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

PART 1: Introduction and Centers X(1) - X(1000)
PART 2: Centers X(1001) - X(3000)
PART 3: Centers X(3001) - X(5000)
PART 4: Centers X(5001) - X(7000)
PART 5: Centers X(7001) - X(10000)
PART 6: Centers X(10001) - X(12000)
PART 7: Centers X(12001) - X(14000)
PART 8: Centers X(14001) - X(16000)
PART 9: Centers X(16001) - X(18000)
PART 10: Centers X(18001) - X(20000)
PART 11: Centers X(20001) - X(22000)
PART 12: Centers X(22001) - X(24000)
PART 13: Centers X(24001) - X(26000)
PART 14: Centers X(26001) - X(28000)
PART 15: Centers X(28001) - X(30000)
PART 16: Centers X(30001) - X(32000)
PART 17: Centers X(32001) - X(34000)
PART 18: Centers X(34001) - X(36000)
PART 19: Centers X(36001) - X(38000)
PART 20: Centers X(38001) - X(40000)
PART 21: Centers X(40001) - X(42000)
PART 22: Centers X(42001) - X(44000)
PART 23: Centers X(44001) - X(46000)
PART 24: Centers X(46001) - X(48000)
PART 25: Centers X(48001) - X(50000)


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}, {8652, 40600}, {34819, 38996}, {37211, 40586}
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}, {4778, 4790}
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(28176)-Dao conjugate of X(32664)
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): {668, 31336}, {1015, 42335}
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(29143)-Dao conjugate of X(32664)
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(28895)-Dao conjugate of X(32664)
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(29022)-Dao conjugate of X(32664)
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}, {28148, 32664}
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(29048)-Dao conjugate of X(32664)
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): {190, 39048}, {513, 35355}, {646, 35111}, {668, 16593}, {1015, 36807}, {1280, 8054}, {1810, 34467}, {6078, 32664}, {35160, 40617}
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(29289)-Dao conjugate of X(32664)
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}, {28847, 40586}
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}, {28196, 40600}
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(4427)-Dao conjugate of X(17239)
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): {907, 40589}, {1015, 23051}, {1086, 18840}, {5190, 8801}, {8054, 39951}, {34817, 39006}
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}, {497, 1146}, {614, 1015}, {1040, 35072}, {1084, 40934}, {1086, 4000}, {1473, 39006}, {1851, 5190}, {2968, 6554}, {3673, 40619}, {4319, 35508}, {5139, 8020}, {5286, 5515}, {7083, 38991}, {7124, 38983}, {7195, 40615}, {7289, 26932}, {8054, 16502}, {14714, 30706}, {15526, 18589}, {17170, 40618}, {17441, 34591}, {21750, 38986}, {22057, 35071}, {27509, 40626}, {28017, 40617}
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}, {3715, 38991}, {3927, 39006}, {4654, 40617}, {4716, 40623}, {4727, 38979}, {4820, 6615}, {8054, 16777}, {30596, 40619}
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}, {40030, 40619}
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}, {37, 15449}, {39, 100}, {82, 1086}, {83, 40619}, {101, 40585}, {115, 18098}, {141, 692}, {213, 3124}, {251, 1015}, {321, 339}, {514, 18108}, {827, 40592}, {1111, 18087}, {1176, 26932}, {1783, 40938}, {4553, 6665}, {4577, 34021}, {4599, 6626}, {4858, 18082}, {8054, 46289}, {10547, 34467}, {21208, 32911}, {21802, 39691}, {34055, 40618}, {34072, 40589}
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}, {40031, 40619}
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}, {3732, 17279}
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): {75, 38960}, {969, 8054}
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): {10, 15527}, {190, 6292}, {1086, 10159}, {3108, 8054}, {3589, 4568}, {4988, 31065}, {6626, 35137}, {7953, 40589}, {15523, 39691}, {39006, 41435}
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): {907, 40592}, {1015, 39951}, {1086, 23051}, {18840, 40619}, {26932, 34817}
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): {1, 39015}, {3, 36147}, {8, 17419}, {9, 8707}, {9, 38992}, {10, 3125}, {141, 35334}, {190, 1211}, {223, 6648}, {244, 14624}, {333, 17197}, {478, 36098}, {661, 4581}, {960, 1018}, {1015, 1220}, {1086, 30710}, {1240, 40619}, {1791, 39006}, {2092, 3699}, {2298, 8054}, {2359, 34467}, {3666, 4033}, {31643, 40615}, {32664, 32736}
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): {8, 17417}, {223, 32038}, {931, 40589}, {941, 8054}, {1015, 31359}, {1086, 34258}, {3699, 34261}, {34259, 39006}, {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): {76, 1111}, {142, 3699}, {190, 40606}, {223, 6606}, {346, 3119}, {668, 1212}, {1015, 32008}, {2346, 8054}, {6605, 38991}, {10482, 39025}, {21453, 40617}, {31618, 40615}, {34467, 47487}
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): {37, 15527}, {100, 6292}, {1015, 3108}, {3589, 4553}, {3954, 39691}, {7953, 40592}, {10159, 40619}, {26932, 41435}, {34021, 35137}
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

underbar



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(28875)-Dao conjugate of X(32664)
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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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

underbar



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}, {664, 16589}, {1146, 32009}, {1400, 3121}, {1434, 17205}, {3739, 4551}, {40439, 40625}
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}, {4778, 47965}, {30679, 40618}
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(514)-Dao conjugate of X(20315)
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): {31, 21252}, {16757, 21178}
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(4427)-Dao conjugate of X(44307)
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}, {83, 1146}, {109, 141}, {115, 18097}, {226, 15449}, {251, 38991}, {339, 349}, {650, 10566}, {651, 40585}, {653, 40938}, {827, 40602}, {1176, 38983}, {1400, 3124}, {1799, 40626}, {3112, 40624}, {4577, 40605}, {4599, 40582}, {4628, 5452}, {6615, 18108}, {6741, 18082}, {20620, 32085}, {34055, 35072}, {39025, 46289}
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

underbar



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}, {521, 1459}
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}, {977, 1015}
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(5557)-Dao conjugate of X(8054)
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}, {3676, 4129}, {6615, 40086}, {8054, 20615}, {34594, 40602}, {37205, 40582}, {38991, 39798}, {39025, 40148}
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}, {32555, 32664}
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}, {32556, 32664}
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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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

underbar



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}, {4777, 4893}, {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}, {994, 1015}, {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): {75, 15611}, {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(3573)-Dao conjugate of X(3836)
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(3478)-Dao conjugate of X(39025)
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): {3551, 8054}, {20906, 31286}
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): {4408, 48008}, {8054, 39742}
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): {8, 2170}, {9, 8706}, {190, 3452}, {646, 3752}, {1015, 1222}, {1086, 32017}, {1261, 38991}, {6558, 12640}, {8054, 23617}, {14829, 24237}, {40420, 40617}
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}, {996, 1015}, {8054, 40401}, {36091, 40595}
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}, {668, 11530}, {8054, 30712}, {31503, 38986}
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): {3296, 8054}, {30679, 39006}
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(4777)-Dao conjugate of X(47779)
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(28883)-Dao conjugate of X(40586)
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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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, CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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 CÚsar 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}, {6, 119}, {9, 36052}, {115, 3657}, {517, 8609}, {913, 36103}, {915, 1249}, {1015, 42769}, {1737, 2323}, {3161, 45393}, {5375, 6099}, {14578, 39175}, {22383, 39002}, {23980, 39173}
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}, {6, 118}, {516, 8608}, {917, 1249}, {1459, 39003}, {35182, 39026}
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

underbar



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(905)-Dao conjugate of X(22383)
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): {311, 44311}, {1459, 4025}, {14714, 44040}, {22391, 40518}
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

underbar



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): {6, 3121}, {10, 8708}, {99, 16589}, {100, 3739}, {115, 32009}, {244, 40433}, {1015, 40408}, {1086, 40439}, {1509, 17205}, {1621, 2486}
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}, {86, 5515}, {662, 40181}, {1036, 40608}, {1084, 2221}, {1444, 17421}, {1472, 38986}, {6741, 30479}
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): {69, 1565}, {100, 15487}, {190, 6554}, {200, 14936}, {514, 48070}, {1018, 18589}, {1086, 30701}, {4000, 6558}, {4006, 17463}, {7123, 8054}, {7131, 40617}, {8817, 40615}
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(210)-Dao conjugate of X(4516)
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): {99, 6554}, {100, 18589}, {115, 30701}, {662, 15487}, {1015, 40403}, {1084, 7123}, {1565, 17206}, {2287, 14936}, {3681, 17463}, {4000, 7256}, {4561, 16583}, {4988, 48070}, {5190, 40411}, {7084, 38986}, {8269, 36908}, {8817, 40622}
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): {31, 3248}, {100, 34832}, {4595, 16604}
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}

underbar



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],