leftri rightri


This is PART 26: Centers X(50001) - X(52000)

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


X(50001) = X(1)X(2)∩X(513)X(4382)

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

X(50001) = 6 X[2] - 5 X[899], 9 X[2] - 10 X[4871], 9 X[2] - 5 X[19998], 3 X[2] - 5 X[29824], 3 X[899] - 4 X[4871], 3 X[899] - 2 X[19998], 15 X[1149] - 16 X[3636], 2 X[4871] - 3 X[29824], X[19998] - 3 X[29824], 3 X[244] - 2 X[4706]

X(50001) lies on these lines: {1, 2}, {38, 49462}, {244, 4706}, {321, 49491}, {354, 49468}, {513, 4382}, {518, 3994}, {672, 3943}, {726, 17145}, {740, 17449}, {750, 49460}, {756, 4891}, {896, 4702}, {902, 32919}, {1266, 30941}, {2239, 49699}, {2308, 32943}, {3056, 40341}, {3120, 4684}, {3315, 4716}, {3696, 17450}, {3756, 4819}, {3873, 4365}, {4392, 49469}, {4465, 4725}, {4490, 9260}, {4519, 31161}, {4671, 49498}, {4681, 22167}, {4686, 13476}, {4727, 20331}, {4850, 49678}, {4851, 30958}, {4883, 21020}, {4966, 33136}, {17154, 28522}, {23473, 32450}, {31035, 49510}, {32915, 49447}, {46901, 49470}, {46904, 49475}, {46909, 49471}

X(50001) = reflection of X(i) in X(j) for these {i,j}: {899, 29824}, {19998, 4871}
X(50001) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 31136, 30970}, {145, 10453, 30942}, {145, 30942, 42}, {3633, 31137, 3240}, {3635, 3741, 29822}, {4871, 19998, 899}, {17135, 42057, 3720}, {19998, 29824, 4871}, {26015, 49763, 4062}


X(50002) = X(65)X(519)∩X(72)X(899)

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

X(50002) = X[3885] - 3 X[20039], 4 X[4871] - 5 X[5439], X[5904] - 3 X[31855]

X(50002) lies on these lines: {65, 519}, {72, 899}, {392, 4003}, {513, 4707}, {518, 4674}, {726, 22306}, {942, 3702}, {960, 3670}, {1149, 37592}, {3753, 4692}, {3868, 19998}, {3885, 20039}, {4018, 34434}, {4871, 5439}, {5902, 49493}, {5904, 24440}

X(50002) = midpoint of X(3868) and X(19998)
X(50002) = reflection of X(i) in X(j) for these {i,j}: {72, 899}, {29824, 942}


X(50003) = X(58)X(5253)∩X(519)X(3868)

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

X(50003) lies on these lines: {58, 5253}, {320, 350}, {519, 3868}, {962, 37482}, {3218, 3909}, {3436, 26871}, {3681, 4001}, {3784, 32859}, {3869, 11573}, {3936, 3937}, {4014, 4442}, {4259, 19998}, {4417, 26910}, {7270, 19809}, {7998, 17347}, {8679, 22294}, {46909, 49537}


X(50004) = EULER LINE INTERCEPT OF X(6329)X(44493)

Barycentrics    a^10-3*(b^2+c^2)*a^8+2*(b^4+10*b^2*c^2+c^4)*a^6+(b^2+c^2)*(2*b^4-21*b^2*c^2+2*c^4)*a^4-(b^2-c^2)^2*(3*b^4+b^2*c^2+3*c^4)*a^2+(b^4-c^4)*(b^2-c^2)^3 : :

See Antreas Hatzipolakis and César Lozada, euclid 5102.

X(50004) lies on these lines: {2, 3}, {6329, 44493}, {9707, 11694}, {11444, 20126}, {15361, 46728}

X(50004) = {X(3530), X(10300)}-harmonic conjugate of X(550)


X(50005) = EULER LINE INTERCEPT OF X(5895)X(44755)

Barycentrics    5*a^10-7*(b^2+c^2)*a^8-2*(b^2-3*c^2)*(3*b^2-c^2)*a^6+(b^2+c^2)*(10*b^4-17*b^2*c^2+10*c^4)*a^4+(b^4-13*b^2*c^2+c^4)*(b^2-c^2)^2*a^2-3*(b^4-c^4)*(b^2-c^2)^3 : :

See Antreas Hatzipolakis and César Lozada, euclid 5102.

X(50005) lies on these lines: {2, 3}, {5895, 44755}, {12291, 15305}, {34796, 43835}


X(50006) = EULER LINE INTERCEPT OF X(567)X(40242)

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

X(50006) = X(382)-5*X(12173), 3*X(550)-5*X(6823), 4*X(550)-5*X(7525)

See Antreas Hatzipolakis and César Lozada, euclid 5102.

X(50006) lies on these lines: {2, 3}, {567, 40242}, {11438, 18379}, {13630, 34786}, {14449, 40909}, {18474, 34798}, {20427, 32316}, {37481, 43837}

X(50006) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (546, 16531, 5), (6240, 44263, 1658)


X(50007) = EULER LINE INTERCEPT OF X(567)X(15361)

Barycentrics    7*a^10-15*(b^2+c^2)*a^8+(2*b^4+17*b^2*c^2+2*c^4)*a^6+2*(b^2+c^2)*(7*b^4-9*b^2*c^2+7*c^4)*a^4-(b^2-c^2)^2*(9*b^4+13*b^2*c^2+9*c^4)*a^2+(b^4-c^4)*(b^2-c^2)^3 : :

X(50007) = 2*X(3)+X(7552), 5*X(3)+4*X(34577), X(20)+8*X(7542)

See Antreas Hatzipolakis and César Lozada, euclid 5102.

X(50007) lies on these lines: {2, 3}, {567, 15361}, {3431, 37779}, {6030, 10193}, {7998, 10628}, {9143, 11464}, {10168, 43584}, {11430, 15360}, {15020, 40107}, {15052, 35266}, {17845, 20391}, {41462, 48378}

X(50007) = anticomplement of X(49674)
X(50007) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 376, 3153), (3, 44262, 376), (186, 549, 2), (10989, 44261, 20), (15702, 18420, 2), (35921, 44214, 2)


X(50008) = EULER LINE INTERCEPT OF X(50)X(7737)

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

X(50008) = 9*X(2)-X(49670), 2*X(4)-3*X(11818), X(4)-3*X(18420), 5*X(4)+3*X(35513), 4*X(140)-3*X(7514)

See Antreas Hatzipolakis and César Lozada, euclid 5102.

X(50008) lies on these lines: {2, 3}, {50, 7737}, {67, 1352}, {68, 13630}, {70, 14861}, {113, 5651}, {125, 37470}, {182, 15118}, {184, 30714}, {265, 18911}, {511, 7706}, {541, 11178}, {542, 8542}, {566, 2549}, {599, 44791}, {1154, 37473}, {1204, 1209}, {1350, 40909}, {1514, 35283}, {1531, 5650}, {1899, 16270}, {2777, 4550}, {3763, 32620}, {3818, 14915}, {4549, 33533}, {5092, 18382}, {5486, 14984}, {5654, 15136}, {5878, 45959}, {5890, 41724}, {5892, 18390}, {6000, 18431}, {6288, 11457}, {6776, 32251}, {7739, 41335}, {8548, 8550}, {8717, 29012}, {9306, 15132}, {9729, 9927}, {9815, 10095}, {10510, 20423}, {10516, 11472}, {10574, 25738}, {10625, 31815}, {11003, 12383}, {11179, 32233}, {11180, 32306}, {11550, 14855}, {12006, 39571}, {12038, 22661}, {12118, 32046}, {12121, 14805}, {12233, 16266}, {12293, 37514}, {12295, 22112}, {12370, 36752}, {12429, 43588}, {13336, 21659}, {13347, 34786}, {13754, 34507}, {14852, 37475}, {15072, 41171}, {15113, 19506}, {15125, 43586}, {15126, 23329}, {16163, 39242}, {16187, 46686}, {17704, 18383}, {18309, 30230}, {18312, 30209}, {18313, 20186}, {18356, 18909}, {18400, 44491}, {18917, 45956}, {18933, 40685}, {19479, 48378}, {20417, 21243}, {20791, 25739}, {26937, 34826}, {32140, 40647}, {35237, 36990}, {35259, 46817}, {35450, 41736}, {39522, 44469}, {43620, 44529}

X(50008) = midpoint of X(i) and X(j) for these {i, j}: {1350, 40909}, {1352, 4846}, {18494, 35243}, {35237, 36990}
X(50008) = reflection of X(i) in X(j) for these (i, j): (4549, 33533), (4550, 24206), (11818, 18420), (31861, 5), (49669, 49671)
X(50008) = complement of X(49669)
X(50008) = anticomplement of X(49671)
X(50008) = intersection, other than A, B, C, of circumconics {{A, B, C, X(23), X(4846)}} and {{A, B, C, X(26), X(14861)}}
X(50008) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 381, 858), (3, 37196, 550), (4, 376, 5189), (5, 549, 5159), (5, 15122, 5094), (5, 47336, 381), (381, 11284, 5), (381, 18325, 4), (549, 47335, 3), (2045, 2046, 6640), (3530, 18377, 6643), (6823, 31833, 26), (7495, 10295, 3), (7528, 37201, 3627), (8703, 44288, 1370), (10996, 14790, 548), (12106, 25338, 4232), (13160, 37118, 1656), (16618, 37458, 26), (16977, 44241, 3), (18572, 44263, 4), (35921, 37978, 3), (37347, 37981, 5)


X(50009) = EULER LINE INTERCEPT OF X(74)X(5449)

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

X(50009) = 3*X(2)-4*X(10024), 2*X(3)-3*X(7552), 3*X(3)-4*X(34577), 3*X(4)-2*X(31724)

See Antreas Hatzipolakis and César Lozada, euclid 5102.

X(50009) lies on these lines: {2, 3}, {74, 5449}, {76, 13219}, {146, 2888}, {156, 12383}, {265, 13491}, {323, 22660}, {1478, 9538}, {1514, 15052}, {1531, 15644}, {1533, 13419}, {1539, 11591}, {1614, 3047}, {2777, 11440}, {2883, 14516}, {3100, 3585}, {3357, 23293}, {3410, 12162}, {3448, 6241}, {3521, 6102}, {3581, 34798}, {3583, 4296}, {4846, 18912}, {5012, 13403}, {5448, 43574}, {5876, 7728}, {5878, 11442}, {5925, 13203}, {6193, 12364}, {6225, 18387}, {6759, 12278}, {7706, 9781}, {7747, 10313}, {7748, 22240}, {8718, 11750}, {9544, 12118}, {9707, 12319}, {10574, 18390}, {10575, 25739}, {10733, 13198}, {11417, 35821}, {11418, 35820}, {11420, 19107}, {11421, 19106}, {11456, 12293}, {12121, 32171}, {12134, 32111}, {12220, 48901}, {12226, 15800}, {12244, 32138}, {12254, 15089}, {12279, 18381}, {12290, 18474}, {12317, 18356}, {12370, 15032}, {12897, 15033}, {12902, 45731}, {13418, 18550}, {13445, 20299}, {13851, 46850}, {14683, 32139}, {14927, 18382}, {15019, 40240}, {15062, 21243}, {16111, 20191}, {19121, 29012}, {20127, 32210}, {22528, 43584}, {22555, 35602}, {26881, 34785}, {32046, 43818}, {34148, 43831}, {34563, 41586}, {43605, 44665}

X(50009) = reflection of X(i) in X(j) for these (i, j): (20, 7488), (3520, 10024), (12086, 1594), (34148, 43831), (35491, 7542)
X(50009) = anticomplement of X(3520)
X(50009) = anticomplementary conjugate of the anticomplement of X(3521)
X(50009) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 16868, 2), (3, 44279, 4), (4, 20, 3153), (4, 7544, 3839), (4, 18420, 3832), (4, 44440, 20), (5, 31726, 4), (381, 44271, 4), (382, 44263, 4), (546, 16042, 3091), (550, 10125, 3), (3520, 10024, 2), (3529, 18569, 5189), (3627, 37946, 3146), (10254, 11250, 6143), (10565, 49135, 20), (37201, 37444, 20)


leftri

Points in a [[b+c,c+a,a+b], [b-c,c-a,a-b]] coordinate system: X(50010)-X(50030)

rightri

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

L1 is the line: (b+c) α + (c+a) β (a+)b γ = 0.

L2 is the line (b-c) α + (c-a) β + (a-b) γ = 0 (Nagel line).

The origin is given by (0,0) = X(239) = a^2 - bc : b^2 - ca : c^2 - ab .

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

u : v : w = -2(a^2 - bc) - (b-c)x + (2a - b - c) y : : ,

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

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

{-((2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2)), (2 (a^3+b^3+c^3))/(a^2+b^2+c^2)}, 69
{-(((a-b) (a-c) (b-c))/(a b+a c+b c)), ((a+b) (a+c) (b+c))/(a b+a c+b c)}, 49755
{-(((a-b) (a-c) (b-c) (a+b+c))/(2 a b c)), 1/2 (a+b+c)}, 49759
{-(((a-b) (a-c) (b-c) (a+b+c))/(2 (a+b) (a+c) (b+c))), 1/2 (a+b+c)}, 49760
{0, -2 (a+b+c)}, 20016
{0, -a-b-c}, 49770
{0, 0}, 239
{0, 1/2 (a+b+c)}, 3008
{0, a+b+c}, 3912
{0, (a^2+b^2+c^2)/(a+b+c)}, 49772
{0, ((a+b) (a+c) (b+c))/(a b+a c+b c)}, 30109
{0, 2 (a+b+c)}, 6542
{0, (2 (a^2+b^2+c^2))/(a+b+c)}, 8
{0, (2 (a b+a c+b c))/(a+b+c)}, 1
{((a-b) (a-c) (b-c) (a+b+c))/(2 a b c), 1/2 (a+b+c)}, 43040
{((a-b) (a-c) (b-c))/(a b+a c+b c), a+b+c}, 49780
{((a-b) (a-c) (b-c))/(a b+a c+b c), ((a+b) (a+c) (b+c))/(a b+a c+b c)}, 20924
{(2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2), (2 (a^3+b^3+c^3))/(a^2+b^2+c^2)}, 30225
{(-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), (2*a*b*c)/(a^2 + b^2 + c^2)}, 50010
{-(((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)), (a^3 + b^3 + c^3)/(a^2 + b^2 + c^2)}, 50011
{-1/2*((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c), -1/2*((a + b)*(a + c)*(b + c))/(a*b + a*c + b*c)}, 50012
{-1/2*((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), (a^3 + b^3 + c^3)/(2*(a^2 + b^2 + c^2))}, 50013
{-1/2*((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c), ((a + b)*(a + c)*(b + c))/(2*(a*b + a*c + b*c))}, 50014
{0, (-2*(a^2 + b^2 + c^2))/(a + b + c)}, 50015
{0, (-2*(a*b + a*c + b*c))/(a + b + c)}, 50016
{0, -((a^2 + b^2 + c^2)/(a + b + c))}, 50017
{0, -((a*b + a*c + b*c)/(a + b + c))}, 50018
{0, (-a - b - c)/2}, 50019
{0, -1/2*(a^2 + b^2 + c^2)/(a + b + c)}, 50020
{0, -1/2*(a*b + a*c + b*c)/(a + b + c)}, 50021
{0, (a^2 + b^2 + c^2)/(2*(a + b + c))}, 50022
{0, (a*b + a*c + b*c)/(a + b + c)}, 50023
{0, (2*(a^3 + b^3 + c^3))/(a^2 + b^2 + c^2)}, 50024
{((a - b)*(a - c)*(b - c))/(2*(a*b + a*c + b*c)), ((a + b)*(a + c)*(b + c))/(2*(a*b + a*c + b*c))}, 50025
{((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), -((a^3 + b^3 + c^3)/(a^2 + b^2 + c^2))}, 50026
{((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), (a^3 + b^3 + c^3)/(a^2 + b^2 + c^2)}, 50027
{((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), ((a + b)*(a + c)*(b + c))/(a^2 + b^2 + c^2)}, 50028
{(2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), (-2*a*b*c)/(a^2 + b^2 + c^2)}, 50029
{(2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2), (-2*(a^3 + b^3 + c^3))/(a^2 + b^2 + c^2)}, 50023


X(50010) = X(63)X(194)∩X(69)X(519)

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

X(50010) = 5 X[17286] - 4 X[49782], 5 X[17304] - 2 X[49778]

X(50010) lies on these lines: {1, 20924}, {2, 49781}, {63, 194}, {69, 519}, {75, 24291}, {76, 3502}, {99, 2382}, {192, 24249}, {515, 1266}, {712, 17738}, {1227, 17160}, {3476, 7195}, {3673, 3905}, {3729, 3734}, {3912, 25527}, {3961, 33934}, {4357, 16086}, {4360, 49779}, {4384, 49758}, {5293, 33944}, {6542, 17184}, {10436, 20893}, {17286, 49782}, {17304, 49778}, {17490, 24266}, {18816, 35169}, {20247, 37639}, {20911, 32945}, {20925, 32920}, {20934, 24255}, {28850, 32922}, {28885, 49709}, {32029, 35102}

X(50010) = anticomplement of X(49781)
X(50010) = {X(20893),X(30117)}-harmonic conjugate of X(10436)


X(50011) = X(6)X(142)∩X(37)X(141)

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

X(50011) = X[193] - 5 X[29590], 3 X[599] - X[49752], 3 X[41140] - X[49783], 5 X[3618] - 7 X[29607], 7 X[3619] - 5 X[17266], 5 X[3620] - X[6542], 4 X[3631] - X[49750], 4 X[3631] + X[49770], X[17310] - 3 X[21356], 3 X[21358] - 2 X[41141], X[32029] - 3 X[37756]

X(50011) lies on these lines: {1, 49776}, {2, 36404}, {6, 142}, {37, 141}, {44, 5845}, {69, 239}, {193, 29590}, {516, 49706}, {518, 1086}, {519, 599}, {524, 31138}, {536, 4437}, {674, 46149}, {990, 1352}, {1266, 9055}, {1386, 17392}, {1575, 9436}, {3094, 46180}, {3618, 27147}, {3619, 17248}, {3620, 3672}, {3631, 49750}, {3663, 49509}, {3668, 43040}, {3751, 6173}, {3763, 5257}, {3834, 25357}, {4260, 24476}, {4319, 12589}, {4327, 12588}, {4356, 49764}, {4398, 49502}, {4648, 16972}, {4684, 4864}, {4688, 49524}, {5224, 27487}, {5249, 37676}, {5847, 49676}, {7174, 32847}, {7289, 27626}, {9004, 20455}, {9025, 35119}, {16517, 17272}, {16605, 21258}, {17119, 49688}, {17170, 39248}, {17234, 49496}, {17310, 21356}, {17325, 49768}, {17395, 49465}, {21358, 41141}, {23980, 35094}, {24199, 49481}, {25023, 25067}, {26015, 27918}, {26543, 49760}, {29331, 48876}, {30379, 34253}, {31139, 47359}, {32029, 37756}

X(50011) = midpoint of X(i) and X(j) for these {i,j}: {69, 239}, {49750, 49770}
X(50011) = reflection of X(i) in X(j) for these {i,j}: {6, 3008}, {3912, 141}
X(50011) = anticomplement of X(49775)
X(50011) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 4000, 16973}, {3755, 49511, 3242}


X(50012) = X(37)X(519)∩X(81)X(239)

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

X(50012) = 3 X[239] - X[20924]

X(50012) lies on these lines: {37, 519}, {81, 239}, {213, 3902}, {758, 4969}, {1015, 4771}, {2238, 4975}, {2795, 4716}, {3735, 5839}, {3759, 24254}, {3780, 4692}, {17147, 40891}, {20016, 49753}, {48864, 49459}

X(50012) = midpoint of X(20016) and X(49753)


X(50013) = X(69)X(239)∩X(141)X(519)

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

X(50013) = X[6] - 3 X[41140], X[69] + 3 X[239], 3 X[599] - X[49750], 3 X[3008] - 2 X[3589], 4 X[3589] - 3 X[49775], 7 X[3619] - 3 X[17310], 5 X[3620] + 3 X[40891], 5 X[3763] - 3 X[3912], X[49688] - 3 X[49772], X[49679] - 3 X[49771], X[6144] - 3 X[49783], 4 X[34573] - 3 X[41141]

X(50013) lies on these lines: {6, 4795}, {69, 239}, {141, 519}, {142, 49684}, {518, 4395}, {599, 49750}, {742, 3008}, {1386, 34824}, {3416, 17290}, {3619, 17310}, {3620, 40891}, {3763, 3912}, {3818, 12610}, {3834, 5846}, {3844, 49766}, {4357, 16521}, {4361, 49688}, {4851, 49679}, {5847, 17067}, {6144, 49783}, {17045, 49768}, {17306, 32847}, {17313, 49681}, {34573, 41141}, {49752, 49770}

X(50013) = midpoint of X(49752) and X(49770)
X(50013) = reflection of X(i) in X(j) for these {i,j}: {49766, 3844}, {49775, 3008}


X(50014) = X(37)X(519)∩X(44)X(517)

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

X(50014) = 3 X[41140] + X[41773], 3 X[4688] - 2 X[20893], 5 X[31238] - 2 X[49780]

X(50014) lies on these lines: {2, 49779}, {37, 519}, {42, 21332}, {44, 517}, {239, 257}, {304, 24735}, {518, 21331}, {594, 49781}, {672, 21888}, {742, 49774}, {1015, 16611}, {1086, 35102}, {1100, 30117}, {1108, 21892}, {1212, 20691}, {1475, 21951}, {1575, 43065}, {1914, 5546}, {2082, 4426}, {2087, 49997}, {2170, 2238}, {2176, 4051}, {2275, 29590}, {3008, 6692}, {3061, 3507}, {3125, 45751}, {3691, 3727}, {3739, 16724}, {3749, 16968}, {3752, 41140}, {3780, 17451}, {3912, 5743}, {3959, 21384}, {4688, 20893}, {4695, 20331}, {5291, 5540}, {8682, 30109}, {9260, 21348}, {9460, 16610}, {9623, 36404}, {10027, 20363}, {16086, 17275}, {16583, 17448}, {16589, 49764}, {16829, 25368}, {17310, 44307}, {17755, 35101}, {18904, 45213}, {19623, 31998}, {21373, 49494}, {21857, 29331}, {21868, 25066}, {25432, 49711}, {25614, 49769}, {28606, 40891}, {30116, 36409}, {31238, 49780}, {35069, 35092}, {35957, 40859}

X(50014) = midpoint of X(i) and X(j) for these {i,j}: {239, 49755}, {35957, 40859}
X(50014) = reflection of X(i) in X(j) for these {i,j}: {37, 49758}, {20924, 3739}, {49777, 3008}
X(50014) = complement of X(49779)
X(50014) = X(4615)-Ceva conjugate of X(513)
X(50014) = crosspoint of X(i) and X(j) for these (i,j): {80, 274}, {88, 256}
X(50014) = crosssum of X(i) and X(j) for these (i,j): {36, 213}, {44, 171}, {2087, 4040}
X(50014) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3691, 3727, 21879}, {4875, 41015, 1107}, {16605, 40133, 16604}


X(50015) = X(1)X(2)∩X(75)X(49681)

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

X(50015) = 3 X[1] - 2 X[49764], 9 X[2] - 8 X[49769], 3 X[8] - 4 X[49772], 4 X[10] - 5 X[29590], 3 X[239] - 2 X[49772], 8 X[3008] - 7 X[9780], 3 X[3241] - 4 X[49771], 5 X[3616] - 4 X[3912], 11 X[5550] - 10 X[17266], 11 X[5550] - 8 X[49766], 3 X[6542] - 4 X[49764], 7 X[9780] - 4 X[49762], 5 X[17266] - 4 X[49766], 2 X[17310] - 3 X[38314], 3 X[17310] - 4 X[49768], 13 X[19877] - 14 X[29607], X[20050] + 4 X[49770], 7 X[20057] - 4 X[49763], 3 X[32847] - 4 X[49769], 9 X[38314] - 8 X[49768], 3 X[238] - 2 X[4439], 6 X[238] - 5 X[4473], 4 X[4439] - 5 X[4473], 4 X[1086] - 3 X[4645], 2 X[1086] - 3 X[32922], 4 X[3246] - 3 X[17264]

X(50015) lies on these lines: {1, 2}, {75, 49681}, {190, 28503}, {238, 4439}, {319, 49465}, {320, 28538}, {452, 49757}, {514, 31291}, {518, 25048}, {524, 24841}, {528, 17160}, {536, 49709}, {537, 20072}, {730, 39362}, {740, 21295}, {742, 4644}, {752, 4440}, {894, 49684}, {944, 29331}, {952, 36716}, {1086, 4645}, {1120, 17962}, {1320, 7261}, {1482, 36663}, {1654, 4407}, {2099, 33949}, {3212, 3476}, {3246, 17264}, {3416, 17227}, {3600, 43040}, {3759, 49688}, {3790, 7290}, {3883, 9791}, {3891, 4388}, {3902, 17762}, {4361, 49679}, {4452, 33869}, {4665, 5263}, {4693, 49700}, {4716, 17765}, {4720, 33954}, {4914, 19786}, {4968, 17789}, {4969, 9041}, {5195, 9802}, {5291, 35092}, {5296, 49756}, {5772, 49775}, {5839, 49509}, {6224, 13235}, {6646, 49455}, {7174, 49754}, {8148, 36732}, {9053, 49706}, {12245, 36699}, {16491, 17368}, {16496, 17363}, {17119, 49720}, {17121, 49529}, {17155, 20101}, {17302, 33076}, {17315, 42819}, {17318, 49746}, {17360, 47358}, {17377, 42871}, {17489, 21226}, {17772, 49675}, {17778, 32923}, {20090, 49479}, {20244, 33865}, {20911, 25303}, {24723, 49463}, {24821, 49710}, {26738, 33070}, {28512, 32857}, {28581, 49695}, {28599, 33150}, {31029, 33148}, {31030, 33112}, {31300, 49532}, {32844, 37759}, {32921, 49506}, {33082, 49464}, {36727, 37705}

X(50015) = midpoint of X(145) and X(20016)
X(50015) = reflection of X(i) in X(j) for these {i,j}: {8, 239}, {4645, 32922}, {4693, 49700}, {6542, 1}, {24821, 49710}, {49762, 3008}
X(50015) = anticomplement of X(32847)
X(50015) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3632, 49560}, {1, 17397, 38314}, {1, 48851, 17397}, {8, 3241, 36534}, {8, 38314, 29611}, {238, 4439, 4473}, {33076, 49472, 17302}, {49764, 49772, 3661}


X(50016) = X(1)X(2)∩X(190)X(740)

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

X(50016) = 4 X[1125] - 5 X[29590], 5 X[1698] - 4 X[3912], 8 X[3008] - 7 X[3624], 7 X[3624] - 4 X[49763], X[3632] + 4 X[49770], 3 X[3679] - 2 X[32847], 3 X[3679] - 4 X[49772], 5 X[17266] - 4 X[49767], 2 X[17310] - 3 X[19875], 3 X[17310] - 4 X[49769], 9 X[19875] - 8 X[49769], 3 X[25055] - 4 X[41140], 9 X[25055] - 8 X[49768], 14 X[29607] - 13 X[34595], 3 X[41140] - 2 X[49768], 2 X[190] - 3 X[1757], 3 X[1757] - 4 X[4753], 3 X[238] - 2 X[4702], 3 X[3685] - 4 X[4759], 3 X[4966] - 4 X[40480], 3 X[17297] - 4 X[25351], 2 X[17374] - 3 X[31151]

X(50016) lies on these lines: {1, 2}, {6, 49459}, {9, 49469}, {40, 29331}, {44, 4693}, {75, 49497}, {80, 6543}, {86, 4732}, {190, 740}, {238, 4702}, {274, 4714}, {319, 4085}, {484, 18206}, {518, 4716}, {524, 24715}, {528, 4969}, {536, 24821}, {537, 17160}, {678, 4954}, {742, 3751}, {846, 3896}, {894, 4709}, {984, 17318}, {1001, 49678}, {1018, 39252}, {1051, 32772}, {1054, 24593}, {1145, 39041}, {2223, 48696}, {2796, 20072}, {3242, 49689}, {3339, 43040}, {3685, 4759}, {3696, 4649}, {3755, 33082}, {3759, 32941}, {3791, 3996}, {3875, 49448}, {3886, 16468}, {3931, 49760}, {4007, 16972}, {4026, 42334}, {4042, 17592}, {4046, 32780}, {4360, 49457}, {4361, 49490}, {4378, 9260}, {4407, 17320}, {4409, 5852}, {4414, 24616}, {4416, 4780}, {4555, 4589}, {4597, 35153}, {4647, 17789}, {4660, 17363}, {4663, 49468}, {4692, 17143}, {4706, 18201}, {4737, 17144}, {4738, 39044}, {4743, 24723}, {4767, 21805}, {4781, 16704}, {4783, 17790}, {4819, 35466}, {4868, 40773}, {4966, 40480}, {5119, 21384}, {5220, 49452}, {5223, 49445}, {5235, 21806}, {5263, 49489}, {5288, 37575}, {5525, 18785}, {5541, 24578}, {15481, 49461}, {16476, 37610}, {16477, 49484}, {16484, 17348}, {16669, 49485}, {17117, 49479}, {17119, 31178}, {17121, 49482}, {17151, 49532}, {17175, 33770}, {17277, 49471}, {17297, 25351}, {17299, 33165}, {17335, 49470}, {17362, 33076}, {17374, 31151}, {17378, 24693}, {17596, 32853}, {17769, 49698}, {17772, 32850}, {20924, 32092}, {21027, 37635}, {23407, 25439}, {32857, 34379}, {32860, 32913}, {32921, 49450}, {49453, 49503}

X(50016) = midpoint of X(8) and X(20016)
X(50016) = reflection of X(i) in X(j) for these {i,j}: {1, 239}, {190, 4753}, {4693, 44}, {6542, 10}, {24821, 49712}, {32847, 49772}, {49761, 49766}, {49763, 3008}
X(50016) = anticomplement of X(49764)
X(50016) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3679, 36531}, {1, 16832, 25055}, {1, 19875, 16831}, {1, 31855, 2664}, {8, 4393, 36480}, {8, 26626, 48802}, {8, 29659, 3679}, {8, 49488, 1}, {145, 16825, 1}, {190, 4753, 1757}, {3241, 16816, 24331}, {3241, 24331, 1}, {3244, 16823, 1}, {3696, 4649, 24342}, {3896, 32864, 846}, {4062, 33139, 29862}, {4361, 49680, 49490}, {4393, 36480, 1}, {4709, 49685, 894}, {17162, 19998, 17763}, {17348, 49475, 16484}, {17763, 19998, 5524}, {20011, 32914, 3979}, {32847, 49772, 3679}, {36480, 49488, 4393}


X(50017) = X(1)X(2)∩X(44)X(28503)

Barycentrics    4*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(50017) = X[8] - 3 X[239], 2 X[8] - 3 X[49772], 2 X[10] - 3 X[41140], X[145] + 3 X[40891], 3 X[551] - 2 X[49767], 4 X[1125] - 3 X[3912], 5 X[1698] - 6 X[3008], 5 X[1698] - 3 X[32847], 2 X[3244] + 3 X[49770], 2 X[3244] - 3 X[49771], 5 X[3616] - 3 X[17310], 7 X[3622] - 3 X[6542], 7 X[3622] - 6 X[49768], 5 X[3623] + 3 X[20016], 7 X[3624] - 6 X[41141], 15 X[29590] - 11 X[46933], 3 X[41140] - X[49762], 3 X[238] - 2 X[2325], 2 X[320] - 3 X[24231], X[320] - 3 X[32922], 3 X[1279] - X[4727], 3 X[1738] - 4 X[4395], 3 X[3932] - 4 X[6687], 3 X[4716] + X[49708], 4 X[17067] - 3 X[31151]

X(50017) lies on these lines: {1, 2}, {44, 28503}, {75, 49684}, {238, 2325}, {320, 5847}, {518, 4969}, {726, 4480}, {740, 49700}, {742, 49483}, {752, 1266}, {984, 3707}, {1086, 28538}, {1279, 4727}, {1386, 17369}, {1738, 4395}, {2345, 16491}, {3212, 4315}, {3246, 3943}, {3416, 17290}, {3696, 4405}, {3717, 4974}, {3755, 49506}, {3759, 49529}, {3883, 32921}, {3932, 6687}, {3946, 33076}, {3950, 15485}, {4301, 28909}, {4353, 33082}, {4357, 49472}, {4361, 49681}, {4416, 49455}, {4431, 49482}, {4464, 49471}, {4649, 4982}, {4667, 31178}, {4684, 17772}, {4693, 17133}, {4700, 49712}, {4702, 4971}, {4716, 5853}, {4873, 7290}, {4989, 33159}, {5839, 16496}, {7278, 20911}, {9053, 49702}, {16478, 49781}, {17067, 31151}, {17160, 28580}, {17360, 49511}, {17362, 49465}, {17363, 49505}, {17388, 42819}, {24393, 49534}, {28522, 49705}, {29331, 34773}, {30331, 49469}, {49499, 49783}

X(50017) = midpoint of X(i) and X(j) for these {i,j}: {17160, 49709}, {49770, 49771}
X(50017) = reflection of X(i) in X(j) for these {i,j}: {3717, 4974}, {3943, 3246}, {4480, 49710}, {6542, 49768}, {24231, 32922}, {32847, 3008}, {49712, 4700}, {49750, 49511}, {49761, 49764}, {49762, 10}, {49763, 1}, {49772, 239}
X(50017) = anticomplement of X(49766)
X(50017) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 17367, 10}, {16823, 29569, 1125}, {17763, 49987, 5121}, {41140, 49762, 10}


X(50018) = X(1)X(2)∩X(44)X(740)

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

X(50018) = X[1] - 3 X[239], X[8] + 3 X[40891], 3 X[10] - 2 X[49766], 2 X[1125] - 3 X[41140], 5 X[1698] - 3 X[17310], 6 X[3008] - 5 X[19862], 5 X[3617] + 3 X[20016], 5 X[3617] - 3 X[32847], 2 X[3626] + 3 X[49770], 2 X[3626] - 3 X[49772], 4 X[3634] - 3 X[3912], 11 X[5550] - 15 X[29590], 3 X[6542] - 7 X[9780], 7 X[9780] - 6 X[49769], 7 X[15808] - 6 X[49768], 15 X[17266] - 17 X[19872], 5 X[19862] - 3 X[49764], 3 X[41140] - X[49763], X[49762] + 3 X[49770], X[49762] - 3 X[49772], 3 X[4716] - X[17160], 3 X[4716] + X[49712], 2 X[3246] - 3 X[4974], 4 X[17067] - 3 X[49676]

X(50018) lies on these lines: {1, 2}, {4, 28909}, {6, 4709}, {44, 740}, {45, 3993}, {75, 49685}, {88, 32919}, {213, 24044}, {274, 49780}, {514, 4784}, {524, 24692}, {536, 4753}, {726, 4716}, {742, 4663}, {752, 4969}, {1100, 4732}, {1107, 4868}, {1757, 28522}, {3246, 4974}, {3579, 29331}, {3686, 16521}, {3696, 16666}, {3743, 49758}, {3745, 4457}, {3759, 49459}, {3875, 49520}, {3923, 16670}, {4058, 16972}, {4072, 16970}, {4085, 17362}, {4361, 49479}, {4407, 17395}, {4439, 4971}, {4660, 5839}, {4672, 49468}, {4693, 4759}, {4700, 28580}, {4852, 49457}, {4887, 34379}, {4923, 38049}, {4970, 32864}, {4991, 5263}, {5221, 43040}, {5750, 16522}, {17067, 49676}, {17348, 49471}, {17349, 49469}, {17374, 25351}, {17595, 32853}, {20924, 28612}, {28503, 49701}, {32921, 49510}, {49449, 49463}, {49450, 49464}, {49453, 49508}, {49455, 49504}, {49503, 49519}

X(50018) = midpoint of X(i) and X(j) for these {i,j}: {17160, 49712}, {20016, 32847}, {49770, 49772}
X(50018) = reflection of X(i) in X(j) for these {i,j}: {4693, 4759}, {6542, 49769}, {17374, 25351}, {49710, 4700}, {49762, 3626}, {49763, 1125}, {49764, 3008}
X(50018) = anticomplement of X(49767)
X(50018) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1698, 29595}, {1, 16815, 1125}, {3696, 49489, 33682}, {3759, 49459, 49482}, {4361, 49497, 49479}, {4716, 49712, 17160}, {16825, 49495, 3244}, {29591, 29633, 3634}, {41140, 49763, 1125}, {49762, 49772, 3626}


X(50019) = X(1)X(2)∩X(44)X(17133)

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

X(50019) = 3 X[2] - 7 X[239], 6 X[2] - 7 X[3008], 9 X[2] - 7 X[3912], 15 X[2] - 7 X[6542], 39 X[2] - 35 X[17266], 11 X[2] - 7 X[17310], 9 X[2] + 7 X[20016], 27 X[2] - 35 X[29590], 45 X[2] - 49 X[29607], X[2] + 7 X[40891], 5 X[2] - 7 X[41140], 8 X[2] - 7 X[41141], 12 X[2] - 7 X[49765], 3 X[2] + 7 X[49770], 3 X[239] - X[3912], 5 X[239] - X[6542], 13 X[239] - 5 X[17266], 11 X[239] - 3 X[17310], 3 X[239] + X[20016], 9 X[239] - 5 X[29590], 15 X[239] - 7 X[29607], X[239] + 3 X[40891], 5 X[239] - 3 X[41140], 8 X[239] - 3 X[41141], 7 X[239] - X[49761], 4 X[239] - X[49765], 3 X[3008] - 2 X[3912], 5 X[3008] - 2 X[6542], 13 X[3008] - 10 X[17266], 11 X[3008] - 6 X[17310], 3 X[3008] + 2 X[20016], 9 X[3008] - 10 X[29590], 15 X[3008] - 14 X[29607], X[3008] + 6 X[40891], 5 X[3008] - 6 X[41140], 4 X[3008] - 3 X[41141], 7 X[3008] - 2 X[49761], X[3008] + 2 X[49770], 5 X[3912] - 3 X[6542], 13 X[3912] - 15 X[17266], 11 X[3912] - 9 X[17310], 3 X[3912] - 5 X[29590], 5 X[3912] - 7 X[29607], X[3912] + 9 X[40891], 5 X[3912] - 9 X[41140], 8 X[3912] - 9 X[41141], 7 X[3912] - 3 X[49761], 4 X[3912] - 3 X[49765], X[3912] + 3 X[49770], 5 X[4668] - 7 X[49772], 13 X[6542] - 25 X[17266], 11 X[6542] - 15 X[17310], 3 X[6542] + 5 X[20016], 9 X[6542] - 25 X[29590], 3 X[6542] - 7 X[29607], X[6542] + 15 X[40891], X[6542] - 3 X[41140], 8 X[6542] - 15 X[41141], 7 X[6542] - 5 X[49761], 4 X[6542] - 5 X[49765], X[6542] + 5 X[49770], 55 X[17266] - 39 X[17310], 15 X[17266] + 13 X[20016], 9 X[17266] - 13 X[29590], 75 X[17266] - 91 X[29607], 5 X[17266] + 39 X[40891], 25 X[17266] - 39 X[41140], 40 X[17266] - 39 X[41141], 35 X[17266] - 13 X[49761], 20 X[17266] - 13 X[49765], 5 X[17266] + 13 X[49770], 9 X[17310] + 11 X[20016], 27 X[17310] - 55 X[29590], 45 X[17310] - 77 X[29607], X[17310] + 11 X[40891], 5 X[17310] - 11 X[41140], 8 X[17310] - 11 X[41141], 21 X[17310] - 11 X[49761], 12 X[17310] - 11 X[49765], 3 X[17310] + 11 X[49770], 3 X[20016] + 5 X[29590], 5 X[20016] + 7 X[29607], X[20016] - 9 X[40891], 5 X[20016] + 9 X[41140], 8 X[20016] + 9 X[41141], 7 X[20016] + 3 X[49761], 4 X[20016] + 3 X[49765], X[20016] - 3 X[49770], 25 X[29590] - 21 X[29607], 5 X[29590] + 27 X[40891], 25 X[29590] - 27 X[41140], 40 X[29590] - 27 X[41141], 35 X[29590] - 9 X[49761], 20 X[29590] - 9 X[49765], 5 X[29590] + 9 X[49770], 7 X[29607] + 45 X[40891], 7 X[29607] - 9 X[41140], 56 X[29607] - 45 X[41141], 49 X[29607] - 15 X[49761], 28 X[29607] - 15 X[49765], 7 X[29607] + 15 X[49770], 5 X[40891] + X[41140], 8 X[40891] + X[41141], 21 X[40891] + X[49761], 12 X[40891] + X[49765], 3 X[40891] - X[49770], 8 X[41140] - 5 X[41141], 21 X[41140] - 5 X[49761], 12 X[41140] - 5 X[49765], 3 X[41140] + 5 X[49770], 21 X[41141] - 8 X[49761], 3 X[41141] - 2 X[49765], 3 X[41141] + 8 X[49770], 4 X[49761] - 7 X[49765], X[49761] + 7 X[49770], X[49765] + 4 X[49770], X[4409] + 7 X[4969]

X(50019) lies on these lines: {1, 2}, {44, 17133}, {75, 4856}, {190, 28313}, {514, 4790}, {516, 4716}, {524, 4887}, {527, 4409}, {536, 4700}, {548, 29331}, {742, 4726}, {1100, 4758}, {1267, 49620}, {1449, 4371}, {2325, 4971}, {3589, 4060}, {3618, 4058}, {3663, 5839}, {3664, 4361}, {3686, 4021}, {3707, 17318}, {3731, 4460}, {3739, 4909}, {3759, 17355}, {3834, 28337}, {3946, 17237}, {4072, 26685}, {4359, 7278}, {4395, 4725}, {4399, 5750}, {4405, 4670}, {4422, 28329}, {4431, 17121}, {4454, 17151}, {4464, 17277}, {4545, 17239}, {4667, 17119}, {4898, 18230}, {4910, 17259}, {4916, 20195}, {4923, 38315}, {5391, 49621}, {6666, 17388}, {8168, 21526}, {16667, 32087}, {17067, 17374}, {17132, 17160}, {17348, 25072}, {17772, 25351}, {20172, 49685}, {27480, 49520}, {27484, 49469}, {28512, 32108}, {32029, 34379}, {38186, 49679}, {43179, 49678}

X(50019) = midpoint of X(i) and X(j) for these {i,j}: {239, 49770}, {3912, 20016}
X(50019) = reflection of X(i) in X(j) for these {i,j}: {3008, 239}, {17374, 17067}, {49765, 3008}
X(50019) = complement of X(49761)
X(50019) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {145, 16833, 29571}, {239, 6542, 41140}, {239, 20016, 3912}, {239, 40891, 49770}, {3008, 49765, 41141}, {3632, 5222, 29594}, {3686, 4852, 4021}, {3912, 41140, 29607}, {3912, 49770, 20016}, {6542, 29607, 3912}, {16816, 29574, 31211}, {17023, 29617, 3626}, {20050, 24599, 29573}, {24603, 29584, 3636}


X(50020) = X(1)X(2)∩X(514)X(4830)

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

X(50020) = X[8] - 5 X[239], 3 X[8] - 5 X[49772], 3 X[239] - X[49772], 9 X[551] - 5 X[49764], 6 X[551] - 5 X[49768], 5 X[3008] - 4 X[3634], 3 X[3008] - 2 X[49769], 7 X[3624] - 5 X[3912], 8 X[3634] - 5 X[49766], 6 X[3634] - 5 X[49769], 5 X[6542] - 13 X[46934], 9 X[19875] - 5 X[32847], 3 X[19875] - 5 X[41140], 25 X[29590] - 17 X[46932], X[32847] - 3 X[41140], 2 X[49764] - 3 X[49768], 3 X[49766] - 4 X[49769], X[4439] - 3 X[4974]

X(50020) lies on these lines: {1, 2}, {514, 4830}, {537, 4700}, {1086, 5847}, {1386, 4665}, {3246, 4971}, {3686, 4407}, {3773, 4989}, {4133, 7290}, {4361, 49684}, {4395, 28538}, {4432, 17133}, {4439, 4974}, {4464, 16484}, {4856, 49479}, {5839, 49505}, {16491, 42696}, {17132, 49710}, {21874, 22036}, {32922, 34379}

X(50020) = midpoint of X(i) and X(j) for these {i,j}: {1, 49770}, {20016, 49763}
X(50020) = reflection of X(i) in X(j) for these {i,j}: {49765, 1125}, {49766, 3008}


X(50021) = X(1)X(2)∩X(190)X(4716)

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

X(50021) = X[1] - 5 X[239], 5 X[3008] - 4 X[19878], 6 X[3828] - 5 X[49769], 3 X[4669] - 5 X[49772], 5 X[6542] - 13 X[19877], 8 X[19878] - 5 X[49767], 3 X[19883] - 5 X[41140], 9 X[19883] - 5 X[49764], 5 X[20016] + 11 X[46933], 19 X[22266] - 5 X[49761], X[32847] + 3 X[40891], 3 X[41140] - X[49764], X[190] + 3 X[4716], X[4702] - 3 X[4974]

X(50021) lies on these lines: {1, 2}, {190, 4716}, {726, 4753}, {740, 4759}, {2796, 4700}, {3696, 4991}, {3759, 4709}, {3993, 17335}, {4125, 17144}, {4361, 49685}, {4670, 49489}, {4702, 4974}, {4725, 25351}, {29331, 31663}

X(50021) = midpoint of X(10) and X(49770)
X(50021) = reflection of X(i) in X(j) for these {i,j}: {49765, 3634}, {49767, 3008}


X(50022) = X(1)X(2)∩X(9)X(4780)

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

X(50022) = X[1] - 3 X[41140], X[8] + 3 X[239], X[8] - 3 X[49772], 2 X[1125] - 3 X[3008], 4 X[1125] - 3 X[49768], 5 X[1698] - 3 X[3912], 5 X[3617] + 3 X[40891], 7 X[3622] - 15 X[29590], X[3633] - 3 X[49771], 4 X[3634] - 3 X[41141], 3 X[3679] - X[49762], 3 X[6542] - 11 X[46933], 7 X[9780] - 3 X[17310], 3 X[41141] - 2 X[49767], X[320] - 3 X[1738], 3 X[1757] - X[4480], 3 X[3932] - X[4727], 3 X[4966] - 5 X[31243], 3 X[4974] - X[49700], 3 X[32922] + X[49714]

X(50022) lies on these lines: {1, 2}, {9, 4780}, {44, 28580}, {142, 49497}, {320, 1738}, {514, 4818}, {516, 49710}, {518, 4395}, {527, 4753}, {740, 2325}, {752, 4700}, {1266, 49712}, {1757, 4480}, {3664, 49685}, {3686, 4085}, {3696, 17369}, {3707, 3755}, {3717, 4716}, {3751, 42697}, {3931, 49758}, {3932, 4727}, {3946, 49457}, {4000, 49505}, {4026, 49756}, {4070, 4771}, {4078, 49486}, {4133, 4873}, {4353, 49510}, {4361, 49529}, {4405, 49524}, {4429, 17360}, {4439, 17133}, {4667, 24693}, {4690, 48821}, {4695, 20456}, {4709, 17355}, {4732, 5750}, {4868, 25092}, {4966, 31243}, {4969, 5847}, {4974, 5853}, {4982, 49489}, {4989, 49473}, {6666, 49471}, {6687, 28581}, {15569, 31285}, {16666, 49725}, {17119, 47359}, {17278, 49680}, {17290, 49511}, {17337, 49475}, {17353, 49459}, {19925, 28909}, {20893, 28612}, {24393, 32921}, {25101, 49469}, {32922, 49714}, {40663, 43054}, {49508, 49519}

X(50022) = midpoint of X(i) and X(j) for these {i,j}: {239, 49772}, {1266, 49712}, {3717, 4716}, {32847, 49770}
X(50022) = reflection of X(i) in X(j) for these {i,j}: {49765, 49769}, {49766, 10}, {49767, 3634}, {49768, 3008}
X(50022) = complement of X(49763)
X(50022) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3634, 49767, 41141}


X(50023) = X(1)X(2)∩X(44)X(537)

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

X(50023) = X[8] - 5 X[29590], 3 X[551] - X[49764], 3 X[551] - 2 X[49768], 5 X[1698] - 7 X[29607], 5 X[3616] - X[6542], 5 X[3616] - 2 X[49767], 7 X[3622] + X[20016], 7 X[3624] - 5 X[17266], 4 X[3634] - X[49762], 4 X[3636] - X[49763], 4 X[3636] + X[49770], 7 X[15808] - 2 X[49765], X[17310] - 3 X[25055], 5 X[19862] - 2 X[49766], 3 X[19883] - 2 X[41141], 3 X[38314] + X[40891], 3 X[41140] + X[49771], 3 X[41140] - X[49772], X[190] - 3 X[238], X[190] + 3 X[32922], 3 X[238] - 2 X[4759], 2 X[4759] + 3 X[32922], X[4753] - 3 X[4974], 2 X[4395] + X[49700], 3 X[1279] - X[4702], 3 X[3836] - 4 X[40480], X[24715] - 3 X[37756], 3 X[37756] + X[49709], 5 X[27191] - 3 X[31151], 3 X[27487] - 5 X[40328], 3 X[38049] - 2 X[49775]

X(50023) lies on these lines: {1, 2}, {6, 49479}, {9, 49455}, {31, 24165}, {37, 49472}, {40, 36699}, {44, 537}, {56, 43040}, {75, 49482}, {106, 3226}, {142, 49684}, {190, 238}, {192, 15485}, {213, 22011}, {244, 24593}, {274, 17200}, {330, 17105}, {333, 17598}, {354, 3791}, {405, 49757}, {514, 659}, {515, 36716}, {516, 49705}, {518, 4753}, {527, 49710}, {528, 4395}, {536, 3246}, {730, 35119}, {740, 1279}, {742, 1386}, {748, 3891}, {750, 24594}, {752, 1086}, {758, 20358}, {902, 4781}, {946, 36663}, {984, 17335}, {993, 22779}, {1001, 3993}, {1107, 16600}, {1266, 2796}, {1319, 16609}, {1385, 29331}, {1621, 4970}, {1738, 17766}, {2308, 17140}, {3210, 8616}, {3230, 17475}, {3242, 49510}, {3315, 32919}, {3550, 17490}, {3685, 28522}, {3696, 49473}, {3751, 49535}, {3758, 31178}, {3759, 49490}, {3769, 17063}, {3792, 25048}, {3821, 3883}, {3834, 28538}, {3836, 5846}, {3846, 17061}, {3923, 4659}, {3932, 17769}, {3966, 26128}, {4000, 4660}, {4011, 4135}, {4085, 17366}, {4090, 4383}, {4115, 16369}, {4257, 24621}, {4359, 17469}, {4360, 16484}, {4361, 4709}, {4366, 16801}, {4388, 33147}, {4392, 24616}, {4407, 17330}, {4409, 17767}, {4422, 4439}, {4429, 49506}, {4434, 16610}, {4514, 33132}, {4597, 18822}, {4641, 42055}, {4645, 28512}, {4649, 4991}, {4653, 33296}, {4663, 49491}, {4665, 48810}, {4672, 49483}, {4676, 49493}, {4693, 17160}, {4717, 17143}, {4767, 32927}, {4780, 30331}, {4852, 42819}, {4865, 24789}, {4914, 28595}, {4966, 17772}, {5074, 21630}, {5220, 49508}, {5233, 17725}, {5257, 49756}, {5259, 43993}, {5267, 37575}, {5284, 32928}, {5587, 36653}, {5603, 28909}, {5847, 49676}, {5853, 49696}, {5977, 41193}, {6381, 39044}, {6629, 18827}, {7176, 10521}, {8666, 49759}, {8692, 17262}, {9041, 49701}, {9053, 49693}, {9423, 16611}, {10436, 16491}, {12699, 36732}, {14621, 27478}, {15254, 49456}, {15492, 49513}, {15950, 16603}, {16468, 24349}, {16478, 17789}, {16487, 17151}, {16496, 49504}, {16583, 17448}, {16704, 17449}, {16706, 33076}, {16973, 49505}, {16974, 49781}, {17119, 48805}, {17123, 32926}, {17127, 17155}, {17144, 33937}, {17278, 49681}, {17336, 49517}, {17348, 49457}, {17349, 49448}, {17350, 49532}, {17352, 33165}, {17395, 49740}, {17597, 32853}, {17716, 19804}, {17739, 41773}, {17770, 24231}, {18480, 36727}, {18785, 39697}, {19796, 33095}, {20924, 31997}, {21241, 32844}, {24542, 32848}, {24715, 28562}, {24841, 49712}, {25440, 37590}, {25529, 27759}, {26724, 33072}, {27191, 31151}, {27487, 40328}, {28508, 32857}, {31161, 41241}, {32843, 33148}, {32861, 33124}, {32911, 32923}, {32947, 33150}, {33071, 33130}, {33075, 33123}, {34063, 37617}, {34379, 49783}, {35173, 35180}, {38049, 49775}, {41190, 48289}, {42871, 49497}, {47539, 47593}, {49478, 49489}

X(50023) = midpoint of X(i) and X(j) for these {i,j}: {1, 239}, {238, 32922}, {3792, 25048}, {4693, 17160}, {24715, 49709}, {24841, 49712}, {47539, 47593}, {49763, 49770}, {49771, 49772}
X(50023) = reflection of X(i) in X(j) for these {i,j}: {10, 3008}, {190, 4759}, {3912, 1125}, {3932, 31289}, {4432, 3246}, {4439, 4422}, {6542, 49767}, {24692, 1086}, {32847, 49769}, {49764, 49768}
X(50023) = complement of X(32847)
X(50023) = anticomplement of X(49769)
X(50023) = crossdifference of every pair of points on line {649, 2276}
X(50023) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3679, 36534}, {1, 4384, 36480}, {1, 16823, 1125}, {1, 16825, 10}, {1, 16832, 48854}, {1, 24331, 551}, {1, 25055, 29570}, {1, 49488, 3244}, {1, 49997, 3009}, {2, 32847, 49769}, {9, 49455, 49520}, {190, 238, 4759}, {551, 49764, 49768}, {614, 4362, 3840}, {748, 3891, 3971}, {1001, 32921, 3993}, {1386, 24325, 33682}, {1621, 32924, 4970}, {3757, 29821, 6685}, {3759, 49490, 49685}, {4361, 32941, 4709}, {4383, 32920, 4090}, {4384, 16826, 29604}, {4384, 36480, 10}, {4852, 42819, 49471}, {7191, 32914, 3741}, {7292, 17763, 4871}, {15254, 49463, 49456}, {16815, 36531, 3828}, {16816, 36534, 3679}, {16825, 36480, 4384}, {17348, 49465, 49457}, {25055, 29609, 1125}, {32844, 33129, 21241}, {37756, 49709, 24715}, {41140, 49771, 49772}


X(50024) = X(1)X(2)∩X(69)X(514)

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

X(50024) = 5 X[3620] - 2 X[49751], 3 X[21356] - X[34342], 3 X[21358] - 2 X[36234]

X(50024) lies on these lines: {1, 2}, {6, 36230}, {69, 514}, {116, 4561}, {141, 24281}, {144, 32106}, {150, 4568}, {190, 544}, {319, 35957}, {346, 32094}, {524, 34362}, {742, 49778}, {952, 4437}, {1016, 17233}, {1043, 4237}, {3620, 49751}, {4361, 6547}, {4766, 4867}, {4851, 36226}, {6631, 17295}, {17347, 32028}, {17362, 45213}, {21356, 34342}, {21358, 36234}, {36205, 41014}

X(50024) = midpoint of X(69) and X(30225)
X(50024) = reflection of X(i) in X(j) for these {i,j}: {6, 36230}, {4482, 4437}, {24281, 141}
X(50024) = isotomic conjugate of the isogonal conjugate of X(46407)
X(50024) = barycentric product X(76)*X(46407)
X(50024) = barycentric quotient X(46407)/X(6)


X(50025) = X(2)X(49753)∩X(81)X(239)

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

X(50025) lies on these lines: {2, 49753}, {10, 7794}, {39, 1212}, {75, 24254}, {81, 239}, {213, 20880}, {238, 2795}, {291, 1739}, {519, 3696}, {538, 17755}, {742, 20893}, {754, 49711}, {758, 1086}, {760, 1738}, {984, 48840}, {1111, 2238}, {2482, 35119}, {3218, 24617}, {3721, 24790}, {3735, 4000}, {3736, 30117}, {3739, 30109}, {3753, 49772}, {3912, 31993}, {3954, 26978}, {4260, 24476}, {4361, 33936}, {4395, 35101}, {4403, 35102}, {4438, 7801}, {5291, 9317}, {5977, 33891}, {7200, 45751}, {16611, 21138}, {16720, 29433}, {16825, 24293}, {16827, 33940}, {17033, 33933}, {17034, 33943}, {20347, 21839}, {20894, 24330}, {24631, 41140}, {25368, 30106}, {26801, 41805}, {27918, 49997}, {31855, 46894}, {35074, 35092}, {35075, 35094}, {35103, 37756}

X(50025) = midpoint of X(i) and X(j) for these {i,j}: {75, 40859}, {239, 20924}
X(50025) = reflection of X(i) in X(j) for these {i,j}: {30109, 3739}, {36226, 49777}, {49758, 3008}
X(50025) = complement of X(49753)
X(50025) = {X(20894),X(46899)}-harmonic conjugate of X(24330)


X(50026) = X(6)X(519)∩X(69)X(239)

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

X(50026) = X[69] - 3 X[239], 2 X[141] - 3 X[41140], 3 X[41140] - X[49750], X[193] + 3 X[40891], 2 X[3629] + 3 X[49770], 2 X[3629] - 3 X[49783], 4 X[3589] - 3 X[3912], 6 X[3008] - 5 X[3763], 5 X[3763] - 3 X[49752], 5 X[3618] - 3 X[17310], 3 X[38047] - 2 X[49766], 3 X[38049] - 2 X[49767], 6 X[41141] - 7 X[47355], X[47279] - 3 X[47539], 5 X[47456] - 3 X[47532]

X(50026) lies on these lines: {1, 49756}, {6, 519}, {37, 49771}, {44, 4899}, {69, 239}, {141, 41140}, {145, 36404}, {193, 40891}, {518, 4969}, {524, 36525}, {742, 3629}, {1100, 3589}, {1386, 49763}, {1449, 32847}, {1914, 3977}, {2325, 49696}, {3008, 3763}, {3618, 4916}, {4461, 20016}, {4700, 49713}, {6542, 49775}, {16666, 49524}, {16884, 49768}, {17330, 49465}, {17362, 49772}, {29331, 48906}, {38047, 49766}, {38049, 49767}, {41141, 47355}, {41747, 46180}, {47279, 47539}, {47456, 47532}, {49504, 49509}

X(50026) = midpoint of X(49770) and X(49783)
X(50026) = reflection of X(i) in X(j) for these {i,j}: {6542, 49775}, {49750, 141}, {49752, 3008}, {49762, 49524}, {49763, 1386}
X(50026) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 49690, 17281}, {41140, 49750, 141}


X(50027) = X(1)X(5319)∩X(6)X(519)

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

X(50027) = 3 X[34362] - X[49778], 4 X[17229] - 3 X[49773]

X(50027) lies on these lines: {1, 5319}, {6, 519}, {44, 952}, {239, 17740}, {620, 35466}, {899, 4530}, {1015, 24216}, {1145, 6184}, {1572, 24247}, {2087, 26015}, {2170, 33136}, {2243, 21578}, {3008, 24281}, {3061, 37716}, {3663, 3735}, {3912, 5718}, {4967, 49774}, {5224, 49755}, {5724, 49762}, {5725, 49766}, {10027, 17242}, {17229, 49773}, {17245, 49777}, {21796, 40937}, {21857, 29331}

X(50027) = midpoint of X(239) and X(30225)
X(50027) = reflection of X(i) in X(j) for these {i,j}: {3912, 36230}, {24281, 3008}
X(50027) = crossdifference of every pair of points on line {9002, 47373}


X(50028) = X(6)X(519)∩X(81)X(239)

Barycentrics    a*(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(50028) lies on these lines: {1, 9351}, {6, 519}, {44, 40091}, {81, 239}, {514, 21007}, {712, 32029}, {940, 41140}, {1015, 3684}, {1016, 20669}, {1100, 30117}, {1107, 4653}, {1573, 16503}, {1914, 45751}, {2087, 4511}, {2238, 16784}, {2241, 8616}, {2280, 16975}, {2323, 35092}, {3008, 37674}, {3726, 5540}, {3735, 16973}, {3751, 10800}, {3759, 49779}, {3780, 5299}, {3875, 7798}, {3912, 4383}, {4251, 17448}, {4361, 20893}, {4400, 29742}, {4435, 6550}, {4906, 16583}, {5276, 16971}, {5277, 17474}, {5309, 33141}, {5839, 16086}, {10027, 23660}, {16466, 49763}, {16781, 49768}, {17266, 37687}, {17310, 32911}, {17750, 49772}, {20331, 48696}, {37679, 41141}, {37685, 40891}, {49773, 49775}

X(50028) = reflection of X(i) in X(j) for these {i,j}: {17299, 49782}, {49773, 49775}
X(50028) = crosspoint of X(81) and X(40400)
X(50028) = crosssum of X(i) and X(j) for these (i,j): {37, 16610}, {244, 14408}
X(50028) = crossdifference of every pair of points on line {9002, 22277}


X(50029) = X(1)X(7760)∩X(63)X(194)

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

X(50029) lies on these lines: {1, 7760}, {6, 24291}, {9, 40859}, {39, 17739}, {63, 194}, {193, 24247}, {257, 7839}, {514, 2484}, {519, 1992}, {538, 17738}, {730, 1757}, {1572, 3729}, {3061, 7754}, {3570, 5529}, {3735, 7798}, {3912, 5712}, {6542, 26223}, {7757, 17596}, {10436, 30109}, {16086, 49754}, {17349, 24249}, {22253, 49518}, {24266, 37683}, {36483, 41232}, {37717, 41624}

X(50029) = reflection of X(6542) in X(49781)


X(50030) = X(1)X(49754)∩X(69)X(239)

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

X(50030) = 4 X[141] - 5 X[29590], 3 X[1992] - 4 X[49783], 5 X[3618] - 4 X[3912], 8 X[3008] - 7 X[3619], 7 X[3619] - 4 X[49750], X[11008] + 4 X[49770], 3 X[16475] - 2 X[49764], 3 X[17310] - 4 X[49775], 3 X[21356] - 4 X[41140]

X(50030) lies on these lines: {1, 49754}, {2, 49752}, {6, 6542}, {69, 239}, {141, 29590}, {190, 9053}, {193, 742}, {344, 16779}, {518, 25048}, {519, 1992}, {524, 903}, {648, 35158}, {1449, 3618}, {3008, 3619}, {3242, 17346}, {3570, 5211}, {3758, 49688}, {3945, 27487}, {5845, 17160}, {6776, 29331}, {7174, 49771}, {9055, 20072}, {11008, 49770}, {16475, 49764}, {17256, 49465}, {17310, 49775}, {17387, 38186}, {17389, 36404}, {20090, 49481}, {21356, 41140}, {46922, 49524}

X(50030) = midpoint of X(193) and X(20016)
X(50030) = reflection of X(i) in X(j) for these {i,j}: {69, 239}, {6542, 6}, {49750, 3008}
X(50030) = anticomplement of X(49752)
X(50030) = {X(16973),X(17363)}-harmonic conjugate of X(69)


X(50031) = X(3)X(12)∩X(11)X(40)

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

See Tran Viet Hung and Francisco Javier García Capitán, euclid 5105.

X(50031) lies on these lines: {1,37364}, {2,5584}, {3,12}, {4,4413}, {5,165}, {10,37374}, {11,40}, {20,1329}, {30,44847}, {36,31799}, {55,6865}, {56,6926}, {119,550}, {210,6245},{376,18242},{411,3035},{442,10164},{495,7987},{496,7991},{515,21031},{516,4187},{517,37722},{631,7680},{908,9943},{958,6890},{962,3816},{1210,7957}, {1376,6253}, {1479,6244}, {1532,31730}, {1698,8727}, {1699,17527}, {1737,31793}, {1836,37560}, {1837,6282}, {2077,10958}, {2829,37403}, {2886,6943}, {3058,10306}, {3085,8273}, {3336,5762}, {3428,5433}, {3452,12688}, {3522,11681}, {3523,25466}, {3576,15888}, {3579,6882}, {3583,31777}, {3584,35202}, {3614,6907}, {3634,8226}, {3654,10943}, {3814,12512},{3817,17575}, {3820,5691}, {3825,5493}, {3826,6828}, {3925,6684}, {4004,4301}, {4193,9778}, {4297,17757}, {4300,37662}, {4679,12705}, {4995,10902}, {4999,6972}, {5056,42356}, {5217,6987}, {5218,15844}, {5221,5758}, {5298,11249}, {5316,21628}, {5326,7688}, {5499,38109}, {5520,36158}, {5536,34753}, {5537,15171}, {5538,37730}, {5660,16143}, {5692,33899}, {5731,12607}, {5763,5902}, {5812,11246}, {5842,6903}, {5918,6260}, {6174,6796}, {6284,6827}, {6361,6963}, {6690,6986}, {6763,13226}, {6833,24953}, {6838,11495}, {6841,11231}, {6842,31663}, {6845,34501}, {6848,31246}, {6894,9342}, {6897,10894}, {6899,11500}, {6916,10895}, {6928,11826}, {6947,11496}, {6952,31260}, {6956,31245}, {6958,7294}, {6967,22753}, {7411,27529}, {7491,24466}, {7580,26364}, {7743,31797}, {7951,16192}, {7956,9589}, {7992,31142}, {8158,10072}, {8726,17718}, {9588,31419}, {9779,13865}, {9841,12678}, {9961,27131}, {10167,21077}, {10175,37447}, {10268,26481}, {10404,37526}, {10588,37108}, {10591,35514}, {10806,34699}, {10860,12679}, {10883,19877}, {10944,37611}, {11227,13407}, {11277,38114}, {11375,30503}, {11471,37432}, {12047,31787}, {12114,34606}, {12565,30827}, {12616,21677}, {12667,31141}, {12680,21075}, {12953,44846}, {14110,40663}, {16117,38752}, {17556,34630}, {18481,37725}, {19754,37078}, {19856,37365}, {21154,26286}, {24390,43174}, {26285,28459}, {26446,37356}, {30384,31798}


leftri

MIYAMOTO-LOZADA CENTERS: X(50032)-X(50040)

rightri

The centers X(50032) - X(50040), except for X(50039), were noted and conjectured by Keita Miyamoto, and confirmed by César Lozada. All the barycentric coordinates and other properties were found by Lozada, who also discovered X(50039).

These centers are associated with circles tangent to the 3 excircles. In particular, X(50037), X(50038), X(50040) involve Hart circles of the excircles. (See Mathworld: Hart's Theorem.)

Here, the notation (O) means a circle with center O. Let (Ea), (Eb), (Ec) denote the excircles, and let (S) be their radical circle. There are 8 lines or circles each of which is tangent to (Ea), (Eb), (Ec) simultaneously. These 8 are:

sidelines AB, BC, CA;
nine-point circle (N);
Apollonius circle (Ap); note that (Ap) is the (S)-inverse of (N);
The three Jenkins circles (Ja), (Jb), (Jc); the A-Jenkins circle (Ja) is the (S)--inverse of BC; and (Jb) and (Jc) are defined cyclically.

Hart's theorem states that generally, other than (Ea), (Eb), (Ec), there are 14 circles in total each of which is tangent to 4 of the 8 simultaneously. Following are the 14 Hart circles of the excircles:

The incircle (I) is tangent to AB, BC, CA, internally tangent to (N).
The Moses hull circle (M) is (internally or externally) tangent to (Ja), (Jb), (Jc), (Ap). (If S lies on (I), then (M) is a line.)
(O1) is tangent to AB and CA, internally tangent to (Jb) and (Jc); the circles (O2) and (O3) are defined cyclically.
(O4) is tangent to BC, internally tangent to (Ap) and (Ja), and externally tangent to (N); the circles (O5) and (O6) are defined cyclically.
(O7) is tangent to BC, internally tangent to (N), and externally tangent to (Jb) and (Jc); the circles (O8) and (O9) are defined cyclically.
(O10) is tangent to AB and CA, and externally tangent to (Ap) and (Ja); the circles (O11) and (O12) are defined cyclically.

Among the 14 Hart circles, the 6 Hart circles (O1), (O2), (O3), (O4), (O5), (O6) are orthogonal to (S), while the 4 Hart circles (M), (O10), (O11), (O12) are the (S)-inverses of the other 4: (I), (O7), (O8), (O9), respectively. Clearly, IM, O7O10, O8O11, O9O12 concur in S = X(10). Also, O1O4, O2O5, O3O6 concur in X(50037).


X(50032) = 1st MIYAMOTO-LOZADA CENTER

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

Denote by Ta the point of tangency of (Ea) with (Ap), and likewise for Tb and Tc. Let ω1 be the circle, other than (Ea), (Eb), (Ec), that is internally tangent to (Ap) and also tangent to CA and AB. Define ω2 and ω3 cyclically. Denote by T1 the point of tangency of ω1 with (Ap), and likewise for T2 and T3. Then TaT1, TbT2, TcT3 concur in X(50032).

Let Ab be the intersection of the ray BA and (Ap), and define Bc and Ca cyclically. Let Ba be the intersection of the ray AB and (Ap), and define Cb and Ac cyclically. Let

A1=TbBa∩TcCa;
B1=TcCb∩TaAb;
C1=TaAc∩TbBc;
A2=TbBc∩TcCb;
B2=TcCa∩TaAc;
C2=TaAb∩TbBa;
Then, A1A2, B1B2, C1C2 concur in X(50032), and TaA2, TbB2, TcC2 concur in X(50033).

Construction: X(50032)

X(50032) lies on these lines: {8, 181}, {40, 43}, {1193, 1682}, {5975, 34459}, {10974, 17647}


X(50033) = 2nd MIYAMOTO-LOZADA CENTER

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

See X(50032). Construction: X(50033)

X(50033) lies on these lines: {3, 6}, {10, 21853}, {19, 2238}, {37, 181}, {758, 38408}, {960, 1213}, {966, 34259}, {1100, 1682}, {3553, 9548}, {3554, 9549}, {5213, 34459}, {9564, 17303}, {9565, 17275}, {10381, 34528}, {10822, 21857}, {10823, 40133}


X(50034) = 3rd MIYAMOTO-LOZADA CENTER

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

Let Fa be the point of tangency of (Ea) with (N), and likewise for Fb and Fc. Let ω1' be the circle internally tangent to (Jb) and (Jc) and externally tangent to (N). Denote by T1' the point of tangency of ω1' with (N). Define ω2', ω3', T2', T3' cyclically.Then FaT1', FbT2', FcT3' concur in X(50034).

In the notation at X(50032), Let Ab' be the (S)-inverse of Ab, and define Bc', Ca', Ac', Ba', Cb' cyclically. Let

A1'=FbBa'∩FcCa', B1'=FcCb'∩FaAb', C1'=FaAc'∩FbBc', A2'=FbBc'∩FcCb', B2'=FcCa'∩FaAc', C2'=FaAb'∩FbBa'.
Then, A1'A2', B1'B2', C1'C2' concur in X(50034), and FaA1', FbB1', FcC1' concur in X(50035), and FaA2', FbB2', FcC2' concur in X(50036).

Construction: X(50034)

X(50034) lies on these lines: {2, 12}, {11, 10459}, {119, 5993}, {495, 21214}, {498, 28383}, {1201, 15888}, {3614, 44411}, {5233, 12607}, {5432, 28348}, {5743, 21031}, {10406, 22299}, {17451, 21025}


X(50035) = 4th MIYAMOTO-LOZADA CENTER

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

See X(50034). Construction: X(50035)

X(50035) lies on these lines: {12, 15281}, {5949, 44411}


X(50036) = 5th MIYAMOTO-LOZADA CENTER

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

See X(50034). Construction: X(50036)

X(50036) lies on these lines: {2, 1444}, {4, 36744}, {5, 6}, {9, 46}, {10, 21853}, {11, 1100}, {12, 37}, {19, 431}, {30, 1030}, {44, 3614}, {45, 10592}, {55, 430}, {80, 11069}, {86, 26019}, {115, 119}, {125, 20623}, {140, 5124}, {198, 407}, {223, 5219}, {226, 7363}, {230, 1333}, {284, 6841}, {325, 3770}, {381, 4254}, {391, 5141}, {403, 1172}, {427, 5275}, {478, 3142}, {495, 16777}, {496, 16884}, {572, 6882}, {573, 6842}, {579, 6881}, {584, 8226}, {594, 17757}, {858, 37675}, {860, 10590}, {862, 1486}, {908, 1211}, {966, 2476}, {1146, 17443}, {1449, 7741}, {1478, 2178}, {1500, 21855}, {1532, 4271}, {1592, 31473}, {1609, 3560}, {1656, 5120}, {1824, 22273}, {1834, 2910}, {2171, 21011}, {2193, 37361}, {2220, 7745}, {2238, 2911}, {2262, 17605}, {2278, 6831}, {2294, 21044}, {2303, 37983}, {2305, 15973}, {2323, 15833}, {2345, 11681}, {2475, 27524}, {2886, 17275}, {3013, 8068}, {3091, 37503}, {3247, 37719}, {3554, 8227}, {3686, 25639}, {3723, 15888}, {3814, 5750}, {3815, 5069}, {3822, 5257}, {3925, 21866}, {3936, 28808}, {3948, 20927}, {3949, 21029}, {3958, 21014}, {4016, 21965}, {4053, 21018}, {4187, 4268}, {4261, 5254}, {4263, 39565}, {4280, 37362}, {4675, 21239}, {5019, 7746}, {5080, 38871}, {5110, 37365}, {5115, 37646}, {5133, 5276}, {5153, 37662}, {5179, 14873}, {5251, 17514}, {5421, 34460}, {5475, 16946}, {5746, 6829}, {5800, 36672}, {5802, 6990}, {5839, 11680}, {6506, 40942}, {6871, 27522}, {6907, 37499}, {6913, 8573}, {6914, 8553}, {7173, 16666}, {7679, 41325}, {7752, 34283}, {7958, 40133}, {8286, 39050}, {8287, 18635}, {8680, 27691}, {8727, 37504}, {8728, 37500}, {11063, 31649}, {12607, 17299}, {13911, 44038}, {16307, 30447}, {16732, 41003}, {17206, 25456}, {17330, 17530}, {17362, 24390}, {17454, 37447}, {17669, 26110}, {18990, 21773}, {19542, 19721}, {20146, 33061}, {20236, 44396}, {20337, 29967}, {20616, 21860}, {21024, 34528}, {21033, 21675}, {21287, 26243}, {21677, 21873}, {21698, 23668}, {21858, 21956}, {21863, 40663}, {22369, 46536}, {24512, 47513}, {25505, 26561}, {25508, 33034}, {26601, 27042}, {27039, 31043}, {31018, 41809}, {31845, 38962}, {33329, 47160}, {33854, 37990}, {34119, 40750}, {36659, 36740}, {37049, 42843}, {37401, 37508}, {37673, 47514}, {40635, 44092}

X(50036) = complement of X(1444)
X(50036) = complementary conjugate of the complement of X(1824)
X(50036) = Cevapoint of X(523) and X(651)
X(50036) = crossdifference of every pair of points on line {X(924), X(2605)}
X(50036) = crosssum of X(i) and X(j) for these (i, j): {512, 48383}, {523, 650}
X(50036) = X(2)-Ceva conjugate of-X(37565)
X(50036) = X(i)-complementary conjugate of-X(j) for these (i, j): (4, 3741), (10, 1368)
X(50036) = perspector of the circumconic {{A, B, C, X(925), X(6742)}}
X(50036) = intersection, other than A, B, C, of circumconics {{A, B, C, X(12), X(68)}} and {{A, B, C, X(46), X(6757)}}
X(50036) = barycentric product X(i)*X(j) for these {i, j}: {1, 23555}, {10, 12047}, {86, 21696}, {661, 18740}
X(50036) = trilinear product X(i)*X(j) for these {i, j}: {6, 23555}, {37, 12047}, {81, 21696}, {512, 18740}
X(50036) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (485, 486, 5707), (1213, 1901, 2245), (1213, 5949, 442), (2245, 8818, 1901), (5747, 5816, 6)


X(50037) = 6th MIYAMOTO-LOZADA CENTER

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

The lines O1O4, O2O5, O3O6 concur in X(50037).

Construction: X(50037)

X(50037) lies on these lines: {1, 2051}, {2, 10465}, {4, 9}, {5, 19858}, {8, 9535}, {12, 19542}, {42, 10454}, {43, 5691}, {65, 9553}, {80, 34458}, {165, 15971}, {181, 1837}, {355, 970}, {386, 515}, {517, 3714}, {946, 30116}, {958, 2050}, {986, 29069}, {1220, 23512}, {1478, 5530}, {1682, 5252}, {1685, 49601}, {1686, 49602}, {1695, 3679}, {3029, 9864}, {3031, 12368}, {3032, 12751}, {3057, 9554}, {3091, 19853}, {3436, 3687}, {3831, 12545}, {3840, 43164}, {4260, 5787}, {4276, 6796}, {4297, 6685}, {5247, 13478}, {5790, 9566}, {5794, 9564}, {5799, 37715}, {5881, 9549}, {6736, 36855}, {7987, 29825}, {8185, 9570}, {9534, 10440}, {9567, 18525}, {9568, 37714}, {9571, 15177}, {10406, 10950}, {10407, 11375}, {10434, 26115}, {10449, 29311}, {10526, 39566}, {11236, 36731}, {11500, 19763}, {12435, 17751}, {12610, 13161}, {13178, 34454}, {13211, 34453}, {13532, 34455}, {15232, 46020}, {21363, 31339}, {24982, 37191}, {26446, 35203}

X(50037) = complement of X(10465)
X(50037) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2051, 44039, 1), (5587, 9548, 10)


X(50038) = 7th MIYAMOTO-LOZADA CENTER

Barycentrics    (b-c)^2*a^2-8*(b+c)*b*c*a-(b^2-c^2)^2 : :

In the notation at X(50034), Let P1 be the point of tangency of (O7) with (N), and define P2 and P3 cyclically. Then T1'P1, T2'P2, T3'P3 concur in X(50038).

Construction: X(50038)

X(50038) lies on these lines: {2, 3304}, {3, 34697}, {4, 34630}, {5, 3654}, {10, 11}, {12, 57}, {21, 6174}, {55, 5129}, {119, 3652}, {120, 31090}, {140, 37725}, {144, 3826}, {210, 8582}, {405, 4995}, {442, 3828}, {443, 31141}, {474, 34606}, {518, 25011}, {519, 17575}, {528, 37162}, {529, 17531}, {936, 10950}, {938, 3711}, {946, 4731}, {958, 6921}, {997, 37734}, {1155, 18250}, {1210, 3983}, {1329, 2476}, {1376, 6872}, {1706, 4679}, {1722, 17602}, {1788, 3715}, {1837, 8580}, {2478, 34612}, {2551, 4413}, {2646, 20103}, {2885, 5743}, {2886, 5154}, {3035, 5260}, {3058, 5084}, {3303, 17559}, {3305, 37828}, {3452, 3698}, {3617, 3816}, {3634, 17757}, {3679, 17527}, {3740, 21677}, {3854, 38092}, {3921, 10916}, {4002, 21616}, {4193, 9710}, {4197, 28610}, {4423, 7080}, {4429, 26046}, {4534, 39244}, {4860, 5815}, {4997, 30543}, {4999, 31235}, {5044, 13601}, {5046, 49732}, {5251, 47742}, {5258, 5298}, {5326, 10955}, {5432, 6857}, {5433, 9708}, {5434, 16408}, {5552, 31259}, {6057, 46937}, {6284, 9709}, {6766, 7958}, {6831, 31399}, {6841, 9956}, {6853, 20400}, {6919, 31140}, {7173, 31419}, {7294, 10956}, {7965, 7989}, {8165, 10895}, {8167, 10528}, {9623, 24954}, {9657, 17580}, {9662, 9679}, {10056, 16853}, {10197, 17590}, {10592, 41859}, {11236, 37462}, {11237, 17582}, {11376, 20196}, {12246, 18242}, {13747, 31157}, {16593, 27025}, {16842, 45701}, {16857, 31452}, {18249, 44848}, {19331, 48833}, {19843, 31246}, {19876, 37719}, {19877, 25466}, {19925, 46916}, {23675, 31197}, {25614, 37661}, {26029, 37164}, {26446, 37406}, {37163, 38757}, {37364, 37714}, {37548, 38471}, {37726, 38099}, {42056, 49609}

X(50038) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 9711, 21031), (2, 21031, 15888), (442, 3828, 34501), (1329, 3925, 3614), (1329, 9780, 3925), (1698, 3820, 12), (2551, 4413, 7354), (3679, 17527, 37722), (3740, 24982, 21677), (8165, 26040, 10895), (11681, 46932, 3826), (24953, 26364, 5326)


X(50039) = 8th MIYAMOTO-LOZADA CENTER

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

The points X(10), X(1682) and X(50038) are collinear, and X(50039) is the trilinear pole of their line.

X(50039) lies on these lines: {190, 4560}, {514, 4552}, {518, 41683}, {522, 3952}, {885, 23343}, {908, 1266}, {2397, 46779}, {2401, 2427}, {3257, 21222}, {4033, 4391}, {5548, 13136}, {16704, 39698}, {17906, 17924}

X(50039) = isogonal conjugate of X(21786)
X(50039) = isotomic conjugate of X(21222)
X(50039) = crosspoint of X(i) and X(j) for these (i, j): {2, 3762}, {8, 46393}
X(50039) = X(i)-Dao conjugate of-X(j) for these (i, j): (6, 23087), (10, 21894)
X(50039) = X(i)-isoconjugate-of-X(j) for these {i, j}: {19, 23087}, {58, 21894}
X(50039) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (3, 23087), (37, 21894)
X(50039) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(3257)}} and {{A, B, C, X(100), X(46480)}}
X(50039) = trilinear pole of the line {10, 11}
X(50039) = barycentric product X(190)*X(14554)
X(50039) = barycentric quotient X(i)/X(j) for these (i, j): (3, 23087), (37, 21894), (101, 5053), (900, 34590)
X(50039) = trilinear product X(100)*X(14554)
X(50039) = trilinear quotient X(i)/X(j) for these (i, j): (10, 21894), (63, 23087), (100, 5053)


X(50040) = 9th MIYAMOTO-LOZADA CENTER

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

Denote by Q1 the point of tangency of (O10) with (Ja), and define Q2 and Q3 cyclically. Then AQ1, BQ2, CQ3 concur in X(50040).

Construction: X(50040)

X(50040) lies on these lines: {388, 32038}, {959, 3616}, {986, 3671}, {2476, 34258}, {5257, 5837}

X(50040) = X(514)-Dao conjugate of-X(3026)
X(50040) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(986)}} and {{A, B, C, X(4), X(261)}}
X(50040) = barycentric product X(959)*X(34258)
X(50040) = barycentric quotient X(i)/X(j) for these (i, j): (941, 958), (959, 940), (1086, 3026)
X(50040) = trilinear product X(i)*X(j) for these {i, j}: {941, 44733}, {959, 31359}
X(50040) = trilinear quotient X(i)/X(j) for these (i, j): (941, 2268), (959, 1468), (1111, 3026)


leftri

Points in a [[a(b-c),b(c-a),c(a-b)], [(b^2-c^2)(a^2-b^2-c^2), (c^2-a^2)(b^2-c^2-a^2), (a^2-b^2)(a^2 - b^2 - c^2)]] coordinate system: X(50041)-X(50073)

rightri

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

L1 is the line: a(b+c) α + b(c+a) β (a+)b γ = 0.

L2 is the line (b^2-c^2)(a^2-b^2-c^2) α + (c^2-a^2)(b^2-c^2-a^2) β + (a^2-b^2)(a^2 - b^2 - c^2) γ = 0 (Euler line).

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

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

u : v : w = -(a-b)(a-c)(b-c)(a^3+b^3+c^3+a^2b+ab^2+b^2c+bc^2+c^2a+a^2c+2abc) - (ab + ac - 2bc)x - (2a^4-b^4-c^4+2b^2c^2-a^2b^2-a^2c^2) y : : ,

where, as functions of a, b, c, the coordinate x is antisymmetric of degree 4, and y is antisymmetric of degree 2.

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

{-2 (a-b) (a-c) (b-c) (a+b+c), -((2 (a-b) (a-c) (b-c))/(a+b+c))}, 8
{-((a-b) (a-c) (b-c) (a+b+c)), -(((a-b) (a-c) (b-c))/(a+b+c))}, 3679
{-(1/2) (a-b) (a-c) (b-c) (a+b+c), -(((a-b) (a-c) (b-c))/(2 (a+b+c)))}, 10
{0, 0}, 2
{0, ((a-b) (a-c) (b-c))/(a+b+c)}, 16394
{1/2 (a-b) (a-c) (b-c) (a+b+c), ((a-b) (a-c) (b-c))/(2 (a+b+c))}, 551
{(a-b) (a-c) (b-c) (a+b+c), ((a-b) (a-c) (b-c))/(a+b+c)}, 1
{2 (a-b) (a-c) (b-c) (a+b+c), (2 (a-b) (a-c) (b-c))/(a+b+c)}, 3241
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), -(((a - b)*(a - c)*(b - c))/(a + b + c))}, 50041
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), -1/2*((a - b)*(a - c)*(b - c))/(a + b + c)}, 50042
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), 0}, 50043
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), ((a - b)*(a - c)*(b - c))/(a + b + c)}, 50044
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), (2*(a - b)*(a - c)*(b - c))/(a + b + c)}, 50045
{-((a - b)*(a - c)*(b - c)*(a + b + c)), (-2*(a - b)*(a - c)*(b - c))/(a + b + c)}, 50046
{-((a - b)*(a - c)*(b - c)*(a + b + c)), -1/2*((a - b)*(a - c)*(b - c))/(a + b + c)}, 50047
{-((a - b)*(a - c)*(b - c)*(a + b + c)), 0}, 50048
{-((a - b)*(a - c)*(b - c)*(a + b + c)), ((a - b)*(a - c)*(b - c))/(a + b + c)}, 50049
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), (-2*(a - b)*(a - c)*(b - c))/(a + b + c)}, 50050
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), -(((a - b)*(a - c)*(b - c))/(a + b + c))}, 50051
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), 0}, 50052
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), ((a - b)*(a - c)*(b - c))/(2*(a + b + c))}, 50053
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), ((a - b)*(a - c)*(b - c))/(a + b + c)}, 50054
{0, (-2*(a - b)*(a - c)*(b - c))/(a + b + c)}, 50055
{0, -(((a - b)*(a - c)*(b - c))/(a + b + c))}, 50056
{0, -(((a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2))}, 50057
{0, -1/2*((a - b)*(a - c)*(b - c))/(a + b + c)}, 50058
{0, ((a - b)*(a - c)*(b - c))/(2*(a + b + c))}, 50059
{0, ((a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2)}, 50060
{0, (2*(a - b)*(a - c)*(b - c))/(a + b + c)}, 50061
{((a - b)*(a - c)*(b - c)*(a + b + c))/2, -1/2*((a - b)*(a - c)*(b - c))/(a + b + c)}, 50062
{((a - b)*(a - c)*(b - c)*(a + b + c))/2, 0}, 50063
{((a - b)*(a - c)*(b - c)*(a + b + c))/2, ((a - b)*(a - c)*(b - c))/(a + b + c)}, 50064
{(a - b)*(a - c)*(b - c)*(a + b + c), (-2*(a - b)*(a - c)*(b - c))/(a + b + c)}, 50065
{(a - b)*(a - c)*(b - c)*(a + b + c), -(((a - b)*(a - c)*(b - c))/(a + b + c))}, 50066
{(a - b)*(a - c)*(b - c)*(a + b + c), -1/2*((a - b)*(a - c)*(b - c))/(a + b + c)}, 50067
{(a - b)*(a - c)*(b - c)*(a + b + c), 0}, 50068
{(a - b)*(a - c)*(b - c)*(a + b + c), ((a - b)*(a - c)*(b - c))/(2*(a + b + c))}, 50069
{(a - b)*(a - c)*(b - c)*(a + b + c), (2*(a - b)*(a - c)*(b - c))/(a + b + c)}, 50070
{2*(a - b)*(a - c)*(b - c)*(a + b + c), 0}, 50071
{2*(a - b)*(a - c)*(b - c)*(a + b + c), ((a - b)*(a - c)*(b - c))/(a + b + c)}, 50072
{(2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c), ((a - b)*(a - c)*(b - c))/(a + b + c)}, 50073


X(50041) = X(2)X(3695)∩X(8)X(30)

Barycentrics    a^4 + a^2*b^2 - 2*b^4 - 6*a*b^2*c - 6*b^3*c + a^2*c^2 - 6*a*b*c^2 - 8*b^2*c^2 - 6*b*c^3 - 2*c^4 : :

X(50041) lies on these lines: {2, 3695}, {8, 30}, {75, 44217}, {321, 381}, {345, 15670}, {405, 42033}, {519, 5710}, {536, 984}, {549, 17740}, {3419, 4431}, {3543, 4461}, {3704, 10056}, {3830, 5016}, {3969, 15934}, {4102, 10449}, {4363, 49744}, {4740, 17678}, {4980, 17528}, {5814, 17781}, {6175, 28605}, {7788, 33935}, {15956, 32087}, {17264, 17542}, {17294, 24473}, {17532, 42029}, {17556, 42034}, {19835, 31152}

X(50041) = {X(8),X(49719)}-harmonic conjugate of X(48800)


X(50042) = X(5)X(321)∩X(8)X(30)

Barycentrics    a^2*b^2 - b^4 - 4*a*b^2*c - 4*b^3*c + a^2*c^2 - 4*a*b*c^2 - 6*b^2*c^2 - 4*b*c^3 - c^4 : :
X(50042) = X[145] - 3 X[16394]

X(50042) lies on these lines: {4, 4461}, {5, 321}, {8, 30}, {10, 536}, {75, 3695}, {140, 17740}, {145, 16394}, {192, 4205}, {306, 6147}, {312, 17527}, {345, 6675}, {346, 11108}, {442, 28605}, {495, 3704}, {942, 2321}, {1089, 3820}, {1278, 16062}, {1329, 4066}, {1368, 19835}, {1698, 6057}, {2886, 42031}, {3159, 5743}, {3627, 5016}, {3703, 4647}, {3729, 5814}, {3813, 4717}, {3831, 48644}, {3932, 28612}, {3933, 33935}, {3974, 9709}, {4046, 5904}, {4125, 9711}, {4187, 4671}, {4363, 49743}, {4431, 5295}, {4527, 35633}, {4658, 17388}, {4686, 23537}, {4788, 37164}, {5695, 15171}, {5708, 34255}, {6535, 24443}, {7206, 28611}, {7227, 43531}, {7483, 33168}, {10386, 32929}, {13728, 17147}, {16085, 17143}, {16458, 19825}, {16817, 42033}, {17759, 37148}, {19276, 20009}, {24390, 33089}, {28503, 30145}

X(50042) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 3927, 49718}, {8, 32933, 49716}, {75, 3695, 8728}, {3703, 4647, 31419}


X(50043) = X(2)X(37)∩X(8)X(30)

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

X(50043) lies on these lines: {2, 37}, {7, 3969}, {8, 30}, {63, 4431}, {306, 4654}, {319, 20078}, {553, 2321}, {3058, 5695}, {3161, 41915}, {3219, 42696}, {3241, 16394}, {3543, 5016}, {3686, 25734}, {3695, 44217}, {3704, 11237}, {3729, 5739}, {4001, 4007}, {4023, 4942}, {4102, 32939}, {4363, 37631}, {4371, 19742}, {4454, 32859}, {4644, 20017}, {4665, 49730}, {5271, 5325}, {5278, 32087}, {5294, 17151}, {5564, 42030}, {7227, 20182}, {7229, 19684}, {7283, 31156}, {10327, 49732}, {10385, 32929}, {16676, 28608}, {17269, 40688}, {18139, 31995}, {19993, 49484}, {20911, 32836}, {24280, 33075}, {26563, 32869}, {29616, 32007}, {29617, 48869}, {30614, 32941}, {32833, 33935}, {32858, 42697}, {33163, 49474}, {33171, 49493}, {35578, 42045}, {37549, 48859}, {41816, 49748}, {42039, 48802}

X(50043) = reflection of X(3241) in X(16394)
X(50043) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4740, 19819}, {2, 42033, 17776}, {75, 42033, 2}, {4664, 19797, 2}, {4686, 32777, 19789}, {4726, 24789, 19826}, {17281, 42051, 2}


X(50044) = X(1)X(536)∩X(8)X(30)

Barycentrics    a^4 - a^2*b^2 + 2*a*b^2*c + 2*b^3*c - a^2*c^2 + 2*a*b*c^2 + 4*b^2*c^2 + 2*b*c^3 : :
X(50044) = 2 X[1] - 3 X[16394]

X(50044) lies on these lines: {1, 536}, {3, 321}, {5, 17740}, {8, 30}, {10, 32934}, {20, 4461}, {21, 28605}, {25, 19835}, {37, 16458}, {46, 3714}, {63, 5295}, {72, 3729}, {75, 405}, {76, 16085}, {190, 9534}, {192, 1010}, {312, 474}, {344, 17529}, {345, 442}, {346, 443}, {377, 3695}, {382, 5016}, {404, 4671}, {596, 17597}, {940, 2901}, {956, 29010}, {958, 4647}, {964, 17147}, {975, 3175}, {993, 42031}, {999, 3702}, {1008, 17759}, {1009, 4441}, {1089, 1376}, {1104, 4686}, {1125, 4387}, {1229, 16410}, {1260, 23661}, {1278, 4195}, {1453, 17151}, {1468, 4365}, {1478, 3704}, {1714, 44416}, {1724, 4361}, {1770, 3416}, {1975, 33935}, {2049, 28606}, {2321, 4292}, {2345, 13728}, {2476, 33168}, {2915, 19845}, {3210, 13740}, {3263, 19309}, {3295, 4968}, {3555, 3886}, {3672, 37037}, {3696, 41229}, {3701, 9709}, {3712, 10198}, {3797, 11321}, {3913, 4692}, {3916, 11679}, {3923, 16466}, {3969, 18541}, {3977, 5791}, {3995, 16454}, {4054, 11374}, {4066, 25440}, {4197, 32849}, {4205, 19822}, {4223, 31130}, {4340, 17314}, {4358, 16408}, {4359, 11108}, {4362, 24850}, {4385, 5687}, {4418, 5711}, {4424, 5793}, {4519, 32636}, {4665, 49728}, {4699, 37035}, {4717, 8666}, {4740, 13735}, {4980, 16418}, {5080, 5827}, {5100, 29028}, {5192, 17495}, {5247, 49474}, {5262, 11354}, {5271, 31445}, {5786, 21375}, {5905, 41014}, {6533, 8167}, {8728, 17776}, {10449, 32939}, {12943, 36974}, {13741, 17490}, {13747, 28808}, {16342, 31025}, {16343, 31993}, {16352, 42715}, {16370, 42029}, {16371, 42034}, {16377, 42720}, {16403, 26227}, {16425, 42713}, {16429, 27802}, {16777, 25526}, {16842, 19804}, {16853, 24589}, {16862, 18743}, {16864, 30829}, {17164, 49492}, {17280, 33833}, {17302, 37036}, {17526, 19789}, {17535, 46938}, {17698, 19785}, {17751, 36279}, {17862, 37244}, {19276, 42044}, {19285, 20336}, {19329, 33931}, {19331, 22034}, {19768, 33940}, {19825, 37314}, {19848, 36011}, {20182, 43531}, {23537, 32777}, {24851, 32778}, {28604, 37039}, {30699, 37176}, {31339, 32936}, {34791, 49485}, {37248, 48380}, {37549, 48863}, {38315, 43993}, {42033, 44217}

X(50044) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 32933, 3927}, {75, 7283, 405}, {4385, 32932, 5687}, {4968, 32929, 3295}


X(50045) = X(2)X(7283)∩X(8)X(30)

Barycentrics    5*a^4 - 4*a^2*b^2 - b^4 + 6*a*b^2*c + 6*b^3*c - 4*a^2*c^2 + 6*a*b*c^2 + 14*b^2*c^2 + 6*b*c^3 - c^4 : :
X(50045) = 4 X[16394] - 3 X[38314]

X(50045) lies on these lines: {2, 7283}, {8, 30}, {75, 31156}, {321, 376}, {345, 6175}, {377, 42033}, {381, 17740}, {536, 3241}, {4217, 42051}, {4363, 49739}, {4454, 49687}, {4461, 15683}, {4968, 10385}, {4980, 11111}, {5016, 15682}, {5434, 5695}, {13735, 19819}, {15677, 28605}, {15956, 31995}, {16393, 42047}, {16394, 38314}, {17776, 44217}, {32836, 41826}

X(50045) = {X(48806),X(49719)}-harmonic conjugate of X(8)


X(50046) = X(8)X(536)∩X(30)X(40)

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

X(50046) lies on these lines: {2, 1104}, {8, 536}, {10, 16394}, {30, 40}, {377, 4688}, {388, 48849}, {519, 10371}, {950, 29594}, {958, 16403}, {1423, 5252}, {4217, 17359}, {4664, 26117}, {4755, 37314}, {10404, 31178}, {11114, 17281}, {13735, 32777}, {14020, 41313}, {24473, 48834}, {42051, 48813}

X(50046) = reflection of X(16394) in X(10)
X(50046) = {X(3679),X(48807)}-harmonic conjugate of X(34612)


X(50047) = X(10)X(536)∩X(30)X(40)

Barycentrics    2*a^3*b + a^2*b^2 + 2*a*b^3 + 3*b^4 + 2*a^3*c + 4*a^2*b*c + 10*a*b^2*c + 8*b^3*c + a^2*c^2 + 10*a*b*c^2 + 10*b^2*c^2 + 2*a*c^3 + 8*b*c^3 + 3*c^4 : :

X(50047) lies on these lines: {2, 3695}, {8, 16394}, {10, 536}, {30, 40}, {519, 5835}, {579, 594}, {942, 29594}, {3295, 48849}, {4205, 4664}, {4688, 8728}, {4740, 16062}, {5687, 16403}, {16052, 42029}, {20653, 31161}, {32778, 39542}, {37148, 41142}, {42051, 48815}

X(50047) = midpoint of X(8) and X(16394)


X(50048) = X(2)X(37)∩X(30)X(40)

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

X(50048) lies on these lines: {2, 37}, {8, 4641}, {10, 32934}, {30, 40}, {63, 594}, {81, 17299}, {306, 4363}, {333, 48628}, {519, 5710}, {527, 8896}, {553, 29594}, {750, 6535}, {940, 2321}, {1089, 5955}, {1211, 3729}, {1836, 32778}, {2218, 16418}, {3219, 17275}, {3305, 17340}, {3416, 4418}, {3661, 32939}, {3681, 46918}, {3696, 33163}, {3751, 4046}, {3773, 3980}, {3782, 4659}, {3923, 3966}, {3943, 5287}, {3969, 4851}, {3977, 5737}, {4001, 4445}, {4361, 5294}, {4383, 17355}, {4421, 16403}, {4643, 32933}, {4665, 5271}, {4675, 32858}, {4795, 42045}, {4863, 33169}, {4873, 17022}, {4886, 17350}, {4967, 19732}, {5241, 30568}, {5249, 17118}, {5256, 17369}, {5268, 6057}, {5278, 28634}, {5564, 37652}, {5712, 7229}, {5739, 17351}, {5750, 20182}, {5880, 15523}, {7283, 48814}, {10385, 48849}, {17116, 18134}, {17119, 26723}, {17163, 33114}, {17228, 26840}, {17276, 32782}, {17284, 40688}, {17314, 37595}, {17332, 25734}, {17333, 41816}, {17344, 20078}, {17389, 33954}, {17718, 33160}, {17723, 32855}, {17781, 49721}, {19723, 48864}, {21020, 33161}, {21085, 32935}, {24342, 33092}, {24549, 29574}, {26065, 42696}, {29010, 33167}, {29649, 48644}, {31141, 39573}, {32780, 49474}, {32783, 49493}, {32860, 38047}, {32945, 49688}, {33171, 49483}, {34255, 37520}, {37650, 41915}, {37653, 48630}

X(50048) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4740, 19796}, {2, 42049, 3666}, {75, 32777, 24789}, {2345, 42049, 2}, {3679, 3929, 49724}, {3679, 48812, 34606}, {4665, 44416, 5271}, {17776, 19825, 3739}, {19797, 42033, 2}, {28605, 32779, 3772}


X(50049) = X(1)X(536)∩X(30)X(40)

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

X(50049) lies on these lines: {1, 536}, {2, 7283}, {30, 40}, {35, 16403}, {72, 49721}, {75, 13735}, {321, 16393}, {405, 4688}, {1008, 41142}, {1010, 4664}, {1724, 16833}, {3175, 19276}, {3338, 31137}, {3761, 16085}, {3811, 31161}, {4195, 4740}, {4234, 42029}, {4292, 29594}, {4294, 48849}, {4755, 16458}, {11112, 17281}, {11354, 42051}, {17274, 33868}, {19290, 35652}, {19797, 48814}, {24473, 48862}, {25526, 29597}, {28605, 37817}, {42033, 48816}

X(50049) = reflection of X(1) in X(16394)


X(50050) = X(8)X(536)∩X(10)X(30)

Barycentrics    2*a^4 - a^3*b - 2*a^2*b^2 - a*b^3 - 2*b^4 - a^3*c - 2*a^2*b*c - 3*a*b^2*c - 2*b^3*c - 2*a^2*c^2 - 3*a*b*c^2 - a*c^3 - 2*b*c^3 - 2*c^4 : :
X(50050) = 5 X[1698] - 3 X[16394]

X(50050) lies on these lines: {1, 48801}, {4, 44417}, {8, 536}, {10, 30}, {37, 7270}, {141, 950}, {377, 3739}, {388, 28015}, {452, 17279}, {516, 5835}, {942, 48835}, {964, 17385}, {1104, 16062}, {1698, 16394}, {1837, 26034}, {2345, 3146}, {2475, 31993}, {2646, 25760}, {3057, 32947}, {3454, 24929}, {3666, 5016}, {3698, 32948}, {3752, 4201}, {3868, 17345}, {3931, 36974}, {3962, 4683}, {4138, 11281}, {4202, 17356}, {4363, 9579}, {4514, 5484}, {4657, 5716}, {4660, 5836}, {4670, 49745}, {4698, 37314}, {5046, 30818}, {5051, 37539}, {5086, 33083}, {5262, 17382}, {5691, 5793}, {5710, 28566}, {5814, 48837}, {6284, 49484}, {6872, 32777}, {7232, 11518}, {10371, 28581}, {10895, 29828}, {11114, 17359}, {12527, 49524}, {12625, 17272}, {15680, 32779}, {15956, 20008}, {16085, 25280}, {16403, 29857}, {16817, 17678}, {16824, 21949}, {17235, 37549}, {17357, 17697}, {17606, 32918}, {17690, 24589}, {17792, 22299}, {18252, 44545}, {19822, 31295}, {30148, 48808}

X(50050) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5016, 17676, 3666}, {7270, 26117, 37}


X(50051) = X(2)X(1104)∩X(10)X(30)

Barycentrics    2*a^4 - 3*a^3*b - 4*a^2*b^2 - 3*a*b^3 - 4*b^4 - 3*a^3*c - 6*a^2*b*c - 9*a*b^2*c - 6*b^3*c - 4*a^2*c^2 - 9*a*b*c^2 - 4*b^2*c^2 - 3*a*c^3 - 6*b*c^3 - 4*c^4 : :
X(50051) = X[16394] - 3 X[19875]

X(50051) lies on these lines: {2, 1104}, {10, 30}, {306, 49739}, {381, 44417}, {536, 984}, {950, 48859}, {2345, 3543}, {3419, 17239}, {3586, 17293}, {3739, 44217}, {4670, 49744}, {4688, 17678}, {4870, 25760}, {5232, 15956}, {5814, 48857}, {5835, 28194}, {6175, 31993}, {11113, 17359}, {15677, 32779}, {16394, 19875}, {26117, 42033}, {31156, 32777}


X(50052) = X(2)X(37)∩X(10)X(30)

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

X(50052) lies on these lines: {2, 37}, {10, 30}, {57, 17293}, {63, 17239}, {81, 17372}, {141, 553}, {226, 7227}, {306, 4670}, {519, 5835}, {940, 17229}, {1211, 17351}, {1999, 4102}, {2321, 6703}, {3017, 5295}, {3058, 49484}, {3578, 4641}, {3679, 5247}, {3687, 17369}, {3696, 32780}, {3773, 4682}, {3844, 3980}, {3929, 17251}, {3969, 37595}, {3982, 7231}, {4363, 4654}, {4428, 48851}, {4519, 29845}, {4663, 21085}, {4665, 40940}, {4706, 29663}, {4884, 19868}, {4886, 16669}, {5235, 43260}, {5294, 17348}, {5743, 17355}, {5814, 48870}, {16832, 28608}, {17022, 17269}, {17118, 25527}, {17237, 32939}, {17275, 26065}, {17286, 37674}, {17345, 32782}, {19732, 28633}, {24177, 34573}, {29615, 41629}, {29667, 49719}, {32783, 49483}, {37652, 42030}, {37683, 48630}

X(50052) = midpoint of X(3679) and X(16394)
X(50052) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17281, 35652}, {2, 19797, 4688}, {2, 42033, 37}, {2, 42051, 17382}, {10, 5325, 49730}, {19808, 42033, 2}, {19822, 32777, 3739}, {19825, 24789, 4739}, {44416, 49730, 5325}


X(50053) = X(2)X(7283)∩X(10)X(30)

Barycentrics    4*a^4 + 3*a^3*b + a^2*b^2 + 3*a*b^3 + b^4 + 3*a^3*c + 6*a^2*b*c + 9*a*b^2*c + 6*b^3*c + a^2*c^2 + 9*a*b*c^2 + 10*b^2*c^2 + 3*a*c^3 + 6*b*c^3 + c^4 : :

X(50053) lies on these lines: {2, 7283}, {10, 30}, {306, 49744}, {376, 2345}, {519, 5710}, {536, 551}, {549, 44417}, {942, 48859}, {965, 17355}, {975, 42032}, {1010, 42033}, {1125, 4387}, {1707, 3679}, {3654, 5793}, {5835, 28204}, {6175, 32779}, {7227, 24929}, {13735, 19797}, {15170, 49484}, {15670, 31993}, {15956, 25590}, {17116, 26728}, {17281, 19276}, {19332, 41313}, {19716, 48863}, {19822, 31156}, {32777, 44217}


X(50054) = X(1)X(536)∩X(10)X(30)

Barycentrics    2*a^4 + a^3*b + a*b^3 + a^3*c + 2*a^2*b*c + 3*a*b^2*c + 2*b^3*c + 3*a*b*c^2 + 4*b^2*c^2 + a*c^3 + 2*b*c^3 : :
X(50054) = X[1] - 3 X[16394]

X(50054) lies on these lines: {1, 536}, {3, 44417}, {8, 4641}, {10, 30}, {20, 2345}, {21, 31993}, {37, 1010}, {40, 5793}, {44, 9534}, {58, 5295}, {65, 4418}, {72, 17351}, {75, 1104}, {141, 4292}, {171, 3714}, {306, 49745}, {319, 20077}, {321, 11115}, {377, 32777}, {404, 30818}, {405, 3739}, {443, 17279}, {515, 5835}, {553, 48859}, {894, 1043}, {942, 48863}, {960, 3923}, {964, 3666}, {975, 19276}, {1008, 1575}, {1009, 21264}, {1125, 48643}, {1220, 4646}, {1453, 4361}, {1468, 3706}, {1724, 17348}, {1909, 16085}, {2475, 32779}, {2901, 37594}, {3555, 49467}, {3683, 31339}, {3696, 5247}, {3744, 4968}, {3752, 13740}, {3758, 20018}, {3772, 37176}, {3812, 3980}, {3916, 10479}, {3967, 5293}, {4005, 32938}, {4201, 17289}, {4223, 30748}, {4252, 11679}, {4304, 7227}, {4313, 7229}, {4340, 4851}, {4358, 19284}, {4359, 11319}, {4652, 37660}, {4657, 37037}, {4688, 13735}, {4689, 26115}, {4690, 49716}, {4698, 16458}, {4719, 25496}, {5178, 33170}, {5192, 16610}, {5217, 16403}, {5262, 42051}, {5436, 25590}, {5737, 31424}, {5743, 12572}, {5782, 37537}, {6682, 8720}, {6872, 19822}, {7222, 11036}, {9565, 42450}, {10404, 33171}, {11109, 25939}, {11112, 17359}, {12618, 20420}, {13725, 17303}, {13727, 44798}, {13728, 17385}, {13741, 16602}, {13742, 17278}, {13745, 19857}, {16454, 44307}, {16583, 24275}, {17355, 30618}, {17357, 33833}, {17384, 37036}, {17526, 24789}, {17539, 31025}, {17609, 32943}, {17697, 19804}, {17698, 23537}, {19808, 26117}, {19827, 37164}, {19879, 24715}, {24537, 25091}, {25526, 28639}, {25917, 32930}, {26011, 37248}, {26051, 33116}, {30148, 48811}, {30942, 32636}, {31238, 37035}, {32771, 37080}, {32929, 37548}, {32941, 34791}, {37095, 42706}, {37402, 38871}, {41813, 49461}

X(50054) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 24850, 4640}, {10, 31730, 44419}, {75, 4195, 1104}, {321, 11115, 37539}, {1010, 7283, 37}, {1220, 32932, 4646}, {44416, 49734, 10}


X(50055) = X(2)X(3)∩X(8)X(536)

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

X(50055) lies on these lines: {1, 48799}, {2, 3}, {8, 536}, {3058, 48801}, {3454, 47040}, {3488, 17184}, {4026, 12943}, {4664, 7270}, {4968, 48849}, {5229, 26115}, {5739, 48837}, {6284, 48805}, {9598, 17281}, {9852, 24443}, {15956, 17274}, {16705, 32006}, {18391, 32950}, {19784, 48826}, {34606, 48829}, {37549, 49741}

X(50055) = anticomplement of X(16394)
X(50055) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20, 16393}, {2, 6872, 13735}, {2, 11114, 4217}, {2, 13735, 17526}, {377, 26117, 37314}, {5051, 16393, 2}, {6872, 16062, 17526}, {11113, 11359, 2}, {13735, 16062, 2}, {13745, 17528, 2}, {14020, 17679, 2}, {16052, 16370, 2}, {17530, 19279, 2}, {17677, 37038, 2}, {17678, 48814, 2}


X(50056) = X(1)X(48801)∩X(2)X(3)

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

X(50056) lies on these lines: {1, 48801}, {2, 3}, {10, 32934}, {387, 49716}, {519, 10371}, {536, 984}, {551, 4138}, {940, 48835}, {956, 32773}, {1211, 48837}, {1478, 4026}, {1714, 49728}, {3058, 48803}, {3419, 4357}, {3454, 19765}, {3586, 17306}, {3940, 26580}, {4252, 25441}, {4383, 48843}, {4653, 30811}, {4972, 9708}, {5434, 48799}, {5739, 48847}, {5774, 33083}, {7776, 16705}, {7784, 25499}, {9654, 26115}, {9668, 24552}, {15934, 17184}, {17202, 48908}, {17274, 24473}, {19723, 48839}, {26034, 37715}, {32950, 36279}, {34606, 48831}, {41816, 48850}

X(50056) = reflection of X(16394) in X(2)
X(50056) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11112, 19290}, {2, 11114, 11354}, {2, 14020, 16857}, {2, 17579, 19276}, {2, 17677, 17532}, {2, 17678, 44217}, {2, 26117, 48814}, {2, 37038, 16370}, {2, 48813, 11112}, {2, 48814, 405}, {2, 49735, 16418}, {377, 4205, 16458}, {442, 13725, 16343}, {5051, 17676, 3}, {16062, 26117, 405}, {16062, 48814, 2}, {37144, 37145, 37320}


X(50057) = X(2)X(3)∩X(536)X(599)

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

X(50057) lies on these lines: {2, 3}, {536, 599}, {940, 7761}, {980, 7784}, {1211, 2549}, {2895, 22253}, {3849, 5006}, {4045, 4383}, {5739, 15048}, {16834, 48842}, {24271, 44526}, {29574, 48840}, {31089, 31859}, {41816, 48869}

X(50057) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 8356, 16431}, {2, 35276, 11288}


X(50058) = X(2)X(3)∩X(10)X(536)

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

X(50058) lies on these lines: {2, 3}, {10, 536}, {387, 49718}, {495, 4026}, {1211, 48847}, {1330, 46922}, {3695, 4664}, {3925, 19871}, {4688, 23537}, {5722, 17306}, {5743, 48843}, {5814, 16834}, {6703, 48835}, {15170, 48803}, {15171, 48805}, {18990, 48799}, {20083, 49728}, {32784, 37715}

X(50058) = complement of X(16394)
X(50058) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13735, 17698}, {2, 17676, 16393}, {2, 17677, 37150}, {2, 26117, 13735}, {2, 48813, 19276}, {4205, 16062, 8728}, {5051, 13728, 5}, {16062, 37164, 4205}, {37144, 37145, 49132}


X(50059) = X(2)X(3)∩X(536)X(551)

Barycentrics    4*a^4 + 4*a^3*b + 3*a^2*b^2 + 4*a*b^3 + b^4 + 4*a^3*c + 8*a^2*b*c + 8*a*b^2*c + 4*b^3*c + 3*a^2*c^2 + 8*a*b*c^2 + 6*b^2*c^2 + 4*a*c^3 + 4*b*c^3 + c^4 : :

X(50059) lies on these lines: {2, 3}, {519, 5835}, {536, 551}, {1125, 48643}, {1387, 43135}, {3679, 5269}, {3940, 5749}, {4264, 17330}, {4363, 39544}, {4653, 17398}, {4665, 49683}, {5743, 48866}, {5750, 24929}, {6703, 48863}, {15170, 48805}, {17303, 37817}, {17369, 30115}, {18990, 48801}, {20083, 49734}, {48811, 49736}

X(50059) = midpoint of X(2) and X(16394)
X(50059) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4195, 48814}, {2, 11112, 48815}, {2, 48814, 4205}, {1010, 17698, 8728}, {2049, 37176, 6675}, {11115, 13728, 550}


X(50060) = X(2)X(3)∩X(6)X(536)

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

X(50060) lies on these lines: {2, 3}, {6, 536}, {940, 3734}, {1211, 7737}, {1384, 26243}, {1724, 16833}, {4383, 7804}, {5247, 48812}, {5739, 18907}, {15956, 35578}, {17294, 48862}, {19684, 24203}, {19719, 29580}, {19723, 48864}, {19732, 24275}, {22253, 37685}, {29594, 48863}, {42028, 48838}

X(50060) = crossdifference of every pair of points on line {647, 9010}
X(50060) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1003, 16436}, {2, 16046, 3}, {384, 41236, 11343}, {11320, 19281, 405}


X(50061) = X(2)X(3)∩X(8)X(4641)

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

X(50061) lies on these lines: {2, 3}, {8, 4641}, {193, 4720}, {536, 3241}, {1707, 3679}, {3476, 28968}, {4293, 24552}, {4307, 49492}, {4339, 4968}, {4644, 49687}, {5434, 48805}, {5716, 42049}, {7354, 48801}, {34612, 48832}

X(50061) = reflection of X(2) in X(16394)
X(50061) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6872, 48814}, {2, 16397, 3524}, {2, 48814, 37314}, {2, 48817, 4217}, {377, 4195, 17526}, {1010, 6872, 37314}, {1010, 48814, 2}, {3529, 37037, 17676}, {11112, 11354, 2}, {11113, 19276, 2}, {13735, 48816, 2}, {13745, 19277, 2}, {16370, 37150, 2}


X(50062) = X(10)X(536)∩X(30)X(551)

Barycentrics    5*a^3*b + 7*a^2*b^2 + 5*a*b^3 + 3*b^4 + 5*a^3*c + 10*a^2*b*c + 7*a*b^2*c + 2*b^3*c + 7*a^2*c^2 + 7*a*b*c^2 - 2*b^2*c^2 + 5*a*c^3 + 2*b*c^3 + 3*c^4 : :

X(50062) lies on these lines: {1, 48799}, {2, 7283}, {10, 536}, {30, 551}, {519, 10371}, {942, 49741}, {1125, 16394}, {1330, 29584}, {2901, 29594}, {4205, 4688}, {4656, 48843}, {4664, 16062}, {4740, 37164}, {4755, 8728}, {5248, 16403}, {5722, 17323}, {13735, 19786}, {17320, 17677}, {17528, 41312}, {35652, 48815}, {37148, 41144}, {37150, 41311}

X(50062) = reflection of X(16394) in X(1125)


X(50063) = X(2)X(37)∩X(30)X(551)

Barycentrics    2*a^3 + 3*a^2*b + 3*a*b^2 + 2*b^3 + 3*a^2*c + 4*a*b*c + 3*a*c^2 + 2*c^3 : :
X(50063) = X[16394] - 3 X[25055]

X(50063) lies on these lines: {1, 48801}, {2, 37}, {30, 551}, {57, 17323}, {81, 17345}, {226, 17045}, {553, 49741}, {940, 17235}, {1100, 27184}, {1104, 48814}, {1125, 48643}, {1155, 29847}, {1211, 4852}, {1386, 4425}, {1999, 17237}, {3187, 4690}, {3589, 4656}, {3663, 6703}, {3683, 29636}, {3687, 17395}, {3723, 18134}, {3745, 32776}, {3782, 4670}, {3821, 4682}, {3834, 5287}, {3838, 29644}, {3929, 24441}, {3946, 5743}, {3967, 29633}, {4003, 29845}, {4009, 29663}, {4364, 40940}, {4389, 29841}, {4415, 17023}, {4417, 17396}, {4640, 29645}, {4641, 29833}, {4654, 7175}, {4708, 5271}, {4854, 49484}, {5087, 29650}, {5249, 28639}, {9639, 30143}, {11679, 17325}, {14829, 17324}, {15254, 29654}, {15569, 26128}, {15668, 23681}, {16394, 25055}, {16519, 16834}, {16666, 33066}, {16777, 25527}, {16830, 21949}, {17022, 17290}, {17184, 17376}, {17231, 34064}, {17249, 37683}, {17254, 41629}, {17265, 25430}, {17304, 37674}, {17372, 32782}, {19722, 31164}, {21342, 29837}, {28609, 41239}, {30568, 47355}, {31019, 37869}, {32775, 37593}, {32780, 49523}, {32783, 49462}

X(50063) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3175, 17359}, {2, 3672, 42049}, {2, 19796, 4688}, {17184, 37595, 17376}, {32774, 44307, 17356}


X(50064) = X(1)X(536)∩X(30)X(551)

Barycentrics    6*a^4 + 5*a^3*b + 4*a^2*b^2 + 5*a*b^3 + 5*a^3*c + 10*a^2*b*c + 7*a*b^2*c + 2*b^3*c + 4*a^2*c^2 + 7*a*b*c^2 + 4*b^2*c^2 + 5*a*c^3 + 2*b*c^3 : :

X(50064) lies on these lines: {1, 536}, {2, 1104}, {30, 551}, {37, 13735}, {56, 16403}, {405, 4755}, {519, 5835}, {958, 48854}, {1008, 41144}, {1010, 4688}, {1043, 29584}, {3666, 16393}, {4195, 4664}, {4292, 49741}, {4304, 17045}, {11111, 41312}, {11112, 17382}, {11354, 35652}, {15668, 16485}, {24473, 35637}, {30142, 48826}, {37038, 41311}

X(50064) = midpoint of X(1) and X(16394)


X(50065) = X(1)X(30)∩X(8)X(536)

Barycentrics    a^4 - a^3*b - 2*a^2*b^2 - a*b^3 - b^4 - a^3*c - 2*a^2*b*c - a*b^2*c - 2*a^2*c^2 - a*b*c^2 + 2*b^2*c^2 - a*c^3 - c^4 : :
X(50065) = 4 X[1125] - 3 X[16394]

X(50065) lies on these lines: {1, 30}, {3, 17720}, {4, 3666}, {8, 536}, {10, 32934}, {11, 988}, {12, 17594}, {20, 37539}, {21, 3772}, {37, 377}, {46, 37715}, {55, 13161}, {56, 24210}, {63, 1834}, {65, 17635}, {72, 48837}, {75, 26117}, {78, 4415}, {145, 32859}, {192, 7270}, {226, 19765}, {312, 4201}, {321, 17676}, {355, 4424}, {387, 4641}, {388, 37548}, {405, 23537}, {443, 44307}, {452, 4000}, {499, 37599}, {515, 37614}, {516, 5710}, {740, 10371}, {908, 4255}, {940, 4292}, {950, 3663}, {958, 3914}, {964, 4657}, {968, 25466}, {975, 11112}, {978, 4679}, {986, 1837}, {993, 36250}, {1001, 23536}, {1043, 27184}, {1072, 11496}, {1104, 6872}, {1125, 16394}, {1193, 24703}, {1210, 17595}, {1478, 3931}, {1479, 17721}, {1714, 31445}, {1770, 5711}, {2218, 20834}, {2292, 5794}, {2352, 37425}, {2475, 28606}, {2478, 3752}, {2650, 33098}, {2901, 48835}, {2975, 33134}, {3011, 16403}, {3085, 4689}, {3120, 10448}, {3146, 3672}, {3159, 48836}, {3175, 48813}, {3436, 4646}, {3585, 5725}, {3670, 5722}, {3710, 17262}, {3714, 26034}, {3739, 37314}, {3744, 4294}, {3755, 12527}, {3797, 33832}, {3868, 17276}, {3869, 33100}, {3916, 5292}, {3924, 33145}, {3944, 11375}, {3951, 17334}, {4003, 36574}, {4189, 33133}, {4195, 19786}, {4202, 17279}, {4217, 17382}, {4302, 5266}, {4304, 34937}, {4340, 37595}, {4346, 15956}, {4352, 4872}, {4364, 49734}, {4383, 12572}, {4414, 21935}, {4423, 24178}, {4428, 28027}, {4640, 5230}, {4652, 37646}, {4673, 5484}, {4850, 5046}, {4862, 11518}, {5016, 17147}, {5047, 17278}, {5084, 16610}, {5137, 13323}, {5178, 7226}, {5252, 29010}, {5260, 33131}, {5262, 11114}, {5271, 49728}, {5290, 37553}, {5436, 23681}, {5530, 10895}, {5691, 5724}, {5717, 20182}, {5718, 9612}, {5721, 7330}, {5835, 28530}, {5930, 6180}, {6376, 16085}, {6850, 37528}, {6925, 15852}, {7283, 16062}, {9791, 31359}, {10459, 33094}, {10624, 37542}, {10896, 24239}, {11319, 32774}, {11320, 19834}, {11376, 37617}, {12953, 17599}, {13725, 31993}, {15338, 17602}, {15680, 33155}, {15803, 37634}, {16706, 17697}, {16817, 48814}, {16859, 26724}, {16865, 33129}, {17064, 24953}, {17275, 26064}, {17596, 24914}, {17679, 41313}, {17690, 31035}, {17718, 37573}, {17719, 37574}, {17751, 32950}, {17781, 48842}, {18178, 26892}, {19796, 19851}, {19808, 37164}, {20018, 33066}, {27802, 37241}, {28011, 49736}, {28029, 41230}, {28808, 37339}, {29028, 37588}, {31424, 35466}, {31730, 37540}, {33144, 37080}, {33151, 34772}, {37732, 37822}, {44302, 46483}

X(50065) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 9579, 49745}, {1, 24851, 1836}, {1, 33095, 12701}, {405, 23537, 24789}, {950, 3663, 37549}, {1479, 37592, 17721}, {3120, 10448, 28628}, {3146, 3672, 5716}, {4414, 21935, 26066}, {4854, 7354, 1}, {6872, 19785, 1104}, {7283, 16062, 32777}, {15338, 17602, 37552}


X(50066) = X(1)X(30)∩X(2)X(7283)

Barycentrics    a^4 - 3*a^3*b - 5*a^2*b^2 - 3*a*b^3 - 2*b^4 - 3*a^3*c - 6*a^2*b*c - 3*a*b^2*c - 5*a^2*c^2 - 3*a*b*c^2 + 4*b^2*c^2 - 3*a*c^3 - 2*c^4 : :
X(50066) = 2 X[16394] - 3 X[25055]

X(50066) lies on these lines: {1, 30}, {2, 7283}, {37, 44217}, {63, 3017}, {72, 48842}, {381, 3666}, {536, 984}, {549, 17720}, {988, 3582}, {1423, 5119}, {1714, 5325}, {3175, 11359}, {3419, 17246}, {3534, 37539}, {3543, 3672}, {3584, 17594}, {3663, 5738}, {3772, 15670}, {3931, 11237}, {4664, 17678}, {5271, 49729}, {5710, 28198}, {5716, 15682}, {6175, 28606}, {10056, 13161}, {10072, 24210}, {10452, 17274}, {11113, 17301}, {11238, 37592}, {15315, 45032}, {15677, 33155}, {16062, 42033}, {16394, 25055}, {17781, 48857}, {18541, 37595}, {19785, 31156}, {19796, 48814}, {24473, 49747}, {28204, 37614}

X(50066) = {X(3058),X(48819)}-harmonic conjugate of X(1)


X(50067) = X(1)X(30)∩X(10)X(536)

Barycentrics    2*a^3*b + 3*a^2*b^2 + 2*a*b^3 + b^4 + 2*a^3*c + 4*a^2*b*c + 2*a*b^2*c + 3*a^2*c^2 + 2*a*b*c^2 - 2*b^2*c^2 + 2*a*c^3 + c^4 : :
X(50067) = 5 X[3616] - 3 X[16394]

X(50067) lies on these lines: {1, 30}, {4, 3672}, {5, 3666}, {10, 536}, {21, 33155}, {35, 17602}, {37, 8728}, {72, 48847}, {75, 4205}, {140, 17720}, {141, 2901}, {192, 3695}, {321, 13728}, {350, 37148}, {382, 5716}, {386, 4415}, {387, 3927}, {405, 19785}, {442, 28606}, {495, 3931}, {496, 20256}, {528, 30145}, {550, 37539}, {938, 15956}, {940, 24470}, {942, 3663}, {952, 37614}, {986, 4941}, {988, 15325}, {1125, 48643}, {1278, 37164}, {1330, 4360}, {1479, 17599}, {1565, 4352}, {1612, 37292}, {1770, 3745}, {1834, 17246}, {2049, 17321}, {2886, 36250}, {3159, 48843}, {3175, 48815}, {3187, 49716}, {3295, 28015}, {3616, 16394}, {3743, 25466}, {3744, 10386}, {3752, 17527}, {3755, 34790}, {3772, 6675}, {3875, 5814}, {3914, 31419}, {3946, 12572}, {3995, 4202}, {4000, 11108}, {4021, 5717}, {4187, 4850}, {4292, 37594}, {4340, 18541}, {4356, 21620}, {4357, 5295}, {4387, 19836}, {4389, 10449}, {4424, 5690}, {4643, 49718}, {4656, 5044}, {4658, 17365}, {4719, 21616}, {4868, 12607}, {5047, 33150}, {5051, 17147}, {5248, 17061}, {5262, 11113}, {5530, 10592}, {5706, 5762}, {5710, 28174}, {5711, 24248}, {5719, 19765}, {5799, 29069}, {6051, 23536}, {7283, 17698}, {7483, 33133}, {7961, 36279}, {10071, 37730}, {10593, 24239}, {11246, 37559}, {12433, 37549}, {13407, 37593}, {13725, 30699}, {13740, 17302}, {16085, 18140}, {16403, 26228}, {16817, 19796}, {17045, 43531}, {17320, 37150}, {17526, 19823}, {17590, 26724}, {17595, 34753}, {17674, 31035}, {17781, 48861}, {19270, 37759}, {19767, 33151}, {19789, 37314}, {19851, 48814}, {20009, 48813}, {20083, 44416}, {20328, 26978}, {20831, 41230}, {24068, 49524}, {24390, 33134}, {24403, 37165}, {24850, 29645}, {24929, 34937}, {27184, 41014}, {30148, 49736}, {31445, 40940}, {33152, 37573}, {33833, 41839}, {37424, 37528}, {37582, 39595}

X(50067) = crosssum of X(55) and X(4275)
X(50067) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3782, 6147}, {37, 23537, 8728}, {192, 16062, 3695}, {387, 4419, 3927}, {3931, 13161, 495}, {7283, 19786, 17698}, {24210, 37592, 496}


X(50068) = X(1)X(30)∩X(2)X(37)

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

X(50068) lies on these lines: {1, 30}, {2, 37}, {6, 17781}, {7, 37595}, {45, 26723}, {63, 17246}, {72, 48857}, {81, 17276}, {226, 4021}, {306, 17318}, {333, 17247}, {376, 37539}, {519, 10371}, {551, 16394}, {553, 940}, {612, 49732}, {968, 17061}, {988, 5298}, {1086, 5287}, {1100, 5905}, {1104, 31156}, {1125, 4387}, {1211, 3875}, {1255, 27186}, {1654, 42030}, {1698, 6057}, {1699, 17726}, {1723, 3929}, {1961, 33149}, {1962, 33143}, {1999, 4389}, {3187, 3578}, {3247, 23681}, {3305, 17366}, {3416, 32776}, {3543, 5716}, {3654, 4424}, {3661, 4102}, {3662, 34064}, {3744, 10385}, {3745, 24248}, {3920, 49719}, {3931, 10056}, {3944, 17600}, {3946, 4383}, {3966, 4425}, {3989, 33128}, {3993, 26128}, {3994, 29663}, {4001, 17255}, {4085, 30615}, {4310, 4883}, {4352, 17078}, {4353, 17597}, {4360, 27184}, {4364, 5271}, {4393, 33066}, {4415, 5256}, {4419, 4641}, {4428, 16403}, {4675, 17019}, {4679, 29821}, {4703, 49477}, {4851, 17184}, {4852, 5739}, {4859, 25430}, {4995, 17594}, {5249, 16777}, {5294, 17262}, {5311, 5880}, {5325, 40940}, {5710, 28194}, {6354, 7190}, {6358, 7264}, {9347, 33102}, {10072, 37592}, {11237, 13161}, {11238, 17599}, {16673, 41867}, {16834, 48848}, {17011, 33151}, {17017, 24703}, {17022, 40688}, {17249, 37653}, {17258, 37652}, {17274, 39773}, {17299, 32782}, {17319, 18134}, {17380, 27064}, {17393, 17778}, {17525, 37817}, {17528, 23604}, {17591, 17728}, {17592, 17718}, {17595, 39595}, {17598, 36482}, {17724, 37553}, {19765, 34937}, {23537, 44217}, {25453, 49456}, {27804, 33122}, {28634, 41809}, {29574, 48840}, {29617, 41816}, {29636, 32936}, {29644, 48643}, {29645, 32934}, {29816, 33094}, {29833, 32933}, {29841, 32939}, {29847, 32845}, {32780, 49445}, {32783, 49452}, {32925, 38047}, {32947, 49681}, {33144, 37593}, {33163, 49523}, {33171, 49462}, {42045, 44302}

X(50068) = reflection of X(16394) in X(551)
X(50068) = crossdifference of every pair of points on line {667, 9404}
X(50068) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4654, 37631}, {1, 33154, 1836}, {1, 48818, 5434}, {2, 192, 42033}, {2, 4740, 19797}, {2, 19819, 4688}, {2, 42033, 32777}, {2, 42044, 17281}, {37, 19785, 24789}, {192, 19786, 32777}, {226, 4021, 20182}, {554, 1081, 10404}, {3782, 37631, 4654}, {3944, 17600, 17723}, {3946, 4656, 4383}, {3995, 32774, 17279}, {4415, 17395, 5256}, {4425, 32921, 3966}, {5311, 33145, 5880}, {15170, 48820, 1}, {17019, 33146, 4675}, {17321, 30699, 31993}, {17382, 35652, 2}, {17399, 42034, 2}, {17592, 33152, 17718}, {17599, 24210, 17721}, {19786, 42033, 2}, {28606, 33155, 3772}, {32776, 32928, 3416}


X(50069) = X(1)X(30)∩X(536)X(551)

Barycentrics    4*a^4 + 6*a^3*b + 7*a^2*b^2 + 6*a*b^3 + b^4 + 6*a^3*c + 12*a^2*b*c + 6*a*b^2*c + 7*a^2*c^2 + 6*a*b*c^2 - 2*b^2*c^2 + 6*a*c^3 + c^4 : :
X(50069) = X[16394] - 3 X[38314]

X(50069) lies on these lines: {1, 30}, {2, 3695}, {72, 48861}, {376, 3672}, {536, 551}, {547, 17720}, {549, 3666}, {553, 37594}, {2901, 48859}, {3584, 17602}, {3723, 26728}, {3830, 5716}, {4021, 24929}, {4364, 49683}, {5719, 20182}, {5736, 15956}, {6175, 33155}, {8703, 37539}, {10072, 17599}, {15670, 28606}, {16394, 38314}, {16519, 48848}, {17395, 30115}, {17698, 42033}, {17726, 38034}, {19785, 44217}, {30142, 49732}


X(50070) = X(1)X(30)∩X(2)X(1104)

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

X(50070) lies on these lines: {1, 30}, {2, 1104}, {37, 31156}, {72, 48870}, {376, 3666}, {381, 17720}, {519, 5710}, {536, 3241}, {551, 4138}, {553, 37549}, {2298, 17281}, {2352, 14636}, {3017, 3419}, {3175, 48817}, {3488, 37595}, {3576, 17726}, {3584, 5725}, {3654, 5264}, {3672, 15683}, {3679, 5269}, {3772, 6175}, {3945, 15956}, {4195, 42033}, {4217, 35652}, {4304, 20182}, {4339, 10385}, {4870, 26098}, {4995, 37552}, {5252, 17716}, {5266, 10056}, {5807, 17359}, {10072, 17721}, {11194, 16403}, {11346, 41313}, {15670, 37817}, {15677, 28606}, {17016, 49719}, {17301, 17579}, {20009, 42032}, {24789, 44217}, {28194, 37614}, {41312, 49735}

X(50070) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 48827, 3058}, {1, 48828, 37631}


X(50071) = X(2)X(37)∩X(30)X(944)

Barycentrics    a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 3*a^2*c + 2*a*b*c - 3*b^2*c + 3*a*c^2 - 3*b*c^2 + c^3 : :
X(50071) = 2 X[16394] - 3 X[38314]

X(50071) lies on these lines: {2, 37}, {30, 944}, {145, 32859}, {1266, 5287}, {3187, 4419}, {3475, 27804}, {3782, 17318}, {3875, 5739}, {4360, 5905}, {4398, 34064}, {4854, 49453}, {5698, 17150}, {7222, 8025}, {16394, 38314}, {16834, 17781}, {17019, 42697}, {17184, 17314}, {17316, 33146}, {17389, 48838}, {19723, 49742}, {19993, 49463}, {24248, 32928}, {24441, 49724}, {30614, 49455}, {32087, 41809}, {33088, 33154}, {33163, 49445}, {33171, 49452}, {42028, 49722}

X(50071) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17147, 42049}, {2, 42049, 17740}, {192, 19785, 17776}, {3175, 17301, 2}, {4664, 19796, 2}, {17320, 42029, 2}


X(50072) = X(1)X(536)∩X(30)X(944)

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

X(50072) lies on these lines: {1, 536}, {2, 3695}, {30, 944}, {72, 16834}, {192, 13735}, {405, 4664}, {519, 10371}, {1010, 4740}, {3295, 16403}, {4688, 16458}, {4980, 19277}, {10441, 24473}, {11354, 42044}, {16393, 17147}, {16401, 37539}, {16483, 49472}, {17378, 33865}, {19290, 42051}, {19796, 44217}, {24441, 49723}

X(50072) = reflection of X(16394) in X(1)


X(50073) = X(1)X(536)∩X(30)X(48830)

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

X(50073) lies on these lines: {1, 536}, {2, 31402}, {30, 48830}, {218, 597}, {405, 41312}, {4426, 41311}, {4755, 17742}, {11321, 37756}, {15668, 16785}, {16403, 37580}, {16502, 46922}, {24549, 29574}, {26626, 33151}, {28609, 41239}, {29584, 39731}, {35103, 37614}


leftri

Points in a [[b-c,c-a,a-b],[a(b-c),b(c-a),c(a-b)]] coordinate system: X(50074)-X(50133)

rightri

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

L1 is the line: (b-c) α + (c-a) β (a-b) γ = 0.

L2 is the line a(b-c) α + b(c-a) β c(a-b) γ = 0.

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

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

u : v : w = -(a-b)(a-c)(b-c) + (-2 a + b + c) x + (a b + a c - 2 b c) y : : ,

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

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

{-((2 (a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2)), -((2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2))}, 69
{-((2 (a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2)), -(((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2)))}, 17372
{-((2 (a-b) (a-c) (b-c))/(a+b+c)), 0}, 8
{-((2 (a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2)), ((a-b) (a-c) (b-c))/(a^2+b^2+c^2)}, 17299
{-(((a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2)), -((2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2))}, 17274
{-(((a-b) (a-c) (b-c) (a+b+c))/(a b+a c+b c)), -((2 (a-b) (a-c) (b-c))/(a b+a c+b c))}, 17333
{-(((a-b) (a-c) (b-c))/(a+b+c)), -(((a-b) (a-c) (b-c))/(a^2+b^2+c^2))}, 48829
{-(((a-b) (a-c) (b-c))/(a+b+c)), -(((a-b) (a-c) (b-c))/(a b+a c+b c))}, 984
{-(((a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2)), -(((a-b) (a-c) (b-c))/(a^2+b^2+c^2))}, 599
{-(((a-b) (a-c) (b-c) (a+b+c))/(a b+a c+b c)), -(((a-b) (a-c) (b-c))/(a b+a c+b c))}, 17346
{-(((a-b) (a-c) (b-c))/(a+b+c)), 0}, 3679
{-(((a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2)), 0}, 17294
{-(((a-b) (a-c) (b-c) (a+b+c))/(a b+a c+b c)), 0}, 29617
{-(((a-b) (a-c) (b-c))/(a+b+c)), ((a-b) (a-c) (b-c))/(2 (a b+a c+b c))}, 3696
{-(((a-b) (a-c) (b-c))/(a+b+c)), (2 (a-b) (a-c) (b-c))/(a b+a c+b c)}, 49474
{-(((a-b) (a-c) (b-c) (a+b+c))/(2 (a^2+b^2+c^2))), -((2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2))}, 3663
{-(((a-b) (a-c) (b-c))/(2 (a+b+c))), -(((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2)))}, 48821
{-(((a-b) (a-c) (b-c) (a+b+c))/(2 (a^2+b^2+c^2))), -(((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2)))}, 141
{-(((a-b) (a-c) (b-c) (a+b+c))/(2 (a b+a c+b c))), -(((a-b) (a-c) (b-c))/(2 (a b+a c+b c)))}, 17330
{-(((a-b) (a-c) (b-c))/(2 (a+b+c))), 0}, 10
{-(((a-b) (a-c) (b-c) (a+b+c))/(2 (a^2+b^2+c^2))), 0}, 29594
{-(((a-b) (a-c) (b-c) (a+b+c))/(2 (a^2+b^2+c^2))), ((a-b) (a-c) (b-c))/(a^2+b^2+c^2)}, 2321
{0, -((2 (a-b) (a-c) (b-c))/(a b+a c+b c))}, 192} {0, -(((a-b) (a-c) (b-c))/(a^2+b^2+c^2))}, 17301
{0, -(((a-b) (a-c) (b-c))/(a b+a c+b c))}, 4664
{0, -(((a-b) (a-c) (b-c) (a+b+c))/(a b c))}, 42044
{0, -(((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2)))}, 17382
{0, -(((a-b) (a-c) (b-c))/(2 (a b+a c+b c)))}, 37
{0, -(((a-b) (a-c) (b-c) (a+b+c))/(2 a b c))}, 3175
{0, 0}, 2
{0, ((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2))}, 17359
{0, ((a-b) (a-c) (b-c))/(2 (a b+a c+b c))}, 4688
{0, ((a-b) (a-c) (b-c) (a+b+c))/(2 a b c)}, 42051
{0, ((a-b) (a-c) (b-c))/(a^2+b^2+c^2)}, 17281
{0, ((a-b) (a-c) (b-c))/(a b+a c+b c)}, 75
{0, (2 (a-b) (a-c) (b-c))/(a b+a c+b c)}, 4740
{((a-b) (a-c) (b-c))/(2 (a+b+c)), -(((a-b) (a-c) (b-c))/(a b+a c+b c))}, 3993
{((a-b) (a-c) (b-c))/(2 (a+b+c)), 0}, 551
{((a-b) (a-c) (b-c) (a+b+c))/(2 (a b+a c+b c)), 0}, 29574
{((a-b) (a-c) (b-c))/(2 (a+b+c)), ((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2))}, 48810
{((a-b) (a-c) (b-c))/(2 (a+b+c)), ((a-b) (a-c) (b-c))/(2 (a b+a c+b c))}, 24325
{((a-b) (a-c) (b-c) (a+b+c))/(2 (a^2+b^2+c^2)), ((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2))}, 597
{((a-b) (a-c) (b-c) (a+b+c))/(2 (a b+a c+b c)), ((a-b) (a-c) (b-c))/(2 (a b+a c+b c))}, 17392
{((a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2), -((2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2))}, 3875
{((a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2), -(((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2)))}, 4852
{((a-b) (a-c) (b-c))/(a+b+c), 0}, 1
{((a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2), 0}, 16834
{((a-b) (a-c) (b-c) (a+b+c))/(a b+a c+b c), 0}, 17389
{((a-b) (a-c) (b-c))/(a+b+c), ((a-b) (a-c) (b-c))/(a^2+b^2+c^2)}, 48805
{((a-b) (a-c) (b-c))/(a+b+c), ((a-b) (a-c) (b-c))/(a b+a c+b c)}, 31178
{((a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2), ((a-b) (a-c) (b-c))/(a^2+b^2+c^2)}, 6
{((a-b) (a-c) (b-c) (a+b+c))/(a b+a c+b c), ((a-b) (a-c) (b-c))/(a b+a c+b c)}, 17378
{(2 (a-b) (a-c) (b-c))/(a+b+c), -(((a-b) (a-c) (b-c))/(a b+a c+b c))}, 49470
{(2 (a-b) (a-c) (b-c))/(a+b+c), 0}, 3241
{(2 (a-b) (a-c) (b-c))/(a+b+c), ((a-b) (a-c) (b-c))/(2 (a b+a c+b c))}, 49478
{(2 (a-b) (a-c) (b-c))/(a+b+c), (2 (a-b) (a-c) (b-c))/(a b+a c+b c)}, 24349
{(2 (a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2), (2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2)}, 1992
{(-2*(a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c), (-2*(a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50074
{(-2*(a - b)*(a - c)*(b - c))/(a + b + c), -(((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c))}, 50075
{(-2*(a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2), -(((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2))}, 50076
{(-2*(a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c), -(((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c))}, 50077
{(-2*(a - b)*(a - c)*(b - c))/(a + b + c), -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c)}, 50078
{(-2*(a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2), 0}, 50079
{-(((a - b)*(a - c)*(b - c))/(a + b + c)), (-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50080
{-(((a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2)), -1/2*((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50081
{-(((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c)), -1/2*((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50082
{-(((a - b)*(a - c)*(b - c))/(a + b + c)), ((a - b)*(a - c)*(b - c)*(a + b + c))/(2*a*b*c)}, 50083
{-(((a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2)), ((a - b)*(a - c)*(b - c))/(2*(a^2 + b^2 + c^2))}, 50084
{-(((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c)), ((a - b)*(a - c)*(b - c))/(2*(a*b + a*c + b*c))}, 50085
{-(((a - b)*(a - c)*(b - c))/(a + b + c)), ((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50086
{-(((a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2)), ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50087
{-(((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c)), ((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50088
{-(((a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2)), (2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50089
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c), (-2*(a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50090
{-1/2*((a - b)*(a - c)*(b - c))/(a + b + c), -(((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2))}, 50091
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2), -(((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2))}, 50092
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c), -(((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c))}, 50093
{-1/2*((a - b)*(a - c)*(b - c))/(a + b + c), -1/2*((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50094
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c), 0}, 50095
{-1/2*((a - b)*(a - c)*(b - c))/(a + b + c), ((a - b)*(a - c)*(b - c))/(2*(a*b + a*c + b*c))}, 50096
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2), ((a - b)*(a - c)*(b - c))/(2*(a^2 + b^2 + c^2))}, 50097
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c), ((a - b)*(a - c)*(b - c))/(2*(a*b + a*c + b*c))}, 50098
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c), ((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50099
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2), (2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50100
{0, (-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50101
{0, -(((a - b)*(a - c)*(b - c)*(a + b + c))/(a^3 + b^3 + c^3))}, 50102
{0, -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a^3 + b^3 + c^3)}, 50103
{0, ((a - b)*(a - c)*(b - c)*(a + b + c))/(2*(a^3 + b^3 + c^3))}, 50104
{0, ((a - b)*(a - c)*(b - c)*(a + b + c))/(a^3 + b^3 + c^3)}, 50105
{0, ((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c)}, 50106
{0, (2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50107
{((a - b)*(a - c)*(b - c)*(a + b + c))/(2*(a^2 + b^2 + c^2)), (-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50108
{((a - b)*(a - c)*(b - c)*(a + b + c))/(2*(a^2 + b^2 + c^2)), -(((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2))}, 50109
{((a - b)*(a - c)*(b - c)*(a + b + c))/(2*(a*b + a*c + b*c)), -(((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c))}, 50110
{((a - b)*(a - c)*(b - c))/(2*(a + b + c)), -1/2*((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50111
{((a - b)*(a - c)*(b - c)*(a + b + c))/(2*(a^2 + b^2 + c^2)), -1/2*((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50112
{((a - b)*(a - c)*(b - c)*(a + b + c))/(2*(a*b + a*c + b*c)), -1/2*((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50113
{((a - b)*(a - c)*(b - c)*(a + b + c))/(2*(a^2 + b^2 + c^2)), 0}, 50114
{((a - b)*(a - c)*(b - c)*(a + b + c))/(2*(a^2 + b^2 + c^2)), ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50115
{((a - b)*(a - c)*(b - c)*(a + b + c))/(2*(a*b + a*c + b*c)), ((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50116
{((a - b)*(a - c)*(b - c))/(2*(a + b + c)), (2*(a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50117
{((a - b)*(a - c)*(b - c)*(a + b + c))/(2*(a^2 + b^2 + c^2)), (2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50118
{((a - b)*(a - c)*(b - c)*(a + b + c))/(2*(a*b + a*c + b*c)), (2*(a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50119
{((a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2), -(((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2))}, 50120
{((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c), -(((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c))}, 50121
{((a - b)*(a - c)*(b - c))/(a + b + c), -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c)}, 50122
{((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c), -1/2*((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50123
{((a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2), ((a - b)*(a - c)*(b - c))/(2*(a^2 + b^2 + c^2))}, 50124
{((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c), ((a - b)*(a - c)*(b - c))/(2*(a*b + a*c + b*c))}, 50125
{((a - b)*(a - c)*(b - c))/(a + b + c), (2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50126
{((a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2), (2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50127
{((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c), (2*(a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50128
{(2*(a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2), 0}, 50129
{(2*(a - b)*(a - c)*(b - c))/(a + b + c), ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50130
{(2*(a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2), ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50131
{(2*(a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c), ((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50132
{(2*(a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c), (2*(a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50133


X(50074) = X(2)X(6)∩X(8)X(752)

Barycentrics    4*a^2 - a*b - 2*b^2 - a*c - b*c - 2*c^2 : :
X(50074) = 3 X[2] - 4 X[17330], 5 X[2] - 4 X[17392], 7 X[2] - 8 X[49731], 9 X[2] - 8 X[49738], 2 X[17330] - 3 X[17346], 5 X[17330] - 3 X[17392], 7 X[17330] - 6 X[49731], 3 X[17330] - 2 X[49738], 3 X[17346] - X[17378], 5 X[17346] - 2 X[17392], 7 X[17346] - 4 X[49731], 9 X[17346] - 4 X[49738], 5 X[17378] - 6 X[17392], 7 X[17378] - 12 X[49731], 3 X[17378] - 4 X[49738], 7 X[17392] - 10 X[49731], 9 X[17392] - 10 X[49738], 9 X[49731] - 7 X[49738], X[192] - 4 X[4416], X[192] + 2 X[17363], X[192] - 3 X[17488], 2 X[4416] + X[17363], 4 X[4416] - 3 X[17488], 2 X[17333] - 3 X[17488], 2 X[17363] + 3 X[17488], X[1278] + 2 X[17347], X[1278] - 4 X[17362], X[17347] + 2 X[17362], 5 X[3617] - 4 X[49725], 8 X[3686] - 5 X[4699], 4 X[3686] - X[17364], 5 X[4699] - 2 X[17364], 4 X[3739] - 3 X[39704], 2 X[3879] - 5 X[17331], 4 X[3879] - 7 X[27268], 10 X[17331] - 7 X[27268], 8 X[4399] - 5 X[4821], 5 X[4687] - 6 X[16590], 8 X[4698] - 9 X[41848], 5 X[4704] - 8 X[17332], 5 X[4704] - 2 X[17377], 4 X[17332] - X[17377], 4 X[4732] - 3 X[24452], 7 X[4772] - 4 X[17365], X[4788] - 4 X[17334]

X(50074) lies on these lines: {2, 6}, {8, 752}, {9, 17310}, {44, 17230}, {75, 4715}, {144, 528}, {145, 49746}, {190, 20055}, {192, 519}, {239, 4741}, {319, 17281}, {320, 16816}, {527, 4740}, {540, 48850}, {545, 1278}, {551, 17248}, {674, 4661}, {754, 48869}, {894, 3679}, {903, 4361}, {1100, 17328}, {1449, 17252}, {1743, 17287}, {3241, 17257}, {3617, 49725}, {3621, 20073}, {3625, 4480}, {3662, 41140}, {3681, 9025}, {3686, 4699}, {3707, 17244}, {3729, 4677}, {3739, 39704}, {3758, 4690}, {3759, 17236}, {3879, 17331}, {3973, 17268}, {4001, 17490}, {4034, 17116}, {4360, 24441}, {4370, 17233}, {4389, 4969}, {4393, 4643}, {4399, 4821}, {4419, 20016}, {4430, 9038}, {4431, 34641}, {4473, 29616}, {4664, 4725}, {4667, 29576}, {4669, 48628}, {4685, 41834}, {4687, 16590}, {4698, 41848}, {4700, 17367}, {4704, 17332}, {4732, 24452}, {4748, 29586}, {4772, 17365}, {4788, 17334}, {4795, 17275}, {4852, 17329}, {4856, 17396}, {4908, 17336}, {4971, 49748}, {5839, 6646}, {7277, 10022}, {7754, 17677}, {7758, 22267}, {11165, 22351}, {15492, 17240}, {16666, 17250}, {16667, 17326}, {16668, 17400}, {16669, 17228}, {16670, 17292}, {16671, 17371}, {16676, 29619}, {16814, 17386}, {16834, 17254}, {16885, 17295}, {17120, 17270}, {17121, 17272}, {17256, 29570}, {17280, 32099}, {17299, 25269}, {17335, 17374}, {17338, 41141}, {17348, 17361}, {17387, 29599}, {18144, 39996}, {20018, 37038}, {24514, 31136}, {28333, 49722}, {28337, 49742}, {28503, 31302}, {28538, 49496}, {31134, 32864}, {31300, 42696}, {37150, 49718}, {48839, 48858}

X(50074) = anticomplement of X(17378)
X(50074) = midpoint of X(17333) and X(17363)
X(50074) = reflection of X(i) in X(j) for these {i,j}: {2, 17346}, {145, 49746}, {192, 17333}, {4740, 29617}, {17333, 4416}, {17378, 17330}, {48858, 48839}
X(50074) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17271, 17238}, {2, 17343, 17271}, {2, 17375, 17313}, {2, 37654, 17349}, {6, 17271, 2}, {6, 17343, 17238}, {44, 17360, 17230}, {69, 17349, 17232}, {69, 37654, 2}, {192, 17488, 17333}, {193, 1654, 17379}, {391, 20080, 17300}, {966, 11008, 20090}, {1743, 17287, 17358}, {3180, 3181, 37683}, {3629, 5224, 37677}, {3686, 17364, 4699}, {3758, 4690, 29593}, {3759, 17344, 17236}, {3879, 17331, 27268}, {4416, 17333, 17488}, {4416, 17363, 192}, {15534, 17251, 46922}, {17121, 17272, 17383}, {17251, 46922, 2}, {17277, 17313, 2}, {17277, 40341, 17375}, {17330, 17378, 2}, {17332, 17377, 4704}, {17335, 17374, 29572}, {17346, 17378, 17330}, {17347, 17362, 1278}, {31303, 37656, 37684}


X(50075) = X(2)X(210)∩X(8)X(536)

Barycentrics    2*a^2*b - 4*a*b^2 + 2*a^2*c - 3*a*b*c - b^2*c - 4*a*c^2 - b*c^2 : :
X(50075) = X[1] + 2 X[49449], 2 X[8] + X[49447], 5 X[8] - 2 X[49468], X[8] + 2 X[49515], 7 X[8] + 2 X[49522], 5 X[49447] + 4 X[49468], X[49447] - 4 X[49515], 7 X[49447] - 4 X[49522], X[49468] + 5 X[49515], 7 X[49468] + 5 X[49522], 7 X[49515] - X[49522], 4 X[10] - X[49499], 2 X[10] + X[49503], X[49499] + 2 X[49503], 5 X[75] - 8 X[4732], X[75] + 2 X[49448], X[75] - 4 X[49457], 2 X[75] + X[49501], 5 X[75] - 2 X[49532], 5 X[3679] - 4 X[4732], 4 X[3679] + X[49501], 5 X[3679] - X[49532], 4 X[4732] + 5 X[49448], 2 X[4732] - 5 X[49457], 16 X[4732] + 5 X[49501], 4 X[4732] - X[49532], X[49448] + 2 X[49457], 4 X[49448] - X[49501], 5 X[49448] + X[49532], 8 X[49457] + X[49501], 10 X[49457] - X[49532], 5 X[49501] + 4 X[49532], 5 X[984] - 2 X[3993], 2 X[984] + X[49450], 4 X[984] - X[49470], X[984] + 2 X[49510], 7 X[984] - X[49678], 5 X[984] + X[49689], 4 X[3993] - 5 X[4664], 4 X[3993] + 5 X[49450], 8 X[3993] - 5 X[49470], X[3993] + 5 X[49510], 14 X[3993] - 5 X[49678], 2 X[3993] + X[49689], X[4664] + 4 X[49510], 7 X[4664] - 2 X[49678], 5 X[4664] + 2 X[49689], 2 X[49450] + X[49470], X[49450] - 4 X[49510], 7 X[49450] + 2 X[49678], 5 X[49450] - 2 X[49689], X[49470] + 8 X[49510], 7 X[49470] - 4 X[49678], 5 X[49470] + 4 X[49689], 14 X[49510] + X[49678], 10 X[49510] - X[49689], 5 X[49678] + 7 X[49689], 4 X[551] - 5 X[4687], 5 X[4687] - 2 X[49490], 5 X[4687] + 4 X[49504], X[49490] + 2 X[49504], X[1278] + 2 X[49513], X[49502] + 2 X[49688], 5 X[1698] - 2 X[49491], 5 X[3617] - 2 X[49483], X[3621] + 2 X[49462], 2 X[3625] + X[49452], 4 X[3626] - X[49493], 2 X[3626] + X[49508], X[49493] + 2 X[49508], X[3632] + 2 X[49456], X[3644] + 4 X[34641], X[3644] + 2 X[49459], X[3644] - 4 X[49520], X[49459] + 2 X[49520], 2 X[3696] + X[31302], 8 X[3828] - 7 X[4751], 7 X[4751] - 4 X[49479], 4 X[3842] - 3 X[25055], 4 X[3842] - X[49498], 3 X[25055] - X[49498], 5 X[4704] - X[20049], 5 X[4704] - 2 X[49475], 4 X[4709] - X[4764], 2 X[4709] + X[49517], X[4764] + 2 X[49517], 4 X[4755] - 3 X[38314], 3 X[38314] - 2 X[49478], 3 X[19875] - 2 X[24325], 3 X[38087] - 2 X[49481], 5 X[40328] - 2 X[49535]

X(50077) lies on these lines: {1, 4753}, {2, 210}, {8, 536}, {10, 17227}, {37, 3241}, {44, 36534}, {75, 537}, {192, 31145}, {312, 4937}, {519, 751}, {527, 49720}, {528, 17333}, {551, 4687}, {726, 4669}, {740, 4677}, {1278, 49513}, {1654, 49502}, {1698, 49491}, {1992, 48856}, {3210, 4113}, {3617, 49483}, {3621, 49462}, {3625, 49452}, {3626, 49493}, {3632, 49456}, {3644, 34641}, {3661, 31349}, {3696, 4740}, {3707, 49771}, {3711, 24627}, {3717, 29594}, {3751, 46922}, {3758, 36480}, {3828, 4751}, {3842, 25055}, {3932, 29577}, {4085, 17249}, {4096, 20942}, {4384, 24841}, {4389, 49772}, {4407, 17250}, {4429, 24393}, {4660, 17329}, {4676, 5220}, {4684, 29600}, {4688, 24349}, {4704, 20049}, {4709, 4764}, {4755, 38314}, {4795, 25384}, {4966, 29582}, {5223, 5263}, {5224, 49529}, {5252, 17950}, {7174, 16834}, {9041, 17330}, {11194, 34247}, {12329, 19326}, {13735, 41229}, {15624, 17549}, {16496, 17277}, {16833, 32922}, {17228, 33165}, {17234, 49505}, {17254, 48829}, {17256, 36479}, {17260, 42871}, {17261, 49460}, {17319, 49680}, {17328, 33076}, {17336, 32941}, {17349, 49465}, {17360, 32847}, {17393, 49497}, {18743, 31137}, {19325, 22769}, {19875, 24325}, {21342, 26038}, {25269, 49485}, {28204, 30273}, {28503, 29617}, {28538, 49496}, {28554, 49474}, {28580, 49748}, {30615, 37653}, {31144, 48851}, {31161, 31330}, {32784, 49697}, {34747, 49471}, {35026, 35167}, {36531, 41847}, {38087, 49481}, {40328, 49535}, {42034, 42054}, {48853, 49536}

X(50075) = midpoint of X(i) and X(j) for these {i,j}: {192, 31145}, {551, 49504}, {3679, 49448}, {4664, 49450}, {4740, 31302}, {31178, 49503}, {34641, 49520}
X(50075) = reflection of X(i) in X(j) for these {i,j}: {75, 3679}, {3241, 37}, {3679, 49457}, {4664, 984}, {4740, 3696}, {4795, 25384}, {20049, 49475}, {24349, 4688}, {31178, 10}, {34747, 49471}, {49459, 34641}, {49470, 4664}, {49478, 4755}, {49479, 3828}, {49490, 551}, {49499, 31178}
X(50075) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 49515, 49447}, {10, 49503, 49499}, {75, 49448, 49501}, {984, 49450, 49470}, {984, 49510, 49450}, {984, 49689, 3993}, {3626, 49508, 49493}, {3751, 48854, 46922}, {4407, 29659, 17250}, {4407, 49701, 29659}, {4709, 49517, 4764}, {4732, 49532, 75}, {4755, 49478, 38314}, {17256, 49714, 36479}, {31137, 42056, 18743}, {36480, 49712, 3758}, {49448, 49457, 75}, {49459, 49520, 3644}


X(50076) = X(2)X(319)∩X(69)X(536)

Barycentrics    3*a^2 + a*b - 3*b^2 + a*c - 2*b*c - 3*c^2 : :
X(50076) = 4 X[69] - X[17276], 2 X[69] + X[17299], 5 X[69] - 2 X[17345], X[69] + 2 X[17372], X[17276] + 2 X[17299], 5 X[17276] - 8 X[17345], X[17276] + 8 X[17372], 5 X[17299] + 4 X[17345], X[17299] - 4 X[17372], X[17345] + 5 X[17372], X[193] - 4 X[17229], 5 X[17281] - 4 X[49726], 5 X[17294] - 2 X[49726], 2 X[2321] + X[40341], 5 X[3620] - 2 X[4852], 2 X[3629] - 5 X[17286], 2 X[3630] + X[3729], 4 X[3631] - X[3875], 4 X[4856] - 7 X[47355], X[6144] - 4 X[17355], 2 X[17351] + X[20080], 2 X[17382] - 3 X[21356]

X(50076) lies on these lines: {2, 319}, {6, 29594}, {8, 4675}, {37, 32099}, {44, 29616}, {45, 49765}, {69, 536}, {141, 16834}, {145, 17237}, {193, 17229}, {320, 4740}, {519, 599}, {524, 17281}, {527, 15533}, {1086, 3632}, {1449, 48635}, {1654, 17386}, {1992, 17359}, {2321, 40341}, {3241, 41311}, {3244, 17325}, {3620, 4852}, {3625, 17119}, {3629, 17286}, {3630, 3729}, {3631, 3875}, {3633, 17395}, {3661, 46922}, {3679, 17392}, {3686, 17311}, {3723, 4916}, {3770, 42034}, {3879, 4445}, {4007, 17365}, {4034, 17245}, {4060, 17118}, {4364, 29605}, {4399, 17298}, {4416, 17309}, {4419, 4727}, {4464, 17323}, {4478, 10436}, {4643, 4664}, {4657, 17287}, {4677, 6173}, {4686, 21296}, {4690, 4755}, {4708, 29585}, {4715, 11160}, {4798, 29593}, {4856, 47355}, {4889, 17321}, {4908, 6172}, {4910, 17302}, {4969, 17284}, {4971, 17274}, {5224, 29580}, {5564, 17375}, {5847, 48805}, {6144, 17355}, {8556, 49554}, {10453, 41144}, {16284, 16732}, {16666, 29611}, {16833, 17278}, {17133, 49747}, {17227, 20016}, {17250, 29588}, {17251, 29574}, {17270, 17390}, {17271, 17389}, {17272, 17388}, {17277, 29582}, {17279, 17295}, {17290, 49770}, {17297, 29617}, {17300, 28634}, {17310, 17346}, {17314, 17344}, {17315, 17343}, {17318, 49761}, {17330, 29573}, {17351, 20080}, {17376, 42696}, {17378, 29615}, {17382, 21356}, {17391, 32025}, {19875, 42334}, {20090, 48630}, {24599, 31243}, {24691, 41142}, {31136, 32852}, {31137, 32861}, {31138, 31145}, {31139, 34641}, {37654, 41310}, {48849, 49478}

X(50076) = midpoint of X(40341) and X(49721)
X(50076) = reflection of X(i) in X(j) for these {i,j}: {6, 29594}, {1992, 17359}, {3875, 49741}, {16834, 141}, {17274, 22165}, {17281, 17294}, {17301, 599}, {49721, 2321}, {49741, 3631}
X(50076) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 17374, 4675}, {69, 17299, 17276}, {69, 17372, 17299}, {319, 4851, 17275}, {319, 17373, 4851}, {3879, 4445, 17303}, {4916, 5232, 3723}, {6542, 17360, 4643}, {17271, 17389, 41312}, {17287, 17377, 4657}, {17295, 17363, 17279}, {17296, 17362, 17278}, {17310, 17346, 41313}


X(50077) = X(2)X(319)∩X(75)X(524)

Barycentrics    4*a^2 - 2*b^2 - 3*b*c - 2*c^2 : :
X(50077) = 5 X[75] - 8 X[4399], 11 X[75] - 8 X[7228], X[75] - 4 X[17362], X[75] + 2 X[17363], 5 X[75] - 2 X[17364], 7 X[75] - 4 X[17365], 5 X[75] - 4 X[49727], 11 X[4399] - 5 X[7228], 2 X[4399] - 5 X[17362], 4 X[4399] + 5 X[17363], 4 X[4399] - X[17364], 14 X[4399] - 5 X[17365], 4 X[4399] - 5 X[29617], 2 X[7228] - 11 X[17362], 4 X[7228] + 11 X[17363], 20 X[7228] - 11 X[17364], 14 X[7228] - 11 X[17365], 4 X[7228] - 11 X[29617], 10 X[7228] - 11 X[49727], 2 X[17362] + X[17363], 10 X[17362] - X[17364], 7 X[17362] - X[17365], 5 X[17362] - X[49727], 5 X[17363] + X[17364], 7 X[17363] + 2 X[17365], 5 X[17363] + 2 X[49727], 7 X[17364] - 10 X[17365], X[17364] - 5 X[29617], 2 X[17365] - 7 X[29617], 5 X[17365] - 7 X[49727], 5 X[29617] - 2 X[49727], X[3644] - 4 X[4416], 8 X[3686] - 5 X[4687], 4 X[3686] - X[17377], 5 X[4687] - 2 X[17377], 5 X[4687] - 4 X[29574], 4 X[3879] - 7 X[4751], 4 X[4688] - 3 X[39704], 8 X[4755] - 9 X[41848], X[4764] + 2 X[17347], 4 X[4889] - 7 X[27268], 5 X[17331] - 2 X[17388], 5 X[17331] - 4 X[49737], 4 X[17390] - 5 X[29622]

X(50077) lies on these lines: {1, 31144}, {2, 319}, {6, 29615}, {8, 1992}, {44, 20055}, {69, 4402}, {75, 524}, {86, 4034}, {145, 17256}, {190, 3632}, {192, 28329}, {193, 5564}, {239, 599}, {320, 11160}, {391, 17315}, {519, 751}, {594, 8584}, {597, 3661}, {749, 4685}, {894, 15534}, {1278, 4912}, {1449, 32025}, {1654, 17393}, {2345, 5032}, {3187, 31143}, {3416, 50030}, {3589, 48640}, {3629, 48628}, {3630, 48627}, {3631, 48637}, {3644, 4416}, {3662, 22165}, {3679, 46922}, {3686, 4687}, {3705, 22329}, {3707, 49761}, {3875, 17329}, {3879, 4751}, {4033, 27424}, {4357, 49543}, {4360, 17328}, {4361, 15533}, {4371, 7321}, {4384, 17387}, {4385, 7812}, {4389, 49770}, {4393, 4690}, {4445, 17121}, {4478, 17368}, {4643, 20016}, {4688, 39704}, {4700, 17354}, {4715, 4740}, {4755, 41848}, {4764, 17132}, {4852, 17249}, {4856, 17381}, {4889, 27268}, {4971, 17333}, {5014, 37857}, {5847, 49720}, {5860, 32802}, {5861, 32801}, {6144, 17116}, {6542, 17335}, {7081, 11163}, {7227, 41149}, {11008, 32087}, {16666, 29593}, {16706, 21356}, {16816, 17374}, {16833, 17297}, {16834, 17271}, {17117, 40341}, {17240, 17349}, {17251, 29584}, {17259, 29620}, {17264, 37654}, {17270, 17400}, {17277, 17386}, {17287, 17370}, {17294, 17342}, {17295, 17341}, {17299, 17336}, {17301, 40891}, {17330, 17389}, {17331, 17388}, {17366, 48638}, {17367, 20582}, {17369, 20583}, {17390, 29622}, {20090, 28634}, {28558, 49474}, {28562, 49459}, {29623, 31285}, {31145, 49698}, {35578, 42696}, {37785, 40713}, {37786, 40714}, {42334, 48809}, {48310, 48635}

X(50077) = midpoint of X(17363) and X(29617)
X(50077) = reflection of X(i) in X(j) for these {i,j}: {75, 29617}, {3644, 49748}, {4664, 17346}, {17364, 49727}, {17377, 29574}, {17388, 49737}, {17389, 17330}, {29574, 3686}, {29617, 17362}, {49727, 4399}, {49748, 4416}
X(50077) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {239, 17360, 17227}, {319, 3759, 17228}, {319, 5839, 3759}, {3686, 17377, 4687}, {4371, 20080, 7321}, {4393, 4690, 17250}, {4399, 17364, 75}, {4445, 17121, 17371}, {4852, 17343, 17249}, {16834, 17271, 17399}, {17348, 17373, 17241}, {17349, 17372, 17240}, {17362, 17363, 75}


X(50078) = X(8)X(536)∩X(72)X(519)

Barycentrics    a^3*b + 2*a^2*b^2 + a*b^3 + a^3*c - 4*a^2*b*c + 5*a*b^2*c - 2*b^3*c + 2*a^2*c^2 + 5*a*b*c^2 - 4*b^2*c^2 + a*c^3 - 2*b*c^3 : :
X(50078) = 4 X[596] - 7 X[4002], 3 X[4731] - 2 X[24165], X[10914] + 2 X[24068], 5 X[25917] - 6 X[42056]

X(50078) lies on these lines: {1, 4009}, {2, 341}, {8, 536}, {10, 4003}, {65, 537}, {72, 519}, {529, 7667}, {551, 25079}, {596, 4002}, {986, 3679}, {3241, 8834}, {3666, 4737}, {3714, 31136}, {3744, 13735}, {3752, 4723}, {3880, 32925}, {3895, 17262}, {3902, 22034}, {3920, 50064}, {3971, 5919}, {4421, 22345}, {4487, 17147}, {4664, 37548}, {4688, 4968}, {4692, 31993}, {4711, 32860}, {4731, 24165}, {4884, 6735}, {4929, 5727}, {5724, 49527}, {9369, 37539}, {9371, 34619}, {10459, 31161}, {10914, 24068}, {11236, 42753}, {17752, 31349}, {23764, 48077}, {25917, 42056}, {28580, 34720}, {30145, 48826}, {31145, 42044}, {33908, 49476}, {34687, 34691}, {37829, 49609}, {42083, 49462}, {48806, 50048}

X(50078) = midpoint of X(31145) and X(42044)
X(50078) = reflection of X(i) in X(j) for these {i,j}: {3241, 35652}, {5919, 3971}, {31165, 42054}, {32860, 4711}, {42051, 3679}
X(50078) = {X(3057),X(49981)}-harmonic conjugate of X(72)


X(50079) = X(1)X(2)∩X(69)X(536)

Barycentrics    3*a^2 + 2*a*b - 3*b^2 + 2*a*c - 4*b*c - 3*c^2 : :
X(50079) = 3 X[2] - 4 X[29594], 7 X[2] - 4 X[49543], 5 X[3616] - 8 X[49560], 5 X[3617] - 2 X[49495], X[3621] + 2 X[49451], 11 X[5550] - 8 X[49477], 7 X[9780] - 4 X[49488], X[16834] - 3 X[17294], 7 X[16834] - 6 X[49543], 3 X[17294] - 2 X[29594], 7 X[17294] - 2 X[49543], X[20050] - 4 X[49458], 7 X[29594] - 3 X[49543], 5 X[69] - 2 X[17276], X[69] + 2 X[17299], 7 X[69] - 4 X[17345], X[69] - 4 X[17372], X[17276] + 5 X[17299], 7 X[17276] - 10 X[17345], X[17276] - 10 X[17372], 7 X[17299] + 2 X[17345], X[17299] + 2 X[17372], X[17345] - 7 X[17372], X[193] - 4 X[2321], 3 X[599] - 2 X[49741], 5 X[3618] - 8 X[17229], 7 X[3619] - 4 X[4852], 5 X[3620] - 2 X[3875], 2 X[3729] + X[20080], 4 X[4133] - X[24280], 4 X[4527] - X[24695], X[11008] - 4 X[17351], 2 X[17301] - 3 X[21356]

X(50079) lies on these lines: {1, 2}, {6, 28337}, {7, 4740}, {69, 536}, {86, 4916}, {192, 32099}, {193, 2321}, {319, 4664}, {329, 39351}, {344, 17309}, {346, 17363}, {391, 17242}, {524, 49721}, {527, 11160}, {537, 41842}, {545, 15533}, {599, 4971}, {966, 17315}, {1043, 16046}, {1268, 28641}, {1278, 21296}, {1909, 42029}, {1992, 4725}, {2345, 17377}, {2784, 9778}, {2809, 4661}, {3208, 3929}, {3618, 17229}, {3619, 4852}, {3620, 3875}, {3672, 17287}, {3729, 20080}, {3879, 4007}, {3913, 21511}, {3928, 4050}, {3945, 48628}, {3948, 25278}, {3969, 26065}, {3975, 20942}, {4000, 17295}, {4052, 38259}, {4060, 10436}, {4072, 25728}, {4133, 24280}, {4371, 17234}, {4399, 17311}, {4402, 17232}, {4419, 17360}, {4421, 4433}, {4445, 17321}, {4452, 17288}, {4460, 17302}, {4461, 17364}, {4464, 17306}, {4478, 16777}, {4527, 24695}, {4643, 4727}, {4648, 5564}, {4688, 4851}, {4755, 17275}, {4869, 17117}, {4889, 17303}, {4910, 17384}, {4969, 17269}, {4980, 34284}, {5232, 17319}, {5839, 17233}, {5881, 7406}, {7229, 20090}, {8666, 21537}, {8715, 21508}, {11008, 17351}, {12513, 21495}, {15534, 49726}, {16884, 48636}, {17133, 17274}, {17240, 37650}, {17264, 37654}, {17268, 37681}, {17300, 32087}, {17301, 21356}, {17374, 42697}, {17375, 31995}, {17755, 49689}, {19738, 26035}, {20533, 31349}, {21281, 42051}, {22165, 28309}, {24524, 42034}, {25298, 28809}, {26104, 48639}, {27480, 28581}, {28333, 40341}, {28605, 33936}, {32850, 39721}, {48821, 49486}

X(50079) = reflection of X(i) in X(j) for these {i,j}: {2, 17294}, {1992, 17281}, {15534, 49726}, {16834, 29594}, {49486, 48821}, {49747, 22165}
X(50079) = anticomplement of X(16834)
X(50079) = X(6016)-anticomplementary conjugate of X(513)
X(50079) = crosssum of X(1015) and X(8657)
X(50079) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3679, 48853}, {2, 145, 29584}, {2, 29577, 29579}, {2, 29583, 29600}, {2, 29584, 26626}, {2, 29585, 29597}, {2, 29616, 29577}, {2, 31145, 29617}, {8, 3241, 48849}, {8, 6542, 17316}, {10, 29597, 2}, {10, 29605, 29585}, {145, 3661, 26626}, {239, 29577, 2}, {239, 29616, 29579}, {319, 17314, 17257}, {3621, 29616, 239}, {3625, 49765, 4384}, {3661, 29584, 2}, {3679, 29574, 2}, {3912, 16833, 2}, {4384, 29600, 2}, {4384, 49765, 29583}, {4445, 17388, 17321}, {4668, 29602, 24603}, {4678, 29624, 29576}, {5222, 20053, 20016}, {5564, 17386, 4648}, {5839, 17233, 26685}, {6542, 20055, 8}, {16815, 29618, 29621}, {16834, 17294, 29594}, {16834, 29594, 2}, {17230, 20016, 5222}, {17299, 17372, 69}, {17309, 17362, 344}, {17310, 29617, 2}, {17389, 29615, 2}, {20050, 29611, 4393}, {29576, 29619, 29624}, {29588, 29593, 3616}


X(50080) = X(1)X(528)∩X(69)X(519)

Barycentrics    a^3 - 4*a^2*b - a*b^2 - 2*b^3 - 4*a^2*c + 2*b^2*c - a*c^2 + 2*b*c^2 - 2*c^3 : :
X(50080) = 2 X[65] + X[15076], X[69] + 2 X[4780], 4 X[3663] - X[16496], X[3875] + 2 X[4660], X[3751] - 4 X[3755], X[3751] + 2 X[24248], 2 X[3755] + X[24248], 2 X[17281] - 3 X[19875], 3 X[19875] - 4 X[48821], 5 X[1698] - 2 X[5695], 5 X[1698] - 4 X[17359], 7 X[3624] - 4 X[49484], X[3632] + 2 X[49453], X[3633] - 4 X[49463], X[3729] - 4 X[4085], 5 X[3763] - 2 X[49485], 4 X[3821] - X[3886], 8 X[3946] - 5 X[16491], X[4655] + 2 X[4743], 2 X[4655] + X[49495], 4 X[4743] - X[49495], 4 X[17382] - 3 X[25055], 3 X[25055] - 2 X[48805], 4 X[17235] - X[49460], 5 X[17304] - 2 X[32941], 2 X[17345] + X[49680], 3 X[38047] - 2 X[49726] a

X(50080) lies on these lines: {1, 528}, {2, 968}, {6, 28534}, {8, 17254}, {30, 1721}, {42, 31164}, {43, 31142}, {65, 15076}, {69, 519}, {75, 48851}, {165, 33135}, {200, 33154}, {516, 16475}, {518, 49747}, {527, 3751}, {536, 984}, {545, 47359}, {740, 17294}, {752, 16834}, {982, 31146}, {988, 45700}, {1040, 3058}, {1213, 3731}, {1266, 36479}, {1698, 5695}, {1711, 3929}, {2783, 5587}, {2999, 33095}, {3158, 33152}, {3241, 4310}, {3416, 4971}, {3624, 49484}, {3632, 49453}, {3633, 49463}, {3666, 31140}, {3672, 48856}, {3729, 4085}, {3749, 19785}, {3750, 23681}, {3763, 49485}, {3821, 3886}, {3870, 33145}, {3931, 17528}, {3946, 16491}, {4000, 47357}, {4312, 4649}, {4357, 48802}, {4419, 49772}, {4429, 17264}, {4442, 29828}, {4512, 33132}, {4645, 17389}, {4646, 11236}, {4654, 42042}, {4655, 4743}, {4659, 29659}, {4677, 28503}, {4693, 17284}, {4702, 17290}, {4709, 17270}, {4725, 49486}, {4850, 10707}, {4854, 5268}, {4859, 15668}, {4862, 49490}, {5231, 17593}, {5256, 33094}, {5263, 17399}, {5266, 34707}, {5429, 29032}, {5902, 44670}, {6174, 17720}, {7232, 49475}, {9580, 29821}, {10389, 33147}, {10436, 48822}, {10712, 26242}, {13161, 34619}, {16831, 24693}, {17151, 33076}, {17156, 32950}, {17235, 49460}, {17272, 49459}, {17296, 49469}, {17297, 49470}, {17298, 49471}, {17304, 32941}, {17320, 48854}, {17345, 49680}, {17346, 24723}, {17396, 38314}, {17591, 24392}, {17889, 37553}, {28297, 49524}, {28530, 38047}, {28609, 42043}, {29327, 36551}, {29573, 31151}, {29658, 35445}, {31162, 48902}, {33068, 39594}, {33128, 35258}, {34606, 50065}, {34612, 50068}, {37756, 49746}, {41312, 49725}, {44663, 48842}, {47358, 49741}, {48812, 48831}

X(50080) = reflection of X(i) in X(j) for these {i,j}: {1, 17301}, {3679, 48829}, {5695, 17359}, {17281, 48821}, {47358, 49741}, {48805, 17382}, {48812, 48831}
X(50080) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3696, 17251, 3679}, {3755, 24248, 3751}, {3914, 17594, 17064}, {4655, 4743, 49495}, {17281, 48821, 19875}, {17320, 49720, 48854}, {17382, 48805, 25055}


X(50081) = X(2)X(319)∩X(69)X(4715)

Barycentrics    2*a^2 + a*b - 4*b^2 + a*c - 2*b*c - 4*c^2 : :
X(50081) = X[69] + 2 X[17229], 2 X[69] + X[17351], 4 X[17229] - X[17351], 5 X[141] - 2 X[3946], 4 X[141] - X[4852], 2 X[141] + X[17372], 8 X[3946] - 5 X[4852], 4 X[3946] + 5 X[17372], 4 X[3946] - 5 X[17382], X[4852] + 2 X[17372], 3 X[599] - X[17274], 5 X[599] - X[49747], X[17274] + 3 X[17294], 5 X[17274] - 3 X[49747], 5 X[17294] + X[49747], X[2321] + 2 X[3631], 2 X[2321] + X[17345], 4 X[3631] - X[17345], X[49484] - 4 X[49560], 2 X[3416] + X[49467], 5 X[3620] - 2 X[17235], 5 X[3620] + X[17299], 2 X[17235] + X[17299], X[3630] + 2 X[17355], X[16834] - 3 X[21358], 5 X[17286] + X[40341], X[17301] - 3 X[21356]

X(50081) lies on these lines: {1, 25503}, {2, 319}, {8, 3834}, {10, 49738}, {37, 17252}, {44, 17230}, {69, 4715}, {75, 31138}, {141, 519}, {142, 4478}, {524, 17359}, {527, 22165}, {536, 599}, {545, 2321}, {551, 17390}, {594, 17376}, {752, 49484}, {903, 4686}, {1654, 16590}, {2345, 4795}, {3241, 4657}, {3416, 49467}, {3620, 17235}, {3625, 4395}, {3626, 34824}, {3630, 17355}, {3632, 17290}, {3661, 4670}, {3663, 28309}, {3664, 10022}, {3679, 3739}, {3686, 41141}, {3696, 31151}, {3706, 31134}, {3723, 17238}, {3879, 17385}, {3912, 4690}, {3936, 27747}, {4000, 31145}, {4007, 4726}, {4034, 17265}, {4043, 39996}, {4058, 7228}, {4060, 7263}, {4361, 4677}, {4364, 49765}, {4370, 4416}, {4389, 4727}, {4393, 48639}, {4399, 21255}, {4405, 4701}, {4479, 18144}, {4643, 29616}, {4648, 28633}, {4681, 17272}, {4688, 17297}, {4698, 17270}, {4708, 17316}, {4718, 17273}, {4739, 17298}, {4755, 17251}, {4869, 28634}, {4908, 17233}, {4910, 20049}, {4969, 29596}, {5847, 48810}, {6542, 17237}, {6687, 29579}, {15492, 17268}, {15668, 19875}, {16666, 17292}, {16668, 17371}, {16669, 17285}, {16671, 17358}, {16706, 40891}, {16814, 17240}, {16816, 31243}, {16834, 21358}, {17133, 49741}, {17227, 20055}, {17279, 32099}, {17286, 40341}, {17301, 21356}, {17312, 31238}, {17325, 29605}, {17326, 46845}, {17327, 25055}, {17336, 17488}, {17346, 29577}, {17356, 17362}, {17357, 17363}, {17375, 39704}, {17377, 17384}, {17379, 48640}, {17387, 29593}, {17389, 41311}, {17395, 49761}, {20050, 26104}, {20530, 31137}, {20582, 28337}, {21264, 31136}, {27776, 31143}, {28297, 41152}, {28503, 49511}, {28581, 48829}, {29575, 31144}, {29600, 49731}, {29619, 39260}

X(50081) = midpoint of X(i) and X(j) for these {i,j}: {69, 17281}, {599, 17294}, {17372, 17382}
X(50081) = reflection of X(i) in X(j) for these {i,j}: {4852, 17382}, {17281, 17229}, {17351, 17281}, {17359, 29594}, {17382, 141}
X(50081) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 17229, 17351}, {141, 17372, 4852}, {319, 17231, 17348}, {2321, 3631, 17345}, {3620, 17299, 17235}, {3661, 17374, 4670}, {3679, 17296, 17313}, {3679, 17313, 3739}, {3879, 48635, 17385}, {4007, 7232, 4726}, {4445, 17296, 3739}, {4445, 17313, 3679}, {4701, 17067, 4405}, {4851, 17239, 28639}, {4908, 17344, 17333}, {17228, 17373, 1100}, {17230, 17360, 44}, {17233, 17333, 4908}, {17238, 17386, 3723}, {17240, 17343, 16814}, {17251, 29573, 4755}, {17270, 17311, 4698}, {17271, 17295, 17310}, {17271, 17310, 37}, {17272, 17309, 4681}, {17287, 17295, 37}, {17287, 17310, 17271}, {17297, 29615, 4688}, {17312, 32025, 31238}, {17346, 29577, 41310}, {17377, 48634, 17384}


X(50082) = X(2)X(319)∩X(8)X(44)

Barycentrics    4*a^2 - a*b - 2*b^2 - a*c - 4*b*c - 2*c^2 : :
X(50082) = X[37] - 4 X[3686], 2 X[37] - 3 X[16590], X[37] + 2 X[17362], 5 X[37] - 2 X[17388], 8 X[3686] - 3 X[16590], 2 X[3686] + X[17362], 10 X[3686] - X[17388], 3 X[16590] - 4 X[17330], 3 X[16590] + 4 X[17362], 15 X[16590] - 4 X[17388], 5 X[17330] - X[17388], 5 X[17362] + X[17388], 5 X[4688] - 4 X[49733], X[17333] - 3 X[17346], X[17333] + 3 X[29617], 5 X[17333] - 3 X[49748], 5 X[17346] - X[49748], 5 X[29617] + X[49748], 2 X[4399] + X[4416], 4 X[4399] - X[4686], 2 X[4416] + X[4686], X[1278] + 3 X[17488], 2 X[3739] + X[17363], 2 X[3879] - 5 X[31238], 5 X[31238] - 4 X[49738], 2 X[4681] - 5 X[17331], 5 X[4687] - 2 X[4889], 4 X[4698] - X[17377], 5 X[4699] - 3 X[39704], X[4718] - 4 X[17332], 2 X[4726] + X[17347], 4 X[4739] - X[17364], 7 X[27268] - 9 X[41848]

X(50082) lies on these lines: {2, 319}, {6, 3679}, {8, 44}, {9, 4677}, {10, 4969}, {37, 519}, {45, 3632}, {69, 31138}, {75, 4715}, {141, 41140}, {193, 4795}, {239, 4690}, {391, 16814}, {524, 4688}, {536, 17333}, {545, 4399}, {551, 1213}, {573, 28204}, {594, 4669}, {599, 16833}, {752, 3696}, {903, 17117}, {966, 3241}, {1266, 4405}, {1278, 17488}, {1333, 4921}, {1386, 42334}, {1449, 19875}, {1654, 4852}, {1766, 34718}, {2238, 31136}, {2321, 4370}, {2325, 4701}, {2345, 16671}, {3214, 5109}, {3244, 39260}, {3247, 34747}, {3578, 42051}, {3625, 3707}, {3626, 4700}, {3629, 4967}, {3630, 24199}, {3633, 16672}, {3634, 4982}, {3656, 5816}, {3739, 17363}, {3828, 4856}, {3834, 16816}, {3875, 24441}, {3879, 31238}, {4007, 16885}, {4060, 17340}, {4285, 10459}, {4361, 17274}, {4364, 49770}, {4371, 17276}, {4377, 25298}, {4384, 17313}, {4393, 4708}, {4445, 17357}, {4478, 17353}, {4545, 17355}, {4664, 28329}, {4668, 16670}, {4681, 17331}, {4685, 21858}, {4687, 4889}, {4698, 17377}, {4699, 39704}, {4718, 17332}, {4726, 17347}, {4739, 17364}, {4740, 4912}, {4745, 5750}, {4755, 17389}, {4816, 4873}, {4898, 16677}, {5257, 46845}, {5288, 19297}, {5564, 17351}, {5847, 49725}, {6144, 25590}, {6173, 15533}, {6687, 17230}, {10914, 21864}, {16521, 50016}, {16522, 36531}, {16668, 17303}, {16723, 29767}, {16834, 17251}, {16884, 25055}, {17121, 17385}, {17133, 49742}, {17229, 17342}, {17235, 17343}, {17256, 20016}, {17270, 17384}, {17277, 17310}, {17278, 32099}, {17287, 17356}, {17294, 41310}, {17334, 28301}, {17335, 20055}, {17337, 41141}, {17359, 29615}, {17379, 28633}, {17395, 50019}, {21866, 34612}, {21872, 34720}, {21873, 31165}, {21949, 31134}, {27268, 41848}, {28337, 29574}, {28503, 49515}, {28580, 49468}, {28581, 49746}, {29584, 31144}, {29601, 31285}, {31137, 37673}, {31139, 40341}, {41816, 50063}

X(50082) = midpoint of X(i) and X(j) for these {i,j}: {17330, 17362}, {17346, 29617}, {17363, 17378}
X(50082) = reflection of X(i) in X(j) for these {i,j}: {37, 17330}, {3879, 49738}, {17330, 3686}, {17378, 3739}, {17389, 4755}, {29574, 49731}
X(50082) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 37654, 17281}, {10, 4969, 16666}, {37, 17330, 16590}, {45, 3632, 4727}, {239, 4690, 17237}, {239, 17271, 17382}, {319, 17348, 17231}, {391, 17299, 16814}, {1654, 40891, 17320}, {3625, 3707, 3943}, {3626, 4700, 17369}, {3686, 17362, 37}, {4399, 4416, 4686}, {4690, 17382, 17271}, {5839, 17275, 1100}, {16816, 17360, 3834}, {16834, 17251, 41311}, {17121, 32025, 17385}, {17271, 17382, 17237}, {17281, 37654, 44}, {17320, 40891, 4852}


X(50083) = X(2)X(3702)∩X(65)X(519)

Barycentrics    (b + c)*(-a^3 - 2*a^2*b - a*b^2 - 2*a^2*c + 6*a*b*c + 2*b^2*c - a*c^2 + 2*b*c^2) : :
X(50083) = 2 X[2901] - 5 X[3698], 4 X[3159] - 7 X[3983], 5 X[3697] - 4 X[4096], 3 X[3921] - 2 X[3971], 5 X[17609] - 8 X[24176], 3 X[19875] - 2 X[35652]

X(50083) lies on these lines: {1, 19290}, {2, 3702}, {8, 32950}, {10, 3175}, {37, 4714}, {65, 519}, {72, 4685}, {517, 32860}, {536, 984}, {551, 37593}, {740, 3753}, {968, 11357}, {995, 4706}, {1089, 21896}, {1214, 34625}, {1278, 4737}, {1402, 16371}, {2901, 3698}, {3159, 3983}, {3241, 3896}, {3303, 19286}, {3579, 27368}, {3697, 4096}, {3714, 3987}, {3902, 17495}, {3914, 16052}, {3921, 3971}, {3967, 31855}, {3992, 22034}, {4047, 37654}, {4052, 21075}, {4234, 32932}, {4361, 5119}, {4365, 4695}, {4642, 5295}, {4646, 4647}, {4686, 4692}, {4711, 28555}, {4717, 30818}, {4868, 31993}, {4975, 16602}, {5835, 48845}, {5902, 28581}, {10371, 48834}, {10691, 41340}, {11113, 28580}, {11239, 19819}, {11346, 32929}, {12514, 19723}, {16351, 17594}, {17156, 36279}, {17530, 49636}, {17609, 24176}, {19875, 35652}, {24390, 49554}, {28612, 37548}, {37589, 39766}, {41015, 48864}, {48812, 50044}, {48831, 50048}, {48832, 50049}

X(50083) = reflection of X(i) in X(j) for these {i,j}: {72, 4685}, {3175, 10}, {3555, 42055}


X(50084) = X(2)X(3723)∩X(8)X(41313)

Barycentrics    2*a^2 + 3*a*b - 4*b^2 + 3*a*c - 6*b*c - 4*c^2 : :
X(50084) = X[4852] - 4 X[17229], X[4852] + 2 X[17299], 2 X[17229] + X[17299], 2 X[597] - 3 X[17359], 4 X[2321] - X[17351], 2 X[2321] + X[17372], X[17351] + 2 X[17372], 5 X[599] - 3 X[17274], X[599] - 3 X[17294], 7 X[599] - 3 X[49747], X[17274] - 5 X[17294], 7 X[17274] - 5 X[49747], 7 X[17294] - X[49747], X[1992] - 3 X[17281], X[3875] - 3 X[21358], 4 X[4535] - X[4663], 3 X[17382] - 4 X[20582], 2 X[20582] - 3 X[29594], 2 X[17235] - 3 X[21356], 5 X[17286] - 3 X[47352], 3 X[19875] - X[49486], 3 X[38087] - X[49495], X[49463] - 4 X[49560]

X(50084) lies on these lines: {2, 3723}, {8, 41313}, {37, 29615}, {44, 20055}, {69, 4912}, {141, 17133}, {321, 20956}, {519, 597}, {524, 2321}, {536, 599}, {594, 28639}, {671, 24076}, {1992, 4725}, {2345, 4889}, {2796, 4527}, {3175, 31143}, {3589, 49543}, {3625, 4422}, {3632, 17269}, {3661, 4727}, {3679, 4755}, {3729, 15533}, {3739, 4007}, {3834, 29616}, {3875, 21358}, {3943, 4690}, {3950, 4478}, {4058, 17390}, {4060, 17243}, {4072, 17332}, {4431, 17376}, {4445, 4681}, {4535, 4663}, {4664, 27495}, {4665, 49765}, {4669, 49731}, {4670, 6542}, {4677, 15485}, {4686, 17295}, {4688, 17310}, {4715, 11160}, {4718, 17287}, {4726, 17296}, {4739, 17311}, {4740, 31138}, {4898, 17327}, {4908, 17346}, {4971, 17382}, {5461, 21081}, {8584, 17355}, {17132, 17345}, {17231, 37756}, {17233, 17338}, {17235, 21356}, {17239, 17314}, {17286, 47352}, {17344, 49748}, {17369, 49761}, {17385, 17388}, {19875, 49486}, {20583, 28337}, {25498, 48636}, {28313, 49741}, {28538, 49484}, {28562, 49485}, {29610, 39260}, {29620, 31238}, {34641, 38210}, {38087, 49495}, {49463, 49560}

X(50084) = midpoint of X(i) and X(j) for these {i,j}: {2, 17299}, {3729, 15533}, {4677, 49460}
X(50084) = reflection of X(i) in X(j) for these {i,j}: {2, 17229}, {4852, 2}, {8584, 17355}, {17345, 22165}, {17382, 29594}, {49543, 3589}
X(50084) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2321, 17372, 17351}, {4007, 17309, 3739}, {17229, 17299, 4852}, {17233, 29617, 41310}, {29617, 41310, 17348}


X(50085) = X(2)X(3723)∩X(8)X(17237)

Barycentrics    4*a^2 + a*b - 2*b^2 + a*c - 8*b*c - 2*c^2 : :
X(50085) = X[37] - 4 X[4399], 3 X[37] - 4 X[49731], 3 X[4399] - X[49731], 3 X[4688] - 2 X[17392], X[4686] + 2 X[17362], 3 X[17333] - 5 X[17346], X[17333] - 5 X[29617], 7 X[17333] - 5 X[49748], X[17346] - 3 X[29617], 7 X[17346] - 3 X[49748], 7 X[29617] - X[49748], 4 X[3686] - X[4718], 2 X[4664] - 3 X[16590], 5 X[4699] - 2 X[4889], 2 X[4726] + X[17363], 4 X[4739] - X[17377], 2 X[17388] - 5 X[31238]

X(50085) lies on these lines: {2, 3723}, {8, 17237}, {37, 4399}, {75, 4725}, {239, 17359}, {519, 3696}, {527, 4686}, {528, 49468}, {536, 17333}, {599, 4677}, {1086, 3625}, {1100, 42696}, {1278, 28322}, {3621, 4675}, {3626, 17395}, {3632, 6173}, {3679, 4716}, {3686, 4718}, {3739, 17389}, {3834, 20055}, {3875, 17251}, {3879, 49733}, {3912, 4405}, {4007, 17357}, {4060, 17366}, {4085, 4669}, {4361, 17231}, {4384, 4727}, {4416, 28297}, {4431, 16669}, {4464, 46845}, {4664, 16590}, {4665, 16666}, {4668, 17325}, {4670, 20016}, {4685, 22289}, {4690, 17160}, {4699, 4889}, {4715, 4740}, {4726, 17363}, {4739, 17377}, {16833, 41310}, {17117, 17297}, {17133, 17330}, {17151, 17344}, {17239, 17399}, {17264, 17348}, {17311, 38093}, {17369, 50019}, {17382, 29615}, {17388, 31238}, {24603, 39260}, {28534, 49474}, {29616, 31243}, {31138, 31145}, {34824, 49761}, {37595, 41821}, {48851, 49486}

X(50085) = midpoint of X(17363) and X(49722)
X(50085) = reflection of X(i) in X(j) for these {i,j}: {3879, 49733}, {4718, 49742}, {17389, 3739}, {49722, 4726}, {49742, 3686}
X(50085) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3632, 17119, 17374}, {4665, 49770, 16666}


X(50086) = X(1)X(4688)∩X(2)X(740)

Barycentrics    2*a^2*b - a*b^2 + 2*a^2*c - 3*a*b*c - 4*b^2*c - a*c^2 - 4*b*c^2 : :
X(50086) = X[1] + 2 X[49468], 5 X[8] - 2 X[49449], 2 X[8] + X[49493], 4 X[8] - X[49503], 5 X[4740] + 2 X[49449], 4 X[4740] + X[49503], 4 X[49449] + 5 X[49493], 8 X[49449] - 5 X[49503], 2 X[49493] + X[49503], 4 X[10] - X[49452], 2 X[37] - 3 X[19875], X[75] + 2 X[4709], 2 X[75] + X[49459], 5 X[75] - 2 X[49479], 4 X[75] - X[49490], 4 X[4709] + X[31178], 4 X[4709] - X[49459], 5 X[4709] + X[49479], 8 X[4709] + X[49490], 5 X[31178] - 4 X[49479], 5 X[49459] + 4 X[49479], 2 X[49459] + X[49490], 8 X[49479] - 5 X[49490], X[192] - 4 X[4732], X[984] - 4 X[3696], 5 X[984] - 2 X[49445], X[984] + 2 X[49474], 7 X[984] - 4 X[49523], 5 X[3679] - X[49445], 7 X[3679] - 2 X[49523], 10 X[3696] - X[49445], 2 X[3696] + X[49474], 7 X[3696] - X[49523], X[49445] + 5 X[49474], 7 X[49445] - 10 X[49523], 7 X[49474] + 2 X[49523], 4 X[551] - 5 X[40328], 5 X[40328] - 2 X[49470], X[1278] + 2 X[49457], 2 X[1278] + X[49517], 4 X[49457] - X[49517], 5 X[1698] - 4 X[4755], 5 X[1698] - 2 X[49462], 4 X[24325] - X[49678], 5 X[3617] - 2 X[49456], X[3621] + 2 X[49491], 2 X[3625] + X[49499], 4 X[3626] - X[49447], X[3632] + 2 X[49483], X[3644] - 6 X[38098], 4 X[3739] - 3 X[25055], 4 X[3739] - X[49469], 3 X[25055] - X[49469], 5 X[4668] - 2 X[49515], 2 X[4686] + X[49448], 5 X[4699] - 3 X[38314], 5 X[4699] - 2 X[49471], 3 X[38314] - 2 X[49471], 4 X[4726] - X[49532], 4 X[4739] - X[49475], 4 X[4746] - X[49508], 7 X[4751] - 6 X[19883], X[4764] + 2 X[49520], 7 X[19876] - 2 X[49461], 2 X[24349] + X[49689]

X(50086) lies on these lines: {1, 4688}, {2, 740}, {8, 537}, {10, 4664}, {37, 19875}, {75, 519}, {76, 4783}, {192, 4732}, {238, 16833}, {518, 4677}, {524, 49531}, {536, 984}, {551, 40328}, {594, 48821}, {726, 4669}, {742, 47359}, {752, 29617}, {982, 31136}, {1278, 28554}, {1698, 4755}, {1738, 29594}, {1757, 49721}, {1921, 4479}, {2667, 48855}, {2796, 17346}, {3241, 24325}, {3617, 49456}, {3621, 49491}, {3625, 49499}, {3626, 49447}, {3632, 49483}, {3644, 38098}, {3654, 29010}, {3706, 17063}, {3739, 25055}, {3758, 50018}, {3828, 3993}, {3836, 29577}, {3875, 48854}, {4046, 17889}, {4061, 33101}, {4085, 48628}, {4361, 48805}, {4363, 50016}, {4384, 4693}, {4395, 29660}, {4431, 33165}, {4432, 16816}, {4457, 32937}, {4659, 49712}, {4660, 5564}, {4665, 29659}, {4668, 49515}, {4685, 42029}, {4686, 49448}, {4699, 38314}, {4706, 29827}, {4716, 16834}, {4726, 49532}, {4739, 49475}, {4745, 28522}, {4746, 49508}, {4751, 19883}, {4764, 49520}, {4780, 4967}, {4923, 24231}, {4971, 49725}, {5247, 50049}, {5295, 24440}, {5902, 44671}, {6542, 24693}, {7201, 11237}, {8298, 47037}, {13634, 24257}, {15485, 49485}, {16393, 27368}, {17116, 49497}, {17117, 32941}, {17160, 36480}, {17225, 49524}, {17230, 25351}, {17271, 49518}, {17294, 31151}, {17318, 36531}, {17320, 48809}, {17333, 28542}, {17360, 24692}, {19876, 49461}, {24248, 42334}, {24342, 49486}, {24349, 31145}, {24357, 28309}, {25124, 48858}, {28605, 31161}, {30271, 34628}, {31317, 40891}, {32087, 48849}, {33076, 42696}, {34641, 49450}, {34747, 49478}, {46922, 49488}

X(50086) = midpoint of X(i) and X(j) for these {i,j}: {8, 4740}, {3679, 49474}, {4688, 49468}, {24349, 31145}, {31178, 49459}
X(50086) = reflection of X(i) in X(j) for these {i,j}: {1, 4688}, {984, 3679}, {3241, 24325}, {3679, 3696}, {3993, 3828}, {4664, 10}, {31178, 75}, {34628, 30271}, {34747, 49478}, {49450, 34641}, {49452, 4664}, {49462, 4755}, {49470, 551}, {49490, 31178}, {49493, 4740}, {49678, 3241}, {49689, 31145}
X(50086) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 49493, 49503}, {75, 4709, 49459}, {75, 49459, 49490}, {1278, 49457, 49517}, {3696, 49474, 984}


X(50087) = X(6)X(519)∩X(8)X(45)

Barycentrics    a^2 + 2*a*b - 2*b^2 + 2*a*c - 4*b*c - 2*c^2 : :
X(50087) = X[6] - 4 X[2321], 11 X[6] - 8 X[4856], X[6] + 2 X[17299], 5 X[6] - 8 X[17355], 11 X[2321] - 2 X[4856], 2 X[2321] + X[17299], 5 X[2321] - 2 X[17355], 4 X[4856] - 11 X[17281], 4 X[4856] + 11 X[17299], 5 X[4856] - 11 X[17355], 5 X[17281] - 4 X[17355], 5 X[17299] + 4 X[17355], 4 X[32941] - X[49679], 2 X[49460] + X[49690], 3 X[599] - 2 X[17274], X[17274] - 3 X[17294], 4 X[17274] - 3 X[49747], 4 X[17294] - X[49747], 4 X[4527] - X[5695], X[3416] + 2 X[4133], X[3729] + 2 X[17372], 2 X[3729] + X[40341], 4 X[17372] - X[40341], 5 X[3763] - 2 X[3875], 5 X[3763] - 8 X[17229], 5 X[3763] - 4 X[17382], X[3875] - 4 X[17229], 4 X[3773] - X[49486], 4 X[4535] - X[49488], 2 X[4852] - 5 X[17286], 4 X[4852] - 7 X[47355], 10 X[17286] - 7 X[47355], X[6144] - 4 X[17351], 2 X[16834] - 3 X[47352], 4 X[17359] - 3 X[47352], 2 X[17301] - 3 X[21358], 3 X[21358] - 4 X[29594], 3 X[21356] - 2 X[49741], 3 X[38315] - 4 X[48810], X[49453] - 4 X[49560]

X(50087) lies on these lines: {1, 4727}, {2, 594}, {6, 519}, {8, 45}, {9, 4677}, {10, 16672}, {37, 3679}, {44, 3632}, {69, 545}, {75, 17309}, {141, 28309}, {145, 17369}, {190, 20055}, {192, 4445}, {219, 36910}, {239, 17269}, {319, 17262}, {344, 4399}, {346, 4370}, {524, 49721}, {527, 15533}, {536, 599}, {551, 4058}, {573, 34718}, {740, 48829}, {752, 4527}, {903, 1278}, {966, 16677}, {1030, 4421}, {1043, 3285}, {1086, 29616}, {1213, 16674}, {1449, 34747}, {1575, 31137}, {1761, 34626}, {1766, 28204}, {1992, 28337}, {2171, 11237}, {2276, 31136}, {2325, 3625}, {2329, 4289}, {2345, 3241}, {3178, 21690}, {3196, 8168}, {3242, 28503}, {3247, 19875}, {3416, 4133}, {3501, 5043}, {3621, 4969}, {3623, 26039}, {3624, 39260}, {3626, 4029}, {3633, 16666}, {3644, 17255}, {3654, 37499}, {3661, 17318}, {3672, 48635}, {3686, 4072}, {3707, 4701}, {3723, 4898}, {3729, 4715}, {3731, 16590}, {3763, 3875}, {3773, 49486}, {3879, 4795}, {3912, 17119}, {3930, 31140}, {3949, 31141}, {3950, 4060}, {3986, 38098}, {4006, 17556}, {4034, 16814}, {4053, 11236}, {4141, 41423}, {4286, 10449}, {4363, 6542}, {4365, 31134}, {4371, 17337}, {4395, 29579}, {4431, 4851}, {4452, 48632}, {4461, 17365}, {4472, 29585}, {4478, 17257}, {4479, 17786}, {4513, 17796}, {4515, 8609}, {4535, 49488}, {4659, 17374}, {4664, 17251}, {4665, 17316}, {4668, 16676}, {4670, 29605}, {4675, 49765}, {4681, 17270}, {4686, 17296}, {4688, 29573}, {4704, 32025}, {4718, 17272}, {4725, 15534}, {4726, 17298}, {4740, 17297}, {4745, 5257}, {4764, 17288}, {4788, 17273}, {4852, 17286}, {4916, 7229}, {5124, 11194}, {5564, 17242}, {5687, 19297}, {5839, 17340}, {5904, 21864}, {6144, 17351}, {7297, 17742}, {10022, 17390}, {11160, 28333}, {11238, 17452}, {15668, 17315}, {16371, 21773}, {16833, 41310}, {16834, 17359}, {17116, 17386}, {17117, 17240}, {17133, 17301}, {17151, 17231}, {17160, 17230}, {17228, 17323}, {17244, 31244}, {17245, 32087}, {17264, 29617}, {17276, 28301}, {17278, 41141}, {17279, 41140}, {17280, 40891}, {17319, 17327}, {17321, 48636}, {17324, 48640}, {17334, 32099}, {17347, 17487}, {17349, 41138}, {17354, 20016}, {17395, 29611}, {17398, 38314}, {17488, 25269}, {17532, 22021}, {17788, 42034}, {18145, 30473}, {21356, 49741}, {21689, 27558}, {21943, 31479}, {22165, 28297}, {25503, 29591}, {27739, 33077}, {29016, 36721}, {29577, 37756}, {29583, 34824}, {29619, 41847}, {31146, 44798}, {31151, 49474}, {36409, 49678}, {38315, 48810}, {49453, 49560}

X(50087) = midpoint of X(17281) and X(17299)
X(50087) = reflection of X(i) in X(j) for these {i,j}: {6, 17281}, {599, 17294}, {1992, 49726}, {3875, 17382}, {16834, 17359}, {17281, 2321}, {17301, 29594}, {17382, 17229}, {49747, 599}
X(50087) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 3943, 45}, {75, 17309, 17311}, {75, 17310, 17313}, {75, 17313, 31139}, {192, 4445, 17253}, {192, 17271, 24441}, {346, 17362, 16885}, {346, 31145, 37654}, {346, 37654, 4370}, {594, 17314, 16777}, {1278, 17295, 7232}, {2321, 17299, 6}, {2345, 17388, 16884}, {3632, 4873, 44}, {3644, 17287, 17255}, {3661, 17318, 17325}, {3729, 17372, 40341}, {3875, 17229, 3763}, {3950, 4060, 17275}, {3950, 17275, 16675}, {4361, 17233, 17267}, {4370, 17362, 37654}, {4370, 37654, 16885}, {4431, 4851, 17118}, {4445, 24441, 17271}, {4664, 29615, 17251}, {4852, 17286, 47355}, {5564, 17242, 17259}, {16834, 17359, 47352}, {17117, 17240, 17265}, {17160, 17230, 17290}, {17271, 24441, 17253}, {17301, 29594, 21358}, {17309, 17313, 17310}, {17310, 17313, 17311}, {17311, 31139, 17313}, {17315, 48628, 15668}, {17319, 48630, 17327}, {31145, 37654, 17362}


X(50088) = X(2)X(594)∩X(75)X(519)

Barycentrics    2*a^2 + a*b - b^2 + a*c - 5*b*c - c^2 : :
X(50088) = 7 X[75] - 4 X[3664], 5 X[75] - 2 X[3879], 4 X[75] - X[17377], 5 X[75] - 3 X[39704], 10 X[3664] - 7 X[3879], 16 X[3664] - 7 X[17377], 8 X[3664] - 7 X[17378], 20 X[3664] - 21 X[39704], 8 X[3879] - 5 X[17377], 4 X[3879] - 5 X[17378], 2 X[3879] - 3 X[39704], 5 X[17377] - 12 X[39704], 5 X[17378] - 6 X[39704], X[192] - 4 X[4399], 2 X[17333] - 3 X[17346], X[17333] - 3 X[29617], 4 X[17333] - 3 X[49748], 4 X[29617] - X[49748], 2 X[1278] + X[17347], X[1278] + 2 X[17362], X[17347] - 4 X[17362], X[3644] - 4 X[3686], 2 X[4416] + X[4764], 2 X[4681] - 3 X[16590], 2 X[4686] + X[17363], 5 X[4699] - 2 X[17388], 5 X[4699] - 4 X[49738], 2 X[4718] - 5 X[17331], 4 X[4726] - X[17364], 8 X[4739] - 5 X[17391], 7 X[4772] - 4 X[17390], X[4788] - 4 X[17332], 5 X[4821] - 2 X[17365], 2 X[17334] - 3 X[17488]

X(50088) lies on these lines: {2, 594}, {6, 40891}, {8, 4389}, {69, 903}, {75, 519}, {86, 3241}, {190, 37654}, {192, 4399}, {239, 17281}, {313, 4479}, {319, 4398}, {320, 3632}, {346, 41138}, {524, 4740}, {536, 17333}, {545, 1278}, {551, 4967}, {740, 49746}, {752, 49474}, {1086, 20055}, {1266, 3625}, {1654, 24441}, {2321, 17342}, {3244, 41847}, {3264, 17144}, {3621, 42697}, {3626, 17250}, {3644, 3686}, {3661, 17382}, {3663, 34641}, {3672, 32025}, {3679, 3875}, {3758, 49770}, {3759, 4431}, {3943, 4405}, {3945, 20049}, {3946, 48630}, {4007, 16706}, {4021, 4745}, {4034, 17258}, {4058, 17371}, {4060, 17228}, {4346, 20052}, {4357, 4669}, {4363, 20016}, {4370, 17349}, {4371, 17277}, {4393, 4665}, {4395, 17230}, {4402, 17283}, {4416, 4764}, {4452, 17273}, {4460, 28626}, {4464, 17394}, {4478, 17236}, {4664, 17133}, {4681, 16590}, {4686, 4715}, {4688, 17389}, {4699, 17388}, {4718, 17331}, {4726, 17364}, {4727, 17244}, {4739, 17391}, {4772, 17390}, {4788, 17332}, {4795, 17116}, {4821, 17365}, {4852, 17381}, {4908, 17348}, {4954, 37670}, {6542, 17119}, {7263, 17373}, {10022, 17379}, {16833, 17264}, {17117, 17234}, {17240, 41141}, {17269, 29590}, {17294, 37756}, {17300, 31139}, {17301, 29615}, {17319, 28634}, {17322, 19875}, {17334, 17488}, {17372, 31138}, {17383, 48636}, {17386, 24199}, {17387, 49761}, {17395, 29593}, {17788, 42029}, {21277, 34700}, {21296, 36588}, {25055, 28653}, {25590, 34747}, {27191, 29616}, {27739, 37759}, {28337, 49727}, {28635, 31248}, {34605, 39765}, {41816, 50071}

X(50088) = reflection of X(i) in X(j) for these {i,j}: {192, 17330}, {17330, 4399}, {17346, 29617}, {17377, 17378}, {17378, 75}, {17388, 49738}, {17389, 4688}, {49722, 4740}, {49748, 17346}
X(50088) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 17160, 4389}, {319, 17151, 4398}, {1266, 3625, 17360}, {1278, 17362, 17347}, {2321, 41140, 17342}, {3679, 3875, 17320}, {3679, 17320, 5224}, {3875, 5564, 5224}, {3879, 39704, 17378}, {3943, 4405, 16816}, {4677, 17151, 17274}, {4677, 17274, 319}, {4852, 48628, 17381}, {5564, 17320, 3679}, {17117, 17299, 17234}, {17342, 41140, 17352}


X(50089) = X(1)X(4527)∩X(2)X(2321)

Barycentrics    a^2 + 3*a*b - 2*b^2 + 3*a*c - 6*b*c - 2*c^2 : :
X(50089) = X[1] - 4 X[4527], 5 X[2] - 4 X[3946], 4 X[2] - 5 X[17286], 4 X[2321] - X[3875], 5 X[2321] - 2 X[3946], 8 X[2321] - 5 X[17286], 5 X[3875] - 8 X[3946], 2 X[3875] - 5 X[17286], 16 X[3946] - 25 X[17286], X[3886] - 4 X[4133], X[3729] + 2 X[17299], 4 X[599] - 3 X[17274], 2 X[599] - 3 X[17294], 5 X[599] - 3 X[49747], 5 X[17274] - 4 X[49747], 5 X[17294] - 2 X[49747], 4 X[597] - 3 X[16834], 2 X[597] - 3 X[17281], 5 X[1698] - 8 X[4535], 2 X[3663] - 3 X[21356], 4 X[3773] - 3 X[19875], 2 X[4688] - 3 X[27474], 2 X[4852] - 3 X[47352], 8 X[17229] - 5 X[17304], 4 X[17229] - 3 X[21358], 5 X[17304] - 6 X[21358], 3 X[17301] - 4 X[20582], 2 X[20583] - 3 X[49726], 3 X[25055] - 2 X[32921]

X(50089) lies on these lines: {1, 4527}, {2, 2321}, {6, 28329}, {9, 29617}, {69, 17132}, {75, 29573}, {86, 4898}, {190, 3632}, {192, 4007}, {239, 4873}, {319, 49748}, {321, 31179}, {344, 4072}, {519, 1992}, {524, 3729}, {527, 11160}, {536, 599}, {594, 41312}, {597, 4971}, {646, 17144}, {671, 43677}, {740, 3679}, {1266, 29616}, {1278, 17296}, {1698, 4535}, {3175, 21810}, {3633, 3758}, {3644, 17272}, {3663, 21356}, {3681, 24394}, {3731, 5564}, {3760, 4033}, {3773, 19875}, {3879, 4461}, {3882, 4050}, {3943, 4384}, {3950, 42696}, {3969, 25527}, {4034, 17261}, {4058, 17321}, {4060, 17257}, {4361, 41310}, {4363, 4727}, {4365, 21829}, {4371, 25101}, {4431, 10436}, {4445, 4718}, {4464, 5749}, {4483, 4921}, {4644, 49761}, {4659, 6542}, {4665, 16831}, {4668, 17256}, {4677, 17346}, {4686, 17298}, {4688, 27474}, {4699, 29620}, {4725, 49721}, {4726, 17311}, {4740, 6173}, {4745, 4780}, {4764, 4862}, {4788, 17287}, {4821, 17312}, {4851, 49727}, {4852, 47352}, {4859, 17240}, {4888, 17386}, {4912, 15533}, {5695, 28538}, {5853, 6172}, {9041, 49451}, {15534, 17351}, {16670, 20016}, {16674, 28633}, {16833, 17264}, {17151, 17233}, {17160, 17284}, {17229, 17304}, {17275, 49737}, {17276, 22165}, {17301, 20582}, {17308, 17318}, {17315, 25590}, {17355, 49543}, {17359, 24277}, {17362, 25728}, {17769, 34747}, {18697, 42029}, {20583, 49726}, {23668, 42041}, {25055, 32921}, {26627, 31011}, {28313, 29594}, {29582, 38093}, {31137, 41142}, {31143, 42044}, {32941, 46922}, {36973, 39351}, {42697, 49765}, {47358, 49446}, {47359, 49495}

X(50089) = reflection of X(i) in X(j) for these {i,j}: {2, 2321}, {3875, 2}, {4780, 4745}, {15533, 17372}, {15534, 17351}, {16834, 17281}, {17274, 17294}, {17276, 22165}, {49446, 47358}, {49495, 47359}, {49543, 17355}
X(50089) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {192, 4007, 17270}, {2321, 3875, 17286}, {4363, 4727, 29605}, {4431, 17314, 10436}, {4686, 17309, 17298}, {4740, 17310, 6173}, {4764, 17295, 4862}, {17151, 17233, 17282}


X(50090) = X(1)X(4480)∩X(2)X(2415)

Barycentrics    2*a^2 - 5*a*b - b^2 - 5*a*c + 4*b*c - c^2 : :
X(50090) = 5 X[37] - 2 X[7228], 3 X[37] - 2 X[49738], 3 X[7228] - 5 X[49738], 5 X[75] - 9 X[41848], 2 X[192] + X[4416], 5 X[192] + X[17363], 5 X[192] + 3 X[17488], 5 X[4416] - 2 X[17363], 5 X[4416] - 6 X[17488], 5 X[17333] - X[17363], 5 X[17333] - 3 X[17488], X[17363] - 3 X[17488], 3 X[4664] - X[17378], 2 X[17378] - 3 X[29574], X[17378] + 3 X[49748], X[29574] + 2 X[49748], X[17330] - 3 X[49742], 2 X[49514] + X[49528], 4 X[49456] - X[49476], X[3644] + 2 X[3686], 2 X[3664] - 5 X[4704], X[3879] - 4 X[4681], X[3879] + 2 X[17334], 2 X[4681] + X[17334], X[3883] + 2 X[49523], X[4686] - 3 X[16590], X[4718] + 2 X[17332], X[4788] + 5 X[17331], 2 X[49447] + X[49466]

X(50090) lies on these lines: {1, 4480}, {2, 2415}, {9, 41140}, {37, 545}, {45, 1266}, {75, 28301}, {141, 4908}, {142, 903}, {144, 3241}, {190, 17023}, {192, 519}, {320, 4029}, {344, 36911}, {527, 4664}, {536, 17330}, {537, 49514}, {551, 894}, {752, 49456}, {984, 28580}, {1654, 4669}, {2321, 17258}, {2325, 4389}, {3244, 20072}, {3589, 36522}, {3644, 3686}, {3662, 41141}, {3664, 4704}, {3672, 25728}, {3679, 4431}, {3707, 17160}, {3717, 48829}, {3828, 17248}, {3875, 37654}, {3879, 4681}, {3883, 28503}, {3912, 4419}, {3946, 17336}, {3950, 6646}, {4021, 17350}, {4058, 17252}, {4060, 17328}, {4072, 17287}, {4078, 31151}, {4098, 17300}, {4357, 17262}, {4370, 17246}, {4398, 6666}, {4440, 29571}, {4454, 16831}, {4473, 31191}, {4488, 38314}, {4659, 24603}, {4686, 16590}, {4688, 28297}, {4718, 17332}, {4741, 49765}, {4745, 48628}, {4755, 28322}, {4788, 17331}, {4795, 16777}, {4887, 17244}, {4896, 29569}, {4898, 20080}, {4912, 17392}, {6172, 16834}, {9957, 41772}, {11239, 45738}, {16675, 31139}, {16676, 42697}, {16696, 17195}, {16706, 41138}, {17133, 17346}, {17243, 31138}, {17254, 29594}, {17276, 17313}, {17787, 18145}, {22002, 22014}, {25255, 25265}, {27754, 33151}, {28313, 29617}, {29007, 41803}, {29597, 35578}, {41310, 49741}, {41311, 49726}, {41312, 49721}, {41313, 49747}, {49447, 49466}

X(50090) = midpoint of X(i) and X(j) for these {i,j}: {192, 17333}, {4664, 49748}, {49447, 49746}
X(50090) = reflection of X(i) in X(j) for these {i,j}: {4416, 17333}, {4688, 49737}, {29574, 4664}, {49466, 49746}, {49727, 4755}
X(50090) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 20073, 4480}, {320, 4029, 29601}, {2325, 4389, 29596}, {3663, 17261, 25101}, {4370, 17246, 17382}, {4370, 17382, 17353}, {4681, 17334, 3879}, {17247, 25269, 17355}, {17262, 24441, 17281}, {17281, 24441, 4357}, {17333, 17363, 17488}


X(50091) = X(2)X(968)∩X(10)X(536)

Barycentrics    5*a^2*b + 2*a*b^2 + 3*b^3 + 5*a^2*c - b^2*c + 2*a*c^2 - b*c^2 + 3*c^3 : :
X(50091) = 2 X[141] + X[4780], X[3755] + 2 X[3821], 2 X[3755] + X[49511], 4 X[3821] - X[49511], X[3663] + 2 X[4085], 2 X[3663] + X[49529], 4 X[4085] - X[49529], X[3625] + 2 X[49463], 2 X[3626] + X[49453], 4 X[3634] - X[5695], 4 X[3844] - X[4133], 2 X[3946] + X[4660], 4 X[3946] - X[49684], 2 X[4660] + X[49684], 4 X[17235] - X[49505], 5 X[19862] - 2 X[49484], 3 X[19883] - 2 X[48810], 3 X[38047] - X[49721], 4 X[34573] - X[49485]

X(50091) lies on these lines: {2, 968}, {10, 536}, {141, 4780}, {142, 214}, {516, 5085}, {518, 49741}, {519, 599}, {537, 3663}, {597, 28534}, {726, 38191}, {740, 29594}, {752, 49630}, {1125, 24693}, {1266, 29659}, {2092, 16052}, {2550, 48854}, {2783, 10175}, {2796, 6034}, {3241, 3662}, {3625, 49463}, {3626, 49453}, {3634, 5695}, {3679, 4357}, {3826, 4755}, {3828, 5257}, {3836, 4356}, {3844, 4133}, {3946, 4660}, {4026, 4688}, {4029, 49769}, {4078, 4429}, {4104, 32776}, {4260, 44663}, {4389, 49772}, {4432, 31191}, {4643, 50022}, {4645, 29584}, {4656, 42056}, {4663, 28333}, {4667, 24692}, {4669, 28503}, {4693, 29596}, {5847, 16834}, {5883, 44670}, {6173, 48830}, {7734, 49736}, {17023, 24715}, {17067, 24331}, {17227, 49763}, {17235, 49505}, {17236, 31145}, {17290, 49768}, {17318, 49766}, {17359, 25354}, {17399, 49720}, {19784, 50049}, {19862, 49484}, {19883, 48810}, {21255, 49471}, {25351, 29571}, {28526, 38047}, {29057, 38146}, {29574, 31151}, {31161, 33145}, {31178, 33149}, {34573, 49485}, {41311, 49725}, {47359, 49747}, {48632, 49475}, {49676, 49691}, {49732, 50063}

X(50091) = midpoint of X(i) and X(j) for these {i,j}: {17301, 48829}, {47359, 49747}
X(50091) = reflection of X(i) in X(j) for these {i,j}: {10, 48821}, {551, 17382}, {17281, 3828}, {48805, 1125}
X(50091) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3663, 4085, 49529}, {3755, 3821, 49511}, {3946, 4660, 49684}, {4026, 4688, 48853}


X(50092) = X(2)X(7)∩X(10)X(537)

Barycentrics    a*b + 3*b^2 + a*c - 2*b*c + 3*c^2 : :
X(50092) = X[69] + 2 X[3946], X[69] + 5 X[17304], 2 X[3946] - 5 X[17304], X[16834] - 5 X[17304], 4 X[141] - X[2321], 2 X[141] + X[3663], 5 X[141] - 2 X[17229], X[141] + 2 X[17235], X[2321] + 2 X[3663], 5 X[2321] - 8 X[17229], X[2321] + 8 X[17235], X[2321] + 4 X[49741], 5 X[3663] + 4 X[17229], X[3663] - 4 X[17235], X[17229] + 5 X[17235], 4 X[17229] - 5 X[29594], 2 X[17229] + 5 X[49741], 4 X[17235] + X[29594], X[29594] + 2 X[49741], X[3416] + 2 X[4353], X[3755] - 4 X[3821], X[3755] + 2 X[49511], 2 X[3821] + X[49511], 2 X[1125] + X[4655], 2 X[3589] + X[17345], 7 X[3619] - X[3729], 5 X[3620] + X[3875], 7 X[3624] - X[24695], 2 X[3631] + X[4852], 4 X[3634] - X[32935], 5 X[3763] + X[17276], 5 X[3763] - 2 X[17355], 5 X[3763] - X[49721], X[17276] + 2 X[17355], 2 X[4085] + X[49505], 2 X[4672] - 5 X[19862], 2 X[22165] + X[49543], 2 X[4856] + X[40341], X[17281] - 3 X[21358], 3 X[21358] + X[49747], X[17294] - 3 X[21356], X[17351] - 4 X[34573]

X(50092) lies on these lines: {2, 7}, {10, 537}, {37, 21255}, {44, 31191}, {69, 3946}, {141, 536}, {190, 29596}, {192, 29577}, {320, 4667}, {392, 2835}, {515, 48799}, {516, 31884}, {518, 48821}, {519, 599}, {524, 17382}, {528, 49630}, {545, 17359}, {551, 752}, {597, 4715}, {942, 50058}, {950, 50055}, {966, 4859}, {1125, 4252}, {1211, 24177}, {1227, 30892}, {1266, 3661}, {1278, 48634}, {1449, 21296}, {1738, 3679}, {2325, 4419}, {2345, 4862}, {2792, 10165}, {3008, 3707}, {3241, 4684}, {3244, 17374}, {3247, 4869}, {3589, 17345}, {3619, 3729}, {3620, 3875}, {3624, 24695}, {3626, 17119}, {3631, 4852}, {3634, 32935}, {3664, 4657}, {3666, 4035}, {3672, 17296}, {3686, 4000}, {3739, 48631}, {3763, 17276}, {3773, 28554}, {3778, 42038}, {3828, 31139}, {3834, 4364}, {3840, 41144}, {3879, 17288}, {3912, 4029}, {3914, 31136}, {3950, 17231}, {3986, 17245}, {4001, 32774}, {4007, 4452}, {4021, 4851}, {4026, 5542}, {4034, 4402}, {4044, 39995}, {4058, 4686}, {4060, 17151}, {4072, 4718}, {4085, 49505}, {4104, 24169}, {4138, 6682}, {4201, 12437}, {4260, 48815}, {4292, 16394}, {4310, 48849}, {4346, 4659}, {4356, 4966}, {4363, 4887}, {4371, 4545}, {4384, 17067}, {4395, 4690}, {4398, 4431}, {4416, 16706}, {4429, 24393}, {4440, 17292}, {4464, 17373}, {4480, 17354}, {4644, 26104}, {4670, 4896}, {4672, 19862}, {4700, 5222}, {4708, 34824}, {4725, 22165}, {4726, 48636}, {4741, 17367}, {4748, 16832}, {4758, 29603}, {4798, 25503}, {4856, 40341}, {4858, 26563}, {4902, 7222}, {4912, 49726}, {4967, 17238}, {4980, 40013}, {4982, 17014}, {5224, 24199}, {5550, 36834}, {5743, 24175}, {5765, 19279}, {5850, 38047}, {5880, 19868}, {7228, 17385}, {7263, 17239}, {7321, 17307}, {16062, 24391}, {16672, 29606}, {16676, 29627}, {16829, 20257}, {16887, 17197}, {17045, 17376}, {17132, 17281}, {17133, 17294}, {17232, 17247}, {17233, 48638}, {17234, 17249}, {17250, 24603}, {17253, 17278}, {17255, 17279}, {17256, 27191}, {17258, 17283}, {17265, 25072}, {17271, 37756}, {17297, 17320}, {17298, 17321}, {17300, 17324}, {17308, 42697}, {17313, 41312}, {17318, 49765}, {17329, 17352}, {17332, 17356}, {17334, 17357}, {17342, 49748}, {17344, 17366}, {17346, 41140}, {17347, 17370}, {17351, 34573}, {17360, 49770}, {17361, 17380}, {17364, 17383}, {17365, 17384}, {17375, 17396}, {17378, 17399}, {17770, 38049}, {18739, 42034}, {19883, 25354}, {20072, 29630}, {21514, 24328}, {24210, 31137}, {24231, 31178}, {24325, 48853}, {24441, 41141}, {24798, 40617}, {25357, 49731}, {26142, 26959}, {26769, 27113}, {26932, 41006}, {28194, 48803}, {28534, 48810}, {30768, 36263}, {31161, 32781}, {37549, 50046}, {41310, 49742}

X(50092) = midpoint of X(i) and X(j) for these {i,j}: {2, 17274}, {69, 16834}, {141, 49741}, {599, 17301}, {3663, 29594}, {17276, 49721}, {17281, 49747}, {47358, 48829}
X(50092) = reflection of X(i) in X(j) for these {i,j}: {2321, 29594}, {3663, 49741}, {16834, 3946}, {17359, 20582}, {29594, 141}, {49721, 17355}, {49741, 17235}
X(50092) = X(37209)-Ceva conjugate of X(514)
X(50092) = barycentric product X(75)*X(4003)
X(50092) = barycentric quotient X(4003)/X(1)
X(50092) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 17306, 5750}, {37, 48632, 21255}, {69, 17304, 3946}, {141, 3663, 2321}, {141, 17235, 3663}, {142, 4357, 5257}, {320, 17023, 4667}, {320, 17305, 17023}, {1086, 17237, 10}, {3008, 4643, 3707}, {3662, 4357, 142}, {3662, 17236, 4357}, {3763, 17276, 17355}, {3821, 49511, 3755}, {3834, 4364, 29571}, {4000, 17272, 3686}, {4346, 29611, 4659}, {4389, 17227, 3912}, {4398, 17228, 4431}, {4407, 25351, 10}, {4419, 17284, 2325}, {4643, 17290, 3008}, {4644, 26104, 29598}, {4657, 7232, 3664}, {4670, 7238, 4896}, {4675, 17325, 1125}, {4686, 48635, 4058}, {4851, 17323, 4021}, {4887, 29604, 4363}, {5224, 48629, 24199}, {6646, 17291, 17353}, {16706, 17273, 4416}, {17231, 17246, 3950}, {17238, 48627, 4967}, {17249, 48637, 17234}, {17257, 17282, 6666}, {17258, 17283, 25101}, {17288, 17302, 3879}, {17297, 17320, 29574}, {17374, 17395, 3244}, {17392, 41311, 551}, {21358, 49747, 17281}, {31138, 41311, 17392}


X(50093) = X(2)X(7)∩X(10)X(190)

Barycentrics    2*a^2 - 3*a*b - b^2 - 3*a*c - c^2 : :
X(50093) = 4 X[37] - X[3879], 2 X[37] + X[4416], X[37] + 2 X[17332], 5 X[37] - 2 X[17390], X[3879] + 2 X[4416], X[3879] + 8 X[17332], 5 X[3879] - 8 X[17390], X[3879] - 8 X[49737], X[4416] - 4 X[17332], 5 X[4416] + 4 X[17390], X[4416] + 4 X[49737], 5 X[17332] + X[17390], 4 X[17332] + X[29574], 4 X[17390] - 5 X[29574], X[17390] - 5 X[49737], X[29574] - 4 X[49737], X[192] + 2 X[3686], X[192] + 5 X[17331], 2 X[3686] - 5 X[17331], 5 X[17331] - X[29617], 2 X[984] + X[3883], 5 X[984] + X[49506], 4 X[984] - X[49527], 7 X[984] - X[49534], 5 X[3883] - 2 X[49506], 2 X[3883] + X[49527], 7 X[3883] + 2 X[49534], 4 X[49506] + 5 X[49527], 7 X[49506] + 5 X[49534], 7 X[49527] - 4 X[49534], 2 X[49516] + X[49521], X[4688] - 3 X[16590], 3 X[16590] - 2 X[49731], 2 X[3664] - 5 X[4687], 2 X[3664] + X[17347], 5 X[4687] + X[17347], 2 X[3739] + X[17334], 2 X[4399] + X[4718], 2 X[4681] + X[17362], 4 X[4698] - X[17365], 5 X[4704] + X[17363], 2 X[7228] - 5 X[31238], X[49466] + 2 X[49515], X[17364] - 7 X[27268], X[17364] - 5 X[29622], 7 X[27268] - 5 X[29622]

X(50093) lies on these lines: {1, 1992}, {2, 7}, {6, 41312}, {10, 190}, {37, 524}, {44, 597}, {45, 599}, {69, 3731}, {72, 13745}, {75, 17132}, {86, 3986}, {141, 16814}, {192, 3686}, {193, 3247}, {198, 16436}, {210, 6007}, {238, 551}, {239, 3707}, {256, 4685}, {261, 37792}, {306, 31143}, {319, 3950}, {320, 29571}, {333, 4656}, {344, 17272}, {346, 17270}, {391, 3875}, {392, 2810}, {516, 49720}, {518, 49740}, {519, 751}, {536, 17330}, {545, 4688}, {645, 6626}, {646, 25280}, {752, 49692}, {846, 4104}, {946, 7609}, {966, 3729}, {1001, 47358}, {1100, 8584}, {1125, 3758}, {1213, 17351}, {1266, 4384}, {1334, 3882}, {1449, 5032}, {1575, 36235}, {1654, 2321}, {1716, 42043}, {1743, 17321}, {1756, 19870}, {2325, 3661}, {2345, 25728}, {2663, 25421}, {3008, 4389}, {3161, 5232}, {3175, 49724}, {3220, 17549}, {3241, 7174}, {3242, 49783}, {3294, 21362}, {3589, 15492}, {3616, 15601}, {3618, 3973}, {3629, 3723}, {3663, 17258}, {3664, 4687}, {3679, 3717}, {3710, 26064}, {3718, 42034}, {3739, 4912}, {3751, 48830}, {3755, 9791}, {3759, 4021}, {3828, 32784}, {3842, 28558}, {3914, 37857}, {3923, 48809}, {3943, 4690}, {3946, 17247}, {3951, 37314}, {4026, 15481}, {4029, 6542}, {4054, 5235}, {4058, 32025}, {4078, 33082}, {4098, 17315}, {4133, 42334}, {4360, 49543}, {4363, 4480}, {4370, 17359}, {4393, 4700}, {4399, 4718}, {4407, 4432}, {4422, 17237}, {4428, 7083}, {4431, 17262}, {4440, 16815}, {4464, 5839}, {4473, 17292}, {4552, 25719}, {4644, 16831}, {4657, 16885}, {4659, 20073}, {4667, 16826}, {4669, 33076}, {4676, 19868}, {4681, 17362}, {4698, 17365}, {4704, 17363}, {4708, 17369}, {4715, 4755}, {4740, 28301}, {4741, 17244}, {4745, 33165}, {4748, 17308}, {4758, 29612}, {4851, 15533}, {4856, 17393}, {4887, 31211}, {5220, 47359}, {5224, 17336}, {5393, 13637}, {5405, 13757}, {5735, 36660}, {5969, 17760}, {6144, 16674}, {6210, 28194}, {7064, 17792}, {7228, 31238}, {7238, 31285}, {7277, 28639}, {7290, 38314}, {8359, 25066}, {9041, 49466}, {10868, 21039}, {11160, 16676}, {11163, 24239}, {11179, 46475}, {11523, 13736}, {12527, 31359}, {14210, 42724}, {15534, 16777}, {15817, 35302}, {15828, 17307}, {16370, 24320}, {16484, 49505}, {16517, 16834}, {16666, 20583}, {16669, 17045}, {16670, 26626}, {16677, 40341}, {16785, 34914}, {16832, 42697}, {16970, 29597}, {17067, 29628}, {17233, 17328}, {17234, 17329}, {17235, 17337}, {17238, 17339}, {17239, 17340}, {17242, 17343}, {17243, 17344}, {17245, 17345}, {17246, 17348}, {17249, 17352}, {17250, 17354}, {17251, 17281}, {17252, 17280}, {17253, 17279}, {17255, 17278}, {17259, 17276}, {17263, 17273}, {17264, 17271}, {17297, 29600}, {17300, 29620}, {17301, 24441}, {17304, 37650}, {17305, 31191}, {17318, 49770}, {17360, 49765}, {17364, 27268}, {17374, 29601}, {17384, 48310}, {17387, 29606}, {19723, 50068}, {19822, 25734}, {22214, 24437}, {24517, 46910}, {24692, 25352}, {24695, 39586}, {25269, 48628}, {27820, 27834}, {28333, 49738}, {28534, 49725}, {28538, 49476}, {29633, 38089}, {32041, 35144}, {41149, 46845}, {41531, 43262}, {41816, 42033}, {44694, 49735}

X(50093) = midpoint of X(i) and X(j) for these {i,j}: {2, 17333}, {75, 49748}, {192, 29617}, {4416, 29574}, {4664, 17346}, {17330, 49742}, {17332, 49737}, {17334, 49727}
X(50093) = reflection of X(i) in X(j) for these {i,j}: {37, 49737}, {3879, 29574}, {4688, 49731}, {17392, 4755}, {29574, 37}, {29617, 3686}, {49727, 3739}
X(50093) = barycentric product X(i)*X(j) for these {i,j}: {75, 4689}, {190, 47784}
X(50093) = barycentric quotient X(i)/X(j) for these {i,j}: {4689, 1}, {47784, 514}
X(50093) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 144, 35578}, {2, 35578, 10436}, {9, 4357, 17353}, {9, 17257, 4357}, {9, 17306, 26685}, {37, 4416, 3879}, {37, 17332, 4416}, {44, 4364, 17023}, {44, 41311, 597}, {45, 599, 41313}, {45, 4643, 3912}, {141, 16814, 25101}, {144, 5296, 10436}, {190, 17256, 10}, {192, 17331, 3686}, {597, 4364, 41311}, {597, 41311, 17023}, {599, 41313, 3912}, {966, 3729, 4967}, {984, 3883, 49527}, {1654, 17261, 2321}, {3161, 5232, 17286}, {4384, 4419, 1266}, {4389, 17335, 3008}, {4422, 17237, 29596}, {4480, 24603, 4363}, {4643, 41313, 599}, {4687, 17347, 3664}, {4688, 16590, 49731}, {5224, 17336, 17355}, {5296, 35578, 2}, {6646, 17260, 142}, {16826, 20072, 4667}, {17247, 17349, 3946}, {17248, 17350, 5750}, {17250, 17354, 29604}, {17258, 17277, 3663}, {17259, 17276, 24199}, {17262, 17275, 4431}, {17263, 17273, 21255}, {17264, 17271, 29594}


X(50094) = X(2)X(38)∩X(10)X(536)

Barycentrics    a^2*b + 4*a*b^2 + a^2*c + 6*a*b*c + b^2*c + 4*a*c^2 + b*c^2 : :
X(50094) = 2 X[1] + X[49449], 5 X[2] - X[24349], 7 X[2] + X[31302], 7 X[2] - 5 X[40328], X[984] + 2 X[3842], 2 X[984] + X[24325], 5 X[984] + X[24349], 3 X[984] + X[31178], 7 X[984] - X[31302], 7 X[984] + 5 X[40328], 4 X[3842] - X[24325], 10 X[3842] - X[24349], 6 X[3842] - X[31178], 14 X[3842] + X[31302], 14 X[3842] - 5 X[40328], 5 X[24325] - 2 X[24349], 3 X[24325] - 2 X[31178], 7 X[24325] + 2 X[31302], 7 X[24325] - 10 X[40328], 3 X[24349] - 5 X[31178], 7 X[24349] + 5 X[31302], 7 X[24349] - 25 X[40328], 7 X[31178] + 3 X[31302], 7 X[31178] - 15 X[40328], X[31302] + 5 X[40328], 2 X[10] + X[49456], 2 X[37] + X[49457], 4 X[37] - X[49471], 7 X[37] - X[49475], 2 X[49457] + X[49471], 7 X[49457] + 2 X[49475], 7 X[49471] - 4 X[49475], X[75] - 3 X[19875], X[192] + 2 X[4732], 4 X[1125] - X[49491], 2 X[1125] + X[49515], X[49491] + 2 X[49515], 5 X[1698] + X[49447], 5 X[3616] + X[49503], 5 X[3617] + X[49452], 7 X[3624] - X[49499], 2 X[3626] + X[49462], 4 X[3634] - X[49483], 2 X[3739] + X[49520], 2 X[4681] + X[4709], 2 X[4681] + 3 X[38098], X[4709] - 3 X[38098], 5 X[4687] - 3 X[25055], 5 X[4687] + X[49448], 3 X[25055] + X[49448], 4 X[4691] - X[49468], 4 X[4698] - 3 X[19883], 4 X[4698] - X[49479], 3 X[19883] - X[49479], 5 X[4699] + X[49517], 5 X[4704] + X[49459], 7 X[4751] - X[49532], 7 X[9780] - X[49493], 2 X[15569] + X[49510], 5 X[19862] + X[49508], 7 X[27268] - 3 X[38314], 7 X[27268] - X[49490], 3 X[38314] - X[49490], 5 X[31238] + X[49513], 3 X[38087] - X[49531]

X(50094) lies on these lines: {1, 4753}, {2, 38}, {9, 48854}, {10, 536}, {37, 519}, {45, 4432}, {75, 3992}, {190, 36531}, {192, 4732}, {381, 29054}, {518, 551}, {528, 49737}, {545, 25384}, {726, 3828}, {740, 3679}, {752, 49692}, {876, 28840}, {1086, 25352}, {1125, 49491}, {1698, 17305}, {1757, 46922}, {2796, 49725}, {3247, 49497}, {3616, 49503}, {3617, 49452}, {3624, 49499}, {3626, 49462}, {3634, 49483}, {3654, 20430}, {3681, 10180}, {3696, 4745}, {3715, 29644}, {3723, 49685}, {3725, 42042}, {3731, 32941}, {3739, 49520}, {3751, 5625}, {3775, 4078}, {3826, 49741}, {3912, 4407}, {3986, 49529}, {3993, 4669}, {4032, 11237}, {4389, 25351}, {4419, 24693}, {4649, 29580}, {4672, 16830}, {4677, 49470}, {4681, 4709}, {4687, 25055}, {4691, 49468}, {4698, 19883}, {4699, 49517}, {4704, 49459}, {4740, 28516}, {4751, 49532}, {4937, 30970}, {4981, 31136}, {5257, 48853}, {5296, 48849}, {5302, 50064}, {6211, 13634}, {7322, 32916}, {9780, 49493}, {15481, 33682}, {15569, 49510}, {16370, 34247}, {16674, 49680}, {16677, 49460}, {16814, 49482}, {16826, 49712}, {16833, 32921}, {17237, 49769}, {17248, 33165}, {17254, 31151}, {17256, 32847}, {17259, 49455}, {17277, 49472}, {17281, 48809}, {17310, 27495}, {17333, 28558}, {17628, 34612}, {18822, 39717}, {19862, 49508}, {19871, 49598}, {24433, 25375}, {24450, 35040}, {25354, 49524}, {27268, 38314}, {27798, 32925}, {28503, 49731}, {28581, 34641}, {29582, 33087}, {29584, 49489}, {29600, 49511}, {31238, 49513}, {32935, 39586}, {35960, 35962}, {38087, 49531}, {40774, 41142}, {47359, 48822}, {48802, 49526}

X(50094) = midpoint of X(i) and X(j) for these {i,j}: {2, 984}, {3654, 20430}, {3679, 4664}, {3993, 4669}, {4677, 49470}, {47359, 49509}, {49725, 49742}
X(50094) = reflection of X(i) in X(j) for these {i,j}: {2, 3842}, {551, 4755}, {3696, 4745}, {4688, 3828}, {24325, 2}
X(50094) = complement of X(31178)
X(50094) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 756, 42056}, {2, 42039, 42055}, {2, 42041, 42054}, {37, 49457, 49471}, {45, 36480, 4432}, {984, 3842, 24325}, {984, 40328, 31302}, {1125, 49515, 49491}


X(50095) = X(1)X(2)∩X(75)X(527)

Barycentrics    2*a^2 - a*b - b^2 - a*c - 4*b*c - c^2 : :
X(50095) = 7 X[2] - 5 X[29622], 2 X[8] + X[49466], 4 X[10] - X[49476], 2 X[17389] - 3 X[29574], X[17389] + 3 X[29617], 7 X[17389] - 15 X[29622], X[29574] + 2 X[29617], 7 X[29574] - 10 X[29622], 7 X[29617] + 5 X[29622], X[37] + 2 X[4399], X[75] + 2 X[3686], 2 X[75] + X[4416], 5 X[75] + X[17347], 3 X[75] - X[49722], 4 X[3686] - X[4416], 10 X[3686] - X[17347], 6 X[3686] + X[49722], 5 X[4416] - 2 X[17347], 3 X[4416] + 2 X[49722], 5 X[17346] - X[17347], 3 X[17346] + X[49722], 3 X[17347] + 5 X[49722], 3 X[4688] - 2 X[49733], 2 X[3696] + X[3883], 3 X[17330] - X[49742], X[1278] + 5 X[17331], 2 X[3664] - 5 X[4699], 2 X[3664] + X[17363], 5 X[4699] + X[17363], 4 X[3739] - X[3879], 2 X[3739] + X[17362], X[3879] + 2 X[17362], X[4686] + 2 X[17332], 4 X[4698] - X[17388], 2 X[4726] + X[17334], 4 X[4739] - X[17365], 7 X[4751] - X[17377], 7 X[4772] - X[17364], 3 X[16590] - 2 X[49737], 2 X[17390] - 5 X[31238]

X(50095) lies on these lines: {1, 2}, {6, 4967}, {9, 4431}, {37, 4399}, {44, 4665}, {63, 5011}, {69, 4034}, {75, 527}, {85, 553}, {99, 333}, {142, 319}, {190, 3707}, {192, 28313}, {193, 25590}, {210, 14839}, {226, 4886}, {241, 25719}, {321, 4115}, {335, 49510}, {344, 4007}, {355, 36731}, {391, 3729}, {516, 27484}, {517, 36728}, {518, 27478}, {524, 4688}, {528, 3696}, {536, 17330}, {538, 42051}, {594, 17348}, {673, 24393}, {728, 42032}, {903, 35177}, {966, 3875}, {1086, 4690}, {1213, 4852}, {1266, 4643}, {1278, 17331}, {1386, 4733}, {1573, 3666}, {1654, 3663}, {2094, 14552}, {2321, 5564}, {2325, 17335}, {2796, 31349}, {3219, 5540}, {3496, 3929}, {3578, 20880}, {3620, 4859}, {3664, 4699}, {3739, 3879}, {3758, 4700}, {3759, 5750}, {3765, 20888}, {3797, 4709}, {3886, 47357}, {3946, 5224}, {3950, 17260}, {3966, 31140}, {3975, 4044}, {3986, 17319}, {3993, 31323}, {3997, 32911}, {4000, 17270}, {4021, 17248}, {4042, 24586}, {4054, 37656}, {4058, 17280}, {4060, 6666}, {4102, 32008}, {4301, 7384}, {4357, 4361}, {4359, 30806}, {4360, 5257}, {4364, 4405}, {4395, 17237}, {4398, 17328}, {4402, 5232}, {4445, 17278}, {4461, 25728}, {4464, 16777}, {4472, 16666}, {4478, 17231}, {4480, 4659}, {4545, 17234}, {4654, 6604}, {4664, 17133}, {4670, 4969}, {4686, 17332}, {4698, 17388}, {4708, 17395}, {4715, 49727}, {4726, 17334}, {4739, 17365}, {4740, 17132}, {4741, 4887}, {4751, 17377}, {4755, 28329}, {4758, 4982}, {4772, 17364}, {4785, 27855}, {4795, 15534}, {4844, 47783}, {4848, 41245}, {4856, 17379}, {4875, 25083}, {4888, 20080}, {4901, 38097}, {4980, 14213}, {5243, 46176}, {5258, 21511}, {5325, 41006}, {5563, 25946}, {5739, 31164}, {5814, 17528}, {5839, 10436}, {5853, 27474}, {5881, 36698}, {6996, 11362}, {7227, 16669}, {7263, 17344}, {7406, 7991}, {7982, 36662}, {8584, 10022}, {8666, 11329}, {8715, 16367}, {12513, 16412}, {12625, 37169}, {14033, 48812}, {14555, 31142}, {15533, 31139}, {16054, 24391}, {16590, 28309}, {16706, 32025}, {17067, 17227}, {17121, 28604}, {17144, 30830}, {17151, 17257}, {17160, 17256}, {17229, 17337}, {17239, 17366}, {17242, 25072}, {17245, 17372}, {17259, 17299}, {17271, 37756}, {17286, 37650}, {17287, 21255}, {17296, 38093}, {17298, 32099}, {17320, 31144}, {17343, 48627}, {17349, 17355}, {17352, 48630}, {17356, 48635}, {17357, 48636}, {17373, 27147}, {17374, 34824}, {17390, 31238}, {17398, 28633}, {17772, 31306}, {17868, 21078}, {18821, 35148}, {19723, 48864}, {19796, 41816}, {19797, 41258}, {20131, 49497}, {20132, 49685}, {20135, 49680}, {20142, 49482}, {20154, 32941}, {20156, 49460}, {20223, 30625}, {20913, 25298}, {20919, 33941}, {21873, 24058}, {22165, 31138}, {24177, 37653}, {24357, 49756}, {24387, 26019}, {25125, 30819}, {27481, 28522}, {27489, 28234}, {27640, 41418}, {28301, 49748}, {28337, 49738}, {28512, 31329}, {28538, 49725}, {30090, 34282}, {30854, 33938}, {32029, 42334}, {32986, 48807}, {33298, 43035}, {35263, 46918}, {37416, 43174}, {40093, 43262}, {50046, 50057}

X(50095) = complement of X(17389)
X(50095) = midpoint of X(i) and X(j) for these {i,j}: {2, 29617}, {75, 17346}, {4399, 49731}, {4740, 17333}, {17362, 17392}
X(50095) = reflection of X(i) in X(j) for these {i,j}: {37, 49731}, {3879, 17392}, {4416, 17346}, {17346, 3686}, {17392, 3739}, {29574, 2}
X(50095) = X(28903)-anticomplementary conjugate of X(513)
X(50095) = X(28868)-complementary conjugate of X(513)
X(50095) = barycentric product X(i)*X(j) for these {i,j}: {75, 15254}, {668, 47811}
X(50095) = barycentric quotient X(i)/X(j) for these {i,j}: {15254, 1}, {47811, 513}
X(50095) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3679, 48802}, {2, 8, 17294}, {2, 3241, 29597}, {2, 6542, 29575}, {2, 16833, 41140}, {2, 17294, 3912}, {2, 17310, 29600}, {2, 29575, 29571}, {2, 29577, 41141}, {2, 29584, 551}, {2, 29615, 29594}, {2, 40891, 29584}, {6, 28634, 4967}, {8, 4384, 3912}, {9, 42696, 4431}, {10, 239, 17023}, {75, 3686, 4416}, {391, 32087, 3729}, {551, 49543, 29584}, {594, 17348, 17353}, {966, 4371, 3875}, {1125, 50019, 4393}, {1654, 17117, 3663}, {2321, 17277, 25101}, {3008, 3626, 3661}, {3008, 3661, 29596}, {3617, 5222, 17308}, {3621, 5308, 29605}, {3625, 16815, 29601}, {3625, 29571, 6542}, {3626, 16816, 29596}, {3632, 16832, 17316}, {3632, 17316, 49761}, {3661, 16816, 3008}, {3679, 16833, 2}, {3739, 17362, 3879}, {3975, 17143, 4044}, {4060, 6666, 17233}, {4361, 17251, 17301}, {4361, 17275, 4357}, {4384, 17294, 2}, {4393, 29576, 1125}, {4402, 5232, 17304}, {4643, 17119, 1266}, {4669, 29594, 29615}, {4678, 24599, 29611}, {4691, 29604, 29593}, {4699, 17363, 3664}, {4701, 31211, 49765}, {4701, 49765, 20055}, {5564, 17277, 2321}, {6542, 16815, 29571}, {6542, 29571, 29601}, {9780, 17014, 29603}, {16815, 29575, 2}, {16826, 20016, 3244}, {17244, 20055, 49765}, {17251, 17301, 4357}, {17275, 17301, 17251}, {17292, 29590, 31191}, {17349, 48628, 17355}, {17367, 29593, 29604}, {24603, 49770, 1}, {29584, 40891, 49543}, {31211, 49765, 17244}, {40713, 40714, 4847}


X(50096) = X(2)X(740)∩X(10)X(536)

Barycentrics    a^2*b - 2*a*b^2 + a^2*c - 6*a*b*c - 5*b^2*c - 2*a*c^2 - 5*b*c^2 : :
X(50096) = 2 X[8] + X[49491], 4 X[10] - X[49456], X[75] + 2 X[4732], 5 X[75] + X[49448], 2 X[75] + X[49457], 11 X[75] + X[49501], 7 X[75] - X[49532], 5 X[3679] - X[49448], 11 X[3679] - X[49501], 7 X[3679] + X[49532], 10 X[4732] - X[49448], 4 X[4732] - X[49457], 22 X[4732] - X[49501], 14 X[4732] + X[49532], 2 X[49448] - 5 X[49457], 11 X[49448] - 5 X[49501], 7 X[49448] + 5 X[49532], 11 X[49457] - 2 X[49501], 7 X[49457] + 2 X[49532], 7 X[49501] + 11 X[49532], 2 X[3696] + X[24325], 5 X[3696] + X[49478], 5 X[4688] - X[49478], 5 X[24325] - 2 X[49478], 2 X[3739] + X[4709], 4 X[3739] - X[49471], 2 X[4709] + X[49471], 2 X[1125] + X[49468], X[3241] - 5 X[4699], 5 X[4699] + X[49459], 5 X[3617] + X[49493], 4 X[3626] - X[49449], 2 X[3626] + X[49483], X[49449] + 2 X[49483], 4 X[3634] - X[49462], 2 X[3842] - 3 X[19875], 2 X[3842] + X[49474], X[4664] - 3 X[19875], 3 X[19875] + X[49474], 5 X[4668] + X[49499], 7 X[4678] - X[49503], 5 X[4687] - 7 X[19876], 4 X[4691] - X[49515], 2 X[4726] + X[49520], 4 X[4739] + X[34641], 4 X[4739] - X[49479], 7 X[4751] - X[49469], 7 X[4772] + X[31145], 7 X[4772] - X[49490], 5 X[4821] + X[49517], 7 X[9780] - X[49452], 2 X[15569] - 3 X[19883], 3 X[25055] - X[49470], 3 X[38314] - 5 X[40328]

X(50096) lies on these lines: {2, 740}, {8, 24693}, {10, 536}, {37, 3828}, {75, 537}, {238, 20160}, {321, 4937}, {518, 3919}, {519, 3696}, {551, 3739}, {599, 49531}, {726, 4745}, {984, 4695}, {1125, 49468}, {1266, 4407}, {2796, 17330}, {3241, 4699}, {3617, 49493}, {3626, 49449}, {3634, 49462}, {3654, 29054}, {3661, 25351}, {3755, 48853}, {3821, 4733}, {3836, 29594}, {3842, 4664}, {3943, 25352}, {3993, 4755}, {4049, 4777}, {4085, 4967}, {4096, 42029}, {4202, 42437}, {4359, 31136}, {4363, 4753}, {4384, 4432}, {4457, 32771}, {4651, 31161}, {4660, 28634}, {4668, 49499}, {4670, 50018}, {4678, 49503}, {4687, 19876}, {4690, 24692}, {4691, 49515}, {4693, 16815}, {4716, 29584}, {4726, 49520}, {4739, 34641}, {4751, 49469}, {4772, 31145}, {4783, 20913}, {4821, 49517}, {4974, 16469}, {4980, 42054}, {5625, 49486}, {5883, 44671}, {9780, 49452}, {15569, 19883}, {16666, 50021}, {16825, 48805}, {17117, 49472}, {17119, 36480}, {17160, 36531}, {17301, 48809}, {17346, 28558}, {17530, 21926}, {19804, 31137}, {21927, 44847}, {24342, 46922}, {24452, 31317}, {24715, 31349}, {25055, 49470}, {25590, 49497}, {28538, 49481}, {29615, 31151}, {32921, 48854}, {32941, 35227}, {33072, 41821}, {34824, 49764}, {35025, 35173}, {38314, 40328}

X(50096) = midpoint of X(i) and X(j) for these {i,j}: {8, 31178}, {75, 3679}, {551, 4709}, {599, 49531}, {984, 4740}, {3241, 49459}, {3696, 4688}, {4664, 49474}, {24715, 31349}, {31145, 49490}, {34641, 49479}
X(50096) = reflection of X(i) in X(j) for these {i,j}: {37, 3828}, {551, 3739}, {3679, 4732}, {3993, 4755}, {4664, 3842}, {24325, 4688}, {49457, 3679}, {49471, 551}, {49491, 31178}
X(50096) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 4732, 49457}, {3626, 49483, 49449}, {3739, 4709, 49471}, {4664, 19875, 3842}, {19875, 49474, 4664}


X(50097) = X(2)X(594)∩X(6)X(28337)

Barycentrics    2*a*b - 3*b^2 + 2*a*c - 4*b*c - 3*c^2 : :
X(50097) = X[141] + 2 X[2321], 5 X[141] - 2 X[3663], X[141] - 4 X[17229], 7 X[141] - 4 X[17235], 5 X[2321] + X[3663], X[2321] + 2 X[17229], 7 X[2321] + 2 X[17235], 4 X[2321] + X[49741], X[3663] - 10 X[17229], 7 X[3663] - 10 X[17235], X[3663] - 5 X[29594], 4 X[3663] - 5 X[49741], 7 X[17229] - X[17235], 8 X[17229] - X[49741], 2 X[17235] - 7 X[29594], 8 X[17235] - 7 X[49741], 4 X[29594] - X[49741], 4 X[3773] - X[49524], 2 X[17294] + X[49726], 2 X[4535] + X[49560], 2 X[3589] - 5 X[17286], 2 X[3589] + X[17299], X[16834] - 5 X[17286], 5 X[17286] + X[17299], X[3629] - 4 X[17355], X[3629] + 2 X[17372], 2 X[17355] + X[17372], X[3630] + 2 X[17351], 2 X[3631] + X[3729], 2 X[3844] + X[4133], X[3875] - 4 X[34573], 3 X[21356] - X[49747]

X(50097) lies on these lines: {2, 594}, {6, 28337}, {8, 4422}, {9, 4478}, {10, 4755}, {37, 48636}, {69, 28333}, {75, 29577}, {141, 536}, {192, 48635}, {319, 17340}, {346, 4445}, {519, 597}, {524, 17281}, {527, 22165}, {537, 4535}, {545, 599}, {740, 48821}, {1086, 4740}, {1213, 17242}, {1278, 48632}, {2325, 4690}, {2345, 17309}, {2901, 50058}, {3008, 4405}, {3589, 16834}, {3629, 17355}, {3630, 17351}, {3631, 3729}, {3644, 48634}, {3661, 3943}, {3679, 3932}, {3703, 31136}, {3739, 4058}, {3844, 4133}, {3875, 34573}, {3912, 4665}, {3950, 17239}, {4007, 4399}, {4029, 4708}, {4060, 17348}, {4072, 4681}, {4363, 29616}, {4370, 17346}, {4395, 17284}, {4431, 7263}, {4461, 7232}, {4472, 17316}, {4643, 4873}, {4659, 7238}, {4669, 30331}, {4670, 49765}, {4677, 33165}, {4686, 48631}, {4720, 30906}, {4725, 8584}, {4726, 21255}, {4727, 17023}, {4733, 19875}, {4764, 48633}, {4798, 29602}, {4851, 7227}, {4966, 31178}, {4969, 17354}, {5564, 17268}, {5846, 48805}, {6172, 36522}, {6535, 31161}, {6542, 17369}, {7228, 17296}, {7231, 17376}, {7277, 17373}, {9055, 27474}, {10022, 17310}, {15569, 48853}, {16666, 49761}, {16672, 25358}, {17119, 29579}, {17133, 17382}, {17160, 29587}, {17228, 17246}, {17240, 17245}, {17247, 48640}, {17251, 49737}, {17264, 17330}, {17265, 32087}, {17271, 49742}, {17274, 28297}, {17280, 17362}, {17287, 17334}, {17289, 17388}, {17292, 17395}, {17295, 17365}, {17297, 49727}, {17301, 20582}, {17303, 29597}, {17313, 49733}, {17315, 17398}, {17318, 29611}, {17342, 29617}, {17786, 27792}, {21085, 42056}, {21356, 49747}, {24044, 24076}, {25350, 31027}, {28329, 48310}, {29573, 49738}, {29618, 41847}, {34641, 49693}

X(50097) = midpoint of X(i) and X(j) for these {i,j}: {69, 49721}, {2321, 29594}, {16834, 17299}, {17281, 17294}
X(50097) = reflection of X(i) in X(j) for these {i,j}: {141, 29594}, {597, 17359}, {16834, 3589}, {17301, 20582}, {29594, 17229}, {49726, 17281}, {49741, 141}
X(50097) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 17269, 4422}, {346, 4445, 17332}, {594, 17233, 17243}, {2321, 17229, 141}, {2345, 17309, 17390}, {3661, 3943, 4364}, {3679, 41313, 49731}, {3912, 4665, 34824}, {4007, 17279, 4399}, {4431, 17231, 7263}, {5564, 17268, 17337}, {17119, 29579, 40480}, {17240, 48628, 17245}, {17242, 48630, 1213}, {17264, 29615, 17330}, {17286, 17299, 3589}, {17293, 17314, 17045}, {17354, 20055, 4969}, {17355, 17372, 3629}


X(50098) = X(2)X(594)∩X(8)X(599)

Barycentrics    2*a^2 - b^2 - 6*b*c - c^2 : :
X(50098) = X[75] + 2 X[4399], 5 X[75] - 2 X[7228], 2 X[75] + X[17362], 5 X[75] + X[17363], 7 X[75] - X[17364], 4 X[75] - X[17365], 5 X[4399] + X[7228], 4 X[4399] - X[17362], 10 X[4399] - X[17363], 14 X[4399] + X[17364], 8 X[4399] + X[17365], 4 X[4399] + X[49727], 4 X[7228] + 5 X[17362], 2 X[7228] + X[17363], 14 X[7228] - 5 X[17364], 8 X[7228] - 5 X[17365], 2 X[7228] + 5 X[29617], 4 X[7228] - 5 X[49727], 5 X[17362] - 2 X[17363], 7 X[17362] + 2 X[17364], 2 X[17362] + X[17365], 7 X[17363] + 5 X[17364], 4 X[17363] + 5 X[17365], X[17363] - 5 X[29617], 2 X[17363] + 5 X[49727], 4 X[17364] - 7 X[17365], X[17364] + 7 X[29617], 2 X[17364] - 7 X[49727], X[17365] + 4 X[29617], 2 X[29617] + X[49727], 5 X[4740] + 3 X[17488], 5 X[17346] - 3 X[17488], X[1278] + 2 X[17332], 2 X[3686] + X[4686], 4 X[3686] - X[17334], 2 X[4686] + X[17334], 4 X[3739] - X[17388], X[3879] - 4 X[4739], X[4416] + 2 X[4726], 5 X[4664] - 9 X[41848], 9 X[41848] - 10 X[49731], 5 X[4699] - 2 X[17390], 7 X[4751] - 5 X[29622], X[4764] + 5 X[17331], 7 X[4772] - X[17377], 5 X[4821] + X[17347]

X(50098) lies on these lines: {2, 594}, {6, 4371}, {7, 15533}, {8, 599}, {10, 17395}, {37, 17133}, {75, 524}, {141, 5564}, {192, 49737}, {239, 597}, {319, 7263}, {519, 3696}, {536, 17330}, {545, 4740}, {591, 32798}, {740, 49740}, {894, 8584}, {1100, 49543}, {1213, 3875}, {1266, 4690}, {1278, 17332}, {1991, 32797}, {1992, 4363}, {2321, 17337}, {2345, 47352}, {3058, 42446}, {3589, 48628}, {3617, 17325}, {3625, 17374}, {3626, 17237}, {3629, 17116}, {3630, 7321}, {3631, 48627}, {3632, 4675}, {3661, 4395}, {3662, 4478}, {3679, 7174}, {3686, 4686}, {3705, 22110}, {3739, 17388}, {3758, 20583}, {3759, 7227}, {3763, 4402}, {3782, 31143}, {3879, 4739}, {3943, 4384}, {4000, 21358}, {4007, 17278}, {4034, 17276}, {4058, 17357}, {4060, 17231}, {4364, 17160}, {4393, 4472}, {4416, 4726}, {4422, 16816}, {4431, 17340}, {4445, 21356}, {4452, 17253}, {4461, 16885}, {4464, 28639}, {4664, 28309}, {4670, 49770}, {4677, 6173}, {4699, 17390}, {4727, 29571}, {4733, 32921}, {4751, 29622}, {4764, 17331}, {4772, 17377}, {4821, 17347}, {4852, 4967}, {4864, 4923}, {5434, 7235}, {5839, 7277}, {5846, 49720}, {6144, 7222}, {6542, 34824}, {6707, 17393}, {7081, 11168}, {7172, 42850}, {7238, 17360}, {8370, 33941}, {10022, 40891}, {11160, 42697}, {16666, 50019}, {16706, 48636}, {16833, 16970}, {17151, 17246}, {17230, 40480}, {17245, 17299}, {17271, 49741}, {17287, 48631}, {17289, 48310}, {17315, 29620}, {17333, 28297}, {17359, 41140}, {17372, 24199}, {17378, 28337}, {17389, 49738}, {19723, 50043}, {28333, 49722}, {29621, 31244}, {31138, 34641}, {31139, 31145}, {31995, 40341}, {34362, 45213}, {34573, 48630}, {37654, 49721}, {37674, 41915}, {48830, 49486}

X(50098) = midpoint of X(i) and X(j) for these {i,j}: {75, 29617}, {1278, 49748}, {4740, 17346}, {17362, 49727}
X(50098) = reflection of X(i) in X(j) for these {i,j}: {192, 49737}, {4664, 49731}, {17362, 29617}, {17365, 49727}, {17378, 49733}, {17388, 29574}, {17389, 49738}, {17392, 4688}, {29574, 3739}, {29617, 4399}, {49727, 75}, {49742, 17330}, {49748, 17332}
X(50098) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 17119, 1086}, {75, 4399, 17362}, {75, 17362, 17365}, {75, 17363, 7228}, {239, 4665, 17369}, {594, 4361, 17366}, {3686, 4686, 17334}, {3875, 28634, 1213}, {4361, 42696, 594}, {4371, 32087, 6}, {4405, 4665, 239}, {4431, 17348, 17340}, {4852, 4967, 17398}, {5564, 17117, 141}, {5564, 37756, 29615}, {5839, 17118, 7277}, {5839, 35578, 15534}, {15534, 17118, 35578}, {15534, 35578, 7277}, {17117, 29615, 37756}, {17151, 17275, 17246}, {29615, 37756, 141}


X(50099) = X(2)X(2321)∩X(75)X(519)

Barycentrics    2*a^2 + a*b - b^2 + a*c - 8*b*c - c^2 : :
X(50099) = 5 X[75] - 2 X[3664], 4 X[75] - X[3879], 7 X[75] - X[17377], 3 X[75] - X[17378], 7 X[75] - 3 X[39704], 8 X[3664] - 5 X[3879], 14 X[3664] - 5 X[17377], 6 X[3664] - 5 X[17378], 14 X[3664] - 15 X[39704], 7 X[3879] - 4 X[17377], 3 X[3879] - 4 X[17378], 7 X[3879] - 12 X[39704], 3 X[17377] - 7 X[17378], X[17377] - 3 X[39704], 7 X[17378] - 9 X[39704], 5 X[17330] - 3 X[49742], 4 X[4399] - X[4416], 2 X[4399] + X[4686], X[4416] + 2 X[4686], X[1278] + 2 X[3686], 4 X[3696] - X[49527], X[3883] + 2 X[49474], 3 X[4688] - 2 X[49738], 3 X[29574] - 4 X[49738], 2 X[4726] + X[17362], X[4718] - 3 X[16590], 4 X[4739] - X[17388], 5 X[4821] + X[17363], X[49466] + 2 X[49468]

X(50099) lies on these lines: {2, 2321}, {7, 31145}, {8, 1266}, {10, 17160}, {37, 28309}, {44, 4405}, {69, 4677}, {75, 519}, {142, 17310}, {307, 41803}, {314, 17195}, {319, 903}, {320, 3625}, {527, 4740}, {536, 17330}, {545, 4399}, {551, 4360}, {594, 17382}, {894, 40891}, {1100, 10022}, {1278, 3686}, {2325, 16816}, {3008, 17342}, {3241, 4464}, {3596, 4479}, {3626, 4389}, {3631, 36525}, {3632, 42697}, {3635, 41847}, {3662, 4060}, {3663, 4669}, {3679, 4357}, {3687, 27739}, {3696, 28503}, {3729, 4371}, {3758, 50019}, {3828, 4021}, {3883, 28580}, {3912, 17119}, {4029, 16815}, {4058, 16706}, {4072, 17263}, {4361, 4431}, {4363, 49770}, {4370, 17348}, {4395, 29596}, {4452, 17270}, {4545, 17343}, {4664, 28313}, {4665, 17023}, {4667, 20016}, {4675, 49761}, {4688, 4971}, {4691, 17250}, {4701, 4887}, {4715, 4726}, {4718, 16590}, {4725, 49727}, {4727, 29601}, {4739, 17388}, {4745, 5224}, {4795, 17118}, {4821, 17363}, {4851, 31139}, {4908, 25101}, {4980, 20234}, {7263, 31138}, {15492, 36522}, {17067, 17230}, {17132, 17346}, {17233, 41141}, {17275, 24441}, {17299, 17313}, {17318, 24603}, {17321, 19875}, {17392, 28329}, {17781, 21273}, {19883, 28653}, {29594, 37756}, {32099, 36588}, {46922, 49543}, {49466, 49468}, {49476, 49725}, {49690, 49750}

X(50099) = midpoint of X(i) and X(j) for these {i,j}: {1278, 17333}, {4740, 29617}
X(50099) = reflection of X(i) in X(j) for these {i,j}: {17333, 3686}, {29574, 4688}, {49476, 49725}
X(50099) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3663, 4669, 17271}, {3875, 32087, 4967}, {4361, 4431, 17353}, {4361, 17281, 41140}, {4399, 4686, 4416}, {4431, 41140, 17281}, {4701, 4887, 17360}, {4727, 34824, 29601}, {5564, 17271, 4669}, {17151, 42696, 4357}, {17281, 41140, 17353}


X(50100) = X(2)X(3950)∩X(141)X(536)

Barycentrics    5*a*b - 3*b^2 + 5*a*c - 10*b*c - 3*c^2 : :
X(50100) = 2 X[141] - 5 X[2321], 8 X[141] - 5 X[3663], 7 X[141] - 10 X[17229], 13 X[141] - 10 X[17235], 4 X[141] - 5 X[29594], 7 X[141] - 5 X[49741], 4 X[2321] - X[3663], 7 X[2321] - 4 X[17229], 13 X[2321] - 4 X[17235], 7 X[2321] - 2 X[49741], 7 X[3663] - 16 X[17229], 13 X[3663] - 16 X[17235], 7 X[3663] - 8 X[49741], 13 X[17229] - 7 X[17235], 8 X[17229] - 7 X[29594], 8 X[17235] - 13 X[29594], 14 X[17235] - 13 X[49741], 7 X[29594] - 4 X[49741], 8 X[4133] + X[4924], 5 X[4133] + X[49536], 5 X[4924] - 8 X[49536], 5 X[3729] + X[20080], X[6144] + 5 X[17299], X[6144] - 5 X[49721], 5 X[17281] - 3 X[47352]

X(50100) lies on these lines: {2, 3950}, {10, 4664}, {75, 4072}, {141, 536}, {190, 3625}, {192, 4058}, {346, 16833}, {519, 1992}, {527, 15533}, {537, 4527}, {551, 32922}, {599, 28301}, {740, 38191}, {1278, 21255}, {3008, 4873}, {3244, 46922}, {3664, 4461}, {3729, 20080}, {3840, 41142}, {3912, 4740}, {3943, 4688}, {3986, 48628}, {3993, 48853}, {4029, 4665}, {4060, 17262}, {4098, 4967}, {4480, 20055}, {4659, 4896}, {4667, 4727}, {4669, 33076}, {4677, 6172}, {4887, 29616}, {4898, 4909}, {4899, 31145}, {4971, 49543}, {6144, 17299}, {16834, 17355}, {17132, 17294}, {17133, 17281}, {17160, 31191}, {17346, 34641}, {17351, 28337}, {17359, 28309}, {17372, 28333}, {22165, 28322}, {24199, 29582}, {25072, 32087}, {28297, 41152}, {28329, 49726}, {28484, 48821}, {28554, 49511}, {31144, 38098}

X(50100) = midpoint of X(17299) and X(49721)
X(50100) = reflection of X(i) in X(j) for these {i,j}: {3663, 29594}, {16834, 17355}, {29594, 2321}, {49741, 17229}
X(50100) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4659, 49765, 4896}, {4898, 7229, 4909}


X(50101) = X(2)X(37)∩X(6)X(545)

Barycentrics    a^2 + 2*a*b + b^2 + 2*a*c - 4*b*c + c^2 : :
X(50101) = 5 X[2] - 4 X[17359], 3 X[2] - 4 X[17382], X[17281] - 3 X[17301], 5 X[17281] - 6 X[17359], 5 X[17301] - 2 X[17359], 3 X[17301] - 2 X[17382], 3 X[17359] - 5 X[17382], X[8] + 2 X[49453], X[69] - 4 X[3663], X[69] + 2 X[3875], 2 X[3663] + X[3875], 2 X[4780] + X[16496], 3 X[38314] - 2 X[48805], X[145] - 4 X[49463], X[193] - 4 X[4852], X[193] + 2 X[17276], 2 X[4852] + X[17276], X[24248] + 2 X[32921], 4 X[1386] - X[24280], 4 X[2321] - 7 X[3619], 2 X[2321] - 5 X[17304], 7 X[3619] - 10 X[17304], 5 X[3616] - 2 X[5695], 5 X[3616] - 4 X[48810], 5 X[3618] - 2 X[3729], 5 X[3618] - 8 X[3946], X[3729] - 4 X[3946], 5 X[3620] - 8 X[17235], 5 X[3620] - 2 X[17299], 4 X[17235] - X[17299], 7 X[3622] - 4 X[49484], 2 X[3755] + X[49446], 2 X[3874] + X[15076], X[3886] - 4 X[4353], 2 X[17294] - 3 X[21356], 4 X[17345] - X[20080], X[24695] - 4 X[49477], 3 X[47352] - 2 X[49726]

X(50101) lies on these lines: {1, 1266}, {2, 37}, {6, 545}, {7, 528}, {8, 4389}, {9, 41140}, {44, 20073}, {45, 4395}, {69, 519}, {86, 16711}, {89, 20092}, {141, 28309}, {144, 3759}, {145, 320}, {190, 5222}, {193, 4715}, {239, 4419}, {314, 16712}, {319, 31145}, {347, 17078}, {348, 11240}, {391, 17258}, {524, 49747}, {527, 1992}, {534, 18655}, {537, 49518}, {551, 4021}, {594, 17323}, {597, 28297}, {599, 4971}, {742, 27480}, {752, 24248}, {966, 17117}, {1086, 17313}, {1100, 4795}, {1386, 24280}, {1441, 11239}, {1444, 11194}, {1654, 4371}, {2321, 3619}, {2783, 5603}, {3161, 17352}, {3212, 34711}, {3244, 4887}, {3247, 24199}, {3262, 3673}, {3264, 18135}, {3596, 18145}, {3616, 5695}, {3617, 17250}, {3618, 3729}, {3620, 17235}, {3621, 17360}, {3622, 41847}, {3635, 4896}, {3662, 17310}, {3679, 4357}, {3755, 49446}, {3758, 4454}, {3834, 29583}, {3873, 44670}, {3874, 15076}, {3879, 4862}, {3886, 4353}, {3943, 17290}, {3945, 4373}, {3950, 17282}, {4025, 23757}, {4029, 17067}, {4217, 5262}, {4310, 49470}, {4329, 34611}, {4352, 17144}, {4361, 17246}, {4363, 17395}, {4364, 17119}, {4370, 17262}, {4393, 4440}, {4399, 17253}, {4402, 17277}, {4431, 17306}, {4460, 17377}, {4464, 34747}, {4470, 17397}, {4480, 16670}, {4648, 17319}, {4659, 17023}, {4665, 17325}, {4669, 17270}, {4675, 29585}, {4677, 17272}, {4689, 26245}, {4725, 11160}, {4734, 25568}, {4741, 20016}, {4768, 25602}, {4851, 31138}, {4858, 28827}, {4869, 17315}, {4873, 29596}, {4912, 5032}, {4916, 17375}, {4941, 24478}, {4945, 37651}, {4967, 19875}, {4970, 33144}, {5224, 32087}, {5232, 5564}, {5552, 23521}, {5749, 17380}, {5839, 6646}, {6172, 49748}, {6173, 29574}, {6604, 22464}, {7190, 36595}, {7222, 17379}, {7228, 16884}, {7229, 17381}, {7232, 17388}, {7263, 16777}, {8822, 28610}, {9436, 31146}, {9776, 34064}, {10022, 17045}, {10444, 28194}, {10521, 34639}, {10528, 17895}, {11112, 50072}, {11235, 41003}, {15533, 28337}, {15534, 28333}, {16475, 28526}, {16672, 34824}, {17116, 17396}, {17133, 17294}, {17139, 33296}, {17150, 42058}, {17220, 41846}, {17224, 17346}, {17227, 29616}, {17254, 29617}, {17255, 17362}, {17261, 37650}, {17273, 32099}, {17292, 26104}, {17305, 29611}, {17309, 48632}, {17311, 48631}, {17324, 48628}, {17335, 24599}, {17336, 37681}, {17345, 20080}, {17350, 17487}, {17361, 20049}, {17390, 36525}, {17861, 45701}, {18600, 30939}, {18697, 48803}, {19276, 50069}, {20043, 33066}, {21433, 26144}, {21606, 27545}, {24654, 32095}, {24695, 49477}, {25055, 25590}, {25101, 36911}, {26039, 29614}, {27191, 29627}, {27549, 49523}, {28313, 29594}, {28530, 38315}, {28555, 38047}, {28562, 33869}, {30479, 50066}, {31134, 33088}, {31151, 33149}, {31164, 42754}, {31178, 48830}, {31302, 49715}, {32922, 49746}, {35578, 46922}, {47352, 49726}, {48806, 48831}, {48856, 49720}

X(50101) = midpoint of X(i) and X(j) for these {i,j}: {3875, 17274}, {48829, 49453}
X(50101) = reflection of X(i) in X(j) for these {i,j}: {2, 17301}, {8, 48829}, {69, 17274}, {599, 49741}, {1992, 16834}, {5695, 48810}, {17274, 3663}, {17281, 17382}, {48806, 48831}, {49721, 597}
X(50101) = anticomplement of X(17281)
X(50101) = isotomic conjugate of the isogonal conjugate of X(16483)
X(50101) = X(13396)-anticomplementary conjugate of X(20295)
X(50101) = crossdifference of every pair of points on line {667, 9032}
X(50101) = barycentric product X(i)*X(j) for these {i,j}: {76, 16483}, {85, 3895}
X(50101) = barycentric quotient X(i)/X(j) for these {i,j}: {3895, 9}, {16483, 6}
X(50101) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1266, 42697}, {2, 346, 17342}, {2, 3672, 17320}, {2, 17320, 17321}, {2, 42044, 42032}, {7, 3241, 17378}, {75, 3672, 17321}, {75, 17320, 2}, {145, 4346, 320}, {192, 4000, 344}, {239, 17333, 37654}, {903, 4360, 17378}, {903, 17378, 7}, {1086, 17318, 17316}, {1278, 17302, 2345}, {2321, 17304, 3619}, {3644, 16706, 346}, {3663, 3875, 69}, {3672, 4452, 75}, {3729, 3946, 3618}, {3943, 17290, 29579}, {3945, 4373, 7321}, {4357, 17151, 42696}, {4360, 4398, 7}, {4360, 17378, 3241}, {4361, 17246, 17257}, {4361, 24441, 17330}, {4363, 17395, 26626}, {4389, 17160, 8}, {4393, 4440, 4644}, {4398, 17378, 903}, {4419, 37654, 17333}, {4454, 17014, 3758}, {4460, 21296, 17377}, {4664, 37756, 2}, {4688, 41312, 2}, {4764, 17289, 4461}, {4852, 17276, 193}, {5564, 17249, 5232}, {7263, 49738, 31139}, {7321, 17393, 3945}, {16706, 17342, 2}, {16777, 31139, 49738}, {17117, 17247, 966}, {17147, 19785, 345}, {17235, 17299, 3620}, {17246, 17330, 24441}, {17262, 17366, 26685}, {17281, 17301, 17382}, {17281, 17382, 2}, {17315, 48629, 4869}, {17319, 48627, 4648}, {17330, 24441, 17257}, {27754, 33129, 2}, {42051, 50068, 2}, {46922, 49722, 35578}


X(50102) = X(1)X(4442)∩X(2)X(37)

Barycentrics    a^3 + a^2*b + a*b^2 + b^3 + a^2*c - 2*b^2*c + a*c^2 - 2*b*c^2 + c^3 : :
X(50102) = X[3891] + 2 X[3914], 2 X[3891] + X[5014], 4 X[3914] - X[5014], X[3187] + 2 X[3782], 2 X[3187] + X[32859], 4 X[3782] - X[32859], 2 X[3791] + X[33098], 4 X[17061] - X[32929], X[32933] - 4 X[40940], 4 X[39544] - X[49687]

X(50102) lies on these lines: {1, 4442}, {2, 37}, {31, 2796}, {226, 31179}, {239, 33151}, {306, 17133}, {519, 3891}, {524, 3187}, {544, 16834}, {551, 24552}, {597, 26223}, {599, 17184}, {726, 33114}, {740, 27476}, {903, 40215}, {1056, 3241}, {1150, 3663}, {1255, 29622}, {1824, 24473}, {1836, 17150}, {1992, 5905}, {1999, 33146}, {3006, 49453}, {3120, 32921}, {3218, 4398}, {3219, 49748}, {3679, 4972}, {3759, 17484}, {3769, 33102}, {3771, 4933}, {3791, 28558}, {3875, 3936}, {3896, 33144}, {3920, 49720}, {3944, 32924}, {3946, 4054}, {3969, 25527}, {3977, 31229}, {4141, 4438}, {4360, 31019}, {4361, 26580}, {4362, 32950}, {4363, 29833}, {4365, 26128}, {4641, 4912}, {4654, 42045}, {4693, 29638}, {4716, 33065}, {4852, 31034}, {4854, 49740}, {4956, 7191}, {4970, 33127}, {5016, 17677}, {5222, 41241}, {5235, 17247}, {5249, 29574}, {5695, 26230}, {6327, 28538}, {7263, 26627}, {7321, 14996}, {13745, 50067}, {16704, 17276}, {17017, 48643}, {17061, 32929}, {17132, 32933}, {17135, 47358}, {17155, 33135}, {17160, 33077}, {17165, 47359}, {17299, 31017}, {17345, 31303}, {17367, 41242}, {17393, 37635}, {17528, 50072}, {17679, 23537}, {17763, 33149}, {17861, 20887}, {17889, 32928}, {18139, 23681}, {19281, 50073}, {20017, 28329}, {21020, 48809}, {21282, 49681}, {21283, 49465}, {24725, 49477}, {25496, 48642}, {26098, 48645}, {27081, 28634}, {27184, 29617}, {27186, 34064}, {27759, 29849}, {28516, 33161}, {28522, 33156}, {28534, 42058}, {28557, 35263}, {28562, 33094}, {29615, 32782}, {29631, 49493}, {29632, 49452}, {29658, 32845}, {29829, 49483}, {29830, 49462}, {29831, 49484}, {29832, 49463}, {31177, 32946}, {32775, 49474}, {32856, 49488}, {32860, 33152}, {32914, 33154}, {32915, 33147}, {32922, 33134}, {32925, 33132}, {32926, 33131}, {33088, 48646}, {33104, 49472}, {33115, 49445}, {33136, 49455}, {33139, 49447}, {33148, 49470}, {37633, 48627}, {37792, 40214}, {37798, 39126}, {39544, 49687}, {49735, 50066}

X(50102) = reflection of X(i) in X(j) for these {i,j}: {33114, 33128}, {33122, 33143}
X(50102) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3995, 41313}, {312, 19830, 33150}, {321, 19785, 32774}, {3120, 32921, 33070}, {3187, 3782, 32859}, {3772, 17147, 33113}, {3891, 3914, 5014}, {4362, 33145, 32950}, {19785, 30699, 321}, {24789, 41313, 2}, {27184, 29617, 31143}, {31993, 41311, 2}


X(50103) = X(1)X(3824)∩X(2)X(37)

Barycentrics    2*a^3 + a^2*b + a*b^2 + 2*b^3 + a^2*c - 2*b^2*c + a*c^2 - 2*b*c^2 + 2*c^3 : :
X(50103) = 2 X[3782] + X[4641], X[3782] + 2 X[40940], X[4641] - 4 X[40940], X[3744] + 2 X[3914], X[3744] - 4 X[17061], X[3914] + 2 X[17061]

X(50103) lies on these lines: {1, 3824}, {2, 37}, {6, 31164}, {31, 28534}, {44, 33151}, {63, 49747}, {210, 33132}, {226, 544}, {278, 38461}, {306, 4971}, {333, 17254}, {354, 33135}, {518, 33128}, {519, 2887}, {527, 3782}, {528, 3744}, {551, 49739}, {553, 34050}, {908, 17366}, {940, 6173}, {1086, 30684}, {1100, 31019}, {1104, 11114}, {1150, 17235}, {1155, 29658}, {1279, 33134}, {1386, 3120}, {1418, 37798}, {1738, 17602}, {1999, 17297}, {2003, 4654}, {2094, 37642}, {3006, 49463}, {3011, 4689}, {3017, 24473}, {3187, 4725}, {3241, 33073}, {3589, 4054}, {3663, 33996}, {3683, 33154}, {3689, 17725}, {3696, 32775}, {3706, 26128}, {3745, 17889}, {3755, 17724}, {3838, 17017}, {3875, 30811}, {3920, 21949}, {3936, 4852}, {3946, 5718}, {3967, 29850}, {3999, 11269}, {4003, 33140}, {4080, 41241}, {4383, 5526}, {4415, 26723}, {4442, 26230}, {4519, 29637}, {4640, 33145}, {4663, 32856}, {4670, 29833}, {4693, 29860}, {4702, 29638}, {4849, 33153}, {4892, 49477}, {5249, 17392}, {5262, 17577}, {5271, 17251}, {5294, 49726}, {5695, 29855}, {6679, 28542}, {6703, 49733}, {7191, 10707}, {7322, 19875}, {9629, 11238}, {10129, 17025}, {11111, 50065}, {11112, 23537}, {13161, 34606}, {13745, 50062}, {16418, 50066}, {16669, 17484}, {16700, 16742}, {16704, 17345}, {17013, 26738}, {17022, 38093}, {17064, 17599}, {17070, 29639}, {17117, 30832}, {17150, 48646}, {17276, 24597}, {17294, 25527}, {17304, 37660}, {17346, 27184}, {17348, 26580}, {17372, 31017}, {17389, 18134}, {17597, 31146}, {17605, 29821}, {19277, 25055}, {20106, 28313}, {20182, 25525}, {21241, 49472}, {21342, 33142}, {24177, 37634}, {24295, 48641}, {25391, 36923}, {28297, 44416}, {28322, 32933}, {28484, 33156}, {28530, 35263}, {28538, 31134}, {28555, 33161}, {28581, 33122}, {28582, 33114}, {29575, 34064}, {29631, 49483}, {29632, 49462}, {29654, 48643}, {29856, 49493}, {29857, 49453}, {29858, 49452}, {33115, 49523}, {33130, 37593}, {33136, 49465}, {33139, 49515}, {33148, 49478}, {33170, 49525}, {33175, 49468}, {37684, 48629}, {39595, 40688}

X(50103) = midpoint of X(33128) and X(33143)
X(50103) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 321, 17359}, {2, 4980, 50052}, {2, 17301, 3666}, {2, 19785, 17301}, {2, 19796, 42051}, {3772, 17301, 2}, {3772, 19785, 3666}, {3782, 40940, 4641}, {3914, 17061, 3744}, {4000, 17720, 16610}, {4442, 26230, 49484}, {16706, 37759, 30818}, {29658, 33149, 1155}, {33129, 33155, 37}, {33132, 33152, 210}, {33133, 33150, 3752}, {33135, 33147, 354}


X(50104) = X(2)X(37)∩X(10)X(3712)

Barycentrics    2*a^3 - a^2*b - a*b^2 + 2*b^3 - a^2*c + 2*b^2*c - a*c^2 + 2*b*c^2 + 2*c^3 : :
X(50104) = 2 X[306] + X[4641], X[306] + 2 X[44416], X[4641] - 4 X[44416], 2 X[3703] + X[3744], X[3782] - 4 X[20106]

X(50104) lies on these lines: {2, 37}, {10, 3712}, {31, 28538}, {38, 4141}, {42, 4933}, {44, 33077}, {55, 3679}, {57, 5525}, {63, 599}, {141, 3977}, {210, 33160}, {306, 524}, {333, 4595}, {354, 33158}, {518, 33156}, {519, 3703}, {544, 29594}, {597, 5294}, {908, 17340}, {940, 16785}, {1150, 17229}, {1155, 29674}, {1214, 34897}, {1279, 33089}, {1386, 32848}, {1992, 26065}, {2321, 35466}, {2796, 2887}, {3006, 49484}, {3187, 28329}, {3218, 17231}, {3219, 31143}, {3306, 17267}, {3683, 32778}, {3689, 33165}, {3695, 37539}, {3696, 33115}, {3706, 4438}, {3729, 30811}, {3745, 33092}, {3748, 33169}, {3749, 4677}, {3782, 17132}, {3844, 4414}, {3912, 37520}, {3929, 10319}, {3936, 17351}, {3967, 29846}, {4001, 22165}, {4003, 29637}, {4030, 4669}, {4062, 4663}, {4376, 4715}, {4427, 48647}, {4519, 33140}, {4640, 15523}, {4690, 4760}, {4693, 29861}, {4702, 33120}, {4849, 33166}, {4912, 32933}, {4914, 8616}, {4956, 29872}, {5233, 17339}, {5241, 25101}, {5249, 49727}, {5256, 47352}, {5291, 17294}, {5302, 20653}, {5325, 49724}, {5695, 29857}, {5718, 17355}, {5846, 35263}, {7283, 17677}, {7801, 25083}, {8299, 31136}, {9909, 20989}, {11111, 50046}, {11237, 48812}, {15492, 37656}, {16704, 17372}, {17133, 40940}, {17240, 37684}, {17261, 30832}, {17284, 17595}, {17285, 24627}, {17286, 37660}, {17299, 24597}, {17345, 31017}, {17528, 50049}, {17594, 19875}, {17599, 25055}, {17605, 27759}, {21342, 33173}, {21949, 29873}, {25697, 36923}, {26223, 31179}, {26230, 49463}, {27184, 49748}, {27739, 31142}, {27757, 41242}, {28204, 28464}, {28484, 33128}, {28534, 31134}, {28555, 33143}, {28581, 33114}, {28582, 33122}, {29574, 37595}, {29631, 49462}, {29632, 49483}, {29641, 49720}, {29855, 49453}, {29856, 49452}, {29858, 49493}, {31164, 49721}, {31445, 49723}, {32775, 49523}, {32780, 37593}, {33136, 49485}, {33139, 49468}, {33148, 49525}, {33163, 47359}, {33170, 49478}, {33171, 47358}, {33175, 49515}, {49735, 50051}

X(50104) = midpoint of X(33156) and X(33161)
X(50104) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17776, 41313}, {2, 28606, 41311}, {2, 41313, 44307}, {2, 42033, 3175}, {10, 3712, 4689}, {306, 44416, 4641}, {345, 32777, 3666}, {17279, 17740, 16610}, {17280, 32851, 30818}, {32779, 32849, 37}, {33157, 33168, 3752}, {33158, 33167, 354}, {33160, 33164, 210}


X(50105) = X(2)X(37)∩X(31)X(519)

Barycentrics    a^3 - a^2*b - a*b^2 + b^3 - a^2*c + 2*b^2*c - a*c^2 + 2*b*c^2 + c^3 : :
X(50105) = 4 X[306] - X[32859], 2 X[306] + X[32933], X[32859] + 2 X[32933], 4 X[3703] - X[5014], 2 X[3703] + X[32929], X[5014] + 2 X[32929], X[3187] - 4 X[44416], 2 X[4641] + X[20017]

X(50105) lies on these lines: {2, 37}, {8, 11111}, {31, 519}, {63, 544}, {81, 17389}, {100, 3790}, {190, 33077}, {306, 527}, {528, 3703}, {726, 33122}, {740, 33114}, {750, 6541}, {846, 3679}, {968, 48851}, {1150, 2321}, {1211, 49742}, {1962, 48822}, {2108, 31137}, {2796, 31134}, {2887, 28542}, {3006, 5695}, {3187, 4971}, {3218, 17233}, {3219, 17346}, {3416, 4427}, {3578, 3929}, {3685, 33089}, {3695, 11112}, {3702, 45700}, {3704, 34606}, {3705, 10707}, {3712, 26227}, {3729, 3936}, {3773, 4414}, {3782, 28297}, {3896, 33163}, {3923, 32848}, {4054, 30834}, {4062, 32935}, {4141, 31136}, {4365, 4438}, {4418, 33092}, {4442, 29857}, {4641, 4725}, {4676, 32842}, {4693, 33120}, {4696, 34619}, {4894, 34649}, {4933, 31161}, {4970, 26061}, {4981, 48802}, {5016, 7283}, {5235, 48628}, {5739, 6172}, {5741, 31142}, {6057, 6174}, {6173, 18139}, {6327, 28534}, {6535, 32916}, {7206, 25440}, {11239, 48806}, {13745, 50047}, {14996, 17315}, {15523, 32934}, {16418, 50041}, {16704, 17299}, {17012, 17354}, {17155, 33158}, {17184, 49747}, {17242, 37633}, {17243, 26627}, {17254, 32782}, {17262, 26580}, {17269, 17595}, {17276, 31017}, {17297, 32858}, {17318, 29833}, {17333, 31143}, {17336, 37656}, {17339, 37680}, {17351, 31034}, {17372, 31303}, {17528, 50044}, {18134, 49722}, {21283, 49485}, {24248, 48647}, {26034, 48648}, {26223, 49726}, {26230, 49453}, {28313, 40940}, {28516, 33143}, {28522, 33128}, {28538, 42058}, {29631, 49452}, {29632, 49493}, {29674, 32845}, {29829, 49462}, {29830, 49483}, {29831, 49463}, {29832, 49484}, {32775, 49445}, {32778, 32936}, {32855, 32930}, {32860, 33164}, {32862, 32932}, {32863, 35596}, {32915, 33167}, {32925, 33160}, {33115, 49474}, {33170, 49470}, {33175, 49447}, {36263, 49560}, {37540, 50000}

X(50105) = reflection of X(i) in X(j) for these {i,j}: {33114, 33161}, {33122, 33156}
X(50105) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17147, 17301}, {2, 17301, 32774}, {2, 50043, 4980}, {306, 32933, 32859}, {321, 345, 33113}, {346, 17740, 4358}, {2321, 3977, 1150}, {3666, 17359, 2}, {3703, 32929, 5014}, {3923, 32848, 33070}, {15523, 32934, 32950}, {17147, 32777, 32774}, {17301, 32777, 2}


X(50106) = X(1)X(39711)∩X(2)X(37)

Barycentrics    a^2*b + a*b^2 + a^2*c - a*b*c - 2*b^2*c + a*c^2 - 2*b*c^2 : :
X(50106) = 5 X[2] - 4 X[35652], 5 X[3175] - 6 X[35652], 4 X[3175] - 3 X[42044], X[3175] - 3 X[42051], 8 X[35652] - 5 X[42044], 2 X[35652] - 5 X[42051], X[42044] - 4 X[42051], 8 X[596] - 5 X[3889], 3 X[3681] - 4 X[4685], 2 X[4685] - 3 X[32860], 3 X[3873] - 4 X[42055], 3 X[17155] - 2 X[42055], 4 X[4096] - 3 X[32925]

X(50106) lies on these lines: {1, 39711}, {2, 37}, {8, 32950}, {38, 49474}, {42, 49493}, {63, 4921}, {81, 3875}, {88, 30567}, {210, 28555}, {239, 11352}, {304, 16711}, {306, 1266}, {314, 18601}, {320, 20017}, {354, 28484}, {519, 3868}, {528, 20243}, {538, 3578}, {553, 17133}, {596, 3889}, {726, 3681}, {740, 3873}, {756, 49445}, {894, 19738}, {903, 39700}, {908, 4052}, {982, 4365}, {1086, 32858}, {1213, 28651}, {1738, 32862}, {1836, 32842}, {2321, 33172}, {2895, 17276}, {2999, 41242}, {3120, 32855}, {3187, 17160}, {3219, 4361}, {3416, 33102}, {3662, 3969}, {3663, 32782}, {3679, 4642}, {3687, 33151}, {3696, 7226}, {3703, 33131}, {3705, 4442}, {3706, 4392}, {3712, 29681}, {3720, 49452}, {3729, 32911}, {3758, 45222}, {3773, 33125}, {3782, 33077}, {3891, 32932}, {3896, 24349}, {3914, 33089}, {3920, 49453}, {3923, 32924}, {3943, 40688}, {3966, 33100}, {3967, 4706}, {3980, 9347}, {3994, 16569}, {4062, 33103}, {4096, 28516}, {4113, 49513}, {4360, 42028}, {4362, 32845}, {4363, 17011}, {4384, 33761}, {4387, 7292}, {4398, 17184}, {4418, 32921}, {4430, 28581}, {4440, 32859}, {4454, 20043}, {4467, 23878}, {4651, 49447}, {4654, 36595}, {4659, 5256}, {4661, 28582}, {4716, 32912}, {4734, 46897}, {4762, 17161}, {4851, 26842}, {4852, 37685}, {4883, 49461}, {4956, 11238}, {4970, 32771}, {5262, 11354}, {5278, 17117}, {5333, 25590}, {5695, 7191}, {5839, 20078}, {5880, 33093}, {6535, 33174}, {6541, 25961}, {7263, 27186}, {7283, 11346}, {8025, 17393}, {9352, 17763}, {10129, 29849}, {11220, 29016}, {11359, 50041}, {11680, 49554}, {15523, 33149}, {16712, 33935}, {16751, 36900}, {16825, 32936}, {17018, 49483}, {17019, 17318}, {17024, 49484}, {17116, 19684}, {17118, 20182}, {17132, 17781}, {17140, 49470}, {17144, 18172}, {17247, 41809}, {17262, 27065}, {17275, 41821}, {17299, 32863}, {17329, 43990}, {17717, 48642}, {17786, 40013}, {17889, 32848}, {18139, 48627}, {18632, 41803}, {18662, 24635}, {19276, 50072}, {19870, 28612}, {20011, 49499}, {20068, 49450}, {20081, 25298}, {20292, 33088}, {20911, 48838}, {23155, 35104}, {24165, 28522}, {24248, 33075}, {24715, 32854}, {26037, 49456}, {26627, 34064}, {27783, 27790}, {28503, 34612}, {28554, 42054}, {28580, 34611}, {29814, 49462}, {29815, 49463}, {30568, 37687}, {31137, 42040}, {31161, 42043}, {32104, 40773}, {32778, 33145}, {32852, 32857}, {32861, 33098}, {32866, 33094}, {32914, 32934}, {32922, 32929}, {32940, 49488}, {32945, 49455}, {33128, 33167}, {33132, 33161}, {33143, 33160}, {33147, 33156}, {37549, 48862}, {37631, 49727}, {37676, 49533}, {41823, 46922}, {48815, 50042}, {48817, 50045}

X(50106) = reflection of X(i) in X(j) for these {i,j}: {2, 42051}, {3681, 32860}, {3873, 17155}, {32915, 24165}, {42044, 2}
X(50106) = anticomplement of X(3175)
X(50106) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {8690, 20295}, {34860, 21287}, {39956, 1330}
X(50106) = barycentric product X(75)*X(17749)
X(50106) = barycentric quotient X(17749)/X(1)
X(50106) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4740, 4980}, {75, 17147, 28606}, {306, 1266, 33146}, {321, 3210, 4850}, {345, 19789, 33129}, {1278, 3210, 321}, {3644, 19804, 3995}, {3666, 4686, 28605}, {3980, 32928, 9347}, {17160, 32939, 3187}, {17301, 50048, 2}, {17320, 19797, 2}, {17740, 30699, 33133}, {29849, 48643, 10129}, {37756, 42033, 2}


X(50107) = X(2)X(37)∩X(8)X(190)

Barycentrics    a^2 - 2*a*b + b^2 - 2*a*c + 4*b*c + c^2 : :
X(50107) = 3 X[2] - 4 X[17359], 5 X[2] - 4 X[17382], 3 X[17281] - X[17301], 3 X[17281] - 2 X[17359], 5 X[17281] - 2 X[17382], 5 X[17301] - 6 X[17382], 5 X[17359] - 3 X[17382], X[8] + 2 X[5695], X[69] - 4 X[2321], X[69] + 2 X[3729], 2 X[2321] + X[3729], X[145] - 4 X[49484], X[193] + 2 X[17299], X[193] - 4 X[17351], X[17299] + 2 X[17351], X[3751] + 2 X[4133], 2 X[3416] + X[24280], 5 X[3616] - 2 X[49453], 5 X[3618] - 2 X[3875], 5 X[3618] - 8 X[17355], X[3875] - 4 X[17355], 7 X[3619] - 4 X[3663], 7 X[3619] - 10 X[17286], 2 X[3663] - 5 X[17286], 5 X[3620] - 8 X[17229], 5 X[3620] - 2 X[17276], 4 X[17229] - X[17276], 7 X[3622] - 4 X[49463], 4 X[3678] - X[15076], 4 X[3773] - X[24248], 2 X[4527] + X[32935], 4 X[4535] - X[4655], 2 X[17274] - 3 X[21356], 3 X[21356] - 4 X[29594], 4 X[17372] - X[20080], 3 X[21358] - 2 X[49741], 3 X[38314] - 4 X[48810], 2 X[49485] + X[49688]

X(50107) lies on these lines: {2, 37}, {6, 4971}, {7, 17233}, {8, 190}, {9, 4431}, {45, 4665}, {69, 527}, {76, 646}, {86, 7229}, {141, 28297}, {144, 319}, {145, 3758}, {189, 4102}, {193, 4725}, {306, 31164}, {313, 30681}, {320, 4454}, {348, 4552}, {391, 5564}, {519, 1992}, {524, 49721}, {534, 17781}, {545, 599}, {594, 17251}, {597, 28309}, {894, 17314}, {903, 39749}, {966, 17261}, {984, 48802}, {1086, 17269}, {1266, 17284}, {1332, 4513}, {1654, 25269}, {1930, 30701}, {2094, 32939}, {2325, 4384}, {2550, 3790}, {2783, 5657}, {3161, 17277}, {3241, 28503}, {3264, 28809}, {3416, 24280}, {3616, 49453}, {3617, 17256}, {3618, 3875}, {3619, 3663}, {3620, 17229}, {3622, 49463}, {3661, 4419}, {3664, 4072}, {3678, 15076}, {3679, 3717}, {3681, 44670}, {3685, 47357}, {3686, 25728}, {3687, 31142}, {3695, 17528}, {3696, 27549}, {3702, 11240}, {3703, 31140}, {3704, 11236}, {3731, 4967}, {3773, 24248}, {3912, 4659}, {3943, 4363}, {3945, 17315}, {3950, 10436}, {3969, 5905}, {3974, 32932}, {3993, 48822}, {4007, 4416}, {4029, 16831}, {4044, 4494}, {4054, 30828}, {4058, 17270}, {4346, 17227}, {4360, 5749}, {4361, 17340}, {4365, 33163}, {4371, 17349}, {4373, 48629}, {4385, 34619}, {4389, 29611}, {4398, 17285}, {4399, 16885}, {4402, 17352}, {4421, 8424}, {4422, 17119}, {4440, 17230}, {4445, 17334}, {4464, 16667}, {4470, 16826}, {4472, 16672}, {4473, 16816}, {4488, 17347}, {4527, 32935}, {4535, 4655}, {4562, 36222}, {4643, 20073}, {4644, 6542}, {4648, 17116}, {4667, 29605}, {4670, 29585}, {4673, 32034}, {4675, 29583}, {4693, 36479}, {4715, 11160}, {4733, 9791}, {4748, 29593}, {4869, 7321}, {4910, 16668}, {4916, 20090}, {5032, 28329}, {5222, 17160}, {5232, 17258}, {5263, 48856}, {5839, 17350}, {6535, 26034}, {6554, 33938}, {6707, 16674}, {7222, 17300}, {7227, 16777}, {7228, 17311}, {7263, 17267}, {7283, 11111}, {10707, 33089}, {11112, 50044}, {11113, 50041}, {15533, 28333}, {15534, 28337}, {16670, 49770}, {16676, 24603}, {16814, 28634}, {16823, 38025}, {16834, 17133}, {17079, 40704}, {17117, 17339}, {17118, 17243}, {17132, 17274}, {17151, 17353}, {17224, 17378}, {17234, 31995}, {17246, 17293}, {17253, 48636}, {17255, 48635}, {17268, 48627}, {17271, 49748}, {17295, 21296}, {17309, 17365}, {17313, 49727}, {17318, 17369}, {17333, 29615}, {17361, 20059}, {17372, 20080}, {17373, 31300}, {17397, 26039}, {17487, 39345}, {17579, 50045}, {17762, 25242}, {17786, 44147}, {18816, 32041}, {19853, 32026}, {20009, 50054}, {20055, 20072}, {20895, 20927}, {21358, 49741}, {22003, 24044}, {24199, 38093}, {26104, 29613}, {28472, 38315}, {28484, 38047}, {29617, 37654}, {29624, 41847}, {30414, 46176}, {31145, 49698}, {32882, 40014}, {32934, 48644}, {33677, 42048}, {34603, 49719}, {36494, 38053}, {36588, 36807}, {36796, 36916}, {38092, 39570}, {38314, 48810}, {48849, 49746}, {49485, 49688}

X(50107) = anticomplement of X(17301)
X(50107) = midpoint of X(3729) and X(17294)
X(50107) = reflection of X(i) in X(j) for these {i,j}: {2, 17281}, {6, 49726}, {69, 17294}, {3241, 48805}, {17274, 29594}, {17294, 2321}, {17301, 17359}, {49747, 141}
X(50107) = X(i)-isoconjugate of X(j) for these (i,j): {604, 34919}, {649, 14074}
X(50107) = X(i)-Dao conjugate of X(j) for these (i,j): {3161, 34919}, {4860, 34522}, {5375, 14074}
X(50107) = trilinear pole of line {14077, 47787}
X(50107) = barycentric product X(i)*X(j) for these {i,j}: {190, 47787}, {312, 8545}, {346, 1996}, {668, 14077}, {3596, 37541}, {3699, 30181}, {5423, 47386}
X(50107) = barycentric quotient X(i)/X(j) for these {i,j}: {8, 34919}, {100, 14074}, {1996, 279}, {8545, 57}, {14077, 513}, {15346, 4860}, {30181, 3676}, {37541, 56}, {46644, 34056}, {47386, 479}, {47787, 514}
X(50107) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 346, 17264}, {2, 3672, 17399}, {2, 17264, 344}, {8, 6172, 17346}, {9, 4431, 42696}, {75, 312, 37788}, {75, 346, 344}, {75, 17264, 2}, {190, 17346, 6172}, {192, 2345, 17321}, {344, 37788, 1997}, {346, 4461, 75}, {594, 17262, 17257}, {594, 49742, 17251}, {1086, 17269, 29579}, {1278, 17280, 4000}, {2321, 3729, 69}, {3161, 32087, 17277}, {3175, 50048, 2}, {3644, 17289, 3672}, {3663, 17286, 3619}, {3875, 17355, 3618}, {3912, 4659, 42697}, {3943, 4363, 17316}, {4361, 17340, 26685}, {4454, 29616, 320}, {4488, 32099, 17347}, {4659, 4873, 3912}, {4671, 17740, 28808}, {4688, 4908, 41313}, {4688, 41313, 2}, {4764, 16706, 4452}, {5564, 17336, 391}, {7321, 17240, 4869}, {17116, 17242, 4648}, {17117, 17339, 37650}, {17160, 17354, 5222}, {17229, 17276, 3620}, {17233, 49722, 17297}, {17251, 17262, 49742}, {17251, 49742, 17257}, {17258, 48630, 5232}, {17261, 48628, 966}, {17274, 29594, 21356}, {17281, 17301, 17359}, {17289, 17399, 2}, {17297, 49722, 7}, {17299, 17351, 193}, {17301, 17359, 2}, {17318, 17369, 26626}, {17342, 37756, 2}, {42029, 42033, 2}


X(50108) = X(2)X(3950)∩X(69)X(519)

Barycentrics    4*a^2 + 5*a*b + b^2 + 5*a*c - 10*b*c + c^2 : :
X(50108) = 2 X[69] - 5 X[3663], X[69] + 5 X[3875], 3 X[69] - 5 X[17274], X[3663] + 2 X[3875], 3 X[3663] - 2 X[17274], 3 X[3875] + X[17274], 2 X[15534] - 5 X[49543], 7 X[597] - 5 X[49726], 5 X[4852] - 2 X[32455], 5 X[2321] - 8 X[34573], 5 X[17382] - 4 X[34573], 10 X[3946] - 7 X[47355], 5 X[17281] - 7 X[47355], X[4924] + 2 X[49446], 3 X[5032] - 5 X[16834], 5 X[17301] - 3 X[21358], 6 X[21358] - 5 X[29594]

X(50108) lies on these lines: {2, 3950}, {6, 28301}, {10, 17160}, {69, 519}, {75, 551}, {145, 4887}, {192, 41140}, {527, 15534}, {536, 597}, {545, 4852}, {903, 3879}, {1266, 3244}, {2321, 17382}, {3241, 3664}, {3625, 4389}, {3633, 4346}, {3635, 42697}, {3668, 41803}, {3672, 3679}, {3686, 24441}, {3755, 28503}, {3828, 17321}, {3945, 36588}, {3946, 17281}, {3986, 17117}, {4000, 41141}, {4029, 4395}, {4058, 17302}, {4060, 17323}, {4072, 16706}, {4357, 4669}, {4370, 4718}, {4398, 4464}, {4402, 25072}, {4416, 40891}, {4419, 50019}, {4460, 4862}, {4656, 27776}, {4726, 10022}, {4745, 42696}, {4908, 17366}, {4909, 31995}, {4924, 49446}, {5032, 16834}, {5224, 38098}, {8584, 28322}, {17121, 17487}, {17133, 17301}, {17271, 34641}, {17272, 31145}, {17310, 21255}, {17318, 29571}, {17342, 31191}, {17376, 36525}, {17388, 31138}, {19875, 32087}, {20049, 21296}, {25590, 38314}, {28329, 49741}, {28484, 48810}, {28580, 32921}, {29600, 37756}, {36911, 37650}

X(50108) = reflection of X(i) in X(j) for these {i,j}: {2321, 17382}, {17281, 3946}, {29594, 17301}
X(50108) = {X(1266),X(3244)}-harmonic conjugate of X(4896)


X(50109) = X(2)X(2321)∩X(6)X(17132)

Barycentrics    4*a^2 + 3*a*b + b^2 + 3*a*c - 6*b*c + c^2 : :
X(50109) = 7 X[2] - 5 X[17286], X[2321] + 2 X[3875], X[2321] - 4 X[3946], 7 X[2321] - 10 X[17286], X[3875] + 2 X[3946], 7 X[3875] + 5 X[17286], 14 X[3946] - 5 X[17286], X[599] - 3 X[17301], X[3755] + 2 X[32921], 2 X[4353] + X[49486], X[3663] + 2 X[4852], 5 X[3663] - 2 X[17345], 5 X[4852] + X[17345], 2 X[17345] + 5 X[49543], X[1992] - 3 X[16834], 5 X[597] - 3 X[49726], X[3244] + 2 X[4743], X[3886] - 3 X[38314], X[4133] - 3 X[19883], 2 X[4527] - 5 X[19862], X[4740] + 3 X[27480], X[4780] + 2 X[49472], 2 X[4856] + X[17276], 3 X[17382] - 2 X[20582], 4 X[20582] - 3 X[29594], X[5695] - 3 X[38023], X[11160] - 3 X[17274], X[17299] - 3 X[21358], 5 X[17304] - 3 X[21356], 2 X[17355] - 3 X[47352]

X(50109) lies on these lines: {2, 2321}, {6, 17132}, {10, 17395}, {141, 28329}, {142, 4360}, {226, 31179}, {239, 3707}, {354, 24394}, {519, 599}, {524, 3663}, {527, 1992}, {536, 597}, {545, 20583}, {551, 740}, {1086, 3244}, {1100, 49727}, {1125, 17119}, {1266, 4393}, {1449, 4452}, {2325, 5222}, {2482, 15349}, {2796, 49477}, {3008, 4029}, {3241, 5853}, {3625, 17237}, {3626, 17325}, {3635, 4675}, {3662, 4464}, {3672, 3686}, {3759, 49748}, {3886, 38314}, {3943, 31191}, {3950, 17366}, {4000, 29573}, {4021, 4361}, {4035, 19785}, {4058, 17384}, {4060, 17306}, {4072, 17357}, {4085, 4669}, {4098, 17337}, {4133, 19883}, {4356, 49740}, {4357, 29617}, {4389, 49770}, {4395, 29571}, {4405, 4708}, {4419, 4700}, {4431, 17380}, {4460, 17296}, {4483, 42028}, {4527, 19862}, {4545, 5232}, {4643, 50019}, {4644, 4982}, {4659, 17014}, {4664, 41140}, {4725, 49741}, {4740, 27480}, {4780, 17392}, {4856, 15534}, {4889, 48631}, {4910, 7232}, {4912, 8584}, {4971, 17382}, {5695, 38023}, {5749, 32105}, {5750, 17151}, {9041, 49463}, {11160, 17274}, {16475, 28557}, {16672, 31211}, {16676, 24599}, {17023, 17160}, {17067, 17316}, {17197, 33296}, {17227, 49761}, {17235, 22165}, {17254, 40891}, {17281, 28313}, {17290, 49765}, {17299, 21358}, {17302, 29615}, {17304, 21356}, {17320, 31144}, {17348, 49737}, {17355, 47352}, {17359, 28309}, {17388, 21255}, {17393, 24199}, {17765, 31138}, {17769, 34641}, {19796, 41823}, {22110, 49554}, {23668, 42038}, {24257, 28194}, {24473, 44661}, {27191, 29601}, {28522, 38049}, {28538, 49630}, {28562, 49684}, {47359, 49453}

X(50109) = midpoint of X(i) and X(j) for these {i,j}: {2, 3875}, {3663, 49543}, {15534, 17276}, {47358, 49486}, {47359, 49453}
X(50109) = reflection of X(i) in X(j) for these {i,j}: {2, 3946}, {2321, 2}, {4669, 4085}, {15534, 4856}, {22165, 17235}, {29594, 17382}, {47358, 4353}, {49543, 4852}
X(50109) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1266, 4393, 4667}, {3008, 17318, 4029}, {3875, 3946, 2321}, {4021, 4361, 5257}, {4360, 37756, 29574}, {29574, 37756, 142}


X(50110) = X(2)X(2321)∩X(9)X(4464)

Barycentrics    2*a^2 + 5*a*b - b^2 + 5*a*c - 4*b*c - c^2 : :
X(50110) = 5 X[37] - 2 X[4399], 3 X[37] - 2 X[49731], 3 X[4399] - 5 X[49731], 2 X[192] + X[3879], 5 X[192] + X[17364], 5 X[3879] - 2 X[17364], X[17364] - 5 X[17389], X[3883] - 4 X[3993], 3 X[4664] - X[17346], 2 X[49470] + X[49527], 2 X[49462] + X[49476], 2 X[17392] - 3 X[29574], 5 X[17392] - 3 X[49727], 5 X[29574] - 2 X[49727], X[3644] + 2 X[3664], 2 X[3686] - 5 X[4704], X[4416] - 4 X[4681], X[4416] + 2 X[17388], 2 X[4681] + X[17388], X[4718] + 2 X[17390], X[4788] + 5 X[17391], 2 X[4889] + X[17334]

X(50110) lies on these lines: {2, 2321}, {9, 4464}, {37, 4399}, {45, 49770}, {69, 4898}, {75, 28313}, {142, 29575}, {145, 6172}, {190, 3244}, {192, 527}, {239, 4029}, {519, 751}, {528, 49462}, {536, 17392}, {551, 32922}, {597, 4908}, {1086, 29601}, {1100, 49726}, {1266, 6173}, {1992, 49684}, {2325, 4393}, {3175, 22012}, {3241, 3685}, {3625, 17256}, {3635, 3758}, {3644, 3664}, {3663, 17297}, {3686, 4704}, {3707, 20016}, {3886, 48856}, {3912, 17290}, {3943, 17023}, {3950, 4360}, {3986, 5564}, {4021, 17233}, {4058, 17322}, {4060, 17248}, {4072, 17289}, {4098, 17277}, {4357, 17294}, {4364, 4727}, {4389, 49765}, {4416, 4681}, {4419, 29605}, {4431, 16777}, {4440, 29619}, {4472, 39260}, {4643, 49761}, {4659, 29585}, {4667, 29588}, {4669, 31144}, {4686, 49733}, {4688, 28309}, {4718, 17390}, {4788, 17391}, {4851, 49747}, {4852, 25101}, {4856, 17336}, {4873, 26626}, {4887, 17387}, {4889, 17334}, {4910, 16885}, {4986, 42724}, {6542, 17254}, {7227, 46845}, {16672, 24603}, {16673, 42696}, {16674, 28634}, {16834, 16970}, {17067, 29572}, {17132, 17378}, {17160, 29571}, {17251, 17299}, {17320, 29594}, {17330, 28329}, {17335, 50019}, {17355, 17393}, {17365, 28322}, {17395, 29596}, {20009, 34701}, {20583, 36522}, {28522, 36494}, {29600, 37756}, {29602, 42697}, {41140, 41313}, {46922, 49482}

X(50110) = midpoint of X(i) and X(j) for these {i,j}: {192, 17389}, {3644, 49722}, {17388, 49742}
X(50110) = reflection of X(i) in X(j) for these {i,j}: {3879, 17389}, {4416, 49742}, {4686, 49733}, {49722, 3664}, {49742, 4681}
X(50110) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3950, 4360, 17353}, {4681, 17388, 4416}


X(50111) = X(1)X(190)∩X(2)X(740)

Barycentrics    5*a^2*b + 2*a*b^2 + 5*a^2*c + 6*a*b*c - b^2*c + 2*a*c^2 - b*c^2 : :
X(50111) = 5 X[1] + X[49447], 2 X[1] + X[49456], 4 X[1] - X[49491], 7 X[1] - X[49499], 5 X[4664] - X[49447], 4 X[4664] + X[49491], 7 X[4664] + X[49499], 2 X[49447] - 5 X[49456], 4 X[49447] + 5 X[49491], 7 X[49447] + 5 X[49499], 2 X[49456] + X[49491], 7 X[49456] + 2 X[49499], 7 X[49491] - 4 X[49499], 4 X[37] - X[49457], 2 X[37] + X[49471], 5 X[37] + X[49475], X[49457] + 2 X[49471], 5 X[49457] + 4 X[49475], 5 X[49471] - 2 X[49475], X[75] - 3 X[25055], X[192] + 3 X[38314], X[31178] - 3 X[38314], X[3993] + 2 X[15569], 2 X[3993] + X[24325], 4 X[15569] - X[24325], 2 X[1125] + X[49462], 2 X[3244] + X[49449], 5 X[3616] - X[4740], 5 X[3616] + X[49452], 7 X[3622] - X[49493], 5 X[3623] + X[49503], 4 X[3634] - X[49468], 2 X[3635] + X[49515], 4 X[3636] - X[49483], 2 X[3842] + X[49470], 2 X[3739] - 3 X[19883], 2 X[4681] + X[49479], 5 X[4687] - 2 X[4732], 5 X[4687] - 3 X[19875], 5 X[4687] + X[49469], 2 X[4732] - 3 X[19875], 2 X[4732] + X[49469], 3 X[19875] + X[49469], 4 X[4698] - X[4709], 5 X[4704] + X[49490], 5 X[16491] + X[49502], 7 X[27268] - X[49459], 3 X[47352] - X[49531]

X(50111) lies on these lines: {1, 190}, {2, 740}, {10, 4755}, {37, 519}, {42, 42056}, {45, 4753}, {75, 4975}, {192, 28554}, {238, 29584}, {518, 3898}, {536, 551}, {752, 29574}, {984, 3241}, {1125, 4688}, {2321, 48853}, {2796, 17392}, {3244, 49449}, {3247, 32941}, {3616, 4740}, {3622, 49493}, {3623, 49503}, {3634, 49468}, {3635, 49515}, {3636, 49483}, {3655, 20430}, {3656, 29054}, {3679, 3842}, {3685, 29580}, {3696, 3828}, {3723, 49482}, {3731, 49497}, {3739, 19883}, {3836, 4356}, {3923, 5625}, {3995, 31161}, {4029, 4439}, {4096, 42042}, {4098, 49529}, {4364, 49764}, {4370, 36409}, {4407, 49763}, {4653, 19623}, {4669, 28581}, {4681, 49479}, {4687, 4732}, {4693, 16826}, {4698, 4709}, {4704, 49490}, {4759, 16666}, {4937, 46897}, {4974, 16834}, {5308, 24693}, {6682, 31137}, {10176, 44671}, {15485, 17393}, {16484, 17000}, {16491, 49502}, {16672, 36480}, {16674, 49460}, {16677, 49680}, {16777, 48805}, {16814, 49685}, {17237, 49767}, {17243, 48821}, {17244, 25351}, {17281, 48822}, {17318, 24331}, {17378, 28558}, {20049, 49689}, {21806, 31035}, {24715, 29569}, {25384, 28309}, {27268, 49459}, {29575, 31151}, {29577, 32784}, {30273, 31162}, {31145, 49678}, {31323, 40891}, {34747, 49450}, {35166, 35956}, {47352, 49531}, {48856, 49526}, {49676, 49741}

X(50111) = midpoint of X(i) and X(j) for these {i,j}: {1, 4664}, {192, 31178}, {551, 3993}, {984, 3241}, {3655, 20430}, {3679, 49470}, {4688, 49462}, {4740, 49452}, {20049, 49689}, {30273, 31162}, {31145, 49678}, {34747, 49450}
X(50111) = reflection of X(i) in X(j) for these {i,j}: {10, 4755}, {551, 15569}, {3679, 3842}, {3696, 3828}, {4688, 1125}, {24325, 551}, {49456, 4664}
X(50111) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 49456, 49491}, {37, 49471, 49457}, {192, 38314, 31178}, {3993, 15569, 24325}, {4687, 49469, 4732}, {16484, 17319, 49472}


X(50112) = X(2)X(594)∩X(6)X(545)

Barycentrics    4*a^2 + 2*a*b + b^2 + 2*a*c - 4*b*c + c^2 : :
X(50112) = X[141] - 4 X[3946], X[141] + 2 X[4852], 5 X[141] - 2 X[17372], 2 X[3946] + X[4852], 10 X[3946] - X[17372], 5 X[4852] + X[17372], X[17372] - 5 X[17382], 3 X[16834] + X[17274], 2 X[16834] + X[49741], X[17274] - 3 X[17301], 2 X[17274] - 3 X[49741], 2 X[3589] + X[3875], X[3629] + 2 X[3663], X[3630] - 4 X[17235], 2 X[3631] - 5 X[17304], X[3729] - 4 X[6329], X[22165] + 2 X[49543], 2 X[4856] + X[17345], 2 X[17359] - 3 X[48310], X[17276] + 2 X[32455], X[17299] - 4 X[34573], 2 X[32921] + X[49524]

X(50112) lies on these lines: {1, 4395}, {2, 594}, {6, 545}, {7, 36525}, {10, 4405}, {37, 41140}, {75, 10022}, {141, 519}, {145, 17290}, {192, 4370}, {239, 4364}, {524, 16834}, {527, 8584}, {536, 597}, {551, 3739}, {599, 28337}, {740, 48810}, {752, 49477}, {903, 17365}, {1086, 4393}, {1100, 7263}, {1213, 17396}, {1266, 16666}, {1386, 28580}, {1449, 4795}, {1992, 28333}, {3241, 4000}, {3244, 3834}, {3589, 3875}, {3617, 25503}, {3621, 26104}, {3629, 3663}, {3630, 17235}, {3631, 17304}, {3635, 17067}, {3672, 17332}, {3679, 4399}, {3729, 6329}, {3759, 17246}, {3782, 45222}, {3828, 25498}, {3879, 31138}, {3943, 17342}, {4021, 17348}, {4029, 6687}, {4363, 17014}, {4371, 17327}, {4389, 4969}, {4398, 7277}, {4402, 15668}, {4407, 50021}, {4422, 5222}, {4445, 31145}, {4460, 17309}, {4464, 17231}, {4472, 17119}, {4478, 4677}, {4665, 17023}, {4669, 17239}, {4690, 50019}, {4725, 22165}, {4727, 29596}, {4856, 17345}, {4887, 4982}, {4889, 21255}, {4908, 17353}, {4910, 17296}, {5839, 17323}, {5846, 48829}, {6707, 25055}, {7222, 36588}, {7227, 17151}, {12610, 28204}, {16475, 28530}, {16672, 31285}, {16706, 17310}, {16711, 18166}, {16833, 41312}, {16884, 31139}, {17027, 25350}, {17117, 17398}, {17121, 17334}, {17133, 17359}, {17160, 17369}, {17237, 49770}, {17245, 17393}, {17262, 36522}, {17271, 17302}, {17276, 32455}, {17294, 20582}, {17299, 34573}, {17305, 20016}, {17316, 40480}, {17319, 17337}, {17351, 28301}, {17356, 41141}, {17377, 48632}, {17383, 48635}, {17384, 48636}, {17392, 29584}, {17399, 29617}, {19722, 19819}, {19875, 28634}, {20180, 46922}, {20181, 49733}, {27191, 29588}, {28329, 29594}, {28472, 38047}, {28484, 38049}, {28503, 32921}, {29235, 36729}, {29601, 31243}, {39704, 48627}

X(50112) = midpoint of X(i) and X(j) for these {i,j}: {1992, 49747}, {3875, 17281}, {4852, 17382}, {16834, 17301}
X(50112) = reflection of X(i) in X(j) for these {i,j}: {141, 17382}, {17281, 3589}, {17294, 20582}, {17382, 3946}, {49726, 597}, {49741, 17301}
X(50112) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4395, 34824}, {239, 17320, 17330}, {239, 17395, 4364}, {3241, 4000, 17313}, {3241, 17313, 17390}, {3672, 37654, 24441}, {3946, 4852, 141}, {4360, 17366, 17243}, {5222, 17318, 4422}, {16833, 41312, 49731}, {17119, 26626, 4472}, {17271, 40891, 17362}, {17302, 40891, 17271}, {17320, 17330, 4364}, {17330, 17395, 17320}, {24441, 37654, 17332}, {29584, 37756, 17392}, {49465, 50013, 141}


X(50113) = X(2)X(594)∩X(6)X(644)

Barycentrics    2*a^2 + 4*a*b - b^2 + 4*a*c - 2*b*c - c^2 : :
X(50113) = 5 X[37] - 2 X[3686], 5 X[37] - 3 X[16590], 4 X[37] - X[17362], 2 X[37] + X[17388], 2 X[3686] - 3 X[16590], 4 X[3686] - 5 X[17330], 8 X[3686] - 5 X[17362], 4 X[3686] + 5 X[17388], 6 X[16590] - 5 X[17330], 12 X[16590] - 5 X[17362], 6 X[16590] + 5 X[17388], X[17362] + 2 X[17388], 2 X[192] + X[17365], X[192] + 2 X[17390], X[17365] - 4 X[17390], 3 X[4664] - X[17333], X[17333] + 3 X[17389], 2 X[17333] - 3 X[49742], 2 X[17389] + X[49742], 4 X[29574] - X[49727], X[3644] + 2 X[7228], X[3644] + 5 X[17391], X[3644] + 3 X[39704], 2 X[7228] - 5 X[17391], 2 X[7228] - 3 X[39704], 5 X[17391] - 3 X[39704], 2 X[3664] + X[4718], X[3879] + 2 X[4681], 2 X[3879] + X[17334], 4 X[4681] - X[17334], 2 X[4399] - 5 X[4687], X[4416] + 2 X[4889], 5 X[4704] - 2 X[17332], 5 X[4704] + X[17377], 2 X[17332] + X[17377]

X(50113) lies on these lines: {1, 3943}, {2, 594}, {6, 644}, {8, 16672}, {9, 13602}, {10, 4727}, {37, 519}, {44, 3244}, {45, 145}, {69, 24441}, {75, 28309}, {86, 10022}, {141, 17310}, {190, 29588}, {192, 545}, {320, 29619}, {346, 16884}, {391, 16677}, {524, 4664}, {536, 17392}, {551, 2321}, {597, 17264}, {740, 49725}, {742, 31342}, {752, 3993}, {903, 17300}, {966, 16674}, {1086, 17313}, {1100, 3950}, {1125, 39260}, {1213, 3247}, {1743, 36911}, {1766, 3655}, {1953, 34699}, {2171, 5434}, {2178, 4421}, {2242, 47040}, {2294, 34612}, {2325, 3635}, {2345, 38314}, {2901, 37150}, {3058, 17452}, {3178, 21689}, {3589, 17242}, {3629, 17261}, {3630, 17258}, {3631, 17247}, {3633, 16676}, {3644, 7228}, {3663, 31138}, {3664, 4718}, {3672, 17311}, {3729, 4795}, {3731, 34747}, {3834, 29601}, {3871, 19297}, {3874, 21864}, {3875, 17245}, {3879, 4681}, {3912, 17382}, {3946, 41141}, {3970, 17444}, {3986, 34641}, {4007, 19875}, {4021, 17231}, {4037, 31161}, {4053, 34606}, {4058, 19883}, {4060, 4745}, {4098, 16814}, {4363, 29585}, {4364, 6542}, {4393, 4422}, {4395, 17244}, {4398, 36525}, {4399, 4687}, {4405, 16815}, {4416, 4889}, {4431, 28639}, {4464, 17348}, {4472, 29570}, {4478, 17248}, {4643, 29605}, {4648, 31139}, {4665, 16826}, {4669, 5257}, {4675, 29602}, {4677, 16673}, {4688, 17133}, {4690, 49761}, {4704, 17332}, {4740, 49733}, {4755, 28329}, {4851, 17246}, {4852, 17337}, {4854, 31134}, {4856, 15492}, {4916, 40341}, {4954, 37675}, {5308, 17119}, {5750, 46845}, {5839, 16675}, {5846, 49746}, {6172, 15534}, {6329, 17339}, {6707, 48628}, {7227, 17394}, {7238, 17387}, {7263, 17317}, {7277, 17262}, {8610, 20691}, {11113, 22021}, {13587, 21773}, {16816, 31285}, {16834, 41313}, {16972, 47359}, {17160, 29569}, {17227, 29618}, {17237, 49765}, {17240, 17396}, {17254, 22165}, {17269, 26626}, {17277, 40891}, {17290, 29583}, {17294, 41312}, {17297, 49741}, {17301, 29573}, {17303, 25055}, {17309, 17321}, {17312, 48631}, {17322, 48636}, {17325, 29616}, {17336, 32455}, {17346, 28337}, {17350, 36522}, {17399, 20582}, {17487, 20090}, {18146, 30473}, {20693, 42056}, {21049, 34619}, {21690, 27577}, {21801, 34749}, {21808, 34720}, {21853, 24473}, {21933, 45701}, {25358, 29593}, {27191, 29589}, {27754, 35466}, {28333, 49748}, {28580, 49462}, {29016, 36722}, {29235, 36730}, {29572, 40480}, {29575, 37756}, {29594, 41311}, {29617, 49731}, {35121, 49751}, {37631, 42044}, {46922, 49726}

X(50113) = midpoint of X(i) and X(j) for these {i,j}: {192, 17378}, {4664, 17389}, {17330, 17388}
X(50113) = reflection of X(i) in X(j) for these {i,j}: {75, 49738}, {4740, 49733}, {17330, 37}, {17346, 49737}, {17362, 17330}, {17365, 17378}, {17378, 17390}, {17392, 29574}, {29617, 49731}, {49727, 17392}, {49742, 4664}
X(50113) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3943, 17369}, {37, 17388, 17362}, {45, 145, 4969}, {192, 17390, 17365}, {1100, 3950, 17340}, {2321, 3723, 17398}, {2325, 3635, 16666}, {3244, 4029, 44}, {3247, 4898, 17299}, {3247, 17299, 1213}, {3644, 17391, 7228}, {3672, 17311, 48632}, {3686, 16590, 17330}, {3879, 4681, 17334}, {4360, 17243, 17366}, {4704, 17377, 17332}, {16777, 17314, 594}, {17160, 29569, 34824}, {17240, 17396, 34573}, {17242, 17393, 3589}, {17247, 17386, 3631}, {17264, 29584, 597}, {17309, 17321, 48635}, {17310, 17319, 17320}, {17310, 17320, 141}, {17315, 17319, 141}, {17315, 17320, 17310}, {17316, 17318, 1086}, {17399, 29577, 20582}


X(50114) = X(1)X(2)∩X(6)X(527)

Barycentrics    4*a^2 + a*b + b^2 + a*c - 2*b*c + c^2 : :
X(50114) = 2 X[2] + X[49543], X[10] + 2 X[49477], 2 X[1125] + X[49488], 5 X[3616] + X[49495], 7 X[3622] - X[49451], 4 X[3636] - X[49458], 3 X[16834] + X[17294], 2 X[16834] + X[29594], 2 X[17294] - 3 X[29594], 2 X[17294] + 3 X[49543], 5 X[19862] - 2 X[49560], 2 X[6] + X[3663], X[6] + 2 X[3946], 5 X[6] + X[17276], 3 X[6] + X[49747], X[3663] - 4 X[3946], 5 X[3663] - 2 X[17276], 3 X[3663] - 2 X[49747], 10 X[3946] - X[17276], 6 X[3946] - X[49747], X[17276] - 5 X[17301], 3 X[17276] - 5 X[49747], 3 X[17301] - X[49747], X[69] + 2 X[4856], X[193] + 5 X[17304], 2 X[1386] + X[3755], 3 X[597] - X[49726], X[2321] - 4 X[3589], X[2321] + 2 X[4852], 2 X[3589] + X[4852], 2 X[3242] + X[4924], 5 X[3618] + X[3875], 5 X[3618] - 2 X[17355], X[3875] + 2 X[17355], X[3629] + 2 X[17235], X[3751] + 2 X[4353], X[3821] + 2 X[4991], 2 X[4085] + X[49684], X[4133] - 4 X[24295], X[4780] + 2 X[49482], 4 X[6329] - X[17351], X[17281] - 3 X[47352], X[17299] - 7 X[47355], X[17345] + 2 X[32455], X[17372] - 4 X[34573], 2 X[49464] + X[49536], 3 X[38023] - X[48805], 2 X[49472] + X[49529], 2 X[49489] + X[49511], X[49505] + 2 X[49685]

X(50114) lies on these lines: {1, 2}, {6, 527}, {7, 16667}, {9, 4021}, {44, 17395}, {57, 1323}, {58, 35935}, {69, 4856}, {81, 17205}, {83, 4052}, {141, 4725}, {142, 1100}, {165, 11200}, {193, 17304}, {218, 50068}, {222, 553}, {223, 38009}, {226, 544}, {238, 4356}, {277, 39948}, {279, 39980}, {335, 49535}, {354, 2809}, {491, 49620}, {492, 49621}, {514, 1643}, {515, 36731}, {516, 16475}, {524, 17382}, {528, 1386}, {536, 597}, {673, 4649}, {740, 38049}, {752, 49630}, {940, 24175}, {946, 36728}, {948, 4654}, {1001, 4989}, {1015, 3752}, {1051, 33147}, {1086, 4667}, {1108, 25065}, {1212, 5325}, {1266, 3758}, {1429, 4251}, {1449, 3664}, {1453, 11111}, {1475, 20367}, {1509, 24378}, {1642, 46907}, {1738, 4349}, {1743, 3672}, {1992, 17274}, {2321, 3589}, {2325, 17318}, {2784, 3817}, {2796, 5182}, {3058, 41339}, {3159, 41249}, {3242, 4924}, {3247, 25072}, {3304, 37272}, {3338, 24590}, {3452, 6603}, {3496, 3928}, {3618, 3875}, {3629, 17235}, {3666, 43065}, {3671, 41245}, {3686, 4657}, {3707, 4364}, {3723, 17337}, {3731, 37681}, {3751, 4353}, {3759, 4357}, {3821, 4991}, {3879, 16706}, {3913, 21526}, {3929, 16572}, {3945, 4859}, {3950, 4360}, {3986, 17277}, {3993, 17755}, {4029, 4422}, {4058, 17289}, {4060, 17293}, {4072, 17280}, {4082, 32928}, {4085, 49684}, {4098, 17319}, {4133, 24295}, {4253, 37555}, {4263, 28358}, {4301, 6996}, {4314, 16478}, {4361, 5750}, {4395, 4670}, {4399, 17385}, {4402, 25590}, {4416, 17121}, {4419, 16670}, {4421, 21539}, {4431, 17368}, {4464, 17233}, {4643, 4700}, {4644, 4887}, {4648, 4909}, {4656, 5526}, {4658, 16054}, {4664, 49521}, {4672, 28542}, {4675, 17067}, {4715, 8584}, {4780, 49482}, {4848, 43053}, {4910, 17309}, {4967, 17381}, {4969, 17237}, {4982, 17290}, {5255, 34639}, {5257, 17045}, {5493, 37416}, {5563, 11349}, {5717, 17528}, {5745, 34522}, {5749, 17151}, {5839, 17306}, {5853, 38185}, {5881, 7402}, {6185, 40767}, {6329, 17351}, {6666, 16777}, {7264, 30807}, {7290, 47357}, {7397, 7982}, {8666, 11343}, {8715, 21477}, {9278, 35066}, {9441, 12194}, {10222, 19512}, {11194, 21509}, {12437, 37326}, {12513, 21514}, {15828, 17261}, {16668, 17365}, {16669, 17246}, {16671, 17334}, {16673, 18230}, {16712, 17206}, {16884, 17278}, {16972, 24266}, {17133, 17281}, {17158, 33941}, {17180, 42028}, {17299, 47355}, {17330, 41311}, {17345, 32455}, {17349, 17396}, {17352, 17393}, {17356, 17390}, {17357, 17388}, {17362, 17384}, {17363, 17383}, {17370, 17377}, {17372, 34573}, {17379, 24199}, {17745, 17781}, {17769, 38191}, {19785, 31164}, {19796, 41258}, {19804, 33936}, {20172, 33682}, {20179, 37756}, {20582, 28337}, {20583, 28333}, {20942, 33938}, {20963, 24215}, {21314, 21454}, {24181, 37631}, {25723, 31225}, {26740, 43047}, {27480, 28522}, {27942, 35113}, {28301, 49721}, {28329, 48310}, {28538, 48821}, {29081, 36727}, {30424, 33149}, {30809, 37723}, {31230, 41687}, {32029, 49464}, {35293, 46908}, {37520, 43057}, {37597, 40133}, {37677, 48627}, {38023, 48805}, {40747, 43266}, {41823, 42033}, {48867, 50060}, {49472, 49529}, {49489, 49511}, {49505, 49685}

X(50114) = midpoint of X(i) and X(j) for these {i,j}: {2, 16834}, {6, 17301}, {1992, 17274}, {4852, 17359}, {8584, 49741}, {29594, 49543}
X(50114) = reflection of X(i) in X(j) for these {i,j}: {2321, 17359}, {3663, 17301}, {17301, 3946}, {17359, 3589}, {29594, 2}, {49543, 16834}
X(50114) = complement of X(17294)
X(50114) = X(28899)-complementary conjugate of X(513)
X(50114) = crosssum of X(6) and X(41423)
X(50114) = crossdifference of every pair of points on line {649, 9029}
X(50114) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 43, 41276}, {1, 3008, 29571}, {1, 3679, 48856}, {1, 5222, 3008}, {1, 31183, 5308}, {2, 3241, 29573}, {2, 4393, 17389}, {2, 17389, 3912}, {2, 29573, 41141}, {2, 29574, 29600}, {2, 29584, 29574}, {2, 40891, 29615}, {6, 3946, 3663}, {8, 29598, 29604}, {145, 17284, 49765}, {239, 17023, 10}, {239, 41251, 30133}, {1086, 4667, 4896}, {1086, 16666, 4667}, {1100, 17366, 142}, {1449, 4000, 3664}, {2999, 39595, 45204}, {3244, 31191, 3912}, {3247, 37650, 25072}, {3589, 4852, 2321}, {3616, 24599, 16832}, {3618, 3875, 17355}, {3623, 29627, 29602}, {3636, 31211, 16831}, {3661, 49770, 3625}, {3759, 17380, 4357}, {3759, 17399, 17346}, {3879, 16706, 21255}, {3912, 4393, 3244}, {3912, 17367, 31191}, {4360, 17353, 3950}, {4384, 26626, 1125}, {4393, 17367, 3912}, {5222, 17014, 1}, {5228, 43035, 10481}, {6542, 29630, 29596}, {16816, 17397, 24603}, {17017, 28125, 1}, {17045, 17348, 5257}, {17121, 17302, 4416}, {17266, 29588, 29601}, {17319, 25101, 4098}, {1734X(50114) = 6, 17380, 17399}, {17346, 17399, 4357}, {17367, 17389, 2}, {17397, 24603, 19862}, {20057, 31189, 29621}, {29604, 50019, 8}


X(50115) = X(2)X(7)∩X(10)X(44)

Barycentrics    4*a^2 - a*b + b^2 - a*c + 2*b*c + c^2 : :
X(50115) = 2 X[6] + X[2321], 5 X[6] - 2 X[4856], 5 X[6] + X[17299], X[6] + 2 X[17355], 5 X[2321] + 4 X[4856], 5 X[2321] - 2 X[17299], X[2321] - 4 X[17355], 2 X[4856] + 5 X[17281], 2 X[4856] + X[17299], X[4856] + 5 X[17355], 5 X[17281] - X[17299], X[17299] - 10 X[17355], 2 X[49482] + X[49529], X[10] + 2 X[4672], 2 X[1125] + X[32935], X[193] + 5 X[17286], 3 X[38047] - X[48829], 4 X[3589] - X[3663], 2 X[3589] + X[17351], X[3663] + 2 X[17351], 5 X[1698] + X[24695], 5 X[3618] + X[3729], 5 X[3618] - 2 X[3946], X[3729] + 2 X[3946], X[3629] + 2 X[17229], 4 X[3634] - X[4655], X[3755] + 2 X[3923], X[4133] + 2 X[49489], X[4852] - 4 X[6329], 3 X[48310] - X[49741], X[4924] + 2 X[49467], X[17301] - 3 X[47352], 3 X[47352] + X[49721], X[17276] - 7 X[47355], X[17345] - 4 X[34573], X[17372] + 2 X[32455], 4 X[24295] - X[49511], 2 X[49473] + X[49536]

X(50115) lies on these lines: {1, 2325}, {2, 7}, {6, 519}, {8, 4700}, {10, 44}, {30, 10445}, {37, 537}, {41, 16393}, {45, 1125}, {75, 41140}, {86, 25101}, {141, 4715}, {145, 4873}, {190, 17023}, {193, 17286}, {198, 16371}, {218, 5782}, {281, 1877}, {284, 4234}, {320, 29596}, {346, 1449}, {374, 2835}, {380, 34607}, {515, 48833}, {516, 36721}, {518, 48810}, {522, 1643}, {524, 17359}, {536, 597}, {545, 3589}, {594, 4669}, {726, 13331}, {903, 16706}, {950, 4217}, {965, 19290}, {966, 3973}, {1086, 31191}, {1100, 3950}, {1213, 15492}, {1220, 5837}, {1266, 17367}, {1386, 28503}, {1405, 4848}, {1698, 24695}, {1743, 2345}, {1766, 28194}, {1901, 16052}, {1992, 17294}, {2182, 11112}, {2183, 16549}, {2257, 34625}, {2264, 34612}, {2267, 16788}, {2297, 2324}, {2329, 5053}, {2792, 10175}, {2796, 6034}, {3008, 4363}, {3161, 3247}, {3217, 19336}, {3244, 3943}, {3501, 4266}, {3616, 16676}, {3618, 3729}, {3625, 4969}, {3629, 17229}, {3634, 4655}, {3636, 16672}, {3664, 4795}, {3692, 11239}, {3723, 4098}, {3731, 25055}, {3739, 10022}, {3745, 4082}, {3755, 3923}, {3758, 3912}, {3759, 4431}, {3828, 16885}, {3834, 4896}, {3879, 17120}, {3932, 4349}, {3986, 15828}, {3993, 36409}, {4007, 31145}, {4021, 17262}, {4035, 32777}, {4058, 16671}, {4060, 4677}, {4072, 16668}, {4078, 33682}, {4133, 49489}, {4195, 12437}, {4254, 4421}, {4270, 42043}, {4286, 20108}, {4344, 4901}, {4389, 4480}, {4416, 17271}, {4419, 29598}, {4422, 4670}, {4440, 29630}, {4470, 16832}, {4473, 16826}, {4643, 29604}, {4644, 17284}, {4657, 24441}, {4659, 5222}, {4664, 49528}, {4676, 49746}, {4725, 8584}, {4741, 29613}, {4745, 17275}, {4747, 29627}, {4758, 16831}, {4852, 6329}, {4859, 7222}, {4887, 17290}, {4912, 48310}, {4924, 49467}, {4967, 17349}, {4971, 49543}, {5120, 11194}, {5220, 19868}, {5227, 48803}, {5263, 24393}, {5550, 31722}, {5735, 36682}, {5783, 19276}, {6687, 34824}, {7227, 17348}, {7228, 17356}, {7229, 37681}, {7277, 17231}, {7359, 8582}, {8557, 45700}, {8715, 37503}, {8804, 11113}, {9300, 49554}, {9359, 40790}, {11235, 40963}, {13539, 20262}, {13735, 41239}, {13740, 24391}, {14439, 35263}, {15601, 39581}, {15668, 25072}, {16517, 48854}, {16548, 33950}, {16667, 17314}, {16786, 49466}, {16829, 39252}, {16834, 17133}, {17045, 36522}, {17067, 42697}, {17121, 40891}, {17132, 17301}, {17234, 39704}, {17238, 17488}, {17242, 37677}, {17264, 29574}, {17268, 20090}, {17269, 49765}, {17276, 47355}, {17278, 31139}, {17292, 20072}, {17302, 17487}, {17321, 25728}, {17332, 17385}, {17334, 17384}, {17335, 24603}, {17336, 17381}, {17339, 17379}, {17345, 34573}, {17347, 17371}, {17352, 24199}, {17357, 17365}, {17358, 17364}, {17372, 32455}, {17392, 29600}, {17396, 25269}, {17399, 49748}, {17766, 38191}, {20227, 42053}, {20582, 28333}, {20583, 28337}, {21101, 31161}, {21211, 45313}, {21526, 24328}, {21629, 28854}, {21803, 22343}, {23617, 36910}, {24165, 46907}, {24295, 49511}, {24386, 33121}, {24487, 46898}, {24502, 36406}, {24725, 30768}, {25590, 37650}, {26061, 31134}, {27747, 35466}, {28534, 48821}, {29057, 38118}, {31151, 33159}, {31349, 49521}, {35113, 36220}, {36595, 37800}, {38408, 49636}, {41311, 49742}, {49473, 49536}

X(50115) = midpoint of X(i) and X(j) for these {i,j}: {6, 17281}, {597, 49726}, {1992, 17294}, {17301, 49721}, {17351, 17382}, {47359, 48805}
X(50115) = reflection of X(i) in X(j) for these {i,j}: {2321, 17281}, {3663, 17382}, {17281, 17355}, {17382, 3589}, {29594, 17359}, {49630, 48821}
X(50115) = complement of X(17274)
X(50115) = crossdifference of every pair of points on line {663, 4491}
X(50115) = barycentric product X(i)*X(j) for these {i,j}: {8, 4315}, {190, 47767}
X(50115) = barycentric quotient X(i)/X(j) for these {i,j}: {4315, 7}, {47767, 514}
X(50115) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2325, 4029}, {2, 17333, 4357}, {2, 17350, 17333}, {2, 35578, 6173}, {6, 17299, 4856}, {6, 17355, 2321}, {8, 16670, 4700}, {9, 5749, 5750}, {9, 5750, 5257}, {10, 44, 3707}, {44, 17369, 10}, {894, 17353, 142}, {1100, 17340, 3950}, {1743, 2345, 3686}, {1743, 3679, 37654}, {2345, 37654, 3679}, {3589, 17351, 3663}, {3618, 3729, 3946}, {3664, 41141, 17313}, {3679, 37654, 3686}, {3758, 3912, 4667}, {3758, 17342, 17378}, {3758, 17354, 3912}, {3943, 16666, 3244}, {3986, 15828, 16814}, {4422, 4670, 29571}, {4795, 17279, 17313}, {4795, 17313, 3664}, {5294, 26223, 226}, {10436, 26685, 6666}, {16814, 17398, 3986}, {17120, 17280, 3879}, {17264, 46922, 29574}, {17279, 17313, 41141}, {17333, 17368, 2}, {17342, 17378, 3912}, {17350, 17368, 4357}, {17354, 17378, 17342}, {17357, 17365, 21255}, {17392, 41310, 29600}, {47352, 49721, 17301}, {49569, 49570, 10175}


X(50116) = X(2)X(7)∩X(10)X(320)

Barycentrics    2*a^2 + a*b - b^2 + a*c + 4*b*c - c^2 : :
X(50116) = X[37] + 2 X[7228], X[75] + 2 X[3664], 2 X[75] + X[3879], 5 X[75] + X[17377], X[75] + 3 X[39704], 4 X[3664] - X[3879], 10 X[3664] - X[17377], 2 X[3664] - 3 X[39704], 5 X[3879] - 2 X[17377], X[3879] - 6 X[39704], X[17377] - 5 X[17378], X[17377] - 15 X[39704], X[17378] - 3 X[39704], 3 X[24452] + X[49490], X[29574] + 2 X[49727], X[3883] - 4 X[24325], X[1278] + 5 X[17391], 2 X[3686] - 5 X[4699], 2 X[3686] + X[17364], 5 X[4699] + X[17364], 4 X[3739] - X[4416], 2 X[3739] + X[17365], X[4416] + 2 X[17365], X[4686] + 2 X[17390], 4 X[4698] - X[17334], 2 X[4726] + X[17388], 4 X[4739] - X[17362], 7 X[4751] - X[17347], 7 X[4772] - X[17363], 3 X[16590] - 2 X[17332], 3 X[16590] - 5 X[31238], 2 X[17332] - 5 X[31238], 2 X[17049] + X[49537], 5 X[17331] - 3 X[17488], 2 X[24349] + X[49527], X[49476] + 2 X[49483]

X(50116) lies on these lines: {1, 1266}, {2, 7}, {6, 4795}, {10, 320}, {37, 545}, {44, 34824}, {45, 4480}, {69, 3679}, {75, 519}, {77, 36595}, {86, 99}, {141, 10022}, {190, 29571}, {192, 28301}, {239, 4667}, {269, 17079}, {314, 42057}, {319, 4669}, {354, 6007}, {376, 10444}, {516, 49746}, {518, 49725}, {524, 4688}, {536, 17392}, {537, 49521}, {594, 17376}, {742, 27478}, {752, 3883}, {942, 37150}, {946, 41874}, {971, 36722}, {1086, 4670}, {1100, 7263}, {1125, 4389}, {1213, 17345}, {1278, 17391}, {1441, 41801}, {1442, 41803}, {1992, 16833}, {2321, 17116}, {2325, 17244}, {2345, 17298}, {2810, 3753}, {3008, 3758}, {3241, 3875}, {3244, 17160}, {3263, 31161}, {3616, 4346}, {3618, 4859}, {3626, 17360}, {3634, 17250}, {3668, 17078}, {3672, 38314}, {3686, 4699}, {3707, 16815}, {3729, 4648}, {3739, 4416}, {3812, 17114}, {3828, 5224}, {3834, 17369}, {3912, 4363}, {3943, 29601}, {3946, 17379}, {3950, 17317}, {3977, 27754}, {3986, 17258}, {4021, 4398}, {4029, 29569}, {4034, 20080}, {4054, 37633}, {4058, 17295}, {4059, 34606}, {4060, 17373}, {4292, 37038}, {4349, 32922}, {4370, 17245}, {4384, 4644}, {4395, 16666}, {4419, 16831}, {4431, 4851}, {4440, 16826}, {4452, 30712}, {4454, 5308}, {4464, 17151}, {4470, 17308}, {4472, 7238}, {4473, 29626}, {4643, 24603}, {4659, 17316}, {4664, 17132}, {4665, 17374}, {4677, 42696}, {4686, 17390}, {4698, 17334}, {4700, 16816}, {4726, 17388}, {4739, 17362}, {4740, 17133}, {4741, 29576}, {4745, 17361}, {4747, 5222}, {4751, 17347}, {4754, 30030}, {4755, 4912}, {4758, 17397}, {4772, 17363}, {4785, 21211}, {4798, 17325}, {4862, 17321}, {4869, 7229}, {4873, 29583}, {4908, 7231}, {4909, 17393}, {4911, 17677}, {5121, 26240}, {5263, 5542}, {5564, 34641}, {5735, 36706}, {5736, 19336}, {5805, 36721}, {5880, 48829}, {7227, 17231}, {7232, 17303}, {7277, 17348}, {10385, 10889}, {10401, 11237}, {10446, 28194}, {10455, 17179}, {13727, 43177}, {14548, 31146}, {15668, 17276}, {15936, 20880}, {15956, 50061}, {16394, 24549}, {16412, 24328}, {16590, 17332}, {16676, 20073}, {17045, 36525}, {17049, 49537}, {17067, 17367}, {17117, 20090}, {17119, 49770}, {17139, 17175}, {17227, 29604}, {17234, 17342}, {17235, 17398}, {17246, 28639}, {17261, 17487}, {17263, 41138}, {17264, 29600}, {17270, 21296}, {17272, 19875}, {17273, 28653}, {17288, 28604}, {17289, 21255}, {17297, 29594}, {17322, 19883}, {17331, 17488}, {17335, 31211}, {17336, 25072}, {17375, 48628}, {17381, 48629}, {17384, 48631}, {17385, 48632}, {17387, 49765}, {17532, 41004}, {17579, 18650}, {18821, 35154}, {19796, 42028}, {19868, 43180}, {20179, 37756}, {23812, 24165}, {24342, 49511}, {24349, 49527}, {24391, 26051}, {24541, 24999}, {24693, 49772}, {24697, 39580}, {24723, 30424}, {25377, 27922}, {25557, 48810}, {27191, 31191}, {27747, 37520}, {28333, 49731}, {28503, 49476}, {28534, 49740}, {28634, 40341}, {30090, 34283}, {30941, 31136}, {30962, 31137}, {31145, 32087}, {31317, 49754}, {32025, 38098}, {32093, 32099}, {32836, 48812}, {33869, 48822}, {36232, 41144}, {37631, 39774}, {41310, 49726}, {41311, 49741}, {41312, 49747}, {41313, 49721}, {47359, 47595}, {49535, 49715}, {49688, 49750}

X(50116) = midpoint of X(i) and X(j) for these {i,j}: {75, 17378}, {4664, 49722}, {4740, 17389}, {7228, 49738}, {17330, 17365}, {17392, 49727}
X(50116) = reflection of X(i) in X(j) for these {i,j}: {37, 49738}, {3879, 17378}, {4416, 17330}, {4688, 49733}, {17330, 3739}, {17378, 3664}, {29574, 17392}, {49742, 4755}
X(50116) = complement of X(17333)
X(50116) = crossdifference of every pair of points on line {663, 14407}
X(50116) = barycentric product X(i)*X(j) for these {i,j}: {75, 37520}, {190, 47891}, {27747, 39704}
X(50116) = barycentric quotient X(i)/X(j) for these {i,j}: {27747, 3679}, {37520, 1}, {47891, 514}
X(50116) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 42697, 1266}, {2, 7, 17274}, {2, 17274, 4357}, {2, 17484, 27776}, {7, 10436, 4357}, {10, 4896, 320}, {69, 25590, 4967}, {75, 3664, 3879}, {75, 39704, 17378}, {86, 903, 17320}, {86, 7321, 3663}, {86, 17320, 551}, {142, 894, 17353}, {551, 3663, 17320}, {894, 26806, 142}, {903, 17320, 3663}, {1086, 4670, 17023}, {1125, 4887, 4389}, {3739, 17365, 4416}, {3834, 17369, 29596}, {3945, 31995, 3875}, {4363, 4675, 3912}, {4363, 17313, 17281}, {4389, 41847, 1125}, {4398, 17394, 4021}, {4472, 7238, 17237}, {4648, 7222, 3729}, {4675, 17281, 17313}, {4699, 17364, 3686}, {4795, 31139, 41140}, {4851, 17118, 4431}, {4869, 7229, 17286}, {4888, 25590, 69}, {7321, 17320, 903}, {10436, 17274, 2}, {16815, 20072, 3707}, {17116, 17300, 2321}, {17234, 17342, 41141}, {17245, 17351, 25101}, {17281, 17313, 3912}, {17350, 27147, 6666}, {17355, 41141, 17342}, {17378, 39704, 3664}, {17379, 48627, 3946}


X(50117) = X(1)X(1278)∩X(10)X(75)

Barycentrics    a*b^2 - 2*a*b*c - 3*b^2*c + a*c^2 - 3*b*c^2 : :
X(50117) = X[8] - 5 X[4821], 10 X[4821] - X[49504], 5 X[4821] + X[49532], X[49504] + 2 X[49532], 3 X[10] - 2 X[984], 5 X[10] - 2 X[49447], X[10] + 2 X[49493], 7 X[10] - 2 X[49517], 3 X[75] - X[984], 5 X[75] - X[49447], 7 X[75] - X[49517], 4 X[75] - X[49520], 5 X[984] - 3 X[49447], X[984] + 3 X[49493], 7 X[984] - 3 X[49517], 4 X[984] - 3 X[49520], X[49447] + 5 X[49493], 7 X[49447] - 5 X[49517], 4 X[49447] - 5 X[49520], 7 X[49493] + X[49517], 4 X[49493] + X[49520], 4 X[49517] - 7 X[49520], 4 X[37] - 5 X[19862], X[3625] - 8 X[4726], X[4709] - 4 X[4726], 3 X[4740] + X[24349], 3 X[4740] - X[49474], 9 X[4740] + X[49498], 6 X[4740] + X[49535], 3 X[24349] - X[49498], 3 X[49474] + X[49498], 2 X[49474] + X[49535], 2 X[49498] - 3 X[49535], 3 X[551] - 2 X[3993], 9 X[551] - 8 X[15569], 3 X[551] - 4 X[24325], 3 X[3993] - 4 X[15569], 2 X[15569] - 3 X[24325], 4 X[3696] - 3 X[4669], 3 X[4669] - 2 X[49510], 3 X[4669] + 4 X[49525], X[49510] + 2 X[49525], X[3244] + 4 X[4686], 5 X[3244] - 4 X[49475], 3 X[3244] - 4 X[49478], X[3244] - 4 X[49483], 5 X[4686] + X[49475], 3 X[4686] + X[49478], 2 X[4686] + X[49479], 3 X[49475] - 5 X[49478], 2 X[49475] - 5 X[49479], X[49475] - 5 X[49483], 2 X[49478] - 3 X[49479], X[49478] - 3 X[49483], 5 X[1698] - 7 X[4772], 5 X[3616] - X[4788], 7 X[3624] - 5 X[4704], 4 X[3634] - 5 X[4699], 2 X[3644] - 7 X[15808], 3 X[3679] - X[31302], 3 X[3817] - 2 X[20430], 2 X[3842] - 3 X[4688], 3 X[4688] - X[49523], 2 X[4664] - 3 X[19883], 3 X[4664] - 5 X[40328], 9 X[19883] - 10 X[40328], 8 X[19878] - 7 X[27268], 3 X[31178] - X[49470], 3 X[34641] - 2 X[49450], X[49505] + 2 X[49533], X[49534] - 3 X[49720]

X(50117) lies on these lines: {1, 1278}, {2, 4135}, {8, 4821}, {10, 75}, {11, 48641}, {37, 19862}, {38, 4980}, {142, 6541}, {192, 1125}, {244, 321}, {335, 29594}, {518, 3625}, {519, 4740}, {536, 551}, {537, 3696}, {596, 42027}, {740, 3244}, {894, 49477}, {982, 42029}, {1086, 3773}, {1089, 20892}, {1215, 42051}, {1698, 4772}, {1757, 17117}, {2321, 49676}, {2796, 3883}, {3159, 29974}, {3210, 6685}, {3416, 24692}, {3616, 4788}, {3624, 4704}, {3626, 49448}, {3634, 4699}, {3635, 49469}, {3644, 15808}, {3661, 27494}, {3679, 31302}, {3706, 42055}, {3729, 16825}, {3739, 28555}, {3741, 4392}, {3751, 50018}, {3758, 4991}, {3775, 4665}, {3790, 49769}, {3797, 27478}, {3817, 20430}, {3826, 4439}, {3836, 7263}, {3842, 4688}, {3923, 4659}, {3953, 22167}, {3971, 4359}, {3994, 24589}, {3995, 25501}, {4058, 49509}, {4065, 25124}, {4066, 20891}, {4072, 38054}, {4133, 5542}, {4297, 29010}, {4361, 32935}, {4363, 32921}, {4365, 17140}, {4399, 5852}, {4407, 4733}, {4431, 24231}, {4440, 33082}, {4527, 4966}, {4535, 17231}, {4647, 20899}, {4649, 17160}, {4664, 19883}, {4671, 4871}, {4685, 17165}, {4716, 49685}, {4732, 49515}, {4764, 49452}, {4970, 32771}, {4974, 17351}, {5263, 49464}, {5493, 29054}, {6532, 22016}, {6686, 17490}, {7321, 32846}, {9055, 49511}, {9330, 32925}, {9843, 20171}, {16604, 20688}, {17063, 42034}, {17118, 49453}, {17146, 50001}, {17147, 43223}, {17151, 49488}, {17154, 31136}, {17340, 31289}, {17362, 17771}, {17365, 17772}, {19789, 25453}, {19796, 32780}, {19819, 33163}, {19820, 33132}, {19878, 27268}, {21241, 33089}, {21927, 24387}, {22295, 49981}, {24215, 33935}, {24603, 27481}, {26128, 50048}, {28484, 49471}, {28562, 49506}, {28581, 49491}, {28582, 49457}, {29603, 31347}, {29635, 30699}, {29674, 48627}, {31025, 46901}, {31178, 49470}, {32922, 49482}, {33159, 37756}, {34641, 49450}, {36480, 49446}, {49459, 49499}, {49505, 49533}, {49531, 49536}, {49534, 49720}

X(50117) = midpoint of X(i) and X(j) for these {i,j}: {1, 1278}, {8, 49532}, {75, 49493}, {3696, 49525}, {4686, 49483}, {4764, 49452}, {24349, 49474}, {49459, 49499}
X(50117) = reflection of X(i) in X(j) for these {i,j}: {10, 75}, {192, 1125}, {3244, 49479}, {3625, 4709}, {3993, 24325}, {4065, 25124}, {42027, 596}, {49448, 3626}, {49456, 3739}, {49469, 3635}, {49479, 49483}, {49504, 8}, {49508, 49457}, {49510, 3696}, {49515, 4732}, {49520, 10}, {49523, 3842}, {49535, 24349}, {49536, 49531}
X(50117) = complement of X(49445)
X(50117) = crosspoint of X(75) and X(27494)
X(50117) = crosssum of X(31) and X(21793)
X(50117) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {321, 24165, 3840}, {3696, 49510, 4669}, {3797, 27478, 29571}, {3993, 24325, 551}, {4066, 24176, 46827}, {4133, 5542, 49764}, {4363, 32921, 33682}, {4365, 17140, 42057}, {4431, 24231, 49560}, {4688, 49523, 3842}, {4740, 24349, 49474}, {17155, 28605, 3741}


X(50118) = X(2)X(2415)∩X(10)X(190)

Barycentrics    4*a^2 - 3*a*b + b^2 - 3*a*c + 6*b*c + c^2 : :
X(50118) = 7 X[2] - 5 X[17304], X[3663] + 2 X[3729], 7 X[3663] - 10 X[17304], X[3663] - 4 X[17355], 7 X[3729] + 5 X[17304], X[3729] + 2 X[17355], 5 X[17304] - 14 X[17355], 2 X[3886] + X[4924], X[2321] + 2 X[17351], 5 X[2321] - 2 X[17372], 5 X[17351] + X[17372], X[599] - 3 X[17281], 2 X[599] - 3 X[29594], X[599] + 3 X[49721], X[29594] + 2 X[49721], X[597] - 3 X[49726], 3 X[17359] - 2 X[20582], 2 X[3946] - 3 X[47352], 2 X[4353] - 3 X[25055], 2 X[4856] - 3 X[5032], X[11160] - 3 X[17294], X[17276] - 3 X[21358], 5 X[17286] - 3 X[21356], 3 X[19875] - X[24248], 3 X[19883] - 4 X[24295], 3 X[38023] - X[49453], 3 X[38314] - X[49446]

X(50118) lies on these lines: {2, 2415}, {6, 17133}, {10, 190}, {86, 4098}, {141, 4912}, {142, 17340}, {346, 3664}, {516, 3543}, {519, 1992}, {524, 2321}, {527, 599}, {536, 597}, {545, 17359}, {551, 726}, {894, 3950}, {1266, 17354}, {1743, 4461}, {1766, 3929}, {2325, 4363}, {2482, 22003}, {3008, 4659}, {3244, 3758}, {3661, 4480}, {3707, 4665}, {3717, 49720}, {3773, 28558}, {3817, 33167}, {3828, 28526}, {3879, 4072}, {3912, 4896}, {3943, 4667}, {3946, 47352}, {3973, 32087}, {4021, 5749}, {4029, 4670}, {4058, 4416}, {4061, 32938}, {4082, 4418}, {4141, 29639}, {4353, 25055}, {4357, 49748}, {4370, 4688}, {4419, 29604}, {4431, 17350}, {4440, 29596}, {4454, 4887}, {4470, 16676}, {4488, 17272}, {4644, 4873}, {4660, 4745}, {4669, 17346}, {4740, 41140}, {4747, 29602}, {4755, 10022}, {4758, 16672}, {4856, 5032}, {4908, 17392}, {4956, 33170}, {4967, 17336}, {4971, 20583}, {5257, 7227}, {5695, 47359}, {5750, 17262}, {6173, 41141}, {6666, 17118}, {8584, 28329}, {9041, 49484}, {10445, 50048}, {11160, 17294}, {11163, 49554}, {15534, 17299}, {15828, 17277}, {16670, 50019}, {16834, 28313}, {17229, 22165}, {17254, 17487}, {17264, 29600}, {17276, 21358}, {17280, 21255}, {17286, 21356}, {17301, 28301}, {17308, 20073}, {17342, 49722}, {17353, 37756}, {17369, 41311}, {17382, 28297}, {17760, 49549}, {17764, 38191}, {17766, 34641}, {17781, 31143}, {19875, 24248}, {19883, 24295}, {20258, 22019}, {25244, 25268}, {28322, 49741}, {28516, 38049}, {28557, 38047}, {29674, 30424}, {35043, 36220}, {36522, 49731}, {38023, 49453}, {38314, 49446}, {46922, 49482}

X(50118) = midpoint of X(i) and X(j) for these {i,j}: {2, 3729}, {5695, 47359}, {15534, 17299}, {17281, 49721}
X(50118) = reflection of X(i) in X(j) for these {i,j}: {2, 17355}, {3663, 2}, {4660, 4745}, {22165, 17229}, {29594, 17281}, {49543, 6}, {49630, 10}
X(50118) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {346, 35578, 29573}, {1266, 17354, 31191}, {2325, 4363, 29571}, {3161, 25590, 25072}, {3729, 17355, 3663}, {4454, 17284, 4887}, {4644, 4873, 49765}, {17340, 49727, 41310}, {29573, 35578, 3664}, {41310, 49727, 142}


X(50119) = X(2)X(2415)∩X(7)X(4431)

Barycentrics    2*a^2 - a*b - b^2 - a*c + 8*b*c - c^2 : :
X(50119) = 5 X[75] - 2 X[3686], 4 X[75] - X[4416], 3 X[75] - X[17346], 7 X[75] - X[17347], 8 X[3686] - 5 X[4416], 6 X[3686] - 5 X[17346], 14 X[3686] - 5 X[17347], 2 X[3686] + 5 X[49722], 3 X[4416] - 4 X[17346], 7 X[4416] - 4 X[17347], X[4416] + 4 X[49722], 7 X[17346] - 3 X[17347], X[17346] + 3 X[49722], X[17347] + 7 X[49722], X[49466] - 4 X[49483], 4 X[17392] - 3 X[29574], X[17392] - 3 X[49727], X[29574] - 4 X[49727], 5 X[4688] - 3 X[16590], 3 X[4688] - 2 X[49731], 9 X[16590] - 10 X[49731], X[1278] + 2 X[3664], X[3879] + 2 X[4686], X[3879] - 4 X[7228], X[4686] + 2 X[7228], 2 X[4726] + X[17365], 4 X[4739] - X[17334], 5 X[4821] + X[17364], X[49476] + 2 X[49493], 2 X[49525] + X[49527]

X(50119) lies on these lines: {2, 2415}, {7, 4431}, {8, 30424}, {10, 4440}, {37, 28297}, {75, 527}, {142, 17264}, {344, 38093}, {519, 4740}, {528, 49466}, {536, 17392}, {545, 4688}, {551, 3685}, {553, 39126}, {1086, 17359}, {1100, 7231}, {1266, 4363}, {1278, 3664}, {2094, 11679}, {2321, 7321}, {3241, 4349}, {3620, 4902}, {3626, 4741}, {3661, 4887}, {3668, 40892}, {3679, 4899}, {3687, 31164}, {3739, 28322}, {3875, 7222}, {3879, 4686}, {3883, 28534}, {3912, 4659}, {3950, 26806}, {4058, 17288}, {4060, 17361}, {4072, 17312}, {4346, 17308}, {4357, 17118}, {4384, 4454}, {4398, 5750}, {4419, 24603}, {4461, 17298}, {4644, 49770}, {4664, 28301}, {4667, 17160}, {4675, 29601}, {4677, 11160}, {4725, 4726}, {4739, 17334}, {4821, 17364}, {4896, 6542}, {4912, 17330}, {4967, 17251}, {4980, 20237}, {7263, 17353}, {10022, 41311}, {10436, 28641}, {16832, 20073}, {16834, 35578}, {17067, 17354}, {17133, 17378}, {17781, 20879}, {19875, 27549}, {20582, 36525}, {20880, 20881}, {22019, 30037}, {24248, 48851}, {24325, 28542}, {28580, 31178}, {31139, 41313}, {34641, 49707}, {36588, 39716}, {39707, 48640}, {48856, 49446}, {49476, 49493}, {49525, 49527}

X(50119) = midpoint of X(i) and X(j) for these {i,j}: {75, 49722}, {1278, 17389}
X(50119) = reflection of X(i) in X(j) for these {i,j}: {37, 49733}, {17389, 3664}, {49742, 3739}
X(50119) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1266, 4363, 17023}, {3729, 24199, 25101}, {3729, 31995, 24199}, {4373, 7229, 17304}, {4384, 4454, 4480}, {4659, 42697, 3912}, {4686, 7228, 3879}


X(50120) = X(2)X(594)∩X(6)X(536)

Barycentrics    3*a^2 + 2*a*b + 2*a*c - 4*b*c : :
X(50120) = 5 X[6] - 2 X[3729], X[6] + 2 X[3875], X[6] - 4 X[4852], 7 X[6] - 4 X[17351], X[3729] + 5 X[3875], X[3729] - 10 X[4852], X[3729] - 5 X[16834], 7 X[3729] - 10 X[17351], 4 X[3729] - 5 X[49721], X[3875] + 2 X[4852], 7 X[3875] + 2 X[17351], 4 X[3875] + X[49721], 7 X[4852] - X[17351], 8 X[4852] - X[49721], 7 X[16834] - 2 X[17351], 4 X[16834] - X[49721], 8 X[17351] - 7 X[49721], X[3242] - 4 X[32921], 5 X[3242] - 8 X[49464], X[3242] + 2 X[49486], 5 X[32921] - 2 X[49464], 2 X[32921] + X[49486], 4 X[49464] + 5 X[49486], X[15534] - 4 X[49543], X[49453] + 2 X[49488], 3 X[38315] - 2 X[48805], 4 X[2321] - 7 X[47355], 4 X[3663] - X[40341], 5 X[3763] - 8 X[3946], 5 X[3763] - 2 X[17299], 5 X[3763] - 4 X[29594], 4 X[3946] - X[17299], 2 X[4780] + X[49681], X[5695] - 4 X[49477], X[6144] + 2 X[17276], 5 X[16491] - 2 X[49485], 2 X[17281] - 3 X[47352], 2 X[17294] - 3 X[21358], 4 X[17382] - 3 X[21358], 5 X[17304] - 2 X[17372], 2 X[49455] + X[49680], X[49460] - 4 X[49472], 2 X[49463] + X[49495]

X(50120) lies on these lines: {1, 4688}, {2, 594}, {6, 536}, {8, 17325}, {37, 16833}, {43, 41144}, {45, 239}, {69, 28337}, {75, 16884}, {145, 1086}, {192, 16885}, {193, 28333}, {319, 17323}, {519, 599}, {524, 49747}, {527, 15534}, {537, 49453}, {545, 1992}, {597, 28309}, {740, 38315}, {903, 39720}, {1100, 17118}, {1213, 4371}, {1449, 4686}, {1743, 4718}, {2321, 47355}, {3241, 17392}, {3244, 4675}, {3632, 17237}, {3633, 17374}, {3644, 17121}, {3663, 40341}, {3672, 17253}, {3679, 4716}, {3696, 48854}, {3739, 29597}, {3759, 17262}, {3763, 3946}, {3834, 29605}, {3879, 4910}, {3943, 5222}, {4000, 4460}, {4007, 17384}, {4021, 17275}, {4363, 4393}, {4384, 4755}, {4389, 20016}, {4395, 17316}, {4399, 17321}, {4402, 17245}, {4415, 20043}, {4419, 4969}, {4428, 16684}, {4445, 17302}, {4452, 17365}, {4464, 4851}, {4643, 49770}, {4659, 16666}, {4665, 26626}, {4725, 15533}, {4727, 17284}, {4764, 17120}, {4780, 49681}, {4889, 17298}, {4980, 19722}, {5308, 31244}, {5425, 6173}, {5564, 17327}, {5695, 49477}, {5814, 50062}, {5839, 17246}, {6144, 17276}, {6542, 17290}, {7232, 17377}, {7277, 32105}, {7290, 49461}, {8584, 28297}, {9055, 27480}, {15668, 17117}, {16475, 28484}, {16491, 49485}, {16674, 17259}, {16675, 17348}, {16677, 17277}, {16706, 17309}, {16971, 36871}, {17014, 17369}, {17027, 41142}, {17133, 17281}, {17251, 17320}, {17255, 17363}, {17265, 17315}, {17269, 17367}, {17278, 29600}, {17294, 17382}, {17304, 17372}, {17305, 20055}, {17313, 17389}, {17346, 24441}, {17359, 24277}, {17398, 32087}, {17399, 29615}, {17599, 31136}, {19819, 37631}, {20155, 20181}, {25503, 29593}, {28554, 49489}, {29583, 40480}, {29585, 34824}, {31138, 34747}, {37654, 49742}, {41140, 41313}, {45659, 48303}, {47040, 49683}, {49455, 49680}, {49460, 49472}, {49463, 49495}

X(50120) = midpoint of X(3875) and X(16834)
X(50120) = reflection of X(i) in X(j) for these {i,j}: {6, 16834}, {69, 49741}, {599, 17301}, {15533, 17274}, {16834, 4852}, {17294, 17382}, {17299, 29594}, {29594, 3946}, {49721, 6}
X(50120) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 17395, 17325}, {239, 17318, 45}, {1100, 17151, 17118}, {3672, 17362, 17253}, {3875, 4852, 6}, {3946, 17299, 3763}, {4000, 4460, 17388}, {4000, 17388, 17311}, {4360, 4361, 16777}, {4393, 4740, 46922}, {4393, 17160, 4363}, {4740, 46922, 4363}, {5564, 17396, 17327}, {17117, 17393, 15668}, {17160, 46922, 4740}, {17259, 17319, 16674}, {17294, 17382, 21358}, {17314, 17366, 17267}, {17320, 29617, 17251}, {17389, 37756, 17313}, {32921, 49486, 3242}


X(50121) = X(2)X(594)∩X(145)X(190)

Barycentrics    2*a^2 + 3*a*b - b^2 + 3*a*c - 3*b*c - c^2 : :
X(50121) = 5 X[192] - 2 X[17334], 4 X[192] - X[17347], 2 X[192] + X[17377], X[192] + 2 X[17388], 8 X[17334] - 5 X[17347], 4 X[17334] + 5 X[17377], X[17334] + 5 X[17388], 4 X[17334] - 5 X[49748], X[17347] + 2 X[17377], X[17347] + 8 X[17388], X[17377] - 4 X[17388], 4 X[17388] + X[49748], 4 X[17389] - X[49722], X[1278] - 4 X[17390], X[3644] + 2 X[3879], 4 X[3664] - X[4764], 4 X[3739] - 5 X[29622], 4 X[4399] - 7 X[27268], 4 X[4681] - X[17363], 2 X[4686] - 5 X[17391], 5 X[4704] - 2 X[17362], 5 X[4704] - 4 X[49737], X[4718] + 2 X[4889], 2 X[4718] + X[17364], 4 X[4889] - X[17364], X[4788] + 2 X[17365]

X(50121) lies on these lines: {1, 4527}, {2, 594}, {8, 31144}, {37, 28329}, {45, 20016}, {75, 17133}, {145, 190}, {192, 524}, {239, 41313}, {320, 29605}, {344, 4460}, {519, 751}, {536, 17378}, {553, 42304}, {597, 3943}, {599, 4389}, {740, 36494}, {1266, 17387}, {1278, 17390}, {2321, 17381}, {2796, 49452}, {3241, 28503}, {3244, 3758}, {3247, 5564}, {3629, 25269}, {3632, 17256}, {3644, 3879}, {3661, 4727}, {3663, 17386}, {3664, 4764}, {3672, 17295}, {3723, 48628}, {3739, 29622}, {3759, 3950}, {3834, 29618}, {3875, 4859}, {3891, 37857}, {3946, 17240}, {4007, 17322}, {4021, 17228}, {4029, 17335}, {4363, 29588}, {4364, 20055}, {4395, 29572}, {4398, 4851}, {4399, 27268}, {4419, 11160}, {4431, 17394}, {4665, 29570}, {4675, 29619}, {4681, 17363}, {4685, 21699}, {4686, 17391}, {4704, 17362}, {4718, 4889}, {4725, 17333}, {4740, 17392}, {4788, 17365}, {4852, 17242}, {4910, 17121}, {4956, 33070}, {5224, 17299}, {6631, 34342}, {6646, 15533}, {8584, 17350}, {8860, 37764}, {11163, 29840}, {15534, 17262}, {16834, 17264}, {17117, 29620}, {17119, 29569}, {17151, 17317}, {17160, 17316}, {17227, 49765}, {17229, 17396}, {17230, 17395}, {17246, 17373}, {17247, 17372}, {17280, 47352}, {17281, 29584}, {17294, 17320}, {17301, 17310}, {17302, 17309}, {17305, 29616}, {17358, 48310}, {17360, 49761}, {17382, 29577}, {17399, 29594}, {20017, 31143}, {20046, 33761}, {20162, 40891}, {27191, 29583}, {27789, 41818}, {28337, 49742}, {28538, 49462}, {29612, 39260}, {33954, 50073}, {34747, 49695}, {41629, 42360}, {42028, 50043}

X(50121) = midpoint of X(17377) and X(49748)
X(50121) = reflection of X(i) in X(j) for these {i,j}: {75, 29574}, {1278, 49727}, {4740, 17392}, {17346, 4664}, {17347, 49748}, {17362, 49737}, {17378, 17389}, {29617, 37}, {49722, 17378}, {49727, 17390}, {49748, 192}
X(50121) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {192, 17377, 17347}, {192, 17388, 17377}, {2321, 17393, 17381}, {3875, 4898, 17315}, {3875, 17315, 17234}, {3875, 29573, 37756}, {3943, 4393, 17354}, {3950, 4464, 3759}, {4029, 49770, 17335}, {4360, 17233, 17380}, {4360, 17314, 17233}, {4718, 4889, 17364}, {4852, 17242, 17352}, {6542, 17318, 4389}, {17299, 17319, 5224}, {17299, 41312, 29615}, {17315, 37756, 29573}, {17319, 29615, 41312}, {29573, 37756, 17234}, {29615, 41312, 5224}


X(50122) = X(1)X(536)∩X(72)X(519)

Barycentrics    a^3*b + 2*a^2*b^2 + a*b^3 + a^3*c + 8*a^2*b*c - a*b^2*c - 2*b^3*c + 2*a^2*c^2 - a*b*c^2 - 4*b^2*c^2 + a*c^3 - 2*b*c^3 : :
X(50122) = 2 X[2901] + X[3057], 5 X[3697] - 6 X[42056], X[4018] - 4 X[35633]

X(50122) lies on these lines: {1, 536}, {2, 3702}, {10, 4519}, {72, 519}, {392, 740}, {517, 32915}, {537, 3555}, {551, 4065}, {986, 31137}, {1212, 4099}, {1402, 16400}, {2292, 31136}, {2646, 47040}, {3241, 42044}, {3679, 3714}, {3685, 13735}, {3697, 42056}, {3752, 4975}, {3875, 16483}, {3902, 3995}, {4018, 35633}, {4420, 4954}, {4647, 4688}, {4664, 4673}, {4692, 22034}, {4717, 31993}, {4742, 17147}, {4755, 19871}, {4852, 5315}, {4854, 50062}, {4868, 30818}, {4891, 5902}, {4918, 10916}, {4956, 17577}, {5049, 17155}, {5692, 28581}, {7743, 29849}, {10179, 28484}, {11112, 28580}, {11240, 25083}, {11552, 17376}, {16393, 32929}, {16466, 16834}, {16474, 17351}, {16833, 31435}, {17314, 30305}, {17320, 17762}, {17533, 49636}, {19875, 31327}, {24473, 42057}, {27480, 35274}, {29584, 41813}, {48799, 50065}, {48801, 50066}, {48803, 50068}, {48819, 50071}

X(50122) = midpoint of X(3241) and X(42044)
X(50122) = reflection of X(i) in X(j) for these {i,j}: {3679, 35652}, {5902, 4891}, {17155, 5049}, {24473, 42057}, {42051, 551}
X(50122) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2901, 3159, 49980}, {19871, 27785, 4755}


X(50123) = X(1)X(4727)∩X(44)X(145)

Barycentrics    4*a^2 + 5*a*b - 2*b^2 + 5*a*c - 4*b*c - 2*c^2 : :
X(50123) = 7 X[37] - 4 X[3686], 4 X[37] - 3 X[16590], 3 X[37] - 2 X[17330], 5 X[37] - 2 X[17362], X[37] + 2 X[17388], 16 X[3686] - 21 X[16590], 6 X[3686] - 7 X[17330], 10 X[3686] - 7 X[17362], 2 X[3686] + 7 X[17388], 9 X[16590] - 8 X[17330], 15 X[16590] - 8 X[17362], 3 X[16590] + 8 X[17388], 5 X[17330] - 3 X[17362], X[17330] + 3 X[17388], X[17362] + 5 X[17388], X[192] + 2 X[4889], X[17378] - 3 X[17389], 7 X[17378] - 3 X[49722], 7 X[17389] - X[49722], 2 X[3879] + X[4718], X[1278] - 3 X[39704], 2 X[4681] + X[17377], X[4686] - 4 X[17390], 3 X[4688] - 4 X[49738], 3 X[29574] - 2 X[49738], 2 X[4726] - 5 X[17391]

X(50123) lies on these lines: {1, 4727}, {2, 3723}, {6, 4898}, {9, 34747}, {10, 39260}, {37, 519}, {44, 145}, {45, 3633}, {192, 4715}, {344, 4910}, {346, 16668}, {536, 17378}, {545, 3879}, {551, 594}, {752, 49462}, {903, 17376}, {1100, 3241}, {1213, 4669}, {1278, 39704}, {3244, 3943}, {3247, 4677}, {3555, 21864}, {3632, 16672}, {3635, 17369}, {3679, 16777}, {3828, 4060}, {3875, 17313}, {3950, 4370}, {4007, 25055}, {4029, 4969}, {4034, 16674}, {4360, 17231}, {4364, 49761}, {4393, 17342}, {4395, 29601}, {4431, 10022}, {4460, 17278}, {4464, 17243}, {4664, 4725}, {4670, 29588}, {4681, 17333}, {4686, 17390}, {4688, 4971}, {4708, 20055}, {4726, 17391}, {4755, 29617}, {4851, 31138}, {4916, 17276}, {5257, 34641}, {5839, 20049}, {6542, 17237}, {16814, 37654}, {16834, 41310}, {16885, 36911}, {17119, 29602}, {17121, 41138}, {17133, 17392}, {17151, 31139}, {17160, 29619}, {17235, 17386}, {17271, 17319}, {17274, 17318}, {17275, 31145}, {17294, 41311}, {17303, 38314}, {17309, 17384}, {17344, 24441}, {17348, 40891}, {17359, 29584}, {17365, 28301}, {17366, 41141}, {17395, 49765}, {21863, 24473}, {28313, 49727}, {28503, 49478}, {28538, 49509}, {28580, 49461}, {29583, 31243}, {31332, 32025}, {32455, 36522}, {49468, 49725}

X(50123) = midpoint of X(17333) and X(17377)
X(50123) = reflection of X(i) in X(j) for these {i,j}: {4688, 29574}, {17333, 4681}, {29617, 4755}, {49468, 49725}
X(50123) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3241, 17281, 1100}, {3241, 17314, 17281}, {3244, 3943, 16666}, {4360, 17310, 17382}, {17310, 17382, 17231}, {17318, 29605, 17374}


X(50124) = X(2)X(319)∩X(6)X(536)

Barycentrics    6*a^2 + a*b + a*c - 2*b*c : :
X(50124) = 7 X[6] - X[3729], 5 X[6] + X[3875], 2 X[6] + X[4852], 4 X[6] - X[17351], 5 X[6] - X[49721], 5 X[3729] + 7 X[3875], 2 X[3729] + 7 X[4852], X[3729] + 7 X[16834], 4 X[3729] - 7 X[17351], 5 X[3729] - 7 X[49721], 2 X[3875] - 5 X[4852], X[3875] - 5 X[16834], 4 X[3875] + 5 X[17351], 2 X[4852] + X[17351], 5 X[4852] + 2 X[49721], 4 X[16834] + X[17351], 5 X[16834] + X[49721], 5 X[17351] - 4 X[49721], X[141] + 2 X[4856], X[193] + 2 X[17235], X[1386] - 4 X[4991], 4 X[1386] - X[49467], 5 X[1386] - 2 X[49473], X[1386] + 2 X[49489], 16 X[4991] - X[49467], 10 X[4991] - X[49473], 2 X[4991] + X[49489], 5 X[49467] - 8 X[49473], X[49467] + 8 X[49489], X[49473] + 5 X[49489], 2 X[4663] + X[49463], X[4663] + 2 X[49477], X[49463] - 4 X[49477], X[2321] - 4 X[6329], 4 X[3589] - X[17372], 5 X[3618] - 2 X[17229], X[3629] + 2 X[3946], 2 X[3629] + X[17345], 4 X[3946] - X[17345], X[3663] + 2 X[32455], X[6144] + 5 X[17304], 3 X[16475] - X[48805], 5 X[16491] + X[49680], X[17294] - 3 X[47352], X[49465] + 2 X[49685], X[49484] + 2 X[49488]

X(50124) lies on these lines: {1, 4755}, {2, 319}, {6, 536}, {37, 17121}, {44, 4393}, {75, 16668}, {141, 4856}, {192, 16671}, {193, 17235}, {239, 4670}, {346, 4910}, {519, 597}, {524, 17382}, {527, 8584}, {537, 4663}, {545, 20583}, {551, 4974}, {1279, 3241}, {1449, 3739}, {1743, 4681}, {1992, 4715}, {2321, 6329}, {3008, 4982}, {3244, 4422}, {3589, 17372}, {3618, 17229}, {3629, 3946}, {3633, 17269}, {3663, 28333}, {3686, 25498}, {3723, 17349}, {3758, 4740}, {3834, 5222}, {3879, 17356}, {3941, 4421}, {4000, 32093}, {4360, 16669}, {4361, 16667}, {4364, 4700}, {4395, 4667}, {4464, 17340}, {4641, 45222}, {4643, 17014}, {4665, 50019}, {4686, 17120}, {4690, 4969}, {4698, 16884}, {4708, 26626}, {4727, 17354}, {4796, 42697}, {4889, 17279}, {4912, 5032}, {4971, 49543}, {5625, 19883}, {5847, 48821}, {6144, 17304}, {6687, 17316}, {15492, 17319}, {15534, 17274}, {16475, 28581}, {16477, 49462}, {16491, 49680}, {16670, 17318}, {16696, 25059}, {16814, 17393}, {17027, 41144}, {17133, 49726}, {17260, 46845}, {17277, 29580}, {17281, 28329}, {17294, 47352}, {17344, 17380}, {17346, 41311}, {17352, 29582}, {17357, 17377}, {17362, 17385}, {17363, 17384}, {17366, 17376}, {17367, 17374}, {17369, 49770}, {17387, 31243}, {17389, 41310}, {17390, 29600}, {17392, 41140}, {18194, 42043}, {37654, 41312}, {49465, 49685}, {49484, 49488}

X(50124) = midpoint of X(i) and X(j) for these {i,j}: {6, 16834}, {1992, 17301}, {3629, 49741}, {3875, 49721}, {15534, 17274}
X(50124) = reflection of X(i) in X(j) for these {i,j}: {4852, 16834}, {17345, 49741}, {17359, 597}, {17372, 29594}, {29594, 3589}, {49741, 3946}
X(50124) = crossdifference of every pair of points on line {4834, 9010}
X(50124) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 4852, 17351}, {239, 16666, 4670}, {239, 46922, 4688}, {1100, 3759, 17348}, {1100, 17348, 28639}, {3629, 3946, 17345}, {4663, 49477, 49463}, {4688, 16666, 46922}, {4688, 46922, 4670}, {4969, 17023, 4690}, {4991, 49489, 1386}


X(50125) = X(1)X(599)∩X(2)X(319)

Barycentrics    4*a^2 + 3*a*b - 2*b^2 + 3*a*c - 2*c^2 : :
X(50125) = X[37] + 2 X[3879], 5 X[37] - 2 X[4416], 7 X[37] - 4 X[17332], X[37] - 4 X[17390], 5 X[37] - 4 X[49737], 5 X[3879] + X[4416], 7 X[3879] + 2 X[17332], X[3879] + 2 X[17390], 5 X[3879] + 2 X[49737], 7 X[4416] - 10 X[17332], X[4416] - 10 X[17390], X[4416] - 5 X[29574], X[17332] - 7 X[17390], 2 X[17332] - 7 X[29574], 5 X[17332] - 7 X[49737], 5 X[17390] - X[49737], 5 X[29574] - 2 X[49737], X[75] + 2 X[4889], 5 X[17378] - X[49722], 5 X[17389] + X[49722], 4 X[3664] - X[4686], 2 X[3664] + X[17388], X[4686] + 2 X[17388], 2 X[3739] + X[17377], 2 X[3739] - 5 X[17391], X[17377] + 5 X[17391], 5 X[17391] - X[29617], 2 X[4681] + X[17364], 4 X[4698] - X[17363], 4 X[4698] - 5 X[29622], X[17363] - 5 X[29622], X[4718] + 2 X[17365], X[4740] - 3 X[39704], 4 X[4755] - 3 X[16590], 3 X[16590] - 2 X[17346], 2 X[17362] - 5 X[31238]

X(50125) lies on these lines: {1, 599}, {2, 319}, {6, 29573}, {9, 15534}, {37, 524}, {44, 1992}, {45, 29602}, {69, 3723}, {75, 4889}, {86, 17372}, {142, 49543}, {145, 4675}, {190, 29619}, {192, 4912}, {193, 16814}, {320, 29588}, {344, 5032}, {519, 3696}, {536, 17378}, {551, 4966}, {597, 3912}, {1086, 3244}, {1386, 49752}, {1449, 17311}, {2482, 37589}, {2796, 49462}, {3175, 42045}, {3241, 4645}, {3247, 40341}, {3416, 48830}, {3629, 15492}, {3633, 17119}, {3635, 17395}, {3664, 4686}, {3714, 49564}, {3731, 6144}, {3739, 17377}, {3834, 4393}, {3908, 8539}, {3943, 4667}, {3945, 4916}, {3950, 7277}, {3970, 7202}, {3993, 28558}, {4357, 22165}, {4360, 17376}, {4363, 4727}, {4364, 39260}, {4377, 30939}, {4422, 20583}, {4464, 7263}, {4552, 14564}, {4643, 11160}, {4657, 21356}, {4664, 4715}, {4665, 49761}, {4668, 36834}, {4670, 6542}, {4681, 17364}, {4690, 16826}, {4698, 17363}, {4700, 29606}, {4708, 17360}, {4718, 17132}, {4740, 39704}, {4755, 16590}, {4852, 17300}, {4856, 17337}, {4909, 17398}, {4969, 29571}, {5222, 31243}, {5266, 7801}, {5425, 6173}, {5847, 49740}, {6687, 29572}, {7810, 37592}, {8584, 16669}, {9041, 49476}, {11168, 24239}, {15533, 16777}, {16667, 17267}, {16668, 17279}, {16726, 20691}, {16834, 17313}, {16884, 17296}, {17019, 31143}, {17023, 20582}, {17225, 49528}, {17229, 17379}, {17235, 17375}, {17240, 37677}, {17251, 29597}, {17271, 29580}, {17277, 29620}, {17287, 25498}, {17295, 17385}, {17297, 17382}, {17310, 17359}, {17312, 17356}, {17314, 35578}, {17315, 17351}, {17319, 17345}, {17354, 29618}, {17362, 31238}, {17369, 49765}, {20055, 41847}, {25101, 32455}, {25536, 32004}, {28337, 49738}, {28562, 49471}, {28581, 49720}, {31139, 34747}, {34824, 49770}, {42028, 50052}, {48828, 48862}

X(50125) = midpoint of X(i) and X(j) for these {i,j}: {3879, 29574}, {17364, 49748}, {17377, 29617}, {17378, 17389}, {17388, 49727}
X(50125) = reflection of X(i) in X(j) for these {i,j}: {37, 29574}, {4416, 49737}, {4686, 49727}, {4688, 17392}, {17346, 4755}, {29574, 17390}, {29617, 3739}, {49727, 3664}, {49748, 4681}
X(50125) = crossdifference of every pair of points on line {2515, 4834}
X(50125) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 599, 41311}, {1, 17374, 17237}, {6, 29573, 41310}, {599, 41311, 17237}, {1100, 4851, 17231}, {1449, 17311, 17357}, {1992, 17316, 41313}, {1992, 41313, 44}, {3664, 17388, 4686}, {3879, 17390, 37}, {3945, 4916, 17299}, {4363, 29605, 4727}, {4393, 17387, 3834}, {4755, 17346, 16590}, {16884, 17296, 17384}, {17297, 29584, 17382}, {17310, 46922, 17359}, {17315, 20090, 17351}, {17360, 29570, 4708}, {17373, 17394, 17239}, {17374, 41311, 599}, {17375, 17393, 17235}, {17377, 17391, 3739}, {17379, 17386, 17229}


X(50126) = X(1)X(536)∩X(9)X(80)

Barycentrics    3*a^3 - 2*a^2*b + a*b^2 - 2*a^2*c + 4*b^2*c + a*c^2 + 4*b*c^2 : :
X(50126) = X[1] + 2 X[5695], 5 X[1] - 2 X[49453], 7 X[1] - 4 X[49463], X[1] - 4 X[49484], 5 X[5695] + X[49453], 7 X[5695] + 2 X[49463], X[5695] + 2 X[49484], 5 X[48805] - X[49453], 7 X[48805] - 2 X[49463], 7 X[49453] - 10 X[49463], X[49453] - 10 X[49484], X[49463] - 7 X[49484], X[6] + 2 X[49485], X[3751] + 2 X[3886], X[3751] - 4 X[3923], X[3886] + 2 X[3923], 2 X[3729] + X[16496], X[3729] + 2 X[32941], X[16496] - 4 X[32941], 3 X[16475] - 2 X[16834], 4 X[960] - X[15076], 5 X[1698] - 4 X[48821], 5 X[3618] - 2 X[4780], 2 X[3875] - 5 X[16491], X[3875] - 4 X[49482], 5 X[16491] - 8 X[49482], 2 X[4660] - 5 X[17286], 4 X[4672] - X[49495], 2 X[17301] - 3 X[25055], 3 X[25055] - 4 X[48810], 2 X[17351] + X[49460], 4 X[17359] - 3 X[19875], 3 X[19875] - 2 X[48829], X[24280] + 2 X[49511], X[49446] - 4 X[49473], 2 X[32935] + X[49451]

X(50126) lies on these lines: {1, 536}, {2, 968}, {6, 49485}, {9, 80}, {30, 12717}, {57, 31137}, {63, 31136}, {238, 16833}, {314, 4234}, {321, 3749}, {390, 48849}, {516, 29594}, {518, 49721}, {519, 1992}, {537, 3729}, {545, 47358}, {551, 4021}, {599, 28534}, {740, 16475}, {752, 17294}, {894, 3241}, {960, 15076}, {1001, 4688}, {1376, 33845}, {1402, 16396}, {1449, 49469}, {1698, 48821}, {1699, 33160}, {1707, 3706}, {1743, 49459}, {1757, 4677}, {1966, 4479}, {2783, 3576}, {2796, 17274}, {3058, 50048}, {3246, 17119}, {3618, 4780}, {3702, 16393}, {3870, 31161}, {3875, 16491}, {4312, 33087}, {4384, 4432}, {4387, 5268}, {4442, 29855}, {4519, 37540}, {4644, 49763}, {4645, 29577}, {4650, 35613}, {4660, 17286}, {4664, 5263}, {4672, 49495}, {4716, 16469}, {4717, 37817}, {4779, 39581}, {4873, 32847}, {4954, 41242}, {5692, 44670}, {6284, 50046}, {7174, 36554}, {7290, 49474}, {9580, 32778}, {10472, 16351}, {10477, 44663}, {15171, 50047}, {16395, 16778}, {16484, 25590}, {16670, 50016}, {16676, 36531}, {17118, 42819}, {17264, 49720}, {17284, 24715}, {17301, 24342}, {17350, 31145}, {17351, 49460}, {17359, 19875}, {24280, 49511}, {24392, 33167}, {24473, 35892}, {25728, 49457}, {28484, 38315}, {28530, 49741}, {28554, 49446}, {30568, 42056}, {32935, 49451}, {41313, 49725}, {42697, 49768}, {46922, 49470}, {47359, 49726}, {48803, 48818}, {48851, 49746}

X(50126) = midpoint of X(5695) and X(48805)
X(50126) = reflection of X(i) in X(j) for these {i,j}: {1, 48805}, {3679, 17281}, {17301, 48810}, {47359, 49726}, {48805, 49484}, {48818, 48803}, {48829, 17359}
X(50126) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3729, 32941, 16496}, {3875, 49482, 16491}, {3886, 3923, 3751}, {4363, 4702, 1}, {4664, 5263, 48854}, {5695, 49484, 1}, {17301, 48810, 25055}, {17359, 48829, 19875}


X(50127) = X(1)X(190)∩X(2)X(7)

Barycentrics    3*a^2 - a*b - a*c + 2*b*c : :
X(50127) = X[1] - 4 X[4672], X[1] + 2 X[32935], 2 X[4672] + X[32935], 2 X[6] + X[3729], 4 X[6] - X[3875], 5 X[6] - 2 X[4852], X[6] + 2 X[17351], 2 X[3729] + X[3875], 5 X[3729] + 4 X[4852], X[3729] - 4 X[17351], 5 X[3875] - 8 X[4852], X[3875] + 8 X[17351], X[3875] + 4 X[49721], 4 X[4852] - 5 X[16834], X[4852] + 5 X[17351], 2 X[4852] + 5 X[49721], X[16834] + 4 X[17351], X[16834] + 2 X[49721], 2 X[10] + X[24695], 2 X[69] - 5 X[17286], X[69] - 4 X[17355], 5 X[17286] - 8 X[17355], 5 X[17286] - 4 X[29594], X[193] + 2 X[2321], 2 X[3751] + X[3886], X[3751] + 2 X[3923], X[3886] - 4 X[3923], X[17294] - 4 X[49726], 4 X[1386] - X[49446], 5 X[1698] - 2 X[4655], 4 X[3589] - X[17276], 8 X[3589] - 5 X[17304], 2 X[17276] - 5 X[17304], 5 X[17304] - 4 X[49741], 5 X[3618] - 2 X[3663], 2 X[3629] + X[17299], 2 X[3755] + X[24280], 5 X[3763] - 2 X[17345], 2 X[4663] + X[5695], 4 X[4663] - X[49495], 2 X[5695] + X[49495], 2 X[17382] - 3 X[47352], 3 X[47352] - X[49747], X[6144] + 2 X[17372], 5 X[16491] - 2 X[49455], X[16496] - 4 X[49482], 4 X[17229] - X[40341], 4 X[17235] - 7 X[47355], 3 X[38047] - 2 X[48821], X[49451] - 4 X[49484], 2 X[49485] + X[49680]

X(50127) lies on these lines: {1, 190}, {2, 7}, {6, 536}, {10, 24695}, {31, 31161}, {37, 25728}, {43, 2230}, {44, 4363}, {45, 4670}, {69, 17286}, {72, 16394}, {75, 1743}, {78, 16393}, {86, 3731}, {141, 28333}, {192, 1449}, {193, 2321}, {228, 16395}, {238, 31178}, {239, 4659}, {284, 16046}, {314, 41629}, {320, 17284}, {344, 3664}, {346, 3879}, {391, 4967}, {518, 48805}, {519, 1992}, {524, 17281}, {528, 47359}, {545, 597}, {599, 4715}, {612, 32938}, {614, 32940}, {645, 17103}, {646, 24524}, {651, 9312}, {666, 24411}, {726, 16475}, {752, 1757}, {758, 48826}, {896, 29828}, {940, 30568}, {964, 3951}, {984, 48854}, {999, 33845}, {1014, 38869}, {1016, 35962}, {1045, 42043}, {1100, 17262}, {1215, 1707}, {1220, 12526}, {1260, 16398}, {1266, 4454}, {1278, 17121}, {1386, 49446}, {1473, 16404}, {1698, 4655}, {1699, 33121}, {2319, 39929}, {2325, 4667}, {2345, 4416}, {2663, 42042}, {2792, 5587}, {2999, 32939}, {3008, 42697}, {3097, 24574}, {3161, 3945}, {3220, 19326}, {3241, 3685}, {3247, 17261}, {3501, 3882}, {3589, 17276}, {3618, 3663}, {3629, 17299}, {3661, 20072}, {3672, 4488}, {3717, 4307}, {3739, 16885}, {3755, 24280}, {3759, 17151}, {3763, 17345}, {3765, 4494}, {3883, 48849}, {3912, 4644}, {3943, 29605}, {3973, 17277}, {3984, 11115}, {4007, 17363}, {4029, 29585}, {4034, 48628}, {4054, 24597}, {4098, 4909}, {4195, 11523}, {4312, 4429}, {4339, 32034}, {4344, 49527}, {4360, 16667}, {4361, 16669}, {4364, 29603}, {4370, 4795}, {4389, 29598}, {4419, 4480}, {4422, 4675}, {4431, 5839}, {4440, 17367}, {4470, 24603}, {4473, 17244}, {4552, 25716}, {4641, 11679}, {4643, 17308}, {4648, 25101}, {4657, 17334}, {4663, 5695}, {4681, 16884}, {4686, 16671}, {4697, 5268}, {4713, 41144}, {4718, 16668}, {4722, 17156}, {4725, 15534}, {4741, 17292}, {4747, 5308}, {4748, 26039}, {4756, 9347}, {4759, 24331}, {4851, 7277}, {4855, 16397}, {4859, 7321}, {4862, 16706}, {4873, 6542}, {4887, 31191}, {4888, 17234}, {4901, 49754}, {4902, 48629}, {4912, 17382}, {4971, 8584}, {5032, 17133}, {5223, 5263}, {5256, 32933}, {5269, 32937}, {5440, 16401}, {5735, 36652}, {5782, 23151}, {5814, 50047}, {6144, 17372}, {6381, 41316}, {6651, 36911}, {7085, 16403}, {7222, 24199}, {7227, 17275}, {7228, 17278}, {7232, 17357}, {7290, 24349}, {9620, 35103}, {10022, 49731}, {10477, 11354}, {11319, 11520}, {11518, 17697}, {12717, 28194}, {14621, 31349}, {15492, 17259}, {15601, 16823}, {15668, 16814}, {15828, 25072}, {16371, 23206}, {16396, 20760}, {16399, 20769}, {16417, 23169}, {16469, 32922}, {16477, 49493}, {16491, 49455}, {16496, 49482}, {16549, 21362}, {16570, 32916}, {16571, 36634}, {16666, 17318}, {16673, 17394}, {16675, 28639}, {16676, 16826}, {16829, 21384}, {16832, 17335}, {17026, 24330}, {17116, 17349}, {17118, 17348}, {17229, 40341}, {17235, 47355}, {17242, 20090}, {17253, 17385}, {17255, 17384}, {17258, 17381}, {17264, 17378}, {17267, 17376}, {17268, 17375}, {17269, 17374}, {17272, 17289}, {17273, 17371}, {17279, 17298}, {17280, 17296}, {17285, 17361}, {17288, 17358}, {17293, 17344}, {17297, 17342}, {17300, 17339}, {17303, 17332}, {17307, 17329}, {17313, 41310}, {17319, 25269}, {17320, 49748}, {17331, 28604}, {17768, 38047}, {17787, 34283}, {18065, 44139}, {18787, 43262}, {19322, 24320}, {19875, 24342}, {20073, 26626}, {20583, 28309}, {20942, 32017}, {21477, 24328}, {23891, 36275}, {24441, 41311}, {24578, 36406}, {24725, 29857}, {25734, 28606}, {26076, 27091}, {26227, 36277}, {27813, 27834}, {28313, 49543}, {28534, 48829}, {28554, 32921}, {28582, 38315}, {29578, 36834}, {29826, 36263}, {29855, 32856}, {31136, 32912}, {31137, 32913}, {31165, 35628}, {31995, 37681}, {33163, 41011}, {35258, 46897}, {36807, 39704}, {37756, 49722}, {39694, 39948}, {41312, 49742}, {44663, 48832}, {47358, 48810}, {49451, 49484}, {49485, 49680}

X(50127) = midpoint of X(i) and X(j) for these {i,j}: {6, 49721}, {3729, 16834}
X(50127) = reflection of X(i) in X(j) for these {i,j}: {69, 29594}, {599, 17359}, {3729, 49721}, {3875, 16834}, {16834, 6}, {17274, 2}, {17276, 49741}, {17281, 49726}, {17294, 17281}, {17301, 597}, {29594, 17355}, {47358, 48810}, {49721, 17351}, {49741, 3589}, {49747, 17382}
X(50127) = X(16975)-Dao conjugate of X(30942)
X(50127) = crossdifference of every pair of points on line {663, 3768}
X(50127) = barycentric product X(i)*X(j) for these {i,j}: {75, 37540}, {190, 47761}
X(50127) = barycentric quotient X(i)/X(j) for these {i,j}: {37540, 1}, {47761, 514}
X(50127) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3729, 3875}, {6, 17351, 3729}, {7, 17353, 17282}, {9, 894, 10436}, {9, 44421, 16574}, {44, 4363, 4384}, {45, 4670, 16831}, {69, 17355, 17286}, {86, 17336, 3731}, {144, 5749, 4357}, {190, 3758, 1}, {190, 46922, 4664}, {192, 17120, 1449}, {320, 17354, 17284}, {391, 7229, 4967}, {894, 17350, 9}, {2325, 4667, 17316}, {2345, 4416, 17270}, {3589, 17276, 17304}, {3751, 3923, 3886}, {3758, 4664, 46922}, {3973, 25590, 17277}, {4370, 17392, 41313}, {4454, 5222, 1266}, {4480, 17023, 4419}, {4643, 17369, 17308}, {4659, 16670, 239}, {4663, 5695, 49495}, {4664, 46922, 1}, {4672, 32935, 1}, {4795, 41313, 17392}, {5294, 5905, 25527}, {6646, 17368, 17306}, {7222, 37650, 24199}, {7277, 17340, 4851}, {7321, 17352, 4859}, {17261, 17379, 3247}, {17264, 17378, 29573}, {17279, 17365, 17298}, {17280, 17364, 17296}, {17289, 17347, 17272}, {17338, 26806, 20195}, {25269, 37677, 17319}, {47352, 49747, 17382}


X(50128) = X(1)X(2796)∩X(2)X(7)

Barycentrics    2*a^2 - b^2 + 3*b*c - c^2 : :
X(50128) = 4 X[37] - 5 X[29622], 5 X[29622] - 2 X[49748], 7 X[75] - 4 X[4399], X[75] - 4 X[7228], 5 X[75] - 2 X[17362], 4 X[75] - X[17363], 2 X[75] + X[17364], X[75] + 2 X[17365], X[4399] - 7 X[7228], 10 X[4399] - 7 X[17362], 16 X[4399] - 7 X[17363], 8 X[4399] + 7 X[17364], 2 X[4399] + 7 X[17365], 8 X[4399] - 7 X[29617], 2 X[4399] - 7 X[49727], 10 X[7228] - X[17362], 16 X[7228] - X[17363], 8 X[7228] + X[17364], 2 X[7228] + X[17365], 8 X[7228] - X[29617], 8 X[17362] - 5 X[17363], 4 X[17362] + 5 X[17364], X[17362] + 5 X[17365], 4 X[17362] - 5 X[29617], X[17362] - 5 X[49727], X[17363] + 2 X[17364], X[17363] + 8 X[17365], X[17363] - 8 X[49727], X[17364] - 4 X[17365], X[17364] + 4 X[49727], 4 X[17365] + X[29617], X[29617] - 4 X[49727], X[192] - 4 X[3664], 2 X[192] - 5 X[17391], 8 X[3664] - 5 X[17391], 5 X[17391] - 4 X[29574], X[4664] - 3 X[39704], 2 X[17392] - 3 X[39704], X[17389] + 2 X[49722], X[1278] + 2 X[3879], X[3644] - 4 X[17390], 4 X[3686] - 7 X[4772], 8 X[3739] - 5 X[17331], 4 X[3739] - X[17347], 5 X[17331] - 2 X[17347], 2 X[4416] - 5 X[4699], 2 X[4686] + X[17377], 5 X[4687] - 2 X[17334], 5 X[4687] - 4 X[49737], 7 X[4751] - 4 X[17332], X[4764] + 2 X[17388]

X(50128) lies on these lines: {1, 2796}, {2, 7}, {6, 7321}, {8, 11160}, {10, 4741}, {37, 4912}, {44, 29628}, {45, 29581}, {69, 7222}, {75, 524}, {86, 17247}, {87, 7189}, {190, 4675}, {192, 3664}, {193, 17117}, {239, 1992}, {319, 15533}, {320, 599}, {335, 545}, {346, 17312}, {350, 34363}, {518, 49720}, {519, 4740}, {536, 17378}, {551, 24231}, {591, 32801}, {594, 7231}, {597, 1086}, {752, 31178}, {903, 4586}, {1100, 4398}, {1213, 17329}, {1266, 4393}, {1278, 3879}, {1654, 25590}, {1836, 29843}, {1991, 32802}, {2321, 17375}, {2325, 29572}, {2345, 17288}, {3227, 44353}, {3241, 4307}, {3589, 48629}, {3620, 7229}, {3623, 15590}, {3631, 48630}, {3644, 17390}, {3663, 17379}, {3673, 8370}, {3679, 4645}, {3686, 4772}, {3705, 7840}, {3729, 4888}, {3739, 17331}, {3759, 7263}, {3782, 29841}, {3834, 17354}, {3873, 6007}, {3875, 20090}, {3912, 4896}, {3943, 17387}, {3945, 17319}, {3946, 37677}, {4000, 17120}, {4054, 37684}, {4141, 29643}, {4310, 38314}, {4346, 4747}, {4361, 15534}, {4364, 29612}, {4371, 11008}, {4384, 20072}, {4389, 4670}, {4395, 20583}, {4416, 4699}, {4419, 16826}, {4431, 17373}, {4454, 17316}, {4461, 32093}, {4470, 29610}, {4472, 17250}, {4480, 29571}, {4643, 29576}, {4648, 17261}, {4659, 6542}, {4665, 17360}, {4676, 25557}, {4686, 17377}, {4687, 17334}, {4688, 4715}, {4697, 29634}, {4751, 17332}, {4764, 17388}, {4796, 16666}, {4862, 17302}, {4869, 17268}, {4887, 17023}, {4902, 17304}, {4911, 7841}, {4967, 17343}, {5032, 17121}, {5224, 17345}, {5263, 47358}, {5308, 20073}, {5564, 40341}, {5764, 16397}, {5860, 32797}, {5861, 32798}, {5880, 47359}, {5969, 33890}, {6625, 34899}, {6645, 7185}, {7032, 7240}, {7198, 25918}, {7227, 17228}, {7232, 17289}, {7238, 17227}, {7812, 33940}, {9041, 49499}, {11329, 24328}, {15668, 17258}, {16670, 29590}, {16706, 47352}, {16823, 24695}, {17232, 17355}, {17233, 17376}, {17234, 17339}, {17235, 17381}, {17237, 29608}, {17241, 17340}, {17245, 17336}, {17246, 17394}, {17249, 17398}, {17253, 28653}, {17255, 17322}, {17262, 17317}, {17264, 17313}, {17272, 28604}, {17273, 17303}, {17280, 17298}, {17281, 17297}, {17287, 21296}, {17320, 49747}, {17330, 28333}, {17335, 34824}, {17342, 49726}, {17349, 24199}, {17358, 21255}, {17359, 31138}, {17370, 48310}, {17371, 48632}, {17399, 49741}, {17743, 24796}, {17768, 49740}, {17951, 19604}, {19883, 26150}, {20080, 32087}, {20892, 34283}, {24248, 48830}, {24325, 28558}, {24330, 31028}, {24342, 48809}, {24411, 39353}, {24692, 29659}, {24693, 49712}, {25760, 31177}, {27447, 43263}, {28534, 49746}, {28538, 49483}, {28562, 49479}, {29641, 32940}, {30424, 49630}, {31143, 32859}, {34573, 48637}, {37608, 49608}, {42028, 50068}, {49738, 49742}

X(50128) = midpoint of X(i) and X(j) for these {i,j}: {17364, 29617}, {17365, 49727}, {17378, 49722}
X(50128) = reflection of X(i) in X(j) for these {i,j}: {75, 49727}, {192, 29574}, {4664, 17392}, {17330, 49733}, {17333, 2}, {17334, 49737}, {17346, 4688}, {17363, 29617}, {17389, 17378}, {29574, 3664}, {29617, 75}, {49727, 7228}, {49742, 49738}, {49748, 37}
X(50128) = barycentric product X(27777)*X(39704)
X(50128) = barycentric quotient X(i)/X(j) for these {i,j}: {10485, 10987}, {27777, 3679}
X(50128) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 35578, 894}, {6, 7321, 48627}, {7, 894, 3662}, {7, 35578, 2}, {9, 26806, 27147}, {69, 7222, 17116}, {69, 17116, 48628}, {75, 17364, 17363}, {75, 17365, 17364}, {86, 17276, 17247}, {142, 17350, 17338}, {190, 4675, 17244}, {192, 3664, 17391}, {193, 31995, 17117}, {320, 4363, 3661}, {894, 3662, 17368}, {894, 17291, 5749}, {903, 46922, 17301}, {1086, 3758, 17367}, {1266, 4667, 4393}, {2345, 17288, 48634}, {3663, 17379, 17396}, {3729, 4888, 17300}, {3729, 17300, 17242}, {3739, 17347, 17331}, {3834, 17354, 29629}, {3943, 17387, 29618}, {4346, 4747, 26626}, {4364, 41847, 29612}, {4389, 4670, 17397}, {4644, 42697, 239}, {4664, 39704, 17392}, {4697, 33103, 29634}, {4795, 17301, 46922}, {6646, 10436, 17248}, {7228, 17365, 75}, {7232, 17289, 48633}, {7238, 17369, 17227}, {7263, 7277, 3759}, {17227, 17369, 29613}, {17234, 17351, 17339}, {17264, 17313, 29582}, {17281, 17297, 29577}, {17313, 49721, 17264}, {26806, 31300, 9}


X(50129) = X(1)X(2)∩X(6)X(4971)

Barycentrics    5*a^2 + 2*a*b - b^2 + 2*a*c - 4*b*c - c^2 : :
X(50129) = 5 X[2] - 4 X[29594], X[2] - 4 X[49543], X[8] - 4 X[49488], X[145] + 2 X[49495], 5 X[3616] - 8 X[49477], 5 X[3623] - 2 X[49451], 11 X[5550] - 8 X[49560], 3 X[16834] - X[17294], 5 X[16834] - 2 X[29594], 5 X[17294] - 6 X[29594], X[17294] - 6 X[49543], 7 X[20057] - 4 X[49458], X[29594] - 5 X[49543], 3 X[6] - 2 X[49726], X[69] - 4 X[4852], 5 X[69] - 8 X[17235], 5 X[4852] - 2 X[17235], 4 X[17235] - 5 X[17301], X[193] + 2 X[3875], 4 X[32029] - X[41842], 5 X[3618] - 2 X[17299], 5 X[3618] - 4 X[17359], 7 X[3619] - 4 X[17372], 5 X[3620] - 8 X[3946], 4 X[3663] - X[20080], X[3729] - 4 X[4856], X[11008] + 2 X[17276], 4 X[17382] - 3 X[21356]

X(50129) lies on these lines: {1, 2}, {6, 4971}, {9, 4464}, {37, 4910}, {69, 4725}, {86, 4371}, {192, 4460}, {193, 527}, {279, 25726}, {319, 17399}, {344, 17388}, {346, 17121}, {391, 17319}, {518, 27480}, {524, 49747}, {528, 32029}, {536, 1992}, {544, 5905}, {545, 15534}, {553, 9312}, {599, 28337}, {952, 36731}, {966, 17393}, {1100, 42696}, {1482, 36728}, {2094, 3210}, {2784, 9812}, {2809, 4430}, {3175, 21874}, {3177, 18662}, {3304, 25946}, {3618, 17299}, {3619, 17372}, {3620, 3946}, {3629, 28297}, {3663, 20080}, {3672, 17254}, {3729, 4856}, {3759, 17264}, {3879, 6173}, {3913, 21495}, {3945, 17117}, {4000, 17297}, {4052, 18845}, {4344, 31317}, {4360, 5839}, {4361, 17392}, {4399, 16884}, {4402, 17300}, {4431, 16667}, {4452, 17364}, {4461, 17120}, {4488, 4788}, {4513, 42032}, {4644, 17160}, {4664, 37654}, {4740, 35578}, {4889, 17278}, {4898, 25101}, {4916, 17234}, {4969, 17318}, {5032, 17133}, {5232, 17396}, {5734, 7384}, {7229, 37677}, {7406, 7982}, {8236, 27484}, {8584, 28309}, {8666, 21508}, {8715, 21537}, {10222, 36662}, {11008, 17276}, {11160, 17274}, {11194, 35276}, {12513, 21511}, {12630, 20533}, {15533, 49741}, {16046, 41629}, {16777, 49731}, {17119, 49733}, {17242, 37681}, {17251, 17321}, {17281, 28329}, {17302, 32099}, {17315, 37650}, {17379, 32087}, {17382, 21356}, {17755, 49678}, {17781, 20111}, {18135, 25298}, {19819, 42045}, {20059, 32105}, {20090, 31995}, {24695, 28542}, {25417, 41821}, {30699, 31164}, {32922, 39721}, {36698, 37727}, {39362, 39363}, {47357, 49470}

X(50129) = reflection of X(i) in X(j) for these {i,j}: {2, 16834}, {69, 17301}, {11160, 17274}, {15533, 49741}, {16834, 49543}, {17299, 17359}, {17301, 4852}, {49721, 8584}
X(50129) = anticomplement of X(17294)
X(50129) = X(28899)-anticomplementary conjugate of X(513)
X(50129) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 145, 17389}, {2, 17389, 17316}, {2, 31145, 29615}, {8, 3241, 48856}, {8, 4393, 26626}, {145, 239, 17316}, {239, 17244, 24599}, {239, 17389, 2}, {239, 29619, 29628}, {3008, 29605, 29583}, {3244, 4384, 29585}, {3244, 50019, 4384}, {3621, 17014, 3661}, {3759, 17314, 26685}, {4360, 5839, 17257}, {4393, 20016, 8}, {5222, 6542, 29579}, {5222, 20050, 6542}, {16816, 29588, 5308}, {16833, 29574, 2}, {20053, 29611, 20055}, {29573, 41140, 2}, {29584, 29617, 2}, {29619, 29621, 17316}, {29619, 29628, 29621}


X(50130) = X(1)X(528)∩X(6)X(519)

Barycentrics    5*a^3 - 2*a^2*b + 4*a*b^2 - b^3 - 2*a^2*c + b^2*c + 4*a*c^2 + b*c^2 - c^3 : :
X(50130) = 2 X[2321] + X[49679], X[17299] - 4 X[32941], X[17299] + 2 X[49681], 4 X[17355] - X[49690], 2 X[32941] + X[49681], X[49460] + 2 X[49684], 4 X[49482] - X[49688], X[145] + 2 X[49484], 2 X[3244] + X[5695], X[3416] - 4 X[49473], 5 X[3623] - 2 X[49463], 4 X[3635] - X[49453], 2 X[17382] - 3 X[38314], 3 X[25055] - 2 X[48821], X[17276] - 4 X[49465]

X(50130) lies on these lines: {1, 528}, {2, 1279}, {6, 519}, {8, 17359}, {33, 428}, {37, 47357}, {145, 3758}, {516, 49747}, {527, 3242}, {529, 48827}, {536, 3241}, {551, 48829}, {752, 47358}, {991, 3655}, {1877, 11237}, {2094, 21342}, {2263, 5434}, {3244, 5695}, {3303, 4185}, {3416, 49473}, {3476, 6610}, {3623, 49463}, {3635, 49453}, {3654, 13329}, {3679, 7290}, {3722, 17723}, {3772, 31140}, {3883, 17251}, {3886, 4971}, {3945, 4373}, {4307, 4864}, {4339, 34610}, {4349, 28580}, {4363, 49771}, {4643, 36534}, {4648, 17382}, {4677, 16469}, {4725, 49467}, {4863, 17469}, {4952, 27064}, {5266, 45700}, {5269, 31146}, {5733, 10222}, {5846, 17294}, {5853, 38185}, {5919, 44670}, {6172, 49515}, {7174, 49742}, {8236, 27475}, {9053, 49726}, {10707, 17720}, {11240, 37539}, {13161, 34706}, {14621, 17389}, {15287, 16417}, {16487, 17337}, {16777, 30331}, {16970, 17330}, {17245, 25055}, {17269, 49762}, {17275, 48802}, {17276, 28534}, {17303, 48851}, {17765, 38047}, {19624, 37610}, {24280, 28322}, {28297, 49446}, {28542, 49455}, {29659, 49708}, {34611, 50068}, {36479, 49699}, {36480, 49700}, {37681, 48630}, {41312, 49746}, {48854, 49740}

X(50130) = reflection of X(i) in X(j) for these {i,j}: {8, 17359}, {3679, 48810}, {17281, 48805}, {17301, 1}, {48829, 551}
X(50130) = crossdifference of every pair of points on line {9002, 22108}
X(50130) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32941, 49681, 17299}, {36534, 49709, 4643}, {47357, 48856, 37}


X(50131) = X(2)X(319)∩X(6)X(519)

Barycentrics    5*a^2 + a*b - b^2 + a*c - 2*b*c - c^2 : :
X(50131) = 5 X[6] - 2 X[2321], X[6] - 4 X[4856], 4 X[6] - X[17299], 7 X[6] - 4 X[17355], X[2321] - 10 X[4856], 4 X[2321] - 5 X[17281], 8 X[2321] - 5 X[17299], 7 X[2321] - 10 X[17355], 8 X[4856] - X[17281], 16 X[4856] - X[17299], 7 X[4856] - X[17355], 7 X[17281] - 8 X[17355], 7 X[17299] - 16 X[17355], 2 X[49497] + X[49681], X[49680] + 2 X[49684], 4 X[49685] - X[49688], X[193] + 2 X[4852], 2 X[193] + X[17276], 4 X[4852] - X[17276], 3 X[16834] - X[17274], 5 X[16834] - 2 X[49741], 2 X[17274] - 3 X[17301], 5 X[17274] - 6 X[49741], 5 X[17301] - 4 X[49741], X[15534] + 2 X[49543], 2 X[3629] + X[3875], 2 X[4743] - 5 X[49488], X[3416] - 4 X[49489], 5 X[3618] - 2 X[17372], 2 X[3630] - 5 X[17304], 2 X[3663] + X[6144], X[3729] - 4 X[32455], 4 X[3946] - X[40341], 8 X[6329] - 5 X[17286], X[11008] + 2 X[17345], 3 X[16475] - 2 X[48810], 4 X[17235] - X[20080], 2 X[29594] - 3 X[47352]

X(50131) lies on these lines: {1, 4285}, {2, 319}, {6, 519}, {8, 16666}, {9, 13602}, {10, 4982}, {37, 3241}, {44, 145}, {45, 3244}, {69, 17382}, {75, 4795}, {192, 4910}, {193, 4715}, {239, 4675}, {344, 4889}, {346, 16671}, {391, 3723}, {524, 16834}, {527, 15534}, {536, 1992}, {545, 3629}, {551, 3686}, {572, 3654}, {573, 3655}, {583, 3169}, {594, 4677}, {597, 17294}, {752, 4743}, {903, 17364}, {966, 38314}, {1213, 25055}, {1333, 41629}, {1404, 41687}, {1405, 37738}, {1449, 3679}, {1743, 4370}, {2345, 16668}, {3416, 49489}, {3618, 17372}, {3630, 17304}, {3632, 17369}, {3633, 3943}, {3635, 3707}, {3644, 17487}, {3663, 6144}, {3664, 31139}, {3729, 28309}, {3751, 28503}, {3758, 20016}, {3770, 4479}, {3829, 50036}, {3879, 17278}, {3885, 21864}, {3896, 42058}, {3946, 40341}, {3973, 36911}, {4000, 31138}, {4034, 17398}, {4277, 17448}, {4360, 17333}, {4363, 49770}, {4384, 49738}, {4393, 4643}, {4399, 10022}, {4416, 24441}, {4421, 36743}, {4422, 29605}, {4460, 4718}, {4464, 17262}, {4657, 17271}, {4667, 17119}, {4669, 5750}, {4690, 26626}, {4727, 20050}, {4908, 16669}, {4916, 37681}, {4971, 8584}, {5032, 28329}, {5153, 42043}, {5165, 20018}, {5222, 17374}, {5296, 46845}, {5564, 37677}, {5847, 48829}, {6329, 17286}, {6542, 17342}, {6687, 29583}, {7277, 17151}, {8252, 49621}, {8253, 49620}, {11008, 17345}, {11194, 36744}, {12513, 37503}, {15933, 31324}, {16475, 48810}, {16522, 36480}, {16833, 17392}, {17014, 17237}, {17121, 17279}, {17133, 49721}, {17235, 20080}, {17242, 41138}, {17258, 17488}, {17269, 49761}, {17311, 41141}, {17335, 29588}, {17346, 29584}, {17379, 28634}, {17384, 32099}, {17387, 29590}, {17389, 41313}, {17772, 38047}, {20057, 39260}, {20090, 39704}, {20583, 49726}, {21769, 42057}, {21866, 34607}, {24693, 50021}, {28297, 41149}, {28580, 49486}, {29594, 47352}, {29597, 49731}, {29617, 46922}, {29764, 39996}, {36409, 49450}, {41662, 49608}

X(50131) = reflection of X(i) in X(j) for these {i,j}: {69, 17382}, {17281, 6}, {17294, 597}, {17299, 17281}, {17301, 16834}, {49726, 20583}
X(50131) = crossdifference of every pair of points on line {4834, 9002}
X(50131) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {193, 4852, 17276}, {1100, 5839, 17275}, {1449, 17362, 17303}, {3241, 37654, 37}, {3244, 4700, 45}, {3633, 16670, 3943}, {3635, 3707, 16672}, {3879, 41140, 17313}, {4667, 50019, 17119}, {17121, 17377, 17279}, {17313, 41140, 17278}, {17346, 29584, 41312}


X(50132) = X(2)X(319)∩X(75)X(519)

Barycentrics    4*a^2 + 2*a*b - 2*b^2 + 2*a*c - b*c - 2*c^2 : :
X(50132) = 5 X[75] - 8 X[3664], X[75] - 4 X[3879], X[75] + 2 X[17377], 2 X[75] - 3 X[39704], 2 X[3664] - 5 X[3879], 4 X[3664] + 5 X[17377], 4 X[3664] - 5 X[17378], 16 X[3664] - 15 X[39704], 2 X[3879] + X[17377], 8 X[3879] - 3 X[39704], 2 X[4709] - 3 X[24452], 4 X[17377] + 3 X[39704], 4 X[17378] - 3 X[39704], X[192] - 4 X[4889], 3 X[4664] - 2 X[17333], 5 X[4664] - 4 X[49742], X[17333] - 3 X[17389], 5 X[17333] - 6 X[49742], 5 X[17389] - 2 X[49742], X[3644] + 2 X[17364], X[3644] - 4 X[17388], X[17364] + 2 X[17388], 5 X[4687] - 4 X[17330], 5 X[4687] - 2 X[17363], 5 X[4687] - 8 X[17390], 10 X[4687] - 9 X[41848], 8 X[17330] - 9 X[41848], X[17363] - 4 X[17390], 4 X[17363] - 9 X[41848], 16 X[17390] - 9 X[41848], 5 X[4704] - 3 X[17488], 7 X[4751] - 4 X[17362], 7 X[4751] - 10 X[17391], 7 X[4751] - 8 X[49738], 2 X[17362] - 5 X[17391], 5 X[17391] - 4 X[49738], X[4764] - 4 X[17365], 6 X[16590] - 7 X[27268], 5 X[29622] - 4 X[49731]

X(50132) lies on these lines: {1, 17250}, {2, 319}, {6, 17240}, {8, 41847}, {45, 29619}, {69, 3241}, {75, 519}, {86, 3679}, {145, 320}, {190, 29605}, {192, 4715}, {193, 4916}, {239, 17313}, {524, 4664}, {545, 3644}, {551, 5224}, {597, 29577}, {599, 17399}, {752, 49470}, {903, 3875}, {1449, 17295}, {1743, 41138}, {1964, 25573}, {1992, 17264}, {3244, 4389}, {3629, 4370}, {3630, 17247}, {3631, 17396}, {3633, 17160}, {3723, 17343}, {3758, 6542}, {3828, 4909}, {3945, 5564}, {3946, 48637}, {4360, 17274}, {4393, 17227}, {4398, 4464}, {4422, 29618}, {4643, 29588}, {4667, 49761}, {4670, 20055}, {4675, 20016}, {4677, 10436}, {4687, 17330}, {4690, 29570}, {4700, 29601}, {4704, 17488}, {4740, 28329}, {4751, 17362}, {4764, 17365}, {4795, 17299}, {4852, 17375}, {4856, 17352}, {4908, 17350}, {4967, 34641}, {4969, 17244}, {4982, 29596}, {5847, 49746}, {6144, 17261}, {7321, 20049}, {10022, 48628}, {10446, 28204}, {15533, 17254}, {16590, 27268}, {16666, 17230}, {16667, 17285}, {16668, 17358}, {16704, 27754}, {16777, 17328}, {16779, 29573}, {16834, 17297}, {16884, 17287}, {17023, 48639}, {17117, 31139}, {17120, 17309}, {17121, 17311}, {17133, 49722}, {17229, 37677}, {17234, 41140}, {17251, 29580}, {17256, 29585}, {17258, 20080}, {17270, 25055}, {17294, 46922}, {17296, 17370}, {17300, 40891}, {17316, 17335}, {17319, 17329}, {17322, 32099}, {17339, 32455}, {17346, 29574}, {17354, 49765}, {17372, 17379}, {17380, 48638}, {17381, 48640}, {17392, 28337}, {18133, 42057}, {19875, 32025}, {20050, 42697}, {20929, 42029}, {20943, 35633}, {24524, 28660}, {28503, 49499}, {28562, 49518}, {29597, 31144}, {29622, 49731}, {31136, 37632}, {31137, 37678}, {31151, 49488}, {39126, 41801}, {49534, 49711}, {49684, 49750}

X(50132) = midpoint of X(17377) and X(17378)
X(50132) = reflection of X(i) in X(j) for these {i,j}: {75, 17378}, {4664, 17389}, {17330, 17390}, {17346, 29574}, {17362, 49738}, {17363, 17330}, {17378, 3879}, {29617, 17392}
X(50132) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17360, 17250}, {6, 17310, 17342}, {6, 17386, 17240}, {69, 3241, 17320}, {69, 17393, 17249}, {75, 17378, 39704}, {193, 4916, 17315}, {193, 17315, 17336}, {599, 29584, 17399}, {1100, 17373, 17228}, {1449, 17295, 17371}, {3241, 17320, 17393}, {3759, 4851, 17241}, {3879, 17377, 75}, {4393, 17374, 17227}, {4687, 17330, 41848}, {4852, 17375, 48629}, {16884, 17287, 17400}, {17121, 17311, 17341}, {17310, 17342, 17240}, {17319, 40341, 17329}, {17342, 17386, 17310}, {17362, 17391, 4751}, {17363, 17390, 4687}, {17364, 17388, 3644}, {17372, 17379, 48630}


X(50133) = X(1)X(4741)∩X(2)X(6)

Barycentrics    4*a^2 + a*b - 2*b^2 + a*c + b*c - 2*c^2 : :
X(50133) = 5 X[2] - 4 X[17330], 3 X[2] - 4 X[17392], 9 X[2] - 8 X[49731], 7 X[2] - 8 X[49738], 6 X[17330] - 5 X[17346], 2 X[17330] - 5 X[17378], 3 X[17330] - 5 X[17392], 9 X[17330] - 10 X[49731], 7 X[17330] - 10 X[49738], X[17346] - 3 X[17378], 3 X[17346] - 4 X[49731], 7 X[17346] - 12 X[49738], 3 X[17378] - 2 X[17392], 9 X[17378] - 4 X[49731], 7 X[17378] - 4 X[49738], 3 X[17392] - 2 X[49731], 7 X[17392] - 6 X[49738], 7 X[49731] - 9 X[49738], X[192] - 4 X[3879], X[192] + 2 X[17364], 2 X[3879] + X[17364], 2 X[48841] - 3 X[48858], X[1278] - 4 X[17365], X[1278] + 2 X[17377], 2 X[17365] + X[17377], X[3644] - 4 X[4889], 8 X[3664] - 5 X[4699], 4 X[3664] - X[17363], 5 X[4699] - 2 X[17363], 2 X[4416] - 5 X[17391], 4 X[4416] - 7 X[27268], 10 X[17391] - 7 X[27268], 2 X[4688] - 3 X[39704], 5 X[4704] - 2 X[17347], 5 X[4704] - 8 X[17390], 5 X[4704] - 4 X[49742], X[17347] - 4 X[17390], 7 X[4772] - 4 X[17362], 7 X[4772] - 8 X[49733], X[4788] - 4 X[17388], 5 X[4821] - 8 X[7228]

X(50133) lies on these lines: {1, 4741}, {2, 6}, {9, 29575}, {44, 17387}, {75, 4725}, {145, 528}, {192, 527}, {239, 6173}, {320, 4393}, {519, 4740}, {540, 48841}, {674, 4430}, {752, 3241}, {754, 48838}, {894, 17294}, {903, 39720}, {1100, 17236}, {1278, 4971}, {1449, 17288}, {1743, 17312}, {1943, 4654}, {1999, 31164}, {2309, 25572}, {2325, 29618}, {3644, 4889}, {3661, 4667}, {3664, 4699}, {3707, 29581}, {3723, 17329}, {3758, 17230}, {3759, 17376}, {3873, 9025}, {4352, 7893}, {4360, 49747}, {4363, 20055}, {4416, 17391}, {4419, 29588}, {4473, 29583}, {4643, 29570}, {4644, 6542}, {4658, 37164}, {4661, 9038}, {4664, 4715}, {4670, 17360}, {4675, 16816}, {4688, 39704}, {4690, 41847}, {4700, 29628}, {4704, 17347}, {4748, 29592}, {4772, 17362}, {4788, 17388}, {4821, 7228}, {4851, 17264}, {4888, 17117}, {4896, 49770}, {5839, 26806}, {6172, 17316}, {6360, 20291}, {7277, 17233}, {11111, 20077}, {11112, 20018}, {11165, 22355}, {14023, 22267}, {14976, 28562}, {16666, 17227}, {16667, 17291}, {16668, 17370}, {16669, 17241}, {16670, 17266}, {16671, 17341}, {16676, 29625}, {16884, 17273}, {17120, 17296}, {17121, 17298}, {17256, 29595}, {17274, 29584}, {17302, 21296}, {17314, 31300}, {17315, 25269}, {17328, 28639}, {17333, 29574}, {17335, 29599}, {17344, 17394}, {17345, 17393}, {17351, 17386}, {20016, 42697}, {28333, 49748}, {28337, 49727}, {28534, 49470}, {28604, 32099}, {30939, 31060}, {31145, 49720}, {33082, 48822}, {48850, 48868}

X(50133) = midpoint of X(i) and X(j) for these {i,j}: {17364, 17389}, {17377, 49722}
X(50133) = reflection of X(i) in X(j) for these {i,j}: {2, 17378}, {192, 17389}, {1278, 49722}, {17333, 29574}, {17346, 17392}, {17347, 49742}, {17362, 49733}, {17389, 3879}, {31145, 49720}, {48850, 48868}, {49722, 17365}, {49742, 17390}
X(50133) = anticomplement of X(17346)
X(50133) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17297, 17232}, {2, 17343, 17251}, {2, 17375, 17297}, {6, 17297, 2}, {6, 17375, 17232}, {44, 17387, 29572}, {69, 17379, 17238}, {69, 20090, 17379}, {86, 17251, 2}, {86, 40341, 17343}, {193, 17300, 17349}, {599, 46922, 2}, {1100, 17361, 17236}, {1449, 17288, 17383}, {3664, 17363, 4699}, {3758, 17374, 17230}, {3879, 17364, 192}, {3945, 20080, 1654}, {4416, 17391, 27268}, {4670, 17360, 29593}, {17120, 17296, 17358}, {17346, 17378, 17392}, {17346, 17392, 2}, {17347, 17390, 4704}, {17365, 17377, 1278}


X(50134) = EULER LINE INTERCEPT OF X(10264)X(11451)

Barycentrics    (b^2+c^2)*a^8-2*(b^4+b^2*c^2+c^4)*a^6-13*(b^2+c^2)*b^2*c^2*a^4+(2*b^4+15*b^2*c^2+2*c^4)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(50134) = 3*X(5)-X(37439), 3*X(381)+X(7485)

See Antreas Hatzipolakis and César Lozada, euclid 5123.

X(50134) lies on these lines: {2, 3}, {10264, 11451}, {17814, 22051}

X(50134) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5, 33332, 5056), (5, 37938, 5071), (3091, 46450, 381), (19709, 37353, 5)


X(50135) = EULER LINE INTERCEPT OF X(113)X(46665)

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

See Antreas Hatzipolakis and César Lozada, euclid 5123.

X(50135) lies on these lines: {2, 3}, {113, 46665}, {115, 5421}, {3564, 15038}, {3580, 13364}, {5449, 27355}, {5475, 13345}, {5480, 23039}, {5891, 19130}, {9722, 15484}, {10540, 37649}, {11442, 45967}, {11695, 18488}, {14561, 18445}, {14627, 31831}, {14845, 21243}, {15047, 18914}, {15087, 18583}, {16655, 37471}, {23300, 32063}, {39601, 49123}

X(50135) = midpoint of X(i) and X(j) for these {i, j}: {4, 15246}, {7550, 37349}
X(50135) = reflection of X(37990) in X(5)
X(50135) = complement of X(44832)
X(50135) = inverse of X(37924) in: MacBeath inconic, nine-point circle
X(50135) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5, 427, 5055), (5, 5066, 403), (5, 5133, 2072), (5, 7403, 1656), (5, 11585, 5079), (5, 13371, 5056), (2072, 5133, 5576), (3091, 18531, 381), (3545, 37353, 5), (13413, 14892, 5), (21308, 48411, 468)


X(50136) = EULER LINE INTERCEPT OF X(143)X(19130)

Barycentrics    (b^2+c^2)*a^8-2*(b^4+b^2*c^2+c^4)*a^6-5*(b^2+c^2)*b^2*c^2*a^4+(2*b^4+7*b^2*c^2+2*c^4)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(50136) = X(4)+3*X(14787), 5*X(5)+X(1907), 3*X(5)-X(7399), 3*X(381)+X(7503)

See Antreas Hatzipolakis and César Lozada, euclid 5123.

X(50136) lies on these lines: {2, 3}, {143, 19130}, {155, 22051}, {156, 8254}, {575, 45732}, {3060, 21230}, {3410, 14627}, {3574, 15060}, {3613, 21474}, {3818, 32046}, {5449, 13364}, {5480, 14449}, {5943, 13561}, {10095, 21243}, {10264, 15043}, {10274, 15426}, {10516, 16266}, {10627, 24206}, {11442, 32165}, {11459, 20424}, {11810, 14693}, {13363, 20299}, {13434, 45731}, {14561, 32140}, {14769, 25147}, {18128, 25555}, {18356, 45969}, {18388, 45958}, {18474, 43575}, {18583, 43588}

X(50136) = midpoint of X(5) and X(7403)
X(50136) = inverse of X(13564) in: orthocentroidal circle, Yff hyperbola
X(50136) = inverse of X(37947) in: MacBeath inconic, nine-point circle
X(50136) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 37353, 5), (5, 427, 3628), (5, 3857, 403), (5, 13371, 547), (5, 33332, 2), (5, 37938, 3090), (381, 18377, 546), (5068, 10255, 5), (5072, 7577, 5), (5169, 40916, 427), (12811, 13413, 5)


X(50137) = EULER LINE INTERCEPT OF X(39)X(1879)

Barycentrics    (b^2+c^2)*a^8-2*(b^4+b^2*c^2+c^4)*a^6-6*(b^2+c^2)*b^2*c^2*a^4+2*(b^2-c^2)^2*(b^4+4*b^2*c^2+c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(50137) = 3*X(381)+X(34864)

See Antreas Hatzipolakis and César Lozada, euclid 5123.

X(50137) lies on these lines: {2, 3}, {39, 1879}, {52, 19130}, {141, 37484}, {156, 14389}, {187, 31607}, {195, 31831}, {567, 12134}, {569, 3818}, {1112, 9827}, {1173, 41724}, {1209, 10110}, {1352, 36749}, {1495, 6689}, {1503, 13353}, {3410, 32358}, {3564, 14627}, {3580, 10095}, {3581, 11745}, {3589, 37471}, {5266, 8068}, {5422, 32140}, {5480, 6243}, {6288, 12241}, {6530, 14978}, {9722, 30435}, {9729, 18488}, {10263, 37636}, {10516, 36747}, {10625, 24206}, {11451, 23294}, {12233, 18435}, {12370, 41171}, {13292, 15038}, {13336, 38317}, {13364, 34826}, {13419, 37513}, {14216, 20300}, {14561, 36753}, {14805, 34782}, {15012, 16003}, {15026, 26879}, {15037, 18914}, {15060, 31810}, {16837, 27353}, {18350, 23292}, {18436, 45089}, {18553, 37505}, {20299, 41580}, {23300, 34780}, {25738, 45967}, {32125, 32767}, {34545, 43588}, {34598, 42671}, {34963, 42660}

X(50137) = midpoint of X(4) and X(37126)
X(50137) = reflection of X(14788) in X(5)
X(50137) = inverse of X(5899) in: MacBeath inconic, nine-point circle
X(50137) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 14786, 3), (4, 37353, 5), (5, 427, 1656), (5, 3850, 403), (5, 5133, 5576), (5, 5576, 2072), (5, 7403, 3), (5, 11585, 5055), (5, 13371, 3090), (5, 33332, 3628), (140, 428, 2937), (381, 1656, 1598), (381, 31724, 546), (858, 34939, 3628), (1312, 1313, 5899), (1595, 7405, 3), (3628, 33332, 858), (3850, 23047, 381), (5068, 7577, 5), (5169, 46336, 427), (7403, 7405, 1595), (7404, 7528, 3), (10255, 19709, 5), (15559, 37990, 140), (23335, 37439, 3526)


X(50138) = EULER LINE INTERCEPT OF X(6)X(18356)

Barycentrics    (b^2+c^2)*a^8-2*(b^4+b^2*c^2+c^4)*a^6-3*(b^2+c^2)*b^2*c^2*a^4+(b^2-c^2)^2*(b^2+2*c^2)*(2*b^2+c^2)*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(50138) = 3*X(5)+X(1595), 5*X(5)-X(6823), 3*X(381)+X(7526), 9*X(381)-X(12173), 3*X(547)-X(16197)

See Antreas Hatzipolakis and César Lozada, euclid 5123.

X(50138) lies on these lines: {2, 3}, {6, 18356}, {51, 34826}, {125, 15026}, {143, 21243}, {156, 3818}, {184, 8254}, {195, 3410}, {343, 14449}, {399, 11804}, {542, 32136}, {567, 45731}, {569, 34514}, {578, 32423}, {1209, 10263}, {1263, 14769}, {3574, 5876}, {3613, 25043}, {5448, 45958}, {5449, 10095}, {5462, 13561}, {6243, 7730}, {6288, 15033}, {6689, 13419}, {6747, 35719}, {6759, 32351}, {7703, 15024}, {7706, 32138}, {10264, 37481}, {10539, 15806}, {11264, 37505}, {11743, 13565}, {11805, 12281}, {12006, 20299}, {12359, 16881}, {13365, 14076}, {13451, 41587}, {13491, 18488}, {14561, 18952}, {15083, 30531}, {15088, 32743}, {18125, 45016}, {18388, 45959}, {18436, 20424}, {18474, 45970}, {18553, 41597}, {18583, 44494}, {18914, 20303}, {19362, 27552}, {21659, 22804}, {22234, 25328}, {23315, 40685}, {24206, 32142}, {25738, 45969}, {32767, 34146}, {37472, 41171}, {39691, 43843}

X(50138) = midpoint of X(140) and X(16198)
X(50138) = complement of X(7525)
X(50138) = inverse of X(2937) in: orthocentroidal circle, Yff hyperbola
X(50138) = inverse of X(37936) in: MacBeath inconic, nine-point circle
X(50138) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 4, 2937), (5, 427, 140), (5, 3858, 403), (5, 7403, 546), (5, 11585, 547), (5, 13371, 3628), (5, 33332, 3), (5, 37938, 1656), (140, 546, 6756), (1594, 37981, 1595), (1656, 37353, 5), (3545, 10255, 5), (3850, 13413, 5), (3851, 7577, 5), (5133, 5576, 5), (5169, 37353, 5189), (15559, 37347, 550), (39504, 49673, 1594)


X(50139) = EULER LINE INTERCEPT OF X(113)X(11695)

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

See Antreas Hatzipolakis and César Lozada, euclid 5123.

X(50139) lies on these lines: {2, 3}, {113, 11695}, {155, 45967}, {373, 5448}, {1506, 49123}, {2883, 40280}, {3580, 14128}, {12606, 41599}, {15060, 26879}, {15873, 37484}, {16252, 37471}, {34783, 37648}, {45303, 45622}

X(50139) = inverse of X(35452) in: MacBeath inconic, nine-point circle
X(50139) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5, 427, 5072), (5, 3628, 403), (5, 11585, 3851), (5, 13371, 3545), (5, 49673, 5133), (1656, 11479, 6640), (7577, 15022, 5)


X(50140) = EULER LINE INTERCEPT OF X(113)X(17853)

Barycentrics    (b^2+c^2)*a^8-2*(b^4+b^2*c^2+c^4)*a^6+5*(b^2+c^2)*b^2*c^2*a^4+(2*b^4-3*b^2*c^2+2*c^4)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(50140) = 3*X(5)+X(1368), 5*X(5)-X(1596), 3*X(5)-X(46030), X(25)-9*X(5055), 3*X(381)+5*X(31255), 3*X(547)-X(6677), 5*X(632)-X(44241)

See Antreas Hatzipolakis and César Lozada, euclid 5123.

X(50140) lies on these lines: {2, 3}, {113, 17853}, {125, 15060}, {155, 32165}, {184, 10272}, {569, 15806}, {1147, 43575}, {1568, 5946}, {1660, 23325}, {3410, 38724}, {4550, 40685}, {5012, 14643}, {5448, 12006}, {5449, 14128}, {5651, 11801}, {5876, 43817}, {6689, 43582}, {9306, 32423}, {10264, 18435}, {12022, 40111}, {13162, 34517}, {13352, 46114}, {13363, 18388}, {14852, 34966}, {14984, 15088}, {15048, 49123}, {17814, 18356}, {18308, 39512}, {18350, 45731}, {19130, 40670}, {20299, 45958}, {20304, 21243}, {20584, 32351}, {30522, 43586}, {43393, 43839}

X(50140) = midpoint of X(i) and X(j) for these {i, j}: {140, 44920}, {1368, 46030}, {12106, 18531}
X(50140) = inverse of X(37950) in: MacBeath inconic, nine-point circle
X(50140) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 18570, 140), (5, 427, 5066), (5, 549, 403), (5, 11585, 546), (5, 13371, 3850), (5, 33332, 3851), (5, 37938, 381), (381, 35452, 4), (1368, 37439, 6677), (1656, 16072, 6644), (3090, 10255, 5), (5055, 7577, 5), (10109, 13413, 5), (31074, 31255, 1368), (39504, 49673, 2072)


X(50141) = EULER LINE INTERCEPT OF X(17814)X(45967)

Barycentrics    (b^2+c^2)*a^8-2*(b^4+b^2*c^2+c^4)*a^6+18*(b^2+c^2)*b^2*c^2*a^4+2*(b^2-c^2)^2*(b^4-8*b^2*c^2+c^4)*a^2-(b^4-c^4)*(b^2-c^2)^3 : :

See Antreas Hatzipolakis and César Lozada, euclid 5123.

X(50141) lies on these lines: {2, 3}, {17814, 45967}

X(50141) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5, 13371, 3544), (5, 35018, 403), (3541, 16868, 235)


X(50142) = EULER LINE INTERCEPT OF X(15068)X(45969)

Barycentrics    (b^2+c^2)*a^8-2*(b^4+b^2*c^2+c^4)*a^6+11*(b^2+c^2)*b^2*c^2*a^4+(2*b^4-9*b^2*c^2+2*c^4)*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(50142) = 5*X(5)+X(30739)

See Antreas Hatzipolakis and César Lozada, euclid 5123.

X(50142) lies on these lines: {2, 3}, {15068, 45969}, {43614, 45731}

X(50142) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (5, 15699, 403), (5, 33332, 5068), (5, 37938, 3545), (547, 44236, 3628), (10255, 15022, 5)


X(50143) = EULER LINE INTERCEPT OF X(39)X(49123)

Barycentrics    (b^2+c^2)*a^8-2*(b^4+b^2*c^2+c^4)*a^6+6*(b^2+c^2)*b^2*c^2*a^4+2*(b^2-c^2)^4*a^2-(b^4-c^4)*(b^2-c^2)^3 : :
X(50143) = 6*X(5)-X(44803)

See Antreas Hatzipolakis and César Lozada, euclid 5123.

X(50143) lies on these lines: {2, 3}, {39, 49123}, {113, 9729}, {155, 32166}, {233, 3003}, {399, 18914}, {567, 9820}, {1503, 43811}, {1568, 5462}, {3047, 10272}, {3580, 11591}, {5449, 32123}, {5475, 40320}, {5651, 9927}, {5654, 36753}, {5876, 26879}, {5892, 43831}, {5907, 43392}, {6146, 18350}, {6689, 12900}, {9306, 44076}, {10516, 44503}, {11064, 37472}, {11441, 18952}, {11745, 15800}, {12161, 45967}, {12241, 22115}, {12606, 41598}, {13198, 13353}, {13321, 31802}, {13565, 15088}, {13567, 18436}, {15056, 26917}, {15058, 26913}, {15068, 18912}, {16657, 37495}, {17814, 25738}, {18911, 32139}, {20299, 36982}, {21659, 43586}, {22660, 37481}, {22802, 37470}, {23039, 41587}, {25739, 43614}, {37649, 41615}, {39503, 46953}, {40111, 43575}, {43573, 43844}, {43588, 43816}, {43821, 44665}, {43845, 45298}

X(50143) = inverse of X(18859) in: MacBeath inconic, nine-point circle
X(50143) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 3520, 140), (5, 140, 403), (5, 427, 3851), (5, 2072, 5576), (5, 7403, 5072), (5, 10224, 5133), (5, 11585, 381), (5, 13371, 3091), (5, 37938, 3850), (5, 49673, 1594), (140, 1885, 3), (1594, 49673, 2072), (3090, 14786, 1656), (5055, 10255, 5), (5056, 7577, 5), (7574, 18369, 6756), (13413, 44904, 5), (16238, 34664, 3)


leftri

Points in a [[2a^2-b^2-c^2,2b^2-c^2-a^2,2c^2-a^2-b^2], [L2 = [(b^2-c^2)(a^2-b^2-c^2), (c^2- a^2)(b^2-c^2-a^2), (a^2- b^2)(a^2-b^2-c^2)]] coordinate system: X(50144)-X(50150)

rightri

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

L1 is the line: (2a^2-b^2-c^2) α + (c^2- a^2)(b^2-c^2-a^2) β + 2c^2-a^2-b^2 γ = 0.

L2 is the line (b^2-c^2)(a^2-b^2-c^2) α + (c^2- a^2)(b^2-c^2-a^2) β + (a^2- b^2)(a^2-b^2-c^2) γ = 0 (Euler line).

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

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

u : v : w = -2(a^6 - a^4(b^2+c^2) - a^2 (b^4 - 3 b^2 c^2 + c^4) + (b^2 - c^2)(b^4 - c^4)) + 3(b^2-c^2) x - (a^2 (2a^2 - b^2 - c^2) - (b^2 - c^2)^2) y : : ,

where, as functions of a, b, c, the coordinate x is antisymmetric of degree 4, and y is symmetric of degree 2.

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

{-2 (a-b) (a-c) (b-c) (a+b+c), 1/2 (a^2+b^2+c^2)}, 16304
{-((2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)), 1/2 (a^2+b^2+c^2)}, 16334
{-((a-b) (a-c) (b-c) (a+b+c)), 1/2 (a^2+b^2+c^2)}, 16309} {-(((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2)), 1/2 (a^2+b^2+c^2), 16321
{-(1/2) (a-b) (a-c) (b-c) (a+b+c), 1/2 (a^2+b^2+c^2)}, 16305
{0, -2 (a^2+b^2+c^2)}, 10989
{0, -a^2-b^2-c^2}, 858
{0, 1/2 (-a^2-b^2-c^2)}, 47097
{0, 0}, 2
{0, 1/2 (a^2+b^2+c^2)}, 468
{0, a^2+b^2+c^2}, 7426
{0, 2 (a^2+b^2+c^2)}, 23
{1/2 (a-b) (a-c) (b-c) (a+b+c), 1/2 (a^2+b^2+c^2)}, 16332
{(a-b) (a-c) (b-c) (a+b+c), 1/2 (a^2+b^2+c^2)}, 16272
{((a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2), 1/2 (a^2+b^2+c^2)}, 16324
{(2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2), 1/2 (a^2+b^2+c^2)}, 16303
{(2 (a^2-b^2) (a^2-c^2) (b^2-c^2))/(a^2+b^2+c^2), 2 (a^2+b^2+c^2)}, 32224
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), 0}, 51045
{(-2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2), 0}, 51046
{((a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2), 0}, 51047
{(a - b)*(a - c)*(b - c)*(a + b + c), ((a + b)*(a + c)*(b + c))/(a + b + c)}, 51048
{(2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2), 0}, 51049
{(2*(a^2 - b^2)*(a^2 - c^2)*(b^2 - c^2))/(a^2 + b^2 + c^2), a^2 + b^2 + c^2}, 51050


X(50144) = X(8)X(30)∩X(325)X(523)

Barycentrics    {-2*(a - b)*(a - c)*(b - c)*(a + b + c), -a^2 - b^2 - c^2}; a^4*b^2 - 2*a^3*b^3 + 2*a*b^5 - b^6 + 2*a^3*b^2*c - 2*b^5*c + a^4*c^2 + 2*a^3*b*c^2 - 2*a^2*b^2*c^2 - 2*a*b^3*c^2 + b^4*c^2 - 2*a^3*c^3 - 2*a*b^2*c^3 + 4*b^3*c^3 + b^2*c^4 + 2*a*c^5 - 2*b*c^5 - c^6 : :
X(50144) = 5 X[3617] - 2 X[47271], 3 X[7426] - 4 X[16305], X[16322] - 3 X[47097], 6 X[16323] - 5 X[37760]

X(50144) lies on these lines: {2, 16272}, {8, 30}, {10, 11809}, {23, 16309}, {325, 523}, {403, 41013}, {956, 37976}, {3580, 6741}, {3617, 47271}, {3681, 4046}, {3935, 5160}, {4081, 5057}, {6742, 11064}, {7426, 16305}, {10149, 34772}, {10989, 31091}, {14985, 46818}, {16322, 30741}, {16323, 37760}, {29855, 47178}, {37963, 47161}

X(50144) = anticomplement of X(16272)
X(50144) = reflection of X(i) in X(j) for these {i,j}: {23, 16309}, {3580, 6741}, {6742, 11064}, {11809, 10}, {46818, 14985}
X(50144) = incircle of anticomplementary triangle inverse of X(44447)


X(50145) = X(2)X(523)∩X(8)X(30)

Barycentrics    a^6 - a^4*b^2 + 3*a^3*b^3 - a^2*b^4 - 3*a*b^5 + b^6 - 3*a^3*b^2*c + 3*b^5*c - a^4*c^2 - 3*a^3*b*c^2 + 3*a^2*b^2*c^2 + 3*a*b^3*c^2 - b^4*c^2 + 3*a^3*c^3 + 3*a*b^2*c^3 - 6*b^3*c^3 - a^2*c^4 - b^2*c^4 - 3*a*c^5 + 3*b*c^5 + c^6 : :
X(50145) = X[8] + 2 X[47272], X[36154] + 2 X[47273], 2 X[13869] - 3 X[38314], 4 X[16305] - 3 X[37907]

X(50145) lies on these lines: {2, 523}, {8, 30}, {519, 47270}, {551, 47274}, {2452, 19738}, {2453, 19723}, {3109, 3241}, {3679, 36154}, {3829, 5520}, {5278, 47285}, {5642, 6742}, {6741, 9140}, {7426, 16309}, {9143, 14985}, {11809, 47496}, {13869, 38314}, {16305, 37907}, {23922, 31143}, {31145, 36171}, {36224, 42045}

X(50145) = midpoint of X(i) and X(j) for these {i,j}: {3679, 47273}, {31145, 36171}
X(50145) = reflection of X(i) in X(j) for these {i,j}: {3241, 3109}, {6742, 5642}, {7426, 16309}, {9140, 6741}, {9143, 14985}, {11809, 47496}, {36154, 3679}, {47274, 551}


X(50146) = X(2)X(523)∩X(30)X(599)

Barycentrics    a^8 + a^4*b^4 - 3*a^2*b^6 + b^8 - 5*a^4*b^2*c^2 + 4*a^2*b^4*c^2 + 3*b^6*c^2 + a^4*c^4 + 4*a^2*b^2*c^4 - 8*b^4*c^4 - 3*a^2*c^6 + 3*b^2*c^6 + c^8 : :
X(50146) = 2 X[141] + X[47285], 4 X[16321] - X[32224], 2 X[11007] - 3 X[21358], 2 X[11007] + X[47284], 3 X[21358] + X[47284], 4 X[20582] + X[47283], 3 X[21356] - X[36163]

X(50146) lies on these lines: {2, 523}, {5, 16279}, {6, 34094}, {30, 599}, {141, 36194}, {183, 7426}, {338, 11632}, {468, 7610}, {524, 1316}, {543, 5181}, {549, 6795}, {597, 2452}, {804, 11006}, {1634, 37991}, {2782, 5648}, {2799, 5465}, {3314, 10989}, {5112, 47556}, {6055, 41359}, {6787, 20403}, {7473, 44134}, {7615, 14120}, {7778, 16312}, {7883, 36187}, {8182, 36180}, {8860, 16324}, {9761, 32461}, {9763, 32460}, {9830, 36882}, {11007, 21358}, {11168, 16320}, {11179, 36177}, {11185, 36196}, {11657, 47597}, {15271, 16316}, {16179, 22492}, {16180, 22491}, {16303, 37637}, {20582, 47283}, {21356, 36163}, {23055, 47239}, {23342, 32833}, {25157, 34316}, {25167, 34315}, {34229, 47171}, {34511, 36157}, {35522, 44155}, {36207, 45331}, {36889, 46869}, {40826, 46296}, {40879, 45662}, {42850, 46992}

X(50146) = midpoint of X(i) and X(j) for these {i,j}: {599, 2453}, {16312, 47097}, {36194, 47285}, {36889, 46869}
X(50146) = reflection of X(i) in X(j) for these {i,j}: {6, 34094}, {2452, 597}, {5112, 47556}, {6795, 549}, {7426, 16321}, {11179, 36177}, {16279, 5}, {32224, 7426}, {36194, 141}
X(50146) = psi-transform of X(9191)


X(50147) = X(2)X(523)∩X(30)X(182)

Barycentrics    2*a^8 - 7*a^4*b^4 + 3*a^2*b^6 + 2*b^8 + 8*a^4*b^2*c^2 - a^2*b^4*c^2 - 3*b^6*c^2 - 7*a^4*c^4 - a^2*b^2*c^4 + 2*b^4*c^4 + 3*a^2*c^6 - 3*b^2*c^6 + 2*c^8 : :
X(50147) = X[1316] - 3 X[47352], 2 X[5159] + X[16333], X[47285] - 7 X[47355]

X(50147) lies on these lines: {2, 523}, {3, 16279}, {6, 36194}, {30, 182}, {376, 35345}, {381, 6795}, {524, 11007}, {543, 15118}, {549, 24975}, {599, 2452}, {804, 5465}, {1316, 47352}, {2492, 5661}, {3111, 20403}, {3329, 10989}, {3589, 34094}, {3815, 16303}, {5158, 37987}, {5159, 9771}, {7426, 7792}, {7610, 47238}, {7668, 11632}, {7790, 36196}, {7827, 36165}, {9158, 46868}, {9479, 11006}, {9832, 46998}, {10168, 36177}, {11168, 16315}, {23878, 33509}, {42286, 46296}, {47285, 47355}

X(50147) = midpoint of X(i) and X(j) for these {i,j}: {3, 16279}, {6, 36194}, {381, 6795}, {599, 2452}, {10989, 32224}, {16303, 47097}
X(50147) = reflection of X(i) in X(j) for these {i,j}: {34094, 3589}, {36177, 10168}


X(50148) = X(1)X(30)∩X(106)X(476)

Barycentrics    (a^2 + a*b + b^2 - c^2)*(a^2 - b^2 + a*c + c^2)*(a^3 + a^2*b - a*b^2 - b^3 + a^2*c - a*b*c + b^2*c - a*c^2 + b*c^2 - c^3) : :
X(50148) = X[1] + 2 X[39751], X[484] + 2 X[31522], 2 X[36195] + X[47274], 4 X[44898] - X[47273]

X(50148) lies on the cubic K086 and these lines: {1, 30}, {2, 6757}, {36, 2687}, {80, 5627}, {106, 476}, {265, 28204}, {381, 41496}, {484, 31522}, {519, 6742}, {523, 24920}, {551, 3615}, {1138, 18593}, {1325, 5563}, {1749, 18285}, {1989, 8609}, {2166, 3582}, {3017, 24443}, {3247, 8818}, {3746, 36001}, {5127, 13486}, {5196, 5557}, {6126, 14158}, {7110, 16307}, {8606, 14799}, {10056, 43682}, {14844, 37701}, {15767, 17404}, {23710, 37979}, {29681, 37907}, {30447, 37719}, {34209, 45926}, {36195, 47274}, {37922, 41345}, {39152, 46078}, {39153, 46074}, {44898, 47273}

X(50148) = isogonal conjugate of X(7343)
X(50148) = X(2166)-Ceva conjugate of X(79)
X(50148) = incircle-inverse of X(11544)
X(50148) = X(484)-cross conjugate of X(19658)
X(50148) = X(i)-isoconjugate of X(j) for these (i,j): {1, 7343}, {35, 3065}, {323, 11075}, {2174, 21739}, {3219, 19302}, {34921, 35057}
X(50148) = X(3)-Dao conjugate of X(7343)
X(50148) = crossdifference of every pair of points on line {9404, 17454}
X(50148) = barycentric product X(i)*X(j) for these {i,j}: {75, 11076}, {79, 17484}, {94, 6126}, {321, 14158}, {484, 30690}, {2160, 17791}, {2166, 40612}, {17483, 19658}, {19297, 20565}
X(50148) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 7343}, {79, 21739}, {484, 3219}, {2160, 3065}, {6126, 323}, {6186, 19302}, {11076, 1}, {14158, 81}, {17484, 319}, {17791, 33939}, {19297, 35}, {21864, 3678}, {30690, 40716}, {42657, 9404}


X(50149) = X(2)X(523)∩X(6)X(30)

Barycentrics    a^8 - 5*a^4*b^4 + 3*a^2*b^6 + b^8 + 7*a^4*b^2*c^2 - 2*a^2*b^4*c^2 - 3*b^6*c^2 - 5*a^4*c^4 - 2*a^2*b^2*c^4 + 4*b^4*c^4 + 3*a^2*c^6 - 3*b^2*c^6 + c^8 : :
X(50149) = 4 X[16303] - X[32224], X[858] + 2 X[16333], X[2453] - 3 X[47352], 2 X[34094] - 3 X[47352], 4 X[3589] - X[47285], 2 X[36177] - 3 X[38064], X[47283] - 6 X[48310]

X(50149) lies on the cubic K909 and these lines: {2, 523}, {3, 45331}, {6, 30}, {263, 8705}, {376, 5467}, {524, 2452}, {597, 1316}, {599, 11007}, {804, 9144}, {858, 11163}, {1551, 9744}, {1989, 49102}, {1992, 36163}, {2453, 34094}, {2793, 5465}, {2794, 15303}, {3014, 6054}, {3018, 6055}, {3106, 34313}, {3107, 34314}, {3589, 47285}, {5201, 15915}, {5309, 21906}, {5640, 9158}, {6128, 9880}, {7426, 16324}, {7610, 16315}, {7622, 40544}, {7735, 46998}, {7806, 37907}, {7812, 36187}, {7827, 38526}, {9513, 14220}, {9832, 22329}, {11168, 47242}, {11184, 47097}, {15271, 47155}, {16319, 47597}, {23055, 47238}, {36177, 38064}, {36180, 37809}, {36185, 37785}, {36186, 37786}, {47283, 48310}

X(50149) = midpoint of X(i) and X(j) for these {i,j}: {1992, 36163}, {2452, 36194}, {6795, 16279}
X(50149) = reflection of X(i) in X(j) for these {i,j}: {599, 11007}, {1316, 597}, {2453, 34094}, {7426, 16324}
X(50149) = psi-transform of X(9185)
X(50149) = crossdifference of every pair of points on line {187, 8675}
X(50149) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2453, 47352, 34094}, {14995, 46127, 2}


X(50150) = X(6)X(30)∩X(351)X(523)

Barycentrics    4*a^8 + 3*a^6*b^2 - 11*a^4*b^4 + 3*a^2*b^6 + b^8 + 3*a^6*c^2 + 16*a^4*b^2*c^2 - 5*a^2*b^4*c^2 - 6*b^6*c^2 - 11*a^4*c^4 - 5*a^2*b^2*c^4 + 10*b^4*c^4 + 3*a^2*c^6 - 6*b^2*c^6 + c^8 : :
X(50150) = 2 X[16303] + X[32224], X[23] + 2 X[16333], 2 X[16321] - 3 X[37907], 2 X[34094] - 3 X[47455]

X(50150) lies on these lines: {2, 16324}, {6, 30}, {23, 16333}, {351, 523}, {468, 7610}, {524, 5112}, {597, 11594}, {1316, 47544}, {1513, 14995}, {1976, 6094}, {2080, 14934}, {3003, 6055}, {3849, 15303}, {5467, 8598}, {6054, 45921}, {11632, 11799}, {16321, 17008}, {34094, 47455}, {37461, 45331}, {42849, 47097}

X(50150) = reflection of X(i) in X(j) for these {i,j}: {2, 16324}, {1316, 47544}
X(50150) = crossdifference of every pair of points on line {574, 8675}


X(50151) = (name pending)

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

See Tran Viet Hung and Francisco Javier García Capitán, euclid 5113.

X(50151) lies on these lines: { }

X(50151) = isogonal conjugate of X(50152)


X(50152) = (name pending)

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

See Tran Viet Hung and Francisco Javier García Capitán, euclid 5113.

X(50152) lies on the inconic with perspector X(4076) and these lines: { }

X(50152) = isogonal conjugate of X(50151)


leftri

Points in a [[a^2 (b^2 - c^2), b^2 (c^2 - a^2), c^2 (a^2 - b^2)], [L2 = [(b^2-c^2)(a^2-b^2-c^2), (c^2- a^2)(b^2-c^2-a^2), (a^2- b^2)(a^2-b^2-c^2)]] coordinate system: X(50144)-X(50150)

rightri

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

L1 is the line: a^2 (b^2 - c^2) α + b^2 (c^2 - a^2) β + c^2 (a^2 - b^2) γ = 0.

L2 is the line (b^2-c^2)(a^2-b^2-c^2) α + (c^2- a^2)(b^2-c^2-a^2) β + (a^2- b^2)(a^2-b^2-c^2) γ = 0 (Euler line).

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

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

u : v : w = - (a^2 - b^2)(a^2 - c^2)(b^2 - c^2)(a^2 + b^2 + c^2) + (2 b^2 c^2 - a^2 b^2 - a^2 c^2) x + (b^4 + c^4 - 2a^4 + a^2 b^2 + a^2 c^2 - 2 b^2 c^2) y : : ,

where, as functions of a, b, c, the coordinate x is antisymmetric of degree 4, and y is antisymmetric of degree 4.

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

{-2 (a-b) (a-c) (b-c) (a+b+c), -((2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c))}, 8
{-2 (a-b) (a-c) (b-c) (a+b+c), -((a-b) (a-c) (b-c) (a+b+c))}, 3578
{-((2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c)), -(((a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c))}, 49717
{-((a-b) (a-c) (b-c) (a+b+c)), -(((a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c))}, 3679
{-((a-b) (a-c) (b-c) (a+b+c)), -(1/2) (a-b) (a-c) (b-c) (a+b+c)}, 49724
{-(1/2) (a-b) (a-c) (b-c) (a+b+c), -(((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a+b+c)))}, 10
{0, -(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c))}, 49735
{0, -(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a+b+c)))}, 13745
{0, 0}, 2
{1/2 (a-b) (a-c) (b-c) (a+b+c), ((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a+b+c))}, 551
{(a-b) (a-c) (b-c) (a+b+c), 1/2 (a-b) (a-c) (b-c) (a+b+c)}, 37631
{(a-b) (a-c) (b-c) (a+b+c), ((a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c)}, 1
{2 (a-b) (a-c) (b-c) (a+b+c), (a-b) (a-c) (b-c) (a+b+c)}, 42045
{(2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c), ((a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c)}, 49749
{2 (a-b) (a-c) (b-c) (a+b+c), (2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c)}, 3241
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), -1/2*((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)}, 50153
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), 0}, 50154
{(-2*(a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c), 0}, 50155
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), ((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)}, 50156
{-(((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c)), -(((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c))}, 50157
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)), -1/2*((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)}, 50158
{-((a - b)*(a - c)*(b - c)*(a + b + c)), 0}, 50159
{-(((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c)), 0}, 50160
{-1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c), -1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c)}, 50161
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), 0}, 50162
{-1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c), 0}, 50163
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), ((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)}, 50164
{0, (-2*(a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c)}, 50165
{0, -((a - b)*(a - c)*(b - c)*(a + b + c))}, 50166
{0, -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))}, 50167
{0, ((a - b)*(a - c)*(b - c)*(a + b + c))/2}, 50168
{0, ((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(2*(a + b + c))}, 50169
{0, (a - b)*(a - c)*(b - c)*(a + b + c)}, 50170
{0, ((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c)}, 50171
{0, (2*(a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c)}, 50172
{((a - b)*(a - c)*(b - c)*(a + b + c))/2, 0}, 50173
{((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(2*(a + b + c)), 0}, 50174
{(a - b)*(a - c)*(b - c)*(a + b + c), (-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)}, 50175
{(a - b)*(a - c)*(b - c)*(a + b + c), -(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c))}, 50176
{(a - b)*(a - c)*(b - c)*(a + b + c), -1/2*((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)}, 50177
{(a - b)*(a - c)*(b - c)*(a + b + c), 0}, 50178
{((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c), 0}, 50179
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c), ((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(2*(a + b + c))}, 50180
{(a - b)*(a - c)*(b - c)*(a + b + c), (a - b)*(a - c)*(b - c)*(a + b + c)}, 50181
{(a - b)*(a - c)*(b - c)*(a + b + c), (2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)}, 50182
{2*(a - b)*(a - c)*(b - c)*(a + b + c), 0}, 50183
{(2*(a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c), 0}, 50184
{(2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c), ((a - b)*(a - c)*(b - c)*(a + b + c))/2}, 50185
{(2*(a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c), (2*(a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c)}, 50186


X(50153) = X(8)X(30)∩X(10)X(538)

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

X(50153) lies on these lines: {8, 30}, {10, 538}, {194, 37148}, {524, 32935}, {726, 15985}, {1655, 4205}, {1909, 3695}, {2049, 22253}, {4385, 15973}, {4658, 24275}, {4754, 49743}, {5739, 36685}, {6057, 37631}, {7754, 33745}, {7798, 43531}, {7839, 13740}, {8728, 34284}, {10449, 48869}, {11108, 27523}, {16062, 20081}, {17527, 28809}, {32847, 49745}, {37159, 47286}


X(50154) = X(2)X(39)∩X(8)X(30)

Barycentrics    a^4*b - a^3*b^2 - a^2*b^3 + a*b^4 + a^4*c + 2*a^3*b*c + 2*a*b^3*c + b^4*c - a^3*c^2 + 6*a*b^2*c^2 + 5*b^3*c^2 - a^2*c^3 + 2*a*b*c^3 + 5*b^2*c^3 + a*c^4 + b*c^4 : :
X(50154) = 2 X[3729] + X[15983]

X(50154) lies on these lines: {2, 39}, {8, 30}, {524, 49721}, {1909, 42033}, {2795, 17163}, {3729, 15983}, {3734, 19742}, {4754, 17316}, {4877, 27604}, {7798, 19717}, {8025, 24275}, {16704, 24271}, {19684, 22253}, {25257, 33941}, {30056, 31995}, {31339, 48818}, {48849, 49735}


X(50155) = X(2)X(39)∩X(8)X(524)

Barycentrics    a^3*b + a*b^3 + a^3*c + 4*a^2*b*c + 4*a*b^2*c + b^3*c + 4*a*b*c^2 + 6*b^2*c^2 + a*c^3 + b*c^3 : :
X(50155) = X[8] + 2 X[4754]

X(50155) lies on these lines: {2, 39}, {8, 524}, {30, 48849}, {75, 17497}, {514, 46895}, {536, 4968}, {1334, 50118}, {1654, 26079}, {1909, 4033}, {3241, 49749}, {3691, 20367}, {3780, 50098}, {4688, 16732}, {7229, 28369}, {7751, 19284}, {7760, 16930}, {7781, 16347}, {7991, 15971}, {8667, 19336}, {8682, 17163}, {13745, 39581}, {15983, 17116}, {15985, 31995}, {16393, 47037}, {17137, 50128}, {17164, 35103}, {17169, 21024}, {17251, 17679}, {21020, 35102}, {26965, 37756}, {28610, 28638}, {42045, 50079}

X(50155) = reflection of X(3241) in X(49749)
X(50155) = {X(26035),X(34284)}-harmonic conjugate of X(26978)


X(50156) = X(1)X(538)∩X(8)X(30)

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

X(50156) lies on these lines: {1, 538}, {3, 26243}, {8, 30}, {58, 24271}, {76, 1009}, {99, 37023}, {194, 1008}, {325, 37049}, {385, 11104}, {405, 34284}, {443, 27523}, {474, 28809}, {511, 3729}, {524, 5695}, {543, 49723}, {1010, 1655}, {1089, 4447}, {1150, 49129}, {1281, 2782}, {1724, 3734}, {1909, 7283}, {1975, 13723}, {2795, 4647}, {3923, 28369}, {4039, 24850}, {4044, 37609}, {4195, 20081}, {4204, 30599}, {4292, 4987}, {4385, 37425}, {4387, 37631}, {5254, 37025}, {6390, 37047}, {7985, 32515}, {9534, 48869}, {10449, 11355}, {11354, 42025}, {13728, 15048}, {13745, 39581}, {15975, 46108}, {15983, 24280}, {15985, 24248}, {17128, 37027}, {17316, 49743}, {24275, 25526}, {28368, 32930}, {31859, 37053}, {37507, 44140}, {39906, 47521}

X(50156) = midpoint of X(15983) and X(24280)
X(50156) = reflection of X(i) in X(j) for these {i,j}: {24248, 15985}, {28369, 3923}

X(50157) = X(1)X(524)∩X(2)X(32)

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

X(50157) lies on these lines: {1, 524}, {2, 32}, {10, 4760}, {30, 48851}, {405, 17251}, {538, 49735}, {540, 48822}, {3578, 17389}, {3954, 50093}, {5283, 17346}, {7759, 16342}, {7764, 16347}, {7768, 16927}, {7794, 16931}, {9766, 16351}, {14023, 37314}, {17294, 49724}, {17392, 25499}, {19336, 47101}, {24956, 31090}, {25683, 26244}, {31144, 33954}, {49717, 49729}

X(50157) = reflection of X(49717) in X(49729)


X(50158) = X(2)X(6)∩X(10)X(538)

Barycentrics    4*a^2*b^2 + 3*a*b^3 + 6*a^2*b*c + 9*a*b^2*c + 3*b^3*c + 4*a^2*c^2 + 9*a*b*c^2 + 4*b^2*c^2 + 3*a*c^3 + 3*b*c^3 : :
X(50158) = 3 X[49717] + X[49749], X[4754] - 7 X[9780]

X(50158) lies on these lines: {2, 6}, {10, 538}, {30, 48809}, {754, 49729}, {1698, 24691}, {2227, 21699}, {3720, 25358}, {3741, 4708}, {4364, 4854}, {4472, 24690}, {4643, 33097}, {4690, 43223}, {4713, 4748}, {4754, 9780}, {4981, 9055}, {5969, 5988}, {6626, 13586}, {19856, 49716}, {25350, 26037}, {25381, 28840}, {30821, 31285}

X(50158) = midpoint of X(2) and X(49717)
X(50158) = complement of X(49749)


X(50159) = X(2)X(39)∩X(30)X(40)

Barycentrics    a^4*b + a*b^4 + a^4*c + 2*a^3*b*c + a^2*b^2*c + 2*a*b^3*c + b^4*c + a^2*b*c^2 + 4*a*b^2*c^2 + 3*b^3*c^2 + 2*a*b*c^3 + 3*b^2*c^3 + a*c^4 + b*c^4 : :
X(50159) = X[3729] + 2 X[15985], 4 X[17355] - X[28369]

X(50159) lies on these lines: {2, 39}, {30, 40}, {81, 24275}, {333, 24271}, {524, 17281}, {754, 3578}, {2782, 33167}, {2795, 21020}, {3729, 15985}, {3734, 5278}, {3761, 32777}, {3912, 4754}, {4647, 49760}, {5737, 24296}, {7798, 19684}, {7804, 19742}, {11286, 19723}, {13745, 48851}, {17116, 30056}, {17251, 50057}, {17310, 42045}, {17355, 28369}, {18206, 21024}, {19701, 22253}, {29573, 37631}, {29574, 49749}


X(50160) = X(2)X(39)∩X(10)X(4754)

Barycentrics    a^3*b + a^2*b^2 + a*b^3 + a^3*c + 4*a^2*b*c + 4*a*b^2*c + b^3*c + a^2*c^2 + 4*a*b*c^2 + 4*b^2*c^2 + a*c^3 + b*c^3 : :
X(50160) = X(50160) = 2 X[10] + X[4754]

X(50160) lies on these lines: {2, 39}, {10, 4754}, {30, 48851}, {519, 49749}, {524, 3416}, {543, 1281}, {668, 28604}, {1018, 7227}, {1111, 3739}, {1213, 25468}, {1698, 25350}, {3578, 27790}, {3761, 17303}, {3928, 28608}, {4692, 25384}, {5007, 16930}, {7751, 16454}, {7760, 16926}, {7780, 19284}, {7781, 16342}, {8667, 19290}, {8682, 21020}, {8716, 16351}, {15985, 25590}, {17175, 21024}, {17251, 44217}, {17294, 37631}, {17739, 49724}, {19276, 47037}, {27478, 46902}, {27798, 35102}, {29615, 42045}, {35101, 46895}

X(50160) = midpoint of X(4754) and X(49717)
X(50160) = reflection of X(49717) in X(10)
X(50160) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 26035, 48860}, {2, 34284, 48840}, {2, 48840, 25499}, {2, 48869, 5283}


X(50161) = X(2)X(32)∩X(30)X(48853)

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

X(50161) lies on these lines: {2, 32}, {30, 48853}, {524, 551}, {538, 13745}, {543, 1281}, {3578, 29580}, {7751, 37314}, {7759, 16343}, {7764, 16342}, {7768, 16929}, {7794, 16927}, {11357, 17251}, {19290, 47101}, {29574, 49724}, {29594, 49730}, {49723, 49749}

X(50161) = midpoint of X(49723) and X(49749)


X(50162) = X(2)X(39)∩X(10)X(30)

Barycentrics    2*a^4*b + a^3*b^2 + a^2*b^3 + 2*a*b^4 + 2*a^4*c + 4*a^3*b*c + 3*a^2*b^2*c + 4*a*b^3*c + 2*b^4*c + a^3*c^2 + 3*a^2*b*c^2 + 6*a*b^2*c^2 + 4*b^3*c^2 + a^2*c^3 + 4*a*b*c^3 + 4*b^2*c^3 + 2*a*c^4 + 2*b*c^4 : :
X(50162) = X[15985] + 2 X[17355]

X(50162) lies on these lines: {2, 39}, {10, 30}, {333, 24275}, {524, 17359}, {553, 21240}, {754, 49724}, {1500, 42033}, {2795, 27798}, {3578, 3661}, {3734, 19732}, {3739, 24208}, {3912, 37631}, {4754, 17284}, {5235, 24271}, {5278, 7804}, {7798, 19701}, {15985, 17355}, {24036, 44417}, {29573, 49749}, {29577, 42045}, {29674, 49744}


X(50163) = X(2)X(39)∩X(10)X(524)

Barycentrics    2*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 2*a^3*c + 8*a^2*b*c + 8*a*b^2*c + 2*b^3*c + 3*a^2*c^2 + 8*a*b*c^2 + 6*b^2*c^2 + 2*a*c^3 + 2*b*c^3 : :
X(50163) = 5 X[1698] + X[4754], 3 X[19875] - X[49717]

X(50163) lies on these lines: {2, 39}, {10, 524}, {30, 48853}, {536, 3743}, {543, 13745}, {1698, 4754}, {2049, 4658}, {3679, 49749}, {3739, 16611}, {5007, 16926}, {5184, 24342}, {7751, 16458}, {7760, 16928}, {7780, 16454}, {7781, 16343}, {8667, 19332}, {8682, 27798}, {15973, 43174}, {17499, 31144}, {17758, 20582}, {19336, 46893}, {19875, 49717}, {20888, 41311}, {24603, 24628}, {35103, 49598}

X(50163) = midpoint of X(3679) and X(49749)


X(50164) = X(1)X(538)∩X(10)X(30)

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

X(50164) lies on these lines: {1, 538}, {10, 30}, {21, 24271}, {39, 1008}, {76, 4195}, {99, 19312}, {187, 11104}, {405, 3734}, {511, 3923}, {516, 15985}, {524, 49484}, {540, 49560}, {543, 13745}, {574, 37053}, {620, 37047}, {625, 37049}, {754, 49716}, {1009, 3934}, {1010, 16589}, {1043, 17499}, {1104, 20888}, {1500, 7283}, {1724, 7804}, {2549, 13725}, {2782, 41193}, {2795, 49598}, {3501, 48883}, {3849, 49723}, {3912, 49745}, {3948, 11115}, {4044, 37539}, {4045, 13728}, {4201, 7847}, {4229, 26244}, {4292, 21240}, {5254, 37044}, {5737, 49130}, {7739, 19766}, {7751, 19761}, {7781, 19758}, {7816, 13723}, {7861, 37025}, {9534, 48864}, {9746, 9840}, {10449, 48817}, {10479, 11355}, {11319, 20913}, {13736, 32815}, {15447, 30818}, {16342, 24296}, {17130, 19768}, {20018, 48869}, {20077, 33297}, {32456, 37023}


X(50165) = X(2)X(3)∩X(145)X(524)

Barycentrics    4*a^4 - a^3*b - 4*a^2*b^2 - a*b^3 - 2*b^4 - a^3*c - 4*a^2*b*c - 4*a*b^2*c - b^3*c - 4*a^2*c^2 - 4*a*b*c^2 + 2*b^2*c^2 - a*c^3 - b*c^3 - 2*c^4 : :
X(50165) = 3 X[2] - 4 X[13745], 2 X[13745] - 3 X[49735], 5 X[3617] - 8 X[49728], X[3621] - 4 X[49716], 7 X[3622] - 4 X[49745], 5 X[20052] - 8 X[49718], 3 X[38314] - 2 X[49744], 11 X[46933] - 8 X[49734]

X(50165) lies on these lines: {1, 17491}, {2, 3}, {8, 49723}, {10, 4781}, {145, 524}, {540, 3241}, {1043, 31143}, {2650, 28558}, {2796, 17164}, {3578, 31145}, {3617, 49728}, {3621, 49716}, {3622, 49745}, {4304, 26580}, {4720, 43990}, {4933, 27558}, {5330, 48907}, {7354, 49740}, {10459, 28562}, {17330, 26770}, {17333, 25237}, {19742, 48837}, {19765, 31179}, {20052, 49718}, {27804, 38456}, {34605, 49746}, {38314, 49744}, {42045, 49739}, {46933, 49734}, {50046, 50105}, {50050, 50104}, {50065, 50102}

X(50165) = reflection of X(i) in X(j) for these {i,j}: {2, 49735}, {8, 49723}, {31145, 3578}, {42045, 49739}
X(50165) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11114, 17537}, {2, 37299, 16397}, {21, 17677, 2}, {405, 17679, 2}, {6872, 17676, 11319}, {11111, 50055, 2}, {11112, 14020, 2}, {11114, 37038, 2}, {11346, 11359, 2}, {15680, 26117, 11115}, {16858, 17678, 2}, {17579, 48814, 2}, {31156, 48813, 2}


X(50166) = X(2)X(3)∩X(500)X(26639)

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

X(50166) lies on these lines: {2, 3}, {500, 26639}, {524, 49747}, {538, 3578}, {540, 16834}, {754, 29584}, {2549, 5278}, {5741, 24296}, {7737, 19684}, {7761, 18139}, {15048, 19742}, {18907, 19717}, {19732, 44526}, {24271, 41809}, {26626, 49745}, {49723, 50095}

X(50166) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11359, 50060, 2}, {17677, 35935, 2}


X(50167) = X(2)X(3)∩X(239)X(49716)

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

X(50167) lies on these lines: {2, 3}, {239, 49716}, {524, 16834}, {538, 42051}, {540, 50114}, {754, 37631}, {1213, 24271}, {1834, 24632}, {2549, 19732}, {4384, 49728}, {5278, 15048}, {5453, 26639}, {5743, 24296}, {7737, 19701}, {7739, 19723}, {16833, 49723}, {17023, 49745}, {17308, 49734}, {18907, 19684}, {19744, 44526}, {19749, 43618}, {26626, 49743}, {29574, 49739}

X(50167) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 48813, 50057}, {21997, 26601, 1375}


X(50168) = X(2)X(3)∩X(524)X(17281)

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

X(50168) lies on these lines: {2, 3}, {524, 17281}, {538, 3175}, {540, 29594}, {754, 49724}, {1211, 24275}, {2549, 19701}, {3661, 49716}, {3912, 49745}, {4384, 49734}, {5278, 18907}, {7737, 19732}, {7739, 19722}, {15048, 19684}, {15936, 35578}, {17056, 24271}, {17308, 49728}, {17316, 49743}, {19749, 43619}, {25007, 48887}, {29573, 49744}

X(50168) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 48817, 50060}


X(50169) = X(2)X(3)∩X(10)X(540)

Barycentrics    2*a^4 + 2*a^3*b + 3*a^2*b^2 + 2*a*b^3 - b^4 + 2*a^3*c + 8*a^2*b*c + 8*a*b^2*c + 2*b^3*c + 3*a^2*c^2 + 8*a*b*c^2 + 6*b^2*c^2 + 2*a*c^3 + 2*b*c^3 - c^4 : :
X(50169) = X[1] + 2 X[49734], X[13442] - 4 X[15973], 3 X[13745] - 2 X[49735], X[8] + 2 X[49743], 4 X[10] - X[49716], 2 X[10] + X[49745], X[49716] + 2 X[49745], 5 X[1698] - 2 X[49728], 5 X[3617] - 2 X[49718], 3 X[19875] - X[49723], 3 X[19875] - 2 X[49730]

X(50169) lies on these lines: {1, 49734}, {2, 3}, {8, 42045}, {10, 540}, {500, 19860}, {511, 3753}, {519, 37631}, {524, 3416}, {543, 5988}, {551, 49739}, {993, 15447}, {1330, 41816}, {1698, 49728}, {1834, 25526}, {3419, 10436}, {3617, 49718}, {3828, 49729}, {4720, 37635}, {5250, 48915}, {5439, 40649}, {6707, 25468}, {7354, 19858}, {9579, 19859}, {9810, 28294}, {13408, 24987}, {17614, 48894}, {19684, 48847}, {19701, 48837}, {19722, 48857}, {19723, 48870}, {19738, 48861}, {19857, 50050}, {19861, 48903}, {19875, 49723}, {24161, 25055}, {24473, 50116}, {24982, 48887}, {26131, 41014}, {26637, 45923}, {27798, 38456}, {29181, 38052}, {41312, 50066}, {41812, 47033}, {50053, 50104}, {50069, 50102}

X(50169) = midpoint of X(i) and X(j) for these {i,j}: {8, 42045}, {3679, 49744}, {46617, 46704}, {49724, 49745}
X(50169) = reflection of X(i) in X(j) for these {i,j}: {13745, 2}, {42045, 49743}, {49716, 49724}, {49723, 49730}, {49724, 10}, {49729, 3828}, {49739, 551}
X(50169) = complement of X(49735)
X(50169) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 376, 16351}, {2, 377, 11359}, {2, 4217, 16857}, {2, 4234, 15670}, {2, 6175, 16052}, {2, 11359, 13728}, {2, 15677, 17553}, {2, 17679, 48815}, {2, 19336, 549}, {2, 31156, 11357}, {2, 48816, 11112}, {2, 48817, 405}, {2, 50061, 16418}, {10, 49745, 49716}, {377, 2049, 13728}, {381, 19332, 2}, {382, 16456, 37314}, {1010, 26051, 442}, {2049, 11359, 2}, {2475, 14005, 4205}, {14007, 26117, 17514}, {17528, 19277, 2}, {17528, 34609, 17532}, {19875, 49723, 49730}, {37153, 48817, 2}


X(50170) = X(2)X(3)∩X(524)X(49721)

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

X(50170) lies on these lines: {2, 3}, {524, 49721}, {538, 17389}, {540, 17294}, {543, 29580}, {754, 3578}, {2549, 19684}, {3734, 18139}, {3936, 24271}, {5278, 7737}, {7739, 19738}, {15048, 19717}, {15936, 50128}, {17316, 49745}, {18907, 19742}, {19701, 44526}, {24275, 41809}, {26639, 48903}, {29574, 49744}, {29585, 49743}

X(50170) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11354, 50057, 2}


X(50171) = X(2)X(3)∩X(8)X(524)

Barycentrics    2*a^4 + a^3*b + a^2*b^2 + a*b^3 - b^4 + a^3*c + 4*a^2*b*c + 4*a*b^2*c + b^3*c + a^2*c^2 + 4*a*b*c^2 + 4*b^2*c^2 + a*c^3 + b*c^3 - c^4 : :
X(50171) = 4 X[13745] - 3 X[49735], 2 X[15971] + X[48890], X[8] - 4 X[49734], X[8] + 2 X[49745], 2 X[49734] + X[49745], X[145] - 4 X[49743], 5 X[3617] - 2 X[49716], 7 X[4678] - 4 X[49718], 7 X[9780] - 4 X[49728], X[10914] + 2 X[49557], 3 X[19875] - 2 X[49729], 3 X[38314] - 2 X[49739]

X(50171) lies on these lines: {1, 4442}, {2, 3}, {8, 524}, {10, 896}, {145, 49743}, {519, 2650}, {540, 1046}, {542, 46483}, {543, 16830}, {551, 23536}, {1043, 26131}, {1213, 26079}, {1330, 31143}, {2292, 2796}, {3178, 4933}, {3241, 37631}, {3617, 49716}, {3710, 50118}, {3868, 50128}, {3897, 48893}, {4678, 49718}, {4720, 17778}, {5252, 28968}, {5262, 37756}, {5554, 48877}, {5722, 26627}, {6284, 49740}, {9780, 49728}, {10404, 47358}, {10483, 19858}, {10914, 49557}, {15936, 20880}, {15938, 26651}, {15988, 48922}, {16948, 25446}, {17330, 26035}, {17378, 34284}, {18139, 48863}, {19684, 48837}, {19717, 48847}, {19722, 48842}, {19738, 48857}, {19860, 48897}, {19875, 49729}, {21020, 38456}, {21674, 24850}, {25005, 48887}, {25385, 49608}, {26064, 31144}, {26978, 49738}, {34606, 49725}, {38314, 49739}, {41312, 50065}, {50049, 50105}, {50054, 50104}, {50064, 50103}

X(50171) = reflection of X(i) in X(j) for these {i,j}: {3241, 37631}, {3578, 3679}, {42045, 49744}, {49723, 10}, {49735, 2}
X(50171) = anticomplement of X(13745)
X(50171) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 377, 17679}, {2, 2475, 17677}, {2, 11114, 14020}, {2, 16397, 37298}, {2, 17677, 5051}, {2, 17679, 4202}, {2, 48817, 11346}, {377, 964, 4202}, {381, 19290, 2}, {964, 17679, 2}, {1010, 2475, 5051}, {1010, 17677, 2}, {11112, 37150, 2}, {11354, 44217, 2}, {16394, 17528, 2}, {17532, 19276, 2}, {19277, 50056, 2}, {49734, 49745, 8}


X(50172) = X(2)X(3)∩X(8)X(540)

Barycentrics    4*a^4 + a^3*b + a*b^3 - 2*b^4 + a^3*c + 4*a^2*b*c + 4*a*b^2*c + b^3*c + 4*a*b*c^2 + 6*b^2*c^2 + a*c^3 + b*c^3 - 2*c^4 : :
X(50172) = 5 X[2] - 4 X[13745], 6 X[13745] - 5 X[49735], X[145] - 4 X[49745], 5 X[3617] - 4 X[49724], 5 X[3617] - 8 X[49734], 5 X[3623] - 8 X[49743], X[3885] - 4 X[49557], 7 X[4678] - 4 X[49716], 11 X[46933] - 8 X[49728]

X(50172) lies on these lines: {2, 3}, {8, 540}, {145, 42045}, {519, 17164}, {524, 31145}, {543, 5992}, {551, 3120}, {3241, 49744}, {3586, 26627}, {3617, 49724}, {3623, 49743}, {3679, 4418}, {3885, 49557}, {3897, 48926}, {4080, 30115}, {4678, 49716}, {17163, 38456}, {19717, 48837}, {19738, 48842}, {19743, 48847}, {24275, 26079}, {24850, 27690}, {46933, 49728}, {50070, 50102}

X(50172) = reflection of X(i) in X(j) for these {i,j}: {145, 42045}, {3241, 49744}, {42045, 49745}, {49724, 49734}
X(50172) = anticomplement of X(49735)
X(50172) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 48817, 11319}, {377, 48817, 2}, {381, 19336, 2}, {964, 11359, 2}, {4234, 6175, 2}, {11114, 48816, 2}, {11346, 44217, 2}, {11354, 17679, 2}, {15680, 26051, 17588}, {16393, 17532, 2}


X(50173) = X(2)X(39)∩X(30)X(551)

Barycentrics    2*a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + 2*a*b^4 + 2*a^4*c + 4*a^3*b*c + 5*a^2*b^2*c + 4*a*b^3*c + 2*b^4*c + 3*a^3*c^2 + 5*a^2*b*c^2 + 2*a*b^2*c^2 + 3*a^2*c^3 + 4*a*b*c^3 + 2*a*c^4 + 2*b*c^4 : :
X(50173) = 5 X[17304] + X[28369]

X(50173) lies on these lines: {2, 39}, {30, 551}, {524, 17382}, {754, 37631}, {1015, 19786}, {2795, 10180}, {3734, 19701}, {4415, 30106}, {4754, 29598}, {5333, 24271}, {6703, 17205}, {7798, 19732}, {7804, 19684}, {16833, 49717}, {17304, 28369}, {19744, 22253}, {24275, 25507}, {41140, 49724}


X(50174) = X(2)X(39)∩X(524)X(551)

Barycentrics    2*a^3*b + 5*a^2*b^2 + 2*a*b^3 + 2*a^3*c + 8*a^2*b*c + 8*a*b^2*c + 2*b^3*c + 5*a^2*c^2 + 8*a*b*c^2 + 2*b^2*c^2 + 2*a*c^3 + 2*b*c^3 : :
X(50174) = 7 X[3624] - X[4754], 3 X[25055] - X[49749]

X(50174) lies on these lines: {1, 49717}, {2, 39}, {524, 551}, {543, 5988}, {754, 13745}, {1015, 17322}, {3624, 4754}, {3849, 49735}, {4364, 39542}, {4698, 24036}, {5007, 16927}, {6707, 17205}, {7751, 16343}, {7759, 37314}, {7760, 16929}, {7780, 16342}, {7781, 16458}, {8682, 10180}, {8716, 19332}, {18904, 41311}, {25055, 49749}, {49730, 50114}

X(50174) = midpoint of X(1) and X(49717)
X(50174) = {X(2),X(5283)}-harmonic conjugate of X(48860)


X(50175) = X(1)X(30)∩X(4)X(980)

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

X(50175) lies on these lines: {1, 30}, {3, 24296}, {4, 980}, {8, 538}, {187, 35915}, {274, 26117}, {377, 2549}, {511, 24248}, {516, 28369}, {524, 49495}, {540, 49488}, {543, 16830}, {940, 49130}, {950, 24214}, {964, 3734}, {986, 48937}, {1010, 24271}, {1834, 18206}, {2223, 13161}, {2292, 2795}, {2475, 40773}, {2794, 46483}, {3146, 4352}, {4045, 4202}, {4384, 49728}, {7270, 25264}, {9534, 48813}, {9840, 37575}, {14005, 24275}, {15048, 16552}, {15447, 17720}, {15971, 44431}, {16823, 49735}, {19318, 24617}, {37522, 49129}, {37555, 48883}


X(50176) = X(1)X(30)∩X(381)X(980)

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

X(50176) lies on these lines: {1, 30}, {381, 980}, {524, 50080}, {538, 3679}, {540, 16834}, {3017, 18206}, {3543, 4352}, {3578, 32950}, {3663, 15982}, {4384, 49729}, {5283, 44217}, {6175, 40773}, {7739, 16552}, {11355, 48840}, {16833, 49723}, {19871, 48812}


X(50177) = X(1)X(30)∩X(10)X(538)

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

X(50177) lies on these lines: {1, 30}, {4, 4352}, {5, 980}, {10, 538}, {76, 37148}, {194, 16062}, {239, 49716}, {274, 4205}, {325, 37159}, {385, 35916}, {442, 40773}, {511, 3663}, {524, 4655}, {540, 49477}, {698, 49519}, {940, 49129}, {942, 24214}, {986, 32515}, {1107, 23537}, {1330, 33296}, {1975, 33745}, {2782, 5988}, {2795, 3743}, {3695, 25264}, {3734, 43531}, {3821, 15985}, {4202, 31036}, {5283, 8728}, {7840, 17677}, {9534, 11359}, {10449, 48838}, {13740, 17128}, {13745, 16823}, {15447, 17602}, {16825, 49728}, {19758, 36477}, {20018, 48813}, {24248, 28369}, {24271, 25526}, {24296, 37522}, {29365, 37548}, {34937, 48893}, {36480, 49734}, {37425, 37590}, {37555, 48882}, {37575, 48930}

X(50177) = midpoint of X(24248) and X(28369)
X(50177) = reflection of X(15985) in X(3821)


X(50178) = X(1)X(30)∩X(2)X(39)

Barycentrics    a^4*b + 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 + a^4*c + 2*a^3*b*c + 3*a^2*b^2*c + 2*a*b^3*c + b^4*c + 2*a^3*c^2 + 3*a^2*b*c^2 - b^3*c^2 + 2*a^2*c^3 + 2*a*b*c^3 - b^2*c^3 + a*c^4 + b*c^4 : :
X(50178) = 2 X[3663] + X[28369], 2 X[15985] - 5 X[17304]

X(50178) lies on these lines: {1, 30}, {2, 39}, {86, 24271}, {213, 17781}, {239, 3578}, {524, 16834}, {536, 18697}, {543, 29580}, {553, 24214}, {754, 29584}, {940, 24296}, {1111, 3666}, {1962, 2795}, {2782, 33152}, {3230, 28368}, {3663, 28369}, {3734, 19684}, {4045, 18139}, {4384, 49730}, {4754, 17023}, {5278, 7798}, {5333, 24275}, {7804, 19717}, {11286, 19722}, {11355, 48855}, {14636, 37575}, {15985, 17304}, {16825, 49729}, {16829, 19796}, {16833, 49724}, {16975, 19785}, {17246, 29382}, {17591, 32515}, {19732, 22253}, {19853, 48806}, {25264, 42033}, {27248, 42032}, {27272, 32026}, {43266, 49749}, {49717, 50095}

X(50178) = crossdifference of every pair of points on line {669, 9404}


X(50179) = X(1)X(524)∩X(2)X(39)

Barycentrics    a^3*b + 3*a^2*b^2 + a*b^3 + a^3*c + 4*a^2*b*c + 4*a*b^2*c + b^3*c + 3*a^2*c^2 + 4*a*b*c^2 + a*c^3 + b*c^3 : :
X(50179) = 4 X[1125] - X[4754]

X(50179) lies on these lines: {1, 524}, {2, 39}, {30, 48854}, {37, 14210}, {213, 50093}, {405, 28619}, {519, 49717}, {536, 4647}, {543, 16830}, {551, 49749}, {597, 16552}, {712, 3989}, {754, 49735}, {764, 28840}, {958, 50073}, {1107, 41311}, {1125, 4465}, {1962, 8682}, {2238, 46913}, {2292, 35103}, {3230, 28369}, {3294, 49737}, {3578, 29584}, {4301, 9840}, {4664, 17762}, {4755, 16601}, {5007, 16931}, {5277, 21937}, {7751, 16342}, {7758, 37314}, {7760, 16927}, {7780, 16347}, {7781, 16454}, {8667, 16351}, {8716, 19290}, {10180, 35102}, {16819, 37756}, {16829, 17320}, {16833, 49730}, {16834, 49724}, {16912, 33955}, {16975, 17321}, {17045, 45751}, {17210, 21024}, {17324, 30056}, {25579, 28609}, {29578, 30566}, {29580, 42045}, {29597, 37631}, {31144, 33296}

X(50179) = reflection of X(49749) in X(551)


X(50180) = X(2)X(6)∩X(538)X(551)

Barycentrics    4*a^3*b + 4*a^2*b^2 + a*b^3 + 4*a^3*c + 10*a^2*b*c + 7*a*b^2*c + b^3*c + 4*a^2*c^2 + 7*a*b*c^2 + 4*b^2*c^2 + a*c^3 + b*c^3 : :
X(50180) = X[49717] + 3 X[49749], 5 X[3616] + X[4754]

X(50180) lies on these lines: {2, 6}, {30, 48822}, {42, 4472}, {43, 4798}, {511, 28600}, {536, 25124}, {538, 551}, {543, 41184}, {3616, 4713}, {3739, 4771}, {4640, 4670}, {4665, 17018}, {4758, 6685}, {4831, 24690}, {16589, 18172}, {17032, 17369}, {28840, 48248}

X(50180) = midpoint of X(2) and X(49749)
X(50180) = complement of X(49717)
X(50180) = {X(4670),X(43223)}-harmonic conjugate of X(25349)


X(50181) = X(1)X(30)∩X(2)X(32)

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

X(50181) lies on these lines: {1, 30}, {2, 32}, {445, 14581}, {524, 17281}, {538, 17389}, {540, 48811}, {940, 36731}, {2895, 24275}, {3578, 3661}, {3954, 17781}, {4045, 19717}, {5712, 24296}, {7761, 19684}, {7804, 18139}, {11287, 19722}, {17308, 49730}, {17778, 24271}

X(50181) = crossdifference of every pair of points on line {3005, 9404}


X(50182) = X(1)X(30)∩X(2)X(40984)

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

X(50182) lies on these lines: {1, 30}, {2, 40984}, {376, 980}, {524, 50130}, {538, 3241}, {754, 49735}, {2223, 14636}, {4352, 15683}, {4720, 24275}, {4754, 49771}, {5283, 31156}, {5337, 13634}, {6740, 11060}, {7865, 25499}, {13745, 48854}, {15677, 40773}, {19853, 48798}, {36480, 49729}


X(50183) = X(2)X(39)∩X(30)X(944)

Barycentrics    a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4 + a^4*c + 2*a^3*b*c + 4*a^2*b^2*c + 2*a*b^3*c + b^4*c + 3*a^3*c^2 + 4*a^2*b*c^2 - 2*a*b^2*c^2 - 3*b^3*c^2 + 3*a^2*c^3 + 2*a*b*c^3 - 3*b^2*c^3 + a*c^4 + b*c^4 : :
X(50183) = 4 X[3663] - X[15983]

X(50183) lies on these lines: {2, 39}, {30, 944}, {524, 49747}, {2795, 27804}, {3663, 15983}, {3734, 19717}, {4754, 26626}, {5278, 22253}, {7798, 19742}, {7804, 19743}, {8025, 24271}, {11286, 19738}, {15048, 18139}, {16714, 25660}, {24296, 37639}, {31179, 36731}


X(50184) = X(2)X(39)∩X(30)X(48856)

Barycentrics    a^3*b + 4*a^2*b^2 + a*b^3 + a^3*c + 4*a^2*b*c + 4*a*b^2*c + b^3*c + 4*a^2*c^2 + 4*a*b*c^2 - 2*b^2*c^2 + a*c^3 + b*c^3 : :
X(50184) = 5 X[3616] - 2 X[4754], 3 X[38314] - 2 X[49749]

X(50184) lies on these lines: {2, 39}, {8, 49717}, {30, 48856}, {37, 7200}, {524, 3241}, {543, 5992}, {551, 4368}, {1962, 35102}, {3578, 50129}, {3616, 4713}, {3989, 46180}, {7751, 16347}, {7760, 16931}, {7781, 19284}, {8682, 27804}, {8716, 19336}, {15983, 17247}, {16714, 24944}, {26759, 32026}, {37631, 42050}, {38314, 49749}

X(50184) = reflection of X(8) in X(49717)
X(50184) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 26770, 48860}, {2, 48840, 26978}, {2, 48869, 26035}, {1655, 16705, 27040}, {5283, 48840, 2}, {25499, 48860, 2}


X(50185) = X(2)X(967)∩X(30)X(48830)

Barycentrics    2*a^4 + 6*a^3*b + 3*a^2*b^2 - b^4 + 6*a^3*c + 12*a^2*b*c + 6*a*b^2*c + 3*a^2*c^2 + 6*a*b*c^2 + 6*b^2*c^2 - c^4 : :
X(50185) = X[4754] + 2 X[49743]

X(50185) lies on these lines: {2, 967}, {30, 48830}, {524, 3416}, {538, 3175}, {540, 48853}, {543, 49739}, {754, 49745}, {1509, 14568}, {4754, 49743}, {6625, 14041}, {8356, 37632}, {11361, 17379}, {13468, 37522}, {17103, 35297}, {23812, 35102}, {25579, 28609}, {42045, 50079}


X(50186) = X(2)X(32)∩X(8)X(524)

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

X(50186) lies on these lines: {2, 32}, {8, 524}, {30, 48856}, {86, 26079}, {540, 48802}, {964, 17251}, {4725, 4968}, {7759, 19284}, {7768, 16930}, {9766, 19336}, {17141, 50128}, {17297, 17686}, {17346, 26035}, {17392, 26978}, {19819, 42045}, {26145, 37675}, {34284, 50133}


X(50187) = X(2)X(3018)∩X(4)X(542)

Barycentrics    4*a^8 - 3*a^6*b^2 - 5*a^4*b^4 + 3*a^2*b^6 + b^8 - 3*a^6*c^2 + 10*a^4*b^2*c^2 - 2*a^2*b^4*c^2 - 9*b^6*c^2 - 5*a^4*c^4 - 2*a^2*b^2*c^4 + 16*b^4*c^4 + 3*a^2*c^6 - 9*b^2*c^6 + c^8 : :
X(50187) = 4 X[3018] - X[35520]

X(50187) lies on these lines: {2, 3018}, {4, 542}, {338, 597}, {351, 523}, {543, 2407}, {599, 19221}, {1990, 44569}, {2452, 11632}, {2482, 14570}, {3014, 41624}, {3260, 40112}, {4558, 8591}, {9512, 14830}, {11054, 41617}, {11078, 18777}, {11092, 18776}, {11163, 14995}, {14999, 17948}, {15912, 34351}, {23055, 47200}

X(50187) = reflection of X(i) in X(j) for these {i,j}: {2, 3018}, {35520, 2}
X(50187) = barycentric product X(316)*X(46338)
X(50187) = barycentric quotient X(46338)/X(67)
X(50187) = {X(648),X(671)}-harmonic conjugate of X(1992)


X(50188) = X(2)X(112)∩X(4)X(74)

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

X(50188) lies on these lines: {2, 112}, {4, 74}, {53, 338}, {69, 648}, {94, 43678}, {98, 36191}, {186, 47220}, {297, 525}, {340, 15262}, {393, 48540}, {459, 671}, {468, 5191}, {470, 37776}, {471, 37775}, {868, 47202}, {1368, 38553}, {2052, 46105}, {2409, 2794}, {2967, 11007}, {3269, 13567}, {5015, 23541}, {6103, 48453}, {6353, 9862}, {7550, 11587}, {7879, 8743}, {8744, 14165}, {9409, 47252}, {13200, 35278}, {14900, 35282}, {15526, 41678}, {16237, 35520}, {16318, 44216}, {34186, 38689}, {34778, 42854}, {37855, 44569}, {37937, 40079}, {42665, 47216}

X(50188) = polar conjugate of X(2697)
X(50188) = polar conjugate of the isogonal conjugate of X(2781)
X(50188) = X(5641)-Ceva conjugate of X(4)
X(50188) = X(48)-isoconjugate of X(2697)
X(50188) = X(i)-Dao conjugate of X(j) for these (i,j): {542, 6103}, {1249, 2697}
X(50188) = cevapoint of X(6103) and X(36201)
X(50188) = crossdifference of every pair of points on line {184, 1636}
X(50188) = X(47216)-lineconjugate of X(42665)
X(50188) = barycentric product X(i)*X(j) for these {i,j}: {264, 2781}, {340, 43090}, {850, 37937}, {5641, 42426}
X(50188) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 2697}, {2781, 3}, {6530, 47110}, {8744, 46340}, {37937, 110}, {40079, 17974}, {42426, 542}, {43090, 265}
X(50188) = {X(297),X(3580)}-harmonic conjugate of X(44146)


X(50189) = X(1)X(9551)∩X(942)X(4868)

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

See Kadir Altintas and César Lozada euclid 5126.

X(50189) lies on these lines: {1, 9551}, {942, 4868}, {3588, 19767}, {3666, 5083}


X(50190) = X(1)X(3)∩X(2)X(3881)

Barycentrics    a*((b+c)*a^2+5*b*c*a-(b^2-c^2)*(b-c)) : :
X(50190) = 5*X(1)+2*X(65), X(1)+6*X(354), 3*X(1)+4*X(942), 9*X(1)-2*X(3057), X(1)-8*X(5045), 5*X(1)-12*X(5049), 8*X(1)-X(5697), 4*X(1)+3*X(5902), 6*X(1)+X(5903), 13*X(1)-6*X(5919), 11*X(1)-4*X(9957), 3*X(1)-10*X(17609), 2*X(1)+5*X(18398), 15*X(1)-8*X(31792), 13*X(1)+8*X(31794), X(35)-8*X(16193), 3*X(36)+4*X(18839), X(40)-8*X(13373), X(65)-15*X(354), 3*X(65)-10*X(942), 9*X(65)+5*X(3057), X(65)+20*X(5045), X(65)+6*X(5049), 16*X(65)+5*X(5697), 8*X(65)-15*X(5902), 12*X(65)-5*X(5903), 13*X(65)+15*X(5919), 11*X(65)+10*X(9957), 3*X(65)+4*X(31792), 13*X(65)-20*X(31794)

See Antreas Hatzipolakis and César Lozada euclid 5128.

X(50190) lies on these lines: {1, 3}, {2, 3881}, {7, 5557}, {8, 3892}, {10, 3889}, {12, 15079}, {38, 27785}, {72, 25055}, {79, 497}, {80, 938}, {81, 30148}, {90, 10390}, {140, 37703}, {145, 5883}, {210, 34595}, {226, 37720}, {388, 37702}, {392, 3901}, {474, 42871}, {499, 3475}, {518, 3624}, {551, 3868}, {553, 40270}, {596, 32915}, {631, 15104}, {758, 3622}, {912, 9624}, {960, 3894}, {984, 31318}, {995, 46190}, {1001, 6763}, {1056, 37710}, {1071, 11522}, {1125, 3873}, {1210, 37719}, {1371, 39795}, {1372, 39794}, {1476, 15173}, {1478, 11037}, {1479, 10248}, {1698, 3555}, {1699, 12675}, {1724, 29820}, {2802, 20057}, {3058, 24470}, {3060, 23157}, {3086, 11038}, {3216, 49490}, {3241, 3754}, {3293, 17063}, {3485, 5083}, {3487, 5443}, {3488, 4317}, {3582, 11374}, {3583, 10404}, {3600, 36975}, {3616, 3874}, {3617, 3833}, {3621, 3918}, {3632, 3812}, {3633, 3753}, {3636, 3869}, {3678, 4430}, {3679, 5439}, {3681, 19862}, {3697, 3848}, {3698, 4677}, {3711, 16863}, {3743, 4392}, {3786, 28618}, {3878, 38314}, {3885, 3919}, {3890, 4084}, {3916, 42819}, {3957, 25440}, {3983, 19876}, {4018, 10179}, {4187, 17051}, {4293, 5441}, {4298, 10483}, {4309, 15228}, {4333, 41864}, {4540, 46931}, {4666, 5259}, {4686, 39711}, {4847, 41859}, {4867, 11520}, {4880, 5250}, {5208, 28619}, {5218, 5442}, {5220, 5506}, {5248, 29817}, {5249, 49627}, {5265, 12432}, {5270, 5722}, {5284, 41872}, {5289, 16126}, {5312, 49478}, {5315, 28011}, {5434, 12433}, {5435, 31452}, {5444, 5703}, {5445, 10056}, {5531, 6918}, {5542, 10394}, {5559, 18490}, {5572, 9614}, {5586, 11034}, {5603, 12005}, {5659, 6989}, {5691, 13374}, {5693, 5901}, {5696, 24390}, {5728, 23708}, {5784, 38024}, {5884, 10595}, {6051, 21342}, {6147, 18393}, {6693, 29638}, {6738, 37706}, {6744, 10572}, {6833, 11218}, {7226, 27784}, {7671, 43180}, {7741, 11019}, {7951, 21620}, {7967, 31870}, {7972, 46681}, {7988, 14872}, {8083, 30420}, {8242, 18408}, {8715, 27003}, {9589, 10167}, {9612, 9844}, {9654, 37718}, {9668, 16118}, {9670, 18541}, {10122, 11036}, {10176, 46934}, {10527, 26725}, {10569, 30290}, {10582, 25542}, {10826, 17626}, {11020, 21625}, {11033, 30408}, {11246, 15172}, {11551, 12053}, {11552, 12701}, {11924, 18409}, {12564, 30294}, {12577, 45287}, {12953, 18530}, {13369, 31162}, {14923, 33815}, {14986, 37735}, {15180, 17097}, {15844, 41556}, {15888, 18395}, {16408, 41711}, {16472, 35197}, {16491, 24476}, {16503, 17736}, {16971, 20271}, {17624, 37708}, {18514, 18527}, {19854, 38053}, {19861, 41696}, {20132, 30137}, {21214, 43220}, {23155, 31757}, {24387, 31019}, {24629, 40006}, {25079, 49491}, {25526, 29652}, {30145, 37633}, {30628, 38054}, {30704, 49276}, {32558, 47320}, {33108, 41862}, {38021, 40263}

X(50190) = Cevapoint of X(513) and X(28196)
X(50190) = crosssum of X(513) and X(28195)
X(50190) = intersection, other than A, B, C, of circumconics {{A, B, C, X(7), X(3746)}} and {{A, B, C, X(35), X(3296)}}
X(50190) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 57, 3746), (1, 484, 3303), (1, 942, 5903), (1, 3333, 36), (1, 3336, 3295), (1, 3337, 55), (1, 3338, 35), (1, 5902, 5697), (1, 10980, 46), (1, 11010, 6767), (1, 11518, 5425), (1, 11529, 11009), (1, 18398, 5902), (1, 37587, 2646), (35, 36946, 1), (65, 5049, 1), (354, 5045, 1), (354, 17609, 942), (942, 5903, 5902), (942, 17609, 1), (942, 31792, 65), (3295, 4860, 3336), (3303, 5708, 484), (3304, 15934, 1), (3333, 44841, 1), (3555, 3742, 1698), (4430, 5550, 3678), (4883, 37592, 1), (5425, 30274, 5902), (5439, 34791, 3679), (5903, 18398, 942), (11019, 13407, 7741), (24928, 44840, 1), (26357, 34471, 3601)


X(50191) = X(1)X(3)∩X(7)X(5551)

Barycentrics    a*(3*(b+c)*a^2+14*b*c*a-3*(b^2-c^2)*(b-c)) : :
X(50191) = 7*X(1)+3*X(65), X(1)+9*X(354), 2*X(1)+3*X(942), 13*X(1)-3*X(3057), X(1)-6*X(5045), 4*X(1)-9*X(5049), 11*X(1)+9*X(5902), 17*X(1)+3*X(5903), 19*X(1)-9*X(5919), 8*X(1)-3*X(9957), X(1)-3*X(17609), X(1)+3*X(18398), 11*X(1)-6*X(31792), 3*X(1)+2*X(31794), 2*X(65)-7*X(942), 13*X(65)+7*X(3057), X(65)+14*X(5045), 17*X(65)-7*X(5903), 8*X(65)+7*X(9957), X(65)+7*X(17609), X(65)-7*X(18398), 11*X(65)+14*X(31792), 9*X(65)-14*X(31794)

See Antreas Hatzipolakis and César Lozada euclid 5128.

X(50191) lies on these lines: {1, 3}, {7, 5551}, {72, 46934}, {495, 31399}, {496, 5542}, {518, 19862}, {553, 15172}, {596, 4891}, {950, 28190}, {971, 11025}, {1056, 5558}, {1125, 3988}, {1387, 12563}, {3243, 16408}, {3296, 5556}, {3555, 9780}, {3617, 3889}, {3622, 24473}, {3623, 4004}, {3625, 3812}, {3626, 34791}, {3634, 3742}, {3698, 4816}, {3723, 24047}, {3753, 20050}, {3824, 26015}, {3873, 4539}, {3874, 4525}, {3916, 29817}, {3982, 40273}, {4018, 38314}, {4292, 28182}, {4298, 28172}, {4311, 15935}, {4353, 21848}, {4355, 9668}, {4666, 31445}, {5572, 11544}, {5722, 11037}, {6051, 17449}, {6147, 7743}, {6744, 18990}, {6797, 46681}, {7173, 13407}, {9579, 18530}, {9589, 11034}, {9624, 31821}, {9812, 43733}, {9856, 12005}, {10404, 18527}, {10592, 21620}, {10593, 11019}, {11036, 11373}, {11038, 11374}, {12019, 18240}, {12245, 18490}, {12577, 37730}, {12675, 15009}, {13374, 31673}, {15570, 25440}, {17051, 21077}, {21625, 39542}, {25557, 49627}, {31601, 39795}, {31602, 39794}

X(50191) = midpoint of X(i) and X(j) for these {i, j}: {3623, 4004}, {3889, 5439}, {17609, 18398}
X(50191) = reflection of X(i) in X(j) for these (i, j): (942, 18398), (10441, 11531), (17609, 5045), (31785, 8148)
X(50191) = Cevapoint of X(513) and X(28214)
X(50191) = crosssum of X(513) and X(28213)
X(50191) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 3338, 5217), (1, 4860, 3579), (354, 5045, 942), (354, 17609, 18398), (942, 5045, 5049), (942, 5049, 9957), (3337, 3748, 31663), (3337, 36946, 3748), (3742, 3881, 34790)


X(50192) = X(1)X(3)∩X(2)X(4533)

Barycentrics    a*(3*(b+c)*a^2+10*b*c*a-3*(b^2-c^2)*(b-c)) : :
X(50192) = 5*X(1)+3*X(65), X(1)-9*X(354), X(1)+3*X(942), 11*X(1)-3*X(3057), X(1)-3*X(5045), 5*X(1)-9*X(5049), 19*X(1)-3*X(5697), 7*X(1)+9*X(5902), 13*X(1)+3*X(5903), 17*X(1)-9*X(5919), 7*X(1)-3*X(9957), 7*X(1)-15*X(17609), X(1)+15*X(18398), 5*X(1)-3*X(31792), X(65)+15*X(354), X(65)-5*X(942), 11*X(65)+5*X(3057), X(65)+5*X(5045), X(65)+3*X(5049), 19*X(65)+5*X(5697), 7*X(65)-15*X(5902), 13*X(65)-5*X(5903), 17*X(65)+15*X(5919), 7*X(65)+5*X(9957), 3*X(65)-5*X(31794)

See Antreas Hatzipolakis and César Lozada euclid 5128.

X(50192) lies on these lines: {1, 3}, {2, 4533}, {5, 5542}, {7, 15008}, {30, 6744}, {72, 5550}, {210, 19872}, {226, 10593}, {355, 11037}, {382, 4355}, {518, 3634}, {553, 15171}, {938, 3296}, {950, 28168}, {952, 12577}, {960, 15808}, {971, 12005}, {1125, 4127}, {1210, 10592}, {1483, 14563}, {2771, 18240}, {3241, 4004}, {3243, 9709}, {3487, 11230}, {3555, 3617}, {3583, 5557}, {3614, 13407}, {3616, 24473}, {3621, 3753}, {3622, 4018}, {3625, 5883}, {3626, 3812}, {3633, 3922}, {3635, 10107}, {3636, 44663}, {3649, 7743}, {3678, 3848}, {3697, 4430}, {3701, 17146}, {3742, 3874}, {3824, 10916}, {3833, 4662}, {3868, 46934}, {3873, 3921}, {3880, 33815}, {3892, 5836}, {3894, 25917}, {3927, 10582}, {3962, 25055}, {4005, 34595}, {4084, 10179}, {4292, 28154}, {4297, 15935}, {4298, 12433}, {4654, 9669}, {5083, 12019}, {5223, 16853}, {5225, 18527}, {5229, 5722}, {5290, 38140}, {5551, 5556}, {5558, 7317}, {5571, 12813}, {5572, 13369}, {5714, 5728}, {5791, 38053}, {5806, 12675}, {5886, 11036}, {5901, 12563}, {6051, 17450}, {6147, 9955}, {6245, 20330}, {6738, 28204}, {6908, 38030}, {8083, 8100}, {8715, 15570}, {9655, 37723}, {9947, 10569}, {9956, 21620}, {10122, 11544}, {10580, 12699}, {11033, 12491}, {11038, 11231}, {11551, 37722}, {13405, 34753}, {14520, 15658}, {15172, 28198}, {15841, 31657}, {16137, 44675}, {16408, 41863}, {17051, 21616}, {17626, 31937}, {18217, 48661}, {18530, 41869}, {18732, 25418}, {18990, 28208}, {21169, 39795}, {21625, 22791}, {24046, 49478}, {24171, 48847}, {24176, 28581}, {24325, 39564}, {24470, 28146}, {28174, 40270}, {29229, 39543}, {31768, 31796}, {35633, 42053}, {46827, 49491}

X(50192) = midpoint of X(i) and X(j) for these {i, j}: {1, 31794}, {7, 15008}, {65, 31792}, {942, 5045}, {950, 31776}, {3635, 10107}, {3812, 3881}, {3874, 5044}, {4292, 31795}, {4298, 12433}, {5571, 12813}, {5806, 12675}, {6583, 13373}, {12005, 13374}, {12577, 17706}, {31768, 31796}
X(50192) = Cevapoint of X(513) and X(28176)
X(50192) = crosssum of X(513) and X(28175)
X(50192) = inverse of X(5131) in: de Longchamps ellipse, incircle
X(50192) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 942, 31794), (1, 1159, 11278), (1, 3338, 5204), (1, 4860, 37582), (1, 5128, 3295), (1, 5204, 24929), (1, 5708, 3579), (65, 5049, 31792), (354, 942, 5045), (354, 18398, 942), (942, 5049, 65), (942, 9957, 5902), (2446, 2447, 5131), (3333, 15934, 1385), (3337, 37080, 5122), (3742, 3874, 5044), (3873, 5439, 34790), (5045, 9940, 16216), (5045, 31792, 5049), (5045, 31794, 1), (5128, 44841, 1), (5902, 17609, 9957), (6147, 11019, 9955), (7373, 11529, 10222), (10916, 25557, 3824)


X(50193) = X(1)X(3)∩X(2)X(4004)

Barycentrics    a*(3*(b+c)*a^2-2*b*c*a-3*(b^2-c^2)*(b-c)) : :
X(50193) = X(1)-3*X(65), 7*X(1)-9*X(354), 2*X(1)-3*X(942), 5*X(1)-3*X(3057), 5*X(1)-6*X(5045), 8*X(1)-9*X(5049), 7*X(1)-3*X(5697), 5*X(1)-9*X(5902), X(1)+3*X(5903), 11*X(1)-9*X(5919), 4*X(1)-3*X(9957), 13*X(1)-15*X(17609), 11*X(1)-15*X(18398), 7*X(1)-6*X(31792), X(3)-3*X(10273), 7*X(65)-3*X(354), 5*X(65)-X(3057), 5*X(65)-2*X(5045), 8*X(65)-3*X(5049), 7*X(65)-X(5697), 5*X(65)-3*X(5902), 11*X(65)-3*X(5919), 4*X(65)-X(9957), 13*X(65)-5*X(17609), 11*X(65)-5*X(18398), 7*X(65)-2*X(31792), 3*X(65)-2*X(31794)

See Antreas Hatzipolakis and César Lozada euclid 5128.

X(50193) lies on these lines: {1, 3}, {2, 4004}, {4, 7319}, {5, 4848}, {7, 7317}, {8, 4018}, {10, 3838}, {20, 11041}, {30, 41551}, {44, 21863}, {45, 21853}, {72, 3617}, {79, 41684}, {145, 24473}, {221, 44414}, {226, 5690}, {355, 4295}, {382, 5727}, {392, 5550}, {474, 11682}, {495, 3671}, {496, 4301}, {516, 21848}, {518, 3625}, {519, 4757}, {631, 4323}, {758, 3626}, {912, 37705}, {946, 10593}, {950, 28174}, {952, 4292}, {960, 3634}, {962, 5722}, {971, 7672}, {1000, 11037}, {1042, 5399}, {1156, 16615}, {1210, 7743}, {1478, 41687}, {1483, 4311}, {1698, 3922}, {1706, 3940}, {1737, 7173}, {1770, 10950}, {1788, 5886}, {1836, 10573}, {1837, 22793}, {1845, 1887}, {1858, 46027}, {1864, 31822}, {1876, 41722}, {1902, 15337}, {2262, 16670}, {2800, 6797}, {2802, 34791}, {2841, 42450}, {3085, 3654}, {3086, 3656}, {3474, 18481}, {3485, 26446}, {3488, 20070}, {3555, 14923}, {3577, 7285}, {3586, 48661}, {3614, 9956}, {3621, 3868}, {3649, 10039}, {3679, 3962}, {3689, 41696}, {3698, 5692}, {3740, 3918}, {3742, 3884}, {3753, 3869}, {3812, 3878}, {3824, 24987}, {3827, 4663}, {3874, 3880}, {3876, 4002}, {3877, 5439}, {3899, 19872}, {3901, 4816}, {3911, 5901}, {3913, 12559}, {3927, 9623}, {3935, 35990}, {3947, 38127}, {3988, 4745}, {4067, 4662}, {4127, 4691}, {4293, 37727}, {4297, 37728}, {4298, 28234}, {4299, 37740}, {4302, 37724}, {4312, 5881}, {4314, 14563}, {4317, 37738}, {4338, 12943}, {4640, 30147}, {4654, 34718}, {4887, 24471}, {5176, 14450}, {5225, 12699}, {5330, 27003}, {5435, 10595}, {5556, 43734}, {5587, 31821}, {5657, 11374}, {5691, 48664}, {5693, 9947}, {5694, 41538}, {5704, 6956}, {5728, 30332}, {5777, 14988}, {5790, 9612}, {5806, 6844}, {5837, 8728}, {5844, 10106}, {5855, 17647}, {5883, 15808}, {5887, 6867}, {6001, 31673}, {6147, 31397}, {6284, 28198}, {6684, 37737}, {6738, 15171}, {6744, 15170}, {7354, 28204}, {7971, 19541}, {8232, 38126}, {8256, 21077}, {9579, 18525}, {9589, 9668}, {9613, 12645}, {9657, 37708}, {9669, 31162}, {9708, 12526}, {10404, 12647}, {10483, 28208}, {10572, 28146}, {10624, 12433}, {10827, 38176}, {11035, 39779}, {11230, 24914}, {11231, 11375}, {11246, 31776}, {11545, 19925}, {11551, 15888}, {11552, 36920}, {11570, 39777}, {11571, 17636}, {11573, 45955}, {11684, 18259}, {12575, 17706}, {12701, 18527}, {12953, 37721}, {13375, 34502}, {13405, 16137}, {13463, 49627}, {13464, 15325}, {15829, 16408}, {16118, 37006}, {16126, 48696}, {16232, 38235}, {16676, 21871}, {16948, 18180}, {17070, 40635}, {17220, 23521}, {17605, 18395}, {17606, 18393}, {17634, 40263}, {18397, 40266}, {18492, 30286}, {19843, 34744}, {19860, 31445}, {20271, 36647}, {21578, 37734}, {21740, 40262}, {26364, 34647}, {31601, 39794}, {31602, 39795}, {31870, 45776}, {33597, 48363}, {34040, 36754}, {34753, 44675}

X(50193) = midpoint of X(i) and X(j) for these {i, j}: {8, 4018}, {65, 5903}, {1770, 10950}, {3555, 14923}, {3868, 10914}, {11571, 17636}, {11575, 34583}, {24474, 25413}
X(50193) = reflection of X(i) in X(j) for these (i, j): (1, 31794), (10, 10107), (942, 65), (960, 3754), (3057, 5045), (3869, 5044), (3878, 3812), (3884, 33815), (4067, 4662), (4127, 4691), (5693, 9947), (5697, 31792), (7957, 31797), (9856, 7686), (9957, 942), (10106, 24470), (10624, 12433), (12575, 17706), (12672, 5806), (14110, 31787), (15171, 6738), (31786, 34339), (31788, 35004), (31793, 31788), (31798, 37562), (34790, 5836), (45287, 31776), (45776, 31870)
X(50193) = Cevapoint of X(513) and X(28222)
X(50193) = crosssum of X(513) and X(28221)
X(50193) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(7319)}} and {{A, B, C, X(55), X(7317)}}
X(50193) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 46, 5204), (1, 1155, 13624), (1, 2093, 5128), (1, 5128, 3), (1, 5204, 1385), (1, 31794, 942), (1, 37567, 3579), (1, 37582, 5126), (46, 1385, 5122), (46, 2099, 1385), (56, 25415, 10222), (65, 3057, 5902), (942, 9957, 5049), (1159, 12702, 1), (2093, 3340, 3), (2099, 5204, 1), (3057, 5902, 5045), (3336, 11009, 1319), (3339, 7982, 999), (3340, 5128, 1), (3671, 11362, 495), (3878, 3919, 3812), (3884, 33815, 3742), (3922, 31165, 1698), (5045, 5902, 942), (5173, 34339, 942), (5563, 11280, 5048), (5708, 8148, 1), (6583, 18838, 942), (7991, 11529, 3295), (10247, 37545, 1420), (12645, 18541, 9613), (13601, 35004, 942), (24474, 37544, 942), (31786, 34339, 11227)


X(50194) = X(1)X(3)∩X(4)X(4323)

Barycentrics    a*(2*a^3-3*(b+c)*a^2-2*(b^2-b*c+c^2)*a+3*(b^2-c^2)*(b-c)) : :
X(50194) = 3*X(1)-X(55), 5*X(1)-X(5119), 3*X(1)+X(25415), X(55)+3*X(2099), 5*X(55)-3*X(5119), 2*X(55)-3*X(24929), 3*X(551)-2*X(6690), 5*X(2099)+X(5119), 2*X(2099)+X(24929), 3*X(2099)-X(25415), 3*X(3241)+X(3434), 3*X(3679)-5*X(31245), 3*X(5049)-2*X(11018), 2*X(5119)-5*X(24929), 3*X(5119)+5*X(25415), 3*X(10247)-X(37533), 9*X(10247)-X(44455), 3*X(11224)+X(41338), 3*X(24929)+2*X(25415), 3*X(37533)-X(44455)

See Antreas Hatzipolakis and César Lozada euclid 5128.

X(50194) lies on these lines: {1, 3}, {2, 11041}, {4, 4323}, {7, 7967}, {8, 6856}, {10, 5855}, {42, 34586}, {80, 17605}, {140, 4848}, {145, 3419}, {200, 40587}, {210, 4867}, {214, 3919}, {226, 952}, {355, 3485}, {381, 5727}, {388, 37727}, {392, 5284}, {404, 4004}, {405, 11682}, {495, 519}, {496, 6738}, {497, 3656}, {498, 41687}, {515, 37728}, {528, 5542}, {551, 6690}, {674, 49465}, {938, 6956}, {946, 37730}, {950, 22791}, {954, 11526}, {960, 30147}, {993, 44663}, {1000, 10578}, {1056, 3241}, {1058, 5734}, {1210, 5901}, {1320, 3957}, {1361, 20122}, {1386, 49682}, {1387, 9952}, {1389, 17097}, {1392, 3296}, {1457, 5396}, {1478, 18407}, {1479, 37724}, {1483, 6147}, {1484, 41558}, {1737, 11230}, {1824, 1870}, {1836, 28160}, {1837, 9955}, {1864, 48667}, {2161, 16666}, {2182, 2364}, {2771, 41695}, {2807, 39543}, {2808, 34930}, {2975, 4018}, {3244, 11263}, {3486, 12699}, {3555, 4861}, {3577, 19541}, {3600, 37000}, {3623, 11036}, {3635, 12563}, {3649, 37734}, {3654, 5218}, {3655, 4293}, {3671, 5842}, {3679, 31245}, {3683, 3899}, {3753, 4511}, {3811, 8168}, {3812, 30144}, {3817, 12019}, {3869, 31445}, {3874, 11260}, {3897, 3916}, {3898, 30329}, {3911, 38028}, {3940, 9623}, {3947, 47745}, {3962, 5258}, {4292, 34773}, {4295, 18481}, {4298, 13607}, {4301, 15171}, {4302, 28198}, {4304, 28174}, {4311, 24470}, {4314, 15174}, {4342, 15170}, {4345, 15933}, {4654, 18499}, {4744, 4973}, {4870, 7951}, {4930, 9708}, {5044, 5730}, {5219, 5790}, {5251, 31165}, {5274, 5603}, {5288, 16126}, {5289, 8167}, {5326, 11231}, {5356, 16884}, {5434, 11551}, {5437, 35272}, {5443, 17606}, {5494, 7978}, {5690, 13411}, {5703, 12245}, {5719, 5844}, {5728, 10698}, {5836, 22836}, {5837, 6675}, {5854, 49626}, {5881, 9654}, {5886, 6859}, {6224, 20292}, {6264, 8581}, {6265, 6797}, {6737, 31419}, {7672, 31658}, {7686, 40257}, {8000, 11523}, {9352, 35271}, {9578, 12645}, {9581, 18493}, {9612, 18525}, {9613, 18526}, {9655, 36999}, {9668, 31162}, {9669, 11522}, {9956, 10573}, {10107, 25440}, {10175, 11545}, {10283, 44675}, {10404, 32900}, {10571, 37698}, {10572, 22793}, {10695, 44858}, {10895, 37711}, {10896, 37721}, {10914, 34772}, {10943, 15844}, {10944, 13407}, {10950, 12047}, {11037, 20057}, {11108, 15829}, {11237, 37708}, {11246, 21578}, {11552, 36975}, {12053, 12433}, {12513, 12559}, {12635, 34790}, {12647, 17718}, {12701, 31795}, {12736, 19907}, {12737, 17625}, {12943, 28208}, {13405, 28234}, {14988, 18389}, {15173, 21398}, {15733, 42871}, {16465, 38460}, {16602, 45763}, {18527, 30384}, {22837, 34791}, {24390, 41575}, {30284, 30295}, {30331, 38454}, {34040, 36742}, {34232, 39756}, {34958, 48347}, {36845, 36867}, {37701, 38176}, {48909, 49557}

X(50194) = midpoint of X(i) and X(j) for these {i, j}: {1, 2099}, {55, 25415}, {145, 3419}, {954, 11526}, {1478, 37740}, {3428, 7982}, {8148, 37584}, {37727, 37820}, {37728, 39542}
X(50194) = reflection of X(i) in X(j) for these (i, j): (7680, 13464), (24929, 1), (31397, 5719), (32613, 15178)
X(50194) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(34471)}} and {{A, B, C, X(7), X(10246)}}
X(50194) = barycentric product X(81)*X(38058)
X(50194) = trilinear product X(58)*X(38058)
X(50194) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 65, 1385), (1, 3338, 1388), (1, 3340, 3), (1, 5425, 354), (1, 5902, 1319), (1, 5903, 2646), (1, 7982, 3295), (1, 11009, 3057), (1, 11280, 3746), (1, 11529, 999), (1, 18421, 3576), (1, 25415, 55), (1, 30323, 3303), (65, 37605, 3336), (942, 25405, 999), (999, 11529, 942), (1159, 10246, 57), (2093, 13384, 3), (2646, 5183, 5010), (2646, 5903, 3579), (3340, 13384, 2093), (4861, 34195, 3555), (5010, 5183, 3579), (5045, 33179, 1), (5048, 44840, 1), (5708, 37624, 1420), (5730, 19860, 5044), (5885, 11567, 1385), (6738, 13464, 496), (10247, 15934, 1), (10573, 11375, 9956), (15178, 31794, 56), (17609, 33176, 1), (24926, 37605, 1385)


X(50195) = X(1)X(3)∩X(12)X(1858)

Barycentrics    a*((b+c)*a^5-(b^2+c^2)*a^4-2*(b^3+c^3)*a^3+2*(b^2-3*b*c+c^2)*(b+c)^2*a^2+(b^4-c^4)*(b-c)*a-(b^2-c^2)^2*(b-c)^2) : :
X(50195) = 3*X(354)-X(2099), X(3419)-3*X(3753), X(5119)+3*X(5902), 5*X(18398)-X(25415)

See Antreas Hatzipolakis and César Lozada euclid 5128.

X(50195) lies on these lines: {1, 3}, {4, 12711}, {8, 16465}, {10, 13567}, {12, 1858}, {19, 1905}, {37, 1182}, {72, 3085}, {210, 18397}, {226, 6001}, {227, 581}, {380, 2262}, {388, 1071}, {442, 18251}, {495, 912}, {498, 5044}, {515, 10391}, {518, 8255}, {528, 5572}, {611, 34381}, {758, 13405}, {910, 2301}, {920, 31445}, {938, 3434}, {950, 5842}, {960, 6690}, {971, 1478}, {1056, 17625}, {1064, 1465}, {1210, 2886}, {1254, 4300}, {1455, 37469}, {1479, 5806}, {1706, 2900}, {1737, 3925}, {1785, 1859}, {1824, 7952}, {1829, 41227}, {1864, 5587}, {1876, 4307}, {1898, 10895}, {2264, 5540}, {2292, 45038}, {2294, 3708}, {2298, 36121}, {2550, 3419}, {2771, 12831}, {2807, 3664}, {3059, 3679}, {3086, 5439}, {3157, 17836}, {3189, 10914}, {3476, 39779}, {3485, 12672}, {3487, 12709}, {3488, 37000}, {3586, 14100}, {3698, 10399}, {3742, 44675}, {3754, 6738}, {3827, 47373}, {3869, 5703}, {3947, 31803}, {4292, 9943}, {4293, 10167}, {4299, 31805}, {4340, 35672}, {4870, 17638}, {5177, 12529}, {5261, 12528}, {5290, 15071}, {5530, 10822}, {5657, 41539}, {5719, 14988}, {5722, 37820}, {5725, 11435}, {5836, 8261}, {5855, 34791}, {5883, 11019}, {5884, 21620}, {5887, 10321}, {5927, 10590}, {6253, 10572}, {6744, 33815}, {6913, 30223}, {7951, 10157}, {9578, 14872}, {9612, 12688}, {9613, 12680}, {9614, 9848}, {9654, 40263}, {9803, 17620}, {9856, 12047}, {9947, 10827}, {10039, 21677}, {10106, 12675}, {10393, 11500}, {10396, 42012}, {10398, 42014}, {10523, 31937}, {10595, 17622}, {11020, 17784}, {11038, 18419}, {12053, 13374}, {12432, 43174}, {12616, 15844}, {12953, 31822}, {13369, 18990}, {13754, 49743}, {17658, 34619}, {18249, 45120}, {18413, 40608}, {20612, 24987}, {20617, 31978}, {21147, 36746}, {24473, 34744}, {33597, 45230}

X(50195) = midpoint of X(i) and X(j) for these {i, j}: {8, 16465}, {55, 65}, {18389, 31397}, {37533, 37562}
X(50195) = reflection of X(i) in X(j) for these (i, j): (1, 11018), (960, 6690), (2886, 3812), (5173, 942)
X(50195) = X(1065)-complementary conjugate of-X(1329)
X(50195) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 171, 46974), (1, 1735, 3666), (1, 5570, 12915), (1, 13750, 942), (1, 17700, 8071), (1, 22766, 1385), (12, 1858, 5777), (55, 2099, 37569), (55, 5172, 10902), (55, 5584, 40292), (65, 354, 11529), (65, 3057, 37625), (65, 7957, 5903), (354, 18838, 942), (942, 12915, 5570), (942, 31788, 65), (999, 10202, 3660), (1454, 26357, 37623), (2093, 5902, 65), (3333, 15016, 37566), (3753, 5728, 18391), (5045, 5885, 942), (5045, 16201, 16217), (7686, 12710, 950), (8071, 17700, 37582), (11529, 37569, 2099), (18397, 31434, 210), (31787, 37544, 46)


X(50196) = X(1)X(3)∩X(11)X(5777)

Barycentrics    a*((b+c)*a^5-(b^2+c^2)*a^4-2*(b^3+c^3)*a^3+2*(b^4+c^4-b*c*(b^2-4*b*c+c^2))*a^2+(b^4-c^4)*(b-c)*a-(b^2-c^2)^2*(b-c)^2) : :
X(50196) = 3*X(1)-2*X(20789), X(46)-5*X(18398), X(56)-3*X(354), 3*X(210)-5*X(31246), X(1898)-3*X(11238), X(3436)+3*X(3873), 3*X(3742)-2*X(6691), 5*X(3889)-X(36977), 3*X(5902)+X(30323), 3*X(16215)-X(20789), 3*X(17728)-X(41538)

See Antreas Hatzipolakis and César Lozada euclid 5128.

X(50196) lies on these lines: {1, 3}, {4, 17625}, {11, 5777}, {72, 3086}, {210, 31246}, {226, 7681}, {392, 30478}, {442, 38055}, {496, 912}, {497, 1071}, {499, 5044}, {518, 1210}, {613, 34381}, {614, 7078}, {938, 3436}, {950, 2829}, {960, 44675}, {971, 1479}, {1058, 12711}, {1066, 1465}, {1125, 18240}, {1478, 5806}, {1496, 28082}, {1737, 21031}, {1828, 28076}, {1858, 37722}, {1876, 4310}, {1898, 11238}, {1902, 15500}, {2082, 22153}, {2191, 42019}, {2260, 21801}, {2360, 18178}, {2550, 11023}, {2841, 12016}, {3085, 5439}, {3476, 17624}, {3488, 37002}, {3555, 18391}, {3562, 7191}, {3586, 12680}, {3681, 5704}, {3742, 6691}, {3812, 8256}, {3868, 14986}, {3874, 11019}, {3881, 6738}, {3889, 36977}, {4193, 17615}, {4294, 10167}, {4302, 31805}, {5274, 12528}, {5572, 10122}, {5603, 12709}, {5693, 37704}, {5722, 10629}, {5836, 5854}, {5887, 11373}, {5927, 10591}, {6001, 12053}, {7686, 10106}, {7741, 10157}, {7743, 10948}, {8581, 9612}, {8679, 9969}, {9581, 14872}, {9613, 9850}, {9614, 12688}, {9669, 40263}, {9856, 30384}, {9943, 10624}, {9947, 10826}, {10391, 12005}, {10580, 11415}, {12608, 15845}, {12764, 17660}, {12943, 31822}, {13369, 15171}, {13607, 46681}, {14523, 43916}, {15325, 31837}, {15524, 18732}, {17634, 31162}, {17728, 41538}, {18251, 24390}, {18450, 33557}, {24025, 24167}, {26201, 31795}, {34791, 38455}, {41537, 41708}

X(50196) = midpoint of X(i) and X(j) for these {i, j}: {65, 2098}, {3874, 21616}, {12680, 37001}, {12764, 17660}
X(50196) = reflection of X(i) in X(j) for these (i, j): (1, 16215), (7681, 13374), (8069, 11018), (8256, 3812), (24928, 5045), (32612, 13373)
X(50196) = X(1067)-complementary conjugate of-X(1329)
X(50196) = inverse of X(2077) in: de Longchamps ellipse, incircle
X(50196) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 354, 16193), (1, 982, 17102), (1, 1771, 3744), (1, 3075, 5266), (1, 5570, 942), (1, 22767, 1385), (65, 354, 3333), (72, 17626, 3086), (942, 9957, 34339), (942, 12915, 1), (942, 31788, 18838), (950, 5083, 12675), (2446, 2447, 2077), (3057, 18838, 31788), (3874, 11019, 44547), (5045, 6583, 942), (10948, 39599, 7743), (17642, 37566, 40)


X(50197) = X(7)X(333)∩X(37)X(226)

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

See Antreas Hatzipolakis and Ercole Suppa euclid 5131.

X(50197) lies on these lines: {7,333}, {37,226}, {57,34824}, {145,388}, {518,39793}, {524,4654}, {1503,33097}, {3475,4854}, {3486,41825}, {4059,5249}, {5226,41804}, {5333,7181}, {25466,27184}


X(50198) = X(9)X(46)∩X(19)X(29)

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

See Antreas Hatzipolakis and Ercole Suppa euclid 5131.

X(50198) lies on these lines: {1,4273}, {2,1762}, {9,46}, {19,29}, {21,2173}, {37,1247}, {44,1046}, {45,846}, {48,3897}, {57,34824}, {230,8557}, {284,25081}, {405,2939}, {610,2217}, {966,21014}, {1054,4286}, {1086,36540}, {1125,1731}, {1732,3306}, {1953,5330}, {2161,6690}, {2256,10912}, {2287,2294}, {2303,40977}, {2328,11221}, {3294,16548}, {3305,21376}, {3646,18598}, {3751,15990}, {3929,10022}, {4357,40530}, {4418,26040}, {4422,24335}, {4472,36483}, {4700,17706}, {5296,27531}, {6191,37145}, {6192,37144}, {8680,16054}, {8756,24987}, {16670,21373}, {17614,18599}, {24435,25255}, {24683,37169}, {26244,29828}

X(50198) = complement of X(41874)
X(50198) = X(9)-beth conjugate of X(18755)
X(50198) = X(4653)-Dao conjugate of X(5235)
X(50198) = X(3822)-Zayin conjugate of X(1762)
X(50198) = crossdifference of every pair of points on line {2605, 42662}


leftri

Points on the Euler line: X(50199)-X(50208)

rightri

In the plane of a triangle ABC, let

P = point on Nagel line;
D = point not on Nagel line or Euler line;
U = point on Nagel line, other than U and G;
L = line through U parallel to PD;
U′ = L^(Euler line).

For centers X(50199)-X(50208), we take P = X(1) and D = X(6). The appearance of (i,j) in the following list means that if if U = X(i) then U' = X(j): (43,50199), (239,50200), (306,50201), (551, 50202), (946, 50203), (997, 50204), (1125,50205), (1210), 50206), (1698,50207), (1737,50208).


X(50199) = X(2)X(3)∩X(43)X(518)

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

X(50199) lies on these lines: {2, 3}, {43, 518}, {55, 3836}, {56, 25453}, {1001, 33109}, {1376, 3763}, {1403, 24169}, {3662, 20760}, {4429, 23853}, {5687, 33171}, {16569, 41229}, {17313, 18185}, {18134, 37502}, {18613, 48829}, {21010, 29654}, {22139, 26657}, {22149, 26840}, {25760, 27639}, {26034, 27628}, {26128, 34247}, {29474, 35612}, {37673, 46838}

X(50199) = reflection of X(405) in X(19267)
X(50199) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4204, 16842}, {2, 16056, 11358}, {2, 35984, 1011}, {2, 37262, 1009}, {2, 37329, 405}, {2, 37467, 16058}, {8728, 16299, 405}, {17522, 35975, 20841}


X(50200) = X(2)X(3)∩X(239)X(335)

Barycentrics    a^5 - a*b^4 - a^3*b*c + a^2*b^2*c - a*b^3*c - b^4*c + a^2*b*c^2 + 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(50200) lies on these lines: {2, 3}, {10, 24588}, {41, 30985}, {81, 26978}, {105, 20556}, {190, 20432}, {218, 5905}, {238, 23682}, {239, 335}, {332, 29964}, {333, 20913}, {516, 25903}, {1111, 20602}, {1441, 26998}, {1959, 9317}, {3008, 24630}, {3219, 20880}, {4254, 27267}, {4271, 28980}, {4366, 27272}, {4384, 41229}, {4426, 24789}, {5247, 23536}, {5249, 41239}, {5278, 34284}, {5300, 32858}, {5302, 16815}, {6002, 26017}, {8301, 20486}, {10404, 17367}, {10446, 26657}, {14829, 24587}, {16609, 19555}, {16706, 41258}, {16752, 33854}, {20335, 20769}, {24632, 29433}, {25593, 33864}, {26085, 32782}, {30807, 31638}, {35285, 48932}

X(50200) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 379, 37233}, {2, 384, 16050}, {2, 4209, 11329}, {2, 11320, 33821}, {2, 14953, 21495}, {2, 16910, 33736}, {2, 16920, 11342}, {2, 17680, 37096}, {2, 19237, 16053}, {2, 26003, 26025}, {16054, 17681, 2}, {17682, 37086, 2}


X(50201) = X(2)X(3)∩X(63)X(141)

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

X(50201) lies on these lines: {2, 3}, {7, 17776}, {37, 3782}, {63, 141}, {209, 306}, {583, 46885}, {942, 41507}, {1104, 26723}, {3695, 3868}, {3772, 41508}, {3912, 42706}, {4260, 16465}, {4304, 48843}, {5279, 33157}, {5294, 18650}, {16608, 40161}, {40940, 49480}

X(50201) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 464, 16368}, {2, 3151, 37086}, {2, 14021, 37323}, {2, 27052, 5}, {2, 37312, 7536}, {440, 37326, 2}, {30810, 37266, 2}


X(50202) = X(2)X(3)∩X(518)X(551)

Barycentrics    4*a^4 - 5*a^2*b^2 + b^4 - 12*a^2*b*c - 12*a*b^2*c - 5*a^2*c^2 - 12*a*b*c^2 - 2*b^2*c^2 + c^4 : :
X(50202) = 5 X[2] - X[377], 7 X[2] + X[6872], 3 X[2] + X[31156], X[2] - 5 X[31259], 17 X[2] - X[31295], X[377] + 5 X[405], 7 X[377] + 5 X[6872], 2 X[377] - 5 X[8728], 3 X[377] + 5 X[31156], X[377] - 25 X[31259], 17 X[377] - 5 X[31295], 3 X[377] - 5 X[44217], 7 X[405] - X[6872], 2 X[405] + X[8728], 3 X[405] - X[31156], X[405] + 5 X[31259], 17 X[405] + X[31295], 3 X[405] + X[44217], 3 X[3524] - X[37426], 3 X[5054] + X[37234], 3 X[5054] - X[44284], 3 X[5055] - X[44229], 2 X[6872] + 7 X[8728], 3 X[6872] - 7 X[31156], X[6872] + 35 X[31259], 17 X[6872] + 7 X[31295], 3 X[6872] + 7 X[44217], 3 X[8728] + 2 X[31156], X[8728] - 10 X[31259], 17 X[8728] - 2 X[31295], 3 X[8728] - 2 X[44217], 3 X[11539] - X[44222], X[31156] + 15 X[31259], 17 X[31156] + 3 X[31295], 85 X[31259] - X[31295], 15 X[31259] - X[44217], 3 X[31295] - 17 X[44217], 3 X[38071] - X[44286], 2 X[1125] + X[5302], 7 X[3624] - X[10404], 3 X[25055] + X[41229]

X(50202) lies on these lines: {1, 48861}, {2, 3}, {10, 48859}, {37, 50069}, {45, 39544}, {141, 49729}, {518, 551}, {553, 31445}, {942, 5325}, {1001, 15170}, {1125, 5302}, {1698, 4995}, {1724, 37631}, {3058, 5259}, {3305, 5719}, {3576, 38108}, {3582, 24953}, {3584, 3820}, {3624, 5298}, {3646, 5506}, {3649, 41872}, {3653, 8583}, {3656, 31435}, {3679, 10389}, {3739, 50053}, {3940, 18230}, {4423, 10072}, {4653, 17337}, {5247, 48823}, {5248, 49732}, {5251, 5434}, {5306, 16589}, {5362, 42633}, {5367, 42634}, {5603, 38043}, {6147, 17781}, {6174, 19876}, {6666, 24929}, {8167, 15325}, {10157, 10165}, {10385, 19855}, {10386, 49719}, {11238, 19854}, {15254, 39542}, {16814, 26728}, {16817, 42033}, {17776, 50041}, {19875, 37702}, {19883, 34646}, {24541, 38022}, {24564, 34773}, {24789, 50066}, {31142, 31157}, {34625, 38025}, {34638, 38204}, {48847, 49739}, {48870, 49743}

X(50202) = midpoint of X(i) and X(j) for these {i,j}: {2, 405}, {31156, 44217}, {37234, 44284}
X(50202) = reflection of X(8728) in X(2)
X(50202) = complement of X(44217)
X(50202) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3524, 16408}, {2, 4187, 15699}, {2, 5084, 5055}, {2, 5129, 3545}, {2, 6857, 5054}, {2, 7483, 11539}, {2, 10304, 17582}, {2, 13745, 48815}, {2, 15670, 549}, {2, 15671, 7483}, {2, 15672, 404}, {2, 16858, 11112}, {2, 16861, 11113}, {2, 17558, 3524}, {2, 17561, 3}, {2, 31156, 44217}, {2, 33029, 33219}, {2, 33255, 33035}, {2, 33309, 37150}, {3, 17561, 15673}, {405, 44217, 31156}, {5054, 16853, 2}, {5054, 37234, 44284}, {6175, 11113, 15687}, {6675, 11108, 17527}, {11108, 16845, 6675}, {11112, 15677, 15686}, {15671, 17536, 2}, {15674, 17534, 13747}, {16845, 17554, 11108}, {16865, 17529, 550}, {17552, 17561, 2}, {19526, 37462, 548}


X(50203) = X(2)X(3)∩X(518)X(936)

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

X(50203) lies on these lines: {2, 3}, {57, 45120}, {78, 5045}, {518, 936}, {580, 25878}, {938, 9709}, {965, 4253}, {1210, 4413}, {1445, 5044}, {1617, 19855}, {3361, 30393}, {3646, 21153}, {3689, 12521}, {5248, 38204}, {7373, 20007}, {10306, 11024}, {11496, 38052}, {12511, 38059}, {12864, 44675}, {31419, 42884}, {34772, 35272}

X(50203) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 404, 16293}, {2, 474, 3149}, {2, 6836, 17527}, {2, 6986, 11108}, {2, 17580, 6864}, {2, 37282, 405}, {2, 37423, 17559}, {3, 6846, 1012}, {3, 16408, 17582}, {404, 17558, 3}, {404, 31259, 20835}, {405, 474, 37270}, {405, 37270, 37426}, {443, 37244, 1012}, {17529, 37249, 19520}, {20835, 31259, 405}


X(50204) = X(2)X(3)∩X(518)X(997)

Barycentrics    a^2*(a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5 - a^4*c + b^4*c - 2*a^3*c^2 - 6*a*b^2*c^2 - 8*b^3*c^2 + 2*a^2*c^3 - 8*b^2*c^3 + a*c^4 + b*c^4 - c^5) : :
X(50204) = 2 X[405] + 3 X[16417], 3 X[16417] - 2 X[37270]

X(50204) lies on these lines: {2, 3}, {36, 7308}, {56, 3715}, {518, 997}, {936, 12875}, {993, 6666}, {1259, 5439}, {1260, 15934}, {1376, 5722}, {1470, 5219}, {1617, 5252}, {1698, 37579}, {1708, 3927}, {1737, 9709}, {3295, 5836}, {3428, 31658}, {3624, 26357}, {3679, 33925}, {3698, 11508}, {3753, 10679}, {4413, 8069}, {4423, 23708}, {4511, 7373}, {5123, 41345}, {5251, 37578}, {5259, 9580}, {5396, 17825}, {5398, 17811}, {5687, 12433}, {5720, 10269}, {5780, 37535}, {5806, 10310}, {5886, 25893}, {7742, 10827}, {8582, 11499}, {8583, 11249}, {10200, 15842}, {10680, 19861}, {10957, 19854}, {11374, 25524}, {12410, 19869}, {16202, 19860}, {16203, 17614}, {25941, 44414}, {31435, 35239}

X(50204) = midpoint of X(405) and X(37270)
X(50204) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6878, 6675}, {2, 6883, 11108}, {2, 6947, 17527}, {2, 37249, 3}, {2, 37313, 37306}, {3, 16411, 16417}, {3, 16853, 16293}, {3, 16857, 13615}, {3, 19250, 5020}, {377, 405, 37234}, {404, 5084, 6985}, {405, 474, 377}, {405, 37282, 3}, {474, 37248, 3}, {631, 37302, 3}, {859, 7484, 3}, {1006, 6854, 1012}, {5047, 37301, 37284}, {6827, 6911, 19541}, {6883, 6911, 6827}, {6913, 37271, 17528}, {11108, 16417, 19541}, {11334, 19265, 11284}, {16370, 37309, 3}, {16410, 37244, 3}, {16422, 28383, 3}, {16453, 37246, 3}, {28466, 37306, 17571}, {37034, 37247, 3}, {37284, 37301, 3}, {37306, 37313, 28466}


X(50205) = X(2)X(3)∩X(518)X(1125)

Barycentrics    2*a^4 - 3*a^2*b^2 + b^4 - 8*a^2*b*c - 8*a*b^2*c - 3*a^2*c^2 - 8*a*b*c^2 - 2*b^2*c^2 + c^4 : :
X(50205) = 9 X[2] - X[377], 3 X[2] + X[405], 15 X[2] + X[6872], 7 X[2] + X[31156], 3 X[2] + 5 X[31259], 33 X[2] - X[31295], 5 X[2] - X[44217], 5 X[5] - X[44286], X[377] + 3 X[405], 5 X[377] + 3 X[6872], X[377] - 3 X[8728], 7 X[377] + 9 X[31156], X[377] + 15 X[31259], 11 X[377] - 3 X[31295], 5 X[377] - 9 X[44217], 5 X[405] - X[6872], 7 X[405] - 3 X[31156], X[405] - 5 X[31259], 11 X[405] + X[31295], 5 X[405] + 3 X[44217], 5 X[631] - X[37426], 5 X[632] - X[44222], 5 X[1656] - X[44229], 7 X[3526] + X[37234], X[6872] + 5 X[8728], 7 X[6872] - 15 X[31156], X[6872] - 25 X[31259], 11 X[6872] + 5 X[31295], X[6872] + 3 X[44217], 7 X[8728] + 3 X[31156], X[8728] + 5 X[31259], 11 X[8728] - X[31295], 5 X[8728] - 3 X[44217], 5 X[15694] - X[44284], 3 X[31156] - 35 X[31259], 33 X[31156] + 7 X[31295], 5 X[31156] + 7 X[44217], 55 X[31259] + X[31295], 25 X[31259] + 3 X[44217], 5 X[31295] - 33 X[44217], 7 X[3624] + X[41229], X[10404] - 13 X[34595], X[5302] + 5 X[19862]

X(50205) lies on these lines: {2, 3}, {8, 15935}, {9, 6147}, {10, 12433}, {11, 25542}, {45, 24159}, {58, 17245}, {84, 38122}, {142, 24470}, {386, 17337}, {496, 4423}, {518, 1125}, {942, 45120}, {946, 31658}, {1001, 15172}, {1213, 4251}, {1490, 38108}, {1698, 5722}, {1724, 49743}, {1730, 48924}, {2550, 10386}, {3295, 19855}, {3333, 3624}, {3361, 5219}, {3452, 4999}, {3487, 18230}, {3584, 50038}, {3616, 3940}, {3634, 6690}, {3646, 5763}, {3695, 16817}, {3712, 28611}, {3820, 10198}, {3824, 12572}, {3826, 5248}, {3925, 5259}, {3968, 32157}, {4253, 17398}, {5022, 5747}, {5030, 24937}, {5241, 25645}, {5250, 28212}, {5251, 18990}, {5273, 5708}, {5278, 49718}, {5284, 24390}, {5305, 16589}, {5432, 9581}, {5506, 26725}, {5599, 26399}, {5600, 26423}, {5692, 16137}, {5745, 34753}, {5806, 6684}, {5844, 19860}, {5883, 18253}, {5901, 31837}, {6284, 41859}, {6594, 12864}, {6688, 34466}, {6691, 19878}, {6705, 10156}, {6714, 39580}, {6769, 26446}, {7330, 31657}, {7789, 36812}, {8167, 26363}, {8257, 28628}, {8583, 37700}, {9711, 10197}, {10165, 38158}, {10176, 11281}, {10593, 31245}, {10943, 25893}, {11544, 41872}, {12511, 42356}, {12609, 15254}, {12684, 21151}, {13405, 20790}, {17277, 41014}, {17776, 50042}, {18139, 49716}, {18249, 31794}, {18482, 31730}, {19874, 24542}, {19875, 37723}, {20195, 31424}, {20418, 38216}, {22791, 31435}, {24789, 50067}, {24936, 37680}, {25072, 34937}, {25878, 36742}, {25917, 37737}, {26105, 31493}, {29571, 37594}, {31494, 34625}, {36750, 37659}, {40273, 40998}

X(50205) = midpoint of X(i) and X(j) for these {i,j}: {405, 8728}, {942, 45120}
X(50205) = complement of X(8728)
X(50205) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 21, 17529}, {2, 405, 8728}, {2, 631, 16863}, {2, 5047, 442}, {2, 6675, 140}, {2, 6857, 16408}, {2, 6910, 16862}, {2, 6921, 16864}, {2, 11108, 5}, {2, 11357, 48815}, {2, 13742, 2049}, {2, 15674, 17531}, {2, 16053, 37326}, {2, 16842, 17527}, {2, 16845, 3}, {2, 16859, 4197}, {2, 16912, 6656}, {2, 16918, 33033}, {2, 17526, 16458}, {2, 17527, 3628}, {2, 17534, 17575}, {2, 17536, 4187}, {2, 17547, 17530}, {2, 17552, 11108}, {2, 17554, 4}, {2, 17558, 17582}, {2, 17559, 1656}, {2, 17570, 2476}, {2, 17588, 17674}, {2, 25875, 47510}, {2, 31259, 405}, {2, 33034, 8361}, {2, 33036, 8362}, {2, 37035, 4205}, {2, 37037, 16456}, {2, 37162, 31254}, {3, 1656, 6864}, {3, 6887, 5}, {4, 17554, 16857}, {5, 549, 6985}, {5, 33335, 8226}, {140, 5066, 11277}, {142, 31445, 24470}, {405, 474, 20835}, {405, 44217, 6872}, {443, 16418, 550}, {452, 17528, 3627}, {631, 37434, 3}, {1001, 31419, 15172}, {1006, 6900, 44238}, {1125, 5044, 5719}, {1125, 6666, 5044}, {1656, 6827, 5}, {3624, 7308, 11374}, {3624, 24953, 15325}, {3634, 6690, 47742}, {3925, 5259, 15171}, {4197, 16859, 11113}, {4423, 19854, 496}, {5055, 6866, 5}, {5084, 17582, 6849}, {6857, 16408, 549}, {6900, 44238, 20420}, {6904, 17561, 17571}, {6904, 17571, 8703}, {6910, 16862, 17564}, {6910, 17564, 12108}, {6913, 6989, 37424}, {15674, 17531, 37298}, {16370, 17563, 33923}, {16370, 37462, 17563}, {16458, 17526, 50059}, {16845, 17582, 17558}, {16860, 17528, 452}, {17547, 31254, 37162}, {17558, 17582, 3}, {24934, 44898, 140}, {31254, 37162, 17530}


X(50206) = X(2)X(3)∩X(518)X(1210)

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

X(50206) lies on these lines: {2, 3}, {11, 936}, {40, 25973}, {78, 496}, {392, 31419}, {518, 1210}, {938, 17757}, {3452, 45120}, {3660, 3814}, {3697, 3820}, {3816, 13411}, {3825, 6700}, {3925, 12701}, {5439, 21617}, {5713, 17825}, {5742, 46196}, {7680, 8582}, {10523, 41229}, {19727, 19754}, {19802, 19839}, {25893, 48482}

X(50206) = complement of X(37282)
X(50206) = orthocentroidal-circle-inverse of X(16410)
X(50206) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 16410}, {2, 411, 13747}, {2, 4193, 6831}, {2, 6835, 474}, {2, 6919, 6865}, {2, 6991, 442}, {2, 11344, 140}, {442, 4187, 5084}, {474, 37359, 8727}, {2478, 25962, 6907}, {3142, 37439, 5}, {3814, 9843, 15844}, {4193, 6890, 37359}, {6881, 11108, 47510}, {6922, 8728, 37282}, {6990, 17582, 37363}


X(50207) = X(2)X(3)∩X(518)X(1698)

Barycentrics    a^4 - 3*a^2*b^2 + 2*b^4 - 10*a^2*b*c - 10*a*b^2*c - 3*a^2*c^2 - 10*a*b*c^2 - 4*b^2*c^2 + 2*c^4 : :
X(50207) = 9 X[2] + X[377], 6 X[2] - X[405], 21 X[2] - X[6872], 3 X[2] + 2 X[8728], 11 X[2] - X[31156], 39 X[2] + X[31295], 4 X[2] + X[44217], 4 X[5] + X[37426], 4 X[140] + X[44229], 2 X[377] + 3 X[405], 7 X[377] + 3 X[6872], X[377] - 6 X[8728], 11 X[377] + 9 X[31156], X[377] + 3 X[31259], 13 X[377] - 3 X[31295], 4 X[377] - 9 X[44217], 7 X[405] - 2 X[6872], X[405] + 4 X[8728], 11 X[405] - 6 X[31156], 13 X[405] + 2 X[31295], 2 X[405] + 3 X[44217], 4 X[547] + X[44284], 4 X[3530] + X[44286], 4 X[3628] + X[44222], 11 X[5070] - X[37234], X[6872] + 14 X[8728], 11 X[6872] - 21 X[31156], X[6872] - 7 X[31259], 13 X[6872] + 7 X[31295], 4 X[6872] + 21 X[44217], 22 X[8728] + 3 X[31156], 2 X[8728] + X[31259], 26 X[8728] - X[31295], 8 X[8728] - 3 X[44217], 3 X[17532] + 2 X[20835], 3 X[31156] - 11 X[31259], 39 X[31156] + 11 X[31295], 4 X[31156] + 11 X[44217], 13 X[31259] + X[31295], 4 X[31259] + 3 X[44217], 4 X[31295] - 39 X[44217], 2 X[5302] - 17 X[19872]

X(50207) lies on these lines: {2, 3}, {10, 41711}, {72, 41867}, {518, 1698}, {1001, 41859}, {1714, 17245}, {3305, 3824}, {3337, 5437}, {3624, 5440}, {3634, 4860}, {3826, 5687}, {3841, 4423}, {3911, 3947}, {3927, 27186}, {5043, 46196}, {5275, 5346}, {5302, 19872}, {5438, 34595}, {5550, 31493}, {10479, 17265}, {19862, 31245}, {19877, 31479}, {25525, 45120}, {31246, 31253}, {34501, 45701}

X(50207) = reflection of X(405) in X(31259)
X(50207) = complement of X(31259)
X(50207) = orthocentroidal-circle-inverse of X(17590)
X(50207) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 17590}, {2, 5, 16854}, {2, 442, 16842}, {2, 2476, 16853}, {2, 4187, 16856}, {2, 4193, 16855}, {2, 4197, 11108}, {2, 4202, 16844}, {2, 4208, 17552}, {2, 5141, 17546}, {2, 6856, 17575}, {2, 8728, 405}, {2, 17529, 474}, {2, 17535, 3526}, {2, 17582, 7483}, {2, 17674, 19273}, {2, 31254, 1656}, {2, 33026, 17540}, {2, 33833, 16343}, {2, 37436, 16845}, {2, 37462, 6675}, {4, 17590, 17542}, {377, 17566, 37282}, {405, 8728, 44217}, {442, 16842, 17556}, {1698, 20195, 5439}, {4197, 11108, 17532}, {4208, 17552, 11113}, {6675, 37462, 16371}, {7483, 17529, 17582}, {7483, 17582, 474}, {11108, 20835, 405}, {11112, 16845, 19526}, {11113, 17552, 17545}, {16845, 37436, 11112}, {16862, 19521, 474}


X(50208) = X(2)X(3)∩X(518)X(1737)

Barycentrics    a^5*b^2 - a^4*b^3 - 2*a^3*b^4 + 2*a^2*b^5 + a*b^6 - b^7 + 2*a^5*b*c - a^4*b^2*c - 4*a^3*b^3*c + 2*a*b^5*c + b^6*c + a^5*c^2 - a^4*b*c^2 + 4*a^3*b^2*c^2 + 2*a^2*b^3*c^2 - a*b^4*c^2 + 3*b^5*c^2 - a^4*c^3 - 4*a^3*b*c^3 + 2*a^2*b^2*c^3 - 4*a*b^3*c^3 - 3*b^4*c^3 - 2*a^3*c^4 - a*b^2*c^4 - 3*b^3*c^4 + 2*a^2*c^5 + 2*a*b*c^5 + 3*b^2*c^5 + a*c^6 + b*c^6 - c^7 : :
X(50208) = 4 X[8728] + 3 X[17533]

X(50208) lies on these lines: {2, 3}, {11, 5440}, {12, 5439}, {392, 3925}, {518, 1737}, {997, 11376}, {1125, 10957}, {1329, 17437}, {1387, 4511}, {1898, 41540}, {2886, 23708}, {3753, 25973}, {3814, 3911}, {5437, 7951}, {5438, 7741}, {8068, 31263}, {10200, 26481}, {10827, 25466}, {18254, 41552}, {31435, 41859}

X(50208) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6826, 37249}, {2, 6854, 474}, {2, 6881, 442}, {2, 6911, 13747}, {5, 1012, 8226}, {5, 6907, 6968}, {5, 6958, 6831}, {5, 8728, 377}, {5, 25962, 442}, {442, 17533, 1532}, {4187, 17529, 7483}, {6826, 37249, 11112}, {6829, 6879, 5}, {6837, 6991, 5}, {6882, 6905, 37374}


X(50209) = X(125)X(418)∩X(577)X(31364)

Barycentrics    a^2*(-a^2+b^2+c^2)*((b^2+c^2)*a^2-(b^2-c^2)^2)*((b^2+c^2)*a^14-(5*b^4+6*b^2*c^2+5*c^4)*a^12+(b^2+c^2)*(10*b^4+b^2*c^2+10*c^4)*a^10-(10*b^8+10*c^8+(5*b^4+8*b^2*c^2+5*c^4)*b^2*c^2)*a^8-(b^2-c^2)^4*b^4*c^4+(b^2+c^2)*(5*b^8+5*c^8-(11*b^4-14*b^2*c^2+11*c^4)*b^2*c^2)*a^6-2*(b^4-c^4)*(b^2-c^2)^3*a^2*b^2*c^2-(b^2-c^2)^2*(b^8+c^8-5*(b^4+b^2*c^2+c^4)*b^2*c^2)*a^4) : :
X(50209) = (S^4-SB^2*SC^2)*(2*S^4+(4*R^2*(5*R^2+SA-5*SW)-SA^2+3*SW^2)*S^2+(2*R^2*(3*SA+8*R^2-7*SW)-SA^2+SB*SC+2*SW^2)*(SA^2-SB*SC)) : :

See Kadir Altintas and César Lozada euclid 5132.

X(50209) lies on these lines: {125, 418}, {577, 31364}


X(50210) = REFLECTION OF X(46604) IN X(5)

Barycentrics    a^24-8*(b^2+c^2)*a^22+(29*b^4+46*b^2*c^2+29*c^4)*a^20-2*(b^2+c^2)*(31*b^4+24*b^2*c^2+31*c^4)*a^18+(83*b^8+83*c^8+(133*b^4+153*b^2*c^2+133*c^4)*b^2*c^2)*a^16+(4*b^8+4*c^8+(15*b^4+16*b^2*c^2+15*c^4)*b^2*c^2)*a^12*b^2*c^2-2*(b^2+c^2)*(31*b^8+31*c^8+2*(2*b^4+19*b^2*c^2+2*c^4)*b^2*c^2)*a^14+(b^4-c^4)*(b^2-c^2)*(62*b^8+62*c^8+(11*b^4+67*b^2*c^2+11*c^4)*b^2*c^2)*a^10-(b^2-c^2)^2*(83*b^12+83*c^12-(9*b^8+9*c^8+(7*b^4+8*b^2*c^2+7*c^4)*b^2*c^2)*b^2*c^2)*a^8+2*(b^4-c^4)*(b^2-c^2)*(31*b^12+31*c^12-(83*b^8+83*c^8-(97*b^4-88*b^2*c^2+97*c^4)*b^2*c^2)*b^2*c^2)*a^6-(b^2-c^2)^4*(29*b^12+29*c^12-2*(22*b^8+22*c^8-(5*b^4+11*b^2*c^2+5*c^4)*b^2*c^2)*b^2*c^2)*a^4+(b^6+c^6)*(b^2-c^2)^6*(8*b^4-13*b^2*c^2+8*c^4)*a^2-(b^4-b^2*c^2+c^4)^2*(b^2-c^2)^8 : :

See Kadir Altintas and César Lozada euclid 5132.

X(50210) lies on this line: {5, 46604}

X(50210) = reflection of X(46604) in X(5)


X(50211) = X(17)X(99)∩X(61)X(115)

Barycentrics    2*sqrt(3)*(3*a^6-5*(b^2+c^2)*a^4+(2*b^4-9*b^2*c^2+2*c^4)*a^2+(b^4-c^4)*(b^2-c^2))*S+a^8+4*(b^2+c^2)*a^6-(15*b^4+13*b^2*c^2+15*c^4)*a^4+(b^2+c^2)*(15*b^4-31*b^2*c^2+15*c^4)*a^2-5*(b^2-c^2)^4 : :

See Kadir Altintas and César Lozada euclid 5132.

X(50211) lies on these lines: {13, 38230}, {17, 99}, {61, 115}, {5459, 22511}, {5470, 42062}, {5615, 46054}, {9115, 10611}, {13350, 23005}, {35230, 47861}


X(50212) = X(18)X(99)∩X(62)X(115)

Barycentrics    -2*sqrt(3)*(3*a^6-5*(b^2+c^2)*a^4+(2*b^4-9*b^2*c^2+2*c^4)*a^2+(b^4-c^4)*(b^2-c^2))*S+a^8+4*(b^2+c^2)*a^6-(15*b^4+13*b^2*c^2+15*c^4)*a^4+(b^2+c^2)*(15*b^4-31*b^2*c^2+15*c^4)*a^2-5*(b^2-c^2)^4: :

See Kadir Altintas and César Lozada euclid 5132.

X(50212) lies on these lines: {14, 38230}, {18, 99}, {62, 115}, {5460, 22510}, {5469, 42063}, {5611, 46053}, {9117, 10612}, {13349, 23004}, {35229, 47862}


X(50213) = X(7684)X(32627)∩X(15609)X(37848)

Barycentrics    ((2*a^14-18*(b^2+c^2)*a^12+2*(31*b^4+52*b^2*c^2+31*c^4)*a^10-2*(b^2+c^2)*(55*b^4+36*b^2*c^2+55*c^4)*a^8+2*(55*b^8+55*c^8+(39*b^4+25*b^2*c^2+39*c^4)*b^2*c^2)*a^6-2*(b^2+c^2)*(31*b^8+31*c^8-25*(3*b^4-b^2*c^2+3*c^4)*b^2*c^2)*a^4+2*(b^2-c^2)^2*(9*b^8+9*c^8-(29*b^4+61*b^2*c^2+29*c^4)*b^2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)^3*(-2*b^4+18*b^2*c^2-2*c^4))*S+sqrt(3)*(a^16-6*(b^2+c^2)*a^14+2*(7*b^4+8*b^2*c^2+7*c^4)*a^12-2*(b^2+c^2)*(7*b^4-12*b^2*c^2+7*c^4)*a^10-(79*b^4+89*b^2*c^2+79*c^4)*b^2*c^2*a^8+2*(b^2+c^2)*(7*b^8+7*c^8+(45*b^4-17*b^2*c^2+45*c^4)*b^2*c^2)*a^6-2*(7*b^12+7*c^12+(26*b^8+26*c^8-(31*b^4+13*b^2*c^2+31*c^4)*b^2*c^2)*b^2*c^2)*a^4+(b^4-c^4)*(b^2-c^2)*(6*b^8+6*c^8+(10*b^4-43*b^2*c^2+10*c^4)*b^2*c^2)*a^2-(b^2-c^2)^4*(b^8+c^8+(b^4-8*b^2*c^2+c^4)*b^2*c^2)))*a^2 : :

See Kadir Altintas and César Lozada euclid 5132.

X(50213) lies on these lines: {7684, 32627}, {15609, 37848}


X(50214) = X(7685)X(32628)∩X(15610)X(37850)

Barycentrics    (-(2*a^14-18*(b^2+c^2)*a^12+2*(31*b^4+52*b^2*c^2+31*c^4)*a^10-2*(b^2+c^2)*(55*b^4+36*b^2*c^2+55*c^4)*a^8+2*(55*b^8+55*c^8+(39*b^4+25*b^2*c^2+39*c^4)*b^2*c^2)*a^6-2*(b^2+c^2)*(31*b^8+31*c^8-25*(3*b^4-b^2*c^2+3*c^4)*b^2*c^2)*a^4+2*(b^2-c^2)^2*(9*b^8+9*c^8-(29*b^4+61*b^2*c^2+29*c^4)*b^2*c^2)*a^2+(b^4-c^4)*(b^2-c^2)^3*(-2*b^4+18*b^2*c^2-2*c^4))*S+sqrt(3)*(a^16-6*(b^2+c^2)*a^14+2*(7*b^4+8*b^2*c^2+7*c^4)*a^12-2*(b^2+c^2)*(7*b^4-12*b^2*c^2+7*c^4)*a^10-(79*b^4+89*b^2*c^2+79*c^4)*b^2*c^2*a^8+2*(b^2+c^2)*(7*b^8+7*c^8+(45*b^4-17*b^2*c^2+45*c^4)*b^2*c^2)*a^6-2*(7*b^12+7*c^12+(26*b^8+26*c^8-(31*b^4+13*b^2*c^2+31*c^4)*b^2*c^2)*b^2*c^2)*a^4+(b^4-c^4)*(b^2-c^2)*(6*b^8+6*c^8+(10*b^4-43*b^2*c^2+10*c^4)*b^2*c^2)*a^2-(b^2-c^2)^4*(b^8+c^8+(b^4-8*b^2*c^2+c^4)*b^2*c^2)))*a^2 : :

See Kadir Altintas and César Lozada euclid 5132.

X(50214) lies on these lines: {7685, 32628}, {15610, 37850}


leftri

Points in a [[(b^4 - c^4, c^4 - a^4, a^4 - b^4 ], (b^2-c^2)(a^2-b^2-c^2), (c^2- a^2)(b^2-c^2-a^2), (a^2- b^2)(a^2-b^2-c^2)]] coordinate system: X(50215)-X(50236)

rightri

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

L1 is the line: (b^4 - c^4) α + (c^4 - a^4) β + (a^4 - b^4) γ = 0.

L2 is the line (b^2-c^2)(a^2-b^2-c^2) α + (c^2- a^2)(b^2-c^2-a^2) β + (a^2- b^2)(a^2-b^2-c^2) γ = 0 (Euler line).

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

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

u : v : w = -(a^2 - b^2)((a^2 - c^2)(b^2 - c^2)(a^2 + b^2 + c^2) + (-2 a^4 + b^4 + c^4) x + (2 a^4 - a^2 b^2 - a^2 c^2 - (b^2 - c^2)^2 ) y : : ,

where, as functions of a, b, c, the coordinate x is antisymmetric of degree 4, and y is antisymmetric of degree 4.

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

{-2 (a-b) (a-c) (b-c) (a+b+c), (a-b) (a-c) (b-c) (a+b+c)}, 3578
{-((2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c)), ((a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c)}, 49717
{-2 (a-b) (a-c) (b-c) (a+b+c), 2 (a-b) (a-c) (b-c) (a+b+c)}, 50154
{-((2 (a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c)), (2 (a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c)}, 50155
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c)), 0}, 50157
{-((a-b) (a-c) (b-c) (a+b+c)), 1/2 (a-b) (a-c) (b-c) (a+b+c)}, 49724
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c)), ((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a+b+c))}, 50158
{-((a-b) (a-c) (b-c) (a+b+c)), (a-b) (a-c) (b-c) (a+b+c)}, 50159
{-((a-b) (a-c) (b-c) (a+b+c)), ((a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c)}, 49723
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c)), ((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c)}, 50160
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a+b+c))), 0}, 50161
{-(1/2) (a-b) (a-c) (b-c) (a+b+c), 1/2 (a-b) (a-c) (b-c) (a+b+c)}, 50162
{-(1/2) (a-b) (a-c) (b-c) (a+b+c), ((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a+b+c))}, 49729
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a+b+c))), ((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a+b+c))}, 50163
{0, -((2 (a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c))}, 50165
{0, -((a-b) (a-c) (b-c) (a+b+c))}, 50166
{0, -(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c))}, 49735
{0, -(1/2) (a-b) (a-c) (b-c) (a+b+c)}, 50167
{0, -(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a+b+c)))}, 13745
{0, 0}, 2
{0, 1/2 (a-b) (a-c) (b-c) (a+b+c)}, 50168
{0, ((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a+b+c))}, 50169
{0, (a-b) (a-c) (b-c) (a+b+c)}, 50170
{0, ((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c)}, 50171
{0, (2 (a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c)}, 50172
{1/2 (a-b) (a-c) (b-c) (a+b+c), -(1/2) (a-b) (a-c) (b-c) (a+b+c)}, 50173
{((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a+b+c)), -(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a+b+c)))}, 50174
{(a-b) (a-c) (b-c) (a+b+c), -((a-b) (a-c) (b-c) (a+b+c))}, 50178
{(a-b) (a-c) (b-c) (a+b+c), -(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c))}, 50182
{(a-b) (a-c) (b-c) (a+b+c), -(((a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c))}, 49744
{((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c), -(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c))}, 50179
{(a-b) (a-c) (b-c) (a+b+c), -(1/2) (a-b) (a-c) (b-c) (a+b+c)}, 37631
{((a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c), -(((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a+b+c)))}, 50180
{(a-b) (a-c) (b-c) (a+b+c), 0}, 50181
{2 (a-b) (a-c) (b-c) (a+b+c), -2 (a-b) (a-c) (b-c) (a+b+c)}, 50183
{(2 (a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c), -((2 (a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c))}, 50184
{2 (a-b) (a-c) (b-c) (a+b+c), -((a-b) (a-c) (b-c) (a+b+c))}, 42045
{(2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c), -(((a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c))}, 49749
{(2 (a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c), 0}, 50186
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), (2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)}, 50215
{-((a - b)*(a - c)*(b - c)*(a + b + c)), -1/2*((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)}, 50216
{-((a - b)*(a - c)*(b - c)*(a + b + c)), 0}, 50217
{-((a - b)*(a - c)*(b - c)*(a + b + c)), 2*(a - b)*(a - c)*(b - c)*(a + b + c)}, 50218
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))}, 50219
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), -1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c)}, 50220
{-1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c), -1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c)}, 50221
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), 0}, 50222
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), (a - b)*(a - c)*(b - c)*(a + b + c)}, 50223
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), ((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)}, 50224
{((a - b)*(a - c)*(b - c)*(a + b + c))/2, -1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c)}, 50225
{((a - b)*(a - c)*(b - c)*(a + b + c))/2, -1/2*((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)}, 50226
{((a - b)*(a - c)*(b - c)*(a + b + c))/2, 0}, 50227
{((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(2*(a + b + c)), 0}, 50228
{((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(2*(a + b + c)), ((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(2*(a + b + c))}, 50229
{((a - b)*(a - c)*(b - c)*(a + b + c))/2, ((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)}, 50230
{(a - b)*(a - c)*(b - c)*(a + b + c), -1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c)}, 50231
{((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c), 0}, 50232
{(a - b)*(a - c)*(b - c)*(a + b + c), ((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)}, 50233
{2*(a - b)*(a - c)*(b - c)*(a + b + c), (-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)}, 50234
{(2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c), -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))}, 50235
{2*(a - b)*(a - c)*(b - c)*(a + b + c), ((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)}, 50236


X(50215) = X(2)X(58)∩X(8)X(30)

Barycentrics    4*a^4 + 3*a^3*b - 2*a^2*b^2 - 3*a*b^3 - 2*b^4 + 3*a^3*c - 6*a*b^2*c - 3*b^3*c - 2*a^2*c^2 - 6*a*b*c^2 - 2*b^2*c^2 - 3*a*c^3 - 3*b*c^3 - 2*c^4 : :
X(50215) = 3 X[2] - 4 X[49729], 3 X[49723] - 2 X[49729], 3 X[49723] - X[49744], X[8] - 4 X[49716], 5 X[8] - 8 X[49718], 5 X[3578] - 4 X[49718], 5 X[49716] - 2 X[49718], 3 X[3241] - 4 X[49739], 3 X[49735] - 2 X[49739], 5 X[3616] - 4 X[37631], 5 X[3616] - 8 X[49728], 11 X[5550] - 8 X[49743], 7 X[9780] - 8 X[49730], 7 X[9780] - 4 X[49745], 4 X[13745] - 3 X[38314], 3 X[38314] - 2 X[42045]

X(50215) lies on these lines: {2, 58}, {8, 30}, {69, 31156}, {239, 50176}, {333, 6175}, {376, 5739}, {381, 1150}, {511, 7985}, {519, 50165}, {524, 3241}, {542, 15983}, {549, 5741}, {551, 6536}, {599, 11346}, {1043, 15678}, {2287, 31155}, {2895, 15677}, {3017, 16704}, {3187, 50066}, {3543, 14552}, {3616, 37631}, {3647, 27558}, {3679, 4418}, {3936, 15670}, {4061, 34638}, {4234, 31143}, {4416, 45744}, {4420, 48897}, {4641, 50051}, {4643, 50070}, {4683, 39766}, {4921, 17677}, {5251, 20290}, {5278, 44217}, {5550, 49743}, {7809, 34016}, {9780, 49730}, {13745, 38314}, {13857, 27721}, {15672, 25650}, {15936, 21296}, {16351, 31179}, {16861, 17297}, {17346, 17579}, {17525, 41014}, {17676, 48857}, {17679, 19723}, {18139, 50202}, {19742, 48835}, {23942, 39563}, {36534, 50182}, {49717, 50186}, {49724, 50171}

X(50215) = reflection of X(i) in X(j) for these {i,j}: {2, 49723}, {8, 3578}, {3241, 49735}, {3578, 49716}, {37631, 49728}, {42045, 13745}, {49744, 49729}, {49745, 49730}, {50171, 49724}, {50172, 3679}, {50186, 49717}
X(50215) = anticomplement of X(49744)
X(50215) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13745, 42045, 38314}, {49723, 49744, 49729}, {49729, 49744, 2}


X(50216) = X(10)X(3849)∩X(30)X(40)

Barycentrics    4*a^6 + 8*a^5*b - 5*a^3*b^3 - 6*a^2*b^4 - 7*a*b^5 - 2*b^6 + 8*a^5*c + 2*a^4*b*c - 11*a^3*b^2*c - 11*a^2*b^3*c - 13*a*b^4*c - 7*b^5*c - 11*a^3*b*c^2 - 12*a^2*b^2*c^2 - 8*a*b^3*c^2 - 6*b^4*c^2 - 5*a^3*c^3 - 11*a^2*b*c^3 - 8*a*b^2*c^3 - 2*b^3*c^3 - 6*a^2*c^4 - 13*a*b*c^4 - 6*b^2*c^4 - 7*a*c^5 - 7*b*c^5 - 2*c^6 : :

X(50216) lies on these lines: {10, 3849}, {30, 40}, {385, 17677}, {524, 4655}, {543, 50153}, {754, 50180}, {7812, 37148}, {7840, 35916}, {9939, 16062}, {11359, 42028}, {13745, 16830}, {22329, 37159}, {29584, 50167}


X(50217) = X(2)X(32)∩X(30)X(40)

Barycentrics    2*a^5 + a^4*b - a^3*b^2 - a^2*b^3 - 2*a*b^4 - b^5 + a^4*c - 2*a^3*b*c - 2*a^2*b^2*c - 2*a*b^3*c - 2*b^4*c - a^3*c^2 - 2*a^2*b*c^2 - 2*a*b^2*c^2 - b^3*c^2 - a^2*c^3 - 2*a*b*c^3 - b^2*c^3 - 2*a*c^4 - 2*b*c^4 - c^5 : :
X(50217) = 2 X[49716] + X[50175]

X(50217) lies on these lines: {2, 32}, {30, 40}, {524, 16834}, {538, 3578}, {543, 50154}, {1654, 24271}, {3849, 50162}, {4045, 19742}, {5278, 7761}, {5739, 24296}, {7848, 18139}, {11287, 19723}, {11355, 48839}, {13745, 48854}, {17251, 50060}, {40891, 50183}, {42045, 50173}, {48809, 49729}, {49716, 50175}, {49730, 50168}

X(50217) = midpoint of X(3578) and X(50166)
X(50217) = reflection of X(i) in X(j) for these {i,j}: {42045, 50173}, {50159, 49724}, {50168, 49730}, {50170, 50162}, {50178, 50167}, {50181, 2}, {50182, 13745}


X(50218) = X(2)X(99)∩X(30)X(40)

Barycentrics    2*a^5 + 3*a^4*b - a^3*b^2 - a^2*b^3 - b^5 + 3*a^4*c + 2*a^3*b*c + 2*a*b^3*c - a^3*c^2 + 6*a*b^2*c^2 + 5*b^3*c^2 - a^2*c^3 + 2*a*b*c^3 + 5*b^2*c^3 - c^5 : :
X(50218) = 2 X[49724] - 3 X[50159], X[42045] - 3 X[50170], 2 X[42045] - 3 X[50181]

X(50218) lies on these lines: {2, 99}, {30, 40}, {524, 3729}, {538, 17389}, {540, 50156}, {754, 50154}, {3578, 3849}, {11159, 19723}, {29597, 50168}, {39586, 50169}, {49735, 50164}, {50162, 50166}

X(50218) = reflection of X(i) in X(j) for these {i,j}: {49735, 50164}, {50166, 50162}, {50175, 50169}, {50178, 50168}, {50181, 50170}


X(50219) = X(2)X(187)∩X(10)X(30)

Barycentrics    4*a^5 + 2*a^4*b - 3*a^3*b^2 - 3*a^2*b^3 - 4*a*b^4 - 2*b^5 + 2*a^4*c - 4*a^3*b*c - 5*a^2*b^2*c - 4*a*b^3*c - 4*b^4*c - 3*a^3*c^2 - 5*a^2*b*c^2 - 2*a*b^2*c^2 - 3*a^2*c^3 - 4*a*b*c^3 - 4*a*c^4 - 4*b*c^4 - 2*c^5 : :
X(50219) = 4 X[49730] - 3 X[50162], X[3578] + 3 X[50166], X[37631] - 3 X[50167], 2 X[37631] - 3 X[50173]

X(50219) lies on these lines: {2, 187}, {10, 30}, {524, 3663}, {538, 3578}, {543, 49724}, {599, 4483}, {754, 37631}, {4393, 50178}, {4660, 11645}, {17397, 50181}

X(50219) = reflection of X(i) in X(j) for these {i,j}: {50164, 49729}, {50173, 50167}


X(50220) = X(10)X(30)∩X(405)X(7865)

Barycentrics    4*a^6 + 2*a^5*b - a^4*b^2 - 4*a^3*b^3 - 7*a^2*b^4 - 4*a*b^5 - 2*b^6 + 2*a^5*c - 4*a^4*b*c - 10*a^3*b^2*c - 10*a^2*b^3*c - 10*a*b^4*c - 4*b^5*c - a^4*c^2 - 10*a^3*b*c^2 - 12*a^2*b^2*c^2 - 10*a*b^3*c^2 - 4*b^4*c^2 - 4*a^3*c^3 - 10*a^2*b*c^3 - 10*a*b^2*c^3 - 4*b^3*c^3 - 7*a^2*c^4 - 10*a*b*c^4 - 4*b^2*c^4 - 4*a*c^5 - 4*b*c^5 - 2*c^6 : :
X(50220) = 4 X[49728] - X[50164]

X(50220) lies on these lines: {10, 30}, {405, 7865}, {538, 49723}, {540, 50173}, {754, 13745}, {1008, 14537}, {1009, 40344}, {4195, 11057}, {7809, 19312}, {7880, 13723}, {16816, 50175}, {29646, 49744}, {41140, 50167}, {49716, 50017}

X(50220) = reflection of X(50162) in X(49729)


X(50221) = X(2)X(187)∩X(30)X(48853)

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

X(50221) lies on these lines: {2, 187}, {30, 48853}, {524, 49465}, {538, 49735}, {754, 13745}, {7775, 16351}, {7843, 16342}, {7849, 16931}, {7873, 16927}, {50160, 50165}

X(50221) = midpoint of X(i) and X(j) for these {i,j}: {49735, 50157}, {50160, 50165}
X(50221) = reflection of X(i) in X(j) for these {i,j}: {50163, 50161}, {50174, 13745}


X(50222) = X(2)X(32)∩X(10)X(30)

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

X(50222) lies on these lines: {2, 32}, {10, 30}, {239, 3578}, {524, 17382}, {538, 42051}, {542, 32115}, {543, 50159}, {3849, 50168}, {4045, 5278}, {5737, 36731}, {7761, 19732}, {9546, 17330}, {16830, 50182}, {17023, 37631}, {24275, 26044}, {29633, 49744}, {49476, 49739}

X(50222) = midpoint of X(i) and X(j) for these {i,j}: {3578, 50178}, {49724, 50167}, {50159, 50166}
X(50222) = reflection of X(50162) in X(49730)
X(50222) = complement of X(50181)


X(50223) = X(2)X(99)∩X(10)X(30)

Barycentrics    2*a^5 + 4*a^4*b + a*b^4 - b^5 + 4*a^4*c + 4*a^3*b*c + 2*a^2*b^2*c + 4*a*b^3*c + b^4*c + 2*a^2*b*c^2 + 8*a*b^2*c^2 + 6*b^3*c^2 + 4*a*b*c^3 + 6*b^2*c^3 + a*c^4 + b*c^4 - c^5 : :
X(50223) = 2 X[49730] - 3 X[50162], X[37631] - 3 X[50168], X[3578] - 3 X[50159], X[3578] + 3 X[50170]

X(50223) lies on these lines: {2, 99}, {10, 30}, {524, 2321}, {538, 3175}, {542, 3923}, {754, 3578}, {3849, 49724}, {6542, 50154}, {16826, 50178}, {49744, 50156}

X(50223) = midpoint of X(i) and X(j) for these {i,j}: {49744, 50156}, {50154, 50181}, {50159, 50170}


X(50224) = X(10)X(30)∩X(538)X(13745)

Barycentrics    2*a^6 - 2*a^5*b - 2*a^4*b^2 - 2*a^3*b^3 - 5*a^2*b^4 - 2*a*b^5 - b^6 - 2*a^5*c - 8*a^4*b*c - 8*a^3*b^2*c - 8*a^2*b^3*c - 8*a*b^4*c - 2*b^5*c - 2*a^4*c^2 - 8*a^3*b*c^2 - 12*a^2*b^2*c^2 - 14*a*b^3*c^2 - 5*b^4*c^2 - 2*a^3*c^3 - 8*a^2*b*c^3 - 14*a*b^2*c^3 - 8*b^3*c^3 - 5*a^2*c^4 - 8*a*b*c^4 - 5*b^2*c^4 - 2*a*c^5 - 2*b*c^5 - c^6 : :
X(50224) = 2 X[49728] + X[50164]

X(50224) lies on these lines: {10, 30}, {538, 13745}, {754, 49717}, {1008, 7753}, {3578, 50182}, {4195, 7811}, {5306, 37044}, {5737, 36721}, {7739, 13725}, {7799, 19312}, {11112, 48860}, {13736, 32836}, {16815, 50175}, {16823, 50178}, {29596, 49745}, {29637, 49744}, {37038, 48864}, {49466, 49739}, {49735, 50159}

X(50224) = midpoint of X(i) and X(j) for these {i,j}: {3578, 50182}, {49735, 50159}


X(50225) = X(1)X(538)∩X(30)X(551)

Barycentrics    6*a^5*b + 5*a^4*b^2 + 4*a^3*b^3 + 5*a^2*b^4 + 6*a^5*c + 12*a^4*b*c + 10*a^3*b^2*c + 10*a^2*b^3*c + 6*a*b^4*c + 5*a^4*c^2 + 10*a^3*b*c^2 + 12*a^2*b^2*c^2 + 10*a*b^3*c^2 + 2*b^4*c^2 + 4*a^3*c^3 + 10*a^2*b*c^3 + 10*a*b^2*c^3 + 4*b^3*c^3 + 5*a^2*c^4 + 6*a*b*c^4 + 2*b^2*c^4 : :
X(50225) = 5 X[1] + X[50156], 2 X[1] + X[50164], 2 X[50156] - 5 X[50164], 7 X[3622] - X[50175], 2 X[3635] + X[50153], 4 X[3636] - X[50177], 3 X[38314] - X[50178]

X(50225) lies on these lines: {1, 538}, {2, 40984}, {30, 551}, {519, 50162}, {754, 13745}, {1008, 9466}, {1009, 44562}, {1982, 14581}, {3241, 50159}, {3622, 50175}, {3635, 50153}, {3636, 50177}, {4195, 7757}, {19868, 50158}, {38314, 50178}, {49735, 50181}, {49739, 50168}

X(50225) = midpoint of X(i) and X(j) for these {i,j}: {2, 50182}, {3241, 50159}, {49735, 50181}, {49739, 50168}
X(50225) = reflection of X(50173) in X(551)


X(50226) = X(2)X(58)∩X(30)X(551)

Barycentrics    2*a^4 + 4*a^3*b + 4*a^2*b^2 + a*b^3 - b^4 + 4*a^3*c + 10*a^2*b*c + 7*a*b^2*c + b^3*c + 4*a^2*c^2 + 7*a*b*c^2 + 4*b^2*c^2 + a*c^3 + b*c^3 - c^4 : :
X(50226) = 2 X[49723] - 3 X[49729], X[49723] + 3 X[49744], X[49729] + 2 X[49744], 5 X[10] - 2 X[49718], X[10] + 2 X[49743], X[49718] + 5 X[49743], 2 X[1125] + X[49745], X[3244] + 2 X[49734], X[3578] - 3 X[19875], 5 X[3616] - X[50165], 4 X[3634] - X[49716], 2 X[3812] + X[49557], X[5836] + 2 X[10108], 5 X[19862] - 2 X[49728], 3 X[25055] - X[49735], 3 X[38314] + X[50172]

X(50226) lies on these lines: {1, 4442}, {2, 58}, {10, 524}, {30, 551}, {86, 316}, {500, 30143}, {511, 5883}, {519, 37631}, {542, 15973}, {543, 50177}, {597, 8728}, {599, 2049}, {754, 50180}, {758, 23812}, {1125, 4892}, {1992, 37153}, {2475, 28619}, {2796, 3743}, {2901, 29574}, {3017, 42028}, {3244, 49734}, {3578, 19875}, {3616, 50165}, {3634, 49716}, {3679, 41812}, {3812, 49557}, {3828, 49724}, {4653, 26109}, {4658, 26051}, {5295, 50125}, {5836, 10108}, {6173, 43169}, {6175, 42025}, {7801, 33745}, {7810, 37148}, {7812, 16062}, {10022, 50047}, {13857, 27687}, {14005, 31143}, {14007, 31144}, {15360, 37158}, {16454, 31179}, {17378, 33297}, {17392, 37150}, {17679, 19684}, {17758, 49738}, {19701, 48835}, {19722, 44217}, {19862, 49728}, {23814, 48050}, {25055, 49735}, {26117, 28620}, {29181, 38054}, {29597, 50170}, {31173, 37159}, {38314, 50172}, {48822, 50181}

X(50226) = midpoint of X(i) and X(j) for these {i,j}: {1, 50171}, {2, 49744}, {3679, 42045}, {13745, 49745}, {37631, 50169}, {50170, 50176}
X(50226) = reflection of X(i) in X(j) for these {i,j}: {13745, 1125}, {49724, 3828}, {49729, 2}
X(50226) = complement of X(49723)
X(50226) = {X(25526),X(26131)}-harmonic conjugate of X(3454)


X(50227) = X(2)X(32)∩X(30)X(551)

Barycentrics    2*a^5 + 4*a^4*b + 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5 + 4*a^4*c + 4*a^3*b*c + 4*a^2*b^2*c + 4*a*b^3*c + b^4*c + 2*a^3*c^2 + 4*a^2*b*c^2 + 4*a*b^2*c^2 + 2*b^3*c^2 + 2*a^2*c^3 + 4*a*b*c^3 + 2*b^2*c^3 + a*c^4 + b*c^4 - c^5 : :
X(50227) = 2 X[49743] + X[50164]

X(50227) lies on these lines: {2, 32}, {30, 551}, {524, 17359}, {538, 3175}, {543, 29580}, {2795, 23812}, {3849, 50167}, {4045, 19684}, {7761, 19701}, {14581, 25986}, {17310, 42045}, {17778, 24275}, {24271, 37635}, {49743, 50164}, {50171, 50182}

X(50227) = midpoint of X(i) and X(j) for these {i,j}: {2, 50181}, {37631, 50168}, {42045, 50159}, {50170, 50178}, {50171, 50182}


X(50228) = X(2)X(32)∩X(10)X(524)

Barycentrics    2*a^4 + 2*a^3*b + 4*a^2*b^2 + 2*a*b^3 - b^4 + 2*a^3*c + 8*a^2*b*c + 8*a*b^2*c + 2*b^3*c + 4*a^2*c^2 + 8*a*b*c^2 + 4*b^2*c^2 + 2*a*c^3 + 2*b*c^3 - c^4 : :
X(50228) = 3 X[2] + X[50186], 2 X[50157] - 3 X[50161], 3 X[50161] + 2 X[50186]

X(50228) lies on these lines: {2, 32}, {10, 524}, {30, 50174}, {538, 50169}, {540, 50158}, {543, 16830}, {1125, 25383}, {2049, 17251}, {3849, 13745}, {7759, 16458}, {7764, 16454}, {7768, 16928}, {7794, 16926}, {9766, 19332}, {16351, 47101}, {19856, 49723}, {37631, 50095}, {49717, 49744}

X(50228) = midpoint of X(i) and X(j) for these {i,j}: {49717, 49744}, {50157, 50186}, {50171, 50179}
X(50228) = reflection of X(50161) in X(2)
X(50228) = complement of X(50157)
X(50228) = {X(2),X(50186)}-harmonic conjugate of X(50157)


X(50229) = X(2)X(187)∩X(30)X(50174)

Barycentrics    4*a^4 + 2*a^3*b + 3*a^2*b^2 + 2*a*b^3 - 2*b^4 + 2*a^3*c + 8*a^2*b*c + 8*a*b^2*c + 2*b^3*c + 3*a^2*c^2 + 8*a*b*c^2 + 6*b^2*c^2 + 2*a*c^3 + 2*b*c^3 - 2*c^4 : : a

X(50229) lies on these lines: {2, 187}, {30, 50174}, {524, 4669}, {538, 50171}, {754, 50163}, {4363, 17730}, {7775, 19290}, {7843, 16454}, {7849, 16930}, {7873, 16926}, {50160, 50186}, {50172, 50179}

X(50229) = midpoint of X(i) and X(j) for these {i,j}: {50160, 50186}, {50172, 50179}
X(50229) = reflection of X(50163) in X(50169)


X(50230) = X(1)X(543)∩X(30)X(551)

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

X(50230) lies on these lines: {1, 543}, {30, 551}, {524, 49484}, {538, 50122}, {754, 49717}, {1008, 7810}, {2482, 11104}, {3849, 13745}, {4195, 7812}, {5461, 37049}, {16823, 50171}, {19758, 34504}, {29584, 50170}, {50095, 50168}

X(50230) = midpoint of X(50170) and X(50182)

X(50231) = X(1)X(30)∩X(2)X(19761)

Barycentrics    2*a^6 + 10*a^5*b + 7*a^4*b^2 + 4*a^3*b^3 + 4*a^2*b^4 - 2*a*b^5 - b^6 + 10*a^5*c + 16*a^4*b*c + 10*a^3*b^2*c + 10*a^2*b^3*c + 4*a*b^4*c - 2*b^5*c + 7*a^4*c^2 + 10*a^3*b*c^2 + 12*a^2*b^2*c^2 + 10*a*b^3*c^2 + b^4*c^2 + 4*a^3*c^3 + 10*a^2*b*c^3 + 10*a*b^2*c^3 + 4*b^3*c^3 + 4*a^2*c^4 + 4*a*b*c^4 + b^2*c^4 - 2*a*c^5 - 2*b*c^5 - c^6 : :
X(50231) = 3 X[38314] - X[50166]

X(50231) lies on these lines: {1, 30}, {2, 19761}, {376, 19758}, {519, 50168}, {524, 48805}, {538, 50122}, {551, 50167}, {754, 13745}, {1008, 37671}, {1009, 9300}, {3241, 50170}, {4195, 7837}, {4307, 15936}, {7865, 13728}, {19868, 49729}, {38314, 50166}, {49763, 50164}

X(50231) = midpoint of X(i) and X(j) for these {i,j}: {3241, 50170}, {50181, 50182}
X(50231) = reflection of X(50167) in X(551)

X(50232) = X(2)X(32)∩X(30)X(48854)

Barycentrics    2*a^4 + a^3*b + 2*a^2*b^2 + a*b^3 - b^4 + a^3*c + 4*a^2*b*c + 4*a*b^2*c + b^3*c + 2*a^2*c^2 + 4*a*b*c^2 + 2*b^2*c^2 + a*c^3 + b*c^3 - c^4 : :
X(50232) = 3 X[50157] - 4 X[50161], X[50157] + 2 X[50186], 2 X[50161] + 3 X[50186]

X(50232) lies on these lines: {2, 32}, {30, 48854}, {86, 25468}, {524, 3416}, {538, 50171}, {540, 48809}, {543, 5992}, {3849, 49735}, {7759, 16454}, {7764, 19284}, {7768, 16926}, {7794, 16930}, {9766, 19290}, {16834, 37631}, {25683, 37675}, {29617, 42045}, {49723, 50158}

X(50232) = midpoint of X(i) and X(j) for these {i,j}: {2, 50186}, {50172, 50184}
X(50232) = reflection of X(i) in X(j) for these {i,j}: {49723, 50158}, {49735, 50174}, {50157, 2}, {50160, 50169}
X(50232) = anticomplement of X(50161)


X(50233) = X(1)X(30)∩X(381)X(19761)

Barycentrics    2*a^6 + 7*a^5*b + 4*a^4*b^2 + a^3*b^3 + a^2*b^4 - 2*a*b^5 - b^6 + 7*a^5*c + 10*a^4*b*c + 4*a^3*b^2*c + 4*a^2*b^3*c + a*b^4*c - 2*b^5*c + 4*a^4*c^2 + 4*a^3*b*c^2 + 6*a^2*b^2*c^2 + 7*a*b^3*c^2 + b^4*c^2 + a^3*c^3 + 4*a^2*b*c^3 + 7*a*b^2*c^3 + 4*b^3*c^3 + a^2*c^4 + a*b*c^4 + b^2*c^4 - 2*a*c^5 - 2*b*c^5 - c^6 : :
X(50233) = 3 X[25055] - 2 X[50167]

X(50233) lies on these lines: {1, 30}, {381, 19761}, {519, 50170}, {524, 50126}, {551, 50166}, {754, 49717}, {1008, 7811}, {1009, 7753}, {3534, 19758}, {3679, 50168}, {7799, 11104}, {25055, 50167}

X(50233) = reflection of X(i) in X(j) for these {i,j}: {3679, 50168}, {49744, 50181}, {50166, 551}, {50176, 37631}


X(50234) = X(2)X(58)∩X(8)X(524)

Barycentrics    4*a^4 + 5*a^3*b + 2*a^2*b^2 - a*b^3 - 2*b^4 + 5*a^3*c + 8*a^2*b*c + 2*a*b^2*c - b^3*c + 2*a^2*c^2 + 2*a*b*c^2 + 2*b^2*c^2 - a*c^3 - b*c^3 - 2*c^4 : :
X(50234) = 5 X[2] - 4 X[49729], 5 X[49723] - 6 X[49729], X[49723] - 3 X[49744], 2 X[49729] - 5 X[49744], 5 X[8] - 8 X[49734], X[8] - 4 X[49745], 2 X[49734] - 5 X[49745], 4 X[49734] - 5 X[50171], 5 X[3616] - 4 X[13745], 5 X[3616] - 8 X[49743], X[3869] - 4 X[49557], 5 X[3890] - 8 X[10108], 11 X[5550] - 8 X[49728], 7 X[9780] - 4 X[49716], 4 X[37631] - 3 X[38314], 3 X[38314] - 2 X[49735]

X(50234) lies on these lines: {1, 17491}, {2, 58}, {3, 31179}, {6, 17679}, {8, 524}, {30, 944}, {81, 17677}, {377, 1992}, {519, 17164}, {542, 15971}, {597, 4202}, {599, 964}, {942, 50003}, {1010, 31143}, {1125, 31029}, {2292, 28558}, {3578, 50169}, {3616, 13745}, {3849, 50175}, {3869, 49557}, {3890, 10108}, {4795, 50046}, {4933, 24850}, {4968, 28538}, {5300, 47359}, {5550, 49728}, {6175, 41629}, {9780, 49716}, {11114, 17139}, {11359, 19738}, {13857, 27686}, {14005, 31144}, {14020, 17392}, {16474, 21282}, {19717, 48835}, {19743, 48843}, {29584, 50176}, {33097, 39766}, {37631, 38314}

X(50234) = reflection of X(i) in X(j) for these {i,j}: {2, 49744}, {8, 50171}, {3241, 42045}, {3578, 50169}, {13745, 49743}, {49735, 37631}, {50165, 1}, {50171, 49745}
X(50234) = anticomplement of X(49723)
X(50234) = {X(37631),X(49735)}-harmonic conjugate of X(38314)


X(50235) = X(1)X(524)∩X(2)X(2271)

Barycentrics    2*a^4 - 6*a^3*b - 5*a^2*b^2 - b^4 - 6*a^3*c - 12*a^2*b*c - 6*a*b^2*c - 5*a^2*c^2 - 6*a*b*c^2 - 2*b^2*c^2 - c^4 : :

X(50235) lies on these lines: {1, 524}, {2, 2271}, {30, 48830}, {538, 49739}, {597, 16783}, {754, 37631}, {3849, 49745}, {3970, 49737}, {5718, 7775}, {6625, 8597}, {7833, 17379}, {8359, 24512}, {8370, 37632}, {8598, 17103}, {19765, 34511}, {20132, 34604}, {26626, 50186}, {29573, 49730}, {29574, 49724}, {34506, 37634}, {50169, 50180}

X(50235) = reflection of X(i) in X(j) for these {i,j}: {49724, 50161}, {50169, 50180}, {50185, 49749}


X(50236) = X(1)X(3849)∩X(30)X(944)

Barycentrics    4*a^6 + 11*a^5*b + 6*a^4*b^2 + a^3*b^3 - 4*a*b^5 - 2*b^6 + 11*a^5*c + 14*a^4*b*c + 4*a^3*b^2*c + 4*a^2*b^3*c - a*b^4*c - 4*b^5*c + 6*a^4*c^2 + 4*a^3*b*c^2 + 6*a^2*b^2*c^2 + 7*a*b^3*c^2 + a^3*c^3 + 4*a^2*b*c^3 + 7*a*b^2*c^3 + 4*b^3*c^3 - a*b*c^4 - 4*a*c^5 - 4*b*c^5 - 2*c^6 : :

X(50236) lies on these lines: {1, 3849}, {30, 944}, {524, 5695}, {754, 49717}, {1008, 9939}, {1009, 7812}, {7840, 11104}, {13745, 50186}, {22329, 37049}, {31179, 49129}, {48822, 50181}


leftri

Points on the Euler line: X(50237)-X(50244)

rightri

As in the preamble just before X(50199), in the plane of a triangle ABC, let

P = point on Nagel line;
D = point not on Nagel line or Euler line;
U = point on Nagel line, other than U and G;
L = line through U parallel to PD;
U′ = L^(Euler line).

For centers X(50237)-X(50244), we take P = X(1) and D = X(6). The appearance of (h,k), n in the following list means that if if U = h*a + k*(b+c) : : , then U' = X(n).

(1,-2), 44217
(1,-1), 377
(1,0), 405
(1,1) ,2
(1,2), 50207
(2,-1), 30
(2,1), 50205
(3,-1), 6872
(3,1), 31259
(4,1), 50202
(5,-3) ,31295
(5,-1), 31156
(1,-3), 50237)
(2,-3), 50238)
(3,-2), 50239
(4,-3), 50240)
(4,-1), 50241
(5,-2), 50242
(6,-1), 50243
(7, -3), 50244


X(50237) = X(2)X(3)∩X(518)X(3617)

Barycentrics    a^4 + 2*a^2*b^2 - 3*b^4 + 10*a^2*b*c + 10*a*b^2*c + 2*a^2*c^2 + 10*a*b*c^2 + 6*b^2*c^2 - 3*c^4 : :
X(50237) = 3 X[2] + 2 X[377], 9 X[2] - 4 X[405], 6 X[2] - X[6872], 3 X[2] - 8 X[8728], 7 X[2] - 2 X[31156], 9 X[2] + X[31295], X[2] + 4 X[44217], 13 X[2] - 8 X[50202], 21 X[2] - 16 X[50205], 3 X[2] - 4 X[50207], X[4] + 4 X[44222], X[20] + 4 X[44229], 3 X[377] + 2 X[405], 4 X[377] + X[6872], X[377] + 4 X[8728], 7 X[377] + 3 X[31156], 6 X[377] - X[31295], X[377] - 6 X[44217], 13 X[377] + 12 X[50202], 7 X[377] + 8 X[50205], X[377] + 2 X[50207], 8 X[405] - 3 X[6872], X[405] - 6 X[8728], 14 X[405] - 9 X[31156], 2 X[405] - 3 X[31259], 4 X[405] + X[31295], X[405] + 9 X[44217], 13 X[405] - 18 X[50202], 7 X[405] - 12 X[50205], X[405] - 3 X[50207], X[2475] + 4 X[44256], 7 X[3090] - 2 X[37234], X[3146] + 4 X[37426], X[3529] + 4 X[44286], X[3543] + 4 X[44284], X[6872] - 16 X[8728], 7 X[6872] - 12 X[31156], X[6872] - 4 X[31259], 3 X[6872] + 2 X[31295], X[6872] + 24 X[44217], 13 X[6872] - 48 X[50202], 7 X[6872] - 32 X[50205], X[6872] - 8 X[50207], 28 X[8728] - 3 X[31156], 4 X[8728] - X[31259], 24 X[8728] + X[31295], 2 X[8728] + 3 X[44217], 13 X[8728] - 3 X[50202], 7 X[8728] - 2 X[50205], 3 X[31156] - 7 X[31259], 18 X[31156] + 7 X[31295], X[31156] + 14 X[44217], 13 X[31156] - 28 X[50202], 3 X[31156] - 8 X[50205], 3 X[31156] - 14 X[50207], 6 X[31259] + X[31295], X[31259] + 6 X[44217], 13 X[31259] - 12 X[50202], 7 X[31259] - 8 X[50205], X[31295] - 36 X[44217], 13 X[31295] + 72 X[50202], 7 X[31295] + 48 X[50205], X[31295] + 12 X[50207], 14 X[36003] - 9 X[36004], 13 X[44217] + 2 X[50202], 21 X[44217] + 4 X[50205], 3 X[44217] + X[50207], 21 X[50202] - 26 X[50205], 6 X[50202] - 13 X[50207], 4 X[50205] - 7 X[50207], 4 X[10404] + 11 X[46933], 7 X[9780] - 2 X[41229], 8 X[5302] - 23 X[46931]

X(50237) lies on these lines: {2, 3}, {8, 27186}, {142, 12649}, {145, 28629}, {518, 3617}, {1788, 5261}, {2550, 10587}, {2886, 10586}, {3085, 26060}, {3218, 9780}, {3436, 3826}, {3621, 40587}, {3634, 4652}, {3841, 10527}, {3925, 12513}, {4413, 10585}, {5178, 38053}, {5249, 11523}, {5250, 28232}, {5258, 20076}, {5302, 8165}, {5550, 31418}, {5716, 26724}, {9342, 10588}, {9578, 30379}, {10528, 25466}, {10529, 33108}, {10590, 19877}, {10599, 11231}, {11236, 34501}, {19860, 28236}, {24645, 24982}, {24987, 38052}, {33130, 36578}, {37723, 38093}

X(50237) = midpoint of X(377) and X(31259)
X(50237) = reflection of X(i) in X(j) for these {i,j}: {31259, 50207}, {50207, 8728}
X(50237) = anticomplement of X(31259)
X(50237) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 377, 6872}, {2, 3146, 16859}, {2, 3522, 15674}, {2, 5177, 5187}, {2, 31295, 405}, {2, 37161, 5046}, {2, 37256, 17558}, {2, 37435, 16865}, {3, 6993, 6870}, {377, 405, 31295}, {377, 8728, 2}, {377, 20835, 37435}, {405, 31295, 6872}, {405, 36003, 4189}, {442, 16408, 6933}, {442, 37462, 2}, {443, 4197, 2}, {631, 31254, 2}, {2476, 17582, 2}, {2478, 17529, 2}, {3090, 17535, 2}, {4202, 37153, 2}, {4208, 37436, 2}, {5177, 5187, 6871}, {6854, 37438, 6838}, {6856, 17531, 2}, {6881, 6897, 6837}, {6901, 6989, 20}, {6931, 16862, 2}, {6933, 16408, 2}, {6933, 37462, 16408}, {8728, 44217, 377}, {17528, 17529, 2478}, {31259, 50207, 2}, {33026, 33840, 2}


X(50238) = X(2)X(3)∩X(518)X(3626)

Barycentrics    2*a^4 + a^2*b^2 - 3*b^4 + 8*a^2*b*c + 8*a*b^2*c + a^2*c^2 + 8*a*b*c^2 + 6*b^2*c^2 - 3*c^4 : :
X(50238) = 3 X[2] + 5 X[377], 9 X[2] - 5 X[405], 21 X[2] - 5 X[6872], 3 X[2] - 5 X[8728], 13 X[2] - 5 X[31156], 33 X[2] - 25 X[31259], 27 X[2] + 5 X[31295], X[2] - 5 X[44217], 7 X[2] - 5 X[50202], 6 X[2] - 5 X[50205], 21 X[2] - 25 X[50207], 3 X[377] + X[405], 7 X[377] + X[6872], 13 X[377] + 3 X[31156], 11 X[377] + 5 X[31259], 9 X[377] - X[31295], X[377] + 3 X[44217], 7 X[377] + 3 X[50202], 2 X[377] + X[50205], 7 X[377] + 5 X[50207], X[382] - 5 X[44229], 7 X[405] - 3 X[6872], X[405] - 3 X[8728], 13 X[405] - 9 X[31156], 11 X[405] - 15 X[31259], 3 X[405] + X[31295], X[405] - 9 X[44217], 7 X[405] - 9 X[50202], 2 X[405] - 3 X[50205], 7 X[405] - 15 X[50207], X[550] - 5 X[44222], X[3529] - 5 X[37426], 13 X[5079] - 5 X[37234], X[6872] - 7 X[8728], 13 X[6872] - 21 X[31156], 11 X[6872] - 35 X[31259], 9 X[6872] + 7 X[31295], X[6872] - 21 X[44217], X[6872] - 3 X[50202], 2 X[6872] - 7 X[50205], X[6872] - 5 X[50207], 13 X[8728] - 3 X[31156], 11 X[8728] - 5 X[31259], 9 X[8728] + X[31295], X[8728] - 3 X[44217], 7 X[8728] - 3 X[50202], 7 X[8728] - 5 X[50207], X[15681] - 5 X[44284], 33 X[31156] - 65 X[31259], 27 X[31156] + 13 X[31295], X[31156] - 13 X[44217], 7 X[31156] - 13 X[50202], 6 X[31156] - 13 X[50205], 21 X[31156] - 65 X[50207], 45 X[31259] + 11 X[31295], 5 X[31259] - 33 X[44217], 35 X[31259] - 33 X[50202], 10 X[31259] - 11 X[50205], 7 X[31259] - 11 X[50207], X[31295] + 27 X[44217], 7 X[31295] + 27 X[50202], 2 X[31295] + 9 X[50205], 7 X[31295] + 45 X[50207], 7 X[44217] - X[50202], 6 X[44217] - X[50205], 21 X[44217] - 5 X[50207], 6 X[50202] - 7 X[50205], 3 X[50202] - 5 X[50207], 7 X[50205] - 10 X[50207]

X(50238) lies on these lines: {2, 3}, {10, 24470}, {142, 12433}, {214, 15808}, {355, 31657}, {518, 3626}, {1125, 31795}, {3339, 9578}, {3632, 11529}, {3636, 40270}, {3753, 24475}, {3822, 47742}, {3824, 5719}, {3925, 5258}, {3982, 15556}, {4413, 10592}, {5250, 28216}, {5692, 11544}, {5790, 11024}, {5817, 48664}, {6147, 11523}, {7354, 41859}, {8583, 38034}, {8715, 25466}, {9654, 26040}, {9655, 19855}, {10175, 34862}, {12436, 34753}, {12513, 31419}, {13369, 18357}, {15174, 41862}, {17757, 26060}, {19860, 28224}, {19925, 31805}, {24467, 38042}, {31494, 34610}, {31673, 38204}

X(50238) = midpoint of X(377) and X(8728)
X(50238) = reflection of X(50205) in X(8728)
X(50238) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3529, 16866}, {2, 17563, 3530}, {2, 17573, 14869}, {377, 44217, 8728}, {443, 5177, 16408}, {443, 17528, 5}, {4197, 11112, 6675}, {5177, 16408, 5}, {5187, 16864, 17527}, {5187, 37462, 16864}, {6675, 11112, 548}, {6856, 16417, 632}, {6872, 50207, 50202}, {8728, 50202, 50207}, {16408, 17528, 5177}, {16418, 37435, 15704}, {16864, 17532, 5187}, {17527, 17532, 3850}, {17532, 37462, 17527}, {17565, 33033, 8359}, {17582, 37161, 381}


X(50239) = X(2)X(3)∩X(518)X(3632)

Barycentrics    3*a^4 - a^2*b^2 - 2*b^4 + 2*a^2*b*c + 2*a*b^2*c - a^2*c^2 + 2*a*b*c^2 + 4*b^2*c^2 - 2*c^4 : :
X(50239) = 3 X[2] - 5 X[377], 6 X[2] - 5 X[405], 9 X[2] - 5 X[6872], 9 X[2] - 10 X[8728], 7 X[2] - 5 X[31156], 27 X[2] - 25 X[31259], 3 X[2] + 5 X[31295], 4 X[2] - 5 X[44217], 11 X[2] - 10 X[50202], 21 X[2] - 20 X[50205], 24 X[2] - 25 X[50207], 3 X[377] - X[6872], 3 X[377] - 2 X[8728], 7 X[377] - 3 X[31156], 9 X[377] - 5 X[31259], 4 X[377] - 3 X[44217], 11 X[377] - 6 X[50202], 7 X[377] - 4 X[50205], 8 X[377] - 5 X[50207], 3 X[405] - 2 X[6872], 3 X[405] - 4 X[8728], 7 X[405] - 6 X[31156], 9 X[405] - 10 X[31259], X[405] + 2 X[31295], 2 X[405] - 3 X[44217], 11 X[405] - 12 X[50202], 7 X[405] - 8 X[50205], 4 X[405] - 5 X[50207], 4 X[546] - 5 X[44229], 4 X[550] - 5 X[37426], 4 X[3530] - 5 X[44222], 7 X[3851] - 5 X[37234], 7 X[6872] - 9 X[31156], 3 X[6872] - 5 X[31259], X[6872] + 3 X[31295], 4 X[6872] - 9 X[44217], 11 X[6872] - 18 X[50202], 7 X[6872] - 12 X[50205], 8 X[6872] - 15 X[50207], 14 X[8728] - 9 X[31156], 6 X[8728] - 5 X[31259], 2 X[8728] + 3 X[31295], 8 X[8728] - 9 X[44217], 11 X[8728] - 9 X[50202], 7 X[8728] - 6 X[50205], 16 X[8728] - 15 X[50207], 27 X[31156] - 35 X[31259], 3 X[31156] + 7 X[31295], 4 X[31156] - 7 X[44217], 11 X[31156] - 14 X[50202], 3 X[31156] - 4 X[50205], 24 X[31156] - 35 X[50207], 5 X[31259] + 9 X[31295], 20 X[31259] - 27 X[44217], 55 X[31259] - 54 X[50202], 35 X[31259] - 36 X[50205], 8 X[31259] - 9 X[50207], 4 X[31295] + 3 X[44217], 11 X[31295] + 6 X[50202], 7 X[31295] + 4 X[50205], 8 X[31295] + 5 X[50207], 4 X[34200] - 5 X[44284], 11 X[44217] - 8 X[50202], 21 X[44217] - 16 X[50205], 6 X[44217] - 5 X[50207], 21 X[50202] - 22 X[50205], 48 X[50202] - 55 X[50207], 32 X[50205] - 35 X[50207], 2 X[3244] - 5 X[10404]

X(50239) lies on these lines: {2, 3}, {8, 9655}, {10, 12943}, {56, 24387}, {72, 9579}, {79, 12635}, {100, 9654}, {149, 7373}, {392, 41869}, {484, 1706}, {518, 3632}, {519, 9657}, {551, 9670}, {938, 12690}, {956, 7354}, {958, 10483}, {1125, 12953}, {1376, 3585}, {1478, 5687}, {1699, 17614}, {1770, 5794}, {1836, 5730}, {2077, 10894}, {2099, 3244}, {2886, 4299}, {2932, 13273}, {3419, 4292}, {3434, 18990}, {3485, 10609}, {3583, 25524}, {3586, 5439}, {3612, 3838}, {3616, 9668}, {3624, 35271}, {3626, 37567}, {3636, 12053}, {3680, 34747}, {3753, 5691}, {3813, 4317}, {3822, 5217}, {3868, 18541}, {3877, 48661}, {3913, 5270}, {4004, 5727}, {4293, 24390}, {4297, 36999}, {4302, 25466}, {4325, 11194}, {4330, 4428}, {4333, 4640}, {4338, 44663}, {4421, 37719}, {4666, 31795}, {4857, 34706}, {5080, 9709}, {5086, 36279}, {5204, 25639}, {5229, 17757}, {5250, 28146}, {5253, 9669}, {5267, 31245}, {5275, 7748}, {5277, 44518}, {5283, 44526}, {5302, 37572}, {5362, 42127}, {5367, 42126}, {5440, 9612}, {5563, 11235}, {5692, 16118}, {5693, 17653}, {5880, 10572}, {6154, 10956}, {6224, 12735}, {7270, 50044}, {7802, 16992}, {8666, 31140}, {8715, 11237}, {9614, 37525}, {9647, 31484}, {9955, 35262}, {10107, 37711}, {10198, 15338}, {10386, 10587}, {10724, 34123}, {10728, 26062}, {10729, 34124}, {10861, 31671}, {10895, 25440}, {10949, 26437}, {11015, 31019}, {11246, 49168}, {11826, 26332}, {12246, 33899}, {12625, 24473}, {12649, 24470}, {15326, 26363}, {16120, 31806}, {17616, 24474}, {17619, 18492}, {18499, 34773}, {19860, 28160}, {19861, 22793}, {19925, 37001}, {26543, 48873}, {31473, 35821}, {37720, 40726}, {43531, 48836}, {48837, 49745}

X(50239) = midpoint of X(377) and X(31295)
X(50239) = reflection of X(i) in X(j) for these {i,j}: {405, 377}, {6872, 8728}
X(50239) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 550, 19535}, {3, 2475, 17532}, {4, 474, 17556}, {4, 6904, 4187}, {4, 6955, 6922}, {4, 11112, 474}, {4, 31775, 37022}, {4, 37435, 11112}, {5, 4190, 16371}, {20, 442, 16370}, {20, 37161, 6857}, {376, 5177, 7483}, {377, 405, 44217}, {377, 6872, 8728}, {405, 44217, 50207}, {443, 3146, 11113}, {443, 11113, 16842}, {452, 17529, 17542}, {546, 17563, 2}, {548, 6910, 19704}, {1657, 17528, 21}, {1836, 17647, 5730}, {2475, 17579, 3}, {2475, 37256, 2476}, {2476, 17579, 37256}, {2476, 37256, 3}, {3522, 6856, 37298}, {3830, 16408, 5046}, {3832, 17567, 17533}, {3843, 16417, 4193}, {3850, 17564, 6931}, {3851, 17573, 2}, {4187, 6904, 474}, {4187, 11112, 6904}, {4188, 17577, 1656}, {4197, 15680, 16418}, {4208, 5059, 11111}, {5073, 11108, 11114}, {5141, 13587, 3526}, {6850, 37468, 7580}, {6857, 37161, 442}, {6872, 8728, 405}, {6921, 6974, 6857}, {7504, 37307, 5054}, {15670, 17576, 19539}, {16418, 17800, 15680}, {17533, 17583, 17567}, {17676, 50171, 2049}, X(50239) = {26051, 37038, 16343}, {26117, 48816, 16458}, {31156, 50205, 405}, {37234, 37282, 405}


X(50240) = X(2)X(3)∩X(518)X(3625)

Barycentrics    4*a^4 - a^2*b^2 - 3*b^4 + 4*a^2*b*c + 4*a*b^2*c - a^2*c^2 + 4*a*b*c^2 + 6*b^2*c^2 - 3*c^4 : :
X(50240) = 3 X[2] - 7 X[377], 9 X[2] - 7 X[405], 15 X[2] - 7 X[6872], 6 X[2] - 7 X[8728], 11 X[2] - 7 X[31156], 39 X[2] - 35 X[31259], 9 X[2] + 7 X[31295], 5 X[2] - 7 X[44217], 8 X[2] - 7 X[50202], 15 X[2] - 14 X[50205], 33 X[2] - 35 X[50207], 3 X[377] - X[405], 5 X[377] - X[6872], 11 X[377] - 3 X[31156], 13 X[377] - 5 X[31259], 3 X[377] + X[31295], 5 X[377] - 3 X[44217], 8 X[377] - 3 X[50202], 5 X[377] - 2 X[50205], 11 X[377] - 5 X[50207], 5 X[405] - 3 X[6872], 2 X[405] - 3 X[8728], 11 X[405] - 9 X[31156], 13 X[405] - 15 X[31259], 5 X[405] - 9 X[44217], 8 X[405] - 9 X[50202], 5 X[405] - 6 X[50205], 11 X[405] - 15 X[50207], 5 X[3627] - 7 X[44286], 5 X[3843] - 7 X[44229], 11 X[5072] - 7 X[37234], 2 X[6872] - 5 X[8728], 11 X[6872] - 15 X[31156], 13 X[6872] - 25 X[31259], 3 X[6872] + 5 X[31295], X[6872] - 3 X[44217], 8 X[6872] - 15 X[50202], 11 X[6872] - 25 X[50207], 11 X[8728] - 6 X[31156], 13 X[8728] - 10 X[31259], 3 X[8728] + 2 X[31295], 5 X[8728] - 6 X[44217], 4 X[8728] - 3 X[50202], 5 X[8728] - 4 X[50205], 11 X[8728] - 10 X[50207], 5 X[14093] - 7 X[44284], 5 X[15712] - 7 X[44222], 5 X[17538] - 7 X[37426], 39 X[31156] - 55 X[31259], 9 X[31156] + 11 X[31295], 5 X[31156] - 11 X[44217], 8 X[31156] - 11 X[50202], 15 X[31156] - 22 X[50205], 3 X[31156] - 5 X[50207], 15 X[31259] + 13 X[31295], 25 X[31259] - 39 X[44217], 40 X[31259] - 39 X[50202], 25 X[31259] - 26 X[50205], 11 X[31259] - 13 X[50207], 5 X[31295] + 9 X[44217], 8 X[31295] + 9 X[50202], 5 X[31295] + 6 X[50205], 11 X[31295] + 15 X[50207], 8 X[44217] - 5 X[50202], 3 X[44217] - 2 X[50205], 33 X[44217] - 25 X[50207], 15 X[50202] - 16 X[50205], 33 X[50202] - 40 X[50207], 22 X[50205] - 25 X[50207], X[3633] - 7 X[10404]

X(50240) lies on these lines: {1, 41865}, {2, 3}, {8, 18541}, {355, 9952}, {495, 8715}, {518, 3625}, {535, 9710}, {2093, 4668}, {2550, 9655}, {3256, 26482}, {3340, 3633}, {3419, 24470}, {3585, 3820}, {3635, 12563}, {3824, 4304}, {3925, 10483}, {4316, 24953}, {4317, 31140}, {4691, 8256}, {4847, 31776}, {5128, 41229}, {5175, 5708}, {5229, 9709}, {5250, 28178}, {5258, 7354}, {5270, 34612}, {5694, 16120}, {5880, 37730}, {7270, 50042}, {9945, 11374}, {10592, 25440}, {10855, 31822}, {10895, 47742}, {11246, 47033}, {11544, 12635}, {12513, 18990}, {14929, 34284}, {17614, 38034}, {17616, 24475}, {17647, 39542}, {19860, 28186}, {19861, 40273}, {26332, 31777}, {26543, 48874}, {31420, 34610}, {31458, 34620}, {48835, 49734}, {48837, 49743}, {48847, 49745}

X(50240) = midpoint of X(405) and X(31295)
X(50240) = reflection of X(i) in X(j) for these {i,j}: {6872, 50205}, {8728, 377}
X(50240) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 11112, 17563}, {5, 17563, 17564}, {20, 17528, 6675}, {377, 6872, 44217}, {377, 31295, 405}, {442, 17579, 550}, {2475, 11112, 5}, {3529, 4208, 16418}, {3851, 19706, 17567}, {4188, 17530, 632}, {4190, 6933, 19537}, {4190, 17532, 140}, {6175, 37256, 7483}, {6871, 16371, 3628}, {6872, 44217, 50205}, {6917, 31775, 8727}, {6933, 19537, 140}, {6951, 37468, 37424}, {7483, 37256, 8703}, {13747, 17577, 5}, {17532, 19537, 6933}, {44217, 50205, 8728}


X(50241) = X(2)X(3)∩X(518)X(3244)

Barycentrics    4*a^4 - 3*a^2*b^2 - b^4 - 4*a^2*b*c - 4*a*b^2*c - 3*a^2*c^2 - 4*a*b*c^2 + 2*b^2*c^2 - c^4 : :
X(50241) = 9 X[2] - 5 X[377], 3 X[2] - 5 X[405], 3 X[2] + 5 X[6872], 6 X[2] - 5 X[8728], X[2] - 5 X[31156], 21 X[2] - 25 X[31259], 21 X[2] - 5 X[31295], 7 X[2] - 5 X[44217], 4 X[2] - 5 X[50202], 9 X[2] - 10 X[50205], 27 X[2] - 25 X[50207], X[377] - 3 X[405], X[377] + 3 X[6872], 2 X[377] - 3 X[8728], X[377] - 9 X[31156], 7 X[377] - 15 X[31259], 7 X[377] - 3 X[31295], 7 X[377] - 9 X[44217], 4 X[377] - 9 X[50202], 3 X[377] - 5 X[50207], X[382] - 5 X[37234], X[405] - 3 X[31156], 7 X[405] - 5 X[31259], 7 X[405] - X[31295], 7 X[405] - 3 X[44217], 4 X[405] - 3 X[50202], 3 X[405] - 2 X[50205], 9 X[405] - 5 X[50207], 7 X[3528] - 5 X[37426], 7 X[3851] - 5 X[44229], 2 X[6872] + X[8728], X[6872] + 3 X[31156], 7 X[6872] + 5 X[31259], 7 X[6872] + X[31295], 7 X[6872] + 3 X[44217], 4 X[6872] + 3 X[50202], 3 X[6872] + 2 X[50205], 9 X[6872] + 5 X[50207], X[8728] - 6 X[31156], 7 X[8728] - 10 X[31259], 7 X[8728] - 2 X[31295], 7 X[8728] - 6 X[44217], 2 X[8728] - 3 X[50202], 3 X[8728] - 4 X[50205], 9 X[8728] - 10 X[50207], 7 X[14869] - 5 X[44222], 7 X[15700] - 5 X[44284], 21 X[31156] - 5 X[31259], 21 X[31156] - X[31295], 7 X[31156] - X[44217], 4 X[31156] - X[50202], 9 X[31156] - 2 X[50205], 27 X[31156] - 5 X[50207], 5 X[31259] - X[31295], 5 X[31259] - 3 X[44217], 20 X[31259] - 21 X[50202], 15 X[31259] - 14 X[50205], 9 X[31259] - 7 X[50207], X[31295] - 3 X[44217], 4 X[31295] - 21 X[50202], 3 X[31295] - 14 X[50205], 9 X[31295] - 35 X[50207], 4 X[44217] - 7 X[50202], 9 X[44217] - 14 X[50205], 27 X[44217] - 35 X[50207], 9 X[50202] - 8 X[50205], 27 X[50202] - 20 X[50207], 6 X[50205] - 5 X[50207], X[3632] - 5 X[41229], 2 X[3626] - 5 X[5302]

X(50241) lies on these lines: {2, 3}, {8, 10386}, {35, 3820}, {63, 12433}, {80, 6154}, {355, 4512}, {392, 34773}, {495, 5248}, {496, 993}, {518, 3244}, {936, 9945}, {944, 5779}, {950, 31445}, {952, 5250}, {956, 15172}, {958, 15171}, {1001, 18990}, {1104, 50067}, {1385, 40998}, {1420, 10404}, {1483, 3877}, {1697, 3632}, {1698, 15338}, {1724, 48847}, {1730, 48915}, {3058, 5258}, {3488, 3927}, {3576, 6259}, {3583, 24953}, {3586, 5791}, {3612, 4679}, {3624, 15326}, {3626, 5302}, {3631, 47038}, {3636, 12577}, {3683, 10572}, {3746, 34606}, {3816, 5267}, {3868, 15935}, {3897, 10283}, {3940, 4313}, {4262, 38930}, {4294, 9708}, {4299, 4423}, {4304, 5044}, {4314, 34790}, {4316, 25542}, {4330, 34612}, {4652, 34753}, {4658, 48846}, {4847, 31795}, {4999, 10593}, {5122, 9843}, {5126, 11813}, {5217, 47742}, {5225, 31493}, {5251, 6284}, {5259, 7354}, {5283, 18907}, {5303, 26127}, {5692, 10543}, {5722, 31424}, {5901, 37826}, {6690, 10592}, {7283, 50042}, {7956, 11012}, {8227, 30264}, {8582, 31663}, {8666, 49736}, {9668, 19843}, {9669, 30478}, {11015, 27065}, {11235, 31458}, {11496, 31799}, {12019, 26066}, {12513, 15170}, {12514, 37730}, {12572, 24929}, {12635, 15174}, {12640, 34641}, {12953, 19854}, {15254, 17647}, {16616, 31730}, {17768, 30143}, {18481, 18540}, {19860, 28174}, {24466, 31423}, {24541, 38034}, {24703, 37737}, {25522, 38761}, {26543, 39884}, {31141, 31452}, {31157, 37720}, {38028, 41012}, {48863, 49728}

X(50241) = midpoint of X(405) and X(6872)
X(50241) = reflection of X(i) in X(j) for these {i,j}: {377, 50205}, {8728, 405}
X(50241) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 550, 17563}, {2, 3528, 17573}, {2, 19535, 3530}, {3, 17527, 17564}, {4, 11106, 16418}, {4, 16418, 6675}, {21, 5046, 7483}, {21, 11113, 5}, {376, 5129, 16408}, {377, 405, 50205}, {377, 50205, 8728}, {382, 16866, 2}, {405, 8728, 50202}, {405, 37426, 50204}, {405, 44217, 31259}, {442, 11114, 3627}, {452, 11111, 3}, {452, 17576, 5084}, {1657, 16857, 443}, {2478, 16370, 140}, {3146, 16845, 17528}, {3522, 17559, 16417}, {3534, 16853, 6904}, {3560, 31789, 8727}, {4187, 4189, 549}, {4187, 17525, 4189}, {4193, 37298, 632}, {4195, 4205, 50059}, {4195, 48814, 4205}, {5046, 7483, 5}, {5047, 15680, 11112}, {5084, 11111, 17576}, {5084, 17576, 3}, {5251, 6284, 31419}, {6868, 6913, 20420}, {6872, 31156, 405}, {6910, 17556, 3628}, {6920, 37468, 5}, {7483, 11113, 5046}, {7489, 7491, 5}, {11112, 15680, 15704}, {11114, 16865, 442}, {11319, 49735, 13728}, {13735, 26117, 17698}, {13736, 48817, 2049}, {13747, 17549, 15712}, {15678, 17536, 37256}, {16859, 17579, 17529}, {17535, 36004, 17583}, {17549, 37162, 13747}, {17698, 26117, 50058}, {31259, 31295, 44217}, {44222, 50206, 8728}


X(50242) = X(2)X(3)∩X(518)X(3633)

Barycentrics    5*a^4 - 3*a^2*b^2 - 2*b^4 - 2*a^2*b*c - 2*a*b^2*c - 3*a^2*c^2 - 2*a*b*c^2 + 4*b^2*c^2 - 2*c^4 : :
X(50242) = 9 X[2] - 7 X[377], 6 X[2] - 7 X[405], 3 X[2] - 7 X[6872], 15 X[2] - 14 X[8728], 5 X[2] - 7 X[31156], 33 X[2] - 35 X[31259], 15 X[2] - 7 X[31295], 8 X[2] - 7 X[44217], 13 X[2] - 14 X[50202], 27 X[2] - 28 X[50205], 36 X[2] - 35 X[50207], 2 X[377] - 3 X[405], X[377] - 3 X[6872], 5 X[377] - 6 X[8728], 5 X[377] - 9 X[31156], 11 X[377] - 15 X[31259], 5 X[377] - 3 X[31295], 8 X[377] - 9 X[44217], 13 X[377] - 18 X[50202], 3 X[377] - 4 X[50205], 4 X[377] - 5 X[50207], 5 X[405] - 4 X[8728], 5 X[405] - 6 X[31156], 11 X[405] - 10 X[31259], 5 X[405] - 2 X[31295], 4 X[405] - 3 X[44217], 13 X[405] - 12 X[50202], 9 X[405] - 8 X[50205], 6 X[405] - 5 X[50207], 8 X[548] - 7 X[37426], 5 X[3843] - 7 X[37234], 8 X[3850] - 7 X[44229], 5 X[6872] - 2 X[8728], 5 X[6872] - 3 X[31156], 11 X[6872] - 5 X[31259], 5 X[6872] - X[31295], 8 X[6872] - 3 X[44217], 13 X[6872] - 6 X[50202], 9 X[6872] - 4 X[50205], 12 X[6872] - 5 X[50207], 2 X[8728] - 3 X[31156], 22 X[8728] - 25 X[31259], 16 X[8728] - 15 X[44217], 13 X[8728] - 15 X[50202], 9 X[8728] - 10 X[50205], 24 X[8728] - 25 X[50207], 8 X[12108] - 7 X[44222], 8 X[14891] - 7 X[44284], 33 X[31156] - 25 X[31259], 3 X[31156] - X[31295], 8 X[31156] - 5 X[44217], 13 X[31156] - 10 X[50202], 27 X[31156] - 20 X[50205], 36 X[31156] - 25 X[50207], 25 X[31259] - 11 X[31295], 40 X[31259] - 33 X[44217], 65 X[31259] - 66 X[50202], 45 X[31259] - 44 X[50205], 12 X[31259] - 11 X[50207], 8 X[31295] - 15 X[44217], 13 X[31295] - 30 X[50202], 9 X[31295] - 20 X[50205], 12 X[31295] - 25 X[50207], 13 X[44217] - 16 X[50202], 27 X[44217] - 32 X[50205], 9 X[44217] - 10 X[50207], 27 X[50202] - 26 X[50205], 72 X[50202] - 65 X[50207], 16 X[50205] - 15 X[50207], 5 X[4668] - 7 X[41229]

X(50242) lies on these lines: {2, 3}, {8, 12732}, {518, 3633}, {529, 4309}, {535, 3303}, {956, 6284}, {993, 12953}, {1001, 10483}, {1376, 4324}, {1388, 4315}, {1621, 9655}, {2098, 3635}, {2975, 9668}, {3255, 15173}, {3586, 3916}, {3812, 4333}, {3913, 4330}, {3940, 11015}, {4297, 12679}, {4302, 5687}, {4316, 25524}, {4317, 49736}, {4428, 5270}, {4666, 31776}, {4668, 11010}, {4857, 11194}, {5119, 32537}, {5248, 12943}, {5250, 28160}, {5267, 10896}, {5362, 42130}, {5367, 42131}, {5441, 12635}, {5563, 34620}, {5985, 38733}, {7373, 20067}, {8666, 9670}, {9656, 10197}, {15172, 20076}, {17619, 35242}, {18480, 35258}, {19860, 28146}, {25522, 35271}, {26333, 30264}, {31473, 42267}, {34739, 37719}, {37730, 44447}

X(50242) = reflection of X(i) in X(j) for these {i,j}: {405, 6872}, {31295, 8728}
X(50242) = crossdifference of every pair of points on line {647, 39521}
X(50242) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17583, 474}, {4, 17576, 7483}, {20, 11113, 474}, {21, 382, 17532}, {376, 4187, 19537}, {377, 405, 50207}, {377, 50207, 44217}, {442, 11111, 19526}, {452, 3529, 11112}, {452, 11112, 16842}, {550, 2478, 16371}, {2476, 15677, 17571}, {3146, 11111, 442}, {3522, 13747, 19705}, {3830, 17571, 2476}, {4193, 37299, 3}, {5073, 16418, 2475}, {6857, 17525, 19539}, {6872, 31295, 31156}, {6938, 31789, 37022}, {7483, 17576, 16370}, {8728, 31156, 405}, {11108, 17800, 17579}, {11114, 15680, 3}, {15681, 16408, 37256}, {17548, 37375, 3526}, {20835, 37234, 405}, {31156, 31295, 8728}, {33032, 33244, 17694}


X(50243) = X(2)X(3)∩X(518)X(3635)

Barycentrics    6*a^4 - 5*a^2*b^2 - b^4 - 8*a^2*b*c - 8*a*b^2*c - 5*a^2*c^2 - 8*a*b*c^2 + 2*b^2*c^2 - c^4 : :
X(50243) = 15 X[2] - 7 X[377], 3 X[2] - 7 X[405], 9 X[2] + 7 X[6872], 9 X[2] - 7 X[8728], X[2] + 7 X[31156], 27 X[2] - 35 X[31259], 39 X[2] - 7 X[31295], 11 X[2] - 7 X[44217], 5 X[2] - 7 X[50202], 6 X[2] - 7 X[50205], 39 X[2] - 35 X[50207], X[377] - 5 X[405], 3 X[377] + 5 X[6872], 3 X[377] - 5 X[8728], X[377] + 15 X[31156], 9 X[377] - 25 X[31259], 13 X[377] - 5 X[31295], 11 X[377] - 15 X[44217], X[377] - 3 X[50202], 2 X[377] - 5 X[50205], 13 X[377] - 25 X[50207], 3 X[405] + X[6872], 3 X[405] - X[8728], X[405] + 3 X[31156], 9 X[405] - 5 X[31259], 13 X[405] - X[31295], 11 X[405] - 3 X[44217], 5 X[405] - 3 X[50202], 13 X[405] - 5 X[50207], X[1657] + 7 X[37234], 11 X[5072] - 7 X[44229], X[6872] - 9 X[31156], 3 X[6872] + 5 X[31259], 13 X[6872] + 3 X[31295], 11 X[6872] + 9 X[44217], 5 X[6872] + 9 X[50202], 2 X[6872] + 3 X[50205], 13 X[6872] + 15 X[50207], X[8728] + 9 X[31156], 3 X[8728] - 5 X[31259], 13 X[8728] - 3 X[31295], 11 X[8728] - 9 X[44217], 5 X[8728] - 9 X[50202], 2 X[8728] - 3 X[50205], 13 X[8728] - 15 X[50207], 11 X[15718] - 7 X[44284], 11 X[21735] - 7 X[37426], 27 X[31156] + 5 X[31259], 39 X[31156] + X[31295], 11 X[31156] + X[44217], 5 X[31156] + X[50202], 6 X[31156] + X[50205], 39 X[31156] + 5 X[50207], 65 X[31259] - 9 X[31295], 55 X[31259] - 27 X[44217], 25 X[31259] - 27 X[50202], 10 X[31259] - 9 X[50205], 13 X[31259] - 9 X[50207], 11 X[31295] - 39 X[44217], 5 X[31295] - 39 X[50202], 2 X[31295] - 13 X[50205], X[31295] - 5 X[50207], 5 X[44217] - 11 X[50202], 6 X[44217] - 11 X[50205], 39 X[44217] - 55 X[50207], 6 X[50202] - 5 X[50205], 39 X[50202] - 25 X[50207], 13 X[50205] - 10 X[50207], X[3625] - 7 X[5302], X[3633] + 7 X[41229]

X(50243) lies on these lines: {2, 3}, {35, 50038}, {518, 3635}, {958, 15172}, {1125, 31776}, {3625, 5302}, {3633, 31393}, {3683, 37730}, {3793, 27269}, {3927, 15935}, {4512, 5690}, {4668, 5727}, {5248, 12607}, {5250, 5844}, {5251, 15171}, {5258, 15170}, {5259, 18990}, {5436, 6147}, {5692, 15174}, {5719, 12572}, {5843, 37615}, {5901, 40998}, {9708, 10386}, {10165, 22792}, {10404, 13462}, {12433, 24391}, {15326, 25542}, {19860, 28212}, {31435, 34773}

X(50243) = midpoint of X(6872) and X(8728)
X(50243) = reflection of X(50205) in X(405)
X(50243) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21, 37162, 37298}, {377, 405, 50202}, {405, 6872, 8728}, {452, 16418, 5}, {5084, 17571, 549}, {6675, 11113, 546}, {11108, 11111, 550}, {11113, 16865, 6675}, {15680, 16861, 17529}, {16370, 17527, 3530}, {16408, 17576, 8703}, {17544, 17579, 17590}


X(50244) = X(2)X(3)∩X(518)X(3644)

Barycentrics    7*a^4 - 4*a^2*b^2 - 3*b^4 - 2*a^2*b*c - 2*a*b^2*c - 4*a^2*c^2 - 2*a*b*c^2 + 6*b^2*c^2 - 3*c^4 : :
X(50244) = 6 X[2] - 5 X[377], 9 X[2] - 10 X[405], 3 X[2] - 5 X[6872], 21 X[2] - 20 X[8728], 4 X[2] - 5 X[31156], 24 X[2] - 25 X[31259], 9 X[2] - 5 X[31295], 11 X[2] - 10 X[44217], 19 X[2] - 20 X[50202], 39 X[2] - 40 X[50205], 51 X[2] - 50 X[50207], 3 X[377] - 4 X[405], 7 X[377] - 8 X[8728], 2 X[377] - 3 X[31156], 4 X[377] - 5 X[31259], 3 X[377] - 2 X[31295], 11 X[377] - 12 X[44217], 19 X[377] - 24 X[50202], 13 X[377] - 16 X[50205], 17 X[377] - 20 X[50207], 2 X[405] - 3 X[6872], 7 X[405] - 6 X[8728], 8 X[405] - 9 X[31156], 16 X[405] - 15 X[31259], 11 X[405] - 9 X[44217], 19 X[405] - 18 X[50202], 13 X[405] - 12 X[50205], 17 X[405] - 15 X[50207], 4 X[546] - 5 X[37234], 11 X[3855] - 10 X[44229], 7 X[6872] - 4 X[8728], 4 X[6872] - 3 X[31156], 8 X[6872] - 5 X[31259], 3 X[6872] - X[31295], 11 X[6872] - 6 X[44217], 19 X[6872] - 12 X[50202], 13 X[6872] - 8 X[50205], 17 X[6872] - 10 X[50207], 16 X[8728] - 21 X[31156], 32 X[8728] - 35 X[31259], 12 X[8728] - 7 X[31295], 22 X[8728] - 21 X[44217], 19 X[8728] - 21 X[50202], 13 X[8728] - 14 X[50205], 34 X[8728] - 35 X[50207], 11 X[15715] - 10 X[44284], 11 X[15720] - 10 X[44222], 6 X[31156] - 5 X[31259], 9 X[31156] - 4 X[31295], 11 X[31156] - 8 X[44217], 19 X[31156] - 16 X[50202], 39 X[31156] - 32 X[50205], 51 X[31156] - 40 X[50207], 15 X[31259] - 8 X[31295], 55 X[31259] - 48 X[44217], 95 X[31259] - 96 X[50202], 65 X[31259] - 64 X[50205], 17 X[31259] - 16 X[50207], 11 X[31295] - 18 X[44217], 19 X[31295] - 36 X[50202], 13 X[31295] - 24 X[50205], 17 X[31295] - 30 X[50207], 19 X[44217] - 22 X[50202], 39 X[44217] - 44 X[50205], 51 X[44217] - 55 X[50207], 39 X[50202] - 38 X[50205], 102 X[50202] - 95 X[50207], 68 X[50205] - 65 X[50207], 4 X[3626] - 5 X[41229]

X(50244) lies on these lines: {2, 3}, {329, 11015}, {518, 3644}, {535, 4309}, {1058, 20067}, {2320, 5556}, {3244, 10624}, {3421, 20066}, {3434, 5258}, {3436, 4302}, {3626, 41229}, {3632, 12526}, {3636, 4311}, {3877, 12688}, {3897, 9812}, {4305, 5057}, {4308, 10404}, {5048, 5180}, {5250, 28164}, {5283, 43618}, {5303, 10591}, {5552, 15338}, {6284, 12513}, {7280, 10584}, {9655, 10587}, {9668, 10529}, {9670, 11240}, {9963, 20007}, {10527, 12953}, {10572, 44447}, {15171, 20076}, {19860, 28150}, {21031, 34626}, {28534, 37724}, {31673, 35258}, {32826, 37670}, {34620, 37722}

X(50244) = reflection of X(i) in X(j) for these {i,j}: {377, 6872}, {31295, 405}
X(50244) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 4189, 6933}, {4, 6914, 6860}, {20, 11114, 2478}, {20, 37267, 36005}, {376, 5046, 6921}, {377, 6872, 31156}, {377, 31156, 31259}, {405, 31295, 377}, {452, 5059, 17579}, {452, 17579, 37462}, {546, 19535, 2}, {1657, 11113, 4190}, {2476, 15678, 17576}, {3543, 17576, 2476}, {3627, 16370, 6871}, {4189, 6933, 6910}, {5084, 11001, 37256}, {6872, 31295, 405}, {6934, 37290, 6957}, {6938, 7491, 6836}, {11111, 33703, 2475}


X(50245) = X(140)X(3366)∩X(1327)X(2041)

Barycentrics    Sin[A] / ((Sqrt[3] + 2)*Cos[A] + 3*Sin[A]) : : (Peter Moses, 9/4/2022)
Barycentrics    1 / ((2 + Sqrt[3])*(-a^2 + b^2 + c^2) + 6*S) : : (Peter Moses, 9/4/2022)
Barycentrics    17 a^4+10 Sqrt[3] a^4+63 a^2 b^2+36 Sqrt[3] a^2 b^2-80 b^4-46 Sqrt[3] b^4+63 a^2 c^2+36 Sqrt[3] a^2 c^2+160 b^2 c^2+92 Sqrt[3] b^2 c^2-80 c^4-46 Sqrt[3] c^4+156 a^2 S+90 Sqrt[3] a^2 S : :
Barycentrics    2 (9 (7+4 Sqrt[3]) S^2+(97+56 Sqrt[3]) SB SC+3 (26+15 Sqrt[3]) S (SB+SC)) : :

See Antreas Hatzipolakis and Ercole Suppa euclid 5142.

X(50245) lies on the Kiepert circumhyperbola and these lines: {13,14814}, {18,42563}, {140,3366}, {397,16966}, {486,42992}, {1327,2041}, {1656,3392}, {2045,5351}, {3391,8960}, {3591,42998}, {6398,10576}, {6433,42177}, {10188,32789}, {10195,42936}, {11480,42237}, {12816,18587}, {12817,18585}, {12819,42245}, {16960,42222}, {36455,43562}, {42095,42238}, {42229,42979}


X(50246) = X(30)X(3391)∩X(381)X(3367)

Barycentrics    Sin[A] / (3*(Sqrt[3] - 2)*Cos[A] - Sin[A]) : : (Peter Moses, 9/4/2022)
Barycentrics    1 / (3*(2 - Sqrt[3])*(-a^2 + b^2 + c^2) + 2*S) : : (Peter Moses, 9/4/2022)
Barycentrics    (239+138 Sqrt[3]) a^4+2 (556+321 Sqrt[3]) (b^2-c^2)^2-a^2 ((1351+780 Sqrt[3]) b^2+(1351+780 Sqrt[3]) c^2+6 (362+209 Sqrt[3]) S) : :
Barycentrics    (1351+780 Sqrt[3]) S^2+9 (97+56 Sqrt[3]) SB SC+3 (362+209 Sqrt[3]) S (SB+SC) : :

See Antreas Hatzipolakis and Ercole Suppa euclid 5142.

X(50246) lies on the Kiepert circumhyperbola and these lines: {2,42198}, {14,32787}, {15,43503}, {16,42639}, {17,15765}, {18,18586}, {30,3391}, {381,3367}, {396,3845}, {485,35731}, {486,16267}, {590,36968}, {1327,36969}, {1328,36468}, {1991,42035}, {2042,10195}, {2043,5352}, {3317,36447}, {3364,36454}, {3366,35822}, {3830,6221}, {6306,40707}, {6561,43476}, {10187,14813}, {11122,33443}, {12816,42284}, {14226,37640}, {14241,36464}, {16809,36448}, {16962,42236}, {22235,42249}, {32788,42506}, {36463,42257}, {36466,36967}, {42133,43567}, {42217,43543}, {42230,42814}, {42237,42586}


leftri

Points in a [[(b^2 - c^2, c^2 - a^2, a^2 - b^2 ], b^2 + c^2, c^2 + a^2, a^2 + b^2]] coordinate system: X(50247)-X(50255)

rightri

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

L1 is the line: (b^2 - c^2) α + (c^2 - a^2) β + (a^2 - b^2) γ = 0.

L2 is the line (b^2 + c^2) α + (c^2 + a^2) β + (a^2 + b^2) γ = 0.

The origin is given by (0, 0) = X(385) = a^4 - b^2 c^2 : b^4 - c^2 a^2 : c^4 - a^2 b^2.

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

u : v : w = 2(a^4 - b^2 c^2) + (-2a^2 + b^2 + c^2) x + (b^2 - c^2) y : : ,

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

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

{-2 (a b+a c+b c), 0}, 17731
{-((2 a b c)/(a+b+c)), 0}, 19623
{1/2 (-a^2-b^2-c^2), 0}, 15480
{0, 0}, 385
{1/2 (a^2+b^2+c^2), 0}, 230
{a^2+b^2+c^2, 0}, 325
{(a^4+b^4+c^4)/(a^2+b^2+c^2), 0}, 15993
{(2 (a^3+b^3+c^3))/(a+b+c), -((2 (a-b) (a-c) (b-c))/(a+b+c))}, 36223
{2 (a^2+b^2+c^2), 0}, 7779
{2 (a+b+c)^2, 0}, 20536
{(2 (a^4+b^4+c^4))/(a^2+b^2+c^2), 0}, 69
{(2 (a^3+b^3+c^3))/(a+b+c), (2 (a-b) (a-c) (b-c))/(a+b+c)}, 8
{(-2*(a^3 + b^3 + c^3))/(a + b + c), (-2*(a - b)*(a - c)*(b - c))/(a + b + c)}, 50247
{-2*(a^2 + b^2 + c^2), 0}, 50248
{(-2*(a^4 + b^4 + c^4))/(a^2 + b^2 + c^2), 0}, 50249
{-((a^3 + b^3 + c^3)/(a + b + c)), -(((a - b)*(a - c)*(b - c))/(a + b + c))}, 50250
{-a^2 - b^2 - c^2, 0}, 50251
{-(a*b) - a*c - b*c, 0}, 50252
{-((a^4 + b^4 + c^4)/(a^2 + b^2 + c^2)), 0}, 50253
{(a^3 + b^3 + c^3)/(a + b + c), ((a - b)*(a - c)*(b - c))/(a + b + c)}, 50254
{(2*a*b*c)/(a + b + c), (-2*(a - b)*(a - c)*(b - c))/(a + b + c)}, 50255


X(50247) = X(8)X(385)∩X(519)X(1281)

Barycentrics    3*a^5 + a^4*b - a^3*b^2 + a^2*b^3 + a*b^4 - b^5 + a^4*c + a^2*b^2*c - b^4*c - a^3*c^2 + a^2*b*c^2 - 3*a*b^2*c^2 - b^3*c^2 + a^2*c^3 - b^2*c^3 + a*c^4 - b*c^4 - c^5 : :
X(50247) = 8 X[230] - 7 X[9780], 4 X[325] - 5 X[3616], 4 X[551] - 3 X[41136], 11 X[5550] - 10 X[7925], 3 X[7809] - 4 X[11725], 2 X[7840] - 3 X[38314], 2 X[13174] - 3 X[33265], 2 X[13178] - 3 X[19570], 8 X[15480] - X[20053]

X(50247) lies on these lines: {1, 7779}, {8, 385}, {21, 17731}, {230, 9780}, {325, 3616}, {519, 1281}, {524, 3241}, {551, 41136}, {754, 7983}, {846, 17389}, {944, 32515}, {1580, 6542}, {2784, 40236}, {4425, 29584}, {5051, 10026}, {5550, 7925}, {5965, 7970}, {7809, 11725}, {7840, 38314}, {7985, 24695}, {8424, 17377}, {13174, 33265}, {13178, 19570}, {15480, 20053}, {20476, 37311}, {20536, 26117}

X(50247) = reflection of X(i) in X(j) for these {i,j}: {8, 385}, {7779, 1}


X(50248) = X(2)X(6)∩X(20)X(20105)

Barycentrics    3*a^4 + a^2*b^2 - b^4 + a^2*c^2 - 3*b^2*c^2 - c^4 : :
X(50248) = 15 X[2] - 16 X[230], 9 X[2] - 8 X[325], 3 X[2] - 4 X[385], 5 X[2] - 4 X[7840], 21 X[2] - 20 X[7925], 11 X[2] - 12 X[8859], 9 X[2] - 16 X[15480], 17 X[2] - 16 X[22110], 7 X[2] - 8 X[22329], 25 X[2] - 24 X[41133], 7 X[2] - 6 X[41136], 47 X[2] - 48 X[41139], 33 X[2] - 32 X[44377], 63 X[2] - 64 X[44381], 31 X[2] - 32 X[44401], 6 X[230] - 5 X[325], 4 X[230] - 5 X[385], 8 X[230] - 5 X[7779], 4 X[230] - 3 X[7840], 28 X[230] - 25 X[7925], 44 X[230] - 45 X[8859], 3 X[230] - 5 X[15480], 17 X[230] - 15 X[22110], 14 X[230] - 15 X[22329], 10 X[230] - 9 X[41133], 56 X[230] - 45 X[41136], 47 X[230] - 45 X[41139], 8 X[230] - 15 X[44367], 11 X[230] - 10 X[44377], 21 X[230] - 20 X[44381], 31 X[230] - 30 X[44401], 2 X[325] - 3 X[385], 4 X[325] - 3 X[7779], 10 X[325] - 9 X[7840], 14 X[325] - 15 X[7925], 22 X[325] - 27 X[8859], 17 X[325] - 18 X[22110], 7 X[325] - 9 X[22329], 25 X[325] - 27 X[41133], 28 X[325] - 27 X[41136], 47 X[325] - 54 X[41139], 4 X[325] - 9 X[44367], 11 X[325] - 12 X[44377], 7 X[325] - 8 X[44381], 31 X[325] - 36 X[44401], 5 X[385] - 3 X[7840], 7 X[385] - 5 X[7925], 11 X[385] - 9 X[8859], and many others

X(50248) lies on these lines: {2, 6}, {20, 20105}, {23, 47154}, {30, 35369}, {76, 20088}, {147, 5965}, {148, 754}, {194, 14023}, {316, 19570}, {340, 41358}, {511, 5984}, {523, 20063}, {538, 14712}, {690, 31374}, {732, 8782}, {736, 6658}, {1078, 7890}, {1353, 37455}, {2549, 9939}, {2896, 4045}, {3552, 32817}, {3564, 40236}, {3734, 34604}, {3767, 7946}, {3793, 13586}, {3849, 8596}, {3933, 33225}, {4590, 31068}, {4788, 20075}, {5007, 46226}, {5286, 7929}, {5305, 7939}, {5309, 7850}, {5319, 7938}, {5346, 7922}, {5355, 7883}, {5368, 7944}, {5992, 17770}, {5999, 34380}, {6179, 7836}, {6392, 33019}, {6655, 7754}, {6781, 8591}, {7408, 38294}, {7533, 36207}, {7746, 7949}, {7751, 7785}, {7755, 7917}, {7758, 7793}, {7762, 16044}, {7767, 7839}, {7768, 7797}, {7780, 7905}, {7790, 41748}, {7794, 10583}, {7798, 7811}, {7812, 17131}, {7827, 7848}, {7828, 7882}, {7829, 32027}, {7833, 22253}, {7845, 14568}, {7854, 7894}, {7856, 7896}, {7857, 7916}, {7879, 7920}, {7900, 32827}, {7906, 33259}, {7921, 33020}, {7924, 14929}, {8267, 8272}, {9751, 33749}, {9855, 47287}, {10313, 39352}, {10487, 25486}, {10989, 47155}, {11898, 13862}, {14036, 21309}, {14645, 14931}, {14976, 43619}, {15717, 21445}, {16316, 37909}, {16895, 43136}, {17165, 20056}, {19689, 30435}, {20072, 33889}, {35511, 46228}, {36811, 39091}, {40000, 40002}

X(50248) = reflection of X(i) in X(j) for these {i,j}: {2, 44367}, {325, 15480}, {7779, 385}, {20094, 14712}, {40898, 3181}, {40899, 3180}
X(50248) = orthoptic-circle-of-Steiner-circumellipe-inverse of X(32525)
X(50248) = anticomplement of X(7779)
X(50248) = anticomplement of the isogonal conjugate of X(46286)
X(50248) = anticomplement of the isotomic conjugate of X(11606)
X(50248) = isotomic conjugate of the anticomplement of X(39091)
X(50248) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {11606, 6327}, {17957, 1369}, {46286, 8}, {46289, 15588}, {46970, 7192}
X(50248) = X(11606)-Ceva conjugate of X(2)
X(50248) = X(39091)-cross conjugate of X(2)
X(50248) = crosssum of X(3124) and X(5113)
X(50248) = crossdifference of every pair of points on line {512, 5041}
X(50248) = barycentric product X(i)*X(j) for these {i,j}: {1916, 36811}, {11606, 39091}
X(50248) = barycentric quotient X(i)/X(j) for these {i,j}: {36811, 385}, {39091, 7779}
X(50248) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 7766, 2}, {183, 6144, 7837}, {325, 15480, 385}, {325, 22329, 44381}, {325, 44381, 7925}, {385, 7779, 2}, {385, 7840, 230}, {385, 7925, 22329}, {385, 39093, 7766}, {385, 39099, 39089}, {1078, 7890, 13571}, {3629, 37671, 3329}, {5286, 7929, 19690}, {6179, 7855, 7836}, {6189, 6190, 3589}, {7735, 7897, 2}, {7751, 7877, 7785}, {7754, 7893, 6655}, {7760, 7826, 2896}, {7762, 17129, 16044}, {7767, 7839, 33021}, {7768, 7805, 7797}, {7779, 44367, 385}, {14614, 40341, 3314}, {16995, 45962, 2}, {20065, 20081, 6658}, {22329, 41136, 2}, {39365, 39366, 6}, {44361, 44362, 69}


X(50249) = X(2)X(6)∩X(115)X(5207)

Barycentrics    3*a^6 + 2*a^2*b^4 - b^6 - a^2*b^2*c^2 - 2*b^4*c^2 + 2*a^2*c^4 - 2*b^2*c^4 - c^6 : :
X(50249) = 3 X[69] - 4 X[15993], 8 X[230] - 7 X[3619], 4 X[325] - 5 X[3618], 3 X[385] - 2 X[15993], 4 X[597] - 3 X[41136], 3 X[1992] - 2 X[39099], 3 X[7840] - 4 X[44380], 3 X[21356] - 4 X[22329], 4 X[115] - 3 X[5207], 4 X[2030] - 3 X[7799], 3 X[5182] - 2 X[7813], 2 X[11646] - 3 X[19570]

X(50249) lies on these lines: {2, 6}, {115, 5207}, {511, 9862}, {542, 43453}, {575, 7905}, {576, 7877}, {698, 20094}, {736, 7737}, {754, 10754}, {895, 43696}, {1351, 40250}, {2030, 7799}, {3926, 38905}, {5038, 13571}, {5039, 10348}, {5052, 45804}, {5182, 7813}, {5476, 7926}, {5965, 10753}, {5969, 14712}, {6776, 32515}, {7768, 44499}, {8288, 19577}, {9863, 11477}, {9983, 13330}, {9993, 35389}, {11646, 19570}, {14023, 32452}, {32220, 37906}, {34380, 35458}

X(50249) = reflection of X(i) in X(j) for these {i,j}: {69, 385}, {7779, 6}
X(50249) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6189, 6190, 7792}, {39365, 39366, 7766}


X(50250) = X(1)X(524)∩X(8)X(385)

Barycentrics    4*a^5 + 2*a^4*b - a^3*b^2 + a^2*b^3 + a*b^4 - b^5 + 2*a^4*c + a^2*b^2*c - b^4*c - a^3*c^2 + a^2*b*c^2 - 4*a*b^2*c^2 - 2*b^3*c^2 + a^2*c^3 - 2*b^2*c^3 + a*c^4 - b*c^4 - c^5 : :
>X(50250) = X[8] - 3 X[385], 2 X[10] - 3 X[22329], X[145] + 3 X[44367], 6 X[230] - 5 X[1698], 3 X[325] - 4 X[1125], 5 X[3616] - 3 X[7840], 7 X[3622] - 3 X[7779], 7 X[3624] - 6 X[22110], X[3633] + 6 X[15480], 2 X[6390] - 3 X[38221], 9 X[8859] - 7 X[9780], 10 X[19862] - 9 X[41133], 17 X[19872] - 18 X[41139], 13 X[34595] - 12 X[44377], 9 X[41136] - 13 X[46934]

X(50250) lies on these lines: {1, 524}, {8, 385}, {10, 22329}, {145, 44367}, {230, 1698}, {325, 1125}, {523, 48324}, {1580, 3712}, {2329, 18253}, {3616, 7840}, {3622, 7779}, {3624, 22110}, {3633, 15480}, {3793, 5184}, {4938, 8772}, {6390, 38221}, {7718, 38294}, {7845, 11725}, {8859, 9780}, {19862, 41133}, {19872, 41139}, {28558, 49550}, {32515, 34773}, {34595, 44377}, {41136, 46934}

X(50250) = reflection of X(i) in X(j) for these {i,j}: {5184, 3793}, {7845, 11725}


X(50251) = X(2)X(6)∩X(5)X(7877)

Barycentrics    4*a^4 + a^2*b^2 - b^4 + a^2*c^2 - 4*b^2*c^2 - c^4 : :
X(50251) = 9 X[2] - 10 X[230], 6 X[2] - 5 X[325], 3 X[2] - 5 X[385], 9 X[2] - 5 X[7779], 7 X[2] - 5 X[7840], 27 X[2] - 25 X[7925], 13 X[2] - 15 X[8859], 3 X[2] - 10 X[15480], 11 X[2] - 10 X[22110], 4 X[2] - 5 X[22329], 16 X[2] - 15 X[41133], 19 X[2] - 15 X[41136], 29 X[2] - 30 X[41139], X[2] - 5 X[44367], 21 X[2] - 20 X[44377], 39 X[2] - 40 X[44381], 19 X[2] - 20 X[44401], 4 X[230] - 3 X[325], 2 X[230] - 3 X[385], 14 X[230] - 9 X[7840], 6 X[230] - 5 X[7925], 26 X[230] - 27 X[8859], X[230] - 3 X[15480], 11 X[230] - 9 X[22110], 8 X[230] - 9 X[22329], 32 X[230] - 27 X[41133], 38 X[230] - 27 X[41136], 29 X[230] - 27 X[41139], 2 X[230] - 9 X[44367], 7 X[230] - 6 X[44377], 13 X[230] - 12 X[44381], 19 X[230] - 18 X[44401], 3 X[325] - 2 X[7779], 7 X[325] - 6 X[7840], 9 X[325] - 10 X[7925], 13 X[325] - 18 X[8859], X[325] - 4 X[15480], 11 X[325] - 12 X[22110], 2 X[325] - 3 X[22329], 8 X[325] - 9 X[41133], 19 X[325] - 18 X[41136], 29 X[325] - 36 X[41139], X[325] - 6 X[44367], 7 X[325] - 8 X[44377], 13 X[325] - 16 X[44381], 19 X[325] - 24 X[44401], 3 X[385] - X[7779], 7 X[385] - 3 X[7840], 9 X[385] - 5 X[7925], 13 X[385] - 9 X[8859], 11 X[385] - 6 X[22110], 4 X[385] - 3 X[22329], 16 X[385] - 9 X[41133], 19 X[385] - 9 X[41136], 29 X[385] - 18 X[41139], X[385] - 3 X[44367], 7 X[385] - 4 X[44377], 13 X[385] - 8 X[44381], 19 X[385] - 12 X[44401], 4 X[3631] - 5 X[15993], 7 X[7779] - 9 X[7840], 3 X[7779] - 5 X[7925], 13 X[7779] - 27 X[8859], X[7779] - 6 X[15480], 11 X[7779] - 18 X[22110], 4 X[7779] - 9 X[22329], 16 X[7779] - 27 X[41133], 19 X[7779] - 27 X[41136], 29 X[7779] - 54 X[41139], X[7779] - 9 X[44367], 7 X[7779] - 12 X[44377], 13 X[7779] - 24 X[44381], 19 X[7779] - 36 X[44401], 27 X[7840] - 35 X[7925], 13 X[7840] - 21 X[8859], 3 X[7840] - 14 X[15480], 11 X[7840] - 14 X[22110], 4 X[7840] - 7 X[22329], 16 X[7840] - 21 X[41133], 19 X[7840] - 21 X[41136], 29 X[7840] - 42 X[41139], X[7840] - 7 X[44367], 3 X[7840] - 4 X[44377], 39 X[7840] - 56 X[44381], 19 X[7840] - 28 X[44401], 65 X[7925] - 81 X[8859], 5 X[7925] - 18 X[15480], 55 X[7925] - 54 X[22110], and many others

X(50251) lies on these lines: {2, 6}, {5, 7877}, {76, 18907}, {98, 34380}, {99, 3793}, {140, 7905}, {187, 14148}, {194, 33275}, {340, 16318}, {523, 8664}, {538, 6781}, {550, 9821}, {736, 19687}, {754, 47286}, {1285, 32836}, {1353, 22712}, {1384, 32833}, {1513, 5965}, {1975, 33239}, {2549, 7750}, {3053, 32820}, {3530, 12054}, {3564, 43460}, {3851, 39663}, {3926, 46453}, {3933, 6179}, {4969, 33891}, {5008, 6661}, {5254, 7893}, {5305, 7768}, {5319, 7879}, {5346, 7896}, {5355, 6656}, {5368, 7849}, {5475, 7751}, {5477, 5976}, {5939, 14645}, {5984, 29181}, {6194, 8550}, {6704, 34571}, {7745, 17129}, {7755, 7882}, {7758, 21843}, {7760, 7767}, {7761, 41748}, {7780, 7890}, {7790, 14929}, {7798, 8356}, {7807, 7855}, {7809, 43291}, {7811, 15048}, {7813, 35297}, {7838, 32992}, {7845, 33228}, {7850, 33184}, {7894, 8362}, {7903, 33249}, {7904, 9607}, {7917, 8361}, {8352, 32457}, {8364, 32027}, {8370, 17131}, {9753, 11898}, {10299, 21445}, {11646, 36849}, {12007, 37455}, {13186, 33921}, {14907, 22253}, {15687, 34733}, {16315, 47629}, {16316, 37897}, {17328, 29634}, {20065, 32819}, {33706, 48906}, {46517, 47155}

X(50251) = reflection of X(i) in X(j) for these {i,j}: {99, 3793}, {325, 385}, {385, 15480}, {7779, 230}, {47287, 6781}
X(50251) = crossdifference of every pair of points on line {512, 7772}
X(50251) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 5304, 7868}, {69, 14614, 7792}, {183, 193, 41624}, {230, 7779, 325}, {325, 385, 22329}, {385, 7779, 230}, {385, 44367, 15480}, {1992, 15589, 11174}, {3630, 5306, 3314}, {5304, 7868, 7792}, {5346, 7896, 8363}, {5355, 7826, 7848}, {5355, 7848, 6656}, {6144, 8667, 7774}, {6189, 6190, 3618}, {7735, 20080, 7788}, {7754, 14023, 7750}, {7774, 8667, 37688}, {7805, 7826, 6656}, {7805, 7848, 5355}, {7840, 44377, 325}, {7868, 14614, 5304}, {9766, 17008, 37647}


X(50252) = X(2)X(6)∩X(115)X(540)

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

X(50252) lies on these lines: {2, 6}, {55, 17388}, {58, 21024}, {115, 540}, {171, 594}, {187, 519}, {237, 20475}, {523, 649}, {538, 6629}, {896, 4037}, {1100, 6682}, {1761, 16557}, {1914, 32919}, {2160, 2319}, {2329, 18253}, {3550, 17299}, {3684, 4969}, {3769, 49509}, {3943, 17735}, {4386, 17362}, {4434, 20693}, {5247, 21025}, {10453, 21793}, {12513, 37023}, {17303, 37604}, {17366, 24586}, {17448, 37592}, {23897, 49745}, {23905, 49728}

X(50252) = midpoint of X(385) and X(17731)
X(50252) = reflection of X(i) in X(j) for these {i,j}: {325, 44379}, {10026, 230}
X(50252) = crossdifference of every pair of points on line {386, 512}
X(50252) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {333, 40750, 1213}, {4386, 32853, 17362}, {6189, 6190, 17379}, {26244, 41629, 6}, {39022, 39023, 17398}


X(50253) = X(2)X(6)∩X(511)X(10991)

Barycentrics    4*a^6 + a^4*b^2 + 2*a^2*b^4 - b^6 + a^4*c^2 - 2*a^2*b^2*c^2 - 3*b^4*c^2 + 2*a^2*c^4 - 3*b^2*c^4 - c^6 : :
X(50253) = 4 X[6] - 3 X[41146], X[69] - 3 X[385], 2 X[69] - 3 X[15993], 2 X[141] - 3 X[22329], X[193] + 3 X[44367], 6 X[230] - 5 X[3763], 3 X[325] - 4 X[3589], 5 X[3618] - 3 X[7840], 7 X[3619] - 9 X[8859], X[6144] + 6 X[15480], 6 X[22110] - 7 X[47355], 3 X[1691] - 2 X[6390], 3 X[2482] - 4 X[38010], 6 X[46998] - 5 X[47452]

X(50253) lies on these lines: {2, 6}, {511, 10991}, {538, 14928}, {575, 7890}, {736, 35432}, {1503, 43453}, {1691, 6390}, {2030, 7813}, {2482, 38010}, {3793, 5104}, {3818, 35389}, {7826, 44499}, {8550, 12251}, {32515, 41747}, {46998, 47452}

X(50253) = reflection of X(i) in X(j) for these {i,j}: {5104, 3793}, {7779, 44380}, {7813, 2030}, {15993, 385}
X(50253) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 7806, 141}, {6189, 6190, 16989}


X(50254) = X(1)X(230)∩X(8)X(385)

Barycentrics    2*a^4*b + a^3*b^2 - a^2*b^3 - a*b^4 + b^5 + 2*a^4*c - a^2*b^2*c + b^4*c + a^3*c^2 - a^2*b*c^2 - 2*b^3*c^2 - a^2*c^3 - 2*b^2*c^3 - a*c^4 + b*c^4 + c^5 : :
X(50254) = X[944] - 3 X[21445], 2 X[946] - 3 X[39663], 5 X[1698] - 4 X[44377], X[3241] - 3 X[8859], 5 X[3617] - X[7779], 7 X[3624] - 8 X[44381], 4 X[3828] - 3 X[41133], 5 X[4668] + 2 X[15480], 5 X[7925] - 7 X[9780], X[7970] - 3 X[38227], X[7983] - 3 X[14568], X[9884] - 3 X[26613], 6 X[10256] - 7 X[31423], 2 X[11711] - 3 X[35297], 3 X[19875] - 2 X[22110], 3 X[25055] - 4 X[44401], 3 X[38047] - 2 X[44380], 3 X[38220] - 4 X[43291]

X(50254) lies on these lines: {1, 230}, {8, 385}, {10, 325}, {30, 5184}, {238, 1146}, {291, 40663}, {511, 40608}, {518, 15993}, {519, 22329}, {523, 10015}, {524, 3416}, {944, 21445}, {946, 39663}, {952, 11364}, {984, 30358}, {1503, 9860}, {1698, 44377}, {3241, 8859}, {3564, 9864}, {3617, 7779}, {3624, 44381}, {3828, 41133}, {4668, 15480}, {5690, 12782}, {7925, 9780}, {7970, 38227}, {7983, 14568}, {8256, 46032}, {8298, 44669}, {9884, 26613}, {10256, 31423}, {11711, 35297}, {13911, 44394}, {13973, 44392}, {19875, 22110}, {23902, 28369}, {25055, 44401}, {26300, 49347}, {26301, 49348}, {34379, 44369}, {35080, 35110}, {38047, 44380}, {38220, 43291}

X(50254) = midpoint of X(i) and X(j) for these {i,j}: {8, 385}, {5184, 13178}
X(50254) = reflection of X(i) in X(j) for these {i,j}: {1, 230}, {325, 10}
X(50254) = crossdifference of every pair of points on line {2278, 41159}


X(50255) = X(55)X(192)∩X(190)X(1580)

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

X(50255) lies on these lines: {21, 19623}, {55, 192}, {190, 1580}, {230, 2345}, {256, 4360}, {325, 17321}, {523, 4491}, {524, 3241}, {536, 1281}, {846, 3769}, {1284, 32922}, {1999, 17611}, {2667, 3979}, {3875, 8245}, {3905, 8931}, {3923, 4234}, {4425, 17320}, {5051, 44396}, {17731, 35623}, {22329, 50107}, {26117, 44370}


leftri

Points in a [[(b^2 - c^2, c^2 - a^2, a^2 - b^2 ], [(b^4 - c^4, c^4 - a^4, a^4 - b^4 ]] coordinate system: X(50256)-X(50279)

rightri

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

L1 is the line: (b^2 - c^2) α + (c^2 - a^2) β + (a^2 - b^2) γ = 0.

L2 is the line (b^4 - c^4) α + (c^4 - a^4) β + (a^4 - b^4) γ = 0.

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

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

u : v : w = (a^2 - b^2)(a^2 - c^2)(b^2 - c^2) + (-2a^2 + b^2 + c^2) x + (2a^4 - b^4 - c^4) y : : ,

where, as functions of a, b, c, the coordinate x is antisymmetric of degree 4, and y is antisymmetric of degree 2.

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

{-2 (a-b) (a-c) (b-c) (a+b+c), -((2 (a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2))}, 50183
{-((2 (a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c)), -((2 (a-b) (a-c) (b-c))/(a+b+c))}, 50184
{-((2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c)), (2 (a-b) (a-c) (b-c))/(a+b+c)}, 50234
{-((a-b) (a-c) (b-c) (a+b+c)), -((2 (a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2))}, 50166
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c)), -((2 (a-b) (a-c) (b-c))/(a+b+c))}, 49735
{-((a-b) (a-c) (b-c) (a+b+c)), -(((a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2))}, 50178
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c)), -(((a-b) (a-c) (b-c))/(a+b+c))}, 50179
{-((a-b) (a-c) (b-c) (a+b+c)), 0}, 42045
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c)), 0}, 49749
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c)), ((a-b) (a-c) (b-c))/(a+b+c)}, 49744
{-(1/2) (a-b) (a-c) (b-c) (a+b+c), -(((a-b) (a-c) (b-c))/(a+b+c))}, 50235
{-(1/2) (a-b) (a-c) (b-c) (a+b+c), -(((a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2))}, 50167
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a+b+c))), -(((a-b) (a-c) (b-c))/(a+b+c))}, 13745
{-(1/2) (a-b) (a-c) (b-c) (a+b+c), -(((a-b) (a-c) (b-c) (a+b+c))/(2 (a^2+b^2+c^2)))}, 50173
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a+b+c))), -(((a-b) (a-c) (b-c))/(2 (a+b+c)))}, 50174
{-(1/2) (a-b) (a-c) (b-c) (a+b+c), 0}, 37631
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a+b+c))), 0}, 50180
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a+b+c))), ((a-b) (a-c) (b-c))/(2 (a+b+c))}, 50226
{0, -(((a-b) (a-c) (b-c))/(a+b+c))}, 50157
{0, -(((a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2))}, 50217
{0, -(((a-b) (a-c) (b-c))/(2 (a+b+c)))}, 50161
{0, -(((a-b) (a-c) (b-c) (a+b+c))/(2 (a^2+b^2+c^2)))}, 50222
{0, 0}, 2
{0, ((a-b) (a-c) (b-c))/(2 (a+b+c))}, 50228
{0, ((a-b) (a-c) (b-c) (a+b+c))/(2 (a^2+b^2+c^2))}, 50227
{0, ((a-b) (a-c) (b-c))/(a+b+c)}, 50232
{0, ((a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2)}, 50181
{0, (2 (a-b) (a-c) (b-c))/(a+b+c)}, 50186
{((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a+b+c)), -(((a-b) (a-c) (b-c))/(2 (a+b+c)))}, 49729
{1/2 (a-b) (a-c) (b-c) (a+b+c), 0}, 49724
{((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a+b+c)), 0}, 50158
{1/2 (a-b) (a-c) (b-c) (a+b+c), ((a-b) (a-c) (b-c) (a+b+c))/(2 (a^2+b^2+c^2))}, 50162
{((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a+b+c)), ((a-b) (a-c) (b-c))/(2 (a+b+c))}, 50163
{1/2 (a-b) (a-c) (b-c) (a+b+c), ((a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2)}, 50168
{((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a+b+c)), ((a-b) (a-c) (b-c))/(a+b+c)}, 50169
{((a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c), -(((a-b) (a-c) (b-c))/(a+b+c))}, 49723
{(a-b) (a-c) (b-c) (a+b+c), 0}, 3578
{((a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c), 0}, 49717
{(a-b) (a-c) (b-c) (a+b+c), ((a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2)}, 50159
{((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c), ((a-b) (a-c) (b-c))/(a+b+c)}, 50160
{(a-b) (a-c) (b-c) (a+b+c), (2 (a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2)}, 50170
{((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c), (2 (a-b) (a-c) (b-c))/(a+b+c)}, 50171
{(2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a+b+c), -((2 (a-b) (a-c) (b-c))/(a+b+c))}, 50215
{2 (a-b) (a-c) (b-c) (a+b+c), (2 (a-b) (a-c) (b-c) (a+b+c))/(a^2+b^2+c^2)}, 50154
{(2 (a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a+b+c), (2 (a-b) (a-c) (b-c))/(a+b+c)}, 50155
{-2*(a - b)*(a - c)*(b - c)*(a + b + c), 0}, 50256
{(-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c), 0}, 50257
{(-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c), ((a - b)*(a - c)*(b - c))/(a + b + c)}, 50258
{-((a - b)*(a - c)*(b - c)*(a + b + c)), -(((a - b)*(a - c)*(b - c))/(a + b + c))}, 50259
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)), -(((a - b)*(a - c)*(b - c))/(a + b + c))}, 50260
{-(((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c)), 0}, 50261
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)), ((a - b)*(a - c)*(b - c))/(2*(a + b + c))}, 50262
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c)), (2*(a - b)*(a - c)*(b - c))/(a + b + c)}, 50263
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), -1/2*((a - b)*(a - c)*(b - c))/(a + b + c)}, 50264
{-1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c), 0}, 50265
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)), ((a - b)*(a - c)*(b - c))/(2*(a + b + c))}, 50266
{0, (-2*(a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2)}, 50267
{0, -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c)}, 50268
{0, (2*(a - b)*(a - c)*(b - c)*(a + b + c))/(a^2 + b^2 + c^2)}, 50269
{((a - b)*(a - c)*(b - c)*(a + b + c))/2, -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b + a*c + b*c)}, 50270
{((a - b)*(a - c)*(b - c)*(a + b + c))/2, ((a - b)*(a - c)*(b - c))/(2*(a + b + c))}, 50271
{(a - b)*(a - c)*(b - c)*(a + b + c), -(((a - b)*(a - c)*(b - c))/(a + b + c))}, 50272
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c), -1/2*((a - b)*(a - c)*(b - c))/(a + b + c)}, 50273
{((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a + b + c), 0}, 50274
{(a - b)*(a - c)*(b - c)*(a + b + c), ((a - b)*(a - c)*(b - c))/(a + b + c)}, 50275
{(2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c), -(((a - b)*(a - c)*(b - c))/(a + b + c))}, 50276
{2*(a - b)*(a - c)*(b - c)*(a + b + c), 0}, 50277
{(2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a + b + c), 0}, 50278
{2*(a - b)*(a - c)*(b - c)*(a + b + c), (2*(a - b)*(a - c)*(b - c))/(a + b + c)}, 50279


X(50256) = X(2)X(6)∩X(30)X(145)

Barycentrics    4*a^3 + 5*a^2*b - a*b^2 - 2*b^3 + 5*a^2*c + 2*a*b*c - b^2*c - a*c^2 - b*c^2 - 2*c^3 : :
X(50256) = 3 X[2] - 4 X[37631], 5 X[2] - 4 X[49724], 9 X[2] - 8 X[49730], X[3578] - 3 X[42045], 5 X[3578] - 6 X[49724], 3 X[3578] - 4 X[49730], 2 X[37631] - 3 X[42045], 5 X[37631] - 3 X[49724], 3 X[37631] - 2 X[49730], 5 X[42045] - 2 X[49724], 9 X[42045] - 4 X[49730], 9 X[49724] - 10 X[49730], 5 X[3616] - 4 X[49729], 5 X[3617] - 8 X[49743], X[3621] - 4 X[49745], 7 X[3622] - 4 X[49716], 5 X[3623] - 4 X[49739], 5 X[3876] - 8 X[10108], 3 X[50178] - 2 X[50219], 3 X[50154] - 4 X[50223], 3 X[50181] - 2 X[50223], 5 X[20052] - 8 X[49734], 4 X[23812] - 3 X[27812], 3 X[38314] - 2 X[49723], 11 X[46933] - 8 X[49718]

X(50256) lies on these lines: {1, 50215}, {2, 6}, {8, 49744}, {30, 145}, {319, 6539}, {320, 45222}, {511, 4430}, {519, 17164}, {527, 25254}, {540, 3241}, {542, 5992}, {553, 17495}, {754, 50183}, {1999, 4080}, {2403, 6002}, {3187, 4654}, {3616, 49729}, {3617, 49743}, {3621, 49745}, {3622, 49716}, {3623, 49739}, {3876, 10108}, {3879, 3995}, {3969, 7277}, {4202, 48861}, {4393, 50178}, {4644, 20017}, {4649, 20290}, {4697, 4938}, {4725, 4980}, {4754, 20055}, {5434, 20040}, {6542, 50154}, {10032, 31301}, {10385, 20064}, {11319, 48870}, {15677, 20077}, {17147, 17364}, {17162, 33097}, {17230, 50162}, {17248, 30562}, {17389, 25237}, {17770, 27804}, {19998, 49732}, {20011, 49719}, {20052, 49734}, {23812, 27812}, {28840, 47900}, {31029, 40940}, {31064, 32004}, {31145, 50171}, {32025, 43260}, {32859, 50068}, {38314, 49723}, {42044, 50132}, {46933, 49718}

X(50256) = reflection of X(i) in X(j) for these {i,j}: {2, 42045}, {8, 49744}, {3578, 37631}, {31145, 50171}, {50154, 50181}, {50165, 3241}, {50172, 50234}, {50215, 1}
X(50256) = anticomplement of X(3578)
X(50256) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2160, 2891}, {6186, 41821}, {28615, 3648}
X(50256) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {599, 19738, 2}, {2895, 8025, 27081}, {2895, 20090, 8025}, {3578, 37631, 2}, {3578, 42045, 37631}, {17778, 20086, 16704}, {31143, 42028, 2}, {41816, 42025, 2}


X(50257) = X(2)X(6)∩X(519)X(50155)

Barycentrics    5*a^3*b + 2*a^2*b^2 - a*b^3 + 5*a^3*c + 8*a^2*b*c + 2*a*b^2*c - b^3*c + 2*a^2*c^2 + 2*a*b*c^2 + 2*b^2*c^2 - a*c^3 - b*c^3 : :
X(50257) = 5 X[2] - 4 X[50158], 3 X[2] - 4 X[50180], X[49717] - 3 X[49749], 5 X[49717] - 6 X[50158], 5 X[49749] - 2 X[50158], 3 X[49749] - 2 X[50180], 3 X[50158] - 5 X[50180], X[145] + 2 X[4754], 5 X[3616] - 4 X[50174], 3 X[38314] - 2 X[50179]

X(50257) lies on these lines: {1, 50184}, {2, 6}, {8, 50160}, {42, 4667}, {145, 4754}, {511, 1002}, {519, 50155}, {527, 4343}, {536, 25295}, {538, 3241}, {540, 48830}, {754, 50234}, {1100, 20347}, {1742, 42042}, {3616, 50174}, {4363, 20011}, {4644, 17018}, {4649, 13576}, {4651, 4670}, {4747, 20012}, {16667, 30949}, {17145, 25368}, {17169, 20970}, {17179, 46913}, {17389, 50154}, {24690, 29822}, {29584, 50183}, {38314, 50179}, {49735, 50235}, {49744, 50186}, {50157, 50215}, {50171, 50185}

X(50257) = reflection of X(i) in X(j) for these {i,j}: {2, 49749}, {8, 50160}, {49717, 50180}, {49735, 50235}, {50171, 50185}, {50184, 1}, {50186, 49744}, {50215, 50157}
X(50257) = anticomplement of X(49717)
X(50257) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20090, 40721, 30941}, {49717, 49749, 50180}, {49717, 50180, 2}


X(50258) = X(2)X(1171)∩X(6)X(25468)

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

X(50258) lies on these lines: {2, 1171}, {6, 25468}, {148, 20090}, {524, 3416}, {538, 17389}, {540, 48822}, {543, 3241}, {754, 50234}, {3578, 50163}, {3892, 15309}, {7277, 21711}, {29597, 37631}, {39586, 49743}, {49495, 49745}, {49717, 50226}, {49723, 50180}, {50161, 50215}

X(50258) = reflection of X(i) in X(j) for these {i,j}: {3578, 50163}, {49717, 50226}, {49723, 50180}, {50157, 49749}, {50160, 50185}, {50179, 37631}, {50215, 50161}, {50232, 49744}


X(50259) = X(1)X(524)∩X(2)X(20970)

Barycentrics    5*a^3*b + 3*a^2*b^2 - a*b^3 + 5*a^3*c + 8*a^2*b*c + 2*a*b^2*c - b^3*c + 3*a^2*c^2 + 2*a*b*c^2 - a*c^3 - b*c^3 : :
X(50259) = 2 X[3244] + X[4754], 3 X[25055] - 2 X[50158], 3 X[38314] - 2 X[50174]

X(50259) lies on these lines: {1, 524}, {2, 20970}, {8, 50163}, {145, 50155}, {213, 29574}, {239, 50228}, {519, 49749}, {538, 3241}, {551, 49717}, {599, 25499}, {754, 29584}, {1992, 5283}, {2650, 35103}, {3244, 4754}, {3578, 29580}, {3679, 50180}, {3849, 50175}, {4297, 48909}, {4393, 50186}, {6161, 28840}, {7775, 31179}, {8584, 16552}, {14712, 20090}, {16834, 37631}, {16971, 28369}, {17389, 50159}, {25055, 50158}, {29597, 49724}, {33954, 46922}, {38314, 50174}, {49488, 50226}, {50215, 50221}

X(50259) = midpoint of X(145) and X(50155)
X(50259) = reflection of X(i) in X(j) for these {i,j}: {8, 50163}, {3578, 50161}, {3679, 50180}, {49717, 551}, {50157, 50235}, {50160, 49749}, {50179, 1}, {50215, 50221}, {50232, 37631}
X(50259) = {X(29584),X(42045)}-harmonic conjugate of X(50178)


X(50260) = X(1)X(524)∩X(2)X(4251)

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

X(50260) lies on these lines: {1, 524}, {2, 4251}, {540, 48830}, {543, 4754}, {754, 49744}, {3578, 29574}, {3970, 50093}, {7775, 37693}, {7810, 24512}, {7812, 37632}, {9939, 17379}, {14210, 27705}, {16784, 28369}, {29573, 49724}, {29633, 50228}, {29659, 50163}, {36479, 50155}, {37631, 50217}, {49717, 50161}, {49743, 50216}, {50180, 50232}, {50186, 50226}

X(50260) = reflection of X(i) in X(j) for these {i,j}: {1, 50235}, {49717, 50161}, {49723, 50157}, {49744, 49749}, {50186, 50226}, {50232, 50180}


X(50261) = X(2)X(6)∩X(30)X(48856)

Barycentrics    2*a^4 + a^3*b + 3*a^2*b^2 + a*b^3 - b^4 + a^3*c + 4*a^2*b*c + 4*a*b^2*c + b^3*c + 3*a^2*c^2 + 4*a*b*c^2 + a*c^3 + b*c^3 - c^4 : :
X(50261) = 3 X[50171] - 4 X[50229], 2 X[50229] - 3 X[50232], 3 X[38314] - 2 X[50235]

X(50261) lies on these lines: {2, 6}, {30, 48856}, {527, 42039}, {538, 50171}, {540, 48854}, {754, 49735}, {1961, 24712}, {4667, 4722}, {5311, 24694}, {7758, 16454}, {14023, 16342}, {19336, 34511}, {24685, 29688}, {38314, 50235}, {39587, 49745}, {50155, 50169}, {50157, 50174}, {50160, 50228}

X(50261) = midpoint of X(50184) and X(50186)
X(50261) = reflection of X(i) in X(j) for these {i,j}: {3578, 49717}, {49735, 50179}, {50155, 50169}, {50157, 50174}, {50160, 50228}, {50171, 50232}


X(50262) = X(1)X(543)∩X(10)X(524)

Barycentrics    2*a^4 + 6*a^3*b + 4*a^2*b^2 - b^4 + 6*a^3*c + 12*a^2*b*c + 6*a*b^2*c + 4*a^2*c^2 + 6*a*b*c^2 + 4*b^2*c^2 - c^4 : :

X(50262) lies on these lines: {1, 543}, {2, 1171}, {10, 524}, {538, 3175}, {540, 50161}, {594, 31013}, {671, 6625}, {754, 49744}, {2482, 17103}, {3849, 49745}, {5712, 34511}, {6542, 50155}, {7621, 24883}, {7810, 37632}, {7812, 17379}, {7827, 20132}, {8682, 23812}, {16826, 50179}, {19765, 34504}, {23903, 36523}, {24051, 24076}, {29615, 42045}, {34506, 37522}, {50157, 50234}

X(50262) = midpoint of X(i) and X(j) for these {i,j}: {37631, 50185}, {42045, 50160}, {49744, 49749}, {49745, 50235}, {50157, 50234}
X(50262) = reflection of X(i) in X(j) for these {i,j}: {50161, 50180}, {50228, 50226}


X(50263) = X(1)X(3849)∩X(8)X(524)

Barycentrics    4*a^4 + 3*a^3*b + 2*a^2*b^2 - 2*b^4 + 3*a^3*c + 6*a^2*b*c + 3*a*b^2*c + 2*a^2*c^2 + 3*a*b*c^2 + 2*b^2*c^2 - 2*c^4 : :
X(50263) = X[4754] - 4 X[49745], 3 X[25055] - 2 X[50221]

X(50263) lies on these lines: {1, 3849}, {8, 524}, {540, 48809}, {754, 49744}, {3679, 50229}, {6625, 44367}, {7775, 37522}, {7812, 24512}, {7840, 17103}, {8352, 23903}, {9939, 37632}, {19856, 49723}, {24704, 41312}, {25055, 50221}, {34506, 37693}, {37631, 50166}, {49743, 50235}, {50157, 50226}, {50158, 50215}

X(50263) = midpoint of X(50186) and X(50234)
X(50263) = reflection of X(i) in X(j) for these {i,j}: {3679, 50229}, {49717, 50232}, {49723, 50228}, {49749, 49744}, {50157, 50226}, {50215, 50158}, {50235, 49743}


X(50264) = X(1)X(538)∩X(524)X(551)

Barycentrics    6*a^3*b + 5*a^2*b^2 + 6*a^3*c + 12*a^2*b*c + 6*a*b^2*c + 5*a^2*c^2 + 6*a*b*c^2 + 2*b^2*c^2 : :
X(50264) = 5 X[1] + X[4754], X[4754] - 5 X[49749], 3 X[25055] - X[49717], 3 X[38314] - X[50179]

X(50264) lies on these lines: {1, 538}, {2, 20970}, {519, 50163}, {524, 551}, {540, 50221}, {543, 49739}, {754, 37631}, {1125, 50158}, {1509, 13586}, {3241, 50160}, {3736, 19276}, {3849, 49744}, {4340, 47102}, {4909, 15985}, {5969, 41193}, {7757, 17379}, {9466, 37632}, {12150, 20132}, {24512, 44562}, {25055, 49717}, {29574, 50162}, {37522, 46893}, {38314, 50179}, {42045, 50157}, {50114, 50228}, {50226, 50229}

X(50264) = midpoint of X(i) and X(j) for these {i,j}: {1, 49749}, {3241, 50160}, {37631, 50235}, {42045, 50157}, {49739, 50185}
X(50264) = reflection of X(i) in X(j) for these {i,j}: {50158, 1125}, {50163, 50180}, {50174, 551}, {50229, 50226}


X(50265) = X(2)X(6)∩X(30)X(48854)

Barycentrics    2*a^4 + 2*a^3*b + 5*a^2*b^2 + 2*a*b^3 - b^4 + 2*a^3*c + 8*a^2*b*c + 8*a*b^2*c + 2*b^3*c + 5*a^2*c^2 + 8*a*b*c^2 + 2*b^2*c^2 + 2*a*c^3 + 2*b*c^3 - c^4 : :
X(50265) = 3 X[13745] - 2 X[50221], 3 X[50174] - X[50221]

X(50265) lies on these lines: {2, 6}, {30, 48854}, {538, 50169}, {543, 50229}, {551, 50235}, {754, 13745}, {3058, 41312}, {4364, 4799}, {4708, 41002}, {7758, 16458}, {14023, 16343}, {16830, 49745}, {19290, 34511}, {39586, 49743}, {39587, 49734}, {49735, 50186}, {50171, 50184}, {50185, 50226}

X(50265) = midpoint of X(i) and X(j) for these {i,j}: {49735, 50186}, {50171, 50184}, {50179, 50232}
X(50265) = reflection of X(i) in X(j) for these {i,j}: {13745, 50174}, {49724, 50158}, {50169, 50228}, {50185, 50226}, {50235, 551}


X(50266) = X(1)X(3849)∩X(10)X(524)

Barycentrics    4*a^4 + 6*a^3*b + 5*a^2*b^2 - 2*b^4 + 6*a^3*c + 12*a^2*b*c + 6*a*b^2*c + 5*a^2*c^2 + 6*a*b*c^2 + 2*b^2*c^2 - 2*c^4 : :
X(50266) = 3 X[37631] - X[50235]

X(50266) lies on these lines: {1, 3849}, {10, 524}, {519, 50229}, {538, 49744}, {540, 50174}, {543, 49745}, {551, 50221}, {754, 37631}, {940, 7775}, {1509, 7840}, {4340, 34511}, {4393, 50186}, {5718, 34506}, {6625, 11054}, {7883, 20132}, {14762, 29438}, {17103, 39785}, {17397, 50157}, {29617, 42045}, {50179, 50234}

X(50266) = midpoint of X(i) and X(j) for these {i,j}: {42045, 50232}, {50179, 50234}
X(50266) = reflection of X(i) in X(j) for these {i,j}: {50163, 50226}, {50221, 551}


X(50267) = X(2)X(32)∩X(8)X(30)

Barycentrics    4*a^5 + 3*a^4*b - a^3*b^2 - a^2*b^3 - 3*a*b^4 - 2*b^5 + 3*a^4*c - 2*a^3*b*c - 2*a^2*b^2*c - 2*a*b^3*c - 3*b^4*c - a^3*c^2 - 2*a^2*b*c^2 - 2*a*b^2*c^2 - b^3*c^2 - a^2*c^3 - 2*a*b*c^3 - b^2*c^3 - 3*a*c^4 - 3*b*c^4 - 2*c^5 : :
X(50267) = 3 X[2] - 4 X[50222], 5 X[2] - 4 X[50227], X[50181] - 3 X[50217], 5 X[50181] - 6 X[50227], 3 X[50217] - 2 X[50222], 5 X[50217] - 2 X[50227], 5 X[50222] - 3 X[50227], 4 X[50216] - X[50234]

X(50267) lies on these lines: {2, 32}, {8, 30}, {524, 49747}, {1150, 36731}, {3849, 50159}, {4393, 50178}, {7761, 19742}, {14929, 18139}, {24271, 43990}, {26626, 37631}, {29593, 50162}, {42045, 50167}, {48802, 49723}, {48856, 49735}, {49488, 50176}, {49724, 50170}, {49729, 50233}, {50182, 50220}, {50216, 50234}

X(50267) = reflection of X(i) in X(j) for these {i,j}: {2, 50217}, {42045, 50167}, {50154, 3578}, {50170, 49724}, {50178, 50219}, {50181, 50222}, {50182, 50220}, {50183, 50166}, {50233, 49729}
X(50267) = anticomplement of X(50181)
X(50267) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {50181, 50217, 50222}, {50181, 50222, 2}


X(50268) = X(2)X(32)∩X(37)X(524)

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

X(50268) lies on these lines: {2, 32}, {37, 524}, {405, 48839}, {540, 551}, {3578, 17310}, {5259, 49723}, {7759, 16349}, {7768, 19224}, {7794, 19237}, {29580, 42045}, {29594, 49724}, {48853, 50169}, {49735, 50178}, {50155, 50218}, {50160, 50170}, {50173, 50221}

X(50268) = {X(50161),X(50227)}-harmonic conjugate of X(2)


X(50269) = X(2)X(32)∩X(30)X(944)

Barycentrics    4*a^5 + 5*a^4*b + a^3*b^2 + a^2*b^3 - a*b^4 - 2*b^5 + 5*a^4*c + 2*a^3*b*c + 2*a^2*b^2*c + 2*a*b^3*c - b^4*c + a^3*c^2 + 2*a^2*b*c^2 + 2*a*b^2*c^2 + b^3*c^2 + a^2*c^3 + 2*a*b*c^3 + b^2*c^3 - a*c^4 - b*c^4 - 2*c^5 : :
X(50269) = 5 X[2] - 4 X[50222], 3 X[2] - 4 X[50227], 3 X[50181] - X[50217], 5 X[50181] - 2 X[50222], 3 X[50181] - 2 X[50227], 5 X[50217] - 6 X[50222], 3 X[50222] - 5 X[50227], X[50234] + 2 X[50236]

X(50269) lies on these lines: {2, 32}, {30, 944}, {524, 49721}, {540, 50233}, {3578, 50168}, {3849, 50178}, {4045, 19743}, {7761, 19717}, {11287, 19738}, {18139, 18907}, {24275, 43990}, {37631, 50166}, {48830, 49744}, {48849, 50171}, {49735, 50231}, {50165, 50182}

X(50269) = reflection of X(i) in X(j) for these {i,j}: {2, 50181}, {3578, 50168}, {49735, 50231}, {50154, 50170}, {50165, 50182}, {50166, 37631}, {50183, 42045}, {50217, 50227}
X(50269) = anticomplement of X(50217)
X(50269) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {50181, 50217, 50227}, {50217, 50227, 2}


X(50270) = X(2)X(58)∩X(37)X(524)

Barycentrics    2*a^5 + 4*a^4*b - 3*a^2*b^3 - 2*a*b^4 - b^5 + 4*a^4*c + 2*a^3*b*c - 7*a^2*b^2*c - 7*a*b^3*c - 2*b^4*c - 7*a^2*b*c^2 - 10*a*b^2*c^2 - 3*b^3*c^2 - 3*a^2*c^3 - 7*a*b*c^3 - 3*b^2*c^3 - 2*a*c^4 - 2*b*c^4 - c^5 : :

X(50270) lies on these lines: {2, 58}, {30, 50095}, {37, 524}, {316, 333}, {754, 49724}, {3578, 17294}, {3679, 50170}, {3912, 49716}, {16833, 50166}, {16834, 49735}, {17023, 49728}, {19723, 50057}, {24603, 49745}, {29597, 42045}, {37631, 50174}, {41140, 50167}, {41229, 41814}, {48802, 50233}, {49717, 50181}


X(50271) = X(2)X(20970)∩X(10)X(524)

Barycentrics    2*a^3*b - 3*a^2*b^2 - 4*a*b^3 + 2*a^3*c - 4*a^2*b*c - 10*a*b^2*c - 4*b^3*c - 3*a^2*c^2 - 10*a*b*c^2 - 6*b^2*c^2 - 4*a*c^3 - 4*b*c^3 : :
X(50271) = 5 X[3617] - X[50155], 3 X[19875] - X[49749]

X(50271) lies on these lines: {2, 20970}, {8, 50179}, {10, 524}, {316, 1654}, {519, 50158}, {538, 3679}, {540, 50229}, {754, 49724}, {1500, 29615}, {3578, 50232}, {3617, 50155}, {3661, 50157}, {3828, 50180}, {3849, 49723}, {3912, 50235}, {4042, 50073}, {16589, 31144}, {19875, 49749}, {21070, 49737}, {29593, 50186}, {29594, 49730}, {49729, 50221}, {50095, 50173}

X(50271) = midpoint of X(i) and X(j) for these {i,j}: {8, 50179}, {3578, 50232}, {3679, 49717}
X(50271) = reflection of X(i) in X(j) for these {i,j}: {50161, 49730}, {50163, 10}, {50174, 50158}, {50180, 3828}, {50221, 49729}


X(50272) = X(1)X(524)∩X(8)X(3849)

Barycentrics    4*a^4 + 3*a^3*b - a^2*b^2 - 3*a*b^3 - 2*b^4 + 3*a^3*c - 6*a*b^2*c - 3*b^3*c - a^2*c^2 - 6*a*b*c^2 - 4*b^2*c^2 - 3*a*c^3 - 3*b*c^3 - 2*c^4 : :
X(50272) = 3 X[50157] - 2 X[50235]

X(50272) lies on these lines: {1, 524}, {8, 3849}, {538, 50215}, {540, 50160}, {599, 33953}, {754, 3578}, {1150, 7775}, {3241, 50221}, {5741, 34506}, {7840, 34016}, {29593, 50186}, {29610, 50228}, {42045, 50161}, {44367, 46707}, {49724, 50232}, {50163, 50234}

X(50272) = reflection of X(i) in X(j) for these {i,j}: {3241, 50221}, {42045, 50161}, {50179, 49723}, {50232, 49724}, {50234, 50163}


X(50273) = X(2)X(1171)∩X(524)X(551)

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

X(50273) lies on these lines: {2, 1171}, {99, 1654}, {524, 551}, {538, 42051}, {540, 50158}, {543, 3679}, {594, 24074}, {754, 49717}, {3578, 29584}, {3956, 15309}, {4115, 17332}, {17251, 19276}, {40891, 50184}, {49728, 50221}, {49730, 50163}, {50215, 50232}

X(50273) = midpoint of X(i) and X(j) for these {i,j}: {3578, 50179}, {49717, 49723}, {50215, 50232}
X(50273) = reflection of X(i) in X(j) for these {i,j}: {50161, 49729}, {50163, 49730}, {50221, 49728}, {50228, 50158}


X(50274) = X(2)X(6)∩X(30)X(48849)

Barycentrics    2*a^4 - a^3*b - a^2*b^2 - a*b^3 - b^4 - a^3*c - 4*a^2*b*c - 4*a*b^2*c - b^3*c - a^2*c^2 - 4*a*b*c^2 - 4*b^2*c^2 - a*c^3 - b*c^3 - c^4 : :
X(50274) = 3 X[49735] - 4 X[50221], 3 X[50157] - 2 X[50221]

X(50274) lies on these lines: {2, 6}, {30, 48849}, {538, 49735}, {540, 48851}, {754, 50160}, {3241, 50235}, {4363, 4450}, {7758, 16342}, {13745, 50184}, {14023, 16454}, {24321, 46483}, {39581, 49716}, {50161, 50179}, {50163, 50232}, {50169, 50186}, {50185, 50234}

X(50274) = reflection of X(i) in X(j) for these {i,j}: {3241, 50235}, {42045, 49749}, {49735, 50157}, {50171, 50160}, {50179, 50161}, {50184, 13745}, {50186, 50169}, {50232, 50163}, {50234, 50185}


X(50275) = X(1)X(50158)∩X(8)X(538)

Barycentrics    3*a^3*b - a^2*b^2 - 3*a*b^3 + 3*a^3*c - 6*a*b^2*c - 3*b^3*c - a^2*c^2 - 6*a*b*c^2 - 4*b^2*c^2 - 3*a*c^3 - 3*b*c^3 : :
X(50275) = 4 X[3626] - X[4754], 3 X[19875] - 2 X[50180]

X(50275) lies on these lines: {1, 50158}, {2, 20970}, {8, 538}, {10, 49749}, {519, 49717}, {524, 3416}, {754, 3578}, {1018, 4478}, {3241, 50174}, {3626, 4754}, {3849, 50215}, {13586, 34016}, {17294, 49724}, {17310, 50161}, {19875, 50180}, {29573, 49730}, {29617, 50178}, {31145, 50184}, {42045, 50228}, {50229, 50234}

X(50275) = midpoint of X(31145) and X(50184)
X(50275) = reflection of X(i) in X(j) for these {i,j}: {1, 50158}, {3241, 50174}, {42045, 50228}, {49749, 10}, {50157, 49724}, {50160, 3679}, {50179, 49717}, {50234, 50229}, {50235, 49730}
X(50275) = {X(3578),X(29615)}-harmonic conjugate of X(50159)


X(50276) = X(1)X(524)∩X(2)X(1171)

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

X(50276) lies on these lines: {1, 524}, {2, 1171}, {8, 543}, {538, 3578}, {540, 48809}, {754, 50215}, {1931, 31143}, {4416, 21839}, {5739, 34511}, {7621, 25446}, {9939, 17343}, {17739, 49724}, {21816, 50093}, {23942, 36523}, {29576, 50163}, {29615, 50218}, {42045, 50174}, {49718, 50216}, {49729, 49749}, {49730, 50185}, {49744, 50158}, {50228, 50234}

X(50276) = reflection of X(i) in X(j) for these {i,j}: {42045, 50174}, {49744, 50158}, {49749, 49729}, {50157, 49723}, {50160, 49724}, {50185, 49730}, {50232, 49717}, {50234, 50228}, {50235, 49728}


X(50277) = X(2)X(6)∩X(8)X(540)

Barycentrics    4*a^3 + 3*a^2*b - 3*a*b^2 - 2*b^3 + 3*a^2*c - 2*a*b*c - 3*b^2*c - 3*a*c^2 - 3*b*c^2 - 2*c^3 : :
X(50277) = 5 X[2] - 4 X[37631], 3 X[2] - 4 X[49724], 7 X[2] - 8 X[49730], 5 X[3578] - 2 X[37631], 3 X[3578] - X[42045], 3 X[3578] - 2 X[49724], 7 X[3578] - 4 X[49730], 6 X[37631] - 5 X[42045], 3 X[37631] - 5 X[49724], 7 X[37631] - 10 X[49730], 7 X[42045] - 12 X[49730], 7 X[49724] - 6 X[49730], X[145] - 4 X[49716], 3 X[50154] - 2 X[50218], 5 X[3617] - 8 X[49718], 5 X[3617] - 4 X[50169], 5 X[3623] - 8 X[49728], 7 X[4678] - 4 X[49745], 3 X[38314] - 4 X[49729], 11 X[46933] - 8 X[49743]

X(50277) lies on these lines: {2, 6}, {8, 540}, {30, 12245}, {145, 49716}, {511, 4661}, {519, 50165}, {754, 50154}, {894, 6539}, {3241, 49723}, {3617, 49718}, {3623, 49728}, {3679, 50234}, {3995, 4416}, {4001, 17495}, {4080, 33066}, {4419, 20046}, {4678, 49745}, {4683, 17162}, {4715, 4980}, {17147, 17363}, {17163, 17770}, {18253, 27571}, {20290, 32864}, {28840, 48145}, {38314, 49729}, {40891, 50183}, {46933, 49743}, {50077, 50106}

X(50277) = reflection of X(i) in X(j) for these {i,j}: {2, 3578}, {145, 49735}, {3241, 49723}, {42045, 49724}, {49735, 49716}, {50165, 50215}, {50169, 49718}, {50172, 8}, {50183, 50217}, {50234, 3679}
X(50277) = anticomplement of X(42045)
X(50277) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 41816, 27081}, {2, 43990, 41816}, {81, 41816, 2}, {81, 43990, 27081}, {1654, 20086, 8025}, {2895, 16704, 31037}, {3578, 42045, 49724}, {5739, 31303, 37639}, {31143, 41629, 2}, {31144, 42025, 2}, {42045, 49724, 2}


X(50278) = X(2)X(6)∩X(8)X(538)

Barycentrics    3*a^3*b - 2*a^2*b^2 - 3*a*b^3 + 3*a^3*c - 6*a*b^2*c - 3*b^3*c - 2*a^2*c^2 - 6*a*b*c^2 - 2*b^2*c^2 - 3*a*c^3 - 3*b*c^3 : :
X(50278) = 3 X[2] - 4 X[50158], 5 X[2] - 4 X[50180], 3 X[49717] - X[49749], 3 X[49717] - 2 X[50158], 5 X[49717] - 2 X[50180], 5 X[49749] - 6 X[50180], 5 X[50158] - 3 X[50180], 5 X[3617] - 2 X[4754], 3 X[38314] - 4 X[50174]

X(50278) lies on these lines: {2, 6}, {8, 538}, {511, 44431}, {519, 50184}, {540, 48802}, {754, 50215}, {3241, 50179}, {3617, 4754}, {3679, 50155}, {3707, 30821}, {4643, 17135}, {4651, 4690}, {4748, 29814}, {5969, 5992}, {13576, 33082}, {17344, 20347}, {19998, 25349}, {29615, 50154}, {29617, 50183}, {38314, 50174}, {50232, 50234}

X(50278) = reflection of X(i) in X(j) for these {i,j}: {2, 49717}, {3241, 50179}, {49749, 50158}, {50155, 3679}, {50234, 50232}
X(50278) = anticomplement of X(49749)
X(50278) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4690, 24690, 4651}, {49717, 49749, 50158}, {49749, 50158, 2}


X(50279) = X(2)X(20970)∩X(8)X(524)

Barycentrics    7*a^3*b - 5*a*b^3 + 7*a^3*c + 4*a^2*b*c - 8*a*b^2*c - 5*b^3*c - 8*a*b*c^2 - 6*b^2*c^2 - 5*a*c^3 - 5*b*c^3 : :
X(50279) = 5 X[8] - 2 X[4754], 4 X[4754] - 5 X[50155], 5 X[3617] - 4 X[50163], 3 X[38314] - 4 X[50158]

X(50279) lies on these lines: {2, 20970}, {8, 524}, {69, 26079}, {145, 50179}, {519, 50184}, {538, 31145}, {599, 26978}, {754, 50154}, {1992, 26035}, {3241, 49717}, {3578, 50079}, {3617, 50163}, {6542, 50157}, {11160, 34284}, {17137, 29617}, {17316, 50235}, {38314, 50158}

X(50279) = reflection of X(i) in X(j) for these {i,j}: {145, 50179}, {3241, 49717}, {50155, 8}


X(50280) = X(2)X(187)∩X(381)X(576)

Barycentrics    8 a^4+7 a^2 b^2-10 b^4+7 a^2 c^2+16 b^2 c^2-10 c^4 : :
Barycentrics    9 S^2+27 SB SC+9 SB SW+9 SC SW-4 SW^2 : :
X(50280) = 2*X(2)-3*X(7603),5*X(2)-3*X(7771),5*X(7603)-2*X(7771)

See Antreas Hatzipolakis and Ercole Suppa euclid 5144.

X(50280) lies on these lines: {2,187}, {39,8352}, {99,8786}, {115,8584}, {381,576}, {524,43457}, {1975,7775}, {1992,18424}, {2782,3845}, {3363,9466}, {3534,9734}, {5007,33006}, {5008,5461}, {6781,9771}, {7694,15682}, {7745,8355}, {7747,27088}, {7753,37350}, {7757,17503}, {7777,32479}, {7785,11054}, {7801,32823}, {7812,39565}, {7821,8370}, {7843,33013}, {7845,15533}, {11632,14160}, {14046,43528}, {14971,18907}, {22329,39601}, {31652,33192}, {36523,41624}


leftri

Points in a [[b-c,c-a,a-b ], [b^3 - c^3, c^3 - a^3, a^3 - b^3 ]] coordinate system: X(50281)-X(50316)

rightri

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

L1 is the line: (b-c) α + (c-a) β + (a-b) γ = 0.

L2 is the line (b^3 - c^3) α + (c^3 - a^3) β + (a^3 - b^3) γ = 0.

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

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

u : v : w = (a-b)(a-c)(b-c)(a+b+c) + (-2a + b + c) x + (2 a^3 - b^3 - c^3) y ,

where, as functions of a, b, c, the coordinate x is antisymmetric of degree 3, and y is antisymmetric of degree 3.

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

{-2 (a-b) (a-c) (b-c), 0}, 3241
{-2 (a-b) (a-c) (b-c), (2 (a-b) (a-c) (b-c))/(a b+a c+b c)}, 50133
{-((2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)), (2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2)}, 1992
{-((a-b) (a-c) (b-c)), -((2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2))}, 17274
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c)), -((2 (a-b) (a-c) (b-c))/(a b+a c+b c))}, 17333
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)), -((2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2))}, 4660
{-((a-b) (a-c) (b-c)), -(((a-b) (a-c) (b-c))/(a b+a c+b c))}, 49746
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c)), -(((a-b) (a-c) (b-c))/(a b+a c+b c))}, 984
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)), -(((a-b) (a-c) (b-c))/(a^2+b^2+c^2))}, 48829
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)), -(((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2)))}, 4085
{-((a-b) (a-c) (b-c)), 0}, 1
{-((a-b) (a-c) (b-c)), ((a-b) (a-c) (b-c))/(a b+a c+b c)}, 17378
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2)), ((a-b) (a-c) (b-c))/(a^2+b^2+c^2)}, 6
{-(1/2) (a-b) (a-c) (b-c), -(((a-b) (a-c) (b-c))/(a^2+b^2+c^2))}, 50092
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a b+a c+b c))), -(((a-b) (a-c) (b-c))/(a b+a c+b c))}, 50093
{-(1/2) (a-b) (a-c) (b-c), -(((a-b) (a-c) (b-c))/(2 (a b+a c+b c)))}, 49740
{-(((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a b+a c+b c))), -(((a-b) (a-c) (b-c))/(2 (a b+a c+b c)))}, 50094
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a^2+b^2+c^2))), -(((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2)))}, 48821
{-(1/2) (a-b) (a-c) (b-c), 0}, 551
{-(1/2) (a-b) (a-c) (b-c), ((a-b) (a-c) (b-c))/(2 (a b+a c+b c))}, 17392
{-(((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a^2+b^2+c^2))), ((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2))}, 597
{-(1/2) (a-b) (a-c) (b-c), (2 (a-b) (a-c) (b-c))/(a+b+c)^2}, 4349
{0, 0}, 2
{((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a b+a c+b c)), -(((a-b) (a-c) (b-c))/(a b+a c+b c))}, 3883
{1/2 (a-b) (a-c) (b-c), -(((a-b) (a-c) (b-c))/(2 (a b+a c+b c)))}, 17330
{((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a^2+b^2+c^2)), -(((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2)))}, 141
{1/2 (a-b) (a-c) (b-c), 0}, 10
{1/2 (a-b) (a-c) (b-c), ((a-b) (a-c) (b-c))/(2 (a b+a c+b c))}, 49725
{((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a b+a c+b c)), ((a-b) (a-c) (b-c))/(2 (a b+a c+b c))}, 24325
{((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a^2+b^2+c^2)), ((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2))}, 48810
{1/2 (a-b) (a-c) (b-c), ((a-b) (a-c) (b-c))/(a^2+b^2+c^2)}, 50115
{((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(2 (a b+a c+b c)), ((a-b) (a-c) (b-c))/(a b+a c+b c)}, 50116
{((a-b) (a-c) (b-c) (a b+a c+b c))/(2 (a^2+b^2+c^2)), ((a-b) (a-c) (b-c))/(a^2+b^2+c^2)}, 49482
{(a-b) (a-c) (b-c), -(((a-b) (a-c) (b-c))/(a b+a c+b c))}, 17346
{((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2), -(((a-b) (a-c) (b-c))/(a^2+b^2+c^2))}, 599
{(a-b) (a-c) (b-c), 0}, 3679
{(a-b) (a-c) (b-c), ((a-b) (a-c) (b-c))/(a b+a c+b c)}, 49720
{((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c), ((a-b) (a-c) (b-c))/(a b+a c+b c)}, 31178
{((a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2), ((a-b) (a-c) (b-c))/(a^2+b^2+c^2)}, 48805
{(a-b) (a-c) (b-c), (2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2)}, 50127
{((a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c), (2 (a-b) (a-c) (b-c))/(a b+a c+b c)}, 50128
{2 (a-b) (a-c) (b-c), -((2 (a-b) (a-c) (b-c))/(a b+a c+b c))}, 50074
{(2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2), -((2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2))}, 69
{(2 (a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c), -(((a-b) (a-c) (b-c))/(a b+a c+b c))}, 49506
{2 (a-b) (a-c) (b-c), 0}, 8
{(2 (a-b) (a-c) (b-c) (a b+a c+b c))/(a^2+b^2+c^2), ((a-b) (a-c) (b-c))/(a^2+b^2+c^2)}, 32941
{(2 (a-b) (a-c) (b-c) (a^2+b^2+c^2))/(a b+a c+b c), (2 (a-b) (a-c) (b-c))/(a b+a c+b c)}, 24349
{-2*(a - b)*(a - c)*(b - c), -(((a - b)*(a - c)*(b - c))/(a + b + c)^2)}, 50281
{(-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), 0}, 50282
{(-2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50283
{-2*(a - b)*(a - c)*(b - c), (2*(a - b)*(a - c)*(b - c))/(a + b + c)^2}, 50284
{-((a - b)*(a - c)*(b - c)), -(((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2))}, 50285
{-(((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c)), 0}, 50286
{-(((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2)), 0}, 50287
{-(((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c)), ((a - b)*(a - c)*(b - c))/(2*(a*b + a*c + b*c))}, 50288
{-(((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c)), (2*(a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50289
{-1/2*((a - b)*(a - c)*(b - c)), -(((a - b)*(a - c)*(b - c))/(a + b + c)^2)}, 50290
{-1/2*((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c), 0}, 50291
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)^3)/(a*b*c), 0}, 50292
{-1/2*((a - b)*(a - c)*(b - c)), ((a - b)*(a - c)*(b - c))/(2*(a + b + c)^2)}, 50293
{-1/2*((a - b)*(a - c)*(b - c)), ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50294
{0, (-2*(a - b)*(a - c)*(b - c))/(a + b + c)^2}, 50295
{0, -(((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c))}, 50296
{0, -1/2*((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50297
{0, -1/2*((a - b)*(a - c)*(b - c))/(a + b + c)^2}, 50298
{0, ((a - b)*(a - c)*(b - c))/(2*(a*b + a*c + b*c))}, 50299
{0, ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50300
{0, ((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50301
{0, ((a - b)*(a - c)*(b - c))/(a + b + c)^2}, 50302
{0, (2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50303
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(2*(a^2 + b^2 + c^2)), (-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50304
{((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(2*(a*b + a*c + b*c)), 0}, 50305
{((a - b)*(a - c)*(b - c)*(a + b + c)^3)/(2*a*b*c), 0}, 50306
{((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(2*(a*b + a*c + b*c)), (2*(a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50307
{(a - b)*(a - c)*(b - c), -(((a - b)*(a - c)*(b - c))/(a + b + c)^2)}, 50308
{(a - b)*(a - c)*(b - c), -1/2*((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50309
{((a - b)*(a - c)*(b - c)*(a^2 + b^2 + c^2))/(a*b + a*c + b*c), 0}, 50310
{((a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), 0}, 50311
{(a - b)*(a - c)*(b - c), ((a - b)*(a - c)*(b - c))/(2*(a + b + c)^2)}, 50312
{(a - b)*(a - c)*(b - c), ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50313
{(a - b)*(a - c)*(b - c), (2*(a - b)*(a - c)*(b - c))/(a + b + c)^2}, 50314
{(2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), -1/2*((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50315
{(2*(a - b)*(a - c)*(b - c)*(a*b + a*c + b*c))/(a^2 + b^2 + c^2), 0}, 50316


X(50281) = X(1)X(75)∩X(2)X(4716)

Barycentrics    a^3 + 3*a^2*b + a*b^2 + 3*a^2*c + 2*a*b*c - b^2*c + a*c^2 - b*c^2 : :
X(50281) = 5 X[3623] - X[4307]

X(50281) lies on these lines: {1, 75}, {2, 4716}, {6, 3993}, {9, 49489}, {10, 4060}, {31, 27804}, {37, 49488}, {43, 34064}, {81, 32934}, {145, 17343}, {192, 4649}, {238, 4393}, {386, 25660}, {516, 1482}, {519, 9348}, {551, 50120}, {726, 17318}, {748, 45222}, {752, 3241}, {894, 49452}, {940, 4970}, {968, 3791}, {984, 17319}, {1001, 49477}, {1100, 3923}, {1125, 4361}, {1255, 26037}, {1449, 4672}, {1483, 29207}, {1698, 48630}, {1738, 29574}, {1757, 4664}, {1962, 3187}, {1999, 17592}, {2345, 4527}, {2550, 4743}, {3210, 4038}, {3242, 3244}, {3247, 3842}, {3623, 4307}, {3685, 29584}, {3696, 3723}, {3706, 29644}, {3711, 4946}, {3741, 20182}, {3751, 49456}, {3773, 17314}, {3775, 17321}, {3821, 4851}, {3836, 17316}, {3879, 4655}, {3896, 5311}, {3924, 27705}, {3932, 50113}, {3969, 29647}, {3980, 37595}, {4021, 49511}, {4026, 17388}, {4068, 5248}, {4133, 5750}, {4349, 28580}, {4362, 37593}, {4363, 28522}, {4365, 19684}, {4419, 17771}, {4432, 16475}, {4460, 39581}, {4644, 17767}, {4645, 29588}, {4657, 49560}, {4663, 4681}, {4667, 28526}, {4670, 28484}, {4710, 18147}, {4732, 39586}, {4734, 17122}, {4852, 15569}, {4854, 32946}, {4891, 29668}, {4966, 17395}, {4971, 48822}, {4974, 16834}, {5220, 49685}, {5222, 31289}, {5271, 10180}, {5695, 16884}, {5712, 48643}, {6541, 38047}, {6542, 32784}, {6682, 39594}, {8715, 20990}, {9345, 17495}, {10453, 17600}, {14996, 32845}, {16672, 50018}, {16801, 49715}, {16830, 49459}, {17011, 25496}, {17013, 32944}, {17018, 32920}, {17019, 32860}, {17117, 40328}, {17233, 29633}, {17242, 33159}, {17248, 42334}, {17275, 25354}, {17300, 33149}, {17301, 49676}, {17302, 33087}, {17315, 29674}, {17363, 24697}, {17377, 33082}, {17378, 32857}, {17380, 29637}, {17389, 32846}, {17593, 37684}, {17599, 42057}, {17769, 36479}, {17778, 33154}, {17779, 30829}, {21806, 26227}, {21883, 23543}, {25351, 29602}, {28581, 36480}, {28606, 32853}, {29016, 48900}, {29572, 31252}, {29580, 50086}, {29597, 50096}, {29814, 32924}, {29829, 32848}, {29833, 33156}, {29837, 32855}, {29841, 33160}, {32926, 42042}, {32936, 37685}, {33064, 50068}, {33098, 42045}, {46845, 49468}, {49446, 49491}, {49453, 49479}, {49455, 49478}, {49457, 49495}, {49458, 49475}, {49510, 49680}

X(50281) = midpoint of X(3244) and X(4356)
X(50281) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3875, 24325}, {1, 4360, 32921}, {1, 10436, 5625}, {1, 24342, 17394}, {1, 49469, 5263}, {1, 49470, 32941}, {1, 49474, 86}, {192, 4649, 32935}, {1100, 49462, 3923}, {1999, 17592, 32916}, {3635, 49464, 42871}, {4852, 15569, 16825}, {5695, 16884, 33682}, {16777, 49486, 10}, {17011, 32915, 25496}, {17018, 32928, 32920}, {17393, 49470, 1}


X(50282) = X(1)X(2)∩X(6)X(528)

Barycentrics    a^3 + 5*a^2*b - a*b^2 + b^3 + 5*a^2*c - b^2*c - a*c^2 - b*c^2 + c^3 : :
X(50282) = X[8] + 2 X[49488], 2 X[10] + X[49495], X[145] - 4 X[49477], 4 X[1125] - X[49451], 5 X[3616] - 2 X[49458], X[4677] + 2 X[49543], 7 X[9780] - 4 X[49560], 3 X[19875] - 2 X[29594], X[69] - 4 X[4085], X[69] + 2 X[49497], 2 X[4085] + X[49497], 2 X[141] + X[49680], X[193] + 2 X[4660], X[193] - 4 X[49685], X[4660] + 2 X[49685], X[3751] + 2 X[3755], 2 X[3751] + X[24248], 4 X[3755] - X[24248], 4 X[3589] - X[49460], 5 X[3618] - 2 X[32941], X[3729] + 2 X[4780], X[3875] + 2 X[49529], 4 X[3946] - X[16496], 2 X[4353] + X[4924], 4 X[4663] - X[24695], 2 X[4743] + X[32935], 2 X[4852] + X[49688], X[49486] + 2 X[49524], 5 X[17304] - 2 X[49505], 2 X[17359] - 3 X[38047], 3 X[38087] - X[50087], 3 X[47352] - 2 X[48810], X[49446] + 2 X[49536]

X(50282) lies on these lines: {1, 2}, {6, 528}, {30, 44414}, {69, 4085}, {80, 32631}, {141, 49680}, {193, 4660}, {212, 10385}, {218, 11113}, {238, 47357}, {344, 49471}, {346, 49469}, {350, 4737}, {376, 9441}, {390, 16468}, {518, 17301}, {524, 48829}, {527, 3751}, {529, 48842}, {535, 48837}, {536, 47359}, {537, 49518}, {540, 50267}, {544, 1478}, {597, 48805}, {599, 48821}, {672, 5119}, {740, 50107}, {752, 1992}, {1002, 2809}, {1009, 3913}, {1203, 34719}, {1386, 50130}, {1738, 6173}, {1757, 6172}, {1834, 11236}, {2094, 32913}, {2099, 5723}, {2177, 24597}, {2276, 43065}, {2308, 20075}, {2345, 49459}, {2550, 4649}, {3097, 11200}, {3247, 38097}, {3416, 4725}, {3475, 33132}, {3550, 37666}, {3589, 49460}, {3618, 32941}, {3672, 49448}, {3717, 50110}, {3729, 4780}, {3875, 49529}, {3896, 33163}, {3914, 31164}, {3945, 38092}, {3946, 16496}, {3993, 27549}, {4000, 49490}, {4026, 17251}, {4038, 26040}, {4310, 49498}, {4353, 4924}, {4419, 49712}, {4429, 17297}, {4441, 4692}, {4452, 49532}, {4479, 17158}, {4644, 24715}, {4645, 50133}, {4663, 24695}, {4664, 49692}, {4674, 36887}, {4714, 33936}, {4722, 44447}, {4743, 28542}, {4852, 49688}, {4859, 38024}, {4971, 49486}, {5032, 28562}, {5220, 49742}, {5228, 5434}, {5247, 11111}, {5526, 37657}, {5695, 49726}, {5706, 34746}, {5710, 34720}, {5712, 32865}, {5734, 36692}, {5839, 33076}, {5853, 16475}, {6603, 21904}, {7982, 36670}, {9041, 50112}, {9803, 18473}, {11522, 36694}, {13632, 34718}, {15485, 37681}, {16484, 37650}, {17264, 49470}, {17274, 50091}, {17279, 49475}, {17304, 49505}, {17314, 33165}, {17320, 50075}, {17321, 49457}, {17359, 28581}, {17366, 42871}, {17382, 47358}, {17399, 49450}, {17720, 21870}, {17732, 17745}, {24210, 31142}, {25072, 38101}, {25568, 33135}, {26098, 31140}, {28503, 50120}, {28538, 50131}, {28580, 50127}, {30573, 47828}, {33144, 50103}, {33159, 49678}, {34744, 42050}, {34745, 37509}, {36695, 37714}, {37676, 48847}, {38087, 50087}, {46922, 49720}, {47352, 48810}, {48801, 48845}, {49446, 49536}, {49744, 50186}, {49749, 50169}, {50115, 50126}

X(50282) = midpoint of X(i) and X(j) for these {i,j}: {8, 50129}, {3751, 50080}, {17294, 49495}
X(50282) = reflection of X(i) in X(j) for these {i,j}: {1, 50114}, {599, 48821}, {5695, 49726}, {17274, 50091}, {17294, 10}, {24248, 50080}, {47358, 17382}, {48801, 48845}, {48805, 597}, {50080, 3755}, {50126, 50115}, {50129, 49488}, {50130, 1386}
X(50282) = crossdifference of every pair of points on line {649, 47329}
X(50282) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 8, 48802}, {8, 26626, 36480}, {10, 48822, 2}, {3751, 3755, 24248}, {4085, 49497, 69}, {4660, 49685, 193}, {29659, 50016, 8}


X(50283) = X(1)X(4753)∩X(6)X(519)

Barycentrics    3*a^3 + 5*a^2*b - a*b^2 + 5*a^2*c - b^2*c - a*c^2 - b*c^2 : :
X(50283) = 4 X[6] - X[32941], 3 X[6] - X[48805], 7 X[6] - X[49460], 5 X[6] - 2 X[49482], 2 X[6] + X[49497], 5 X[6] + X[49680], X[6] + 2 X[49685], 2 X[4856] + X[49529], 3 X[32941] - 4 X[48805], 7 X[32941] - 4 X[49460], 5 X[32941] - 8 X[49482], X[32941] + 2 X[49497], 5 X[32941] + 4 X[49680], X[32941] + 8 X[49685], 7 X[48805] - 3 X[49460], 5 X[48805] - 6 X[49482], 2 X[48805] + 3 X[49497], 5 X[48805] + 3 X[49680], X[48805] + 6 X[49685], 5 X[49460] - 14 X[49482], 2 X[49460] + 7 X[49497], 5 X[49460] + 7 X[49680], X[49460] + 14 X[49685], 4 X[49482] + 5 X[49497], 2 X[49482] + X[49680], X[49482] + 5 X[49685], 5 X[49497] - 2 X[49680], X[49497] - 4 X[49685], X[49680] - 10 X[49685], X[193] + 2 X[4085], 4 X[4663] - X[32935], 2 X[4663] + X[49488], X[32935] + 2 X[49488], 2 X[3751] + X[32921], 5 X[3751] + X[49446], X[3751] + 2 X[49489], 5 X[16834] - X[49446], 5 X[32921] - 2 X[49446], X[32921] - 4 X[49489], X[49446] - 10 X[49489], X[3242] - 4 X[4991], 2 X[3629] + X[4660], 2 X[4672] + X[49495], 2 X[4743] + X[24695], 3 X[38047] - X[50076], X[48799] - 3 X[48857]

X(50283) lies on these lines: {1, 4753}, {2, 3775}, {6, 519}, {9, 50111}, {10, 4758}, {86, 19875}, {145, 4439}, {193, 4085}, {238, 3241}, {239, 31178}, {516, 5102}, {518, 50124}, {524, 48821}, {528, 8584}, {536, 4663}, {537, 3751}, {726, 50120}, {740, 50127}, {752, 1992}, {894, 50086}, {984, 29584}, {1449, 48854}, {1698, 17387}, {1743, 49471}, {1757, 4664}, {3187, 31161}, {3242, 4991}, {3629, 4660}, {3655, 37510}, {3679, 46922}, {3686, 48853}, {3736, 18192}, {3758, 50016}, {3773, 50079}, {3842, 29597}, {3875, 28554}, {4363, 50018}, {4393, 49712}, {4407, 26626}, {4421, 37507}, {4432, 16670}, {4655, 50091}, {4667, 24693}, {4669, 33682}, {4672, 49495}, {4677, 5263}, {4716, 4740}, {4722, 32934}, {4743, 24695}, {4929, 16468}, {4946, 37540}, {11194, 37502}, {14621, 40891}, {15534, 48829}, {16666, 36480}, {16671, 49475}, {16786, 49701}, {16833, 24325}, {17119, 50021}, {17120, 49459}, {17121, 49490}, {17259, 19883}, {17277, 25055}, {17330, 48822}, {17349, 38314}, {17360, 36478}, {20160, 29622}, {25496, 31136}, {28558, 50080}, {29577, 33159}, {31151, 50133}, {34379, 50092}, {37654, 48830}, {38047, 50076}, {48799, 48857}, {49486, 49721}

X(50283) = midpoint of X(i) and X(j) for these {i,j}: {3751, 16834}, {15534, 48829}, {47359, 50131}, {49486, 49721}, {49495, 50126}
X(50283) = reflection of X(i) in X(j) for these {i,j}: {4655, 50091}, {16834, 49489}, {32921, 16834}, {50079, 3773}, {50126, 4672}
X(50283) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 49497, 32941}, {6, 49680, 49482}, {6, 49685, 49497}, {3751, 49489, 32921}, {4663, 49488, 32935}, {4667, 50022, 24693}


X(50284) = X(1)X(69)∩X(2)X(3791)

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

X(50284) lies on these lines: {1, 69}, {2, 3791}, {6, 3932}, {7, 32921}, {8, 4649}, {10, 1449}, {81, 33088}, {144, 49456}, {145, 740}, {192, 24695}, {193, 984}, {238, 17316}, {344, 16468}, {346, 4672}, {390, 49471}, {391, 3842}, {516, 944}, {519, 4349}, {726, 4644}, {752, 3241}, {1001, 17390}, {1100, 3416}, {1125, 17296}, {1279, 50125}, {1386, 4851}, {1482, 29207}, {1503, 48909}, {1738, 16834}, {1743, 4078}, {1757, 1992}, {1961, 14555}, {1999, 26098}, {2308, 17776}, {2345, 33682}, {2550, 49488}, {3332, 28850}, {3474, 4970}, {3616, 17238}, {3618, 29674}, {3619, 29646}, {3623, 28498}, {3629, 5220}, {3635, 4356}, {3672, 4655}, {3685, 17389}, {3686, 39586}, {3751, 4899}, {3773, 5749}, {3775, 32099}, {3790, 17120}, {3823, 50124}, {3836, 5222}, {3891, 42045}, {3912, 16475}, {3923, 17314}, {3945, 24325}, {3966, 37595}, {3993, 5698}, {4000, 49477}, {4026, 16884}, {4028, 5269}, {4310, 49472}, {4344, 32941}, {4360, 24248}, {4362, 5712}, {4393, 4645}, {4419, 17770}, {4438, 37666}, {4447, 37502}, {4454, 28516}, {4648, 16825}, {4676, 17315}, {4716, 50129}, {4725, 48802}, {4753, 5686}, {4852, 5880}, {4889, 49484}, {4916, 49482}, {4966, 38315}, {5018, 6604}, {5263, 17377}, {5311, 5739}, {5695, 17388}, {5846, 36479}, {5849, 24316}, {5905, 32928}, {6211, 14912}, {6542, 20145}, {6682, 37655}, {7174, 34379}, {7222, 50117}, {7226, 20086}, {8236, 49700}, {10453, 40718}, {11269, 33070}, {14996, 32842}, {16469, 29573}, {16477, 26685}, {16666, 38047}, {16823, 17391}, {16830, 17363}, {17011, 26034}, {17013, 33086}, {17163, 20046}, {17284, 38049}, {17318, 17768}, {17365, 49453}, {17378, 32922}, {17393, 24723}, {17778, 33144}, {18048, 36574}, {18141, 29821}, {18788, 25406}, {19785, 32949}, {20064, 27804}, {20069, 32937}, {20872, 35707}, {20930, 23689}, {24280, 49452}, {24342, 42696}, {24597, 29643}, {25496, 34255}, {26065, 33092}, {26626, 32784}, {28538, 48830}, {29606, 38059}, {29627, 31289}, {29658, 30828}, {29671, 37642}, {30699, 33097}, {32847, 50030}, {32857, 50101}, {33073, 33137}, {33093, 33163}, {33098, 50071}, {38053, 50023}, {38200, 50022}, {39587, 49457}, {47357, 49705}, {49478, 49681}

X(50284) = midpoint of X(145) and X(4307)
X(50284) = reflection of X(4356) in X(3635)
X(50284) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 33082, 17321}, {145, 20090, 24349}, {33093, 37685, 33163}


X(50285) = X(1)X(320)∩X(2)X(38)

Barycentrics    a^3 + 3*a*b^2 + b^3 + 3*a*c^2 + c^3 : :
X(50285) = 2 X[1] + X[4655], 4 X[1125] - X[32935], X[69] + 2 X[49472], 2 X[141] + X[49455], X[3242] + 2 X[3821], X[3416] + 2 X[49464], 4 X[4353] - X[32921], 2 X[4353] + X[49511], X[32921] + 2 X[49511], 5 X[3616] - 2 X[4672], 7 X[3622] - X[24695], 2 X[3663] + X[32941], 2 X[3773] + X[49446], 4 X[3946] - X[49497], 2 X[3946] + X[49505], X[49497] + 2 X[49505], 2 X[4085] + X[16496], 2 X[4085] - 5 X[17304], X[16496] + 5 X[17304], X[4660] - 4 X[17235], X[4660] + 2 X[49465], 2 X[17235] + X[49465], 2 X[4743] + X[49451], X[17276] + 2 X[49482], X[24248] + 2 X[49473], 3 X[25055] - X[50127], X[49453] + 2 X[49560]

X(50285) lies on these lines: {1, 320}, {2, 38}, {10, 17067}, {45, 1125}, {69, 49472}, {141, 28503}, {190, 29660}, {238, 17333}, {518, 17382}, {519, 599}, {527, 551}, {528, 49741}, {545, 3923}, {553, 1460}, {726, 17281}, {740, 50101}, {896, 29831}, {903, 5263}, {990, 28854}, {1086, 24693}, {1386, 4715}, {1626, 4428}, {2792, 10246}, {2796, 48805}, {2835, 3898}, {3616, 4672}, {3622, 24695}, {3662, 31151}, {3663, 28580}, {3672, 49471}, {3677, 3846}, {3679, 3775}, {3736, 16712}, {3773, 49446}, {3782, 29652}, {3836, 7174}, {3946, 49497}, {4000, 49457}, {4078, 41141}, {4085, 16496}, {4260, 48844}, {4334, 17078}, {4364, 24331}, {4384, 4407}, {4415, 29668}, {4419, 4432}, {4425, 17597}, {4439, 17284}, {4643, 50023}, {4650, 29838}, {4657, 49479}, {4660, 17235}, {4683, 17024}, {4688, 48809}, {4703, 7191}, {4743, 49451}, {4753, 5222}, {4865, 17184}, {4908, 49523}, {4966, 50113}, {4974, 37654}, {5625, 9791}, {5850, 38046}, {6173, 48854}, {7292, 27776}, {9041, 48821}, {10199, 24433}, {12263, 24397}, {14020, 28082}, {15485, 17258}, {16475, 17771}, {16484, 17247}, {16706, 49448}, {16825, 17330}, {17227, 32847}, {17236, 33076}, {17271, 32922}, {17276, 49482}, {17279, 49520}, {17280, 49517}, {17289, 49532}, {17291, 33165}, {17302, 49490}, {17305, 24841}, {17310, 33087}, {17313, 49676}, {17318, 49764}, {17323, 42871}, {17342, 29637}, {17354, 24821}, {17357, 49513}, {17367, 49712}, {17370, 49501}, {17469, 42058}, {17591, 33126}, {17598, 27184}, {17599, 33064}, {17716, 26840}, {17725, 24627}, {17770, 38315}, {21342, 29635}, {24231, 50116}, {24248, 49473}, {24457, 48295}, {24715, 36534}, {24725, 29823}, {25055, 50127}, {25557, 49738}, {26230, 36263}, {27754, 29632}, {28542, 50126}, {28554, 50107}, {28562, 50130}, {29633, 49499}, {29648, 32940}, {29666, 32938}, {29686, 32933}, {29815, 33067}, {29819, 32859}, {29853, 33761}, {31136, 50102}, {31162, 39553}, {33122, 46901}, {33143, 46909}, {41311, 48822}, {42057, 50068}, {48802, 50096}, {49453, 49560}, {49463, 50081}, {49477, 50131}, {49488, 50112}

X(50285) = midpoint of X(i) and X(j) for these {i,j}: {1, 17274}, {3242, 48829}, {17301, 47358}, {48805, 49747}, {49453, 50087}, {49463, 50081}
X(50285) = reflection of X(i) in X(j) for these {i,j}: {3923, 48810}, {4655, 17274}, {32935, 50115}, {48829, 3821}, {49488, 50112}, {50087, 49560}, {50115, 1125}, {50131, 49477}
X(50285) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {38, 26128, 4438}, {1086, 36480, 24693}, {3946, 49505, 49497}, {4353, 49511, 32921}, {16496, 17304, 4085}, {17235, 49465, 4660}, {17305, 24841, 29659}, {26150, 31302, 33159}


X(50286) = X(1)X(2)∩X(37)X(49746)

Barycentrics    2*a^3 + 3*a*b^2 - b^3 + 3*a*b*c + 3*a*c^2 - c^3 : :
X(50286) = X[8] + 2 X[49476], 4 X[551] - 5 X[29622], 5 X[3616] - 2 X[49466], 4 X[3842] - X[49506], X[17363] - 4 X[49457], X[17364] + 2 X[49448], 2 X[17365] + X[49501], 5 X[17391] - 2 X[49490], 2 X[24325] + X[49534], X[24349] + 2 X[49527], 3 X[24452] - X[49493], 3 X[39704] - X[49499]

X(50286) lies on these lines: {1, 2}, {37, 49746}, {45, 49709}, {75, 28503}, {86, 49688}, {192, 28580}, {377, 48838}, {388, 7185}, {516, 50090}, {518, 17378}, {524, 50075}, {528, 4664}, {536, 49720}, {537, 50128}, {538, 50171}, {545, 49447}, {644, 5276}, {664, 5252}, {752, 984}, {903, 5880}, {952, 44430}, {964, 48864}, {1022, 48164}, {2550, 50101}, {3126, 44550}, {3219, 42058}, {3242, 17313}, {3251, 47804}, {3303, 16048}, {3416, 17271}, {3654, 13634}, {3655, 13635}, {3662, 31151}, {3696, 50088}, {3699, 17723}, {3717, 50115}, {3746, 17522}, {3790, 5263}, {3819, 3873}, {3822, 31084}, {3842, 49506}, {3895, 40131}, {3913, 19310}, {3932, 17342}, {4085, 17396}, {4202, 48844}, {4344, 27549}, {4349, 4899}, {4370, 4676}, {4385, 37150}, {4421, 19326}, {4429, 17382}, {4518, 5724}, {4645, 7174}, {4660, 17247}, {4675, 24841}, {4715, 49515}, {4844, 47771}, {4863, 34064}, {4908, 49484}, {4968, 33933}, {5846, 17330}, {5847, 50074}, {5881, 7379}, {5886, 24808}, {7385, 7982}, {7951, 31126}, {9041, 17392}, {9053, 49738}, {9269, 47802}, {11194, 19325}, {12513, 19314}, {14005, 33955}, {14421, 44429}, {15668, 49690}, {16496, 17300}, {17000, 49497}, {17234, 49465}, {17242, 32941}, {17248, 33076}, {17259, 49679}, {17264, 48805}, {17277, 49681}, {17297, 47358}, {17315, 49460}, {17317, 42871}, {17320, 32850}, {17339, 49482}, {17346, 28538}, {17349, 49684}, {17363, 49457}, {17364, 49448}, {17365, 49501}, {17368, 33165}, {17375, 49505}, {17379, 49529}, {17391, 49490}, {17399, 48821}, {17679, 48840}, {19277, 48804}, {21554, 37727}, {21807, 34611}, {22116, 43262}, {24325, 49534}, {24349, 49527}, {24441, 24723}, {24452, 49493}, {27184, 31134}, {28534, 49748}, {28581, 50123}, {30580, 47809}, {31169, 34606}, {33309, 48824}, {36404, 37654}, {36409, 50082}, {39605, 47745}, {39704, 49499}, {41313, 50130}, {46922, 47359}, {48627, 49455}, {49450, 50132}, {49470, 50113}, {49735, 50217}

X(50286) = midpoint of X(i) and X(j) for these {i,j}: {49450, 50132}, {49527, 50116}
X(50286) = reflection of X(i) in X(j) for these {i,j}: {75, 49725}, {3241, 29574}, {17333, 984}, {24349, 50116}, {29617, 3679}, {49470, 50113}, {49746, 37}, {50088, 3696}
X(50286) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 10, 17367}, {2, 31145, 48849}, {8, 39587, 16830}, {10, 49762, 8}, {10, 50017, 16816}, {145, 16816, 50017}, {145, 29569, 1}, {3679, 48854, 2}, {3920, 29641, 29634}, {3932, 48810, 17342}, {17320, 32850, 48829}, {29660, 49769, 29629}, {32847, 36480, 3661}


X(50287) = X(1)X(2)∩X(6)X(752)

Barycentrics    a^3 + 3*a^2*b + b^3 + 3*a^2*c + c^3 : :
X(50287) = X[8] + 2 X[49477], 2 X[10] + X[49488], 4 X[1125] - X[49458], 5 X[1698] + X[49495], 5 X[1698] - 2 X[49560], 7 X[3624] - X[49451], 2 X[4745] + X[49543], X[17294] - 3 X[19875], X[49495] + 2 X[49560], X[6] + 2 X[4085], 2 X[6] + X[4660], 4 X[4085] - X[4660], X[69] + 2 X[49685], 2 X[141] + X[49497], X[17281] - 3 X[38047], X[3416] + 2 X[49489], 4 X[3589] - X[32941], 5 X[3618] - 2 X[49482], X[3751] + 2 X[3821], 2 X[3755] + X[3923], 5 X[3763] + X[49680], 2 X[3773] + X[49486], X[3886] - 4 X[24295], 4 X[3946] - X[49455], 2 X[3946] + X[49529], X[49455] + 2 X[49529], 2 X[4353] + X[49536], X[4655] + 2 X[4663], 2 X[4743] + X[5695], X[4780] + 2 X[17355], X[32921] + 2 X[49524], 3 X[38023] - X[50130], 3 X[38087] + X[50120], 3 X[47352] - X[48805], 7 X[47355] - X[49460], 2 X[49472] + X[49688], 2 X[49481] + X[49526]

X(50287) lies on these lines: {1, 2}, {6, 752}, {69, 49685}, {141, 49497}, {238, 49746}, {516, 14853}, {518, 17382}, {524, 48821}, {527, 50091}, {528, 597}, {529, 48845}, {535, 5091}, {537, 17301}, {540, 50217}, {545, 32935}, {726, 50101}, {740, 17281}, {903, 33149}, {984, 17320}, {1009, 8715}, {1022, 47824}, {1643, 29066}, {1738, 50116}, {1757, 17333}, {2276, 4868}, {2308, 42058}, {2345, 4709}, {2550, 33682}, {2784, 5587}, {2796, 50080}, {2809, 5883}, {2901, 21802}, {3251, 47822}, {3339, 7185}, {3416, 49489}, {3589, 32941}, {3618, 49482}, {3654, 13632}, {3655, 13633}, {3672, 49520}, {3696, 36409}, {3751, 3821}, {3755, 3923}, {3758, 24715}, {3759, 33076}, {3763, 49680}, {3773, 49486}, {3826, 49738}, {3836, 17313}, {3844, 50081}, {3886, 24295}, {3896, 26061}, {3932, 50113}, {3946, 49455}, {4000, 49479}, {4026, 17330}, {4301, 36670}, {4310, 49535}, {4353, 49536}, {4360, 33165}, {4385, 4479}, {4389, 49712}, {4407, 17325}, {4429, 4649}, {4439, 17318}, {4643, 4753}, {4644, 24692}, {4655, 4663}, {4657, 49457}, {4658, 33955}, {4670, 24693}, {4675, 25351}, {4693, 17354}, {4716, 50088}, {4722, 32950}, {4732, 17303}, {4734, 33167}, {4743, 5695}, {4780, 17355}, {4795, 5880}, {4908, 49462}, {4970, 33163}, {4972, 31134}, {5220, 24441}, {5247, 37038}, {5657, 10186}, {5853, 38049}, {7174, 49697}, {8299, 25439}, {9269, 48216}, {9345, 24988}, {10791, 32115}, {11355, 48867}, {11522, 36692}, {14421, 47823}, {15621, 19263}, {16469, 49705}, {16475, 17766}, {16484, 17352}, {16670, 49710}, {16706, 49490}, {17271, 32784}, {17279, 49471}, {17280, 49469}, {17289, 49459}, {17302, 49448}, {17342, 33159}, {17357, 49475}, {17399, 50075}, {17592, 33118}, {17765, 38315}, {18481, 19703}, {20456, 24464}, {23888, 48244}, {24203, 37678}, {25539, 49689}, {27754, 33115}, {28503, 32921}, {28538, 50124}, {28542, 49721}, {28612, 33933}, {28854, 36721}, {30580, 47827}, {31161, 50102}, {31178, 37756}, {32846, 50132}, {32948, 37685}, {33082, 50074}, {33114, 46904}, {33128, 46897}, {36693, 37714}, {36722, 48900}, {37150, 48848}, {37676, 48808}, {38023, 50130}, {38087, 50120}, {41312, 50094}, {41313, 50111}, {42054, 50068}, {47352, 48805}, {47355, 49460}, {48832, 48842}, {48833, 48837}, {49472, 49688}, {49481, 49526}, {49749, 50226}

X(50287) = midpoint of X(i) and X(j) for these {i,j}: {6, 48829}, {3416, 50131}, {3679, 16834}, {3751, 17274}, {3755, 50115}, {17301, 47359}, {48831, 48857}, {48832, 48842}, {48833, 48837}, {49486, 50087}, {49524, 50112}, {50080, 50127}
X(50287) = reflection of X(i) in X(j) for these {i,j}: {3923, 50115}, {4660, 48829}, {17274, 3821}, {29594, 3828}, {32921, 50112}, {32941, 48810}, {48808, 48843}, {48810, 3589}, {48829, 4085}, {50081, 3844}, {50087, 3773}, {50131, 49489}
X(50287) = crossdifference of every pair of points on line {649, 9011}
X(50287) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1698, 17244}, {2, 3679, 48809}, {2, 48830, 551}, {6, 4085, 4660}, {10, 3244, 49766}, {10, 50018, 8}, {42, 25453, 3771}, {1698, 49495, 49560}, {3946, 49529, 49455}, {4429, 17378, 31151}, {4649, 31151, 17378}, {5222, 36479, 50023}, {17018, 29850, 29642}, {17023, 49772, 36480}, {36478, 50016, 3661}, {49477, 50018, 49488}


X(50288) = X(1)X(3836)∩X(2)X(49506)

Barycentrics    2*a^3 + 2*a*b^2 - b^3 + 2*a*b*c + 2*a*c^2 - c^3 : :
X(50288) = 5 X[3696] - 3 X[50085], 5 X[984] - 3 X[17333], 3 X[17378] - X[49498], 3 X[17389] - X[49678], X[49474] - 3 X[49720]

X(50288) lies on these lines: {1, 3836}, {2, 49506}, {6, 49693}, {8, 4649}, {10, 1386}, {37, 17766}, {75, 17769}, {142, 3244}, {145, 4716}, {192, 17764}, {516, 49456}, {519, 3696}, {524, 49510}, {528, 3993}, {537, 49527}, {612, 3846}, {740, 49476}, {750, 29832}, {752, 984}, {1001, 49700}, {1086, 49464}, {1738, 49472}, {1961, 4514}, {2550, 32921}, {2796, 49523}, {2887, 3920}, {3416, 3775}, {3626, 4545}, {3632, 5564}, {3664, 49491}, {3717, 4672}, {3744, 29653}, {3745, 29673}, {3751, 49701}, {3773, 5263}, {3791, 25006}, {3826, 50023}, {3842, 3883}, {3874, 9049}, {3878, 20713}, {3912, 49473}, {3923, 4439}, {3932, 49482}, {3961, 33073}, {3989, 4450}, {4030, 43223}, {4078, 4432}, {4307, 32935}, {4349, 49529}, {4360, 4743}, {4407, 33082}, {4416, 28498}, {4434, 29639}, {4438, 5269}, {4655, 7174}, {4663, 49697}, {4667, 49536}, {4682, 29655}, {4753, 24393}, {4851, 49458}, {4970, 34612}, {4972, 29816}, {5014, 5311}, {5205, 17722}, {5297, 32844}, {5847, 49457}, {5852, 49508}, {5853, 49471}, {5880, 49455}, {6541, 49484}, {6679, 17716}, {9041, 49535}, {9053, 49479}, {9347, 33120}, {10327, 25496}, {10459, 30034}, {10944, 30097}, {15254, 49705}, {15481, 49710}, {16484, 49704}, {16825, 49681}, {16830, 33076}, {17024, 25961}, {17122, 29840}, {17300, 49675}, {17334, 28508}, {17364, 49503}, {17378, 49498}, {17389, 49678}, {17602, 21241}, {17763, 21242}, {17767, 49447}, {17768, 49520}, {17770, 49515}, {17771, 49448}, {19701, 29669}, {20020, 32920}, {20090, 49707}, {21026, 26230}, {24349, 49534}, {25957, 29815}, {28337, 34641}, {28503, 50117}, {28542, 49445}, {29569, 49708}, {29606, 43179}, {29844, 37674}, {30818, 49994}, {32772, 33091}, {32783, 48651}, {32926, 33109}, {32927, 33112}, {32928, 33110}, {32945, 33093}, {33087, 36534}, {33152, 48649}, {33682, 49524}, {34379, 49449}, {41011, 42054}, {42819, 49696}, {46897, 49996}, {49465, 49676}, {49467, 49764}, {49474, 49720}, {49489, 49772}

X(50288) = midpoint of X(i) and X(j) for these {i,j}: {3632, 17377}, {17364, 49503}, {24349, 49534}
X(50288) = reflection of X(i) in X(j) for these {i,j}: {3244, 17390}, {3883, 3842}, {17362, 3626}, {49491, 3664}
X(50288) = complement of X(49506)
X(50288) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 32850, 4085}, {10, 49684, 4974}, {612, 4865, 3846}, {3416, 36480, 3775}, {3920, 33072, 2887}, {5263, 32847, 3773}, {17317, 49695, 1}, {17716, 29641, 6679}, {32926, 33109, 48643}


X(50289) = X(1)X(2896)∩X(2)X(3883)

Barycentrics    2*a^3 + a*b^2 - b^3 + a*b*c + a*c^2 - c^3 : :
X(50289) = 4 X[1] - 5 X[17391], 3 X[17389] - 2 X[49470], 2 X[24349] - 3 X[50128], 4 X[984] - 3 X[17333], 5 X[3617] - 4 X[3686], 4 X[3696] - 3 X[29617], 2 X[3696] - 3 X[49720], 4 X[15569] - 3 X[49746], 3 X[17378] - 2 X[49478], 5 X[29622] - 4 X[49740], 2 X[49461] - 3 X[50121], 2 X[49525] - 3 X[49722]

X(50289) lies on these lines: {1, 2896}, {2, 3883}, {4, 41261}, {6, 32850}, {7, 145}, {8, 193}, {10, 16468}, {31, 29641}, {37, 28566}, {55, 33073}, {57, 29840}, {63, 20101}, {75, 5846}, {81, 5014}, {100, 33070}, {171, 3705}, {181, 25306}, {192, 516}, {238, 17338}, {239, 2550}, {320, 3242}, {335, 528}, {390, 17316}, {518, 17364}, {519, 4740}, {524, 49450}, {527, 31302}, {537, 49534}, {551, 26150}, {608, 5174}, {612, 4388}, {750, 32844}, {752, 984}, {902, 29643}, {940, 4514}, {962, 20009}, {1001, 17244}, {1279, 17234}, {1376, 33071}, {1386, 4429}, {1401, 3873}, {1469, 3888}, {1738, 49684}, {1836, 32926}, {1892, 1897}, {1999, 3434}, {2263, 3870}, {2285, 3169}, {2298, 5016}, {2308, 33117}, {2796, 49445}, {2886, 3769}, {2887, 17716}, {3006, 17126}, {3052, 33116}, {3187, 33110}, {3218, 29832}, {3219, 20064}, {3241, 4310}, {3244, 24231}, {3306, 5211}, {3416, 3661}, {3550, 29671}, {3616, 17291}, {3617, 3686}, {3623, 15600}, {3644, 28530}, {3664, 49466}, {3685, 17242}, {3688, 3869}, {3696, 28538}, {3717, 17350}, {3744, 18134}, {3745, 29841}, {3749, 29839}, {3755, 4393}, {3758, 49524}, {3790, 3923}, {3791, 32865}, {3823, 17352}, {3826, 29628}, {3844, 29613}, {3868, 9052}, {3886, 6542}, {3891, 20292}, {3896, 49719}, {3920, 6327}, {3932, 4676}, {3935, 31034}, {3938, 32949}, {3961, 32946}, {3980, 32866}, {3993, 21829}, {4026, 17397}, {4298, 17480}, {4312, 4440}, {4318, 10571}, {4327, 36846}, {4349, 17379}, {4362, 33109}, {4398, 49463}, {4418, 32854}, {4434, 17717}, {4450, 28606}, {4671, 50000}, {4672, 33165}, {4678, 5772}, {4684, 17375}, {4696, 34283}, {4697, 33169}, {4702, 29618}, {4764, 28472}, {4788, 28557}, {4847, 37683}, {4864, 17376}, {4892, 17725}, {4894, 37559}, {4901, 49754}, {5015, 5711}, {5219, 37764}, {5223, 20072}, {5247, 28026}, {5311, 32947}, {5542, 49771}, {5554, 5807}, {5698, 17261}, {5710, 7270}, {5852, 49501}, {5880, 32922}, {5905, 20020}, {6646, 7174}, {7081, 26098}, {7321, 49679}, {8616, 29653}, {9053, 17365}, {9436, 41354}, {10327, 27064}, {10528, 28739}, {12588, 21280}, {12648, 40862}, {12649, 41246}, {13576, 17027}, {14923, 35104}, {14942, 31038}, {14996, 29835}, {15485, 49705}, {15569, 49746}, {15570, 49699}, {16706, 38315}, {16823, 27147}, {16830, 17248}, {17000, 33076}, {17017, 32948}, {17150, 33131}, {17184, 29815}, {17233, 49484}, {17238, 19868}, {17247, 24723}, {17254, 48856}, {17257, 39587}, {17297, 50130}, {17347, 28570}, {17374, 49467}, {17377, 28581}, {17378, 49478}, {17469, 25957}, {17599, 33068}, {17763, 33104}, {17764, 49452}, {17765, 49490}, {17767, 49517}, {17768, 49447}, {17769, 49493}, {17770, 49448}, {17771, 49503}, {17772, 49459}, {20045, 31019}, {20154, 29576}, {21241, 29658}, {21282, 33134}, {24325, 49506}, {24552, 33078}, {24620, 49987}, {24692, 49464}, {24715, 32921}, {24725, 32927}, {25006, 37652}, {25496, 33079}, {25527, 29838}, {25716, 41352}, {25959, 26230}, {26015, 37684}, {26223, 33091}, {26227, 33112}, {26685, 39570}, {26986, 27091}, {28494, 49456}, {28498, 49457}, {28508, 49520}, {28534, 49523}, {28599, 29667}, {29575, 47357}, {29577, 48805}, {29622, 49740}, {29649, 33106}, {29652, 33085}, {29655, 37604}, {29659, 33682}, {29674, 49482}, {29816, 32776}, {29819, 33125}, {31134, 32775}, {31145, 35578}, {32772, 33074}, {32846, 32941}, {32851, 37540}, {32852, 32945}, {32857, 49455}, {32920, 33097}, {32928, 33094}, {32929, 33093}, {32932, 33088}, {32937, 41011}, {33082, 36480}, {33087, 49473}, {33149, 49472}, {36534, 49511}, {37608, 49613}, {42871, 49695}, {49461, 50121}, {49525, 49722}

X(50289) = reflection of X(i) in X(j) for these {i,j}: {145, 3879}, {192, 49476}, {3869, 3688}, {17347, 49515}, {17363, 8}, {29617, 49720}, {31302, 49527}, {49466, 3664}, {49499, 17365}, {49506, 24325}
X(50289) = anticomplement of X(3883)
X(50289) = X(1390)-anticomplementary conjugate of X(3436)
X(50289) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4645, 3662}, {8, 4307, 894}, {31, 33072, 29641}, {171, 4865, 3705}, {940, 4514, 29843}, {1386, 4429, 17367}, {2887, 17716, 29634}, {3416, 5263, 3661}, {3745, 32773, 29841}, {3920, 6327, 27184}, {3923, 32847, 3790}, {3932, 4676, 17339}, {4312, 49446, 4440}, {5880, 32922, 48627}, {5880, 49681, 32922}, {17300, 49704, 1}


X(50290) = X(1)X(69)∩X(2)X(968)

Barycentrics    (b + c)*(3*a^2 + 2*a*b + b^2 + 2*a*c + c^2) : :
X(50290) = 3 X[551] - X[4349], 5 X[3616] - X[4307]

X(50290) lies on these lines: {1, 69}, {2, 968}, {3, 142}, {8, 17248}, {9, 38194}, {10, 37}, {42, 4104}, {45, 38047}, {86, 24723}, {141, 15569}, {226, 1284}, {238, 17023}, {306, 1962}, {307, 42289}, {344, 1698}, {515, 46475}, {518, 4364}, {519, 9348}, {527, 48822}, {528, 25357}, {536, 48853}, {551, 752}, {579, 12514}, {726, 24357}, {894, 9791}, {960, 4260}, {984, 4899}, {986, 17065}, {1211, 4028}, {1215, 4656}, {1255, 33078}, {1385, 29207}, {1386, 17045}, {1503, 48894}, {1621, 5310}, {1721, 36706}, {1757, 50093}, {1770, 25526}, {1836, 19701}, {2292, 3778}, {2385, 24315}, {2550, 39586}, {2796, 24358}, {2887, 10180}, {3008, 20156}, {3244, 17772}, {3338, 29747}, {3416, 16777}, {3452, 6685}, {3589, 15254}, {3616, 3662}, {3622, 17236}, {3634, 5955}, {3663, 24325}, {3664, 4655}, {3671, 41003}, {3672, 39581}, {3678, 22312}, {3679, 50110}, {3686, 49488}, {3687, 17592}, {3717, 29659}, {3739, 39580}, {3751, 17257}, {3775, 49471}, {3790, 4704}, {3812, 15488}, {3822, 30444}, {3823, 4755}, {3826, 4698}, {3828, 41313}, {3836, 29571}, {3844, 17243}, {3896, 41809}, {3912, 32784}, {3923, 5750}, {3946, 16825}, {3966, 20182}, {3989, 29685}, {4021, 32921}, {4138, 17056}, {4363, 28526}, {4389, 24231}, {4416, 4649}, {4429, 4687}, {4431, 49452}, {4472, 28530}, {4640, 6703}, {4642, 22174}, {4643, 34379}, {4645, 16826}, {4647, 19857}, {4663, 17332}, {4665, 28484}, {4667, 17770}, {4670, 17768}, {4676, 17381}, {4682, 44419}, {4708, 28581}, {4714, 42724}, {4716, 50095}, {4854, 31993}, {4924, 49449}, {4966, 17237}, {4967, 49474}, {4974, 50114}, {5019, 33682}, {5224, 49470}, {5249, 16778}, {5263, 17322}, {5287, 26034}, {5294, 29647}, {5316, 33845}, {5333, 20292}, {5550, 27147}, {5695, 17303}, {5745, 29635}, {5853, 36480}, {6051, 13728}, {6682, 11019}, {6690, 49631}, {7174, 36479}, {7235, 21967}, {7283, 19865}, {7611, 10175}, {8424, 12579}, {8582, 25099}, {10436, 24248}, {11263, 16580}, {11362, 31395}, {15485, 29646}, {15808, 28494}, {16475, 26626}, {16593, 25351}, {16672, 49766}, {16801, 49711}, {16823, 17302}, {17019, 33083}, {17021, 33086}, {17061, 50063}, {17235, 25557}, {17246, 49483}, {17247, 24349}, {17250, 49763}, {17275, 49486}, {17320, 32922}, {17325, 49768}, {17339, 26083}, {17353, 29633}, {17384, 17764}, {19684, 41011}, {19854, 28420}, {19860, 25023}, {19868, 32941}, {23381, 36025}, {24169, 25501}, {24199, 33149}, {25101, 33159}, {25349, 28600}, {25371, 29057}, {25496, 40998}, {25498, 49484}, {26251, 31035}, {26580, 29822}, {27626, 31435}, {28022, 37592}, {28606, 33089}, {29574, 32846}, {29594, 50111}, {29598, 38187}, {29837, 38000}, {30331, 49473}, {31191, 31289}, {32857, 50116}, {32916, 39595}, {33076, 49476}, {33092, 39597}, {49478, 49505}, {49515, 49536}, {49693, 50094}, {49756, 50018}

X(50290) = midpoint of X(i) and X(j) for these {i,j}: {10, 4356}, {7174, 36479}
X(50290) = crossdifference of every pair of points on line {2484, 3733}
X(50290) = barycentric product X(i)*X(j) for these {i,j}: {10, 26626}, {190, 47998}, {321, 16475}, {3695, 31910}
X(50290) = barycentric quotient X(i)/X(j) for these {i,j}: {16475, 81}, {26626, 86}, {47998, 514}
X(50290) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3883, 49684}, {1, 4357, 49511}, {1, 33082, 3879}, {10, 37, 4078}, {10, 3950, 3773}, {10, 3986, 3842}, {10, 3993, 2321}, {10, 4133, 594}, {10, 4780, 3696}, {10, 25354, 5257}, {37, 4026, 10}, {238, 17023, 38049}, {594, 49462, 4133}, {1001, 1486, 5248}, {1001, 4657, 1125}, {1125, 3821, 142}, {1211, 37593, 4028}, {1213, 3696, 10}, {3717, 29659, 38191}, {3755, 5257, 10}, {3842, 4085, 10}, {3931, 4205, 10}, {4425, 43223, 226}, {4649, 24697, 4416}, {31191, 38059, 31289}, {33149, 40328, 24199}, {41311, 49740, 551}


X(50291) = X(1)X(2)∩X(37)X(528)

Barycentrics    2*a^3 + a^2*b + 4*a*b^2 - b^3 + a^2*c + 6*a*b*c + b^2*c + 4*a*c^2 + b*c^2 - c^3 : :
X(50291) = 2 X[10] + X[49476], 4 X[1125] - X[49466], 5 X[29622] - 3 X[38314], 2 X[3664] + X[49448], 4 X[3842] - X[3883], X[3879] + 2 X[49457], 2 X[7228] + X[49513], 2 X[24325] + X[49527], 5 X[40328] + X[49534]

X(50291) lies on these lines: {1, 2}, {37, 528}, {86, 49529}, {241, 5434}, {355, 39605}, {515, 44430}, {518, 17392}, {527, 984}, {536, 49725}, {537, 49521}, {538, 50169}, {547, 15251}, {726, 50119}, {740, 50110}, {752, 49692}, {1001, 50130}, {1266, 24693}, {1323, 7179}, {1390, 10712}, {1449, 38097}, {1573, 43065}, {1738, 17301}, {1757, 4349}, {2550, 50080}, {2796, 50090}, {3242, 38086}, {3263, 4692}, {3416, 17251}, {3664, 49448}, {3672, 38092}, {3696, 4971}, {3746, 4223}, {3753, 14839}, {3842, 3883}, {3879, 49457}, {3913, 19309}, {3925, 50103}, {3932, 17359}, {3997, 5276}, {4029, 4693}, {4078, 5263}, {4104, 33073}, {4301, 7385}, {4307, 6172}, {4421, 19322}, {4429, 17399}, {4645, 17254}, {4648, 16496}, {4649, 24393}, {4656, 33109}, {4664, 28580}, {4667, 49712}, {4688, 28503}, {4714, 26234}, {4737, 30758}, {4755, 49740}, {4780, 17319}, {4844, 47766}, {5011, 5119}, {5257, 33076}, {5283, 11355}, {5316, 17722}, {5750, 33165}, {5846, 49731}, {5847, 17346}, {5880, 49747}, {5882, 21554}, {5988, 13178}, {6173, 7174}, {6998, 11362}, {7228, 49513}, {7322, 26098}, {7390, 7991}, {7407, 37714}, {8273, 21487}, {8666, 19314}, {8715, 19310}, {9041, 49481}, {9300, 40133}, {9441, 13634}, {10175, 24808}, {11113, 14537}, {11194, 19323}, {12513, 19313}, {13161, 17528}, {13745, 50222}, {15485, 25072}, {15668, 49688}, {16475, 38057}, {16491, 37650}, {16857, 48824}, {17000, 49685}, {17133, 50086}, {17245, 49465}, {17259, 49681}, {17277, 49684}, {17297, 49511}, {17300, 49505}, {17313, 47358}, {17320, 50091}, {17330, 28538}, {17378, 50075}, {17781, 42041}, {19701, 30615}, {20715, 31165}, {24199, 49455}, {24210, 31140}, {24325, 49527}, {24441, 24699}, {24452, 28301}, {25101, 49482}, {25439, 26241}, {27785, 34719}, {28297, 49523}, {28313, 49474}, {28534, 49742}, {28542, 49456}, {31151, 50092}, {34379, 50133}, {34720, 37548}, {34746, 37528}, {40328, 49534}, {41310, 48810}, {41311, 48821}, {41312, 48829}, {41313, 48805}, {44217, 48840}, {49447, 49722}, {49483, 49733}, {49744, 50261}, {50096, 50099}, {50176, 50184}

X(50291) = midpoint of X(i) and X(j) for these {i,j}: {8, 17389}, {4664, 49720}, {17378, 50075}, {49447, 49722}, {49476, 50095}
X(50291) = reflection of X(i) in X(j) for these {i,j}: {49483, 49733}, {49740, 4755}, {50093, 50094}, {50095, 10}, {50099, 50096}
X(50291) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 8, 48851}, {2, 39587, 48856}, {2, 48856, 1}, {17244, 36534, 49768}, {30116, 41276, 1}, {32847, 36531, 10}, {36440, 36458, 41140}, {39586, 48851, 2}


X(50292) = X(1)X(2)∩X(37)X(49724)

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

X(50292) lies on these lines: {1, 2}, {37, 49724}, {63, 17314}, {81, 2321}, {192, 4001}, {312, 17377}, {319, 34064}, {321, 3879}, {333, 17315}, {524, 3175}, {527, 42044}, {540, 2901}, {553, 17133}, {594, 37595}, {599, 50068}, {940, 17299}, {1029, 4052}, {1211, 17372}, {1255, 5257}, {1817, 12437}, {1992, 42032}, {2136, 39592}, {2895, 4656}, {3058, 28538}, {3219, 3950}, {3305, 5839}, {3578, 50093}, {3663, 32863}, {3664, 28605}, {3666, 17388}, {3755, 33078}, {3782, 17374}, {3891, 4684}, {3913, 11350}, {3914, 32846}, {3943, 4641}, {3946, 33172}, {3977, 37683}, {3995, 4416}, {4007, 19822}, {4029, 33761}, {4030, 49475}, {4034, 25430}, {4035, 33133}, {4046, 4682}, {4054, 17778}, {4078, 32864}, {4102, 40438}, {4133, 4418}, {4356, 33083}, {4527, 4697}, {4663, 6057}, {4725, 35652}, {4780, 32948}, {4851, 5249}, {4889, 44417}, {4916, 5712}, {4921, 5325}, {4971, 42051}, {4980, 50116}, {5294, 17233}, {5295, 50169}, {5847, 32915}, {6173, 19819}, {8715, 11340}, {11246, 28484}, {11523, 37185}, {14210, 42715}, {16435, 37727}, {17242, 37652}, {17274, 50071}, {17295, 19786}, {17296, 19785}, {17297, 19796}, {17298, 19789}, {17309, 32777}, {17311, 24789}, {17319, 37653}, {17355, 37685}, {17362, 44307}, {17363, 41839}, {17373, 27184}, {17378, 42029}, {17386, 18134}, {17390, 31993}, {19723, 41313}, {19742, 25101}, {21255, 33150}, {23120, 37672}, {24210, 32852}, {30615, 49680}, {30713, 30939}, {31164, 42047}, {32925, 34379}, {32928, 49511}, {32943, 49684}, {37631, 50125}, {41629, 42033}, {42034, 50132}, {48834, 50066}, {48862, 50070}, {50043, 50089}, {50048, 50087}, {50052, 50084}, {50063, 50081}

X(50292) = reflection of X(i) in X(j) for these {i,j}: {17781, 3175}, {50106, 553}
X(50292) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {145, 34255, 5256}, {1999, 6542, 306}, {3187, 3912, 26723}, {3687, 49761, 20017}, {33088, 39594, 26015}, {40940, 49765, 32858}


X(50293) = X(1)X(75)∩X(2)X(3791)

Barycentrics    2*a^3 + 3*a^2*b + 2*a*b^2 + 3*a^2*c + 4*a*b*c + b^2*c + 2*a*c^2 + b*c^2 : :
X(50293) = 3 X[551] + X[4349], X[3332] + 3 X[10186], 7 X[3622] + X[4307]

X(50293) lies on these lines: {1, 75}, {2, 3791}, {6, 3842}, {8, 43985}, {10, 1100}, {31, 10180}, {37, 4672}, {38, 8025}, {141, 1125}, {145, 31313}, {238, 16826}, {319, 19856}, {335, 4432}, {516, 550}, {537, 24358}, {551, 752}, {726, 4670}, {756, 19717}, {894, 49456}, {940, 6682}, {984, 17379}, {1001, 16679}, {1215, 5311}, {1255, 32930}, {1449, 39586}, {1621, 40592}, {1698, 3759}, {1757, 46922}, {2345, 4535}, {3187, 27798}, {3332, 10186}, {3616, 17300}, {3622, 4307}, {3624, 17307}, {3634, 4991}, {3635, 49467}, {3685, 29580}, {3715, 19739}, {3720, 30982}, {3723, 3993}, {3739, 49477}, {3741, 37595}, {3745, 37869}, {3773, 5750}, {3775, 3879}, {3782, 23812}, {3821, 17045}, {3828, 50124}, {3836, 17023}, {3923, 16777}, {3941, 5248}, {3952, 19741}, {3980, 20182}, {4096, 19722}, {4356, 17764}, {4362, 19701}, {4363, 28516}, {4364, 17770}, {4407, 34379}, {4434, 9347}, {4645, 29586}, {4649, 16830}, {4655, 17321}, {4667, 17771}, {4682, 6685}, {4687, 16468}, {4697, 28606}, {4716, 29584}, {4732, 16884}, {4909, 19868}, {5287, 25496}, {5333, 32914}, {5711, 21769}, {5849, 24317}, {5901, 29207}, {6541, 17369}, {6703, 29671}, {15569, 49482}, {15668, 16825}, {16475, 16831}, {16477, 17260}, {16525, 17750}, {17019, 32772}, {17021, 32944}, {17056, 29645}, {17232, 25539}, {17234, 29646}, {17243, 24295}, {17297, 25055}, {17317, 29637}, {17320, 32857}, {17322, 33082}, {17381, 29674}, {17390, 49560}, {17391, 33087}, {17396, 33149}, {17397, 32784}, {17450, 29823}, {17469, 30562}, {17599, 42053}, {17793, 37632}, {24331, 38315}, {24478, 24923}, {25351, 26626}, {26109, 33130}, {27691, 39897}, {28558, 41312}, {28595, 29647}, {29571, 31289}, {29630, 31252}, {29650, 37674}, {29841, 33111}, {32775, 37635}, {32913, 42028}, {33064, 37631}, {42025, 42055}, {46845, 49462}

X(50293) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 86, 24325}, {1, 5263, 49471}, {1, 10436, 32921}, {1, 17394, 5625}, {1, 24325, 49472}, {1, 24342, 4360}, {1, 43997, 75}, {1, 49474, 17393}, {10, 1100, 49489}, {37, 33682, 4672}, {940, 29644, 6682}, {1386, 28639, 1125}, {3634, 4991, 17348}, {3745, 37869, 43223}, {4649, 16830, 49457}, {5311, 19684, 1215}, {29571, 38049, 31289}


X(50294) = X(1)X(527)∩X(6)X(519)

Barycentrics    8*a^3 + a^2*b + 4*a*b^2 - b^3 + a^2*c + b^2*c + 4*a*c^2 + b*c^2 - c^3 : :
X(50294) = 5 X[1] + X[24695], X[2321] - 4 X[49482], X[2321] + 2 X[49684], 2 X[4856] + X[49460], 2 X[17355] + X[49681], 2 X[49482] + X[49684], X[17301] - 3 X[38315], 4 X[1386] - X[3755], X[3244] + 2 X[4672], 2 X[3635] + X[32935], 4 X[3636] - X[4655], X[17274] - 3 X[38314], 2 X[3946] - 5 X[16491], 5 X[16491] - X[50080], 3 X[38023] - X[48829]

X(50294) lies on these lines: {1, 527}, {2, 3883}, {6, 519}, {9, 48856}, {226, 17469}, {354, 2835}, {516, 17301}, {524, 50224}, {528, 1386}, {537, 3993}, {551, 752}, {553, 2263}, {1100, 30331}, {1456, 5434}, {2094, 3677}, {2550, 4989}, {3241, 3685}, {3244, 4672}, {3246, 29571}, {3332, 31162}, {3452, 17716}, {3635, 32935}, {3636, 4655}, {3663, 28534}, {3679, 16469}, {3686, 48802}, {3707, 36480}, {3758, 49771}, {3886, 50129}, {3945, 17274}, {3946, 16491}, {4029, 4432}, {4307, 6173}, {4315, 6610}, {4339, 34701}, {4353, 49747}, {4646, 34639}, {4648, 16487}, {4684, 50133}, {4971, 49484}, {5263, 50095}, {5695, 28313}, {5733, 13464}, {5750, 48851}, {5846, 17359}, {5853, 16475}, {6172, 7174}, {8692, 25072}, {15287, 40726}, {15601, 39587}, {16020, 38093}, {16370, 21002}, {16468, 24393}, {16970, 48854}, {17023, 49709}, {17133, 50126}, {17245, 19883}, {17251, 19868}, {17264, 49476}, {17354, 49762}, {17382, 49630}, {17766, 38049}, {19875, 37650}, {28297, 49463}, {28503, 50118}, {28538, 29594}, {28542, 49472}, {28562, 50091}, {28580, 50109}, {31140, 40940}, {32922, 50119}, {38023, 48829}, {41140, 49720}

X(50294) = midpoint of X(i) and X(j) for these {i,j}: {6, 50130}, {3241, 50127}, {3886, 50129}
X(50294) = reflection of X(i) in X(j) for these {i,j}: {3755, 50114}, {29594, 48810}, {49630, 17382}, {49747, 4353}, {50080, 3946}, {50092, 551}, {50114, 1386}
X(50294) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {551, 4349, 17392}, {1279, 17392, 551}, {3241, 3685, 50110}, {49482, 49684, 2321}


X(50295) = X(1)X(69)∩X(2)X(31)

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 : :
X(50295) = 2 X[4643] + X[36479], 5 X[4748] - 2 X[36480]

X(50295) lies on these lines: {1, 69}, {2, 31}, {3, 16872}, {4, 9}, {6, 4026}, {7, 4655}, {8, 192}, {11, 37660}, {21, 7295}, {37, 3416}, {42, 5739}, {43, 14555}, {44, 38047}, {45, 3932}, {55, 1211}, {72, 3779}, {75, 23690}, {141, 1001}, {144, 32935}, {145, 17343}, {193, 4649}, {200, 4104}, {219, 15984}, {306, 968}, {307, 2263}, {319, 49470}, {329, 1215}, {333, 32773}, {344, 29674}, {345, 846}, {346, 3773}, {348, 5018}, {377, 28287}, {388, 1423}, {390, 3775}, {391, 4085}, {405, 7083}, {406, 2212}, {443, 27626}, {474, 28271}, {497, 3741}, {511, 35628}, {518, 4643}, {519, 4356}, {524, 48830}, {527, 48851}, {528, 17251}, {537, 48849}, {594, 5695}, {599, 4966}, {726, 4419}, {756, 10327}, {894, 24695}, {908, 29828}, {958, 1503}, {960, 3781}, {986, 24478}, {992, 37148}, {993, 3220}, {997, 1064}, {1008, 5224}, {1009, 20992}, {1125, 4349}, {1150, 11269}, {1279, 17237}, {1284, 12588}, {1330, 26110}, {1352, 31394}, {1376, 4192}, {1386, 4657}, {1441, 4331}, {1478, 1756}, {1479, 10479}, {1621, 32782}, {1698, 17353}, {1699, 18229}, {1724, 19784}, {1738, 4384}, {1742, 36706}, {1757, 29659}, {1780, 19854}, {1836, 31993}, {1962, 32852}, {2198, 26085}, {2308, 29647}, {2886, 5737}, {2895, 17018}, {3219, 29667}, {3240, 37656}, {3242, 17253}, {3243, 49505}, {3332, 19843}, {3434, 31330}, {3454, 10198}, {3474, 3980}, {3475, 29651}, {3579, 5955}, {3616, 17300}, {3617, 17764}, {3618, 16468}, {3619, 15485}, {3620, 16484}, {3621, 49534}, {3622, 17375}, {3626, 4901}, {3632, 49527}, {3634, 15601}, {3661, 3685}, {3662, 16823}, {3666, 3966}, {3672, 32921}, {3679, 3717}, {3683, 32777}, {3686, 3755}, {3687, 17594}, {3696, 17275}, {3705, 38000}, {3720, 33080}, {3731, 4078}, {3739, 5880}, {3750, 33084}, {3751, 4416}, {3757, 27184}, {3790, 17261}, {3821, 4000}, {3826, 17259}, {3827, 24316}, {3831, 5084}, {3840, 26105}, {3842, 5296}, {3844, 15254}, {3886, 17270}, {3914, 5271}, {3925, 19732}, {3931, 5814}, {3971, 3974}, {3989, 32854}, {3993, 17314}, {3996, 41816}, {4007, 4133}, {4028, 37553}, {4034, 4780}, {4042, 49724}, {4096, 5423}, {4138, 25525}, {4201, 41886}, {4205, 5711}, {4295, 49598}, {4312, 25590}, {4359, 32950}, {4362, 4425}, {4363, 17768}, {4364, 5846}, {4368, 20539}, {4383, 41002}, {4389, 32922}, {4407, 17765}, {4413, 5241}, {4414, 17740}, {4418, 19822}, {4429, 17277}, {4432, 20533}, {4438, 5273}, {4450, 41809}, {4454, 17767}, {4470, 28508}, {4644, 17770}, {4659, 28526}, {4665, 28530}, {4670, 28570}, {4672, 5749}, {4676, 17289}, {4679, 30818}, {4683, 5905}, {4690, 28581}, {4691, 15593}, {4708, 28566}, {4748, 17766}, {4851, 15569}, {4864, 47358}, {4972, 5278}, {4974, 5222}, {4981, 5014}, {5051, 5230}, {5220, 17332}, {5223, 49529}, {5235, 14009}, {5250, 22370}, {5257, 16970}, {5284, 33172}, {5311, 6536}, {5361, 33142}, {5484, 36858}, {5550, 25539}, {5554, 25024}, {5686, 49693}, {5712, 32946}, {5745, 7710}, {5752, 22301}, {5772, 6172}, {5774, 37715}, {5794, 50050}, {5839, 49488}, {6646, 24349}, {6653, 29593}, {7226, 33090}, {7232, 25557}, {7262, 26065}, {7270, 31359}, {7301, 16865}, {8616, 32783}, {8692, 34573}, {9623, 28849}, {9711, 34807}, {9780, 25611}, {10371, 37548}, {10449, 15824}, {10453, 37653}, {10472, 48902}, {10477, 21746}, {10516, 30847}, {11679, 24210}, {13723, 23868}, {13728, 16466}, {14552, 32853}, {15310, 36474}, {15523, 17776}, {16043, 29991}, {16342, 29981}, {16469, 29598}, {16475, 17023}, {16496, 49466}, {16676, 49766}, {16704, 29829}, {16830, 17248}, {16832, 38052}, {16833, 50091}, {17239, 49484}, {17246, 49453}, {17250, 49709}, {17256, 32850}, {17258, 49447}, {17271, 49746}, {17274, 24231}, {17276, 49483}, {17299, 49462}, {17316, 32846}, {17325, 38315}, {17328, 49450}, {17329, 49499}, {17330, 48829}, {17344, 49478}, {17362, 49486}, {17559, 46827}, {17592, 32861}, {17725, 26245}, {17755, 24715}, {18141, 26102}, {18228, 44431}, {18517, 48887}, {19785, 32776}, {19789, 33145}, {19804, 33068}, {19853, 26045}, {20011, 43990}, {20017, 27804}, {20075, 32945}, {20078, 32940}, {21020, 33094}, {22097, 36844}, {22793, 39564}, {24331, 38053}, {24336, 29054}, {24441, 28503}, {24477, 29655}, {24597, 29631}, {24655, 25681}, {24691, 28600}, {24703, 44417}, {25568, 29670}, {26037, 32948}, {26132, 33130}, {26227, 26580}, {26228, 32775}, {26363, 37530}, {27065, 29679}, {28250, 50199}, {28538, 41312}, {28558, 35578}, {28562, 48809}, {28605, 33100}, {28606, 33075}, {29635, 37642}, {29640, 30828}, {29685, 32912}, {29814, 32863}, {29822, 31034}, {29830, 31017}, {29837, 37683}, {30478, 48932}, {30699, 33154}, {30970, 33104}, {31018, 32931}, {31144, 49720}, {31211, 38204}, {31419, 48944}, {32099, 49471}, {32857, 42697}, {32862, 33761}, {35892, 39543}, {36534, 49704}, {38316, 49768}, {40091, 48803}, {42696, 49474}, {48831, 48839}, {49492, 49735}, {49515, 49688}, {49698, 50075}, {49754, 50016}, {50080, 50095}

X(50295) = reflection of X(i) in X(j) for these {i,j}: {3332, 48900}, {4349, 1125}, {48802, 17251}
X(50295) = complement of X(4307)
X(50295) = crossdifference of every pair of points on line {1459, 2484}
X(50295) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17272, 49511}, {1, 33082, 69}, {2, 4388, 26098}, {2, 33083, 26034}, {7, 39581, 24325}, {8, 9791, 192}, {8, 17257, 984}, {10, 3923, 2345}, {10, 4660, 2550}, {75, 24723, 24248}, {238, 32784, 2}, {333, 32773, 33137}, {748, 32781, 2}, {756, 33074, 10327}, {846, 32778, 345}, {960, 17792, 3781}, {966, 2550, 10}, {984, 24697, 17257}, {984, 33076, 8}, {1215, 4703, 329}, {1621, 32782, 33171}, {2345, 5698, 3923}, {3219, 29667, 33163}, {3617, 27549, 33165}, {3757, 27184, 33144}, {3821, 16825, 4000}, {3844, 15254, 17279}, {3846, 32916, 2}, {3883, 4357, 1}, {4655, 24325, 7}, {4683, 32771, 5905}, {5743, 44419, 1376}, {7262, 32780, 26065}, {7290, 17306, 1125}, {9780, 26685, 33159}, {16468, 29633, 3618}, {16469, 29598, 38049}, {17123, 33174, 2}, {17332, 49524, 5220}, {19822, 44447, 4418}, {24331, 49676, 38053}, {24697, 33076, 984}, {25760, 32917, 2}, {25960, 32918, 2}, {26102, 33085, 18141}, {28606, 33075, 33088}, {29651, 33064, 3475}, {31330, 32947, 3434}, {32776, 32914, 19785}, {32946, 43223, 5712}, {42334, 49459, 8}


X(50296) = X(1)X(524)∩X(2)X(31)

Barycentrics    2*a^3 - a^2*b - a*b^2 - b^3 - a^2*c - 3*a*b*c - b^2*c - a*c^2 - b*c^2 - c^3 : :
X(50296) = X[984] + 2 X[3883], 2 X[984] + X[49506], 5 X[984] - 2 X[49527], 4 X[984] - X[49534], 4 X[3883] - X[49506], 5 X[3883] + X[49527], 8 X[3883] + X[49534], 5 X[49506] + 4 X[49527], 2 X[49506] + X[49534], X[49506] + 4 X[50093], 8 X[49527] - 5 X[49534], X[49527] - 5 X[50093], X[49534] - 8 X[50093], 4 X[3686] - X[49459], 2 X[4416] + X[49490], 2 X[17392] - 3 X[25055], 4 X[17332] - X[49448], 5 X[17331] - 2 X[49457], 2 X[17334] + X[49532], X[17347] + 2 X[49479], 2 X[17362] + X[49469], X[17363] + 2 X[49471], 3 X[19875] - 2 X[49725], 3 X[19875] - 4 X[49731], 3 X[38314] - X[50133], 2 X[49466] + X[49503]

X(50296) lies on these lines: {1, 524}, {2, 31}, {8, 4439}, {9, 80}, {10, 598}, {21, 7301}, {30, 6210}, {37, 28538}, {43, 41002}, {44, 29659}, {45, 32847}, {69, 16484}, {75, 2796}, {141, 15485}, {256, 49735}, {320, 24331}, {333, 33141}, {355, 7609}, {392, 9025}, {516, 40840}, {519, 751}, {527, 31178}, {537, 17333}, {540, 48825}, {542, 31394}, {551, 4357}, {597, 4026}, {599, 1001}, {674, 5692}, {726, 49748}, {740, 27481}, {846, 3966}, {908, 27777}, {968, 32861}, {993, 24436}, {1125, 17227}, {1150, 24217}, {1211, 8616}, {1386, 41311}, {1423, 5434}, {1621, 31143}, {1654, 32941}, {1698, 15601}, {1738, 49630}, {1757, 47359}, {1992, 4649}, {2177, 37656}, {3058, 49724}, {3219, 33169}, {3241, 17257}, {3246, 17237}, {3305, 33079}, {3416, 41313}, {3550, 5743}, {3654, 6211}, {3661, 4432}, {3683, 32778}, {3685, 29615}, {3686, 49459}, {3707, 49772}, {3717, 4669}, {3750, 5739}, {3757, 4703}, {3758, 49710}, {3763, 8692}, {3828, 17353}, {3886, 42334}, {3915, 26064}, {4085, 17349}, {4141, 33089}, {4239, 5363}, {4356, 49543}, {4384, 24715}, {4389, 50023}, {4407, 36534}, {4416, 49490}, {4423, 33085}, {4450, 26037}, {4512, 33160}, {4655, 16823}, {4657, 38023}, {4660, 17277}, {4683, 33103}, {4688, 28534}, {4690, 4702}, {4740, 28542}, {4912, 49483}, {4933, 33077}, {4966, 22165}, {5224, 49482}, {5235, 33104}, {5263, 31144}, {5271, 33095}, {5278, 32865}, {5284, 33080}, {5737, 33106}, {5846, 49737}, {5847, 29574}, {6172, 48849}, {7083, 16418}, {7290, 17392}, {7295, 16370}, {9041, 17332}, {9791, 32921}, {12699, 38330}, {15254, 29674}, {15569, 50125}, {16569, 44419}, {16815, 24693}, {16825, 24723}, {16833, 50080}, {16885, 38087}, {17132, 49493}, {17133, 49452}, {17247, 49472}, {17251, 48805}, {17256, 36480}, {17258, 49455}, {17306, 28640}, {17331, 49457}, {17334, 49532}, {17344, 42819}, {17347, 49479}, {17360, 49764}, {17362, 49469}, {17363, 49471}, {17389, 50111}, {17579, 28287}, {17725, 26580}, {17755, 50096}, {17768, 49727}, {19732, 33109}, {19875, 33159}, {19883, 25539}, {21358, 29637}, {24325, 28558}, {24695, 35578}, {25351, 29628}, {27065, 33074}, {28329, 49462}, {28498, 29622}, {28503, 49742}, {28580, 50086}, {29573, 32846}, {29633, 47352}, {29651, 33066}, {31019, 31177}, {31179, 32843}, {31339, 50171}, {32854, 33761}, {32914, 33154}, {33075, 33092}, {34645, 49729}, {36479, 49712}, {38314, 50133}, {39704, 49711}, {41140, 50091}, {46922, 48822}, {48851, 50127}, {49466, 49503}, {49474, 50098}, {49521, 50088}

X(50296) = midpoint of X(i) and X(j) for these {i,j}: {3241, 50074}, {3883, 50093}, {17346, 49746}, {49470, 50077}
X(50296) = reflection of X(i) in X(j) for these {i,j}: {1, 49740}, {984, 50093}, {3679, 17330}, {17378, 551}, {17389, 50111}, {49474, 50098}, {49720, 10}, {49725, 49731}, {50086, 50095}, {50121, 3993}, {50125, 15569}, {50128, 24325}
X(50296) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 33076, 33165}, {10, 4759, 17354}, {748, 33083, 33174}, {846, 3966, 32855}, {984, 3883, 49506}, {984, 49506, 49534}, {1001, 33082, 33087}, {1992, 48830, 4649}, {3246, 17237, 29660}, {3757, 4703, 33101}, {4407, 49700, 36534}, {5263, 31144, 48809}, {5278, 32947, 32865}, {16825, 24723, 33149}, {17256, 49709, 36480}, {49725, 49731, 19875}


X(50297) = X(2)X(31)∩X(10)X(528)

Barycentrics    2*a^3 - 2*a^2*b - 2*a*b^2 - b^3 - 2*a^2*c - 6*a*b*c - 2*b^2*c - 2*a*c^2 - 2*b*c^2 - c^3 : :
X(50297) = 2 X[3686] + X[49471], 5 X[3616] - X[50133], 2 X[3842] + X[3883], X[17378] - 3 X[25055], 3 X[19875] - X[49720], 5 X[17331] + X[49490], 2 X[17332] + X[49479], 3 X[19883] - 2 X[49738], 3 X[38314] + X[50074]

X(50297) lies on these lines: {1, 4407}, {2, 31}, {6, 48822}, {9, 48851}, {10, 528}, {30, 45305}, {37, 519}, {45, 4439}, {75, 28542}, {391, 49497}, {516, 36728}, {524, 551}, {527, 24325}, {537, 50093}, {674, 10176}, {726, 49742}, {740, 50095}, {966, 32941}, {1001, 3775}, {1125, 17237}, {1213, 49482}, {1654, 16484}, {2796, 4688}, {3246, 4708}, {3616, 50133}, {3679, 3773}, {3707, 4753}, {3715, 29669}, {3739, 28534}, {3797, 50086}, {3828, 24295}, {3842, 3883}, {3892, 9038}, {3986, 49684}, {3993, 4971}, {4085, 17277}, {4134, 9054}, {4364, 50023}, {4384, 50080}, {4425, 50103}, {4643, 24331}, {4655, 6173}, {4660, 17259}, {4669, 4923}, {4670, 49710}, {4690, 49764}, {4703, 31164}, {4725, 15569}, {4755, 28538}, {4759, 17369}, {4974, 50114}, {5224, 15485}, {5235, 10707}, {5241, 6174}, {5296, 48856}, {6172, 32935}, {8692, 17327}, {11114, 31339}, {16370, 23868}, {16815, 24715}, {16823, 17254}, {16825, 17301}, {16832, 24693}, {17250, 29660}, {17260, 33076}, {17272, 17322}, {17289, 19875}, {17297, 33082}, {17331, 49490}, {17332, 49479}, {17333, 31178}, {17335, 29659}, {17389, 17772}, {17767, 49722}, {17768, 49733}, {19732, 31140}, {19883, 21255}, {24692, 34824}, {28297, 50117}, {28503, 49737}, {28554, 50090}, {28558, 50116}, {28580, 50096}, {29575, 32846}, {36479, 49701}, {36480, 49700}, {36531, 49709}, {37654, 48830}, {38314, 50074}, {41002, 43223}, {42057, 49724}, {48805, 48809}, {48853, 50115}, {49462, 50085}, {49730, 49736}

X(50297) = midpoint of X(i) and X(j) for these {i,j}: {1, 17346}, {3679, 49746}, {17330, 49740}, {17333, 31178}, {49462, 50085}
X(50297) = reflection of X(i) in X(j) for these {i,j}: {10, 49731}, {17392, 1125}, {49725, 3828}
X(50297) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17256, 4407}, {966, 47357, 48802}, {3679, 17264, 3773}, {47357, 48802, 32941}


X(50298) = X(2)X(31)∩X(10)X(37)

Barycentrics    (b + c)*(2*a^2 + 2*a*b + b^2 + 2*a*c + b*c + c^2) : :
X(50298) = 9 X[2] - X[4307], 3 X[10] + X[4356], X[4407] - 4 X[4708], X[4349] - 5 X[19862], X[7174] + 3 X[48851]

X(50298) lies on these lines: {1, 319}, {2, 31}, {5, 516}, {10, 37}, {42, 41809}, {65, 27691}, {86, 33082}, {140, 29207}, {141, 1125}, {142, 39580}, {306, 10180}, {321, 6536}, {405, 23868}, {518, 4407}, {537, 48853}, {551, 4966}, {726, 4364}, {846, 19808}, {894, 24697}, {984, 3778}, {993, 19266}, {1001, 16846}, {1211, 43223}, {1284, 16603}, {1503, 48932}, {1654, 4649}, {1698, 4429}, {1738, 24603}, {1757, 17256}, {3616, 17238}, {3624, 17234}, {3662, 40328}, {3678, 22277}, {3679, 50121}, {3685, 29610}, {3686, 49489}, {3717, 50094}, {3739, 3821}, {3797, 29576}, {3823, 25352}, {3827, 24317}, {3828, 17359}, {3844, 4698}, {3879, 5625}, {3896, 8013}, {3914, 27798}, {3923, 17303}, {3966, 29644}, {3995, 48644}, {4038, 37653}, {4349, 17245}, {4357, 24231}, {4363, 17767}, {4425, 31993}, {4432, 26582}, {4472, 17768}, {4643, 17771}, {4647, 42714}, {4655, 10436}, {4657, 16825}, {4665, 28522}, {4670, 17770}, {4672, 5750}, {4687, 29674}, {4699, 33149}, {4974, 17023}, {4981, 29685}, {5018, 17095}, {5233, 29825}, {5235, 29631}, {5247, 19865}, {5248, 16848}, {5263, 19856}, {5278, 29647}, {5333, 32949}, {5550, 17232}, {5737, 29635}, {5743, 6685}, {5846, 25358}, {6210, 7380}, {6651, 24715}, {7174, 48851}, {8040, 15523}, {8053, 16292}, {9780, 17280}, {9791, 28604}, {12579, 50054}, {13728, 27633}, {14815, 21035}, {15569, 17239}, {16468, 17381}, {16475, 29603}, {16593, 38059}, {16823, 17326}, {16826, 32846}, {16830, 33076}, {16929, 30175}, {17045, 49477}, {17237, 49676}, {17246, 50117}, {17247, 49493}, {17251, 48822}, {17257, 32935}, {17260, 33159}, {17264, 19875}, {17275, 49488}, {17277, 29633}, {17307, 29637}, {17321, 32921}, {17398, 33682}, {17400, 29646}, {17765, 36480}, {19701, 32946}, {19732, 25453}, {19822, 32934}, {19832, 29859}, {19857, 49598}, {19868, 49473}, {21085, 37593}, {21242, 30970}, {24342, 24723}, {26115, 26772}, {27081, 29822}, {29640, 30832}, {29653, 48651}, {29659, 49693}, {29846, 31247}, {30571, 31027}, {31025, 48641}, {32850, 36531}, {36534, 49691}, {40999, 42289}, {48628, 49452}

X(50298) = midpoint of X(17251) and X(48822)
X(50298) = crossdifference of every pair of points on line {3250, 3733}
X(50298) = barycentric product X(i)*X(j) for these {i,j}: {10, 17397}, {850, 28860}, {3695, 31907}, {3952, 28859}
X(50298) = barycentric quotient X(i)/X(j) for these {i,j}: {17397, 86}, {28859, 7192}, {28860, 110}
X(50298) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5224, 3775}, {2, 32784, 3836}, {10, 37, 3773}, {10, 3755, 4732}, {10, 3986, 4078}, {10, 3993, 594}, {10, 4026, 4085}, {10, 4709, 4733}, {10, 5257, 3842}, {10, 25354, 37}, {594, 3993, 4527}, {1213, 4026, 10}, {1386, 25498, 1125}, {3616, 17238, 33087}, {3634, 24295, 17385}, {4425, 31993, 48643}, {15254, 17385, 24295}, {15569, 17239, 49560}, {24723, 28653, 24342}


X(50299) = X(2)X(31)∩X(10)X(524)

Barycentrics    2*a^3 + 2*a^2*b + 2*a*b^2 - b^3 + 2*a^2*c + 6*a*b*c + 2*b^2*c + 2*a*c^2 + 2*b*c^2 - c^3 : :
X(50299) = 2 X[3664] + X[49457], X[3879] + 2 X[4732], X[4709] + 2 X[17390], 2 X[7228] + X[49520], X[17346] - 3 X[19875], 5 X[17391] + X[49459], 3 X[25055] - X[49746], 3 X[39704] + X[50075]

X(50299) lies on these lines: {1, 4743}, {2, 31}, {10, 524}, {37, 2796}, {44, 25352}, {86, 4085}, {142, 214}, {210, 23812}, {319, 3679}, {320, 4407}, {519, 3696}, {527, 50094}, {537, 49521}, {597, 3826}, {599, 3775}, {674, 5883}, {726, 49727}, {740, 27478}, {984, 50128}, {1125, 15810}, {1961, 48643}, {2550, 48830}, {3664, 49457}, {3685, 29620}, {3739, 28538}, {3755, 5625}, {3773, 24342}, {3821, 41311}, {3828, 5750}, {3842, 28558}, {3879, 4732}, {3923, 41313}, {3945, 49497}, {4078, 50118}, {4349, 4974}, {4363, 4439}, {4364, 24692}, {4429, 43997}, {4432, 29571}, {4648, 32941}, {4655, 39586}, {4660, 15668}, {4664, 28542}, {4675, 36480}, {4685, 37631}, {4693, 29569}, {4709, 17390}, {4755, 28534}, {4956, 17021}, {5311, 50102}, {5333, 32948}, {5434, 30097}, {5880, 41312}, {6173, 48854}, {7228, 49520}, {9041, 49479}, {16826, 24715}, {16828, 49723}, {17023, 25351}, {17132, 49456}, {17245, 49482}, {17278, 38023}, {17346, 19875}, {17369, 49769}, {17389, 50086}, {17391, 49459}, {17764, 29622}, {17767, 49748}, {17768, 49737}, {17772, 29617}, {19808, 48651}, {19870, 49744}, {19874, 50234}, {21242, 37633}, {24199, 49472}, {24331, 49700}, {25055, 49746}, {26580, 31177}, {28503, 49733}, {28554, 50119}, {28580, 50111}, {29597, 50080}, {29615, 32846}, {29653, 50104}, {29659, 41847}, {31143, 32949}, {31144, 33082}, {32935, 35578}, {34824, 50023}, {38049, 38204}, {39704, 50075}, {47359, 49693}, {48822, 48829}, {49474, 50121}

X(50299) = midpoint of X(i) and X(j) for these {i,j}: {1, 49720}, {984, 50128}, {3679, 17378}, {3696, 50125}, {17389, 50086}, {17392, 49725}, {49474, 50121}
X(50299) = reflection of X(i) in X(j) for these {i,j}: {551, 49738}, {17330, 3828}, {49740, 1125}, {50093, 3842}
X(50299) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 4667, 4753}, {320, 36531, 4407}, {599, 48809, 3775}


X(50300) = X(2)X(31)∩X(6)X(519)

Barycentrics    3*a^3 + a^2*b + a*b^2 + a^2*c + b^2*c + a*c^2 + b*c^2 : :
X(50300) = X[1] + 2 X[4672], 2 X[1] + X[32935], 4 X[4672] - X[32935], 2 X[6] + X[32941], 5 X[6] + X[49460], X[6] + 2 X[49482], 4 X[6] - X[49497], 7 X[6] - X[49680], 5 X[6] - 2 X[49685], 2 X[17355] + X[49684], 5 X[32941] - 2 X[49460], X[32941] - 4 X[49482], 2 X[32941] + X[49497], 7 X[32941] + 2 X[49680], 5 X[32941] + 4 X[49685], 5 X[48805] - X[49460], 4 X[48805] + X[49497], 7 X[48805] + X[49680], 5 X[48805] + 2 X[49685], X[49460] - 10 X[49482], 4 X[49460] + 5 X[49497], 7 X[49460] + 5 X[49680], X[49460] + 2 X[49685], 8 X[49482] + X[49497], 14 X[49482] + X[49680], 5 X[49482] + X[49685], 7 X[49497] - 4 X[49680], 5 X[49497] - 8 X[49685], 5 X[49680] - 14 X[49685], X[17274] - 3 X[25055], 3 X[38049] - X[50091], 2 X[1386] + X[3923], 4 X[1386] - X[32921], 2 X[3923] + X[32921], 3 X[38315] + X[49721], 3 X[16475] - X[16834], 3 X[16475] + X[50126], 4 X[1125] - X[4655], X[17301] - 3 X[38023], X[3416] - 4 X[24295], 4 X[3589] - X[4660], 5 X[3616] + X[24695], 5 X[3618] - 2 X[4085], X[3729] + 5 X[16491], X[3729] + 2 X[49472], 5 X[16491] - 2 X[49472], X[3751] + 2 X[49473], X[3886] + 2 X[49489], X[4523] + 2 X[12722], 2 X[4663] + X[49458], 4 X[4991] - X[49486], X[5695] + 2 X[49477], 2 X[17351] + X[49455], 3 X[47352] - X[48829], 2 X[49484] + X[49488]

X(50300) lies on these lines: {1, 190}, {2, 31}, {6, 519}, {8, 16477}, {9, 48854}, {44, 36480}, {45, 4759}, {86, 2163}, {239, 50086}, {320, 29660}, {516, 5085}, {524, 48810}, {527, 551}, {528, 597}, {535, 16792}, {536, 1386}, {612, 42056}, {614, 4697}, {726, 38315}, {740, 16475}, {894, 31178}, {960, 50064}, {1125, 4252}, {1150, 21747}, {1193, 16393}, {1449, 49471}, {1707, 6682}, {1743, 49457}, {1757, 50075}, {1836, 29654}, {2267, 16503}, {2308, 24552}, {2792, 5886}, {2796, 17301}, {2835, 5883}, {3008, 24693}, {3052, 6685}, {3241, 4649}, {3246, 4670}, {3286, 19247}, {3304, 19532}, {3416, 24295}, {3589, 4660}, {3616, 24695}, {3618, 4085}, {3654, 37510}, {3679, 5263}, {3683, 29644}, {3685, 29584}, {3729, 16491}, {3736, 4234}, {3745, 4011}, {3751, 49473}, {3886, 49489}, {4349, 29600}, {4363, 50023}, {4393, 4693}, {4415, 29842}, {4421, 37502}, {4450, 29663}, {4479, 30940}, {4523, 12722}, {4640, 29650}, {4641, 29652}, {4643, 49710}, {4663, 49458}, {4667, 49768}, {4683, 29648}, {4688, 16825}, {4702, 16666}, {4753, 16670}, {4755, 15254}, {4865, 5294}, {4892, 29855}, {4974, 16469}, {4991, 49486}, {5057, 29636}, {5248, 16300}, {5695, 49477}, {5749, 48849}, {5750, 48853}, {5847, 29594}, {6210, 13634}, {7083, 19322}, {7290, 24325}, {7295, 19326}, {8692, 15668}, {15601, 39586}, {16370, 20992}, {16394, 16466}, {16476, 16829}, {16484, 17379}, {16668, 49475}, {16786, 36479}, {17017, 32934}, {17024, 32940}, {17025, 32845}, {17120, 49490}, {17121, 49459}, {17277, 19875}, {17290, 24692}, {17330, 48809}, {17335, 36531}, {17351, 49455}, {17354, 32847}, {17359, 28538}, {17367, 24715}, {17368, 33076}, {17382, 28534}, {17469, 26223}, {17716, 27064}, {17766, 38047}, {17768, 49741}, {17772, 50079}, {18169, 42028}, {19251, 20470}, {19290, 27623}, {20172, 41140}, {20179, 49720}, {20292, 29852}, {21242, 24597}, {24703, 29645}, {24723, 29646}, {24725, 26230}, {26128, 41011}, {28503, 49726}, {28542, 50101}, {28562, 47352}, {28580, 50114}, {29057, 38029}, {29577, 32846}, {29634, 33096}, {29659, 49709}, {29666, 33067}, {29684, 32950}, {29686, 32859}, {29815, 32938}, {29819, 32933}, {29823, 36263}, {29826, 36277}, {29831, 32856}, {29834, 33151}, {29838, 33101}, {31137, 32942}, {32943, 37685}, {36534, 49712}, {37654, 48802}, {45223, 48855}, {47358, 49706}, {48803, 48870}, {48822, 49740}, {49484, 49488}, {49560, 50076}

X(50300) = midpoint of X(i) and X(j) for these {i,j}: {1, 50127}, {6, 48805}, {5695, 50120}, {16834, 50126}, {47359, 50130}, {48803, 48870}, {49484, 50124}
X(50300) = reflection of X(i) in X(j) for these {i,j}: {4655, 50092}, {4660, 48821}, {32935, 50127}, {32941, 48805}, {48805, 49482}, {48821, 3589}, {48826, 48866}, {49488, 50124}, {50076, 49560}, {50092, 1125}, {50120, 49477}, {50127, 4672}
X(50300) = crossdifference of every pair of points on line {3250, 3768}
X(50300) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 4672, 32935}, {6, 32941, 49497}, {6, 49460, 49685}, {6, 49482, 32941}, {9, 48854, 50094}, {31, 25496, 32916}, {1386, 3923, 32921}, {2308, 24552, 32853}, {3246, 4670, 24331}, {3729, 16491, 49472}, {4974, 50096, 16833}, {16475, 50126, 16834}, {17469, 26223, 32920}


X(50301) = X(1)X(528)∩X(2)X(31)

Barycentrics    2*a^3 + a^2*b + a*b^2 - b^3 + a^2*c + 3*a*b*c + b^2*c + a*c^2 + b*c^2 - c^3 : :
X(50301) = 4 X[3664] - X[49490], 2 X[3879] + X[49459], 2 X[4709] + X[17377], 3 X[24452] - X[50086], 5 X[1698] - 4 X[49731], 2 X[17330] - 3 X[19875], 2 X[3883] - 5 X[40328], 3 X[25055] - 4 X[49738], 3 X[25055] - 2 X[49740], 4 X[4732] - X[17363], 4 X[7228] - X[49532], X[17364] + 2 X[49457], 2 X[17365] + X[49448], 4 X[17390] - X[49469], 5 X[17391] - 2 X[49471], 4 X[24325] - X[49506], 2 X[24349] + X[49534], 2 X[49476] + X[49493]

X(50301) lies on these lines: {1, 528}, {2, 31}, {7, 48856}, {8, 50133}, {10, 3758}, {30, 1742}, {37, 28534}, {69, 48802}, {75, 519}, {81, 32865}, {86, 4660}, {149, 9345}, {192, 28542}, {239, 24693}, {320, 36480}, {516, 27475}, {524, 3416}, {527, 984}, {535, 30116}, {537, 50128}, {551, 3821}, {612, 31164}, {674, 5902}, {726, 49722}, {740, 17389}, {894, 33165}, {940, 31140}, {1054, 17723}, {1155, 29657}, {1698, 49731}, {1738, 4349}, {1743, 17303}, {1836, 1961}, {2177, 37635}, {2550, 4649}, {2792, 44430}, {2796, 4664}, {2886, 37604}, {3120, 9347}, {3241, 32921}, {3306, 17722}, {3434, 4038}, {3550, 17056}, {3685, 29575}, {3696, 4725}, {3745, 17889}, {3753, 9025}, {3826, 16468}, {3834, 29660}, {3883, 40328}, {3894, 9054}, {3920, 33103}, {3923, 17264}, {3932, 49726}, {3944, 4682}, {3980, 32855}, {4026, 43997}, {4085, 17379}, {4223, 7301}, {4334, 5434}, {4363, 32847}, {4389, 24692}, {4407, 4741}, {4418, 33092}, {4429, 33682}, {4432, 17244}, {4643, 36531}, {4644, 49712}, {4648, 16484}, {4654, 8270}, {4655, 16830}, {4657, 25055}, {4667, 49772}, {4670, 29659}, {4688, 28538}, {4693, 17316}, {4697, 29641}, {4715, 25384}, {4716, 50129}, {4732, 17363}, {4783, 24524}, {4859, 16491}, {4888, 16496}, {4924, 34641}, {4971, 49474}, {5249, 17716}, {5263, 17297}, {5268, 31142}, {5269, 33130}, {5276, 10712}, {5287, 33095}, {5297, 24725}, {5311, 20292}, {5363, 7465}, {5711, 17528}, {5717, 24440}, {5718, 6174}, {5846, 49733}, {5847, 50095}, {6172, 24695}, {6180, 11237}, {7228, 49532}, {7290, 38093}, {7321, 49455}, {9352, 29688}, {9440, 10056}, {10436, 33076}, {10448, 37299}, {10459, 34605}, {10707, 24217}, {12652, 31162}, {14996, 33136}, {15310, 36490}, {15485, 17245}, {16475, 38052}, {16779, 48821}, {17019, 33094}, {17234, 49482}, {17251, 33082}, {17271, 48809}, {17274, 48854}, {17294, 32846}, {17300, 32941}, {17302, 38314}, {17313, 48805}, {17333, 28558}, {17335, 25352}, {17354, 49769}, {17359, 29674}, {17364, 49457}, {17365, 49448}, {17367, 25351}, {17387, 49764}, {17390, 49469}, {17391, 49471}, {17400, 19883}, {17469, 27186}, {17725, 31019}, {17768, 49742}, {17772, 31314}, {19684, 32948}, {19871, 49723}, {20090, 49497}, {21242, 37684}, {24199, 49684}, {24325, 49506}, {24331, 49709}, {24349, 49534}, {24697, 39586}, {26627, 32844}, {28297, 49445}, {28322, 49523}, {28503, 49727}, {28580, 29574}, {28604, 50074}, {29020, 36732}, {29207, 36728}, {29573, 50126}, {29617, 50096}, {29640, 37540}, {29644, 33068}, {29676, 37520}, {29816, 33146}, {29847, 48646}, {31160, 40401}, {32857, 49747}, {32949, 33084}, {33072, 33169}, {33106, 37674}, {34606, 49745}, {34612, 37631}, {35596, 36263}, {37298, 37603}, {37607, 45700}, {42043, 49732}, {48627, 49472}, {49452, 50110}, {49476, 49493}

X(50301) = midpoint of X(i) and X(j) for these {i,j}: {8, 50133}, {17378, 49720}, {49476, 50119}
X(50301) = reflection of X(i) in X(j) for these {i,j}: {1, 17392}, {3679, 49725}, {17333, 50094}, {17346, 10}, {29617, 50096}, {31178, 50116}, {48825, 48868}, {49452, 50110}, {49493, 50119}, {49740, 49738}, {49746, 551}
X(50301) = crossdifference of every pair of points on line {3250, 22108}
X(50301) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5880, 33149}, {551, 3821, 17399}, {612, 33097, 33101}, {750, 33112, 17717}, {940, 33109, 33141}, {3980, 33073, 32855}, {5311, 20292, 33154}, {25352, 49710, 17335}, {33104, 37633, 24217}, {34612, 37631, 42042}, {49738, 49740, 25055}


X(50302) = X(1)X(75)∩X(2)X(31)

Barycentrics    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(50302) = 3 X[2] + X[4307], 2 X[4670] + X[36480], X[7174] - 3 X[48854], 3 X[551] - X[4356], 2 X[4407] + X[4644]

X(50302) lies on these lines: {1, 75}, {2, 31}, {3, 142}, {5, 29207}, {6, 10}, {8, 4649}, {9, 3842}, {37, 3923}, {42, 19684}, {55, 11358}, {56, 19533}, {57, 6682}, {58, 19858}, {63, 4697}, {69, 3775}, {81, 31330}, {85, 5018}, {87, 1220}, {226, 1460}, {244, 26627}, {306, 19719}, {312, 1961}, {321, 5311}, {354, 29652}, {388, 7175}, {405, 20992}, {498, 41263}, {515, 37474}, {518, 4670}, {519, 4923}, {524, 48809}, {528, 48822}, {537, 7174}, {551, 4356}, {595, 16690}, {612, 1215}, {673, 25351}, {726, 4363}, {730, 5145}, {756, 26223}, {870, 1921}, {873, 18064}, {894, 984}, {940, 3741}, {942, 35632}, {958, 20258}, {964, 2309}, {968, 10180}, {993, 3286}, {1100, 3696}, {1150, 30970}, {1193, 16454}, {1211, 32946}, {1279, 24331}, {1376, 6685}, {1386, 3739}, {1400, 37149}, {1449, 4732}, {1463, 36487}, {1468, 16738}, {1471, 17077}, {1503, 14529}, {1621, 5333}, {1698, 16468}, {1699, 23512}, {1724, 16828}, {1738, 17023}, {1742, 13727}, {1757, 3758}, {1761, 5327}, {1836, 4425}, {1918, 5264}, {1962, 32929}, {2050, 3817}, {2177, 19740}, {2209, 26115}, {2295, 40728}, {2304, 41239}, {2305, 25354}, {2308, 5278}, {2345, 3773}, {2550, 4085}, {2784, 36942}, {2796, 41312}, {2886, 6703}, {2975, 30035}, {3008, 38049}, {3072, 5713}, {3187, 21020}, {3210, 17600}, {3242, 49479}, {3244, 49460}, {3306, 29826}, {3332, 37570}, {3589, 3826}, {3616, 16484}, {3617, 37677}, {3624, 15485}, {3625, 49680}, {3626, 49685}, {3634, 17259}, {3661, 20132}, {3664, 19868}, {3666, 3980}, {3677, 42053}, {3679, 46922}, {3685, 16826}, {3706, 37595}, {3720, 24552}, {3723, 49462}, {3729, 49456}, {3742, 29668}, {3744, 29651}, {3745, 4362}, {3751, 49457}, {3752, 29650}, {3754, 31778}, {3757, 17716}, {3771, 17056}, {3772, 29645}, {3783, 37632}, {3791, 5271}, {3816, 37365}, {3822, 29046}, {3827, 24315}, {3835, 16874}, {3840, 37674}, {3841, 20083}, {3844, 17385}, {3891, 29816}, {3912, 20131}, {3914, 19834}, {3920, 32771}, {3925, 25453}, {3931, 20227}, {3932, 17369}, {3946, 20181}, {3989, 32933}, {3993, 5695}, {3996, 42042}, {4011, 44307}, {4026, 4660}, {4030, 29669}, {4038, 10453}, {4078, 17355}, {4096, 7322}, {4340, 19866}, {4344, 39581}, {4357, 4655}, {4359, 17017}, {4361, 49477}, {4364, 17768}, {4366, 17397}, {4384, 4974}, {4386, 41333}, {4389, 32857}, {4393, 4716}, {4407, 4644}, {4418, 28606}, {4419, 17767}, {4423, 25501}, {4429, 17381}, {4432, 16831}, {4434, 29828}, {4470, 17769}, {4472, 5846}, {4512, 17188}, {4527, 17314}, {4643, 17770}, {4650, 38000}, {4651, 19717}, {4659, 28516}, {4667, 34379}, {4675, 49676}, {4676, 4687}, {4682, 29649}, {4685, 19722}, {4693, 29570}, {4698, 15254}, {4703, 41011}, {4708, 28570}, {4709, 16884}, {4733, 17362}, {4758, 5853}, {4798, 17766}, {4805, 50232}, {4851, 49560}, {4946, 19745}, {4966, 17392}, {4970, 20182}, {4972, 29647}, {4981, 32912}, {5014, 29685}, {5015, 16800}, {5016, 27714}, {5132, 25440}, {5224, 19856}, {5247, 19853}, {5249, 5329}, {5250, 37232}, {5297, 32931}, {5363, 31019}, {5437, 9746}, {5550, 19278}, {5710, 28365}, {5791, 8258}, {5955, 17748}, {5988, 5989}, {6210, 6998}, {6211, 44430}, {6541, 17281}, {6650, 29592}, {6692, 49631}, {7083, 19309}, {7226, 32940}, {7295, 19310}, {7301, 19318}, {7413, 25525}, {8025, 17135}, {8033, 17149}, {8616, 25507}, {8692, 19878}, {9259, 41193}, {9345, 29824}, {9347, 17763}, {9454, 16788}, {9780, 16477}, {10022, 28503}, {10448, 11115}, {10479, 37559}, {11269, 21242}, {11680, 29845}, {12588, 16603}, {13610, 31359}, {14005, 27644}, {14199, 40783}, {14829, 37604}, {14996, 32919}, {15310, 36477}, {15569, 28639}, {15808, 19274}, {16458, 16466}, {16469, 16832}, {16476, 16819}, {16478, 16817}, {16496, 49491}, {16706, 29646}, {16801, 49709}, {16823, 40328}, {16834, 50096}, {16849, 21246}, {16872, 36015}, {16926, 17033}, {17000, 33076}, {17011, 32860}, {17018, 32945}, {17019, 32915}, {17061, 29842}, {17065, 24923}, {17116, 49493}, {17118, 49453}, {17234, 29637}, {17244, 20137}, {17248, 24697}, {17257, 24695}, {17279, 24295}, {17289, 20159}, {17291, 25539}, {17300, 33087}, {17318, 28522}, {17319, 49452}, {17321, 24248}, {17322, 24723}, {17325, 24692}, {17363, 42334}, {17368, 33159}, {17399, 25055}, {17592, 32932}, {17599, 24165}, {17720, 25385}, {17733, 37594}, {17765, 36479}, {17778, 33084}, {17889, 19786}, {18046, 29486}, {18134, 32783}, {18139, 24943}, {19273, 19862}, {19279, 19883}, {19281, 23682}, {19329, 23868}, {19741, 19998}, {19804, 29821}, {19808, 32778}, {19822, 33088}, {19863, 37522}, {20133, 27255}, {20135, 29571}, {20140, 27020}, {20142, 29576}, {20145, 29593}, {20148, 27091}, {20150, 45223}, {20153, 29581}, {20154, 24603}, {20155, 29594}, {20157, 38059}, {20174, 28612}, {20292, 32776}, {21005, 23803}, {23568, 25637}, {23812, 33064}, {24231, 50116}, {24653, 37576}, {24669, 28629}, {24725, 26580}, {24731, 30963}, {24789, 29654}, {25371, 29054}, {26037, 32911}, {26102, 32942}, {26109, 29839}, {26131, 27270}, {26446, 37510}, {26724, 29852}, {27184, 33097}, {27186, 29648}, {28562, 40096}, {28605, 32928}, {28618, 37288}, {28626, 30332}, {28699, 44706}, {28849, 44356}, {29016, 30147}, {29020, 36663}, {29057, 46475}, {29584, 50086}, {29597, 50111}, {29631, 33108}, {29634, 33130}, {29636, 33129}, {29641, 32780}, {29643, 32779}, {29653, 32777}, {29657, 32851}, {29659, 32850}, {29664, 33119}, {29667, 33072}, {29682, 33113}, {29814, 32943}, {29815, 32923}, {29829, 33136}, {29833, 33128}, {29837, 33141}, {29841, 33135}, {29847, 33133}, {29854, 33157}, {30942, 37633}, {31191, 38048}, {32773, 33109}, {32782, 32949}, {32864, 37685}, {33175, 37635}, {36534, 49675}, {36834, 38316}, {37150, 37715}, {37593, 37869}, {38315, 50023}, {39914, 45782}, {46845, 49461}, {47359, 49697}, {48810, 49738}, {49455, 49483}, {49458, 49478}, {49696, 50130}, {50094, 50127}

X(50302) = midpoint of X(10) and X(4349)
X(50302) = crossdifference of every pair of points on line {798, 834}
X(50302) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 75, 32921}, {1, 1740, 3736}, {1, 3886, 49471}, {1, 5263, 32941}, {1, 10436, 24325}, {1, 18792, 2274}, {1, 24342, 75}, {1, 43997, 86}, {1, 49474, 4360}, {2, 171, 32916}, {2, 4645, 32784}, {2, 17126, 32917}, {2, 26098, 3846}, {2, 32772, 25496}, {2, 33107, 25960}, {2, 33112, 25760}, {8, 4649, 49497}, {8, 17379, 4649}, {9, 39586, 3842}, {10, 33682, 6}, {55, 19701, 43223}, {81, 31330, 32853}, {86, 1010, 3736}, {86, 5263, 1}, {171, 238, 5156}, {894, 984, 32935}, {894, 16830, 984}, {1001, 8053, 5248}, {1001, 15668, 1125}, {1100, 3696, 49488}, {1125, 3821, 4657}, {1125, 49482, 1001}, {1386, 3739, 16825}, {1698, 16468, 17277}, {2049, 5711, 10}, {2049, 5765, 5783}, {2886, 6703, 29635}, {3416, 17303, 10}, {3624, 37603, 19270}, {3664, 19868, 49511}, {3745, 31993, 4362}, {3791, 27798, 5271}, {3842, 4672, 9}, {3920, 32771, 32920}, {3980, 29644, 3666}, {4384, 16475, 4974}, {4418, 28606, 32934}, {4429, 17381, 29633}, {4657, 5880, 3821}, {4682, 44417, 29649}, {5625, 49471, 1}, {5695, 16777, 3993}, {17118, 49453, 50117}, {17394, 49470, 1}, {19808, 33073, 32778}, {19856, 33082, 5224}, {27186, 29648, 33123}, {28639, 49484, 15569}, {29597, 50126, 50111}


X(50303) = X(1)X(527)∩X(2)X(31)

Barycentrics    5*a^3 + a^2*b + a*b^2 - b^3 + a^2*c + b^2*c + a*c^2 + b*c^2 - c^3 : :
X(50303) = 2 X[1] + X[24695], X[8] - 4 X[4672], X[69] - 4 X[49482], X[145] + 2 X[32935], X[193] + 2 X[32941], 3 X[16475] - X[50080], 3 X[16475] - 2 X[50114], 5 X[3751] - 2 X[4924], 4 X[1386] - X[24248], 5 X[3616] - 2 X[4655], 5 X[3618] - 2 X[4660], 2 X[3629] + X[49460], 2 X[3663] - 5 X[16491], X[3729] + 2 X[49684], 2 X[17351] + X[49681], 2 X[17382] - 3 X[38023], 3 X[38315] - X[49747], X[24280] + 2 X[32921], 3 X[25055] - 2 X[50092], 4 X[32455] - X[49680], 3 X[47352] - 2 X[48821]

X(50303) lies on these lines: {1, 527}, {2, 31}, {6, 528}, {8, 4672}, {58, 45700}, {69, 49482}, {145, 4693}, {192, 537}, {193, 32941}, {329, 17716}, {332, 4234}, {376, 1064}, {390, 4649}, {516, 16475}, {518, 50130}, {519, 1992}, {524, 48805}, {540, 48803}, {551, 3664}, {553, 34036}, {597, 48829}, {599, 48810}, {740, 50129}, {982, 2094}, {984, 4344}, {1001, 17392}, {1386, 17301}, {1457, 4334}, {1468, 11240}, {1738, 16469}, {1743, 2345}, {1795, 10072}, {1834, 34706}, {1836, 50103}, {2308, 3434}, {2550, 16468}, {2792, 5429}, {2796, 50101}, {2835, 5902}, {3246, 4675}, {3416, 17359}, {3474, 29821}, {3616, 4655}, {3618, 4660}, {3629, 49460}, {3663, 16491}, {3685, 17389}, {3729, 49684}, {3758, 36479}, {3883, 48851}, {3945, 16484}, {4295, 16478}, {4392, 35596}, {4432, 17316}, {4648, 15485}, {4659, 50017}, {4676, 17264}, {4677, 4923}, {4715, 47358}, {4725, 49484}, {4795, 24357}, {4865, 26065}, {4888, 16487}, {4971, 5695}, {5222, 24715}, {5230, 17577}, {5255, 34619}, {5263, 17346}, {5269, 31142}, {5363, 35988}, {5434, 6180}, {5625, 9791}, {5710, 34606}, {5712, 8616}, {5744, 17722}, {5749, 33076}, {5846, 49726}, {5847, 17294}, {5905, 17469}, {6173, 7290}, {6174, 37540}, {7277, 42871}, {7301, 37254}, {8424, 11194}, {8692, 17245}, {9812, 33135}, {9965, 17598}, {10385, 14547}, {10707, 11269}, {11031, 28610}, {11112, 16466}, {12652, 28194}, {14523, 24473}, {15507, 21010}, {16670, 49772}, {16834, 28580}, {17017, 44447}, {17281, 28538}, {17351, 49681}, {17382, 38023}, {17399, 24723}, {17491, 29831}, {17768, 38315}, {19993, 32940}, {20020, 32938}, {20072, 36534}, {21747, 24597}, {24280, 28542}, {24725, 26228}, {25055, 50092}, {26105, 37604}, {28297, 49453}, {28322, 49463}, {28503, 49721}, {28566, 38047}, {29207, 36731}, {29639, 36277}, {31140, 33137}, {31164, 33144}, {31165, 50070}, {31178, 35578}, {32455, 49680}, {32922, 49722}, {33088, 50105}, {33106, 37642}, {33141, 37666}, {33682, 48822}, {34607, 42043}, {34630, 37537}, {34745, 36750}, {34749, 37542}, {36480, 49710}, {37427, 37570}, {37681, 38092}, {42697, 50023}, {46922, 48830}, {47352, 48821}, {48831, 48867}, {48854, 50093}

X(50303) = reflection of X(i) in X(j) for these {i,j}: {599, 48810}, {3416, 17359}, {3679, 50115}, {17274, 551}, {17301, 1386}, {24248, 17301}, {48829, 597}, {48831, 48867}, {50080, 50114}, {50107, 3923}
X(50303) = crossdifference of every pair of points on line {3250, 23650}
X(50303) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3758, 49709, 36479}, {4344, 6172, 48856}, {5263, 17346, 48802}, {6172, 48856, 984}, {16475, 50080, 50114}, {21747, 33104, 24597}, {46922, 49746, 48830}


X(50304) = X(1)X(17236)∩X(2)X(21747)

Barycentrics    2*a^3 - a*b^2 - 2*b^3 - b^2*c - a*c^2 - b*c^2 - 2*c^3 : :
X(50304) = X[4780] - 3 X[49630], 3 X[17274] - X[49455], 5 X[141] - 3 X[48810], 6 X[48810] - 5 X[49482], 3 X[599] - X[32941], 3 X[3416] + X[17276], 3 X[4655] - X[17276], X[3629] - 3 X[48821], 3 X[3821] - 2 X[3946], 4 X[3946] - 3 X[49477], 3 X[3923] - 5 X[17286], 3 X[15533] + X[49680], X[40341] + 3 X[48829], 3 X[48829] - X[49497], X[49485] - 3 X[50081], X[49684] - 3 X[50092]

X(50304) lies on these lines: {1, 17236}, {2, 21747}, {8, 4821}, {9, 49769}, {10, 894}, {42, 20290}, {69, 519}, {75, 24692}, {141, 752}, {171, 30832}, {238, 17283}, {319, 4709}, {320, 33076}, {516, 1352}, {524, 4085}, {528, 3631}, {537, 17345}, {540, 15985}, {551, 17300}, {599, 28562}, {726, 3416}, {740, 17372}, {758, 17792}, {896, 48647}, {902, 31017}, {966, 3828}, {984, 17329}, {1125, 4349}, {1150, 21241}, {1386, 28498}, {2321, 2796}, {2550, 3626}, {2887, 35466}, {2895, 4685}, {3629, 48821}, {3662, 50023}, {3679, 17116}, {3741, 6327}, {3773, 17768}, {3821, 3946}, {3836, 17337}, {3840, 4388}, {3844, 4672}, {3883, 49676}, {3923, 17286}, {3945, 48822}, {3971, 4683}, {3993, 17315}, {4001, 29673}, {4090, 33066}, {4135, 33099}, {4432, 17231}, {4439, 17334}, {4450, 33081}, {4482, 11161}, {4527, 28530}, {4535, 28546}, {4641, 28595}, {4669, 50119}, {4690, 4732}, {4693, 17295}, {4741, 49448}, {4759, 17279}, {4859, 16825}, {4888, 48851}, {4914, 42055}, {4970, 32852}, {5232, 48809}, {5692, 25279}, {5695, 28550}, {5839, 50021}, {5846, 49464}, {5880, 28634}, {6646, 32847}, {6685, 26034}, {9857, 46180}, {10197, 27267}, {15485, 17232}, {15533, 49680}, {16484, 17297}, {17120, 36478}, {17229, 28534}, {17235, 28538}, {17252, 36531}, {17272, 36480}, {17275, 24693}, {17277, 31151}, {17296, 49767}, {17298, 24331}, {17339, 29674}, {17344, 49457}, {17347, 33165}, {17348, 25351}, {17351, 28558}, {17353, 49710}, {17360, 49459}, {17361, 49490}, {17363, 50018}, {17364, 29659}, {17373, 49469}, {17374, 49471}, {17381, 32784}, {17766, 49511}, {17771, 49524}, {19879, 20077}, {20064, 24943}, {20101, 32783}, {21282, 31136}, {21296, 36479}, {24165, 33067}, {24248, 28522}, {24728, 39885}, {26840, 32866}, {28494, 49484}, {28566, 49473}, {29660, 48633}, {30056, 49723}, {32843, 33086}, {32850, 49510}, {32859, 33074}, {32861, 33068}, {32863, 32947}, {32949, 33083}, {33109, 37653}, {40341, 48829}, {44416, 48651}, {49485, 50081}, {49684, 50092}

X(50304) = midpoint of X(i) and X(j) for these {i,j}: {69, 4660}, {3416, 4655}, {24728, 39885}, {40341, 49497}
X(50304) = reflection of X(i) in X(j) for these {i,j}: {4672, 3844}, {49472, 17235}, {49477, 3821}, {49482, 141}, {49685, 4085}
X(50304) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 32857, 50117}, {319, 24715, 4709}, {320, 33076, 49479}, {1150, 31134, 21241}, {2895, 32948, 4685}, {4388, 33085, 3840}, {4645, 33082, 10}, {4683, 33078, 3971}, {6327, 33080, 3741}, {6646, 32847, 49520}, {24723, 32846, 3993}, {26034, 32946, 6685}, {32852, 32950, 4970}, {32863, 32947, 42057}, {32949, 33083, 43223}, {33066, 33079, 4090}, {33067, 33075, 24165}, {40341, 48829, 49497}


X(50305) = X(1)X(2)∩X(11)X(27747)

Barycentrics    2*a^3 - 3*a^2*b - b^3 - 3*a^2*c - 6*a*b*c - 3*b^2*c - 3*b*c^2 - c^3 : :
X(50305) = 2 X[10] + X[49466], 4 X[1125] - X[49476], X[17389] - 3 X[38314], X[3883] + 2 X[24325], 2 X[3686] + X[49490], 4 X[3842] - X[49527], 2 X[4399] + X[49475], X[4416] + 2 X[49479], 3 X[16590] - X[49515], 5 X[40328] + X[49506]

X(50305) lies on these lines: {1, 2}, {11, 27747}, {30, 50268}, {37, 28503}, {75, 28580}, {86, 49684}, {105, 5251}, {142, 31151}, {210, 6688}, {238, 50115}, {392, 14839}, {405, 48864}, {518, 17330}, {527, 31178}, {528, 4688}, {536, 49740}, {537, 50093}, {538, 13745}, {545, 49483}, {594, 42819}, {726, 50090}, {730, 49563}, {740, 50099}, {752, 3883}, {903, 24723}, {966, 16496}, {993, 26241}, {1001, 17281}, {1111, 26234}, {1213, 49465}, {1279, 48810}, {1447, 4315}, {1482, 39605}, {1573, 3290}, {1654, 49505}, {1738, 48829}, {2321, 16484}, {2796, 50119}, {3246, 17369}, {3303, 16849}, {3304, 16852}, {3416, 17313}, {3686, 49490}, {3707, 49712}, {3739, 49725}, {3751, 37654}, {3842, 49527}, {3913, 19313}, {3997, 5315}, {4026, 17382}, {4049, 47797}, {4223, 5258}, {4301, 7379}, {4331, 36595}, {4356, 50108}, {4370, 15254}, {4399, 49475}, {4416, 49479}, {4421, 19323}, {4660, 24199}, {4665, 4702}, {4733, 49467}, {4780, 17117}, {4844, 47757}, {4966, 50081}, {4967, 32941}, {4968, 14020}, {5249, 31134}, {5276, 16474}, {5542, 33082}, {5731, 9746}, {5846, 49738}, {5847, 17378}, {5880, 31139}, {5882, 6998}, {5988, 7983}, {6666, 33165}, {7380, 13464}, {7407, 11522}, {8666, 19310}, {8715, 19314}, {9041, 49731}, {9710, 14019}, {11194, 19322}, {11362, 21554}, {12513, 19309}, {13725, 48838}, {13728, 48844}, {15485, 17355}, {15569, 50113}, {15668, 49681}, {16351, 19758}, {16490, 37675}, {16590, 49515}, {16801, 17000}, {17251, 47358}, {17256, 24841}, {17259, 49688}, {17271, 49511}, {17274, 24231}, {17275, 42871}, {17277, 49529}, {17320, 32922}, {17333, 24349}, {17392, 28538}, {17718, 27739}, {19277, 48824}, {19290, 19761}, {19898, 19942}, {21198, 47800}, {24216, 37660}, {25354, 49464}, {25557, 31138}, {27754, 33089}, {28234, 44430}, {28301, 49493}, {28309, 49462}, {28534, 49727}, {28634, 49460}, {33940, 37038}, {34379, 50074}, {34610, 42048}, {37756, 50091}, {40328, 49506}, {40551, 45664}, {47357, 50126}, {49470, 50088}, {49478, 50082}, {49723, 50274}, {50110, 50111}, {50163, 50225}, {50169, 50227}, {50171, 50233}

X(50305) = midpoint of X(i) and X(j) for these {i,j}: {75, 49746}, {3241, 29617}, {3883, 50116}, {17333, 24349}, {49470, 50088}, {49478, 50082}
X(50305) = reflection of X(i) in X(j) for these {i,j}: {29574, 551}, {49725, 3739}, {50110, 50111}, {50113, 15569}, {50116, 24325}
X(50305) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 8, 49763}, {2, 3241, 48854}, {2, 48849, 3679}, {8, 3616, 29583}, {8, 16815, 10}, {8, 17244, 49766}, {10, 1125, 29596}, {551, 48853, 2}, {1125, 49766, 17244}, {3244, 39580, 16830}, {4384, 36479, 49772}, {24603, 49771, 36480}, {29596, 49466, 49476}


X(50306) = X(1)X(2)∩X(6)X(50048)

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

X(50306) lies on these lines: {1, 2}, {6, 50048}, {63, 5839}, {524, 42051}, {527, 50106}, {536, 17781}, {1211, 4852}, {1266, 32859}, {1386, 4046}, {1449, 19822}, {1738, 32852}, {1817, 24391}, {2321, 32911}, {2895, 3663}, {3175, 4971}, {3210, 4001}, {3305, 17314}, {3666, 17362}, {3686, 28606}, {3707, 33761}, {3755, 33075}, {3759, 5294}, {3875, 5739}, {3879, 4359}, {3883, 3896}, {3914, 4716}, {3945, 41915}, {3946, 32782}, {3950, 27065}, {3966, 49486}, {3969, 17353}, {3977, 37652}, {4035, 33129}, {4104, 32928}, {4133, 32930}, {4360, 4886}, {4361, 5249}, {4371, 5712}, {4383, 17299}, {4399, 31993}, {4416, 17147}, {4431, 26223}, {4641, 4969}, {4654, 19819}, {4656, 37656}, {4688, 37631}, {4780, 32947}, {4856, 37685}, {4967, 19684}, {4980, 20234}, {4986, 42715}, {5814, 50056}, {5847, 32860}, {5905, 17151}, {6762, 39592}, {8666, 11340}, {10371, 48801}, {11350, 12513}, {12625, 37185}, {17117, 17778}, {17133, 42044}, {17155, 34379}, {17160, 33066}, {17275, 20182}, {17320, 41816}, {17374, 40688}, {17377, 19804}, {17388, 44307}, {17600, 42334}, {17788, 42029}, {19701, 28634}, {19797, 46922}, {23119, 37672}, {24177, 32863}, {28329, 35652}, {28538, 34612}, {31143, 50109}, {32924, 49511}, {32945, 49684}, {41002, 49462}, {41011, 49474}, {42045, 50116}, {48842, 50046}, {48861, 50047}, {48870, 50049}, {49724, 50082}, {50043, 50127}, {50052, 50124}, {50068, 50120}

X(50306) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 20043, 5256}, {239, 306, 26723}, {3210, 17363, 4001}, {3687, 49770, 3187}, {4716, 32861, 3914}, {14459, 32914, 4028}, {41816, 41823, 17320}


X(50307) = X(1)X(7)∩X(2)X(1707)

Barycentrics    2*a^3 + a^2*b - b^3 + a^2*c + 2*a*b*c + b^2*c + b*c^2 - c^3 : :
X(50307) = 2 X[3993] - 3 X[29574], 3 X[354] - 2 X[39543], X[24349] - 3 X[50128], 2 X[50117] - 3 X[50119], X[3883] - 3 X[50116], 2 X[24325] - 3 X[50116], 4 X[3842] - 3 X[50093], 7 X[9780] - 5 X[17331], 2 X[15569] - 3 X[17392], 3 X[17378] - X[49470], 3 X[31178] - X[49506], 3 X[39704] - X[49746], X[49450] - 3 X[49720], X[49461] - 3 X[50125]

X(50307) lies on these lines: {1, 7}, {2, 1707}, {6, 1738}, {8, 17116}, {9, 24695}, {10, 894}, {11, 37520}, {31, 5249}, {35, 41430}, {37, 17768}, {44, 3826}, {46, 573}, {56, 31394}, {57, 6210}, {58, 12609}, {65, 511}, {75, 5847}, {79, 2298}, {81, 3914}, {85, 4008}, {86, 24723}, {98, 109}, {142, 238}, {190, 4078}, {191, 5279}, {192, 28526}, {306, 4418}, {320, 5263}, {329, 5268}, {335, 2796}, {354, 29349}, {498, 28739}, {518, 17365}, {519, 4740}, {524, 3696}, {527, 984}, {528, 49478}, {537, 49527}, {545, 49523}, {553, 982}, {595, 28026}, {608, 1838}, {611, 6180}, {612, 5905}, {613, 5228}, {726, 49476}, {740, 3879}, {750, 908}, {752, 3883}, {756, 17781}, {940, 1836}, {942, 15310}, {946, 37469}, {968, 44447}, {978, 12436}, {986, 5717}, {1001, 4675}, {1086, 1386}, {1111, 23689}, {1125, 3662}, {1155, 5718}, {1158, 5713}, {1210, 41246}, {1266, 32921}, {1279, 25557}, {1284, 37609}, {1400, 1756}, {1430, 30687}, {1441, 1733}, {1471, 30379}, {1698, 3973}, {1719, 3101}, {1737, 5823}, {1743, 38052}, {1777, 12047}, {1785, 1892}, {1837, 48938}, {1876, 13750}, {1908, 16592}, {1957, 30686}, {1961, 4656}, {2308, 26723}, {2321, 32846}, {2385, 18161}, {2550, 3751}, {2646, 48929}, {2876, 24476}, {2887, 4697}, {2956, 9612}, {3008, 16468}, {3011, 17126}, {3057, 29309}, {3058, 4883}, {3218, 29639}, {3306, 5121}, {3338, 28017}, {3416, 4363}, {3452, 17122}, {3474, 5712}, {3475, 3749}, {3487, 37552}, {3550, 13405}, {3616, 17324}, {3634, 17368}, {3649, 29097}, {3666, 11246}, {3679, 35578}, {3685, 17300}, {3687, 3980}, {3717, 32935}, {3739, 28570}, {3744, 29105}, {3745, 3782}, {3755, 4649}, {3757, 20101}, {3758, 4429}, {3784, 10473}, {3790, 49766}, {3821, 14621}, {3828, 26083}, {3836, 4672}, {3838, 37646}, {3842, 28558}, {3844, 17369}, {3886, 49763}, {3896, 42045}, {3911, 17717}, {3912, 3923}, {3920, 17483}, {3925, 4641}, {3931, 49743}, {3932, 17351}, {3944, 37604}, {3946, 33149}, {3977, 29643}, {3982, 17716}, {4000, 16475}, {4001, 31330}, {4003, 17726}, {4026, 4670}, {4028, 17778}, {4031, 17722}, {4032, 29057}, {4035, 33160}, {4038, 33095}, {4054, 17763}, {4104, 33066}, {4114, 17598}, {4133, 6542}, {4252, 28628}, {4357, 4655}, {4415, 4682}, {4424, 49744}, {4640, 17056}, {4648, 5698}, {4650, 5745}, {4654, 5269}, {4663, 7277}, {4671, 49990}, {4676, 17234}, {4684, 32941}, {4690, 4733}, {4715, 49725}, {4718, 28556}, {4780, 20090}, {4795, 48829}, {4847, 32913}, {4849, 49732}, {4851, 5695}, {4854, 37595}, {4859, 16469}, {4860, 17721}, {4966, 17376}, {4989, 17067}, {5045, 29229}, {5057, 37633}, {5222, 7613}, {5255, 21620}, {5257, 24697}, {5264, 13407}, {5266, 6147}, {5272, 9776}, {5273, 16570}, {5294, 25957}, {5297, 17484}, {5311, 33098}, {5327, 18589}, {5710, 10404}, {5711, 13161}, {5719, 37589}, {5725, 36279}, {5750, 32784}, {5846, 7228}, {5850, 49448}, {5852, 49515}, {5853, 49490}, {5902, 29353}, {5903, 29311}, {6173, 7290}, {6646, 16830}, {7191, 26842}, {7321, 32922}, {9347, 33151}, {9778, 41825}, {9780, 17331}, {9791, 16826}, {10039, 28968}, {11019, 33106}, {12512, 37574}, {12527, 20348}, {13411, 37603}, {14996, 33134}, {15254, 17245}, {15320, 18166}, {15569, 17392}, {15601, 20195}, {15936, 50233}, {16056, 20967}, {16466, 24178}, {16476, 17050}, {16706, 38049}, {16823, 26806}, {16824, 20077}, {16825, 24199}, {17011, 33102}, {17019, 33100}, {17064, 37642}, {17127, 27186}, {17132, 49445}, {17257, 39586}, {17291, 19862}, {17316, 24280}, {17355, 29674}, {17378, 28580}, {17388, 28484}, {17390, 28530}, {17491, 26580}, {17595, 17723}, {17605, 37634}, {17718, 37540}, {17764, 49471}, {17765, 49491}, {17766, 49466}, {17767, 49456}, {17771, 49457}, {17889, 40940}, {18193, 21454}, {18391, 48878}, {19684, 32950}, {19857, 41812}, {20059, 39587}, {20138, 49710}, {21255, 29637}, {21282, 29835}, {23578, 27846}, {23659, 24443}, {23812, 43223}, {23958, 29680}, {24177, 29821}, {24295, 29596}, {24309, 37576}, {24393, 49712}, {24470, 37592}, {24541, 26573}, {24703, 37674}, {24988, 41241}, {25006, 32912}, {25959, 30768}, {26015, 33104}, {26102, 40998}, {26728, 49480}, {27003, 33107}, {28079, 36574}, {28194, 48825}, {28198, 48823}, {28503, 49525}, {28538, 49727}, {28542, 50110}, {28557, 49452}, {29632, 35263}, {29681, 30652}, {31138, 48810}, {31151, 33159}, {31178, 49506}, {31317, 50095}, {31397, 40862}, {31730, 37573}, {32772, 33067}, {32850, 49529}, {32939, 33073}, {32940, 33072}, {33131, 37685}, {37593, 37631}, {39542, 48934}, {39704, 49746}, {42697, 50017}, {46922, 50091}, {49450, 49720}, {49461, 50125}, {49482, 49676}

X(50307) = midpoint of X(i) and X(j) for these {i,j}: {8, 17364}, {65, 49537}
X(50307) = reflection of X(i) in X(j) for these {i,j}: {1, 3664}, {3883, 24325}, {4416, 10}, {21746, 942}, {49462, 17390}, {49466, 49479}, {49483, 7228}
X(50307) = crosspoint of X(7) and X(14621)
X(50307) = crosssum of X(55) and X(2276)
X(50307) = barycentric product X(109)*X(28959)
X(50307) = barycentric quotient X(28959)/X(35519)
X(50307) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 7, 24231}, {1, 4312, 24248}, {1, 32857, 3663}, {6, 5880, 1738}, {7, 4307, 1}, {7, 4344, 4310}, {57, 26098, 24239}, {81, 20292, 3914}, {171, 33097, 226}, {320, 5263, 49511}, {481, 482, 3674}, {750, 24725, 908}, {894, 4645, 10}, {940, 1836, 24210}, {1961, 33099, 4656}, {2550, 3751, 49772}, {2550, 4644, 3751}, {3218, 33112, 29639}, {3474, 5712, 17594}, {3663, 4349, 1}, {3663, 30424, 32857}, {3755, 4667, 4649}, {3821, 33682, 17023}, {3836, 4672, 17353}, {3883, 50116, 24325}, {3944, 37604, 39595}, {3980, 32946, 3687}, {4295, 4340, 1}, {4307, 4310, 4344}, {4310, 4344, 1}, {4339, 11036, 1}, {4349, 30424, 3663}, {4418, 32949, 306}, {4649, 24715, 3755}, {4650, 33111, 5745}, {4654, 5269, 33144}, {4860, 17721, 24216}, {17122, 33096, 3452}, {17126, 31019, 3011}, {17376, 49484, 4966}, {17778, 32932, 4028}, {24342, 33082, 10}, {24692, 33682, 3821}, {30425, 30426, 4295}, {32913, 33109, 4847}


X(50308) = X(1)X(319)∩X(6)X(10)

Barycentrics    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(50308) = 3 X[10] - X[4349], 5 X[3617] - X[4307]

X(50308) lies on these lines: {1, 319}, {2, 3791}, {6, 10}, {8, 192}, {9, 3773}, {43, 4886}, {45, 6541}, {55, 21085}, {69, 24325}, {75, 4655}, {141, 16825}, {238, 3661}, {239, 32784}, {321, 4703}, {333, 4438}, {346, 4535}, {355, 382}, {518, 4690}, {519, 9348}, {551, 50076}, {594, 3923}, {599, 49676}, {726, 4643}, {752, 1757}, {966, 3842}, {982, 37653}, {1001, 4445}, {1029, 33110}, {1125, 4851}, {1211, 4362}, {1215, 5739}, {1386, 17239}, {1698, 17381}, {1738, 50095}, {1962, 20017}, {2345, 4672}, {2550, 4732}, {2887, 5271}, {2895, 32771}, {3578, 32912}, {3616, 17373}, {3617, 4307}, {3624, 17317}, {3625, 4356}, {3631, 25557}, {3678, 5752}, {3685, 29615}, {3687, 32916}, {3696, 4660}, {3703, 49724}, {3741, 3966}, {3757, 33084}, {3759, 29633}, {3790, 17331}, {3821, 4361}, {3836, 4384}, {3844, 17348}, {3846, 11679}, {3883, 32941}, {3932, 17330}, {3974, 4096}, {3993, 17299}, {4007, 4527}, {4011, 41002}, {4026, 17362}, {4034, 4085}, {4042, 29673}, {4060, 4133}, {4283, 9534}, {4357, 32921}, {4359, 33080}, {4363, 17770}, {4407, 7174}, {4416, 32935}, {4419, 28516}, {4545, 4780}, {4645, 24693}, {4649, 17363}, {4651, 33074}, {4657, 49477}, {4659, 17767}, {4665, 17768}, {4668, 17764}, {4669, 28580}, {4676, 48630}, {4678, 28494}, {4683, 28605}, {4697, 19822}, {4716, 29617}, {4725, 48822}, {4865, 31330}, {4966, 24331}, {4980, 33098}, {4981, 32854}, {4989, 19862}, {5018, 33298}, {5232, 49472}, {5235, 29643}, {5263, 32025}, {5278, 15523}, {5311, 41809}, {5361, 33119}, {5564, 24723}, {5690, 29207}, {5737, 29671}, {5743, 29649}, {5839, 49489}, {5846, 36480}, {5849, 24315}, {5880, 28634}, {6327, 21020}, {6646, 49493}, {12588, 16609}, {15254, 17229}, {15569, 17372}, {16468, 17289}, {16475, 17308}, {16477, 17368}, {16777, 25354}, {16823, 17287}, {17117, 33149}, {17163, 33094}, {17165, 43990}, {17228, 29637}, {17253, 49453}, {17258, 49445}, {17271, 32922}, {17276, 50117}, {17277, 29674}, {17284, 31289}, {17293, 24295}, {17300, 40328}, {17307, 29646}, {17328, 49447}, {17343, 24349}, {17344, 49483}, {17349, 33159}, {19732, 29653}, {19742, 26061}, {19804, 33085}, {19868, 49684}, {24248, 42696}, {24715, 33888}, {24725, 31025}, {26037, 33078}, {26128, 32782}, {28538, 48809}, {28653, 43997}, {29604, 38049}, {29628, 31252}, {29658, 30832}, {29667, 32864}, {29847, 31247}, {30970, 33070}, {31037, 33127}, {31143, 33065}, {31993, 32946}, {32099, 39581}, {32780, 37652}, {32855, 38000}, {32860, 33083}, {32917, 33077}, {32926, 41816}, {32931, 37656}, {33099, 42029}, {33102, 41821}, {48805, 49705}, {49510, 49688}, {49752, 50023}, {49754, 49772}, {50079, 50111}

X(50308) = midpoint of X(3625) and X(4356)
X(50308) = reflection of X(7174) in X(4407)
X(50308) = crossdifference of every pair of points on line {834, 20981}
X(50308) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17270, 3775}, {8, 1654, 984}, {10, 33682, 17303}, {75, 33082, 4655}, {333, 32778, 4438}, {1001, 4445, 49560}, {3416, 17275, 10}, {4026, 17362, 49488}, {5564, 24723, 49474}, {16823, 17287, 33087}, {31330, 33075, 4865}, {32782, 32914, 26128}, {33076, 42334, 8}


X(50309) = X(10)X(524)∩X(37)X(519)

Barycentrics    2*a^3 + 2*a^2*b - 4*a*b^2 - b^3 + 2*a^2*c - 6*a*b*c - 4*b^2*c - 4*a*c^2 - 4*b*c^2 - c^3 : :
X(50309) = 2 X[3686] + X[49457], 3 X[17330] - X[49740], 3 X[3679] - X[49720], 3 X[17346] + X[49720], 2 X[4399] + X[49520], X[4416] + 2 X[4732], X[4709] + 2 X[17332], X[17378] - 3 X[19875], 5 X[17331] + X[49459]

X(50309) lies on these lines: {2, 3775}, {6, 48809}, {8, 4439}, {10, 524}, {37, 519}, {239, 4407}, {391, 32941}, {527, 50096}, {528, 4669}, {537, 50095}, {551, 4974}, {599, 3836}, {726, 50098}, {740, 50093}, {752, 1757}, {966, 48830}, {984, 29617}, {1213, 49685}, {1654, 4085}, {2796, 3696}, {2887, 31143}, {3626, 28562}, {3707, 4432}, {3773, 6651}, {3826, 22165}, {3828, 17392}, {3842, 29574}, {3846, 4042}, {3993, 49737}, {4364, 50018}, {4399, 49520}, {4416, 4732}, {4677, 49746}, {4685, 49724}, {4709, 17332}, {4743, 24697}, {4745, 49725}, {5883, 9038}, {6541, 50084}, {8584, 33682}, {9041, 49510}, {16825, 47358}, {17133, 49456}, {17224, 50091}, {17256, 50016}, {17270, 17378}, {17275, 47359}, {17331, 49459}, {17333, 28542}, {17374, 25352}, {17395, 50021}, {17771, 50128}, {17772, 50077}, {21085, 50104}, {21242, 37656}, {28554, 50099}, {28604, 50074}, {37654, 48802}, {41310, 49560}, {41312, 49488}, {49474, 49748}

X(50309) = midpoint of X(i) and X(j) for these {i,j}: {984, 29617}, {3679, 17346}, {4677, 49746}, {17333, 50086}, {49474, 49748}
X(50309) = reflection of X(i) in X(j) for these {i,j}: {551, 49731}, {3993, 49737}, {17392, 3828}, {29574, 3842}, {49725, 4745}


X(50310) = X(1)X(2)∩X(75)X(528)

Barycentrics    2*a^3 - 2*a^2*b + a*b^2 - b^3 - 2*a^2*c - 3*a*b*c - 2*b^2*c + a*c^2 - 2*b*c^2 - c^3 : :
X(50310) = X[8] + 2 X[49466], 5 X[3616] - 2 X[49476], 6 X[25055] - 5 X[29622], 2 X[29574] - 3 X[38314], 2 X[3883] + X[24349], 4 X[3842] - X[49534], 5 X[17331] - 2 X[49448], 4 X[17332] - X[49501], X[17363] + 2 X[49490], X[17364] - 4 X[49479], 2 X[24325] + X[49506]

X(50310) lies on these lines: {1, 2}, {75, 528}, {85, 5434}, {86, 49681}, {319, 42871}, {344, 38025}, {428, 5342}, {516, 50119}, {518, 17346}, {527, 3883}, {536, 49746}, {537, 17333}, {538, 49735}, {752, 31178}, {956, 26241}, {1001, 3790}, {1121, 4586}, {1279, 17359}, {1447, 3476}, {1573, 26242}, {1621, 50105}, {1654, 16496}, {2099, 7179}, {2263, 40892}, {3058, 42029}, {3242, 17251}, {3246, 17354}, {3263, 3902}, {3416, 17297}, {3654, 13635}, {3655, 13634}, {3662, 33076}, {3681, 5943}, {3685, 47357}, {3842, 49534}, {3877, 14839}, {3913, 19314}, {4026, 17399}, {4030, 19804}, {4363, 49709}, {4388, 31164}, {4391, 45322}, {4421, 19325}, {4431, 30331}, {4514, 31140}, {4643, 24841}, {4645, 6173}, {4647, 34719}, {4660, 48627}, {4664, 28503}, {4676, 49726}, {4688, 49720}, {4725, 49478}, {4740, 28580}, {4844, 44435}, {4886, 41711}, {4914, 18134}, {4968, 11114}, {4971, 49470}, {4980, 34611}, {5015, 17528}, {5224, 49465}, {5258, 17522}, {5263, 50130}, {5337, 19336}, {5564, 49460}, {5734, 7407}, {5844, 44430}, {5846, 17392}, {5847, 50133}, {5881, 7385}, {6998, 37727}, {7379, 7982}, {7380, 10222}, {9041, 17330}, {9053, 49731}, {9791, 49446}, {10031, 37670}, {11057, 17579}, {11194, 17798}, {11346, 48864}, {12513, 19310}, {15485, 17339}, {15668, 49679}, {16284, 37671}, {16484, 17242}, {16857, 48804}, {17000, 32941}, {17233, 42819}, {17247, 49455}, {17259, 49690}, {17271, 47358}, {17277, 49688}, {17286, 35227}, {17298, 38024}, {17301, 32922}, {17331, 49448}, {17332, 49501}, {17338, 33165}, {17343, 49505}, {17349, 49529}, {17363, 49490}, {17364, 49479}, {17378, 28538}, {17379, 49684}, {17396, 49472}, {17549, 37586}, {17762, 34699}, {24325, 49506}, {24723, 49747}, {26234, 30806}, {27184, 32923}, {27186, 28599}, {28322, 49525}, {28534, 49483}, {28542, 49493}, {28581, 50085}, {30583, 47804}, {31156, 48869}, {32773, 50103}, {37756, 48829}, {42034, 49736}, {49447, 49742}, {50160, 50182}, {50171, 50181}

X(50310) = midpoint of X(49466) and X(50095)
X(50310) = reflection of X(i) in X(j) for these {i,j}: {8, 50095}, {4664, 49740}, {17389, 1}, {49447, 49742}, {49720, 4688}, {49722, 49483}, {50075, 17330}, {50128, 31178}
X(50310) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 48851, 2}, {2, 145, 48856}, {2, 48856, 16830}, {10, 29660, 29613}, {10, 49771, 36534}, {145, 39581, 16830}, {24331, 32847, 17244}, {29659, 50023, 17367}, {39581, 48856, 2}, {47357, 50107, 3685}


X(50311) = X(1)X(2)∩X(38)X(50105)

Barycentrics    a^3 - a^2*b + 2*a*b^2 + b^3 - a^2*c + 2*b^2*c + 2*a*c^2 + 2*b*c^2 + c^3 : :
X(50311) = X[1] + 2 X[49560], 2 X[10] + X[49458], 4 X[1125] - X[49488], 5 X[1698] + X[49451], 5 X[3616] - 2 X[49477], 5 X[3616] - X[50129], 7 X[3624] - X[49495], X[16834] - 3 X[25055], 3 X[38314] + X[50079], X[69] + 2 X[49482], 4 X[141] - X[4660], 2 X[141] + X[32941], X[4660] + 2 X[32941], X[3923] + 2 X[49511], 2 X[2321] + X[49455], X[3242] + 2 X[3773], X[3416] + 2 X[49473], 4 X[3589] - X[49497], 5 X[3618] - 2 X[49685], X[3751] - 4 X[24295], 5 X[3763] - 2 X[4085], 5 X[3763] + X[49460], 2 X[4085] + X[49460], 2 X[3821] + X[3886], 2 X[3844] + X[49467], X[4133] + 2 X[4353], 2 X[4527] + X[49453], X[4655] + 2 X[49484], X[16496] + 5 X[17286], 2 X[17229] + X[49465], 2 X[17235] + X[49485], X[17299] + 2 X[49472], 2 X[17355] + X[49505], 3 X[21358] - X[48829], 3 X[38023] - X[50131], 7 X[47355] - X[49680]

X(50311) lies on these lines: {1, 2}, {38, 50105}, {45, 4407}, {69, 49482}, {141, 528}, {238, 17346}, {346, 49520}, {350, 33934}, {376, 48925}, {516, 10519}, {518, 17359}, {524, 48810}, {527, 3923}, {529, 48859}, {535, 11355}, {537, 17281}, {540, 48811}, {544, 993}, {599, 752}, {726, 50107}, {740, 17301}, {966, 38025}, {984, 17264}, {1001, 3775}, {1009, 8666}, {1386, 4725}, {1654, 15485}, {2239, 37610}, {2321, 49455}, {2345, 49479}, {2784, 3576}, {2796, 17274}, {2809, 3789}, {2887, 31140}, {3242, 3773}, {3246, 4690}, {3416, 49473}, {3589, 49497}, {3618, 49685}, {3654, 13633}, {3655, 13632}, {3673, 4479}, {3685, 17254}, {3706, 26128}, {3751, 24295}, {3763, 4085}, {3814, 30959}, {3821, 3886}, {3834, 24693}, {3844, 49467}, {3996, 33174}, {4000, 4709}, {4133, 4353}, {4234, 17206}, {4310, 50117}, {4334, 40892}, {4389, 4693}, {4432, 4643}, {4439, 17269}, {4441, 4717}, {4527, 49453}, {4653, 30966}, {4655, 28534}, {4657, 49471}, {4702, 17237}, {4732, 17278}, {4800, 23888}, {4863, 28595}, {4966, 17392}, {4971, 32921}, {5049, 28600}, {5195, 30946}, {5224, 16484}, {5263, 17297}, {5695, 28542}, {6173, 49676}, {6541, 7174}, {8616, 37653}, {10707, 25760}, {11522, 36693}, {11813, 30961}, {16371, 17798}, {16496, 17286}, {16706, 49459}, {17227, 24715}, {17228, 33076}, {17229, 49465}, {17235, 49485}, {17239, 42819}, {17279, 49457}, {17280, 49448}, {17285, 33165}, {17289, 49490}, {17293, 42871}, {17299, 49472}, {17302, 49469}, {17342, 50075}, {17354, 49712}, {17355, 49505}, {17384, 49475}, {17399, 49470}, {17772, 38315}, {20347, 33866}, {20582, 48821}, {21242, 30811}, {21356, 28562}, {21358, 48829}, {21747, 31303}, {24217, 30832}, {24231, 50119}, {24552, 32946}, {25539, 49678}, {25557, 49733}, {25590, 38024}, {28503, 50097}, {28538, 50081}, {28580, 50092}, {30583, 47822}, {31017, 33104}, {31151, 49720}, {31164, 33064}, {32782, 32943}, {32935, 49726}, {32942, 33084}, {32945, 33172}, {33156, 46909}, {33159, 49450}, {36692, 37714}, {37756, 50086}, {38023, 50131}, {41312, 50111}, {41313, 50094}, {42055, 50048}, {47355, 49680}, {48801, 48862}, {49717, 49729}

X(50311) = midpoint of X(i) and X(j) for these {i,j}: {1, 17294}, {599, 48805}, {3416, 50130}, {3886, 50080}, {5695, 49747}, {17274, 50126}, {17281, 47358}, {48801, 48862}
X(50311) = reflection of X(i) in X(j) for these {i,j}: {17294, 49560}, {32935, 49726}, {48821, 20582}, {49488, 50114}, {50080, 3821}, {50114, 1125}, {50129, 49477}, {50130, 49473}
X(50311) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2, 48822}, {2, 48802, 10}, {10, 49768, 24331}, {141, 32941, 4660}, {3741, 33171, 3771}, {3763, 49460, 4085}, {10453, 32783, 29635}, {17135, 24943, 25453}, {17230, 36534, 32847}, {24552, 33081, 32946}, {29611, 36479, 10}, {31330, 33173, 29642}


X(50312) = X(1)X(5564)∩X(10)X(37)

Barycentrics    (b + c)*(2*a*b + b^2 + 2*a*c + 3*b*c + c^2) : :
X(50312) = 5 X[10] - X[4356], X[4407] + 2 X[4665], X[4307] + 7 X[4678], X[4349] + 3 X[4669]

X(50312) lies on these lines: {1, 5564}, {2, 4716}, {8, 4649}, {10, 37}, {75, 3775}, {306, 27798}, {313, 4647}, {319, 24342}, {321, 8013}, {516, 3627}, {551, 50085}, {726, 4407}, {752, 1757}, {756, 48644}, {894, 42334}, {984, 48628}, {1125, 4405}, {1211, 48643}, {1698, 17233}, {1738, 50096}, {2887, 20360}, {3617, 17764}, {3626, 3629}, {3634, 17243}, {3661, 3836}, {3678, 20713}, {3686, 4672}, {3739, 49560}, {3821, 17239}, {3826, 48636}, {3828, 50097}, {3923, 17275}, {3925, 48651}, {4007, 39586}, {4046, 43223}, {4307, 4678}, {4349, 4669}, {4360, 19856}, {4363, 17771}, {4364, 28522}, {4365, 41809}, {4384, 31289}, {4399, 49477}, {4431, 49456}, {4437, 25351}, {4643, 17767}, {4651, 6539}, {4655, 17270}, {4684, 4967}, {4688, 49676}, {4690, 17770}, {4699, 33087}, {4708, 28484}, {4745, 28580}, {4899, 49457}, {4974, 50095}, {5224, 49474}, {5271, 6679}, {5750, 49489}, {7235, 16603}, {7270, 13610}, {10479, 24530}, {15569, 28633}, {16825, 28634}, {17238, 33149}, {17248, 49452}, {17251, 28542}, {17271, 32857}, {17303, 49488}, {17348, 24295}, {17362, 33682}, {17377, 43997}, {17748, 39564}, {17769, 36480}, {19797, 32913}, {19822, 32853}, {19868, 49472}, {21027, 48647}, {21085, 31993}, {21954, 22206}, {25526, 40438}, {26580, 48641}, {29587, 31252}, {29593, 32784}, {29615, 32846}, {29674, 48630}, {31330, 33089}, {32025, 33082}, {32917, 46918}, {32921, 42696}, {32924, 41821}, {33099, 41816}

X(50312) = barycentric product X(i)*X(j) for these {i,j}: {10, 29576}, {4033, 48024}
X(50312) = barycentric quotient X(i)/X(j) for these {i,j}: {29576, 86}, {48024, 1019}
X(50312) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 28604, 4649}, {10, 594, 3773}, {10, 2321, 3842}, {10, 3696, 4085}, {10, 3993, 1213}, {10, 4058, 4078}, {10, 4133, 5257}, {10, 4709, 4026}, {594, 4733, 10}, {4026, 4709, 4743}, {4058, 4078, 4535}


X(50313) = X(2)X(38)∩X(6)X(519)

Barycentrics    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(50313) = 2 X[2321] + X[49497], X[17299] + 2 X[49685], 4 X[17355] - X[32941], 2 X[17355] + X[49529], X[32941] + 2 X[49529], 2 X[49482] + X[49688], X[8] + 2 X[4672], 4 X[10] - X[4655], 2 X[10] + X[32935], X[4655] + 2 X[32935], X[3923] + 2 X[49524], X[17301] - 3 X[38047], 3 X[38087] - X[48829], 3 X[38087] + X[49721], X[3242] - 4 X[24295], 4 X[3589] - X[49455], 5 X[3617] + X[24695], 5 X[3618] - 2 X[49472], X[3729] + 2 X[4085], X[3751] + 2 X[3773], 2 X[4527] + X[49495], X[4660] + 2 X[17351], X[17274] - 3 X[19875]

X(50313) lies on these lines: {1, 4439}, {2, 38}, {6, 519}, {8, 4672}, {9, 48851}, {10, 527}, {37, 48822}, {42, 50105}, {190, 29659}, {346, 49471}, {516, 38144}, {518, 17359}, {528, 3923}, {545, 48821}, {551, 41313}, {597, 28503}, {726, 17301}, {740, 50107}, {752, 1757}, {894, 33165}, {1654, 7229}, {1738, 50119}, {2345, 48802}, {2792, 5790}, {2796, 38087}, {2887, 31164}, {3242, 24295}, {3589, 49455}, {3617, 24695}, {3618, 49472}, {3654, 48875}, {3661, 49712}, {3683, 29669}, {3729, 4085}, {3751, 3773}, {3758, 32847}, {3775, 5223}, {3790, 4649}, {3821, 49747}, {3826, 49733}, {3828, 31139}, {3836, 6173}, {3846, 31142}, {3932, 17392}, {3967, 29635}, {3994, 29829}, {4026, 49742}, {4234, 5009}, {4370, 49740}, {4389, 24821}, {4407, 17308}, {4422, 24331}, {4429, 49722}, {4432, 36479}, {4527, 49495}, {4657, 49520}, {4660, 17351}, {4663, 4725}, {4667, 49766}, {4675, 49769}, {4685, 50048}, {4697, 10327}, {4703, 29667}, {4865, 26223}, {4884, 29650}, {4902, 5224}, {4908, 36409}, {4971, 49488}, {5294, 32920}, {5749, 48856}, {5772, 6172}, {5905, 28595}, {9041, 48810}, {10707, 33120}, {16475, 17769}, {16484, 17339}, {16706, 49532}, {17132, 50091}, {17156, 48644}, {17254, 32784}, {17269, 49764}, {17279, 49479}, {17280, 49490}, {17289, 49448}, {17297, 29674}, {17302, 49517}, {17350, 33076}, {17369, 36480}, {17371, 49501}, {17381, 25055}, {17384, 49513}, {17399, 29633}, {17577, 36568}, {19584, 24484}, {20172, 50095}, {21629, 28194}, {24725, 31079}, {24841, 29660}, {25351, 42697}, {25378, 30578}, {25453, 50103}, {26251, 36263}, {27064, 33169}, {28554, 50101}, {28580, 50118}, {29057, 38116}, {29637, 49499}, {29670, 44416}, {29673, 31140}, {29679, 32940}, {31151, 50128}, {32846, 50133}, {32921, 50114}, {33086, 35596}, {33161, 46897}, {36224, 44370}, {42033, 42042}, {48830, 50111}, {49489, 50129}

X(50313) = midpoint of X(i) and X(j) for these {i,j}: {3679, 50127}, {3729, 50080}, {3751, 17294}, {17281, 47359}, {48829, 49721}, {49524, 49726}, {49688, 50130}
X(50313) = reflection of X(i) in X(j) for these {i,j}: {3923, 49726}, {17294, 3773}, {32921, 50114}, {49747, 3821}, {50080, 4085}, {50092, 3828}, {50129, 49489}, {50130, 49482}
X(50313) = crossdifference of every pair of points on line {8632, 9002}
X(50313) = barycentric product X(190)*X(48235)
X(50313) = barycentric quotient X(48235)/X(514)
X(50313) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 4363, 24693}, {10, 32935, 4655}, {1215, 33163, 4438}, {1757, 3679, 17346}, {17165, 26061, 26128}, {17355, 49529, 32941}, {24821, 36478, 4389}, {26223, 33162, 4865}, {29667, 32938, 4703}, {38087, 49721, 48829}


X(50314) = X(1)X(75)∩X(4)X(9)

Barycentrics    a^3 + a*b^2 + 2*a*b*c + 2*b^2*c + a*c^2 + 2*b*c^2 : :
X(50314) = X[4659] + 2 X[36480]

X(50314) lies on these lines: {1, 75}, {2, 968}, {3, 10472}, {4, 9}, {5, 5955}, {6, 3696}, {7, 49511}, {8, 193}, {31, 5271}, {37, 5695}, {43, 2258}, {46, 10479}, {55, 31993}, {57, 3741}, {63, 4418}, {65, 10477}, {81, 17156}, {82, 39708}, {100, 29828}, {141, 5880}, {165, 18229}, {171, 11679}, {191, 1760}, {192, 16830}, {200, 1215}, {238, 4384}, {239, 16475}, {261, 11104}, {307, 4331}, {310, 18056}, {312, 5268}, {321, 612}, {329, 4104}, {333, 1707}, {346, 4078}, {355, 29207}, {390, 39581}, {452, 41921}, {517, 35628}, {518, 4363}, {519, 4349}, {527, 48802}, {528, 24358}, {536, 48854}, {594, 3416}, {596, 23051}, {614, 4359}, {673, 4432}, {726, 4659}, {730, 40875}, {752, 1757}, {846, 45048}, {936, 27384}, {940, 3706}, {942, 35892}, {946, 21246}, {958, 50054}, {984, 3729}, {993, 4221}, {1001, 3739}, {1008, 1716}, {1054, 29827}, {1089, 46738}, {1100, 49468}, {1125, 4000}, {1155, 37660}, {1211, 1836}, {1279, 4688}, {1350, 43173}, {1376, 3185}, {1386, 4361}, {1402, 11358}, {1441, 2263}, {1449, 4709}, {1503, 5794}, {1698, 4429}, {1699, 3846}, {1721, 13727}, {1722, 13740}, {1743, 4672}, {1944, 3332}, {2049, 3931}, {2082, 26035}, {2292, 17872}, {2328, 44734}, {2385, 24316}, {2783, 46475}, {2796, 48809}, {2886, 37360}, {2999, 25496}, {3158, 29670}, {3187, 17163}, {3242, 17118}, {3243, 49458}, {3247, 3993}, {3305, 26037}, {3306, 30942}, {3434, 19822}, {3579, 39564}, {3616, 17396}, {3617, 17350}, {3624, 16706}, {3632, 17772}, {3661, 4645}, {3663, 19868}, {3677, 24165}, {3683, 19732}, {3687, 26098}, {3702, 16454}, {3703, 50048}, {3723, 49461}, {3731, 3842}, {3749, 3757}, {3755, 5750}, {3771, 25525}, {3775, 4312}, {3786, 3869}, {3789, 24330}, {3821, 17306}, {3823, 17359}, {3826, 17279}, {3836, 17284}, {3840, 5437}, {3844, 17293}, {3870, 32771}, {3883, 4967}, {3891, 4980}, {3896, 19684}, {3920, 28605}, {3925, 32777}, {3932, 17281}, {3971, 7322}, {4011, 7308}, {4026, 17303}, {4028, 5712}, {4042, 4641}, {4133, 17314}, {4195, 16824}, {4310, 31995}, {4344, 32087}, {4357, 24248}, {4362, 5269}, {4364, 28530}, {4365, 5311}, {4387, 44307}, {4407, 17767}, {4413, 30818}, {4414, 30970}, {4416, 24695}, {4419, 28526}, {4431, 49476}, {4461, 39587}, {4512, 27798}, {4514, 19797}, {4640, 5737}, {4643, 17768}, {4644, 34379}, {4649, 49459}, {4651, 26223}, {4654, 33064}, {4665, 5846}, {4666, 32943}, {4667, 4923}, {4668, 28498}, {4670, 28581}, {4671, 5297}, {4675, 4966}, {4676, 17277}, {4679, 5241}, {4684, 50116}, {4686, 49453}, {4690, 28570}, {4693, 16831}, {4697, 32853}, {4699, 16823}, {4716, 16834}, {4726, 49463}, {4733, 17275}, {4850, 29826}, {4873, 6541}, {4970, 29644}, {4974, 16469}, {4981, 32933}, {5018, 9312}, {5044, 48944}, {5219, 25385}, {5220, 17351}, {5222, 38049}, {5223, 32935}, {5224, 24723}, {5231, 21242}, {5247, 31327}, {5248, 41230}, {5249, 33171}, {5250, 31339}, {5256, 32772}, {5272, 19804}, {5287, 32915}, {5295, 5711}, {5336, 33745}, {5438, 48932}, {5552, 27254}, {5573, 29668}, {5725, 37150}, {5739, 41011}, {5743, 24703}, {5772, 38191}, {5793, 5836}, {5853, 36479}, {5902, 38485}, {5936, 30332}, {5988, 46236}, {6051, 16458}, {6173, 49676}, {6358, 8270}, {6382, 7093}, {6651, 29576}, {7193, 24264}, {7222, 49505}, {7227, 49524}, {7283, 19853}, {7290, 16825}, {8769, 31359}, {9623, 28850}, {9780, 17260}, {9791, 17248}, {10030, 40719}, {10371, 49745}, {10389, 29651}, {11683, 12526}, {13588, 16778}, {15254, 17259}, {15569, 15668}, {16468, 20179}, {16484, 40328}, {16491, 17117}, {16496, 17116}, {16667, 49489}, {16777, 49462}, {16973, 49531}, {17119, 38315}, {17122, 30567}, {17251, 28534}, {17257, 24280}, {17270, 33082}, {17274, 32857}, {17282, 29637}, {17286, 29674}, {17294, 32846}, {17296, 49560}, {17298, 33087}, {17304, 33149}, {17308, 17738}, {17318, 28484}, {17369, 36404}, {17370, 34595}, {17599, 42051}, {17733, 37554}, {17740, 29639}, {17754, 24727}, {17889, 25527}, {19701, 37593}, {19808, 32773}, {19860, 26665}, {19861, 26538}, {19875, 41138}, {20162, 31306}, {20292, 32782}, {20883, 23555}, {21085, 32946}, {21283, 29835}, {22184, 23543}, {23681, 26128}, {24231, 42697}, {24331, 38316}, {24336, 29057}, {24392, 29655}, {24452, 31151}, {24850, 31424}, {25006, 33163}, {25055, 37756}, {26227, 31025}, {26627, 29824}, {27186, 33173}, {29327, 36477}, {29642, 41867}, {29648, 33150}, {29664, 33168}, {29667, 33110}, {29673, 36483}, {29705, 29713}, {29846, 31266}, {29855, 33129}, {29857, 32779}, {30142, 42031}, {31019, 33175}, {31164, 33065}, {31178, 49675}, {31183, 31289}, {31211, 38059}, {32778, 33109}, {32780, 32865}, {32917, 35258}, {32926, 42029}, {33077, 33112}, {33084, 33097}, {33111, 33160}, {37049, 46826}, {37095, 44119}, {37553, 43223}, {38053, 49768}, {42871, 49467}, {47358, 49727}, {49446, 49493}, {49451, 49490}, {49455, 50117}, {49460, 49478}

X(50314) = midpoint of X(i) and X(j) for these {i,j}: {8, 4307}, {4659, 7174}, {4667, 4923}
X(50314) = reflection of X(i) in X(j) for these {i,j}: {4356, 1125}, {7174, 36480}
X(50314) = X(26643)-Ceva conjugate of X(5275)
X(50314) = crossdifference of every pair of points on line {798, 1459}
X(50314) = barycentric product X(i)*X(j) for these {i,j}: {10, 26643}, {75, 5275}, {190, 7662}
X(50314) = barycentric quotient X(i)/X(j) for these {i,j}: {5275, 1}, {7662, 514}, {26643, 86}
X(50314) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 17151, 32921}, {1, 24342, 10436}, {1, 25590, 24325}, {1, 49474, 3875}, {2, 32929, 968}, {2, 32932, 17594}, {8, 894, 3751}, {10, 3923, 9}, {31, 21020, 5271}, {75, 5263, 1}, {86, 49470, 1}, {165, 18229, 32916}, {940, 3706, 39594}, {1100, 49468, 49486}, {2345, 2550, 10}, {3242, 17118, 49483}, {3739, 49484, 1001}, {3741, 3980, 57}, {3775, 4655, 17272}, {3836, 24693, 38052}, {3886, 10436, 1}, {4312, 17272, 4655}, {4359, 24552, 614}, {4418, 31330, 63}, {4429, 17289, 1698}, {4649, 49459, 49495}, {4709, 33682, 49488}, {5835, 49734, 5794}, {16469, 16833, 4974}, {16825, 49482, 7290}, {17284, 38052, 3836}, {17889, 32783, 25527}, {19804, 32942, 5272}, {24165, 29652, 3677}, {24325, 32941, 1}, {26037, 32930, 3305}, {32771, 32945, 3870}, {32772, 32860, 5256}, {32779, 33108, 29857}, {32935, 49457, 5223}, {33112, 46918, 33077}, {33682, 49488, 1449}, {43997, 49469, 1}, {49458, 49479, 3243}


X(50315) = X(1)X(319)∩X(2)X(49497)

Barycentrics    2*a^2*b - 2*a*b^2 - b^3 + 2*a^2*c - 2*b^2*c - 2*a*c^2 - 2*b*c^2 - c^3 : :
X(50315) = 5 X[141] - 3 X[48821], 5 X[4085] - 6 X[48821], 3 X[3773] - 4 X[17229], 2 X[17229] - 3 X[49560], 3 X[599] - X[4660], 3 X[599] + X[49460], X[3663] - 3 X[49511], X[3629] - 3 X[48810], 5 X[3763] - X[49680], X[4780] - 3 X[50092], X[4924] - 3 X[38191], X[16496] + 3 X[17294], X[17299] + 3 X[47358], 3 X[47358] - X[49455], 3 X[29594] - X[49529], X[40341] + 3 X[48805], X[49681] + 3 X[50076]

X(50315) lies on these lines: {1, 319}, {2, 49497}, {8, 3836}, {10, 4966}, {31, 31303}, {37, 4407}, {69, 752}, {141, 519}, {142, 4732}, {145, 32784}, {354, 21085}, {518, 3773}, {524, 49482}, {528, 3631}, {537, 2321}, {551, 1213}, {594, 49479}, {599, 4660}, {726, 4527}, {740, 3663}, {984, 17242}, {1086, 4709}, {1125, 17348}, {1211, 42057}, {1654, 16484}, {2796, 17345}, {2887, 17135}, {2891, 5247}, {2895, 32943}, {3241, 17238}, {3242, 17769}, {3244, 4026}, {3416, 17765}, {3589, 49685}, {3626, 3826}, {3629, 48810}, {3632, 4429}, {3661, 49490}, {3662, 49459}, {3679, 17234}, {3686, 49768}, {3687, 24216}, {3696, 49676}, {3706, 33064}, {3717, 49449}, {3741, 5718}, {3750, 37653}, {3759, 29660}, {3763, 49680}, {3771, 31187}, {3790, 49503}, {3821, 4743}, {3846, 10453}, {3886, 4655}, {3912, 49457}, {3923, 17771}, {3932, 49510}, {3936, 21242}, {3943, 49520}, {3996, 33085}, {4023, 4871}, {4028, 6682}, {4042, 29642}, {4046, 24165}, {4062, 46909}, {4133, 28516}, {4357, 49471}, {4389, 49469}, {4416, 4432}, {4439, 17233}, {4445, 42871}, {4519, 21093}, {4648, 48802}, {4663, 24295}, {4672, 34379}, {4684, 4967}, {4690, 42819}, {4693, 6646}, {4702, 17344}, {4711, 25108}, {4753, 17353}, {4780, 50092}, {4783, 20892}, {4851, 36480}, {4886, 29820}, {4909, 19868}, {4924, 38191}, {5233, 31137}, {5695, 17767}, {5847, 49473}, {6541, 49515}, {6679, 24597}, {10449, 37716}, {15485, 17346}, {15668, 48809}, {16496, 17294}, {16706, 50016}, {16823, 42334}, {17156, 26128}, {17165, 48644}, {17228, 29659}, {17230, 33165}, {17237, 49475}, {17240, 50075}, {17243, 49767}, {17249, 49470}, {17275, 24331}, {17276, 28542}, {17280, 49712}, {17287, 33076}, {17288, 24715}, {17295, 32847}, {17298, 24693}, {17299, 47358}, {17317, 36531}, {17327, 48822}, {17360, 49700}, {17362, 50023}, {17366, 50018}, {17373, 36534}, {17766, 49467}, {17770, 49484}, {20011, 32781}, {20012, 33174}, {21255, 25351}, {21283, 31134}, {22165, 28562}, {24199, 50096}, {29594, 49529}, {29673, 48651}, {29674, 49450}, {30942, 37651}, {31178, 48628}, {31289, 37650}, {32856, 48641}, {32863, 32945}, {32864, 33173}, {32919, 33175}, {33162, 48652}, {40341, 48805}, {48627, 50086}, {49506, 49691}, {49681, 50076}

X(50315) = midpoint of X(i) and X(j) for these {i,j}: {69, 32941}, {2321, 49505}, {3416, 49458}, {3886, 4655}, {4660, 49460}, {17299, 49455}, {17345, 49485}, {17372, 49465}
X(50315) = reflection of X(i) in X(j) for these {i,j}: {3773, 49560}, {4085, 141}, {4663, 24295}, {4743, 3821}, {49489, 1125}, {49685, 3589}
X(50315) = complement of X(49497)
X(50315) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 33087, 3836}, {599, 49460, 4660}, {3706, 33064, 48643}, {3936, 31136, 21242}, {4357, 49763, 49471}, {10453, 33084, 3846}, {17135, 31017, 33136}, {17135, 33081, 2887}, {17233, 49448, 4439}, {17299, 47358, 49455}, {29674, 49450, 49693}, {31017, 33136, 2887}, {32853, 33171, 6679}, {33081, 33136, 31017}


X(50316) = X(1)X(2)∩X(6)X(48810)

Barycentrics    a^3 - 3*a^2*b + 3*a*b^2 + b^3 - 3*a^2*c + 3*b^2*c + 3*a*c^2 + 3*b*c^2 + c^3 : :
X(50316) = X[8] + 2 X[49458], X[8] - 4 X[49560], 2 X[10] + X[49451], 4 X[1125] - X[49495], 5 X[3616] - 2 X[49488], 7 X[3622] - 4 X[49477], 3 X[25055] - 2 X[50114], 3 X[38314] - X[50129], X[49458] + 2 X[49560], X[69] + 2 X[32941], 2 X[141] + X[49460], X[193] - 4 X[49482], 2 X[2321] + X[16496], X[3416] + 2 X[49467], 4 X[3589] - X[49680], 5 X[3618] - 2 X[49497], 7 X[3619] - 4 X[4085], 5 X[3620] - 2 X[4660], X[3729] + 2 X[49505], 2 X[3886] + X[24248], X[3886] + 2 X[49511], X[24248] - 4 X[49511], 2 X[4133] + X[49446], X[24695] - 4 X[49484], 2 X[4780] - 5 X[17304], 4 X[17229] - X[49688], X[17276] + 2 X[49485], 5 X[17286] - 2 X[49529], X[17299] + 2 X[49465], 2 X[17372] + X[49681], 3 X[21358] - 2 X[48821], 3 X[38023] - 2 X[50124]

X(50316) lies on these lines: {1, 2}, {6, 48810}, {11, 27739}, {69, 752}, {141, 48829}, {193, 49482}, {238, 37654}, {344, 49457}, {346, 49448}, {390, 33082}, {391, 15485}, {392, 3789}, {497, 33084}, {518, 17281}, {524, 48805}, {527, 50126}, {528, 599}, {529, 11355}, {536, 47358}, {537, 50107}, {540, 50233}, {544, 47039}, {545, 5695}, {594, 42871}, {740, 50101}, {956, 8299}, {966, 16484}, {1001, 17330}, {1009, 12513}, {1111, 4441}, {1146, 5289}, {1279, 50082}, {1386, 50131}, {2238, 16483}, {2321, 16496}, {2345, 49490}, {2550, 31151}, {2784, 5731}, {2809, 5692}, {3242, 28503}, {3303, 16850}, {3416, 49467}, {3434, 31134}, {3550, 37655}, {3589, 49680}, {3618, 49497}, {3619, 4085}, {3620, 4660}, {3672, 49469}, {3685, 17333}, {3706, 33144}, {3729, 49505}, {3751, 50115}, {3886, 17274}, {4000, 49459}, {4034, 35227}, {4046, 17597}, {4133, 49446}, {4310, 49474}, {4331, 36589}, {4353, 50108}, {4370, 5220}, {4419, 4693}, {4461, 49532}, {4479, 4673}, {4543, 47828}, {4643, 4702}, {4657, 49475}, {4684, 50116}, {4715, 24695}, {4720, 30965}, {4780, 17304}, {4904, 30945}, {4908, 49515}, {4966, 17313}, {5263, 17378}, {5315, 37657}, {5734, 36693}, {5739, 32943}, {5880, 31138}, {5881, 36670}, {8616, 14552}, {9041, 50097}, {11522, 36695}, {12702, 19703}, {13464, 36672}, {13633, 34718}, {13745, 49717}, {16486, 37673}, {16801, 17349}, {17229, 49688}, {17251, 49740}, {17264, 50075}, {17271, 49746}, {17275, 42819}, {17276, 49485}, {17286, 49529}, {17297, 49720}, {17299, 49465}, {17320, 49470}, {17321, 49471}, {17342, 49450}, {17359, 47359}, {17360, 49709}, {17372, 49681}, {17382, 28581}, {17718, 27747}, {17757, 30959}, {17784, 33085}, {19277, 48823}, {20075, 33080}, {21242, 30828}, {21283, 31017}, {21358, 48821}, {24477, 33160}, {25557, 31139}, {27549, 49510}, {28309, 49453}, {28538, 50076}, {30305, 30946}, {30384, 30961}, {32922, 50088}, {33159, 49689}, {34648, 43170}, {36694, 37714}, {38023, 50124}, {38076, 43167}, {42032, 42054}, {48808, 48837}, {48811, 48870}, {48832, 48859}, {48833, 48863}, {49486, 50112}, {49723, 50278}, {50080, 50092}

X(50316) = midpoint of X(i) and X(j) for these {i,j}: {3241, 50079}, {3242, 50087}, {3886, 17274}, {48829, 49460}, {49467, 50081}, {50076, 50130}
X(50316) = reflection of X(i) in X(j) for these {i,j}: {6, 48810}, {3416, 50081}, {3679, 29594}, {3751, 50115}, {16834, 551}, {17274, 49511}, {24248, 17274}, {47359, 17359}, {48829, 141}, {48832, 48859}, {48833, 48863}, {48837, 48808}, {48870, 48811}, {49486, 50112}, {50080, 50092}, {50108, 4353}, {50131, 1386}
X(50316) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3632, 50017}, {2, 3241, 48830}, {8, 3616, 16816}, {8, 29579, 10}, {551, 48809, 2}, {3886, 49511, 24248}, {4966, 49725, 17313}, {17135, 33171, 33137}, {29660, 50016, 5222}, {36480, 49764, 17316}, {49458, 49560, 8}


X(50317) = X(1)X(3)∩X(4)X(500)

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

See Kadir Altintas and Ercole Suppa euclid 5148.

X(50317) lies on these lines: {1,3}, {2,5396}, {4,500}, {5,581}, {6,6883}, {10,37698}, {30,991}, {37,912}, {42,26446}, {43,11231}, {73,11374}, {81,1006}, {140,386}, {273,1442}, {387,6989}, {394,405}, {498,2594}, {511,6176}, {515,24220}, {580,4658}, {582,6986}, {631,19767}, {632,17749}, {943,3562}, {952,30116}, {975,5788}, {995,38028}, {997,5737}, {1064,3720}, {1150,4511}, {1437,13733}, {1656,37732}, {1724,36750}, {1742,28146}, {1765,3247}, {1834,37438}, {1836,4337}, {3085,5399}, {3110,31848}, {3191,3927}, {3216,3526}, {3560,17814}, {3682,5791}, {3743,5884}, {3794,19260}, {3920,5767}, {3945,6987}, {4257,7508}, {4300,12699}, {4306,6147}, {4340,6868}, {4414,12081}, {4551,31479}, {4648,6826}, {4649,39523}, {4653,6914}, {5055,5400}, {5070,22392}, {5145,32515}, {5262,37151}, {5287,18446}, {5312,31423}, {5492,15071}, {5603,29814}, {5657,17018}, {5693,27785}, {5712,6827}, {5718,6882}, {5720,17022}, {5721,6881}, {5722,14547}, {5732,18506}, {5752,13731}, {5769,30115}, {5887,6051}, {6001,15569}, {6149,15175}, {6505,41930}, {6829,45926}, {6830,45944}, {6840,37635}, {6852,24936}, {6878,24597}, {6905,37633}, {6911,37674}, {6971,37693}, {7100,43682}, {7534,46883}, {8583,16457}, {9306,36011}, {9840,37482}, {9956,37699}, {10393,37696}, {10454,46704}, {10459,37727}, {10571,37737}, {11230,26102}, {13738,18180}, {14828,36027}, {14996,37106}, {16343,19861}, {16418,17194}, {16451,41723}, {16455,22076}, {16458,19860}, {16577,18389}, {17019,18444}, {18178,19763}, {20117,27784}, {24281,29331}, {28459,37631}, {37697,45126}

X(50317) = trilinear quotient X(i)/X(j) for these (i, j): (1,37523,942), (3,45923,1754), (3,45931,37530), (1385,37536,3), (1764,3576,3)


leftri

Points on the Euler line: X(50318)-X(50325)

rightri

In the plane of a triangle ABC, let

P = point on Nagel line;
D = point not on Nagel line or Euler line;
U = point on Nagel line, other than U and G;
L = line through U parallel to PD;
U′ = L^(Euler line).

For centers X(50199)-X(50208), we take P = X(8) and D = X(6). The appearance of (i,j) in the following list means that if if U = X(i) then U' = X(j): (10,50318), (239,50319), (3187,50320), (3241,50321), (3621,50322), (3679,50323), (3811,50324), (4362,50325)


X(50318) = X(2)X(3)∩X(10)X(1386)

Barycentrics    2*a^4 + 4*a^3*b + 5*a^2*b^2 + 4*a*b^3 + b^4 + 4*a^3*c + 8*a^2*b*c + 8*a*b^2*c + 4*b^3*c + 5*a^2*c^2 + 8*a*b*c^2 + 6*b^2*c^2 + 4*a*c^3 + 4*b*c^3 + c^4 : :
X(50318) = 3 X[2] + X[964], 9 X[2] - X[17676], 3 X[964] + X[17676], 3 X[13728] - X[17676]

X(50318) lies on these lines: {2, 3}, {6, 49718}, {10, 1386}, {141, 43531}, {942, 5750}, {1125, 17061}, {1213, 4264}, {1330, 17307}, {1698, 5269}, {2345, 50042}, {2901, 17045}, {3624, 17720}, {3634, 6679}, {3695, 17289}, {3927, 5749}, {4026, 15171}, {4657, 50067}, {5105, 17398}, {5295, 17023}, {5717, 29604}, {5814, 17308}, {9708, 19866}, {10449, 17381}, {15172, 24552}, {16828, 25992}, {17384, 23537}, {19784, 31419}, {19865, 32942}, {19868, 34790}, {20582, 50226}, {24931, 37662}, {25499, 50177}, {26035, 50153}, {39564, 40940}, {48843, 49734}, {48866, 49728}

X(50318) = midpoint of X(964) and X(13728)
X(50318) = complement of X(13728)
X(50318) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 964, 13728}, {2, 2049, 8728}, {2, 5047, 17514}, {2, 13740, 4205}, {2, 13742, 16844}, {2, 14005, 17529}, {2, 16845, 16457}, {2, 16903, 33035}, {2, 17526, 16343}, {2, 17589, 17674}, {2, 17697, 37039}, {2, 17698, 6675}, {2, 37036, 17698}, {2, 37037, 3}, {2, 37176, 19273}, {3, 37037, 50059}, {141, 43531, 49743}, {405, 474, 37250}, {405, 37255, 48930}, {4202, 50169, 50238}, {11319, 13745, 50243}, {11354, 13725, 50241}, {13742, 16844, 50202}


X(50319) = X(2)X(3)∩X(239)X(5846)

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

X(50319) lies on these lines: {2, 3}, {239, 5846}, {1086, 20432}, {3661, 26561}, {3836, 23682}, {4766, 28254}, {17397, 26590}, {17757, 27044}, {20913, 21024}, {24222, 29716}, {26558, 29610}, {33172, 34284}

X(50319) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6656, 26601}, {2, 11320, 17540}, {2, 33840, 37096}


X(50320) = X(2)X(3)∩X(141)X(321)

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

X(50320) lies on these lines: {2, 3}, {141, 321}, {1230, 5254}, {2345, 32933}, {3187, 5014}, {17011, 26561}, {17019, 26590}, {18136, 46738}, {21287, 32911}, {32782, 44147}, {33172, 44140}, {45222, 48847}

X(50320) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 32974, 7381}, {7866, 11350, 2}


X(50321) = X(2)X(3)∩X(6)X(50215)

Barycentrics    a^4 - 3*a^3*b - 5*a^2*b^2 - 3*a*b^3 - 2*b^4 - 3*a^3*c - 6*a^2*b*c - 6*a*b^2*c - 3*b^3*c - 5*a^2*c^2 - 6*a*b*c^2 - 2*b^2*c^2 - 3*a*c^3 - 3*b*c^3 - 2*c^4 : :
X(50321) = X[964] - 4 X[13728], X[964] + 2 X[17676], 2 X[13728] + X[17676]

X(50321) lies on these lines: {2, 3}, {6, 50215}, {8, 48842}, {141, 49739}, {321, 50066}, {540, 19738}, {551, 31134}, {599, 3241}, {1150, 3017}, {2345, 50045}, {3578, 48857}, {3666, 50051}, {3679, 4981}, {4026, 5434}, {4657, 50070}, {4720, 17238}, {4968, 48818}, {5278, 48843}, {7788, 16705}, {7865, 25499}, {11237, 26115}, {17147, 50041}, {17237, 49687}, {17251, 50184}, {19684, 48835}, {19722, 50234}, {32784, 49492}, {42045, 48834}, {48840, 50310}, {48845, 49724}, {48861, 49716}

X(50321) = midpoint of X(2) and X(17676)
X(50321) = reflection of X(i) in X(j) for these {i,j}: {2, 13728}, {964, 2}
X(50321) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11359, 17679}, {2, 48813, 50171}, {2, 49735, 11346}, {2, 50165, 11354}, {13728, 17676, 964}, {13745, 48815, 2}


X(50322) = X(2)X(3)∩X(8)X(20064)

Barycentrics    3*a^4 + a^3*b + a*b^3 - b^4 + a^3*c + 2*a^2*b*c + 2*a*b^2*c + b^3*c + 2*a*b*c^2 + 4*b^2*c^2 + a*c^3 + b*c^3 - c^4 : :
X(50322) = 3 X[2] - 4 X[964], 9 X[2] - 8 X[13728], 3 X[964] - 2 X[13728], 4 X[13728] - 3 X[17676]

X(50322) lies on these lines: {2, 3}, {8, 20064}, {193, 3621}, {1043, 31034}, {4302, 26115}, {4339, 20045}, {4450, 5793}, {5016, 50054}, {5278, 49734}, {5716, 17147}, {7354, 24552}, {7737, 26035}, {9579, 17184}, {9657, 48805}, {14923, 37516}, {17154, 36579}, {17165, 20035}, {19741, 19783}, {20077, 31303}, {24275, 26085}, {28619, 48841}

X(50322) = reflection of X(17676) in X(964)
X(50322) = anticomplement of X(17676)
X(50322) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 37435, 17690}, {4, 11115, 2}, {4, 50061, 11115}, {377, 11319, 2}, {377, 48817, 11319}, {382, 16394, 5051}, {964, 17676, 2}, {2049, 50242, 49735}, {2475, 4195, 2}, {2478, 19284, 2}, {11319, 50172, 377}, {11354, 50239, 4202}, {13725, 50244, 50165}, {16865, 26051, 2}, {16909, 33841, 2}, {16910, 17688, 2}, {16913, 33820, 2}, {17537, 19284, 2478}, {17589, 37314, 2}, {19281, 31015, 2}, {19281, 50170, 31015}, {26643, 31049, 2}, {33703, 37037, 50055}, {48817, 50172, 2}


X(50323) = X(2)X(3)∩X(8)X(48861)

Barycentrics    4*a^4 + 6*a^3*b + 7*a^2*b^2 + 6*a*b^3 + b^4 + 6*a^3*c + 12*a^2*b*c + 12*a*b^2*c + 6*b^3*c + 7*a^2*c^2 + 12*a*b*c^2 + 10*b^2*c^2 + 6*a*c^3 + 6*b*c^3 + c^4 : :
X(50323) = 5 X[2] - X[17676], 2 X[964] + X[13728], 5 X[964] + X[17676], 5 X[13728] - 2 X[17676]

X(50323) lies on these lines: {1, 48859}, {2, 3}, {8, 48861}, {141, 49744}, {321, 50069}, {597, 3679}, {1724, 49730}, {2345, 50041}, {3666, 50053}, {4657, 50066}, {4968, 48820}, {15170, 24552}, {17385, 50051}, {25499, 50176}, {37631, 43531}, {48860, 50291}, {48863, 49739}, {48866, 49729}, {48867, 49724}, {48870, 49716}

X(50323) = midpoint of X(2) and X(964)
X(50323) = reflection of X(13728) in X(2)
X(50323) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11354, 13745}, {2, 17561, 16343}, {2, 50171, 48815}


X(50324) = X(2)X(3)∩X(141)X(500)

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

X(50324) lies on these lines: {2, 3}, {141, 500}, {582, 3589}, {943, 28780}, {3811, 5396}, {4026, 12699}, {4357, 40263}, {4420, 33075}, {5266, 5718}, {5480, 48882}, {5742, 25066}, {13408, 43531}, {14389, 35193}, {17306, 41854}, {19130, 35203}, {19784, 35239}, {21850, 48928}, {24206, 48893}, {36750, 41610}, {37552, 37693}, {48876, 48907}


X(50325) = X(2)X(3)∩X(12)X(32778)

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

X(50325) lies on these lines: {2, 3}, {12, 32778}, {495, 33088}, {1836, 32784}, {1961, 17720}, {2886, 4362}, {2887, 3838}, {3822, 29671}, {4640, 17385}, {25466, 29644}, {25639, 29645}

X(50325) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 37316, 6675}


leftri

Points in a [[b c, c a, a b], [a^2, b^2, c^2]] coordinate system: X(50326)-X(50359)

rightri

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

L1 is the line: b c α + c a β + a b γ = 0.

L2 is the line a^2 α + b^2 β + c^2 γ = 0.

The origin is given by (0, 0) = X(1491) = a(b-c)(b^2+bc+c^2) : : .

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

u : v : w = a(b - c)(b^2 + b c + c^2) - a(b - c) x - (b^2 - c^2) y ,

where, as functions of a, b, c, the coordinate x is antisymmetric of degree 3, and y is antisymmetric of degree 3.

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

{-2 (a^2+b^2+c^2), -2 (a^2+b^2+c^2)}, 47925
{-2 (a b+a c+b c), -2 (a b+a c+b c)}, 47928
{-((2 a b c)/(a+b+c)), -((2 a b c)/(a+b+c))}, 4490
{-2 (a b+a c+b c), -a b-a c-b c}, 47666
{-2 (a b+a c+b c), 1/2 (-a b-a c-b c)}, 47993
{-2 (a b+a c+b c), 0}, 48024
{-2 (a b+a c+b c), 1/2 (a^2+b^2+c^2)}, 48046
{-2 (a^2+b^2+c^2), a b+a c+b c}, 47685
{-2 (a b+a c+b c), a b+a c+b c}, 48080
{-2 (a+b+c)^2, a b+a c+b c}, 48079
{-((2 a b c)/(a+b+c)), a b+a c+b c}, 7650
{-((2 a b c)/(a+b+c)), (2 (a+b) (a+c) (b+c))/(a+b+c)}, 48392
{-((2 (a+b) (a+c) (b+c))/(a+b+c)), (2 a b c)/(a+b+c)}, 48123
{-a b-a c-b c, -2 (a^2+b^2+c^2)}, 47702
{-a b-a c-b c, -2 (a b+a c+b c)}, 47934
{-a b-a c-b c, -2 (a+b+c)^2}, 47669
{-a^2-b^2-c^2, -a^2-b^2-c^2}, 47968
{-a b-a c-b c, -a^2-b^2-c^2}, 47701
{-a b-a c-b c, -a b-a c-b c}, 4824
{-a b-a c-b c, -(a+b+c)^2}, 4988
{-(a+b+c)^2, -a^2-b^2-c^2}, 47944
{-(a+b+c)^2, -a b-a c-b c}, 47945
{-((a b c)/(a+b+c)), -((a b c)/(a+b+c))}, 4705
{-a b-a c-b c, 1/2 (-a^2-b^2-c^2)}, 47998
{-a b-a c-b c, 1/2 (-a b-a c-b c)}, 48002
{-a b-a c-b c, -(1/2) (a+b+c)^2}, 4841
{-(a+b+c)^2, 1/2 (-a^2-b^2-c^2)}, 47988
{-a b-a c-b c, 0}, 661
{-((a b c)/(a+b+c)), 0}, 47842
{-a b-a c-b c, 1/2 (a^2+b^2+c^2)}, 48047
{-a b-a c-b c, 1/2 (a b+a c+b c)}, 4806
{-a b-a c-b c, 1/2 (a+b+c)^2}, 3700
{-((a b c)/(a+b+c)), ((a+b) (a+c) (b+c))/(2 (a+b+c))}, 31946
{-a^2-b^2-c^2, a b+a c+b c}, 46403
{-a b-a c-b c, a^2+b^2+c^2}, 4088
{-a b-a c-b c, a b+a c+b c}, 4010
{-a b-a c-b c, (a+b+c)^2}, 4024
{-(a+b+c)^2, a b+a c+b c}, 20295
{-((a b c)/(a+b+c)), a b+a c+b c}, 30591
{-((a b c)/(a+b+c)), ((a+b) (a+c) (b+c))/(a+b+c)}, 1577
{-(((a+b) (a+c) (b+c))/(a+b+c)), (a b c)/(a+b+c)}, 14349
{-a b-a c-b c, 2 (a^2+b^2+c^2)}, 47700
{-a b-a c-b c, 2 (a b+a c+b c)}, 4804
{-a b-a c-b c, 2 (a+b+c)^2}, 4838
{-(a+b+c)^2, 2 (a b+a c+b c)}, 4810
{-((a b c)/(a+b+c)), (2 a b c)/(a+b+c)}, 48350
{1/2 (-a^2-b^2-c^2), -a^2-b^2-c^2}, 47960
{-(1/2) (a+b+c)^2, -a^2-b^2-c^2}, 47961
{1/2 (-a^2-b^2-c^2), 1/2 (-a^2-b^2-c^2)}, 48007
{1/2 (-a b-a c-b c), 1/2 (-a b-a c-b c)}, 48010
{-(1/2) (a+b+c)^2, 1/2 (-a^2-b^2-c^2)}, 47995
{-((a b c)/(2 (a+b+c))), -((a b c)/(2 (a+b+c)))}, 48012
{1/2 (-a^2-b^2-c^2), 0}, 2526
{1/2 (-a b-a c-b c), 0}, 48030
{-(1/2) (a+b+c)^2, 0}, 48027
{1/2 (-a^2-b^2-c^2), 1/2 (a+b+c)^2}, 49285
{1/2 (-a b-a c-b c), 1/2 (a b+a c+b c)}, 3835
{-(1/2) (a+b+c)^2, 1/2 (a^2+b^2+c^2)}, 48039
{-((a b c)/(2 (a+b+c))), ((a+b) (a+c) (b+c))/(2 (a+b+c))}, 21260
{-(((a+b) (a+c) (b+c))/(2 (a+b+c))), (a b c)/(2 (a+b+c))}, 48059
{1/2 (-a^2-b^2-c^2), a b+a c+b c}, 48089
{1/2 (-a b-a c-b c), a b+a c+b c}, 48090
{-(1/2) (a+b+c)^2, a b+a c+b c}, 4106
{1/2 (-a^2-b^2-c^2), 2 (a b+a c+b c)}, 48125
{0, -a b-a c-b c}, 47975
{0, 1/2 (-a^2-b^2-c^2)}, 3004
{0, 0}, 1491
{0, 1/2 (a b+a c+b c)}, 3837
{0, 1/2 (a+b+c)^2}, 48396
{0, ((a+b) (a+c) (b+c))/(2 (a+b+c))}, 44316
{0, a b+a c+b c}, 693
{0, 2 (a b+a c+b c)}, 48120
{1/2 (a^2+b^2+c^2), -(1/2) (a+b+c)^2}, 45745
{1/2 (a b+a c+b c), 1/2 (-a b-a c-b c)}, 48017
{1/2 (a+b+c)^2, 1/2 (-a^2-b^2-c^2)}, 4025
{1/2 (a^2+b^2+c^2), 0}, 650
{1/2 (a^2+b^2+c^2), 1/2 (a^2+b^2+c^2)}, 48062
{1/2 (a^2+b^2+c^2), 1/2 (a b+a c+b c)}, 4874
{1/2 (a^2+b^2+c^2), 1/2 (a+b+c)^2}, 6590
{1/2 (a b+a c+b c), 1/2 (a b+a c+b c)}, 24720
{1/2 (a+b+c)^2, 1/2 (a^2+b^2+c^2)}, 48069
{(a b c)/(2 (a+b+c)), (a b c)/(2 (a+b+c))}, 48066
{1/2 (a^2+b^2+c^2), a b+a c+b c}, 7662
{1/2 (a^2+b^2+c^2), (a+b+c)^2}, 48397
{1/2 (a b+a c+b c), a b+a c+b c}, 48098
{1/2 (a+b+c)^2, a b+a c+b c}, 43067
{1/2 (a^2+b^2+c^2), (2 a b c)/(a+b+c)}, 6129
{1/2 (a b+a c+b c), 2 (a b+a c+b c)}, 48127
{1/2 (a+b+c)^2, 2 (a b+a c+b c)}, 48134
{a^2+b^2+c^2, -a b-a c-b c}, 17494
{a b+a c+b c, -a^2-b^2-c^2}, 16892
{(a b c)/(a+b+c), -(((a+b) (a+c) (b+c))/(a+b+c))}, 48409
{((a+b) (a+c) (b+c))/(a+b+c), -((a b c)/(a+b+c))}, 1734
{(a+b+c)^2, 1/2 (-a^2-b^2-c^2)}, 4897
{a^2+b^2+c^2, 0}, 659
{a b+a c+b c, 0}, 2254
{(a+b+c)^2, 0}, 4784
{a^2+b^2+c^2, 1/2 (a^2+b^2+c^2)}, 47890
{a^2+b^2+c^2, 1/2 (a b+a c+b c)}, 48248
{a^2+b^2+c^2, a^2+b^2+c^2}, 48103
{a^2+b^2+c^2, a b+a c+b c}, 47694
{a^2+b^2+c^2, (a b c)/(a+b+c)}, 4057
{a b+a c+b c, a b+a c+b c}, 21146
{a b+a c+b c, (a+b+c)^2}, 47703
{(a+b+c)^2, a b+a c+b c}, 7192
{(a+b+c)^2, (a b c)/(a+b+c)}, 4840
{(a b c)/(a+b+c), (a b c)/(a+b+c)}, 2530
{(a^3+b^3+c^3)/(a+b+c), (a b c)/(a+b+c)}, 3737
{((a+b) (a+c) (b+c))/(a+b+c), (a b c)/(a+b+c)}, 23800
{a b+a c+b c, 2 (a b+a c+b c)}, 47672
{(a^3+b^3+c^3)/(a+b+c), (2 a b c)/(a+b+c)}, 2605
{2 (a^2+b^2+c^2), a b+a c+b c}, 47697
{2 (a b+a c+b c), a b+a c+b c}, 48108
{2 (a+b+c)^2, a b+a c+b c}, 48107
{2 (a^2+b^2+c^2), 2 (a^2+b^2+c^2)}, 48140
{2 (a b+a c+b c), 2 (a b+a c+b c)}, 48143
{(2 a b c)/(a+b+c), (2 a b c)/(a+b+c)}, 3777
{-2*(a*b + a*c + b*c), (a + b + c)^2/2}, 50326
{(-2*a*b*c)/(a + b + c), ((a + b)*(a + c)*(b + c))/(a + b + c)}, 50327
{-a^2 - b^2 - c^2, 0}, 50328
{-(a*b) - a*c - b*c, ((a + b)*(a + c)*(b + c))/(a + b + c)}, 50329
{-((a*b*c)/(a + b + c)), (a*b*c)/(a + b + c)}, 50330
{-(((a + b)*(a + c)*(b + c))/(a + b + c)), ((a + b)*(a + c)*(b + c))/(a + b + c)}, 50331
{-(a*b) - a*c - b*c, (2*a*b*c)/(a + b + c)}, 50332
{0, (a^2 + b^2 + c^2)/2}, 50333
{0, ((a + b)*(a + c)*(b + c))/(a + b + c)}, 50334
{(a*b + a*c + b*c)/2, 0}, 50335
{(a + b + c)^2/2, 0}, 50336
{((a + b)*(a + c)*(b + c))/(2*(a + b + c)), ((a + b)*(a + c)*(b + c))/(2*(a + b + c))}, 50337
{a*b + a*c + b*c, (-2*a*b*c)/(a + b + c)}, 50338
{(a + b + c)^2, -2*(a*b + a*c + b*c)}, 50339
{a^2 + b^2 + c^2, -a^2 - b^2 - c^2}, 50340
{a*b + a*c + b*c, -(a*b) - a*c - b*c}, 50341
{(a + b + c)^2, -a^2 - b^2 - c^2}, 50342
{(a + b + c)^2, -(a*b) - a*c - b*c}, 50343
{(a + b + c)^2, -((a*b*c)/(a + b + c))}, 50344
{(a*b*c)/(a + b + c), -((a*b*c)/(a + b + c))}, 50345
{(a^3 + b^3 + c^3)/(a + b + c), -((a*b*c)/(a + b + c))}, 50346
{a^2 + b^2 + c^2, (-a^2 - b^2 - c^2)/2}, 50347
{a*b + a*c + b*c, (-a^2 - b^2 - c^2)/2}, 50348
{(a^3 + b^3 + c^3)/(a + b + c), 0}, 50349
{((a + b)*(a + c)*(b + c))/(a + b + c), 0}, 50350
{(a^3 + b^3 + c^3)/(a + b + c), (a^3 + b^3 + c^3)/(a + b + c)}, 50351
{((a + b)*(a + c)*(b + c))/(a + b + c), ((a + b)*(a + c)*(b + c))/(a + b + c)}, 50352
{a^2 + b^2 + c^2, (2*a*b*c)/(a + b + c)}, 50353
{a*b + a*c + b*c, (2*a*b*c)/(a + b + c)}, 50354
{(2*(a + b)*(a + c)*(b + c))/(a + b + c), (-2*a*b*c)/(a + b + c)}, 50355
{2*(a*b + a*c + b*c), -(a*b) - a*c - b*c}, 50356
{2*(a*b + a*c + b*c), (-a^2 - b^2 - c^2)/2}, 50357
{2*(a^2 + b^2 + c^2), 0}, 50358
{2*(a*b + a*c + b*c), 0}, 50359


X(50326) = X(100)X(190)∩X(513)X(3700)

Barycentrics    (b - c)*(-3*a^2*b + b^3 - 3*a^2*c - 2*a*b*c + 3*b^2*c + 3*b*c^2 + c^3) : :
X(50326) = 2 X[2977] - 3 X[30565], 2 X[649] - 3 X[48231], 2 X[650] - 3 X[48166], 2 X[676] - 3 X[4800], 3 X[4010] - X[48326], 3 X[23770] - 2 X[48326], 3 X[1639] - 2 X[9508], X[2254] - 3 X[4120], 2 X[2254] - 3 X[48182], 3 X[3716] - 2 X[13246], 4 X[3716] - 3 X[26275], 8 X[13246] - 9 X[26275], 4 X[3239] - 3 X[47807], 2 X[3798] - 3 X[47803], 4 X[3835] - 3 X[48178], 2 X[4025] - 3 X[47799], X[4467] - 3 X[47821], 4 X[4885] - 3 X[48245], 3 X[4931] - X[47703], 3 X[4944] - X[7659], 2 X[7659] - 3 X[48249], 3 X[4958] + X[48032], 2 X[17069] - 3 X[47822], 3 X[21297] - X[49301], 2 X[25380] - 3 X[45661], 5 X[26798] - 3 X[48159], X[26853] - 3 X[48250], 3 X[31147] - X[47973], 2 X[47132] - 3 X[48172], 3 X[47769] - X[47975], 3 X[47772] - X[48408], 3 X[47786] - X[48015], 2 X[48015] - 3 X[48163], 3 X[47790] - X[48108], 3 X[47826] - X[48277], 3 X[47832] - X[47971], 3 X[47870] - X[49283], X[48148] - 3 X[48416]

X(50326) lies on these lines: {100, 190}, {513, 3700}, {522, 48000}, {523, 8663}, {525, 48267}, {649, 48231}, {650, 48166}, {676, 4800}, {690, 10015}, {812, 48055}, {824, 47998}, {918, 4010}, {1491, 14321}, {1639, 9508}, {2254, 4120}, {2786, 3716}, {3004, 4806}, {3239, 47807}, {3566, 4391}, {3667, 4522}, {3798, 47803}, {3835, 48178}, {3910, 48265}, {4024, 48021}, {4025, 47799}, {4040, 29232}, {4170, 29288}, {4367, 4990}, {4382, 48078}, {4467, 47821}, {4490, 4843}, {4500, 4778}, {4724, 48266}, {4762, 48040}, {4804, 48082}, {4810, 6084}, {4841, 48028}, {4874, 4897}, {4885, 48245}, {4931, 47703}, {4940, 48007}, {4944, 7659}, {4958, 48032}, {4977, 20295}, {6002, 48299}, {6005, 48395}, {6367, 47994}, {7178, 29200}, {7265, 29142}, {7662, 28846}, {17069, 47822}, {21104, 48090}, {21120, 29284}, {21297, 49301}, {22037, 23887}, {23875, 48403}, {25380, 45661}, {26798, 48159}, {26853, 48250}, {28175, 49273}, {28195, 49294}, {28213, 49298}, {28851, 48394}, {28855, 49292}, {28878, 48134}, {28894, 47983}, {29126, 49279}, {29148, 48290}, {29198, 48280}, {29240, 49276}, {29278, 48336}, {29328, 47890}, {30520, 49295}, {31147, 47973}, {44449, 47694}, {47132, 48172}, {47656, 47941}, {47671, 47904}, {47691, 49272}, {47696, 48079}, {47704, 48112}, {47769, 47975}, {47772, 48408}, {47786, 48015}, {47790, 48108}, {47826, 48277}, {47832, 47971}, {47870, 49283}, {47989, 48049}, {48036, 48268}, {48076, 48142}, {48102, 48114}, {48148, 48416}

X(50326) = midpoint of X(i) and X(j) for these {i,j}: {4024, 48021}, {4382, 48078}, {4724, 48266}, {4804, 48082}, {4810, 48083}, {20295, 49275}, {25259, 48080}, {44449, 47694}, {47656, 47941}, {47665, 47699}, {47671, 47904}, {47691, 49272}, {47696, 48079}, {47704, 48112}, {48036, 48268}, {48076, 48142}, {48102, 48114}
X(50326) = reflection of X(i) in X(j) for these {i,j}: {1491, 14321}, {3004, 4806}, {4367, 4990}, {4841, 48028}, {4897, 4874}, {21104, 48090}, {23770, 4010}, {47989, 48049}, {47998, 48043}, {48007, 4940}, {48047, 48270}, {48163, 47786}, {48182, 4120}, {48249, 4944}, {48290, 49288}, {48396, 3700}, {48400, 48267}
X(50326) = crossdifference of every pair of points on line {1015, 16466}


X(50327) = X(10)X(522)∩X(513)X(1577)

Barycentrics    b*(b - c)*c*(-a^2 + a*b + b^2 + a*c + 2*b*c + c^2) : :
X(50327) = 2 X[905] - 3 X[48207], X[1459] - 3 X[47832], X[4560] - 3 X[48165], 2 X[8043] - 3 X[47794], 2 X[14838] - 3 X[48181], X[20293] + 3 X[48172], X[17496] - 3 X[48209], 2 X[31947] - 3 X[48186], 3 X[48186] - X[48321], 2 X[40086] - 3 X[48184]

X(50327) lies on these lines: {10, 522}, {513, 1577}, {514, 30591}, {523, 4391}, {656, 48264}, {693, 4806}, {784, 47842}, {814, 4057}, {834, 4010}, {900, 2517}, {905, 48207}, {1269, 3261}, {1459, 3720}, {1491, 31946}, {2523, 24961}, {3716, 48297}, {3733, 4874}, {3762, 4802}, {3907, 48302}, {4064, 21118}, {4086, 4777}, {4397, 28183}, {4404, 28165}, {4408, 4509}, {4436, 18740}, {4462, 28175}, {4474, 48303}, {4560, 48165}, {4768, 28205}, {4778, 4823}, {4801, 28213}, {4840, 29170}, {4978, 28195}, {6586, 21960}, {8043, 47794}, {8702, 48339}, {14208, 48029}, {14838, 48181}, {17135, 20293}, {17496, 48209}, {18072, 18133}, {23282, 29017}, {23290, 46110}, {23880, 48168}, {25501, 47831}, {25512, 31947}, {29066, 48306}, {35353, 40013}

X(50327) = midpoint of X(i) and X(j) for these {i,j}: {656, 48264}, {1577, 4985}, {2517, 4811}, {3762, 4815}, {4064, 21118}, {4391, 7650}, {4474, 48303}
X(50327) = reflection of X(i) in X(j) for these {i,j}: {1491, 31946}, {3733, 4874}, {4036, 4791}, {48297, 3716}, {48321, 31947}
X(50327) = X(4490)-Dao conjugate of X(4500)
X(50327) = crossdifference of every pair of points on line {5019, 7113}
X(50327) = barycentric product X(i)*X(j) for these {i,j}: {75, 48277}, {693, 17275}, {4391, 11375}
X(50327) = barycentric quotient X(i)/X(j) for these {i,j}: {11375, 651}, {17275, 100}, {48277, 1}
X(50327) = {X(48186),X(48321)}-harmonic conjugate of X(31947)


X(50328) = X(2)X(48248)∩X(44)X(513)

Barycentrics    a*(b - c)*(a^2 + 2*b^2 + b*c + 2*c^2) : :
X(50328) = 2 X[649] - 3 X[48244], 4 X[650] - 3 X[659], 2 X[650] - 3 X[1491], X[650] - 3 X[2526], 8 X[650] - 9 X[47827], 4 X[650] - 9 X[48160], 7 X[650] - 9 X[48193], 10 X[650] - 9 X[48226], X[659] - 4 X[2526], 2 X[659] - 3 X[47827], X[659] - 3 X[48160], 7 X[659] - 12 X[48193], 5 X[659] - 6 X[48226], 4 X[1491] - 3 X[47827], 2 X[1491] - 3 X[48160], 7 X[1491] - 6 X[48193], 5 X[1491] - 3 X[48226], 3 X[2254] - X[4979], 8 X[2526] - 3 X[47827], 4 X[2526] - 3 X[48160], 7 X[2526] - 3 X[48193], 10 X[2526] - 3 X[48226], 2 X[4724] - 3 X[48162], 2 X[4782] - 3 X[47828], 3 X[4784] - 2 X[4979], X[4784] + 2 X[48020], X[4813] - 3 X[48023], X[4979] + 3 X[48020], 3 X[47810] - X[48032], 7 X[47827] - 8 X[48193], 5 X[47827] - 4 X[48226], 4 X[48030] - 3 X[48162], 7 X[48160] - 4 X[48193], 5 X[48160] - 2 X[48226], 10 X[48193] - 7 X[48226], X[4810] - 4 X[48042], 3 X[4810] - 4 X[49287], 3 X[24719] - 2 X[49287], 3 X[48042] - X[49287], X[26824] - 3 X[46403], X[47654] + 3 X[47687], 2 X[667] - 3 X[47893], 3 X[47893] - 4 X[48066], 2 X[676] - 3 X[48178], 2 X[693] - 3 X[48167], 3 X[2530] - 2 X[3960], 4 X[3960] - 3 X[4367], 4 X[2490] - 3 X[48247], 4 X[3835] - 3 X[4800], 6 X[3837] - 5 X[26985], 4 X[3837] - 3 X[47833], 2 X[3837] - 3 X[48164], 5 X[26985] - 3 X[47694], 10 X[26985] - 9 X[47833], 5 X[26985] - 9 X[48164], 2 X[47694] - 3 X[47833], X[47694] - 3 X[48164], X[4814] + 3 X[48122], 2 X[4369] - 3 X[36848], 2 X[4401] - 3 X[47888], 3 X[4448] - 4 X[25666], 2 X[4791] - 3 X[31149], 3 X[4809] - 4 X[21212], 4 X[4874] - 5 X[30795], 2 X[4874] - 3 X[44429], 4 X[4874] - 3 X[48251], 5 X[30795] - 6 X[44429], 5 X[30795] - 2 X[47697], 5 X[30795] - 3 X[48251], 3 X[44429] - X[47697], 2 X[47697] - 3 X[48251], 3 X[4879] - 2 X[4895], X[4895] - 3 X[48131], 4 X[4885] - 3 X[48234], 3 X[4927] - 2 X[47132], 3 X[4948] - 2 X[17494], X[17494] - 3 X[48157], 3 X[4951] - 2 X[48271], 2 X[7662] - 3 X[48184], 2 X[8689] - 3 X[47778], 3 X[21146] - 2 X[49291], 4 X[21260] - 3 X[47872], 4 X[23815] - 3 X[47889], 4 X[24720] - 3 X[48253], 3 X[25569] - 2 X[48324], 5 X[27013] - 6 X[48229], 7 X[27115] - 6 X[45314], 7 X[27138] - 6 X[48183], X[47664] + 3 X[47685], X[47664] - 3 X[47975], 3 X[31131] - X[47660], 5 X[31209] - 6 X[45323], X[47662] - 3 X[48187], X[47693] - 3 X[48169], X[47695] - 3 X[48159], X[47696] - 3 X[47808], 3 X[47808] - 2 X[48405], 3 X[47812] - X[48153], 3 X[47822] - 2 X[48063], X[47974] - 3 X[48549], 2 X[48008] - 3 X[48225]

X(50328) lies on these lines: {2, 48248}, {44, 513}, {256, 23838}, {512, 48086}, {514, 4774}, {522, 4810}, {523, 2528}, {663, 48100}, {667, 47893}, {676, 48178}, {693, 48167}, {764, 4160}, {814, 48410}, {830, 2530}, {900, 3004}, {1654, 28209}, {1734, 48596}, {2490, 48247}, {3309, 48092}, {3667, 47877}, {3728, 40471}, {3738, 4477}, {3777, 8678}, {3835, 4800}, {3837, 26985}, {3900, 48616}, {4010, 48050}, {4040, 48059}, {4041, 48116}, {4057, 27630}, {4083, 4814}, {4369, 36848}, {4382, 4777}, {4401, 47888}, {4448, 25666}, {4449, 48137}, {4770, 21385}, {4778, 47985}, {4791, 31149}, {4802, 47925}, {4809, 21212}, {4833, 27644}, {4834, 48018}, {4874, 30795}, {4879, 4895}, {4885, 48234}, {4905, 48586}, {4927, 47132}, {4948, 17494}, {4951, 48271}, {4963, 4977}, {4983, 42325}, {6004, 14349}, {6005, 48603}, {6006, 48041}, {6372, 47948}, {7192, 30966}, {7662, 48184}, {8689, 47778}, {9002, 20983}, {9013, 27469}, {11068, 47984}, {17166, 48406}, {18004, 49275}, {21123, 23656}, {21146, 49291}, {21260, 47872}, {21343, 48335}, {23815, 47889}, {24720, 48253}, {25569, 48324}, {27013, 48229}, {27115, 45314}, {27138, 48183}, {27673, 28284}, {28151, 47919}, {28195, 47909}, {28220, 47908}, {28225, 47885}, {28355, 28399}, {28396, 28398}, {28840, 49717}, {29070, 48409}, {29144, 47958}, {29198, 47912}, {29204, 47923}, {29362, 47664}, {29370, 47677}, {31131, 47660}, {31209, 45323}, {47662, 48187}, {47693, 48169}, {47695, 48159}, {47696, 47808}, {47700, 47931}, {47701, 47999}, {47812, 48153}, {47822, 48063}, {47901, 48146}, {47905, 48151}, {47910, 47953}, {47913, 47956}, {47924, 48621}, {47927, 47964}, {47929, 47967}, {47934, 48115}, {47940, 48108}, {47944, 47989}, {47946, 47992}, {47949, 48613}, {47951, 48599}, {47969, 48002}, {47970, 48005}, {47973, 48077}, {47974, 48549}, {48008, 48225}, {48015, 48035}, {48017, 48593}, {48047, 48083}, {48054, 48351}, {48056, 48102}, {48069, 48589}, {48073, 48590}, {48088, 48604}, {48089, 48120}, {48093, 48367}, {48097, 48139}, {48098, 48142}, {48106, 48585}, {48129, 48338}, {48148, 48583}

X(50328) = midpoint of X(i) and X(j) for these {i,j}: {1734, 48596}, {2254, 48020}, {4041, 48116}, {4905, 48586}, {47685, 47975}, {47700, 47931}, {47901, 48146}, {47905, 48151}, {47934, 48115}, {47940, 48108}, {47973, 48077}, {48015, 48035}, {48017, 48593}, {48069, 48589}, {48073, 48590}, {48106, 48585}, {48148, 48583}
X(50328) = reflection of X(i) in X(j) for these {i,j}: {659, 1491}, {663, 48100}, {667, 48066}, {1491, 2526}, {4010, 48050}, {4040, 48059}, {4367, 2530}, {4449, 48137}, {4724, 48030}, {4784, 2254}, {4810, 24719}, {4834, 48018}, {4879, 48131}, {4948, 48157}, {4963, 47945}, {4983, 48052}, {17166, 48406}, {21343, 48335}, {21385, 4770}, {24719, 48042}, {47694, 3837}, {47696, 48405}, {47697, 4874}, {47701, 47999}, {47827, 48160}, {47833, 48164}, {47910, 47953}, {47913, 47956}, {47924, 48621}, {47927, 47964}, {47929, 47967}, {47944, 47989}, {47946, 47992}, {47949, 48613}, {47969, 48002}, {47970, 48005}, {48024, 48027}, {48083, 48047}, {48102, 48056}, {48120, 48089}, {48123, 48092}, {48139, 48097}, {48142, 48098}, {48251, 44429}, {48323, 3777}, {48336, 14349}, {48338, 48129}, {48351, 48054}, {48367, 48093}, {48599, 47951}, {48604, 48088}, {49275, 18004}
X(50328) = anticomplement of X(48248)
X(50328) = X(14492)-Ceva conjugate of X(11)
X(50328) = X(2)-isoconjugate of X(28864)
X(50328) = X(28864)-Dao conjugate of X(32664)
X(50328) = crossdifference of every pair of points on line {1, 5007}
X(50328) = barycentric product X(i)*X(j) for these {i,j}: {1, 28863}, {513, 17292}
X(50328) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 28864}, {17292, 668}, {28863, 75}
X(50328) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {659, 1491, 47827}, {659, 48160, 1491}, {667, 48066, 47893}, {1491, 2526, 48160}, {3837, 47694, 47833}, {4724, 48030, 48162}, {4874, 44429, 30795}, {4874, 47697, 48251}, {30795, 48251, 4874}, {44429, 47697, 4874}, {47694, 48164, 3837}, {47696, 47808, 48405}


X(50329) = X(513)X(1577)∩X(523)X(661)

Barycentrics    (b - c)*(b + c)*(-a^3 - a^2*b - a^2*c + b^2*c + b*c^2) : :
X(50329) = X[14288] + 2 X[48267], X[4064] - 3 X[4120], X[4729] - 4 X[21714], 2 X[9508] - 3 X[48205], 2 X[31947] - 3 X[47839]

X(50329) lies on these lines: {430, 38360}, {512, 4036}, {513, 1577}, {522, 4129}, {523, 661}, {525, 21121}, {656, 900}, {798, 6133}, {810, 48302}, {814, 48297}, {834, 4391}, {2254, 44316}, {2310, 7668}, {2517, 48080}, {2605, 2787}, {2786, 21187}, {3657, 15232}, {3716, 4057}, {3733, 6002}, {3766, 20948}, {3835, 28623}, {4086, 4132}, {4106, 14208}, {4145, 4404}, {4369, 4840}, {4729, 21714}, {4777, 48551}, {4802, 48093}, {4977, 47906}, {6129, 21894}, {7253, 9013}, {7649, 48269}, {8061, 29078}, {8672, 30591}, {8676, 44426}, {9508, 48205}, {15313, 16228}, {17217, 18160}, {17478, 29324}, {20981, 24506}, {24287, 42327}, {24346, 37014}, {26983, 48209}, {27045, 48204}, {28175, 48279}, {31947, 47839}, {40086, 48151}

X(50329) = midpoint of X(i) and X(j) for these {i,j}: {2517, 48080}, {4086, 4170}, {7649, 48269}
X(50329) = reflection of X(i) in X(j) for these {i,j}: {656, 31946}, {2254, 44316}, {3733, 8062}, {4057, 3716}, {4840, 4369}, {23282, 3700}, {47842, 4129}, {48151, 40086}
X(50329) = X(i)-Ceva conjugate of X(j) for these (i,j): {7649, 523}, {48269, 3566}
X(50329) = X(i)-isoconjugate of X(j) for these (i,j): {81, 29014}, {100, 15376}, {163, 39700}
X(50329) = X(i)-Dao conjugate of X(j) for these (i,j): {115, 39700}, {306, 4561}, {8054, 15376}, {29014, 40586}
X(50329) = crosspoint of X(4) and X(3952)
X(50329) = crosssum of X(i) and X(j) for these (i,j): {3, 3733}, {3670, 23800}
X(50329) = crossdifference of every pair of points on line {58, 15376}
X(50329) = barycentric product X(i)*X(j) for these {i,j}: {10, 29013}, {514, 2901}, {523, 3187}, {661, 18147}, {850, 5301}, {1577, 1724}, {14618, 42463}
X(50329) = barycentric quotient X(i)/X(j) for these {i,j}: {42, 29014}, {523, 39700}, {649, 15376}, {1724, 662}, {2901, 190}, {3187, 99}, {5301, 110}, {18147, 799}, {29013, 86}, {42463, 4558}


X(50330) = X(1)X(38469)∩X(36)X(238)

Barycentrics    a*(b - c)*(b + c)*(a*b + b^2 + a*c + c^2) : :
X(50330) = 2 X[3733] - 3 X[14419], 3 X[14419] - 4 X[31947], 2 X[4036] - 3 X[14431], X[4705] + 2 X[48350], 3 X[14431] - 4 X[31946], X[1769] + 2 X[48059], X[4397] - 3 X[47814], 2 X[4874] - 3 X[48186], 2 X[6133] - 3 X[47794], X[7253] - 3 X[47840], 2 X[8062] - 3 X[47839], X[47694] - 3 X[48173], X[47844] - 3 X[48209]

X(50330) lies on these lines: {1, 38469}, {2, 4581}, {36, 238}, {512, 656}, {514, 24459}, {521, 48136}, {522, 1491}, {523, 1577}, {647, 661}, {650, 21389}, {663, 832}, {665, 48022}, {764, 4977}, {784, 7650}, {826, 4064}, {1649, 8034}, {1769, 48059}, {2254, 2499}, {2517, 21260}, {2526, 17115}, {2533, 27711}, {2605, 9013}, {3004, 4509}, {3005, 47701}, {3120, 3259}, {3122, 38363}, {3125, 41179}, {3667, 48066}, {3777, 4778}, {4041, 4139}, {4079, 8061}, {4129, 27576}, {4132, 4730}, {4140, 21099}, {4397, 47814}, {4466, 35094}, {4490, 28147}, {4601, 35147}, {4775, 15313}, {4802, 47725}, {4811, 48410}, {4874, 48186}, {4879, 35057}, {4934, 20975}, {6004, 48340}, {6129, 8678}, {6133, 47794}, {6161, 48306}, {6370, 21121}, {6371, 17420}, {6586, 48025}, {7253, 47840}, {7927, 14429}, {8062, 47839}, {8648, 39480}, {9508, 29487}, {14434, 42758}, {17066, 30765}, {18210, 38982}, {20293, 48298}, {20294, 47708}, {21124, 42661}, {23752, 42768}, {23765, 28229}, {27293, 47694}, {28161, 48012}, {28398, 48023}, {28623, 48267}, {39011, 39015}, {47844, 48209}

X(50330) = midpoint of X(i) and X(j) for these {i,j}: {661, 4017}, {4811, 48410}, {14349, 21189}, {17420, 48131}, {20293, 48298}, {20294, 47708}, {47842, 48350}
X(50330) = reflection of X(i) in X(j) for these {i,j}: {2517, 21260}, {3733, 31947}, {4036, 31946}, {4086, 21051}, {4705, 47842}, {6161, 48306}, {48393, 30591}
X(50330) = complement of X(4581)
X(50330) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 17197}, {31, 3125}, {100, 3831}, {101, 44417}, {109, 3812}, {110, 49598}, {163, 6703}, {692, 5750}, {765, 6371}, {960, 124}, {1193, 11}, {1211, 21253}, {1331, 37613}, {1333, 24195}, {1415, 39595}, {2092, 8287}, {2149, 3910}, {2269, 26932}, {2292, 125}, {2300, 1086}, {3666, 116}, {3725, 115}, {3882, 141}, {4267, 34589}, {4357, 21252}, {17420, 46100}, {20967, 1146}, {22074, 16596}, {22076, 34846}, {22345, 2968}, {24471, 17059}, {40153, 17761}, {40976, 6506}, {42661, 24040}
X(50330) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 3125}, {12, 3120}, {56, 18210}, {513, 6371}, {693, 3910}, {3004, 21124}, {38470, 1}
X(50330) = X(i)-isoconjugate of X(j) for these (i,j): {21, 36098}, {58, 8707}, {81, 36147}, {86, 32736}, {100, 2363}, {101, 14534}, {110, 1220}, {162, 1791}, {163, 30710}, {190, 1169}, {284, 6648}, {333, 8687}, {643, 961}, {648, 2359}, {662, 2298}, {1240, 1576}, {1798, 1897}, {4556, 14624}, {4570, 4581}, {32739, 40827}, {36050, 40452}
X(50330) = X(i)-Dao conjugate of X(j) for these (i,j): {2, 3125}, {10, 8707}, {21, 38992}, {81, 39015}, {99, 1211}, {100, 960}, {115, 30710}, {124, 40452}, {125, 1791}, {244, 1220}, {261, 17197}, {333, 17419}, {645, 2092}, {668, 3666}, {1015, 14534}, {1084, 2298}, {1240, 4858}, {1798, 34467}, {2363, 8054}, {6648, 40590}, {31643, 40622}, {32736, 40600}, {36098, 40611}, {36147, 40586}, {40619, 40827}
X(50330) = crosspoint of X(i) and X(j) for these (i,j): {86, 8052}, {513, 523}, {693, 7178}, {3004, 48131}
X(50330) = crosssum of X(i) and X(j) for these (i,j): {100, 110}, {513, 5262}, {692, 5546}, {32736, 36147}
X(50330) = crossdifference of every pair of points on line {21, 37}
X(50330) = barycentric product X(i)*X(j) for these {i,j}: {1, 21124}, {10, 48131}, {37, 3004}, {42, 4509}, {65, 3910}, {226, 17420}, {274, 42661}, {321, 6371}, {429, 905}, {512, 20911}, {513, 1211}, {514, 2292}, {523, 3666}, {525, 1829}, {649, 18697}, {650, 41003}, {656, 1848}, {661, 4357}, {663, 45196}, {667, 1228}, {693, 2092}, {850, 2300}, {960, 7178}, {1019, 20653}, {1193, 1577}, {2269, 4077}, {2354, 14208}, {2530, 27067}, {3120, 3882}, {3261, 3725}, {3669, 3704}, {3674, 4041}, {3676, 21033}, {3687, 4017}, {3700, 24471}, {3835, 45197}, {4036, 40153}, {4079, 16739}, {4705, 16705}, {7192, 21810}, {14618, 22345}, {15413, 44092}, {17108, 47711}, {17924, 22076}, {20906, 45218}, {21051, 27455}, {22097, 24006}, {24002, 40966}
X(50330) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 8707}, {42, 36147}, {65, 6648}, {213, 32736}, {429, 6335}, {512, 2298}, {513, 14534}, {523, 30710}, {647, 1791}, {649, 2363}, {661, 1220}, {667, 1169}, {693, 40827}, {810, 2359}, {960, 645}, {1193, 662}, {1211, 668}, {1228, 6386}, {1400, 36098}, {1402, 8687}, {1577, 1240}, {1829, 648}, {1848, 811}, {2092, 100}, {2269, 643}, {2292, 190}, {2300, 110}, {2354, 162}, {3004, 274}, {3125, 4581}, {3666, 99}, {3674, 4625}, {3687, 7257}, {3704, 646}, {3725, 101}, {3882, 4600}, {3910, 314}, {3965, 7256}, {4267, 4612}, {4357, 799}, {4509, 310}, {4705, 14624}, {6371, 81}, {6589, 40452}, {7178, 31643}, {7180, 961}, {16705, 4623}, {17420, 333}, {18210, 15420}, {18697, 1978}, {20653, 4033}, {20911, 670}, {20967, 5546}, {21033, 3699}, {21035, 35334}, {21124, 75}, {21810, 3952}, {22076, 1332}, {22097, 4592}, {22345, 4558}, {22383, 1798}, {24471, 4573}, {40966, 644}, {41003, 4554}, {42550, 44765}, {42661, 37}, {44092, 1783}, {45196, 4572}, {45197, 4598}, {45218, 932}, {48131, 86}
X(50330) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3733, 31947, 14419}, {4036, 31946, 14431}, {4079, 8061, 24290}


X(50331) = X(512)X(2517)∩X(513)X(1577)

Barycentrics    (b - c)*(-(a^3*b) - a^2*b^2 - a^3*c - a^2*b*c + b^3*c - a^2*c^2 + 2*b^2*c^2 + b*c^3) : :
X(50331) = 2 X[14288] + X[48267], X[4017] - 3 X[4728], 2 X[9508] - 3 X[48228], 3 X[14431] - 2 X[20316], X[20293] - 3 X[30709]

X(50331) lies on these lines: {512, 2517}, {513, 1577}, {522, 1491}, {523, 4992}, {656, 21260}, {667, 8062}, {693, 8672}, {802, 4486}, {814, 3737}, {832, 7253}, {834, 4036}, {900, 21189}, {1459, 2787}, {1919, 24506}, {2530, 28623}, {3837, 23800}, {4017, 4728}, {4063, 6133}, {4083, 4086}, {4139, 4397}, {4391, 6371}, {4581, 20295}, {4778, 48265}, {4815, 48090}, {4874, 29487}, {5214, 47948}, {6004, 44444}, {6089, 20294}, {8678, 39547}, {9508, 48228}, {14431, 20316}, {20293, 30709}, {21191, 24287}, {27293, 48243}, {28147, 48279}, {29070, 46385}, {29324, 48281}

X(50331) = midpoint of X(i) and X(j) for these {i,j}: {4581, 20295}, {5214, 47948}, {7253, 21301}
X(50331) = reflection of X(i) in X(j) for these {i,j}: {656, 21260}, {667, 8062}, {4063, 6133}, {4815, 48090}, {23800, 3837}
X(50331) = crossdifference of every pair of points on line {172, 4275}
X(50331) = barycentric product X(1577)*X(27660)
X(50331) = barycentric quotient X(27660)/X(662)


X(50332) = X(512)X(656)∩X(513)X(663)

Barycentrics    a*(b - c)*(b + c)*(a^2 + 2*a*b + b^2 + 2*a*c + c^2) : :
X(50332) = X[1769] + 2 X[48123], X[4822] + 2 X[48350], 2 X[4369] - 3 X[48209], X[4397] - 3 X[4776], X[4404] - 3 X[48551], X[4581] - 3 X[47840], 2 X[8062] - 3 X[47840], 2 X[6133] - 3 X[47822], 3 X[21052] - 4 X[31946], 2 X[21187] - 3 X[47797], 5 X[24924] - 6 X[48207], 4 X[25666] - 3 X[48204], 2 X[43927] - 3 X[47813]

X(50332) lies on these lines: {512, 656}, {513, 663}, {514, 4815}, {522, 4170}, {523, 661}, {830, 48307}, {832, 4775}, {834, 17420}, {2517, 3835}, {3250, 48022}, {3942, 4934}, {4041, 4132}, {4057, 8635}, {4086, 4129}, {4139, 4705}, {4160, 48293}, {4369, 48209}, {4397, 4776}, {4404, 48551}, {4502, 48033}, {4581, 8062}, {4778, 48335}, {4784, 28372}, {4802, 47918}, {4826, 8061}, {4879, 38469}, {4977, 48334}, {4983, 8672}, {6005, 23800}, {6133, 47822}, {8678, 48303}, {11934, 42312}, {15313, 48338}, {20315, 48069}, {21052, 31946}, {21102, 48400}, {21187, 47797}, {23752, 48403}, {24924, 48207}, {25666, 48204}, {28147, 47959}, {28155, 47997}, {28161, 48054}, {28623, 48080}, {35057, 48337}, {43927, 47813}, {44444, 48050}, {46385, 48099}, {46393, 47136}, {48281, 48348}, {48302, 48322}, {48332, 48342}

X(50332) = midpoint of X(i) and X(j) for these {i,j}: {4017, 4822}, {42312, 48023}
X(50332) = reflection of X(i) in X(j) for these {i,j}: {1459, 48136}, {2517, 3835}, {4017, 48350}, {4041, 47842}, {4086, 4129}, {4581, 8062}, {21102, 48400}, {23752, 48403}, {44444, 48050}, {46385, 48099}, {48069, 20315}, {48150, 48306}, {48281, 48348}, {48322, 48302}, {48342, 48332}
X(50332) = X(47995)-Ceva conjugate of X(48402)
X(50332) = crossdifference of every pair of points on line {9, 58}
X(50332) = barycentric product X(i)*X(j) for these {i,j}: {1, 48402}, {37, 47995}, {514, 3931}, {523, 5256}, {525, 7713}, {661, 17321}, {905, 39579}, {1577, 16466}, {4017, 14555}, {4077, 4254}, {5250, 7178}
X(50332) = barycentric quotient X(i)/X(j) for these {i,j}: {3931, 190}, {4254, 643}, {5250, 645}, {5256, 99}, {7713, 648}, {14555, 7257}, {16466, 662}, {17321, 799}, {39579, 6335}, {47995, 274}, {48402, 75}
X(50332) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 42664, 8611}, {4581, 47840, 8062}


X(50333) = X(2)X(676)∩X(4)X(9521)

Barycentrics    (a - b - c)*(b - c)*(a*b - b^2 + a*c - c^2) : :
X(50333) = 5 X[2] - 4 X[45318], 5 X[676] - 6 X[45318], 12 X[45318] - 5 X[47695], X[3904] + 2 X[4528], 2 X[659] - 3 X[47884], 4 X[2977] - 3 X[47884], X[693] - 3 X[47808], 5 X[1491] - 3 X[47877], 5 X[3004] - 6 X[47877], 4 X[3837] - 3 X[4927], 2 X[3837] - 3 X[48182], 3 X[4927] - 2 X[23770], X[23770] - 3 X[48182], 3 X[44429] - X[47691], 3 X[44435] - X[47692], X[45746] - 3 X[48175], X[47689] + 3 X[48175], X[47690] - 3 X[48187], X[47975] + 3 X[48187], 3 X[1639] - 2 X[3716], 5 X[631] - 4 X[44819], X[4088] + 2 X[4925], 3 X[1638] - 2 X[4458], 3 X[1638] - 4 X[25380], X[1769] - 3 X[14429], 2 X[1769] - 3 X[25923], 4 X[2490] - 3 X[47804], 4 X[2505] - X[49301], 2 X[4147] - 3 X[44729], X[21120] - 3 X[44729], 4 X[3812] - 3 X[30691], 2 X[4369] - 3 X[48232], X[4467] - 3 X[48242], 3 X[4763] - 2 X[13246], 2 X[4874] - 3 X[47807], 2 X[4885] - 3 X[47806], X[47123] - 3 X[47806], 3 X[4893] - X[47972], X[4895] - 3 X[14432], X[47945] + 3 X[48254], 3 X[48254] - X[49283], 3 X[31131] - X[46403], 3 X[31131] + X[48408], 3 X[6545] - X[47705], 3 X[6546] - X[48032], X[7192] - 3 X[48252], 2 X[7662] - 3 X[47788], X[7662] - 3 X[48200], 3 X[14430] - X[21132], 2 X[17069] - 3 X[47828], X[17494] + 3 X[48169], X[47687] - 3 X[48169], 3 X[19875] - 2 X[44566], 2 X[20517] - 3 X[41800], 3 X[21052] - X[21118], 4 X[25666] - 3 X[48179], 7 X[27115] - 3 X[48239], X[47968] - 3 X[48160], 6 X[30792] - 5 X[30795], 5 X[31209] - 3 X[47798], 4 X[31287] - 3 X[47800], 2 X[34958] - 3 X[47795], 3 X[36848] - X[48326], X[47131] - 3 X[47802], 2 X[47132] - 3 X[47833], X[47652] - 3 X[48164], X[47660] - 3 X[48208], X[47688] - 3 X[48159], X[47693] + 3 X[48157], X[47694] - 3 X[47809], X[47696] - 3 X[48236], X[47697] - 3 X[47771], X[47699] - 3 X[48549], X[47701] - 3 X[47810], X[47704] - 3 X[47812], X[47708] - 3 X[47814], X[47712] - 3 X[47816], X[47716] - 3 X[48556], X[47720] - 3 X[47819], 3 X[48171] - X[49275], 3 X[48231] - 2 X[48248], X[48398] - 3 X[48545]

X(50333) lies on these lines: {2, 676}, {4, 9521}, {8, 3904}, {10, 10015}, {11, 123}, {72, 928}, {75, 23684}, {100, 190}, {120, 20621}, {325, 523}, {337, 876}, {513, 4468}, {514, 2526}, {519, 45341}, {522, 650}, {525, 1734}, {631, 44819}, {649, 48077}, {784, 48395}, {824, 48017}, {885, 6559}, {918, 2254}, {1125, 48286}, {1499, 49277}, {1638, 4458}, {1769, 14429}, {2490, 47804}, {2505, 49301}, {2530, 4808}, {2799, 5988}, {2826, 3762}, {2827, 13227}, {3126, 43042}, {3667, 11067}, {3738, 14740}, {3800, 14349}, {3810, 4147}, {3812, 30691}, {3900, 6332}, {3910, 4041}, {4063, 28481}, {4152, 6068}, {4369, 48232}, {4391, 6362}, {4467, 48242}, {4500, 4928}, {4560, 29278}, {4705, 29142}, {4762, 49285}, {4763, 13246}, {4770, 29312}, {4777, 47784}, {4778, 48095}, {4802, 48007}, {4841, 48010}, {4874, 47807}, {4885, 47123}, {4893, 47972}, {4895, 14432}, {4963, 4977}, {5087, 42763}, {5592, 28521}, {6084, 20344}, {6087, 34188}, {6129, 20315}, {6545, 47705}, {6546, 48032}, {6556, 24128}, {7178, 17072}, {7192, 48252}, {7659, 28846}, {7662, 47788}, {7927, 48059}, {14321, 48080}, {14425, 44433}, {14430, 21132}, {16594, 23757}, {16892, 47700}, {17069, 47828}, {17494, 47687}, {17724, 24353}, {19875, 44566}, {20508, 25128}, {20517, 41800}, {21051, 48400}, {21052, 21118}, {21104, 24720}, {21260, 48403}, {21301, 29162}, {23729, 48050}, {23875, 48018}, {24003, 24025}, {24097, 42020}, {24396, 24415}, {25604, 48228}, {25666, 48179}, {26231, 26275}, {27115, 48239}, {28147, 47960}, {28169, 47880}, {28175, 47968}, {28183, 47827}, {28191, 47919}, {28213, 48140}, {28217, 47885}, {28221, 48226}, {28229, 48132}, {28423, 48243}, {28851, 48073}, {28859, 47985}, {28882, 48042}, {29021, 48012}, {29047, 48066}, {29144, 47998}, {29168, 48005}, {29208, 48100}, {30520, 48015}, {30787, 30790}, {31209, 47798}, {31287, 47800}, {32679, 41014}, {34894, 43728}, {34958, 47795}, {36848, 48326}, {47131, 47802}, {47132, 47833}, {47652, 48164}, {47660, 48208}, {47663, 47685}, {47679, 47714}, {47683, 47723}, {47688, 48159}, {47693, 48157}, {47694, 47809}, {47696, 48236}, {47697, 47771}, {47698, 48108}, {47699, 48549}, {47701, 47810}, {47703, 47934}, {47704, 47812}, {47707, 48410}, {47708, 47814}, {47711, 48409}, {47712, 47816}, {47715, 48407}, {47716, 48556}, {47720, 47819}, {47940, 49282}, {47943, 48146}, {47973, 48118}, {47988, 48027}, {48020, 48101}, {48023, 48106}, {48138, 48585}, {48171, 49275}, {48231, 48248}, {48398, 48545}

X(50333) = midpoint of X(i) and X(j) for these {i,j}: {8, 3904}, {649, 48077}, {1734, 48272}, {2254, 4088}, {2530, 4808}, {4041, 48278}, {4397, 20294}, {6332, 44448}, {16892, 47700}, {17494, 47687}, {45746, 47689}, {46403, 48408}, {47663, 47685}, {47679, 47714}, {47683, 47723}, {47690, 47975}, {47698, 48108}, {47703, 47934}, {47707, 48410}, {47711, 48409}, {47715, 48407}, {47940, 49282}, {47943, 48146}, {47945, 49283}, {47973, 48118}, {48020, 48101}, {48023, 48106}, {48035, 48060}, {48039, 48069}, {48138, 48585}
X(50333) = reflection of X(i) in X(j) for these {i,j}: {8, 4528}, {659, 2977}, {2254, 4925}, {3004, 1491}, {3700, 4522}, {4458, 25380}, {4841, 48010}, {4927, 48182}, {4976, 4913}, {6129, 20315}, {7178, 17072}, {10015, 10}, {21104, 24720}, {21120, 4147}, {23729, 48050}, {23770, 3837}, {25923, 14429}, {26275, 28602}, {42763, 5087}, {43042, 3126}, {44433, 14425}, {47123, 4885}, {47695, 676}, {47788, 48200}, {47890, 48062}, {47988, 48027}, {47998, 48030}, {48046, 48047}, {48055, 48056}, {48080, 14321}, {48274, 48396}, {48286, 1125}, {48400, 21051}, {48402, 48012}, {48403, 21260}
X(50333) = complement of X(47695)
X(50333) = anticomplement of X(676)
X(50333) = isogonal conjugate of X(32735)
X(50333) = isotomic conjugate of X(927)
X(50333) = anticomplement of the isogonal conjugate of X(677)
X(50333) = isotomic conjugate of the anticomplement of X(1566)
X(50333) = isotomic conjugate of the complement of X(14732)
X(50333) = isotomic conjugate of the isogonal conjugate of X(926)
X(50333) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {100, 152}, {103, 149}, {677, 8}, {911, 4440}, {2338, 37781}, {18025, 21293}, {24016, 36845}, {32642, 192}, {32668, 4452}, {35184, 4430}, {36039, 2}, {36101, 150}, {40116, 5905}
X(50333) = X(692)-complementary conjugate of X(39048)
X(50333) = X(i)-Ceva conjugate of X(j) for these (i,j): {668, 4437}, {883, 3912}, {1026, 3932}, {3699, 40609}, {4518, 11}, {4583, 312}, {35574, 345}, {36796, 1146}, {36802, 8}, {36803, 40997}, {42720, 3693}
X(50333) = X(1566)-cross conjugate of X(2)
X(50333) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32735}, {6, 36146}, {7, 32666}, {31, 927}, {32, 34085}, {56, 36086}, {57, 919}, {59, 1027}, {100, 1416}, {101, 1462}, {105, 109}, {108, 36057}, {294, 1461}, {560, 46135}, {604, 666}, {651, 1438}, {653, 32658}, {667, 39293}, {673, 1415}, {884, 7045}, {885, 24027}, {934, 2195}, {1024, 1262}, {1025, 41934}, {1106, 36802}, {1110, 43930}, {1445, 32644}, {1617, 36041}, {1813, 8751}, {1814, 32674}, {4564, 43929}, {4565, 18785}, {5228, 36138}, {5377, 43924}, {6614, 28071}, {32724, 40719}, {32739, 34018}, {34036, 35185}, {34160, 36093}, {36059, 36124}
X(50333) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 36086}, {2, 927}, {3, 32735}, {6, 39014}, {7, 35094}, {9, 36146}, {11, 105}, {56, 38989}, {57, 38980}, {100, 40609}, {108, 20621}, {109, 39046}, {241, 17435}, {241, 23973}, {294, 35508}, {513, 3126}, {514, 43930}, {518, 2283}, {522, 885}, {651, 6184}, {656, 23696}, {658, 36905}, {659, 3716}, {664, 17755}, {666, 3161}, {673, 1146}, {884, 17115}, {918, 43042}, {919, 5452}, {926, 8638}, {934, 39063}, {1015, 1462}, {1027, 6615}, {1086, 35509}, {1416, 8054}, {1438, 38991}, {1447, 27918}, {1617, 5519}, {1633, 17060}, {1814, 35072}, {2195, 14714}, {2481, 40624}, {2968, 14942}, {2976, 4925}, {5228, 39012}, {6180, 48315}, {6374, 46135}, {6376, 34085}, {6552, 36802}, {6631, 39293}, {6741, 13576}, {20620, 36124}, {31637, 40626}, {34018, 40619}, {36057, 38983}
X(50333) = cevapoint of X(i) and X(j) for these (i,j): {2, 14732}, {516, 24980}
X(50333) = crosspoint of X(i) and X(j) for these (i,j): {8, 36802}, {99, 37202}, {100, 26703}, {190, 18025}, {668, 36796}, {883, 3912}, {3263, 42720}, {4583, 40217}
X(50333) = crosssum of X(i) and X(j) for these (i,j): {512, 39690}, {513, 3827}, {884, 1438}
X(50333) = crossdifference of every pair of points on line {32, 56}
X(50333) = barycentric product X(i)*X(j) for these {i,j}: {8, 918}, {11, 42720}, {76, 926}, {241, 4397}, {312, 2254}, {314, 24290}, {333, 4088}, {346, 43042}, {514, 3717}, {518, 4391}, {521, 46108}, {522, 3912}, {561, 46388}, {646, 3675}, {650, 3263}, {665, 3596}, {668, 17435}, {672, 35519}, {693, 3693}, {883, 1146}, {885, 4437}, {1025, 24026}, {1026, 4858}, {1502, 8638}, {1818, 46110}, {1861, 6332}, {1876, 15416}, {2283, 23978}, {2284, 34387}, {2321, 23829}, {2340, 3261}, {3126, 36796}, {3239, 9436}, {3267, 37908}, {3700, 30941}, {3716, 40217}, {3900, 40704}, {3930, 18155}, {3932, 4560}, {4041, 18157}, {4086, 18206}, {4546, 10029}, {4925, 6557}, {5089, 35518}, {25083, 44426}, {35094, 36802}, {36795, 42758}
X(50333) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 36146}, {2, 927}, {6, 32735}, {8, 666}, {9, 36086}, {41, 32666}, {55, 919}, {75, 34085}, {76, 46135}, {190, 39293}, {241, 934}, {346, 36802}, {513, 1462}, {518, 651}, {521, 1814}, {522, 673}, {644, 5377}, {649, 1416}, {650, 105}, {652, 36057}, {657, 2195}, {663, 1438}, {665, 56}, {672, 109}, {693, 34018}, {883, 1275}, {884, 41934}, {885, 6185}, {918, 7}, {926, 6}, {1025, 7045}, {1026, 4564}, {1086, 43930}, {1146, 885}, {1458, 1461}, {1566, 676}, {1818, 1813}, {1861, 653}, {1876, 32714}, {1946, 32658}, {2170, 1027}, {2223, 1415}, {2254, 57}, {2283, 1262}, {2284, 59}, {2310, 1024}, {2340, 101}, {2356, 32674}, {3064, 36124}, {3126, 241}, {3239, 14942}, {3263, 4554}, {3271, 43929}, {3286, 4565}, {3596, 36803}, {3675, 3669}, {3688, 46163}, {3693, 100}, {3700, 13576}, {3716, 6654}, {3717, 190}, {3900, 294}, {3912, 664}, {3930, 4551}, {3932, 4552}, {4041, 18785}, {4081, 28132}, {4088, 226}, {4130, 28071}, {4163, 6559}, {4391, 2481}, {4397, 36796}, {4437, 883}, {4712, 1025}, {4843, 14625}, {4925, 5435}, {5089, 108}, {5236, 36118}, {6184, 2283}, {6332, 31637}, {8638, 32}, {9436, 658}, {14430, 36816}, {14439, 23703}, {14936, 884}, {17435, 513}, {18157, 4625}, {18206, 1414}, {18344, 8751}, {20683, 4559}, {20752, 36059}, {23829, 1434}, {24290, 65}, {25083, 6516}, {28143, 14197}, {30941, 4573}, {33299, 35333}, {34591, 23696}, {34855, 4617}, {35094, 43042}, {35293, 23890}, {35519, 18031}, {36819, 37136}, {37908, 112}, {39014, 8638}, {39063, 23973}, {39749, 41075}, {40141, 35185}, {40704, 4569}, {42341, 6180}, {42720, 4998}, {42758, 1465}, {42771, 3310}, {43042, 279}, {44448, 31638}, {46108, 18026}, {46388, 31}
X(50333) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 47695, 676}, {659, 2977, 47884}, {3837, 23770, 4927}, {4458, 25380, 1638}, {17494, 48169, 47687}, {21120, 44729, 4147}, {23770, 48182, 3837}, {31131, 48408, 46403}, {47123, 47806, 4885}, {47689, 48175, 45746}, {47945, 48254, 49283}, {47975, 48187, 47690}


X(50334) = X(325)X(523)∩X(513)X(1577)

Barycentrics    b*(b - c)*c*(a^2 + a*b + b^2 + a*c + 2*b*c + c^2) : :
X(50334) = 3 X[693] + X[4397], 3 X[2517] - X[4397], 3 X[1577] - X[4985], 2 X[650] - 3 X[48205], X[4560] - 3 X[48246], 4 X[4885] - 3 X[48207], X[6129] - 3 X[45320], 2 X[8043] - 3 X[48228], 2 X[14838] - 3 X[48230], X[17494] - 3 X[48204], 5 X[26985] - 3 X[48209], 2 X[31947] - 3 X[47795], 3 X[47832] - X[48340]

X(50334) lies on these lines: {325, 523}, {513, 1577}, {514, 4036}, {522, 4823}, {650, 24960}, {768, 4444}, {814, 3733}, {834, 2533}, {900, 7650}, {2605, 29066}, {3737, 47724}, {3762, 28195}, {3777, 40086}, {3810, 21111}, {3907, 48283}, {4057, 4874}, {4086, 4802}, {4132, 48273}, {4374, 29078}, {4391, 4977}, {4404, 28151}, {4411, 4509}, {4462, 28213}, {4474, 48342}, {4560, 48246}, {4768, 28165}, {4777, 4815}, {4778, 4791}, {4801, 28175}, {4811, 28217}, {4828, 29370}, {4840, 18155}, {4885, 48207}, {6129, 45320}, {6133, 29362}, {6362, 44426}, {7649, 49285}, {8043, 48228}, {8062, 29051}, {14208, 48027}, {14838, 48230}, {17494, 48204}, {20954, 29328}, {21121, 29017}, {21260, 47842}, {21301, 47844}, {23752, 48278}, {24720, 28623}, {26985, 48209}, {27610, 48103}, {31947, 47795}, {40166, 47136}, {44444, 47694}, {47832, 48340}, {48292, 48295}

X(50334) = midpoint of X(i) and X(j) for these {i,j}: {693, 2517}, {3737, 47724}, {4086, 4978}, {4474, 48342}, {7649, 49285}, {21301, 47844}, {23752, 48278}, {44444, 47694}
X(50334) = reflection of X(i) in X(j) for these {i,j}: {1491, 44316}, {3777, 40086}, {4057, 4874}, {30591, 4823}, {47842, 21260}, {48292, 48295}, {48297, 8062}
X(50334) = polar conjugate of the isogonal conjugate of X(2523)
X(50334) = X(i)-Dao conjugate of X(j) for these (i,j): {48085, 48275}, {48123, 48404}
X(50334) = crossdifference of every pair of points on line {32, 2174}
X(50334) = barycentric product X(i)*X(j) for these {i,j}: {75, 48275}, {264, 2523}, {523, 30599}, {693, 17303}, {1577, 25526}, {3261, 5311}, {4391, 10404}, {20565, 30600}
X(50334) = barycentric quotient X(i)/X(j) for these {i,j}: {2523, 3}, {5311, 101}, {10404, 651}, {17303, 100}, {25526, 662}, {30599, 99}, {30600, 35}, {48275, 1}


X(50335) = X(44)X(513)∩X(75)X(693)

Barycentrics    a*(b - c)*(a*b - 2*b^2 + a*c - b*c - 2*c^2) : :
X(50335) = X[649] - 3 X[48244], 2 X[650] - 3 X[48213], X[659] - 3 X[47828], X[661] - 3 X[1491], X[661] + 3 X[2254], 5 X[661] - 9 X[47810], 7 X[661] - 3 X[48021], 5 X[661] - 3 X[48024], 4 X[661] - 3 X[48028], 2 X[661] - 3 X[48030], 5 X[1491] - 3 X[47810], 7 X[1491] - X[48021], 5 X[1491] - X[48024], 4 X[1491] - X[48028], 5 X[2254] + 3 X[47810], 7 X[2254] + X[48021], 5 X[2254] + X[48024], 4 X[2254] + X[48028], 2 X[2254] + X[48030], 3 X[2526] + X[4790], 4 X[4394] - 3 X[4782], 2 X[4394] - 3 X[9508], X[4724] - 3 X[47827], X[4784] + 3 X[48160], 21 X[47810] - 5 X[48021], 3 X[47810] - X[48024], 12 X[47810] - 5 X[48028], 6 X[47810] - 5 X[48030], 5 X[48021] - 7 X[48024], 4 X[48021] - 7 X[48028], 2 X[48021] - 7 X[48030], X[48023] - 3 X[48160], 4 X[48024] - 5 X[48028], 2 X[48024] - 5 X[48030], X[48029] - 3 X[48193], X[48032] - 3 X[48226], X[693] - 3 X[36848], X[47131] - 3 X[47754], 2 X[48018] + X[48100], 4 X[48018] + X[48129], 4 X[48066] - X[48129], 4 X[21212] - 3 X[48212], 4 X[24720] - X[48127], 3 X[24720] - X[48399], 2 X[48017] + X[48098], 4 X[48017] + X[48127], 3 X[48017] + X[48399], 3 X[48098] - 2 X[48399], 3 X[48127] - 4 X[48399], X[663] - 3 X[47893], 2 X[676] - 3 X[48215], 3 X[905] - X[48327], 2 X[48327] - 3 X[48330], 3 X[1734] - X[4730], 2 X[1734] + X[48137], 3 X[1734] + X[48335], 3 X[2530] + X[4730], 3 X[2530] - X[48335], 2 X[4730] + 3 X[48137], 3 X[48137] - 2 X[48335], X[3700] - 3 X[48182], 2 X[3716] - 3 X[48197], X[4010] - 3 X[44429], X[4040] - 3 X[47888], X[4122] - 3 X[47808], X[4369] - 3 X[45328], X[4382] - 3 X[48167], 3 X[4448] - 5 X[31209], X[4467] + 3 X[31131], 2 X[4905] + X[47922], 3 X[4800] - 5 X[30835], 3 X[21146] - X[47675], X[47653] + 3 X[48254], X[47675] + 3 X[47975], 2 X[47675] - 3 X[48135], 2 X[47975] + X[48135], X[4804] - 3 X[48184], X[4824] - 3 X[48175], X[48108] + 3 X[48175], 2 X[48108] + X[48620], 6 X[48175] - X[48620], 2 X[4874] - 3 X[48216], 4 X[25380] - 3 X[48216], 4 X[4885] - 3 X[48202], X[4922] - 3 X[44550], 3 X[4948] - X[47926], X[47964] + 2 X[48073], 4 X[48010] - X[48610], 4 X[48073] + X[48610], X[47967] + 2 X[48075], 4 X[48012] - X[48609], 4 X[48075] + X[48609], X[7192] + 3 X[48157], 2 X[7662] - 3 X[48221], 2 X[8689] - 3 X[45314], 3 X[14419] - X[48324], X[17494] - 3 X[48225], X[23729] - 3 X[48163], X[24719] - 3 X[48164], 5 X[24924] - 3 X[48234], 2 X[25666] - 3 X[45323], 5 X[26985] - 3 X[48189], 3 X[47812] - X[48120], 5 X[30795] - 3 X[47832], 2 X[31286] - 3 X[48229], 3 X[48229] - X[48248], 4 X[31287] - 3 X[45666], 3 X[44435] - X[48349], X[46403] + 3 X[48242], X[47660] - 3 X[48235], X[47677] + 3 X[48187], X[47694] - 3 X[47823], X[47695] - 3 X[48227], X[47701] - 3 X[47877], 3 X[47795] - X[48305], 3 X[47796] - X[48301], 3 X[47806] - X[49286], 3 X[47814] - X[48265], 3 X[47816] - X[48267], 3 X[47819] - X[48279], 3 X[47830] - X[48063], 3 X[47885] - X[48102], X[47946] - 3 X[48549], X[47962] - 3 X[48190], X[47969] - 3 X[48176], 2 X[48000] - 3 X[48191], 2 X[48069] + X[48621], 2 X[48015] + X[48097], X[48142] - 3 X[48253], 3 X[48185] - X[49275], 3 X[48188] - X[49273], 3 X[48200] - X[48271], 3 X[48249] - X[48276], X[48273] - 3 X[48556]

X(50335) lies on these lines: {44, 513}, {75, 693}, {512, 48018}, {514, 4770}, {522, 3837}, {523, 3776}, {663, 47893}, {676, 48215}, {764, 46032}, {824, 25381}, {900, 3835}, {905, 48327}, {1022, 4825}, {1734, 2530}, {2533, 48410}, {3004, 29144}, {3126, 19584}, {3667, 4806}, {3700, 48182}, {3716, 48197}, {3777, 4041}, {3960, 48344}, {4010, 4926}, {4040, 47888}, {4122, 47808}, {4132, 8665}, {4151, 23815}, {4369, 45328}, {4382, 48167}, {4444, 4762}, {4448, 31209}, {4467, 31131}, {4486, 28898}, {4490, 48151}, {4524, 47329}, {4560, 29274}, {4705, 4905}, {4778, 47954}, {4800, 30835}, {4802, 21146}, {4804, 28205}, {4814, 21343}, {4824, 28195}, {4834, 48086}, {4874, 25380}, {4885, 21264}, {4913, 29362}, {4922, 44550}, {4948, 47926}, {4977, 47964}, {6004, 14838}, {6005, 48059}, {6372, 47967}, {7192, 48157}, {7662, 48221}, {8674, 42319}, {8689, 45314}, {8714, 21260}, {9001, 17792}, {14419, 48324}, {16892, 29204}, {17494, 48225}, {19947, 48295}, {21301, 29152}, {23729, 48163}, {24719, 48164}, {24924, 48234}, {25666, 45323}, {26042, 26049}, {26078, 27345}, {26985, 48189}, {27633, 27674}, {28151, 47672}, {28165, 47812}, {28183, 48394}, {28199, 47934}, {28209, 47996}, {28217, 48043}, {28220, 47666}, {28225, 47993}, {29202, 48278}, {29236, 48321}, {29280, 48272}, {29328, 48050}, {30765, 45342}, {30795, 47832}, {31286, 48229}, {31287, 45666}, {39386, 48037}, {43931, 45782}, {44435, 48349}, {46403, 48242}, {47660, 48235}, {47677, 48187}, {47694, 47823}, {47695, 48227}, {47701, 47877}, {47795, 48305}, {47796, 48301}, {47806, 49286}, {47814, 48265}, {47816, 48267}, {47819, 48279}, {47830, 48063}, {47885, 48102}, {47925, 48146}, {47928, 48148}, {47931, 48140}, {47946, 48549}, {47957, 48005}, {47962, 48190}, {47968, 48106}, {47969, 48176}, {47973, 48103}, {47999, 48611}, {48000, 48191}, {48007, 48069}, {48015, 48062}, {48056, 48614}, {48142, 48253}, {48185, 49275}, {48188, 49273}, {48200, 48271}, {48249, 48276}, {48273, 48556}

X(50335) = midpoint of X(i) and X(j) for these {i,j}: {1022, 4825}, {1491, 2254}, {1734, 2530}, {2533, 48410}, {3777, 4041}, {4490, 48151}, {4705, 4905}, {4730, 48335}, {4784, 48023}, {4814, 21343}, {4824, 48108}, {4834, 48086}, {7659, 48027}, {21146, 47975}, {24720, 48017}, {47925, 48146}, {47928, 48148}, {47931, 48140}, {47934, 48143}, {47968, 48106}, {47973, 48103}, {48007, 48069}, {48010, 48073}, {48012, 48075}, {48015, 48062}, {48018, 48066}
X(50335) = reflection of X(i) in X(j) for these {i,j}: {4782, 9508}, {4874, 25380}, {47922, 4705}, {47954, 48002}, {47957, 48005}, {47964, 48010}, {47967, 48012}, {48028, 48030}, {48030, 1491}, {48090, 3837}, {48093, 48059}, {48097, 48062}, {48098, 24720}, {48100, 48066}, {48127, 48098}, {48129, 48100}, {48135, 21146}, {48137, 2530}, {48248, 31286}, {48295, 19947}, {48330, 905}, {48331, 14838}, {48344, 3960}, {48609, 47967}, {48610, 47964}, {48611, 47999}, {48614, 48056}, {48620, 4824}, {48621, 48007}
X(50335) = X(2)-isoconjugate of X(30554)
X(50335) = X(30554)-Dao conjugate of X(32664)
X(50335) = crossdifference of every pair of points on line {1, 2251}
X(50335) = barycentric product X(i)*X(j) for these {i,j}: {1, 30519}, {513, 17230}, {514, 49448}, {656, 31916}, {9461, 20568}
X(50335) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 30554}, {9461, 44}, {17230, 668}, {30519, 75}, {31916, 811}, {49448, 190}
X(50335) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1491, 48024, 47810}, {1734, 48335, 4730}, {2530, 4730, 48335}, {4784, 48160, 48023}, {4874, 25380, 48216}, {48108, 48175, 4824}, {48229, 48248, 31286}


X(50336) = X(3)X(667)∩X(44)X(513)

Barycentrics    a*(b - c)*(a^2 + 2*a*b - b^2 + 2*a*c - c^2) : :
X(50336) = 3 X[667] - X[6161], 2 X[6161] - 3 X[48329], X[661] - 3 X[47828], X[1491] - 3 X[48244], 3 X[1635] - X[4724], 4 X[2516] - 3 X[48226], 2 X[4784] + X[48027], X[4784] + 3 X[48244], X[4813] - 3 X[47810], 3 X[4893] - X[48021], X[7659] + 2 X[9508], 2 X[7659] + X[48029], 4 X[9508] - X[48029], 3 X[47777] - 2 X[48028], 3 X[47827] - X[48024], X[48026] - 3 X[48193], X[48027] - 6 X[48244], X[48028] - 3 X[48213], 2 X[48030] - 3 X[48193], 3 X[48249] - X[48396], X[693] - 3 X[47824], 2 X[4874] - 3 X[47761], X[1577] - 3 X[48573], 2 X[1960] - 3 X[30234], 2 X[4834] + X[48616], 2 X[4522] - 3 X[48200], 2 X[3239] - 3 X[47807], 2 X[3716] - 3 X[47803], 4 X[31286] - 3 X[47803], 2 X[3676] - 3 X[48245], X[23770] - 3 X[48245], X[3700] - 3 X[48232], 2 X[3835] - 3 X[47802], X[3835] - 3 X[48575], 4 X[25380] - 3 X[47802], 2 X[25380] - 3 X[48575], X[4010] - 3 X[47823], 2 X[4885] - 3 X[47823], X[4122] - 3 X[48235], X[4170] - 3 X[47795], 3 X[4379] - X[4804], X[4382] - 3 X[47812], X[4391] - 3 X[47836], 3 X[4453] - X[47691], X[4467] + 3 X[48252], X[47690] - 3 X[48252], 4 X[4521] - 3 X[48166], X[4775] - 3 X[14419], X[47963] - 3 X[48210], 2 X[48000] - 3 X[48210], 3 X[45328] - X[48050], 2 X[4806] - 3 X[47760], X[4806] - 3 X[48229], X[4810] - 3 X[48184], 2 X[23813] - 3 X[48184], X[4824] - 3 X[48225], 6 X[48225] - X[48608], 3 X[4948] - X[47928], X[4983] - 3 X[47888], X[24719] - 3 X[36848], 3 X[6546] - X[48078], X[7192] + 3 X[48242], X[47975] - 3 X[48242], 4 X[7658] - 3 X[47799], X[17166] - 3 X[48570], X[20295] - 3 X[44429], 2 X[20317] - 3 X[47835], 3 X[47835] - X[48265], 4 X[21212] - 3 X[48192], 5 X[24924] - 3 X[47832], X[25259] - 3 X[47809], 2 X[25666] - 3 X[47830], 3 X[47830] - X[48043], X[26853] + 3 X[48164], 5 X[27013] - 3 X[47804], X[47953] - 3 X[48190], 2 X[48010] - 3 X[48190], 3 X[31148] - X[48142], 3 X[31150] - X[47969], 5 X[31209] - 3 X[47821], 5 X[31250] - 6 X[48216], 4 X[31287] - 3 X[47822], X[31290] - 3 X[48549], 4 X[43061] - 3 X[48231], 3 X[44550] - X[48298], 3 X[45313] - X[48063], 3 X[45320] - 2 X[48090], X[47123] - 3 X[47758], X[47666] - 3 X[47825], X[47672] - 3 X[48579], X[47688] - 3 X[48422], X[47689] - 3 X[48254], X[47692] - 3 X[48241], X[47694] - 3 X[47762], X[47696] - 3 X[48567], X[47699] - 3 X[47782], X[47701] - 3 X[47886], 3 X[47771] - X[49275], 3 X[47775] - X[47941], 3 X[47778] - X[48037], 3 X[47783] - X[47979], 3 X[47785] - X[48006], 3 X[47806] - X[48269], 3 X[47837] - X[48267], 3 X[47877] - X[47944], 3 X[47885] - X[48083], 3 X[47893] - X[48123], X[47940] - 3 X[48157], X[47945] - 3 X[48175], X[48107] + 3 X[48175], X[47946] - 3 X[48176], X[47954] - 3 X[48191], X[47974] - 3 X[48240], X[48120] - 3 X[48253], 3 X[48159] - X[49298], 3 X[48171] - X[49272], 3 X[48227] - X[48349], 3 X[48236] - X[49273], X[48273] - 3 X[48569]

X(50336) lies on these lines: {2, 48080}, {3, 667}, {10, 29148}, {44, 513}, {46, 4063}, {65, 876}, {377, 21301}, {442, 21260}, {512, 905}, {514, 4818}, {521, 7234}, {522, 3798}, {523, 4025}, {669, 24562}, {676, 2487}, {690, 49280}, {693, 47824}, {764, 36279}, {812, 24720}, {830, 48018}, {900, 4786}, {918, 48062}, {1019, 1734}, {1159, 14421}, {1577, 48573}, {1960, 30234}, {2517, 18155}, {2530, 4834}, {2533, 23880}, {2646, 4162}, {2785, 7636}, {2786, 4522}, {2976, 28217}, {2977, 4468}, {3004, 47961}, {3239, 47807}, {3251, 37606}, {3566, 6332}, {3667, 3716}, {3676, 23770}, {3700, 48232}, {3733, 8646}, {3777, 8712}, {3803, 6004}, {3835, 25380}, {3837, 4106}, {3887, 7634}, {3900, 4367}, {3960, 29350}, {4010, 4885}, {4040, 6050}, {4041, 48144}, {4088, 47971}, {4122, 28898}, {4170, 47795}, {4185, 18344}, {4190, 31291}, {4259, 9010}, {4378, 4730}, {4379, 4804}, {4380, 46403}, {4382, 47812}, {4391, 47836}, {4401, 42325}, {4449, 4729}, {4453, 47691}, {4458, 47131}, {4467, 47690}, {4498, 48151}, {4507, 6371}, {4521, 48166}, {4705, 48607}, {4750, 4777}, {4761, 48321}, {4762, 21146}, {4763, 6006}, {4775, 14419}, {4778, 47963}, {4785, 45328}, {4802, 16892}, {4806, 47760}, {4810, 23813}, {4811, 30024}, {4824, 48225}, {4926, 48220}, {4932, 48017}, {4944, 48217}, {4948, 47928}, {4977, 47962}, {4983, 47888}, {5880, 6008}, {6002, 17072}, {6003, 15599}, {6005, 14838}, {6372, 47965}, {6546, 48078}, {7192, 47975}, {7465, 26249}, {7483, 31288}, {7650, 18154}, {7658, 47799}, {8639, 22089}, {11068, 48055}, {14018, 17924}, {14837, 48400}, {15309, 47956}, {17166, 48570}, {17494, 48108}, {17528, 31149}, {20295, 44429}, {20317, 26066}, {21051, 29170}, {21188, 48403}, {21189, 29487}, {21192, 29021}, {21212, 48192}, {22092, 45907}, {23789, 29302}, {24601, 37233}, {24666, 42312}, {24924, 47832}, {25259, 47809}, {25299, 25981}, {25511, 48246}, {25537, 25925}, {25666, 47830}, {25901, 37228}, {26248, 47808}, {26853, 48164}, {27013, 47804}, {27527, 48243}, {27622, 28255}, {27929, 28867}, {28147, 49291}, {28161, 49292}, {28195, 47920}, {28199, 47923}, {28209, 48560}, {28225, 48001}, {28319, 30580}, {28373, 47521}, {28628, 47841}, {28840, 47953}, {28846, 48047}, {29198, 47921}, {30519, 48222}, {30520, 48103}, {30792, 47786}, {31148, 48142}, {31150, 47969}, {31209, 47821}, {31250, 48216}, {31287, 47822}, {31290, 48549}, {39386, 48214}, {43061, 48231}, {44550, 48298}, {45313, 48063}, {45320, 48090}, {45674, 48211}, {45746, 49283}, {47123, 47758}, {47663, 49301}, {47666, 47825}, {47672, 48579}, {47676, 48408}, {47677, 47693}, {47688, 48422}, {47689, 48254}, {47692, 48241}, {47694, 47762}, {47696, 48567}, {47699, 47782}, {47701, 47886}, {47703, 48277}, {47771, 49275}, {47775, 47941}, {47778, 48037}, {47783, 47979}, {47785, 48006}, {47806, 48269}, {47837, 48267}, {47877, 47944}, {47885, 48083}, {47890, 48096}, {47893, 48123}, {47909, 48147}, {47912, 48149}, {47914, 47964}, {47915, 47967}, {47926, 48148}, {47930, 48118}, {47931, 48138}, {47932, 48119}, {47934, 48141}, {47935, 48122}, {47940, 48157}, {47943, 48104}, {47945, 48107}, {47946, 48176}, {47948, 48110}, {47950, 47999}, {47951, 48007}, {47952, 48002}, {47954, 48191}, {47955, 48005}, {47960, 48617}, {47966, 48003}, {47968, 48606}, {47974, 48240}, {47976, 48086}, {47982, 48067}, {47985, 48071}, {48008, 48073}, {48011, 48075}, {48013, 48039}, {48016, 48042}, {48056, 48087}, {48059, 48091}, {48066, 48092}, {48074, 48601}, {48095, 48622}, {48097, 48124}, {48098, 48125}, {48100, 48128}, {48120, 48253}, {48145, 48598}, {48159, 49298}, {48171, 49272}, {48227, 48349}, {48236, 49273}, {48271, 48405}, {48273, 48569}, {48603, 48624}, {48605, 48621}

X(50336) = midpoint of X(i) and X(j) for these {i,j}: {649, 2254}, {650, 7659}, {1019, 1734}, {1491, 4784}, {2526, 4790}, {2530, 4834}, {4025, 48069}, {4041, 48144}, {4063, 4905}, {4088, 47971}, {4378, 4730}, {4380, 46403}, {4449, 4729}, {4467, 47690}, {4498, 48151}, {4761, 48321}, {4932, 48017}, {4979, 48023}, {7192, 47975}, {16892, 48106}, {17494, 48108}, {45746, 49283}, {47663, 49301}, {47676, 48408}, {47677, 47693}, {47703, 48277}, {47909, 48147}, {47912, 48149}, {47923, 48146}, {47926, 48148}, {47930, 48118}, {47931, 48138}, {47932, 48119}, {47934, 48141}, {47935, 48122}, {47943, 48104}, {47945, 48107}, {47948, 48110}, {47973, 48101}, {47976, 48086}, {47982, 48067}, {47985, 48071}, {48008, 48073}, {48011, 48075}, {48013, 48039}, {48015, 48060}, {48016, 48042}, {48018, 48064}, {48074, 48601}, {48145, 48598}, {48603, 48624}
X(50336) = reflection of X(i) in X(j) for these {i,j}: {650, 9508}, {659, 4394}, {676, 2487}, {3716, 31286}, {3835, 25380}, {4010, 4885}, {4040, 6050}, {4106, 3837}, {4162, 48330}, {4468, 2977}, {4810, 23813}, {4944, 48217}, {7662, 4369}, {23770, 3676}, {47131, 4458}, {47760, 48229}, {47777, 48213}, {47786, 30792}, {47802, 48575}, {47914, 47964}, {47915, 47967}, {47950, 47999}, {47951, 48007}, {47952, 48002}, {47953, 48010}, {47955, 48005}, {47956, 48012}, {47961, 3004}, {47963, 48000}, {47966, 48003}, {48026, 48030}, {48027, 1491}, {48029, 650}, {48043, 25666}, {48055, 11068}, {48087, 48056}, {48088, 48062}, {48089, 24720}, {48091, 48059}, {48092, 48066}, {48096, 47890}, {48099, 14838}, {48124, 48097}, {48125, 48098}, {48126, 21146}, {48128, 48100}, {48134, 43067}, {48136, 905}, {48211, 45674}, {48265, 20317}, {48271, 48405}, {48329, 667}, {48332, 3960}, {48346, 3669}, {48400, 14837}, {48403, 21188}, {48605, 48621}, {48606, 47968}, {48607, 4705}, {48608, 4824}, {48615, 48103}, {48616, 2530}, {48617, 47960}, {48618, 47965}, {48619, 47962}, {48622, 48095}
X(50336) = complement of X(48080)
X(50336) = X(39981)-complementary conjugate of X(116)
X(50336) = X(i)-isoconjugate of X(j) for these (i,j): {2, 28847}, {100, 39954}, {101, 39721}, {692, 40028}
X(50336) = X(i)-Dao conjugate of X(j) for these (i,j): {1015, 39721}, {1086, 40028}, {8054, 39954}, {28847, 32664}
X(50336) = crosspoint of X(i) and X(j) for these (i,j): {57, 6183}, {100, 1002}
X(50336) = crosssum of X(i) and X(j) for these (i,j): {9, 6182}, {513, 1001}
X(50336) = crossdifference of every pair of points on line {1, 2271}
X(50336) = barycentric product X(i)*X(j) for these {i,j}: {1, 28846}, {81, 48047}, {513, 17316}, {514, 3751}, {649, 30758}, {656, 14013}, {1019, 4078}, {3669, 27549}, {8769, 14291}
X(50336) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 28847}, {513, 39721}, {514, 40028}, {649, 39954}, {3751, 190}, {4078, 4033}, {14013, 811}, {14291, 18156}, {17316, 668}, {27549, 646}, {28846, 75}, {30758, 1978}, {48047, 321}
X(50336) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3716, 31286, 47803}, {3835, 25380, 47802}, {3835, 48575, 25380}, {4010, 47823, 4885}, {4467, 48252, 47690}, {4784, 48244, 1491}, {4810, 48184, 23813}, {7192, 48242, 47975}, {7659, 9508, 48029}, {23770, 48245, 3676}, {47830, 48043, 25666}, {47835, 48265, 20317}, {47953, 48190, 48010}, {47963, 48210, 48000}, {48026, 48193, 48030}, {48107, 48175, 47945}


X(50337) = X(2)X(4040)∩X(10)X(514)

Barycentrics    (b - c)*(a^2*b - a*b^2 + a^2*c + b^2*c - a*c^2 + b*c^2) : :
X(50337) = X[1] - 3 X[47796], X[21302] + 3 X[47796], 3 X[10] - 2 X[4147], X[10] + 2 X[24720], X[2530] - 3 X[36848], X[2533] + 3 X[36848], X[4147] - 3 X[17072], 2 X[4147] + 3 X[23789], X[4147] + 3 X[24720], 2 X[17072] + X[23789], 3 X[3837] - X[4992], 2 X[20517] - 3 X[21181], 3 X[21181] - 4 X[21188], 3 X[551] - 2 X[48294], X[649] - 3 X[48573], X[659] - 3 X[47837], X[661] - 3 X[47816], X[663] - 3 X[47795], 2 X[1125] - 3 X[47795], X[667] - 3 X[47823], X[1019] - 3 X[47824], X[21301] + 3 X[47824], 3 X[1577] - X[48264], 3 X[2254] + X[48264], 5 X[1698] - 3 X[47793], 5 X[1698] - X[47970], 3 X[47793] - X[47970], 4 X[3634] - X[4724], 4 X[3634] - 3 X[47794], X[4724] - 3 X[47794], X[3737] - 3 X[48246], X[3762] - 3 X[21052], X[3762] + 2 X[23796], 3 X[21052] + 2 X[23796], 3 X[21052] + X[48151], X[3803] - 3 X[47761], 6 X[3828] - X[47929], X[4041] + 3 X[47812], X[4978] - 3 X[47812], X[4063] - 3 X[47836], X[46403] + 3 X[47836], X[4807] + 2 X[23815], X[4170] - 3 X[4728], X[4367] - 3 X[48569], X[4761] + 3 X[48556], X[48131] - 3 X[48556], X[4775] - 3 X[47841], 3 X[4776] - X[48081], 2 X[4791] + X[23795], 2 X[4794] - 5 X[19862], X[4794] - 3 X[48218], 5 X[19862] - 6 X[48218], 3 X[21183] + X[44448], 3 X[6545] - X[47716], X[14349] - 3 X[44429], 3 X[14430] + X[23738], 3 X[14431] - X[48265], 4 X[25380] - X[48284], 3 X[19883] - 2 X[45316], 5 X[24924] - 3 X[47818], 5 X[24924] - X[48150], 3 X[47818] - X[48150], 5 X[30795] - 3 X[47839], 5 X[30795] - X[48336], 3 X[47839] - X[48336], 5 X[30835] - 3 X[47838], 5 X[30835] - X[48367], 3 X[47838] - X[48367], 3 X[31148] + X[47905], 5 X[31251] - 3 X[47822], 5 X[31251] - X[48351], 3 X[47822] - X[48351], 2 X[31288] - 3 X[48216], 3 X[48216] - X[48331], X[46385] - 3 X[48228], X[47685] + 3 X[48565], X[47706] + 3 X[48422], 3 X[47802] - X[48099], 3 X[47804] - X[48111], 3 X[47808] - X[48272], 3 X[47814] - X[47959], 3 X[47814] + X[48108], 3 X[47815] - X[47977], 3 X[47817] - X[48032], 3 X[47819] - X[48335], 3 X[47820] - X[48324], 3 X[47833] - X[48305], 3 X[47840] - X[48352], 3 X[47889] - X[48291], 3 X[47893] - X[48288], X[47912] + 3 X[48579], X[48021] - 3 X[48551], X[48065] - 3 X[48196], X[48086] - 3 X[48164], 3 X[48184] - X[48273], 3 X[48186] - X[48340], 3 X[48207] - X[48306], 3 X[48209] - X[48307], 3 X[48230] - X[48297], X[48329] - 3 X[48564]

X(50337) lies on these lines: {1, 21302}, {2, 4040}, {8, 48282}, {10, 514}, {512, 3837}, {513, 3814}, {519, 4449}, {522, 4823}, {551, 48294}, {649, 23791}, {650, 29186}, {659, 47837}, {661, 47816}, {663, 1125}, {667, 47823}, {693, 1734}, {830, 4369}, {891, 48406}, {905, 29066}, {993, 44408}, {1019, 21301}, {1210, 21185}, {1577, 2254}, {1698, 47793}, {1838, 46110}, {2517, 23800}, {3244, 48287}, {3261, 23790}, {3309, 4885}, {3634, 4724}, {3716, 42325}, {3737, 48246}, {3741, 4379}, {3762, 21052}, {3766, 23828}, {3776, 29047}, {3803, 47761}, {3828, 47929}, {3835, 6005}, {3840, 47779}, {3900, 48295}, {3907, 3960}, {4025, 29062}, {4041, 4978}, {4063, 46403}, {4083, 4807}, {4170, 4728}, {4357, 4406}, {4367, 48569}, {4374, 24462}, {4391, 4905}, {4401, 31286}, {4522, 23875}, {4560, 47724}, {4707, 48278}, {4730, 48279}, {4761, 48131}, {4775, 47841}, {4776, 48081}, {4778, 20316}, {4791, 23795}, {4794, 19862}, {4808, 48326}, {4834, 24719}, {4847, 21183}, {4874, 6004}, {4960, 47945}, {4961, 49287}, {4977, 48005}, {5267, 39476}, {6332, 29304}, {6372, 21051}, {6545, 29673}, {6548, 33120}, {6734, 49300}, {7178, 23887}, {7192, 47948}, {9029, 49511}, {9508, 29070}, {10916, 47123}, {14349, 44429}, {14430, 23738}, {14431, 48265}, {14838, 25380}, {15309, 24718}, {16737, 16887}, {16889, 24170}, {16892, 47711}, {17066, 40474}, {17212, 21304}, {17734, 21173}, {17750, 21791}, {18004, 29252}, {19883, 45316}, {19947, 29298}, {21124, 47715}, {21204, 29655}, {22037, 29200}, {23879, 48396}, {24232, 31647}, {24924, 47818}, {25440, 48387}, {25627, 47996}, {25666, 48058}, {26037, 47775}, {28209, 47994}, {28225, 47987}, {28521, 48345}, {28840, 48613}, {29033, 48575}, {29158, 48069}, {29190, 49285}, {29302, 48089}, {29667, 48156}, {29679, 47773}, {30795, 47839}, {30835, 47838}, {31040, 47763}, {31148, 47905}, {31251, 47822}, {31288, 48216}, {31330, 47780}, {34958, 48286}, {36568, 47725}, {37998, 49676}, {46385, 48228}, {46827, 48063}, {47672, 48407}, {47679, 47703}, {47685, 48565}, {47706, 48422}, {47802, 48099}, {47804, 48111}, {47808, 48272}, {47814, 47959}, {47815, 47977}, {47817, 48032}, {47819, 48335}, {47820, 48324}, {47833, 48305}, {47840, 48352}, {47889, 48291}, {47893, 48288}, {47912, 48579}, {48021, 48551}, {48065, 48196}, {48086, 48164}, {48184, 48273}, {48186, 48340}, {48207, 48306}, {48209, 48307}, {48230, 48297}, {48329, 48564}

X(50337) = midpoint of X(i) and X(j) for these {i,j}: {1, 21302}, {8, 48282}, {10, 23789}, {693, 1734}, {1019, 21301}, {1577, 2254}, {2517, 23800}, {2530, 2533}, {3762, 48151}, {4041, 4978}, {4063, 46403}, {4374, 24462}, {4391, 4905}, {4560, 47724}, {4705, 21146}, {4707, 48278}, {4730, 48279}, {4761, 48131}, {4791, 48075}, {4808, 48326}, {4823, 48018}, {4834, 24719}, {4960, 47945}, {7192, 47948}, {16892, 47711}, {17072, 24720}, {21124, 47715}, {47672, 48407}, {47679, 47703}, {47959, 48108}
X(50337) = reflection of X(i) in X(j) for these {i,j}: {10, 17072}, {663, 1125}, {3244, 48287}, {3777, 23814}, {4129, 21260}, {4401, 31286}, {14838, 25380}, {20517, 21188}, {23789, 24720}, {23795, 48075}, {48058, 25666}, {48151, 23796}, {48284, 14838}, {48286, 34958}, {48331, 31288}
X(50337) = complement of X(4040)
X(50337) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 40619}, {100, 40607}, {2350, 1086}, {13476, 11}, {17758, 116}, {39950, 17761}, {40216, 21252}, {43076, 1125}
X(50337) = X(100)-isoconjugate of X(34443)
X(50337) = X(i)-Dao conjugate of X(j) for these (i,j): {38, 4553}, {8054, 34443}
X(50337) = crosspoint of X(75) and X(8050)
X(50337) = crosssum of X(31) and X(4057)
X(50337) = crossdifference of every pair of points on line {1914, 2174}
X(50337) = barycentric product X(i)*X(j) for these {i,j}: {10, 26822}, {513, 18040}, {514, 17165}, {693, 16549}, {3261, 20990}, {4025, 17915}, {7192, 21067}, {7199, 21865}, {22164, 46107}
X(50337) = barycentric quotient X(i)/X(j) for these {i,j}: {649, 34443}, {16549, 100}, {17165, 190}, {17915, 1897}, {18040, 668}, {20990, 101}, {21067, 3952}, {21865, 1018}, {22164, 1331}, {26822, 86}, {40585, 4553}
X(50337) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {663, 47795, 1125}, {1698, 47970, 47793}, {2533, 36848, 2530}, {4041, 47812, 4978}, {4761, 48556, 48131}, {20517, 21188, 21181}, {21052, 48151, 3762}, {21301, 47824, 1019}, {21302, 47796, 1}, {24924, 48150, 47818}, {30795, 48336, 47839}, {30835, 48367, 47838}, {31251, 48351, 47822}, {46403, 47836, 4063}, {47814, 48108, 47959}, {48216, 48331, 31288}


X(50338) = X(10)X(4985)∩X(240)X(522)

Barycentrics    a*(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(50338) = 3 X[656] - 2 X[21189], 4 X[1734] - X[1769], 3 X[1734] - X[21189], 3 X[1769] - 4 X[21189], 3 X[1635] - 2 X[4057], 2 X[3716] - 3 X[48204], 3 X[4728] - 4 X[44316], 2 X[8062] - 3 X[48243], 3 X[14413] - 2 X[48292], 4 X[25380] - 3 X[48209], X[42312] - 3 X[47828]

X(50338) lies on these lines: {10, 4985}, {240, 522}, {513, 4041}, {523, 2254}, {650, 48340}, {659, 23954}, {812, 44444}, {834, 4729}, {900, 17420}, {905, 48303}, {1459, 3900}, {1635, 4057}, {2509, 45755}, {2530, 4139}, {2605, 4895}, {3309, 46385}, {3716, 48204}, {3733, 48322}, {3737, 3887}, {3837, 24382}, {3960, 48293}, {4017, 4777}, {4036, 48264}, {4081, 22084}, {4086, 8714}, {4132, 48131}, {4171, 6586}, {4397, 28623}, {4728, 44316}, {4730, 6371}, {4802, 48151}, {4811, 20316}, {4814, 43924}, {4905, 28147}, {4926, 6615}, {6129, 6608}, {6362, 21102}, {6366, 21103}, {8043, 48306}, {8062, 48243}, {8648, 48391}, {14077, 48342}, {14413, 48292}, {14838, 48307}, {15313, 17418}, {21173, 35057}, {21187, 47695}, {21727, 48021}, {21832, 48033}, {23687, 49285}, {23738, 28175}, {23800, 28161}, {23874, 44448}, {25380, 48209}, {28155, 48075}, {42312, 47828}, {43927, 48153}

X(50338) = midpoint of X(4814) and X(43924)
X(50338) = reflection of X(i) in X(j) for these {i,j}: {656, 1734}, {1769, 656}, {4811, 20316}, {4895, 2605}, {4985, 10}, {7650, 17072}, {23800, 48018}, {47695, 21187}, {48153, 43927}, {48264, 4036}, {48293, 3960}, {48303, 905}, {48306, 8043}, {48307, 14838}, {48322, 3733}, {48340, 650}
X(50338) = X(1)-Dao conjugate of X(46660)
X(50338) = crosspoint of X(75) and X(37212)
X(50338) = crosssum of X(i) and X(j) for these (i,j): {31, 4979}, {656, 3743}
X(50338) = crossdifference of every pair of points on line {48, 1449}
X(50338) = barycentric product X(i)*X(j) for these {i,j}: {514, 34790}, {1577, 17524}, {1887, 6332}, {37212, 46660}
X(50338) = barycentric quotient X(i)/X(j) for these {i,j}: {1887, 653}, {17524, 662}, {34790, 190}, {46660, 4978}


X(50339) = X(512)X(47683)∩X(513)X(4963)

Barycentrics    (b - c)*(-a^3 - 2*a^2*b + 2*a*b^2 - 2*a^2*c + 3*a*b*c + 2*b^2*c + 2*a*c^2 + 2*b*c^2) : :
X(50339) = 3 X[4963] - 2 X[47903], X[47903] - 3 X[47934], 2 X[47914] - 3 X[47928], 5 X[47926] - 3 X[47927], 9 X[659] - 8 X[8689], 3 X[659] - 4 X[48008], 5 X[659] - 4 X[48063], 2 X[8689] - 3 X[48008], 10 X[8689] - 9 X[48063], 3 X[47885] - 2 X[49286], 5 X[48008] - 3 X[48063], 3 X[4784] - 2 X[7192], 4 X[650] - 3 X[4800], 2 X[661] - 3 X[4948], 5 X[661] - 6 X[45676], 5 X[4948] - 4 X[45676], 2 X[693] - 3 X[48244], 3 X[1491] - 2 X[4106], 4 X[4106] - 3 X[4810], 2 X[3835] - 3 X[48225], 2 X[3837] - 3 X[48242], 3 X[4010] - 4 X[25666], 2 X[4010] - 3 X[47827], 3 X[4913] - 2 X[25666], 4 X[4913] - 3 X[47827], 8 X[25666] - 9 X[47827], 3 X[4367] - 2 X[48291], 2 X[4382] - 3 X[48167], 4 X[4394] - 3 X[48234], 2 X[4500] - 3 X[48235], 3 X[4560] - 2 X[48289], 3 X[4879] - 4 X[48289], 4 X[4782] - 3 X[48251], 3 X[4804] - 5 X[24924], 2 X[4804] - 3 X[47833], 6 X[9508] - 5 X[24924], 4 X[9508] - 3 X[47833], 10 X[24924] - 9 X[47833], 2 X[4806] - 3 X[47825], 2 X[4820] - 3 X[4951], 3 X[4824] - 2 X[47991], 2 X[4940] - 3 X[48190], 2 X[24719] - 3 X[48160], 4 X[48017] - 3 X[48160], 3 X[25569] - 2 X[48339], 5 X[26985] - 6 X[48229], 7 X[27115] - 6 X[48183], 3 X[47975] - X[48079], 5 X[30795] - 6 X[47828], 5 X[30795] - 4 X[48090], 3 X[47828] - 2 X[48090], 5 X[30835] - 6 X[48213], 7 X[31207] - 6 X[48202], 4 X[31286] - 3 X[48189], 3 X[36848] - 2 X[49289], 3 X[47776] - 2 X[48248], 3 X[47823] - 2 X[48394], 3 X[47877] - 2 X[49295], 3 X[47893] - 2 X[48273], 2 X[48043] - 3 X[48176], 2 X[48080] - 3 X[48162], 2 X[48120] - 3 X[48253], 2 X[48127] - 3 X[48579]

X(50339) lies on these lines: {512, 47683}, {513, 4963}, {522, 659}, {523, 4467}, {649, 2529}, {650, 4800}, {661, 4948}, {693, 48244}, {900, 17494}, {1491, 4106}, {3835, 48225}, {3837, 48242}, {4010, 4913}, {4151, 4367}, {4382, 48167}, {4394, 48234}, {4500, 48235}, {4560, 4879}, {4724, 4926}, {4730, 4774}, {4782, 28205}, {4802, 47930}, {4804, 9508}, {4806, 47825}, {4814, 29236}, {4820, 4951}, {4824, 47991}, {4932, 28169}, {4940, 48190}, {7659, 48143}, {21196, 48349}, {21343, 48321}, {24719, 48017}, {25569, 48339}, {26078, 26854}, {26277, 48187}, {26985, 48229}, {27115, 48183}, {28151, 48141}, {28165, 48142}, {28183, 47694}, {28217, 47969}, {28396, 30061}, {29144, 48277}, {29150, 48407}, {29328, 47975}, {30795, 47828}, {30835, 48213}, {31207, 48202}, {31286, 48189}, {36848, 49289}, {47776, 48248}, {47823, 48394}, {47877, 49295}, {47893, 48273}, {48043, 48176}, {48080, 48162}, {48120, 48253}, {48127, 48579}

X(50339) = reflection of X(i) in X(j) for these {i,j}: {4010, 4913}, {4774, 4730}, {4804, 9508}, {4810, 1491}, {4879, 4560}, {4963, 47934}, {21343, 48321}, {24719, 48017}, {48143, 7659}, {48349, 21196}
X(50339) = crossdifference of every pair of points on line {2275, 5313}
X(50339) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4010, 4913, 47827}, {4804, 9508, 47833}, {24719, 48017, 48160}, {47828, 48090, 30795}


X(50340) = X(23)X(385)∩X(37)X(650)

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(50340) = 3 X[659] - 2 X[47890], 3 X[44433] - X[47660], 3 X[44433] - 2 X[48248], X[47659] - 3 X[47694], X[47659] - 9 X[48239], X[47661] + 3 X[47695], X[47693] - 3 X[47805], X[47694] - 3 X[48239], 4 X[47890] - 3 X[48103], X[23731] - 3 X[47701], 2 X[23731] - 3 X[47944], 4 X[47960] - 3 X[47968], X[47971] + 3 X[47972], 2 X[3835] - 3 X[48177], 4 X[676] - 3 X[47833], 3 X[47833] - 2 X[48396], X[693] - 3 X[48223], X[20295] - 3 X[48158], 4 X[2487] - 3 X[48249], 2 X[2526] - 3 X[47877], 4 X[3239] - 3 X[4951], 2 X[3700] - 3 X[4800], 2 X[3776] - 3 X[48224], 2 X[3837] - 3 X[47797], X[47687] - 3 X[47797], 2 X[4369] - 3 X[4809], 2 X[4500] - 3 X[48189], 2 X[4522] - 3 X[47822], 3 X[4724] - X[48117], 3 X[48083] - 2 X[48117], 2 X[4806] - 3 X[48161], 2 X[4874] - 3 X[47798], X[47690] - 3 X[47798], 2 X[4885] - 3 X[48211], 2 X[6590] - 3 X[48234], 4 X[17069] - 3 X[48244], 2 X[18004] - 3 X[47821], 4 X[21212] - 3 X[36848], 2 X[24720] - 3 X[48227], 3 X[25569] - 2 X[48290], 5 X[27013] - 3 X[48254], 7 X[27115] - 6 X[28602], 2 X[48062] - 3 X[48226], X[47650] - 3 X[47691], 5 X[30795] - 6 X[47799], 5 X[30835] - 6 X[48195], 7 X[31207] - 6 X[48217], 5 X[31209] - 3 X[48187], 4 X[31286] - 3 X[48235], 4 X[31287] - 3 X[48200], 4 X[34958] - 3 X[47889], X[46403] - 3 X[48203], X[47685] - 3 X[48174], X[47689] - 3 X[47804], 3 X[47804] - 2 X[48405], X[47700] - 3 X[47811], 3 X[47811] - 2 X[48056], 3 X[47702] + X[48145], X[47706] - 3 X[47815], X[47710] - 3 X[47817], X[47714] - 3 X[47818], X[47718] - 3 X[47820], 3 X[47872] - 2 X[48395], 3 X[47887] - 2 X[48098], 3 X[48006] - X[48038], 3 X[48024] - 2 X[48038], 2 X[48047] - 3 X[48162], 2 X[48050] - 3 X[48552], X[48118] - 3 X[48572], 3 X[48184] - 2 X[49285]

X(50340) lies on these lines: {1, 29312}, {23, 385}, {37, 650}, {513, 16892}, {514, 4922}, {522, 1491}, {525, 48336}, {649, 29144}, {663, 29017}, {667, 29021}, {676, 47833}, {690, 48352}, {693, 26234}, {812, 48349}, {814, 47708}, {824, 4375}, {826, 4040}, {891, 47727}, {900, 3004}, {1019, 29168}, {1577, 29086}, {1960, 29166}, {2487, 48249}, {2526, 4926}, {2533, 4142}, {2804, 4477}, {2977, 28187}, {3239, 4951}, {3667, 48007}, {3700, 4800}, {3716, 4122}, {3762, 29110}, {3776, 48224}, {3801, 29051}, {3837, 47687}, {3904, 48289}, {3906, 49276}, {3910, 4879}, {4063, 7927}, {4170, 29106}, {4367, 29142}, {4369, 4809}, {4391, 29074}, {4401, 29164}, {4458, 21146}, {4498, 29208}, {4500, 48189}, {4522, 47822}, {4707, 29188}, {4724, 48083}, {4762, 47131}, {4774, 10015}, {4775, 23876}, {4778, 47925}, {4782, 48106}, {4794, 29318}, {4802, 48132}, {4806, 48161}, {4808, 48003}, {4874, 47690}, {4885, 48211}, {4977, 49302}, {6590, 48234}, {7265, 29194}, {11068, 28169}, {17069, 48244}, {18004, 47821}, {21185, 48392}, {21212, 36848}, {23805, 24180}, {23875, 48351}, {23879, 48305}, {23887, 48288}, {24720, 48227}, {25259, 29370}, {25569, 48290}, {27013, 48254}, {27115, 28602}, {28147, 48140}, {28151, 48095}, {28161, 48062}, {28165, 47885}, {28183, 47827}, {28220, 47919}, {28221, 48160}, {29025, 47709}, {29037, 48265}, {29062, 48267}, {29070, 47712}, {29078, 48080}, {29098, 47713}, {29146, 48300}, {29172, 47728}, {29190, 48273}, {29200, 48367}, {29204, 48094}, {29250, 47707}, {29278, 48400}, {29284, 48338}, {29354, 47970}, {29358, 48065}, {29362, 47650}, {30795, 47799}, {30835, 48195}, {31094, 31131}, {31207, 48217}, {31209, 48187}, {31286, 48235}, {31287, 48200}, {34958, 47889}, {46403, 48203}, {47123, 48120}, {47132, 48274}, {47685, 48174}, {47689, 47804}, {47700, 47811}, {47702, 48145}, {47706, 47815}, {47710, 47817}, {47714, 47818}, {47718, 47820}, {47872, 48395}, {47887, 48098}, {47999, 48020}, {48006, 48024}, {48030, 48077}, {48047, 48162}, {48050, 48552}, {48061, 48604}, {48118, 48572}, {48184, 49285}, {48286, 48291}

X(50340) = reflection of X(i) in X(j) for these {i,j}: {2533, 4142}, {3904, 48289}, {4122, 3716}, {4774, 10015}, {4808, 48003}, {21146, 4458}, {47660, 48248}, {47682, 1960}, {47687, 3837}, {47689, 48405}, {47690, 4874}, {47700, 48056}, {47944, 47701}, {48020, 47999}, {48024, 48006}, {48077, 48030}, {48083, 4724}, {48103, 659}, {48106, 4782}, {48120, 47123}, {48274, 47132}, {48291, 48286}, {48300, 48331}, {48392, 21185}, {48396, 676}, {48585, 48621}, {48604, 48061}, {49279, 4794}
X(50340) = crossdifference of every pair of points on line {36, 39}
X(50340) = barycentric product X(514)*X(33076)
X(50340) = barycentric quotient X(33076)/X(190)
X(50340) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {676, 48396, 47833}, {44433, 47660, 48248}, {47687, 47797, 3837}, {47689, 47804, 48405}, {47690, 47798, 4874}, {47700, 47811, 48056}


X(50341) = X(75)X(693)∩X(512)X(48409)

Barycentrics    (b - c)*(-(a^2*b) + 2*a*b^2 - a^2*c + 2*a*b*c + b^2*c + 2*a*c^2 + b*c^2) : :
X(50341) = 2 X[693] - 3 X[36848], 2 X[47131] - 3 X[48224], 3 X[4824] - 2 X[47666], 5 X[4824] - 2 X[47941], 7 X[4824] - 4 X[47954], 5 X[4824] - 4 X[47964], 5 X[47666] - 3 X[47941], 4 X[47666] - 3 X[47946], 7 X[47666] - 6 X[47954], 5 X[47666] - 6 X[47964], X[47666] - 3 X[47975], 4 X[47941] - 5 X[47946], 7 X[47941] - 10 X[47954], X[47941] - 5 X[47975], 7 X[47946] - 8 X[47954], 5 X[47946] - 8 X[47964], X[47946] - 4 X[47975], 5 X[47954] - 7 X[47964], 2 X[47954] - 7 X[47975], 2 X[47964] - 5 X[47975], 3 X[1491] - 2 X[3835], 4 X[3835] - 3 X[4010], X[3835] - 3 X[48017], X[4010] - 4 X[48017], 3 X[2254] - X[47672], 3 X[21146] - 2 X[47672], 4 X[650] - 3 X[4448], 2 X[650] - 3 X[48225], 3 X[1635] - 2 X[48248], 3 X[1638] - 2 X[47132], 2 X[1960] - 3 X[45671], 2 X[3716] - 3 X[47827], 2 X[4369] - 3 X[48244], 3 X[4800] - 4 X[25666], 2 X[4806] - 3 X[47810], 3 X[4809] - 4 X[17069], X[4810] - 3 X[48160], 2 X[48050] - 3 X[48160], 6 X[4874] - 7 X[31207], 2 X[4874] - 3 X[47828], 7 X[31207] - 9 X[47828], 4 X[4885] - 3 X[48189], 2 X[48030] - 3 X[48175], X[48080] - 3 X[48175], 3 X[4948] - 2 X[48000], 2 X[6590] - 3 X[48235], 2 X[7662] - 3 X[47823], 6 X[9508] - 5 X[27013], 2 X[9508] - 3 X[48242], 5 X[27013] - 3 X[47694], 5 X[27013] - 9 X[48242], X[47694] - 3 X[48242], X[20295] - 3 X[48157], 3 X[21145] - 2 X[49300], 5 X[24924] - 6 X[48229], 4 X[25380] - 3 X[47833], 7 X[27115] - 6 X[45666], 7 X[27138] - 6 X[45342], 3 X[44429] - 2 X[48090], 5 X[30835] - 6 X[45323], 5 X[31209] - 6 X[48213], 4 X[31286] - 3 X[48234], 3 X[44550] - 2 X[48344], 2 X[47123] - 3 X[48227], X[47659] - 3 X[48254], X[47665] - 3 X[48187], 2 X[48028] - 3 X[48549], 2 X[48029] - 3 X[48176], 2 X[48063] - 3 X[48226], 3 X[48167] - 2 X[49289], 3 X[48184] - 2 X[48394], 3 X[48185] - 2 X[49286], 3 X[48188] - 2 X[48271], 3 X[48253] - 2 X[49292]

X(50341) lies on these lines: {75, 693}, {512, 48409}, {513, 4380}, {514, 4730}, {522, 1491}, {523, 2254}, {650, 2276}, {659, 4913}, {661, 900}, {784, 1734}, {824, 24326}, {905, 48301}, {1635, 48248}, {1638, 47132}, {1960, 45671}, {2526, 24719}, {2530, 4151}, {3004, 48349}, {3667, 48010}, {3716, 47827}, {3762, 4770}, {3779, 9001}, {3837, 4804}, {3887, 48288}, {3960, 48291}, {4083, 48410}, {4170, 48059}, {4369, 48244}, {4705, 8714}, {4778, 47928}, {4782, 47697}, {4800, 25666}, {4802, 48108}, {4806, 28221}, {4809, 17069}, {4810, 48050}, {4874, 31207}, {4885, 48189}, {4895, 48289}, {4922, 48321}, {4925, 48396}, {4926, 48030}, {4948, 48000}, {4961, 48603}, {4962, 48043}, {4977, 47934}, {6006, 47996}, {6161, 48284}, {6367, 47715}, {6372, 48407}, {6590, 48235}, {7662, 47823}, {9508, 27013}, {14838, 48305}, {17072, 48392}, {20295, 48157}, {21035, 21727}, {21051, 48264}, {21145, 49300}, {24720, 28161}, {24924, 48229}, {25380, 47833}, {27115, 45666}, {27138, 45342}, {28147, 48073}, {28151, 47675}, {28165, 48098}, {28169, 48399}, {28175, 48148}, {28187, 47812}, {28205, 44429}, {28209, 47917}, {28217, 48002}, {28225, 47910}, {29078, 48077}, {29144, 45746}, {29150, 47948}, {29168, 47679}, {29170, 47912}, {29188, 47683}, {29204, 47677}, {29328, 48023}, {30765, 48182}, {30835, 45323}, {31209, 48213}, {31286, 48234}, {39386, 47993}, {44550, 48344}, {47123, 48227}, {47659, 48254}, {47665, 48187}, {48012, 48267}, {48028, 48549}, {48029, 48176}, {48056, 49275}, {48063, 48226}, {48066, 48273}, {48167, 49289}, {48184, 48394}, {48185, 49286}, {48188, 48271}, {48253, 49292}

X(50341) = reflection of X(i) in X(j) for these {i,j}: {659, 4913}, {1491, 48017}, {2533, 1734}, {3762, 4770}, {4010, 1491}, {4170, 48059}, {4448, 48225}, {4804, 3837}, {4810, 48050}, {4824, 47975}, {4895, 48289}, {4922, 48321}, {6161, 48284}, {21146, 2254}, {24719, 2526}, {47694, 9508}, {47697, 4782}, {47941, 47964}, {47946, 4824}, {48021, 48002}, {48024, 48010}, {48080, 48030}, {48120, 24720}, {48143, 48073}, {48264, 21051}, {48265, 4705}, {48267, 48012}, {48273, 48066}, {48279, 2530}, {48291, 3960}, {48301, 905}, {48305, 14838}, {48349, 3004}, {48392, 17072}, {48396, 4925}, {49275, 48056}
X(50341) = crossdifference of every pair of points on line {172, 2251}
X(50341) = barycentric product X(514)*X(49457)
X(50341) = barycentric quotient X(49457)/X(190)
X(50341) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4810, 48160, 48050}, {47694, 48242, 9508}, {48080, 48175, 48030}


X(50342) = X(1)X(690)∩X(2)X(18004)

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(50342) = X[46403] - 3 X[48571], 3 X[16892] - X[47943], 2 X[47943] - 3 X[47968], 3 X[47944] - 4 X[47961], 3 X[47971] + X[47972], 3 X[4367] - 4 X[39545], 3 X[4367] - 2 X[48290], 3 X[649] - X[48118], 3 X[48103] - 2 X[48118], 3 X[659] - 2 X[48055], 4 X[48055] - 3 X[48083], 4 X[676] - 3 X[4800], 3 X[1019] - X[47726], 3 X[1491] - 2 X[48039], 3 X[4025] - X[48039], 3 X[1635] - 2 X[48056], 6 X[1638] - 5 X[30795], 4 X[2487] - 3 X[47807], 4 X[3676] - 3 X[48184], 2 X[3700] - 3 X[47833], 2 X[3716] - 3 X[4809], 2 X[3835] - 3 X[48227], 2 X[3837] - 3 X[4453], X[4088] - 3 X[4750], 3 X[4750] - 2 X[9508], 4 X[4394] - 3 X[47885], 3 X[47885] - 2 X[48088], 3 X[4448] - 4 X[13246], 2 X[4468] - 3 X[48226], 2 X[4500] - 3 X[48238], 2 X[4522] - 3 X[47823], X[4730] - 3 X[30595], 2 X[4806] - 3 X[47797], X[44449] - 3 X[47797], 2 X[4940] - 3 X[48192], 2 X[14321] - 3 X[47799], 4 X[17069] - 3 X[47827], 3 X[47827] - 2 X[48047], X[20295] - 3 X[48241], 5 X[27013] - 3 X[48171], 3 X[27486] - X[47698], 2 X[48043] - 3 X[48177], X[47690] - 3 X[47755], 5 X[30835] - 6 X[48215], 7 X[31207] - 6 X[48199], 4 X[31286] - 3 X[48185], X[47693] - 3 X[47763], 3 X[47762] - 2 X[48405], 3 X[47782] - 2 X[48002], 3 X[47804] - X[49272], 3 X[47811] - 2 X[48048], 3 X[47811] - X[48112], 3 X[47822] - 2 X[48270], 3 X[47877] - 2 X[48027], 3 X[47878] - 2 X[47964], 3 X[47886] - 2 X[48030], 3 X[47887] - 2 X[48090], 3 X[47887] - X[48266], 3 X[47894] - X[47945], 3 X[47930] + X[48626], 2 X[48046] - 3 X[48162], 2 X[48049] - 3 X[48552], X[48079] - 3 X[48174], 3 X[48234] - 2 X[49286], 3 X[48253] - 2 X[48396]

X(50342) lies on these lines: {1, 690}, {2, 18004}, {38, 2254}, {149, 900}, {388, 18006}, {512, 47727}, {513, 16892}, {522, 21146}, {523, 4467}, {525, 4367}, {649, 48103}, {659, 918}, {663, 29200}, {667, 23875}, {676, 4800}, {693, 29078}, {812, 48326}, {814, 47722}, {826, 1019}, {876, 23829}, {1125, 22037}, {1491, 4025}, {1577, 29090}, {1635, 48056}, {1638, 30795}, {1960, 49276}, {2487, 47807}, {2528, 3733}, {2533, 29037}, {2785, 4922}, {2786, 4010}, {2787, 4707}, {3566, 4879}, {3667, 49295}, {3676, 48184}, {3700, 47833}, {3716, 4809}, {3776, 24719}, {3798, 48062}, {3801, 6002}, {3835, 48227}, {3837, 4453}, {3874, 3887}, {3906, 47682}, {3910, 48323}, {4040, 29252}, {4063, 29354}, {4088, 4750}, {4122, 4369}, {4142, 48265}, {4378, 23876}, {4394, 47885}, {4448, 13246}, {4449, 29284}, {4468, 48226}, {4500, 48238}, {4522, 47823}, {4705, 21192}, {4730, 30595}, {4761, 29110}, {4777, 7659}, {4782, 48094}, {4790, 4802}, {4806, 44449}, {4824, 21196}, {4830, 28890}, {4834, 29047}, {4841, 4963}, {4874, 25259}, {4940, 48192}, {4948, 45669}, {4951, 47758}, {4977, 47653}, {4978, 29106}, {5307, 16230}, {7662, 28898}, {8674, 11670}, {14270, 39578}, {14321, 47799}, {14779, 28175}, {17069, 47827}, {20295, 48241}, {20517, 48267}, {21222, 24097}, {24287, 35352}, {24400, 24442}, {24415, 24447}, {26853, 47688}, {27013, 48171}, {27486, 47698}, {28846, 48024}, {28855, 47946}, {28867, 48224}, {28871, 48001}, {28878, 47910}, {28906, 48043}, {28910, 47963}, {29017, 48144}, {29058, 47724}, {29150, 47712}, {29170, 47708}, {29194, 47715}, {29204, 48106}, {29216, 48273}, {29248, 47719}, {29280, 48300}, {29292, 47711}, {29312, 48320}, {29328, 47691}, {29340, 47680}, {29358, 48064}, {29362, 47676}, {29370, 47690}, {30520, 48622}, {30579, 44010}, {30835, 48215}, {31207, 48199}, {31286, 48185}, {32478, 48337}, {45745, 47928}, {47693, 47763}, {47762, 48405}, {47782, 48002}, {47804, 49272}, {47811, 48048}, {47822, 48270}, {47877, 48027}, {47878, 47964}, {47886, 48030}, {47887, 48090}, {47894, 47945}, {47930, 48626}, {47990, 48019}, {48028, 48076}, {48046, 48162}, {48049, 48552}, {48060, 48140}, {48079, 48174}, {48143, 49296}, {48234, 49286}, {48248, 49275}, {48253, 48396}

X(50342) = midpoint of X(26853) and X(47688)
X(50342) = reflection of X(i) in X(j) for these {i,j}: {876, 23829}, {1491, 4025}, {4010, 4458}, {4088, 9508}, {4122, 4369}, {4705, 21192}, {4784, 4897}, {4810, 23770}, {4824, 21196}, {4948, 45669}, {4951, 47758}, {4963, 4841}, {22037, 1125}, {24097, 21222}, {24719, 3776}, {25259, 4874}, {44449, 4806}, {47928, 45745}, {47937, 48611}, {47968, 16892}, {48019, 47990}, {48047, 17069}, {48062, 3798}, {48076, 48028}, {48083, 659}, {48088, 4394}, {48094, 4782}, {48103, 649}, {48112, 48048}, {48140, 48060}, {48143, 49296}, {48265, 4142}, {48266, 48090}, {48267, 20517}, {48290, 39545}, {49275, 48248}, {49276, 1960}
X(50342) = anticomplement of X(18004)
X(50342) = anticomplement of the isogonal conjugate of X(17940)
X(50342) = anticomplement of the isotomic conjugate of X(17930)
X(50342) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1333, 39368}, {1929, 3448}, {2702, 2895}, {4556, 20538}, {4610, 20560}, {6650, 21294}, {17930, 6327}, {17940, 8}, {17962, 21221}, {35148, 21287}, {37135, 1330}
X(50342) = X(17930)-Ceva conjugate of X(2)
X(50342) = crosspoint of X(i) and X(j) for these (i,j): {99, 335}, {1268, 35148}
X(50342) = crosssum of X(i) and X(j) for these (i,j): {512, 1914}, {2308, 5029}
X(50342) = crossdifference of every pair of points on line {2503, 2653}
X(50342) = barycentric product X(i)*X(j) for these {i,j}: {514, 32846}, {2786, 19936}
X(50342) = barycentric quotient X(i)/X(j) for these {i,j}: {19936, 35148}, {32846, 190}
X(50342) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4088, 4750, 9508}, {4394, 48088, 47885}, {17069, 48047, 47827}, {39545, 48290, 4367}, {44449, 47797, 4806}, {47811, 48112, 48048}, {47887, 48266, 48090}


X(50343) = X(2)X(4010)∩X(100)X(190)

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(50343) = 3 X[2] - 4 X[9508], 5 X[2] - 4 X[45342], 7 X[2] - 8 X[45691], 5 X[4010] - 6 X[45342], 7 X[4010] - 12 X[45691], 5 X[9508] - 3 X[45342], 7 X[9508] - 6 X[45691], 7 X[45342] - 10 X[45691], 4 X[10] - 3 X[30709], 2 X[659] - 3 X[47776], 4 X[2977] - 3 X[30565], 3 X[4560] - 2 X[48288], 5 X[649] - 3 X[48578], 2 X[47690] - 3 X[48254], 5 X[47694] - 6 X[48578], 4 X[48069] - 3 X[48254], 4 X[650] - 3 X[47821], 3 X[47821] - 2 X[48080], 2 X[661] - 3 X[47825], 4 X[4913] - 3 X[47825], 2 X[693] - 3 X[47824], 2 X[1491] - 3 X[48242], X[20295] - 3 X[48242], 2 X[1577] - 3 X[47836], 3 X[1635] - 2 X[3716], 5 X[3616] - 6 X[14419], 2 X[4724] - 3 X[48240], 4 X[48008] - 3 X[48240], 2 X[3700] - 3 X[47809], 2 X[3835] - 3 X[47828], 4 X[3837] - 3 X[21297], 2 X[3837] - 3 X[48244], 2 X[4810] - 3 X[21297], X[4810] - 3 X[48244], 4 X[4025] - 3 X[48241], 2 X[47691] - 3 X[48241], 2 X[4106] - 3 X[44429], 2 X[4122] - 3 X[48208], 2 X[4170] - 3 X[47840], 4 X[14838] - 3 X[47840], 4 X[4369] - 3 X[47834], 2 X[4804] - 3 X[47834], 3 X[4379] - 2 X[48394], 2 X[4382] - 3 X[48170], 4 X[24720] - 3 X[48170], 4 X[4394] - 3 X[47804], 3 X[4453] - 2 X[23770], 2 X[4458] - 3 X[4750], 3 X[4728] - 4 X[25380], 4 X[4782] - 3 X[47805], 4 X[48017] - 3 X[48157], 2 X[48023] - 3 X[48157], 2 X[4806] - 3 X[47827], 2 X[4823] - 3 X[48573], 4 X[4874] - 5 X[27013], 4 X[4874] - 3 X[48172], 5 X[27013] - 3 X[48172], 3 X[4893] - 2 X[48043], 4 X[4925] - 3 X[31131], 2 X[4940] - 3 X[48193], 3 X[4948] - 2 X[48002], 3 X[47774] - 4 X[48002], 2 X[4992] - 3 X[47893], 2 X[7662] - 3 X[47762], 7 X[9780] - 6 X[14431], 2 X[13246] - 3 X[45679], 2 X[14288] - 3 X[26078], 4 X[17069] - 3 X[47797], 4 X[19947] - 3 X[30592], 2 X[23729] - 3 X[48159], 2 X[24719] - 3 X[48164], 2 X[25259] - 3 X[48171], 4 X[48062] - 3 X[48171], 5 X[26985] - 6 X[47823], 5 X[26985] - 4 X[48090], 3 X[47823] - 2 X[48090], 7 X[27115] - 6 X[47822], 5 X[30795] - 6 X[48229], 5 X[30835] - 6 X[47830], 3 X[48203] - 2 X[48349], 3 X[31148] - 2 X[49292], 3 X[31150] - 2 X[48029], 7 X[31207] - 6 X[47831], 4 X[31286] - 3 X[47832], 3 X[44435] - 2 X[49295], 3 X[44550] - 2 X[48332], 3 X[47759] - 4 X[48030], 2 X[48030] - 3 X[48225], 3 X[47771] - 2 X[49286], 3 X[47772] - 4 X[48056], 3 X[47775] - 2 X[48024], 3 X[47780] - 2 X[48120], 3 X[47781] - 2 X[47983], 3 X[47782] - 2 X[47998], 3 X[47793] - 2 X[48267], 3 X[47796] - 2 X[48273], 3 X[47810] - 2 X[48049], 3 X[47812] - 2 X[49289], 3 X[47826] - 2 X[48037], 3 X[47869] - 4 X[48098], 3 X[47870] - 4 X[48405], 3 X[47892] - 2 X[48055], 2 X[48026] - 3 X[48549], 2 X[48027] - 3 X[48175], X[48079] - 3 X[48175], 2 X[48028] - 3 X[48176], 3 X[48236] - 2 X[48271], 3 X[48252] - 2 X[48396], 2 X[48326] - 3 X[48571], 2 X[48399] - 3 X[48579]

X(50343) lies on these lines: {2, 4010}, {8, 2787}, {10, 30709}, {55, 16158}, {98, 28471}, {100, 190}, {145, 4922}, {149, 13277}, {291, 812}, {512, 4560}, {513, 4380}, {514, 50016}, {522, 649}, {523, 4467}, {650, 47821}, {656, 25299}, {661, 4913}, {669, 7253}, {690, 49274}, {693, 47824}, {784, 4834}, {814, 21302}, {824, 47693}, {875, 4155}, {876, 18009}, {885, 18785}, {891, 21222}, {897, 5466}, {918, 48408}, {1019, 4151}, {1282, 2786}, {1491, 20295}, {1577, 47836}, {1635, 3716}, {1734, 21301}, {1768, 21381}, {2526, 6008}, {2775, 6361}, {3571, 24403}, {3616, 14419}, {3667, 4724}, {3700, 47809}, {3798, 47123}, {3835, 47828}, {3837, 4810}, {3907, 4729}, {4025, 47691}, {4041, 6002}, {4063, 8714}, {4083, 17496}, {4106, 44429}, {4122, 48208}, {4145, 17154}, {4170, 14838}, {4369, 4804}, {4378, 48304}, {4379, 48394}, {4382, 24720}, {4394, 47804}, {4441, 14296}, {4453, 23770}, {4458, 4750}, {4490, 29170}, {4522, 48266}, {4705, 29150}, {4707, 49303}, {4728, 25380}, {4762, 7659}, {4765, 48006}, {4773, 44433}, {4777, 47763}, {4778, 47926}, {4782, 4926}, {4785, 48017}, {4802, 47677}, {4806, 47827}, {4808, 29090}, {4811, 30061}, {4813, 48010}, {4818, 47958}, {4823, 48573}, {4830, 48032}, {4874, 27013}, {4893, 48043}, {4905, 29302}, {4925, 31131}, {4932, 28161}, {4940, 48193}, {4948, 47774}, {4961, 48066}, {4962, 48063}, {4992, 47893}, {5075, 49629}, {6084, 49301}, {6089, 19642}, {7662, 47762}, {8674, 14683}, {9780, 14431}, {13246, 45679}, {14288, 26078}, {15309, 48407}, {16892, 47688}, {17069, 47797}, {19947, 30592}, {21124, 29118}, {21146, 26824}, {21192, 47712}, {21196, 47701}, {21832, 24578}, {23729, 48159}, {24623, 47695}, {24719, 48164}, {25259, 48062}, {26277, 47808}, {26985, 47823}, {27045, 48204}, {27115, 47822}, {27167, 48209}, {27293, 48243}, {27486, 48158}, {28132, 46388}, {28147, 48141}, {28169, 48577}, {28221, 48248}, {28225, 47927}, {28840, 47934}, {28846, 47698}, {28863, 48146}, {28882, 47973}, {29216, 48272}, {29270, 48018}, {29350, 48298}, {30519, 48118}, {30795, 48229}, {30835, 47830}, {31095, 48203}, {31148, 49292}, {31150, 48029}, {31207, 47831}, {31286, 47832}, {35025, 35030}, {35028, 35033}, {39698, 41683}, {44435, 49295}, {44449, 48047}, {44550, 48332}, {45745, 47699}, {47686, 48015}, {47696, 48060}, {47759, 48030}, {47771, 49286}, {47772, 48056}, {47775, 48024}, {47780, 48120}, {47781, 47983}, {47782, 47998}, {47793, 48267}, {47796, 48273}, {47810, 48049}, {47812, 49289}, {47826, 48037}, {47869, 48098}, {47870, 48405}, {47890, 49275}, {47892, 48055}, {47938, 48404}, {47989, 49297}, {47992, 48019}, {48000, 48021}, {48007, 49298}, {48026, 48549}, {48027, 48079}, {48028, 48176}, {48050, 48114}, {48073, 48119}, {48088, 49272}, {48103, 49273}, {48236, 48271}, {48252, 48396}, {48284, 48352}, {48326, 48571}, {48399, 48579}

X(50343) = reflection of X(i) in X(j) for these {i,j}: {8, 4730}, {145, 4922}, {149, 13277}, {661, 4913}, {4010, 9508}, {4170, 14838}, {4382, 24720}, {4724, 48008}, {4804, 4369}, {4810, 3837}, {4813, 48010}, {7192, 4784}, {17166, 1019}, {20295, 1491}, {21297, 48244}, {21301, 1734}, {25259, 48062}, {26824, 21146}, {31290, 4824}, {44433, 4773}, {44449, 48047}, {46403, 2254}, {47123, 3798}, {47686, 48015}, {47688, 16892}, {47690, 48069}, {47691, 4025}, {47693, 48106}, {47694, 649}, {47696, 48060}, {47699, 45745}, {47701, 21196}, {47712, 21192}, {47759, 48225}, {47774, 4948}, {47938, 48404}, {47939, 47953}, {47941, 47962}, {47945, 47975}, {47958, 4818}, {47969, 17494}, {48006, 4765}, {48019, 47992}, {48021, 48000}, {48023, 48017}, {48032, 4830}, {48079, 48027}, {48080, 650}, {48108, 7659}, {48114, 48050}, {48119, 48073}, {48142, 4932}, {48158, 27486}, {48266, 4522}, {48298, 48321}, {48304, 4378}, {48352, 48284}, {49272, 48088}, {49273, 48103}, {49275, 47890}, {49297, 47989}, {49298, 48007}, {49303, 4707}
X(50343) = anticomplement of X(4010)
X(50343) = anticomplement of the isotomic conjugate of X(4589)
X(50343) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {99, 20554}, {110, 17794}, {163, 33888}, {291, 3448}, {292, 21221}, {335, 21294}, {660, 1330}, {662, 20345}, {692, 39367}, {741, 149}, {805, 4388}, {813, 2895}, {1333, 39362}, {1576, 30667}, {1808, 34188}, {1911, 148}, {1922, 21220}, {2196, 39352}, {2311, 37781}, {4562, 21287}, {4584, 69}, {4589, 6327}, {4639, 315}, {14598, 25054}, {17938, 21226}, {18268, 4440}, {18827, 21293}, {34067, 1654}, {36066, 17135}, {37128, 150}, {39276, 25049}
X(50343) = X(4589)-Ceva conjugate of X(2)
X(50343) = X(18268)-isoconjugate of X(40529)
X(50343) = X(35068)-Dao conjugate of X(40529)
X(50343) = crosspoint of X(i) and X(j) for these (i,j): {99, 673}, {190, 18827}, {1268, 4562}, {2363, 36086}
X(50343) = crosssum of X(i) and X(j) for these (i,j): {512, 672}, {513, 20718}, {649, 3747}, {2254, 2292}, {2308, 8632}
X(50343) = crossdifference of every pair of points on line {1015, 1193}
X(50343) = barycentric quotient X(740)/X(40529)
X(50343) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 48080, 47821}, {661, 4913, 47825}, {3837, 4810, 21297}, {4010, 9508, 2}, {4025, 47691, 48241}, {4170, 14838, 47840}, {4369, 4804, 47834}, {4382, 24720, 48170}, {4724, 48008, 48240}, {4810, 48244, 3837}, {20295, 48242, 1491}, {25259, 48062, 48171}, {27013, 48172, 4874}, {47690, 48069, 48254}, {47823, 48090, 26985}, {48017, 48023, 48157}, {48079, 48175, 48027}


X(50344) = X(484)X(513)∩X(512)X(1326)

Barycentrics    a^2*(b - c)*(a + 2*b + c)*(a + b + 2*c) : :
X(50344) = 2 X[2605] - 3 X[3733], 3 X[649] - X[48340], 3 X[4057] - 2 X[48340], 3 X[1019] - X[48293], 2 X[4806] - 3 X[48205], 2 X[31946] - 3 X[47836]

X(50344) lies on these lines: {484, 513}, {512, 1326}, {522, 31010}, {523, 4467}, {649, 4057}, {660, 4436}, {691, 6578}, {834, 43924}, {876, 40438}, {889, 6540}, {900, 4581}, {901, 8701}, {1019, 4132}, {1126, 6371}, {1171, 9178}, {1255, 43928}, {1796, 35365}, {2483, 28615}, {2489, 43925}, {2640, 9282}, {4036, 29150}, {4491, 17990}, {4570, 4629}, {4596, 17929}, {4806, 48205}, {4983, 8043}, {9142, 28471}, {10566, 26853}, {14560, 36069}, {16874, 18105}, {20295, 44316}, {20954, 29328}, {21121, 29118}, {23836, 32635}, {31946, 47836}, {33670, 46611}

X(50344) = midpoint of X(26853) and X(44444)
X(50344) = reflection of X(i) in X(j) for these {i,j}: {4057, 649}, {4840, 4784}, {4983, 8043}, {20295, 44316}
X(50344) = isogonal conjugate of X(4427)
X(50344) = isogonal conjugate of the anticomplement of X(3120)
X(50344) = isogonal conjugate of the complement of X(44006)
X(50344) = isogonal conjugate of the isotomic conjugate of X(4608)
X(50344) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {4629, 18133}, {34594, 2891}
X(50344) = X(i)-Ceva conjugate of X(j) for these (i,j): {4629, 6}, {6540, 1255}, {6578, 1171}, {8701, 1126}
X(50344) = X(i)-cross conjugate of X(j) for these (i,j): {3122, 6}, {4491, 23345}, {17990, 3572}
X(50344) = X(i)-isoconjugate of X(j) for these (i,j): {1, 4427}, {2, 35342}, {57, 30729}, {59, 4985}, {75, 35327}, {81, 4115}, {99, 1962}, {100, 1125}, {101, 4359}, {109, 3702}, {110, 4647}, {162, 41014}, {163, 1230}, {190, 1100}, {312, 36075}, {430, 4592}, {553, 644}, {643, 3649}, {648, 3958}, {651, 3686}, {660, 4974}, {662, 1213}, {664, 3683}, {668, 2308}, {692, 1269}, {765, 4977}, {799, 20970}, {811, 22080}, {901, 4975}, {932, 4970}, {1016, 4979}, {1018, 8025}, {1252, 4978}, {1332, 1839}, {1414, 4046}, {1492, 3775}, {1783, 4001}, {1897, 3916}, {2355, 4561}, {3257, 4969}, {3616, 35339}, {3647, 6742}, {3699, 32636}, {3903, 4697}, {4065, 34594}, {4103, 30581}, {4557, 16709}, {4564, 4976}, {4567, 4988}, {4570, 30591}, {4575, 44143}, {4588, 4717}, {4596, 8040}, {4600, 4983}, {4610, 21816}, {4856, 27834}, {4966, 36086}, {4984, 5376}, {4989, 37223}, {4990, 7045}, {6335, 22054}, {6367, 24041}, {6533, 8701}, {8663, 24037}, {15322, 41818}, {15455, 17454}, {17746, 43190}, {30593, 40521}
X(50344) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 4427}, {11, 3702}, {115, 1230}, {125, 41014}, {136, 44143}, {206, 35327}, {244, 4647}, {430, 5139}, {512, 8663}, {513, 4977}, {661, 4978}, {1015, 4359}, {1084, 1213}, {1086, 1269}, {1125, 8054}, {1962, 38986}, {3005, 6367}, {3683, 39025}, {3686, 38991}, {3775, 38995}, {3835, 4992}, {3916, 34467}, {4001, 39006}, {4046, 40608}, {4115, 40586}, {4966, 38989}, {4975, 38979}, {4985, 6615}, {4988, 40627}, {4990, 17115}, {5452, 30729}, {14434, 30592}, {17423, 22080}, {20970, 38996}, {32664, 35342}
X(50344) = cevapoint of X(i) and X(j) for these (i,j): {512, 649}, {513, 4132}, {523, 44316}
X(50344) = crosspoint of X(i) and X(j) for these (i,j): {1126, 8701}, {1171, 6578}, {1255, 6540}, {37212, 40438}
X(50344) = crosssum of X(i) and X(j) for these (i,j): {2, 14779}, {513, 3743}, {514, 6707}, {522, 18253}, {523, 3634}, {1125, 4977}, {1213, 6367}, {1962, 4979}, {3683, 4976}, {3686, 4990}, {4647, 4985}, {4988, 8040}
X(50344) = trilinear pole of line {1015, 3124}
X(50344) = crossdifference of every pair of points on line {1100, 1125}
X(50344) = barycentric product X(i)*X(j) for these {i,j}: {1, 47947}, {6, 4608}, {58, 31010}, {115, 6578}, {244, 37212}, {512, 32014}, {513, 1255}, {514, 1126}, {523, 1171}, {649, 1268}, {661, 40438}, {667, 32018}, {693, 28615}, {1015, 6540}, {1086, 8701}, {1796, 7649}, {3120, 4629}, {3122, 4632}, {3125, 4596}, {3669, 32635}, {3676, 33635}, {3733, 6539}, {4102, 43924}, {23345, 31011}
X(50344) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 4427}, {31, 35342}, {32, 35327}, {42, 4115}, {55, 30729}, {244, 4978}, {512, 1213}, {513, 4359}, {514, 1269}, {523, 1230}, {647, 41014}, {649, 1125}, {650, 3702}, {661, 4647}, {663, 3686}, {665, 4966}, {667, 1100}, {669, 20970}, {798, 1962}, {810, 3958}, {1015, 4977}, {1019, 16709}, {1084, 8663}, {1126, 190}, {1171, 99}, {1255, 668}, {1268, 1978}, {1357, 30724}, {1397, 36075}, {1459, 4001}, {1635, 4975}, {1646, 30592}, {1796, 4561}, {1919, 2308}, {1960, 4969}, {2170, 4985}, {2489, 430}, {2501, 44143}, {2605, 3578}, {3049, 22080}, {3063, 3683}, {3121, 4983}, {3122, 4988}, {3124, 6367}, {3125, 30591}, {3248, 4979}, {3250, 3775}, {3271, 4976}, {3709, 4046}, {3733, 8025}, {4057, 45222}, {4079, 8013}, {4378, 4410}, {4596, 4601}, {4608, 76}, {4629, 4600}, {4893, 4717}, {4979, 6533}, {6377, 4992}, {6539, 27808}, {6540, 31625}, {6578, 4590}, {7180, 3649}, {8632, 4974}, {8643, 4856}, {8656, 4982}, {8701, 1016}, {14936, 4990}, {20979, 4970}, {20981, 4697}, {21758, 4973}, {22383, 3916}, {28615, 100}, {31010, 313}, {32014, 670}, {32018, 6386}, {32635, 646}, {33635, 3699}, {37212, 7035}, {40438, 799}, {43924, 553}, {43925, 31900}, {47947, 75}


X(50345) = X(484)X(513)∩X(522)X(1491)

Barycentrics    a*(b - c)*(a*b^2 + b^3 + 3*b^2*c + a*c^2 + 3*b*c^2 + c^3) : :
X(50345) = X[4811] - 3 X[47814], 2 X[4874] - 3 X[48228], 3 X[26078] - X[47844], X[47694] - 3 X[48243]

X(50345) lies on these lines: {484, 513}, {522, 1491}, {523, 2530}, {650, 8662}, {764, 4802}, {784, 2517}, {832, 17418}, {834, 4730}, {900, 47842}, {2254, 8672}, {3126, 10472}, {3667, 48012}, {3777, 28147}, {3837, 4815}, {4041, 6371}, {4057, 8043}, {4139, 48131}, {4397, 48410}, {4490, 4778}, {4761, 4977}, {4770, 6363}, {4811, 47814}, {4874, 48228}, {4985, 21051}, {6004, 46385}, {6161, 48297}, {7650, 21260}, {8062, 48305}, {21173, 38469}, {23765, 28191}, {26078, 47844}, {28161, 48066}, {28183, 48350}, {29070, 44444}, {30591, 44316}, {34258, 35353}, {47694, 48243}

X(50345) = midpoint of X(4397) and X(48410)
X(50345) = reflection of X(i) in X(j) for these {i,j}: {4057, 8043}, {4815, 3837}, {4985, 21051}, {6161, 48297}, {7650, 21260}, {30591, 44316}, {48305, 8062}
X(50345) = crosspoint of X(693) and X(47915)
X(50345) = crossdifference of every pair of points on line {172, 1100}


X(50346) = X(1)X(523)∩X(484)X(513)

Barycentrics    a*(b - c)*(a^3 - a*b^2 - a*b*c - 3*b^2*c - a*c^2 - 3*b*c^2) : :
X(50346) = 3 X[1] - 4 X[2605], 5 X[1] - 4 X[48292], 3 X[1] - 2 X[48293], 2 X[2605] - 3 X[3737], 5 X[2605] - 3 X[48292], 5 X[3737] - 2 X[48292], 3 X[3737] - X[48293], 6 X[48292] - 5 X[48293], 3 X[17418] - X[43924], 3 X[21173] - 2 X[43924], 3 X[4040] - 2 X[48340], 3 X[46385] - X[48340], X[6615] - 3 X[47811], 5 X[1698] - 6 X[48204], 7 X[3624] - 6 X[48209], 13 X[34595] - 12 X[48207], 2 X[47843] - 3 X[48228]

X(50346) lies on these lines: {1, 523}, {43, 47825}, {484, 513}, {514, 4581}, {522, 3465}, {612, 48208}, {614, 48203}, {650, 1758}, {663, 28161}, {846, 6615}, {1019, 8672}, {1027, 39977}, {1459, 28147}, {1698, 48204}, {1743, 3287}, {1781, 21127}, {2517, 47724}, {2640, 39344}, {2957, 5400}, {2999, 47782}, {3624, 48209}, {3667, 4724}, {3709, 3731}, {3907, 4404}, {4017, 14838}, {4041, 6003}, {4132, 4833}, {4139, 48337}, {4151, 7253}, {4374, 25590}, {4397, 29066}, {4436, 46973}, {4449, 28155}, {4551, 14985}, {4777, 48297}, {4789, 17022}, {4794, 42312}, {4802, 48281}, {4815, 8062}, {4948, 42043}, {4962, 48065}, {5010, 48391}, {5256, 46915}, {5268, 47809}, {5272, 47797}, {5287, 47792}, {6371, 21385}, {7161, 23838}, {7178, 34496}, {7199, 10436}, {7280, 48382}, {7649, 49300}, {7951, 8819}, {9359, 24376}, {10980, 34954}, {13610, 35347}, {16569, 47827}, {17420, 48003}, {21180, 23752}, {21184, 45746}, {23511, 47784}, {25502, 47833}, {26102, 47834}, {28151, 48283}, {28165, 48302}, {28169, 48303}, {28183, 48306}, {28191, 48342}, {28225, 47929}, {28471, 45710}, {34595, 48207}, {47843, 48228}

X(50346) = reflection of X(i) in X(j) for these {i,j}: {1, 3737}, {4017, 14838}, {4040, 46385}, {4815, 8062}, {17420, 48003}, {21173, 17418}, {21189, 650}, {23752, 21180}, {42312, 4794}, {47724, 2517}, {48282, 1459}, {48293, 2605}, {48307, 48297}, {49300, 7649}
X(50346) = excentral-isogonal conjugate of X(33811)
X(50346) = X(46187)-anticomplementary conjugate of X(3448)
X(50346) = X(4551)-Ceva conjugate of X(1)
X(50346) = X(i)-Dao conjugate of X(j) for these (i,j): {4560, 18155}, {18698, 24224}
X(50346) = crosspoint of X(i) and X(j) for these (i,j): {100, 40430}, {651, 40438}
X(50346) = crosssum of X(i) and X(j) for these (i,j): {513, 2650}, {523, 3614}, {649, 3725}, {650, 1962}
X(50346) = crossdifference of every pair of points on line {1100, 2245}
X(50346) = barycentric product X(i)*X(j) for these {i,j}: {100, 24224}, {514, 5260}, {4551, 40625}
X(50346) = barycentric quotient X(i)/X(j) for these {i,j}: {5260, 190}, {24224, 693}, {40625, 18155}
X(50346) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2605, 48293, 1}, {3737, 48293, 2605}


X(50347) = X(21)X(884)∩X(23)X(385)

Barycentrics    (a - b - c)*(b - c)*(2*a^2 + a*b + b^2 + a*c + c^2) : :
X(50347) = 3 X[659] - X[48103], X[17494] + 3 X[48239], 3 X[44433] - X[47694], X[47660] - 3 X[47805], X[47693] - 3 X[48250], X[47695] - 3 X[48239], 3 X[47890] - 2 X[48103], 3 X[48240] - X[48408], 3 X[3004] - 2 X[48007], X[47979] - 3 X[48006], 3 X[47988] - 4 X[47990], 2 X[47990] - 3 X[47998], 3 X[1639] - 2 X[4522], 3 X[4040] - X[49276], 2 X[676] - 3 X[47798], X[693] - 3 X[47798], 2 X[1491] - 3 X[47784], 3 X[4724] - X[48078], 3 X[1638] - 2 X[24720], 4 X[2487] - 3 X[47824], 4 X[2490] - 3 X[47809], 3 X[47884] - 2 X[48062], 2 X[2977] - 3 X[48226], 2 X[3835] - 3 X[48179], 2 X[3837] - 3 X[47799], X[4088] - 3 X[47811], X[4122] - 3 X[4448], 3 X[4809] - X[21146], 2 X[21146] - 3 X[47891], 2 X[4874] - 3 X[26275], 4 X[4874] - 3 X[47788], 3 X[26275] - X[48396], 3 X[47788] - 2 X[48396], 2 X[4885] - 3 X[47800], 3 X[47800] - X[49285], 3 X[4893] - X[48077], 2 X[4925] - 3 X[47828], 3 X[4927] - 2 X[48089], X[48089] - 3 X[48211], X[47691] - 3 X[48223], 3 X[6545] - X[48115], 3 X[6546] - X[47700], X[6590] - 3 X[47801], 2 X[14321] - 3 X[47821], 2 X[18004] - 3 X[48166], X[20295] - 3 X[48161], X[24719] - 3 X[48177], 5 X[27013] - 3 X[48252], 7 X[27115] - 3 X[48169], 5 X[31209] - 3 X[47808], 4 X[31286] - 3 X[48232], 4 X[31287] - 3 X[47806], 3 X[44435] - X[47685], X[46403] - 3 X[47797], X[47652] - 3 X[48203], X[47656] - 3 X[48237], X[47686] - 3 X[48174], X[47689] - 3 X[47771], X[47690] - 3 X[47804], 3 X[47701] - X[47902], X[47703] - 3 X[47813], X[47707] - 3 X[47815], X[47711] - 3 X[47817], X[47715] - 3 X[47818], X[47719] - 3 X[47820], 3 X[47756] - 2 X[48050], 3 X[47781] - X[47940], 3 X[47783] - X[48035], 3 X[47876] - 2 X[48010], 3 X[47887] - X[48119], 3 X[48055] - 2 X[48614], X[48094] - 3 X[48572], 3 X[48231] - 2 X[48405], 3 X[48241] - X[49301], X[48275] - 3 X[48578]

X(50347) lies on these lines: {2, 47687}, {21, 884}, {23, 385}, {513, 3004}, {514, 3803}, {522, 650}, {525, 4040}, {649, 47972}, {663, 3910}, {667, 29142}, {676, 693}, {814, 48400}, {824, 48063}, {830, 48402}, {900, 1491}, {918, 4724}, {1499, 48352}, {1577, 4205}, {1638, 24720}, {1960, 29312}, {2254, 17069}, {2487, 47824}, {2490, 47809}, {2496, 4777}, {2517, 25009}, {2526, 3667}, {2826, 48321}, {2915, 14344}, {2977, 28183}, {3566, 48336}, {3704, 4041}, {3743, 4151}, {3798, 7659}, {3800, 4063}, {3835, 48179}, {3837, 47799}, {3907, 21120}, {4017, 23740}, {4088, 47811}, {4122, 4448}, {4142, 7178}, {4369, 13246}, {4391, 29278}, {4394, 48069}, {4401, 29021}, {4458, 21104}, {4477, 42337}, {4762, 47123}, {4778, 47960}, {4782, 29144}, {4794, 23876}, {4809, 21146}, {4811, 35518}, {4874, 26275}, {4885, 47800}, {4893, 48077}, {4925, 47828}, {4927, 48089}, {4962, 48193}, {4977, 47676}, {4978, 34958}, {4988, 48153}, {6006, 47880}, {6084, 47691}, {6366, 47729}, {6545, 48115}, {6546, 47700}, {6590, 47801}, {7662, 48274}, {10015, 29066}, {11068, 28161}, {13745, 21201}, {14321, 47821}, {14349, 28481}, {14425, 48187}, {16892, 48032}, {18004, 48166}, {20295, 48161}, {20517, 29186}, {21124, 48150}, {21130, 28294}, {21185, 23882}, {21192, 42325}, {21385, 47727}, {21611, 23684}, {23770, 29362}, {23875, 48065}, {23887, 48284}, {24719, 48177}, {26732, 48264}, {27013, 48252}, {27115, 48169}, {28147, 48095}, {28179, 48140}, {28187, 47885}, {28191, 48132}, {28209, 47968}, {28221, 47827}, {28229, 47919}, {28423, 48173}, {28851, 48009}, {28867, 48037}, {28886, 47980}, {28902, 47941}, {29017, 48299}, {29070, 48403}, {29086, 48395}, {29162, 47708}, {29232, 48267}, {30520, 48061}, {30725, 48325}, {31209, 47808}, {31286, 48232}, {31287, 47806}, {39386, 47877}, {39545, 48320}, {44435, 47685}, {45746, 47697}, {46403, 47797}, {47132, 48120}, {47652, 48203}, {47656, 48237}, {47663, 47692}, {47686, 48174}, {47689, 47771}, {47690, 47804}, {47701, 47902}, {47702, 48101}, {47703, 47813}, {47707, 47815}, {47711, 47817}, {47715, 47818}, {47719, 47820}, {47756, 48050}, {47781, 47940}, {47783, 48035}, {47876, 48010}, {47887, 48119}, {47923, 48105}, {48029, 48046}, {48055, 48614}, {48094, 48572}, {48231, 48405}, {48241, 49301}, {48275, 48578}

X(50347) = complement of X(47687)
X(50347) = midpoint of X(i) and X(j) for these {i,j}: {649, 47972}, {4025, 48014}, {4988, 48153}, {16892, 48032}, {17494, 47695}, {21124, 48150}, {21385, 47727}, {45746, 47697}, {47663, 47692}, {47676, 47974}, {47702, 48101}, {47923, 48105}
X(50347) = reflection of X(i) in X(j) for these {i,j}: {693, 676}, {2254, 17069}, {3700, 3716}, {4369, 13246}, {4927, 48211}, {4978, 34958}, {7178, 4142}, {7659, 3798}, {21104, 4458}, {30725, 48325}, {47788, 26275}, {47890, 659}, {47891, 4809}, {47988, 47998}, {48046, 48029}, {48069, 4394}, {48120, 47132}, {48187, 14425}, {48274, 7662}, {48290, 1960}, {48299, 48331}, {48320, 39545}, {48396, 4874}, {49285, 4885}
X(50347) = X(109)-isoconjugate of X(1390)
X(50347) = X(11)-Dao conjugate of X(1390)
X(50347) = crossdifference of every pair of points on line {39, 56}
X(50347) = barycentric product X(i)*X(j) for these {i,j}: {333, 47701}, {514, 3883}, {522, 17023}, {650, 26234}, {1386, 4391}, {1890, 6332}, {4026, 4560}, {5244, 7253}, {18155, 21840}, {21764, 35519}, {22390, 46110}, {42030, 47902}
X(50347) = barycentric quotient X(i)/X(j) for these {i,j}: {650, 1390}, {1386, 651}, {1890, 653}, {3883, 190}, {4026, 4552}, {5244, 4566}, {17023, 664}, {21764, 109}, {21840, 4551}, {22390, 1813}, {26234, 4554}, {39251, 23703}, {47701, 226}, {47902, 4654}
X(50347) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 47798, 676}, {4874, 48396, 47788}, {17494, 48239, 47695}, {26275, 48396, 4874}, {47800, 49285, 4885}


X(50348) = X(2)X(49275)∩X(513)X(3004)

Barycentrics    (b - c)*(-(a^2*b) + 2*a*b^2 + b^3 - a^2*c + b^2*c + 2*a*c^2 + b*c^2 + c^3) : :
X(50348) = 3 X[21115] - X[47704], 3 X[47878] - X[47927], 2 X[676] - 3 X[48227], 3 X[1635] - X[48102], 3 X[1638] - 2 X[4874], 2 X[48050] - 3 X[48163], 2 X[2977] - 3 X[47828], 3 X[47828] - X[48094], 2 X[3239] - 3 X[47802], 2 X[3716] - 3 X[47799], 4 X[21212] - 3 X[47799], 2 X[3835] - 3 X[48178], X[4024] - 3 X[47812], X[4122] - 3 X[36848], 2 X[4369] - 3 X[48245], 3 X[4453] - X[47694], 2 X[4522] - 3 X[48182], X[4724] - 3 X[47886], X[4804] - 3 X[6545], 2 X[4806] - 3 X[47756], 3 X[4893] - X[48078], 3 X[4927] - 2 X[48090], 2 X[4990] - 3 X[47841], 3 X[6546] - X[48113], X[7265] - 3 X[48556], 4 X[7658] - 3 X[47803], X[20295] - 3 X[48159], 3 X[21120] - 2 X[24093], X[25259] - 3 X[44429], 4 X[25380] - 3 X[47807], 4 X[25666] - 3 X[48166], 3 X[26275] - 2 X[48063], 5 X[27013] - 3 X[48250], 4 X[31286] - 3 X[48231], 3 X[44435] - X[48080], 3 X[44550] - X[47728], 2 X[47132] - 3 X[47887], X[47660] - 3 X[47824], X[47689] + 3 X[48434], X[47691] - 3 X[48422], X[47692] - 5 X[48433], X[47693] - 3 X[48252], X[47695] - 3 X[48241], X[47696] - 3 X[47762], X[47698] - 3 X[48175], 3 X[47781] - X[47941], 3 X[47782] - X[47969], 3 X[47783] - X[48036], 3 X[47785] - X[48061], 3 X[47809] - X[49273], 3 X[47810] - X[48082], 3 X[47827] - X[48083], 3 X[47877] - X[48024], 3 X[47885] - X[48604], X[48087] - 3 X[48193], X[48103] - 3 X[48244], 3 X[48213] - X[48614], 3 X[48232] - 2 X[48405], 3 X[48242] - X[48408], 3 X[48242] + X[49302], X[48275] - 3 X[48579]

X(50348) lies on these lines: {2, 49275}, {513, 3004}, {514, 4818}, {522, 3776}, {523, 2254}, {525, 2530}, {649, 4841}, {650, 48055}, {659, 17069}, {676, 48227}, {824, 24720}, {900, 24719}, {905, 48299}, {918, 1491}, {1635, 48102}, {1638, 4874}, {1734, 29288}, {2522, 43060}, {2786, 48050}, {2977, 47828}, {3239, 47802}, {3566, 48131}, {3676, 7662}, {3700, 3837}, {3716, 21212}, {3777, 3910}, {3798, 4778}, {3801, 6362}, {3835, 48178}, {3960, 48290}, {4024, 47812}, {4088, 47930}, {4122, 36848}, {4369, 48245}, {4380, 47686}, {4453, 47694}, {4467, 46403}, {4522, 30519}, {4724, 47886}, {4750, 28209}, {4784, 47968}, {4786, 28220}, {4802, 48069}, {4804, 6545}, {4806, 47756}, {4843, 48279}, {4885, 49286}, {4893, 48078}, {4905, 29142}, {4927, 48090}, {4976, 29362}, {4979, 47943}, {4988, 48148}, {4990, 47841}, {6372, 48402}, {6546, 48113}, {7265, 48556}, {7658, 47803}, {7659, 47960}, {8714, 48403}, {9508, 47890}, {11068, 48096}, {17494, 49301}, {19947, 49290}, {20295, 48159}, {21120, 24093}, {21124, 48151}, {23729, 29328}, {23789, 23879}, {23875, 48066}, {25259, 44429}, {25380, 47807}, {25666, 48166}, {26275, 48063}, {27013, 48250}, {28175, 47923}, {28195, 48060}, {28213, 47931}, {28478, 48616}, {28846, 48027}, {28851, 48010}, {28855, 47992}, {28863, 48249}, {28878, 47953}, {29021, 48075}, {29047, 48018}, {29200, 48100}, {29240, 48321}, {29252, 48059}, {29284, 48137}, {30520, 48062}, {31286, 48231}, {34958, 48305}, {44435, 48080}, {44550, 47728}, {45674, 48247}, {45746, 48108}, {47132, 47887}, {47653, 49283}, {47660, 47824}, {47676, 47975}, {47677, 47690}, {47689, 48434}, {47691, 48422}, {47692, 48433}, {47693, 48252}, {47695, 48241}, {47696, 47762}, {47698, 48175}, {47781, 47941}, {47782, 47969}, {47783, 48036}, {47785, 48061}, {47809, 49273}, {47810, 48082}, {47827, 48083}, {47877, 48024}, {47885, 48604}, {47971, 48023}, {48030, 48046}, {48087, 48193}, {48098, 48274}, {48103, 48244}, {48104, 48598}, {48119, 48277}, {48213, 48614}, {48232, 48405}, {48242, 48408}, {48275, 48579}, {48280, 48406}, {48394, 48415}

X(50348) = midpoint of X(i) and X(j) for these {i,j}: {649, 47973}, {2254, 16892}, {4025, 48015}, {4088, 47930}, {4380, 47686}, {4467, 46403}, {4784, 47968}, {4979, 47943}, {4988, 48148}, {7659, 47960}, {17494, 49301}, {21124, 48151}, {45746, 48108}, {47653, 49283}, {47673, 47703}, {47676, 47975}, {47677, 47690}, {47923, 48106}, {47931, 48101}, {47971, 48023}, {47982, 48013}, {48104, 48598}, {48119, 48277}, {48408, 49302}
X(50348) = reflection of X(i) in X(j) for these {i,j}: {659, 17069}, {3700, 3837}, {3716, 21212}, {7662, 3676}, {23770, 3776}, {47890, 9508}, {47988, 47999}, {47989, 48007}, {47998, 3004}, {48046, 48030}, {48047, 1491}, {48055, 650}, {48094, 2977}, {48096, 11068}, {48247, 45674}, {48274, 48098}, {48280, 48406}, {48290, 3960}, {48299, 905}, {48305, 34958}, {48394, 48415}, {48396, 24720}, {49286, 4885}, {49290, 19947}
X(50348) = complement of X(49275)
X(50348) = barycentric product X(514)*X(49511)
X(50348) = barycentric quotient X(49511)/X(190)
X(50348) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3716, 21212, 47799}, {47828, 48094, 2977}, {48242, 49302, 48408}


X(50349) = X(1)X(523)∩X(44)X(513)

Barycentrics    a*(b - c)*(a^3 - a*b^2 - a*b*c - 2*b^2*c - a*c^2 - 2*b*c^2) : :
X(50349) = 2 X[1] - 3 X[2605], X[1] - 3 X[3737], 4 X[1] - 3 X[48292], 5 X[1] - 3 X[48293], 5 X[2605] - 2 X[48293], 4 X[3737] - X[48292], 5 X[3737] - X[48293], 5 X[48292] - 4 X[48293], X[4724] + 3 X[17418], X[4724] - 3 X[46385], 2 X[4794] - 3 X[48297], 4 X[4794] - 3 X[48306], 3 X[2517] - X[47721], 8 X[3634] - 9 X[48205], X[4804] - 3 X[45686], 11 X[5550] - 9 X[48209], 7 X[9780] - 9 X[48204], X[17166] - 3 X[47845], 10 X[19862] - 9 X[48207], 2 X[47843] - 3 X[48230]

X(50349) lies on these lines: {1, 523}, {42, 4948}, {44, 513}, {45, 3709}, {512, 4833}, {514, 21112}, {522, 4794}, {663, 4777}, {900, 4040}, {1459, 4802}, {2517, 47721}, {2613, 37140}, {2617, 14985}, {3240, 47825}, {3614, 8819}, {3634, 48205}, {3733, 8672}, {3738, 48003}, {4017, 31947}, {4041, 8674}, {4145, 4879}, {4449, 28151}, {4705, 9013}, {4789, 17021}, {4804, 45686}, {4824, 27970}, {4926, 48340}, {4977, 10015}, {5204, 48382}, {5217, 48391}, {5297, 47809}, {5550, 48209}, {6006, 48065}, {7199, 41847}, {7292, 47797}, {8062, 30591}, {8675, 44410}, {9001, 47965}, {9780, 48204}, {14288, 29070}, {17012, 47782}, {17013, 46915}, {17166, 47845}, {19862, 48207}, {27773, 47822}, {28147, 48283}, {28161, 48302}, {28165, 48303}, {28169, 48294}, {28175, 48281}, {28179, 48282}, {28183, 48307}, {28195, 43052}, {28199, 48342}, {28205, 42312}, {28209, 47970}, {28220, 47929}, {30950, 47833}, {36283, 36285}, {47843, 48230}

X(50349) = midpoint of X(17418) and X(46385)
X(50349) = reflection of X(i) in X(j) for these {i,j}: {656, 8043}, {2605, 3737}, {4017, 31947}, {30591, 8062}, {48292, 2605}, {48306, 48297}
X(50349) = X(5397)-Ceva conjugate of X(11)
X(50349) = crosssum of X(523) and X(7951)
X(50349) = crossdifference of every pair of points on line {1, 2245}
X(50349) = X(i)-lineconjugate of X(j) for these (i,j): {44, 2245}, {523, 1}
X(50349) = barycentric product X(i)*X(j) for these {i,j}: {514, 5251}, {1577, 9275}
X(50349) = barycentric quotient X(i)/X(j) for these {i,j}: {5251, 190}, {9275, 662}


X(50350) = X(44)X(513)∩X(523)X(1734)

Barycentrics    a*(b - c)*(a^2*b - b^3 + a^2*c + a*b*c - b^2*c - b*c^2 - c^3) : :
X(50350) = 3 X[656] - X[17420], 3 X[2254] + X[17420], 2 X[8043] - 3 X[47828], X[46385] - 3 X[47828], 3 X[2457] - X[21118], 2 X[3716] - 3 X[48181], X[7253] - 3 X[48246], 2 X[8062] - 3 X[48230], 4 X[25380] - 3 X[48230], X[21102] - 3 X[30574], X[39547] - 3 X[48569], 3 X[47824] - X[47844]

X(50350) lies on these lines: {44, 513}, {514, 11795}, {521, 7629}, {522, 4823}, {523, 1734}, {663, 31947}, {832, 3733}, {834, 2530}, {900, 21189}, {905, 2605}, {1459, 8674}, {1769, 4926}, {2457, 21118}, {2523, 7252}, {3309, 48306}, {3716, 48181}, {3798, 48044}, {3887, 48302}, {3900, 48292}, {3960, 35057}, {4017, 4777}, {4025, 48084}, {4036, 17072}, {4041, 4802}, {4057, 6004}, {4449, 8702}, {4778, 48075}, {4905, 4977}, {4962, 24457}, {6370, 20294}, {6586, 24290}, {7253, 48246}, {8062, 25380}, {9209, 48182}, {14315, 28221}, {14838, 48297}, {21102, 30574}, {21186, 23604}, {21252, 22084}, {21262, 24287}, {21727, 47928}, {22091, 34948}, {23189, 48390}, {23687, 23770}, {24462, 29078}, {28195, 48151}, {31946, 48267}, {39547, 48569}, {47824, 47844}

X(50350) = midpoint of X(i) and X(j) for these {i,j}: {656, 2254}, {1734, 23800}
X(50350) = reflection of X(i) in X(j) for these {i,j}: {663, 31947}, {2605, 905}, {4036, 17072}, {8062, 25380}, {30591, 47843}, {46385, 8043}, {48267, 31946}, {48283, 3960}, {48297, 14838}
X(50350) = X(2)-isoconjugate of X(29041)
X(50350) = X(29041)-Dao conjugate of X(32664)
X(50350) = crossdifference of every pair of points on line {1, 584}
X(50350) = barycentric product X(i)*X(j) for these {i,j}: {1, 23875}, {513, 32858}, {514, 5904}, {1577, 4278}
X(50350) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 29041}, {4278, 662}, {5904, 190}, {23875, 75}, {32858, 668}
X(50350) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 8061, 48025}, {8062, 25380, 48230}, {46385, 47828, 8043}


X(50351) = X(1)X(523)∩X(10)X(514)

Barycentrics    (b - c)*(a^3 - a*b^2 + b^3 - a*b*c - a*c^2 + c^3) : :
X(50351) = 2 X[1] - 3 X[30580], 3 X[30583] - 4 X[32212], 3 X[1022] - 4 X[24099], 5 X[1698] - 6 X[28602], 4 X[3634] - 3 X[4049], 3 X[4448] - 2 X[21201], 2 X[4458] - 3 X[14419], 2 X[4791] - 3 X[48185], 3 X[6545] - 4 X[19947], 3 X[6546] - X[21132], 2 X[7178] - 3 X[47837], 3 X[14413] - X[47705], 3 X[25569] - 2 X[48286], 3 X[47839] - 2 X[48403], X[47721] - 3 X[48187], X[47722] - 3 X[47808], 2 X[48400] - 3 X[48553]

X(50351) lies on these lines: {1, 523}, {2, 49303}, {10, 514}, {72, 513}, {512, 3869}, {522, 5592}, {650, 16583}, {659, 23887}, {661, 29029}, {667, 23877}, {690, 49274}, {784, 48300}, {814, 48272}, {826, 4560}, {879, 1175}, {891, 3904}, {900, 49276}, {1019, 6763}, {1022, 1224}, {1027, 29142}, {1643, 45745}, {1698, 28602}, {1734, 29082}, {1960, 47695}, {2254, 29102}, {2785, 4730}, {2787, 4088}, {2826, 12738}, {2977, 10015}, {3251, 28161}, {3309, 37585}, {3634, 4049}, {3762, 48056}, {3801, 14838}, {3837, 47680}, {3906, 4467}, {3907, 4808}, {3960, 48326}, {4041, 29094}, {4367, 8666}, {4374, 33933}, {4448, 21201}, {4458, 14419}, {4608, 5466}, {4707, 9508}, {4777, 49462}, {4789, 17244}, {4791, 48185}, {4804, 49290}, {4874, 49300}, {4948, 50287}, {4983, 29118}, {6332, 48273}, {6545, 19947}, {6546, 21132}, {6550, 6634}, {7178, 24914}, {7192, 34016}, {7199, 33943}, {8043, 21121}, {8045, 48393}, {8578, 17418}, {14349, 29025}, {14413, 47705}, {14421, 28147}, {16892, 29224}, {17367, 47782}, {17494, 29312}, {17496, 29354}, {17739, 47890}, {21124, 29154}, {21301, 29336}, {23879, 38348}, {23894, 23905}, {24114, 47679}, {25569, 48286}, {25681, 47839}, {28840, 50276}, {29070, 48278}, {29098, 48131}, {29110, 47700}, {29120, 47959}, {29122, 48030}, {29126, 48047}, {29128, 47701}, {29132, 48024}, {29138, 48005}, {29140, 48054}, {29158, 48123}, {29184, 48059}, {29328, 49277}, {29362, 49278}, {29569, 47792}, {31290, 46707}, {47684, 47975}, {47721, 48187}, {47722, 47808}, {48299, 48305}, {48400, 48553}

X(50351) = midpoint of X(i) and X(j) for these {i,j}: {3904, 48408}, {47683, 47726}, {47684, 47975}
X(50351) = reflection of X(i) in X(j) for these {i,j}: {3762, 48056}, {3801, 14838}, {4707, 9508}, {4804, 49290}, {6161, 5592}, {10015, 2977}, {21121, 8043}, {47680, 3837}, {47695, 1960}, {47727, 48289}, {48273, 6332}, {48291, 48290}, {48305, 48299}, {48326, 3960}, {48393, 8045}, {49300, 4874}
X(50351) = complement of X(49303)
X(50351) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {765, 3448}, {1016, 21294}, {1101, 17154}, {1110, 148}, {1252, 21221}, {4567, 150}, {4570, 149}, {4600, 21293}, {6632, 21287}, {23990, 21220}, {31615, 2893}
X(50351) = crosssum of X(8661) and X(17455)
X(50351) = crossdifference of every pair of points on line {1914, 2245}
X(50351) = barycentric product X(i)*X(j) for these {i,j}: {514, 33115}, {523, 25536}, {4608, 24956}
X(50351) = barycentric quotient X(i)/X(j) for these {i,j}: {24956, 4427}, {25536, 99}, {33115, 190}


X(50352) = X(10)X(514)∩X(512)X(693)

Barycentrics    (b - c)*(a^2*b + a^2*c + a*b*c + b^2*c + b*c^2) : :
X(50352) = 2 X[10] + X[48143], 3 X[36848] - 2 X[48066], 2 X[650] - 3 X[47837], X[663] - 3 X[4379], 2 X[905] - 3 X[48569], X[48288] - 3 X[48569], 2 X[1960] - 3 X[47820], X[48144] - 3 X[48579], 2 X[3716] - 3 X[47875], 3 X[47875] - X[48351], 3 X[48238] - X[48301], X[4761] + 2 X[48098], X[4367] - 3 X[48253], 3 X[4448] - 2 X[48065], X[4560] - 3 X[47824], 3 X[4728] - X[4822], X[4730] + 2 X[48399], 2 X[4770] + X[47675], 3 X[4776] - 2 X[48053], 3 X[14431] - X[47949], 2 X[4782] - 3 X[48566], X[4879] - 3 X[47889], 3 X[47889] - 2 X[48295], 4 X[4885] - 3 X[47839], 3 X[47839] - 2 X[48099], 2 X[6050] - 3 X[47761], 2 X[9508] - 3 X[48573], 2 X[14838] - 3 X[47823], X[17166] - 3 X[47780], X[21302] + 3 X[47780], X[17494] - 3 X[47836], 3 X[21052] - X[47918], 3 X[21052] + X[48148], 2 X[23815] - 3 X[47812], 3 X[47812] - X[48131], 5 X[24924] - 4 X[31288], 4 X[25380] - 3 X[47888], 4 X[25666] - 5 X[31251], 5 X[26985] - 3 X[47840], X[47721] + 3 X[48570], 3 X[44429] - 2 X[48059], X[47666] - 3 X[47814], 3 X[47814] - 2 X[48005], 3 X[47793] - X[47969], 3 X[47813] - X[48150], 3 X[47815] - X[47974], 3 X[47816] - 2 X[48030], 3 X[47818] - 2 X[48331], 3 X[47822] - 2 X[48058], 3 X[47832] - X[48367], 3 X[47833] - X[48336], 3 X[47835] - 2 X[48003], 2 X[48028] - 3 X[48551], 2 X[48029] - 3 X[48553], 2 X[48100] - 3 X[48556], X[48123] - 3 X[48184]

X(50352) lies on these lines: {1, 29366}, {10, 514}, {512, 693}, {513, 1577}, {522, 30595}, {523, 1734}, {525, 48396}, {649, 29070}, {650, 47837}, {659, 29186}, {661, 21260}, {663, 3720}, {667, 4369}, {784, 2254}, {788, 7199}, {812, 4834}, {814, 1019}, {826, 47690}, {832, 47844}, {891, 4801}, {905, 48288}, {918, 48395}, {1269, 4406}, {1960, 47820}, {2517, 8672}, {2787, 48144}, {3309, 7662}, {3716, 47875}, {3762, 29198}, {3800, 23770}, {3801, 29021}, {3835, 4983}, {3837, 14349}, {3887, 48238}, {3900, 48291}, {3907, 4378}, {4010, 4823}, {4040, 4874}, {4041, 47672}, {4063, 29362}, {4083, 4761}, {4122, 23875}, {4129, 48024}, {4151, 48120}, {4170, 48090}, {4367, 29066}, {4374, 40495}, {4391, 6372}, {4448, 48065}, {4449, 29298}, {4474, 48341}, {4498, 48119}, {4507, 29771}, {4560, 47824}, {4707, 29017}, {4728, 4822}, {4730, 48399}, {4770, 47675}, {4774, 48323}, {4776, 48053}, {4778, 14431}, {4782, 48566}, {4784, 29013}, {4791, 48265}, {4802, 48407}, {4806, 48081}, {4844, 48287}, {4879, 47889}, {4885, 47839}, {4897, 29232}, {4922, 48343}, {4932, 24287}, {4960, 47948}, {4977, 21051}, {6004, 47694}, {6050, 47761}, {6367, 47656}, {6545, 29685}, {6590, 24290}, {7178, 29142}, {7192, 21301}, {7265, 29200}, {7927, 47691}, {7950, 47689}, {8045, 49279}, {8678, 43067}, {8714, 48392}, {9313, 48152}, {9508, 48573}, {14838, 47823}, {15313, 39547}, {17135, 17166}, {17494, 47836}, {20317, 47966}, {21052, 47918}, {21104, 29288}, {21124, 47703}, {21348, 21837}, {23755, 48278}, {23815, 47812}, {24561, 26640}, {24924, 31288}, {25259, 29252}, {25380, 47888}, {25501, 47779}, {25512, 47795}, {25666, 31251}, {26985, 47840}, {28195, 47967}, {28209, 47942}, {28220, 47957}, {28840, 31149}, {29025, 47680}, {29033, 48064}, {29047, 48326}, {29058, 47755}, {29074, 47723}, {29082, 47682}, {29090, 47971}, {29098, 48106}, {29102, 48300}, {29144, 47712}, {29146, 47714}, {29166, 47718}, {29168, 47708}, {29174, 47725}, {29182, 47721}, {29204, 47710}, {29208, 47716}, {29272, 47684}, {29274, 48568}, {29312, 47719}, {29324, 48320}, {29332, 47726}, {29336, 47722}, {29350, 48279}, {29354, 47676}, {44429, 48059}, {47666, 47814}, {47729, 48328}, {47793, 47969}, {47813, 48150}, {47815, 47974}, {47816, 48030}, {47818, 48331}, {47822, 48058}, {47832, 48367}, {47833, 48336}, {47835, 48003}, {47912, 48141}, {47941, 47994}, {47946, 47997}, {48028, 48551}, {48029, 48553}, {48100, 48556}, {48111, 48248}, {48123, 48184}, {48335, 48406}

X(50352) = midpoint of X(i) and X(j) for these {i,j}: {1019, 47724}, {2533, 21146}, {4041, 47672}, {4391, 48108}, {4474, 48341}, {4490, 48143}, {4498, 48119}, {4707, 47715}, {4761, 4978}, {4774, 48323}, {4960, 47948}, {7192, 21301}, {17166, 21302}, {21124, 47703}, {23755, 48278}, {47676, 47707}, {47912, 48141}, {47918, 48148}
X(50352) = reflection of X(i) in X(j) for these {i,j}: {661, 21260}, {667, 4369}, {2530, 24720}, {3777, 23789}, {4010, 4823}, {4040, 4874}, {4170, 48090}, {4490, 10}, {4705, 17072}, {4824, 48012}, {4879, 48295}, {4922, 48343}, {4978, 48098}, {4983, 3835}, {14349, 3837}, {47666, 48005}, {47729, 48328}, {47941, 47994}, {47946, 47997}, {47959, 21051}, {47966, 20317}, {48024, 4129}, {48081, 4806}, {48099, 4885}, {48111, 48248}, {48131, 23815}, {48265, 4791}, {48267, 1577}, {48273, 693}, {48288, 905}, {48305, 7662}, {48335, 48406}, {48351, 3716}, {49279, 8045}
X(50352) = crossdifference of every pair of points on line {584, 1185}
X(50352) = barycentric product X(i)*X(j) for these {i,j}: {514, 32771}, {693, 17750}, {876, 41250}
X(50352) = barycentric quotient X(i)/X(j) for these {i,j}: {17750, 100}, {32771, 190}, {41250, 874}
X(50352) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4879, 47889, 48295}, {4885, 48099, 47839}, {21052, 48148, 47918}, {21302, 47780, 17166}, {47666, 47814, 48005}, {47812, 48131, 23815}, {47875, 48351, 3716}, {48288, 48569, 905}


X(50353) = X(23)X(385)∩X(513)X(663)

Barycentrics    a*(b - c)*(a^3 + a^2*b + a^2*c - a*b*c + b^2*c + b*c^2) : :
X(50353) = 2 X[2605] - 3 X[25569], 2 X[656] - 3 X[28284], 2 X[3837] - 3 X[48209], X[44444] - 3 X[48209], 2 X[4036] - 3 X[47872], X[4397] - 3 X[47804], 2 X[6133] - 3 X[47804], X[4404] - 3 X[47817], 2 X[4491] + X[48323], 3 X[4809] - 2 X[21187], 3 X[8643] - X[17418], 2 X[21051] - 3 X[48165], 2 X[21260] - 3 X[48186], X[21301] - 3 X[48173], 5 X[30795] - 4 X[44316], 5 X[30795] - 6 X[48207], 2 X[44316] - 3 X[48207], 4 X[31288] - 3 X[48228], 2 X[31946] - 3 X[48168], 4 X[31947] - 3 X[47893], X[47136] - 3 X[47801]

X(50353) lies on these lines: {1, 6371}, {23, 385}, {37, 2483}, {512, 48307}, {513, 663}, {521, 48327}, {522, 667}, {649, 21348}, {656, 28284}, {676, 28095}, {798, 4435}, {814, 7650}, {832, 21189}, {834, 4879}, {891, 48293}, {900, 3733}, {1255, 43928}, {1491, 25537}, {1919, 3287}, {1960, 3737}, {2517, 4874}, {2787, 4985}, {2978, 4784}, {3716, 7234}, {3835, 24676}, {3837, 26097}, {4036, 47872}, {4040, 8672}, {4063, 4139}, {4083, 48303}, {4132, 21349}, {4140, 47127}, {4378, 4778}, {4397, 6133}, {4401, 28161}, {4404, 47817}, {4491, 4977}, {4809, 21187}, {4815, 29070}, {6003, 48345}, {6004, 23800}, {6363, 48281}, {8638, 23400}, {8643, 17418}, {8654, 20294}, {9002, 48283}, {9013, 28396}, {16695, 47844}, {17420, 38469}, {20906, 26277}, {21051, 48165}, {21260, 48186}, {21301, 48173}, {21343, 48292}, {22096, 24840}, {25884, 25926}, {26249, 47798}, {28225, 48343}, {28355, 28399}, {30795, 31003}, {31288, 48228}, {31946, 48168}, {31947, 47893}, {32626, 39200}, {39386, 46610}, {39480, 39577}, {42337, 48387}, {46385, 48331}, {47136, 47801}, {48342, 48344}

X(50353) = midpoint of X(i) and X(j) for these {i,j}: {649, 42312}, {4017, 48150}, {17420, 48322}, {21189, 48324}
X(50353) = reflection of X(i) in X(j) for these {i,j}: {659, 4057}, {1459, 48330}, {2517, 4874}, {3737, 1960}, {4397, 6133}, {4879, 48302}, {21343, 48292}, {44444, 3837}, {46385, 48331}, {48281, 48328}, {48336, 48306}, {48342, 48344}
X(50353) = isogonal conjugate of the anticomplement of X(38992)
X(50353) = X(6648)-Ceva conjugate of X(6)
X(50353) = X(100)-isoconjugate of X(45989)
X(50353) = X(8054)-Dao conjugate of X(45989)
X(50353) = crosspoint of X(i) and X(j) for these (i,j): {1, 8707}, {251, 8687}
X(50353) = crosssum of X(i) and X(j) for these (i,j): {1, 6371}, {141, 3910}, {513, 3812}, {521, 37613}, {522, 3831}
X(50353) = crossdifference of every pair of points on line {9, 39}
X(50353) = barycentric product X(i)*X(j) for these {i,j}: {513, 27064}, {514, 5255}, {6648, 38992}
X(50353) = barycentric quotient X(i)/X(j) for these {i,j}: {649, 45989}, {5255, 190}, {27064, 668}, {38992, 3910}
X(50353) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {669, 47694, 659}, {4397, 47804, 6133}, {44316, 48207, 30795}, {44444, 48209, 3837}


X(50354) = X(513)X(663)∩X(514)X(656)

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(50354) = 3 X[1769] - 2 X[6615], X[1769] + 2 X[48151], 2 X[2605] - 3 X[14413], 3 X[4017] - X[6615], X[6615] + 3 X[48151], 3 X[2457] - 2 X[10015], 2 X[3716] - 3 X[48209], 3 X[4453] - 2 X[21187], 2 X[6133] - 3 X[47823], 2 X[8062] - 3 X[47796], 4 X[25380] - 3 X[48204], 3 X[31148] - 2 X[43927]

X(50354) lies on these lines: {513, 663}, {514, 656}, {521, 48342}, {522, 4905}, {523, 2254}, {661, 6586}, {693, 28623}, {764, 6371}, {832, 4378}, {834, 48334}, {905, 46385}, {918, 4064}, {1734, 28147}, {2457, 10015}, {2517, 24720}, {2530, 8672}, {3309, 48303}, {3676, 7649}, {3716, 48209}, {3733, 22379}, {3737, 3960}, {3887, 48293}, {4041, 4802}, {4057, 48032}, {4391, 47843}, {4449, 15313}, {4453, 21187}, {4462, 20316}, {4466, 23771}, {4468, 20315}, {4509, 23829}, {4778, 21189}, {4815, 8714}, {4840, 4979}, {4895, 48292}, {4977, 17420}, {6003, 48281}, {6133, 47823}, {7178, 21102}, {8062, 47796}, {8648, 48382}, {11125, 30724}, {14288, 40086}, {15179, 23838}, {20294, 47676}, {20507, 23739}, {21103, 30725}, {21172, 30723}, {23226, 44408}, {24457, 39386}, {25380, 48204}, {28155, 48018}, {28161, 48075}, {30591, 48264}, {31148, 43927}, {35057, 48282}, {38469, 48323}, {42325, 48307}, {47842, 47918}

X(50354) = midpoint of X(i) and X(j) for these {i,j}: {4017, 48151}, {17420, 23738}, {20294, 47676}
X(50354) = reflection of X(i) in X(j) for these {i,j}: {656, 23800}, {1459, 3669}, {1769, 4017}, {2517, 24720}, {3737, 3960}, {4391, 47843}, {4462, 20316}, {4468, 20315}, {4895, 48292}, {4979, 4840}, {7649, 3676}, {11125, 30724}, {14288, 40086}, {21102, 7178}, {21103, 30725}, {21172, 30723}, {46385, 905}, {47918, 47842}, {48032, 4057}, {48264, 30591}, {48340, 6129}
X(50354) = isogonal conjugate of the polar conjugate of X(23595)
X(50354) = X(i)-Ceva conjugate of X(j) for these (i,j): {58, 244}, {3668, 1086}, {36048, 57}
X(50354) = X(i)-isoconjugate of X(j) for these (i,j): {8, 15439}, {100, 943}, {101, 40435}, {190, 2259}, {200, 36048}, {346, 32651}, {644, 2982}, {692, 40422}, {906, 40447}, {1175, 3952}, {1794, 1897}, {4557, 40412}, {4574, 40395}, {4587, 40573}, {35320, 44687}
X(50354) = X(i)-Dao conjugate of X(j) for these (i,j): {78, 39007}, {190, 18591}, {200, 15607}, {313, 16732}, {442, 3699}, {668, 16585}, {943, 8054}, {1015, 40435}, {1086, 40422}, {1794, 34467}, {4033, 40937}, {5190, 40447}, {6609, 36048}
X(50354) = crosspoint of X(i) and X(j) for these (i,j): {57, 36048}, {1019, 3676}
X(50354) = crosssum of X(1018) and X(3939)
X(50354) = crossdifference of every pair of points on line {9, 943}
X(50354) = barycentric product X(i)*X(j) for these {i,j}: {3, 23595}, {81, 23752}, {442, 1019}, {513, 5249}, {514, 942}, {525, 46883}, {693, 2260}, {905, 1838}, {1088, 33525}, {1841, 4025}, {2294, 7192}, {3261, 40956}, {3669, 6734}, {3676, 40937}, {3824, 48074}, {3960, 45926}, {4077, 46882}, {4303, 17924}, {7199, 40952}, {7649, 18607}, {14208, 46890}, {14547, 24002}, {14597, 46107}, {17094, 46884}, {17096, 40967}
X(50354) = barycentric quotient X(i)/X(j) for these {i,j}: {442, 4033}, {513, 40435}, {514, 40422}, {604, 15439}, {649, 943}, {667, 2259}, {942, 190}, {1019, 40412}, {1106, 32651}, {1407, 36048}, {1838, 6335}, {1841, 1897}, {2260, 100}, {2294, 3952}, {4303, 1332}, {5249, 668}, {6734, 646}, {7649, 40447}, {8021, 7259}, {14547, 644}, {14597, 1331}, {18607, 4561}, {22383, 1794}, {23207, 4587}, {23595, 264}, {23752, 321}, {33525, 200}, {40937, 3699}, {40952, 1018}, {40956, 101}, {40967, 30730}, {40978, 4557}, {43923, 40573}, {43924, 2982}, {45926, 36804}, {46882, 643}, {46883, 648}, {46884, 36797}, {46890, 162}


X(50355) = X(8)X(29324)∩X(10)X(48267)

Barycentrics    a*(b - c)*(2*a*b - b^2 + 2*a*c - b*c - c^2) : :
X(50355) = 3 X[1491] - 2 X[14349], 5 X[1491] - 4 X[48059], 3 X[1734] - X[14349], 5 X[1734] - 2 X[48059], 4 X[1734] - X[48123], 5 X[14349] - 6 X[48059], 4 X[14349] - 3 X[48123], 8 X[48059] - 5 X[48123], 5 X[4041] - X[47906], 4 X[4041] - X[47913], 3 X[4041] - X[47918], 5 X[4041] - 2 X[47922], 7 X[4041] - 2 X[48609], 5 X[4490] - 2 X[47906], 3 X[4490] - 2 X[47918], 5 X[4490] - 4 X[47922], 7 X[4490] - 4 X[48609], 4 X[47906] - 5 X[47913], 3 X[47906] - 5 X[47918], 7 X[47906] - 10 X[48609], 3 X[47913] - 4 X[47918], 5 X[47913] - 8 X[47922], 7 X[47913] - 8 X[48609], 5 X[47918] - 6 X[47922], 7 X[47918] - 6 X[48609], 7 X[47922] - 5 X[48609], 3 X[667] - 2 X[48345], 2 X[905] - 3 X[48244], X[4879] - 3 X[48244], 3 X[1635] - 2 X[48331], 3 X[2254] - X[48334], X[3777] + 2 X[4729], 3 X[3777] - 2 X[48334], 3 X[4729] + X[48334], 2 X[3716] - 3 X[47835], 2 X[4040] - 3 X[48226], 2 X[4162] - 3 X[25569], 3 X[4705] - 2 X[47997], 5 X[4705] - 2 X[48594], 4 X[47997] - 3 X[48024], 5 X[47997] - 3 X[48594], 5 X[48024] - 4 X[48594], 2 X[4806] - 3 X[47814], 2 X[4874] - 3 X[47836], 3 X[4951] - 2 X[7265], 2 X[4990] - 3 X[47807], 2 X[4992] - 3 X[44429], 2 X[8045] - 3 X[48235], 3 X[14419] - 2 X[48294], 4 X[25380] - 3 X[47841], 3 X[47810] - 2 X[48093], 3 X[47827] - 2 X[48099], 3 X[47828] - X[48338], 3 X[47893] - 2 X[48136], 2 X[48092] - 3 X[48160], 3 X[48184] - 2 X[48273], 3 X[48234] - 2 X[48305], 2 X[48248] - 3 X[48565], 2 X[48295] - 3 X[48569], X[48339] - 3 X[48573]

X(50355) lies on these lines: {8, 29324}, {10, 48267}, {512, 1491}, {513, 4041}, {514, 4730}, {522, 2533}, {650, 48336}, {659, 3309}, {663, 9508}, {667, 3887}, {690, 48272}, {764, 48075}, {784, 4761}, {814, 21302}, {830, 4834}, {891, 4905}, {900, 4391}, {905, 4879}, {1635, 48331}, {2254, 3777}, {2530, 29350}, {3667, 4147}, {3669, 21343}, {3716, 47835}, {3900, 4367}, {3960, 48333}, {4010, 17072}, {4040, 48226}, {4063, 6004}, {4088, 29200}, {4139, 23800}, {4151, 48120}, {4162, 25569}, {4170, 21260}, {4369, 48301}, {4394, 48329}, {4401, 6161}, {4467, 29074}, {4526, 22222}, {4560, 29366}, {4705, 6005}, {4770, 47959}, {4774, 23880}, {4775, 14838}, {4782, 48150}, {4784, 8678}, {4806, 47814}, {4807, 8714}, {4808, 23875}, {4814, 48144}, {4822, 48030}, {4843, 48396}, {4874, 47836}, {4895, 48330}, {4926, 48264}, {4951, 7265}, {4983, 48012}, {4990, 47807}, {4992, 44429}, {8045, 48235}, {14077, 48323}, {14419, 48294}, {16892, 29208}, {17494, 29246}, {21051, 48080}, {21124, 29144}, {21301, 29328}, {24720, 48279}, {25380, 47841}, {28217, 48401}, {29226, 48151}, {29280, 47700}, {29284, 48278}, {29298, 48321}, {32478, 49277}, {47810, 48093}, {47827, 48099}, {47828, 48338}, {47893, 48136}, {47928, 48407}, {47967, 48021}, {48003, 48351}, {48005, 48081}, {48092, 48160}, {48184, 48273}, {48234, 48305}, {48248, 48565}, {48295, 48569}, {48339, 48573}

X(50355) = midpoint of X(i) and X(j) for these {i,j}: {2254, 4729}, {4814, 48144}
X(50355) = reflection of X(i) in X(j) for these {i,j}: {663, 9508}, {764, 48075}, {1491, 1734}, {2530, 48018}, {3777, 2254}, {4010, 17072}, {4170, 21260}, {4490, 4041}, {4775, 14838}, {4822, 48030}, {4879, 905}, {4895, 48330}, {4983, 48012}, {6161, 4401}, {21343, 3669}, {23765, 4905}, {47906, 47922}, {47913, 4490}, {47928, 48407}, {47959, 4770}, {48021, 47967}, {48024, 4705}, {48080, 21051}, {48081, 48005}, {48123, 1491}, {48150, 4782}, {48265, 4147}, {48267, 10}, {48279, 24720}, {48301, 4369}, {48329, 4394}, {48333, 3960}, {48336, 650}, {48351, 48003}, {48392, 2533}
X(50355) = crosssum of X(513) and X(4640)
X(50355) = crossdifference of every pair of points on line {1449, 5573}
X(50355) = barycentric product X(i)*X(j) for these {i,j}: {1, 48270}, {513, 17242}
X(50355) = barycentric quotient X(i)/X(j) for these {i,j}: {17242, 668}, {48270, 75}
X(50355) = {X(4879),X(48244)}-harmonic conjugate of X(905)


X(50356) = X(1)X(44550)∩X(10)X(1734)

Barycentrics    (b - c)*(-2*a^2*b + 2*a*b^2 - 2*a^2*c + a*b*c + b^2*c + 2*a*c^2 + b*c^2) : :
X(50356) = 2 X[1] - 3 X[44550], 2 X[10] - 3 X[1734], 4 X[10] - 3 X[4391], X[145] - 3 X[17496], 4 X[4824] - 3 X[47666], 5 X[4824] - 3 X[47946], 3 X[4824] - 2 X[47954], 7 X[4824] - 6 X[47964], 2 X[4824] - 3 X[47975], 3 X[47666] - 2 X[47941], 5 X[47666] - 4 X[47946], 9 X[47666] - 8 X[47954], 7 X[47666] - 8 X[47964], 5 X[47941] - 6 X[47946], 3 X[47941] - 4 X[47954], 7 X[47941] - 12 X[47964], X[47941] - 3 X[47975], 9 X[47946] - 10 X[47954], 7 X[47946] - 10 X[47964], 2 X[47946] - 5 X[47975], 7 X[47954] - 9 X[47964], 4 X[47954] - 9 X[47975], 4 X[47964] - 7 X[47975], 3 X[693] - 2 X[4804], 3 X[693] - 4 X[24720], 5 X[693] - 6 X[47812], 5 X[693] - 4 X[48394], 3 X[2254] - X[4804], 3 X[2254] - 2 X[24720], 5 X[2254] - 3 X[47812], 5 X[2254] - 2 X[48394], 3 X[4453] - 2 X[47123], 5 X[4804] - 9 X[47812], 5 X[4804] - 6 X[48394], 10 X[24720] - 9 X[47812], 5 X[24720] - 3 X[48394], 3 X[47812] - 2 X[48394], 3 X[47675] - 4 X[48143], 3 X[48108] - 2 X[48143], 2 X[650] - 3 X[48242], 3 X[661] - 2 X[48037], 2 X[661] - 3 X[48175], 3 X[48017] - X[48037], 4 X[48017] - 3 X[48175], 4 X[48037] - 9 X[48175], 4 X[1491] - 3 X[4776], 3 X[1491] - 2 X[4806], 9 X[4776] - 8 X[4806], 3 X[4776] - 2 X[48080], 4 X[4806] - 3 X[48080], 6 X[905] - 5 X[3616], 3 X[1635] - 2 X[48063], 2 X[3700] - 3 X[47808], 4 X[4925] - 3 X[47808], 4 X[3716] - 5 X[31209], 2 X[3716] - 3 X[47828], 5 X[31209] - 6 X[47828], 2 X[4010] - 3 X[44429], 2 X[4106] - 3 X[48164], 2 X[4122] - 3 X[48187], 4 X[4369] - 3 X[48237], 4 X[4394] - 3 X[47805], 2 X[4724] - 3 X[31150], 4 X[4913] - 3 X[31150], 3 X[21146] - 2 X[48127], 2 X[4794] - 3 X[45671], 2 X[4874] - 3 X[48244], 4 X[4885] - 3 X[48172], 11 X[5550] - 12 X[44561], 4 X[48010] - 3 X[48548], 2 X[48021] - 3 X[48548], 2 X[6590] - 3 X[48252], 2 X[7662] - 3 X[47824], 4 X[9508] - 3 X[47804], 7 X[9780] - 6 X[45664], 4 X[17069] - 3 X[47798], 4 X[23770] - 5 X[48421], 5 X[24924] - 6 X[48575], 4 X[25380] - 3 X[47832], 2 X[48024] - 3 X[48549], 3 X[36848] - 2 X[48090], 2 X[47131] - 3 X[48241], 2 X[47132] - 3 X[48245], 2 X[47691] - 3 X[48422], 2 X[47694] - 3 X[47762], 3 X[47782] - 2 X[48006], 3 X[47809] - 2 X[49286], 3 X[47810] - 2 X[48043], 3 X[47814] - 2 X[48267], 3 X[47819] - 2 X[48273], 3 X[47820] - 2 X[48305], 3 X[47825] - 2 X[48029], 3 X[47892] - 2 X[48061], 2 X[48027] - 3 X[48157], 4 X[48062] - 3 X[48557], 3 X[48557] - 2 X[49275], 3 X[48159] - 2 X[49295], 3 X[48174] - 2 X[48349], 3 X[48208] - 2 X[48271], 4 X[48396] - 3 X[48423], 3 X[48579] - 2 X[49292]

X(50356) lies on these lines: {1, 44550}, {10, 1734}, {145, 3900}, {512, 48410}, {513, 4380}, {514, 4729}, {522, 693}, {523, 47674}, {649, 47697}, {650, 48242}, {656, 4811}, {661, 3667}, {812, 47685}, {824, 47689}, {900, 1491}, {905, 3616}, {1577, 48018}, {1635, 48063}, {2526, 20295}, {2786, 48077}, {3126, 17244}, {3309, 4560}, {3700, 4925}, {3716, 31209}, {3835, 4962}, {3837, 28221}, {3887, 47729}, {3960, 48339}, {4010, 4926}, {4041, 4462}, {4088, 49272}, {4106, 48164}, {4122, 48187}, {4151, 4801}, {4170, 48066}, {4369, 48237}, {4394, 47805}, {4397, 28623}, {4724, 4913}, {4777, 21146}, {4778, 47934}, {4785, 48020}, {4794, 45671}, {4818, 47701}, {4874, 48244}, {4885, 48172}, {4895, 48325}, {4932, 48153}, {4978, 48075}, {5550, 44561}, {6005, 48409}, {6006, 48010}, {6590, 48252}, {7192, 7659}, {7253, 16751}, {7662, 47824}, {9508, 47804}, {9780, 45664}, {14077, 21222}, {16892, 47692}, {17069, 47798}, {17072, 48264}, {21196, 47972}, {21302, 23880}, {23770, 48421}, {23809, 24184}, {23879, 47718}, {24924, 48575}, {25380, 47832}, {28147, 48148}, {28161, 47672}, {28183, 48120}, {28205, 48098}, {28209, 47928}, {28217, 48024}, {28225, 47917}, {28898, 49447}, {29628, 45322}, {30519, 47700}, {30765, 48545}, {36848, 48090}, {39386, 48002}, {44449, 48039}, {47131, 48241}, {47132, 48245}, {47651, 47973}, {47652, 48015}, {47655, 47703}, {47660, 48069}, {47662, 48106}, {47665, 47690}, {47691, 48422}, {47694, 47762}, {47782, 48006}, {47809, 49286}, {47810, 48043}, {47814, 48267}, {47819, 48273}, {47820, 48305}, {47825, 48029}, {47892, 48061}, {47982, 49297}, {47985, 48019}, {48008, 48032}, {48023, 48079}, {48027, 48157}, {48042, 48114}, {48062, 48557}, {48159, 49295}, {48174, 48349}, {48208, 48271}, {48396, 48423}, {48579, 49292}

X(50356) = reflection of X(i) in X(j) for these {i,j}: {661, 48017}, {693, 2254}, {1577, 48018}, {3700, 4925}, {4170, 48066}, {4391, 1734}, {4462, 4041}, {4724, 4913}, {4801, 4905}, {4804, 24720}, {4811, 656}, {4895, 48325}, {4978, 48075}, {7192, 7659}, {20295, 2526}, {24457, 23809}, {44449, 48039}, {47651, 47973}, {47652, 48015}, {47655, 47703}, {47660, 48069}, {47662, 48106}, {47665, 47690}, {47666, 47975}, {47672, 48073}, {47675, 48108}, {47692, 16892}, {47695, 4025}, {47697, 649}, {47701, 4818}, {47729, 48321}, {47939, 47945}, {47941, 4824}, {47972, 21196}, {47974, 17494}, {48014, 4765}, {48019, 47985}, {48021, 48010}, {48032, 48008}, {48079, 48023}, {48080, 1491}, {48114, 48042}, {48153, 4932}, {48264, 17072}, {48339, 3960}, {49272, 4088}, {49275, 48062}, {49297, 47982}
X(50356) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1002, 33650}, {1415, 27484}, {2279, 37781}, {8693, 329}, {32041, 21286}, {32724, 10025}, {36138, 30807}, {37138, 3436}, {42290, 150}
X(50356) = crosspoint of X(75) and X(32041)
X(50356) = crossdifference of every pair of points on line {41, 2242}
X(50356) = barycentric product X(i)*X(j) for these {i,j}: {514, 49450}, {522, 31225}
X(50356) = barycentric quotient X(i)/X(j) for these {i,j}: {31225, 664}, {49450, 190}
X(50356) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 48017, 48175}, {1491, 48080, 4776}, {2254, 4804, 24720}, {3700, 4925, 47808}, {3716, 47828, 31209}, {4724, 4913, 31150}, {4804, 24720, 693}, {4824, 47941, 47666}, {47812, 48394, 693}, {47941, 47975, 4824}, {48010, 48021, 48548}, {48062, 49275, 48557}


X(50357) = X(149)X(900)∩X(513)X(3004)

Barycentrics    (b - c)*(3*a + b + c)*(-(a*b) + b^2 - a*c + c^2) : :
X(50357) = X[47695] - 3 X[48571], 3 X[3004] - 2 X[47998], 3 X[4025] - X[48014], X[47982] - 3 X[48015], 3 X[4905] - X[49278], 3 X[649] - X[48105], 2 X[676] - 3 X[4453], 3 X[2254] - X[4088], 3 X[2254] - 2 X[4925], 3 X[1638] - 2 X[3716], 3 X[1639] - 4 X[25380], 4 X[2487] - 3 X[47804], 4 X[2505] - 3 X[31131], 4 X[2527] - 3 X[48250], 2 X[2976] - 3 X[44433], 2 X[2977] - 3 X[48244], X[48083] - 3 X[48244], 2 X[4010] - 3 X[4927], 3 X[4773] - 2 X[4830], 3 X[4750] - X[48032], 3 X[4786] - X[48068], 2 X[4806] - 3 X[48178], 2 X[4874] - 3 X[48245], 2 X[4990] - 3 X[47796], 2 X[7662] - 3 X[47891], 4 X[9508] - 3 X[47884], 3 X[47884] - 2 X[48055], 2 X[14321] - 3 X[44429], 3 X[16892] - X[47702], 2 X[18004] - 3 X[48182], 4 X[21212] - 3 X[48179], 3 X[27486] - X[47974], 4 X[31287] - 3 X[48546], X[44449] - 3 X[48164], X[47697] - 3 X[47755], 3 X[47756] - 2 X[48043], 3 X[47784] - 2 X[48029], 3 X[47788] - 2 X[49286], 3 X[47808] - X[49272], 3 X[47824] - X[49275], 3 X[47828] - X[48078], 3 X[47876] - 2 X[48001], 3 X[47890] - 2 X[48096], 3 X[47973] - X[48598], 3 X[48249] - 2 X[48405], 3 X[48252] - X[49273]

X(50357) lies on these lines: {149, 900}, {513, 3004}, {514, 7659}, {522, 21104}, {523, 47674}, {525, 4905}, {649, 48105}, {676, 4453}, {824, 48073}, {918, 2254}, {1491, 48046}, {1499, 48335}, {1638, 3716}, {1639, 25380}, {2487, 47804}, {2505, 31131}, {2526, 28846}, {2527, 48250}, {2785, 30725}, {2826, 4707}, {2976, 44433}, {2977, 48083}, {3566, 3777}, {3667, 3776}, {3700, 24720}, {3910, 48151}, {4010, 4927}, {4394, 48061}, {4700, 4706}, {4724, 17069}, {4750, 48032}, {4784, 4977}, {4786, 48068}, {4801, 4843}, {4806, 48178}, {4874, 48245}, {4990, 47796}, {6084, 49301}, {6366, 21222}, {7662, 47891}, {9508, 47884}, {14321, 44429}, {16892, 47702}, {18004, 48182}, {21146, 48274}, {21212, 48179}, {23795, 23887}, {23829, 39775}, {23875, 48075}, {27486, 28209}, {28225, 48404}, {28851, 48017}, {28867, 48042}, {28886, 47985}, {28898, 49285}, {28902, 47945}, {30520, 48069}, {31287, 48546}, {39386, 48239}, {39545, 48324}, {44449, 48164}, {47697, 47755}, {47756, 48043}, {47784, 48029}, {47788, 49286}, {47808, 49272}, {47824, 49275}, {47828, 48078}, {47876, 48001}, {47890, 48096}, {47973, 48598}, {48249, 48405}, {48252, 49273}

X(50357) = reflection of X(i) in X(j) for these {i,j}: {3700, 24720}, {4088, 4925}, {4724, 17069}, {4841, 4818}, {47988, 48007}, {48046, 1491}, {48055, 9508}, {48061, 4394}, {48083, 2977}, {48274, 21146}, {48324, 39545}
X(50357) = X(i)-isoconjugate of X(j) for these (i,j): {105, 8694}, {673, 34074}, {919, 25430}, {1438, 4606}, {2334, 36086}, {4627, 18785}, {4866, 32735}, {5936, 32666}, {34820, 36146}
X(50357) = X(i)-Dao conjugate of X(j) for these (i,j): {2334, 38989}, {4606, 6184}, {4624, 36905}, {5936, 35094}, {8694, 39046}, {25430, 38980}, {34820, 39014}
X(50357) = crossdifference of every pair of points on line {1438, 2334}
X(50357) = barycentric product X(i)*X(j) for these {i,j}: {241, 4811}, {391, 43042}, {514, 4684}, {518, 4801}, {918, 3616}, {2254, 19804}, {3263, 4790}, {3717, 30723}, {3912, 4778}, {3932, 48580}, {4088, 42028}, {4765, 9436}, {4815, 18206}, {4822, 18157}, {4830, 40217}, {4841, 30941}, {5257, 23829}
X(50357) = barycentric quotient X(i)/X(j) for these {i,j}: {391, 36802}, {518, 4606}, {665, 2334}, {672, 8694}, {918, 5936}, {926, 34820}, {1449, 36086}, {2223, 34074}, {2254, 25430}, {3286, 4627}, {3361, 36146}, {3616, 666}, {3675, 47915}, {4684, 190}, {4765, 14942}, {4778, 673}, {4790, 105}, {4801, 2481}, {4811, 36796}, {4822, 18785}, {4827, 28071}, {4830, 6654}, {4841, 13576}, {9436, 4624}, {18206, 4614}, {21454, 927}, {30941, 4633}
X(50357) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2254, 4088, 4925}, {9508, 48055, 47884}, {48083, 48244, 2977}


X(50358) = X(44)X(513)∩X(512)X(48111)

Barycentrics    a*(b - c)*(2*a^2 + b^2 - b*c + c^2) : :
X(50358) = 2 X[650] - 3 X[659], 4 X[650] - 3 X[1491], 5 X[650] - 3 X[2526], 10 X[650] - 9 X[47827], 14 X[650] - 9 X[48160], 11 X[650] - 9 X[48193], 8 X[650] - 9 X[48226], 5 X[659] - 2 X[2526], 5 X[659] - 3 X[47827], 7 X[659] - 3 X[48160], 11 X[659] - 6 X[48193], 4 X[659] - 3 X[48226], 5 X[1491] - 4 X[2526], 5 X[1491] - 6 X[47827], 7 X[1491] - 6 X[48160], 11 X[1491] - 12 X[48193], 2 X[1491] - 3 X[48226], 2 X[2526] - 3 X[47827], 14 X[2526] - 15 X[48160], 11 X[2526] - 15 X[48193], 8 X[2526] - 15 X[48226], 4 X[4394] - 3 X[48244], 3 X[4724] - X[4813], 2 X[4813] - 3 X[48024], X[4979] + 3 X[48032], 3 X[47811] - X[48020], 3 X[47811] - 2 X[48030], 7 X[47827] - 5 X[48160], 11 X[47827] - 10 X[48193], 4 X[47827] - 5 X[48226], X[48023] - 3 X[48572], 2 X[48027] - 3 X[48162], 11 X[48160] - 14 X[48193], 4 X[48160] - 7 X[48226], 8 X[48193] - 11 X[48226], X[47664] + 3 X[47697], 3 X[667] - 2 X[3960], 3 X[3777] - 4 X[3960], 2 X[693] - 3 X[48234], 3 X[48234] - 4 X[48248], 4 X[2490] - 3 X[48182], 4 X[2527] - 3 X[48249], 2 X[3776] - 3 X[4809], 4 X[3803] - X[23765], 2 X[3835] - 3 X[4448], 3 X[4448] - 4 X[8689], 2 X[3837] - 3 X[47804], X[47685] - 3 X[47804], 3 X[4010] - 2 X[49287], 3 X[48063] - X[49287], X[4895] - 3 X[48150], 2 X[4106] - 3 X[4800], 3 X[4498] - X[4814], 6 X[4874] - 5 X[26985], 2 X[4874] - 3 X[47805], 4 X[4874] - 3 X[48184], 5 X[26985] - 3 X[46403], 5 X[26985] - 9 X[47805], 10 X[26985] - 9 X[48184], X[46403] - 3 X[47805], 2 X[46403] - 3 X[48184], 4 X[4885] - 3 X[48167], 4 X[6050] - 3 X[47893], 2 X[7662] - 3 X[48251], 4 X[13246] - 3 X[48227], 2 X[21051] - 3 X[47815], 2 X[21260] - 3 X[47817], 2 X[23815] - 3 X[47818], 3 X[25569] - 2 X[48332], 5 X[26777] - 3 X[48157], X[26824] - 3 X[47694], 2 X[26824] - 3 X[48120], 7 X[27115] - 6 X[45323], 5 X[30795] - 6 X[47803], 5 X[30835] - 6 X[45666], 5 X[31209] - 6 X[45314], 4 X[31286] - 3 X[36848], 4 X[31288] - 3 X[48556], 3 X[44433] - X[47652], X[47651] - 3 X[48223], X[47686] - 3 X[47798], X[47687] - 3 X[48250], 3 X[48250] - 2 X[48405], X[47688] - 3 X[48239], 3 X[47813] - 2 X[48098], 3 X[47813] - X[48115], 3 X[47820] - 2 X[48406], 3 X[47822] - 2 X[48050], 3 X[47833] - 2 X[48089], X[48119] - 3 X[48578], 3 X[48143] - 4 X[49291], 3 X[48189] - 2 X[49289]

X(50358) lies on these lines: {44, 513}, {512, 48111}, {514, 4922}, {522, 48072}, {523, 8664}, {667, 3777}, {693, 48234}, {830, 4490}, {891, 48324}, {900, 4380}, {983, 23838}, {1027, 40746}, {1960, 48335}, {2490, 48182}, {2527, 48249}, {2530, 4401}, {2832, 4378}, {2977, 39386}, {3004, 28209}, {3667, 48062}, {3716, 24719}, {3776, 4809}, {3803, 4367}, {3835, 4448}, {3837, 47685}, {4010, 48063}, {4040, 48123}, {4057, 8654}, {4063, 6004}, {4083, 4895}, {4106, 4800}, {4491, 21005}, {4498, 4814}, {4777, 47932}, {4778, 47968}, {4802, 48153}, {4834, 42325}, {4874, 26985}, {4879, 8712}, {4885, 48167}, {4963, 47963}, {4977, 47676}, {4983, 48065}, {6006, 11068}, {6050, 47893}, {6133, 44444}, {6161, 29350}, {6372, 47977}, {7662, 48251}, {9002, 18183}, {13246, 48227}, {20983, 47330}, {21051, 47815}, {21118, 29244}, {21132, 29156}, {21260, 47817}, {21343, 48327}, {23815, 47818}, {25569, 48332}, {26777, 48157}, {26824, 29362}, {27115, 45323}, {28151, 48132}, {28195, 47933}, {28217, 47885}, {28220, 47960}, {28225, 48007}, {28882, 48349}, {29070, 48392}, {29078, 49275}, {29144, 48101}, {29198, 47936}, {29204, 48130}, {29226, 48322}, {29238, 48264}, {29302, 48305}, {29324, 31291}, {29370, 49273}, {30795, 47803}, {30835, 45666}, {31209, 45314}, {31286, 36848}, {31288, 48556}, {44433, 47652}, {47651, 48223}, {47686, 47798}, {47687, 48250}, {47688, 48239}, {47700, 48097}, {47701, 48599}, {47813, 48098}, {47820, 48406}, {47822, 48050}, {47833, 48089}, {47901, 48621}, {47905, 47967}, {47910, 47969}, {47913, 47970}, {47940, 48002}, {47944, 48006}, {47946, 48009}, {47949, 48623}, {47964, 48583}, {47999, 48585}, {48005, 48586}, {48056, 48077}, {48059, 48596}, {48061, 48083}, {48100, 48116}, {48102, 48604}, {48119, 48578}, {48131, 48331}, {48143, 49291}, {48189, 49289}, {48330, 48334}, {48333, 48345}

X(50358) = reflection of X(i) in X(j) for these {i,j}: {693, 48248}, {1491, 659}, {2254, 4782}, {2530, 4401}, {3777, 667}, {3835, 8689}, {4010, 48063}, {4367, 3803}, {4879, 48329}, {4963, 47963}, {4983, 48065}, {21343, 48327}, {23765, 4367}, {24719, 3716}, {44444, 6133}, {46403, 4874}, {47685, 3837}, {47687, 48405}, {47700, 48097}, {47901, 48621}, {47905, 47967}, {47910, 47969}, {47913, 47970}, {47940, 48002}, {47944, 48006}, {47946, 48009}, {47949, 48623}, {48020, 48030}, {48024, 4724}, {48077, 48056}, {48083, 48061}, {48115, 48098}, {48116, 48100}, {48120, 47694}, {48123, 4040}, {48131, 48331}, {48184, 47805}, {48333, 48345}, {48334, 48330}, {48335, 1960}, {48583, 47964}, {48585, 47999}, {48586, 48005}, {48596, 48059}, {48599, 47701}, {48604, 48102}
X(50358) = X(14458)-Ceva conjugate of X(11)
X(50358) = X(2)-isoconjugate of X(28883)
X(50358) = X(28883)-Dao conjugate of X(32664)
X(50358) = crosssum of X(513) and X(49465)
X(50358) = crossdifference of every pair of points on line {1, 7772}
X(50358) = barycentric product X(i)*X(j) for these {i,j}: {1, 28882}, {81, 48349}, {513, 17367}, {656, 31908}, {693, 5332}, {1019, 4085}, {1022, 49700}, {7192, 46907}
X(50358) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 28883}, {4085, 4033}, {5332, 100}, {17367, 668}, {28882, 75}, {31908, 811}, {46907, 3952}, {48349, 321}, {49700, 24004}
X(50358) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {659, 1491, 48226}, {693, 48248, 48234}, {2526, 47827, 1491}, {3835, 8689, 4448}, {4874, 46403, 48184}, {46403, 47805, 4874}, {47685, 47804, 3837}, {47687, 48250, 48405}, {47811, 48020, 48030}, {47813, 48115, 48098}


X(50359) = X(44)X(513)∩X(142)X(3835)

Barycentrics    a*(b - c)*(2*a*b - b^2 + 2*a*c + b*c - c^2) : :
X(50359) = 2 X[650] - 3 X[48244], 3 X[659] - 4 X[4394], 2 X[661] - 3 X[1491], X[661] - 3 X[2254], 7 X[661] - 9 X[47810], 5 X[661] - 3 X[48021], 4 X[661] - 3 X[48024], 7 X[661] - 6 X[48028], 5 X[661] - 6 X[48030], 7 X[1491] - 6 X[47810], 5 X[1491] - 2 X[48021], 7 X[1491] - 4 X[48028], 5 X[1491] - 4 X[48030], 7 X[2254] - 3 X[47810], 5 X[2254] - X[48021], 4 X[2254] - X[48024], 7 X[2254] - 2 X[48028], 5 X[2254] - 2 X[48030], 2 X[4724] - 3 X[48226], 3 X[4784] - 2 X[4790], X[4790] - 3 X[7659], 4 X[9508] - 3 X[48226], 15 X[47810] - 7 X[48021], 12 X[47810] - 7 X[48024], 3 X[47810] - 2 X[48028], 15 X[47810] - 14 X[48030], 3 X[47827] - 2 X[48029], 4 X[48021] - 5 X[48024], 7 X[48021] - 10 X[48028], 7 X[48024] - 8 X[48028], 5 X[48024] - 8 X[48030], 2 X[48027] - 3 X[48160], 5 X[48028] - 7 X[48030], 2 X[3835] - 3 X[36848], 3 X[3777] - 2 X[48335], 3 X[4905] - X[48335], 3 X[21146] - 2 X[48399], 4 X[48073] - X[48120], 3 X[48073] - X[48399], 3 X[48120] - 4 X[48399], X[47675] - 3 X[48108], 2 X[47675] - 3 X[48143], 2 X[676] - 3 X[48245], 2 X[47132] - 3 X[47891], 3 X[1734] - 2 X[4770], 3 X[4490] - 4 X[4770], 4 X[2487] - 3 X[26275], 4 X[2527] - 3 X[48247], 4 X[48075] - X[48123], 2 X[4806] - 3 X[44429], 3 X[4367] - 2 X[48327], 2 X[4010] - 3 X[48184], 4 X[24720] - 3 X[48184], 2 X[3716] - 3 X[47823], 2 X[4106] - 3 X[48167], 4 X[4369] - 3 X[48234], 3 X[4448] - 4 X[31286], X[47913] - 4 X[48018], X[47910] - 4 X[48017], 2 X[4794] - 3 X[14419], 3 X[4800] - 4 X[4885], 2 X[4874] - 3 X[47824], 3 X[4948] - 2 X[47962], 3 X[4951] - 2 X[25259], 2 X[4992] - 3 X[47819], 2 X[7662] - 3 X[48253], 2 X[8689] - 3 X[45313], 2 X[14321] - 3 X[48182], 2 X[18004] - 3 X[47808], 4 X[21212] - 3 X[48177], 4 X[25380] - 3 X[47822], 2 X[25666] - 3 X[45328], 3 X[31131] - X[44449], 7 X[31207] - 6 X[45666], 5 X[31209] - 6 X[48229], X[31290] - 3 X[48157], 3 X[44550] - 2 X[48289], 3 X[47762] - 2 X[48248], 3 X[47812] - 2 X[48090], 3 X[47877] - 2 X[47998], 3 X[47885] - 2 X[48055], 3 X[47888] - 2 X[48058], 3 X[47893] - 2 X[48099], X[47941] - 3 X[48175], 2 X[48002] - 3 X[48175], 4 X[48015] - X[48599], X[47969] - 3 X[48242], 2 X[47993] - 3 X[48549], 2 X[48000] - 3 X[48225], 2 X[48001] - 3 X[48176], 4 X[48069] - X[48604], 3 X[48187] - X[49272], 3 X[48252] - 2 X[48405], 3 X[48252] - X[49275], 3 X[48254] - X[49273]

X(50359) lies on these lines: {44, 513}, {142, 3835}, {512, 3777}, {514, 4730}, {522, 21146}, {523, 47674}, {667, 39476}, {676, 48245}, {690, 49278}, {693, 900}, {764, 29350}, {905, 48336}, {1019, 6004}, {1734, 4490}, {2344, 35355}, {2487, 26275}, {2527, 48247}, {2530, 6005}, {2976, 4806}, {3309, 4367}, {3667, 4010}, {3669, 4879}, {3716, 47823}, {3733, 8654}, {3776, 48349}, {3837, 28217}, {3887, 4378}, {3900, 48323}, {3960, 4775}, {4041, 29198}, {4083, 23765}, {4106, 48167}, {4170, 23815}, {4369, 48234}, {4444, 4785}, {4448, 31286}, {4486, 28867}, {4560, 29246}, {4705, 47913}, {4729, 23738}, {4776, 8661}, {4777, 47672}, {4778, 4824}, {4794, 14419}, {4800, 4885}, {4802, 48148}, {4804, 4926}, {4810, 48089}, {4822, 48100}, {4833, 16751}, {4874, 47824}, {4895, 48344}, {4925, 48047}, {4940, 30765}, {4948, 47962}, {4951, 25259}, {4962, 48394}, {4977, 47663}, {4983, 48066}, {4992, 47819}, {7662, 48253}, {8053, 16874}, {8689, 45313}, {8714, 48392}, {9002, 22277}, {14321, 48182}, {14838, 48351}, {15599, 41430}, {16892, 29144}, {17072, 48265}, {17496, 29366}, {18004, 47808}, {21212, 48177}, {21301, 29170}, {21302, 29324}, {23789, 48273}, {25380, 47822}, {25666, 45328}, {26049, 26078}, {26144, 27193}, {27674, 28284}, {28165, 48135}, {28195, 47934}, {28205, 48127}, {28209, 47666}, {28220, 47917}, {28225, 47946}, {28851, 49701}, {29078, 47687}, {29188, 48321}, {29200, 48278}, {29204, 47930}, {29252, 48272}, {29328, 46403}, {31131, 44449}, {31207, 45666}, {31209, 48229}, {31290, 48157}, {44550, 48289}, {47762, 48248}, {47812, 48090}, {47877, 47998}, {47885, 48055}, {47888, 48058}, {47893, 48099}, {47902, 48621}, {47904, 47964}, {47906, 47967}, {47925, 47973}, {47938, 47999}, {47941, 48002}, {47942, 48005}, {47944, 48007}, {47949, 48012}, {47968, 48015}, {47969, 48242}, {47993, 48549}, {48000, 48225}, {48001, 48176}, {48056, 48078}, {48059, 48081}, {48062, 48083}, {48069, 48103}, {48097, 48113}, {48106, 48140}, {48187, 49272}, {48252, 48405}, {48254, 49273}

X(50359) = midpoint of X(4729) and X(23738)
X(50359) = reflection of X(i) in X(j) for these {i,j}: {1491, 2254}, {2530, 48075}, {3777, 4905}, {4010, 24720}, {4170, 23815}, {4490, 1734}, {4705, 48018}, {4724, 9508}, {4775, 3960}, {4784, 7659}, {4804, 48098}, {4810, 48089}, {4822, 48100}, {4824, 48017}, {4879, 3669}, {4895, 48344}, {4983, 48066}, {21146, 48073}, {23765, 48151}, {47902, 48621}, {47904, 47964}, {47906, 47967}, {47910, 4824}, {47913, 4705}, {47925, 47973}, {47928, 47975}, {47938, 47999}, {47941, 48002}, {47942, 48005}, {47944, 48007}, {47946, 48010}, {47949, 48012}, {47968, 48015}, {48021, 48030}, {48024, 1491}, {48032, 4782}, {48047, 4925}, {48078, 48056}, {48080, 3837}, {48081, 48059}, {48083, 48062}, {48103, 48069}, {48113, 48097}, {48120, 21146}, {48123, 2530}, {48140, 48106}, {48143, 48108}, {48265, 17072}, {48273, 23789}, {48336, 905}, {48349, 3776}, {48351, 14838}, {48599, 47968}, {48604, 48103}, {49275, 48405}
X(50359) = X(2)-isoconjugate of X(28852)
X(50359) = X(28852)-Dao conjugate of X(32664)
X(50359) = crosssum of X(513) and X(42819)
X(50359) = crossdifference of every pair of points on line {1, 9351}
X(50359) = barycentric product X(i)*X(j) for these {i,j}: {1, 28851}, {513, 17244}, {514, 49490}, {1022, 49701}
X(50359) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 28852}, {17244, 668}, {28851, 75}, {49490, 190}, {49701, 24004}
X(50359) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4010, 24720, 48184}, {4724, 9508, 48226}, {47941, 48175, 48002}, {48252, 49275, 48405}


leftri

Radical traces of circumcircle and other circles: X(50360)-X(50390)

rightri

This preamble and centers X(50360)-X(50390) were contributed by César Eliud Lozada, June 4, 2022.

The appearance of (Ω, n) in the following list means that the radical trace of the circumcircle of ABC and circle Ω is X(n):

(Adams circle, 50360), (anticomplementary circle, 858), (Apollonius circle, 50361), (Bevan circle, 1155), (Brocard circle, 187), (Conway circle, 50362), (Dao-Moses-Telv circle, 50363), (Dou circle, 9720), (Dou circles radical circle, 50364), (1st Droz-Farny circle, 44452), (Ehrmann circle, 6), (Euler-Gergonne-Soddy circle, 50365), (excircles radical circle, 50366), (extangents circle, 50367), (Fuhrmann circle, 50368), (Gallatly circle, 2021), (GEOS circle, 50369), (half-Moses circle, 50370), (hexyl circle, 50371), (Hatzipolakis-Suppa circle, 4), (Hutson-Parry circle, 9179), (incentral circle, 50372), (incircle, 3660), (intangents circle, 50373), (Kenmotu circle, 50374), (Kenmotu-outer, 50375), (1st Lemoine circle, 1691), (2nd Lemoine circle, 1692), (3rd Lemoine circle, 50376), (Lester circle, 50377), (Longuet-Higgins circle, 50378), (Lucas Circles Radical(+1), 187), (Lucas Circles Radical(-1), 187), (Lucas(+1) inner circle, 187), (Lucas(-1) inner , 187), (Mandart circle, 50379), (mixtilinear circle, 50380), (inner-Montesdeoca-Lemoine circle, 187), (outer-Montesdeoca-Lemoine circle, 187), (Moses circle, 2030), (Moses circles radical circle, 35901), (Moses-Longuet-Higgins circle, 3660), (Moses-parry circle, 50381), (inner-Napoleon circle, 32461), (outer-Napoleon circle, 32460), (1st Neuberg circle, 50382), (Neuberg circles radical circle, 32531), (nine-point circle, 468), (orthocentroidal circle, 468), (orthoptic circle of Steiner inellipse, 468), (Parry circle, 9129), (polar circle, 468), (power circles radical circle (ABC obtuse only), 858), (reflection circle, 50383), (Schoute circle, 6), (sine-triple-angle circle , 50384), (Spieker circle, 50385), (Stammler circles radical circle, 3), (1st Steiner circle, 47090), (2nd Steiner circle, 50386), (Stevanovic circle , 46408), (tangential circle, 468), (Taylor circle, 50387), (inner-Vecten circle, 50388), (outer-Vecten circle, 50389), (Yff contact circle , 50390)

Circles in cursive characters can be consulted in the Alphabetical Index of Terms in ETC. All other circles can be viewed in Wolfram's Triangle Circles.


X(50360) = RADICAL TRACE {CIRCUMCIRCLE, ADAMS CIRCLE}

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

X(50360) lies on these lines: {1, 3}, {2389, 30379}

X(50360) = inverse of X(45227) in: de Longchamps ellipse, incircle
X(50360) = X(37912)-of-intouch triangle
X(50360) = {X(2446), X(2447)}-harmonic conjugate of X(45227)


X(50361) = RADICAL TRACE {CIRCUMCIRCLE, APOLLONIUS CIRCLE}

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

X(50361) lies on these lines: {3, 6}, {230, 517}, {392, 37047}, {512, 650}, {612, 40966}, {625, 5241}, {692, 32758}, {3230, 3291}, {5277, 22076}, {7745, 34466}, {7746, 15488}, {21843, 37521}

X(50361) = midpoint of X(187) and X(5164)
X(50361) = perspector of the circumconic {{A, B, C, X(110), X(941)}}
X(50361) = inverse of X(4263) in: Brocard inellipse, Moses circle
X(50361) = inverse of X(36744) in circumcircle
X(50361) = crossdifference of every pair of points on line {X(523), X(940)}
X(50361) = X(6)-daleth conjugate of-X(4263)
X(50361) = X(6)-Hirst inverse of-X(36744)
X(50361) = X(512)-vertex conjugate of-X(36744)
X(50361) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (187, 1692, 5006), (1379, 1380, 36744), (2028, 2029, 4263)


X(50362) = RADICAL TRACE {CIRCUMCIRCLE, CONWAY CIRCLE}

Barycentrics    a*((b^2+c^2)*a^3-(b^2+c^2)*(b^2-b*c+c^2)*a-(b^2-c^2)*(b-c)*b*c) : :
X(50362) = X(100)-3*X(33852) = 2*X(1155)-3*X(34583)

X(50362) lies on these lines: {1, 3}, {2, 38472}, {11, 511}, {51, 3816}, {100, 33852}, {181, 37634}, {238, 18191}, {320, 350}, {343, 23304}, {404, 22300}, {499, 5752}, {518, 17763}, {674, 26015}, {692, 37449}, {740, 38484}, {858, 21252}, {908, 8679}, {970, 5433}, {1125, 18180}, {1193, 18178}, {1216, 26470}, {1329, 16980}, {1355, 3326}, {1401, 3782}, {1469, 17720}, {1479, 37482}, {1836, 3784}, {1985, 5087}, {2050, 17617}, {2225, 5701}, {2392, 11813}, {2594, 19513}, {2807, 37374}, {2886, 3917}, {2975, 22299}, {2979, 11680}, {3006, 4553}, {3025, 3027}, {3056, 17721}, {3218, 20718}, {3706, 35626}, {3720, 18165}, {3742, 37869}, {3792, 33140}, {3794, 32942}, {3819, 3925}, {3826, 5650}, {3911, 29311}, {3937, 17768}, {4259, 11269}, {4999, 22076}, {5176, 17751}, {5211, 25048}, {5253, 41723}, {5579, 47007}, {7186, 33106}, {7354, 15488}, {7681, 45186}, {7998, 33108}, {11573, 12047}, {13391, 48933}, {14829, 22275}, {15571, 15635}, {15608, 31842}, {15644, 15908}, {16699, 22065}, {19546, 45885}, {20605, 35326}, {21807, 24434}, {21865, 33170}, {22325, 32918}, {23155, 31053}, {23638, 37663}, {24387, 31737}, {24703, 26892}, {29828, 30800}, {35628, 37660}, {40663, 45955}, {41012, 42450}

X(50362) = midpoint of X(i) and X(j) for these {i, j}: {36, 38474}, {18330, 35459}
X(50362) = reflection of X(484) in X(35059)
X(50362) = anticomplement of X(38472)
X(50362) = perspector of the circumconic {{A, B, C, X(274), X(651)}}
X(50362) = inverse of X(1764) in Conway circle
X(50362) = inverse of X(3666) in: de Longchamps ellipse, incircle
X(50362) = inverse of X(16678) in circumcircle
X(50362) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(18155)}} and {{A, B, C, X(55), X(7253)}}
X(50362) = Cevapoint of X(513) and X(2703)
X(50362) = crosssum of X(513) and X(2787)
X(50362) = X(513)-vertex conjugate of-X(16678)
X(50362) = reflection of X(i) in the line X(j)X(k) for these (i, j, k): (11, 512, 4369), (36, 11813, 23789)
X(50362) = X(41202)-of-intouch triangle
X(50362) = X(47153)-of-2nd Conway triangle
X(50362) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (940, 5078, 5061), (1381, 1382, 16678), (2446, 2447, 3666), (14829, 35614, 22275), (35645, 37521, 55)


X(50363) = RADICAL TRACE {CIRCUMCIRCLE, DAO-MOSES-TELV CIRCLE}

Barycentrics    a^2*(a^16-3*(b^2+c^2)*a^14+2*(b^4+5*b^2*c^2+c^4)*a^12+(b^2+c^2)*(b^4-10*b^2*c^2+c^4)*a^10-3*(4*b^4-11*b^2*c^2+4*c^4)*b^2*c^2*a^8-(b^2+c^2)*(b^8+c^8-b^2*c^2*(17*b^4-33*b^2*c^2+17*c^4))*a^6-(b^2-c^2)^2*(2*b^8+2*c^8-b^2*c^2*(5*b^4-27*b^2*c^2+5*c^4))*a^4+3*(b^4-c^4)*(b^2-c^2)*(b^4+c^4+b*c*(b^2-b*c-c^2))*(b^4+c^4-b*c*(b^2+b*c-c^2))*a^2-(b^2-c^2)^4*(b^4+4*b^2*c^2+c^4)*(b^4-b^2*c^2+c^4)) : :

X(50363) lies on these lines: {3, 1637}, {25, 1989}, {125, 15538}, {2492, 35901}, {11063, 47327}, {44467, 46942}

X(50363) = isogonal conjugate of the antigonal conjugate of X(44769)
X(50363) = inverse of X(3) in Dao-Moses-Telv circle
X(50363) = inverse of X(1637) in circumcircle
X(50363) = reflection of X(3) in the line X(6644)X(34218)
X(50363) = inverse of X(35901) in Moses-Parry circle


X(50364) = RADICAL TRACE {CIRCUMCIRCLE, DOU CIRCLES RADICAL CIRCLE}

Barycentrics    a^2*(a^2+b^2-c^2)*(a^2-b^2+c^2)*(a^12-4*(b^2+c^2)*a^10+(7*b^4+11*b^2*c^2+7*c^4)*a^8-(b^2+c^2)*(8*b^4+3*b^2*c^2+8*c^4)*a^6+(7*b^8+7*c^8+(b^4+12*b^2*c^2+c^4)*b^2*c^2)*a^4-(b^2+c^2)*(4*b^8+4*c^8-(7*b^4-10*b^2*c^2+7*c^4)*b^2*c^2)*a^2+(b^8+c^8+2*(b^4-b^2*c^2+c^4)*b^2*c^2)*(b^2-c^2)^2) : :

X(50364) lies on these lines: {3, 2501}, {25, 53}, {112, 12824}, {378, 6792}

X(50364) = isogonal conjugate of the antigonal conjugate of X(4558)
X(50364) = circumperp conjugate of the anticomplement of X(39533)
X(50364) = inverse of X(3) in radical circle of Dou circles
X(50364) = reflection of X(3) in the line X(6644)X(37813)
X(50364) = inverse of X(2501) in circumcircle


X(50365) = RADICAL TRACE {CIRCUMCIRCLE, EULER-GERGONNE-SODDY CIRCLE}

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

X(50365) lies on these lines: {2, 3}, {347, 523}

X(50365) = crossdifference of every pair of points on line {X(647), X(8554)}


X(50366) = RADICAL TRACE {CIRCUMCIRCLE, EXCIRCLES RADICAL CIRCLE}

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

X(50366) lies on these lines: {3, 10}, {35, 46878}, {78, 27379}, {124, 516}, {171, 45206}, {226, 14455}, {243, 281}, {406, 498}, {522, 650}, {929, 5179}, {1155, 26932}, {1465, 25968}, {1861, 44425}, {2222, 26703}, {3011, 4858}, {3452, 4011}, {3579, 20306}, {3911, 26013}, {4640, 41883}, {5552, 10538}, {6051, 13411}, {6181, 46835}, {6690, 6708}, {6718, 34050}, {23528, 27380}, {28826, 32929}, {28923, 29830}, {36002, 45281}

X(50366) = midpoint of X(929) and X(5179)
X(50366) = reflection of X(34050) in X(6718)
X(50366) = complement of the antigonal conjugate of X(5179)
X(50366) = isogonal conjugate of the antigonal conjugate of X(8048)
X(50366) = perspector of the circumconic {{A, B, C, X(8), X(44765)}}
X(50366) = center of the circumconic {{A, B, C, X(929), X(5179)}}
X(50366) = inverse of X(197) in circumcircle
X(50366) = inverse of X(5745) in Spieker circle
X(50366) = Cevapoint of X(522) and X(929)
X(50366) = crossdifference of every pair of points on line {X(56), X(6589)}
X(50366) = crosssum of X(522) and X(928)
X(50366) = X(929)-Ceva conjugate of-X(522)
X(50366) = X(55)-complementary conjugate of-X(20623)
X(50366) = center of circle {{X(101), X(929), X(5179)}}
X(50366) = X(197)-vertex conjugate of-X(522)


X(50367) = RADICAL TRACE {CIRCUMCIRCLE, EXTANGENTS CIRCLE}

Barycentrics    a*(2*a^14+(b+c)*a^13-6*(b^2+c^2)*a^12-(b+c)*(5*b^2+b*c+5*c^2)*a^11+(3*b^4+3*c^4-4*b*c*(b-c)^2)*a^10+2*(b+c)*(4*b^4+4*c^4+b*c*(b^2+4*b*c+c^2))*a^9+(7*b^6+7*c^6+2*b*c*(b^2+b*c+c^2)*(5*b^2-3*b*c+5*c^2))*a^8-2*(b^6+c^6)*(b+c)*a^7-2*(4*b^6+4*c^6-(5*b^4+5*c^4-8*b*c*(b^2-b*c+c^2))*b*c)*(b+c)^2*a^6-(b+c)*(7*b^8+7*c^8+2*b*c*(b^3-b*c^2+c^3)*(b^3-b^2*c+c^3))*a^5-2*(b^2-c^2)^2*(b^4+c^4+b*c*(b^2+4*b*c+c^2))*b*c*a^4+(b^2-c^2)^2*(b+c)*(7*b^6+7*c^6+b*c*(b^2+4*b*c+c^2)*(b^2-b*c+c^2))*a^3+(b^4-c^4)*(b^2-c^2)*(b+c)^2*(3*b^4+3*c^4-4*b*c*(b^2-b*c+c^2))*a^2-2*(b^6-c^6)*(b^2-c^2)^3*(b+c)*a-(b^2-c^2)^4*(b^3-c^3)^2) : :

X(50367) lies on these lines: {3, 3101}


X(50368) = RADICAL TRACE {CIRCUMCIRCLE, FUHRMANN CIRCLE}

Barycentrics    (b+c)*a^6-(b^2+c^2)*a^5-(b^2-c^2)*(b-c)*a^4+(2*b^2+3*b*c+2*c^2)*(b-c)^2*a^3-(b^2-c^2)*(b-c)*(b^2+3*b*c+c^2)*a^2-(b^2-c^2)*(b-c)*(b^3+c^3)*a+(b^3+c^3)*(b^2-c^2)^2 : :
X(50368) = 5*X(1698)-X(3465)

X(50368) lies on these lines: {2, 45272}, {3, 10}, {8, 34030}, {109, 5081}, {117, 517}, {124, 6001}, {240, 522}, {929, 29306}, {1698, 3465}, {1706, 36568}, {1788, 44696}, {3583, 24410}, {6699, 40558}, {6718, 46974}, {6734, 23528}, {7683, 44545}, {8582, 16870}, {10538, 38945}, {12053, 36576}, {18339, 45766}, {18340, 25005}, {20306, 33899}, {23541, 45269}, {24982, 24984}

X(50368) = midpoint of X(i) and X(j) for these {i, j}: {109, 5081}, {10538, 38945}, {18339, 45766}
X(50368) = reflection of X(46974) in X(6718)
X(50368) = complement of X(45272)
X(50368) = perspector of the circumconic {{A, B, C, X(92), X(44765)}}
X(50368) = inverse of X(23843) in circumcircle
X(50368) = Cevapoint of X(522) and X(2765)
X(50368) = crossdifference of every pair of points on line {X(48), X(6589)}
X(50368) = crosssum of X(522) and X(2849)
X(50368) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {4, 18339, 45766}, {109, 1309, 5081}, {10538, 38945, 45272}
X(50368) = X(21268)-of-Wasat triangle
X(50368) = X(5962)-of-4th Euler triangle
X(50368) = X(522)-vertex conjugate of-X(23843)


X(50369) = RADICAL TRACE {CIRCUMCIRCLE, GEOS CIRCLE}

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

X(50369) lies on these lines: {2, 92}, {3, 4885}


X(50370) = RADICAL TRACE {CIRCUMCIRCLE, HALF-MOSES CIRCLE}

Barycentrics    a^2*(13*(b^2+c^2)*a^4-2*(4*b^4+3*b^2*c^2+4*c^4)*a^2+(b^2+c^2)*(3*b^4-8*b^2*c^2+3*c^4)) : :
X(50370) = 3*X(39)+5*X(187) = X(39)-5*X(2021) = X(187)+3*X(2021) = 3*X(2024)+X(5104)

X(50370) lies on these lines: {3, 6}, {538, 32459}, {625, 15491}, {3793, 41672}, {3849, 8358}, {5140, 33885}, {5148, 9331}, {5194, 9336}, {7757, 46453}, {9741, 11055}, {11257, 37689}, {14069, 39266}, {18907, 44562}, {33191, 34229}

X(50370) = X(50370)-of-circumsymmedial triangle
X(50370) = crossdifference of every pair of points on line {X(523), X(8556)}


X(50371) = RADICAL TRACE {CIRCUMCIRCLE, HEXYL CIRCLE}

Barycentrics    a*(2*a^6-3*(b+c)*a^5-(3*b-c)*(b-3*c)*a^4+2*(b+c)*(3*b^2-4*b*c+3*c^2)*a^3-8*(b^2-b*c+c^2)*b*c*a^2-(b^2-c^2)*(b-c)*(3*b^2-2*b*c+3*c^2)*a+(b^2-c^2)^2*(b-c)^2) : :
X(50371) = 3*X(36)-X(5536) = 3*X(36)-5*X(7987) = X(40)-3*X(2077) = 2*X(40)-3*X(13528) = 3*X(165)-X(3245) = 3*X(484)-7*X(16192) = X(1155)+2*X(35459) = 3*X(1319)-4*X(1385) = 2*X(1482)-3*X(5048) = X(1482)+3*X(35000) = X(3218)-3*X(38693) = 3*X(3576)-2*X(5126) = 3*X(3814)-2*X(19925) = 2*X(3911)-3*X(21154) = X(5048)+2*X(35000) = 6*X(5123)-5*X(5818) = 3*X(5183)-8*X(31663) = X(5536)+3*X(5538) = X(5536)-5*X(7987) = 3*X(5538)+5*X(7987)

X(50371) lies on these lines: {1, 3}, {4, 5087}, {8, 6966}, {20, 5057}, {72, 5450}, {78, 12114}, {101, 2182}, {102, 1308}, {104, 518}, {210, 22758}, {214, 516}, {224, 12671}, {376, 28534}, {377, 22835}, {404, 7686}, {515, 5440}, {535, 4297}, {840, 30237}, {908, 2829}, {934, 2745}, {944, 32049}, {946, 11112}, {952, 3689}, {953, 1292}, {960, 6906}, {971, 6326}, {997, 1012}, {1004, 22753}, {1071, 22836}, {1125, 15908}, {1158, 5730}, {1295, 3100}, {1389, 10107}, {1455, 22350}, {1456, 34586}, {1512, 3035}, {1753, 11363}, {1768, 4867}, {1836, 6948}, {1837, 6891}, {1878, 37194}, {2717, 28291}, {2743, 28233}, {2800, 17613}, {3218, 38693}, {3486, 6926}, {3560, 25917}, {3652, 44782}, {3683, 6914}, {3812, 6940}, {3814, 6700}, {3838, 6951}, {3911, 21154}, {3916, 31806}, {3935, 38669}, {3962, 24467}, {4190, 24558}, {4299, 5812}, {4305, 6865}, {4511, 6001}, {4640, 6950}, {4679, 6930}, {4855, 11500}, {4870, 28458}, {4881, 36003}, {5080, 6836}, {5086, 6972}, {5123, 5794}, {5176, 6890}, {5253, 13374}, {5603, 5880}, {5660, 10742}, {5691, 31160}, {5693, 34862}, {5761, 10404}, {5901, 31777}, {6261, 37022}, {6681, 9843}, {6684, 37298}, {6705, 6737}, {6736, 12616}, {6850, 11375}, {6893, 24954}, {6897, 28628}, {6915, 16616}, {6922, 10572}, {6923, 17605}, {6938, 24703}, {6958, 17606}, {6961, 24914}, {6977, 26066}, {7483, 8582}, {7701, 31821}, {8227, 17528}, {9521, 42763}, {9943, 21740}, {11260, 12245}, {11496, 19861}, {11715, 25416}, {11813, 37468}, {12047, 31775}, {12672, 30144}, {12675, 34772}, {12680, 37700}, {12688, 45770}, {13369, 37733}, {14414, 45884}, {15015, 44425}, {16132, 31805}, {17768, 38759}, {18242, 27385}, {20418, 26015}, {34474, 48363}, {34526, 38902}, {35514, 42819}, {41389, 48695}

X(50371) = midpoint of X(i) and X(j) for these {i, j}: {1, 5537}, {3, 35459}, {20, 5057}, {36, 5538}, {1768, 4867}, {2717, 47621}, {3935, 38669}, {4511, 6909}, {10609, 37374}
X(50371) = reflection of X(i) in X(j) for these (i, j): (4, 5087), (1155, 3), (1512, 3035), (5535, 5122), (13528, 2077), (14872, 17615), (22765, 18857), (26015, 20418), (37725, 6745)
X(50371) = isogonal conjugate of the antigonal conjugate of X(3427)
X(50371) = circumperp conjugate of X(55)
X(50371) = Gibert-Burek-Moses concurrent circles image of X(2093)
X(50371) = inverse of X(3428) in circumcircle
X(50371) = inverse of X(6282) in hexyl circle
X(50371) = intersection, other than A, B, C, of circumconics {{A, B, C, X(55), X(2745)}} and {{A, B, C, X(57), X(2716)}}
X(50371) = X(21)-beth conjugate of-X(3660)
X(50371) = X(513)-vertex conjugate of-X(3428)
X(50371) = (2nd circumperp)-isotomic conjugate-of-X(28291)
X(50371) = center of circles {{ X(i), X(j), X(k) }} for these {i, j, k}: {103, 2717, 47621}, {1768, 4867, 34464}, {3935, 38669, 38682}
X(50371) = X(468)-of-hexyl triangle
X(50371) = X(858)-of-2nd circumperp triangle
X(50371) = X(1155)-of-ABC-X3 reflections triangle
X(50371) = X(5087)-of-anti-Euler triangle
X(50371) = X(5537)-of-anti-Aquila triangle
X(50371) = X(10295)-of-1st circumperp triangle
X(50371) = X(10297)-of-excentral triangle
X(50371) = X(18839)-of-2nd circumperp tangential triangle
X(50371) = X(35459)-of-anti-X3-ABC reflections triangle
X(50371) = X(37928)-of-incircle-circles triangle
X(50371) = X(45171)-of-intouch triangle
X(50371) = X(47309)-of-excenters-reflections triangle
X(50371) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 36, 3660), (1, 40293, 37566), (3, 37606, 3576), (78, 12114, 14872), (1155, 2646, 1319), (1155, 5048, 65), (1381, 1382, 3428), (1385, 1482, 20323), (1385, 33596, 37080), (2077, 5537, 10310), (2077, 35459, 14110), (3576, 6282, 3428), (3576, 37569, 999), (5536, 7987, 36), (5538, 7987, 5536), (5603, 6955, 5880), (7957, 37605, 11249), (7987, 37571, 1385), (10269, 37533, 354), (10306, 35000, 5537), (13624, 31793, 11012), (15178, 31798, 11014), (21740, 37403, 9943), (24474, 32612, 32636), (24929, 37606, 2646), (26290, 26291, 1617), (26365, 26366, 10246), (37562, 46920, 11011), (38013, 38014, 1319)


X(50372) = RADICAL TRACE {CIRCUMCIRCLE, INCENTRAL CIRCLE}

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

X(50372) lies on these lines: {3, 2941}, {661, 2605}


X(50373) = RADICAL TRACE {CIRCUMCIRCLE, INTANGENTS CIRCLE}

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

X(50373) lies on these lines: {3, 3100}, {73, 663}


X(50374) = RADICAL TRACE {CIRCUMCIRCLE, KENMOTU CIRCLE}

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

X(50374) lies on these lines: {3, 6}, {590, 32432}, {639, 7749}, {3767, 26441}, {7388, 31481}, {11294, 31411}, {13663, 31173}, {32435, 32491}, {32436, 44647}

X(50374) = reflection of X(50375) in X(32)
X(50374) = isogonal conjugate of the isotomic conjugate of X(44392)
X(50374) = barycentric product X(6)*X(44392)
X(50374) = trilinear product X(31)*X(44392)
X(50374) = perspector of the circumconic {{A, B, C, X(110), X(8577)}}
X(50374) = inverse of X(5062) in: Brocard inellipse, Moses circle
X(50374) = inverse of X(12968) in circumcircle
X(50374) = crossdifference of every pair of points on line {X(492), X(523)}
X(50374) = crosssum of X(6) and X(44391)
X(50374) = X(6)-daleth conjugate of-X(5062)
X(50374) = X(6)-Hirst inverse of-X(12968)
X(50374) = X(512)-vertex conjugate of-X(12968)
X(50374) = X(2459)-of-1st Kenmotu-centers triangle
X(50374) = X(50374)-of-circumsymmedial triangle
X(50374) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 45578, 1505), (32, 1504, 5062), (187, 1570, 6566), (187, 1692, 50375), (371, 41410, 5017), (1379, 1380, 12968), (1691, 2021, 50375), (1691, 2460, 187), (1692, 6566, 5062), (2028, 2029, 5062), (2032, 5162, 50375), (2460, 6424, 1692), (5052, 10631, 50375), (6424, 12963, 32)


X(50375) = RADICAL TRACE {CIRCUMCIRCLE, OUTER-KENMOTU CIRCLE}

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

X(50375) lies on these lines: {3, 6}, {615, 32435}, {640, 7749}, {3767, 8982}, {8996, 44527}, {13783, 31173}, {32432, 32490}, {32433, 44648}

X(50375) = reflection of X(50374) in X(32)
X(50375) = isogonal conjugate of the isotomic conjugate of X(44394)
X(50375) = barycentric product X(6)*X(44394)
X(50375) = trilinear product X(31)*X(44394)
X(50375) = perspector of the circumconic {{A, B, C, X(110), X(8576)}}
X(50375) = inverse of X(5058) in: Brocard inellipse, Moses circle
X(50375) = inverse of X(12963) in circumcircle
X(50375) = crossdifference of every pair of points on line {X(491), X(523)}
X(50375) = crosssum of X(6) and X(44390)
X(50375) = X(6)-daleth conjugate of-X(5058)
X(50375) = X(6)-Hirst inverse of-X(12963)
X(50375) = X(512)-vertex conjugate of-X(12963)
X(50375) = X(2460)-of-2nd Kenmotu-centers triangle
X(50375) = X(50375)-of-circumsymmedial triangle
X(50375) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 45579, 1504), (32, 1505, 5058), (187, 1570, 6567), (187, 1692, 50374), (372, 41411, 5017), (1379, 1380, 12963), (1505, 9675, 35841), (1691, 2021, 50374), (1691, 2459, 187), (1692, 6567, 5058), (2028, 2029, 5058), (2032, 5162, 50374), (2459, 6423, 1692), (5052, 10631, 50374), (6423, 12968, 32), (9675, 39764, 5058)


X(50376) = RADICAL TRACE {CIRCUMCIRCLE, 3rd LEMOINE CIRCLE}

Barycentrics    4*a^18+67*(b^2+c^2)*a^16+2*(67*b^4+583*b^2*c^2+67*c^4)*a^14+2*(b^2+c^2)*(2*b^4+1581*b^2*c^2+2*c^4)*a^12-2*(71*b^8+71*c^8-(1033*b^4+3060*b^2*c^2+1033*c^4)*b^2*c^2)*a^10-5*(b^2+c^2)*(10*b^8+10*c^8+(96*b^4+61*b^2*c^2+96*c^4)*b^2*c^2)*a^8+2*(13*b^12+13*c^12-(14*b^8+14*c^8+(1508*b^4+2557*b^2*c^2+1508*c^4)*b^2*c^2)*b^2*c^2)*a^6-(b^2+c^2)*(20*b^12+20*c^12-(516*b^8+516*c^8+(573*b^4-4138*b^2*c^2+573*c^4)*b^2*c^2)*b^2*c^2)*a^4-2*(b^4-c^4)^2*(11*b^8+11*c^8+(2*b^4-99*b^2*c^2+2*c^4)*b^2*c^2)*a^2-(b^4-4*b^2*c^2+c^4)*(b^2-c^2)^2*(b^2+c^2)^5 : :

X(50376) lies on these lines: {3, 8145}


X(50377) = RADICAL TRACE {CIRCUMCIRCLE, LESTER CIRCLE}

Barycentrics    a^2*(a^16-6*(b^2+c^2)*a^14+(14*b^4+31*b^2*c^2+14*c^4)*a^12-7*(b^2+c^2)*(2*b^4+7*b^2*c^2+2*c^4)*a^10+3*(23*b^4+31*b^2*c^2+23*c^4)*b^2*c^2*a^8+2*(b^2+c^2)*(7*b^8+7*c^8-32*(b^4+c^4)*b^2*c^2)*a^6-(14*b^12+14*c^12-(27*b^8+27*c^8+(21*b^4+25*b^2*c^2+21*c^4)*b^2*c^2)*b^2*c^2)*a^4+3*(b^2+c^2)*(2*b^12+2*c^12-(5*b^8+5*c^8-3*(b^4-b^2*c^2+c^4)*b^2*c^2)*b^2*c^2)*a^2-(b^2-c^2)^4*(b^8+c^8+(3*b^4+b^2*c^2+3*c^4)*b^2*c^2))*(a^2+c*a+c^2-b^2)*(a^2-c*a+c^2-b^2)*(a^2+b*a+b^2-c^2)*(a^2-b*a+b^2-c^2) : :

X(50377) lies on these lines: {3, 1116}, {231, 1989}

X(50377) = isogonal conjugate of the antigonal conjugate of X(10411)
X(50377) = reflection of X(3) in the line X(186)X(8754)
X(50377) = inverse of X(15475) in circumcircle


X(50378) = RADICAL TRACE {CIRCUMCIRCLE, LONGUET-HIGGINS CIRCLE}

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

X(50378) lies on these lines: {3, 962}, {81, 501}, {100, 4966}, {244, 1326}, {659, 3004}, {4860, 17013}, {5536, 16586}

X(50378) = isogonal conjugate of the antigonal conjugate of X(13476)
X(50378) = reflection of X(3) in the line X(4977)X(39210)
X(50378) = inverse of X(1621) in circumcircle


X(50379) = RADICAL TRACE {CIRCUMCIRCLE, MANDART CIRCLE}

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

X(50379) lies on these lines: {3, 960}, {405, 15524}, {521, 3239}, {5087, 44993}, {11375, 37744}

X(50379) = perspector of the circumconic {{A, B, C, X(280), X(46640)}}
X(50379) = crossdifference of every pair of points on line {X(221), X(6588)}


X(50380) = RADICAL TRACE {CIRCUMCIRCLE, MIXTILINEAR CIRCLE}

Barycentrics    a^2*(a^8-(b+c)*a^7-3*(2*b^2-3*b*c+2*c^2)*a^6+(b+c)*(12*b^2-13*b*c+12*c^2)*a^5-3*(b^2+12*b*c+c^2)*(b^2-b*c+c^2)*a^4-(b+c)*(9*b^4+9*c^4-2*b*c*(24*b^2-29*b*c+24*c^2))*a^3+(8*b^6+8*c^6-(15*b^4+15*c^4+2*b*c*(b^2-b*c+c^2))*b*c)*a^2-(b^2-c^2)*(b-c)*(2*b^4+2*c^4-b*c*(b^2-6*b*c+c^2))*a-(b^2-c^2)^2*(b-c)^2*b*c) : :

X(50380) lies on these lines: {3, 8147}


X(50381) = RADICAL TRACE {CIRCUMCIRCLE, MOSES-PARRY CIRCLE}

Barycentrics    a^2*(a^14-3*(b^2+c^2)*a^12-(b^4-16*b^2*c^2+c^4)*a^10+(b^2+c^2)*(5*b^4-18*b^2*c^2+5*c^4)*a^8-(b^8+c^8+b^2*c^2*(12*b^4-35*b^2*c^2+12*c^4))*a^6-(b^2+c^2)*(b^8+c^8-b^2*c^2*(14*b^4-27*b^2*c^2+14*c^4))*a^4+(b^8+c^8-2*b^2*c^2*(b^4+6*b^2*c^2+c^4))*(b^2-c^2)^2*a^2+(b^4-c^4)*(b^2-c^2)*(-b^8-c^8+2*b^2*c^2*(b^4+c^4))) : :
X(50381) = X(1296)-3*X(38699) = X(1297)-3*X(38698) = X(10749)-3*X(38796) = X(10766)-3*X(36696) = 2*X(34841)-3*X(38804)

X(50381) lies on these lines: {3, 2492}, {25, 111}, {126, 6720}, {127, 6719}, {132, 23699}, {1296, 38699}, {1297, 38698}, {2781, 28662}, {2794, 5512}, {2854, 28343}, {9129, 9517}, {10749, 38796}, {10766, 36696}, {15560, 18876}, {16317, 36168}, {16318, 46619}, {33962, 38608}, {34841, 38804}

X(50381) = midpoint of X(111) and X(112)
X(50381) = reflection of X(i) in X(j) for these (i, j): (126, 6720), (127, 6719)
X(50381) = isogonal conjugate of the antigonal conjugate of X(17708)
X(50381) = inverse of X(3) in Moses-Parry circle
X(50381) = inverse of X(2492) in circumcircle
X(50381) = reflection of X(3) in the line X(6644)X(14649)
X(50381) = crossdifference of every pair of points on line {X(14417), X(41359)}


X(50382) = RADICAL TRACE {CIRCUMCIRCLE, 1st NEUBERG CIRCLE}

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

X(50382) lies on these lines: {3, 736}, {669, 7467}


X(50383) = RADICAL TRACE {CIRCUMCIRCLE, REFLECTION CIRCLE}

Barycentrics    a^2*((b^2+c^2)*a^14-(7*b^4+6*b^2*c^2+7*c^4)*a^12+3*(b^2+c^2)*(7*b^4-2*b^2*c^2+7*c^4)*a^10-(35*b^8+35*c^8+b^2*c^2*(13*b^4+12*b^2*c^2+13*c^4))*a^8+(b^2+c^2)*(35*b^8+35*c^8-b^2*c^2*(46*b^4-49*b^2*c^2+46*c^4))*a^6-(b^2-c^2)^2*(21*b^8+21*c^8+2*b^2*c^2*(6*b^4+7*b^2*c^2+6*c^4))*a^4+(b^4-c^4)*(b^2-c^2)*(7*b^8+7*c^8-b^2*c^2*(14*b^4-15*b^2*c^2+14*c^4))*a^2-(b^4+b^2*c^2+c^4)*(b^2-c^2)^6) : :

X(50383) lies on the cubic K418 and these lines: {3, 54}, {1510, 12077}, {6746, 32409}, {12233, 16337}, {12359, 16336}, {19552, 25738}, {32744, 43588}

X(50383) = perspector of the circumconic {{A, B, C, X(3459), X(18315)}}
X(50383) = crossdifference of every pair of points on line {X(195), X(12077)}
X(50383) = X(i)-line conjugate of-X(j) for these (i, j): (3, 195), (54, 195), (97, 195)


X(50384) = RADICAL TRACE {CIRCUMCIRCLE, SINE TRIPLE-ANGLE CIRCLE}

Barycentrics    a^2*(2*a^14-6*(b^2+c^2)*a^12+(5*b^4+14*b^2*c^2+5*c^4)*a^10-9*(b^2+c^2)*b^2*c^2*a^8-4*(b^4-3*b^2*c^2+c^4)*b^2*c^2*a^6-2*(b^4-c^4)*(b^2-c^2)*(b^4-3*b^2*c^2+c^4)*a^4+(b^4-c^4)^2*(b^2-c^2)^2*a^2-(b^4-c^4)*(b^2-c^2)^3*b^2*c^2)*(-a^2+b^2+c^2) : :

X(50384) lies on these lines: {3, 49}

X(50384) = crossdifference of every pair of points on line {X(2501), X(8571)}


X(50385) = RADICAL TRACE {CIRCUMCIRCLE, SPIEKER CIRCLE}

Barycentrics    10*a^6-9*(b+c)*a^5-(5*b-c)*(b-5*c)*a^4+2*(b+c)*(7*b^2-16*b*c+7*c^2)*a^3-8*(b^2+3*b*c+c^2)*(b-c)^2*a^2-(b^2-c^2)*(b-c)*(5*b^2-6*b*c+5*c^2)*a+(3*b^2-2*b*c+3*c^2)*(b^2-c^2)^2 : :

X(50385) lies on these lines: {3, 10}, {522, 2490}, {3731, 5218}, {7288, 8056}

X(50385) = crossdifference of every pair of points on line {X(6589), X(8572)}


X(50386) = RADICAL TRACE {CIRCUMCIRCLE, 2nd STEINER CIRCLE}

Barycentrics    a^2*(a^16-4*(b^2+c^2)*a^14+3*(b^2+2*c^2)*(2*b^2+c^2)*a^12-(4*b^2+c^2)*(b^2+4*c^2)*(b^2+c^2)*a^10+11*(b^4+3*b^2*c^2+c^4)*b^2*c^2*a^8+(b^2+c^2)*(4*b^8+4*c^8-b^2*c^2*(7*b^4+12*b^2*c^2+7*c^4))*a^6-(6*b^12+6*c^12-(6*b^8+6*c^8-b^2*c^2*(3*b^4-19*b^2*c^2+3*c^4))*b^2*c^2)*a^4+(b^2+c^2)*(2*b^6-2*c^6-b^2*c^2*(2*b^2-3*c^2))*(2*b^6-2*c^6-b^2*c^2*(3*b^2-2*c^2))*a^2-(b^6-c^6)*(b^2-c^2)*(b^4+c^4)*(b^4-b^2*c^2+c^4)) : :

X(50386) lies on these lines: {3, 8151}, {23, 325}

X(50386) = inverse of X(11123) in circumcircle
X(50386) = X(468)-of-Steiner triangle


X(50387) = RADICAL TRACE {CIRCUMCIRCLE, TAYLOR CIRCLE}

Barycentrics    a^2*((b^2+c^2)*a^6-(3*b^4-4*b^2*c^2+3*c^4)*a^4+3*(b^4-c^4)*(b^2-c^2)*a^2-(b^4+c^4)*(b^2-c^2)^2) : :
X(50387) = X(187)+3*X(15544)

X(50387) lies on these lines: {3, 6}, {51, 7737}, {113, 36472}, {115, 6000}, {185, 3767}, {230, 13754}, {232, 47421}, {373, 31415}, {460, 512}, {625, 37648}, {974, 15341}, {1299, 2715}, {1506, 11695}, {2713, 41368}, {3054, 10170}, {3124, 3331}, {3291, 45938}, {3815, 5892}, {3917, 21843}, {5254, 40647}, {5286, 10574}, {5305, 13630}, {5462, 7745}, {5475, 5943}, {5477, 8681}, {5663, 43291}, {5890, 7735}, {5891, 37637}, {5907, 7746}, {5946, 18907}, {6688, 7603}, {6759, 44527}, {7736, 15045}, {7747, 10110}, {7748, 46850}, {7749, 11793}, {7755, 13382}, {10575, 44518}, {12162, 13881}, {14855, 44526}, {15028, 31404}, {15030, 43620}, {15072, 43448}, {16310, 25711}, {18424, 46847}, {32125, 35605}, {39565, 44870}

X(50387) = isogonal conjugate of the antigonal conjugate of X(6504)
X(50387) = polar conjugate of the isotomic conjugate of X(47195)
X(50387) = barycentric product X(4)*X(47195)
X(50387) = trilinear product X(19)*X(47195)
X(50387) = perspector of the circumconic {{A, B, C, X(110), X(393)}}
X(50387) = inverse of X(800) in: Brocard inellipse, Moses circle
X(50387) = inverse of X(1609) in circumcircle
X(50387) = Cevapoint of X(512) and X(2713)
X(50387) = crossdifference of every pair of points on line {X(394), X(523)}
X(50387) = crosssum of X(i) and X(j) for these (i, j): {6, 44389}, {512, 2797}
X(50387) = X(6)-daleth conjugate of-X(800)
X(50387) = X(6)-Hirst inverse of-X(1609)
X(50387) = X(512)-vertex conjugate of-X(1609)
X(50387) = X(8074)-of-orthic triangle
X(50387) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1379, 1380, 1609), (2028, 2029, 800)


X(50388) = RADICAL TRACE {CIRCUMCIRCLE, INNER-VECTEN CIRCLE}

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

X(50388) lies on the cubic K038 and these lines: {3, 640}, {6563, 14326}

X(50388) = inverse of X(44199) in circumcircle


X(50389) = RADICAL TRACE {CIRCUMCIRCLE, OUTER-VECTEN CIRCLE}

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

X(50389) lies on the cubic K038 and these lines: {3, 639}, {6563, 14325}

X(50389) = inverse of X(44196) in circumcircle


X(50390) = RADICAL TRACE {CIRCUMCIRCLE, YFF CONTACT CIRCLE}

Barycentrics    2*a^12-6*(b+c)*a^11+(5*b^2+16*b*c+5*c^2)*a^10+(b+c)*(b^2-10*b*c+c^2)*a^9-(b^2+c^2)*(b^2+13*b*c+c^2)*a^8-(b+c)*(5*b^4+5*c^4-22*b*c*(b^2+c^2))*a^7+(4*b^6+4*c^6+(7*b^4+7*c^4-b*c*(43*b^2-6*b*c+43*c^2))*b*c)*a^6+(b+c)*(6*b^6+6*c^6-b*c*(36*b^2-5*b*c+36*c^2)*(b-c)^2)*a^5-(11*b^8+11*c^8-(26*b^6+26*c^6-(10*b^4+10*c^4+b*c*(31*b^2-48*b*c+31*c^2))*b*c)*b*c)*a^4+(b^2-c^2)*(b-c)*(5*b^6+5*c^6-b^2*c^2*(7*b^2-16*b*c+7*c^2))*a^3+(b^8+c^8-(3*b^4+3*c^4+4*b*c*(b^2-b*c+c^2))*(b^2-b*c+c^2)*b*c)*(b-c)^2*a^2-(b^3+c^3)*(b-c)^4*(b^4+c^4+3*b*c*(b^2+c^2))*a+(b^2-c^2)^2*(b-c)^2*b*c*(b^2-b*c+c^2)^2 : :

X(50390) lies on these lines: {3, 5592}, {2183, 3006}


X(50391) = X(2)X(3)∩X(1724)X(49734)

Barycentrics    4*a^4 + 2*a^3*b + a^2*b^2 + 2*a*b^3 - b^4 + 2*a^3*c + 4*a^2*b*c + 4*a*b^2*c + 2*b^3*c + a^2*c^2 + 4*a*b*c^2 + 6*b^2*c^2 + 2*a*c^3 + 2*b*c^3 - c^4 : :
X(50391) = 3 X[2] - 5 X[964], 6 X[2] - 5 X[13728], 9 X[2] - 5 X[17676], 9 X[2] - 10 X[50318], 7 X[2] - 5 X[50321], 3 X[2] + 5 X[50322], 4 X[2] - 5 X[50323], 3 X[964] - X[17676], 3 X[964] - 2 X[50318], 7 X[964] - 3 X[50321], 4 X[964] - 3 X[50323], 3 X[13728] - 2 X[17676], 3 X[13728] - 4 X[50318], 7 X[13728] - 6 X[50321], X[13728] + 2 X[50322], 2 X[13728] - 3 X[50323], 7 X[17676] - 9 X[50321], X[17676] + 3 X[50322], 4 X[17676] - 9 X[50323], 14 X[50318] - 9 X[50321], 2 X[50318] + 3 X[50322], 8 X[50318] - 9 X[50323], 3 X[50321] + 7 X[50322], 4 X[50321] - 7 X[50323], 4 X[50322] + 3 X[50323]

X(50391) lies on these lines: {2, 3}, {1724, 49734}, {3629, 3632}, {5716, 50044}, {9657, 48803}, {18907, 26035}, {18990, 24552}, {28619, 48846}, {48863, 49745}

X(50391) = midpoint of X(964) and X(50322)
X(50391) = reflection of X(i) in X(j) for these {i,j}: {13728, 964}, {17676, 50318}
X(50391) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {964, 13728, 50323}, {964, 17676, 50318}, {2049, 6872, 13745}, {3146, 37037, 50056}, {3627, 50059, 5051}, {4202, 50172, 50240}, {11319, 50171, 8728}, {17676, 50318, 13728}, {17697, 48816, 17529}, {19281, 50168, 30810}


X(50392) = X(658)X(14543)∩X(4573)X(4626)

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

See Ercole Suppa, euclid 5164.

X(50392) lies on these lines: {658,14543}, {4573,4626}

X(50392) = X(i)-isoconjugate of X(j) for these (i,j): (657,3601), (3063,20007), (3601,657), (4130,4252), (4252,4130), (5273,8641)
X(50392) = X(i)-reciprocal conjugate of X(j) for these {i,j}: {658,5273}, {664,20007}, {934,3601}, {4626,3945}, {5665,3900}
X(50392) = barycentric product X(i)*X(j) for these (i,j): (4569,5665), (4626,43533)
X(50392) = barycentric quotient X(i)/X(j) for these {i,j}: {658,5273}, {664,20007}, {934,3601}, {4626,3945}, {5665,3900}
X(50392) = trilinear product X(i)*X(j) for these (i,j): (658,5665), (4617,43533)
X(50392) = trilinear quotient X(i)/X(j) for these (i,j): (658,3601), (4554,20007), (4569,5273), (4617,4252), (5665,657)
X(50392) = trilinear pole of the line: {7, 950}


X(50393) = X(2)X(3)∩X(518)X(3619)

Barycentrics    a^4 - 4*a^2*b^2 + 3*b^4 - 14*a^2*b*c - 14*a*b^2*c - 4*a^2*c^2 - 14*a*b*c^2 - 6*b^2*c^2 + 3*c^4 : :
X(50393) = 6 X[2] + X[377], 9 X[2] - 2 X[405], 15 X[2] - X[6872], 3 X[2] + 4 X[8728], 8 X[2] - X[31156], 12 X[2] - 5 X[31259], 27 X[2] + X[31295], 5 X[2] + 2 X[44217], 11 X[2] - 4 X[50202], 15 X[2] - 8 X[50205], 3 X[2] - 10 X[50207], 9 X[2] + 5 X[50237], 27 X[2] + 8 X[50238], 33 X[2] + 2 X[50239], 45 X[2] + 4 X[50240], 39 X[2] - 4 X[50241], 51 X[2] - 2 X[50242], 57 X[2] - 8 X[50243], 36 X[2] - X[50244], 5 X[3] + 2 X[44286], 3 X[377] + 4 X[405], 5 X[377] + 2 X[6872], X[377] - 8 X[8728], 4 X[377] + 3 X[31156], 2 X[377] + 5 X[31259], 9 X[377] - 2 X[31295], 5 X[377] - 12 X[44217], 11 X[377] + 24 X[50202], 5 X[377] + 16 X[50205], X[377] + 20 X[50207], 3 X[377] - 10 X[50237], 9 X[377] - 16 X[50238], 11 X[377] - 4 X[50239], 15 X[377] - 8 X[50240], 13 X[377] + 8 X[50241], 17 X[377] + 4 X[50242], 19 X[377] + 16 X[50243], 6 X[377] + X[50244], 10 X[405] - 3 X[6872], X[405] + 6 X[8728], 16 X[405] - 9 X[31156], 8 X[405] - 15 X[31259], 6 X[405] + X[31295], 5 X[405] + 9 X[44217], 11 X[405] - 18 X[50202], 5 X[405] - 12 X[50205], X[405] - 15 X[50207], 2 X[405] + 5 X[50237], 3 X[405] + 4 X[50238], 11 X[405] + 3 X[50239], 5 X[405] + 2 X[50240], 13 X[405] - 6 X[50241], 17 X[405] - 3 X[50242], 19 X[405] - 12 X[50243], 8 X[405] - X[50244], 5 X[631] + 2 X[44229], 5 X[1656] + 2 X[44222], 5 X[3091] + 2 X[37426], 8 X[3628] - X[37234], 5 X[5071] + 2 X[44284], X[6872] + 20 X[8728], 8 X[6872] - 15 X[31156], 4 X[6872] - 25 X[31259], 9 X[6872] + 5 X[31295], X[6872] + 6 X[44217], 11 X[6872] - 60 X[50202], X[6872] - 8 X[50205], X[6872] - 50 X[50207], 3 X[6872] + 25 X[50237], 9 X[6872] + 40 X[50238], 11 X[6872] + 10 X[50239], 3 X[6872] + 4 X[50240], 13 X[6872] - 20 X[50241], 17 X[6872] - 10 X[50242], 19 X[6872] - 40 X[50243], 12 X[6872] - 5 X[50244], 32 X[8728] + 3 X[31156], 16 X[8728] + 5 X[31259], 36 X[8728] - X[31295], 10 X[8728] - 3 X[44217], 11 X[8728] + 3 X[50202], 5 X[8728] + 2 X[50205], 2 X[8728] + 5 X[50207], 12 X[8728] - 5 X[50237], 9 X[8728] - 2 X[50238], 22 X[8728] - X[50239], 15 X[8728] - X[50240], 13 X[8728] + X[50241], 34 X[8728] + X[50242], 19 X[8728] + 2 X[50243], and many others

X(50393) lies on these lines: {2, 3}, {518, 3619}, {3193, 25878}, {3306, 3634}, {3434, 41859}, {3824, 31018}, {3871, 40333}, {4855, 19862}, {5435, 10404}, {5714, 35595}, {6734, 20195}, {8164, 46932}, {10584, 34595}, {11523, 41867}, {12620, 26015}, {26131, 37650}

X(50393) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 377, 31259}, {2, 2475, 17552}, {2, 3091, 17534}, {2, 4197, 2478}, {2, 4208, 5047}, {2, 5177, 17536}, {2, 5187, 16853}, {2, 6871, 16842}, {2, 6872, 50205}, {2, 6919, 17546}, {2, 8728, 377}, {2, 17582, 6921}, {2, 37436, 21}, {2, 37462, 6910}, {2, 50237, 405}, {140, 6877, 6860}, {377, 405, 50244}, {377, 31259, 31156}, {405, 8728, 50237}, {405, 44217, 50240}, {405, 50237, 377}, {405, 50238, 31295}, {405, 50240, 6872}, {405, 50244, 31156}, {442, 16853, 5187}, {4197, 17536, 5177}, {4208, 20835, 377}, {5177, 17536, 2478}, {6872, 44217, 377}, {6991, 37407, 10431}, {8728, 37270, 37436}, {8728, 50205, 44217}, {8728, 50207, 2}, {31259, 50244, 405}, {31295, 50237, 50238}, {31295, 50238, 377}, {44217, 50205, 6872}, {50205, 50240, 405}


X(50394) = X(2)X(3)∩X(518)X(3634)

Barycentrics    2*a^4 - 5*a^2*b^2 + 3*b^4 - 16*a^2*b*c - 16*a*b^2*c - 5*a^2*c^2 - 16*a*b*c^2 - 6*b^2*c^2 + 3*c^4 : :
X(50394) = 15 X[2] + X[377], 9 X[2] - X[405], 33 X[2] - X[6872], 3 X[2] + X[8728], 17 X[2] - X[31156], 21 X[2] - 5 X[31259], 63 X[2] + X[31295], 7 X[2] + X[44217], 5 X[2] - X[50202], 3 X[2] + 5 X[50207], 27 X[2] + 5 X[50237], 9 X[2] + X[50238], 39 X[2] + X[50239], 27 X[2] + X[50240], 21 X[2] - X[50241], 57 X[2] - X[50242], 15 X[2] - X[50243], 81 X[2] - X[50244], 3 X[377] + 5 X[405], 11 X[377] + 5 X[6872], X[377] - 5 X[8728], 17 X[377] + 15 X[31156], 7 X[377] + 25 X[31259], 21 X[377] - 5 X[31295], 7 X[377] - 15 X[44217], X[377] + 3 X[50202], X[377] + 5 X[50205], X[377] - 25 X[50207], 9 X[377] - 25 X[50237], 3 X[377] - 5 X[50238], 13 X[377] - 5 X[50239], 9 X[377] - 5 X[50240], 7 X[377] + 5 X[50241], 19 X[377] + 5 X[50242], 27 X[377] + 5 X[50244], 11 X[405] - 3 X[6872], X[405] + 3 X[8728], 17 X[405] - 9 X[31156], 7 X[405] - 15 X[31259], 7 X[405] + X[31295], 7 X[405] + 9 X[44217], 5 X[405] - 9 X[50202], X[405] - 3 X[50205], X[405] + 15 X[50207], 3 X[405] + 5 X[50237], 13 X[405] + 3 X[50239], 3 X[405] + X[50240], 7 X[405] - 3 X[50241], 19 X[405] - 3 X[50242], 5 X[405] - 3 X[50243], 9 X[405] - X[50244], 7 X[3090] + X[37426], 7 X[3526] + X[44229], X[6872] + 11 X[8728], 17 X[6872] - 33 X[31156], 7 X[6872] - 55 X[31259], 21 X[6872] + 11 X[31295], 7 X[6872] + 33 X[44217], 5 X[6872] - 33 X[50202], X[6872] - 11 X[50205], X[6872] + 55 X[50207], 9 X[6872] + 55 X[50237], 3 X[6872] + 11 X[50238], 13 X[6872] + 11 X[50239], 9 X[6872] + 11 X[50240], 7 X[6872] - 11 X[50241], 19 X[6872] - 11 X[50242], 5 X[6872] - 11 X[50243], 27 X[6872] - 11 X[50244], 17 X[8728] + 3 X[31156], 7 X[8728] + 5 X[31259], 21 X[8728] - X[31295], 7 X[8728] - 3 X[44217], 5 X[8728] + 3 X[50202], X[8728] - 5 X[50207], 9 X[8728] - 5 X[50237], 3 X[8728] - X[50238], 13 X[8728] - X[50239], 9 X[8728] - X[50240], 7 X[8728] + X[50241], 19 X[8728] + X[50242], 5 X[8728] + X[50243], 27 X[8728] + X[50244], 7 X[14869] + X[44286], 7 X[15703] + X[44284], 21 X[31156] - 85 X[31259], 63 X[31156] + 17 X[31295], 7 X[31156] + 17 X[44217], 5 X[31156] - 17 X[50202], 3 X[31156] - 17 X[50205], 3 X[31156] + 85 X[50207], and many others

X(50394) lies on these lines: {2, 3}, {518, 3634}, {3579, 38204}, {3646, 38034}, {3824, 6666}, {3826, 8715}, {3925, 15172}, {5534, 38042}, {5709, 38171}, {5791, 20195}, {5812, 38113}, {6147, 41867}, {6260, 38318}, {6668, 6692}, {10404, 31231}, {15171, 41859}, {18139, 49718}, {19872, 41229}, {22793, 38059}, {31420, 38025}, {31446, 38093}

X(50394) = midpoint of X(i) and X(j) for these {i,j}: {377, 50243}, {405, 50238}, {8728, 50205}
X(50394) = complement of X(50205)
X(50394) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4197, 17590}, {2, 6856, 16855}, {2, 6933, 16856}, {2, 8728, 50205}, {2, 16863, 632}, {2, 17529, 6675}, {2, 31254, 17575}, {2, 50207, 8728}, {5, 549, 6851}, {140, 547, 37356}, {377, 50202, 50243}, {405, 8728, 50238}, {405, 31295, 50241}, {405, 44217, 31295}, {405, 50237, 50240}, {632, 6911, 140}, {1656, 6908, 5}, {4208, 16857, 3627}, {6933, 16856, 17527}, {8728, 50202, 377}, {8728, 50240, 50237}, {8728, 50241, 44217}, {17536, 36003, 405}, {31259, 31295, 405}, {31259, 44217, 50241}, {50205, 50238, 405}, {50205, 50243, 50202}, {50237, 50240, 50238}


X(50395) = X(2)X(3)∩X(518)X(3828)

Barycentrics    2*a^4 - 7*a^2*b^2 + 5*b^4 - 24*a^2*b*c - 24*a*b^2*c - 7*a^2*c^2 - 24*a*b*c^2 - 10*b^2*c^2 + 5*c^4 : :
X(50395) = 7 X[2] + X[377], 5 X[2] - X[405], 17 X[2] - X[6872], 9 X[2] - X[31156], 13 X[2] - 5 X[31259], 31 X[2] + X[31295], 3 X[2] + X[44217], X[2] - 5 X[50207], 11 X[2] + 5 X[50237], 4 X[2] + X[50238], 19 X[2] + X[50239], 13 X[2] + X[50240], 11 X[2] - X[50241], 29 X[2] - X[50242], 8 X[2] - X[50243], 41 X[2] - X[50244], 5 X[377] + 7 X[405], 17 X[377] + 7 X[6872], X[377] - 7 X[8728], 9 X[377] + 7 X[31156], 13 X[377] + 35 X[31259], 31 X[377] - 7 X[31295], 3 X[377] - 7 X[44217], 3 X[377] + 7 X[50202], 2 X[377] + 7 X[50205], X[377] + 35 X[50207], 11 X[377] - 35 X[50237], 4 X[377] - 7 X[50238], 19 X[377] - 7 X[50239], 13 X[377] - 7 X[50240], 11 X[377] + 7 X[50241], 29 X[377] + 7 X[50242], 8 X[377] + 7 X[50243], 41 X[377] + 7 X[50244], 17 X[405] - 5 X[6872], X[405] + 5 X[8728], 9 X[405] - 5 X[31156], 13 X[405] - 25 X[31259], 31 X[405] + 5 X[31295], 3 X[405] + 5 X[44217], 3 X[405] - 5 X[50202], 2 X[405] - 5 X[50205], X[405] - 25 X[50207], 11 X[405] + 25 X[50237], 4 X[405] + 5 X[50238], 19 X[405] + 5 X[50239], 13 X[405] + 5 X[50240], 11 X[405] - 5 X[50241], 29 X[405] - 5 X[50242], 8 X[405] - 5 X[50243], 41 X[405] - 5 X[50244], 3 X[3545] + X[37426], 3 X[5054] + X[44229], 3 X[5055] + X[44284], X[6872] + 17 X[8728], and many others

X(50395) lies on these lines: {2, 3}, {518, 3828}, {3017, 17245}, {3058, 41859}, {3634, 34753}, {3925, 15170}, {4973, 5302}, {5325, 24470}, {5550, 18530}, {8583, 38022}, {10156, 10172}, {10171, 33575}, {11544, 41862}, {18527, 19862}, {24789, 50069}, {26446, 38036}

X(50395) = midpoint of X(i) and X(j) for these {i,j}: {2, 8728}, {44217, 50202}
X(50395) = reflection of X(50205) in X(2)
X(50395) = complement of X(50202)
X(50395) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3545, 16853}, {2, 16408, 11539}, {2, 17582, 5054}, {2, 37436, 17561}, {2, 44217, 50202}, {8728, 50202, 44217}, {8728, 50205, 50238}, {8728, 50241, 50237}, {50205, 50238, 50243}


X(50396) = X(2)X(3)∩X(518)X(3919)

Barycentrics    4*a^4 + a^2*b^2 - 5*b^4 + 12*a^2*b*c + 12*a*b^2*c + a^2*c^2 + 12*a*b*c^2 + 10*b^2*c^2 - 5*c^4 : :
X(50396) = X[2] + 3 X[377], 5 X[2] - 3 X[405], 11 X[2] - 3 X[6872], 2 X[2] - 3 X[8728], 7 X[2] - 3 X[31156], 19 X[2] - 15 X[31259], 13 X[2] + 3 X[31295], X[2] - 3 X[44217], 4 X[2] - 3 X[50202], 7 X[2] - 6 X[50205], 13 X[2] - 15 X[50207], 7 X[2] - 15 X[50237], X[2] - 6 X[50238], 7 X[2] + 3 X[50239], 4 X[2] + 3 X[50240], 8 X[2] - 3 X[50241], 17 X[2] - 3 X[50242], 13 X[2] - 6 X[50243], 23 X[2] - 3 X[50244], 5 X[377] + X[405], 11 X[377] + X[6872], 2 X[377] + X[8728], 7 X[377] + X[31156], 19 X[377] + 5 X[31259], 13 X[377] - X[31295], 4 X[377] + X[50202], 7 X[377] + 2 X[50205], 13 X[377] + 5 X[50207], 7 X[377] + 5 X[50237], X[377] + 2 X[50238], 7 X[377] - X[50239], 4 X[377] - X[50240], 8 X[377] + X[50241], 17 X[377] + X[50242], 13 X[377] + 2 X[50243], 23 X[377] + X[50244], 11 X[405] - 5 X[6872], 2 X[405] - 5 X[8728], 7 X[405] - 5 X[31156], 19 X[405] - 25 X[31259], 13 X[405] + 5 X[31295], X[405] - 5 X[44217], 4 X[405] - 5 X[50202], 7 X[405] - 10 X[50205], 13 X[405] - 25 X[50207], 7 X[405] - 25 X[50237], X[405] - 10 X[50238], 7 X[405] + 5 X[50239], 4 X[405] + 5 X[50240], 8 X[405] - 5 X[50241], 17 X[405] - 5 X[50242], 13 X[405] - 10 X[50243], 23 X[405] - 5 X[50244], X[3534] - 3 X[44284], X[3830] - 3 X[44229], and many others

X(50396) lies on these lines: {2, 3}, {495, 49732}, {518, 3919}, {3679, 5586}, {3828, 5302}, {5288, 5434}, {9945, 25525}, {10543, 41862}, {11024, 38074}, {12751, 38202}, {15935, 27186}, {17614, 38022}, {23536, 48820}, {23537, 50069}, {37631, 48847}, {48835, 49730}, {48845, 50226}, {48857, 49743}, {48861, 49744}

X(50396) = midpoint of X(i) and X(j) for these {i,j}: {377, 44217}, {3679, 10404}, {31156, 50239}, {50202, 50240}
X(50396) = reflection of X(i) in X(j) for these {i,j}: {5302, 3828}, {8728, 44217}, {31156, 50205}, {44217, 50238}, {50202, 8728}, {50241, 50202}
X(50396) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3534, 15673}, {2, 11001, 16418}, {2, 11112, 8703}, {2, 15679, 11113}, {2, 16371, 11812}, {2, 17532, 5066}, {2, 17579, 17525}, {2, 37299, 15675}, {377, 8728, 50240}, {377, 50237, 50239}, {377, 50238, 8728}, {8728, 50240, 50241}, {11113, 15679, 33699}, {17525, 17579, 19710}, {17561, 37435, 15681}, {17679, 50169, 48815}, {31295, 50207, 50243}, {50205, 50237, 8728}, {50237, 50239, 50205}


X(50397) = X(2)X(3)∩X(518)X(4677)

Barycentrics    5*a^4 - a^2*b^2 - 4*b^4 + 6*a^2*b*c + 6*a*b^2*c - a^2*c^2 + 6*a*b*c^2 + 8*b^2*c^2 - 4*c^4 : :
X(50397) = X[2] - 3 X[377], 4 X[2] - 3 X[405], 7 X[2] - 3 X[6872], 5 X[2] - 6 X[8728], 5 X[2] - 3 X[31156], 17 X[2] - 15 X[31259], 5 X[2] + 3 X[31295], 2 X[2] - 3 X[44217], 7 X[2] - 6 X[50202], 13 X[2] - 12 X[50205], 14 X[2] - 15 X[50207], 11 X[2] - 15 X[50237], 7 X[2] - 12 X[50238], 2 X[2] + 3 X[50239], X[2] + 6 X[50240], 11 X[2] - 6 X[50241], 10 X[2] - 3 X[50242], 19 X[2] - 12 X[50243], 13 X[2] - 3 X[50244], 4 X[377] - X[405], 7 X[377] - X[6872], 5 X[377] - 2 X[8728], 5 X[377] - X[31156], 17 X[377] - 5 X[31259], 5 X[377] + X[31295], 7 X[377] - 2 X[50202], 13 X[377] - 4 X[50205], 14 X[377] - 5 X[50207], 11 X[377] - 5 X[50237], 7 X[377] - 4 X[50238], 2 X[377] + X[50239], X[377] + 2 X[50240], 11 X[377] - 2 X[50241], 10 X[377] - X[50242], 19 X[377] - 4 X[50243], 13 X[377] - X[50244], 7 X[405] - 4 X[6872], 5 X[405] - 8 X[8728], 5 X[405] - 4 X[31156], 17 X[405] - 20 X[31259], 5 X[405] + 4 X[31295], 7 X[405] - 8 X[50202], 13 X[405] - 16 X[50205], 7 X[405] - 10 X[50207], 11 X[405] - 20 X[50237], 7 X[405] - 16 X[50238], X[405] + 2 X[50239], X[405] + 8 X[50240], 11 X[405] - 8 X[50241], 5 X[405] - 2 X[50242], 19 X[405] - 16 X[50243], 13 X[405] - 4 X[50244], 2 X[3534] - 3 X[37426], 2 X[3845] - 3 X[44229], 5 X[6872] - 14 X[8728], 5 X[6872] - 7 X[31156], 17 X[6872] - 35 X[31259], 5 X[6872] + 7 X[31295], 2 X[6872] - 7 X[44217], 13 X[6872] - 28 X[50205], 2 X[6872] - 5 X[50207], 11 X[6872] - 35 X[50237], X[6872] - 4 X[50238], 2 X[6872] + 7 X[50239], X[6872] + 14 X[50240], 11 X[6872] - 14 X[50241], 10 X[6872] - 7 X[50242], 19 X[6872] - 28 X[50243], 13 X[6872] - 7 X[50244], 2 X[8703] - 3 X[44284], 34 X[8728] - 25 X[31259], 2 X[8728] + X[31295], 4 X[8728] - 5 X[44217], 7 X[8728] - 5 X[50202], 13 X[8728] - 10 X[50205], 28 X[8728] - 25 X[50207], 22 X[8728] - 25 X[50237], 7 X[8728] - 10 X[50238], 4 X[8728] + 5 X[50239], X[8728] + 5 X[50240], 11 X[8728] - 5 X[50241], 4 X[8728] - X[50242], 19 X[8728] - 10 X[50243], 26 X[8728] - 5 X[50244], 2 X[12100] - 3 X[44222], 2 X[15673] - 3 X[44256], 5 X[19709] - 3 X[37234], 17 X[31156] - 25 X[31259], 2 X[31156] - 5 X[44217], and many others

X(50397) lies on these lines: {2, 3}, {518, 4677}, {519, 10404}, {553, 3419}, {1478, 49732}, {3695, 50045}, {4968, 48800}, {5250, 28202}, {5275, 11648}, {5300, 48804}, {5302, 19875}, {5687, 11237}, {7270, 50041}, {9776, 12690}, {11057, 16992}, {17000, 19569}, {17614, 38021}, {19701, 48836}, {19860, 28208}, {23536, 48824}, {23537, 50070}, {25055, 34706}, {31159, 40726}, {37631, 48837}, {48842, 49744}, {48857, 49745}

X(50397) = midpoint of X(i) and X(j) for these {i,j}: {31156, 31295}, {44217, 50239}
X(50397) = reflection of X(i) in X(j) for these {i,j}: {405, 44217}, {6872, 50202}, {31156, 8728}, {44217, 377}, {50202, 50238}, {50242, 31156}
X(50397) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3534, 16370}, {2, 3845, 17556}, {2, 11001, 17525}, {2, 13587, 15701}, {2, 15678, 16418}, {2, 15679, 3830}, {2, 15682, 11113}, {2, 17577, 19709}, {2, 17579, 3534}, {2, 19708, 37298}, {2, 41106, 17533}, {377, 6872, 50238}, {377, 31295, 8728}, {377, 50239, 405}, {377, 50240, 50239}, {1657, 4197, 19526}, {3534, 17528, 2}, {4208, 15683, 17561}, {6872, 50207, 405}, {6872, 50238, 50207}, {8728, 31295, 50242}, {8728, 50242, 405}, {10109, 17564, 2}, {11112, 17532, 16371}, {15685, 16418, 15678}, {16417, 19709, 2}, {16418, 37285, 16370}, {17528, 17579, 16370}, {17679, 50172, 11354}, {50239, 50242, 31295}


X(50398) = X(2)X(3)∩X(518)X(3622)

Barycentrics    5*a^4 - 6*a^2*b^2 + b^4 - 14*a^2*b*c - 14*a*b^2*c - 6*a^2*c^2 - 14*a*b*c^2 - 2*b^2*c^2 + c^4 : :
X(50398) = 9 X[2] - 2 X[377], 3 X[2] + 4 X[405], 6 X[2] + X[6872], 15 X[2] - 8 X[8728], 5 X[2] + 2 X[31156], 3 X[2] - 10 X[31259], 15 X[2] - X[31295], 11 X[2] - 4 X[44217], X[2] - 8 X[50202], 9 X[2] - 16 X[50205], 27 X[2] - 20 X[50207], 12 X[2] - 5 X[50237], 51 X[2] - 16 X[50238], 39 X[2] - 4 X[50239], 57 X[2] - 8 X[50240], 27 X[2] + 8 X[50241], 45 X[2] + 4 X[50242], 33 X[2] + 16 X[50243], 33 X[2] + 2 X[50244], X[377] + 6 X[405], 4 X[377] + 3 X[6872], 5 X[377] - 12 X[8728], 5 X[377] + 9 X[31156], X[377] - 15 X[31259], 10 X[377] - 3 X[31295], 11 X[377] - 18 X[44217], X[377] - 36 X[50202], X[377] - 8 X[50205], 3 X[377] - 10 X[50207], 8 X[377] - 15 X[50237], 17 X[377] - 24 X[50238], 13 X[377] - 6 X[50239], 19 X[377] - 12 X[50240], 3 X[377] + 4 X[50241], 5 X[377] + 2 X[50242], 11 X[377] + 24 X[50243], 11 X[377] + 3 X[50244], 8 X[405] - X[6872], 5 X[405] + 2 X[8728], 10 X[405] - 3 X[31156], 2 X[405] + 5 X[31259], 20 X[405] + X[31295], 11 X[405] + 3 X[44217], X[405] + 6 X[50202], 3 X[405] + 4 X[50205], 9 X[405] + 5 X[50207], 16 X[405] + 5 X[50237], 17 X[405] + 4 X[50238], 13 X[405] + X[50239], 19 X[405] + 2 X[50240], and many others

X(50398) lies on these lines: {2, 3}, {518, 3622}, {1125, 31018}, {3616, 27065}, {3935, 12521}, {4423, 10586}, {5251, 20076}, {5260, 10587}, {5265, 10404}, {5281, 46932}, {5284, 10529}, {5302, 46934}, {5550, 31053}, {5703, 35595}, {18230, 34772}, {19855, 20075}, {19861, 38059}, {20066, 40333}

X(50398) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 405, 6872}, {2, 5129, 5187}, {2, 6872, 50237}, {2, 15676, 3523}, {2, 15680, 37436}, {2, 16865, 4190}, {2, 17544, 452}, {2, 31295, 8728}, {21, 17552, 2}, {377, 31156, 50242}, {377, 31259, 50205}, {377, 50205, 2}, {377, 50242, 31295}, {405, 8728, 31156}, {405, 31259, 2}, {405, 44217, 50243}, {405, 50202, 31259}, {405, 50204, 21}, {405, 50205, 377}, {405, 50207, 50241}, {631, 17534, 2}, {5047, 16845, 2}, {6832, 6992, 6870}, {6857, 17536, 2}, {6910, 16842, 2}, {6921, 16853, 2}, {8728, 31156, 31295}, {8728, 50242, 377}, {15670, 16853, 6921}, {16418, 17590, 37462}, {17526, 37035, 2}, {17546, 17567, 2}, {17590, 37462, 2}, {31156, 31295, 6872}, {36003, 50203, 17572}, {44217, 50243, 50244}, {50205, 50241, 50207}, {50207, 50241, 377}


X(50399) = X(2)X(3)∩X(518)X(938)

Barycentrics    a^7 - a^6*b - a^5*b^2 + a^4*b^3 - a^3*b^4 + a^2*b^5 + a*b^6 - b^7 - a^6*c - 4*a^5*b*c - a^4*b^2*c + 4*a^3*b^3*c + a^2*b^4*c + b^6*c - a^5*c^2 - a^4*b*c^2 + 18*a^3*b^2*c^2 + 14*a^2*b^3*c^2 - a*b^4*c^2 + 3*b^5*c^2 + a^4*c^3 + 4*a^3*b*c^3 + 14*a^2*b^2*c^3 - 3*b^4*c^3 - a^3*c^4 + a^2*b*c^4 - a*b^2*c^4 - 3*b^3*c^4 + a^2*c^5 + 3*b^2*c^5 + a*c^6 + b*c^6 - c^7 : :

X(50399) lies on these lines: {2, 3}, {497, 25917}, {518, 938}, {1058, 20007}, {1210, 18250}, {1445, 12572}, {3434, 31435}, {3436, 21620}, {3646, 48482}, {4321, 5290}, {5302, 5704}, {5703, 25681}, {6735, 7160}, {12649, 34790}, {18228, 45120}, {26127, 27383}

X(50399) = anticomplement of X(50203)
X(50399) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 452, 6986}, {2, 2478, 6836}, {2, 6872, 37282}, {2, 6894, 443}, {2, 6919, 6828}, {2, 20846, 6921}, {4, 5084, 5129}, {4, 8728, 377}, {4, 37108, 6925}, {405, 50206, 2}, {3149, 17527, 2}, {4187, 16293, 2}, {5046, 37161, 4}, {6864, 17559, 2}, {14022, 19520, 6837}


X(50400) = X(2)X(3)∩X(518)X(1999)

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

X(50400) lies on these lines: {2, 3}, {63, 20171}, {238, 3914}, {518, 1999}, {572, 17182}, {1089, 11679}, {1746, 17185}, {2278, 31631}, {5135, 24703}, {5271, 17755}, {5745, 21065}, {5928, 27184}, {27064, 41260}

X(50400) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7560, 11329}, {1889, 16353, 377}


X(50401) = X(2)X(3)∩X(74)X(512)

Barycentrics    a^2*(a^14*b^2 - 4*a^12*b^4 + 5*a^10*b^6 - 5*a^6*b^10 + 4*a^4*b^12 - a^2*b^14 + a^14*c^2 + a^10*b^4*c^2 - 7*a^8*b^6*c^2 + 3*a^6*b^8*c^2 + 2*a^4*b^10*c^2 + 3*a^2*b^12*c^2 - 3*b^14*c^2 - 4*a^12*c^4 + a^10*b^2*c^4 + 6*a^8*b^4*c^4 + 3*a^6*b^6*c^4 - 3*a^4*b^8*c^4 - 12*a^2*b^10*c^4 + 9*b^12*c^4 + 5*a^10*c^6 - 7*a^8*b^2*c^6 + 3*a^6*b^4*c^6 - 6*a^4*b^6*c^6 + 10*a^2*b^8*c^6 - 9*b^10*c^6 + 3*a^6*b^2*c^8 - 3*a^4*b^4*c^8 + 10*a^2*b^6*c^8 + 6*b^8*c^8 - 5*a^6*c^10 + 2*a^4*b^2*c^10 - 12*a^2*b^4*c^10 - 9*b^6*c^10 + 4*a^4*c^12 + 3*a^2*b^2*c^12 + 9*b^4*c^12 - a^2*c^14 - 3*b^2*c^14) : :
X(50401) = 3 X[186] - 2 X[237], 5 X[37952] - 4 X[44221], 3 X[38704] - 2 X[47079]

X(50401 )lies on these lines: {2, 3}, {74, 512}, {98, 477}, {111, 841}, {1294, 40118}, {1297, 32710}, {1300, 2697}, {2493, 47414}, {2693, 3563}, {2770, 43660}, {6000, 47213}, {9181, 43576}, {14979, 29011}, {34175, 40079}, {38704, 47079}, {39201, 47003}, {44468, 47427}

X(50401) = reflection of X(i) in X(j) for these {i,j}: {4, 36189}, {7464, 47620}, {7468, 3}
X(50401) = circumcircle-inverse of X(7422)
X(50401) = orthoptic-circle-of-Steiner-inellipse-inverse of X(3134)
X(50401) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 186, 37937}, {1113, 1114, 7422}, {5000, 5001, 7480}, {5002, 5003, 40049}, {5004, 5005, 7471}, {7418, 46585, 7422}, {36164, 36166, 7422}, {40894, 40895, 7482}, {42789, 42790, 7473}


X(50402) = X(2)X(3)∩X(105)X(477)

Barycentrics    a*(a^13*b - a^12*b^2 - 3*a^11*b^3 + 3*a^10*b^4 + 2*a^9*b^5 - 2*a^8*b^6 + 2*a^7*b^7 - 2*a^6*b^8 - 3*a^5*b^9 + 3*a^4*b^10 + a^3*b^11 - a^2*b^12 + a^13*c - 2*a^9*b^4*c - 2*a^7*b^6*c + 3*a^5*b^8*c + 2*a^3*b^10*c - 2*a*b^12*c - a^12*c^2 + 3*a^9*b^3*c^2 - a^8*b^4*c^2 - 2*a^7*b^5*c^2 + 4*a^6*b^6*c^2 - 2*a^5*b^7*c^2 - a^4*b^8*c^2 - 2*a^3*b^9*c^2 + 3*a*b^11*c^2 - b^12*c^2 - 3*a^11*c^3 + 3*a^9*b^2*c^3 + a^7*b^4*c^3 + a^5*b^6*c^3 - 6*a^3*b^8*c^3 + 4*a*b^10*c^3 + 3*a^10*c^4 - 2*a^9*b*c^4 - a^8*b^2*c^4 + a^7*b^3*c^4 - 2*a^6*b^4*c^4 + a^5*b^5*c^4 - 2*a^4*b^6*c^4 + 7*a^3*b^7*c^4 - a^2*b^8*c^4 - 7*a*b^9*c^4 + 3*b^10*c^4 + 2*a^9*c^5 - 2*a^7*b^2*c^5 + a^5*b^4*c^5 - 2*a^3*b^6*c^5 - 3*a*b^8*c^5 - 2*a^8*c^6 - 2*a^7*b*c^6 + 4*a^6*b^2*c^6 + a^5*b^3*c^6 - 2*a^4*b^4*c^6 - 2*a^3*b^5*c^6 + 4*a^2*b^6*c^6 + 5*a*b^7*c^6 - 2*b^8*c^6 + 2*a^7*c^7 - 2*a^5*b^2*c^7 + 7*a^3*b^4*c^7 + 5*a*b^6*c^7 - 2*a^6*c^8 + 3*a^5*b*c^8 - a^4*b^2*c^8 - 6*a^3*b^3*c^8 - a^2*b^4*c^8 - 3*a*b^5*c^8 - 2*b^6*c^8 - 3*a^5*c^9 - 2*a^3*b^2*c^9 - 7*a*b^4*c^9 + 3*a^4*c^10 + 2*a^3*b*c^10 + 4*a*b^3*c^10 + 3*b^4*c^10 + a^3*c^11 + 3*a*b^2*c^11 - a^2*c^12 - 2*a*b*c^12 - b^2*c^12) :
: Barycentrics    a*((b+c)*a^13-(b^2+c^2)*a^12-3*(b^3+c^3)*a^11+3*(b^4+c^4)*a^10+(b+c)*(2*b^4+2*c^4-b*c*(4*b^2-7*b*c+4*c^2))*a^9-(b^2+c^2)*(2*b^4-b^2*c^2+2*c^4)*a^8+(b+c)*(2*b^6+2*c^6-(4*b^4+4*c^4-b*c*(2*b^2-b*c+2*c^2))*b*c)*a^7-2*(b^8+c^8-b^2*c^2*(2*b^4-b^2*c^2+2*c^4))*a^6-(b^3+c^3)*(b-c)^2*(3*b^4+3*c^4+b*c*(3*b^2+5*b*c+3*c^2))*a^5+(b^4-c^4)*(b^2-c^2)*(3*b^4+2*b^2*c^2+3*c^4)*a^4+(b^2-c^2)*(b-c)*(b^8+c^8+(b^2+c^2)*(3*b^4+3*c^4+b*c*(2*b-c)*(b-2*c))*b*c)*a^3-(b^8+c^8+2*b^2*c^2*(b^2+c^2)^2)*(b^2-c^2)^2*a^2-(b^3-c^3)*b*c*(b^2-c^2)^3*(2*b^2-3*b*c+2*c^2)*a-(b^4-c^4)*(b^2-c^2)^3*b^2*c^2) : :

X(50402) lies on these lines: {2, 3}, {74, 2752}, {98, 2687}, {104, 842}, {105, 477}, {841, 9061}, {915, 2697}, {1295, 40118}, {2693, 15344}, {2694, 3563}, {26703, 32710}

X(50402) = reflection of X(i) in X(j) for these {i,j}: {4, 37986}, {7475, 3}
X(50402) = circumcircle-inverse of X(7425)
X(50402) = orthoptic-circle-of-Steiner-inellipe-inverse of X(3139)
X(50402) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 186, 37965}, {1113, 1114, 7425}, {5000, 5001, 37966}, {5004, 5005, 7477}, {7418, 14127, 7425}, {7422, 7427, 7425}, {7423, 7429, 7425}, {36166, 46618, 7425}, {42789, 42790, 7476}, {46585, 46586, 7425}


X(50403) = X(2)X(3)∩X(109)X(476)

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

X(50403) lies on these lines: {2, 3}, {109, 476}, {110, 522}, {523, 14544}, {691, 9056}, {1291, 26709}, {1304, 41906}, {3233, 7253}, {10420, 26704}

X(50403) = circumcircle-inverse of X(7450)
X(50403) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1113, 1114, 7450}, {7471, 7477, 7479}


X(50404) = X(2)X(3)∩X(7)X(109)

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

X(50404) lies on these lines: {2, 3}, {7, 109}, {63, 17165}, {100, 27514}, {103, 9056}, {595, 4295}, {1071, 39572}, {3011, 4292}, {3060, 19742}, {3796, 19684}, {3868, 20045}, {4304, 29639}, {5012, 19717}, {5208, 37639}, {5249, 26230}, {5273, 33166}, {5278, 33586}, {8822, 37670}, {9085, 41906}, {9965, 26245}, {10444, 35258}, {14544, 18161}, {15080, 19740}, {16992, 42697}, {20347, 26236}, {24553, 35260}, {25000, 32269}, {29828, 31424}

X(50404) = anticomplement of X(37330)
X(50404) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 23, 36007}, {468, 37050, 2}, {4224, 7413, 2}, {5004, 5005, 7420}, {7465, 7474, 2}, {21554, 33849, 2}


X(50405) = X(308)X(393)∩X(10002)X(10548)

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

See Antreas Hatzipolakis and Ercole Suppa, euclid 5167.

X(50405) lies on these lines: {308,393}, {10002,10548}


X(50406) = X(264)X(9465)∩X(308)X(393)

Barycentrics    (a^2+b^2) (a^2+b^2-c^2) (a^2+c^2) (a^2-b^2+c^2) (a^4 b^2-b^6+a^4 c^2-4 a^2 b^2 c^2+5 b^4 c^2+5 b^2 c^4-c^6) : :
Barycentrics    SB SC (SB+SW) (SC+SW) (4 S^2 (3 R^2-SW)-SA (3 SA-SW) SW) : :

See Antreas Hatzipolakis and Ercole Suppa, euclid 5167.

X(50406) lies on these lines: {2,21459}, {69,10549}, {83,40138}, {193,10550}, {264,9465}, {308,393}, {1249,18092}, {9308,17500}, {16890,32000}, {32085,43981}


X(50407) = X(2)X(3)∩X(10)X(48870)

Barycentrics    5*a^4 + 6*a^3*b + 8*a^2*b^2 + 6*a*b^3 - b^4 + 6*a^3*c + 18*a^2*b*c + 18*a*b^2*c + 6*b^3*c + 8*a^2*c^2 + 18*a*b*c^2 + 14*b^2*c^2 + 6*a*c^3 + 6*b*c^3 - c^4 : :
X(50407) = 4 X[2049] - X[13725]

X(50407) lies on thesse lines: {2, 3}, {10, 48870}, {69, 49744}, {345, 50053}, {1992, 3679}, {17303, 50051}, {17321, 50066}, {19701, 49739}, {19766, 48842}, {28606, 50045}, {30699, 50069}, {31993, 50070}, {43531, 48857}, {48869, 50291}

X(50407) = reflection of X(i) in X(j) for these {i,j}: {2, 2049}, {13725, 2}
X(50407) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4195, 17561}, {2, 10304, 19270}, {2, 50171, 48813}, {964, 37153, 13742}, {16903, 33251, 2}, {19277, 37150, 2}, {44217, 50323, 2}, {50169, 50323, 44217}


X(50408) = X(2)X(3)∩X(8)X(193)

Barycentrics    3*a^4 + 2*a^3*b + 2*a^2*b^2 + 2*a*b^3 - b^4 + 2*a^3*c + 6*a^2*b*c + 6*a*b^2*c + 2*b^3*c + 2*a^2*c^2 + 6*a*b*c^2 + 6*b^2*c^2 + 2*a*c^3 + 2*b*c^3 - c^4 : :
X(50408) = 3 X[2] - 4 X[2049]

X(50408) lies on thesse lines: {1, 30699}, {2, 3}, {6, 49734}, {8, 193}, {10, 1707}, {69, 49745}, {75, 5716}, {145, 3902}, {314, 3945}, {321, 20009}, {345, 50054}, {388, 5263}, {391, 4274}, {950, 10436}, {1043, 5712}, {1220, 2550}, {2292, 24280}, {2345, 7270}, {2899, 5268}, {3600, 10475}, {3616, 23536}, {3617, 5300}, {3622, 33155}, {3757, 4339}, {4299, 19863}, {4300, 19860}, {4340, 10449}, {4357, 9579}, {5016, 19822}, {5250, 12717}, {5266, 26245}, {5698, 31359}, {5731, 35635}, {5836, 37516}, {5921, 46483}, {9710, 48832}, {10454, 10455}, {11160, 50234}, {11518, 50116}, {14534, 37666}, {14552, 20077}, {17140, 36579}, {17303, 50050}, {17321, 50065}, {19684, 19783}, {19766, 43531}, {20880, 44735}, {25242, 31087}, {28620, 48841}, {32815, 50175}, {34258, 45784}, {37549, 42697}

X(50408) = reflection of X(13725) in X(2049)
X(50408) = anticomplement of X(13725)
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3146, 26117}, {2, 3522, 19278}, {2, 4190, 37339}, {2, 6872, 13736}, {2, 31295, 17676}, {2, 33244, 17689}, {2, 37435, 4201}, {2, 50322, 6872}, {4, 1010, 2}, {377, 964, 2}, {377, 37314, 17680}, {382, 19277, 4205}, {405, 37153, 2}, {405, 37425, 37175}, {405, 50169, 37153}, {405, 50391, 48817}, {442, 16394, 37176}, {442, 37176, 2}, {443, 13740, 2}, {964, 17686, 17697}, {964, 50171, 377}, {2049, 13725, 2}, {2475, 6872, 6994}, {2478, 16454, 2}, {4195, 26051, 2}, {4197, 17526, 2}, {5192, 37462, 2}, {8728, 11354, 13742}, {8728, 13742, 2}, {11103, 37155, 4194}, {11114, 14005, 37314}, {13728, 50239, 48813}, {13740, 48816, 443}, {13741, 17582, 2}, {14005, 37314, 2}, {16062, 37037, 2}, {17676, 50172, 31295}, {17688, 33028, 2}, {24570, 47510, 2}, {25519, 37154, 2}, {33026, 33821, 2}, {37153, 48817, 405}, {43531, 48837, 19766}, {48817, 50169, 2}, {50169, 50391, 405}, {50240, 50318, 11359}


X(50409) = X(2)X(3)∩X(10)X(48847)

Barycentrics    4*a^3*b + 7*a^2*b^2 + 4*a*b^3 + b^4 + 4*a^3*c + 12*a^2*b*c + 12*a*b^2*c + 4*b^3*c + 7*a^2*c^2 + 12*a*b*c^2 + 6*b^2*c^2 + 4*a*c^3 + 4*b*c^3 + c^4 : :
X(50409) = 3 X[2] + X[13725]

X(50409) lies on these lines: {2, 3}, {10, 48847}, {58, 17398}, {141, 1125}, {386, 1213}, {496, 19863}, {1353, 25898}, {1698, 37715}, {3295, 19866}, {3624, 37554}, {3634, 48843}, {3666, 19857}, {3828, 48845}, {3846, 19862}, {4026, 19858}, {4260, 5044}, {4357, 6147}, {5224, 41014}, {5263, 10386}, {5550, 18139}, {5750, 31445}, {8040, 14815}, {10436, 24470}, {11246, 41812}, {17325, 24159}, {17392, 28620}, {17717, 34595}, {19684, 49716}, {19701, 49743}, {19856, 37573}, {25512, 37609}, {28606, 50042}, {31993, 50067}, {43531, 49728}, {48861, 49730}

X(50409) = midpoint of X(2049) and X(13725)
X(50409) = complement of X(2049)
X(50409) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 405, 50318}, {2, 443, 16456}, {2, 3552, 16899}, {2, 4201, 14007}, {2, 4205, 5}, {2, 11110, 17698}, {2, 13725, 2049}, {2, 13728, 8728}, {2, 16343, 6675}, {2, 16844, 50205}, {2, 16904, 7770}, {2, 19273, 140}, {2, 26117, 19280}, {2, 37039, 4205}, {3, 16846, 16848}, {405, 19266, 48930}, {964, 13745, 50241}, {4026, 19858, 31419}, {7824, 16902, 2}, {8728, 13728, 48815}, {11354, 13736, 50243}, {11359, 37153, 50238}, {17676, 50169, 50240}, {19280, 26117, 37150}, {26117, 37150, 3627}


X(50410) = X(2)X(3)∩X(551)X(599)

Barycentrics    a^4 - 6*a^3*b - 11*a^2*b^2 - 6*a*b^3 - 2*b^4 - 6*a^3*c - 18*a^2*b*c - 18*a*b^2*c - 6*b^3*c - 11*a^2*c^2 - 18*a*b*c^2 - 8*b^2*c^2 - 6*a*c^3 - 6*b*c^3 - 2*c^4 : :
X(50410) = X[2049] + 2 X[13725]

X(50410) lies on these lines: {2, 3}, {6, 49729}, {10, 48842}, {551, 599}, {3017, 5737}, {3679, 17592}, {3940, 17248}, {4653, 17327}, {10385, 19866}, {11238, 19863}, {17251, 50174}, {17303, 50053}, {17321, 50069}, {19684, 50215}, {19701, 49744}, {19722, 49723}, {19744, 48843}, {19766, 48861}, {19783, 49718}, {25498, 37817}, {28606, 50041}, {31993, 50066}, {48857, 49730}, {48870, 49728}

X(50410) = midpoint of X(2) and X(13725)
X(50410) = reflection of X(2049) in X(2)
X(50410) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13745, 11354}, {2, 17561, 17698}, {2, 19270, 5054}, {2, 31156, 50323}, {2, 33187, 16903}, {2, 37038, 19277}, {2, 50321, 44217}, {13745, 50323, 31156}, {31156, 50323, 11354}, {44217, 50321, 11359}


X(50411) = X(2)X(3)∩X(239)X(1738)

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

X(50411) lies on these lines: {2, 3}, {239, 1738}, {1654, 34283}, {1999, 23536}, {4440, 20432}, {6002, 25008}, {20533, 27272}, {20880, 26840}, {23537, 41251}, {24726, 41874}, {26035, 26044}, {26048, 26073}, {34284, 37653}

X(50411) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {379, 33840, 2}, {6656, 16054, 2}, {17670, 37086, 2}, {24610, 33841, 2}, {33833, 41236, 2}, {37096, 37233, 2}, {50200, 50319, 2}


X(50412) = X(2)X(3)∩X(31)X(306)

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

X(50412) lies on these lines: {2, 3}, {6, 345}, {31, 306}, {321, 5336}, {894, 19684}, {1724, 3687}, {2268, 5294}, {2298, 17776}, {3187, 49492}, {3782, 17321}, {5278, 32779}, {11679, 37817}, {19757, 26626}, {27064, 27396}

X(50412) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3151, 33736}, {13740, 37265, 2}, {17526, 37419, 2}, {19542, 49128, 19645}


X(50413) = 75TH HATZIPOLAKIS-MOSES-EULER POINT

Barycentrics    16*a^18 - 58*a^16*b^2 + 67*a^14*b^4 - 10*a^12*b^6 - 21*a^10*b^8 + 6*a^8*b^10 - 31*a^6*b^12 + 58*a^4*b^14 - 31*a^2*b^16 + 4*b^18 - 58*a^16*c^2 + 196*a^14*b^2*c^2 - 180*a^12*b^4*c^2 - 31*a^10*b^6*c^2 + 83*a^8*b^8*c^2 + 26*a^6*b^10*c^2 - 90*a^4*b^12*c^2 + 73*a^2*b^14*c^2 - 19*b^16*c^2 + 67*a^14*c^4 - 180*a^12*b^2*c^4 + 192*a^10*b^4*c^4 - 29*a^8*b^6*c^4 - 95*a^6*b^8*c^4 - 6*a^4*b^10*c^4 + 19*b^14*c^4 - 10*a^12*c^6 - 31*a^10*b^2*c^6 - 29*a^8*b^4*c^6 + 150*a^6*b^6*c^6 + 34*a^4*b^8*c^6 - 121*a^2*b^10*c^6 + 17*b^12*c^6 - 21*a^10*c^8 + 83*a^8*b^2*c^8 - 95*a^6*b^4*c^8 + 34*a^4*b^6*c^8 + 158*a^2*b^8*c^8 - 21*b^10*c^8 + 6*a^8*c^10 + 26*a^6*b^2*c^10 - 6*a^4*b^4*c^10 - 121*a^2*b^6*c^10 - 21*b^8*c^10 - 31*a^6*c^12 - 90*a^4*b^2*c^12 + 17*b^6*c^12 + 58*a^4*c^14 + 73*a^2*b^2*c^14 + 19*b^4*c^14 - 31*a^2*c^16 - 19*b^2*c^16 + 4*c^18 : :

See Antreas Hatzipolakis and Peter Moses, euclid 5170.

X(50413) lies on this line: {2, 3}


X(50414) = ISOGONAL CONJUGATE OF X(14863)

Barycentrics    a^2*(4*a^8 - 11*a^6*b^2 + 9*a^4*b^4 - a^2*b^6 - b^8 - 11*a^6*c^2 + 4*a^4*b^2*c^2 + a^2*b^4*c^2 + 6*b^6*c^2 + 9*a^4*c^4 + a^2*b^2*c^4 - 10*b^4*c^4 - a^2*c^6 + 6*b^2*c^6 - c^8) : :
X(50414) = 11 X[3] - 3 X[64], X[3] - 9 X[154], 5 X[3] + 3 X[1498], 7 X[3] - 3 X[3357], X[3] + 3 X[6759], 23 X[3] - 15 X[8567], X[3] - 3 X[10282], 17 X[3] - 9 X[10606], 5 X[3] - 9 X[11202], 13 X[3] - 9 X[11204], 13 X[3] + 3 X[12315], 19 X[3] - 3 X[13093], X[3] + 15 X[14530], 7 X[3] - 15 X[17821], 7 X[3] + 9 X[32063], 25 X[3] - 9 X[35450], X[64] - 33 X[154], 5 X[64] + 11 X[1498], 7 X[64] - 11 X[3357], X[64] + 11 X[6759], 23 X[64] - 55 X[8567], X[64] - 11 X[10282], 17 X[64] - 33 X[10606], 5 X[64] - 33 X[11202], 13 X[64] - 33 X[11204], 13 X[64] + 11 X[12315], 19 X[64] - 11 X[13093], X[64] + 55 X[14530], 7 X[64] - 55 X[17821], 7 X[64] + 33 X[32063], 25 X[64] - 33 X[35450], 15 X[154] + X[1498], 21 X[154] - X[3357], 3 X[154] + X[6759], 69 X[154] - 5 X[8567], 3 X[154] - X[10282], 17 X[154] - X[10606], 5 X[154] - X[11202], 13 X[154] - X[11204], 39 X[154] + X[12315], 57 X[154] - X[13093], 3 X[154] + 5 X[14530], 21 X[154] - 5 X[17821], 7 X[154] + X[32063], 25 X[154] - X[35450], 7 X[1498] + 5 X[3357], X[1498] - 5 X[6759], 23 X[1498] + 25 X[8567], X[1498] + 5 X[10282], 17 X[1498] + 15 X[10606], X[1498] + 3 X[11202], 13 X[1498] + 15 X[11204], 13 X[1498] - 5 X[12315], 19 X[1498] + 5 X[13093], X[1498] - 25 X[14530], 7 X[1498] + 25 X[17821], 7 X[1498] - 15 X[32063], 5 X[1498] + 3 X[35450], X[3357] + 7 X[6759], 23 X[3357] - 35 X[8567], X[3357] - 7 X[10282], 17 X[3357] - 21 X[10606], 5 X[3357] - 21 X[11202], 13 X[3357] - 21 X[11204], 13 X[3357] + 7 X[12315], 19 X[3357] - 7 X[13093], X[3357] + 35 X[14530], X[3357] - 5 X[17821], X[3357] + 3 X[32063], 25 X[3357] - 21 X[35450], 23 X[6759] + 5 X[8567], 17 X[6759] + 3 X[10606], 5 X[6759] + 3 X[11202], 13 X[6759] + 3 X[11204], 13 X[6759] - X[12315], 19 X[6759] + X[13093], X[6759] - 5 X[14530], 7 X[6759] + 5 X[17821], 7 X[6759] - 3 X[32063], 25 X[6759] + 3 X[35450], 5 X[8567] - 23 X[10282], 85 X[8567] - 69 X[10606], 25 X[8567] - 69 X[11202], 65 X[8567] - 69 X[11204], 65 X[8567] + 23 X[12315], 95 X[8567] - 23 X[13093], X[8567] + 23 X[14530], 7 X[8567] - 23 X[17821], 35 X[8567] + 69 X[32063], 125 X[8567] - 69 X[35450], 17 X[10282] - 3 X[10606], 5 X[10282] - 3 X[11202], 13 X[10282] - 3 X[11204], 13 X[10282] + X[12315], 19 X[10282] - X[13093], X[10282] + 5 X[14530], 7 X[10282] - 5 X[17821], 7 X[10282] + 3 X[32063], 25 X[10282] - 3 X[35450], 5 X[10606] - 17 X[11202], 13 X[10606] - 17 X[11204], 39 X[10606] + 17 X[12315], 57 X[10606] - 17 X[13093], 3 X[10606] + 85 X[14530], 21 X[10606] - 85 X[17821], 7 X[10606] + 17 X[32063], 25 X[10606] - 17 X[35450], 13 X[11202] - 5 X[11204], 39 X[11202] + 5 X[12315], 57 X[11202] - 5 X[13093], 3 X[11202] + 25 X[14530], 21 X[11202] - 25 X[17821], 7 X[11202] + 5 X[32063], 5 X[11202] - X[35450], 3 X[11204] + X[12315], 57 X[11204] - 13 X[13093], 3 X[11204] + 65 X[14530], 21 X[11204] - 65 X[17821], 7 X[11204] + 13 X[32063], 25 X[11204] - 13 X[35450], 19 X[12315] + 13 X[13093], X[12315] - 65 X[14530], 7 X[12315] + 65 X[17821], 7 X[12315] - 39 X[32063], 25 X[12315] + 39 X[35450], X[13093] + 95 X[14530], 7 X[13093] - 95 X[17821], 7 X[13093] + 57 X[32063], 25 X[13093] - 57 X[35450], 7 X[14530] + X[17821], 35 X[14530] - 3 X[32063], 125 X[14530] + 3 X[35450], 5 X[17821] + 3 X[32063], 125 X[17821] - 21 X[35450], 25 X[32063] + 7 X[35450], X[15801] - 9 X[32379], 3 X[26] + X[15083], 3 X[156] + X[17714], 3 X[156] - X[41597], 3 X[159] + X[576], 3 X[206] - X[575], 3 X[206] + X[15581], X[546] - 3 X[16252], 3 X[549] + X[44762], 5 X[632] - 9 X[10192], 5 X[632] - 3 X[20299], 3 X[10192] - X[20299], 4 X[3628] - 3 X[32767], 3 X[1660] + X[7530], 2 X[12103] - 3 X[32903], 3 X[2883] + X[15704], 7 X[3090] + 9 X[11206], 7 X[3090] - 3 X[18381], 3 X[11206] + X[18381], 5 X[3091] + 3 X[9833], 5 X[3091] - 3 X[18383], X[3146] + 3 X[34785], 11 X[3525] - 3 X[14216], 11 X[3525] - 27 X[35260], X[14216] - 9 X[35260], X[3529] + 3 X[22802], X[3627] + 3 X[34782], 7 X[3857] - 3 X[41362], 5 X[5076] + 3 X[17845], 13 X[5079] - 9 X[23325], X[5609] + 3 X[15647], 3 X[5878] + 5 X[17538], X[6247] - 3 X[10182], 3 X[6247] - 7 X[14869], 9 X[10182] - 7 X[14869], 3 X[41725] + X[45187], 3 X[9924] + 5 X[11482], 3 X[9934] + 5 X[15034], X[9968] + 3 X[15577], X[10222] + 3 X[40660], 13 X[10303] - 9 X[23329], 13 X[10303] + 3 X[34781], 3 X[23329] + X[34781], 4 X[12108] - 3 X[25563], 8 X[12108] - 9 X[46265], 2 X[25563] - 3 X[46265], 3 X[13289] + X[14094], 3 X[13293] - 7 X[15020], X[15105] - 5 X[46853], 9 X[19153] - 5 X[22234], 3 X[23042] + X[39879], 3 X[31166] + X[34507], 3 X[32743] - 5 X[38795]

See Antreas Hatzipolakis and Peter Moses, euclid 5173.

X(50414) lies on these lines: {2, 14864}, {3, 64}, {4, 36809}, {5, 45185}, {22, 15606}, {23, 15801}, {24, 13382}, {26, 15083}, {30, 14862}, {49, 13598}, {51, 11423}, {52, 32237}, {54, 26863}, {61, 30402}, {62, 30403}, {110, 15644}, {140, 23060}, {156, 511}, {159, 576}, {184, 10110}, {185, 26882}, {186, 43806}, {206, 575}, {389, 1495}, {428, 12242}, {542, 13383}, {546, 8254}, {549, 44762}, {578, 5198}, {632, 10192}, {1092, 33524}, {1173, 13366}, {1199, 44106}, {1493, 5446}, {1503, 3628}, {1511, 14641}, {1531, 41482}, {1660, 7530}, {1971, 5007}, {2393, 22330}, {2777, 12103}, {2883, 15704}, {3090, 11206}, {3091, 9833}, {3146, 34785}, {3292, 12088}, {3525, 14216}, {3529, 22802}, {3627, 34782}, {3746, 10535}, {3857, 41362}, {5076, 17845}, {5079, 23325}, {5092, 13154}, {5237, 10675}, {5238, 10676}, {5562, 26881}, {5563, 26888}, {5609, 10628}, {5878, 17538}, {5943, 15047}, {6247, 10182}, {6419, 10533}, {6420, 10534}, {6427, 17819}, {6428, 17820}, {6453, 12970}, {6454, 12964}, {6519, 19088}, {6522, 19087}, {7517, 34986}, {7556, 41725}, {7592, 44082}, {7712, 11444}, {9544, 45186}, {9705, 37925}, {9707, 11430}, {9781, 13472}, {9820, 29012}, {9924, 11482}, {9934, 15034}, {9968, 15577}, {10095, 15516}, {10096, 45732}, {10112, 37971}, {10222, 40660}, {10303, 23329}, {10984, 35264}, {11264, 25338}, {11381, 11464}, {11403, 19357}, {11422, 34750}, {11426, 44731}, {11432, 41424}, {11456, 35479}, {11645, 13371}, {11820, 41427}, {12105, 41589}, {12106, 15012}, {12107, 13754}, {12108, 25563}, {12111, 41398}, {12112, 16835}, {13289, 14094}, {13293, 15020}, {13367, 13474}, {13488, 15152}, {14915, 32171}, {15105, 46853}, {15311, 44245}, {15448, 18914}, {15580, 41593}, {16625, 37440}, {16836, 35265}, {16982, 44668}, {17704, 43586}, {18128, 44232}, {18378, 21849}, {18475, 44870}, {19153, 22234}, {22352, 43598}, {23042, 39879}, {23411, 25555}, {31166, 34507}, {32445, 35007}, {32743, 38795}, {35259, 37515}, {37514, 40284}, {37946, 43579}, {43602, 47486}

X(50414) = midpoint of X(i) and X(j) for these {i,j}: {5, 45185}, {575, 15581}, {6759, 10282}, {9833, 18383}, {15580, 41593}, {17714, 41597}
X(50414) = isogonal conjugate of X(14863)
X(50414) = complement of X(14864)
X(50414) = X(3)-Dao conjugate of X(14863)
X(50414) = barycentric quotient X(6)/X(14863)
X(50414) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {154, 6759, 10282}, {154, 14530, 6759}, {156, 17714, 41597}, {184, 10594, 37505}, {206, 15581, 575}, {1495, 1614, 389}, {3357, 6759, 32063}, {6759, 11202, 1498}, {9707, 26883, 11430}, {10594, 37505, 10110}, {13367, 14157, 13474}, {17821, 32063, 3357}


X(50415) = X(2)X(3)∩X(511)X(3679)

Barycentrics    a^6*b + a^5*b^2 + a^4*b^3 + a^3*b^4 - 2*a^2*b^5 - 2*a*b^6 + a^6*c - 4*a^5*b*c + 2*a^4*b^2*c + 5*a^3*b^3*c - a^2*b^4*c - a*b^5*c - 2*b^6*c + a^5*c^2 + 2*a^4*b*c^2 + 2*a^3*b^2*c^2 + 5*a^2*b^3*c^2 + 2*a*b^4*c^2 - 2*b^5*c^2 + a^4*c^3 + 5*a^3*b*c^3 + 5*a^2*b^2*c^3 + 2*a*b^3*c^3 + 4*b^4*c^3 + a^3*c^4 - a^2*b*c^4 + 2*a*b^2*c^4 + 4*b^3*c^4 - 2*a^2*c^5 - a*b*c^5 - 2*b^2*c^5 - 2*a*c^6 - 2*b*c^6 : :
X(50415) = 4 X[549] - 3 X[14636], 3 X[5054] - 2 X[48930], X[9840] + 2 X[15971], X[9840] - 4 X[15973], X[15971] + 2 X[15973], X[37425] + 2 X[46704], 4 X[10] - X[48936], 2 X[355] + X[48921], 5 X[1698] - 2 X[48939], 2 X[18480] + X[48916], X[18525] + 2 X[48927], 3 X[19875] - X[48883], 3 X[25055] - 2 X[48894], 3 X[38066] - X[48928], 3 X[38074] - X[48877]

X(50415) lies on these lines: {2, 3}, {10, 48936}, {355, 48921}, {500, 10459}, {511, 3679}, {519, 48909}, {542, 6126}, {1201, 48903}, {1698, 48939}, {3419, 30035}, {3582, 28385}, {3654, 48917}, {3656, 48931}, {9668, 44843}, {9955, 28352}, {11237, 49745}, {18480, 48916}, {18493, 28370}, {18525, 48927}, {19782, 48862}, {19875, 48883}, {21214, 38021}, {25055, 48894}, {28194, 48899}, {28198, 48915}, {28208, 48926}, {38066, 48928}, {38074, 48877}

X(50415) = midpoint of X(2) and X(15971)
X(50415) = reflection of X(i) in X(j) for these {i,j}: {2, 15973}, {3656, 48931}, {9840, 2}, {48917, 3654}
X(50415) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15971, 15973, 9840}


X(50416) = X(2)X(3)∩X(511)X(1698)

Barycentrics    a^6*b + a^5*b^2 - 3*a^4*b^3 - 3*a^3*b^4 + 2*a^2*b^5 + 2*a*b^6 + a^6*c + 4*a^5*b*c - 2*a^4*b^2*c - 7*a^3*b^3*c - a^2*b^4*c + 3*a*b^5*c + 2*b^6*c + a^5*c^2 - 2*a^4*b*c^2 - 6*a^3*b^2*c^2 - 7*a^2*b^3*c^2 - 2*a*b^4*c^2 + 2*b^5*c^2 - 3*a^4*c^3 - 7*a^3*b*c^3 - 7*a^2*b^2*c^3 - 6*a*b^3*c^3 - 4*b^4*c^3 - 3*a^3*c^4 - a^2*b*c^4 - 2*a*b^2*c^4 - 4*b^3*c^4 + 2*a^2*c^5 + 3*a*b*c^5 + 2*b^2*c^5 + 2*a*c^6 + 2*b*c^6 : :
X(50416) = 6 X[2] - X[9840], 9 X[2] + X[15971], 3 X[2] + 2 X[15973], 4 X[5] + X[37425], 8 X[140] - 3 X[14636], 4 X[140] + X[46704], 7 X[3526] - 2 X[48930], 3 X[9840] + 2 X[15971], X[9840] + 4 X[15973], 3 X[14636] + 2 X[46704], X[15971] - 6 X[15973], 4 X[10] + X[48909], X[500] + 4 X[9956], 3 X[1699] + 2 X[48919], 7 X[3624] - 2 X[48894], 16 X[3634] - X[48936], 2 X[5453] + 3 X[5790], 3 X[5587] + 2 X[48893], 4 X[6684] + X[48899], 4 X[9955] + X[48915], 6 X[10175] - X[48937], 6 X[11230] - X[48903], 6 X[11231] - X[48882], 17 X[19872] - 2 X[48939], 4 X[24206] + X[48922], 6 X[26446] - X[48917], 3 X[26446] + 2 X[48931], X[48917] + 4 X[48931], 7 X[31423] - 2 X[35203], 4 X[48887] + X[48921]

X(50416) lies on these lines: {2, 3}, {10, 48909}, {500, 9956}, {511, 1698}, {1699, 48919}, {3624, 48894}, {3634, 48936}, {4754, 24318}, {5453, 5790}, {5587, 48893}, {5965, 28369}, {6684, 48899}, {9955, 48915}, {10175, 48937}, {10895, 15447}, {11230, 48903}, {11231, 48882}, {19872, 48939}, {24206, 48922}, {26446, 48917}, {31423, 35203}, {31479, 49743}, {48887, 48921}

X(50416) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15973, 9840}, {140, 46704, 14636}, {26446, 48931, 48917}


X(50417) = X(2)X(3)∩X(511)X(9780)

Barycentrics    a^6*b + a^5*b^2 - 4*a^4*b^3 - 4*a^3*b^4 + 3*a^2*b^5 + 3*a*b^6 + a^6*c + 6*a^5*b*c - 3*a^4*b^2*c - 10*a^3*b^3*c - a^2*b^4*c + 4*a*b^5*c + 3*b^6*c + a^5*c^2 - 3*a^4*b*c^2 - 8*a^3*b^2*c^2 - 10*a^2*b^3*c^2 - 3*a*b^4*c^2 + 3*b^5*c^2 - 4*a^4*c^3 - 10*a^3*b*c^3 - 10*a^2*b^2*c^3 - 8*a*b^3*c^3 - 6*b^4*c^3 - 4*a^3*c^4 - a^2*b*c^4 - 3*a*b^2*c^4 - 6*b^3*c^4 + 3*a^2*c^5 + 4*a*b*c^5 + 3*b^2*c^5 + 3*a*c^6 + 3*b*c^6 : :
X(50417) = 9 X[2] - 2 X[9840], 6 X[2] + X[15971], 3 X[2] + 4 X[15973], 5 X[631] + 2 X[46704], 5 X[3091] + 2 X[37425], 11 X[3525] - 4 X[48930], 4 X[9840] + 3 X[15971], X[9840] + 6 X[15973], 13 X[10303] - 6 X[14636], X[15971] - 8 X[15973], 2 X[500] + 5 X[5818], 5 X[3617] + 2 X[48909], 8 X[3634] - X[48883], 11 X[5550] - 4 X[48894], 6 X[5587] + X[48923], 3 X[5657] + 4 X[48931], 3 X[9812] + 4 X[48919], 8 X[9956] - X[48877], 6 X[10175] + X[48897], 6 X[26446] + X[48941], 6 X[38042] + X[48907], 5 X[40330] + 2 X[48922], 23 X[46931] - 2 X[48936]

X(50417) lies on these lines: {2, 3}, {500, 5818}, {511, 9780}, {3617, 48909}, {3634, 48883}, {5229, 15447}, {5550, 48894}, {5587, 48923}, {5657, 48931}, {8164, 49743}, {9812, 48919}, {9956, 48877}, {10175, 48897}, {10588, 49745}, {26446, 48941}, {38042, 48907}, {40330, 48922}, {46931, 48936}

X(50417) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15973, 15971}


X(50418) = X(2)X(3)∩X(511)X(1125)

Barycentrics    2*a^6*b + 2*a^5*b^2 - 3*a^4*b^3 - 3*a^3*b^4 + a^2*b^5 + a*b^6 + 2*a^6*c + 2*a^5*b*c - a^4*b^2*c - 5*a^3*b^3*c - 2*a^2*b^4*c + 3*a*b^5*c + b^6*c + 2*a^5*c^2 - a^4*b*c^2 - 6*a^3*b^2*c^2 - 5*a^2*b^3*c^2 - a*b^4*c^2 + b^5*c^2 - 3*a^4*c^3 - 5*a^3*b*c^3 - 5*a^2*b^2*c^3 - 6*a*b^3*c^3 - 2*b^4*c^3 - 3*a^3*c^4 - 2*a^2*b*c^4 - a*b^2*c^4 - 2*b^3*c^4 + a^2*c^5 + 3*a*b*c^5 + b^2*c^5 + a*c^6 + b*c^6 : :
X(50418) = 3 X[2] + X[9840], 9 X[2] - X[15971], X[4] + 3 X[14636], 5 X[631] - X[37425], 5 X[1656] - X[46704], 3 X[9840] + X[15971], X[15971] - 3 X[15973], 3 X[3576] + X[48937], 5 X[3616] - X[48909], 7 X[3624] + X[48883], X[5453] - 3 X[38028], 11 X[5550] + X[48936], 3 X[5603] + X[48917], 3 X[5886] + X[48882], 5 X[8227] - X[48899], 3 X[10164] - X[48919], 3 X[10165] - X[48893], 3 X[11230] - X[48931], 5 X[19862] + X[48939], 3 X[26446] + X[48903]

X(50418) lies on these lines: {2, 3}, {10, 48894}, {511, 1125}, {613, 28369}, {946, 25354}, {988, 50177}, {1385, 48887}, {1423, 6147}, {1503, 48932}, {3035, 49734}, {3564, 15985}, {3576, 48937}, {3616, 48909}, {3624, 48883}, {3846, 4999}, {5432, 37574}, {5433, 17717}, {5453, 21214}, {5550, 48936}, {5603, 48917}, {5690, 37529}, {5844, 10459}, {5886, 10476}, {5901, 35631}, {8227, 48899}, {8981, 39385}, {9959, 49598}, {10164, 48919}, {10165, 48893}, {11230, 48931}, {15325, 37607}, {16828, 37619}, {19858, 31394}, {19862, 48939}, {20258, 31445}, {22791, 48924}, {24470, 30097}, {26446, 48903}, {28365, 36742}, {28389, 37737}, {32515, 37592}, {37573, 37715}

X(50418) = midpoint of X(i) and X(j) for these {i,j}: {5, 48930}, {10, 48894}, {946, 35203}, {1385, 48887}, {9840, 15973}, {9959, 49598}, {22791, 48924}
X(50418) = complement of X(15973)
X(50418) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9840, 15973}, {5, 549, 19543}, {6998, 11110, 3}


X(50419) = X(2)X(3)∩X(145)X(511)

Barycentrics    3*a^6*b + 3*a^5*b^2 - 2*a^4*b^3 - 2*a^3*b^4 - a^2*b^5 - a*b^6 + 3*a^6*c - 2*a^5*b*c + a^4*b^2*c - 3*a^2*b^4*c + 2*a*b^5*c - b^6*c + 3*a^5*c^2 + a^4*b*c^2 - 4*a^3*b^2*c^2 + a*b^4*c^2 - b^5*c^2 - 2*a^4*c^3 - 4*a*b^3*c^3 + 2*b^4*c^3 - 2*a^3*c^4 - 3*a^2*b*c^4 + a*b^2*c^4 + 2*b^3*c^4 - a^2*c^5 + 2*a*b*c^5 - b^2*c^5 - a*c^6 - b*c^6 : :
X(50419) = 3 X[2] - 4 X[9840], 9 X[2] - 8 X[15973], 5 X[3091] - 4 X[46704], 5 X[3522] - 4 X[37425], 7 X[3523] - 8 X[48930], 3 X[9840] - 2 X[15973], 2 X[13442] - 3 X[49735], 12 X[14636] - 11 X[15717], 3 X[15971] - 4 X[15973], 5 X[3617] - 8 X[48939], X[3621] - 4 X[48936], 7 X[3622] - 8 X[48894], 5 X[3623] - 4 X[48909], 3 X[5731] - 2 X[48897], 3 X[7967] - 2 X[48907], 5 X[10595] - 4 X[48933]

X(50419) lies on these lines: {2, 3}, {8, 48883}, {40, 4427}, {145, 511}, {390, 28369}, {516, 10459}, {573, 26770}, {944, 20041}, {962, 33100}, {1201, 4297}, {1503, 15983}, {3600, 49745}, {3617, 48939}, {3621, 48936}, {3622, 48894}, {3623, 48909}, {3924, 24728}, {4294, 37610}, {5731, 48897}, {6284, 28386}, {7967, 48907}, {9812, 10465}, {10595, 48933}, {12245, 48928}, {15326, 28385}, {17164, 29057}, {20067, 38568}, {20076, 46483}, {20892, 30271}, {48903, 48941}

X(50419) = reflection of X(i) in X(j) for these {i,j}: {8, 48883}, {12245, 48928}, {15971, 9840}, {48941, 48903}
X(50419) = anticomplement of X(15971)
X(50419) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 376, 19543}, {9840, 15971, 2}


X(50420) = X(2)X(3)∩X(511)X(3616)

Barycentrics    3*a^6*b + 3*a^5*b^2 - 4*a^4*b^3 - 4*a^3*b^4 + a^2*b^5 + a*b^6 + 3*a^6*c + 2*a^5*b*c - a^4*b^2*c - 6*a^3*b^3*c - 3*a^2*b^4*c + 4*a*b^5*c + b^6*c + 3*a^5*c^2 - a^4*b*c^2 - 8*a^3*b^2*c^2 - 6*a^2*b^3*c^2 - a*b^4*c^2 + b^5*c^2 - 4*a^4*c^3 - 6*a^3*b*c^3 - 6*a^2*b^2*c^3 - 8*a*b^3*c^3 - 2*b^4*c^3 - 4*a^3*c^4 - 3*a^2*b*c^4 - a*b^2*c^4 - 2*b^3*c^4 + a^2*c^5 + 4*a*b*c^5 + b^2*c^5 + a*c^6 + b*c^6 : :
X(50420) = 3 X[2] + 2 X[9840], 6 X[2] - X[15971], 9 X[2] - 4 X[15973], X[4] + 4 X[48930], X[20] - 6 X[14636], 7 X[3090] - 2 X[46704], 7 X[3523] - 2 X[37425], 4 X[9840] + X[15971], 3 X[9840] + 2 X[15973], 3 X[15971] - 8 X[15973], X[8] + 4 X[48894], X[944] + 4 X[48887], X[962] + 4 X[35203], 4 X[1125] + X[48883], 4 X[1385] + X[48877], 6 X[3576] - X[48923], 7 X[3622] - 2 X[48909], 11 X[5550] + 4 X[48939], 3 X[5603] + 2 X[48882], 3 X[5657] + 2 X[48903], 3 X[5731] + 2 X[48937], 6 X[5886] - X[48941], 4 X[5901] + X[48928], 4 X[9959] + X[17164], 6 X[10165] - X[48897], 3 X[11203] + 2 X[49598], X[46483] + 4 X[49728], 6 X[38028] - X[48907], 13 X[46934] + 2 X[48936]

X(50420) lies on these lines: {2, 3}, {8, 48894}, {511, 3616}, {944, 48887}, {946, 6536}, {962, 35203}, {1125, 48883}, {1385, 48877}, {3576, 48923}, {3622, 48909}, {5550, 48939}, {5603, 48882}, {5657, 48903}, {5731, 48937}, {5886, 48941}, {5901, 48928}, {5965, 15983}, {7288, 49745}, {9959, 17164}, {10165, 48897}, {10459, 28234}, {10470, 48888}, {11203, 49598}, {19874, 37619}, {30478, 46483}, {31458, 49729}, {38028, 48907}, {46934, 48936}

X(50420) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9840, 15971}


X(50421) = X(2)X(3)∩X(511)X(551)

Barycentrics    4*a^6*b + 4*a^5*b^2 - 5*a^4*b^3 - 5*a^3*b^4 + a^2*b^5 + a*b^6 + 4*a^6*c + 2*a^5*b*c - a^4*b^2*c - 7*a^3*b^3*c - 4*a^2*b^4*c + 5*a*b^5*c + b^6*c + 4*a^5*c^2 - a^4*b*c^2 - 10*a^3*b^2*c^2 - 7*a^2*b^3*c^2 - a*b^4*c^2 + b^5*c^2 - 5*a^4*c^3 - 7*a^3*b*c^3 - 7*a^2*b^2*c^3 - 10*a*b^3*c^3 - 2*b^4*c^3 - 5*a^3*c^4 - 4*a^2*b*c^4 - a*b^2*c^4 - 2*b^3*c^4 + a^2*c^5 + 5*a*b*c^5 + b^2*c^5 + a*c^6 + b*c^6 : :
X(50421) = 5 X[2] - X[15971], X[376] - 3 X[14636], 3 X[3524] - X[37425], 3 X[5055] - X[46704], 5 X[9840] + X[15971], 2 X[9840] + X[15973], 2 X[15971] - 5 X[15973], X[500] - 3 X[3653], 2 X[1125] + X[48939], 5 X[3616] + X[48936], 3 X[25055] + X[48883], 3 X[38021] - X[48899], 3 X[38022] - X[48933], 3 X[38064] - X[48922], 3 X[38314] - X[48909]

X(50421) lies on these lines: {2, 3}, {500, 3653}, {511, 551}, {519, 48894}, {542, 15985}, {1125, 48939}, {1201, 5453}, {3616, 48936}, {3654, 48903}, {3656, 48882}, {3750, 49739}, {5298, 49745}, {5719, 28387}, {19870, 37619}, {25055, 48883}, {28194, 35203}, {28204, 48887}, {28352, 48927}, {38021, 48899}, {38022, 48933}, {38064, 48922}, {38314, 48909}

X(50421) = midpoint of X(i) and X(j) for these {i,j}: {2, 9840}, {3654, 48903}, {3656, 48882}
X(50421) = reflection of X(15973) in X(2)
X(50421) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {}


X(50422) = X(2)X(3)∩X(511)X(3241)

Barycentrics    5*a^6*b + 5*a^5*b^2 - 4*a^4*b^3 - 4*a^3*b^4 - a^2*b^5 - a*b^6 + 5*a^6*c - 2*a^5*b*c + a^4*b^2*c - 2*a^3*b^3*c - 5*a^2*b^4*c + 4*a*b^5*c - b^6*c + 5*a^5*c^2 + a^4*b*c^2 - 8*a^3*b^2*c^2 - 2*a^2*b^3*c^2 + a*b^4*c^2 - b^5*c^2 - 4*a^4*c^3 - 2*a^3*b*c^3 - 2*a^2*b^2*c^3 - 8*a*b^3*c^3 + 2*b^4*c^3 - 4*a^3*c^4 - 5*a^2*b*c^4 + a*b^2*c^4 + 2*b^3*c^4 - a^2*c^5 + 4*a*b*c^5 - b^2*c^5 - a*c^6 - b*c^6 : :
X(50422) = 5 X[2] - 4 X[15973], 3 X[3524] - 4 X[48930], 3 X[3545] - 2 X[46704], 4 X[9840] - X[15971], 5 X[9840] - 2 X[15973], 3 X[10304] - 2 X[37425], 6 X[14636] - 5 X[15692], 5 X[15971] - 8 X[15973], X[8] - 4 X[48939], X[145] + 2 X[48936], 3 X[38074] - 4 X[48887], 3 X[38314] - 4 X[48894]

X(50422) lies on these lines: {2, 3}, {8, 48939}, {145, 48936}, {511, 3241}, {519, 48883}, {542, 15983}, {1201, 48897}, {3058, 28386}, {3656, 48941}, {4293, 44843}, {4304, 28387}, {10459, 28194}, {28204, 48877}, {28369, 49739}, {28370, 48916}, {29181, 47357}, {34610, 46483}, {38074, 48887}, {38314, 48894}

X(50422) = reflection of X(i) in X(j) for these {i,j}: {2, 9840}, {15971, 2}, {48941, 3656}
X(50422) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {}


X(50423) = X(2)X(3)∩X(42)X(511)

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

X(50423) lies on these lines: {2, 3}, {42, 511}, {43, 48883}, {55, 28369}, {524, 15621}, {899, 48939}, {1503, 23359}, {1742, 10434}, {3240, 48936}, {3720, 48894}, {4300, 48893}, {4307, 23853}, {10459, 48919}, {15447, 16678}, {15985, 44419}, {17018, 48909}, {23361, 49734}

X(50423) = midpoint of X(37331) and X(37425)
X(50423) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5004, 5005, 19312}, {9840, 37425, 15971}


X(50424) = X(2)X(3)∩X(239)X(511)

Barycentrics    a^7*b + a^6*b^2 - a^3*b^5 - a^2*b^6 + a^7*c + a^4*b^3*c - a^2*b^5*c - a*b^6*c + a^6*c^2 - b^6*c^2 + a^4*b*c^3 + a*b^4*c^3 + a*b^3*c^4 + 2*b^4*c^4 - a^3*c^5 - a^2*b*c^5 - a^2*c^6 - a*b*c^6 - b^2*c^6 : :
X(50424) = 3 X[13635] - 2 X[15977]

X(50424) lies on these lines: {2, 3}, {7, 28369}, {63, 3765}, {239, 511}, {515, 30059}, {516, 3747}, {517, 40886}, {649, 4391}, {673, 29181}, {1423, 18655}, {1503, 4645}, {1764, 20913}, {4384, 48883}, {4393, 48909}, {5249, 49612}, {5279, 17787}, {6650, 24833}, {12545, 23536}, {13478, 24587}, {16815, 48939}, {16816, 48936}, {16826, 48894}, {18650, 30097}, {20432, 29069}, {41245, 49745}

X(50424) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 15970, 48890}


X(50425) = X(2)X(3)∩X(387)X(511)

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

X(50425) lies on these lines: {2, 3}, {10, 24728}, {40, 1423}, {387, 511}, {573, 5286}, {944, 5015}, {1072, 28388}, {1201, 37611}, {1330, 6776}, {1350, 1834}, {1714, 48883}, {2551, 24320}, {3085, 37619}, {3421, 42461}, {3428, 28386}, {3430, 48837}, {3587, 28387}, {4340, 37527}, {4385, 5657}, {5254, 37499}, {5691, 19879}, {5706, 28369}, {5767, 15983}, {5786, 15985}, {7080, 20760}, {7952, 37613}, {8193, 10629}, {10449, 10519}, {12607, 24328}, {15852, 28358}, {17132, 43174}, {37508, 43448}, {37823, 46264}

X(50425) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 631, 13740}, {6827, 6850, 34938}, {9840, 19514, 28383}


X(50426) = X(2)X(3)∩X(511)X(1714)

Barycentrics    a^7 + a^6*b - a^5*b^2 + a^4*b^3 + a^3*b^4 - 3*a^2*b^5 - a*b^6 + b^7 + a^6*c - 2*a^5*b*c + a^4*b^2*c + 2*a^3*b^3*c - a^2*b^4*c - b^6*c - a^5*c^2 + a^4*b*c^2 - 2*a^3*b^2*c^2 + a*b^4*c^2 - 3*b^5*c^2 + a^4*c^3 + 2*a^3*b*c^3 + 3*b^4*c^3 + a^3*c^4 - a^2*b*c^4 + a*b^2*c^4 + 3*b^3*c^4 - 3*a^2*c^5 - 3*b^2*c^5 - a*c^6 - b*c^6 + c^7 : : X(50426) lies on these lines: {2, 3}, {40, 17889}, {46, 1423}, {65, 33144}, {387, 48909}, {511, 1714}, {602, 28356}, {1329, 24320}, {1834, 19782}, {2646, 17721}, {3178, 24257}, {3980, 6684}, {5292, 37521}, {5300, 39572}, {5552, 20760}, {10198, 37619}, {17757, 42461}, {22766, 28385}, {26066, 46844}, {28370, 35459}

X(50426) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5000, 5001, 28099}


X(50427) = X(2)X(3)∩X(551)X(48842)

Barycentrics    a^4 + 2*a^3*b + 5*a^2*b^2 + 2*a*b^3 - 2*b^4 + 2*a^3*c + 14*a^2*b*c + 14*a*b^2*c + 2*b^3*c + 5*a^2*c^2 + 14*a*b*c^2 + 8*b^2*c^2 + 2*a*c^3 + 2*b*c^3 - 2*c^4 : :

X(50427) lies on these lines: {2, 3}, {6, 50226}, {10, 599}, {551, 48842}, {1992, 49743}, {3295, 49720}, {3927, 50128}, {5278, 50234}, {5295, 29573}, {5711, 50299}, {11160, 49718}, {11237, 19870}, {17251, 50163}, {19723, 49744}, {19732, 49723}, {19744, 48835}, {23537, 41312}, {43531, 47352}, {48834, 49730}

X(50427) = reflection of X(11357) in X(2)
X(50427) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 377, 13745}, {2, 11359, 50410}, {2, 13745, 16844}, {2, 44217, 11359}, {2, 48816, 16418}, {2, 48817, 50202}, {2, 50169, 11354}, {2, 50171, 405}, {8728, 37153, 2049}


X(50428) = X(2)X(3)∩X(551)X(48837)

Barycentrics    3*a^4 + 2*a^3*b + 4*a^2*b^2 + 2*a*b^3 - 3*b^4 + 2*a^3*c + 14*a^2*b*c + 14*a*b^2*c + 2*b^3*c + 4*a^2*c^2 + 14*a*b*c^2 + 10*b^2*c^2 + 2*a*c^3 + 2*b*c^3 - 3*c^4 : :

X(50428) lies on these lines: {2, 3}, {10, 48834}, {69, 3679}, {387, 42028}, {551, 48837}, {1478, 19870}, {1992, 49744}, {3828, 48835}, {4340, 41629}, {5800, 49725}, {14548, 17180}, {19723, 49745}, {19766, 48845}, {48838, 50291}, {48857, 50226}, {48862, 49734}

X(50428) = anticomplement of X(11357)
X(50428) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 377, 48813}, {2, 11354, 13742}, {2, 48813, 13725}, {2, 50169, 50407}, {2, 50171, 48817}, {2, 50172, 31156}, {2, 50408, 11354}, {377, 37153, 13725}, {442, 19290, 2}, {2049, 48815, 2}, {8728, 11354, 2}, {8728, 50408, 13742}, {16052, 19332, 2}, {17528, 19332, 16052}, {37153, 48813, 2}, {44217, 50169, 2}


X(50429) = X(2)X(3)∩X(8)X(11160)

Barycentrics    7*a^4 + 2*a^3*b + 2*a^2*b^2 + 2*a*b^3 - 5*b^4 + 2*a^3*c + 14*a^2*b*c + 14*a*b^2*c + 2*b^3*c + 2*a^2*c^2 + 14*a*b*c^2 + 14*b^2*c^2 + 2*a*c^3 + 2*b*c^3 - 5*c^4 : :
X(50429) = 5 X[2] - 4 X[11357]

X(50429) lies on these lines: {2, 3}, {8, 11160}, {193, 50234}, {388, 49720}, {599, 49734}, {1992, 49745}, {4968, 31145}, {5716, 37756}, {9579, 50093}, {23536, 38314}, {48837, 50226}

X(50429) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 31295, 50165}, {2, 50165, 13736}, {2, 50171, 50408}, {377, 50171, 2}, {11359, 50407, 2}, {13745, 37153, 2}, {44217, 48817, 2}, {48813, 50169, 2}, {50169, 50397, 48813}


X(50430) = X(1)X(1992)∩X(2)X(3)

Barycentrics    5*a^4 - 2*a^3*b - 8*a^2*b^2 - 2*a*b^3 - b^4 - 2*a^3*c - 14*a^2*b*c - 14*a*b^2*c - 2*b^3*c - 8*a^2*c^2 - 14*a*b*c^2 - 2*b^2*c^2 - 2*a*c^3 - 2*b*c^3 - c^4 : :

X(50430) lies on these lines: {1, 1992}, {2, 3}, {69, 49723}, {551, 48870}, {597, 19766}, {599, 49728}, {958, 49740}, {1104, 41312}, {4294, 49720}, {4653, 14555}, {5247, 48830}, {5283, 37654}, {5302, 47359}, {7609, 31435}, {7737, 50230}, {11160, 49716}, {11179, 48894}, {19723, 49739}, {48862, 49730}, {48869, 50305}

X(50430) = reflection of X(2) in X(11357)
X(50430) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6872, 50171}, {2, 13736, 13745}, {2, 13745, 13725}, {2, 31156, 48817}, {2, 48817, 50407}, {2, 49735, 48813}, {2, 50165, 377}, {2, 50171, 37153}, {405, 13725, 13742}, {405, 13736, 13725}, {405, 13745, 2}, {11359, 50202, 2}, {16844, 50241, 50408}, {16865, 37314, 37176}


X(50431) = X(2)X(3)∩X(8)X(17116)

Barycentrics    5*a^4 + 2*a^3*b + 2*a^2*b^2 + 2*a*b^3 - 3*b^4 + 2*a^3*c + 10*a^2*b*c + 10*a*b^2*c + 2*b^3*c + 2*a^2*c^2 + 10*a*b*c^2 + 10*b^2*c^2 + 2*a*c^3 + 2*b*c^3 - 3*c^4 : :
X(50431) = 9 X[2] - 8 X[16844], 3 X[2] - 4 X[37153], 3 X[13736] - 4 X[16844], 2 X[16844] - 3 X[37153]

X(50431) lies on these lines: {2, 3}, {8, 17116}, {10, 16570}, {69, 49734}, {193, 49745}, {3621, 4968}, {3622, 23536}, {3623, 30589}, {4678, 5300}, {9579, 17257}, {11851, 42697}, {12625, 50116}, {19783, 48837}, {20008, 20880}, {20019, 20090}, {34282, 34284}, {37683, 43533}

X(50431) = reflection of X(13736) in X(37153)
X(50431) = anticomplement of X(13736)
X(50431) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 26051, 2}, {377, 50171, 50408}, {377, 50408, 2}, {2049, 50240, 48813}, {4195, 4208, 2}, {6871, 19284, 2}, {11319, 50237, 2}, {13736, 37153, 2}, {17697, 37436, 2}, {44217, 50391, 13742}, {50169, 50239, 13725}


X(50432) = X(2)X(3)∩X(141)X(3634)

Barycentrics    4*a^3*b + 9*a^2*b^2 + 4*a*b^3 - b^4 + 4*a^3*c + 20*a^2*b*c + 20*a*b^2*c + 4*b^3*c + 9*a^2*c^2 + 20*a*b*c^2 + 10*b^2*c^2 + 4*a*c^3 + 4*b*c^3 - c^4 : :
X(50432) = 9 X[2] - X[13736], 3 X[2] + X[37153], X[13736] - 3 X[16844], X[13736] + 3 X[37153]

X(50432) lies on these lines: {2, 3}, {141, 3634}, {495, 16828}, {496, 25512}, {1125, 48847}, {1698, 33084}, {3824, 5257}, {6707, 20083}, {15888, 19871}, {18139, 19877}, {19732, 49743}, {19878, 48843}, {29571, 39564}

X(50432) = midpoint of X(16844) and X(37153)
X(50432) = complement of X(16844)
X(50432) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 443, 16457}, {2, 2049, 50205}, {2, 4197, 17514}, {2, 8728, 50409}, {2, 14007, 17698}, {2, 16458, 6675}, {2, 37153, 16844}, {4197, 17514, 50058}, {8728, 17527, 47514}, {8728, 50409, 48815}, {11357, 50408, 50243}


X(50433) = ISOGONAL CONJUGATE OF X(14165)

Barycentrics    a^2*(a^2 - b^2 - c^2)^2*(a^2 - a*b + b^2 - c^2)*(a^2 + a*b + b^2 - c^2)*(a^2 - b^2 - a*c + c^2)*(a^2 - b^2 + a*c + c^2) : :
Barycentrics    Sin[A]^2/(3 - Tan[A]^2) : :

X(50433) lies on these lines: {6, 13}, {49, 41335}, {94, 275}, {184, 5158}, {216, 5961}, {287, 328}, {323, 1494}, {394, 15526}, {476, 26717}, {577, 3269}, {1141, 6570}, {2088, 14910}, {2393, 14560}, {3003, 19627}, {3284, 11079}, {5422, 18883}, {5663, 39176}, {6344, 40402}, {8749, 15395}, {9033, 14582}, {11004, 39358}, {11081, 41893}, {11086, 41892}, {14254, 27359}, {15032, 18316}, {15851, 31676}, {18400, 38943}, {18558, 32320}, {23128, 39170}

X(50433) = isogonal conjugate of X(14165)
X(50433) = isogonal conjugate of the polar conjugate of X(265)
X(50433) = X(94)-Ceva conjugate of X(5961)
X(50433) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14165}, {19, 340}, {92, 186}, {107, 32679}, {158, 323}, {162, 44427}, {526, 823}, {811, 47230}, {1096, 7799}, {1748, 5962}, {1969, 34397}, {2052, 6149}, {2088, 23999}, {2190, 14918}, {2290, 8795}, {2624, 6528}, {3268, 24019}, {6198, 17923}, {6521, 22115}, {8552, 36126}, {8747, 42701}, {11062, 40440}, {14590, 24006}, {14920, 36119}, {16080, 35201}
X(50433) = X(i)-Dao conjugate of X(j) for these (i,j): {3, 14165}, {5, 14918}, {6, 340}, {125, 44427}, {130, 2081}, {186, 22391}, {323, 1147}, {393, 15295}, {1511, 14920}, {2052, 14993}, {2972, 41078}, {3268, 35071}, {5664, 38999}, {6503, 7799}, {8552, 46093}, {17423, 47230}, {32679, 38985}, {39170, 46106}
X(50433) = cevapoint of X(i) and X(j) for these (i,j): {216, 3284}, {1636, 3269}
X(50433) = crosspoint of X(5504) and X(14919)
X(50433) = crosssum of X(i) and X(j) for these (i,j): {403, 1990}, {2081, 16186}, {35235, 47230}
X(50433) = trilinear pole of line {418, 34983}
X(50433) = crossdifference of every pair of points on line {526, 1986}
X(50433) = barycentric product X(i)*X(j) for these {i,j}: {3, 265}, {68, 5961}, {94, 577}, {110, 43083}, {184, 328}, {255, 2166}, {343, 11077}, {394, 1989}, {418, 46138}, {476, 520}, {525, 32662}, {656, 36061}, {822, 32680}, {1092, 6344}, {1141, 5562}, {1636, 39290}, {1650, 15395}, {1807, 7100}, {3265, 14560}, {3269, 39295}, {3431, 18478}, {3926, 11060}, {3964, 18384}, {4558, 14582}, {5504, 39170}, {11064, 11079}, {12028, 13754}, {14356, 17974}, {14585, 20573}, {14592, 32661}, {18557, 32640}, {18558, 44769}, {18817, 23606}, {23968, 35911}, {24018, 32678}, {31676, 34483}, {32320, 46456}, {35139, 39201}, {36296, 40710}, {36297, 40709}
X(50433) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 340}, {6, 14165}, {94, 18027}, {184, 186}, {216, 14918}, {217, 11062}, {265, 264}, {328, 18022}, {394, 7799}, {418, 1154}, {476, 6528}, {520, 3268}, {577, 323}, {647, 44427}, {822, 32679}, {1141, 8795}, {1636, 5664}, {1989, 2052}, {2351, 5962}, {3049, 47230}, {3284, 14920}, {3990, 42701}, {5562, 1273}, {5961, 317}, {8606, 5081}, {11060, 393}, {11077, 275}, {11079, 16080}, {14560, 107}, {14575, 34397}, {14582, 14618}, {14585, 50}, {14595, 6344}, {15395, 42308}, {17434, 41078}, {18384, 1093}, {18478, 44135}, {18479, 381}, {18558, 41079}, {19627, 36423}, {20975, 35235}, {23606, 22115}, {32320, 8552}, {32661, 14590}, {32662, 648}, {32678, 823}, {34980, 16186}, {36061, 811}, {36296, 471}, {36297, 470}, {39170, 44138}, {39201, 526}, {42293, 2081}, {43083, 850}


X(50434) = ANTICOMPLEMENT OF X(1514)

Barycentrics    4*a^10 - 5*a^8*b^2 - 8*a^6*b^4 + 14*a^4*b^6 - 4*a^2*b^8 - b^10 - 5*a^8*c^2 + 30*a^6*b^2*c^2 - 18*a^4*b^4*c^2 - 10*a^2*b^6*c^2 + 3*b^8*c^2 - 8*a^6*c^4 - 18*a^4*b^2*c^4 + 28*a^2*b^4*c^4 - 2*b^6*c^4 + 14*a^4*c^6 - 10*a^2*b^2*c^6 - 2*b^4*c^6 - 4*a^2*c^8 + 3*b^2*c^8 - c^10 : :
X(50434) = 3 X[3] - 2 X[46817], 3 X[32111] - 4 X[46817], X[146] - 3 X[2071], 3 X[2071] - 2 X[11064], 3 X[376] - X[12112], 3 X[403] - 4 X[6699], 2 X[468] - 3 X[15055], 4 X[10564] - 3 X[40112], 3 X[858] - 2 X[1531], 2 X[1495] - 3 X[44280], 4 X[37853] - 3 X[44280], 2 X[1533] - 3 X[7426], 2 X[1539] - 3 X[2072], 5 X[3522] - 3 X[35265], 3 X[5622] - 2 X[47571], 2 X[16163] - 3 X[16386], 3 X[16386] - X[46818], 2 X[10272] - 3 X[34152], 3 X[10304] - 2 X[35266], 3 X[14644] - 2 X[47309], 3 X[15041] - X[18325], 5 X[15059] - 4 X[37984], 3 X[15061] - 2 X[47336], 4 X[15448] - 5 X[37952], 3 X[21663] - 2 X[32223], 4 X[32223] - 3 X[47096], 3 X[38701] - 2 X[47148], 3 X[38788] - 2 X[47335]

X(50434) lies on these lines: {2, 1514}, {3, 32111}, {20, 64}, {30, 74}, {146, 2071}, {323, 17838}, {376, 12112}, {378, 4846}, {403, 6699}, {468, 15055}, {511, 10990}, {541, 10564}, {548, 18350}, {550, 11459}, {858, 1531}, {1495, 37853}, {1499, 3268}, {1515, 4240}, {1533, 7426}, {1539, 2072}, {1559, 47109}, {1657, 32140}, {3146, 18931}, {3184, 44436}, {3522, 35265}, {3529, 12293}, {3543, 37643}, {3564, 15054}, {3589, 7527}, {3818, 26156}, {5622, 47571}, {5925, 37444}, {6000, 12825}, {6696, 50009}, {6800, 35485}, {7464, 12244}, {7706, 35484}, {7728, 15122}, {8703, 26881}, {10192, 35493}, {10272, 34152}, {10295, 12292}, {10297, 10721}, {10304, 35266}, {10546, 44273}, {10575, 35491}, {10605, 37644}, {10606, 37638}, {11413, 20427}, {11440, 44683}, {11441, 12250}, {11442, 35450}, {11598, 32125}, {11799, 12041}, {12103, 41482}, {12290, 44240}, {12317, 44665}, {12358, 44246}, {12379, 14982}, {12412, 18859}, {13292, 43806}, {13339, 13623}, {13488, 43601}, {14644, 47309}, {15041, 18325}, {15059, 37984}, {15061, 47336}, {15062, 31829}, {15072, 46444}, {15080, 44285}, {15305, 44241}, {15448, 37952}, {15559, 43577}, {16252, 35497}, {18323, 34584}, {21663, 32223}, {34005, 46850}, {34224, 34350}, {34622, 39899}, {34801, 44831}, {35492, 39242}, {36164, 47324}, {37077, 37648}, {37636, 44458}, {38701, 47148}, {38788, 47335}, {39434, 46968}

X(50434) = midpoint of X(7464) and X(12244)
X(50434) = reflection of X(i) in X(j) for these {i,j}: {20, 20725}, {146, 11064}, {1495, 37853}, {3580, 74}, {7728, 15122}, {10295, 16111}, {10721, 10297}, {11799, 12041}, {32111, 3}, {32125, 11598}, {46818, 16163}, {47096, 21663}, {47323, 46632}, {47324, 36164}
X(50434) = anticomplement of X(1514)
X(50434) = cevapoint of X(2935) and X(35237)
X(50434) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 64, 14516}, {146, 2071, 11064}, {378, 4846, 14389}, {1495, 37853, 44280}, {12250, 30552, 11441}, {16386, 46818, 16163}, {34778, 48905, 69}


X(50435) = REFLECTION OF X(110) IN X(403)

Barycentrics    a^10 - 2*a^8*b^2 + a^6*b^4 - a^4*b^6 + 2*a^2*b^8 - b^10 - 2*a^8*c^2 + 5*a^6*b^2*c^2 - a^4*b^4*c^2 - 5*a^2*b^6*c^2 + 3*b^8*c^2 + a^6*c^4 - a^4*b^2*c^4 + 6*a^2*b^4*c^4 - 2*b^6*c^4 - a^4*c^6 - 5*a^2*b^2*c^6 - 2*b^4*c^6 + 2*a^2*c^8 + 3*b^2*c^8 - c^10 : :
X(50435) = 2 X[4] + X[41724], 2 X[3580] + X[10733], 3 X[9140] - X[13445], X[323] - 4 X[7687], 2 X[1495] - 3 X[46451], 2 X[1531] + X[37779], 2 X[2072] - 3 X[14644], 3 X[14644] - X[43574], 5 X[3091] - 2 X[3292], 7 X[3832] - 8 X[44872], 8 X[5159] - 11 X[15025], X[5921] + 2 X[32127], 4 X[6699] - 3 X[37948], X[7464] - 4 X[36253], 4 X[10257] - 5 X[15059], X[10296] + 2 X[41586], 4 X[10297] - 7 X[15044], 4 X[10297] - X[23061], 7 X[15044] - X[23061], 2 X[10564] - 5 X[15081], 4 X[11801] - X[37477], X[12383] - 3 X[37943], X[14094] - 4 X[47336], 2 X[14156] - 3 X[23515], 3 X[14643] - 2 X[40111], 3 X[14643] - 4 X[46031], 5 X[15027] - 2 X[37950], 3 X[15035] - 4 X[44452], 5 X[15051] - 8 X[47296], 3 X[15055] - 2 X[16386], 3 X[15061] - 2 X[34152], 2 X[16163] - 3 X[37941], 3 X[37941] - 4 X[44673], X[18859] - 3 X[38724], X[23236] - 4 X[44961], 4 X[32223] - 3 X[37940], 4 X[37968] - 3 X[38723]

X(50435) lies on these lines: {2, 11430}, {3, 26913}, {4, 52}, {5, 15033}, {15, 44713}, {16, 44714}, {20, 21663}, {22, 18396}, {23, 18400}, {24, 9938}, {26, 12289}, {30, 74}, {49, 13406}, {54, 10024}, {110, 403}, {113, 539}, {125, 2071}, {140, 43821}, {155, 35488}, {185, 50009}, {186, 17702}, {193, 3818}, {235, 14516}, {323, 1568}, {378, 14852}, {381, 1993}, {389, 34007}, {399, 46449}, {511, 3153}, {520, 16229}, {542, 37784}, {546, 6288}, {567, 46029}, {568, 44263}, {1147, 16868}, {1154, 7723}, {1209, 35500}, {1351, 18386}, {1370, 18918}, {1495, 46451}, {1503, 47096}, {1531, 37779}, {1594, 15136}, {1614, 15761}, {1885, 15062}, {1899, 15072}, {1994, 18388}, {2070, 12902}, {2072, 14644}, {2888, 5907}, {2931, 37970}, {2979, 18531}, {3091, 3292}, {3146, 18381}, {3410, 15030}, {3448, 6000}, {3519, 31834}, {3520, 5449}, {3541, 15123}, {3543, 11550}, {3545, 37645}, {3564, 10151}, {3830, 34514}, {3832, 44872}, {3843, 12160}, {3845, 41628}, {5012, 12022}, {5133, 16657}, {5159, 15025}, {5640, 18420}, {5663, 31726}, {5921, 32127}, {6030, 16618}, {6193, 18504}, {6240, 41587}, {6241, 25738}, {6243, 18377}, {6640, 11704}, {6699, 37948}, {6759, 34799}, {6761, 46106}, {6815, 15028}, {7464, 36253}, {7488, 21659}, {7505, 11449}, {7527, 21243}, {7547, 36747}, {7552, 18475}, {7574, 13391}, {7577, 13352}, {7691, 12605}, {7728, 44283}, {7951, 9637}, {9729, 43816}, {9820, 35487}, {9936, 45014}, {10055, 11446}, {10071, 19367}, {10112, 43831}, {10149, 12903}, {10201, 11464}, {10224, 37495}, {10257, 15059}, {10263, 18379}, {10295, 15133}, {10296, 41586}, {10297, 15044}, {10539, 44958}, {10540, 11563}, {10564, 15081}, {10574, 18912}, {10689, 34334}, {11250, 43608}, {11412, 18404}, {11440, 12359}, {11441, 12429}, {11454, 35481}, {11455, 44276}, {11457, 12279}, {11468, 34350}, {11572, 13598}, {11591, 43865}, {11649, 32273}, {11750, 12088}, {11799, 14157}, {11801, 37477}, {12038, 14940}, {12084, 23294}, {12086, 20299}, {12121, 15646}, {12163, 35490}, {12241, 13160}, {12272, 18385}, {12290, 31725}, {12310, 37954}, {12324, 15077}, {12383, 37943}, {12897, 14865}, {13142, 23047}, {13353, 43575}, {13403, 14118}, {13470, 13564}, {13567, 15053}, {13619, 32110}, {14094, 47336}, {14130, 34826}, {14156, 23515}, {14449, 15800}, {14568, 34211}, {14643, 40111}, {14982, 41720}, {15027, 37950}, {15035, 44452}, {15043, 39571}, {15045, 50008}, {15051, 47296}, {15054, 15311}, {15055, 16386}, {15061, 34152}, {15066, 16072}, {15078, 26958}, {16000, 45788}, {16013, 46939}, {16163, 37941}, {16196, 22808}, {18350, 44235}, {18356, 18439}, {18383, 45186}, {18394, 18569}, {18405, 33586}, {18430, 44288}, {18440, 40318}, {18859, 38724}, {18911, 20791}, {22466, 23308}, {22804, 44056}, {23236, 44961}, {23325, 31074}, {26879, 43601}, {29012, 37945}, {30510, 34104}, {30744, 37497}, {31101, 37480}, {31180, 37483}, {31830, 38848}, {32223, 37940}, {34153, 44234}, {34484, 45286}, {34664, 37636}, {34783, 44279}, {34864, 43835}, {35480, 37489}, {35491, 44158}, {37925, 44407}, {37968, 38723}, {38397, 49669}, {40647, 43808}, {43588, 43602}, {44280, 44569}, {44862, 45308}

X(50435) = midpoint of X(2070) and X(12902)
X(50435) = reflection of X(i) in X(j) for these {i,j}: {20, 21663}, {110, 403}, {323, 1568}, {1568, 7687}, {2071, 125}, {3153, 13851}, {7728, 44283}, {10540, 11563}, {12121, 15646}, {13619, 32110}, {14157, 11799}, {16163, 44673}, {18403, 10113}, {22115, 5}, {25739, 265}, {34153, 44234}, {37477, 37938}, {37938, 11801}, {40111, 46031}, {43574, 2072}, {44280, 44569}
X(50435) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {158, 146}, {1096, 39358}, {2159, 46717}, {2349, 6527}, {8749, 6360}, {15459, 7192}, {16080, 4329}, {24000, 14611}, {32695, 4560}, {36119, 20}, {42308, 21295}
X(50435) = crosspoint of X(i) and X(j) for these (i,j): {801, 1494}, {6528, 39295}
X(50435) = crosssum of X(i) and X(j) for these (i,j): {800, 1495}, {2088, 39201}, {9409, 47421}
X(50435) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 68, 12111}, {4, 11442, 15305}, {24, 12293, 12278}, {26, 12289, 41482}, {378, 14852, 23293}, {1899, 44440, 15072}, {3060, 18392, 4}, {7505, 12118, 11449}, {10024, 12370, 54}, {10263, 18379, 31724}, {12022, 15760, 5012}, {12241, 13160, 13434}, {12359, 18560, 11440}, {12429, 37197, 11441}, {13567, 38323, 15053}, {14644, 43574, 2072}, {15044, 23061, 10297}, {15761, 44076, 1614}, {16163, 44673, 37941}, {18356, 18439, 43895}, {18356, 44271, 18439}, {31725, 32140, 12290}, {40111, 46031, 14643}


X(50436) = EULER LINE INTERCEPT OF X(147)X(38661)

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

See Tran Quang Hung and Francisco Javier García Capitán, euclid 5178.

X(50436) lies on these lines: {2,3}, {147,38661}, {385,2420}, {2407,12215}, {4048,40879}, {5149,5649}, {5664,8290}


X(50437) = EULER LINE INTERCEPT OF X(6)X(877)

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

See Tran Quang Hung and Peter Moses, euclid 5181.

X(50437) lies on the cubic K553 and these lines: {2, 3}, {6, 877}, {76, 249}, {99, 6531}, {112, 39931}, {648, 5182}, {1691, 44132}, {2967, 10352}, {3269, 31636}, {4048, 44144}, {5108, 18020}, {7754, 34211}, {32697, 47736}, {34359, 36794}, {34473, 45031}, {35912, 39646}


X(50438) = X(10)X(37)∩X(516)X(5318)

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

See César Lozada, euclid 5180.

X(50438) lies on these lines: {10, 37}, {516, 5318}, {11488, 37830}


X(50439) = X(10)X(37)∩X(516)X(5321)

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

See César Lozada, euclid 5180.

X(50439) lies on these lines: {10, 37}, {516, 5321}, {11489, 37833}


X(50440) = X(11)X(1211)∩X(114)X(325)

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

See César Lozada, euclid 5180.

X(50440) lies on these lines: {1, 16613}, {8, 3903}, {10, 4531}, {11, 1211}, {72, 4109}, {75, 30546}, {114, 325}, {115, 14839}, {210, 3773}, {238, 1914}, {291, 16592}, {440, 2968}, {442, 4904}, {518, 10026}, {620, 3110}, {644, 37014}, {661, 4712}, {674, 44396}, {740, 3027}, {760, 5164}, {960, 1146}, {1282, 21383}, {2886, 8286}, {3056, 27688}, {3688, 46826}, {3742, 3756}, {3779, 27556}, {3932, 20723}, {4010, 4155}, {4087, 40717}, {4417, 10477}, {4553, 8287}, {20337, 20358}, {20590, 20865}, {25304, 27704}, {35078, 50254}

X(50440) = midpoint of X(8) and X(3903)
X(50440) = reflection of X(i) in X(j) for these (i, j): (3110, 620), (40608, 10)
X(50440) = complement of the isogonal conjugate of X(1284)
X(50440) = complementary conjugate of the complement of X(1284)
X(50440) = crossdifference of every pair of points on the line {X(876), X(1910)}
X(50440) = crosssum of X(874) and X(22373)
X(50440) = X(8)-beth conjugate of-X(40608)
X(50440) = X(8)-Ceva conjugate of-X(740)
X(50440) = X(i)-complementary conjugate of-X(j) for these (i, j): (56, 740), (65, 3836), (226, 20541), (238, 960), (239, 21246)
X(50440) = X(325)-Dao conjugate of-X(8033)
X(50440) = X(i)-isoconjugate-of-X(j) for these {i, j}: {98, 741}, {875, 36036}, {876, 36084}
X(50440) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (237, 18268), (325, 40017), (511, 37128), (740, 1821), (862, 6531)
X(50440) = perspector of the circumconic {{A, B, C, X(1959), X(2396)}}
X(50440) = center of the circumconic {{A, B, C, X(8), X(3903)}}
X(50440) = barycentric product X(i)*X(j) for these {i, j}: {8, 16591}, {325, 2238}, {511, 3948}, {740, 1959}, {862, 6393}, {874, 3569}
X(50440) = barycentric quotient X(i)/X(j) for these (i, j): (237, 18268), (325, 40017), (511, 37128), (740, 1821), (862, 6531), (874, 43187)
X(50440) = trilinear product X(i)*X(j) for these {i, j}: {9, 16591}, {237, 35544}, {325, 3747}, {350, 5360}, {511, 740}, {1284, 44694}
X(50440) = trilinear quotient X(i)/X(j) for these (i, j): (325, 18827), (511, 741), (740, 98), (874, 36036), (1755, 18268)
X(50440) = {X(17793), X(45162)}-harmonic conjugate of X(46842)


X(50441) = X(2)X(11)∩X(8)X(348)

Barycentrics    ((b+c)*a-b^2-c^2)*(2*a^3-(b+c)*a^2-(b^2-c^2)*(b-c)) : :
X(50441) = 5*X(1698)-4*X(40483), 5*X(3617)-X(39351), 7*X(9780)-5*X(31640)

See César Lozada, euclid 5180.

X(50441) lies on these lines: {1, 4904}, {2, 11}, {8, 348}, {10, 1146}, {40, 2883}, {77, 30620}, {118, 516}, {197, 7580}, {198, 11677}, {200, 223}, {291, 24396}, {307, 3059}, {325, 32850}, {347, 4012}, {480, 28739}, {518, 1362}, {519, 35094}, {545, 24411}, {676, 24014}, {918, 2254}, {958, 36706}, {972, 35514}, {984, 24449}, {1086, 36219}, {1145, 3126}, {1214, 2968}, {1282, 5845}, {1329, 36652}, {1375, 40910}, {1458, 39066}, {1565, 2809}, {1575, 8608}, {1698, 40483}, {1818, 4966}, {1834, 16613}, {1861, 3693}, {1944, 38454}, {2293, 25964}, {2310, 21914}, {3030, 38992}, {3174, 18634}, {3617, 39351}, {3717, 40883}, {3752, 3755}, {3846, 20103}, {3870, 6505}, {3935, 40612}, {3939, 36949}, {4081, 4552}, {4085, 40533}, {4357, 15587}, {4364, 24341}, {4417, 43290}, {4706, 8758}, {4733, 6741}, {5400, 5743}, {5438, 25914}, {5819, 44431}, {5836, 40608}, {5842, 36027}, {5852, 40868}, {5880, 40719}, {6067, 17077}, {6603, 28849}, {8226, 44411}, {8256, 9311}, {8286, 13405}, {9504, 17755}, {9780, 31640}, {10025, 17768}, {10186, 34522}, {11495, 27509}, {14100, 25019}, {15624, 23305}, {15726, 40880}, {19868, 20540}, {20935, 31627}, {24248, 24352}, {25355, 49524}, {26006, 41339}, {26932, 35338}, {29207, 41327}, {31038, 49470}, {36845, 49486}, {39035, 44669}, {39050, 46393}, {39959, 49688}

X(50441) = midpoint of X(8) and X(664)
X(50441) = reflection of X(i) in X(j) for these (i, j): (1, 17044), (1146, 10)
X(50441) = complement of X(14942)
X(50441) = complementary conjugate of the complement of X(1458)
X(50441) = crossdifference of every pair of points on line {X(665), X(911)}
X(50441) = crosssum of X(926) and X(44408)
X(50441) = X(8)-beth conjugate of-X(1146)
X(50441) = X(i)-Ceva conjugate of-X(j) for these (i, j): (2, 40869), (8, 518), (664, 918)
X(50441) = X(i)-complementary conjugate of-X(j) for these (i, j): (6, 34852), (7, 20544), (31, 40869), (56, 518), (57, 20335)
X(50441) = X(i)-daleth conjugate of-X(j) for these (i, j): (2, 16593), (516, 17747)
X(50441) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 9503), (241, 7), (676, 11)
X(50441) = X(i)-Hirst inverse of-X(j) for these (i, j): {2, 20533}, {516, 40869}
X(50441) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 9503}, {103, 105}, {673, 911}, {677, 1027}
X(50441) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 9503), (241, 43736), (516, 673), (518, 36101), (665, 2424)
X(50441) = perspector of the circumconic {{A, B, C, X(666), X(2398)}}
X(50441) = center of the circumconic {{A, B, C, X(8), X(664)}}
X(50441) = inverse of X(16593) in Steiner inellipse
X(50441) = inverse of X(20533) in Steiner circumellipse
X(50441) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(34337)}} and {{A, B, C, X(11), X(1566)}}
X(50441) = barycentric product X(i)*X(j) for these {i, j}: {8, 39063}, {75, 9502}, {516, 3912}, {518, 30807}, {672, 35517}, {676, 42720}
X(50441) = barycentric quotient X(i)/X(j) for these (i, j): (1, 9503), (241, 43736), (516, 673), (518, 36101), (665, 2424), (672, 103)
X(50441) = trilinear product X(i)*X(j) for these {i, j}: {2, 9502}, {9, 39063}, {241, 40869}, {516, 518}, {665, 42719}, {672, 30807}
X(50441) = trilinear quotient X(i)/X(j) for these (i, j): (2, 9503), (516, 105), (518, 103), (672, 911), (676, 1027), (910, 1438)


X(50442) = X(8)X(908)∩X(189)X(226)

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

See César Lozada, euclid 5180.

X(50442) lies on these lines: {2, 20223}, {7, 34234}, {8, 908}, {29, 5703}, {92, 5226}, {189, 226}, {312, 3262}, {329, 333}, {344, 4997}, {2399, 3239}, {2994, 31053}, {4518, 30741}, {4945, 36596}, {5328, 26591}, {5603, 36921}, {5744, 30608}, {5942, 21739}, {6557, 30852}, {7020, 41013}, {9776, 40420}, {17316, 17947}, {18228, 40435}, {27287, 46880}, {33077, 46873}

X(50442) = isotomic conjugate of X(5744)
X(50442) = polar conjugate of X(34231)
X(50442) = crosspoint of X(i) and X(j) for these (i, j): {2, 5219}, {7, 5603}, {75, 31397}, {273, 7682}
X(50442) = X(i)-cross conjugate of-X(j) for these (i, j): (1000, 36588), (1512, 18815)
X(50442) = X(i)-Dao conjugate of-X(j) for these (i, j): (9, 3576), (281, 37410)
X(50442) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 3576}, {48, 34231}
X(50442) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 3576), (4, 34231)
X(50442) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(36100)}} and {{A, B, C, X(2), X(8)}}
X(50442) = trilinear pole of the line {522, 10015}
X(50442) = barycentric product X(i)*X(j) for these {i, j}: {75, 3577}, {903, 36925}, {1268, 44730}
X(50442) = barycentric quotient X(i)/X(j) for these (i, j): (1, 3576), (4, 34231)
X(50442) = trilinear product X(i)*X(j) for these {i, j}: {2, 3577}, {88, 36925}, {1255, 44730}
X(50442) = trilinear quotient X(i)/X(j) for these (i, j): (2, 3576), (92, 34231)


X(50443) = X(1)X(5)∩X(40)X(499)

Barycentrics    (a-b-c) (a^3-3 a (b-c)^2-2 (b-c)^2 (b+c)) : :
X(50443) = (r-2 R) X(1) + 4r X(5)

See Angel Montesdeoca, euclid 5183 and HG060622

X(50443) lies on these lines: {1,5}, {2,1697}, {3,7743}, {4,1420}, {7,7285}, {8,18220}, {9,10527}, {10,7962}, {36,4333}, {40,499}, {46,3582}, {55,3624}, {56,1699}, {57,946}, {65,11522}, {78,24392}, {84,1519}, {104,7704}, {142,10384}, {145,30852}, {149,4855}, {165,5433}, {200,3813}, {226,11037}, {318,4939}, {381,9613}, {382,5126}, {388,3817}, {390,5550}, {392,5705}, {442,15845}, {443,497}, {498,31393}, {515,10591}, {516,7288}, {551,3486}, {590,31432}, {614,33178}, {631,10624}, {908,6762}, {936,24390}, {942,18493}, {950,3616}, {960,5231}, {962,3911}, {995,2654}, {997,24387}, {999,9612}, {1058,10389}, {1111,47444}, {1155,9589}, {1210,3340}, {1319,5691}, {1320,7705}, {1329,4853}, {1385,3586}, {1467,8727}, {1479,3576}, {1532,12650}, {1656,9957}, {1698,3057}, {1702,9661}, {1737,6978}, {1788,4301}, {1836,3361}, {1858,18398}, {1864,5045}, {2078,3149}, {2093,22791}, {2098,3679}, {2136,5552}, {2170,23058}, {2646,11238}, {2886,8583}, {3085,37556}, {3090,31397}, {3091,10106}, {3158,27385}, {3295,11230}, {3304,5290}, {3333,4654}, {3338,18393}, {3339,17728}, {3359,26492}, {3434,5438}, {3452,26129}, {3475,21625}, {3476,19925}, {3485,11019}, {3487,44841}, {3583,37618}, {3600,9779}, {3612,4857}, {3617,4345}, {3622,31266}, {3632,5048}, {3634,4342}, {3646,19854}, {3649,10980}, {3660,12688}, {3680,6735}, {3742,12711}, {3746,11502}, {3812,31249}, {3829,5794}, {3832,4308}, {3872,4193}, {3895,27529}, {3928,11415}, {3953,24430}, {4187,9623}, {4293,18483}, {4294,10165}, {4297,5225}, {4312,32636}, {4313,46934}, {4315,5229}, {4321,42356}, {4511,12625}, {4512,4999}, {4666,10393}, {4679,5234}, {4848,5704}, {4862,24798}, {4915,21031}, {4997,44720}, {5044,17642}, {5070,31436}, {5082,6700}, {5083,12528}, {5087,12513}, {5119,31423}, {5122,48661}, {5123,10912}, {5154,38460}, {5175,24558}, {5193,12114}, {5217,38031}, {5218,12575}, {5249,10586}, {5251,10966}, {5259,26357}, {5265,9812}, {5432,34595}, {5434,30308}, {5436,24541}, {5450,16174}, {5563,22760}, {5570,5693}, {5573,28018}, {5795,6919}, {5836,17622}, {5853,27383}, {5904,18839}, {6284,7987}, {6667,13463}, {6684,30305}, {6734,15829}, {6763,7082}, {6982,10572}, {7080,21627}, {7308,19843}, {7354,13462}, {7701,33593}, {7702,34789}, {7966,10786}, {7991,24914}, {8256,34640}, {8580,24954}, {9336,11998}, {9668,13624}, {9670,37600}, {9856,37566}, {10085,41690}, {10157,16215}, {10171,10588}, {10385,19883}, {10388,31419}, {10392,11038}, {10395,11523}, {10398,20330}, {10573,16200}, {10582,28628}, {10584,24982}, {10707,34701}, {10889,17322}, {10895,20323}, {10965,48696}, {11035,17604}, {11224,41687}, {11510,44425}, {11531,40663}, {11680,19861}, {11681,36846}, {11997,40328}, {12541,27525}, {12589,16475}, {12629,17757}, {12699,15325}, {12953,37605}, {13253,20118}, {13274,15015}, {13464,18391}, {13888,19038}, {13942,19037}, {14923,15558}, {15171,30282}, {15299,38036}, {15717,30332}, {16004,35242}, {16189,30286}, {16485,40950}, {17064,21214}, {17282,26093}, {18240,31803}, {18395,30323}, {18492,45287}, {18525,25405}, {18991,44624}, {18992,44623}, {19003,19030}, {19004,19029}, {21075,34625}, {21616,31142}, {22753,37583}, {24174,45269}, {24179,41010}, {25440,32557}, {26363,31435}, {28082,45272}, {28151,44448}, {28194,41348}, {30478,40998}, {31401,31426}, {31433,31455}, {31479,31792}, {31795,37606}, {32558,35262}, {34716,37375}, {38150,42884}


X(50444) = X(1)X(5)∩X(165)X(499)

Barycentrics    (a-b-c) (a^3-5 a (b-c)^2-4 (b-c)^2 (b+c)) : :
X(50444) = (r-4 R) X(1) + 8r X(5)

See Angel Montesdeoca, euclid 5183 and HG060622

X(50444) lies on these lines: {1,5}, {2,12575}, {4,13462}, {40,7743}, {46,45035}, {55,16863}, {84,22835}, {140,31508}, {165,499}, {390,19862}, {497,3624}, {519,5828}, {936,24387}, {942,38021}, {946,3339}, {950,25055}, {1000,31399}, {1125,4208}, {1158,16174}, {1210,11522}, {1329,4915}, {1420,10896}, {1479,6916}, {1482,30286}, {1519,7992}, {1538,10864}, {1656,31393}, {1698,9819}, {1699,3086}, {1737,11531}, {2098,4668}, {3057,19875}, {3062,10305}, {3333,9955}, {3337,30223}, {3452,4866}, {3576,9669}, {3582,15803}, {3586,30389}, {3600,12571}, {3601,11238}, {3617,8275}, {3626,4345}, {3634,9785}, {3646,31493}, {3680,5123}, {3813,4882}, {3814,12629}, {3817,5290}, {3825,9623}, {3828,4862}, {3832,4315}, {3911,9589}, {4193,4853}, {4298,9779}, {4301,5704}, {4314,5550}, {4321,7678}, {4342,9780}, {4847,26129}, {4855,10707}, {4857,30282}, {4900,6736}, {5045,17604}, {5055,31792}, {5087,6762}, {5154,36846}, {5223,21616}, {5226,21625}, {5231,41012}, {5234,10527}, {5281,19878}, {5433,9580}, {5438,11235}, {5691,10591}, {5734,16236}, {5833,26363}, {6260,9851}, {6847,24644}, {7962,17606}, {7991,30384}, {8580,24390}, {8583,11680}, {9583,35803}, {9588,30305}, {9612,10072}, {9671,37605}, {10039,30315}, {10043,16207}, {10270,26492}, {10394,38024}, {10572,30392}, {10573,16189}, {10980,12047}, {11019,11036}, {11519,17757}, {11529,18493}, {12127,12607}, {12528,18240}, {12701,31231}, {13407,30343}, {15079,30323}, {15325,41869}, {18492,24928}, {19003,44623}, {19004,44624}, {22760,37587}, {23681,28018}, {24392,25681}, {25079,46872}, {30294,31788}, {30337,31434}, {34628,37618}, {37828,45310}


X(50445) = X(1)X(15476)∩X(1100)X(8287)

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

See Kadir Altintas and César Lozada, euclid 5184.

X(50445) lies on these lines: {1, 15476}, {1100, 8287}, {1963, 40214}, {3982, 6610}, {5045, 5144}, {8044, 25417}

X(50445) = midpoint of X(1) and X(15476)


X(50446) = X(24)X(50209)∩X(11387)X(43976)

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

See Kadir Altintas and César Lozada, euclid 5184.

X(50446) lies on these lines: {24, 50209}, {11387, 43976}, {31364, 42400}


X(50447) = X(3)X(6)∩X(3526)X(30465)

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

See Kadir Altintas and César Lozada, euclid 5184.

X(50447) lies on these lines: {3, 6}, {3526, 30465}, {11555, 16960}


X(50448) = X(3)X(6)∩X(3526)X(30468)

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

See Kadir Altintas and César Lozada, euclid 5184.

X(50448) lies on these lines: {3, 6}, {3526, 30468}, {11556, 16961}


leftri

Points in a [[b c, c a, a b], [a^3, b^3, c^3]] coordinate system: X(50449)-X(50459)

rightri

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

L1 is the line: b c α + c a β + a b γ = 0.

L2 is the line a^3 α + b^3 β + c^3 γ = 0.

The origin is given by (0, 0) = X(8061) = a(b^4 - c^4) : : .

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

u : v : w = a(b^4 - c^4) - a(b - c) x - (b^3 - c^3) y ,

where, as functions of a, b, c, the coordinate x is symmetric of degree 3, and y is symmetric of degree 2.

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

{-(a+b+c)^3, -((a b c)/(a+b+c))}, 47947
{-((a+b+c) (a b+a c+b c)), -((a b c)/(a+b+c))}, 47959
{-((a+b) (a+c) (b+c)), 0}, 661
{-(1/2) (a+b) (a+c) (b+c), ((a+b) (a+c) (b+c))/(2 (a+b+c))}, 4129
{0, 0}, 8061
{0, ((a+b) (a+c) (b+c))/(a+b+c)}, 1577
{1/2 (a^3+b^3+c^3), 1/2 (a b+a c+b c)}, 8060
{1/2 (a^3+b^3+c^3), (a b c)/(2 (a+b+c))}, 14838
{a b c, -a^2-b^2-c^2}, 16892
{(a+b+c) (a^2+b^2+c^2), -((a b c)/(a+b+c))}, 4063
{a b c, a b+a c+b c}, 693
{a b c, (a+b+c)^2}, 4024
{-2*(a + b)*(a + c)*(b + c), -(((a + b)*(a + c)*(b + c))/(a + b + c))}, 50449
{-2*a*b*c, a*b + a*c + b*c}, 50450
{-(a*b*c), a*b + a*c + b*c}, 50451
{-((a + b)*(a + c)*(b + c)), a*b + a*c + b*c}, 50452
{-1/2*(a*b*c), -1/2*(a^3 + b^3 + c^3)/(a + b + c)}, 50453
{a*b*c, 0}, 50454
{(a + b + c)*(a^2 + b^2 + c^2), 0}, 50455
{a^3 + b^3 + c^3, (a*b*c)/(a + b + c)}, 50456
{(a + b)*(a + c)*(b + c), (2*(a + b)*(a + c)*(b + c))/(a + b + c)}, 50457
{a^3 + b^3 + c^3, (2*a*b*c)/(a + b + c)}, 50458
{(a^4 + b^4 + c^4)/(a + b + c), (2*a*b*c)/(a + b + c)}, 50459


X(50449) = X(512)X(4824)∩X(514)X(661)

Barycentrics    (b - c)*(b + c)*(2*a^2 + 2*a*b + 2*a*c + b*c) : :
X(50449) = 3 X[661] - 2 X[4129], 4 X[661] - 3 X[48551], 3 X[1577] - 4 X[4129], 2 X[1577] - 3 X[48551], X[3762] - 4 X[47996], 8 X[4129] - 9 X[48551], X[4391] - 3 X[48548], 3 X[4776] - 2 X[4823], 2 X[47997] - 3 X[48548], 2 X[1019] - 3 X[45671], X[4761] - 4 X[48002], 2 X[7192] - 3 X[48568], 4 X[14838] - 3 X[48568]

X(50449) lies on these lines: {512, 4824}, {514, 661}, {523, 4170}, {525, 4841}, {656, 4778}, {798, 1019}, {810, 4040}, {2530, 4977}, {3124, 7208}, {4151, 4822}, {4367, 4963}, {4369, 4960}, {4705, 4761}, {7192, 14838}

X(50449) = midpoint of X(i) and X(j) for these {i,j}: {4367, 4963}, {4822, 47934}, {47917, 48131}
X(50449) = reflection of X(i) in X(j) for these {i,j}: {693, 48054}, {1577, 661}, {3762, 47959}, {4170, 4983}, {4391, 47997}, {4705, 48002}, {4761, 4705}, {4960, 4369}, {4978, 14349}, {7192, 14838}, {47679, 4841}, {47959, 47996}, {48407, 4824}
X(50449) = X(28148)-complementary conjugate of X(3739)
X(50449) = X(i)-isoconjugate of X(j) for these (i,j): {6, 43356}, {110, 39983}, {163, 39708}
X(50449) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 43356}, {115, 39708}, {244, 39983}
X(50449) = crosssum of X(i) and X(j) for these (i,j): {48, 46382}, {3720, 46385}
X(50449) = crossdifference of every pair of points on line {31, 2667}
X(50449) = barycentric product X(i)*X(j) for these {i,j}: {10, 48107}, {321, 48064}, {523, 17394}, {1577, 37685}, {14208, 17562}
X(50449) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 43356}, {523, 39708}, {661, 39983}, {17394, 99}, {17562, 162}, {37685, 662}, {48064, 81}, {48107, 86}
X(50449) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {661, 1577, 48551}, {4391, 48548, 47997}, {7192, 14838, 48568}


X(50450) = X(75)X(4391)∩X(320)X(350)

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

X(50450) lies on these lines: {75, 4391}, {319, 3900}, {320, 350}, {824, 3762}, {1577, 4406}, {1734, 5224}, {2786, 4791}, {3261, 4985}, {4357, 8714}

X(50450) = X(29213)-anticomplementary conjugate of X(2)
X(50450) = X(14077)-Dao conjugate of X(47787)
X(50450) = cevapoint of X(29212) and X(47787)
X(50450) = barycentric product X(i)*X(j) for these {i,j}: {75, 27486}, {693, 17346}, {4262, 40495}
X(50450) = barycentric quotient X(i)/X(j) for these {i,j}: {4262, 692}, {17346, 100}, {27486, 1}
X(50450) = {X(4811),X(15413)}-harmonic conjugate of X(20954)


X(50451) = X(75)X(4036)∩X(320)X(350)

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

X(50451) lies on these lines: {75, 4036}, {192, 4140}, {319, 8702}, {320, 350}, {522, 4357}, {656, 4467}, {824, 4391}, {1269, 3261}, {1577, 2786}, {3766, 4509}

X(50451) = X(29038)-anticomplementary conjugate of X(2)
X(50451) = X(i)-Ceva conjugate of X(j) for these (i,j): {1577, 693}, {4374, 20906}
X(50451) = X(i)-isoconjugate of X(j) for these (i,j): {100, 18757}, {101, 2248}, {112, 15377}, {692, 13610}, {6625, 32739}, {34069, 40777}
X(50451) = X(i)-Dao conjugate of X(j) for these (i,j): {1, 6627}, {86, 662}, {1015, 2248}, {1086, 13610}, {4705, 21196}, {6625, 40619}, {8054, 18757}, {15377, 34591}
X(50451) = crosspoint of X(i) and X(j) for these (i,j): {75, 4623}, {668, 40033}
X(50451) = crossdifference of every pair of points on line {213, 7122}
X(50451) = barycentric product X(i)*X(j) for these {i,j}: {75, 21196}, {514, 17762}, {693, 1654}, {846, 3261}, {850, 38814}, {1577, 6626}, {2905, 14208}, {4213, 15413}, {4391, 17084}, {4623, 6627}, {7192, 27569}, {7199, 21085}, {14844, 18160}, {18155, 27691}, {18755, 40495}
X(50451) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 2248}, {514, 13610}, {649, 18757}, {656, 15377}, {693, 6625}, {824, 40777}, {846, 101}, {1654, 100}, {2905, 162}, {4213, 1783}, {6626, 662}, {6627, 4705}, {7199, 40164}, {17084, 651}, {17762, 190}, {18755, 692}, {21085, 1018}, {21196, 1}, {21879, 4557}, {22139, 906}, {24381, 2295}, {27569, 3952}, {27691, 4551}, {27954, 4579}, {38814, 110}, {39921, 37135}, {40722, 1492}, {40751, 825}
X(50451) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 18158, 4036}, {693, 4811, 23794}, {4509, 4985, 3766}, {7199, 30591, 693}, {7650, 15413, 693}, {20954, 48084, 693}


X(50452) = X(103)X(9073)∩X(320)X(350)

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

X(50452) lies on these lines: {103, 9073}, {320, 350}, {649, 4486}, {661, 824}, {1491, 4467}, {2786, 3835}, {3004, 4806}, {3837, 4897}, {4406, 14288}

X(50452) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 48080, 20295}, {693, 48107, 21146}, {43067, 48090, 693}


X(50453) = X(10)X(523)∩X(241)X(514)

Barycentrics    (b - c)*(b + c)*(a*b + b^2 + a*c - b*c + c^2) : :
X(50453) = X[4841] + 3 X[7178], X[4841] - 3 X[48402], X[43052] + 3 X[47880], 3 X[4129] - 2 X[14321], 3 X[4129] - X[22037], 3 X[1577] - X[4024], X[4024] + 3 X[21124], X[4122] - 3 X[14431]

X(50453) lies on these lines: {10, 523}, {241, 514}, {525, 4129}, {661, 4707}, {690, 4806}, {824, 4791}, {830, 4142}, {850, 1577}, {3800, 4807}, {3801, 4705}, {4122, 14431}, {4160, 4458}

X(50453) = midpoint of X(i) and X(j) for these {i,j}: {661, 4707}, {1577, 21124}, {3004, 10015}, {3801, 4705}, {7178, 48402}
X(50453) = reflection of X(i) in X(j) for these {i,j}: {3960, 21212}, {22037, 14321}
X(50453) = X(9070)-complementary conjugate of X(141)
X(50453) = X(i)-Ceva conjugate of X(j) for these (i,j): {39706, 1086}, {44435, 48350}
X(50453) = X(i)-isoconjugate of X(j) for these (i,j): {110, 40401}, {163, 996}, {1333, 9059}, {3285, 36091}
X(50453) = X(i)-Dao conjugate of X(j) for these (i,j): {37, 9059}, {115, 996}, {244, 40401}, {47766, 47845}
X(50453) = crossdifference of every pair of points on line {55, 2206}
X(50453) = barycentric product X(i)*X(j) for these {i,j}: {10, 44435}, {75, 48350}, {313, 9002}, {321, 48335}, {514, 26580}, {523, 4389}, {661, 33934}, {693, 4424}, {850, 995}, {1577, 4850}, {3877, 4077}, {4024, 16712}, {4080, 23888}, {5233, 7178}, {21130, 30588}
X(50453) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 9059}, {523, 996}, {661, 40401}, {995, 110}, {3877, 643}, {4266, 5546}, {4389, 99}, {4424, 100}, {4674, 36091}, {4850, 662}, {5233, 645}, {9002, 58}, {16712, 4610}, {21042, 4767}, {21130, 5235}, {23206, 4575}, {23888, 16704}, {26580, 190}, {33934, 799}, {44435, 86}, {48335, 81}, {48350, 1}
X(50453) = {X(4129),X(22037)}-harmonic conjugate of X(14321)


X(50454) = X(44)X(513)∩X(321)X(693)

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

X(50454) lies on these lines: {44, 513}, {321, 693}, {905, 5029}, {2530, 3250}, {2786, 3835}, {3700, 3837}, {4750, 4776}, {6004, 8632}

X(50454) = crossdifference of every pair of points on line {1, 2210}
X(50454) = barycentric product X(i)*X(j) for these {i,j}: {513, 29674}, {514, 49509}, {650, 36482}, {661, 30965}
X(50454) = barycentric quotient X(i)/X(j) for these {i,j}: {29674, 668}, {30965, 799}, {36482, 4554}, {49509, 190}
X(50454) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {656, 48033, 20979}, {661, 2254, 649}, {661, 48019, 48024}, {2530, 24290, 3250}, {48026, 48030, 661}, {48031, 50350, 798}


X(50455) = X(44)X(513)∩X(802)X(10566)

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

X(50455) lies on these lines: {44, 513}, {802, 10566}, {824, 4063}, {834, 8632}, {1919, 6371}, {3250, 4057}, {4491, 4502}, {4817, 7199}, {4832, 8659}

X(50455) = isogonal conjugate of the isotomic conjugate of X(47958)
X(50455) = X(i)-Ceva conjugate of X(j) for these (i,j): {28506, 55}, {33952, 17017}
X(50455) = crosspoint of X(17017) and X(33952)
X(50455) = crosssum of X(649) and X(29816)
X(50455) = crossdifference of every pair of points on line {1, 3773}
X(50455) = barycentric product X(i)*X(j) for these {i,j}: {6, 47958}, {513, 17017}, {649, 4657}, {667, 33945}, {1015, 33952}, {3966, 43924}
X(50455) = barycentric quotient X(i)/X(j) for these {i,j}: {4657, 1978}, {17017, 668}, {33945, 6386}, {33952, 31625}, {47958, 76}
X(50455) = {X(649),X(20979)}-harmonic conjugate of X(2483)


X(50456) = X(36)X(238)∩X(99)X(101)

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

X(50456) lies on these lines: {36, 238}, {99, 101}, {105, 741}, {171, 5040}, {514, 1919}, {659, 8300}, {812, 4366}, {824, 4560}, {1429, 7212}, {1577, 8060}, {3776, 4817}, {8061, 14838}

X(50456) = reflection of X(i) in X(j) for these {i,j}: {1577, 8060}, {8061, 14838}
X(50456) = X(i)-Ceva conjugate of X(j) for these (i,j): {4584, 81}, {4596, 8298}, {34594, 18205}
X(50456) = X(i)-cross conjugate of X(j) for these (i,j): {27918, 1429}, {40623, 1}
X(50456) = X(i)-isoconjugate of X(j) for these (i,j): {10, 813}, {37, 660}, {42, 4562}, {101, 43534}, {213, 4583}, {291, 1018}, {292, 3952}, {321, 34067}, {335, 4557}, {661, 5378}, {741, 4103}, {756, 4584}, {762, 36066}, {805, 21021}, {872, 4639}, {1252, 35352}, {1400, 36801}, {1500, 4589}, {1911, 4033}, {1922, 27808}, {3721, 8684}, {3774, 41072}, {3862, 4613}, {3954, 36081}, {4518, 4559}, {4551, 4876}, {4552, 7077}, {21803, 37134}, {21818, 41209}, {37128, 40521}
X(50456) = X(i)-Dao conjugate of X(j) for these (i,j): {10, 40623}, {321, 35119}, {334, 40620}, {660, 40589}, {661, 35352}, {665, 4088}, {762, 38978}, {1015, 43534}, {1018, 39029}, {3837, 21053}, {3952, 19557}, {4033, 6651}, {4103, 8299}, {4562, 40592}, {4583, 6626}, {5378, 36830}, {27808, 39028}, {36801, 40582}
X(50456) = cevapoint of X(659) and X(8632)
X(50456) = crosspoint of X(81) and X(4584)
X(50456) = crosssum of X(i) and X(j) for these (i,j): {37, 21832}, {512, 21830}, {523, 20486}, {661, 3930}, {4024, 20659}, {4088, 15523}
X(50456) = crossdifference of every pair of points on line {37, 3122}
X(50456) = barycentric product X(i)*X(j) for these {i,j}: {21, 43041}, {58, 3766}, {81, 812}, {86, 659}, {99, 27846}, {238, 7192}, {239, 1019}, {274, 8632}, {286, 22384}, {350, 3733}, {513, 33295}, {649, 30940}, {662, 27918}, {693, 5009}, {741, 27855}, {757, 4010}, {804, 7303}, {873, 4455}, {905, 31905}, {1014, 3716}, {1178, 14296}, {1414, 4124}, {1428, 18155}, {1429, 4560}, {1434, 4435}, {1447, 3737}, {1509, 21832}, {1914, 7199}, {2185, 7212}, {2201, 15419}, {3570, 16726}, {3573, 17205}, {3684, 17096}, {3685, 7203}, {3808, 40415}, {4107, 40432}, {4131, 34856}, {4155, 6628}, {4164, 32010}, {4375, 37128}, {4584, 35119}, {4610, 39786}, {7252, 10030}, {17212, 18786}, {17217, 34252}, {17493, 18200}, {17925, 20769}, {18197, 39914}, {23597, 40773}
X(50456) = barycentric quotient X(i)/X(j) for these {i,j}: {21, 36801}, {58, 660}, {81, 4562}, {86, 4583}, {110, 5378}, {238, 3952}, {239, 4033}, {244, 35352}, {350, 27808}, {513, 43534}, {593, 4584}, {659, 10}, {757, 4589}, {812, 321}, {1019, 335}, {1333, 813}, {1428, 4551}, {1429, 4552}, {1509, 4639}, {1914, 1018}, {2206, 34067}, {2210, 4557}, {2238, 4103}, {3684, 30730}, {3716, 3701}, {3733, 291}, {3737, 4518}, {3747, 40521}, {3766, 313}, {3808, 2887}, {4010, 1089}, {4107, 3963}, {4124, 4086}, {4155, 6535}, {4164, 1215}, {4375, 3948}, {4435, 2321}, {4448, 3992}, {4455, 756}, {4508, 4377}, {4800, 4125}, {4810, 4066}, {5009, 100}, {5027, 21803}, {7192, 334}, {7199, 18895}, {7203, 7233}, {7212, 6358}, {7252, 4876}, {7303, 18829}, {8632, 37}, {14296, 1237}, {16695, 41531}, {16726, 4444}, {18197, 40848}, {18200, 30669}, {21832, 594}, {22384, 72}, {27846, 523}, {27855, 35544}, {27918, 1577}, {30665, 3773}, {30940, 1978}, {31905, 6335}, {33295, 668}, {38348, 6541}, {38367, 21830}, {38813, 8684}, {38989, 4088}, {39786, 4024}, {43041, 1441}, {46387, 3954}, {46390, 762}
X(50456) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1019, 3737, 4481}, {4164, 4455, 238}


X(50457) = X(512)X(4804)∩X(514)X(661)

Barycentrics    (b - c)*(b + c)*(a^2 + a*b + a*c + 2*b*c) : :
X(50457) = 3 X[661] - 4 X[4129], 5 X[661] - 6 X[48551], 3 X[1577] - 2 X[4129], 5 X[1577] - 3 X[48551], 10 X[4129] - 9 X[48551], 3 X[4728] - 4 X[4823], 3 X[4728] - 2 X[14349], 3 X[4789] - 2 X[8045], 4 X[4791] - X[47917], 5 X[7178] - 4 X[7657], 8 X[7657] - 5 X[21124], 2 X[905] - 3 X[4379], 2 X[4490] - 3 X[14430], 2 X[4707] + X[4838], 3 X[4931] - 2 X[7265]

X(50457) lies on these lines: {338, 3942}, {512, 4804}, {514, 661}, {523, 656}, {525, 4024}, {663, 7662}, {784, 2254}, {798, 4498}, {810, 4449}, {905, 4379}, {4010, 4822}, {4077, 7216}, {4151, 4729}, {4369, 4560}, {4490, 4802}, {4707, 4838}, {4931, 7265}, {5214, 6003}, {6002, 7192}

X(50457) = midpoint of X(i) and X(j) for these {i,j}: {4024, 23755}, {4462, 47675}, {4707, 47678}
X(50457) = reflection of X(i) in X(j) for these {i,j}: {661, 1577}, {663, 7662}, {2254, 50352}, {4041, 2533}, {4560, 4369}, {4729, 4761}, {4801, 48399}, {4804, 48393}, {4822, 4010}, {4838, 47678}, {14349, 4823}, {21124, 7178}, {47917, 47959}, {47918, 4391}, {47959, 4791}, {48131, 693}, {48149, 7192}, {48300, 6590}, {48334, 4978}
X(50457) = X(i)-complementary conjugate of X(j) for these (i,j): {28162, 3739}, {31503, 116}
X(50457) = X(43067)-Ceva conjugate of X(8672)
X(50457) = X(i)-isoconjugate of X(j) for these (i,j): {6, 931}, {21, 32693}, {101, 5331}, {110, 941}, {112, 34259}, {163, 31359}, {662, 2258}, {692, 37870}, {959, 5546}, {1576, 34258}, {2194, 32038}, {14574, 40828}
X(50457) = X(i)-Dao conjugate of X(j) for these (i,j): {9, 931}, {21, 17417}, {115, 31359}, {244, 941}, {643, 34261}, {1015, 5331}, {1084, 2258}, {1086, 37870}, {1214, 32038}, {4858, 34258}, {32693, 40611}, {34259, 34591}, {40622, 44733}
X(50457) = crosssum of X(i) and X(j) for these (i,j): {3737, 10458}, {4258, 21789}
X(50457) = crossdifference of every pair of points on line {31, 284}
X(50457) = barycentric product X(i)*X(j) for these {i,j}: {10, 43067}, {75, 8672}, {226, 23880}, {321, 48144}, {514, 31993}, {523, 10436}, {525, 5307}, {561, 8639}, {661, 34284}, {850, 1468}, {940, 1577}, {958, 4077}, {1441, 17418}, {1867, 4025}, {3676, 3714}, {4185, 14208}, {5019, 20948}, {7178, 11679}
X(50457) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 931}, {226, 32038}, {512, 2258}, {513, 5331}, {514, 37870}, {523, 31359}, {656, 34259}, {661, 941}, {940, 662}, {958, 643}, {1400, 32693}, {1468, 110}, {1577, 34258}, {1867, 1897}, {2268, 5546}, {3713, 7259}, {3714, 3699}, {4017, 959}, {4185, 162}, {5019, 163}, {5307, 648}, {7178, 44733}, {8639, 31}, {8672, 1}, {10436, 99}, {11679, 645}, {17418, 21}, {20948, 40828}, {23880, 333}, {31993, 190}, {34284, 799}, {43067, 86}, {48144, 81}
X(50457) = {X(4823),X(14349)}-harmonic conjugate of X(4728)


X(50458) = X(513)X(663)∩X(514)X(8632)

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

X(50458) lies on these lines: {513, 663}, {514, 8632}, {824, 4560}, {905, 5029}, {918, 1919}, {1019, 3250}, {2786, 6332}, {4107, 4391}, {4435, 4498}

X(50458) = crossdifference of every pair of points on line {9, 3778}
X(50458) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {663, 48144, 48131}, {48329, 48330, 663}


X(50459) = X(1)X(824)∩X(513)X(663)

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

X(50459) lies on these lines: {1, 824}, {512, 1919}, {513, 663}, {650, 3745}, {810, 8061}, {1402, 8641}, {1980, 3005}, {8632, 9313}

X(50459) = X(668)-isoconjugate of X(3415)
X(50459) = crosspoint of X(1) and X(825)
X(50459) = crosssum of X(i) and X(j) for these (i,j): {1, 824}, {522, 17023}
X(50459) = crossdifference of every pair of points on line {9, 1760}
X(50459) = barycentric product X(i)*X(j) for these {i,j}: {512, 24632}, {513, 5282}, {514, 37586}, {649, 3416}, {652, 1892}, {21123, 26270}
X(50459) = barycentric quotient X(i)/X(j) for these {i,j}: {1892, 46404}, {1919, 3415}, {3416, 1978}, {5282, 668}, {24632, 670}, {37586, 190}


X(50460) = X(115)X(125)∩X(275)X(23286)

Barycentrics    (b^2-c^2)(a^14 b^2-4 a^12 b^4+4 a^10 b^6+4 a^8 b^8-11 a^6 b^10+8 a^4 b^12-2 a^2 b^14+a^14 c^2-2 a^12 b^2 c^2+3 a^10 b^4 c^2-11 a^8 b^6 c^2+19 a^6 b^8 c^2-12 a^4 b^10 c^2+a^2 b^12 c^2+b^14 c^2-4 a^12 c^4+3 a^10 b^2 c^4+8 a^8 b^4 c^4-8 a^6 b^6 c^4-4 a^4 b^8 c^4+9 a^2 b^10 c^4-4 b^12 c^4+4 a^10 c^6-11 a^8 b^2 c^6-8 a^6 b^4 c^6+16 a^4 b^6 c^6-8 a^2 b^8 c^6+7 b^10 c^6+4 a^8 c^8+19 a^6 b^2 c^8-4 a^4 b^4 c^8-8 a^2 b^6 c^8-8 b^8 c^8-11 a^6 c^10-12 a^4 b^2 c^10+9 a^2 b^4 c^10+7 b^6 c^10+8 a^4 c^12+a^2 b^2 c^12-4 b^4 c^12-2 a^2 c^14+b^2 c^14) : :
Barycentrics    (SB-SC) (2 S^4-(4 R^2-SW)^2 (9 SA^2-6 SA SW-SW^2)-3 S^2 (32 R^4+12 R^2 SA-SA^2-20 R^2 SW-2 SA SW+3 SW^2)) : :

See Tran Quang Hung and Ercole Suppa, euclid 5188.

X(50460) lies on these lines: {115,125}, {275,23286}, {2052,23290}

X(50460) = X(3269)-Hirst inverse of X(42731)


X(50461) = X(265)-CEVA CONJUGATE OF X(3)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - 3*a^4*c^2 - a^2*b^2*c^2 + b^4*c^2 + 3*a^2*c^4 + b^2*c^4 - c^6) : :
X(50461) = X(50461) = X[3] - 4 X[3292], 5 X[3] - 4 X[21663], 5 X[3292] - X[21663], X[12164] + 2 X[15136], 2 X[21663] - 5 X[22115], 2 X[323] + X[399], 5 X[323] + X[12112], 4 X[323] - X[37496], 5 X[399] - 2 X[12112], 2 X[399] + X[37496], 4 X[12112] + 5 X[37496], 2 X[125] - 5 X[40113], 2 X[186] - 3 X[32609], X[32608] - 3 X[32609], X[32608] - 4 X[40111], 3 X[32609] - 4 X[40111], 4 X[15091] - X[43704], 3 X[381] - 2 X[50435], 4 X[1495] - 3 X[37956], 4 X[1511] - 3 X[37955], 2 X[1511] - 3 X[43572], 5 X[1656] - 2 X[41724], 4 X[2072] - 3 X[38724], 4 X[10272] - X[37779], 4 X[10272] - 3 X[37943], X[37779] - 3 X[37943], 2 X[3581] - 3 X[37922], 2 X[5609] + X[23061], 4 X[5609] - X[37924], 2 X[23061] + X[37924], 2 X[13445] - 3 X[18859], X[13445] - 3 X[43574], X[12308] + 2 X[37477], 4 X[7575] - 7 X[15039], 2 X[10510] + X[32254], 5 X[38794] - 4 X[44673], X[12317] - 3 X[44450], 4 X[13392] - 3 X[16532], 2 X[14094] + X[35001], 4 X[14156] - 3 X[15061], 5 X[15040] - 4 X[15646], 3 X[15041] - 4 X[34152], 9 X[15046] - 8 X[46031], 5 X[20125] - 3 X[46451], 2 X[31726] - 3 X[38789], 3 X[35265] - 2 X[37936]

X(50461) lies on the cubic K1278 and these lines: {2, 15037}, {3, 49}, {5, 195}, {6, 5055}, {30, 146}, {51, 21308}, {52, 12316}, {54, 11591}, {68, 10255}, {110, 1154}, {115, 45769}, {125, 40113}, {140, 43845}, {143, 15801}, {154, 37494}, {156, 2937}, {186, 32608}, {265, 539}, {381, 1993}, {382, 11441}, {403, 19504}, {511, 5899}, {520, 34983}, {524, 45016}, {547, 34545}, {549, 15032}, {550, 43605}, {567, 5891}, {568, 9306}, {1157, 15770}, {1173, 18874}, {1199, 3628}, {1351, 9971}, {1353, 45967}, {1493, 13434}, {1495, 37956}, {1498, 17800}, {1511, 37955}, {1614, 6101}, {1656, 5422}, {1657, 32139}, {1807, 23071}, {1986, 37917}, {1995, 13321}, {2071, 10620}, {2072, 3564}, {2914, 10272}, {2930, 11649}, {3043, 37970}, {3060, 7545}, {3153, 32423}, {3193, 37230}, {3289, 22121}, {3410, 39504}, {3448, 37938}, {3470, 15766}, {3526, 7592}, {3534, 11456}, {3545, 11004}, {3581, 37922}, {3819, 13339}, {3830, 18451}, {3843, 36747}, {3845, 15052}, {3851, 17814}, {4653, 28453}, {4658, 36750}, {5012, 15067}, {5054, 15066}, {5070, 17825}, {5073, 37498}, {5093, 9027}, {5097, 14845}, {5462, 22462}, {5504, 11559}, {5576, 31831}, {5609, 13391}, {5612, 5616}, {5648, 19140}, {5654, 10254}, {5663, 13445}, {5876, 14130}, {5889, 45735}, {5907, 37472}, {5944, 7691}, {5965, 14643}, {6000, 12308}, {6102, 15053}, {6193, 18404}, {6243, 10539}, {6640, 11411}, {6759, 37484}, {7100, 23070}, {7488, 12307}, {7502, 9544}, {7506, 12160}, {7575, 15039}, {7579, 15069}, {7666, 17506}, {8614, 13465}, {8681, 18449}, {9706, 10610}, {9716, 49671}, {9936, 25738}, {10095, 41578}, {10112, 43821}, {10170, 13366}, {10201, 45794}, {10217, 10661}, {10218, 10662}, {10264, 46114}, {10282, 17824}, {10510, 19377}, {10564, 17838}, {10601, 15703}, {10625, 47748}, {11064, 12364}, {11427, 14787}, {11440, 35498}, {11444, 32046}, {11793, 13353}, {11898, 19139}, {12046, 46084}, {12086, 33541}, {12118, 18562}, {12162, 37495}, {12227, 38794}, {12301, 47750}, {12310, 45780}, {12317, 44450}, {12370, 43835}, {12902, 18403}, {13150, 13512}, {13292, 50143}, {13346, 18439}, {13352, 18435}, {13392, 16532}, {13619, 34153}, {14094, 35001}, {14118, 31834}, {14156, 15061}, {14269, 44413}, {14449, 34484}, {14516, 31724}, {14683, 46450}, {14831, 43586}, {15018, 15699}, {15033, 15060}, {15040, 15646}, {15041, 34152}, {15046, 46031}, {15106, 40112}, {15123, 19458}, {15137, 18400}, {15246, 44324}, {15316, 21400}, {15533, 44493}, {15681, 37483}, {15694, 17811}, {15781, 44715}, {15800, 45286}, {15806, 21230}, {16661, 33542}, {18364, 43394}, {18917, 37669}, {20125, 46451}, {20806, 39899}, {23292, 48411}, {24981, 44407}, {31626, 46025}, {31726, 38789}, {32063, 44457}, {32136, 43651}, {32165, 43816}, {34380, 37971}, {34782, 48669}, {35265, 37936}, {36752, 46219}, {38896, 43965}, {44282, 44555}

X(50461) = midpoint of X(i) and X(j) for these {i,j}: {12308, 35452}, {14157, 23061}, {14683, 46450}
X(50461) = reflection of X(i) in X(j) for these {i,j}: {3, 22115}, {186, 40111}, {265, 1568}, {2070, 110}, {3448, 37938}, {5899, 10540}, {10264, 46114}, {10620, 2071}, {12902, 18403}, {13619, 34153}, {14157, 5609}, {18859, 43574}, {22115, 3292}, {32608, 186}, {35452, 37477}, {37924, 14157}, {37955, 43572}, {39562, 22151}, {44555, 44282}
X(50461) = isotomic conjugate of the polar conjugate of X(11063)
X(50461) = isogonal conjugate of the polar conjugate of X(37779)
X(50461) = X(i)-Ceva conjugate of X(j) for these (i,j): {265, 3}, {1568, 15781}, {10272, 15766}, {37779, 11063}, {46751, 40604}
X(50461) = X(i)-isoconjugate of X(j) for these (i,j): {19, 13582}, {92, 14579}, {158, 43704}, {1263, 2190}, {1291, 24006}, {3471, 36119}
X(50461) = X(i)-Dao conjugate of X(j) for these (i,j): {5, 1263}, {6, 13582}, {323, 340}, {1147, 43704}, {1511, 3471}, {2970, 8562}, {10413, 44427}, {14106, 16336}, {14579, 22391}
X(50461) = cevapoint of X(195) and X(399)
X(50461) = crosssum of X(8754) and X(47230)
X(50461) = crossdifference of every pair of points on line {2501, 6748}
X(50461) = barycentric product X(i)*X(j) for these {i,j}: {3, 37779}, {63, 1749}, {69, 11063}, {265, 40604}, {343, 1157}, {394, 37943}, {525, 47053}, {3284, 46751}, {3470, 11064}, {4558, 45147}, {4563, 6140}, {5612, 40710}, {5616, 40709}, {10272, 14919}, {18695, 19306}, {32662, 45790}
X(50461) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 13582}, {184, 14579}, {216, 1263}, {577, 43704}, {1157, 275}, {1749, 92}, {2914, 14165}, {3284, 3471}, {3470, 16080}, {5612, 471}, {5616, 470}, {6140, 2501}, {8562, 44427}, {9380, 38539}, {10272, 46106}, {10413, 2970}, {11063, 4}, {19306, 2190}, {32661, 1291}, {36296, 46072}, {36297, 46076}, {37779, 264}, {37943, 2052}, {38542, 9381}, {40604, 340}, {45147, 14618}, {47053, 648}, {50433, 15392}
X(50461) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15087, 15037}, {3, 3167, 9703}, {3, 34783, 43807}, {5, 195, 14627}, {5, 1994, 15038}, {49, 5562, 3}, {52, 18350, 13621}, {54, 11591, 34864}, {143, 43598, 18369}, {155, 394, 18445}, {156, 11412, 2937}, {184, 23039, 3}, {186, 40111, 32609}, {195, 15038, 1994}, {323, 399, 37496}, {394, 18445, 3}, {1092, 15083, 34783}, {1092, 34783, 3}, {1147, 18436, 3}, {1199, 3628, 15047}, {1493, 14128, 13434}, {1614, 6101, 13564}, {1993, 15068, 381}, {1994, 15038, 14627}, {3289, 22146, 22121}, {5562, 41597, 49}, {5609, 23061, 37924}, {5612, 5616, 11063}, {5876, 34148, 14130}, {5891, 34986, 567}, {6243, 10539, 18378}, {7691, 9705, 5944}, {11064, 12364, 19456}, {11441, 16266, 382}, {12316, 13621, 52}, {14516, 31724, 48675}, {15801, 43598, 143}, {17814, 36749, 3851}, {32608, 32609, 186}


X(50462) = X(265)-CEVA CONJUGATE OF X(7100)

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

X(50462) lies on the cubic K1278 and these lines: {3, 7100}, {5, 79}, {30, 3464}, {484, 31522}, {517, 26700}, {579, 2160}, {582, 6149}, {1325, 13486}, {1725, 5221}, {3615, 27003}, {5127, 37582}, {5535, 29374}, {5902, 7073}, {11076, 14158}, {14844, 39542}, {36058, 36061}

X(50462) = isotomic conjugate of the polar conjugate of X(11076)
X(50462) = X(265)-Ceva conjugate of X(7100)
X(50462) = X(i)-isoconjugate of X(j) for these (i,j): {4, 7343}, {3065, 6198}, {14975, 40716}
X(50462) = X(i)-Dao conjugate of X(j) for these (i,j): {340, 3218}, {7343, 36033}
X(50462) = cevapoint of X(3336) and X(3464)
X(50462) = barycentric product X(i)*X(j) for these {i,j}: {63, 50148}, {69, 11076}, {265, 40612}, {306, 14158}, {7100, 17484}, {23071, 30690}, {40709, 46075}, {40710, 46071}
X(50462) = barycentric quotient X(i)/X(j) for these {i,j}: {48, 7343}, {7100, 21739}, {11076, 4}, {14158, 27}, {19297, 6198}, {23071, 3219}, {40612, 340}, {46071, 471}, {46075, 470}, {50148, 92}
X(50462) = {X(46071),X(46075)}-harmonic conjugate of X(11076)


X(50463) = X(3)X(15958)∩X(5)X(49)

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

X(50463) lies on the cubic K1278 and these lines: {3, 15958}, {5, 49}, {30, 3484}, {94, 37127}, {97, 46091}, {216, 5961}, {264, 18831}, {436, 6344}, {933, 5663}, {1154, 18401}, {1511, 18315}, {5562, 19210}, {6662, 34148}, {7100, 36059}, {8798, 41597}, {13599, 32046}, {14586, 22146}, {15781, 44715}, {22115, 34900}, {25044, 34783}, {31504, 46092}

X(50463) = isotomic conjugate of the polar conjugate of X(11077)
X(50463) = X(1636)-cross conjugate of X(18315)
X(50463) = X(i)-isoconjugate of X(j) for these (i,j): {19, 14918}, {92, 11062}, {158, 1154}, {340, 2181}, {823, 2081}, {1096, 1273}, {1953, 14165}, {2052, 2290}, {6149, 13450}, {24019, 41078}
X(50463) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 14918}, {1147, 1154}, {1273, 6503}, {11062, 22391}, {13450, 14993}, {14569, 15295}, {35071, 41078}
X(50463) = cevapoint of X(54) and X(3484)
X(50463) = trilinear pole of line {577, 17434}
X(50463) = barycentric product X(i)*X(j) for these {i,j}: {69, 11077}, {94, 19210}, {95, 50433}, {97, 265}, {328, 14533}, {394, 1141}, {577, 46138}, {14560, 15414}, {14592, 15958}, {18315, 43083}, {35139, 46088}
X(50463) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 14918}, {54, 14165}, {97, 340}, {184, 11062}, {265, 324}, {394, 1273}, {520, 41078}, {577, 1154}, {1141, 2052}, {1989, 13450}, {5961, 467}, {11060, 14569}, {11077, 4}, {14533, 186}, {14582, 23290}, {15958, 14590}, {19210, 323}, {23286, 44427}, {32662, 35360}, {36296, 6116}, {36297, 6117}, {39201, 2081}, {43083, 18314}, {46088, 526}, {46138, 18027}, {46966, 16813}, {50433, 5}


X(50464) = X(5)X(34298)∩X(30)X(74)

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

X(50464) lies on the cubic K1278 and these lines: {5, 34298}, {30, 74}, {49, 3470}, {186, 46788}, {250, 5663}, {525, 12028}, {1154, 44769}, {1511, 40384}, {2693, 12041}, {3284, 11079}, {4550, 11074}, {5961, 11589}, {6000, 14560}, {7514, 35910}, {10421, 30522}, {14254, 38937}, {14264, 18445}, {14919, 22115}, {15311, 43090}, {15781, 44715}, {16077, 43752}, {18848, 32138}, {31621, 33533}, {35908, 39522}, {39170, 39174}

X(50464) = isotomic conjugate of the polar conjugate of X(11079)
X(50464) = X(i)-cross conjugate of X(j) for these (i,j): {577, 14919}, {2972, 43083}, {17434, 44769}
X(50464) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 14920}, {1147, 1511}, {1986, 39174}, {5664, 35071}, {6148, 6503}, {14165, 36896}, {22391, 39176}, {34334, 39170}, {35201, 36033}
X(50464) = cevapoint of X(i) and X(j) for these (i,j): {3, 44715}, {74, 38933}
X(50464) = trilinear pole of line {1636, 50433}
X(50464) = X(i)-isoconjugate of X(j) for these (i,j): {4, 35201}, {19, 14920}, {92, 39176}, {158, 1511}, {186, 1784}, {1096, 6148}, {2173, 14165}, {3258, 24000}, {5664, 24019}, {24001, 47230}
X(50464) = barycentric product X(i)*X(j) for these {i,j}: {69, 11079}, {265, 14919}, {328, 18877}, {394, 5627}, {520, 39290}, {1494, 50433}, {3926, 40355}, {15395, 15526}, {32662, 34767}, {39377, 40710}, {39378, 40709}, {43083, 44769}
X(50464) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 14920}, {48, 35201}, {74, 14165}, {184, 39176}, {265, 46106}, {394, 6148}, {520, 5664}, {577, 1511}, {3269, 3258}, {5627, 2052}, {11079, 4}, {14380, 44427}, {14919, 340}, {15395, 23582}, {18479, 18487}, {18877, 186}, {32662, 4240}, {34980, 47414}, {36061, 24001}, {36296, 6111}, {36297, 6110}, {39290, 6528}, {39377, 471}, {39378, 470}, {40355, 393}, {43083, 41079}, {44715, 14918}, {50433, 30}
X(50464) = {X(39377),X(39378)}-harmonic conjugate of X(11079)


X(50465) = X(3)X(36296)∩X(5)X(13)

Barycentrics    a^2*(a^2 - b^2 - c^2)*(Sqrt[3]*(a^2 - b^2 - c^2) + 2*S)*(Sqrt[3]*(a^2 + b^2 - c^2) + 2*S)*(Sqrt[3]*(a^2 - b^2 + c^2) + 2*S) : :
Barycentrics    Cos[A]*Cos[A + Pi/6]*Sec[A - Pi/6]*Sin[A] : :
X(50465) = X[38943] - 3 X[41889]

X(50465) lies on the cubics K908 and K1278 and these lines: {3, 36296}, {5, 13}, {16, 1511}, {30, 5668}, {61, 6102}, {265, 10218}, {450, 36306}, {471, 11078}, {511, 5995}, {3284, 11079}, {3292, 38414}, {3457, 11486}, {5504, 39380}, {5663, 5669}, {10217, 11064}, {11142, 22238}, {14368, 17403}, {36211, 40667}, {36839, 46789}, {38413, 47482}

X(50465) = isotomic conjugate of the polar conjugate of X(11081)
X(50465) = isogonal conjugate of the polar conjugate of X(11078)
X(50465) = X(i)-Ceva conjugate of X(j) for these (i,j): {11078, 11081}, {39377, 3}
X(50465) = X(i)-isoconjugate of X(j) for these (i,j): {19, 11092}, {92, 11086}, {162, 23284}, {470, 2154}, {1094, 6344}
X(50465) = X(i)-Dao conjugate of X(j) for these (i,j): {6, 11092}, {16, 11094}, {125, 23284}, {340, 11126}, {470, 40581}, {11086, 22391}
X(50465) = cevapoint of X(62) and X(5668)
X(50465) = crosssum of X(463) and X(1990)
X(50465) = barycentric product X(i)*X(j) for these {i,j}: {3, 11078}, {13, 44719}, {16, 40709}, {69, 11081}, {265, 11130}, {299, 36296}, {300, 46113}, {323, 10217}, {532, 47481}, {4558, 23283}, {6104, 40712}, {6148, 39380}, {8552, 36839}, {23871, 38414}, {36208, 40710}, {36211, 44718}, {39377, 41888}
X(50465) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 11092}, {16, 470}, {184, 11086}, {647, 23284}, {3457, 8738}, {5995, 36309}, {6104, 473}, {10217, 94}, {11078, 264}, {11080, 6344}, {11081, 4}, {11083, 46926}, {11130, 340}, {11134, 10633}, {16186, 43961}, {22115, 11131}, {23283, 14618}, {32585, 11600}, {32662, 36840}, {34395, 8739}, {36208, 471}, {36296, 14}, {36297, 36210}, {36839, 46456}, {38414, 23896}, {39377, 36311}, {39380, 5627}, {40581, 11094}, {40709, 301}, {44712, 33529}, {44719, 298}, {46112, 36209}, {46113, 15}, {47481, 11117}, {50433, 10218}
X(50465) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 62, 11083}, {16, 36208, 11081}, {16, 40581, 48366}


X(50466) = X(3)X(36297)∩X(5)X(14)

Barycentrics    a