2094, 14829}, {2796, 31178}, {3241, 49453}, {3618, 4373}, {3644, 3664}, {3662, 17359}, {3663, 17381}, {3679, 4655}, {3729, 6173}, {3879, 4764}, {4361, 31300}, {4417, 31164}, {4431, 17361}, {4461, 17295}, {4480, 17335}, {4644, 17160}, {4664, 17132}, {4665, 4741}, {4675, 29575}, {4677, 49714}, {4686, 4725}, {4688, 4912}, {4699, 17334}, {4715, 29617}, {4718, 17391}, {4726, 17363}, {4739, 17331}, {4772, 17332}, {4788, 17390}, {4795, 29584}, {4821, 17362}, {4862, 17289}, {4887, 17227}, {4888, 17315}, {4896, 17387}, {4902, 17286}, {4908, 29582}, {4967, 17329}, {5224, 17116}, {6172, 17277}, {6646, 17118}, {7227, 17236}, {7229, 17307}, {7231, 17246}, {7238, 17230}, {7263, 17350}, {15534, 40891}, {17119, 20072}, {17164, 34605}, {17245, 25269}, {17255, 28604}, {17258, 25590}, {17262, 26806}, {17263, 38093}, {17336, 24199}, {17345, 48628}, {17351, 17352}, {17355, 48629}, {17358, 48631}, {17781, 20921}, {20059, 42696}, {20928, 42029}, {22003, 24063}, {24280, 47357}, {24693, 24821}, {24723, 48851}, {24833, 36551}, {28301, 29574}, {28534, 49483}, {29577, 31138}, {31140, 36223}, {35578, 46922}, {39707, 48637}

X(49722) = reflection of X(i) in X(j) for these {i,j}: {192, 17392}, {17333, 4688}, {17346, 75}, {17347, 17346}, {17392, 7228}
X(49722) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {894, 4398, 17380}, {1278, 17365, 17377}, {3729, 6173, 17264}, {3729, 7321, 17234}, {4363, 4440, 4389}, {4454, 42697, 190}, {6173, 17264, 17234}, {7321, 17264, 6173}, {17116, 17276, 5224}, {17351, 48627, 17352}


X(49723) = X(1)X(524)∩X(2)X(58)

Barycentrics    2*a^4 + a^3*b - 2*a^2*b^2 - 2*a*b^3 - b^4 + a^3*c - 2*a^2*b*c - 5*a*b^2*c - 2*b^3*c - 2*a^2*c^2 - 5*a*b*c^2 - 2*b^2*c^2 - 2*a*c^3 - 2*b*c^3 - c^4 : :
X(49723) = 3 X[25055] - 2 X[37631], 5 X[25917] - 2 X[49557]

X(49723) lies on these lines: {1, 524}, {2, 58}, {10, 896}, {21, 31143}, {30, 40}, {44, 19867}, {333, 17677}, {340, 1982}, {405, 599}, {511, 5692}, {519, 2292}, {530, 5699}, {531, 5700}, {542, 5258}, {551, 41815}, {597, 13728}, {1008, 7812}, {1009, 7810}, {1010, 31144}, {1654, 14712}, {1992, 13725}, {2245, 11112}, {2482, 37023}, {2796, 4647}, {2895, 4653}, {3017, 4921}, {3647, 20653}, {4195, 9939}, {4234, 41816}, {4256, 37656}, {4933, 21081}, {5032, 19766}, {5251, 33082}, {5278, 17679}, {5315, 28369}, {5463, 11097}, {5464, 11098}, {5526, 15984}, {7283, 29615}, {7801, 13723}, {7817, 37025}, {7840, 19312}, {9534, 32480}, {11101, 15360}, {11160, 13736}, {11163, 37053}, {11263, 31177}, {11359, 19723}, {11645, 48939}, {13735, 17271}, {13857, 27685}, {15983, 16499}, {16342, 31179}, {16394, 17251}, {16948, 24931}, {17346, 37038}, {17579, 48852}, {17768, 46895}, {19742, 48843}, {19924, 48936}, {22110, 37047}, {25055, 37631}, {25917, 49557}, {28558, 49598}, {31173, 37049}, {31855, 44419}, {38330, 48899}

X(49723) = reflection of X(i) in X(j) for these {i,j}: {1, 13745}, {42045, 551}, {48899, 38330}


X(49724) = X(2)X(6)∩X(30)X(40)

Barycentrics    2*a^3 - 3*a*b^2 - b^3 - 4*a*b*c - 3*b^2*c - 3*a*c^2 - 3*b*c^2 - c^3 : :
X(49724) = 2 X[3578] + X[37631], 3 X[3578] + X[42045], 3 X[37631] - 2 X[42045], 2 X[9958] + X[48928]

X(49724) lies on these lines: {2, 6}, {8, 4918}, {10, 540}, {30, 40}, {63, 17275}, {210, 511}, {257, 29617}, {306, 4690}, {312, 17331}, {321, 17332}, {340, 25986}, {519, 3743}, {538, 42051}, {545, 4980}, {553, 4059}, {594, 3219}, {846, 4046}, {896, 8013}, {1376, 15447}, {1834, 26064}, {1999, 17256}, {3187, 4364}, {3666, 3686}, {3672, 30711}, {3691, 22097}, {3712, 21085}, {3719, 40997}, {3739, 4001}, {3741, 41002}, {3782, 4643}, {3826, 33080}, {3925, 33082}, {3943, 33761}, {3969, 4478}, {4023, 32916}, {4026, 32864}, {4030, 49457}, {4061, 4689}, {4204, 18185}, {4384, 40688}, {4399, 17147}, {4416, 31993}, {4418, 4733}, {4445, 17776}, {4651, 44419}, {4658, 17514}, {4665, 32933}, {4854, 24697}, {4886, 38000}, {4969, 17011}, {4981, 5846}, {5249, 17344}, {5257, 37595}, {5258, 48930}, {5294, 17239}, {5686, 29181}, {5839, 20182}, {9013, 48247}, {9810, 14425}, {9958, 48928}, {11112, 48852}, {11113, 48839}, {11346, 48859}, {12555, 31142}, {14206, 42708}, {15973, 21031}, {16418, 40980}, {17118, 20078}, {17163, 28530}, {17237, 26723}, {17252, 19786}, {17253, 19785}, {17254, 19796}, {17255, 19789}, {17270, 32777}, {17272, 24789}, {17328, 27184}, {17333, 42029}, {17334, 28605}, {17362, 28606}, {17768, 21020}, {17770, 27798}, {18253, 20653}, {25055, 39948}, {26724, 48632}, {28503, 42039}, {28610, 28638}, {28840, 47890}, {29615, 42033}, {31156, 48862}, {33079, 36483}, {33157, 48635}, {37038, 48850}, {40891, 41823}, {44217, 48834}

X(49724) = midpoint of X(2) and X(3578)
X(49724) = reflection of X(i) in X(j) for these {i,j}: {9810, 14425}, {37631, 2}
X(49724) = complement of X(42045)
X(49724) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1654, 41816}, {2, 1992, 19722}, {2, 41816, 1211}, {333, 1211, 35466}, {333, 1654, 1211}, {333, 41816, 2}, {846, 42334, 4046}, {966, 14552, 940}, {1150, 5743, 37634}, {2895, 5235, 17056}, {4643, 5271, 3782}, {5737, 5739, 5718}, {14555, 37660, 37663}, {16704, 41809, 6703}, {31144, 41629, 2}


X(49725) = X(2)X(11)∩X(10)X(44)

Barycentrics    2*a^3 + 3*a*b^2 - b^3 + 6*a*b*c + 3*b^2*c + 3*a*c^2 + 3*b*c^2 - c^3 : :
X(49725) = X[984] + 3 X[24452], 2 X[4709] + X[17388], 4 X[4732] - X[17362], 2 X[7228] + X[49448], X[17365] + 2 X[49457], 2 X[17390] + X[49459], 3 X[39704] + X[49450]

X(49725) lies on these lines: {1, 4395}, {2, 11}, {8, 17378}, {10, 44}, {37, 28580}, {75, 28503}, {141, 31151}, {516, 36722}, {519, 3696}, {524, 3416}, {529, 48816}, {545, 984}, {551, 3755}, {599, 48802}, {674, 3753}, {1010, 9710}, {1086, 24693}, {1211, 31134}, {1213, 4660}, {1386, 41140}, {1738, 17382}, {3241, 49486}, {3242, 31139}, {3712, 27754}, {3723, 4780}, {3828, 24295}, {3913, 37153}, {3923, 4370}, {3932, 17281}, {3945, 49680}, {4023, 33112}, {4078, 4908}, {4085, 17398}, {4307, 37654}, {4364, 24715}, {4407, 24692}, {4432, 25352}, {4472, 29659}, {4645, 17271}, {4648, 49460}, {4665, 32847}, {4702, 29571}, {4709, 17388}, {4732, 17362}, {4966, 17313}, {4981, 11246}, {5057, 27776}, {5192, 34501}, {5241, 33104}, {5278, 42058}, {5743, 33109}, {5880, 17274}, {5902, 9054}, {6173, 47358}, {6284, 14020}, {6703, 32865}, {7227, 33165}, {7228, 49448}, {9041, 31178}, {9708, 48833}, {11113, 19870}, {12607, 26051}, {13745, 19871}, {16815, 49709}, {16830, 17320}, {17245, 32941}, {17301, 48854}, {17333, 17768}, {17337, 49482}, {17365, 49457}, {17390, 49459}, {19274, 31458}, {19277, 48831}, {19336, 31157}, {19853, 37038}, {19875, 33159}, {20716, 42056}, {24199, 49465}, {24248, 24441}, {25590, 49688}, {28301, 49523}, {28309, 49474}, {29291, 36720}, {29660, 40480}, {31138, 49511}, {38047, 38200}, {39587, 49453}, {39704, 49450}

X(49725) = midpoint of X(8) and X(17378)
X(49725) = reflection of X(17330) in X(10)
X(49725) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 2550, 48829}, {2, 5263, 48810}, {2, 48829, 4026}, {3826, 48810, 2}, {24693, 36480, 1086}, {24715, 36531, 4364}


X(49726) = X(2)X(45)∩X(6)X(4971)

Barycentrics    4*a^2 - 2*a*b + b^2 - 2*a*c + 4*b*c + c^2 : :
X(49726) = 5 X[141] - 2 X[17345], X[141] + 2 X[17351], X[141] - 4 X[17355], X[17345] + 5 X[17351], X[17345] - 10 X[17355], X[17345] - 5 X[17359], X[17351] + 2 X[17355], 3 X[17281] - X[17294], 2 X[3923] + X[49524], 2 X[2321] + X[3629], 2 X[3589] + X[3729], X[3630] - 4 X[17229], 2 X[3631] - 5 X[17286], X[3875] - 4 X[6329], 2 X[17382] - 3 X[48310], X[17276] - 4 X[34573], X[17299] + 2 X[32455]

X(49726) lies on these lines: {2, 45}, {6, 4971}, {9, 7227}, {10, 28534}, {44, 4665}, {141, 527}, {142, 7231}, {144, 17293}, {346, 17390}, {519, 4527}, {524, 17281}, {528, 3923}, {536, 597}, {537, 48810}, {551, 49456}, {594, 17346}, {599, 28333}, {894, 17243}, {1213, 17336}, {1743, 4399}, {1992, 28337}, {2321, 3629}, {2325, 4670}, {2345, 6172}, {2796, 48821}, {3161, 15668}, {3589, 3729}, {3630, 17229}, {3631, 17286}, {3663, 28322}, {3731, 6707}, {3758, 3943}, {3875, 6329}, {3973, 28634}, {4072, 4889}, {4395, 4659}, {4416, 48636}, {4431, 16669}, {4480, 17237}, {4488, 17255}, {4644, 17269}, {4669, 49710}, {4688, 49516}, {4715, 22165}, {4795, 29573}, {4798, 16676}, {4852, 28313}, {4908, 29574}, {4967, 15492}, {5220, 48802}, {5749, 17045}, {5835, 34606}, {6173, 7228}, {6174, 32931}, {6534, 48820}, {7222, 17265}, {7229, 17259}, {7238, 17284}, {7263, 17353}, {7277, 17233}, {9041, 48805}, {10707, 33170}, {16475, 28472}, {16522, 29584}, {16561, 36483}, {16834, 28309}, {17116, 17337}, {17118, 26685}, {17120, 17388}, {17132, 17382}, {17245, 17339}, {17246, 17368}, {17254, 17289}, {17261, 17398}, {17274, 20582}, {17276, 34573}, {17280, 17297}, {17285, 31300}, {17299, 32455}, {17303, 25728}, {17313, 35578}, {17347, 48635}, {17357, 48631}, {17358, 48632}, {17381, 25269}, {19875, 24697}, {24828, 36490}, {25382, 36220}, {28530, 38047}, {28555, 38049}, {29243, 36551}, {29582, 39704}, {31140, 33163}, {31164, 32777}

X(49726) = midpoint of X(i) and X(j) for these {i,j}: {3729, 17301}, {17351, 17359}
X(49726) = reflection of X(i) in X(j) for these {i,j}: {141, 17359}, {17274, 20582}, {17301, 3589}, {17359, 17355}, {22165, 29594}
X(49726) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {190, 17369, 4364}, {894, 17264, 17392}, {894, 17340, 17243}, {2345, 6172, 17251}, {4363, 4422, 34824}, {5749, 17262, 17045}, {6172, 17251, 17332}, {17264, 17392, 17243}, {17340, 17392, 17264}, {17351, 17355, 141}


X(49727) = X(2)X(45)∩X(6)X(4402)

Barycentrics    2*a^2 - b^2 + 6*b*c - c^2 : :
X(49727) = 5 X[75] - 2 X[4399], X[75] + 2 X[7228], 4 X[75] - X[17362], 7 X[75] - X[17363], 5 X[75] + X[17364], 2 X[75] + X[17365], 3 X[75] - X[29617], X[4399] + 5 X[7228], 8 X[4399] - 5 X[17362], 14 X[4399] - 5 X[17363], 2 X[4399] + X[17364], 4 X[4399] + 5 X[17365], 6 X[4399] - 5 X[29617], 8 X[7228] + X[17362], 14 X[7228] + X[17363], 10 X[7228] - X[17364], 4 X[7228] - X[17365], 6 X[7228] + X[29617], 7 X[17362] - 4 X[17363], 5 X[17362] + 4 X[17364], X[17362] + 2 X[17365], 3 X[17362] - 4 X[29617], 5 X[17363] + 7 X[17364], 2 X[17363] + 7 X[17365], 3 X[17363] - 7 X[29617], 2 X[17364] - 5 X[17365], 3 X[17364] + 5 X[29617], 3 X[17365] + 2 X[29617], 3 X[17392] - 2 X[29574], X[1278] + 2 X[17390], 2 X[3664] + X[4686], 4 X[3664] - X[17388], 2 X[4686] + X[17388], 4 X[3739] - X[17334], X[3879] + 2 X[4726], X[4416] - 4 X[4739], 3 X[4664] - 5 X[29622], 5 X[4699] - 2 X[17332], X[4764] + 5 X[17391], 7 X[4772] - X[17347], 5 X[4821] + X[17377], X[17389] - 3 X[39704]

X(49727) lies on these lines: {2, 45}, {6, 4402}, {7, 594}, {8, 15533}, {37, 17132}, {75, 524}, {141, 7321}, {142, 17340}, {239, 8584}, {320, 4665}, {519, 49468}, {527, 4688}, {528, 31178}, {536, 17392}, {551, 28542}, {591, 32797}, {597, 894}, {1213, 17276}, {1266, 4670}, {1278, 17390}, {1447, 11168}, {1991, 32798}, {1992, 4361}, {2345, 21358}, {2796, 24325}, {2886, 24411}, {3035, 27777}, {3058, 4459}, {3589, 48627}, {3598, 42850}, {3629, 17117}, {3630, 5564}, {3631, 48628}, {3661, 7238}, {3662, 7227}, {3663, 17398}, {3664, 4686}, {3679, 5880}, {3729, 17245}, {3739, 4912}, {3758, 4395}, {3759, 20583}, {3763, 7229}, {3879, 4726}, {3943, 4659}, {4000, 47352}, {4371, 6144}, {4398, 17045}, {4413, 12035}, {4416, 4739}, {4418, 24409}, {4431, 17376}, {4452, 16884}, {4461, 17311}, {4478, 17361}, {4644, 4969}, {4664, 28297}, {4667, 49543}, {4669, 49713}, {4699, 17332}, {4740, 4971}, {4755, 28322}, {4764, 17391}, {4772, 17347}, {4795, 16834}, {4821, 17377}, {4862, 17303}, {4887, 17237}, {4888, 17299}, {4896, 17374}, {4908, 29600}, {4967, 17345}, {6173, 17281}, {6646, 31144}, {6707, 17247}, {7179, 22110}, {7232, 21356}, {8370, 33940}, {9041, 24349}, {10436, 17246}, {11160, 42696}, {16706, 48310}, {17243, 26806}, {17288, 48636}, {17289, 48631}, {17337, 17351}, {17346, 28333}, {17389, 28309}, {17483, 31143}, {20180, 46922}, {25382, 30982}, {29594, 31138}, {32087, 40341}, {34573, 48629}

X(49727) = midpoint of X(4740) and X(17378)
X(49727) = reflection of X(17330) in X(4688)
X(49727) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 17118, 594}, {75, 7228, 17365}, {75, 17364, 4399}, {75, 17365, 17362}, {320, 29615, 22165}, {597, 7263, 37756}, {597, 37756, 17366}, {894, 7263, 17366}, {894, 37756, 597}, {1086, 4363, 17369}, {1266, 4670, 17395}, {3664, 4686, 17388}, {4346, 4470, 17325}, {4363, 42697, 1086}, {4644, 17119, 4969}, {4659, 4675, 3943}, {4665, 22165, 29615}, {7222, 31995, 6}, {7231, 7263, 894}, {7321, 17116, 141}, {17276, 25590, 1213}, {17351, 24199, 17337}


X(49728) = X(1)X(524)∩X(10)X(30)

Barycentrics    2*a^4 - 3*a^2*b^2 - 2*a*b^3 - b^4 - 4*a^2*b*c - 6*a*b^2*c - 2*b^3*c - 3*a^2*c^2 - 6*a*b*c^2 - 2*b^2*c^2 - 2*a*c^3 - 2*b*c^3 - c^4 : :
X(49728) = X[1] - 3 X[13745], X[145] + 3 X[3578], 5 X[3616] - 3 X[37631], 7 X[3622] - 3 X[42045]

X(49728) lies on these lines: {1, 524}, {2, 4252}, {3, 5743}, {4, 5737}, {6, 13725}, {8, 4918}, {9, 13442}, {10, 30}, {12, 32917}, {20, 966}, {21, 1211}, {32, 37044}, {58, 4205}, {69, 13736}, {72, 17332}, {86, 20077}, {141, 405}, {145, 3578}, {187, 6537}, {220, 15984}, {325, 6626}, {333, 1834}, {377, 19732}, {386, 48839}, {404, 5241}, {443, 17259}, {500, 997}, {511, 960}, {540, 1125}, {594, 7283}, {740, 12579}, {754, 19868}, {846, 3704}, {896, 27714}, {936, 48897}, {940, 37314}, {958, 1503}, {968, 10371}, {993, 48930}, {1008, 7745}, {1010, 1213}, {1043, 1654}, {1086, 16817}, {1104, 4357}, {1191, 28369}, {1193, 41002}, {1329, 15973}, {1330, 11110}, {1376, 15592}, {1453, 4657}, {1724, 3589}, {1992, 19783}, {2176, 15989}, {2475, 5235}, {2478, 37660}, {2551, 15971}, {3454, 6675}, {3564, 48894}, {3616, 37631}, {3622, 42045}, {3649, 4683}, {3712, 20653}, {3739, 4292}, {3763, 13742}, {3815, 37053}, {3846, 4999}, {3936, 17588}, {4026, 5247}, {4195, 5224}, {4199, 4267}, {4201, 17277}, {4255, 14555}, {4340, 15668}, {4389, 19851}, {4472, 19857}, {4647, 28530}, {4653, 41014}, {4660, 9710}, {4754, 39581}, {4854, 27368}, {5051, 35466}, {5232, 11106}, {5233, 19278}, {5260, 33083}, {5273, 48890}, {5278, 17676}, {5289, 48909}, {5433, 25960}, {5436, 17272}, {5453, 30144}, {5718, 16342}, {5739, 19765}, {5741, 16347}, {5794, 48937}, {5835, 12514}, {6284, 31330}, {6707, 17514}, {7354, 31339}, {7379, 26244}, {7789, 13723}, {8728, 48835}, {9534, 17330}, {10381, 18165}, {10449, 48814}, {10479, 11113}, {11101, 32269}, {11111, 17251}, {11115, 41809}, {11357, 48834}, {12572, 44417}, {13408, 26363}, {13567, 37228}, {15670, 25645}, {15672, 24946}, {15674, 30831}, {15823, 46878}, {16052, 24880}, {16699, 45802}, {16824, 24723}, {16859, 33172}, {16865, 32782}, {17123, 25914}, {17245, 37035}, {17265, 17552}, {17327, 37037}, {17337, 33833}, {17346, 20018}, {17398, 37039}, {17539, 27081}, {17553, 24936}, {17557, 26131}, {17677, 25446}, {17768, 49598}, {19266, 19762}, {19270, 37662}, {19723, 48845}, {19744, 37153}, {19760, 37175}, {19843, 48935}, {20420, 48888}, {21616, 48931}, {22325, 23841}, {24220, 31774}, {24384, 32459}, {24570, 26958}, {24703, 48899}, {24953, 25760}, {25906, 26543}, {25992, 32781}, {30478, 46483}, {31156, 48859}, {37047, 44377}, {41229, 49524}

X(49728) = midpoint of X(13442) and X(48883)
X(49728) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 31445, 44416}, {21, 26064, 1211}, {58, 4205, 6703}, {333, 26117, 1834}, {1330, 11110, 17056}, {1724, 13728, 3589}, {17514, 25526, 6707}


X(49729) = X(2)X(58)∩X(10)X(30)

Barycentrics    2*a^4 - 4*a^2*b^2 - 3*a*b^3 - b^4 - 6*a^2*b*c - 9*a*b^2*c - 3*b^3*c - 4*a^2*c^2 - 9*a*b*c^2 - 4*b^2*c^2 - 3*a*c^3 - 3*b*c^3 - c^4 : :
X(49729) = 3 X[25055] - X[42045]

X(49729) lies on these lines: {1, 3578}, {2, 58}, {10, 30}, {15, 37831}, {16, 37834}, {333, 3017}, {376, 966}, {381, 5737}, {511, 10176}, {519, 3743}, {524, 551}, {542, 15985}, {549, 5743}, {599, 11357}, {846, 3679}, {993, 14636}, {1125, 37631}, {1211, 15670}, {1654, 4653}, {2092, 17330}, {2305, 19276}, {3584, 32917}, {4234, 31144}, {4364, 49683}, {4407, 49686}, {5224, 7811}, {5235, 6175}, {5278, 48843}, {6626, 7799}, {13725, 48857}, {15671, 25645}, {15936, 17272}, {16418, 17251}, {17256, 30115}, {17553, 31143}, {19732, 44217}, {23897, 39563}, {25055, 42045}, {31156, 48863}, {31446, 48890}, {37038, 48852}

X(49729) = midpoint of X(1) and X(3578)
X(49729) = reflection of X(37631) in X(1125)
X(49729) = {X(2),X(48870)}-harmonic conjugate of X(43531)


X(49730) = X(2)X(6)∩X(10)X(30)

Barycentrics    2*a^3 - 2*a^2*b - 5*a*b^2 - b^3 - 2*a^2*c - 8*a*b*c - 5*b^2*c - 5*a*c^2 - 5*b*c^2 - c^3 : :
X(49730) = 3 X[2] + X[3578], 5 X[2] - X[42045], 5 X[3578] + 3 X[42045], 5 X[37631] - 3 X[42045]

X(49730) lies on these lines: {2, 6}, {10, 30}, {45, 42032}, {63, 2160}, {375, 511}, {405, 48859}, {530, 49571}, {531, 49572}, {540, 3828}, {553, 3739}, {594, 42033}, {846, 4733}, {958, 14636}, {1503, 9746}, {1761, 3929}, {2049, 48870}, {3017, 4205}, {3058, 31330}, {3219, 5341}, {3679, 3704}, {3712, 8013}, {3928, 28608}, {3943, 4102}, {3989, 28472}, {4364, 5271}, {4399, 28606}, {4415, 17256}, {4428, 48802}, {4472, 4641}, {4643, 4654}, {4708, 40940}, {4980, 28297}, {4981, 9053}, {4995, 32917}, {5434, 31339}, {6175, 26064}, {7231, 20078}, {9711, 15973}, {13725, 48842}, {17332, 17781}, {17362, 42030}, {17768, 27798}, {17776, 48636}, {18163, 46196}, {19859, 48828}, {21020, 28530}, {29181, 38057}, {30970, 41002}, {32419, 49623}, {32421, 49622}, {37150, 48839}

X(49730) = midpoint of X(i) and X(j) for these {i,j}: {3578, 37631}, {3679, 13745}
X(49730) = complement of X(37631)
X(49730) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3578, 37631}, {2, 19723, 597}, {333, 1213, 6703}, {333, 26044, 1213}, {966, 5737, 5743}


X(49731) = X(2)X(6)∩X(10)X(528)

Barycentrics    2*a^2 - 4*a*b - b^2 - 4*a*c - 4*b*c - c^2 : :
X(49731) = 3 X[2] + X[17346], 5 X[2] - X[17378], 3 X[17330] - X[17346], 5 X[17330] + X[17378], 3 X[17330] + X[17392], 5 X[17346] + 3 X[17378], 3 X[17378] - 5 X[17392], 2 X[37] + X[4399], 4 X[3739] - X[7228], 2 X[3739] + X[17332], X[7228] + 2 X[17332], X[4688] + 3 X[16590], X[3686] + 2 X[4698], 2 X[3686] + X[17390], 4 X[4698] - X[17390], X[4416] + 5 X[31238], X[4664] - 9 X[41848], 5 X[4687] + X[17362], 5 X[4687] - X[17389], 5 X[4699] + X[17334], 7 X[4751] + 5 X[17331], 7 X[4751] - X[17365], 5 X[17331] + X[17365], X[17049] + 2 X[40607], X[17388] - 7 X[27268], X[48841] + 3 X[48852]

X(49731) lies on these lines: {2, 6}, {9, 7227}, {10, 528}, {30, 48860}, {37, 4399}, {44, 4472}, {45, 4665}, {75, 28297}, {144, 7231}, {210, 9054}, {319, 29575}, {344, 48636}, {519, 3842}, {527, 3739}, {545, 4688}, {551, 4974}, {573, 36728}, {594, 17260}, {674, 3740}, {752, 3823}, {1001, 48802}, {1086, 16815}, {3008, 4708}, {3161, 28635}, {3617, 17269}, {3679, 3932}, {3686, 4698}, {3707, 4670}, {3731, 28634}, {3742, 9038}, {3834, 31211}, {3912, 31285}, {3986, 4852}, {4361, 5296}, {4363, 6172}, {4364, 4384}, {4405, 17318}, {4416, 31238}, {4478, 17243}, {4643, 6173}, {4663, 39580}, {4664, 28309}, {4681, 28313}, {4687, 17362}, {4690, 29571}, {4699, 17334}, {4739, 28322}, {4748, 17290}, {4751, 17331}, {4798, 16670}, {4967, 16814}, {4969, 16826}, {5257, 17045}, {5816, 36731}, {6174, 32917}, {6666, 17239}, {6687, 29604}, {7263, 17257}, {16667, 28640}, {16675, 42696}, {16816, 17395}, {16833, 41312}, {16857, 48859}, {17023, 25358}, {17049, 40607}, {17224, 17382}, {17229, 25072}, {17237, 40480}, {17248, 17366}, {17250, 29628}, {17252, 48632}, {17253, 48631}, {17263, 48635}, {17272, 38093}, {17293, 18230}, {17328, 27147}, {17335, 17369}, {17355, 28633}, {17360, 29581}, {17388, 27268}, {19875, 33159}, {24754, 25356}, {26037, 44419}, {27791, 30579}, {28337, 29574}, {31311, 32025}, {31333, 32101}, {31339, 34606}, {41140, 41311}, {48809, 48810}, {48841, 48852}, {48846, 48850}, {48851, 49524}

X(49731) = midpoint of X(i) and X(j) for these {i,j}: {2, 17330}, {573, 36728}, {17346, 17392}, {17362, 17389}, {48846, 48850}
X(49731) = complement of X(17392)
X(49731) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 966, 17251}, {2, 1654, 17297}, {2, 17251, 141}, {2, 17297, 17245}, {2, 17346, 17392}, {44, 24603, 4472}, {391, 15668, 3629}, {966, 17259, 141}, {1213, 17277, 3589}, {1654, 17245, 3631}, {3686, 4698, 17390}, {3739, 17332, 7228}, {4364, 4384, 4395}, {4643, 16832, 34824}, {4643, 34824, 7238}, {4751, 17331, 17365}, {5224, 17337, 34573}, {5232, 17265, 141}, {5257, 17348, 17045}, {16815, 17256, 1086}, {17243, 17275, 4478}, {17251, 17259, 2}, {17330, 17392, 17346}, {17335, 29576, 17369}, {17349, 17398, 6329}


X(49732) = X(2)X(11)∩X(10)X(30)

Barycentrics    2*a^3 - 2*a^2*b + a*b^2 - b^3 - 2*a^2*c + 4*a*b*c + b^2*c + a*c^2 + b*c^2 - c^3 : :
X(49732) = 5 X[2] - X[34611], 5 X[3058] - 3 X[34611], X[3058] + 3 X[34612], X[34611] + 5 X[34612], 3 X[210] - X[17781], 4 X[12436] - X[34791], X[1770] + 5 X[3697], 5 X[3617] + X[7354], 2 X[3626] + X[18990], 4 X[3634] - X[15171], 4 X[3918] - X[37730], 7 X[3922] - X[41575], 7 X[4002] - X[10572], X[4292] + 2 X[4662], 5 X[5071] - X[34629], 5 X[5818] + X[11826], 3 X[26446] - X[28459], X[6284] - 7 X[9780], X[6737] + 2 X[10107], X[11113] - 3 X[19875], X[11362] + 2 X[37281], 2 X[15172] - 5 X[19862], 5 X[15694] - X[34745], 2 X[19925] + X[31777], X[20420] + 2 X[43174], X[34697] - 3 X[38074], X[37430] + 3 X[38074], X[34699] - 3 X[38314], X[40998] - 3 X[46916]

X(49732) lies on these lines: {2, 11}, {3, 9710}, {4, 9711}, {8, 5221}, {10, 30}, {12, 6175}, {35, 15670}, {42, 37631}, {46, 529}, {75, 37671}, {141, 41454}, {165, 38200}, {200, 4654}, {210, 17768}, {355, 28458}, {375, 15310}, {376, 958}, {377, 11237}, {381, 1329}, {404, 5298}, {428, 1861}, {442, 3584}, {443, 3913}, {474, 3813}, {511, 22278}, {515, 10178}, {516, 3740}, {517, 10170}, {518, 553}, {519, 942}, {524, 4685}, {527, 9954}, {535, 4745}, {545, 24336}, {547, 25639}, {549, 4999}, {594, 2160}, {678, 29689}, {936, 31162}, {960, 28194}, {993, 8703}, {997, 3656}, {1056, 8168}, {1086, 3961}, {1125, 15170}, {1155, 25006}, {1211, 32948}, {1503, 10174}, {1574, 7753}, {1575, 9300}, {1722, 48827}, {1738, 17061}, {1770, 3697}, {2475, 21031}, {2551, 3543}, {2796, 4096}, {2829, 5790}, {3090, 31420}, {3158, 38052}, {3189, 11024}, {3241, 34720}, {3303, 37462}, {3306, 4863}, {3419, 17699}, {3452, 18482}, {3474, 5220}, {3524, 19843}, {3534, 9708}, {3578, 4651}, {3582, 6691}, {3592, 31486}, {3617, 7354}, {3626, 18990}, {3634, 15171}, {3648, 32635}, {3649, 4420}, {3654, 28452}, {3681, 5852}, {3689, 5249}, {3711, 5905}, {3715, 44447}, {3742, 5853}, {3746, 17529}, {3749, 17278}, {3750, 17245}, {3753, 44669}, {3755, 4682}, {3814, 5066}, {3820, 3845}, {3838, 6745}, {3870, 25557}, {3871, 26060}, {3918, 37730}, {3922, 41575}, {3932, 32932}, {3938, 40688}, {3971, 28530}, {3980, 49524}, {3996, 4966}, {4001, 4113}, {4002, 10572}, {4023, 6327}, {4030, 4359}, {4046, 33078}, {4085, 6703}, {4126, 32933}, {4292, 4662}, {4309, 16842}, {4386, 5306}, {4415, 24715}, {4418, 14985}, {4450, 41002}, {4660, 5743}, {4695, 5724}, {4854, 5297}, {4857, 17575}, {4906, 24175}, {4942, 5423}, {5044, 28198}, {5047, 34501}, {5054, 18543}, {5055, 26364}, {5071, 31418}, {5080, 15679}, {5082, 25524}, {5087, 20103}, {5241, 32947}, {5251, 17525}, {5260, 15338}, {5267, 34200}, {5437, 17051}, {5438, 25055}, {5524, 33097}, {5537, 8226}, {5687, 10056}, {5695, 42032}, {5711, 48857}, {5818, 11826}, {5840, 38042}, {5841, 38112}, {5842, 26446}, {6173, 41548}, {6284, 9780}, {6737, 10107}, {6904, 12513}, {6923, 38757}, {6951, 37725}, {6980, 20400}, {7263, 32920}, {7489, 10993}, {7742, 16371}, {7924, 26558}, {8580, 24703}, {8616, 17337}, {8666, 17563}, {8715, 8728}, {9041, 42055}, {9053, 24165}, {9350, 33104}, {9712, 14070}, {9713, 9909}, {9776, 42871}, {9778, 38057}, {10022, 24334}, {10164, 38201}, {10176, 28174}, {10691, 34822}, {11111, 34626}, {11113, 19875}, {11362, 37281}, {13463, 19861}, {13587, 31157}, {13745, 19870}, {13846, 31484}, {15172, 19862}, {15621, 16056}, {15692, 30478}, {15694, 31493}, {16417, 45700}, {16857, 34707}, {17070, 21949}, {17366, 17716}, {17392, 42042}, {17528, 45701}, {17531, 37722}, {17533, 31159}, {17561, 19855}, {17579, 34606}, {17602, 33131}, {17647, 28204}, {17750, 48848}, {18141, 49460}, {19054, 31413}, {19276, 48831}, {19925, 31777}, {20070, 45085}, {20420, 43174}, {22758, 38759}, {24177, 49465}, {24434, 42039}, {24693, 29670}, {24694, 25355}, {24987, 32157}, {25135, 28562}, {25351, 29656}, {25681, 38021}, {26066, 37428}, {27186, 37703}, {28503, 42051}, {28556, 32925}, {28580, 35652}, {29651, 34824}, {29672, 40480}, {30145, 48820}, {30308, 30827}, {30613, 42454}, {31145, 34749}, {31453, 41945}, {31491, 31652}, {32865, 37646}, {33109, 37662}, {33136, 37634}, {34605, 34689}, {34625, 40726}, {34697, 37430}, {34699, 38314}, {34728, 44442}, {37375, 44847}, {40998, 46916}

X(49732) = midpoint of X(i) and X(j) for these {i,j}: {2, 34612}, {8, 5434}, {355, 28458}, {376, 34746}, {3241, 34720}, {3543, 34630}, {3654, 28452}, {3679, 11112}, {3681, 11246}, {17579, 34606}, {30613, 42454}, {31145, 34749}, {34605, 34689}, {34697, 37430}, {34728, 44442}
X(49732) = reflection of X(15170) in X(1125)
X(49732) = complement of X(3058)
X(49732) = complement of the isogonal conjugate of X(41431)
X(49732) = X(41431)-complementary conjugate of X(10)
X(49732) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 100, 4995}, {2, 3434, 11238}, {2, 3829, 45310}, {2, 4995, 6690}, {2, 10385, 1001}, {2, 11238, 3816}, {2, 17784, 10385}, {2, 31140, 3829}, {2, 34607, 4428}, {10, 3579, 18253}, {10, 31730, 5302}, {100, 3925, 6690}, {1376, 2550, 2886}, {1376, 2886, 3035}, {1706, 5794, 8256}, {3434, 4413, 3816}, {3925, 4995, 2}, {4413, 11238, 2}, {5687, 44217, 10056}, {9350, 33104, 37663}, {10056, 44217, 25466}, {10385, 26040, 2}, {17784, 26040, 1001}, {25440, 31419, 4999}, {37430, 38074, 34697}


X(49733) = X(2)X(45)∩X(10)X(7238)

Barycentrics    2*a^2 + 2*a*b - b^2 + 2*a*c + 8*b*c - c^2 : :
X(49733) = 5 X[75] + X[17388], 3 X[75] + X[17389], 2 X[75] + X[17390], 7 X[75] + 5 X[17391], 3 X[17388] - 5 X[17389], 2 X[17388] - 5 X[17390], 7 X[17388] - 25 X[17391], X[17388] - 5 X[17392], 2 X[17389] - 3 X[17390], 7 X[17389] - 15 X[17391], X[17389] - 3 X[17392], 7 X[17390] - 10 X[17391], 5 X[17391] - 7 X[17392], 2 X[3739] + X[7228], 4 X[3739] - X[17332], 2 X[7228] + X[17332], 2 X[3664] + X[4399], X[3664] + 2 X[4739], X[4399] - 4 X[4739], 5 X[4699] - X[17346], 5 X[4699] + X[17365], 7 X[4751] - X[17334], 7 X[4772] - X[17362], X[29617] + 3 X[39704]

X(49733) lies on these lines: {2, 45}, {7, 17251}, {9, 7231}, {10, 7238}, {37, 28297}, {75, 4971}, {141, 6173}, {142, 7227}, {524, 4688}, {527, 3739}, {528, 24325}, {551, 49484}, {594, 17297}, {1125, 28542}, {1213, 7321}, {2094, 5737}, {3589, 24199}, {3630, 4888}, {3631, 4967}, {3663, 6707}, {3664, 4399}, {3679, 22165}, {3943, 29575}, {4395, 4670}, {4478, 17376}, {4665, 4675}, {4690, 4896}, {4698, 28322}, {4699, 17346}, {4700, 4796}, {4708, 4887}, {4726, 28313}, {4751, 17334}, {4755, 17132}, {4772, 17362}, {4795, 8584}, {5235, 35596}, {5743, 31164}, {5880, 48851}, {6172, 7222}, {7229, 17265}, {7263, 10436}, {9041, 31178}, {15668, 31995}, {15828, 17351}, {17116, 17245}, {17118, 17243}, {17279, 38093}, {17298, 48636}, {17303, 48631}, {17330, 28333}, {17340, 27147}, {17378, 28337}, {17395, 41847}, {17398, 17399}, {24348, 36220}, {25385, 45310}, {28309, 29574}, {28604, 48632}, {29617, 39704}

X(49733) = midpoint of X(i) and X(j) for these {i,j}: {75, 17392}, {17346, 17365}
X(49733) = reflection of X(17390) in X(17392)
X(49733) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3664, 4739, 4399}, {3739, 7228, 17332}, {4363, 34824, 4422}, {4795, 16833, 8584}, {4888, 28634, 3630}, {7263, 10436, 17045}


X(49734) = X(8)X(524)∩X(10)X(30)

Barycentrics    2*a^4 + a^2*b^2 + 2*a*b^3 - b^4 + 4*a^2*b*c + 6*a*b^2*c + 2*b^3*c + a^2*c^2 + 6*a*b*c^2 + 6*b^2*c^2 + 2*a*c^3 + 2*b*c^3 - c^4 : :
X(49734) = X[145] - 3 X[37631], 5 X[1698] - 3 X[13745], 3 X[3578] - 7 X[4678], X[3621] + 3 X[42045]

X(49734) lies on these lines: {4, 5743}, {8, 524}, {10, 30}, {20, 5737}, {29, 25659}, {141, 377}, {145, 37631}, {230, 23897}, {256, 24438}, {386, 37150}, {442, 25645}, {452, 17259}, {511, 5836}, {540, 3626}, {594, 7270}, {950, 3739}, {958, 37425}, {964, 3589}, {966, 3146}, {997, 48903}, {1010, 1834}, {1043, 17056}, {1125, 17070}, {1211, 2475}, {1213, 26117}, {1376, 9840}, {1503, 5794}, {1698, 13745}, {1706, 48883}, {1714, 16394}, {2049, 48837}, {2292, 28530}, {2345, 48890}, {2550, 5793}, {2886, 15973}, {2975, 15447}, {3578, 4678}, {3621, 42045}, {3712, 21674}, {3868, 7228}, {4190, 37660}, {4202, 34573}, {4234, 25446}, {4361, 5716}, {4395, 5262}, {4418, 21677}, {4643, 9579}, {4720, 26131}, {4968, 9053}, {5046, 5241}, {5224, 32819}, {5235, 15680}, {5292, 19276}, {6247, 6850}, {6284, 31339}, {6707, 14005}, {6872, 19732}, {7263, 37549}, {7354, 31330}, {8728, 48863}, {9623, 48897}, {10449, 48816}, {10454, 10472}, {10479, 11112}, {11115, 35466}, {12514, 48915}, {12625, 25590}, {13736, 19744}, {15338, 32917}, {15888, 32945}, {15936, 20008}, {16052, 24931}, {17265, 37436}, {17337, 17697}, {17679, 20582}, {19284, 37634}, {19766, 48842}, {24220, 31782}, {24384, 44377}, {25440, 48930}, {28368, 37542}, {37642, 43533}, {40587, 48907}, {43531, 48847}, {44217, 48859}, {44669, 49598}

X(49734) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 24850, 18253}, {1010, 1834, 6703}, {1043, 26051, 17056}


X(49735) = X(1)X(540)∩X(2)X(3)

Barycentrics    2*a^4 - a^3*b - 3*a^2*b^2 - a*b^3 - b^4 - a^3*c - 4*a^2*b*c - 4*a*b^2*c - b^3*c - 3*a^2*c^2 - 4*a*b*c^2 - a*c^3 - b*c^3 - c^4 : :
X(49735) = 4 X[9840] - X[48890], 3 X[14636] - 2 X[38430], X[2292] - 4 X[12579], X[46483] - 4 X[48894], 2 X[37631] - 3 X[38314], 2 X[48903] + X[48935]

X(49735) lies on these lines: {1, 540}, {2, 3}, {8, 4918}, {511, 3877}, {515, 11203}, {519, 2292}, {524, 3241}, {528, 12746}, {536, 49512}, {543, 1281}, {551, 4425}, {644, 15984}, {846, 3679}, {1043, 26064}, {1284, 5434}, {1654, 4720}, {1962, 38456}, {3058, 8240}, {3655, 30285}, {3897, 46483}, {3936, 4653}, {4450, 30116}, {4643, 49687}, {4660, 30056}, {4854, 39766}, {4972, 5251}, {5250, 48883}, {5278, 48837}, {5300, 48807}, {5330, 48909}, {8245, 34628}, {9959, 28204}, {15936, 17274}, {16086, 33761}, {17614, 48926}, {18139, 48835}, {19723, 48842}, {19738, 48870}, {19742, 48847}, {19861, 48897}, {24850, 27714}, {24929, 26580}, {30055, 32947}, {30366, 41856}, {35623, 48841}, {37631, 38314}, {48903, 48935}

X(49735) = reflection of X(i) in X(j) for these {i,j}: {2, 13745}, {42045, 1}, {46617, 48930}
X(49735) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 376, 19336}, {2, 6872, 48817}, {2, 11359, 4202}, {2, 15677, 4234}, {2, 17676, 11359}, {2, 31156, 11346}, {2, 48813, 17679}, {2, 48814, 14020}, {2, 48817, 964}, {20, 37314, 16454}, {21, 26117, 5051}, {381, 16351, 2}, {405, 11359, 2}, {405, 17676, 4202}, {855, 4199, 21}, {4201, 5047, 17674}, {6175, 17553, 2}, {6872, 13725, 964}, {11357, 44217, 2}, {13725, 48817, 2}, {15670, 16052, 2}, {17556, 19279, 2}, {37038, 48814, 2}


X(49736) = X(1)X(529)∩X(2)X(11)

Barycentrics    2*a^3 - 2*a^2*b + a*b^2 - b^3 - 2*a^2*c - 4*a*b*c + b^2*c + a*c^2 + b*c^2 - c^3 : :
X(49736) = 5 X[1] - X[34690], 5 X[11113] + X[34690], 3 X[2] + X[34611], 3 X[3058] - X[34611], 3 X[3058] + X[34612], X[10] + 2 X[15172], 2 X[3884] + X[37730], 2 X[1125] + X[15171], X[5434] - 3 X[38314], X[11114] + 3 X[38314], 3 X[3524] + X[34629], 3 X[3545] - X[34746], 3 X[3576] - X[37429], X[11112] - 3 X[25055], 5 X[3616] + X[6284], 5 X[3616] - X[17579], 7 X[3622] - X[7354], 4 X[3636] - X[18990], 3 X[3653] - X[28458], 2 X[3812] + X[10624], X[3878] + 2 X[12433], 5 X[3890] + X[10950], 3 X[5055] + X[34745], X[5836] + 2 X[12575], 3 X[5886] - X[28452], 7 X[9624] - X[37468], 3 X[10304] - X[34630], 5 X[10595] + X[11827], 5 X[10595] - X[34617], 2 X[12572] + X[34791], X[12572] + 2 X[40270], X[34791] - 4 X[40270], 2 X[13464] + X[31789], 2 X[15006] + X[15587], 2 X[15178] + X[37290], X[17647] + 2 X[31795], 3 X[19875] + X[34719], 3 X[19883] + X[34649], X[34698] - 5 X[37624]

X(49736) lies on these lines: {1, 529}, {2, 11}, {5, 10197}, {8, 34699}, {10, 15172}, {12, 37375}, {21, 31157}, {30, 551}, {35, 6691}, {57, 17051}, {145, 34689}, {226, 42819}, {329, 42871}, {354, 17768}, {376, 40726}, {377, 9670}, {381, 16202}, {388, 34739}, {392, 44669}, {405, 3813}, {428, 1848}, {442, 4857}, {452, 12513}, {474, 4309}, {496, 4999}, {498, 3847}, {515, 10179}, {516, 3742}, {517, 5892}, {518, 40998}, {519, 960}, {524, 42057}, {527, 5572}, {535, 25405}, {545, 24424}, {549, 10199}, {553, 3660}, {902, 37634}, {903, 41874}, {908, 3748}, {938, 34744}, {944, 34697}, {952, 3898}, {958, 1058}, {962, 34618}, {968, 17721}, {1086, 29820}, {1125, 7743}, {1211, 32943}, {1279, 17061}, {1329, 3295}, {1388, 3485}, {1479, 17532}, {1503, 10181}, {1532, 34486}, {1697, 8256}, {1699, 38316}, {1836, 4666}, {1962, 17726}, {2136, 3679}, {2177, 37663}, {2310, 24434}, {2478, 3303}, {2796, 42053}, {2829, 10246}, {2951, 6173}, {3086, 34741}, {3175, 28503}, {3241, 5330}, {3246, 40940}, {3304, 6872}, {3305, 4863}, {3315, 33100}, {3428, 10596}, {3452, 30331}, {3488, 5289}, {3524, 34629}, {3545, 10786}, {3576, 37429}, {3582, 37298}, {3584, 8070}, {3612, 9614}, {3616, 6284}, {3622, 7354}, {3636, 18990}, {3653, 28458}, {3655, 6261}, {3656, 28459}, {3663, 4906}, {3683, 26015}, {3687, 4702}, {3740, 5853}, {3746, 4187}, {3750, 37662}, {3756, 17596}, {3812, 10624}, {3820, 25439}, {3840, 44419}, {3870, 4679}, {3871, 26127}, {3873, 5852}, {3877, 5855}, {3878, 12433}, {3890, 10950}, {3913, 5084}, {3919, 28212}, {3929, 31146}, {3932, 4514}, {3943, 32866}, {3951, 15007}, {3967, 49466}, {3971, 9053}, {4011, 49524}, {4030, 4358}, {4104, 49467}, {4192, 18613}, {4294, 25524}, {4321, 4654}, {4364, 24694}, {4388, 4966}, {4422, 29673}, {4432, 29655}, {4640, 11019}, {4656, 49465}, {4664, 41624}, {4676, 29843}, {4762, 17115}, {4847, 15254}, {4854, 7191}, {4860, 44447}, {4865, 17243}, {4883, 41011}, {4884, 29844}, {4891, 5847}, {5046, 15888}, {5055, 34745}, {5057, 29817}, {5087, 13405}, {5204, 10586}, {5220, 36845}, {5241, 32945}, {5253, 15338}, {5259, 24390}, {5298, 17549}, {5327, 42028}, {5426, 16173}, {5443, 38027}, {5698, 10580}, {5701, 21795}, {5719, 11813}, {5743, 32941}, {5836, 12575}, {5840, 38028}, {5841, 10283}, {5842, 5886}, {5880, 9580}, {5883, 28174}, {5919, 38455}, {6057, 33090}, {6668, 7741}, {6675, 24387}, {6688, 22278}, {6703, 49482}, {6871, 9671}, {6914, 20418}, {6929, 38757}, {6965, 37725}, {7373, 34740}, {7483, 37720}, {7489, 37726}, {7681, 10267}, {8071, 10072}, {8236, 25568}, {8583, 41864}, {8616, 24217}, {8715, 17527}, {9041, 42054}, {9624, 37468}, {9669, 10198}, {9710, 11108}, {9713, 16541}, {9785, 34687}, {9812, 38053}, {10022, 25363}, {10032, 35596}, {10056, 17556}, {10177, 38454}, {10269, 38759}, {10284, 31806}, {10304, 34630}, {10386, 25440}, {10587, 10895}, {10595, 11827}, {10691, 17382}, {10916, 18253}, {11111, 11194}, {11240, 31156}, {12572, 34791}, {13100, 15677}, {13463, 19860}, {13464, 31789}, {13615, 42842}, {13867, 31165}, {14555, 49460}, {14986, 34742}, {15006, 15587}, {15178, 37290}, {15485, 33141}, {15862, 34641}, {15933, 34695}, {16418, 45700}, {16484, 17056}, {16503, 17747}, {16866, 31458}, {17135, 41002}, {17155, 28556}, {17245, 33109}, {17246, 17598}, {17320, 41003}, {17337, 32865}, {17340, 33169}, {17534, 34501}, {17577, 31936}, {17647, 31795}, {17728, 35258}, {19875, 34719}, {19883, 34649}, {21031, 37162}, {21625, 34646}, {22791, 30143}, {23711, 37295}, {24165, 28530}, {24316, 24441}, {24982, 32157}, {25378, 29848}, {28194, 31788}, {28198, 40296}, {30264, 45977}, {30568, 49688}, {30624, 41006}, {31018, 41711}, {31053, 37703}, {31162, 37428}, {31190, 31508}, {31249, 35445}, {31445, 49627}, {32049, 37556}, {33094, 40688}, {34698, 37624}, {35989, 41341}, {37080, 41012}, {37715, 40091}, {37718, 38058}

X(49736) = midpoint of X(i) and X(j) for these {i,j}: {1, 11113}, {2, 3058}, {8, 34699}, {145, 34689}, {944, 34697}, {962, 34618}, {3241, 34606}, {3656, 28459}, {5434, 11114}, {6284, 17579}, {11827, 34617}, {31162, 37428}, {34611, 34612}
X(49736) = reflection of X(22278) in X(6688)
X(49736) = complement of X(34612)
X(49736) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 390, 34607}, {2, 497, 11235}, {2, 10385, 4421}, {2, 11235, 2886}, {2, 11238, 3829}, {2, 34607, 1376}, {2, 34611, 34612}, {2, 47357, 4428}, {11, 1621, 6690}, {55, 3816, 3035}, {149, 5284, 3925}, {390, 26105, 1376}, {496, 5248, 4999}, {497, 1001, 2886}, {1001, 11235, 2}, {1279, 24210, 17061}, {1836, 4666, 25557}, {2478, 3303, 12607}, {2478, 11239, 31141}, {3058, 34612, 34611}, {3303, 31141, 11239}, {3434, 4423, 3826}, {3913, 5084, 9711}, {4432, 29655, 44416}, {8616, 24217, 37646}, {9580, 10582, 5880}, {11114, 38314, 5434}, {11239, 31141, 12607}, {12572, 40270, 34791}, {16484, 33106, 17056}, {26105, 34607, 2}, {29820, 33095, 1086}


X(49737) = X(1)X(8584)∩X(2)X(45)

Barycentrics    2*a^2 - 6*a*b - b^2 - 6*a*c - c^2 : :
X(49737) = 7 X[37] - X[3879], 5 X[37] + X[4416], 2 X[37] + X[17332], 4 X[37] - X[17390], 3 X[37] - X[29574], 5 X[3879] + 7 X[4416], 2 X[3879] + 7 X[17332], 4 X[3879] - 7 X[17390], 3 X[3879] - 7 X[29574], 2 X[4416] - 5 X[17332], 4 X[4416] + 5 X[17390], 3 X[4416] + 5 X[29574], 2 X[17332] + X[17390], 3 X[17332] + 2 X[29574], 3 X[17390] - 4 X[29574], X[4399] + 2 X[4681], 3 X[4664] + X[29617], 3 X[17330] - X[29617], 5 X[4687] + X[17334], 4 X[4698] - X[7228], 5 X[4704] + X[17362], 5 X[17331] + X[17388], 3 X[17333] + 5 X[29622], 3 X[17392] - 5 X[29622], X[17365] - 7 X[27268]

X(49737) lies on these lines: {1, 8584}, {2, 45}, {9, 597}, {37, 524}, {69, 16677}, {141, 3731}, {193, 16674}, {320, 29620}, {344, 21358}, {527, 4755}, {551, 15254}, {594, 31144}, {599, 16675}, {984, 9041}, {1100, 20583}, {1213, 17261}, {1992, 16777}, {2325, 4708}, {2796, 3842}, {3161, 17327}, {3247, 3629}, {3589, 16814}, {3686, 28329}, {3707, 49543}, {3723, 32455}, {3739, 17132}, {3828, 28542}, {3943, 17256}, {3950, 4478}, {3986, 6707}, {4029, 4690}, {4098, 17372}, {4357, 20582}, {4361, 32105}, {4399, 4681}, {4643, 16676}, {4657, 48310}, {4664, 4971}, {4687, 17334}, {4688, 28297}, {4698, 4912}, {4704, 17362}, {4748, 17269}, {5032, 16884}, {5220, 48830}, {5257, 7227}, {5296, 17262}, {5525, 34914}, {6329, 15492}, {7238, 29571}, {9039, 10179}, {13663, 30413}, {13783, 30412}, {15533, 17316}, {15534, 16672}, {15668, 35578}, {16521, 29584}, {16590, 28309}, {16696, 21826}, {17225, 49516}, {17235, 25072}, {17245, 17258}, {17246, 17260}, {17247, 17337}, {17248, 17340}, {17253, 21356}, {17321, 47352}, {17323, 18230}, {17331, 17388}, {17333, 17392}, {17335, 17395}, {17336, 17398}, {17346, 28337}, {17365, 27268}, {19297, 35276}, {25101, 34573}, {27549, 38087}

X(49737) = midpoint of X(i) and X(j) for these {i,j}: {4664, 17330}, {17333, 17392}
X(49737) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 41312, 597}, {37, 17332, 17390}, {45, 4364, 4422}, {597, 41312, 17045}, {3986, 17351, 6707}, {4357, 41310, 20582}, {4643, 29573, 22165}, {16675, 17257, 17243}


X(49738) = X(2)X(6)∩X(37)X(545)

Barycentrics    2*a^2 + 4*a*b - b^2 + 4*a*c + 4*b*c - c^2 : :
X(49738) = 5 X[2] - X[17346], 3 X[2] + X[17378], 5 X[17330] - 3 X[17346], X[17330] + 3 X[17392], 3 X[17346] + 5 X[17378], X[17346] + 5 X[17392], X[17378] - 3 X[17392], 2 X[37] + X[7228], 4 X[3739] - X[4399], 5 X[3739] + X[4889], 2 X[3739] + X[17390], 5 X[4399] + 4 X[4889], X[4399] + 2 X[17390], 2 X[4889] - 5 X[17390], X[3664] + 2 X[4698], 2 X[3664] + X[17332], 4 X[4698] - X[17332], X[3879] + 5 X[31238], X[4416] - 3 X[16590], X[4664] - 5 X[29622], 5 X[4687] - X[17333], 5 X[4687] + X[17365], 5 X[4687] + 3 X[39704], X[17333] + 3 X[39704], X[17365] - 3 X[39704], 5 X[4699] + X[17388], 7 X[4751] - X[17362], 7 X[4751] + 5 X[17391], X[17362] + 5 X[17391], 5 X[17331] - 9 X[41848], X[17334] - 7 X[27268]

X(49738) lies on these lines: {1, 4395}, {2, 6}, {7, 24441}, {9, 4795}, {30, 6176}, {37, 545}, {44, 31285}, {75, 28309}, {142, 214}, {145, 4405}, {320, 29578}, {354, 9054}, {428, 17171}, {519, 3739}, {527, 4755}, {594, 17310}, {674, 3742}, {752, 1125}, {894, 4370}, {903, 17246}, {991, 36722}, {1086, 16826}, {1100, 41140}, {3241, 4361}, {3616, 17290}, {3636, 17067}, {3663, 36525}, {3664, 4698}, {3679, 4478}, {3723, 24199}, {3740, 9038}, {3758, 29581}, {3828, 17239}, {3848, 9025}, {3879, 31238}, {3912, 4472}, {3943, 29569}, {3986, 17345}, {4000, 38314}, {4026, 31151}, {4357, 31138}, {4363, 5308}, {4364, 4675}, {4389, 29595}, {4416, 16590}, {4422, 4670}, {4470, 17269}, {4657, 25055}, {4664, 28297}, {4665, 17316}, {4669, 17372}, {4677, 28634}, {4681, 28301}, {4687, 17333}, {4688, 4971}, {4699, 17388}, {4745, 28633}, {4751, 17362}, {4798, 17284}, {4969, 16815}, {5257, 17376}, {5550, 25503}, {5750, 41141}, {6173, 41312}, {7227, 10022}, {7231, 17262}, {7263, 16777}, {7277, 17260}, {7865, 48815}, {9041, 49481}, {10197, 16608}, {13745, 25499}, {15569, 28580}, {16672, 42697}, {16696, 17180}, {17023, 40480}, {17119, 29585}, {17224, 17359}, {17227, 29612}, {17237, 25358}, {17244, 17342}, {17264, 29620}, {17296, 19875}, {17301, 29597}, {17305, 29592}, {17306, 28640}, {17311, 48636}, {17312, 28653}, {17318, 29624}, {17321, 48631}, {17322, 48632}, {17331, 41848}, {17334, 27268}, {17351, 36522}, {17354, 29599}, {17366, 17394}, {17374, 24603}, {17387, 29576}, {17395, 29570}, {17529, 28619}, {18144, 18146}, {18145, 25660}, {18643, 34828}, {19277, 48859}, {19883, 21255}, {24325, 28503}, {26104, 46934}, {27191, 29586}, {28562, 40344}, {29580, 37756}, {30578, 40434}, {30588, 37691}, {48816, 48846}, {48821, 48822}

X(49738) = midpoint of X(i) and X(j) for these {i,j}: {2, 17392}, {991, 36722}, {4688, 29574}, {17330, 17378}, {17333, 17365}, {48816, 48846}
X(49738) = complement of X(17330)
X(49738) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 34824, 4395}, {2, 3945, 37654}, {2, 4648, 17313}, {2, 17271, 1213}, {2, 17300, 17271}, {2, 17313, 141}, {2, 17378, 17330}, {2, 37654, 17259}, {86, 17245, 3589}, {141, 15668, 6707}, {142, 551, 17382}, {142, 28639, 17045}, {551, 17382, 17045}, {1213, 17300, 3631}, {3664, 4698, 17332}, {3739, 17390, 4399}, {3945, 17259, 3629}, {4364, 4675, 7238}, {4470, 29621, 17269}, {4648, 15668, 141}, {4670, 29571, 4422}, {4675, 16831, 4364}, {4687, 39704, 17333}, {4751, 17391, 17362}, {4869, 17327, 141}, {10022, 17243, 17281}, {10022, 17281, 7227}, {10436, 17243, 7227}, {10436, 17281, 10022}, {15668, 17313, 2}, {17234, 17398, 34573}, {17244, 41847, 17369}, {17284, 36834, 4798}, {17312, 28653, 48635}, {17330, 17392, 17378}, {17333, 39704, 17365}, {17337, 17379, 6329}, {17382, 28639, 551}, {17394, 27147, 17366}


X(49739) = X(1)X(30)∩X(2)X(1043)

Barycentrics    2*a^4 - 6*a^3*b - 7*a^2*b^2 - b^4 - 6*a^3*c - 12*a^2*b*c - 6*a*b^2*c - 7*a^2*c^2 - 6*a*b*c^2 + 2*b^2*c^2 - c^4 : :

X(49739) lies on these lines: {1, 30}, {2, 1043}, {6, 31156}, {55, 14636}, {58, 17525}, {81, 15677}, {145, 3578}, {376, 940}, {381, 5718}, {387, 17561}, {405, 48857}, {511, 5919}, {519, 3743}, {524, 3241}, {528, 4343}, {529, 31880}, {549, 37634}, {597, 11346}, {855, 18185}, {941, 17330}, {999, 15447}, {1213, 4720}, {1724, 48861}, {1962, 44669}, {1989, 6740}, {3017, 4653}, {3303, 9840}, {3304, 37425}, {3338, 48915}, {3488, 20182}, {3543, 5712}, {3584, 37715}, {3672, 15936}, {3679, 4046}, {3746, 48930}, {3945, 15683}, {4038, 15326}, {4304, 37595}, {4340, 11001}, {4364, 49687}, {4870, 24210}, {4995, 37573}, {5066, 37693}, {5283, 48848}, {5710, 10385}, {5724, 37593}, {6175, 17056}, {8236, 29181}, {8703, 37522}, {10470, 31782}, {11112, 48855}, {11113, 48841}, {15671, 24883}, {15679, 26131}, {15933, 37549}, {15973, 37722}, {16486, 28368}, {17392, 17579}, {18635, 31155}, {19686, 20132}, {19722, 48817}, {20323, 48893}, {28460, 45923}, {32636, 48919}, {34606, 42042}, {37038, 48858}, {37080, 48894}, {37556, 48883}, {37563, 48924}, {44217, 48837}

X(49739) = midpoint of X(145) and X(3578)
X(49739) = reflection of X(37631) in X(1)
X(49739) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3017, 4653, 15670}, {3017, 15670, 35466}


X(49740) = X(1)X(524)∩X(2)X(11)

Barycentrics    2*a^3 - 4*a^2*b - a*b^2 - b^3 - 4*a^2*c - 6*a*b*c - b^2*c - a*c^2 - b*c^2 - c^3 : :
X(49740) = 2 X[3686] + X[49475], X[17362] + 2 X[49471], X[3883] + 2 X[15569], 2 X[4399] + X[49469], X[17378] - 3 X[38314], 2 X[17332] + X[49490], X[17334] + 2 X[49479]

X(49740) lies on these lines: {1, 524}, {2, 11}, {6, 48830}, {9, 47359}, {10, 4702}, {30, 31394}, {37, 519}, {45, 36479}, {141, 16484}, {142, 49630}, {238, 597}, {344, 31311}, {391, 49680}, {392, 674}, {529, 48814}, {540, 48823}, {545, 24357}, {551, 752}, {599, 4966}, {952, 7611}, {966, 49460}, {984, 9041}, {1086, 24331}, {1125, 15810}, {1213, 32941}, {1284, 5434}, {1486, 16370}, {2177, 5241}, {2796, 24325}, {3241, 17346}, {3246, 17023}, {3247, 49681}, {3303, 37314}, {3416, 29573}, {3589, 15485}, {3616, 17305}, {3618, 8692}, {3655, 46475}, {3679, 3932}, {3723, 49684}, {3731, 49688}, {3750, 5743}, {3813, 11110}, {3883, 15569}, {3886, 4733}, {3902, 42724}, {4078, 4669}, {4085, 17337}, {4199, 18613}, {4309, 16458}, {4357, 42819}, {4399, 49469}, {4415, 29651}, {4422, 29659}, {4432, 17369}, {4649, 8584}, {4657, 25055}, {4660, 17245}, {4664, 28503}, {4665, 4693}, {4688, 28580}, {4967, 49485}, {5257, 30331}, {5692, 9054}, {5695, 39581}, {5698, 35578}, {6703, 8616}, {7290, 38023}, {9025, 10179}, {9710, 37035}, {10022, 24358}, {10072, 16351}, {12513, 13736}, {14020, 34606}, {15172, 19858}, {16342, 37722}, {16674, 49679}, {16677, 49690}, {16814, 49529}, {16823, 37756}, {16826, 49709}, {16857, 48831}, {17018, 41002}, {17051, 24627}, {17132, 49483}, {17133, 49462}, {17243, 33076}, {17257, 42871}, {17273, 17321}, {17279, 19875}, {17281, 48851}, {17332, 49490}, {17334, 49479}, {17365, 28558}, {17384, 19883}, {17398, 49482}, {17549, 20872}, {17677, 25466}, {19871, 34719}, {20582, 32784}, {22165, 33082}, {24715, 34824}, {24723, 25557}, {25354, 49473}, {25378, 37691}, {26102, 44419}, {26580, 37703}, {27759, 29640}, {29617, 31323}, {29633, 48310}

X(49740) = midpoint of X(i) and X(j) for these {i,j}: {3241, 17346}, {3883, 29574}, {29617, 49470}
X(49740) = reflection of X(i) in X(j) for these {i,j}: {17392, 551}, {29574, 15569}
X(49740) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 47357, 48805}, {1279, 41311, 551}, {3679, 41313, 3932}


X(49741) = X(1)X(7238)∩X(2)X(45)

Barycentrics    2*a*b + 3*b^2 + 2*a*c - 4*b*c + 3*c^2 : :
X(49741) = 5 X[141] - 2 X[2321], X[141] + 2 X[3663], 7 X[141] - 4 X[17229], X[141] - 4 X[17235], 3 X[141] - 2 X[29594], X[2321] + 5 X[3663], 7 X[2321] - 10 X[17229], X[2321] - 10 X[17235], 3 X[2321] - 5 X[29594], 7 X[3663] + 2 X[17229], X[3663] + 2 X[17235], 3 X[3663] + X[29594], X[17229] - 7 X[17235], 6 X[17229] - 7 X[29594], 6 X[17235] - X[29594], X[16834] + 3 X[17274], X[16834] - 3 X[17301], 4 X[3821] - X[49524], 2 X[3589] + X[17276], 2 X[3589] - 5 X[17304], X[17276] + 5 X[17304], X[3629] - 4 X[3946], X[3629] + 2 X[17345], 2 X[3946] + X[17345], X[3630] + 2 X[4852], 2 X[3631] + X[3875], X[3729] - 4 X[34573]

X(49741) lies on these lines: {1, 7238}, {2, 45}, {6, 28333}, {7, 17045}, {37, 48631}, {38, 19945}, {69, 28337}, {141, 536}, {142, 4755}, {192, 48632}, {320, 17395}, {519, 4743}, {524, 16834}, {527, 597}, {537, 3821}, {551, 5126}, {594, 4398}, {599, 4971}, {1213, 17249}, {1266, 4665}, {1278, 48635}, {1621, 38530}, {2486, 3829}, {2796, 48810}, {3122, 42040}, {3123, 42038}, {3589, 17276}, {3629, 3946}, {3630, 4852}, {3631, 3875}, {3644, 48633}, {3662, 4664}, {3672, 7232}, {3679, 33149}, {3729, 34573}, {3834, 29600}, {3943, 17227}, {4000, 17255}, {4021, 17376}, {4026, 31178}, {4357, 4688}, {4395, 4643}, {4399, 17272}, {4405, 4690}, {4407, 4745}, {4445, 4452}, {4478, 17151}, {4657, 4862}, {4670, 4887}, {4675, 29597}, {4681, 21255}, {4686, 48636}, {4715, 8584}, {4741, 4969}, {4764, 48634}, {4912, 48310}, {4980, 30713}, {5750, 7231}, {5880, 48854}, {6173, 41312}, {6646, 17366}, {7227, 17306}, {7277, 17380}, {7321, 17324}, {9041, 48829}, {16706, 17334}, {17132, 17359}, {17242, 48637}, {17245, 17247}, {17254, 17330}, {17258, 17337}, {17273, 17362}, {17281, 20582}, {17288, 17388}, {17291, 17340}, {17294, 28309}, {17302, 17365}, {17320, 17392}, {17327, 31995}, {24169, 42056}, {24248, 48805}, {29574, 31138}, {31004, 41142}, {31136, 33145}, {31137, 33154}

X(49741) = midpoint of X(i) and X(j) for these {i,j}: {17274, 17301}, {24248, 48805}
X(49741) = reflection of X(i) in X(j) for these {i,j}: {597, 17382}, {17281, 20582}, {48821, 3821}, {49524, 48821}
X(49741) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 17323, 17045}, {1086, 4364, 34824}, {1086, 4389, 4364}, {1266, 17237, 4665}, {3662, 17246, 17243}, {3663, 17235, 141}, {3672, 7232, 17390}, {3946, 17345, 3629}, {4000, 17255, 17332}, {4398, 17236, 594}, {4419, 17290, 4422}, {4440, 17305, 17369}, {4657, 4862, 7228}, {7321, 17324, 17398}, {17247, 48629, 17245}, {17249, 48627, 1213}, {17254, 37756, 17330}, {17276, 17304, 3589}, {17325, 42697, 4472}


X(49742) = X(2)X(45)∩X(6)X(6172)

Barycentrics    2*a^2 - 4*a*b - b^2 - 4*a*c + 2*b*c - c^2 : :
X(49742) = 5 X[37] - 2 X[3664], 2 X[37] + X[17334], 4 X[37] - X[17365], 4 X[3664] + 5 X[17334], 8 X[3664] - 5 X[17365], 4 X[3664] - 5 X[17392], 2 X[17334] + X[17365], X[192] + 2 X[17332], 2 X[192] + X[17362], 4 X[17332] - X[17362], 3 X[4664] - X[17389], 3 X[17333] + X[17389], X[3644] + 2 X[4399], X[3644] + 5 X[17331], 2 X[4399] - 5 X[17331], 2 X[3686] + X[4718], X[4416] + 2 X[4681], 2 X[4416] + X[17388], 4 X[4681] - X[17388], 5 X[4687] - 2 X[7228], 5 X[4704] + X[17347], 5 X[4704] - 2 X[17390], X[17347] + 2 X[17390], 5 X[29622] - 3 X[39704]

X(49742) lies on these lines: {2, 45}, {6, 6172}, {7, 16675}, {9, 17246}, {10, 28542}, {37, 527}, {44, 17395}, {75, 28297}, {141, 17254}, {144, 7277}, {192, 4971}, {320, 29575}, {344, 17255}, {346, 17253}, {519, 49449}, {524, 4664}, {528, 984}, {536, 17330}, {551, 4672}, {594, 17251}, {597, 17320}, {846, 24345}, {1213, 3729}, {2094, 37674}, {2242, 47039}, {2292, 34606}, {2310, 3058}, {2325, 17237}, {3161, 3763}, {3241, 15534}, {3242, 47357}, {3589, 17247}, {3629, 17319}, {3630, 17315}, {3631, 17242}, {3644, 4399}, {3663, 16814}, {3672, 16885}, {3679, 24697}, {3686, 4718}, {3731, 4902}, {3739, 28322}, {3929, 8557}, {3943, 4643}, {3945, 16674}, {3946, 15492}, {3950, 17344}, {4021, 16669}, {4029, 17374}, {4271, 29740}, {4310, 38025}, {4331, 11237}, {4357, 17340}, {4395, 17335}, {4403, 21822}, {4414, 6174}, {4416, 4681}, {4478, 17328}, {4480, 4670}, {4644, 16672}, {4648, 16677}, {4656, 37646}, {4657, 25728}, {4665, 17256}, {4675, 16676}, {4687, 7228}, {4688, 17132}, {4704, 17347}, {4715, 29574}, {4755, 4912}, {4795, 29597}, {4862, 38093}, {4908, 29594}, {4969, 17318}, {5224, 25269}, {5296, 17118}, {5695, 48802}, {5698, 48856}, {5919, 9039}, {6068, 28125}, {6329, 17396}, {6646, 17243}, {7227, 17248}, {7238, 17244}, {7263, 17260}, {8584, 29584}, {9791, 49524}, {16561, 36540}, {16590, 28301}, {17045, 17350}, {17056, 31164}, {17235, 25101}, {17249, 17339}, {17252, 48636}, {17263, 48631}, {17274, 41313}, {17310, 22165}, {17323, 26685}, {17342, 20582}, {17351, 17398}, {17378, 28333}, {17393, 32455}, {24828, 36551}, {28309, 29617}, {29069, 36728}, {29243, 36490}, {29600, 31138}, {29622, 39704}, {31142, 37662}, {32935, 48822}, {34612, 42041}, {35596, 37633}

X(49742) = midpoint of X(i) and X(j) for these {i,j}: {192, 17346}, {4664, 17333}, {17334, 17392}
X(49742) = reflection of X(i) in X(j) for these {i,j}: {17346, 17332}, {17362, 17346}, {17365, 17392}, {17392, 37}
X(49742) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 17246, 17366}, {37, 17334, 17365}, {45, 4419, 1086}, {144, 16777, 7277}, {190, 4364, 17369}, {192, 17332, 17362}, {344, 17255, 48632}, {346, 17253, 48635}, {3644, 17331, 4399}, {3663, 16814, 17337}, {3731, 17276, 17245}, {4416, 4681, 17388}, {4704, 17347, 17390}, {17242, 17329, 3631}, {17247, 17336, 3589}, {17249, 17339, 34573}, {17254, 17261, 17264}, {17254, 17264, 141}, {17257, 17262, 594}, {17258, 17261, 141}, {17258, 17264, 17254}


X(49743) = X(1)X(30)∩X(5)X(940)

Barycentrics    2*a^4 + 4*a^3*b + 3*a^2*b^2 - b^4 + 4*a^3*c + 8*a^2*b*c + 4*a*b^2*c + 3*a^2*c^2 + 4*a*b*c^2 + 2*b^2*c^2 - c^4 : :
X(49743) = X[1] - 3 X[37631], X[8] + 3 X[42045], 3 X[3578] - 7 X[9780], 5 X[3616] - 3 X[13745], 3 X[23812] - X[49598]

X(49743) lies on these lines: {1, 30}, {3, 4340}, {4, 3945}, {5, 940}, {6, 8728}, {7, 48941}, {8, 42045}, {10, 524}, {12, 2003}, {21, 37635}, {35, 15447}, {40, 14521}, {46, 48924}, {56, 48930}, {57, 48882}, {58, 6675}, {69, 2049}, {81, 442}, {86, 1330}, {140, 5398}, {141, 43531}, {193, 37153}, {226, 37594}, {316, 33770}, {323, 46441}, {325, 1509}, {377, 48847}, {386, 48868}, {387, 17528}, {388, 46704}, {394, 47510}, {495, 611}, {496, 26098}, {511, 942}, {517, 10108}, {540, 1125}, {550, 19765}, {581, 20420}, {740, 49564}, {750, 47742}, {894, 3695}, {896, 27577}, {938, 15936}, {966, 16456}, {999, 9840}, {1010, 17778}, {1056, 15971}, {1100, 23537}, {1154, 13750}, {1210, 48887}, {1211, 25526}, {1419, 5290}, {1503, 4349}, {1654, 14007}, {1697, 48915}, {1770, 37593}, {1834, 4658}, {1993, 47516}, {2303, 21530}, {2475, 41819}, {2476, 14996}, {2895, 14005}, {2901, 17390}, {2906, 37989}, {3085, 22117}, {3178, 4697}, {3295, 4307}, {3333, 48883}, {3338, 17723}, {3454, 6703}, {3487, 13442}, {3488, 48923}, {3578, 9780}, {3616, 13745}, {3628, 37634}, {3666, 24470}, {3743, 17768}, {3745, 13407}, {3824, 40940}, {3879, 5295}, {3927, 4644}, {3933, 33745}, {3953, 17726}, {4065, 28530}, {4187, 37633}, {4197, 37685}, {4202, 19717}, {4255, 17563}, {4648, 11108}, {4682, 21077}, {4733, 41814}, {5051, 8025}, {5333, 17514}, {5396, 37281}, {5542, 29181}, {5570, 13391}, {5703, 48935}, {5706, 37424}, {5707, 6907}, {5708, 48928}, {5713, 8727}, {5716, 15934}, {5719, 37539}, {5722, 48937}, {5725, 34380}, {5739, 16458}, {5762, 37528}, {5814, 10436}, {6051, 41011}, {6097, 8069}, {6390, 17103}, {6625, 47286}, {6656, 20132}, {6701, 17070}, {6842, 45931}, {6881, 36750}, {7535, 37492}, {7762, 16062}, {7767, 37148}, {7952, 46467}, {8367, 29438}, {10449, 17378}, {11036, 48890}, {11110, 20077}, {11112, 19767}, {11359, 19766}, {11374, 37554}, {13728, 19684}, {13740, 17300}, {14268, 48921}, {15325, 37607}, {15670, 16948}, {15989, 17750}, {16052, 42028}, {16266, 37438}, {16290, 37507}, {16454, 31034}, {16466, 28368}, {17527, 37674}, {17529, 32911}, {17698, 18134}, {19280, 37653}, {19714, 47514}, {19722, 48815}, {19783, 48813}, {20018, 48816}, {20090, 26051}, {23812, 49598}, {24390, 33112}, {24902, 35466}, {24928, 48894}, {24929, 48893}, {25446, 41629}, {25512, 41002}, {28174, 37548}, {31777, 37529}, {34753, 37520}, {35203, 37582}, {35612, 37482}, {36279, 48917}, {37401, 45923}, {37469, 45933}, {44217, 48861}

X(49743) = midpoint of X(i) and X(j) for these {i,j}: {500, 13408}, {942, 49557}, {13442, 46483}
X(49743) = crosssum of X(55) and X(4272)
X(49743) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 79, 4854}, {1, 6147, 39544}, {58, 17056, 6675}, {81, 26131, 442}, {86, 1330, 4205}, {1010, 17778, 41014}, {3664, 5717, 942}, {4340, 5712, 3}, {5333, 26064, 17514}, {5713, 36746, 8727}, {5718, 37522, 140}, {16948, 24936, 15670}, {20077, 26109, 11110}, {37634, 37693, 3628}


X(49744) = X(1)X(30)∩X(2)X(58)

Barycentrics    2*a^4 + 3*a^3*b + 2*a^2*b^2 - b^4 + 3*a^3*c + 6*a^2*b*c + 3*a*b^2*c + 2*a^2*c^2 + 3*a*b*c^2 + 2*b^2*c^2 - c^4 : :
X(49744) = 2 X[13408] + X[48897], X[65] + 2 X[49557], X[3057] - 4 X[10108], 2 X[13745] - 3 X[25055]

X(49744) lies on these lines: {1, 30}, {2, 58}, {6, 44217}, {10, 3578}, {36, 14636}, {65, 49557}, {81, 3017}, {171, 3584}, {314, 17378}, {376, 5712}, {377, 48857}, {381, 940}, {511, 5902}, {519, 2650}, {524, 3416}, {542, 6126}, {547, 37634}, {549, 5718}, {551, 4425}, {553, 3670}, {986, 46617}, {1099, 1111}, {1401, 18398}, {1509, 7809}, {2303, 31154}, {2475, 4658}, {3057, 10108}, {3336, 48882}, {3338, 48883}, {3534, 19765}, {3543, 3945}, {3582, 37607}, {3583, 4038}, {3647, 27577}, {3746, 37425}, {4307, 37610}, {4653, 15677}, {4754, 32847}, {4973, 29688}, {5010, 15447}, {5221, 48928}, {5264, 10056}, {5270, 46704}, {5315, 28368}, {5337, 13632}, {5429, 26725}, {5563, 9840}, {5711, 8614}, {5733, 6925}, {6625, 19570}, {6906, 45933}, {7753, 24512}, {7799, 17103}, {7811, 37632}, {7924, 20132}, {7951, 37604}, {10072, 26098}, {11113, 17392}, {11114, 48855}, {11359, 19722}, {13407, 39572}, {13745, 25055}, {15670, 17056}, {15671, 16948}, {15672, 24936}, {15973, 37719}, {16474, 33109}, {17596, 38430}, {17677, 42028}, {17678, 46922}, {17679, 19738}, {18139, 48866}, {18541, 20182}, {19336, 31179}, {19684, 48835}, {19717, 48843}, {22392, 37281}, {23812, 38456}, {23903, 39563}, {26117, 28619}, {28198, 37548}, {35203, 37524}, {37080, 48926}, {37496, 45923}, {37563, 48915}, {37571, 48893}, {37702, 48937}

X(49744) = reflection of X(i) in X(j) for these {i,j}: {1, 37631}, {3578, 10}
X(49744) = crossdifference of every pair of points on line {9404, 42664}
X(49744) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 48870, 1724}, {81, 6175, 3017}, {3058, 48823, 1}, {4654, 48828, 1}


X(49745) = X(1)X(30)∩X(8)X(524)

Barycentrics    2*a^4 + 2*a^3*b + a^2*b^2 - b^4 + 2*a^3*c + 4*a^2*b*c + 2*a*b^2*c + a^2*c^2 + 2*a*b*c^2 + 2*b^2*c^2 - c^4 : :
X(49745) = 2 X[1] - 3 X[37631], X[145] - 3 X[42045], 4 X[1125] - 3 X[13745], 3 X[3578] - 5 X[3617], 3 X[10180] - 2 X[12579]

X(49745) lies on these lines: {1, 30}, {2, 4252}, {3, 5718}, {4, 940}, {5, 37522}, {6, 377}, {7, 5716}, {8, 524}, {10, 540}, {11, 37607}, {12, 171}, {20, 5712}, {21, 17056}, {23, 229}, {29, 18635}, {31, 25466}, {36, 48930}, {46, 5725}, {55, 37425}, {56, 9840}, {57, 48883}, {58, 442}, {65, 511}, {81, 1834}, {86, 26117}, {140, 37693}, {141, 964}, {145, 42045}, {162, 25987}, {221, 388}, {226, 3429}, {316, 1509}, {325, 17103}, {333, 20077}, {385, 6625}, {386, 11112}, {404, 37662}, {443, 4383}, {452, 4648}, {474, 37663}, {484, 48924}, {495, 5264}, {516, 37548}, {517, 49557}, {529, 10459}, {538, 49476}, {581, 37468}, {582, 44222}, {597, 17679}, {601, 7680}, {603, 15844}, {611, 48922}, {750, 1329}, {851, 4267}, {894, 7270}, {896, 18253}, {950, 3664}, {960, 41011}, {980, 49132}, {986, 11246}, {988, 17723}, {1010, 1211}, {1012, 5713}, {1043, 17778}, {1046, 21677}, {1056, 37542}, {1086, 5262}, {1104, 5249}, {1125, 4892}, {1155, 5530}, {1191, 28368}, {1210, 37520}, {1213, 1778}, {1220, 4645}, {1319, 48894}, {1386, 23536}, {1408, 37527}, {1453, 24789}, {1468, 2886}, {1478, 5711}, {1714, 17528}, {1724, 8728}, {1737, 48887}, {1754, 37424}, {1764, 31774}, {1770, 3931}, {1785, 46467}, {1837, 48937}, {1884, 18165}, {1901, 2303}, {2099, 48909}, {2292, 17768}, {2295, 15989}, {2305, 37232}, {2476, 37646}, {2478, 37674}, {2646, 48893}, {2650, 44669}, {2975, 33112}, {3085, 37540}, {3146, 3945}, {3178, 3712}, {3286, 37225}, {3333, 17721}, {3475, 4339}, {3486, 48923}, {3564, 5252}, {3578, 3617}, {3585, 37559}, {3589, 4202}, {3666, 4292}, {3670, 24470}, {3677, 4355}, {3704, 4418}, {3710, 17351}, {3744, 21620}, {3745, 13161}, {3813, 33104}, {3836, 25992}, {3868, 17365}, {3925, 5247}, {3936, 11115}, {4185, 36740}, {4190, 4255}, {4195, 18134}, {4205, 25526}, {4217, 17313}, {4220, 5323}, {4234, 25650}, {4257, 7483}, {4265, 37231}, {4295, 37614}, {4296, 6354}, {4313, 41825}, {4331, 15832}, {4689, 31730}, {4860, 36574}, {4888, 11518}, {4968, 5846}, {4999, 33105}, {5046, 37633}, {5047, 17245}, {5051, 6703}, {5119, 48915}, {5177, 37642}, {5204, 14636}, {5221, 48936}, {5228, 15970}, {5253, 33107}, {5255, 15888}, {5266, 13407}, {5269, 5290}, {5292, 17532}, {5300, 49524}, {5398, 37438}, {5429, 24161}, {5432, 37603}, {5433, 17717}, {5706, 6850}, {5707, 6923}, {5721, 6917}, {5741, 19284}, {5743, 16454}, {6175, 24883}, {6604, 15982}, {6655, 20132}, {6831, 37469}, {6836, 37501}, {6897, 36745}, {6907, 37530}, {6916, 37537}, {7745, 24512}, {7750, 37632}, {7823, 17379}, {7952, 46468}, {9534, 48816}, {9612, 17720}, {9654, 9958}, {9957, 10108}, {10180, 12579}, {10391, 40950}, {10479, 37150}, {10544, 39793}, {11113, 48868}, {11114, 17392}, {11319, 18139}, {11374, 17775}, {11826, 37529}, {12047, 48931}, {12436, 16610}, {12572, 44307}, {13567, 24537}, {13725, 19701}, {13728, 43531}, {14621, 26561}, {15338, 37573}, {15668, 37314}, {15680, 37635}, {15976, 37609}, {15991, 21281}, {16052, 25441}, {16783, 18907}, {17016, 20292}, {17128, 17300}, {17234, 17697}, {17530, 45939}, {17572, 37651}, {17579, 19767}, {17589, 41809}, {17676, 19684}, {17718, 37552}, {17726, 37592}, {18391, 48877}, {18679, 44698}, {19715, 37193}, {19722, 19766}, {19732, 37153}, {19734, 37191}, {19738, 48845}, {19760, 35980}, {19761, 36474}, {20088, 20147}, {23292, 24984}, {24231, 29317}, {24239, 32636}, {24929, 48926}, {24953, 33111}, {25557, 28082}, {25914, 32944}, {26115, 44419}, {30811, 37176}, {33106, 37722}, {33863, 37661}, {34380, 41687}, {36279, 48928}, {37161, 37666}, {37281, 37732}, {37360, 37823}, {37436, 37650}, {37447, 45924}, {37462, 37679}, {37567, 48917}, {37568, 48919}, {37675, 38930}, {38456, 49598}, {44217, 48870}, {45923, 47032}

X(49745) = midpoint of X(15971) and X(46483)
X(49745) = reflection of X(9957) in X(10108)
X(49745) = crosspoint of X(7) and X(14534)
X(49745) = crosssum of X(i) and X(j) for these (i,j): {55, 2092}, {4267, 45236}
X(49745) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 24851, 4854}, {1, 33097, 3649}, {4, 4340, 940}, {5, 37522, 37634}, {7, 5716, 37549}, {20, 5712, 19765}, {21, 26131, 17056}, {58, 442, 35466}, {81, 2475, 1834}, {388, 4307, 5710}, {896, 21674, 18253}, {1010, 1330, 1211}, {3178, 24850, 3712}, {3585, 37559, 37715}, {4292, 5717, 3666}, {5266, 13407, 17724}, {6917, 36742, 5721}, {9612, 37554, 17720}, {14005, 26064, 1213}, {17717, 37608, 5433}, {20077, 26051, 333}, {43531, 48835, 13728}


X(49746) = X(2)X(11)∩X(8)X(45)

Barycentrics    2*a^3 - 3*a^2*b - b^3 - 3*a^2*c - 3*a*b*c - c^3 : :
X(49746) = 2 X[3883] + X[49470], 2 X[3993] + X[49506], 2 X[17392] - 3 X[38314], X[17347] + 2 X[49490], X[17363] + 2 X[49475], X[17377] - 4 X[49471], 3 X[24452] - 5 X[40328], X[49447] + 2 X[49466]

X(49746) lies on these lines: {1, 320}, {2, 11}, {8, 45}, {10, 17342}, {21, 23855}, {75, 28580}, {81, 42058}, {190, 36479}, {192, 28503}, {518, 17333}, {519, 751}, {524, 3241}, {545, 24349}, {551, 3821}, {674, 3877}, {903, 24248}, {962, 41874}, {968, 4514}, {1010, 4309}, {1220, 4217}, {1279, 17382}, {1654, 49460}, {2099, 17950}, {2177, 5233}, {2263, 17078}, {2796, 31178}, {3006, 27754}, {3052, 29837}, {3246, 17367}, {3303, 26117}, {3416, 17310}, {3616, 17290}, {3661, 4702}, {3662, 42819}, {3679, 3773}, {3685, 17281}, {3748, 27184}, {3750, 4417}, {3755, 41140}, {3790, 4908}, {3935, 27776}, {3979, 4703}, {4030, 41839}, {4085, 15485}, {4344, 17392}, {4357, 30331}, {4364, 36534}, {4370, 49524}, {4419, 24841}, {4425, 17715}, {4432, 17354}, {4450, 29814}, {4512, 33121}, {4640, 29843}, {4645, 17313}, {4660, 16484}, {4666, 33068}, {4715, 49478}, {4901, 36911}, {5224, 32941}, {5235, 21283}, {5919, 9025}, {6646, 42871}, {7174, 49695}, {7976, 24429}, {10389, 33126}, {15171, 37150}, {16496, 17258}, {17233, 33076}, {17247, 49465}, {17254, 47358}, {17261, 49688}, {17304, 35227}, {17319, 49681}, {17329, 49505}, {17336, 49529}, {17347, 49490}, {17363, 49475}, {17377, 49471}, {17381, 49482}, {17389, 28538}, {17393, 49684}, {18134, 31134}, {18613, 37467}, {19278, 37722}, {20012, 41002}, {24331, 24715}, {24452, 40328}, {24457, 47729}, {24697, 49458}, {29651, 33095}, {29817, 32950}, {31144, 48802}, {31349, 49531}, {33071, 37553}, {33309, 48831}, {40891, 49486}, {46922, 48830}, {48628, 49485}, {49447, 49466}

X(49746) = reflection of X(i) in X(j) for these {i,j}: {8, 17330}, {17378, 1}
X(49746) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 48829, 4429}, {1001, 48829, 2}, {4026, 48810, 2}, {4085, 15485, 17352}, {4432, 29659, 17354}, {4660, 16484, 17234}


X(49747) = X(2)X(45)∩X(6)X(527)

Barycentrics    a^2 - 2*a*b - 2*b^2 - 2*a*c + 4*b*c - 2*c^2 : :
X(49747) = X[6] - 4 X[3663], 5 X[6] - 8 X[3946], X[6] + 2 X[17276], 5 X[3663] - 2 X[3946], 2 X[3663] + X[17276], 4 X[3946] + 5 X[17276], 4 X[3946] - 5 X[17301], 2 X[4655] + X[49453], X[3242] + 2 X[24248], 3 X[599] - 2 X[17294], 3 X[17274] - X[17294], 2 X[3729] - 5 X[3763], X[3729] - 4 X[17235], 5 X[3763] - 8 X[17235], 5 X[3763] - 4 X[17359], X[3875] + 2 X[17345], 2 X[3875] + X[40341], 4 X[17345] - X[40341], 4 X[4660] - X[49690], 4 X[4852] - X[6144], 4 X[17382] - 3 X[47352], 2 X[17281] - 3 X[21358], 5 X[17304] - 2 X[17351], 10 X[17304] - 7 X[47355], 4 X[17351] - 7 X[47355], 3 X[38087] - 4 X[48821], 4 X[49455] - X[49679]

X(49747) lies on these lines: {1, 28534}, {2, 45}, {6, 527}, {7, 16777}, {37, 4862}, {38, 4492}, {55, 24405}, {69, 4971}, {75, 17251}, {141, 28297}, {142, 16675}, {144, 17366}, {192, 7232}, {320, 17318}, {344, 48631}, {346, 48632}, {519, 4655}, {528, 3242}, {536, 599}, {537, 48829}, {894, 17323}, {966, 4373}, {982, 24338}, {986, 11236}, {1213, 31995}, {1266, 4643}, {1278, 4445}, {1423, 5036}, {1427, 4654}, {1992, 28333}, {2310, 11238}, {2796, 48805}, {3123, 4484}, {3247, 4902}, {3285, 35935}, {3644, 17288}, {3662, 17262}, {3666, 31164}, {3670, 17556}, {3672, 16884}, {3679, 49493}, {3723, 4888}, {3729, 3763}, {3731, 38093}, {3752, 31142}, {3875, 4725}, {3928, 8557}, {4000, 6172}, {4310, 47357}, {4331, 5434}, {4357, 17118}, {4361, 4398}, {4392, 10707}, {4403, 17461}, {4443, 4947}, {4452, 17362}, {4461, 48635}, {4644, 17395}, {4648, 16674}, {4656, 37682}, {4659, 17237}, {4660, 49690}, {4664, 17313}, {4675, 4887}, {4681, 17298}, {4686, 17272}, {4715, 15534}, {4718, 17296}, {4726, 17270}, {4740, 17271}, {4741, 17160}, {4764, 17287}, {4788, 17295}, {4821, 32025}, {4852, 6144}, {4859, 16814}, {4912, 17382}, {4942, 33174}, {5220, 33149}, {5695, 28542}, {6534, 48804}, {6545, 23352}, {7222, 17398}, {7228, 17321}, {7238, 17316}, {7263, 17257}, {7277, 20059}, {7321, 15668}, {10269, 38531}, {11114, 37549}, {11160, 28337}, {15934, 48841}, {16677, 17245}, {16969, 24214}, {17116, 17249}, {17117, 17329}, {17132, 17281}, {17151, 17344}, {17227, 17269}, {17236, 17293}, {17258, 17259}, {17261, 17265}, {17268, 48637}, {17283, 25269}, {17299, 28313}, {17304, 17351}, {17314, 45789}, {17333, 37756}, {17356, 25728}, {17380, 31300}, {17388, 21296}, {17483, 20182}, {17596, 24406}, {17597, 33100}, {17599, 33098}, {17768, 38315}, {21342, 31146}, {22165, 28309}, {24341, 24434}, {24399, 24464}, {24833, 36490}, {24851, 34706}, {28301, 29594}, {28580, 47358}, {29069, 36731}, {29573, 31138}, {29580, 39704}, {33155, 35596}, {34605, 37614}, {38087, 48821}, {42764, 45320}, {44663, 48818}, {48851, 49483}, {49455, 49679}

X(49747) = midpoint of X(17276) and X(17301)
X(49747) = reflection of X(i) in X(j) for these {i,j}: {6, 17301}, {599, 17274}, {3729, 17359}, {15534, 16834}, {17301, 3663}, {17359, 17235}
X(49747) = crossdifference of every pair of points on line {1960, 9029}
X(49747) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 17246, 16777}, {75, 17254, 17251}, {75, 17255, 17253}, {192, 7232, 17311}, {903, 24441, 31139}, {1086, 4419, 45}, {1266, 4643, 17119}, {1278, 17273, 4445}, {3644, 17288, 17309}, {3662, 17262, 17267}, {3663, 17276, 6}, {3672, 17365, 16884}, {3729, 17235, 3763}, {3875, 17345, 40341}, {4000, 17334, 16885}, {4346, 4419, 1086}, {4363, 4389, 17325}, {4389, 4440, 4363}, {4398, 6646, 4361}, {4409, 17369, 4454}, {7321, 17247, 15668}, {17116, 17249, 17327}, {17251, 17254, 17253}, {17251, 17255, 17254}, {17258, 48627, 17259}, {17261, 48629, 17265}, {17304, 17351, 47355}


X(49748) = X(2)X(45)∩X(192)X(524)

Barycentrics    2*a^2 - 3*a*b - b^2 - 3*a*c + 3*b*c - c^2 : :
X(49748) = 6 X[37] - 5 X[29622], X[192] + 2 X[17334], 2 X[192] + X[17347], 4 X[192] - X[17377], 5 X[192] - 2 X[17388], 4 X[17334] - X[17347], 8 X[17334] + X[17377], 5 X[17334] + X[17388], 2 X[17347] + X[17377], 5 X[17347] + 4 X[17388], 5 X[17377] - 8 X[17388], 3 X[4664] - 2 X[29574], 3 X[17378] - 4 X[29574], 3 X[17333] - X[29617], 3 X[17346] - 2 X[29617], X[1278] - 4 X[17332], X[3644] + 2 X[4416], 4 X[3686] - X[4764], 4 X[4681] - X[17364], 2 X[4686] - 5 X[17331], 5 X[4704] - 2 X[17365], 2 X[4718] + X[17363], X[4788] + 2 X[17362], 4 X[7228] - 7 X[27268]

X(49748) lies on these lines: {2, 45}, {9, 4398}, {37, 4912}, {55, 36224}, {75, 17132}, {86, 35578}, {141, 25269}, {144, 1992}, {192, 524}, {320, 29573}, {346, 17273}, {519, 49447}, {527, 4664}, {536, 17333}, {551, 4676}, {597, 17246}, {599, 6646}, {894, 41312}, {984, 2796}, {1266, 17335}, {1278, 17332}, {2321, 17329}, {2325, 17227}, {3161, 17283}, {3241, 5698}, {3644, 4416}, {3662, 41310}, {3663, 15828}, {3679, 24723}, {3685, 47358}, {3686, 4764}, {3717, 49630}, {3729, 5224}, {3731, 7321}, {3758, 4480}, {3943, 4741}, {3950, 17361}, {4029, 17387}, {4141, 25760}, {4393, 8584}, {4431, 17328}, {4461, 32025}, {4488, 17321}, {4643, 29615}, {4659, 17256}, {4675, 29620}, {4681, 17364}, {4686, 17331}, {4688, 28322}, {4704, 17365}, {4715, 17389}, {4718, 17363}, {4740, 17330}, {4788, 17362}, {4795, 29580}, {4796, 39260}, {4862, 17263}, {4908, 29577}, {4933, 33065}, {6542, 15533}, {7228, 27268}, {7238, 29572}, {9041, 31302}, {11160, 17314}, {15534, 17318}, {16675, 26806}, {16706, 25728}, {16777, 31300}, {16814, 48627}, {17234, 17261}, {17235, 17339}, {17236, 17340}, {17242, 17345}, {17247, 17351}, {17249, 17355}, {17254, 17281}, {17255, 17280}, {17257, 31144}, {17264, 17274}, {17302, 47352}, {17383, 48310}, {17484, 31179}, {17488, 28309}, {19786, 25734}, {20078, 34064}, {21093, 27777}, {25101, 48629}, {28538, 49523}, {28558, 49456}, {28562, 49520}, {29582, 31138}, {29643, 31177}

X(49748) = reflection of X(i) in X(j) for these {i,j}: {4740, 17330}, {17346, 17333}, {17378, 4664}
X(49748) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {190, 4389, 17354}, {190, 4419, 4389}, {192, 17334, 17347}, {192, 17347, 17377}, {3663, 17336, 17352}, {3729, 17258, 5224}, {4419, 20073, 190}, {6646, 17262, 17233}, {17246, 17350, 17380}, {17247, 17351, 17381}, {17261, 17276, 17234}


X(49749) = X(1)X(538)∩X(2)X(6)

Barycentrics    3*a^3*b + 2*a^2*b^2 + 3*a^3*c + 6*a^2*b*c + 3*a*b^2*c + 2*a^2*c^2 + 3*a*b*c^2 + 2*b^2*c^2 : :
X(49749) = 2 X[1] + X[4754]

X(49749) lies on these lines: {1, 538}, {2, 6}, {30, 48830}, {42, 2234}, {511, 9746}, {527, 13097}, {536, 2667}, {540, 48822}, {1045, 42042}, {1281, 5969}, {3248, 3720}, {3664, 4987}, {3758, 17032}, {4038, 4396}, {4363, 17018}, {4368, 5625}, {4375, 28840}, {4441, 16884}, {4470, 20012}, {4472, 4651}, {4665, 20011}, {4667, 24690}, {4697, 4760}, {4713, 29814}, {4798, 26037}, {8299, 33682}, {8716, 19765}, {13586, 17103}, {16666, 24592}, {16834, 25426}, {17045, 20347}, {17175, 20970}, {17180, 46913}, {17394, 24514}, {24724, 33097}, {25349, 29822}, {29580, 39916}, {37619, 41430}

X(49749) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {86, 40721, 2238}, {4667, 43223, 24690}, {17379, 37632, 24512}

leftri

Points in a [[a,b,c], [b-c,c-a,a-b]] coordinate system: X(49750)-X(49783)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1, L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1 is the line: a α + b β c γ = 0.

L2 is the line (b-c) α + (c-a) β + (a-b) γ = 0 (Nagel line).

The origin is given by (0,0) = X(3912) = b^2 + c^2 - a b - a c : : .

Barycentrics u : v : w for a triangle center U = (x, y) in this system are given by

u : v : w = b^2 + c^2 - a(b + c) + (b-c) x + (2a - b - c) y : : ,

where, as functions of a, b, c, the coordinate x is antisymmetric of degree 1, and y is symmetric of degree 2.

The appearance of {x, y}, k in the following list means that (x, y) = X(k).

{-((2 (a-b) (a-c) (b-c))/(a b+a c+b c)), (2 a b c)/(a b+a c+b c)}, 41773
{-(((a-b) (a-c) (b-c))/(a^2+b^2+c^2)), (a^3+b^3+c^3)/(a^2+b^2+c^2)}, 24281
{0, -a-b-c}, 6542
{0, -((a^2+b^2+c^2)/(a+b+c))}, 32847
{0, 0}, 3912
{0, 1/2 (a+b+c)}, 3008
{0, a+b+c}, 239
{0, (a^2+b^2+c^2)/(a+b+c)}, 1
{0, (a b+a c+b c)/(a+b+c)}, 10
{0, (a b c)/(a b+a c+b c)}, 30109
{((a-b) (a-c) (b-c) (a+b+c))/(2 a b c), 1/2 (a+b+c)}, 43040
{((a-b) (a-c) (b-c))/(a^2+b^2+c^2), (a^3+b^3+c^3)/(a^2+b^2+c^2)}, 6
{((a-b) (a-c) (b-c))/(a b+a c+b c), (a b c)/(a b+a c+b c)}, 20924
{((a-b) (a-c) (b-c))/(a b+a c+b c), (a^3+b^3+c^3)/(a b+a c+b c)}, 3879
{((a-b) (a-c) (b-c))/(a b+a c+b c), (2 a b c)/(a b+a c+b c)}, 20893
{(-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), (-2*(a^3 + b^3 + c^3))/(a^2 + b^2 + c^2)}, 49750
{(-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), (a^3 + b^3 + c^3)/(a^2 + b^2 + c^2)}, 49751
{-(((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)), -((a^3 + b^3 + c^3)/(a^2 + b^2 + c^2))}, 49752
{-(((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)), -((a*b*c)/(a*b + a*c + b*c))}, 49753
{-(((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)), -((a^3 + b^3 + c^3)/(a*b + a*c + b*c))}, 49754
{-(((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)), (a*b*c)/(a*b + a*c + b*c)}, 49755
{-1/2*((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c), -1/2*(a^3 + b^3 + c^3)/(a*b + a*c + b*c)}, 49756
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c), (-a - b - c)/2}, 49757
{-1/2*((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c), ((a + b)*(a + c)*(b + c))/(2*(a*b + a*c + b*c))}, 49758
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c), (a + b + c)/2}, 49759
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/((a + b)*(a + c)*(b + c)), (a + b + c)/2}, 49760
{0, -2*(a + b + c)}, 49761
{0, (-2*(a^2 + b^2 + c^2))/(a + b + c)}, 49762
{0, (-2*(a*b + a*c + b*c))/(a + b + c)}, 49763
{0, -((a*b + a*c + b*c)/(a + b + c))}, 49764
{0, (-a - b - c)/2}, 49765
{0, -1/2*(a^2 + b^2 + c^2)/(a + b + c)}, 49766
{0, -1/2*(a*b + a*c + b*c)/(a + b + c)}, 49767
{0, (a^2 + b^2 + c^2)/(2*(a + b + c))}, 49768
{0, (a*b + a*c + b*c)/(2*(a + b + c))}, 49769
{0, 2*(a + b + c)}, 49770
{0, (2*(a^2 + b^2 + c^2))/(a + b + c)}, 49771
{0, (2*(a*b + a*c + b*c))/(a + b + c)}, 49772
{0, (2*a*b*c)/(a^2 + b^2 + c^2)}, 49773
{0, (2*a*b*c)/(a*b + a*c + b*c)}, 49774
{((a - b)*(a - c)*(b - c))/(2*(a^2 + b^2 + c^2)), (a^3 + b^3 + c^3)/(2*(a^2 + b^2 + c^2))}, 49775
{((a - b)*(a - c)*(b - c))/(2*(a*b + a*c + b*c)), (a^3 + b^3 + c^3)/(2*(a*b + a*c + b*c))}, 49776
{((a - b)*(a - c)*(b - c))/(2*(a*b + a*c + b*c)), ((a + b)*(a + c)*(b + c))/(2*(a*b + a*c + b*c))}, 49777
{((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), -((a^3 + b^3 + c^3)/(a^2 + b^2 + c^2))}, 49778
{((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c), -((a*b*c)/(a*b + a*c + b*c))}, 49779
{((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c), 0}, 49780
{((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), (a*b*c)/(a^2 + b^2 + c^2)}, 49781
{((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), (2*a*b*c)/(a^2 + b^2 + c^2)}, 49782
{(2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), (2*(a^3 + b^3 + c^3))/(a^2 + b^2 + c^2)}, 49783


X(49750) = X(6)X(3879)∩X(69)X(519)

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

X(49750) = 2 X[6] - 3 X[3912], 4 X[141] - 3 X[41140], 3 X[6542] + X[20080], X[193] - 3 X[17310], 3 X[239] - 5 X[3620], 6 X[3008] - 7 X[3619], 5 X[3618] - 6 X[41141]

X(49750) lies on these lines: {6, 3879}, {69, 519}, {141, 41140}, {144, 6542}, {193, 17310}, {239, 3620}, {524, 4908}, {742, 3630}, {1266, 9053}, {3008, 3619}, {3618, 41141}, {4357, 49465}, {4899, 49711}, {5847, 49709}, {17360, 49511}, {17378, 49529}, {29601, 36404}, {38191, 41847}


X(49751) = X(6)X(514)∩X(69)X(519)

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

X(49751) = X[6] - 3 X[24281], X[69] + 3 X[34342], 2 X[3589] - 3 X[36234], 7 X[3619] - 3 X[30225], 5 X[3763] - 3 X[34362], 4 X[34573] - 3 X[36230]

X(49751) lies on these lines: {6, 514}, {7, 6549}, {69, 519}, {106, 664}, {192, 6633}, {1442, 30117}, {3212, 4257}, {3589, 36234}, {3619, 30225}, {3672, 24864}, {3723, 36226}, {3763, 34362}, {4360, 4555}, {6788, 23816}, {8649, 21138}, {17321, 25031}, {17366, 35092}, {17393, 35962}, {25269, 32094}, {34573, 36230}, {37651, 46790}

X(49751) = {X(6788),X(38941)}-harmonic conjugate of X(23816)


X(49752) = X(69)X(192)∩X(141)X(239)

Barycentrics    a^4 + a*b^3 - b^4 - a^2*b*c + a*b^2*c + a*b*c^2 - 2*b^2*c^2 + a*c^3 - c^4 : :
X(49752) = 4 X[3008] - 5 X[3763], 4 X[3589] - 5 X[17266], 7 X[3619] - 5 X[29590], 5 X[3620] - X[20016], 3 X[17297] - X[32029], 3 X[27487] - 2 X[49481], 3 X[21356] - X[40891], 3 X[21358] - 2 X[41140], 7 X[29607] - 8 X[34573], 4 X[41141] - 3 X[47352]

X(49752) lies on these lines: {6, 3879}, {7, 49533}, {69, 192}, {141, 239}, {320, 9055}, {335, 24699}, {518, 3792}, {519, 599}, {524, 4370}, {1086, 9053}, {1352, 29331}, {3008, 3763}, {3589, 17266}, {3619, 29590}, {3620, 20016}, {3844, 42334}, {3943, 5845}, {4675, 49479}, {5846, 49695}, {5847, 49705}, {15526, 35093}, {16973, 17296}, {17119, 49690}, {17237, 33076}, {17297, 32029}, {17299, 47595}, {17300, 27487}, {17361, 49502}, {17386, 49496}, {17392, 49524}, {21356, 40891}, {21358, 41140}, {29573, 36404}, {29607, 34573}, {41141, 47352}

X(49752) = midpoint of X(69) and X(6542)
X(49752) = reflection of X(i) in X(j) for these {i,j}: {6, 3912}, {239, 141}


X(49753) = X(1)X(7760)∩X(76)X(85)

Barycentrics    a^2*b^2 - a*b^3 + a^2*b*c + a^2*c^2 - b^2*c^2 - a*c^3 : :
X(49753) = 2 X[20893] - 3 X[27487]

X(49753) lies on these lines: {1, 7760}, {37, 40859}, {75, 30109}, {76, 85}, {99, 3509}, {190, 758}, {192, 3735}, {239, 5278}, {257, 1500}, {274, 21808}, {335, 538}, {346, 24282}, {350, 18061}, {514, 4079}, {519, 751}, {536, 21331}, {666, 35145}, {668, 3930}, {671, 4562}, {712, 3797}, {760, 3685}, {894, 24275}, {982, 7757}, {1016, 3508}, {1655, 2895}, {1739, 41142}, {1909, 3970}, {2292, 32026}, {2795, 4645}, {3125, 17759}, {3662, 4045}, {3721, 25264}, {3758, 48866}, {3760, 18055}, {3807, 3992}, {3943, 35101}, {3985, 33948}, {4006, 25280}, {4043, 18714}, {4396, 30113}, {4555, 35144}, {4568, 20947}, {4680, 32847}, {5525, 18047}, {7894, 16787}, {14210, 33946}, {14568, 17719}, {16600, 33296}, {16829, 21332}, {17137, 25237}, {17141, 26770}, {17143, 17451}, {17233, 33936}, {17280, 24254}, {17762, 21070}, {18059, 40463}, {18140, 33299}, {20247, 27109}, {20893, 27487}, {20955, 40006}, {21090, 41324}, {24036, 37686}, {24293, 29674}, {24349, 48869}, {27097, 41805}, {29960, 33940}, {29966, 33933}, {31317, 48864}

X(49753) = reflection of X(i) in X(j) for these {i,j}: {75, 30109}, {20924, 3912}, {40859, 37}
X(49753) = {X(17760),X(21071)}-harmonic conjugate of X(33939)


X(49754) = X(6)X(3879)∩X(519)X(751)

Barycentrics    2*a^4 - a^3*b + 2*a^2*b^2 - b^4 - a^3*c + a*b^2*c - b^3*c + 2*a^2*c^2 + a*b*c^2 - 2*b^2*c^2 - b*c^3 - c^4 : :
X(49754) = 2 X[3664] - 3 X[27487]

X(49754) lies on these lines: {6, 3879}, {9, 6542}, {10, 7760}, {190, 17766}, {239, 1654}, {519, 751}, {524, 17755}, {527, 33888}, {742, 4416}, {1757, 3717}, {3008, 5224}, {3664, 27487}, {3758, 33165}, {4438, 14614}, {4460, 17257}, {9025, 20670}, {17251, 41140}, {17306, 29590}, {17362, 49516}, {17772, 49692}, {17789, 34283}, {29574, 36409}, {33159, 46922}

X(49754) = midpoint of X(6542) and X(17363)
X(49754) = reflection of X(i) in X(j) for these {i,j}: {239, 3686}, {3879, 3912}, {49711, 17755}


X(49755) = X(2)X(21332)∩X(190)X(517)

Barycentrics    a^2*b^2 - a*b^3 - a^2*b*c + a*b^2*c + a^2*c^2 + a*b*c^2 - b^2*c^2 - a*c^3 : :
X(49755) = 2 X[20924] - 3 X[27487], 3 X[27487] - 4 X[30109]

X(49755) lies on these lines: {2, 21332}, {37, 10027}, {75, 46180}, {92, 17789}, {99, 5011}, {183, 34522}, {190, 517}, {194, 3959}, {239, 257}, {320, 35102}, {325, 1146}, {330, 20271}, {335, 21331}, {350, 2170}, {514, 1921}, {519, 751}, {1121, 4518}, {1655, 3727}, {1909, 17451}, {1959, 3975}, {3061, 3452}, {3177, 21281}, {3227, 4694}, {3263, 33946}, {3570, 4511}, {3693, 4595}, {3721, 21226}, {3726, 9263}, {3770, 17443}, {3797, 35101}, {3807, 4723}, {4051, 17144}, {4695, 41142}, {5179, 41324}, {5739, 6542}, {6381, 18061}, {6631, 40872}, {7187, 20255}, {16086, 29331}, {16583, 34063}, {17266, 41793}, {17466, 17793}, {17760, 33938}, {18159, 20335}, {18161, 20923}, {20179, 24291}, {20955, 29960}, {21138, 33891}, {21808, 25303}, {23636, 30631}, {25280, 33299}, {26562, 33947}, {28850, 32850}, {29968, 41875}, {29988, 30006}, {30030, 33943}, {30036, 33930}, {30038, 33944}, {35070, 35092}, {35145, 35148}, {37686, 43065}

X(49755) = midpoint of X(3912) and X(41773)
X(49755) = reflection of X(i) in X(j) for these {i,j}: {335, 21331}, {10027, 37}, {20924, 30109}
X(49755) = crossdifference of every pair of points on line {1918, 7234}
X(49755) = {X(20924),X(30109)}-harmonic conjugate of X(27487)


X(49756) = X(6)X(3879)∩X(37)X(519)

Barycentrics    2*a^4 - a^3*b + 3*a^2*b^2 - a*b^3 - b^4 - a^3*c + 2*a^2*b*c + a*b^2*c - 2*b^3*c + 3*a^2*c^2 + a*b*c^2 - 2*b^2*c^2 - a*c^3 - 2*b*c^3 - c^4 : :
X(49756) = X[3879] - 3 X[3912], 3 X[17310] + X[17363]

X(49756) lies on these lines: {6, 3879}, {9, 32847}, {37, 519}, {44, 3932}, {45, 3883}, {239, 966}, {344, 17310}, {391, 6542}, {742, 17332}, {1213, 3008}, {1279, 4969}, {2243, 3977}, {2246, 32848}, {2325, 17766}, {3707, 4078}, {3943, 5853}, {4357, 16521}, {4657, 41140}, {5276, 32779}, {7855, 34847}, {16517, 17272}, {16593, 17374}, {17357, 41141}, {20924, 34283}


X(49757) = X(9)X(192)∩X(76)X(85)

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

X(49757) lies on these lines: {4, 32847}, {9, 192}, {57, 25242}, {72, 519}, {76, 85}, {321, 17451}, {329, 6542}, {514, 3700}, {516, 20715}, {726, 20358}, {1229, 30097}, {3008, 3666}, {3061, 20173}, {3693, 16609}, {3911, 25083}, {3930, 30807}, {3971, 4517}, {3995, 40886}, {5777, 29331}, {16603, 40997}, {17266, 25525}, {17310, 28609}, {17452, 22040}, {17742, 24268}, {20171, 20258}, {20432, 20891}, {20703, 23682}, {22016, 22021}

X(49757) = reflection of X(43040) in X(3912)


X(49758) = X(32)X(169)∩X(37)X(519)

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

X(49758) lies on these lines: {1, 9351}, {2, 20924}, {6, 15934}, {9, 3735}, {32, 169}, {37, 519}, {38, 46902}, {39, 1212}, {44, 758}, {45, 9708}, {63, 36283}, {75, 48864}, {115, 5179}, {187, 910}, {213, 17451}, {238, 760}, {239, 5278}, {514, 6586}, {665, 6550}, {672, 3125}, {712, 17755}, {742, 30109}, {766, 3271}, {966, 16086}, {1015, 3290}, {1104, 5007}, {1107, 16600}, {1149, 2087}, {1211, 3912}, {1279, 2809}, {1319, 8649}, {1500, 16601}, {1572, 16970}, {1574, 16605}, {1575, 16611}, {1738, 2795}, {1739, 20331}, {1914, 5540}, {2082, 2241}, {2161, 15898}, {2170, 3230}, {2242, 40131}, {2243, 21372}, {2246, 2251}, {3294, 3727}, {3570, 30113}, {3666, 41140}, {3691, 3954}, {3721, 16552}, {3726, 45751}, {3730, 3959}, {3739, 20893}, {3767, 6554}, {3772, 5309}, {3780, 3970}, {3934, 25994}, {4000, 7739}, {4253, 20271}, {4403, 44664}, {4422, 35101}, {4526, 33905}, {4695, 14439}, {5011, 17735}, {5452, 16502}, {5819, 7737}, {6547, 40880}, {7746, 46835}, {7765, 23537}, {8609, 23980}, {8624, 18785}, {10027, 35957}, {10459, 21802}, {14839, 49692}, {16549, 21951}, {16975, 26242}, {17279, 33936}, {17353, 24254}, {20432, 26035}, {20963, 21808}, {21796, 40937}, {21892, 25078}, {24282, 26685}, {24735, 33937}, {25070, 30646}, {26690, 29607}, {28659, 29544}

X(49758) = midpoint of X(i) and X(j) for these {i,j}: {44, 21331}, {10027, 35957}
X(49758) = reflection of X(20893) in X(3739)
X(49758) = complement of X(20924)
X(49758) = complement of the isotomic conjugate of X(2161)
X(49758) = X(i)-complementary conjugate of X(j) for these (i,j): {32, 214}, {80, 626}, {213, 31845}, {560, 16586}, {759, 21240}, {1411, 17046}, {2006, 17047}, {2161, 2887}, {2205, 35069}, {6187, 141}, {11060, 25639}, {18359, 21235}, {20566, 40379}, {32675, 17072}, {34079, 3741}, {34857, 21245}, {47318, 23301}
X(49758) = crosspoint of X(2) and X(2161)
X(49758) = crosssum of X(6) and X(3218)
X(49758) = crossdifference of every pair of points on line {8053, 16874}
X(49758) = barycentric product X(1)*X(33136)
X(49758) = barycentric quotient X(33136)/X(75)
X(49758) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {169, 16968, 32}, {1212, 16583, 39}, {3290, 43065, 1015}, {16601, 41015, 1500}, {16605, 25066, 1574}, {16611, 24036, 1575}, {21332, 46907, 1}


X(49759) = X(72)X(519)∩X(241)X(514)

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

X(49759) lies on these lines: {9, 29001}, {34, 979}, {63, 194}, {72, 519}, {241, 514}, {516, 20670}, {666, 1438}, {1146, 26012}, {1404, 14543}, {1429, 3732}, {2170, 30807}, {2398, 8647}, {3056, 21084}, {3061, 3452}, {4530, 48381}, {6542, 31018}, {22343, 23688}, {23524, 23677}, {27321, 27338}, {29331, 31837}, {29607, 31224}, {29984, 29988}, {34059, 36638}

X(49759) = reflection of X(43040) in X(3008)
X(49759) = crossdifference of every pair of points on line {55, 23655}


X(49760) = X(2)X(20955)∩X(37)X(319)

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

X(49760) lies on these lines: {2, 20955}, {37, 319}, {44, 18722}, {63, 3959}, {65, 1046}, {85, 24789}, {210, 3507}, {238, 3512}, {239, 257}, {241, 514}, {385, 3290}, {518, 20590}, {519, 3743}, {742, 15985}, {1108, 28366}, {1211, 3912}, {1581, 24479}, {1931, 9278}, {1959, 2238}, {2287, 44302}, {3125, 18206}, {3752, 29590}, {4383, 7146}, {4658, 30117}, {5291, 20602}, {7200, 16752}, {14543, 27970}, {15586, 16702}, {16583, 17739}, {17266, 30832}, {17310, 41816}, {17451, 37676}, {17789, 27319}, {18161, 27623}, {20016, 28606}, {20597, 46195}, {23668, 45705}, {25067, 26671}, {28369, 40977}, {29331, 37528}, {29607, 41806}

X(49760) = X(i)-complementary conjugate of X(j) for these (i,j): {32, 35114}, {28482, 141}, {35162, 626}
X(49760) = X(17930)-Ceva conjugate of X(513)
X(49760) = crosspoint of X(i) and X(j) for these (i,j): {256, 1929}, {274, 7261}
X(49760) = crosssum of X(i) and X(j) for these (i,j): {171, 1757}, {213, 17798}
X(49760) = crossdifference of every pair of points on line {55, 7234}
X(49760) = barycentric product X(81)*X(23947)
X(49760) = barycentric quotient X(23947)/X(321)
X(49760) = {X(17789),X(27321)}-harmonic conjugate of X(31993)


X(49761) = X(1)X(2)∩X(44)X(28337)

Barycentrics    4*a^2 + 3*a*b - 3*b^2 + 3*a*c - 4*b*c - 3*c^2 : :
X(49761) = 9 X[2] - 7 X[239], 15 X[2] - 14 X[3008], 6 X[2] - 7 X[3912], 3 X[2] - 7 X[6542], 33 X[2] - 35 X[17266], 5 X[2] - 7 X[17310], 15 X[2] - 7 X[20016], 39 X[2] - 35 X[29590], 51 X[2] - 49 X[29607], 11 X[2] - 7 X[40891], 8 X[2] - 7 X[41140], 13 X[2] - 14 X[41141], 5 X[239] - 6 X[3008], 2 X[239] - 3 X[3912], X[239] - 3 X[6542], 11 X[239] - 15 X[17266], 5 X[239] - 9 X[17310], 5 X[239] - 3 X[20016], 13 X[239] - 15 X[29590], 17 X[239] - 21 X[29607], 11 X[239] - 9 X[40891], 8 X[239] - 9 X[41140], 13 X[239] - 18 X[41141], 4 X[3008] - 5 X[3912], 2 X[3008] - 5 X[6542], 22 X[3008] - 25 X[17266], 2 X[3008] - 3 X[17310], 26 X[3008] - 25 X[29590], 34 X[3008] - 35 X[29607], 22 X[3008] - 15 X[40891], 16 X[3008] - 15 X[41140], 13 X[3008] - 15 X[41141], 11 X[3912] - 10 X[17266], 5 X[3912] - 6 X[17310], 5 X[3912] - 2 X[20016], 13 X[3912] - 10 X[29590], 17 X[3912] - 14 X[29607], 11 X[3912] - 6 X[40891], 4 X[3912] - 3 X[41140], 13 X[3912] - 12 X[41141], 5 X[4668] - 7 X[32847], 11 X[6542] - 5 X[17266], 5 X[6542] - 3 X[17310], 5 X[6542] - X[20016], 13 X[6542] - 5 X[29590], 17 X[6542] - 7 X[29607], 11 X[6542] - 3 X[40891], 8 X[6542] - 3 X[41140], 13 X[6542] - 6 X[41141], 25 X[17266] - 33 X[17310], 25 X[17266] - 11 X[20016], 13 X[17266] - 11 X[29590], 85 X[17266] - 77 X[29607], 5 X[17266] - 3 X[40891], 40 X[17266] - 33 X[41140], 65 X[17266] - 66 X[41141], 3 X[17310] - X[20016], 39 X[17310] - 25 X[29590], 51 X[17310] - 35 X[29607], 11 X[17310] - 5 X[40891], 8 X[17310] - 5 X[41140], 13 X[17310] - 10 X[41141], 13 X[20016] - 25 X[29590], 17 X[20016] - 35 X[29607], 11 X[20016] - 15 X[40891], 8 X[20016] - 15 X[41140], 13 X[20016] - 30 X[41141], 85 X[29590] - 91 X[29607], 55 X[29590] - 39 X[40891], 40 X[29590] - 39 X[41140], 5 X[29590] - 6 X[41141], 77 X[29607] - 51 X[40891], 56 X[29607] - 51 X[41140], 91 X[29607] - 102 X[41141], 8 X[40891] - 11 X[41140], 13 X[40891] - 22 X[41141], 13 X[41140] - 16 X[41141], X[4480] - 4 X[4727], 3 X[1266] - 4 X[7238], 2 X[7238] - 3 X[17374], 2 X[4700] - 3 X[17264]

X(49761) lies on these lines: {1, 2}, {44, 28337}, {86, 4060}, {141, 4464}, {142, 17386}, {320, 17133}, {514, 4838}, {524, 4480}, {536, 4409}, {594, 4889}, {742, 3630}, {1086, 28329}, {1266, 4971}, {1992, 4873}, {2321, 3758}, {3627, 29331}, {3663, 17373}, {3686, 17315}, {3723, 4478}, {3763, 4910}, {3879, 4363}, {3943, 4725}, {3946, 17295}, {3950, 17363}, {4021, 17287}, {4029, 17346}, {4044, 24524}, {4058, 17379}, {4072, 17350}, {4098, 17331}, {4114, 43040}, {4357, 17372}, {4416, 17314}, {4432, 17772}, {4440, 28313}, {4460, 17304}, {4693, 5847}, {4700, 17264}, {4740, 4896}, {4851, 17119}, {4856, 17280}, {4898, 17257}, {4909, 28604}, {4916, 10436}, {4967, 17390}, {5839, 25101}, {8162, 21986}, {8168, 16412}, {17309, 17353}, {21839, 24081}, {24133, 33905}, {24821, 34379}, {27478, 49459}, {27481, 49504}, {31342, 49457}

X(49761) = reflection of X(i) in X(j) for these {i,j}: {1266, 17374}, {3912, 6542}, {20016, 3008}
X(49761) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 29574, 24603}, {8, 29605, 29574}, {145, 17294, 17023}, {3008, 17310, 3912}, {3879, 17299, 4431}, {6542, 20016, 17310}, {16816, 29618, 29600}, {16834, 29616, 29596}, {17310, 20016, 3008}, {17372, 17388, 4357}, {17389, 20055, 10}, {20050, 29616, 16834}, {29588, 29615, 1125}


X(49762) = X(1)X(2)∩X(44)X(3717)

Barycentrics    4*a^3 - a^2*b + 4*a*b^2 - 3*b^3 - a^2*c + 2*a*b*c - 3*b^2*c + 4*a*c^2 - 3*b*c^2 - 3*c^3 : :
X(49762) = 2 X[1] - 3 X[3912], X[1] - 3 X[32847], 4 X[10] - 3 X[41140], X[145] - 3 X[17310], 3 X[239] - 5 X[3617], 6 X[3008] - 7 X[9780], 5 X[3616] - 6 X[41141], X[3621] + 3 X[6542], 7 X[4678] - 3 X[40891], 15 X[17266] - 13 X[46934], 21 X[29607] - 23 X[46931], 2 X[44] - 3 X[3717], 2 X[3246] - 3 X[3932], 3 X[4645] - 2 X[4887], 3 X[4899] - 2 X[49712], 4 X[17067] - 3 X[32922], X[17160] - 3 X[32850]

X(49762) lies on these lines: {1, 2}, {44, 3717}, {45, 3883}, {514, 47685}, {678, 32848}, {742, 49515}, {752, 4480}, {1266, 28503}, {1738, 17769}, {2325, 49709}, {3246, 3932}, {3416, 49527}, {3674, 5252}, {3879, 49688}, {3895, 17742}, {4029, 49746}, {4078, 49506}, {4346, 49446}, {4645, 4887}, {4684, 9053}, {4851, 49690}, {4896, 24349}, {4899, 5847}, {4901, 16670}, {4968, 20893}, {8168, 37580}, {9041, 17374}, {16666, 49524}, {17067, 32922}, {17160, 32850}, {17242, 30331}, {17279, 49679}, {17353, 49681}, {18788, 28236}, {29331, 37705}, {33165, 49684}, {49459, 49528}, {49511, 49534}

X(49762) = reflection of X(i) in X(j) for these {i,j}: {3912, 32847}, {49709, 2325}
X(49762) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {145, 29579, 1}, {3617, 29608, 10}, {29601, 49466, 1}


X(49763) = X(1)X(2)∩X(238)X(4700)

Barycentrics    5*a^2*b - 2*a*b^2 - b^3 + 5*a^2*c + 2*a*b*c - 3*b^2*c - 2*a*c^2 - 3*b*c^2 - c^3 : :
X(49763) = X[8] - 3 X[17310], 2 X[10] - 3 X[3912], X[145] + 3 X[6542], 3 X[239] - 5 X[3616], 4 X[1125] - 3 X[41140], 5 X[1698] - 6 X[41141], 6 X[3008] - 7 X[3624], 7 X[3622] - 3 X[40891], X[3632] - 3 X[32847], 15 X[17266] - 13 X[19877], 3 X[238] - 2 X[4700], X[1266] - 3 X[4684], 2 X[1266] - 3 X[24231], 3 X[1738] - 4 X[3834], 2 X[3834] - 3 X[4966], 3 X[3685] - X[20072], 3 X[3717] - 2 X[49701], 3 X[4899] - 2 X[49713], 3 X[6541] - X[49713]

X(49763) lies on these lines: {1, 2}, {141, 49475}, {142, 49459}, {192, 49505}, {238, 4700}, {320, 28580}, {514, 4170}, {518, 3943}, {524, 4702}, {527, 4693}, {528, 17374}, {740, 1266}, {742, 49462}, {984, 4029}, {1738, 3834}, {2321, 49490}, {2325, 49712}, {3246, 4969}, {3662, 4780}, {3663, 49469}, {3685, 20072}, {3686, 16484}, {3696, 34824}, {3717, 49701}, {3755, 33087}, {3790, 49536}, {3879, 32941}, {3902, 20913}, {3948, 4742}, {3950, 49448}, {4035, 33141}, {4046, 4883}, {4078, 49450}, {4133, 24349}, {4297, 28909}, {4357, 49471}, {4389, 49470}, {4431, 49479}, {4464, 49472}, {4527, 49491}, {4647, 20893}, {4690, 49740}, {4709, 24199}, {4727, 28503}, {4819, 16610}, {4851, 20181}, {4867, 5179}, {4899, 6541}, {5542, 49474}, {5846, 49699}, {5847, 49709}, {5853, 32846}, {16496, 17314}, {16666, 48810}, {17233, 49529}, {17269, 47359}, {17279, 49680}, {17299, 42871}, {17309, 49688}, {17318, 47358}, {17353, 49497}, {17360, 49746}, {17362, 42819}, {17365, 49485}, {17377, 49684}, {17387, 49720}, {17388, 49465}, {22791, 29331}, {24393, 49689}, {25557, 49468}, {29311, 38485}, {30991, 33134}

X(49763) = reflection of X(i) in X(j) for these {i,j}: {1738, 4966}, {4899, 6541}, {4969, 3246}, {24231, 4684}, {49712, 2325}
X(49763) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 17244, 10}, {4028, 10453, 24239}, {33087, 49678, 3755}


X(49764) = X(1)X(2)∩X(37)X(4407)

Barycentrics    3*a^2*b - a*b^2 - b^3 + 3*a^2*c + 2*a*b*c - 2*b^2*c - a*c^2 - 2*b*c^2 - c^3 : :
X(49764) = 4 X[3008] - 5 X[19862], 5 X[3616] - X[20016], 7 X[3624] - 5 X[29590], 4 X[3634] - 5 X[17266], 3 X[17310] - X[32847], 8 X[19878] - 7 X[29607], 3 X[19883] - 2 X[41140], 3 X[25055] - X[40891], 2 X[4439] - 3 X[6541], X[1086] - 3 X[4966], 2 X[1086] - 3 X[49676], 3 X[1757] - 5 X[4473], 3 X[17264] - X[49712], 3 X[17297] - X[24715]

X(49764) lies on these lines: {1, 2}, {37, 4407}, {141, 49471}, {142, 4709}, {319, 16484}, {320, 2796}, {514, 4010}, {518, 4439}, {524, 4432}, {537, 3943}, {726, 4684}, {740, 1086}, {742, 3993}, {752, 4702}, {946, 29331}, {1279, 17772}, {1509, 33954}, {1757, 4473}, {2321, 49479}, {3120, 31029}, {3246, 4725}, {3662, 49469}, {3671, 43040}, {3685, 17770}, {3773, 49478}, {3775, 4708}, {3790, 49498}, {3821, 17227}, {3836, 28581}, {3846, 4891}, {3879, 49482}, {3896, 24169}, {3923, 4644}, {3932, 49697}, {3948, 4975}, {3950, 49505}, {4078, 49510}, {4085, 17231}, {4133, 5542}, {4422, 4753}, {4425, 33081}, {4429, 49678}, {4527, 49483}, {4649, 24295}, {4653, 6626}, {4660, 17296}, {4665, 24325}, {4717, 17762}, {4732, 17245}, {4780, 21255}, {4851, 32941}, {4864, 17769}, {5846, 49696}, {5847, 49705}, {15485, 17363}, {17233, 49490}, {17234, 49459}, {17240, 33165}, {17242, 49448}, {17243, 49457}, {17264, 49712}, {17267, 49680}, {17279, 49497}, {17295, 33076}, {17297, 24715}, {17309, 42871}, {17311, 49460}, {17313, 24693}, {17314, 49455}, {17353, 49685}, {17372, 42819}, {17376, 49485}, {17388, 49472}, {17766, 32846}, {20432, 42031}, {20893, 33935}, {24231, 28522}, {24692, 28580}, {25385, 26738}, {28538, 49700}, {32784, 48639}, {32915, 33064}, {34587, 35068}

X(49764) = midpoint of X(i) and X(j) for these {i,j}: {1, 6542}, {320, 4693}, {4702, 17374}
X(49764) = reflection of X(i) in X(j) for these {i,j}: {10, 3912}, {239, 1125}, {4753, 4422}, {49676, 4966}, {49697, 3932}, {49710, 4432}
X(49764) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17308, 48822}, {1, 49560, 10}, {10, 15808, 39580}, {306, 42057, 29655}, {3241, 17230, 29659}, {3661, 29586, 24603}, {3679, 17244, 25352}, {3679, 25352, 10}, {3775, 15569, 25354}, {3950, 49505, 49520}, {17231, 49475, 4085}, {33087, 49470, 3821}


X(49765) = X(1)X(2)∩X(69)X(3950)

Barycentrics    2*a^2 + 3*a*b - 3*b^2 + 3*a*c - 2*b*c - 3*c^2 : :
X(49765) = 9 X[2] - 5 X[239], 6 X[2] - 5 X[3008], 3 X[2] - 5 X[3912], 3 X[2] + 5 X[6542], 21 X[2] - 25 X[17266], X[2] - 5 X[17310], 21 X[2] - 5 X[20016], 33 X[2] - 25 X[29590], 39 X[2] - 35 X[29607], 13 X[2] - 5 X[40891], 7 X[2] - 5 X[41140], 4 X[2] - 5 X[41141], 2 X[239] - 3 X[3008], X[239] - 3 X[3912], X[239] + 3 X[6542], 7 X[239] - 15 X[17266], X[239] - 9 X[17310], 7 X[239] - 3 X[20016], 11 X[239] - 15 X[29590], 13 X[239] - 21 X[29607], 13 X[239] - 9 X[40891], 7 X[239] - 9 X[41140], 4 X[239] - 9 X[41141], X[3008] + 2 X[6542], 7 X[3008] - 10 X[17266], X[3008] - 6 X[17310], 7 X[3008] - 2 X[20016], 11 X[3008] - 10 X[29590], 13 X[3008] - 14 X[29607], 13 X[3008] - 6 X[40891], 7 X[3008] - 6 X[41140], 2 X[3008] - 3 X[41141], X[3632] - 5 X[32847], 7 X[3912] - 5 X[17266], X[3912] - 3 X[17310], 7 X[3912] - X[20016], 11 X[3912] - 5 X[29590], 13 X[3912] - 7 X[29607], 13 X[3912] - 3 X[40891], 7 X[3912] - 3 X[41140], 4 X[3912] - 3 X[41141], 7 X[6542] + 5 X[17266], X[6542] + 3 X[17310], 7 X[6542] + X[20016], 11 X[6542] + 5 X[29590], 13 X[6542] + 7 X[29607], 13 X[6542] + 3 X[40891], 7 X[6542] + 3 X[41140], 4 X[6542] + 3 X[41141], 5 X[17266] - 21 X[17310], 5 X[17266] - X[20016], 11 X[17266] - 7 X[29590], 65 X[17266] - 49 X[29607], 65 X[17266] - 21 X[40891], 5 X[17266] - 3 X[41140], 20 X[17266] - 21 X[41141], 21 X[17310] - X[20016], 33 X[17310] - 5 X[29590], 39 X[17310] - 7 X[29607], 13 X[17310] - X[40891], 7 X[17310] - X[41140], 4 X[17310] - X[41141], 11 X[20016] - 35 X[29590], 13 X[20016] - 49 X[29607], 13 X[20016] - 21 X[40891], X[20016] - 3 X[41140], 4 X[20016] - 21 X[41141], 65 X[29590] - 77 X[29607], 65 X[29590] - 33 X[40891], 35 X[29590] - 33 X[41140], 20 X[29590] - 33 X[41141], 7 X[29607] - 3 X[40891], 49 X[29607] - 39 X[41140], 28 X[29607] - 39 X[41141], 7 X[40891] - 13 X[41140], 4 X[40891] - 13 X[41141], 4 X[41140] - 7 X[41141], X[4693] + 3 X[32846], 3 X[4887] - 4 X[7238], X[1266] - 3 X[17297], 3 X[4684] - X[24841], X[4969] - 3 X[41310], X[47312] - 5 X[47532]

X(49765) lies on these lines: {1, 2}, {69, 3950}, {141, 4021}, {142, 17119}, {320, 17132}, {335, 28522}, {514, 3700}, {516, 4693}, {524, 2325}, {527, 3943}, {536, 4887}, {546, 29331}, {597, 4982}, {742, 3631}, {1086, 4727}, {1266, 17297}, {1449, 4916}, {2321, 3664}, {3589, 4889}, {3644, 49518}, {3663, 17296}, {3672, 4898}, {3686, 17243}, {3707, 41313}, {3723, 48635}, {3729, 4072}, {3731, 32099}, {3739, 4060}, {3758, 3879}, {3834, 4971}, {3875, 21255}, {3946, 17231}, {3982, 4059}, {3986, 17270}, {4007, 4648}, {4029, 4643}, {4058, 10436}, {4098, 17257}, {4353, 33087}, {4357, 17295}, {4371, 20195}, {4395, 28329}, {4416, 17242}, {4422, 4700}, {4431, 17300}, {4432, 4437}, {4445, 5257}, {4461, 4888}, {4464, 16706}, {4478, 4698}, {4644, 4873}, {4659, 4896}, {4667, 17281}, {4684, 24841}, {4856, 17240}, {4869, 17151}, {4901, 4924}, {4909, 5750}, {4967, 17317}, {4969, 41310}, {5232, 16673}, {5525, 7291}, {5850, 20533}, {5936, 31312}, {6541, 34379}, {6666, 17362}, {6996, 28236}, {6999, 28228}, {7402, 16200}, {9038, 40521}, {11343, 25439}, {11349, 48696}, {17239, 25358}, {17312, 24199}, {17363, 25101}, {20080, 25728}, {21868, 31198}, {22034, 22036}, {27474, 49479}, {27475, 49459}, {28639, 48636}, {32852, 40998}, {36662, 38155}, {38186, 49690}, {43179, 49506}, {43180, 49493}, {47312, 47532}

X(49765) = midpoint of X(i) and X(j) for these {i,j}: {1086, 4727}, {3912, 6542}, {3943, 17374}
X(49765) = reflection of X(i) in X(j) for these {i,j}: {3008, 3912}, {4700, 4422}
X(49765) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 29594, 29604}, {1, 29616, 29594}, {2, 29601, 29606}, {2, 29605, 3244}, {2, 29618, 29601}, {8, 29573, 29571}, {8, 29621, 16832}, {2321, 4851, 3664}, {3008, 3912, 41141}, {3621, 29627, 16833}, {3625, 29600, 4384}, {3626, 29606, 2}, {3633, 5222, 49543}, {3661, 29574, 1125}, {3686, 17243, 25072}, {3879, 17233, 17355}, {3912, 41140, 17266}, {4384, 29583, 29600}, {4393, 29577, 29596}, {4851, 17309, 2321}, {5750, 17390, 4909}, {6542, 17310, 3912}, {16832, 29573, 29621}, {16832, 29621, 29571}, {16834, 29579, 31191}, {17023, 17389, 3635}, {17229, 17390, 5750}, {17230, 17389, 17023}, {17231, 17388, 3946}, {17233, 17386, 3879}, {17240, 17377, 17353}, {17242, 17373, 4416}, {17243, 17372, 3686}, {17266, 20016, 41140}, {17294, 17316, 10}, {17295, 17315, 4357}, {17296, 17314, 3663}, {17299, 17311, 142}, {17308, 29585, 551}, {17353, 17377, 4856}, {24603, 29615, 4691}, {29569, 29615, 24603}


X(49766) = X(1)X(2)∩X(44)X(3932)

Barycentrics    2*a^3 + a^2*b + 2*a*b^2 - 3*b^3 + a^2*c + 4*a*b*c - 3*b^2*c + 2*a*c^2 - 3*b*c^2 - 3*c^3 : :
X(49766) = X[1] - 3 X[3912], X[1] + 3 X[32847], X[8] + 3 X[17310], 3 X[239] - 7 X[9780], 2 X[1125] - 3 X[41141], 5 X[1698] - 3 X[41140], 3 X[3008] - 4 X[3634], 5 X[3617] + 3 X[6542], 11 X[5550] - 15 X[17266], 15 X[29590] - 23 X[46931], 3 X[40891] - 11 X[46933], X[44] - 3 X[3932], X[1266] - 3 X[31151], 3 X[1738] - X[17160], 3 X[3717] - X[49712], 3 X[32846] + X[49712], 3 X[3836] - 2 X[17067]

X(49766) lies on these lines: {1, 2}, {44, 3932}, {45, 3416}, {514, 4522}, {516, 6541}, {527, 4439}, {726, 4887}, {752, 2325}, {1266, 31151}, {1738, 17160}, {2550, 4133}, {3246, 5846}, {3703, 37520}, {3717, 32846}, {3834, 28503}, {3836, 17067}, {3879, 33165}, {3943, 28580}, {3950, 4660}, {4060, 4732}, {4082, 32946}, {4385, 20924}, {4422, 28538}, {4645, 28526}, {4780, 17314}, {4851, 49529}, {4901, 49536}, {17132, 24692}, {17267, 49681}, {17279, 49684}, {17296, 49505}, {17311, 49688}, {17601, 33092}, {18357, 29331}, {18788, 28164}, {21255, 49455}, {28909, 43174}, {33087, 49527}

X(49766) = midpoint of X(i) and X(j) for these {i,j}: {3717, 32846}, {3912, 32847}
X(49766) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 29596, 1125}, {1, 29674, 29596}, {8, 29583, 1}, {29596, 49476, 1}, {29674, 49476, 1125}


X(49767) = X(1)X(2)∩X(3)X(28909)

Barycentrics    4*a^2*b - a*b^2 - 2*b^3 + 4*a^2*c + 4*a*b*c - 3*b^2*c - a*c^2 - 3*b*c^2 - 2*c^3 : :
X(49767) = X[1] + 3 X[17310], X[10] - 3 X[3912], X[145] + 3 X[32847], 3 X[239] - 7 X[3624], 3 X[3008] - 4 X[19878], 5 X[3616] + 3 X[6542], 2 X[3634] - 3 X[41141], 11 X[5550] - 3 X[40891], 5 X[19862] - 3 X[41140], X[3943] + 3 X[4966], X[1266] - 3 X[49676], 3 X[3717] - X[49713], 3 X[3932] - X[49701], X[4693] + 3 X[17297], 3 X[17297] - X[24692], X[4753] - 3 X[41310], 3 X[32846] + X[49709]

X(49767) lies on these lines: {1, 2}, {3, 28909}, {514, 4806}, {524, 4759}, {726, 3943}, {740, 3834}, {1266, 28522}, {3649, 43040}, {3685, 28508}, {3717, 49713}, {3790, 49535}, {3932, 49701}, {3993, 4389}, {4029, 49511}, {4432, 17374}, {4527, 25557}, {4684, 6541}, {4693, 17297}, {4702, 28562}, {4709, 17234}, {4717, 20913}, {4753, 41310}, {4851, 49482}, {4933, 24593}, {7238, 28542}, {9955, 29331}, {15485, 17373}, {16484, 17295}, {17231, 49471}, {17232, 49469}, {17233, 49479}, {17240, 49490}, {17241, 49459}, {17242, 49520}, {17267, 49497}, {17279, 49685}, {17311, 32941}, {20893, 42031}, {28512, 32846}

X(49767) = midpoint of X(i) and X(j) for these {i,j}: {4432, 17374}, {4684, 6541}, {4693, 24692}
X(49767) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17230, 10}, {4693, 17297, 24692}


X(49768) = X(1)X(2)∩X(9)X(49505)

Barycentrics    2*a^3 - 3*a^2*b + 2*a*b^2 + b^3 - 3*a^2*c - 4*a*b*c + b^2*c + 2*a*c^2 + b*c^2 + c^3 : :
X(49768) = 3 X[1] + X[32847], X[8] - 5 X[17266], X[239] - 5 X[3616], 7 X[3622] + X[6542], 3 X[3912] - X[32847], 11 X[5550] - 7 X[29607], X[17310] + 3 X[38314], 3 X[25055] - X[41140], 5 X[29590] - 13 X[46934], X[24692] - 3 X[49676], 3 X[1279] + X[17374], 3 X[4966] - X[17374], 3 X[1738] - 5 X[27191], 3 X[3685] + X[4440], X[4440] - 3 X[24231], 3 X[17264] + X[24841], 3 X[17297] + X[49709], 3 X[27487] + X[49470]

X(49768) lies on these lines: {1, 2}, {9, 49505}, {11, 30823}, {39, 3991}, {45, 47358}, {106, 35574}, {141, 42819}, {142, 20181}, {214, 17060}, {238, 4684}, {304, 20893}, {344, 16496}, {497, 4138}, {514, 3716}, {515, 36654}, {516, 24692}, {518, 4422}, {524, 3246}, {527, 4432}, {528, 3834}, {537, 2325}, {726, 24225}, {742, 15569}, {908, 24709}, {1001, 4643}, {1086, 4702}, {1266, 4693}, {1279, 4966}, {1319, 43054}, {1323, 39775}, {1738, 27191}, {1930, 4717}, {2796, 4887}, {3242, 4078}, {3243, 49536}, {3664, 49482}, {3673, 18156}, {3685, 4440}, {3702, 20432}, {3712, 3999}, {3717, 49675}, {3749, 18141}, {3826, 49467}, {3836, 5853}, {3883, 33087}, {3923, 5542}, {3932, 4864}, {3946, 49471}, {3950, 49455}, {3977, 17449}, {3993, 4353}, {4000, 4780}, {4104, 4423}, {4357, 16484}, {4416, 15485}, {4515, 16604}, {4653, 16887}, {4660, 21255}, {4670, 48810}, {4675, 48805}, {4851, 49684}, {4891, 17061}, {4901, 15600}, {4989, 49489}, {5249, 32943}, {5901, 29331}, {6666, 49457}, {7238, 28534}, {7263, 49485}, {12263, 46180}, {15570, 49524}, {17227, 49746}, {17237, 49740}, {17243, 49465}, {17264, 24841}, {17267, 49688}, {17278, 49460}, {17279, 42871}, {17296, 35227}, {17297, 49709}, {17311, 49681}, {17353, 49490}, {17355, 49479}, {17366, 49475}, {17464, 34587}, {17718, 30824}, {18788, 28228}, {20662, 41391}, {21320, 33845}, {24210, 33124}, {24216, 32851}, {25101, 49448}, {25557, 49484}, {27487, 49470}, {28849, 35094}, {30818, 37703}, {33064, 40998}

X(49768) = midpoint of X(i) and X(j) for these {i,j}: {1, 3912}, {238, 4684}, {1086, 4702}, {1266, 4693}, {1279, 4966}, {3685, 24231}, {3717, 49675}, {3932, 4864}
X(49768) = reflection of X(3008) in X(1125)
X(49768) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17284, 36479}, {1, 25055, 26626}, {1, 29598, 48830}, {1, 29660, 17023}, {1, 29674, 49466}, {1, 49476, 3635}, {10, 551, 24331}, {16832, 48802, 10}, {17023, 17284, 31211}, {17023, 29660, 1125}, {17279, 42871, 49529}, {17284, 36479, 10}, {21255, 30331, 4660}, {29585, 38314, 1}, {29596, 29659, 3828}, {29611, 48851, 10}, {29672, 42057, 40940}, {29674, 49466, 3626}


X(49769) = X(1)X(2)∩X(12)X(43040)

Barycentrics    a*b^2 - 2*b^3 + 4*a*b*c - b^2*c + a*c^2 - b*c^2 - 2*c^3 : :
X(49769) = X[1] - 5 X[17266], 3 X[2] + X[32847], X[239] - 5 X[1698], X[6542] + 7 X[9780], X[17310] + 3 X[19875], 13 X[19877] - 5 X[29590], X[20016] - 17 X[46932], X[190] + 3 X[31151], X[24692] - 3 X[31151], X[1086] - 3 X[3836], X[1086] + 3 X[3932], 3 X[3836] + X[4439], 3 X[3932] - X[4439], X[984] + 3 X[27487], X[4432] - 3 X[41310], 5 X[4473] + 3 X[4645], 3 X[17264] + X[24715], 3 X[17297] + X[49712], 5 X[31252] - X[32922]

X(49769) lies on these lines: {1, 2}, {12, 43040}, {76, 4125}, {121, 20532}, {141, 4407}, {190, 24692}, {238, 28512}, {334, 4013}, {344, 4660}, {514, 3837}, {516, 36716}, {536, 25351}, {537, 3834}, {726, 1086}, {740, 3823}, {742, 3842}, {752, 4422}, {984, 17227}, {1089, 20432}, {1738, 6541}, {2325, 2796}, {3662, 49520}, {3717, 49676}, {3773, 3826}, {3814, 20486}, {3817, 36653}, {3821, 4078}, {3822, 46180}, {3952, 31029}, {3971, 25957}, {3993, 4429}, {4009, 4892}, {4080, 4937}, {4085, 17243}, {4090, 18134}, {4135, 17889}, {4297, 36699}, {4358, 21026}, {4432, 28562}, {4473, 4645}, {4684, 49697}, {4709, 17233}, {4732, 17229}, {4753, 17374}, {4851, 49685}, {4966, 49693}, {4997, 27759}, {5743, 48651}, {5846, 31289}, {6376, 20924}, {6687, 28538}, {9956, 29331}, {17231, 49457}, {17232, 49448}, {17234, 33165}, {17240, 49459}, {17241, 49490}, {17263, 33076}, {17264, 24715}, {17267, 32941}, {17279, 49482}, {17281, 24693}, {17282, 49455}, {17297, 49712}, {17311, 49497}, {17356, 49472}, {17789, 46937}, {18483, 36727}, {19925, 36663}, {24165, 25961}, {24193, 24196}, {24988, 32848}, {26083, 43997}, {26446, 28909}, {26738, 32931}, {28503, 40480}, {28595, 44307}, {31252, 32922}, {31673, 36732}, {33087, 49510}, {33159, 33682}, {35127, 35134}, {48629, 49517}

X(49769) = midpoint of X(i) and X(j) for these {i,j}: {10, 3912}, {190, 24692}, {1086, 4439}, {1738, 6541}, {3717, 49676}, {3836, 3932}, {4684, 49697}, {4753, 17374}, {4966, 49693}
X(49769) = reflection of X(i) in X(j) for these {i,j}: {3008, 3634}, {4759, 4422}
X(49769) = crossdifference of every pair of points on line {649, 21793}
X(49769) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 551, 29659}, {10, 25352, 3828}, {10, 49560, 3626}, {190, 31151, 24692}, {1086, 3932, 4439}, {3836, 4439, 1086}, {4358, 21026, 21241}, {17234, 33165, 49479}, {17244, 29659, 551}, {19875, 29593, 10}, {25961, 32862, 24165}, {29679, 29854, 43223}


X(49770) = X(1)X(2)∩X(6)X(4431)

Barycentrics    4*a^2 + a*b - b^2 + a*c - 4*b*c - c^2 : :
X(49770) = 3 X[2] - 5 X[239], 9 X[2] - 10 X[3008], 6 X[2] - 5 X[3912], 9 X[2] - 5 X[6542], 27 X[2] - 25 X[17266], 7 X[2] - 5 X[17310], 3 X[2] + 5 X[20016], 21 X[2] - 25 X[29590], 33 X[2] - 35 X[29607], X[2] - 5 X[40891], 4 X[2] - 5 X[41140], 11 X[2] - 10 X[41141], 3 X[239] - 2 X[3008], 3 X[239] - X[6542], 9 X[239] - 5 X[17266], 7 X[239] - 3 X[17310], 7 X[239] - 5 X[29590], 11 X[239] - 7 X[29607], X[239] - 3 X[40891], 4 X[239] - 3 X[41140], 11 X[239] - 6 X[41141], 4 X[3008] - 3 X[3912], 6 X[3008] - 5 X[17266], 14 X[3008] - 9 X[17310], 2 X[3008] + 3 X[20016], 14 X[3008] - 15 X[29590], 22 X[3008] - 21 X[29607], 2 X[3008] - 9 X[40891], 8 X[3008] - 9 X[41140], 11 X[3008] - 9 X[41141], 3 X[3912] - 2 X[6542], 9 X[3912] - 10 X[17266], 7 X[3912] - 6 X[17310], X[3912] + 2 X[20016], 7 X[3912] - 10 X[29590], 11 X[3912] - 14 X[29607], X[3912] - 6 X[40891], 2 X[3912] - 3 X[41140], 11 X[3912] - 12 X[41141], 3 X[6542] - 5 X[17266], 7 X[6542] - 9 X[17310], X[6542] + 3 X[20016], 7 X[6542] - 15 X[29590], 11 X[6542] - 21 X[29607], X[6542] - 9 X[40891], 4 X[6542] - 9 X[41140], 11 X[6542] - 18 X[41141], 35 X[17266] - 27 X[17310], 5 X[17266] + 9 X[20016], 7 X[17266] - 9 X[29590], 55 X[17266] - 63 X[29607], 5 X[17266] - 27 X[40891], 20 X[17266] - 27 X[41140], 55 X[17266] - 54 X[41141], 3 X[17310] + 7 X[20016], 3 X[17310] - 5 X[29590], 33 X[17310] - 49 X[29607], X[17310] - 7 X[40891], 4 X[17310] - 7 X[41140], 11 X[17310] - 14 X[41141], 7 X[20016] + 5 X[29590], 11 X[20016] + 7 X[29607], X[20016] + 3 X[40891], 4 X[20016] + 3 X[41140], 11 X[20016] + 6 X[41141], 55 X[29590] - 49 X[29607], 5 X[29590] - 21 X[40891], 20 X[29590] - 21 X[41140], 55 X[29590] - 42 X[41141], 7 X[29607] - 33 X[40891], 28 X[29607] - 33 X[41140], 7 X[29607] - 6 X[41141], 4 X[40891] - X[41140], 11 X[40891] - 2 X[41141], 11 X[41140] - 8 X[41141], X[4480] - 4 X[4969], 3 X[4716] - X[24715], 4 X[17067] - 3 X[17297]

X(49770) lies on these lines: {1, 2}, {6, 4431}, {37, 4464}, {44, 4971}, {75, 4667}, {142, 17377}, {190, 4700}, {193, 17151}, {319, 3946}, {391, 4460}, {514, 4380}, {524, 1266}, {527, 17160}, {536, 4480}, {550, 29331}, {742, 3629}, {894, 4856}, {1086, 4725}, {1100, 4399}, {1323, 25726}, {1449, 42696}, {1654, 4021}, {1738, 17772}, {1992, 4659}, {2321, 3759}, {3618, 4007}, {3663, 4741}, {3664, 17117}, {3686, 4360}, {3707, 4664}, {3875, 4416}, {3879, 4361}, {3883, 49486}, {3943, 28329}, {3950, 17349}, {3982, 7247}, {4029, 17335}, {4031, 43040}, {4034, 17321}, {4044, 17144}, {4058, 17368}, {4060, 17289}, {4072, 17339}, {4133, 16468}, {4357, 4690}, {4371, 10436}, {4395, 17374}, {4402, 17298}, {4405, 4688}, {4422, 4727}, {4478, 17384}, {4545, 32025}, {4665, 16666}, {4709, 31317}, {4716, 5847}, {4726, 7277}, {4732, 31306}, {4862, 20080}, {4889, 17245}, {4910, 16777}, {4982, 46922}, {5228, 25719}, {5257, 17393}, {5288, 21511}, {5564, 5750}, {5850, 41845}, {6381, 25298}, {6666, 17315}, {6996, 28234}, {6999, 28236}, {7227, 16668}, {7377, 47745}, {7406, 11531}, {9436, 43066}, {11278, 36728}, {14621, 49685}, {16200, 36662}, {16367, 25439}, {16884, 28634}, {17067, 17297}, {17121, 17355}, {17132, 20072}, {17269, 17299}, {17304, 32099}, {17314, 25101}, {17348, 17388}, {17366, 17372}, {17373, 21255}, {17755, 28581}, {20172, 49497}, {21495, 48696}, {21874, 22034}, {24133, 33920}, {27478, 49490}, {27480, 49448}, {27484, 30331}, {28522, 33888}, {36867, 37075}, {36920, 43053}, {40459, 47991}, {49459, 49684}

X(49770) = midpoint of X(239) and X(20016)
X(49770) = reflection of X(i) in X(j) for these {i,j}: {190, 4700}, {3912, 239}, {4727, 4422}, {6542, 3008}, {17374, 4395}
X(49770) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20050, 29605}, {2, 29605, 29601}, {2, 29619, 29606}, {8, 16834, 17023}, {8, 17014, 17308}, {10, 49543, 4393}, {145, 4384, 29574}, {239, 3912, 41140}, {239, 6542, 3008}, {239, 17310, 29590}, {1100, 4399, 4967}, {3008, 6542, 3912}, {3621, 5222, 17294}, {3633, 16833, 17316}, {3875, 5839, 4416}, {3879, 4361, 24199}, {4393, 29617, 10}, {4690, 4852, 17395}, {4690, 17395, 4357}, {4701, 29604, 29615}, {4852, 17362, 4357}, {5222, 17294, 29596}, {16816, 17389, 29571}, {16834, 17308, 17014}, {17014, 17308, 17023}, {17362, 17395, 4690}, {17367, 20055, 29594}, {20016, 40891, 239}


X(49771) = X(1)X(2)∩X(44)X(9041)

Barycentrics    4*a^3 - 3*a^2*b + 4*a*b^2 - b^3 - 3*a^2*c - 2*a*b*c - b^2*c + 4*a*c^2 - b*c^2 - c^3 : :
X(49771) = 3 X[1] - X[32847], 5 X[3617] - 7 X[29607], X[3621] - 5 X[29590], 7 X[3622] - 5 X[17266], 5 X[3623] - X[6542], 3 X[3912] - 2 X[32847], 3 X[38314] - 2 X[41141], X[4440] + 3 X[49704], X[1266] + 2 X[49699], X[4480] - 4 X[49700], 3 X[1279] - 2 X[4422], 3 X[3717] - 4 X[4422], 3 X[4684] - 2 X[17374], 3 X[4864] - X[17374], 3 X[24231] - 2 X[24692], 5 X[27191] - 3 X[32850]

X(49771) lies on these lines: {1, 2}, {44, 9041}, {63, 30614}, {192, 30331}, {238, 4899}, {344, 35227}, {390, 49446}, {514, 47692}, {516, 4440}, {518, 3271}, {527, 24841}, {528, 1266}, {537, 4480}, {726, 49696}, {740, 49691}, {742, 49478}, {1001, 49527}, {1120, 1438}, {1279, 3717}, {1317, 39775}, {1483, 29331}, {1738, 17765}, {1930, 3902}, {2099, 3674}, {2325, 16786}, {3242, 3883}, {3476, 7195}, {3879, 42871}, {3950, 16779}, {4078, 49534}, {4297, 17480}, {4344, 4747}, {4357, 49465}, {4416, 16496}, {4431, 32941}, {4434, 24216}, {4464, 49475}, {4513, 16502}, {4684, 4864}, {4702, 28503}, {4720, 33953}, {4851, 49679}, {4929, 27549}, {4952, 37679}, {5847, 49675}, {5853, 32922}, {7976, 46180}, {7991, 11851}, {16468, 49536}, {16487, 26685}, {17279, 49690}, {17353, 49688}, {17721, 30824}, {17724, 30823}, {17766, 24231}, {20924, 39731}, {24199, 24693}, {24709, 32927}, {24715, 49708}, {27191, 32850}, {49490, 49496}, {49506, 49511}

X(49771) = midpoint of X(i) and X(j) for these {i,j}: {145, 239}, {24715, 49708}, {24841, 49709}, {32922, 49695}
X(49771) = reflection of X(i) in X(j) for these {i,j}: {8, 3008}, {3717, 1279}, {3912, 1}, {4684, 4864}, {4899, 238}
X(49771) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 145, 49476}, {1, 29598, 38314}, {1, 29633, 3636}, {1, 29659, 551}, {1, 36479, 17023}, {145, 39567, 8}, {17023, 49466, 36479}, {17316, 24599, 17284}, {42871, 49681, 3879}


X(49772) = X(1)X(2)∩X(44)X(528)

Barycentrics    3*a^2*b - 2*a*b^2 + b^3 + 3*a^2*c - 2*a*b*c - b^2*c - 2*a*c^2 - b*c^2 + c^3 : :
X(49772) = X[145] - 5 X[29590], 5 X[3616] - 7 X[29607], 5 X[3617] - X[6542], 3 X[3679] - X[32847], 7 X[4678] + X[20016], 7 X[9780] - 5 X[17266], 3 X[19875] - 2 X[41141], 2 X[1086] - 3 X[1738], 4 X[1086] - 3 X[24231], X[1266] + 2 X[49701], 3 X[3717] - 2 X[4439], X[4439] - 3 X[49693], 3 X[3685] - 5 X[4473], 2 X[4395] + X[49702], X[24841] - 3 X[37756], 3 X[37756] + X[49714]

X(49772) lies on these lines: {1, 2}, {44, 528}, {75, 49529}, {76, 4737}, {80, 294}, {142, 49490}, {190, 28580}, {192, 4780}, {210, 24210}, {218, 3419}, {226, 32865}, {238, 3939}, {241, 40663}, {484, 7291}, {514, 1734}, {515, 9441}, {516, 1757}, {517, 20683}, {518, 1086}, {527, 24715}, {537, 1266}, {666, 28849}, {726, 4899}, {740, 3717}, {742, 3696}, {752, 4753}, {908, 21805}, {984, 3755}, {1145, 6184}, {1211, 4113}, {1212, 20691}, {1500, 16601}, {1707, 17784}, {1711, 20588}, {1834, 4662}, {2082, 3730}, {2321, 33165}, {2325, 4693}, {2550, 3751}, {2796, 4480}, {2886, 4849}, {3035, 31201}, {3036, 6603}, {3175, 4126}, {3212, 10481}, {3452, 33141}, {3501, 16572}, {3555, 24178}, {3662, 49505}, {3663, 49448}, {3681, 3914}, {3685, 4473}, {3686, 33076}, {3689, 35466}, {3711, 17720}, {3758, 49720}, {3759, 49684}, {3790, 4133}, {3821, 49510}, {3823, 4966}, {3826, 49478}, {3836, 4684}, {3879, 49497}, {3932, 28581}, {3944, 21060}, {3948, 4723}, {3950, 49469}, {3973, 5838}, {3996, 33118}, {4000, 16496}, {4001, 32948}, {4026, 4708}, {4078, 49470}, {4085, 4357}, {4104, 32773}, {4119, 4771}, {4356, 38210}, {4361, 49688}, {4363, 47359}, {4383, 4863}, {4395, 9041}, {4398, 49501}, {4416, 4660}, {4422, 4702}, {4429, 17227}, {4431, 4709}, {4641, 34612}, {4643, 48829}, {4645, 34379}, {4661, 33131}, {4670, 49725}, {4674, 6549}, {4692, 20888}, {4714, 20893}, {4732, 4967}, {4738, 6381}, {4743, 49456}, {4792, 46790}, {4848, 43040}, {4851, 49680}, {4924, 5542}, {4956, 30578}, {4969, 28538}, {4974, 17765}, {5223, 24248}, {5228, 5252}, {5294, 32945}, {5316, 24217}, {5690, 29331}, {5718, 21870}, {5723, 36920}, {5773, 21578}, {5844, 15251}, {5847, 32850}, {5850, 32857}, {6376, 17158}, {6666, 16484}, {9053, 49694}, {9778, 16570}, {9803, 18461}, {12782, 46180}, {13161, 34790}, {15485, 30331}, {16610, 24216}, {16676, 38097}, {17051, 31197}, {17064, 25568}, {17132, 24821}, {17237, 48821}, {17243, 49475}, {17278, 42871}, {17279, 49460}, {17290, 47358}, {17335, 49746}, {17337, 42819}, {17340, 49485}, {17353, 32941}, {17366, 49465}, {17757, 20544}, {17781, 33094}, {21868, 40133}, {24199, 49479}, {24349, 49536}, {24391, 24440}, {24789, 41711}, {24841, 37756}, {26738, 33108}, {28562, 49710}, {28603, 33922}, {28909, 38155}, {32921, 49527}, {32922, 49698}, {33087, 49689}, {33110, 41011}, {33149, 49503}, {35115, 35134}, {35127, 35131}, {36205, 41687}, {49521, 49526}

X(49772) = midpoint of X(i) and X(j) for these {i,j}: {8, 239}, {24715, 49712}, {24841, 49714}, {32922, 49698}
X(49772) = reflection of X(i) in X(j) for these {i,j}: {1, 3008}, {3717, 49693}, {3912, 10}, {4684, 3836}, {4693, 2325}, {4702, 4422}, {4899, 49697}, {4966, 3823}, {24231, 1738}
X(49772) = crossdifference of every pair of points on line {649, 2280}
X(49772) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 551, 25352}, {10, 3625, 49560}, {10, 39580, 9780}, {10, 48853, 29576}, {43, 4847, 24239}, {145, 16020, 1}, {899, 26015, 5121}, {1737, 31855, 38471}, {3661, 5222, 29571}, {3679, 29659, 10}, {3755, 24393, 984}, {3935, 33139, 3011}, {4085, 49457, 4357}, {4429, 49450, 49511}, {4685, 29673, 3687}, {4924, 5542, 49498}, {5524, 33140, 6745}, {17014, 48856, 1}, {17367, 36534, 551}, {20012, 29641, 4028}, {21805, 33136, 908}, {33165, 49459, 2321}, {37756, 49714, 24841}


X(49773) = X(1)X(2)∩X(169)X(30701)

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

X(49773) lies on these lines: {1, 2}, {169, 30701}, {514, 15416}, {515, 4482}, {517, 4437}, {668, 5179}, {1565, 40883}, {2321, 33936}, {2809, 3717}, {3933, 4515}, {4103, 5074}, {4119, 21232}, {17671, 44720}, {20642, 21587}, {20928, 44723}, {30730, 33864}


X(49774) = X(1)X(2)∩X(75)X(46180)

Barycentrics    a^2*b^2 - a*b^3 - 2*a^2*b*c + 2*a*b^2*c - b^3*c + a^2*c^2 + 2*a*b*c^2 - a*c^3 - b*c^3 : :
X(49774) = X(49774) = 2 X[20893] + X[41773]

X(49774) lies on these lines: {1, 2}, {75, 46180}, {76, 20257}, {304, 4051}, {514, 4374}, {517, 17755}, {538, 1266}, {668, 20335}, {730, 1738}, {956, 24586}, {1107, 25349}, {1573, 4357}, {1909, 17050}, {2170, 3263}, {2176, 24735}, {3691, 17152}, {3717, 14839}, {3735, 49521}, {3753, 24631}, {3836, 44359}, {4659, 48869}, {5288, 29473}, {6381, 17761}, {6547, 20549}, {9055, 21331}, {9296, 40875}, {9369, 27000}, {9436, 43059}, {10009, 20924}, {14213, 20432}, {17144, 21071}, {17448, 20255}, {17760, 33937}, {20491, 45213}, {21226, 24214}, {21281, 21384}, {21332, 24326}, {23579, 26825}, {24190, 24215}, {24231, 44353}, {33821, 37588}

X(49774) = complement of X(10027)
X(49774) = midpoint of X(20924) and X(35957)
X(49774) = reflection of X(i) in X(j) for these {i,j}: {3912, 30109}, {40859, 3008}
X(49774) = crossdifference of every pair of points on line {649, 2209}
X(49774) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 30030, 29968}, {8, 30036, 29960}, {10, 30038, 29991}, {145, 30057, 29966}, {239, 27321, 3008}, {239, 30059, 3912}, {6542, 29988, 3912}


X(49775) = X(6)X(3879)∩X(239)X(2345)

Barycentrics    2*a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3 + b^4 - 3*a^3*c - 2*a^2*b*c - a*b^2*c + 3*a^2*c^2 - a*b*c^2 + 2*b^2*c^2 - a*c^3 + c^4 : :
X(49775) = X[69] - 5 X[17266], X[239] - 5 X[3618], X[4437] - 3 X[41310], 3 X[16475] + X[32847], 3 X[17264] + X[32029], 3 X[27487] + X[49496], X[41140] - 3 X[47352]

X(49775) lies on these lines: {2, 36404}, {6, 3879}, {69, 17266}, {141, 6666}, {182, 12618}, {239, 2345}, {344, 16973}, {518, 4422}, {519, 597}, {524, 41141}, {742, 3008}, {2325, 9055}, {3242, 41313}, {3834, 5845}, {3844, 49731}, {4363, 38186}, {4437, 41310}, {16475, 32847}, {17023, 24357}, {17251, 38088}, {17264, 32029}, {17265, 47595}, {17269, 49688}, {17352, 27487}, {17355, 49481}, {18583, 29331}, {20530, 40869}, {24256, 46180}, {25101, 49509}, {41140, 47352}

X(49775) = midpoint of X(6) and X(3912)
X(49775) = reflection of X(3008) in X(3589)


X(49776) = X(6)X(3879)∩X(239)X(4648)

Barycentrics    2*a^4 - a^3*b - a^2*b^2 + 3*a*b^3 - b^4 - a^3*c - 6*a^2*b*c + a*b^2*c + 2*b^3*c - a^2*c^2 + a*b*c^2 - 2*b^2*c^2 + 3*a*c^3 + 2*b*c^3 - c^4 : :
X(49776) = X[239] - 5 X[17391], 5 X[17266] - X[17363], X[17377] + 3 X[27487]

X(49776) lies on these lines: {6, 3879}, {239, 4648}, {519, 3696}, {599, 3883}, {742, 17390}, {1086, 4864}, {1100, 3008}, {1279, 4966}, {3686, 17231}, {3945, 6542}, {4675, 42871}, {17266, 17363}, {17377, 27487}, {28350, 30059}

X(49776) = midpoint of X(3879) and X(3912)


X(49777) = X(2)X(21332)∩X(239)X(940)

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

X(49777) lies on these lines: {2, 21332}, {37, 46180}, {44, 35102}, {75, 10027}, {85, 2176}, {115, 5074}, {230, 17044}, {239, 940}, {514, 6586}, {517, 1086}, {519, 3696}, {672, 7200}, {742, 20924}, {1111, 3230}, {1149, 27918}, {1214, 43040}, {1279, 28850}, {1441, 28350}, {1447, 9259}, {1575, 21232}, {1914, 9317}, {1920, 25111}, {1921, 25129}, {2238, 30806}, {3008, 6692}, {3212, 20271}, {3290, 21138}, {3673, 16969}, {3727, 26978}, {3912, 17056}, {4713, 20925}, {5088, 17735}, {7176, 33863}, {7278, 20963}, {9312, 16968}, {16827, 20955}, {17752, 33943}, {20930, 27623}, {24281, 29331}, {27020, 41805}, {29365, 40091}, {35075, 35080}, {35110, 35119}, {41240, 41875}

X(49777) = midpoint of X(i) and X(j) for these {i,j}: {75, 10027}, {20924, 40859}
X(49777) = crossdifference of every pair of points on line {4507, 8053}
X(49777) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3290, 43037, 21138}, {20925, 35274, 4713}


X(49778) = X(6)X(519)∩X(80)X(4876)

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

X(49778) lies on these lines: {6, 519}, {80, 4876}, {115, 3936}, {239, 32779}, {952, 3943}, {966, 16086}, {3735, 4660}, {3912, 17720}, {4144, 4867}, {4671, 6542}, {17244, 24262}, {17300, 20234}, {17386, 20444}, {17398, 30117}, {23972, 35122}, {29331, 32431}

X(49778) = midpoint of X(6542) and X(30225)
X(49778) = reflection of X(i) in X(j) for these {i,j}: {239, 36230}, {24281, 3912}


X(49779) = X(1)X(20955)∩X(75)X(519)

Barycentrics    b*c*(-3*a^2 + a*b + b^2 + a*c - b*c + c^2) : :
X(49779) = 3 X[75] - 4 X[20893], 2 X[20893] - 3 X[20924], 3 X[3912] - X[41773]

X(49779) lies on these lines: {1, 20955}, {8, 33943}, {10, 41875}, {75, 519}, {85, 2099}, {145, 33930}, {190, 35102}, {239, 940}, {274, 4714}, {298, 7026}, {299, 7043}, {304, 4737}, {312, 17310}, {319, 16086}, {320, 517}, {321, 1909}, {335, 35101}, {350, 4742}, {514, 4079}, {668, 3992}, {742, 10027}, {1168, 4555}, {1966, 6631}, {3061, 3452}, {3244, 33940}, {3263, 4487}, {3293, 41805}, {3632, 33933}, {3930, 33946}, {3938, 40038}, {4125, 33939}, {4359, 40891}, {4479, 20925}, {4642, 33947}, {4674, 17179}, {4851, 17788}, {4868, 16712}, {4975, 18145}, {5525, 33951}, {7187, 20691}, {7200, 17759}, {8682, 36226}, {9260, 20906}, {9460, 20568}, {10026, 21604}, {17143, 20894}, {17386, 20444}, {17394, 30117}, {20911, 25303}, {20930, 29331}, {20934, 33093}, {21232, 37686}, {21272, 30941}, {21606, 33920}, {27739, 30829}, {30109, 35957}, {33677, 37788}, {35511, 42713}

X(49779) = reflection of X(i) in X(j) for these {i,j}: {75, 20924}, {35957, 30109}, {40859, 36226}
X(49779) = X(18359)-Ceva conjugate of X(75)
X(49779) = X(320)-Dao conjugate of X(3218)
X(49779) = barycentric product X(i)*X(j) for these {i,j}: {75, 20072}, {668, 45674}, {1969, 23166}
X(49779) = barycentric quotient X(i)/X(j) for these {i,j}: {20072, 1}, {23166, 48}, {45674, 513}
X(49779) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 20955, 33944}, {304, 24524, 33938}, {350, 30806, 18159}, {668, 14210, 20947}, {16284, 18156, 6376}


X(49780) = X(75)X(519)∩X(239)X(14996)

Barycentrics    b*c*(-4*a^2 + a*b + 2*b^2 + a*c - 2*b*c + 2*c^2) : :
X(49780) = 2 X[75] - 3 X[20893], X[75] - 3 X[20924], 3 X[27487] - X[35957]

X(49780) lies on these lines: {75, 519}, {239, 14996}, {350, 20568}, {514, 661}, {536, 4403}, {551, 33934}, {742, 36226}, {1125, 20955}, {3244, 33930}, {3263, 4738}, {3625, 33933}, {3626, 33943}, {3634, 41875}, {3635, 33940}, {3636, 33944}, {3761, 4671}, {3902, 20894}, {4357, 42285}, {4495, 4555}, {4510, 4693}, {7278, 20911}, {16086, 32099}, {16284, 33942}, {17274, 17461}, {21605, 33937}, {24589, 41140}, {27487, 35957}, {29982, 41773}, {30829, 41141}

X(49780) = reflection of X(20893) in X(20924)
X(49780) = X(i)-isoconjugate of X(j) for these (i,j): {6, 28317}, {32, 35170}
X(49780) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 28317), (6376, 35170), (35124, 1)
X(49780) = barycentric product X(i)*X(j) for these {i,j}: {75, 4715}, {1978, 14422}
X(49780) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 28317}, {75, 35170}, {4715, 1}, {14422, 649}
X(49780) = {X(14210),X(30806)}-harmonic conjugate of X(6381)


X(49781) = X(6)X(519)∩X(76)X(85)

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

X(49781) lies on these lines: {6, 519}, {9, 16086}, {76, 85}, {115, 35123}, {142, 20893}, {239, 5294}, {344, 24249}, {345, 24266}, {346, 24247}, {514, 48031}, {515, 2325}, {730, 6541}, {3663, 4045}, {3693, 21859}, {3932, 28850}, {3954, 22026}, {4070, 5440}, {4109, 5741}, {4119, 43065}, {4136, 25066}, {4437, 35102}, {5750, 30117}, {6542, 26223}, {7739, 49455}, {17280, 24291}, {17310, 17778}, {17776, 24268}, {17790, 30109}, {23980, 35122}, {24169, 46902}, {24255, 29653}


X(49782) = X(6)X(519)∩X(37)X(48843)

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

X(49782) lies on these lines: {6, 519}, {37, 48843}, {116, 40883}, {321, 1930}, {346, 16086}, {514, 15416}, {2161, 2325}, {2345, 30117}, {3008, 32777}, {3772, 21096}, {4103, 5179}, {4119, 24036}, {4153, 4417}, {4169, 6735}, {4568, 5074}, {17233, 20924}, {21024, 22425}, {21069, 46738}


X(49783) = X(6)X(3879)∩X(7)X(193)

Barycentrics    4*a^4 - 3*a^3*b + 3*a^2*b^2 + a*b^3 - b^4 - 3*a^3*c - 4*a^2*b*c + a*b^2*c + 3*a^2*c^2 + a*b*c^2 - 2*b^2*c^2 + a*c^3 - c^4 : :
X(49783) = 5 X[3620] - 7 X[29607], 3 X[5032] - X[17310], X[20080] - 5 X[29590]

X(49783) lies on these lines: {6, 3879}, {7, 193}, {69, 3008}, {190, 49695}, {518, 3271}, {519, 1992}, {524, 31138}, {527, 32029}, {742, 3629}, {1266, 5845}, {1353, 29331}, {3570, 5121}, {3620, 29607}, {3758, 49529}, {4416, 16973}, {4480, 9055}, {5032, 17310}, {5847, 32850}, {9025, 20455}, {17346, 49511}, {20080, 29590}, {29574, 36404}, {32451, 46180}

X(49783) = midpoint of X(193) and X(239)
X(49783) = reflection of X(i) in X(j) for these {i,j}: {69, 3008}, {3912, 6}


X(49784) = EXTERNAL PAVLOV-MOSES POINT

Barycentrics    2*(a^2 + 3*b^2 + 3*c^2 - (1 + Sqrt[5])*(b^2 + c^2))*S + Sqrt[7 - 2*(1 + Sqrt[5])]*((-1 + Sqrt[5])*a^2*(a^2 - b^2 - c^2) + 4*S^2) : :
X(49784) = 3*X[2] - (3 + Sqrt[5])*X[5402]

See X(3381), X(5401), and X(49785).

X(49784) lies on the cubic K906 and these lines: {2, 3380}, {1352, 49785}


X(49785) = INTERNAL PAVLOV-MOSES POINT

Barycentrics    2*(a^2 + 3*b^2 + 3*c^2 - (1 + Sqrt[5])*(b^2 + c^2))*S - Sqrt[7 - 2*(1 + Sqrt[5])]*((-1 + Sqrt[5])*a^2*(a^2 - b^2 - c^2) + 4*S^2) : :
X(49785) = 3*X[2] - (3 + Sqrt[5])*X[3382]

See X(3381), X(5401), and X(49784).

X(49785) lies on the cubic K906 and these lines: {2, 3382}, {1352, 49784}


X(49786) = X(2)X(1327)∩X(6)X(13769)

Barycentrics    3*(4*a^4 - 5*a^2*b^2 + b^4 - 5*a^2*c^2 - 2*b^2*c^2 + c^4) - 2*(a^2 + 4*b^2 + 4*c^2)*S : :
X(49786) = 4 X[2] - X[1327], 5 X[2] + X[13678], X[2] + 2 X[13701], 2 X[2] + X[13712], 7 X[2] - X[33456], 5 X[1327] + 4 X[13678], X[1327] + 8 X[13701], X[1327] + 2 X[13712], 7 X[1327] - 4 X[33456], X[13669] + 2 X[13684], X[13678] - 10 X[13701], 2 X[13678] - 5 X[13712], 7 X[13678] + 5 X[33456], X[13681] + 2 X[13700], 4 X[13701] - X[13712], 14 X[13701] + X[33456], 7 X[13712] + 2 X[33456], 2 X[33470] + X[36380], 2 X[33471] + X[36376], X[376] + 2 X[48778], 2 X[381] + X[13666], 2 X[549] + X[13692], 2 X[551] + X[13688], 10 X[641] - X[12322], 8 X[641] + X[42260], 4 X[12322] + 5 X[42260], X[3534] + 2 X[22806], 2 X[3679] + X[13702], 5 X[5071] - 2 X[13687], 2 X[8703] + X[49361], 2 X[11049] + X[13689], 16 X[11812] - X[13690], 8 X[12100] + X[13691], X[13674] - 7 X[15702], X[13679] - 7 X[19876], X[13713] - 7 X[15703], 5 X[15693] + X[48677], 5 X[15694] - 2 X[49114], 10 X[15713] - X[49362], 11 X[15721] - 2 X[48780]

X(49786) lies on the cubic K906 and these lines: {2, 1327}, {6, 13769}, {376, 48778}, {381, 13666}, {486, 7618}, {524, 19145}, {549, 1352}, {551, 13688}, {590, 13662}, {641, 11147}, {3534, 22806}, {3679, 13702}, {4995, 13696}, {5071, 13687}, {5298, 13695}, {5418, 33364}, {7585, 13720}, {8703, 49361}, {11049, 13689}, {11812, 13690}, {12100, 13691}, {13651, 13846}, {13674, 15702}, {13679, 19876}, {13713, 15703}, {13831, 32786}, {13847, 19099}, {15533, 35255}, {15693, 48677}, {15694, 49114}, {15713, 49362}, {15721, 48780}, {26361, 26615}, {26619, 42603}, {41895, 43559}

X(49786) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13701, 13712}, {2, 13712, 1327}, {13704, 13706, 2}


X(49787) = X(2)X(1328)∩X(6)X(13833)

Barycentrics    3*(4*a^4 - 5*a^2*b^2 + b^4 - 5*a^2*c^2 - 2*b^2*c^2 + c^4) + 2*(a^2 + 4*b^2 + 4*c^2)*S : :
X(49787) = 4 X[2] - X[1328], 5 X[2] + X[13798], X[2] + 2 X[13821], 2 X[2] + X[13835], 7 X[2] - X[33457], 5 X[1328] + 4 X[13798], X[1328] + 8 X[13821], X[1328] + 2 X[13835], 7 X[1328] - 4 X[33457], X[13789] + 2 X[13804], X[13798] - 10 X[13821], 2 X[13798] - 5 X[13835], 7 X[13798] + 5 X[33457], X[13801] + 2 X[13820], 4 X[13821] - X[13835], 14 X[13821] + X[33457], 7 X[13835] + 2 X[33457], 2 X[33472] + X[36381], 2 X[33473] + X[36377], X[376] + 2 X[48779], 2 X[381] + X[13786], 2 X[549] + X[13812], 2 X[551] + X[13808], 10 X[642] - X[12323], 8 X[642] + X[42261], 4 X[12323] + 5 X[42261], X[3534] + 2 X[22807], 2 X[3679] + X[13822], 5 X[5071] - 2 X[13807], 2 X[8703] + X[49364], 2 X[11049] + X[13809], 16 X[11812] - X[13811], 8 X[12100] + X[13810], X[13794] - 7 X[15702], X[13799] - 7 X[19876], X[13836] - 7 X[15703], 5 X[15693] + X[48678], 5 X[15694] - 2 X[49115], 10 X[15713] - X[49363], 11 X[15721] - 2 X[48781]

X(49787) lies on the cubic K906 and these lines: {2, 1328}, {6, 13833}, {376, 48779}, {381, 13786}, {485, 7618}, {524, 19146}, {549, 1352}, {551, 13808}, {615, 13782}, {642, 11147}, {3534, 22807}, {3679, 13822}, {4995, 13816}, {5071, 13807}, {5298, 13815}, {5420, 33365}, {7586, 13843}, {8703, 49364}, {11049, 13809}, {11812, 13811}, {12100, 13810}, {13770, 13847}, {13794, 15702}, {13799, 19876}, {13832, 32785}, {13836, 15703}, {13846, 19100}, {15533, 35256}, {15693, 48678}, {15694, 49115}, {15713, 49363}, {15721, 48781}, {26362, 26616}, {26620, 42602}, {41895, 43558}

X(49787) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13821, 13835}, {2, 13835, 1328}, {13824, 13826, 2}


X(49788) = X(2)X(187)∩X(69)X(44773)

Barycentrics    8*a^8 - 19*a^6*b^2 + 24*a^4*b^4 - 7*a^2*b^6 - 4*b^8 - 19*a^6*c^2 + 27*a^4*b^2*c^2 + 27*a^2*b^4*c^2 - b^6*c^2 + 24*a^4*c^4 + 27*a^2*b^2*c^4 + 6*b^4*c^4 - 7*a^2*c^6 - b^2*c^6 - 4*c^8 : :
X(49788) = X[8182] - 4 X[15810], 8 X[40344] + X[44678]

X(49788) lies on the cubic K906 and these lines: {2, 187}, {69, 44773}, {524, 32447}, {574, 11161}, {1352, 7618}, {6054, 7622}, {7608, 7775}, {7615, 37242}, {7619, 43461}, {11178, 19911}, {34507, 34511}


X(49789) = X(2)X(4048)∩X(3)X(31982)

Barycentrics    a^10 + a^8*b^2 - a^6*b^4 - 2*a^4*b^6 + a^8*c^2 - 3*a^6*b^2*c^2 - 9*a^4*b^4*c^2 - 3*a^2*b^6*c^2 + b^8*c^2 - a^6*c^4 - 9*a^4*b^2*c^4 - 8*a^2*b^4*c^4 - 2*a^4*c^6 - 3*a^2*b^2*c^6 + b^2*c^8 : :

X(49789) lies on these lines: {2, 4048}, {3, 31982}, {83, 3094}, {182, 732}, {2076, 20088}, {3098, 18548}, {5149, 10007}, {6308, 26316}, {8178, 40108}, {10519, 35701}, {29012, 32190}
on K906

X(49789) = midpoint of X(3098) and X(18548)
X(49789) = reflection of X(8177) in X(8150)
X(49789) = {X(8290),X(24273)}-harmonic conjugate of X(4048)


X(49790) = X(2)X(7598)∩X(3)X(485)

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

X(49790) lies on the cubic K906 and these lines: {2, 7598}, {3, 485}, {20, 32499}, {140, 49221}, {182, 8997}, {371, 492}, {486, 11315}, {488, 7793}, {491, 6228}, {524, 19145}, {631, 3103}, {1151, 6289}, {1513, 9757}, {2459, 3068}, {3054, 9600}, {3094, 31958}, {3102, 16925}, {3564, 35255}, {5420, 6422}, {6118, 7389}, {6200, 6811}, {6250, 10576}, {6278, 9680}, {6337, 13877}, {6423, 19103}, {6449, 48660}, {6564, 35947}, {8960, 13924}, {8981, 12968}, {9646, 18988}, {9661, 13082}, {9681, 45024}, {9744, 45539}, {9987, 39647}, {12257, 33371}, {13637, 32421}, {13879, 35812}, {22625, 42258}, {22635, 35731}, {23311, 40288}, {31463, 39655}, {36656, 42260}, {45462, 45522}

X(49790) = reflection of X(i) in X(j) for these {i,j}: {485, 590}, {492, 641}
X(49790) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 13882, 485}, {485, 12124, 32495}, {11315, 15883, 486}, {32497, 49104, 485}, {35812, 35832, 13879}


X(49791) = X(2)X(7599)∩X(3)X(486)

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

X(49791) lies on the cubic K906 and these lines: {2, 7599}, {3, 486}, {20, 32498}, {140, 49220}, {182, 13989}, {372, 491}, {485, 11316}, {487, 7793}, {492, 6229}, {524, 19146}, {631, 3102}, {1152, 6290}, {1513, 9758}, {2460, 3069}, {3054, 13711}, {3094, 31958}, {3103, 16925}, {3564, 35256}, {5418, 6421}, {6119, 7388}, {6251, 10577}, {6337, 13930}, {6396, 6813}, {6424, 19104}, {6450, 48659}, {6565, 35946}, {8396, 9680}, {9744, 45538}, {9986, 39647}, {12256, 33370}, {12963, 13966}, {13757, 32419}, {13933, 35813}, {22596, 42259}, {23312, 40289}, {36655, 42261}, {45463, 45523}

X(49791) = reflection of X(i) in X(j) for these {i,j}: {486, 615}, {491, 642}
X(49791) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 13934, 486}, {486, 12123, 32492}, {11316, 15884, 485}, {32494, 49103, 486}, {35813, 35833, 13933}


X(49792) = X(2)X(694)∩X(3)X(698)

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

X(49792) lies on the cubic K906 and these lines: {2, 694}, {3, 698}, {69, 44771}, {194, 1691}, {511, 7759}, {538, 32429}, {732, 6776}, {3098, 39603}, {6393, 44453}, {18768, 46264}, {31670, 31982}, {32449, 40825}

X(49792) = midpoint of X(18768) and X(46264)
X(49792) = reflection of X(31981) in X(8177)


X(49793) = X(2)X(2782)∩X(3)X(31958)

Barycentrics    3*a^10*b^2 - 10*a^8*b^4 + 14*a^6*b^6 - 8*a^4*b^8 + a^2*b^10 + 3*a^10*c^2 - 19*a^8*b^2*c^2 + 22*a^6*b^4*c^2 + 8*a^4*b^6*c^2 - 7*a^2*b^8*c^2 - b^10*c^2 - 10*a^8*c^4 + 22*a^6*b^2*c^4 + 30*a^4*b^4*c^4 + 12*a^2*b^6*c^4 + 14*a^6*c^6 + 8*a^4*b^2*c^6 + 12*a^2*b^4*c^6 + 2*b^6*c^6 - 8*a^4*c^8 - 7*a^2*b^2*c^8 + a^2*c^10 - b^2*c^10 : :

X(49793) lies on the cubic K906 and these lines: {2, 2782}, {3, 31958}, {5, 8179}, {39, 11261}, {69, 44775}, {183, 32515}, {262, 316}, {524, 32447}, {3095, 3785}, {5024, 32519}, {6194, 35002}, {12054, 40923}, {13334, 32149}

leftri

Centers related to Fermat-Dao-Nhi triangles: X(49794)-X(49978)

rightri

This preamble and centers X(49794)-X(49978) were contributed by César Eliud Lozada, May 26, 2022.

Fermat-Dao-Nhi triangles were introduced in the preamble just before X(33602).


X(49794) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND ANTI-ARTZT

Barycentrics    sqrt(3)*(a^2+b^2+c^2)*(6*a^4+(b^2+c^2)*a^2-(b^2-3*c^2)*(3*b^2-c^2))-S*(31*a^4+18*(b^2+c^2)*a^2-5*b^4+18*b^2*c^2-5*c^4) : :

X(49794) lies on these lines: {5863, 12154}, {8593, 35749}, {11159, 49844}, {12155, 35690}, {33603, 40672}

X(49794) = perspector (anti-Artzt, 1st inner-Fermat-Dao-Nhi)


X(49795) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND ANTI-ARTZT

Barycentrics    sqrt(3)*(a^2+b^2+c^2)*(6*a^4+(b^2+c^2)*a^2-(b^2-3*c^2)*(3*b^2-c^2))+S*(31*a^4+18*(b^2+c^2)*a^2-5*b^4+18*b^2*c^2-5*c^4) : :

X(49795) lies on these lines: {5862, 12155}, {8593, 36327}, {11159, 49843}, {12154, 35694}, {33602, 40671}

X(49795) = perspector (anti-Artzt, 1st outer-Fermat-Dao-Nhi)


X(49796) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND 1st ANTI-BROCARD

Barycentrics    -6*sqrt(3)*(4*a^8-4*(b^2+c^2)*a^6-3*(b^4+c^4)*a^4+10*(b^6+c^6)*a^2-7*b^8-7*c^8+2*b^2*c^2*(7*b^4-12*b^2*c^2+7*c^4))*(a^2+b^2+c^2)*S+23*a^12-23*(b^2+c^2)*a^10+(76*b^4+81*b^2*c^2+76*c^4)*a^8-2*(b^2+c^2)*(85*b^4+27*b^2*c^2+85*c^4)*a^6+(211*b^8+211*c^8+2*b^2*c^2*(95*b^4+72*b^2*c^2+95*c^4))*a^4-(b^2+c^2)*(131*b^8+131*c^8-2*b^2*c^2*(133*b^4-227*b^2*c^2+133*c^4))*a^2+(b^2-c^2)^2*(14*b^8+14*c^8-(31*b^4-72*b^2*c^2+31*c^4)*b^2*c^2) : :

X(49796) lies on these lines: {5978, 36318}, {5979, 15682}, {7840, 35749}

X(49796) = perspector (1st anti-Brocard, 1st inner-Fermat-Dao-Nhi)


X(49797) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND 1st ANTI-BROCARD

Barycentrics    6*sqrt(3)*(4*a^8-4*(b^2+c^2)*a^6-3*(b^4+c^4)*a^4+10*(b^6+c^6)*a^2-7*b^8-7*c^8+2*b^2*c^2*(7*b^4-12*b^2*c^2+7*c^4))*(a^2+b^2+c^2)*S+23*a^12-23*(b^2+c^2)*a^10+(76*b^4+81*b^2*c^2+76*c^4)*a^8-2*(b^2+c^2)*(85*b^4+27*b^2*c^2+85*c^4)*a^6+(211*b^8+211*c^8+2*b^2*c^2*(95*b^4+72*b^2*c^2+95*c^4))*a^4-(b^2+c^2)*(131*b^8+131*c^8-2*b^2*c^2*(133*b^4-227*b^2*c^2+133*c^4))*a^2+(b^2-c^2)^2*(14*b^8+14*c^8-(31*b^4-72*b^2*c^2+31*c^4)*b^2*c^2) : :

X(49797) lies on these lines: {5978, 15682}, {5979, 36320}, {7840, 36327}

X(49797) = perspector (1st anti-Brocard, 1st outer-Fermat-Dao-Nhi)


X(49798) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND ANTI-MCCAY

Barycentrics    -2*(53*a^6-61*(b^2+c^2)*a^4+(47*b^4-18*b^2*c^2+47*c^4)*a^2-(b^2+c^2)*(19*b^4-30*b^2*c^2+19*c^4))*S+(37*a^8-68*(b^2+c^2)*a^6+2*(35*b^4+16*b^2*c^2+35*c^4)*a^4-4*(b^2+c^2)*(8*b^4-7*b^2*c^2+8*c^4)*a^2+b^8+2*(2*b^4-b^2*c^2+2*c^4)*b^2*c^2+c^8)*sqrt(3) : :

X(49798) lies on these lines: {5863, 8595}, {8594, 35690}, {9855, 35749}

X(49798) = perspector (anti-McCay, 1st inner-Fermat-Dao-Nhi)


X(49799) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND ANTI-MCCAY

Barycentrics    2*(53*a^6-61*(b^2+c^2)*a^4+(47*b^4-18*b^2*c^2+47*c^4)*a^2-(b^2+c^2)*(19*b^4-30*b^2*c^2+19*c^4))*S+(37*a^8-68*(b^2+c^2)*a^6+2*(35*b^4+16*b^2*c^2+35*c^4)*a^4-4*(b^2+c^2)*(8*b^4-7*b^2*c^2+8*c^4)*a^2+b^8+2*(2*b^4-b^2*c^2+2*c^4)*b^2*c^2+c^8)*sqrt(3) : :

X(49799) lies on these lines: {5862, 8594}, {8595, 35694}, {9855, 36327}

X(49799) = perspector (anti-McCay, 1st outer-Fermat-Dao-Nhi)


X(49800) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND ARTZT

Barycentrics    -12*sqrt(3)*(a^2+b^2+c^2)*(2*a^4+5*(b^2+c^2)*a^2-7*(b^2-c^2)^2)*S+23*a^8-144*(b^2+c^2)*a^6+2*(175*b^4+232*b^2*c^2+175*c^4)*a^4-16*(b^2+c^2)*(18*b^4-29*b^2*c^2+18*c^4)*a^2+(59*b^4-98*b^2*c^2+59*c^4)*(b^2-c^2)^2 : :

X(49800) lies on these lines: {381, 49850}, {3545, 49939}, {5066, 49801}, {5863, 9760}, {6054, 35749}, {6114, 33603}, {9749, 36318}, {9750, 15682}, {9762, 35690}, {41099, 49895}, {44219, 49849}

X(49800) = perspector (Artzt, 1st inner-Fermat-Dao-Nhi)


X(49801) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND ARTZT

Barycentrics    12*sqrt(3)*(a^2+b^2+c^2)*(2*a^4+5*(b^2+c^2)*a^2-7*(b^2-c^2)^2)*S+23*a^8-144*(b^2+c^2)*a^6+2*(175*b^4+232*b^2*c^2+175*c^4)*a^4-16*(b^2+c^2)*(18*b^4-29*b^2*c^2+18*c^4)*a^2+(59*b^4-98*b^2*c^2+59*c^4)*(b^2-c^2)^2 : :

X(49801) lies on these lines: {381, 49849}, {3545, 49940}, {5066, 49800}, {5862, 9762}, {6054, 36327}, {6115, 33602}, {9749, 15682}, {9750, 36320}, {9760, 35694}, {41099, 49896}

X(49801) = perspector (Artzt, 1st outer-Fermat-Dao-Nhi)


X(49802) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND 1st BROCARD

Barycentrics    -6*sqrt(3)*(a^2+b^2+c^2)*(4*a^4-4*(b^2+c^2)*a^2-7*b^4-7*c^4)*S+23*a^8+39*(b^2+c^2)*a^6-(25*b^4+13*b^2*c^2+25*c^4)*a^4-(b^2+c^2)*(51*b^4+160*b^2*c^2+51*c^4)*a^2+7*(2*b^4+7*b^2*c^2+2*c^4)*(b^2-c^2)^2 : :

X(49802) lies on these lines: {599, 35749}, {619, 49828}, {3642, 36318}, {3643, 15682}, {5071, 33410}, {19710, 49897}, {33624, 43228}

X(49802) = perspector (1st Brocard, 1st inner-Fermat-Dao-Nhi)


X(49803) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND 1st BROCARD

Barycentrics    6*sqrt(3)*(a^2+b^2+c^2)*(4*a^4-4*(b^2+c^2)*a^2-7*b^4-7*c^4)*S+23*a^8+39*(b^2+c^2)*a^6-(25*b^4+13*b^2*c^2+25*c^4)*a^4-(b^2+c^2)*(51*b^4+160*b^2*c^2+51*c^4)*a^2+7*(2*b^4+7*b^2*c^2+2*c^4)*(b^2-c^2)^2 : :

X(49803) lies on these lines: {599, 36327}, {618, 49829}, {3642, 15682}, {3643, 36320}, {5071, 33411}, {19710, 49898}, {33622, 43229}

X(49803) = perspector (1st Brocard, 1st outer-Fermat-Dao-Nhi)


X(49804) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND 1st BROCARD-REFLECTED

Barycentrics    2*sqrt(3)*(a^2+b^2+c^2)*(4*a^4+3*(b^2+c^2)*a^2+14*b^2*c^2)*S+24*a^8-8*(b^2+c^2)*a^6-(20*b^4+93*b^2*c^2+20*c^4)*a^4+2*(b^2+c^2)*(2*b^4-29*b^2*c^2+2*c^4)*a^2+7*(b^2-c^2)^2*b^2*c^2 : :

X(49804) lies on these lines: {22689, 36322}

X(49804) = perspector (1st Brocard-reflected, 1st inner-Fermat-Dao-Nhi)


X(49805) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND 1st BROCARD-REFLECTED

Barycentrics    -2*sqrt(3)*(a^2+b^2+c^2)*(4*a^4+3*(b^2+c^2)*a^2+14*b^2*c^2)*S+24*a^8-8*(b^2+c^2)*a^6-(20*b^4+93*b^2*c^2+20*c^4)*a^4+2*(b^2+c^2)*(2*b^4-29*b^2*c^2+2*c^4)*a^2+7*(b^2-c^2)^2*b^2*c^2 : :

X(49805) lies on these lines: {22687, 36323}

X(49805) = perspector (1st Brocard-reflected, 1st outer-Fermat-Dao-Nhi)


X(49806) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND INNER-FERMAT

Barycentrics    -14*sqrt(3)*(7*a^2+b^2+c^2)*S+43*a^4+76*(b^2+c^2)*a^2-119*(b^2-c^2)^2 : :

X(49806) lies on these lines: {2, 49912}, {14, 33624}, {3104, 41120}, {5066, 36318}, {5071, 16626}, {33561, 49855}, {33606, 35750}, {33609, 47866}, {35749, 41135}, {36329, 49816}, {36330, 49830}

X(49806) = perspector (inner-Fermat, 1st inner-Fermat-Dao-Nhi)
X(49806) = anticomplement of X(49912)


X(49807) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND INNER-FERMAT

Barycentrics    14*sqrt(3)*(7*a^2-5*b^2-5*c^2)*S+101*a^4-94*(b^2+c^2)*a^2-7*(b^2-c^2)^2 : :
X(49807) = 3*X(33613)-X(49911)

X(49807) lies on these lines: {2, 33613}, {616, 36324}, {3104, 49827}, {3839, 16626}, {11160, 49808}, {15682, 48655}, {15697, 36320}, {20094, 36327}, {33622, 42511}, {36967, 49856}, {40898, 49901}, {47865, 49817}

X(49807) = reflection of X(2) in X(33613)
X(49807) = perspector (inner-Fermat, 1st outer-Fermat-Dao-Nhi)
X(49807) = anticomplement of X(49911)


X(49808) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND OUTER-FERMAT

Barycentrics    -14*sqrt(3)*(7*a^2-5*b^2-5*c^2)*S+101*a^4-94*(b^2+c^2)*a^2-7*(b^2-c^2)^2 : :
X(49808) = 3*X(33612)-X(49914)

X(49808) lies on these lines: {2, 33612}, {617, 36326}, {3105, 49826}, {3839, 16627}, {11160, 49807}, {15682, 48656}, {15697, 36318}, {20094, 35749}, {33624, 42510}, {36968, 49857}, {40899, 49902}, {47866, 49818}

X(49808) = reflection of X(2) in X(33612)
X(49808) = perspector (outer-Fermat, 1st inner-Fermat-Dao-Nhi)
X(49808) = X(33603)-of-outer-Fermat triangle
X(49808) = anticomplement of X(49914)


X(49809) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND OUTER-FERMAT

Barycentrics    14*sqrt(3)*(7*a^2+b^2+c^2)*S+43*a^4+76*(b^2+c^2)*a^2-119*(b^2-c^2)^2 : :

X(49809) lies on these lines: {2, 49913}, {13, 33622}, {3105, 41119}, {5066, 36320}, {5071, 16627}, {33560, 49858}, {33607, 36331}, {33608, 47865}, {35751, 49819}, {35752, 49831}, {36327, 41135}

X(49809) = perspector (outer-Fermat, 1st outer-Fermat-Dao-Nhi)
X(49809) = X(33607)-of-outer-Fermat triangle
X(49809) = anticomplement of X(49913)


X(49810) = HOMOTHETIC CENTER OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND 4th FERMAT-DAO

Barycentrics    18*sqrt(3)*S*a^2+2*a^4-13*(b^2+c^2)*a^2+11*(b^2-c^2)^2 : :

X(49810) lies on these lines: {2, 18}, {4, 42533}, {6, 10109}, {14, 15682}, {16, 49824}, {20, 43427}, {62, 41099}, {376, 42993}, {381, 42503}, {395, 3534}, {398, 15693}, {3090, 43426}, {3411, 3543}, {3830, 42148}, {3845, 10653}, {3860, 42920}, {5055, 42899}, {5066, 42153}, {5071, 42506}, {5079, 42898}, {5334, 43245}, {5335, 42521}, {5339, 19710}, {5340, 42420}, {5469, 35749}, {5863, 22490}, {8703, 42149}, {10654, 12100}, {11001, 16963}, {11485, 42513}, {11489, 15719}, {11539, 42419}, {11540, 43208}, {12821, 33605}, {15640, 42972}, {15685, 42160}, {15687, 42508}, {15697, 16964}, {15698, 41944}, {15701, 42089}, {15702, 42991}, {15711, 42509}, {15713, 16645}, {15716, 42147}, {15721, 42504}, {16242, 41971}, {16530, 35750}, {16808, 37641}, {16809, 43781}, {16961, 19708}, {16966, 42953}, {16967, 49862}, {18581, 19709}, {18582, 33607}, {22237, 42161}, {22238, 33699}, {22511, 36318}, {22572, 35690}, {22604, 36333}, {22633, 36332}, {22690, 36322}, {22891, 36326}, {25161, 36328}, {25167, 36336}, {25168, 36337}, {25169, 36341}, {25170, 36343}, {25214, 36354}, {33606, 41107}, {36330, 47856}, {36968, 42901}, {37835, 42952}, {41021, 41031}, {41091, 41127}, {41100, 49873}, {41103, 41130}, {41121, 42111}, {42093, 43109}, {42113, 43417}, {42117, 46332}, {42129, 42984}, {42479, 43463}, {42519, 49905}, {42580, 43013}, {42589, 43419}, {42626, 42917}, {42817, 42911}, {42910, 49947}, {42931, 43778}, {43003, 43494}, {43005, 49907}, {43015, 43403}, {43239, 44580}, {43242, 43400}, {43243, 49827}, {43365, 43369}, {43425, 49140}, {43554, 49813}, {43645, 43870}, {49570, 49577}

X(49810) = homothetic center (4th Fermat-Dao, 1st inner-Fermat-Dao-Nhi)
X(49810) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 16268, 49859), (2, 42507, 40694), (2, 42999, 42532), (6, 10109, 49811), (14, 42977, 15682), (14, 49812, 42510), (11543, 49948, 41120), (15682, 42977, 42510), (15682, 49812, 42977), (16268, 42507, 2), (16961, 41108, 49861), (18581, 43229, 41119), (33606, 41107, 43404), (37641, 41122, 41112), (40694, 49859, 2), (41120, 49948, 10653), (42103, 42634, 10653), (42104, 42510, 46334)


X(49811) = HOMOTHETIC CENTER OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND 3rd FERMAT-DAO

Barycentrics    -18*sqrt(3)*S*a^2+2*a^4-13*(b^2+c^2)*a^2+11*(b^2-c^2)^2 : :

X(49811) lies on these lines: {2, 17}, {4, 42532}, {6, 10109}, {13, 15682}, {15, 49825}, {20, 43426}, {61, 41099}, {376, 42992}, {381, 42502}, {396, 3534}, {397, 15693}, {3090, 43427}, {3412, 3543}, {3830, 42147}, {3845, 10654}, {3860, 42921}, {5055, 42898}, {5066, 42156}, {5071, 42507}, {5079, 42899}, {5334, 42520}, {5335, 43244}, {5339, 42419}, {5340, 19710}, {5470, 36327}, {5862, 22489}, {8703, 42152}, {10653, 12100}, {11001, 16962}, {11486, 42512}, {11488, 15719}, {11539, 42420}, {11540, 43207}, {12820, 33604}, {15640, 42973}, {15685, 42161}, {15687, 42509}, {15697, 16965}, {15698, 41943}, {15701, 42092}, {15702, 42990}, {15711, 42508}, {15713, 16644}, {15716, 42148}, {15721, 42505}, {16241, 41972}, {16529, 36331}, {16808, 43782}, {16809, 37640}, {16960, 19708}, {16966, 49861}, {16967, 42952}, {18581, 33606}, {18582, 19709}, {22235, 42160}, {22236, 33699}, {22510, 36320}, {22571, 35694}, {22602, 36335}, {22631, 36334}, {22688, 36323}, {22846, 36324}, {25151, 36325}, {25157, 36338}, {25158, 36339}, {25159, 36340}, {25160, 36342}, {25217, 36321}, {33607, 41108}, {35730, 35736}, {35752, 47855}, {36763, 36768}, {36967, 42900}, {37832, 42953}, {41020, 41030}, {41101, 49874}, {41122, 42114}, {42094, 43108}, {42112, 43416}, {42118, 46332}, {42132, 42985}, {42478, 43464}, {42518, 49906}, {42581, 43012}, {42588, 43418}, {42625, 42916}, {42818, 42910}, {42911, 49948}, {42930, 43777}, {43002, 43493}, {43004, 49908}, {43014, 43404}, {43238, 44580}, {43242, 49826}, {43243, 43399}, {43364, 43368}, {43424, 49140}, {43555, 49812}, {43646, 43869}, {49569, 49581}

X(49811) = homothetic center (3rd Fermat-Dao, 1st outer-Fermat-Dao-Nhi)
X(49811) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 16267, 49860), (2, 42506, 40693), (2, 42998, 42533), (6, 10109, 49810), (13, 42976, 15682), (13, 49813, 42511), (11542, 49947, 41119), (15682, 42976, 42511), (15682, 49813, 42976), (16267, 42506, 2), (16960, 41107, 49862), (18582, 43228, 41120), (33607, 41108, 43403), (37640, 41121, 41113), (40693, 49860, 2), (41119, 49947, 10654), (42105, 42511, 46335), (42106, 42633, 10654)


X(49812) = HOMOTHETIC CENTER OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND 8th FERMAT-DAO

Barycentrics    3*sqrt(3)*a^2-5*S : :
X(49812) = 6*X(5343)-X(42515) = X(5343)-10*X(42989) = 3*X(5343)-5*X(49824) = X(42515)-10*X(49824) = 6*X(42989)-X(49824)

X(49812) lies on these lines: {2, 6}, {3, 49876}, {4, 3411}, {5, 49874}, {13, 42472}, {14, 15682}, {15, 15719}, {16, 11001}, {18, 5071}, {30, 5343}, {39, 33616}, {61, 15702}, {62, 3545}, {115, 35749}, {376, 5237}, {381, 5344}, {398, 10304}, {547, 43207}, {549, 42999}, {631, 41944}, {3091, 42519}, {3364, 35737}, {3524, 5238}, {3525, 16962}, {3529, 42993}, {3534, 5334}, {3543, 5349}, {3544, 42990}, {3830, 11543}, {3832, 43201}, {3839, 5350}, {3845, 11486}, {3855, 42973}, {5055, 42998}, {5066, 5335}, {5321, 15640}, {5339, 15683}, {5365, 15684}, {5366, 23046}, {5471, 36327}, {6108, 36318}, {6114, 36319}, {6151, 46204}, {6449, 15764}, {6775, 33625}, {6782, 36344}, {7685, 41033}, {8703, 42119}, {9113, 46453}, {9115, 35750}, {10109, 42974}, {10299, 42991}, {10303, 43100}, {10646, 43482}, {10653, 12816}, {10654, 19708}, {11481, 43429}, {11485, 11812}, {11540, 42633}, {12101, 42125}, {12817, 33605}, {13875, 36332}, {13928, 36333}, {14269, 42924}, {14482, 49953}, {15685, 42816}, {15690, 42115}, {15692, 16773}, {15693, 42479}, {15695, 42117}, {15697, 42154}, {15698, 41101}, {15700, 42925}, {15701, 42121}, {15705, 42944}, {15708, 22236}, {15710, 42150}, {15713, 42516}, {15715, 42780}, {15721, 43239}, {15722, 42419}, {16241, 43464}, {16242, 42504}, {16808, 33602}, {16965, 42636}, {16966, 42513}, {16967, 42480}, {18581, 41106}, {19107, 43330}, {19709, 42142}, {19711, 42116}, {22237, 42148}, {22574, 35690}, {22692, 36322}, {22848, 33615}, {22893, 36326}, {25173, 36328}, {25187, 36336}, {25188, 36337}, {25189, 36341}, {25190, 36343}, {25219, 36354}, {30414, 46845}, {33607, 42915}, {33699, 42133}, {34755, 43399}, {35007, 37173}, {35694, 40672}, {36330, 47858}, {36358, 41640}, {36359, 41642}, {36445, 42227}, {36463, 42228}, {36836, 43480}, {36843, 43770}, {36967, 43301}, {36969, 43368}, {37835, 41119}, {41023, 41031}, {41091, 41126}, {41095, 41130}, {41648, 49578}, {41943, 42596}, {41990, 42922}, {42085, 42631}, {42087, 43237}, {42089, 43309}, {42091, 43419}, {42092, 42976}, {42106, 42800}, {42107, 43540}, {42140, 42943}, {42143, 42420}, {42151, 42972}, {42152, 42597}, {42155, 42778}, {42161, 42436}, {42432, 42805}, {42478, 42982}, {42488, 43446}, {42494, 42599}, {42506, 42911}, {42508, 42941}, {42512, 43014}, {42520, 42897}, {42528, 43331}, {42529, 42893}, {42532, 43015}, {42625, 43466}, {42801, 46333}, {42910, 49907}, {43193, 43774}, {43198, 44580}, {43200, 43372}, {43242, 43401}, {43246, 43403}, {43247, 43416}, {43555, 49811}, {43633, 43784}, {49572, 49577}

X(49812) = intersection, other than A, B, C, of circumconics {{A, B, C, X(69), X(33606)}} and {{A, B, C, X(83), X(49813)}}
X(49812) = X(2)-Ceva conjugate of-X(33617)
X(49812) = X(31)-complementary conjugate of-X(33617)
X(49812) = homothetic center (8th Fermat-Dao, 1st inner-Fermat-Dao-Nhi)
X(49812) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 6, 49813), (2, 395, 49861), (2, 37785, 5862), (2, 43228, 11488), (2, 49861, 11489), (2, 49948, 37641), (4, 41100, 42588), (14, 42510, 15682), (14, 42977, 42510), (16, 41113, 11001), (16, 42507, 41113), (18, 42521, 41121), (395, 37641, 11489), (395, 43229, 49906), (395, 49948, 2), (11489, 37641, 37640), (15682, 42510, 42120), (16268, 41100, 41120), (16645, 43228, 2), (16963, 40694, 376), (23303, 49905, 2), (36446, 37641, 19053), (36447, 36464, 37641), (36465, 37641, 19054), (37641, 49861, 2), (37641, 49906, 49862), (41100, 41120, 4), (41107, 49904, 18581), (41122, 42533, 10653), (42154, 42792, 15697), (42510, 49810, 14), (42977, 49810, 15682), (43202, 43769, 3543), (43229, 49906, 2), (43404, 49875, 3845), (49906, 49948, 43229)


X(49813) = HOMOTHETIC CENTER OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND 7th FERMAT-DAO

Barycentrics    3*sqrt(3)*a^2+5*S : :
X(49813) = 6*X(5344)-X(42514) = X(5344)-10*X(42988) = 3*X(5344)-5*X(49825) = X(42514)-10*X(49825) = 6*X(42988)-X(49825)

X(49813) lies on these lines: {2, 6}, {3, 49875}, {4, 3412}, {5, 49873}, {13, 15682}, {14, 42473}, {15, 11001}, {16, 15719}, {17, 5071}, {30, 5344}, {39, 33617}, {61, 3545}, {62, 15702}, {115, 36327}, {376, 5238}, {381, 5343}, {397, 10304}, {547, 43208}, {549, 42998}, {631, 41943}, {2981, 46204}, {3091, 42518}, {3390, 35737}, {3524, 5237}, {3525, 16963}, {3529, 42992}, {3534, 5335}, {3543, 5350}, {3544, 42991}, {3830, 11542}, {3832, 43202}, {3839, 5349}, {3845, 11485}, {3855, 42972}, {5055, 42999}, {5066, 5334}, {5318, 15640}, {5340, 15683}, {5365, 23046}, {5366, 15684}, {5472, 35749}, {6109, 36320}, {6115, 36344}, {6450, 15764}, {6772, 33623}, {6783, 36319}, {7684, 41032}, {8703, 42120}, {9112, 36769}, {9117, 36331}, {10109, 42975}, {10299, 42990}, {10303, 43107}, {10645, 43481}, {10653, 19708}, {10654, 12817}, {11480, 43428}, {11486, 11812}, {11540, 42634}, {12101, 42128}, {12816, 33604}, {13876, 36334}, {13929, 36335}, {14269, 42925}, {14482, 49952}, {15685, 42815}, {15690, 42116}, {15692, 16772}, {15693, 42478}, {15695, 42118}, {15697, 42155}, {15698, 41100}, {15700, 42924}, {15701, 42124}, {15705, 42945}, {15708, 22238}, {15710, 42151}, {15713, 42517}, {15715, 42779}, {15721, 43238}, {15722, 42420}, {16241, 42505}, {16242, 43463}, {16809, 33603}, {16964, 42635}, {16966, 42481}, {16967, 42512}, {18582, 41106}, {19106, 43331}, {19709, 42139}, {19711, 42115}, {22235, 42147}, {22573, 35694}, {22691, 36323}, {22847, 36324}, {22892, 33614}, {25178, 36325}, {25183, 36338}, {25184, 36339}, {25185, 36340}, {25186, 36342}, {25220, 36321}, {30415, 46845}, {33606, 42914}, {33699, 42134}, {34754, 43400}, {35007, 37172}, {35690, 40671}, {35731, 35736}, {35752, 47857}, {36350, 41630}, {36351, 41632}, {36445, 42230}, {36463, 42229}, {36764, 36768}, {36767, 41620}, {36836, 43769}, {36843, 43479}, {36968, 43300}, {36970, 43369}, {37832, 41120}, {41022, 41030}, {41638, 49582}, {41944, 42597}, {41990, 42923}, {42086, 42632}, {42088, 43236}, {42089, 42977}, {42090, 43418}, {42092, 43308}, {42103, 42799}, {42110, 43541}, {42141, 42942}, {42146, 42419}, {42149, 42596}, {42150, 42973}, {42154, 42777}, {42160, 42435}, {42431, 42806}, {42479, 42983}, {42489, 43447}, {42495, 42598}, {42507, 42910}, {42509, 42940}, {42513, 43015}, {42521, 42896}, {42528, 42892}, {42529, 43330}, {42533, 43014}, {42626, 43465}, {42802, 46333}, {42911, 49908}, {43194, 43773}, {43197, 44580}, {43199, 43373}, {43243, 43402}, {43246, 43417}, {43247, 43404}, {43554, 49810}, {43632, 43783}, {49571, 49581}

X(49813) = intersection, other than A, B, C, of circumconics {{A, B, C, X(69), X(33607)}} and {{A, B, C, X(83), X(49812)}}
X(49813) = X(2)-Ceva conjugate of-X(33616)
X(49813) = X(31)-complementary conjugate of-X(33616)
X(49813) = homothetic center (7th Fermat-Dao, 1st outer-Fermat-Dao-Nhi)
X(49813) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 6, 49812), (2, 396, 49862), (2, 37786, 5863), (2, 43229, 11489), (2, 49862, 11488), (2, 49947, 37640), (4, 41101, 42589), (13, 42511, 15682), (13, 42976, 42511), (15, 41112, 11001), (15, 42506, 41112), (17, 42520, 41122), (396, 37640, 11488), (396, 43228, 49905), (396, 49947, 2), (11488, 37640, 37641), (15682, 42511, 42119), (16267, 41101, 41119), (16644, 43229, 2), (16962, 40693, 376), (23302, 49906, 2), (36446, 36465, 37640), (36447, 37640, 19054), (36464, 37640, 19053), (37640, 49862, 2), (37640, 49905, 49861), (41101, 41119, 4), (41108, 49903, 18582), (41121, 42532, 10654), (42155, 42791, 15697), (42511, 49811, 13), (42976, 49811, 15682), (43201, 43770, 3543), (43228, 49905, 2), (43403, 49876, 3845), (49905, 49947, 43228)


X(49814) = HOMOTHETIC CENTER OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND 1st HALF-DIAMONDS-CENTRAL

Barycentrics    -22*S*(25*a^2+7*b^2+7*c^2)+(11*a^4+212*(b^2+c^2)*a^2-223*(b^2-c^2)^2)*sqrt(3) : :

X(49814) lies on these lines: {2, 41971}, {5, 36318}, {14, 49830}, {530, 49863}, {5460, 35749}, {5863, 33476}, {6774, 15682}, {10304, 33418}, {22891, 36326}, {33412, 47865}, {33474, 35690}, {33615, 36331}, {35750, 49910}, {36330, 49816}

X(49814) = perspector (1st inner-Fermat-Dao-Nhi, 1st half-diamonds-central)


X(49815) = HOMOTHETIC CENTER OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND 2nd HALF-DIAMONDS-CENTRAL

Barycentrics    22*S*(25*a^2+7*b^2+7*c^2)+(11*a^4+212*(b^2+c^2)*a^2-223*(b^2-c^2)^2)*sqrt(3) : :

X(49815) lies on these lines: {2, 41972}, {5, 36320}, {13, 49831}, {531, 49864}, {5459, 36327}, {5862, 33477}, {6771, 15682}, {10304, 33419}, {22846, 36324}, {33413, 47866}, {33475, 35694}, {33614, 35750}, {35752, 49819}, {36331, 49909}

X(49815) = perspector (1st outer-Fermat-Dao-Nhi, 2nd half-diamonds-central)
X(49815) = X(49909)-of-outer-Fermat triangle


X(49816) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND 1st HALF-DIAMONDS

Barycentrics    22*(-3*a^2+15*c^2+15*b^2)*S+(209*a^4-256*(b^2+c^2)*a^2+47*(b^2-c^2)^2)*sqrt(3) : :

X(49816) lies on these lines: {2, 42894}, {619, 33624}, {15682, 22797}, {15693, 36318}, {15702, 49106}, {21356, 49819}, {33618, 35750}, {36326, 42510}, {36329, 49806}, {36330, 49814}

X(49816) = perspector (1st inner-Fermat-Dao-Nhi, 1st half-diamonds)


X(49817) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND 1st HALF-DIAMONDS

Barycentrics    66*(13*a^2+b^2+c^2)*S+(187*a^4+166*(b^2+c^2)*a^2-353*(b^2-c^2)^2)*sqrt(3) : :

X(49817) lies on these lines: {2, 43033}, {13, 36324}, {10304, 49106}, {15682, 47610}, {22797, 36320}, {47865, 49807}

X(49817) = perspector (1st outer-Fermat-Dao-Nhi, 1st half-diamonds)


X(49818) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND 2nd HALF-DIAMONDS

Barycentrics    -66*(13*a^2+b^2+c^2)*S+(187*a^4+166*(b^2+c^2)*a^2-353*(b^2-c^2)^2)*sqrt(3) : :

X(49818) lies on these lines: {2, 43032}, {14, 36326}, {10304, 49105}, {15682, 47611}, {22796, 36318}, {47866, 49808}

X(49818) = perspector (1st inner-Fermat-Dao-Nhi, 2nd half-diamonds)
X(49818) = X(33615)-of-outer-Fermat triangle


X(49819) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND 2nd HALF-DIAMONDS

Barycentrics    -22*(-3*a^2+15*c^2+15*b^2)*S+(209*a^4-256*(b^2+c^2)*a^2+47*(b^2-c^2)^2)*sqrt(3) : :

X(49819) lies on these lines: {2, 42895}, {618, 33622}, {15682, 22796}, {15693, 36320}, {15702, 49105}, {21356, 49816}, {33619, 36331}, {33623, 36768}, {35751, 49809}, {35752, 49815}, {36324, 42511}, {36327, 36767}

X(49819) = perspector (1st outer-Fermat-Dao-Nhi, 2nd half-diamonds)
X(49819) = X(33619)-of-outer-Fermat triangle


X(49820) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND 1st HALF-SQUARES

Barycentrics    3*(8*(b^2+c^2)*S-21*a^4+12*(b^2+c^2)*a^2+9*(b^2-c^2)^2)*sqrt(3)+8*(11*a^2-7*b^2-7*c^2)*S-7*a^4-40*(b^2+c^2)*a^2+47*(b^2-c^2)^2 : :

X(49820) lies on these lines: {2, 49930}, {33442, 36332}, {36329, 49822}

X(49820) = perspector (1st inner-Fermat-Dao-Nhi, 1st half-squares)
X(49820) = anticomplement of X(49930)


X(49821) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND 1st HALF-SQUARES

Barycentrics    3*(8*(b^2+c^2)*S-21*a^4+12*(b^2+c^2)*a^2+9*(b^2-c^2)^2)*sqrt(3)-8*(11*a^2-7*b^2-7*c^2)*S+7*a^4+40*(b^2+c^2)*a^2-47*(b^2-c^2)^2 : :

X(49821) lies on these lines: {2, 49929}, {33440, 36334}, {35751, 49823}

X(49821) = perspector (1st outer-Fermat-Dao-Nhi, 1st half-squares)
X(49821) = anticomplement of X(49929)


X(49822) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND 2nd HALF-SQUARES

Barycentrics    3*(-8*(b^2+c^2)*S-21*a^4+12*(b^2+c^2)*a^2+9*(b^2-c^2)^2)*sqrt(3)+8*(11*a^2-7*b^2-7*c^2)*S+7*a^4+40*(b^2+c^2)*a^2-47*(b^2-c^2)^2 : :

X(49822) lies on these lines: {2, 49928}, {33443, 36333}, {36329, 49820}

X(49822) = perspector (1st inner-Fermat-Dao-Nhi, 2nd half-squares)
X(49822) = anticomplement of X(49928)


X(49823) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND 2nd HALF-SQUARES

Barycentrics    3*(-8*(b^2+c^2)*S-21*a^4+12*(b^2+c^2)*a^2+9*(b^2-c^2)^2)*sqrt(3)-8*(11*a^2-7*b^2-7*c^2)*S-7*a^4-40*(b^2+c^2)*a^2+47*(b^2-c^2)^2 : :

X(49823) lies on these lines: {2, 49927}, {33441, 36335}, {35751, 49821}

X(49823) = perspector (1st outer-Fermat-Dao-Nhi, 2nd half-squares)
X(49823) = anticomplement of X(49927)


X(49824) = HOMOTHETIC CENTER OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND 4th ISODYNAMIC-DAO

Barycentrics    -12*S*a^2*sqrt(3)+7*a^4+4*(b^2+c^2)*a^2-11*(b^2-c^2)^2 : :
X(49824) = 5*X(5343)+4*X(42989) = 3*X(5343)+2*X(49812) = X(42515)+9*X(49812) = 6*X(42989)-5*X(49812)

X(49824) lies on these lines: {2, 14}, {4, 33603}, {5, 49862}, {6, 41099}, {13, 42481}, {16, 49810}, {18, 15692}, {20, 16268}, {30, 5343}, {115, 36318}, {298, 32892}, {376, 5339}, {381, 42775}, {382, 43109}, {395, 11001}, {398, 3545}, {547, 42495}, {631, 42791}, {1503, 41031}, {3091, 41121}, {3146, 42993}, {3411, 43425}, {3412, 42952}, {3522, 41944}, {3524, 42153}, {3534, 11543}, {3543, 5365}, {3830, 37641}, {3839, 41112}, {3845, 5335}, {3851, 43246}, {3860, 42974}, {5032, 41118}, {5056, 16962}, {5066, 37640}, {5068, 42991}, {5071, 42163}, {5321, 15682}, {5344, 12816}, {5349, 42899}, {5366, 14269}, {5471, 36320}, {5480, 41030}, {5863, 31694}, {6110, 49841}, {6775, 31684}, {6782, 35750}, {8703, 11489}, {10109, 11485}, {10299, 43100}, {10303, 41973}, {10304, 16964}, {10653, 12817}, {11160, 33627}, {11486, 33699}, {12100, 42119}, {12101, 43772}, {15640, 36970}, {15683, 16963}, {15685, 42140}, {15687, 43202}, {15688, 43003}, {15693, 42117}, {15695, 42818}, {15697, 42085}, {15698, 16645}, {15701, 43108}, {15702, 42147}, {15703, 42925}, {15708, 42150}, {15709, 42599}, {15710, 43194}, {15713, 42129}, {15715, 43239}, {15716, 42122}, {15719, 42942}, {16267, 42920}, {16809, 41119}, {16961, 42631}, {16965, 43476}, {18582, 43232}, {19107, 42977}, {19708, 33605}, {19709, 42139}, {19710, 42126}, {19711, 42628}, {22856, 36324}, {23249, 36450}, {23259, 36467}, {23303, 43482}, {31696, 35690}, {31698, 36333}, {31700, 36332}, {31702, 36322}, {31704, 36326}, {31706, 33624}, {31708, 36328}, {31710, 35749}, {31712, 36336}, {31714, 36337}, {31716, 36343}, {31718, 36341}, {31720, 36354}, {33416, 42953}, {33604, 42166}, {35404, 43769}, {35736, 42239}, {36446, 45384}, {36465, 45385}, {36843, 46333}, {36969, 43032}, {38071, 42776}, {41106, 42110}, {41107, 42134}, {41124, 41130}, {42086, 42533}, {42107, 43542}, {42127, 43398}, {42132, 42516}, {42135, 42478}, {42141, 42634}, {42145, 42514}, {42161, 43547}, {42419, 42473}, {42436, 43495}, {42472, 42496}, {42474, 49905}, {42508, 43401}, {42520, 49860}, {42688, 43198}, {42690, 42923}, {42778, 42792}, {42804, 43400}, {42911, 42976}, {42912, 43247}, {42918, 49903}, {42935, 43551}, {42943, 42987}, {43005, 43870}, {43335, 43540}, {43364, 43418}, {43466, 46335}, {43630, 46332}, {49577, 49597}

X(49824) = homothetic center (1st inner-Fermat-Dao-Nhi, 4th isodynamic-Dao)
X(49824) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 14, 49873), (2, 5334, 49827), (2, 41108, 49876), (2, 41113, 5334), (2, 49873, 43404), (4, 43229, 49826), (6, 41099, 49825), (14, 5334, 43404), (14, 41108, 41120), (14, 41113, 2), (14, 43419, 18581), (3534, 11543, 49861), (3543, 42972, 5365), (3830, 37641, 49875), (5334, 49873, 2), (5334, 49876, 41108), (10654, 41122, 2), (11489, 42589, 8703), (16963, 42160, 15683), (18581, 41101, 2), (36970, 42510, 15640), (37641, 43417, 42133), (40694, 42972, 3543), (41108, 41120, 2), (41108, 49876, 49827), (41108, 49908, 42511), (41113, 41120, 41108), (41113, 49873, 49827), (41120, 42511, 49908), (42133, 49875, 3830), (42139, 49813, 19709), (42511, 49908, 2), (42816, 43417, 37641), (42983, 43541, 10653), (43404, 49827, 2)


X(49825) = HOMOTHETIC CENTER OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND 3rd ISODYNAMIC-DAO

Barycentrics    12*S*a^2*sqrt(3)+7*a^4+4*(b^2+c^2)*a^2-11*(b^2-c^2)^2 : :
X(49825) = 5*X(5344)+4*X(42988) = 3*X(5344)+2*X(49813) = X(42514)+9*X(49813) = 6*X(42988)-5*X(49813)

X(49825) lies on these lines: {2, 13}, {4, 33602}, {5, 49861}, {6, 41099}, {14, 42480}, {15, 49811}, {17, 15692}, {20, 16267}, {30, 5344}, {115, 36320}, {299, 32892}, {376, 5340}, {381, 42776}, {382, 43108}, {396, 11001}, {397, 3545}, {547, 42494}, {631, 42792}, {1503, 41030}, {3091, 41122}, {3146, 42992}, {3411, 42953}, {3412, 43424}, {3522, 41943}, {3524, 42156}, {3534, 11542}, {3543, 5366}, {3830, 37640}, {3839, 41113}, {3845, 5334}, {3851, 43247}, {3860, 42975}, {5032, 41117}, {5056, 16963}, {5066, 37641}, {5068, 42990}, {5071, 42166}, {5318, 15682}, {5343, 12817}, {5350, 42898}, {5365, 14269}, {5472, 36318}, {5480, 41031}, {5862, 31693}, {6111, 49842}, {6772, 31683}, {6783, 36331}, {8703, 11488}, {10109, 11486}, {10299, 43107}, {10303, 41974}, {10304, 16965}, {10654, 12816}, {11160, 33626}, {11485, 33699}, {12100, 42120}, {12101, 43771}, {15640, 36969}, {15683, 16962}, {15685, 42141}, {15687, 43201}, {15688, 43002}, {15693, 42118}, {15695, 42817}, {15697, 42086}, {15698, 16644}, {15701, 43109}, {15702, 42148}, {15703, 42924}, {15708, 42151}, {15709, 42598}, {15710, 43193}, {15713, 42132}, {15715, 43238}, {15716, 42123}, {15719, 42943}, {16268, 42921}, {16808, 41120}, {16960, 42632}, {16964, 43475}, {18581, 43233}, {19106, 42976}, {19708, 33604}, {19709, 42142}, {19710, 42127}, {19711, 42627}, {22900, 36326}, {23249, 36468}, {23259, 36449}, {23302, 43481}, {31695, 35694}, {31697, 36335}, {31699, 36334}, {31701, 36323}, {31703, 36324}, {31705, 33622}, {31707, 36325}, {31709, 36327}, {31711, 36338}, {31713, 36339}, {31715, 36340}, {31717, 36342}, {31719, 36321}, {33417, 42952}, {33605, 42163}, {35404, 43770}, {35736, 35740}, {36447, 45385}, {36464, 45384}, {36836, 46333}, {36970, 43033}, {38071, 42775}, {41106, 42107}, {41108, 42133}, {42085, 42532}, {42110, 43543}, {42126, 43397}, {42129, 42517}, {42138, 42479}, {42140, 42633}, {42144, 42515}, {42160, 43546}, {42420, 42472}, {42435, 43496}, {42473, 42497}, {42475, 49906}, {42509, 43402}, {42521, 49859}, {42689, 43197}, {42691, 42922}, {42777, 42791}, {42803, 43399}, {42910, 42977}, {42913, 43246}, {42919, 49904}, {42934, 43550}, {42942, 42986}, {43004, 43869}, {43334, 43541}, {43365, 43419}, {43465, 46334}, {43631, 46332}, {49581, 49596}

X(49825) = homothetic center (1st outer-Fermat-Dao-Nhi, 3rd isodynamic-Dao)
X(49825) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 13, 49874), (2, 5335, 49826), (2, 41107, 49875), (2, 41112, 5335), (2, 49874, 43403), (4, 43228, 49827), (6, 41099, 49824), (13, 5335, 43403), (13, 41107, 41119), (13, 41112, 2), (13, 43418, 18582), (3534, 11542, 49862), (3543, 42973, 5366), (3830, 37640, 49876), (5335, 49874, 2), (5335, 49875, 41107), (10653, 41121, 2), (11488, 42588, 8703), (16962, 42161, 15683), (18582, 41100, 2), (36969, 42511, 15640), (37640, 43416, 42134), (40693, 42973, 3543), (41107, 41119, 2), (41107, 49875, 49826), (41107, 49907, 42510), (41112, 41119, 41107), (41112, 49874, 49826), (41119, 42510, 49907), (42134, 49876, 3830), (42142, 49812, 19709), (42510, 49907, 2), (42815, 43416, 37640), (42982, 43540, 10654), (43403, 49826, 2)


X(49826) = HOMOTHETIC CENTER OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND 2nd LEMOINE-DAO

Barycentrics    12*S*a^2*sqrt(3)+11*a^4-4*(b^2+c^2)*a^2-7*(b^2-c^2)^2 : :
X(49826) = 2*X(42588)+3*X(42998) = 11*X(42588)+3*X(43770) = 2*X(42588)+X(49876) = 11*X(42998)-2*X(43770) = 3*X(42998)-X(49876) = 6*X(43770)-11*X(49876)

X(49826) lies on these lines: {2, 13}, {3, 43109}, {4, 33603}, {6, 15682}, {14, 43365}, {15, 15697}, {17, 15708}, {20, 41974}, {30, 42588}, {61, 15683}, {62, 3839}, {376, 397}, {381, 5344}, {395, 41106}, {396, 19708}, {546, 43201}, {1152, 35736}, {1656, 43246}, {3091, 42973}, {3105, 49808}, {3146, 41973}, {3411, 3854}, {3522, 16962}, {3524, 42148}, {3528, 42794}, {3534, 37640}, {3543, 16965}, {3545, 5340}, {3830, 5334}, {3832, 16268}, {3845, 37641}, {3860, 42139}, {5055, 42924}, {5056, 41944}, {5066, 11486}, {5071, 22238}, {5073, 42515}, {5237, 15721}, {5318, 41099}, {5321, 43398}, {5343, 42161}, {5351, 43495}, {5365, 15687}, {5863, 11296}, {6775, 36319}, {7486, 10187}, {8703, 42120}, {8716, 33458}, {10109, 42128}, {10303, 42958}, {10304, 40693}, {10646, 49903}, {10654, 15640}, {11001, 42087}, {11481, 43542}, {11485, 19710}, {11488, 12100}, {11489, 19709}, {11542, 15693}, {11737, 42775}, {12101, 42975}, {12817, 43553}, {15681, 43769}, {15685, 42119}, {15692, 16267}, {15694, 42590}, {15695, 42912}, {15698, 42508}, {15699, 42494}, {15701, 42815}, {15702, 33604}, {15705, 41943}, {15709, 36843}, {15710, 16772}, {15711, 42496}, {15713, 42115}, {15714, 43635}, {15716, 42124}, {15717, 42992}, {15719, 16644}, {16241, 49860}, {16808, 42977}, {16809, 43781}, {16963, 42162}, {18581, 42533}, {22513, 36318}, {22580, 35690}, {22612, 36333}, {22641, 36332}, {22708, 36322}, {22862, 33624}, {22907, 36326}, {23023, 36328}, {23024, 36336}, {23025, 36337}, {23026, 36341}, {23027, 36343}, {23028, 36354}, {23046, 42989}, {23249, 36467}, {23259, 36450}, {33417, 41972}, {33602, 43555}, {33607, 42530}, {33699, 42127}, {34200, 42988}, {34755, 42804}, {35381, 42984}, {35403, 43202}, {36330, 47864}, {36344, 41745}, {36448, 42216}, {36449, 43257}, {36466, 42215}, {36468, 43256}, {36969, 41113}, {40694, 42521}, {41031, 41039}, {41091, 41116}, {41097, 41130}, {41101, 42086}, {42088, 43777}, {42090, 43244}, {42097, 43482}, {42106, 49859}, {42122, 42516}, {42131, 42633}, {42141, 42589}, {42142, 42913}, {42149, 43016}, {42158, 42632}, {42166, 42611}, {42416, 43640}, {42432, 43311}, {42480, 42546}, {42506, 42631}, {42512, 43010}, {42518, 42957}, {42581, 43480}, {42626, 43106}, {42682, 42941}, {42683, 43502}, {42818, 43247}, {42893, 42903}, {42914, 43033}, {42919, 43020}, {42920, 43008}, {42940, 43488}, {43006, 43541}, {43017, 43369}, {43022, 43485}, {43031, 43399}, {43108, 43111}, {43226, 43233}, {43242, 49811}, {43371, 43484}, {49577, 49605}

X(49826) = homothetic center (1st inner-Fermat-Dao-Nhi, 2nd Lemoine-Dao)
X(49826) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 5335, 49825), (2, 10653, 49875), (2, 41107, 5335), (2, 41112, 49874), (2, 49825, 43403), (4, 43229, 49824), (6, 15682, 49827), (13, 42510, 2), (16, 41119, 2), (62, 12816, 41120), (3845, 37641, 49873), (5066, 11486, 49861), (5318, 49948, 41099), (5335, 49874, 41112), (5335, 49875, 2), (8703, 42974, 49813), (10653, 41107, 2), (10653, 41112, 41100), (12816, 41120, 3839), (16267, 42151, 15692), (16644, 42792, 15719), (41099, 49948, 43404), (41100, 41107, 41112), (41100, 41112, 2), (41107, 49875, 49825), (41112, 49874, 49825), (42120, 49813, 8703), (42134, 49873, 3845), (42155, 43228, 11001), (42503, 49948, 42987), (42511, 46334, 20), (42943, 49905, 15698)


X(49827) = HOMOTHETIC CENTER OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND 1st LEMOINE-DAO

Barycentrics    -12*S*a^2*sqrt(3)+11*a^4-4*(b^2+c^2)*a^2-7*(b^2-c^2)^2 : :
X(49827) = 2*X(42589)+3*X(42999) = 11*X(42589)+3*X(43769) = 2*X(42589)+X(49875) = 11*X(42999)-2*X(43769) = 3*X(42999)-X(49875) = 6*X(43769)-11*X(49875)

X(49827) lies on these lines: {2, 14}, {3, 43108}, {4, 33602}, {6, 15682}, {13, 43364}, {16, 15697}, {18, 15708}, {20, 41973}, {30, 42589}, {61, 3839}, {62, 15683}, {376, 398}, {381, 5343}, {395, 19708}, {396, 41106}, {546, 43202}, {1151, 35736}, {1656, 43247}, {3091, 42972}, {3104, 49807}, {3146, 41974}, {3412, 3854}, {3522, 16963}, {3524, 42147}, {3528, 42793}, {3534, 37641}, {3543, 16964}, {3545, 5339}, {3830, 5335}, {3832, 16267}, {3845, 37640}, {3860, 42142}, {5055, 42925}, {5056, 41943}, {5066, 11485}, {5071, 22236}, {5073, 42514}, {5238, 15721}, {5318, 43397}, {5321, 41099}, {5344, 42160}, {5352, 43496}, {5366, 15687}, {5862, 11295}, {6772, 36344}, {7486, 10188}, {8703, 42119}, {8716, 33459}, {10109, 42125}, {10303, 42959}, {10304, 40694}, {10645, 49904}, {10653, 15640}, {11001, 42088}, {11480, 43543}, {11486, 19710}, {11488, 19709}, {11489, 12100}, {11543, 15693}, {11737, 42776}, {12101, 42974}, {12816, 43552}, {15681, 43770}, {15685, 42120}, {15692, 16268}, {15694, 42591}, {15695, 42913}, {15698, 42509}, {15699, 42495}, {15701, 42816}, {15702, 33605}, {15705, 41944}, {15709, 36836}, {15710, 16773}, {15711, 42497}, {15713, 42116}, {15714, 43634}, {15716, 42121}, {15717, 42993}, {15719, 16645}, {16242, 49859}, {16808, 43782}, {16809, 42976}, {16962, 42159}, {18582, 42532}, {22512, 36320}, {22579, 35694}, {22611, 36335}, {22640, 36334}, {22707, 36323}, {22861, 36324}, {22906, 33622}, {23017, 36325}, {23018, 36338}, {23019, 36339}, {23020, 36340}, {23021, 36342}, {23022, 36321}, {23046, 42988}, {23249, 36449}, {23259, 36468}, {33416, 41971}, {33603, 43554}, {33606, 42531}, {33699, 42126}, {34200, 42989}, {34754, 42803}, {35381, 42985}, {35403, 43201}, {35752, 47863}, {36319, 41746}, {36448, 42215}, {36450, 43256}, {36466, 42216}, {36467, 43257}, {36768, 36772}, {36970, 41112}, {40693, 42520}, {41030, 41038}, {41100, 42085}, {42087, 43778}, {42091, 43245}, {42096, 43481}, {42103, 49860}, {42123, 42517}, {42130, 42634}, {42139, 42912}, {42140, 42588}, {42152, 43017}, {42157, 42631}, {42163, 42610}, {42415, 43639}, {42431, 43310}, {42481, 42545}, {42507, 42632}, {42513, 43011}, {42519, 42956}, {42580, 43479}, {42625, 43105}, {42682, 43501}, {42683, 42940}, {42817, 43246}, {42892, 42902}, {42915, 43032}, {42918, 43021}, {42921, 43009}, {42941, 43487}, {43007, 43540}, {43016, 43368}, {43023, 43486}, {43030, 43400}, {43109, 43110}, {43227, 43232}, {43243, 49810}, {43370, 43483}, {49581, 49604}

X(49827) = homothetic center (1st outer-Fermat-Dao-Nhi, 1st Lemoine-Dao)
X(49827) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 5334, 49824), (2, 10654, 49876), (2, 41108, 5334), (2, 41113, 49873), (2, 49824, 43404), (4, 43228, 49825), (6, 15682, 49826), (14, 42511, 2), (15, 41120, 2), (61, 12817, 41119), (3845, 37640, 49874), (5066, 11485, 49862), (5321, 49947, 41099), (5334, 49873, 41113), (5334, 49876, 2), (8703, 42975, 49812), (10654, 41108, 2), (10654, 41113, 41101), (12817, 41119, 3839), (16268, 42150, 15692), (16645, 42791, 15719), (41099, 49947, 43403), (41101, 41108, 41113), (41101, 41113, 2), (41108, 49876, 49824), (41113, 49873, 49824), (42119, 49812, 8703), (42133, 49874, 3845), (42154, 43229, 11001), (42502, 49947, 42986), (42510, 46335, 20), (42942, 49906, 15698)


X(49828) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND MCCAY

Barycentrics    2*sqrt(3)*(157*a^4-206*(b^2+c^2)*a^2+49*(b^2-c^2)^2)*S+109*a^6-217*(b^2+c^2)*a^4+13*(11*b^4-6*b^2*c^2+11*c^4)*a^2-35*(b^4-c^4)*(b^2-c^2) : :

X(49828) lies on these lines: {3, 35749}, {619, 49802}, {5066, 33625}, {5863, 13084}, {6771, 49877}, {10124, 49830}, {13083, 35690}, {15709, 22493}, {15713, 33624}, {33603, 41971}, {44580, 49919}

X(49828) = perspector (1st inner-Fermat-Dao-Nhi, McCay)


X(49829) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND MCCAY

Barycentrics    -2*sqrt(3)*(157*a^4-206*(b^2+c^2)*a^2+49*(b^2-c^2)^2)*S+109*a^6-217*(b^2+c^2)*a^4+13*(11*b^4-6*b^2*c^2+11*c^4)*a^2-35*(b^4-c^4)*(b^2-c^2) : :

X(49829) lies on these lines: {3, 36327}, {618, 49803}, {5066, 33623}, {5862, 13083}, {6774, 49878}, {10124, 49831}, {13084, 35694}, {15709, 22494}, {15713, 33622}, {33602, 41972}, {44580, 49920}

X(49829) = perspector (1st outer-Fermat-Dao-Nhi, McCay)


X(49830) = HOMOTHETIC CENTER OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND OUTER-NAPOLEON

Barycentrics    14*(-7*a^2+11*b^2+11*c^2)*S+(97*a^4-104*(b^2+c^2)*a^2+7*(b^2-c^2)^2)*sqrt(3) : :

X(49830) lies on these lines: {2, 42799}, {3, 36318}, {14, 49814}, {530, 49879}, {628, 47865}, {5464, 35749}, {5613, 15682}, {5863, 9886}, {9763, 35690}, {10124, 49828}, {14144, 36326}, {33603, 36331}, {33624, 42977}, {33625, 47867}, {35750, 42625}, {36330, 49806}

X(49830) = perspector (1st inner-Fermat-Dao-Nhi, outer-Napoleon)
X(49830) = X(49814)-of-outer-Fermat triangle
X(49830) = anticomplement of X(49910)


X(49831) = HOMOTHETIC CENTER OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND INNER-NAPOLEON

Barycentrics    -14*(-7*a^2+11*b^2+11*c^2)*S+(97*a^4-104*(b^2+c^2)*a^2+7*(b^2-c^2)^2)*sqrt(3) : :

X(49831) lies on these lines: {2, 42800}, {3, 36320}, {13, 49815}, {531, 49880}, {627, 47866}, {5463, 36327}, {5617, 15682}, {5862, 9885}, {9761, 35694}, {10124, 49829}, {14145, 36324}, {33602, 35750}, {33608, 36767}, {33622, 36768}, {33623, 36769}, {35752, 49809}, {36331, 42626}

X(49831) = perspector (1st outer-Fermat-Dao-Nhi, inner-Napoleon)
X(49831) = X(49921)-of-outer-Fermat triangle
X(49831) = anticomplement of X(49909)


X(49832) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND 1st NEUBERG

Barycentrics    18*(4*a^4+7*(b^2+c^2)*a^2-11*b^4-8*b^2*c^2-11*c^4)*S*a^2+(72*a^8-148*(b^2+c^2)*a^6+(134*b^4-15*b^2*c^2+134*c^4)*a^4-2*(b^2+c^2)*(29*b^4-80*b^2*c^2+29*c^4)*a^2-49*(b^2-c^2)^2*b^2*c^2)*sqrt(3) : :

X(49832) lies on these lines: {6295, 36336}, {14830, 35749}, {33389, 36322}

X(49832) = perspector (1st inner-Fermat-Dao-Nhi, 1st Neuberg)


X(49833) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND 1st NEUBERG

Barycentrics    -18*(4*a^4+7*(b^2+c^2)*a^2-11*b^4-8*b^2*c^2-11*c^4)*S*a^2+(72*a^8-148*(b^2+c^2)*a^6+(134*b^4-15*b^2*c^2+134*c^4)*a^4-2*(b^2+c^2)*(29*b^4-80*b^2*c^2+29*c^4)*a^2-49*(b^2-c^2)^2*b^2*c^2)*sqrt(3) : :

X(49833) lies on these lines: {6582, 36338}, {14830, 36327}, {33388, 36323}

X(49833) = perspector (1st outer-Fermat-Dao-Nhi, 1st Neuberg)


X(49834) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND 2nd NEUBERG

Barycentrics    -6*sqrt(3)*(4*a^6+(3*b^4+20*b^2*c^2+3*c^4)*a^2-7*(b^4-c^4)*(b^2-c^2))*S+23*a^8-85*(b^2+c^2)*a^6+(169*b^4+251*b^2*c^2+169*c^4)*a^4-(b^2+c^2)*(121*b^4-174*b^2*c^2+121*c^4)*a^2+7*(2*b^4-3*b^2*c^2+2*c^4)*(b^2-c^2)^2 : :

X(49834) lies on these lines: {6299, 36337}, {35749, 48657}

X(49834) = perspector (1st inner-Fermat-Dao-Nhi, 2nd Neuberg)


X(49835) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND 2nd NEUBERG

Barycentrics    6*sqrt(3)*(4*a^6+(3*b^4+20*b^2*c^2+3*c^4)*a^2-7*(b^4-c^4)*(b^2-c^2))*S+23*a^8-85*(b^2+c^2)*a^6+(169*b^4+251*b^2*c^2+169*c^4)*a^4-(b^2+c^2)*(121*b^4-174*b^2*c^2+121*c^4)*a^2+7*(2*b^4-3*b^2*c^2+2*c^4)*(b^2-c^2)^2 : :

X(49835) lies on these lines: {6298, 36339}, {36327, 48657}

X(49835) = perspector (1st outer-Fermat-Dao-Nhi, 2nd Neuberg)


X(49836) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND INNER-VECTEN

Barycentrics    3*(14*(b^2+c^2)*S-8*a^4+(b^2+c^2)*a^2+7*(b^2-c^2)^2)*sqrt(3)+14*(7*a^2-2*b^2-2*c^2)*S+62*a^4-97*(b^2+c^2)*a^2+35*(b^2-c^2)^2 : :

X(49836) lies on these lines: {6303, 36333}

X(49836) = perspector (1st inner-Fermat-Dao-Nhi, inner-Vecten)


X(49837) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND INNER-VECTEN

Barycentrics    -3*(14*(b^2+c^2)*S-8*a^4+(b^2+c^2)*a^2+7*(b^2-c^2)^2)*sqrt(3)+14*(7*a^2-2*b^2-2*c^2)*S+62*a^4-97*(b^2+c^2)*a^2+35*(b^2-c^2)^2 : :

X(49837) lies on these lines: {6302, 36335}

X(49837) = perspector (1st outer-Fermat-Dao-Nhi, inner-Vecten)


X(49838) = PERSPECTOR OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI AND OUTER-VECTEN

Barycentrics    -3*(-14*(b^2+c^2)*S-8*a^4+(b^2+c^2)*a^2+7*(b^2-c^2)^2)*sqrt(3)-14*(7*a^2-2*b^2-2*c^2)*S+62*a^4-97*(b^2+c^2)*a^2+35*(b^2-c^2)^2 : :

X(49838) lies on these lines: {6307, 36332}

X(49838) = perspector (1st inner-Fermat-Dao-Nhi, outer-Vecten)


X(49839) = PERSPECTOR OF THESE TRIANGLES: 1st OUTER-FERMAT-DAO-NHI AND OUTER-VECTEN

Barycentrics    3*(-14*(b^2+c^2)*S-8*a^4+(b^2+c^2)*a^2+7*(b^2-c^2)^2)*sqrt(3)-14*(7*a^2-2*b^2-2*c^2)*S+62*a^4-97*(b^2+c^2)*a^2+35*(b^2-c^2)^2 : :

X(49839) lies on these lines: {6306, 36334}

X(49839) = perspector (1st outer-Fermat-Dao-Nhi, outer-Vecten)


X(49840) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI TO VU-DAO-X(15)-ISODYNAMIC

Barycentrics    -2*(5*a^8-5*(b^2+c^2)*a^6-(9*b^4-23*b^2*c^2+9*c^4)*a^4+13*(b^4-c^4)*(b^2-c^2)*a^2-(4*b^4+13*b^2*c^2+4*c^4)*(b^2-c^2)^2)*S+3*sqrt(3)*(2*a^10-2*(b^2+c^2)*a^8-(5*b^4-12*b^2*c^2+5*c^4)*a^6+7*(b^4-c^4)*(b^2-c^2)*a^4-(b^2-c^2)^2*(b^4+8*b^2*c^2+c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3) : :
X(49840) = 7*X(2)-6*X(46466) = 3*X(39352)-2*X(49931) = 12*X(46466)-7*X(49841) = 3*X(46466)-7*X(49932) = 9*X(46466)-7*X(49971) = X(49841)-4*X(49932) = 3*X(49841)-4*X(49971) = 3*X(49932)-X(49971)

The reciprocal orthologic center of these triangles is X(14).

X(49840) lies on the circumcircles of triangles {1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi} and these lines: {2, 46466}, {2777, 41132}, {6110, 49873}, {23870, 35749}, {35750, 41022}, {39352, 49931}, {41031, 41067}

X(49840) = reflection of X(i) in X(j) for these (i, j): (2, 49932), (49841, 2)
X(49840) = parallelogic center (2nd inner-Fermat-Dao-Nhi, Vu-Dao-X(15)-isodynamic)
X(49840) = orthologic center (1st inner-Fermat-Dao-Nhi, Vu-Dao-X(15)-isodynamic)
X(49840) = anticomplement of X(49971)


X(49841) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI TO VU-DAO-X(15)-ISODYNAMIC

Barycentrics    -2*(7*a^8-7*(b^2+c^2)*a^6-(9*b^4-25*b^2*c^2+9*c^4)*a^4+11*(b^4-c^4)*(b^2-c^2)*a^2-(2*b^4+11*b^2*c^2+2*c^4)*(b^2-c^2)^2)*S+3*sqrt(3)*(2*a^10-2*(b^2+c^2)*a^8-(5*b^4-12*b^2*c^2+5*c^4)*a^6+7*(b^4-c^4)*(b^2-c^2)*a^4-(b^2-c^2)^2*(b^4+8*b^2*c^2+c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3) : :
X(49841) = 5*X(2)-6*X(46466) = 3*X(39358)-2*X(41092) = 12*X(46466)-5*X(49840) = 9*X(46466)-5*X(49932) = 3*X(46466)-5*X(49971) = 3*X(49840)-4*X(49932) = X(49840)-4*X(49971) = X(49932)-3*X(49971)

The reciprocal parallelogic center of these triangles is X(4).

X(49841) lies on the circumcircles of triangles {1st inner-Fermat-Dao-Nhi, 2nd inner-Fermat-Dao-Nhi} and these lines: {2, 46466}, {2777, 49842}, {6110, 49824}, {15640, 35749}, {23870, 35750}, {39358, 41092}, {41033, 41067}

X(49841) = reflection of X(i) in X(j) for these (i, j): (2, 49971), (49840, 2)
X(49841) = parallelogic center (1st inner-Fermat-Dao-Nhi, Vu-Dao-X(15)-isodynamic)
X(49841) = orthologic center (2nd inner-Fermat-Dao-Nhi, Vu-Dao-X(15)-isodynamic)
X(49841) = anticomplement of X(49932)


X(49842) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st INNER-FERMAT-DAO-NHI TO VU-DAO-X(16)-ISODYNAMIC

Barycentrics    2*(7*a^8-7*(b^2+c^2)*a^6-(9*b^4-25*b^2*c^2+9*c^4)*a^4+11*(b^4-c^4)*(b^2-c^2)*a^2-(2*b^4+11*b^2*c^2+2*c^4)*(b^2-c^2)^2)*S+3*sqrt(3)*(2*a^10-2*(b^2+c^2)*a^8-(5*b^4-12*b^2*c^2+5*c^4)*a^6+7*(b^4-c^4)*(b^2-c^2)*a^4-(b^2-c^2)^2*(b^4+8*b^2*c^2+c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3) : :
X(49842) = 5*X(2)-6*X(46465) = 4*X(36768)-3*X(36774) = 2*X(36769)-3*X(36788) = 3*X(39358)-2*X(49971) = 4*X(41092)-X(41132) = 5*X(41092)-3*X(46465) = 3*X(41092)-X(49931) = 5*X(41132)-12*X(46465) = 3*X(41132)-4*X(49931) = 9*X(46465)-5*X(49931)

The reciprocal parallelogic center of these triangles is X(4).

X(49842) lies on the circumcircles of triangles {1st outer-Fermat-Dao-Nhi, 2nd outer-Fermat-Dao-Nhi} and these lines: {2, 41092}, {2777, 49841}, {6111, 49825}, {15640, 36327}, {23871, 36331}, {36768, 36774}, {36769, 36788}, {39358, 49971}, {41032, 41066}

X(49842) = reflection of X(i) in X(j) for these (i, j): (2, 41092), (41132, 2)
X(49842) = parallelogic center (1st outer-Fermat-Dao-Nhi, Vu-Dao-X(16)-isodynamic)
X(49842) = orthologic center (2nd outer-Fermat-Dao-Nhi, Vu-Dao-X(16)-isodynamic)
X(49842) = anticomplement of X(49931)


X(49843) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND ANTI-ARTZT

Barycentrics    -S*(3*a^4+22*(b^2+c^2)*a^2+3*b^4-14*b^2*c^2+3*c^4)*sqrt(3)+3*(a^2+b^2+c^2)*(8*a^4-3*(b^2+c^2)*a^2-(b^2-c^2)^2+4*b^2*c^2) : :

X(49843) lies on these lines: {5862, 12154}, {8593, 35750}, {11159, 49795}, {12155, 35691}, {33605, 40672}

X(49843) = perspector (anti-Artzt, 2nd inner-Fermat-Dao-Nhi)


X(49844) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND ANTI-ARTZT

Barycentrics    S*(3*a^4+22*(b^2+c^2)*a^2+3*b^4-14*b^2*c^2+3*c^4)+sqrt(3)*(a^2+b^2+c^2)*(8*a^4-3*(b^2+c^2)*a^2-(b^2-c^2)^2+4*b^2*c^2) : :

X(49844) lies on these lines: {5863, 12155}, {8593, 36331}, {11159, 49794}, {12154, 35695}, {33604, 40671}

X(49844) = perspector (anti-Artzt, 2nd outer-Fermat-Dao-Nhi)


X(49845) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND 1st ANTI-BROCARD

Barycentrics    -6*sqrt(3)*(8*a^8-8*(b^2+c^2)*a^6+3*(b^4+c^4)*a^4+2*(b^6+c^6)*a^2-5*b^8-5*c^8+2*b^2*c^2*(5*b^4-6*b^2*c^2+5*c^4))*(a^2+b^2+c^2)*S+11*a^12-11*(b^2+c^2)*a^10+(106*b^4+153*b^2*c^2+106*c^4)*a^8-2*(b^2+c^2)*(97*b^4+27*b^2*c^2+97*c^4)*a^6+(187*b^8+187*c^8+2*b^2*c^2*(47*b^4+72*b^2*c^2+47*c^4))*a^4-(b^2+c^2)*(119*b^8+119*c^8-2*b^2*c^2*(109*b^4-143*b^2*c^2+109*c^4))*a^2+(b^2-c^2)^2*(20*b^8+20*c^8-b^2*c^2*(43*b^4-36*b^2*c^2+43*c^4)) : :

X(49845) lies on these lines: {5978, 36344}, {5979, 11001}, {7840, 35750}

X(49845) = perspector (1st anti-Brocard, 2nd inner-Fermat-Dao-Nhi)


X(49846) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND 1st ANTI-BROCARD

Barycentrics    6*sqrt(3)*(a^2+b^2+c^2)*(8*a^8-8*(b^2+c^2)*a^6+3*(b^4+c^4)*a^4+2*(b^6+c^6)*a^2-5*b^8-5*c^8+2*b^2*c^2*(5*b^4-6*b^2*c^2+5*c^4))*S+11*a^12-11*(b^2+c^2)*a^10+(106*b^4+153*b^2*c^2+106*c^4)*a^8-2*(b^2+c^2)*(97*b^4+27*b^2*c^2+97*c^4)*a^6+(187*b^8+187*c^8+2*b^2*c^2*(47*b^4+72*b^2*c^2+47*c^4))*a^4-(b^2+c^2)*(119*b^8+119*c^8-2*b^2*c^2*(109*b^4-143*b^2*c^2+109*c^4))*a^2+(20*b^8+20*c^8-b^2*c^2*(43*b^4-36*b^2*c^2+43*c^4))*(b^2-c^2)^2 : :

X(49846) lies on these lines: {5978, 11001}, {5979, 36319}, {7840, 36331}

X(49846) = perspector (1st anti-Brocard, 2nd outer-Fermat-Dao-Nhi)


X(49847) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND ANTI-MCCAY

Barycentrics    2*(3*a^6+13*(b^2+c^2)*a^4-(23*b^4+6*b^2*c^2+23*c^4)*a^2+(3*b^2+c^2)*(b^2+3*c^2)*(b^2+c^2))*S+(29*a^8-44*(b^2+c^2)*a^6+2*(19*b^4+12*b^2*c^2+19*c^4)*a^4-4*(b^2+c^2)*(2*b^4+b^2*c^2+2*c^4)*a^2-7*b^8+2*(14*b^4-17*b^2*c^2+14*c^4)*b^2*c^2-7*c^8)*sqrt(3) : :

X(49847) lies on these lines: {5862, 8595}, {8594, 35691}, {9855, 35750}

X(49847) = perspector (anti-McCay, 2nd inner-Fermat-Dao-Nhi)


X(49848) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND ANTI-MCCAY

Barycentrics    -2*(3*a^6+13*(b^2+c^2)*a^4-(23*b^4+6*b^2*c^2+23*c^4)*a^2+(3*b^2+c^2)*(b^2+3*c^2)*(b^2+c^2))*S+(29*a^8-44*(b^2+c^2)*a^6+2*(19*b^4+12*b^2*c^2+19*c^4)*a^4-4*(b^2+c^2)*(2*b^4+b^2*c^2+2*c^4)*a^2-7*b^8+2*(14*b^4-17*b^2*c^2+14*c^4)*b^2*c^2-7*c^8)*sqrt(3) : :

X(49848) lies on these lines: {5863, 8594}, {8595, 35695}, {9855, 36331}

X(49848) = perspector (anti-McCay, 2nd outer-Fermat-Dao-Nhi)


X(49849) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND ARTZT

Barycentrics    -12*sqrt(3)*(a^2+b^2+c^2)*(4*a^4+(b^2+c^2)*a^2-5*(b^2-c^2)^2)*S+11*a^8-180*(b^2+c^2)*a^6+2*(169*b^4+172*b^2*c^2+169*c^4)*a^4-4*(b^2+c^2)*(63*b^4-86*b^2*c^2+63*c^4)*a^2+(83*b^4-50*b^2*c^2+83*c^4)*(b^2-c^2)^2 : :

X(49849) lies on these lines: {4, 49895}, {381, 49801}, {3845, 49850}, {5862, 9760}, {6054, 35750}, {6114, 33605}, {9749, 36344}, {9750, 11001}, {9762, 35691}, {41106, 49939}, {44219, 49800}

X(49849) = perspector (Artzt, 2nd inner-Fermat-Dao-Nhi)


X(49850) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND ARTZT

Barycentrics    12*sqrt(3)*(a^2+b^2+c^2)*(4*a^4+(b^2+c^2)*a^2-5*(b^2-c^2)^2)*S+11*a^8-180*(b^2+c^2)*a^6+2*(169*b^4+172*b^2*c^2+169*c^4)*a^4-4*(b^2+c^2)*(63*b^4-86*b^2*c^2+63*c^4)*a^2+(83*b^4-50*b^2*c^2+83*c^4)*(b^2-c^2)^2 : :

X(49850) lies on these lines: {4, 49896}, {381, 49800}, {3845, 49849}, {5863, 9762}, {6054, 36331}, {6115, 33604}, {9749, 11001}, {9750, 36319}, {9760, 35695}, {41106, 49940}

X(49850) = perspector (Artzt, 2nd outer-Fermat-Dao-Nhi)


X(49851) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND 1st BROCARD

Barycentrics    -2*sqrt(3)*(13*a^4-38*(b^2+c^2)*a^2-35*b^4-50*b^2*c^2-35*c^4)*S+(83*a^4-58*(b^2+c^2)*a^2-25*(b^2-c^2)^2)*(a^2+b^2+c^2) : :

X(49851) lies on these lines: {599, 35750}, {619, 49877}, {3545, 33410}, {3642, 36344}, {3643, 11001}, {15690, 49897}, {33627, 43229}

X(49851) = perspector (1st Brocard, 2nd inner-Fermat-Dao-Nhi)


X(49852) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND 1st BROCARD

Barycentrics    2*sqrt(3)*(13*a^4-38*(b^2+c^2)*a^2-35*b^4-50*b^2*c^2-35*c^4)*S+(83*a^4-58*(b^2+c^2)*a^2-25*(b^2-c^2)^2)*(a^2+b^2+c^2) : :

X(49852) lies on these lines: {599, 36331}, {618, 49878}, {3545, 33411}, {3642, 11001}, {3643, 36319}, {15690, 49898}, {33626, 43228}

X(49852) = perspector (1st Brocard, 2nd outer-Fermat-Dao-Nhi)


X(49853) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND 1st BROCARD-REFLECTED

Barycentrics    2*sqrt(3)*(a^2+b^2+c^2)*(8*a^4-3*(b^2+c^2)*a^2+10*b^2*c^2)*S+12*a^8+10*(b^2+c^2)*a^6-(20*b^4+57*b^2*c^2+20*c^4)*a^4-2*(b^2+c^2)*(b^4+11*b^2*c^2+c^4)*a^2-5*(b^2-c^2)^2*b^2*c^2 : :

X(49853) lies on these lines: {22689, 36347}

X(49853) = perspector (1st Brocard-reflected, 2nd inner-Fermat-Dao-Nhi)


X(49854) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND 1st BROCARD-REFLECTED

Barycentrics    -2*sqrt(3)*(a^2+b^2+c^2)*(8*a^4-3*(b^2+c^2)*a^2+10*b^2*c^2)*S+12*a^8+10*(b^2+c^2)*a^6-(20*b^4+57*b^2*c^2+20*c^4)*a^4-2*(b^2+c^2)*(b^4+11*b^2*c^2+c^4)*a^2-5*(b^2-c^2)^2*b^2*c^2 : :

X(49854) lies on these lines: {22687, 36345}

X(49854) = perspector (1st Brocard-reflected, 2nd outer-Fermat-Dao-Nhi)


X(49855) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND INNER-FERMAT

Barycentrics    19*a^4+16*(b^2+c^2)*a^2-35*(b^2-c^2)^2-10*sqrt(3)*S*(5*a^2-c^2-b^2) : :
X(49855) = 4*X(33606)-X(33609) = 3*X(33606)-X(49952) = 3*X(33609)-4*X(49952)

X(49855) lies on these lines: {2, 33606}, {14, 33627}, {148, 35750}, {299, 49946}, {533, 33412}, {616, 36368}, {624, 36324}, {628, 33415}, {1992, 49858}, {3104, 41113}, {3545, 16626}, {3845, 36344}, {12817, 35749}, {33459, 35691}, {33561, 49806}, {33611, 36330}, {33625, 37785}, {36327, 49861}, {36329, 49879}

X(49855) = reflection of X(i) in X(j) for these (i, j): (2, 33606), (33609, 2)
X(49855) = perspector (inner-Fermat, 2nd inner-Fermat-Dao-Nhi)
X(49855) = anticomplement of X(49952)


X(49856) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND INNER-FERMAT

Barycentrics    269*a^4-214*(b^2+c^2)*a^2-55*(b^2-c^2)^2+10*sqrt(3)*S*(5*a^2-7*b^2-7*c^2) : :

X(49856) lies on these lines: {2, 49951}, {616, 36346}, {3104, 49876}, {3543, 16626}, {11001, 48655}, {35752, 49866}, {36967, 49807}

X(49856) = perspector (inner-Fermat, 2nd outer-Fermat-Dao-Nhi)
X(49856) = anticomplement of X(49951)


X(49857) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND OUTER-FERMAT

Barycentrics    269*a^4-214*(b^2+c^2)*a^2-55*(b^2-c^2)^2-10*sqrt(3)*S*(5*a^2-7*b^2-7*c^2) : :

X(49857) lies on these lines: {2, 49954}, {617, 36352}, {3105, 49875}, {3543, 16627}, {11001, 48656}, {36330, 49867}, {36968, 49808}

X(49857) = perspector (outer-Fermat, 2nd inner-Fermat-Dao-Nhi)
X(49857) = X(33605)-of-outer-Fermat triangle
X(49857) = anticomplement of X(49954)


X(49858) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND OUTER-FERMAT

Barycentrics    19*a^4+16*(b^2+c^2)*a^2-35*(b^2-c^2)^2+10*sqrt(3)*S*(5*a^2-c^2-b^2) : :
X(49858) = 4*X(33607)-X(33608) = 3*X(33607)-X(49953) = 3*X(33608)-4*X(49953)

X(49858) lies on these lines: {2, 33607}, {13, 33626}, {148, 36331}, {298, 49945}, {532, 33413}, {617, 36366}, {623, 36326}, {627, 33414}, {1992, 49855}, {3105, 41112}, {3545, 16627}, {3845, 36319}, {12816, 36327}, {33458, 35695}, {33560, 49809}, {33610, 35752}, {33623, 37786}, {35749, 49862}, {35751, 49880}, {36767, 49868}

X(49858) = reflection of X(i) in X(j) for these (i, j): (2, 33607), (33608, 2)
X(49858) = perspector (outer-Fermat, 2nd outer-Fermat-Dao-Nhi)
X(49858) = X(12816)-of-outer-Fermat triangle
X(49858) = anticomplement of X(49953)


X(49859) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND 4th FERMAT-DAO

Barycentrics    18*sqrt(3)*S*a^2+4*a^4-17*(b^2+c^2)*a^2+13*(b^2-c^2)^2 : :

X(49859) lies on these lines: {2, 18}, {4, 42977}, {6, 42518}, {14, 11001}, {16, 15640}, {20, 43425}, {62, 41106}, {395, 3830}, {396, 42951}, {398, 15701}, {1656, 42899}, {3090, 49903}, {3091, 43427}, {3411, 3839}, {3524, 42993}, {3534, 42149}, {3845, 42153}, {5055, 42898}, {5066, 18581}, {5334, 43645}, {5339, 15690}, {5469, 35750}, {5862, 22490}, {8703, 11543}, {10109, 40693}, {10646, 42589}, {10653, 12816}, {10654, 15693}, {11489, 15698}, {11540, 22236}, {11812, 16645}, {12100, 42150}, {12101, 22238}, {15682, 16963}, {15695, 16773}, {15697, 42085}, {15705, 41973}, {15709, 42991}, {15716, 43774}, {15722, 43100}, {16242, 49827}, {16530, 35749}, {16809, 49875}, {16967, 42512}, {18582, 42502}, {19107, 33603}, {19708, 41944}, {19709, 42166}, {19710, 42160}, {19711, 43239}, {22237, 42972}, {22511, 36344}, {22572, 35691}, {22604, 36357}, {22633, 36356}, {22690, 36347}, {22891, 36352}, {25161, 36354}, {25167, 36358}, {25168, 36359}, {25169, 36360}, {25170, 36361}, {25214, 36328}, {33417, 43555}, {33699, 42151}, {34755, 42588}, {36329, 47856}, {37641, 41119}, {37835, 42506}, {38071, 42420}, {41021, 41033}, {41091, 41103}, {41100, 43005}, {41101, 42089}, {41121, 42982}, {41127, 41130}, {42104, 42913}, {42105, 43109}, {42106, 49826}, {42132, 42910}, {42141, 43476}, {42142, 43233}, {42436, 42776}, {42495, 42973}, {42504, 42983}, {42521, 49825}, {42627, 49947}, {42628, 43208}, {42916, 43428}, {42934, 43253}, {42935, 43201}, {42952, 42986}, {43194, 46332}, {43196, 46334}, {43245, 43870}, {44020, 49907}, {49570, 49578}

X(49859) = homothetic center (4th Fermat-Dao, 2nd inner-Fermat-Dao-Nhi)
X(49859) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 16268, 49810), (2, 42999, 42976), (2, 49810, 40694), (16, 33606, 49873), (18, 42507, 42532), (395, 41120, 42510), (395, 42503, 3830), (3830, 42503, 41120), (11489, 43482, 43484), (11543, 49906, 41113), (12816, 41122, 42139), (16268, 49904, 2), (16961, 41122, 49812), (16961, 43543, 10653), (18581, 49948, 41112), (33605, 49861, 42631), (37641, 49908, 41119), (37835, 42897, 43542), (41099, 42533, 10653), (41099, 49812, 42533), (41100, 43475, 43465), (41119, 49908, 42111), (41122, 42533, 41099), (41122, 49812, 10653), (42778, 42818, 10654), (43543, 49812, 41122)


X(49860) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND 3rd FERMAT-DAO

Barycentrics    -18*sqrt(3)*S*a^2+4*a^4-17*(b^2+c^2)*a^2+13*(b^2-c^2)^2 : :

X(49860) lies on these lines: {2, 17}, {4, 42976}, {6, 42518}, {13, 11001}, {15, 15640}, {20, 43424}, {61, 41106}, {395, 42950}, {396, 3830}, {397, 15701}, {1656, 42898}, {3090, 49904}, {3091, 43426}, {3412, 3839}, {3524, 42992}, {3534, 42152}, {3845, 42156}, {5055, 42899}, {5066, 18582}, {5335, 43646}, {5340, 15690}, {5470, 36331}, {5863, 22489}, {8703, 11542}, {10109, 40694}, {10645, 42588}, {10653, 15693}, {10654, 12817}, {11488, 15698}, {11540, 22238}, {11812, 16644}, {12100, 42151}, {12101, 22236}, {15682, 16962}, {15695, 16772}, {15697, 42086}, {15705, 41974}, {15709, 42990}, {15716, 43773}, {15722, 43107}, {16241, 49826}, {16529, 36327}, {16808, 49876}, {16966, 42513}, {18581, 42503}, {19106, 33602}, {19708, 41943}, {19709, 42163}, {19710, 42161}, {19711, 43238}, {22235, 42973}, {22510, 36319}, {22571, 35695}, {22602, 36349}, {22631, 36348}, {22688, 36345}, {22846, 36346}, {25151, 36321}, {25157, 36350}, {25158, 36351}, {25159, 36353}, {25160, 36355}, {25217, 36325}, {33416, 43554}, {33699, 42150}, {34754, 42589}, {35730, 35737}, {35751, 47855}, {36763, 36769}, {37640, 41120}, {37832, 42507}, {38071, 42419}, {41020, 41032}, {41100, 42092}, {41101, 43004}, {41122, 42983}, {42103, 49827}, {42104, 43108}, {42105, 42912}, {42129, 42911}, {42139, 43232}, {42140, 43475}, {42435, 42775}, {42494, 42972}, {42505, 42982}, {42520, 49824}, {42627, 43207}, {42628, 49948}, {42917, 43429}, {42934, 43202}, {42935, 43252}, {42953, 42987}, {43193, 46332}, {43195, 46335}, {43244, 43869}, {44019, 49908}, {49569, 49582}

X(49860) = homothetic center (3rd Fermat-Dao, 2nd outer-Fermat-Dao-Nhi)
X(49860) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 16267, 49811), (2, 42998, 42977), (2, 49811, 40693), (15, 33607, 49874), (17, 42506, 42533), (396, 41119, 42511), (396, 42502, 3830), (3830, 42502, 41119), (11488, 43481, 43483), (11542, 49905, 41112), (12817, 41121, 42142), (16267, 49903, 2), (16960, 41121, 49813), (16960, 43542, 10654), (18582, 49947, 41113), (33604, 49862, 42632), (37640, 49907, 41120), (37832, 42896, 43543), (41099, 42532, 10654), (41099, 49813, 42532), (41101, 43476, 43466), (41120, 49907, 42114), (41121, 42532, 41099), (41121, 49813, 10654), (42777, 42817, 10653), (43542, 49813, 41121)


X(49861) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND 8th FERMAT-DAO

Barycentrics    3*sqrt(3)*a^2-7*S : :
X(49861) = 3*X(5365)-7*X(49873)

X(49861) lies on these lines: {2, 6}, {3, 43108}, {4, 16963}, {5, 49825}, {14, 11001}, {16, 12817}, {18, 3545}, {20, 42792}, {30, 5365}, {39, 33614}, {61, 15709}, {62, 5071}, {115, 35750}, {376, 5351}, {381, 5366}, {382, 42514}, {398, 15692}, {547, 42998}, {549, 42989}, {3090, 3411}, {3146, 43202}, {3364, 35736}, {3524, 5352}, {3528, 42993}, {3529, 42972}, {3533, 41943}, {3534, 11543}, {3543, 42153}, {3544, 42636}, {3830, 42120}, {3839, 22238}, {3845, 42127}, {3860, 42134}, {5054, 42999}, {5066, 11486}, {5067, 16267}, {5321, 43333}, {5334, 8703}, {5335, 19709}, {5343, 15681}, {5344, 38071}, {5471, 36331}, {6108, 36344}, {6114, 36320}, {6447, 15765}, {6448, 18585}, {6455, 15764}, {6782, 36318}, {7685, 41031}, {9115, 35749}, {10109, 42129}, {10299, 43427}, {10304, 16773}, {10646, 43494}, {10653, 41106}, {10654, 15698}, {11481, 15697}, {11485, 15713}, {12100, 42975}, {12816, 34755}, {13875, 36356}, {13928, 36357}, {15640, 42503}, {15683, 22237}, {15685, 43417}, {15693, 42121}, {15695, 42816}, {15705, 42147}, {15707, 42925}, {15708, 43239}, {15715, 42150}, {15719, 16242}, {15721, 22236}, {15759, 43198}, {16241, 42516}, {16809, 43475}, {16961, 19708}, {16966, 49811}, {16967, 33607}, {18581, 41099}, {19107, 42515}, {19710, 42115}, {22235, 43236}, {22574, 35691}, {22692, 36347}, {22848, 33617}, {22893, 36352}, {25173, 36354}, {25187, 36358}, {25188, 36359}, {25189, 36360}, {25190, 36361}, {25219, 36328}, {31652, 37172}, {33416, 42976}, {33603, 33606}, {33612, 33624}, {33699, 42125}, {33703, 42908}, {35695, 40672}, {36327, 49855}, {36329, 47858}, {36336, 41640}, {36337, 41642}, {36969, 43292}, {37832, 42513}, {37835, 41112}, {41023, 41033}, {41091, 41095}, {41121, 42910}, {41126, 41130}, {41648, 49577}, {42088, 43541}, {42092, 42532}, {42095, 43771}, {42116, 44580}, {42141, 42519}, {42148, 42776}, {42152, 42520}, {42159, 42938}, {42160, 46333}, {42161, 42801}, {42163, 43769}, {42436, 42921}, {42472, 43101}, {42502, 42982}, {42508, 43465}, {42626, 43870}, {42628, 42974}, {42632, 43482}, {42692, 43478}, {42815, 43246}, {42911, 43004}, {42940, 43772}, {42942, 42983}, {42988, 47599}, {43015, 43463}, {43545, 49903}, {49572, 49578}, {49869, 49871}

X(49861) = X(2)-Ceva conjugate of-X(33615)
X(49861) = X(31)-complementary conjugate of-X(33615)
X(49861) = homothetic center (8th Fermat-Dao, 2nd inner-Fermat-Dao-Nhi)
X(49861) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 6, 49862), (2, 395, 49812), (2, 37785, 5863), (2, 43229, 37640), (2, 49812, 37641), (2, 49906, 11489), (16, 41120, 15682), (16, 49904, 41120), (376, 41113, 42589), (395, 11489, 37641), (395, 49906, 2), (3534, 11543, 49824), (11489, 37640, 16645), (11489, 49812, 2), (15682, 43543, 41120), (16242, 42511, 15719), (16268, 42149, 376), (16645, 43229, 2), (16645, 49948, 49905), (16963, 41122, 42510), (22236, 43100, 15721), (23303, 49947, 2), (36447, 36450, 37641), (36464, 36467, 37641), (37640, 49905, 49813), (40694, 41944, 3524), (41120, 49904, 43543), (41122, 42510, 4), (42139, 42588, 3845), (42631, 49859, 33605), (42818, 42913, 43404), (42913, 43404, 42120), (42977, 49908, 10653), (49905, 49948, 43229)


X(49862) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND 7th FERMAT-DAO

Barycentrics    3*sqrt(3)*a^2+7*S : :
X(49862) = 3*X(5366)-7*X(49874)

X(49862) lies on these lines: {2, 6}, {3, 43109}, {4, 16962}, {5, 49824}, {13, 11001}, {15, 12816}, {17, 3545}, {20, 42791}, {30, 5366}, {39, 33615}, {61, 5071}, {62, 15709}, {115, 36331}, {376, 5352}, {381, 5365}, {382, 42515}, {397, 15692}, {547, 42999}, {549, 42988}, {3090, 3412}, {3146, 43201}, {3390, 35736}, {3524, 5351}, {3528, 42992}, {3529, 42973}, {3533, 41944}, {3534, 11542}, {3543, 42156}, {3544, 42635}, {3830, 42119}, {3839, 22236}, {3845, 42126}, {3860, 42133}, {5054, 42998}, {5066, 11485}, {5067, 16268}, {5318, 43332}, {5334, 19709}, {5335, 8703}, {5343, 38071}, {5344, 15681}, {5472, 35750}, {6109, 36319}, {6115, 36318}, {6447, 18585}, {6448, 15765}, {6456, 15764}, {6783, 36320}, {7684, 41030}, {9112, 36768}, {9117, 36327}, {10109, 42132}, {10299, 43426}, {10304, 16772}, {10645, 43493}, {10653, 15698}, {10654, 41106}, {11480, 15697}, {11486, 15713}, {12100, 42974}, {12817, 34754}, {13876, 36348}, {13929, 36349}, {15640, 42502}, {15683, 22235}, {15685, 43416}, {15693, 42124}, {15695, 42815}, {15705, 42148}, {15707, 42924}, {15708, 43238}, {15715, 42151}, {15719, 16241}, {15721, 22238}, {15759, 43197}, {16242, 42517}, {16808, 43476}, {16960, 19708}, {16966, 33606}, {16967, 49810}, {18582, 41099}, {19106, 42514}, {19710, 42116}, {22237, 43237}, {22573, 35695}, {22691, 36345}, {22847, 36346}, {22892, 33616}, {25178, 36321}, {25183, 36350}, {25184, 36351}, {25185, 36353}, {25186, 36355}, {25220, 36325}, {31652, 37173}, {33417, 42977}, {33602, 33607}, {33613, 33622}, {33699, 42128}, {33703, 42909}, {35691, 40671}, {35731, 35737}, {35749, 49858}, {35751, 47857}, {36338, 41630}, {36339, 41632}, {36764, 36769}, {36767, 49870}, {36970, 43293}, {37832, 41113}, {37835, 42512}, {41022, 41032}, {41122, 42911}, {41638, 49581}, {42087, 43540}, {42089, 42533}, {42098, 43772}, {42115, 44580}, {42140, 42518}, {42147, 42775}, {42149, 42521}, {42160, 42802}, {42161, 46333}, {42162, 42939}, {42166, 43770}, {42435, 42920}, {42473, 43104}, {42503, 42983}, {42509, 43466}, {42625, 43869}, {42627, 42975}, {42631, 43481}, {42693, 43477}, {42816, 43247}, {42910, 43005}, {42941, 43771}, {42943, 42982}, {42989, 47599}, {43014, 43464}, {43544, 49904}, {49571, 49582}

X(49862) = X(2)-Ceva conjugate of-X(33614)
X(49862) = X(31)-complementary conjugate of-X(33614)
X(49862) = homothetic center (7th Fermat-Dao, 2nd outer-Fermat-Dao-Nhi)
X(49862) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 6, 49861), (2, 396, 49813), (2, 37786, 5862), (2, 43228, 37641), (2, 49813, 37640), (2, 49905, 11488), (15, 41119, 15682), (15, 49903, 41119), (376, 41112, 42588), (396, 11488, 37640), (396, 49905, 2), (3534, 11542, 49825), (11488, 37641, 16644), (11488, 49813, 2), (15682, 43542, 41119), (16241, 42510, 15719), (16267, 42152, 376), (16644, 43228, 2), (16644, 49947, 49906), (16962, 41121, 42511), (22238, 43107, 15721), (23302, 49948, 2), (36446, 36449, 37640), (36465, 36468, 37640), (37641, 49906, 49812), (40693, 41943, 3524), (41119, 49903, 43542), (41121, 42511, 4), (42142, 42589, 3845), (42632, 49860, 33604), (42817, 42912, 43403), (42912, 43403, 42119), (42976, 49907, 10654), (49906, 49947, 43228)


X(49863) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND 1st HALF-DIAMONDS-CENTRAL

Barycentrics    (13*a^4-224*(b^2+c^2)*a^2+211*(b^2-c^2)^2)*sqrt(3)+26*S*(23*a^2+5*c^2+5*b^2) : :

X(49863) lies on these lines: {5, 36344}, {14, 49879}, {530, 49814}, {616, 49910}, {5460, 35750}, {5862, 33476}, {6774, 11001}, {15692, 33418}, {15723, 49877}, {22891, 36352}, {33412, 35752}, {33474, 35691}, {33617, 36327}, {35749, 49950}, {36329, 49865}

X(49863) = perspector (2nd inner-Fermat-Dao-Nhi, 1st half-diamonds-central)


X(49864) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND 2nd HALF-DIAMONDS-CENTRAL

Barycentrics    (13*a^4-224*(b^2+c^2)*a^2+211*(b^2-c^2)^2)*sqrt(3)-26*S*(23*a^2+5*c^2+5*b^2) : :

X(49864) lies on these lines: {5, 36319}, {13, 49880}, {531, 49815}, {617, 49909}, {5459, 36331}, {5863, 33477}, {6771, 11001}, {15692, 33419}, {15723, 49878}, {22846, 36346}, {33413, 36330}, {33475, 35695}, {33616, 35749}, {35751, 49868}, {36327, 49949}

X(49864) = perspector (2nd outer-Fermat-Dao-Nhi, 2nd half-diamonds-central)
X(49864) = X(49949)-of-outer-Fermat triangle


X(49865) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND 1st HALF-DIAMONDS

Barycentrics    (377*a^4-484*(b^2+c^2)*a^2+107*(b^2-c^2)^2)*sqrt(3)+78*(a^2+7*c^2+7*b^2)*S : :

X(49865) lies on these lines: {619, 33627}, {11001, 22797}, {15701, 36344}, {15709, 49106}, {33620, 35749}, {36329, 49863}

X(49865) = perspector (2nd inner-Fermat-Dao-Nhi, 1st half-diamonds)


X(49866) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND 1st HALF-DIAMONDS

Barycentrics    91*a^4+142*(b^2+c^2)*a^2-233*(b^2-c^2)^2+26*sqrt(3)*S*(11*a^2-b^2-c^2) : :

X(49866) lies on these lines: {13, 36346}, {5032, 49867}, {11001, 47610}, {15692, 49106}, {22797, 36319}, {35752, 49856}

X(49866) = perspector (2nd outer-Fermat-Dao-Nhi, 1st half-diamonds)


X(49867) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND 2nd HALF-DIAMONDS

Barycentrics    91*a^4+142*(b^2+c^2)*a^2-233*(b^2-c^2)^2-26*sqrt(3)*S*(11*a^2-b^2-c^2) : :

X(49867) lies on these lines: {14, 36352}, {5032, 49866}, {11001, 47611}, {15692, 49105}, {22796, 36344}, {36330, 49857}

X(49867) = perspector (2nd inner-Fermat-Dao-Nhi, 2nd half-diamonds)
X(49867) = X(33617)-of-outer-Fermat triangle


X(49868) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND 2nd HALF-DIAMONDS

Barycentrics    (377*a^4-484*(b^2+c^2)*a^2+107*(b^2-c^2)^2)*sqrt(3)-78*(a^2+7*c^2+7*b^2)*S : :

X(49868) lies on these lines: {618, 33626}, {11001, 22796}, {15701, 36319}, {15709, 49105}, {33621, 36327}, {35751, 49864}, {36767, 49858}

X(49868) = perspector (2nd outer-Fermat-Dao-Nhi, 2nd half-diamonds)
X(49868) = X(33621)-of-outer-Fermat triangle


X(49869) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND 1st HALF-SQUARES

Barycentrics    3*(32*(b^2+c^2)*S-39*a^4+48*(b^2+c^2)*a^2-9*(b^2-c^2)^2)*sqrt(3)-16*(a^2+10*b^2+10*c^2)*S+205*a^4-248*(b^2+c^2)*a^2+43*(b^2-c^2)^2 : :

X(49869) lies on these lines: {2, 49970}, {33442, 36356}, {49861, 49871}

X(49869) = perspector (2nd inner-Fermat-Dao-Nhi, 1st half-squares)
X(49869) = anticomplement of X(49970)


X(49870) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND 1st HALF-SQUARES

Barycentrics    -3*(32*(b^2+c^2)*S-39*a^4+48*(b^2+c^2)*a^2-9*(b^2-c^2)^2)*sqrt(3)-16*(a^2+10*b^2+10*c^2)*S+205*a^4-248*(b^2+c^2)*a^2+43*(b^2-c^2)^2 : :

X(49870) lies on these lines: {2, 49969}, {33440, 36348}, {36767, 49862}

X(49870) = perspector (2nd outer-Fermat-Dao-Nhi, 1st half-squares)
X(49870) = anticomplement of X(49969)


X(49871) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND 2nd HALF-SQUARES

Barycentrics    -3*(-32*(b^2+c^2)*S-39*a^4+48*(b^2+c^2)*a^2-9*(b^2-c^2)^2)*sqrt(3)+16*(a^2+10*b^2+10*c^2)*S+205*a^4-248*(b^2+c^2)*a^2+43*(b^2-c^2)^2 : :

X(49871) lies on these lines: {2, 49968}, {33443, 36357}, {49861, 49869}

X(49871) = perspector (2nd inner-Fermat-Dao-Nhi, 2nd half-squares)
X(49871) = anticomplement of X(49968)


X(49872) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND 2nd HALF-SQUARES

Barycentrics    3*(-32*(b^2+c^2)*S-39*a^4+48*(b^2+c^2)*a^2-9*(b^2-c^2)^2)*sqrt(3)+16*(a^2+10*b^2+10*c^2)*S+205*a^4-248*(b^2+c^2)*a^2+43*(b^2-c^2)^2 : :

X(49872) lies on these lines: {2, 49967}, {33441, 36349}, {36767, 49862}

X(49872) = perspector (2nd outer-Fermat-Dao-Nhi, 2nd half-squares)
X(49872) = anticomplement of X(49967)


X(49873) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND 4th ISODYNAMIC-DAO

Barycentrics    -12*S*sqrt(3)*a^2+5*a^4+8*(b^2+c^2)*a^2-13*(b^2-c^2)^2 : :
X(49873) = 3*X(5365)+4*X(49861)

X(49873) lies on these lines: {2, 14}, {3, 42589}, {4, 33605}, {5, 49813}, {6, 14226}, {13, 42983}, {16, 15640}, {18, 10304}, {20, 42972}, {30, 5365}, {115, 36344}, {376, 5343}, {381, 42776}, {382, 43202}, {395, 15682}, {397, 33602}, {398, 5071}, {546, 43208}, {549, 43634}, {1503, 41033}, {3091, 41119}, {3146, 16963}, {3524, 5339}, {3534, 11489}, {3543, 12817}, {3545, 42156}, {3830, 11543}, {3832, 42993}, {3839, 5344}, {3845, 37641}, {5054, 43108}, {5055, 42495}, {5066, 42139}, {5068, 16267}, {5321, 11001}, {5335, 41099}, {5340, 42899}, {5349, 43502}, {5471, 36319}, {5480, 41032}, {5862, 31694}, {6110, 49840}, {6199, 36464}, {6395, 36447}, {6782, 35749}, {7486, 41943}, {8703, 42130}, {10109, 11488}, {10646, 43032}, {10653, 42507}, {11481, 42519}, {11486, 12101}, {11540, 42116}, {11812, 42129}, {12816, 42103}, {14892, 42988}, {15022, 42991}, {15683, 42149}, {15685, 42818}, {15687, 42989}, {15690, 42126}, {15692, 16964}, {15693, 42119}, {15695, 42121}, {15698, 42154}, {15701, 42117}, {15702, 42599}, {15705, 42157}, {15708, 42953}, {15709, 42147}, {15710, 43239}, {15711, 42628}, {15715, 43100}, {15719, 23303}, {15721, 42150}, {16242, 43466}, {16645, 19708}, {16809, 41112}, {16961, 46334}, {19709, 37640}, {19710, 42140}, {22235, 42481}, {22856, 36346}, {31696, 35691}, {31698, 36357}, {31700, 36356}, {31702, 36347}, {31704, 36352}, {31706, 33627}, {31708, 36354}, {31710, 35750}, {31712, 36358}, {31714, 36359}, {31716, 36361}, {31718, 36360}, {31720, 36328}, {33459, 34505}, {33699, 42120}, {34200, 43770}, {35403, 42924}, {35404, 42514}, {35737, 42239}, {36446, 42639}, {36465, 42640}, {36970, 49904}, {41091, 41124}, {41100, 49810}, {41944, 42160}, {42086, 42977}, {42088, 43333}, {42089, 42632}, {42091, 43641}, {42093, 42778}, {42101, 43481}, {42105, 43476}, {42114, 49903}, {42127, 42517}, {42155, 42987}, {42161, 43475}, {42433, 43017}, {42472, 43246}, {42506, 42918}, {42512, 43335}, {42513, 42529}, {42532, 42911}, {42533, 43011}, {42626, 43464}, {42687, 43305}, {42791, 43482}, {42817, 43110}, {42913, 43329}, {42934, 43479}, {42963, 43416}, {43015, 43364}, {43242, 43478}, {43480, 43632}, {49578, 49597}

X(49873) = homothetic center (2nd inner-Fermat-Dao-Nhi, 4th isodynamic-Dao)
X(49873) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 14, 49824), (2, 5334, 49876), (2, 41113, 49827), (2, 41120, 43404), (2, 49824, 5334), (4, 49948, 49875), (6, 41106, 49874), (14, 41120, 2), (14, 41122, 41113), (14, 43404, 5334), (16, 33606, 49859), (3543, 22237, 16268), (3830, 11543, 49812), (3830, 43109, 42141), (3845, 37641, 49826), (3845, 49826, 42134), (10654, 49908, 2), (11001, 33603, 5321), (12817, 16268, 42510), (12817, 42510, 3543), (16268, 42159, 3543), (18581, 41108, 2), (37835, 42511, 2), (41099, 43229, 5335), (41113, 41120, 41122), (41113, 41122, 2), (41113, 49827, 5334), (42139, 42975, 43403), (42159, 42510, 12817), (43100, 43194, 15715), (43404, 49824, 2), (49824, 49827, 41113)


X(49874) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND 3rd ISODYNAMIC-DAO

Barycentrics    12*S*sqrt(3)*a^2+5*a^4+8*(b^2+c^2)*a^2-13*(b^2-c^2)^2 : :
X(49874) = 3*X(5366)+4*X(49862)

X(49874) lies on these lines: {2, 13}, {3, 42588}, {4, 33604}, {5, 49812}, {6, 14226}, {14, 42982}, {15, 15640}, {17, 10304}, {20, 42973}, {30, 5366}, {115, 36319}, {376, 5344}, {381, 42775}, {382, 43201}, {396, 15682}, {397, 5071}, {398, 33603}, {546, 43207}, {549, 43635}, {1503, 41032}, {3091, 41120}, {3146, 16962}, {3524, 5340}, {3534, 11488}, {3543, 12816}, {3545, 42153}, {3830, 11542}, {3832, 42992}, {3839, 5343}, {3845, 37640}, {5054, 43109}, {5055, 42494}, {5066, 42142}, {5068, 16268}, {5318, 11001}, {5334, 41099}, {5339, 42898}, {5350, 43501}, {5472, 36344}, {5480, 41033}, {5863, 31693}, {6111, 41132}, {6199, 36446}, {6395, 36465}, {6783, 36327}, {7486, 41944}, {8703, 42131}, {10109, 11489}, {10645, 43033}, {10654, 42506}, {11480, 42518}, {11485, 12101}, {11540, 42115}, {11812, 42132}, {12817, 42106}, {14892, 42989}, {15022, 42990}, {15683, 42152}, {15685, 42817}, {15687, 42988}, {15690, 42127}, {15692, 16965}, {15693, 42120}, {15695, 42124}, {15698, 42155}, {15701, 42118}, {15702, 42598}, {15705, 42158}, {15708, 42952}, {15709, 42148}, {15710, 43238}, {15711, 42627}, {15715, 43107}, {15719, 23302}, {15721, 42151}, {16241, 43465}, {16644, 19708}, {16808, 41113}, {16960, 46335}, {19709, 37641}, {19710, 42141}, {22237, 42480}, {22900, 36352}, {31695, 35695}, {31697, 36349}, {31699, 36348}, {31701, 36345}, {31703, 36346}, {31705, 33626}, {31707, 36321}, {31709, 36331}, {31711, 36350}, {31713, 36351}, {31715, 36353}, {31717, 36355}, {31719, 36325}, {33458, 34505}, {33699, 42119}, {34200, 43769}, {35403, 42925}, {35404, 42515}, {35737, 35740}, {36447, 42640}, {36464, 42639}, {36969, 49903}, {41101, 49811}, {41943, 42161}, {42085, 42976}, {42087, 43332}, {42090, 43642}, {42092, 42631}, {42094, 42777}, {42102, 43482}, {42104, 43475}, {42111, 49904}, {42126, 42516}, {42154, 42986}, {42160, 43476}, {42434, 43016}, {42473, 43247}, {42507, 42919}, {42512, 42528}, {42513, 43334}, {42532, 43010}, {42533, 42910}, {42625, 43463}, {42686, 43304}, {42792, 43481}, {42818, 43111}, {42912, 43328}, {42935, 43480}, {42962, 43417}, {43014, 43365}, {43243, 43477}, {43479, 43633}, {49582, 49596}

X(49874) = homothetic center (2nd outer-Fermat-Dao-Nhi, 3rd isodynamic-Dao)
X(49874) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 13, 49825), (2, 5335, 49875), (2, 41112, 49826), (2, 41119, 43403), (2, 49825, 5335), (4, 49947, 49876), (6, 41106, 49873), (13, 41119, 2), (13, 41121, 41112), (13, 43403, 5335), (15, 33607, 49860), (3543, 22235, 16267), (3830, 11542, 49813), (3830, 43108, 42140), (3845, 37640, 49827), (3845, 49827, 42133), (10653, 49907, 2), (11001, 33602, 5318), (12816, 16267, 42511), (12816, 42511, 3543), (16267, 42162, 3543), (18582, 41107, 2), (37832, 42510, 2), (41099, 43228, 5334), (41112, 41119, 41121), (41112, 41121, 2), (41112, 49826, 5335), (42142, 42974, 43404), (42162, 42511, 12816), (43107, 43193, 15715), (43403, 49825, 2), (49825, 49826, 41112)


X(49875) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND 2nd LEMOINE-DAO

Barycentrics    12*S*sqrt(3)*a^2+13*a^4-8*(b^2+c^2)*a^2-5*(b^2-c^2)^2 : :
X(49875) = 4*X(42589)-9*X(42999) = 5*X(42589)+9*X(43769) = 2*X(42589)-3*X(49827) = 5*X(42999)+4*X(43769) = 3*X(42999)-2*X(49827) = 6*X(43769)+5*X(49827)

X(49875) lies on these lines: {2, 13}, {3, 49813}, {4, 33605}, {6, 11001}, {14, 43397}, {17, 15721}, {20, 41101}, {30, 42589}, {62, 3543}, {299, 32896}, {376, 22236}, {381, 5366}, {395, 41099}, {396, 15698}, {397, 3524}, {631, 42518}, {1152, 35737}, {3091, 16963}, {3105, 49857}, {3146, 43253}, {3522, 42990}, {3523, 16267}, {3534, 42120}, {3545, 5344}, {3830, 37641}, {3839, 16965}, {3845, 11486}, {3853, 43202}, {5056, 43424}, {5066, 11489}, {5071, 5340}, {5237, 15708}, {5318, 41106}, {5334, 15682}, {5351, 43252}, {5352, 10304}, {5365, 42165}, {5862, 11296}, {6773, 39838}, {6775, 36320}, {8703, 37640}, {9541, 36449}, {10109, 42142}, {10303, 33607}, {10646, 42506}, {10654, 42429}, {11480, 43304}, {11481, 15719}, {11485, 15690}, {11488, 15693}, {11540, 42132}, {11542, 15701}, {11543, 42517}, {11812, 42115}, {12100, 42974}, {12101, 42127}, {12816, 18581}, {12817, 40694}, {14893, 42989}, {15640, 41108}, {15681, 43108}, {15683, 42158}, {15685, 42420}, {15686, 43634}, {15692, 40693}, {15695, 42123}, {15697, 36968}, {15702, 36843}, {15703, 42494}, {15705, 42152}, {15709, 42156}, {15713, 42922}, {15715, 16772}, {15716, 43003}, {15717, 41943}, {15722, 42817}, {16241, 41972}, {16268, 42161}, {16809, 49859}, {16962, 43495}, {17504, 42988}, {17578, 42972}, {19106, 43474}, {19708, 42943}, {19709, 42913}, {19710, 42119}, {19711, 42496}, {22513, 36344}, {22580, 35691}, {22612, 36357}, {22641, 36356}, {22708, 36347}, {22862, 33627}, {22907, 36352}, {23023, 36354}, {23024, 36358}, {23025, 36359}, {23026, 36360}, {23027, 36361}, {23028, 36328}, {23046, 42495}, {33603, 42093}, {33699, 42141}, {34200, 43002}, {34755, 49908}, {35381, 43328}, {35418, 42435}, {36318, 41745}, {36329, 47864}, {36969, 41120}, {36970, 42521}, {37835, 43540}, {41033, 41039}, {41091, 41097}, {41116, 41130}, {41944, 42162}, {41990, 42917}, {42087, 43305}, {42090, 43646}, {42091, 42632}, {42092, 49903}, {42094, 43543}, {42098, 42956}, {42100, 43006}, {42102, 42503}, {42105, 43541}, {42121, 42985}, {42131, 42416}, {42147, 46333}, {42149, 42973}, {42160, 43008}, {42419, 42584}, {42436, 42965}, {42479, 42923}, {42480, 44017}, {42505, 42933}, {42528, 42976}, {42613, 42994}, {42625, 42791}, {42777, 43463}, {42778, 43501}, {42889, 43772}, {42899, 43502}, {42941, 43780}, {42961, 43368}, {42991, 49140}, {43020, 49904}, {43028, 43494}, {43104, 43464}, {43399, 43478}, {49578, 49605}

X(49875) = homothetic center (2nd inner-Fermat-Dao-Nhi, 2nd Lemoine-Dao)
X(49875) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 5335, 49874), (2, 10653, 49826), (2, 41107, 49825), (2, 41112, 43403), (2, 49826, 5335), (4, 49948, 49873), (6, 11001, 49876), (16, 41107, 49907), (16, 41112, 2), (397, 42792, 49905), (3534, 43109, 42120), (3830, 37641, 49824), (3830, 42118, 42588), (3830, 49824, 42133), (3845, 11486, 49812), (3845, 49812, 43404), (5318, 49906, 41106), (10653, 41100, 2), (10653, 42510, 41107), (12100, 42974, 49862), (15682, 43229, 5334), (36968, 42511, 15697), (37641, 42588, 3830), (41100, 41107, 42510), (41107, 42510, 2), (41107, 49825, 5335), (41107, 49907, 41112), (41108, 42086, 15640), (42155, 43229, 15682), (42417, 42418, 42508), (42792, 49905, 3524), (42943, 49947, 19708), (43008, 43485, 42160), (49825, 49826, 41107)


X(49876) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND 1st LEMOINE-DAO

Barycentrics    -12*S*sqrt(3)*a^2+13*a^4-8*(b^2+c^2)*a^2-5*(b^2-c^2)^2 : :
X(49876) = 4*X(42588)-9*X(42998) = 5*X(42588)+9*X(43770) = 2*X(42588)-3*X(49826) = 5*X(42998)+4*X(43770) = 3*X(42998)-2*X(49826) = 6*X(43770)+5*X(49826)

X(49876) lies on these lines: {2, 14}, {3, 49812}, {4, 33604}, {6, 11001}, {13, 43398}, {18, 15721}, {20, 41100}, {30, 42588}, {61, 3543}, {298, 32896}, {376, 22238}, {381, 5365}, {395, 15698}, {396, 41099}, {398, 3524}, {631, 42519}, {1151, 35737}, {3091, 16962}, {3104, 49856}, {3146, 43252}, {3522, 42991}, {3523, 16268}, {3534, 42119}, {3545, 5343}, {3830, 37640}, {3839, 16964}, {3845, 11485}, {3853, 43201}, {5056, 43425}, {5066, 11488}, {5071, 5339}, {5238, 15708}, {5321, 41106}, {5335, 15682}, {5351, 10304}, {5352, 43253}, {5366, 42164}, {5863, 11295}, {6770, 39838}, {6772, 36318}, {8703, 37641}, {9541, 36467}, {10109, 42139}, {10303, 33606}, {10645, 42507}, {10653, 42430}, {11480, 15719}, {11481, 43305}, {11486, 15690}, {11489, 15693}, {11540, 42129}, {11542, 42516}, {11543, 15701}, {11812, 42116}, {12100, 42975}, {12101, 42126}, {12816, 40693}, {12817, 18582}, {14893, 42988}, {15640, 41107}, {15681, 43109}, {15683, 42157}, {15685, 42419}, {15686, 43635}, {15692, 40694}, {15695, 42122}, {15697, 36967}, {15702, 36836}, {15703, 42495}, {15705, 42149}, {15709, 42153}, {15713, 42923}, {15715, 16773}, {15716, 43002}, {15717, 41944}, {15722, 42818}, {16242, 41971}, {16267, 42160}, {16808, 49860}, {16963, 43496}, {17504, 42989}, {17578, 42973}, {19107, 43473}, {19708, 42942}, {19709, 42912}, {19710, 42120}, {19711, 42497}, {22512, 36319}, {22579, 35695}, {22611, 36349}, {22640, 36348}, {22707, 36345}, {22861, 36346}, {22906, 33626}, {23017, 36321}, {23018, 36350}, {23019, 36351}, {23020, 36353}, {23021, 36355}, {23022, 36325}, {23046, 42494}, {33602, 42094}, {33699, 42140}, {34200, 43003}, {34754, 49907}, {35381, 43329}, {35418, 42436}, {35751, 47863}, {36320, 41746}, {36769, 36772}, {36969, 42520}, {36970, 41119}, {37832, 43541}, {41032, 41038}, {41943, 42159}, {41990, 42916}, {42088, 43304}, {42089, 49904}, {42090, 42631}, {42091, 43645}, {42093, 43542}, {42095, 42957}, {42099, 43007}, {42101, 42502}, {42104, 43540}, {42124, 42984}, {42130, 42415}, {42148, 46333}, {42152, 42972}, {42161, 43009}, {42420, 42585}, {42435, 42964}, {42478, 42922}, {42481, 44018}, {42504, 42932}, {42529, 42977}, {42612, 42995}, {42626, 42792}, {42777, 43502}, {42778, 43464}, {42888, 43771}, {42898, 43501}, {42940, 43779}, {42960, 43369}, {42990, 49140}, {43021, 49903}, {43029, 43493}, {43101, 43463}, {43400, 43477}, {49582, 49604}

X(49876) = homothetic center (2nd outer-Fermat-Dao-Nhi, 1st Lemoine-Dao)
X(49876) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 5334, 49873), (2, 10654, 49827), (2, 41108, 49824), (2, 41113, 43404), (2, 49827, 5334), (4, 49947, 49874), (6, 11001, 49875), (15, 41108, 49908), (15, 41113, 2), (398, 42791, 49906), (3534, 43108, 42119), (3830, 37640, 49825), (3830, 42117, 42589), (3830, 49825, 42134), (3845, 11485, 49813), (3845, 49813, 43403), (5321, 49905, 41106), (10654, 41101, 2), (10654, 42511, 41108), (12100, 42975, 49861), (15682, 43228, 5335), (36967, 42510, 15697), (37640, 42589, 3830), (41101, 41108, 42511), (41107, 42085, 15640), (41108, 42511, 2), (41108, 49824, 5334), (41108, 49908, 41113), (42154, 43228, 15682), (42417, 42418, 42509), (42791, 49906, 3524), (42942, 49948, 19708), (43009, 43486, 42161), (49824, 49827, 41108)


X(49877) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND MCCAY

Barycentrics    2*sqrt(3)*(133*a^4-158*(b^2+c^2)*a^2+25*(b^2-c^2)^2)*S+37*a^6-145*(b^2+c^2)*a^4+11*(13*b^4+6*b^2*c^2+13*c^4)*a^2-35*(b^4-c^4)*(b^2-c^2) : :

X(49877) lies on these lines: {3, 35750}, {547, 49879}, {619, 49851}, {3845, 33611}, {5862, 13084}, {6771, 49828}, {11812, 33627}, {13083, 35691}, {15702, 33418}, {15723, 49863}, {19711, 49919}, {33605, 42511}

X(49877) = perspector (2nd inner-Fermat-Dao-Nhi, McCay)


X(49878) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND MCCAY

Barycentrics    -2*sqrt(3)*(133*a^4-158*(b^2+c^2)*a^2+25*(b^2-c^2)^2)*S+37*a^6-145*(b^2+c^2)*a^4+11*(13*b^4+6*b^2*c^2+13*c^4)*a^2-35*(b^4-c^4)*(b^2-c^2) : :

X(49878) lies on these lines: {3, 36331}, {547, 49880}, {618, 49852}, {3845, 33610}, {5863, 13083}, {6774, 49829}, {11812, 33626}, {13084, 35695}, {15702, 33419}, {15723, 49864}, {19711, 49920}, {33604, 42510}

X(49878) = perspector (2nd outer-Fermat-Dao-Nhi, McCay)


X(49879) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND OUTER-NAPOLEON

Barycentrics    (121*a^4-116*(b^2+c^2)*a^2-5*(b^2-c^2)^2)*sqrt(3)-10*S*(5*a^2-13*b^2-13*c^2) : :

X(49879) lies on these lines: {2, 43500}, {3, 36344}, {14, 49863}, {530, 49830}, {547, 49877}, {616, 49922}, {628, 35752}, {5464, 35750}, {5613, 11001}, {5862, 9886}, {9763, 35691}, {14144, 36352}, {33605, 36327}, {33627, 47867}, {35749, 49962}, {36329, 49855}

X(49879) = perspector (2nd inner-Fermat-Dao-Nhi, outer-Napoleon)
X(49879) = X(49863)-of-outer-Fermat triangle
X(49879) = anticomplement of X(49950)


X(49880) = HOMOTHETIC CENTER OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND INNER-NAPOLEON

Barycentrics    (121*a^4-116*(b^2+c^2)*a^2-5*(b^2-c^2)^2)*sqrt(3)+10*S*(5*a^2-13*b^2-13*c^2) : :

X(49880) lies on these lines: {2, 43499}, {3, 36319}, {13, 49864}, {531, 49831}, {547, 49878}, {617, 49921}, {627, 36330}, {5463, 36331}, {5617, 11001}, {5863, 9885}, {9761, 35695}, {14145, 36346}, {33604, 35749}, {33610, 36768}, {33626, 36769}, {35751, 49858}, {36327, 49961}

X(49880) = perspector (2nd outer-Fermat-Dao-Nhi, inner-Napoleon)
X(49880) = X(49961)-of-outer-Fermat triangle
X(49880) = anticomplement of X(49949)


X(49881) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND 1st NEUBERG

Barycentrics    6*sqrt(3)*(8*a^4+5*(b^2+c^2)*a^2-13*b^4-16*b^2*c^2-13*c^4)*S*a^2+36*a^8-142*(b^2+c^2)*a^6+(122*b^4+21*b^2*c^2+122*c^4)*a^4-8*(b^2+c^2)*(2*b^4-17*b^2*c^2+2*c^4)*a^2-25*(b^2-c^2)^2*b^2*c^2 : :

X(49881) lies on these lines: {6295, 36358}, {14830, 35750}, {33389, 36347}

X(49881) = perspector (2nd inner-Fermat-Dao-Nhi, 1st Neuberg)


X(49882) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND 1st NEUBERG

Barycentrics    -6*sqrt(3)*(8*a^4+5*(b^2+c^2)*a^2-13*b^4-16*b^2*c^2-13*c^4)*S*a^2+36*a^8-142*(b^2+c^2)*a^6+(122*b^4+21*b^2*c^2+122*c^4)*a^4-8*(b^2+c^2)*(2*b^4-17*b^2*c^2+2*c^4)*a^2-25*(b^2-c^2)^2*b^2*c^2 : :

X(49882) lies on these lines: {6582, 36350}, {14830, 36331}, {33388, 36345}

X(49882) = perspector (2nd outer-Fermat-Dao-Nhi, 1st Neuberg)


X(49883) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND 2nd NEUBERG

Barycentrics    -6*sqrt(3)*(8*a^6-(3*b^4-4*b^2*c^2+3*c^4)*a^2-5*(b^4-c^4)*(b^2-c^2))*S+11*a^8-97*(b^2+c^2)*a^6+(127*b^4+131*b^2*c^2+127*c^4)*a^4-(b^2+c^2)*(61*b^4-66*b^2*c^2+61*c^4)*a^2+5*(4*b^4+3*b^2*c^2+4*c^4)*(b^2-c^2)^2 : :

X(49883) lies on these lines: {6299, 36359}, {35750, 48657}, {36352, 36362}

X(49883) = perspector (2nd inner-Fermat-Dao-Nhi, 2nd Neuberg)


X(49884) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND 2nd NEUBERG

Barycentrics    6*sqrt(3)*(8*a^6-(3*b^4-4*b^2*c^2+3*c^4)*a^2-5*(b^4-c^4)*(b^2-c^2))*S+11*a^8-97*(b^2+c^2)*a^6+(127*b^4+131*b^2*c^2+127*c^4)*a^4-(b^2+c^2)*(61*b^4-66*b^2*c^2+61*c^4)*a^2+5*(4*b^4+3*b^2*c^2+4*c^4)*(b^2-c^2)^2 : :

X(49884) lies on these lines: {6298, 36351}, {36331, 48657}, {36346, 36363}

X(49884) = perspector (2nd outer-Fermat-Dao-Nhi, 2nd Neuberg)


X(49885) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND INNER-VECTEN

Barycentrics    -3*(-10*(b^2+c^2)*S+16*a^4-11*(b^2+c^2)*a^2-5*(b^2-c^2)^2)*sqrt(3)+10*(5*a^2-4*b^2-4*c^2)*S+86*a^4-91*(b^2+c^2)*a^2+5*(b^2-c^2)^2 : :

X(49885) lies on these lines: {6303, 36357}

X(49885) = perspector (2nd inner-Fermat-Dao-Nhi, inner-Vecten)


X(49886) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND INNER-VECTEN

Barycentrics    3*(-10*(b^2+c^2)*S+16*a^4-11*(b^2+c^2)*a^2-5*(b^2-c^2)^2)*sqrt(3)+10*(5*a^2-4*b^2-4*c^2)*S+86*a^4-91*(b^2+c^2)*a^2+5*(b^2-c^2)^2 : :

X(49886) lies on these lines: {6302, 36349}

X(49886) = perspector (2nd outer-Fermat-Dao-Nhi, inner-Vecten)


X(49887) = PERSPECTOR OF THESE TRIANGLES: 2nd INNER-FERMAT-DAO-NHI AND OUTER-VECTEN

Barycentrics    3*(10*(b^2+c^2)*S+16*a^4-11*(b^2+c^2)*a^2-5*(b^2-c^2)^2)*sqrt(3)-10*(5*a^2-4*b^2-4*c^2)*S+86*a^4-91*(b^2+c^2)*a^2+5*(b^2-c^2)^2 : :

X(49887) lies on these lines: {6307, 36356}

X(49887) = perspector (2nd inner-Fermat-Dao-Nhi, outer-Vecten)


X(49888) = PERSPECTOR OF THESE TRIANGLES: 2nd OUTER-FERMAT-DAO-NHI AND OUTER-VECTEN

Barycentrics    -3*(10*(b^2+c^2)*S+16*a^4-11*(b^2+c^2)*a^2-5*(b^2-c^2)^2)*sqrt(3)-10*(5*a^2-4*b^2-4*c^2)*S+86*a^4-91*(b^2+c^2)*a^2+5*(b^2-c^2)^2 : :

X(49888) lies on these lines: {6306, 36348}

X(49888) = perspector (2nd outer-Fermat-Dao-Nhi, outer-Vecten)


X(49889) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND ANTI-ARTZT

Barycentrics    sqrt(3)*(a^2+b^2+c^2)*(9*a^4-5*(b^2+c^2)*a^2+4*b^2*c^2)-2*S*(7*a^4-15*(b^2+c^2)*a^2-2*(b^2-c^2)^2+8*b^2*c^2) : :

X(49889) lies on these lines: {2, 33383}, {5859, 12155}, {8593, 36329}, {11159, 49934}, {12154, 35692}, {33607, 40671}

X(49889) = perspector (anti-Artzt, 3rd inner-Fermat-Dao-Nhi)


X(49890) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND ANTI-ARTZT

Barycentrics    2*S*(7*a^4-15*(b^2+c^2)*a^2-2*(b^2-c^2)^2+8*b^2*c^2)+sqrt(3)*(a^2+b^2+c^2)*(9*a^4-5*(b^2+c^2)*a^2+4*b^2*c^2) : :

X(49890) lies on these lines: {2, 33382}, {5858, 12154}, {8593, 35751}, {11159, 49933}, {12155, 35696}, {33606, 40672}

X(49890) = perspector (anti-Artzt, 3rd outer-Fermat-Dao-Nhi)


X(49891) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND 1st ANTI-BROCARD

Barycentrics    6*sqrt(3)*(a^2+b^2+c^2)*(5*a^8-5*(b^2+c^2)*a^6+3*(b^4+c^4)*a^4-(b^6+c^6)*a^2-2*b^8-2*c^8+b^2*c^2*(4*b^4-3*b^2*c^2+4*c^4))*S+a^12-(b^2+c^2)*a^10+2*(31*b^4+54*b^2*c^2+31*c^4)*a^8-(b^2+c^2)*(106*b^4+27*b^2*c^2+106*c^4)*a^6+(89*b^8+89*c^8+5*b^2*c^2*(4*b^4+9*b^2*c^2+4*c^4))*a^4-(b^2+c^2)*(55*b^8+55*c^8-b^2*c^2*(109*b^4-116*b^2*c^2+109*c^4))*a^2+(10*b^8+10*c^8-b^2*c^2*(26*b^4-9*b^2*c^2+26*c^4))*(b^2-c^2)^2 : :

X(49891) lies on these lines: {2, 16650}, {3534, 5978}, {5979, 36362}, {7840, 36329}

X(49891) = perspector (1st anti-Brocard, 3rd inner-Fermat-Dao-Nhi)


X(49892) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND 1st ANTI-BROCARD

Barycentrics    -6*sqrt(3)*(a^2+b^2+c^2)*(5*a^8-5*(b^2+c^2)*a^6+3*(b^4+c^4)*a^4-(b^6+c^6)*a^2-2*b^8-2*c^8+b^2*c^2*(4*b^4-3*b^2*c^2+4*c^4))*S+a^12-(b^2+c^2)*a^10+2*(31*b^4+54*b^2*c^2+31*c^4)*a^8-(b^2+c^2)*(106*b^4+27*b^2*c^2+106*c^4)*a^6+(89*b^8+89*c^8+5*b^2*c^2*(4*b^4+9*b^2*c^2+4*c^4))*a^4-(b^2+c^2)*(55*b^8+55*c^8-b^2*c^2*(109*b^4-116*b^2*c^2+109*c^4))*a^2+(b^2-c^2)^2*(10*b^8+10*c^8-b^2*c^2*(26*b^4-9*b^2*c^2+26*c^4)) : :

X(49892) lies on these lines: {2, 16651}, {3534, 5979}, {5978, 36363}, {7840, 35751}

X(49892) = perspector (1st anti-Brocard, 3rd outer-Fermat-Dao-Nhi)


X(49893) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND ANTI-MCCAY

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

X(49893) lies on these lines: {2, 16648}, {5859, 8594}, {8595, 35692}, {9855, 36329}, {16529, 36366}, {35955, 49921}

X(49893) = perspector (anti-McCay, 3rd inner-Fermat-Dao-Nhi)


X(49894) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND ANTI-MCCAY

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

X(49894) lies on these lines: {2, 16649}, {5858, 8595}, {8594, 35696}, {9855, 35751}, {16530, 36368}, {35955, 49922}

X(49894) = perspector (anti-McCay, 3rd outer-Fermat-Dao-Nhi)


X(49895) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND ARTZT

Barycentrics    6*sqrt(3)*(a^2+b^2+c^2)*(5*a^4-(b^2+c^2)*a^2-4*(b^2-c^2)^2)*S+a^8-99*(b^2+c^2)*a^6+(169*b^4+154*b^2*c^2+169*c^4)*a^4-(b^2+c^2)*(117*b^4-154*b^2*c^2+117*c^4)*a^2+2*(23*b^4-8*b^2*c^2+23*c^4)*(b^2-c^2)^2 : :

X(49895) lies on these lines: {2, 33385}, {4, 49849}, {381, 49940}, {3534, 9749}, {3830, 49896}, {3845, 9760}, {5859, 9762}, {6054, 36329}, {6115, 33607}, {9750, 36362}, {10109, 33407}, {15701, 49897}, {41099, 49800}

X(49895) = perspector (Artzt, 3rd inner-Fermat-Dao-Nhi)


X(49896) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND ARTZT

Barycentrics    -6*sqrt(3)*(a^2+b^2+c^2)*(5*a^4-(b^2+c^2)*a^2-4*(b^2-c^2)^2)*S+a^8-99*(b^2+c^2)*a^6+(169*b^4+154*b^2*c^2+169*c^4)*a^4-(b^2+c^2)*(117*b^4-154*b^2*c^2+117*c^4)*a^2+2*(23*b^4-8*b^2*c^2+23*c^4)*(b^2-c^2)^2 : :

X(49896) lies on these lines: {2, 33384}, {4, 49850}, {381, 49939}, {3534, 9750}, {3830, 49895}, {3845, 9762}, {5858, 9760}, {6054, 35751}, {6114, 33606}, {9749, 36363}, {10109, 33406}, {15701, 49898}, {41099, 49801}, {44219, 49940}

X(49896) = perspector (Artzt, 3rd outer-Fermat-Dao-Nhi)


X(49897) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND 1st BROCARD

Barycentrics    2*sqrt(3)*(7*a^4-11*(b^2+c^2)*a^2-8*b^4-8*b^2*c^2-8*c^4)*S+(23*a^4-19*(b^2+c^2)*a^2-4*(b^2-c^2)^2)*(a^2+b^2+c^2) : :

X(49897) lies on these lines: {76, 11295}, {381, 33411}, {599, 36329}, {618, 49919}, {2896, 35931}, {3534, 3642}, {3643, 36362}, {5858, 36373}, {15685, 49942}, {15690, 49851}, {15695, 49898}, {15701, 49895}, {19710, 49802}, {36366, 49947}

X(49897) = perspector (1st Brocard, 3rd inner-Fermat-Dao-Nhi)


X(49898) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND 1st BROCARD

Barycentrics    -2*sqrt(3)*(7*a^4-11*(b^2+c^2)*a^2-8*b^4-8*b^2*c^2-8*c^4)*S+(23*a^4-19*(b^2+c^2)*a^2-4*(b^2-c^2)^2)*(a^2+b^2+c^2) : :

X(49898) lies on these lines: {76, 11296}, {381, 33410}, {599, 35751}, {619, 49920}, {2896, 35932}, {3534, 3643}, {3642, 36363}, {5859, 36378}, {15685, 49941}, {15690, 49852}, {15695, 49897}, {15701, 49896}, {19710, 49803}, {36368, 49948}, {36775, 49962}

X(49898) = perspector (1st Brocard, 3rd outer-Fermat-Dao-Nhi)


X(49899) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND 1st BROCARD-REFLECTED

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

X(49899) lies on these lines: {194, 35917}, {5472, 36366}, {22687, 36364}

X(49899) = perspector (1st Brocard-reflected, 3rd inner-Fermat-Dao-Nhi)


X(49900) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND 1st BROCARD-REFLECTED

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

X(49900) lies on these lines: {194, 35918}, {5471, 36368}, {22689, 36365}

X(49900) = perspector (1st Brocard-reflected, 3rd outer-Fermat-Dao-Nhi)


X(49901) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND INNER-FERMAT

Barycentrics    23*a^4-19*(b^2+c^2)*a^2-4*(b^2-c^2)^2+2*sqrt(3)*(a^2-2*b^2-2*c^2)*S : :
X(49901) = X(12816)+2*X(33610) = 3*X(12816)-2*X(33623) = X(22844)+2*X(42434) = X(22890)+2*X(36958) = 3*X(33610)+X(33623) = 3*X(42062)-2*X(47865)

X(49901) lies on these lines: {2, 10646}, {3, 21360}, {30, 16626}, {99, 36329}, {524, 42632}, {530, 22895}, {531, 36386}, {533, 22844}, {599, 15695}, {616, 33624}, {618, 42100}, {623, 42429}, {3104, 7757}, {3534, 5463}, {3830, 49919}, {5210, 35752}, {5351, 37351}, {5464, 8703}, {5474, 22507}, {5858, 36967}, {5859, 35751}, {5862, 9741}, {5995, 41092}, {6674, 33415}, {6778, 33376}, {10645, 33458}, {11298, 42433}, {11301, 42158}, {13084, 49908}, {15681, 21359}, {16645, 49946}, {16652, 44667}, {19710, 49953}, {22114, 42157}, {31168, 35932}, {33387, 42431}, {33459, 35692}, {33607, 42062}, {33608, 36331}, {35304, 41107}, {35696, 36373}, {35749, 49911}, {36368, 42154}, {36767, 38412}, {37170, 43633}, {40898, 49807}, {41407, 43228}, {42036, 46893}, {42506, 45879}

X(49901) = midpoint of X(2) and X(33610)
X(49901) = reflection of X(i) in X(j) for these (i, j): (6778, 33376), (12816, 2)
X(49901) = complement of X(33623)
X(49901) = perspector (inner-Fermat, 3rd inner-Fermat-Dao-Nhi)
X(49901) = X(33459)-of-outer-Fermat triangle
X(49901) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (599, 15695, 49902), (33459, 46335, 36330)


X(49902) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND OUTER-FERMAT

Barycentrics    23*a^4-19*(b^2+c^2)*a^2-4*(b^2-c^2)^2-2*sqrt(3)*(a^2-2*b^2-2*c^2)*S : :
X(49902) = X(12817)+2*X(33611) = 3*X(12817)-2*X(33625) = X(22843)+2*X(36959) = X(22845)+2*X(42433) = 3*X(33611)+X(33625) = 3*X(42063)-2*X(47866)

X(49902) lies on these lines: {2, 10645}, {3, 21359}, {30, 16627}, {99, 35751}, {524, 42631}, {530, 36388}, {531, 22849}, {532, 22845}, {599, 15695}, {617, 33622}, {619, 42099}, {624, 42430}, {3105, 7757}, {3534, 5464}, {3830, 49920}, {5210, 36330}, {5352, 37352}, {5463, 8703}, {5473, 22509}, {5858, 36329}, {5859, 36968}, {5863, 9741}, {5994, 49971}, {6673, 33414}, {6777, 33377}, {10646, 33459}, {11297, 42434}, {11302, 42157}, {13083, 49907}, {15681, 21360}, {16644, 49945}, {16653, 44666}, {19710, 49952}, {22113, 42158}, {31168, 35931}, {33386, 42432}, {33458, 35696}, {33606, 42063}, {33609, 35750}, {35303, 41108}, {35692, 36378}, {36327, 49914}, {36366, 42155}, {37171, 43632}, {40899, 49808}, {41020, 44250}, {41406, 43229}, {42035, 46893}, {42507, 45880}

X(49902) = midpoint of X(2) and X(33611)
X(49902) = reflection of X(i) in X(j) for these (i, j): (6777, 33377), (12817, 2)
X(49902) = complement of X(33625)
X(49902) = perspector (outer-Fermat, 3rd outer-Fermat-Dao-Nhi)
X(49902) = X(33606)-of-outer-Fermat triangle
X(49902) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (599, 15695, 49901), (33458, 46334, 35752)


X(49903) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND 3rd FERMAT-DAO

Barycentrics    -18*sqrt(3)*a^2*S+5*a^4-19*(b^2+c^2)*a^2+14*(b^2-c^2)^2 : :

X(49903) lies on these lines: {2, 17}, {5, 43426}, {6, 49904}, {13, 3534}, {14, 16960}, {15, 12816}, {16, 15713}, {30, 42502}, {61, 5066}, {381, 3412}, {396, 3845}, {397, 11812}, {549, 42992}, {3090, 49859}, {3545, 42991}, {3830, 16962}, {3857, 42995}, {5054, 42505}, {5055, 42507}, {5238, 19710}, {5318, 42632}, {5335, 42631}, {5340, 15695}, {5351, 43107}, {5352, 15697}, {5470, 36329}, {5859, 22489}, {8703, 16965}, {10109, 11543}, {10124, 42420}, {10646, 49826}, {10653, 15719}, {10654, 43365}, {11001, 42152}, {11485, 12817}, {11486, 42530}, {11488, 19708}, {11539, 42979}, {11540, 23302}, {11542, 12100}, {12101, 42166}, {14269, 42509}, {15640, 42162}, {15685, 42434}, {15690, 16772}, {15692, 41974}, {15694, 42990}, {15699, 42898}, {15701, 16644}, {15714, 42959}, {16268, 42598}, {16529, 36330}, {16961, 42911}, {16966, 49948}, {16967, 43229}, {17538, 43424}, {18582, 41106}, {19107, 42511}, {19711, 42148}, {22510, 36362}, {22571, 35692}, {22602, 36371}, {22631, 36370}, {22688, 36364}, {22846, 33624}, {23046, 41973}, {25151, 36367}, {25157, 36373}, {25158, 36375}, {25159, 36376}, {25160, 36377}, {25217, 36387}, {33416, 43548}, {33417, 42974}, {33699, 42813}, {34755, 43494}, {35018, 42899}, {35730, 35734}, {35751, 36763}, {36383, 41104}, {36769, 47855}, {36836, 43546}, {36969, 49874}, {37640, 41122}, {37835, 42952}, {41020, 41026}, {41985, 42593}, {41990, 42633}, {42085, 43366}, {42087, 42892}, {42092, 49875}, {42097, 43033}, {42106, 42589}, {42107, 43007}, {42108, 42912}, {42110, 42799}, {42114, 49873}, {42118, 43483}, {42119, 43471}, {42121, 43469}, {42123, 43334}, {42124, 43418}, {42132, 49906}, {42138, 43475}, {42155, 43010}, {42158, 42504}, {42474, 42481}, {42499, 43484}, {42508, 43238}, {42581, 42988}, {42635, 42967}, {42684, 43324}, {42791, 42900}, {42800, 42982}, {42888, 43108}, {42897, 42910}, {42913, 43207}, {42916, 42941}, {42918, 49824}, {42928, 43481}, {42942, 44015}, {43006, 43554}, {43008, 43027}, {43021, 49876}, {43244, 46332}, {43465, 46334}, {43545, 49861}, {49569, 49579}

X(49903) = homothetic center (3rd Fermat-Dao, 3rd inner-Fermat-Dao-Nhi)
X(49903) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 16267, 42506), (2, 22495, 36386), (2, 49860, 16267), (14, 49947, 42520), (15, 41119, 12816), (17, 42506, 2), (396, 3845, 42976), (396, 41121, 41101), (3845, 42976, 41101), (16960, 49907, 49947), (18582, 49813, 41108), (37832, 43228, 49908), (41101, 41121, 16808), (41119, 49862, 15), (41121, 42976, 3845), (42106, 42589, 43476), (42518, 43332, 49947), (43542, 49862, 41119), (49907, 49947, 14)


X(49904) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND 4th FERMAT-DAO

Barycentrics    18*sqrt(3)*a^2*S+5*a^4-19*(b^2+c^2)*a^2+14*(b^2-c^2)^2 : :

X(49904) lies on these lines: {2, 18}, {5, 43427}, {6, 49903}, {13, 16961}, {14, 3534}, {15, 15713}, {16, 12817}, {30, 42503}, {62, 5066}, {381, 3411}, {395, 3845}, {398, 11812}, {549, 42993}, {3090, 49860}, {3545, 42990}, {3830, 16963}, {3857, 42994}, {5054, 42504}, {5055, 42506}, {5237, 19710}, {5321, 42631}, {5334, 42632}, {5339, 15695}, {5351, 15697}, {5352, 43100}, {5469, 35751}, {5858, 22490}, {8703, 16964}, {10109, 11542}, {10124, 42419}, {10645, 49827}, {10653, 43364}, {10654, 15719}, {11001, 42149}, {11485, 42531}, {11486, 12816}, {11489, 19708}, {11539, 42978}, {11540, 23303}, {11543, 12100}, {12101, 42163}, {14269, 42508}, {15640, 42159}, {15685, 42433}, {15690, 16773}, {15692, 41973}, {15694, 42991}, {15699, 42899}, {15701, 16645}, {15714, 42958}, {16267, 42599}, {16530, 35752}, {16960, 42910}, {16966, 43228}, {16967, 49947}, {17538, 43425}, {18581, 41106}, {19106, 42510}, {19711, 42147}, {22511, 36363}, {22572, 35696}, {22604, 36374}, {22633, 36372}, {22690, 36365}, {22891, 33622}, {23046, 41974}, {25161, 36369}, {25167, 36378}, {25168, 36379}, {25169, 36380}, {25170, 36381}, {25214, 36389}, {33416, 42975}, {33417, 43549}, {33699, 42814}, {34754, 43493}, {35018, 42898}, {36382, 41105}, {36402, 41103}, {36403, 41127}, {36768, 46855}, {36843, 43547}, {36970, 49873}, {37641, 41121}, {37832, 42953}, {41021, 41027}, {41985, 42592}, {41990, 42634}, {42086, 43367}, {42088, 42893}, {42089, 49876}, {42096, 43032}, {42103, 42588}, {42107, 42800}, {42109, 42913}, {42110, 43006}, {42111, 49874}, {42117, 43484}, {42120, 43472}, {42121, 43419}, {42122, 43335}, {42124, 43470}, {42129, 49905}, {42135, 43476}, {42154, 43011}, {42157, 42505}, {42475, 42480}, {42498, 43483}, {42509, 43239}, {42580, 42989}, {42636, 42966}, {42685, 43325}, {42792, 42901}, {42799, 42983}, {42889, 43109}, {42896, 42911}, {42912, 43208}, {42917, 42940}, {42919, 49825}, {42929, 43482}, {42943, 44016}, {43007, 43555}, {43009, 43026}, {43020, 49875}, {43245, 46332}, {43466, 46335}, {43544, 49862}, {47856, 47867}, {49570, 49583}

X(49904) = homothetic center (4th Fermat-Dao, 3rd outer-Fermat-Dao-Nhi)
X(49904) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 16268, 42507), (2, 22496, 36388), (2, 49859, 16268), (13, 49948, 42521), (16, 41120, 12817), (18, 42507, 2), (395, 3845, 42977), (395, 41122, 41100), (3845, 42977, 41100), (16961, 49908, 49948), (18581, 49812, 41107), (37835, 43229, 49907), (41100, 41122, 16809), (41120, 49861, 16), (41122, 42977, 3845), (42103, 42588, 43475), (42519, 43333, 49948), (43543, 49861, 41120), (49908, 49948, 13)


X(49905) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND 7th FERMAT-DAO

Barycentrics    3*sqrt(3)*a^2+8*S : :
X(49905) = 3*X(36836)+4*X(41119) = X(36836)-4*X(42152) = X(36836)+2*X(42156) = 5*X(36836)+4*X(42162) = 3*X(36836)+10*X(42518) = X(41119)+3*X(42152) = 2*X(41119)-3*X(42156) = 5*X(41119)-3*X(42162) = 2*X(41119)-5*X(42518) = 2*X(42152)+X(42156) = 5*X(42152)+X(42162) = 6*X(42152)+5*X(42518) = 5*X(42156)-2*X(42162) = 3*X(42156)-5*X(42518)

X(49905) lies on these lines: {2, 6}, {3, 16267}, {5, 41113}, {13, 3534}, {14, 42132}, {15, 3830}, {16, 15701}, {17, 381}, {18, 42610}, {30, 36836}, {39, 33620}, {61, 5055}, {62, 15694}, {115, 36329}, {376, 5340}, {397, 3524}, {398, 5071}, {542, 36763}, {547, 42153}, {549, 36843}, {631, 43107}, {1350, 6771}, {1656, 3412}, {2979, 11624}, {3146, 42587}, {3390, 35735}, {3522, 43002}, {3526, 16963}, {3543, 42166}, {3545, 5339}, {3839, 42147}, {3843, 42908}, {3845, 18582}, {3851, 42972}, {3854, 43202}, {3860, 42117}, {5023, 35304}, {5054, 22238}, {5066, 10654}, {5070, 42979}, {5079, 42991}, {5210, 35752}, {5237, 15707}, {5238, 15681}, {5318, 11001}, {5321, 41106}, {5334, 43104}, {5335, 19708}, {5351, 15718}, {5352, 15689}, {5463, 22892}, {5472, 35751}, {6109, 36362}, {6115, 36383}, {6410, 15764}, {6425, 18585}, {6426, 15765}, {6783, 36382}, {7684, 41028}, {7746, 22493}, {8703, 11542}, {9112, 36767}, {9117, 36330}, {10109, 41120}, {10124, 42149}, {10304, 42945}, {10645, 15695}, {10646, 43420}, {10653, 12100}, {11301, 34509}, {11481, 15693}, {11485, 19709}, {11539, 43239}, {11540, 42089}, {11737, 42159}, {11812, 42092}, {12101, 42085}, {12816, 36967}, {13876, 36370}, {13929, 36371}, {14093, 42158}, {14269, 42939}, {14892, 42920}, {14893, 42921}, {15640, 42087}, {15682, 42094}, {15684, 42813}, {15685, 36969}, {15686, 42161}, {15687, 42150}, {15688, 16965}, {15690, 42086}, {15692, 42148}, {15698, 42508}, {15699, 40694}, {15702, 42491}, {15703, 16268}, {15708, 42774}, {15709, 16773}, {15711, 43109}, {15719, 42986}, {15720, 42990}, {15721, 42944}, {15722, 42115}, {15759, 42118}, {15815, 35303}, {16242, 43199}, {16966, 42975}, {16967, 42481}, {17504, 42151}, {18581, 42512}, {19107, 43368}, {19710, 42097}, {22235, 42165}, {22331, 37340}, {22332, 37341}, {22573, 35692}, {22691, 36364}, {22847, 33624}, {23046, 42160}, {25178, 36367}, {25183, 36373}, {25184, 36375}, {25185, 36376}, {25186, 36377}, {25220, 36387}, {32460, 47284}, {33416, 42521}, {33417, 42533}, {33604, 43493}, {33605, 43101}, {33608, 33626}, {33699, 42096}, {34754, 42952}, {35402, 42890}, {35403, 42432}, {35696, 40671}, {35731, 35734}, {35750, 49911}, {36393, 41630}, {36395, 41632}, {36439, 42246}, {36457, 42248}, {36768, 41745}, {36769, 47857}, {36968, 42815}, {36970, 42688}, {38071, 42925}, {38335, 42157}, {41022, 41026}, {41099, 42093}, {41638, 49580}, {41944, 42936}, {42088, 42588}, {42101, 43482}, {42109, 43540}, {42111, 42419}, {42114, 43417}, {42129, 49904}, {42131, 43010}, {42142, 42940}, {42164, 42494}, {42430, 44015}, {42434, 42980}, {42472, 43541}, {42474, 49824}, {42475, 43404}, {42500, 43463}, {42504, 42528}, {42519, 49810}, {42611, 42989}, {42629, 43033}, {42630, 43369}, {42634, 43103}, {42687, 43465}, {42800, 43372}, {42802, 42814}, {42910, 43208}, {42914, 43024}, {42928, 43294}, {42949, 43100}, {42982, 43236}, {43015, 43545}, {43195, 43331}, {43207, 44580}, {43226, 43245}, {43232, 43309}, {43330, 43497}, {43479, 43773}, {49571, 49579}

X(49905) = complement of the isotomic conjugate of X(33604)
X(49905) = X(2)-Ceva conjugate of-X(33621)
X(49905) = X(31)-complementary conjugate of-X(33621)
X(49905) = homothetic center (7th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi)
X(49905) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 6, 49906), (2, 396, 49947), (2, 33458, 599), (2, 37640, 43229), (2, 37786, 5858), (2, 43228, 49948), (2, 43229, 16645), (2, 49812, 23303), (2, 49813, 43228), (2, 49862, 396), (2, 49947, 6), (396, 11488, 16644), (396, 16644, 6), (396, 23302, 37640), (396, 43228, 49813), (11001, 49874, 5318), (11488, 49862, 2), (13846, 13847, 396), (15693, 41100, 11481), (16267, 41943, 3), (16268, 42488, 15703), (16644, 16645, 23302), (16644, 49947, 2), (16645, 37640, 6), (16645, 49948, 49861), (18582, 42511, 3845), (23302, 37640, 16645), (23302, 43229, 2), (36969, 42632, 15685), (41106, 49876, 5321), (41108, 42976, 11485), (41120, 42911, 10109), (42117, 43246, 3860), (42124, 42496, 10653), (42529, 43004, 13), (43228, 49813, 49947), (43228, 49948, 6), (43229, 49861, 49948), (49813, 49861, 37640), (49947, 49948, 43228)


X(49906) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND 8th FERMAT-DAO

Barycentrics    3*sqrt(3)*a^2-8*S : :
X(49906) = 3*X(36843)+4*X(41120) = X(36843)-4*X(42149) = X(36843)+2*X(42153) = 5*X(36843)+4*X(42159) = 3*X(36843)+10*X(42519) = X(41120)+3*X(42149) = 2*X(41120)-3*X(42153) = 5*X(41120)-3*X(42159) = 2*X(41120)-5*X(42519) = 2*X(42149)+X(42153) = 5*X(42149)+X(42159) = 6*X(42149)+5*X(42519) = 5*X(42153)-2*X(42159) = 3*X(42153)-5*X(42519)

X(49906) lies on these lines: {2, 6}, {3, 16268}, {5, 41112}, {13, 42129}, {14, 3534}, {15, 15701}, {16, 3830}, {17, 42611}, {18, 381}, {30, 36843}, {39, 33621}, {61, 15694}, {62, 5055}, {115, 35751}, {376, 5339}, {397, 5071}, {398, 3524}, {547, 42156}, {549, 36836}, {631, 43100}, {1350, 6774}, {1656, 3411}, {2979, 11626}, {3146, 42586}, {3364, 35735}, {3522, 43003}, {3526, 16962}, {3543, 42163}, {3545, 5340}, {3839, 42148}, {3843, 42909}, {3845, 18581}, {3851, 42973}, {3854, 43201}, {3860, 42118}, {5023, 35303}, {5054, 22236}, {5066, 10653}, {5070, 42978}, {5079, 42990}, {5210, 36330}, {5237, 15681}, {5238, 15707}, {5318, 41106}, {5321, 11001}, {5334, 19708}, {5335, 43101}, {5351, 15689}, {5352, 15718}, {5464, 22848}, {5471, 36329}, {6108, 36363}, {6114, 36382}, {6409, 15764}, {6425, 15765}, {6426, 18585}, {6772, 36768}, {6782, 36383}, {7685, 41029}, {7746, 22494}, {8703, 11543}, {9115, 35752}, {10109, 41119}, {10124, 42152}, {10304, 42944}, {10645, 43421}, {10646, 15695}, {10654, 12100}, {11302, 34508}, {11480, 15693}, {11486, 19709}, {11539, 43238}, {11540, 42092}, {11737, 42162}, {11812, 42089}, {12101, 42086}, {12817, 36968}, {13875, 36372}, {13928, 36374}, {14093, 42157}, {14269, 42938}, {14892, 42921}, {14893, 42920}, {15640, 42088}, {15682, 42093}, {15684, 42814}, {15685, 36970}, {15686, 42160}, {15687, 42151}, {15688, 16964}, {15690, 42085}, {15692, 42147}, {15698, 42509}, {15699, 40693}, {15702, 42490}, {15703, 16267}, {15708, 42773}, {15709, 16772}, {15711, 43108}, {15719, 42987}, {15720, 42991}, {15721, 42945}, {15722, 42116}, {15759, 42117}, {15815, 35304}, {16241, 43200}, {16966, 42480}, {16967, 42974}, {17504, 42150}, {18582, 42513}, {19106, 43369}, {19710, 42096}, {22237, 42164}, {22331, 37341}, {22332, 37340}, {22574, 35696}, {22692, 36365}, {22893, 33622}, {23046, 42161}, {25173, 36369}, {25187, 36378}, {25188, 36379}, {25189, 36380}, {25190, 36381}, {25219, 36389}, {32461, 47284}, {33416, 42532}, {33417, 42520}, {33604, 43104}, {33605, 43494}, {33609, 33627}, {33699, 42097}, {34755, 42953}, {35402, 42891}, {35403, 42431}, {35692, 40672}, {36331, 49914}, {36398, 41640}, {36399, 41642}, {36402, 41095}, {36403, 41126}, {36439, 42249}, {36457, 42247}, {36967, 42816}, {36969, 42689}, {38071, 42924}, {38335, 42158}, {41023, 41027}, {41099, 42094}, {41648, 49584}, {41943, 42937}, {42087, 42589}, {42102, 43481}, {42108, 43541}, {42111, 43416}, {42114, 42420}, {42130, 43011}, {42132, 49903}, {42139, 42941}, {42165, 42495}, {42429, 44016}, {42433, 42981}, {42473, 43540}, {42474, 43403}, {42475, 49825}, {42501, 43464}, {42505, 42529}, {42518, 49811}, {42610, 42988}, {42629, 43368}, {42630, 43032}, {42633, 43102}, {42686, 43466}, {42799, 43373}, {42801, 42813}, {42911, 43207}, {42915, 43025}, {42929, 43295}, {42948, 43107}, {42983, 43237}, {43014, 43544}, {43196, 43330}, {43208, 44580}, {43227, 43244}, {43233, 43308}, {43331, 43498}, {43480, 43774}, {47858, 47867}, {49572, 49583}

X(49906) = complement of the isotomic conjugate of X(33605)
X(49906) = X(2)-Ceva conjugate of-X(33620)
X(49906) = X(31)-complementary conjugate of-X(33620)
X(49906) = homothetic center (8th Fermat-Dao, 3rd outer-Fermat-Dao-Nhi)
X(49906) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 6, 49905), (2, 395, 49948), (2, 33459, 599), (2, 37641, 43228), (2, 37785, 5859), (2, 43228, 16644), (2, 43229, 49947), (2, 49812, 43229), (2, 49813, 23302), (2, 49861, 395), (2, 49948, 6), (395, 11489, 16645), (395, 16645, 6), (395, 23303, 37641), (395, 43229, 49812), (11001, 49873, 5321), (11489, 49861, 2), (13846, 13847, 395), (15693, 41101, 11480), (16267, 42489, 15703), (16268, 41944, 3), (16644, 16645, 23303), (16644, 37641, 6), (16644, 49947, 49862), (16645, 49948, 2), (18581, 42510, 3845), (23303, 37641, 16644), (23303, 43228, 2), (36970, 42631, 15685), (41106, 49875, 5318), (41107, 42977, 11486), (41119, 42910, 10109), (42118, 43247, 3860), (42121, 42497, 10654), (42528, 43005, 14), (43228, 49862, 49947), (43229, 49812, 49948), (43229, 49947, 6), (49812, 49862, 37641), (49947, 49948, 43229)


X(49907) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND 15th FERMAT-DAO

Barycentrics    -6*S*sqrt(3)*a^2+a^4-11*(b^2+c^2)*a^2+10*(b^2-c^2)^2 : :
X(49907) = X(5352)-10*X(42598) = 7*X(5352)-10*X(42945) = 7*X(42598)-X(42945)

X(49907) lies on these lines: {2, 13}, {4, 41943}, {5, 16267}, {6, 25565}, {14, 16960}, {15, 3845}, {17, 381}, {18, 5055}, {20, 42979}, {30, 5352}, {61, 3545}, {62, 547}, {140, 42792}, {303, 33560}, {376, 42494}, {395, 42502}, {396, 5066}, {397, 15699}, {398, 11737}, {546, 43108}, {549, 42158}, {550, 43107}, {631, 10188}, {632, 41974}, {1656, 16963}, {3090, 3411}, {3091, 42972}, {3366, 42241}, {3367, 35740}, {3389, 42602}, {3390, 42603}, {3412, 3851}, {3524, 42162}, {3529, 42543}, {3530, 42592}, {3534, 12816}, {3543, 5238}, {3830, 16644}, {3839, 42152}, {3855, 41973}, {3860, 42110}, {5054, 16965}, {5056, 42953}, {5068, 43253}, {5071, 16268}, {5072, 42991}, {5237, 11539}, {5318, 12100}, {5339, 42435}, {5340, 15694}, {5344, 15708}, {5350, 15686}, {5351, 15702}, {5469, 5613}, {5858, 22894}, {5859, 22493}, {6777, 22566}, {8703, 23302}, {9113, 18584}, {9114, 35693}, {9763, 36388}, {10109, 11542}, {10124, 42148}, {10304, 42431}, {10645, 11001}, {10646, 11812}, {10654, 41106}, {11303, 41114}, {11305, 21360}, {11451, 30440}, {11480, 42430}, {11485, 43428}, {11486, 42985}, {11488, 36970}, {11540, 43109}, {11543, 42777}, {12101, 42627}, {12103, 42909}, {12820, 42626}, {13083, 49902}, {14093, 43550}, {14269, 42157}, {14892, 42163}, {14893, 42432}, {15060, 30439}, {15640, 42932}, {15681, 43238}, {15682, 42099}, {15684, 42434}, {15685, 42094}, {15687, 16772}, {15689, 42490}, {15690, 42941}, {15692, 42161}, {15693, 36968}, {15695, 42100}, {15697, 42134}, {15698, 42086}, {15701, 33417}, {15707, 43193}, {15709, 42151}, {15710, 43447}, {15711, 42088}, {15713, 42943}, {15716, 42127}, {15719, 43248}, {15723, 36843}, {16645, 42533}, {16773, 47599}, {16967, 42974}, {17504, 42165}, {17538, 42959}, {18546, 36775}, {18581, 33606}, {18585, 35730}, {19708, 42092}, {19710, 42138}, {19711, 42500}, {21359, 34509}, {22495, 33459}, {22577, 35692}, {22607, 36371}, {22636, 36370}, {22695, 36364}, {22849, 33624}, {22855, 36368}, {22997, 47866}, {23004, 47867}, {23046, 42147}, {25166, 36329}, {25182, 36367}, {25199, 36373}, {25200, 36375}, {25201, 36376}, {25202, 36377}, {25228, 36387}, {25236, 36330}, {31705, 45879}, {33604, 43549}, {33605, 42495}, {33699, 42124}, {34200, 43633}, {34754, 49876}, {35403, 43194}, {35733, 35734}, {36382, 46053}, {36438, 42233}, {36449, 42274}, {36453, 42236}, {36456, 42234}, {36468, 42277}, {36469, 42238}, {36757, 47354}, {36765, 41105}, {36836, 38335}, {37640, 41120}, {37641, 42914}, {38071, 42814}, {41024, 41026}, {41971, 43466}, {41985, 42948}, {41986, 43774}, {41990, 42135}, {42091, 43540}, {42093, 43305}, {42095, 42896}, {42104, 43645}, {42106, 42512}, {42107, 42633}, {42115, 42498}, {42120, 42796}, {42121, 42800}, {42123, 42903}, {42143, 42503}, {42154, 43227}, {42159, 43009}, {42160, 42939}, {42474, 43015}, {42480, 42818}, {42593, 46935}, {42594, 42686}, {42599, 42779}, {42625, 43548}, {42635, 43547}, {42636, 42978}, {42793, 45760}, {42892, 43474}, {42895, 43028}, {42908, 43502}, {42910, 49812}, {42924, 43100}, {42930, 43463}, {42947, 43002}, {42963, 43032}, {43003, 43771}, {43005, 49810}, {43012, 47478}, {43029, 43033}, {43103, 44580}, {43233, 43306}, {44020, 49859}, {49575, 49579}

X(49907) = homothetic center (15th Fermat-Dao, 3rd inner-Fermat-Dao-Nhi)
X(49907) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 13, 41100), (2, 18582, 41121), (2, 41100, 16242), (2, 41112, 16), (2, 41119, 41107), (2, 41121, 13), (2, 43403, 41112), (2, 49825, 42510), (2, 49874, 10653), (5, 43228, 41122), (6, 49908, 42507), (13, 16966, 16242), (13, 33416, 10653), (13, 37832, 16966), (16, 37832, 42911), (16, 41107, 49875), (16, 43403, 13), (12816, 16241, 3534), (16267, 41122, 43228), (16966, 41100, 2), (18582, 37832, 13), (18582, 42911, 43403), (19709, 49947, 14), (37832, 41121, 2), (41106, 49862, 10654), (41107, 41119, 13), (41107, 41121, 41119), (41112, 42911, 2), (41112, 49875, 41107), (41113, 49813, 61), (41119, 42510, 49825), (41120, 49860, 37640), (42156, 42581, 18), (42488, 42973, 549), (42506, 49908, 6), (42510, 49825, 41107), (42911, 43403, 16), (43104, 43229, 10109)


X(49908) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND 16th FERMAT-DAO

Barycentrics    6*S*sqrt(3)*a^2+a^4-11*(b^2+c^2)*a^2+10*(b^2-c^2)^2 : :
X(49908) = X(5351)-10*X(42599) = 7*X(5351)-10*X(42944) = 7*X(42599)-X(42944)

X(49908) lies on these lines: {2, 14}, {4, 41944}, {5, 16268}, {6, 25565}, {13, 16961}, {16, 3845}, {17, 5055}, {18, 381}, {20, 42978}, {30, 5351}, {61, 547}, {62, 3545}, {140, 42791}, {302, 33561}, {376, 42495}, {395, 5066}, {396, 42503}, {397, 11737}, {398, 15699}, {546, 43109}, {549, 42157}, {550, 43100}, {631, 10187}, {632, 41973}, {1656, 16962}, {3090, 3412}, {3091, 42973}, {3364, 42602}, {3365, 42603}, {3391, 42239}, {3392, 42240}, {3411, 3851}, {3524, 42159}, {3529, 42544}, {3530, 42593}, {3534, 12817}, {3543, 5237}, {3830, 16645}, {3839, 42149}, {3855, 41974}, {3860, 42107}, {5054, 16964}, {5056, 42952}, {5068, 43252}, {5071, 16267}, {5072, 42990}, {5238, 11539}, {5321, 12100}, {5339, 15694}, {5340, 42436}, {5343, 15708}, {5349, 15686}, {5352, 15702}, {5470, 5617}, {5858, 22494}, {5859, 22850}, {6778, 22566}, {8703, 23303}, {9112, 18584}, {9116, 35697}, {9761, 36386}, {10109, 11543}, {10124, 42147}, {10304, 42432}, {10645, 11812}, {10646, 11001}, {10653, 41106}, {11304, 41115}, {11306, 21359}, {11451, 30439}, {11481, 42429}, {11485, 42984}, {11486, 43429}, {11489, 36969}, {11540, 43108}, {11542, 42778}, {12101, 42628}, {12103, 42908}, {12821, 42625}, {13084, 49901}, {14093, 43551}, {14269, 42158}, {14892, 42166}, {14893, 42431}, {15060, 30440}, {15640, 42933}, {15681, 43239}, {15682, 42100}, {15684, 42433}, {15685, 42093}, {15687, 16773}, {15689, 42491}, {15690, 42940}, {15692, 42160}, {15693, 36967}, {15695, 42099}, {15697, 42133}, {15698, 42085}, {15701, 33416}, {15707, 43194}, {15709, 42150}, {15710, 43446}, {15711, 42087}, {15713, 42942}, {15716, 42126}, {15719, 43249}, {15723, 36836}, {16644, 42532}, {16772, 47599}, {16966, 42975}, {17504, 42164}, {17538, 42958}, {18582, 33607}, {19708, 42089}, {19710, 42135}, {19711, 42501}, {21360, 34508}, {22496, 33458}, {22578, 35696}, {22608, 36374}, {22637, 36372}, {22696, 36365}, {22895, 33622}, {22901, 36366}, {22998, 47865}, {23005, 36769}, {23046, 42148}, {25156, 35751}, {25177, 36369}, {25203, 36378}, {25204, 36379}, {25205, 36380}, {25206, 36381}, {25227, 36389}, {25235, 35752}, {31706, 45880}, {31710, 36768}, {33604, 42494}, {33605, 43548}, {33699, 42121}, {34200, 43632}, {34755, 49875}, {35403, 43193}, {36383, 46054}, {36402, 41093}, {36403, 41131}, {36438, 42232}, {36450, 42277}, {36452, 42237}, {36456, 42231}, {36467, 42274}, {36470, 42235}, {36758, 47354}, {36843, 38335}, {37640, 42915}, {37641, 41119}, {38071, 42813}, {41025, 41027}, {41972, 43465}, {41985, 42949}, {41986, 43773}, {41990, 42138}, {42090, 43541}, {42094, 43304}, {42098, 42897}, {42103, 42513}, {42105, 43646}, {42110, 42634}, {42116, 42499}, {42119, 42795}, {42122, 42902}, {42124, 42799}, {42146, 42502}, {42155, 43226}, {42161, 42938}, {42162, 43008}, {42475, 43014}, {42481, 42817}, {42592, 46935}, {42595, 42687}, {42598, 42780}, {42626, 43549}, {42635, 42979}, {42636, 43546}, {42794, 45760}, {42893, 43473}, {42894, 43029}, {42909, 43501}, {42911, 49813}, {42925, 43107}, {42931, 43464}, {42946, 43003}, {42962, 43033}, {43002, 43772}, {43004, 49811}, {43013, 47478}, {43028, 43032}, {43102, 44580}, {43232, 43307}, {44019, 49860}, {49576, 49583}

X(49908) = homothetic center (16th Fermat-Dao, 3rd outer-Fermat-Dao-Nhi)
X(49908) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 14, 41101), (2, 18581, 41122), (2, 41101, 16241), (2, 41113, 15), (2, 41120, 41108), (2, 41122, 14), (2, 43404, 41113), (2, 49824, 42511), (2, 49873, 10654), (5, 43229, 41121), (6, 49907, 42506), (14, 16967, 16241), (14, 33417, 10654), (14, 37835, 16967), (15, 37835, 42910), (15, 41108, 49876), (15, 43404, 14), (12817, 16242, 3534), (16268, 41121, 43229), (16967, 41101, 2), (18581, 37835, 14), (18581, 42910, 43404), (19709, 49948, 13), (37835, 41122, 2), (41106, 49861, 10653), (41108, 41120, 14), (41108, 41122, 41120), (41112, 49812, 62), (41113, 42910, 2), (41113, 49876, 41108), (41119, 49859, 37641), (41120, 42511, 49824), (42153, 42580, 17), (42489, 42972, 549), (42507, 49907, 6), (42511, 49824, 41108), (42910, 43404, 15), (43101, 43228, 10109)


X(49909) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND 2nd HALF-DIAMONDS-CENTRAL

Barycentrics    (7*a^4-59*(b^2+c^2)*a^2+52*(b^2-c^2)^2)*sqrt(3)-14*S*(11*a^2+2*b^2+2*c^2) : :

X(49909) lies on these lines: {2, 42800}, {5, 36362}, {13, 49921}, {531, 49949}, {617, 49864}, {3524, 33419}, {3534, 6771}, {5459, 36329}, {5859, 33477}, {15694, 49919}, {22846, 33624}, {33413, 36327}, {33475, 35692}, {33619, 35752}, {36331, 49815}, {36769, 49913}

X(49909) = perspector (3rd inner-Fermat-Dao-Nhi, 2nd half-diamonds-central)
X(49909) = complement of X(49831)


X(49910) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND 1st HALF-DIAMONDS-CENTRAL

Barycentrics    (7*a^4-59*(b^2+c^2)*a^2+52*(b^2-c^2)^2)*sqrt(3)+14*S*(11*a^2+2*b^2+2*c^2) : :

X(49910) lies on these lines: {2, 42799}, {5, 36363}, {14, 49922}, {18, 36768}, {530, 49950}, {616, 49863}, {3524, 33418}, {3534, 6774}, {5460, 35751}, {5858, 33476}, {15694, 49920}, {22891, 33622}, {33412, 35749}, {33474, 35696}, {33618, 36330}, {35750, 49814}, {47867, 49912}

X(49910) = perspector (3rd outer-Fermat-Dao-Nhi, 1st half-diamonds-central)
X(49910) = complement of X(49830)


X(49911) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND 1st HALF-DIAMONDS

Barycentrics    7*a^4+40*(b^2+c^2)*a^2-47*(b^2-c^2)^2+14*sqrt(3)*S*(5*a^2-b^2-c^2) : :
X(49911) = 3*X(33613)-2*X(49807)

X(49911) lies on these lines: {2, 33613}, {13, 33624}, {148, 36329}, {1992, 49914}, {3524, 49106}, {3534, 47610}, {11812, 49919}, {12101, 33625}, {22797, 36362}, {33602, 36331}, {33611, 47865}, {35749, 49901}, {35750, 49905}

X(49911) = reflection of X(33613) in X(2)
X(49911) = perspector (3rd inner-Fermat-Dao-Nhi, 1st half-diamonds)
X(49911) = complement of X(49807)


X(49912) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND 1st HALF-DIAMONDS

Barycentrics    119*a^4-157*(b^2+c^2)*a^2+38*(b^2-c^2)^2+14*sqrt(3)*(a^2+4*c^2+4*b^2)*S : :

X(49912) lies on these lines: {2, 49806}, {619, 36368}, {3534, 22797}, {6672, 36346}, {11812, 36363}, {15694, 49106}, {21358, 49913}, {35751, 41134}, {47867, 49910}

X(49912) = perspector (3rd outer-Fermat-Dao-Nhi, 1st half-diamonds)
X(49912) = complement of X(49806)


X(49913) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND 2nd HALF-DIAMONDS

Barycentrics    119*a^4-157*(b^2+c^2)*a^2+38*(b^2-c^2)^2-14*sqrt(3)*(a^2+4*c^2+4*b^2)*S : :

X(49913) lies on these lines: {2, 49809}, {618, 36366}, {3534, 22796}, {6671, 36352}, {11812, 36362}, {15694, 49105}, {21358, 49912}, {33607, 36768}, {36329, 41134}, {36769, 49909}

X(49913) = perspector (3rd inner-Fermat-Dao-Nhi, 2nd half-diamonds)
X(49913) = complement of X(49809)


X(49914) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND 2nd HALF-DIAMONDS

Barycentrics    7*a^4+40*(b^2+c^2)*a^2-47*(b^2-c^2)^2-14*sqrt(3)*S*(5*a^2-b^2-c^2) : :
X(49914) = 3*X(33612)-2*X(49808)

X(49914) lies on these lines: {2, 33612}, {14, 33622}, {148, 35751}, {1992, 49911}, {3524, 49105}, {3534, 47611}, {11812, 49920}, {12101, 33623}, {22796, 36363}, {33603, 35750}, {33610, 47866}, {36327, 49902}, {36331, 49906}

X(49914) = reflection of X(33612) in X(2)
X(49914) = perspector (3rd outer-Fermat-Dao-Nhi, 2nd half-diamonds)
X(49914) = X(33618)-of-outer-Fermat triangle
X(49914) = complement of X(49808)


X(49915) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND 1st HALF-SQUARES

Barycentrics    3*(50*(b^2+c^2)*S-57*a^4+75*(b^2+c^2)*a^2-18*(b^2-c^2)^2)*sqrt(3)+10*(11*a^2+20*b^2+20*c^2)*S-272*a^4+355*(b^2+c^2)*a^2-83*(b^2-c^2)^2 : :

X(49915) lies on these lines: {33440, 36370}

X(49915) = perspector (3rd inner-Fermat-Dao-Nhi, 1st half-squares)


X(49916) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND 1st HALF-SQUARES

Barycentrics    -3*(50*(b^2+c^2)*S-57*a^4+75*(b^2+c^2)*a^2-18*(b^2-c^2)^2)*sqrt(3)+10*(11*a^2+20*b^2+20*c^2)*S-272*a^4+355*(b^2+c^2)*a^2-83*(b^2-c^2)^2 : :

X(49916) lies on these lines: {33442, 36372}

X(49916) = perspector (3rd outer-Fermat-Dao-Nhi, 1st half-squares)


X(49917) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND 2nd HALF-SQUARES

Barycentrics    -3*(-50*(b^2+c^2)*S-57*a^4+75*(b^2+c^2)*a^2-18*(b^2-c^2)^2)*sqrt(3)-10*(11*a^2+20*b^2+20*c^2)*S-272*a^4+355*(b^2+c^2)*a^2-83*(b^2-c^2)^2 : :

X(49917) lies on these lines: {33441, 36371}

X(49917) = perspector (3rd inner-Fermat-Dao-Nhi, 2nd half-squares)


X(49918) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND 2nd HALF-SQUARES

Barycentrics    3*(-50*(b^2+c^2)*S-57*a^4+75*(b^2+c^2)*a^2-18*(b^2-c^2)^2)*sqrt(3)-10*(11*a^2+20*b^2+20*c^2)*S-272*a^4+355*(b^2+c^2)*a^2-83*(b^2-c^2)^2 : :

X(49918) lies on these lines: {33443, 36374}

X(49918) = perspector (3rd outer-Fermat-Dao-Nhi, 2nd half-squares)


X(49919) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND MCCAY

Barycentrics    -2*sqrt(3)*(31*a^4-35*(b^2+c^2)*a^2+4*(b^2-c^2)^2)*S+a^6-28*(b^2+c^2)*a^4+5*(7*b^4+6*b^2*c^2+7*c^4)*a^2-8*(b^4-c^4)*(b^2-c^2) : :

X(49919) lies on these lines: {2, 13103}, {3, 22493}, {381, 49921}, {618, 49897}, {621, 8703}, {3534, 41038}, {3830, 49901}, {5054, 33419}, {5859, 13083}, {6774, 49959}, {11812, 49911}, {12100, 33624}, {13084, 35692}, {15694, 49909}, {15701, 36366}, {15722, 49960}, {16628, 35931}, {19711, 49877}, {33417, 33607}, {44580, 49828}

X(49919) = perspector (3rd inner-Fermat-Dao-Nhi, McCay)


X(49920) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND MCCAY

Barycentrics    2*sqrt(3)*(31*a^4-35*(b^2+c^2)*a^2+4*(b^2-c^2)^2)*S+a^6-28*(b^2+c^2)*a^4+5*(7*b^4+6*b^2*c^2+7*c^4)*a^2-8*(b^4-c^4)*(b^2-c^2) : :

X(49920) lies on these lines: {2, 13102}, {3, 22494}, {381, 49922}, {619, 49898}, {622, 8703}, {3534, 41039}, {3830, 49902}, {5054, 33418}, {5858, 13084}, {6771, 49960}, {11812, 49914}, {12100, 33622}, {13083, 35696}, {15694, 49910}, {15701, 36368}, {15722, 49959}, {16629, 35932}, {19711, 49878}, {33416, 33606}, {44580, 49829}

X(49920) = perspector (3rd outer-Fermat-Dao-Nhi, McCay)


X(49921) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND INNER-NAPOLEON

Barycentrics    (17*a^4-16*(b^2+c^2)*a^2-(b^2-c^2)^2)*sqrt(3)+2*S*(2*a^2-7*b^2-7*c^2) : :
X(49921) = 7*X(2)-3*X(43540) = 5*X(36767)-3*X(38412)

X(49921) lies on these lines: {2, 5318}, {3, 36362}, {13, 49909}, {18, 11295}, {381, 49919}, {530, 42817}, {531, 49961}, {617, 49880}, {627, 35931}, {3534, 5617}, {5463, 36329}, {5859, 9885}, {9761, 35692}, {11180, 19708}, {14145, 15533}, {22495, 42939}, {33607, 35752}, {35304, 40922}, {35750, 49905}, {35751, 36366}, {35955, 49893}, {36330, 43245}, {36331, 42626}, {36767, 38412}

X(49921) = perspector (3rd inner-Fermat-Dao-Nhi, inner-Napoleon)


X(49922) = HOMOTHETIC CENTER OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND OUTER-NAPOLEON

Barycentrics    (17*a^4-16*(b^2+c^2)*a^2-(b^2-c^2)^2)*sqrt(3)-2*S*(2*a^2-7*b^2-7*c^2) : :
X(49922) = 7*X(2)-3*X(43541)

X(49922) lies on these lines: {2, 5321}, {3, 36363}, {14, 49910}, {17, 11296}, {381, 49920}, {530, 49962}, {531, 42818}, {616, 49879}, {628, 35749}, {3534, 5613}, {5464, 35751}, {5858, 9886}, {9763, 35696}, {11180, 19708}, {14144, 15533}, {22496, 42938}, {33606, 36330}, {35303, 40921}, {35750, 42625}, {35752, 43244}, {35955, 49894}, {36329, 36368}, {36331, 49906}

X(49922) = perspector (3rd outer-Fermat-Dao-Nhi, outer-Napoleon)
X(49922) = X(49910)-of-outer-Fermat triangle


X(49923) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND 1st NEUBERG

Barycentrics    -6*sqrt(3)*(5*a^4+2*(b^2+c^2)*a^2-7*b^4-10*b^2*c^2-7*c^4)*S*a^2+9*a^8-71*(b^2+c^2)*a^6+(61*b^4+24*b^2*c^2+61*c^4)*a^4+(b^2+c^2)*(b^4+68*b^2*c^2+c^4)*a^2-8*(b^2-c^2)^2*b^2*c^2 : :

X(49923) lies on these lines: {6582, 36373}, {14711, 36755}, {14830, 36329}, {33388, 36364}

X(49923) = perspector (3rd inner-Fermat-Dao-Nhi, 1st Neuberg)


X(49924) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND 1st NEUBERG

Barycentrics    6*sqrt(3)*(5*a^4+2*(b^2+c^2)*a^2-7*b^4-10*b^2*c^2-7*c^4)*S*a^2+9*a^8-71*(b^2+c^2)*a^6+(61*b^4+24*b^2*c^2+61*c^4)*a^4+(b^2+c^2)*(b^4+68*b^2*c^2+c^4)*a^2-8*(b^2-c^2)^2*b^2*c^2 : :

X(49924) lies on these lines: {6295, 36378}, {14711, 36756}, {14830, 35751}, {33389, 36365}

X(49924) = perspector (3rd outer-Fermat-Dao-Nhi, 1st Neuberg)


X(49925) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND 2nd NEUBERG

Barycentrics    6*sqrt(3)*(5*a^6-(3*b^4+2*b^2*c^2+3*c^4)*a^2-2*(b^4-c^4)*(b^2-c^2))*S+a^8-53*(b^2+c^2)*a^6+(59*b^4+52*b^2*c^2+59*c^4)*a^4-(b^2+c^2)*(17*b^4-24*b^2*c^2+17*c^4)*a^2+2*(5*b^4+6*b^2*c^2+5*c^4)*(b^2-c^2)^2 : :

X(49925) lies on these lines: {3095, 22496}, {6298, 36375}, {33624, 36344}, {36329, 48657}, {48905, 49926}

X(49925) = perspector (3rd inner-Fermat-Dao-Nhi, 2nd Neuberg)


X(49926) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND 2nd NEUBERG

Barycentrics    -6*sqrt(3)*(5*a^6-(3*b^4+2*b^2*c^2+3*c^4)*a^2-2*(b^4-c^4)*(b^2-c^2))*S+a^8-53*(b^2+c^2)*a^6+(59*b^4+52*b^2*c^2+59*c^4)*a^4-(b^2+c^2)*(17*b^4-24*b^2*c^2+17*c^4)*a^2+2*(5*b^4+6*b^2*c^2+5*c^4)*(b^2-c^2)^2 : :

X(49926) lies on these lines: {3095, 22495}, {6299, 36379}, {33622, 36319}, {35751, 48657}, {48905, 49925}

X(49926) = perspector (3rd outer-Fermat-Dao-Nhi, 2nd Neuberg)


X(49927) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND INNER-VECTEN

Barycentrics    -3*(2*(b^2+c^2)*S-5*a^4+4*(b^2+c^2)*a^2+(b^2-c^2)^2)*sqrt(3)+2*(4*a^2-5*c^2-5*b^2)*S+26*a^4-25*(b^2+c^2)*a^2-(b^2-c^2)^2 : :

X(49927) lies on these lines: {2, 49823}, {6302, 36371}, {15293, 33446}, {45385, 49928}, {47865, 49929}

X(49927) = perspector (3rd inner-Fermat-Dao-Nhi, inner-Vecten)
X(49927) = complement of X(49823)


X(49928) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND INNER-VECTEN

Barycentrics    3*(2*(b^2+c^2)*S-5*a^4+4*(b^2+c^2)*a^2+(b^2-c^2)^2)*sqrt(3)+2*(4*a^2-5*c^2-5*b^2)*S+26*a^4-25*(b^2+c^2)*a^2-(b^2-c^2)^2 : :

X(49928) lies on these lines: {2, 49822}, {6303, 36374}, {15293, 33444}, {45385, 49927}, {47866, 49930}

X(49928) = perspector (3rd outer-Fermat-Dao-Nhi, inner-Vecten)
X(49928) = complement of X(49822)


X(49929) = PERSPECTOR OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI AND OUTER-VECTEN

Barycentrics    3*(-2*(b^2+c^2)*S-5*a^4+4*(b^2+c^2)*a^2+(b^2-c^2)^2)*sqrt(3)-2*(4*a^2-5*c^2-5*b^2)*S+26*a^4-25*(b^2+c^2)*a^2-(b^2-c^2)^2 : :

X(49929) lies on these lines: {2, 49821}, {6306, 36370}, {15294, 33447}, {45384, 49930}, {47865, 49927}

X(49929) = perspector (3rd inner-Fermat-Dao-Nhi, outer-Vecten)
X(49929) = complement of X(49821)


X(49930) = PERSPECTOR OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI AND OUTER-VECTEN

Barycentrics    -3*(-2*(b^2+c^2)*S-5*a^4+4*(b^2+c^2)*a^2+(b^2-c^2)^2)*sqrt(3)-2*(4*a^2-5*c^2-5*b^2)*S+26*a^4-25*(b^2+c^2)*a^2-(b^2-c^2)^2 : :

X(49930) lies on these lines: {2, 49820}, {6307, 36372}, {15294, 33445}, {45384, 49929}, {47866, 49928}

X(49930) = perspector (3rd outer-Fermat-Dao-Nhi, outer-Vecten)
X(49930) = complement of X(49820)


X(49931) = PARALLELOGIC CENTER OF THESE TRIANGLES: 3rd INNER-FERMAT-DAO-NHI TO VU-DAO-X(16)-ISODYNAMIC

Barycentrics    2*(4*a^8-4*(b^2+c^2)*a^6-(9*(b^2-c^2)^2-4*b^2*c^2)*a^4+14*(b^4-c^4)*(b^2-c^2)*a^2-(5*b^4+14*b^2*c^2+5*c^4)*(b^2-c^2)^2)*S+3*sqrt(3)*(2*a^10-2*(b^2+c^2)*a^8-(5*b^4-12*b^2*c^2+5*c^4)*a^6+7*(b^4-c^4)*(b^2-c^2)*a^4-(b^2-c^2)^2*(b^4+8*b^2*c^2+c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3) : :
X(49931) = 4*X(2)-3*X(46465) = X(35751)-3*X(36774) = 5*X(36767)-3*X(36788) = 3*X(39352)-X(49840) = X(41092)+2*X(41132) = 2*X(41092)-3*X(46465) = 3*X(41092)-2*X(49842) = 4*X(41132)+3*X(46465) = 3*X(41132)+X(49842) = 9*X(46465)-4*X(49842)

The reciprocal parallelogic center of these triangles is X(4).

X(49931) lies on the circumcircles of triangles {3rd inner-Fermat-Dao-Nhi, 4th inner-Fermat-Dao-Nhi} and these lines: {2, 41092}, {2777, 49932}, {6111, 41119}, {11001, 36319}, {23871, 36330}, {35751, 36774}, {36767, 36788}, {39352, 49840}, {41028, 41066}

X(49931) = midpoint of X(2) and X(41132)
X(49931) = reflection of X(41092) in X(2)
X(49931) = complement of X(49842)
X(49931) = orthologic center (4th inner-Fermat-Dao-Nhi, Vu-Dao-X(16)-isodynamic)
X(49931) = parallelogic center (3rd inner-Fermat-Dao-Nhi, Vu-Dao-X(16)-isodynamic)
X(49931) = {X(2), X(41092)}-harmonic conjugate of X(46465)


X(49932) = PARALLELOGIC CENTER OF THESE TRIANGLES: 3rd OUTER-FERMAT-DAO-NHI TO VU-DAO-X(15)-ISODYNAMIC

Barycentrics    -2*(4*a^8-4*(b^2+c^2)*a^6-(9*(b^2-c^2)^2-4*b^2*c^2)*a^4+14*(b^4-c^4)*(b^2-c^2)*a^2-(5*b^4+14*b^2*c^2+5*c^4)*(b^2-c^2)^2)*S+3*sqrt(3)*(2*a^10-2*(b^2+c^2)*a^8-(5*b^4-12*b^2*c^2+5*c^4)*a^6+7*(b^4-c^4)*(b^2-c^2)*a^4-(b^2-c^2)^2*(b^4+8*b^2*c^2+c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3) : :
X(49932) = 4*X(2)-3*X(46466) = 3*X(39352)-X(41132) = 3*X(46466)+4*X(49840) = 9*X(46466)-4*X(49841) = 3*X(46466)-2*X(49971) = 3*X(49840)+X(49841) = 2*X(49840)+X(49971) = 2*X(49841)-3*X(49971)

The reciprocal parallelogic center of these triangles is X(4).

X(49932) lies on the circumcircles of triangles {3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi} and these lines: {2, 46466}, {2777, 49931}, {6110, 41120}, {11001, 35751}, {23870, 35752}, {39352, 41132}, {41029, 41067}

X(49932) = midpoint of X(2) and X(49840)
X(49932) = reflection of X(49971) in X(2)
X(49932) = complement of X(49841)
X(49932) = orthologic center (4th outer-Fermat-Dao-Nhi, Vu-Dao-X(15)-isodynamic)
X(49932) = parallelogic center (3rd outer-Fermat-Dao-Nhi, Vu-Dao-X(15)-isodynamic)
X(49932) = {X(2), X(49971)}-harmonic conjugate of X(46466)


X(49933) = PERSPECTOR OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND ANTI-ARTZT

Barycentrics    2*(21*a^4+11*(b^2+c^2)*a^2-2*(b^2-3*c^2)*(3*b^2-c^2))*S+sqrt(3)*(a^2+b^2+c^2)*(5*a^4+3*(b^2+c^2)*a^2-4*b^4+12*b^2*c^2-4*c^4) : :

X(49933) lies on these lines: {2, 9989}, {5858, 12155}, {8593, 36330}, {11159, 49890}, {12154, 35693}, {12816, 40671}, {22666, 35943}

X(49933) = perspector (anti-Artzt, 4th inner-Fermat-Dao-Nhi)


X(49934) = PERSPECTOR OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND ANTI-ARTZT

Barycentrics    -2*(21*a^4+11*(b^2+c^2)*a^2-2*(b^2-3*c^2)*(3*b^2-c^2))*S+sqrt(3)*(a^2+b^2+c^2)*(5*a^4+3*(b^2+c^2)*a^2-4*b^4+12*b^2*c^2-4*c^4) : :

X(49934) lies on these lines: {2, 9988}, {5859, 12154}, {8593, 35752}, {11159, 49889}, {12155, 35697}, {12817, 40672}, {22665, 35942}

X(49934) = perspector (anti-Artzt, 4th outer-Fermat-Dao-Nhi)


X(49935) = PERSPECTOR OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND 1st ANTI-BROCARD

Barycentrics    6*sqrt(3)*(a^2+b^2+c^2)*(a^8-(b^2+c^2)*a^6-3*(b^4+c^4)*a^4+7*(b^6+c^6)*a^2-4*b^8-4*c^8+b^2*c^2*(8*b^4-15*b^2*c^2+8*c^4))*S+13*a^12-13*(b^2+c^2)*a^10+4*(8*b^4+9*b^2*c^2+8*c^4)*a^8-(b^2+c^2)*(82*b^4+27*b^2*c^2+82*c^4)*a^6+(113*b^8+113*c^8+b^2*c^2*(116*b^4+45*b^2*c^2+116*c^4))*a^4-(b^2+c^2)*(67*b^8+67*c^8-b^2*c^2*(157*b^4-284*b^2*c^2+157*c^4))*a^2+(4*b^8+4*c^8-(14*b^4-45*b^2*c^2+14*c^4)*b^2*c^2)*(b^2-c^2)^2 : :

X(49935) lies on these lines: {3830, 5978}, {5979, 36382}, {7840, 36330}

X(49935) = perspector (1st anti-Brocard, 4th inner-Fermat-Dao-Nhi)


X(49936) = PERSPECTOR OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND 1st ANTI-BROCARD

Barycentrics    -6*sqrt(3)*(a^2+b^2+c^2)*(a^8-(b^2+c^2)*a^6-3*(b^4+c^4)*a^4+7*(b^6+c^6)*a^2-4*b^8-4*c^8+b^2*c^2*(8*b^4-15*b^2*c^2+8*c^4))*S+13*a^12-13*(b^2+c^2)*a^10+4*(8*b^4+9*b^2*c^2+8*c^4)*a^8-(b^2+c^2)*(82*b^4+27*b^2*c^2+82*c^4)*a^6+(113*b^8+113*c^8+b^2*c^2*(116*b^4+45*b^2*c^2+116*c^4))*a^4-(b^2+c^2)*(67*b^8+67*c^8-b^2*c^2*(157*b^4-284*b^2*c^2+157*c^4))*a^2+(b^2-c^2)^2*(4*b^8+4*c^8-b^2*c^2*(14*b^4-45*b^2*c^2+14*c^4)) : :

X(49936) lies on these lines: {3830, 5979}, {5978, 36383}, {7840, 35752}

X(49936) = perspector (1st anti-Brocard, 4th outer-Fermat-Dao-Nhi)


X(49937) = PERSPECTOR OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND ANTI-MCCAY

Barycentrics    2*(21*a^6-22*(b^2+c^2)*a^4+2*(7*b^4-6*b^2*c^2+7*c^4)*a^2-(b^2+c^2)*(6*b^4-11*b^2*c^2+6*c^4))*S+(11*a^8-23*(b^2+c^2)*a^6+2*(13*b^4+6*b^2*c^2+13*c^4)*a^4-(b^2+c^2)*(14*b^4-17*b^2*c^2+14*c^4)*a^2+2*b^8-(5*b^4-8*b^2*c^2+5*c^4)*b^2*c^2+2*c^8)*sqrt(3) : :

X(49937) lies on these lines: {5858, 8594}, {8595, 35693}, {9855, 36330}

X(49937) = perspector (anti-McCay, 4th inner-Fermat-Dao-Nhi)


X(49938) = PERSPECTOR OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND ANTI-MCCAY

Barycentrics    2*(21*a^6-22*(b^2+c^2)*a^4+2*(7*b^4-6*b^2*c^2+7*c^4)*a^2-(b^2+c^2)*(6*b^4-11*b^2*c^2+6*c^4))*S-(11*a^8-23*(b^2+c^2)*a^6+2*(13*b^4+6*b^2*c^2+13*c^4)*a^4-(b^2+c^2)*(14*b^4-17*b^2*c^2+14*c^4)*a^2+2*b^8-(5*b^4-8*b^2*c^2+5*c^4)*b^2*c^2+2*c^8)*sqrt(3) : :

X(49938) lies on these lines: {5859, 8595}, {8594, 35697}, {9855, 35752}

X(49938) = perspector (anti-McCay, 4th outer-Fermat-Dao-Nhi)


X(49939) = PERSPECTOR OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND ARTZT

Barycentrics    6*sqrt(3)*(a^2+b^2+c^2)*(a^4+7*(b^2+c^2)*a^2-8*(b^2-c^2)^2)*S+13*a^8-63*(b^2+c^2)*a^6+(181*b^4+274*b^2*c^2+181*c^4)*a^4-(b^2+c^2)*(153*b^4-274*b^2*c^2+153*c^4)*a^2+2*(11*b^4-32*b^2*c^2+11*c^4)*(b^2-c^2)^2 : :

X(49939) lies on these lines: {381, 49896}, {3545, 49800}, {3830, 9749}, {5066, 9760}, {5858, 9762}, {6054, 36330}, {6115, 12816}, {9750, 36382}, {19709, 49940}, {41106, 49849}

X(49939) = perspector (Artzt, 4th inner-Fermat-Dao-Nhi)


X(49940) = PERSPECTOR OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND ARTZT

Barycentrics    -6*sqrt(3)*(a^2+b^2+c^2)*(a^4+7*(b^2+c^2)*a^2-8*(b^2-c^2)^2)*S+13*a^8-63*(b^2+c^2)*a^6+(181*b^4+274*b^2*c^2+181*c^4)*a^4-(b^2+c^2)*(153*b^4-274*b^2*c^2+153*c^4)*a^2+2*(11*b^4-32*b^2*c^2+11*c^4)*(b^2-c^2)^2 : :

X(49940) lies on these lines: {381, 49895}, {3545, 49801}, {3830, 9750}, {5066, 9762}, {5859, 9760}, {6054, 35752}, {6114, 12817}, {9749, 36383}, {19709, 49939}, {41106, 49850}, {44219, 49896}

X(49940) = perspector (Artzt, 4th outer-Fermat-Dao-Nhi)


X(49941) = PERSPECTOR OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND 1st BROCARD

Barycentrics    -2*sqrt(3)*(5*a^4+11*(b^2+c^2)*a^2+8*b^4+32*b^2*c^2+8*c^4)*S+(11*a^4+5*(b^2+c^2)*a^2-16*(b^2-c^2)^2)*(a^2+b^2+c^2) : :

X(49941) lies on these lines: {599, 36330}, {618, 49959}, {2896, 11295}, {3642, 3830}, {3643, 36382}, {5055, 33411}, {5859, 36395}, {15685, 49898}, {36386, 49948}

X(49941) = perspector (1st Brocard, 4th inner-Fermat-Dao-Nhi)


X(49942) = PERSPECTOR OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND 1st BROCARD

Barycentrics    2*sqrt(3)*(5*a^4+11*(b^2+c^2)*a^2+8*b^4+32*b^2*c^2+8*c^4)*S+(11*a^4+5*(b^2+c^2)*a^2-16*(b^2-c^2)^2)*(a^2+b^2+c^2) : :

X(49942) lies on these lines: {599, 35752}, {619, 49960}, {2896, 11296}, {3642, 36383}, {3643, 3830}, {5055, 33410}, {5858, 36399}, {15685, 49897}, {36388, 49947}

X(49942) = perspector (1st Brocard, 4th outer-Fermat-Dao-Nhi)


X(49943) = PERSPECTOR OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND 1st BROCARD-REFLECTED

Barycentrics    -2*sqrt(3)*(a^2+b^2+c^2)*(a^4+3*(b^2+c^2)*a^2+8*b^2*c^2)*S+15*a^8-7*(b^2+c^2)*a^6-(13*b^4+60*b^2*c^2+13*c^4)*a^4+(b^2+c^2)*(5*b^4-44*b^2*c^2+5*c^4)*a^2+8*(b^2-c^2)^2*b^2*c^2 : :

X(49943) lies on these lines: {9115, 36386}, {22687, 36384}, {35917, 45017}

X(49943) = perspector (1st Brocard-reflected, 4th inner-Fermat-Dao-Nhi)


X(49944) = PERSPECTOR OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND 1st BROCARD-REFLECTED

Barycentrics    2*sqrt(3)*(a^2+b^2+c^2)*(a^4+3*(b^2+c^2)*a^2+8*b^2*c^2)*S+15*a^8-7*(b^2+c^2)*a^6-(13*b^4+60*b^2*c^2+13*c^4)*a^4+(b^2+c^2)*(5*b^4-44*b^2*c^2+5*c^4)*a^2+8*(b^2-c^2)^2*b^2*c^2 : :

X(49944) lies on these lines: {9117, 36388}, {22689, 36385}, {35918, 45017}

X(49944) = perspector (1st Brocard-reflected, 4th outer-Fermat-Dao-Nhi)


X(49945) = PERSPECTOR OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND OUTER-FERMAT

Barycentrics    5*a^4+17*(b^2+c^2)*a^2-22*(b^2-c^2)^2+4*sqrt(3)*(4*a^2+b^2+c^2)*S : :
X(49945) = 2*X(33602)+X(33619)

X(49945) lies on these lines: {2, 33602}, {13, 36386}, {115, 36330}, {298, 49858}, {597, 49946}, {3105, 9466}, {3830, 5459}, {5055, 16627}, {5340, 33414}, {5460, 19709}, {5859, 33560}, {16644, 49902}, {22845, 42156}, {33458, 40727}, {33459, 42815}, {33621, 36769}, {35752, 49953}, {47865, 49961}

X(49945) = midpoint of X(2) and X(33602)
X(49945) = reflection of X(33619) in X(2)
X(49945) = perspector (outer-Fermat, 4th inner-Fermat-Dao-Nhi)
X(49945) = inverse of X(49947) in Kiepert circumhyperbola


X(49946) = PERSPECTOR OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND INNER-FERMAT

Barycentrics    5*a^4+17*(b^2+c^2)*a^2-22*(b^2-c^2)^2-4*sqrt(3)*(4*a^2+b^2+c^2)*S : :
X(49946) = 2*X(33603)+X(33618)

X(49946) lies on these lines: {2, 33603}, {14, 36388}, {115, 35752}, {299, 49855}, {597, 49945}, {3104, 9466}, {3830, 5460}, {5055, 16626}, {5339, 33415}, {5459, 19709}, {5858, 33561}, {16645, 49901}, {22844, 42153}, {33458, 42816}, {33459, 40727}, {33620, 47867}, {35697, 36768}, {36330, 49952}, {47866, 49962}

X(49946) = midpoint of X(2) and X(33603)
X(49946) = reflection of X(33618) in X(2)
X(49946) = perspector (inner-Fermat, 4th outer-Fermat-Dao-Nhi)
X(49946) = inverse of X(49948) in Kiepert circumhyperbola


X(49947) = HOMOTHETIC CENTER OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND 7th FERMAT-DAO

Barycentrics    3*sqrt(3)*a^2+4*S : :
X(49947) = X(5340)+2*X(22236) = X(5340)-4*X(40693) = 3*X(5340)-4*X(41112) = 5*X(5340)+4*X(42150) = 7*X(5340)-4*X(42161) = 3*X(5340)+4*X(42511) = 4*X(5340)+X(42587) = 2*X(5340)+X(43194) = X(22236)+2*X(40693) = 3*X(22236)+2*X(41112) = 5*X(22236)-2*X(42150) = 7*X(22236)+2*X(42161) = 3*X(22236)-2*X(42511) = 8*X(22236)-X(42587) = 4*X(22236)-X(43194) = 9*X(22236)+16*X(43207) = 3*X(40693)-X(41112) = 5*X(40693)+X(42150) = 7*X(40693)-X(42161) = 3*X(40693)+X(42511) = 16*X(40693)+X(42587) = 8*X(40693)+X(43194) = 9*X(40693)-8*X(43207)

X(49947) lies on these lines: {2, 6}, {3, 3412}, {4, 33604}, {5, 41120}, {13, 3830}, {14, 16960}, {15, 3534}, {16, 15693}, {17, 5055}, {18, 15703}, {20, 42586}, {25, 14173}, {30, 5340}, {32, 22495}, {39, 33618}, {61, 381}, {62, 5054}, {115, 36330}, {376, 397}, {382, 42635}, {398, 3545}, {530, 19781}, {532, 11301}, {533, 11305}, {547, 40694}, {549, 22238}, {1152, 15764}, {1351, 6771}, {1384, 9112}, {1656, 16268}, {2307, 11237}, {3053, 35304}, {3060, 11624}, {3364, 36469}, {3365, 36453}, {3390, 35734}, {3411, 46219}, {3524, 16772}, {3525, 43100}, {3526, 41944}, {3543, 42147}, {3592, 18585}, {3594, 15765}, {3839, 42166}, {3845, 10654}, {3851, 42991}, {5013, 35303}, {5064, 8740}, {5066, 18582}, {5071, 42598}, {5079, 42993}, {5237, 15700}, {5238, 15688}, {5318, 15682}, {5321, 41099}, {5334, 33603}, {5335, 11001}, {5351, 15706}, {5352, 14093}, {5470, 13102}, {5472, 35752}, {6109, 36382}, {6115, 36363}, {6770, 36990}, {6772, 47857}, {6775, 47867}, {6783, 36362}, {7684, 41026}, {7755, 21359}, {8259, 11304}, {8703, 10653}, {8716, 35943}, {9115, 36764}, {9117, 36329}, {10109, 18581}, {10304, 42148}, {10645, 42631}, {10646, 15716}, {11297, 34509}, {11451, 11626}, {11481, 12100}, {11486, 15701}, {11539, 42149}, {11540, 42121}, {11543, 42911}, {11812, 42124}, {12101, 42117}, {12817, 16808}, {12820, 42905}, {13876, 36390}, {13929, 36391}, {14269, 16964}, {14893, 42160}, {15640, 42119}, {15681, 16965}, {15683, 42165}, {15684, 42157}, {15685, 36967}, {15687, 42162}, {15689, 42158}, {15690, 42118}, {15692, 42945}, {15694, 16963}, {15695, 36968}, {15696, 41974}, {15697, 42088}, {15698, 42792}, {15702, 16773}, {15705, 43003}, {15708, 42944}, {15713, 42092}, {15723, 42936}, {16242, 42533}, {16809, 43032}, {16966, 42507}, {16967, 49904}, {17504, 42924}, {17578, 43201}, {18584, 41621}, {19708, 42943}, {19710, 42086}, {19711, 42420}, {19780, 45879}, {21734, 42794}, {22331, 37172}, {22332, 37173}, {22487, 33375}, {22494, 30435}, {22573, 35693}, {22691, 36384}, {22847, 33627}, {22892, 33621}, {23046, 42921}, {25154, 47855}, {25178, 36387}, {25183, 36393}, {25184, 36395}, {25185, 25186}, {25220, 36367}, {33416, 43199}, {33602, 42134}, {33610, 35931}, {33699, 42085}, {34200, 42151}, {34754, 36969}, {35381, 43489}, {35697, 40671}, {35731, 35735}, {35822, 42237}, {35823, 42235}, {36366, 49897}, {36373, 41630}, {36375, 41632}, {36388, 49942}, {36439, 42230}, {36457, 42229}, {36768, 41620}, {36769, 41745}, {36970, 42128}, {37832, 41122}, {37835, 42132}, {38071, 42159}, {38335, 42813}, {41022, 41028}, {41638, 49579}, {41746, 47866}, {42087, 42982}, {42089, 42634}, {42111, 43247}, {42115, 43030}, {42127, 43418}, {42129, 43333}, {42140, 43540}, {42164, 43773}, {42419, 43417}, {42477, 43548}, {42481, 43031}, {42488, 42989}, {42497, 42512}, {42503, 43101}, {42516, 42589}, {42546, 49139}, {42611, 47599}, {42627, 49859}, {42682, 43364}, {42691, 43226}, {42693, 42803}, {42775, 43202}, {42800, 42892}, {42818, 43878}, {42910, 49810}, {42919, 43007}, {42951, 43024}, {42984, 43545}, {43104, 43404}, {43297, 43308}, {43302, 43304}, {49571, 49580}, {49953, 49961}

X(49947) = midpoint of X(41112) and X(42511)
X(49947) = reflection of X(42587) in X(43194)
X(49947) = complement of the isotomic conjugate of X(33602)
X(49947) = inverse of X(49945) in Kiepert circumhyperbola
X(49947) = intersection, other than A, B, C, of circumconics {{A, B, C, X(69), X(33604)}} and {{A, B, C, X(83), X(49948)}}
X(49947) = X(2)-Ceva conjugate of-X(33619)
X(49947) = X(31)-complementary conjugate of-X(33619)
X(49947) = homothetic center (7th Fermat-Dao, 4th inner-Fermat-Dao-Nhi)
X(49947) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 396, 49905), (2, 1992, 33459), (2, 5859, 599), (2, 37640, 43228), (2, 37786, 5859), (2, 43228, 6), (2, 49813, 396), (2, 49861, 23303), (2, 49905, 16644), (2, 49948, 16645), (6, 396, 16644), (6, 11488, 43028), (6, 16644, 16645), (6, 49905, 2), (6, 49906, 43229), (395, 396, 11488), (395, 43028, 16645), (396, 37640, 6), (396, 43228, 2), (5859, 14614, 15534), (10654, 41119, 3845), (12100, 42510, 11481), (13846, 13847, 16644), (15682, 49825, 5318), (16644, 16645, 43029), (16644, 49948, 2), (16773, 43107, 15702), (18582, 41113, 5066), (32787, 32788, 37640), (32787, 36468, 6), (32788, 36449, 6), (36449, 36468, 396), (37640, 49813, 2), (41099, 49827, 5321), (41101, 42506, 13), (41107, 42976, 15), (42520, 49903, 14), (42817, 42975, 37832), (43108, 43416, 33699), (43228, 49813, 49905), (49862, 49906, 16644), (49874, 49876, 4)


X(49948) = HOMOTHETIC CENTER OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND 8th FERMAT-DAO

Barycentrics    3*sqrt(3)*a^2-4*S : :
X(49948) = X(5339)+2*X(22238) = X(5339)-4*X(40694) = 3*X(5339)-4*X(41113) = 5*X(5339)+4*X(42151) = 7*X(5339)-4*X(42160) = 3*X(5339)+4*X(42510) = 4*X(5339)+X(42586) = 2*X(5339)+X(43193) = X(22238)+2*X(40694) = 3*X(22238)+2*X(41113) = 5*X(22238)-2*X(42151) = 7*X(22238)+2*X(42160) = 3*X(22238)-2*X(42510) = 8*X(22238)-X(42586) = 4*X(22238)-X(43193) = 9*X(22238)+16*X(43208) = 3*X(40694)-X(41113) = 5*X(40694)+X(42151) = 7*X(40694)-X(42160) = 3*X(40694)+X(42510) = 16*X(40694)+X(42586) = 8*X(40694)+X(43193) = 9*X(40694)-8*X(43208)

X(49948) lies on these lines: {2, 6}, {3, 3411}, {4, 33605}, {5, 41119}, {13, 16961}, {14, 3830}, {15, 15693}, {16, 3534}, {17, 15703}, {18, 5055}, {20, 42587}, {25, 14179}, {30, 5339}, {32, 22496}, {39, 33619}, {61, 5054}, {62, 381}, {115, 35752}, {376, 398}, {382, 42636}, {397, 3545}, {531, 19780}, {532, 11306}, {533, 11302}, {547, 40693}, {549, 22236}, {1151, 15764}, {1351, 6774}, {1384, 9113}, {1656, 16267}, {3053, 35303}, {3060, 11626}, {3364, 35734}, {3389, 36452}, {3390, 36470}, {3412, 46219}, {3524, 16773}, {3525, 43107}, {3526, 41943}, {3543, 42148}, {3592, 15765}, {3594, 18585}, {3839, 42163}, {3845, 10653}, {3851, 42990}, {5013, 35304}, {5064, 8739}, {5066, 18581}, {5071, 42599}, {5079, 42992}, {5237, 15688}, {5238, 15700}, {5318, 41099}, {5321, 15682}, {5334, 11001}, {5335, 33602}, {5351, 14093}, {5352, 15706}, {5469, 13103}, {5471, 36330}, {6108, 36383}, {6114, 36362}, {6772, 36769}, {6773, 36990}, {6775, 47858}, {6782, 36363}, {7127, 11238}, {7685, 41027}, {7755, 21360}, {8260, 11303}, {8703, 10654}, {8716, 35942}, {9115, 35751}, {10109, 18582}, {10304, 42147}, {10645, 15716}, {10646, 42632}, {11142, 40579}, {11298, 34508}, {11451, 11624}, {11480, 12100}, {11485, 15701}, {11539, 42152}, {11540, 42124}, {11542, 42910}, {11812, 42121}, {12101, 42118}, {12816, 16809}, {12821, 42904}, {13875, 36392}, {13928, 36394}, {14269, 16965}, {14893, 42161}, {15640, 42120}, {15681, 16964}, {15683, 42164}, {15684, 42158}, {15685, 36968}, {15687, 42159}, {15689, 42157}, {15690, 42117}, {15692, 42944}, {15694, 16962}, {15695, 36967}, {15696, 41973}, {15697, 42087}, {15698, 42791}, {15702, 16772}, {15705, 43002}, {15708, 42945}, {15713, 42089}, {15723, 42937}, {16241, 42532}, {16808, 43033}, {16966, 49903}, {16967, 42506}, {17504, 42925}, {17578, 43202}, {18584, 41620}, {19708, 42942}, {19710, 42085}, {19711, 42419}, {19781, 45880}, {21734, 42793}, {22331, 37173}, {22332, 37172}, {22488, 33374}, {22493, 30435}, {22574, 35697}, {22692, 36385}, {22848, 33620}, {22893, 33626}, {23046, 42920}, {25164, 47856}, {25173, 36389}, {25187, 36398}, {25188, 36399}, {25189, 25190}, {25219, 36369}, {33417, 43200}, {33603, 42133}, {33611, 35932}, {33699, 42086}, {34200, 42150}, {34755, 36970}, {35381, 43490}, {35693, 40672}, {35822, 42238}, {35823, 42236}, {36368, 49898}, {36378, 41640}, {36379, 41642}, {36386, 49941}, {36402, 41126}, {36403, 41095}, {36439, 42227}, {36457, 42228}, {36969, 42125}, {37832, 42129}, {37835, 41121}, {38071, 42162}, {38335, 42814}, {41023, 41029}, {41648, 49583}, {41745, 47865}, {41746, 47867}, {42088, 42983}, {42092, 42633}, {42114, 43246}, {42116, 43031}, {42126, 43419}, {42132, 43332}, {42141, 43541}, {42165, 43774}, {42420, 43416}, {42476, 43549}, {42480, 43030}, {42489, 42988}, {42496, 42513}, {42502, 43104}, {42517, 42588}, {42545, 49139}, {42610, 47599}, {42628, 49860}, {42683, 43365}, {42690, 43227}, {42692, 42804}, {42776, 43201}, {42799, 42893}, {42817, 43877}, {42911, 49811}, {42918, 43006}, {42950, 43025}, {42985, 43544}, {43101, 43403}, {43296, 43309}, {43303, 43305}, {49572, 49584}, {49952, 49962}

X(49948) = midpoint of X(41113) and X(42510)
X(49948) = reflection of X(42586) in X(43193)
X(49948) = complement of the isotomic conjugate of X(33603)
X(49948) = inverse of X(49946) in Kiepert circumhyperbola
X(49948) = intersection, other than A, B, C, of circumconics {{A, B, C, X(69), X(33605)}} and {{A, B, C, X(83), X(49947)}}
X(49948) = X(2)-Ceva conjugate of-X(33618)
X(49948) = X(31)-complementary conjugate of-X(33618)
X(49948) = homothetic center (8th Fermat-Dao, 4th outer-Fermat-Dao-Nhi)
X(49948) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 1992, 33458), (2, 5858, 599), (2, 37641, 43229), (2, 37785, 5858), (2, 43228, 49905), (2, 43229, 6), (2, 49812, 395), (2, 49862, 23302), (2, 49906, 16645), (2, 49947, 16644), (6, 395, 16645), (6, 11489, 43029), (6, 16645, 16644), (6, 49905, 43228), (6, 49906, 2), (395, 396, 11489), (395, 37641, 6), (395, 43229, 2), (396, 43029, 16644), (5858, 14614, 15534), (10653, 41120, 3845), (12100, 42511, 11480), (13846, 13847, 16645), (15682, 49824, 5321), (16644, 16645, 43028), (16645, 49947, 2), (16772, 43100, 15702), (18581, 41112, 5066), (32787, 32788, 37641), (32787, 36450, 6), (32788, 36467, 6), (36450, 36467, 395), (37641, 49812, 2), (41099, 49826, 5318), (41100, 42507, 14), (41108, 42977, 16), (42521, 49904, 13), (42818, 42974, 37835), (43109, 43417, 33699), (43229, 49861, 49905), (49861, 49905, 16645), (49873, 49875, 4)


X(49949) = HOMOTHETIC CENTER OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND 2nd HALF-DIAMONDS-CENTRAL

Barycentrics    10*(13*a^2+4*b^2+4*c^2)*S+(5*a^4+53*(b^2+c^2)*a^2-58*(b^2-c^2)^2)*sqrt(3) : :

X(49949) lies on these lines: {2, 43499}, {5, 36382}, {13, 49961}, {17, 47867}, {376, 33419}, {531, 49909}, {3830, 6771}, {5459, 36330}, {5858, 33477}, {15703, 49959}, {22489, 44015}, {22494, 33411}, {22846, 33627}, {33475, 35693}, {33560, 36331}, {33621, 35751}, {36327, 49864}, {47865, 49953}

X(49949) = perspector (4th inner-Fermat-Dao-Nhi, 2nd half-diamonds-central)
X(49949) = complement of X(49880)


X(49950) = HOMOTHETIC CENTER OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND 1st HALF-DIAMONDS-CENTRAL

Barycentrics    -10*(13*a^2+4*b^2+4*c^2)*S+(5*a^4+53*(b^2+c^2)*a^2-58*(b^2-c^2)^2)*sqrt(3) : :

X(49950) lies on these lines: {2, 43500}, {5, 36383}, {14, 49962}, {18, 36769}, {376, 33418}, {530, 49910}, {3830, 6774}, {5460, 35752}, {5859, 33476}, {15703, 49960}, {22490, 44016}, {22493, 33410}, {22891, 33626}, {33474, 35697}, {33561, 35750}, {33620, 36329}, {35749, 49863}, {47866, 49952}

X(49950) = perspector (4th outer-Fermat-Dao-Nhi, 1st half-diamonds-central)
X(49950) = complement of X(49879)


X(49951) = PERSPECTOR OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND 1st HALF-DIAMONDS

Barycentrics    55*a^4+52*(b^2+c^2)*a^2+10*sqrt(3)*(7*a^2+b^2+c^2)*S-107*(b^2-c^2)^2 : :

X(49951) lies on these lines: {2, 49856}, {13, 33627}, {376, 49106}, {3830, 47610}, {22797, 36382}, {31683, 35749}, {33604, 36327}, {33613, 35752}, {35750, 49953}, {36330, 41135}

X(49951) = perspector (4th inner-Fermat-Dao-Nhi, 1st half-diamonds)
X(49951) = complement of X(49856)


X(49952) = PERSPECTOR OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND 1st HALF-DIAMONDS

Barycentrics    -10*sqrt(3)*(a^2-2*b^2-2*c^2)*S+35*a^4-43*(b^2+c^2)*a^2+8*(b^2-c^2)^2 : :
X(49952) = X(33606)+2*X(33609) = 3*X(33606)-2*X(49855) = 3*X(33609)+X(49855)

X(49952) lies on these lines: {2, 33606}, {99, 35752}, {533, 33386}, {599, 15722}, {617, 44016}, {619, 36388}, {1657, 21360}, {3830, 5464}, {5054, 49106}, {5463, 12100}, {6672, 33624}, {10124, 21359}, {11300, 33465}, {12817, 47867}, {14482, 49813}, {19710, 49902}, {33626, 41100}, {35697, 36775}, {36330, 49946}, {36331, 49954}, {47866, 49950}, {49948, 49962}

X(49952) = midpoint of X(2) and X(33609)
X(49952) = reflection of X(33606) in X(2)
X(49952) = complement of X(49855)
X(49952) = perspector (4th outer-Fermat-Dao-Nhi, 1st half-diamonds)
X(49952) = {X(599), X(15722)}-harmonic conjugate of X(49953)


X(49953) = PERSPECTOR OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND 2nd HALF-DIAMONDS

Barycentrics    10*sqrt(3)*(a^2-2*b^2-2*c^2)*S+35*a^4-43*(b^2+c^2)*a^2+8*(b^2-c^2)^2 : :
X(49953) = X(33607)+2*X(33608) = 3*X(33607)-2*X(49858) = 3*X(33608)+X(49858)

X(49953) lies on these lines: {2, 33607}, {99, 36330}, {532, 33387}, {599, 15722}, {616, 44015}, {618, 36386}, {1657, 21359}, {3830, 5463}, {5054, 49105}, {5464, 12100}, {5858, 36767}, {6671, 33622}, {10124, 21360}, {11299, 33464}, {12816, 36769}, {14482, 49812}, {19710, 49901}, {33627, 41101}, {35750, 49951}, {35751, 38412}, {35752, 49945}, {47865, 49949}, {49947, 49961}

X(49953) = midpoint of X(2) and X(33608)
X(49953) = reflection of X(33607) in X(2)
X(49953) = complement of X(49858)
X(49953) = perspector (4th inner-Fermat-Dao-Nhi, 2nd half-diamonds)
X(49953) = {X(599), X(15722)}-harmonic conjugate of X(49952)


X(49954) = PERSPECTOR OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND 2nd HALF-DIAMONDS

Barycentrics    55*a^4+52*(b^2+c^2)*a^2-10*sqrt(3)*(7*a^2+b^2+c^2)*S-107*(b^2-c^2)^2 : :

X(49954) lies on these lines: {2, 49857}, {14, 33626}, {376, 49105}, {3830, 47611}, {22796, 36383}, {31684, 36327}, {33605, 35749}, {33612, 36330}, {35752, 41135}, {36331, 49952}

X(49954) = perspector (4th outer-Fermat-Dao-Nhi, 2nd half-diamonds)
X(49954) = X(33620)-of-outer-Fermat triangle
X(49954) = complement of X(49857)


X(49955) = PERSPECTOR OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND 1st HALF-SQUARES

Barycentrics    128*a^4-13*(b^2+c^2)*a^2-2*(37*a^2-8*b^2-8*c^2)*S-3*(21*a^4-3*(b^2+c^2)*a^2-2*(b^2+c^2)*S-18*(b^2-c^2)^2)*sqrt(3)-115*(b^2-c^2)^2 : :

X(49955) lies on these lines: {2, 42195}, {33366, 35949}, {33440, 36390}, {35752, 49957}

X(49955) = perspector (4th inner-Fermat-Dao-Nhi, 1st half-squares)


X(49956) = PERSPECTOR OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND 1st HALF-SQUARES

Barycentrics    128*a^4-13*(b^2+c^2)*a^2-2*(37*a^2-8*b^2-8*c^2)*S+3*(21*a^4-3*(b^2+c^2)*a^2-2*(b^2+c^2)*S-18*(b^2-c^2)^2)*sqrt(3)-115*(b^2-c^2)^2 : :

X(49956) lies on these lines: {2, 42196}, {33368, 35949}, {33442, 36392}, {36330, 49958}

X(49956) = perspector (4th outer-Fermat-Dao-Nhi, 1st half-squares)


X(49957) = PERSPECTOR OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND 2nd HALF-SQUARES

Barycentrics    128*a^4-13*(b^2+c^2)*a^2+2*(37*a^2-8*b^2-8*c^2)*S+3*(21*a^4-3*(b^2+c^2)*a^2+2*(b^2+c^2)*S-18*(b^2-c^2)^2)*sqrt(3)-115*(b^2-c^2)^2 : :

X(49957) lies on these lines: {2, 42197}, {33369, 35948}, {33441, 36391}, {35752, 49955}

X(49957) = perspector (4th inner-Fermat-Dao-Nhi, 2nd half-squares)


X(49958) = PERSPECTOR OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND 2nd HALF-SQUARES

Barycentrics    128*a^4-13*(b^2+c^2)*a^2+2*(37*a^2-8*b^2-8*c^2)*S-3*(21*a^4-3*(b^2+c^2)*a^2+2*(b^2+c^2)*S-18*(b^2-c^2)^2)*sqrt(3)-115*(b^2-c^2)^2 : :

X(49958) lies on these lines: {2, 42198}, {33367, 35948}, {33443, 36394}, {36330, 49956}

X(49958) = perspector (4th outer-Fermat-Dao-Nhi, 2nd half-squares)


X(49959) = PERSPECTOR OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND MCCAY

Barycentrics    -2*sqrt(3)*(43*a^4-59*(b^2+c^2)*a^2+16*(b^2-c^2)^2)*S+37*a^6-64*(b^2+c^2)*a^4+7*(5*b^4-6*b^2*c^2+5*c^4)*a^2-8*(b^4-c^4)*(b^2-c^2) : :
X(49959) = 5*X(19709)-12*X(43549)

X(49959) lies on these lines: {3, 32909}, {618, 49941}, {3534, 33625}, {5858, 13083}, {6774, 49919}, {12816, 16967}, {13084, 35693}, {15693, 33627}, {15694, 33419}, {15703, 49949}, {15722, 49920}

X(49959) = perspector (4th inner-Fermat-Dao-Nhi, McCay)


X(49960) = PERSPECTOR OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND MCCAY

Barycentrics    2*sqrt(3)*(43*a^4-59*(b^2+c^2)*a^2+16*(b^2-c^2)^2)*S+37*a^6-64*(b^2+c^2)*a^4+7*(5*b^4-6*b^2*c^2+5*c^4)*a^2-8*(b^4-c^4)*(b^2-c^2) : :
X(49960) = 5*X(19709)-12*X(43548)

X(49960) lies on these lines: {3, 32907}, {619, 49942}, {3534, 33623}, {5859, 13084}, {6771, 49920}, {12817, 16966}, {13083, 35697}, {15693, 33626}, {15694, 33418}, {15703, 49950}, {15722, 49919}

X(49960) = perspector (4th outer-Fermat-Dao-Nhi, McCay)


X(49961) = HOMOTHETIC CENTER OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND INNER-NAPOLEON

Barycentrics    4*(4*a^2-5*b^2-5*c^2)*S+(11*a^4-13*(b^2+c^2)*a^2+2*(b^2-c^2)^2)*sqrt(3) : :
X(49961) = 5*X(2)-3*X(43542) = 5*X(15694)-4*X(33419) = 3*X(31683)-X(35749)

X(49961) lies on these lines: {2, 11486}, {3, 36382}, {13, 49949}, {298, 36331}, {531, 49921}, {627, 11295}, {3830, 5617}, {5463, 15300}, {5858, 9885}, {5862, 33619}, {9761, 35693}, {11179, 11898}, {12816, 35751}, {14145, 33627}, {15534, 36386}, {15694, 33419}, {22493, 42434}, {31683, 35749}, {33386, 42491}, {33474, 42951}, {36327, 49880}, {47865, 49945}, {49947, 49953}

X(49961) = perspector (4th inner-Fermat-Dao-Nhi, inner-Napoleon)
X(49961) = {X(36386), X(36767)}-harmonic conjugate of X(15534)


X(49962) = HOMOTHETIC CENTER OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND OUTER-NAPOLEON

Barycentrics    -4*(4*a^2-5*b^2-5*c^2)*S+(11*a^4-13*(b^2+c^2)*a^2+2*(b^2-c^2)^2)*sqrt(3) : :
X(49962) = 5*X(2)-3*X(43543) = 5*X(15694)-4*X(33418) = 3*X(31684)-X(36327)

X(49962) lies on these lines: {2, 11485}, {3, 36383}, {14, 49950}, {299, 35750}, {530, 49922}, {599, 36767}, {628, 11296}, {3830, 5613}, {5464, 15300}, {5859, 9886}, {5863, 33618}, {9763, 35697}, {11179, 11898}, {12817, 36329}, {14144, 33626}, {15534, 36388}, {15694, 33418}, {22494, 42433}, {31684, 36327}, {33387, 42490}, {33475, 42950}, {35749, 49879}, {36775, 49898}, {47866, 49946}, {49948, 49952}

X(49962) = perspector (4th outer-Fermat-Dao-Nhi, outer-Napoleon)
X(49962) = X(49950)-of-outer-Fermat triangle
X(49962) = {X(15693), X(22165)}-harmonic conjugate of X(49961)


X(49963) = PERSPECTOR OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND 1st NEUBERG

Barycentrics    -6*sqrt(3)*(a^4+4*(b^2+c^2)*a^2-5*b^4-2*b^2*c^2-5*c^4)*S*a^2+45*a^8-77*(b^2+c^2)*a^6+(73*b^4-12*b^2*c^2+73*c^4)*a^4-(b^2+c^2)*(41*b^4-92*b^2*c^2+41*c^4)*a^2-32*(b^2-c^2)^2*b^2*c^2 : :

X(49963) lies on these lines: {6582, 36393}, {14830, 36330}, {33388, 36384}, {33878, 49964}

X(49963) = perspector (4th inner-Fermat-Dao-Nhi, 1st Neuberg)


X(49964) = PERSPECTOR OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND 1st NEUBERG

Barycentrics    6*sqrt(3)*(a^4+4*(b^2+c^2)*a^2-5*b^4-2*b^2*c^2-5*c^4)*S*a^2+45*a^8-77*(b^2+c^2)*a^6+(73*b^4-12*b^2*c^2+73*c^4)*a^4-(b^2+c^2)*(41*b^4-92*b^2*c^2+41*c^4)*a^2-32*(b^2-c^2)^2*b^2*c^2 : :

X(49964) lies on these lines: {6295, 36398}, {14830, 35752}, {33389, 36385}, {33878, 49963}

X(49964) = perspector (4th outer-Fermat-Dao-Nhi, 1st Neuberg)


X(49965) = PERSPECTOR OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND 2nd NEUBERG

Barycentrics    6*sqrt(3)*(a^6+(3*b^4+14*b^2*c^2+3*c^4)*a^2-4*(b^4-c^4)*(b^2-c^2))*S+13*a^8-41*(b^2+c^2)*a^6+(101*b^4+172*b^2*c^2+101*c^4)*a^4-11*(b^2+c^2)*(7*b^4-12*b^2*c^2+7*c^4)*a^2+4*(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2 : :

X(49965) lies on these lines: {6298, 36395}, {36330, 48657}

X(49965) = perspector (4th inner-Fermat-Dao-Nhi, 2nd Neuberg)


X(49966) = PERSPECTOR OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND 2nd NEUBERG

Barycentrics    -6*sqrt(3)*(a^6+(3*b^4+14*b^2*c^2+3*c^4)*a^2-4*(b^4-c^4)*(b^2-c^2))*S+13*a^8-41*(b^2+c^2)*a^6+(101*b^4+172*b^2*c^2+101*c^4)*a^4-11*(b^2+c^2)*(7*b^4-12*b^2*c^2+7*c^4)*a^2+4*(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^2 : :

X(49966) lies on these lines: {6299, 36399}, {35752, 48657}

X(49966) = perspector (4th outer-Fermat-Dao-Nhi, 2nd Neuberg)


X(49967) = PERSPECTOR OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND INNER-VECTEN

Barycentrics    -4*S*(14*S-8*a^2+b^2+c^2)+3*(a^4+(b^2+c^2)*a^2-4*(b^2+c^2)*S-2*(b^2-c^2)^2)*sqrt(3) : :

X(49967) lies on these lines: {2, 49872}, {6302, 36391}

X(49967) = perspector (4th inner-Fermat-Dao-Nhi, inner-Vecten)
X(49967) = complement of X(49872)


X(49968) = PERSPECTOR OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND INNER-VECTEN

Barycentrics    -4*S*(14*S-8*a^2+b^2+c^2)-3*(a^4+(b^2+c^2)*a^2-4*(b^2+c^2)*S-2*(b^2-c^2)^2)*sqrt(3) : :

X(49968) lies on these lines: {2, 49871}, {6303, 36394}

X(49968) = perspector (4th outer-Fermat-Dao-Nhi, inner-Vecten)
X(49968) = complement of X(49871)


X(49969) = PERSPECTOR OF THESE TRIANGLES: 4th INNER-FERMAT-DAO-NHI AND OUTER-VECTEN

Barycentrics    4*S*(-14*S-8*a^2+b^2+c^2)-3*(a^4+(b^2+c^2)*a^2+4*(b^2+c^2)*S-2*(b^2-c^2)^2)*sqrt(3) : :

X(49969) lies on these lines: {2, 49870}, {6306, 36390}

X(49969) = perspector (4th inner-Fermat-Dao-Nhi, outer-Vecten)
X(49969) = complement of X(49870)


X(49970) = PERSPECTOR OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI AND OUTER-VECTEN

Barycentrics    4*S*(-14*S-8*a^2+b^2+c^2)+3*(a^4+(b^2+c^2)*a^2+4*(b^2+c^2)*S-2*(b^2-c^2)^2)*sqrt(3) : :

X(49970) lies on these lines: {2, 49869}, {6307, 36392}

X(49970) = perspector (4th outer-Fermat-Dao-Nhi, outer-Vecten)
X(49970) = complement of X(49869)


X(49971) = PARALLELOGIC CENTER OF THESE TRIANGLES: 4th OUTER-FERMAT-DAO-NHI TO VU-DAO-X(15)-ISODYNAMIC

Barycentrics    -2*(8*a^8-8*(b^2+c^2)*a^6-(9*b^4-26*b^2*c^2+9*c^4)*a^4+10*(b^4-c^4)*(b^2-c^2)*a^2-(b^4+10*b^2*c^2+c^4)*(b^2-c^2)^2)*S+3*sqrt(3)*(2*a^10-2*(b^2+c^2)*a^8-(5*b^4-12*b^2*c^2+5*c^4)*a^6+7*(b^4-c^4)*(b^2-c^2)*a^4-(b^2-c^2)^2*(b^4+8*b^2*c^2+c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3) : :
X(49971) = 2*X(2)-3*X(46466) = 3*X(39358)-X(49842) = 9*X(46466)-2*X(49840) = 3*X(46466)+2*X(49841) = 3*X(46466)-X(49932) = X(49840)+3*X(49841) = 2*X(49840)-3*X(49932) = 2*X(49841)+X(49932)

The reciprocal parallelogic center of these triangles is X(4).

X(49971) lies on the circumcircles of triangles {3rd outer-Fermat-Dao-Nhi, 4th outer-Fermat-Dao-Nhi} and these lines: {2, 46466}, {2777, 41092}, {5994, 49902}, {6110, 41113}, {15682, 35752}, {23870, 35751}, {39358, 49842}, {41027, 41067}

X(49971) = midpoint of X(2) and X(49841)
X(49971) = reflection of X(49932) in X(2)
X(49971) = complement of X(49840)
X(49971) = orthologic center (3rd outer-Fermat-Dao-Nhi, Vu-Dao-X(15)-isodynamic)
X(49971) = parallelogic center (4th outer-Fermat-Dao-Nhi, Vu-Dao-X(15)-isodynamic)
X(49971) = {X(46466), X(49932)}-harmonic conjugate of X(2)


X(49972) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ALTINTAS-ISODYNAMIC TO 1st TRI-SQUARES-CENTRAL

Barycentrics    2*S*(9*(b^2+c^2)*a^4-6*(b^2-c^2)^2*a^2-3*(b^4-c^4)*(b^2-c^2)+2*(10*a^4+(b^2+c^2)*a^2-11*(b^2-c^2)^2)*S)*sqrt(3)+2*(14*a^6+7*(b^2+c^2)*a^4-8*(b^4-3*b^2*c^2+c^4)*a^2-13*(b^4-c^4)*(b^2-c^2))*S+12*a^8-3*(b^2+c^2)*a^6+3*(3*b^2+c^2)*(b^2+3*c^2)*a^4-9*(b^2-c^2)^2*(b^2+c^2)*a^2-3*(b^2-c^2)^2*(3*b^4+2*b^2*c^2+3*c^4) : :
X(49972) = X(23002)-3*X(41036) = 3*X(25159)-X(41020) = X(25201)+3*X(41024)

The reciprocal orthologic center of these triangles is X(13705).

X(49972) lies on these lines: {4, 25193}, {115, 13687}, {530, 41050}, {1503, 31715}, {13706, 41040}, {23002, 41036}, {23020, 41038}, {25159, 41020}, {25185, 41022}, {25201, 41024}, {33486, 41034}, {35757, 41018}, {36340, 41030}, {36353, 41032}, {36376, 41026}, {36396, 41028}, {36786, 41019}

X(49972) = orthologic center (1st Altintas-isodynamic, 1st tri-squares-central)


X(49973) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ALTINTAS-ISODYNAMIC TO 1st TRI-SQUARES-CENTRAL

Barycentrics    -2*S*(9*(b^2+c^2)*a^4-6*(b^2-c^2)^2*a^2-3*(b^4-c^4)*(b^2-c^2)+2*(10*a^4+(b^2+c^2)*a^2-11*(b^2-c^2)^2)*S)*sqrt(3)+2*(14*a^6+7*(b^2+c^2)*a^4-8*(b^4-3*b^2*c^2+c^4)*a^2-13*(b^4-c^4)*(b^2-c^2))*S+12*a^8-3*(b^2+c^2)*a^6+3*(3*b^2+c^2)*(b^2+3*c^2)*a^4-9*(b^2-c^2)^2*(b^2+c^2)*a^2-3*(b^2-c^2)^2*(3*b^4+2*b^2*c^2+3*c^4) : :
X(49973) = X(23011)-3*X(41037) = 3*X(25169)-X(41021) = X(25205)+3*X(41025)

The reciprocal orthologic center of these triangles is X(13703).

X(49973) lies on these lines: {4, 25197}, {115, 13687}, {531, 41049}, {1503, 31718}, {13704, 41041}, {23011, 41037}, {23026, 41039}, {25169, 41021}, {25189, 41023}, {25205, 41025}, {33487, 41035}, {36341, 41031}, {36360, 41033}, {36380, 41027}, {36400, 41029}

X(49973) = orthologic center (2nd Altintas-isodynamic, 1st tri-squares-central)


X(49974) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 1st ALTINTAS-ISODYNAMIC TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    2*S*(9*(b^2+c^2)*a^4-6*(b^2-c^2)^2*a^2-3*(b^4-c^4)*(b^2-c^2)-2*(10*a^4+(b^2+c^2)*a^2-11*(b^2-c^2)^2)*S)*sqrt(3)-2*(14*a^6+7*(b^2+c^2)*a^4-8*(b^4-3*b^2*c^2+c^4)*a^2-13*(b^4-c^4)*(b^2-c^2))*S+12*a^8-3*(b^2+c^2)*a^6+3*(3*b^2+c^2)*(b^2+3*c^2)*a^4-9*(b^2-c^2)^2*(b^2+c^2)*a^2-3*(b^2-c^2)^2*(3*b^4+2*b^2*c^2+3*c^4) : :
X(49974) = X(23003)-3*X(41036) = 3*X(25160)-X(41020) = X(25202)+3*X(41024)

The reciprocal orthologic center of these triangles is X(13825).

X(49974) lies on these lines: {4, 25194}, {115, 13807}, {530, 41048}, {1503, 31717}, {13826, 41040}, {23003, 41036}, {23021, 41038}, {25160, 41020}, {25186, 41022}, {25202, 41024}, {33488, 41034}, {35758, 41018}, {36342, 41030}, {36355, 41032}, {36377, 41026}, {36397, 41028}, {36787, 41019}

X(49974) = orthologic center (1st Altintas-isodynamic, 2nd tri-squares-central)


X(49975) = ORTHOLOGIC CENTER OF THESE TRIANGLES: 2nd ALTINTAS-ISODYNAMIC TO 2nd TRI-SQUARES-CENTRAL

Barycentrics    -2*S*(9*(b^2+c^2)*a^4-6*(b^2-c^2)^2*a^2-3*(b^4-c^4)*(b^2-c^2)-2*(10*a^4+(b^2+c^2)*a^2-11*(b^2-c^2)^2)*S)*sqrt(3)-2*(14*a^6+7*(b^2+c^2)*a^4-8*(b^4-3*b^2*c^2+c^4)*a^2-13*(b^4-c^4)*(b^2-c^2))*S+12*a^8-3*(b^2+c^2)*a^6+3*(3*b^2+c^2)*(b^2+3*c^2)*a^4-9*(b^2-c^2)^2*(b^2+c^2)*a^2-3*(b^2-c^2)^2*(3*b^4+2*b^2*c^2+3*c^4) : :
X(49975) = X(23012)-3*X(41037) = 3*X(25170)-X(41021) = X(25206)+3*X(41025)

The reciprocal orthologic center of these triangles is X(13823).

X(49975) lies on these lines: {4, 25198}, {115, 13807}, {531, 41051}, {1503, 31716}, {13824, 41041}, {23012, 41037}, {23027, 41039}, {25170, 41021}, {25190, 41023}, {25206, 41025}, {33489, 41035}, {36343, 41031}, {36361, 41033}, {36381, 41027}, {36401, 41029}

X(49975) = orthologic center (2nd Altintas-isodynamic, 2nd tri-squares-central)


X(49976) = PARALLELOGIC CENTER OF THESE TRIANGLES: 1st ALTINTAS-ISODYNAMIC TO VU-DAO-X(16)-ISODYNAMIC

Barycentrics    2*sqrt(3)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*((b^2+c^2)*a^2-b^4-c^4)*(2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)*S+6*(b^2+c^2)*a^12-(5*b^4+14*b^2*c^2+5*c^4)*a^10-(b^2+c^2)*(17*b^4-40*b^2*c^2+17*c^4)*a^8+2*(b^2-c^2)^2*(11*b^4+12*b^2*c^2+11*c^4)*a^6-4*(b^4-c^4)^2*(b^2+c^2)*a^4-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^4*a^2-(b^4-c^4)*(b^2-c^2)^3*(b^4+4*b^2*c^2+c^4) : :

The reciprocal parallelogic center of these triangles is X(4).

X(49976) lies on the circumcircle of 1st Altintas-isodynamic triangle and these lines: {1503, 6111}, {23871, 41070}, {36774, 41019}, {39838, 41023}, {41016, 41066}, {41026, 49931}, {41028, 41092}, {41030, 49842}, {41032, 41132}

X(49976) = parallelogic center (1st Altintas-isodynamic, Vu-Dao-X(16)-isodynamic)
X(49976) = reflection of X(41066) in X(41016)


X(49977) = PARALLELOGIC CENTER OF THESE TRIANGLES: 2nd ALTINTAS-ISODYNAMIC TO VU-DAO-X(15)-ISODYNAMIC

Barycentrics    -2*sqrt(3)*(a^2+b^2-c^2)*(a^2-b^2+c^2)*((b^2+c^2)*a^2-b^4-c^4)*(2*a^4-(b^2+c^2)*a^2-(b^2-c^2)^2)*S+6*(b^2+c^2)*a^12-(5*b^4+14*b^2*c^2+5*c^4)*a^10-(b^2+c^2)*(17*b^4-40*b^2*c^2+17*c^4)*a^8+2*(b^2-c^2)^2*(11*b^4+12*b^2*c^2+11*c^4)*a^6-4*(b^4-c^4)^2*(b^2+c^2)*a^4-(-4*b^2*c^2+(b^2-c^2)^2)*(b^2-c^2)^4*a^2-(b^4-c^4)*(b^2-c^2)^3*(b^4+4*b^2*c^2+c^4) : :

The reciprocal parallelogic center of these triangles is X(4).

X(49977) lies on the circumcircle of 2nd Altintas-isodynamic triangle and these lines: {1503, 6110}, {23870, 41071}, {39838, 41022}, {41017, 41067}, {41027, 49932}, {41029, 49971}, {41031, 49841}, {41033, 49840}

X(49977) = parallelogic center (2nd Altintas-isodynamic, Vu-Dao-X(15)-isodynamic)
X(49977) = reflection of X(41067) in X(41017)


X(49978) = PERSPECTOR OF THESE TRIANGLES: 1st ANTI-BROCARD AND 1st PAMFILOS-ZHOU

Barycentrics    (2*(b^2-c^2)*(b-c)*a^16-4*b^2*c^2*a^15-2*(b^3+c^3)*(4*b^2+b*c+4*c^2)*a^14+2*(b^2+c^2)^3*a^13+2*(b+c)*(b^4+c^4-b*c*(11*b^2-13*b*c+11*c^2))*b*c*a^12-2*(4*b^8+4*c^8-(b^6+c^6-(3*b^4+3*c^4-b*c*(5*b^2+14*b*c+5*c^2))*b*c)*b*c)*a^11+2*(b+c)*(4*b^8+4*c^8-(4*b^6+4*c^6-(27*b^4+27*c^4-b*c*(14*b^2-45*b*c+14*c^2))*b*c)*b*c)*a^10-2*(8*b^8+8*c^8+(14*b^6+14*c^6+(19*b^4+19*c^4+2*b*c*(5*b^2+9*b*c+5*c^2))*b*c)*b*c)*b*c*a^9-2*(b+c)*(b^10+c^10+(5*b^6+5*c^6+(6*b^4+6*c^4-b*c*(17*b^2-25*b*c+17*c^2))*b*c)*b^2*c^2)*a^8+4*(2*b^12+2*c^12+(7*b^10+7*c^10+(10*b^8+10*c^8+(12*b^6+12*c^6+(9*b^4+9*c^4+b*c*(8*b^2-b*c+8*c^2))*b*c)*b*c)*b*c)*b*c)*a^7+2*(b+c)*(b^10+c^10+(3*b^8+3*c^8+(7*b^6+7*c^6-4*(9*b^4+9*c^4-b*c*(5*b^2-22*b*c+5*c^2))*b*c)*b*c)*b*c)*b*c*a^6-2*(b^12+c^12+(6*b^10+6*c^10-(12*b^8+12*c^8-(6*b^6+6*c^6-(9*b^4+9*c^4-2*b*c*(7*b^2+6*b*c+7*c^2))*b*c)*b*c)*b*c)*b*c)*(b+c)^2*a^5+2*(b+c)*(b^12+c^12+(7*b^10+7*c^10+(b^8+c^8+(37*b^6+37*c^6+(7*b^4+7*c^4-20*b*c*(2*b^2-b*c+2*c^2))*b*c)*b*c)*b*c)*b*c)*b*c*a^4+2*(b^14+c^14+(b^12+c^12-(5*b^10+5*c^10-(4*b^8+4*c^8+(27*b^6+27*c^6+(5*b^4+5*c^4-b*c*(23*b^2+12*b*c+23*c^2))*b*c)*b*c)*b*c)*b*c)*b*c)*b*c*a^3-2*(b+c)*(3*b^12+3*c^12-(11*b^8+11*c^8-(4*b^6+4*c^6-(21*b^4+21*c^4-2*b*c*(6*b^2+7*b*c+6*c^2))*b*c)*b*c)*b^2*c^2)*b^2*c^2*a^2-2*(b^2-c^2)^4*(b^4+4*b^2*c^2+c^4)*b^3*c^3*a-2*(b^4-c^4)*b^4*c^4*(b^3-c^3)*(b^4-4*b^2*c^2+c^4))*S+b*c*a^19+(b^2+b*c+c^2)*(b^2-3*b*c+c^2)*a^17+(b^2-c^2)*(b-c)*b*c*a^16-(2*b^6+2*c^6+(6*b^4+6*c^4-b*c*(5*b^2-22*b*c+5*c^2))*b*c)*a^15+(b+c)*(b^6+c^6-(2*b^4+2*c^4-(4*b^2-7*b*c+4*c^2)*b*c)*b*c)*a^14+(6*b^6+6*c^6-11*(2*b^4+2*c^4-(b-c)^2*b*c)*b*c)*b*c*a^13-(b+c)*(2*b^8+2*c^8-(3*b^6+3*c^6-(2*b^4+2*c^4-(10*b^2+9*b*c+10*c^2)*b*c)*b*c)*b*c)*a^12+(2*b^10+2*c^10+(28*b^6+28*c^6+(37*b^4+37*c^4+(19*b^2+99*b*c+19*c^2)*b*c)*b*c)*b^2*c^2)*a^11-(b+c)*(14*b^8+14*c^8+(8*b^6+8*c^6+(30*b^4+30*c^4+(14*b^2+5*b*c+14*c^2)*b*c)*b*c)*b*c)*b*c*a^10-(b^12+c^12+(6*b^10+6*c^10+(18*b^8+18*c^8+(36*b^6+36*c^6-(29*b^4+29*c^4-(11*b^2-45*b*c+11*c^2)*b*c)*b*c)*b*c)*b*c)*b*c)*a^9+(b+c)*(2*b^12+2*c^12+(25*b^10+25*c^10+(8*b^8+8*c^8+(37*b^6+37*c^6+(6*b^4+6*c^4+(27*b^2-5*b*c+27*c^2)*b*c)*b*c)*b*c)*b*c)*b*c)*a^8+(6*b^12+6*c^12+(9*b^10+9*c^10+(4*b^8+4*c^8-(47*b^6+47*c^6+4*(15*b^4+15*c^4+(13*b^2+31*b*c+13*c^2)*b*c)*b*c)*b*c)*b*c)*b*c)*b*c*a^7-(b+c)*(b^14+c^14+(16*b^12+16*c^12-(19*b^8+19*c^8+(4*b^6+4*c^6-(4*b^4+4*c^4-(7*b^2-120*b*c+7*c^2)*b*c)*b*c)*b*c)*b^2*c^2)*b*c)*a^6+(2*b^14+2*c^14+(4*b^12+4*c^12+(27*b^10+27*c^10+(68*b^8+68*c^8+(57*b^6+57*c^6-2*(11*b^2+42*b*c+11*c^2)*b^2*c^2)*b*c)*b*c)*b*c)*b*c)*b*c*a^5+(3*b^12+3*c^12-(6*b^10+6*c^10+(3*b^8+3*c^8-(11*b^6+11*c^6+(39*b^4+39*c^4-(89*b^2-92*b*c+89*c^2)*b*c)*b*c)*b*c)*b*c)*b*c)*(b+c)^3*b*c*a^4-(b^16+c^16+(6*b^14+6*c^14+(3*b^12+3*c^12+(7*b^10+7*c^10-(15*b^8+15*c^8+(75*b^6+75*c^6+(15*b^4+15*c^4-2*(27*b^2+10*b*c+27*c^2)*b*c)*b*c)*b*c)*b*c)*b*c)*b*c)*b*c)*b*c*a^3-(b^2-c^2)*(b-c)*(2*b^10+2*c^10+(4*b^8+4*c^8+(5*b^6+5*c^6+(8*b^4+8*c^4-(13*b^2+28*b*c+13*c^2)*b*c)*b*c)*b*c)*b*c)*b^3*c^3*a^2+(b^2-c^2)^2*(b^12+c^12-(4*b^8+4*c^8+(b^6+c^6+b*c*(3*b-2*c)*(2*b-3*c)*(b+c)^2)*b*c)*b^2*c^2)*b^2*c^2*a-(b^4-c^4)*(b^2-c^2)^2*b^5*c^5*(b^3-c^3) : :

X(49978) lies on these lines: {1916, 7594}, {8304, 11945}, {8305, 11946}, {39652, 39869}

X(49978) = perspector (1st anti-Brocard, 1st Pamfilos-Zhou)

leftri

Points in a [[bc,ca,ab], [b-c,c-a,a-b]] coordinate system: X(49979)-X(50003)

rightri

If L1 and L2 are lines that meet in a point P not at infinity, then a [L1, L2]-coordinate system is a bivariate coordinate system having L1 as x-axis, L2 as y-axis, and P as origin. In this section, L1 and L2 are the following lines:

L1 is the line: bc α + ca β ab γ = 0.

L2 is the line (b-c) α + (c-a) β + (a-b) γ = 0 (Nagel line).

The origin is given by (0,0) = X(899) = a(2bc-ab-ac) : : .

Barycentrics u : v : w for a triangle center U = (x, y) in this system are given by

u : v : w = -a(a b + a c - 2 b c) - a(b-c) x + (2a - b - c) y : : ,

where, as functions of a, b, c, the coordinate x is antisymmetric of degree 1, and y is symmetric of degree 2.

The appearance of {x, y}, k in the following list means that (x, y) = X(k).

{-(((a-b) (a-c) (b-c) (a+b+c))/(2 a b c)), (a^3+b^3+c^3)/(a+b+c)}, 72
{0, -a b-a c-b c}, 19998
{0, -((a b c)/(a+b+c))}, 31855
{0, 0}, 899
{0, 1/2 (a b+a c+b c)}, 4871
{0, a b+a c+b c}, 29824
{0, (2 a b c)/(a+b+c)}, 1149
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c), (a + b + c)^2/2}, 49979
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c), (a + b + c)^2}, 49980
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c), a^2 + b^2 + c^2}, 49981
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c), a^2 + a*b + b^2 + a*c + b*c + c^2}, 49982
{0, -2*(a*b + a*c + b*c)}, 49983
{0, (-2*a*b*c)/(a + b + c)}, 49984
{0, -(a + b + c)^2}, 49985
{0, -1/2*(a + b + c)^2}, 49986
{0, (-a^2 - b^2 - c^2)/2}, 49987
{0, (-(a*b) - a*c - b*c)/2}, 49988
{0, (-a^2 + 2*a*b - b^2 + 2*a*c + 2*b*c - c^2)/2}, 49989
{0, (a + b + c)^2/2}, 49990
{0, (a^2 + b^2 + c^2)/2}, 49991
{0, (a*b*c)/(2*(a + b + c))}, 49992
{0, ((a + b)*(a + c)*(b + c))/(2*(a + b + c))}, 49993
{0, (a^2 + a*b + b^2 + a*c + b*c + c^2)/2}, 49994
{0, (a + b + c)^2}, 49995
{0, a^2 + b^2 + c^2}, 49996
{0, (a*b*c)/(a + b + c)}, 49997
{0, (a^3 + b^3 + c^3)/(a + b + c)}, 49998
{0, ((a + b)*(a + c)*(b + c))/(a + b + c)}, 49999
{0, a^2 + a*b + b^2 + a*c + b*c + c^2}, 50000
{0, 2*(a*b + a*c + b*c)}, 50001
{((a - b)*(a - c)*(b - c)*(a + b + c))/(2*a*b*c), -((a^3 + b^3 + c^3)/(a + b + c))}, 50002
{((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c), a*b + a*c + b*c}, 50003


X(49979) = X(45)X(899)∩X(72)X(519)

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

X(49979) lies on these lines: {45, 899}, {51, 22034}, {72, 519}, {373, 4686}, {375, 4365}, {513, 3700}, {674, 3994}, {4009, 6007}


X(49980) = X(37)X(899)∩X(72)X(519)

Barycentrics    a*(b + c)*(a^3*b - a*b^3 + a^3*c + 4*a^2*b*c + 2*a*b^2*c - b^3*c + 2*a*b*c^2 - 6*b^2*c^2 - a*c^3 - b*c^3) : :
X(49980) = 3 X[210] - 2 X[19998], 3 X[354] - 4 X[29824], 7 X[3983] - 6 X[31855]

X(49980) lies on these lines: {37, 899}, {72, 519}, {210, 3896}, {321, 354}, {513, 4024}, {740, 22045}, {3698, 3714}, {3702, 34791}, {3909, 31011}, {3931, 3983}, {3994, 44671}, {4015, 4065}, {4871, 31993}, {14464, 21873}


X(49981) = X(38)X(210)∩X(72)X(519)

Barycentrics    a*(a^3*b^2 - a*b^4 + 2*a^3*b*c - 4*a^2*b^2*c + 5*a*b^3*c - b^4*c + a^3*c^2 - 4*a^2*b*c^2 + 4*a*b^2*c^2 - 3*b^3*c^2 + 5*a*b*c^3 - 3*b^2*c^3 - a*c^4 - b*c^4) : :
X(49981) = 3 X[210] - 2 X[899], 3 X[354] - 4 X[4871], 3 X[3681] - X[19998], 5 X[3890] - 3 X[20039]

X(49981) lies on these lines: {38, 210}, {72, 519}, {341, 3868}, {354, 4871}, {513, 4088}, {518, 3952}, {726, 22313}, {986, 31855}, {3681, 17147}, {3689, 23845}, {3881, 25079}, {3890, 20039}, {4696, 5836}, {18191, 32927}, {42083, 44671}


X(49982) = X(72)X(519)∩X(192)X(19998)

Barycentrics    a*(a^3*b^2 - a*b^4 + 2*a^3*b*c + 3*a*b^3*c - b^4*c + a^3*c^2 + 4*a*b^2*c^2 - 5*b^3*c^2 + 3*a*b*c^3 - 5*b^2*c^3 - a*c^4 - b*c^4) : :
X(49982) = 3 X[3873] - 5 X[29824], 5 X[899] - 6 X[3740]

X(49982) lies on these lines: {72, 519}, {192, 19998}, {210, 4970}, {312, 3873}, {513, 4122}, {518, 3994}, {756, 899}, {942, 1089}, {2292, 4662}, {4871, 24325}, {22275, 32925}, {22295, 49474}, {22313, 28522}


X(49983) = X(1)X(2)∩X(513)X(4963)

Barycentrics    5*a^2*b - 2*a*b^2 + 5*a^2*c - 2*a*b*c - 2*b^2*c - 2*a*c^2 - 2*b*c^2 : :
X(49983) = 6 X[2] - 7 X[899], 15 X[2] - 14 X[4871], 3 X[2] - 7 X[19998], 9 X[2] - 7 X[29824], 5 X[899] - 4 X[4871], 3 X[899] - 2 X[29824], 2 X[4871] - 5 X[19998], 6 X[4871] - 5 X[29824], 3 X[19998] - X[29824], 2 X[4009] - 3 X[21805]

X(49983) lies on these lines: {1, 2}, {513, 4963}, {672, 4969}, {750, 49680}, {1962, 4113}, {2238, 4727}, {2239, 49702}, {2308, 3996}, {3681, 49452}, {3779, 6144}, {3896, 49456}, {4009, 21805}, {4465, 28329}, {4519, 4849}, {4819, 32848}, {4850, 49689}, {4873, 37657}, {8168, 16405}, {17147, 49508}, {31161, 49468}, {32860, 49499}, {46901, 49450}

X(49983) = reflection of X(899) in X(19998)
X(49983) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 42, 30970}, {3240, 3632, 31136}, {3625, 4946, 2}, {4685, 20011, 3720}


X(49984) = X(1)X(2)∩X(513)X(4041)

Barycentrics    a*(a^2*b + a*b^2 + a^2*c + 4*a*b*c - 4*b^2*c + a*c^2 - 4*b*c^2) : :
X(49984) = 2 X[1] - 5 X[899], 4 X[1] - 5 X[1149], X[1] - 5 X[31855], X[1149] - 4 X[31855], 7 X[4678] + 5 X[19998], 10 X[4871] - 13 X[19877], X[20014] - 5 X[20039], 5 X[29824] - 11 X[46933]

X(49984) lies on these lines: {1, 2}, {513, 4041}, {517, 21805}, {518, 4695}, {740, 4723}, {902, 48696}, {999, 9350}, {1457, 36920}, {1458, 40663}, {1469, 9039}, {1574, 17474}, {1739, 17449}, {2177, 9708}, {2292, 4662}, {2347, 16885}, {3666, 4711}, {3691, 20691}, {3780, 21868}, {3989, 4868}, {4300, 5690}, {4383, 8168}, {4642, 34790}, {4731, 49478}, {4737, 32860}, {4742, 24003}, {6767, 17125}, {16418, 17782}, {17757, 33136}, {21342, 21896}

X(49984) = reflection of X(i) in X(j) for these {i,j}: {899, 31855}, {1149, 899}, {4742, 24003}, {17449, 1739}
X(49984) = crossdifference of every pair of points on line {649, 1449}
X(49984) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 3214, 1193}, {145, 6048, 27627}, {3293, 3626, 10459}, {20014, 27625, 1}


X(49985) = X(1)X(2)∩X(513)X(4988)

Barycentrics    2*a^3 + 4*a^2*b - b^3 + 4*a^2*c - 2*a*b*c - 3*b^2*c - 3*b*c^2 - c^3 : :
X(49985) = 2 X[899] + X[14464]

X(49985) lies on these lines: {1, 2}, {513, 4988}, {896, 4969}, {1086, 4938}, {3120, 4716}, {3722, 4819}, {3994, 4971}, {4009, 28329}, {4414, 5839}, {4527, 41241}, {4706, 4725}, {4886, 6536}, {17362, 46904}

X(49985) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {239, 14459, 4062}


X(49986) = X(1)X(2)∩X(513)X(4841)

Barycentrics    2*a^3 + 5*a^2*b - b^3 + 5*a^2*c - 4*a*b*c - 3*b^2*c - 3*b*c^2 - c^3 : :
X(49986) = 5 X[899] + X[14464]

X(49986) lies on these lines: {1, 2}, {513, 4841}, {524, 4706}, {896, 4700}, {908, 4716}, {1155, 4969}, {1279, 4819}, {3686, 46904}, {3994, 17133}, {4009, 4971}, {4023, 4852}, {17495, 34379}, {32860, 41011}

X(49986) = {X(5212),X(49770)}-harmonic conjugate of X(17763)


X(49987) = X(1)X(2)∩X(513)X(3004)

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

X(49987) lies on these lines: {1, 2}, {142, 33070}, {238, 3977}, {244, 5847}, {513, 3004}, {516, 17495}, {524, 3999}, {528, 4706}, {750, 49684}, {908, 32922}, {982, 4001}, {1266, 5057}, {1699, 19789}, {1738, 32844}, {2246, 4700}, {3246, 3712}, {3315, 4684}, {3452, 3891}, {3677, 5739}, {3686, 46909}, {3717, 37680}, {3739, 17726}, {3883, 4850}, {4009, 28503}, {4023, 49465}, {4078, 17125}, {4082, 26688}, {4349, 26627}, {4353, 26580}, {4361, 17721}, {4392, 4416}, {4413, 49681}, {4679, 49453}, {4887, 17491}, {5249, 33071}, {5542, 31034}, {5846, 16610}, {5850, 17154}, {6327, 24177}, {7290, 17740}, {17147, 40998}, {17353, 33089}, {17449, 34379}, {17769, 24003}, {24165, 41011}, {24199, 33112}, {24200, 24692}, {24210, 32924}, {24216, 32919}, {24231, 32843}, {31018, 49446}

X(49987) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {239, 5211, 26015}, {5212, 49771, 3935}, {7290, 17740, 35263}, {7292, 32842, 3912}


X(49988) = X(1)X(2)∩X(513)X(4507)

Barycentrics    4*a^2*b - a*b^2 + 4*a^2*c - 4*a*b*c - b^2*c - a*c^2 - b*c^2 : :
X(49988) = 3 X[2] - 5 X[899], 6 X[2] - 5 X[4871], 3 X[2] + 5 X[19998], 9 X[2] - 5 X[29824], 3 X[899] - X[29824], X[4871] + 2 X[19998], 3 X[4871] - 2 X[29824], 3 X[19998] + X[29824]

X(49988) lies on these lines: {1, 2}, {210, 4970}, {513, 4507}, {537, 4706}, {726, 21805}, {740, 4009}, {750, 49685}, {1155, 4753}, {1469, 4031}, {1575, 4969}, {2238, 2325}, {2276, 3707}, {3629, 17792}, {3681, 49508}, {3689, 4974}, {3699, 4716}, {3711, 32921}, {3952, 28522}, {3971, 49452}, {4003, 49449}, {4023, 4085}, {4090, 32860}, {4113, 6682}, {4152, 17793}, {4392, 49504}, {4395, 20335}, {4405, 21264}, {4413, 49497}, {4457, 44417}, {4465, 17133}, {4480, 17759}, {4681, 40607}, {4700, 20331}, {4709, 32931}, {4849, 49483}, {4850, 49510}, {4982, 24512}, {16373, 25439}, {17369, 21904}, {19546, 28234}, {21870, 24325}, {24003, 28581}, {24165, 49499}, {24620, 49498}, {30829, 49678}, {35992, 48696}, {42054, 49522}, {42056, 49462}

X(49988) = midpoint of X(899) and X(19998)
X(49988) = reflection of X(4871) in X(899)
X(49988) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {43, 4685, 3741}, {3633, 16569, 30947}, {3633, 30947, 42057}, {4651, 30970, 4691}, {4691, 6685, 30970}, {16569, 20012, 42057}, {20012, 30947, 3633}, {26038, 42042, 25501}


X(49989) = X(1)X(2)∩X(513)X(11934)

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

X(49989) lies on these lines: {1, 2}, {11, 4864}, {100, 24216}, {149, 24231}, {244, 5853}, {513, 11934}, {516, 17449}, {528, 3999}, {908, 49675}, {1738, 3315}, {2292, 40270}, {3058, 21342}, {3689, 3756}, {3722, 3911}, {3873, 41011}, {3914, 17597}, {4009, 9041}, {4414, 30331}, {4434, 49691}, {4684, 32844}, {5048, 6075}, {5219, 15600}, {5542, 33104}, {5718, 15570}, {12437, 32577}, {17125, 24393}, {17145, 34379}, {17154, 28526}, {17460, 28234}, {17721, 42871}, {18193, 20075}, {23710, 42070}, {24386, 33127}, {25531, 49698}, {27918, 49776}

X(49989) = crossdifference of every pair of points on line {218, 649}
X(49989) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 10916, 28027}, {1, 26015, 3011}, {1, 31146, 11269}


X(49990) = X(1)X(2)∩X(513)X(3700)

Barycentrics    2*a^3 + a^2*b - b^3 + a^2*c + 4*a*b*c - 3*b^2*c - 3*b*c^2 - c^3 : :
X(49990) = 7 X[899] - X[14464]

X(49990) lies on these lines: {1, 2}, {312, 41011}, {513, 3700}, {524, 4009}, {527, 3994}, {750, 2321}, {896, 2325}, {908, 32846}, {1150, 4078}, {1155, 3943}, {3452, 32852}, {3717, 32919}, {3790, 37684}, {3879, 32931}, {3911, 32848}, {3950, 4414}, {3952, 34379}, {3971, 4001}, {3977, 6541}, {3999, 28503}, {4023, 17372}, {4030, 4891}, {4082, 32912}, {4358, 5847}, {4413, 17299}, {4656, 33080}, {4684, 32927}, {4706, 4971}, {11246, 22034}, {17231, 17602}, {17311, 17718}, {17772, 24003}, {21255, 33143}, {24210, 33078}

X(49990) = crossdifference of every pair of points on line {649, 16466}
X(49990) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3912, 17763, 3011}, {5212, 49761, 14459}, {6745, 49765, 4062}, {9458, 14459, 5212}


X(49991) = X(1)X(2)∩X(513)X(4468)

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

X(49991) lies on these lines: {1, 2}, {100, 2751}, {329, 6555}, {513, 4468}, {515, 4723}, {516, 3952}, {528, 4009}, {750, 49529}, {908, 3699}, {1150, 24393}, {1376, 30615}, {1738, 32927}, {1810, 34234}, {2177, 4078}, {2201, 8756}, {2246, 2325}, {2550, 4054}, {3158, 17776}, {3218, 4899}, {3416, 3711}, {3452, 5014}, {3681, 4001}, {3689, 3932}, {3710, 5687}, {3740, 4030}, {3823, 17724}, {3967, 34612}, {3994, 28580}, {3999, 9041}, {4019, 40659}, {4082, 32929}, {4090, 41011}, {4104, 33074}, {4126, 4640}, {4358, 4939}, {4413, 49688}, {4434, 49693}, {4706, 28503}, {4767, 5057}, {4850, 49527}, {4901, 17740}, {4952, 17597}, {5100, 41012}, {5300, 21075}, {5423, 17784}, {5573, 30614}, {5744, 10005}, {5847, 21805}, {6327, 21060}, {8256, 42378}, {9053, 16610}, {9778, 25734}, {11682, 44722}, {17765, 24003}, {18908, 49131}, {20075, 30568}, {24589, 46916}, {25531, 49695}, {27549, 35258}, {32851, 43290}

X(49991) = crossdifference of every pair of points on line {649, 16502}
X(49991) = barycentric product X(i)*X(j) for these {i,j}: {75, 41391}, {306, 14954}
X(49991) = barycentric quotient X(i)/X(j) for these {i,j}: {14954, 27}, {41391, 1}, {46537, 17205}
X(49991) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 5205, 26015}, {10, 976, 25904}, {100, 3717, 3977}, {200, 10327, 306}, {3006, 17780, 6745}, {3699, 32850, 908}, {4901, 46917, 17740}, {5212, 49762, 32842}


X(49992) = X(1)X(2)∩X(513)X(4401)

Barycentrics    a*(2*a^2*b + 2*a*b^2 + 2*a^2*c - 2*a*b*c - 3*b^2*c + 2*a*c^2 - 3*b*c^2) : :
X(49992) = X[1] + 5 X[899], 3 X[1] - 5 X[1149], 3 X[1] + 5 X[31855], 3 X[899] + X[1149], 3 X[899] - X[31855], 5 X[4871] - 8 X[19878], 5 X[20039] + 3 X[31145]

X(49992) lies on these lines: {1, 2}, {36, 37680}, {44, 4973}, {72, 24167}, {88, 4880}, {513, 4401}, {758, 16610}, {982, 4134}, {993, 37679}, {1203, 17531}, {1464, 3911}, {1738, 11813}, {2234, 4759}, {3052, 25440}, {3752, 10176}, {3822, 37663}, {3892, 4849}, {3894, 9335}, {4067, 24046}, {4084, 24174}, {4256, 17123}, {4694, 21805}, {4794, 45323}, {5251, 37687}, {5400, 28164}, {5883, 16602}, {6681, 35466}, {8053, 8692}, {9350, 37610}, {16669, 21892}, {16814, 21796}, {17535, 37559}, {19335, 29353}, {20984, 28256}, {25591, 42031}, {26724, 37701}

X(49992) = midpoint of X(i) and X(j) for these {i,j}: {1149, 31855}, {4694, 21805}
X(49992) = reflection of X(24168) in X(16610)
X(49992) = crossdifference of every pair of points on line {649, 16777}
X(49992) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 28257, 19878}, {899, 1149, 31855}, {978, 16569, 995}, {978, 17749, 10}, {995, 16569, 10}, {995, 17749, 16569}, {3216, 27627, 1125}, {3293, 28352, 3636}


X(49993) = X(1)X(2)∩X(513)X(3814)

Barycentrics    a^2*b^2 + a*b^3 - 2*a^2*b*c - 3*a*b^2*c + b^3*c + a^2*c^2 - 3*a*b*c^2 + 2*b^2*c^2 + a*c^3 + b*c^3 : :
X(49993) = X[10] + 2 X[4871], X[899] - 4 X[3634], 5 X[1698] + X[29824], 5 X[1698] - X[31855], 5 X[3616] - X[20039], 13 X[19877] - X[19998]

X(49993) lies on these lines: {1, 2}, {121, 17757}, {244, 3992}, {513, 3814}, {517, 34587}, {596, 3701}, {726, 24168}, {750, 48866}, {758, 24003}, {958, 19248}, {993, 19261}, {1089, 24176}, {1215, 3833}, {1376, 19250}, {1574, 21070}, {1739, 4358}, {3159, 24443}, {3263, 21208}, {3264, 40039}, {3670, 4075}, {3726, 4103}, {3754, 25079}, {4013, 43922}, {4125, 24165}, {4245, 25440}, {4297, 19550}, {4413, 48863}, {4694, 4723}, {4695, 4975}, {4968, 6532}, {5123, 34589}, {5248, 19239}, {5267, 16374}, {5793, 16863}, {6381, 17205}, {6693, 25992}, {7951, 25961}, {9039, 49511}, {11813, 11814}, {17265, 31479}, {17761, 20530}, {18140, 24170}, {19549, 44039}, {21026, 38979}, {21251, 34832}, {24046, 24068}, {24166, 33932}, {25531, 40091}, {26688, 49500}, {46914, 49755}

X(49993) = midpoint of X(i) and X(j) for these {i,j}: {244, 3992}, {1739, 4358}, {4694, 4723}, {4695, 4975}, {17757, 34590}, {29824, 31855}
X(49993) = reflection of X(1149) in X(1125)
X(49993) = complement of the isotomic conjugate of X(40039)
X(49993) = X(i)-complementary conjugate of X(j) for these (i,j): {39698, 141}, {40039, 2887}
X(49993) = crosspoint of X(2) and X(40039)
X(49993) = crossdifference of every pair of points on line {649, 16685}
X(49993) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3634, 3831, 10}, {3741, 3828, 10}, {10459, 19847, 1125}, {20340, 49769, 10}, {24046, 46937, 24068}


X(49994) = X(1)X(2)∩X(513)X(4522)

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

X(49994) lies on these lines: {1, 2}, {100, 6541}, {513, 4522}, {752, 4009}, {1155, 4439}, {1215, 23812}, {2243, 2325}, {2796, 3994}, {3699, 32846}, {3932, 4434}, {3952, 17770}, {3974, 3980}, {3992, 38456}, {4358, 17766}, {4425, 33079}, {4645, 21093}, {5846, 24003}, {11814, 32844}, {16610, 17769}, {24169, 32926}, {30829, 49506}, {32919, 49697}, {32927, 49676}

X(49994) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10327, 29649, 29673}


X(49995) = X(1)X(2)∩X(513)X(4024)

Barycentrics    2*a^3 + 2*a^2*b - b^3 + 2*a^2*c + 2*a*b*c - 3*b^2*c - 3*b*c^2 - c^3 : :
X(49995) = 4 X[899] - X[14464]

X(49995) lies on these lines: {1, 2}, {81, 6535}, {513, 4024}, {524, 3994}, {750, 17299}, {896, 3943}, {1155, 4727}, {1255, 8040}, {3120, 32846}, {4009, 4725}, {4358, 17772}, {4414, 17314}, {4427, 31011}, {4706, 28329}, {4722, 6057}, {6536, 34064}, {6541, 16704}, {17295, 32775}, {17296, 33143}, {17309, 33156}, {17315, 32917}, {17373, 33065}, {17374, 32856}, {17377, 32931}, {17388, 46904}, {32949, 48642}, {33135, 48650}

X(49995) = crossdifference of every pair of points on line {649, 1203}
X(49995) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6542, 17763, 4062}


X(49996) = X(1)X(2)∩X(513)X(4088)

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

X(49996) lies on these lines: {1, 2}, {31, 30615}, {244, 9053}, {513, 4088}, {528, 3994}, {678, 3712}, {750, 49688}, {756, 4030}, {902, 3717}, {2246, 3943}, {3120, 32850}, {3689, 32848}, {3699, 32844}, {3722, 3932}, {3952, 17766}, {4358, 17765}, {4413, 49690}, {4450, 42054}, {4530, 49778}, {4850, 49534}, {4901, 33161}, {5846, 21805}, {6535, 32945}, {16704, 49697}, {17724, 21026}, {20871, 23858}, {21093, 21282}, {32919, 49698}, {33110, 48642}, {33126, 48650}, {42039, 44419}, {42720, 49754}, {46901, 49527}

X(49996) = crossdifference of every pair of points on line {649, 5299}
X(49996) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3935, 32847, 4062}, {3938, 10327, 29687}, {3961, 33091, 15523}, {32850, 32927, 3120}


X(49997) = X(1)X(2)∩X(36)X(238)

Barycentrics    a*(a^2*b + a*b^2 + a^2*c - 2*a*b*c - b^2*c + a*c^2 - b*c^2) : :
X(49997) = X[1] + 2 X[899], 4 X[1125] - X[29824], 2 X[1149] + X[31855], 5 X[3616] + X[19998], 7 X[3624] - 4 X[4871], X[4674] - 4 X[16610], X[17495] + 2 X[34587]

X(49997) lies on these lines: {1, 2}, {9, 5069}, {35, 16374}, {36, 238}, {38, 10176}, {39, 3294}, {40, 19550}, {44, 39982}, {46, 11512}, {55, 19261}, {56, 1724}, {57, 49500}, {58, 5253}, {63, 26747}, {72, 3953}, {87, 2163}, {100, 40091}, {101, 33854}, {105, 35333}, {106, 24625}, {171, 5315}, {191, 1050}, {213, 16604}, {214, 12746}, {226, 1450}, {244, 758}, {320, 17179}, {392, 3752}, {404, 595}, {474, 1191}, {484, 1054}, {495, 37663}, {515, 5400}, {517, 1739}, {518, 4694}, {538, 4465}, {740, 4975}, {748, 993}, {896, 4973}, {956, 37679}, {957, 2093}, {958, 19239}, {960, 3670}, {982, 5692}, {992, 17053}, {999, 4383}, {1001, 16357}, {1015, 2238}, {1018, 1575}, {1046, 3337}, {1052, 1757}, {1064, 10165}, {1089, 25079}, {1104, 17614}, {1107, 46196}, {1203, 20744}, {1279, 5440}, {1319, 4551}, {1376, 16483}, {1385, 37732}, {1420, 37694}, {1453, 19257}, {1457, 3911}, {1464, 5298}, {1519, 33810}, {1616, 5687}, {1621, 4256}, {1738, 30384}, {1740, 15485}, {1743, 2260}, {1745, 7963}, {1754, 22753}, {1759, 39248}, {1777, 40293}, {1914, 35342}, {1929, 17946}, {2170, 16611}, {2176, 16549}, {2234, 4432}, {2235, 24491}, {2275, 16552}, {2300, 28244}, {2802, 4695}, {3052, 16371}, {3057, 3987}, {3073, 37561}, {3120, 11813}, {3218, 43922}, {3246, 35338}, {3295, 19248}, {3304, 19253}, {3683, 37599}, {3684, 16784}, {3746, 19249}, {3751, 9039}, {3753, 16602}, {3825, 21935}, {3869, 24046}, {3878, 24443}, {3881, 46190}, {3884, 4642}, {3915, 25440}, {3940, 17597}, {3976, 5904}, {3992, 24003}, {4022, 49448}, {4216, 7280}, {4255, 19534}, {4257, 17127}, {4274, 28249}, {4281, 28619}, {4306, 5265}, {4359, 46895}, {4653, 5284}, {4719, 6051}, {4859, 34830}, {4880, 18201}, {5010, 8616}, {5204, 19251}, {5217, 19252}, {5247, 5563}, {5251, 17123}, {5258, 19244}, {5259, 19259}, {5288, 19242}, {5291, 9259}, {5396, 38028}, {5433, 37558}, {5443, 24161}, {5697, 24440}, {5710, 16408}, {5730, 17054}, {5886, 24789}, {5888, 41432}, {5902, 17063}, {5903, 24174}, {6160, 16589}, {6533, 49598}, {7208, 35102}, {7288, 10571}, {7299, 34880}, {7987, 19262}, {8666, 32577}, {9370, 41426}, {9549, 10439}, {9567, 39550}, {9624, 37529}, {9708, 16499}, {9709, 37542}, {10914, 45219}, {12047, 24178}, {12053, 22072}, {13624, 48897}, {15325, 34586}, {15803, 45047}, {16417, 37540}, {16466, 25524}, {16489, 48696}, {16600, 39244}, {16685, 46838}, {16971, 21904}, {16975, 37673}, {17064, 23708}, {17152, 24170}, {17164, 24176}, {17205, 20347}, {17495, 34587}, {17757, 24222}, {17889, 18393}, {18140, 34063}, {19263, 37575}, {19267, 41229}, {19275, 37602}, {19291, 37587}, {20227, 21078}, {20228, 21892}, {21077, 23675}, {21119, 47716}, {21363, 37620}, {21616, 23536}, {23537, 41012}, {24631, 46899}, {24806, 31231}, {25466, 37693}, {25917, 37592}, {27195, 37686}, {28554, 42083}, {33130, 37701}, {33944, 41805}, {35262, 37817}, {37618, 37836}, {39542, 40688}, {41002, 49723}, {46894, 49777}

X(49997) = midpoint of X(i) and X(j) for these {i,j}: {1, 31855}, {8, 20039}, {899, 1149}
X(49997) = reflection of X(i) in X(j) for these {i,j}: {1, 1149}, {1739, 16610}, {3992, 24003}, {4674, 1739}, {31855, 899}, {34590, 15325}
X(49997) = isotomic conjugate of X(40039)
X(49997) = isogonal conjugate of the isotomic conjugate of X(39995)
X(49997) = X(14554)-complementary conjugate of X(21245)
X(49997) = X(i)-Ceva conjugate of X(j) for these (i,j): {106, 1}, {37680, 44}
X(49997) = X(34587)-cross conjugate of X(1)
X(49997) = X(i)-isoconjugate of X(j) for these (i,j): {6, 39698}, {31, 40039}
X(49997) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 40039), (9, 39698), (4358, 3264), (34587, 10)
X(49997) = crosspoint of X(i) and X(j) for these (i,j): {86, 88}, {3257, 7035}
X(49997) = crosssum of X(i) and X(j) for these (i,j): {1, 31855}, {42, 44}, {1635, 3248}, {2087, 4705}
X(49997) = crossdifference of every pair of points on line {37, 649}
X(49997) = barycentric product X(i)*X(j) for these {i,j}: {1, 17495}, {6, 39995}, {88, 34587}, {92, 23169}
X(49997) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 39698}, {2, 40039}, {17495, 75}, {23169, 63}, {26844, 39995}, {34587, 4358}, {39995, 76}
X(49997) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 978, 3216}, {1, 3216, 3293}, {1, 6048, 3632}, {1, 16569, 3679}, {2, 995, 1}, {8, 27625, 17749}, {10, 1201, 1}, {42, 551, 1}, {239, 25510, 29456}, {239, 27166, 29769}, {386, 3616, 1}, {392, 3752, 4424}, {474, 1191, 5264}, {614, 997, 1}, {869, 24331, 1}, {976, 30148, 1}, {978, 21214, 1}, {992, 17053, 21061}, {1015, 2238, 45751}, {1125, 1193, 1}, {1125, 25512, 3624}, {1193, 28352, 1125}, {1201, 27627, 10}, {1376, 16483, 37610}, {1575, 3230, 1018}, {3741, 28247, 16569}, {3811, 28011, 1}, {3924, 30144, 1}, {4511, 7292, 30117}, {4511, 30117, 1}, {5313, 25055, 1}, {7191, 30115, 1}, {7292, 45763, 1}, {10459, 28257, 3634}, {16466, 25524, 37522}, {16827, 26959, 29433}, {17123, 37617, 5251}, {17749, 28370, 1}, {22350, 44675, 1}, {22836, 28082, 1}, {23511, 46943, 1}, {27625, 28370, 8}, {28247, 28360, 3741}, {28248, 28361, 3840}, {28254, 28371, 3912}, {29818, 49686, 1}, {30117, 45763, 4511}, {38460, 47622, 1}


X(49998) = X(1)X(2)∩X(72)X(513)

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

X(49998) lies on these lines: {1, 2}, {69, 4089}, {72, 513}, {80, 3699}, {516, 30196}, {952, 4738}, {1023, 2321}, {1043, 7206}, {1479, 44722}, {2087, 17362}, {3940, 4680}, {3992, 44669}, {4571, 10058}, {4756, 9963}, {4867, 32850}, {4899, 21578}, {9897, 21290}, {13744, 23343}, {16489, 49695}, {21090, 30729}, {32099, 38941}, {37706, 44720}

X(49998) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 6790, 1}, {8, 17780, 10}


X(49999) = X(1)X(2)∩X(513)X(1577)

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

X(49999) = X[8] + 5 X[29824], 6 X[551] - 5 X[1149], 5 X[899] - 8 X[3634], 7 X[3624] - 10 X[4871], 9 X[19875] - 5 X[31855], 5 X[19998] - 17 X[46932]

X(49999) lies on these lines: {1, 2}, {80, 30866}, {190, 4880}, {312, 5902}, {320, 18145}, {321, 5883}, {354, 4692}, {484, 3685}, {513, 1577}, {517, 4975}, {518, 3992}, {668, 41851}, {740, 1739}, {750, 48863}, {758, 4358}, {942, 1089}, {1203, 13741}, {1269, 7321}, {1478, 18141}, {2802, 4742}, {2901, 24443}, {3336, 7283}, {3583, 4645}, {3701, 3874}, {3702, 3754}, {3706, 4714}, {3714, 5439}, {3761, 30962}, {3812, 4647}, {3814, 3936}, {3822, 18139}, {3833, 4359}, {3881, 4696}, {3894, 32937}, {3967, 24473}, {4011, 49500}, {4084, 25253}, {4125, 17165}, {4385, 18398}, {4387, 36279}, {4423, 5774}, {4653, 32918}, {4680, 5722}, {4720, 9342}, {4869, 10590}, {4966, 17757}, {4973, 24593}, {5251, 14829}, {5295, 28611}, {5561, 7155}, {5687, 18613}, {5692, 18743}, {5904, 46937}, {6381, 30941}, {7270, 37702}, {7951, 18134}, {13740, 37559}, {16549, 21071}, {17057, 17241}, {17164, 33815}, {17242, 24223}, {17297, 31160}, {17361, 18133}, {17495, 24168}, {18409, 40893}, {20963, 21025}, {31318, 31359}

X(49999) = reflection of X(17495) in X(24168)


X(50000) = X(1)X(2)∩X(513)X(4122)

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

X(50000) lies on these lines: {1, 2}, {244, 17769}, {513, 4122}, {752, 3994}, {896, 4439}, {902, 6541}, {2243, 3943}, {3175, 4450}, {3416, 26580}, {3717, 16704}, {3769, 32862}, {3790, 17126}, {3883, 31035}, {3952, 5847}, {3974, 26223}, {4009, 28538}, {4358, 5846}, {4434, 32848}, {4480, 31301}, {5223, 31303}, {17184, 32926}, {17339, 30653}, {17602, 48647}, {17772, 21805}, {24210, 28599}, {32846, 32927}, {32928, 33079}

X(50000) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {17763, 32847, 3006}, {32926, 33078, 17184}



This is the end of PART 25: Centers X(48001) - X(50000)

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)