| PART 1: | Introduction and Centers X(1) - X(1000) | PART 2: | Centers X(1001) - X(3000) | PART 3: | Centers X(3001) - X(5000) |
| PART 4: | Centers X(5001) - X(7000) | PART 5: | Centers X(7001) - X(10000) | PART 6: | Centers X(10001) - X(12000) |
| PART 7: | Centers X(12001) - X(14000) | PART 8: | Centers X(14001) - X(16000) | PART 9: | Centers X(16001) - X(18000) |
| PART 10: | Centers X(18001) - X(20000) | PART 11: | Centers X(20001) - X(22000) | PART 12: | Centers X(22001) - X(24000) |
| PART 13: | Centers X(24001) - X(26000) | PART 14: | Centers X(26001) - X(28000) | PART 15: | Centers X(28001) - X(30000) |
| PART 16: | Centers X(30001) - X(32000) | PART 17: | Centers X(32001) - X(34000) | PART 18: | Centers X(34001) - X(36000) |
| PART 19: | Centers X(36001) - X(38000) | PART 20: | Centers X(38001) - X(40000) | PART 21: | Centers X(40001) - X(42000) |
| PART 22: | Centers X(42001) - X(44000) | PART 23: | Centers X(44001) - X(46000) | PART 24: | Centers X(46001) - X(48000) |
| PART 25: | Centers X(48001) - X(50000) | PART 26: | Centers X(50001) - X(52000) | PART 27: | Centers X(52001) - X(54000) |
| PART 28: | Centers X(54001) - X(56000) | PART 29: | Centers X(56001) - X(58000) | PART 30: | Centers X(58001) - X(60000) |
| PART 31: | Centers X(60001) - X(62000) | PART 32: | Centers X(62001) - X(64000) | PART 33: | Centers X(64001) - X(66000) |
| PART 34: | Centers X(66001) - X(68000) | PART 35: | Centers X(68001) - X(70000) | PART 36: | Centers X(70001) - X(72000) |
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}
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) 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}
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)
See Antreas Hatzipolakis and César Lozada, euclid 5102.
X(50005) lies on these lines: {2, 3}, {5895, 44755}, {12291, 15305}, {34796, 43835}
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)
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)
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)
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)
Points in a [[b+c,c+a,a+b], [b-c,c-a,a-b]] coordinate system: X(50010)-X(50030)
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
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)
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}
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)
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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) 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)
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}
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) 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) 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)
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)
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}
MIYAMOTO-LOZADA CENTERS: X(50032)-X(50040)
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).
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}
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}
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}
See X(50034). Construction: X(50035)
X(50035) lies on these lines: {12, 15281}, {5949, 44411}
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)
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)
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)
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)
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)
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)
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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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}
Points in a [[b-c,c-a,a-b],[a(b-c),b(c-a),c(a-b)]] coordinate system: X(50074)-X(50133)
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) 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(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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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), (5375, 14074), (34522, 4860)
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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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}
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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) 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) 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) 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) 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) 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) 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) 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}
See Tran Viet Hung and Francisco Javier García Capitán, euclid 5113.
X(50151) lies on these lines: { }
X(50151) = isogonal conjugate of X(50152)
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)
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)
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) 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) 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) 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) 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(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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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): (1249, 2697), (6103, 542)
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)
See Kadir Altintas and César Lozada euclid 5126.
X(50189) lies on these lines: {1, 9551}, {942, 4868}, {3588, 19767}, {3666, 5083}
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)
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)
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)
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)
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)
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)
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)
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}
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}
Points on the Euler line: X(50199)-X(50208)
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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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}
See Kadir Altintas and César Lozada euclid 5132.
X(50209) lies on these lines: {125, 418}, {577, 31364}
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)
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}
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}
See Kadir Altintas and César Lozada euclid 5132.
X(50213) lies on these lines: {7684, 32627}, {15609, 37848}
See Kadir Altintas and César Lozada euclid 5132.
X(50214) lies on these lines: {7685, 32628}, {15610, 37850}
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)
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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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(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(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) 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) 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) 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) 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}
Points on the Euler line: X(50237)-X(50244)
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) 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) 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) 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) 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) 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) 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) 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) 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}
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}
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}
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)
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) 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) 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) 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) 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) 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) 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) 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) 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) 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}
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)
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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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}
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}
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)
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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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}
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)
Points on the Euler line: X(50318)-X(50325)
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) 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) 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) 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) 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) 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) 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) 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) 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}
Points in a [[b c, c a, a b], [a^2, b^2, c^2]] coordinate system: X(50326)-X(50359)
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) 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) 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(4500)-Dao conjugate of X(4490)
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) 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(32664)-Dao conjugate of X(28864)
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) 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), (40586, 29014)
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) 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): (10, 8707), (115, 30710), (124, 40452), (125, 1791), (244, 1220), (960, 100), (1015, 14534), (1084, 2298), (1211, 99), (2092, 645), (3125, 2), (3666, 668), (4858, 1240), (8054, 2363), (17197, 261), (17419, 333), (34467, 1798), (38992, 21), (39015, 81), (40586, 36147), (40590, 6648), (40600, 32736), (40611, 36098), (40619, 40827), (40622, 31643)
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) 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) 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) 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), (9, 36146), (11, 105), (241, 23973), (514, 43930), (518, 2283), (522, 885), (656, 23696), (918, 43042), (926, 8638), (1015, 1462), (1146, 673), (2968, 14942), (3126, 513), (3161, 666), (3716, 659), (4925, 2976), (5452, 919), (5519, 1617), (6184, 651), (6374, 46135), (6376, 34085), (6552, 36802), (6615, 1027), (6631, 39293), (6741, 13576), (8054, 1416), (14714, 2195), (17060, 1633), (17115, 884), (17435, 241), (17755, 664), (20620, 36124), (20621, 108), (27918, 1447), (35072, 1814), (35094, 7), (35508, 294), (35509, 1086), (36905, 658), (38980, 57), (38983, 36057), (38989, 56), (38991, 1438), (39012, 5228), (39014, 6), (39046, 109), (39063, 934), (40609, 100), (40619, 34018), (40624, 2481), (40626, 31637), (48315, 6180)
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) 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): (48275, 48085), (48404, 48123)
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) 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(32664)-Dao conjugate of X(30554)
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) 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), (32664, 28847)
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) 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) 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(46660)-Dao conjugate of X(1)
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) 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) 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) 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) 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) 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) 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), (512, 8663), (513, 4977), (661, 4978), (1015, 4359), (1084, 1213), (1086, 1269), (3005, 6367), (3835, 4992), (5139, 430), (5452, 30729), (6615, 4985), (8054, 1125), (14434, 30592), (17115, 4990), (17423, 22080), (32664, 35342), (34467, 3916), (38979, 4975), (38986, 1962), (38989, 4966), (38991, 3686), (38995, 3775), (38996, 20970), (39006, 4001), (39025, 3683), (40586, 4115), (40608, 4046), (40627, 4988)
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) 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) 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), (24224, 18698)
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) 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) 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) 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) 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(32664)-Dao conjugate of X(29041)
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) 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) 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) 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) 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): (442, 3699), (1015, 40435), (1086, 40422), (5190, 40447), (6609, 36048), (8054, 943), (15607, 200), (16585, 668), (16732, 313), (18591, 190), (34467, 1794), (39007, 78), (40937, 4033)
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) 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) 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) 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): (6184, 4606), (35094, 5936), (36905, 4624), (38980, 25430), (38989, 2334), (39014, 34820), (39046, 8694)
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) 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(32664)-Dao conjugate of X(28883)
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) 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(32664)-Dao conjugate of X(28852)
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}
Radical traces of circumcircle and other circles: X(50360)-X(50390)
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) 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) 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) 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) 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) 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) lies on these lines: {2, 3}, {347, 523}
X(50365) = crossdifference of every pair of points on line {X(647), X(8554)}
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) lies on these lines: {3, 3101}
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) lies on these lines: {2, 92}, {3, 4885}
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) 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) lies on these lines: {3, 2941}, {661, 2605}
X(50373) lies on these lines: {3, 3100}, {73, 663}
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) 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) lies on these lines: {3, 8145}
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) 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) 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) lies on these lines: {3, 8147}
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) lies on these lines: {3, 736}, {669, 7467}
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) lies on these lines: {3, 49}
X(50384) = crossdifference of every pair of points on line {X(2501), X(8571)}
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) 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) 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) lies on the cubic K038 and these lines: {3, 640}, {6563, 14326}
X(50388) = inverse of X(44199) in circumcircle
X(50389) lies on the cubic K038 and these lines: {3, 639}, {6563, 14325}
X(50389) = inverse of X(44196) in circumcircle
X(50390) lies on these lines: {3, 5592}, {2183, 3006}
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}
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) 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) 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) 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) 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) 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) 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) 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) 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 )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) 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) 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) 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}
See Antreas Hatzipolakis and Ercole Suppa, euclid 5167.
X(50405) lies on these lines: {308,393}, {10002,10548}
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) 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) 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) 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) 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) 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) 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}
See Antreas Hatzipolakis and Peter Moses, euclid 5170.
X(50413) lies on this line: {2, 3}
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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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) 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(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5000, 5001, 28099}
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) 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) 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) 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) 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) 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) 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), (1147, 323), (1511, 14920), (2972, 41078), (6503, 7799), (14993, 2052), (15295, 393), (17423, 47230), (22391, 186), (35071, 3268), (38985, 32679), (38999, 5664), (39170, 46106), (46093, 8552)
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) 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) 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}
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}
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}
See César Lozada, euclid 5180.
X(50438) lies on these lines: {10, 37}, {516, 5318}, {11488, 37830}
See César Lozada, euclid 5180.
X(50439) lies on these lines: {10, 37}, {516, 5321}, {11489, 37833}
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)
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)
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)
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}
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}
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)
See Kadir Altintas and César Lozada, euclid 5184.
X(50446) lies on these lines: {24, 50209}, {11387, 43976}, {31364, 42400}
See Kadir Altintas and César Lozada, euclid 5184.
X(50447) lies on these lines: {3, 6}, {3526, 30465}, {11555, 16960}
See Kadir Altintas and César Lozada, euclid 5184.
X(50448) lies on these lines: {3, 6}, {3526, 30468}, {11556, 16961}
Points in a [[b c, c a, a b], [a^3, b^3, c^3]] coordinate system: X(50449)-X(50459)
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) 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) 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(47787)-Dao conjugate of X(14077)
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) 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): (86, 662), (1015, 2248), (1086, 13610), (6627, 1), (8054, 18757), (21196, 4705), (34591, 15377), (40619, 6625)
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) 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) 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) 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) 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) 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): (661, 35352), (665, 4088), (1015, 43534), (3837, 21053), (6626, 4583), (6651, 4033), (8299, 4103), (19557, 3952), (35119, 321), (36830, 5378), (38978, 762), (39028, 27808), (39029, 1018), (40582, 36801), (40589, 660), (40592, 4562), (40620, 334), (40623, 10)
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) 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), (115, 31359), (244, 941), (1015, 5331), (1084, 2258), (1086, 37870), (1214, 32038), (4858, 34258), (17417, 21), (34261, 643), (34591, 34259), (40611, 32693), (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) 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) 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}
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) 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), (8562, 2970), (10413, 44427), (16336, 14106), (22391, 14579)
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) 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): (3218, 340), (36033, 7343)
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) 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), (6503, 1273), (14993, 13450), (15295, 14569), (22391, 11062), (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) 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), (6503, 6148), (22391, 39176), (35071, 5664), (36033, 35201), (36896, 14165), (39170, 34334), (39174, 1986)
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) 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), (11126, 340), (22391, 11086), (40581, 470)
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) lies on the cubics K908 and K1278 and these lines: {3, 36297}, {5, 14}, {15, 1511}, {30, 5669}, {62, 6102}, {265, 10217}, {450, 36309}, {470, 11092}, {511, 5994}, {3284, 11079}, {3292, 38413}, {3458, 11485}, {5504, 39381}, {5663, 5668}, {10218, 11064}, {11141, 22236}, {14369, 17402}, {36210, 40668}, {36840, 46789}, {38414, 47481}
X(50466) = isotomic conjugate of the polar conjugate of X(11086)
X(50466) = isogonal conjugate of the polar conjugate of X(11092)
X(50466) = X(i)-Ceva conjugate of X(j) for these (i,j): {11092, 11086}, {39378, 3}
X(50466) = X(i)-isoconjugate of X(j) for these (i,j): {19, 11078}, {92, 11081}, {162, 23283}, {471, 2153}, {1095, 6344}
X(50466) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 11078), (15, 11093), (125, 23283), (11127, 340), (22391, 11081), (40580, 471)
X(50466) = cevapoint of X(61) and X(5669)
X(50466) = crosssum of X(462) and X(1990)
X(50466) = barycentric product X(i)*X(j) for these {i,j}: {3, 11092}, {14, 44718}, {15, 40710}, {69, 11086}, {265, 11131}, {298, 36297}, {301, 46112}, {323, 10218}, {533, 47482}, {4558, 23284}, {6105, 40711}, {6148, 39381}, {8552, 36840}, {23870, 38413}, {36209, 40709}, {36210, 44719}, {39378, 41887}
X(50466) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 11078}, {15, 471}, {184, 11081}, {647, 23283}, {3458, 8737}, {5994, 36306}, {6105, 472}, {10218, 94}, {11085, 6344}, {11086, 4}, {11088, 46925}, {11092, 264}, {11131, 340}, {11137, 10632}, {16186, 43962}, {22115, 11130}, {23284, 14618}, {32586, 11601}, {32662, 36839}, {34394, 8740}, {36209, 470}, {36296, 36211}, {36297, 13}, {36840, 46456}, {38413, 23895}, {39378, 36308}, {39381, 5627}, {40580, 11093}, {40710, 300}, {44711, 33530}, {44718, 299}, {46112, 16}, {46113, 36208}, {47482, 11118}, {50433, 10217}
X(50466) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 61, 11088}, {15, 36209, 11086}, {15, 40580, 48365}
X(50467) lies on the cubic K1278 and these lines: {5, 1117}, {30, 2132}, {265, 14919}, {399, 15773}, {5158, 10217}, {5609, 15395}, {14254, 39290}, {14264, 40355}, {14385, 14805}, {15790, 40391}, {40384, 47055}
X(50467) = isotomic conjugate of the polar conjugate of X(11074)
X(50467) = X(14919)-Ceva conjugate of X(11079)
X(50467) = X(i)-isoconjugate of X(j) for these (i,j): {1138, 35201}, {19223, 24000}
X(50467) = X(i)-Dao conjugate of X(j) for these (i, j): (1989, 46106), (14919, 340)
X(50467) = cevapoint of X(2132) and X(3470)
X(50467) = crosspoint of X(265) and X(14993)
X(50467) = barycentric product X(i)*X(j) for these {i,j}: {69, 11074}, {1272, 11079}, {14919, 14993}
X(50467) = barycentric quotient X(i)/X(j) for these {i,j}: {399, 14920}, {3269, 19223}, {11074, 4}, {11079, 1138}, {14993, 46106}, {19303, 35201}, {50433, 20123}
X(50468) lies on the cubic K1278 and these lines: {3, 36296}, {5, 8837}, {13, 15}, {61, 143}, {216, 5961}, {265, 10663}, {343, 465}, {473, 8838}, {549, 41889}, {3457, 11485}, {5944, 8839}, {5995, 13350}, {8604, 42619}, {10645, 36208}, {11082, 27361}, {11142, 22236}, {16021, 16463}, {38414, 47481}
X(50468) = isotomic conjugate of the polar conjugate of X(11083)
X(50468) = isogonal conjugate of the polar conjugate of X(8838)
X(50468) = X(8838)-Ceva conjugate of X(11083)
X(50468) = X(i)-isoconjugate of X(j) for these (i,j): {92, 8603}, {93, 35198}, {2962, 10633}
X(50468) = X(i)-Dao conjugate of X(j) for these (i, j): (10640, 470), (11130, 340), (22391, 8603)
X(50468) = cevapoint of X(15) and X(8837)
X(50468) = barycentric product X(i)*X(j) for these {i,j}: {3, 8838}, {61, 40709}, {69, 11083}, {265, 11126}, {302, 36296}, {328, 11135}, {6104, 40710}, {6671, 47481}, {10217, 11146}, {11082, 44180}, {11581, 44718}, {23872, 38414}
X(50468) = barycentric quotient X(i)/X(j) for these {i,j}: {49, 11127}, {61, 470}, {184, 8603}, {2965, 10633}, {3457, 8741}, {6104, 471}, {8604, 562}, {8838, 264}, {10632, 14165}, {11082, 93}, {11083, 4}, {11126, 340}, {11135, 186}, {16463, 8737}, {36296, 17}, {36297, 11600}, {38414, 32036}, {40709, 34389}, {44180, 11133}, {46112, 37848}
X(50468) = {X(61),X(6104)}-harmonic conjugate of X(11083)
X(50469) lies on the cubic K1278 and these lines: {3, 36297}, {5, 8839}, {14, 16}, {62, 143}, {216, 5961}, {265, 10664}, {343, 466}, {472, 8836}, {3458, 11486}, {5944, 8837}, {5994, 13349}, {10646, 36209}, {11087, 27361}, {11141, 22238}, {16022, 16464}, {38413, 47482}
X(50469) = isotomic conjugate of the polar conjugate of X(11088)
X(50469) = isogonal conjugate of the polar conjugate of X(8836)
X(50469) = X(8836)-Ceva conjugate of X(11088)
X(50469) = X(i)-isoconjugate of X(j) for these (i,j): {92, 8604}, {93, 35199}, {2962, 10632}
X(50469) = X(i)-Dao conjugate of X(j) for these (i, j): (10639, 471), (11131, 340), (22391, 8604)
X(50469) = cevapoint of X(16) and X(8839)
X(50469) = barycentric product X(i)*X(j) for these {i,j}: {3, 8836}, {62, 40710}, {69, 11088}, {265, 11127}, {303, 36297}, {328, 11136}, {6105, 40709}, {6672, 47482}, {10218, 11145}, {11087, 44180}, {11582, 44719}, {23873, 38413}
X(50469) = barycentric quotient X(i)/X(j) for these {i,j}: {49, 11126}, {62, 471}, {184, 8604}, {2965, 10632}, {3458, 8742}, {6105, 470}, {8603, 562}, {8836, 264}, {10633, 14165}, {11087, 93}, {11088, 4}, {11127, 340}, {11136, 186}, {16464, 8738}, {36296, 11601}, {36297, 18}, {38413, 32037}, {40710, 34390}, {44180, 11132}, {46113, 37850}
X(50469) = {X(62),X(6105)}-harmonic conjugate of X(11088)
See César Lozada, euclid 5193.
X(50470) lies on this line: {2, 3}
X(50470) = reflection of X(3) in X(13448)
See César Lozada, euclid 5193.
X(50471) lies on the 2nd Steiner circle and these lines: {3, 14769}, {4, 195}, {5, 14652}, {128, 5099}, {157, 381}, {1553, 31726}, {1656, 15366}, {6592, 46450}, {8146, 14130}, {12091, 18403}, {13505, 34514}, {13512, 31723}, {13556, 22823}, {14674, 31976}, {14877, 14978}, {21731, 25149}, {23319, 45735}, {34418, 39504}
X(50471) = reflection of X(i) in X(j) for these (i, j): (3, 14769), (14652, 5)
X(50471) = X(99)-Ceva conjugate of-X(24978)
See César Lozada, euclid 5193.
X(50472) lies on the circumcircles of triangles Ehrmann-side and Johnson and on these lines: {3, 16221}, {4, 16978}, {5, 10420}, {30, 925}, {265, 924}, {381, 42424}, {382, 38580}, {403, 13557}, {523, 13556}, {1304, 43995}, {2070, 23181}, {6033, 11799}, {7728, 13417}, {10745, 36184}, {14980, 31724}, {18403, 21268}, {31723, 38953}
X(50472) = reflection of X(i) in X(j) for these (i, j): (3, 16221), (10420, 5), (13557, 403), (18403, 21268)
See César Lozada, euclid 5193.
X(50473) lies on these lines: {30, 137}, {136, 14106}
See César Lozada, euclid 5193.
X(50474) lies on the Yiu circle and these lines: {5663, 6150}, {25044, 43966}
See César Lozada, euclid 5193.
X(50475) lies on these lines: {136, 35591}, {137, 523}, {1154, 32215}, {10096, 16337}, {24306, 32423}
See Antreas Hatzipolakis, César Lozada and Peter Moses, euclid 5194 and euclid 5195.
X(50476) lies on these lines: {3, 43838}, {5, 399}, {30, 143}, {49, 13392}, {54, 140}, {125, 8254}, {265, 43600}, {542, 32205}, {546, 25739}, {547, 43836}, {548, 3581}, {550, 43818}, {567, 43608}, {575, 13561}, {632, 45968}, {1154, 44862}, {1199, 22051}, {1493, 46114}, {1514, 3861}, {1899, 50138}, {2918, 12107}, {3521, 3853}, {3530, 13292}, {3564, 16239}, {3580, 34004}, {3627, 43835}, {3628, 15806}, {3850, 18914}, {5012, 34577}, {5422, 50136}, {5462, 13163}, {5501, 8902}, {5690, 43830}, {5892, 11264}, {5898, 36966}, {5943, 23409}, {7583, 43867}, {7584, 43868}, {7592, 49673}, {7728, 43612}, {9730, 45970}, {10020, 43810}, {10095, 18128}, {10116, 13363}, {10125, 32046}, {10224, 18952}, {10264, 13434}, {10627, 11225}, {11433, 17714}, {11441, 50142}, {11802, 13358}, {11803, 34564}, {12006, 32423}, {12121, 43603}, {12289, 37481}, {13142, 44245}, {13567, 18282}, {14683, 22462}, {15012, 30522}, {15043, 45731}, {15108, 44756}, {15172, 43819}, {15557, 42400}, {16982, 17712}, {18912, 46029}, {20127, 43611}, {33332, 34545}, {34153, 43597}, {36753, 39504}, {43866, 48154}
X(50476) = midpoint of X(i) and X(j) for these {i, j}: {140, 32165}, {3530, 13292}, {3628, 43588}, {3850, 18914}, {8254, 27552}, {10095, 18128}, {13142, 44245}, {13630, 43575}, {16982, 17712}
X(50476) = reflection of X(13163) in X(5462)
X(50476) = crosspoint of X(95) and X(11538)
X(50476) = crosssum of X(51) and X(15109)
X(50476) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (125, 36153, 8254), (140, 11245, 32165), (1199, 37938, 22051), (3448, 15047, 5), (13630, 43573, 43575), (15037, 43808, 5), (15806, 43817, 3628), (18128, 32068, 10095), (43588, 45298, 3628), (43816, 43845, 5)
See Antreas Hatzipolakis and César Lozada, euclid 5194.
X(50477) lies on these lines: {61, 302}, {8259, 15609}
See Antreas Hatzipolakis and César Lozada, euclid 5194.
X(50478) lies on these lines: {62, 303}, {8260, 15610}
See Antreas Hatzipolakis, César Lozada and Peter Moses, euclid 5194 and euclid 5195.
X(50479) lies on these lines: {5, 51}, {54, 47065}, {137, 5501}, {434, 11576}, {10285, 10610}, {13856, 19268}, {27196, 33545}
X(50479) = midpoint of X(8254) and X(14051)
X(50479) = crosssum of X(54) and X(15345)
X(50480) lies on the cubics K528 and K1279, the curve Q066, and these lines: {2, 38937}, {20, 14911}, {30, 15262}, {146, 2071}, {34170, 46106}
X(50480) = isogonal conjugate of X(2935)
X(50480) = cyclocevian conjugate of X(2986)
X(50480) = isotomic conjugate of the anticomplement of X(8749)
X(50480) = X(i)-cross conjugate of X(j) for these (i,j): {5897, 3346}, {8749, 2}, {11744, 4}, {34178, 1138}
X(50480) = cevapoint of X(i) and X(j) for these (i,j): {3, 17838}, {512, 39008}, {523, 16177}
X(50480) = trilinear pole of line {9033, 46425}
X(50480) = barycentric quotient X(6)/X(2935)
Points in a [[b c, c a, a b], [b^2 c^2, c^2 a^2, a^2 b^2]] coordinate system: X(50481)-X(50526)
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^2 c^2 α + c^2 a^2 β + a^2 b^2 γ = 0.
The origin is given by (0, 0) = X(649) = a^2 (b - c) : : .
Barycentrics u : v : w for a triangle center U = (x,y) in this system are given by
u : v : w = -a^3 b c (b-c) - a(b-c) x + a^2(b^2-c^2) y ,
where, as functions of a, b, c, the coordinate x is symmetric 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 c (a+b+c), -((2 a b c)/(a+b+c))}, 47912
{-2 (a b+a c+b c) (a^2+b^2+c^2), -2 (a^2+b^2+c^2)}, 47923
{-2 (a b+a c+b c)^2, -2 (a b+a c+b c)}, 47926
{-2 a b c (a+b+c), -a b-a c-b c}, 20983
{-2 a b c (a+b+c), 0}, 4813
{-a b c (a+b+c), -((2 a b c)/(a+b+c))}, 4041
{-a b c (a+b+c), -((a b c)/(a+b+c))}, 4705
{-((a+b) (a+c) (b+c) (a+b+c)), -(a+b+c)^2}, 48277
{-(a+b+c)^2 (a b+a c+b c), -(a+b+c)^2}, 4988
{-((a b+a c+b c) (a^2+b^2+c^2)), -a^2-b^2-c^2}, 16892
{-(a b+a c+b c)^2, -a b-a c-b c}, 17494
{-a b c (a+b+c), -((a b c)/(2 (a+b+c)))}, 48005
{-a b c (a+b+c), 0}, 661
{-a b c (a+b+c), (a b c)/(2 (a+b+c))}, 48053
{-a b c (a+b+c), (a b c)/(a+b+c)}, 4983
{-a b c (a+b+c), (2 a b c)/(a+b+c)}, 4822
{-(1/2) a b c (a+b+c), 1/2 (-a b-a c-b c)}, 4507
{-(1/2) (a+b) (a+c) (b+c) (a+b+c), -(1/2) (a+b+c)^2}, 4976
{-(1/2) (a+b+c)^2 (a b+a c+b c), -(1/2) (a+b+c)^2}, 45745
{-(1/2) (a b+a c+b c) (a^2+b^2+c^2), 1/2 (-a^2-b^2-c^2)}, 4025
{-(1/2) (a b+a c+b c)^2, 1/2 (-a b-a c-b c)}, 48008
{-(1/2) a b c (a+b+c), 0}, 650
{-(1/2) a b c (a+b+c), (a b c)/(a+b+c)}, 48099
{0, -((a b c)/(a+b+c))}, 4834
{0, 0}, 649
{0, a b+a c+b c}, 2978
{0, (a b c)/(a+b+c)}, 667
{0, (2 a b c)/(a+b+c)}, 663
{1/2 a b c (a+b+c), 0}, 4790
{1/2 (a+b) (a+c) (b+c) (a+b+c), 1/2 (a+b+c)^2}, 48276
{1/2 (a+b+c)^2 (a b+a c+b c), 1/2 (a+b+c)^2}, 49293
{1/2 (a b+a c+b c) (a^2+b^2+c^2), 1/2 (a^2+b^2+c^2)}, 48060
{1/2 (a b+a c+b c)^2, 1/2 (a b+a c+b c)}, 4932
{a b c (a+b+c), 0}, 4979
{(a+b) (a+c) (b+c) (a+b+c), (a+b+c)^2}, 48275
{(a b+a c+b c) (a^2+b^2+c^2), a^2+b^2+c^2}, 48101
{(a b+a c+b c)^2, a b+a c+b c}, 7192
{2 (a b+a c+b c) (a^2+b^2+c^2), 2 (a^2+b^2+c^2)}, 48138
{2 (a b+a c+b c)^2, 2 (a b+a c+b c)}, 48141
{-2*a*b*c*(a + b + c), -2*(a*b + a*c + b*c)}, 50481
{-2*(a + b)*(a + c)*(b + c)*(a + b + c), -2*(a + b + c)^2}, 50482
{-(a*b*c*(a + b + c)), -2*(a*b + a*c + b*c)}, 50483
{-((a + b + c)^2*(a*b + a*c + b*c)), -2*(a*b + a*c + b*c)}, 50484
{-(a*b + a*c + b*c)^2, -2*(a*b + a*c + b*c)}, 50485
{-(a*b*c*(a + b + c)), -a^2 - b^2 - c^2}, 50486
{-(a*b*c*(a + b + c)), -(a*b) - a*c - b*c}, 50487
{-(a*b*c*(a + b + c)), -(((a + b)*(a + c)*(b + c))/(a + b + c))}, 50488
{-((a + b + c)^2*(a*b + a*c + b*c)), -(a*b) - a*c - b*c}, 50489
{-(a*b*c*(a + b + c)), (-a^2 - b^2 - c^2)/2}, 50490
{-(a*b*c*(a + b + c)), (-(a*b) - a*c - b*c)/2}, 50491
{-(a*b*c*(a + b + c)), -1/2*(a + b + c)^2}, 50492
{-(a*b*c*(a + b + c)), -1/2*((a + b)*(a + c)*(b + c))/(a + b + c)}, 50493
{-(a*b*c*(a + b + c)), (a^2 + b^2 + c^2)/2}, 50494
{-(a*b*c*(a + b + c)), (a + b + c)^2/2}, 50495
{-(a*b*c*(a + b + c)), a^2 + b^2 + c^2}, 50496
{-(a*b*c*(a + b + c)), a*b + a*c + b*c}, 50497
{-(a*b*c*(a + b + c)), (a + b + c)^2}, 50498
{-1/2*(a*b*c*(a + b + c)), (-2*a*b*c)/(a + b + c)}, 50499
{-1/2*(a*b*c*(a + b + c)), -(a*b) - a*c - b*c}, 50500
{-1/2*(a*b*c*(a + b + c)), -((a*b*c)/(a + b + c))}, 50501
{-1/2*((a + b + c)^2*(a*b + a*c + b*c)), -(a*b) - a*c - b*c}, 50502
{-1/2*(a*b*c*(a + b + c)), (-a^2 - b^2 - c^2)/2}, 50503
{-1/2*(a*b*c*(a + b + c)), -1/2*(a*b*c)/(a + b + c)}, 50504
{-1/2*((a*b + a*c + b*c)*(a^2 + b^2 + c^2)), 0}, 50505
{-1/2*(a*b*c*(a + b + c)), (a^2 + b^2 + c^2)/2}, 50506
{-1/2*(a*b*c*(a + b + c)), (a*b*c)/(2*(a + b + c))}, 50507
{-1/2*(a*b*c*(a + b + c)), (2*a*b*c)/(a + b + c)}, 50508
{0, (-2*a*b*c)/(a + b + c)}, 50509
{0, (a*b + a*c + b*c)/2}, 50510
{0, (a + b + c)^2/2}, 50511
{0, (a*b*c)/(2*(a + b + c))}, 50512
{(a*b*c*(a + b + c))/2, (a^2 + b^2 + c^2)/2}, 50513
{(a*b*c*(a + b + c))/2, (a*b + a*c + b*c)/2}, 50514
{(a*b*c*(a + b + c))/2, (a*b*c)/(a + b + c)}, 50515
{(a*b + a*c + b*c)^2/2, a*b + a*c + b*c}, 50516
{(a*b*c*(a + b + c))/2, (2*a*b*c)/(a + b + c)}, 50517
{((a + b)*(a + c)*(b + c)*(a + b + c))/2, 2*(a*b + a*c + b*c)}, 50518
{((a + b + c)^2*(a*b + a*c + b*c))/2, 2*(a*b + a*c + b*c)}, 50519
{(a*b + a*c + b*c)^2, -(a*b) - a*c - b*c}, 50520
{a*b*c*(a + b + c), a*b + a*c + b*c}, 50521
{(a + b + c)^2*(a*b + a*c + b*c), (a + b + c)^2}, 50522
{a*b*c*(a + b + c), (2*a*b*c)/(a + b + c)}, 50523
{(a*b + a*c + b*c)^2, 2*(a*b + a*c + b*c)}, 50524
{2*a*b*c*(a + b + c), 0}, 50525
{2*a*b*c*(a + b + c), (2*a*b*c)/(a + b + c)}, 50526
X(50481) lies on these lines: {1, 27673}, {8, 20295}, {42, 649}, {512, 4813}, {513, 4963}, {798, 8655}, {834, 48023}, {1734, 27469}, {2978, 4893}, {3063, 8635}, {3779, 9002}, {3835, 31330}, {4083, 4382}, {4807, 23803}, {4979, 9010}, {5216, 48012}, {6005, 31290}, {9040, 47971}, {10459, 28398}, {20012, 26853}, {25637, 30835}, {26037, 30023}, {26822, 48573}
X(50481) = reflection of X(i) in X(j) for these {i,j}: {4813, 20983}, {5216, 48012}
X(50481) = isogonal conjugate of the isotomic conjugate of X(48012)
X(50481) = crosssum of X(i) and X(j) for these (i,j): {1, 27673}, {514, 32776}
X(50481) = crossdifference of every pair of points on line {239, 20893}
X(50481) = barycentric product X(i)*X(j) for these {i,j}: {6, 48012}, {31, 47665}, {37, 5216}, {667, 48630}
X(50481) = barycentric quotient X(i)/X(j) for these {i,j}: {5216, 274}, {47665, 561}, {48012, 76}, {48630, 6386}
X(50482) lies on these lines: {513, 47669}, {514, 14779}, {522, 4813}, {523, 649}, {650, 4838}, {661, 4777}, {663, 6367}, {812, 47657}, {824, 47661}, {1635, 48397}, {2786, 47667}, {3239, 4024}, {3700, 28187}, {3835, 46915}, {4025, 47671}, {4369, 47655}, {4379, 20522}, {4382, 45746}, {4435, 29146}, {4467, 48141}, {4468, 48429}, {4500, 30835}, {4608, 4932}, {4762, 47673}, {4789, 31207}, {4790, 28151}, {4802, 4979}, {4839, 29248}, {4841, 28183}, {4926, 48019}, {4928, 48424}, {4984, 28155}, {5029, 9131}, {6590, 28169}, {17422, 49300}, {20909, 29771}, {25666, 48423}, {28205, 48026}, {28840, 47668}, {28863, 47664}, {28882, 47654}, {28890, 48435}, {28894, 47932}, {28898, 47917}, {29078, 47909}, {30565, 48430}, {31010, 47794}, {31147, 48404}, {31286, 47792}, {43067, 47670}, {47659, 48008}, {47665, 48000}, {47757, 48418}, {47886, 48274}, {47894, 48399}, {47920, 48112}
X(50482) = reflection of X(i) in X(j) for these {i,j}: {649, 48277}, {4024, 45745}, {4382, 45746}, {4608, 4932}, {4813, 4988}, {4838, 650}, {47655, 4369}, {47656, 21196}, {47659, 48008}, {47665, 48000}, {47670, 43067}, {47671, 4025}, {47908, 47667}, {47923, 47673}, {47926, 47661}, {48112, 47920}, {48117, 47926}, {48138, 47932}, {48141, 4467}, {48266, 4841}, {48275, 4976}, {48429, 4468}
X(50482) = crossdifference of every pair of points on line {386, 7280}
X(50482) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 4838, 47873}, {4024, 45745, 4893}, {4500, 47782, 30835}, {4841, 48266, 48544}, {4976, 48275, 649}, {21196, 47656, 4379}, {48275, 48277, 4976}
X(50483) lies on these lines: {244, 7063}, {512, 661}, {513, 4963}, {693, 4761}, {788, 4979}, {834, 2254}, {1635, 2978}, {3804, 4832}, {3835, 4807}, {4083, 47672}, {4086, 48080}, {4132, 4804}, {4155, 4838}, {4826, 46390}, {5216, 16751}, {6005, 47666}, {8635, 21007}, {9400, 48114}, {20983, 48019}, {21052, 22320}
X(50483) = reflection of X(i) in X(j) for these {i,j}: {2978, 4507}, {48019, 20983}
X(50483) = isogonal conjugate of the isotomic conjugate of X(48407)
X(50483) = X(47915)-Ceva conjugate of X(3709)
X(50483) = X(i)-isoconjugate of X(j) for these (i,j): {86, 6013}, {99, 10013}
X(50483) = X(i)-Dao conjugate of X(j) for these (i, j): (38986, 10013), (40600, 6013)
X(50483) = crosspoint of X(2334) and X(4557)
X(50483) = crosssum of X(i) and X(j) for these (i,j): {1019, 10458}, {3616, 7192}, {3720, 48144}
X(50483) = crossdifference of every pair of points on line {81, 4384}
X(50483) = barycentric product X(i)*X(j) for these {i,j}: {6, 48407}, {37, 6005}, {42, 47666}, {321, 8655}, {512, 4687}, {661, 17018}, {3700, 16878}, {4024, 39673}
X(50483) = barycentric quotient X(i)/X(j) for these {i,j}: {213, 6013}, {798, 10013}, {4079, 46772}, {4687, 670}, {6005, 274}, {8639, 17110}, {8655, 81}, {16878, 4573}, {17018, 799}, {39673, 4610}, {47666, 310}, {48407, 76}
X(50483) = {X(2978),X(4507)}-harmonic conjugate of X(1635)
X(50484) lies on these lines: {1, 27647}, {8, 4160}, {42, 661}, {512, 4988}, {513, 4963}, {649, 4041}, {650, 8655}, {669, 4705}, {798, 21727}, {830, 17494}, {2512, 21828}, {3779, 9013}, {4086, 47694}, {4369, 31330}, {4807, 4932}, {10459, 28372}, {17166, 25299}, {20012, 31290}, {23506, 48030}, {24924, 30970}, {26115, 27045}, {27648, 48012}
X(50484) = crosssum of X(1) and X(27647)
X(50484) = crossdifference of every pair of points on line {5256, 18206}
X(50485) lies on these lines: {512, 17494}, {513, 4963}, {649, 4083}, {659, 4093}, {661, 9400}, {669, 4063}, {693, 4507}, {788, 4380}, {890, 18197}, {891, 7192}, {2978, 29350}, {4139, 47694}, {4155, 47660}, {4782, 8655}, {4785, 20983}, {4807, 23791}, {6371, 50343}, {6373, 26853}, {14404, 48049}, {14426, 26798}, {25142, 31147}, {26854, 47836}, {29226, 48141}, {30665, 48101}
X(50485) = reflection of X(i) in X(j) for these {i,j}: {693, 4507}, {2978, 48008}
X(50485) = {X(4782),X(23506)}-harmonic conjugate of X(8655)
X(50486) lies on these lines: {31, 649}, {512, 661}, {513, 16892}, {669, 21828}, {834, 4724}, {891, 48130}, {3005, 4455}, {3056, 9002}, {3804, 7180}, {3835, 25760}, {3869, 4468}, {4083, 48094}, {4088, 4132}, {4139, 47700}, {4170, 14208}, {4388, 20295}, {6005, 47995}, {6371, 48032}, {6372, 47916}, {7234, 8034}, {8655, 43060}, {8672, 47702}, {21125, 47652}, {27730, 50298}, {28005, 32944}
X(50486) = isogonal conjugate of the isotomic conjugate of X(47712)
X(50486) = X(46149)-Ceva conjugate of X(27846)
X(50486) = X(190)-isoconjugate of X(40398)
X(50486) = X(21249)-Dao conjugate of X(668)
X(50486) = crosssum of X(i) and X(j) for these (i,j): {100, 4568}, {514, 33123}
X(50486) = crossdifference of every pair of points on line {81, 3912}
X(50486) = barycentric product X(i)*X(j) for these {i,j}: {6, 47712}, {31, 27712}, {42, 47652}, {251, 21125}, {512, 16706}, {513, 16600}, {523, 5299}, {649, 4972}, {661, 7191}, {798, 33940}, {2501, 7293}, {3122, 33951}, {4017, 33950}, {4079, 33955}, {4514, 7180}, {10566, 20969}, {17192, 18105}, {17456, 18108}, {17924, 23203}
X(50486) = barycentric quotient X(i)/X(j) for these {i,j}: {667, 40398}, {4972, 1978}, {5299, 99}, {7191, 799}, {7293, 4563}, {16600, 668}, {16706, 670}, {20969, 4568}, {21125, 8024}, {23203, 1332}, {27712, 561}, {33940, 4602}, {33950, 7257}, {47652, 310}, {47712, 76}
X(50486) = {X(8034),X(8664)}-harmonic conjugate of X(7234)
X(50487) lies on these lines: {6, 16874}, {8, 30203}, {10, 3835}, {42, 649}, {43, 29487}, {100, 805}, {209, 9313}, {512, 661}, {513, 4380}, {650, 2978}, {667, 18266}, {668, 886}, {669, 798}, {692, 32729}, {693, 2533}, {810, 8639}, {834, 1491}, {838, 4834}, {881, 21814}, {891, 47672}, {1980, 3063}, {2254, 6371}, {3124, 7063}, {3214, 9433}, {3293, 29807}, {3805, 4467}, {4010, 4036}, {4024, 4155}, {4079, 8663}, {4139, 4804}, {4391, 22324}, {4397, 48080}, {4649, 18200}, {4651, 9400}, {4685, 4785}, {4776, 25142}, {4790, 9010}, {4879, 25537}, {4897, 9040}, {4979, 6373}, {5040, 7252}, {6005, 47996}, {6006, 22312}, {6372, 47917}, {8013, 21720}, {8672, 47934}, {9002, 22277}, {9286, 24534}, {9508, 16751}, {14474, 27013}, {14838, 39548}, {15630, 21833}, {15632, 22280}, {17217, 25299}, {20711, 21834}, {21005, 21007}, {21820, 23610}, {22279, 36848}, {22305, 40603}, {24921, 29647}, {26115, 27345}, {27674, 48136}, {29226, 47675}, {30665, 47660}, {31286, 43223}, {40516, 42455}
X(50487) = reflection of X(i) in X(j) for these {i,j}: {649, 4507}, {2533, 22320}, {2978, 650}, {39548, 14838}
X(50487) = isogonal conjugate of X(4623)
X(50487) = isogonal conjugate of the isotomic conjugate of X(4705)
X(50487) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {18298, 21293}, {40737, 149}, {40770, 4440}, {40778, 39345}
X(50487) = X(i)-Ceva conjugate of X(j) for these (i,j): {10, 21835}, {42, 3121}, {65, 21823}, {100, 21814}, {181, 3124}, {512, 4079}, {668, 37}, {692, 213}, {1500, 1084}, {1824, 21833}, {3952, 21820}, {4553, 21802}, {21859, 21815}, {40504, 3125}, {40516, 4516}, {40521, 1500}
X(50487) = X(i)-cross conjugate of X(j) for these (i,j): {1084, 1500}, {7063, 7109}
X(50487) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 4623), (10, 670), (11, 18021), (37, 4602), (115, 6385), (244, 310), (512, 513), (523, 40495), (1084, 274), (3005, 693), (3121, 16748), (3124, 16703), (4075, 6386), (5139, 286), (5375, 34537), (5452, 4631), (6741, 40072), (8054, 873), (9296, 44168), (15267, 4569), (17423, 1444), (32664, 4610), (38978, 350), (38982, 40075), (38986, 86), (38988, 16741), (38996, 81), (39010, 30938), (39025, 261), (39026, 24037), (40586, 799), (40600, 99), (40603, 4609), (40607, 668), (40608, 314), (40611, 4625), (40627, 7199)
X(50487) = cevapoint of X(512) and X(9402)
X(50487) = crosspoint of X(i) and X(j) for these (i,j): {37, 668}, {100, 18098}, {213, 692}, {512, 798}, {1500, 40521}
X(50487) = crosssum of X(i) and X(j) for these (i,j): {2, 17166}, {6, 16692}, {75, 18158}, {81, 667}, {99, 799}, {274, 693}, {513, 16696}, {514, 4425}, {1019, 18169}, {1444, 15413}, {2530, 18182}, {3733, 18166}, {4107, 4368}, {7192, 16705}, {7199, 16709}
X(50487) = crossdifference of every pair of points on line {81, 239}
X(50487) = X(i)-isoconjugate of X(j) for these (i,j): {1, 4623}, {2, 4610}, {21, 4625}, {27, 4563}, {57, 4631}, {58, 670}, {60, 4572}, {76, 4556}, {81, 799}, {85, 4612}, {86, 99}, {100, 873}, {109, 18021}, {110, 310}, {163, 6385}, {190, 1509}, {249, 3261}, {261, 664}, {274, 662}, {286, 4592}, {314, 1414}, {333, 4573}, {350, 36066}, {513, 24037}, {514, 4590}, {522, 7340}, {552, 3699}, {593, 1978}, {645, 1434}, {648, 17206}, {649, 34537}, {658, 7058}, {668, 757}, {689, 17187}, {693, 24041}, {763, 4033}, {811, 1444}, {849, 6386}, {892, 6629}, {905, 46254}, {1014, 7257}, {1019, 4601}, {1043, 4616}, {1098, 4569}, {1101, 40495}, {1269, 6578}, {1333, 4602}, {1429, 36806}, {1790, 6331}, {1919, 44168}, {2185, 4554}, {2206, 4609}, {2287, 4635}, {3120, 31614}, {3676, 6064}, {3952, 6628}, {4025, 18020}, {4107, 39292}, {4131, 23999}, {4558, 44129}, {4560, 4620}, {4565, 28660}, {4567, 7199}, {4577, 16887}, {4584, 30940}, {4589, 33295}, {4593, 16696}, {4594, 17103}, {4596, 16709}, {4598, 7304}, {4599, 16703}, {4600, 7192}, {4603, 8033}, {4615, 16704}, {4622, 30939}, {4632, 8025}, {4633, 42028}, {4636, 6063}, {5209, 17929}, {6540, 30593}, {7054, 46406}, {7649, 47389}, {16741, 36085}, {17200, 35137}, {17209, 43187}, {17731, 17930}, {20924, 37140}, {23582, 30805}, {30938, 36133}, {36069, 40075}
X(50487) = barycentric product X(i)*X(j) for these {i,j}: {1, 4079}, {6, 4705}, {10, 798}, {12, 3063}, {31, 4024}, {32, 4036}, {37, 512}, {42, 661}, {65, 3709}, {72, 2489}, {100, 3124}, {101, 2643}, {110, 21833}, {115, 692}, {163, 21043}, {181, 650}, {210, 7180}, {213, 523}, {228, 2501}, {291, 46390}, {292, 4155}, {313, 1924}, {321, 669}, {513, 1500}, {514, 872}, {594, 667}, {646, 1356}, {647, 1824}, {649, 756}, {656, 2333}, {657, 1254}, {663, 2171}, {668, 1084}, {693, 7109}, {762, 3733}, {810, 1826}, {850, 2205}, {875, 4037}, {906, 8754}, {1015, 40521}, {1018, 3122}, {1042, 4171}, {1089, 1919}, {1109, 32739}, {1110, 21131}, {1255, 8663}, {1332, 2971}, {1334, 4017}, {1400, 4041}, {1402, 3700}, {1415, 4092}, {1427, 4524}, {1577, 1918}, {1783, 20975}, {1946, 8736}, {1973, 4064}, {1978, 4117}, {1980, 28654}, {2084, 18082}, {2161, 42666}, {2197, 18344}, {2200, 24006}, {2281, 48395}, {2298, 42661}, {2350, 21727}, {2395, 5360}, {2533, 40729}, {2610, 6187}, {2623, 21807}, {3005, 18098}, {3049, 41013}, {3121, 3952}, {3125, 4557}, {3248, 4103}, {3271, 21859}, {3669, 7064}, {3690, 6591}, {3708, 8750}, {3903, 21823}, {3954, 18105}, {4083, 6378}, {4105, 7147}, {4130, 7143}, {4515, 7250}, {4516, 4559}, {4554, 7063}, {4567, 22260}, {4601, 23099}, {4674, 14407}, {4770, 28658}, {5380, 21906}, {6354, 8641}, {6367, 28615}, {6386, 9427}, {7140, 22383}, {7148, 20979}, {9178, 21839}, {9278, 17990}, {9426, 27801}, {15320, 21837}, {15630, 42717}, {18001, 20693}, {18070, 41267}, {21046, 32676}, {21051, 21759}, {21056, 34248}, {21353, 42653}, {21816, 50344}, {21828, 34857}, {21834, 23493}, {28625, 48005}, {35352, 41333}
X(50487) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 4623}, {10, 4602}, {31, 4610}, {37, 670}, {42, 799}, {55, 4631}, {100, 34537}, {101, 24037}, {115, 40495}, {181, 4554}, {213, 99}, {228, 4563}, {321, 4609}, {351, 16741}, {512, 274}, {523, 6385}, {560, 4556}, {594, 6386}, {649, 873}, {650, 18021}, {661, 310}, {667, 1509}, {668, 44168}, {669, 81}, {688, 16696}, {692, 4590}, {756, 1978}, {762, 27808}, {798, 86}, {810, 17206}, {872, 190}, {888, 30938}, {906, 47389}, {1042, 4635}, {1084, 513}, {1254, 46406}, {1334, 7257}, {1356, 3669}, {1400, 4625}, {1402, 4573}, {1415, 7340}, {1500, 668}, {1824, 6331}, {1918, 662}, {1919, 757}, {1922, 36066}, {1924, 58}, {1980, 593}, {2084, 16887}, {2086, 14296}, {2171, 4572}, {2175, 4612}, {2200, 4592}, {2205, 110}, {2333, 811}, {2489, 286}, {2610, 40075}, {2643, 3261}, {2971, 17924}, {3005, 16703}, {3049, 1444}, {3063, 261}, {3121, 7192}, {3122, 7199}, {3124, 693}, {3700, 40072}, {3709, 314}, {4024, 561}, {4036, 1502}, {4041, 28660}, {4064, 40364}, {4079, 75}, {4117, 649}, {4128, 16737}, {4155, 1921}, {4455, 30940}, {4557, 4601}, {4705, 76}, {5360, 2396}, {6378, 18830}, {7063, 650}, {7064, 646}, {7077, 36806}, {7109, 100}, {7143, 36838}, {7234, 8033}, {8034, 16727}, {8640, 7304}, {8641, 7058}, {8663, 4359}, {8664, 16707}, {8750, 46254}, {9402, 34021}, {9426, 1333}, {9427, 667}, {9447, 4636}, {14407, 30939}, {18082, 37204}, {18098, 689}, {20975, 15413}, {21043, 20948}, {21056, 18837}, {21727, 18152}, {21755, 17212}, {21814, 4576}, {21815, 3888}, {21823, 4374}, {21833, 850}, {21835, 17217}, {21837, 33297}, {22260, 16732}, {23099, 3125}, {23216, 22383}, {23610, 3121}, {32739, 24041}, {40521, 31625}, {40729, 4594}, {42068, 6591}, {42661, 20911}, {42666, 20924}, {46390, 350}
X(50487) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {42, 649, 7234}, {661, 21727, 4705}, {3063, 8646, 1980}
X(50488) lies on these lines: {512, 661}, {513, 48409}, {649, 838}, {656, 2530}, {667, 788}, {834, 14349}, {891, 50457}, {1577, 4083}, {4086, 4132}, {4129, 4147}, {4507, 4834}, {4761, 22320}, {4905, 9002}, {4992, 31946}, {6005, 48010}, {6372, 47904}, {17478, 48333}, {26983, 47836}, {27045, 47840}
X(50488) = reflection of X(i) in X(j) for these {i,j}: {4761, 22320}, {4834, 4507}
X(50488) = isogonal conjugate of the isotomic conjugate of X(47842)
X(50488) = X(i)-Ceva conjugate of X(j) for these (i,j): {834, 42664}, {28625, 3121}
X(50488) = X(i)-isoconjugate of X(j) for these (i,j): {81, 37218}, {86, 835}, {99, 43531}, {799, 2214}, {4600, 43927}
X(50488) = X(i)-Dao conjugate of X(j) for these (i, j): (38986, 43531), (38996, 2214), (39016, 274), (40586, 37218), (40600, 835), (41849, 4602)
X(50488) = crosspoint of X(941) and X(3952)
X(50488) = crosssum of X(i) and X(j) for these (i,j): {2, 47844}, {835, 37218}, {940, 3733}, {2478, 4560}, {3670, 14349}
X(50488) = crossdifference of every pair of points on line {75, 81}
X(50488) = barycentric product X(i)*X(j) for these {i,j}: {1, 42664}, {6, 47842}, {31, 23879}, {37, 834}, {42, 14349}, {213, 45746}, {321, 8637}, {386, 661}, {469, 810}, {512, 28606}, {656, 44103}, {669, 33935}, {798, 5224}, {1333, 23282}, {1919, 42714}, {3121, 33948}, {3876, 7180}
X(50488) = barycentric quotient X(i)/X(j) for these {i,j}: {42, 37218}, {213, 835}, {386, 799}, {669, 2214}, {798, 43531}, {834, 274}, {3121, 43927}, {5224, 4602}, {8637, 81}, {14349, 310}, {23282, 27801}, {23879, 561}, {28606, 670}, {33935, 4609}, {42664, 75}, {44103, 811}, {45746, 6385}, {47842, 76}
X(50488) = {X(798),X(810)}-harmonic conjugate of X(667)
X(50489) lies on these lines: {10, 4932}, {42, 4813}, {512, 4988}, {513, 4380}, {649, 4705}, {661, 669}, {2533, 7192}, {2978, 8678}, {4010, 27575}, {4024, 9279}, {4088, 8672}, {4367, 27647}, {4474, 48141}, {4781, 40501}, {4979, 21727}, {6372, 48101}, {21146, 27610}, {22319, 29198}, {23506, 48093}, {27648, 48030}, {28374, 48027}
X(50489) = X(32042)-Ceva conjugate of X(37)
X(50489) = X(48005)-Dao conjugate of X(4802)
X(50489) = crosssum of X(4840) and X(18166)
X(50489) = crossdifference of every pair of points on line {17011, 20963}
X(50490) lies on these lines: {512, 661}, {513, 3004}, {647, 4455}, {650, 9313}, {669, 1402}, {834, 48029}, {876, 25537}, {891, 48094}, {926, 20983}, {2488, 6363}, {2499, 2978}, {3005, 3709}, {3310, 8640}, {3804, 7234}, {4010, 14208}, {4083, 4468}, {4088, 4139}, {4108, 26983}, {4132, 48047}, {5996, 27045}, {6372, 47958}, {8651, 21828}, {8672, 47701}, {17115, 21107}
X(50490) = reflection of X(2978) in X(2499)
X(50490) = isogonal conjugate of the isotomic conjugate of X(48403)
X(50490) = X(i)-Ceva conjugate of X(j) for these (i,j): {1427, 3121}, {2333, 3122}
X(50490) = X(i)-isoconjugate of X(j) for these (i,j): {190, 40403}, {643, 8817}, {645, 7131}, {662, 30701}, {670, 7084}, {799, 7123}, {1037, 7257}, {1043, 8269}, {1332, 40411}, {1790, 42384}, {4567, 48070}, {7259, 30705}
X(50490) = X(i)-Dao conjugate of X(j) for these (i, j): (1084, 30701), (6554, 670), (15487, 799), (17463, 33932), (18589, 668), (38996, 7123), (40627, 48070)
X(50490) = crosspoint of X(512) and X(7250)
X(50490) = crosssum of X(i) and X(j) for these (i,j): {99, 7256}, {100, 4561}
X(50490) = crossdifference of every pair of points on line {81, 7123}
X(50490) = barycentric product X(i)*X(j) for these {i,j}: {6, 48403}, {25, 21107}, {42, 48398}, {497, 7180}, {512, 4000}, {513, 16583}, {514, 40934}, {523, 16502}, {614, 661}, {647, 1851}, {649, 3914}, {650, 40961}, {693, 21750}, {798, 3673}, {1427, 17115}, {1473, 2501}, {1633, 3125}, {2082, 4017}, {2489, 17170}, {3122, 3732}, {3669, 40965}, {3709, 7195}, {4025, 8020}, {4041, 28017}, {4319, 7216}, {6554, 7250}, {6591, 17441}, {7083, 7178}, {7192, 21813}, {7649, 23620}, {17924, 22363}, {21015, 43925}
X(50490) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 30701}, {614, 799}, {667, 40403}, {669, 7123}, {1473, 4563}, {1633, 4601}, {1824, 42384}, {1851, 6331}, {1924, 7084}, {2082, 7257}, {3122, 48070}, {3673, 4602}, {3914, 1978}, {4000, 670}, {4319, 7258}, {5324, 4631}, {7083, 645}, {7180, 8817}, {7250, 30705}, {8020, 1897}, {16502, 99}, {16583, 668}, {21107, 305}, {21750, 100}, {21813, 3952}, {22363, 1332}, {23620, 4561}, {28017, 4625}, {30706, 7256}, {40934, 190}, {40961, 4554}, {40965, 646}, {48398, 310}, {48403, 76}
X(50490) = {X(669),X(8034)}-harmonic conjugate of X(7180)
X(50491) lies on these lines: {1, 25537}, {6, 23570}, {8, 26148}, {10, 23301}, {42, 669}, {43, 18197}, {181, 7180}, {512, 661}, {513, 4507}, {647, 17990}, {649, 6373}, {650, 788}, {667, 23655}, {693, 891}, {798, 3221}, {834, 48030}, {1491, 6371}, {2254, 6363}, {2978, 4893}, {3063, 8633}, {3240, 36270}, {3700, 4155}, {3709, 4093}, {3805, 21196}, {3835, 4083}, {4010, 4086}, {4132, 4806}, {4394, 9010}, {4651, 44445}, {4685, 25423}, {4824, 8672}, {6085, 50359}, {6372, 47666}, {8640, 20979}, {9002, 50335}, {9009, 22277}, {9040, 17069}, {9400, 48049}, {14321, 22276}, {17072, 23818}, {19998, 31299}, {21260, 25627}, {22183, 22226}, {22191, 22222}, {24534, 45902}, {24674, 47835}, {24747, 26102}, {25473, 29633}, {25686, 32783}, {29226, 48399}, {30700, 50452}, {31003, 31330}, {43223, 44451}, {43931, 45313}
X(50491) = midpoint of X(649) and X(20983)
X(50491) = reflection of X(3835) in X(25142)
X(50491) = isogonal conjugate of the isotomic conjugate of X(21051)
X(50491) = X(42328)-complementary conjugate of X(116)
X(50491) = X(i)-Ceva conjugate of X(j) for these (i,j): {43, 6377}, {749, 1015}, {798, 512}, {3952, 3971}, {4033, 1500}, {4083, 21834}, {6376, 40610}, {20691, 21835}
X(50491) = X(i)-cross conjugate of X(j) for these (i,j): {21834, 512}, {21835, 20691}
X(50491) = crosspoint of X(i) and X(j) for these (i,j): {6, 3903}, {42, 3952}, {4033, 6376}, {4083, 20979}
X(50491) = crosssum of X(i) and X(j) for these (i,j): {2, 4367}, {81, 16695}, {86, 3733}, {932, 4598}, {1019, 18192}, {4560, 37373}, {7192, 33947}, {27455, 43931}
X(50491) = crossdifference of every pair of points on line {81, 330}
X(50491) = X(i)-isoconjugate of X(j) for these (i,j): {58, 18830}, {81, 4598}, {86, 932}, {87, 99}, {110, 6384}, {163, 6383}, {274, 34071}, {330, 662}, {645, 7153}, {670, 7121}, {799, 2162}, {811, 23086}, {1019, 5383}, {1414, 7155}, {2053, 4625}, {2319, 4573}, {4565, 27424}, {4584, 39914}, {4589, 34252}, {4600, 43931}, {4610, 16606}, {4623, 23493}, {5546, 7209}, {6331, 15373}, {27644, 32039}
X(50491) = X(i)-Dao conjugate of X(j) for these (i, j): (10, 18830), (75, 4602), (115, 6383), (244, 6384), (798, 1019), (1084, 330), (3835, 7192), (4083, 17217), (6377, 310), (17423, 23086), (21051, 4374), (38986, 87), (38996, 2162), (40586, 4598), (40598, 670), (40600, 932), (40608, 7155), (40610, 274)
X(50491) = barycentric product X(i)*X(j) for these {i,j}: {1, 21834}, {6, 21051}, {10, 20979}, {37, 4083}, {42, 3835}, {43, 661}, {181, 27527}, {192, 512}, {210, 43051}, {213, 20906}, {321, 8640}, {513, 20691}, {523, 2176}, {594, 16695}, {649, 3971}, {668, 21835}, {669, 6382}, {756, 18197}, {798, 6376}, {1018, 3123}, {1400, 4147}, {1403, 3700}, {1423, 4041}, {1438, 21959}, {1500, 17217}, {1577, 2209}, {1824, 25098}, {1826, 22090}, {2501, 20760}, {3121, 36863}, {3122, 4595}, {3208, 4017}, {3212, 3709}, {3690, 17921}, {3952, 6377}, {4024, 38832}, {4033, 38986}, {4079, 33296}, {4086, 41526}, {4455, 40848}, {4557, 21138}, {4674, 14408}, {4705, 27644}, {7140, 23092}, {7180, 27538}, {9426, 40367}, {16606, 25142}, {16742, 40521}, {18107, 21035}, {21762, 27808}, {21832, 41531}, {23493, 23886}
X(50491) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 18830}, {42, 4598}, {43, 799}, {192, 670}, {213, 932}, {512, 330}, {523, 6383}, {661, 6384}, {669, 2162}, {798, 87}, {1403, 4573}, {1423, 4625}, {1918, 34071}, {1924, 7121}, {2176, 99}, {2209, 662}, {3049, 23086}, {3121, 43931}, {3123, 7199}, {3208, 7257}, {3709, 7155}, {3835, 310}, {3971, 1978}, {4017, 7209}, {4041, 27424}, {4079, 42027}, {4083, 274}, {4147, 28660}, {4455, 39914}, {4557, 5383}, {4729, 27496}, {6376, 4602}, {6377, 7192}, {6382, 4609}, {8640, 81}, {14408, 30939}, {16695, 1509}, {18197, 873}, {20691, 668}, {20760, 4563}, {20906, 6385}, {20979, 86}, {21051, 76}, {21762, 3733}, {21834, 75}, {21835, 513}, {22090, 17206}, {22386, 7254}, {23493, 32039}, {24533, 8033}, {25142, 31008}, {27527, 18021}, {27644, 4623}, {38832, 4610}, {38986, 1019}, {40610, 17217}, {41526, 1414}, {41531, 4639}
X(50491) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {43, 18197, 24533}, {3835, 25142, 14426}
X(50492) lies on these lines: {512, 661}, {513, 4841}, {647, 798}, {649, 854}, {650, 834}, {891, 48275}, {3239, 29350}, {3700, 4132}, {3709, 42664}, {4024, 4139}, {4083, 6590}, {4790, 9002}, {4979, 6363}, {4988, 8672}, {7178, 8712}, {14298, 47136}, {17217, 24622}, {21099, 21719}, {47130, 48269}, {47995, 48402}
X(50492) = isogonal conjugate of the isotomic conjugate of X(48402)
X(50492) = crossdifference of every pair of points on line {8, 81}
X(50492) = barycentric product X(i)*X(j) for these {i,j}: {1, 50332}, {6, 48402}, {42, 47995}, {512, 17321}, {513, 3931}, {523, 16466}, {656, 7713}, {661, 5256}, {1459, 39579}, {4017, 5250}, {4254, 7178}, {7180, 14555}
X(50492) = barycentric quotient X(i)/X(j) for these {i,j}: {3931, 668}, {4254, 645}, {5250, 7257}, {5256, 799}, {7713, 811}, {16466, 99}, {17321, 670}, {47995, 310}, {48402, 76}, {50332, 75}
X(50492) = {X(4832),X(7180)}-harmonic conjugate of X(649)
X(50493) lies on these lines: {39, 21763}, {386, 16695}, {512, 661}, {650, 838}, {656, 6363}, {667, 20456}, {669, 20865}, {798, 6373}, {810, 1960}, {834, 48054}, {891, 1577}, {970, 6002}, {1924, 20970}, {2084, 46390}, {3111, 24504}, {3124, 42655}, {4083, 4129}, {4139, 50329}, {6050, 9010}, {6371, 47842}, {6372, 47946}, {8637, 20861}, {8711, 20969}, {9002, 48066}, {17478, 48296}, {21260, 25142}, {22076, 30583}, {26983, 47837}, {27045, 47839}
X(50493) = midpoint of X(667) and X(20983)
X(50493) = reflection of X(21260) in X(25142)
X(50493) = isogonal conjugate of the isotomic conjugate of X(31946)
X(50493) = X(i)-Ceva conjugate of X(j) for these (i,j): {667, 512}, {20983, 3221}
X(50493) = X(i)-isoconjugate of X(j) for these (i,j): {99, 39748}, {110, 40010}, {662, 35058}, {799, 39964}
X(50493) = X(i)-Dao conjugate of X(j) for these (i, j): (244, 40010), (321, 6386), (1084, 35058), (31946, 7192), (38986, 39748), (38996, 39964)
X(50493) = crosspoint of X(6) and X(3952)
X(50493) = crosssum of X(i) and X(j) for these (i,j): {2, 3733}, {4193, 4560}
X(50493) = crossdifference of every pair of points on line {81, 4360}
X(50493) = barycentric product X(i)*X(j) for these {i,j}: {6, 31946}, {58, 21720}, {512, 17147}, {513, 21858}, {523, 16685}, {649, 3159}, {661, 3216}, {667, 40603}, {669, 40034}, {798, 18133}, {2501, 22458}
X(50493) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 35058}, {661, 40010}, {669, 39964}, {798, 39748}, {3159, 1978}, {3216, 799}, {4079, 42471}, {16685, 99}, {17147, 670}, {18133, 4602}, {21720, 313}, {21858, 668}, {22458, 4563}, {31946, 76}, {40034, 4609}, {40603, 6386}
X(50494) lies on these lines: {42, 42664}, {512, 661}, {513, 4468}, {647, 7234}, {669, 3709}, {834, 48027}, {891, 47958}, {926, 2978}, {2483, 21005}, {2484, 8646}, {2489, 4079}, {2533, 14208}, {3005, 7180}, {3250, 23655}, {3804, 4455}, {4083, 47995}, {4088, 8672}, {4108, 27045}, {4132, 47998}, {4139, 47701}, {4374, 25299}, {5996, 26983}, {6363, 48020}, {6371, 20983}, {6372, 48094}, {6590, 8678}, {8034, 8665}, {9313, 48026}
X(50494) = isogonal conjugate of the isotomic conjugate of X(48395)
X(50494) = X(i)-isoconjugate of X(j) for these (i,j): {81, 37215}, {86, 1310}, {670, 1472}, {799, 2221}, {1036, 4625}, {1245, 4623}, {1414, 30479}, {2339, 4573}, {17206, 36099}
X(50494) = X(i)-Dao conjugate of X(j) for these (i, j): (5515, 310), (8678, 47844), (38996, 2221), (40181, 799), (40586, 37215), (40600, 1310), (40608, 30479)
X(50494) = crosspoint of X(2484) and X(8678)
X(50494) = crosssum of X(1310) and X(37215)
X(50494) = crossdifference of every pair of points on line {81, 2221}
X(50494) = barycentric product X(i)*X(j) for these {i,j}: {6, 48395}, {10, 2484}, {37, 8678}, {42, 6590}, {213, 2517}, {321, 8646}, {388, 3709}, {512, 2345}, {612, 661}, {647, 7102}, {798, 4385}, {1010, 4079}, {1460, 3700}, {1500, 47844}, {1824, 2522}, {2285, 4041}, {2303, 4705}, {2333, 23874}, {2501, 7085}, {3900, 8898}, {3974, 7180}, {4024, 44119}, {4130, 10376}, {4171, 4320}, {4524, 7365}
X(50494) = barycentric quotient X(i)/X(j) for these {i,j}: {42, 37215}, {213, 1310}, {612, 799}, {669, 2221}, {1460, 4573}, {1924, 1472}, {2285, 4625}, {2303, 4623}, {2345, 670}, {2484, 86}, {2517, 6385}, {3709, 30479}, {4320, 4635}, {4385, 4602}, {6590, 310}, {7085, 4563}, {7102, 6331}, {8646, 81}, {8678, 274}, {8898, 4569}, {10376, 36838}, {44119, 4610}, {48395, 76}
X(50495) lies on these lines: {512, 661}, {513, 3700}, {523, 24089}, {647, 4079}, {649, 3709}, {834, 48026}, {3239, 6005}, {4024, 8672}, {4132, 4841}, {4139, 4988}, {4468, 20296}, {4813, 6371}, {6363, 48019}, {6372, 48275}, {7180, 42664}, {17159, 24622}
X(50495) = crosssum of X(4560) and X(37265)
X(50495) = crossdifference of every pair of points on line {81, 3616}
X(50495) = barycentric product X(661)*X(5287)
X(50495) = barycentric quotient X(5287)/X(799)
X(50496) lies on these lines: {512, 661}, {513, 4088}, {649, 21003}, {830, 47660}, {834, 48023}, {891, 47916}, {2483, 8635}, {3005, 7234}, {3709, 3804}, {4079, 18105}, {4083, 47958}, {4132, 47701}, {4139, 47702}, {4455, 8664}, {4468, 6005}, {4707, 21125}, {4761, 14208}, {4813, 9313}, {6371, 48020}, {6372, 48130}, {6586, 8655}, {8672, 47700}, {8678, 48275}, {29350, 47995}
X(50496) = isogonal conjugate of the isotomic conjugate of X(47711)
X(50496) = X(86)-isoconjugate of X(831)
X(50496) = X(40600)-Dao conjugate of X(831)
X(50496) = crosspoint of X(830) and X(2483)
X(50496) = crosssum of X(i) and X(j) for these (i,j): {514, 32772}, {6536, 21124}
X(50496) = crossdifference of every pair of points on line {81, 5299}
X(50496) = barycentric product X(i)*X(j) for these {i,j}: {6, 47711}, {10, 2483}, {37, 830}, {42, 47660}, {321, 8635}, {512, 17289}, {513, 28594}, {523, 5280}, {661, 3920}, {798, 33941}, {2501, 5314}, {3669, 4538}, {3709, 7247}
X(50496) = barycentric quotient X(i)/X(j) for these {i,j}: {213, 831}, {830, 274}, {2483, 86}, {3920, 799}, {4538, 646}, {5280, 99}, {5314, 4563}, {8635, 81}, {17289, 670}, {28594, 668}, {33941, 4602}, {47660, 310}, {47711, 76}
X(50496) = {X(3005),X(7234)}-harmonic conjugate of X(21828)
X(50497) lies on these lines: {320, 350}, {512, 661}, {649, 4455}, {788, 4813}, {834, 48024}, {891, 47917}, {2254, 2499}, {2488, 6615}, {3005, 4079}, {3120, 38989}, {3121, 38978}, {3122, 39011}, {3805, 44449}, {3808, 49297}, {3835, 6005}, {4040, 29807}, {4083, 47666}, {4132, 4824}, {4139, 47934}, {4155, 4988}, {4507, 4893}, {4784, 25537}, {4804, 8672}, {4806, 23301}, {4979, 8027}, {5040, 16874}, {6371, 48021}, {6372, 47672}, {6373, 48019}, {8034, 8663}, {9400, 17494}, {9508, 24948}, {15309, 39548}, {20983, 48026}, {23655, 48338}, {26049, 47821}, {27193, 47824}, {27674, 50336}, {27854, 48049}, {29198, 47675}, {29350, 47996}
X(50497) = reflection of X(20983) in X(48026)
X(50497) = complement of the isogonal conjugate of X(4436)
X(50497) = isogonal conjugate of the isotomic conjugate of X(48393)
X(50497) = medial-isogonal conjugate of X(2486)
X(50497) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {9401, 149}, {9403, 148}
X(50497) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 2486}, {6, 17205}, {31, 3121}, {101, 4698}, {110, 10180}, {662, 36812}, {692, 25092}, {765, 6372}, {1252, 48000}, {2667, 115}, {3691, 26932}, {3706, 124}, {3720, 11}, {3739, 116}, {4059, 17059}, {4436, 10}, {4891, 5510}, {16589, 8287}, {18089, 44312}, {18166, 17761}, {20888, 21252}, {20963, 1086}, {21020, 125}, {21753, 16592}, {21820, 6627}, {22060, 2968}, {22369, 16573}, {39793, 8286}, {48264, 46100}
X(50497) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 3121}, {513, 6372}, {1500, 3122}, {13476, 3125}, {34585, 1015}
X(50497) = X(i)-isoconjugate of X(j) for these (i,j): {86, 8708}, {99, 40433}, {100, 40439}, {190, 40408}, {662, 32009}
X(50497) = X(i)-Dao conjugate of X(j) for these (i, j): (1084, 32009), (2486, 17143), (3121, 2), (3739, 668), (8054, 40439), (16589, 670), (38986, 40433), (40600, 8708)
X(50497) = crosspoint of X(512) and X(513)
X(50497) = crosssum of X(i) and X(j) for these (i,j): {99, 100}, {667, 1206}
X(50497) = crossdifference of every pair of points on line {81, 213}
X(50497) = barycentric product X(i)*X(j) for these {i,j}: {6, 48393}, {37, 6372}, {42, 47672}, {512, 3739}, {513, 16589}, {514, 2667}, {523, 20963}, {649, 21020}, {650, 39793}, {656, 40975}, {661, 3720}, {693, 21753}, {798, 20888}, {1019, 21699}, {1400, 48264}, {2501, 22060}, {3005, 18089}, {3125, 4436}, {3669, 4111}, {3691, 4017}, {3706, 7180}, {3709, 4059}, {4079, 17175}, {4705, 18166}, {7192, 21820}, {17924, 22369}
X(50497) = barycentric quotient X(i)/X(j) for these {i,j}: {213, 8708}, {512, 32009}, {649, 40439}, {667, 40408}, {798, 40433}, {2667, 190}, {3691, 7257}, {3720, 799}, {3739, 670}, {4111, 646}, {4436, 4601}, {6372, 274}, {16589, 668}, {18089, 689}, {18166, 4623}, {20888, 4602}, {20963, 99}, {21020, 1978}, {21699, 4033}, {21753, 100}, {21820, 3952}, {22060, 4563}, {22369, 1332}, {39793, 4554}, {40975, 811}, {47672, 310}, {48264, 28660}, {48393, 76}
X(50497) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4010, 21146, 30591}, {48080, 48108, 4811}
X(50498) lies on these lines: {37, 4790}, {321, 48079}, {512, 661}, {513, 4024}, {514, 24089}, {649, 4057}, {834, 4813}, {875, 2978}, {1245, 10097}, {4064, 48106}, {4132, 4988}, {4139, 47669}, {4526, 4979}, {4826, 21828}, {4838, 8672}, {4932, 22043}, {4940, 31993}, {6005, 6590}, {6371, 48019}, {7234, 8663}, {7265, 47660}, {15309, 47678}, {22044, 49293}, {24083, 31286}, {24084, 47789}
X(50498) = isogonal conjugate of the isotomic conjugate of X(47678)
X(50498) = X(8694)-Ceva conjugate of X(42)
X(50498) = X(86)-isoconjugate of X(15322)
X(50498) = X(40600)-Dao conjugate of X(15322)
X(50498) = crosspoint of X(101) and X(28625)
X(50498) = crosssum of X(i) and X(j) for these (i,j): {21, 4765}, {514, 5333}, {8025, 48580}
X(50498) = crossdifference of every pair of points on line {81, 1125}
X(50498) = barycentric product X(i)*X(j) for these {i,j}: {6, 47678}, {37, 15309}, {512, 28653}, {661, 17019}
X(50498) = barycentric quotient X(i)/X(j) for these {i,j}: {213, 15322}, {15309, 274}, {17019, 799}, {28653, 670}, {47678, 76}
X(50499) lies on these lines: {19, 18344}, {40, 3309}, {55, 667}, {65, 876}, {512, 650}, {513, 4041}, {514, 7659}, {649, 3900}, {663, 4394}, {798, 4130}, {905, 29350}, {926, 17410}, {1019, 14077}, {1491, 48128}, {1635, 48338}, {1734, 2526}, {2093, 4905}, {2254, 8712}, {2484, 4827}, {2550, 6008}, {3566, 48062}, {3667, 4163}, {3716, 48559}, {3779, 9010}, {3803, 3887}, {3910, 48069}, {3925, 21260}, {4106, 17072}, {4132, 6129}, {4380, 21302}, {4705, 48026}, {4730, 4790}, {4761, 23882}, {4770, 47956}, {4775, 6050}, {4782, 37568}, {4807, 29013}, {4820, 48395}, {4843, 6590}, {4885, 47836}, {4940, 47814}, {4983, 47777}, {4990, 47766}, {4992, 47802}, {5263, 27419}, {5592, 28579}, {6005, 47965}, {6182, 21389}, {9508, 48136}, {10902, 39227}, {14349, 48193}, {17784, 31291}, {20317, 48080}, {21677, 29150}, {23880, 50343}, {28478, 50333}, {28898, 47707}, {29200, 48088}, {30234, 48294}, {31250, 47837}, {31287, 47840}, {37080, 48330}, {45320, 48273}, {48012, 48091}, {48125, 50352}, {48304, 48570}, {48339, 48566}, {48616, 50335}
X(50499) = midpoint of X(i) and X(j) for these {i,j}: {649, 4729}, {4380, 21302}, {4730, 4834}
X(50499) = reflection of X(i) in X(j) for these {i,j}: {663, 4394}, {2526, 1734}, {3669, 50336}, {3803, 48011}, {4106, 17072}, {4162, 667}, {4775, 6050}, {4790, 4834}, {4820, 48395}, {47915, 4490}, {47956, 4770}, {48026, 4705}, {48080, 20317}, {48091, 48012}, {48125, 50352}, {48128, 1491}, {48136, 9508}, {48329, 4782}, {48616, 50335}
X(50499) = crossdifference of every pair of points on line {940, 1449}
X(50500) lies on these lines: {512, 650}, {513, 4380}, {788, 4790}, {834, 50336}, {891, 48133}, {2978, 4394}, {3063, 16874}, {4083, 43067}, {4106, 9400}, {4132, 7662}, {4155, 48397}, {4369, 29350}, {4834, 7234}, {4979, 9010}, {6005, 48000}, {6371, 7659}, {6372, 47920}, {8646, 21007}, {9040, 48013}, {25511, 47836}, {27166, 47761}, {30665, 49281}
X(50500) = reflection of X(i) in X(j) for these {i,j}: {650, 4507}, {2978, 4394}
X(50500) = crossdifference of every pair of points on line {940, 4384}
X(50501) lies on these lines: {10, 29013}, {100, 29241}, {484, 513}, {512, 650}, {514, 4818}, {522, 48395}, {525, 48062}, {649, 4041}, {659, 3309}, {663, 1635}, {667, 3900}, {693, 47836}, {812, 17072}, {830, 48011}, {891, 3669}, {905, 4083}, {1491, 48092}, {1960, 4162}, {2254, 4498}, {2490, 4990}, {2509, 9313}, {2516, 4775}, {2530, 8712}, {2533, 23882}, {2832, 48075}, {2977, 3566}, {3716, 48561}, {3777, 48244}, {3803, 4782}, {3887, 4401}, {3960, 48346}, {4010, 47835}, {4025, 29288}, {4091, 9373}, {4106, 21260}, {4139, 6129}, {4147, 6002}, {4151, 7662}, {4155, 21348}, {4160, 48064}, {4170, 47794}, {4367, 14077}, {4380, 21301}, {4391, 50343}, {4453, 47720}, {4467, 47707}, {4490, 4784}, {4762, 50352}, {4770, 4790}, {4801, 47824}, {4807, 29066}, {4814, 48322}, {4822, 4893}, {4885, 47837}, {4895, 8643}, {4905, 21385}, {4959, 8656}, {4978, 48573}, {4979, 47912}, {6005, 48003}, {6367, 48397}, {6372, 7659}, {6588, 42666}, {14419, 48333}, {14837, 48403}, {14838, 29350}, {15309, 48607}, {17166, 47762}, {20295, 47814}, {20317, 48267}, {20517, 47131}, {21051, 29328}, {21124, 48106}, {21188, 23770}, {21192, 29047}, {21302, 47776}, {23875, 48088}, {27013, 47820}, {29051, 48008}, {29142, 48069}, {29158, 50453}, {29170, 48401}, {29200, 48056}, {29252, 48087}, {29284, 49280}, {29302, 48089}, {30202, 34948}, {30234, 48330}, {31209, 47840}, {31286, 48564}, {31287, 47839}, {47694, 48565}, {47718, 48254}, {47719, 48252}, {47777, 48053}, {47793, 48080}, {47810, 48121}, {47811, 48367}, {47818, 48339}, {47823, 48279}, {47827, 48123}, {47828, 48131}, {47935, 48023}, {48005, 48026}, {48012, 48027}, {48030, 48091}, {48059, 48128}, {48066, 48616}, {48129, 48213}, {48226, 48336}, {48232, 48280}, {48242, 48410}, {48392, 50339}
X(50501) = midpoint of X(i) and X(j) for these {i,j}: {649, 4041}, {659, 50355}, {663, 4729}, {667, 4730}, {1734, 4063}, {2254, 4498}, {4380, 21301}, {4391, 50343}, {4467, 47707}, {4490, 4784}, {4705, 4834}, {4814, 48322}, {4905, 21385}, {4979, 47912}, {7659, 47921}, {21124, 48106}, {47935, 48023}, {47948, 47976}, {48392, 50339}
X(50501) = reflection of X(i) in X(j) for these {i,j}: {663, 6050}, {667, 4394}, {905, 9508}, {3803, 4782}, {4106, 21260}, {4162, 1960}, {4990, 2490}, {23770, 21188}, {47131, 20517}, {47955, 47967}, {47956, 4705}, {47966, 47965}, {48026, 48005}, {48027, 48012}, {48029, 48003}, {48089, 50337}, {48091, 48030}, {48092, 1491}, {48099, 650}, {48128, 48059}, {48136, 14838}, {48267, 20317}, {48273, 4885}, {48327, 667}, {48329, 4401}, {48332, 905}, {48346, 3960}, {48403, 14837}, {48616, 48066}
X(50501) = X(20315)-Dao conjugate of X(693)
X(50501) = crosspoint of X(i) and X(j) for these (i,j): {19, 100}, {3451, 36082}
X(50501) = crosssum of X(i) and X(j) for these (i,j): {63, 513}, {514, 21616}
X(50501) = crossdifference of every pair of points on line {940, 1100}
X(50501) = barycentric product X(i)*X(j) for these {i,j}: {1, 48269}, {19, 20315}, {101, 17888}, {513, 17314}, {523, 1778}, {649, 46937}, {650, 1788}, {693, 14974}, {2501, 14868}
X(50501) = barycentric quotient X(i)/X(j) for these {i,j}: {1778, 99}, {1788, 4554}, {14868, 4563}, {14974, 100}, {17314, 668}, {17888, 3261}, {20315, 304}, {46937, 1978}, {48269, 75}
X(50501) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {663, 1635, 6050}, {1635, 4729, 663}, {4394, 4730, 48327}, {47837, 48273, 4885}, {48128, 48193, 48059}
X(50502) lies on these lines: {512, 45745}, {513, 4380}, {649, 4041}, {650, 669}, {693, 25299}, {830, 48008}, {1491, 28374}, {2512, 6589}, {2978, 3900}, {4083, 45746}, {4160, 4932}, {4397, 30061}, {4449, 28372}, {4705, 8640}, {4841, 9313}, {6050, 8655}, {26854, 44429}, {27293, 47814}, {27647, 48136}, {29198, 47663}, {29226, 47653}
X(50502) = crossdifference of every pair of points on line {980, 5256}
X(50503) lies on these lines: {31, 649}, {512, 650}, {513, 3004}, {659, 834}, {663, 21005}, {667, 43060}, {669, 6589}, {830, 48404}, {891, 48095}, {2488, 6371}, {3005, 6586}, {3310, 3804}, {3776, 20517}, {3835, 3846}, {3878, 11068}, {4083, 47890}, {4132, 48062}, {4367, 23768}, {4841, 8678}, {6372, 47960}, {6608, 9437}, {8655, 21828}, {9002, 18183}, {9029, 20983}, {26148, 35519}, {28423, 47840}, {35518, 48080}
X(50503) = isogonal conjugate of the isotomic conjugate of X(47708)
X(50503) = crosssum of X(514) and X(26128)
X(50503) = crossdifference of every pair of points on line {940, 3912}
X(50503) = barycentric product X(i)*X(j) for these {i,j}: {6, 47708}, {649, 32773}
X(50503) = barycentric quotient X(i)/X(j) for these {i,j}: {32773, 1978}, {47708, 76}
X(50594) lies on these lines: {2, 48273}, {10, 814}, {100, 29103}, {512, 650}, {513, 47987}, {514, 9508}, {522, 6133}, {523, 20517}, {525, 2977}, {649, 4705}, {659, 1734}, {661, 4834}, {663, 4730}, {667, 1635}, {693, 47837}, {784, 4913}, {812, 21260}, {826, 48062}, {830, 4782}, {834, 8043}, {891, 905}, {1019, 4490}, {1491, 4063}, {1577, 47835}, {1960, 2516}, {2254, 47936}, {2490, 4843}, {2530, 4498}, {2787, 4147}, {3251, 4959}, {3777, 21385}, {3837, 29302}, {3887, 48331}, {3960, 29226}, {4010, 47794}, {4025, 29354}, {4040, 48226}, {4083, 14838}, {4129, 29328}, {4151, 4874}, {4155, 6586}, {4170, 47822}, {4380, 47814}, {4394, 4770}, {4449, 14419}, {4468, 29252}, {4522, 29106}, {4524, 33969}, {4728, 31251}, {4729, 4775}, {4763, 31288}, {4784, 47959}, {4790, 47956}, {4801, 48569}, {4804, 47875}, {4807, 29366}, {4814, 8643}, {4893, 4983}, {4905, 48244}, {4960, 47928}, {4976, 48395}, {4978, 47823}, {4990, 14425}, {4992, 47829}, {6139, 18344}, {6367, 6590}, {6372, 47965}, {7265, 48185}, {7659, 47966}, {14077, 48328}, {14349, 47827}, {15309, 47967}, {17069, 29288}, {17072, 23791}, {17166, 27013}, {17494, 47836}, {18004, 29216}, {21051, 29013}, {21146, 48573}, {21301, 47776}, {23770, 41800}, {23815, 25380}, {23875, 48056}, {23879, 48405}, {24719, 47816}, {27115, 47840}, {27486, 47707}, {29025, 50453}, {29148, 48401}, {29168, 48069}, {29362, 50337}, {31209, 47839}, {47715, 48235}, {47716, 48227}, {47717, 48224}, {47793, 48267}, {47795, 48279}, {47804, 48305}, {47810, 47935}, {47811, 48351}, {47815, 50356}, {47818, 48301}, {47820, 48291}, {47872, 50339}, {47888, 48131}, {47893, 48335}, {47970, 50359}, {47975, 48565}, {48080, 48553}, {48081, 48162}, {48092, 48193}, {48093, 48194}, {48100, 48213}, {48160, 48596}, {48176, 50449}, {48204, 50331}, {48225, 48409}, {48229, 48406}, {48407, 48566}
X(50504) = midpoint of X(i) and X(j) for these {i,j}: {649, 4705}, {659, 1734}, {661, 4834}, {663, 4730}, {667, 4041}, {1019, 4490}, {1491, 4063}, {2530, 4498}, {3777, 21385}, {4040, 50355}, {4729, 4775}, {4784, 47959}, {4790, 47956}, {4807, 48284}, {4960, 47928}, {4976, 48395}, {7659, 47966}, {17072, 48008}, {17494, 50352}, {47965, 50336}, {47970, 50359}, {48011, 48012}, {48267, 50343}
X(50504) = reflection of X(i) in X(j) for these {i,j}: {1960, 6050}, {6050, 2516}, {23815, 25380}
X(50504) = complement of X(48273)
X(50504) = crosssum of X(513) and X(4641)
X(50504) = crossdifference of every pair of points on line {940, 4850}
X(50504) = barycentric product X(i)*X(j) for these {i,j}: {1, 48266}, {513, 17299}, {650, 24914}
X(50504) = barycentric quotient X(i)/X(j) for these {i,j}: {17299, 668}, {24914, 4554}, {48266, 75}
X(50504) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1635, 4041, 667}, {4498, 47828, 2530}, {17494, 47836, 50352}, {47793, 50343, 48267}, {48226, 50355, 4040}
X(50505) lies on these lines: {44, 513}, {512, 4025}, {663, 28372}, {669, 905}, {830, 4932}, {834, 50348}, {1019, 8646}, {1734, 18197}, {2530, 8640}, {2978, 3309}, {3004, 9313}, {3005, 25098}, {3716, 30023}, {3798, 6005}, {4083, 16892}, {4391, 25299}, {4455, 27674}, {6371, 48015}, {6372, 48060}, {7192, 8678}, {8672, 48069}, {17494, 48410}, {20907, 47128}, {26854, 47819}, {27167, 48564}, {27293, 44429}, {27647, 48099}, {29198, 48101}, {29226, 47923}
X(50505) = crossdifference of every pair of points on line {1, 21750}
X(50505) = barycentric product X(513)*X(27248)
X(50505) = barycentric quotient X(27248)/X(668)
X(50505) = {X(2530),X(8640)}-harmonic conjugate of X(28374)
X(50506) lies on these lines: {512, 650}, {513, 4468}, {514, 22284}, {649, 21003}, {661, 9313}, {669, 6586}, {834, 1491}, {891, 47960}, {2483, 8646}, {2484, 16874}, {2526, 4524}, {3004, 4083}, {3005, 6589}, {3261, 25299}, {4105, 9437}, {4477, 8676}, {6005, 11068}, {6372, 48095}, {7234, 43060}, {8678, 48276}, {9002, 20983}, {21123, 23655}, {28423, 47836}
X(50506) = isogonal conjugate of the isotomic conjugate of X(47707)
X(50506) = crosssum of X(514) and X(25496)
X(50506) = crossdifference of every pair of points on line {940, 16502}
X(50506) = barycentric product X(6)*X(47707)
X(50506) = barycentric quotient X(47707)/X(76)
X(50507) lies on these lines: {1, 4490}, {2, 50352}, {10, 29366}, {42, 663}, {512, 650}, {513, 4401}, {514, 1125}, {649, 4983}, {659, 14349}, {661, 667}, {693, 47839}, {764, 47929}, {784, 3716}, {814, 4129}, {830, 48030}, {832, 47842}, {891, 47965}, {905, 6372}, {1019, 48024}, {1491, 3216}, {1577, 47822}, {1635, 4822}, {1639, 48395}, {1734, 47827}, {1946, 2520}, {1960, 8678}, {2254, 47888}, {2530, 4724}, {2533, 16828}, {2832, 48137}, {2977, 3800}, {3624, 48143}, {3669, 47966}, {3777, 47970}, {3803, 48027}, {3835, 29070}, {3837, 29186}, {3887, 48194}, {3900, 4770}, {3960, 29198}, {4010, 47838}, {4025, 29252}, {4041, 4775}, {4063, 48123}, {4083, 48003}, {4147, 29298}, {4160, 47967}, {4367, 47959}, {4369, 31288}, {4378, 47918}, {4391, 48288}, {4455, 8637}, {4468, 29354}, {4522, 29086}, {4560, 47821}, {4730, 48338}, {4761, 47835}, {4782, 48093}, {4784, 48081}, {4794, 48012}, {4806, 29013}, {4905, 47893}, {4978, 47841}, {4992, 29302}, {6005, 9508}, {6332, 29312}, {6367, 45745}, {6546, 29686}, {6589, 42653}, {7927, 48062}, {8053, 48387}, {8643, 47912}, {14077, 48347}, {14321, 29232}, {14419, 47826}, {15309, 48028}, {17072, 29188}, {17166, 47775}, {17494, 47840}, {18004, 29062}, {19947, 48009}, {21003, 48031}, {21051, 29066}, {21124, 49279}, {21146, 47795}, {21192, 29200}, {21260, 25666}, {27115, 47836}, {27647, 28255}, {29047, 48056}, {29058, 47765}, {29082, 50453}, {29090, 48270}, {29150, 48043}, {29168, 48006}, {29226, 48348}, {29246, 50337}, {29256, 49280}, {29266, 48269}, {30234, 47955}, {31209, 47837}, {39798, 40464}, {42325, 50335}, {43067, 48564}, {46385, 50330}, {47666, 47820}, {47683, 48392}, {47708, 50351}, {47710, 48188}, {47711, 48185}, {47712, 48177}, {47777, 47956}, {47796, 47969}, {47810, 48150}, {47811, 48131}, {47818, 50449}, {47819, 47974}, {47828, 48367}, {47832, 48393}, {47875, 50457}, {47913, 48320}, {47921, 48332}, {47922, 48344}, {47941, 48570}, {47975, 48305}, {48086, 50358}, {48108, 48569}, {48111, 50328}, {48122, 48572}, {48176, 48301}, {48179, 48403}, {48265, 48321}, {48272, 50340}, {48289, 48401}, {48299, 48402}, {48340, 50345}, {48352, 50355}
X(50507) = midpoint of X(i) and X(j) for these {i,j}: {1, 4490}, {649, 4983}, {650, 48099}, {659, 14349}, {661, 667}, {663, 4705}, {764, 47929}, {905, 48029}, {1019, 48024}, {1491, 4040}, {1734, 48336}, {1960, 48005}, {2254, 48351}, {2530, 4724}, {3669, 47966}, {3777, 47970}, {3803, 48027}, {3960, 48004}, {4041, 4775}, {4063, 48123}, {4129, 48284}, {4367, 47959}, {4378, 47918}, {4391, 48288}, {4401, 48054}, {4560, 48267}, {4730, 48338}, {4782, 48093}, {4784, 48081}, {4794, 48012}, {4822, 4834}, {14419, 47826}, {14838, 48058}, {17494, 48273}, {21003, 48031}, {21124, 49279}, {46385, 50330}, {47683, 48392}, {47708, 50351}, {47842, 48297}, {47913, 48320}, {47921, 48332}, {47922, 48344}, {47949, 48144}, {47965, 48136}, {47967, 48330}, {47975, 48305}, {48030, 48331}, {48045, 48064}, {48065, 48066}, {48086, 50358}, {48111, 50328}, {48265, 48321}, {48272, 50340}, {48289, 48401}, {48299, 48402}, {48301, 48407}, {48340, 50345}, {48352, 50355}
X(50507) = reflection of X(i) in X(j) for these {i,j}: {4369, 31288}, {21260, 25666}
X(50507) = complement of X(50352)
X(50507) = isogonal conjugate of the isotomic conjugate of X(50327)
X(50507) = crossdifference of every pair of points on line {940, 3218}
X(50507) = barycentric product X(i)*X(j) for these {i,j}: {1, 48277}, {6, 50327}, {513, 17275}, {650, 11375}
X(50507) = barycentric quotient X(i)/X(j) for these {i,j}: {11375, 4554}, {17275, 668}, {48277, 75}, {50327, 76}
X(50507) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {663, 4893, 4705}, {1635, 4822, 4834}, {4367, 48162, 47959}, {4560, 47821, 48267}, {14419, 47949, 48144}, {17494, 47840, 48273}, {47826, 48144, 47949}, {47827, 48336, 1734}, {47888, 48351, 2254}, {48123, 48226, 4063}, {48176, 48301, 48407}, {48288, 48553, 4391}
X(50508) lies on these lines: {1, 48081}, {512, 650}, {513, 663}, {661, 3900}, {667, 4790}, {830, 48091}, {891, 47966}, {905, 6005}, {1734, 48193}, {2526, 3309}, {3064, 44705}, {3616, 48570}, {3803, 4794}, {3887, 48054}, {3907, 48043}, {3910, 48006}, {4079, 4130}, {4083, 47921}, {4106, 29051}, {4160, 47955}, {4162, 4775}, {4170, 23882}, {4449, 48021}, {4705, 4825}, {4724, 8712}, {4729, 4893}, {4761, 47838}, {4776, 21302}, {4806, 29366}, {4813, 48322}, {4834, 6050}, {4843, 45745}, {4879, 47915}, {4885, 47840}, {4895, 47912}, {4940, 21301}, {4944, 48395}, {4979, 8643}, {4990, 6590}, {4992, 29246}, {6004, 48092}, {6372, 48332}, {7655, 50330}, {14077, 47959}, {14837, 48179}, {15309, 48294}, {17072, 47760}, {20317, 47821}, {21343, 47913}, {22037, 29196}, {23880, 48080}, {28470, 48049}, {28478, 50347}, {29021, 49280}, {29170, 48289}, {29198, 48346}, {29208, 48088}, {29226, 48618}, {29278, 48269}, {29288, 48087}, {29350, 47965}, {30234, 48064}, {30235, 44410}, {31250, 47839}, {31287, 47836}, {31291, 48079}, {43052, 48400}, {45320, 50352}, {47709, 49274}, {47914, 48291}, {47942, 48282}, {47949, 48333}, {47956, 48053}, {48027, 48093}, {48028, 48607}, {48085, 48324}, {48125, 48273}, {48287, 48594}, {48339, 50449}
X(50508) = midpoint of X(i) and X(j) for these {i,j}: {1, 48081}, {661, 48338}, {663, 4822}, {4162, 48026}, {4449, 48021}, {4775, 4983}, {4813, 48322}, {4879, 48024}, {4895, 47912}, {14349, 48352}, {21343, 47913}, {31291, 48079}, {47709, 49274}, {47942, 48282}, {47949, 48333}, {47959, 48337}, {48085, 48324}, {48121, 48150}, {48123, 48336}, {48131, 48367}, {48287, 48594}, {48339, 50449}
X(50508) = reflection of X(i) in X(j) for these {i,j}: {650, 48099}, {2526, 14349}, {3669, 48136}, {3803, 4794}, {4162, 4775}, {4790, 667}, {4834, 6050}, {6590, 4990}, {7655, 50330}, {7659, 905}, {21301, 4940}, {43052, 48400}, {47915, 48024}, {47921, 48029}, {47955, 48045}, {47956, 48053}, {47965, 48058}, {48026, 4983}, {48027, 48093}, {48089, 4992}, {48125, 48273}, {48128, 48123}, {48607, 48028}, {48616, 48129}
X(50508) = crossdifference of every pair of points on line {9, 940}
X(50508) = barycentric product X(i)*X(j) for these {i,j}: {513, 5296}, {514, 37553}
X(50508) = barycentric quotient X(i)/X(j) for these {i,j}: {5296, 668}, {37553, 190}
X(50509) lies on these lines: {1, 48064}, {187, 237}, {513, 4041}, {514, 50016}, {525, 48106}, {650, 4822}, {657, 4832}, {659, 48367}, {830, 47976}, {834, 43924}, {891, 48341}, {1019, 4449}, {1491, 48121}, {1635, 48099}, {1734, 48023}, {2254, 48122}, {2484, 9313}, {2533, 29328}, {2786, 47707}, {3566, 48300}, {3716, 48565}, {3835, 47836}, {3900, 4790}, {4040, 48011}, {4063, 4724}, {4083, 4784}, {4105, 8676}, {4151, 48142}, {4160, 48110}, {4163, 6006}, {4170, 47832}, {4379, 48273}, {4380, 29051}, {4382, 50352}, {4401, 48352}, {4474, 6002}, {4705, 4813}, {4707, 29158}, {4729, 4814}, {4761, 29013}, {4774, 29152}, {4782, 48336}, {4785, 21301}, {4806, 47835}, {4843, 48276}, {4893, 4983}, {4932, 17166}, {4959, 48322}, {4978, 48579}, {4990, 47767}, {4992, 47823}, {7659, 8712}, {9508, 48123}, {14349, 47828}, {17072, 20295}, {21260, 31147}, {21302, 26853}, {23875, 48118}, {28470, 48016}, {28478, 48069}, {29200, 48103}, {29208, 50342}, {29216, 47711}, {29252, 48117}, {29270, 47724}, {29288, 47971}, {29294, 47710}, {29302, 48119}, {30835, 47837}, {31207, 47839}, {31286, 47840}, {32478, 49279}, {47793, 48043}, {47810, 48091}, {47814, 48049}, {47826, 48003}, {47827, 48093}, {47893, 48129}, {47909, 48407}, {47938, 48402}, {47956, 48019}, {47965, 48021}, {48005, 48544}, {48012, 48085}, {48018, 48086}, {48027, 48597}, {48100, 48244}, {48131, 50336}, {48266, 48395}, {48295, 48568}, {48304, 48580}, {48305, 48578}, {48351, 48572}, {48595, 48613}
X(50509) = midpoint of X(i) and X(j) for these {i,j}: {4729, 4979}, {21302, 26853}
X(50509) = reflection of X(i) in X(j) for these {i,j}: {1, 48064}, {649, 4834}, {663, 649}, {4040, 48011}, {4382, 50352}, {4449, 1019}, {4724, 4063}, {4813, 4705}, {4814, 4729}, {4822, 650}, {4959, 48322}, {17166, 4932}, {20295, 17072}, {47906, 47921}, {47909, 48407}, {47911, 4490}, {47912, 4041}, {47929, 4498}, {47938, 48402}, {48019, 47956}, {48021, 47965}, {48023, 1734}, {48081, 48003}, {48085, 48012}, {48086, 48018}, {48121, 1491}, {48122, 2254}, {48123, 9508}, {48131, 50336}, {48144, 4784}, {48151, 7659}, {48266, 48395}, {48278, 48069}, {48336, 4782}, {48338, 667}, {48352, 4401}, {48367, 659}, {48582, 48607}, {48595, 48613}, {48597, 48027}
X(50509) = isogonal conjugate of the isotomic conjugate of X(28147)
X(50509) = X(28148)-Ceva conjugate of X(6)
X(50509) = X(i)-isoconjugate of X(j) for these (i,j): {75, 28148}, {100, 28626}, {190, 39948}, {651, 30711}
X(50509) = X(i)-Dao conjugate of X(j) for these (i, j): (206, 28148), (8054, 28626), (38991, 30711)
X(50509) = crosspoint of X(6) and X(28148)
X(50509) = crosssum of X(i) and X(j) for these (i,j): {1, 48064}, {2, 28147}, {514, 3624}, {522, 5273}
X(50509) = crossdifference of every pair of points on line {2, 1449}
X(50509) = barycentric product X(i)*X(j) for these {i,j}: {1, 48026}, {6, 28147}, {512, 25507}, {513, 3247}, {649, 9780}, {650, 3339}, {667, 42029}, {3947, 7252}, {3951, 6591}
X(50509) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 28148}, {649, 28626}, {663, 30711}, {667, 39948}, {3247, 668}, {3339, 4554}, {9780, 1978}, {25507, 670}, {28147, 76}, {42029, 6386}, {48026, 75}
X(50509) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 48338, 667}, {667, 48338, 663}, {4775, 8643, 663}, {48003, 48081, 47826}
X(50510) lies on these lines: {187, 237}, {513, 3716}, {650, 788}, {659, 3737}, {661, 6373}, {834, 4782}, {891, 17494}, {926, 4477}, {2497, 21123}, {2530, 28372}, {3063, 23575}, {3709, 46386}, {3766, 6372}, {4063, 39548}, {4083, 48008}, {4155, 4976}, {4394, 4507}, {4724, 6363}, {4893, 20983}, {4979, 8027}, {14426, 25666}, {16874, 21786}, {21196, 30665}, {21260, 30023}, {22383, 23570}, {23506, 48294}, {25142, 47778}, {25636, 47794}, {27293, 47839}, {27453, 30060}, {27647, 48059}, {32009, 43928}
X(50510) = midpoint of X(i) and X(j) for these {i,j}: {649, 2978}, {4063, 39548}
X(50510) = reflection of X(i) in X(j) for these {i,j}: {4507, 4394}, {4932, 43931}
X(50510) = X(787)-complementary conjugate of X(2)
X(50510) = X(i)-Ceva conjugate of X(j) for these (i,j): {86, 1015}, {904, 3271}, {23493, 3248}, {38832, 23470}
X(50510) = X(i)-isoconjugate of X(j) for these (i,j): {100, 40418}, {101, 1221}, {190, 1258}, {1018, 40409}
X(50510) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 1221), (3122, 10), (3741, 3952), (8054, 40418), (21838, 1978)
X(50510) = crosspoint of X(649) and X(7192)
X(50510) = crosssum of X(i) and X(j) for these (i,j): {100, 18047}, {190, 4557}, {514, 6685}, {523, 27042}, {3952, 4595}
X(50510) = crossdifference of every pair of points on line {2, 1258}
X(50510) = barycentric product X(i)*X(j) for these {i,j}: {86, 40627}, {512, 16738}, {513, 1107}, {514, 2309}, {649, 3741}, {661, 18169}, {663, 30097}, {667, 20891}, {693, 1197}, {1019, 3728}, {3733, 21024}, {3737, 45208}, {4560, 39780}, {7192, 21838}, {7649, 22065}, {17924, 22389}, {18091, 21123}
X(50510) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 1221}, {649, 40418}, {667, 1258}, {1107, 668}, {1197, 100}, {2309, 190}, {3728, 4033}, {3733, 40409}, {3741, 1978}, {16738, 670}, {18169, 799}, {20891, 6386}, {21024, 27808}, {21700, 4103}, {21838, 3952}, {22065, 4561}, {22389, 1332}, {23212, 4574}, {23473, 33946}, {30097, 4572}, {39780, 4552}, {40627, 10}, {45216, 4595}
X(50510) = {X(649),X(663)}-harmonic conjugate of X(8640)
X(50511) lies on these lines: {187, 237}, {513, 3700}, {650, 834}, {661, 6371}, {891, 4988}, {1021, 5216}, {2483, 7252}, {2484, 22383}, {3835, 30864}, {4083, 45745}, {4132, 4976}, {4139, 48277}, {4526, 4979}, {4765, 29350}, {4790, 21348}, {4813, 6363}, {6085, 48019}, {6332, 48060}, {8672, 48275}, {9002, 48026}, {20952, 21437}, {25084, 27673}, {25258, 26853}
X(50511) = crossdifference of every pair of points on line {2, 5711}
X(50511) = {X(649),X(3250)}-harmonic conjugate of X(647)
X(50512) lies on these lines: {58, 18001}, {187, 237}, {249, 17940}, {513, 4401}, {514, 4782}, {650, 47956}, {659, 1019}, {690, 48299}, {798, 6373}, {830, 9508}, {891, 4063}, {905, 48616}, {926, 48387}, {1125, 4992}, {1491, 48586}, {1577, 29340}, {1635, 4705}, {1919, 4832}, {2483, 17990}, {2527, 29278}, {2530, 48116}, {2533, 29182}, {3700, 29266}, {3716, 29150}, {3733, 5009}, {3801, 29184}, {3803, 6004}, {3835, 31288}, {3906, 48300}, {4010, 47818}, {4040, 4784}, {4083, 48011}, {4106, 48564}, {4142, 29029}, {4369, 29070}, {4378, 4498}, {4380, 47820}, {4391, 29176}, {4394, 4770}, {4458, 29098}, {4707, 29272}, {4730, 48322}, {4790, 48099}, {4791, 29152}, {4809, 47712}, {4823, 29238}, {4874, 29013}, {4897, 29252}, {4905, 50358}, {4973, 4974}, {4976, 6367}, {4979, 4983}, {6005, 48331}, {7178, 29336}, {8045, 29106}, {8714, 48248}, {13246, 29118}, {14419, 48131}, {15309, 47994}, {17072, 45313}, {17166, 47776}, {20295, 47839}, {20517, 29025}, {21146, 48568}, {21260, 25126}, {21301, 27013}, {21385, 48323}, {24626, 29770}, {24719, 47795}, {25537, 29807}, {25569, 48337}, {26853, 47840}, {27673, 28255}, {29058, 47767}, {29062, 48405}, {29136, 48400}, {29168, 50347}, {29226, 48343}, {29256, 47682}, {29268, 48565}, {29270, 48090}, {29350, 48330}, {29354, 47890}, {30234, 48136}, {30724, 32636}, {31207, 31251}, {31291, 47836}, {46403, 48569}, {47762, 50352}, {47804, 48267}, {47811, 47949}, {47813, 48393}, {47817, 48265}, {47827, 47948}, {47888, 48023}, {47893, 48086}, {47947, 48162}, {47959, 48226}, {47969, 48580}, {47976, 48123}, {48024, 48110}, {48111, 50359}, {48305, 50343}, {48306, 50344}, {48324, 50355}
X(50512) = midpoint of X(i) and X(j) for these {i,j}: {649, 667}, {659, 1019}, {663, 4834}, {2483, 21003}, {3803, 50336}, {4040, 4784}, {4063, 4367}, {4378, 4498}, {4380, 48273}, {4401, 48064}, {4730, 48322}, {4790, 48099}, {4905, 50358}, {4979, 4983}, {21385, 48323}, {47949, 48149}, {47976, 48123}, {48024, 48110}, {48045, 48074}, {48111, 50359}, {48305, 50343}, {48306, 50344}, {48324, 50355}
X(50512) = reflection of X(i) in X(j) for these {i,j}: {1960, 667}, {3835, 31288}, {4992, 1125}, {21260, 31286}, {48005, 650}, {48059, 14838}, {48296, 48328}, {48347, 48330}
X(50512) = isogonal conjugate of X(6540)
X(50512) = isogonal conjugate of the anticomplement of X(35076)
X(50512) = isogonal conjugate of the complement of X(39348)
X(50512) = isogonal conjugate of the isotomic conjugate of X(4977)
X(50512) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 6540), (206, 8701), (513, 4608), (1015, 32018), (1084, 6539), (1125, 27808), (1213, 1978), (3120, 313), (3647, 668), (8054, 1268), (16726, 310), (32664, 37212), (35076, 76), (38991, 4102), (39025, 32635), (40589, 4632), (40627, 31010)
X(50512) = crosspoint of X(i) and X(j) for these (i,j): {6, 8701}, {649, 3733}, {1100, 4427}, {2308, 35327}, {32636, 36075}
X(50512) = crosssum of X(i) and X(j) for these (i,j): {2, 4977}, {10, 31010}, {190, 3952}, {513, 44307}, {514, 3634}, {523, 41809}, {1255, 50344}, {1268, 4608}, {6367, 6537}
X(50512) = crossdifference of every pair of points on line {2, 594}
X(50512) = X(i)-Ceva conjugate of X(j) for these (i,j): {42, 3248}, {58, 1015}, {4427, 1100}, {6186, 3271}, {8701, 6}, {35327, 2308}, {35342, 20970}
X(50512) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6540}, {2, 37212}, {10, 4596}, {37, 4632}, {75, 8701}, {100, 1268}, {101, 32018}, {190, 1255}, {321, 4629}, {651, 4102}, {662, 6539}, {664, 32635}, {668, 1126}, {765, 4608}, {1016, 47947}, {1018, 32014}, {1089, 6578}, {1171, 4033}, {1796, 6335}, {1978, 28615}, {3257, 31011}, {3952, 40438}, {4554, 33635}, {4567, 31010}, {5380, 31013}, {7035, 50344}, {37211, 43260}
X(50512) = barycentric product X(i)*X(j) for these {i,j}: {1, 4979}, {6, 4977}, {11, 36075}, {31, 4978}, {55, 30724}, {56, 4976}, {58, 4988}, {71, 46542}, {81, 4983}, {106, 4984}, {244, 35342}, {430, 7254}, {512, 8025}, {513, 1100}, {514, 2308}, {553, 663}, {593, 6367}, {604, 4985}, {647, 31900}, {649, 1125}, {650, 32636}, {667, 4359}, {739, 30592}, {798, 16709}, {905, 2355}, {1015, 4427}, {1019, 1962}, {1086, 35327}, {1213, 3733}, {1269, 1919}, {1333, 30591}, {1357, 30729}, {1407, 4990}, {1459, 1839}, {1509, 8663}, {2162, 4992}, {3572, 4974}, {3649, 7252}, {3669, 3683}, {3686, 43924}, {3916, 6591}, {4079, 30593}, {4705, 30581}, {4966, 43929}, {4969, 23345}, {7192, 20970}, {7649, 22054}, {8701, 35076}, {17924, 23201}, {17925, 22080}, {41014, 43925}
X(50512) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 6540}, {31, 37212}, {32, 8701}, {58, 4632}, {512, 6539}, {513, 32018}, {553, 4572}, {649, 1268}, {663, 4102}, {667, 1255}, {1015, 4608}, {1100, 668}, {1125, 1978}, {1213, 27808}, {1333, 4596}, {1919, 1126}, {1960, 31011}, {1962, 4033}, {1977, 50344}, {1980, 28615}, {2206, 4629}, {2308, 190}, {2355, 6335}, {3063, 32635}, {3122, 31010}, {3248, 47947}, {3683, 646}, {3733, 32014}, {4079, 6538}, {4359, 6386}, {4427, 31625}, {4834, 43260}, {4974, 27853}, {4976, 3596}, {4977, 76}, {4978, 561}, {4979, 75}, {4983, 321}, {4984, 3264}, {4985, 28659}, {4988, 313}, {4992, 6382}, {6367, 28654}, {8025, 670}, {8663, 594}, {16709, 4602}, {20970, 3952}, {22054, 4561}, {23201, 1332}, {30581, 4623}, {30591, 27801}, {30592, 35543}, {30724, 6063}, {31900, 6331}, {32636, 4554}, {35327, 1016}, {35342, 7035}, {36075, 4998}, {46542, 44129}
X(50512) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 663, 4834}, {667, 4775, 8643}, {667, 4834, 663}, {4380, 47820, 48273}, {21301, 27013, 47837}, {47811, 48149, 47949}
X(50513) lies on these lines: {31, 649}, {512, 4162}, {513, 4468}, {834, 4784}, {890, 6589}, {3835, 3836}, {3874, 29350}, {4083, 4897}, {4524, 6085}, {6371, 7659}, {8640, 43060}, {9002, 22277}, {21143, 23655}
X(50513) = isogonal conjugate of the isotomic conjugate of X(47720)
X(50513) = crossdifference of every pair of points on line {3912, 4383}
X(50513) = barycentric product X(6)*X(47720)
X(50513) = barycentric quotient X(47720)/X(76)
X(50514) lies on these lines: {1, 9433}, {31, 8654}, {42, 649}, {512, 4162}, {513, 3716}, {650, 6373}, {665, 1912}, {1635, 20983}, {1980, 21758}, {2978, 4979}, {3020, 3025}, {3635, 29350}, {3733, 23092}, {3776, 3808}, {3912, 6004}, {3937, 38989}, {4083, 4504}, {4394, 9010}, {4524, 9032}, {4763, 25142}, {6363, 43051}, {6686, 31286}, {8633, 21003}, {9400, 48016}, {14426, 31287}, {14474, 31207}, {18200, 40763}, {20340, 29717}, {21005, 21786}, {26102, 29738}, {27013, 43928}, {39548, 47976}, {47330, 50335}
X(50514) = midpoint of X(i) and X(j) for these {i,j}: {2978, 4979}, {39548, 47976}
X(50514) = reflection of X(i) in X(j) for these {i,j}: {4369, 43931}, {4507, 649}
X(50514) = isogonal conjugate of the isotomic conjugate of X(3777)
X(50514) = X(i)-Ceva conjugate of X(j) for these (i,j): {7, 1015}, {3888, 2275}, {7121, 3248}, {7192, 3776}
X(50514) = X(i)-Dao conjugate of X(j) for these (i, j): (1086, 7034), (2887, 3952), (3271, 8), (8054, 7033), (19602, 4505), (32664, 4621), (41771, 6386)
X(50514) = crosspoint of X(2275) and X(3888)
X(50514) = crosssum of X(i) and X(j) for these (i,j): {3699, 4595}, {4033, 4557}
X(50514) = crossdifference of every pair of points on line {239, 312}
X(50514) = X(i)-isoconjugate of X(j) for these (i,j): {2, 4621}, {100, 7033}, {190, 17743}, {350, 8684}, {646, 7132}, {668, 983}, {692, 7034}, {1018, 38810}, {3113, 3799}, {3407, 3807}, {3596, 8685}, {3773, 33514}, {3952, 40415}, {4610, 43265}, {27808, 38813}
X(50514) = barycentric product X(i)*X(j) for these {i,j}: {6, 3777}, {31, 3776}, {292, 3808}, {513, 2275}, {514, 7032}, {604, 3810}, {649, 982}, {650, 7248}, {663, 41777}, {667, 3662}, {798, 33947}, {810, 31917}, {875, 33891}, {1015, 3888}, {1019, 3778}, {1333, 3801}, {1919, 33930}, {3056, 3669}, {3061, 43924}, {3063, 7185}, {3116, 4817}, {3248, 33946}, {3676, 20665}, {3721, 3733}, {3784, 6591}, {3794, 7180}, {3863, 4367}, {3865, 20981}, {4531, 17096}, {7192, 16584}, {7199, 40935}, {7203, 20684}, {20284, 43931}
X(50514) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 4621}, {514, 7034}, {649, 7033}, {667, 17743}, {982, 1978}, {1919, 983}, {1922, 8684}, {2275, 668}, {3056, 646}, {3094, 4505}, {3116, 3807}, {3117, 3799}, {3662, 6386}, {3721, 27808}, {3733, 38810}, {3776, 561}, {3777, 76}, {3778, 4033}, {3801, 27801}, {3808, 1921}, {3810, 28659}, {3888, 31625}, {4531, 30730}, {4817, 46281}, {7032, 190}, {7248, 4554}, {9006, 3774}, {16584, 3952}, {20284, 36863}, {20665, 3699}, {21751, 4557}, {21815, 40521}, {22364, 4574}, {33947, 4602}, {40935, 1018}, {41777, 4572}
X(50515) lies on these lines: {1, 47976}, {36, 238}, {512, 4162}, {514, 4830}, {649, 4041}, {650, 47956}, {659, 47913}, {661, 6050}, {663, 4979}, {830, 48018}, {1635, 47912}, {2504, 48574}, {2533, 28475}, {3309, 4784}, {3835, 48564}, {3900, 4834}, {3960, 48616}, {4129, 47803}, {4160, 48011}, {4367, 48332}, {4378, 8712}, {4380, 17166}, {4394, 4705}, {4401, 15309}, {4449, 47935}, {4724, 48149}, {4782, 47922}, {4794, 48074}, {4820, 29266}, {4822, 8643}, {4932, 29051}, {4940, 47839}, {4959, 48322}, {4990, 28217}, {6004, 7659}, {6005, 48329}, {6008, 48273}, {6590, 29232}, {7662, 29013}, {14838, 48027}, {20295, 47820}, {21260, 47761}, {21301, 47762}, {23738, 48144}, {27013, 47814}, {28478, 48290}, {28591, 39386}, {29070, 43067}, {29090, 48271}, {29158, 47131}, {29170, 48248}, {29288, 48060}, {29354, 48095}, {31288, 47760}, {31291, 47763}, {34958, 49295}, {46403, 48570}, {47707, 48567}, {47811, 47911}, {47826, 48582}, {47828, 47905}, {47840, 48079}, {47906, 48572}, {48003, 48607}, {48108, 48580}, {48264, 48578}, {48294, 48624}, {48343, 48346}
X(50515) = midpoint of X(i) and X(j) for these {i,j}: {1, 47976}, {663, 4979}, {4040, 48110}, {4380, 17166}, {4449, 47935}, {4724, 48149}, {4794, 48074}, {48294, 48624}
X(50515) = reflection of X(i) in X(j) for these {i,j}: {661, 6050}, {4705, 4394}, {47956, 650}, {47965, 4782}, {47966, 659}, {48027, 14838}, {48029, 4401}, {48092, 905}, {48099, 667}, {48332, 4367}, {48346, 48343}, {48607, 48003}, {48616, 3960}, {49295, 34958}, {50336, 48064}
X(50515) = crosssum of X(i) and X(j) for these (i,j): {1, 47976}, {513, 5287}
X(50515) = crossdifference of every pair of points on line {37, 3305}
X(50515) = barycentric product X(1)*X(49293)
X(50515) = barycentric quotient X(49293)/X(75)
X(50516) lies on these lines: {1, 8640}, {2, 20983}, {38, 21350}, {81, 1980}, {320, 350}, {512, 4932}, {649, 4083}, {650, 24534}, {659, 1459}, {667, 18173}, {669, 48330}, {788, 4369}, {891, 48008}, {940, 21005}, {1491, 28372}, {3221, 21191}, {3741, 23803}, {3805, 6590}, {3808, 48398}, {3835, 6373}, {3999, 4782}, {4025, 30665}, {4164, 22383}, {4380, 8027}, {4394, 38238}, {4411, 35560}, {4790, 9400}, {4885, 9010}, {6363, 48063}, {9002, 48248}, {14404, 31209}, {17494, 29226}, {18180, 30234}, {20979, 24666}, {21051, 30023}, {21348, 46386}, {21392, 32913}, {23503, 23572}, {23655, 24533}, {23791, 23815}, {24768, 28398}, {25126, 25627}, {25299, 25301}, {27045, 48197}, {27167, 48216}, {27293, 47841}, {27453, 30095}, {27647, 48030}, {28475, 37536}, {29198, 48141}, {38247, 43928}
X(50516) = midpoint of X(2978) and X(7192)
X(50516) = reflection of X(i) in X(j) for these {i,j}: {649, 43931}, {20983, 25142}
X(50516) = complement of X(20983)
X(50516) = anticomplement of X(25142)
X(50516) = isogonal conjugate of the isotomic conjugate of X(23807)
X(50516) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {32039, 69}, {34071, 21219}
X(50516) = X(i)-Ceva conjugate of X(j) for these (i,j): {667, 513}, {18197, 649}
X(50516) = X(i)-cross conjugate of X(j) for these (i,j): {3221, 23572}, {23807, 513}
X(50516) = X(i)-isoconjugate of X(j) for these (i,j): {42, 3222}, {100, 3223}, {101, 2998}, {190, 3224}, {668, 34248}, {692, 18832}, {1897, 3504}, {4628, 42551}, {8750, 43714}, {32739, 40162}
X(50516) = X(i)-Dao conjugate of X(j) for these (i, j): (76, 6386), (1015, 2998), (1086, 18832), (8054, 3223), (21191, 4083), (26932, 43714), (32746, 668), (34467, 3504), (40592, 3222), (40619, 40162)
X(50516) = crosspoint of X(i) and X(j) for these (i,j): {1, 18830}, {86, 32039}
X(50516) = crosssum of X(i) and X(j) for these (i,j): {1, 8640}, {649, 23457}, {667, 23538}
X(50516) = crossdifference of every pair of points on line {43, 213}
X(50516) = barycentric product X(i)*X(j) for these {i,j}: {1, 21191}, {6, 23807}, {57, 25128}, {58, 20910}, {75, 23572}, {81, 23301}, {194, 513}, {274, 3221}, {286, 2524}, {310, 23503}, {514, 1740}, {522, 1424}, {649, 17149}, {650, 17082}, {662, 21144}, {667, 6374}, {693, 1613}, {757, 21056}, {905, 3186}, {1019, 21080}, {1919, 18837}, {3676, 7075}, {3733, 22028}, {6385, 9491}, {7192, 21877}, {11325, 15413}, {13476, 27168}, {14296, 47642}, {17924, 20794}, {38834, 48084}
X(50516) = barycentric quotient X(i)/X(j) for these {i,j}: {81, 3222}, {194, 668}, {513, 2998}, {514, 18832}, {649, 3223}, {667, 3224}, {693, 40162}, {905, 43714}, {1424, 664}, {1613, 100}, {1740, 190}, {1919, 34248}, {2524, 72}, {2530, 42551}, {3186, 6335}, {3221, 37}, {4164, 39927}, {6374, 6386}, {7075, 3699}, {9491, 213}, {11325, 1783}, {17082, 4554}, {17149, 1978}, {20794, 1332}, {20910, 313}, {21056, 1089}, {21080, 4033}, {21144, 1577}, {21191, 75}, {21877, 3952}, {22028, 27808}, {22383, 3504}, {23301, 321}, {23503, 42}, {23572, 1}, {23807, 76}, {25128, 312}, {27168, 17143}
X(50516) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 8640, 23506}, {2, 20983, 25142}, {20979, 24666, 25537}, {21191, 25128, 23301}, {24674, 24755, 2}
X(50517) lies on these lines: {8, 48565}, {512, 4162}, {513, 663}, {514, 3803}, {649, 3900}, {650, 667}, {659, 47921}, {661, 8643}, {693, 31291}, {798, 4827}, {814, 7662}, {830, 905}, {832, 7655}, {1019, 3309}, {1577, 28475}, {1946, 23865}, {1960, 48026}, {2484, 4130}, {2522, 8635}, {3804, 49293}, {3887, 48064}, {4040, 47942}, {4041, 4394}, {4063, 14077}, {4147, 48559}, {4160, 4401}, {4163, 43061}, {4369, 28470}, {4449, 8712}, {4462, 47805}, {4762, 17166}, {4794, 15309}, {4820, 29232}, {4885, 21301}, {4940, 47840}, {4979, 48338}, {4990, 48269}, {6005, 48345}, {6182, 17410}, {6590, 29278}, {8642, 21789}, {8656, 47912}, {8713, 43042}, {14838, 30234}, {17072, 47761}, {17496, 47697}, {20317, 47804}, {21051, 47803}, {21185, 29126}, {21260, 31250}, {21302, 47762}, {23880, 47694}, {25901, 25925}, {28585, 48568}, {29025, 47131}, {29037, 48271}, {29051, 43067}, {29070, 48125}, {29158, 48286}, {29162, 47123}, {29288, 48095}, {29324, 48248}, {29354, 48124}, {31287, 47814}, {39227, 39577}, {47777, 47956}, {47881, 48395}, {47915, 47957}, {47955, 48058}, {47976, 48337}, {48032, 48341}, {48110, 48352}, {48111, 48320}, {48323, 50358}, {48328, 48332}, {48344, 48346}, {48563, 50352}
X(50517) = midpoint of X(i) and X(j) for these {i,j}: {649, 48322}, {693, 31291}, {1019, 48324}, {4162, 4790}, {4979, 48338}, {17496, 47697}, {47976, 48337}, {48032, 48341}, {48110, 48352}, {48111, 48320}, {48144, 48150}, {48149, 48367}, {48323, 50358}
X(50517) = reflection of X(i) in X(j) for these {i,j}: {650, 667}, {2526, 905}, {3669, 4367}, {4041, 4394}, {4162, 48327}, {4163, 43061}, {4705, 6050}, {7659, 1019}, {21301, 4885}, {47915, 48029}, {47921, 659}, {47955, 48058}, {47965, 4401}, {48026, 48099}, {48029, 48331}, {48099, 1960}, {48128, 48136}, {48136, 48330}, {48193, 30234}, {48269, 4990}, {48332, 48328}, {48346, 48344}
X(50517) = crosssum of X(i) and X(j) for these (i,j): {513, 37674}, {521, 10319}
X(50517) = crossdifference of every pair of points on line {9, 2999}
X(50517) = barycentric product X(i)*X(j) for these {i,j}: {513, 5749}, {514, 5269}, {650, 3600}, {3669, 7172}
X(50517) = barycentric quotient X(i)/X(j) for these {i,j}: {3600, 4554}, {5269, 190}, {5749, 668}, {7172, 646}
X(50517) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {667, 4705, 6050}, {4705, 6050, 650}, {21260, 48564, 31250}, {21301, 47820, 4885}
X(50518) lies on these lines: {72, 49288}, {210, 3239}, {354, 4025}, {512, 48276}, {513, 4382}, {518, 25259}, {521, 4985}, {650, 663}, {652, 3683}, {693, 44319}, {926, 3700}, {1639, 4524}, {1836, 46400}, {2488, 4976}, {2499, 4841}, {3309, 43067}, {3555, 29212}, {3706, 35519}, {3716, 35057}, {3887, 4369}, {4083, 48095}, {4132, 48106}, {4171, 46388}, {4394, 8655}, {6589, 37593}, {7662, 15313}, {9029, 48269}, {9443, 48087}, {14077, 47962}, {18154, 21302}, {21894, 23655}, {42325, 49291}
X(50518) = reflection of X(i) in X(j) for these {i,j}: {72, 49288}, {4841, 2499}, {4976, 2488}, {44319, 693}
X(50518) = X(2350)-complementary conjugate of X(40618)
X(50518) = X(18155)-Ceva conjugate of X(650)
X(50518) = X(i)-isoconjugate of X(j) for these (i,j): {7, 6577}, {109, 8049}, {651, 39797}, {664, 34444}, {1414, 40504}, {1415, 39735}, {4565, 40515}, {4573, 40147}
X(50518) = X(i)-Dao conjugate of X(j) for these (i, j): (11, 8049), (42, 4551), (1146, 39735), (38991, 39797), (39025, 34444), (40608, 40504), (40624, 40005)
X(50518) = crosspoint of X(314) and X(644)
X(50518) = crosssum of X(1402) and X(3669)
X(50518) = crossdifference of every pair of points on line {57, 39797}
X(50518) = barycentric product X(i)*X(j) for these {i,j}: {9, 8714}, {521, 17911}, {522, 16552}, {650, 17135}, {663, 18137}, {3737, 21070}, {3900, 17077}, {4041, 29767}, {4391, 8053}, {4560, 22271}, {18155, 40586}, {22126, 44426}
X(50518) = barycentric quotient X(i)/X(j) for these {i,j}: {41, 6577}, {522, 39735}, {650, 8049}, {663, 39797}, {3063, 34444}, {3709, 40504}, {4041, 40515}, {4391, 40005}, {8053, 651}, {8714, 85}, {16552, 664}, {17077, 4569}, {17135, 4554}, {17911, 18026}, {18137, 4572}, {22126, 6516}, {22271, 4552}, {29767, 4625}, {40586, 4551}
X(50519) lies on these lines: {1, 28374}, {8, 30061}, {42, 650}, {145, 14077}, {512, 49293}, {513, 4382}, {518, 48271}, {521, 47694}, {649, 3900}, {669, 48327}, {693, 10453}, {926, 6590}, {1021, 8642}, {2488, 45745}, {2978, 8678}, {3056, 9001}, {3309, 7192}, {3700, 9029}, {3873, 47677}, {3887, 4932}, {4083, 48101}, {4391, 25301}, {4500, 37998}, {4524, 47766}, {4782, 8702}, {4885, 30942}, {9443, 48094}, {18197, 48324}, {23791, 48295}
X(50519) = reflection of X(45745) in X(2488)
X(50519) = crosssum of X(1) and X(28374)
X(50519) = crossdifference of every pair of points on line {2999, 20367}
X(50520) lies on these lines: {512, 7192}, {513, 4380}, {649, 2664}, {659, 50344}, {660, 4427}, {669, 2106}, {875, 40439}, {876, 8663}, {901, 8708}, {2978, 43931}, {3572, 4979}, {4155, 4608}, {4507, 47775}, {4822, 27647}, {7659, 28374}, {8655, 48064}, {9361, 39337}, {9400, 26824}, {15148, 43925}, {15630, 43920}, {23345, 40433}, {27045, 47836}, {27167, 47840}, {27648, 50336}, {29350, 48141}, {32009, 43928}, {39548, 48580}, {40408, 43926}, {43927, 47694}
X(50520) = isogonal conjugate of X(4436)
X(50520) = isogonal conjugate of the anticomplement of X(2486)
X(50520) = isotomic conjugate of the anticomplement of X(3121)
X(50520) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {8708, 1654}, {32009, 21221}, {40408, 4440}, {40433, 148}, {40439, 149}
X(50520) = X(8708)-Ceva conjugate of X(40433)
X(50520) = X(i)-cross conjugate of X(j) for these (i,j): {3121, 2}, {16726, 1}, {47776, 43928}
X(50520) = cevapoint of X(i) and X(j) for these (i,j): {512, 513}, {514, 42327}, {523, 21260}
X(50520) = crosspoint of X(8708) and X(40433)
X(50520) = crosssum of X(i) and X(j) for these (i,j): {3720, 6372}, {21020, 48264}
X(50520) = trilinear pole of line {1015, 1084}
X(50520) = crossdifference of every pair of points on line {3691, 3720}
X(50520) = X(i)-isoconjugate of X(j) for these (i,j): {1, 4436}, {59, 48264}, {99, 2667}, {100, 3720}, {101, 3739}, {109, 3706}, {110, 21020}, {190, 20963}, {643, 39793}, {651, 3691}, {662, 16589}, {692, 20888}, {765, 6372}, {799, 21753}, {811, 22369}, {1018, 18166}, {1252, 47672}, {1293, 4891}, {1332, 40975}, {1414, 4111}, {1897, 22060}, {3939, 4059}, {4557, 17175}, {4570, 48393}, {4610, 21820}, {18089, 46148}
X(50520) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 4436), (11, 3706), (244, 21020), (513, 6372), (661, 47672), (1015, 3739), (1084, 16589), (1086, 20888), (6615, 48264), (8054, 3720), (17423, 22369), (34467, 22060), (38986, 2667), (38991, 3691), (38996, 21753), (40608, 4111), (40617, 4059), (40620, 16748), (50330, 48393)
X(50520) = barycentric product X(i)*X(j) for these {i,j}: {513, 32009}, {514, 40433}, {523, 40408}, {661, 40439}, {1086, 8708}
X(50520) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 4436}, {244, 47672}, {512, 16589}, {513, 3739}, {514, 20888}, {649, 3720}, {650, 3706}, {661, 21020}, {663, 3691}, {667, 20963}, {669, 21753}, {798, 2667}, {1015, 6372}, {1019, 17175}, {2170, 48264}, {3049, 22369}, {3125, 48393}, {3669, 4059}, {3709, 4111}, {3733, 18166}, {4040, 29773}, {4079, 21699}, {4367, 4754}, {4394, 4891}, {7180, 39793}, {7192, 16748}, {8708, 1016}, {18108, 18089}, {22383, 22060}, {32009, 668}, {40408, 99}, {40433, 190}, {40439, 799}
X(50521) lies on these lines: {1, 29545}, {42, 649}, {81, 18108}, {320, 350}, {512, 4895}, {650, 9010}, {661, 6373}, {667, 838}, {688, 3005}, {891, 47932}, {1912, 3250}, {2488, 6363}, {2499, 6085}, {2512, 9009}, {3244, 29350}, {3805, 47660}, {3808, 47652}, {3835, 3840}, {4083, 4380}, {4374, 35560}, {4467, 30665}, {4785, 42057}, {5040, 21005}, {6005, 48071}, {6372, 48147}, {7252, 21003}, {8034, 23751}, {8635, 21758}, {9002, 18183}, {9040, 47890}, {9400, 26853}, {14434, 30835}, {14474, 31286}, {23656, 45882}, {24666, 28398}, {25128, 30094}, {25142, 31209}, {26102, 29426}, {27013, 38238}, {29226, 47664}, {43931, 47762}, {47330, 50328}
X(50521) = reflection of X(20983) in X(650)
X(50521) = isogonal conjugate of the isotomic conjugate of X(2530)
X(50521) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {3495, 37781}, {39746, 150}, {43687, 3448}
X(50521) = X(i)-Ceva conjugate of X(j) for these (i,j): {81, 3121}, {513, 2530}, {4553, 39}, {13476, 1015}, {18830, 16720}, {46148, 21814}
X(50521) = X(2084)-cross conjugate of X(21123)
X(50521) = cevapoint of X(688) and X(2084)
X(50521) = crosspoint of X(i) and X(j) for these (i,j): {39, 4553}, {513, 667}, {1415, 1431}, {17187, 46148}
X(50521) = crosssum of X(i) and X(j) for these (i,j): {1, 29545}, {75, 18072}, {83, 18108}, {100, 668}, {514, 24169}, {693, 33940}, {4039, 4375}, {4391, 7081}, {4580, 18709}, {8640, 17752}, {10566, 18082}
X(50521) = crossdifference of every pair of points on line {83, 213}
X(50521) = X(i)-isoconjugate of X(j) for these (i,j): {10, 4577}, {37, 4593}, {42, 689}, {76, 4628}, {82, 668}, {83, 190}, {99, 18082}, {100, 3112}, {101, 308}, {213, 37204}, {251, 1978}, {306, 42396}, {313, 827}, {321, 4599}, {350, 36081}, {645, 18097}, {692, 18833}, {799, 18098}, {1016, 10566}, {1331, 46104}, {1799, 1897}, {1918, 42371}, {4039, 41209}, {4561, 32085}, {4567, 18070}, {4594, 18099}, {5383, 18107}, {6335, 34055}, {6386, 46289}, {7035, 18108}, {16894, 33515}, {27801, 34072}, {32739, 40016}
X(50521) = X(i)-Dao conjugate of X(j) for these (i, j): (39, 6386), (141, 668), (798, 18107), (1015, 308), (1086, 18833), (3124, 321), (5521, 46104), (6626, 37204), (8054, 3112), (15449, 27801), (21123, 18081), (34021, 42371), (34452, 100), (34467, 1799), (38986, 18082), (38996, 18098), (40585, 1978), (40589, 4593), (40592, 689), (40619, 40016), (40627, 18070)
X(50521) = barycentric product X(i)*X(j) for these {i,j}: {1, 21123}, {6, 2530}, {31, 16892}, {32, 48084}, {38, 649}, {39, 513}, {48, 21108}, {58, 8061}, {81, 3005}, {86, 2084}, {141, 667}, {244, 46148}, {274, 688}, {291, 46387}, {427, 22383}, {512, 16696}, {514, 1964}, {604, 48278}, {650, 1401}, {661, 17187}, {665, 46149}, {669, 16703}, {693, 3051}, {798, 16887}, {810, 17171}, {826, 1333}, {905, 1843}, {1015, 4553}, {1019, 21035}, {1459, 17442}, {1634, 3125}, {1635, 46150}, {1919, 1930}, {1923, 3261}, {1980, 8024}, {2087, 46162}, {2170, 46153}, {2203, 2525}, {3049, 16747}, {3063, 3665}, {3121, 4576}, {3248, 4568}, {3669, 3688}, {3675, 46163}, {3676, 40972}, {3733, 3954}, {3917, 6591}, {4020, 7649}, {6385, 9494}, {7117, 46152}, {7192, 21814}, {7199, 41267}, {8041, 18108}, {14399, 46147}, {14419, 46154}, {15413, 27369}, {17924, 20775}, {18210, 35325}, {19606, 23807}, {21760, 35367}, {21828, 46160}, {21832, 46159}, {23224, 27376}, {33299, 43924}, {40495, 41331}
X(50521) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 1978}, {39, 668}, {58, 4593}, {81, 689}, {86, 37204}, {141, 6386}, {274, 42371}, {513, 308}, {514, 18833}, {560, 4628}, {649, 3112}, {667, 83}, {669, 18098}, {688, 37}, {693, 40016}, {798, 18082}, {826, 27801}, {1333, 4577}, {1401, 4554}, {1634, 4601}, {1843, 6335}, {1919, 82}, {1922, 36081}, {1923, 101}, {1964, 190}, {1977, 18108}, {1980, 251}, {2084, 10}, {2203, 42396}, {2206, 4599}, {2530, 76}, {2531, 3954}, {3005, 321}, {3051, 100}, {3122, 18070}, {3248, 10566}, {3688, 646}, {3954, 27808}, {4020, 4561}, {4553, 31625}, {6591, 46104}, {8061, 313}, {9494, 213}, {16696, 670}, {16703, 4609}, {16887, 4602}, {16892, 561}, {17187, 799}, {20775, 1332}, {21035, 4033}, {21108, 1969}, {21123, 75}, {21814, 3952}, {22383, 1799}, {27369, 1783}, {38986, 18107}, {40972, 3699}, {41267, 1018}, {41272, 5380}, {41331, 692}, {46148, 7035}, {46149, 36803}, {46159, 4639}, {46387, 350}, {48084, 1502}, {48278, 28659}
X(50521) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {650, 20983, 14404}, {667, 22383, 1980}
X(5022) lies on these lines: {239, 514}, {513, 4024}, {523, 4979}, {650, 2457}, {661, 1639}, {693, 23731}, {812, 47671}, {824, 48107}, {900, 4838}, {918, 48147}, {1635, 4841}, {2527, 47876}, {2533, 21720}, {2786, 47659}, {3004, 31148}, {3239, 48544}, {3700, 28209}, {3835, 47791}, {4106, 47937}, {4120, 4778}, {4379, 47995}, {4394, 47878}, {4406, 20909}, {4444, 6546}, {4468, 47908}, {4500, 48079}, {4608, 26853}, {4728, 47988}, {4762, 48104}, {4785, 47656}, {4789, 48049}, {4790, 4802}, {4893, 28229}, {4897, 47673}, {4963, 48056}, {4976, 28175}, {6084, 48145}, {6545, 41850}, {6589, 21103}, {7653, 47880}, {7662, 47938}, {13401, 42462}, {17422, 21102}, {20295, 48416}, {21053, 50352}, {21104, 47916}, {21108, 43925}, {21116, 47652}, {23729, 47900}, {23770, 47902}, {28220, 47874}, {28225, 47873}, {28840, 47660}, {28851, 47662}, {28855, 49273}, {28867, 47665}, {28878, 48117}, {28882, 47675}, {28886, 49272}, {28894, 47971}, {28898, 48438}, {28902, 48112}, {30565, 47991}, {30835, 47789}, {31147, 47981}, {31207, 47783}, {31286, 47781}, {47762, 48404}, {47769, 47984}, {47771, 47996}, {47780, 48414}, {47790, 48041}, {47808, 47985}, {47809, 47992}, {47813, 47998}, {47832, 47983}, {47833, 47990}, {47885, 47964}, {47887, 47961}, {47890, 47917}, {47903, 48046}, {47907, 48398}, {47909, 48062}, {47939, 48270}, {47950, 48412}, {47960, 48425}, {47999, 48253}, {48000, 48567}, {48001, 48250}, {48006, 48578}, {48007, 48579}, {48076, 48271}, {48094, 49281}, {48108, 50454}, {48114, 48274}, {48399, 49298}, {48583, 50333}, {49289, 49297}
X(50522) = midpoint of X(4608) and X(26853)
X(50522) = reflection of X(i) in X(j) for these {i,j}: {649, 49293}, {661, 48276}, {4024, 48275}, {4813, 6590}, {4963, 48056}, {4988, 649}, {16892, 7192}, {23731, 693}, {45746, 4932}, {47652, 49291}, {47667, 48008}, {47669, 4976}, {47673, 4897}, {47900, 23729}, {47902, 23770}, {47903, 48046}, {47904, 48055}, {47907, 48398}, {47908, 4468}, {47909, 48062}, {47916, 21104}, {47917, 47890}, {47923, 49296}, {47926, 48060}, {47937, 4106}, {47938, 7662}, {47939, 48270}, {47943, 21146}, {47958, 43067}, {48019, 3700}, {48076, 48271}, {48079, 4500}, {48082, 47660}, {48094, 49281}, {48101, 49282}, {48114, 48274}, {48266, 48397}, {48277, 4790}, {48428, 47971}, {48429, 47659}, {48583, 50333}, {49297, 49289}, {49298, 48399}
X(50522) = X(17398)-Dao conjugate of X(33948)
X(50522) = crosspoint of X(514) and X(43927)
X(50522) = crossdifference of every pair of points on line {42, 595}
X(50522) = barycentric product X(514)*X(17398)
X(50522) = barycentric quotient X(17398)/X(190)
X(50522) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 4765, 14435}, {4765, 48576, 649}, {4790, 48277, 4984}, {4813, 6590, 4120}, {4932, 45746, 4750}, {43067, 47958, 6545}, {47652, 49291, 21116}, {48266, 48275, 48397}, {48266, 48397, 4024}
X(50523) lies on these lines: {10, 48566}, {512, 4895}, {513, 663}, {514, 50017}, {522, 47718}, {649, 4041}, {650, 47912}, {659, 47918}, {661, 667}, {784, 48153}, {812, 17166}, {814, 50457}, {830, 1019}, {905, 48023}, {1491, 47905}, {1577, 47813}, {1635, 4705}, {1734, 48064}, {1960, 4983}, {2530, 48020}, {3803, 4724}, {3835, 47820}, {3900, 4790}, {3960, 48086}, {4024, 29232}, {4040, 15309}, {4063, 4160}, {4083, 47935}, {4129, 47818}, {4147, 48565}, {4369, 21301}, {4378, 48334}, {4401, 47811}, {4490, 4782}, {4504, 48298}, {4729, 4834}, {4794, 48081}, {4804, 29013}, {4813, 8643}, {4893, 6050}, {4932, 28470}, {6002, 47694}, {6005, 48110}, {6372, 48032}, {7192, 29051}, {8656, 48026}, {14392, 48387}, {14419, 48059}, {14838, 47810}, {17072, 47762}, {21003, 48022}, {21118, 29126}, {21260, 24924}, {21302, 47763}, {23057, 48337}, {23738, 48320}, {23755, 29240}, {23882, 48142}, {24561, 25008}, {24720, 48570}, {25900, 25901}, {28372, 28373}, {28882, 47720}, {29037, 47660}, {29047, 48146}, {29070, 47672}, {29098, 47705}, {29114, 49300}, {29118, 47695}, {29150, 48305}, {29152, 48392}, {29186, 48148}, {29198, 47936}, {29238, 48120}, {29278, 48276}, {29288, 48101}, {29328, 48301}, {29340, 48393}, {29350, 47976}, {29354, 48130}, {30835, 48564}, {31148, 50352}, {31286, 47814}, {39545, 47943}, {47796, 48050}, {47819, 48042}, {47826, 47955}, {47840, 48049}, {47911, 48029}, {47942, 48065}, {47947, 48058}, {47966, 48572}, {47967, 48226}, {48024, 48331}, {48045, 48584}, {48066, 48586}, {48114, 48273}, {48248, 48265}, {48284, 50449}, {48327, 48338}, {48335, 48343}, {48345, 48352}, {48568, 50337}
X(50523) = midpoint of X(i) and X(j) for these {i,j}: {4979, 48322}, {7192, 31291}, {48110, 48324}, {48149, 48150}
X(50523) = reflection of X(i) in X(j) for these {i,j}: {661, 667}, {1734, 48064}, {2254, 1019}, {4041, 649}, {4490, 4782}, {4724, 3803}, {4729, 4834}, {4813, 48099}, {4822, 663}, {4895, 48322}, {4983, 1960}, {21301, 4369}, {23738, 48320}, {47905, 1491}, {47906, 4724}, {47911, 48029}, {47912, 650}, {47918, 659}, {47936, 50358}, {47942, 48065}, {47947, 48058}, {47948, 14838}, {47956, 6050}, {47959, 4401}, {48019, 4983}, {48020, 2530}, {48021, 4040}, {48022, 21003}, {48023, 905}, {48024, 48331}, {48081, 4794}, {48086, 3960}, {48114, 48273}, {48116, 3777}, {48121, 48136}, {48122, 3669}, {48123, 48330}, {48131, 4367}, {48151, 48144}, {48264, 47694}, {48265, 48248}, {48298, 4504}, {48334, 4378}, {48335, 48343}, {48338, 48327}, {48352, 48345}, {48367, 48329}, {48582, 48024}, {48584, 48045}, {48586, 48066}, {48597, 48123}, {50449, 48284}
X(50523) = X(961)-Ceva conjugate of X(2170)
X(50523) = X(8)-isoconjugate of X(29279)
X(50523) = crosssum of X(100) and X(3882)
X(50523) = crossdifference of every pair of points on line {9, 5256}
X(50523) = barycentric product X(i)*X(j) for these {i,j}: {1, 48276}, {57, 29278}, {513, 5750}, {514, 3745}, {649, 4968}, {650, 4298}
X(50523) = barycentric quotient X(i)/X(j) for these {i,j}: {604, 29279}, {3745, 190}, {4298, 4554}, {4968, 1978}, {5750, 668}, {29278, 312}, {48276, 75}
X(50523) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4367, 48131, 14413}, {4401, 47959, 47811}, {4813, 8643, 48099}, {6050, 47956, 4893}, {14838, 47948, 47810}
X(50524) lies on these lines: {1, 669}, {8, 25299}, {42, 24533}, {239, 24626}, {512, 7192}, {513, 4382}, {514, 2978}, {649, 4083}, {659, 2605}, {693, 788}, {838, 48273}, {875, 3873}, {891, 17494}, {1193, 28286}, {3221, 17217}, {3661, 21726}, {3700, 9040}, {3720, 25537}, {3741, 31003}, {3805, 4024}, {3835, 20983}, {4041, 28372}, {4106, 9010}, {4132, 4784}, {4139, 50343}, {4145, 50339}, {4147, 30023}, {4155, 4467}, {4374, 9402}, {4507, 47762}, {4705, 27647}, {4932, 29350}, {4979, 9400}, {6371, 39547}, {6373, 20295}, {7180, 10473}, {8640, 48333}, {8655, 48330}, {9286, 14296}, {10453, 26148}, {14404, 25666}, {14426, 27138}, {16874, 18199}, {16892, 30665}, {17135, 44445}, {17458, 20598}, {21301, 25301}, {21763, 21836}, {23301, 31330}, {23570, 37685}, {24747, 30950}, {24943, 25686}, {25126, 26037}, {25128, 30968}, {25142, 30835}, {25473, 29647}, {25636, 47841}, {26815, 27016}, {27045, 47839}, {27167, 47837}, {28374, 48332}, {29226, 47926}
X(50524) = reflection of X(20983) in X(3835)
X(50524) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {87, 148}, {110, 41840}, {330, 21221}, {662, 21219}, {932, 1654}, {2162, 21220}, {4556, 36857}, {4565, 36858}, {4573, 20537}, {4596, 36856}, {4598, 2895}, {4610, 17149}, {4625, 20350}, {6383, 21294}, {6384, 3448}, {7121, 25054}, {18830, 1330}, {34071, 1655}, {36066, 2227}
X(50524) = X(18196)-Ceva conjugate of X(21763)
X(50524) = X(21836)-cross conjugate of X(42327)
X(50524) = X(101)-isoconjugate of X(42328)
X(50524) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 42328), (42327, 512)
X(50524) = crosspoint of X(i) and X(j) for these (i,j): {1, 670}, {18830, 32009}
X(50524) = crosssum of X(i) and X(j) for these (i,j): {1, 669}, {512, 22199}, {647, 23420}, {649, 23427}, {663, 23441}, {667, 23417}, {3005, 23445}, {8640, 20963}
X(50524) = crossdifference of every pair of points on line {43, 2229}
X(50524) = barycentric product X(i)*X(j) for these {i,j}: {1, 42327}, {10, 18196}, {38, 18106}, {75, 21763}, {86, 21836}, {92, 22387}, {512, 34022}, {513, 25264}
X(50524) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 42328}, {18106, 3112}, {18196, 86}, {21763, 1}, {21836, 10}, {22387, 63}, {25264, 668}, {34022, 670}, {42327, 75}
X(50524) = {X(1),X(18197)}-harmonic conjugate of X(669)
X(50525) lies on these lines: {2, 48041}, {44, 513}, {512, 4959}, {514, 14779}, {693, 48577}, {812, 47675}, {900, 48275}, {905, 48597}, {918, 48104}, {1019, 48074}, {2529, 4944}, {2786, 49282}, {3004, 47937}, {3239, 48576}, {3667, 4024}, {3700, 39386}, {3776, 49297}, {3798, 47981}, {3835, 47763}, {4025, 23731}, {4063, 47911}, {4106, 31148}, {4120, 49284}, {4369, 31147}, {4379, 4932}, {4380, 28840}, {4382, 4785}, {4467, 28859}, {4498, 15309}, {4750, 47995}, {4762, 48147}, {4770, 4834}, {4776, 31207}, {4778, 4988}, {4822, 8643}, {4830, 47941}, {4838, 4926}, {4897, 47958}, {4940, 24924}, {4949, 47881}, {4960, 29270}, {4976, 28209}, {4977, 48277}, {4984, 28225}, {5029, 9811}, {6006, 6590}, {6008, 47672}, {6545, 49294}, {6546, 48038}, {8632, 48122}, {11068, 48034}, {14350, 47766}, {14838, 48595}, {16892, 47907}, {17494, 47908}, {21212, 48543}, {24719, 48579}, {26798, 47779}, {28195, 47669}, {28217, 47873}, {28846, 48067}, {28855, 47663}, {28867, 47660}, {28906, 49273}, {29328, 48142}, {30520, 48145}, {30835, 47762}, {31150, 47991}, {31286, 47759}, {31290, 48008}, {43061, 47764}, {43067, 48114}, {47774, 48588}, {47775, 47984}, {47776, 47996}, {47780, 49287}, {47805, 48037}, {47886, 47988}, {47890, 48076}, {47900, 47960}, {47903, 47962}, {47923, 47971}, {47924, 50342}, {47939, 48000}, {47947, 48011}, {47965, 48582}, {47985, 48242}, {47986, 48240}, {48003, 48584}, {48060, 48082}, {48064, 48085}, {48080, 48578}, {48095, 48112}, {48110, 48144}, {48149, 48341}, {48270, 48567}, {48327, 48338}, {48585, 50357}
X(50525) = reflection of X(i) in X(j) for these {i,j}: {649, 4979}, {661, 4790}, {1019, 48074}, {4024, 49293}, {4063, 48624}, {4382, 7192}, {4498, 47976}, {4813, 649}, {7192, 48071}, {16892, 48013}, {17494, 48016}, {20295, 4932}, {23731, 4025}, {31290, 48008}, {47900, 47960}, {47903, 47962}, {47907, 16892}, {47908, 17494}, {47911, 4063}, {47912, 4834}, {47923, 47971}, {47924, 50342}, {47926, 4380}, {47937, 3004}, {47939, 48000}, {47941, 4830}, {47947, 48011}, {47958, 4897}, {47981, 3798}, {48019, 650}, {48020, 7659}, {48023, 4784}, {48034, 11068}, {48076, 47890}, {48079, 4369}, {48082, 48060}, {48085, 48064}, {48101, 48067}, {48112, 48095}, {48114, 43067}, {48117, 48101}, {48121, 1019}, {48138, 48104}, {48141, 48107}, {48144, 48110}, {48266, 48276}, {48341, 48149}, {48582, 47965}, {48584, 48003}, {48585, 50357}, {48592, 31286}, {48595, 14838}, {48597, 905}, {49297, 3776}
X(50525) = anticomplement of X(48041)
X(50525) = X(i)-Ceva conjugate of X(j) for these (i,j): {39948, 244}, {39983, 1015}
X(50525) = X(48053)-cross conjugate of X(28195)
X(50525) = X(i)-isoconjugate of X(j) for these (i,j): {2, 28196}, {100, 27789}, {101, 28650}, {765, 48587}
X(50525) = X(i)-Dao conjugate of X(j) for these (i, j): (513, 48587), (1015, 28650), (8054, 27789), (32664, 28196)
X(50525) = crosssum of X(i) and X(j) for these (i,j): {513, 46845}, {27789, 48587}
X(50525) = crossdifference of every pair of points on line {1, 4134}
X(50525) = barycentric product X(i)*X(j) for these {i,j}: {1, 28195}, {81, 47669}, {86, 48053}, {513, 3624}, {514, 16884}, {656, 31901}, {661, 42025}, {3669, 4034}, {3733, 42031}, {14838, 43261}
X(50525) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 28196}, {513, 28650}, {649, 27789}, {1015, 48587}, {3624, 668}, {4034, 646}, {16884, 190}, {28195, 75}, {31901, 811}, {42025, 799}, {42031, 27808}, {43261, 15455}, {47669, 321}, {48053, 10}
X(50525) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {649, 4813, 4893}, {649, 48544, 650}, {650, 48019, 48544}, {661, 4790, 649}, {661, 4979, 4790}, {4369, 48079, 31147}, {4932, 20295, 4379}, {31286, 48592, 47759}, {47762, 48049, 30835}, {48019, 48544, 4813}, {48266, 48276, 47873}
X(50526) lies on these lines: {512, 4959}, {513, 663}, {649, 4705}, {659, 47911}, {661, 6050}, {667, 4813}, {830, 48110}, {1019, 48023}, {1635, 47956}, {3667, 47719}, {3803, 48021}, {4040, 48594}, {4041, 4790}, {4160, 47976}, {4401, 47826}, {4724, 15309}, {4729, 4814}, {4785, 17166}, {4825, 4834}, {4932, 21301}, {4960, 29033}, {4983, 8643}, {8656, 48019}, {17072, 47763}, {24720, 48580}, {28470, 48071}, {29013, 48142}, {29037, 49282}, {29051, 48107}, {29070, 48141}, {29232, 48275}, {29288, 48104}, {29354, 48138}, {47811, 47955}, {47820, 48049}, {47828, 47948}, {47840, 48041}, {47905, 50336}, {47949, 48572}, {48029, 48582}, {48050, 48570}, {48058, 48584}, {48267, 48578}, {48577, 50352}
X(50526) = reflection of X(i) in X(j) for these {i,j}: {4041, 4790}, {4813, 667}, {21301, 4932}, {47905, 50336}, {47911, 659}, {47912, 649}, {47947, 4401}, {47948, 48064}, {48019, 48099}, {48021, 3803}, {48023, 1019}, {48121, 4367}, {48122, 48144}, {48582, 48029}, {48584, 48058}, {48597, 48136}
X(50526) = crossdifference of every pair of points on line {9, 17011}
X(50526) = barycentric product X(650)*X(4355)
X(50526) = barycentric quotient X(4355)/X(4554)
X(50526) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4401, 47947, 47826}, {47948, 48064, 47828}
X(50527) lies on the cubic K1279 and these lines: {1, 7}, {30, 1411}, {47, 9961}, {74, 484}, {1717, 37558}, {1772, 36002}, {2647, 16118}
X(50527) = {X(1042),X(4354)}-harmonic conjugate of X(1)
X(50528) lies on the cubic K1279 and these lines: {1, 30}, {3, 1709}, {4, 12520}, {9, 7688}, {20, 224}, {36, 7171}, {40, 64}, {46, 1858}, {65, 37411}, {78, 31730}, {84, 11012}, {102, 36984}, {165, 5720}, {376, 997}, {411, 1158}, {515, 3434}, {516, 18446}, {517, 41711}, {550, 45770}, {610, 2935}, {758, 2900}, {912, 41338}, {936, 4640}, {946, 4666}, {958, 41871}, {960, 37426}, {962, 3957}, {971, 3428}, {990, 1064}, {999, 14100}, {1001, 1012}, {1071, 12704}, {1470, 45633}, {1479, 34489}, {1699, 18443}, {1728, 1898}, {1745, 12940}, {1750, 3925}, {1766, 30269}, {1770, 6869}, {2077, 10860}, {2771, 37584}, {2951, 6282}, {3149, 9943}, {3333, 10391}, {3338, 13369}, {3359, 44425}, {3465, 8270}, {3529, 21740}, {3587, 5692}, {3651, 12514}, {3679, 18528}, {3715, 5584}, {3811, 6361}, {3869, 33557}, {3870, 28194}, {3935, 34632}, {3962, 12702}, {4295, 10393}, {4297, 6938}, {4300, 5311}, {4512, 37286}, {4880, 5709}, {4915, 5881}, {5250, 35989}, {5251, 18540}, {5534, 7991}, {5691, 6923}, {5787, 15908}, {5886, 7965}, {6259, 11827}, {6765, 44663}, {6836, 12608}, {6838, 12616}, {6851, 12047}, {6889, 12617}, {6899, 21616}, {6914, 7987}, {6924, 16209}, {6974, 10165}, {7701, 31424}, {7995, 10268}, {8227, 8726}, {8583, 16370}, {9122, 12262}, {9612, 10953}, {9812, 18444}, {9841, 37561}, {10085, 11249}, {10167, 22753}, {10382, 11529}, {10582, 38021}, {10826, 37406}, {10902, 12705}, {11014, 12650}, {12511, 31803}, {12671, 18237}, {12679, 31789}, {12680, 22770}, {13624, 28444}, {15681, 35459}, {16117, 40266}, {17532, 18492}, {19860, 31673}, {20835, 31435}, {22793, 37615}, {24703, 37428}, {24806, 36985}, {28146, 37533}, {28160, 36999}, {28534, 34626}, {28628, 37447}, {35239, 40263}, {37022, 37837}, {37356, 37692}
X(50528) = midpoint of X(1) and X(41860)
X(50528) = reflection of X(i) in X(j) for these {i,j}: {40, 7580}, {1709, 3}, {5691, 6923}, {6938, 4297}, {10431, 946}, {37569, 18446}, {41869, 1836}, {44447, 31730}
X(50528) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 16143, 41854}, {40, 1490, 17857}, {411, 9961, 1158}, {997, 43178, 376}, {1490, 12565, 40}, {1750, 30503, 5587}, {5692, 41853, 3587}, {16132, 41869, 1}, {35239, 40263, 41229}
X(50529) lies on the cubic K1279 and these lines: {20, 254}, {30, 50}, {64, 155}, {74, 35465}, {7464, 10420}, {39986, 47195}
X(50529) = barycentric product X(2986)*X(18451)
X(50529) = barycentric quotient X(18451)/X(3580)
X(50530) lies on the cubic K1279 and these lines: {1, 378}, {9, 15941}, {30, 16548}, {40, 64}, {74, 484}, {223, 5119}, {610, 3587}, {1745, 11010}, {2939, 2940}, {2941, 31730}, {3468, 37563}, {5715, 11471}, {10605, 18397}
X(50530) = excentral isogonal conjugate of X(1718)
X(50530) = {X(40),X(16389)}-harmonic conjugate of X(1490)
X(50531) lies on the cubic K1279 and these lines: {20, 6148}, {154, 1511}, {3172, 39176}, {4354, 40933}
X(50531) = isogonal conjugate of X(50434)
X(50531) = isogonal conjugate of the anticomplement of X(1514)
X(50531) = crosssum of X(2935) and X(35237)
X(50531) = barycentric quotient X(6)/X(50434)
See Tran Quang Hung, Francisco Javier García Capitán and Peter Moses, euclid 5202 and euclid 5204.
X(50532) lies on these lines: {2, 3}, {122, 2040}, {1379, 47296}, {3284, 39023}, {3557, 13567}, {6190, 40996}, {14631, 23292}, {15526, 39022}
X(50532) = X(i)-complementary conjugate of X(j) for these (i,j): {48, 3414}, {656, 2039}, {810, 39023}, {1379, 8062}, {3414, 20305}, {5639, 226}, {6190, 21259}
X(50532) = X(i)-Ceva conjugate of X(j) for these (i,j): {253, 3414}, {6190, 525}
Points in an orthogonal [[b-c, c-a, a-b], [2 a^2 - 3a (b+c) - b^2 - c^2 + 6 b c, 2 b^2 - 3 b (c+a) - c^2 - a^2 + 6 c a , 2c^2 - 3 c (a+b) - a^2 - b^2 + 6 a b]] coordinate system: X(50533)-X(50536)
The origin is given by (0, 0) = X(2) = 1 : 1 : 1 : : .
Barycentrics u : v : w for a triangle center U = (x,y) in this system are given by
u : v : w = -2(a^3 + b^3 + c^3 + 9 a b c - 2 a^2 b - 2 a b^2 - 2 b^2 c - 2 b c^2 - 2 c^2 a - 2 c a^2) + (-2 a + b + c) x + 3(b - c)(3 a - b - c) y : : ,
where, as functions of a, b, c, the coordinate x is symmetric of degree 4, and y is symmetric of degree 4.
The appearance of {x, y}, k in the following list means that (x, y) = X(k).
{-a^2-b^2-c^2, 0}, 5121
{0, 0}, 2}
{2 (a^2+b^2+c^2), 0}, 5205}
{-2*(a^2 + b^2 + c^2), 0}, X(50533)
{-a^2 - b^2 - c^2, -(((a - b)*(a - c)*(b - c)*(a + b + c))/((a + b)*(a + c)*(b + c)))}, X(50534)
{(a^2 + b^2 + c^2)/2, 0}, X(50535)
{2*(a^2 + b^2 + c^2), ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, X(50536)
X(50533) lies on these lines: {1, 2}, {11, 37756}, {126, 5516}, {244, 31177}, {524, 3756}, {903, 19634}, {1054, 28562}, {1366, 1447}, {2726, 4588}, {3667, 4750}, {3737, 45673}, {4370, 39059}, {4679, 49748}, {4715, 26273}, {4956, 17495}, {5233, 47358}, {9053, 12035}, {16067, 19796}, {17132, 17777}, {17721, 49720}, {17722, 50299}, {18201, 28558}, {24627, 50296}, {25531, 41310}, {25533, 37792}, {26240, 39704}, {43055, 49709}
X(50533) = midpoint of X(2) and X(5211)
X(50533) = reflection of X(i) in X(j) for these {i,j}: {2, 5121}, {5205, 2}
X(50533) = orthoptic-circle-of-Steiner-inellipse-inverse of X(551)
X(50533) = orthoptic-circle-of-Steiner-circumellipe inverse of X(3241)}
X(50533) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5121, 5211, 5205}
X(50534) lies on these lines: {21, 45763}, {210, 846}, {381, 24174}, {519, 2292}, {1385, 3073}, {2254, 3667}, {9978, 47625}, {23848, 24436}, {35623, 38473}
X(50535) lies on these lines: {1, 2}, {124, 3836}, {142, 30754}, {516, 1293}, {1054, 28526}, {1155, 16594}, {1738, 37758}, {2718, 9104}, {2885, 11260}, {3041, 40538}, {3452, 4655}, {3667, 3716}, {3699, 24216}, {3823, 6667}, {3911, 24003}, {4009, 43055}, {4138, 30827}, {4358, 17888}, {5057, 30855}, {17132, 26273}, {21242, 46916}
X(50535) = midpoint of X(i) and X(j) for these {i,j}: {3699, 24216}, {5121, 5205}
X(50535) = complement of X(5121)
X(50535) = Spieker-circle-inverse of X(20103)
X(50535) = orthoptic-circle-of-the-Steiner-inellipse-inverse of X(8)
X(50535) = orthoptic-circle-of-the-Steiner-circumellipse-inverse of X(3621)
X(50535) = psi-transform of X(24280)
X(50535) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5205, 5121}, {2, 37762, 3011}, {4871, 6745, 49768}
X(50536) lies on the cubic K1275 and these lines: {6, 519}, {187, 4370}, {649, 3239}, {2325, 7113}
X(50536) = crossdifference of every pair of points on line {1201, 9002}
See Tran Quang Hung and Francisco Javier García Capitán, euclid 5203.
X(50537) lies on this line: {511, 7470}
Points in a [[a^4, b^4, c^4], [b^2 c^2, c^2 a^2, a^2 b^2]] coordinate system: X(50538)-X(50556)
The origin is given by (0, 0) = X(50549) = a^2 (b^6 - c^6) : : .
Barycentrics u : v : w for a triangle center U = (x,y) in this system are given by
a^2 (b^6 - c^6) + (b^4 - c^4) x + a^2 (b^2 - c^2) y : : ,
where, as functions of a, b, c, the coordinate x is symmetric of degree 4, and y is symmetric of degree 4.
The appearance of {x, y}, k in the following list means that (x, y) = X(k).
{-a b c (a+b+c), (a b+a c+b c)^2}, 24290
{1/2 (-a^4-b^4-c^4), 0}, 47126
{1/2 (-a^4-b^4-c^4), 1/2 (a^2+b^2+c^2)^2}, 33294
{0, 1/2 (a^4+b^4+c^4)}, 647
{0, a^4+b^4+c^4}, 5027
{0, (a^2+b^2+c^2)^2}, 14318
{1/2 (a^4+b^4+c^4), 0}, 6333
{-2*a*b*c*(a + b + c), -(a*b + a*c + b*c)^2}, 50538
{-(a*b*c*(a + b + c)), (a^4 + b^4 + c^4)/2}, 50539
{-(a*b*c*(a + b + c)), (a + b + c)*(a^3 + b^3 + c^3)}, 50540
{-((a + b + c)^2*(a*b + a*c + b*c)), (a*b + a*c + b*c)^2}, 50541
{-a^4 - b^4 - c^4, (a^2 + b^2 + c^2)^2}, 50542
{(-a^4 - b^4 - c^4)/2, -(a^2 + b^2 + c^2)^2}, 50543
{-1/2*(a*b*c*(a + b + c)), ((a + b + c)*(a^3 + b^3 + c^3))/2}, 50544
{-1/2*(a^2 + b^2 + c^2)^2, (a^4 + b^4 + c^4)/2}, 50545
{-1/2*(a^2 + b^2 + c^2)^2, (a^2 + b^2 + c^2)^2/2}, 50546
{(-a^4 - b^4 - c^4)/2, a^4 + b^4 + c^4}, 50547
{(-a^4 - b^4 - c^4)/2, (a^2 + b^2 + c^2)^2}, 50548
{0, 0}, 50549
{0, (a^2 + b^2 + c^2)^2/2}, 50550
{(a^4 + b^4 + c^4)/2, (-a^4 - b^4 - c^4)/2}, 50551
{(a^4 + b^4 + c^4)/2, a^4 + b^4 + c^4}, 50552
{(a^2 + b^2 + c^2)^2/2, (a^4 + b^4 + c^4)/2}, 50553
{(a^2 + b^2 + c^2)^2, (a^4 + b^4 + c^4)/2}, 50554
{a*b*c*(a + b + c), (a*b + a*c + b*c)^2}, 50555
{(a*b + a*c + b*c)^2, (a + b + c)*(a^3 + b^3 + c^3)}, 50556
{(a*b + a*c + b*c)^2, 2*a*b*c*(a + b + c)}, 50557
X(50538) lies on these lines: {325, 523}, {351, 650}, {512, 4813}, {649, 9279}, {661, 4155}, {690, 48082}, {740, 48000}, {804, 17494}, {876, 4608}, {888, 50521}, {2530, 47671}, {2978, 9402}, {3777, 47674}, {4024, 4705}, {4490, 25259}, {4770, 42666}, {4988, 8034}, {9147, 26777}, {11176, 27115}, {21020, 47672}, {21349, 47658}, {23768, 47668}, {25258, 47825}, {26985, 45689}, {47703, 50345}
X(50538) = reflection of X(i) in X(j) for these {i,j}: {8663, 661}, {42661, 4705}, {42666, 4770}
X(50538) = X(i)-Ceva conjugate of X(j) for these (i,j): {321, 3124}, {523, 48393}, {762, 2643}, {4436, 16589}
X(50538) = X(i)-isoconjugate of X(j) for these (i,j): {110, 40439}, {662, 40408}, {757, 8708}, {4556, 32009}, {24041, 50520}
X(50538) = X(i)-Dao conjugate of X(j) for these (i, j): (244, 40439), (1084, 40408), (3005, 50520), (3121, 81), (3739, 99), (16589, 4623), (40607, 8708)
X(50538) = crosspoint of X(i) and X(j) for these (i,j): {523, 4705}, {4436, 16589}
X(50538) = crosssum of X(40408) and X(50520)
X(50538) = crossdifference of every pair of points on line {32, 593}
X(50538) = barycentric product X(i)*X(j) for these {i,j}: {37, 48393}, {115, 4436}, {321, 50497}, {514, 21699}, {523, 16589}, {594, 6372}, {661, 21020}, {693, 21820}, {756, 47672}, {850, 21753}, {1577, 2667}, {2171, 48264}, {3700, 39793}, {3720, 4024}, {3739, 4705}, {4036, 20963}, {4064, 40975}, {4079, 20888}, {4111, 7178}, {14618, 22369}
X(50538) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 40408}, {661, 40439}, {1500, 8708}, {2667, 662}, {3124, 50520}, {3706, 4631}, {3720, 4610}, {3739, 4623}, {4079, 40433}, {4111, 645}, {4436, 4590}, {4705, 32009}, {6372, 1509}, {16589, 99}, {21020, 799}, {21699, 190}, {21753, 110}, {21820, 100}, {22369, 4558}, {39793, 4573}, {47672, 873}, {48393, 274}, {50497, 81}
X(50539) lies on these lines: {512, 661}, {523, 2509}, {525, 650}, {647, 826}, {665, 48300}, {2484, 8672}, {3709, 4064}, {8045, 16612}
X(50539) = crossdifference of every pair of points on line {22, 81}
X(50540) lies on these lines: {239, 7927}, {512, 661}, {523, 4107}, {690, 47892}, {826, 4467}, {1635, 5113}, {4155, 4435}, {4477, 14318}
X(50540) = crosssum of X(1019) and X(17799)
X(50540) = barycentric product X(21832)*X(32780)
X(50540) = barycentric quotient X(32780)/X(4639)
X(50541) lies on these lines: {512, 4988}, {525, 661}, {826, 4024}, {3250, 16892}, {3309, 48277}, {3566, 4841}, {3700, 3801}, {3800, 47669}, {3906, 4120}, {4064, 8061}, {28481, 48019}, {47708, 48269}, {48278, 50454}
X(50541) = reflection of X(4024) in X(24290)
X(50541) = barycentric product X(i)*X(j) for these {i,j}: {10, 50348}, {523, 49511}
X(50541) = barycentric quotient X(i)/X(j) for these {i,j}: {49511, 99}, {50348, 86}
X(50542) lies on these lines: {6, 33907}, {148, 690}, {826, 14318}, {2799, 3506}, {3569, 20859}, {3804, 7950}, {5113, 14420}, {6333, 9208}, {9479, 14316}, {24256, 24284}
X(50542) = X(46970)-anticomplementary conjugate of X(21289)
X(50542) = crosspoint of X(1916) and X(4577)
X(50542) = crosssum of X(i) and X(j) for these (i,j): {1691, 3005}, {5007, 5113}
X(50542) = crossdifference of every pair of points on line {11205, 14153}
X(50543) lies on these lines: {83, 5466}, {512, 33294}, {523, 2525}, {804, 3806}, {826, 44445}, {850, 7927}, {2799, 8665}, {3005, 11123}, {3800, 9134}
X(50544) lies on these lines: {512, 650}, {523, 2487}, {647, 4155}, {669, 1635}, {812, 23301}, {1960, 50518}, {3221, 50514}, {3700, 17990}, {4041, 7234}, {4151, 31286}, {4728, 31279}, {4763, 44451}, {6089, 12075}, {8672, 50336}, {16751, 50524}, {18154, 47837}, {25511, 48273}, {27527, 50343}, {44445, 47776}
X(50544) = midpoint of X(4041) and X(8639)
X(50544) = crossdifference of every pair of points on line {940, 11329}
X(50544) = barycentric product X(661)*X(32853)
X(50544) = barycentric quotient X(32853)/X(799)
X(50544) = {X(650),X(50501)}-harmonic conjugate of X(4507)
X(50545) lies on these lines: {23, 385}, {351, 14316}, {512, 3806}, {525, 3005}, {647, 826}, {2525, 3906}, {2528, 3265}, {3566, 8665}, {3800, 8664}, {3804, 7927}, {4122, 27731}, {7950, 8651}, {8029, 41927}, {23878, 47126}
X(50545) = reflection of X(2528) in X(3265)
X(50545) = crosssum of X(512) and X(5359)
X(50545) = crossdifference of every pair of points on line {22, 39}
X(50545) = barycentric product X(523)*X(7800)
X(50545) = barycentric quotient X(7800)/X(99)
X(50545) = {X(2528),X(17414)}-harmonic conjugate of X(3265)
X(50546) lies on these lines: {512, 3806}, {523, 14318}, {525, 4486}, {826, 33294}, {1637, 3906}, {2528, 9210}, {9208, 14316}
X(50546) = crossdifference of every pair of points on line {1915, 6800}
X(50547) lies on these lines: {441, 525}, {512, 33294}, {690, 5996}, {826, 5027}, {879, 1176}, {2799, 3288}, {3050, 23881}, {3906, 45687}, {9030, 47138}, {12077, 14316}
X(50547) = reflection of X(i) in X(j) for these {i,j}: {2525, 24284}, {6333, 647}, {12077, 14316}
X(50547) = crossdifference of every pair of points on line {25, 20859}
X(50547) = barycentric product X(525)*X(7792)
X(50547) = barycentric quotient X(7792)/X(648)
X(50548) lies on these lines: {512, 33294}, {523, 3804}, {525, 47128}, {669, 2799}, {690, 850}, {804, 12077}, {826, 14318}, {924, 16230}, {1637, 23301}, {2501, 3566}, {2525, 9479}, {3005, 14420}, {6563, 8651}, {8704, 41300}, {9147, 41298}, {9979, 12075}, {14417, 44451}, {18105, 23881}, {31279, 44564}
X(50548) = reflection of X(i) in X(j) for these {i,j}: {6563, 8651}, {44445, 12075}, {47126, 33294}
X(50548) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {3565, 21289}, {4599, 19583}, {38252, 39346}
X(50548) = crosspoint of X(i) and X(j) for these (i,j): {4, 4577}, {10159, 35136}
X(50548) = crosssum of X(i) and X(j) for these (i,j): {3, 3005}, {5007, 8651}
X(50548) = crossdifference of every pair of points on line {3167, 9605}
X(50548) = barycentric product X(523)*X(7762)
X(50548) = barycentric quotient X(7762)/X(99)
X(50548) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6563, 8651, 45687}, {9979, 44445, 12075}
X(50549) lies on these lines: {141, 523}, {187, 237}, {525, 4486}, {690, 5996}, {808, 4580}, {826, 850}, {2492, 9012}, {2514, 3221}, {3906, 9148}, {7950, 46562}, {9044, 9171}, {12073, 45687}
X(50549) = midpoint of X(i) and X(j) for these {i,j}: {3005, 3569}, {6333, 47126}
X(50549) = reflection of X(i) in X(j) for these {i,j}: {669, 5113}, {5027, 647}
X(50549) = isogonal conjugate of X(33514)
X(50549) = isotomic conjugate of the isogonal conjugate of X(17415)
X(50549) = X(i)-Ceva conjugate of X(j) for these (i,j): {327, 115}, {47643, 20975}
X(50549) = X(i)-isoconjugate of X(j) for these (i,j): {1, 33514}, {110, 3113}, {163, 3114}, {560, 9063}, {662, 3407}, {789, 38813}, {799, 18898}, {811, 43722}, {825, 38810}, {1492, 40415}, {1576, 46281}, {1933, 41073}, {4599, 14617}, {4613, 7305}, {5384, 7255}, {8840, 36084}
X(50549) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 33514), (115, 3114), (244, 3113), (1084, 3407), (2887, 1492), (3124, 14617), (4858, 46281), (6374, 9063), (6784, 182), (10335, 670), (16584, 37133), (17423, 43722), (19602, 99), (38987, 8840), (38995, 40415), (38996, 18898)
X(50549) = crosspoint of X(825) and X(38831)
X(50549) = crosssum of X(i) and X(j) for these (i,j): {523, 7792}, {824, 6679}, {4586, 34069}, {9006, 40377}
X(50549) = crossdifference of every pair of points on line {2, 1501}
X(50549) = barycentric product X(i)*X(j) for these {i,j}: {76, 17415}, {512, 3314}, {523, 3094}, {647, 5117}, {656, 46507}, {788, 20234}, {824, 3778}, {850, 3117}, {882, 9865}, {1491, 3721}, {1502, 9006}, {1577, 3116}, {2275, 4122}, {2276, 3801}, {2887, 3250}, {4475, 7239}, {4481, 7237}, {14295, 42061}, {18899, 44173}, {21751, 30870}, {23285, 43977}
X(50549) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 33514}, {76, 9063}, {512, 3407}, {523, 3114}, {661, 3113}, {669, 18898}, {1491, 38810}, {1577, 46281}, {1916, 41073}, {2887, 37133}, {3005, 14617}, {3049, 43722}, {3094, 99}, {3116, 662}, {3117, 110}, {3250, 40415}, {3314, 670}, {3569, 8840}, {3721, 789}, {3778, 4586}, {5117, 6331}, {9006, 32}, {9865, 880}, {16584, 1492}, {17415, 6}, {18899, 1576}, {20234, 46132}, {21751, 34069}, {40935, 825}, {42061, 805}, {43977, 827}, {46386, 38813}, {46507, 811}
X(50549) = {X(669),X(9210)}-harmonic conjugate of X(5113)
X(50550) lies on these lines: {110, 12833}, {187, 237}, {206, 924}, {688, 2485}, {690, 30474}, {826, 33294}, {882, 1843}, {1499, 11176}, {2492, 9009}, {3566, 24284}, {3818, 11182}, {3906, 14420}, {4550, 21905}, {5652, 15724}, {9023, 46001}, {9030, 22105}, {20987, 21006}, {25423, 45336}
X(50550) = midpoint of X(i) and X(j) for these {i,j}: {351, 11186}, {669, 3569}
X(50550) = reflection of X(i) in X(j) for these {i,j}: {647, 5113}, {5027, 8651}, {24284, 44451}
X(50550) = X(42359)-complementary conjugate of X(21253)
X(50550) = crosspoint of X(110) and X(263)
X(50550) = crosssum of X(183) and X(523)
X(50550) = crossdifference of every pair of points on line {2, 12215}
X(50550) = barycentric product X(i)*X(j) for these {i,j}: {512, 7774}, {523, 5017}
X(50550) = barycentric quotient X(i)/X(j) for these {i,j}: {5017, 99}, {7774, 670}
X(50551) lies on these lines: {512, 6333}, {525, 4486}, {550, 1499}, {647, 690}, {669, 46546}, {1640, 31279}, {2501, 11182}, {3566, 5027}, {3906, 47126}
X(50551) = crossdifference of every pair of points on line {1915, 1995}
X(50552) lies on these lines: {325, 523}, {512, 2525}, {525, 669}, {647, 826}, {690, 3804}, {2395, 11123}, {2799, 47128}, {3566, 8664}, {3800, 8665}, {3801, 27731}, {3806, 7950}, {3906, 8651}, {5489, 40689}, {8642, 49279}, {8654, 48299}, {12075, 31174}, {28374, 29017}, {30476, 47126}, {41300, 45687}
X(50552) = midpoint of X(669) and X(2528)
X(50552) = reflection of X(i) in X(j) for these {i,j}: {3005, 3265}, {47126, 30476}
X(50552) = X(6572)-complementary conjugate of X(21235)
X(50552) = X(i)-Ceva conjugate of X(j) for these (i,j): {6572, 141}, {40831, 3124}
X(50552) = crosspoint of X(99) and X(31360)
X(50552) = crossdifference of every pair of points on line {22, 32}
X(50552) = barycentric product X(523)*X(7795)
X(50552) = barycentric quotient X(7795)/X(99)
X(50553) lies on these lines: {2, 12075}, {230, 231}, {512, 6333}, {525, 6562}, {669, 2799}, {804, 2525}, {826, 5027}, {1632, 9514}, {1799, 41298}, {2896, 12073}, {3005, 11123}, {3268, 44445}, {8651, 33294}, {8664, 32473}, {9134, 30476}, {9168, 30785}, {14417, 23301}, {21006, 23881}, {31299, 32478}
X(50553) = reflection of X(i) in X(j) for these {i,j}: {16230, 46953}, {33294, 8651}, {47126, 647}
X(50553) = anticomplement of X(12075)
X(50553) = X(40405)-anticomplementary conjugate of X(21294)
X(50553) = crossdifference of every pair of points on line {3, 20859}
X(50553) = barycentric product X(523)*X(7807)
X(50553) = barycentric quotient X(7807)/X(99)
X(50553) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14325, 14326, 647}, {45687, 47126, 647}
X(50554) lies on these lines: {512, 2528}, {523, 2525}, {525, 3804}, {647, 826}, {669, 3906}, {3005, 7950}, {3265, 3806}, {28374, 29318}, {31174, 47126}
X(50554) = reflection of X(3806) in X(3265)
X(50554) = crossdifference of every pair of points on line {22, 30435}
X(50555) lies on these lines: {1, 7252}, {512, 4895}, {525, 4978}, {661, 3954}, {826, 4024}, {3569, 7927}
X(50555) = crossdifference of every pair of points on line {5135, 7465}
X(50556) lies on these lines: {512, 7192}, {513, 4509}, {514, 4435}, {523, 3875}, {525, 1019}, {661, 24285}, {667, 4025}, {693, 6004}, {826, 4467}, {832, 15413}, {3004, 4040}, {3309, 43067}, {4367, 23829}, {4369, 24290}, {7199, 39547}, {7950, 17161}, {8632, 16892}, {8659, 17494}, {23785, 50353}, {24286, 48288}, {24601, 25259}, {26248, 47837}, {47995, 48351}
X(50556) = reflection of X(i) in X(j) for these {i,j}: {661, 24285}, {17494, 8659}, {24290, 4369}, {48288, 24286}
X(50556) = X(30555)-anticomplementary conjugate of X(1654)
X(50557) lies on these lines: {325, 523}, {512, 7192}, {514, 42664}, {525, 4801}, {647, 17494}, {1577, 4988}, {2611, 23989}, {4025, 4151}, {4077, 30572}, {4108, 26248}, {4132, 43067}, {4139, 47780}, {4374, 17161}, {4391, 47667}, {4467, 7199}, {4762, 36900}, {4789, 25667}, {4815, 14208}, {4978, 16892}, {7650, 47699}, {8672, 20295}, {9979, 47124}, {17894, 28169}, {18154, 47782}, {20950, 47654}, {20952, 47658}, {23878, 47869}, {24622, 46915}, {26824, 31296}, {26985, 30476}, {29771, 47660}
X(50557) = midpoint of X(26824) and X(31296)
X(50557) = reflection of X(i) in X(j) for these {i,j}: {850, 693}, {17494, 647}
X(50557) = isotomic conjugate of X(43356)
X(50557) = isotomic conjugate of the anticomplement of X(38967)
X(50557) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2215, 148}, {36077, 5905}, {36080, 1654}
X(50557) = X(38967)-cross conjugate of X(2)
X(50557) = X(i)-isoconjugate of X(j) for these (i,j): {31, 43356}, {163, 39983}, {1576, 39708}
X(50557) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 43356), (115, 39983), (4858, 39708)
X(50557) = crossdifference of every pair of points on line {32, 21753}
X(50557) = barycentric product X(i)*X(j) for these {i,j}: {75, 50449}, {313, 48064}, {321, 48107}, {850, 37685}, {1577, 17394}, {3267, 17562}
X(50557) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 43356}, {523, 39983}, {1577, 39708}, {17394, 662}, {17562, 112}, {37685, 110}, {48064, 58}, {48107, 81}, {50449, 1}
X(50557) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 47655, 35519}, {693, 47657, 3261}
See Kadir Altintas and César Lozada, euclid 5219.
X(50558) lies on these lines: {1, 30}, {3, 16777}, {31, 8143}, {37, 582}, {47, 45065}, {220, 36754}, {273, 6198}, {942, 18477}, {946, 29065}, {1100, 40263}, {3187, 48887}, {3579, 5311}, {3811, 4971}, {5396, 29235}, {5398, 31445}, {5752, 16519}, {6985, 20182}, {9955, 17017}, {13369, 37595}, {17045, 50324}, {29016, 48900}, {46475, 48882}
X(50558) = {X(1), X(4654)}-harmonic conjugate of X(7100)
X(50559) lies on these lines: {7, 2886}, {63, 348}, {85, 4359}, {144, 9533}, {219, 30682}, {329, 658}, {345, 7055}, {479, 28610}, {527, 47386}, {664, 9778}, {1088, 9965}, {1260, 6516}, {1996, 5905}, {2094, 17079}, {2898, 17768}, {3218, 17093}, {3784, 10167}, {5698, 31526}, {20078, 37780}, {35312, 44447}
X(50559) = isotomic conjugate of the polar conjugate of X(3160)
X(50559) = X(69)-Ceva conjugate of X(348)
X(50559) = X(i)-isoconjugate of X(j) for these (i,j): {25, 19605}, {33, 11051}, {607, 3062}, {2212, 10405}
X(50559) = X(i)-Dao conjugate of X(j) for these (i, j): (7, 4), (6505, 19605), (13609, 3064)
X(50559) = barycentric product X(i)*X(j) for these {i,j}: {63, 31627}, {69, 3160}, {77, 16284}, {144, 348}, {165, 7182}, {304, 1419}, {345, 9533}, {3718, 17106}, {6063, 22117}
X(50559) = barycentric quotient X(i)/X(j) for these {i,j}: {63, 19605}, {77, 3062}, {144, 281}, {165, 33}, {222, 11051}, {348, 10405}, {1419, 19}, {3160, 4}, {3207, 607}, {7056, 36620}, {7182, 44186}, {7658, 3064}, {9533, 278}, {16284, 318}, {17106, 34}, {22117, 55}, {31627, 92}
X(50559) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {63, 7056, 348}, {144, 9533, 31627}
X(50560) lies on these lines: {7, 17049}, {69, 4569}, {75, 1088}, {85, 24199}, {346, 4554}, {518, 47393}, {3596, 4572}, {3662, 17435}, {3729, 40864}, {3912, 40593}, {6007, 31604}
X(50560) = isotomic conjugate of the isogonal conjugate of X(3160)
X(50560) = X(76)-Ceva conjugate of X(6063)
X(50560) = X(i)-isoconjugate of X(j) for these (i,j): {32, 19605}, {41, 11051}, {2175, 3062}, {9447, 10405}, {9448, 44186}
X(50560) = X(i)-Dao conjugate of X(j) for these (i, j): (7, 6), (144, 38293), (3160, 11051), (4130, 35508), (6376, 19605), (7658, 3022), (13609, 663), (40133, 1200), (40593, 3062)
X(50560) = cevapoint of X(16284) and X(31627)
X(50560) = barycentric product X(i)*X(j) for these {i,j}: {75, 31627}, {76, 3160}, {85, 16284}, {144, 6063}, {165, 20567}, {561, 1419}, {3207, 41283}, {3596, 9533}, {4572, 7658}, {17106, 28659}
X(50560) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 11051}, {75, 19605}, {85, 3062}, {144, 55}, {165, 41}, {1419, 31}, {3160, 6}, {3207, 2175}, {6063, 10405}, {7658, 663}, {9533, 56}, {13609, 3022}, {16284, 9}, {17106, 604}, {20567, 44186}, {21060, 1334}, {31627, 1}, {43182, 1200}
X(50560) = {X(346),X(34019)}-harmonic conjugate of X(4554)
X(50561) lies on the cubic K970 and these lines: {2, 17113}, {6, 41351}, {7, 354}, {9, 658}, {75, 4569}, {77, 4626}, {85, 10004}, {144, 9533}, {347, 30682}, {3160, 45228}, {4000, 41356}, {8732, 37757}, {9311, 41777}, {14189, 38285}, {16706, 30705}, {17158, 41789}, {20059, 37780}, {25722, 35312}, {30854, 39063}, {42311, 45834}
X(50561) = isotomic conjugate of the isogonal conjugate of X(17106)
X(50561) = X(85)-Ceva conjugate of X(1088)
X(50561) = X(i)-cross conjugate of X(j) for these (i,j): {3160, 31627}, {43182, 144}
X(50561) = X(i)-isoconjugate of X(j) for these (i,j): {41, 19605}, {220, 11051}, {1253, 3062}, {10405, 14827}
X(50561) = X(i)-Dao conjugate of X(j) for these (i, j): (7, 9), (3160, 19605), (7658, 24010), (13609, 3900), (17113, 3062)
X(50561) = cevapoint of X(i) and X(j) for these (i,j): {7, 17113}, {3160, 9533}
X(50561) = crosspoint of X(i) and X(j) for these (i,j): {85, 31627}, {4569, 24011}
X(50561) = crosssum of X(8641) and X(24012)
X(50561) = barycentric product X(i)*X(j) for these {i,j}: {7, 31627}, {75, 9533}, {76, 17106}, {85, 3160}, {144, 1088}, {279, 16284}, {1419, 6063}, {4569, 7658}, {13609, 24011}
X(50561) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 19605}, {144, 200}, {165, 220}, {269, 11051}, {279, 3062}, {1088, 10405}, {1419, 55}, {3160, 9}, {3207, 1253}, {7658, 3900}, {9533, 1}, {13609, 24010}, {16284, 346}, {17106, 6}, {21060, 4515}, {22117, 1802}, {23062, 36620}, {31627, 8}
X(50561) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 23062, 1088}, {7, 31526, 14100}, {23062, 47374, 7}
X(50562) lies on these lines: {7, 10167}, {144, 9533}, {210, 4566}, {226, 857}, {658, 3219}, {1088, 10004}, {1750, 34059}, {1920, 46406}, {5905, 7056}, {10394, 31526}, {14256, 18228}, {31527, 36991}
X(50562) = X(1441)-Ceva conjugate of X(1446)
X(50562) = X(i)-isoconjugate of X(j) for these (i,j): {2194, 19605}, {2328, 11051}
X(50562) = X(i)-Dao conjugate of X(j) for these (i, j): (7, 21), (1214, 19605), (13609, 1021), (36908, 11051)
X(50562) = barycentric product X(i)*X(j) for these {i,j}: {144, 1446}, {226, 31627}, {313, 17106}, {321, 9533}, {349, 1419}, {1088, 21060}, {1441, 3160}, {3668, 16284}
X(50562) = barycentric quotient X(i)/X(j) for these {i,j}: {144, 2287}, {165, 2328}, {226, 19605}, {1419, 284}, {1427, 11051}, {1446, 10405}, {3160, 21}, {3668, 3062}, {7658, 1021}, {9533, 81}, {16284, 1043}, {17106, 58}, {21060, 200}, {21872, 220}, {31627, 333}
X(50563) lies on these lines: {7, 11523}, {72, 307}, {144, 1419}, {226, 21029}, {329, 34059}, {348, 3951}, {527, 3188}, {1231, 4101}, {1441, 3671}, {2475, 25719}, {3146, 25718}, {4566, 21075}, {5905, 9312}, {6872, 25716}, {7176, 41572}, {16865, 25723}, {31821, 41007}
X(50563) = X(306)-Ceva conjugate of X(307)
X(50563) = X(i)-isoconjugate of X(j) for these (i,j): {1172, 11051}, {1474, 19605}, {2204, 10405}, {2299, 3062}
X(50563) = X(i)-Dao conjugate of X(j) for these (i, j): (7, 27), (226, 3062)
X(50563) = barycentric product X(i)*X(j) for these {i,j}: {72, 31627}, {144, 307}, {165, 1231}, {306, 3160}, {348, 21060}, {349, 22117}, {1214, 16284}, {1419, 20336}, {3710, 9533}, {7182, 21872}
X(50563) = barycentric quotient X(i)/X(j) for these {i,j}: {72, 19605}, {73, 11051}, {144, 29}, {165, 1172}, {307, 10405}, {1214, 3062}, {1231, 44186}, {1419, 28}, {3160, 27}, {3207, 2299}, {16284, 31623}, {17106, 1396}, {21060, 281}, {21872, 33}, {22117, 284}, {31627, 286}
X(50564) lies on the circumconic {{A,B,C,X(2),X(6)}} and these lines: {6, 9125}, {111, 1499}, {647, 34898}, {690, 21448}, {6791, 9178}
X(50564) = X(662)-isoconjugate of X(33962)
X(50564) = X(i)-Dao conjugate of X(j) for these (i, j): (1084, 33962), (1648, 6077)
X(50564) = barycentric product X(523)*X(6093)
X(50564) = barycentric quotient X(i)/X(j) for these {i,j}: {512, 33962}, {1649, 6077}, {6093, 99}
X(50565) lies on these lines: {111, 1499}, {524, 5914}, {542, 14858}, {1640, 45294}, {5108, 21448}, {5912, 9209}, {5913, 5915}, {9486, 47077}
X(50566) lies on these lines: {2, 6}, {111, 1499}, {542, 31654}, {843, 9084}, {6791, 34806}, {9146, 14515}
X(50566) = midpoint of X(9146) and X(14515)
X(50566) = reflection of X(i) in X(j) for these {i,j}: {6792, 14858}, {34806, 6791}
X(50567) lies on these lines: {2, 5503}, {6, 620}, {69, 74}, {76, 22677}, {98, 10519}, {110, 38940}, {114, 325}, {115, 141}, {125, 4576}, {126, 1648}, {147, 10513}, {148, 3620}, {182, 38748}, {183, 6055}, {187, 524}, {193, 5182}, {316, 19924}, {538, 15993}, {543, 599}, {576, 7763}, {597, 9167}, {621, 41060}, {622, 41061}, {626, 44453}, {670, 44155}, {671, 19662}, {690, 5181}, {732, 1569}, {754, 5104}, {1007, 20423}, {1176, 3044}, {1350, 2794}, {1351, 15561}, {1352, 10008}, {1503, 38738}, {1916, 16986}, {1975, 10992}, {1992, 41134}, {2030, 35297}, {2782, 14994}, {2786, 4437}, {2799, 3569}, {2854, 15357}, {2936, 22241}, {2979, 4121}, {3094, 4045}, {3266, 41586}, {3564, 33813}, {3589, 22848}, {3618, 33231}, {3619, 14061}, {3763, 6034}, {3818, 39809}, {3926, 5171}, {3933, 5188}, {4027, 50248}, {4563, 5972}, {4904, 24199}, {5017, 5149}, {5039, 10352}, {5050, 38750}, {5099, 47557}, {5107, 44380}, {5108, 10418}, {5157, 39834}, {5186, 41584}, {5207, 29317}, {5461, 21358}, {5468, 5642}, {5480, 36519}, {5590, 13653}, {5591, 13773}, {5847, 11711}, {5860, 13760}, {5861, 13640}, {5939, 37671}, {5965, 12215}, {5971, 15360}, {6033, 33878}, {6036, 34229}, {6054, 37668}, {6388, 32525}, {6721, 8781}, {6776, 21166}, {7665, 35279}, {7764, 13330}, {7767, 10991}, {7769, 25555}, {7776, 38745}, {7777, 22486}, {7788, 35705}, {7794, 46283}, {7799, 39099}, {7807, 44499}, {8591, 11161}, {8593, 11160}, {9140, 14360}, {9766, 11173}, {9830, 15300}, {9880, 11178}, {10330, 24981}, {10542, 32954}, {11180, 12117}, {11477, 20399}, {12828, 34336}, {12829, 15480}, {14356, 39374}, {14639, 40330}, {14971, 20582}, {15452, 39873}, {15483, 34511}, {15533, 36521}, {16989, 36849}, {18358, 22515}, {18440, 38730}, {18553, 32819}, {18906, 23514}, {19905, 32836}, {20398, 32828}, {20774, 32001}, {22247, 47352}, {23235, 32830}, {29181, 39838}, {30786, 45311}, {31128, 45291}, {31670, 32827}, {31884, 38747}, {35022, 40341}, {37485, 39857}
X(50567) = midpoint of X(i) and X(j) for these {i,j}: {69, 99}, {6033, 33878}, {8591, 11161}, {8593, 11160}, {11180, 12117}, {18440, 38730}
X(50567) = reflection of X(i) in X(j) for these {i,j}: {6, 620}, {115, 141}, {193, 41672}, {671, 19662}, {5099, 47557}, {5107, 44380}, {5477, 5026}, {9880, 11178}, {14928, 99}, {18800, 2482}, {22515, 18358}, {38749, 3098}, {39809, 3818}, {46264, 38736}
X(50567) = isotomic conjugate of X(9154)
X(50567) = complement of X(10754)
X(50567) = isotomic conjugate of the isogonal conjugate of X(9155)
X(50567) = X(36892)-Ceva conjugate of X(511)
X(50567) = X(i)-isoconjugate of X(j) for these (i,j): {31, 9154}, {98, 923}, {111, 1910}, {248, 36128}, {293, 8753}, {897, 1976}, {1821, 32740}, {2395, 36142}, {2422, 36085}, {2715, 23894}, {6531, 36060}, {9178, 36084}, {10097, 36104}, {14601, 46277}, {14908, 36120}, {19626, 46273}
X(50567) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 9154), (132, 8753), (524, 5967), (1560, 6531), (2482, 98), (3291, 36874), (5976, 671), (6593, 1976), (11672, 111), (21905, 15630), (23992, 2395), (35088, 5466), (38987, 9178), (38988, 2422), (39000, 10097), (39039, 36128), (39040, 897), (40601, 32740), (41172, 8430), (46094, 14908), (50440, 5547)
X(50567) = crossdifference of every pair of points on line {1976, 2422}
X(50567) = barycentric product X(i)*X(j) for these {i,j}: {76, 9155}, {126, 36892}, {297, 6390}, {325, 524}, {468, 6393}, {511, 3266}, {690, 2396}, {877, 14417}, {896, 46238}, {1959, 14210}, {2421, 35522}, {2799, 5468}, {3292, 44132}, {4230, 45807}, {4235, 6333}, {5967, 32458}, {5968, 36792}, {7813, 20022}, {16702, 42703}, {36212, 44146}
X(50567) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 9154}, {126, 36874}, {187, 1976}, {232, 8753}, {237, 32740}, {240, 36128}, {297, 17983}, {325, 671}, {351, 2422}, {468, 6531}, {511, 111}, {524, 98}, {684, 10097}, {690, 2395}, {896, 1910}, {1755, 923}, {1959, 897}, {2396, 892}, {2421, 691}, {2482, 5967}, {2799, 5466}, {3266, 290}, {3289, 14908}, {3292, 248}, {3569, 9178}, {3712, 15628}, {4235, 685}, {5026, 40820}, {5467, 2715}, {5468, 2966}, {5642, 35906}, {5967, 41932}, {5968, 10630}, {6333, 14977}, {6390, 287}, {6393, 30786}, {6786, 14609}, {7813, 20021}, {9155, 6}, {9418, 19626}, {14210, 1821}, {14417, 879}, {14567, 14601}, {14966, 32729}, {18872, 34238}, {21906, 15630}, {23200, 14600}, {23889, 36084}, {23997, 36142}, {24039, 36036}, {33752, 10561}, {35522, 43665}, {35910, 9139}, {36212, 895}, {36790, 5968}, {36823, 10422}, {36892, 44182}, {41167, 8430}, {42717, 5380}, {43034, 7316}, {44132, 46111}, {44146, 16081}, {45662, 34369}, {45672, 36822}, {46238, 46277}
X(50567) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {193, 5182, 41672}, {671, 21356, 19662}, {1648, 45672, 126}, {2482, 5477, 5026}, {3763, 6034, 6722}, {5026, 5477, 18800}, {5468, 7664, 5642}, {5976, 32458, 114}, {14501, 14502, 325}
X(50568) lies the Kiepert circumhyperbola of the Brocard triangle, the cubic K551, and these lines: {99, 7746}, {1352, 49784}
X(50568) = midpoint of X(49784) and X(49785)
X(50569) lies the Kiepert circumhyperbola of the Brocard triangle, the cubic K551, and this line: {99, 7746}
X(50570) lies on the Kiepert circumhyperbola of the Brocard triangle and these lines: {2, 7765}, {3, 148}, {4, 19569}, {5, 13571}, {17, 628}, {18, 627}, {76, 35005}, {115, 2896}, {193, 576}, {194, 3090}, {385, 546}, {532, 41122}, {533, 41121}, {599, 5025}, {629, 42673}, {630, 42672}, {631, 38226}, {632, 7783}, {633, 16630}, {634, 16631}, {671, 33260}, {1656, 38231}, {1698, 3729}, {2996, 10303}, {3094, 3619}, {3146, 7793}, {3180, 33465}, {3181, 33464}, {3529, 17008}, {3544, 7774}, {3589, 7797}, {3616, 38222}, {3618, 38232}, {3627, 14712}, {3628, 47286}, {3630, 15514}, {3767, 10000}, {3851, 7837}, {3857, 7762}, {5007, 14568}, {5072, 7754}, {5079, 7777}, {5286, 33261}, {5309, 33020}, {5461, 7909}, {5485, 32976}, {5487, 40706}, {5488, 40707}, {5982, 33382}, {5983, 33383}, {6392, 15022}, {6655, 41135}, {6658, 18546}, {7610, 33275}, {7615, 10807}, {7620, 33244}, {7749, 20094}, {7751, 32993}, {7758, 33011}, {7760, 33024}, {7779, 39565}, {7794, 9166}, {7796, 18362}, {7836, 13881}, {7843, 44367}, {7887, 40727}, {7905, 39601}, {7907, 34505}, {7938, 10008}, {7946, 33006}, {8363, 46226}, {8584,
33013}, {8591, 11149}, {8667, 14062}, {8859, 19687}, {9939, 32996}, {11177, 40279}, {11303, 49898}, {11304, 49897}, {11305, 49942}, {11306, 49941}, {11361, 22331}, {13468, 33256}, {14042, 22329}, {14045, 37671}, {14869, 17006}, {15031, 20088}, {16042, 19577}, {17128, 43291}, {17244, 31266}, {20081, 43620}, {22844, 33412}, {22845, 33413}, {22847, 44030}, {22861, 22914}, {22869, 22907}, {22893, 44032}, {23055, 33254}, {31652, 32457}, {32480, 33012}, {32836, 33277}, {32885, 33258}, {33283, 46951}, {33626, 36368}, {33627, 36366}, {38734, 39652}
X(50570) = midpoint of X(22113) and X(22114)
X(50570) = reflection of X(i) in X(j) for these {i,j}: {627, 18}, {628, 17}
X(50570) = {X(5),X(19570)}-harmonic conjugate of X(13571)
X(50571) lies on the Kiepert circumhyperbola of the Brocard triangle and these lines: {2, 11147}, {3, 9167}, {6, 12040}, {76, 7610}, {230, 9741}, {524, 10008}, {543, 13881}, {549, 1352}, {599, 620}, {2482, 37637}, {2896, 33274}, {3053, 9770}, {3094, 7622}, {3642, 13706}, {3643, 13704}, {3815, 18842}, {5054, 7697}, {5077, 22247}, {5210, 22110}, {5215, 11165}, {6228, 13700}, {6229, 13820}, {7619, 11286}, {7868, 10807}, {7907, 34505}, {9166, 33233}, {9740, 32841}, {9766, 26613}, {9771, 32839}, {11149, 35955}, {11159, 18584}, {11184, 35297}, {11301, 42672}, {11302, 42673}, {11742, 31275}, {13769, 13833}, {14971, 44518}, {15533, 21843}, {15597, 32885}, {15693, 15810}, {18311, 45681}, {31274, 44541}, {33224, 48310}, {33692, 37671}, {38748, 40248}
X(50571) = midpoint of X(i) and X(j) for these {i,j}: {2, 11147}, {49786, 49787}
X(50571) = {X(7622),X(11288)}-harmonic conjugate of X(47352)
X(50572) lies on these lines: {3, 69}, {99, 32001}, {253, 32831}, {264, 1007}, {317, 8979}, {325, 6527}, {1272, 39118}, {4558, 11008}, {4847, 42696}, {6389, 37669}, {7763, 32000}, {8797, 20563}, {8968, 13430}, {10607, 20080}, {13441, 32805}, {14615, 32818}, {16774, 43705}, {20477, 32006}, {40405, 40819}
X(50572) = isotomic conjugate of the isogonal conjugate of X(12164)
X(50572) = X(253)-Ceva conjugate of X(69)
X(50572) = X(1973)-isoconjugate of X(43670)
X(50572) = X(i)-Dao conjugate of X(j) for these (i, j): (6337, 43670), (37669, 20)
X(50572) = crosspoint of X(44326) and X(47389)
X(50572) = barycentric product X(i)*X(j) for these {i,j}: {76, 12164}, {3926, 6622}, {32605, 34403}
X(50572) = barycentric quotient X(i)/X(j) for these {i,j}: {69, 43670}, {6622, 393}, {12164, 6}, {32605, 1249}
X(50572) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 40697, 6337}, {3926, 41005, 69}
X(50573) lies on these lines: {2, 7}, {5, 11662}, {44, 5723}, {80, 516}, {390, 28234}, {518, 1317}, {519, 12730}, {528, 36920}, {651, 1323}, {971, 12691}, {1155, 5851}, {2801, 21578}, {3035, 44785}, {3257, 43762}, {3973, 37800}, {4304, 10394}, {4315, 5692}, {4867, 14151}, {5220, 5252}, {5251, 8543}, {5720, 8544}, {5722, 5729}, {5727, 30332}, {5728, 15935}, {5850, 7677}, {5856, 26015}, {6326, 18450}, {7671, 18412}, {7675, 21168}, {7951, 30312}, {15254, 15950}, {15297, 41012}, {15726, 33519}, {28534, 40663}, {30295, 44425}, {34919, 35258}, {37701, 43180}
X(50573) = midpoint of X(144) and X(3218)
X(50573) = reflection of X(i) in X(j) for these {i,j}: {7, 3911}, {908, 9}, {30379, 37787}, {44785, 3035}
X(50573) = barycentric quotient X(18801)/X(26015)
X(50573) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 3911, 30379}, {7, 37787, 3911}, {9, 41563, 41572}, {9, 41572, 21617}, {908, 30379, 21617}, {3218, 37787, 1445}, {6172, 12848, 8545}
See Angel Montesdeoca, euclid 5222 and HG310521
X(50574) lies on these lines: {1,523}, {11,7137}, {12,2614}, {229,4367}, {245,1109}, {514,12071}, {522,12579}, {1365,12064}, {2292,4041}, {2613,14985}, {4086,4647}, {4467,6626}, {9293,23938}, {23879,27929}, {35347,41501}, {37140,39138}
Points in a [[b-c, c-a, a-b], [b^2 c^2 (b^2 - c^2), c^2 a^2 (c^2 - a^2), a^2 b^2 (a^2 - b^2)]] coordinate system: X(50575)-X(50638)
The origin is given by (0, 0) = X(386) = a^2 (b^2 + c^2 + a b + a c + b c) : : .
Barycentrics u : v : w for a triangle center U = (x,y) in this system are given by
U = a^2 (a-b)(a-c)(b-c)(b^2 + c^2 + a b + a c + b c) + (-2 a + b + c) x + a^2 (a^2 b^2 + a^2 c^2 - b^4 - c^4) y : : ,
where, as functions of a, b, c, the coordinate x is antisymmetric of degree 6, and y is antisymmetric of degree 1.
The appearance of {x, y}, k in the following list means that (x, y) = X(k).
{-((a-b) (a+b) (a-c) (b-c) (a+c) (b+c)), 0}, 20018
{-((a-b) (a-c) (b-c) (a^3+b^3+c^3)), ((a-b) (a-c) (b-c) (a+b+c))/(a b c)}, 3868
{-a (a-b) b (a-c) (b-c) c, (2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2)}, 3751
{0, -(((a-b) (a-c) (b-c))/(2 (a b+a c+b c)))}, 4263
{0, 0}, 386
{0, ((a-b) (a-c) (b-c))/(a^2+b^2+c^2)}, 6
{1/2 (a-b) (a-c) (b-c) (a+b+c) (a b+a c+b c), -(((a-b) (a-c) (b-c))/(a^2+b^2+c^2))}, 49511
{1/2 (a-b) (a+b) (a-c) (b-c) (a+c) (b+c), -(((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2)))}, 141
{1/2 a (a-b) b (a-c) (b-c) c, ((a-b) (a-c) (b-c))/(2 (a^2+b^2+c^2))}, 1386
{(a-b) (a+b) (a-c) (b-c) (a+c) (b+c), -((2 (a-b) (a-c) (b-c))/(a^2+b^2+c^2))}, 69
{a (a-b) b (a-c) (b-c) c, 0}, 1
{(a-b) (a+b) (a-c) (b-c) (a+c) (b+c), 0}, 10449
{(a-b) (a+b) (a-c) (b-c) (a+c) (b+c), ((a-b) (a-c) (b-c))/(a b+a c+b c)}, 34282
{2 a (a-b) b (a-c) (b-c) c, -(((a-b) (a-c) (b-c))/(a^2+b^2+c^2))}, 3242
{-2*a*(a - b)*b*(a - c)*(b - c)*c, 0}, 50575
{-(a*(a - b)*b*(a - c)*(b - c)*c), (-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50576
{-((a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c)), (-2*(a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50577
{-(a*(a - b)*b*(a - c)*(b - c)*c), -(((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c))}, 50578
{-((a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c)), -(((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c))}, 50579
{-(a*(a - b)*b*(a - c)*(b - c)*c), -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c)}, 50580
{-(a*(a - b)*b*(a - c)*(b - c)*c), 0}, 50581
{-((a - b)*(a - c)*(b - c)*(a^3 + b^3 + c^3)), 0}, 50582
{-(a*(a - b)*b*(a - c)*(b - c)*c), ((a - b)*(a - c)*(b - c)*(a + b + c))/(2*a*b*c)}, 50583
{-(a*(a - b)*b*(a - c)*(b - c)*c), ((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50584
{-(a*(a - b)*b*(a - c)*(b - c)*c), ((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c)}, 50585
{-((a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c)), ((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c)}, 50586
{-1/2*(a*(a - b)*b*(a - c)*(b - c)*c), 0}, 50587
{-1/2*((a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c)), , 50588
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)*(a^2 + b^2 + c^2)), 0}, 50589
{-1/2*((a - b)*(a - c)*(b - c)*(a + b + c)*(a*b + a*c + b*c)), 0}, 50590
{0, -(((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2))}, 50591
{0, -(((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c))}, 50592
{0, -(((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c))}, 50593
{0, -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c)}, 50594
{0, ((a - b)*(a - c)*(b - c))/(2*(a^2 + b^2 + c^2))}, 50595
{0, ((a - b)*(a - c)*(b - c))/(2*(a*b + a*c + b*c))}, 50596
{0, ((a - b)*(a - c)*(b - c)*(a + b + c))/(2*a*b*c)}, 50597
{0, ((a - b)*(a - c)*(b - c))/(a + b + c)^2}, 50598
{0, ((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c)}, 50599
{0, (2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50600
{((a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c))/2, -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c)}, 50601
{((a - b)*(a - c)*(b - c)*(a + b + c)^3)/2, -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c)}, 50602
{((a - b)*(a - c)*(b - c)*(a + b + c)*(a*b + a*c + b*c))/2, -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c)}, 50603
{(a*(a - b)*b*(a - c)*(b - c)*c)/2, 0}, 50604
{((a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c))/2, 0}, 50605
{((a - b)*(a - c)*(b - c)*(a + b + c)^3)/2, 0}, 50606
{((a - b)*(a - c)*(b - c)*(a + b + c)*(a^2 + b^2 + c^2))/2, 0}, 50607
{((a - b)*(a - c)*(b - c)*(a + b + c)*(a*b + a*c + b*c))/2, 0}, 50608
{((a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c))/2, ((a - b)*(a - c)*(b - c))/(2*(a^2 + b^2 + c^2))}, 50609
{((a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c))/2, ((a - b)*(a - c)*(b - c)*(a + b + c))/(2*a*b*c)}, 50610
{((a - b)*(a - c)*(b - c)*(a + b + c)*(a*b + a*c + b*c))/2, ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50611
{a*(a - b)*b*(a - c)*(b - c)*c, (-2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50612
{a*(a - b)*b*(a - c)*(b - c)*c, (-2*(a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50613
{a*(a - b)*b*(a - c)*(b - c)*c, (-2*(a - b)*(a - c)*(b - c))/(a + b + c)^2}, 50614
{a*(a - b)*b*(a - c)*(b - c)*c, -(((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2))}, 50615
{a*(a - b)*b*(a - c)*(b - c)*c, -(((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c))}, 50616
{a*(a - b)*b*(a - c)*(b - c)*c, -(((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c))}, 50617
{a*(a - b)*b*(a - c)*(b - c)*c, -(((a - b)*(a - c)*(b - c)*(a + b + c))/((a + b)*(a + c)*(b + c)))}, 50618
{(a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c), -(((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c))}, 50619
{a*(a - b)*b*(a - c)*(b - c)*c, -1/2*((a - b)*(a - c)*(b - c))/(a*b + a*c + b*c)}, 50620
{a*(a - b)*b*(a - c)*(b - c)*c, -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c)}, 50621
{a*(a - b)*b*(a - c)*(b - c)*c, -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/((a + b)*(a + c)*(b + c))}, 50622
{(a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c), -1/2*((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c)}, 50623
{(a - b)*(a - c)*(b - c)*(a^3 + b^3 + c^3), 0}, 50624
{(a - b)*(a - c)*(b - c)*(a + b + c)*(a*b + a*c + b*c), 0}, 50625
{a*(a - b)*b*(a - c)*(b - c)*c, ((a - b)*(a - c)*(b - c)*(a + b + c))/(2*a*b*c)}, 50626
{a*(a - b)*b*(a - c)*(b - c)*c, ((a - b)*(a - c)*(b - c)*(a + b + c))/(2*(a + b)*(a + c)*(b + c))}, 50627
{(a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c), ((a - b)*(a - c)*(b - c)*(a + b + c))/(2*a*b*c)}, 50628
{a*(a - b)*b*(a - c)*(b - c)*c, ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50629
{a*(a - b)*b*(a - c)*(b - c)*c, ((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c)}, 50630
{a*(a - b)*b*(a - c)*(b - c)*c, ((a - b)*(a - c)*(b - c)*(a + b + c))/((a + b)*(a + c)*(b + c))}, 50631
{(a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c), ((a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50632
{(a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c), ((a - b)*(a - c)*(b - c)*(a + b + c))/(a*b*c)}, 50633
{(a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c), ((a - b)*(a - c)*(b - c)*(a + b + c))/((a + b)*(a + c)*(b + c))}, 50634
{a*(a - b)*b*(a - c)*(b - c)*c, (2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50635
{(a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c), (2*(a - b)*(a - c)*(b - c))/(a^2 + b^2 + c^2)}, 50636
{2*a*(a - b)*b*(a - c)*(b - c)*c, 0}, 50637
{2*(a - b)*(a + b)*(a - c)*(b - c)*(a + c)*(b + c), 0}, 50638
X(50575) lies on these lines: {1, 2}, {45, 4263}, {58, 3913}, {72, 17461}, {500, 34718}, {511, 12702}, {872, 49678}, {956, 33771}, {991, 11362}, {996, 1043}, {1126, 5710}, {1191, 22141}, {1357, 5221}, {1468, 48696}, {1739, 3889}, {2177, 5258}, {2334, 4658}, {2901, 4737}, {3691, 9331}, {3730, 3780}, {3736, 49680}, {3754, 49490}, {3871, 16948}, {3873, 3987}, {3875, 44147}, {3881, 24440}, {3892, 24174}, {3997, 4050}, {4002, 4883}, {4253, 20691}, {4256, 12513}, {4257, 8715}, {4270, 17299}, {4285, 50087}, {4695, 18398}, {4849, 9957}, {5045, 21896}, {5145, 49497}, {5247, 25439}, {5400, 5734}, {5711, 8168}, {11010, 32912}, {24046, 34791}, {28234, 37699}, {31187, 31480}, {33136, 37719}, {37529, 47745}, {37530, 38665}, {37567, 39796}, {39742, 49498}
X(50575) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3214, 17749}, {1, 3216, 28370}, {145, 3293, 995}, {3240, 20050, 1}, {3241, 28370, 1}
X(50576) lies on these lines: {1, 17792}, {6, 3550}, {9, 3507}, {40, 511}, {42, 25304}, {43, 3056}, {69, 519}, {141, 33141}, {238, 10387}, {386, 16475}, {614, 25279}, {1716, 3688}, {2177, 15988}, {3679, 15985}, {3749, 22370}, {4263, 6184}, {4787, 21371}, {5847, 20018}, {24471, 49490}, {25144, 25502}, {26543, 32865}, {28369, 42042}
X(50577) lies on these lines: {2, 4263}, {20, 185}, {145, 21746}, {192, 519}, {385, 19544}, {386, 17379}, {573, 37683}, {1654, 10449}, {3210, 17364}, {3664, 17490}, {4357, 20168}, {4643, 20170}, {10453, 23659}, {17000, 19313}, {17331, 41839}, {20090, 24621}, {36744, 44352}
X(50577) = reflection of X(34282) in X(4263)
X(50577) = anticomplement of X(34282)
X(50577) = {X(4263),X(34282)}-harmonic conjugate of X(2)
X(50578) lies on these lines: {1, 51}, {10, 25279}, {36, 386}, {40, 511}, {519, 3869}, {978, 23638}, {986, 8679}, {2979, 3214}, {3616, 20962}, {3917, 6048}, {4646, 9037}, {5255, 37516}, {5687, 7186}, {11573, 24440}, {18178, 37716}, {23155, 24443}, {23157, 24046}, {49557, 50301}
X(50578) = crossdifference of every pair of points on line {46383, 48277}
X(50579) lies on these lines: {1, 22172}, {20, 185}, {72, 17363}, {81, 386}, {145, 3060}, {192, 29958}, {519, 3869}, {959, 3227}, {960, 17346}, {970, 37683}, {1043, 37516}, {2478, 3948}, {3210, 23154}, {3882, 37030}, {3884, 48839}, {4417, 18178}, {9534, 30054}, {9957, 48814}, {22076, 37652}, {30022, 34282}, {31034, 41723}, {34283, 35104}, {42450, 49470}, {48816, 49557}
X(50580) lies on these lines: {1, 5943}, {40, 511}, {42, 16980}, {56, 181}, {72, 519}, {474, 3030}, {956, 1682}, {986, 2810}, {2183, 4263}, {2276, 23630}, {2551, 10449}, {3056, 6765}, {3214, 3917}, {3271, 3295}, {3421, 10480}, {3688, 34790}, {3811, 10544}, {3819, 6048}, {3913, 37516}, {4385, 35104}, {4642, 23154}, {4646, 8679}, {12109, 49490}, {12607, 18178}, {14872, 40965}, {15803, 42043}, {16473, 20959}, {21075, 21334}, {29958, 37598}, {40966, 41229}
X(50581) lies on these lines: {1, 2}, {5, 33141}, {6, 979}, {9, 1500}, {21, 2177}, {31, 3871}, {37, 4662}, {40, 511}, {46, 32913}, {55, 5247}, {58, 3550}, {72, 37598}, {76, 3875}, {87, 1126}, {100, 1468}, {171, 5687}, {210, 37548}, {213, 3208}, {238, 3295}, {244, 3889}, {269, 5933}, {341, 872}, {354, 24174}, {355, 37529}, {405, 3750}, {442, 32865}, {500, 3654}, {517, 37699}, {518, 986}, {581, 11362}, {595, 2209}, {740, 4385}, {846, 41229}, {940, 2334}, {941, 3731}, {942, 24440}, {958, 37573}, {960, 4849}, {964, 32945}, {982, 3555}, {984, 1716}, {988, 6762}, {991, 43174}, {993, 33771}, {1043, 4281}, {1044, 2093}, {1047, 2947}, {1054, 3338}, {1064, 12245}, {1100, 21868}, {1203, 37610}, {1220, 3996}, {1254, 7672}, {1282, 1773}, {1330, 4660}, {1334, 37657}, {1376, 37607}, {1449, 17750}, {1453, 3749}, {1466, 9363}, {1475, 17756}, {1479, 36855}, {1697, 20683}, {1724, 3746}, {1738, 21620}, {1739, 18398}, {1740, 4649}, {1743, 2269}, {1745, 5903}, {1757, 12514}, {1834, 12607}, {2099, 37694}, {2176, 21904}, {2271, 2329}, {2276, 3780}, {2292, 3681}, {2321, 4270}, {2476, 33136}, {2551, 4878}, {2594, 24806}, {2663, 50314}, {2901, 22016}, {3057, 21870}, {3072, 44414}, {3073, 10679}, {3158, 5429}, {3247, 16589}, {3294, 9331}, {3303, 4383}, {3339, 4334}, {3340, 4551}, {3579, 4650}, {3689, 37539}, {3695, 33165}, {3697, 6051}, {3701, 32915}, {3702, 32931}, {3704, 49524}, {3714, 28581}, {3723, 25614}, {3725, 44720}, {3728, 3743}, {3729, 17499}, {3736, 49497}, {3737, 4770}, {3744, 16478}, {3752, 3976}, {3755, 13161}, {3795, 37590}, {3812, 21896}, {3813, 37662}, {3868, 4642}, {3873, 24443}, {3874, 49498}, {3876, 21805}, {3881, 24046}, {3896, 4696}, {3915, 32911}, {3916, 17601}, {3927, 49712}, {3944, 21077}, {3956, 27784}, {3983, 44307}, {3987, 5902}, {4050, 20970}, {4085, 16062}, {4187, 24217}, {4251, 7220}, {4252, 4421}, {4255, 12513}, {4256, 8666}, {4267, 15621}, {4272, 17299}, {4285, 17281}, {4322, 5435}, {4335, 5223}, {4339, 10460}, {4343, 5686}, {4360, 6376}, {4424, 5904}, {4641, 37568}, {4658, 18792}, {4663, 24696}, {4851, 20255}, {4852, 25102}, {4859, 17758}, {4865, 5100}, {4868, 49448}, {4968, 32860}, {5045, 17063}, {5082, 26098}, {5109, 50131}, {5119, 26893}, {5145, 49685}, {5192, 32943}, {5261, 42289}, {5264, 17977}, {5295, 49459}, {5400, 11522}, {5453, 5690}, {5814, 33076}, {6361, 24695}, {7718, 40976}, {7772, 50028}, {7982, 15488}, {9350, 17531}, {9355, 12705}, {9364, 34046}, {9709, 17122}, {9710, 17056}, {9798, 37576}, {10381, 11523}, {10436, 34282}, {10476, 45955}, {11010, 49500}, {11108, 16484}, {12699, 33096}, {13407, 17889}, {13740, 32941}, {16466, 37588}, {16474, 37522}, {16610, 17609}, {17054, 42871}, {17144, 37678}, {17151, 20888}, {17296, 21240}, {17298, 24190}, {17314, 21071}, {17319, 27269}, {17388, 21025}, {17717, 24390}, {17718, 24161}, {17754, 20963}, {18194, 49489}, {20162, 26687}, {21075, 24210}, {21746, 23841}, {23447, 24528}, {23853, 35206}, {24068, 49445}, {24214, 36854}, {24524, 33296}, {25294, 32925}, {25440, 37608}, {31327, 31993}, {31419, 33111}, {34612, 49745}, {37523, 40663}, {37549, 41711}, {37555, 37676}, {37663, 37722}, {39972, 43531}, {48812, 50164}, {48825, 49732}, {49743, 50301}
X(50581) = midpoint of X(8) and X(20018)
X(50581) = reflection of X(i) in X(j) for these {i,j}: {1, 386}, {986, 4646}, {10449, 10}
X(50581) = X(i)-Ceva conjugate of X(j) for these (i,j): {940, 3731}, {2334, 1}
X(50581) = X(513)-isoconjugate of X(43350)
X(50581) = X(39026)-Dao conjugate of X(43350)
X(50581) = crosspoint of X(4606) and X(7035)
X(50581) = crosssum of X(3248) and X(4790)
X(50581) = barycentric product X(1)*X(41839)
X(50581) = barycentric quotient X(i)/X(j) for these {i,j}: {101, 43350}, {41839, 75}
X(50581) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 43, 978}, {1, 200, 5293}, {1, 1698, 26102}, {1, 3216, 21214}, {1, 3293, 43}, {1, 5529, 19861}, {1, 6048, 2}, {1, 16569, 1125}, {1, 31855, 1698}, {1, 42043, 386}, {2, 3214, 6048}, {6, 3913, 5255}, {6, 20691, 3501}, {8, 42, 1}, {8, 19767, 10459}, {8, 26115, 31330}, {40, 3751, 1046}, {42, 10459, 19767}, {42, 45216, 41268}, {43, 21214, 3216}, {58, 8715, 3550}, {100, 1468, 37603}, {145, 1193, 1}, {145, 3240, 1193}, {976, 17016, 1}, {993, 33771, 37574}, {995, 3244, 1}, {1149, 3623, 1}, {1201, 3241, 1}, {1724, 3746, 8616}, {1834, 12607, 37716}, {2276, 3780, 21384}, {2594, 41687, 24806}, {3216, 21214, 978}, {3632, 5312, 1}, {3633, 5313, 1}, {3752, 34791, 3976}, {3931, 34790, 984}, {3935, 17016, 976}, {3938, 5262, 1}, {3957, 28082, 1}, {4255, 12513, 37617}, {10459, 19767, 1}, {15955, 22836, 1}, {21896, 49478, 3812}, {24440, 49490, 942}, {26115, 31330, 1698}, {30107, 40006, 17284}, {34772, 49487, 1}
X(50582) lies on these lines: {1, 2}, {7, 11851}, {65, 50289}, {75, 49734}, {192, 950}, {257, 17363}, {377, 48627}, {452, 17261}, {511, 3868}, {894, 5716}, {1697, 49704}, {1837, 32926}, {1897, 5090}, {2893, 3875}, {3212, 3879}, {3550, 49609}, {3662, 7270}, {3710, 17339}, {3891, 5086}, {3905, 7179}, {3913, 41346}, {4389, 50050}, {4440, 9579}, {4514, 37614}, {5016, 27184}, {5135, 49681}, {5175, 30699}, {5434, 34860}, {5691, 49446}, {5794, 32922}, {5795, 49527}, {7772, 49778}, {10106, 17480}, {11518, 17300}, {11520, 17778}, {12527, 31302}, {12635, 33071}, {12642, 28386}, {16496, 43749}, {17116, 50408}, {17242, 17743}, {17247, 26117}, {20911, 34282}, {24391, 37683}, {24524, 44153}, {31995, 50431}, {33070, 34195}, {49745, 50128}
X(50582) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 10, 29634}, {145, 12649, 1999}, {145, 29840, 1}, {3244, 49613, 1}, {3710, 17697, 17339}, {7270, 37549, 3662}
X(50583) lies on these lines: {1, 3819}, {10, 21746}, {40, 511}, {51, 3214}, {55, 386}, {65, 519}, {71, 4263}, {181, 5687}, {209, 37568}, {674, 4646}, {986, 9052}, {1469, 6765}, {2177, 22076}, {2550, 10449}, {3216, 28353}, {3293, 23638}, {3688, 3931}, {3780, 23630}, {3812, 49725}, {3913, 4259}, {3976, 40649}, {4260, 5255}, {4385, 6007}, {4660, 10381}, {4849, 42450}, {5082, 10473}, {5943, 6048}, {8715, 10974}, {9710, 18165}, {12109, 24440}, {12514, 20683}, {17784, 20018}, {37567, 39796}
X(50584) lies on these lines: {1, 28350}, {40, 511}, {43, 5943}, {75, 519}, {238, 386}, {978, 39543}, {1002, 25570}, {1743, 2276}, {2293, 16476}, {3240, 23659}, {3809, 22167}, {4307, 20018}, {4650, 41430}, {17331, 21805}, {17349, 23634}, {22277, 24696}, {24220, 33141}
X(50584 = {X(1045),X(3779)}-harmonic conjugate of X(12782)
X(50585) lies on these lines: {1, 3917}, {31, 35}, {40, 511}, {51, 6048}, {519, 3868}, {674, 986}, {942, 50301}, {3060, 3214}, {3178, 25308}, {3295, 3792}, {3550, 10974}, {3874, 50289}, {4259, 5255}, {4645, 10449}, {4646, 9047}, {5300, 47033}, {8715, 41329}, {9780, 20961}, {11573, 49490}, {17748, 25306}, {18180, 32865}, {20018, 20101}, {33141, 37536}
X(50586) lies on these lines: {1, 28375}, {7, 17143}, {20, 185}, {21, 386}, {72, 17333}, {145, 2979}, {377, 5208}, {387, 3794}, {519, 3868}, {942, 48816}, {1043, 4259}, {3555, 50289}, {3786, 13725}, {3881, 48868}, {4195, 4260}, {4201, 10477}, {5692, 12579}, {10461, 37467}, {12109, 17490}, {16980, 20012}, {17378, 34791}, {22836, 30362}, {26051, 35612}, {31424, 42043}, {35998, 40571}
X(50587) lies on these lines: {1, 2}, {6, 8715}, {35, 16948}, {37, 4015}, {44, 4263}, {71, 16670}, {72, 4868}, {171, 1126}, {209, 37568}, {210, 3743}, {227, 12432}, {404, 16474}, {474, 2334}, {511, 3579}, {516, 37699}, {581, 43174}, {740, 4066}, {758, 4646}, {872, 3993}, {942, 22278}, {1089, 3896}, {1100, 1574}, {1203, 3871}, {1215, 42031}, {1500, 21904}, {1724, 2177}, {1918, 16477}, {2163, 37307}, {2292, 4134}, {2321, 4272}, {2594, 4848}, {2650, 3919}, {2901, 4125}, {3159, 4090}, {3454, 4085}, {3647, 4689}, {3671, 4551}, {3678, 3931}, {3697, 37593}, {3699, 41813}, {3736, 49685}, {3740, 27784}, {3746, 32911}, {3752, 3881}, {3755, 21077}, {3873, 24167}, {3879, 24170}, {3918, 21896}, {3934, 4852}, {3971, 4065}, {3997, 20691}, {4006, 21840}, {4067, 4424}, {4084, 4642}, {4255, 8666}, {4270, 17355}, {4285, 50115}, {4301, 37732}, {4356, 4878}, {4647, 46897}, {4705, 4794}, {4856, 5105}, {4970, 24068}, {5220, 22312}, {5247, 33771}, {5396, 11362}, {6043, 15792}, {6538, 21803}, {6684, 37698}, {6701, 21949}, {6796, 44414}, {7173, 39583}, {7373, 8688}, {10176, 37548}, {10593, 44411}, {12607, 48847}, {16466, 25439}, {16666, 21858}, {18398, 24168}, {19925, 37529}, {22300, 50193}, {23638, 31757}, {24046, 49490}, {24176, 49479}, {24387, 37662}, {24440, 33815}, {24597, 31452}, {31730, 48916}, {32141, 39523}, {33136, 37693}, {34282, 41847}, {35468, 36277}, {37582, 41682}, {37619, 48936}, {37651, 37720}, {49732, 49743}
X(50587) = X(25417)-Ceva conjugate of X(37)
X(50587) = X(58)-isoconjugate of X(39711)
X(50587) = X(10)-Dao conjugate of X(39711)
X(50587) = barycentric product X(i)*X(j) for these {i,j}: {37, 17393}, {100, 48551}, {1018, 48079}, {3952, 48011}
X(50587) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 39711}, {17393, 274}, {48011, 7192}, {48079, 7199}, {48551, 693}
X(50587) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 43, 17749}, {1, 899, 19862}, {1, 3214, 10}, {1, 3216, 28352}, {1, 3293, 3214}, {1, 17749, 1125}, {1, 27627, 15808}, {1, 28352, 551}, {42, 3214, 1}, {42, 3293, 10}, {2650, 3987, 3919}, {3755, 21077, 36250}, {3931, 4849, 3678}, {20691, 20970, 3997}
X(50588) lies on these lines: {1, 2}, {511, 550}, {579, 4856}, {1043, 48866}, {1330, 48836}, {3454, 48847}, {3988, 49456}, {4065, 5692}, {4067, 4970}, {4286, 50131}, {4464, 18147}, {5132, 8666}, {5156, 49685}, {9569, 10454}, {16287, 25439}, {16709, 34282}, {18137, 49678}, {19526, 19750}, {19543, 28234}, {35999, 48696}, {41014, 48843}
X(50588) = midpoint of X(386) and X(20018)
X(50588) = reflection of X(10449) in X(20108)
X(50588) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {386, 10449, 20108}
X(50589) lies on these lines: {1, 2}, {3, 49681}, {58, 49684}, {596, 50307}, {3430, 5882}, {3678, 49527}, {3710, 5315}, {3879, 3881}, {3891, 12047}, {3914, 43993}, {4255, 49679}, {4865, 23537}, {4914, 13728}, {5846, 37592}, {12609, 32922}, {12699, 49453}, {13407, 33070}, {15172, 49462}, {21077, 33071}, {21616, 32926}, {41014, 49465}
X(50589) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 32866, 10}
X(50590) lies on these lines: {1, 2}, {3, 49497}, {58, 49685}, {511, 31728}, {596, 49535}, {2321, 20970}, {2901, 4090}, {3169, 4253}, {3678, 3993}, {3707, 4263}, {4065, 4134}, {4085, 41014}, {4255, 49680}, {4663, 24850}, {4727, 28622}, {4753, 31445}, {4970, 5904}, {5044, 49471}, {5266, 49489}, {5882, 15489}, {8715, 19762}, {20691, 23447}, {21071, 21904}, {21080, 49452}, {22278, 34791}, {22316, 49483}, {37529, 45305}
X(50590) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3216, 28360}, {1, 4685, 10}, {42, 20012, 4685}, {43, 35633, 46827}
X(50591) lies on these lines: {1, 17792}, {3, 6}, {42, 1403}, {55, 22418}, {56, 3778}, {69, 4201}, {141, 1834}, {142, 17054}, {387, 10519}, {518, 986}, {519, 599}, {694, 39967}, {936, 21892}, {940, 37099}, {960, 1716}, {984, 3507}, {990, 9620}, {1104, 27626}, {1191, 10387}, {1193, 3056}, {1352, 48837}, {1738, 5794}, {1818, 2277}, {2176, 3781}, {2273, 3220}, {3192, 12294}, {3662, 7270}, {3751, 3928}, {3905, 4357}, {4191, 20966}, {5480, 37662}, {5732, 9593}, {7191, 25308}, {7481, 8705}, {9534, 15985}, {16969, 37819}, {17065, 25524}, {17597, 33073}, {18906, 37678}, {19765, 40432}, {19767, 28369}, {20108, 47355}, {25354, 50410}, {30940, 34282}, {37467, 37676}, {48847, 48876}, {49529, 49609}
X(50591) = midpoint of X(69) and X(20018)
X(50591) = reflection of X(i) in X(j) for these {i,j}: {6, 386}, {10449, 141}
X(50591) = {X(6),X(31884)}-harmonic conjugate of X(4252)
X(50592) lies on these lines: {1, 22172}, {3, 6}, {42, 3060}, {256, 49488}, {519, 751}, {726, 34283}, {986, 17770}, {1654, 10449}, {1707, 42043}, {1757, 12514}, {3664, 24046}, {3670, 17364}, {3764, 4649}, {4443, 49489}, {4476, 37657}, {4646, 15310}, {4850, 50003}, {5224, 30939}, {5739, 35623}, {15955, 31394}, {17381, 20108}, {20966, 37685}, {37662, 48934}, {48837, 48878}
X(50592) = reflection of X(386) in X(4263)
X(50592) = {X(4277),X(37516)}-harmonic conjugate of X(3736)
X(50593) lies on these lines: {1, 3060}, {3, 6}, {10, 25308}, {43, 31737}, {143, 50317}, {519, 3869}, {960, 48839}, {982, 23156}, {986, 2392}, {1698, 20962}, {1993, 17104}, {2895, 5046}, {2979, 3216}, {3678, 17346}, {3884, 48814}, {3917, 17749}, {3953, 23155}, {3976, 23157}, {4193, 17182}, {5400, 11444}, {5890, 48897}, {7186, 25440}, {9037, 37592}, {9957, 48841}, {11010, 49500}, {11412, 37732}, {11573, 24046}, {15680, 20018}, {17566, 20108}, {21849, 48855}, {31034, 35637}, {48868, 49557}
X(50593) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5752, 37516, 58}
X(50594) lies on these lines: {1, 51}, {3, 6}, {5, 18178}, {9, 4158}, {10, 23638}, {35, 26890}, {60, 1994}, {72, 519}, {209, 37568}, {993, 1682}, {1211, 4187}, {1397, 39582}, {1401, 23156}, {1724, 22076}, {1829, 37226}, {2347, 3682}, {2478, 3948}, {2915, 44085}, {3056, 3811}, {3060, 19767}, {3216, 3917}, {3271, 5248}, {3670, 23154}, {3678, 3688}, {3743, 15049}, {3752, 11573}, {3819, 17749}, {3890, 14020}, {3909, 4202}, {3931, 42450}, {4424, 42448}, {4719, 9037}, {5044, 17330}, {5119, 26893}, {5453, 5946}, {5462, 50317}, {5562, 18163}, {5718, 18180}, {5810, 6929}, {5836, 37150}, {6872, 20018}, {7483, 18191}, {8679, 37592}, {10108, 17392}, {10393, 11436}, {10478, 19754}, {10544, 22836}, {13747, 20108}, {14531, 22392}, {14855, 48916}, {17104, 34986}, {19366, 45126}, {21334, 21616}, {21746, 31757}, {23841, 30116}, {31792, 48846}, {34466, 37646}, {37536, 37662}
X(50594) = crossdifference of every pair of points on line {523, 46383}
X(50594) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 5752, 10974}, {581, 4266, 19763}
X(50595) lies on these lines: {3, 6}, {141, 20108}, {387, 14561}, {519, 597}, {1203, 2330}, {1469, 5313}, {1834, 19130}, {2108, 42043}, {3056, 5312}, {3216, 28369}, {3618, 10449}, {5292, 38317}, {5476, 48857}, {5480, 48847}, {7804, 24267}, {10477, 19246}, {11175, 39961}, {14994, 37678}, {17499, 41622}, {24206, 37662}, {37594, 41656}, {48837, 48901}
X(50595) = midpoint of X(6) and X(386)
X(50595) = reflection of X(141) in X(20108)
X(50595) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 2271, 5039}, {39, 4279, 48886}
X(50596) lies on these lines: {1, 28350}, {3, 6}, {42, 3917}, {274, 3945}, {291, 39980}, {519, 3696}, {995, 39543}, {1193, 21746}, {1206, 23653}, {1500, 3781}, {1834, 24220}, {3522, 45784}, {4646, 29311}, {4648, 10449}, {11112, 50307}, {17337, 20108}, {37662, 48888}, {48837, 48902}, {48847, 48934}
X(50596) = midpoint of X(20018) and X(34282)
X(50596) = reflection of X(4263) in X(386)
X(50596) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3736, 4260, 39}
X(50597) lies on these lines: {1, 3917}, {3, 6}, {46, 32913}, {51, 3216}, {60, 6636}, {65, 519}, {181, 25440}, {209, 3916}, {377, 5208}, {674, 37592}, {993, 10822}, {1125, 21746}, {1437, 5347}, {1469, 3811}, {1780, 16064}, {1834, 37536}, {2194, 20833}, {2646, 49480}, {2979, 19767}, {3293, 16980}, {3792, 37573}, {4190, 20018}, {4719, 9047}, {5045, 17392}, {5292, 37521}, {5447, 50317}, {5482, 37646}, {5784, 22011}, {5891, 48903}, {5943, 17749}, {7483, 20108}, {8728, 18165}, {10381, 48835}, {10441, 48837}, {12109, 24046}, {12609, 49676}, {15556, 30493}, {17733, 39780}, {18178, 48847}, {20961, 27627}, {36987, 48897}, {37522, 40952}, {37732, 45186}
X(50597) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 4259, 10974}, {4256, 41329, 970}, {12109, 40649, 24046}
X(50598) lies on these lines: {1, 20765}, {3, 6}, {69, 37148}, {81, 11358}, {86, 2049}, {171, 42043}, {238, 16418}, {332, 33745}, {387, 15973}, {405, 27644}, {519, 4923}, {940, 18792}, {992, 16846}, {999, 2274}, {1010, 17379}, {1193, 28383}, {1203, 36635}, {1613, 40734}, {1740, 4649}, {2309, 16466}, {3167, 22130}, {9909, 44118}, {10458, 16345}, {11108, 27623}, {13588, 37685}, {16395, 17126}, {17000, 19311}, {17259, 20108}, {17277, 19273}, {17349, 19270}, {19276, 46922}, {19533, 19767}, {19757, 27660}, {23092, 23654}
X(50598) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3736, 3}, {6, 4255, 4279}, {1740, 4649, 5711}
X(50599) lies on these lines: {1, 2979}, {3, 6}, {22, 17104}, {51, 17749}, {320, 34282}, {519, 3868}, {942, 48868}, {978, 31757}, {994, 17647}, {2475, 10449}, {2476, 33172}, {3060, 3216}, {3624, 20961}, {3754, 48816}, {3792, 5248}, {3794, 20083}, {3878, 37038}, {3881, 17378}, {5044, 16590}, {9047, 37592}, {10627, 50317}, {17676, 18417}, {20018, 20086}, {23039, 48903}, {23157, 49490}, {31738, 37529}, {37521, 45939}, {37567, 39796}
X(50599) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4259, 37482, 58}
X(50600) lies on these lines: {1, 22214}, {3, 6}, {193, 10449}, {519, 1992}, {595, 611}, {995, 1469}, {1724, 15988}, {1834, 21850}, {3017, 20423}, {3192, 6403}, {3242, 4930}, {3293, 25304}, {3618, 20108}, {5292, 14853}, {6210, 15953}, {10479, 15983}, {14561, 45939}, {18583, 37646}, {24046, 24471}, {25898, 43531}, {37662, 48876}
X(50600) = midpoint of X(193) and X(10449)
X(50600) = reflection of X(386) in X(6)
X(50600) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 4252, 5050}, {6, 33863, 5034}
X(50601) lies on these lines: {5, 141}, {10, 51}, {21, 386}, {44, 4263}, {72, 519}, {80, 5016}, {2895, 5046}, {3060, 10479}, {3688, 4075}, {3754, 37150}, {3794, 45939}, {3831, 31737}, {4015, 17330}, {4271, 8715}, {5752, 48863}, {7483, 20108}, {8240, 22836}, {10974, 48866}, {13724, 30144}, {13740, 41329}
X(50602) lies on these lines: {37, 386}, {65, 42031}, {72, 519}, {210, 3743}, {321, 3868}, {511, 22036}, {2321, 10974}, {3678, 3993}, {3713, 27802}, {3881, 49479}, {3931, 14973}, {3995, 20018}, {5295, 5836}, {5439, 31993}, {5752, 17299}, {5784, 22011}, {10108, 50125}, {21061, 31424}
X(50603) lies on these lines: {1, 28356}, {8, 20962}, {10, 5943}, {72, 519}, {238, 386}, {511, 946}, {1125, 21746}, {1479, 4388}, {2887, 25639}, {3056, 17733}, {3678, 3883}, {4857, 18417}, {5044, 50297}, {5752, 32941}, {10974, 49482}, {18180, 21242}, {26098, 35632}
X(50604) lies on these lines: {1, 2}, {6, 8666}, {21, 5315}, {31, 5267}, {38, 4067}, {39, 3997}, {58, 37617}, {65, 26740}, {73, 4315}, {81, 5563}, {106, 931}, {214, 37539}, {392, 3743}, {501, 2363}, {511, 1385}, {517, 4719}, {758, 37592}, {872, 49510}, {941, 41418}, {942, 34434}, {946, 36250}, {993, 16466}, {999, 23361}, {1064, 4297}, {1100, 4263}, {1191, 5248}, {1203, 2975}, {1449, 2183}, {1450, 37558}, {1457, 3671}, {1491, 48294}, {1834, 24387}, {2176, 25092}, {2274, 33682}, {2321, 5153}, {2646, 49480}, {2650, 3953}, {2802, 4646}, {3057, 4868}, {3264, 17393}, {3585, 33107}, {3663, 17139}, {3666, 3878}, {3670, 4084}, {3677, 12559}, {3736, 49482}, {3745, 17614}, {3752, 3754}, {3755, 49600}, {3813, 48847}, {3825, 37715}, {3884, 3931}, {3898, 37548}, {3901, 4392}, {3919, 24443}, {3946, 13464}, {3988, 49515}, {4003, 4018}, {4255, 8715}, {4256, 5255}, {4270, 4856}, {4298, 10571}, {4850, 5903}, {5105, 17355}, {5109, 50115}, {5253, 37559}, {5258, 32911}, {5396, 5882}, {5443, 33133}, {5710, 25440}, {5730, 17599}, {5902, 24167}, {6176, 15178}, {7280, 17126}, {8692, 16866}, {9619, 16972}, {11263, 23536}, {13370, 17074}, {13607, 37698}, {16483, 19765}, {17061, 37737}, {17152, 25599}, {17351, 32450}, {17394, 34282}, {17448, 20970}, {17609, 43220}, {21620, 34586}, {22045, 34587}, {24046, 33815}, {25405, 38472}, {25439, 37542}, {28236, 37699}, {33071, 36974}, {33771, 37588}, {37573, 40091}, {37620, 48917}
X(50604) = midpoint of X(1) and X(386)
X(50604) = reflection of X(10) in X(20108)
X(50604) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 42, 3244}, {1, 78, 30145}, {1, 614, 30143}, {1, 978, 30116}, {1, 995, 1125}, {1, 997, 30142}, {1, 1193, 10}, {1, 1201, 551}, {1, 3216, 10459}, {1, 5262, 49682}, {1, 5312, 145}, {1, 5313, 8}, {1, 34772, 49686}, {978, 30116, 3634}, {1193, 10459, 3216}, {3216, 10459, 10}
X(50605) lies on these lines: {1, 2}, {3, 48863}, {4, 48835}, {5, 141}, {35, 32918}, {36, 35999}, {38, 1089}, {39, 21024}, {55, 16302}, {58, 13740}, {72, 30818}, {75, 24046}, {76, 16887}, {79, 33067}, {121, 9711}, {140, 6176}, {191, 32930}, {312, 3159}, {321, 3670}, {333, 13741}, {405, 37660}, {515, 19543}, {549, 48859}, {579, 17355}, {594, 1574}, {595, 32942}, {596, 982}, {726, 4066}, {940, 43531}, {942, 44417}, {946, 31778}, {958, 16286}, {964, 10457}, {966, 17559}, {984, 4075}, {993, 16287}, {996, 12513}, {999, 5793}, {1043, 4256}, {1078, 33954}, {1150, 1724}, {1191, 5774}, {1203, 32944}, {1211, 4187}, {1213, 4263}, {1215, 3874}, {1376, 16414}, {1393, 6358}, {1479, 26034}, {1573, 21025}, {1834, 48843}, {2049, 37674}, {2051, 10441}, {2140, 21240}, {2276, 21070}, {2321, 4261}, {2476, 33172}, {2887, 25639}, {2901, 3666}, {3336, 4418}, {3452, 34831}, {3579, 49484}, {3663, 44140}, {3701, 46909}, {3702, 4424}, {3714, 37592}, {3734, 49129}, {3739, 39564}, {3746, 32943}, {3752, 5295}, {3814, 50362}, {3821, 36250}, {3824, 3834}, {3825, 3846}, {3836, 3841}, {3923, 16574}, {3936, 37693}, {3953, 4968}, {4015, 49457}, {4065, 32915}, {4193, 17182}, {4195, 4257}, {4201, 48836}, {4203, 4278}, {4234, 48865}, {4251, 26244}, {4252, 11354}, {4267, 19243}, {4286, 17281}, {4357, 18147}, {4363, 5708}, {4429, 29484}, {4438, 16301}, {4647, 24443}, {4653, 19270}, {4660, 29492}, {4721, 24690}, {4857, 32947}, {4894, 33074}, {5132, 8715}, {5156, 49482}, {5165, 50115}, {5204, 16400}, {5224, 30939}, {5235, 17536}, {5241, 17575}, {5248, 32916}, {5259, 32917}, {5263, 29437}, {5264, 24552}, {5267, 16452}, {5439, 31993}, {5692, 25591}, {5737, 11108}, {5743, 17527}, {5745, 16290}, {5786, 19517}, {5791, 17279}, {5883, 49598}, {5904, 32931}, {5955, 15571}, {6245, 12618}, {6532, 17063}, {6693, 17698}, {6703, 50318}, {7283, 24627}, {7504, 30831}, {7741, 25760}, {7761, 36685}, {7800, 36674}, {7865, 36729}, {8258, 24295}, {9708, 16291}, {10176, 25079}, {10408, 10473}, {10476, 50037}, {11263, 25385}, {12571, 45305}, {12572, 14058}, {13478, 37415}, {15171, 44419}, {15488, 37365}, {16453, 25440}, {16552, 27040}, {16607, 17046}, {16842, 19732}, {16853, 17259}, {17143, 29454}, {17205, 34284}, {17289, 29453}, {17595, 50044}, {17686, 29473}, {17758, 30945}, {18046, 32784}, {18099, 29568}, {18140, 30966}, {18398, 32771}, {18792, 27145}, {18840, 36682}, {19646, 48937}, {19792, 23537}, {21020, 28611}, {21067, 49509}, {21071, 25092}, {21077, 49511}, {21208, 33945}, {24165, 24167}, {24174, 28612}, {24275, 33863}, {24430, 44040}, {24718, 45324}, {24900, 48284}, {25526, 37633}, {25961, 41859}, {26064, 37162}, {26819, 39748}, {32772, 37559}, {32861, 41822}, {33159, 41681}, {33297, 37678}, {33953, 37670}, {36974, 37717}, {37582, 50054}, {37620, 44039}, {37662, 41014}, {47694, 50337}
X(50605) = midpoint of X(i) and X(j) for these {i,j}: {386, 10449}, {3714, 37592}, {10476, 50037}
X(50605) = reflection of X(386) in X(20108)
X(50605) = complement of X(386)
X(50605) = anticomplement of X(20108)
X(50605) = complement of the isogonal conjugate of X(43531)
X(50605) = X(i)-complementary conjugate of X(j) for these (i,j): {513, 5515}, {667, 39016}, {835, 513}, {2214, 2}, {2217, 34281}, {37218, 3835}, {43531, 10}, {43927, 11}
X(50605) = crossdifference of every pair of points on line {649, 3050}
X(50605) = barycentric product X(10)*X(27163)
X(50605) = barycentric quotient X(27163)/X(86)
X(50605) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1698, 26115}, {2, 8, 3216}, {2, 386, 20108}, {2, 5292, 20083}, {2, 9534, 17749}, {2, 10449, 386}, {2, 10479, 10}, {5, 141, 3454}, {10, 3840, 1125}, {10, 46827, 3634}, {10, 49993, 1698}, {38, 1089, 24068}, {58, 13740, 48866}, {75, 24046, 24176}, {1150, 5192, 1724}, {1698, 31330, 10}, {3741, 3831, 10}, {13740, 14829, 58}, {17135, 26030, 3293}, {17698, 37646, 6693}, {17748, 49560, 21081}, {21240, 21264, 2140}, {26102, 31855, 995}, {26115, 29824, 1}, {27020, 31027, 40006}, {29827, 30942, 3840}, {30942, 31330, 29824}, {30957, 31339, 3624}
X(50606) lies on these lines: {1, 2}, {3, 17299}, {58, 2321}, {511, 22036}, {594, 37594}, {1770, 4365}, {3159, 4416}, {3175, 49716}, {3723, 50409}, {3943, 31445}, {4007, 37554}, {4035, 24160}, {4102, 50053}, {4104, 41814}, {4252, 50087}, {4371, 17582}, {4527, 24850}, {4686, 24470}, {5044, 17362}, {5295, 49734}, {6147, 17374}, {11110, 17315}, {12047, 32852}, {12609, 32846}, {12699, 47353}, {17229, 17698}, {17296, 24159}, {17372, 21245}, {21616, 32861}, {42031, 50307}
X(50607) lies on these lines: {1, 2}, {3, 49688}, {58, 49529}, {72, 4030}, {405, 30615}, {908, 4894}, {1770, 17165}, {2271, 17299}, {2321, 4251}, {3430, 11362}, {3678, 3883}, {3710, 3746}, {3717, 5248}, {3967, 15171}, {4255, 49690}, {4514, 21616}, {4533, 41002}, {4696, 10572}, {5014, 12047}, {5015, 21077}, {5266, 49524}, {5300, 13407}, {7772, 50026}, {9053, 37592}, {12609, 32850}, {23537, 32920}, {23850, 37577}
X(50608) lies on these lines: {1, 2}, {3, 23379}, {4, 43164}, {21, 32943}, {38, 3702}, {39, 2321}, {58, 49482}, {75, 3976}, {141, 3813}, {210, 25079}, {314, 3663}, {354, 49598}, {404, 32945}, {442, 21242}, {496, 3846}, {511, 946}, {516, 10476}, {594, 16604}, {596, 42027}, {740, 37592}, {962, 35621}, {986, 4673}, {988, 3886}, {1043, 37617}, {1058, 50295}, {1107, 21071}, {1150, 3915}, {1211, 37722}, {1215, 3555}, {1330, 33106}, {1468, 24552}, {1764, 5493}, {2140, 21255}, {2292, 46909}, {2887, 24390}, {3159, 22016}, {3295, 32916}, {3303, 37660}, {3333, 50314}, {3338, 3980}, {3454, 24387}, {3671, 10473}, {3678, 49510}, {3681, 25591}, {3686, 21769}, {3697, 24003}, {3750, 19270}, {3775, 21257}, {3817, 39550}, {3836, 31419}, {3871, 32918}, {3878, 14058}, {3881, 49479}, {3889, 32771}, {3902, 4642}, {3923, 44421}, {3931, 6682}, {3950, 25092}, {3953, 4647}, {4011, 41229}, {4135, 24068}, {4202, 33136}, {4252, 48805}, {4253, 17355}, {4255, 49460}, {4263, 5257}, {4297, 37425}, {4301, 10441}, {4315, 10475}, {4342, 10480}, {4357, 34282}, {4432, 31445}, {4441, 24214}, {4655, 12699}, {4719, 28581}, {5044, 49457}, {5045, 24325}, {5100, 33079}, {5247, 32942}, {5255, 14829}, {5263, 37607}, {5266, 49473}, {5289, 34831}, {5542, 35620}, {5837, 34589}, {8666, 19762}, {10371, 17721}, {10465, 28164}, {10471, 17205}, {10477, 49505}, {11110, 16484}, {11362, 15489}, {12047, 33064}, {12053, 21334}, {12545, 31964}, {12609, 49676}, {13407, 25385}, {15825, 30331}, {16062, 33141}, {16466, 32853}, {17050, 30945}, {17393, 41849}, {17448, 21024}, {17474, 26035}, {17600, 41813}, {17609, 31993}, {19804, 31327}, {20257, 21240}, {20888, 24215}, {20911, 24172}, {21020, 46190}, {21628, 43159}, {21629, 35635}, {21630, 38484}, {22167, 23414}, {23853, 25440}, {24161, 33124}, {24850, 49484}, {27318, 48628}, {32865, 33833}, {33939, 49521}, {34791, 44417}, {34860, 42029}, {35626, 49600}, {41014, 50315}, {49728, 49736}
X(50608) = midpoint of X(i) and X(j) for these {i,j}: {1, 10449}, {986, 4673}
X(50608) = reflection of X(386) in X(1125)
X(50608) = X(i)-complementary conjugate of X(j) for these (i,j): {513, 38961}, {43350, 513}
X(50608) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3632, 20037}, {1, 3741, 10}, {1, 10453, 35633}, {1, 19863, 43223}, {2, 8, 6048}, {8, 3831, 10}, {8, 26094, 899}, {8, 30942, 3831}, {10, 3840, 46827}, {10, 49627, 29655}, {596, 42031, 50117}, {1201, 31136, 8}, {3953, 4647, 24165}, {19863, 43223, 19862}, {26801, 31027, 29960}
X(50609) lies on these lines: {5, 141}, {6, 10449}, {182, 48863}, {386, 3589}, {519, 597}, {1104, 17353}, {1469, 30942}, {3416, 37717}, {3507, 33159}, {3618, 20018}, {3741, 20545}, {3831, 17792}, {4136, 5750}, {5743, 50440}, {10479, 15985}, {25144, 46827}, {48835, 48901}
X(50609) = midpoint of X(6) and X(10449)
X(50609) = reflection of X(386) in X(3589)
X(50610) lies on these lines: {5, 141}, {10, 3917}, {65, 519}, {81, 386}, {1215, 23156}, {2475, 10449}, {2594, 25440}, {2979, 10479}, {3741, 31737}, {3840, 31757}, {3909, 37693}, {10441, 48835}, {13747, 20108}, {14829, 41329}, {15049, 25079}, {18178, 48843}, {30034, 30172}, {37482, 48863}
X(50611) lies on these lines: {6, 519}, {69, 33106}, {141, 3829}, {386, 38049}, {511, 946}, {3056, 3741}, {3507, 17353}, {3618, 42043}, {3840, 17792}, {5847, 10449}, {10387, 32916}, {15983, 31136}, {15988, 32943}, {16475, 20018}, {21242, 26543}, {25304, 30942}, {28369, 42057}
X(50612) lies on these lines: {1, 256}, {6, 11194}, {69, 519}, {141, 37716}, {386, 988}, {388, 24231}, {518, 986}, {982, 1465}, {1350, 5255}, {3094, 3501}, {3098, 3550}, {3242, 10912}, {3507, 49448}, {3749, 22097}, {5587, 24230}, {10449, 13161}, {12588, 37708}, {24248, 39898}, {31670, 33106}, {37676, 42043}, {45989, 45990}
X(50612) = reflection of X(i) in X(j) for these {i,j}: {3751, 386}, {10449, 49511}
X(50613) lies on these lines: {1, 256}, {9, 3507}, {10, 7155}, {43, 23659}, {87, 3778}, {192, 519}, {350, 17272}, {386, 2309}, {573, 3550}, {751, 872}, {894, 4787}, {982, 49537}, {986, 15310}, {1740, 3764}, {1742, 17596}, {1743, 2276}, {1757, 12514}, {3122, 24661}, {3551, 3663}, {3679, 17787}, {3731, 4876}, {3944, 45305}, {4443, 18194}, {5255, 48875}, {10446, 33106}, {10449, 21299}, {16571, 24478}, {17065, 25528}, {17331, 33889}, {17379, 23633}, {17591, 29353}, {24598, 36646}, {25304, 40790}, {37617, 48908}, {39742, 50128}
X(50613) = crossdifference of every pair of points on line {3287, 48323}
X(50613) = {X(256),X(3056)}-harmonic conjugate of X(1)
X(50614) lies on these lines: {1, 256}, {4, 3663}, {9, 386}, {238, 16418}, {519, 4356}, {936, 21796}, {971, 37592}, {984, 1716}, {1008, 3729}, {1864, 3666}, {3677, 4654}, {3731, 16850}, {3997, 5756}, {4263, 16517}, {4353, 45305}, {4357, 10449}, {6211, 17594}, {16290, 27626}, {17247, 26117}, {17257, 20018}, {28606, 44694}, {32784, 37715}, {37474, 37617}
X(50614) = {X(1),X(256)}-harmonic conjugate of X(6210)
X(50615) lies on these lines: {1, 256}, {6, 8666}, {182, 37617}, {355, 24212}, {386, 518}, {519, 599}, {3098, 5255}, {3550, 14810}, {3677, 4551}, {4263, 16973}, {5252, 37549}, {5725, 21620}, {17597, 17723}, {20108, 38047}, {24206, 37716}, {33106, 48901}, {33895, 49465}
X(50616) lies on these lines: {1, 256}, {8, 23659}, {9, 1500}, {238, 386}, {516, 986}, {519, 751}, {553, 982}, {573, 5255}, {950, 37598}, {983, 3746}, {988, 1742}, {991, 37617}, {1125, 41886}, {1386, 4443}, {3550, 48886}, {3664, 3976}, {3764, 5263}, {3923, 12782}, {4283, 50300}, {4357, 34282}, {4676, 21035}, {8616, 40984}, {10449, 15824}, {10877, 37539}, {13161, 45305}, {15310, 37592}, {16475, 24575}, {17065, 24923}, {17591, 29349}, {18046, 32784}, {24478, 50314}, {29712, 33165}, {33106, 48902}, {37716, 48888}
X(50617) lies on these lines: {1, 256}, {10, 25306}, {31, 35}, {56, 7186}, {80, 5016}, {519, 3869}, {960, 50296}, {970, 3550}, {984, 42450}, {995, 31737}, {1191, 3792}, {1201, 2979}, {1479, 4388}, {1682, 37574}, {3060, 10459}, {3617, 20962}, {3917, 21214}, {3976, 11573}, {4294, 20018}, {5119, 26893}, {5255, 5752}, {7741, 25760}, {7998, 28352}, {8616, 22076}, {10441, 33106}, {10822, 16468}, {18178, 33141}, {28370, 33884}, {29958, 49448}, {30116, 31757}, {31778, 37717}, {33104, 41723}, {37482, 37617}, {48825, 49557}
X(50617) = crossdifference of every pair of points on line {3287, 48275}
X(50617) = {X(1),X(6210)}-harmonic conjugate of X(30362)
X(50618) lies on these lines: {1, 256}, {21, 386}, {30, 986}, {500, 37617}, {519, 2292}, {846, 41229}, {982, 49745}, {984, 49728}, {988, 48897}, {3293, 18235}, {3550, 35203}, {3670, 4292}, {3931, 17611}, {3953, 49744}, {3976, 49743}, {4220, 37522}, {4263, 16552}, {4424, 10572}, {5255, 48882}, {7283, 17741}, {8229, 37693}, {9959, 37548}, {10449, 26117}, {10950, 24430}, {11115, 20966}, {12782, 50164}, {17596, 37425}, {24174, 50169}, {24440, 49734}, {24443, 50171}, {33106, 48899}, {37599, 48926}, {37716, 48887}, {37717, 46704}, {41813, 50255}
X(50619) lies on these lines: {1, 28356}, {4, 69}, {8, 3060}, {21, 386}, {51, 9534}, {519, 3869}, {674, 4385}, {960, 48814}, {1043, 5752}, {1479, 35614}, {1757, 12514}, {1812, 4222}, {2476, 33172}, {3678, 48839}, {3714, 9047}, {3794, 5292}, {3884, 48841}, {4195, 10974}, {4259, 13740}, {4680, 5086}, {6872, 20018}, {7283, 26893}, {9052, 34283}, {11111, 34259}, {12047, 33064}, {14829, 37482}, {16574, 48897}, {17346, 34790}, {17378, 49557}, {20961, 31339}, {21849, 48850}, {22836, 30366}, {41329, 48863}
X(50620) lies on these lines: {1, 256}, {37, 519}, {39, 49482}, {386, 1001}, {516, 37592}, {551, 28358}, {986, 29309}, {2092, 32941}, {3058, 3666}, {4261, 48805}, {4277, 49460}, {5255, 48886}, {5263, 24530}, {17321, 34282}, {21796, 36480}, {33106, 48940}, {37599, 41430}, {37617, 48929}
X(50621) lies on these lines: {1, 256}, {8, 23638}, {38, 42448}, {51, 10459}, {55, 386}, {60, 41432}, {72, 519}, {181, 5710}, {213, 2269}, {390, 20018}, {497, 10449}, {958, 3271}, {959, 4344}, {960, 3688}, {970, 5255}, {982, 17114}, {1125, 20359}, {1191, 10387}, {1201, 3917}, {1203, 2330}, {1208, 4300}, {1364, 10966}, {1573, 20594}, {1697, 20683}, {2646, 49480}, {3430, 41346}, {3550, 15489}, {3671, 20358}, {3813, 18178}, {3819, 21214}, {3915, 22076}, {3954, 17452}, {4298, 49537}, {4314, 49705}, {4673, 35104}, {5250, 40966}, {5263, 9565}, {5432, 20108}, {5650, 28352}, {7998, 28370}, {10108, 48823}, {12053, 21334}, {12513, 37516}, {12688, 12721}, {15488, 33106}, {16975, 23630}, {20684, 23544}, {37555, 46850}, {39789, 42397}
X(50621) = crosspoint of X(8) and X(1036)
X(50621) = crosssum of X(56) and X(388)
X(50621) = crossdifference of every pair of points on line {3287, 48276}
X(50621) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3056, 10544}, {1, 48883, 28386}
X(50622) lies on these lines: {1, 256}, {20, 980}, {21, 40984}, {30, 37592}, {39, 4195}, {386, 405}, {391, 941}, {519, 3743}, {950, 3666}, {988, 37425}, {1043, 2092}, {3752, 49734}, {3764, 9565}, {3883, 49728}, {3931, 37730}, {4298, 49745}, {4339, 50182}, {5255, 35203}, {5266, 48930}, {10449, 13725}, {11106, 14930}, {14636, 37552}, {15973, 24239}, {15981, 37573}, {17596, 48919}, {37617, 48893}
X(50622) = crosssum of X(940) and X(28369)
X(50622) = {X(1),X(48883)}-harmonic conjugate of X(28369)
X(50623) lies on these lines: {4, 69}, {8, 51}, {9, 1500}, {10, 21746}, {72, 519}, {75, 12109}, {78, 13724}, {386, 405}, {452, 20018}, {674, 3714}, {942, 37150}, {964, 40952}, {970, 1043}, {986, 6007}, {1724, 40984}, {3876, 14020}, {3883, 34790}, {3913, 4271}, {4192, 10461}, {4260, 13740}, {4274, 5255}, {4385, 9052}, {4662, 17330}, {4673, 45955}, {5943, 9534}, {6284, 22275}, {9564, 37573}, {10544, 17733}, {10974, 48863}, {16574, 37425}, {16980, 17135}, {19646, 29472}
X(50623) = {X(4),X(10477)}-harmonic conjugate of X(10381)
X(50624) lies on these lines: {1, 2}, {341, 37730}, {511, 48935}, {944, 25406}, {1222, 37727}, {1265, 3488}, {1330, 11523}, {2099, 5100}, {4273, 17299}, {4385, 44669}, {4514, 5730}, {4645, 12559}, {4680, 41696}, {4737, 10950}, {4867, 4894}, {5015, 12635}, {5084, 44722}, {5135, 49688}, {5300, 34195}, {10572, 32937}, {11015, 32933}, {12433, 18743}, {17336, 50241}, {17647, 24349}, {17679, 26729}, {18990, 49499}, {24524, 44150}, {30615, 37724}, {36926, 37721}, {37080, 42378}
X(50625) lies on these lines: {1, 2}, {3, 49460}, {39, 17299}, {58, 32941}, {75, 3881}, {320, 34282}, {354, 28612}, {511, 12699}, {595, 32853}, {596, 39742}, {758, 4673}, {964, 16474}, {1043, 4278}, {1126, 25496}, {1150, 3746}, {1724, 32943}, {2140, 17296}, {2321, 4253}, {2891, 4388}, {3058, 49716}, {3159, 49448}, {3454, 33141}, {3555, 3706}, {3678, 49450}, {3686, 40270}, {3696, 5045}, {3702, 5904}, {3813, 41014}, {3873, 4647}, {3875, 16887}, {3876, 4975}, {3894, 17164}, {3902, 5903}, {3953, 32860}, {3966, 41814}, {3976, 49459}, {3996, 25440}, {4015, 18743}, {4101, 30384}, {4134, 19582}, {4359, 50190}, {4417, 24387}, {4684, 12609}, {4702, 31445}, {4793, 33815}, {4966, 31419}, {4981, 27785}, {5100, 40012}, {5264, 32919}, {5266, 49467}, {5288, 49492}, {5295, 34791}, {5741, 37720}, {6763, 32929}, {8715, 14829}, {10404, 39793}, {12513, 19762}, {15170, 49718}, {17144, 33297}, {17314, 25092}, {21070, 21384}, {24349, 42031}, {28581, 37592}, {28634, 36812}, {30941, 32104}, {31162, 48877}, {32945, 37522}, {45955, 50037}
X(50625) = X(39711)-anticomplementary conjugate of X(1330)
X(50625) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 29824, 1698}
X(50626) lies on these lines: {1, 256}, {7, 17143}, {51, 1201}, {56, 181}, {58, 41346}, {65, 519}, {73, 10475}, {145, 46716}, {213, 23630}, {373, 28352}, {388, 10449}, {551, 28389}, {956, 10822}, {959, 3227}, {960, 50093}, {970, 37617}, {978, 23841}, {986, 45955}, {1191, 3271}, {1193, 16980}, {1203, 19369}, {1357, 5221}, {1400, 4263}, {1460, 34046}, {1463, 3671}, {1573, 45208}, {2175, 22654}, {2300, 40969}, {3028, 47018}, {3216, 28385}, {3339, 7248}, {3361, 42043}, {3600, 20018}, {3779, 6762}, {3879, 24471}, {3881, 35650}, {3892, 49564}, {3917, 10459}, {3976, 12109}, {4014, 4295}, {4259, 12513}, {4673, 6007}, {5045, 48823}, {5433, 20108}, {5484, 35614}, {5640, 28370}, {5691, 12126}, {5943, 21214}, {7066, 22759}, {8666, 10974}, {10404, 39793}, {12680, 12723}, {13161, 35631}, {18732, 30493}, {20970, 41526}, {24440, 40649}, {28037, 37543}
X(50626) = X(7)-Ceva conjugate of X(21471)
X(50626) = crosssum of X(55) and X(391)
X(50626) = crossdifference of every pair of points on line {3287, 4976}
X(50626) = barycentric product X(i)*X(j) for these {i,j}: {651, 50345}, {2334, 21471}
X(50626) = barycentric quotient X(50345)/X(4391)
X(50626) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {65, 1401, 17114}, {1193, 16980, 23638}
X(50627) lies on these lines: {1, 256}, {274, 3945}, {386, 474}, {519, 37631}, {962, 50175}, {988, 48917}, {2274, 9565}, {5255, 48893}, {5266, 5453}, {5399, 5711}, {5712, 10449}, {9575, 15984}, {10106, 49745}, {15936, 41805}, {19860, 28368}, {20108, 37634}, {35203, 37617}, {37539, 43034}, {37599, 48924}
X(50628) lies on these lines: {4, 69}, {8, 3917}, {65, 519}, {141, 18178}, {312, 29958}, {321, 23154}, {386, 474}, {942, 3879}, {946, 35626}, {970, 14829}, {986, 35104}, {1150, 22076}, {1211, 4187}, {1722, 28350}, {2810, 4385}, {3680, 45989}, {3702, 42448}, {3714, 8679}, {3812, 17392}, {3819, 9534}, {3831, 23638}, {3872, 47521}, {3882, 13731}, {5295, 11573}, {5883, 49564}, {6904, 20018}, {9565, 37607}, {10371, 41822}, {10822, 32853}, {12053, 21334}, {16574, 48917}, {16980, 17751}, {21746, 35633}, {32863, 41723}, {37150, 49557}, {37536, 41014}
X(50628) = {X(69),X(10441)}-harmonic conjugate of X(10381)
X(50629) lies on these lines: {1, 256}, {6, 519}, {182, 5255}, {386, 1386}, {611, 37542}, {613, 5710}, {940, 24216}, {995, 17792}, {1428, 5264}, {2329, 5039}, {2330, 37610}, {3098, 37617}, {3550, 5092}, {3729, 41622}, {3818, 33106}, {4263, 16972}, {15989, 49740}, {19130, 37716}, {20228, 36479}, {28365, 50305}, {37552, 38029}, {48827, 48922}
X(50629) = reflection of X(386) in X(1386)
X(50629) = crossdifference of every pair of points on line {3287, 9002}
X(50630) lies on these lines: {1, 256}, {36, 386}, {43, 16980}, {46, 32913}, {51, 21214}, {181, 37608}, {519, 3868}, {942, 48825}, {958, 3792}, {1201, 3060}, {1408, 5363}, {1478, 10449}, {1743, 23630}, {2650, 23155}, {2979, 10459}, {3622, 20961}, {3877, 12579}, {3944, 35631}, {4293, 20018}, {5255, 37482}, {5640, 28352}, {5710, 7186}, {5752, 37617}, {8666, 41329}, {11002, 28370}, {11009, 49454}, {12047, 33064}, {15803, 42043}, {16569, 23841}, {25306, 49613}, {37536, 37716}
X(50630) = crossdifference of every pair of points on line {3287, 48277}
X(50630) = {X(28386),X(48909)}-harmonic conjugate of X(1)
X(50631) lies on these lines: {1, 256}, {81, 386}, {171, 2594}, {500, 5255}, {519, 2650}, {1724, 15988}, {3061, 15989}, {3550, 48893}, {3936, 37693}, {4340, 20018}, {10449, 17778}, {10471, 34282}, {10944, 49745}, {17596, 48917}, {18169, 22076}, {33106, 48937}, {37617, 48882}, {37716, 48931}, {45287, 46483}
X(50631) = {X(28369),X(48909)}-harmonic conjugate of X(1)
X(50632) lies on these lines: {4, 69}, {6, 519}, {141, 16052}, {182, 1043}, {386, 3589}, {405, 25101}, {983, 1724}, {1011, 3977}, {3098, 14829}, {3729, 11355}, {4052, 49505}, {4417, 19130}, {5480, 41014}, {5774, 10387}, {11346, 17339}, {11357, 25072}, {19723, 30615}
X(50632) = crossdifference of every pair of points on line {3049, 9002}
X(50633) lies on these lines: {4, 69}, {8, 2979}, {10, 25279}, {75, 11573}, {81, 386}, {222, 19845}, {270, 394}, {519, 3868}, {942, 17378}, {1043, 37482}, {1320, 15315}, {2476, 3909}, {3057, 37038}, {3714, 9037}, {3754, 48868}, {3917, 9534}, {4190, 20018}, {4193, 17182}, {4385, 8679}, {4417, 37536}, {4968, 23155}, {5187, 31026}, {5752, 14829}, {5836, 48816}, {7283, 26892}, {7535, 28965}, {10916, 25306}, {10974, 37683}, {13740, 37516}, {16062, 18178}, {17391, 43220}, {18134, 18180}, {25253, 30438}
X(50634) lies on these lines: {4, 69}, {30, 4673}, {75, 49743}, {312, 49716}, {341, 49718}, {386, 16454}, {500, 1043}, {519, 2650}, {524, 4385}, {3578, 3701}, {3886, 48897}, {3902, 45287}, {4205, 30939}, {4417, 48931}, {5295, 49557}, {14829, 48882}, {17144, 50177}, {28612, 50226}, {41014, 48933}, {46937, 49724}
X(50635) lies on these lines: {1, 256}, {6, 979}, {171, 613}, {182, 3550}, {386, 16475}, {519, 1992}, {611, 37588}, {978, 17792}, {1193, 25304}, {1350, 37617}, {1352, 33106}, {1428, 37603}, {2108, 42043}, {3416, 37717}, {3507, 16468}, {3729, 32451}, {3749, 14547}, {3915, 15988}, {3976, 24471}, {4339, 20018}, {5480, 37716}, {5847, 10449}, {10387, 37573}, {16496, 29698}
X(50636) lies on these lines: {4, 69}, {6, 1043}, {8, 3056}, {9, 1265}, {304, 5728}, {312, 1864}, {332, 33745}, {341, 18247}, {345, 14547}, {386, 3618}, {518, 4673}, {519, 1992}, {894, 5716}, {1350, 14829}, {1469, 10453}, {3486, 3685}, {3786, 14555}, {3944, 49511}, {3974, 7077}, {4417, 5480}, {5739, 26096}, {7008, 44189}, {17135, 20557}, {17751, 25304}, {17789, 24349}, {21850, 41014}, {24282, 32118}, {24342, 50407}
X(50636) = reflection of X(i) in X(j) for these {i,j}: {69, 10449}, {20018, 6}
X(50637) lies on these lines: {1, 2}, {21, 16499}, {31, 5288}, {37, 31792}, {38, 5697}, {58, 12513}, {106, 474}, {511, 1482}, {581, 37727}, {595, 956}, {596, 17480}, {872, 49689}, {944, 48897}, {958, 40091}, {984, 3884}, {986, 2802}, {991, 5882}, {993, 37588}, {996, 1222}, {1120, 43531}, {1320, 15315}, {1457, 37709}, {1483, 5453}, {1573, 16969}, {1616, 9708}, {2476, 24222}, {2975, 37610}, {3057, 17461}, {3303, 4653}, {3445, 16408}, {3476, 4306}, {3670, 14923}, {3722, 37571}, {3730, 16975}, {3736, 49460}, {3754, 3976}, {3880, 37592}, {3885, 4424}, {3913, 4256}, {3915, 5258}, {3918, 17063}, {3999, 4004}, {4051, 16600}, {4127, 49503}, {4253, 17448}, {4257, 5255}, {4263, 16777}, {4360, 34282}, {4390, 5299}, {4414, 37563}, {4482, 7770}, {4595, 7786}, {5044, 45219}, {5105, 17299}, {5109, 50087}, {5145, 32941}, {5266, 11260}, {5270, 33104}, {5275, 9327}, {5818, 32486}, {5836, 24046}, {7174, 29740}, {8715, 37617}, {10571, 10944}, {11009, 49454}, {11108, 16486}, {11533, 13541}, {13161, 49600}, {13744, 38504}, {16496, 29698}, {17054, 40587}, {17715, 35016}, {21342, 50193}, {24387, 37716}, {29066, 29739}, {31514, 38496}, {33895, 49465}
X(50637) = midpoint of X(145) and X(10449)
X(50637) = reflection of X(386) in X(1)
X(50637) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 8, 995}, {1, 1698, 1149}, {1, 3632, 1193}, {1, 3633, 42}, {1, 3679, 1201}, {1, 3961, 30144}, {1, 19861, 47622}, {1, 49494, 5262}, {8, 3241, 20041}, {956, 37542, 595}, {1201, 3679, 17749}, {1222, 13740, 996}, {5255, 8666, 4257}
X(50638) lies on these lines: {1, 2}, {382, 511}, {579, 17299}, {1043, 4257}, {3754, 49459}, {3901, 4365}, {4720, 37522}, {5156, 49460}, {5165, 50087}, {5288, 16452}, {7855, 36707}, {12433, 17362}, {16451, 48696}, {31794, 49468}, {48839, 49718}, {48841, 49728}, {48868, 49734}
X(50638) = reflection of X(386) in X(10449)
X(50639) lies on these lines: {2, 5503}, {6, 41134}, {20, 542}, {32, 1992}, {69, 543}, {76, 338}, {99, 524}, {115, 21356}, {141, 9166}, {193, 18800}, {325, 9877}, {511, 6054}, {597, 7807}, {1641, 4563}, {2799, 39905}, {3618, 9167}, {3619, 14971}, {3620, 19662}, {4576, 10717}, {5026, 15534}, {5107, 41137}, {5181, 9144}, {5461, 14064}, {5477, 36521}, {5648, 15342}, {5976, 11163}, {6034, 7944}, {6055, 10519}, {6390, 16508}, {6393, 22110}, {7608, 15850}, {7799, 41146}, {7929, 8596}, {7983, 47358}, {8366, 10542}, {8724, 10753}, {8787, 33235}, {9169, 45672}, {9830, 11057}, {9884, 28538}, {10554, 35356}, {10722, 19924}, {10723, 47353}, {11006, 48953}, {11054, 15993}, {11178, 14639}, {11179, 21166}, {11180, 23698}, {11632, 48876}, {11646, 22165}, {14061, 21358}, {14916, 35279}, {14928, 20080}, {15300, 47102}, {19911, 39099}, {20423, 23234}, {22247, 31401}, {23055, 46236}, {25562, 31670}, {40341, 45018}
X(50639) = midpoint of X(8591) and X(11160)
X(50639) = reflection of X(i) in X(j) for these {i,j}: {2, 50567}, {193, 18800}, {671, 599}, {1992, 2482}, {5477, 36521}, {7983, 47358}, {8593, 99}, {9144, 5181}, {10723, 47353}, {10753, 8724}, {10754, 2}, {11054, 15993}, {11161, 69}, {11632, 48876}, {11646, 22165}, {15342, 5648}, {15534, 5026}, {22486, 5976}, {31670, 25562}, {39099, 39785}
X(50639) = crossdifference of every pair of points on line {9135, 9171}
X(50639) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1992, 2482, 5182}, {3620, 41135, 19662}
X(50640) lies on these lines: {2, 694}, {6, 39652}, {20, 22679}, {39, 10754}, {69, 2782}, {76, 22677}, {99, 511}, {325, 9772}, {524, 11152}, {542, 11057}, {698, 15993}, {1350, 5989}, {1569, 14645}, {1975, 44453}, {2076, 19120}, {2482, 22486}, {3095, 6337}, {3098, 5152}, {3552, 5026}, {4027, 5017}, {5052, 5182}, {5104, 8289}, {6393, 15980}, {6655, 11646}, {7863, 32452}, {9607, 32476}, {9830, 33264}, {13354, 21166}, {14994, 19905}, {19911, 41137}, {35705, 40236}
X(50640) = reflection of X(i) in X(j) for these {i,j}: {76, 50567}, {1916, 3094}, {10754, 39}, {13330, 5026}, {18906, 5976}, {22486, 2482}, {32451, 1569}, {43532, 22677}
X(50640) = {X(25332),X(36790)}-harmonic conjugate of X(40708)
X(50641) lies on these lines: {2, 98}, {4, 10754}, {20, 50567}, {69, 2794}, {76, 15069}, {99, 1503}, {141, 34473}, {325, 22664}, {511, 10722}, {620, 25406}, {671, 47353}, {690, 41737}, {1350, 11057}, {1351, 22505}, {2782, 18440}, {2784, 3663}, {3023, 39891}, {3027, 39892}, {3564, 6033}, {3618, 36519}, {3619, 38737}, {3767, 5477}, {3818, 14639}, {5152, 45018}, {5254, 11646}, {5969, 10723}, {6321, 39884}, {6337, 14981}, {7795, 10991}, {7828, 8550}, {8716, 9830}, {9166, 47354}, {9863, 34507}, {9873, 23235}, {10516, 14061}, {10519, 38749}, {11645, 12117}, {11898, 38744}, {12184, 39873}, {12185, 39897}, {13188, 48662}, {14645, 39838}, {14927, 38738}, {14982, 15342}, {15561, 48906}, {15581, 33802}, {18358, 38224}, {18768, 36997}, {20774, 43976}, {21166, 46264}, {22573, 41042}, {22574, 41043}, {32451, 38383}, {32469, 32476}, {33340, 39887}, {33341, 39888}, {38704, 47557}, {38741, 48876}, {38743, 39899}, {39803, 39879}, {41134, 43273}
X(50641) = midpoint of X(i) and X(j) for these {i,j}: {147, 5921}, {11898, 38744}, {13188, 48662}
X(50641) = reflection of X(i) in X(j) for these {i,j}: {20, 50567}, {98, 1352}, {671, 47353}, {1351, 22505}, {5477, 38745}, {6321, 39884}, {6776, 114}, {8593, 6054}, {10723, 36990}, {10753, 6033}, {10754, 4}, {11161, 11180}, {11179, 25562}, {14927, 38738}, {15342, 14982}, {32451, 38383}, {38664, 11646}, {38741, 48876}
X(50641) = reflection of X(41737) in the Fermat line
X(50641) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {114, 6776, 5182}, {11179, 25562, 23234}
X(50642) lies on these lines: {6, 8057}, {125, 14117}, {419, 2501}, {523, 47454}, {525, 3239}, {1499, 1514}, {3619, 4143}
X(50642) = X(32676)-complementary conjugate of X(7710)
X(50642) = crossdifference of every pair of points on line {154, 3917}
X(50642) = barycentric product X(523)*X(14927)
X(50642) = barycentric quotient X(14927)/X(99)
X(50643) lies on these lines: {2, 6002}, {98, 2384}, {111, 44873}, {649, 3239}, {4729, 7172}, {4893, 28470}, {6998, 28312}, {17496, 44435}, {28468, 47773}, {28478, 47771}, {28490, 48156}
X(50644) lies on these lines: {6, 38359}, {74, 5915}, {323, 401}, {523, 47281}, {647, 14471}, {690, 9209}, {2501, 3566}, {2519, 6753}
X(50644) = crosssum of X(8651) and X(39764)
X(50644) = crossdifference of every pair of points on line {51, 3167}
Intersection of radical axes involving apollonian circles: X(50645)-X(50686)
This preamble and centers X(50645)-X(50686) were contributed by César Eliud Lozada, June 13, 2022.
Let ABC be a triangle. Let A', A" be the points at which the A-internal and the A-external angle bisectors cut BC. The circle with diameter A'A" is called the A-apollonian circle of ABC, and the B- and the C- apollonian circles are built similarly.
Let Ω be any other circle and let ra, rb, rc be the radical axes of Ω and the A-, B- and C- apollonian circles of ABC, respectively. Then ra, rb, rc concur in a point on the Brocard axis of ABC.
If X, Y, Z are the powers of Ω with respect to A, B, C, respectively, then Q(Ω), the point of intersection of ra, rb, rc, is:
Q(Ω) = a^2*(-a^2*b^2*c^2+(a^2-b^2)*Y*b^2+(a^2-c^2)*Z*c^2) : b^2*(-a^2*b^2*c^2+(b^2-c^2)*c^2*Z+(b^2-a^2)*X*a^2) : c^2*(-a^2*b^2*c^2+(c^2-a^2)*X*a^2+(-b^2+c^2)*Y*b^2)
If Ω is a circle with center O* = x0:y0:z0 and radius ρ, then
Q(O*, ρ) = a^2*(b^2*((-(b^2+c^2)*a^2+c^4+b^4)*ρ^2-a^2*c^2*(-a^2+b^2+c^2))*y0^2+c^2*((-(b^2+c^2)*a^2+c^4+b^4)*ρ^2-a^2*b^2*(-a^2+b^2+c^2))*z0^2+a^2*((-(b^2+c^2)*a^2+c^4+b^4)*ρ^2-b^2*c^2*(-a^2+b^2+c^2))*x0^2-2*b*c*(((b^2+c^2)*a^2-b^4-c^4)*ρ^2+a^2*b^2*c^2)*y0*z0+a*c*((-2*(b^2+c^2)*a^2+2*b^4+2*c^4)*ρ^2+b^2*(a^4-(2*b^2+c^2)*a^2+(b^2-c^2)*b^2))*z0*x0+a*b*((-2*(b^2+c^2)*a^2+2*b^4+2*c^4)*ρ^2+c^2*(a^4-(b^2+2*c^2)*a^2-(b^2-c^2)*c^2))*x0*y0) : :
Here, if we make ρ = 0, we can name Q(O*, ρ=0) = Q(O*) as the apollonian image of O*, to be considered later.
In the following list, (Ω, n) indicates that Q(Ω) = X(n):
(anti-Artzt circle, 50672), (anticomplementary circle, 50645), (Artzt circle, 50673), (Bevan circle, 579), (2nd Brocard circle, 3094), (1st Brocard circle, 574), (circumcircle, 6), ((circumcircle, incircle)-inverter, 14520), (Conway circle, 50646), (Dao-Moses-Telv circle, 3), (Dao-symmedial circle, 39), (Dou circle, 50647), (Dou circles radical circle, 3), (1st Droz-Farny circle, 50648), (2nd Droz-Farny circle, 50649), (Ehrmann circle, 6), (1st Evans circle, 573), (2nd Evans circle, 573), (excircles radical circle, 50650), (Fuhrmann circle, 50651), (Gallatly circle, 50652), (GEOS circle, 50653), (half-Moses circle, 50654), (hexyl circle, 50656), (Hatzipolakis-Suppa circle, 50655), (Hung circle, 50674), (Hutson-Parry circle, 574), (incentral circle, 50657), (incircle, 50658), (incircle of anticomplementary triangle, 50686), (incircle-of-orthic triangle, 50675), (Johnson triangle circumcircle, 50676), (Kenmotu circle, 371), (outer-Kenmotu, 372), (1st Lemoine circle, 50659), (2nd Lemoine (or cosine) circle, 5050), (Lester circle, 50660), (Longuet-Higgins circle, 50661), (2nd Lozada circle, 50679), (3rd Lozada circle, 50680), (4th Lozada circle, 50681), (5th Lozada circle, 5050), (6th Lozada circle, 50682), (7th Lozada circle, 50683), (8th Lozada circle, 50684), (9th Lozada circle, 50685), (10th Lozada circle, 371), (11th Lozada circle, 372), (Lucas(+1) circles radical circle, 6221), (Lucas(-1) circles radical circle, 6398), (Lucas(+1) inner, 6468), (Lucas(-1) inner, 6469), (mixtilinear incircles radical circle, 50677), (inner Montesdeoca-Lemoine circle, 50662), (outer Montesdeoca-Lemoine circle, 50663), (Moses circle, 50664), (Moses-Parry circle, 3), (inner-Napoleon circle, 3106), (outer-Napoleon circle, 3107), (Neuberg circles radical circle, 50665), (Nguyen-Moses circle, 11477), (nine-point circle, 570), (orthocentroidal circle, 566), (orthoptic circle of Steiner inellipse, 39), (orthosymmedial circle, 50678), (polar circle, 216), (power circles radical circle, 50666), (reflection circle, 50667), (Stammler circle, 37517), (1st Steiner circle, 50668), (2nd Steiner circle, 50669), (Stevanovic circle, 3), (symmedial circle, 50670), (tangential circle, 571), (Taylor circle, 50671), (Yff contact circle, 573)
Definition of these central circles can be found in the Alphabetical Index of Terms in ETC or in Wolfram's Triangle Circles.
X(50645) lies on these lines: {2, 20819}, {3, 6}, {4, 28728}, {66, 36214}, {69, 23635}, {160, 9019}, {193, 20975}, {206, 6660}, {264, 305}, {311, 37988}, {393, 2967}, {418, 40681}, {1176, 46546}, {1370, 3164}, {1634, 9973}, {1843, 36212}, {1916, 8264}, {1993, 40947}, {2393, 20794}, {2450, 39113}, {2971, 32827}, {2979, 22062}, {3060, 22087}, {3148, 20806}, {3167, 33582}, {3964, 12167}, {3981, 8265}, {6033, 13556}, {7499, 7792}, {7667, 41624}, {7778, 14767}, {7795, 42442}, {7796, 40035}, {9407, 19122}, {9766, 34609}, {9969, 11328}, {12220, 20775}, {12836, 18170}, {13409, 40680}, {14575, 37183}, {14790, 32428}, {16043, 22424}, {16327, 46517}, {21213, 44089}, {21531, 41760}, {23335, 45279}, {23646, 35892}, {24318, 29673}, {25332, 40697}, {26870, 42441}, {27369, 28710}, {31099, 40896}, {31360, 42313}, {31952, 34146}, {37466, 42406}, {44376, 45838}
X(50645) = midpoint of X(3164) and X(44443)
X(50645) = barycentric product X(i)*X(j) for these {i, j}: {343, 19197}, {1502, 33728}
X(50645) = trilinear product X(561)*X(33728)
X(50645) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 3001, 50666), (570, 3313, 3), (3095, 50666, 6), (13351, 41328, 11171)
X(50646) lies on these lines: {3, 6}, {76, 24523}, {516, 10441}, {517, 49475}, {940, 21746}, {980, 3056}, {1742, 1764}, {3271, 27623}, {3664, 3784}, {3817, 3840}, {3819, 16345}, {3888, 29981}, {4297, 29311}, {4416, 26892}, {5650, 16355}, {10436, 22412}, {10446, 20788}, {15310, 22793}, {31394, 50317}
X(50646) = reflection of X(i) in X(j) for these (i, j): (5752, 48886), (48902, 37536)
X(50647) lies on these lines: {3, 6}, {4, 47731}, {1299, 8882}, {1843, 6754}, {1879, 12162}, {2165, 13754}, {9722, 12359}, {39111, 47328}, {40939, 47421}
X(50647) = barycentric product X(24)*X(12359)
X(50647) = trilinear product X(47)*X(9722)
X(50647) = intersection, other than A, B, C, of circumconics {{A, B, C, X(3), X(12359)}} and {{A, B, C, X(6), X(9722)}}
X(50647) = X(281)-of-orthic triangle, when ABC is acute
X(50647) = {X(12239), X(12240)}-harmonic conjugate of X(52)
X(50648) lies on these lines: {3, 6}, {5, 34981}, {49, 7669}, {54, 14060}, {264, 7769}, {1594, 39530}, {7558, 7828}, {13371, 23333}, {13561, 15345}, {14160, 33842}, {14570, 37121}, {15122, 16333}, {15850, 34834}, {23635, 41714}, {34507, 36212}, {37335, 43811}, {37444, 42329}
X(50648) = {X(14630), X(14631)}-harmonic conjugate of X(36753)
X(50649) lies on these lines: {3, 6}, {4, 2393}, {5, 5181}, {24, 19136}, {25, 34787}, {30, 15074}, {49, 45016}, {51, 468}, {54, 1177}, {69, 6816}, {74, 43812}, {141, 23308}, {143, 34351}, {184, 11470}, {185, 1205}, {193, 41716}, {206, 9707}, {235, 1843}, {373, 11746}, {381, 43130}, {427, 41603}, {524, 5562}, {542, 12162}, {597, 40929}, {599, 11793}, {895, 7527}, {1181, 9914}, {1216, 39571}, {1352, 9927}, {1495, 15582}, {1503, 1885}, {1593, 8549}, {1974, 15577}, {1992, 5889}, {2854, 15030}, {2904, 45110}, {2979, 11433}, {3060, 7493}, {3091, 11188}, {3516, 10249}, {3520, 5622}, {3541, 23327}, {3542, 6403}, {3564, 5876}, {3567, 35486}, {3618, 15028}, {3819, 26958}, {3917, 13567}, {5012, 37929}, {5133, 27365}, {5446, 20423}, {5489, 8675}, {5650, 47296}, {5890, 35485}, {5891, 18390}, {5907, 8681}, {6241, 6776}, {6288, 18553}, {6291, 45862}, {6406, 45863}, {7503, 41614}, {7507, 23049}, {7526, 8548}, {7998, 37643}, {8537, 15033}, {8540, 19365}, {8541, 11424}, {8584, 14831}, {9019, 12233}, {9027, 11459}, {9920, 19596}, {9925, 15068}, {9968, 11456}, {9970, 32245}, {9971, 10110}, {10182, 47455}, {10192, 44079}, {10263, 16618}, {10282, 18374}, {10516, 14913}, {10558, 19330}, {10752, 15032}, {10982, 45015}, {11179, 40647}, {11180, 15058}, {11412, 11821}, {11429, 19369}, {11649, 11799}, {11695, 47352}, {12038, 15462}, {12111, 15531}, {12220, 37201}, {12298, 14233}, {12299, 14230}, {12309, 17814}, {12584, 38851}, {12593, 38676}, {13142, 31807}, {13248, 15472}, {13367, 44102}, {13417, 44109}, {13754, 32284}, {14094, 16510}, {14118, 37784}, {14130, 39562}, {14641, 46264}, {14912, 22829}, {15026, 16238}, {15118, 37118}, {15274, 34854}, {15303, 25711}, {15581, 26883}, {15873, 41585}, {16227, 47460}, {17040, 43695}, {17710, 29181}, {18350, 43829}, {18475, 45171}, {18560, 36201}, {18925, 41719}, {19118, 23041}, {19128, 45172}, {19130, 41714}, {19149, 19459}, {19153, 19357}, {21969, 44210}, {22151, 34148}, {22467, 43815}, {24206, 50143}, {25406, 30552}, {31725, 48901}, {32142, 48876}, {32205, 38079}, {32260, 32274}, {32411, 44214}, {34469, 34778}, {34622, 43273}, {34786, 36990}, {34986, 41615}, {37072, 46057}, {37648, 41673}, {41729, 46444}, {43586, 43811}, {43604, 43810}, {44870, 47353}
X(50649) = midpoint of X(i) and X(j) for these {i, j}: {4, 15073}, {6, 44439}, {193, 41716}, {1351, 18438}, {6467, 12294}
X(50649) = reflection of X(i) in X(j) for these (i, j): (3, 44479), (52, 576), (185, 8550), (389, 44495), (1350, 11574), (1843, 5480), (3313, 9967), (6403, 9969), (6776, 32366), (14831, 8584), (15069, 5907), (19161, 6), (32260, 32274), (37473, 389), (37511, 182), (41714, 19130)
X(50649) = intersection, other than A, B, C, of circumconics {{A, B, C, X(32), X(14457)}} and {{A, B, C, X(54), X(14961)}}
X(50649) = X(5698)-of-orthic triangle, when ABC is acute
X(50649) = X(13200)-of-1st orthosymmedial triangle
X(50649) = X(15073)-of-Euler triangle
X(50649) = X(34787)-of-anti-Ara triangle
X(50649) = X(43130)-of-anti-Ehrmann-mid triangle
X(50649) = X(44479)-of-X3-ABC reflections triangle
X(50649) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 1351, 44492), (6, 37473, 389), (184, 11470, 34117), (185, 40673, 8550), (389, 13348, 1192), (389, 37473, 19161), (389, 44479, 35371), (389, 44495, 6), (576, 578, 6), (1351, 36749, 576), (1593, 10602, 8549), (6243, 11426, 389), (6403, 14853, 9969), (8538, 13352, 44469), (15644, 46363, 9786)
X(50650) lies on these lines: {1, 22071}, {3, 6}, {5, 46838}, {36, 2197}, {37, 140}, {952, 21858}, {1400, 13006}, {1470, 22132}, {1575, 37365}, {1765, 3216}, {1766, 2277}, {2077, 16470}, {2260, 22059}, {2286, 40293}, {2303, 6940}, {2815, 22092}, {3666, 3911}, {4868, 37528}, {5301, 26285}, {6700, 17355}, {6996, 24530}, {10446, 24598}, {12610, 27633}, {14792, 22056}, {17053, 24046}, {19542, 37663}
X(50650) = {X(216), X(579)}-harmonic conjugate of X(3002)
X(50651) lies on these lines: {3, 6}, {184, 23860}, {1736, 33149}, {3772, 22069}
X(50652) lies on these lines: {3, 6}, {114, 9478}, {140, 732}, {141, 40108}, {193, 22677}, {262, 46264}, {538, 10168}, {542, 44562}, {1352, 7786}, {1503, 11272}, {2782, 3589}, {3564, 10007}, {3618, 7709}, {3818, 9744}, {6248, 7803}, {6661, 46267}, {6683, 24206}, {7697, 47355}, {7757, 38064}, {7763, 14994}, {7976, 38116}, {8152, 46850}, {11257, 14561}, {12782, 38029}, {13108, 40332}, {14853, 32522}, {14881, 44882}, {15819, 17008}, {18583, 32516}, {22486, 33266}, {22682, 48884}, {24256, 32448}, {25561, 42849}, {32449, 49111}
X(50652) = midpoint of X(i) and X(j) for these {i, j}: {39, 182}, {3098, 35439}, {5092, 44423}, {6248, 32429}, {14881, 44882}, {18583, 32516}, {24256, 32448}, {32449, 49111}
X(50652) = reflection of X(i) in X(j) for these (i, j): (24206, 6683), (44500, 15516)
X(50652) = inverse of X(2022) in half-Moses circle
X(50652) = X(50652)-of-circumsymmedial triangle
X(50652) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (182, 576, 35429), (182, 3098, 35423), (575, 5092, 39750), (2011, 2012, 574), (2021, 11171, 13334), (8160, 8161, 37479), (12020, 12021, 35431), (21163, 35439, 3098), (32429, 38317, 6248), (32448, 38110, 24256), (39498, 39750, 5092)
X(50653) lies on these lines: {3, 6}, {218, 2197}, {1596, 1865}, {1723, 40590}, {1766, 8608}, {1880, 17905}, {6554, 40937}, {8776, 22134}
X(50653) = {X(40590), X(43046)}-harmonic conjugate of X(1723)
X(50654) lies on these lines: {3, 6}, {6683, 18358}, {7786, 39874}, {37667, 41622}, {44562, 48906}
X(50654) = X(50654)-of-circumsymmedial triangle
X(50654) = {X(575), X(5092)}-harmonic conjugate of X(41412)
X(50655) lies on these lines: {3, 6}, {13481, 35908}
X(50656) lies on these lines: {3, 6}, {19, 1818}, {516, 6261}, {1742, 6282}, {3587, 41430}, {3601, 6210}, {3781, 15830}, {5709, 29311}, {6045, 16455}, {6245, 17748}, {6824, 48888}, {6826, 24220}, {6847, 48878}, {6989, 20083}, {8727, 48938}, {16056, 37521}, {20420, 48902}, {24929, 31394}, {31395, 41276}, {37281, 48934}
X(50656) = {X(3), X(48908)}-harmonic conjugate of X(50658)
X(50657) lies on these lines: {1, 8818}, {3, 6}, {37, 3013}, {661, 17438}, {1442, 8287}, {2174, 20982}, {2594, 21741}, {20277, 20279}, {37701, 50036}
X(50657) = barycentric product X(i)*X(j) for these {i, j}: {35, 11263}, {758, 47054}
X(50657) = perspector of the circumconic {{A, B, C, X(110), X(47054)}}
X(50657) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(21794)}} and {{A, B, C, X(35), X(15792)}}
X(50657) = crossdifference of every pair of points on line {X(523), X(1749)}
X(50658) lies on these lines: {1, 46850}, {3, 6}, {7, 22440}, {37, 2808}, {51, 37262}, {57, 1742}, {142, 45305}, {241, 29957}, {443, 48878}, {516, 942}, {1362, 9440}, {1442, 3270}, {2174, 38599}, {2807, 11700}, {3664, 11018}, {3819, 8731}, {5446, 48927}, {5453, 40647}, {5907, 33536}, {5943, 16056}, {6000, 50317}, {6210, 8726}, {6826, 48938}, {6851, 48902}, {7411, 40952}, {7675, 45963}, {8727, 24220}, {8728, 48888}, {9940, 15310}, {10202, 29349}, {10446, 14548}, {10477, 36706}, {11227, 29353}, {12109, 15852}, {13476, 38454}, {13598, 48897}, {17049, 28850}, {17065, 32462}, {17603, 49537}, {18443, 31394}, {24474, 29309}, {29311, 31793}
X(50658) = midpoint of X(1742) and X(21746)
X(50658) = (Ascella)-isogonal conjugate-of-X(5745)
X(50658) = X(264)-of-Ascella triangle, when ABC is acute
X(50658) = X(50645)-of-inverse-in-incircle triangle, when ABC is acute
X(50658) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 5751, 4260), (3, 48908, 50656)
X(50659) lies on these lines: {2, 12215}, {3, 6}, {22, 20965}, {25, 10329}, {69, 7824}, {110, 15302}, {114, 10516}, {115, 38317}, {141, 7763}, {183, 732}, {193, 33004}, {232, 19124}, {263, 41275}, {353, 35265}, {378, 2211}, {384, 3618}, {394, 14153}, {543, 5149}, {597, 1003}, {599, 30532}, {613, 31448}, {694, 37344}, {698, 31859}, {1078, 32451}, {1180, 42295}, {1194, 43650}, {1352, 31401}, {1428, 2276}, {1503, 3815}, {1506, 3818}, {1597, 33874}, {1613, 7484}, {1915, 3796}, {1971, 23041}, {1975, 24256}, {1992, 33273}, {1993, 8041}, {2023, 5026}, {2056, 17811}, {2275, 2330}, {2422, 39495}, {2548, 46264}, {2549, 14561}, {3051, 7485}, {3060, 38862}, {3231, 40916}, {3291, 22112}, {3499, 31521}, {3589, 4048}, {3763, 3788}, {3981, 10601}, {5103, 7841}, {5152, 5182}, {5207, 7777}, {5309, 10168}, {5359, 11205}, {5422, 20859}, {5475, 29012}, {5999, 7736}, {6329, 33235}, {6593, 38661}, {6688, 34481}, {6704, 7834}, {6776, 31400}, {7496, 9463}, {7514, 18371}, {7735, 37455}, {7739, 38064}, {7745, 44882}, {7747, 48898}, {7748, 19130}, {7751, 41622}, {7754, 8177}, {7756, 48901}, {7783, 18906}, {7784, 35701}, {7786, 38907}, {7815, 14994}, {7875, 8290}, {9467, 18872}, {9574, 16475}, {9609, 37123}, {9620, 38029}, {11284, 20998}, {11676, 14853}, {12588, 31497}, {14688, 34241}, {15048, 38110}, {15069, 31492}, {16419, 21001}, {18440, 31467}, {18898, 39951}, {20806, 22416}, {23660, 37576}, {24206, 31455}, {28343, 38663}, {28662, 38662}, {31396, 39870}, {31406, 48906}, {31428, 39885}, {31457, 40107}, {31463, 45511}, {32217, 37903}, {32291, 48787}, {32292, 48786}, {32305, 46301}, {37283, 46337}, {39590, 48884}, {41517, 45146}, {44519, 48910}
X(50659) = midpoint of X(574) and X(5034)
X(50659) = reflection of X(i) in X(j) for these (i, j): (6, 5034), (35378, 1692), (35429, 182)
X(50659) = isogonal conjugate of the isotomic conjugate of X(16990)
X(50659) = barycentric product X(6)*X(16990)
X(50659) = trilinear product X(31)*X(16990)
X(50659) = inverse of X(5017) in 1st Brocard circle
X(50659) = inverse of X(46305) in 2nd Brocard circle
X(50659) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(5017)}} and {{A, B, C, X(6), X(16990)}}
X(50659) = Cevapoint of X(6) and X(11175)
X(50659) = crossdifference of every pair of points on line {X(523), X(50550)}
X(50659) = crosssum of X(6) and X(11174)
X(50659) = X(50659)-of-circumsymmedial triangle
X(50659) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 5017), (6, 5013, 3094), (6, 5085, 1691), (6, 5116, 3), (6, 15514, 5093), (6, 15815, 1350), (6, 44453, 1351), (39, 182, 6), (187, 42852, 6), (574, 39498, 5116), (575, 5028, 6), (1570, 39561, 6), (1670, 12050, 6), (1671, 12051, 6), (1691, 13331, 6), (2011, 2012, 11171), (3053, 34873, 3), (3094, 5038, 6), (3094, 12055, 5013), (5038, 12055, 3094), (5039, 17508, 187), (5052, 37512, 3098), (5085, 47619, 3), (6421, 19145, 6), (6422, 19146, 6), (8177, 32449, 7754), (9605, 40825, 6), (9737, 13354, 1350), (12962, 12969, 5041), (17508, 42852, 5039), (39764, 44499, 6)
X(50660) lies on these lines: {2, 13582}, {3, 6}, {23, 3815}, {24, 31492}, {44, 14792}, {45, 14793}, {53, 14865}, {186, 6749}, {230, 7496}, {231, 7765}, {393, 35475}, {395, 11146}, {396, 11145}, {597, 35296}, {632, 9722}, {1506, 7545}, {1599, 13847}, {1600, 13846}, {1658, 31450}, {1990, 3520}, {1995, 9609}, {2549, 49671}, {2937, 9698}, {3055, 16042}, {3087, 44879}, {3131, 8015}, {3132, 8014}, {3148, 19596}, {3292, 9604}, {3518, 6748}, {3589, 44180}, {3628, 44537}, {3763, 9723}, {4996, 17369}, {5254, 7550}, {5306, 15246}, {5475, 37924}, {5702, 23040}, {6636, 9300}, {6794, 14354}, {7279, 17366}, {7464, 47275}, {7492, 7736}, {7512, 9606}, {7555, 31406}, {7556, 31400}, {7669, 37457}, {7738, 46262}, {7748, 9220}, {7753, 30537}, {9607, 37126}, {9700, 31467}, {10311, 37920}, {11284, 44524}, {12106, 31401}, {13472, 22101}, {17330, 37293}, {31457, 43809}, {31861, 44526}, {34437, 43718}, {35473, 40138}, {37637, 40916}, {37950, 47322}, {38862, 38872}, {41476, 41478}
X(50660) = complement of the isotomic conjugate of X(45972)
X(50660) = inverse of X(11063) in 1st Brocard circle
X(50660) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(11063)}} and {{A, B, C, X(4), X(15037)}}
X(50660) = Cevapoint of X(6) and X(30537)
X(50660) = crossdifference of every pair of points on line {X(523), X(6140)}
X(50660) = crosssum of X(6) and X(15018)
X(50660) = X(2)-Ceva conjugate of-X(45973)
X(50660) = X(31)-complementary conjugate of-X(45973)
X(50660) = (medial)-isotomic conjugate-of-X(45973)
X(50660) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 11063), (6, 3053, 33886), (32, 13337, 6), (39, 50, 6), (371, 372, 15037), (566, 5063, 6), (570, 3284, 41335), (574, 5063, 566), (577, 13351, 6), (2965, 5421, 6), (3284, 31652, 570), (3284, 41335, 6), (5421, 22052, 2965), (11063, 15109, 3), (22236, 22238, 36752), (31489, 44522, 1995)
X(50661) lies on these lines: {3, 6}, {87, 27626}, {261, 8033}, {610, 39252}, {993, 49479}, {2175, 23853}, {2663, 3601}, {4224, 16998}, {6857, 26110}, {8731, 37632}, {11328, 16574}, {17065, 23863}, {18169, 35612}, {18206, 20794}
X(50662) lies on these lines: {3, 6}, {1495, 41379}, {44109, 46770}
X(50662) = inverse of X(187) in inner Montesdeoca-Lemoine circle
X(50662) = inverse of X(8161) in Schoute circle
X(50662) = intersection, other than A, B, C, of circumconics {{A, B, C, X(74), X(8161)}} and {{A, B, C, X(111), X(50663)}}
X(50662) = X(50662)-of-circumsymmedial triangle
X(50662) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 187, 50663), (15, 16, 8161), (39, 5092, 50663), (1342, 38720, 12021), (5008, 41413, 50663)
X(50663) lies on these lines: {3, 6}, {1495, 41378}, {44109, 46771}
X(50663) = inverse of X(187) in outer Montesdeoca-Lemoine circle
X(50663) = inverse of X(8160) in Schoute circle
X(50663) = intersection, other than A, B, C, of circumconics {{A, B, C, X(74), X(8160)}} and {{A, B, C, X(111), X(50662)}}
X(50663) = X(50663)-of-circumsymmedial triangle
X(50663) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (6, 187, 50662), (15, 16, 8160), (39, 5092, 50662), (1343, 38721, 12020), (5008, 41413, 50662)
X(50664) lies on these lines: {2, 43150}, {3, 6}, {4, 42785}, {30, 6329}, {51, 15080}, {69, 15702}, {74, 34155}, {140, 3631}, {141, 10168}, {159, 10250}, {184, 6688}, {193, 15708}, {323, 3819}, {373, 10546}, {524, 11812}, {542, 547}, {549, 3629}, {597, 3845}, {631, 7905}, {1176, 13446}, {1199, 19150}, {1216, 36153}, {1352, 5067}, {1353, 3630}, {1386, 11278}, {1495, 5012}, {1503, 3850}, {1511, 5892}, {1843, 47485}, {1992, 15719}, {1994, 41462}, {2979, 44111}, {3055, 6036}, {3292, 15082}, {3431, 15045}, {3533, 3619}, {3543, 5476}, {3545, 3618}, {3564, 16239}, {3620, 33748}, {3763, 15723}, {3832, 11572}, {3853, 13470}, {3917, 11004}, {3934, 13196}, {3973, 46475}, {5054, 40341}, {5056, 6776}, {5059, 14853}, {5422, 34417}, {5480, 29323}, {5622, 19140}, {5640, 5645}, {5643, 35265}, {5650, 11422}, {5651, 12045}, {5907, 15032}, {5946, 17710}, {6000, 41593}, {6248, 10359}, {6636, 34565}, {6676, 32068}, {6771, 6782}, {6774, 6783}, {7499, 11225}, {8541, 44878}, {8546, 12039}, {8549, 23042}, {8550, 24206}, {8562, 8675}, {8584, 19711}, {9027, 32154}, {9306, 10219}, {9716, 33879}, {9969, 37936}, {9976, 10821}, {9977, 13367}, {10249, 34779}, {10601, 26864}, {11001, 31670}, {11178, 39899}, {11202, 34777}, {11451, 44110}, {11456, 44870}, {11464, 41714}, {11695, 32046}, {11738, 43697}, {12006, 44668}, {12042, 44562}, {12099, 40291}, {12100, 20583}, {12112, 46847}, {12834, 44106}, {13363, 41579}, {13434, 46850}, {13596, 44102}, {14355, 15630}, {14848, 48910}, {15061, 41731}, {15066, 34986}, {15107, 21849}, {15301, 32448}, {15686, 21850}, {15690, 19924}, {15988, 36006}, {16200, 16491}, {16496, 38029}, {18440, 25561}, {19128, 34484}, {20299, 41729}, {20415, 42146}, {20416, 42143}, {20423, 48880}, {20425, 43030}, {20426, 43031}, {21747, 37619}, {23327, 34776}, {25406, 33703}, {32414, 42849}, {32450, 44224}, {32455, 41983}, {33751, 41981}, {34567, 41435}, {35228, 39125}, {35500, 43596}, {37527, 37680}, {38155, 39870}, {38335, 43273}, {43130, 43815}, {45298, 47296}, {47281, 47569}, {48904, 49133}, {48905, 48943}
X(50664) = midpoint of X(i) and X(j) for these {i, j}: {3, 5097}, {6, 5092}, {140, 12007}, {182, 575}, {576, 14810}, {1353, 40107}, {6776, 18553}, {8546, 12039}, {8550, 24206}, {12100, 20583}, {13354, 44423}, {15516, 20190}, {19130, 48906}, {20299, 41729}, {21850, 48892}, {31670, 48891}, {35228, 39125}, {46264, 48895}, {48905, 48943}
X(50664) = reflection of X(i) in X(j) for these (i, j): (15516, 575), (20190, 182), (22330, 15516)
X(50664) = complement of X(43150)
X(50664) = inverse of X(37512) in Schoute circle
X(50664) = inverse of X(37517) in 1st Brocard circle
X(50664) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(37517)}} and {{A, B, C, X(39), X(14483)}}
X(50664) = crossdifference of every pair of points on line {X(523), X(47445)}
X(50664) = X(5097)-of-anti-X3-ABC reflections triangle
X(50664) = X(50664)-of-circumsymmedial triangle
X(50664) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 37517), (3, 39561, 5097), (6, 182, 5092), (6, 5033, 41413), (6, 5085, 33878), (6, 12017, 3098), (6, 33878, 576), (6, 37517, 5097), (15, 16, 37512), (182, 576, 5085), (182, 3098, 12017), (182, 5050, 575), (182, 17508, 10541), (182, 22234, 17508), (182, 39561, 3), (575, 5092, 6), (575, 5097, 39561), (575, 20190, 22330), (576, 5085, 14810), (1351, 10541, 17508), (3098, 12017, 5092), (5012, 15018, 1495), (5033, 41413, 38010), (5092, 39750, 38010), (5092, 43147, 8589), (13336, 37505, 13348), (13353, 15037, 37513), (15037, 37513, 389), (17508, 22234, 1351), (22352, 44107, 15107), (37517, 39561, 6), (39899, 47355, 11178), (45410, 45551, 43120)
X(50665) lies on these lines: {3, 6}, {193, 32518}, {262, 8921}, {880, 10104}, {7777, 32531}, {11059, 23216}, {20794, 21444}
The radical circle of the power-circles is also called the De Longchamps circle.
X(50666) lies on these lines: {2, 3186}, {3, 6}, {5, 43976}, {22, 44089}, {53, 15980}, {69, 20819}, {141, 19602}, {160, 17710}, {206, 19576}, {237, 12220}, {264, 21531}, {325, 1368}, {339, 44166}, {1176, 43722}, {1249, 2967}, {1843, 11328}, {1916, 2998}, {1974, 6660}, {2165, 38224}, {2790, 6033}, {2971, 16041}, {2972, 16051}, {3148, 26206}, {3164, 37190}, {3784, 22064}, {3785, 22424}, {3867, 44230}, {3964, 10602}, {3981, 40377}, {5159, 16313}, {6389, 39080}, {6467, 20794}, {6676, 7792}, {6776, 44716}, {7386, 7774}, {7467, 22240}, {7494, 16989}, {7778, 20208}, {8681, 22152}, {9971, 35222}, {10349, 28723}, {10691, 41624}, {11585, 14059}, {12167, 37344}, {12294, 31952}, {12836, 18194}, {14575, 22151}, {14603, 40073}, {15561, 42406}, {16098, 42407}, {18374, 33801}, {18589, 20254}, {19121, 46546}, {20775, 22087}, {20806, 40947}, {20821, 22169}, {23333, 44388}, {30172, 35552}, {34828, 44380}, {37452, 45921}, {38739, 46262}
X(50666) = midpoint of X(9307) and X(14615)
X(50666) = reflection of X(i) in X(j) for these (i, j): (30262, 3), (43976, 5)
X(50666) = complement of X(3186)
X(50666) = isogonal conjugate of the polar conjugate of X(5025)
X(50666) = isotomic conjugate of the polar conjugate of X(3981)
X(50666) = complementary conjugate of the complement of X(3504)
X(50666) = barycentric product X(i)*X(j) for these {i, j}: {3, 5025}, {69, 3981}, {1176, 40379}
X(50666) = trilinear product X(i)*X(j) for these {i, j}: {48, 5025}, {63, 3981}
X(50666) = inverse of X(37893) in 1st Brocard circle
X(50666) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(37893)}} and {{A, B, C, X(3), X(5025)}}
X(50666) = Cevapoint of X(525) and X(4609)
X(50666) = crosssum of X(i) and X(j) for these (i, j): {520, 44451}, {525, 9426}
X(50666) = X(48)-complementary conjugate of-X(6374)
X(50666) = X(30262)-of-ABC-X3 reflections triangle
X(50666) = X(43976)-of-Johnson triangle
X(50666) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 6, 37893), (6, 3001, 50645), (6, 50645, 3095), (216, 11574, 3), (17710, 34990, 160), (20819, 20975, 69), (20821, 22169, 22370)
X(50667) lies on these lines: {3, 6}, {1154, 2963}, {5889, 18353}, {16336, 34520}
X(50667) = {X(371), X(372)}-harmonic conjugate of X(15787)
X(50668) lies on these lines: {3, 6}, {160, 45186}, {311, 32830}, {428, 21668}, {1907, 13051}, {3613, 27356}, {5480, 36212}, {39506, 50135}
X(50669) lies on these lines: {3, 6}, {22, 7778}, {69, 7669}, {99, 44166}, {141, 37183}, {157, 599}, {160, 2916}, {308, 34885}, {325, 6636}, {376, 41761}, {548, 45921}, {1576, 20819}, {3148, 3763}, {3447, 36163}, {4558, 17710}, {5152, 33769}, {5938, 7801}, {7467, 44521}, {7782, 40073}, {7792, 15246}, {7818, 11641}, {7832, 33717}, {7835, 37898}, {7881, 33802}, {7934, 37902}, {10519, 37813}, {14907, 42407}, {19121, 34990}, {19596, 33801}, {34573, 37335}, {40341, 40947}
X(50669) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 37485, 8553), (160, 46546, 2916), (3001, 37893, 6), (5157, 9737, 13351)
X(50670) lies on these lines: {3, 6}, {83, 14950}, {316, 8272}, {3589, 15449}, {9482, 22352}
X(50671) lies on these lines: {3, 6}, {53, 40647}, {233, 11695}, {393, 10574}, {3087, 15043}, {5462, 6748}, {6000, 36412}, {9826, 32438}, {15053, 41758}, {15466, 32002}, {40641, 44084}
X(50672) lies on these lines: {3, 6}, {110, 1003}, {3231, 12525}, {5108, 6232}, {5468, 35925}, {5651, 11286}, {11003, 13586}
X(50673) lies on these lines: {3, 6}, {111, 13860}, {381, 5106}, {3231, 35934}, {6232, 11676}
X(50674) lies on these lines: {3, 6}, {6876, 11495}
X(50675) lies on these lines: {3, 6}, {51, 40680}, {264, 6524}, {3164, 6995}, {5943, 6389}, {9822, 41005}, {10110, 42353}, {14767, 46737}, {26870, 45186}, {34608, 47383}, {34854, 45198}, {40981, 46832}
X(50676) lies on these lines: {2, 22353}, {3, 6}, {131, 18388}, {160, 11649}, {264, 328}, {3153, 3164}, {3818, 23635}, {7547, 39530}, {7777, 16188}, {10224, 18121}, {14575, 34218}, {18122, 46029}, {18377, 18380}, {22515, 44263}, {34507, 44716}
X(50676) = complement of the circumtangential-isogonal conjugate of X(184)
X(50677) lies on these lines: {1, 1418}, {3, 6}, {4, 17245}, {20, 4648}, {21, 25878}, {37, 5732}, {40, 49478}, {44, 21153}, {45, 971}, {55, 1407}, {56, 2293}, {141, 36706}, {154, 16064}, {220, 1818}, {241, 7675}, {269, 3601}, {376, 3332}, {516, 4675}, {548, 5733}, {603, 1253}, {631, 17337}, {940, 7411}, {968, 5918}, {990, 16777}, {1001, 1742}, {1005, 25934}, {1086, 21151}, {1191, 4300}, {1279, 3576}, {1427, 10383}, {1434, 3522}, {1456, 37600}, {1471, 5204}, {1615, 16588}, {1721, 15569}, {1834, 37108}, {2263, 2646}, {3052, 15931}, {3207, 3220}, {3445, 30389}, {3523, 37650}, {3752, 10857}, {3755, 43151}, {4189, 37659}, {4191, 17810}, {4210, 33586}, {5646, 16373}, {5759, 17365}, {6610, 30282}, {7290, 7987}, {7431, 46890}, {7580, 37674}, {8572, 15287}, {8726, 15852}, {10178, 17594}, {10387, 37575}, {10516, 36474}, {12618, 17267}, {12652, 42819}, {13633, 38072}, {13727, 15668}, {15688, 45942}, {15717, 37681}, {15750, 44100}, {16466, 35202}, {16885, 31658}, {17119, 29016}, {17194, 37270}, {17259, 48878}, {17265, 36652}, {17276, 43177}, {17334, 36996}, {17811, 20835}, {17825, 37309}, {19541, 37682}, {28014, 37328}, {29181, 36698}, {34046, 37601}, {35986, 37633}, {36674, 48910}, {36990, 49131}, {38692, 44858}, {48872, 49132}
X(50677) = crossdifference of every pair of points on line {X(523), X(14282)}
X(50677) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 500, 36745), (3, 991, 6), (3, 1350, 37499), (3, 33878, 48886), (3, 37474, 5085), (3, 37501, 4252), (55, 22053, 1407), (1151, 1152, 4258), (4300, 8273, 1191), (8726, 15852, 17054)
X(50678) lies on these lines: {2, 1625}, {3, 6}, {5, 3331}, {140, 217}, {184, 35324}, {232, 5892}, {401, 15018}, {458, 46106}, {549, 3289}, {1656, 32445}, {2207, 15805}, {2211, 38110}, {3054, 45938}, {3767, 48262}, {3851, 38297}, {5012, 32661}, {5054, 40805}, {5056, 41367}, {5422, 35941}, {7749, 45935}, {8744, 37124}, {9419, 40108}, {10986, 15080}, {11360, 40951}, {11451, 33885}, {13630, 22416}, {14535, 17825}, {14845, 33842}, {14855, 33843}, {15045, 22240}, {15066, 37067}, {18907, 20965}, {34573, 34850}, {42459, 47301}
X(50679) lies on these lines: {3, 6}, {5892, 6128}, {20791, 34288}
X(50680) lies on these lines: {3, 6}, {487, 26362}, {3595, 32488}, {6459, 23334}, {8946, 11473}, {12222, 13639}, {12257, 43408}, {13934, 45523}, {32492, 42268}, {35265, 41419}, {49019, 49103}, {49039, 49220}
X(50680) = X(50680)-of-circumsymmedial triangle
X(50680) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 371, 8375), (187, 11477, 50681), (371, 9732, 6424), (371, 12313, 6422), (1351, 6221, 2460), (3364, 3389, 43118), (9737, 44656, 372), (9738, 44509, 3)
X(50681) lies on these lines: {3, 6}, {488, 26361}, {3593, 32489}, {6460, 23334}, {8948, 11474}, {12221, 13759}, {12256, 43407}, {13882, 45522}, {32495, 42269}, {49018, 49104}, {49038, 49221}
X(50681) = X(50681)-of-circumsymmedial triangle
X(50681) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 372, 8376), (187, 11477, 50680), (372, 9733, 6423), (372, 12314, 6421), (1351, 6398, 2459), (3365, 3390, 43119), (9737, 44657, 371), (9739, 44510, 3)
X(50682) lies on these lines: {3, 6}, {9117, 38317}, {10516, 22997}, {16962, 22490}, {38136, 43451}
X(50682) = X(50682)-of-circumsymmedial triangle
X(50682) = {X(187), X(15520)}-harmonic conjugate of X(50683)
X(50683) lies on these lines: {3, 6}, {9115, 38317}, {10516, 22998}, {16963, 22489}, {38136, 43452}
X(50683) = X(50683)-of-circumsymmedial triangle
X(50683) = {X(187), X(15520)}-harmonic conjugate of X(50682)
X(50684) lies on these lines: {3, 6}, {114, 9756}, {141, 10256}, {193, 21445}, {2065, 14253}, {3564, 7763}, {3589, 37348}, {3818, 36519}, {6776, 32829}, {7631, 35364}, {7694, 15980}, {7803, 38110}, {9744, 48906}, {9754, 37451}, {10352, 13860}, {21850, 39656}, {37334, 39141}, {45554, 48743}, {45555, 48742}
X(50684) = X(50684)-of-circumsymmedial triangle
X(50684) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 182, 35429), (3, 1351, 35383), (39, 182, 5050), (182, 5092, 35423), (182, 9737, 1692), (1692, 9737, 1351), (5092, 13355, 3)
X(50685) lies on these lines: {3, 6}, {69, 35930}, {193, 11676}, {2882, 18534}, {3564, 20065}, {3852, 39879}, {6321, 48910}, {7770, 48876}, {9753, 37688}, {11285, 18583}, {13860, 17008}, {14984, 38661}
X(50685) = reflection of X(i) in X(j) for these (i, j): (3, 5017), (13355, 41413)
X(50685) = X(5017)-of-X3-ABC reflections triangle
X(50685) = X(50685)-of-circumsymmedial triangle
X(50685) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3098, 35423, 3), (5052, 5171, 35429)
X(50686) lies on these lines: {3, 6}, {2175, 23857}, {3570, 49127}, {3882, 20794}, {4220, 16997}, {6010, 30487}, {10446, 19522}, {23355, 39225}
X(50687) lies on these lines: {2, 3}, {6, 43507}, {8, 34648}, {13, 42104}, {14, 42105}, {61, 49825}, {62, 49824}, {68, 46851}, {145, 31162}, {147, 8596}, {165, 38076}, {315, 32869}, {316, 10513}, {390, 11237}, {395, 42141}, {396, 42140}, {485, 43257}, {486, 43256}, {519, 9812}, {538, 23334}, {597, 14927}, {598, 43951}, {671, 5984}, {754, 7620}, {962, 31145}, {1131, 32787}, {1132, 32788}, {1327, 35821}, {1328, 35820}, {1503, 5032}, {1698, 34638}, {1699, 38314}, {1992, 36990}, {2794, 41135}, {2979, 46847}, {3058, 5229}, {3060, 32062}, {3068, 42575}, {3069, 42574}, {3241, 5691}, {3424, 41895}, {3586, 15933}, {3590, 42577}, {3591, 42576}, {3592, 43376}, {3594, 43377}, {3600, 11238}, {3616, 34628}, {3617, 34632}, {3620, 47354}, {3621, 12699}, {3622, 18483}, {3623, 3656}, {3655, 33697}, {3679, 20070}, {3785, 32893}, {4297, 30308}, {4669, 9589}, {4678, 18480}, {4846, 14487}, {5175, 17781}, {5225, 5434}, {5261, 10385}, {5274, 12943}, {5286, 14537}, {5334, 36969}, {5335, 36970}, {5343, 42161}, {5344, 42160}, {5355, 14075}, {5365, 16965}, {5366, 16964}, {5556, 6738}, {5603, 28208}, {5657, 28202}, {5731, 38021}, {5921, 48901}, {6000, 11002}, {6033, 35369}, {6053, 9143}, {6054, 20094}, {6425, 41952}, {6426, 41951}, {6435, 23249}, {6436, 23259}, {6494, 7583}, {6495, 7584}, {6498, 7581}, {6499, 7582}, {7585, 42284}, {7586, 42283}, {7694, 32480}, {7737, 39563}, {7739, 14930}, {7750, 32872}, {7768, 32892}, {7773, 32841}, {7799, 32827}, {7809, 32815}, {7811, 32834}, {7917, 32830}, {7999, 46852}, {8591, 10723}, {8972, 42263}, {9140, 13202}, {9541, 42604}, {9542, 18538}, {9543, 35786}, {9545, 13482}, {9778, 19875}, {9779, 25055}, {9880, 10722}, {10056, 18513}, {10072, 18514}, {10152, 46808}, {10653, 42133}, {10654, 42134}, {10706, 12295}, {10710, 20096}, {10711, 20095}, {10714, 38956}, {11004, 44413}, {11057, 32828}, {11160, 47353}, {11179, 48884}, {11180, 20080}, {11185, 32874}, {11239, 41698}, {11381, 21849}, {11439, 13598}, {11451, 13570}, {11480, 43873}, {11481, 43874}, {11542, 43482}, {11543, 43481}, {11645, 14853}, {12111, 21969}, {12112, 39522}, {12243, 22515}, {12278, 32605}, {12512, 19876}, {12528, 31822}, {12816, 40693}, {12817, 40694}, {12820, 42635}, {12821, 42636}, {13172, 22566}, {13445, 34417}, {13474, 14831}, {13754, 16981}, {13846, 42271}, {13847, 42272}, {13941, 42264}, {14235, 48476}, {14239, 48477}, {14458, 38259}, {14492, 18845}, {14848, 33748}, {14907, 32885}, {15031, 32870}, {15072, 16226}, {15431, 32269}, {15811, 43605}, {16001, 36318}, {16002, 36320}, {16241, 42112}, {16242, 42113}, {16267, 19107}, {16268, 19106}, {16621, 34799}, {16644, 42108}, {16645, 42109}, {16962, 42085}, {16963, 42086}, {17013, 18506}, {17503, 47586}, {18492, 46933}, {18525, 20014}, {19053, 23261}, {19054, 23251}, {20049, 22793}, {20059, 31672}, {20423, 48895}, {20582, 48872}, {21356, 29181}, {22235, 42147}, {22237, 42148}, {22615, 23253}, {22644, 23263}, {25406, 38072}, {25561, 48873}, {25565, 48896}, {28198, 38074}, {31412, 41945}, {31730, 46932}, {32819, 32840}, {32822, 32879}, {32826, 32833}, {32837, 48913}, {35242, 46930}, {35510, 36889}, {35770, 43515}, {35771, 43516}, {35787, 43407}, {36413, 36430}, {36836, 42775}, {36843, 42776}, {36967, 42106}, {36968, 42103}, {37640, 42094}, {37641, 42093}, {37749, 44987}, {38077, 38693}, {38084, 38754}, {40330, 48904}, {41100, 42159}, {41101, 42162}, {41107, 42481}, {41108, 42480}, {41119, 43475}, {41120, 43476}, {41121, 42150}, {41122, 42151}, {41943, 42921}, {41944, 42920}, {41946, 42561}, {41957, 43799}, {41958, 43800}, {41979, 42725}, {41980, 42726}, {42095, 43100}, {42098, 43107}, {42099, 42911}, {42100, 42910}, {42101, 42155}, {42102, 42154}, {42107, 42625}, {42110, 42626}, {42111, 42528}, {42114, 42529}, {42119, 43364}, {42120, 43365}, {42125, 43242}, {42126, 42982}, {42127, 42983}, {42128, 43243}, {42135, 43543}, {42136, 42974}, {42137, 42975}, {42138, 43542}, {42139, 42943}, {42142, 42942}, {42149, 46334}, {42152, 46335}, {42163, 43769}, {42164, 43773}, {42165, 43774}, {42166, 43770}, {42215, 42540}, {42216, 42539}, {42262, 43209}, {42265, 43210}, {42266, 42602}, {42267, 42603}, {42270, 42414}, {42273, 42413}, {42429, 42918}, {42430, 42919}, {42431, 42510}, {42432, 42511}, {42494, 43194}, {42495, 43193}, {42514, 43239}, {42515, 43238}, {42537, 42638}, {42538, 42637}, {42627, 43493}, {42628, 43494}, {42629, 43782}, {42630, 43781}, {42633, 42803}, {42634, 42804}, {42727, 46473}, {42728, 46476}, {42785, 46264}, {42813, 49874}, {42814, 49873}, {42904, 43020}, {42905, 43021}, {43016, 43311}, {43017, 43310}, {43032, 43233}, {43033, 43232}, {43338, 43888}, {43339, 43887}, {43572, 46261}, {43632, 49907}, {43633, 49908}, {47102, 47617}
X(50687) = midpoint of X(i) and X(j) for these {i,j}: {382, 5055}, {3524, 15682}, {3543, 3839}, {3830, 38335}, {11001, 35409}, {11539, 35404}, {15684, 15688}, {33699, 38071}
X(50687) = reflection of X(i) in X(j) for these {i,j}: {2, 3839}, {3, 38071}, {4, 38335}, {20, 3524}, {165, 38076}, {376, 5055}, {550, 47599}, {3524, 381}, {3534, 11539}, {3545, 14269}, {3839, 4}, {5054, 23046}, {5055, 3845}, {5731, 38021}, {8703, 14892}, {9778, 19875}, {10304, 3545}, {11001, 15688}, {11539, 546}, {12103, 14890}, {14892, 3861}, {15072, 16226}, {15681, 45759}, {15688, 5}, {15689, 15699}, {15691, 41984}, {15699, 41987}, {15704, 41982}, {25406, 38072}, {35409, 15684}, {38071, 14893}, {38314, 1699}, {38320, 428}, {38335, 15687}, {38693, 38077}, {38754, 38084}, {41982, 11737}, {45759, 5066}, {46333, 3}, {49135, 35409}
X(50687) = anticomplement of X(10304)
X(50687) = orthoptic-circle-of-Steiner-circumellipse-inverse of X(37904)
X(50687) = anticomplement of the isogonal conjugate of X(14490)
X(50687) = X(14490)-anticomplementary conjugate of X(8)
X(50687) = crosspoint of X(43540) and X(43541)
X(50687) = crosssum of X(11480) and X(11481)
X(50687) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 376, 15717}, {2, 381, 5068}, {2, 3146, 15683}, {2, 3543, 3146}, {2, 5059, 376}, {2, 15683, 3522}, {2, 17578, 3543}, {2, 19686, 33201}, {2, 21734, 549}, {3, 381, 10109}, {3, 3830, 35434}, {3, 14893, 41099}, {3, 35434, 33699}, {4, 376, 3845}, {4, 382, 3091}, {4, 3090, 3861}, {4, 3146, 3832}, {4, 3529, 3843}, {4, 3543, 2}, {4, 3545, 14269}, {4, 3627, 20}, {4, 3830, 3543}, {4, 15682, 381}, {4, 17578, 3146}, {4, 33703, 546}, {4, 35480, 6623}, {4, 41099, 14893}, {4, 44438, 7378}, {4, 44440, 37349}, {5, 11001, 15692}, {5, 15684, 11001}, {5, 15688, 15709}, {5, 15691, 15701}, {5, 15692, 2}, {5, 15759, 15723}, {5, 49137, 21735}, {13, 43400, 42104}, {14, 43399, 42105}, {20, 381, 2}, {20, 3091, 140}, {20, 3543, 15682}, {20, 10304, 15689}, {20, 11541, 5059}, {20, 15721, 8703}, {20, 46935, 3}, {20, 49135, 49137}, {140, 382, 11541}, {140, 3524, 15708}, {140, 3627, 382}, {140, 3845, 381}, {140, 11541, 20}, {140, 12101, 41988}, {140, 15685, 376}, {140, 15691, 15759}, {140, 41986, 15699}, {140, 41988, 3845}, {376, 382, 15640}, {376, 3091, 2}, {376, 3845, 3091}, {376, 5055, 15708}, {376, 5067, 15693}, {376, 11541, 15685}, {376, 15640, 5059}, {376, 15682, 11541}, {376, 15685, 20}, {376, 15723, 15692}, {376, 17504, 10304}, {381, 382, 15685}, {381, 3534, 5070}, {381, 3627, 15682}, {381, 3830, 3627}, {381, 5073, 8703}, {381, 8703, 3090}, {381, 12101, 4}, {381, 12811, 41106}, {381, 14269, 41987}, {381, 14891, 5071}, {381, 15682, 20}, {381, 15684, 15691}, {381, 15685, 140}, {381, 15689, 15699}, {381, 15699, 3545}, {381, 15701, 5}, {381, 35403, 41988}, {381, 41990, 3855}, {381, 49137, 15701}, {382, 3091, 5059}, {382, 3845, 376}, {382, 5059, 3146}, {382, 12102, 4}, {382, 14269, 17504}, {382, 15693, 35400}, {382, 35402, 3830}, {382, 35403, 3845}, {382, 46853, 33703}, {452, 6175, 2}, {546, 3534, 5071}, {546, 33703, 3523}, {546, 35404, 3534}, {546, 41981, 5}, {547, 1657, 19708}, {547, 10303, 2}, {547, 19708, 10303}, {548, 15703, 15719}, {549, 3529, 15697}, {549, 3843, 41106}, {549, 5056, 2}, {549, 15697, 21734}, {549, 41106, 5056}, {549, 45762, 381}, {550, 19709, 15702}, {550, 45760, 3}, {550, 47599, 15706}, {1656, 15686, 15698}, {1657, 3855, 10303}, {2043, 2044, 3525}, {3090, 5073, 20}, {3090, 8703, 15721}, {3090, 15721, 2}, {3091, 3543, 15640}, {3091, 3856, 3854}, {3091, 5059, 15717}, {3091, 15640, 376}, {3091, 15708, 5055}, {3146, 3832, 3522}, {3146, 3839, 15705}, {3146, 5068, 20}, {3146, 15717, 5059}, {3522, 3832, 15022}, {3523, 5071, 2}, {3524, 3545, 15699}, {3524, 15689, 10304}, {3524, 15709, 15701}, {3524, 15710, 14891}, {3526, 15690, 15715}, {3528, 3850, 46936}, {3529, 3843, 5056}, {3529, 5056, 21734}, {3529, 41106, 549}, {3529, 45757, 10304}, {3534, 5070, 14891}, {3534, 5071, 3523}, {3534, 11539, 15710}, {3534, 35404, 33703}, {3534, 46853, 376}, {3543, 3830, 17578}, {3543, 3845, 5059}, {3543, 15640, 382}, {3543, 15692, 15684}, {3544, 15719, 15703}, {3545, 10304, 2}, {3545, 11001, 41983}, {3545, 14269, 3839}, {3627, 3861, 5073}, {3627, 12101, 381}, {3627, 15682, 3543}, {3627, 15687, 12101}, {3627, 41988, 15685}, {3627, 44903, 33699}, {3830, 5076, 15687}, {3830, 12101, 15682}, {3830, 12102, 376}, {3830, 15687, 4}, {3830, 35401, 5076}, {3830, 35403, 382}, {3832, 15683, 2}, {3839, 10304, 3545}, {3839, 15640, 15708}, {3839, 15708, 3091}, {3839, 49135, 15709}, {3845, 3853, 35402}, {3845, 12102, 35403}, {3845, 15640, 2}, {3845, 15687, 12102}, {3845, 15704, 11737}, {3845, 35400, 5067}, {3845, 35403, 4}, {3845, 35404, 46853}, {3850, 19710, 15694}, {3850, 49136, 3528}, {3853, 5076, 4}, {3853, 15687, 3830}, {3854, 46935, 5068}, {3855, 19708, 547}, {3856, 14893, 3845}, {3858, 17800, 3525}, {3860, 15686, 1656}, {3861, 5073, 3090}, {3861, 8703, 381}, {3861, 15682, 15721}, {5054, 5055, 41985}, {5054, 14269, 23046}, {5054, 23046, 3545}, {5054, 35418, 15705}, {5055, 15708, 2}, {5055, 15759, 15709}, {5056, 15697, 549}, {5066, 15681, 631}, {5066, 18586, 36454}, {5066, 18587, 36436}, {5066, 35407, 376}, {5067, 41982, 15708}, {5068, 15682, 15683}, {5070, 33703, 20}, {5070, 49137, 41981}, {5071, 15710, 11539}, {5071, 33703, 3534}, {5072, 15695, 10124}, {5129, 44217, 2}, {5177, 31156, 2}, {6658, 32980, 33205}, {6661, 33180, 2}, {6871, 15677, 2}, {6995, 31133, 2}, {7398, 31152, 2}, {7486, 15702, 2}, {7527, 18534, 37913}, {7530, 13596, 10298}, {7924, 32971, 2}, {8370, 33210, 2}, {8597, 33016, 33272}, {9818, 37945, 7492}, {9880, 10722, 11177}, {10109, 44903, 3}, {10109, 47598, 15699}, {10124, 15695, 10299}, {10304, 15708, 17504}, {11001, 15684, 49135}, {11001, 15691, 20}, {11001, 15709, 15688}, {11001, 21735, 15691}, {11348, 44216, 2}, {11539, 15710, 3523}, {11737, 15693, 5067}, {11737, 15704, 15693}, {11737, 35400, 376}, {12102, 41988, 12101}, {14044, 33280, 32972}, {14063, 19686, 2}, {14066, 33279, 32971}, {14269, 15689, 381}, {14269, 47598, 41099}, {14784, 14785, 46853}, {14893, 15682, 46935}, {14893, 33699, 3}, {14893, 44903, 381}, {15640, 15717, 15683}, {15681, 15716, 44245}, {15682, 15685, 15640}, {15682, 15691, 49135}, {15682, 41987, 10304}, {15682, 41988, 3091}, {15684, 15701, 49137}, {15687, 35402, 376}, {15688, 15709, 15692}, {15688, 41984, 3524}, {15689, 15699, 3524}, {15689, 41983, 21735}, {15689, 41987, 3545}, {15691, 15701, 21735}, {15691, 49137, 11001}, {15692, 49135, 11001}, {15693, 15704, 376}, {15693, 35400, 15704}, {15694, 19710, 3528}, {15694, 46936, 2}, {15694, 49136, 19710}, {15697, 41106, 2}, {15698, 49138, 15686}, {15699, 17504, 140}, {15699, 41986, 5055}, {15699, 41987, 381}, {15701, 15723, 140}, {15701, 21735, 15692}, {15701, 41984, 15709}, {15701, 49137, 15691}, {15702, 19709, 7486}, {15706, 19709, 47599}, {15706, 44580, 3524}, {15706, 47599, 15702}, {15707, 44682, 3524}, {15709, 21735, 3524}, {15709, 35409, 11001}, {15759, 41983, 17504}, {16044, 33263, 2}, {17504, 41985, 5054}, {21735, 49137, 20}, {22615, 43503, 35822}, {22644, 43504, 35823}, {32966, 33266, 2}, {32972, 33246, 2}, {32979, 33019, 33025}, {33006, 35927, 2}, {33016, 33272, 2}, {33198, 33223, 2}, {33199, 33224, 2}, {35822, 43503, 23253}, {35823, 43504, 23263}, {36436, 36454, 15681}, {36445, 36463, 5}, {37640, 42094, 43540}, {37640, 42940, 43466}, {37641, 42093, 43541}, {37641, 42941, 43465}, {41099, 44903, 46935}, {41990, 44682, 547}, {42093, 42941, 37641}, {42094, 42940, 37640}, {43465, 43478, 43541}, {43465, 43541, 37641}, {43466, 43477, 43540}, {43466, 43540, 37640}, {43477, 43540, 42094}, {43478, 43541, 42093}, {43507, 43508, 6}, {45758, 47478, 15699}, {46333, 47598, 10304}
X(50688) lies on these lines: {2, 3}, {6, 43405}, {13, 43018}, {14, 43019}, {15, 43364}, {16, 43365}, {61, 42104}, {62, 42105}, {64, 18296}, {68, 46848}, {79, 18221}, {145, 22793}, {193, 48901}, {390, 3585}, {393, 36431}, {397, 42478}, {398, 42479}, {485, 43883}, {486, 43884}, {515, 10248}, {590, 10147}, {615, 10148}, {962, 3632}, {1131, 6561}, {1132, 6560}, {1327, 43376}, {1328, 43377}, {1539, 14683}, {1587, 43507}, {1588, 43508}, {1699, 3636}, {1899, 34563}, {2093, 7319}, {2777, 15044}, {2979, 40247}, {3060, 13474}, {3087, 15860}, {3244, 5691}, {3303, 5229}, {3304, 5225}, {3411, 49873}, {3412, 49874}, {3583, 3600}, {3586, 11036}, {3592, 42284}, {3594, 42283}, {3622, 28160}, {3626, 7991}, {3629, 36990}, {3746, 5261}, {3868, 31822}, {3951, 5175}, {3982, 11518}, {4031, 9579}, {4293, 18514}, {4294, 18513}, {4301, 34747}, {4678, 28174}, {5007, 43448}, {5237, 42103}, {5238, 42106}, {5265, 10483}, {5274, 5563}, {5304, 7747}, {5334, 42161}, {5335, 42160}, {5343, 16965}, {5344, 16964}, {5349, 37641}, {5350, 37640}, {5351, 42113}, {5352, 42112}, {5365, 10653}, {5366, 10654}, {5395, 14488}, {5446, 11455}, {5480, 33748}, {5556, 11529}, {5603, 33697}, {5656, 34786}, {5889, 32062}, {5921, 11008}, {5984, 22515}, {6154, 10724}, {6225, 18405}, {6241, 11002}, {6419, 22615}, {6420, 22644}, {6425, 31412}, {6426, 42272}, {6427, 23267}, {6428, 23273}, {6447, 13886}, {6448, 13939}, {6453, 8972}, {6454, 13941}, {6486, 43337}, {6487, 43336}, {6488, 42265}, {6489, 42262}, {6496, 43788}, {6497, 43787}, {6519, 18538}, {6522, 18762}, {6564, 43512}, {6565, 43511}, {6776, 22330}, {7585, 23253}, {7586, 23263}, {7620, 14023}, {7687, 15021}, {7748, 37665}, {7758, 23334}, {7982, 9812}, {7989, 28158}, {8960, 43257}, {8976, 9543}, {9541, 35786}, {9542, 42258}, {9545, 26883}, {9589, 34648}, {9656, 10385}, {9778, 18492}, {9780, 28150}, {9781, 14915}, {9961, 16616}, {10110, 12279}, {10113, 38626}, {10152, 35711}, {10519, 48904}, {10625, 16261}, {10721, 36253}, {10722, 38734}, {10723, 38745}, {10725, 38769}, {10726, 38781}, {10733, 24981}, {10734, 38801}, {11004, 32139}, {11185, 32868}, {11381, 16625}, {11412, 46849}, {11439, 45186}, {11444, 46847}, {11469, 18387}, {11482, 39874}, {12112, 36749}, {12244, 15027}, {12250, 18383}, {12295, 14094}, {12690, 20008}, {12699, 20054}, {12820, 22235}, {12821, 22237}, {12943, 14986}, {13202, 15054}, {13452, 17505}, {13598, 15305}, {13665, 43560}, {13785, 43561}, {14241, 31487}, {14516, 16656}, {14561, 48942}, {14639, 35021}, {14641, 15024}, {14853, 22234}, {15012, 15072}, {15029, 16163}, {15034, 46686}, {15045, 44863}, {15052, 37498}, {15077, 15741}, {15801, 32340}, {15808, 28164}, {16658, 34799}, {16772, 42775}, {16773, 42776}, {16835, 32533}, {17852, 42259}, {18480, 20070}, {18843, 43951}, {19106, 42159}, {19107, 42162}, {20080, 39884}, {20094, 22505}, {20095, 22799}, {20096, 38630}, {22236, 42102}, {22238, 42101}, {22682, 32522}, {22938, 38631}, {23235, 39809}, {31404, 31652}, {31663, 46931}, {32826, 37668}, {33698, 43537}, {34632, 37714}, {35007, 37689}, {35812, 43523}, {35813, 43524}, {36836, 42108}, {36843, 42109}, {36969, 42613}, {36970, 42612}, {37667, 50570}, {37832, 42932}, {37835, 42933}, {38140, 46932}, {38664, 39838}, {38686, 38956}, {40330, 43621}, {40693, 43540}, {40694, 43541}, {41112, 41973}, {41113, 41974}, {41244, 41914}, {42090, 42581}, {42091, 42580}, {42093, 42165}, {42094, 42164}, {42096, 42598}, {42097, 42599}, {42099, 43869}, {42100, 43870}, {42119, 42166}, {42120, 42163}, {42136, 43473}, {42137, 43474}, {42150, 42939}, {42151, 42938}, {42153, 43401}, {42156, 43402}, {42157, 43403}, {42158, 43404}, {42215, 43520}, {42216, 43519}, {42263, 43879}, {42264, 43880}, {42488, 42798}, {42489, 42797}, {42494, 42942}, {42495, 42943}, {42584, 43464}, {42585, 43463}, {42781, 43771}, {42782, 43772}, {42803, 43556}, {42804, 43557}, {42815, 42888}, {42816, 42889}, {42896, 42967}, {42897, 42966}, {42900, 43251}, {42901, 43250}, {42908, 42990}, {42909, 42991}, {42920, 43633}, {42921, 43632}, {42962, 43630}, {42963, 43631}, {42988, 43482}, {42989, 43481}, {43566, 43570}, {43567, 43571}, {43605, 44413}
X(50688) = midpoint of X(i) and X(j) for these {i,j}: {382, 3851}, {15682, 15702}
X(50688) = reflection of X(i) in X(j) for these {i,j}: {3, 3857}, {20, 3523}, {3523, 3832}, {3528, 3851}, {3832, 4}, {14869, 546}, {15698, 381}, {15703, 3845}, {44904, 3861}
X(50688) = anticomplement of X(3528)
X(50688) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 382, 49135}, {2, 546, 3091}, {2, 3146, 3529}, {2, 3522, 3530}, {2, 3528, 3523}, {2, 3832, 3851}, {2, 15681, 10304}, {2, 15683, 15688}, {2, 17504, 15721}, {2, 49135, 20}, {3, 381, 12812}, {3, 546, 3544}, {3, 3091, 46936}, {3, 3146, 49140}, {3, 3544, 2}, {3, 3857, 3090}, {3, 5076, 12102}, {3, 12102, 4}, {3, 12812, 3525}, {3, 26863, 14002}, {3, 35419, 49134}, {3, 46936, 10303}, {3, 49140, 20}, {4, 20, 3839}, {4, 376, 3843}, {4, 382, 2}, {4, 631, 3845}, {4, 3146, 3091}, {4, 3529, 546}, {4, 3543, 20}, {4, 3545, 3861}, {4, 3627, 3146}, {4, 3830, 17578}, {4, 3855, 14269}, {4, 5073, 3854}, {4, 10431, 13729}, {4, 13488, 7409}, {4, 15682, 5}, {4, 17578, 3543}, {4, 33699, 15717}, {4, 33703, 381}, {4, 35409, 3859}, {4, 35480, 3089}, {4, 35490, 3088}, {4, 49138, 41099}, {5, 5059, 10304}, {5, 10299, 2}, {5, 11540, 1656}, {5, 15681, 10299}, {5, 15682, 5059}, {5, 38335, 4}, {5, 49136, 17538}, {20, 3091, 10303}, {20, 3839, 5056}, {20, 5056, 15692}, {20, 15708, 3522}, {20, 46936, 3}, {140, 15684, 49138}, {376, 3843, 5068}, {376, 38071, 2}, {381, 382, 49139}, {381, 3522, 7486}, {381, 15704, 3525}, {381, 33703, 3522}, {381, 49139, 3530}, {382, 546, 3529}, {382, 3529, 3146}, {382, 3530, 33703}, {382, 14269, 550}, {382, 15687, 4}, {382, 15688, 5073}, {546, 550, 5079}, {546, 3529, 2}, {546, 3627, 382}, {546, 3628, 38071}, {546, 5079, 3855}, {546, 12103, 35018}, {546, 14869, 3851}, {546, 49136, 10299}, {546, 49139, 3525}, {550, 3855, 2}, {550, 14269, 3855}, {550, 15700, 3528}, {631, 3845, 3854}, {631, 5073, 15683}, {631, 35018, 2}, {632, 3627, 33699}, {1131, 6561, 42522}, {1132, 6560, 42523}, {1656, 11001, 21734}, {1656, 21734, 15721}, {1657, 3545, 15717}, {1657, 3861, 3545}, {1657, 15697, 20}, {1657, 15717, 15697}, {1657, 35403, 3861}, {2043, 2044, 15709}, {2045, 42281, 35732}, {2046, 42280, 42282}, {3090, 3528, 14869}, {3090, 3529, 3528}, {3090, 3832, 3091}, {3090, 14869, 2}, {3090, 15698, 3525}, {3091, 3146, 20}, {3091, 3523, 3090}, {3091, 3543, 3146}, {3091, 10303, 5056}, {3091, 15697, 632}, {3091, 15704, 15708}, {3091, 49140, 3}, {3146, 3529, 49135}, {3146, 3627, 3543}, {3146, 3854, 12103}, {3146, 5059, 49136}, {3146, 17578, 3627}, {3522, 7486, 15708}, {3525, 15704, 3522}, {3525, 15708, 10303}, {3525, 33703, 15704}, {3528, 3851, 2}, {3528, 15702, 10299}, {3529, 3544, 3}, {3529, 10299, 17538}, {3529, 17538, 15681}, {3530, 15713, 15720}, {3530, 35018, 47598}, {3533, 15696, 15705}, {3533, 35416, 3146}, {3534, 3858, 5067}, {3543, 3839, 15640}, {3543, 10304, 15682}, {3543, 49135, 382}, {3545, 15717, 46935}, {3545, 34200, 2}, {3627, 3853, 5076}, {3627, 5076, 4}, {3627, 12101, 49137}, {3627, 12102, 3}, {3627, 15687, 546}, {3627, 38335, 17538}, {3628, 49137, 376}, {3830, 3853, 4}, {3830, 5076, 3627}, {3832, 5059, 15702}, {3839, 10303, 3091}, {3839, 15640, 15692}, {3843, 12101, 4}, {3843, 15720, 38071}, {3843, 49137, 3628}, {3845, 5073, 631}, {3845, 12103, 5072}, {3845, 47598, 381}, {3850, 17800, 3524}, {3850, 35404, 17800}, {3851, 14869, 3090}, {3854, 5072, 3091}, {3854, 15683, 631}, {3859, 15686, 46219}, {3861, 33699, 1657}, {3861, 35403, 4}, {5056, 15640, 20}, {5059, 10304, 20}, {5066, 15696, 3533}, {5068, 15713, 7486}, {5071, 15707, 2}, {5072, 5073, 12103}, {5072, 12103, 631}, {5076, 17578, 3091}, {5076, 49136, 38335}, {5079, 14269, 546}, {7409, 34603, 10565}, {7486, 33703, 20}, {11113, 37161, 17554}, {11361, 32982, 33198}, {11737, 15710, 2}, {12812, 15704, 3}, {14041, 32981, 33199}, {14042, 33279, 2}, {14044, 33007, 32980}, {14062, 33280, 2}, {14066, 33017, 32979}, {14784, 14785, 33923}, {14891, 15703, 15702}, {14893, 44245, 41991}, {15156, 15157, 37945}, {15682, 17538, 49136}, {15682, 49136, 3146}, {15683, 35434, 3543}, {15687, 17578, 49135}, {15687, 34200, 35403}, {15687, 38071, 12101}, {15688, 35018, 631}, {15690, 33703, 5059}, {15690, 47598, 14891}, {15697, 46935, 15717}, {15701, 15717, 3523}, {15704, 49139, 3529}, {15721, 15722, 15708}, {17538, 49136, 5059}, {18586, 18587, 35404}, {19696, 33006, 439}, {23253, 35821, 7585}, {23263, 35820, 7586}, {32971, 33019, 33210}, {32979, 33017, 33202}, {32980, 33007, 33203}, {32993, 33193, 32989}, {33002, 40246, 33209}, {33018, 33192, 32990}, {33699, 35403, 3545}, {35732, 42282, 3522}, {36436, 36454, 44903}, {41099, 49138, 140}, {41991, 44245, 1656}, {42104, 42134, 43466}, {42105, 42133, 43465}, {42133, 43465, 42983}, {42134, 43466, 42982}, {42153, 43401, 43769}, {42156, 43402, 43770}, {42268, 43407, 13941}, {42269, 43408, 8972}, {42280, 42281, 1657}, {43405, 43406, 6}, {47752, 47753, 37939}
X(50689) lies on these lines: {2, 3}, {6, 18296}, {10, 10248}, {13, 5343}, {14, 5344}, {51, 11439}, {52, 16261}, {61, 42106}, {62, 42103}, {69, 32894}, {145, 1699}, {146, 36253}, {147, 38734}, {148, 38745}, {149, 38757}, {150, 38769}, {151, 38781}, {165, 46931}, {185, 13570}, {194, 22682}, {316, 32834}, {325, 32879}, {355, 20052}, {390, 10895}, {393, 15860}, {395, 42776}, {396, 42775}, {397, 43540}, {398, 43541}, {516, 46933}, {575, 42785}, {576, 5921}, {590, 9543}, {615, 17852}, {946, 3623}, {962, 4678}, {1131, 3071}, {1132, 3070}, {1173, 32533}, {1498, 34545}, {1539, 15027}, {1587, 35787}, {1588, 35786}, {2777, 15025}, {2996, 43951}, {3060, 44870}, {3068, 42578}, {3069, 42579}, {3085, 18514}, {3086, 18513}, {3303, 5225}, {3304, 5229}, {3316, 9542}, {3339, 5556}, {3340, 7319}, {3411, 49875}, {3412, 49876}, {3424, 18845}, {3448, 15044}, {3531, 14843}, {3567, 16194}, {3585, 14986}, {3590, 31454}, {3592, 31412}, {3594, 42284}, {3600, 10896}, {3616, 12571}, {3617, 7991}, {3621, 7982}, {3622, 5691}, {3746, 10590}, {3785, 15031}, {3817, 30389}, {3984, 5175}, {4301, 31145}, {4846, 46848}, {4857, 31410}, {5237, 42105}, {5238, 42104}, {5254, 14930}, {5265, 12943}, {5281, 12953}, {5286, 39590}, {5334, 42162}, {5335, 42159}, {5349, 22235}, {5350, 22237}, {5351, 42111}, {5352, 42114}, {5365, 40693}, {5366, 40694}, {5422, 15811}, {5462, 11455}, {5550, 28164}, {5563, 10591}, {5587, 20070}, {5640, 11381}, {5656, 18383}, {5881, 20049}, {5890, 46849}, {5893, 32064}, {5943, 12279}, {5984, 14639}, {6053, 14683}, {6223, 26842}, {6248, 44434}, {6337, 32895}, {6361, 38140}, {6411, 43406}, {6412, 43405}, {6419, 23259}, {6420, 23249}, {6425, 8972}, {6426, 13941}, {6427, 23273}, {6428, 23267}, {6429, 43383}, {6430, 43382}, {6447, 18538}, {6448, 18762}, {6453, 22615}, {6454, 22644}, {6459, 43508}, {6460, 43507}, {6488, 42263}, {6489, 42264}, {6519, 42225}, {6522, 42226}, {6564, 23263}, {6565, 23253}, {6748, 36413}, {6776, 22234}, {7585, 23261}, {7586, 23251}, {7620, 7758}, {7687, 15054}, {7693, 9815}, {7768, 32874}, {7772, 43448}, {7782, 32871}, {7850, 32868}, {7860, 46951}, {7917, 11185}, {7965, 11681}, {7989, 9778}, {8252, 42414}, {8253, 42413}, {8596, 14981}, {8976, 42604}, {9544, 11424}, {9545, 46261}, {9581, 21454}, {9588, 38076}, {9716, 32605}, {9842, 27131}, {9968, 20079}, {10110, 15305}, {10113, 38632}, {10147, 42258}, {10148, 42259}, {10513, 32882}, {10519, 48895}, {10541, 14927}, {10574, 32062}, {10586, 41698}, {10721, 20397}, {10722, 20398}, {10723, 20399}, {10724, 20400}, {10725, 20401}, {10982, 43605}, {10984, 46865}, {11002, 12111}, {11003, 26883}, {11004, 11441}, {11236, 12632}, {11425, 35265}, {11440, 34417}, {11451, 46850}, {11465, 14855}, {11477, 20080}, {11482, 39884}, {11485, 43778}, {11486, 43777}, {11488, 42164}, {11489, 42165}, {11522, 34648}, {12112, 36753}, {12248, 38141}, {12250, 23325}, {12251, 22681}, {12290, 44871}, {12295, 15034}, {12323, 32814}, {12324, 23324}, {12699, 38176}, {12816, 42993}, {12817, 42992}, {13202, 15021}, {13472, 17505}, {13474, 15043}, {13598, 15056}, {13665, 23275}, {13785, 23269}, {13951, 42605}, {14023, 23334}, {14094, 46686}, {14360, 38801}, {14484, 38259}, {14853, 22330}, {14907, 32870}, {14915, 15024}, {15020, 36518}, {15030, 16981}, {15052, 36747}, {15058, 46852}, {15431, 37643}, {16644, 43770}, {16645, 43769}, {16657, 34799}, {16808, 42160}, {16809, 42161}, {16960, 42964}, {16961, 42965}, {16962, 42908}, {16963, 42909}, {16964, 43403}, {16965, 43404}, {16982, 18436}, {18424, 35007}, {18480, 20014}, {19053, 43377}, {19054, 43376}, {20054, 37712}, {20065, 50570}, {20218, 42854}, {21628, 25005}, {22236, 42101}, {22238, 42102}, {22331, 37689}, {22334, 31371}, {22505, 38627}, {22515, 38628}, {22799, 38631}, {22938, 38629}, {23235, 35369}, {26216, 33842}, {26330, 45863}, {26331, 45862}, {30531, 48675}, {31404, 43457}, {31415, 31652}, {32785, 42271}, {32786, 42272}, {32815, 32841}, {32816, 32840}, {32826, 32831}, {32827, 32830}, {32880, 37668}, {35812, 43257}, {35813, 43256}, {36836, 42110}, {36843, 42107}, {36969, 42920}, {36970, 42921}, {37640, 43773}, {37641, 43774}, {37665, 44518}, {38136, 39874}, {40247, 45186}, {42087, 42472}, {42088, 42473}, {42093, 42166}, {42094, 42163}, {42096, 43869}, {42097, 43870}, {42119, 42598}, {42120, 42599}, {42135, 42983}, {42136, 43243}, {42137, 43242}, {42138, 42982}, {42144, 43463}, {42145, 43464}, {42147, 42494}, {42148, 42495}, {42154, 43478}, {42155, 43477}, {42262, 43511}, {42265, 43512}, {42274, 43407}, {42277, 43408}, {42433, 42593}, {42434, 42592}, {42496, 42803}, {42497, 42804}, {42694, 42779}, {42695, 42780}, {42813, 42999}, {42814, 42998}, {42900, 43005}, {42901, 43004}, {42910, 43633}, {42911, 43632}, {42924, 43543}, {42925, 43542}, {42942, 43479}, {42943, 43480}, {42962, 42986}, {42963, 42987}, {42972, 49825}, {42973, 49824}, {43201, 43229}, {43202, 43228}, {43238, 43402}, {43239, 43401}, {43248, 43400}, {43249, 43399}, {43250, 44015}, {43251, 44016}, {46730, 48912}
X(50689) = midpoint of X(i) and X(j) for these {i,j}: {4, 3855}, {3830, 15723}
X(50689) = reflection of X(i) in X(j) for these {i,j}: {20, 21735}, {3525, 5072}, {5056, 3855}, {5072, 41991}, {15717, 5056}, {15720, 5}, {21735, 5070}, {41991, 546}
X(50689) = anticomplement of X(15717)
X(50689) = orthocentroidal circle inverse of X(17578)
X(50689) = orthoptic-circle-of-Steiner-circumellipse-inverse of X(37910)
X(50689) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 17578}, {2, 3832, 3854}, {2, 5059, 21734}, {2, 17578, 5059}, {3, 381, 12811}, {3, 3091, 15022}, {3, 3544, 46936}, {3, 3627, 11541}, {3, 3857, 3544}, {3, 11541, 20}, {3, 12811, 3090}, {3, 15022, 2}, {4, 5, 3543}, {4, 376, 3853}, {4, 381, 20}, {4, 546, 3091}, {4, 631, 3830}, {4, 3090, 3627}, {4, 3091, 3146}, {4, 3529, 5076}, {4, 3545, 382}, {4, 3832, 2}, {4, 3839, 3832}, {4, 3843, 3839}, {4, 3850, 49135}, {4, 3854, 5059}, {4, 3856, 10304}, {4, 3857, 49140}, {4, 3858, 3523}, {4, 6849, 37437}, {4, 6893, 37433}, {4, 6957, 6895}, {4, 7394, 34007}, {4, 7528, 50009}, {4, 7559, 37104}, {4, 23046, 7486}, {4, 23047, 7378}, {4, 33703, 15687}, {4, 35488, 7487}, {4, 37197, 6995}, {4, 41099, 5}, {4, 41106, 33703}, {5, 550, 47598}, {5, 3522, 2}, {5, 3524, 46935}, {5, 3529, 10303}, {5, 3534, 3533}, {5, 3543, 3522}, {5, 3627, 44245}, {5, 5073, 3524}, {5, 5076, 3529}, {5, 11812, 1656}, {5, 12101, 5073}, {5, 14269, 4}, {5, 44903, 140}, {20, 381, 5068}, {20, 3091, 3090}, {20, 3523, 8703}, {20, 3524, 3522}, {20, 3543, 5073}, {20, 3627, 3146}, {20, 5056, 15721}, {20, 5068, 2}, {20, 5070, 15717}, {20, 15721, 21735}, {20, 46935, 3524}, {140, 3627, 49137}, {140, 15682, 20}, {140, 45762, 3861}, {376, 3851, 7486}, {381, 3090, 3091}, {381, 3627, 3090}, {381, 3830, 15699}, {381, 3861, 4}, {381, 5055, 41990}, {381, 5073, 5}, {381, 8703, 3545}, {381, 12101, 3524}, {381, 14269, 12101}, {381, 14892, 41106}, {381, 15685, 14892}, {381, 35403, 14891}, {381, 38335, 15701}, {382, 3523, 15683}, {382, 3545, 3523}, {382, 3628, 17538}, {382, 3858, 3545}, {382, 5056, 35418}, {382, 14893, 4}, {439, 32963, 2}, {546, 3091, 3832}, {546, 3627, 381}, {546, 3628, 3858}, {546, 3861, 3627}, {546, 12102, 3857}, {546, 12103, 3856}, {546, 14269, 3529}, {546, 14893, 3628}, {547, 17800, 10299}, {631, 3830, 49135}, {631, 15706, 3523}, {632, 3853, 49136}, {632, 49136, 376}, {1656, 3856, 41106}, {1656, 15685, 44682}, {1656, 15687, 33703}, {1656, 33703, 10304}, {1657, 5066, 5067}, {1657, 5067, 15692}, {1995, 11403, 12086}, {2476, 11106, 2}, {2478, 37161, 2}, {2676, 3832, 2675}, {3070, 43560, 42540}, {3071, 43561, 42539}, {3090, 3091, 5068}, {3090, 3525, 5070}, {3090, 3529, 3524}, {3090, 3627, 20}, {3090, 11541, 3}, {3090, 21735, 3525}, {3090, 44245, 10303}, {3091, 3146, 2}, {3091, 3543, 10303}, {3091, 3839, 546}, {3091, 5056, 5072}, {3091, 5076, 3522}, {3091, 10303, 5}, {3091, 46936, 3544}, {3091, 49140, 46936}, {3146, 3522, 3529}, {3146, 3832, 3091}, {3146, 15022, 3}, {3522, 5068, 46935}, {3523, 15715, 15717}, {3524, 3529, 44245}, {3524, 5073, 20}, {3524, 12101, 3543}, {3524, 15682, 44903}, {3524, 41099, 381}, {3525, 3855, 5072}, {3525, 5072, 5056}, {3525, 15720, 10303}, {3525, 17538, 15715}, {3525, 41991, 3091}, {3529, 3543, 3146}, {3529, 5076, 3543}, {3529, 10303, 3522}, {3529, 44245, 20}, {3541, 21451, 2}, {3543, 3839, 41099}, {3543, 10303, 3529}, {3543, 15694, 15683}, {3543, 46935, 20}, {3544, 3857, 3091}, {3544, 12102, 49140}, {3544, 46936, 15022}, {3545, 15683, 2}, {3545, 17538, 3628}, {3627, 5072, 21735}, {3627, 12101, 5076}, {3627, 12811, 3}, {3627, 15699, 15704}, {3627, 41990, 12108}, {3627, 44245, 5073}, {3627, 49137, 15682}, {3628, 15704, 15706}, {3628, 17538, 3523}, {3830, 3850, 631}, {3830, 5079, 15704}, {3832, 5068, 381}, {3832, 15717, 3855}, {3839, 3861, 5068}, {3843, 3845, 4}, {3845, 41987, 381}, {3850, 3853, 19711}, {3850, 3861, 41988}, {3850, 15704, 5079}, {3850, 34200, 5}, {3851, 3853, 376}, {3851, 49136, 632}, {3853, 23046, 3851}, {3854, 17578, 2}, {3855, 5072, 3091}, {3855, 15721, 5068}, {3855, 35401, 3523}, {3856, 15687, 1656}, {3857, 12102, 3}, {3857, 49140, 15022}, {3858, 14893, 382}, {3858, 17538, 3091}, {3860, 38335, 5071}, {5047, 13615, 16865}, {5056, 15717, 2}, {5056, 15721, 5070}, {5070, 15716, 140}, {5070, 21735, 15721}, {5071, 15640, 15705}, {5071, 15705, 2}, {5071, 38335, 15640}, {5072, 15723, 5079}, {5072, 41991, 3855}, {5073, 5076, 3627}, {5073, 44245, 3529}, {5073, 46935, 3522}, {5076, 10303, 3146}, {5076, 41099, 3091}, {5079, 15699, 3090}, {5079, 15704, 631}, {5141, 17576, 2}, {5154, 37267, 2}, {5187, 37435, 2}, {5691, 9779, 3622}, {6459, 43508, 43520}, {6459, 43879, 43883}, {6460, 43507, 43519}, {6460, 43880, 43884}, {6655, 32991, 2}, {6912, 36002, 20846}, {7394, 7409, 2}, {7530, 35500, 38435}, {7989, 9778, 46932}, {8703, 15694, 3524}, {9812, 19925, 3617}, {10109, 23046, 381}, {10299, 17800, 15697}, {11286, 33292, 33182}, {11361, 32972, 33201}, {12101, 44245, 3627}, {12102, 46936, 3146}, {13615, 36002, 35986}, {14035, 32980, 2}, {14041, 32971, 33200}, {14042, 33006, 32973}, {14062, 33016, 32974}, {14063, 32979, 2}, {14068, 32993, 2}, {14269, 41099, 3543}, {14782, 14783, 19709}, {14784, 14785, 15712}, {14892, 15687, 15685}, {14892, 44682, 1656}, {15044, 38791, 3448}, {15687, 41106, 10304}, {15691, 41990, 5055}, {15696, 35018, 15702}, {15699, 41988, 3830}, {15703, 49133, 46853}, {15721, 21735, 15717}, {15723, 35416, 15704}, {16044, 32982, 2}, {16194, 44863, 3567}, {16865, 17572, 37248}, {16924, 33025, 2}, {18586, 18587, 15686}, {19687, 32984, 33203}, {19696, 32998, 35287}, {21565, 21568, 11350}, {32961, 33205, 2}, {32962, 33023, 2}, {32966, 32981, 2}, {32971, 33200, 2}, {32972, 33201, 2}, {32983, 33229, 33202}, {32995, 33019, 2}, {32996, 33018, 2}, {32997, 33024, 2}, {33011, 33244, 2}, {33013, 33279, 32990}, {33030, 33050, 2}, {33051, 33056, 2}, {33699, 35018, 15696}, {33703, 41106, 1656}, {33703, 44682, 20}, {35403, 38071, 11001}, {35732, 42282, 3523}, {36436, 36454, 15700}, {42101, 42142, 43466}, {42101, 43466, 43474}, {42102, 42139, 43465}, {42102, 43465, 43473}, {42103, 43226, 42134}, {42106, 43227, 42133}, {42280, 42281, 1656}, {43364, 43365, 6}, {43771, 43772, 6}, {44903, 49137, 3529}, {46853, 49133, 46333}, {46936, 49140, 3}
X(50690) lies on these lines: {2, 3}, {6, 43519}, {99, 32881}, {315, 32880}, {316, 32840}, {323, 15811}, {371, 43432}, {372, 43433}, {397, 43466}, {398, 43465}, {485, 6478}, {486, 6479}, {516, 4678}, {962, 20014}, {1131, 42263}, {1132, 42264}, {1151, 3590}, {1152, 3591}, {1204, 48912}, {1498, 11004}, {3068, 43560}, {3069, 43561}, {3070, 6441}, {3071, 6442}, {3592, 43411}, {3594, 43412}, {3617, 5493}, {3621, 5691}, {3622, 10248}, {3623, 9812}, {5334, 42901}, {5335, 42900}, {5339, 42141}, {5340, 42140}, {5343, 42104}, {5344, 42105}, {5349, 22237}, {5350, 22235}, {5365, 42086}, {5366, 42085}, {5890, 12002}, {5921, 48884}, {5984, 39809}, {6361, 38176}, {6439, 8972}, {6440, 13941}, {6447, 14241}, {6448, 14226}, {6453, 43503}, {6454, 43504}, {6459, 43507}, {6460, 43508}, {6476, 42275}, {6477, 42276}, {7320, 9580}, {7585, 42271}, {7586, 42272}, {7768, 32826}, {7860, 32830}, {7917, 32815}, {8960, 43408}, {9543, 31412}, {9589, 31145}, {9780, 28158}, {10513, 32819}, {10723, 35369}, {11002, 12279}, {12512, 46931}, {13202, 14683}, {13421, 18439}, {13598, 16981}, {15105, 18405}, {16960, 43781}, {16961, 43782}, {16964, 44018}, {16965, 44017}, {18553, 43621}, {19106, 42999}, {19107, 42998}, {20052, 41869}, {20070, 31673}, {20080, 36990}, {20094, 39838}, {22236, 43540}, {22238, 43541}, {23251, 43376}, {23261, 43377}, {29323, 42785}, {32824, 32879}, {33884, 44870}, {34507, 48943}, {36836, 43877}, {36843, 43878}, {38259, 47586}, {40693, 42909}, {40694, 42908}, {41100, 43425}, {41101, 43424}, {41973, 42161}, {41974, 42160}, {42087, 42494}, {42088, 42495}, {42099, 42979}, {42100, 42978}, {42108, 43473}, {42109, 43474}, {42133, 42158}, {42134, 42157}, {42136, 43777}, {42137, 43778}, {42139, 43480}, {42142, 43479}, {42225, 42522}, {42226, 42523}, {42283, 43511}, {42284, 43512}, {42510, 43427}, {42511, 43426}, {42892, 43403}, {42893, 43404}, {42924, 42983}, {42925, 42982}, {42942, 43477}, {42943, 43478}, {43016, 43022}, {43017, 43023}, {43193, 43553}, {43194, 43552}, {43209, 43410}, {43210, 43409}, {43413, 43879}, {43414, 43880}, {43624, 46476}, {43625, 46473}
X(50690) = midpoint of X(3146) and X(3832)
X(50690) = reflection of X(i) in X(j) for these {i,j}: {20, 3090}, {3523, 4}, {3622, 10248}, {3857, 3853}, {8703, 45762}, {11001, 15700}
X(50690) = orthoptic-circle-of-Steiner-circumellipse-inverse of X(47316)
X(50690) = crosspoint of X(43556) and X(43557)
X(50690) = crosssum of X(36836) and X(36843)
X(50690) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 382, 35404}, {3, 47599, 631}, {4, 20, 5068}, {4, 376, 3850}, {4, 550, 3091}, {4, 1656, 3839}, {4, 1657, 5056}, {4, 3146, 5059}, {4, 3522, 3854}, {4, 3523, 3832}, {4, 3529, 1656}, {4, 3533, 546}, {4, 5059, 2}, {4, 5073, 20}, {4, 10299, 3858}, {4, 11541, 21735}, {4, 15682, 5073}, {4, 21735, 381}, {4, 33703, 550}, {4, 49135, 3522}, {4, 49138, 3533}, {5, 35384, 3529}, {20, 140, 3522}, {20, 3091, 3524}, {20, 3543, 3627}, {20, 15682, 3146}, {20, 46935, 21735}, {20, 49137, 15683}, {20, 49140, 15685}, {140, 3851, 3090}, {381, 11541, 20}, {381, 21735, 46935}, {381, 44682, 3090}, {381, 46935, 5068}, {382, 3543, 3146}, {382, 3627, 15682}, {382, 35416, 3845}, {546, 49138, 10304}, {548, 41099, 46936}, {550, 3830, 4}, {1656, 3853, 4}, {1657, 3858, 10299}, {1657, 5056, 3522}, {3090, 3524, 3526}, {3090, 3528, 15701}, {3091, 15683, 21734}, {3091, 21734, 2}, {3091, 33703, 15683}, {3146, 3522, 49135}, {3146, 3543, 17578}, {3146, 3830, 21734}, {3146, 15683, 33703}, {3146, 15705, 49134}, {3146, 17578, 2}, {3522, 3854, 2}, {3522, 5068, 140}, {3522, 49135, 5059}, {3524, 3861, 3091}, {3524, 33703, 49137}, {3524, 49137, 20}, {3526, 12108, 15702}, {3529, 3839, 15717}, {3529, 3853, 3839}, {3529, 8703, 20}, {3544, 15696, 15708}, {3627, 3861, 3830}, {3627, 5073, 4}, {3627, 8703, 3853}, {3627, 15682, 20}, {3830, 33703, 3091}, {3830, 49137, 3861}, {3832, 3851, 3854}, {3839, 3857, 3832}, {3843, 11001, 10303}, {3845, 17538, 7486}, {3845, 49134, 17538}, {3850, 5076, 4}, {3850, 49139, 376}, {3853, 15684, 3529}, {3854, 5059, 3522}, {3855, 15704, 15692}, {3858, 10299, 5056}, {3861, 15759, 12811}, {3861, 33703, 20}, {3861, 44245, 41986}, {3861, 49137, 3524}, {5056, 49135, 1657}, {5059, 17578, 4}, {5068, 5073, 5059}, {5070, 5073, 49139}, {5073, 15685, 49133}, {5076, 49139, 3850}, {5349, 42120, 22237}, {5350, 42119, 22235}, {7486, 17538, 15705}, {11737, 35404, 15684}, {12101, 15682, 15640}, {12102, 17800, 3545}, {12108, 15684, 33703}, {12811, 15689, 631}, {14093, 33703, 49140}, {14869, 44682, 44580}, {14893, 15696, 3544}, {15022, 15717, 47598}, {15640, 23046, 15683}, {15684, 15707, 35384}, {15687, 49136, 631}, {15698, 15702, 15707}, {15704, 38335, 3855}, {15721, 49140, 20}, {17800, 35434, 12102}, {36445, 36463, 45757}, {41992, 49136, 3529}, {42104, 42431, 5343}, {42105, 42432, 5344}, {43473, 43496, 43556}, {43474, 43495, 43557}, {43519, 43520, 6}
X(50691) lies on these lines: {2, 3}, {8, 28232}, {17, 42112}, {18, 42113}, {193, 48943}, {315, 32877}, {316, 32824}, {371, 43376}, {372, 43377}, {390, 5270}, {397, 42140}, {398, 42141}, {516, 4668}, {962, 3633}, {1131, 42542}, {1132, 42541}, {1151, 43409}, {1152, 43410}, {1587, 6435}, {1588, 6436}, {3590, 6564}, {3591, 6565}, {3600, 4857}, {3616, 28172}, {3617, 28146}, {3620, 29317}, {3621, 48661}, {3623, 28186}, {3625, 5691}, {3630, 36990}, {4114, 9579}, {4691, 5493}, {5237, 42513}, {5238, 42512}, {5274, 10483}, {5286, 14075}, {5318, 43243}, {5321, 43242}, {5334, 42431}, {5335, 42432}, {5339, 42109}, {5340, 42108}, {5343, 42086}, {5344, 42085}, {5346, 43448}, {5349, 42097}, {5350, 42096}, {5365, 42104}, {5366, 42105}, {5818, 28154}, {5882, 9812}, {5921, 48910}, {5965, 48904}, {6409, 43786}, {6410, 43785}, {6437, 42570}, {6438, 42571}, {6459, 43411}, {6460, 43412}, {7320, 9613}, {7581, 43519}, {7582, 43520}, {7585, 22644}, {7586, 22615}, {7748, 34571}, {7755, 43618}, {7781, 23334}, {7860, 32815}, {8960, 23253}, {8972, 42266}, {9542, 31412}, {9692, 43879}, {10575, 11002}, {10595, 28190}, {11220, 31822}, {11480, 42775}, {11481, 42776}, {11522, 28164}, {11542, 43473}, {11543, 43474}, {12250, 14864}, {12279, 13382}, {12512, 22266}, {13886, 43560}, {13939, 43561}, {13941, 42267}, {14927, 33748}, {14929, 32882}, {15105, 32064}, {16960, 22235}, {16961, 22237}, {16981, 34783}, {17852, 41951}, {19106, 41973}, {19107, 41974}, {20052, 28212}, {20053, 28234}, {22236, 43422}, {22238, 43423}, {23249, 42522}, {23259, 42523}, {23263, 42276}, {23269, 42225}, {23275, 42226}, {32826, 32878}, {32875, 37668}, {34507, 43621}, {35369, 38744}, {35812, 43503}, {35813, 43504}, {35814, 43571}, {35815, 43570}, {40693, 43424}, {40694, 43425}, {41969, 42578}, {41970, 42579}, {42021, 46851}, {42099, 42921}, {42100, 42920}, {42101, 42495}, {42102, 42494}, {42103, 43870}, {42106, 43869}, {42144, 42988}, {42145, 42989}, {42147, 42516}, {42148, 42517}, {42283, 42414}, {42284, 42413}, {42433, 43400}, {42434, 43399}, {42435, 42992}, {42436, 42993}, {42472, 42949}, {42473, 42948}, {42561, 43414}, {42629, 43776}, {42630, 43775}, {42910, 42958}, {42911, 42959}, {42990, 49827}, {42991, 49826}, {43238, 43873}, {43239, 43874}, {43364, 43471}, {43365, 43472}, {43426, 43540}, {43427, 43541}
X(50691) = midpoint of X(i) and X(j) for these {i,j}: {1656, 5073}, {3146, 17578}, {15640, 15692}, {15696, 35407}, {17538, 33703}
X(50691) = reflection of X(i) in X(j) for these {i,j}: {20, 3091}, {631, 5076}, {632, 3853}, {1657, 15712}, {3091, 17578}, {3522, 4}, {3529, 15696}, {3843, 3627}, {5071, 3830}, {11001, 15694}, {15683, 19708}, {15693, 15687}, {15704, 48154}, {15714, 12101}, {17538, 3843}, {19708, 35403}, {35414, 11001}, {35434, 33699}, {41099, 35434}
X(50691) = anticomplement of X(17538)
X(50691) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3146, 33703}, {2, 3522, 15712}, {2, 3832, 5072}, {2, 3843, 3091}, {2, 15683, 15689}, {2, 15686, 10304}, {2, 15706, 15721}, {2, 21735, 3523}, {2, 33703, 49140}, {2, 49140, 20}, {3, 4, 3854}, {3, 382, 33699}, {3, 3854, 46935}, {4, 20, 5056}, {4, 140, 3832}, {4, 376, 3851}, {4, 550, 5068}, {4, 631, 3858}, {4, 1657, 2}, {4, 3146, 49135}, {4, 3522, 3091}, {4, 3529, 140}, {4, 5056, 3839}, {4, 5059, 3523}, {4, 5073, 5059}, {4, 10299, 381}, {4, 21735, 3850}, {4, 33703, 1657}, {4, 49135, 20}, {4, 49138, 10299}, {5, 11541, 15683}, {20, 3091, 15692}, {20, 3146, 15640}, {20, 3839, 10303}, {20, 46936, 10304}, {140, 3830, 4}, {140, 49133, 3529}, {376, 23046, 2}, {382, 3146, 3543}, {382, 15682, 3146}, {382, 15684, 3627}, {546, 11001, 15717}, {546, 44580, 5}, {546, 49134, 11001}, {548, 3627, 38335}, {550, 5068, 3523}, {631, 12812, 2}, {631, 17538, 14093}, {632, 46853, 19711}, {1593, 37945, 38435}, {1656, 3522, 3523}, {1656, 3843, 3850}, {1657, 3627, 4}, {1657, 3843, 15712}, {1657, 3850, 21735}, {1657, 15712, 17538}, {2043, 2044, 15719}, {3091, 3523, 1656}, {3091, 3543, 17578}, {3091, 15697, 631}, {3091, 49140, 17538}, {3146, 3543, 20}, {3146, 3627, 49140}, {3146, 5059, 5073}, {3522, 17578, 4}, {3522, 41099, 46935}, {3523, 5059, 20}, {3523, 49135, 5059}, {3528, 3845, 15022}, {3528, 15022, 15721}, {3529, 3830, 3832}, {3529, 3832, 10304}, {3529, 5071, 15696}, {3529, 10304, 20}, {3534, 12102, 3855}, {3543, 10304, 3830}, {3543, 15640, 3839}, {3543, 49135, 4}, {3545, 14891, 2}, {3545, 15704, 21734}, {3627, 5073, 21735}, {3627, 12812, 5076}, {3627, 15684, 33703}, {3627, 23046, 3853}, {3627, 33703, 2}, {3830, 35407, 15696}, {3830, 49133, 140}, {3832, 5071, 3091}, {3832, 10304, 46936}, {3843, 14093, 12812}, {3843, 17538, 2}, {3845, 49137, 3528}, {3850, 15712, 1656}, {3850, 21735, 2}, {3850, 33703, 5059}, {3851, 3853, 4}, {3853, 35411, 3544}, {3853, 49136, 376}, {3856, 44903, 3}, {3858, 5076, 4}, {3858, 15712, 12812}, {3859, 15693, 3090}, {3861, 15681, 3525}, {5059, 5068, 550}, {5059, 5073, 49135}, {5071, 41099, 38071}, {5072, 49133, 1657}, {5076, 14093, 3843}, {8597, 33280, 32982}, {10109, 14893, 23046}, {12103, 14269, 5067}, {12812, 14093, 631}, {14066, 33271, 2}, {14784, 14785, 44245}, {14813, 14814, 15688}, {14893, 46333, 2}, {15684, 33699, 46333}, {15684, 33703, 3146}, {15686, 15696, 17538}, {15687, 17800, 3090}, {15689, 49139, 1657}, {15696, 46936, 15692}, {15704, 48154, 15695}, {15708, 19708, 15692}, {15712, 17538, 3522}, {15714, 41989, 3526}, {15721, 49137, 20}, {17538, 41099, 45760}, {17578, 35407, 10304}, {17578, 35414, 546}, {19711, 49136, 49138}, {23253, 42275, 43512}, {23263, 42276, 43511}, {35502, 44454, 12087}, {42104, 42158, 5365}, {42105, 42157, 5366}, {42133, 42151, 22237}, {42134, 42150, 22235}, {42278, 42279, 15685}
X(50692) lies on these lines: {2, 3}, {8, 28158}, {145, 9589}, {185, 16981}, {316, 32841}, {390, 9657}, {395, 43557}, {396, 43556}, {485, 9692}, {515, 20014}, {516, 3621}, {962, 28172}, {1131, 9543}, {1132, 43338}, {1151, 43507}, {1152, 43508}, {2794, 35369}, {3411, 5343}, {3412, 5344}, {3600, 9670}, {3620, 48872}, {3623, 4301}, {4302, 31410}, {4325, 14986}, {4678, 5691}, {5334, 43633}, {5335, 43632}, {5365, 36968}, {5366, 36967}, {5734, 13607}, {5881, 20052}, {5921, 29317}, {6221, 43340}, {6398, 43341}, {6425, 43376}, {6426, 43377}, {6429, 42570}, {6430, 42571}, {6435, 42275}, {6436, 42276}, {6488, 43409}, {6489, 43410}, {6498, 42215}, {6499, 42216}, {7585, 42272}, {7586, 42271}, {7737, 34571}, {7765, 14075}, {7782, 32873}, {7796, 32879}, {7802, 32894}, {7850, 32830}, {8960, 43526}, {8972, 43560}, {9541, 42540}, {9607, 14930}, {9681, 23249}, {9778, 37714}, {10147, 41952}, {10148, 41951}, {10248, 46934}, {11002, 46850}, {11431, 13403}, {11439, 33884}, {11488, 43473}, {11489, 43474}, {12007, 48910}, {12245, 28182}, {12324, 37779}, {12512, 46932}, {13941, 43561}, {14907, 32872}, {15305, 15606}, {15752, 47296}, {16192, 46930}, {16644, 43552}, {16645, 43553}, {16964, 42113}, {16965, 42112}, {20054, 28228}, {20080, 29181}, {21454, 37723}, {22235, 42942}, {22237, 42943}, {23241, 34549}, {23253, 35812}, {23259, 35814}, {23263, 35813}, {23269, 31487}, {28168, 37727}, {31414, 42258}, {31670, 33749}, {32815, 32880}, {32816, 32881}, {35265, 45248}, {37640, 43496}, {37641, 43495}, {40330, 48879}, {42085, 42934}, {42086, 42935}, {42093, 42685}, {42094, 42684}, {42096, 43465}, {42097, 43466}, {42101, 43870}, {42102, 43869}, {42104, 42433}, {42105, 42434}, {42108, 43193}, {42109, 43194}, {42126, 43242}, {42127, 43243}, {42130, 42982}, {42131, 42983}, {42140, 42148}, {42141, 42147}, {42149, 42429}, {42152, 42430}, {42157, 42965}, {42158, 42964}, {42164, 43769}, {42165, 43770}, {42259, 43382}, {42494, 42626}, {42495, 42625}, {42539, 43431}, {42586, 49812}, {42587, 49813}, {42815, 43634}, {42816, 43635}, {42888, 42987}, {42889, 42986}, {42920, 43545}, {42921, 43544}, {43302, 43636}, {43303, 43637}, {43601, 48912}
X(50692) = reflection of X(i) in X(j) for these {i,j}: {4, 49136}, {20, 33703}, {3146, 49135}, {3529, 5073}, {3845, 35408}, {5059, 3146}, {11541, 49133}, {15682, 35400}, {15683, 15640}, {33703, 49134}, {49135, 11541}, {49138, 382}, {49139, 3627}, {49140, 4}
X(50692) = anticomplement of X(5059)
X(50692) = orthoptic-circle-of-Steiner-circumellipse-inverse of X(37911)
X(50692) = anticomplement of the isogonal conjugate of X(43691)
X(50692) = X(43691)-anticomplementary conjugate of X(8)
X(50692) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3854, 2}, {3, 33699, 4}, {3, 41099, 46935}, {4, 20, 15717}, {4, 376, 3628}, {4, 548, 7486}, {4, 549, 3091}, {4, 3090, 23046}, {4, 3529, 3534}, {4, 3534, 10303}, {4, 5072, 3839}, {4, 7486, 3832}, {4, 10304, 15022}, {4, 15640, 3146}, {4, 15698, 5072}, {4, 15704, 10304}, {4, 15709, 3857}, {4, 17538, 15709}, {4, 17800, 20}, {4, 46333, 3}, {4, 49136, 15640}, {4, 49140, 15683}, {5, 20, 3522}, {5, 3529, 20}, {5, 3853, 14269}, {5, 12101, 3843}, {5, 15694, 5067}, {5, 46853, 11812}, {20, 382, 3832}, {20, 3091, 3528}, {20, 3146, 17578}, {20, 3523, 15696}, {20, 3543, 5}, {20, 3832, 21734}, {20, 7486, 548}, {20, 17578, 2}, {20, 17800, 15683}, {20, 33703, 3146}, {20, 49135, 33703}, {20, 49140, 17800}, {382, 548, 4}, {382, 1657, 5070}, {382, 3832, 17578}, {382, 5070, 3853}, {382, 17800, 548}, {382, 49138, 20}, {546, 35421, 140}, {548, 3628, 44682}, {548, 7486, 15717}, {548, 15717, 21734}, {549, 3533, 10303}, {549, 3860, 5055}, {550, 5072, 15698}, {550, 10109, 3}, {1657, 3528, 20}, {1657, 3853, 3528}, {1657, 14269, 44245}, {1657, 14892, 17538}, {1657, 15682, 3091}, {1657, 35434, 3}, {2041, 2042, 15682}, {2043, 2044, 15715}, {3091, 5056, 14892}, {3146, 3522, 3543}, {3146, 3832, 382}, {3146, 5059, 2}, {3146, 15683, 4}, {3146, 49138, 21734}, {3522, 5068, 15720}, {3526, 10304, 15717}, {3526, 17800, 15704}, {3528, 3853, 3091}, {3528, 15682, 3853}, {3529, 3543, 3522}, {3529, 5073, 3543}, {3529, 15682, 3533}, {3533, 14269, 3091}, {3534, 5055, 34200}, {3534, 10303, 3522}, {3534, 14269, 549}, {3534, 33699, 41099}, {3534, 44903, 46333}, {3534, 49136, 5073}, {3543, 5073, 3146}, {3543, 10303, 4}, {3544, 33923, 15721}, {3627, 5055, 4}, {3627, 11001, 3523}, {3627, 15696, 3855}, {3627, 49139, 11001}, {3830, 3857, 4}, {3830, 17538, 5056}, {3830, 35381, 3845}, {3832, 15717, 7486}, {3832, 21734, 2}, {3839, 3859, 3832}, {3843, 15696, 15713}, {3843, 15720, 5}, {3845, 21735, 46936}, {3853, 35400, 33703}, {3853, 44245, 5}, {3855, 11001, 15696}, {3855, 15696, 3523}, {3856, 17800, 46333}, {3856, 47598, 5}, {3857, 15709, 5056}, {5059, 17578, 20}, {5073, 44245, 15682}, {5073, 49137, 12101}, {7486, 49138, 15683}, {7585, 42272, 43519}, {7586, 42271, 43520}, {10303, 46935, 47598}, {10303, 49140, 3529}, {10304, 15640, 15684}, {11001, 15682, 3860}, {11001, 15696, 20}, {11541, 33703, 49134}, {12086, 39568, 37913}, {14269, 15682, 3543}, {14269, 35400, 35384}, {14269, 44245, 3533}, {14784, 14785, 15686}, {15022, 15717, 3526}, {15640, 49135, 49136}, {15640, 49140, 4}, {15683, 15717, 20}, {15683, 49140, 5059}, {15684, 15704, 4}, {15684, 17800, 3526}, {15706, 44904, 3525}, {17578, 21734, 3832}, {17800, 49134, 49136}, {33699, 44903, 47598}, {33703, 49134, 49135}, {33703, 49138, 382}, {33923, 38335, 3544}, {34200, 49139, 3529}, {36445, 36463, 41985}, {37899, 44442, 30769}, {42271, 42414, 7586}, {42272, 42413, 7585}, {44903, 47598, 3534}, {49135, 49140, 15640}, {49136, 49140, 3146}
X(50693) lies on these lines: {2, 3}, {6, 42574}, {8, 12512}, {15, 43300}, {16, 43301}, {40, 3621}, {61, 42091}, {62, 42090}, {69, 43691}, {98, 35369}, {99, 32840}, {100, 44846}, {144, 3984}, {145, 4297}, {146, 15034}, {147, 38736}, {148, 38747}, {149, 38759}, {150, 38771}, {151, 38783}, {165, 3617}, {193, 44882}, {194, 22676}, {315, 32841}, {316, 32835}, {325, 32881}, {389, 16981}, {390, 3304}, {394, 16936}, {395, 43770}, {396, 43769}, {489, 32814}, {515, 4678}, {516, 3622}, {569, 43576}, {575, 48873}, {576, 48885}, {590, 42414}, {615, 42413}, {944, 20014}, {962, 26842}, {1038, 9539}, {1078, 32872}, {1131, 41954}, {1132, 41953}, {1151, 43883}, {1152, 43884}, {1278, 30271}, {1350, 20080}, {1420, 30332}, {1587, 6453}, {1588, 6454}, {1614, 8717}, {1620, 37643}, {1975, 32880}, {2777, 15020}, {2951, 19861}, {2975, 11495}, {2979, 45187}, {3060, 15012}, {3085, 4316}, {3086, 4324}, {3098, 5921}, {3164, 47381}, {3184, 38686}, {3218, 9841}, {3219, 37551}, {3241, 5493}, {3303, 3600}, {3448, 15021}, {3592, 6460}, {3594, 6459}, {3618, 48872}, {3620, 14927}, {3623, 5731}, {3624, 10248}, {3746, 4293}, {3819, 11439}, {3868, 31805}, {3869, 5918}, {3917, 12279}, {3926, 7850}, {3928, 12536}, {3951, 20007}, {4294, 5563}, {4302, 14986}, {4313, 11518}, {4430, 7957}, {4661, 12680}, {4788, 30273}, {5023, 37689}, {5188, 20081}, {5204, 5274}, {5206, 43448}, {5217, 5261}, {5237, 5334}, {5238, 5335}, {5265, 6284}, {5281, 7354}, {5286, 35007}, {5304, 22331}, {5318, 43869}, {5321, 43870}, {5343, 43632}, {5344, 43633}, {5351, 42085}, {5352, 42086}, {5447, 12290}, {5537, 20067}, {5609, 12244}, {5640, 17704}, {5656, 50414}, {5691, 46933}, {5732, 20059}, {5882, 34632}, {5889, 36987}, {5894, 11206}, {5895, 35260}, {5972, 15023}, {5984, 23235}, {6030, 34563}, {6200, 43336}, {6221, 43787}, {6223, 26792}, {6282, 20214}, {6361, 10222}, {6396, 43337}, {6398, 43788}, {6409, 8972}, {6410, 13941}, {6411, 31412}, {6412, 42561}, {6419, 9541}, {6420, 42260}, {6425, 7585}, {6426, 7586}, {6447, 42216}, {6448, 42215}, {6449, 23267}, {6450, 23273}, {6455, 13886}, {6456, 13939}, {6488, 31454}, {6560, 35815}, {6561, 35814}, {6776, 48892}, {7583, 9542}, {7712, 11449}, {7735, 44519}, {7737, 31652}, {7750, 10513}, {7771, 32826}, {7782, 32831}, {7811, 32824}, {7860, 32837}, {7929, 8721}, {7987, 9812}, {7998, 11381}, {7999, 14915}, {8142, 17494}, {8236, 10390}, {8567, 32064}, {8591, 10991}, {8960, 43342}, {9143, 10990}, {9540, 42267}, {9589, 34638}, {9729, 11002}, {9780, 16192}, {9833, 32903}, {9862, 14692}, {10164, 46932}, {10442, 30712}, {10519, 41482}, {10541, 29181}, {10543, 18221}, {10574, 16625}, {10645, 42161}, {10646, 42160}, {10721, 38795}, {10722, 38751}, {10723, 38740}, {10727, 38775}, {10728, 38763}, {10732, 38787}, {10733, 38729}, {10992, 11177}, {11003, 13346}, {11004, 37498}, {11220, 31793}, {11257, 20105}, {11412, 14855}, {11459, 14641}, {11468, 41398}, {11469, 40911}, {11477, 12007}, {11480, 43465}, {11481, 43466}, {11482, 33748}, {11485, 43242}, {11486, 43243}, {11488, 42165}, {11489, 42164}, {11542, 42689}, {11543, 42688}, {11821, 35240}, {12111, 13348}, {12289, 17712}, {12383, 38788}, {12437, 28610}, {12632, 34610}, {12651, 29817}, {12699, 31666}, {13172, 38742}, {13199, 38754}, {13202, 15029}, {13452, 34483}, {13472, 13623}, {13846, 43376}, {13847, 43377}, {13935, 42266}, {14023, 34504}, {14094, 16111}, {14360, 38803}, {14537, 31407}, {14561, 48920}, {14654, 38798}, {14683, 15054}, {14689, 38689}, {14853, 20190}, {14907, 32830}, {14912, 48874}, {14996, 37501}, {15018, 46945}, {15025, 38727}, {15072, 15644}, {15077, 43713}, {15305, 40247}, {15513, 43619}, {15515, 31404}, {15589, 32882}, {16772, 22235}, {16773, 22237}, {16964, 42796}, {16965, 42795}, {16982, 37481}, {17852, 32788}, {18220, 37605}, {18481, 20052}, {18909, 37779}, {18945, 21663}, {19925, 46931}, {20057, 28228}, {20066, 43161}, {20085, 46684}, {20094, 38664}, {20095, 24466}, {20096, 38668}, {20097, 38684}, {20098, 38685}, {20099, 38688}, {20218, 40897}, {20725, 35265}, {20791, 45186}, {22236, 42120}, {22238, 42119}, {22332, 37665}, {23236, 38626}, {23269, 35255}, {23275, 35256}, {28172, 31423}, {30652, 37570}, {31414, 41963}, {31670, 33750}, {32522, 44434}, {32523, 48673}, {32785, 42272}, {32786, 42271}, {34469, 39874}, {34628, 43174}, {36836, 42088}, {36843, 42087}, {36967, 42934}, {36968, 42935}, {37515, 46865}, {37537, 37685}, {37640, 43193}, {37641, 43194}, {38665, 38761}, {38666, 38773}, {38667, 38785}, {38675, 38805}, {38807, 44987}, {40693, 42529}, {40694, 42528}, {41971, 42150}, {41972, 42151}, {42096, 42599}, {42097, 42598}, {42099, 42159}, {42100, 42162}, {42104, 42580}, {42105, 42581}, {42108, 43365}, {42109, 43364}, {42111, 43468}, {42112, 42954}, {42113, 42955}, {42114, 43467}, {42115, 42983}, {42116, 42982}, {42121, 42690}, {42124, 42691}, {42136, 43464}, {42137, 43463}, {42139, 43299}, {42140, 42163}, {42141, 42166}, {42142, 43298}, {42147, 42625}, {42148, 42626}, {42153, 43480}, {42156, 43479}, {42262, 43508}, {42265, 43507}, {42429, 42488}, {42430, 42489}, {42431, 43403}, {42432, 43404}, {42480, 42511}, {42481, 42510}, {42490, 42494}, {42491, 42495}, {42631, 42991}, {42632, 42990}, {42694, 42937}, {42695, 42936}, {42779, 42891}, {42780, 42890}, {42793, 49906}, {42794, 49905}, {42813, 43544}, {42814, 43545}, {42932, 43542}, {42933, 43543}, {42942, 43495}, {42943, 43496}, {42948, 43478}, {42949, 43477}, {43252, 49947}, {43256, 43526}, {43257, 43525}
X(50693) = midpoint of X(i) and X(j) for these {i,j}: {20, 3523}, {3857, 15704}
X(50693) = reflection of X(i) in X(j) for these {i,j}: {4, 3526}, {381, 19711}, {3090, 3}, {3523, 3528}, {3543, 41106}, {3832, 3523}, {3851, 44682}, {5066, 45761}, {9780, 16192}, {10248, 3624}, {15700, 8703}, {41106, 15700}, {45762, 11812}
X(50693) = anticomplement of X(3832)
X(50693) = orthoptic-circle-of-Steiner-circumellipse-inverse of X(47315)
X(50693) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20, 5059}, {2, 3522, 21734}, {2, 5059, 17578}, {2, 17578, 3854}, {3, 4, 10303}, {3, 20, 3146}, {3, 381, 12108}, {3, 382, 632}, {3, 546, 631}, {3, 550, 17538}, {3, 632, 3524}, {3, 1657, 546}, {3, 3090, 3523}, {3, 3146, 2}, {3, 3529, 3091}, {3, 3534, 15704}, {3, 3627, 3525}, {3, 5072, 549}, {3, 5076, 140}, {3, 10303, 15717}, {3, 11403, 40916}, {3, 11541, 46936}, {3, 12082, 44802}, {3, 12103, 3529}, {3, 12108, 10299}, {3, 15681, 5076}, {3, 15696, 44245}, {3, 15704, 4}, {3, 16661, 7492}, {3, 17538, 20}, {3, 17800, 5072}, {3, 33524, 23}, {3, 33532, 12088}, {3, 35407, 5070}, {3, 36002, 17572}, {3, 44245, 376}, {3, 49136, 3628}, {3, 49137, 5}, {3, 49140, 15022}, {4, 20, 15683}, {4, 376, 548}, {4, 548, 10304}, {4, 549, 7486}, {4, 631, 5055}, {4, 3090, 3857}, {4, 3528, 15698}, {4, 3529, 49136}, {4, 3534, 20}, {4, 3628, 3091}, {4, 10303, 15022}, {4, 10304, 15717}, {4, 15698, 3526}, {4, 15704, 49140}, {4, 15709, 5}, {4, 15717, 2}, {4, 17800, 15640}, {4, 33703, 33699}, {4, 46333, 17800}, {4, 49140, 3146}, {5, 550, 15691}, {5, 1657, 35409}, {5, 11001, 49135}, {5, 15684, 4}, {5, 15688, 21735}, {5, 21735, 15692}, {5, 41981, 15688}, {5, 41984, 1656}, {15, 43300, 43302}, {16, 43301, 43303}, {20, 376, 3522}, {20, 548, 15717}, {20, 3091, 3529}, {20, 3522, 2}, {20, 3528, 3832}, {20, 3543, 1657}, {20, 7411, 37435}, {20, 7486, 17800}, {20, 8703, 5068}, {20, 10303, 49140}, {20, 10304, 4}, {20, 15692, 49135}, {20, 15697, 550}, {20, 21734, 17578}, {20, 46219, 35414}, {20, 49135, 11001}, {20, 49140, 15704}, {140, 5076, 3544}, {140, 15681, 33703}, {140, 15722, 631}, {140, 33703, 3839}, {376, 550, 20}, {376, 3524, 15695}, {376, 3534, 10304}, {376, 11001, 15688}, {376, 15689, 15697}, {376, 15691, 15692}, {376, 17538, 3}, {381, 46853, 10299}, {382, 3524, 5056}, {382, 5066, 4}, {382, 15695, 33923}, {382, 33923, 3524}, {439, 6655, 2}, {546, 631, 46936}, {546, 1657, 11541}, {546, 8703, 3}, {546, 11541, 3543}, {546, 46936, 5068}, {548, 550, 3534}, {548, 3526, 3528}, {548, 3534, 4}, {548, 5066, 33923}, {548, 10304, 3522}, {548, 12103, 3628}, {548, 15684, 21735}, {548, 15704, 3}, {548, 17538, 49140}, {549, 3534, 46333}, {549, 17800, 4}, {549, 44904, 3526}, {549, 46333, 15640}, {550, 15690, 15696}, {550, 15696, 376}, {550, 44245, 3}, {631, 1657, 3543}, {631, 3543, 5068}, {631, 5068, 2}, {631, 11541, 546}, {631, 15700, 3523}, {632, 33923, 3}, {1003, 33226, 33202}, {1131, 42264, 43519}, {1132, 42263, 43520}, {1657, 8703, 631}, {1657, 46936, 3146}, {3090, 3528, 3}, {3091, 3529, 3146}, {3091, 3628, 15022}, {3091, 3839, 41991}, {3091, 10303, 3628}, {3146, 3522, 3}, {3146, 15022, 4}, {3146, 15683, 49140}, {3146, 15705, 46936}, {3146, 15717, 15022}, {3522, 15683, 15717}, {3522, 15717, 10304}, {3523, 3832, 2}, {3523, 15698, 15717}, {3524, 15698, 45761}, {3525, 3529, 3627}, {3525, 3627, 3091}, {3526, 3857, 3090}, {3526, 15698, 3523}, {3528, 3529, 14869}, {3528, 46333, 44904}, {3529, 12103, 20}, {3529, 17538, 12103}, {3529, 49136, 49140}, {3530, 5073, 3545}, {3530, 19710, 5073}, {3534, 10304, 15683}, {3534, 15688, 15684}, {3534, 15695, 5066}, {3534, 15706, 15681}, {3534, 15759, 11001}, {3543, 8703, 15705}, {3543, 11541, 3146}, {3543, 15705, 2}, {3543, 46936, 546}, {3544, 5076, 3839}, {3544, 15706, 10303}, {3544, 33703, 5076}, {3544, 41991, 3091}, {3552, 33023, 2}, {3552, 33207, 33023}, {3628, 12103, 15704}, {3628, 14869, 3526}, {3628, 15704, 49136}, {3628, 49136, 4}, {3830, 15710, 15721}, {3830, 15712, 5067}, {3832, 5068, 41106}, {3832, 15717, 3526}, {3839, 10304, 15706}, {3843, 12100, 3533}, {3850, 44903, 49134}, {3851, 44682, 15702}, {3853, 15720, 5071}, {3853, 45759, 15720}, {3855, 5054, 46935}, {3857, 14869, 3628}, {3857, 15698, 10303}, {3857, 44904, 5072}, {4189, 37435, 2}, {4190, 17576, 2}, {4190, 37299, 17576}, {4297, 9778, 145}, {5055, 10304, 15705}, {5055, 15704, 11541}, {5055, 35435, 33699}, {5055, 41983, 15709}, {5059, 21734, 2}, {5067, 15710, 15712}, {5067, 15712, 15721}, {5068, 15705, 631}, {5072, 7486, 15022}, {5072, 46333, 49140}, {5073, 14093, 3530}, {5731, 20070, 3623}, {5731, 31730, 20070}, {6455, 42226, 13886}, {6456, 42225, 13939}, {6655, 33208, 439}, {6872, 36004, 37267}, {6872, 37267, 2}, {6904, 11106, 2}, {7408, 15246, 2}, {7411, 37022, 4189}, {7486, 15640, 4}, {7585, 42638, 9543}, {7791, 33201, 2}, {7791, 33268, 35927}, {7791, 35927, 33201}, {7807, 33247, 33210}, {7833, 32973, 33025}, {7833, 33254, 32973}, {7987, 9812, 46934}, {8356, 33239, 33198}, {8357, 33191, 33182}, {8703, 15722, 19708}, {8703, 35409, 15692}, {10299, 49138, 381}, {10303, 10304, 3}, {10303, 15022, 2}, {10303, 15704, 3146}, {10303, 49140, 4}, {10304, 15640, 549}, {10304, 15683, 2}, {10304, 15692, 15759}, {10304, 15704, 15022}, {10304, 49140, 10303}, {11001, 15688, 15692}, {11001, 15709, 15684}, {11001, 21735, 5}, {11001, 41983, 3543}, {11413, 37198, 6636}, {11414, 22467, 37913}, {12103, 41991, 15681}, {12108, 46853, 3}, {12111, 13348, 33884}, {13586, 32974, 33205}, {13586, 33253, 32974}, {13587, 50244, 6919}, {14068, 33022, 2}, {14093, 19710, 3545}, {14782, 14783, 15703}, {14813, 14814, 49133}, {14927, 31884, 3620}, {15022, 15683, 3146}, {15022, 15717, 10303}, {15515, 43618, 31404}, {15640, 46333, 15683}, {15681, 15706, 33699}, {15681, 19708, 3839}, {15682, 34200, 15708}, {15683, 15717, 4}, {15684, 15688, 15759}, {15684, 15759, 15709}, {15685, 15720, 3853}, {15685, 45759, 5071}, {15686, 15695, 3524}, {15686, 33923, 382}, {15686, 35418, 2}, {15688, 15691, 11001}, {15688, 15709, 10304}, {15688, 49137, 3}, {15689, 15690, 376}, {15689, 15696, 550}, {15691, 21735, 20}, {15691, 41981, 5}, {15692, 49135, 5}, {15693, 49134, 3850}, {15694, 49133, 3861}, {15696, 15697, 3522}, {15700, 15701, 41983}, {15701, 15759, 15698}, {15701, 49135, 3832}, {15702, 44682, 3523}, {15704, 49136, 3529}, {15704, 49140, 15683}, {15709, 15759, 15692}, {15759, 41981, 548}, {16925, 33200, 2}, {16925, 33267, 33272}, {16925, 33272, 33200}, {17548, 31295, 2}, {17576, 37435, 37228}, {19708, 33703, 140}, {21735, 35409, 631}, {26617, 26618, 14039}, {31670, 33751, 33750}, {32964, 32982, 2}, {32964, 33264, 32982}, {32965, 32981, 2}, {32965, 33265, 32981}, {32973, 33025, 2}, {32974, 33205, 2}, {32979, 33004, 2}, {32980, 33259, 2}, {32985, 33234, 33180}, {32986, 33235, 33181}, {32991, 33012, 2}, {32997, 33014, 2}, {33004, 33193, 32979}, {33007, 33275, 32990}, {33008, 33257, 32971}, {33017, 33276, 32989}, {33051, 33062, 2}, {33192, 33259, 32980}, {33207, 33252, 3552}, {33208, 33243, 6655}, {33238, 35297, 33199}, {33244, 33260, 2}, {33250, 35955, 16043}, {33273, 33280, 32987}, {33274, 33279, 32988}, {35404, 46332, 15707}, {35471, 35485, 3088}, {35732, 42282, 3543}, {36445, 36463, 41983}, {41981, 49135, 3522}, {42258, 42637, 7586}, {42259, 42638, 7585}, {42280, 42281, 38335}, {42490, 42941, 42494}, {42491, 42940, 42495}, {42574, 42575, 6}, {43382, 43383, 6}
X(50694) lies on these lines: {2, 3}, {33, 17134}, {40, 4651}, {42, 516}, {165, 26037}, {390, 5712}, {515, 17135}, {517, 20011}, {573, 9778}, {581, 962}, {966, 42316}, {2356, 18659}, {3198, 30807}, {3720, 4297}, {3741, 28164}, {3995, 30273}, {4359, 30271}, {4450, 5739}, {4685, 5493}, {5080, 27517}, {5691, 31330}, {5731, 29814}, {5752, 6361}, {6685, 28158}, {8025, 37474}, {9589, 42042}, {9812, 10478}, {10382, 18655}, {10441, 48923}, {10444, 20347}, {10453, 10454}, {12717, 32929}, {14547, 17220}, {17165, 29054}, {20012, 20070}, {20075, 31034}, {29181, 37676}, {29349, 48918}, {29822, 41869}
X(50694) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 37400, 2}, {20, 3146, 50419}, {1817, 14004, 36007}, {6818, 37262, 2}, {7580, 49130, 19645}
X(50695) lies on these lines: {2, 3}, {7, 10393}, {8, 41338}, {78, 516}, {165, 12617}, {354, 3486}, {390, 3485}, {515, 12649}, {517, 20013}, {938, 3338}, {944, 3889}, {962, 6261}, {1210, 4299}, {1434, 5738}, {1445, 10392}, {1490, 5905}, {1858, 3474}, {1898, 15726}, {1902, 20243}, {3218, 9799}, {3332, 19767}, {3434, 6253}, {3601, 21617}, {3616, 43161}, {3869, 7957}, {3876, 5759}, {4294, 5703}, {4302, 13411}, {5552, 44425}, {5558, 15933}, {5691, 6734}, {5698, 15587}, {5887, 6361}, {6700, 28158}, {7987, 38150}, {9778, 9800}, {9960, 9965}, {10528, 11500}, {10586, 22753}, {11471, 24611}, {12528, 20078}, {12608, 41869}, {12688, 44447}, {12699, 33597}, {12943, 15844}, {13373, 18481}, {21628, 35258}, {28160, 37002}
X(50695) = reflection of X(i) in X(j) for these {i,j}: {20, 6934}, {6836, 3149}
X(50695) = anticomplement of X(6836)
X(50695) = orthocentroidal-circle-inverse of X(6870)}
X(50695) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 6870}, {2, 3146, 6895}, {3, 4, 6837}, {3, 5, 6878}, {3, 6835, 2}, {3, 37387, 4228}, {3, 37447, 6974}, {4, 20, 6872}, {4, 376, 3560}, {4, 411, 2}, {4, 631, 6841}, {4, 2476, 3832}, {4, 3529, 7491}, {4, 6825, 3091}, {4, 6838, 6871}, {4, 6853, 6866}, {4, 6857, 10883}, {4, 6867, 3839}, {4, 6869, 20}, {4, 6876, 6824}, {4, 6985, 6838}, {4, 6988, 6828}, {4, 31384, 3089}, {20, 3091, 6987}, {20, 6904, 3522}, {376, 6864, 6986}, {377, 11344, 2}, {382, 37406, 4}, {411, 6828, 6988}, {474, 50399, 2}, {631, 6991, 2}, {1006, 6849, 6886}, {1006, 6886, 50398}, {1657, 6918, 37428}, {2478, 37229, 2}, {3149, 6836, 2}, {3149, 37022, 37282}, {3529, 6948, 20}, {3651, 6826, 37112}, {5059, 37256, 20}, {5125, 27379, 2}, {6824, 6876, 3523}, {6826, 37112, 50237}, {6828, 6988, 2}, {6831, 6962, 2}, {6840, 6848, 5187}, {6851, 6905, 6890}, {6853, 6866, 5056}, {6864, 6986, 2}, {6865, 6915, 2}, {6868, 6988, 37423}, {6889, 44229, 6993}, {6925, 37468, 31295}, {6927, 6943, 2}, {7580, 20420, 377}, {37411, 37468, 6925}
X(50696) lies on these lines: {2, 3}, {7, 10382}, {9, 9778}, {33, 347}, {40, 9800}, {55, 8232}, {57, 5809}, {63, 36991}, {72, 20070}, {200, 329}, {226, 390}, {342, 44695}, {515, 15239}, {517, 20015}, {950, 3600}, {962, 1490}, {971, 9965}, {1699, 43161}, {1864, 3474}, {1998, 6223}, {2094, 30304}, {2900, 7674}, {3488, 5049}, {3586, 4293}, {3935, 5758}, {3957, 18446}, {4294, 9612}, {4297, 10582}, {4533, 5777}, {4666, 5731}, {4847, 5175}, {4872, 17093}, {5311, 11200}, {5658, 20075}, {5728, 11220}, {5732, 9776}, {5735, 41561}, {5759, 5927}, {5762, 20214}, {6260, 41869}, {7964, 38057}, {8580, 12572}, {9779, 25525}, {9801, 32932}, {9961, 44547}, {11201, 28125}, {11495, 26040}, {11523, 12632}, {12511, 19855}, {13257, 20095}, {14552, 48878}, {15931, 38037}, {18481, 31822}, {20103, 28158}, {28146, 37822}
X(50696) = reflection of X(i) in X(j) for these {i,j}: {329, 1750}, {10430, 57}
X(50696) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3146, 10431}, {4, 20, 452}, {4, 376, 6913}, {4, 442, 3832}, {4, 3529, 31789}, {4, 3651, 6846}, {4, 6843, 3839}, {4, 6908, 3091}, {4, 7580, 2}, {4, 37411, 37421}, {4, 37421, 5177}, {20, 3091, 37423}, {20, 3839, 6992}, {20, 17580, 3522}, {1864, 3474, 12848}, {3651, 6846, 3523}, {4190, 5059, 20}, {5084, 37271, 2}, {6835, 33557, 37108}, {6835, 37108, 37436}, {7580, 13615, 7411}, {7580, 19541, 35990}, {10431, 36002, 2}
X(50697) lies on these lines: {2, 3}, {144, 5739}, {306, 516}, {329, 45744}, {515, 3187}, {517, 20017}, {573, 3219}, {581, 17011}, {952, 20046}, {966, 44416}, {990, 5256}, {1848, 17134}, {1999, 10454}, {3672, 3782}, {5271, 5691}, {5738, 21454}, {5751, 11220}, {5752, 12528}, {5905, 17147}, {7282, 17080}, {9778, 33083}, {9812, 33112}, {10319, 20291}, {10444, 17184}, {10445, 26223}, {10464, 17185}, {10478, 31019}, {20064, 29207}, {20106, 28158}, {21270, 24310}, {28164, 40940}, {30807, 42699}, {37499, 41809}, {41820, 44736}
X(50697) = reflection of X(19645) in X(19542)
X(50697) = anticomplement of X(19645)
X(50697) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3151, 31015}, {4, 37419, 2}, {379, 440, 2}, {469, 1817, 2}, {857, 11347, 2}, {2476, 37265, 2}, {3146, 6999, 31015}, {5125, 27404, 2}, {19542, 19645, 2}
X(50698) lies on these lines: {2, 3}, {8, 1763}, {33, 4329}, {40, 3710}, {57, 5807}, {145, 17441}, {154, 26668}, {165, 12618}, {197, 11677}, {321, 3198}, {390, 3744}, {391, 39690}, {516, 612}, {517, 20020}, {614, 4297}, {910, 2345}, {940, 29181}, {944, 19993}, {962, 3920}, {1211, 36990}, {1427, 3600}, {1503, 5739}, {1766, 3161}, {1824, 20061}, {2000, 36850}, {2220, 5304}, {2895, 5921}, {3598, 17863}, {4299, 24239}, {4383, 44882}, {5069, 37665}, {5285, 28739}, {5731, 7191}, {10382, 18650}, {14555, 14927}, {15589, 44140}, {20076, 29840}, {20110, 26893}, {21287, 37668}, {25406, 32911}, {31670, 37527}, {37521, 48873}, {37674, 48872}
X(50698) = reflection of X(26118) in X(19544)
X(50698) = anticomplement of X(26118)
X(50698) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3146, 37456}, {4, 4220, 2}, {25, 26052, 2}, {1370, 35996, 2}, {2478, 37099, 2}, {5000, 5001, 7521}, {5004, 5005, 13730}, {6997, 7465, 2}, {7386, 33849, 2}, {7392, 37261, 2}, {7580, 49132, 37419}, {19544, 26118, 2}
X(50699) lies on these lines: {2, 3}, {8, 21370}, {81, 25406}, {390, 3666}, {515, 10327}, {516, 614}, {517, 19993}, {612, 4297}, {940, 44882}, {944, 20020}, {962, 7191}, {1040, 4329}, {1211, 31884}, {1333, 5304}, {1350, 5739}, {1766, 40184}, {3220, 27540}, {3424, 40013}, {3600, 7365}, {3757, 10465}, {3920, 5731}, {4261, 37665}, {4302, 24239}, {4383, 29181}, {4696, 7172}, {5014, 17740}, {5921, 32863}, {9812, 12610}, {10383, 18650}, {14927, 18141}, {15589, 44147}, {18788, 33088}, {20075, 29840}, {36844, 37577}, {37521, 46264}, {37679, 48872}, {41011, 43173}
X(50699) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 26118, 2}, {4, 19649, 2}, {20, 452, 50419}, {1370, 37449, 2}, {4224, 7386, 2}, {4228, 46336, 2}, {5002, 5003, 27505}, {5004, 5005, 37034}
X(50700) lies on these lines: {2, 3}, {7, 1490}, {57, 9799}, {78, 962}, {84, 1445}, {144, 5777}, {165, 21628}, {386, 3332}, {390, 946}, {497, 6253}, {515, 938}, {516, 936}, {517, 20007}, {580, 37681}, {581, 3945}, {944, 5045}, {952, 20008}, {1071, 21454}, {1125, 38150}, {1210, 3361}, {1537, 20095}, {1699, 4294}, {1750, 4292}, {3085, 44425}, {3474, 12688}, {3487, 5805}, {3488, 5806}, {3811, 7674}, {4308, 12650}, {5044, 5759}, {5217, 7965}, {5225, 36999}, {5226, 5715}, {5229, 15844}, {5248, 38037}, {5256, 9121}, {5261, 26332}, {5274, 48482}, {5281, 6796}, {5435, 6245}, {5584, 26040}, {5603, 33597}, {5704, 31673}, {5705, 19925}, {5720, 5758}, {5732, 12436}, {5763, 31671}, {5817, 31445}, {5882, 15933}, {5932, 7177}, {6326, 16134}, {6361, 9856}, {7982, 12632}, {8166, 9669}, {9776, 10884}, {9778, 12705}, {9812, 27383}, {9843, 28164}, {9960, 44547}, {9965, 12528}, {10051, 45287}, {10394, 12671}, {10445, 27382}, {10857, 18219}, {11024, 30503}, {11036, 18446}, {11372, 31730}, {12512, 21153}, {12664, 12848}, {12672, 20070}, {14986, 22753}, {15811, 37537}, {18221, 31870}, {18482, 40262}, {21279, 38859}, {24470, 36996}, {31363, 40395}, {31419, 38149}, {31672, 34862}, {35250, 38140}, {37530, 37666}
X(50700) = reflection of X(i) in X(j) for these {i,j}: {376, 19706}, {6865, 6918}
X(50700) = anticomplement of X(6865)
X(50700) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20, 37423}, {2, 3146, 6836}, {2, 3522, 6986}, {2, 3832, 6828}, {2, 6894, 3091}, {2, 37267, 37282}, {3, 4, 37434}, {3, 5, 16845}, {3, 6846, 17558}, {3, 6849, 6846}, {3, 6864, 2}, {3, 6918, 50203}, {4, 631, 8727}, {4, 1532, 3832}, {4, 3149, 2}, {4, 6834, 6844}, {4, 6848, 3091}, {4, 6880, 6845}, {4, 6905, 6847}, {4, 6927, 6831}, {4, 6935, 37447}, {4, 37468, 3146}, {5, 6869, 6987}, {5, 6987, 5129}, {5, 6988, 2}, {20, 3091, 452}, {20, 5056, 6992}, {20, 5129, 6987}, {20, 17580, 3}, {377, 36002, 37421}, {411, 6835, 2}, {411, 6915, 37229}, {443, 7580, 37108}, {443, 16293, 2}, {1750, 4292, 6223}, {3091, 3523, 6884}, {3091, 17558, 6846}, {3146, 4190, 20}, {3149, 6831, 6927}, {3651, 6854, 37407}, {3832, 5141, 3091}, {6825, 44229, 6843}, {6826, 6908, 4208}, {6826, 6985, 6908}, {6828, 6962, 2}, {6831, 6927, 2}, {6834, 6844, 5056}, {6836, 6915, 2}, {6838, 6839, 5177}, {6840, 6953, 6919}, {6846, 6849, 3091}, {6847, 6905, 3523}, {6851, 6911, 6926}, {6865, 6918, 2}, {6869, 6987, 20}, {7580, 19521, 3}, {14004, 25876, 37054}, {17567, 50206, 2}, {19541, 20420, 4}, {37281, 37411, 6916}
X(50701) lies on these lines: {2, 3}, {7, 18446}, {8, 5709}, {11, 36999}, {40, 5837}, {56, 6253}, {57, 515}, {65, 9942}, {78, 5758}, {84, 1708}, {104, 8732}, {142, 3576}, {145, 24474}, {278, 46974}, {329, 5720}, {347, 1060}, {355, 37623}, {387, 37530}, {388, 11500}, {390, 5603}, {391, 5755}, {497, 5842}, {516, 997}, {517, 17784}, {579, 5822}, {581, 4340}, {610, 10445}, {912, 9965}, {942, 944}, {946, 3601}, {950, 5804}, {952, 2095}, {962, 4511}, {971, 2096}, {1064, 4307}, {1071, 37544}, {1119, 38554}, {1155, 14647}, {1465, 34231}, {1466, 7354}, {1467, 4311}, {1478, 44425}, {1490, 4292}, {1498, 37537}, {1512, 5744}, {1519, 9812}, {1537, 9945}, {1699, 4302}, {1737, 4299}, {2550, 3428}, {2551, 11827}, {3085, 6796}, {3086, 37583}, {3358, 5825}, {3474, 6001}, {3485, 37837}, {3486, 7686}, {3487, 33597}, {3488, 11018}, {3586, 7682}, {3587, 9778}, {3622, 24299}, {3940, 5762}, {4260, 6776}, {4295, 6261}, {4297, 8726}, {4304, 10383}, {4309, 11522}, {5082, 22770}, {5138, 14853}, {5218, 7680}, {5225, 7681}, {5229, 18242}, {5261, 10786}, {5265, 10785}, {5273, 21165}, {5397, 45100}, {5587, 5745}, {5715, 13411}, {5721, 37642}, {5731, 9776}, {5770, 20067}, {5771, 5790}, {5787, 37002}, {5791, 5818}, {5841, 18491}, {5881, 24391}, {5882, 11518}, {5908, 43213}, {6224, 9946}, {6260, 9579}, {6361, 12672}, {6705, 31673}, {7080, 11499}, {7171, 10430}, {7713, 36986}, {7956, 9668}, {7967, 15934}, {7982, 12437}, {8729, 9837}, {9709, 31799}, {9940, 18481}, {9956, 35250}, {10165, 41867}, {10532, 11491}, {10588, 10894}, {10698, 20095}, {10806, 45977}, {11012, 19843}, {11023, 34489}, {11374, 40262}, {11407, 34628}, {12116, 14986}, {12248, 13226}, {12512, 21628}, {12671, 44547}, {12691, 41563}, {12705, 31730}, {18493, 38033}, {18517, 26286}, {20066, 33596}, {20070, 37585}, {20075, 37533}, {20076, 37532}, {21164, 28164}, {28146, 35249}, {34610, 34746}, {34617, 38665}, {34739, 38757}, {37584, 48363}
X(50701) = reflection of X(i) in X(j) for these {i,j}: {4, 19541}, {20, 6948}, {329, 5720}, {497, 22753}, {3586, 7682}, {5768, 57}, {6827, 6911}, {9580, 946}, {9668, 7956}, {10430, 7171}
X(50701) = anticomplement of X(6827)
X(50701) = orthocentroidal-circle-inverse of X(6844)
X(50701) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 6844}, {2, 20, 6987}, {2, 3146, 6840}, {2, 3522, 37106}, {2, 6839, 6843}, {3, 4, 6847}, {3, 5, 6857}, {3, 443, 37407}, {3, 6826, 2}, {3, 6841, 6892}, {3, 6869, 20}, {3, 6885, 6904}, {3, 6989, 3523}, {3, 7497, 4224}, {3, 8727, 6935}, {3, 8728, 631}, {3, 20420, 4}, {3, 28452, 6826}, {3, 37281, 443}, {3, 44229, 6824}, {4, 376, 1012}, {4, 631, 6831}, {4, 3149, 6848}, {4, 6834, 3091}, {4, 6880, 6830}, {4, 6905, 2}, {4, 6906, 37434}, {4, 6927, 5}, {4, 6934, 20}, {4, 6935, 8727}, {4, 6941, 3832}, {4, 6942, 6833}, {4, 6968, 3839}, {4, 6969, 381}, {4, 6977, 6845}, {5, 6868, 452}, {5, 6954, 2}, {20, 452, 6868}, {20, 3091, 6872}, {20, 6904, 3}, {20, 17580, 37423}, {21, 6835, 6846}, {140, 6858, 2}, {376, 6854, 1006}, {377, 411, 6908}, {404, 6836, 6926}, {443, 37306, 2}, {631, 6829, 2}, {1006, 6854, 2}, {2043, 2044, 11111}, {2478, 6915, 6964}, {3090, 6936, 5129}, {3146, 37256, 20}, {3149, 37468, 4}, {3522, 37434, 6906}, {3523, 6993, 2}, {3523, 37436, 6989}, {3528, 6878, 21161}, {3651, 6897, 37108}, {4188, 6895, 6890}, {4189, 6894, 6837}, {4297, 12436, 8726}, {5603, 37000, 390}, {5691, 15803, 6245}, {5731, 9776, 18443}, {5805, 24929, 5603}, {6796, 26332, 3085}, {6824, 44229, 3091}, {6825, 6917, 5177}, {6827, 6911, 2}, {6830, 6880, 2}, {6830, 6905, 6880}, {6832, 6875, 17558}, {6833, 6942, 3523}, {6850, 6985, 37421}, {6863, 37230, 6867}, {6869, 6885, 3}, {6875, 6900, 6832}, {6876, 6901, 6889}, {6880, 6938, 6992}, {6881, 8727, 6830}, {6882, 6970, 2}, {6889, 6901, 4208}, {6909, 35977, 3}, {6916, 7580, 37427}, {6918, 31789, 5084}, {6928, 6944, 6919}, {6928, 37251, 6944}, {6935, 8727, 6847}, {6946, 6947, 2}, {7580, 11112, 6916}, {10883, 17549, 6974}, {14784, 14785, 31789}, {16417, 37364, 631}, {17579, 36002, 6925}, {17580, 37423, 631}, {37421, 37435, 6850}
X(50702) lies on theselines: {2, 3}, {8, 1764}, {42, 12545}, {78, 10444}, {145, 10441}, {165, 31339}, {390, 19765}, {515, 17751}, {516, 1193}, {517, 20040}, {940, 3600}, {944, 37536}, {959, 3474}, {1038, 17134}, {1150, 5786}, {1754, 34281}, {2944, 4418}, {3616, 10470}, {3831, 28164}, {4293, 37522}, {5396, 48941}, {5482, 18481}, {8142, 27674}, {10437, 17183}, {10446, 19767}, {10476, 17135}, {13329, 27660}, {15338, 21321}, {15509, 27410}, {19734, 37501}, {20036, 20070}, {20051, 45955}, {20076, 37639}, {26030, 50037}, {26251, 39573}
X(50702) = reflection of X(4) in X(19648)
X(50702) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 20, 50419}, {10470, 24220, 3616}
See Kadir Altintas and César Lozada, euclid 5233.
X(50703) lies on the quartic Q161 and these lines: {30, 80}, {140, 47307}, {21739, 48698}
X(50703) = midpoint of X(3065) and X(14452)
See Kadir Altintas and César Lozada, euclid 5233.
X(50704) lies on the quartic Q161 and these lines: {30, 5685}, {140, 3467}
X(50704) = midpoint of X(5685) and X(19658)
See Kadir Altintas and César Lozada, euclid 5233.
X(50705) lies on the quartic Q161 and these lines: {4, 1389}, {30, 1807}, {140, 3460}
X(50705) = midpoint of X(3465) and X(34300)
X(50706) lies on these lines: {2, 3}, {512, 3268}, {2387, 2979}, {2393, 6148}
X(50707 lies on these lines: {2, 3}, {51, 2387}, {115, 1495}, {184, 5309}, {230, 5191}, {512, 1637}, {1976, 1989}, {2393, 6128}, {3580, 6033}
X(50707) = crossdifference of every pair of points on line {647, 15066}
X(50707) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25, 21177, 237}, {419, 2450, 44887}, {1316, 1513, 47526}
See Antreas Hatzipolakis and César Lozada, euclid 5237.
X(50708) lies on the cubics K439, K467 and these lines: {2, 21357}, {3, 12325}, {4, 12175}, {5, 195}, {12, 35197}, {30, 511}, {49, 34577}, {52, 13368}, {54, 140}, {68, 10224}, {110, 10096}, {125, 46114}, {128, 24147}, {137, 31674}, {143, 6153}, {155, 13406}, {193, 11818}, {265, 43965}, {323, 33565}, {382, 13422}, {399, 43893}, {403, 2914}, {546, 6288}, {548, 7691}, {549, 45968}, {550, 12254}, {562, 14106}, {858, 15137}, {930, 6343}, {1141, 14140}, {1147, 10125}, {1157, 14072}, {1209, 1493}, {1216, 11264}, {1263, 19552}, {1511, 14049}, {1568, 11801}, {1658, 6193}, {1853, 16266}, {1993, 39504}, {2070, 5898}, {2072, 11804}, {2917, 12107}, {3530, 10610}, {3574, 3850}, {3575, 6242}, {3580, 11597}, {3627, 48675}, {3819, 11232}, {3853, 15800}, {3861, 13142}, {5159, 15124}, {5498, 12359}, {5562, 45970}, {5690, 9905}, {5876, 43581}, {5889, 45971}, {5899, 14683}, {5972, 47117}, {6101, 15532}, {6146, 21660}, {6150, 6592}, {6152, 6756}, {6243, 13423}, {6286, 15171}, {6515, 12106}, {6689, 15605}, {7356, 18990}, {7502, 45794}, {7514, 11898}, {7575, 25714}, {7583, 12965}, {7584, 12971}, {7730, 41628}, {9833, 17846}, {9920, 11206}, {9935, 32359}, {9936, 17824}, {10020, 47360}, {10095, 23409}, {10112, 11591}, {10115, 16881}, {10116, 10627}, {10124, 45298}, {10126, 14143}, {10192, 10274}, {10205, 35720}, {10212, 44158}, {10264, 43574}, {10272, 11702}, {10285, 25043}, {10289, 13856}, {10297, 25740}, {10619, 18914}, {10677, 11542}, {10678, 11543}, {11017, 40240}, {11225, 13363}, {11250, 11411}, {11412, 45731}, {11558, 43580}, {11563, 46440}, {11577, 32377}, {11600, 46076}, {11601, 46072}, {11808, 44056}, {12010, 41597}, {12026, 16336}, {12105, 41596}, {12108, 20585}, {12118, 15332}, {12134, 14449}, {12164, 44279}, {12242, 13565}, {12280, 14516}, {12291, 34224}, {12300, 13488}, {12317, 35452}, {12362, 12606}, {12370, 31834}, {12383, 32608}, {12421, 15136}, {12429, 18377}, {12605, 22815}, {12811, 20584}, {13079, 15172}, {13383, 41615}, {13419, 13421}, {13469, 15425}, {13490, 41713}, {14156, 40685}, {15069, 39522}, {15334, 18016}, {15350, 32226}, {15392, 34308}, {15557, 35719}, {15644, 45732}, {15699, 45967}, {15957, 23338}, {16532, 32609}, {18403, 36853}, {18583, 19150}, {19468, 31804}, {19940, 31879}, {23410, 41578}, {32166, 34421}, {32338, 44076}, {36749, 50136}, {37947, 46818}, {41586, 44264}, {44324, 44325}
X(50708) = isogonal conjugate of X(33643)
X(50708) = circumnormal-isogonal conjugate of X(33639)
X(50708) = Cevapoint of X(i) and X(j) for these (i, j): {3, 39431}, {140, 1263}
X(50708) = crosssum of X(140) and X(1157)
X(50708) = X(1263)-Ceva conjugate of-X(140)
X(50708) = X(3)-vertex conjugate of-X(13152)
See Antreas Hatzipolakis and César Lozada, euclid 5237.
X(50709) lies on these lines: {4, 1620}, {20, 5893}, {30, 511}, {64, 49135}, {74, 15153}, {154, 15683}, {382, 6696}, {546, 10193}, {1498, 49138}, {1514, 13619}, {1597, 15578}, {1853, 3146}, {2883, 3529}, {2935, 37925}, {3060, 40928}, {3153, 20725}, {3543, 23332}, {3627, 23329}, {3830, 23328}, {5059, 5895}, {5073, 6247}, {5878, 49137}, {5925, 33703}, {6240, 16656}, {8567, 17578}, {9781, 18560}, {9833, 49139}, {10117, 37944}, {10182, 15690}, {10606, 15682}, {11202, 19710}, {11204, 15687}, {12102, 25563}, {13202, 37931}, {13293, 37936}, {13473, 47296}, {14216, 49134}, {15105, 49133}, {15704, 16252}, {16621, 34797}, {17800, 34782}, {17845, 49140}, {18376, 35404}, {20427, 49136}, {22049, 42452}, {23315, 47096}, {23325, 33699}, {30517, 47030}, {33702, 35515}, {33923, 46265}, {38794, 44246}, {38795, 47308}, {40196, 48905}
X(50709) = isogonal conjugate of X(50710)
See Antreas Hatzipolakis and César Lozada, euclid 5237.
X(50710) lies on the circumcircle and these lines: {107, 17578}, {110, 8567}
X(50710) = isogonal conjugate of X(50709)
X(50710) = intersection, other than A, B, C, of circumcircle and circumconic {{A, B, C, X(3), X(17578)}}
See Antreas Hatzipolakis and César Lozada, euclid 5237.
X(50711) lies on these lines: {13, 37753}, {14, 37752}, {30, 511}, {67, 50567}, {74, 38738}, {98, 12383}, {99, 3448}, {110, 115}, {114, 265}, {125, 620}, {146, 10723}, {147, 48982}, {148, 14683}, {399, 6321}, {671, 9143}, {895, 5477}, {1511, 6036}, {2482, 9140}, {2502, 42344}, {2930, 11646}, {2931, 39854}, {2948, 13178}, {3580, 47326}, {5026, 25328}, {5182, 25320}, {5461, 5642}, {5465, 36523}, {5609, 38734}, {5655, 9880}, {5972, 6722}, {6033, 12902}, {6055, 14849}, {6721, 20304}, {7728, 39809}, {7756, 38523}, {8980, 10819}, {9862, 48951}, {9864, 12407}, {10264, 33813}, {10620, 38730}, {10733, 39838}, {10754, 11061}, {10820, 13967}, {11005, 14981}, {11006, 15300}, {11557, 39806}, {11623, 30714}, {11711, 13605}, {11720, 11725}, {11724, 12261}, {11800, 39835}, {12041, 38736}, {12042, 34153}, {12121, 38749}, {12302, 39860}, {12308, 38733}, {12310, 39857}, {12317, 13172}, {12412, 39828}, {13188, 15545}, {14643, 23514}, {14644, 36519}, {15027, 38751}, {15034, 38740}, {15035, 38737}, {15040, 38739}, {15041, 38731}, {15059, 31274}, {15061, 38748}, {15100, 39807}, {15102, 39808}, {15561, 38724}, {16163, 38747}, {16278, 24981}, {18331, 23235}, {18332, 23236}, {20399, 33512}, {22247, 45311}, {32609, 38224}, {35834, 49370}, {35835, 49369}, {36739, 36955}
X(50711) = isogonal conjugate of X(50712)
See Antreas Hatzipolakis and César Lozada, euclid 5237.
X(50712) lies on the circumcircle and these lines: {107, 17578}, {110, 8567}lies on the circumcircle and these lines: {476, 5099}, {691, 35936}, {2709, 38613}, {5461, 14734}, {10425, 14729}, {45773, 50386}
X(50712) = isogonal conjugate of X(50711)
X(50712) = intersection, other than A, B, C, of circumcircle and circumconic {{A, B, C, X(186), X(2065)}}
X(50713) lies on these lines: {2, 3}, {518, 4004}, {3633, 5425}, {3828, 9656}, {4114, 4691}, {9654, 26060}, {9671, 19883}, {11041, 20053}
X(50713) = midpoint of X(377) and X(50237)
X(50713) = reflection of X(i) in X(j) for these {i,j}: {405, 50207}, {31259, 8728}, {50207, 50237}
X(50713) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 377, 50240}, {2, 1657, 19538}, {2, 50240, 50242}, {2, 50242, 405}, {377, 405, 50397}, {377, 8728, 50239}, {377, 44217, 405}, {377, 50238, 44217}, {442, 17583, 2}, {443, 17532, 16862}, {443, 37161, 4187}, {4187, 37161, 17532}, {8728, 31259, 50207}, {8728, 50239, 405}, {8728, 50240, 50243}, {8728, 50243, 2}, {15674, 15696, 16370}, {31259, 50237, 8728}, {44217, 50207, 50237}, {44217, 50239, 8728}, {50238, 50396, 377}
X(50714) lies on these lines: {2, 3}, {518, 4539}, {1125, 3715}, {3158, 19875}, {3582, 8167}, {3624, 5302}, {3655, 24564}, {10404, 19862}, {16817, 50041}, {24473, 45120}
X(50714) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 376, 17529}, {2, 377, 50395}, {2, 405, 44217}, {2, 549, 16862}, {2, 5047, 381}, {2, 11346, 50427}, {2, 13742, 50323}, {2, 15670, 474}, {2, 15671, 5054}, {2, 16845, 15670}, {2, 16857, 17532}, {2, 16859, 6175}, {2, 16861, 17528}, {2, 17542, 17556}, {2, 31156, 8728}, {2, 31259, 50202}, {2, 44217, 50207}, {2, 50202, 405}, {2, 50398, 31156}, {405, 8728, 50242}, {405, 16862, 37426}, {405, 50207, 50239}, {405, 50397, 31156}, {442, 17554, 17545}, {8728, 31156, 50397}, {8728, 50397, 44217}, {8728, 50398, 405}, {15670, 17590, 2}, {15694, 16855, 2}, {16845, 17590, 474}, {31156, 50397, 50242}, {31259, 50205, 405}, {44217, 50242, 50397}, {50202, 50205, 2}
X(50715) lies on these lines: {2, 3}, {55, 3823}, {518, 614}, {958, 23675}, {1473, 17282}, {3953, 5272}, {4423, 4698}, {7083, 25957}, {11365, 19846}, {18139, 37492}, {29641, 37502}, {29850, 37580}
X(50715) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 405, 16353}, {2, 1370, 14019}, {2, 4228, 474}, {2, 5047, 37060}, {2, 16048, 25}, {2, 16067, 31255}, {2, 25494, 7484}, {405, 50199, 20835}
X(50716) lies on these lines: {2, 3}, {78, 5138}, {518, 976}, {2218, 3739}, {3666, 28082}, {3980, 5248}, {5259, 17889}, {5293, 36504}, {10404, 36503}
X(50716) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 405, 37329}, {3, 37065, 37255}, {21, 16451, 13723}
X(50717) lies on these lines: {2, 3}, {10, 27628}, {56, 3589}, {518, 872}, {978, 41229}, {992, 5069}, {5259, 33109}, {5302, 27627}, {18235, 24443}, {27634, 28252}, {28250, 31339}, {29492, 46877}
X(50717) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13738, 37255}, {2, 27655, 474}, {405, 16299, 37329}, {405, 50199, 377}, {405, 50203, 16353}, {11319, 35984, 37425}, {16062, 19238, 13724}, {16299, 19267, 405}, {19260, 33833, 47521}
X(50718) lies on the Moses-Parry circle, the cubic K936, and these lines: {4, 187}, {5, 5523}, {6, 7699}, {53, 403}, {111, 5094}, {112, 381}, {115, 7577}, {232, 39601}, {264, 8430}, {378, 2079}, {427, 5913}, {458, 8429}, {1157, 8882}, {1235, 32966}, {1249, 3545}, {1346, 8106}, {1347, 8105}, {1560, 5169}, {1594, 49123}, {1995, 8428}, {2165, 3087}, {3054, 10295}, {3091, 41370}, {3569, 7703}, {3851, 8743}, {5066, 16318}, {5068, 41361}, {5889, 8571}, {6032, 44467}, {6103, 43457}, {6143, 7748}, {6240, 42391}, {7547, 10312}, {7749, 34797}, {9166, 36794}, {9756, 10735}, {10254, 22240}, {10311, 18362}, {13509, 23325}, {14585, 18394}, {18392, 32661}, {18472, 18572}, {19709, 45141}, {21397, 31861}, {27371, 44958}, {27376, 35487}, {35480, 37637}, {39157, 40103}
X(50718) = nine-point-circle-inverse of X(5523)
X(50718) = orthocentroidal-circle-inverse of X(112)
X(50718) = polar-circle-inverse of X(187)
X(50718) = polar conjugate of the isotomic conjugate of X(38397)
X(50718) = barycentric product X(4)*X(38397)
X(50718) = barycentric quotient X(38397)/X(69)
X(50718) = {X(7547),X(13881)}-harmonic conjugate of X(10312)
X(50719) lies on the circumcircle of the outer Vecten triangle and these lines: {2, 33343}, {4, 32495}, {5, 6230}, {6, 13}, {15, 48722}, {16, 48724}, {30, 44392}, {98, 486}, {99, 492}, {114, 371}, {147, 1588}, {148, 22601}, {325, 32419}, {372, 2794}, {485, 6568}, {543, 591}, {590, 13670}, {615, 12042}, {620, 6200}, {671, 1328}, {1124, 12184}, {1132, 32498}, {1151, 15561}, {1152, 38741}, {1327, 19058}, {1335, 12185}, {1504, 45542}, {2088, 48736}, {2459, 48726}, {2460, 37459}, {2782, 3071}, {3069, 9862}, {3070, 22505}, {3103, 38383}, {3311, 38743}, {3312, 38744}, {3845, 49214}, {5420, 34473}, {5860, 33432}, {6036, 10577}, {6054, 13653}, {6302, 32553}, {6303, 32552}, {6319, 22484}, {6321, 23261}, {6396, 13989}, {6409, 38750}, {6410, 38742}, {6419, 38745}, {6423, 48660}, {6424, 44534}, {6453, 20399}, {6560, 10722}, {6569, 43571}, {6721, 8414}, {7584, 49213}, {8252, 38739}, {8980, 10576}, {9660, 15452}, {9677, 39805}, {9733, 12601}, {9741, 49097}, {9864, 35775}, {10053, 44622}, {10069, 44624}, {10723, 22615}, {10991, 13967}, {11177, 38424}, {11724, 35763}, {11725, 45398}, {12221, 33340}, {12305, 38738}, {12829, 49221}, {13178, 45426}, {13640, 42277}, {13847, 14830}, {13874, 45420}, {13968, 49363}, {14061, 42274}, {14639, 42268}, {14651, 33431}, {14981, 35878}, {15357, 35826}, {21166, 42260}, {22502, 42269}, {22515, 42283}, {22566, 32787}, {25559, 35759}, {25560, 42236}, {32421, 47286}, {32459, 44390}, {32492, 35684}, {33342, 33457}, {33813, 42258}, {34127, 42583}, {35610, 45444}, {35753, 41061}, {35768, 45460}, {35777, 39828}, {35787, 45440}, {35801, 45490}, {35803, 45492}, {35808, 45458}, {35820, 39838}, {35835, 49369}, {35850, 41060}, {38224, 42262}, {38730, 42263}, {39857, 45428}, {41020, 42231}, {41021, 42233}, {42215, 49266}, {46053, 48725}, {46054, 48723}
X(50719) = midpoint of X(i) and X(j) for these {i,j}: {4, 33430}, {486, 22501}, {591, 49311}, {5860, 33432}, {12221, 33340}, {13748, 49309}, {22484, 22562}, {22601, 22603}, {33342, 33457}, {33440, 33442}, {35821, 35879}, {49305, 49307}
X(50719) = reflection of X(i) in X(j) for these {i,j}: {6230, 5}, {13926, 486}, {49213, 7584}
X(50719) = orthocentroidal-circle-inverse of X(6564)
X(50719) = crossdifference of every pair of points on line {526, 49268}
X(50719) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 45438, 6564}, {3071, 49355, 3102}, {6565, 35824, 115}, {6565, 39893, 6564}, {8980, 36519, 10576}, {10722, 19108, 6560}, {13989, 38749, 6396}, {31862, 31863, 6564}
X(50720) lies on the circumcircle of the inner Vecten triangle and these lines: {2, 33342}, {4, 32492}, {5, 6231}, {6, 13}, {15, 48723}, {16, 48725}, {30, 44394}, {98, 485}, {99, 491}, {114, 372}, {147, 1587}, {148, 22630}, {325, 32421}, {371, 2794}, {486, 6569}, {543, 1991}, {590, 12042}, {615, 13790}, {620, 6396}, {671, 1327}, {1124, 12185}, {1131, 32499}, {1151, 38741}, {1152, 15561}, {1328, 19057}, {1335, 12184}, {1505, 45543}, {2088, 48737}, {2459, 37459}, {2460, 48727}, {2782, 3070}, {3068, 9862}, {3071, 22505}, {3102, 38383}, {3311, 38744}, {3312, 38743}, {3845, 49215}, {5418, 34473}, {5861, 33433}, {6036, 10576}, {6054, 13773}, {6200, 8997}, {6306, 32553}, {6307, 32552}, {6320, 22485}, {6321, 23251}, {6409, 38742}, {6410, 38750}, {6420, 38745}, {6423, 44534}, {6424, 48659}, {6454, 20399}, {6561, 10722}, {6568, 43570}, {6721, 8406}, {7583, 49212}, {8253, 38739}, {8960, 8980}, {9732, 12602}, {9741, 49096}, {9864, 35774}, {10053, 31472}, {10069, 44623}, {10577, 13967}, {10723, 22644}, {11177, 38423}, {11724, 35762}, {11725, 45399}, {12222, 33341}, {12306, 38738}, {12829, 49220}, {13178, 45427}, {13760, 42274}, {13846, 14830}, {13908, 49362}, {13927, 45421}, {14061, 42277}, {14639, 42269}, {14651, 31412}, {14981, 35879}, {15357, 35827}, {21166, 42261}, {22501, 42268}, {22515, 42284}, {22566, 32788}, {25559, 42237}, {25560, 42238}, {31411, 43449}, {32419, 47286}, {32459, 44391}, {32495, 35685}, {33343, 33456}, {33813, 42259}, {34127, 42582}, {35611, 45445}, {35754, 41061}, {35769, 45461}, {35776, 39828}, {35786, 45441}, {35800, 45491}, {35802, 45493}, {35809, 45459}, {35821, 39838}, {35834, 49370}, {35851, 41060}, {38224, 42265}, {38730, 42264}, {39857, 45429}, {41020, 42232}, {41021, 42234}, {42216, 49267}, {46053, 48724}, {46054, 48722}
X(50720) = midpoint of X(i) and X(j) for these {i,j}: {4, 33431}, {485, 22502}, {1991, 49312}, {5861, 33433}, {12222, 33341}, {13749, 49310}, {22485, 22563}, {22630, 22632}, {33343, 33456}, {33441, 33443}, {35820, 35878}, {49306, 49308}
X(50720) = reflection of X(i) in X(j) for these {i,j}: {6231, 5}, {13873, 485}, {49212, 7583}
X(50720) = orthocentroidal-circle-inverse of X(6565)
X(50720) = crossdifference of every pair of points on line {526, 49269}
X(50720) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 45439, 6565}, {3070, 49356, 3103}, {6564, 35825, 115}, {6564, 39894, 6565}, {8997, 38749, 6200}, {10722, 19109, 6561}, {13967, 36519, 10577}, {31862, 31863, 6565}
X(50721) lies on these lines: {4, 6568}, {6, 13}, {98, 1132}, {99, 26619}, {114, 13653}, {486, 9739}, {615, 38736}, {620, 18762}, {625, 32419}, {671, 14226}, {1328, 13968}, {1588, 6230}, {2794, 14233}, {3069, 39809}, {3071, 6036}, {6055, 13773}, {6320, 33432}, {6321, 12314}, {6423, 22819}, {6721, 13873}, {6722, 42215}, {7584, 45862}, {8277, 39831}, {8997, 42274}, {9862, 13790}, {9880, 19108}, {10723, 13939}, {13670, 14061}, {13926, 35021}, {13943, 39812}, {13951, 38738}, {13967, 23261}, {14639, 33430}, {16001, 42246}, {16002, 42247}, {23259, 38749}, {23275, 34473}, {32421, 32457}, {35874, 42264}, {38730, 45385}, {38735, 49212}, {42573, 49214}
X(50721) = midpoint of X(i) and X(j) for these {i,j}: {1328, 13968}, {13967, 23261}
X(50721) = orthocentroidal-circle-inverse of X(13665)
X(50721) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6565, 35823, 5475}, {31862, 31863, 13665}
X(50722) lies on these lines: {4, 6569}, {6, 13}, {98, 1131}, {99, 26620}, {114, 13773}, {485, 8997}, {590, 38736}, {620, 18538}, {625, 32421}, {671, 14241}, {1327, 13908}, {1587, 6231}, {2794, 14230}, {3068, 39809}, {3070, 6036}, {6055, 13653}, {6319, 33433}, {6321, 12313}, {6424, 22820}, {6721, 13926}, {6722, 42216}, {7583, 45863}, {8276, 39831}, {8976, 36762}, {8980, 23251}, {9862, 13670}, {9880, 19109}, {10723, 13886}, {13790, 14061}, {13873, 35021}, {13889, 39812}, {13989, 42277}, {14639, 33431}, {16001, 42248}, {16002, 42249}, {19055, 31414}, {23249, 38749}, {23269, 34473}, {32419, 32457}, {35873, 42263}, {38730, 45384}, {38735, 49213}, {42572, 49215}
X(50722) = midpoint of X(i) and X(j) for these {i,j}: {1327, 13908}, {8980, 23251}
X(50722) = orthocentroidal-circle-inverse of X(13785)
X(50722) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6564, 35822, 5475}, {31862, 31863, 13785}
X(50723) lies on these lines: {6, 13}, {98, 3316}, {99, 1271}, {114, 6215}, {147, 13773}, {543, 5861}, {615, 48779}, {620, 5591}, {671, 43566}, {1161, 22810}, {2482, 13821}, {2782, 5875}, {2794, 5871}, {5589, 13178}, {5595, 39857}, {6036, 26341}, {6230, 6281}, {6231, 10514}, {6279, 22502}, {6321, 11916}, {7813, 32421}, {8974, 11177}, {8997, 10991}, {10517, 21166}, {11370, 11725}, {11623, 33430}, {11824, 38738}, {13760, 13949}, {13933, 49213}, {35246, 38736}, {38737, 45552}, {38740, 45550}
X(50723) = midpoint of X(i) and X(j) for these {i,j}: {5861, 9882}, {5871, 6227}, {6270, 6271}
X(50723) = reflection of X(i) in X(j) for these {i,j}: {14981, 6230}, {33430, 11623}
X(50723) = crossdifference of every pair of points on line {526, 19110}
X(50724) lies on these lines: {6, 13}, {98, 3317}, {99, 1270}, {114, 6214}, {147, 13653}, {543, 5860}, {590, 48778}, {620, 5590}, {671, 43567}, {1160, 22809}, {2482, 13701}, {2782, 5874}, {2794, 5870}, {5588, 13178}, {5594, 39857}, {6036, 26348}, {6230, 10515}, {6231, 6278}, {6280, 22501}, {6321, 11917}, {7813, 32419}, {8975, 13640}, {10518, 21166}, {10991, 13989}, {11177, 13773}, {11371, 11725}, {11623, 33431}, {11825, 38738}, {13879, 49212}, {23251, 37839}, {35247, 38736}, {38737, 45553}, {38740, 45551}
X(50724) = midpoint of X(i) and X(j) for these {i,j}: {5860, 9883}, {5870, 6226}, {6268, 6269}
X(50724) = reflection of X(i) in X(j) for these {i,j}: {14981, 6231}, {33431, 11623}
X(50724) = crossdifference of every pair of points on line {526, 19111}
X(50725) lies on these lines: {2, 3}, {7, 12625}, {8, 4312}, {144, 9579}, {145, 3671}, {388, 12632}, {2550, 8170}, {3600, 3813}, {3617, 12527}, {3621, 17483}, {3623, 41870}, {4018, 20052}, {4373, 50582}, {4452, 7247}, {4461, 7270}, {4654, 12536}, {4678, 20078}, {4900, 20054}, {5175, 21454}, {5229, 21031}, {5232, 49734}, {5691, 43182}, {5836, 12125}, {8583, 10248}, {11024, 31673}, {38149, 40267}
X(50725) = reflection of X(11106) in X(4208)
X(50725) = anticomplement of X(11106)
X(50725) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 31295, 5059}, {2, 37256, 21734}, {2, 50692, 6872}, {20, 37161, 2}, {377, 3146, 2}, {377, 11114, 37436}, {404, 5068, 2}, {442, 8727, 4193}, {2475, 37435, 2}, {2476, 15717, 2}, {3522, 5177, 2}, {3529, 17528, 17558}, {3832, 6904, 2}, {4208, 11106, 2}, {5177, 17579, 3522}, {6871, 37267, 2}, {16915, 33200, 2}, {17565, 32979, 2}, {32980, 33062, 2}, {32982, 33058, 2}, {33023, 33030, 2}, {33201, 33841, 2}
X(50726) lies on these lines: {2, 3}, {9, 3824}, {10, 15934}, {55, 41859}, {142, 3634}, {191, 41862}, {210, 942}, {277, 26100}, {495, 19855}, {999, 19854}, {1001, 3841}, {1125, 12437}, {1159, 28629}, {3059, 16216}, {3295, 3925}, {3358, 38318}, {3454, 17259}, {3579, 31671}, {3587, 3646}, {3601, 34595}, {3624, 24929}, {3626, 36867}, {3763, 4260}, {3826, 6600}, {3828, 24391}, {3927, 5249}, {4423, 9669}, {5044, 25525}, {5122, 31263}, {5138, 47355}, {5219, 37544}, {5251, 9655}, {5259, 9668}, {5273, 24470}, {5292, 17245}, {5534, 5790}, {5705, 20195}, {5707, 25878}, {5709, 11231}, {5714, 18230}, {5715, 31658}, {5745, 37545}, {5787, 10175}, {5789, 9940}, {5805, 6684}, {6173, 31446}, {6245, 10172}, {6260, 38108}, {6767, 31419}, {7373, 19843}, {7778, 36812}, {7879, 16994}, {7988, 37551}, {8167, 25639}, {8227, 31793}, {8583, 37533}, {8818, 37500}, {9708, 25466}, {9945, 31272}, {9956, 18443}, {10306, 38121}, {10896, 25542}, {11230, 37531}, {11495, 12558}, {11518, 19875}, {11928, 25893}, {12436, 31253}, {12513, 31494}, {12620, 49627}, {12645, 19860}, {13151, 18525}, {15668, 20083}, {15937, 48887}, {17234, 25446}, {17265, 50605}, {17284, 39564}, {17811, 45931}, {18483, 38059}, {18493, 37585}, {18541, 31445}, {19812, 19852}, {19872, 31246}, {24541, 35272}, {24880, 37674}, {31420, 47357}, {36499, 40328}, {37682, 45939}, {38031, 48482}
X(50726) = midpoint of X(4208) and X(16845)
X(50726) = reflection of X(16866) in X(16845)
X(50726) = complement of X(16845)
X(50726) = orthocentroidal circle inverse of X(50205)
X(50726) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 50205}, {2, 5, 16853}, {2, 442, 11108}, {2, 443, 6675}, {2, 2476, 16842}, {2, 2478, 17590}, {2, 4187, 16855}, {2, 4193, 16854}, {2, 4197, 405}, {2, 4202, 16343}, {2, 4208, 16845}, {2, 5141, 17534}, {2, 5154, 17546}, {2, 5177, 17552}, {2, 6175, 50714}, {2, 6856, 17527}, {2, 6933, 17575}, {2, 8728, 3}, {2, 13728, 16457}, {2, 14019, 19319}, {2, 16062, 16844}, {2, 16408, 3526}, {2, 16911, 33217}, {2, 17529, 16408}, {2, 17582, 140}, {2, 25962, 37224}, {2, 33026, 7819}, {2, 33035, 32954}, {2, 33180, 33027}, {2, 33833, 19273}, {2, 37153, 17698}, {2, 37436, 6857}, {2, 37462, 7483}, {2, 47516, 37244}, {2, 50393, 17529}, {3, 5055, 6841}, {3, 5070, 6861}, {4, 50205, 16857}, {5, 140, 6865}, {5, 6989, 3}, {5, 37411, 381}, {5, 50394, 2}, {140, 6826, 3}, {142, 3634, 5791}, {142, 5791, 5708}, {377, 16418, 1657}, {405, 474, 37301}, {405, 1004, 37292}, {405, 4197, 17528}, {405, 17528, 382}, {442, 1004, 17528}, {442, 11108, 381}, {442, 17590, 2478}, {443, 6675, 3}, {443, 6857, 37267}, {443, 17559, 6851}, {549, 6869, 3}, {631, 20420, 3}, {1698, 41867, 942}, {2478, 17590, 11108}, {3090, 37407, 8727}, {3826, 10198, 9709}, {6675, 8728, 443}, {6856, 17527, 5055}, {6910, 17573, 15693}, {7483, 16417, 15720}, {7483, 37462, 16417}, {8727, 37407, 3}, {11108, 16408, 16410}, {11108, 37271, 3}, {11108, 37292, 405}, {11111, 50240, 17800}, {11112, 17571, 15696}, {11113, 31259, 16860}, {14782, 14783, 37423}, {16056, 16290, 3}, {17561, 50396, 15681}, {17698, 37153, 19277}, {19526, 50713, 17579}, {19538, 50397, 15680}, {37267, 37436, 443}
X(50727) lies on these lines: {2, 3}, {10, 41870}, {551, 24392}, {553, 1698}, {1058, 3841}, {2346, 38092}, {3017, 4648}, {3475, 3679}, {3584, 26040}, {3681, 3921}, {3826, 8164}, {3828, 5850}, {5178, 38314}, {5550, 18527}, {10056, 41859}, {10175, 21151}, {11237, 19855}, {13407, 19875}, {18530, 46934}, {19883, 34701}, {26446, 38172}, {32635, 46932}
X(50727) = midpoint of X(2) and X(4208)
X(50727) = reflection of X(16845) in X(2)
X(50727) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 377, 17561}, {2, 442, 3545}, {2, 443, 3524}, {2, 452, 50714}, {2, 474, 15709}, {2, 3543, 50202}, {2, 3545, 17559}, {2, 3839, 11108}, {2, 4190, 15671}, {2, 10304, 6675}, {2, 17580, 5054}, {2, 33039, 33220}, {2, 33278, 16912}, {2, 44217, 376}, {2, 50687, 17554}, {377, 17561, 11001}, {381, 50395, 2}, {15699, 16863, 2}, {17525, 37435, 46333}, {17528, 50202, 3543}
See Kadir Altintas and César Lozada, euclid 5245.
X(50728) lies on these lines: {2, 3}, {1147, 34292}
See Angel Montesdeoca, euclid 5247 and HG120622.
X(50729) lies on these lines: {2,11166}, {51,17430}, {184,15534}, {353,47075}, {524,47074}, {597,10183}, {3906,11123}, {31961,31962}
X(50729) = midpoint of the orthocenters of these triangles: 4th Brocard and circumsymmedial
See Angel Montesdeoca, euclid 5247 and HG120622.
X(50730) lies on these lines: {2,47589}, {3,47591}, {4,47590}, {30,31748}, {381,13378}, {3091,47592}, {3543,5032}, {14269,46673}
X(50730) = reflection of X(2) in X(47589)
See Antreas Hatzipolakis and Ercole Suppa, euclid 5249.
X(50731) lies on these lines: {3,115}, {76,47389}
X(50731) = X(1581)-isoconjugate of X(35296)
X(50731) = X(i)-reciprocal conjugate of X(j) for these {i,j}: {1691,35296}, {5027,6132}
X(50731) = barycentric product X(804)*X(44768)
X(50731) = barycentric quotient X(i)/X(j) for these {i,j}: {1691,35296}, {5027,6132}
X(50731) = trilinear quotient X(1580)/X(35296)
X(50731) = intersection, other than A, B, C, of circumconics {A, B, C, X(2), X(44534)} and {A, B, C, X(3), X(419)}
See Antreas Hatzipolakis and Ercole Suppa, euclid 5249.
X(50732) lies on these lines: {3,114}, {1316,15391}, {14265,41760}
X(50732) = X(1581)-isoconjugate of X(37183)
X(50732) = barycentric product X(i)*X(j) for these (i,j): (804,44767), (3978,39644)
X(50732) = trilinear product X(1966)*X(39644)
X(50732) = trilinear quotient X(1580)/X(37183)
X(50732) = intersection, other than A, B, C, of circumconics {A, B, C, X(3), X(419)} and {A, B, C, X(4), X(6033)}
See Antreas Hatzipolakis and Ercole Suppa, euclid 5249.
X(50733) lies on these lines: {3,119}, {1459,3924}
X(50733) = intersection, other than A, B, C, of circumconics {A, B, C, X(3), X(953)} and {A, B, C, X(4), X(10742)}
See Antreas Hatzipolakis and Ercole Suppa, euclid 5249.
X(50734) lies on this line: {3,118}
X(50734) = intersection, other than A, B, C, of circumconics {A, B, C, X(3), X(1946)} and {A, B, C, X(4), X(10741)}
X(50735) lies on these lines: {2, 3}, {7, 193}, {63, 3691}, {966, 8822}, {4292, 4384}, {4304, 16831}, {4307, 23682}, {4313, 16826}, {4393, 11036}, {4454, 20432}, {5249, 26626}, {5273, 29576}, {9965, 20880}, {11520, 50129}, {12536, 17389}, {14552, 34284}, {17014, 33150}, {17257, 18655}, {19719, 19752}, {19791, 20009}, {20913, 37655}, {24588, 41785}, {24603, 31424}
X(50735) = reflection of X(37169) in X(37075)
X(50735) = anticomplement of X(37169)
X(50735) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 31295, 31015}, {4, 16054, 2}, {377, 379, 2}, {377, 4198, 50408}, {377, 48890, 50431}, {442, 24609, 2}, {443, 37086, 2}, {2476, 24580, 2}, {5177, 24604, 2}, {6175, 24608, 2}, {6933, 24581, 2}, {16412, 36662, 2}, {37075, 37169, 2}
X(50736) lies on these lines: {2, 3}, {8, 31164}, {10, 6172}, {388, 31140}, {390, 34649}, {519, 5290}, {535, 19843}, {938, 6173}, {1330, 43533}, {1770, 18231}, {2094, 6734}, {2550, 11236}, {2886, 34610}, {3241, 21620}, {3600, 31418}, {3679, 4295}, {3822, 5281}, {4305, 25055}, {4312, 5775}, {4333, 19876}, {4745, 4866}, {5175, 11036}, {5229, 34606}, {5261, 34619}, {5265, 25639}, {5703, 34701}, {5714, 20007}, {5716, 50103}, {5806, 38073}, {6147, 20008}, {6174, 10588}, {6744, 38024}, {7613, 37717}, {8165, 31160}, {9947, 38074}, {10248, 31435}, {11024, 19925}, {11037, 31146}, {11237, 34720}, {12520, 34648}, {13161, 48856}, {17706, 41865}, {25466, 34706}, {28609, 45039}, {30478, 34620}, {38202, 38757}
X(50736) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3146, 11111}, {2, 3522, 37298}, {2, 3832, 17556}, {2, 11111, 17558}, {2, 13587, 15721}, {2, 15683, 16370}, {2, 17528, 4208}, {2, 17577, 3091}, {2, 17579, 10304}, {2, 31295, 37299}, {2, 37161, 17528}, {2, 50687, 11113}, {4, 4208, 5129}, {4, 17528, 2}, {4, 37161, 4208}, {377, 3091, 17580}, {377, 17577, 2}, {442, 3146, 17558}, {442, 11111, 2}, {443, 17556, 2}, {2475, 5177, 20}, {2476, 37435, 3523}, {3090, 17564, 2}, {3545, 37430, 6847}, {3843, 50238, 17559}, {5071, 16417, 2}, {6856, 37298, 2}, {6856, 50239, 3522}, {6871, 6904, 5056}, {16857, 50727, 2}, {17532, 50397, 17530}, {25466, 34706, 47357}, {37108, 37428, 10304}, {41099, 50396, 2}
X(50737) lies on these lines: {2, 3}, {144, 3679}, {388, 34699}, {2550, 34739}, {3419, 20059}, {3600, 11235}, {4293, 31159}, {5229, 34612}, {5261, 34607}, {5281, 34626}, {5556, 6737}, {5905, 31145}, {9579, 28610}, {20007, 28609}, {31473, 43508}, {34625, 34637}, {34648, 36991}
X(50737) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36004, 15717}, {2, 50689, 37375}, {4, 50240, 17580}, {20, 17532, 2}, {2475, 3146, 37161}, {3146, 37161, 11106}, {3839, 11112, 2}, {6871, 36004, 2}, {6904, 37375, 2}, {15692, 17530, 2}, {33031, 33272, 2}
X(50738) lies on these lines: {2, 3}, {8, 34639}, {144, 4304}, {390, 34610}, {527, 4313}, {3241, 4314}, {3600, 34620}, {4294, 5288}, {4298, 38314}, {5281, 11236}, {6172, 20007}, {6174, 8165}, {10385, 34749}, {30282, 46873}, {30478, 34706}, {34625, 34649}
X(50738) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11111, 11106}, {2, 17578, 17577}, {2, 37299, 3522}, {2, 50725, 17528}, {20, 11111, 2}, {21, 5059, 37161}, {3091, 37298, 2}, {3523, 17556, 2}, {3529, 17558, 50725}, {3543, 16370, 2}, {6172, 34701, 20007}, {6872, 37299, 2}, {10304, 11113, 2}, {15680, 17576, 3146}, {15721, 17533, 2}, {17528, 17558, 2}, {17538, 50241, 17580}, {33032, 35287, 2}, {34620, 47357, 3600}
X(50739) lies on these lines: {2, 3}, {10, 34701}, {55, 34720}, {144, 5719}, {527, 3487}, {528, 19843}, {535, 10198}, {551, 3333}, {553, 3361}, {958, 34619}, {966, 4262}, {993, 1056}, {1058, 5248}, {1125, 5698}, {1621, 11240}, {2094, 3616}, {3085, 34606}, {3486, 3679}, {3488, 5745}, {3646, 9841}, {3653, 5887}, {3869, 5045}, {4251, 37654}, {4252, 17392}, {4256, 37650}, {4257, 4648}, {4258, 17330}, {4294, 24953}, {4313, 5791}, {4428, 34625}, {4512, 5603}, {4653, 37642}, {4677, 31436}, {4995, 22760}, {4999, 47743}, {5010, 26040}, {5044, 10394}, {5057, 5550}, {5217, 19855}, {5218, 5251}, {5250, 10595}, {5259, 7288}, {5265, 8543}, {5266, 48856}, {5273, 24929}, {5275, 46453}, {5281, 9708}, {5292, 48841}, {5703, 6172}, {6690, 8164}, {10165, 21151}, {10167, 33574}, {10199, 26105}, {10385, 34719}, {10572, 19875}, {10588, 31160}, {11024, 31663}, {12436, 38093}, {12437, 31446}, {13411, 31142}, {15254, 34919}, {16020, 37599}, {16992, 32817}, {18231, 37730}, {19883, 28617}, {25466, 34620}, {26543, 39874}, {28534, 28628}, {31418, 34706}, {31419, 34707}, {31473, 43510}, {37552, 50291}, {37573, 50282}
X(50739) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20, 17528}, {2, 21, 11111}, {2, 452, 17556}, {2, 3523, 17564}, {2, 6872, 17577}, {2, 11111, 4}, {2, 11113, 3545}, {2, 15692, 16417}, {2, 15697, 50396}, {2, 16370, 376}, {2, 17525, 15682}, {2, 17556, 3090}, {2, 17577, 6856}, {2, 33032, 32984}, {2, 37298, 631}, {2, 37299, 377}, {3, 16845, 17582}, {3, 17558, 16845}, {3, 17560, 17562}, {3, 50205, 17580}, {21, 6857, 4}, {140, 16866, 5129}, {405, 631, 17559}, {405, 37298, 2}, {442, 17576, 3529}, {443, 4189, 3528}, {452, 7483, 3090}, {549, 16857, 2}, {3560, 6988, 4}, {5084, 6910, 3525}, {5248, 30478, 1058}, {5248, 45700, 47357}, {6675, 17528, 2}, {6675, 17571, 20}, {6855, 6868, 4}, {6856, 6872, 4}, {6857, 11111, 2}, {6904, 19535, 21735}, {6910, 16865, 5084}, {6954, 7489, 6939}, {7483, 17556, 2}, {7483, 19526, 452}, {11108, 17564, 2}, {15670, 16370, 2}, {15671, 17579, 2}, {15674, 37299, 2}, {15717, 17554, 16408}, {16417, 50202, 2}, {16912, 32964, 33043}, {16914, 33055, 32968}, {30478, 47357, 45700}, {45700, 47357, 1058}
X(50740) lies on these lines: {2, 3}, {10, 1159}, {46, 19876}, {65, 19875}, {519, 28628}, {527, 5791}, {528, 10198}, {551, 5794}, {999, 31245}, {1698, 31142}, {2886, 6767}, {3295, 31140}, {3454, 17251}, {3624, 37606}, {3634, 5880}, {3679, 41696}, {3822, 9708}, {3824, 5705}, {3828, 12609}, {3841, 9709}, {3925, 31479}, {3927, 31164}, {3940, 31266}, {4259, 21358}, {4428, 34649}, {5248, 34706}, {5292, 17392}, {5550, 10609}, {5714, 6172}, {5745, 18541}, {5784, 38093}, {7373, 25466}, {8148, 24987}, {8583, 35459}, {9654, 19854}, {9655, 24953}, {9940, 38065}, {10056, 34720}, {10172, 38108}, {10592, 19855}, {11231, 38052}, {14110, 38021}, {15934, 25525}, {17346, 25446}, {17647, 19883}, {25542, 34879}, {26543, 44456}, {30147, 34700}, {31418, 47357}, {31419, 34619}, {31473, 45385}, {34339, 38083}, {34595, 37600}, {37541, 41859}, {38024, 50192}
X(50740) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 377, 37298}, {2, 381, 16857}, {2, 442, 17528}, {2, 443, 17564}, {2, 2476, 17556}, {2, 5177, 11111}, {2, 6175, 16370}, {2, 11111, 6675}, {2, 16417, 15694}, {2, 17528, 3}, {2, 17532, 16418}, {2, 17556, 11108}, {2, 17564, 3526}, {2, 17577, 405}, {2, 17678, 19279}, {2, 37375, 17542}, {2, 44217, 16417}, {2, 50396, 15693}, {5, 50394, 17559}, {5, 50726, 16853}, {381, 5054, 28459}, {1656, 8728, 16863}, {2475, 17571, 17800}, {2476, 11108, 3851}, {3545, 6889, 37428}, {3824, 5705, 5708}, {4193, 50207, 16855}, {5177, 6675, 382}, {6856, 8728, 1656}, {11108, 37240, 3}, {15765, 18585, 6987}, {16418, 17532, 3830}, {17528, 37224, 3830}, {17577, 31254, 2}, {25466, 31493, 7373}, {37224, 37240, 37284}
X(50741) lies on these lines: {2, 3}, {9, 3828}, {10, 5714}, {72, 5828}, {226, 3679}, {274, 32823}, {388, 5288}, {497, 31159}, {519, 3487}, {527, 5833}, {529, 19843}, {551, 3488}, {938, 3824}, {943, 4421}, {950, 25055}, {1056, 2886}, {1058, 11235}, {1698, 3474}, {2550, 3822}, {2551, 3841}, {3085, 34612}, {3241, 3419}, {3296, 10916}, {3421, 33108}, {3600, 31493}, {3616, 18527}, {3622, 18530}, {3646, 12571}, {3654, 5758}, {3820, 40333}, {3838, 34647}, {3913, 31420}, {3925, 10590}, {4293, 31157}, {4669, 11523}, {5082, 11239}, {5175, 38314}, {5229, 19854}, {5261, 31419}, {5292, 48868}, {5436, 19883}, {5587, 5658}, {5715, 28194}, {5746, 17330}, {5811, 9956}, {5817, 10175}, {6690, 34626}, {6701, 49168}, {7680, 35514}, {7951, 26040}, {8232, 38092}, {9612, 19875}, {9780, 20292}, {10197, 34607}, {10202, 10861}, {10477, 21356}, {10895, 19855}, {11237, 34689}, {18446, 34627}, {18528, 19860}, {21168, 26446}, {25639, 47743}, {31140, 34699}, {34610, 34637}, {41014, 43533}
X(50741) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3543, 16418}, {2, 5177, 17532}, {2, 6871, 37375}, {2, 11112, 3524}, {2, 11114, 17561}, {2, 15640, 15673}, {2, 16371, 15702}, {2, 17530, 5071}, {2, 17532, 4}, {2, 33031, 14033}, {2, 36004, 6910}, {2, 37375, 5084}, {2, 50397, 19708}, {4, 3525, 6936}, {4, 5067, 6920}, {5, 4208, 17582}, {377, 6856, 631}, {442, 5177, 4}, {442, 17532, 2}, {443, 2476, 3090}, {546, 50726, 5129}, {1656, 50238, 17580}, {2475, 6857, 3529}, {2550, 3822, 8164}, {3090, 6951, 6935}, {3091, 8728, 17559}, {4197, 6871, 5084}, {4197, 37375, 2}, {5084, 6871, 3855}, {6843, 6907, 4}, {6867, 37438, 6865}, {6874, 6897, 6956}, {6881, 6939, 3090}, {6881, 6982, 6939}, {6937, 6984, 4}, {7483, 37435, 3528}, {16417, 17528, 50396}, {17530, 44217, 2}, {17565, 33052, 32978}, {25466, 31418, 1058}
X(50742) lies on these lines: {1, 28610}, {2, 3}, {7, 551}, {55, 34689}, {63, 3241}, {144, 24929}, {390, 993}, {392, 11220}, {497, 31157}, {519, 4313}, {958, 34607}, {1056, 34740}, {2550, 34626}, {3600, 5248}, {3617, 11015}, {3672, 37817}, {3679, 4304}, {3868, 31792}, {3928, 15933}, {3945, 4653}, {4252, 48846}, {4292, 25055}, {4428, 34610}, {4512, 5731}, {4640, 34744}, {4677, 12536}, {4745, 31446}, {5044, 9859}, {5218, 31141}, {5258, 12632}, {5261, 10197}, {5265, 5267}, {5281, 45701}, {5325, 34701}, {5698, 34647}, {5703, 28609}, {6172, 7675}, {6690, 34739}, {10385, 34699}, {10391, 31165}, {10461, 48858}, {10572, 18231}, {11020, 24473}, {11024, 12512}, {11036, 38314}, {11194, 47357}, {11235, 30478}, {14986, 34742}, {18228, 30282}, {19723, 19752}, {20007, 31445}
X(50742) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3146, 17532}, {2, 11114, 3839}, {2, 15678, 15640}, {2, 17549, 15692}, {2, 36004, 6904}, {2, 37375, 5056}, {3, 11106, 5129}, {3, 50243, 17559}, {20, 21, 17558}, {20, 10303, 37163}, {20, 17558, 4208}, {21, 17576, 20}, {21, 20835, 37106}, {376, 16418, 2}, {405, 3522, 17580}, {452, 4189, 3523}, {548, 16866, 17582}, {3524, 37429, 37108}, {3529, 6675, 37161}, {5084, 19535, 15717}, {5177, 15680, 49135}, {6856, 50242, 17578}, {6857, 17532, 2}, {6904, 16865, 17554}, {6910, 37375, 2}, {11001, 15673, 2}, {11111, 16370, 2}, {11112, 17561, 2}, {16370, 17525, 11111}, {16865, 36004, 2}, {17549, 31156, 2}
X(50743) lies on these lines: {1, 2}, {523, 2525}, {3703, 49484}, {3717, 32844}, {3914, 49453}, {3977, 17766}, {4133, 21283}, {4865, 32935}, {4899, 32843}, {5288, 7465}, {5853, 32848}, {8229, 28234}, {17718, 49690}, {21282, 28526}, {25760, 49527}, {31034, 49536}, {33070, 49529}, {33114, 49684}, {37449, 48696}
X(50743) = reflection of X(3011) in X(3006)
X(50743) = crossdifference of every pair of points on line {649, 30435}
X(50743) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {26015, 32847, 49990}, {32842, 49772, 49986}
X(50744) lies on these lines: {1, 2}, {55, 4001}, {100, 4684}, {329, 4779}, {516, 17491}, {518, 3712}, {523, 4468}, {902, 34379}, {2177, 49511}, {2280, 3707}, {2325, 3930}, {3243, 17740}, {3295, 4101}, {3689, 4966}, {3696, 37703}, {3722, 4938}, {3750, 24697}, {3751, 35263}, {3755, 33122}, {3886, 4054}, {3936, 5853}, {3996, 5249}, {4023, 42819}, {4035, 5014}, {4414, 49505}, {4427, 5850}, {4780, 33143}, {4899, 32849}, {5718, 49467}, {5739, 10389}, {17602, 49475}, {17718, 49460}, {17724, 28581}, {17725, 49678}, {28580, 32856}, {31280, 33136}, {33156, 49529}, {33161, 49536}
X(50744) = crossdifference of every pair of points on line {649, 5021}
X(50744) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3912, 3935, 49991}
X(50745) lies on these lines: {1, 2}, {226, 37610}, {484, 24231}, {495, 3744}, {515, 24222}, {517, 17724}, {523, 21185}, {908, 40091}, {988, 31452}, {1279, 17757}, {1478, 3749}, {1626, 8069}, {1738, 48696}, {1785, 5146}, {3746, 13161}, {3748, 37715}, {3871, 23537}, {3911, 4694}, {3914, 25439}, {3915, 21077}, {3921, 17337}, {3953, 6684}, {4186, 45061}, {4723, 24542}, {4995, 37599}, {5049, 37634}, {5119, 33144}, {5255, 13407}, {5264, 21620}, {5266, 15888}, {5434, 37589}, {5886, 17783}, {6767, 17720}, {7743, 37691}, {8715, 23536}, {11374, 37542}, {12047, 37588}, {17597, 26446}, {17715, 37716}, {17719, 30384}, {17721, 31479}, {23675, 25440}
X(50745) = crossdifference of every pair of points on line {649, 36743}
X(50745) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3584, 24239}, {10, 1125, 25967}
X(50746) lies on these lines: {37, 519}, {321, 17775}, {523, 661}, {536, 22047}, {3834, 24062}, {4115, 4908}, {4370, 21839}, {4681, 24090}, {4686, 24050}, {16672, 17162}, {16777, 39766}, {17374, 22003}, {22021, 40085}, {22034, 24066}
X(50747) lies on these lines: {12, 1089}, {37, 3011}, {72, 519}, {190, 2651}, {321, 2886}, {523, 661}, {958, 39766}, {1155, 22003}, {1621, 3995}, {1834, 2292}, {3035, 42701}, {3925, 42708}, {3932, 27692}, {4358, 25652}, {4387, 12635}, {5220, 17162}, {5791, 50068}, {7235, 21676}
X(50748) lies on these lines: {1, 2}, {55, 4655}, {100, 49676}, {523, 3716}, {527, 4760}, {528, 4892}, {537, 3712}, {740, 17724}, {902, 17770}, {2177, 3821}, {2784, 39572}, {2796, 32856}, {3475, 3980}, {3685, 21093}, {3689, 3836}, {3722, 3936}, {3748, 3846}, {3749, 32946}, {3750, 4425}, {3996, 33130}, {4011, 25568}, {4417, 17715}, {4428, 4703}, {4434, 4966}, {4438, 41711}, {4743, 50103}, {5718, 49473}, {5853, 21241}, {6541, 32927}, {11813, 14513}, {17602, 49471}, {17718, 25385}, {17725, 49470}, {17782, 32950}, {21242, 49467}, {21805, 24542}, {24169, 33124}, {24295, 46897}, {24325, 37703}, {32843, 49705}, {32844, 49696}, {32851, 49675}, {33115, 49697}, {48641, 49485}
X(50748) = midpoint of X(i) and X(j) for these {i,j}: {3722, 3936}, {4062, 20045}
X(50748) = crossdifference of every pair of points on line {649, 33863}
X(50748) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {42, 29656, 29654}, {2177, 33122, 3821}, {3750, 33126, 4425}, {3771, 3870, 29673}, {3935, 29632, 10}, {3957, 29846, 29655}, {3961, 29839, 29653}, {6745, 49768, 4871}, {17018, 29848, 29645}, {17718, 32941, 25385}
X(50749) lies on these lines: {1, 2}, {484, 33148}, {495, 49480}, {523, 21179}, {595, 33096}, {758, 17724}, {1279, 3814}, {1283, 37919}, {1459, 50337}, {3744, 3822}, {3746, 36250}, {3772, 25439}, {3892, 37646}, {3919, 26728}, {3992, 24542}, {4868, 17061}, {4906, 11231}, {5255, 11263}, {6684, 24167}, {11813, 17719}, {16483, 17783}, {24160, 37588}, {33127, 37610}, {33129, 48696}
X(50749) = crossdifference of every pair of points on line {649, 5124}
X(50749) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {17719, 40091, 11813}
X(50750) lies on these lines: {1, 2}, {35, 33067}, {523, 50507}, {3454, 37080}, {3694, 39798}, {4065, 34937}, {4256, 33124}, {4653, 33126}, {4703, 5248}, {5010, 33069}, {17718, 48863}, {26725, 32945}, {32943, 37701}, {47373, 49511}
X(50751) lies on these lines: {75, 519}, {313, 45095}, {321, 17775}, {325, 523}, {527, 20956}, {536, 20912}, {1227, 30806}, {1269, 1441}, {2325, 21591}, {3943, 21417}, {4358, 4957}, {21428, 30588}, {21601, 30608}, {24209, 30939}
X(50751) = X(32)-isoconjugate of X(43757)
X(50751) = X(6376)-Dao conjugate of X(43757)
X(50751) = barycentric product X(1978)*X(14315)
X(50751) = barycentric quotient X(i)/X(j) for these {i,j}: {75, 43757}, {4358, 36818}, {14315, 649}
X(50751) = {X(3262),X(35550)}-harmonic conjugate of X(3264)
X(50752) lies on these lines: {1, 2}, {63, 4138}, {120, 50366}, {226, 4438}, {345, 17064}, {516, 8229}, {523, 4885}, {527, 4892}, {536, 17070}, {620, 44908}, {908, 33115}, {1368, 34851}, {1738, 32851}, {2886, 49484}, {2887, 5745}, {3035, 3823}, {3120, 3977}, {3263, 24209}, {3416, 31187}, {3712, 28580}, {3717, 17719}, {3751, 30828}, {3772, 49453}, {3817, 4011}, {3819, 25137}, {3836, 3911}, {3838, 44416}, {3914, 33113}, {3936, 34379}, {4009, 37691}, {4035, 32853}, {4054, 33161}, {4078, 17720}, {4422, 5087}, {4703, 5325}, {5249, 33119}, {5267, 7465}, {5294, 33105}, {5750, 37661}, {5847, 35466}, {5943, 25135}, {6796, 16434}, {12572, 37330}, {15082, 25108}, {17353, 17717}, {17355, 25385}, {17718, 49529}, {17723, 38049}, {17725, 49527}, {17783, 30615}, {17785, 33124}, {20544, 37370}, {24210, 33116}, {25639, 37315}, {28236, 39572}, {30811, 49511}, {30834, 33114}, {31204, 33075}, {31229, 33070}, {31245, 32777}, {31266, 33163}, {31280, 32856}, {33073, 41806}, {33104, 35263}, {33121, 41878}, {39559, 49598}
X(50752) = midpoint of X(i) and X(j) for these {i,j}: {3006, 3011}, {3120, 3977}
X(50752) = complement of X(3011)
X(50752) = orthoptic-circle-of-Steiner-inellipse-inverse of X(6790)
X(50752) = X(i)-complementary conjugate of X(j) for these (i,j): {9085, 226}, {29241, 513}, {35365, 11}
X(50752) = crossdifference of every pair of points on line {649, 3053}
X(50752) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3006, 3011}, {2, 29639, 1125}, {2, 29826, 19862}, {2, 29857, 10}, {2, 30741, 1}, {2, 30751, 3741}, {2, 30752, 3840}, {2, 30762, 8}, {2, 30763, 3912}, {2, 30768, 3634}, {26015, 29632, 49768}, {29657, 29856, 17023}, {29862, 33140, 3912}
X(50753) lies on these lines: {1, 2}, {55, 4035}, {226, 5695}, {516, 3936}, {523, 3239}, {527, 3712}, {2321, 17718}, {3755, 30811}, {3886, 30828}, {3911, 4966}, {3977, 5850}, {4021, 32775}, {4023, 6666}, {4082, 25568}, {4101, 18249}, {4353, 33122}, {4417, 40998}, {4684, 32851}, {4706, 17067}, {4887, 32845}, {4892, 28580}, {4933, 17132}, {5218, 17296}, {5542, 17740}, {17355, 33156}, {17776, 21060}, {31034, 35263}, {33849, 45765}
X(50753) = midpoint of X(3011) and X(4062)
X(50753) = crossdifference of every pair of points on line {649, 4252}
X(50753) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3771, 4028, 40940}, {30741, 49451, 4847}
X(50754) lies on these lines: {1, 2}, {197, 23391}, {516, 4442}, {523, 2527}, {527, 4831}, {896, 17132}, {1150, 4353}, {3686, 17602}, {3712, 17133}, {3962, 40962}, {4021, 32917}, {4535, 6679}, {4892, 5847}, {4989, 30818}, {5850, 16704}, {17070, 28538}
X(50754) = crossdifference of every pair of points on line {649, 4255}
X(50754) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {239, 37764, 5212}, {5212, 37764, 6745}
X(50755) lies on these lines: {1, 2}, {6, 25385}, {11, 4974}, {81, 23812}, {116, 31655}, {149, 49705}, {226, 19369}, {230, 4771}, {238, 643}, {320, 17731}, {333, 4425}, {523, 2487}, {524, 4892}, {740, 3712}, {896, 2796}, {897, 18201}, {1086, 35087}, {1150, 3821}, {1386, 21242}, {1757, 21093}, {2325, 4037}, {2651, 5057}, {2784, 8229}, {2886, 3791}, {3120, 16704}, {3218, 20369}, {3291, 16611}, {3706, 6679}, {3759, 17717}, {3769, 32865}, {3772, 32853}, {3911, 7235}, {3923, 24597}, {3936, 4938}, {3944, 37652}, {3977, 28522}, {3980, 37642}, {4119, 4727}, {4527, 50104}, {4641, 48643}, {4647, 8258}, {4683, 4921}, {4689, 4743}, {4716, 32851}, {4831, 28558}, {4969, 10026}, {4970, 5745}, {4987, 50252}, {5235, 25354}, {5361, 32776}, {5372, 33125}, {5718, 49489}, {5847, 21241}, {6541, 33115}, {6703, 27798}, {6758, 17495}, {7683, 35099}, {8542, 34830}, {11814, 37680}, {14829, 24169}, {17064, 32946}, {17351, 48641}, {17602, 49457}, {17718, 49497}, {17725, 49450}, {17728, 24371}, {17766, 33136}, {17889, 37683}, {30832, 42334}, {31187, 49486}, {31229, 33156}, {31730, 46623}, {32864, 33133}, {32919, 33129}, {32927, 49697}, {33097, 41629}, {33160, 41806}, {36263, 50102}
X(50755) = midpoint of X(i) and X(j) for these {i,j}: {896, 4442}, {3120, 16704}, {4062, 17162}
X(50755) = reflection of X(4892) in X(17070)
X(50755) = complement of X(4062)
X(50755) = X(i)-complementary conjugate of X(j) for these (i,j): {28, 5181}, {58, 16597}, {81, 126}, {111, 1211}, {286, 34517}, {513, 5099}, {667, 23992}, {671, 21245}, {691, 513}, {892, 21260}, {895, 21530}, {897, 3454}, {923, 1213}, {1333, 2482}, {5380, 31946}, {7316, 442}, {8753, 50036}, {14908, 18591}, {32729, 650}, {32740, 16589}, {36060, 440}, {36085, 3835}, {36142, 514}, {43926, 11}
X(50755) = X(892)-Ceva conjugate of X(514)
X(50755) = crossdifference of every pair of points on line {649, 18755}
X(50755) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 17162, 4062}, {8, 25459, 1698}, {10, 17763, 49994}, {333, 33135, 4425}, {1150, 33128, 3821}, {1757, 37759, 21093}, {1999, 33138, 29653}, {3187, 24892, 29671}, {3741, 40940, 29654}, {3772, 32853, 33064}, {4362, 33137, 29673}, {4938, 31280, 3936}, {6745, 50022, 49988}, {14829, 33132, 24169}, {17763, 33139, 10}, {18201, 37756, 24200}, {24883, 27368, 10}, {29833, 30970, 1125}, {32914, 33142, 29655}, {32919, 33129, 49676}
X(50756) lies on these lines: {1, 2}, {31, 4365}, {38, 49463}, {44, 3994}, {69, 33143}, {100, 4716}, {319, 32775}, {321, 2308}, {333, 3989}, {523, 649}, {524, 32856}, {536, 896}, {545, 4831}, {660, 43758}, {726, 16704}, {740, 902}, {750, 4361}, {752, 4442}, {1150, 32921}, {2177, 49486}, {2895, 33152}, {3120, 5847}, {3416, 33128}, {3706, 17469}, {3712, 4971}, {3722, 28581}, {3745, 21020}, {3759, 32931}, {3769, 32860}, {3772, 32852}, {3875, 4414}, {3891, 32853}, {3923, 21747}, {3936, 17772}, {3969, 6679}, {3971, 19742}, {4133, 35263}, {4358, 4974}, {4360, 32917}, {4427, 28522}, {4650, 50106}, {4655, 50102}, {4663, 31161}, {4671, 16468}, {4697, 4980}, {4725, 4938}, {4852, 46904}, {4933, 28329}, {5294, 6535}, {5372, 17591}, {5846, 33136}, {7262, 42044}, {14829, 32924}, {16477, 41242}, {17061, 33081}, {17126, 49474}, {17155, 37683}, {17160, 32845}, {17299, 33156}, {17362, 17602}, {17363, 33065}, {17449, 32919}, {19785, 33080}, {19796, 33067}, {20475, 21522}, {21282, 28512}, {24165, 37639}, {24597, 33161}, {28508, 44006}, {30699, 33098}, {31025, 33682}, {32843, 37759}, {32846, 33129}, {32848, 35466}, {32861, 33133}, {32863, 33147}, {32864, 32926}, {32925, 37652}, {32940, 41629}, {33075, 33135}, {33078, 33132}, {33082, 33155}, {33085, 33150}, {36263, 49453}, {41011, 48642}, {46897, 49489}, {46909, 49472}
X(50756) = midpoint of X(17162) and X(20045)
X(50756) = reflection of X(i) in X(j) for these {i,j}: {4062, 3011}, {32848, 35466}
X(50756) = X(513)-isoconjugate of X(29341)
X(50756) = X(39026)-Dao conjugate of X(29341)
X(50756) = crossdifference of every pair of points on line {386, 649}
X(50756) = X(i)-lineconjugate of X(j) for these (i,j): {1, 386}, {523, 649}
X(50756) = barycentric product X(190)*X(29340)
X(50756) = barycentric quotient X(i)/X(j) for these {i,j}: {101, 29341}, {29340, 514}
X(50756) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {239, 17763, 899}, {321, 3791, 2308}, {333, 32928, 3989}, {1150, 32921, 46901}, {1999, 32914, 3720}, {3187, 4362, 42}, {3187, 26227, 49488}, {3741, 17150, 29819}, {3935, 50016, 49983}, {4362, 49488, 26227}, {6745, 50019, 49986}, {11679, 17017, 31241}, {15523, 40940, 29867}, {26227, 49488, 42}, {32919, 32922, 17449}
X(50757) lies on these lines: {1, 2}, {11, 30447}, {21, 36250}, {30, 17070}, {36, 759}, {58, 11263}, {79, 16948}, {81, 26725}, {230, 16611}, {238, 5127}, {515, 45926}, {523, 8043}, {540, 4892}, {754, 25383}, {758, 35466}, {993, 3772}, {1086, 4973}, {1104, 25639}, {1203, 46441}, {1324, 20470}, {1834, 35016}, {2392, 18191}, {2886, 49480}, {3028, 35063}, {3246, 7743}, {3743, 6675}, {3817, 45924}, {3833, 37634}, {3841, 37539}, {3911, 24168}, {4037, 24956}, {4256, 33132}, {4257, 17889}, {4653, 33135}, {4854, 15670}, {4868, 6690}, {4974, 44396}, {4975, 24542}, {4999, 16579}, {5010, 33131}, {5247, 24160}, {5248, 16430}, {5251, 33133}, {5267, 17512}, {5298, 39751}, {5745, 33996}, {5883, 37646}, {5886, 45923}, {6149, 33593}, {6629, 24187}, {6681, 16610}, {6693, 49598}, {6701, 49745}, {7267, 25468}, {8143, 10021}, {11116, 24178}, {13605, 37791}, {16429, 24789}, {17064, 37817}, {17127, 18393}, {17647, 41501}, {17737, 21090}, {19623, 49676}, {21173, 23789}, {21630, 40091}, {21949, 37589}, {25385, 48866}, {32911, 37701}, {35193, 41012}, {37662, 38062}, {37756, 41134}
X(50757) = X(i)-complementary conjugate of X(j) for these (i,j): {58, 31845}, {759, 3454}, {849, 214}, {1408, 6739}, {1411, 34829}, {2206, 35069}, {24624, 21245}, {32671, 514}, {34079, 1211}, {36069, 513}, {37140, 3835}
X(50757) = crosspoint of X(86) and X(21907)
X(50757) = crosssum of X(42) and X(17796)
X(50757) = crossdifference of every pair of points on line {649, 1030}
X(50757) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3624, 24936}, {1, 24880, 10}, {1, 24902, 21674}, {58, 24161, 11263}, {21674, 24902, 3634}, {25645, 27368, 21081}, {30115, 33138, 10}
X(50758) lies on these lines: {1, 2}, {516, 16704}, {523, 4025}, {527, 4442}, {740, 3977}, {896, 28580}, {1150, 3755}, {1738, 32919}, {2321, 33114}, {3120, 34379}, {3706, 5294}, {3751, 4054}, {3879, 33108}, {3886, 24597}, {3896, 5745}, {3914, 4001}, {3946, 46909}, {3999, 4395}, {4133, 33161}, {4414, 4780}, {4416, 33134}, {4431, 33170}, {4684, 33129}, {4831, 28534}, {5196, 6629}, {5847, 33136}, {17718, 49680}, {17725, 49689}, {19742, 40998}, {21242, 49489}, {24210, 32864}, {25385, 49685}, {28581, 35466}, {33128, 49511}, {33143, 49505}
X(50758) = midpoint of X(3006) and X(17162)
X(50758) = crossdifference of every pair of points on line {649, 2271}
X(50758) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {239, 26015, 49987}, {3886, 24597, 35263}, {3914, 32853, 4001}, {17156, 33137, 306}, {17763, 49772, 49991}
X(50759) lies on these lines: {1, 2}, {36, 1738}, {212, 12053}, {238, 30384}, {517, 35466}, {523, 905}, {529, 17070}, {946, 1724}, {956, 3772}, {993, 3914}, {999, 24789}, {1104, 24390}, {1108, 39798}, {1468, 12609}, {1478, 17064}, {1733, 23580}, {1739, 3911}, {2217, 23604}, {2933, 7742}, {2975, 23537}, {3434, 37817}, {3753, 37646}, {3873, 26728}, {3915, 49600}, {3931, 24953}, {3987, 6684}, {4383, 5886}, {4424, 5745}, {4641, 39542}, {4646, 7483}, {4742, 24542}, {4875, 5305}, {5179, 17737}, {5247, 12047}, {5251, 24210}, {5258, 13161}, {5429, 33109}, {5563, 24178}, {5725, 31245}, {5791, 37614}, {6675, 37548}, {8053, 40292}, {8666, 23536}, {9708, 17720}, {11112, 21949}, {11230, 37663}, {11551, 32913}, {13407, 24161}, {15325, 16610}, {16474, 26725}, {16485, 24392}, {16968, 21073}, {21241, 38456}, {31157, 37599}, {31419, 37539}, {33132, 37617}, {34612, 37589}, {34937, 40967}
X(50759) = midpoint of X(3006) and X(39766)
X(50759) = crossdifference of every pair of points on line {649, 36744}
X(50759) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3008, 44675, 49997}, {15955, 24880, 24987}, {24892, 49487, 10}
X(50760) lies on these lines: {1, 4762}, {2, 48295}, {519, 693}, {523, 45341}, {551, 31150}, {650, 25055}, {891, 48234}, {1734, 45328}, {3241, 29066}, {3244, 47721}, {3679, 14077}, {4151, 44550}, {4160, 31147}, {4411, 50086}, {4777, 14421}, {4885, 19875}, {5692, 9443}, {8760, 31162}, {9015, 47356}, {9397, 31159}, {17494, 38314}, {19883, 31209}, {26824, 48285}, {28147, 45686}, {29350, 31148}, {30583, 48202}, {31161, 48423}, {45667, 45671}, {48120, 48296}, {48291, 48335}
X(50760) = midpoint of X(i) and X(j) for these {i,j}: {2, 48304}, {3241, 47869}
X(50760) = reflection of X(i) in X(j) for these {i,j}: {2, 48295}, {3679, 45320}, {30583, 48202}, {31150, 551}, {45671, 45667}, {50086, 4411}
X(50761) lies on these lines: {1, 17494}, {10, 4885}, {145, 47724}, {514, 4775}, {519, 693}, {523, 48296}, {551, 650}, {891, 48248}, {1125, 31209}, {3241, 26824}, {3244, 29066}, {3635, 47729}, {3679, 26985}, {3900, 23789}, {4151, 4449}, {4160, 48049}, {4301, 8760}, {4342, 11934}, {4411, 4709}, {4669, 45320}, {4717, 21438}, {4762, 48285}, {4777, 49479}, {4828, 49459}, {4844, 48399}, {4932, 29350}, {8714, 21222}, {9001, 49505}, {9015, 49684}, {10197, 28834}, {14421, 50341}, {19883, 31287}, {25055, 27115}, {26777, 38314}, {34587, 47874}
X(50761) = midpoint of X(i) and X(j) for these {i,j}: {1, 48304}, {145, 47724}, {21343, 48291}
X(50761) = reflection of X(i) in X(j) for these {i,j}: {10, 48295}, {4669, 45320}, {4709, 4411}, {47729, 3635}, {48284, 1}
X(50762) lies on these lines: {2, 824}, {321, 45320}, {536, 693}, {3666, 31150}, {17147, 47869}, {23876, 48571}
X(50762) = midpoint of X(17147) and X(47869)
X(50762) = reflection of X(i) in X(j) for these {i,j}: {321, 45320}, {31150, 3666}
X(50763) lies on these lines: {2, 4777}, {37, 31150}, {75, 45320}, {192, 47869}, {536, 693}, {4411, 4740}, {4664, 4762}, {4687, 44567}, {14077, 50075}, {31178, 48295}, {47721, 49462}
X(50763) = midpoint of X(192) and X(47869)
X(50763) = reflection of X(i) in X(j) for these {i,j}: {75, 45320}, {4740, 4411}, {31150, 37}, {31178, 48295}
X(50764) lies on these lines: {1, 45320}, {2, 29066}, {8, 47869}, {10, 31150}, {514, 31131}, {519, 693}, {551, 47729}, {650, 19875}, {663, 45324}, {667, 45332}, {1698, 44567}, {3241, 48295}, {3251, 48202}, {3679, 4762}, {3828, 48284}, {4040, 45664}, {4049, 48223}, {4411, 31178}, {4677, 14077}, {4728, 4844}, {4761, 4785}, {4774, 48167}, {4775, 45342}, {4777, 50086}, {4885, 25055}, {9015, 47359}, {14349, 31149}, {17072, 45671}, {26985, 38314}, {28294, 47788}, {31145, 48304}, {38098, 47664}, {44550, 50337}, {44553, 47687}, {44566, 50347}, {45323, 48288}, {45328, 48321}, {45340, 48289}, {45660, 46385}, {47683, 48190}, {48234, 48324}
X(50764) = midpoint of X(i) and X(j) for these {i,j}: {8, 47869}, {3679, 47724}, {4774, 48167}, {31145, 48304}, {31150, 47721}, {44553, 47687}
X(50764) = reflection of X(i) in X(j) for these {i,j}: {1, 45320}, {663, 45324}, {667, 45332}, {3241, 48295}, {3251, 48202}, {4040, 45664}, {4775, 45342}, {14349, 31149}, {31150, 10}, {31178, 4411}, {44550, 50337}, {45671, 17072}, {46385, 45660}, {47683, 48190}, {47729, 551}, {48223, 4049}, {48284, 3828}, {48288, 45323}, {48289, 45340}, {48321, 45328}, {48324, 48234}, {48335, 48167}, {50347, 44566}
X(50765) lies on these lines: {6, 29066}, {518, 693}, {650, 38047}, {1386, 47729}, {1577, 9029}, {2533, 9010}, {3242, 48295}, {3416, 9001}, {3751, 9015}, {4663, 47721}, {4761, 9002}, {4762, 47359}, {4777, 49531}, {9040, 50352}, {14077, 49688}, {38315, 48285}, {45320, 47358}
X(50765) = midpoint of X(3751) and X(47724)
X(50765) = reflection of X(i) in X(j) for these {i,j}: {3242, 48295}, {47358, 45320}, {47729, 1386}
X(50766) lies on these lines: {2, 9015}, {6, 45320}, {69, 47869}, {141, 31150}, {524, 693}, {599, 4762}, {650, 21358}, {3763, 44567}, {4885, 47352}, {8760, 47353}, {9001, 15533}, {17494, 21356}, {29066, 47358}, {47356, 48295}
X(50766) = midpoint of X(69) and X(47869)
X(50766) = reflection of X(i) in X(j) for these {i,j}: {6, 45320}, {31150, 141}, {47356, 48295}
X(50767) lies on these lines: {1, 650}, {8, 26985}, {145, 26824}, {514, 4895}, {519, 693}, {551, 31209}, {891, 48324}, {1491, 48296}, {1734, 3960}, {1938, 5697}, {3241, 17494}, {3244, 47664}, {3633, 47724}, {3635, 48284}, {3679, 4885}, {3900, 4905}, {4041, 48287}, {4160, 4813}, {4162, 47970}, {4411, 49459}, {4490, 48347}, {4677, 45320}, {4729, 48343}, {4730, 48344}, {4777, 49490}, {4794, 23057}, {4825, 9269}, {4844, 47672}, {4879, 47959}, {4959, 42325}, {4979, 29350}, {5903, 9366}, {6182, 25415}, {6366, 49300}, {7951, 15280}, {7962, 11934}, {7982, 8760}, {8702, 23800}, {9001, 16496}, {9015, 49681}, {9373, 30323}, {9397, 11009}, {10056, 28834}, {14349, 48333}, {14421, 50335}, {16474, 22383}, {17460, 48557}, {19875, 31250}, {21189, 48293}, {21343, 48335}, {21385, 48327}, {24948, 48855}, {25055, 31287}, {27115, 38314}, {29226, 48111}, {34747, 48125}, {47942, 48338}, {48081, 48337}
X(50767) = midpoint of X(i) and X(j) for these {i,j}: {145, 48304}, {3633, 47724}
X(50767) = reflection of X(i) in X(j) for these {i,j}: {8, 48295}, {1491, 48296}, {1734, 4449}, {4041, 48287}, {4490, 48347}, {4677, 45320}, {4729, 48343}, {4730, 48344}, {4814, 3960}, {4825, 9269}, {4905, 48282}, {14349, 48333}, {17494, 48285}, {21189, 48293}, {21385, 48327}, {47729, 3244}, {47942, 48338}, {47959, 4879}, {47970, 4162}, {48081, 48337}, {48284, 3635}, {48335, 21343}, {49459, 4411}
X(50767) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3241, 17494, 48285}, {3960, 4814, 1734}, {4449, 4814, 3960}
X(50768) lies on these lines: {38, 17230}, {17250, 17450}
See Ercole Suppa and César Lozada, euclid 5254.
X(50769) lies on these lines: {3, 6}, {22156, 40214}, {28482, 39633}
See Ercole Suppa and César Lozada, euclid 5254.
X(50770) lies on these lines: {3, 8612}, {3481, 34576}
Points in a [[b^2 - c^2, c^2 - a^2, a^2 - b^2[, [a^2 - b^2 - c^2, b^2 - c^2 - a^2, c^2 - a^2 - b^2)]] coordinate system: X(50771)-X(50776)
The origin is given by (0, 0) = X(230) = 2 a^4 + b^4 + c^4 - a^2 b^2 - a^2 c^2 - 2 b^2 c^2 : : .
Barycentrics u : v : w for a triangle center U = (x,y) in this system are given by
U = 2 a^4 + b^4 + c^4 - a^2 b^2 - a^2 c^2 - 2 b^2 c^2 + (2 a^2 - b^2 - c^2) x + 2(b^2 - c^2) y : : ,
where, as functions of a, b, c, the coordinate x is antisymmetric 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).
{-((a^3+b^3+c^3)/(a+b+c)), -(((a-b) (a-c) (b-c))/(2 (a+b+c)))}, 24348
{-a^2-b^2-c^2, 0}, 325
{-(a+b+c)^2, 0}, 10026
{-((a^3+b^3+c^3)/(a+b+c)), ((a-b) (a-c) (b-c))/(2 (a+b+c))}, 10
{1/2 (-a^2-b^2-c^2), 0}, 44377
{0, 0}, 230
{a^2+b^2+c^2, 0}, 385
{a b+a c+b c, 0}, 44379
{(a+b+c)^2, 0}, 50252
{(a b c)/(a+b+c), 0}, 44378
{2 (a^2+b^2+c^2), 0}, 15480
{-2*(a^2 + b^2 + c^2), 0}, 50771
{(-2*(a^3 + b^3 + c^3))/(a + b + c), ((a - b)*(a - c)*(b - c))/(a + b + c)}, 50772
{-((a^3 + b^3 + c^3)/(a + b + c)), 0}, 50773
{(a^2 + b^2 + c^2)/2, 0}, 50774
{(a^3 + b^3 + c^3)/(a + b + c), -1/2*((a - b)*(a - c)*(b - c))/(a + b + c)}, 50775
{(2*(a^3 + b^3 + c^3))/(a + b + c), -(((a - b)*(a - c)*(b - c))/(a + b + c))}, 50776
X(50771) lies on these lines: {2, 6}, {5, 7855}, {30, 7813}, {114, 34380}, {140, 7826}, {147, 29181}, {315, 31859}, {523, 2525}, {546, 6248}, {550, 30270}, {574, 14929}, {620, 3793}, {736, 8357}, {754, 6390}, {1975, 33280}, {3053, 32818}, {3529, 15428}, {3544, 39663}, {3705, 17365}, {3734, 3933}, {3849, 14148}, {3926, 33239}, {3972, 7762}, {5008, 8368}, {5023, 32831}, {5026, 12830}, {5041, 8364}, {5254, 7758}, {5305, 7821}, {5346, 33186}, {5355, 8360}, {5965, 35021}, {6656, 7905}, {6781, 39785}, {7179, 17362}, {7227, 30179}, {7238, 33891}, {7750, 7906}, {7764, 7767}, {7784, 9607}, {7798, 33184}, {7799, 32459}, {7800, 9606}, {7801, 18907}, {7805, 8361}, {7807, 7871}, {7809, 47286}, {7818, 15048}, {7819, 7838}, {7820, 41750}, {7823, 32820}, {7848, 8359}, {7850, 8356}, {7854, 31406}, {7894, 8363}, {7896, 8362}, {7900, 32819}, {7908, 8369}, {7926, 8370}, {7939, 13571}, {10256, 14869}, {12007, 37450}, {13881, 32823}, {14711, 43457}, {16316, 47312}, {16320, 37897}, {17246, 29840}, {17344, 24239}, {17768, 49544}, {18358, 44422}, {20065, 32821}, {32457, 37350}, {32827, 34505}, {37900, 47245}, {47242, 47629}
X(50771) = midpoint of X(i) and X(j) for these {i,j}: {325, 7779}, {7813, 7845}
X(50771) = reflection of X(i) in X(j) for these {i,j}: {230, 325}, {385, 44377}, {3793, 620}, {15480, 230}
X(50771) = complement of X(50251)
X(50771) = crossdifference of every pair of points on line {512, 30435}
X(50771) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 9766, 3815}, {141, 7774, 9300}, {193, 7778, 5306}, {230, 325, 22110}, {325, 385, 44377}, {325, 22329, 7925}, {325, 50248, 44381}, {325, 50251, 2}, {385, 44377, 230}, {1007, 8667, 3054}, {1007, 20080, 8667}, {3314, 41624, 3589}, {3933, 7759, 7745}, {6189, 6190, 3620}, {7736, 10513, 599}, {7758, 7776, 5254}, {7759, 7916, 3933}, {7762, 7796, 7789}, {7764, 7882, 7767}, {7774, 7788, 141}, {7779, 7840, 325}, {7779, 41136, 50248}, {7792, 7837, 32455}, {7796, 7949, 7762}, {7821, 7890, 5305}, {7837, 7897, 7792}, {7838, 7895, 7819}, {7855, 7903, 5}, {7871, 7877, 7807}, {7905, 7917, 6656}, {7906, 7946, 7750}, {7925, 22329, 44381}, {7925, 41136, 325}, {7925, 50248, 22329}, {9770, 15533, 11168}, {9770, 15589, 31489}, {11163, 16990, 15491}, {15480, 22110, 230}, {15491, 22165, 16990}, {15533, 31489, 15589}, {15589, 31489, 11168}, {22329, 44381, 230}, {39022, 39023, 3763}, {41136, 50248, 7925}, {44384, 44385, 44380}
X(50772) lies on these lines: {1, 44377}, {8, 325}, {10, 230}, {145, 7925}, {385, 3617}, {519, 22110}, {523, 4528}, {524, 3416}, {1385, 10256}, {1503, 9864}, {1698, 44381}, {3241, 41133}, {3828, 41139}, {4678, 7779}, {4691, 15480}, {4769, 5690}, {5818, 39663}, {5846, 44380}, {7983, 33228}, {19875, 44401}, {22329, 50247}, {44392, 45444}, {44394, 45445}
X(50772) = midpoint of X(8) and X(325)
X(50772) = reflection of X(i) in X(j) for these {i,j}: {1, 44377}, {230, 10}
X(50773) lies on these lines: {2, 6}, {10, 523}, {115, 545}, {190, 31057}, {1698, 24345}, {3109, 49728}, {4205, 6788}, {4422, 8287}, {5949, 7228}, {6537, 23991}, {6626, 14588}, {7238, 20337}, {9024, 50440}, {9780, 36223}, {17058, 40480}, {17332, 46826}, {17768, 20546}, {23897, 31644}, {23992, 35121}, {25469, 26081}, {36154, 49734}, {44419, 47403}
X(50773) = midpoint of X(10) and X(24348)
X(50773) = crosssum of X(6) and X(5170)
X(50773) = crossdifference of every pair of points on line {512, 3285}
X(50773) = {X(39022),X(39023)}-harmonic conjugate of X(3936)
X(50774) lies on these lines: {2, 6}, {30, 32457}, {98, 29181}, {115, 3793}, {140, 7805}, {511, 35021}, {523, 8651}, {538, 32459}, {549, 7798}, {550, 5171}, {736, 19697}, {754, 43291}, {1447, 4395}, {2980, 27364}, {3053, 32815}, {3528, 21445}, {3530, 13334}, {3628, 7838}, {3632, 50254}, {3855, 39663}, {4045, 5305}, {5023, 6392}, {5254, 14907}, {5346, 8362}, {5355, 8359}, {5965, 10011}, {6036, 34380}, {6179, 7745}, {7081, 7227}, {7751, 7789}, {7755, 7767}, {7793, 33275}, {7826, 8361}, {7844, 14929}, {7848, 8360}, {7877, 33249}, {7896, 33186}, {8369, 17131}, {9752, 15069}, {9769, 25328}, {11054, 47287}, {12007, 37451}, {13881, 32827}, {16315, 46517}, {16316, 46998}, {20850, 33582}, {21843, 22253}, {22712, 32449}, {37900, 47242}, {47155, 47312}, {47238, 47629}
X(50774) = midpoint of X(i) and X(j) for these {i,j}: {115, 3793}, {230, 385}, {325, 15480}
X(50774) = reflection of X(i) in X(j) for these {i,j}: {325, 44381}, {44377, 230}
X(50774) = crossdifference of every pair of points on line {512, 5013}
X(50774) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 385, 50251}, {6, 34229, 15491}, {6, 37667, 13468}, {183, 5306, 3589}, {230, 325, 44381}, {230, 15480, 325}, {230, 44377, 44401}, {325, 385, 15480}, {325, 44381, 44377}, {385, 7925, 44367}, {385, 8859, 7779}, {385, 22329, 230}, {3815, 14614, 32455}, {5304, 15271, 597}, {7735, 8667, 141}, {7766, 37688, 9300}, {13468, 15491, 34229}, {14614, 17008, 3815}, {15534, 23055, 9771}, {17004, 41624, 3055}, {39022, 39023, 3618}
X(50775) lies on these lines: {1, 257}, {2, 50247}, {10, 230}, {30, 11599}, {40, 21445}, {99, 38221}, {316, 38220}, {325, 1125}, {511, 11710}, {519, 22329}, {523, 1960}, {524, 551}, {538, 11711}, {736, 12263}, {740, 41193}, {754, 11725}, {1385, 32515}, {1513, 2784}, {2796, 8598}, {3564, 21636}, {3616, 7779}, {3622, 50248}, {3624, 7925}, {3636, 50251}, {3679, 8859}, {3849, 12258}, {3923, 4234}, {3993, 24929}, {4039, 8772}, {4205, 10026}, {5184, 7983}, {5847, 15993}, {5965, 11724}, {6675, 44379}, {6998, 49488}, {7840, 25055}, {8983, 44394}, {9864, 38227}, {9881, 26613}, {11110, 17731}, {13174, 13586}, {13178, 14568}, {13971, 44392}, {15903, 17770}, {16475, 39099}, {19862, 44377}, {19883, 22110}, {19925, 39663}, {38049, 44380}, {38314, 44367}
X(50775) = midpoint of X(i) and X(j) for these {i,j}: {1, 385}, {325, 50250}, {5184, 7983}
X(50775) = reflection of X(i) in X(j) for these {i,j}: {10, 230}, {325, 1125}
X(50775) = crossdifference of every pair of points on line {4286, 45882}
X(50776) lies on these lines: {1, 524}, {8, 22329}, {10, 230}, {145, 385}, {325, 3616}, {518, 5148}, {523, 48327}, {1125, 22110}, {1698, 44401}, {1959, 4831}, {3242, 50253}, {3617, 8859}, {3622, 7840}, {3623, 44367}, {3624, 44377}, {3632, 50254}, {3634, 41139}, {3635, 15480}, {4062, 8772}, {5550, 41133}, {5698, 50255}, {20057, 50251}, {32459, 38221}
X(50776) = midpoint of X(i) and X(j) for these {i,j}: {1, 50250}, {325, 50247}, {3242, 50253}
X(50777) lies on these lines: {1, 4759}, {2, 726}, {10, 536}, {37, 537}, {45, 50023}, {75, 3828}, {192, 3679}, {518, 3898}, {519, 751}, {545, 50299}, {740, 4669}, {752, 49742}, {1125, 17354}, {1266, 25352}, {1757, 29584}, {2796, 50090}, {3241, 4704}, {3244, 49515}, {3625, 49462}, {3626, 49452}, {3634, 49493}, {3635, 49503}, {3636, 49499}, {3666, 42056}, {3696, 38098}, {3731, 49455}, {3775, 50097}, {3836, 49741}, {3842, 4688}, {3923, 48854}, {3943, 4407}, {3995, 31136}, {4029, 49764}, {4078, 50092}, {4090, 28606}, {4098, 49505}, {4356, 49697}, {4389, 49769}, {4419, 24692}, {4681, 34641}, {4685, 42041}, {4687, 49517}, {4699, 19876}, {4718, 4732}, {4740, 19875}, {4745, 28522}, {4755, 19883}, {4971, 50309}, {5220, 50283}, {6541, 29594}, {15481, 50124}, {15569, 49535}, {16676, 24331}, {16814, 49472}, {16826, 24821}, {17023, 31349}, {17132, 49519}, {17258, 50304}, {17261, 49482}, {17318, 50018}, {17319, 49685}, {17320, 49521}, {18145, 21443}, {19862, 49483}, {20430, 28194}, {22220, 42038}, {24349, 25055}, {25354, 48853}, {27268, 49532}, {28503, 49737}, {28542, 49725}, {28562, 50286}, {29600, 49676}, {31137, 41839}, {31145, 49469}, {31161, 43223}, {31302, 38314}, {33682, 50127}, {35126, 36217}, {36480, 50126}, {38089, 49481}, {41312, 50313}, {41313, 50285}, {42039, 42057}, {48809, 50107}, {49471, 49504}, {49692, 50114}, {49721, 50302}, {49748, 50301}
X(50777) = midpoint of X(i) and X(j) for these {i,j}: {192, 3679}, {551, 49520}, {984, 4664}, {3241, 49448}, {4688, 49523}, {4740, 49445}, {31145, 49469}, {31178, 49447}, {49456, 50094}, {49748, 50301}, {50090, 50291}
X(50777) = reflection of X(i) in X(j) for these {i,j}: {10, 50094}, {75, 3828}, {551, 37}, {3993, 4664}, {4688, 3842}, {4709, 3679}, {24325, 4755}, {31178, 1125}, {34641, 49457}, {49479, 551}, {50086, 4745}, {50117, 4688}, {50297, 49737}
X(50777) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 49520, 49479}, {984, 3993, 49510}, {3842, 49523, 50117}, {4364, 4439, 10}, {4755, 24325, 19883}, {19875, 49445, 4740}
X(50778) lies on these lines: {1, 4688}, {2, 4891}, {8, 4755}, {37, 519}, {145, 4664}, {518, 3899}, {528, 50125}, {536, 3241}, {537, 3244}, {551, 3696}, {984, 34747}, {1100, 48805}, {1279, 16834}, {2805, 10031}, {3623, 4740}, {3635, 49483}, {3655, 30271}, {3679, 15569}, {3723, 48854}, {3739, 38314}, {3823, 29582}, {3842, 34641}, {3883, 28337}, {4684, 49741}, {4686, 31178}, {4702, 16666}, {4718, 49490}, {4725, 49746}, {4727, 36479}, {4732, 19883}, {4898, 49690}, {4908, 47359}, {4966, 50091}, {5919, 44671}, {9041, 50110}, {15492, 49497}, {16669, 50283}, {16814, 49680}, {17231, 48821}, {17237, 49763}, {17299, 48849}, {20049, 49450}, {20430, 34748}, {22034, 31161}, {25055, 31238}, {28329, 50310}, {30273, 34631}, {31136, 37593}, {31138, 50080}, {36480, 39260}, {41310, 50282}, {41311, 50316}, {46922, 49484}, {47357, 50131}, {50085, 50305}
X(50778) = midpoint of X(i) and X(j) for these {i,j}: {145, 4664}, {984, 34747}, {3241, 49470}, {3679, 49678}, {20049, 49450}, {20430, 34748}, {30273, 34631}, {31178, 49469}
X(50778) = reflection of X(i) in X(j) for these {i,j}: {8, 4755}, {3679, 15569}, {3696, 551}, {4686, 31178}, {4688, 1}, {30271, 3655}, {34641, 3842}, {49468, 4688}, {49478, 3241}, {49515, 4664}, {50082, 49740}, {50085, 50305}
X(50778) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {49461, 49478, 49525}, {49470, 49478, 49461}, {49471, 49475, 37}
X(50779) lies on these lines: {2, 742}, {6, 4664}, {37, 524}, {75, 47352}, {141, 3986}, {518, 3898}, {536, 597}, {537, 1386}, {599, 29575}, {984, 47356}, {1992, 49509}, {3589, 4688}, {3618, 4740}, {3739, 48310}, {3970, 50259}, {3997, 35103}, {4133, 49524}, {4687, 21358}, {4704, 5032}, {5476, 29010}, {9055, 36522}, {11179, 20430}, {16834, 36404}, {16972, 50127}, {21356, 27268}, {28538, 50094}, {31178, 38023}, {38047, 50086}, {41311, 49516}
X(50779) = midpoint of X(i) and X(j) for these {i,j}: {6, 4664}, {599, 49496}, {984, 47356}, {1992, 49509}, {11179, 20430}
X(50779) = reflection of X(i) in X(j) for these {i,j}: {141, 4755}, {4688, 3589}, {49481, 597}
X(50780) lies on these lines: {141, 45313}, {524, 649}, {597, 4785}, {3589, 31147}, {3835, 48310}, {8584, 9002}, {20295, 47352}, {21358, 27013}, {47762, 50766}
X(50780) = reflection of X(i) in X(j) for these {i,j}: {141, 45313}, {31147, 3589}
X(50781) lies on these lines: {1, 21356}, {2, 5847}, {6, 3828}, {10, 524}, {40, 11180}, {69, 3679}, {141, 551}, {182, 38068}, {306, 4933}, {376, 39885}, {516, 47353}, {518, 3919}, {519, 599}, {528, 50081}, {542, 38430}, {549, 39870}, {553, 12588}, {576, 31399}, {597, 3844}, {740, 49630}, {752, 29594}, {946, 11178}, {1125, 21358}, {1352, 28194}, {1386, 19883}, {1738, 29617}, {1992, 19875}, {2321, 2796}, {2836, 4134}, {3241, 3620}, {3618, 19876}, {3626, 24693}, {3631, 9041}, {3634, 47352}, {3707, 49769}, {3751, 11160}, {3763, 38023}, {3773, 28558}, {3912, 50296}, {4026, 50125}, {4054, 31177}, {4078, 33082}, {4104, 31143}, {4133, 50084}, {4429, 50077}, {4643, 49766}, {4645, 29615}, {4655, 17132}, {4725, 48821}, {4745, 15533}, {4780, 17372}, {5032, 9780}, {5476, 10175}, {5480, 38076}, {5882, 40107}, {6684, 11179}, {9053, 41152}, {9143, 32261}, {9881, 11161}, {11362, 34507}, {11645, 31730}, {11898, 38066}, {12258, 19662}, {13178, 50639}, {15069, 43174}, {15534, 38047}, {16496, 31145}, {17227, 50017}, {17271, 50291}, {17290, 50020}, {17294, 28580}, {17297, 50305}, {17360, 49772}, {17392, 48853}, {17772, 49543}, {18583, 38083}, {19924, 31673}, {20423, 38146}, {24248, 50089}, {28202, 39884}, {28204, 48876}, {28534, 50097}, {28542, 50100}, {28562, 49560}, {29573, 50295}, {29574, 32846}, {29600, 50297}, {31151, 50095}, {38021, 40330}, {38087, 40341}, {38098, 49524}, {50079, 50080}
X(50781) = midpoint of X(i) and X(j) for these {i,j}: {40, 11180}, {69, 3679}, {376, 39885}, {599, 3416}, {3751, 11160}, {9143, 32261}, {9881, 11161}, {13178, 50639}, {15533, 47359}, {16496, 31145}, {24248, 50089}, {34641, 49505}, {48829, 50076}, {50079, 50080}
X(50781) = reflection of X(i) in X(j) for these {i,j}: {6, 3828}, {551, 141}, {597, 3844}, {946, 11178}, {1386, 20582}, {4133, 50084}, {11179, 6684}, {12258, 19662}, {39870, 549}, {47356, 1125}, {47359, 4745}, {49511, 599}, {49529, 3679}, {49684, 551}, {50109, 3821}, {50118, 3773}
X(50781) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3828, 38089}, {1386, 20582, 19883}, {4745, 47359, 38191}, {21358, 47356, 1125}
X(50782) lies on these lines: {519, 599}, {524, 3617}, {1698, 47352}, {3616, 21358}, {3623, 21356}, {3631, 31145}, {3679, 40341}, {3763, 16491}, {6144, 38087}, {19862, 47356}, {28174, 47353}, {28202, 36990}
X(50782) = reflection of X(47356) in X(19862)
X(50783) lies on these lines: {1, 21358}, {2, 5846}, {6, 3679}, {8, 524}, {10, 47352}, {45, 32847}, {55, 4933}, {69, 903}, {141, 3241}, {145, 17305}, {182, 38066}, {517, 47353}, {518, 4677}, {519, 599}, {528, 50087}, {540, 48804}, {542, 34718}, {551, 3763}, {742, 50075}, {752, 49721}, {1350, 28204}, {1386, 19875}, {1482, 11178}, {1992, 49524}, {2550, 50098}, {3052, 50104}, {3620, 20049}, {3625, 24692}, {3654, 43273}, {3656, 10516}, {3828, 38023}, {3844, 25055}, {3883, 41313}, {3886, 50084}, {4643, 49762}, {4663, 4668}, {4669, 5847}, {4678, 5032}, {4745, 38047}, {4914, 37674}, {5476, 5790}, {5480, 38074}, {5642, 32298}, {5690, 11179}, {5695, 28562}, {5969, 34673}, {6144, 49529}, {9053, 22165}, {9780, 48310}, {11180, 12245}, {11645, 12702}, {14077, 50766}, {14621, 29615}, {16491, 19876}, {16777, 33076}, {17251, 50286}, {17269, 49709}, {17290, 50015}, {17294, 49706}, {17313, 50310}, {17392, 48849}, {18525, 19924}, {18583, 38081}, {19596, 37546}, {20423, 38144}, {20582, 38314}, {28194, 36990}, {28503, 49747}, {29594, 50130}, {29617, 32850}, {34641, 40341}, {34747, 49465}, {41146, 50772}, {41312, 49476}, {48809, 50288}
X(50783) = midpoint of X(i) and X(j) for these {i,j}: {69, 31145}, {11180, 12245}
X(50783) = reflection of X(i) in X(j) for these {i,j}: {6, 3679}, {599, 3416}, {1482, 11178}, {1992, 49524}, {3241, 141}, {3242, 599}, {3886, 50084}, {11179, 5690}, {15534, 47359}, {32298, 5642}, {34747, 49465}, {41146, 50772}, {43273, 3654}, {47356, 10}, {47359, 4669}, {49679, 3241}, {49681, 551}, {49684, 3828}, {49688, 34641}, {49690, 31145}, {50120, 48829}, {50130, 29594}
X(50783) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3679, 38087}, {10, 47356, 47352}, {3828, 38023, 47355}, {3828, 49684, 38023}
X(50784) lies on these lines: {141, 38023}, {519, 599}, {524, 1698}, {1352, 28202}, {3616, 17387}, {3620, 28538}, {3629, 19876}, {3631, 3679}, {3828, 40341}, {3844, 11160}, {4933, 33080}, {6144, 38089}, {15533, 38047}, {19862, 21358}, {22165, 47359}, {28150, 47353}, {31253, 47352}
X(50784) = reflection of X(47356) in X(3616)
X(50785) lies on these lines: {6, 19876}, {69, 38087}, {519, 599}, {524, 9780}, {3622, 21356}, {3624, 21358}, {3828, 6144}, {15808, 47356}, {28146, 47353}
X(50785) = reflection of X(i) in X(j) for these {i,j}: {6, 19876}, {47356, 15808}
X(50786) lies on these lines: {69, 34641}, {193, 3679}, {519, 599}, {524, 3626}, {551, 3619}, {1992, 38098}, {3244, 21356}, {3589, 3828}, {3620, 34747}, {3634, 47356}, {3636, 21358}, {4669, 34379}, {4745, 5847}, {11160, 49536}, {15534, 38191}, {28194, 39884}, {28228, 47353}, {31145, 49505}, {49766, 50296}
X(50786) = midpoint of X(i) and X(j) for these {i,j}: {69, 34641}, {11160, 49536}, {31145, 49505}
X(50786) = reflection of X(47356) in X(3634)
X(50787) lies on these lines: {2, 34379}, {10, 21356}, {69, 551}, {141, 3828}, {518, 3968}, {519, 599}, {524, 1125}, {1992, 19883}, {2796, 50567}, {3241, 17324}, {3620, 3679}, {3624, 5032}, {3631, 28538}, {3634, 21358}, {3636, 47356}, {3653, 11898}, {3763, 38089}, {4297, 11180}, {4663, 31253}, {4933, 33081}, {5476, 10171}, {5846, 41152}, {5847, 22165}, {11160, 25055}, {11178, 19925}, {11599, 50639}, {15534, 38049}, {15692, 39878}, {16496, 34641}, {17132, 49560}, {17227, 50022}, {17360, 50020}, {19878, 47352}, {24231, 29615}, {27487, 50075}, {28164, 47353}, {28194, 48876}, {33087, 50093}, {38023, 40341}, {38076, 40330}, {38315, 41150}, {40107, 43174}, {49768, 50296}
X(50787) = midpoint of X(i) and X(j) for these {i,j}: {69, 551}, {599, 49511}, {3679, 49505}, {4297, 11180}, {11599, 50639}, {16496, 34641}
X(50787) = reflection of X(i) in X(j) for these {i,j}: {3828, 141}, {19925, 11178}, {47356, 3636}
X(50788) lies on these lines: {69, 3828}, {518, 41152}, {519, 599}, {524, 3634}, {551, 3620}, {1125, 21356}, {11178, 12571}, {11180, 12512}, {11898, 38068}, {19876, 20080}, {19878, 21358}, {22165, 34379}, {28158, 47353}, {38089, 40341}
X(50788) = midpoint of X(i) and X(j) for these {i,j}: {69, 3828}, {11180, 12512}
X(50788) = reflection of X(12571) in X(11178)
X(50789) lies on these lines: {6, 34641}, {8, 47356}, {141, 34747}, {193, 28538}, {519, 599}, {524, 3632}, {551, 49679}, {3241, 3619}, {3244, 21358}, {3589, 3679}, {3626, 47352}, {3630, 9041}, {4663, 20052}, {4669, 38047}, {4677, 5846}, {4745, 38315}, {4933, 32854}, {16475, 41153}, {20049, 49465}, {20050, 21356}, {28204, 48873}, {28234, 47353}, {38087, 49684}, {41313, 49506}
X(50789) = reflection of X(i) in X(j) for these {i,j}: {6, 34641}, {20049, 49465}, {34747, 141}, {47356, 8}, {47359, 4677}, {49679, 551}, {49681, 3679}, {49688, 31145}
X(50789) = {X(3679),X(49681)}-harmonic conjugate of X(38023)
X(50790) lies on these lines: {1, 41310}, {2, 9053}, {6, 644}, {8, 21358}, {45, 49771}, {69, 20049}, {141, 31145}, {145, 524}, {518, 3899}, {519, 599}, {542, 34748}, {551, 38087}, {952, 47353}, {1483, 11179}, {3243, 50125}, {3244, 47356}, {3621, 21356}, {3622, 48310}, {3679, 3763}, {3938, 4933}, {4864, 29573}, {5476, 10247}, {5846, 15533}, {5969, 34685}, {6144, 49681}, {8148, 19924}, {10168, 37624}, {11178, 12645}, {11645, 18526}, {16496, 28538}, {16973, 50123}, {28194, 48872}, {28204, 36990}, {28329, 49451}, {30614, 37674}, {38023, 49529}, {38314, 49524}, {38315, 47359}, {41312, 49466}, {41313, 49527}, {47595, 50108}, {49467, 50089}, {49704, 49748}, {49721, 50130}
X(50790) = midpoint of X(i) and X(j) for these {i,j}: {69, 20049}, {16496, 34747}
X(50790) = reflection of X(i) in X(j) for these {i,j}: {6, 3241}, {599, 3242}, {3679, 49465}, {11179, 1483}, {12645, 11178}, {31145, 141}, {47356, 3244}, {49679, 34747}, {49688, 551}, {49690, 3679}, {49721, 50130}, {50089, 49467}
X(50790) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {551, 38087, 47355}, {551, 49688, 38087}, {16496, 49679, 40341}, {49465, 49690, 3763}
X(50791) lies on these lines: {141, 38087}, {519, 599}, {524, 3616}, {551, 40341}, {1350, 28202}, {1698, 21358}, {3241, 3631}, {3617, 21356}, {3620, 9041}, {6144, 38023}, {15533, 38315}, {19862, 47352}, {27474, 28582}, {28160, 47353}
X(50792) lies on these lines: {69, 38023}, {141, 19876}, {519, 599}, {524, 3624}, {3622, 47356}, {9780, 21356}, {28172, 47353}
X(50792) = reflection of X(i) in X(j) for these {i,j}: {19876, 141}, {47356, 3622}
X(50793) lies on these lines: {2, 3}, {518, 4731}, {3826, 11237}, {3828, 41229}, {3841, 10072}, {5288, 41859}, {5302, 19877}, {9780, 10404}, {24564, 31162}, {26723, 48828}
X(50793) = anticomplement of X(50714)
X(50793) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 377, 31156}, {2, 3543, 5047}, {2, 4190, 15670}, {2, 4208, 6175}, {2, 6175, 2478}, {2, 6872, 50202}, {2, 10304, 15671}, {2, 15677, 16845}, {2, 17572, 15702}, {2, 31156, 31259}, {2, 44217, 377}, {2, 50237, 44217}, {2, 50429, 11346}, {377, 8728, 50393}, {377, 31259, 50244}, {377, 50393, 31259}, {381, 17529, 2}, {405, 44217, 50396}, {405, 50395, 2}, {443, 50727, 2}, {547, 16862, 2}, {4197, 37436, 37462}, {4208, 44256, 377}, {6872, 50238, 377}, {8728, 44217, 2}, {8728, 44222, 17529}, {8728, 50237, 377}, {8728, 50238, 50207}, {8728, 50396, 50395}, {15670, 50726, 2}, {31156, 50393, 2}, {31295, 50713, 377}, {36445, 36463, 6851}, {44217, 50207, 50397}, {44217, 50397, 50238}, {50202, 50207, 2}, {50202, 50238, 50397}, {50202, 50397, 6872}, {50205, 50713, 31295}, {50207, 50238, 6872}, {50207, 50397, 50202}, {50239, 50394, 50398}, {50395, 50396, 405}
X(50794) lies on these lines: {2, 3}, {518, 3922}, {3617, 26842}, {3925, 20076}, {5249, 20013}, {5554, 38052}, {10586, 24387}, {20060, 40333}, {31420, 38314}, {41229, 46933}
X(50794) = midpoint of X(377) and X(50393)
X(50794) = reflection of X(50398) in X(50393)
X(50794) = anticomplement of X(50398)
X(50794) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 377, 31295}, {2, 50693, 15676}, {377, 8728, 6872}, {377, 31156, 50240}, {377, 31259, 50239}, {377, 44217, 50237}, {377, 50237, 2}, {377, 50244, 50397}, {405, 50396, 377}, {443, 50741, 17531}, {2475, 37436, 2}, {4190, 4197, 2}, {5187, 17582, 2}, {6175, 17582, 5187}, {6871, 37462, 2}, {6872, 8728, 2}, {6872, 50237, 8728}, {6886, 6951, 3146}, {8728, 50238, 50713}, {8728, 50239, 31259}, {8728, 50713, 377}, {17528, 37462, 6871}, {31259, 50239, 6872}, {44217, 50238, 377}, {44217, 50713, 8728}, {50205, 50397, 50244}, {50207, 50240, 31156}, {50393, 50398, 2}
X(50795) lies on these lines: {2, 3}, {518, 3624}, {3916, 20195}, {4423, 24387}, {5302, 30827}, {5316, 19878}, {5439, 45120}, {10198, 50038}, {19862, 21060}, {31494, 38314}, {34595, 41229}
X(50795) = midpoint of X(50393) and X(50398)
X(50795) = reflection of X(405) in X(50398)
X(50795) = complement of X(50393)
X(50795) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 377, 50394}, {2, 405, 50207}, {2, 5047, 50726}, {2, 6675, 16862}, {2, 7483, 16864}, {2, 16845, 17529}, {2, 17534, 1656}, {2, 17552, 442}, {2, 17590, 16842}, {2, 31259, 8728}, {2, 50205, 405}, {2, 50398, 50393}, {2, 50714, 44217}, {377, 50202, 405}, {405, 8728, 50239}, {405, 16862, 37270}, {405, 44217, 50242}, {405, 50205, 50714}, {405, 50207, 44217}, {405, 50397, 50241}, {405, 50713, 6872}, {442, 17552, 17542}, {2476, 6857, 37284}, {5047, 50726, 17532}, {6872, 8728, 50713}, {6872, 50713, 50239}, {8728, 31259, 405}, {8728, 50202, 50243}, {8728, 50205, 31259}, {8728, 50239, 44217}, {8728, 50243, 377}, {11108, 37282, 405}, {11108, 50740, 37162}, {15670, 17582, 19537}, {16845, 17529, 16370}, {50202, 50394, 377}, {50205, 50394, 50202}, {50207, 50239, 8728}, {50207, 50714, 405}, {50237, 50241, 50397}, {50241, 50395, 50237}, {50243, 50394, 8728}
X(50796) lies on these lines: {1, 3545}, {2, 515}, {3, 3828}, {4, 3679}, {5, 551}, {8, 3839}, {10, 30}, {35, 28461}, {40, 3543}, {80, 226}, {140, 38083}, {165, 11001}, {182, 38089}, {355, 381}, {376, 5691}, {382, 38066}, {516, 3654}, {517, 3845}, {518, 47354}, {528, 6246}, {535, 28452}, {546, 4301}, {547, 1385}, {549, 4297}, {553, 1478}, {597, 39870}, {631, 19876}, {671, 9864}, {730, 44422}, {944, 5071}, {950, 10056}, {952, 3817}, {993, 18491}, {1125, 3655}, {1210, 5434}, {1327, 35774}, {1328, 35775}, {1490, 50741}, {1656, 3653}, {1698, 3524}, {1699, 4677}, {1837, 11237}, {1992, 39885}, {2043, 36440}, {2044, 36458}, {2321, 32431}, {2771, 3919}, {2784, 11632}, {2796, 6321}, {2800, 5927}, {3058, 31397}, {3091, 3241}, {3244, 9955}, {3488, 5726}, {3525, 30315}, {3529, 9588}, {3534, 26446}, {3582, 45287}, {3584, 10572}, {3585, 4848}, {3586, 10385}, {3617, 34632}, {3625, 22791}, {3626, 12699}, {3627, 5493}, {3632, 34631}, {3634, 5054}, {3635, 18493}, {3636, 18526}, {3751, 11180}, {3754, 40263}, {3814, 15842}, {3818, 49529}, {3832, 7982}, {3850, 10222}, {3851, 37727}, {3854, 5734}, {3855, 11522}, {3860, 5844}, {3947, 37730}, {4015, 37585}, {4052, 38309}, {4304, 4995}, {4311, 5298}, {4428, 6913}, {4654, 18391}, {4691, 12702}, {4701, 8148}, {4870, 10950}, {5067, 30389}, {5068, 9624}, {5080, 17781}, {5086, 21075}, {5248, 18518}, {5251, 21161}, {5252, 11238}, {5261, 15933}, {5270, 6900}, {5290, 17706}, {5450, 16371}, {5461, 11710}, {5476, 38146}, {5480, 28538}, {5603, 30308}, {5657, 15682}, {5690, 15687}, {5727, 10590}, {5777, 44663}, {5837, 18517}, {5847, 20423}, {5886, 19709}, {5901, 11737}, {6054, 13178}, {6256, 9948}, {6260, 7700}, {6713, 38104}, {6735, 49719}, {6738, 9654}, {6796, 16370}, {6841, 12437}, {6918, 40726}, {6990, 37719}, {7377, 41140}, {7384, 17310}, {7686, 9947}, {7967, 7988}, {7987, 15702}, {8185, 44837}, {8226, 37725}, {8227, 13607}, {8703, 10164}, {8715, 37234}, {9140, 12368}, {9143, 12407}, {9616, 43257}, {9623, 18529}, {9778, 15640}, {9779, 16200}, {9780, 10304}, {10072, 10106}, {10109, 11230}, {10171, 10246}, {10445, 17330}, {10516, 47358}, {10591, 37709}, {10706, 13211}, {10707, 10863}, {10709, 13532}, {10718, 12784}, {10902, 16858}, {11019, 12019}, {11112, 12616}, {11113, 34746}, {11178, 49511}, {11231, 12100}, {11274, 11729}, {11499, 28444}, {11500, 16418}, {11518, 31410}, {11530, 31420}, {11539, 13624}, {11709, 45311}, {11715, 45310}, {11812, 17502}, {12053, 37710}, {12101, 28174}, {12103, 31447}, {12114, 16417}, {12512, 15681}, {12608, 17577}, {13912, 41945}, {13975, 41946}, {14831, 31760}, {14872, 24473}, {14893, 22793}, {15686, 31663}, {15690, 28190}, {15692, 31423}, {15699, 19862}, {15705, 46932}, {15708, 19877}, {15808, 47478}, {15843, 25639}, {16174, 17618}, {16239, 31666}, {16616, 34790}, {16980, 31751}, {17525, 38058}, {17604, 39779}, {18358, 49505}, {18524, 28453}, {18761, 25440}, {19130, 49684}, {19710, 28168}, {20117, 31165}, {21031, 37447}, {21636, 22566}, {22266, 41983}, {23841, 31728}, {24042, 37820}, {24391, 44229}, {28146, 33699}, {29057, 49630}, {29594, 36728}, {31425, 50693}, {31657, 38094}, {31658, 38101}, {31659, 38105}, {31871, 37562}, {35242, 46933}, {35403, 48661}, {35822, 49602}, {35823, 49601}, {36006, 37561}, {36946, 37702}, {36990, 38087}, {36991, 38092}, {37298, 40260}, {38047, 43273}, {38065, 43176}, {38072, 47356}, {38075, 47357}, {38144, 47353}, {45715, 48778}, {45716, 48779}, {48852, 50037}, {48903, 50587}, {48937, 50415}
(50796) = midpoint of X(i) and X(j) for these {i,j}: {1, 34627}, {4, 3679}, {8, 31162}, {10, 34648}, {40, 3543}, {80, 10711}, {355, 381}, {376, 5691}, {671, 9864}, {1992, 39885}, {3241, 5881}, {3632, 34631}, {3654, 3830}, {3655, 18525}, {3751, 11180}, {4301, 34641}, {5603, 37712}, {5690, 15687}, {6054, 13178}, {7982, 31145}, {9140, 12368}, {9143, 12407}, {10706, 13211}, {10707, 12751}, {10709, 13532}, {10718, 12784}, {11112, 34697}, {11113, 34746}, {12699, 34718}, {14872, 24473}, {34632, 41869}, {34640, 34717}, {34647, 34700}, {47353, 47359}, {48937, 50415}
(50796) = reflection of X(i) in X(j) for these {i,j}: {3, 3828}, {376, 6684}, {381, 19925}, {549, 9956}, {551, 5}, {946, 381}, {1385, 547}, {3241, 13464}, {3576, 10172}, {3654, 4745}, {3655, 1125}, {3817, 38140}, {4297, 549}, {5882, 551}, {5901, 11737}, {10164, 38042}, {10165, 10175}, {10175, 5587}, {10246, 10171}, {11274, 11729}, {11362, 3679}, {11709, 45311}, {11710, 5461}, {11715, 45310}, {14831, 31760}, {15681, 12512}, {15686, 31663}, {21636, 22566}, {22793, 14893}, {24473, 31870}, {31162, 18483}, {31165, 20117}, {31673, 34648}, {34638, 3579}, {34648, 18480}, {34718, 3626}, {34748, 3635}, {38127, 5790}, {38155, 38138}, {39870, 597}, {49511, 11178}
(50796) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3828, 38068}, {4, 38074, 3679}, {8, 3839, 31162}, {8, 18492, 18483}, {10, 18480, 31673}, {10, 31673, 31730}, {355, 946, 47745}, {355, 19925, 946}, {376, 5818, 19875}, {376, 19875, 6684}, {547, 1385, 19883}, {551, 38076, 5}, {944, 5071, 25055}, {1482, 12571, 946}, {1698, 34628, 3524}, {3091, 3241, 38021}, {3091, 5881, 13464}, {3241, 38021, 13464}, {3545, 34627, 1}, {3617, 50687, 34632}, {3654, 4745, 38127}, {3654, 5790, 4745}, {3655, 5055, 1125}, {3679, 37714, 38074}, {3830, 5790, 3654}, {3839, 31162, 18483}, {5055, 18525, 3655}, {5603, 41106, 30308}, {5691, 5818, 6684}, {5691, 19875, 376}, {5881, 38021, 3241}, {7989, 25055, 5071}, {9955, 37705, 3244}, {14269, 34718, 12699}, {15178, 38022, 551}, {18357, 18480, 10}, {18492, 31162, 3839}, {31399, 38068, 3828}, {34632, 50687, 41869}, {38144, 47353, 47359}
X(50797) lies on these lines: {2, 28224}, {3, 38074}, {8, 14269}, {10, 15688}, {20, 38081}, {30, 3617}, {145, 38071}, {165, 3534}, {355, 381}, {382, 3679}, {515, 15693}, {546, 31145}, {551, 5079}, {944, 15703}, {952, 19709}, {1656, 28204}, {1657, 38066}, {1698, 5054}, {3241, 3851}, {3545, 3623}, {3616, 5055}, {3622, 47478}, {3654, 28150}, {3655, 19862}, {3828, 15720}, {3830, 28174}, {3839, 8148}, {3855, 20049}, {4668, 18480}, {4816, 31162}, {5066, 10247}, {5071, 37624}, {5072, 5881}, {5076, 28194}, {5657, 15685}, {5690, 15684}, {5818, 15694}, {5844, 41099}, {7967, 10109}, {9780, 15707}, {9956, 15723}, {11001, 38112}, {12245, 14893}, {12702, 34648}, {14093, 28208}, {15695, 28186}, {15700, 19875}, {15701, 38042}, {15706, 18481}, {17504, 46933}, {18518, 28443}, {23046, 34631}, {28158, 35384}, {28198, 35434}, {37727, 38076}, {38099, 38753}
X(50797) = midpoint of X(i) and X(j) for these {i,j}: {3616, 34627}, {4816, 31162}
X(50797) = reflection of X(i) in X(j) for these {i,j}: {3655, 19862}, {15694, 5818}, {34718, 4668}, {34748, 3623}, {37624, 5071}
X(50797) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3545, 37705, 34748}, {5055, 34627, 18526}, {18357, 34627, 5055}, {18480, 34718, 38335}
X(50798) lies on these lines: {1, 5055}, {2, 952}, {3, 3679}, {4, 31145}, {5, 3241}, {8, 30}, {10, 3655}, {40, 15681}, {55, 9897}, {80, 11238}, {100, 18515}, {119, 3829}, {140, 38081}, {145, 3545}, {165, 15695}, {182, 38087}, {200, 35459}, {355, 381}, {376, 5690}, {382, 28194}, {515, 3534}, {517, 3830}, {528, 5779}, {547, 1483}, {549, 944}, {551, 1656}, {956, 18524}, {958, 28443}, {962, 15687}, {999, 37708}, {1159, 4654}, {1351, 28538}, {1352, 9041}, {1376, 12773}, {1385, 15694}, {1657, 11362}, {2072, 47593}, {2095, 28452}, {3058, 12647}, {3090, 38022}, {3091, 20049}, {3242, 11178}, {3295, 37711}, {3434, 10742}, {3476, 11545}, {3524, 3617}, {3526, 3653}, {3543, 12245}, {3576, 15701}, {3579, 4668}, {3582, 37707}, {3584, 37706}, {3616, 15699}, {3621, 3839}, {3624, 32900}, {3625, 12699}, {3626, 15688}, {3632, 8148}, {3633, 9955}, {3818, 49690}, {3843, 7982}, {3845, 5844}, {3850, 5734}, {3851, 10222}, {3871, 28461}, {3893, 31937}, {3913, 13743}, {3940, 5176}, {4297, 14093}, {4421, 12331}, {4428, 7489}, {4678, 10304}, {4691, 15706}, {4701, 31673}, {4745, 15693}, {4746, 31730}, {4816, 41869}, {4870, 10827}, {4915, 18528}, {5066, 5603}, {5070, 15178}, {5071, 5901}, {5072, 13464}, {5073, 7991}, {5252, 15934}, {5434, 5708}, {5476, 38144}, {5493, 49137}, {5534, 50740}, {5550, 47599}, {5559, 9670}, {5563, 43731}, {5587, 10247}, {5642, 12898}, {5657, 8703}, {5687, 26321}, {5691, 15684}, {5727, 6767}, {5731, 12100}, {5816, 50113}, {5846, 20423}, {5886, 38155}, {5899, 37546}, {6684, 15700}, {6713, 38099}, {6914, 38665}, {6980, 37725}, {7373, 37709}, {7377, 40891}, {7970, 22566}, {7987, 15718}, {7989, 33179}, {8185, 37956}, {8197, 45380}, {8200, 11208}, {8204, 45379}, {8207, 11207}, {9053, 47354}, {9655, 41687}, {9778, 19710}, {9780, 11539}, {9812, 12101}, {9864, 48657}, {9947, 23340}, {9956, 15703}, {10056, 10950}, {10072, 10944}, {10109, 10283}, {10164, 15716}, {10589, 12735}, {10711, 12531}, {10914, 40266}, {10942, 17530}, {10943, 17533}, {11001, 28186}, {11112, 34698}, {11113, 34745}, {11179, 49524}, {11194, 11499}, {11237, 37710}, {11278, 18492}, {11680, 11698}, {11849, 28444}, {12438, 20128}, {12513, 37251}, {12751, 31140}, {13587, 32153}, {13607, 19883}, {13624, 15707}, {13632, 48802}, {13846, 35788}, {13847, 35789}, {14848, 47356}, {14872, 25413}, {14986, 43734}, {15640, 28178}, {15682, 28174}, {15685, 28160}, {15696, 43174}, {15709, 46933}, {15720, 38068}, {16200, 30308}, {16202, 16857}, {16417, 37535}, {16418, 37621}, {17549, 32141}, {17781, 18499}, {18323, 47490}, {18440, 49688}, {18519, 35000}, {19130, 49679}, {19540, 31136}, {19876, 46219}, {19877, 47598}, {19914, 34612}, {20050, 38071}, {20052, 50687}, {20053, 23046}, {20057, 47478}, {21677, 28460}, {22793, 35403}, {28212, 33699}, {29010, 50075}, {29617, 36731}, {31479, 37740}, {31657, 38092}, {31658, 38097}, {31659, 38100}, {32537, 37234}, {34689, 34746}, {34697, 34720}, {35822, 35843}, {35823, 35842}, {36279, 41684}, {36728, 50079}, {37545, 45287}, {38034, 41106}, {38067, 43175}, {39899, 49529}, {40726, 45976}, {44265, 47488}, {48903, 50575}, {48907, 50415}
X(50798) = midpoint of X(i) and X(j) for these {i,j}: {4, 31145}, {8, 34627}, {381, 12645}, {3543, 12245}, {3621, 34631}, {3625, 34648}, {3632, 31162}, {3679, 5881}, {10711, 12531}, {18525, 34718}, {34689, 34746}, {34697, 34720}, {34700, 34717}
X(50798) = reflection of X(i) in X(j) for these {i,j}: {3, 3679}, {376, 5690}, {381, 355}, {944, 549}, {962, 15687}, {1482, 381}, {1483, 547}, {3241, 5}, {3242, 11178}, {3534, 3654}, {3576, 38176}, {3654, 4669}, {3655, 10}, {4930, 11236}, {5603, 38138}, {5731, 38112}, {5882, 3828}, {5886, 38155}, {7967, 38042}, {7970, 22566}, {8148, 31162}, {10246, 5790}, {10247, 5587}, {11179, 49524}, {12699, 34648}, {12702, 34718}, {12898, 5642}, {15681, 40}, {15684, 5691}, {16200, 38140}, {18525, 34627}, {18526, 3655}, {20128, 12438}, {28460, 21677}, {31162, 18480}, {34627, 37705}, {34628, 3579}, {34631, 22791}, {34698, 11112}, {34718, 8}, {34745, 11113}, {34747, 10222}, {34748, 1}, {37727, 551}, {44265, 47488}, {48657, 9864}, {48661, 3543}, {48667, 10711}, {48907, 50415}
X(50798) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3679, 38066}, {8, 18525, 12702}, {8, 37705, 18525}, {10, 3655, 5054}, {145, 18357, 18493}, {355, 12645, 1482}, {355, 47745, 12645}, {547, 1483, 38314}, {1385, 19875, 15694}, {3241, 38074, 5}, {3579, 34628, 15689}, {3621, 3839, 34631}, {3632, 18480, 8148}, {3653, 3828, 3526}, {3828, 5882, 3653}, {3839, 34631, 22791}, {5054, 18526, 3655}, {5055, 34748, 1}, {5818, 38314, 547}, {8148, 14269, 31162}, {9956, 25055, 15703}, {10222, 37714, 3851}, {12699, 34648, 38335}, {15703, 37624, 25055}, {18480, 31162, 14269}, {34747, 37714, 38021}, {34747, 38021, 10222}
X(50799) lies on these lines: {1, 38071}, {2, 17502}, {3, 38076}, {4, 28202}, {5, 3653}, {10, 14269}, {20, 38083}, {30, 1698}, {40, 14893}, {165, 33699}, {355, 381}, {382, 3828}, {515, 19709}, {517, 41099}, {546, 3679}, {547, 5691}, {549, 7989}, {550, 19876}, {551, 3851}, {952, 30308}, {1657, 38068}, {1699, 3860}, {3091, 28204}, {3241, 3855}, {3534, 10175}, {3543, 9956}, {3545, 3616}, {3576, 10109}, {3579, 50687}, {3617, 3839}, {3623, 9955}, {3624, 47478}, {3634, 15688}, {3654, 3845}, {3830, 26446}, {3832, 38074}, {3843, 28194}, {3850, 37727}, {3854, 10222}, {3856, 7982}, {3857, 5881}, {3858, 37714}, {3859, 11522}, {4297, 15703}, {4654, 12019}, {4668, 18357}, {4677, 38138}, {4816, 22791}, {5054, 31253}, {5055, 18481}, {5066, 5886}, {5071, 28208}, {5076, 31399}, {5818, 28198}, {6684, 15684}, {7991, 38081}, {9588, 12102}, {10164, 15685}, {10172, 15701}, {10283, 41990}, {10304, 33697}, {11001, 11231}, {11698, 41858}, {11737, 25055}, {12101, 38042}, {12737, 38077}, {12811, 38022}, {14892, 34773}, {15686, 31423}, {15687, 19875}, {15693, 28164}, {15695, 28172}, {15699, 34628}, {15704, 30315}, {15713, 28190}, {16192, 44903}, {18483, 34718}, {19708, 28168}, {37733, 38078}, {38104, 38753}
X(50799) = midpoint of X(i) and X(j) for these {i,j}: {3623, 34627}, {4668, 31162}, {19862, 34648}
X(50799) = reflection of X(3655) in X(3616)
X(50799) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3545, 18480, 3655}, {3845, 5587, 3654}, {5055, 34648, 18481}, {18357, 23046, 31162}
X(50800) lies on these lines: {2, 28186}, {3, 19876}, {4, 38066}, {8, 23046}, {10, 38335}, {30, 9780}, {40, 35403}, {355, 381}, {546, 38074}, {551, 5072}, {944, 11737}, {952, 41106}, {1656, 38076}, {1657, 3828}, {1698, 15689}, {3241, 3850}, {3534, 10164}, {3545, 3622}, {3616, 14892}, {3624, 5055}, {3634, 15706}, {3653, 5079}, {3654, 28232}, {3655, 15808}, {3679, 3843}, {3715, 12702}, {3830, 5587}, {3839, 4678}, {3845, 5790}, {3851, 9624}, {3860, 38138}, {3861, 38081}, {4297, 15723}, {5054, 34648}, {5066, 10283}, {5068, 38022}, {5657, 12101}, {5691, 15694}, {5818, 15687}, {7988, 10246}, {7989, 15703}, {9955, 34748}, {9956, 15681}, {10175, 15693}, {10247, 30308}, {11231, 15695}, {14893, 48661}, {15682, 38042}, {15684, 19875}, {15688, 31673}, {15696, 38068}, {15698, 28190}, {15701, 28160}, {18491, 28453}, {18493, 20057}, {19877, 45759}, {31399, 49136}, {38087, 48889}, {46333, 46932}
X(50800) = midpoint of X(20057) and X(34627)
X(50800) = reflection of X(i) in X(j) for these {i,j}: {3, 19876}, {3655, 15808}, {15703, 7989}, {34718, 4678}
X(50800) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3839, 18357, 34718}, {34627, 38071, 18493}
X(50801) lies on these lines: {2, 28236}, {4, 34641}, {8, 34648}, {10, 3524}, {20, 3679}, {30, 3626}, {140, 3828}, {355, 381}, {376, 38098}, {515, 4745}, {516, 4669}, {517, 12101}, {547, 13607}, {551, 3090}, {952, 10109}, {1125, 15699}, {3091, 34747}, {3241, 5068}, {3244, 3545}, {3534, 38127}, {3617, 34628}, {3625, 31162}, {3627, 28194}, {3632, 3839}, {3634, 3655}, {3635, 14892}, {3636, 5055}, {3653, 31399}, {3654, 15685}, {3830, 28228}, {3845, 28234}, {4301, 31145}, {4668, 34632}, {4691, 15689}, {4701, 18480}, {4746, 31673}, {5070, 5882}, {5073, 11362}, {5493, 11541}, {5690, 44903}, {5790, 15701}, {5818, 19883}, {6684, 14891}, {7991, 50690}, {11180, 49536}, {11237, 12563}, {11278, 23046}, {11522, 20049}, {11540, 31662}, {11737, 33179}, {12512, 15691}, {12811, 13464}, {15716, 26446}, {15721, 19875}, {16200, 41106}, {18483, 41987}, {18492, 34631}, {18526, 19878}, {28224, 44580}, {28232, 33699}, {31253, 41984}, {38081, 44682}, {38140, 41990}, {38191, 43273}, {40273, 45762}
X(50801) = midpoint of X(i) and X(j) for these {i,j}: {4, 34641}, {8, 34648}, {10, 34627}, {381, 47745}, {551, 5881}, {3625, 31162}, {4301, 31145}, {11180, 49536}, {31673, 34718}, {37712, 38155}
X(50801) = reflection of X(i) in X(j) for these {i,j}: {3655, 3634}, {13607, 547}, {33179, 11737}, {34718, 4746}, {43174, 3679}
X(50801) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3241, 37714, 38076}, {5881, 38074, 551}
X(50802) lies on these lines: {1, 3839}, {2, 165}, {4, 551}, {5, 3828}, {10, 3545}, {11, 553}, {30, 1125}, {40, 5071}, {114, 2796}, {140, 28202}, {226, 11238}, {355, 381}, {376, 8227}, {382, 3653}, {497, 43179}, {515, 3845}, {517, 3956}, {527, 3829}, {535, 22835}, {546, 13464}, {547, 6684}, {549, 12512}, {671, 21636}, {726, 44422}, {950, 4870}, {952, 3860}, {962, 19875}, {1385, 15687}, {1537, 38077}, {1538, 49736}, {1656, 38068}, {1698, 34632}, {2784, 12258}, {3058, 13405}, {3090, 5493}, {3091, 3679}, {3241, 3832}, {3244, 18492}, {3524, 19862}, {3534, 10165}, {3543, 4297}, {3576, 15682}, {3579, 15699}, {3582, 4292}, {3584, 10624}, {3616, 34628}, {3624, 10304}, {3625, 34631}, {3626, 22791}, {3627, 38022}, {3634, 5055}, {3635, 18480}, {3636, 3655}, {3646, 50727}, {3654, 10175}, {3671, 10591}, {3830, 5886}, {3843, 5882}, {3851, 11362}, {3854, 31145}, {3855, 7982}, {3858, 10222}, {3861, 15178}, {3884, 16616}, {3944, 4353}, {3947, 9614}, {4052, 14484}, {4298, 10072}, {4342, 10590}, {4428, 19541}, {4654, 11019}, {4669, 5587}, {4677, 38155}, {4691, 34718}, {4701, 18357}, {4746, 8148}, {4856, 32431}, {5054, 19878}, {5056, 9589}, {5057, 10032}, {5068, 7991}, {5072, 31399}, {5087, 20103}, {5219, 10385}, {5226, 30331}, {5267, 28461}, {5274, 5542}, {5325, 24703}, {5584, 19536}, {5603, 28236}, {5691, 38314}, {5714, 21625}, {5715, 45700}, {5734, 34747}, {5806, 44663}, {5818, 38098}, {5847, 47354}, {5850, 24386}, {5901, 14893}, {6054, 11599}, {6175, 41012}, {6738, 10896}, {6744, 9669}, {6745, 49719}, {7377, 41141}, {7384, 41140}, {7681, 12558}, {7704, 34637}, {7987, 10248}, {8703, 11230}, {9588, 15022}, {9612, 12577}, {9770, 17132}, {9956, 11737}, {10056, 12575}, {10109, 10172}, {10124, 31663}, {10151, 47593}, {10246, 41150}, {10478, 42057}, {10706, 13605}, {10707, 21635}, {10711, 21630}, {10863, 31140}, {11231, 28232}, {11237, 12053}, {11372, 38073}, {11680, 17781}, {11812, 28178}, {12047, 12563}, {12100, 28146}, {12101, 28160}, {13374, 31871}, {13912, 42602}, {13975, 42603}, {15690, 28154}, {15703, 48661}, {15708, 34595}, {15709, 35242}, {15721, 16192}, {15759, 28182}, {16189, 20049}, {17502, 19710}, {17578, 30389}, {17604, 30329}, {17618, 34612}, {18249, 25639}, {18481, 38335}, {20423, 34379}, {24473, 31803}, {25935, 31048}, {28172, 33699}, {28234, 38140}, {36990, 38023}, {36991, 38024}, {38035, 47353}, {38049, 43273}, {38146, 47359}, {38176, 41990}, {48764, 48778}, {48765, 48779}
X(50802) = midpoint of X(i) and X(j) for these {i,j}: {1, 34648}, {4, 551}, {10, 31162}, {381, 946}, {547, 40273}, {549, 22793}, {671, 21636}, {1385, 15687}, {1699, 3817}, {3244, 34627}, {3543, 4297}, {3625, 34631}, {3655, 31673}, {3679, 4301}, {5901, 14893}, {6054, 11599}, {7982, 34641}, {9812, 10164}, {10706, 13605}, {10707, 21635}, {10711, 21630}, {24473, 31803}, {34638, 41869}
X(50802) = reflection of X(i) in X(j) for these {i,j}: {381, 12571}, {3655, 3636}, {3828, 5}, {6684, 547}, {9956, 11737}, {10171, 3817}, {12512, 549}, {19925, 381}, {31663, 10124}, {34718, 4691}, {43174, 3828}
X(50802) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3839, 34648}, {2, 9779, 30308}, {2, 30308, 3817}, {4, 38021, 551}, {376, 8227, 19883}, {946, 12571, 19925}, {1699, 7988, 9812}, {1699, 9779, 3817}, {1699, 30308, 2}, {3091, 3679, 38076}, {3524, 41869, 34638}, {3543, 25055, 4297}, {3545, 31162, 10}, {3616, 50687, 34628}, {3654, 19709, 10175}, {3655, 14269, 31673}, {3817, 10164, 7988}, {4301, 38076, 3679}, {7982, 38074, 34641}, {7988, 9812, 10164}, {9955, 18483, 1125}, {14269, 18493, 3655}, {18493, 31673, 3636}, {19862, 34638, 3524}
X(50803) lies on these lines: {2, 28164}, {4, 3828}, {5, 31666}, {10, 3839}, {30, 3634}, {355, 381}, {382, 38068}, {515, 5066}, {516, 3845}, {517, 3860}, {546, 28194}, {551, 3091}, {962, 38098}, {1125, 3545}, {1698, 34638}, {1699, 4669}, {3146, 19876}, {3241, 3854}, {3524, 31253}, {3543, 7989}, {3626, 31162}, {3627, 38083}, {3635, 34627}, {3636, 18480}, {3653, 5072}, {3679, 3832}, {3817, 7967}, {3830, 10175}, {3843, 43174}, {3850, 28204}, {3855, 38021}, {3857, 13464}, {3861, 28202}, {4297, 5071}, {4301, 38074}, {4691, 18483}, {4745, 5587}, {4746, 18357}, {5055, 19878}, {5493, 50689}, {5691, 19883}, {5886, 41150}, {6684, 15687}, {6744, 10895}, {7384, 41141}, {8703, 10172}, {9956, 14893}, {10109, 28160}, {10164, 15682}, {10171, 19709}, {11231, 33699}, {11539, 33697}, {11737, 28208}, {11812, 28168}, {12100, 28172}, {12101, 28150}, {13624, 47478}, {15705, 19872}, {19862, 34628}, {30315, 50688}, {31730, 38335}, {34379, 47354}, {34641, 37714}, {36990, 38089}, {36991, 38094}, {38146, 47353}
X(50803) = midpoint of X(i) and X(j) for these {i,j}: {4, 3828}, {381, 19925}, {1125, 34648}, {3543, 12512}, {3626, 31162}, {3635, 34627}, {6684, 15687}, {9956, 14893}
X(50803) = reflection of X(12571) in X(381)
X(50803) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 38076, 3828}, {1698, 50687, 34638}, {3545, 18492, 34648}, {3545, 34648, 1125}
X(50804) lies on these lines: {1, 15699}, {2, 38176}, {3, 34641}, {5, 34747}, {8, 3524}, {10, 34748}, {20, 28204}, {30, 3632}, {40, 15691}, {140, 3653}, {165, 952}, {355, 381}, {515, 15685}, {517, 15682}, {551, 5070}, {1385, 15721}, {1483, 19875}, {1698, 41984}, {2136, 3652}, {3090, 3241}, {3244, 5055}, {3534, 28236}, {3545, 20050}, {3576, 44580}, {3579, 20052}, {3621, 12699}, {3625, 15689}, {3626, 5054}, {3627, 5881}, {3633, 14892}, {3830, 28234}, {3839, 11278}, {3845, 37712}, {3861, 7982}, {4669, 15701}, {4678, 32900}, {4701, 18526}, {4745, 10246}, {4816, 34773}, {5066, 16200}, {5068, 10222}, {5071, 33179}, {5073, 28194}, {5690, 14891}, {5844, 12101}, {5882, 38066}, {5886, 10109}, {8148, 34648}, {9955, 20014}, {11531, 15687}, {11541, 28202}, {12245, 28208}, {12811, 38021}, {13607, 15694}, {15693, 38127}, {15713, 30392}, {18480, 20053}, {19709, 38155}, {22791, 41987}, {25439, 28453}, {30308, 38138}, {31162, 37705}, {32214, 44847}, {38083, 46935}, {44265, 47534}
X(50804) = midpoint of X(i) and X(j) for these {i,j}: {3621, 34627}, {20053, 34631}
X(50804) = reflection of X(i) in X(j) for these {i,j}: {3, 34641}, {381, 47745}, {3654, 4677}, {3655, 8}, {8148, 34648}, {11531, 15687}, {12699, 34627}, {18481, 34718}, {20049, 10222}, {31162, 37705}, {34631, 18480}, {34718, 3625}, {34747, 5}, {34748, 10}, {37727, 3679}, {44265, 47534}
X(50804) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3679, 37727, 3653}, {13607, 38098, 15694}, {20049, 38074, 10222}
X(50805) lies on these lines: {1, 5054}, {2, 5844}, {3, 3241}, {4, 20049}, {5, 31145}, {8, 5055}, {30, 145}, {40, 14093}, {355, 381}, {376, 1483}, {382, 7982}, {517, 3534}, {547, 10595}, {549, 12245}, {551, 3526}, {944, 15681}, {952, 3830}, {956, 28453}, {962, 15684}, {1000, 28465}, {1351, 9041}, {1385, 15700}, {1656, 3679}, {1657, 28194}, {3090, 38081}, {3244, 3655}, {3295, 28443}, {3524, 3623}, {3545, 3621}, {3576, 15716}, {3617, 15699}, {3622, 11539}, {3632, 18493}, {3633, 11278}, {3635, 15706}, {3653, 11362}, {3654, 10164}, {3839, 20014}, {3851, 5734}, {4301, 5076}, {4421, 22765}, {4669, 5886}, {4677, 5790}, {5070, 38022}, {5072, 16189}, {5079, 13464}, {5559, 31480}, {5603, 19709}, {5657, 15701}, {5690, 15694}, {5691, 35434}, {5697, 17637}, {5731, 15695}, {5882, 15696}, {5901, 15703}, {7967, 8703}, {7970, 48657}, {9053, 20423}, {9589, 49133}, {9655, 11280}, {10385, 37728}, {11001, 28212}, {11009, 11237}, {11194, 11849}, {11207, 11876}, {11208, 11875}, {11531, 28198}, {11898, 28538}, {12000, 16418}, {12001, 16417}, {12626, 20128}, {12653, 18499}, {12773, 25416}, {13846, 35810}, {13847, 35811}, {14269, 20050}, {15682, 28224}, {15685, 28174}, {15686, 20070}, {15689, 34632}, {15707, 20057}, {15723, 25055}, {16191, 30308}, {17612, 19706}, {18323, 47536}, {18357, 20053}, {18440, 49679}, {18543, 41575}, {20054, 38071}, {23960, 31160}, {24473, 25413}, {26726, 41711}, {28202, 49137}, {28208, 48661}, {28456, 37547}, {34698, 34749}, {34699, 34745}, {35381, 41150}, {37958, 47491}, {38138, 41106}, {39899, 49681}, {41985, 46931}, {44265, 47493}, {46933, 47599}, {46934, 47598}
X(50805) = midpoint of X(i) and X(j) for these {i,j}: {4, 20049}, {145, 34631}, {3633, 31162}, {7982, 34747}, {8148, 34748}, {20050, 34627}, {34710, 34743}
X(50805) = reflection of X(i) in X(j) for these {i,j}: {3, 3241}, {376, 1483}, {381, 1482}, {3655, 3244}, {3679, 10222}, {5790, 16200}, {8148, 34631}, {12245, 549}, {12645, 381}, {12702, 3655}, {15681, 944}, {15684, 962}, {18525, 31162}, {18526, 34748}, {20070, 15686}, {20128, 12626}, {25413, 24473}, {31145, 5}, {31160, 23960}, {31162, 11278}, {34627, 22791}, {34632, 34773}, {34641, 13464}, {34698, 34749}, {34718, 1}, {34745, 34699}, {34748, 145}, {44265, 47493}, {48657, 7970}
X(50805) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 34718, 5054}, {145, 8148, 18526}, {551, 38066, 3526}, {3633, 11278, 18525}, {3654, 10246, 15693}, {3655, 12702, 15688}, {3679, 9624, 38083}, {5690, 38314, 15694}, {18525, 31162, 38335}, {22791, 34627, 14269}, {34632, 34773, 15689}
X(50806) lies on these lines: {1, 14269}, {2, 28174}, {3, 28202}, {5, 38066}, {8, 38071}, {20, 38022}, {30, 3616}, {40, 15703}, {355, 381}, {376, 40273}, {382, 551}, {516, 15693}, {517, 19709}, {546, 3241}, {547, 962}, {549, 48661}, {944, 14893}, {952, 41099}, {1125, 15688}, {1385, 15684}, {1656, 28194}, {1657, 3653}, {1698, 5055}, {1699, 3830}, {3534, 5886}, {3543, 5901}, {3545, 3617}, {3576, 15685}, {3582, 37545}, {3623, 3839}, {3624, 15707}, {3654, 3817}, {3655, 18483}, {3679, 3851}, {3828, 5079}, {3843, 11522}, {3845, 5603}, {3850, 38074}, {3855, 31145}, {3858, 5734}, {4301, 5072}, {4654, 7743}, {4668, 8148}, {4677, 38140}, {5054, 12699}, {5066, 5790}, {5073, 9624}, {5550, 17504}, {5657, 10109}, {5731, 33699}, {6361, 11539}, {7991, 38083}, {8227, 15694}, {8703, 9812}, {9589, 46219}, {9778, 11812}, {9780, 47478}, {10248, 35404}, {10283, 12101}, {11001, 38028}, {11230, 15701}, {11238, 15934}, {12811, 38081}, {15681, 22793}, {15687, 38314}, {15689, 41869}, {15695, 28146}, {15697, 28182}, {15699, 34632}, {15700, 19883}, {15706, 31730}, {15713, 28216}, {18357, 20052}, {18480, 34748}, {18526, 34648}, {19708, 28178}, {19914, 38077}, {23046, 34627}, {28208, 35403}, {28465, 31671}, {29622, 36731}, {30389, 49134}, {34773, 50687}, {35272, 50397}, {38026, 38753}
X(50806) = midpoint of X(i) and X(j) for these {i,j}: {1698, 31162}, {20052, 34631}, {35403, 37624}
X(50806) = reflection of X(i) in X(j) for these {i,j}: {15694, 8227}, {19709, 30308}, {34718, 3617}
X(50806) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3545, 22791, 34718}, {3655, 18483, 38335}, {5055, 31162, 12702}, {9955, 31162, 5055}, {22793, 25055, 15681}
X(50807) lies on these lines: {1, 23046}, {2, 28146}, {4, 3653}, {5, 19876}, {30, 3624}, {40, 11737}, {355, 381}, {517, 41106}, {546, 38021}, {551, 3843}, {1125, 38335}, {1698, 14892}, {1699, 3654}, {3090, 28202}, {3545, 9780}, {3576, 12101}, {3622, 3655}, {3679, 3850}, {3817, 3830}, {3828, 5072}, {3832, 28204}, {3845, 5886}, {3851, 28194}, {3854, 38074}, {3856, 11522}, {3858, 37727}, {3859, 7982}, {3860, 38034}, {3861, 38022}, {4297, 35403}, {5055, 18483}, {5068, 38083}, {5071, 22793}, {5079, 38068}, {5881, 41991}, {7967, 9779}, {7987, 35404}, {7988, 8703}, {8227, 15687}, {10171, 15693}, {10248, 15702}, {11230, 15682}, {12512, 15723}, {14269, 15808}, {14893, 25055}, {15640, 17502}, {15684, 19883}, {15689, 19862}, {15698, 28154}, {15699, 41869}, {15701, 28150}, {15706, 19878}, {18480, 20057}, {18493, 34648}, {19709, 26446}, {19872, 45757}, {19875, 40273}, {31162, 38071}, {34595, 45759}, {34773, 41987}, {35242, 47599}, {38023, 48889}
X(50807) = midpoint of X(10248) and X(15702)
X(50807) = reflection of X(i) in X(j) for these {i,j}: {3655, 3622}, {19876, 5}
X(50807) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1699, 5066, 3654}, {3839, 9955, 3655}, {3845, 30308, 5886}
X(50808) lies on these lines: {1, 10304}, {2, 165}, {3, 551}, {4, 3828}, {5, 28202}, {7, 31508}, {8, 34628}, {10, 30}, {20, 3679}, {35, 3671}, {36, 4342}, {40, 376}, {46, 4314}, {55, 553}, {57, 10385}, {98, 1293}, {100, 10032}, {171, 4356}, {200, 43178}, {226, 4995}, {306, 4781}, {355, 15681}, {381, 6684}, {484, 4304}, {515, 3534}, {517, 3892}, {527, 4421}, {528, 13226}, {535, 13528}, {537, 30271}, {546, 31447}, {547, 22793}, {548, 5882}, {549, 946}, {550, 11362}, {631, 38021}, {726, 33706}, {901, 2688}, {902, 24177}, {952, 15690}, {962, 15692}, {966, 41456}, {991, 42042}, {1125, 3524}, {1155, 3058}, {1210, 37572}, {1385, 34200}, {1482, 14093}, {1657, 38066}, {1698, 3839}, {1742, 42043}, {1764, 42057}, {1770, 3584}, {2094, 7994}, {2100, 15159}, {2101, 15158}, {2482, 21636}, {2771, 4525}, {2784, 9881}, {2801, 5918}, {2938, 50118}, {2951, 6172}, {3090, 31425}, {3091, 19876}, {3098, 49505}, {3146, 9588}, {3158, 5850}, {3241, 3522}, {3244, 3655}, {3339, 15933}, {3474, 4654}, {3486, 41348}, {3509, 3950}, {3523, 9589}, {3528, 7982}, {3529, 38074}, {3543, 19875}, {3545, 3634}, {3550, 3663}, {3576, 19708}, {3578, 4061}, {3616, 15705}, {3624, 15708}, {3625, 15689}, {3626, 34627}, {3627, 31399}, {3635, 34631}, {3636, 15710}, {3748, 4031}, {3753, 17525}, {3830, 26446}, {3845, 10175}, {3911, 11238}, {3919, 44255}, {3929, 10860}, {3986, 37508}, {4082, 4427}, {4084, 37585}, {4114, 37703}, {4229, 41629}, {4292, 10056}, {4311, 11010}, {4312, 5281}, {4315, 5119}, {4349, 17594}, {4420, 16143}, {4677, 15697}, {4689, 37631}, {4691, 46333}, {4745, 5657}, {4785, 15599}, {4847, 49719}, {4848, 15338}, {5054, 12699}, {5055, 18483}, {5059, 37714}, {5066, 11231}, {5071, 12571}, {5128, 6738}, {5267, 35239}, {5298, 12053}, {5434, 37568}, {5476, 38118}, {5480, 38089}, {5537, 7411}, {5584, 16370}, {5587, 15682}, {5603, 15698}, {5690, 15686}, {5691, 15683}, {5698, 20103}, {5732, 28610}, {5759, 28609}, {5790, 15685}, {5805, 38094}, {5847, 43273}, {5881, 17538}, {5886, 15693}, {5901, 14891}, {6055, 11599}, {6173, 43151}, {6174, 21635}, {6745, 44447}, {7688, 21161}, {7753, 31396}, {7957, 24473}, {7964, 17613}, {7987, 20070}, {8227, 15702}, {8591, 9860}, {8616, 24175}, {8715, 37426}, {9143, 9904}, {9300, 31443}, {9441, 12194}, {9591, 37940}, {9616, 19054}, {9624, 10299}, {9740, 17132}, {9774, 28562}, {9780, 50687}, {9955, 11539}, {9956, 15687}, {10072, 10624}, {10124, 40273}, {10165, 12100}, {10172, 19709}, {10222, 33923}, {10310, 12511}, {10440, 15310}, {10443, 50115}, {10578, 43180}, {10710, 28346}, {10980, 43179}, {11112, 34618}, {11113, 34630}, {11160, 39878}, {11177, 13174}, {11220, 15104}, {11230, 11812}, {11278, 41982}, {11522, 15717}, {12101, 28182}, {12575, 15803}, {13624, 45759}, {13912, 35822}, {13975, 35823}, {14537, 31398}, {15064, 15726}, {15170, 21625}, {15178, 46853}, {15691, 47745}, {15694, 48661}, {15695, 28234}, {15707, 18493}, {15709, 19878}, {15711, 38028}, {15712, 38022}, {15713, 38034}, {15759, 17502}, {15808, 17504}, {16174, 38069}, {16226, 31757}, {17533, 50031}, {18788, 29574}, {19710, 28160}, {19722, 37078}, {21734, 30389}, {22266, 23046}, {28154, 33699}, {28168, 38112}, {28190, 38176}, {28538, 44882}, {28854, 29600}, {30315, 50689}, {31145, 50693}, {31793, 44663}, {31884, 47358}, {35578, 43173}, {35986, 41561}, {36698, 41141}, {37062, 48867}, {37416, 41140}, {37427, 45701}, {37540, 50068}, {37545, 40270}, {37619, 41430}, {38087, 48872}, {41338, 43175}, {41945, 49227}, {41946, 49226}, {42053, 43162}, {43172, 50116}, {48881, 49529}, {48897, 50587}, {48917, 50590}
X(50808) = midpoint of X(i) and X(j) for these {i,j}: {1, 34632}, {8, 34628}, {10, 34638}, {20, 3679}, {40, 376}, {165, 9778}, {355, 15681}, {551, 5493}, {2094, 7994}, {2100, 15159}, {2101, 15158}, {2951, 6172}, {3241, 7991}, {3534, 3654}, {3655, 12702}, {3928, 34607}, {5690, 15686}, {5691, 15683}, {6361, 31162}, {7957, 24473}, {8591, 9860}, {9143, 9904}, {11112, 34618}, {11113, 34630}, {11160, 39878}, {11177, 13174}, {11220, 15104}, {18481, 34718}, {34639, 34646}, {34701, 34744}, {34711, 34716}
X(50808) = reflection of X(i) in X(j) for these {i,j}: {4, 3828}, {376, 12512}, {381, 6684}, {549, 31663}, {551, 3}, {946, 549}, {1385, 34200}, {3244, 3655}, {3543, 19925}, {3625, 34718}, {3679, 43174}, {3817, 10164}, {4297, 376}, {4301, 551}, {4669, 3654}, {5901, 14891}, {6173, 43151}, {9812, 10171}, {10164, 165}, {10710, 28346}, {11599, 6055}, {15687, 9956}, {21635, 6174}, {21636, 2482}, {22793, 547}, {31162, 1125}, {34627, 3626}, {34631, 3635}, {34638, 31730}, {34641, 11362}, {34648, 10}, {38155, 5657}, {40273, 10124}
X(50808) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9812, 30308}, {2, 30308, 10171}, {3, 5493, 4301}, {4, 3828, 38076}, {40, 12512, 4297}, {549, 946, 19883}, {962, 15692, 25055}, {3474, 13405, 30424}, {3474, 35445, 13405}, {3524, 6361, 31162}, {3524, 31162, 1125}, {3543, 19875, 19925}, {3579, 31730, 10}, {3653, 13464, 551}, {4640, 49732, 5325}, {5325, 49732, 10}, {6361, 35242, 1125}, {10304, 34632, 1}, {12702, 15688, 3655}, {15689, 34718, 18481}, {16192, 25055, 15692}, {31162, 35242, 3524}
X(50809) lies on these lines: {1, 15710}, {2, 28174}, {4, 28202}, {30, 3617}, {40, 376}, {145, 15688}, {165, 15698}, {484, 10385}, {516, 41099}, {517, 19708}, {549, 20070}, {550, 31145}, {551, 10299}, {631, 11522}, {952, 15697}, {962, 15702}, {1698, 3545}, {3090, 5493}, {3146, 38066}, {3241, 3528}, {3524, 3579}, {3529, 3679}, {3533, 38021}, {3534, 28224}, {3622, 17504}, {3623, 10304}, {3654, 9778}, {3828, 3855}, {4668, 31730}, {4816, 34628}, {5071, 28198}, {5073, 38081}, {5603, 15719}, {5657, 15682}, {5690, 15683}, {5790, 15640}, {5844, 15695}, {7967, 8703}, {7991, 21735}, {8148, 45759}, {8193, 37948}, {9589, 38068}, {9952, 13199}, {10247, 15759}, {10283, 15716}, {10595, 15692}, {12645, 15691}, {14269, 46933}, {15693, 28212}, {15707, 46934}, {15708, 22791}, {15709, 19862}, {15714, 37624}, {15715, 31663}, {17538, 28204}, {19709, 28216}, {20052, 34718}, {26446, 41106}, {28232, 30308}, {31673, 35409}, {33703, 38074}, {38071, 46932}, {46930, 47478}
X(50809) = midpoint of X(i) and X(j) for these {i,j}: {3616, 34632}, {4816, 34628}
X(50809) = reflection of X(i) in X(j) for these {i,j}: {10595, 15692}, {20052, 34718}, {31162, 19862}, {34627, 4668}, {34631, 3623}, {37624, 15714}
X(50809) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3579, 34632, 3524}, {3654, 9778, 11001}, {10304, 12702, 34631}, {31663, 38314, 15715}, {31730, 34627, 46333}
X(50810) lies on these lines: {1, 3524}, {2, 392}, {3, 3241}, {4, 3679}, {5, 38066}, {8, 30}, {10, 3545}, {20, 28204}, {40, 376}, {55, 5427}, {57, 1000}, {104, 6244}, {140, 5734}, {145, 3579}, {165, 7967}, {186, 37546}, {329, 1145}, {355, 3543}, {381, 962}, {484, 3476}, {515, 4677}, {516, 4669}, {527, 12115}, {528, 5759}, {529, 37430}, {546, 38081}, {549, 1482}, {551, 631}, {553, 1056}, {599, 39898}, {938, 15170}, {946, 5071}, {952, 3534}, {958, 28461}, {1006, 4428}, {1058, 4848}, {1064, 42043}, {1071, 31797}, {1125, 15709}, {1159, 10578}, {1327, 35788}, {1328, 35789}, {1350, 9041}, {1385, 15692}, {1480, 32911}, {1483, 34200}, {1512, 31142}, {1621, 44455}, {1699, 38127}, {1708, 3488}, {1766, 37654}, {1788, 5697}, {2096, 28610}, {2098, 5298}, {2099, 4995}, {2183, 36916}, {2482, 7970}, {2771, 4661}, {2800, 5658}, {2802, 24477}, {2975, 35448}, {3058, 18391}, {3090, 3828}, {3146, 28202}, {3244, 15710}, {3245, 3474}, {3295, 15933}, {3416, 11180}, {3421, 17781}, {3428, 4421}, {3485, 3584}, {3486, 11010}, {3487, 5903}, {3522, 20049}, {3523, 3653}, {3525, 9588}, {3526, 38022}, {3528, 5882}, {3529, 5493}, {3533, 9624}, {3544, 31399}, {3576, 15698}, {3587, 3895}, {3616, 5054}, {3617, 3839}, {3621, 18481}, {3622, 11278}, {3623, 13624}, {3625, 34638}, {3626, 34648}, {3632, 31730}, {3651, 3913}, {3830, 28174}, {3845, 5790}, {3855, 38076}, {3871, 35239}, {3889, 40296}, {3919, 38053}, {4221, 41629}, {4293, 5183}, {4294, 41687}, {4295, 11237}, {4311, 41348}, {4317, 5559}, {4345, 15325}, {4654, 31397}, {4668, 31673}, {4678, 18480}, {4691, 18492}, {4745, 5587}, {5055, 9780}, {5056, 38083}, {5066, 38112}, {5067, 11522}, {5218, 25415}, {5273, 40587}, {5281, 50194}, {5303, 35251}, {5325, 9623}, {5434, 37567}, {5476, 38116}, {5480, 38087}, {5537, 6950}, {5550, 11539}, {5642, 7978}, {5714, 10039}, {5731, 5844}, {5758, 17532}, {5805, 38092}, {5846, 43273}, {5901, 15694}, {6055, 7983}, {6174, 10698}, {6684, 10595}, {6769, 50739}, {6776, 28538}, {6876, 8715}, {6940, 40726}, {6986, 37622}, {6990, 9710}, {7288, 30323}, {7397, 41140}, {7580, 38665}, {7681, 44847}, {7688, 25439}, {7987, 15715}, {8158, 16417}, {8193, 44837}, {9143, 12778}, {9779, 19709}, {9955, 46933}, {10164, 15719}, {10165, 11224}, {10175, 30308}, {10246, 12100}, {10247, 15693}, {10248, 14893}, {10283, 11812}, {10306, 16370}, {10310, 11194}, {10444, 50099}, {10519, 47358}, {10679, 28466}, {11111, 49163}, {11112, 34617}, {11113, 34629}, {11207, 11823}, {11208, 11822}, {11238, 30305}, {11239, 37562}, {11248, 17549}, {11249, 13587}, {11826, 34717}, {11827, 34700}, {12101, 38138}, {12246, 34630}, {12513, 37403}, {12536, 44238}, {12645, 15681}, {12703, 47357}, {13607, 16192}, {13634, 48856}, {14110, 34625}, {14269, 18357}, {14839, 33706}, {14923, 37585}, {15178, 15717}, {15640, 28146}, {15677, 16139}, {15683, 28208}, {15685, 28186}, {15687, 48661}, {15688, 20050}, {15689, 18526}, {15699, 18493}, {15700, 37624}, {15701, 38028}, {16236, 31508}, {16371, 22770}, {17310, 36698}, {17504, 20057}, {17561, 19860}, {19053, 35775}, {19054, 35774}, {19065, 35610}, {19066, 35611}, {19705, 34474}, {19710, 28224}, {19883, 31423}, {19925, 38098}, {20066, 35250}, {20067, 35249}, {24473, 31788}, {28150, 37712}, {28216, 33699}, {28458, 34605}, {28459, 34611}, {28647, 49178}, {29054, 50086}, {30147, 31669}, {31798, 37427}, {34618, 34720}, {34619, 44663}, {37416, 40891}, {37499, 50113}, {37939, 49553}, {41338, 48363}, {48881, 49690}, {48882, 50422}, {48897, 50575}, {48941, 50415}
X(50810) = midpoint of X(i) and X(j) for these {i,j}: {8, 34632}, {20, 31145}, {376, 12245}, {3543, 20070}, {3625, 34638}, {3632, 34628}, {3679, 7991}, {5493, 34641}, {6361, 34627}, {12645, 15681}, {12702, 34718}, {34618, 34720}, {34630, 34689}, {34711, 34744}
X(50810) = reflection of X(i) in X(j) for these {i,j}: {2, 3654}, {4, 3679}, {8, 34718}, {145, 3655}, {376, 40}, {381, 5690}, {551, 43174}, {944, 376}, {962, 381}, {1482, 549}, {1483, 34200}, {1699, 38127}, {3241, 3}, {3543, 355}, {3655, 3579}, {3679, 11362}, {4301, 3828}, {5603, 5657}, {5881, 34641}, {6361, 34632}, {7967, 165}, {7970, 2482}, {7978, 5642}, {7982, 551}, {7983, 6055}, {9143, 12778}, {9812, 5790}, {10698, 6174}, {10711, 1145}, {11180, 3416}, {11224, 10165}, {15677, 16139}, {16200, 10164}, {20049, 37727}, {20050, 34748}, {24473, 31788}, {31162, 10}, {34605, 28458}, {34611, 28459}, {34617, 11112}, {34627, 8}, {34628, 31730}, {34629, 11113}, {34631, 1}, {34632, 12702}, {34648, 3626}, {34747, 5882}, {34748, 34773}, {39898, 599}, {41869, 34648}, {48661, 15687}, {48941, 50415}, {50422, 48882}
X(50810) = anticomplement of X(3656)
X(50810) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3654, 5657}, {4, 3679, 38074}, {8, 12702, 6361}, {10, 31162, 3545}, {40, 12245, 944}, {145, 10304, 3655}, {549, 1482, 38314}, {946, 19875, 5071}, {962, 5690, 5818}, {3245, 12647, 3474}, {3524, 34631, 1}, {3579, 3655, 10304}, {3828, 4301, 38021}, {3828, 38021, 3090}, {5493, 5881, 3529}, {6684, 11531, 10595}, {6684, 25055, 15702}, {7982, 43174, 631}, {7991, 11362, 4}, {9588, 13464, 3525}, {10595, 15702, 25055}, {15688, 34748, 34773}, {28610, 37429, 2096}, {34632, 34718, 34627}
X(50811) lies on these lines: {1, 30}, {2, 515}, {3, 3679}, {4, 551}, {5, 3653}, {8, 10304}, {10, 3524}, {20, 3241}, {35, 22759}, {36, 5727}, {40, 376}, {57, 21578}, {63, 6224}, {80, 31231}, {98, 28560}, {140, 19876}, {145, 31730}, {165, 952}, {191, 28460}, {200, 10609}, {214, 10711}, {355, 549}, {381, 1385}, {382, 11522}, {516, 7967}, {517, 3534}, {518, 43273}, {527, 43161}, {528, 5732}, {529, 37428}, {535, 18446}, {537, 30273}, {542, 33535}, {546, 38022}, {547, 7989}, {550, 7991}, {553, 4293}, {599, 39885}, {631, 3828}, {632, 30315}, {671, 11710}, {730, 33706}, {946, 3543}, {956, 7688}, {962, 13607}, {993, 21161}, {1012, 4428}, {1071, 34620}, {1125, 3545}, {1158, 37299}, {1319, 3586}, {1350, 28538}, {1388, 9614}, {1420, 10072}, {1478, 13384}, {1482, 15681}, {1483, 11531}, {1490, 11113}, {1503, 47358}, {1657, 9589}, {1698, 5054}, {1699, 3830}, {1702, 41945}, {1703, 41946}, {1837, 5298}, {1992, 39870}, {2043, 36444}, {2044, 36462}, {2077, 4421}, {2093, 15326}, {2320, 31266}, {2482, 9864}, {2646, 9613}, {2771, 3899}, {2779, 23155}, {2796, 13172}, {2800, 10031}, {3090, 38076}, {3146, 13464}, {3149, 40726}, {3244, 6361}, {3304, 37411}, {3333, 3486}, {3339, 37739}, {3340, 4299}, {3361, 37730}, {3428, 30283}, {3476, 4304}, {3488, 4315}, {3522, 11362}, {3523, 38068}, {3526, 31666}, {3528, 34641}, {3529, 4301}, {3579, 3632}, {3582, 9581}, {3584, 3612}, {3600, 15933}, {3601, 10056}, {3616, 3839}, {3617, 15705}, {3622, 18483}, {3624, 5055}, {3626, 15710}, {3633, 4880}, {3634, 15709}, {3635, 46333}, {3651, 8666}, {3751, 11179}, {3817, 41099}, {3845, 5886}, {3869, 10032}, {3872, 49719}, {3877, 15678}, {3897, 6175}, {4034, 37508}, {4192, 31137}, {4302, 7962}, {4305, 10106}, {4312, 50194}, {4316, 25415}, {4317, 6869}, {4324, 30323}, {4333, 11009}, {4512, 17525}, {4668, 45759}, {4669, 5657}, {4745, 10164}, {4870, 9612}, {4995, 5252}, {5010, 37708}, {5059, 5734}, {5066, 7988}, {5071, 19883}, {5119, 7171}, {5219, 37525}, {5248, 28461}, {5250, 7701}, {5251, 18519}, {5259, 18761}, {5288, 35239}, {5450, 17549}, {5476, 38029}, {5480, 38023}, {5493, 17538}, {5563, 6985}, {5603, 15682}, {5642, 12368}, {5690, 16192}, {5693, 12680}, {5722, 13462}, {5790, 15693}, {5805, 38024}, {5818, 15702}, {5844, 15690}, {5901, 15687}, {5903, 13369}, {6054, 11711}, {6055, 13178}, {6174, 12751}, {6261, 11114}, {6326, 28459}, {6453, 31440}, {6684, 15692}, {6769, 34618}, {6796, 13587}, {7280, 37711}, {7397, 41141}, {7411, 38669}, {7415, 41629}, {7580, 31146}, {7753, 9619}, {7966, 10860}, {7972, 38761}, {8148, 32900}, {8235, 49735}, {8715, 37403}, {8726, 34746}, {9041, 44882}, {9140, 11709}, {9300, 9592}, {9582, 49232}, {9583, 32787}, {9615, 49601}, {9623, 49732}, {9625, 9909}, {9626, 14070}, {9668, 25405}, {9778, 15697}, {9780, 15708}, {9799, 50742}, {9812, 15640}, {9850, 9957}, {9860, 14830}, {9875, 11632}, {9880, 38220}, {9897, 38602}, {9904, 12898}, {9943, 34626}, {9955, 14269}, {9956, 15694}, {10247, 15685}, {10267, 28444}, {10269, 44425}, {10283, 28190}, {10303, 31399}, {10386, 30337}, {10444, 17378}, {10465, 48858}, {10698, 11274}, {10706, 11720}, {10707, 11715}, {10708, 11714}, {10709, 11700}, {10710, 11712}, {10716, 11713}, {10718, 12265}, {10726, 47115}, {10827, 37616}, {10864, 11111}, {10884, 17579}, {10902, 12114}, {10950, 15803}, {11012, 11194}, {11014, 12520}, {11015, 36846}, {11112, 12650}, {11171, 22650}, {11180, 49511}, {11224, 19710}, {11227, 19706}, {11230, 19709}, {11231, 15701}, {11236, 33597}, {11372, 43175}, {11500, 16371}, {11525, 17784}, {11539, 18357}, {11812, 38042}, {12100, 26446}, {12101, 38034}, {12248, 33337}, {12513, 37426}, {12645, 14093}, {12647, 35445}, {12675, 24473}, {13151, 41867}, {13253, 38753}, {13634, 48851}, {14110, 34740}, {14563, 21454}, {15338, 37738}, {15626, 19254}, {15684, 22793}, {15699, 34595}, {15704, 16189}, {15711, 38112}, {15712, 38081}, {15713, 38138}, {15715, 38098}, {15716, 38176}, {15719, 38155}, {15931, 22758}, {15935, 30350}, {16191, 28216}, {16475, 20423}, {16491, 31670}, {16496, 46264}, {17310, 37416}, {17504, 37705}, {17533, 18242}, {17556, 37837}, {17857, 34606}, {18421, 37728}, {18443, 28452}, {18493, 33697}, {20049, 50693}, {20076, 41863}, {21842, 50443}, {24608, 25935}, {24728, 28562}, {26321, 28443}, {26364, 45036}, {30503, 34612}, {31136, 37400}, {31156, 31435}, {31434, 37600}, {31662, 38140}, {31805, 34707}, {33179, 48661}, {34557, 35734}, {34625, 37427}, {34630, 34699}, {34690, 37531}, {35238, 48696}, {35243, 37546}, {35404, 40273}, {36698, 41140}, {37062, 48862}, {37356, 37719}, {37364, 37725}, {37406, 37720}, {37499, 50082}, {39874, 49505}, {47321, 47333}, {48881, 49681}, {48893, 50415}, {48905, 49465}, {48923, 50422}, {48937, 50421}
X(50811) = midpoint of X(i) and X(j) for these {i,j}: {1, 34628}, {20, 3241}, {145, 34632}, {376, 944}, {962, 15683}, {1482, 15681}, {1483, 15686}, {3244, 34638}, {3655, 18481}, {6361, 34631}, {7991, 34747}, {12680, 31165}, {12702, 34748}, {18526, 34718}, {34618, 34749}, {34630, 34699}, {34701, 34716}, {48923, 50422}
X(50811) = reflection of X(i) in X(j) for these {i,j}: {1, 3655}, {4, 551}, {40, 376}, {191, 28460}, {355, 549}, {376, 4297}, {381, 1385}, {671, 11710}, {1699, 10246}, {1992, 39870}, {3241, 5882}, {3543, 946}, {3576, 5731}, {3632, 34718}, {3633, 34748}, {3654, 8703}, {3655, 34773}, {3679, 3}, {3751, 11179}, {4677, 3654}, {5587, 3576}, {5690, 34200}, {5691, 381}, {5693, 31165}, {5790, 17502}, {5881, 3679}, {6054, 11711}, {6361, 34638}, {7701, 15677}, {7982, 3241}, {9140, 11709}, {9860, 14830}, {9864, 2482}, {9875, 11632}, {10698, 11274}, {10706, 11720}, {10707, 11715}, {10708, 11714}, {10709, 11700}, {10710, 11712}, {10711, 214}, {10716, 11713}, {10718, 12265}, {11180, 49511}, {11372, 47357}, {12368, 5642}, {12407, 9140}, {12751, 6174}, {13178, 6055}, {15684, 22793}, {15687, 5901}, {16200, 7967}, {22650, 11171}, {24473, 12675}, {31142, 37611}, {31145, 11362}, {31162, 1}, {31165, 31786}, {34627, 10}, {34628, 18481}, {34631, 3244}, {34632, 31730}, {34641, 43174}, {34648, 1125}, {34718, 3579}, {34747, 37727}, {35404, 40273}, {37625, 24473}, {37712, 26446}, {38140, 31662}, {39885, 599}, {41869, 31162}, {47321, 47333}, {47357, 43175}, {48937, 50421}, {50415, 48893}
X(50811) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5441, 41864}, {4, 551, 38021}, {20, 5882, 7982}, {165, 4677, 3654}, {355, 549, 19875}, {355, 7987, 31423}, {381, 1385, 25055}, {381, 25055, 8227}, {382, 15178, 11522}, {549, 19875, 31423}, {550, 37727, 7991}, {551, 38021, 9624}, {631, 38074, 3828}, {944, 4297, 40}, {1125, 34648, 3545}, {1319, 3586, 37704}, {1385, 5691, 8227}, {1657, 10222, 9589}, {3476, 4304, 31393}, {3486, 4311, 3333}, {3524, 34627, 10}, {3543, 38314, 946}, {3545, 34648, 18492}, {3579, 18526, 3632}, {3654, 8703, 165}, {3655, 34628, 31162}, {3679, 9588, 38066}, {3845, 5886, 30308}, {5691, 25055, 381}, {7966, 10860, 12703}, {7987, 19875, 549}, {12245, 12512, 40}, {12680, 31786, 5693}, {13624, 18525, 1698}, {15326, 37740, 2093}, {15688, 18526, 34718}, {15688, 34718, 3579}, {15689, 34748, 12702}, {18481, 34773, 1}, {19883, 19925, 5071}
X(50812) lies on these lines: {1, 15688}, {2, 28150}, {3, 28202}, {30, 1698}, {40, 376}, {78, 10032}, {165, 3534}, {355, 15691}, {381, 16192}, {382, 19876}, {515, 15697}, {516, 19708}, {517, 15695}, {548, 7982}, {550, 3679}, {551, 3528}, {1125, 15710}, {1699, 12100}, {3146, 38068}, {3522, 5734}, {3524, 19862}, {3529, 3828}, {3543, 31423}, {3545, 31253}, {3576, 3656}, {3579, 4668}, {3616, 10304}, {3623, 34632}, {3624, 17504}, {3653, 9589}, {3654, 15690}, {3817, 15719}, {4816, 18481}, {5073, 38083}, {5587, 11001}, {5691, 15686}, {5881, 50693}, {5886, 15759}, {6684, 15683}, {7987, 14093}, {7988, 15701}, {7989, 15684}, {8227, 15692}, {9588, 12103}, {9624, 21735}, {9778, 16200}, {9955, 15706}, {10164, 15682}, {10175, 15640}, {11230, 15716}, {11522, 46853}, {12699, 45759}, {15673, 38052}, {15681, 19875}, {15693, 28146}, {15696, 28204}, {15700, 22793}, {15707, 34595}, {15708, 18483}, {15711, 28178}, {15713, 28182}, {15715, 19883}, {19709, 28154}, {19710, 26446}, {19872, 38071}, {22791, 41982}, {25055, 34200}, {28158, 41099}, {30315, 49136}, {33703, 38076}, {34648, 46333}, {37727, 41981}, {38028, 46332}
X(50812) = midpoint of X(i) and X(j) for these {i,j}: {3623, 34632}, {4668, 34628}, {19862, 34638}
X(50812) = reflection of X(i) in X(j) for these {i,j}: {7987, 14093}, {8227, 15692}, {30308, 15693}, {31162, 3616}
X(50812) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3524, 34638, 41869}, {3579, 15689, 34628}, {10304, 31730, 31162}, {15681, 31663, 19875}
X(50813) lies on these lines: {2, 28146}, {3, 38022}, {4, 19876}, {8, 15689}, {10, 46333}, {20, 38074}, {30, 9780}, {40, 376}, {165, 11001}, {516, 15698}, {548, 3241}, {551, 21735}, {946, 15715}, {962, 34200}, {3522, 10222}, {3523, 28202}, {3524, 3624}, {3528, 28194}, {3534, 5657}, {3543, 31663}, {3545, 34638}, {3579, 4678}, {3616, 45759}, {3622, 3656}, {3623, 35418}, {3653, 21734}, {3654, 15697}, {3679, 17538}, {3828, 33703}, {5550, 15706}, {5603, 19708}, {5731, 15695}, {5818, 15683}, {7718, 35489}, {8148, 15688}, {8703, 9778}, {9779, 11812}, {9812, 15693}, {10164, 41099}, {10248, 15703}, {10299, 38021}, {12103, 38066}, {12699, 15705}, {14093, 38314}, {14891, 48661}, {15701, 28178}, {15702, 16192}, {15709, 41869}, {15710, 15808}, {15718, 40273}, {15721, 22793}, {17578, 38083}, {19877, 38335}, {28150, 41106}, {28204, 50693}, {31425, 38076}, {31447, 49140}
X(50813) = midpoint of X(20057) and X(34632)
X(50813) = reflection of X(i) in X(j) for these {i,j}: {4, 19876}, {10248, 15703}, {15702, 16192}, {31162, 15808}, {34627, 4678}
X(50813) = {X(34638),X(35242)}-harmonic conjugate of X(3545)
X(50814) lies on these lines: {1, 15705}, {2, 28228}, {5, 3828}, {8, 34638}, {10, 3839}, {20, 34641}, {30, 3626}, {40, 376}, {515, 19710}, {516, 3654}, {517, 12100}, {551, 3523}, {553, 5183}, {946, 15703}, {1125, 3656}, {1657, 11362}, {3146, 3679}, {3241, 21734}, {3244, 10304}, {3245, 13405}, {3522, 34747}, {3524, 3636}, {3525, 4301}, {3534, 28236}, {3543, 38098}, {3579, 3635}, {3625, 34628}, {3633, 35418}, {3634, 31162}, {3845, 28232}, {3854, 9589}, {3860, 28174}, {4669, 28164}, {4677, 9778}, {4691, 6361}, {4701, 31730}, {4746, 34627}, {5657, 41106}, {5690, 35404}, {6684, 10124}, {8703, 28234}, {9588, 46936}, {9955, 45757}, {10032, 12527}, {10165, 15722}, {10171, 28212}, {11278, 17504}, {11531, 15692}, {12103, 28204}, {12108, 13464}, {12571, 19875}, {13607, 34200}, {14891, 33179}, {14893, 19925}, {15681, 47745}, {15682, 38155}, {15698, 16200}, {15708, 15808}, {31253, 47599}, {31447, 38022}, {31797, 44663}, {33699, 38176}, {34631, 35242}, {37568, 41547}, {38068, 46219}
X(50814) = midpoint of X(i) and X(j) for these {i,j}: {8, 34638}, {10, 34632}, {20, 34641}, {551, 7991}, {3625, 34628}, {3679, 5493}, {6361, 34648}, {15681, 47745}, {31730, 34718}, {34639, 34744}, {34646, 34711}
X(50814) = reflection of X(i) in X(j) for these {i,j}: {3828, 43174}, {4701, 34718}, {4745, 3654}, {13607, 34200}, {31162, 3634}, {33179, 14891}, {34627, 4746}, {34648, 4691}
X(50814) = {X(3654),X(3830)}-harmonic conjugate of X(38127)
X(50815) lies on these lines: {1, 34638}, {2, 28164}, {3, 3828}, {10, 10304}, {20, 551}, {30, 1125}, {40, 376}, {165, 4669}, {355, 14093}, {515, 4745}, {516, 3534}, {517, 15690}, {548, 28204}, {549, 19925}, {550, 10222}, {553, 15326}, {631, 38076}, {946, 15681}, {1385, 15686}, {1657, 3653}, {1698, 15705}, {2796, 38738}, {3241, 5493}, {3244, 34632}, {3522, 3679}, {3524, 3634}, {3529, 38021}, {3543, 7987}, {3545, 19878}, {3576, 11001}, {3579, 4701}, {3624, 50687}, {3626, 15688}, {3635, 3655}, {3636, 31162}, {3654, 15695}, {3817, 15682}, {3830, 10165}, {3839, 19862}, {3845, 10171}, {4301, 17538}, {4315, 10385}, {4668, 35418}, {4691, 34627}, {5054, 31253}, {5066, 28168}, {5587, 15698}, {5603, 41150}, {5691, 15692}, {5731, 11224}, {5882, 15696}, {5886, 15685}, {6684, 28208}, {7989, 15721}, {9583, 43256}, {9952, 38759}, {9956, 14891}, {10164, 19708}, {10172, 11812}, {10175, 15693}, {11194, 12511}, {11230, 33699}, {11231, 15711}, {12100, 28160}, {12103, 13464}, {15640, 30308}, {15678, 40998}, {15683, 25055}, {15691, 28198}, {15699, 33697}, {15709, 18492}, {15712, 38083}, {15713, 38140}, {15715, 31423}, {15717, 19876}, {15759, 28186}, {16138, 28460}, {16858, 35202}, {17504, 18480}, {19710, 28150}, {21735, 38074}, {22793, 44903}, {28182, 31662}, {28534, 43181}, {31447, 38081}, {31666, 38022}, {31805, 44663}, {34379, 43273}, {37062, 48865}, {37416, 41141}, {38023, 48872}, {41869, 46333}
X(50815) = midpoint of X(i) and X(j) for these {i,j}: {1, 34638}, {10, 34628}, {20, 551}, {376, 4297}, {946, 15681}, {1385, 15686}, {3241, 5493}, {3244, 34632}, {3655, 31730}, {22793, 44903}, {34639, 34716}, {34646, 34701}
X(50815) = reflection of X(i) in X(j) for these {i,j}: {3543, 12571}, {3635, 3655}, {3828, 3}, {6684, 34200}, {9956, 14891}, {10171, 17502}, {12512, 376}, {19925, 549}, {31162, 3636}, {34627, 4691}, {34648, 3634}
X(50815) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3524, 34648, 3634}, {3543, 7987, 19883}, {3543, 19883, 12571}, {3655, 15689, 31730}, {10304, 34628, 10}
X(50816) lies on these lines: {2, 28158}, {20, 3828}, {30, 3634}, {40, 376}, {165, 4745}, {515, 15690}, {516, 8703}, {548, 15178}, {549, 12571}, {550, 38081}, {551, 3522}, {946, 14093}, {1125, 10304}, {1657, 38068}, {2796, 38747}, {3524, 19878}, {3529, 38076}, {3534, 26446}, {3576, 41150}, {3579, 4746}, {3626, 34628}, {3635, 34632}, {3636, 3656}, {3679, 50693}, {3817, 15698}, {3839, 31253}, {4691, 15689}, {5059, 19876}, {5493, 16189}, {6684, 15686}, {10164, 11001}, {10171, 15693}, {10172, 33699}, {10175, 15685}, {10247, 15695}, {11812, 28154}, {12100, 28150}, {15681, 19925}, {15683, 16192}, {15691, 31663}, {15696, 43174}, {15705, 19862}, {15710, 41869}, {15714, 22793}, {15759, 28146}, {17504, 18483}, {21735, 38021}, {28178, 46332}, {28202, 33923}, {28204, 44245}, {34200, 40273}, {34648, 35242}, {38089, 48872}
X(50816) = midpoint of X(i) and X(j) for these {i,j}: {20, 3828}, {376, 12512}, {1125, 34638}, {3626, 34628}, {3635, 34632}, {6684, 15686}, {15681, 19925}, {15691, 31663}
X(50816) = reflection of X(12571) in X(549)
X(50816) = {X(10304),X(34638)}-harmonic conjugate of X(1125)
X(50817) lies on these lines: {1, 5054}, {2, 16200}, {3, 34747}, {4, 34641}, {5, 3656}, {8, 3839}, {10, 34631}, {30, 3632}, {40, 376}, {145, 15705}, {355, 14893}, {381, 11531}, {517, 3830}, {551, 3525}, {952, 19710}, {1385, 15718}, {1482, 15703}, {1657, 7991}, {1698, 47599}, {1699, 3860}, {1749, 5119}, {3146, 5881}, {3241, 3523}, {3244, 3524}, {3543, 47745}, {3545, 3626}, {3576, 3654}, {3579, 34748}, {3621, 34632}, {3625, 34627}, {3633, 3655}, {3636, 15709}, {3653, 9588}, {3828, 9624}, {3929, 12703}, {4301, 38074}, {4654, 12647}, {4668, 8148}, {4669, 5587}, {4701, 34648}, {4745, 5603}, {4816, 12699}, {5055, 11278}, {5071, 38098}, {5559, 11518}, {5690, 10124}, {5691, 35404}, {5790, 30308}, {5882, 20049}, {10222, 38066}, {10246, 15722}, {10304, 20050}, {11001, 28236}, {11230, 16191}, {11238, 36920}, {12645, 28198}, {12702, 34628}, {13464, 46936}, {13607, 15692}, {14923, 31938}, {15640, 28232}, {15682, 28228}, {15693, 30392}, {15694, 33179}, {15708, 20057}, {16189, 19876}, {19709, 38176}, {20052, 31673}, {20053, 31730}, {21161, 25439}, {28202, 49134}, {31423, 38314}, {33923, 37727}, {38155, 41099}
X(50817) = midpoint of X(3621) and X(34632)
X(50817) = reflection of X(i) in X(j) for these {i,j}: {1, 34718}, {4, 34641}, {3241, 11362}, {3543, 47745}, {3633, 3655}, {5881, 31145}, {7982, 3679}, {11531, 381}, {20049, 5882}, {31162, 8}, {34627, 3625}, {34628, 12702}, {34631, 10}, {34648, 4701}, {34747, 3}, {34748, 3579}, {41869, 34627}
X(50817) = {X(3679),X(7982)}-harmonic conjugate of X(38021)
X(50818) lies on these lines: {1, 3545}, {2, 952}, {3, 31145}, {4, 1392}, {8, 3524}, {10, 15709}, {20, 20049}, {30, 145}, {40, 376}, {104, 4421}, {355, 5071}, {381, 1483}, {497, 7972}, {499, 43734}, {515, 11224}, {517, 11001}, {528, 36996}, {547, 37624}, {549, 12645}, {551, 3090}, {553, 11041}, {631, 3679}, {956, 21161}, {962, 28208}, {1000, 3065}, {1056, 37740}, {1058, 37738}, {1317, 10711}, {1327, 35810}, {1328, 35811}, {1385, 15702}, {1482, 3543}, {3242, 11180}, {3244, 31162}, {3295, 28461}, {3523, 38066}, {3525, 3653}, {3526, 38081}, {3529, 28194}, {3533, 3828}, {3534, 5844}, {3576, 4669}, {3579, 20053}, {3616, 32900}, {3617, 5054}, {3621, 10304}, {3622, 5055}, {3623, 3839}, {3632, 15710}, {3633, 6361}, {3635, 34648}, {3654, 5731}, {3830, 28224}, {3845, 10247}, {3855, 38021}, {3929, 7966}, {4677, 5657}, {4678, 15708}, {5056, 38022}, {5067, 15178}, {5274, 12735}, {5603, 28236}, {5690, 15692}, {5818, 13607}, {6776, 9041}, {6873, 15888}, {6876, 12513}, {6896, 37724}, {6950, 38669}, {7397, 17310}, {7982, 33703}, {8164, 37708}, {8192, 44837}, {9053, 43273}, {9143, 12898}, {9624, 38076}, {9798, 37939}, {9897, 10589}, {10056, 37707}, {10072, 37706}, {10283, 19709}, {10299, 34641}, {10785, 34717}, {10786, 34700}, {11194, 11491}, {11207, 11844}, {11208, 11843}, {11237, 37734}, {11274, 12751}, {11362, 21735}, {11539, 46933}, {12248, 20075}, {12702, 20014}, {15640, 28186}, {15677, 19919}, {15681, 20070}, {15685, 28212}, {15688, 20054}, {15699, 46934}, {15701, 38112}, {15705, 20052}, {15933, 37739}, {16202, 16858}, {16203, 36006}, {18480, 20057}, {18481, 20050}, {19875, 47745}, {22791, 50687}, {28202, 49138}, {31423, 38098}, {34617, 34749}, {34629, 34699}, {36698, 40891}, {37711, 47743}, {37907, 47476}, {46931, 47598}
X(50818) = midpoint of X(i) and X(j) for these {i,j}: {20, 20049}, {3633, 34628}, {18526, 34748}, {20050, 34632}
X(50818) = reflection of X(i) in X(j) for these {i,j}: {4, 3241}, {8, 3655}, {145, 34748}, {376, 944}, {381, 1483}, {3241, 37727}, {3543, 1482}, {3621, 34718}, {3679, 5882}, {5881, 551}, {6361, 34628}, {9143, 12898}, {10711, 1317}, {11180, 3242}, {12245, 376}, {12645, 549}, {12751, 11274}, {20070, 15681}, {31145, 3}, {31162, 3244}, {34617, 34749}, {34627, 1}, {34629, 34699}, {34631, 145}, {34632, 18481}, {34648, 3635}, {34718, 34773}
X(50818) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 34627, 3545}, {8, 3655, 3524}, {355, 38314, 5071}, {551, 5881, 38074}, {551, 38074, 3090}, {3621, 10304, 34718}, {3654, 5731, 19708}, {3679, 30389, 38068}, {6361, 34628, 46333}, {34718, 34773, 10304}
X(50819) lies on these lines: {2, 17502}, {3, 38074}, {8, 15688}, {10, 15710}, {20, 3656}, {30, 3616}, {40, 376}, {515, 19708}, {517, 15697}, {550, 3241}, {551, 3529}, {952, 15695}, {962, 15686}, {1385, 15683}, {1482, 15691}, {1698, 3524}, {3146, 3653}, {3522, 28204}, {3528, 3679}, {3533, 38076}, {3534, 5731}, {3545, 19862}, {3576, 15682}, {3579, 20052}, {3617, 10304}, {3623, 3655}, {3828, 10299}, {3839, 13624}, {5071, 7987}, {5073, 38022}, {5550, 14269}, {5587, 15719}, {5603, 11001}, {5657, 8703}, {5691, 15702}, {5790, 15759}, {5818, 15692}, {5886, 15640}, {9778, 15690}, {9779, 33699}, {9780, 17504}, {9812, 15685}, {10165, 41106}, {10246, 19710}, {10385, 21578}, {15681, 38314}, {15689, 34632}, {15693, 28186}, {15706, 18357}, {15707, 19877}, {15708, 18480}, {15709, 31253}, {15715, 19875}, {15716, 38042}, {16189, 17538}, {17578, 31666}, {18525, 45759}, {19709, 28190}, {28164, 41099}, {28172, 30308}, {30389, 49138}, {31162, 46333}, {31730, 34631}, {33703, 38021}, {33923, 38066}, {37705, 41982}, {38112, 46332}
X(50819) = midpoint of X(1698) and X(34628)
X(50819) = reflection of X(i) in X(j) for these {i,j}: {3623, 3655}, {5071, 7987}, {5818, 15692}, {34627, 3617}, {34648, 31253}
X(50819) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10304, 18481, 34627}, {15689, 34773, 34632}
X(50820) lies on these lines: {1, 15689}, {2, 28172}, {3, 19876}, {20, 38021}, {30, 3624}, {40, 376}, {165, 15695}, {548, 3679}, {550, 3656}, {551, 17538}, {1125, 46333}, {1698, 45759}, {1699, 19710}, {3524, 18492}, {3534, 3576}, {3617, 35418}, {3622, 31162}, {3646, 15677}, {3653, 12103}, {3828, 21735}, {5587, 19708}, {5691, 34200}, {7713, 35489}, {7982, 15696}, {7987, 15681}, {7989, 15700}, {8227, 15683}, {8703, 26446}, {9617, 32787}, {9780, 10304}, {10299, 38076}, {14093, 19875}, {15685, 17502}, {15686, 25055}, {15688, 18525}, {15690, 16200}, {15697, 28232}, {15698, 28164}, {15701, 28168}, {15705, 31673}, {15707, 33697}, {15710, 34648}, {15715, 19925}, {15808, 41869}, {16192, 28208}, {19872, 41983}, {20057, 31730}, {21734, 38068}, {28194, 50693}, {28202, 30389}, {31425, 38074}, {34595, 38335}
X(50820) = reflection of X(i) in X(j) for these {i,j}: {7989, 15700}, {19876, 3}, {31162, 3622}
X(50820) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {15685, 17502, 30308}, {15688, 34628, 35242}
X(50821) lies on these lines: {1, 5054}, {2, 392}, {3, 3679}, {4, 28202}, {5, 3828}, {8, 3524}, {10, 30}, {20, 38074}, {35, 28443}, {40, 381}, {46, 11237}, {65, 3584}, {72, 13145}, {100, 21161}, {140, 551}, {145, 15708}, {165, 3534}, {182, 28538}, {210, 2771}, {355, 376}, {495, 553}, {498, 50193}, {500, 3214}, {515, 4745}, {516, 3845}, {519, 549}, {528, 12619}, {535, 10225}, {546, 5493}, {547, 946}, {550, 38081}, {572, 50082}, {631, 3241}, {632, 13464}, {942, 10056}, {944, 15692}, {952, 4669}, {962, 5071}, {993, 15813}, {1125, 11278}, {1210, 15170}, {1350, 38087}, {1386, 10168}, {1480, 37679}, {1482, 15694}, {1656, 7991}, {1657, 37714}, {1698, 5055}, {1699, 19709}, {1737, 3058}, {1788, 5045}, {2093, 31479}, {2550, 18407}, {3017, 4646}, {3057, 3582}, {3085, 31794}, {3219, 10711}, {3245, 17605}, {3359, 3929}, {3416, 11179}, {3452, 12611}, {3523, 31145}, {3526, 7982}, {3530, 5882}, {3533, 5734}, {3543, 5818}, {3545, 9780}, {3564, 50781}, {3576, 4677}, {3616, 15709}, {3617, 10304}, {3624, 8148}, {3625, 41983}, {3626, 17504}, {3628, 4301}, {3632, 15707}, {3634, 15699}, {3689, 13151}, {3698, 37585}, {3817, 10109}, {3830, 5587}, {3839, 6361}, {3844, 11178}, {3851, 9589}, {3860, 28216}, {3968, 44257}, {3983, 40263}, {4297, 34200}, {4304, 11545}, {4420, 33858}, {4421, 28466}, {4423, 44455}, {4428, 6883}, {4654, 31434}, {4662, 13369}, {4668, 15706}, {4678, 15705}, {4691, 37705}, {4870, 5903}, {4995, 24929}, {5044, 37828}, {5066, 10175}, {5070, 11522}, {5072, 30315}, {5085, 50783}, {5119, 11238}, {5122, 5252}, {5126, 12647}, {5128, 9654}, {5183, 7951}, {5251, 28453}, {5260, 28461}, {5298, 24928}, {5432, 50194}, {5434, 10039}, {5453, 50587}, {5476, 38167}, {5537, 7489}, {5642, 11699}, {5691, 15681}, {5694, 31788}, {5722, 10385}, {5726, 18541}, {5731, 15698}, {5732, 38097}, {5759, 38092}, {5812, 50741}, {5837, 47742}, {5844, 10165}, {5885, 24473}, {5901, 10124}, {6174, 22935}, {6175, 16139}, {6427, 31440}, {7688, 18524}, {7967, 15719}, {7987, 12645}, {8227, 15703}, {8983, 43211}, {9140, 12778}, {9300, 31398}, {9578, 31776}, {9591, 37956}, {9624, 46219}, {9626, 34006}, {9708, 35238}, {9709, 35239}, {9710, 37356}, {9711, 37406}, {9778, 15682}, {9812, 41106}, {9860, 48657}, {9864, 14830}, {9881, 11632}, {9940, 34619}, {9947, 37427}, {9957, 10072}, {10172, 28228}, {10199, 10284}, {10245, 34712}, {10246, 15701}, {10257, 47593}, {10306, 16857}, {10310, 28444}, {10916, 32157}, {11001, 28168}, {11010, 17606}, {11024, 50727}, {11171, 22697}, {11194, 32612}, {11236, 26921}, {11239, 13373}, {11248, 16418}, {11249, 16417}, {11518, 31480}, {11530, 31494}, {11531, 15723}, {11698, 15481}, {11724, 22247}, {11737, 40273}, {12101, 28178}, {12245, 15702}, {12261, 45311}, {12331, 15931}, {12512, 15686}, {12607, 44222}, {13846, 35774}, {13847, 35775}, {13971, 43212}, {13973, 31439}, {14093, 16192}, {14269, 41869}, {14891, 47745}, {15687, 19925}, {15688, 18525}, {15690, 28186}, {15711, 28236}, {15713, 28234}, {15720, 34747}, {15759, 28224}, {15764, 34557}, {15765, 36458}, {15908, 44847}, {16004, 18250}, {16174, 38084}, {16370, 26285}, {16371, 26286}, {17549, 26086}, {17757, 17781}, {18236, 31937}, {18395, 37568}, {18483, 38071}, {18492, 38335}, {18583, 38089}, {18585, 36440}, {19710, 28164}, {19862, 47598}, {20423, 38047}, {21031, 37401}, {21077, 49107}, {22266, 45757}, {22332, 31444}, {22792, 40256}, {24466, 38099}, {26487, 34744}, {26492, 34711}, {28150, 33699}, {28458, 34606}, {28459, 34612}, {28460, 47033}, {29010, 50096}, {30264, 38100}, {31165, 37562}, {31394, 41310}, {31395, 41311}, {31758, 31840}, {31837, 35004}, {34339, 45701}, {34634, 43934}, {34790, 40296}, {35597, 37291}, {35822, 49227}, {35823, 49226}, {36920, 37525}, {37600, 41684}, {37619, 50104}, {38064, 47356}, {38067, 47357}, {38116, 47359}, {41945, 49602}, {41946, 49601}, {42042, 50317}, {48882, 50415}
X(50821) = midpoint of X(i) and X(j) for these {i,j}: {1, 34718}, {2, 3654}, {3, 3679}, {8, 3655}, {40, 381}, {165, 5790}, {355, 376}, {549, 5690}, {551, 11362}, {3416, 11179}, {3632, 34748}, {3828, 43174}, {5657, 26446}, {5691, 15681}, {5882, 34641}, {6175, 16139}, {9140, 12778}, {9860, 48657}, {9864, 14830}, {9881, 11632}, {10164, 38127}, {10711, 12515}, {11171, 22697}, {12699, 34632}, {12702, 31162}, {18481, 34627}, {18525, 34628}, {28458, 34606}, {28459, 34612}, {28460, 47033}, {31145, 37727}, {31165, 37562}, {31673, 34638}, {31730, 34648}, {48882, 50415}
X(50821) = reflection of X(i) in X(j) for these {i,j}: {5, 3828}, {376, 31663}, {381, 9956}, {549, 6684}, {551, 140}, {946, 547}, {1385, 549}, {1386, 10168}, {3241, 15178}, {3655, 13624}, {4297, 34200}, {5901, 10124}, {7967, 31662}, {10222, 551}, {11178, 3844}, {11230, 11231}, {11231, 26446}, {11699, 5642}, {11724, 22247}, {12261, 45311}, {15686, 12512}, {15687, 19925}, {17502, 10164}, {22793, 381}, {22935, 6174}, {24473, 5885}, {31162, 9955}, {31840, 31758}, {33697, 34648}, {34648, 18357}, {34748, 32900}, {38034, 10172}, {38140, 38042}, {38176, 38112}, {40273, 11737}
X(50821) = complement of X(3656)
X(50821) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5657, 3654}, {3, 38066, 3679}, {5, 3828, 38083}, {8, 3524, 3655}, {10, 3579, 18480}, {10, 31730, 18357}, {40, 7989, 48661}, {40, 9956, 22793}, {40, 19875, 381}, {140, 11362, 10222}, {381, 19875, 9956}, {551, 38068, 140}, {631, 3241, 3653}, {1482, 15694, 25055}, {1698, 12702, 9955}, {1698, 31162, 5055}, {3241, 3653, 15178}, {3524, 3655, 13624}, {3530, 5882, 31666}, {3545, 34632, 12699}, {3579, 33697, 31730}, {3617, 10304, 34627}, {3654, 26446, 2}, {4421, 28466, 32613}, {5054, 34718, 1}, {5055, 12702, 31162}, {5055, 31162, 9955}, {5493, 31399, 546}, {5690, 6684, 1385}, {5901, 10124, 19883}, {7991, 19876, 38021}, {9780, 34632, 3545}, {10304, 34627, 18481}, {11362, 38068, 551}, {12245, 15702, 38314}, {15688, 18525, 34628}, {15709, 34631, 3616}, {18357, 31730, 33697}, {18357, 33697, 18480}, {19876, 38021, 1656}, {25055, 31423, 15694}, {34628, 35242, 15688}
X(50822) lies on these lines: {5, 38066}, {8, 17504}, {10, 38071}, {30, 3617}, {40, 35404}, {355, 44903}, {519, 549}, {550, 3679}, {632, 16189}, {952, 15711}, {1698, 3656}, {3241, 14869}, {3524, 20052}, {3530, 31145}, {3564, 50782}, {3616, 11539}, {3621, 15707}, {3623, 5054}, {3627, 5493}, {3654, 3845}, {3655, 4816}, {3858, 28194}, {4668, 45759}, {4678, 15688}, {4745, 28150}, {5657, 8703}, {5790, 33699}, {5844, 15713}, {7967, 44580}, {8148, 47599}, {10124, 12245}, {10247, 11540}, {12645, 14891}, {12702, 23046}, {15720, 20049}, {19710, 28160}, {28204, 46853}, {34631, 47598}, {34748, 41983}, {46933, 47478}
X(50822) = midpoint of X(i) and X(j) for these {i,j}: {3616, 34718}, {3655, 4816}
X(50822) = {X(3654),X(38112)}-harmonic conjugate of X(3845)
X(50823) lies on these lines: {1, 11539}, {2, 5844}, {3, 31145}, {5, 3656}, {8, 30}, {10, 15699}, {40, 15686}, {55, 28463}, {140, 3241}, {145, 5054}, {165, 952}, {355, 15687}, {376, 12645}, {381, 12245}, {515, 19710}, {517, 3845}, {519, 549}, {546, 38074}, {547, 1482}, {550, 11362}, {551, 632}, {631, 20049}, {944, 34200}, {962, 14893}, {1353, 28538}, {3058, 41684}, {3524, 3621}, {3534, 28224}, {3545, 4678}, {3564, 50783}, {3576, 19711}, {3579, 4701}, {3616, 47598}, {3617, 5055}, {3623, 15709}, {3625, 34773}, {3626, 22791}, {3627, 28194}, {3632, 3655}, {3653, 14869}, {3748, 15935}, {3828, 10222}, {3830, 28212}, {3857, 4301}, {3871, 28443}, {3913, 5428}, {4668, 18357}, {4691, 11278}, {4745, 10171}, {4746, 18480}, {4816, 18481}, {4860, 12647}, {4995, 37728}, {5066, 5790}, {5453, 50575}, {5476, 38165}, {5550, 41984}, {5603, 10109}, {5657, 12100}, {5731, 15759}, {5734, 35018}, {5818, 11737}, {5881, 15704}, {5882, 44682}, {5886, 16191}, {5901, 19875}, {7967, 15693}, {9041, 48876}, {9780, 47599}, {9956, 38098}, {10124, 38314}, {10246, 11812}, {10248, 41988}, {10304, 18526}, {10573, 15170}, {10595, 15703}, {11238, 11545}, {12000, 17542}, {13243, 37429}, {13464, 38083}, {15178, 38068}, {15682, 28216}, {15684, 20070}, {15702, 37624}, {15707, 20054}, {15708, 20014}, {15712, 37727}, {15713, 26446}, {18493, 47478}, {18583, 38087}, {19877, 41985}, {19883, 33179}, {19914, 28459}, {20053, 41983}, {28174, 33699}, {28178, 37712}, {28198, 35404}, {28208, 44903}, {34667, 43934}, {35842, 41946}, {35843, 41945}, {37546, 37936}, {37950, 47490}, {38028, 38127}, {38034, 38176}, {43174, 46853}, {43211, 44635}, {43212, 44636}, {44266, 47488}
X(50823) = midpoint of X(i) and X(j) for these {i,j}: {3, 31145}, {8, 34718}, {376, 12645}, {381, 12245}, {3621, 34748}, {3632, 3655}, {3654, 4677}, {11362, 34641}, {12702, 34627}, {15684, 20070}, {18525, 34632}
X(50823) = reflection of X(i) in X(j) for these {i,j}: {5, 3679}, {549, 5690}, {944, 34200}, {962, 14893}, {1482, 547}, {1483, 549}, {3241, 140}, {8703, 3654}, {10222, 3828}, {10283, 38112}, {15686, 40}, {15687, 355}, {31162, 18357}, {38028, 38127}, {38034, 38176}, {44266, 47488}
X(50823) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 3679, 38081}, {3241, 38066, 140}, {3524, 3621, 34748}, {3617, 34631, 5055}, {3828, 10222, 38022}, {18357, 31162, 23046}
X(50824) lies on these lines: {1, 30}, {2, 952}, {3, 3241}, {5, 551}, {8, 5054}, {10, 11539}, {40, 34200}, {55, 10074}, {140, 3653}, {145, 3524}, {165, 15759}, {182, 9041}, {355, 547}, {376, 1482}, {381, 944}, {497, 22938}, {515, 3845}, {516, 19710}, {517, 3892}, {519, 549}, {528, 31657}, {546, 38021}, {548, 7982}, {550, 10222}, {553, 50194}, {572, 50113}, {631, 31145}, {632, 3828}, {946, 15687}, {962, 15681}, {993, 28463}, {1125, 15699}, {1317, 4995}, {1319, 37728}, {1387, 11238}, {1388, 10072}, {1484, 3829}, {1621, 12773}, {1656, 38074}, {1657, 5734}, {1698, 47598}, {1699, 12101}, {2771, 3898}, {2886, 33337}, {2975, 28443}, {3242, 11179}, {3244, 13624}, {3476, 5719}, {3523, 20049}, {3530, 30389}, {3534, 5731}, {3543, 10595}, {3545, 3622}, {3564, 47358}, {3576, 3654}, {3579, 3635}, {3582, 10950}, {3584, 10944}, {3616, 5055}, {3617, 15709}, {3621, 15708}, {3623, 10304}, {3624, 47599}, {3627, 13464}, {3628, 5881}, {3633, 41983}, {3636, 18480}, {3813, 5499}, {3816, 11698}, {3830, 5603}, {3839, 18493}, {3850, 9624}, {3853, 11522}, {3860, 30308}, {3873, 44255}, {3877, 17525}, {3897, 15670}, {3957, 35459}, {4297, 15686}, {4301, 15704}, {4421, 10269}, {4428, 6914}, {4668, 14890}, {4669, 10165}, {4677, 11812}, {4745, 11231}, {4870, 45287}, {4930, 34610}, {5066, 5886}, {5085, 50790}, {5250, 19919}, {5298, 21842}, {5330, 15677}, {5428, 8666}, {5432, 7972}, {5476, 38040}, {5587, 10109}, {5657, 15693}, {5691, 14893}, {5763, 46920}, {5818, 15703}, {6049, 7373}, {6361, 15689}, {6924, 40726}, {7489, 38669}, {7508, 34486}, {7970, 14830}, {7987, 14891}, {7991, 33923}, {8148, 15688}, {8227, 11737}, {9140, 12898}, {9778, 15695}, {9884, 11632}, {9955, 23046}, {9956, 19883}, {10056, 34471}, {10124, 19875}, {10164, 19711}, {10168, 49524}, {10245, 34730}, {10248, 35434}, {10267, 11194}, {10609, 49719}, {10704, 14666}, {11001, 28178}, {11114, 34698}, {11171, 22713}, {11207, 45621}, {11208, 45620}, {11230, 28236}, {11237, 37737}, {11274, 11715}, {11362, 15712}, {11724, 22566}, {12115, 22799}, {12245, 15692}, {12645, 15694}, {12737, 34612}, {13369, 31792}, {13587, 37535}, {13911, 43211}, {13973, 43212}, {14869, 34641}, {15325, 37740}, {15682, 28190}, {15683, 48661}, {15685, 28182}, {15690, 16200}, {15707, 20050}, {15711, 17502}, {15714, 31663}, {15845, 25405}, {16189, 44245}, {16202, 16370}, {16203, 16371}, {16239, 19876}, {17549, 37621}, {17564, 24927}, {17579, 34745}, {18444, 37429}, {18583, 38023}, {19907, 49736}, {20423, 38315}, {22793, 35404}, {24475, 44663}, {26321, 28461}, {26487, 34700}, {26492, 34717}, {28160, 33699}, {28460, 34195}, {28538, 48876}, {29580, 36728}, {31666, 43174}, {32787, 35763}, {32788, 35762}, {34352, 37298}, {34551, 36440}, {34552, 36458}, {34595, 41985}, {34606, 37733}, {34656, 43934}, {35018, 37714}, {35641, 41946}, {35642, 41945}, {37950, 47491}, {38029, 47359}, {38140, 41150}, {44266, 47495}, {48906, 49465}, {48907, 50422}
X(50824) = midpoint of X(i) and X(j) for these {i,j}: {1, 3655}, {3, 3241}, {8, 34748}, {145, 34718}, {376, 1482}, {381, 944}, {549, 1483}, {551, 5882}, {962, 15681}, {3242, 11179}, {3679, 37727}, {4930, 34610}, {5731, 10247}, {7967, 10246}, {7970, 14830}, {8148, 34632}, {9140, 12898}, {9884, 11632}, {10704, 14666}, {11114, 34698}, {11171, 22713}, {11274, 11715}, {12699, 34628}, {12702, 34631}, {15683, 48661}, {17579, 34745}, {18481, 31162}, {18526, 34627}, {28460, 34195}, {48907, 50422}
X(50824) = reflection of X(i) in X(j) for these {i,j}: {5, 551}, {40, 34200}, {355, 547}, {381, 5901}, {549, 1385}, {551, 15178}, {3543, 40273}, {3654, 12100}, {3679, 140}, {5690, 549}, {5691, 14893}, {10164, 31662}, {15686, 4297}, {15687, 946}, {22566, 11724}, {34627, 18357}, {34648, 9955}, {34773, 3655}, {35404, 22793}, {38028, 10246}, {38034, 10283}, {38042, 38028}, {38112, 10165}, {38138, 11230}, {44266, 47495}, {49524, 10168}
X(50824) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 34773, 22791}, {5, 551, 38022}, {145, 3524, 34718}, {355, 25055, 547}, {381, 37624, 38314}, {381, 38314, 5901}, {631, 31145, 38066}, {632, 38081, 3828}, {944, 37624, 5901}, {944, 38314, 381}, {1385, 1483, 5690}, {1385, 13607, 1483}, {3576, 3654, 12100}, {3616, 18526, 18357}, {3616, 34627, 5055}, {3623, 10304, 34631}, {3653, 3679, 140}, {3653, 37727, 3679}, {5054, 34748, 8}, {5055, 18526, 34627}, {5055, 34627, 18357}, {5882, 15178, 5}, {8148, 15688, 34632}, {9955, 34648, 23046}, {10304, 34631, 12702}, {31666, 43174, 44682}
X(50825) lies on these lines: {2, 28174}, {3, 38074}, {5, 28202}, {8, 15707}, {10, 17504}, {30, 1698}, {40, 10124}, {140, 3656}, {165, 5066}, {355, 14891}, {515, 15711}, {517, 15713}, {519, 549}, {546, 19876}, {547, 31423}, {550, 3828}, {551, 14869}, {632, 28194}, {944, 15718}, {952, 15693}, {962, 15723}, {1482, 15721}, {3241, 15720}, {3523, 38066}, {3524, 3617}, {3530, 3679}, {3564, 50784}, {3576, 44580}, {3579, 15699}, {3616, 5054}, {3623, 15708}, {3627, 38083}, {3634, 38071}, {3653, 9588}, {3654, 11812}, {3655, 4668}, {3845, 11231}, {4745, 17502}, {5085, 50782}, {5587, 15690}, {5657, 15701}, {5790, 15698}, {5818, 14093}, {5886, 11540}, {5901, 15702}, {8703, 10164}, {9780, 15688}, {9956, 15686}, {10032, 27529}, {10175, 33699}, {10304, 18357}, {11522, 45760}, {11539, 19862}, {12100, 26446}, {12512, 35404}, {12699, 47599}, {12702, 15709}, {14269, 19877}, {14892, 41869}, {15687, 31663}, {15691, 16192}, {15695, 28190}, {15703, 40273}, {15705, 18525}, {15706, 34627}, {15710, 46933}, {15712, 28204}, {15714, 28208}, {16239, 38021}, {19708, 28186}, {19709, 28178}, {19711, 38112}, {19875, 34200}, {19925, 44903}, {23046, 31730}, {28182, 41099}, {28216, 30308}, {28466, 33814}, {31162, 47598}, {38081, 44682}
X(50825) = midpoint of X(i) and X(j) for these {i,j}: {3623, 34718}, {3655, 4668}, {5818, 14093}
X(50825) = {X(3654),X(11812)}-harmonic conjugate of X(38028)
X(50826) lies on these lines: {2, 28212}, {3, 38081}, {5, 19876}, {8, 41983}, {10, 45759}, {30, 9780}, {140, 5734}, {165, 33699}, {355, 15714}, {519, 549}, {632, 4301}, {952, 19711}, {1698, 23046}, {3241, 12108}, {3524, 4678}, {3530, 38066}, {3564, 50785}, {3579, 38071}, {3616, 14890}, {3617, 15706}, {3622, 5054}, {3624, 3656}, {3627, 3828}, {3654, 10283}, {3679, 15712}, {3845, 10175}, {3857, 28202}, {3858, 38083}, {3860, 9778}, {4995, 15935}, {5657, 11812}, {5731, 12100}, {5790, 15759}, {5818, 15691}, {5844, 15701}, {6361, 47478}, {7967, 15722}, {8703, 26446}, {9588, 14869}, {9955, 15699}, {9956, 35404}, {10164, 15711}, {11231, 28232}, {12702, 47598}, {14892, 19877}, {15686, 19875}, {15689, 46933}, {15698, 28224}, {17504, 37705}, {18493, 41984}, {19710, 28172}, {20057, 34718}, {26062, 50395}, {28204, 44682}, {31663, 44903}, {33923, 38074}, {34632, 47599}, {38022, 43174}, {38335, 46932}
X(50826) = midpoint of X(20057) and X(34718)
X(50826) = reflection of X(5) in X(19876)
X(50826) = {X(3654),X(15713)}-harmonic conjugate of X(10283)
X(50827) lies on these lines: {1, 15709}, {2, 16200}, {3, 34641}, {4, 3679}, {8, 10304}, {10, 3656}, {30, 3626}, {40, 15683}, {355, 15684}, {376, 47745}, {381, 38098}, {515, 3534}, {516, 33699}, {517, 3956}, {519, 549}, {548, 28204}, {551, 3526}, {631, 34747}, {952, 15759}, {1125, 47598}, {1698, 34631}, {3241, 10303}, {3244, 5054}, {3524, 3632}, {3564, 50786}, {3579, 4746}, {3617, 31162}, {3625, 3655}, {3628, 3828}, {3635, 14890}, {3636, 11539}, {3830, 28232}, {3845, 28228}, {3857, 38081}, {4301, 5072}, {4668, 31730}, {4677, 5657}, {4678, 31673}, {4691, 18483}, {4995, 36920}, {5071, 11531}, {5085, 50789}, {5176, 10032}, {5493, 49136}, {5844, 11540}, {5881, 50693}, {5882, 15717}, {7486, 7982}, {8703, 28236}, {10124, 33179}, {10172, 38112}, {11001, 37712}, {11278, 15699}, {12007, 28538}, {12245, 19875}, {12702, 34648}, {15022, 31399}, {15640, 28150}, {15708, 20050}, {18525, 34638}, {20423, 38191}, {21161, 48696}, {31662, 44580}
X(50827) = midpoint of X(i) and X(j) for these {i,j}: {3, 34641}, {10, 34718}, {376, 47745}, {3625, 3655}, {3654, 4669}, {3679, 11362}, {5882, 31145}, {12702, 34648}, {18525, 34638}, {31673, 34632}, {31730, 34627}
X(50827) = reflection of X(i) in X(j) for these {i,j}: {10172, 38112}, {13464, 3828}, {13607, 549}, {33179, 10124}
X(50827) = {X(3679),X(7991)}-harmonic conjugate of X(38074)
X(50828) lies on these lines: {1, 3524}, {2, 515}, {3, 551}, {5, 31666}, {8, 15708}, {10, 3655}, {20, 38021}, {21, 16005}, {30, 1125}, {36, 553}, {40, 15692}, {140, 3828}, {165, 15698}, {214, 5745}, {355, 15694}, {376, 946}, {381, 4297}, {516, 8703}, {517, 12100}, {519, 549}, {527, 10269}, {534, 28454}, {535, 18857}, {547, 19925}, {548, 28202}, {550, 38022}, {599, 39870}, {631, 3679}, {632, 38083}, {943, 13370}, {944, 15702}, {950, 3582}, {952, 4745}, {997, 5325}, {1319, 4995}, {1350, 38023}, {1482, 15700}, {1656, 38076}, {1698, 15709}, {1699, 11001}, {2482, 11710}, {2646, 5298}, {2771, 11694}, {2796, 33813}, {2800, 11227}, {3058, 37600}, {3241, 3523}, {3244, 15707}, {3522, 9624}, {3525, 19876}, {3528, 11522}, {3530, 15178}, {3533, 37714}, {3534, 5886}, {3543, 8227}, {3545, 3624}, {3564, 50787}, {3579, 3636}, {3584, 10106}, {3601, 40270}, {3612, 10072}, {3616, 10304}, {3622, 15705}, {3625, 34748}, {3634, 11539}, {3635, 41983}, {3654, 10164}, {3817, 3830}, {3839, 5550}, {3845, 11230}, {3860, 28190}, {3884, 40296}, {3911, 37525}, {4292, 4870}, {4304, 11238}, {4311, 11237}, {4669, 15701}, {4677, 7967}, {4701, 32900}, {5055, 18481}, {5066, 10171}, {5071, 5691}, {5085, 47358}, {5126, 13405}, {5259, 28461}, {5265, 15933}, {5267, 28443}, {5303, 10032}, {5434, 13411}, {5435, 14563}, {5444, 21578}, {5450, 16418}, {5603, 19708}, {5642, 11709}, {5657, 15719}, {5732, 38025}, {5759, 38024}, {5844, 44580}, {5881, 10303}, {5884, 31165}, {5901, 12512}, {6001, 33574}, {6055, 11711}, {6174, 11715}, {6261, 50739}, {6361, 15710}, {6796, 16417}, {7982, 15717}, {7988, 41099}, {7991, 10299}, {8583, 17561}, {8726, 40257}, {9583, 19053}, {9588, 34747}, {9589, 21735}, {9779, 15640}, {9812, 15697}, {9940, 44663}, {9956, 10124}, {10056, 37618}, {10109, 28186}, {10222, 15712}, {10245, 34642}, {10283, 15711}, {10385, 30282}, {10595, 15715}, {10902, 13587}, {11019, 37606}, {11111, 12608}, {11179, 49511}, {11231, 15713}, {11263, 28460}, {11540, 28224}, {12017, 49505}, {12101, 28168}, {12114, 16857}, {12117, 38220}, {12571, 15687}, {12699, 15688}, {12702, 15706}, {14830, 21636}, {14831, 31738}, {14891, 31663}, {15670, 17614}, {15671, 24564}, {15672, 16132}, {15677, 41012}, {15682, 30308}, {15686, 22793}, {15689, 18493}, {15690, 28146}, {15691, 40273}, {15699, 18480}, {15718, 37624}, {15720, 34641}, {15721, 31423}, {15759, 28174}, {17525, 34123}, {17549, 37561}, {18357, 31253}, {19706, 38122}, {19710, 28158}, {19843, 45036}, {20423, 38049}, {22791, 45759}, {23046, 33697}, {24387, 44222}, {24466, 38026}, {24473, 31806}, {28216, 46332}, {28352, 48897}, {28463, 38602}, {30264, 38027}, {37526, 40256}, {38093, 43161}, {38118, 47359}, {41869, 46934}, {43211, 49618}, {43212, 49619}, {48893, 50421}
X(50828) = midpoint of X(i) and X(j) for these {i,j}: {3, 551}, {10, 3655}, {376, 946}, {381, 4297}, {549, 1385}, {599, 39870}, {2482, 11710}, {3241, 11362}, {3244, 34718}, {3576, 10165}, {3625, 34748}, {3679, 5882}, {5642, 11709}, {5731, 10175}, {5884, 31165}, {5901, 34200}, {6055, 11711}, {6174, 11715}, {7967, 38127}, {10164, 10246}, {11179, 49511}, {11263, 28460}, {12699, 34638}, {14830, 21636}, {14831, 31738}, {15686, 22793}, {15691, 40273}, {17502, 38028}, {18481, 34648}, {24473, 31806}, {31162, 31730}, {31673, 34628}, {34641, 37727}, {48893, 50421}
X(50828) = reflection of X(i) in X(j) for these {i,j}: {3828, 140}, {6684, 549}, {9956, 10124}, {12512, 34200}, {13464, 551}, {15687, 12571}, {19925, 547}, {31663, 14891}
X(50828) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3653, 551}, {376, 25055, 946}, {631, 3679, 38068}, {631, 30389, 5882}, {944, 15702, 19875}, {1385, 6684, 13607}, {3525, 38074, 19876}, {3530, 15178, 43174}, {3545, 34628, 31673}, {3616, 10304, 31162}, {3622, 15705, 34632}, {3624, 34628, 3545}, {3654, 15693, 10164}, {3655, 5054, 10}, {4297, 19883, 381}, {5055, 18481, 34648}, {5882, 38068, 3679}, {7987, 25055, 376}, {10246, 15693, 3654}, {10304, 31162, 31730}, {12699, 15688, 34638}, {15692, 38314, 40}, {15705, 34632, 35242}, {15709, 34627, 1698}, {19862, 34648, 5055}, {19876, 38074, 31399}, {37727, 38066, 34641}
X(50829) lies on these lines: {1, 15708}, {2, 165}, {3, 3828}, {10, 3524}, {20, 19876}, {30, 3634}, {40, 15702}, {140, 28194}, {355, 15700}, {376, 19925}, {381, 12512}, {515, 12100}, {517, 11812}, {519, 549}, {547, 12571}, {550, 38083}, {551, 631}, {553, 5432}, {908, 10032}, {944, 38098}, {946, 15694}, {952, 44580}, {991, 36634}, {1125, 3656}, {1155, 41546}, {1350, 38089}, {1698, 10304}, {2796, 6036}, {3241, 9588}, {3523, 3679}, {3525, 5493}, {3530, 28204}, {3534, 10175}, {3543, 16192}, {3545, 34638}, {3564, 50788}, {3576, 4669}, {3579, 11539}, {3582, 12575}, {3584, 4298}, {3624, 34632}, {3626, 3655}, {3628, 28202}, {3635, 34718}, {3653, 11362}, {3654, 10165}, {3748, 3911}, {3845, 10172}, {3860, 28154}, {4297, 15692}, {4301, 10303}, {4691, 13624}, {4745, 15693}, {4860, 13405}, {5055, 31253}, {5066, 28150}, {5085, 50781}, {5218, 44841}, {5281, 43179}, {5325, 20103}, {5587, 19708}, {5732, 38101}, {5759, 38094}, {5818, 15715}, {5882, 38066}, {7610, 17132}, {7989, 15683}, {8703, 11231}, {9780, 15705}, {9955, 47598}, {9956, 34200}, {10056, 12577}, {10109, 28146}, {10124, 28198}, {10299, 38074}, {10385, 31231}, {11540, 28174}, {13464, 14869}, {14891, 28208}, {15672, 25011}, {15688, 31673}, {15690, 28172}, {15699, 18483}, {15706, 18481}, {15709, 19862}, {15711, 38042}, {15713, 28228}, {15721, 25055}, {15722, 38127}, {15759, 28160}, {16112, 43151}, {16226, 31737}, {17502, 19711}, {18480, 45759}, {19710, 38140}, {24466, 38104}, {28190, 46332}, {30264, 38105}, {30315, 50693}, {30389, 31145}, {31188, 31508}, {31439, 43212}, {38028, 41150}
X(50829) = midpoint of X(i) and X(j) for these {i,j}: {3, 3828}, {165, 10171}, {376, 19925}, {381, 12512}, {547, 31663}, {549, 6684}, {551, 43174}, {3626, 3655}, {3635, 34718}, {9956, 34200}
X(50829) = reflection of X(12571) in X(547)
X(50829) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9778, 30308}, {3, 38068, 3828}, {20, 19876, 38076}, {40, 15702, 19883}, {1698, 10304, 34648}, {3525, 31425, 5493}, {3545, 35242, 34638}, {3654, 15701, 10165}, {9780, 15705, 34628}, {14869, 31447, 13464}, {15692, 19875, 4297}, {15709, 31162, 19862}
X(50830) lies on these lines: {1, 47598}, {4, 31145}, {5, 34641}, {8, 5055}, {30, 3632}, {140, 34747}, {145, 15709}, {517, 33699}, {519, 549}, {952, 3534}, {3241, 3526}, {3244, 11539}, {3524, 20054}, {3564, 50789}, {3621, 10304}, {3625, 22791}, {3626, 15699}, {3628, 3679}, {3633, 14890}, {3654, 15759}, {3656, 4677}, {3845, 28234}, {3856, 7982}, {4669, 38042}, {4745, 10283}, {5054, 20050}, {5493, 15704}, {10109, 16200}, {10222, 38081}, {10303, 20049}, {11278, 38071}, {11531, 14893}, {11540, 38028}, {12101, 37712}, {12245, 15683}, {12645, 15684}, {12702, 46333}, {15640, 28174}, {15687, 47745}, {15706, 20053}, {15713, 38127}, {18357, 20052}, {19710, 28236}, {25439, 28463}, {33179, 38098}, {44266, 47534}
X(50830) = midpoint of X(i) and X(j) for these {i,j}: {3621, 34718}, {20053, 34748}
X(50830) = reflection of X(i) in X(j) for these {i,j}: {5, 34641}, {11531, 14893}, {15687, 47745}, {34631, 18357}, {34747, 140}, {34773, 34718}, {44266, 47534}
X(50831) lies on these lines: {1, 15699}, {3, 20049}, {5, 3241}, {8, 11539}, {30, 145}, {140, 31145}, {517, 19710}, {519, 549}, {547, 12645}, {550, 7991}, {551, 38081}, {632, 3679}, {944, 15686}, {952, 1699}, {956, 28463}, {1353, 9041}, {1482, 10248}, {3244, 9955}, {3524, 20014}, {3564, 50790}, {3617, 47598}, {3621, 5054}, {3622, 47599}, {3623, 5055}, {3627, 4301}, {3633, 3655}, {3654, 15711}, {3857, 5881}, {3858, 10222}, {4669, 38028}, {4677, 38112}, {5066, 10247}, {5657, 19711}, {5731, 5844}, {5882, 46853}, {7967, 12100}, {10124, 37624}, {10175, 10283}, {10246, 15713}, {10595, 11737}, {12245, 34200}, {14869, 38066}, {15178, 34641}, {15709, 20052}, {17504, 20050}, {23046, 34627}, {28224, 33699}, {37938, 47593}, {37950, 47536}, {41984, 46933}, {41985, 46934}, {44266, 47493}
X(50831) = midpoint of X(i) and X(j) for these {i,j}: {3, 20049}, {145, 34748}, {3633, 3655}, {18526, 34631}, {20050, 34718}, {34747, 37727}
X(50831) = reflection of X(i) in X(j) for these {i,j}: {5, 3241}, {549, 1483}, {12245, 34200}, {12645, 547}, {15686, 944}, {15687, 1482}, {31145, 140}, {34641, 15178}, {44266, 47493}
X(50832) lies on these lines: {1, 17504}, {2, 28224}, {5, 3653}, {30, 3616}, {140, 38081}, {145, 15707}, {517, 15711}, {519, 549}, {550, 551}, {632, 28204}, {944, 10124}, {946, 44903}, {952, 15713}, {1125, 38071}, {1482, 14891}, {1698, 3655}, {3241, 3530}, {3524, 3623}, {3564, 50791}, {3576, 3656}, {3617, 5054}, {3622, 15688}, {3627, 38022}, {3654, 19711}, {3679, 14869}, {3817, 3845}, {4297, 35404}, {5066, 5731}, {5550, 47478}, {5603, 15690}, {5657, 44580}, {5790, 11540}, {5844, 15693}, {5886, 33699}, {5901, 15686}, {6361, 41982}, {7967, 15701}, {7987, 15714}, {7988, 41990}, {8148, 15705}, {9778, 46332}, {10246, 12100}, {10247, 15698}, {10595, 14093}, {11812, 38112}, {12108, 38066}, {12245, 15718}, {12645, 15721}, {13624, 45759}, {14269, 46934}, {15178, 44682}, {15646, 47593}, {15687, 25055}, {15692, 37624}, {15695, 28216}, {15699, 19862}, {15706, 34631}, {15708, 20052}, {15709, 18526}, {15720, 31145}, {15935, 37525}, {16239, 38074}, {18481, 23046}, {18525, 47599}, {19708, 28212}, {19710, 28150}, {28190, 30308}, {28194, 31666}, {34200, 38314}, {34627, 47598}, {34718, 41983}
X(50832) = midpoint of X(i) and X(j) for these {i,j}: {1698, 3655}, {10595, 14093}, {15692, 37624}, {20052, 34748}
X(50832) = reflection of X(15714) in X(7987)
X(50832) = {X(3655),X(11539)}-harmonic conjugate of X(37705)
X(50833) lies on these lines: {1, 41983}, {2, 28186}, {3, 38022}, {30, 3624}, {140, 19876}, {165, 3656}, {517, 19711}, {519, 549}, {547, 7987}, {551, 15712}, {946, 15714}, {952, 15701}, {1125, 45759}, {1698, 14890}, {3524, 3622}, {3530, 3653}, {3534, 9779}, {3564, 50792}, {3576, 11812}, {3616, 15706}, {3654, 44580}, {3679, 12108}, {3828, 31666}, {3845, 10171}, {4669, 31662}, {4678, 15708}, {5054, 9780}, {5550, 15689}, {5603, 15716}, {5657, 15722}, {5886, 15759}, {5901, 15692}, {8227, 15691}, {8703, 10165}, {10246, 15719}, {10247, 15693}, {11230, 19710}, {11539, 13624}, {14093, 40273}, {14869, 28204}, {14891, 25055}, {14892, 34595}, {15686, 19883}, {15698, 28174}, {15707, 20057}, {15709, 18357}, {15710, 18493}, {15711, 28232}, {15713, 38042}, {15718, 38314}, {15808, 17504}, {18481, 47598}, {19862, 23046}, {19872, 45758}, {28194, 44682}, {33923, 38021}, {34628, 47599}, {35271, 50396}
X(50833) = reflection of X(19876) in X(140)
X(50834) lies on these lines: {2, 5850}, {7, 3828}, {9, 551}, {10, 527}, {142, 38101}, {144, 3679}, {390, 519}, {516, 4669}, {518, 3898}, {528, 34641}, {1757, 50114}, {2550, 38098}, {2801, 4134}, {3062, 34632}, {3244, 47357}, {3524, 43176}, {3625, 5698}, {4356, 49742}, {4701, 30332}, {4745, 5686}, {5432, 21060}, {5542, 15325}, {5729, 21625}, {5779, 28194}, {5785, 28610}, {5805, 38076}, {5845, 50781}, {5852, 38204}, {10589, 31142}, {11019, 41700}, {15558, 31165}, {15828, 49505}, {17768, 38210}, {18230, 38024}, {19878, 30340}, {24393, 28534}, {31657, 38068}, {34639, 34790}, {38093, 43180}, {49515, 50294}
X(50834) = midpoint of X(i) and X(j) for these {i,j}: {144, 3679}, {3062, 34632}, {5223, 6172}
X(50834) = reflection of X(i) in X(j) for these {i,j}: {7, 3828}, {551, 9}, {3244, 47357}, {38201, 5686}
X(50834) = {X(7),X(3828)}-harmonic conjugate of X(38094)
X(50835) lies on these lines: {2, 210}, {7, 3679}, {8, 527}, {9, 3241}, {10, 30340}, {142, 38097}, {144, 528}, {145, 5220}, {200, 18450}, {390, 519}, {391, 50310}, {480, 11194}, {516, 4677}, {551, 18230}, {2346, 16418}, {3059, 34744}, {3189, 50738}, {3243, 38314}, {3421, 45043}, {3621, 5698}, {3623, 15254}, {3632, 30332}, {3656, 5817}, {3672, 49448}, {3751, 48856}, {3828, 38024}, {3940, 14151}, {3945, 50291}, {3951, 12632}, {4346, 49772}, {4452, 49501}, {4543, 6006}, {4668, 30424}, {4669, 5850}, {4678, 5880}, {4745, 38052}, {4882, 8544}, {4899, 17294}, {5071, 20330}, {5232, 49529}, {5265, 30318}, {5274, 31142}, {5542, 19875}, {5759, 28204}, {5805, 38074}, {5819, 50082}, {5845, 50783}, {6173, 24393}, {6600, 17549}, {7426, 47508}, {9041, 37654}, {9780, 38093}, {12125, 34711}, {16496, 37681}, {17297, 39570}, {18228, 31146}, {18254, 34625}, {20007, 34610}, {20070, 34720}, {24599, 24841}, {25557, 46933}, {28194, 36991}, {30308, 38158}, {30331, 34747}, {31657, 38066}, {34718, 35514}, {34784, 40269}, {36479, 49713}, {36922, 50573}, {38025, 42871}, {41325, 50087}, {48802, 49510}, {48851, 49536}, {49449, 50313}, {49450, 50107}, {49504, 50311}, {49712, 50303}
X(50835) = midpoint of X(144) and X(31145)
X(50835) = reflection of X(i) in X(j) for these {i,j}: {7, 3679}, {145, 47357}, {390, 6172}, {3241, 9}, {6172, 5223}, {6173, 24393}, {7426, 47508}, {11038, 5686}, {34747, 30331}, {35514, 34718}, {47357, 5220}
X(50835) = {X(7),X(3679)}-harmonic conjugate of X(38092)
X(50836) lies on these lines: {1, 527}, {2, 165}, {7, 551}, {9, 80}, {10, 30332}, {21, 5735}, {30, 11372}, {36, 1001}, {55, 31142}, {63, 31146}, {142, 18393}, {144, 3241}, {238, 50080}, {376, 2951}, {390, 519}, {392, 15726}, {405, 9589}, {452, 7991}, {484, 8257}, {518, 3899}, {535, 8545}, {752, 29573}, {758, 7671}, {946, 50739}, {954, 4428}, {960, 5696}, {1279, 49747}, {1519, 3524}, {1617, 4654}, {1621, 31164}, {1697, 34606}, {1698, 15254}, {1743, 50282}, {2094, 10980}, {2478, 9588}, {2550, 3583}, {2801, 3877}, {3058, 3929}, {3062, 34628}, {3428, 16418}, {3452, 31508}, {3616, 30424}, {3622, 43180}, {3624, 5880}, {3632, 4693}, {3636, 30340}, {3653, 31657}, {3656, 5762}, {3663, 16487}, {3683, 9580}, {3685, 17294}, {3729, 50310}, {3731, 50291}, {3822, 30311}, {3825, 30312}, {3826, 17533}, {3828, 18230}, {3878, 10394}, {3883, 50107}, {3886, 17346}, {3923, 48851}, {3928, 49736}, {4034, 49485}, {4293, 9814}, {4297, 50738}, {4301, 11106}, {4432, 17284}, {4669, 5686}, {4677, 5853}, {4679, 6174}, {4859, 15485}, {4888, 16484}, {4908, 50783}, {5044, 34707}, {5129, 5493}, {5231, 10707}, {5234, 10624}, {5248, 8543}, {5250, 5691}, {5426, 17525}, {5542, 38314}, {5572, 24473}, {5692, 15733}, {5728, 44663}, {5759, 28194}, {5766, 12572}, {5779, 28204}, {5795, 34711}, {5805, 38021}, {5845, 47358}, {5850, 8236}, {5902, 10177}, {6666, 19876}, {7174, 49742}, {7290, 17301}, {7982, 50241}, {9623, 36976}, {9624, 17571}, {9965, 30350}, {10382, 10385}, {10582, 44447}, {11112, 31435}, {11194, 42884}, {11495, 16371}, {12705, 37428}, {12848, 18421}, {13528, 31658}, {14100, 31165}, {15587, 34626}, {15677, 39778}, {15692, 43151}, {15837, 31141}, {16236, 50573}, {16469, 50114}, {16833, 28580}, {16857, 28198}, {17251, 49484}, {17272, 50311}, {17276, 35227}, {17528, 41869}, {17530, 42356}, {17564, 35242}, {17576, 30389}, {17784, 30393}, {18250, 34639}, {19861, 37299}, {20073, 49771}, {20588, 34611}, {22793, 50740}, {24280, 50119}, {24715, 31183}, {25509, 33068}, {26333, 35514}, {26446, 38180}, {31156, 43166}, {31160, 31434}, {31393, 36973}, {31424, 45700}, {34630, 37551}, {34719, 41229}, {34749, 37556}, {35031, 35093}, {37606, 44785}, {41325, 50115}, {42335, 50302}, {48849, 50118}, {49746, 50127}, {50297, 50314}
X(50836) = midpoint of X(i) and X(j) for these {i,j}: {144, 3241}, {390, 6172}, {3062, 34628}, {5698, 47357}, {14100, 31165}
X(50836) = reflection of X(i) in X(j) for these {i,j}: {1, 47357}, {7, 551}, {2951, 376}, {3241, 30331}, {3679, 9}, {4312, 6173}, {5223, 6172}, {5902, 10177}, {6173, 1001}, {24473, 5572}, {34628, 43161}
X(50836) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 551, 38024}, {1001, 6173, 25055}, {4312, 25055, 6173}, {18230, 38092, 3828}, {49742, 50130, 7174}, {50126, 50296, 3679}
X(50837) lies on these lines: {9, 3828}, {144, 551}, {390, 519}, {516, 3654}, {518, 41149}, {527, 1125}, {3062, 34638}, {3524, 41705}, {3626, 5698}, {3635, 47357}, {4701, 5220}, {4746, 30332}, {4930, 42871}, {5845, 50787}, {5850, 38316}, {11038, 41150}, {18230, 38094}, {30424, 31253}
X(50837) = midpoint of X(i) and X(j) for these {i,j}: {144, 551}, {3062, 34638}
X(50837) = reflection of X(i) in X(j) for these {i,j}: {3635, 47357}, {3828, 9}
X(50838) lies on these lines: {2, 38210}, {7, 34641}, {8, 43180}, {9, 34747}, {142, 3679}, {390, 519}, {518, 4677}, {527, 3632}, {3243, 19875}, {3633, 47357}, {3656, 38139}, {4669, 38052}, {4745, 11038}, {4746, 30340}, {4924, 48856}, {4995, 10383}, {5845, 50789}, {17294, 49707}, {20049, 30331}, {20052, 30424}, {20059, 31145}, {24393, 25055}, {30308, 38154}, {38097, 42871}
X(50838) = reflection of X(i) in X(j) for these {i,j}: {7, 34641}, {3633, 47357}, {20049, 30331}, {34747, 9}
X(50839) lies on these lines: {2, 3158}, {7, 528}, {8, 4702}, {9, 31145}, {144, 20049}, {145, 527}, {390, 519}, {551, 38092}, {962, 34719}, {1001, 17547}, {2094, 20075}, {2403, 6006}, {2550, 38314}, {3543, 43166}, {3622, 38093}, {3635, 30340}, {3655, 35514}, {3679, 18230}, {3829, 7679}, {3880, 7671}, {3895, 37787}, {4308, 34701}, {4421, 7677}, {4677, 5686}, {5220, 20053}, {5435, 31146}, {5698, 20050}, {5730, 9785}, {5758, 34745}, {5819, 50113}, {5828, 34619}, {5845, 50790}, {5880, 20057}, {6223, 34629}, {6762, 50738}, {6764, 11111}, {7320, 12536}, {7673, 44663}, {7676, 11194}, {9797, 34610}, {10304, 43175}, {10578, 31140}, {25055, 40333}, {28204, 36991}, {31165, 34784}, {32087, 50310}, {34632, 43161}, {41325, 50131}, {41857, 50737}, {49704, 50129}
X(50839) = midpoint of X(i) and X(j) for these {i,j}: {144, 20049}, {6172, 12630}
X(50839) = reflection of X(i) in X(j) for these {i,j}: {7, 3241}, {8, 47357}, {3543, 43166}, {3679, 30331}, {6172, 390}, {31145, 9}, {34632, 43161}, {34784, 31165}, {35514, 3655}
X(50840) lies on these lines: {2, 10032}, {9, 38092}, {144, 42819}, {390, 519}, {527, 3616}, {3617, 5698}, {3623, 47357}, {4668, 30332}, {5220, 20052}, {5759, 28202}, {5845, 50791}, {15683, 16112}, {16133, 16857}, {20059, 38025}, {28534, 40333}, {31165, 40269}
X(50840) = reflection of X(3623) in X(47357)
X(50841) lies on these lines: {2, 2802}, {10, 528}, {11, 3828}, {40, 10711}, {100, 993}, {119, 28194}, {214, 519}, {376, 12751}, {535, 6735}, {549, 11715}, {551, 3035}, {553, 10956}, {900, 36912}, {952, 4669}, {1125, 13996}, {1320, 25055}, {1387, 19883}, {2800, 3654}, {2801, 5657}, {3036, 38098}, {3545, 14217}, {3626, 10609}, {3653, 38762}, {3656, 38752}, {3874, 34619}, {3887, 4448}, {4301, 20400}, {4677, 10031}, {4745, 17525}, {4781, 25030}, {5054, 12737}, {5055, 16174}, {5493, 38757}, {5528, 38097}, {5541, 6702}, {5726, 8545}, {5848, 50781}, {6154, 38099}, {6265, 34718}, {6633, 32043}, {6713, 38068}, {7972, 31145}, {8068, 38105}, {8715, 37721}, {9588, 38669}, {10056, 12736}, {10199, 37828}, {12119, 34627}, {12331, 38066}, {13199, 38074}, {13205, 16418}, {13464, 38763}, {16417, 22560}, {17780, 36923}, {19876, 31272}, {21630, 45310}, {22799, 28202}, {25005, 34719}, {25440, 37709}, {26364, 34711}, {28204, 33814}, {31235, 38026}, {33337, 34641}, {34632, 34789}, {37725, 43174}, {41191, 45314}
X(50841) = midpoint of X(i) and X(j) for these {i,j}: {40, 10711}, {100, 3679}, {376, 12751}, {1145, 6174}, {4677, 10031}, {5541, 10707}, {6265, 34718}, {7972, 31145}, {12119, 34627}, {33337, 34641}, {34632, 34789}
X(50841) = reflection of X(i) in X(j) for these {i,j}: {11, 3828}, {214, 6174}, {551, 3035}, {10707, 6702}, {11274, 214}, {11715, 549}, {15863, 3679}, {21630, 45310}, {41191, 45314}
X(50841) = barycentric product X(3245)*X(4358)
X(50841) = barycentric quotient X(3245)/X(88)
X(50841) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11, 3828, 38104}, {4677, 15015, 10031}, {5541, 19875, 10707}, {10707, 19875, 6702}
X(50842) lies on these lines: {2, 5854}, {8, 190}, {11, 3679}, {100, 8168}, {165, 952}, {210, 2802}, {214, 519}, {529, 18802}, {551, 25416}, {900, 4543}, {1320, 45310}, {1387, 19875}, {3035, 3241}, {3036, 10707}, {3625, 10609}, {3828, 38026}, {3916, 4701}, {4370, 4530}, {4428, 13278}, {4668, 12019}, {4745, 34122}, {5552, 34710}, {5559, 50038}, {5848, 50783}, {6154, 34641}, {6702, 38098}, {6713, 38066}, {6876, 38665}, {7173, 34640}, {8068, 38100}, {10031, 24477}, {10711, 12245}, {12735, 34747}, {14740, 31165}, {16370, 25438}, {24466, 28204}, {25055, 26726}, {34610, 36972}, {34689, 34718}, {34749, 49169}, {37406, 37725}, {39776, 44663}
X(50842) = midpoint of X(i) and X(j) for these {i,j}: {100, 31145}, {10711, 12245}
X(50842) = reflection of X(i) in X(j) for these {i,j}: {11, 3679}, {1317, 6174}, {1320, 45310}, {3241, 3035}, {6174, 1145}, {10707, 3036}, {25416, 551}, {31165, 14740}, {34747, 12735}
X(50842) = {X(11),X(3679)}-harmonic conjugate of X(38099)
X(50843) lies on these lines: {1, 528}, {2, 952}, {3, 12776}, {11, 551}, {30, 1537}, {80, 25055}, {100, 999}, {104, 16370}, {119, 17533}, {145, 34753}, {214, 519}, {354, 2802}, {376, 10698}, {381, 11729}, {392, 2801}, {405, 38669}, {442, 15178}, {474, 38665}, {499, 34700}, {535, 12831}, {542, 31525}, {900, 3251}, {944, 10711}, {997, 41701}, {1023, 4370}, {1320, 9945}, {1385, 37298}, {1387, 3488}, {1388, 45700}, {1483, 17564}, {2095, 34631}, {2771, 17525}, {2800, 10167}, {3035, 3679}, {3036, 19875}, {3158, 5854}, {3244, 13996}, {3304, 48713}, {3616, 12019}, {3653, 6713}, {3655, 6265}, {3656, 5840}, {3828, 15863}, {3829, 5533}, {4187, 5882}, {4421, 10087}, {4428, 10058}, {4870, 18976}, {4881, 5844}, {4996, 41345}, {5054, 19914}, {5083, 24473}, {5330, 37299}, {5730, 34610}, {5794, 12750}, {5848, 47358}, {5881, 20400}, {5901, 17577}, {6154, 44840}, {6246, 38077}, {6326, 46947}, {6667, 9897}, {6702, 19883}, {7373, 13279}, {7483, 20418}, {8068, 38027}, {10074, 11194}, {10090, 40726}, {10199, 10950}, {10222, 10993}, {10596, 10738}, {11114, 34773}, {11219, 30392}, {11570, 44663}, {11715, 15670}, {12119, 31162}, {12331, 16417}, {12611, 28208}, {12619, 38069}, {12738, 19861}, {12773, 16418}, {12848, 14151}, {13243, 50742}, {13253, 38759}, {13587, 22765}, {13607, 17614}, {13747, 37727}, {16865, 38631}, {17528, 37624}, {17549, 38602}, {17572, 38629}, {17660, 31165}, {19704, 38693}, {19705, 34474}, {21578, 25558}, {22836, 34749}, {22837, 34720}, {24466, 25485}, {24982, 32900}, {28174, 36005}, {28234, 35271}, {30144, 34606}, {34628, 34789}, {34747, 35023}, {35094, 35124}, {35457, 36004}, {38066, 38762}
X(50843) = midpoint of X(i) and X(j) for these {i,j}: {2, 10031}, {100, 3241}, {214, 11274}, {376, 10698}, {551, 33337}, {944, 10711}, {1317, 6174}, {3655, 6265}, {3679, 7972}, {6224, 10707}, {12119, 31162}, {17660, 31165}, {34628, 34789}
X(50843) = reflection of X(i) in X(j) for these {i,j}: {11, 551}, {80, 45310}, {381, 11729}, {1145, 6174}, {1317, 11274}, {3241, 12735}, {3679, 3035}, {6174, 214}, {10707, 1387}, {11274, 33812}, {12690, 10707}, {15863, 3828}, {24473, 5083}, {25416, 3241}, {34122, 34123}
X(50843) = X(106)-isoconjugate of X(24297)
X(50843) = X(214)-Dao conjugate of X(24297)
X(50843) = barycentric product X(4358)*X(5126)
X(50843) = barycentric quotient X(i)/X(j) for these {i,j}: {44, 24297}, {5126, 88}
X(50843) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11, 551, 38026}, {80, 25055, 45310}, {100, 12735, 25416}, {214, 1317, 1145}, {214, 33812, 1317}, {214, 41553, 5440}, {1317, 1319, 41556}, {1320, 9945, 12732}, {1387, 6224, 12690}, {3828, 15863, 38099}, {6224, 38314, 10707}, {10707, 38314, 1387}, {31235, 38099, 3828}
X(50844) lies on these lines: {2, 5426}, {100, 551}, {214, 519}, {376, 21635}, {528, 1125}, {549, 22935}, {678, 14028}, {952, 4745}, {1768, 15692}, {2771, 12100}, {2802, 3742}, {3035, 3828}, {3524, 6326}, {3543, 15017}, {3634, 10609}, {3653, 12331}, {3679, 33337}, {4297, 10711}, {4669, 10031}, {4855, 10199}, {5054, 10265}, {5528, 38025}, {5541, 38314}, {5848, 50787}, {6154, 38026}, {6224, 19875}, {7972, 34641}, {9803, 15708}, {9945, 45310}, {10707, 19883}, {12019, 31253}, {12119, 34648}, {13146, 15672}, {13199, 38021}, {13587, 35204}, {15688, 16128}, {16861, 46816}, {21630, 25055}, {28194, 33814}, {31235, 38104}, {34638, 34789}, {38068, 38762}
X(50844) = midpoint of X(i) and X(j) for these {i,j}: {100, 551}, {214, 6174}, {376, 21635}, {549, 22935}, {1145, 11274}, {3679, 33337}, {4297, 10711}, {4669, 10031}, {7972, 34641}, {9945, 45310}, {12119, 34648}, {34638, 34789}
X(50844) = reflection of X(i) in X(j) for these {i,j}: {3828, 3035}, {10707, 33709}
X(50844) = barycentric product X(519)*X(35596)
X(50844) = barycentric quotient X(35596)/X(903)
X(50844) = {X(10707),X(19883)}-harmonic conjugate of X(33709)
X(50845) lies on these lines: {100, 3828}, {214, 519}, {528, 3634}, {551, 12653}, {952, 44580}, {2802, 3848}, {4669, 15015}, {5528, 38101}, {5541, 19883}, {5848, 50788}, {6154, 38104}, {6224, 38098}, {7993, 15708}, {10711, 12512}, {12331, 38068}, {13199, 38076}, {19876, 20095}, {34123, 41150}
X(50845) = midpoint of X(i) and X(j) for these {i,j}: {100, 3828}, {10711, 12512}
X(50846) lies on these lines: {11, 3241}, {100, 20049}, {145, 528}, {214, 519}, {551, 38099}, {952, 1699}, {2093, 6154}, {3035, 31145}, {3036, 38314}, {3633, 13996}, {3679, 12735}, {4669, 34123}, {5848, 50790}, {5854, 10031}, {10711, 10893}, {12531, 45310}, {15863, 38026}, {34699, 34748}
X(50846) = midpoint of X(i) and X(j) for these {i,j}: {100, 20049}, {7972, 34747}
X(50846) = reflection of X(i) in X(j) for these {i,j}: {11, 3241}, {1145, 11274}, {3679, 12735}, {6174, 1317}, {12531, 45310}, {31145, 3035}
X(50847) lies on these lines: {2, 37830}, {10, 530}, {13, 3828}, {14, 2796}, {516, 41042}, {519, 5463}, {542, 38430}, {551, 618}, {553, 12942}, {616, 3679}, {966, 49571}, {3634, 22489}, {4669, 36769}, {4745, 35751}, {5460, 11599}, {5478, 38076}, {5617, 28194}, {5699, 49588}, {6771, 38068}, {8591, 9900}, {11705, 19883}, {16001, 31399}, {20252, 38083}, {33440, 36458}, {33441, 36440}, {36386, 49580}
X(50847) = midpoint of X(i) and X(j) for these {i,j}: {616, 3679}, {5463, 12781}, {8591, 9900}
X(50847) = reflection of X(i) in X(j) for these {i,j}: {13, 3828}, {551, 618}, {11599, 5460}
X(50848) lies on these lines: {8, 530}, {10, 22489}, {13, 3679}, {517, 41042}, {519, 5463}, {542, 34718}, {551, 36770}, {616, 31145}, {618, 3241}, {2482, 7974}, {3656, 36765}, {4669, 35752}, {4677, 35751}, {5460, 7983}, {5473, 28204}, {5478, 38074}, {6771, 38066}, {9114, 9881}, {9780, 48311}, {11362, 41020}, {11705, 19875}, {13178, 22577}, {20252, 38081}, {22493, 44659}, {22580, 49524}, {28194, 36961}
X(50848) = midpoint of X(616) and X(31145)
X(50848) = reflection of X(i) in X(j) for these {i,j}: {13, 3679}, {3241, 618}, {5463, 12781}, {7974, 2482}, {7975, 5463}, {7983, 5460}, {9114, 9881}, {22577, 13178}, {22580, 49524}
X(50849) lies on these lines: {1, 530}, {13, 551}, {515, 41042}, {519, 5463}, {542, 3655}, {616, 3241}, {618, 3679}, {671, 11706}, {1125, 22489}, {1386, 22580}, {2482, 12780}, {3624, 48311}, {3653, 6771}, {3828, 36770}, {4669, 36767}, {4677, 36768}, {5459, 9901}, {5460, 13178}, {5464, 11711}, {5473, 28194}, {5478, 38021}, {5617, 28204}, {6302, 36444}, {6306, 36462}, {8595, 44660}, {11599, 22577}, {11705, 38314}, {11707, 37786}, {11725, 31695}, {12337, 16371}, {16370, 22773}, {20252, 38022}, {35931, 44659}
X(50849) = midpoint of X(i) and X(j) for these {i,j}: {616, 3241}, {5463, 7975}
X(50849) = reflection of X(i) in X(j) for these {i,j}: {13, 551}, {671, 11706}, {3679, 618}, {5464, 11711}, {9901, 5459}, {12780, 2482}, {12781, 5463}, {13178, 5460}, {22577, 11599}, {22580, 1386}, {31695, 11725}, {37786, 11707}
X(50849) = {X(9901),X(25055)}-harmonic conjugate of X(5459)
X(50850) lies on these lines: {2, 37833}, {10, 531}, {13, 2796}, {14, 3828}, {516, 41043}, {519, 5464}, {542, 38430}, {551, 619}, {553, 12941}, {617, 3679}, {966, 49572}, {3634, 22490}, {4669, 47867}, {4745, 36329}, {5459, 11599}, {5479, 38076}, {5613, 28194}, {5700, 49589}, {6774, 38068}, {8591, 9901}, {11706, 19883}, {16002, 31399}, {20253, 38083}, {33442, 36440}, {33443, 36458}, {36388, 49584}
X(50850) = midpoint of X(i) and X(j) for these {i,j}: {617, 3679}, {5464, 12780}, {8591, 9901}
X(50850) = reflection of X(i) in X(j) for these {i,j}: {14, 3828}, {551, 619}, {11599, 5459}
X(50851) lies on these lines: {8, 531}, {10, 22490}, {14, 3679}, {517, 41043}, {519, 5464}, {542, 34718}, {617, 31145}, {619, 3241}, {2482, 7975}, {4669, 36330}, {4677, 36329}, {5459, 7983}, {5474, 28204}, {5479, 38074}, {6774, 38066}, {9116, 9881}, {9780, 48312}, {11362, 41021}, {11706, 19875}, {13178, 22578}, {20253, 38081}, {22494, 44660}, {22579, 49524}, {28194, 36962}
X(50851) = midpoint of X(617) and X(31145)
X(50851) = reflection of X(i) in X(j) for these {i,j}: {14, 3679}, {3241, 619}, {5464, 12780}, {7974, 5464}, {7975, 2482}, {7983, 5459}, {9116, 9881}, {22578, 13178}, {22579, 49524}
X(50852) lies on these lines: {1, 531}, {14, 551}, {515, 41043}, {519, 5464}, {542, 3655}, {617, 3241}, {619, 3679}, {671, 11705}, {1125, 22490}, {1386, 22579}, {2482, 12781}, {3624, 48312}, {3653, 6774}, {5459, 13178}, {5460, 9900}, {5463, 11711}, {5474, 28194}, {5479, 38021}, {5613, 28204}, {6303, 36462}, {6307, 36444}, {8594, 44659}, {11599, 22578}, {11706, 38314}, {11708, 37785}, {11725, 31696}, {12336, 16371}, {16370, 22774}, {20253, 38022}, {35932, 44660}
X(50852) = midpoint of X(i) and X(j) for these {i,j}: {617, 3241}, {5464, 7974}
X(50852) = reflection of X(i) in X(j) for these {i,j}: {14, 551}, {671, 11705}, {3679, 619}, {5463, 11711}, {9900, 5460}, {12780, 5464}, {12781, 2482}, {13178, 5459}, {22578, 11599}, {22579, 1386}, {31696, 11725}, {37785, 11708}
X(50852) = {X(9900),X(25055)}-harmonic conjugate of X(5460)
X(50853) lies on these lines: {1, 623}, {2, 11707}, {8, 621}, {10, 15}, {30, 12781}, {40, 22896}, {316, 44660}, {355, 511}, {515, 14538}, {516, 36992}, {517, 20428}, {531, 3679}, {532, 9901}, {740, 49575}, {1125, 40334}, {1698, 6671}, {5587, 7684}, {5611, 5790}, {5657, 36993}, {6672, 38221}, {6684, 21158}, {7975, 21359}, {9903, 22651}, {10791, 36759}, {13350, 26446}, {18481, 36755}, {19875, 45879}, {19876, 48313}, {19925, 41036}, {22511, 50775}
X(50853) = midpoint of X(8) and X(621)
X(50853) = reflection of X(i) in X(j) for these {i,j}: {1, 623}, {15, 10}, {18481, 36755}
X(50853) = anticomplement of X(11707)
X(50854) lies on these lines: {1, 531}, {2, 44659}, {15, 551}, {511, 3656}, {621, 3241}, {623, 3679}, {3624, 48313}, {3653, 13350}, {3828, 40334}, {5184, 45880}, {7684, 38021}, {11705, 37786}, {11707, 38314}, {14538, 28194}, {20428, 28204}, {25055, 45879}
X(50854) = midpoint of X(621) and X(3241)
X(50854) = reflection of X(i) in X(j) for these {i,j}: {15, 551}, {3679, 623}, {5184, 45880}, {37786, 11705}
X(50855) lies on these lines: {2, 14}, {6, 22496}, {13, 524}, {16, 3849}, {18, 37341}, {30, 5463}, {61, 7817}, {62, 7812}, {69, 16808}, {141, 16809}, {187, 16645}, {298, 316}, {300, 35139}, {302, 10646}, {303, 42915}, {325, 9762}, {376, 44666}, {381, 511}, {395, 18907}, {396, 22489}, {532, 42973}, {533, 5459}, {543, 23004}, {549, 21158}, {597, 36757}, {618, 35931}, {624, 42918}, {627, 43633}, {633, 34509}, {635, 11304}, {671, 43538}, {804, 9162}, {858, 34314}, {1352, 41043}, {1992, 37170}, {2459, 36452}, {2460, 36470}, {3104, 7841}, {3105, 7775}, {3107, 11163}, {3180, 33560}, {3524, 36993}, {3526, 21401}, {3534, 36755}, {3545, 7684}, {3679, 44659}, {3734, 11295}, {3763, 42125}, {5054, 13350}, {5055, 5611}, {5099, 34316}, {5215, 42129}, {5318, 35752}, {5461, 22510}, {5470, 22573}, {5476, 20426}, {5858, 41107}, {5859, 41121}, {5862, 41112}, {5863, 31705}, {5965, 32907}, {6144, 42815}, {6582, 40707}, {6672, 26613}, {6694, 43776}, {6782, 43275}, {7615, 42036}, {7617, 9763}, {7801, 37333}, {7810, 37332}, {8352, 22576}, {9114, 9885}, {10168, 32909}, {11001, 49901}, {11008, 42895}, {11095, 49723}, {11168, 44219}, {11185, 22575}, {11289, 42993}, {11297, 42972}, {11298, 16268}, {11300, 39554}, {11302, 39555}, {11586, 40709}, {11645, 48655}, {11707, 25055}, {12100, 49902}, {12155, 22998}, {14541, 16626}, {15534, 42974}, {16002, 47517}, {16242, 33474}, {16635, 43276}, {16964, 37340}, {16966, 33475}, {18546, 31711}, {19106, 35751}, {19780, 49906}, {19924, 22796}, {20582, 37351}, {22110, 36765}, {22329, 22511}, {22577, 22894}, {22844, 42161}, {22845, 42598}, {22849, 36388}, {22997, 33477}, {29181, 41024}, {31695, 31703}, {31696, 46855}, {32455, 43030}, {32459, 35304}, {33458, 49907}, {33459, 41100}, {33624, 42952}, {34317, 41022}, {35229, 42489}, {36368, 43229}, {36767, 42099}, {36770, 42942}, {37144, 50226}, {37172, 42157}, {40335, 42095}, {40341, 42128}, {41017, 47354}, {42816, 47355}, {42975, 47352}
X(50855) = midpoint of X(i) and X(j) for these {i,j}: {2, 621}, {13, 22493}, {9114, 25166}, {19106, 35751}, {22849, 36388}
X(50855) = reflection of X(i) in X(j) for these {i,j}: {2, 623}, {13, 31693}, {15, 2}, {3534, 36755}, {8594, 619}, {15534, 44498}, {22495, 13}, {23005, 8352}, {34314, 858}, {34316, 5099}, {35304, 44383}, {35752, 5318}, {35931, 618}, {36330, 33518}, {36366, 31705}, {36967, 35304}, {37786, 5459}
X(50855) = anticomplement of X(45879)
X(50855) = {circumcircle-of-inner-Napoleon-triangle-inverse of X(5464)}
X(50855) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 617, 13083}, {2, 18581, 22490}, {2, 22491, 14}, {15, 623, 40334}, {69, 22492, 22494}, {302, 35932, 13084}, {621, 623, 15}, {5459, 37786, 16267}, {5863, 41119, 36366}, {9114, 36766, 9885}, {9761, 11296, 16}, {11303, 34508, 62}, {13084, 35932, 10646}, {14538, 20428, 36992}, {16808, 22494, 22492}, {22493, 31693, 22495}, {33474, 35303, 16242}, {47361, 47362, 5464}
X(50856) lies on these lines: {1, 624}, {2, 11708}, {8, 622}, {10, 16}, {30, 12780}, {40, 22851}, {316, 44659}, {355, 511}, {515, 14539}, {516, 36994}, {517, 20429}, {530, 3679}, {533, 9900}, {740, 49576}, {1125, 40335}, {1698, 6672}, {5587, 7685}, {5615, 5790}, {5657, 36995}, {6671, 38221}, {6684, 21159}, {7974, 21360}, {9903, 22652}, {10791, 36760}, {13349, 26446}, {18481, 36756}, {19875, 45880}, {19876, 48314}, {19925, 41037}, {22510, 50775}
X(50856) = midpoint of X(8) and X(622)
X(50856) = reflection of X(i) in X(j) for these {i,j}: {1, 624}, {16, 10}, {18481, 36756}
X(50856) = anticomplement of X(11708)
X(50857) lies on these lines: {1, 530}, {2, 44660}, {16, 551}, {511, 3656}, {622, 3241}, {624, 3679}, {3624, 48314}, {3653, 13349}, {3828, 40335}, {5184, 45879}, {7685, 38021}, {11706, 37785}, {11708, 38314}, {14539, 28194}, {20429, 28204}, {25055, 45880}
X(50857) = midpoint of X(622) and X(3241)
X(50857) = reflection of X(i) in X(j) for these {i,j}: {16, 551}, {3679, 624}, {5184, 45879}, {37785, 11706}
X(50858) lies on these lines: {2, 13}, {6, 22495}, {14, 524}, {15, 3849}, {17, 37340}, {30, 5464}, {61, 7812}, {62, 7817}, {69, 16809}, {141, 16808}, {187, 16644}, {299, 316}, {301, 35139}, {302, 42914}, {303, 10645}, {325, 9760}, {376, 44667}, {381, 511}, {395, 22490}, {396, 18907}, {532, 5460}, {533, 42972}, {543, 23005}, {549, 21159}, {597, 36758}, {619, 35932}, {623, 42919}, {628, 43632}, {634, 34508}, {636, 11303}, {671, 43539}, {804, 9163}, {858, 34313}, {1352, 41042}, {1992, 37171}, {2459, 36469}, {2460, 36453}, {3104, 7775}, {3105, 7841}, {3106, 11163}, {3181, 33561}, {3524, 36995}, {3526, 21402}, {3534, 36756}, {3545, 7685}, {3679, 44660}, {3734, 11296}, {3763, 42128}, {5054, 13349}, {5055, 5615}, {5099, 34315}, {5215, 42132}, {5321, 36330}, {5461, 22511}, {5469, 22574}, {5476, 20425}, {5858, 41122}, {5859, 41108}, {5862, 31706}, {5863, 41113}, {5965, 32909}, {6144, 42816}, {6295, 40706}, {6671, 26613}, {6695, 43775}, {6783, 43274}, {7615, 42035}, {7617, 9761}, {7801, 37332}, {7810, 37333}, {8352, 22575}, {9116, 9886}, {10168, 32907}, {11001, 49902}, {11008, 42894}, {11096, 49723}, {11185, 22576}, {11290, 42992}, {11292, 35730}, {11297, 16267}, {11298, 42973}, {11299, 39555}, {11301, 39554}, {11645, 48656}, {11708, 25055}, {12100, 49901}, {12154, 22997}, {14540, 16627}, {15534, 42975}, {15743, 40710}, {16001, 47519}, {16241, 33475}, {16634, 43277}, {16965, 37341}, {16967, 33474}, {18546, 31712}, {19107, 36329}, {19781, 49905}, {19924, 22797}, {20582, 37352}, {22110, 44219}, {22329, 22510}, {22578, 22850}, {22844, 42599}, {22845, 42160}, {22895, 36386}, {22998, 33476}, {29181, 41025}, {31695, 46854}, {31696, 31704}, {32455, 43031}, {32459, 35303}, {33458, 41101}, {33459, 49908}, {33622, 42953}, {34318, 41023}, {35230, 42488}, {36366, 43228}, {37145, 50226}, {37173, 42158}, {40334, 42098}, {40341, 42125}, {41016, 47354}, {42815, 47355}, {42974, 47352}
X(50858) = midpoint of X(i) and X(j) for these {i,j}: {2, 622}, {14, 22494}, {9116, 25156}, {19107, 36329}, {22895, 36386}
X(50858) = reflection of X(i) in X(j) for these {i,j}: {2, 624}, {14, 31694}, {16, 2}, {3534, 36756}, {8595, 618}, {15534, 44497}, {22496, 14}, {23004, 8352}, {34313, 858}, {34315, 5099}, {35303, 44382}, {35752, 33517}, {35932, 619}, {36330, 5321}, {36368, 31706}, {36968, 35303}, {37785, 5460}
X(50858) = anticomplement of X(45880)
X(50858) = {circumcircle-of-outer-Napoleon-triangle-inverse of X(5463)}
X(50858) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 616, 13084}, {2, 18582, 22489}, {2, 22492, 13}, {16, 624, 40335}, {69, 22491, 22493}, {303, 35931, 13083}, {622, 624, 16}, {5460, 37785, 16268}, {5862, 41120, 36368}, {9763, 11295, 15}, {11304, 34509, 61}, {13083, 35931, 10645}, {14539, 20429, 36994}, {16809, 22493, 22491}, {22494, 31694, 22496}, {33475, 35304, 16241}, {47363, 47364, 5463}
X(50859) lies on these lines: {2, 17}, {3, 21359}, {5, 49953}, {6, 22892}, {13, 38412}, {14, 99}, {16, 37352}, {18, 11297}, {30, 16626}, {61, 33387}, {298, 11132}, {299, 33417}, {376, 44666}, {381, 5463}, {519, 22896}, {524, 41943}, {531, 14144}, {533, 37007}, {543, 11602}, {549, 5464}, {599, 5050}, {616, 16808}, {619, 34540}, {621, 42529}, {623, 36968}, {624, 22895}, {630, 42597}, {2482, 32909}, {3058, 22905}, {3181, 6671}, {3524, 22532}, {3534, 48666}, {3545, 22832}, {3582, 22930}, {3584, 22929}, {3643, 16967}, {3830, 22795}, {5054, 49106}, {5055, 16629}, {5064, 22482}, {5309, 16645}, {5434, 22904}, {5470, 14904}, {5858, 7764}, {5862, 42152}, {5982, 8592}, {6054, 16652}, {6670, 11122}, {6674, 38223}, {7757, 25167}, {7865, 22746}, {8259, 43229}, {8716, 42035}, {9761, 11301}, {10611, 22489}, {10653, 31705}, {11237, 18973}, {11238, 22910}, {11295, 36767}, {11300, 13084}, {11302, 16242}, {11304, 41115}, {11305, 41100}, {11307, 35689}, {11489, 14482}, {11739, 25055}, {13712, 36455}, {13835, 36437}, {13846, 49238}, {13847, 49239}, {16268, 37340}, {16635, 31704}, {19070, 32787}, {19071, 32788}, {19875, 22652}, {20377, 47865}, {22490, 22891}, {22845, 42490}, {22893, 23303}, {22900, 37832}, {22902, 34612}, {22903, 34606}, {22931, 45701}, {22932, 45700}, {31168, 45880}, {32455, 43232}, {33413, 49809}, {33415, 42489}, {33464, 49913}, {34508, 41101}, {35304, 36330}, {37172, 41108}, {41118, 41122}
X(50859) = midpoint of X(i) and X(j) for these {i,j}: {2, 627}, {17, 36386}, {3534, 48666}, {22113, 33622}, {22508, 22569}, {22844, 36366}
X(50859) = reflection of X(i) in X(j) for these {i,j}: {2, 629}, {17, 2}, {3830, 22795}, {22488, 22685}, {22844, 36386}, {33626, 33465}, {36366, 17}, {36386, 627}, {47865, 20377}
X(50859) = Thomson-isogonal conjugate of X(10645)
X(50859) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36386, 36366}, {17, 627, 22844}, {302, 618, 14}, {302, 30472, 40707}, {627, 629, 17}, {6673, 22113, 17}
X(50860) lies on these lines: {2, 18}, {3, 21360}, {5, 49952}, {6, 22848}, {13, 99}, {15, 37351}, {17, 11298}, {30, 16627}, {62, 33386}, {141, 36770}, {298, 33416}, {299, 11133}, {376, 44667}, {381, 5464}, {519, 22851}, {524, 41944}, {530, 14145}, {532, 37008}, {543, 11603}, {549, 5463}, {599, 5050}, {617, 16809}, {618, 34541}, {622, 42528}, {623, 22849}, {624, 36967}, {629, 42596}, {2482, 32907}, {3058, 22860}, {3180, 6672}, {3524, 22531}, {3534, 48665}, {3545, 22831}, {3582, 22885}, {3584, 22884}, {3642, 16966}, {3830, 22794}, {5054, 49105}, {5055, 16628}, {5064, 22481}, {5309, 16644}, {5434, 22859}, {5469, 14905}, {5859, 7764}, {5863, 42149}, {5983, 8592}, {6054, 16653}, {6669, 11121}, {6673, 38223}, {7757, 25157}, {7865, 22745}, {8260, 43228}, {8716, 42036}, {9763, 11302}, {10612, 22490}, {10654, 31706}, {11237, 18972}, {11238, 22865}, {11299, 13083}, {11301, 16241}, {11303, 41114}, {11306, 41101}, {11308, 35688}, {11488, 14482}, {11740, 25055}, {13712, 36437}, {13835, 36455}, {13846, 49236}, {13847, 49237}, {16267, 37341}, {16634, 31703}, {19069, 32788}, {19072, 32787}, {19875, 22651}, {20378, 47866}, {22489, 22846}, {22844, 42491}, {22847, 23302}, {22856, 37835}, {22857, 34612}, {22858, 34606}, {22886, 45701}, {22887, 45700}, {31168, 45879}, {32455, 43233}, {33412, 49806}, {33414, 42488}, {33465, 49912}, {34509, 41100}, {35303, 35752}, {37173, 41107}, {41117, 41121}
X(50860) = midpoint of X(i) and X(j) for these {i,j}: {2, 628}, {18, 36388}, {3534, 48665}, {22114, 33624}, {22506, 22567}, {22845, 36368}
X(50860) = reflection of X(i) in X(j) for these {i,j}: {2, 630}, {18, 2}, {3830, 22794}, {22487, 22683}, {22845, 36388}, {33627, 33464}, {36368, 18}, {36388, 628}, {47866, 20378}
X(50860) = Thomson-isogonal conjugate of X(10646)
X(50860) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36388, 36368}, {18, 628, 22845}, {303, 619, 13}, {303, 30471, 40706}, {628, 630, 18}, {6674, 22114, 18}
X(50861) lies on these lines: {1, 5800}, {2, 5285}, {4, 9}, {8, 2893}, {20, 3220}, {25, 21015}, {30, 24320}, {33, 21062}, {55, 440}, {57, 7386}, {63, 1370}, {66, 72}, {197, 7580}, {198, 49132}, {201, 11392}, {212, 11393}, {219, 1503}, {220, 36990}, {226, 612}, {238, 1479}, {329, 2835}, {377, 4357}, {387, 16470}, {388, 3668}, {405, 1486}, {427, 7085}, {442, 23305}, {443, 17306}, {497, 7070}, {515, 30265}, {518, 41004}, {519, 31158}, {534, 3679}, {950, 3755}, {958, 13442}, {984, 1478}, {1001, 30810}, {1006, 15177}, {1125, 31261}, {1350, 26932}, {1352, 3781}, {1368, 20266}, {1376, 19542}, {1473, 7667}, {1631, 36017}, {1698, 40530}, {1751, 2195}, {1782, 21364}, {1836, 43214}, {1853, 26942}, {1899, 26893}, {2323, 6776}, {2475, 17257}, {2478, 17353}, {2876, 10477}, {3218, 16063}, {3219, 7391}, {3305, 6997}, {3306, 46336}, {3419, 3696}, {3421, 4901}, {3434, 3883}, {3436, 3717}, {3487, 30142}, {3538, 37526}, {3575, 26935}, {3617, 10251}, {3651, 39582}, {3688, 12588}, {3690, 11550}, {3718, 7270}, {3869, 21280}, {3925, 7522}, {3928, 26929}, {3929, 44442}, {4086, 8768}, {4302, 7295}, {4307, 5746}, {4362, 20539}, {4429, 37086}, {4647, 10869}, {4847, 36844}, {5046, 26685}, {5064, 26867}, {5080, 27549}, {5225, 15601}, {5227, 36851}, {5263, 37445}, {5273, 37456}, {5709, 6643}, {5745, 26118}, {5776, 29207}, {6284, 7083}, {6358, 7102}, {6360, 34186}, {6684, 21160}, {6925, 40880}, {7193, 46264}, {7308, 7392}, {7330, 34938}, {7394, 27065}, {7557, 9780}, {9895, 12699}, {9958, 18517}, {10996, 37551}, {11113, 48829}, {12329, 23300}, {12782, 46181}, {14790, 26921}, {15940, 28194}, {17532, 49725}, {17903, 44695}, {18531, 37584}, {19854, 25516}, {21376, 44447}, {21530, 37547}, {24701, 34381}, {26032, 27184}, {26872, 32064}, {26885, 31383}, {26933, 31152}, {27410, 48890}, {27540, 50698}, {28287, 37191}, {28731, 37444}, {30733, 49553}, {31327, 33076}, {32784, 37093}, {33094, 40973}
X(50861) = midpoint of X(8) and X(4329)
X(50861) = reflection of X(i) in X(j) for these {i,j}: {1, 18589}, {19, 10}
X(50861) = barycentric product X(10)*X(24606)
X(50861) = barycentric quotient X(24606)/X(86)
X(50861) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 26939, 9}, {20, 27509, 3220}, {1368, 37581, 20266}
X(50862) lies on these lines: {1, 50687}, {2, 28164}, {3, 38076}, {4, 551}, {10, 30}, {20, 3828}, {40, 38098}, {355, 15684}, {376, 19925}, {381, 4297}, {382, 28194}, {515, 3656}, {516, 4669}, {517, 33699}, {519, 962}, {548, 38083}, {550, 38068}, {553, 12943}, {946, 15687}, {1125, 3839}, {1385, 14893}, {1482, 35434}, {2796, 10723}, {3146, 3679}, {3241, 17578}, {3244, 31162}, {3522, 19876}, {3524, 18492}, {3534, 10164}, {3545, 19862}, {3576, 41099}, {3625, 34627}, {3626, 34632}, {3627, 4301}, {3634, 10304}, {3653, 3843}, {3654, 28150}, {3655, 18483}, {3817, 3845}, {3853, 5882}, {3856, 31666}, {3860, 11230}, {4314, 11237}, {4315, 11238}, {4677, 28228}, {4745, 15640}, {5066, 10165}, {5076, 13464}, {5086, 10032}, {5434, 21625}, {5587, 11001}, {5731, 30308}, {5732, 38094}, {6684, 15681}, {7406, 41141}, {7989, 15692}, {7991, 50691}, {8703, 10175}, {9588, 49140}, {9589, 31145}, {9956, 15686}, {10109, 17502}, {10171, 41106}, {10172, 15693}, {11231, 15690}, {11362, 28202}, {12100, 38140}, {12101, 28186}, {12512, 15683}, {12571, 25055}, {13473, 47593}, {13624, 38071}, {14269, 15808}, {15685, 26446}, {15689, 22266}, {15704, 31399}, {15708, 31253}, {17547, 35202}, {28154, 38127}, {28198, 35404}, {31165, 31871}, {31663, 44903}, {33703, 38074}, {35242, 46333}, {37714, 49135}, {38066, 49136}, {38073, 43176}, {38089, 44882}, {38104, 38759}, {38204, 50396}
X(50862) = midpoint of X(i) and X(j) for these {i,j}: {355, 15684}, {3146, 3679}, {3543, 5691}, {9589, 31145}, {34627, 41869}
X(50862) = reflection of X(i) in X(j) for these {i,j}: {10, 34648}, {20, 3828}, {376, 19925}, {551, 4}, {946, 15687}, {1385, 14893}, {3244, 31162}, {3625, 34627}, {3655, 18483}, {4297, 381}, {5493, 3679}, {15681, 6684}, {15683, 12512}, {15686, 9956}, {31165, 31871}, {34628, 1125}, {34632, 3626}, {34638, 10}, {34648, 31673}, {44903, 31663}
X(50862) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {381, 4297, 19883}, {3655, 38335, 18483}, {3839, 34628, 1125}, {15683, 19875, 12512}
X(50863) lies on these lines: {2, 17502}, {30, 3617}, {382, 31145}, {519, 962}, {1698, 10304}, {3146, 28202}, {3241, 50688}, {3616, 3839}, {3622, 14269}, {3623, 3656}, {3653, 3854}, {3679, 49135}, {3830, 28224}, {4668, 34632}, {5059, 38074}, {7967, 12101}, {10595, 35403}, {12245, 35404}, {15640, 28150}, {15682, 28174}, {15684, 20070}, {15688, 46932}, {15697, 28164}, {15710, 46931}, {15721, 19925}, {17504, 46930}, {17578, 28204}, {18357, 46333}, {19708, 28190}, {19862, 34628}, {20052, 33697}, {28186, 41099}, {28194, 50691}, {38066, 49138}, {38081, 49137}
X(50863) = reflection of X(i) in X(j) for these {i,j}: {1698, 34648}, {10595, 35403}, {20052, 34627}, {34628, 19862}, {34632, 4668}
X(50864) lies on these lines: {1, 3839}, {2, 515}, {3, 38074}, {4, 1392}, {8, 30}, {10, 10304}, {20, 3679}, {40, 15683}, {80, 5435}, {145, 31162}, {165, 4745}, {355, 376}, {381, 944}, {388, 15933}, {516, 4677}, {517, 15682}, {519, 962}, {528, 36991}, {535, 28610}, {548, 38081}, {549, 5818}, {550, 38066}, {551, 3091}, {553, 5727}, {938, 5434}, {952, 3830}, {1385, 5071}, {1482, 10248}, {1483, 14893}, {1698, 15708}, {2094, 9803}, {2784, 9875}, {3086, 7319}, {3090, 3653}, {3146, 5881}, {3476, 11238}, {3486, 11237}, {3523, 3828}, {3524, 9780}, {3525, 38083}, {3534, 5657}, {3545, 3616}, {3583, 4345}, {3584, 4305}, {3585, 4323}, {3621, 41869}, {3622, 18492}, {3623, 18483}, {3626, 34638}, {3654, 9778}, {3832, 5882}, {3845, 5603}, {3851, 38022}, {3854, 9624}, {3855, 15178}, {3860, 10283}, {3889, 16616}, {4297, 15692}, {4301, 34747}, {4308, 10072}, {4313, 10056}, {4428, 6912}, {4511, 18528}, {4669, 28164}, {4678, 31730}, {5054, 18357}, {5055, 5550}, {5056, 38076}, {5059, 11362}, {5066, 10246}, {5252, 10385}, {5493, 49140}, {5690, 15681}, {5732, 38092}, {5748, 6224}, {5768, 28452}, {5790, 8703}, {5844, 33699}, {5886, 41106}, {5905, 20085}, {6049, 10591}, {6253, 34700}, {6915, 40726}, {7406, 17310}, {7486, 30389}, {7967, 9779}, {7982, 17578}, {7987, 15721}, {7989, 19883}, {7991, 34641}, {8185, 37940}, {8591, 9864}, {9041, 36990}, {9143, 12368}, {9589, 50691}, {9613, 11037}, {9799, 17579}, {9956, 15702}, {10303, 19876}, {10430, 37429}, {10728, 18499}, {10914, 12125}, {11114, 34697}, {11160, 39885}, {11177, 13178}, {11231, 15719}, {11491, 28444}, {11500, 17549}, {12100, 38138}, {12114, 13587}, {12245, 28198}, {12512, 38098}, {12528, 44663}, {12536, 37433}, {12645, 15684}, {12647, 30332}, {12699, 20050}, {13464, 50689}, {13624, 15709}, {14269, 18526}, {14647, 36005}, {15685, 28190}, {15690, 38112}, {15693, 38042}, {15705, 46933}, {15717, 38068}, {16191, 28236}, {18391, 37006}, {18493, 23046}, {18761, 28461}, {19541, 38669}, {19708, 26446}, {19925, 25055}, {20053, 33697}, {20070, 47745}, {22791, 34748}, {28202, 33703}, {34557, 35736}, {34711, 34717}, {35403, 40273}, {35404, 48661}, {37546, 37945}, {38075, 43175}, {38087, 44882}, {38099, 38759}, {48923, 50415}, {48937, 50422}
X(50864) = midpoint of X(i) and X(j) for these {i,j}: {3146, 31145}, {12645, 15684}
X(50864) = reflection of X(i) in X(j) for these {i,j}: {1, 34648}, {8, 34627}, {20, 3679}, {145, 31162}, {376, 355}, {944, 381}, {962, 3543}, {1482, 15687}, {1483, 14893}, {3241, 4}, {3543, 5691}, {3655, 18480}, {6224, 10711}, {6361, 34718}, {7991, 34641}, {8591, 9864}, {9143, 12368}, {11001, 3654}, {11114, 34697}, {11160, 39885}, {11177, 13178}, {15681, 5690}, {15683, 40}, {17579, 34746}, {20049, 7982}, {20050, 34631}, {31145, 5881}, {31162, 31673}, {34627, 18525}, {34628, 10}, {34631, 12699}, {34632, 8}, {34638, 3626}, {34711, 34717}, {34718, 37705}, {34744, 34700}, {34747, 4301}, {34748, 22791}, {48661, 35404}, {48923, 50415}, {50422, 48937}
X(50864) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 34648, 3839}, {10, 34628, 10304}, {145, 50687, 31162}, {381, 944, 38314}, {3545, 3655, 3616}, {3654, 11001, 9778}, {3655, 18480, 3545}, {4297, 19875, 15692}, {6361, 37705, 8}, {31162, 31673, 50687}, {34748, 38335, 22791}
X(50865) lies on these lines: {1, 30}, {2, 165}, {3, 28202}, {4, 3679}, {5, 19876}, {7, 30350}, {8, 34648}, {10, 3839}, {20, 551}, {40, 381}, {57, 11238}, {63, 10032}, {147, 2796}, {200, 5057}, {226, 10385}, {355, 15687}, {376, 946}, {382, 7982}, {388, 30337}, {392, 50397}, {497, 553}, {511, 45829}, {515, 11224}, {517, 3830}, {519, 962}, {527, 3062}, {528, 1750}, {547, 31423}, {548, 38022}, {549, 8227}, {550, 3653}, {671, 9860}, {952, 33699}, {1001, 41853}, {1058, 4355}, {1125, 10304}, {1282, 10710}, {1385, 15681}, {1478, 9819}, {1479, 3339}, {1482, 15684}, {1490, 34629}, {1572, 11648}, {1597, 37546}, {1695, 48852}, {1697, 11237}, {1698, 3545}, {1702, 35822}, {1703, 35823}, {1709, 3928}, {1768, 10707}, {1770, 3361}, {1864, 5903}, {1992, 39878}, {2093, 3583}, {2100, 10720}, {2101, 10719}, {2550, 30393}, {2807, 21969}, {2948, 10706}, {2951, 6173}, {2999, 33094}, {3090, 38068}, {3091, 3828}, {3097, 44422}, {3146, 3241}, {3340, 12953}, {3434, 5223}, {3524, 3624}, {3529, 13464}, {3534, 3576}, {3579, 5055}, {3582, 15803}, {3586, 18421}, {3601, 4870}, {3627, 5881}, {3628, 31425}, {3632, 31673}, {3633, 34631}, {3654, 3845}, {3671, 15933}, {3715, 12702}, {3731, 33109}, {3746, 37411}, {3832, 38076}, {3843, 38066}, {3851, 38083}, {3860, 38042}, {3877, 15679}, {3914, 16469}, {3925, 41858}, {3929, 11372}, {3973, 32865}, {4297, 15683}, {4300, 48855}, {4318, 9577}, {4330, 6869}, {4338, 4857}, {4421, 42843}, {4428, 7580}, {4666, 43178}, {4668, 18480}, {4669, 28228}, {4863, 31672}, {4995, 5219}, {5054, 9955}, {5066, 26446}, {5071, 6684}, {5073, 10222}, {5079, 31447}, {5119, 5726}, {5128, 10896}, {5231, 44447}, {5250, 6175}, {5290, 10624}, {5298, 50443}, {5325, 5698}, {5400, 36634}, {5537, 19541}, {5541, 10711}, {5550, 15705}, {5584, 16857}, {5603, 11001}, {5657, 28232}, {5690, 14893}, {5715, 16208}, {5731, 28158}, {5732, 38024}, {5734, 49135}, {5735, 10431}, {5805, 10857}, {5812, 34746}, {5882, 33703}, {5886, 8703}, {5901, 15686}, {5927, 15104}, {6054, 13174}, {6174, 15017}, {6259, 34699}, {6261, 40265}, {6282, 28452}, {7308, 18482}, {7406, 41140}, {7753, 9593}, {7962, 12943}, {7967, 28172}, {7992, 45648}, {7993, 14217}, {7994, 31142}, {8148, 33697}, {8580, 24703}, {8591, 21636}, {8983, 9585}, {9140, 9904}, {9591, 44837}, {9612, 10056}, {9616, 13846}, {9620, 14537}, {9625, 18324}, {9668, 11529}, {9670, 11518}, {9801, 50119}, {9856, 31165}, {10136, 31527}, {10165, 19708}, {10175, 41106}, {10246, 15685}, {10247, 28168}, {10248, 19925}, {10439, 15310}, {10442, 17274}, {10446, 42057}, {10580, 30424}, {10582, 20292}, {10708, 39156}, {10718, 12408}, {10724, 13253}, {10728, 12653}, {10738, 12767}, {11012, 28444}, {11177, 11599}, {11230, 15693}, {11278, 34748}, {11495, 38093}, {12100, 38034}, {12101, 28212}, {12512, 15692}, {12645, 35434}, {12650, 34617}, {12700, 34697}, {12705, 31159}, {12915, 31391}, {13405, 30332}, {13462, 30384}, {13541, 44984}, {13624, 15689}, {15071, 24473}, {15178, 17800}, {15228, 23708}, {15601, 21949}, {15640, 28164}, {15688, 18493}, {15690, 38028}, {15694, 31663}, {15695, 17502}, {15708, 19862}, {16191, 28186}, {16200, 28160}, {16475, 43273}, {16487, 23681}, {16491, 48905}, {16496, 48910}, {16833, 28854}, {17578, 31145}, {17605, 35445}, {17606, 41348}, {17768, 24392}, {18201, 21267}, {18393, 30282}, {18788, 36731}, {19710, 28182}, {19722, 49130}, {20049, 50690}, {21363, 48940}, {23511, 24715}, {26040, 36835}, {28459, 30503}, {28538, 36990}, {29181, 47358}, {29229, 37521}, {30363, 37443}, {31164, 34611}, {31435, 44217}, {33179, 35400}, {34556, 35735}, {34640, 34716}, {34641, 50688}, {34647, 34701}, {34706, 44663}, {37022, 40726}, {38023, 44882}, {38026, 38759}, {47310, 47321}
X(50865) = midpoint of X(i) and X(j) for these {i,j}: {381, 48661}, {962, 3543}, {1482, 15684}, {3146, 3241}, {3679, 9589}, {31162, 41869}
X(50865) = reflection of X(i) in X(j) for these {i,j}: {1, 31162}, {8, 34648}, {20, 551}, {40, 381}, {165, 1699}, {355, 15687}, {376, 946}, {381, 22793}, {549, 40273}, {1282, 10710}, {1699, 9812}, {1768, 10707}, {2100, 10720}, {2101, 10719}, {2948, 10706}, {2951, 6173}, {3241, 4301}, {3632, 34627}, {3633, 34631}, {3654, 3845}, {3655, 22791}, {3679, 4}, {3928, 11235}, {5493, 3828}, {5541, 10711}, {5690, 14893}, {5691, 3543}, {7991, 3679}, {7994, 31142}, {8591, 21636}, {9778, 3817}, {9860, 671}, {9904, 9140}, {11177, 11599}, {12408, 10718}, {13174, 6054}, {15071, 24473}, {15104, 5927}, {15681, 1385}, {15683, 4297}, {15686, 5901}, {30304, 31146}, {31162, 12699}, {31165, 9856}, {34627, 31673}, {34628, 1}, {34632, 10}, {34638, 1125}, {34701, 34647}, {34716, 34640}, {34718, 18480}, {34747, 7982}, {34748, 11278}, {39156, 10708}, {39878, 1992}, {41338, 31140}, {47321, 47310}
X(50865) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1699, 30308}, {2, 30308, 7988}, {4, 7991, 37714}, {4, 9589, 7991}, {8, 50687, 34648}, {20, 11522, 30389}, {40, 381, 19875}, {165, 1699, 7988}, {165, 30308, 2}, {376, 946, 25055}, {376, 25055, 7987}, {381, 19875, 7989}, {497, 4312, 10980}, {962, 5691, 11531}, {1058, 4355, 30343}, {1125, 34638, 10304}, {1770, 9614, 3361}, {1836, 3058, 4654}, {1836, 9580, 1}, {3058, 4654, 1}, {3091, 5493, 9588}, {3091, 9588, 30315}, {3649, 41864, 1}, {3654, 3845, 5587}, {3839, 34632, 10}, {4654, 9580, 3058}, {5735, 10431, 30304}, {6361, 18483, 1698}, {9579, 12701, 1}, {9955, 35242, 34595}, {10248, 20070, 19925}, {11362, 38074, 3679}, {12512, 19883, 15692}, {12699, 41869, 1}, {15683, 38314, 4297}, {22793, 48661, 40}, {34718, 38335, 18480}
X(50866) lies on these lines: {30, 1698}, {40, 35404}, {165, 15640}, {382, 3679}, {519, 962}, {551, 50688}, {1699, 3830}, {3146, 9588}, {3529, 19876}, {3576, 12101}, {3616, 34628}, {3617, 34648}, {3624, 14269}, {3627, 3656}, {3653, 12102}, {3828, 49135}, {3839, 19862}, {3853, 38021}, {4668, 31673}, {4816, 41869}, {5059, 38076}, {5657, 15682}, {7989, 15683}, {7991, 50690}, {8227, 35403}, {9583, 43503}, {9617, 42639}, {9956, 35400}, {10304, 31253}, {11522, 17578}, {15679, 38052}, {15687, 25055}, {15688, 19872}, {18526, 31162}, {28164, 30308}, {28172, 41099}, {28174, 33699}, {28208, 35434}, {30315, 49140}, {31447, 35407}, {37714, 50691}, {38068, 49138}, {38083, 49137}
X(50866) = reflection of X(i) in X(j) for these {i,j}: {3617, 34648}, {8227, 35403}, {34628, 3616}
X(50867) lies on these lines: {2, 28172}, {4, 3653}, {20, 19876}, {30, 9780}, {519, 962}, {3241, 3627}, {3579, 35409}, {3616, 38335}, {3622, 18483}, {3624, 3839}, {3654, 15682}, {3656, 20057}, {3679, 50691}, {3828, 49140}, {3830, 5603}, {4678, 31673}, {5882, 17578}, {5901, 35401}, {9583, 43566}, {9779, 12101}, {10248, 28208}, {11001, 11231}, {15808, 34628}, {19877, 46333}, {28168, 41106}, {28194, 50690}, {28212, 33699}
X(50867) = reflection of X(i) in X(j) for these {i,j}: {20, 19876}, {34628, 15808}, {34632, 4678}
X(50868) lies on these lines: {3, 3828}, {30, 3626}, {515, 3845}, {519, 962}, {547, 19925}, {551, 3832}, {1125, 3545}, {1482, 35402}, {3146, 34641}, {3244, 50687}, {3634, 15708}, {3635, 3656}, {3636, 3839}, {3679, 5059}, {3830, 28236}, {3853, 28204}, {4297, 15702}, {4669, 28158}, {4691, 34638}, {4701, 34627}, {4745, 5657}, {4746, 34632}, {5067, 38076}, {5587, 15719}, {10171, 31662}, {11362, 49133}, {11539, 18480}, {11812, 28186}, {12512, 15686}, {13607, 14893}, {13624, 41985}, {15640, 37712}, {15682, 28228}, {15683, 38098}, {15684, 47745}, {15685, 38127}, {15690, 28160}, {17578, 34747}, {18357, 41982}, {28234, 33699}, {30308, 41150}
X(50868) = midpoint of X(i) and X(j) for these {i,j}: {3146, 34641}, {15684, 47745}
X(50868) = reflection of X(i) in X(j) for these {i,j}: {1125, 34648}, {4701, 34627}, {13607, 14893}, {34628, 3634}, {34632, 4746}, {34638, 4691}
X(50869) lies on these lines: {2, 28158}, {4, 3828}, {10, 50687}, {30, 1125}, {355, 35434}, {376, 12571}, {381, 12512}, {382, 3656}, {515, 33699}, {516, 3654}, {519, 962}, {551, 3146}, {946, 15684}, {1699, 15640}, {2796, 39838}, {3241, 50690}, {3545, 31253}, {3626, 34648}, {3627, 28194}, {3634, 3839}, {3635, 31162}, {3636, 34628}, {3653, 49136}, {3679, 17578}, {3817, 11001}, {3843, 38068}, {3845, 11231}, {3853, 28202}, {3860, 10172}, {4691, 34632}, {4701, 31673}, {5066, 28154}, {5493, 50688}, {5603, 15682}, {5731, 41150}, {6684, 14893}, {7988, 15697}, {8703, 10171}, {9589, 34641}, {10164, 41099}, {10165, 15685}, {10248, 25055}, {10304, 19878}, {12101, 28146}, {12699, 34748}, {14269, 31730}, {15679, 40998}, {15683, 19883}, {15687, 19925}, {19876, 50689}, {22793, 35404}, {28459, 43151}, {33703, 38021}
X(50869) = midpoint of X(i) and X(j) for these {i,j}: {551, 3146}, {946, 15684}, {9589, 34641}, {22793, 35404}, {34648, 41869}
X(50869) = reflection of X(i) in X(j) for these {i,j}: {376, 12571}, {3626, 34648}, {3635, 31162}, {3828, 4}, {6684, 14893}, {12512, 381}, {19925, 15687}, {34628, 3636}, {34632, 4691}, {34638, 3634}
X(50869) = {X(3839),X(34638)}-harmonic conjugate of X(3634)
X(50870) lies on these lines: {30, 3634}, {382, 38066}, {516, 33699}, {519, 962}, {551, 17578}, {946, 35434}, {1125, 50687}, {1699, 41150}, {3146, 3828}, {3627, 13464}, {3679, 50690}, {3830, 5886}, {3839, 19878}, {4691, 6361}, {4746, 31673}, {5587, 15682}, {12101, 28172}, {12571, 15687}, {15684, 19925}, {19876, 50692}, {33703, 38076}, {38068, 49136}
X(50870) = midpoint of X(i) and X(j) for these {i,j}: {3146, 3828}, {15684, 19925}
X(50870) = reflection of X(i) in X(j) for these {i,j}: {4691, 34648}, {12571, 15687}
X(50871) lies on these lines: {1, 3545}, {2, 28236}, {3, 3679}, {4, 34747}, {8, 34628}, {10, 15708}, {20, 34641}, {30, 3632}, {40, 15686}, {145, 34648}, {165, 4669}, {355, 547}, {376, 47745}, {381, 33179}, {515, 4677}, {519, 962}, {551, 5056}, {944, 15702}, {952, 1699}, {1385, 15723}, {1698, 3655}, {3241, 3832}, {3244, 3839}, {3533, 19876}, {3576, 11812}, {3624, 18526}, {3625, 34632}, {3626, 10304}, {3633, 11278}, {3653, 16239}, {3654, 15690}, {3828, 30389}, {3850, 37727}, {3853, 7982}, {4301, 20049}, {4701, 34638}, {4745, 5731}, {4816, 34718}, {5059, 7991}, {5067, 5882}, {5071, 13607}, {5290, 37706}, {5790, 31662}, {7989, 38314}, {9897, 10074}, {11274, 15017}, {12645, 28208}, {15640, 28228}, {15682, 28234}, {15692, 38098}, {15693, 38176}, {18480, 34748}, {19708, 38127}, {19711, 26446}, {20050, 50687}, {22793, 35401}, {28194, 33703}, {28198, 35400}, {28202, 49133}, {31673, 34631}, {34690, 34746}, {34697, 34719}, {34700, 34716}, {34701, 34717}, {34773, 41983}, {35242, 41982}
X(50871) = reflection of X(i) in X(j) for these {i,j}: {1, 34627}, {20, 34641}, {145, 34648}, {376, 47745}, {3633, 31162}, {3655, 37705}, {3679, 5881}, {7991, 31145}, {11531, 3543}, {20049, 4301}, {31162, 18525}, {34628, 8}, {34631, 31673}, {34632, 3625}, {34638, 4701}, {34690, 34746}, {34701, 34717}, {34716, 34700}, {34719, 34697}, {34747, 4}, {34748, 18480}
X(50871) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11278, 38335, 31162}, {30392, 37712, 38155}
X(50872) lies on these lines: {1, 10304}, {2, 392}, {4, 31145}, {8, 3839}, {20, 3241}, {30, 145}, {40, 15692}, {376, 1482}, {381, 12245}, {390, 25415}, {515, 15640}, {519, 962}, {549, 10595}, {551, 3523}, {553, 7962}, {944, 15683}, {952, 15682}, {1145, 46873}, {1320, 9965}, {1480, 37685}, {1483, 15681}, {1699, 4669}, {2071, 47593}, {2093, 4345}, {2099, 10385}, {2102, 15159}, {2103, 15158}, {3057, 11036}, {3090, 38066}, {3091, 3679}, {3146, 20049}, {3244, 34628}, {3303, 37105}, {3340, 15933}, {3522, 10222}, {3524, 3622}, {3525, 38022}, {3534, 7967}, {3545, 3617}, {3579, 15705}, {3582, 18220}, {3600, 30323}, {3616, 15708}, {3621, 12699}, {3623, 3655}, {3632, 34648}, {3635, 34638}, {3653, 15717}, {3828, 7486}, {3830, 5844}, {3832, 38074}, {3851, 38081}, {3899, 5686}, {4294, 11280}, {4428, 37106}, {4745, 30308}, {5054, 46934}, {5055, 46933}, {5056, 11362}, {5059, 28202}, {5071, 5690}, {5493, 16189}, {5559, 31410}, {5731, 11224}, {5790, 41106}, {5881, 50688}, {5901, 15702}, {5921, 28538}, {6172, 43166}, {7406, 40891}, {7970, 8591}, {7978, 9143}, {7983, 11177}, {7989, 38098}, {8158, 16370}, {8703, 10247}, {9589, 34747}, {9624, 38068}, {9778, 16200}, {9812, 28234}, {10246, 19708}, {10248, 47745}, {10283, 15693}, {10303, 13464}, {10306, 13587}, {10442, 50108}, {10704, 37749}, {11001, 28174}, {11160, 39898}, {11240, 37625}, {11521, 48858}, {12645, 15687}, {15178, 21734}, {15685, 28216}, {15699, 46931}, {15719, 38028}, {15721, 25055}, {17549, 22770}, {18480, 20052}, {18493, 46932}, {18525, 20054}, {19876, 46935}, {20050, 41869}, {20053, 31673}, {20057, 31730}, {23340, 37427}, {34200, 37624}, {34640, 34744}, {34647, 34711}, {37705, 38335}, {37907, 47471}
X(50872) = midpoint of X(i) and X(j) for these {i,j}: {3146, 20049}, {9589, 34747}
X(50872) = reflection of X(i) in X(j) for these {i,j}: {8, 31162}, {20, 3241}, {145, 34631}, {376, 1482}, {3241, 7982}, {3543, 962}, {3621, 34627}, {3632, 34648}, {3655, 11278}, {3679, 4301}, {5731, 11224}, {6172, 43166}, {6361, 3655}, {7991, 551}, {8591, 7970}, {9143, 7978}, {9778, 16200}, {11160, 39898}, {11177, 7983}, {12245, 381}, {12645, 15687}, {15158, 2103}, {15159, 2102}, {15681, 1483}, {15683, 944}, {20070, 376}, {31145, 4}, {34627, 12699}, {34628, 3244}, {34631, 8148}, {34632, 1}, {34638, 3635}, {34711, 34647}, {34718, 22791}, {34744, 34640}, {37749, 10704}
X(50872) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 34632, 10304}, {8, 31162, 3839}, {40, 38314, 15692}, {3545, 34718, 3617}, {3621, 50687, 34627}, {3654, 5603, 2}, {5734, 7991, 3523}, {6361, 11278, 3623}, {12699, 34627, 50687}, {22791, 34718, 3545}
X(50873) lies on these lines: {2, 28150}, {4, 28202}, {30, 3616}, {376, 10248}, {382, 3241}, {519, 962}, {551, 49135}, {944, 35404}, {1698, 3839}, {3146, 13464}, {3534, 9779}, {3617, 34632}, {3623, 31162}, {3653, 49138}, {3656, 7967}, {3679, 50688}, {3830, 28174}, {3845, 9778}, {3853, 38074}, {3854, 38068}, {4668, 34648}, {5059, 38021}, {5657, 12101}, {5731, 15640}, {5734, 50691}, {5818, 35403}, {5901, 35400}, {6361, 38335}, {9780, 14269}, {9955, 46333}, {10304, 19862}, {12102, 38066}, {12571, 15721}, {12953, 15933}, {15697, 28158}, {17578, 28194}, {19708, 28154}, {19709, 28182}, {20052, 31673}, {22793, 38314}, {28146, 41099}, {28224, 33699}, {31253, 34638}, {33697, 34631}, {38022, 49137}
X(50873) = reflection of X(i) in X(j) for these {i,j}: {3623, 31162}, {4668, 34648}, {5818, 35403}, {15697, 30308}, {34632, 3617}, {34638, 31253}
X(50873) = {X(41869),X(50687)}-harmonic conjugate of X(34632)
X(50874) lies on these lines: {4, 19876}, {30, 3624}, {382, 11522}, {519, 962}, {551, 50691}, {1698, 38335}, {1699, 15682}, {3622, 34628}, {3627, 3679}, {3656, 28186}, {3830, 5587}, {4678, 34648}, {5901, 35404}, {9588, 50688}, {9780, 50687}, {9956, 35401}, {15640, 30308}, {15684, 25055}, {17578, 43174}, {19872, 23046}, {34595, 46333}, {34718, 41869}
X(50874) = reflection of X(i) in X(j) for these {i,j}: {4678, 34648}, {19876, 4}, {34628, 3622}
See Antreas Hatzipolakis and Peter Moses, euclid 5261.
X(50875) lies on this line: {10272, 14354}
X(50876) lies on these lines: {10, 541}, {74, 3828}, {113, 551}, {125, 38076}, {146, 3679}, {381, 13605}, {515, 5655}, {519, 7978}, {542, 34648}, {553, 12373}, {2771, 3845}, {2781, 50781}, {2784, 9144}, {2948, 3543}, {3545, 33535}, {3656, 38789}, {4297, 5642}, {4301, 38791}, {5691, 9143}, {7728, 28194}, {9140, 19925}, {11709, 19883}, {12041, 38068}
X(50876) = midpoint of X(i) and X(j) for these {i,j}: {146, 3679}, {2948, 3543}, {5691, 9143}, {10706, 12368}
X(50876) = reflection of X(i) in X(j) for these {i,j}: {74, 3828}, {551, 113}, {4297, 5642}, {9140, 19925}, {13605, 381}
X(50877) lies on these lines: {8, 541}, {74, 3679}, {110, 28204}, {113, 3241}, {125, 38074}, {146, 31145}, {355, 9140}, {381, 7984}, {519, 7978}, {542, 34627}, {944, 5642}, {952, 5655}, {2771, 15679}, {2781, 50783}, {5071, 11735}, {5818, 45311}, {5881, 14094}, {9041, 14982}, {10721, 28194}, {10752, 28538}, {11709, 19875}, {12041, 38066}, {12778, 28208}
X(50877) = midpoint of X(146) and X(31145)
X(50877) = reflection of X(i) in X(j) for these {i,j}: {74, 3679}, {944, 5642}, {3241, 113}, {7978, 10706}, {7984, 381}, {9140, 355}, {10706, 12368}
X(50878) lies on these lines: {1, 541}, {40, 5642}, {74, 551}, {110, 28194}, {113, 3679}, {125, 38021}, {146, 3241}, {376, 11720}, {381, 13211}, {517, 5655}, {519, 7978}, {542, 31162}, {946, 9140}, {962, 9143}, {2781, 47358}, {3653, 12041}, {3656, 5663}, {4301, 14094}, {5493, 15034}, {5881, 38791}, {7728, 28204}, {7982, 15063}, {7991, 16534}, {8227, 45311}, {9588, 38795}, {9589, 30714}, {9624, 20417}, {9860, 11656}, {9904, 11723}, {11522, 16003}, {11699, 28198}, {11709, 38314}, {12121, 28202}, {12327, 16371}, {12898, 28208}, {12900, 19876}, {13464, 15054}, {14982, 28538}, {15029, 31399}, {16370, 22583}
X(50878) = midpoint of X(i) and X(j) for these {i,j}: {146, 3241}, {962, 9143}, {7978, 10706}
X(50878) = reflection of X(i) in X(j) for these {i,j}: {40, 5642}, {74, 551}, {376, 11720}, {3679, 113}, {9140, 946}, {9860, 11656}, {12368, 10706}, {13211, 381}
X(50879) lies on these lines: {2, 2784}, {4, 2796}, {10, 542}, {98, 3828}, {114, 551}, {115, 38076}, {147, 3679}, {355, 48657}, {381, 11599}, {515, 8724}, {516, 9881}, {519, 6054}, {543, 34648}, {553, 12184}, {671, 19925}, {946, 22566}, {950, 12350}, {1125, 23234}, {2482, 4297}, {3543, 13174}, {3656, 38743}, {3817, 12258}, {4301, 38745}, {5587, 12243}, {5691, 8591}, {6033, 28194}, {6684, 14830}, {9884, 28236}, {10106, 12351}, {10175, 49102}, {11177, 19875}, {11710, 19883}, {12042, 38068}, {12117, 28164}
X(50879) = midpoint of X(i) and X(j) for these {i,j}: {147, 3679}, {355, 48657}, {3543, 13174}, {5691, 8591}, {6054, 9864}
X(50879) = reflection of X(i) in X(j) for these {i,j}: {98, 3828}, {551, 114}, {671, 19925}, {946, 22566}, {4297, 2482}, {11599, 381}, {14830, 6684}, {21636, 6054}
X(50880) lies on these lines: {1, 23234}, {8, 542}, {80, 10070}, {98, 3679}, {99, 28204}, {114, 3241}, {115, 38074}, {147, 31145}, {355, 671}, {381, 7983}, {515, 9881}, {519, 6054}, {543, 34627}, {944, 2482}, {952, 8724}, {1482, 22566}, {2784, 4669}, {3655, 41134}, {5071, 11725}, {5461, 5818}, {5587, 12258}, {5690, 14830}, {5790, 49102}, {5881, 23235}, {9875, 37712}, {10054, 37710}, {10722, 28194}, {10753, 28538}, {10944, 12351}, {10950, 12350}, {11710, 19875}, {12042, 38066}, {12645, 48657}, {12751, 49150}, {19057, 49602}, {19058, 49601}, {34673, 34718}
X(50880) = midpoint of X(i) and X(j) for these {i,j}: {147, 31145}, {12645, 48657}
X(50880) = reflection of X(i) in X(j) for these {i,j}: {98, 3679}, {671, 355}, {944, 2482}, {1482, 22566}, {3241, 114}, {6054, 9864}, {7970, 6054}, {7983, 381}, {9884, 8724}, {12117, 9881}, {14830, 5690}
X(50881) lies on these lines: {1, 542}, {10, 23234}, {40, 2482}, {65, 12351}, {98, 551}, {99, 28194}, {114, 3679}, {115, 38021}, {147, 3241}, {355, 22566}, {376, 11711}, {381, 13178}, {515, 9884}, {516, 12117}, {517, 8724}, {519, 6054}, {543, 31162}, {671, 946}, {962, 8591}, {1012, 22565}, {1385, 14830}, {1482, 48657}, {1519, 49150}, {1699, 9875}, {1836, 18969}, {2782, 3656}, {2796, 4301}, {3057, 12350}, {3149, 12326}, {3653, 12042}, {3655, 34636}, {5182, 12197}, {5184, 37461}, {5461, 8227}, {5603, 12243}, {5881, 38745}, {5886, 49102}, {6033, 28204}, {6055, 9860}, {6721, 19876}, {7982, 14981}, {9588, 38751}, {9589, 10992}, {9624, 11623}, {10054, 12047}, {10070, 30384}, {11177, 11710}, {11632, 38220}, {11656, 11723}, {12178, 16371}, {12348, 12672}, {12354, 12701}, {12356, 12608}, {13464, 38664}, {16370, 22504}, {22247, 31423}, {28202, 38730}, {41813, 49549}
X(50881) = midpoint of X(i) and X(j) for these {i,j}: {147, 3241}, {962, 8591}, {1482, 48657}, {6054, 7970}
X(50881) = reflection of X(i) in X(j) for these {i,j}: {40, 2482}, {98, 551}, {355, 22566}, {376, 11711}, {671, 946}, {3679, 114}, {5184, 37461}, {6054, 21636}, {6055, 11724}, {9860, 6055}, {9864, 6054}, {9875, 9880}, {9881, 8724}, {11177, 11710}, {11656, 11723}, {12243, 12258}, {13178, 381}, {14830, 1385}
X(50881) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1699, 9875, 9880}, {5603, 12243, 12258}, {6055, 11724, 25055}, {7970, 21636, 9864}, {9860, 25055, 6055}, {11177, 38314, 11710}
X(50882) lies on these lines: {114, 3828}, {147, 551}, {516, 8724}, {519, 6054}, {542, 1125}, {671, 12571}, {946, 48657}, {2482, 12512}, {2796, 14981}, {3634, 23234}, {3817, 12243}, {4298, 12351}, {9881, 28228}, {10171, 49102}, {11177, 19883}, {12117, 28158}, {12350, 12575}, {19925, 22566}
X(50882) = midpoint of X(i) and X(j) for these {i,j}: {147, 551}, {946, 48657}, {6054, 21636}
X(50882) = reflection of X(i) in X(j) for these {i,j}: {671, 12571}, {3828, 114}, {12512, 2482}, {19925, 22566}
X(50883) lies on these lines: {8, 23234}, {98, 3241}, {114, 31145}, {145, 542}, {147, 20049}, {517, 9884}, {519, 6054}, {543, 34631}, {671, 1482}, {1483, 14830}, {2482, 12245}, {3656, 14639}, {5461, 10595}, {5844, 8724}, {9041, 10753}, {9875, 11224}, {9881, 28234}, {10054, 11009}, {10247, 49102}, {10722, 28204}, {12258, 16200}, {12645, 22566}, {19057, 35642}, {19058, 35641}, {34685, 34748}, {34718, 41134}
X(50883) = midpoint of X(147) and X(20049)
X(50883) = reflection of X(i) in X(j) for these {i,j}: {98, 3241}, {671, 1482}, {6054, 7970}, {12117, 9884}, {12245, 2482}, {12645, 22566}, {14830, 1483}, {31145, 114}
X(50884) lies on these lines: {1, 41135}, {2, 9875}, {10, 543}, {99, 3828}, {114, 38076}, {115, 551}, {148, 1654}, {381, 21636}, {515, 11632}, {519, 671}, {535, 11608}, {542, 34648}, {553, 13182}, {1125, 9166}, {2784, 12243}, {3543, 9860}, {3634, 41134}, {3654, 12355}, {3656, 38732}, {4297, 6055}, {4301, 38734}, {4745, 9881}, {5026, 38089}, {5461, 11711}, {5691, 11177}, {5969, 50781}, {6054, 19925}, {6321, 28194}, {8591, 19875}, {8596, 13174}, {9884, 38220}, {11161, 34379}, {12258, 36523}, {12780, 22578}, {12781, 22577}, {14971, 19862}, {33813, 38068}
X(50884) = midpoint of X(i) and X(j) for these {i,j}: {2, 9875}, {148, 3679}, {671, 13178}, {3543, 9860}, {3654, 12355}, {5691, 11177}, {8596, 13174}, {12780, 22578}, {12781, 22577}
X(50884) = reflection of X(i) in X(j) for these {i,j}: {99, 3828}, {551, 115}, {4297, 6055}, {6054, 19925}, {9881, 4745}, {11599, 671}, {11711, 5461}, {12258, 36523}, {21636, 381}
X(50884) = {X(5461),X(11711)}-harmonic conjugate of X(19883)
X(50885) lies on these lines: {1, 9166}, {2, 9884}, {8, 543}, {10, 41134}, {98, 28204}, {99, 3679}, {114, 38074}, {115, 3241}, {145, 41135}, {148, 31145}, {355, 6054}, {381, 7970}, {518, 11161}, {519, 671}, {542, 34627}, {551, 14061}, {944, 6055}, {952, 11632}, {2796, 34641}, {3416, 50639}, {3616, 14971}, {3654, 12117}, {3656, 14639}, {4669, 9881}, {4677, 9875}, {5026, 38087}, {5071, 11724}, {5459, 7974}, {5460, 7975}, {5461, 38314}, {5881, 38664}, {5969, 34673}, {8593, 47359}, {9041, 11646}, {9167, 9780}, {10723, 28194}, {10754, 28538}, {11711, 19875}, {33813, 38066}, {45018, 49529}
X(50885) = midpoint of X(i) and X(j) for these {i,j}: {148, 31145}, {4677, 9875}
X(50885) = reflection of X(i) in X(j) for these {i,j}: {99, 3679}, {671, 13178}, {944, 6055}, {3241, 115}, {6054, 355}, {7970, 381}, {7974, 5459}, {7975, 5460}, {7983, 671}, {8593, 47359}, {9881, 4669}, {9884, 2}, {12117, 3654}, {50639, 3416}
X(50886) lies on these lines: {1, 543}, {2, 9881}, {8, 41135}, {10, 9166}, {40, 6055}, {86, 99}, {98, 28194}, {114, 38021}, {115, 3679}, {148, 3241}, {376, 11710}, {381, 9864}, {517, 11632}, {519, 671}, {524, 24711}, {542, 31162}, {946, 6054}, {962, 11177}, {1125, 41134}, {1698, 14971}, {2482, 11725}, {2782, 3656}, {2784, 49543}, {3624, 9167}, {3653, 33813}, {3654, 49102}, {3828, 14061}, {4301, 38664}, {4677, 36523}, {4870, 12350}, {5026, 38023}, {5184, 22329}, {5459, 12780}, {5460, 12781}, {5461, 19875}, {5463, 11706}, {5464, 11705}, {5847, 11161}, {5881, 38734}, {5969, 34636}, {6321, 28204}, {6722, 19876}, {7974, 22578}, {7975, 22577}, {7991, 11623}, {8591, 11711}, {8598, 38221}, {9588, 38740}, {9589, 10991}, {9830, 47356}, {9900, 31696}, {9901, 31695}, {11522, 14981}, {11646, 28538}, {13173, 16371}, {13464, 23235}, {14830, 28198}, {14928, 16491}, {16370, 22514}, {16475, 18800}, {16823, 31129}, {28202, 38741}, {30790, 39580}, {49511, 50639}
X(50886) = midpoint of X(i) and X(j) for these {i,j}: {148, 3241}, {671, 7983}, {962, 11177}, {7974, 22578}, {7975, 22577}
X(50886) = reflection of X(i) in X(j) for these {i,j}: {2, 12258}, {40, 6055}, {99, 551}, {376, 11710}, {671, 11599}, {2482, 11725}, {3654, 49102}, {3679, 115}, {5184, 22329}, {5463, 11706}, {5464, 11705}, {6054, 946}, {8591, 11711}, {9864, 381}, {9881, 2}, {9900, 31696}, {9901, 31695}, {12780, 5459}, {12781, 5460}, {13174, 2482}, {13178, 671}, {50639, 49511}
X(50886) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 12258, 38220}, {2482, 11725, 25055}, {7983, 11599, 13178}, {8591, 38314, 11711}, {9881, 38220, 2}, {13174, 25055, 2482}
X(50887) lies on these lines: {10, 41135}, {115, 121}, {148, 551}, {516, 11632}, {519, 671}, {543, 1125}, {2784, 9880}, {3634, 9166}, {4745, 36523}, {5969, 50787}, {6054, 12571}, {6055, 12512}, {8591, 19883}, {8596, 25055}, {14971, 31253}, {19878, 41134}
X(50887) = midpoint of X(i) and X(j) for these {i,j}: {148, 551}, {671, 11599}
X(50887) = reflection of X(i) in X(j) for these {i,j}: {3828, 115}, {6054, 12571}, {12512, 6055}
X(50888) lies on these lines: {1, 41134}, {8, 9166}, {99, 3241}, {115, 31145}, {145, 543}, {148, 20049}, {519, 671}, {542, 34631}, {1482, 6054}, {3242, 50639}, {3617, 14971}, {3621, 41135}, {3622, 9167}, {3679, 14061}, {4669, 38220}, {4677, 12258}, {5844, 11632}, {5846, 11161}, {5969, 34685}, {6055, 12245}, {9041, 10754}, {10723, 28204}, {45018, 49681}
X(50888) = midpoint of X(148) and X(20049)
X(50888) = reflection of X(i) in X(j) for these {i,j}: {99, 3241}, {671, 7983}, {4677, 12258}, {6054, 1482}, {12245, 6055}, {31145, 115}, {50639, 3242}
X(50889) lies on these lines: {2, 5426}, {10, 528}, {11, 551}, {30, 10265}, {80, 519}, {100, 3828}, {119, 38076}, {149, 3679}, {210, 2802}, {214, 19883}, {381, 21635}, {547, 22935}, {553, 13273}, {900, 4049}, {952, 3817}, {1145, 38098}, {1387, 11274}, {1484, 28204}, {1768, 3543}, {2771, 3845}, {2796, 10769}, {2801, 38152}, {2805, 50096}, {3035, 38104}, {3241, 9897}, {3545, 6326}, {3655, 12747}, {3839, 9803}, {4745, 40998}, {6174, 6702}, {6224, 25055}, {6246, 7682}, {6264, 34627}, {9024, 50781}, {9581, 10199}, {9669, 34700}, {10031, 16173}, {10427, 38094}, {10609, 19862}, {10711, 19925}, {10738, 28194}, {11219, 28164}, {11263, 17577}, {12247, 31162}, {12653, 31145}, {14269, 16128}, {15863, 34641}, {16858, 35204}, {17549, 46816}, {20085, 33812}, {33814, 38068}, {34638, 46684}
X(50889) = midpoint of X(i) and X(j) for these {i,j}: {80, 10707}, {149, 3679}, {1768, 3543}, {3241, 9897}, {3655, 12747}, {6174, 12690}, {6264, 34627}, {10711, 49176}, {12247, 31162}, {12653, 31145}
X(50889) = reflection of X(i) in X(j) for these {i,j}: {100, 3828}, {214, 45310}, {551, 11}, {6174, 6702}, {10711, 19925}, {11274, 1387}, {21630, 10707}, {21635, 381}, {22935, 547}, {33337, 551}, {34638, 46684}, {34641, 15863}, {34648, 6246}
X(50889) = {X(214),X(45310)}-harmonic conjugate of X(19883)
X(50890) lies on these lines: {2, 952}, {8, 190}, {11, 3241}, {21, 38665}, {30, 19914}, {80, 519}, {100, 993}, {104, 13587}, {119, 38074}, {145, 12019}, {149, 3421}, {214, 19875}, {355, 10711}, {381, 10698}, {404, 5881}, {515, 36005}, {527, 20119}, {535, 41684}, {551, 7972}, {666, 35170}, {900, 36593}, {1145, 9963}, {1317, 38314}, {1484, 17533}, {1537, 3839}, {2096, 12247}, {2476, 37725}, {2771, 15679}, {2801, 37712}, {2802, 3681}, {3035, 38099}, {3036, 6174}, {3617, 10609}, {3655, 12619}, {3828, 33337}, {3871, 37711}, {4193, 37726}, {4669, 15678}, {5047, 38216}, {5055, 19907}, {5071, 11729}, {5252, 14151}, {5330, 12645}, {5660, 38155}, {5690, 37299}, {6175, 12751}, {6246, 31162}, {6594, 38097}, {6702, 11274}, {6797, 24473}, {6915, 12776}, {8164, 12735}, {8666, 43731}, {9024, 50783}, {10199, 37707}, {10427, 38092}, {10529, 43734}, {10573, 34605}, {10724, 28194}, {10755, 28538}, {10896, 34710}, {11112, 37705}, {11219, 28236}, {11698, 17530}, {12331, 16370}, {12515, 28208}, {12532, 17636}, {12730, 47357}, {12747, 34718}, {12773, 16371}, {15015, 38213}, {17566, 20418}, {19883, 33812}, {20049, 25416}, {25485, 38021}, {28534, 36920}, {30308, 38161}, {33814, 38066}, {34628, 46684}, {34648, 34789}, {47745, 49176}
X(50890) = midpoint of X(i) and X(j) for these {i,j}: {149, 31145}, {3679, 9897}, {10707, 12531}, {12247, 34627}, {12747, 34718}
X(50890) = reflection of X(i) in X(j) for these {i,j}: {100, 3679}, {1317, 45310}, {1320, 10707}, {3241, 11}, {3655, 12619}, {3679, 15863}, {5660, 38155}, {6174, 3036}, {6224, 6174}, {7972, 551}, {10031, 2}, {10698, 381}, {10707, 80}, {10711, 355}, {11274, 6702}, {12730, 47357}, {15015, 38213}, {20049, 25416}, {24473, 6797}, {31162, 6246}, {33337, 3828}, {34628, 46684}, {34789, 34648}
X(50890) = X(24297)-anticomplementary conjugate of X(21290)
X(50890) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {80, 12531, 1320}, {1145, 20085, 9963}, {1317, 45310, 38314}, {6702, 11274, 25055}, {9897, 15863, 100}
X(50891) lies on these lines: {1, 528}, {2, 2802}, {10, 30855}, {11, 3679}, {30, 12737}, {35, 13279}, {80, 519}, {88, 14028}, {100, 551}, {104, 28194}, {119, 38021}, {149, 1478}, {214, 9802}, {376, 11715}, {381, 12751}, {499, 34711}, {517, 11219}, {535, 38460}, {900, 1022}, {903, 4089}, {946, 10711}, {952, 1699}, {1000, 17057}, {1145, 19875}, {1387, 5541}, {1388, 34707}, {1482, 49176}, {1537, 7993}, {1647, 4792}, {1698, 13996}, {2932, 40726}, {3035, 38026}, {3120, 10700}, {3545, 16174}, {3582, 17652}, {3632, 12019}, {3653, 33814}, {3655, 12119}, {3746, 48713}, {3828, 31272}, {3885, 37735}, {4301, 38669}, {4342, 5251}, {4345, 45043}, {4677, 5854}, {4857, 13272}, {5434, 20586}, {5441, 34649}, {5559, 24387}, {5603, 5660}, {5697, 45700}, {5903, 11240}, {5919, 26725}, {6224, 11274}, {6246, 34627}, {6264, 31162}, {6265, 34699}, {6594, 38025}, {6667, 19876}, {7982, 37356}, {7991, 20418}, {9024, 47358}, {9897, 25416}, {9951, 11570}, {9963, 33812}, {10031, 15679}, {10057, 11235}, {10199, 14923}, {10222, 37230}, {10389, 15015}, {10738, 28204}, {10912, 17556}, {11009, 12750}, {11114, 22837}, {11522, 37725}, {11524, 21031}, {11571, 24473}, {11604, 24302}, {12247, 34631}, {12619, 34718}, {12641, 13143}, {12747, 34748}, {12758, 34625}, {13205, 16371}, {13464, 38665}, {13541, 24222}, {15863, 31145}, {16370, 22560}, {18421, 41556}, {22791, 34749}, {25415, 31146}, {28202, 38753}, {30308, 38038}, {34632, 46684}, {37298, 37563}, {45035, 49169}, {47033, 49600}
X(50891) = midpoint of X(i) and X(j) for these {i,j}: {149, 3241}, {1320, 10707}, {3679, 12653}, {6264, 31162}, {9897, 34747}, {12247, 34631}, {12747, 34748}, {31160, 41702}
X(50891) = reflection of X(i) in X(j) for these {i,j}: {80, 10707}, {100, 551}, {376, 11715}, {1145, 45310}, {3679, 11}, {5541, 6174}, {5660, 5603}, {6174, 1387}, {6224, 11274}, {7972, 3241}, {10707, 21630}, {10711, 946}, {11571, 24473}, {12119, 3655}, {12751, 381}, {31145, 15863}, {31160, 30384}, {34627, 6246}, {34632, 46684}, {34718, 12619}, {34747, 25416}, {34789, 31162}
X(50891) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {80, 1320, 26726}, {1145, 45310, 19875}, {1320, 21630, 80}, {1387, 6174, 25055}, {5541, 25055, 6174}
X(50892) lies on these lines: {11, 3828}, {80, 519}, {149, 551}, {528, 1125}, {952, 3860}, {1484, 28194}, {2802, 3740}, {3839, 7993}, {4669, 37718}, {4701, 12019}, {6174, 33709}, {6264, 34648}, {9024, 50787}, {9802, 19875}, {10711, 12571}, {11274, 12690}, {12653, 34641}, {20107, 34639}
X(50892) = midpoint of X(i) and X(j) for these {i,j}: {149, 551}, {6264, 34648}, {10707, 21630}, {11274, 12690}, {12653, 34641}
X(50892) = reflection of X(i) in X(j) for these {i,j}: {3828, 11}, {6174, 33709}, {10711, 12571}
X(50893) lies on these lines: {2, 38213}, {11, 34747}, {80, 519}, {100, 34641}, {165, 952}, {528, 3632}, {1317, 19875}, {2802, 4661}, {3035, 3679}, {3036, 25055}, {3241, 15863}, {3656, 38141}, {4669, 10031}, {4816, 10609}, {6246, 34631}, {9024, 50789}, {10711, 47745}, {12119, 34718}, {12619, 34748}, {12735, 38099}, {20095, 31145}, {25485, 38074}, {28204, 38753}, {30308, 38156}, {33812, 38098}, {34627, 34789}
X(50893) =reflection of X(i) in X(j) for these {i,j}: {100, 34641}, {3241, 15863}, {7972, 3679}, {10031, 4669}, {10711, 47745}, {12119, 34718}, {26726, 10707}, {34631, 6246}, {34747, 11}, {34748, 12619}, {34789, 34627}
X(50894) lies on these lines: {2, 5854}, {11, 31145}, {80, 519}, {100, 999}, {145, 528}, {149, 20049}, {900, 2403}, {952, 3830}, {1145, 38314}, {1482, 10711}, {2802, 3873}, {3623, 13996}, {3679, 31272}, {4669, 16173}, {4853, 38216}, {5541, 11274}, {7317, 10527}, {7320, 25875}, {9024, 50790}, {9041, 10755}, {10724, 28204}, {12019, 20053}, {12653, 34747}, {13587, 25438}, {37251, 38665}
X(50894) = midpoint of X(i) and X(j) for these {i,j}: {149, 20049}, {12653, 34747}
X(50894) = reflection of X(i) in X(j) for these {i,j}: {100, 3241}, {3241, 25416}, {5541, 11274}, {10707, 1320}, {10711, 1482}, {12531, 10707}, {31145, 11}
X(50895) lies on these lines: {2, 2784}, {10, 544}, {101, 3828}, {116, 551}, {118, 38076}, {150, 3679}, {519, 10695}, {2801, 3753}, {2809, 4669}, {2810, 50781}, {3543, 39156}, {10171, 15735}, {10710, 19925}, {10739, 28194}, {11712, 19883}, {19875, 28346}, {28345, 38101}, {38068, 38599}
X(50895) = midpoint of X(i) and X(j) for these {i,j}: {150, 3679}, {3543, 39156}
X(50895) = reflection of X(i) in X(j) for these {i,j}: {101, 3828}, {551, 116}, {10710, 19925}, {15735, 10171}
X(50895) = psi-transform of X(9779)
X(50896) lies on these lines: {1, 116}, {2, 11712}, {4, 48357}, {8, 150}, {10, 98}, {80, 885}, {103, 515}, {118, 5587}, {239, 31126}, {242, 29043}, {291, 23596}, {355, 2808}, {516, 10725}, {517, 10739}, {519, 10695}, {523, 24713}, {544, 1282}, {692, 21045}, {740, 41327}, {910, 28901}, {928, 13532}, {938, 14760}, {944, 11714}, {946, 10697}, {952, 50441}, {1111, 18343}, {1125, 31273}, {1362, 5252}, {1698, 6710}, {1837, 3022}, {1899, 17860}, {2550, 2801}, {2772, 12368}, {2774, 13211}, {2786, 13178}, {2802, 10770}, {2810, 3416}, {2812, 38955}, {2813, 38479}, {2825, 12784}, {3576, 6712}, {3617, 20096}, {3661, 31073}, {3939, 21091}, {4297, 38692}, {4858, 21293}, {5011, 28845}, {5090, 5185}, {5176, 34932}, {5179, 28849}, {5688, 34112}, {5691, 39156}, {5790, 38572}, {5847, 10756}, {6246, 10772}, {6684, 38690}, {8227, 11728}, {9518, 13280}, {9956, 38764}, {10175, 15735}, {10573, 18413}, {10727, 31673}, {10741, 18480}, {11028, 18391}, {11231, 38774}, {14942, 34906}, {18421, 34929}, {18481, 38601}, {18525, 38574}, {24712, 31131}, {24980, 30858}, {26446, 38599}, {28160, 38765}, {28345, 38057}, {31423, 38772}, {34457, 50037}, {40910, 48381}, {46073, 50438}, {46077, 50439}
X(50896) = midpoint of X(i) and X(j) for these {i,j}: {8, 150}, {5691, 39156}, {18525, 38574}
X(50896) = reflection of X(i) in X(j) for these {i,j}: {1, 116}, {101, 10}, {944, 11714}, {10697, 946}, {10727, 31673}, {10741, 18480}, {10772, 6246}, {15735, 10175}, {18481, 38601}
X(50896) = anticomplement of X(11712)
X(50896) = barycentric product X(10)*X(24619)
X(50896) = barycentric quotient X(24619)/X(86)
X(50897) lies on these lines: {8, 544}, {101, 3679}, {103, 28204}, {116, 3241}, {118, 38074}, {150, 31145}, {355, 10710}, {381, 10697}, {519, 10695}, {551, 31273}, {2784, 4669}, {2809, 4677}, {2810, 50783}, {5071, 11728}, {5790, 15735}, {5881, 38668}, {10725, 28194}, {10756, 28538}, {11712, 19875}, {28345, 38097}, {28346, 38098}, {38066, 38599}
X(50897) = midpoint of X(150) and X(31145)
X(50897) = reflection of X(i) in X(j) for these {i,j}: {101, 3679}, {3241, 116}, {10695, 10708}, {10697, 381}, {10710, 355}, {15735, 5790}
X(50898) lies on these lines: {1, 544}, {2, 2809}, {101, 551}, {103, 28194}, {116, 3679}, {118, 38021}, {150, 3241}, {376, 11714}, {497, 34930}, {519, 10695}, {528, 1565}, {946, 10710}, {1282, 11726}, {1621, 34928}, {2801, 3892}, {2808, 3656}, {2810, 47358}, {3653, 38599}, {3828, 31273}, {4301, 38668}, {9589, 33521}, {10072, 18413}, {10739, 28204}, {11712, 38314}, {13464, 38666}, {13576, 34578}, {19883, 28346}, {28202, 38765}, {28345, 38025}, {30384, 34934}
X(50898) = midpoint of X(i) and X(j) for these {i,j}: {150, 3241}, {10695, 10708}
X(50898) = reflection of X(i) in X(j) for these {i,j}: {101, 551}, {376, 11714}, {3679, 116}, {10710, 946}
X(50899) lies on these lines: {1, 117}, {2, 11713}, {4, 80}, {8, 151}, {10, 102}, {20, 14690}, {109, 515}, {124, 5587}, {355, 2818}, {388, 12016}, {516, 10726}, {517, 10740}, {519, 10696}, {944, 11700}, {946, 10703}, {1361, 1837}, {1364, 5252}, {1698, 6711}, {1795, 45287}, {2773, 12368}, {2779, 13211}, {2785, 9864}, {2792, 13178}, {2802, 10771}, {2816, 11362}, {2853, 12784}, {3040, 5794}, {3576, 6718}, {3738, 12751}, {4297, 38697}, {5790, 38573}, {5847, 10757}, {6684, 38691}, {7967, 47115}, {8227, 11734}, {9532, 13280}, {9956, 38776}, {10732, 31673}, {10747, 18480}, {11231, 38786}, {18481, 38607}, {18525, 38579}, {26446, 38600}, {28160, 38777}, {31423, 38784}, {34459, 50037}
X(50899) = midpoint of X(i) and X(j) for these {i,j}: {8, 151}, {18525, 38579}
X(50899) = reflection of X(i) in X(j) for these {i,j}: {1, 117}, {20, 14690}, {102, 10}, {944, 11700}, {10703, 946}, {10732, 31673}, {10747, 18480}, {10777, 6246}, {13532, 355}, {18481, 38607}
X(50899) = anticomplement of X(11713)
X(50900) lies on these lines: {102, 3679}, {109, 28204}, {117, 3241}, {124, 38074}, {151, 31145}, {355, 10716}, {381, 10703}, {519, 10696}, {2817, 4677}, {5071, 11734}, {5881, 38674}, {10726, 28194}, {10757, 28538}, {11713, 19875}, {14690, 34628}, {38066, 38600}
X(50900) = midpoint of X(151) and X(31145)
X(50900) = reflection of X(i) in X(j) for these {i,j}: {102, 3679}, {3241, 117}, {10696, 10709}, {10703, 381}, {10716, 355}, {34628, 14690}
X(50901) = X(509) lies on these lines: {2, 2817}, {102, 551}, {109, 28194}, {117, 3679}, {124, 38021}, {151, 3241}, {376, 11700}, {381, 13532}, {519, 10696}, {946, 10716}, {1845, 10072}, {2818, 3656}, {3653, 38600}, {4301, 38674}, {10740, 28204}, {11713, 38314}, {11727, 25055}, {13464, 38667}, {14690, 34632}, {28202, 38777}
X(50901) = midpoint of X(i) and X(j) for these {i,j}: {151, 3241}, {10696, 10709}
X(50901) = reflection of X(i) in X(j) for these {i,j}: {102, 551}, {376, 11700}, {3679, 117}, {10716, 946}, {13532, 381}, {34632, 14690}
X(50902) lies on these lines: {103, 3828}, {116, 38076}, {118, 551}, {152, 3679}, {376, 28346}, {519, 10697}, {544, 34648}, {1282, 3543}, {2784, 12243}, {2801, 38152}, {3656, 38767}, {4301, 38769}, {10708, 19925}, {10741, 28194}, {11714, 19883}, {38068, 38601}
X(50902) = midpoint of X(i) and X(j) for these {i,j}: {152, 3679}, {1282, 3543}
X(50902) = reflection of X(i) in X(j) for these {i,j}: {103, 3828}, {376, 28346}, {551, 118}, {10708, 19925}
X(50903) lies on these lines: {1, 118}, {2, 11714}, {4, 2809}, {7, 80}, {8, 152}, {10, 103}, {101, 515}, {116, 5587}, {165, 38773}, {355, 2808}, {388, 11028}, {516, 3732}, {517, 10741}, {519, 10697}, {944, 11712}, {946, 10695}, {1056, 14760}, {1282, 5691}, {1362, 1837}, {1385, 38764}, {1482, 38767}, {1698, 6712}, {2772, 13211}, {2774, 12368}, {2784, 13178}, {2786, 9864}, {2802, 10772}, {2807, 3419}, {2820, 3762}, {2823, 3421}, {2825, 13280}, {3022, 5252}, {3033, 50037}, {3041, 5794}, {3576, 6710}, {3579, 38765}, {3679, 39156}, {3887, 12751}, {4297, 28346}, {5790, 38574}, {5847, 10758}, {6246, 10770}, {6684, 38692}, {7982, 38769}, {7987, 38772}, {8227, 11726}, {9518, 12784}, {10175, 31273}, {10590, 34930}, {10725, 31673}, {10739, 18480}, {12702, 38768}, {13624, 38774}, {15735, 28236}, {18328, 28850}, {18481, 38599}, {18525, 38572}, {26446, 38601}, {28345, 43161}, {30389, 38775}, {31663, 38766}, {35242, 38771}
X(50903) = midpoint of X(i) and X(j) for these {i,j}: {8, 152}, {1282, 5691}, {12702, 38768}, {18525, 38572}
X(50903) = reflection of X(i) in X(j) for these {i,j}: {1, 118}, {103, 10}, {944, 11712}, {4297, 28346}, {10695, 946}, {10725, 31673}, {10739, 18480}, {10770, 6246}, {18481, 38599}, {38765, 3579}, {43161, 28345}
X(50903) = anticomplement of X(11714)
X(50903) = {X(4297),X(28346)}-harmonic conjugate of X(38690)
X(50904) lies on these lines: {101, 28204}, {103, 3679}, {116, 38074}, {118, 3241}, {152, 31145}, {355, 10708}, {381, 10695}, {519, 10697}, {528, 18328}, {544, 34627}, {952, 15735}, {2801, 37712}, {4845, 37708}, {5071, 11726}, {5727, 44858}, {5881, 38666}, {9897, 34931}, {10727, 28194}, {10758, 28538}, {11714, 19875}, {38066, 38601}
X(50904) = midpoint of X(152) and X(31145)
X(50904) = reflection of X(i) in X(j) for these {i,j}: {103, 3679}, {3241, 118}, {10695, 381}, {10697, 10710}, {10708, 355}
X(50905) lies on these lines: {101, 28194}, {103, 551}, {116, 38021}, {118, 3679}, {152, 3241}, {376, 11712}, {516, 15735}, {519, 10697}, {544, 31162}, {946, 10708}, {2784, 49543}, {2808, 3656}, {3653, 38601}, {4301, 38666}, {4342, 44858}, {5881, 38769}, {9588, 38775}, {9589, 33520}, {10741, 28204}, {11714, 38314}, {11728, 25055}, {13464, 38668}, {15730, 30305}
X(50905) = midpoint of X(i) and X(j) for these {i,j}: {152, 3241}, {10697, 10710}
X(50905) = reflection of X(i) in X(j) for these {i,j}: {103, 551}, {376, 11712}, {3679, 118}, {10708, 946}
X(50906) lies on these lines: {11, 38076}, {80, 14151}, {104, 3828}, {119, 551}, {153, 3679}, {355, 11263}, {381, 21630}, {519, 1519}, {528, 34648}, {553, 12763}, {952, 3817}, {2800, 4669}, {2801, 3753}, {3543, 5541}, {3545, 6264}, {3656, 38755}, {3814, 11698}, {4297, 6174}, {4301, 38757}, {5071, 33709}, {5660, 10031}, {6326, 34627}, {6831, 37725}, {9897, 10590}, {10707, 19925}, {10742, 28194}, {11715, 19883}, {12019, 21625}, {13253, 31145}, {15017, 38314}, {16128, 34718}, {20418, 38104}, {38068, 38602}
X(50906) = midpoint of X(i) and X(j) for these {i,j}: {153, 3679}, {3543, 5541}, {6326, 34627}, {10711, 12751}, {13253, 31145}, {16128, 34718}
X(50906) = reflection of X(i) in X(j) for these {i,j}: {104, 3828}, {551, 119}, {4297, 6174}, {10707, 19925}, {21630, 381}, {21635, 10711}
X(50907) lies on these lines: {2, 952}, {8, 37430}, {11, 38074}, {100, 28204}, {104, 3679}, {119, 3241}, {153, 31145}, {355, 10707}, {376, 1145}, {381, 1320}, {519, 1519}, {528, 16112}, {944, 6174}, {1387, 5071}, {1537, 34631}, {2800, 4677}, {3090, 38026}, {3419, 12531}, {3813, 6941}, {4861, 12738}, {5818, 45310}, {5881, 6906}, {6940, 38669}, {6975, 37726}, {9780, 38069}, {10728, 28194}, {10759, 28538}, {11715, 19875}, {14217, 34648}, {19907, 34748}, {19914, 28458}, {20418, 38099}, {21669, 32537}, {25485, 34747}, {34629, 49169}, {38038, 41106}, {38066, 38602}, {47033, 47745}
X(50907) = midpoint of X(153) and X(31145)
X(50907) = reflection of X(i) in X(j) for these {i,j}: {104, 3679}, {376, 1145}, {944, 6174}, {1320, 381}, {3241, 119}, {10698, 10711}, {10707, 355}, {10711, 12751}, {14217, 34648}, {34631, 1537}, {34747, 25485}, {34748, 19907}
X(50908) lies on these lines: {1, 12831}, {2, 2800}, {11, 11529}, {30, 6265}, {40, 6174}, {80, 381}, {100, 28194}, {104, 551}, {119, 3679}, {153, 3241}, {214, 376}, {354, 2771}, {515, 10031}, {517, 5660}, {519, 1519}, {528, 1537}, {549, 12515}, {944, 11274}, {946, 10707}, {952, 1699}, {1317, 3586}, {1768, 11729}, {2801, 3892}, {2802, 25568}, {3058, 12739}, {3090, 38104}, {3524, 46684}, {3543, 6224}, {3545, 12247}, {3582, 11571}, {3583, 5048}, {3624, 38069}, {3653, 38602}, {3654, 3899}, {3655, 12678}, {3839, 6246}, {4301, 38665}, {4512, 34123}, {4870, 17638}, {5055, 12619}, {5071, 6702}, {5434, 12740}, {5693, 45700}, {5881, 34640}, {5886, 11219}, {5901, 7701}, {6264, 13257}, {6713, 12767}, {6738, 47744}, {7982, 37725}, {8227, 45310}, {9588, 38763}, {9589, 10993}, {9624, 20418}, {9803, 16174}, {9809, 11715}, {10056, 12758}, {10072, 11570}, {10609, 41869}, {10728, 33337}, {11014, 34606}, {11114, 40257}, {11522, 37726}, {12019, 38077}, {12332, 16371}, {12665, 34625}, {12737, 34697}, {12738, 22791}, {12747, 14269}, {13464, 38669}, {15017, 19875}, {15863, 38074}, {16205, 34747}, {16370, 22775}, {19077, 35823}, {19078, 35822}, {22836, 34629}, {22935, 28198}, {28452, 45764}, {30144, 37430}, {30305, 41553}, {30308, 37718}, {34719, 37700}, {37704, 41556}, {37735, 40266}, {38161, 41106}
X(50908) = midpoint of X(i) and X(j) for these {i,j}: {153, 3241}, {381, 48667}, {3543, 6224}, {3655, 16128}, {3679, 13253}, {6326, 31162}, {10698, 10711}
X(50908) = reflection of X(i) in X(j) for these {i,j}: {40, 6174}, {80, 381}, {104, 551}, {376, 214}, {381, 12611}, {944, 11274}, {3241, 25485}, {3655, 19907}, {3679, 119}, {10707, 946}, {10711, 21635}, {11219, 5886}, {12515, 549}, {12751, 10711}, {14217, 31162}, {31162, 1537}, {49176, 10707}
X(50908) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1537, 6326, 14217}, {6265, 34789, 12119}, {10698, 21635, 12751}, {12611, 48667, 80}
X(50909) lies on these lines: {119, 3828}, {153, 551}, {381, 42871}, {519, 1519}, {952, 3860}, {2800, 4745}, {3839, 5531}, {5660, 28164}, {6174, 12512}, {6326, 34648}, {9809, 19875}, {10707, 12571}, {11698, 28194}, {13253, 34641}, {15017, 19883}, {19925, 33592}
X(50909) = midpoint of X(i) and X(j) for these {i,j}: {153, 551}, {6326, 34648}, {10711, 21635}, {13253, 34641}
X(50909) = reflection of X(i) in X(j) for these {i,j}: {3828, 119}, {10707, 12571}, {12512, 6174}
X(50910) lies on these lines: {2, 38128}, {4, 34710}, {40, 11274}, {104, 3241}, {119, 31145}, {145, 34629}, {153, 20049}, {376, 1317}, {381, 12531}, {517, 10031}, {519, 1519}, {528, 34617}, {952, 3830}, {1482, 10707}, {1537, 34627}, {3036, 5071}, {3090, 38099}, {3149, 38665}, {3622, 38069}, {3679, 25485}, {6174, 12245}, {7972, 28194}, {9041, 10759}, {9624, 38104}, {10595, 45310}, {10728, 28204}, {13253, 34747}, {15863, 38021}, {19705, 34474}, {19907, 34718}, {38156, 41106}
X(50910) = midpoint of X(i) and X(j) for these {i,j}: {153, 20049}, {13253, 34747}
X(50910) = reflection of X(i) in X(j) for these {i,j}: {40, 11274}, {104, 3241}, {376, 1317}, {3679, 25485}, {10707, 1482}, {10711, 10698}, {12245, 6174}, {12531, 381}, {31145, 119}, {34627, 1537}, {34718, 19907}
X(50911) lies on these lines: {1, 120}, {2, 11716}, {8, 150}, {9, 80}, {10, 105}, {294, 20495}, {355, 28915}, {515, 1292}, {516, 10729}, {517, 10743}, {519, 10699}, {668, 32850}, {1111, 2550}, {1358, 5252}, {1438, 20482}, {1698, 6714}, {1837, 3021}, {2775, 12368}, {2788, 9864}, {2795, 13178}, {2802, 10773}, {2820, 3762}, {2826, 12751}, {2835, 3421}, {2836, 13211}, {2838, 13280}, {3617, 20097}, {4297, 38712}, {4528, 6084}, {4847, 24618}, {4863, 16833}, {5511, 5587}, {5790, 38575}, {5847, 10760}, {6684, 38694}, {9519, 21290}, {9523, 12784}, {15521, 18480}, {18481, 38619}, {18525, 38589}, {26446, 38603}, {31673, 44983}, {33970, 34122}
X(50911) = midpoint of X(i) and X(j) for these {i,j}: {8, 20344}, {18525, 38589}
X(50911) = reflection of X(i) in X(j) for these {i,j}: {1, 120}, {105, 10}, {15521, 18480}, {18481, 38619}, {44983, 31673}
X(50911) = anticomplement of X(11716)
X(50912) lies on these lines: {8, 190}, {105, 3679}, {120, 3241}, {519, 10699}, {1292, 28204}, {2809, 4677}, {5511, 38074}, {5881, 38684}, {9041, 18343}, {9519, 37712}, {10729, 28194}, {10760, 28538}, {11716, 19875}, {20344, 31145}, {33970, 38099}, {38066, 38603}
X(50912) = midpoint of X(20344) and X(31145)
X(50912) = reflection of X(i) in X(j) for these {i,j}: {105, 3679}, {3241, 120}, {10699, 10712}
X(50913) lies on these lines: {1, 528}, {2, 2809}, {105, 551}, {120, 3679}, {392, 2836}, {519, 10699}, {527, 45765}, {537, 34892}, {1292, 28194}, {3241, 20344}, {3653, 38603}, {3656, 28915}, {3912, 4767}, {4301, 38684}, {5511, 38021}, {5540, 11730}, {6084, 30580}, {10743, 28204}, {11716, 38314}, {13464, 38670}, {33970, 38026}
X(50913) = midpoint of X(i) and X(j) for these {i,j}: {3241, 20344}, {10699, 10712}
X(50913) = reflection of X(i) in X(j) for these {i,j}: {105, 551}, {3679, 120}
X(50914) lies on these lines: {1, 121}, {2, 11717}, {8, 80}, {10, 106}, {515, 1293}, {516, 10730}, {517, 10744}, {519, 3699}, {956, 34139}, {1054, 3679}, {1120, 23869}, {1357, 5252}, {1698, 6715}, {1837, 6018}, {2776, 12368}, {2789, 9864}, {2796, 4669}, {2810, 3416}, {2827, 4768}, {2841, 13532}, {2842, 13211}, {2844, 13280}, {3617, 20098}, {3632, 13541}, {4297, 38713}, {4487, 41684}, {4792, 21093}, {5510, 5587}, {5657, 14664}, {5790, 38576}, {5847, 10761}, {6684, 38695}, {7972, 17780}, {9527, 12784}, {12531, 49998}, {12653, 30566}, {15522, 18480}, {18481, 38620}, {18525, 38590}, {24003, 24864}, {26446, 38604}, {31673, 44984}, {33337, 43290}, {42020, 49169}
X(50914) = midpoint of X(i) and X(j) for these {i,j}: {8, 21290}, {3632, 13541}, {18525, 38590}
X(50914) = reflection of X(i) in X(j) for these {i,j}: {1, 121}, {106, 10}, {1120, 23869}, {10700, 11814}, {15522, 18480}, {18481, 38620}, {44984, 31673}
X(50914) = anticomplement of X(11717)
X(50914) = barycentric product X(312)*X(20586)
X(50914) = barycentric quotient X(20586)/X(57)
X(50914) = {X(10700),X(10713)}-harmonic conjugate of X(11814)
X(50915) lies on these lines: {1, 24709}, {2, 2802}, {86, 99}, {121, 3679}, {190, 14028}, {519, 3699}, {524, 47626}, {1054, 11731}, {1120, 21087}, {1293, 28194}, {2810, 47358}, {2842, 3794}, {3241, 21290}, {3524, 14664}, {3616, 4781}, {3653, 38604}, {4301, 38685}, {4792, 25377}, {5510, 38021}, {5603, 9519}, {10744, 28204}, {11717, 17777}, {13464, 38671}, {16370, 34139}
X(50915) = midpoint of X(i) and X(j) for these {i,j}: {3241, 21290}, {3679, 13541}, {10700, 10713}
X(50915) = reflection of X(i) in X(j) for these {i,j}: {106, 551}, {3679, 121}, {10713, 11814}
X(50916) lies on these lines: {1, 122}, {2, 11718}, {8, 34186}, {10, 107}, {40, 2777}, {80, 2803}, {133, 5587}, {165, 3184}, {515, 1294}, {516, 10152}, {517, 10745}, {519, 10701}, {1698, 6716}, {1837, 7158}, {2790, 9864}, {2797, 13178}, {2802, 10775}, {2816, 11362}, {2828, 12751}, {2846, 13532}, {2848, 13280}, {3324, 5252}, {3576, 34842}, {3579, 23240}, {3679, 9530}, {4297, 38714}, {5657, 5667}, {5790, 38577}, {5847, 10762}, {6684, 23239}, {8193, 14673}, {8227, 36520}, {9033, 13211}, {9528, 47033}, {12699, 49117}, {14703, 15177}, {18480, 22337}, {18481, 38621}, {18525, 38591}, {26446, 38605}, {31673, 44985}
X(50916) = midpoint of X(i) and X(j) for these {i,j}: {8, 34186}, {18525, 38591}
X(50916) = reflection of X(i) in X(j) for these {i,j}: {1, 122}, {107, 10}, {12699, 49117}, {18481, 38621}, {22337, 18480}, {23240, 3579}, {44985, 31673}
X(50916) = anticomplement of X(11718)
X(50917) lies on these lines: {1, 123}, {2, 11719}, {8, 151}, {10, 108}, {40, 1145}, {72, 2778}, {80, 2804}, {515, 1295}, {516, 10731}, {517, 10746}, {519, 10702}, {1359, 5252}, {1698, 6717}, {1837, 3318}, {2791, 9864}, {2798, 13178}, {2802, 10776}, {2812, 38955}, {2818, 15499}, {2823, 3421}, {2849, 4768}, {2850, 13211}, {4297, 38715}, {4528, 6087}, {5587, 25640}, {5790, 38578}, {5847, 10763}, {6684, 38696}, {6735, 49207}, {18339, 24031}, {18480, 33566}, {18481, 38622}, {18525, 38592}, {26446, 38606}, {31673, 44986}, {44692, 48358}
X(50917) =midpoint of X(i) and X(j) for these {i,j}: {8, 34188}, {18525, 38592}
X(50917) =reflection of X(i) in X(j) for these {i,j}: {1, 123}, {108, 10}, {18481, 38622}, {33566, 18480}, {44986, 31673}
X(50917) =anticomplement of X(11719)
X(50918) lies on these lines: {2, 2800}, {102, 28194}, {109, 551}, {117, 38021}, {124, 3679}, {376, 11713}, {519, 10703}, {946, 10709}, {2818, 3656}, {3241, 33650}, {3524, 14690}, {3653, 38607}, {4301, 38667}, {5881, 38781}, {9588, 38787}, {10747, 28204}, {11700, 38314}, {11734, 25055}, {13464, 38674}
X(50918) = midpoint of X(i) and X(j) for these {i,j}: {3241, 33650}, {10703, 10716}
X(50918) = reflection of X(i) in X(j) for these {i,j}: {109, 551}, {376, 11713}, {3679, 124}, {10709, 946}, {13532, 10716}
X(50919) lies on these lines: {10, 542}, {110, 3828}, {113, 38076}, {125, 551}, {265, 28194}, {376, 12407}, {515, 20126}, {519, 7984}, {541, 34648}, {547, 11699}, {553, 12903}, {1511, 38068}, {1992, 32261}, {2854, 50781}, {3448, 3679}, {3543, 9904}, {3656, 38724}, {4301, 36253}, {5609, 31399}, {5882, 20379}, {6593, 38089}, {9143, 19875}, {10264, 28204}, {10272, 38083}, {10706, 19925}, {11231, 11694}, {11720, 19883}, {12317, 38074}, {13169, 34379}, {13464, 15027}, {15081, 38021}, {25328, 28538}, {25330, 50783}, {25335, 38087}, {33535, 34627}
X(50919) = midpoint of X(i) and X(j) for these {i,j}: {376, 12407}, {1992, 32261}, {3448, 3679}, {3543, 9904}, {9140, 13211}, {33535, 34627}
X(50919) = reflection of X(i) in X(j) for these {i,j}: {110, 3828}, {551, 125}, {10706, 19925}, {11699, 547}, {11720, 45311}, {13605, 9140}
X(50919) = {X(11720),X(45311)}-harmonic conjugate of X(19883)
X(50920) lies on these lines: {8, 542}, {67, 9041}, {74, 28204}, {110, 3679}, {113, 38074}, {125, 3241}, {355, 10706}, {381, 7978}, {518, 13169}, {519, 7984}, {541, 34627}, {549, 12898}, {551, 15059}, {597, 32298}, {895, 28538}, {952, 20126}, {1511, 38066}, {2854, 50783}, {3448, 31145}, {3656, 14644}, {4301, 15044}, {5071, 11723}, {5881, 15054}, {5882, 15057}, {6593, 38087}, {10272, 38081}, {10733, 28194}, {11694, 38112}, {11720, 19875}, {13464, 15025}, {34319, 49524}, {38314, 45311}, {41720, 47359}
X(50920) = midpoint of X(3448) and X(31145)
X(50920) = reflection of X(i) in X(j) for these {i,j}: {110, 3679}, {3241, 125}, {7978, 381}, {7984, 9140}, {9140, 13211}, {10706, 355}, {12898, 549}, {32298, 597}, {34319, 49524}, {41720, 47359}
X(50921) lies on these lines: {1, 542}, {67, 28538}, {74, 28194}, {110, 551}, {113, 38021}, {125, 3679}, {265, 28204}, {354, 2771}, {376, 11709}, {381, 12261}, {392, 2836}, {517, 20126}, {519, 7984}, {541, 31162}, {549, 12778}, {597, 32278}, {599, 32238}, {946, 10706}, {1386, 34319}, {1511, 3653}, {2842, 3794}, {2854, 47358}, {2948, 5642}, {3241, 3448}, {3564, 47593}, {3656, 5663}, {3828, 15059}, {4301, 15054}, {5465, 38220}, {5493, 15021}, {5621, 37546}, {5847, 13169}, {5881, 36253}, {6593, 38023}, {6723, 19876}, {7982, 16003}, {7991, 20417}, {9041, 25328}, {9143, 11720}, {9144, 12258}, {9588, 38729}, {9589, 10990}, {9624, 16534}, {10272, 38022}, {11522, 15063}, {11694, 38028}, {13204, 16371}, {13464, 14094}, {15057, 43174}, {15081, 38074}, {15178, 23236}, {15303, 16475}, {16370, 22586}, {19875, 45311}, {20127, 28202}, {25330, 50790}, {44569, 47321}
X(50921) = midpoint of X(i) and X(j) for these {i,j}: {3241, 3448}, {7984, 9140}, {31162, 33535}
X(50921) = reflection of X(i) in X(j) for these {i,j}: {110, 551}, {376, 11709}, {381, 12261}, {599, 32238}, {2948, 5642}, {3679, 125}, {5642, 11735}, {9140, 13605}, {9143, 11720}, {9144, 12258}, {10706, 946}, {12368, 381}, {12778, 549}, {13211, 9140}, {32278, 597}, {34319, 1386}, {47321, 44569}
X(50921) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2948, 25055, 5642}, {5642, 11735, 25055}, {7984, 13605, 13211}, {9143, 38314, 11720}
X(50922) lies on these lines: {125, 3828}, {516, 20126}, {519, 7984}, {542, 1125}, {551, 3448}, {2796, 15357}, {2854, 50787}, {9143, 19883}, {10264, 28194}, {10706, 12571}, {12317, 38021}, {15081, 38076}, {20379, 43174}, {25330, 47358}, {25335, 38023}, {33535, 34648}
X(50922) = midpoint of X(i) and X(j) for these {i,j}: {551, 3448}, {9140, 13605}, {33535, 34648}
X(50922) = reflection of X(i) in X(j) for these {i,j}: {3828, 125}, {10706, 12571}
X(50923) lies on these lines: {110, 3241}, {125, 31145}, {145, 542}, {519, 7984}, {541, 34631}, {895, 9041}, {1482, 10706}, {2854, 50790}, {3448, 20049}, {3679, 15059}, {5844, 20126}, {5846, 13169}, {5881, 15044}, {10733, 28204}, {13464, 15029}, {28538, 32244}
X(50923) = midpoint of X(3448) and X(20049)
X(50923) = reflection of X(i) in X(j) for these {i,j}: {110, 3241}, {9140, 7984}, {10706, 1482}, {31145, 125}
X(50924) lies on these lines: {1, 126}, {2, 11721}, {8, 14360}, {10, 111}, {40, 23699}, {80, 2805}, {355, 33962}, {515, 1296}, {516, 10734}, {517, 10748}, {518, 36883}, {519, 10704}, {543, 3679}, {1698, 6719}, {1837, 6019}, {2780, 12368}, {2793, 9864}, {2802, 10779}, {2813, 38479}, {2830, 12751}, {2852, 13532}, {2854, 3416}, {3325, 5252}, {3576, 40556}, {3617, 20099}, {3654, 32424}, {4297, 38716}, {5512, 5587}, {5657, 14654}, {5790, 11258}, {5847, 10765}, {5886, 40340}, {6684, 38698}, {9172, 19875}, {9956, 38796}, {11231, 38806}, {14650, 26446}, {14657, 15177}, {18480, 22338}, {18481, 38623}, {18525, 38593}, {28160, 38797}, {28662, 38047}, {31423, 38804}, {31673, 44987}
X(50924) = midpoint of X(i) and X(j) for these {i,j}: {8, 14360}, {18525, 38593}
X(50924) = reflection of X(i) in X(j) for these {i,j}: {1, 126}, {111, 10}, {18481, 38623}, {22338, 18480}, {44987, 31673}
X(50924) = anticomplement of X(11721)
X(50925) lies on these lines: {8, 543}, {111, 3679}, {126, 3241}, {519, 10704}, {1296, 28204}, {2854, 50783}, {5512, 38074}, {5690, 14666}, {5881, 38688}, {9041, 36883}, {10734, 28194}, {10765, 28538}, {11721, 19875}, {14360, 31145}, {14650, 38066}, {28662, 38087}, {32424, 34718}
X(50925) = midpoint of X(14360) and X(31145)
X(50925) = reflection of X(i) in X(j) for these {i,j}: {111, 3679}, {3241, 126}, {10704, 10717}, {14666, 5690}
X(50926) lies on these lines: {1, 543}, {111, 551}, {126, 3679}, {519, 10704}, {962, 37749}, {1296, 28194}, {1385, 14666}, {2854, 47358}, {3241, 14360}, {3653, 14650}, {3655, 32424}, {3656, 33962}, {4301, 38688}, {5512, 38021}, {9172, 25055}, {10748, 28204}, {11721, 38314}, {13464, 38675}, {28202, 38797}, {28538, 36883}, {28662, 38023}
X(50926) = midpoint of X(i) and X(j) for these {i,j}: {962, 37749}, {3241, 14360}, {10704, 10717}
X(50926) = reflection of X(i) in X(j) for these {i,j}: {111, 551}, {3679, 126}, {14666, 1385}
See Ivan Pavlov, euclid 5264.
X(50927) lies on the nine-point circle and these lines: {5, 15613}, {122, 6823}, {125, 146}, {136, 1906}, {3258, 47096}, {46436, 46517}
X(50927) = reflection of X(15613) in X(5)
X(50927) = antipode of X(15613) in nine-point circle
See Ivan Pavlov, euclid 5264.
X(50928) lies on the nine-point circle and these lines: {4, 931}, {115, 4263}, {125, 2476}, {136, 1904}, {12558, 42425}
X(50928) = midpoint of X(4) and X(931)
X(50928) = complement of the circumperp conjugate of X(931)
X(50928) = complementary conjugate of the circumnormal-isogonal conjugate of X(931)
X(50928) = Poncelet point of X(931)
X(50928) = center of the circumconic {{A, B, C, X(4), X(931)}}
See Ivan Pavlov, euclid 5264.
X(50929) lies on the nine-point circle and these lines: {4, 38968}, {122, 47514}, {125, 469}
See Ivan Pavlov, euclid 5264.
X(50930) lies on the nine-point circle and these lines: {4, 972}, {11, 278}, {12, 31893}, {116, 6245}, {123, 8727}, {125, 44403}, {235, 38966}, {21664, 50946}, {42772, 44993}
X(50930) = midpoint of X(4) and X(40117)
X(50930) = complement of the circumperp conjugate of X(40117)
X(50930) = complementary conjugate of the circumnormal-isogonal conjugate of X(40117)
X(50930) = orthoassociate of X(972)
X(50930) = Poncelet point of X(40117)
X(50930) = center of the circumconic {{A, B, C, X(4), X(40117)}}
X(50930) = inverse of X(972) in polar circle
See Ivan Pavlov, euclid 5264.
X(50931) lies on the nine-point circle and these lines: {2, 28159}, {4, 4588}, {5, 15614}, {11, 5902}, {5520, 47321}
X(50931) = midpoint of X(4) and X(4588)
X(50931) = reflection of X(15614) in X(5)
X(50931) = complement of X(28159)
X(50931) = complementary conjugate of X(28160)
X(50931) = Poncelet point of X(4588)
X(50931) = center of the circumconic {{A, B, C, X(4), X(4588)}}
X(50931) = antipode of X(15614) in nine-point circle
X(50931) = X(4)-Ceva conjugate of-X(28160)
X(50931) = X(1)-complementary conjugate of-X(28160)
See Ivan Pavlov, euclid 5264.
X(50932) lies on the nine-point circle and these lines: {11, 3333}, {21664, 50944}
X(50933) lies on the nine-point circle and these lines: {2, 2723}, {4, 929}, {5, 15612}, {11, 1465}, {113, 39212}, {116, 515}, {117, 514}, {118, 522}, {124, 516}, {125, 851}, {223, 35580}, {650, 20623}, {1521, 2807}, {1699, 3259}, {1785, 38966}, {2222, 15608}, {5179, 5514}, {5587, 46415}, {19925, 46670}, {25640, 39536}
X(50933) = midpoint of X(4) and X(929)
X(50933) = reflection of X(15612) in X(5)
X(50933) = complement of X(2723)
X(50933) = Stevanovic-circle-inverse of X(20623)
X(50933) = complement of the isogonal conjugate of X(2807)
X(50933) = medial-isogonal conjugate of X(2807)
X(50933) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 2807}, {2807, 10}
X(50933) = X(4)-Ceva conjugate of X(2807)
X(50934) lies on the nine-point circle and these lines: {2, 14388}, {4, 11636}, {5, 46657}, {111, 13994}, {115, 3845}, {125, 5169}, {127, 10254}, {136, 10301}, {381, 15922}, {3258, 7426}, {5099, 44961}, {5480, 12494}, {9993, 9999}, {13413, 46654}, {18323, 38971}
X(50934) = midpoint of X(4) and X(11636)
X(50934) = reflection of X(46657) in X(5)
X(50934) = complement of X(14388)
X(50934) = complement of the isogonal conjugate of X(11645)
X(50934) = medial-isogonal conjugate of X(11645)
X(50934) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 11645}, {31, 16308}, {11645, 10}, {41358, 226}
X(50934) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 16308}, {4, 11645}
X(50934) = X(16308)-Dao conjugate of X(2)
X(50934) = barycentric quotient X(16308)/X(14388)
X(50935) lies on the nine-point circle and these lines: {2, 43660}, {4, 1302}, {30, 46436}, {113, 9003}, {122, 15760}, {125, 381}, {132, 11251}, {135, 6623}, {136, 1596}, {3258, 11799}, {5099, 16334}, {7574, 46437}, {10297, 16177}, {16188, 36169}, {16221, 37984}, {18531, 35968}, {44263, 45182}
X(50935) = midpoint of X(4) and X(1302)
X(50935) = complement of X(43660)
X(50935) = orthocentroidal-circle-inverse of X(11472)
X(50935) = complement of the isogonal conjugate of X(14915)
X(50935) = medial isogonal conjugate of X(14915)
X(50935) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 14915}, {31, 16303}, {14915, 10}
X(50935) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 16303}, {4, 14915}
X(50935) = X(16303)-Dao conjugate of X(2)
X(50935) = barycentric quotient X(16303)/X(43660)
X(50936) lies on the nine-point circle and these lines: {2, 15323}, {4, 932}, {5, 5518}, {11, 982}, {92, 5521}, {115, 23447}, {116, 3825}, {123, 20545}, {946, 44948}, {1699, 20375}, {5511, 26470}, {6841, 44950}, {11680, 11689}
X(50936) = midpoint of X(4) and X(932)
X(50936) = reflection of X(5518) in X(5)
X(50936) = complement of X(15323)
X(50936) = complement of the isogonal conjugate of X(15310)
X(50936) = medial-isogonal conjugate of X(15310)
X(50936) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 15310}, {6, 43040}, {15310, 10}
X(50936) = X(4)-Ceva conjugate of X(15310)
X(50937) lies on the nine-point circle and these lines: {2, 5897}, {4, 122}, {5, 35968}, {115, 393}, {123, 15763}, {125, 235}, {127, 1596}, {131, 11251}, {136, 37197}, {403, 16177}, {1559, 44436}, {1906, 46662}, {3089, 15613}, {3258, 10151}, {6389, 6624}, {13613, 20265}, {15311, 46065}, {33504, 44909}, {35488, 35969}, {37981, 46436}, {37984, 38971}, {38977, 44225}, {43831, 47600}
X(50937) = midpoint of X(4) and X(1301)
X(50937) = reflection of X(35968) in X(5)
X(50937) = complement of X(5897)
X(50937) = polar-circle-inverse of X(1294)
X(50937) = complement of the isogonal conjugate of X(15311)
X(50937) = medial isogonal conjugate of X(15311)
X(50937) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 15311}, {15311, 10}
X(50937) = X(4)-Ceva conjugate of X(15311)
X(50937) = barycentric product X(1559)*X(46065)
X(50938) lies on the nine-point circle and these lines: {2, 1301}, {4, 127}, {25, 125}, {113, 2967}, {115, 235}, {122, 427}, {123, 37362}, {232, 33504}, {403, 38971}, {428, 20625}, {468, 16177}, {1560, 46425}, {1596, 14672}, {3258, 37981}, {3575, 46654}, {5064, 46662}, {5099, 10151}, {5139, 37197}, {5512, 6623}, {12145, 15526}, {13526, 13613}, {20208, 33584}, {35594, 40949}, {42426, 47225}, {46436, 47166}
X(50938) = midpoint of X(4) and X(1289)
X(50938) = complement of X(34168)
X(50938) = polar-circle-inverse of X(1297)
X(50938) = orthoptic-circle-of-Steiner-inellipse-inverse of X(1301)
X(50938) = complement of the isogonal conjugate of X(34146)
X(50938) = medial-isogonal conjugate of X(34146)
X(50938) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 34146}, {31, 16318}, {34146, 10}
X(50938) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 16318}, {4, 34146}
X(50938) = X(16318)-Dao conjugate of X(2)
X(50938) = barycentric quotient X(16318)/X(34168)
X(50939) lies on the nine-point circle and these lines: {4, 1288}, {5, 35969}, {24, 125}, {115, 14576}, {122, 13371}, {127, 31723}, {235, 15241}, {6640, 35968}, {11819, 20625}, {16177, 44452}
X(50939) = midpoint of X(4) and X(1288)
X(50939) = reflection of X(35969) in X(5)
X(50940) lies on the nine-point circle and these lines: {4, 14733}, {5, 46415}, {11, 971}, {119, 3900}, {123, 5087}, {513, 44993}, {517, 5514}, {1566, 2717}, {3259, 7956}, {5511, 22835}, {5886, 15612}, {20620, 23710}, {31844, 46396}
X(50940) = reflection of X(46415) in X(5)
X(50940) = X(6)-complementary conjugate of X(43047)
X(50941) lies on the cubic K010 and these lines: {2, 99}, {476, 691}, {523, 23348}, {892, 2395}, {895, 5967}, {1316, 5968}, {1640, 14999}, {1649, 47293}, {2394, 2396}, {2408, 34574}, {2502, 32221}, {5467, 23288}, {5468, 17708}, {7472, 8371}, {8029, 47291}, {9168, 47288}, {11123, 47289}, {16092, 45662}, {17948, 45331}, {21460, 46124}
X(50941) = X(i)-isoconjugate of X(j) for these (i,j): {842, 2642}, {896, 14998}, {922, 14223}
X(50941) = X(i)-Dao conjugate of X(j) for these (i, j): (15899, 14998), (23967, 690), (35582, 23992), (39061, 14223), (42426, 14273)
X(50941) = cevapoint of X(i) and X(j) for these (i,j): {1640, 45662}, {2493, 20403}
X(50941) = trilinear pole of line {542, 1550}
X(50941) = barycentric product X(i)*X(j) for these {i,j}: {99, 16092}, {542, 892}, {671, 14999}, {7473, 30786}
X(50941) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 14998}, {542, 690}, {671, 14223}, {691, 842}, {892, 5641}, {895, 35909}, {1640, 1648}, {2247, 2642}, {5191, 351}, {5968, 23350}, {6041, 21906}, {6103, 14273}, {7473, 468}, {14999, 524}, {16092, 523}, {34761, 5967}, {36827, 46157}, {42743, 9155}, {45662, 1649}
X(50941) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2407, 14977, 892}, {4226, 5466, 691}
X(50942) lies on the cubic K010 and these lines: {2, 1637}, {468, 1649}, {523, 868}, {524, 18311}, {690, 5967}, {842, 2770}, {2394, 2395}, {2396, 2407}, {2793, 34174}, {5466, 10415}, {5486, 9003}, {5641, 18823}, {5664, 6390}, {9164, 45331}, {13574, 44010}, {24975, 36953}, {35522, 43084}
X(50942) = X(i)-isoconjugate of X(j) for these (i,j): {163, 16092}, {542, 36142}, {691, 2247}, {923, 14999}, {5191, 36085}, {7473, 36060}
X(50942) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 16092), (1560, 7473), (1648, 45662), (1649, 1640), (2482, 14999), (21905, 6041), (23992, 542), (35582, 23967), (38988, 5191), (48317, 6103)
X(50942) = cevapoint of X(2492) and X(20403)
X(50942) = trilinear pole of line {690, 2682}
X(50942) = barycentric product X(i)*X(j) for these {i,j}: {524, 14223}, {690, 5641}, {842, 35522}, {1648, 6035}, {3266, 14998}, {5967, 34765}, {35909, 44146}, {35911, 37778}
X(50942) = barycentric quotient X(i)/X(j) for these {i,j}: {351, 5191}, {468, 7473}, {523, 16092}, {524, 14999}, {690, 542}, {842, 691}, {1648, 1640}, {1649, 45662}, {2642, 2247}, {5641, 892}, {5967, 34761}, {9155, 42743}, {14223, 671}, {14273, 6103}, {14998, 111}, {21906, 6041}, {23350, 5968}, {35909, 895}, {46157, 36827}
X(50942) = {X(7417),X(9168)}-harmonic conjugate of X(47219)
X(50943) lies on the cubic K010 and these lines: {2, 3904}, {514, 42754}, {519, 23757}, {953, 2726}, {996, 23887}, {1000, 6366}, {1016, 2397}, {3762, 14628}, {23808, 37629}, {30725, 40218}, {35168, 46136}, {40437, 43728}
X(50943) = X(i)-isoconjugate of X(j) for these (i,j): {901, 2265}, {952, 32665}
X(50943) = X(i)-Dao conjugate of X(j) for these (i, j): (3310, 35013), (35092, 952), (38979, 2265)
X(50943) = trilinear pole of line {900, 3259}
X(50943) = barycentric product X(900)*X(46136)
X(50943) = barycentric quotient X(i)/X(j) for these {i,j}: {900, 952}, {953, 901}, {1635, 2265}, {3259, 35013}, {6550, 6075}, {30725, 43043}, {46041, 1320}, {46136, 4555}
X(50944) lies on the cubics K010, K011, K190, and K242, and these lines: {2, 2593}, {4, 16070}, {99, 112}, {523, 1113}, {525, 8115}, {879, 15461}, {2575, 6776}, {2580, 4560}, {3267, 46813}, {14618, 46815}, {15164, 23878}
X(50944) = reflection of X(i) in X(j) for these {i,j}: {2593, 8106}, {22340, 46811}
X(50944) = anticomplement of the isotomic conjugate of X(39298)
X(50944) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {163, 14807}, {1101, 22340}, {1113, 21294}, {1822, 13219}, {2576, 3448}, {39298, 6327}, {44123, 21221}
X(50944) = X(i)-Ceva conjugate of X(j) for these (i,j): {99, 1113}, {648, 8115}, {6331, 15164}, {39298, 2}
X(50944) = X(i)-cross conjugate of X(j) for these (i,j): {523, 22340}, {525, 2593}, {647, 2575}, {15167, 15461}
X(50944) = X(i)-isoconjugate of X(j) for these (i,j): {162, 15166}, {163, 1313}, {656, 41942}, {661, 15460}, {662, 44126}, {1114, 2578}, {1823, 8105}, {2574, 2577}, {2581, 42668}, {2582, 44124}, {14499, 36131}
X(50944) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 1313), (125, 15166), (1084, 44126), (1312, 8105), (2575, 647), (8106, 523), (15167, 2574), (36830, 15460), (39008, 14499), (40596, 41942), (46811, 525)
X(50944) = cevapoint of X(i) and X(j) for these (i,j): {523, 8106}, {525, 46811}, {647, 2575}
X(50944) = crosspoint of X(i) and X(j) for these (i,j): {99, 46813}, {648, 46815}, {6331, 15164}
X(50944) = crosssum of X(3049) and X(42668)
X(50944) = trilinear pole of line {125, 1312}
X(50944) = crossdifference of every pair of points on line {15166, 20975}
X(50944) = barycentric product X(i)*X(j) for these {i,j}: {99, 1312}, {670, 44125}, {850, 15461}, {1113, 22340}, {2575, 15164}, {2580, 2583}, {2593, 8115}, {3267, 41941}, {6331, 15167}, {8106, 46813}, {14500, 16077}, {46811, 46815}
X(50944) = barycentric quotient X(i)/X(j) for these {i,j}: {110, 15460}, {112, 41942}, {512, 44126}, {523, 1313}, {647, 15166}, {1113, 1114}, {1312, 523}, {1822, 1823}, {2575, 2574}, {2576, 2577}, {2579, 2578}, {2580, 2581}, {2583, 2582}, {2585, 2584}, {2586, 2587}, {2589, 2588}, {2593, 2592}, {8106, 8105}, {8115, 8116}, {9033, 14499}, {14500, 9033}, {15164, 15165}, {15167, 647}, {15461, 110}, {22340, 22339}, {39241, 39240}, {39298, 39299}, {41941, 112}, {42667, 42668}, {44067, 44068}, {44123, 44124}, {44125, 512}, {46166, 46167}, {46811, 46814}, {46813, 46810}, {46815, 46812}
X(50944) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {99, 39298, 4235}, {648, 39298, 2407}
X(50945) lies on the cubics K010, K011, K190, and K242, and these lines: {2, 2592}, {4, 16071}, {99, 112}, {523, 1114}, {525, 8116}, {879, 15460}, {2574, 6776}, {2581, 4560}, {3267, 46810}, {14618, 46812}, {15165, 23878}
X(50945) = reflection of X(i) in X(j) for these {i,j}: {2592, 8105}, {22339, 46814}
X(50945) = anticomplement of the isotomic conjugate of X(39299)
X(50945) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {163, 14808}, {1101, 22339}, {1114, 21294}, {1823, 13219}, {2577, 3448}, {39299, 6327}, {44124, 21221}
X(50945) = X(i)-Ceva conjugate of X(j) for these (i,j): {99, 1114}, {648, 8116}, {6331, 15165}, {39299, 2}
X(50945) = X(i)-cross conjugate of X(j) for these (i,j): {523, 22339}, {525, 2592}, {647, 2574}, {15166, 15460}
X(50945) = X(i)-isoconjugate of X(j) for these (i,j): {162, 15167}, {163, 1312}, {656, 41941}, {661, 15461}, {662, 44125}, {1113, 2579}, {1822, 8106}, {2575, 2576}, {2580, 42667}, {2583, 44123}, {14500, 36131}
X(50945) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 1312), (125, 15167), (1084, 44125), (1313, 8106), (2574, 647), (8105, 523), (15166, 2575), (36830, 15461), (39008, 14500), (40596, 41941), (46814, 525)
X(50945) = cevapoint of X(i) and X(j) for these (i,j): {523, 8105}, {525, 46814}, {647, 2574}
X(50945) = crosspoint of X(i) and X(j) for these (i,j): {99, 46810}, {648, 46812}, {6331, 15165}
X(50945) = crosssum of X(3049) and X(42667)
X(50945) = trilinear pole of line {125, 1313}
X(50945) = crossdifference of every pair of points on line {15167, 20975}
X(50945) = barycentric product X(i)*X(j) for these {i,j}: {99, 1313}, {670, 44126}, {850, 15460}, {1114, 22339}, {2574, 15165}, {2581, 2582}, {2592, 8116}, {3267, 41942}, {6331, 15166}, {8105, 46810}, {14499, 16077}, {46812, 46814}
X(50945) = barycentric quotient X(i)/X(j) for these {i,j}: {110, 15461}, {112, 41941}, {512, 44125}, {523, 1312}, {647, 15167}, {1114, 1113}, {1313, 523}, {1823, 1822}, {2574, 2575}, {2577, 2576}, {2578, 2579}, {2581, 2580}, {2582, 2583}, {2584, 2585}, {2587, 2586}, {2588, 2589}, {2592, 2593}, {8105, 8106}, {8116, 8115}, {9033, 14500}, {14499, 9033}, {15165, 15164}, {15166, 647}, {15460, 110}, {22339, 22340}, {39240, 39241}, {39299, 39298}, {41942, 112}, {42668, 42667}, {44068, 44067}, {44124, 44123}, {44126, 512}, {46167, 46166}, {46810, 46813}, {46812, 46815}, {46814, 46811}
X(50945) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {99, 39299, 4235}, {648, 39299, 2407}
X(50946) lies on the X-parabola of ABC (see X(12065)) and these lines: {476, 38861}, {523, 2070}, {850, 924}, {1166, 2413}, {1179, 18808}, {1510, 11583}, {2501, 3050}, {3447, 15959}, {5466, 40393}, {10412, 20188}, {15047, 38539}, {15328, 40441}
X(50946) = polar conjugate of X(41677)
X(50946) = isogonal conjugate of the anticomplement of X(8901)
X(50946) = X(2216)-anticomplementary conjugate of X(11671)
X(50946) = X(i)-isoconjugate of X(j) for these (i,j): {48, 41677}, {101, 16698}, {162, 1216}, {163, 37636}, {570, 662}, {811, 23195}, {1209, 36134}, {1238, 32676}, {1594, 4575}, {4592, 47328}
X(50946) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 37636), (125, 1216), (136, 1594), (137, 1209), (338, 1225), (1015, 16698), (1084, 570), (1249, 41677), (5139, 47328), (15450, 42445), (15526, 1238), (17423, 23195), (20625, 41590), (45161, 41578)
X(50946) = cevapoint of X(i) and X(j) for these (i,j): {512, 12077}, {523, 1510}
X(50946) = trilinear pole of line {115, 137}
X(50946) = crossdifference of every pair of points on line {570, 1216}
X(50946) = barycentric product X(i)*X(j) for these {i,j}: {523, 40393}, {525, 1179}, {1166, 18314}, {1577, 2216}, {14618, 40441}, {15412, 40449}
X(50946) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 41677}, {512, 570}, {513, 16698}, {523, 37636}, {525, 1238}, {647, 1216}, {1166, 18315}, {1179, 648}, {2216, 662}, {2489, 47328}, {2501, 1594}, {3049, 23195}, {12077, 1209}, {15451, 42445}, {16040, 41590}, {18314, 1225}, {40393, 99}, {40441, 4558}, {40449, 14570}
X(50947) lies on these lines: {2, 8901}, {3, 2888}, {22, 147}, {99, 925}, {100, 48391}, {107, 43351}, {110, 351}, {323, 44886}, {476, 20189}, {542, 23217}, {930, 25149}, {933, 14590}, {1995, 7665}, {2439, 14586}, {3135, 45794}, {3964, 26283}, {4230, 11794}, {7468, 47293}, {7495, 20775}, {8907, 16391}, {9155, 45237}, {11005, 13558}, {12121, 46585}, {14611, 40049}, {14918, 19189}, {14966, 35319}, {15019, 35222}, {23195, 37636}, {23286, 43969}
X(50947) = anticomplement of X(8901)
X(50947) = isogonal conjugate of the polar conjugate of X(41677)
X(50947) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {249, 21271}, {1101, 3}, {1625, 21221}, {2617, 3448}, {4575, 44003}, {14570, 21294}, {23357, 17479}, {24000, 5889}, {24041, 2979}
X(50947) = X(14587)-Ceva conjugate of X(3)
X(50947) = X(i)-isoconjugate of X(j) for these (i,j): {523, 2216}, {656, 1179}, {661, 40393}, {1166, 2618}, {2616, 40449}, {24006, 40441}
X(50947) = X(i)-Dao conjugate of X(j) for these (i, j): (570, 18314), (1209, 523), (36830, 40393), (37636, 41298), (40596, 1179)
X(50947) = crosspoint of X(i) and X(j) for these (i,j): {99, 18315}, {110, 930}
X(50947) = crosssum of X(i) and X(j) for these (i,j): {512, 12077}, {523, 1510}
X(50947) = trilinear pole of line {570, 1216}
X(50947) = crossdifference of every pair of points on line {115, 137}
X(50947) = barycentric product X(i)*X(j) for these {i,j}: {3, 41677}, {99, 570}, {100, 16698}, {110, 37636}, {112, 1238}, {648, 1216}, {1209, 18315}, {1225, 14586}, {1594, 4558}, {4563, 47328}, {6331, 23195}, {16039, 41590}, {18831, 42445}
X(50947) = barycentric quotient X(i)/X(j) for these {i,j}: {110, 40393}, {112, 1179}, {163, 2216}, {570, 523}, {1209, 18314}, {1216, 525}, {1225, 15415}, {1238, 3267}, {1594, 14618}, {1625, 40449}, {14586, 1166}, {16698, 693}, {23195, 647}, {32661, 40441}, {37636, 850}, {41677, 264}, {42445, 6368}, {47328, 2501}
X(50947) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {110, 23181, 15329}, {110, 36829, 23181}, {1634, 23181, 110}, {1634, 36829, 15329}
See Kadir Altintas and Ercole Suppa, euclid 5269.
X(50948) lies on this line: {3, 6}
X(50948) = trilinear quotient X(3)/X(36744)
X(50949) lies on these lines: {1, 20582}, {2, 5846}, {8, 599}, {10, 597}, {141, 519}, {517, 47354}, {518, 3919}, {524, 3416}, {528, 50097}, {536, 49630}, {542, 5690}, {551, 3844}, {594, 49720}, {752, 49726}, {984, 17225}, {1350, 34627}, {1352, 34718}, {1386, 3828}, {1503, 3654}, {1698, 38023}, {1992, 3617}, {2836, 50919}, {3241, 21358}, {3242, 21356}, {3589, 19875}, {3619, 49679}, {3620, 49690}, {3629, 38098}, {3630, 49529}, {3631, 49688}, {3703, 4141}, {3755, 28329}, {3763, 38314}, {3773, 28562}, {3883, 41310}, {3932, 50296}, {4364, 32847}, {4645, 49727}, {4663, 4691}, {4677, 9053}, {4678, 11160}, {4711, 9004}, {4745, 5847}, {4971, 48829}, {5233, 12035}, {5648, 50920}, {5657, 43273}, {5790, 20423}, {5818, 38072}, {9055, 50086}, {9881, 12783}, {11179, 38066}, {15533, 50782}, {17237, 49762}, {17243, 33076}, {17313, 48849}, {17390, 48830}, {22791, 25561}, {25055, 34573}, {28208, 48881}, {28309, 50080}, {28337, 50282}, {28503, 49741}, {29615, 32850}, {31143, 33091}, {32217, 47496}, {34631, 40330}, {34632, 36990}, {34641, 49511}, {38086, 40333}, {41152, 50784}, {41311, 49476}, {47353, 50810}, {48798, 48862}, {48804, 48834}, {48851, 49738}, {49737, 50295}
X(50949) = midpoint of X(i) and X(j) for these {i,j}: {2, 50783}, {8, 599}, {1350, 34627}, {1352, 34718}, {3242, 31145}, {3416, 3679}, {4669, 50781}, {4677, 47358}, {4745, 50786}, {5648, 50920}, {34632, 36990}, {34641, 49511}, {47353, 50810}, {48798, 48862}, {48804, 48834}
X(50949) = reflection of X(i) in X(j) for these {i,j}: {1, 20582}, {551, 3844}, {597, 10}, {1386, 3828}, {22165, 50781}, {22791, 25561}, {32217, 47496}, {47356, 3589}, {49524, 3679}, {50112, 48821}
X(50949) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1386, 3828, 48310}, {1992, 3617, 38087}, {19875, 47356, 3589}, {21356, 31145, 3242}
X(50950) lies on these lines: {1, 599}, {2, 5847}, {6, 19875}, {8, 11160}, {10, 1992}, {30, 39885}, {40, 542}, {63, 4141}, {69, 519}, {141, 16491}, {165, 43273}, {319, 49720}, {518, 4677}, {524, 3416}, {528, 50076}, {540, 48812}, {551, 21356}, {597, 1698}, {612, 31143}, {752, 17294}, {1350, 34628}, {1352, 31162}, {1386, 21358}, {1699, 47354}, {1707, 50104}, {2796, 50089}, {3241, 49511}, {3242, 34747}, {3524, 39870}, {3564, 3654}, {3619, 19883}, {3620, 38314}, {3624, 20582}, {3630, 49688}, {3631, 49681}, {3632, 9041}, {3655, 48876}, {3729, 28558}, {3844, 19876}, {3879, 48830}, {3886, 28562}, {4645, 29617}, {4654, 12588}, {4663, 38087}, {4669, 34379}, {4725, 48829}, {4769, 14645}, {4851, 49740}, {4933, 35258}, {5587, 20423}, {5695, 50084}, {5846, 22165}, {5880, 50098}, {5921, 34632}, {5969, 9875}, {7982, 34507}, {7989, 38072}, {7991, 15069}, {8550, 9588}, {8584, 38047}, {9001, 50764}, {9053, 50789}, {9780, 38089}, {9830, 13174}, {9956, 14848}, {10516, 30308}, {11008, 38098}, {11178, 38021}, {11180, 28194}, {11477, 37714}, {11898, 34718}, {14927, 34638}, {15534, 50782}, {16833, 31151}, {17133, 24248}, {17225, 49445}, {17270, 48809}, {17271, 48854}, {17378, 48851}, {17594, 32852}, {18440, 28198}, {19662, 38220}, {20080, 49529}, {24452, 40341}, {24695, 50118}, {24723, 50121}, {28208, 33878}, {28534, 50087}, {28580, 50079}, {29573, 32846}, {29574, 50295}, {29594, 50303}, {29615, 50314}, {29828, 31179}, {31144, 39586}, {31423, 38064}, {32220, 47496}, {38315, 50785}, {41152, 50792}, {47353, 50865}, {48805, 50081}, {48821, 50131}, {49496, 50094}, {50091, 50129}, {50299, 50308}
X(50950) = midpoint of X(i) and X(j) for these {i,j}: {8, 11160}, {5921, 34632}, {11898, 34718}, {15533, 50783}
X(50950) = reflection of X(i) in X(j) for these {i,j}: {1, 599}, {2, 50781}, {1992, 10}, {3241, 49511}, {3655, 48876}, {3679, 3416}, {3751, 3679}, {4669, 50786}, {4677, 50783}, {5695, 50084}, {14927, 34638}, {24695, 50118}, {31162, 1352}, {32220, 47496}, {34628, 1350}, {34747, 3242}, {47356, 141}, {47358, 22165}, {48805, 50081}, {48818, 48834}, {49496, 50094}, {50126, 17294}, {50129, 50091}, {50131, 48821}, {50303, 29594}, {50865, 47353}
X(50950) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {141, 47356, 25055}, {3844, 47352, 19876}, {20582, 38023, 3624}, {25055, 47356, 16491}, {32846, 50296, 29573}
X(50951) lies on these lines: {2, 9053}, {8, 597}, {10, 9041}, {141, 28635}, {518, 3968}, {519, 3589}, {524, 3416}, {545, 49630}, {599, 3617}, {1386, 34641}, {1992, 4678}, {3241, 48310}, {3625, 38089}, {3626, 20583}, {3631, 38098}, {3632, 38023}, {3654, 29181}, {3696, 17225}, {3717, 49737}, {4141, 33162}, {4669, 5846}, {4677, 38047}, {4901, 41312}, {5476, 38165}, {5480, 34718}, {5790, 47354}, {5847, 41149}, {6329, 47356}, {7227, 49720}, {8584, 50783}, {8705, 47488}, {11178, 38081}, {12245, 38072}, {12645, 38064}, {16475, 41153}, {19875, 34573}, {22165, 50785}, {28297, 48829}, {31145, 47352}, {32218, 47496}, {33165, 49740}, {34627, 44882}, {38029, 50804}, {38035, 50817}, {38040, 50830}, {38046, 50838}, {38116, 50798}, {38144, 50810}, {38185, 50835}, {38192, 50842}, {38314, 49690}, {48804, 48845}
X(50951) = midpoint of X(i) and X(j) for these {i,j}: {8, 597}, {1386, 34641}, {3679, 49524}, {5476, 50823}, {5480, 34718}, {8584, 50783}, {34627, 44882}, {48804, 48845}
X(50951) = reflection of X(i) in X(j) for these {i,j}: {20582, 10}, {32218, 47496}, {47356, 6329}
X(50951) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 38087, 597}, {38165, 50823, 5476}
X(50952) lies on these lines: {1, 1992}, {2, 34379}, {6, 16590}, {10, 11160}, {30, 39878}, {69, 19875}, {193, 519}, {518, 3899}, {524, 3416}, {542, 5691}, {551, 5032}, {576, 11522}, {597, 3624}, {599, 1698}, {1351, 31162}, {1353, 3655}, {1699, 20423}, {1757, 29573}, {2796, 49495}, {3629, 16496}, {3632, 28538}, {3633, 9041}, {3654, 34380}, {3894, 9004}, {4141, 32912}, {4416, 48830}, {4677, 5847}, {4715, 50080}, {4912, 49486}, {5220, 50125}, {5850, 49543}, {5921, 34648}, {6776, 34628}, {8227, 14848}, {8584, 16475}, {9589, 11477}, {9624, 11482}, {9881, 14645}, {10436, 50309}, {11008, 49529}, {14853, 30308}, {15533, 50785}, {16491, 32455}, {17274, 50283}, {19872, 20582}, {19876, 21356}, {20583, 38023}, {22165, 38047}, {28198, 44456}, {28208, 39899}, {28558, 49497}, {31145, 49536}, {32935, 50089}, {38314, 49505}, {48851, 50074}, {49630, 50282}
X(50952) = reflection of X(i) in X(j) for these {i,j}: {1, 1992}, {599, 4663}, {3655, 1353}, {3679, 3751}, {5921, 34648}, {11160, 10}, {16496, 47356}, {17274, 50283}, {31145, 49536}, {31162, 1351}, {34628, 6776}, {47356, 3629}, {47358, 8584}, {50089, 32935}
X(50952) = {X(8584),X(47358)}-harmonic conjugate of X(16475)
X(50953) lies on these lines: {1, 38087}, {2, 38191}, {69, 38098}, {145, 38089}, {518, 50791}, {519, 3618}, {524, 3416}, {597, 3632}, {1698, 9041}, {1992, 3626}, {3242, 19876}, {3620, 49529}, {3633, 38023}, {3656, 38165}, {3763, 16496}, {4141, 17594}, {4668, 28538}, {4677, 16475}, {4745, 50788}, {5476, 50817}, {11531, 38072}, {21356, 49536}, {25055, 49688}, {26726, 38090}, {28301, 50080}, {28322, 48829}, {34747, 47352}, {37712, 43273}, {38116, 50811}, {38118, 50818}, {38144, 50865}, {38146, 50872}, {38167, 50805}, {38190, 50836}, {38192, 50891}, {38194, 50839}, {38197, 50894}
X(50954) lies on these lines: {30, 3620}, {69, 14269}, {141, 15688}, {193, 38071}, {381, 524}, {382, 599}, {518, 50797}, {542, 1656}, {546, 11160}, {547, 5921}, {549, 48662}, {597, 5079}, {1503, 15693}, {1992, 3851}, {3534, 29012}, {3564, 19709}, {3618, 5055}, {3619, 15707}, {3763, 5054}, {3818, 38335}, {3839, 44456}, {5032, 11737}, {5066, 5093}, {5072, 14848}, {5847, 50806}, {6776, 15703}, {10109, 14912}, {10516, 39561}, {10519, 15685}, {11161, 38743}, {11539, 39874}, {11645, 14093}, {13169, 38789}, {15046, 15303}, {15681, 21356}, {15684, 48876}, {15694, 40330}, {15700, 21358}, {15706, 46264}, {15720, 20582}, {15723, 24206}, {19924, 35434}, {34379, 50799}, {34380, 41099}, {35400, 48874}, {38083, 39878}, {40107, 49137}
X(50954) = midpoint of X(3618) and X(11180)
X(50954) = reflection of X(i) in X(j) for these {i,j}: {3763, 11178}, {15694, 40330}
X(50954) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5055, 11180, 39899}, {11178, 18440, 5054}, {11180, 18358, 5055}, {14848, 25561, 5072}, {15069, 25561, 14848}, {21356, 39884, 15681}
X(50955) lies on these lines: {2, 3167}, {3, 67}, {4, 11160}, {5, 1992}, {6, 5055}, {25, 15360}, {30, 69}, {114, 7610}, {141, 5054}, {182, 9703}, {183, 6054}, {193, 3545}, {343, 8780}, {376, 5921}, {381, 524}, {394, 13857}, {511, 3830}, {518, 50798}, {539, 19588}, {547, 1353}, {549, 6776}, {568, 29959}, {575, 5070}, {576, 3851}, {597, 1656}, {637, 48659}, {638, 48660}, {754, 50685}, {1003, 34623}, {1154, 11188}, {1350, 11645}, {1384, 15993}, {1482, 28538}, {1499, 44206}, {1503, 3534}, {1570, 18362}, {1975, 12117}, {1995, 44555}, {2393, 23039}, {2782, 5077}, {3090, 38079}, {3098, 15689}, {3242, 34748}, {3314, 11177}, {3410, 31133}, {3416, 34718}, {3519, 7529}, {3524, 3620}, {3526, 8550}, {3543, 39884}, {3580, 47597}, {3618, 15699}, {3619, 11539}, {3630, 31670}, {3631, 15688}, {3653, 39870}, {3654, 50781}, {3655, 49511}, {3656, 5847}, {3763, 10168}, {3818, 14269}, {3839, 20080}, {3843, 11477}, {3845, 34380}, {4995, 39900}, {5032, 5071}, {5066, 14853}, {5079, 20583}, {5085, 15701}, {5092, 15707}, {5093, 5476}, {5094, 40112}, {5182, 10104}, {5298, 39901}, {5477, 37637}, {5562, 34725}, {5613, 9761}, {5617, 9763}, {5642, 37638}, {5644, 11225}, {5663, 13169}, {5790, 47359}, {5846, 50805}, {5872, 11306}, {5873, 11305}, {5891, 8681}, {5969, 12355}, {6055, 7778}, {6144, 19130}, {6243, 43130}, {6391, 16072}, {6792, 21448}, {7503, 9925}, {7577, 11405}, {7788, 35458}, {7840, 13860}, {7841, 12243}, {7883, 39646}, {8548, 11704}, {8556, 35429}, {8584, 14561}, {8703, 10519}, {8860, 23234}, {9041, 12645}, {9140, 15066}, {9143, 26864}, {9830, 13188}, {9880, 14645}, {9996, 22253}, {10011, 23055}, {10056, 39873}, {10072, 39897}, {10170, 40673}, {10304, 39874}, {10706, 32244}, {10753, 22566}, {10983, 37345}, {11008, 38071}, {11185, 44369}, {11284, 41724}, {11318, 49102}, {11426, 14787}, {11442, 31152}, {11444, 15074}, {11459, 14984}, {11591, 15073}, {12007, 48310}, {12100, 25406}, {12134, 34726}, {12188, 19905}, {12429, 34664}, {12583, 20128}, {13321, 16776}, {13564, 15581}, {13692, 41491}, {13812, 41490}, {13862, 44367}, {14093, 44882}, {14530, 31166}, {14643, 15303}, {14826, 44212}, {14927, 15686}, {15068, 41614}, {15561, 18800}, {15683, 48874}, {15684, 19924}, {15685, 29012}, {15695, 31884}, {15703, 24206}, {15711, 33750}, {15716, 21167}, {16266, 45034}, {17813, 23325}, {18323, 47552}, {18350, 44470}, {19118, 37943}, {19544, 31143}, {19662, 38224}, {20987, 37956}, {21970, 26255}, {22329, 37071}, {22493, 41043}, {22494, 41042}, {25154, 37824}, {25164, 37825}, {25562, 38743}, {28204, 39885}, {28453, 36740}, {32220, 47334}, {32225, 35259}, {32234, 38397}, {32609, 44751}, {32808, 48678}, {32809, 48677}, {34379, 50796}, {35403, 48901}, {36757, 49905}, {36758, 49906}, {37451, 42850}, {38136, 41106}, {44265, 47473}
X(50955) = midpoint of X(i) and X(j) for these {i,j}: {4, 11160}, {69, 11180}, {376, 5921}, {381, 11898}, {599, 15069}, {10706, 32244}, {15533, 47353}, {15681, 48662}
X(50955) = reflection of X(i) in X(j) for these {i,j}: {3, 599}, {6, 11178}, {376, 48876}, {381, 1352}, {568, 29959}, {576, 25561}, {599, 34507}, {1351, 381}, {1353, 547}, {1992, 5}, {3543, 39884}, {3654, 50781}, {3655, 49511}, {3830, 47353}, {5093, 10516}, {6776, 549}, {8550, 20582}, {10753, 22566}, {11178, 43150}, {11179, 141}, {12188, 19905}, {14927, 15686}, {15534, 5476}, {15681, 1350}, {15683, 48874}, {15684, 36990}, {17813, 23325}, {18440, 11180}, {20128, 12583}, {20423, 47354}, {32220, 47334}, {34718, 3416}, {34748, 3242}, {39899, 11179}, {40673, 10170}, {44265, 47473}, {48679, 10706}
X(50955) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 1992, 14848}, {6, 11178, 5055}, {69, 18440, 33878}, {141, 11179, 5054}, {141, 39899, 12017}, {182, 21358, 15694}, {183, 6054, 40248}, {576, 25561, 38072}, {1352, 11898, 1351}, {1352, 20423, 47354}, {1992, 14848, 11482}, {3818, 40341, 44456}, {5032, 5071, 18583}, {5054, 11179, 12017}, {5054, 39899, 11179}, {5093, 19709, 5476}, {5476, 10516, 19709}, {5476, 15534, 5093}, {6776, 21356, 549}, {8550, 20582, 38064}, {9140, 15066, 32216}, {9143, 47596, 26864}, {10516, 15534, 5476}, {11477, 18553, 3843}, {15068, 41614, 45016}, {15069, 34507, 3}, {20423, 47354, 381}, {20582, 38064, 3526}, {22491, 22492, 20112}, {24206, 47352, 15703}, {25561, 38072, 3851}
X(50956) lies on these lines: {2, 6030}, {4, 25561}, {5, 10541}, {6, 38071}, {30, 3763}, {141, 14269}, {376, 48889}, {381, 524}, {382, 20582}, {511, 41099}, {518, 50799}, {542, 3091}, {546, 599}, {547, 36990}, {576, 3854}, {597, 3851}, {1350, 14893}, {1503, 19709}, {1992, 3855}, {3098, 50687}, {3543, 24206}, {3545, 3618}, {3620, 3839}, {3845, 10516}, {3850, 38072}, {3856, 11477}, {3857, 15069}, {5055, 46264}, {5066, 14561}, {5068, 25565}, {5071, 11645}, {5085, 10109}, {5476, 41106}, {5846, 50806}, {7394, 15360}, {9053, 50797}, {10304, 48884}, {11180, 19130}, {11539, 48905}, {11737, 39884}, {12811, 38079}, {14639, 25562}, {14892, 48906}, {15534, 38136}, {15685, 21167}, {15687, 21358}, {15688, 34573}, {15702, 48898}, {15703, 44882}, {15708, 48892}, {15709, 42786}, {15710, 48891}, {18358, 23046}, {19708, 29323}, {19924, 40330}, {21356, 48901}, {31884, 33699}, {38140, 47359}, {38335, 43621}, {40107, 50689}, {42775, 44512}, {42776, 44511}, {47355, 47478}
X(50956) = reflection of X(i) in X(j) for these {i,j}: {3620, 11178}, {11179, 3618}
X(50956) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {381, 47354, 20423}, {3545, 3818, 11179}, {3839, 11178, 31670}, {5066, 47353, 14561}, {11737, 39884, 47352}, {15687, 21358, 48873}, {20423, 47354, 1352}
X(50957) lies on these lines: {3, 25561}, {30, 3619}, {69, 23046}, {141, 38335}, {381, 524}, {518, 50800}, {542, 3851}, {597, 5072}, {599, 3843}, {1350, 35403}, {1657, 20582}, {1992, 3850}, {3091, 14848}, {3534, 21167}, {3545, 18440}, {3564, 41106}, {3618, 14892}, {3763, 15689}, {3818, 5055}, {3830, 10516}, {3839, 18358}, {5050, 19709}, {5068, 38079}, {5071, 39884}, {5079, 38064}, {5847, 50807}, {6776, 11737}, {10124, 14927}, {10519, 12101}, {11178, 14269}, {11180, 38071}, {11482, 18553}, {11540, 33750}, {11645, 15703}, {14893, 21356}, {15681, 24206}, {15684, 21358}, {15687, 40330}, {15694, 36990}, {15701, 29012}, {15706, 34573}, {15707, 48905}, {15718, 48898}, {15723, 44882}, {25562, 38732}, {35401, 48904}, {35434, 48873}, {47352, 48662}
X(50957) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11178, 14269, 33878}, {19709, 47353, 5050}, {21358, 48889, 15684}
X(50958) lies on these lines: {5, 20583}, {20, 599}, {30, 3631}, {69, 50687}, {140, 542}, {141, 3524}, {381, 524}, {511, 12101}, {518, 50801}, {547, 12007}, {597, 3090}, {1503, 8703}, {1992, 5068}, {3545, 3629}, {3564, 10109}, {3589, 11178}, {3627, 34507}, {3839, 40341}, {3861, 18553}, {5055, 6329}, {5066, 5965}, {5070, 8550}, {5097, 11737}, {5102, 41106}, {5476, 41149}, {5921, 15721}, {8584, 10516}, {9041, 47745}, {9053, 50804}, {10168, 41984}, {10170, 44323}, {11160, 50689}, {11179, 34573}, {11645, 15691}, {12811, 25561}, {14892, 18358}, {15682, 22165}, {15685, 41152}, {15689, 18440}, {21356, 44882}, {23046, 37517}, {40107, 44245}, {40330, 48310}, {41988, 48889}, {44903, 48876}, {47599, 50664}
X(50958) = midpoint of X(i) and X(j) for these {i,j}: {141, 11180}, {597, 15069}, {22165, 47353}
X(50958) = reflection of X(i) in X(j) for these {i,j}: {3589, 11178}, {5097, 11737}, {11179, 34573}, {12007, 547}, {20583, 5}, {41149, 5476}, {44323, 10170}
X(50959) lies on these lines: {2, 21167}, {4, 597}, {5, 20582}, {6, 3839}, {30, 3589}, {140, 25565}, {141, 3545}, {182, 15687}, {373, 47311}, {376, 48310}, {381, 524}, {382, 38064}, {511, 5066}, {518, 50802}, {542, 546}, {547, 19924}, {549, 48901}, {575, 3861}, {576, 3858}, {599, 3091}, {698, 44422}, {946, 9041}, {962, 38087}, {1350, 5071}, {1386, 34648}, {1503, 3845}, {1699, 47359}, {1992, 3832}, {2393, 13570}, {3098, 15699}, {3524, 48910}, {3543, 44882}, {3564, 3860}, {3618, 50687}, {3627, 38079}, {3629, 11180}, {3631, 11178}, {3656, 9053}, {3818, 23046}, {3830, 14561}, {3843, 8550}, {3850, 25561}, {3853, 25555}, {3854, 11160}, {3855, 11477}, {3856, 18553}, {3857, 34507}, {5050, 41153}, {5054, 48881}, {5055, 31670}, {5085, 15682}, {5103, 14492}, {5133, 15360}, {5169, 44569}, {5461, 40927}, {5691, 38023}, {5846, 50796}, {5847, 50803}, {6034, 7745}, {6249, 9880}, {6329, 11179}, {7000, 13663}, {7374, 13783}, {7533, 40112}, {8584, 14853}, {8703, 38317}, {8705, 47332}, {8724, 44230}, {9300, 43450}, {9770, 14484}, {10124, 14810}, {10297, 25488}, {10304, 47355}, {10516, 22165}, {10541, 17578}, {10706, 25328}, {11645, 14893}, {11737, 24206}, {12007, 48889}, {12100, 29317}, {12101, 29012}, {12811, 40107}, {12816, 36758}, {12817, 36757}, {13860, 44401}, {13862, 22110}, {14891, 48885}, {15686, 48904}, {15688, 43621}, {15692, 48872}, {15694, 48873}, {17504, 48880}, {17508, 19710}, {19925, 28538}, {20192, 47296}, {22682, 37350}, {23292, 35266}, {25566, 32423}, {30308, 47358}, {31105, 37648}, {31162, 49524}, {31166, 41362}, {32218, 47334}, {32419, 36725}, {32421, 36724}, {33699, 38110}, {35404, 48898}, {36794, 42874}, {36991, 38086}, {38047, 50865}, {38049, 50862}, {38315, 50864}, {38335, 46264}, {42785, 48906}
X(50959) = midpoint of X(i) and X(j) for these {i,j}: {4, 597}, {182, 15687}, {381, 5480}, {549, 48901}, {1386, 34648}, {3543, 44882}, {3629, 11180}, {3845, 5476}, {8584, 47353}, {10168, 48895}, {10706, 25328}, {11178, 21850}, {14893, 18583}, {15686, 48904}, {20423, 47354}, {31162, 49524}, {31166, 41362}, {35404, 48898}
X(50959) = reflection of X(i) in X(j) for these {i,j}: {140, 25565}, {3631, 11178}, {11179, 6329}, {14810, 10124}, {20582, 5}, {24206, 11737}, {25561, 3850}, {32218, 47334}, {48885, 14891}
X(50959) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 38072, 597}, {381, 20423, 47354}, {3543, 47352, 44882}, {3845, 38136, 5476}, {5480, 47354, 20423}, {14853, 41099, 47353}, {14853, 47353, 8584}, {21850, 38071, 11178}
X(50960) lies on these lines: {4, 20582}, {30, 34573}, {141, 3839}, {381, 524}, {511, 3860}, {518, 50803}, {542, 3850}, {546, 25561}, {547, 48889}, {549, 48896}, {597, 3091}, {599, 3832}, {1503, 5066}, {1992, 3854}, {3545, 3589}, {3763, 50687}, {3818, 6329}, {3845, 29181}, {3855, 20583}, {3859, 18553}, {5071, 44882}, {5072, 38064}, {5092, 47478}, {5133, 35266}, {5846, 50802}, {7533, 44569}, {9041, 19925}, {9053, 50796}, {10109, 29012}, {10168, 14892}, {10516, 41099}, {11178, 23046}, {11180, 32455}, {11539, 48884}, {11645, 11737}, {11812, 29323}, {12571, 28538}, {12811, 25565}, {13862, 44401}, {14561, 41153}, {14853, 41149}, {14893, 24206}, {14912, 41106}, {15682, 21167}, {15691, 48942}, {17504, 42786}, {34507, 41991}, {36990, 48310}, {38335, 48881}, {40670, 46847}, {41983, 48891}, {41987, 48895}, {47598, 48892}
X(50960) = midpoint of X(i) and X(j) for these {i,j}: {4, 20582}, {546, 25561}, {547, 48889}, {11180, 32455}, {14893, 24206}, {15691, 48942}, {40670, 46847}
X(50960) = reflection of X(25565) in X(12811)
X(50961) lies on these lines: {2, 5965}, {6, 15699}, {20, 542}, {30, 40341}, {68, 38545}, {69, 3431}, {114, 9740}, {140, 599}, {182, 15721}, {193, 11178}, {315, 12243}, {381, 524}, {511, 11455}, {518, 50804}, {576, 5068}, {597, 5070}, {1350, 15691}, {1353, 21358}, {1503, 15685}, {1656, 20583}, {1992, 3090}, {3545, 7926}, {3564, 8703}, {3620, 10168}, {3627, 15069}, {3629, 5055}, {3630, 15689}, {3631, 5054}, {3763, 41984}, {3839, 37517}, {3861, 11477}, {5032, 24206}, {5066, 5102}, {5071, 5097}, {5085, 44580}, {5485, 13449}, {5921, 19924}, {6055, 37668}, {6144, 14892}, {10109, 14561}, {11180, 20080}, {12007, 15694}, {12101, 34380}, {12811, 38072}, {14891, 48876}, {15360, 45794}, {15701, 22165}, {15709, 50664}, {21850, 41987}, {34379, 50801}, {38029, 50787}, {38116, 50781}, {38118, 50788}, {38176, 47359}, {44903, 48873}
X(50961) = midpoint of X(11180) and X(20080)
X(50961) = reflection of X(i) in X(j) for these {i,j}: {193, 11178}, {1992, 34507}, {11179, 69}, {31670, 11180}
X(50962) lies on these lines: {2, 5093}, {3, 1992}, {5, 11160}, {6, 5054}, {30, 193}, {69, 5055}, {182, 15700}, {195, 44492}, {323, 47597}, {376, 1353}, {381, 524}, {382, 542}, {511, 3534}, {518, 50805}, {549, 5032}, {576, 599}, {597, 3526}, {1350, 14093}, {1993, 15360}, {2080, 11165}, {3167, 35266}, {3543, 48662}, {3545, 20080}, {3564, 3830}, {3620, 15699}, {3629, 11179}, {3656, 34379}, {3751, 34718}, {5050, 8584}, {5070, 38079}, {5072, 34507}, {5085, 15716}, {5094, 44555}, {5097, 15723}, {5102, 5476}, {5642, 21970}, {5648, 45016}, {5847, 50798}, {5889, 34622}, {5921, 15687}, {5965, 47353}, {5969, 32520}, {6144, 18440}, {6243, 34726}, {6776, 15681}, {7754, 12243}, {7774, 40248}, {7840, 37071}, {8550, 15696}, {8703, 14912}, {8724, 14645}, {9041, 24844}, {9925, 18378}, {10519, 15701}, {10753, 48657}, {11004, 47596}, {11008, 11180}, {11159, 32515}, {11161, 38732}, {11178, 40341}, {12017, 15706}, {12645, 28538}, {13169, 38724}, {13340, 40673}, {13391, 15531}, {13857, 18449}, {13860, 44367}, {14561, 22165}, {14853, 19709}, {14984, 41720}, {15303, 32609}, {15689, 48906}, {15694, 48876}, {15695, 25406}, {15698, 33748}, {15703, 18583}, {15720, 20583}, {20126, 39562}, {21969, 34382}, {22112, 40912}, {28202, 39878}, {28443, 37492}, {32216, 37644}, {32284, 37484}, {34609, 41628}, {34780, 34788}, {35001, 47280}, {35381, 41153}, {35403, 39884}, {35434, 36990}, {37958, 47549}, {44265, 47541}
X(50962) = midpoint of X(11008) and X(11180)
X(50962) = reflection of X(i) in X(j) for these {i,j}: {3, 1992}, {376, 1353}, {381, 1351}, {599, 576}, {5921, 15687}, {11160, 5}, {11179, 3629}, {11180, 21850}, {11898, 381}, {13340, 40673}, {15533, 5476}, {15681, 6776}, {33878, 11179}, {34718, 3751}, {40341, 11178}, {44265, 47541}, {48657, 10753}, {48662, 3543}
X(50962) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {193, 44456, 39899}, {576, 599, 14848}, {599, 14848, 1656}, {5102, 15533, 5476}, {6144, 37517, 18440}, {11179, 33878, 15688}, {11180, 21850, 14269}, {18583, 21356, 15703}
X(50963) lies on these lines: {2, 38136}, {3, 38072}, {4, 14848}, {6, 14269}, {20, 38079}, {30, 3618}, {69, 38071}, {182, 15684}, {381, 524}, {382, 597}, {511, 19709}, {518, 50806}, {542, 3843}, {546, 1992}, {599, 3851}, {1350, 15703}, {1657, 38064}, {3527, 18125}, {3534, 14561}, {3543, 18583}, {3545, 3620}, {3564, 41099}, {3589, 15688}, {3619, 47478}, {3654, 38146}, {3763, 5055}, {3830, 5050}, {3839, 18440}, {3845, 14853}, {3855, 11160}, {5020, 13857}, {5032, 39884}, {5054, 31670}, {5070, 25565}, {5079, 20582}, {5085, 15685}, {5093, 47353}, {5846, 50797}, {5847, 50799}, {6034, 30435}, {6249, 34505}, {6776, 14893}, {8724, 10983}, {9993, 40248}, {10109, 10519}, {10168, 15689}, {10541, 49134}, {11001, 38110}, {11178, 44456}, {11179, 38335}, {11180, 23046}, {11477, 25561}, {11645, 35403}, {11737, 21356}, {15681, 47352}, {15693, 29181}, {15694, 19924}, {15695, 29317}, {15700, 48310}, {15701, 38317}, {15702, 48874}, {15706, 48881}, {15707, 47355}, {17800, 25555}, {20190, 49139}, {23049, 32063}, {25406, 33699}, {35400, 48898}, {38090, 38753}, {46267, 48904}, {48906, 50687}
X(50963) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3830, 5476, 5050}, {10168, 48910, 15689}, {47352, 48901, 15681}, {48310, 48873, 15700}
X(50964) lies on these lines: {2, 29317}, {4, 20190}, {6, 23046}, {20, 25565}, {30, 47355}, {381, 524}, {511, 41106}, {518, 50807}, {542, 3832}, {546, 38072}, {547, 48873}, {597, 3843}, {599, 3850}, {1350, 11737}, {3091, 40107}, {3524, 48895}, {3543, 48896}, {3545, 3619}, {3589, 38335}, {3763, 14892}, {3839, 11179}, {3845, 14561}, {3855, 25561}, {3859, 11477}, {3860, 38136}, {3861, 38079}, {5054, 43621}, {5071, 48901}, {5072, 20582}, {5085, 12101}, {5476, 14912}, {5846, 50800}, {6997, 13857}, {10124, 48872}, {10168, 50687}, {14269, 46264}, {14893, 47352}, {14927, 46267}, {15069, 41991}, {15640, 17508}, {15682, 38317}, {15684, 48310}, {15692, 48904}, {15699, 48910}, {15705, 48879}, {15709, 48880}, {15715, 48920}, {15721, 48885}, {35403, 44882}, {38087, 40273}, {41987, 48906}, {46333, 48943}
X(50964) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3839, 19130, 11179}, {3860, 38136, 47353}
X(50965) lies on these lines: {2, 21167}, {3, 597}, {4, 20582}, {6, 10304}, {20, 599}, {22, 35266}, {30, 141}, {40, 9041}, {69, 41467}, {165, 47359}, {182, 34200}, {376, 524}, {381, 48873}, {511, 8584}, {518, 50808}, {541, 33851}, {542, 550}, {547, 48901}, {548, 8550}, {549, 5480}, {575, 46853}, {576, 33923}, {631, 38072}, {632, 25565}, {698, 33706}, {1351, 14093}, {1352, 15681}, {1353, 33751}, {1503, 3534}, {1992, 3522}, {2076, 5306}, {2781, 44261}, {3242, 34632}, {3416, 34628}, {3524, 3589}, {3528, 11477}, {3543, 21358}, {3545, 34573}, {3564, 15690}, {3618, 15705}, {3619, 50687}, {3627, 25561}, {3629, 11179}, {3630, 15689}, {3631, 11180}, {3763, 3839}, {3844, 34648}, {3845, 29317}, {4297, 28538}, {5054, 31670}, {5085, 19708}, {5092, 45759}, {5102, 33750}, {5188, 5969}, {5476, 12100}, {5651, 47312}, {5846, 50811}, {5847, 50815}, {5999, 11168}, {6329, 15710}, {6393, 11057}, {7470, 12243}, {7492, 40112}, {7555, 11694}, {7987, 38023}, {7998, 47313}, {8542, 47337}, {8546, 41463}, {8598, 22676}, {9019, 36987}, {9053, 50810}, {9740, 46944}, {9830, 38738}, {10168, 17504}, {10516, 15682}, {10519, 11001}, {10541, 21734}, {11160, 50693}, {11511, 47114}, {11539, 19130}, {11645, 15686}, {11812, 38317}, {12103, 34507}, {12117, 12122}, {13567, 15360}, {13857, 44210}, {14269, 43621}, {14561, 15693}, {14853, 15698}, {14891, 18583}, {14892, 42786}, {14893, 48904}, {14912, 41149}, {15069, 17538}, {15105, 15581}, {15107, 20192}, {15158, 15163}, {15159, 15162}, {15533, 15697}, {15534, 25406}, {15683, 21356}, {15687, 24206}, {15691, 48898}, {15692, 47352}, {15704, 40107}, {15708, 47355}, {15711, 38110}, {15712, 38079}, {15713, 38136}, {15759, 17508}, {16063, 44569}, {17225, 30273}, {19127, 37480}, {19710, 29012}, {19905, 38730}, {22110, 37182}, {25329, 38726}, {25555, 44682}, {32217, 47333}, {34379, 50816}, {34638, 49511}, {35243, 35707}, {35404, 48889}, {37283, 43576}, {37517, 41982}, {38071, 48895}, {39561, 46332}, {39884, 44903}, {45303, 47314}
X(50965) = midpoint of X(i) and X(j) for these {i,j}: {20, 599}, {376, 1350}, {381, 48873}, {549, 48874}, {1352, 15681}, {3242, 34632}, {3416, 34628}, {3543, 48872}, {11001, 47353}, {11178, 48880}, {11179, 33878}, {11180, 48905}, {15158, 15163}, {15159, 15162}, {15683, 36990}, {15686, 48876}, {19905, 38730}, {34638, 49511}, {39884, 44903}
X(50965) = reflection of X(i) in X(j) for these {i,j}: {4, 20582}, {182, 34200}, {549, 14810}, {597, 3}, {3627, 25561}, {3629, 11179}, {5476, 12100}, {5480, 549}, {11180, 3631}, {11477, 20583}, {15686, 48885}, {15687, 24206}, {18583, 14891}, {21167, 31884}, {21850, 10168}, {32217, 47333}, {34648, 3844}, {35404, 48889}, {44882, 376}, {44903, 48920}, {48898, 15691}, {48901, 547}, {48904, 14893}
X(50965) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {549, 5480, 48310}, {3098, 48881, 141}, {10519, 11001, 47353}, {14810, 48874, 5480}, {15683, 21356, 36990}, {15688, 33878, 11179}, {17504, 21850, 10168}, {21358, 48872, 3543}
X(50966) lies on these lines: {2, 38136}, {4, 25561}, {6, 15710}, {30, 3620}, {69, 48891}, {193, 15688}, {376, 524}, {511, 19708}, {518, 50809}, {542, 17538}, {550, 11160}, {597, 10299}, {599, 3529}, {1992, 3528}, {3098, 3524}, {3533, 38072}, {3543, 48874}, {3545, 3763}, {3564, 15697}, {3855, 20582}, {5032, 34200}, {5071, 19924}, {5093, 15759}, {5847, 50819}, {5921, 15686}, {7386, 15360}, {8584, 33750}, {8703, 14912}, {10304, 33878}, {10519, 15682}, {11001, 29012}, {11180, 46333}, {11541, 40107}, {11898, 15691}, {14810, 15715}, {14848, 15717}, {14853, 15719}, {15683, 48876}, {15695, 34380}, {15698, 31884}, {15708, 21850}, {21356, 48873}, {29181, 41099}, {34379, 50812}, {37485, 37948}, {44456, 45759}
X(50966) = {X(11180),X(48881)}-harmonic conjugate of X(46333)
X(50967) lies on these lines: {2, 51}, {3, 1992}, {4, 599}, {6, 3524}, {20, 542}, {30, 69}, {74, 30256}, {98, 9740}, {140, 14848}, {141, 3545}, {148, 19905}, {182, 5032}, {193, 3098}, {206, 43572}, {376, 524}, {381, 21356}, {394, 35266}, {518, 50810}, {519, 24728}, {549, 1351}, {575, 15717}, {576, 3523}, {597, 631}, {842, 6082}, {944, 28538}, {1007, 40248}, {1352, 3543}, {1353, 34200}, {1503, 11001}, {2482, 10753}, {2781, 5648}, {3066, 44833}, {3089, 15606}, {3090, 20582}, {3091, 40107}, {3146, 34507}, {3242, 34631}, {3416, 34627}, {3526, 38079}, {3528, 8550}, {3529, 15069}, {3530, 11482}, {3534, 3564}, {3589, 15709}, {3618, 5054}, {3619, 5055}, {3620, 3839}, {3629, 15710}, {3630, 46333}, {3631, 48910}, {3818, 50687}, {3832, 25561}, {3926, 8724}, {4549, 41721}, {5050, 12100}, {5071, 5480}, {5085, 8584}, {5092, 15705}, {5093, 15693}, {5102, 15719}, {5107, 21843}, {5171, 5182}, {5181, 10706}, {5188, 34511}, {5286, 44453}, {5562, 34621}, {5622, 37480}, {5642, 10752}, {5657, 47359}, {5846, 50818}, {5847, 50811}, {5864, 37173}, {5865, 37172}, {5921, 11645}, {5965, 15697}, {5969, 12243}, {6054, 37668}, {6055, 10754}, {6090, 37904}, {6174, 10759}, {7417, 14916}, {7426, 47468}, {7486, 25565}, {7493, 40112}, {7618, 8722}, {7736, 11173}, {7840, 37182}, {8182, 18860}, {8681, 36987}, {8703, 25406}, {9041, 12245}, {9774, 46944}, {9830, 13172}, {9888, 14645}, {10168, 15708}, {10299, 20583}, {10513, 43460}, {10516, 41099}, {10602, 18931}, {11008, 15688}, {11161, 23698}, {11177, 14931}, {11433, 43957}, {11694, 45016}, {11821, 34664}, {11898, 14927}, {12017, 17504}, {12324, 34614}, {13169, 17702}, {13330, 31400}, {13340, 14984}, {13635, 37654}, {13860, 42850}, {14269, 18358}, {14639, 19662}, {14912, 15534}, {14994, 32869}, {15035, 15303}, {15066, 26255}, {15073, 15644}, {15078, 37488}, {15640, 29317}, {15682, 22165}, {15684, 39884}, {15689, 39899}, {15694, 18583}, {15701, 38110}, {15702, 47352}, {15993, 43448}, {16051, 44569}, {16063, 44555}, {16475, 50828}, {17508, 33748}, {17578, 18553}, {17813, 23328}, {18800, 21166}, {18906, 46951}, {19782, 50430}, {20080, 46264}, {21161, 36740}, {23291, 31152}, {26118, 31143}, {26516, 44486}, {26521, 44485}, {28194, 39898}, {30775, 37638}, {31162, 49511}, {31423, 38089}, {32216, 37643}, {32220, 47333}, {32521, 32828}, {33266, 39141}, {33522, 44210}, {33851, 34319}, {34379, 50808}, {34781, 34787}, {37478, 41720}, {37483, 41614}, {37485, 44837}, {37645, 47596}, {37665, 44839}, {37907, 47569}, {39874, 40341}, {39875, 41946}, {39876, 41945}, {42522, 44474}, {42523, 44473}, {43150, 43621}, {43934, 45816}, {44471, 45523}, {44472, 45522}, {44493, 50007}, {47582, 47597}
X(50967) = midpoint of X(i) and X(j) for these {i,j}: {20, 11160}, {5921, 15683}, {11898, 15681}
X(50967) = reflection of X(i) in X(j) for these {i,j}: {4, 599}, {148, 19905}, {193, 11179}, {376, 1350}, {381, 48876}, {1351, 549}, {1353, 34200}, {1992, 3}, {3543, 1352}, {5102, 21167}, {6054, 50567}, {6776, 376}, {7426, 47468}, {10706, 5181}, {10752, 5642}, {10753, 2482}, {10754, 6055}, {10759, 6174}, {11179, 3098}, {11180, 69}, {11477, 597}, {14853, 10519}, {14912, 31884}, {14927, 15681}, {15681, 48874}, {15682, 47353}, {15683, 48873}, {15684, 39884}, {17813, 23328}, {31162, 49511}, {31670, 11178}, {32220, 47333}, {34319, 33851}, {34627, 3416}, {34631, 3242}, {37517, 10168}, {47353, 22165}
X(50967) = anticomplement of X(20423)
X(50967) = Thomson-isogonal conjugate of X(33850)
X(50967) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {193, 10304, 11179}, {381, 21356, 40330}, {381, 48876, 21356}, {3098, 11179, 10304}, {3620, 3839, 11178}, {5032, 15692, 182}, {5480, 21358, 5071}, {11178, 31670, 3839}, {11898, 48874, 14927}, {14912, 31884, 33750}, {20582, 38072, 3090}, {40341, 48881, 39874}
X(50968) lies on these lines: {3, 38072}, {6, 15688}, {20, 47354}, {30, 3763}, {376, 524}, {381, 48885}, {511, 15695}, {518, 50812}, {542, 15696}, {548, 11477}, {549, 48872}, {550, 599}, {597, 3528}, {1352, 15691}, {1503, 15697}, {3098, 15689}, {3524, 48910}, {3529, 20582}, {3534, 29012}, {3589, 15710}, {3618, 10304}, {3620, 48905}, {5054, 48880}, {5085, 8703}, {5102, 33748}, {5846, 50819}, {9053, 50809}, {10516, 11001}, {11539, 43621}, {14093, 19924}, {14269, 48879}, {14561, 15759}, {14810, 15681}, {15069, 50693}, {15682, 21167}, {15684, 48920}, {15686, 36990}, {15693, 29317}, {15700, 48901}, {15703, 48904}, {15706, 19130}, {15715, 48310}, {15716, 38317}, {17504, 47355}, {17800, 25561}, {19708, 29181}, {21850, 41982}, {31663, 38087}, {31670, 45759}, {33923, 38064}, {34200, 47352}, {38110, 46332}
X(50968) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3534, 31884, 47353}, {14810, 15681, 21358}, {34200, 48873, 47352}
X(50969) lies on these lines: {2, 29317}, {3, 38079}, {20, 18553}, {30, 3619}, {69, 15689}, {141, 46333}, {376, 524}, {518, 50813}, {542, 50693}, {548, 1992}, {576, 3522}, {597, 21735}, {599, 17538}, {3098, 11180}, {3524, 47355}, {3528, 10541}, {3534, 10519}, {3543, 14810}, {3618, 45759}, {3839, 48880}, {5050, 8703}, {5071, 48872}, {5092, 10304}, {5480, 15715}, {5847, 50820}, {10299, 38072}, {11001, 31884}, {12017, 41982}, {14093, 48874}, {14848, 46853}, {14853, 19708}, {14927, 15691}, {15683, 40330}, {15686, 21356}, {15688, 44456}, {15692, 48873}, {15695, 25406}, {15698, 29181}, {15705, 31670}, {15709, 48910}, {15721, 48901}, {20582, 33703}, {21167, 41099}, {21734, 38064}, {25561, 49135}
X(50970) lies on these lines: {3, 20583}, {5, 20582}, {6, 15705}, {30, 3631}, {141, 3839}, {376, 524}, {511, 12100}, {518, 50814}, {542, 12103}, {597, 3523}, {599, 3146}, {1503, 19710}, {1992, 21734}, {2979, 35266}, {3098, 32455}, {3524, 6329}, {3589, 5054}, {3629, 10304}, {3830, 29181}, {5097, 14891}, {5102, 15698}, {5480, 15703}, {5965, 15690}, {6144, 35418}, {8584, 31884}, {9053, 50817}, {9770, 46944}, {10519, 41106}, {12007, 34200}, {12102, 40107}, {14893, 19924}, {15644, 16270}, {15711, 39561}, {17504, 37517}, {19130, 45757}, {35404, 48876}, {41152, 47353}
X(50970) = reflection of X(i) in X(j) for these {i,j}: {5097, 14891}, {12007, 34200}, {20583, 3}, {47353, 41152}
X(50971) lies on these lines: {3, 20582}, {20, 597}, {30, 3589}, {141, 10304}, {182, 15686}, {376, 524}, {511, 15690}, {518, 50815}, {542, 548}, {549, 48898}, {550, 576}, {599, 3522}, {1352, 14093}, {1386, 34638}, {1503, 8703}, {1657, 38064}, {1992, 50693}, {2916, 37941}, {3524, 34573}, {3529, 38072}, {3530, 25561}, {3534, 5050}, {3543, 48310}, {3631, 15688}, {3763, 15705}, {3818, 17504}, {3845, 17508}, {3853, 25565}, {4297, 9041}, {5066, 29323}, {5085, 11001}, {5476, 19710}, {5480, 15681}, {5846, 50808}, {5847, 50816}, {5894, 31166}, {7492, 44569}, {7667, 13857}, {8550, 15696}, {8584, 15697}, {8705, 47031}, {9053, 50811}, {9830, 38747}, {10124, 48889}, {10516, 15698}, {10519, 41152}, {11178, 45759}, {11179, 15689}, {11645, 33751}, {12007, 48885}, {12100, 29012}, {12117, 44251}, {12512, 28538}, {14561, 15685}, {14853, 41153}, {14891, 24206}, {14927, 21358}, {15516, 15691}, {15682, 33750}, {15683, 47352}, {15687, 48896}, {15692, 36990}, {15699, 48884}, {15714, 39884}, {17225, 30271}, {19708, 21167}, {22165, 31884}, {25488, 47340}, {26881, 35266}, {32218, 47333}, {33699, 38317}, {34628, 49524}, {37182, 44401}, {44903, 48901}, {46333, 48910}, {47355, 50687}
X(50971) = midpoint of X(i) and X(j) for these {i,j}: {20, 597}, {182, 15686}, {376, 44882}, {549, 48898}, {1386, 34638}, {5476, 19710}, {5480, 15681}, {5894, 31166}, {10168, 48891}, {11179, 48881}, {15687, 48896}, {34628, 49524}, {44903, 48901}
X(50971) = reflection of X(i) in X(j) for these {i,j}: {3853, 25565}, {20582, 3}, {24206, 14891}, {25561, 3530}, {32218, 47333}, {32455, 11179}, {34200, 33751}, {48889, 10124}
X(50971) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11179, 15689, 48881}, {19708, 47353, 21167}
X(50972) lies on these lines: {20, 20582}, {30, 34573}, {376, 524}, {518, 50816}, {542, 44245}, {547, 48920}, {548, 575}, {549, 48904}, {597, 3522}, {599, 50693}, {1503, 15690}, {3534, 47354}, {3589, 10304}, {5085, 41153}, {5093, 15695}, {5476, 8703}, {5480, 14093}, {5846, 50815}, {6329, 12017}, {9041, 12512}, {9053, 50808}, {10168, 41982}, {11001, 21167}, {11539, 48879}, {14810, 15691}, {15689, 18440}, {15697, 31884}, {15706, 43621}, {15710, 48910}, {15714, 48901}, {15759, 29317}, {21735, 38072}, {25406, 41149}, {34200, 48885}, {41983, 48895}, {45759, 48880}, {47478, 48943}, {48310, 48872}
X(50972) = midpoint of X(i) and X(j) for these {i,j}: {20, 20582}, {547, 48920}, {14810, 15691}, {34200, 48885}
X(50973) lies on these lines: {2, 5102}, {5, 599}, {6, 5054}, {30, 40341}, {69, 3839}, {182, 15718}, {193, 15705}, {376, 524}, {394, 15360}, {511, 3830}, {518, 50817}, {542, 1657}, {576, 46219}, {597, 3525}, {631, 20583}, {1351, 15703}, {1352, 14893}, {1992, 3523}, {3146, 11160}, {3524, 3629}, {3534, 5965}, {3545, 3631}, {3564, 19710}, {3630, 11180}, {3763, 47599}, {5050, 15722}, {5055, 37517}, {5085, 12100}, {5097, 15694}, {6144, 11179}, {6329, 15709}, {8550, 21734}, {8584, 10519}, {10124, 47352}, {10304, 11008}, {10516, 22165}, {11178, 44456}, {11412, 15738}, {11898, 19924}, {12007, 15692}, {12108, 38064}, {14269, 43150}, {14848, 40107}, {15701, 39561}, {15707, 50664}, {20080, 48905}, {20126, 37483}, {21167, 41149}, {33878, 48891}, {34379, 50814}, {35404, 36990}, {38035, 50787}, {38127, 47359}, {38144, 50781}, {38146, 50788}
X(50973) = reflection of X(i) in X(j) for these {i,j}: {6144, 11179}, {11180, 3630}, {11477, 599}, {15069, 11160}, {44456, 11178}, {47353, 15533}, {48910, 11180}
X(50973) = {X(599),X(11477)}-harmonic conjugate of X(38072)
X(50974) lies on these lines: {2, 3167}, {3, 11160}, {4, 542}, {6, 3545}, {30, 193}, {69, 3431}, {98, 9770}, {141, 15709}, {159, 37939}, {182, 15702}, {376, 524}, {381, 1353}, {511, 11001}, {518, 50818}, {549, 11898}, {575, 5067}, {597, 3090}, {599, 631}, {1007, 6055}, {1092, 43812}, {1351, 3543}, {1352, 5071}, {1503, 15534}, {1899, 13857}, {3091, 14848}, {3525, 34507}, {3533, 20582}, {3534, 34380}, {3544, 25561}, {3618, 11178}, {3619, 10168}, {3620, 5054}, {3751, 34627}, {3832, 11482}, {3839, 18440}, {3845, 5093}, {3855, 20583}, {5056, 38079}, {5085, 15719}, {5102, 41149}, {5476, 41106}, {5477, 6054}, {5642, 37643}, {5655, 25321}, {5847, 50810}, {5890, 8681}, {5965, 19708}, {6114, 37641}, {6115, 37640}, {6144, 46333}, {6353, 35266}, {6403, 14831}, {6515, 15360}, {6792, 50565}, {6804, 9936}, {6811, 13639}, {6813, 13759}, {7392, 12834}, {7410, 31144}, {7493, 44555}, {7774, 11177}, {8584, 14853}, {8598, 41400}, {8724, 32985}, {9041, 24817}, {9140, 30775}, {9143, 20772}, {9925, 22467}, {9974, 23269}, {9975, 23275}, {10304, 20080}, {10385, 39900}, {10519, 15533}, {11004, 31105}, {11008, 46264}, {11147, 47113}, {11161, 14651}, {11459, 40673}, {11477, 33703}, {12007, 40330}, {12017, 15708}, {12111, 32284}, {12117, 14645}, {12245, 28538}, {13482, 19124}, {13754, 15531}, {14002, 32254}, {14913, 16226}, {14927, 19924}, {14981, 37809}, {15032, 41614}, {15058, 44495}, {15687, 48662}, {15692, 48876}, {15710, 40341}, {16051, 40112}, {17040, 34801}, {18445, 37784}, {18917, 20126}, {18918, 21639}, {19459, 44837}, {21850, 50687}, {21969, 41715}, {22234, 25565}, {28194, 39878}, {28461, 37492}, {32225, 35260}, {32621, 35921}, {32984, 49102}, {33224, 39141}, {34379, 50811}, {34608, 41628}, {36757, 49813}, {36758, 49812}, {37182, 44367}, {37667, 40248}, {38074, 39885}, {39898, 47356}, {43598, 44489}, {45406, 49049}, {45407, 49048}
X(50974) = reflection of X(i) in X(j) for these {i,j}: {4, 1992}, {69, 11179}, {376, 6776}, {381, 1353}, {599, 8550}, {3543, 1351}, {5921, 381}, {6054, 5477}, {6403, 14831}, {10706, 5095}, {11160, 3}, {11180, 6}, {11459, 40673}, {11898, 549}, {15069, 597}, {34627, 3751}, {39898, 47356}, {47353, 8584}, {48662, 15687}
X(50974) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 11180, 3545}, {69, 11179, 3524}, {182, 21356, 15702}, {193, 39899, 39874}, {381, 1353, 5032}, {5032, 5921, 381}, {8584, 47353, 14853}, {9140, 37645, 30775}, {9143, 37644, 26255}, {14853, 47353, 41099}, {26288, 26289, 8716}
X(50975) lies on these lines: {2, 6030}, {20, 575}, {30, 3618}, {69, 15688}, {141, 15710}, {182, 15683}, {376, 524}, {511, 15697}, {518, 50819}, {542, 3522}, {549, 14927}, {550, 1992}, {597, 3529}, {599, 3528}, {1351, 15691}, {1503, 19708}, {3146, 38064}, {3524, 3763}, {3534, 5093}, {3543, 48898}, {3545, 48905}, {3564, 15695}, {3619, 17504}, {3620, 10304}, {3818, 15708}, {3839, 5092}, {5032, 48873}, {5050, 19710}, {5073, 38079}, {5085, 15682}, {5846, 50809}, {5847, 50812}, {5921, 33751}, {7386, 35266}, {8703, 10519}, {10168, 50687}, {10299, 20582}, {10303, 25561}, {10516, 15719}, {10541, 49138}, {11001, 14853}, {11178, 15705}, {11179, 37517}, {11645, 15692}, {12250, 31166}, {14561, 15640}, {14848, 15704}, {15689, 48906}, {15698, 47353}, {15700, 39884}, {15702, 36990}, {15706, 18358}, {15715, 21358}, {18440, 45759}, {20190, 49135}, {21356, 34200}, {25555, 50692}, {25565, 50689}, {33703, 38072}
X(50975) = reflection of X(i) in X(j) for these {i,j}: {11180, 3620}, {40330, 15692}
X(50975) = {X(10304),X(46264)}-harmonic conjugate of X(11180)
X(50976) lies on these lines: {3, 25561}, {6, 15689}, {20, 38072}, {30, 47355}, {376, 524}, {381, 33751}, {518, 50820}, {548, 599}, {550, 20423}, {597, 17538}, {3534, 5085}, {3589, 46333}, {3619, 10304}, {3620, 35418}, {3763, 45759}, {5055, 48891}, {5102, 15690}, {5846, 50813}, {7716, 35489}, {8703, 47353}, {10516, 19708}, {11477, 15696}, {12103, 38064}, {14093, 21358}, {15681, 48904}, {15685, 17508}, {15686, 47352}, {15688, 18440}, {15691, 48872}, {15694, 48896}, {15695, 31884}, {15701, 29323}, {15707, 48884}, {15718, 48889}, {20582, 21735}, {25565, 49136}, {34200, 36990}
X(50976) = {X(14093),X(48898)}-harmonic conjugate of X(21358)
X(50977) lies on these lines: {2, 51}, {3, 67}, {4, 25561}, {5, 20582}, {6, 5054}, {20, 18553}, {30, 141}, {69, 3431}, {76, 9302}, {99, 19905}, {125, 21766}, {140, 576}, {147, 9774}, {182, 524}, {183, 6055}, {193, 15708}, {298, 5981}, {299, 5980}, {343, 43957}, {376, 1352}, {381, 1350}, {518, 50821}, {547, 5480}, {573, 13633}, {574, 15993}, {575, 631}, {632, 38079}, {754, 35424}, {991, 13632}, {1092, 44491}, {1176, 43572}, {1351, 15694}, {1385, 28538}, {1469, 3584}, {1503, 8703}, {1656, 25565}, {2030, 21843}, {2393, 23329}, {2781, 15067}, {2782, 44774}, {2794, 25562}, {3017, 50591}, {3056, 3582}, {3094, 5309}, {3242, 34718}, {3314, 6054}, {3416, 3655}, {3523, 11160}, {3526, 11477}, {3530, 8550}, {3534, 29012}, {3543, 40330}, {3545, 3619}, {3564, 12100}, {3589, 11539}, {3618, 15709}, {3620, 10304}, {3630, 41983}, {3631, 17504}, {3653, 47356}, {3654, 47358}, {3763, 5055}, {3830, 10516}, {3839, 48895}, {3845, 29181}, {4265, 28443}, {5017, 7753}, {5032, 15516}, {5039, 9300}, {5050, 15534}, {5077, 19662}, {5085, 5965}, {5097, 15702}, {5104, 5475}, {5108, 16760}, {5138, 28465}, {5171, 8369}, {5182, 33274}, {5207, 11057}, {5418, 44502}, {5420, 44501}, {5447, 18281}, {5498, 11255}, {5642, 15066}, {5651, 7426}, {5690, 9041}, {5846, 50824}, {5847, 50828}, {5969, 49102}, {6034, 7746}, {6036, 7610}, {6228, 13804}, {6229, 13684}, {6393, 37671}, {6698, 32273}, {6699, 9976}, {6771, 9763}, {6774, 9761}, {6776, 15692}, {6791, 20481}, {7495, 40112}, {7496, 44555}, {7516, 43573}, {7552, 7999}, {7607, 7616}, {7748, 12355}, {7778, 40248}, {7818, 35387}, {7822, 9821}, {7827, 12251}, {7833, 12117}, {7834, 32521}, {7840, 37455}, {7841, 9880}, {7855, 12054}, {7937, 43453}, {8182, 47113}, {8262, 49671}, {8359, 9737}, {8541, 37118}, {8542, 15122}, {8548, 20191}, {8549, 25563}, {8584, 11812}, {8722, 37461}, {8981, 44474}, {9019, 44287}, {9023, 16235}, {9053, 50823}, {9140, 41462}, {9143, 15080}, {9306, 35266}, {9540, 44482}, {9735, 35304}, {9736, 35303}, {9829, 14916}, {9830, 33813}, {9971, 13340}, {9977, 32348}, {10018, 11470}, {10124, 18583}, {10170, 44275}, {10182, 19153}, {10193, 10249}, {10257, 11511}, {10282, 31166}, {10303, 22330}, {10541, 33749}, {10546, 37909}, {10625, 14787}, {10754, 17004}, {11001, 29323}, {11130, 46824}, {11131, 46825}, {11161, 21166}, {11173, 31489}, {11303, 25154}, {11304, 25164}, {11694, 19127}, {11898, 15700}, {12017, 15707}, {12177, 41134}, {12220, 44450}, {13085, 13086}, {13087, 13088}, {13169, 15035}, {13330, 31455}, {13334, 34511}, {13348, 43130}, {13391, 16776}, {13586, 43152}, {13634, 17297}, {13635, 17271}, {13700, 13820}, {13732, 49723}, {13910, 43211}, {13935, 44481}, {13966, 44473}, {13972, 43212}, {14093, 33751}, {14178, 14182}, {14269, 48910}, {14540, 37332}, {14541, 37333}, {14568, 43147}, {14643, 25566}, {14666, 36883}, {14869, 20583}, {14880, 42787}, {14912, 15719}, {14994, 32429}, {15061, 44751}, {15074, 50004}, {15303, 38793}, {15330, 19154}, {15462, 41720}, {15520, 15713}, {15681, 36990}, {15683, 48920}, {15684, 48872}, {15686, 39884}, {15687, 48874}, {15688, 18440}, {15689, 48905}, {15698, 25406}, {15699, 21850}, {15706, 39899}, {15710, 39874}, {15711, 41152}, {15810, 18860}, {16187, 32269}, {16266, 44494}, {16789, 37480}, {18800, 38748}, {19510, 50008}, {19649, 31143}, {20192, 47582}, {20299, 34787}, {20819, 50676}, {21163, 39785}, {21243, 31152}, {21554, 31144}, {22110, 37451}, {22329, 37450}, {22866, 22911}, {25556, 38794}, {26446, 47359}, {29573, 46475}, {30270, 37345}, {30739, 44569}, {31173, 37348}, {31401, 44500}, {32135, 38750}, {32216, 37638}, {32223, 47597}, {32267, 35259}, {34118, 34785}, {34155, 44493}, {34200, 44882}, {34331, 40929}, {34379, 50829}, {34621, 44870}, {34776, 35228}, {35001, 47448}, {35356, 40251}, {35375, 47101}, {37340, 47068}, {37341, 47066}, {40916, 41586}, {41614, 49672}, {41714, 44441}, {42089, 44497}, {42092, 44498}, {42149, 44511}, {42152, 44512}, {43621, 50687}, {44456, 47355}, {44513, 49105}, {44514, 49106}, {45303, 47311}, {47097, 47468}
X(50977) = midpoint of X(i) and X(j) for these {i,j}: {3, 599}, {69, 11179}, {99, 19905}, {376, 1352}, {381, 1350}, {549, 48876}, {3098, 11178}, {3242, 34718}, {3416, 3655}, {3534, 47353}, {3543, 48873}, {3654, 47358}, {5648, 20126}, {6055, 50567}, {7818, 35387}, {9971, 13340}, {11180, 46264}, {14666, 36883}, {15681, 36990}, {15684, 48872}, {15686, 39884}, {15687, 48874}, {16789, 44218}, {22677, 22712}, {47097, 47468}
X(50977) = reflection of X(i) in X(j) for these {i,j}: {4, 25561}, {5, 20582}, {6, 10168}, {182, 549}, {376, 14810}, {381, 24206}, {576, 597}, {597, 140}, {599, 40107}, {1992, 575}, {3543, 48889}, {3818, 11178}, {5097, 46267}, {5476, 2}, {5480, 547}, {10249, 10193}, {11178, 141}, {11179, 5092}, {11180, 43150}, {15520, 38110}, {15681, 48885}, {15683, 48920}, {17508, 21167}, {18583, 10124}, {19140, 5642}, {19153, 10182}, {19154, 15330}, {31166, 10282}, {34507, 599}, {44882, 34200}, {48896, 15686}, {48898, 376}, {48901, 381}, {48904, 15687}
X(50977) = complement of X(20423)
X(50977) = crossdifference of every pair of points on line {2492, 3288}
X(50977) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5476, 38317}, {3, 40107, 34507}, {6, 5054, 10168}, {69, 3524, 11179}, {141, 3098, 3818}, {141, 48881, 18358}, {376, 21356, 1352}, {381, 21358, 24206}, {631, 1992, 38064}, {1350, 21358, 381}, {1350, 24206, 48901}, {1351, 15694, 47352}, {1352, 14810, 48898}, {1656, 38072, 25565}, {1992, 38064, 575}, {3098, 3818, 48880}, {3098, 48884, 48881}, {3524, 11179, 5092}, {3526, 11477, 25555}, {3620, 10304, 11180}, {3620, 46264, 43150}, {3642, 3643, 7761}, {3763, 19130, 42786}, {3763, 33878, 19130}, {5650, 32225, 2}, {10124, 18583, 48310}, {10304, 11180, 46264}, {13083, 13084, 5569}, {13087, 13088, 34506}, {15066, 47596, 5642}, {18358, 48881, 48884}, {18358, 48884, 3818}, {31884, 47353, 3534}, {32216, 37638, 45311}, {40330, 48873, 48889}
X(50978) lies on these lines: {2, 5093}, {3, 11160}, {5, 599}, {6, 11539}, {30, 69}, {140, 1992}, {141, 15699}, {182, 524}, {193, 5054}, {343, 13857}, {376, 11898}, {511, 3845}, {518, 50823}, {542, 550}, {547, 1351}, {576, 20582}, {597, 632}, {1350, 13666}, {1352, 15687}, {1483, 28538}, {1503, 19710}, {3524, 20080}, {3545, 44456}, {3564, 8703}, {3618, 47598}, {3619, 47599}, {3620, 5055}, {3627, 34507}, {3628, 14848}, {3629, 10168}, {3630, 45759}, {3631, 11178}, {3857, 25561}, {3933, 8724}, {5032, 15694}, {5050, 11812}, {5085, 19711}, {5097, 48310}, {5562, 16105}, {5648, 16789}, {5846, 50831}, {5847, 50824}, {5921, 15681}, {5965, 15711}, {6776, 34200}, {7750, 12117}, {7840, 37451}, {8550, 44682}, {8584, 38110}, {9544, 44210}, {10109, 14853}, {10154, 35266}, {10304, 39899}, {10519, 12100}, {11179, 17504}, {11482, 16239}, {11645, 44903}, {11694, 34351}, {11737, 40330}, {12017, 41983}, {13169, 32423}, {14645, 49102}, {14869, 38064}, {14912, 15693}, {15069, 15704}, {15360, 44212}, {15534, 15713}, {15683, 48662}, {15689, 39874}, {15759, 25406}, {18358, 23046}, {18583, 21358}, {19662, 38229}, {19924, 35404}, {28463, 36740}, {30739, 44555}, {33699, 47353}, {34379, 50821}, {37450, 44367}, {37668, 40248}, {37950, 47552}, {38035, 50792}, {38112, 47359}, {38136, 41152}, {38144, 50785}, {39561, 41149}, {43957, 45794}, {44266, 47473}
X(50978) = midpoint of X(i) and X(j) for these {i,j}: {3, 11160}, {376, 11898}, {5921, 15681}, {11179, 40341}, {11180, 33878}, {15683, 48662}
X(50978) = reflection of X(i) in X(j) for these {i,j}: {5, 599}, {549, 48876}, {576, 20582}, {597, 40107}, {1351, 547}, {1353, 549}, {1992, 140}, {3629, 10168}, {6776, 34200}, {11178, 3631}, {15686, 1350}, {15687, 1352}, {21850, 11178}, {33699, 47353}, {35404, 39884}, {41720, 11694}, {44266, 47473}, {44903, 48874}
X(50978) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {576, 20582, 38079}, {1351, 21356, 547}, {11178, 21850, 38071}
X(50979) lies on these lines: {2, 3167}, {3, 1992}, {4, 14848}, {5, 542}, {6, 30}, {20, 11482}, {49, 43815}, {69, 5054}, {140, 599}, {141, 10168}, {182, 524}, {184, 35266}, {193, 3524}, {376, 1351}, {381, 6776}, {389, 15074}, {397, 25154}, {398, 25164}, {428, 39588}, {511, 8584}, {518, 50824}, {546, 38072}, {547, 1352}, {548, 11477}, {550, 576}, {567, 5622}, {568, 44261}, {613, 15170}, {631, 11160}, {632, 20582}, {952, 47359}, {1199, 31802}, {1350, 34200}, {1368, 13366}, {1483, 9041}, {1495, 20192}, {1503, 3845}, {1596, 44102}, {1692, 5306}, {1993, 43957}, {2393, 5946}, {2456, 41624}, {2781, 45956}, {2782, 18800}, {3098, 32455}, {3329, 11177}, {3363, 8593}, {3398, 5182}, {3530, 10541}, {3534, 5093}, {3545, 18440}, {3546, 43908}, {3582, 39873}, {3584, 39897}, {3589, 11178}, {3618, 5055}, {3620, 15709}, {3627, 22234}, {3628, 15069}, {3629, 5092}, {3655, 3751}, {3656, 16475}, {3763, 47598}, {3815, 5477}, {3818, 6329}, {3830, 14853}, {3839, 39874}, {4663, 34773}, {5012, 15360}, {5034, 9300}, {5038, 31406}, {5066, 14561}, {5071, 5921}, {5085, 12100}, {5097, 15686}, {5102, 15690}, {5254, 9880}, {5309, 39764}, {5480, 11645}, {5642, 37648}, {5648, 8263}, {5663, 15303}, {5690, 28538}, {5846, 50823}, {5847, 50821}, {5890, 44285}, {5892, 8681}, {5901, 38023}, {5965, 15713}, {5967, 34094}, {5969, 32448}, {6036, 9771}, {6054, 7792}, {6102, 44479}, {6144, 41983}, {6467, 16226}, {6644, 32621}, {6661, 39141}, {6677, 17809}, {6770, 44219}, {6771, 33474}, {6774, 33475}, {6800, 37904}, {7426, 11003}, {7495, 44555}, {7575, 8546}, {7592, 34664}, {7709, 8598}, {7734, 37672}, {7735, 40248}, {7840, 37450}, {8370, 12243}, {8541, 37458}, {8548, 36752}, {8549, 31166}, {9007, 45681}, {9053, 50831}, {9140, 14389}, {9143, 15018}, {9729, 32284}, {9730, 14984}, {9956, 38089}, {9967, 14831}, {9977, 36966}, {10109, 10516}, {10124, 21358}, {10192, 32068}, {10301, 15019}, {10304, 33878}, {10485, 15993}, {10519, 15693}, {10753, 14830}, {10765, 14666}, {11002, 47313}, {11008, 15707}, {11161, 38224}, {11237, 39901}, {11238, 39900}, {11405, 18533}, {11416, 44239}, {11422, 30739}, {11431, 16195}, {11579, 34319}, {11693, 32114}, {11799, 43697}, {11812, 15533}, {11842, 19661}, {11898, 15694}, {12042, 41672}, {12117, 32467}, {12161, 44503}, {13169, 15061}, {13330, 32516}, {13335, 14645}, {13363, 29959}, {13394, 32225}, {13434, 43812}, {13630, 50649}, {14614, 35429}, {14810, 15714}, {14869, 40107}, {14893, 36990}, {14927, 15684}, {15026, 43130}, {15032, 45016}, {15037, 39562}, {15045, 15531}, {15073, 37481}, {15087, 22151}, {15520, 19710}, {15688, 44456}, {15691, 48873}, {15703, 40330}, {15704, 22330}, {15708, 20080}, {15711, 17508}, {15712, 20190}, {15759, 31884}, {16042, 32254}, {16473, 34634}, {18400, 23326}, {18449, 44249}, {18571, 47280}, {18911, 47097}, {19116, 44657}, {19117, 44656}, {19127, 44490}, {19130, 23046}, {19149, 44804}, {19153, 44275}, {19662, 34127}, {19711, 21167}, {22249, 47276}, {22329, 37451}, {24206, 46267}, {26255, 26864}, {28204, 39870}, {29012, 33699}, {31804, 36753}, {32046, 34351}, {32216, 37645}, {32305, 41595}, {32414, 35021}, {34331, 50476}, {34379, 50828}, {34613, 45034}, {35404, 48901}, {35707, 37936}, {35822, 49229}, {35823, 49228}, {35840, 41946}, {35841, 41945}, {36757, 43228}, {36758, 43229}, {37455, 44367}, {37644, 47596}, {37827, 37967}, {37950, 47549}, {38021, 39878}, {38029, 47358}, {38116, 50783}, {38118, 50781}, {38322, 44494}, {40647, 44495}, {41631, 42634}, {41641, 42633}, {43595, 44480}, {44266, 47544}, {44903, 48898}, {44961, 47458}, {47031, 47463}, {47277, 47333}, {47308, 47462}, {47310, 47461}, {47332, 47459}, {47334, 47457}, {47335, 47464}, {47336, 47460}, {47355, 47599}
X(50979) = midpoint of X(i) and X(j) for these {i,j}: {3, 1992}, {6, 11179}, {376, 1351}, {381, 6776}, {549, 1353}, {597, 8550}, {3655, 3751}, {5050, 14912}, {5093, 25406}, {5477, 6055}, {8549, 31166}, {8593, 11632}, {9730, 40673}, {9967, 14831}, {10753, 14830}, {10765, 14666}, {11180, 39899}, {11579, 34319}, {14927, 15684}, {20126, 41720}, {20423, 43273}, {47277, 47333}
X(50979) = reflection of X(i) in X(j) for these {i,j}: {5, 597}, {141, 10168}, {381, 18583}, {549, 182}, {576, 20583}, {597, 575}, {599, 140}, {1350, 34200}, {1352, 547}, {3845, 5476}, {5648, 11694}, {10168, 50664}, {11178, 3589}, {11180, 18358}, {15686, 44882}, {15687, 5480}, {18553, 25565}, {24206, 46267}, {25561, 25555}, {29959, 13363}, {34507, 20582}, {35404, 48901}, {36990, 14893}, {38110, 5050}, {39884, 381}, {44266, 47544}, {44903, 48898}, {47334, 47457}, {47353, 5066}, {48873, 15691}, {48874, 376}, {48876, 549}, {48906, 11179}
X(50979) = crossdifference of every pair of points on line {8675, 39232}
X(50979) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 597, 38079}, {6, 43273, 20423}, {6, 48906, 21850}, {141, 10168, 11539}, {182, 1353, 48876}, {182, 12007, 1353}, {376, 5032, 1351}, {575, 8550, 5}, {575, 33749, 8550}, {599, 38064, 140}, {1352, 47352, 547}, {3589, 11178, 15699}, {3618, 11180, 5055}, {3618, 39899, 18358}, {3845, 5476, 38136}, {5055, 11180, 18358}, {5055, 39899, 11180}, {5622, 41720, 20126}, {5648, 15462, 11694}, {6776, 18583, 39884}, {10653, 10654, 44526}, {11179, 20423, 43273}, {11842, 37461, 19661}, {11898, 15694, 21356}, {14561, 47353, 5066}, {14912, 33748, 5050}, {24206, 46267, 48310}, {41979, 41980, 43619}
X(50980) lies on these lines: {2, 38136}, {30, 3763}, {69, 15707}, {140, 20423}, {141, 17504}, {182, 524}, {511, 15713}, {518, 50825}, {542, 15712}, {547, 48874}, {550, 20582}, {597, 14869}, {599, 3530}, {631, 11482}, {1350, 10124}, {1351, 15721}, {1352, 14891}, {1503, 15711}, {1992, 15720}, {3098, 15699}, {3524, 3620}, {3564, 15693}, {3618, 5054}, {3619, 15688}, {5066, 31884}, {5085, 44580}, {5102, 11812}, {5846, 50832}, {6776, 15718}, {8703, 21167}, {9053, 50822}, {10303, 14848}, {10304, 18358}, {10516, 15690}, {10519, 15701}, {11178, 45759}, {11179, 41983}, {11180, 15706}, {11539, 21850}, {11540, 14561}, {11645, 15714}, {11694, 15132}, {11737, 48873}, {12100, 43273}, {12108, 38064}, {14093, 40330}, {14810, 15687}, {14892, 48910}, {15686, 24206}, {15700, 21356}, {15702, 18583}, {15704, 25561}, {15705, 18440}, {15709, 33878}, {15759, 47353}, {16239, 38072}, {21358, 34200}, {23046, 48881}, {31670, 47599}, {34573, 38071}, {41982, 48905}
X(50980) = midpoint of X(14093) and X(40330)
X(50980) = {X(21358),X(34200)}-harmonic conjugate of X(39884)
X(50981) lies on these lines: {30, 3619}, {69, 41983}, {140, 14848}, {141, 45759}, {182, 524}, {518, 50826}, {542, 44682}, {550, 47354}, {599, 15712}, {1352, 15714}, {1992, 12108}, {3098, 38071}, {3524, 39899}, {3564, 19711}, {3618, 14890}, {3620, 15706}, {3627, 20582}, {3763, 23046}, {3845, 29317}, {5847, 50833}, {8703, 47353}, {10519, 11812}, {11539, 20423}, {12100, 25406}, {14810, 44903}, {14891, 21356}, {14912, 15722}, {15686, 21358}, {15687, 48872}, {15691, 40330}, {15699, 19130}, {15701, 34380}, {15711, 21167}, {17504, 43273}, {24206, 35404}, {31884, 33699}, {33878, 47598}
X(50982) lies on these lines: {2, 5102}, {4, 599}, {6, 15709}, {30, 3631}, {69, 10304}, {140, 20583}, {141, 5055}, {182, 524}, {511, 5066}, {518, 50827}, {542, 548}, {597, 3526}, {1177, 34483}, {1350, 15683}, {1352, 15684}, {1503, 3534}, {1992, 10303}, {3524, 40341}, {3564, 15759}, {3589, 46114}, {3628, 20582}, {3629, 5054}, {3630, 11179}, {3856, 25561}, {5097, 10124}, {5480, 21356}, {5965, 12100}, {6329, 11539}, {7486, 11477}, {8550, 11160}, {9053, 50830}, {10168, 14890}, {10302, 14485}, {10519, 15533}, {11008, 15708}, {11178, 23046}, {11180, 46333}, {11540, 34380}, {13607, 28538}, {15022, 38072}, {15069, 50693}, {15520, 41153}, {15640, 47353}, {15699, 37517}, {15704, 34507}, {15713, 39561}, {29181, 33699}
X(50982) = midpoint of X(i) and X(j) for these {i,j}: {3630, 11179}, {8550, 11160}, {11180, 48881}
X(50982) = reflection of X(i) in X(j) for these {i,j}: {5097, 10124}, {12007, 549}, {20582, 40107}, {20583, 140}, {32455, 10168}
X(50983) lies on these lines: {2, 154}, {3, 597}, {6, 3524}, {20, 38072}, {30, 3589}, {40, 38023}, {69, 15708}, {140, 542}, {141, 5054}, {182, 524}, {373, 37904}, {376, 5480}, {381, 44882}, {511, 12100}, {518, 50828}, {546, 25565}, {547, 11645}, {548, 25555}, {550, 38079}, {575, 3530}, {576, 15712}, {599, 631}, {944, 38087}, {1350, 15692}, {1351, 15700}, {1352, 15694}, {1385, 9041}, {1428, 4995}, {1691, 9300}, {1992, 3523}, {2330, 5298}, {2781, 16836}, {2916, 37939}, {3098, 6329}, {3313, 16226}, {3534, 14561}, {3545, 47355}, {3564, 11812}, {3576, 47359}, {3618, 10304}, {3628, 25561}, {3629, 15707}, {3654, 38029}, {3655, 49524}, {3763, 11180}, {3818, 15699}, {3839, 48905}, {3845, 38317}, {4297, 38089}, {5026, 6055}, {5050, 8584}, {5055, 46264}, {5066, 29012}, {5071, 36990}, {5096, 21161}, {5306, 50659}, {5476, 8703}, {5621, 7550}, {5622, 5648}, {5732, 38088}, {5759, 38086}, {5846, 50821}, {5847, 50829}, {5892, 9019}, {5893, 34664}, {5969, 13334}, {6034, 12117}, {6036, 9830}, {6247, 31166}, {6684, 28538}, {6696, 37515}, {6776, 15702}, {7395, 15579}, {7464, 38402}, {7495, 44569}, {7496, 40112}, {7575, 25488}, {7736, 20194}, {7789, 8724}, {8369, 37479}, {8705, 18579}, {8722, 19661}, {9053, 50824}, {9172, 14688}, {10124, 24206}, {10303, 15069}, {10519, 15534}, {11001, 33750}, {11178, 11539}, {11477, 15717}, {11695, 33591}, {11737, 48889}, {12101, 29323}, {12108, 40107}, {13331, 33706}, {13339, 15462}, {13857, 23292}, {14093, 48873}, {14810, 14891}, {14853, 19708}, {14869, 34507}, {14890, 43150}, {14912, 15533}, {14984, 44323}, {15303, 38727}, {15448, 22112}, {15686, 48901}, {15687, 48898}, {15688, 31670}, {15690, 29317}, {15691, 33751}, {15698, 31884}, {15701, 22165}, {15706, 33878}, {15711, 41153}, {15714, 48874}, {15721, 21356}, {16239, 18553}, {18358, 47598}, {18583, 19924}, {18800, 38737}, {19127, 44218}, {19153, 23328}, {19710, 38136}, {19711, 39561}, {19905, 38739}, {21163, 27088}, {21850, 45759}, {22110, 37450}, {22329, 37455}, {23046, 48884}, {24466, 38090}, {25329, 38728}, {26316, 44380}, {30264, 38091}, {31521, 44883}, {32455, 41983}, {34380, 41149}, {35404, 48896}, {35486, 41585}, {36703, 45870}, {37451, 44401}, {37648, 47596}, {38047, 50811}, {38049, 50808}, {38068, 39870}, {38315, 50810}, {43650, 44210}, {44903, 48904}, {49102, 49112}
X(50983) = midpoint of X(i) and X(j) for these {i,j}: {3, 597}, {141, 11179}, {182, 549}, {376, 5480}, {381, 44882}, {599, 8550}, {3655, 49524}, {5026, 6055}, {5050, 21167}, {5092, 10168}, {5476, 8703}, {6247, 31166}, {9172, 14688}, {10192, 10249}, {11178, 48906}, {15686, 48901}, {15687, 48898}, {17508, 38110}, {18583, 34200}, {19127, 44218}, {19153, 23328}, {35404, 48896}, {43273, 47354}, {44903, 48904}
X(50983) = reflection of X(i) in X(j) for these {i,j}: {546, 25565}, {3589, 10168}, {11178, 34573}, {14810, 14891}, {15691, 33751}, {18583, 46267}, {20582, 140}, {20583, 575}, {24206, 10124}, {25561, 3628}, {48889, 11737}
X(50983) = complement of X(47354)
X(50983) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 25406, 47353}, {2, 43273, 47354}, {3, 38064, 597}, {376, 47352, 5480}, {631, 10541, 8550}, {5054, 11179, 141}, {5054, 12017, 11179}, {5476, 17508, 8703}, {6776, 15702, 21358}, {8703, 38110, 5476}, {11178, 11539, 34573}, {11180, 15709, 3763}, {11539, 48906, 11178}, {13083, 13084, 12040}, {44882, 48310, 381}
X(50984) lies on these lines: {2, 21167}, {3, 20582}, {6, 15708}, {30, 34573}, {141, 3524}, {182, 524}, {511, 11812}, {518, 50829}, {542, 3530}, {547, 14810}, {548, 25561}, {597, 631}, {599, 3523}, {1350, 15702}, {1352, 15700}, {1503, 10193}, {3098, 11539}, {3525, 38072}, {3564, 41152}, {3589, 5054}, {3619, 15705}, {3631, 11179}, {3763, 10304}, {3818, 45759}, {5050, 41149}, {5055, 48881}, {5085, 15719}, {5092, 41983}, {5093, 15701}, {5476, 15713}, {5480, 15694}, {5846, 50828}, {6329, 10168}, {6684, 9041}, {7496, 44569}, {7499, 13857}, {8584, 10519}, {9053, 50821}, {10109, 29317}, {10124, 19924}, {10516, 19708}, {10541, 11160}, {11178, 17504}, {11645, 14891}, {12108, 22330}, {14893, 48885}, {15691, 48889}, {15692, 21358}, {15698, 47353}, {15703, 48873}, {15706, 46264}, {15710, 48905}, {15714, 48898}, {15715, 40330}, {15720, 20583}, {15721, 47352}, {15759, 29012}, {16239, 25565}, {17508, 19711}, {19130, 47598}, {22110, 37455}, {23046, 42786}, {24206, 34200}, {37450, 44401}, {38071, 48880}, {38110, 41153}, {41987, 48943}, {47478, 48895}
X(50984) = midpoint of X(i) and X(j) for these {i,j}: {3, 20582}, {547, 14810}, {548, 25561}, {3631, 11179}, {14893, 48885}, {15691, 48889}, {24206, 34200}
X(50984) = reflection of X(i) in X(j) for these {i,j}: {6329, 10168}, {25565, 16239}
X(50984) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1350, 15702, 48310}, {15692, 21358, 44882}
X(50985) lies on these lines: {4, 11160}, {6, 43513}, {30, 40341}, {69, 5055}, {182, 524}, {193, 15709}, {511, 33699}, {518, 50830}, {542, 15704}, {548, 43273}, {599, 3628}, {632, 20583}, {1992, 3526}, {3534, 3564}, {3629, 11539}, {3630, 21850}, {3631, 15699}, {3856, 11477}, {3857, 34507}, {5054, 11008}, {5066, 10516}, {5102, 10109}, {5965, 8703}, {6144, 14890}, {7486, 14848}, {7850, 44369}, {10304, 20080}, {11540, 15534}, {11898, 15684}, {33878, 46333}, {34379, 50827}, {37517, 38071}, {38040, 50787}, {38165, 50781}, {38167, 50788}, {38317, 41152}
X(50986) lies on these lines: {5, 1992}, {6, 15699}, {30, 193}, {69, 11539}, {140, 11160}, {182, 524}, {511, 19710}, {518, 50831}, {542, 3627}, {547, 5032}, {550, 43273}, {576, 3858}, {599, 632}, {1351, 15687}, {3564, 3845}, {3620, 47598}, {3629, 19130}, {3630, 10168}, {3857, 15069}, {5050, 15713}, {5054, 20080}, {5066, 5093}, {5476, 41149}, {5847, 50823}, {5921, 14893}, {5965, 8584}, {6144, 11179}, {6776, 15686}, {7762, 12243}, {8550, 46853}, {8703, 25406}, {10154, 15360}, {10519, 19711}, {11008, 17504}, {11178, 32455}, {11180, 23046}, {12100, 14912}, {15701, 33748}, {20126, 37495}, {20583, 34507}, {22165, 38110}, {34379, 50824}, {35266, 41588}, {37451, 44367}, {44266, 47541}, {44903, 48872}
X(50986) = midpoint of X(6144) and X(11179)
X(50986) = reflection of X(i) in X(j) for these {i,j}: {5, 1992}, {549, 1353}, {3630, 10168}, {5476, 41149}, {5921, 14893}, {11160, 140}, {11178, 32455}, {11898, 547}, {15686, 6776}, {15687, 1351}, {34507, 20583}, {44266, 47541}
X(50986) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5032, 11898, 547}, {20583, 34507, 38079}
X(50987) lies on these lines: {5, 10541}, {6, 17504}, {30, 3618}, {182, 524}, {193, 15707}, {511, 15711}, {518, 50832}, {542, 632}, {548, 14848}, {550, 597}, {575, 44682}, {599, 14869}, {1351, 14891}, {1992, 3530}, {3564, 15713}, {3589, 38071}, {3620, 5054}, {3627, 38079}, {3763, 11179}, {3845, 29012}, {5032, 15700}, {5050, 12100}, {5066, 25406}, {5085, 8703}, {5092, 45759}, {5093, 15698}, {5476, 19710}, {5480, 44903}, {5622, 11694}, {5846, 50822}, {5847, 50825}, {5921, 15723}, {6776, 10124}, {10168, 15699}, {10519, 44580}, {11160, 15720}, {11180, 47598}, {11898, 15721}, {14561, 33699}, {14853, 15690}, {14912, 15701}, {15686, 18583}, {15687, 47352}, {15693, 34380}, {15705, 44456}, {15709, 39899}, {15719, 33748}, {18440, 47599}, {20126, 37471}, {23046, 46264}, {35266, 43650}, {35404, 44882}, {39884, 48310}
X(50987) = midpoint of X(3763) and X(11179)
X(50987) = {X(10168),X(48906)}-harmonic conjugate of X(15699)
X(50988) lies on these lines: {3, 38079}, {6, 41983}, {30, 47355}, {140, 43273}, {182, 524}, {511, 19711}, {518, 50833}, {542, 14869}, {597, 15712}, {599, 12108}, {3524, 33878}, {3530, 11477}, {3564, 15701}, {3589, 45759}, {3618, 15706}, {3619, 5054}, {3763, 14890}, {3845, 17508}, {5050, 15719}, {5085, 11812}, {5092, 11539}, {5093, 15693}, {5476, 15711}, {5480, 15714}, {5846, 50826}, {8703, 29317}, {10124, 39884}, {10168, 17504}, {10519, 15722}, {11540, 47353}, {12017, 15708}, {12100, 20423}, {14561, 15759}, {14848, 15717}, {14853, 15716}, {14891, 47352}, {15686, 48310}, {15692, 18583}, {15709, 18358}, {19709, 33750}, {19710, 38317}, {33923, 38072}, {46264, 47598}, {47478, 48905}
X(50988) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10168, 17504, 21850}, {14891, 47352, 48874}
X(50989) lies on these lines: {2, 6}, {518, 50782}, {542, 15695}, {1350, 19710}, {1352, 12101}, {3534, 15069}, {3564, 15711}, {3830, 34507}, {5066, 11477}, {5085, 44580}, {5847, 50791}, {6034, 41148}, {7768, 11317}, {7784, 11054}, {7908, 50571}, {8550, 15719}, {10488, 36521}, {11165, 15602}, {11179, 19711}, {11180, 48872}, {11898, 15716}, {15515, 39785}, {15685, 29012}, {15701, 40107}, {15759, 48876}, {28313, 50076}, {28322, 50087}, {33683, 40344}, {33699, 47353}, {34379, 50784}, {38047, 50788}, {38315, 41150}, {47276, 47314}, {47359, 50785}
X(50989) = midpoint of X(3618) and X(11160)
X(50989) = reflection of X(3763) in X(599)
X(50989) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 22165, 15533}, {599, 6144, 21358}, {599, 15533, 15534}, {599, 40341, 47352}, {599, 47355, 21356}, {3631, 11160, 21358}, {3631, 21358, 599}, {6144, 8584, 15534}, {8584, 22165, 3631}, {11160, 21358, 6144}, {15533, 15534, 40341}, {15533, 22165, 599}, {32808, 32809, 37688}
X(50990) lies on these lines: {2, 6}, {76, 32532}, {376, 34507}, {487, 6496}, {488, 6497}, {511, 41099}, {518, 50784}, {542, 19708}, {1351, 10109}, {1352, 15682}, {1353, 11540}, {1444, 21497}, {1503, 15697}, {3524, 40107}, {3534, 11180}, {3564, 15693}, {3785, 27088}, {4677, 50781}, {4745, 50788}, {4748, 29622}, {5077, 32836}, {5846, 50791}, {6337, 7810}, {6393, 32896}, {6776, 12100}, {7386, 32255}, {7761, 45796}, {7794, 32985}, {7854, 33215}, {7929, 40246}, {8354, 10008}, {8550, 15708}, {8703, 10519}, {9053, 50782}, {10304, 15069}, {11001, 29012}, {11054, 33190}, {11161, 15300}, {11178, 41106}, {11179, 15719}, {11317, 32006}, {11898, 15701}, {13169, 43653}, {14826, 37904}, {15640, 47353}, {15698, 25406}, {15716, 48906}, {16935, 34614}, {17274, 28313}, {17294, 28301}, {17361, 35578}, {18440, 19710}, {19709, 40330}, {22493, 37171}, {22494, 37170}, {28322, 50081}, {29583, 49737}, {29615, 42697}, {29616, 49748}, {32099, 37756}, {33699, 33878}, {37350, 46951}, {47313, 47473}, {49830, 49831}
X(50990) = reflection of X(i) in X(j) for these {i,j}: {1992, 3618}, {3620, 599}
X(50990) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11160, 15534}, {2, 22165, 69}, {69, 141, 11008}, {69, 599, 21356}, {69, 3620, 3618}, {69, 21356, 1992}, {141, 15534, 2}, {599, 22165, 2}, {1992, 21356, 3619}, {3631, 41152, 22165}, {20582, 40341, 5032}, {22165, 41152, 599}, {32808, 32809, 15589}, {32810, 32811, 34229}
X(50991) lies on these lines: {2, 6}, {30, 18553}, {140, 33749}, {182, 15713}, {184, 37283}, {316, 10302}, {511, 5066}, {518, 3968}, {542, 12100}, {545, 29594}, {549, 34507}, {575, 10124}, {576, 15699}, {626, 8355}, {698, 14711}, {1086, 29615}, {1350, 15682}, {1352, 3534}, {1503, 8703}, {2854, 3819}, {2896, 9855}, {2930, 15246}, {3098, 19710}, {3363, 7818}, {3524, 15069}, {3564, 11812}, {3661, 7238}, {3662, 4478}, {3663, 50084}, {3818, 33699}, {3830, 29181}, {3845, 11178}, {3860, 25561}, {3912, 49737}, {3917, 8705}, {4364, 29573}, {4395, 17227}, {4399, 17287}, {4445, 48631}, {4669, 9041}, {4677, 9053}, {4690, 40480}, {4971, 50081}, {5054, 8550}, {5064, 41585}, {5071, 11477}, {5092, 44580}, {5181, 43957}, {5351, 35303}, {5352, 35304}, {5480, 19709}, {5846, 50781}, {5847, 50788}, {5891, 47332}, {5969, 19662}, {6390, 15602}, {6656, 11054}, {6676, 32257}, {6776, 15719}, {7227, 17228}, {7228, 17288}, {7232, 48636}, {7484, 8546}, {7620, 32532}, {7745, 32027}, {7780, 8365}, {7789, 7810}, {7794, 8359}, {7801, 15515}, {7811, 35954}, {7849, 8360}, {7854, 8369}, {7860, 8370}, {7879, 11317}, {7883, 8352}, {7908, 12040}, {7934, 45796}, {8182, 15603}, {8354, 15300}, {8681, 44323}, {8787, 9167}, {9055, 36525}, {9466, 37350}, {9830, 36521}, {10109, 24206}, {10150, 44496}, {10168, 11540}, {10516, 41099}, {10519, 11001}, {10541, 15721}, {11179, 15701}, {11180, 19708}, {11444, 40929}, {11645, 15690}, {11649, 44324}, {11898, 38064}, {12101, 18358}, {15360, 35283}, {15685, 48881}, {15695, 18440}, {15697, 31884}, {15698, 21167}, {15759, 43150}, {16252, 44262}, {16776, 21969}, {17045, 50125}, {17128, 40246}, {17132, 17229}, {17133, 17235}, {17230, 49748}, {17231, 50093}, {17236, 50121}, {17237, 29574}, {17250, 29622}, {17272, 41313}, {17274, 28297}, {17293, 35578}, {17294, 28309}, {17296, 41312}, {17332, 41310}, {17345, 50118}, {17359, 28333}, {17362, 48633}, {17365, 48634}, {17366, 48638}, {17369, 48639}, {17372, 50109}, {17382, 28337}, {17390, 41311}, {17758, 50271}, {17782, 44419}, {18579, 44201}, {19711, 48906}, {21521, 37503}, {22330, 48154}, {22493, 37351}, {22494, 37352}, {25488, 47558}, {25555, 47599}, {29577, 49742}, {31138, 49733}, {32113, 47314}, {32154, 34986}, {32218, 37904}, {33087, 49740}, {36792, 39998}, {37901, 47448}, {40330, 41106}, {46267, 47598}, {47359, 50792}, {48834, 48859}, {50076, 50112}
X(50991) = midpoint of X(i) and X(j) for these {i,j}: {2, 22165}, {69, 597}, {141, 599}, {549, 34507}, {1992, 3630}, {3629, 11160}, {3631, 20582}, {3663, 50084}, {8584, 15533}, {11178, 48876}, {11180, 44882}, {17274, 50097}, {17294, 49741}, {17345, 50118}, {17372, 50109}, {48834, 48859}, {50076, 50112}, {50081, 50092}
X(50991) = reflection of X(i) in X(j) for these {i,j}: {575, 10124}, {597, 34573}, {1992, 6329}, {3589, 20582}, {3631, 599}, {12007, 10168}, {20582, 141}, {20583, 3589}, {22165, 41152}, {32218, 47556}, {32455, 597}
X(50991) = complement of X(8584)
X(50991) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 69, 15534}, {2, 599, 22165}, {2, 15533, 8584}, {2, 15534, 597}, {69, 141, 34573}, {69, 21358, 597}, {69, 34573, 32455}, {141, 597, 21358}, {141, 3629, 3619}, {141, 3630, 3763}, {141, 3631, 3589}, {141, 22165, 2}, {591, 1991, 9740}, {597, 21358, 34573}, {599, 21356, 141}, {599, 21358, 69}, {599, 22165, 41152}, {1992, 3763, 48310}, {1992, 48310, 6329}, {3619, 11160, 47352}, {3620, 21356, 599}, {3630, 3763, 6329}, {3630, 48310, 1992}, {3631, 32455, 69}, {5032, 47355, 597}, {7778, 42850, 15597}, {8584, 22165, 15533}, {11160, 47352, 3629}, {15534, 21358, 2}, {15534, 32455, 41149}, {17287, 48632, 4399}, {17288, 48635, 7228}, {20582, 22165, 41149}, {21358, 34573, 20582}, {22165, 41152, 3631}, {32455, 34573, 3589}, {33458, 33459, 8667}, {39107, 39108, 41136}, {49921, 49922, 19708}
X(50992) lies on these lines: {2, 6}, {7, 50077}, {315, 11054}, {316, 5485}, {319, 35578}, {487, 6456}, {488, 6455}, {511, 11455}, {518, 50789}, {542, 11001}, {575, 15709}, {576, 5071}, {1350, 15697}, {1351, 5066}, {1352, 41099}, {1353, 11812}, {1370, 32244}, {1444, 21498}, {2930, 37913}, {2979, 9027}, {3363, 46951}, {3533, 46267}, {3534, 3564}, {3543, 15069}, {3545, 34507}, {3751, 4745}, {3830, 11180}, {3839, 11477}, {3845, 34380}, {3926, 27088}, {4643, 39260}, {4644, 29615}, {4669, 34379}, {4715, 50079}, {5050, 15713}, {5095, 38282}, {5569, 45796}, {5921, 15640}, {5965, 19708}, {6179, 33197}, {6193, 44261}, {6337, 7855}, {6390, 11147}, {6776, 8703}, {7426, 47552}, {7615, 7845}, {7751, 32984}, {7758, 31652}, {7760, 33230}, {7768, 33190}, {7776, 8355}, {7793, 12151}, {7813, 8182}, {7826, 15515}, {7863, 14023}, {7893, 9855}, {7946, 33006}, {8352, 32006}, {8550, 15692}, {8593, 36521}, {9741, 14907}, {9830, 14976}, {10519, 12100}, {10754, 36523}, {11159, 32836}, {11161, 14645}, {11179, 15698}, {11188, 21969}, {11482, 15699}, {12017, 44580}, {14711, 18906}, {14853, 19709}, {14912, 15719}, {15300, 47102}, {15693, 48876}, {15695, 39899}, {15702, 40107}, {16475, 50787}, {16491, 41150}, {17257, 50125}, {17274, 49543}, {18440, 33699}, {19710, 33878}, {20081, 40246}, {20423, 41106}, {21296, 37756}, {21972, 45312}, {22495, 37170}, {22496, 37171}, {29617, 42697}, {31145, 49722}, {32029, 36525}, {32064, 47314}, {32220, 47551}, {32827, 40727}, {33223, 41748}, {37901, 47276}, {39874, 48891}, {42696, 50128}, {42791, 49921}, {42792, 49922}, {43542, 44498}, {43543, 44497}, {43572, 44470}
X(50992) = midpoint of X(11160) and X(20080)
X(50992) = reflection of X(i) in X(j) for these {i,j}: {2, 15533}, {69, 11160}, {193, 599}, {599, 3630}, {1992, 69}, {3543, 15069}, {6144, 597}, {7426, 47552}, {11008, 1992}, {11160, 40341}, {11180, 11898}, {15534, 22165}, {32220, 47551}, {37901, 47276}
X(50992) = isotomic conjugate of X(32532)
X(50992) = anticomplement of X(15534)
X(50992) = anticomplement of the isogonal conjugate of X(40103)
X(50992) = isotomic conjugate of the isogonal conjugate of X(15655)
X(50992) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {33638, 7192}, {40103, 8}
X(50992) = X(31)-isoconjugate of X(32532)
X(50992) = X(2)-Dao conjugate of X(32532)
X(50992) = barycentric product X(76)*X(15655)
X(50992) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 32532}, {15655, 6}
X(50992) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 193, 8584}, {2, 11160, 15533}, {2, 15533, 69}, {69, 193, 3619}, {69, 1992, 21356}, {69, 11008, 3618}, {193, 3630, 69}, {325, 9740, 23055}, {591, 1991, 15597}, {599, 3619, 21356}, {599, 8584, 2}, {1992, 21356, 3618}, {5858, 5859, 13468}, {5860, 7840, 32810}, {5861, 7840, 32811}, {6144, 15533, 41152}, {6189, 6190, 41133}, {8584, 41153, 6}, {11008, 21356, 1992}, {15533, 15534, 22165}, {15534, 22165, 2}, {20080, 40341, 69}, {32808, 32809, 37668}, {32810, 32811, 1007}, {33622, 33624, 19708}, {35750, 36331, 11001}, {39365, 39366, 41136}
X(50993) lies on these lines: {2, 6}, {30, 47448}, {381, 40107}, {511, 19709}, {518, 50791}, {542, 15040}, {549, 15069}, {576, 15703}, {1350, 3830}, {1352, 8703}, {1503, 19708}, {1620, 44273}, {2930, 7485}, {3094, 14711}, {3096, 11054}, {3098, 15685}, {3242, 4677}, {3534, 29012}, {3564, 15713}, {3844, 38087}, {3845, 10516}, {3860, 31670}, {4361, 48638}, {4363, 48639}, {4437, 36525}, {4445, 37756}, {4663, 19876}, {4669, 47358}, {4745, 49511}, {4912, 17286}, {5013, 39785}, {5023, 7810}, {5054, 10541}, {5055, 11477}, {5066, 48876}, {5077, 7865}, {5085, 15701}, {5092, 15722}, {5207, 14030}, {5846, 50782}, {5847, 50784}, {7232, 48634}, {7784, 8352}, {7794, 22332}, {7795, 27088}, {7801, 15815}, {7815, 12151}, {7818, 50280}, {7849, 11318}, {7853, 40727}, {7854, 22331}, {7883, 11317}, {8550, 15702}, {8716, 31168}, {9466, 44453}, {9544, 37283}, {10109, 20423}, {10168, 11898}, {10302, 17503}, {10488, 41134}, {10519, 15682}, {11001, 36990}, {11179, 11812}, {11180, 15698}, {11291, 17852}, {11645, 15695}, {11646, 15300}, {12100, 43273}, {12101, 48910}, {15067, 39484}, {15640, 48872}, {15681, 18553}, {15690, 48905}, {15759, 46264}, {16672, 17237}, {16675, 17231}, {17118, 17228}, {17119, 17227}, {17235, 50089}, {17250, 29620}, {17253, 41313}, {17267, 50093}, {17269, 49748}, {17272, 41310}, {17274, 28322}, {17290, 29617}, {17291, 50077}, {17293, 50128}, {17296, 41311}, {17304, 28329}, {17306, 50125}, {17311, 41312}, {17323, 50121}, {17325, 29574}, {17387, 25503}, {17814, 44262}, {18358, 33699}, {18906, 33291}, {24206, 38072}, {24441, 29577}, {25561, 33878}, {28301, 29594}, {28313, 50087}, {32113, 47311}, {32257, 34319}, {36194, 47284}, {36523, 50567}, {36792, 40022}, {37904, 43653}, {38047, 50792}, {38315, 50785}, {40330, 41099}, {41150, 49684}, {44580, 48906}, {46219, 46267}, {47097, 47276}, {47313, 47556}, {47359, 50787}, {47445, 47473}, {49543, 50076}, {50081, 50120}
X(50993) = midpoint of X(599) and X(3763)
X(50993) = reflection of X(599) in X(3620)
X(50993) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 69, 8584}, {2, 599, 15533}, {2, 8584, 47352}, {2, 15533, 6}, {2, 22165, 15534}, {69, 20582, 47352}, {141, 599, 21358}, {141, 3620, 3763}, {141, 21356, 599}, {599, 15534, 22165}, {599, 21358, 6}, {599, 47352, 69}, {8584, 20582, 2}, {8584, 41152, 69}, {13846, 13847, 7735}, {15533, 21358, 2}, {15534, 22165, 15533}, {20582, 41152, 8584}, {41152, 47352, 15533}
X(50994) lies on these lines: {2, 6}, {376, 40107}, {511, 41106}, {518, 50792}, {542, 15036}, {1350, 15640}, {1352, 11001}, {3524, 34507}, {3534, 10519}, {3564, 15701}, {3830, 48876}, {4669, 50787}, {4677, 49511}, {4745, 49536}, {4748, 29620}, {5050, 11540}, {5066, 40330}, {5846, 50785}, {6776, 15693}, {7494, 32257}, {7794, 33215}, {7800, 39785}, {7801, 47061}, {7812, 18840}, {7831, 9741}, {7854, 32985}, {7870, 39142}, {7879, 8352}, {7918, 11054}, {8355, 32828}, {8358, 32896}, {8550, 15721}, {8703, 11180}, {9027, 44299}, {10008, 32892}, {10109, 14853}, {11055, 14994}, {11161, 36521}, {11178, 41099}, {11185, 17503}, {11482, 47599}, {11487, 44275}, {12100, 25406}, {12101, 33878}, {14927, 15697}, {15069, 15692}, {15682, 29317}, {15690, 18440}, {15722, 39899}, {17228, 35578}, {17274, 50100}, {19709, 38136}, {32006, 32027}, {32983, 50280}, {33522, 47313}, {36523, 50639}, {40802, 46212}, {47314, 47473}, {49879, 49880}
X(50994) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 8584, 3618}, {2, 11160, 8584}, {2, 15533, 1992}, {141, 3631, 6144}, {141, 15533, 2}, {141, 41152, 15533}, {599, 3620, 21356}, {599, 15533, 41152}, {599, 21356, 69}, {599, 21358, 3631}, {1992, 21356, 141}, {3618, 3631, 69}, {3631, 21358, 11160}, {8584, 21358, 2}, {11160, 21358, 3618}, {20080, 47352, 1992}, {32810, 32811, 183}
X(50995) lies on these lines: {1, 6}, {2, 38086}, {5, 38143}, {7, 141}, {8, 5819}, {10, 38185}, {19, 3059}, {40, 4515}, {55, 3930}, {56, 33299}, {57, 44798}, {63, 3693}, {69, 144}, {78, 3207}, {101, 3940}, {140, 38115}, {142, 3763}, {169, 34790}, {198, 480}, {200, 910}, {210, 40131}, {239, 49502}, {329, 17747}, {390, 5846}, {474, 17736}, {511, 5779}, {516, 2321}, {524, 6172}, {527, 599}, {528, 50087}, {529, 24247}, {594, 2550}, {673, 4361}, {674, 42014}, {728, 12526}, {742, 17262}, {966, 5686}, {971, 1350}, {1125, 38046}, {1146, 3421}, {1156, 9024}, {1213, 38057}, {1352, 5762}, {1376, 3509}, {1400, 41712}, {1418, 21446}, {1503, 5759}, {1696, 21033}, {1706, 7323}, {1759, 4006}, {1761, 2938}, {2099, 4390}, {2178, 5096}, {2280, 41711}, {2285, 8581}, {2551, 21049}, {3290, 37679}, {3304, 39244}, {3338, 25068}, {3436, 40997}, {3496, 3913}, {3589, 18230}, {3620, 20059}, {3628, 38164}, {3634, 38187}, {3681, 26241}, {3686, 49688}, {3694, 37499}, {3713, 5279}, {3729, 27474}, {3730, 3927}, {3811, 4258}, {3818, 31671}, {3827, 21871}, {3844, 38052}, {3869, 4513}, {3943, 5698}, {3950, 5847}, {3991, 12514}, {4383, 26242}, {4534, 34689}, {4908, 15533}, {5022, 25066}, {5085, 31658}, {5257, 38047}, {5480, 5817}, {5542, 5750}, {5696, 16548}, {5711, 28594}, {5732, 31884}, {5805, 10516}, {5815, 6554}, {5816, 38144}, {5838, 5839}, {5843, 48876}, {5848, 6068}, {5850, 17355}, {5853, 17299}, {6173, 21358}, {6600, 36744}, {6666, 38186}, {6667, 38188}, {6668, 38189}, {6776, 21168}, {8545, 34377}, {9041, 37654}, {10387, 14100}, {10519, 36996}, {10895, 21029}, {12572, 21096}, {15668, 27475}, {16593, 17267}, {17119, 49533}, {17259, 49481}, {17261, 49496}, {17275, 24393}, {17276, 50011}, {17277, 27484}, {17330, 48849}, {17349, 32029}, {17362, 49690}, {17388, 49679}, {17398, 38053}, {17595, 17756}, {17597, 33854}, {17738, 49507}, {20672, 23151}, {21044, 31141}, {21060, 40869}, {21075, 46835}, {24206, 38107}, {24352, 30946}, {26039, 30340}, {28538, 50836}, {28739, 39063}, {29181, 36991}, {30331, 49681}, {31672, 48910}, {34371, 36973}, {34820, 39273}, {40341, 49752}, {41338, 44424}, {47357, 50113}, {47358, 50115}, {50131, 50790}
X(50995) = midpoint of X(69) and X(144)
X(50995) = reflection of X(i) in X(j) for these {i,j}: {6, 9}, {7, 141}, {31671, 3818}, {48910, 31672}, {49681, 30331}
X(50995) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 16777, 38315}, {6, 49509, 3242}, {9, 22021, 954}, {37, 44, 16970}, {44, 16973, 6}, {63, 3693, 42316}, {72, 17742, 220}, {144, 346, 41325}, {728, 12526, 21872}, {1759, 4006, 5687}, {3930, 5282, 55}, {5279, 41228, 5781}, {5904, 17744, 218}, {6666, 38186, 47355}, {16503, 42871, 16884}
X(50996) lies on these lines: {2, 210}, {7, 594}, {9, 1992}, {69, 527}, {141, 5936}, {144, 11160}, {390, 28538}, {524, 6172}, {528, 50079}, {542, 5759}, {597, 18230}, {673, 9041}, {2550, 29615}, {3619, 38093}, {3929, 39273}, {4078, 5223}, {4663, 29624}, {5220, 17316}, {5698, 6542}, {5817, 20423}, {5845, 15533}, {5846, 50839}, {5847, 50836}, {6173, 21356}, {6600, 16436}, {11178, 38073}, {15254, 29585}, {16496, 50114}, {17389, 47357}, {20582, 38086}, {29580, 38025}, {34379, 50834}, {36731, 39898}, {49680, 50129}
X(50996) = midpoint of X(144) and X(11160)
X(50996) = reflection of X(i) in X(j) for these {i,j}: {7, 599}, {1992, 9}
X(50997) lies on these lines: {2, 5845}, {6, 527}, {7, 597}, {9, 599}, {142, 38088}, {144, 1992}, {390, 9041}, {516, 47359}, {518, 3899}, {524, 6172}, {528, 49721}, {542, 5779}, {971, 43273}, {2550, 38087}, {3242, 47357}, {5220, 32847}, {5223, 28538}, {5476, 38143}, {5542, 38023}, {5762, 20423}, {5805, 38072}, {5817, 47354}, {5819, 35578}, {5846, 50835}, {5847, 50834}, {6173, 47352}, {9053, 50839}, {10168, 38065}, {10541, 43177}, {18230, 20582}, {21358, 47595}, {31657, 38064}, {34379, 50837}, {38093, 47355}
X(50997) = midpoint of X(144) and X(1992)
X(50997) = reflection of X(i) in X(j) for these {i,j}: {7, 597}, {599, 9}, {3242, 47357}
X(50997) = {X(7),X(597)}-harmonic conjugate of X(38086)
X(50998) lies on these lines: {1, 597}, {2, 9053}, {8, 20582}, {141, 519}, {145, 599}, {518, 3898}, {524, 3241}, {542, 1483}, {545, 50130}, {551, 48310}, {742, 50778}, {952, 47354}, {1350, 34631}, {1352, 34748}, {1992, 3623}, {3244, 28538}, {3416, 34747}, {3589, 38314}, {3616, 38087}, {3629, 16496}, {3630, 49681}, {3631, 49679}, {3654, 21167}, {3655, 44882}, {3844, 34641}, {4141, 4884}, {4364, 49771}, {4665, 36534}, {4864, 29574}, {5648, 50923}, {5846, 22165}, {6703, 30614}, {7174, 49737}, {7263, 49720}, {7967, 43273}, {7977, 9884}, {10247, 20423}, {10595, 38072}, {16590, 50026}, {17133, 49467}, {17225, 49470}, {20049, 21356}, {20057, 20583}, {21358, 31145}, {25055, 49688}, {25561, 37705}, {32217, 47472}, {34573, 49690}, {37624, 38064}, {41152, 50791}, {41310, 49527}, {41311, 49466}, {47353, 50818}, {48856, 49738}, {49630, 49741}
X(50998) = midpoint of X(i) and X(j) for these {i,j}: {2, 50790}, {145, 599}, {1350, 34631}, {1352, 34748}, {3241, 3242}, {3416, 34747}, {5648, 50923}, {16496, 47356}, {47353, 50818}
X(50998) = reflection of X(i) in X(j) for these {i,j}: {8, 20582}, {597, 1}, {3629, 47356}, {22165, 47358}, {32217, 47472}, {34641, 3844}, {37705, 25561}, {44882, 3655}, {48845, 48820}, {49524, 551}
X(50998) = {X(551),X(49524)}-harmonic conjugate of X(48310)
X(50999) lies on these lines: {1, 1992}, {2, 210}, {6, 38314}, {7, 49720}, {8, 599}, {30, 39898}, {69, 519}, {141, 28635}, {145, 4741}, {193, 17488}, {344, 49448}, {345, 4141}, {346, 49501}, {524, 3241}, {537, 50107}, {542, 944}, {551, 3751}, {597, 3616}, {1350, 34632}, {1352, 34627}, {1386, 5032}, {2796, 49458}, {2895, 30614}, {3416, 31145}, {3476, 17950}, {3618, 25055}, {3619, 19875}, {3620, 49688}, {3622, 4663}, {3624, 38089}, {3630, 49679}, {3631, 49690}, {3654, 10519}, {3655, 6776}, {3679, 21356}, {3828, 49536}, {3877, 9004}, {3886, 17132}, {4310, 37756}, {4644, 36534}, {4669, 50787}, {4677, 50781}, {4684, 29573}, {4702, 20073}, {4715, 50130}, {4912, 24280}, {5263, 35578}, {5603, 20423}, {5731, 43273}, {5734, 11477}, {5846, 15533}, {5848, 10031}, {5901, 14848}, {7174, 29574}, {7426, 47477}, {8584, 38315}, {9053, 22165}, {9780, 20582}, {9881, 9941}, {10404, 50429}, {11008, 49684}, {11178, 38074}, {11180, 28204}, {11898, 34748}, {12329, 13587}, {12513, 25906}, {14927, 34628}, {16973, 37654}, {17133, 49446}, {17227, 49714}, {17257, 42871}, {17271, 48849}, {17321, 48830}, {17333, 47357}, {17378, 48856}, {17549, 22769}, {20015, 33068}, {20080, 49681}, {21358, 49524}, {27549, 41310}, {28503, 50079}, {31144, 39581}, {31178, 48802}, {32220, 47472}, {34718, 48876}, {41152, 50785}, {41312, 49478}, {41313, 49515}, {47353, 50864}, {48809, 49479}, {49495, 50109}, {49675, 50296}, {50282, 50285}
X(50999) = midpoint of X(i) and X(j) for these {i,j}: {145, 11160}, {11898, 34748}, {15533, 50790}
X(50999) = reflection of X(i) in X(j) for these {i,j}: {2, 47358}, {8, 599}, {193, 47356}, {1992, 1}, {3241, 3242}, {3679, 49511}, {3751, 551}, {4669, 50787}, {4677, 50781}, {6776, 3655}, {7426, 47477}, {14927, 34628}, {31145, 3416}, {32220, 47472}, {34627, 1352}, {34632, 1350}, {34718, 48876}, {47356, 49465}, {48798, 48834}, {49495, 50109}, {49536, 3828}, {50107, 50316}, {50282, 50285}, {50783, 22165}, {50864, 47353}
X(50999) = anticomplement of X(47359)
X(50999) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3679, 49511, 21356}, {16496, 49505, 69}, {20582, 38087, 9780}
X(51000) lies on these lines: {1, 599}, {2, 5846}, {6, 519}, {8, 597}, {10, 38023}, {31, 4141}, {141, 38314}, {145, 190}, {182, 34718}, {355, 38072}, {517, 43273}, {518, 3899}, {524, 3241}, {528, 50120}, {542, 1482}, {551, 3416}, {752, 49747}, {952, 20423}, {1279, 29573}, {1350, 3655}, {1351, 34748}, {1386, 3679}, {2550, 38086}, {2796, 49453}, {3036, 38090}, {3616, 20582}, {3623, 11160}, {3626, 38089}, {3633, 4663}, {3654, 5085}, {3656, 47353}, {3751, 34747}, {3763, 25055}, {3883, 41312}, {3886, 28329}, {4252, 50589}, {4265, 11194}, {4307, 49727}, {4361, 49720}, {4363, 50015}, {4421, 5096}, {4669, 38047}, {4677, 16475}, {4745, 38049}, {4912, 49446}, {5032, 20049}, {5476, 38144}, {5480, 34627}, {5603, 47354}, {5690, 38064}, {5847, 15533}, {5853, 49543}, {5969, 7976}, {6144, 16496}, {6776, 34631}, {7290, 41310}, {7983, 9830}, {8584, 9053}, {8593, 50888}, {9024, 10031}, {10168, 38066}, {10222, 15069}, {10541, 11362}, {11477, 37727}, {12645, 14848}, {16491, 19875}, {16777, 49740}, {16884, 48830}, {16972, 50082}, {17119, 50017}, {17225, 24349}, {17301, 49630}, {17318, 49709}, {17330, 48856}, {17389, 49706}, {18493, 25561}, {20045, 31179}, {20050, 20583}, {22165, 50791}, {24393, 38088}, {28198, 48905}, {28208, 48910}, {28503, 49721}, {28558, 49455}, {28562, 32921}, {29815, 31143}, {31139, 50301}, {31145, 49524}, {31162, 36990}, {32113, 47472}, {34628, 48872}, {34632, 44882}, {37756, 50289}, {38029, 50821}, {38035, 50796}, {38116, 50823}, {38118, 50827}, {38146, 50801}, {40341, 49465}, {41313, 49476}, {41720, 50923}, {47276, 47491}, {47277, 47535}, {47280, 47489}, {47357, 50113}, {47450, 47495}, {47453, 47496}, {47455, 47488}, {47457, 47494}, {47458, 47490}, {47459, 47531}, {47460, 47533}, {47464, 47536}, {47466, 47537}, {48798, 48845}, {48820, 48834}, {49484, 50089}, {50075, 50779}
X(51000) = midpoint of X(i) and X(j) for these {i,j}: {145, 1992}, {1351, 34748}, {3751, 34747}, {6776, 34631}, {8593, 50888}, {15534, 50790}, {41720, 50923}, {47277, 47535}, {47356, 49681}
X(51000) = reflection of X(i) in X(j) for these {i,j}: {6, 47356}, {8, 597}, {599, 1}, {1350, 3655}, {3242, 3241}, {3416, 551}, {3679, 1386}, {15533, 47358}, {17281, 50294}, {31145, 49524}, {32113, 47472}, {34627, 5480}, {34632, 44882}, {34718, 182}, {36990, 31162}, {47353, 3656}, {47356, 49684}, {47494, 47457}, {48798, 48845}, {48804, 48867}, {48834, 48820}, {48862, 48824}, {48872, 34628}, {49721, 50303}, {50075, 50779}, {50087, 48805}, {50089, 49484}, {50783, 2}, {50789, 4669}, {50798, 5476}
X(51000) = crossdifference of every pair of points on line {2515, 9002}
X(51000) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 49679, 49690}, {6, 49681, 49679}, {8, 597, 38087}, {551, 3416, 21358}, {1386, 3679, 47352}, {5476, 50798, 38144}, {38047, 50789, 4669}, {38315, 50783, 2}, {49681, 49684, 6}
X(50101 lies on these lines: {1, 11160}, {2, 5847}, {8, 1992}, {69, 38314}, {193, 519}, {518, 50839}, {524, 3241}, {542, 962}, {597, 9780}, {599, 3616}, {752, 50129}, {1351, 34627}, {1353, 34718}, {1386, 21356}, {3620, 25055}, {3654, 14912}, {3679, 5032}, {3751, 31145}, {3839, 39885}, {4141, 33088}, {4307, 29617}, {4933, 35261}, {5550, 38023}, {5698, 50121}, {5818, 14848}, {5839, 49720}, {5846, 15534}, {5921, 31162}, {6776, 34632}, {8584, 50783}, {9041, 20050}, {9778, 43273}, {9779, 47354}, {9884, 14645}, {10304, 39870}, {11008, 49681}, {16834, 49630}, {17133, 24280}, {20080, 49684}, {20583, 38087}, {22165, 38315}, {28198, 39874}, {38089, 46933}, {47357, 50132}, {48856, 50074}, {50079, 50303}, {50284, 50296}
X(51001) = reflection of X(i) in X(j) for these {i,j}: {8, 1992}, {69, 47356}, {5921, 31162}, {11160, 1}, {31145, 3751}, {34627, 1351}, {34632, 6776}, {34718, 1353}, {50079, 50303}, {50783, 8584}
X(51001) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 47356, 38314}, {16475, 50781, 2}
X(51002) lies on these lines: {2, 210}, {6, 527}, {7, 1992}, {9, 597}, {141, 38093}, {142, 599}, {239, 5880}, {516, 43273}, {524, 6173}, {528, 16834}, {542, 5805}, {971, 20423}, {1001, 38023}, {1386, 47357}, {2550, 28538}, {3243, 4929}, {3416, 50095}, {4384, 25557}, {4663, 5222}, {5220, 17023}, {5476, 38145}, {5698, 17014}, {5735, 8550}, {5779, 14848}, {5845, 8584}, {5853, 49543}, {6172, 17320}, {6600, 21539}, {10168, 38067}, {11180, 38073}, {11477, 43177}, {15254, 26626}, {16475, 50836}, {16973, 17392}, {17294, 49688}, {17389, 32029}, {20195, 20582}, {24393, 38087}, {24599, 30340}, {29574, 42871}, {31658, 38064}, {36404, 49742}, {38143, 47353}, {38150, 47354}, {38185, 50783}, {38187, 50781}, {49681, 50129}
X(51002) = midpoint of X(7) and X(1992)
X(51002) = reflection of X(i) in X(j) for these {i,j}: {9, 597}, {599, 142}, {47357, 1386}, {47595, 6173}
X(51002) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 597, 38088}, {599, 38086, 142}
X(51003) lies on these lines: {1, 599}, {2, 210}, {6, 16590}, {8, 48639}, {10, 9041}, {38, 4141}, {44, 29660}, {69, 38314}, {141, 519}, {392, 2836}, {515, 47354}, {524, 551}, {527, 48810}, {528, 49630}, {536, 50285}, {537, 17359}, {542, 1385}, {597, 1125}, {742, 50111}, {984, 41310}, {1211, 4906}, {1279, 50296}, {1350, 31162}, {1352, 3655}, {1469, 4870}, {1698, 38087}, {1992, 3616}, {2796, 49484}, {3098, 28198}, {3241, 3416}, {3242, 3679}, {3246, 4643}, {3524, 39898}, {3576, 43273}, {3589, 19883}, {3619, 49688}, {3620, 49681}, {3622, 11160}, {3631, 49684}, {3653, 11179}, {3662, 49720}, {3663, 49485}, {3696, 37756}, {3706, 50102}, {3739, 48809}, {3751, 47352}, {3763, 16496}, {3818, 28208}, {3821, 49467}, {3828, 49524}, {3834, 36480}, {3923, 4912}, {3993, 17225}, {4003, 33175}, {4026, 15570}, {4353, 17133}, {4357, 42819}, {4364, 49768}, {4389, 4702}, {4641, 29686}, {4657, 48830}, {4669, 9053}, {4677, 50790}, {4690, 50023}, {4708, 24331}, {4715, 50300}, {4864, 32784}, {4933, 46901}, {4966, 29574}, {5846, 50781}, {5847, 22165}, {5886, 20423}, {5969, 12258}, {7191, 31143}, {8227, 38072}, {8584, 34379}, {9624, 11477}, {9830, 11711}, {10222, 40107}, {11178, 28204}, {12329, 16417}, {15178, 34507}, {15254, 50093}, {15533, 38315}, {15534, 16475}, {15569, 41312}, {15808, 20583}, {16418, 22769}, {16491, 40341}, {16823, 31144}, {17227, 36534}, {17229, 49455}, {17235, 32941}, {17274, 28534}, {17280, 49513}, {17292, 24841}, {17301, 50316}, {17302, 49475}, {17304, 49460}, {17306, 42871}, {17313, 48854}, {17345, 28558}, {17348, 50309}, {17356, 49457}, {17357, 49448}, {17358, 49501}, {17384, 49490}, {17385, 49479}, {17395, 49763}, {18480, 25561}, {19862, 38089}, {19868, 25557}, {21342, 32783}, {24231, 49727}, {24476, 31165}, {25539, 49498}, {26150, 49450}, {27777, 29827}, {28329, 32921}, {28503, 29594}, {28562, 49473}, {28580, 49741}, {29615, 32922}, {29637, 49515}, {31136, 50103}, {31138, 50301}, {31178, 49509}, {34573, 49529}, {34627, 40330}, {34628, 36990}, {42055, 50052}, {42057, 50063}, {44663, 48803}, {47097, 47477}, {47353, 50811}, {47357, 47595}, {47473, 47593}, {48818, 48862}, {48824, 48834}, {49453, 50089}, {49463, 49560}, {49676, 50299}, {49747, 50126}
X(51003) = midpoint of X(i) and X(j) for these {i,j}: {1, 599}, {2, 47358}, {69, 47356}, {551, 49511}, {1350, 31162}, {1352, 3655}, {3241, 3416}, {3242, 3679}, {4677, 50790}, {5648, 50921}, {17274, 48805}, {17301, 50316}, {24476, 31165}, {31178, 49509}, {34628, 36990}, {47097, 47477}, {47353, 50811}, {47357, 47595}, {47473, 47593}, {48818, 48862}, {48824, 48834}, {49453, 50089}, {49463, 50084}, {49747, 50126}, {50285, 50311}
X(51003) = reflection of X(i) in X(j) for these {i,j}: {10, 20582}, {597, 1125}, {1386, 551}, {3679, 3844}, {4663, 597}, {18480, 25561}, {22165, 50787}, {49524, 3828}, {50084, 49560}
X(51003) = complement of X(47359)
X(51003) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 38314, 47356}, {1992, 3616, 38023}, {3241, 21356, 3416}, {3242, 21358, 3679}, {3679, 21358, 3844}, {38315, 50791, 15533}
X(51004) lies on these lines: {1, 11160}, {2, 34379}, {6, 19883}, {10, 599}, {69, 519}, {142, 50309}, {193, 25055}, {306, 4141}, {518, 3919}, {524, 551}, {542, 4297}, {597, 19862}, {1125, 1992}, {1350, 34638}, {1352, 34648}, {2796, 50639}, {3244, 28538}, {3416, 34641}, {3620, 19875}, {3625, 9041}, {3630, 49684}, {3631, 38098}, {3655, 11898}, {3664, 48809}, {3679, 49536}, {3751, 3828}, {3817, 20423}, {4133, 17132}, {4134, 9004}, {4663, 20582}, {4677, 50786}, {4684, 50296}, {4741, 49763}, {4745, 50788}, {5847, 15533}, {5921, 34628}, {8584, 38049}, {10304, 39878}, {11178, 38076}, {12258, 14645}, {15534, 50791}, {15808, 38023}, {17271, 48853}, {17272, 48830}, {17344, 49740}, {17361, 49720}, {20080, 38314}, {24231, 29617}, {28558, 50315}, {31144, 39580}, {38047, 50792}, {38191, 41152}, {40341, 47356}, {47353, 50862}, {49560, 50118}
X(51004) = midpoint of X(i) and X(j) for these {i,j}: {1, 11160}, {3655, 11898}, {5921, 34628}, {15533, 47358}, {40341, 47356}
X(51004) = reflection of X(i) in X(j) for these {i,j}: {2, 50787}, {10, 599}, {551, 49511}, {1992, 1125}, {3751, 3828}, {4663, 20582}, {4669, 50781}, {4677, 50786}, {4745, 50788}, {34638, 1350}, {34641, 3416}, {34648, 1352}, {49536, 3679}, {50118, 49560}, {50781, 22165}, {50862, 47353}
X(51004) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3751, 21356, 3828}, {4663, 20582, 38089}
X(51005) lies on these lines: {1, 1992}, {2, 5847}, {6, 519}, {10, 597}, {30, 39870}, {69, 25055}, {141, 19883}, {193, 16491}, {238, 29574}, {355, 14848}, {515, 20423}, {516, 43273}, {518, 3898}, {524, 551}, {528, 50124}, {542, 946}, {575, 11362}, {576, 5882}, {599, 1125}, {740, 49543}, {752, 49630}, {1100, 49740}, {1351, 3655}, {1449, 48830}, {2308, 4141}, {2796, 49477}, {3011, 31179}, {3241, 3751}, {3244, 4432}, {3416, 3828}, {3545, 39885}, {3616, 11160}, {3618, 19875}, {3626, 38087}, {3629, 49505}, {3654, 5050}, {3663, 28558}, {3686, 48809}, {3755, 4991}, {3758, 50017}, {3759, 49720}, {3817, 47354}, {3844, 48310}, {3892, 9004}, {3923, 17133}, {4029, 4759}, {4078, 16468}, {4133, 28329}, {4301, 8550}, {4349, 4974}, {4363, 50020}, {4667, 50023}, {4669, 5846}, {4672, 50118}, {4676, 50121}, {4700, 36480}, {4725, 48810}, {4745, 38047}, {4870, 39897}, {4933, 35263}, {5182, 9881}, {5476, 38146}, {5480, 34648}, {6329, 38098}, {6684, 38064}, {6702, 38090}, {6776, 31162}, {8593, 50886}, {9830, 11599}, {9956, 38079}, {10168, 38068}, {11161, 38220}, {11179, 28194}, {11180, 38021}, {11194, 37492}, {11482, 37727}, {15533, 50787}, {15534, 34379}, {16469, 29573}, {16477, 49476}, {16834, 28580}, {17132, 32921}, {17225, 50117}, {19862, 20582}, {19925, 38072}, {21850, 28208}, {23536, 50234}, {25555, 31399}, {28198, 48906}, {28534, 50112}, {28542, 50108}, {31178, 49496}, {32455, 49465}, {34638, 44882}, {34641, 49524}, {37654, 48854}, {37756, 50307}, {38029, 50828}, {38035, 47353}, {38116, 50827}, {38118, 50821}, {38144, 50801}, {41011, 50102}, {41140, 50301}, {41720, 50921}, {46922, 50305}, {47277, 47472}, {47456, 47562}, {47457, 47496}, {47459, 47488}, {47460, 47492}, {47461, 47494}, {47462, 47489}, {47463, 47493}, {47464, 47491}, {47541, 47593}, {50126, 50129}, {50290, 50296}
X(51005) = midpoint of X(i) and X(j) for these {i,j}: {1, 1992}, {6, 47356}, {1351, 3655}, {3241, 3751}, {6776, 31162}, {8593, 50886}, {15534, 47358}, {16834, 50303}, {31178, 49496}, {41720, 50921}, {47277, 47472}, {47541, 47593}, {48805, 50131}, {50126, 50129}
X(51005) = reflection of X(i) in X(j) for these {i,j}: {10, 597}, {551, 1386}, {599, 1125}, {3416, 3828}, {4663, 20583}, {15533, 50787}, {34638, 44882}, {34641, 49524}, {34648, 5480}, {38049, 16475}, {47353, 50802}, {47496, 47457}, {49511, 551}, {49684, 47356}, {50091, 50114}, {50109, 49477}, {50118, 4672}, {50777, 50779}, {50781, 2}, {50783, 4745}, {50796, 5476}
X(51005) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 49684, 49529}, {10, 597, 38089}, {599, 38023, 1125}, {3241, 5032, 3751}, {3416, 47352, 3828}, {5476, 50796, 38146}, {15534, 38315, 47358}, {38035, 47353, 50802}, {38047, 50783, 4745}, {38049, 50781, 2}
X(51006) lies on these lines: {1, 597}, {2, 5846}, {6, 38314}, {141, 16491}, {145, 38087}, {238, 49737}, {390, 38086}, {518, 4532}, {519, 3589}, {524, 551}, {542, 5901}, {545, 50300}, {599, 3616}, {944, 38072}, {1125, 20582}, {1317, 38090}, {1482, 38064}, {1483, 38079}, {1992, 3622}, {3241, 47352}, {3243, 38088}, {3244, 38089}, {3636, 20583}, {3655, 5480}, {3656, 38029}, {3679, 48310}, {4141, 29819}, {4353, 4912}, {4472, 50023}, {4971, 48810}, {5476, 38040}, {5603, 43273}, {5734, 10541}, {5847, 50788}, {5886, 47354}, {6034, 9884}, {6082, 9097}, {6329, 49465}, {7290, 41312}, {8584, 16475}, {8705, 47495}, {9053, 38049}, {9055, 50111}, {9830, 11725}, {10246, 20423}, {11178, 38022}, {12258, 12264}, {14848, 37624}, {17045, 49740}, {17225, 24325}, {17366, 49720}, {17382, 49630}, {18357, 25565}, {19875, 49681}, {19883, 34573}, {22165, 50792}, {28333, 50285}, {28337, 50311}, {29831, 31179}, {31162, 44882}, {34379, 41149}, {37734, 38091}, {38035, 50811}, {38046, 50836}, {38050, 50843}, {38116, 50805}, {38144, 50818}, {38165, 50831}, {38185, 50839}, {38192, 50846}, {47544, 47593}, {48805, 50112}, {48820, 48867}, {48824, 48845}, {49463, 50118}, {49484, 50109}, {49741, 50303}
X(51006) = midpoint of X(i) and X(j) for these {i,j}: {1, 597}, {141, 47356}, {551, 1386}, {3241, 49524}, {3655, 5480}, {5476, 50824}, {8584, 47358}, {17382, 50294}, {31162, 44882}, {47544, 47593}, {48805, 50112}, {48820, 48867}, {48824, 48845}, {49463, 50118}, {49484, 50109}, {49741, 50303}
X(51006) = reflection of X(i) in X(j) for these {i,j}: {18357, 25565}, {20582, 1125}
X(51006) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 38023, 597}, {3241, 47352, 49524}, {16475, 47358, 8584}, {16491, 25055, 47356}, {25055, 47356, 141}, {38040, 50824, 5476}
X(51007) lies on these lines: {2, 10755}, {5, 38147}, {6, 3035}, {10, 38192}, {11, 141}, {69, 100}, {104, 10519}, {119, 511}, {140, 38119}, {142, 38188}, {149, 3620}, {182, 38760}, {214, 5847}, {518, 1145}, {524, 6174}, {528, 599}, {576, 38763}, {900, 4437}, {952, 3416}, {1125, 38050}, {1176, 3045}, {1317, 5846}, {1332, 40560}, {1350, 2829}, {1351, 38752}, {1352, 5840}, {1386, 34123}, {1469, 10956}, {1503, 24466}, {1768, 5227}, {1862, 41584}, {2787, 50567}, {2802, 49511}, {3098, 38761}, {3242, 5854}, {3564, 33814}, {3589, 31235}, {3619, 31272}, {3628, 38168}, {3631, 6154}, {3634, 38197}, {3763, 6667}, {3844, 34122}, {4553, 26932}, {4585, 26231}, {4996, 5849}, {5050, 38762}, {5181, 8674}, {5845, 6068}, {5856, 47595}, {6393, 38643}, {6666, 38195}, {6668, 38199}, {6776, 34474}, {9037, 17757}, {9041, 50842}, {10707, 21356}, {10742, 33878}, {10993, 34507}, {11477, 20400}, {12119, 39885}, {12735, 49681}, {12831, 34377}, {18358, 22938}, {21358, 45310}, {23513, 24206}, {25416, 49465}, {28538, 50843}, {31884, 38759}, {35023, 40341}, {37726, 40107}
X(51007) = midpoint of X(i) and X(j) for these {i,j}: {69, 100}, {10742, 33878}, {12119, 39885}
X(51007) = reflection of X(i) in X(j) for these {i,j}: {6, 3035}, {11, 141}, {22938, 18358}, {25416, 49465}, {38761, 3098}, {49681, 12735}
X(51007) = complement of X(10755)
X(51008) lies on these lines: {2, 5848}, {6, 528}, {11, 597}, {100, 1992}, {119, 542}, {376, 10759}, {518, 50843}, {524, 6174}, {575, 37726}, {576, 10993}, {599, 3035}, {952, 47359}, {1145, 28538}, {1317, 9041}, {1387, 38023}, {2787, 18800}, {2829, 43273}, {3036, 38087}, {4663, 10609}, {5032, 10755}, {5182, 13194}, {5476, 38147}, {5840, 20423}, {5846, 50842}, {5847, 50841}, {6154, 8539}, {6702, 38089}, {6713, 38064}, {6776, 10711}, {8068, 38091}, {8550, 37725}, {8584, 9024}, {8674, 15303}, {9053, 50846}, {10168, 38069}, {10738, 14848}, {15069, 20400}, {16475, 50891}, {16792, 38060}, {20582, 31235}, {34379, 50844}, {34507, 38763}, {45310, 47352}
X(51008) = midpoint of X(i) and X(j) for these {i,j}: {100, 1992}, {376, 10759}, {6776, 10711}
X(51008) = reflection of X(i) in X(j) for these {i,j}: {11, 597}, {599, 3035}
X(51008) = {X(11),X(597)}-harmonic conjugate of X(38090)
X(51009) lies on these lines: {2, 38091}, {5, 38148}, {6, 4999}, {10, 38193}, {12, 141}, {69, 2975}, {140, 38120}, {142, 38189}, {511, 26470}, {518, 10039}, {524, 31157}, {529, 599}, {758, 24476}, {952, 3416}, {1125, 38051}, {1350, 5842}, {1352, 5841}, {1503, 30264}, {3056, 10959}, {3242, 5855}, {3589, 31260}, {3620, 20060}, {3628, 38169}, {3634, 38198}, {3763, 6668}, {3844, 38058}, {4996, 5848}, {5227, 6763}, {5846, 37734}, {5857, 47595}, {6666, 38196}, {6667, 38199}, {9047, 24390}, {10519, 11491}, {24206, 38109}
X(51009) = midpoint of X(69) and X(2975)
X(51009) = reflection of X(i) in X(j) for these {i,j}: {6, 4999}, {12, 141}
X(51010) lies on these lines: {2, 16941}, {6, 618}, {13, 141}, {14, 5969}, {15, 524}, {32, 9115}, {69, 74}, {298, 511}, {299, 5980}, {302, 5476}, {396, 41751}, {518, 12781}, {530, 599}, {532, 22687}, {576, 627}, {619, 6582}, {621, 19924}, {622, 11178}, {634, 40107}, {1350, 41022}, {1352, 44463}, {1469, 12942}, {1503, 5473}, {3056, 12952}, {3094, 3643}, {3589, 36770}, {3630, 42929}, {3763, 6669}, {5092, 30471}, {5459, 21358}, {5478, 10516}, {5480, 36765}, {5846, 7975}, {5858, 6782}, {5965, 14145}, {6034, 6670}, {6770, 10519}, {8368, 42913}, {8584, 36767}, {9041, 50848}, {9116, 9830}, {9916, 37485}, {9989, 34507}, {11307, 44512}, {12205, 42534}, {12588, 18974}, {12589, 13076}, {14538, 36776}, {15533, 36769}, {15534, 36768}, {19130, 40707}, {19662, 31695}, {20194, 41409}, {20582, 22489}, {21360, 46054}, {22165, 35751}, {22796, 31670}, {23005, 35697}, {23024, 25183}, {28538, 50849}, {29181, 36961}, {31694, 42035}, {33878, 48655}, {36757, 36782}
X(51010) = midpoint of X(i) and X(j) for these {i,j}: {69, 616}, {33878, 48655}
X(51010) = reflection of X(i) in X(j) for these {i,j}: {6, 618}, {13, 141}, {6772, 3643}, {22513, 3642}, {22580, 2}, {23024, 25183}, {25154, 11178}, {31670, 22796}, {31695, 19662}, {41745, 22687}
X(51010) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {298, 5979, 5617}, {5463, 36775, 35304}
X(51011) lies on these lines: {2, 14136}, {6, 36764}, {13, 599}, {15, 524}, {69, 530}, {141, 22489}, {298, 9762}, {511, 22493}, {518, 50848}, {531, 50639}, {532, 12155}, {542, 1350}, {597, 36770}, {616, 11160}, {618, 1992}, {622, 22576}, {1384, 9115}, {3619, 48311}, {5459, 21356}, {5460, 10754}, {5464, 50567}, {5470, 19662}, {5847, 50849}, {5858, 14645}, {5969, 35693}, {7615, 42035}, {7975, 28538}, {11129, 35932}, {11295, 22906}, {11646, 22577}, {15534, 36386}, {20423, 36765}, {21358, 42132}, {22165, 35752}, {34379, 50847}
X(51011) = midpoint of X(616) and X(11160)
X(51011) = reflection of X(i) in X(j) for these {i,j}: {13, 599}, {1992, 618}, {5464, 50567}, {10754, 5460}, {22577, 11646}, {22580, 141}
X(51011) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {141, 22580, 22489}, {9114, 35751, 5473}
X(51012) lies on these lines: {2, 98}, {6, 530}, {13, 597}, {14, 9830}, {15, 524}, {30, 12155}, {381, 40671}, {396, 9762}, {511, 8595}, {518, 50849}, {531, 22687}, {543, 10654}, {574, 9115}, {575, 11304}, {599, 618}, {616, 1992}, {1503, 31693}, {2782, 12154}, {3589, 22489}, {5026, 5464}, {5321, 22576}, {5334, 31696}, {5459, 42098}, {5460, 11646}, {5472, 22492}, {5476, 25154}, {5478, 38072}, {5846, 50848}, {5847, 50847}, {5969, 9116}, {5979, 37786}, {5980, 37785}, {6777, 50855}, {6782, 9761}, {7606, 46053}, {7841, 44514}, {7975, 9041}, {8546, 13859}, {8550, 37340}, {8584, 35751}, {8594, 35917}, {11146, 32599}, {11296, 41022}, {11632, 40672}, {11705, 38023}, {12781, 28538}, {13103, 14848}, {14645, 42511}, {15533, 36768}, {15534, 36769}, {18581, 33477}, {20252, 38079}, {20429, 44506}, {20582, 36770}, {22165, 36388}, {22490, 46054}, {22495, 36757}, {22574, 42975}, {32553, 45879}, {32907, 37171}, {35690, 49827}, {35691, 49876}, {35697, 41108}, {36765, 47354}, {37341, 41020}, {41751, 43229}, {41752, 43228}, {47355, 48311}
X(51012) = midpoint of X(616) and X(1992)
X(51012) = reflection of X(i) in X(j) for these {i,j}: {13, 597}, {599, 618}, {5464, 5026}, {11646, 5460}, {19905, 6774}, {22580, 6}, {25154, 5476}
X(51012) = {X(15),X(5463)}-harmonic conjugate of X(9885)
X(51013) lies on these lines: {2, 16940}, {6, 619}, {13, 5969}, {14, 141}, {16, 524}, {32, 9117}, {69, 74}, {298, 5981}, {299, 383}, {303, 5476}, {395, 41753}, {487, 35748}, {518, 12780}, {531, 599}, {533, 22689}, {576, 628}, {618, 6295}, {621, 11178}, {622, 19924}, {633, 40107}, {1350, 41023}, {1352, 44459}, {1469, 12941}, {1503, 5474}, {3056, 12951}, {3094, 3642}, {3589, 41943}, {3630, 42928}, {3763, 6670}, {5092, 30472}, {5460, 21358}, {5479, 10516}, {5846, 7974}, {5859, 6783}, {5965, 14144}, {6034, 6669}, {6773, 10519}, {8368, 42912}, {9041, 50851}, {9114, 9830}, {9915, 37485}, {9988, 34507}, {11308, 44511}, {12204, 42534}, {12588, 18975}, {12589, 13075}, {15533, 47867}, {19130, 40706}, {19662, 31696}, {20194, 41408}, {20582, 22490}, {21359, 46053}, {22165, 36329}, {22797, 31670}, {23004, 35693}, {23018, 25187}, {28538, 50852}, {29181, 36962}, {31693, 42036}, {33878, 48656}
X(51013) = midpoint of X(i) and X(j) for these {i,j}: {69, 617}, {33878, 48656}
X(51013) = reflection of X(i) in X(j) for these {i,j}: {6, 619}, {14, 141}, {6775, 3642}, {22512, 3643}, {22579, 2}, {23018, 25187}, {25164, 11178}, {31670, 22797}, {31696, 19662}, {41746, 22689}
X(51013) = {X(299),X(5978)}-harmonic conjugate of X(5613)
X(51014) lies on these lines: {2, 14137}, {14, 599}, {16, 524}, {69, 531}, {141, 22490}, {299, 9760}, {487, 35686}, {511, 22494}, {518, 50851}, {530, 50639}, {533, 12154}, {542, 1350}, {617, 11160}, {619, 1992}, {621, 22575}, {1384, 9117}, {3619, 48312}, {5459, 10754}, {5460, 21356}, {5463, 50567}, {5469, 19662}, {5847, 50852}, {5859, 14645}, {5969, 35697}, {7615, 42036}, {7974, 28538}, {11128, 35931}, {11296, 22862}, {11646, 22578}, {15534, 36388}, {21358, 42129}, {22165, 36330}, {34379, 50850}
X(51014) = midpoint of X(617) and X(11160)
X(51014) = reflection of X(i) in X(j) for these {i,j}: {14, 599}, {1992, 619}, {5463, 50567}, {10754, 5459}, {22578, 11646}, {22579, 141}
X(51014) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {141, 22579, 22490}, {9116, 36329, 5474}
X(51015) lies on these lines: {2, 98}, {6, 531}, {13, 9830}, {14, 597}, {16, 524}, {30, 12154}, {381, 40672}, {395, 9760}, {511, 8594}, {518, 50852}, {530, 22689}, {543, 10653}, {574, 9117}, {575, 11303}, {599, 619}, {617, 1992}, {1152, 35686}, {1503, 31694}, {2782, 12155}, {3589, 22490}, {5026, 5463}, {5318, 22575}, {5335, 31695}, {5459, 11646}, {5460, 42095}, {5471, 22491}, {5476, 25164}, {5479, 38072}, {5846, 50851}, {5847, 50850}, {5969, 9114}, {5978, 37785}, {5981, 37786}, {6778, 50858}, {6783, 9763}, {7606, 46054}, {7841, 44513}, {7974, 9041}, {8546, 13858}, {8550, 37341}, {8584, 36329}, {8595, 35918}, {11145, 32599}, {11295, 41023}, {11632, 40671}, {11706, 38023}, {12780, 28538}, {13102, 14848}, {14645, 42510}, {15534, 47867}, {18582, 33476}, {20253, 38079}, {20428, 44505}, {22165, 36386}, {22489, 46053}, {22496, 36758}, {22573, 42974}, {32552, 45880}, {32909, 37170}, {35693, 41107}, {35694, 49826}, {35695, 49875}, {37340, 41021}, {41753, 43228}, {41754, 43229}, {47355, 48312}
X(51015) = midpoint of X(617) and X(1992)
X(51015) = reflection of X(i) in X(j) for these {i,j}: {14, 597}, {599, 619}, {5463, 5026}, {11646, 5459}, {19905, 6771}, {22579, 6}, {25164, 5476}
X(51015) = {X(16),X(5464)}-harmonic conjugate of X(9886)
X(51016) lies on these lines: {4, 69}, {6, 623}, {13, 524}, {15, 141}, {18, 3589}, {182, 302}, {183, 5613}, {193, 42982}, {298, 542}, {299, 11178}, {303, 24206}, {325, 5617}, {518, 50853}, {531, 599}, {616, 11645}, {625, 18581}, {698, 25199}, {732, 23000}, {1350, 44666}, {1503, 14538}, {1691, 6672}, {2030, 11489}, {3098, 9988}, {3416, 44659}, {3618, 42987}, {3620, 43243}, {3629, 42779}, {3631, 42630}, {3763, 6671}, {5031, 40335}, {5872, 14880}, {5965, 44488}, {5969, 23004}, {5989, 22507}, {7684, 10516}, {7773, 16626}, {7797, 22114}, {7805, 40693}, {7834, 40694}, {8360, 11543}, {10519, 36993}, {11133, 12215}, {21358, 45879}, {22491, 31173}, {22736, 24273}, {28538, 50854}, {29181, 36992}, {34573, 42955}, {36755, 46264}, {36759, 42534}, {37341, 41406}, {43333, 47352}
X(51016) = midpoint of X(69) and X(621)
X(51016) = reflection of X(i) in X(j) for these {i,j}: {6, 623}, {15, 141}, {193, 44498}, {22580, 31693}, {23024, 31711}, {46264, 36755}
X(51016) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {316, 621, 20428}, {621, 5207, 3818}, {36757, 40334, 3589}
X(51017) lies on these lines: {2, 51}, {6, 531}, {13, 524}, {15, 597}, {30, 12155}, {141, 42915}, {182, 35932}, {518, 50854}, {542, 20428}, {576, 11303}, {599, 623}, {621, 1992}, {3849, 10653}, {5104, 45880}, {5459, 8586}, {5464, 42536}, {5475, 22491}, {5480, 31694}, {5611, 14848}, {5978, 37786}, {7684, 38072}, {8352, 25154}, {8594, 11300}, {8705, 34315}, {9830, 23004}, {10796, 12154}, {11305, 11477}, {11317, 25164}, {11707, 38023}, {13350, 38064}, {14538, 35304}, {19924, 35931}, {20582, 40334}, {22492, 31173}, {28538, 50853}, {32460, 47574}, {43273, 44666}, {44659, 47359}, {45879, 47352}, {47355, 48313}
X(51017) = midpoint of X(621) and X(1992)
X(51017) = reflection of X(i) in X(j) for these {i,j}: {15, 597}, {599, 623}, {1992, 44498}, {5104, 45880}
X(51018) lies on these lines: {4, 69}, {6, 624}, {14, 524}, {16, 141}, {17, 3589}, {182, 303}, {183, 5617}, {193, 42983}, {298, 11178}, {299, 542}, {302, 24206}, {325, 5613}, {518, 50856}, {530, 599}, {617, 11645}, {625, 18582}, {698, 25203}, {732, 23009}, {1350, 44667}, {1503, 14539}, {1691, 6671}, {2030, 11488}, {3098, 9989}, {3416, 44660}, {3618, 42986}, {3620, 43242}, {3629, 42780}, {3631, 42629}, {3763, 6672}, {5031, 40334}, {5873, 14880}, {5965, 44487}, {5969, 23005}, {5989, 22509}, {7685, 10516}, {7773, 16627}, {7797, 22113}, {7805, 40694}, {7834, 40693}, {8360, 11542}, {10519, 36995}, {11132, 12215}, {21358, 45880}, {22492, 31173}, {22737, 24273}, {28538, 50857}, {29181, 36994}, {34573, 42954}, {36756, 46264}, {36760, 42534}, {37340, 41407}, {43332, 47352}
X(51018) = midpoint of X(69) and X(622)
X(51018) = reflection of X(i) in X(j) for these {i,j}: {6, 624}, {16, 141}, {193, 44497}, {22579, 31694}, {23018, 31712}, {46264, 36756}
X(51018) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {316, 622, 20429}, {622, 5207, 3818}, {36758, 40335, 3589}
X(51019) lies on these lines: {2, 51}, {6, 530}, {14, 524}, {16, 597}, {30, 12154}, {141, 42914}, {182, 35931}, {518, 50857}, {542, 20429}, {576, 11304}, {599, 624}, {622, 1992}, {3849, 10654}, {5104, 45879}, {5460, 8586}, {5463, 42536}, {5475, 22492}, {5480, 31693}, {5615, 14848}, {5979, 37785}, {7685, 38072}, {8352, 25164}, {8595, 11299}, {8705, 34316}, {9830, 23005}, {10796, 12155}, {11306, 11477}, {11317, 25154}, {11708, 38023}, {13349, 38064}, {14539, 35303}, {19924, 35932}, {20582, 40335}, {22491, 31173}, {28538, 50856}, {32461, 47574}, {43273, 44667}, {44660, 47359}, {45880, 47352}, {47355, 48314}
X(51019) = midpoint of X(622) and X(1992)
X(51019) = reflection of X(i) in X(j) for these {i,j}: {16, 597}, {599, 624}, {1992, 44497}, {5104, 45879}
X(51020) lies on these lines: {6, 629}, {16, 3631}, {17, 141}, {54, 69}, {302, 5097}, {511, 16626}, {518, 22896}, {524, 41943}, {532, 599}, {542, 14144}, {1350, 44666}, {1352, 44463}, {1469, 22904}, {1503, 22890}, {3056, 22905}, {3094, 22737}, {3412, 3629}, {3620, 22113}, {3763, 6673}, {5613, 5982}, {5846, 22912}, {5969, 11602}, {6674, 38232}, {10516, 22832}, {10519, 22532}, {12588, 18973}, {12589, 22910}, {22165, 36386}, {22508, 33462}, {22523, 42534}, {22657, 37485}, {22795, 31670}, {24206, 40707}, {33878, 48666}, {40341, 43238}
X(51020) = midpoint of X(i) and X(j) for these {i,j}: {69, 627}, {33878, 48666}
X(51020) = reflection of X(i) in X(j) for these {i,j}: {6, 629}, {17, 141}, {31670, 22795}
X(51021) lies on these lines: {6, 630}, {15, 3631}, {18, 141}, {54, 69}, {303, 5097}, {511, 16627}, {518, 22851}, {524, 41944}, {533, 599}, {542, 14145}, {1350, 44667}, {1352, 44459}, {1469, 22859}, {1503, 22843}, {3056, 22860}, {3094, 22736}, {3411, 3629}, {3620, 22114}, {3763, 6674}, {5617, 5983}, {5846, 22867}, {5969, 11603}, {6673, 38232}, {10516, 22831}, {10519, 22531}, {12588, 18972}, {12589, 22865}, {22165, 36388}, {22506, 33463}, {22522, 42534}, {22656, 37485}, {22794, 31670}, {24206, 40706}, {33878, 48665}, {40341, 43239}
X(51021) = midpoint of X(i) and X(j) for these {i,j}: {69, 628}, {33878, 48665}
X(51021) = reflection of X(i) in X(j) for these {i,j}: {6, 630}, {18, 141}, {31670, 22794}
X(51022) lies on these lines: {4, 597}, {6, 43507}, {20, 20582}, {30, 141}, {182, 14893}, {381, 44882}, {511, 33699}, {518, 50862}, {524, 3543}, {542, 3627}, {547, 48898}, {549, 33751}, {550, 25561}, {599, 3146}, {1351, 35434}, {1352, 15684}, {1503, 3830}, {1597, 35707}, {1992, 17578}, {3534, 21167}, {3545, 48905}, {3589, 3839}, {3630, 11180}, {3843, 38064}, {3844, 34638}, {3845, 29012}, {3853, 8550}, {3858, 25565}, {3860, 38317}, {5085, 41099}, {5092, 38071}, {5476, 12101}, {5480, 11645}, {5691, 9041}, {5846, 50865}, {5847, 50869}, {5893, 31166}, {6247, 7540}, {7519, 44569}, {8703, 29323}, {9019, 32062}, {9053, 50864}, {9830, 39838}, {10109, 17508}, {10168, 23046}, {10304, 34573}, {10516, 11001}, {11160, 50690}, {11168, 40236}, {11179, 38335}, {11539, 48892}, {14269, 46264}, {14810, 44903}, {14927, 47352}, {15360, 34603}, {15682, 22165}, {15683, 21358}, {15686, 24206}, {16656, 34725}, {19924, 35404}, {20583, 50688}, {21356, 48872}, {30775, 41424}, {31133, 35266}, {32217, 47310}, {34200, 48896}, {34379, 50870}, {34648, 49524}, {45303, 47313}, {45759, 48891}
X(51022) = midpoint of X(i) and X(j) for these {i,j}: {599, 3146}, {1352, 15684}, {3543, 36990}, {11180, 48910}, {15682, 47353}, {35404, 39884}
X(51022) = reflection of X(i) in X(j) for these {i,j}: {20, 20582}, {182, 14893}, {549, 48889}, {550, 25561}, {597, 4}, {3630, 11180}, {5476, 12101}, {5480, 15687}, {15686, 24206}, {22165, 47353}, {31166, 5893}, {32217, 47310}, {34638, 3844}, {35404, 48942}, {44882, 381}, {44903, 14810}, {48881, 11178}, {48896, 34200}, {48898, 547}, {49524, 34648}
X(51022) = {X(381),X(44882)}-harmonic conjugate of X(48310)
X(51023) lies on these lines: {2, 154}, {4, 542}, {6, 3839}, {20, 599}, {30, 69}, {141, 10304}, {147, 9770}, {182, 5071}, {193, 50687}, {376, 1352}, {381, 6776}, {511, 11455}, {518, 50864}, {524, 3543}, {543, 50641}, {546, 14848}, {549, 40330}, {575, 3855}, {597, 3091}, {631, 18553}, {962, 28538}, {1007, 6054}, {1350, 15683}, {1351, 15687}, {1353, 14893}, {1499, 14977}, {1513, 23055}, {2393, 15305}, {2777, 13169}, {2794, 11161}, {3058, 39891}, {3090, 25561}, {3146, 11160}, {3410, 33522}, {3416, 34632}, {3523, 20582}, {3524, 3619}, {3529, 34507}, {3534, 10519}, {3544, 25565}, {3545, 3618}, {3564, 3830}, {3620, 48905}, {3751, 34648}, {3763, 15708}, {3832, 8550}, {3845, 14853}, {3851, 38079}, {3861, 11482}, {4232, 44569}, {5032, 5480}, {5050, 5066}, {5054, 18358}, {5055, 48906}, {5092, 15709}, {5182, 32984}, {5207, 14458}, {5434, 39892}, {5476, 14912}, {5622, 46261}, {5642, 30775}, {5846, 50872}, {5847, 50865}, {6000, 11188}, {6090, 47311}, {6241, 43130}, {6337, 8724}, {6792, 15638}, {7000, 13757}, {7374, 13637}, {7390, 31144}, {7426, 47474}, {7486, 10541}, {7519, 44555}, {7540, 11411}, {7735, 11177}, {7989, 38089}, {8352, 46034}, {8681, 32062}, {8721, 33215}, {9140, 26255}, {9143, 14982}, {9744, 10033}, {9862, 19905}, {9873, 12117}, {10298, 19596}, {10385, 12588}, {10991, 37809}, {11001, 29012}, {11008, 31670}, {11439, 50649}, {11442, 15360}, {11477, 17578}, {11550, 13857}, {11694, 18281}, {11898, 15684}, {12017, 15699}, {12203, 33230}, {12324, 38323}, {13851, 18919}, {14002, 16010}, {14118, 15581}, {14269, 39899}, {14561, 41106}, {14645, 36997}, {14826, 31152}, {15072, 29959}, {15533, 15640}, {15681, 48876}, {15692, 21358}, {15693, 33750}, {15697, 31884}, {15702, 24206}, {16475, 50802}, {16655, 34621}, {17538, 40107}, {18451, 22151}, {18931, 20126}, {19662, 34473}, {20080, 48910}, {20987, 37940}, {21850, 38335}, {23291, 44212}, {28194, 39885}, {28204, 39898}, {31099, 40112}, {31143, 50698}, {32220, 47310}, {33699, 34380}, {34229, 43460}, {34379, 50862}, {34628, 49511}, {34697, 39889}, {34746, 39890}, {35822, 39876}, {35823, 39875}, {36757, 41119}, {36758, 41120}, {36883, 37749}, {37182, 42850}, {37941, 44883}, {38021, 39870}, {40671, 41042}, {40672, 41043}, {40673, 46847}, {43150, 46333}
X(51023) = midpoint of X(i) and X(j) for these {i,j}: {381, 48662}, {3146, 11160}, {3543, 5921}, {11898, 15684}
X(51023) = reflection of X(i) in X(j) for these {i,j}: {2, 47353}, {20, 599}, {69, 11180}, {376, 1352}, {381, 39884}, {1351, 15687}, {1353, 14893}, {1992, 4}, {3543, 36990}, {3751, 34648}, {6776, 381}, {7426, 47474}, {9143, 14982}, {9862, 19905}, {11061, 10706}, {11160, 15069}, {11177, 11646}, {11179, 3818}, {11180, 18440}, {14927, 376}, {15072, 29959}, {15681, 48876}, {15683, 1350}, {32220, 47310}, {34628, 49511}, {34632, 3416}, {37749, 36883}, {39874, 11179}, {40673, 46847}, {43273, 47354}, {46264, 11178}
X(51023) = anticomplement of X(43273)
X(51023) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 1352, 21356}, {3524, 11178, 3619}, {3545, 11179, 3618}, {3545, 39874, 11179}, {3818, 11179, 3545}, {3818, 39874, 3618}, {9140, 26255, 37643}, {9143, 31105, 37645}, {9214, 14833, 36894}, {11178, 46264, 3524}, {14912, 41099, 5476}, {14927, 21356, 376}, {21358, 44882, 15692}, {25561, 38064, 3090}, {39884, 48662, 6776}, {43273, 47353, 47354}, {43273, 47354, 2}
X(51024) lies on these lines: {2, 21167}, {3, 38072}, {4, 599}, {6, 30}, {20, 597}, {25, 13857}, {40, 38087}, {69, 50687}, {141, 3839}, {182, 15681}, {376, 5480}, {381, 1350}, {382, 542}, {511, 3830}, {516, 47359}, {518, 50865}, {524, 3543}, {547, 48874}, {548, 38079}, {549, 48873}, {550, 38064}, {575, 17800}, {576, 5073}, {962, 9041}, {1351, 11645}, {1352, 15687}, {1386, 34628}, {1498, 34613}, {1503, 15534}, {1657, 14848}, {1992, 3146}, {2781, 18405}, {2930, 10706}, {3053, 6034}, {3091, 20582}, {3098, 5055}, {3242, 31162}, {3416, 34648}, {3524, 47355}, {3526, 25565}, {3534, 5085}, {3545, 3763}, {3564, 33699}, {3589, 10304}, {3627, 15069}, {3654, 38144}, {3818, 38335}, {3843, 25561}, {3845, 10516}, {4297, 38023}, {5032, 14927}, {5050, 15685}, {5054, 19130}, {5076, 34507}, {5092, 15689}, {5093, 29323}, {5097, 35400}, {5102, 29012}, {5642, 41424}, {5691, 28538}, {5732, 38086}, {5846, 50864}, {5847, 50862}, {7519, 40112}, {7540, 37498}, {7747, 10542}, {8550, 33703}, {8584, 15640}, {8703, 14561}, {9053, 50872}, {9830, 10723}, {10168, 15688}, {10387, 11237}, {10488, 10753}, {10519, 41099}, {10606, 23049}, {10717, 37751}, {10719, 15163}, {10720, 15162}, {11001, 14853}, {11160, 17578}, {11163, 40236}, {11178, 14269}, {11180, 40341}, {11425, 34726}, {11482, 49134}, {11898, 35434}, {12017, 48879}, {12100, 38136}, {12512, 38089}, {13598, 34725}, {14093, 48885}, {14810, 15694}, {14893, 48876}, {15360, 23293}, {15683, 44882}, {15686, 18583}, {15690, 38110}, {15692, 48310}, {15693, 38317}, {15695, 17508}, {15696, 25555}, {16936, 34614}, {17810, 31152}, {17813, 36201}, {17834, 18488}, {17845, 31166}, {18534, 19596}, {19905, 22515}, {20126, 37489}, {20583, 49135}, {21969, 34146}, {21970, 45311}, {23326, 50709}, {25566, 32609}, {31099, 44569}, {31105, 37638}, {31860, 47597}, {32113, 47310}, {32216, 34417}, {34379, 50869}, {34603, 37672}, {34632, 49524}, {35228, 37939}, {35403, 48889}, {35707, 37945}, {35822, 36718}, {35823, 36734}, {36757, 46335}, {36758, 46334}, {37182, 42849}, {37517, 48943}, {38047, 50808}, {38049, 50815}, {38090, 38759}, {38191, 50814}, {38315, 50811}, {38402, 41463}, {44456, 48884}, {46267, 48920}, {47031, 47455}, {47276, 47309}, {47332, 47450}, {47333, 47453}, {47336, 47448}, {48662, 48942}
X(51024) = midpoint of X(i) and X(j) for these {i,j}: {1351, 15684}, {1992, 3146}, {11179, 43621}
X(51024) = reflection of X(i) in X(j) for these {i,j}: {20, 597}, {376, 5480}, {381, 48901}, {599, 4}, {1350, 381}, {1352, 15687}, {2930, 10706}, {3242, 31162}, {3416, 34648}, {3534, 5476}, {10488, 10753}, {10606, 23049}, {11178, 48895}, {11179, 21850}, {15162, 10720}, {15163, 10719}, {15533, 47353}, {15681, 182}, {15683, 44882}, {15684, 48904}, {15686, 18583}, {17845, 31166}, {19905, 22515}, {32113, 47310}, {33878, 11178}, {34628, 1386}, {34632, 49524}, {36990, 3543}, {37751, 10717}, {40341, 11180}, {43273, 20423}, {47353, 3830}, {48872, 376}, {48873, 549}, {48874, 547}, {48876, 14893}, {48880, 10168}, {48905, 11179}, {48920, 46267}
X(51024) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 5480, 47352}, {381, 1350, 21358}, {3534, 5476, 5085}, {10168, 48880, 15688}, {11178, 48895, 14269}, {14269, 33878, 11178}, {20423, 43273, 6}, {21850, 43621, 48905}, {21850, 48905, 6}, {31670, 43621, 21850}, {31670, 48910, 6}, {42154, 42155, 7737}, {42263, 42264, 43618}, {47352, 48872, 376}, {48905, 48910, 43621}
X(51025) lies on these lines: {3, 20582}, {4, 20583}, {6, 42539}, {30, 3631}, {518, 50868}, {524, 3543}, {542, 3853}, {547, 11645}, {597, 3832}, {599, 5059}, {1351, 35402}, {1503, 3845}, {3545, 3589}, {3629, 50687}, {3818, 11539}, {3839, 6329}, {5092, 41985}, {5102, 41149}, {9053, 50871}, {10516, 15719}, {10519, 11001}, {12007, 14893}, {15686, 39884}, {15690, 29012}, {15702, 44882}, {15708, 34573}, {16239, 25561}, {18358, 41982}, {20423, 32455}, {35401, 48662}, {44323, 46847}
X(51025) = reflection of X(i) in X(j) for these {i,j}: {12007, 14893}, {20583, 4}, {44323, 46847}
X(51026) lies on these lines: {4, 20582}, {30, 3589}, {141, 50687}, {382, 8550}, {518, 50869}, {524, 3543}, {597, 3146}, {599, 17578}, {1352, 35434}, {1503, 33699}, {1992, 50690}, {3627, 34507}, {3631, 48910}, {3830, 29181}, {3839, 34573}, {5480, 15684}, {5846, 50862}, {5847, 50870}, {9053, 50865}, {10124, 48920}, {11737, 48885}, {12101, 29317}, {12102, 25561}, {12103, 25565}, {14269, 48881}, {14853, 15682}, {15683, 48310}, {15687, 48874}, {15699, 48879}, {21167, 41099}, {23046, 48880}, {25406, 41153}, {32218, 47310}, {32455, 39874}, {33703, 38072}, {34603, 35266}, {35403, 48873}, {35404, 48901}, {38064, 49136}, {38335, 43621}
X(51026) = midpoint of X(i) and X(j) for these {i,j}: {597, 3146}, {5480, 15684}, {15687, 48904}, {35404, 48901}
X(51026) = reflection of X(i) in X(j) for these {i,j}: {12103, 25565}, {20582, 4}, {25561, 12102}, {32218, 47310}, {48885, 11737}, {48920, 10124}
X(51027) lies on these lines: {3, 67}, {6, 3545}, {30, 40341}, {69, 41467}, {141, 15708}, {147, 7610}, {182, 15723}, {381, 5097}, {518, 50871}, {524, 3543}, {547, 1352}, {597, 5056}, {1350, 13666}, {1503, 11001}, {1853, 13857}, {1992, 3832}, {3091, 20583}, {3564, 3845}, {3629, 3839}, {3631, 10304}, {3654, 50782}, {3763, 11179}, {3830, 5965}, {3850, 38072}, {3853, 11477}, {5054, 43150}, {5059, 11160}, {5067, 8550}, {5071, 12007}, {5085, 11812}, {5655, 25331}, {6054, 37637}, {6144, 18440}, {6776, 15702}, {7778, 11177}, {9143, 37638}, {10516, 39561}, {10541, 20582}, {10706, 16176}, {11008, 50687}, {11178, 39899}, {11531, 28538}, {11645, 11898}, {12243, 44518}, {14848, 18553}, {15303, 38792}, {16239, 38064}, {18800, 38746}, {19924, 35400}, {22165, 31884}, {34379, 50868}, {35401, 48901}, {38155, 47359}, {41983, 48906}
X(51027) = reflection of X(i) in X(j) for these {i,j}: {6, 11180}, {599, 15069}, {15534, 47353}, {16176, 10706}, {39899, 11178}
X(51027) = {X(5102),X(47353)}-harmonic conjugate of X(3845)
X(51028) lies on these lines: {2, 51}, {4, 11160}, {6, 10304}, {20, 1992}, {30, 193}, {69, 3839}, {376, 1351}, {518, 50872}, {524, 3543}, {542, 3146}, {575, 21734}, {576, 3522}, {597, 3523}, {599, 3091}, {631, 14848}, {1350, 15692}, {1353, 15681}, {1503, 15640}, {2104, 15159}, {2105, 15158}, {3098, 15705}, {3524, 33878}, {3525, 38079}, {3528, 11482}, {3534, 14912}, {3545, 3620}, {3546, 13421}, {3564, 15682}, {3618, 15708}, {3751, 34632}, {3830, 34380}, {3854, 25561}, {4232, 40112}, {5050, 19708}, {5056, 38072}, {5071, 48876}, {5093, 8703}, {5102, 33748}, {5304, 11173}, {5480, 21356}, {5648, 32605}, {5847, 50864}, {6243, 20126}, {6392, 12243}, {6776, 15683}, {7486, 20582}, {8369, 40268}, {8584, 15697}, {8591, 10753}, {9143, 10752}, {9543, 44656}, {9974, 43512}, {9975, 43511}, {10754, 11177}, {10765, 37749}, {11008, 48910}, {11054, 46034}, {11179, 37517}, {11180, 20080}, {11898, 15687}, {12017, 15710}, {12250, 34788}, {13482, 19131}, {15022, 40107}, {15069, 50688}, {15520, 33750}, {15534, 29181}, {15702, 18583}, {15717, 38064}, {15719, 38110}, {15721, 47352}, {15741, 38323}, {18906, 32869}, {19783, 48936}, {30308, 50787}, {30769, 44569}, {31099, 44555}, {33586, 35266}, {34379, 50865}, {34507, 50689}, {35404, 48662}, {37907, 47571}
X(51028) = reflection of X(i) in X(j) for these {i,j}: {20, 1992}, {376, 1351}, {1992, 11477}, {5921, 3543}, {8591, 10753}, {9143, 10752}, {11160, 4}, {11177, 10754}, {11179, 37517}, {11180, 31670}, {11898, 15687}, {15158, 2105}, {15159, 2104}, {15681, 1353}, {15683, 6776}, {20080, 11180}, {34632, 3751}, {37749, 10765}, {48662, 35404}
X(51028) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 1351, 5032}, {5476, 10519, 2}, {11180, 31670, 50687}, {20080, 50687, 11180}
X(51029) lies on these lines: {4, 25561}, {30, 3618}, {376, 48904}, {382, 1992}, {518, 50873}, {524, 3543}, {597, 49135}, {599, 50688}, {3146, 43273}, {3524, 48895}, {3545, 43621}, {3619, 14269}, {3620, 47354}, {3763, 3839}, {5059, 38072}, {5846, 50863}, {5847, 50866}, {6776, 35404}, {10519, 12101}, {11179, 48943}, {12156, 14912}, {14927, 15684}, {15640, 25406}, {15687, 21356}, {15710, 48879}, {18583, 35400}, {19130, 46333}, {21735, 25565}, {29317, 41099}, {35403, 40330}, {38064, 49138}, {38079, 49137}
X(51029) = reflection of X(40330) in X(35403)
See Kadir Altintas and César Lozada, euclid 5272.
X(51030) lies on these lines: {5, 6509}, {216, 417}, {5907, 44715}
X(51030) = isogonal conjugate of X(51031)
See Kadir Altintas and César Lozada, euclid 5272.
X(51031) lies on these lines: {4, 54}, {6, 14249}, {20, 26880}, {107, 389}, {133, 40240}, {185, 436}, {264, 11441}, {324, 43605}, {399, 14978}, {450, 9729}, {801, 35602}, {933, 43917}, {1093, 7592}, {1105, 34148}, {1181, 2052}, {1304, 14894}, {1597, 45062}, {1885, 10152}, {1941, 34986}, {3087, 33871}, {3091, 36794}, {3542, 43462}, {6616, 40065}, {9786, 37070}, {11426, 41372}, {12162, 37127}, {12241, 34170}, {13382, 40664}, {13450, 15032}, {14152, 40448}, {14627, 34334}, {15760, 43995}, {16080, 26879}, {19347, 41365}
X(51031) = isogonal conjugate of X(51030)
X(51031) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 1614, 8884), (4, 1629, 19169), (4, 6759, 1629)
See Kadir Altintas and César Lozada, euclid 5272.
X(51032) lies on these lines: {15619, 43831}, {18403, 40449}, {31867, 43917}
X(51032) = isogonal conjugate of X(51033)
X(51032) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(38436)}} and {{A, B, C, X(4), X(5)}}
See Kadir Altintas and César Lozada, euclid 5272.
X(51033) lies on these lines: {2, 12278}, {3, 54}, {4, 39242}, {6, 38438}, {20, 6030}, {110, 5907}, {140, 265}, {154, 11439}, {184, 11440}, {186, 5462}, {389, 38448}, {427, 41482}, {549, 45970}, {567, 15331}, {569, 15053}, {578, 10298}, {631, 5449}, {1147, 3431}, {1181, 11454}, {1199, 32110}, {1204, 11003}, {1209, 12383}, {1511, 34864}, {1593, 26881}, {1614, 15062}, {1620, 38441}, {1656, 18379}, {1657, 34513}, {1658, 15033}, {3060, 11425}, {3091, 11202}, {3448, 10619}, {3515, 5640}, {3516, 6800}, {3520, 10575}, {3523, 18911}, {3567, 18324}, {5059, 35268}, {5422, 15750}, {5663, 18364}, {5876, 9705}, {5888, 7509}, {5892, 46865}, {5944, 14130}, {6146, 9140}, {6644, 11465}, {7488, 11430}, {7503, 11449}, {7526, 11464}, {7527, 10282}, {7542, 50435}, {7550, 15020}, {7575, 38848}, {7722, 15055}, {7998, 35602}, {9706, 13754}, {9707, 15305}, {9729, 37941}, {9730, 17506}, {9786, 38446}, {10024, 10733}, {10095, 37922}, {10110, 37940}, {10114, 38727}, {10125, 43821}, {10212, 38728}, {10263, 13482}, {10540, 43613}, {10546, 11479}, {10821, 12235}, {11413, 15080}, {11444, 47391}, {11591, 43572}, {12006, 37955}, {12038, 35921}, {12100, 32165}, {12111, 19357}, {12429, 38397}, {13142, 15360}, {13339, 15036}, {13353, 15646}, {13564, 43576}, {14128, 32609}, {14449, 37472}, {14805, 37814}, {14915, 35478}, {15023, 20190}, {15043, 32534}, {15072, 35477}, {15078, 37476}, {15463, 40441}, {16659, 44218}, {17845, 31236}, {18580, 23294}, {19467, 23293}, {19481, 48375}, {20191, 43808}, {21649, 40632}, {32171, 43598}, {32210, 43806}, {35265, 44870}, {35472, 36752}, {35482, 44407}, {35500, 43614}, {37471, 43615}, {41462, 43652}, {43816, 44673}, {44082, 50689}
X(51033) = isogonal conjugate of X(51032)
X(51033) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 5012, 43601), (3, 34148, 7691), (3, 43394, 43574), (569, 21844, 15053), (1614, 18570, 15062), (3516, 6800, 12279), (5944, 14130, 14157), (7691, 34148, 23061), (11425, 38444, 3060), (13353, 15646, 43597), (13367, 14118, 110), (14805, 37814, 43651), (32534, 37506, 15043), (37814, 43651, 43584)
preaamble pending
X(51034) lies on these lines: {1, 4755}, {2, 210}, {6, 48854}, {8, 4664}, {9, 48805}, {10, 537}, {37, 519}, {44, 36480}, {45, 4702}, {75, 4723}, {391, 49681}, {524, 50291}, {527, 49725}, {528, 50093}, {536, 984}, {551, 3842}, {726, 4745}, {740, 4669}, {756, 31136}, {966, 48849}, {1100, 50283}, {1125, 49449}, {1213, 48853}, {1698, 49503}, {1738, 49741}, {3175, 42041}, {3241, 15569}, {3246, 17335}, {3247, 49680}, {3617, 4740}, {3626, 49456}, {3634, 49491}, {3723, 49497}, {3731, 49460}, {3739, 19875}, {3741, 42056}, {3828, 24325}, {3932, 29594}, {3967, 31330}, {3993, 34641}, {4026, 24393}, {4113, 28606}, {4357, 48821}, {4364, 49772}, {4428, 20967}, {4533, 19863}, {4663, 16830}, {4668, 49452}, {4670, 36531}, {4677, 28581}, {4681, 49459}, {4686, 4732}, {4687, 38314}, {4690, 32847}, {4691, 49522}, {4698, 25055}, {4699, 49501}, {4708, 29659}, {4709, 4718}, {4715, 25384}, {4726, 49517}, {4739, 49532}, {4753, 16666}, {4966, 29600}, {5220, 50127}, {5247, 50064}, {5263, 15481}, {5302, 13735}, {5838, 47357}, {5846, 50779}, {5904, 19871}, {6687, 29660}, {7174, 16833}, {9041, 49731}, {9780, 49499}, {10707, 27776}, {12329, 19322}, {15492, 49482}, {15624, 16370}, {16394, 41229}, {16496, 17259}, {16814, 32941}, {16815, 24841}, {17239, 33165}, {17245, 49505}, {17260, 42819}, {17261, 49485}, {17277, 49465}, {17281, 48802}, {17310, 31323}, {17333, 28534}, {17346, 28538}, {17395, 50022}, {19323, 22769}, {19870, 24473}, {19876, 40328}, {19883, 49504}, {20430, 34718}, {28333, 50307}, {28503, 50095}, {28580, 49742}, {29054, 50796}, {30273, 34627}, {31145, 49470}, {31161, 31993}, {31238, 49479}, {34747, 49689}, {36479, 49702}, {37654, 47356}, {41310, 50311}, {41311, 50287}, {41312, 50282}, {41313, 50316}, {42039, 42051}, {48809, 50313}, {48851, 49509}, {49692, 50296}, {49697, 50298}, {49721, 50314}
X(51034) = midpoint of X(i) and X(j) for these {i,j}: {2, 50075}, {8, 4664}, {551, 49510}, {984, 3679}, {3241, 49450}, {3993, 34641}, {4669, 50777}, {4688, 49515}, {4740, 49447}, {17333, 49720}, {17346, 50286}, {20430, 34718}, {30273, 34627}, {31145, 49470}, {31178, 49448}, {34747, 49689}, {49457, 50094}
X(51034) = reflection of X(i) in X(j) for these {i,j}: {1, 4755}, {37, 50094}, {551, 3842}, {3241, 15569}, {3696, 3679}, {4688, 10}, {24325, 3828}, {31178, 3739}, {49462, 4664}, {49478, 551}, {49483, 4688}, {50082, 50309}, {50096, 4745}, {50305, 49731}, {50778, 50111}
X(51034) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 4407, 17237}, {10, 49515, 49483}, {37, 50778, 50111}, {984, 3696, 49523}, {3626, 49456, 49468}, {3842, 49510, 49478}, {4732, 49520, 4686}, {17335, 36534, 3246}, {19875, 31178, 3739}, {19875, 49448, 31178}, {36531, 49712, 4670}, {37654, 48856, 47356}
X(51035) lies on these lines: {1, 190}, {2, 726}, {10, 4740}, {37, 25055}, {38, 31137}, {75, 3992}, {145, 49508}, {192, 519}, {518, 3899}, {536, 984}, {545, 50301}, {551, 24349}, {740, 4677}, {752, 49748}, {1698, 4688}, {1757, 16834}, {2325, 29660}, {2796, 50286}, {3241, 3993}, {3416, 17225}, {3624, 4755}, {3632, 49452}, {3633, 49462}, {3644, 49457}, {3717, 50091}, {3729, 48854}, {3828, 50117}, {3842, 19876}, {3932, 49741}, {3994, 29827}, {4096, 36634}, {4360, 50283}, {4389, 4439}, {4419, 32847}, {4659, 36531}, {4669, 28522}, {4681, 49490}, {4704, 38314}, {4709, 4788}, {4718, 49459}, {4732, 4764}, {5220, 50120}, {5247, 50072}, {6534, 17157}, {6541, 29577}, {7174, 36554}, {7226, 31136}, {9055, 47359}, {15485, 17261}, {16475, 50779}, {16569, 42056}, {17132, 50291}, {17246, 33165}, {17262, 48805}, {17264, 50285}, {17318, 49712}, {17320, 50313}, {17336, 49472}, {19883, 27268}, {20430, 31162}, {22220, 42040}, {24231, 29600}, {25269, 49482}, {28297, 49725}, {28503, 49742}, {28516, 50096}, {28542, 49720}, {28606, 31161}, {29054, 50865}, {29582, 49676}, {29674, 50092}, {30273, 34628}, {31145, 49510}, {31151, 49747}, {34747, 49470}, {36814, 46795}, {37598, 50078}, {40328, 49525}, {42039, 42044}, {42041, 50106}, {42043, 42054}, {48830, 49528}, {49461, 49689}, {49471, 49501}, {49521, 50101}, {49543, 50834}, {49722, 50299}, {50088, 50309}
X(51035) = midpoint of X(i) and X(j) for these {i,j}: {3241, 31302}, {3679, 49445}, {4664, 49447}, {4688, 49522}, {31178, 49517}
X(51035) = reflection of X(i) in X(j) for these {i,j}: {1, 4664}, {2, 50777}, {75, 50094}, {3241, 3993}, {3679, 984}, {4664, 49456}, {4677, 50075}, {4740, 10}, {24349, 551}, {31145, 49510}, {31162, 20430}, {31178, 37}, {34628, 30273}, {34747, 49470}, {49474, 3679}, {49483, 4755}, {49493, 4688}, {49498, 3241}, {49532, 31178}, {49722, 50299}, {50088, 50309}, {50117, 3828}, {50296, 49742}
X(51035) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {37, 31178, 25055}, {37, 49517, 49532}, {75, 50094, 19875}, {192, 49448, 49469}, {192, 49520, 49448}, {984, 49445, 49474}, {984, 49523, 49445}, {3993, 31302, 49498}, {4681, 49513, 49490}, {4937, 46901, 2}, {17261, 49455, 15485}, {25055, 49532, 31178}, {49447, 49456, 1}, {49452, 49515, 3632}, {49462, 49503, 3633}
X(51036) lies on these lines: {2, 4891}, {8, 4675}, {10, 4755}, {75, 4487}, {518, 3919}, {519, 3739}, {536, 984}, {537, 3626}, {740, 4745}, {3617, 4664}, {3823, 29594}, {3828, 15569}, {4113, 31161}, {4668, 49483}, {4678, 4740}, {4681, 4709}, {4698, 19875}, {4725, 49725}, {4726, 49457}, {4739, 31178}, {4852, 48854}, {4923, 29600}, {15601, 49484}, {17239, 48821}, {17348, 48805}, {17382, 48802}, {22271, 44663}, {24325, 34641}, {25055, 49475}, {28329, 50291}, {28484, 50777}, {28534, 50309}, {28582, 50075}, {28633, 48853}, {28634, 48849}, {29054, 50827}, {30271, 34627}, {31145, 49478}, {31238, 38314}, {34747, 40328}, {49720, 50082}, {50085, 50286}
X(51036) = midpoint of X(i) and X(j) for these {i,j}: {8, 4688}, {3679, 3696}, {4664, 49468}, {4669, 50096}, {4709, 50094}, {4740, 49515}, {24325, 34641}, {30271, 34627}, {31145, 49478}, {49720, 50082}, {50085, 50286}
X(51036) = reflection of X(i) in X(j) for these {i,j}: {4681, 50094}, {4755, 10}, {15569, 3828}, {31178, 4739}
X(51036) = complement of X(50778)
X(51036) = {X(4709),X(38098)}-harmonic conjugate of X(50094)
X(51037) lies on these lines: {1, 4740}, {2, 28522}, {75, 4975}, {192, 19875}, {519, 1278}, {536, 984}, {537, 3632}, {726, 4677}, {1698, 4664}, {3241, 50117}, {3624, 4688}, {3633, 49493}, {3644, 50094}, {3751, 17225}, {4365, 31137}, {4686, 31178}, {4716, 49721}, {4755, 19872}, {4764, 28554}, {4772, 19883}, {4816, 49468}, {4821, 38314}, {17160, 50300}, {20049, 49535}, {24349, 34747}, {28309, 50301}, {28516, 50075}, {28542, 50088}, {29674, 50100}, {31302, 34641}, {32857, 50079}, {33149, 50097}, {42038, 50106}
X(51037) = reflection of X(i) in X(j) for these {i,j}: {1, 4740}, {3241, 50117}, {3644, 50094}, {3679, 49474}, {20049, 49535}, {31178, 4686}, {31302, 34641}, {34747, 24349}, {49445, 3679}, {49452, 4688}, {49469, 31178}
X(51038) lies on these lines: {3, 4755}, {4, 4664}, {5, 4688}, {30, 37}, {75, 3545}, {192, 3839}, {381, 536}, {515, 50111}, {518, 3656}, {537, 946}, {549, 30271}, {726, 44422}, {740, 50796}, {742, 47354}, {952, 50778}, {984, 31162}, {1503, 50779}, {3091, 4740}, {3524, 4687}, {3543, 30273}, {3655, 15569}, {3739, 5055}, {3845, 29010}, {3993, 34648}, {4681, 14269}, {4686, 38071}, {4698, 5054}, {4704, 50687}, {4718, 23046}, {5587, 50086}, {9955, 49483}, {10056, 11997}, {10304, 27268}, {11180, 49496}, {15699, 31238}, {18357, 49468}, {18480, 49462}, {18483, 49456}, {18492, 49452}, {22791, 49515}, {28194, 50094}, {28484, 50799}, {28522, 50803}, {28555, 50807}, {28581, 50798}, {28582, 50806}, {29054, 50777}, {29597, 37474}, {31178, 38021}, {34627, 49470}, {34631, 49450}
X(51038) = midpoint of X(i) and X(j) for these {i,j}: {4, 4664}, {381, 20430}, {984, 31162}, {3543, 30273}, {3993, 34648}, {11180, 49496}, {34627, 49470}, {34631, 49450}
X(51038) = reflection of X(i) in X(j) for these {i,j}: {3, 4755}, {3655, 15569}, {4688, 5}, {30271, 549}
X(51039) lies on these lines: {3, 4664}, {5, 4740}, {30, 192}, {37, 5054}, {75, 5055}, {381, 536}, {518, 50805}, {537, 1482}, {726, 3656}, {740, 50798}, {984, 34718}, {1278, 3545}, {1352, 17225}, {1656, 4688}, {3524, 4704}, {3526, 4755}, {3644, 14269}, {3654, 50777}, {3655, 3993}, {3830, 29010}, {3839, 4788}, {4451, 48804}, {4681, 15688}, {4699, 15699}, {4718, 38335}, {5050, 50779}, {5790, 50086}, {8148, 49447}, {9055, 20423}, {10246, 50111}, {11539, 27268}, {12702, 49456}, {14093, 30271}, {15681, 30273}, {18493, 49493}, {18525, 49452}, {18526, 49462}, {28484, 50797}, {28516, 50806}, {28522, 50796}, {31162, 49445}, {31302, 34631}, {34748, 49470}, {38066, 50094}, {44456, 49502}
X(51039) = midpoint of X(i) and X(j) for these {i,j}: {31162, 49445}, {31302, 34631}
X(51039) = reflection of X(i) in X(j) for these {i,j}: {3, 4664}, {381, 20430}, {3654, 50777}, {3655, 3993}, {4740, 5}, {15681, 30273}, {34718, 984}, {34748, 49470}
X(51040) lies on these lines: {2, 29010}, {3, 4688}, {4, 4740}, {5, 4664}, {30, 75}, {37, 5055}, {192, 3545}, {355, 537}, {381, 536}, {517, 50086}, {518, 50798}, {549, 30273}, {726, 50796}, {740, 3656}, {742, 20423}, {1278, 3839}, {1656, 4755}, {3524, 4699}, {3644, 38071}, {3654, 29054}, {3655, 24325}, {3696, 34718}, {3739, 5054}, {3818, 49533}, {4686, 14269}, {4687, 15699}, {4726, 38335}, {4739, 15688}, {4751, 11539}, {4764, 23046}, {4772, 10304}, {4821, 50687}, {5480, 17225}, {5886, 50111}, {8148, 49468}, {9055, 47354}, {9955, 49452}, {10247, 50778}, {11178, 49509}, {11179, 49481}, {14561, 50779}, {15681, 30271}, {16833, 37510}, {18357, 49447}, {18358, 49502}, {18480, 49493}, {18493, 49462}, {18525, 49483}, {24349, 34627}, {28204, 31178}, {28484, 50806}, {28516, 50799}, {28522, 50802}, {28555, 50800}, {28581, 50805}, {28582, 50797}, {31162, 49474}, {34648, 50117}, {34748, 49478}, {37705, 49499}
X(51040) = midpoint of X(i) and X(j) for these {i,j}: {4, 4740}, {24349, 34627}, {31162, 49474}, {34648, 50117}
X(51040) = reflection of X(i) in X(j) for these {i,j}: {3, 4688}, {3654, 50096}, {3655, 24325}, {4664, 5}, {11179, 49481}, {15681, 30271}, {20430, 381}, {30273, 549}, {34718, 3696}, {34748, 49478}, {49509, 11178}
X(51041) lies on these lines: {4, 4688}, {5, 4755}, {30, 3739}, {37, 3545}, {75, 3839}, {381, 536}, {518, 47354}, {537, 19925}, {726, 50803}, {740, 50802}, {1699, 50086}, {3091, 4664}, {3524, 31238}, {3543, 30271}, {3656, 28581}, {3696, 31162}, {3817, 50111}, {3832, 4740}, {4681, 38071}, {4698, 5055}, {4699, 50687}, {4726, 23046}, {4739, 14269}, {4751, 10304}, {5066, 29010}, {5071, 30273}, {5603, 50778}, {18492, 49483}, {24325, 34648}, {25939, 30976}, {28582, 50799}, {34627, 49478}, {34628, 40328}, {38076, 50094}
X(51041) = midpoint of X(i) and X(j) for these {i,j}: {4, 4688}, {3543, 30271}, {3696, 31162}, {24325, 34648}, {34627, 49478}
X(51041) = reflection of X(4755) in X(5)
X(51042) lies on these lines: {3, 4688}, {4, 4755}, {20, 4664}, {30, 37}, {75, 10304}, {165, 50086}, {376, 536}, {516, 50111}, {517, 50778}, {518, 43273}, {537, 4297}, {726, 50815}, {740, 50808}, {984, 34628}, {3522, 4740}, {3524, 3739}, {3545, 4698}, {3579, 49468}, {3655, 49478}, {3839, 4687}, {3842, 34648}, {3993, 34638}, {4686, 15688}, {4699, 15705}, {4718, 15689}, {4739, 15710}, {4751, 15708}, {5054, 31238}, {8703, 29010}, {15569, 31162}, {15681, 20430}, {18481, 49515}, {27268, 50687}, {28484, 50812}, {28522, 50816}, {28555, 50820}, {28581, 50810}, {28582, 50819}, {29181, 50779}, {31730, 49462}, {34632, 49470}
X(51042) = midpoint of X(i) and X(j) for these {i,j}: {20, 4664}, {376, 30273}, {984, 34628}, {3993, 34638}, {15681, 20430}, {34632, 49470}
X(51042) = reflection of X(i) in X(j) for these {i,j}: {4, 4755}, {4688, 3}, {30271, 376}, {31162, 15569}, {34648, 3842}, {49478, 3655}
X(51043) lies on these lines: {2, 29010}, {3, 4740}, {4, 4664}, {30, 192}, {37, 3545}, {75, 3524}, {376, 536}, {518, 50818}, {537, 944}, {631, 4688}, {726, 50811}, {740, 50810}, {984, 34627}, {1278, 10304}, {1350, 17225}, {3090, 4755}, {3543, 20430}, {3655, 24349}, {3739, 15709}, {3839, 4704}, {3993, 31162}, {4451, 48798}, {4686, 15710}, {4699, 5054}, {4718, 46333}, {4772, 15708}, {4821, 15705}, {5055, 27268}, {5603, 50111}, {5657, 50086}, {6361, 49452}, {9055, 43273}, {11180, 49509}, {14853, 50779}, {28484, 50809}, {28516, 50819}, {28522, 50808}, {34628, 49445}, {34631, 49470}, {38074, 50094}, {39874, 49502}
X(51043) = midpoint of X(34628) and X(49445)
X(51043) = reflection of X(i) in X(j) for these {i,j}: {4, 4664}, {376, 30273}, {3543, 20430}, {4740, 3}, {11180, 49509}, {24349, 3655}, {31162, 3993}, {34627, 984}, {34631, 49470}
X(51044) lies on these lines: {3, 4664}, {4, 4688}, {20, 4740}, {30, 75}, {37, 3524}, {40, 537}, {192, 10304}, {376, 536}, {515, 50086}, {518, 50810}, {549, 20430}, {631, 4755}, {726, 33706}, {740, 50811}, {742, 43273}, {990, 13634}, {1766, 13635}, {3098, 49502}, {3534, 29010}, {3545, 3739}, {3576, 50111}, {3579, 49447}, {3644, 15688}, {3654, 50075}, {3655, 49470}, {3696, 34627}, {3839, 4699}, {4681, 15710}, {4687, 5054}, {4698, 15709}, {4704, 15705}, {4726, 46333}, {4751, 5055}, {4764, 15689}, {4772, 50687}, {5085, 50779}, {6361, 49483}, {7967, 50778}, {11179, 49496}, {12702, 49499}, {13632, 17399}, {13633, 17342}, {15708, 27268}, {17225, 44882}, {24325, 31162}, {24349, 34632}, {28194, 31178}, {28484, 50819}, {28516, 50812}, {28522, 50815}, {28555, 50813}, {28581, 50818}, {28582, 50809}, {29584, 37474}, {31730, 49493}, {34628, 49474}, {34631, 49478}, {34638, 50117}, {34718, 49450}, {35242, 49456}, {48881, 49533}
X(51044) = midpoint of X(i) and X(j) for these {i,j}: {20, 4740}, {24349, 34632}, {34628, 49474}, {34638, 50117}
X(51044) = reflection of X(i) in X(j) for these {i,j}: {4, 4688}, {376, 30271}, {4664, 3}, {20430, 549}, {30273, 376}, {31162, 24325}, {34627, 3696}, {34631, 49478}, {49450, 34718}, {49470, 3655}, {49496, 11179}, {50075, 3654}
X(51045) lies on these lines: {2, 29010}, {3, 4664}, {5, 4755}, {30, 37}, {75, 5054}, {140, 4688}, {192, 3524}, {376, 20430}, {381, 30273}, {511, 50779}, {517, 50111}, {518, 50824}, {536, 549}, {537, 1385}, {631, 4740}, {726, 50828}, {740, 50821}, {984, 3655}, {1278, 15708}, {3545, 27268}, {3644, 15707}, {3653, 31178}, {3739, 11539}, {4681, 17504}, {4687, 5055}, {4698, 15699}, {4699, 15709}, {4704, 10304}, {4718, 41983}, {5844, 50778}, {7611, 29365}, {10168, 49481}, {11179, 49509}, {12017, 49502}, {13624, 49456}, {13632, 17264}, {13633, 17320}, {26446, 50086}, {28204, 50094}, {28484, 50825}, {28522, 50829}, {28555, 50833}, {28581, 50823}, {28582, 50832}, {29584, 37510}, {30271, 34200}, {31238, 47598}, {32900, 49449}, {34718, 49470}, {34748, 49450}
X(51045) = midpoint of X(i) and X(j) for these {i,j}: {3, 4664}, {376, 20430}, {381, 30273}, {984, 3655}, {11179, 49509}, {34718, 49470}, {34748, 49450}
X(51045) = reflection of X(i) in X(j) for these {i,j}: {5, 4755}, {4688, 140}, {30271, 34200}, {49481, 10168}
X(51046) lies on these lines: {3, 192}, {4, 4704}, {5, 37}, {30, 4664}, {75, 140}, {182, 9055}, {517, 3993}, {518, 1353}, {536, 549}, {537, 50824}, {550, 4681}, {631, 1278}, {632, 3739}, {726, 1385}, {740, 5690}, {742, 48876}, {952, 984}, {1009, 25245}, {1656, 27268}, {3523, 4788}, {3525, 4772}, {3526, 4699}, {3530, 3644}, {3564, 49509}, {3576, 49445}, {3628, 4687}, {3696, 38112}, {3842, 38042}, {3995, 4192}, {4032, 6147}, {4360, 37510}, {4686, 14869}, {4688, 11539}, {4718, 15712}, {4740, 5054}, {4751, 16239}, {4755, 15699}, {4764, 12108}, {4821, 10303}, {5844, 49470}, {5882, 49520}, {6684, 28522}, {7201, 24470}, {7967, 31302}, {8703, 30271}, {10165, 50117}, {10246, 24349}, {10283, 15569}, {10386, 11997}, {15178, 49479}, {16577, 20256}, {17262, 37474}, {17479, 21319}, {19540, 41839}, {19546, 31035}, {22791, 29054}, {24325, 38028}, {26446, 49474}, {28204, 50777}, {28606, 37365}, {29069, 48934}, {29343, 48888}, {32141, 34247}, {32453, 32515}, {32900, 49508}, {34380, 49496}, {34773, 49456}, {37727, 49448}, {38110, 49481}
X(51046) = midpoint of X(i) and X(j) for these {i,j}: {3, 192}, {5882, 49520}, {20430, 30273}, {37727, 49448}
X(51046) = reflection of X(i) in X(j) for these {i,j}: {5, 37}, {75, 140}, {49479, 15178}
X(51046) = {X(4664),X(30273)}-harmonic conjugate of X(20430)
X(51047) lies on these lines: {5, 4664}, {30, 192}, {37, 15699}, {75, 11539}, {140, 4740}, {518, 50831}, {536, 549}, {537, 1483}, {632, 4688}, {726, 50824}, {740, 50823}, {1278, 5054}, {3524, 4788}, {3644, 17504}, {3655, 49445}, {3845, 29010}, {4681, 38071}, {4699, 47598}, {4704, 5055}, {4718, 45759}, {4821, 15709}, {10283, 50111}, {15686, 30273}, {15687, 20430}, {17225, 48876}, {27268, 47599}, {28484, 50822}, {28516, 50832}, {28522, 50821}, {31302, 34748}, {37705, 49456}, {38081, 50094}, {38112, 50086}
X(51047) = midpoint of X(i) and X(j) for these {i,j}: {3655, 49445}, {31302, 34748}
X(51047) = reflection of X(i) in X(j) for these {i,j}: {5, 4664}, {4740, 140}, {15686, 30273}, {15687, 20430}
X(51048) lies on these lines: {3, 4740}, {5, 4688}, {30, 75}, {37, 11539}, {140, 4664}, {182, 17225}, {192, 5054}, {518, 50823}, {536, 549}, {537, 5690}, {547, 20430}, {632, 4755}, {726, 50821}, {740, 50824}, {952, 50086}, {1278, 3524}, {3545, 4772}, {3655, 49474}, {3739, 15699}, {4686, 17504}, {4687, 47598}, {4699, 5055}, {4704, 15709}, {4726, 45759}, {4739, 38071}, {4751, 47599}, {4764, 41983}, {4788, 15708}, {4821, 10304}, {8703, 29010}, {15686, 30271}, {24349, 34718}, {28484, 50832}, {28516, 50825}, {28522, 50828}, {28555, 50826}, {28581, 50831}, {28582, 50822}, {30273, 34200}, {38028, 50111}, {38110, 50779}
X(51048) = midpoint of X(i) and X(j) for these {i,j}: {3, 4740}, {3655, 49474}, {24349, 34718}
X(51048) = reflection of X(i) in X(j) for these {i,j}: {5, 4688}, {4664, 140}, {15686, 30271}, {20430, 547}, {30273, 34200}
X(51049) lies on these lines: {3, 4688}, {30, 3739}, {37, 5054}, {75, 3524}, {140, 4755}, {192, 15708}, {381, 30271}, {518, 50821}, {536, 549}, {537, 6684}, {631, 4664}, {726, 50829}, {740, 50828}, {3523, 4740}, {3545, 4751}, {3576, 50086}, {3582, 11997}, {3655, 3696}, {4686, 15707}, {4687, 15709}, {4698, 11539}, {4699, 10304}, {4726, 41983}, {4739, 17504}, {4772, 15705}, {5055, 31238}, {10165, 50111}, {10246, 50778}, {12100, 29010}, {15692, 30273}, {15694, 20430}, {16833, 37474}, {28581, 50824}, {28582, 50825}, {31162, 40328}, {34718, 49478}, {38068, 50094}
X(51049) = midpoint of X(i) and X(j) for these {i,j}: {3, 4688}, {381, 30271}, {3655, 3696}, {34718, 49478}
X(51049) = reflection of X(4755) in X(140)
X(51050) lies on these lines: {2, 210}, {6, 4755}, {37, 524}, {69, 4664}, {75, 21356}, {141, 4688}, {335, 3696}, {536, 599}, {537, 3773}, {726, 50787}, {740, 49630}, {742, 22165}, {984, 29573}, {1386, 29580}, {3008, 49449}, {3242, 16834}, {3416, 50079}, {3620, 4373}, {3631, 17225}, {3661, 49483}, {3739, 21358}, {3797, 49513}, {3912, 49515}, {3962, 26759}, {3967, 31027}, {4005, 27097}, {4663, 16826}, {4698, 47352}, {5032, 27268}, {5846, 50778}, {5847, 50111}, {6542, 24723}, {9041, 50095}, {9055, 36525}, {11160, 49496}, {11180, 30273}, {15569, 47356}, {15624, 16436}, {16496, 16833}, {17284, 49503}, {17389, 28538}, {17738, 49467}, {20155, 48854}, {20582, 49481}, {25730, 43216}, {27474, 28582}, {27480, 50789}, {28484, 50784}, {28522, 50788}, {28555, 50792}, {28581, 50783}, {29584, 49465}, {29600, 49505}, {29604, 49491}, {29611, 49499}, {29616, 49447}, {29620, 31323}, {49456, 49765}, {49741, 50011}
X(51050) = midpoint of X(i) and X(j) for these {i,j}: {69, 4664}, {599, 49509}, {4740, 49502}, {11160, 49496}, {11180, 30273}, {49518, 50089}
X(51050) = reflection of X(i) in X(j) for these {i,j}: {6, 4755}, {4688, 141}, {47356, 15569}, {49481, 20582}
X(51051) lies on these lines: {2, 742}, {6, 4688}, {37, 21358}, {69, 4740}, {75, 524}, {141, 4664}, {192, 21356}, {518, 4677}, {519, 24293}, {536, 599}, {537, 3416}, {597, 49496}, {726, 50781}, {740, 47358}, {1992, 49481}, {3631, 49502}, {3739, 47352}, {3763, 4755}, {3797, 49748}, {4751, 48310}, {4772, 5032}, {4777, 50766}, {9055, 22165}, {11178, 20430}, {24325, 47356}, {24357, 29574}, {28484, 50791}, {28516, 50784}, {28522, 50787}, {28538, 31178}, {28555, 50785}, {28581, 50790}, {28582, 50782}, {29594, 50011}, {41313, 49516}, {47359, 50096}, {47595, 50076}, {49706, 50126}, {49752, 50079}
X(51051) = midpoint of X(69) and X(4740)
X(51051) = reflection of X(i) in X(j) for these {i,j}: {6, 4688}, {1992, 49481}, {4664, 141}, {20430, 11178}, {47356, 24325}, {47359, 50096}, {49496, 597}, {49507, 50084}, {49509, 599}, {49533, 4740}
X(51051) = anticomplement of X(50779)
X(51052) lies on these lines: {7, 37}, {9, 75}, {55, 10025}, {63, 20173}, {85, 1334}, {142, 4389}, {144, 145}, {516, 984}, {527, 4664}, {528, 17333}, {536, 5838}, {537, 50836}, {740, 5223}, {742, 17262}, {894, 1001}, {960, 25242}, {971, 30273}, {1253, 36086}, {1278, 27484}, {1423, 39258}, {1447, 24352}, {1633, 7676}, {1697, 30625}, {1742, 42079}, {2082, 32024}, {2170, 31169}, {2550, 17257}, {3208, 16284}, {3212, 21872}, {3644, 49759}, {3662, 16593}, {3665, 27129}, {3673, 3730}, {3693, 30946}, {3696, 4461}, {3732, 5119}, {3739, 7229}, {3758, 16503}, {3797, 25269}, {3826, 17248}, {3842, 38052}, {3993, 5850}, {4032, 42309}, {4059, 27253}, {4416, 5853}, {4431, 24393}, {4480, 49499}, {4488, 24349}, {4517, 39350}, {4704, 20059}, {4751, 6666}, {4911, 17732}, {5762, 20430}, {5779, 29010}, {5836, 27288}, {5845, 17334}, {6168, 31627}, {6180, 14189}, {6646, 20533}, {7179, 17747}, {7672, 20718}, {8236, 49478}, {8545, 8680}, {9318, 41423}, {11025, 13476}, {11038, 15569}, {11372, 29054}, {11495, 34247}, {16601, 17753}, {16728, 17183}, {17158, 21384}, {17302, 38186}, {17305, 20195}, {17319, 42871}, {17351, 24357}, {17379, 42819}, {17484, 27491}, {17691, 30618}, {17787, 21615}, {24248, 49692}, {26101, 32007}, {27489, 31018}, {27538, 40883}, {30331, 49490}, {30332, 49515}, {30568, 44792}, {36976, 44670}, {38059, 40328}
X(51052) = midpoint of X(144) and X(192)
X(51052) = reflection of X(i) in X(j) for these {i,j}: {7, 37}, {75, 9}, {49490, 30331}
X(51052) = barycentric product X(200)*X(47393)
X(51052) = barycentric quotient X(47393)/X(1088)
X(51052) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 37, 27475}, {192, 20073, 49514}, {192, 49496, 49470}, {192, 49514, 49447}, {3057, 3177, 9311}, {3729, 49516, 75}, {4416, 49507, 49450}, {4419, 41325, 7}, {6646, 20533, 47595}, {24352, 42316, 1447}
X(51053) lies on these lines: {2, 210}, {7, 4688}, {9, 3759}, {75, 527}, {142, 48638}, {144, 4740}, {239, 5220}, {516, 50086}, {528, 29617}, {536, 5838}, {537, 673}, {726, 50834}, {740, 50836}, {984, 50114}, {1001, 29584}, {3008, 49503}, {3243, 29597}, {4384, 49499}, {4393, 15254}, {4607, 37131}, {4751, 38093}, {4755, 18230}, {4901, 17294}, {5222, 49515}, {6173, 17271}, {7671, 44671}, {8236, 50778}, {16593, 29577}, {16832, 49491}, {17251, 49481}, {17284, 49449}, {17349, 49502}, {25557, 29576}, {28484, 50840}, {28522, 50837}, {28581, 50839}, {29580, 42871}, {29594, 33165}, {30332, 49468}, {47357, 49470}, {49452, 50019}
X(51053) = midpoint of X(144) and X(4740)
X(51053) = reflection of X(i) in X(j) for these {i,j}: {7, 4688}, {4664, 9}, {49470, 47357}
X(51054) lies on these lines: {1, 4740}, {2, 740}, {8, 4664}, {75, 4742}, {145, 537}, {192, 519}, {518, 50839}, {528, 50121}, {536, 3241}, {551, 49474}, {984, 31145}, {1278, 31178}, {1738, 29582}, {2796, 50133}, {3242, 17225}, {3616, 4688}, {3621, 49456}, {3623, 49493}, {3644, 49475}, {3679, 3993}, {3685, 16469}, {3875, 35227}, {3896, 27538}, {4360, 48805}, {4393, 4693}, {4676, 50124}, {4677, 50777}, {4699, 25055}, {4704, 49459}, {4709, 19875}, {4755, 9780}, {4780, 17242}, {4788, 28554}, {4970, 31137}, {4971, 49746}, {5695, 46922}, {16394, 41813}, {17133, 50310}, {17233, 48821}, {17310, 50080}, {17318, 36534}, {17319, 48854}, {17350, 50283}, {17389, 28580}, {17393, 49485}, {20014, 49503}, {20049, 31302}, {20050, 49447}, {20053, 49515}, {20054, 49449}, {20057, 49483}, {20430, 34627}, {24723, 50076}, {25269, 49497}, {28534, 50132}, {28581, 50075}, {29054, 50872}, {29577, 50091}, {29580, 50314}, {29584, 50126}, {30273, 34632}, {34747, 49445}, {48628, 48853}, {49720, 50113}, {49740, 50088}, {50110, 50286}
X(51054) = midpoint of X(i) and X(j) for these {i,j}: {20049, 31302}, {34747, 49445}
X(51054) = reflection of X(i) in X(j) for these {i,j}: {8, 4664}, {1278, 31178}, {3241, 49470}, {3679, 3993}, {4664, 49462}, {4677, 50777}, {4740, 1}, {20049, 49678}, {24349, 3241}, {31145, 984}, {31178, 49471}, {34627, 20430}, {34632, 30273}, {49459, 50094}, {49468, 4755}, {49474, 551}, {49720, 50113}, {50086, 50111}, {50088, 49740}, {50286, 50110}
X(51054) = anticomplement of X(50086)
X(51054) = {X(50086),X(50111)}-harmonic conjugate of X(2)
X(51055) lies on these lines: {1, 190}, {2, 210}, {8, 4675}, {10, 48639}, {37, 38314}, {69, 48849}, {75, 519}, {86, 16496}, {145, 4740}, {312, 31161}, {320, 36479}, {524, 50310}, {527, 49746}, {528, 50128}, {536, 3241}, {551, 984}, {726, 11055}, {894, 42871}, {903, 50080}, {1125, 49503}, {1215, 31137}, {1278, 49475}, {1698, 49449}, {2099, 40862}, {3243, 5263}, {3244, 49493}, {3616, 4755}, {3623, 49462}, {3635, 49452}, {3636, 49508}, {3644, 28554}, {3655, 30273}, {3662, 48821}, {3679, 17297}, {3685, 49721}, {3696, 31145}, {3717, 29600}, {3759, 50283}, {3828, 40328}, {3932, 29582}, {4085, 48629}, {4307, 49695}, {4429, 5542}, {4644, 49709}, {4667, 49771}, {4670, 36534}, {4677, 50096}, {4684, 29594}, {4687, 25055}, {4704, 49513}, {4715, 24357}, {4751, 19875}, {4764, 49469}, {4828, 50764}, {4850, 17146}, {4883, 32937}, {4966, 29577}, {5224, 48853}, {7174, 29597}, {9041, 17392}, {12329, 19325}, {13587, 15624}, {14621, 20162}, {15569, 31302}, {16484, 17336}, {16834, 32922}, {17116, 49460}, {17117, 49680}, {17227, 29659}, {17234, 49529}, {17241, 33165}, {17271, 48851}, {17300, 49688}, {17310, 31317}, {17313, 49481}, {17320, 48830}, {17333, 49740}, {17335, 24331}, {17342, 50313}, {17346, 50305}, {17350, 42819}, {17354, 49768}, {17361, 33076}, {17379, 49465}, {17387, 32847}, {17389, 28503}, {17393, 49455}, {17399, 50285}, {17450, 30829}, {18137, 39739}, {19326, 22769}, {19767, 34860}, {20050, 49468}, {20090, 49681}, {21870, 24620}, {24231, 50091}, {25352, 49713}, {25492, 50191}, {26102, 42056}, {28538, 50133}, {28580, 49722}, {29054, 50811}, {30271, 34632}, {31136, 32771}, {34230, 46795}, {34247, 40726}, {34641, 49689}, {34747, 49474}, {36480, 41847}, {37756, 50282}, {38315, 50779}, {42034, 42057}, {42042, 42055}, {42043, 42053}, {47356, 49496}, {48630, 50315}, {49528, 50294}, {49678, 50117}
X(51055) = midpoint of X(i) and X(j) for these {i,j}: {145, 4740}, {551, 49535}, {3241, 24349}, {3679, 49498}, {4664, 49499}, {31178, 49490}, {34747, 49474}
X(51055) = reflection of X(i) in X(j) for these {i,j}: {8, 4688}, {75, 31178}, {984, 551}, {3241, 49478}, {3679, 24325}, {4664, 1}, {4677, 50096}, {4740, 49483}, {17333, 49740}, {17346, 50305}, {30273, 3655}, {31145, 3696}, {31178, 49479}, {34632, 30271}, {49447, 4664}, {49448, 50094}, {49450, 3679}, {49470, 3241}, {49496, 47356}, {49510, 3828}, {49515, 4755}, {49689, 34641}, {49720, 50116}, {50075, 2}, {50286, 17392}
X(51055) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 49491, 49499}, {1, 49499, 49447}, {24325, 49498, 49450}, {24331, 49712, 17335}, {24349, 49478, 49470}, {25055, 49448, 50094}, {25055, 50094, 4687}, {49471, 49532, 3644}, {49479, 49490, 75}
X(51056) lies on these lines: {2, 726}, {8, 537}, {75, 4723}, {192, 28554}, {518, 50789}, {519, 1278}, {536, 3241}, {551, 49445}, {3210, 31161}, {3616, 4664}, {3679, 31302}, {3729, 16487}, {4398, 48821}, {4454, 50015}, {4659, 36534}, {4678, 49508}, {4688, 9780}, {4699, 49517}, {4704, 25055}, {4726, 49501}, {4755, 49522}, {4772, 19875}, {4788, 49479}, {4821, 49448}, {5550, 49456}, {16816, 24821}, {17090, 24816}, {17116, 48854}, {17132, 50310}, {17247, 48853}, {20049, 49498}, {20050, 49499}, {20057, 49452}, {24231, 29577}, {28297, 49746}, {28503, 49722}, {28582, 50075}, {31145, 49474}, {32922, 49721}, {34747, 49535}, {46922, 49453}, {50119, 50286}
X(51056) = reflection of X(i) in X(j) for these {i,j}: {8, 4740}, {192, 31178}, {3241, 24349}, {3679, 50117}, {4664, 49483}, {4740, 49493}, {20049, 49498}, {31145, 49474}, {31302, 3679}, {34747, 49535}, {49445, 551}, {49447, 4688}, {49517, 50094}, {49522, 4755}, {50286, 50119}
X(51056) = {X(192),X(31178)}-harmonic conjugate of X(38314)
X(51057) lies on these lines: {2, 210}, {7, 4664}, {9, 4755}, {37, 527}, {142, 594}, {335, 29575}, {516, 50111}, {528, 29574}, {536, 6173}, {537, 4078}, {673, 15570}, {1001, 20155}, {3243, 16833}, {3696, 17294}, {3739, 38093}, {3838, 31038}, {3912, 25557}, {4344, 15569}, {5220, 16831}, {5698, 29624}, {5845, 50779}, {5853, 50778}, {5880, 17316}, {6545, 28910}, {15254, 16826}, {16834, 42871}, {17389, 49475}, {29571, 49515}, {29580, 42819}, {29606, 43180}, {29621, 30340}, {29627, 49499}, {31178, 38024}, {31211, 49449}, {38052, 50086}, {49468, 49765}, {49478, 50114}
X(51057) = midpoint of X(7) and X(4664)
X(51057) = reflection of X(i) in X(j) for these {i,j}: {9, 4755}, {4688, 142}, {47357, 15569}
X(51058) lies on these lines: {1, 6}, {2, 3930}, {7, 192}, {8, 21808}, {35, 17736}, {39, 3976}, {42, 26242}, {43, 3290}, {55, 3509}, {65, 3208}, {69, 49516}, {75, 142}, {141, 24357}, {144, 1959}, {145, 4051}, {226, 20173}, {244, 17756}, {281, 14943}, {312, 21101}, {321, 31006}, {344, 17755}, {346, 11038}, {354, 3693}, {390, 17452}, {516, 3993}, {527, 4664}, {528, 50113}, {536, 6173}, {579, 39258}, {594, 3826}, {672, 3873}, {673, 4360}, {726, 3950}, {728, 11518}, {740, 2294}, {742, 4851}, {908, 27491}, {942, 3501}, {966, 36479}, {971, 20430}, {982, 2276}, {986, 1500}, {1002, 4712}, {1018, 5902}, {1046, 14974}, {1056, 24247}, {1213, 29659}, {1278, 29583}, {1334, 3868}, {1400, 7672}, {1429, 1445}, {1475, 3889}, {1575, 17063}, {1621, 5282}, {1631, 15624}, {1698, 4006}, {1759, 3746}, {1914, 17715}, {1921, 17786}, {1953, 5819}, {2099, 4919}, {2170, 3241}, {2178, 37576}, {2243, 10987}, {2268, 30284}, {2277, 3774}, {2280, 3957}, {2298, 49530}, {2325, 49499}, {2344, 2346}, {2345, 24325}, {2667, 41265}, {2805, 5528}, {3116, 23462}, {3174, 19589}, {3218, 41423}, {3295, 3496}, {3572, 21834}, {3616, 33299}, {3617, 21921}, {3622, 39244}, {3644, 29601}, {3684, 3870}, {3686, 49450}, {3696, 4007}, {3697, 25086}, {3721, 22426}, {3730, 3874}, {3739, 17265}, {3742, 44798}, {3797, 17242}, {3812, 4515}, {3842, 3949}, {3862, 41886}, {3879, 49496}, {3881, 4253}, {3892, 24036}, {3932, 49531}, {3938, 5276}, {3943, 25557}, {3961, 5275}, {3962, 4520}, {3985, 32937}, {4029, 49447}, {4043, 22048}, {4050, 5836}, {4058, 38204}, {4071, 18134}, {4072, 38054}, {4073, 19586}, {4098, 49520}, {4119, 29641}, {4326, 11997}, {4328, 21446}, {4336, 28071}, {4385, 21071}, {4424, 9331}, {4650, 17735}, {4681, 29602}, {4687, 6666}, {4688, 38093}, {4698, 29598}, {4699, 29579}, {4709, 49766}, {4751, 29596}, {4771, 20012}, {4873, 49483}, {4898, 49469}, {5011, 25439}, {5045, 25066}, {5257, 24393}, {5316, 27489}, {5686, 21033}, {5805, 29010}, {5845, 17390}, {5853, 49470}, {5880, 49452}, {6006, 21143}, {6600, 19557}, {7179, 31038}, {7718, 17442}, {9055, 16593}, {9310, 34772}, {9327, 30144}, {9574, 18193}, {11495, 18788}, {12607, 21049}, {13407, 21073}, {14828, 24333}, {15668, 25384}, {15888, 40997}, {16547, 16550}, {16549, 18398}, {16583, 50581}, {16728, 18164}, {17018, 21840}, {17158, 20257}, {17248, 27495}, {17263, 49715}, {17279, 38186}, {17280, 31317}, {17281, 31178}, {17299, 32847}, {17303, 29637}, {17355, 49479}, {17362, 49689}, {17388, 49678}, {17398, 29660}, {17474, 26690}, {17592, 41269}, {17596, 31477}, {17737, 33127}, {17760, 18156}, {17868, 27480}, {17889, 21956}, {18230, 26626}, {20116, 25078}, {20171, 21617}, {20271, 20691}, {20680, 24578}, {20693, 37673}, {21096, 21620}, {21801, 24484}, {24326, 30945}, {26244, 29670}, {27479, 31019}, {28910, 48335}, {29676, 37661}, {29960, 39731}, {30090, 30693}, {30748, 30822}, {31402, 36574}, {31409, 37717}, {32771, 40463}, {33945, 40006}, {36279, 41322}, {36528, 40750}, {37658, 41711}, {38052, 49474}, {43929, 48307}, {47357, 50111}, {48830, 50094}, {49502, 49521}, {50086, 50087}
X(51058) = midpoint of X(7) and X(192)
X(51058) = reflection of X(i) in X(j) for these {i,j}: {9, 37}, {75, 142}, {47357, 50111}, {49490, 42871}
X(51058) = crosssum of X(1) and X(16779)
X(51058) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 9, 16503}, {1, 5280, 16787}, {1, 5525, 16788}, {1, 17742, 41239}, {1, 17744, 16783}, {37, 49509, 984}, {75, 17233, 27474}, {75, 17241, 27487}, {75, 27475, 142}, {145, 17451, 4051}, {192, 335, 49518}, {354, 3693, 17754}, {942, 3991, 3501}, {2276, 3726, 982}, {3555, 16601, 21384}, {3870, 40131, 3684}, {3889, 25082, 1475}, {3912, 49528, 75}, {4431, 27478, 75}, {17233, 36494, 75}, {20271, 20691, 24440}, {27268, 27484, 18230}
X(51059) lies on these lines: {2, 28522}, {10, 4664}, {75, 19883}, {192, 519}, {536, 551}, {537, 3244}, {726, 11055}, {740, 4669}, {984, 34641}, {1125, 4740}, {1278, 25055}, {2796, 50110}, {3241, 49445}, {3625, 49456}, {3644, 31178}, {3828, 49474}, {4681, 4709}, {4688, 19862}, {4704, 19875}, {4718, 28554}, {4788, 38314}, {6541, 50091}, {17225, 49511}, {17262, 50283}, {17318, 50300}, {20430, 34648}, {28309, 50297}, {28484, 50096}, {28542, 50113}, {28558, 50123}, {30273, 34638}, {31302, 34747}, {49461, 49510}, {49721, 50281}
X(51059) = midpoint of X(i) and X(j) for these {i,j}: {3241, 49445}, {3644, 31178}, {4664, 49452}, {31302, 34747}
X(51059) = reflection of X(i) in X(j) for these {i,j}: {10, 4664}, {551, 3993}, {4669, 50777}, {4709, 50094}, {4740, 1125}, {34638, 30273}, {34641, 984}, {34648, 20430}, {49474, 3828}, {49535, 3241}, {50094, 4681}, {50117, 551}
X(51059) = {X(4709),X(50094)}-harmonic conjugate of X(38098)
X(51060) lies on these lines: {1, 4740}, {2, 726}, {10, 537}, {37, 19883}, {75, 519}, {192, 25055}, {518, 3919}, {536, 551}, {545, 50297}, {740, 50778}, {752, 49727}, {984, 3828}, {1125, 4664}, {1278, 38314}, {1386, 17225}, {2796, 50119}, {3241, 49474}, {3625, 49491}, {3626, 49499}, {3634, 49447}, {3636, 49452}, {3663, 48853}, {3679, 24349}, {3696, 34641}, {3739, 49520}, {3842, 49525}, {4090, 4359}, {4361, 50283}, {4363, 50023}, {4439, 34824}, {4659, 24331}, {4660, 31995}, {4691, 49503}, {4699, 19875}, {4726, 49471}, {4732, 49504}, {4739, 38098}, {4745, 50075}, {4751, 49517}, {4755, 19862}, {4772, 49448}, {4821, 49469}, {4980, 42057}, {6534, 21080}, {6541, 29600}, {7263, 48821}, {7321, 50304}, {16815, 24821}, {16825, 50127}, {17116, 49482}, {17117, 49685}, {17118, 48805}, {17119, 50018}, {17140, 31136}, {24342, 49464}, {24357, 28301}, {24692, 42697}, {25557, 50097}, {25590, 48854}, {28503, 49733}, {28542, 49740}, {28562, 50310}, {29054, 50808}, {29594, 49676}, {30271, 34638}, {31145, 49498}, {31317, 41140}, {38049, 50779}, {46922, 49477}, {48822, 50101}, {49722, 50296}
X(51060) = midpoint of X(i) and X(j) for these {i,j}: {1, 4740}, {75, 31178}, {551, 50117}, {3241, 49474}, {3679, 24349}, {4664, 49493}, {4688, 49483}, {31145, 49498}, {34641, 49535}, {49722, 50296}, {50119, 50305}
X(51060) = reflection of X(i) in X(j) for these {i,j}: {10, 4688}, {551, 24325}, {984, 3828}, {3993, 551}, {4664, 1125}, {4669, 50096}, {34638, 30271}, {34641, 3696}, {49456, 4755}, {49479, 31178}, {49510, 3679}, {49520, 50094}, {50075, 4745}, {50094, 3739}, {50299, 49733}, {50777, 2}
X(51060) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {75, 49479, 4709}, {24325, 50117, 3993}
X(51061) lies on these lines: {1, 4688}, {2, 210}, {37, 25055}, {75, 4742}, {141, 48853}, {142, 48821}, {519, 3739}, {536, 551}, {537, 1125}, {3241, 3696}, {3246, 4670}, {3555, 19871}, {3616, 4664}, {3622, 4740}, {3624, 49515}, {3679, 40328}, {4472, 49768}, {4648, 48849}, {4681, 28554}, {4698, 19883}, {4699, 49475}, {4715, 50297}, {4739, 49471}, {4796, 49710}, {4883, 31136}, {4906, 19701}, {5049, 44671}, {5550, 49499}, {10436, 42819}, {15254, 50127}, {15624, 16417}, {15668, 48854}, {15808, 49456}, {16823, 46922}, {16825, 50124}, {17313, 48851}, {17348, 50283}, {17382, 48822}, {17392, 28538}, {19862, 49491}, {19875, 31238}, {19876, 49498}, {24841, 29578}, {25501, 42056}, {25557, 50092}, {25590, 49485}, {27268, 49513}, {28522, 41150}, {28534, 49740}, {28580, 49733}, {28581, 50096}, {28582, 50777}, {28633, 50315}, {29054, 50828}, {29580, 32922}, {30271, 31162}, {31139, 50080}, {31161, 44307}, {31243, 36478}, {34595, 49503}, {46934, 49447}, {49741, 50290}
X(51061) = midpoint of X(i) and X(j) for these {i,j}: {1, 4688}, {37, 31178}, {551, 24325}, {3241, 3696}, {3679, 49478}, {4664, 49483}, {4740, 49462}, {17392, 50305}, {30271, 31162}, {49479, 50094}, {49740, 50116}, {50086, 50778}
X(51061) = reflection of X(i) in X(j) for these {i,j}: {4755, 1125}, {15569, 551}, {50094, 4698}
X(51061) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 50086, 50778}, {4670, 24331, 3246}, {4688, 50778, 50086}, {19883, 49479, 50094}, {19883, 50094, 4698}, {25055, 31178, 37}
X(51062) lies on these lines: {11, 37}, {75, 3035}, {100, 192}, {119, 29010}, {149, 4704}, {214, 726}, {518, 1317}, {528, 4664}, {536, 6174}, {537, 50843}, {740, 1145}, {900, 20681}, {952, 984}, {1537, 29054}, {2397, 8299}, {2802, 3993}, {2805, 4681}, {2829, 30273}, {3644, 35023}, {3739, 31235}, {3842, 34122}, {4552, 21320}, {4687, 6667}, {5840, 20430}, {5848, 49509}, {5854, 49470}, {7201, 24465}, {7972, 49448}, {8680, 12831}, {10609, 49456}, {12735, 49490}, {13996, 49462}, {15015, 49445}, {24325, 34123}, {24845, 36942}, {25416, 49471}, {27268, 31272}, {27950, 39185}, {33337, 49520}
X(51062) = midpoint of X(i) and X(j) for these {i,j}: {100, 192}, {7972, 49448}, {33337, 49520}
X(51062) = reflection of X(i) in X(j) for these {i,j}: {11, 37}, {75, 3035}, {25416, 49471}, {49490, 12735}
X(51062) = {X(4552),X(21320)}-harmonic conjugate of X(23772)
X(51063) lies on these lines: {2, 30271}, {3, 4687}, {4, 75}, {5, 4751}, {20, 37}, {30, 4664}, {153, 2805}, {165, 3842}, {192, 3146}, {382, 3644}, {388, 11997}, {515, 49470}, {516, 984}, {517, 48878}, {518, 962}, {536, 3543}, {537, 50865}, {740, 5691}, {742, 36990}, {746, 36997}, {950, 7201}, {971, 10446}, {990, 6996}, {1278, 17578}, {1503, 49496}, {1699, 24325}, {1766, 13727}, {1824, 18750}, {3091, 3739}, {3522, 27268}, {3523, 4698}, {3627, 4764}, {3673, 32118}, {3817, 40328}, {3832, 4699}, {3839, 4688}, {3993, 28164}, {4032, 9579}, {4301, 49490}, {4681, 49135}, {4686, 50688}, {4704, 5059}, {4718, 50691}, {4732, 37714}, {4740, 50687}, {4755, 10304}, {4772, 50689}, {4788, 50690}, {5056, 31238}, {5263, 12717}, {5728, 17753}, {5731, 15569}, {5732, 27475}, {5927, 9535}, {6895, 20171}, {7377, 12618}, {7991, 49457}, {7996, 50314}, {9589, 49448}, {9812, 24349}, {10394, 17220}, {10431, 20173}, {10723, 44970}, {10724, 44968}, {12610, 36652}, {12699, 49499}, {16706, 36670}, {17278, 36692}, {17303, 36693}, {17394, 37474}, {19546, 31233}, {25091, 37109}, {26011, 30971}, {28194, 50075}, {28228, 49510}, {28236, 49678}, {28606, 50694}, {28653, 36672}, {29054, 41869}, {29181, 49509}, {34628, 50111}, {34648, 50086}, {48910, 49502}
X(51063) = midpoint of X(i) and X(j) for these {i,j}: {192, 3146}, {9589, 49448}
X(51063) = reflection of X(i) in X(j) for these {i,j}: {20, 37}, {75, 4}, {7991, 49457}, {30273, 20430}, {34628, 50111}, {49490, 4301}, {50086, 34648}
X(51063) = anticomplement of X(30271)
X(51063) = {X(20430),X(30273)}-harmonic conjugate of X(4664)
X(51064) lies on these lines: {4, 4740}, {20, 4664}, {30, 192}, {37, 10304}, {75, 3839}, {376, 20430}, {518, 50872}, {536, 3543}, {537, 962}, {726, 50865}, {740, 50864}, {984, 34632}, {1278, 50687}, {3091, 4688}, {3523, 4755}, {3524, 27268}, {3545, 4699}, {3993, 34628}, {4687, 15708}, {5731, 50111}, {7201, 15933}, {7996, 48854}, {15682, 29010}, {15683, 30273}, {15692, 30271}, {17225, 36990}, {24349, 31162}, {25406, 50779}, {28484, 50863}, {28516, 50873}, {28522, 50862}, {34648, 49474}
X(51064) = reflection of X(i) in X(j) for these {i,j}: {20, 4664}, {376, 20430}, {4740, 4}, {15683, 30273}, {24349, 31162}, {34628, 3993}, {34632, 984}, {49474, 34648}
X(51065) lies on these lines: {4, 4664}, {20, 4688}, {30, 75}, {37, 3839}, {192, 50687}, {381, 30273}, {516, 50086}, {518, 50864}, {536, 3543}, {537, 5691}, {726, 50862}, {740, 50865}, {984, 34648}, {1699, 50111}, {3091, 4755}, {3146, 4740}, {3524, 4751}, {3545, 4687}, {3696, 34632}, {3739, 10304}, {3830, 29010}, {15683, 30271}, {15687, 20430}, {15708, 31238}, {24325, 34628}, {28484, 50873}, {28516, 50866}, {28522, 50869}, {28555, 50867}, {28581, 50872}, {28582, 50863}, {29054, 50075}, {31162, 49470}, {31673, 49447}, {34627, 49450}
X(51065) = midpoint of X(3146) and X(4740)
X(51065) = reflection of X(i) in X(j) for these {i,j}: {20, 4688}, {984, 34648}, {4664, 4}, {15683, 30271}, {20430, 15687}, {30273, 381}, {34628, 24325}, {34632, 3696}, {49450, 34627}, {49470, 31162}
X(51066) lies on these lines: {1, 2}, {30, 37714}, {40, 3830}, {80, 31508}, {165, 3534}, {191, 15679}, {355, 8703}, {376, 9588}, {381, 7991}, {390, 38101}, {484, 3929}, {515, 19708}, {516, 50840}, {517, 19709}, {518, 50791}, {549, 5881}, {944, 38068}, {952, 15713}, {958, 19704}, {962, 38076}, {1268, 50132}, {1320, 38104}, {1376, 19705}, {1482, 38083}, {1656, 16189}, {1699, 38127}, {2550, 18513}, {2551, 18514}, {3219, 16558}, {3245, 3715}, {3305, 5541}, {3339, 11237}, {3416, 8584}, {3543, 43174}, {3545, 11362}, {3576, 15701}, {3579, 15685}, {3654, 3845}, {3655, 11812}, {3656, 7988}, {3681, 3968}, {3697, 44663}, {3711, 5425}, {3731, 4908}, {3746, 16857}, {3751, 15533}, {3817, 50872}, {3826, 38024}, {3839, 9589}, {3860, 12699}, {3869, 4540}, {3901, 3918}, {3913, 17542}, {3921, 5692}, {3973, 17330}, {3983, 5903}, {3992, 42034}, {4002, 5904}, {4085, 50089}, {4312, 38092}, {4338, 50736}, {4413, 37587}, {4421, 5251}, {4428, 48696}, {4445, 31312}, {4512, 50841}, {4654, 5726}, {4662, 24473}, {4664, 4732}, {4688, 49448}, {4695, 42041}, {4714, 42029}, {4731, 5902}, {4738, 19804}, {4748, 28301}, {4755, 49459}, {4859, 28635}, {4866, 17528}, {4888, 5936}, {4902, 5232}, {4912, 17251}, {4995, 5727}, {5010, 9708}, {5054, 30389}, {5055, 7982}, {5066, 5690}, {5071, 11522}, {5223, 38097}, {5258, 16371}, {5288, 40726}, {5298, 37709}, {5493, 50687}, {5657, 15682}, {5691, 11001}, {5731, 50829}, {5793, 16401}, {5818, 28194}, {5882, 15702}, {5886, 16191}, {6174, 9897}, {6684, 15698}, {7280, 9709}, {7741, 44847}, {7987, 15693}, {8275, 10589}, {8666, 36006}, {8715, 16858}, {9593, 39593}, {9624, 15699}, {9710, 17530}, {9711, 17533}, {9778, 50862}, {9812, 50803}, {9819, 11238}, {9900, 36329}, {9901, 35751}, {9902, 11055}, {9956, 11531}, {10164, 50801}, {10165, 50818}, {10175, 50827}, {10222, 15703}, {10436, 32101}, {10711, 12767}, {11224, 50817}, {11230, 50805}, {11231, 30392}, {11539, 37727}, {11540, 50824}, {11852, 34582}, {12100, 26446}, {12101, 41869}, {12780, 47866}, {12781, 47865}, {12782, 14711}, {13178, 15300}, {13624, 15722}, {14093, 31447}, {15015, 38213}, {15534, 50782}, {15621, 19293}, {15640, 34648}, {15695, 28208}, {15719, 50871}, {15759, 18481}, {15803, 19706}, {16173, 50842}, {16475, 50783}, {16490, 37682}, {16496, 21358}, {16667, 50082}, {16673, 50087}, {17271, 25590}, {17313, 28633}, {17525, 47033}, {17768, 38200}, {18145, 32104}, {18357, 33699}, {18492, 28198}, {19711, 37705}, {19925, 34632}, {20582, 49688}, {21356, 49529}, {22165, 47359}, {22650, 33706}, {22651, 36388}, {22652, 36386}, {22697, 44422}, {26726, 38026}, {28297, 33165}, {28484, 50086}, {28516, 50096}, {28582, 51034}, {28611, 44720}, {30393, 31140}, {31425, 34200}, {32557, 50894}, {34122, 50891}, {34773, 44580}, {35750, 50847}, {36331, 50850}, {37710, 38100}, {37720, 50038}, {38047, 50949}, {38057, 50836}, {38059, 50839}, {38155, 50864}, {38191, 50994}, {38210, 50835}, {41229, 50397}, {41990, 50807}, {43997, 50283}, {47311, 47321}, {47313, 47496}, {47358, 50951}, {48310, 49681}, {49474, 50094}, {49524, 50991}, {50047, 50066}, {50049, 50051}, {50777, 51037}, {50781, 50952}, {50786, 51001}, {50789, 51006}, {50808, 50863}
X(51066) = midpoint of X(i) and X(j) for these {i,j}: {1698, 3679}, {3241, 20052}, {3654, 50799}, {47359, 50784}
X(51066) = reflection of X(i) in X(j) for these {i,j}: {551, 31253}, {3623, 551}, {3654, 50822}, {3679, 3617}, {4668, 3679}, {5071, 31399}, {11522, 5071}, {14093, 31447}, {19862, 3828}, {50950, 50782}
X(51066) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 19875, 19876}, {2, 3679, 4677}, {2, 4677, 1}, {2, 4745, 3679}, {8, 3828, 25055}, {8, 25055, 34747}, {8, 38098, 3679}, {8, 46931, 3636}, {10, 3617, 1698}, {10, 3626, 46933}, {10, 3679, 19875}, {10, 4691, 9780}, {10, 4745, 2}, {10, 38098, 3828}, {1698, 3617, 4668}, {1698, 3623, 34595}, {1698, 4668, 1}, {1698, 4816, 3616}, {3582, 3584, 10321}, {3617, 46933, 20052}, {3623, 9780, 31253}, {3626, 46933, 3624}, {3632, 9780, 34595}, {3632, 34595, 1}, {3634, 4678, 3633}, {3634, 34641, 38314}, {3654, 5587, 50865}, {3679, 3828, 34747}, {3679, 19875, 1}, {3679, 25055, 8}, {3828, 38098, 8}, {4677, 19875, 2}, {4678, 38314, 34641}, {4691, 9780, 3632}, {9780, 31253, 1698}, {9956, 34718, 38021}, {20053, 46930, 15808}, {25055, 34747, 1}, {30286, 31434, 1}, {34641, 38314, 3633}, {34718, 38021, 11531}, {50796, 50809, 50866}, {50797, 50821, 50812}
X(51067) lies on these lines: {1, 2}, {355, 15685}, {515, 15695}, {946, 38081}, {3036, 5325}, {3654, 28150}, {3845, 11362}, {3860, 40273}, {4058, 4908}, {4297, 38066}, {4301, 5066}, {4537, 44663}, {4688, 49504}, {4732, 49513}, {5493, 15682}, {5657, 50801}, {5690, 28202}, {5790, 50799}, {5881, 15698}, {5882, 11812}, {9778, 50868}, {10164, 15716}, {10172, 50805}, {10175, 50823}, {11001, 43174}, {12101, 28174}, {15711, 28204}, {15722, 26446}, {15759, 28224}, {15828, 17330}, {17768, 38210}, {19710, 28160}, {19711, 38112}, {21630, 38099}, {22165, 49529}, {28484, 50777}, {28516, 51034}, {28582, 50096}, {34379, 50953}, {34718, 38076}, {37712, 50815}, {38191, 50949}, {38213, 50889}, {41152, 49536}, {44580, 47745}, {47359, 50782}, {49505, 50991}, {50781, 50951}, {50784, 51004}, {50814, 50866}
X(51067) = midpoint of X(i) and X(j) for these {i,j}: {3617, 3679}, {3654, 50797}, {47359, 50782}
X(51067) = reflection of X(i) in X(j) for these {i,j}: {551, 1698}, {3616, 3828}, {51004, 50784}
X(51067) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 10, 15808}, {10, 3244, 22266}, {10, 34641, 19883}, {551, 4669, 4677}, {1698, 5550, 31253}, {3626, 4677, 4669}, {3626, 19878, 8}, {3654, 38155, 50862}, {3679, 4691, 38098}, {3679, 4745, 4669}, {3679, 19875, 4678}, {3679, 38098, 10}, {3828, 41150, 2}, {4669, 4745, 10}, {4669, 38098, 4745}, {4816, 31253, 3244}, {19875, 46930, 3828}
X(51068) lies on these lines: {1, 2}, {40, 15640}, {165, 50801}, {329, 45116}, {355, 11001}, {515, 50820}, {516, 50874}, {517, 41106}, {518, 50792}, {944, 15693}, {952, 15701}, {962, 41099}, {966, 4908}, {3036, 5273}, {3534, 5657}, {3654, 15682}, {3830, 5690}, {3839, 11362}, {3845, 5790}, {3913, 16861}, {3968, 4430}, {4723, 42029}, {4732, 4740}, {5055, 5734}, {5066, 5818}, {5587, 50827}, {5603, 10109}, {5731, 12100}, {5852, 38203}, {5881, 15692}, {5882, 15721}, {5936, 17378}, {6361, 33699}, {8584, 38087}, {8703, 34627}, {9778, 28172}, {9779, 50872}, {9956, 34631}, {10164, 50871}, {10175, 50817}, {10246, 11540}, {10248, 28194}, {10595, 38083}, {11231, 50804}, {12101, 12702}, {12780, 36327}, {12781, 35749}, {15533, 49524}, {15534, 50949}, {15679, 21677}, {15683, 43174}, {15690, 18525}, {15698, 28204}, {15709, 37727}, {15719, 26446}, {15722, 18526}, {15759, 37705}, {16210, 34582}, {17249, 32087}, {17271, 31995}, {17313, 28635}, {19708, 50821}, {19709, 38034}, {21296, 32025}, {22165, 50785}, {22651, 36346}, {22652, 36352}, {22851, 33627}, {22896, 33626}, {24393, 38092}, {28232, 50796}, {28555, 51034}, {28626, 32089}, {32101, 50088}, {32558, 50894}, {36521, 50885}, {37714, 50687}, {38128, 50907}, {38191, 50950}, {38200, 50835}, {38204, 50838}, {47314, 47488}, {47359, 50992}, {50045, 50047}, {50096, 51056}, {50781, 50953}, {50993, 50999}
X(51068) = reflection of X(i) in X(j) for these {i,j}: {3241, 3622}, {3622, 19876}, {4678, 3679}, {15808, 3828}, {19876, 10}
X(51068) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3617, 4745}, {2, 4677, 3241}, {8, 10, 5550}, {8, 9780, 20057}, {10, 3622, 9780}, {10, 3626, 3633}, {10, 3633, 46931}, {10, 4677, 2}, {10, 19872, 46933}, {3241, 5550, 38314}, {3616, 3626, 8}, {3621, 25055, 3241}, {3626, 19875, 31145}, {3633, 46931, 3616}, {3679, 4745, 2}, {3679, 19875, 3626}, {3679, 38098, 3617}, {4668, 20050, 8}, {4668, 46933, 20050}, {4678, 9780, 8}, {4691, 38098, 3679}, {5550, 20057, 3622}, {5690, 38074, 34632}, {19875, 31145, 3616}, {34718, 38081, 5818}
X(51069) lies on these lines: {1, 2}, {40, 38076}, {165, 50862}, {214, 38099}, {355, 15693}, {376, 31425}, {381, 31399}, {515, 12100}, {516, 3845}, {517, 10109}, {946, 38066}, {952, 11540}, {993, 19705}, {1145, 38104}, {1213, 4908}, {1385, 38081}, {1739, 42039}, {2550, 38101}, {2796, 36522}, {3416, 38089}, {3534, 26446}, {3543, 9588}, {3579, 33699}, {3653, 47745}, {3654, 10175}, {3656, 10171}, {3740, 3968}, {3746, 17547}, {3751, 50990}, {3812, 4540}, {3817, 50810}, {3830, 19925}, {3839, 5493}, {3844, 50991}, {3860, 28198}, {3918, 44663}, {3921, 5883}, {3983, 24473}, {3992, 4980}, {4002, 31165}, {4015, 33815}, {4125, 42029}, {4297, 15698}, {4301, 5071}, {4547, 31794}, {4688, 49513}, {4708, 28301}, {4731, 10176}, {4732, 4755}, {4793, 18743}, {4937, 27812}, {5055, 11362}, {5066, 9956}, {5223, 38094}, {5258, 36006}, {5542, 38097}, {5587, 15682}, {5657, 41106}, {5690, 38083}, {5691, 15697}, {5790, 15701}, {5791, 19706}, {5818, 11001}, {5881, 15702}, {5882, 15694}, {6684, 8703}, {7988, 50872}, {7989, 34632}, {8715, 16857}, {9881, 50887}, {10164, 19708}, {10165, 50798}, {10172, 38112}, {10304, 37714}, {11230, 50823}, {11231, 15713}, {11274, 31235}, {11812, 28204}, {13464, 15699}, {15178, 47598}, {15534, 38047}, {15640, 34638}, {15673, 50845}, {15675, 47033}, {15685, 31673}, {15686, 31447}, {15690, 18357}, {15716, 18481}, {15719, 38155}, {15759, 28208}, {16189, 46935}, {17273, 32089}, {17533, 50038}, {18480, 19710}, {19704, 25440}, {21358, 49529}, {22165, 34379}, {24168, 42038}, {25351, 36525}, {25639, 44847}, {28186, 46332}, {28522, 50096}, {28562, 49731}, {31423, 34627}, {32557, 50842}, {34122, 50841}, {34560, 36466}, {35752, 50847}, {36330, 50850}, {38034, 50822}, {38049, 50783}, {38052, 50834}, {38054, 50835}, {38087, 49511}, {38138, 50825}, {38176, 50824}, {38191, 47358}, {38201, 50836}, {38213, 50843}, {47311, 47496}, {47359, 50787}, {49523, 50094}, {50786, 51005}, {50994, 51004}
X(51069) = midpoint of X(i) and X(j) for these {i,j}: {2, 4745}, {10, 3828}, {381, 43174}, {551, 3626}, {1125, 3679}, {3241, 4701}, {3635, 34641}, {3654, 50802}, {3740, 3968}, {4732, 4755}, {9881, 50887}, {10171, 38127}, {10172, 38112}, {12512, 34648}, {47359, 50787}, {50786, 51005}
X(51069) = reflection of X(i) in X(j) for these {i,j}: {551, 19878}, {3634, 3828}, {4746, 3679}
X(51069) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 10, 4745}, {2, 4677, 551}, {8, 19876, 19883}, {10, 1698, 3626}, {10, 3634, 4691}, {10, 9780, 1125}, {10, 19875, 3828}, {10, 46932, 4701}, {145, 9780, 1698}, {1125, 3626, 145}, {1698, 3626, 19878}, {1698, 4677, 2}, {1698, 19878, 3634}, {3617, 25055, 34641}, {3634, 4691, 3636}, {3634, 4746, 1125}, {3654, 10175, 50802}, {3679, 19875, 9780}, {3679, 38314, 3625}, {3828, 4745, 2}, {4745, 41150, 4746}, {19876, 19883, 31253}, {25055, 34641, 3635}
X(51070) lies on these lines: {1, 2}, {515, 15690}, {516, 33699}, {517, 3860}, {518, 41152}, {726, 51036}, {952, 44580}, {3534, 43174}, {3654, 15685}, {3655, 15722}, {3817, 50817}, {3830, 11362}, {4013, 36593}, {4301, 41106}, {4536, 44663}, {4738, 4980}, {4793, 42034}, {5493, 15640}, {5657, 50815}, {5686, 50837}, {5690, 19710}, {5790, 50802}, {5846, 41153}, {5847, 41149}, {5881, 19708}, {5882, 15701}, {6684, 19711}, {10165, 50804}, {11230, 50830}, {12101, 28194}, {12245, 38076}, {12512, 34627}, {12645, 38068}, {15533, 49529}, {15711, 28236}, {15716, 38066}, {15759, 28204}, {17249, 50099}, {19925, 34718}, {28158, 50814}, {28228, 50796}, {28522, 51034}, {34379, 50949}, {38034, 38176}, {38049, 50789}, {38054, 50838}, {38112, 50828}, {38127, 50798}, {38155, 50810}, {38191, 50783}, {38201, 50835}, {38213, 50842}, {47311, 47492}, {47359, 50786}, {49461, 50094}, {49505, 50994}, {49688, 50993}, {50781, 50989}
X(51070) = midpoint of X(i) and X(j) for these {i,j}: {8, 3828}, {551, 4701}, {1125, 34641}, {3626, 3679}, {3635, 31145}, {3654, 50801}, {4669, 4745}, {12512, 34627}, {19925, 34718}, {47359, 50786}
X(51070) = reflection of X(i) in X(j) for these {i,j}: {3636, 3828}, {4691, 3679}
X(51070) = anticomplement of X(41150)
X(51070) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 3679, 38098}, {8, 38098, 3828}, {10, 3244, 19872}, {10, 3621, 1125}, {10, 3625, 3622}, {10, 4669, 4677}, {10, 25055, 3828}, {1125, 3626, 4668}, {3241, 46931, 25055}, {3617, 3633, 10}, {3621, 20057, 3633}, {3626, 4691, 4746}, {3626, 4745, 4669}, {3679, 4669, 4745}, {4691, 4746, 3634}, {20057, 22266, 1125}
X(51071) lies on these lines: {1, 2}, {6, 4098}, {20, 16189}, {30, 4301}, {37, 49504}, {40, 19708}, {45, 4982}, {55, 19704}, {56, 19705}, {81, 16490}, {86, 50099}, {100, 37602}, {142, 50112}, {165, 50814}, {214, 14563}, {226, 1317}, {354, 2802}, {355, 19709}, {376, 5493}, {381, 13464}, {392, 4134}, {495, 3829}, {514, 3251}, {515, 3656}, {516, 7967}, {517, 3892}, {518, 3898}, {524, 49465}, {527, 30331}, {528, 5542}, {529, 15170}, {535, 3058}, {536, 49471}, {537, 3993}, {540, 49739}, {545, 4667}, {549, 11362}, {553, 2099}, {597, 49529}, {599, 49681}, {726, 11055}, {730, 14711}, {740, 50778}, {752, 4356}, {758, 5919}, {903, 4896}, {942, 34639}, {944, 15682}, {946, 1483}, {952, 3817}, {956, 8162}, {960, 4537}, {962, 34628}, {993, 4428}, {999, 4421}, {1001, 50283}, {1100, 3950}, {1120, 41434}, {1255, 24857}, {1266, 39704}, {1319, 33595}, {1320, 5425}, {1385, 12100}, {1386, 9041}, {1392, 43732}, {1482, 3534}, {1699, 50864}, {1992, 16496}, {2098, 4314}, {2321, 50123}, {2550, 38094}, {2784, 50881}, {2796, 7983}, {3036, 38104}, {3057, 3881}, {3081, 16211}, {3242, 15534}, {3243, 43179}, {3246, 49713}, {3247, 4856}, {3295, 5267}, {3303, 8666}, {3304, 8715}, {3339, 6049}, {3416, 50993}, {3452, 15935}, {3476, 4654}, {3488, 28609}, {3524, 31425}, {3543, 5734}, {3545, 5881}, {3555, 3884}, {3576, 15698}, {3579, 15759}, {3653, 6684}, {3654, 10164}, {3663, 11057}, {3664, 50101}, {3671, 5434}, {3723, 3986}, {3746, 17549}, {3754, 17609}, {3839, 11522}, {3860, 18480}, {3874, 9957}, {3875, 4909}, {3878, 31792}, {3879, 17273}, {3880, 5049}, {3885, 18398}, {3889, 5697}, {3893, 3918}, {3899, 4430}, {3913, 16417}, {3928, 31393}, {3946, 17313}, {3947, 4870}, {3987, 46190}, {3997, 16971}, {4021, 17274}, {4029, 4370}, {4058, 17388}, {4072, 16884}, {4090, 34587}, {4125, 4975}, {4133, 49473}, {4135, 31161}, {4141, 35263}, {4234, 4658}, {4311, 11009}, {4349, 28580}, {4353, 15600}, {4357, 50132}, {4359, 4793}, {4360, 50108}, {4424, 42038}, {4432, 36522}, {4464, 17394}, {4653, 41629}, {4664, 49490}, {4670, 28309}, {4688, 4709}, {4692, 4742}, {4694, 42040}, {4700, 16672}, {4715, 49700}, {4717, 42029}, {4740, 49469}, {4755, 49457}, {4762, 48285}, {4780, 17392}, {4795, 17318}, {4803, 25507}, {4848, 5298}, {4852, 49738}, {4895, 23795}, {4924, 4991}, {4969, 16590}, {5071, 9624}, {5159, 47537}, {5257, 46845}, {5258, 16858}, {5281, 8275}, {5435, 16236}, {5450, 12000}, {5541, 27003}, {5563, 13587}, {5587, 50801}, {5603, 28236}, {5625, 49467}, {5657, 50817}, {5686, 50838}, {5690, 15713}, {5710, 16401}, {5731, 11224}, {5741, 21088}, {5745, 36867}, {5750, 50087}, {5790, 50804}, {5844, 10165}, {5846, 50781}, {5847, 15533}, {5850, 8236}, {5853, 38054}, {5854, 50841}, {5886, 38155}, {5901, 10109}, {6174, 25416}, {6702, 38026}, {6796, 12001}, {7373, 25440}, {7962, 10385}, {7972, 10707}, {7974, 36330}, {7975, 35752}, {7977, 12156}, {7980, 22484}, {7981, 22485}, {7991, 10304}, {8027, 29350}, {8148, 15695}, {8227, 38074}, {9053, 38049}, {9588, 15708}, {9589, 15683}, {9778, 50816}, {9802, 26842}, {9812, 50869}, {9875, 50887}, {9881, 50888}, {9884, 50886}, {9956, 38022}, {10031, 15679}, {10107, 50191}, {10175, 10283}, {10176, 10179}, {10595, 19925}, {11038, 50839}, {11112, 34699}, {11113, 34749}, {11114, 34690}, {11207, 11367}, {11208, 11366}, {11236, 37739}, {11237, 37738}, {11238, 37740}, {11260, 15673}, {11263, 49600}, {11278, 15690}, {11373, 34717}, {11374, 34700}, {11529, 34607}, {11531, 12512}, {11711, 36521}, {11813, 37728}, {12005, 23340}, {12053, 33176}, {12101, 31673}, {12245, 15719}, {12258, 36523}, {12437, 33895}, {12513, 16418}, {12531, 33709}, {12559, 34610}, {12577, 34701}, {12625, 50741}, {12630, 38092}, {12640, 17564}, {12781, 36767}, {13624, 15711}, {14891, 31666}, {14923, 33815}, {15569, 49510}, {15621, 19252}, {15640, 28164}, {15677, 16126}, {15678, 34195}, {15685, 18481}, {15692, 30389}, {15699, 31399}, {15863, 45310}, {15888, 17530}, {15934, 19706}, {16173, 50890}, {16484, 49685}, {16489, 32911}, {16777, 50131}, {17045, 50081}, {17079, 25716}, {17132, 49455}, {17133, 32941}, {17180, 33296}, {17256, 31332}, {17319, 50090}, {17382, 17390}, {17395, 31138}, {17460, 39697}, {17533, 37722}, {17556, 37724}, {17579, 34719}, {17766, 49630}, {17793, 36524}, {18146, 24524}, {18185, 19247}, {18483, 18526}, {19710, 28198}, {19722, 48863}, {19738, 48866}, {21161, 34486}, {21358, 49679}, {21627, 50396}, {22165, 28538}, {22791, 28208}, {22867, 36368}, {22912, 36366}, {23789, 48287}, {24393, 38101}, {26446, 50827}, {28522, 51054}, {28554, 49462}, {28581, 50096}, {30308, 50803}, {31150, 50767}, {31151, 49695}, {31178, 49470}, {31447, 41983}, {33682, 48805}, {34123, 50842}, {34379, 50999}, {34502, 39781}, {34582, 49585}, {34612, 44840}, {35610, 42525}, {35611, 42524}, {35751, 50849}, {36329, 50852}, {36768, 50847}, {37429, 43177}, {37904, 47472}, {37911, 47564}, {38028, 38127}, {38053, 38201}, {38089, 49524}, {38112, 50830}, {38220, 50885}, {38315, 47359}, {38496, 48824}, {42819, 50124}, {43531, 48862}, {44635, 49548}, {44636, 49547}, {45667, 50337}, {46922, 49482}, {47097, 47489}, {47311, 47493}, {47352, 49688}, {47729, 50760}, {49675, 49705}, {49676, 49691}, {49710, 49742}, {50053, 50064}, {50062, 50069}, {50070, 50072}, {50092, 50125}, {50100, 50121}, {50787, 50950}, {50844, 50894}
X(51071) = midpoint of X(i) and X(j) for these {i,j}: {1, 3241}, {8, 34747}, {40, 34631}, {145, 3679}, {355, 34748}, {376, 7982}, {381, 37727}, {551, 3244}, {599, 49681}, {944, 31162}, {962, 34628}, {1482, 3655}, {1992, 16496}, {3057, 24473}, {3242, 47356}, {3243, 47357}, {3555, 31165}, {3632, 20049}, {3633, 31145}, {3654, 50805}, {3899, 4430}, {4664, 49490}, {4688, 49475}, {4740, 49469}, {4795, 17318}, {5731, 11224}, {6174, 25416}, {7967, 16200}, {7972, 10707}, {9589, 15683}, {9881, 50888}, {9884, 50886}, {10031, 50891}, {11112, 34699}, {11113, 34749}, {11114, 34690}, {11531, 34632}, {15677, 16126}, {17579, 34719}, {31138, 49699}, {31150, 50767}, {31151, 49695}, {31178, 49470}, {34637, 34649}, {47097, 47489}, {47358, 51000}, {47359, 50790}, {47493, 47593}, {47729, 50760}, {49578, 49582}, {50070, 50072}
X(51071) = reflection of X(i) in X(j) for these {i,j}: {8, 3828}, {10, 551}, {381, 13464}, {549, 15178}, {551, 1}, {3241, 3635}, {3244, 3241}, {3625, 3679}, {3654, 50828}, {3655, 13607}, {3679, 1125}, {3828, 3636}, {3919, 354}, {4067, 31165}, {4084, 24473}, {4134, 392}, {4297, 3655}, {4669, 2}, {4677, 4745}, {4709, 4688}, {4780, 50109}, {5493, 376}, {5883, 5049}, {9875, 50887}, {10164, 10246}, {10175, 10283}, {10176, 10179}, {11274, 12735}, {11362, 549}, {15863, 45310}, {24473, 3881}, {31145, 3626}, {31165, 3884}, {33337, 11274}, {34627, 19925}, {34632, 12512}, {34638, 4297}, {34641, 10}, {34648, 946}, {34718, 6684}, {38098, 25055}, {38127, 38028}, {38155, 5886}, {38201, 38053}, {47357, 43179}, {49457, 4755}, {49510, 50094}, {49520, 4664}, {49529, 597}, {50053, 50064}, {50062, 50069}, {50094, 15569}, {50096, 51061}, {50109, 49472}, {50117, 31178}, {50118, 49482}, {50337, 45667}, {50777, 50111}, {50781, 51003}, {50884, 12258}, {50950, 50787}, {51004, 47358}
X(51071) = complement of X(4677)
X(51071) = anticomplement of X(4745)
X(51071) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 8, 3636}, {1, 145, 1125}, {1, 3244, 10}, {1, 3623, 3635}, {1, 3632, 3622}, {1, 3633, 3616}, {1, 3635, 3244}, {1, 3679, 38314}, {1, 34747, 25055}, {1, 36846, 30147}, {2, 4669, 10}, {2, 4677, 4745}, {6, 4098, 15828}, {8, 3616, 46931}, {8, 3636, 19862}, {8, 3828, 38098}, {8, 19862, 10}, {8, 25055, 3828}, {10, 551, 19883}, {145, 1125, 3625}, {145, 38314, 3679}, {145, 41150, 4669}, {145, 46930, 3621}, {551, 4669, 2}, {551, 19862, 25055}, {551, 19883, 15808}, {551, 38098, 19862}, {1100, 50113, 50115}, {1125, 3625, 10}, {1125, 4691, 46930}, {1125, 4746, 9780}, {1125, 38314, 551}, {1482, 13607, 4297}, {1483, 33179, 946}, {1698, 20050, 4701}, {3057, 3881, 4084}, {3241, 38314, 145}, {3244, 3625, 145}, {3244, 38098, 34747}, {3555, 3884, 4067}, {3616, 3633, 3626}, {3616, 31145, 19875}, {3621, 3624, 4691}, {3622, 3632, 3634}, {3623, 20057, 1}, {3633, 19875, 31145}, {3636, 3828, 25055}, {3636, 25055, 551}, {3636, 34747, 38098}, {3653, 34718, 6684}, {3654, 10246, 50828}, {3654, 50828, 10164}, {3679, 38314, 1125}, {3828, 25055, 19862}, {3828, 38098, 10}, {3993, 49478, 49535}, {4360, 50116, 50108}, {4677, 4745, 4669}, {5550, 20014, 4668}, {5882, 10222, 4301}, {10056, 10072, 10320}, {10246, 50805, 3654}, {10595, 34627, 38021}, {11019, 49626, 10}, {14923, 50190, 33815}, {19862, 38098, 3828}, {19875, 31145, 3626}, {19875, 46931, 3828}, {19883, 34641, 10}, {25055, 34747, 8}, {29574, 29584, 50114}, {29574, 50114, 29600}, {31792, 34791, 3878}, {33176, 37734, 12053}, {34627, 38021, 19925}, {34718, 37624, 3653}, {36444, 36462, 31145}, {38315, 50790, 47359}, {46922, 50110, 50118}, {49465, 49684, 49505}, {50113, 50115, 3950}
X(51072) lies on these lines: {1, 2}, {100, 19704}, {355, 15682}, {390, 38097}, {515, 15697}, {516, 50866}, {517, 41099}, {518, 50784}, {944, 12100}, {952, 15693}, {962, 3845}, {1320, 38099}, {1482, 10109}, {1483, 11540}, {2975, 19705}, {3036, 9802}, {3161, 17330}, {3303, 17547}, {3416, 50992}, {3534, 5690}, {3543, 11362}, {3654, 9778}, {3655, 15719}, {3656, 38176}, {3830, 28174}, {3902, 20942}, {3913, 16858}, {3951, 50737}, {4528, 44553}, {4723, 42034}, {4737, 4980}, {4738, 28605}, {4740, 49457}, {4748, 28309}, {4908, 17275}, {5066, 5790}, {5071, 5734}, {5226, 36920}, {5232, 50099}, {5296, 50087}, {5587, 50872}, {5657, 8703}, {5686, 50840}, {5731, 15698}, {5749, 50082}, {5818, 19709}, {5847, 50953}, {5881, 10304}, {5882, 15708}, {7229, 50074}, {7967, 50804}, {7991, 50687}, {8584, 50783}, {9041, 50993}, {9588, 15705}, {9776, 45116}, {9812, 50796}, {10247, 50830}, {10989, 47492}, {11160, 49529}, {11415, 33559}, {11531, 38076}, {11812, 38112}, {12245, 41106}, {12513, 36006}, {12630, 38025}, {12645, 15701}, {12702, 33699}, {12780, 36331}, {12781, 35750}, {15300, 50885}, {15533, 50782}, {15534, 49524}, {15640, 28150}, {15675, 44669}, {15678, 21677}, {15679, 17768}, {15690, 37705}, {15702, 37727}, {15716, 34773}, {17271, 32087}, {17794, 36524}, {18525, 19710}, {19708, 28204}, {20070, 34648}, {20582, 49690}, {21356, 49688}, {22651, 36324}, {22652, 36326}, {22851, 33624}, {22896, 33622}, {26446, 50818}, {26726, 38104}, {28466, 38665}, {28484, 51034}, {28516, 50086}, {28582, 50075}, {28635, 49738}, {32025, 50101}, {34122, 50894}, {37712, 50808}, {38042, 50805}, {38057, 50839}, {38127, 50811}, {38155, 50865}, {38210, 50836}, {38213, 50891}, {47313, 47488}, {47865, 50848}, {47866, 50851}, {48310, 49679}, {50045, 50046}, {50786, 50952}, {50791, 50991}
X(51072) = midpoint of X(i) and X(j) for these {i,j}: {3623, 31145}, {3679, 4668}, {19862, 34641}
X(51072) = reflection of X(i) in X(j) for these {i,j}: {3241, 3616}, {3617, 3679}, {5734, 5071}, {31145, 4816}, {50782, 50949}, {50809, 3654}, {50999, 50791}
X(51072) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 10, 46930}, {1, 3679, 38098}, {2, 4669, 8}, {8, 10, 20050}, {8, 3617, 3616}, {8, 5550, 3632}, {8, 9780, 20053}, {8, 19877, 3621}, {8, 20057, 3625}, {8, 38314, 31145}, {10, 4816, 3623}, {10, 31145, 38314}, {3616, 20050, 3623}, {3617, 3623, 10}, {3617, 4668, 8}, {3617, 20052, 1698}, {3621, 4746, 8}, {3625, 25055, 20049}, {3625, 46933, 20057}, {3626, 4678, 8}, {3654, 50864, 9778}, {3679, 4669, 2}, {3679, 4677, 4745}, {3679, 19875, 4691}, {4669, 4745, 4677}, {4677, 4745, 2}, {4691, 34641, 19875}, {19875, 34641, 145}, {20049, 25055, 20057}, {20049, 46933, 25055}, {20050, 38314, 3241}, {20057, 31253, 3616}, {31145, 38314, 20050}, {34718, 38074, 962}, {50797, 50810, 50873}, {50798, 50822, 50819}
X(51073) lies on these lines: {1, 2}, {3, 10172}, {5, 10164}, {21, 33696}, {35, 9342}, {36, 17535}, {40, 5067}, {55, 16854}, {56, 16864}, {72, 3833}, {79, 31254}, {100, 17546}, {140, 4297}, {142, 5852}, {165, 5056}, {191, 35595}, {320, 31252}, {354, 4015}, {355, 46219}, {373, 31757}, {375, 23156}, {392, 3918}, {474, 5267}, {515, 3526}, {516, 3090}, {547, 3579}, {549, 31673}, {590, 49547}, {615, 49548}, {631, 19925}, {632, 9956}, {726, 4751}, {942, 4134}, {946, 3628}, {958, 16863}, {960, 3919}, {962, 46935}, {984, 24167}, {993, 16408}, {1001, 16855}, {1015, 25614}, {1089, 24589}, {1111, 25585}, {1203, 37687}, {1213, 3707}, {1224, 39962}, {1376, 16853}, {1385, 16239}, {1656, 3817}, {1699, 7486}, {1724, 17124}, {1738, 17371}, {2325, 3986}, {2802, 4002}, {3035, 50205}, {3057, 3968}, {3068, 49619}, {3069, 49618}, {3091, 12512}, {3336, 27065}, {3361, 31188}, {3452, 11263}, {3523, 7989}, {3524, 18492}, {3525, 5587}, {3530, 38140}, {3533, 3576}, {3545, 34638}, {3555, 3956}, {3583, 26060}, {3619, 34379}, {3650, 6701}, {3663, 28653}, {3671, 24914}, {3678, 5439}, {3697, 3881}, {3698, 3884}, {3701, 6533}, {3717, 25539}, {3739, 28555}, {3740, 3874}, {3754, 25917}, {3812, 4084}, {3814, 5122}, {3822, 17529}, {3823, 49700}, {3824, 5325}, {3825, 3925}, {3826, 3847}, {3832, 16192}, {3836, 6687}, {3839, 50874}, {3841, 4187}, {3842, 31238}, {3844, 38049}, {3848, 34790}, {3851, 28150}, {3857, 28154}, {3868, 4537}, {3876, 4525}, {3878, 10107}, {3892, 4662}, {3911, 3947}, {3921, 17609}, {3950, 16674}, {3971, 24176}, {3988, 24473}, {3993, 4698}, {4065, 4519}, {4066, 4359}, {4067, 5044}, {4075, 24165}, {4078, 17384}, {4098, 4873}, {4193, 41859}, {4298, 10588}, {4301, 5070}, {4314, 5432}, {4315, 5433}, {4349, 17337}, {4358, 28611}, {4364, 28322}, {4395, 6541}, {4405, 28633}, {4413, 5248}, {4423, 8715}, {4480, 17248}, {4535, 50109}, {4663, 20582}, {4687, 49452}, {4755, 51059}, {4758, 17251}, {4896, 17250}, {4973, 5302}, {4982, 17275}, {5010, 16859}, {5032, 50788}, {5054, 34648}, {5055, 18483}, {5057, 31263}, {5071, 41869}, {5183, 11813}, {5217, 17542}, {5218, 41864}, {5220, 38101}, {5251, 5303}, {5257, 16814}, {5259, 17534}, {5264, 17125}, {5265, 5726}, {5296, 15828}, {5316, 12609}, {5326, 10543}, {5691, 10303}, {5692, 33815}, {5745, 37545}, {5750, 16885}, {5847, 47355}, {5880, 6666}, {5882, 38042}, {5901, 38127}, {5943, 31737}, {6361, 50802}, {6667, 21630}, {6681, 24953}, {6702, 10609}, {6721, 21636}, {6722, 11599}, {6723, 13605}, {6834, 21628}, {6853, 12617}, {6931, 40998}, {7746, 31396}, {7815, 49545}, {7988, 46936}, {8164, 12577}, {8167, 9709}, {8185, 40916}, {8227, 43174}, {8252, 13883}, {8253, 13936}, {8258, 41817}, {8983, 32789}, {9167, 50884}, {9588, 28228}, {9940, 15064}, {9955, 15699}, {10124, 18357}, {10170, 31728}, {10173, 31746}, {10304, 50803}, {10576, 13975}, {10577, 13912}, {10585, 31224}, {10589, 12575}, {11108, 25440}, {11230, 11362}, {11278, 41985}, {11284, 49553}, {11539, 13624}, {11695, 31732}, {12019, 38104}, {12100, 33697}, {12558, 50031}, {13893, 32786}, {13947, 32785}, {13971, 32790}, {14869, 28160}, {15178, 41992}, {15694, 18481}, {15703, 28194}, {15707, 50799}, {15708, 50815}, {16583, 25089}, {16668, 17398}, {17067, 25503}, {17095, 43186}, {17259, 33682}, {17327, 21255}, {17353, 24697}, {17357, 50290}, {17385, 25354}, {18249, 30827}, {18525, 50828}, {18743, 28612}, {19248, 23361}, {19253, 23383}, {19315, 37576}, {19646, 41430}, {19744, 43531}, {19827, 23537}, {19886, 19983}, {19933, 19957}, {19999, 27918}, {20195, 38054}, {21358, 50792}, {21635, 38133}, {22793, 35018}, {23789, 47794}, {23795, 25380}, {24206, 38118}, {24231, 26083}, {24325, 49508}, {24390, 34501}, {24719, 31251}, {27268, 28522}, {28168, 44682}, {28178, 44904}, {28346, 31273}, {28494, 50298}, {30424, 38094}, {31197, 37592}, {31243, 49676}, {31262, 38411}, {31287, 48284}, {31289, 49705}, {31447, 40273}, {31658, 38151}, {32900, 38028}, {33337, 34122}, {34573, 49511}, {34633, 43957}, {37453, 49542}, {37559, 37680}, {38047, 49505}, {38069, 50906}, {38093, 43180}, {38108, 43182}, {40328, 49499}, {44381, 50775}, {47352, 50785}, {47599, 50821}, {48065, 48196}, {48310, 50781}, {48311, 50847}, {48312, 50850}, {49449, 51061}, {49522, 50777}, {50687, 50816}
X(51073) = midpoint of X(i) and X(j) for these {i,j}: {1, 4678}, {2, 19876}, {10, 15808}, {3090, 31423}, {3523, 7989}, {3624, 9780}, {3832, 16192}
X(51073) = reflection of X(i) in X(j) for these {i,j}: {10, 9780}, {3622, 1125}, {15808, 3624}, {34638, 50813}, {34648, 50800}
X(51073) = complement of X(3624)
X(51073) = complement of the isotomic conjugate of X(28650)
X(51073) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 28651}, {27789, 141}, {28196, 513}, {28650, 2887}, {48587, 116}
X(51073) = crosspoint of X(2) and X(28650)
X(51073) = barycentric product X(75)*X(46845)
X(51073) = barycentric quotient X(46845)/X(1)
X(51073) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2, 19878}, {1, 10, 4669}, {1, 1698, 46933}, {1, 3634, 22266}, {1, 3679, 20053}, {1, 3828, 10}, {1, 19877, 3828}, {1, 19878, 19883}, {1, 46933, 4691}, {2, 8, 34595}, {2, 10, 19862}, {2, 1698, 1125}, {2, 3634, 10}, {2, 3828, 19883}, {2, 9780, 3624}, {2, 19855, 10200}, {2, 19872, 31253}, {2, 19874, 19864}, {2, 19877, 1}, {2, 26030, 25512}, {2, 46930, 8}, {2, 46931, 3616}, {2, 46932, 5550}, {8, 34595, 1125}, {8, 46930, 1698}, {10, 551, 3625}, {10, 1125, 3244}, {10, 3625, 38098}, {10, 19862, 551}, {10, 19883, 1}, {10, 22266, 3828}, {10, 34641, 3617}, {40, 5067, 10171}, {100, 17546, 25542}, {140, 10175, 4297}, {165, 5056, 12571}, {632, 9956, 10165}, {1125, 1698, 10}, {1125, 3244, 551}, {1125, 3622, 15808}, {1125, 3634, 1698}, {1125, 3828, 4691}, {1125, 4691, 1}, {1385, 31399, 38155}, {1656, 6684, 3817}, {1698, 3633, 19875}, {1698, 34595, 8}, {1698, 46933, 3828}, {3244, 19862, 1125}, {3545, 50829, 34638}, {3616, 19875, 3626}, {3616, 31145, 1}, {3616, 46931, 19875}, {3617, 3635, 34641}, {3617, 25055, 3635}, {3622, 3624, 1125}, {3622, 46933, 4678}, {3624, 19876, 9780}, {3626, 3634, 46931}, {3626, 19875, 10}, {3628, 11231, 946}, {3634, 3828, 19877}, {3634, 19878, 3828}, {3634, 31253, 2}, {3636, 46932, 10}, {3679, 5550, 3636}, {3812, 10176, 4084}, {3817, 6684, 5493}, {3826, 17527, 25639}, {3828, 4691, 46933}, {3828, 19877, 22266}, {3828, 19878, 1}, {3828, 19883, 4669}, {3836, 6687, 49710}, {3925, 17575, 3825}, {4358, 28611, 42031}, {4413, 16842, 5248}, {4669, 19883, 551}, {4691, 19878, 1125}, {4691, 46933, 10}, {5044, 5883, 4067}, {5550, 46932, 3679}, {5705, 20103, 10}, {9342, 17536, 35}, {10588, 31231, 4298}, {19877, 19878, 10}, {19877, 20053, 46932}, {19877, 46933, 1698}, {19878, 19883, 19862}, {19878, 22266, 4669}, {19883, 22266, 10}, {19883, 46933, 3244}, {20582, 38089, 51004}
X(51074) lies on these lines: {2, 28150}, {3, 50869}, {4, 50819}, {5, 28202}, {10, 38071}, {30, 19862}, {355, 381}, {515, 30308}, {516, 19709}, {546, 551}, {1125, 14269}, {1698, 3545}, {1699, 38127}, {3091, 28194}, {3146, 50820}, {3534, 10171}, {3544, 19876}, {3579, 14892}, {3616, 3839}, {3617, 31162}, {3623, 18492}, {3655, 50868}, {3679, 3855}, {3817, 3845}, {3828, 3851}, {3830, 10165}, {3832, 5882}, {3850, 11362}, {3854, 50817}, {3857, 4301}, {3858, 28204}, {3860, 28224}, {4297, 14893}, {4669, 38140}, {5054, 50816}, {5055, 31253}, {5066, 10175}, {5493, 12811}, {5587, 50872}, {5603, 50871}, {5847, 50956}, {7988, 15682}, {9955, 23046}, {10109, 10164}, {10265, 38077}, {10516, 50784}, {11001, 50874}, {11230, 12101}, {11737, 22793}, {12512, 15703}, {12699, 50814}, {13464, 50818}, {15687, 19883}, {15688, 19878}, {15693, 28158}, {15699, 34638}, {15713, 28154}, {28484, 51041}, {28516, 51038}, {31447, 41989}, {33699, 50833}, {34379, 50963}, {38042, 41990}, {38139, 50834}, {38141, 50889}, {38335, 50870}, {38732, 50882}, {38743, 50887}, {38755, 50892}, {38789, 50922}
X(51074) = midpoint of X(i) and X(j) for these {i,j}: {3617, 31162}, {3656, 50797}, {30308, 41099}, {50799, 50806}, {50809, 50865}, {50811, 50863}, {50812, 50873}, {50819, 50866}
X(51074) = reflection of X(i) in X(j) for these {i,j}: {50796, 50799}, {50806, 50802}, {50808, 50825}, {50819, 50828}
X(51074) = complement of X(50812)
X(51074) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 50873, 50812}, {4, 50819, 50866}, {381, 3656, 50803}, {381, 50802, 50796}, {381, 50806, 50799}, {381, 50807, 50802}, {1698, 50865, 50809}, {3616, 50863, 50811}, {3656, 50799, 50797}, {3656, 50800, 50801}, {3656, 50803, 50796}, {9955, 23046, 34648}, {12571, 50802, 50807}, {19925, 50798, 50796}, {50796, 50802, 946}, {50797, 50806, 3656}, {50800, 50801, 50796}, {50801, 50803, 50800}, {50802, 50803, 3656}
X(51075) lies on these lines: {1, 50687}, {2, 28228}, {4, 50868}, {5, 50827}, {10, 50872}, {20, 551}, {30, 3636}, {140, 28194}, {355, 381}, {515, 12101}, {516, 8703}, {517, 10109}, {962, 15721}, {1125, 3524}, {1385, 44903}, {1699, 50864}, {3090, 3828}, {3091, 34641}, {3241, 50689}, {3244, 3839}, {3545, 3626}, {3616, 34638}, {3627, 13464}, {3634, 15699}, {3635, 34648}, {3654, 10171}, {3679, 5068}, {3817, 4745}, {3832, 34747}, {3845, 28236}, {3861, 28204}, {4669, 30308}, {4677, 9779}, {4691, 9955}, {4701, 34631}, {4870, 12575}, {5066, 28234}, {5070, 43174}, {5603, 15682}, {5847, 50958}, {5886, 15701}, {5901, 15691}, {7982, 38076}, {7991, 46935}, {9624, 21735}, {10164, 50809}, {10165, 15716}, {10304, 15808}, {10516, 50786}, {11230, 50825}, {11278, 38071}, {11531, 38098}, {12100, 28232}, {12512, 25055}, {12699, 15689}, {13607, 15687}, {14891, 28198}, {14893, 33179}, {15685, 28158}, {16200, 41099}, {18480, 50831}, {18493, 19878}, {19862, 34632}, {28174, 44580}, {28202, 44245}, {34628, 50873}, {38022, 44682}, {38034, 38176}, {38083, 50822}, {38155, 41106}, {41869, 50819}, {50878, 50922}, {50881, 50887}, {50882, 50886}, {50891, 50909}, {50892, 50908}
X(51075) = midpoint of X(i) and X(j) for these {i,j}: {1125, 31162}, {3635, 34648}, {3656, 50802}, {3828, 4301}, {4701, 34631}, {13607, 15687}, {14893, 33179}, {50811, 50869}, {50815, 50865}, {50878, 50922}, {50881, 50887}, {50882, 50886}, {50891, 50909}, {50892, 50908}
X(51075) = reflection of X(i) in X(j) for these {i,j}: {50803, 50802}, {50816, 50828}
X(51075) = complement of X(50814)
X(51075) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {381, 50804, 50796}, {551, 50865, 50815}, {946, 3656, 50802}, {946, 50796, 50806}, {3656, 50799, 1482}, {3656, 50806, 50796}, {3656, 50807, 50805}, {4301, 38021, 3828}, {50796, 50804, 50801}, {50796, 50806, 50802}, {50801, 50802, 381}, {50802, 50803, 12571}, {50805, 50806, 50807}, {50805, 50807, 50796}
X(51076) lies on these lines: {2, 28158}, {4, 50815}, {5, 50829}, {30, 19878}, {355, 381}, {515, 3860}, {516, 5066}, {551, 3832}, {1125, 3839}, {1699, 4745}, {3090, 50812}, {3091, 3828}, {3545, 3634}, {3626, 50872}, {3635, 50871}, {3636, 34648}, {3679, 3854}, {3817, 41099}, {3830, 10171}, {3845, 11230}, {3850, 28194}, {3855, 38076}, {3856, 28204}, {3857, 38081}, {3858, 50824}, {4691, 31162}, {4746, 50817}, {5071, 12512}, {5072, 38068}, {5657, 41106}, {5847, 50960}, {7988, 50866}, {10109, 28150}, {10172, 50825}, {10304, 50874}, {10516, 50788}, {12811, 28202}, {13464, 41991}, {14639, 50882}, {18483, 38071}, {18492, 50818}, {19862, 50687}, {23046, 34773}, {28228, 38112}, {28522, 51041}, {30308, 50864}, {31253, 34638}, {34379, 50959}, {38140, 50823}
X(51076) = midpoint of X(i) and X(j) for these {i,j}: {381, 12571}, {3636, 34648}, {4691, 31162}, {50802, 50803}, {50815, 50870}, {50816, 50869}
X(51076) = complement of X(50816)
X(51076) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 50869, 50816}, {4, 50815, 50870}, {381, 50802, 50803}, {381, 50807, 50796}, {946, 50796, 50805}, {946, 50799, 50801}, {12571, 50803, 50802}, {19925, 50802, 3656}, {50796, 50805, 50801}, {50796, 50807, 50802}, {50799, 50805, 50796}, {50801, 50802, 946}
X(51077) lies on these lines: {1, 3524}, {2, 16200}, {3, 50814}, {4, 34747}, {5, 34641}, {10, 15699}, {20, 3241}, {30, 3244}, {140, 551}, {145, 31162}, {355, 381}, {376, 11531}, {515, 11224}, {516, 15685}, {517, 3892}, {547, 38098}, {549, 33179}, {553, 25415}, {952, 12101}, {1125, 34718}, {1385, 14891}, {1483, 28198}, {3057, 10122}, {3090, 3679}, {3534, 28228}, {3545, 3632}, {3623, 34632}, {3625, 14892}, {3626, 5055}, {3627, 4301}, {3633, 18483}, {3635, 3655}, {3636, 5054}, {3653, 43174}, {3654, 10165}, {3828, 5070}, {3830, 28236}, {3839, 20050}, {4297, 15691}, {4669, 5844}, {4677, 5603}, {4701, 18493}, {4745, 5886}, {5066, 38155}, {5068, 5734}, {5073, 37727}, {5288, 28461}, {5298, 33176}, {5493, 44245}, {5690, 19883}, {5731, 50820}, {5817, 50838}, {5846, 50958}, {5847, 50961}, {5881, 20049}, {6684, 15721}, {7967, 50819}, {7991, 21735}, {9624, 46935}, {9812, 50863}, {10164, 44580}, {10246, 15716}, {10283, 50822}, {10304, 20057}, {10445, 50123}, {10516, 50789}, {10595, 19875}, {10711, 26726}, {11001, 28232}, {11009, 14526}, {11522, 38074}, {11539, 15808}, {12245, 25055}, {12699, 34748}, {12811, 38076}, {13600, 44663}, {15178, 44682}, {15698, 30392}, {15711, 31662}, {18480, 41987}, {18492, 20014}, {19862, 41984}, {22791, 34648}, {29054, 50778}, {34617, 34719}, {34629, 34690}, {34638, 34773}, {37712, 41099}, {38028, 50826}, {38034, 41990}, {38118, 51006}, {40273, 41988}, {47090, 47593}, {50690, 50873}, {50878, 50923}, {50881, 50888}, {50883, 50886}, {50891, 50910}, {50894, 50908}
X(51077) = midpoint of X(i) and X(j) for these {i,j}: {1, 34631}, {4, 34747}, {145, 31162}, {376, 11531}, {3241, 7982}, {3633, 34627}, {3655, 8148}, {3656, 50805}, {5881, 20049}, {10711, 26726}, {12699, 34748}, {34617, 34719}, {34629, 34690}, {34640, 34743}, {34647, 34710}, {50811, 50872}, {50818, 50865}, {50878, 50923}, {50881, 50888}, {50883, 50886}, {50891, 50910}, {50894, 50908}
X(51077) = reflection of X(i) in X(j) for these {i,j}: {376, 13607}, {549, 33179}, {551, 10222}, {3655, 3635}, {3679, 13464}, {5882, 3241}, {10165, 10247}, {11362, 551}, {31673, 31162}, {31730, 3655}, {34627, 18483}, {34638, 34773}, {34641, 5}, {34648, 22791}, {34718, 1125}, {47745, 381}, {50796, 3656}, {50798, 50802}, {50804, 50801}, {50808, 50824}, {50810, 50828}, {50817, 50827}
X(51077) = complement of X(50817)
X(51077) = anticomplement of X(50827)
X(51077) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 50810, 50828}, {2, 50817, 50827}, {355, 3656, 50806}, {355, 50803, 50796}, {355, 50806, 50803}, {381, 50801, 50796}, {381, 50804, 50801}, {551, 11362, 38068}, {1482, 50805, 3656}, {3241, 50872, 50811}, {3635, 8148, 31730}, {3656, 50796, 946}, {3656, 50798, 50802}, {3656, 50804, 381}, {5734, 31145, 38021}, {7982, 50811, 50872}, {19925, 50797, 50796}, {47745, 50796, 50801}, {50797, 50807, 19925}, {50798, 50802, 50796}, {50801, 50804, 47745}
X(51078) lies on these lines: {2, 28172}, {4, 19876}, {5, 50833}, {10, 23046}, {355, 381}, {382, 50816}, {515, 41106}, {546, 5493}, {551, 3850}, {3091, 50811}, {3524, 50866}, {3534, 50870}, {3545, 3624}, {3576, 50863}, {3579, 41987}, {3622, 18492}, {3634, 38335}, {3817, 50824}, {3828, 3843}, {3830, 50829}, {3832, 28194}, {3839, 9780}, {3845, 10175}, {3854, 38021}, {3855, 5882}, {3857, 28204}, {3858, 11362}, {3860, 28212}, {3861, 38083}, {4297, 11737}, {4301, 41991}, {4678, 31162}, {5055, 50815}, {5066, 11230}, {5587, 50827}, {5657, 28232}, {5847, 50964}, {10164, 12101}, {10165, 19709}, {10172, 15682}, {10516, 50792}, {12512, 35403}, {13464, 50871}, {14269, 31730}, {14892, 19862}, {15689, 31253}, {15808, 34648}, {18483, 50810}, {19872, 46333}, {28555, 51041}, {30308, 50818}, {33697, 47478}, {34379, 50957}, {34638, 50825}, {38089, 48889}, {38098, 40273}, {38141, 50906}, {50687, 50812}, {50689, 50873}
X(51078) = midpoint of X(i) and X(j) for these {i,j}: {4, 19876}, {4678, 31162}, {15808, 34648}, {50800, 50807}, {50813, 50874}, {50820, 50867}
X(51078) = reflection of X(i) in X(j) for these {i,j}: {50796, 50800}, {50808, 50826}
X(51078) = complement of X(50820)
X(51078) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 50867, 50820}, {4, 50813, 50874}, {381, 50799, 50802}, {381, 50800, 50807}, {381, 50803, 50796}, {3656, 19925, 50796}, {12571, 19925, 12645}, {12571, 50801, 50806}, {12645, 50806, 3656}, {19876, 50874, 50813}, {47745, 50796, 50797}, {50799, 50802, 50796}, {50802, 50803, 50799}
X(51079) lies on these lines: {2, 50866}, {3, 38076}, {10, 15688}, {20, 50802}, {30, 19862}, {40, 376}, {515, 15695}, {516, 15697}, {548, 50821}, {550, 551}, {946, 15691}, {1698, 10304}, {3522, 37714}, {3524, 31253}, {3528, 3828}, {3534, 5886}, {3545, 50870}, {3616, 50865}, {3617, 34628}, {3634, 15710}, {3656, 15689}, {3817, 11001}, {4301, 50693}, {4669, 28224}, {5059, 50874}, {5493, 44245}, {5847, 50968}, {8703, 10164}, {10165, 19710}, {10171, 15640}, {10172, 15716}, {10175, 15759}, {11231, 46332}, {11362, 41981}, {15681, 19883}, {15685, 50807}, {15690, 28174}, {15693, 28172}, {15696, 28194}, {15704, 50833}, {15708, 50867}, {15711, 28168}, {17525, 38059}, {18480, 41982}, {18481, 50827}, {19708, 28164}, {28516, 51042}, {31663, 38098}, {31673, 45759}, {31730, 50824}, {31884, 50784}, {33923, 38068}, {34379, 50975}, {37705, 50822}, {38155, 50864}, {43174, 50871}
X(51079) = midpoint of X(i) and X(j) for these {i,j}: {3617, 34628}, {50809, 50811}, {50812, 50819}
X(51079) = reflection of X(i) in X(j) for these {i,j}: {34648, 1698}, {50796, 50825}, {50806, 50828}, {50808, 50812}, {50819, 50815}, {50862, 50799}, {50873, 50802}
X(51079) = complement of X(50866)
X(51079) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 50811, 50816}, {376, 50815, 50808}, {376, 50819, 50812}, {376, 50820, 50815}, {12512, 50810, 50808}, {50808, 50815, 4297}, {50809, 50819, 50811}, {50811, 50812, 50809}, {50811, 50813, 50814}, {50811, 50816, 50808}, {50813, 50814, 50808}, {50814, 50816, 50813}, {50815, 50816, 50811}
X(51080) lies on these lines: {2, 50868}, {3, 50801}, {5, 31666}, {10, 15705}, {30, 3636}, {40, 376}, {515, 12100}, {516, 19710}, {551, 3146}, {1125, 3839}, {1385, 35404}, {1657, 3656}, {3522, 34641}, {3523, 3828}, {3534, 28228}, {3576, 41106}, {3625, 35418}, {3626, 10304}, {3634, 5054}, {3635, 34638}, {3679, 21734}, {3830, 5886}, {3860, 28160}, {4691, 37705}, {4745, 37712}, {5731, 28158}, {5847, 50970}, {8703, 28236}, {10124, 28208}, {10165, 50799}, {12101, 31662}, {12103, 28194}, {12571, 14893}, {13607, 15686}, {13624, 47599}, {14093, 47745}, {15640, 30392}, {15688, 50804}, {15690, 28234}, {15698, 38155}, {15703, 19925}, {15808, 50687}, {18480, 50833}, {19878, 34648}, {28204, 33923}, {30308, 50867}, {30389, 50866}, {31730, 50805}, {31884, 50786}, {34747, 50693}, {35408, 40273}, {38068, 50797}, {38127, 50798}
X(51080) = midpoint of X(i) and X(j) for these {i,j}: {1125, 34628}, {3635, 34638}, {13607, 15686}, {50811, 50815}
X(51080) = reflection of X(i) in X(j) for these {i,j}: {34648, 19878}, {50803, 50828}, {50816, 50815}, {50870, 50802}
X(51080) = complement of X(50868)
X(51080) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 50817, 50808}, {4297, 50808, 50819}, {4297, 50811, 50815}, {50808, 50817, 50814}, {50808, 50819, 50815}, {50811, 50812, 944}, {50811, 50819, 50808}, {50811, 50820, 50818}, {50814, 50815, 376}, {50818, 50819, 50820}, {50818, 50820, 50808}
X(51081) lies on these lines: {2, 50870}, {3, 50803}, {20, 50869}, {30, 19878}, {40, 376}, {516, 15690}, {550, 38022}, {551, 50693}, {3522, 3828}, {3523, 50866}, {3534, 10165}, {3634, 10304}, {3636, 34638}, {3656, 15696}, {4691, 34628}, {4746, 50871}, {5790, 15695}, {5847, 50972}, {8703, 11231}, {9588, 50864}, {10171, 15685}, {10248, 19883}, {12571, 15681}, {12699, 15689}, {14093, 19925}, {15688, 50796}, {15697, 50865}, {15705, 31253}, {15759, 28172}, {18483, 50833}, {21735, 38076}, {28168, 46332}, {28194, 44245}, {28204, 41981}, {28228, 50824}, {31884, 50788}, {34379, 50971}, {38066, 50801}
X(51081) = midpoint of X(i) and X(j) for these {i,j}: {3636, 34638}, {4691, 34628}, {12571, 15681}, {50815, 50816}
X(51081) = complement of X(50870)
X(51081) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 50815, 50816}, {376, 50820, 50808}, {4297, 50808, 50818}, {4297, 50812, 50814}, {12512, 50815, 50811}, {50808, 50818, 50814}, {50808, 50820, 50815}, {50812, 50818, 50808}, {50814, 50815, 4297}
X(51082) lies on these lines: {1, 3839}, {2, 28236}, {3, 34641}, {4, 50868}, {5, 551}, {8, 15705}, {10, 3655}, {20, 34747}, {30, 3244}, {40, 376}, {145, 34628}, {355, 15703}, {381, 13607}, {515, 3656}, {516, 50839}, {517, 19710}, {549, 38098}, {553, 37740}, {946, 14893}, {952, 4669}, {1125, 34627}, {1385, 10124}, {1483, 28208}, {1657, 28194}, {2784, 9884}, {3146, 3241}, {3523, 3679}, {3524, 3626}, {3525, 3828}, {3534, 28234}, {3545, 3636}, {3576, 4745}, {3623, 50866}, {3625, 34773}, {3632, 10304}, {3633, 34632}, {3635, 31162}, {3653, 46219}, {3817, 7967}, {3860, 28224}, {4421, 30283}, {4677, 5731}, {5055, 15808}, {5493, 12103}, {5734, 50867}, {5846, 50970}, {5847, 50973}, {5886, 50800}, {6684, 15718}, {7982, 49138}, {7991, 20049}, {8545, 30331}, {8703, 50830}, {9812, 50874}, {10165, 50832}, {10246, 50797}, {10443, 50131}, {10519, 50786}, {10711, 33812}, {11001, 28228}, {11179, 49536}, {11274, 21635}, {11362, 33923}, {11531, 15683}, {11812, 38176}, {12108, 38068}, {13464, 50806}, {13624, 50825}, {15682, 16200}, {15685, 28232}, {15687, 33179}, {15713, 31662}, {15722, 26446}, {18357, 45757}, {18481, 34638}, {18525, 50799}, {19862, 47599}, {19925, 38314}, {20053, 35418}, {20057, 50687}, {21734, 31145}, {31673, 32900}, {31884, 50789}, {35409, 41869}, {38146, 51006}, {38191, 50983}, {38693, 50893}, {50843, 50906}, {50844, 50907}
X(51082) = midpoint of X(i) and X(j) for these {i,j}: {20, 34747}, {145, 34628}, {3633, 34632}, {3655, 18526}, {7991, 20049}, {11531, 15683}, {18481, 34748}, {50811, 50818}
X(51082) = reflection of X(i) in X(j) for these {i,j}: {10, 3655}, {381, 13607}, {551, 5882}, {3817, 7967}, {4301, 3241}, {5881, 3828}, {10711, 33812}, {15687, 33179}, {21635, 11274}, {31145, 43174}, {31162, 3635}, {34627, 1125}, {34638, 18481}, {34641, 3}, {34648, 1}, {47745, 549}, {49536, 11179}, {50796, 50824}, {50798, 50828}, {50804, 50827}, {50808, 50811}, {50810, 50815}, {50817, 50814}, {50862, 3656}, {50864, 50802}, {50871, 50801}, {50906, 50843}, {50907, 50844}
X(51082) = complement of X(50871)
X(51082) = anticomplement of X(50801)
X(51082) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 50864, 50802}, {2, 50871, 50801}, {3, 50804, 50827}, {40, 50811, 50819}, {40, 50816, 50808}, {40, 50819, 50816}, {376, 50814, 50808}, {376, 50817, 50814}, {549, 47745, 38098}, {944, 50818, 50811}, {3655, 50798, 50828}, {5882, 50796, 50824}, {12512, 50809, 50808}, {50796, 50824, 551}, {50798, 50828, 10}, {50802, 50864, 34648}, {50804, 50827, 34641}, {50808, 50811, 4297}, {50809, 50820, 12512}, {50810, 50811, 50815}, {50810, 50815, 50808}, {50811, 50817, 376}
X(51083) lies on these lines: {2, 50874}, {3, 50807}, {10, 15689}, {20, 19876}, {40, 376}, {165, 50801}, {548, 551}, {550, 50796}, {3522, 50865}, {3524, 50869}, {3529, 50870}, {3534, 10164}, {3616, 35418}, {3624, 10304}, {3634, 46333}, {3656, 15695}, {3817, 19708}, {3828, 17538}, {4678, 34628}, {5493, 50824}, {5847, 50976}, {8703, 10165}, {9588, 50693}, {9780, 34648}, {11001, 50803}, {12103, 38068}, {12571, 15715}, {12699, 15688}, {14093, 19883}, {15690, 28186}, {15696, 38066}, {15698, 28158}, {16191, 50872}, {19862, 45759}, {31673, 50825}, {31884, 50792}, {34379, 50969}
X(51083) = midpoint of X(i) and X(j) for these {i,j}: {20, 19876}, {4678, 34628}, {15808, 34638}, {50813, 50820}
X(51083) = reflection of X(i) in X(j) for these {i,j}: {34648, 9780}, {50796, 50826}, {50808, 50813}, {50862, 50800}
X(51083) = complement of X(50874)
X(51083) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 50812, 50815}, {376, 50813, 50820}, {376, 50816, 50808}, {12245, 50819, 50811}, {12512, 50811, 50808}, {50812, 50815, 50808}, {50815, 50816, 50812}
X(51084) lies on these lines: {1, 15707}, {2, 17502}, {3, 28202}, {5, 50815}, {20, 50807}, {30, 19862}, {40, 15718}, {140, 38083}, {355, 15721}, {376, 10248}, {381, 50866}, {515, 15713}, {516, 15711}, {517, 15693}, {519, 549}, {547, 50862}, {551, 3530}, {631, 28204}, {946, 14891}, {1125, 17504}, {1698, 5054}, {3523, 3653}, {3524, 3579}, {3545, 50867}, {3576, 15701}, {3617, 3655}, {3624, 15688}, {3654, 15719}, {3679, 15720}, {3817, 15690}, {3828, 14869}, {3830, 50820}, {3845, 50870}, {4297, 10124}, {5055, 33697}, {5085, 50791}, {5550, 15710}, {5691, 15723}, {5847, 50980}, {5886, 15698}, {7987, 15694}, {7988, 15685}, {8227, 14093}, {8703, 11230}, {9955, 10304}, {9956, 15702}, {10164, 44580}, {10165, 12100}, {10171, 33699}, {10175, 11540}, {10246, 15722}, {11231, 11812}, {11278, 41983}, {11539, 18480}, {12108, 38068}, {12571, 44903}, {12699, 15705}, {14269, 34595}, {14890, 18357}, {15178, 50805}, {15686, 50869}, {15692, 28198}, {15695, 28154}, {15699, 50803}, {15700, 25055}, {15706, 31162}, {15709, 18481}, {15712, 28194}, {16239, 38076}, {19708, 28146}, {19709, 28168}, {19711, 38028}, {19878, 38071}, {19883, 22793}, {20052, 32900}, {21151, 50840}, {23961, 28466}, {26446, 50818}, {28484, 51049}, {28516, 51045}, {30389, 38066}, {31423, 50871}, {31673, 47599}, {34379, 50987}, {34628, 50800}, {34648, 47598}, {34773, 50801}, {38022, 44682}, {45759, 50816}
X(51084) = midpoint of X(i) and X(j) for these {i,j}: {3617, 3655}, {3656, 50809}, {7987, 15694}, {8227, 14093}, {15695, 30308}, {50797, 50811}, {50799, 50819}, {50806, 50812}, {50822, 50824}, {50825, 50832}
X(51084) = reflection of X(i) in X(j) for these {i,j}: {50821, 50825}, {50832, 50828}
X(51084) = complement of X(50799)
X(51084) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 50819, 50799}, {3, 50806, 50812}, {549, 50824, 50829}, {549, 50828, 50821}, {549, 50832, 50825}, {549, 50833, 50828}, {1698, 50811, 50797}, {3616, 50809, 3656}, {6684, 50823, 50821}, {15700, 25055, 31663}, {19883, 34200, 22793}, {50821, 50828, 1385}, {50822, 50832, 50824}, {50824, 50825, 50822}, {50824, 50826, 50827}, {50824, 50829, 50821}, {50826, 50827, 50821}, {50827, 50829, 50826}, {50828, 50829, 50824}
X(51085) lies on these lines: {1, 10304}, {2, 28236}, {3, 50814}, {4, 551}, {10, 15709}, {30, 3636}, {381, 50868}, {515, 5066}, {516, 3534}, {517, 15759}, {519, 549}, {548, 15178}, {631, 34641}, {944, 19883}, {946, 15684}, {952, 11540}, {1125, 3655}, {3241, 15717}, {3244, 3524}, {3523, 34747}, {3526, 3653}, {3545, 15808}, {3576, 15698}, {3616, 34648}, {3622, 34628}, {3626, 5054}, {3628, 28204}, {3632, 15708}, {3634, 47598}, {3635, 15706}, {3679, 10303}, {3857, 38022}, {4297, 15683}, {4298, 24926}, {4301, 50693}, {4669, 7967}, {4691, 14890}, {4701, 34748}, {4745, 10165}, {4746, 32900}, {5072, 50799}, {5493, 50813}, {5731, 15640}, {5847, 50982}, {5901, 50870}, {7982, 50809}, {8703, 28228}, {9588, 20049}, {10175, 50797}, {10283, 28158}, {11278, 45759}, {11522, 50692}, {12100, 28234}, {12512, 37624}, {12571, 28208}, {12577, 34471}, {13464, 15704}, {15022, 38076}, {15690, 28232}, {15694, 47745}, {15701, 38127}, {15702, 38098}, {15705, 20057}, {16200, 19708}, {18481, 50806}, {18526, 31253}, {19862, 34627}, {19925, 25055}, {23046, 34773}, {28164, 33699}, {31162, 46333}, {31673, 50807}, {33179, 34200}, {34638, 50820}, {35774, 43525}, {35775, 43526}, {37727, 38068}, {37931, 47593}, {43176, 47357}
X(51085) = midpoint of X(i) and X(j) for these {i,j}: {549, 13607}, {1125, 3655}, {3241, 43174}, {3656, 50815}, {3828, 5882}, {4701, 34748}, {33179, 34200}, {43176, 47357}, {50802, 50811}, {50824, 50828}
X(51085) = reflection of X(50829) in X(50828)
X(51085) = complement of X(50801)
X(51085) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {549, 50830, 50821}, {551, 50811, 50802}, {1385, 50821, 50832}, {1385, 50824, 50828}, {3653, 5882, 3828}, {13607, 50828, 50827}, {50821, 50830, 50827}, {50821, 50832, 50828}, {50824, 50825, 1483}, {50824, 50832, 50821}, {50824, 50833, 50831}, {50827, 50828, 549}, {50831, 50832, 50833}, {50831, 50833, 50821}
X(51086) lies on these lines: {2, 28164}, {3, 50802}, {10, 15708}, {20, 50874}, {30, 19878}, {376, 12571}, {381, 50870}, {515, 11812}, {516, 12100}, {517, 41150}, {519, 549}, {551, 3523}, {631, 3828}, {946, 15700}, {1125, 3524}, {3525, 38076}, {3526, 50799}, {3530, 28194}, {3534, 10171}, {3545, 50820}, {3576, 4745}, {3624, 15705}, {3626, 50818}, {3634, 5054}, {3635, 50817}, {3636, 8148}, {3653, 43174}, {3654, 15722}, {3655, 4691}, {3656, 10165}, {3817, 19708}, {4297, 15702}, {4301, 50809}, {4746, 50804}, {5085, 50787}, {5790, 15701}, {5847, 50984}, {7987, 15721}, {7989, 50863}, {8227, 15715}, {8703, 28158}, {10109, 28172}, {10164, 15719}, {10299, 38021}, {10303, 30315}, {10304, 19862}, {11230, 15711}, {11540, 28160}, {12108, 28204}, {12512, 15692}, {15035, 50922}, {15688, 50807}, {15694, 19925}, {15698, 50812}, {15706, 31730}, {15709, 31253}, {15713, 17502}, {15720, 38068}, {15759, 28150}, {15808, 34632}, {18483, 45759}, {20070, 25055}, {21151, 50837}, {21154, 50844}, {21166, 50887}, {28154, 46332}, {28522, 51049}, {30389, 34641}, {34379, 50983}, {34473, 50882}, {34474, 50892}, {38067, 43176}, {38693, 50909}, {38760, 50845}
X(51086) = midpoint of X(i) and X(j) for these {i,j}: {376, 12571}, {3655, 4691}, {50802, 50816}, {50803, 50815}, {50828, 50829}
X(51086) = complement of X(50803)
X(51086) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 50815, 50803}, {3, 50802, 50816}, {549, 50828, 50829}, {549, 50833, 50821}, {1385, 50821, 50831}, {1385, 50825, 50827}, {3624, 15705, 34638}, {6684, 50828, 50824}, {15692, 19883, 12512}, {15709, 34648, 31253}, {50821, 50831, 50827}, {50821, 50833, 50828}, {50825, 50831, 50821}, {50827, 50828, 1385}
X(51087) lies on these lines: {1, 5055}, {2, 38176}, {3, 34747}, {4, 1392}, {5, 50801}, {8, 15709}, {10, 47598}, {30, 3244}, {140, 34641}, {145, 3579}, {381, 33179}, {515, 33699}, {517, 3534}, {519, 549}, {547, 47745}, {548, 5882}, {551, 3628}, {944, 15683}, {952, 3817}, {1482, 15684}, {1864, 31792}, {3524, 20050}, {3526, 3679}, {3545, 20057}, {3623, 9955}, {3625, 14890}, {3626, 11539}, {3632, 5054}, {3633, 13624}, {3635, 18480}, {3636, 15699}, {3653, 10303}, {3654, 7967}, {3829, 32213}, {3830, 16200}, {3845, 28236}, {3857, 13464}, {4421, 23961}, {4669, 11231}, {4677, 10246}, {4745, 38028}, {4870, 37707}, {5072, 5881}, {5288, 28443}, {5603, 50807}, {5731, 50809}, {5844, 15759}, {5846, 50982}, {5847, 50985}, {7972, 50194}, {7982, 17800}, {7991, 50820}, {8148, 34628}, {8703, 28234}, {9041, 12007}, {9956, 38314}, {10109, 38155}, {10124, 38098}, {10172, 41150}, {10247, 50806}, {11194, 33862}, {11224, 28168}, {11274, 22935}, {11531, 15681}, {11812, 38127}, {12645, 25055}, {12702, 50812}, {13606, 22936}, {15022, 38074}, {15640, 28160}, {15687, 50868}, {15693, 31662}, {15701, 30392}, {15704, 28194}, {15708, 20054}, {15717, 20049}, {15808, 47599}, {18481, 34631}, {18526, 31162}, {19709, 37712}, {19710, 28228}, {19875, 37624}, {21627, 49107}, {22793, 50862}, {34690, 34745}, {34698, 34719}, {34773, 50815}, {38021, 50800}, {38167, 51006}, {43150, 49465}, {50693, 50819}
X(51087) = midpoint of X(i) and X(j) for these {i,j}: {1, 34748}, {3, 34747}, {145, 3655}, {3241, 37727}, {3633, 34718}, {3656, 50818}, {8148, 34628}, {11531, 15681}, {18481, 34631}, {18526, 31162}, {34690, 34745}, {34698, 34719}, {50805, 50811}, {50824, 50831}
X(51087) = reflection of X(i) in X(j) for these {i,j}: {381, 33179}, {549, 13607}, {3579, 3655}, {3655, 32900}, {3679, 15178}, {10222, 3241}, {17502, 7967}, {22935, 11274}, {33697, 31162}, {34627, 9955}, {34641, 140}, {34718, 13624}, {47745, 547}, {50821, 50824}, {50823, 50828}, {50830, 50827}
X(51087) = complement of X(50804)
X(51087) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {145, 32900, 3579}, {549, 50827, 50821}, {549, 50830, 50827}, {1483, 50831, 50824}, {3241, 50818, 3656}, {3656, 37727, 50818}, {5690, 50824, 50832}, {5690, 50829, 50821}, {5690, 50832, 50829}, {6684, 50822, 50821}, {50821, 50824, 1385}, {50822, 50833, 6684}, {50823, 50824, 50828}, {50823, 50828, 50821}, {50824, 50830, 549}
X(51088) lies on these lines: {2, 28146}, {3, 19876}, {5, 50869}, {10, 41983}, {140, 50808}, {165, 50806}, {376, 50867}, {381, 50874}, {515, 19711}, {517, 15701}, {519, 549}, {550, 50803}, {551, 12108}, {631, 3656}, {1698, 15706}, {3523, 28204}, {3524, 9780}, {3526, 28202}, {3530, 38068}, {3534, 50866}, {3576, 15722}, {3579, 3624}, {3622, 11278}, {3634, 45759}, {3655, 4678}, {3679, 31666}, {3828, 15712}, {3845, 50816}, {4677, 31662}, {5055, 50812}, {5085, 50785}, {5587, 15716}, {5790, 15693}, {5847, 50988}, {5886, 50809}, {8703, 28172}, {9955, 15709}, {9956, 15692}, {10124, 22793}, {10164, 11812}, {10172, 19710}, {10175, 15759}, {10222, 15720}, {10304, 33697}, {11230, 15713}, {11231, 12100}, {11539, 50802}, {13624, 15707}, {14869, 28194}, {14890, 19862}, {15178, 50817}, {15694, 31663}, {15698, 28160}, {15700, 28208}, {15702, 28198}, {15703, 16192}, {15714, 19925}, {15717, 50819}, {15718, 19875}, {15719, 26446}, {15721, 20070}, {17504, 18480}, {19872, 38335}, {23046, 31253}, {28555, 51049}, {31730, 47598}, {33923, 38076}, {34200, 50862}, {34379, 50981}, {34638, 47599}, {38176, 44580}, {44903, 50870}
X(51088) = midpoint of X(i) and X(j) for these {i,j}: {3, 19876}, {3655, 4678}, {15700, 31423}, {15703, 16192}, {50800, 50820}, {50807, 50813}, {50826, 50833}
X(51088) = reflection of X(50821) in X(50826)
X(51088) = complement of X(50807)
X(51088) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 50813, 50807}, {3, 50800, 50820}, {549, 50825, 50828}, {549, 50826, 50833}, {549, 50829, 50821}, {6684, 50824, 50821}, {19876, 50820, 50800}, {50825, 50828, 50821}, {50828, 50829, 50825}
X(51089) lies on these lines: {2, 38191}, {69, 34747}, {141, 34641}, {193, 3241}, {518, 3898}, {519, 599}, {524, 3244}, {551, 3589}, {597, 49536}, {3619, 3679}, {3626, 21358}, {3630, 28538}, {3632, 21356}, {3635, 47356}, {3636, 47352}, {3828, 49688}, {4669, 9053}, {5032, 20057}, {5846, 51004}, {5847, 50992}, {10516, 50801}, {10519, 50817}, {11178, 47745}, {11179, 13607}, {15808, 48310}, {17133, 49458}, {17765, 49630}, {19883, 49524}, {20582, 38098}, {28194, 48873}, {28204, 39884}, {28236, 47353}, {29574, 49675}, {31884, 50814}, {34379, 51000}, {38049, 47359}, {41153, 51006}, {49473, 50118}, {49543, 51050}, {49771, 50296}
X(51089) = midpoint of X(i) and X(j) for these {i,j}: {69, 34747}, {3241, 16496}, {47358, 50790}
X(51089) = reflection of X(i) in X(j) for these {i,j}: {551, 49465}, {4669, 51003}, {11179, 13607}, {34641, 141}, {47356, 3635}, {47745, 11178}, {49529, 551}, {49536, 597}, {49684, 3241}, {49688, 3828}, {50109, 49464}, {50118, 49473}, {50781, 47358}, {50783, 50787}, {50789, 50786}
X(51089) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {551, 49529, 38089}, {599, 50786, 50781}, {599, 50789, 50786}, {3242, 50790, 47358}, {3416, 47358, 50791}, {3416, 50788, 50781}, {3416, 50791, 50788}, {47358, 50781, 49511}, {47358, 50783, 50787}, {47358, 50789, 599}, {50783, 50787, 50781}
X(51090) lies on these lines: {1, 144}, {2, 4312}, {3, 43182}, {4, 9}, {5, 38151}, {6, 4356}, {7, 1125}, {8, 25728}, {20, 3062}, {31, 4656}, {37, 4349}, {44, 3755}, {55, 21060}, {63, 11019}, {72, 4314}, {140, 38123}, {142, 3647}, {149, 3219}, {162, 2328}, {165, 18228}, {190, 3883}, {191, 1210}, {210, 6154}, {214, 5851}, {226, 3683}, {238, 3663}, {329, 4512}, {386, 4335}, {390, 519}, {392, 4315}, {405, 3671}, {452, 6738}, {480, 8715}, {497, 3929}, {515, 5779}, {518, 3244}, {527, 551}, {528, 4669}, {553, 4423}, {673, 2796}, {726, 51052}, {748, 24177}, {752, 4078}, {758, 5728}, {936, 2951}, {946, 5762}, {954, 5248}, {956, 4342}, {958, 4301}, {960, 971}, {962, 5234}, {991, 24708}, {997, 5732}, {1155, 5316}, {1279, 17334}, {1329, 38130}, {1376, 50808}, {1385, 5843}, {1445, 9843}, {1621, 17781}, {1699, 5273}, {1707, 39595}, {1898, 40661}, {2325, 3416}, {2801, 33337}, {2802, 6068}, {2886, 5325}, {3008, 24248}, {3035, 3452}, {3059, 3678}, {3243, 43179}, {3305, 44447}, {3339, 5129}, {3474, 7308}, {3576, 36996}, {3589, 38187}, {3616, 20059}, {3625, 4133}, {3626, 5686}, {3628, 38172}, {3634, 18230}, {3635, 8236}, {3636, 11038}, {3650, 5439}, {3664, 24695}, {3672, 16469}, {3685, 4416}, {3686, 5695}, {3696, 3707}, {3717, 17336}, {3731, 4307}, {3781, 29353}, {3811, 4326}, {3814, 3826}, {3817, 5745}, {3821, 4759}, {3828, 40333}, {3840, 4368}, {3868, 41861}, {3869, 18412}, {3874, 5572}, {3876, 25722}, {3911, 4679}, {3928, 26105}, {3950, 5847}, {3986, 50302}, {4000, 15601}, {4021, 16475}, {4026, 50115}, {4058, 50308}, {4061, 32929}, {4084, 30329}, {4134, 15733}, {4294, 6743}, {4298, 31435}, {4304, 5692}, {4353, 4419}, {4357, 4676}, {4361, 28557}, {4384, 24280}, {4429, 49630}, {4432, 5845}, {4480, 24349}, {4645, 25101}, {4655, 21255}, {4666, 20078}, {4667, 15569}, {4672, 50290}, {4684, 17347}, {4700, 49486}, {4862, 16020}, {4877, 5327}, {4923, 49485}, {4924, 49712}, {4969, 49461}, {4989, 17301}, {5044, 15587}, {5218, 31142}, {5250, 12527}, {5263, 50093}, {5267, 43177}, {5436, 12563}, {5705, 12571}, {5735, 26363}, {5784, 44238}, {5791, 18483}, {5794, 31672}, {5809, 49168}, {5811, 10268}, {5852, 42819}, {5856, 21630}, {5880, 6666}, {5904, 30628}, {6067, 24387}, {6173, 19883}, {6246, 38127}, {6667, 38207}, {6668, 38208}, {6700, 21153}, {6737, 6872}, {6744, 30330}, {6745, 31018}, {7144, 13755}, {7262, 24210}, {7613, 31183}, {7672, 50573}, {7675, 22836}, {7989, 18231}, {7992, 37423}, {8165, 9588}, {8232, 10198}, {8543, 41572}, {8545, 12573}, {8580, 9778}, {8666, 42884}, {8732, 10200}, {9623, 28228}, {9708, 28194}, {9791, 17023}, {9965, 10582}, {10165, 31657}, {10176, 15726}, {10177, 20116}, {10384, 12575}, {10392, 11113}, {10624, 41229}, {10889, 17733}, {10980, 28610}, {11495, 25440}, {12560, 12848}, {13609, 15855}, {15485, 24231}, {15808, 38053}, {15837, 21075}, {15931, 41561}, {16112, 17647}, {16468, 50114}, {16825, 28526}, {17123, 24175}, {17243, 28570}, {17257, 19868}, {17261, 49476}, {17332, 49484}, {17348, 28530}, {17353, 24723}, {17596, 45204}, {18232, 24389}, {18253, 18482}, {20073, 49446}, {20533, 29594}, {25639, 42356}, {25681, 38122}, {25917, 31391}, {26066, 38108}, {26580, 35263}, {26723, 33100}, {27484, 49474}, {28164, 36991}, {29571, 50307}, {30147, 41563}, {30478, 38036}, {31302, 49771}, {31399, 38179}, {31418, 31446}, {41845, 50095}, {49445, 50017}, {49527, 49709}, {49742, 50294}, {50118, 50296}
X(51090) = midpoint of X(i) and X(j) for these {i,j}: {1, 144}, {9, 5698}, {20, 3062}, {72, 14100}, {390, 5223}, {3869, 18412}, {5759, 11372}, {5904, 30628}, {6172, 50836}, {36996, 41705}
X(51090) = reflection of X(i) in X(j) for these {i,j}: {7, 1125}, {10, 9}, {142, 15254}, {2951, 12512}, {3059, 3678}, {3243, 43179}, {3244, 30331}, {3874, 5572}, {4084, 30329}, {5542, 1001}, {5880, 6666}, {6172, 50837}, {15587, 5044}, {24393, 15481}, {30424, 142}, {31671, 18483}, {35514, 43174}, {36996, 43176}, {43182, 3}, {50834, 6172}
X(51090) = complement of X(4312)
X(51090) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 18249, 10}, {7, 1125, 38054}, {9, 41325, 17355}, {40, 18250, 10}, {63, 40998, 11019}, {142, 15254, 38059}, {142, 38059, 19862}, {165, 18228, 20103}, {329, 4512, 13405}, {390, 6172, 5223}, {390, 50835, 12630}, {452, 12526, 6738}, {1001, 5542, 551}, {2551, 43174, 10}, {3243, 47357, 43179}, {3452, 4640, 10164}, {3576, 36996, 43176}, {3576, 41705, 36996}, {4419, 7290, 4353}, {5223, 50836, 390}, {5745, 24703, 3817}, {5880, 6666, 38204}, {12514, 12572, 10}, {15254, 30424, 19862}, {17355, 50295, 10}, {18230, 38052, 3634}, {30424, 38059, 142}, {31018, 35258, 6745}, {31594, 31595, 6554}, {49520, 49705, 3244}, {50836, 50837, 50834}, {50836, 50840, 50837}
X(51091) lies on these lines: {1, 2}, {515, 33699}, {516, 15685}, {517, 15690}, {518, 41149}, {553, 1317}, {726, 50778}, {946, 34748}, {952, 3860}, {1385, 19711}, {1483, 19710}, {3534, 5882}, {3543, 16189}, {3655, 12512}, {3656, 28236}, {3830, 37727}, {3845, 10222}, {4021, 50132}, {4297, 34631}, {4301, 15682}, {4370, 4982}, {4856, 16814}, {4908, 16668}, {4909, 50099}, {5066, 13464}, {5493, 15697}, {5603, 50803}, {5731, 50816}, {5844, 44580}, {5846, 41152}, {5847, 50998}, {5854, 50844}, {5881, 41106}, {7967, 50808}, {7982, 11001}, {8236, 50834}, {8692, 49685}, {9053, 41153}, {9812, 50870}, {10164, 50817}, {10175, 50804}, {10246, 50829}, {10247, 50796}, {10595, 38076}, {11224, 28158}, {11231, 50830}, {11274, 25416}, {11362, 15693}, {11531, 34638}, {11812, 15178}, {12100, 43174}, {12101, 28204}, {12437, 19706}, {12571, 34627}, {12630, 38024}, {13607, 15759}, {15481, 43179}, {15533, 49681}, {15534, 49684}, {15711, 17502}, {15722, 34718}, {16200, 50818}, {16669, 50113}, {16675, 50131}, {17355, 50123}, {22165, 49465}, {25716, 43186}, {28228, 50811}, {28522, 51055}, {34379, 51000}, {34637, 34719}, {34649, 34690}, {34710, 37545}, {37624, 38068}, {37904, 47491}, {38138, 50801}, {41147, 50887}, {47097, 47537}, {47311, 47489}, {47358, 50989}, {47538, 47593}, {49471, 49513}, {49505, 50992}, {49679, 50993}, {50786, 51003}, {50790, 51005}, {50805, 50814}
X(51091) = midpoint of X(i) and X(j) for these {i,j}: {10, 34747}, {145, 551}, {946, 34748}, {3241, 3244}, {3625, 20049}, {3633, 34641}, {4297, 34631}, {11274, 25416}, {11531, 34638}, {34637, 34719}, {34649, 34690}, {47097, 47537}, {47538, 47593}, {50790, 51005}
X(51091) = reflection of X(i) in X(j) for these {i,j}: {3626, 551}, {3635, 3241}, {3679, 3636}, {3828, 1}, {4701, 3828}, {12512, 3655}, {31145, 4691}, {34627, 12571}, {34641, 3634}, {50786, 51003}
X(51091) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3633, 4678}, {1, 4701, 1125}, {1, 20014, 10}, {1, 31145, 19883}, {145, 3623, 5550}, {3623, 20053, 1}, {3633, 38314, 34641}, {3635, 31253, 20057}, {3828, 4669, 4745}, {4691, 19883, 3828}, {4701, 4745, 4669}, {19883, 31145, 4691}, {20049, 20057, 25055}, {20049, 25055, 3625}, {20057, 46933, 1}, {34641, 38314, 3634}
X(51092) lies on these lines: {1, 2}, {515, 50873}, {517, 15697}, {518, 50840}, {944, 28202}, {952, 41099}, {1317, 21454}, {1482, 15682}, {1483, 3534}, {3242, 50992}, {3543, 37727}, {3654, 31662}, {3830, 28224}, {3839, 10222}, {3845, 34748}, {3871, 19705}, {4373, 17378}, {4460, 30712}, {4740, 49475}, {4747, 28309}, {5066, 10247}, {5603, 50799}, {5731, 50812}, {5844, 15693}, {5846, 50791}, {7967, 8703}, {7974, 36331}, {7975, 35750}, {7982, 15683}, {8148, 19710}, {8584, 50790}, {9812, 50866}, {10109, 12645}, {10246, 50825}, {10595, 19709}, {10989, 47489}, {11001, 28174}, {11160, 49681}, {11812, 50822}, {12100, 12245}, {15178, 15721}, {15300, 50888}, {15533, 50998}, {15570, 38092}, {15640, 28160}, {15678, 31888}, {15692, 31666}, {15698, 50824}, {15713, 37624}, {15719, 34718}, {16189, 17578}, {16200, 50864}, {16677, 37654}, {18146, 25296}, {18526, 33699}, {21356, 49679}, {22867, 33624}, {22912, 33622}, {28484, 51055}, {28516, 51054}, {28582, 50778}, {32093, 50101}, {33179, 38074}, {37909, 47491}, {47313, 47493}, {50782, 50991}
X(51092) = midpoint of X(i) and X(j) for these {i,j}: {1698, 34747}, {20049, 20052}
X(51092) = reflection of X(i) in X(j) for these {i,j}: {3623, 3241}, {4668, 551}, {31145, 3617}, {34641, 31253}
X(51092) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 145, 20054}, {1, 3633, 4746}, {1, 20054, 46932}, {1, 46932, 3622}, {2, 3621, 4669}, {145, 3623, 3617}, {145, 46933, 20050}, {145, 46934, 20014}, {3241, 38314, 3635}, {3617, 20054, 20052}, {3623, 20052, 1}, {3635, 34747, 38314}, {4668, 46933, 3617}, {4669, 38314, 2}, {20014, 20057, 46934}, {34747, 38314, 3621}
X(51093) lies on these lines: {1, 2}, {4, 16189}, {6, 4898}, {7, 50108}, {9, 13602}, {30, 7982}, {35, 11194}, {36, 4421}, {40, 1483}, {44, 36911}, {55, 8275}, {57, 1317}, {100, 11274}, {106, 36593}, {149, 18513}, {165, 7967}, {191, 6762}, {193, 50090}, {355, 5066}, {376, 5882}, {381, 5881}, {484, 3895}, {515, 11224}, {516, 50839}, {517, 3534}, {518, 3899}, {524, 16496}, {528, 3243}, {529, 30323}, {535, 34611}, {536, 49469}, {537, 49445}, {549, 9588}, {553, 3476}, {597, 16491}, {599, 49465}, {664, 21314}, {726, 51054}, {740, 51037}, {750, 4954}, {752, 49695}, {758, 10032}, {858, 47537}, {940, 16490}, {942, 19706}, {944, 11001}, {946, 34627}, {952, 1699}, {956, 4428}, {962, 15640}, {996, 32943}, {999, 48696}, {1100, 50087}, {1120, 2163}, {1320, 5561}, {1376, 37602}, {1385, 15693}, {1449, 17281}, {1482, 3830}, {1697, 6763}, {1757, 49691}, {1768, 12703}, {1992, 49684}, {2093, 34607}, {2094, 21578}, {2098, 4930}, {2099, 4654}, {2136, 3338}, {2550, 38024}, {2796, 49446}, {2800, 50910}, {2802, 3873}, {3036, 38026}, {3058, 7962}, {3081, 12626}, {3158, 5854}, {3189, 18217}, {3242, 15533}, {3247, 17330}, {3251, 9260}, {3295, 5288}, {3303, 5258}, {3304, 16417}, {3340, 4355}, {3416, 50991}, {3524, 11362}, {3543, 4301}, {3545, 13464}, {3555, 3901}, {3576, 3654}, {3586, 28609}, {3653, 5690}, {3664, 4460}, {3680, 5557}, {3681, 3898}, {3723, 4034}, {3731, 37654}, {3746, 12513}, {3748, 36922}, {3750, 16499}, {3751, 8584}, {3759, 31333}, {3761, 4479}, {3813, 17530}, {3817, 50801}, {3829, 7951}, {3839, 5734}, {3860, 18492}, {3871, 7280}, {3874, 3885}, {3875, 4888}, {3879, 4862}, {3880, 5902}, {3881, 14923}, {3893, 5045}, {3902, 4980}, {3913, 5563}, {3922, 50191}, {3928, 5119}, {3929, 31393}, {3946, 4916}, {3973, 4856}, {4007, 16884}, {4018, 34620}, {4297, 15697}, {4304, 28610}, {4305, 34646}, {4316, 20075}, {4324, 20076}, {4338, 34637}, {4360, 17274}, {4370, 16670}, {4383, 16489}, {4464, 17151}, {4644, 28301}, {4649, 48805}, {4653, 4921}, {4659, 4795}, {4664, 49448}, {4684, 50091}, {4688, 49459}, {4692, 42034}, {4693, 49721}, {4704, 49504}, {4715, 17318}, {4720, 42025}, {4737, 4975}, {4738, 18743}, {4740, 49479}, {4762, 50767}, {4803, 5333}, {4851, 50112}, {4852, 4859}, {4864, 31151}, {4867, 31142}, {4870, 9578}, {4873, 16666}, {4889, 17296}, {4900, 14563}, {4909, 32087}, {4910, 17390}, {4929, 16468}, {4969, 16676}, {4995, 13384}, {5010, 25439}, {5048, 5727}, {5054, 15178}, {5055, 9624}, {5223, 47357}, {5251, 6767}, {5264, 16401}, {5290, 10944}, {5298, 41687}, {5425, 6173}, {5426, 10389}, {5542, 12630}, {5559, 31436}, {5587, 10247}, {5603, 30308}, {5657, 15719}, {5687, 40726}, {5692, 5919}, {5731, 50808}, {5836, 50190}, {5839, 16673}, {5846, 22165}, {5847, 50992}, {5886, 10109}, {5903, 24473}, {5904, 9957}, {6172, 30331}, {6174, 12735}, {6256, 16207}, {6264, 37533}, {7174, 50296}, {7290, 49534}, {7308, 15935}, {7426, 47491}, {7966, 41338}, {7974, 36329}, {7975, 35751}, {7976, 11055}, {7987, 12245}, {7989, 10595}, {8148, 15685}, {8162, 9708}, {8186, 11208}, {8187, 11207}, {8192, 9591}, {8227, 12645}, {8236, 50835}, {8666, 17549}, {8715, 13587}, {9053, 16475}, {9331, 16975}, {9612, 34640}, {9613, 11009}, {9614, 34647}, {9778, 50815}, {9779, 50803}, {9802, 17483}, {9812, 50862}, {9819, 10385}, {9875, 50886}, {9881, 36521}, {9884, 50888}, {9897, 10707}, {9900, 47866}, {9901, 47865}, {9902, 14711}, {10165, 50827}, {10246, 15701}, {10436, 50088}, {10711, 25485}, {10826, 34717}, {10827, 34700}, {10912, 50397}, {10914, 18398}, {10980, 11041}, {11011, 11237}, {11113, 11523}, {11160, 49505}, {11235, 37708}, {11236, 37711}, {11260, 37571}, {11278, 18526}, {11280, 12559}, {11518, 11524}, {11520, 17579}, {11525, 44841}, {11529, 34612}, {11533, 49735}, {11540, 38028}, {11852, 16211}, {11910, 34582}, {12101, 22791}, {12258, 50885}, {12531, 30852}, {12607, 17533}, {12625, 17532}, {12644, 30408}, {12646, 30420}, {12699, 33699}, {12702, 15695}, {12781, 36768}, {13174, 15300}, {13178, 36523}, {13407, 21627}, {13624, 15716}, {13888, 49232}, {13942, 49233}, {14584, 36909}, {14976, 28562}, {15170, 34606}, {15485, 49497}, {15569, 49689}, {15675, 35016}, {15679, 34195}, {15690, 34773}, {15692, 43174}, {15700, 31425}, {15706, 31666}, {15713, 26446}, {15718, 31447}, {15759, 35242}, {15803, 34711}, {16173, 50893}, {16191, 28236}, {16205, 41698}, {16206, 48482}, {16484, 49680}, {16590, 16672}, {16667, 17314}, {16777, 50082}, {17078, 25716}, {17160, 39704}, {17179, 33296}, {17271, 17393}, {17272, 17320}, {17297, 49472}, {17306, 50081}, {17319, 50074}, {17556, 37721}, {17728, 50842}, {18145, 24524}, {18481, 19710}, {18514, 20060}, {18613, 19293}, {19738, 48863}, {20070, 34638}, {21630, 31053}, {22650, 44422}, {22713, 33706}, {22867, 36388}, {22912, 36386}, {24222, 33141}, {24393, 38025}, {24715, 36525}, {24857, 25430}, {25303, 32104}, {25590, 50099}, {28224, 50866}, {28313, 35578}, {28329, 49460}, {28337, 41312}, {28444, 37622}, {28466, 34486}, {28503, 50126}, {28522, 51056}, {28554, 49499}, {28580, 50284}, {28581, 50086}, {31140, 50194}, {31150, 48285}, {31178, 49474}, {31231, 36920}, {31423, 37624}, {32049, 37702}, {32941, 46922}, {33076, 50076}, {33087, 48821}, {33176, 50443}, {33595, 37525}, {34379, 51001}, {34657, 34667}, {34674, 34685}, {34689, 37724}, {34712, 34729}, {34714, 34737}, {36767, 50848}, {36769, 50849}, {37556, 41229}, {37718, 50890}, {37904, 47493}, {38023, 49524}, {38034, 50799}, {38047, 50953}, {38140, 50797}, {39948, 50048}, {39980, 42049}, {44553, 48286}, {47097, 47536}, {47311, 47535}, {47313, 47540}, {47314, 47538}, {47321, 47472}, {47352, 49690}, {47724, 50760}, {47867, 50852}, {47869, 50761}, {48167, 48296}, {48807, 48819}, {48812, 48824}, {49450, 50094}, {49511, 50990}, {49675, 50080}, {49708, 49747}, {49709, 49748}, {49723, 49739}, {50041, 50064}, {50046, 50069}, {50049, 50070}, {50066, 50072}, {50075, 50111}, {50121, 50127}, {50781, 50994}, {50783, 50993}, {50789, 50949}
X(51093) = midpoint of X(i) and X(j) for these {i,j}: {1, 34747}, {8, 20049}, {145, 3241}, {599, 49679}, {944, 34631}, {1482, 34748}, {3633, 3679}, {9884, 50888}, {10031, 50894}, {11531, 34628}, {20050, 31145}, {31178, 49678}, {34690, 34719}, {34699, 34749}, {47097, 47536}, {50790, 51000}
X(51093) = reflection of X(i) in X(j) for these {i,j}: {1, 3241}, {8, 551}, {40, 3655}, {100, 11274}, {165, 7967}, {376, 5882}, {381, 10222}, {551, 3635}, {599, 49465}, {1699, 16200}, {1992, 49684}, {3241, 3244}, {3543, 4301}, {3621, 34641}, {3625, 3828}, {3632, 3679}, {3633, 34747}, {3654, 50824}, {3655, 1483}, {3679, 1}, {3681, 3898}, {3751, 47356}, {4659, 4795}, {4664, 49471}, {4677, 2}, {4740, 49479}, {5223, 47357}, {5587, 10247}, {5691, 31162}, {5692, 5919}, {5881, 381}, {5903, 24473}, {5904, 31165}, {6172, 30331}, {6173, 42871}, {6174, 12735}, {7426, 47491}, {7991, 376}, {9875, 50886}, {9897, 10707}, {10711, 25485}, {11160, 49505}, {11531, 34631}, {11852, 16211}, {19876, 20057}, {20070, 34638}, {24473, 34791}, {31140, 50194}, {31145, 10}, {31150, 48285}, {31151, 4864}, {31159, 11011}, {31160, 5048}, {31162, 1482}, {31165, 9957}, {31178, 49478}, {34606, 15170}, {34627, 946}, {34628, 944}, {34632, 4297}, {34641, 1125}, {34690, 34749}, {34718, 1385}, {34719, 34699}, {34747, 145}, {37712, 5603}, {44553, 48286}, {47321, 47472}, {47358, 50998}, {47724, 50760}, {47869, 50761}, {48167, 48296}, {48807, 48819}, {48812, 48824}, {49448, 4664}, {49450, 50094}, {49459, 4688}, {49474, 31178}, {49577, 49579}, {49581, 49583}, {49688, 597}, {49723, 49739}, {50041, 50064}, {50046, 50069}, {50049, 50070}, {50066, 50072}, {50075, 50111}, {50089, 32941}, {50126, 50130}, {50783, 51003}, {50789, 50949}, {50817, 3654}, {50885, 12258}, {50950, 47358}
X(51093) = anticomplement of X(4669)
X(51093) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 8, 3624}, {1, 145, 3633}, {1, 3625, 19872}, {1, 3632, 1698}, {1, 3633, 3632}, {1, 3679, 25055}, {1, 4668, 1125}, {1, 4677, 2}, {1, 19875, 551}, {1, 20050, 4816}, {1, 30286, 44675}, {1, 34595, 3636}, {2, 8, 4745}, {2, 4677, 3679}, {2, 4745, 19875}, {8, 551, 19875}, {8, 3635, 1}, {8, 19875, 3679}, {8, 46934, 10}, {10, 3623, 1}, {145, 3244, 1}, {145, 3623, 20050}, {551, 3624, 25055}, {551, 4745, 2}, {551, 19875, 3624}, {1125, 3621, 4668}, {1125, 20057, 1}, {1317, 26726, 5541}, {3241, 3633, 25055}, {3241, 20049, 551}, {3241, 20050, 38314}, {3241, 34747, 3679}, {3241, 38314, 3623}, {3555, 5697, 3901}, {3576, 50817, 3654}, {3616, 20014, 3625}, {3617, 3636, 34595}, {3621, 20057, 1125}, {3621, 46932, 8}, {3622, 20053, 3626}, {3623, 20014, 46930}, {3623, 20050, 10}, {3623, 31145, 38314}, {3624, 3679, 19875}, {3632, 25055, 3679}, {3635, 20049, 19875}, {3654, 50824, 3576}, {3679, 25055, 1698}, {4360, 50132, 17274}, {4393, 29605, 17284}, {4746, 15808, 46933}, {5550, 20052, 4691}, {5603, 50796, 30308}, {5881, 10222, 11522}, {7972, 25416, 12653}, {9780, 20054, 4701}, {10056, 10072, 10321}, {10530, 11239, 45701}, {10530, 11240, 45700}, {10595, 47745, 7989}, {11239, 45700, 3584}, {11240, 45701, 3582}, {11278, 18526, 41869}, {12245, 13607, 7987}, {12645, 33179, 8227}, {16834, 17389, 29573}, {19872, 20014, 3632}, {19875, 19876, 46932}, {19876, 34641, 3679}, {20014, 41150, 4677}, {20050, 38314, 31145}, {29574, 50129, 16833}, {29585, 49770, 16832}, {30308, 37712, 50796}, {31145, 38314, 10}, {36444, 36462, 34747}, {38314, 46934, 551}, {49469, 49490, 49532}, {49470, 49498, 49445}, {49475, 49490, 49469}, {49478, 49678, 49474}, {50113, 50131, 9}, {50120, 50125, 6173}
X(51094) lies on these lines: {1, 2}, {165, 50805}, {382, 16189}, {515, 50874}, {517, 50820}, {952, 50807}, {1483, 34628}, {3534, 11531}, {3830, 16200}, {4908, 16667}, {5066, 37712}, {5587, 50831}, {5844, 50833}, {5846, 50792}, {5881, 38071}, {7967, 50813}, {7982, 15681}, {7991, 15688}, {10222, 14269}, {10247, 30308}, {11001, 28232}, {11224, 28146}, {11278, 15685}, {11737, 37714}, {13607, 19708}, {15687, 37727}, {15693, 30392}, {15698, 28234}, {15700, 30389}, {16191, 28186}, {19709, 33179}, {28212, 50811}, {28555, 50778}, {37718, 50846}, {41099, 50871}, {47314, 47540}
X(51094) = reflection of X(i) in X(j) for these {i,j}: {3679, 3622}, {4678, 551}, {19876, 1}
X(51094) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3244, 3635, 20050}, {3622, 20052, 9780}, {3636, 4669, 2}, {3679, 19862, 19875}, {3679, 25055, 19877}, {20050, 20057, 3622}
X(51095) lies on these lines: {1, 2}, {515, 50870}, {517, 50816}, {952, 50803}, {1317, 3982}, {3534, 28228}, {3845, 28236}, {4796, 28301}, {4856, 16677}, {5066, 33179}, {5844, 50829}, {5846, 50788}, {5854, 50845}, {5882, 15681}, {6154, 11274}, {7967, 50815}, {8236, 50837}, {8703, 13607}, {10222, 15687}, {10247, 50802}, {11278, 19710}, {11362, 15707}, {11531, 15697}, {12100, 28234}, {12512, 34631}, {12630, 38094}, {13464, 38071}, {14269, 37727}, {15682, 16200}, {15700, 43174}, {15713, 50827}, {15719, 50817}, {16189, 49135}, {17378, 39707}, {17504, 31666}, {19705, 25439}, {19708, 50814}, {19709, 50801}, {19925, 34748}, {28522, 50778}, {34379, 50998}, {47311, 47540}, {47312, 47491}, {50786, 50993}
X(51095) = midpoint of X(i) and X(j) for these {i,j}: {145, 3828}, {3241, 3635}, {3626, 34747}, {12512, 34631}, {19925, 34748}
X(51095) = reflection of X(i) in X(j) for these {i,j}: {4691, 551}, {4745, 41150}
X(51095) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3633, 46932}, {1, 4745, 41150}, {2, 4677, 38098}, {2, 20050, 4677}, {2, 34641, 4745}, {1125, 46931, 19878}, {3244, 15808, 145}, {3244, 20057, 3626}, {20054, 20057, 1}
X(51096) lies on these lines: {1, 2}, {30, 47537}, {515, 50805}, {516, 50818}, {517, 19710}, {518, 51059}, {537, 49461}, {944, 34638}, {946, 3860}, {952, 12101}, {1385, 44580}, {1386, 41153}, {1482, 34648}, {1483, 15711}, {2784, 50883}, {2802, 50846}, {3242, 50989}, {3534, 5493}, {3654, 15716}, {3817, 50798}, {3830, 4301}, {3839, 16189}, {3950, 50131}, {4098, 37654}, {4297, 15690}, {4398, 4464}, {4536, 31165}, {4539, 5919}, {4664, 49504}, {4898, 15828}, {4908, 16671}, {4910, 21255}, {5066, 10222}, {5603, 50801}, {5731, 50814}, {5844, 15759}, {5846, 51004}, {5847, 50790}, {5850, 50839}, {5881, 41099}, {5882, 8703}, {7967, 50817}, {7982, 15682}, {7991, 15697}, {8236, 50838}, {8584, 49684}, {8666, 19704}, {8715, 19705}, {9041, 41149}, {9053, 51005}, {9812, 50868}, {9963, 26726}, {10164, 19711}, {10165, 50823}, {10246, 50827}, {10247, 50804}, {11224, 50864}, {11362, 12100}, {11599, 41147}, {11710, 41151}, {11725, 41148}, {12258, 41154}, {13464, 19709}, {13607, 34718}, {15178, 15713}, {15492, 50123}, {15533, 49505}, {15534, 49681}, {15685, 28194}, {15695, 28234}, {15698, 43174}, {15722, 50828}, {16200, 50802}, {16496, 50992}, {28164, 50872}, {28204, 33699}, {28236, 50862}, {28581, 51060}, {34637, 34749}, {34649, 34699}, {37712, 50803}, {37904, 47489}, {38034, 50796}, {38076, 47745}, {38191, 51006}, {41152, 49511}, {47311, 47536}, {47356, 49536}, {49465, 50991}, {49475, 49520}, {49535, 49678}, {50777, 50778}, {50781, 50998}
X(51096) = midpoint of X(i) and X(j) for these {i,j}: {1, 20049}, {145, 34747}, {3241, 3633}, {3679, 20050}
X(51096) = reflection of X(i) in X(j) for these {i,j}: {10, 3241}, {551, 3244}, {3625, 551}, {3632, 3828}, {3679, 3635}, {31145, 1125}, {34637, 34749}, {34638, 944}, {34641, 1}, {34648, 1482}, {34649, 34699}, {34718, 13607}, {49504, 4664}, {49536, 47356}, {50777, 50778}, {50781, 50998}
X(51096) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2, 41150}, {1, 8, 31253}, {1, 20054, 4746}, {10, 3622, 19862}, {10, 4677, 4669}, {10, 19883, 19876}, {551, 3625, 38098}, {3241, 3621, 25055}, {3244, 19862, 3635}, {3623, 4701, 15808}, {3626, 34595, 10}, {3633, 34595, 20014}, {4464, 50132, 50108}, {4691, 46931, 10}, {4745, 34641, 4669}, {4745, 41150, 2}
X(51097) lies on these lines: {1, 2}, {30, 16189}, {165, 15759}, {515, 50866}, {517, 15695}, {952, 30308}, {1317, 4654}, {1449, 4908}, {1482, 15685}, {1483, 31162}, {1699, 50818}, {3534, 7982}, {3576, 15716}, {3654, 19711}, {3655, 11531}, {3656, 12101}, {3830, 10222}, {3845, 37727}, {3928, 16558}, {4301, 15640}, {4421, 37587}, {4902, 17378}, {4910, 31312}, {5066, 5881}, {5603, 50871}, {5844, 50825}, {5846, 50784}, {5882, 11001}, {5886, 50831}, {7967, 50819}, {7987, 15711}, {7988, 50798}, {7991, 8703}, {8236, 50840}, {9624, 10109}, {10246, 15722}, {10247, 50806}, {10283, 50804}, {10980, 12735}, {11224, 19710}, {11274, 12653}, {11362, 15719}, {11518, 19706}, {11522, 41099}, {12100, 30389}, {13464, 41106}, {13607, 34631}, {15015, 50894}, {15178, 15701}, {15533, 49465}, {15534, 16496}, {15570, 38024}, {15678, 16126}, {15693, 31447}, {16173, 50846}, {16191, 28150}, {16200, 28160}, {16475, 50790}, {16667, 50113}, {16673, 50131}, {19709, 37714}, {22165, 49681}, {24858, 39980}, {28484, 50778}, {28516, 51055}, {28538, 50989}, {33179, 34748}, {37712, 50797}, {38316, 50838}, {41149, 47356}, {47313, 47491}, {50782, 51003}, {50791, 50950}
X(51097) = midpoint of X(i) and X(j) for these {i,j}: {3241, 3623}, {4668, 34747}
X(51097) = reflection of X(i) in X(j) for these {i,j}: {3617, 551}, {3654, 50832}, {3679, 3616}, {50782, 51003}, {50950, 50791}
X(51097) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 19876, 38314}, {1, 34747, 19875}, {2, 41150, 25055}, {3244, 3634, 145}, {3616, 46933, 19862}, {3617, 3623, 20057}, {3621, 19883, 3679}, {3632, 38314, 19876}, {3633, 20057, 1}, {3679, 25055, 3634}, {3679, 34595, 19875}, {4669, 41150, 2}, {33179, 34748, 38021}
X(51098) lies on these lines: {2, 5850}, {7, 551}, {10, 30340}, {30, 43176}, {142, 3828}, {516, 3534}, {518, 3968}, {519, 1056}, {527, 1125}, {528, 33812}, {726, 51057}, {971, 50802}, {2801, 50909}, {3634, 38093}, {3635, 5880}, {3636, 30424}, {3654, 38123}, {3679, 38094}, {4312, 38314}, {4353, 17392}, {4669, 38052}, {4677, 38201}, {4896, 50303}, {5220, 31253}, {5762, 50828}, {5856, 50844}, {6172, 19883}, {9352, 13405}, {11038, 50839}, {20195, 38101}, {21151, 50808}, {27475, 50777}, {28194, 31657}, {31162, 43182}, {34379, 51002}, {34641, 38092}, {34648, 38073}, {36996, 38021}, {38046, 51005}, {38049, 50997}, {38098, 40333}, {38107, 50796}, {38111, 50821}, {38122, 50829}, {38150, 50803}, {38187, 47359}, {38316, 41150}
X(51098) = midpoint of X(i) and X(j) for these {i,j}: {7, 551}, {5542, 6173}, {30424, 47357}, {31162, 43182}
X(51098) = reflection of X(i) in X(j) for these {i,j}: {3828, 142}, {47357, 3636}
X(51098) = complement of X(50834)
X(51098) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 38024, 551}, {25557, 43180, 1125}
X(51099) lies on these lines: {1, 527}, {2, 210}, {7, 528}, {8, 17297}, {9, 551}, {10, 38093}, {30, 47507}, {55, 2094}, {65, 34711}, {69, 50310}, {142, 3679}, {144, 42819}, {145, 5880}, {226, 31146}, {376, 37569}, {381, 20330}, {388, 30318}, {390, 5048}, {495, 41555}, {497, 31164}, {516, 7967}, {519, 1056}, {529, 15933}, {535, 3488}, {537, 51058}, {553, 4321}, {599, 48849}, {938, 11236}, {942, 34619}, {966, 49505}, {971, 3656}, {1001, 6172}, {1022, 6006}, {1159, 10427}, {1319, 12848}, {2345, 49479}, {2346, 17549}, {2801, 3892}, {3189, 11112}, {3242, 17392}, {3244, 43180}, {3296, 3811}, {3452, 30350}, {3474, 3957}, {3485, 3889}, {3486, 34605}, {3487, 3881}, {3543, 12678}, {3555, 28629}, {3616, 5220}, {3622, 15254}, {3635, 30424}, {3653, 31658}, {3654, 38030}, {3655, 43161}, {3748, 9965}, {3828, 20195}, {3886, 50119}, {3945, 49465}, {4000, 49490}, {4298, 34701}, {4307, 4864}, {4310, 17301}, {4313, 34620}, {4402, 49680}, {4428, 28610}, {4452, 49475}, {4454, 4702}, {4648, 16496}, {4669, 38054}, {4677, 38052}, {4684, 17294}, {4745, 38204}, {4860, 6174}, {4869, 49688}, {4870, 8232}, {5049, 10177}, {5223, 25055}, {5252, 30275}, {5298, 41712}, {5328, 17051}, {5572, 34647}, {5731, 38454}, {5732, 28194}, {5735, 5882}, {5744, 37703}, {5762, 50824}, {5766, 34471}, {5784, 11036}, {5805, 28204}, {5809, 11238}, {5850, 38316}, {5856, 50843}, {6600, 16371}, {7222, 32941}, {7672, 11239}, {7675, 10385}, {7677, 42885}, {7982, 43177}, {8236, 15678}, {8543, 22759}, {9041, 17313}, {9776, 41711}, {9850, 34640}, {10056, 30274}, {10072, 18412}, {10707, 12831}, {11495, 34632}, {15185, 34625}, {15590, 49453}, {17146, 17740}, {17251, 39581}, {17264, 49499}, {17316, 24841}, {17373, 31145}, {18221, 32049}, {18391, 38055}, {19870, 22312}, {19875, 24393}, {20057, 30332}, {21151, 50810}, {21153, 50828}, {24231, 50080}, {24325, 48802}, {24349, 50107}, {24470, 34707}, {24473, 34744}, {26105, 31142}, {28538, 47595}, {30329, 45701}, {31140, 36845}, {31178, 50316}, {31995, 49460}, {32922, 39721}, {34627, 38073}, {34631, 35514}, {34641, 38094}, {34718, 38065}, {35167, 36221}, {35578, 48805}, {38048, 51006}, {38107, 50798}, {38111, 50823}, {38122, 50821}, {38150, 50796}, {38315, 50997}, {42047, 42057}, {42049, 42055}, {48830, 50285}, {48851, 49511}, {49446, 50110}, {49491, 50313}, {49675, 50301}
X(51099) = midpoint of X(i) and X(j) for these {i,j}: {7, 3241}, {3243, 6173}, {34631, 35514}
X(51099) = reflection of X(i) in X(j) for these {i,j}: {9, 551}, {381, 20330}, {2550, 6173}, {3241, 42871}, {3679, 142}, {5698, 47357}, {6172, 1001}, {6173, 5542}, {10177, 5049}, {34632, 11495}, {38053, 11038}, {38057, 38053}, {38200, 38054}, {43161, 3655}, {47357, 1}
X(51099) = complement of X(50835)
X(51099) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 14151, 3476}, {9, 551, 38025}, {145, 30340, 5880}, {3242, 17392, 48856}, {3243, 5542, 2550}, {3475, 3873, 24477}, {3679, 38024, 142}, {6172, 38314, 1001}, {11529, 41570, 2550}, {20195, 38097, 3828}, {51002, 51057, 2}
X(51100) lies on these lines: {1, 50839}, {2, 165}, {7, 3679}, {8, 43180}, {9, 3828}, {10, 527}, {142, 214}, {376, 43151}, {377, 43177}, {390, 25055}, {443, 4301}, {518, 3919}, {519, 1056}, {740, 51057}, {971, 50796}, {1001, 16417}, {1125, 38093}, {1698, 50840}, {1738, 4349}, {2801, 3753}, {2951, 3543}, {3008, 50303}, {3059, 24473}, {3241, 38024}, {3244, 25557}, {3545, 11372}, {3624, 30332}, {3632, 30340}, {3634, 5698}, {3654, 38121}, {3655, 38065}, {3656, 38107}, {3663, 50291}, {3664, 50282}, {3717, 49722}, {3754, 5784}, {3755, 17392}, {3814, 3826}, {3823, 49726}, {3833, 10177}, {4078, 28542}, {4208, 5735}, {4297, 6253}, {4312, 6172}, {4315, 30379}, {4353, 7613}, {4356, 50080}, {4645, 50095}, {4745, 5850}, {4896, 49772}, {5251, 30295}, {5493, 8728}, {5691, 43181}, {5762, 50821}, {5805, 28194}, {5847, 51002}, {5853, 38054}, {5856, 50841}, {5883, 15733}, {6006, 21198}, {6684, 50740}, {8582, 17577}, {9776, 31146}, {10175, 38216}, {11019, 31140}, {11024, 19925}, {11362, 50238}, {11495, 16418}, {12436, 45700}, {12512, 50739}, {15587, 30329}, {17057, 50573}, {17532, 38076}, {17564, 19862}, {18230, 19876}, {19706, 38122}, {20195, 38025}, {21060, 31164}, {21151, 50811}, {21255, 50311}, {24175, 33109}, {24199, 50310}, {24393, 38098}, {24715, 29571}, {25351, 31191}, {26040, 31142}, {28204, 31657}, {28580, 29600}, {28629, 34701}, {29594, 31151}, {31162, 35514}, {31658, 38068}, {34648, 43182}, {36996, 38074}, {38046, 51000}, {38047, 50997}, {38086, 47356}, {38111, 50824}, {38185, 47359}, {38187, 51005}, {38314, 43179}, {41141, 50126}, {43172, 50428}, {49725, 50092}
X(51100) = midpoint of X(i) and X(j) for these {i,j}: {7, 3679}, {2550, 6173}, {2951, 3543}, {3059, 24473}, {4312, 6172}, {31162, 35514}, {34648, 43182}
X(51100) = reflection of X(i) in X(j) for these {i,j}: {9, 3828}, {376, 43151}, {551, 142}, {5542, 6173}, {10177, 3833}, {30331, 551}, {34638, 11495}, {38059, 38204}, {38204, 38052}, {38210, 38200}, {47357, 1125}
X(51100) = complement of X(50836)
X(51100) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 38092, 3679}, {9, 3828, 38101}, {10, 5880, 30424}, {551, 38094, 142}, {1738, 50301, 50114}, {4312, 19875, 6172}, {6172, 40333, 19875}, {35514, 38073, 31162}, {38093, 47357, 1125}, {50091, 50299, 551}, {50096, 50781, 4669}, {50114, 50301, 4349}
X(51101) lies on these lines: {1, 50835}, {2, 38210}, {7, 34747}, {142, 34641}, {144, 3241}, {145, 30424}, {153, 34648}, {516, 50839}, {518, 3898}, {519, 1056}, {527, 3244}, {528, 34637}, {551, 3940}, {3626, 38093}, {3633, 43180}, {3635, 47357}, {3874, 34639}, {4669, 38204}, {4677, 11038}, {4745, 38053}, {5748, 31146}, {6172, 43179}, {8236, 50840}, {10167, 50808}, {19883, 24393}, {21151, 50817}, {31145, 38024}, {38107, 50804}, {38111, 50830}, {38122, 50827}, {38150, 50801}, {38194, 51006}, {49536, 49775}, {49675, 50114}
X(51101) = midpoint of X(7) and X(34747)
X(51101) = reflection of X(i) in X(j) for these {i,j}: {551, 42871}, {6172, 43179}, {30331, 3241}, {34641, 142}, {47357, 3635}
X(51101) = complement of X(50838)
X(51102) lies on these lines: {1, 38093}, {2, 3158}, {7, 31145}, {8, 527}, {9, 80}, {10, 47357}, {142, 3241}, {200, 17605}, {381, 43166}, {516, 4669}, {518, 4677}, {519, 1056}, {551, 20195}, {971, 50798}, {1001, 19536}, {1449, 50282}, {2136, 34720}, {2801, 50897}, {3247, 50291}, {3434, 31142}, {3524, 43175}, {3626, 5698}, {3632, 5880}, {3633, 25557}, {3656, 38150}, {3755, 48856}, {3826, 25055}, {3828, 30331}, {3872, 10031}, {3928, 34612}, {3929, 49719}, {4305, 34701}, {4662, 34706}, {4668, 5220}, {4678, 30332}, {4701, 30424}, {4745, 38057}, {4863, 5437}, {4882, 11236}, {4901, 50107}, {5082, 15829}, {5176, 36973}, {5223, 28534}, {5231, 6174}, {5438, 45700}, {5686, 50840}, {5732, 28204}, {5762, 50823}, {5846, 51002}, {5856, 50842}, {5927, 15104}, {6006, 21129}, {6172, 24393}, {6762, 11112}, {6765, 17528}, {6900, 7982}, {7174, 50080}, {7962, 45043}, {9041, 47595}, {11237, 12560}, {11495, 34628}, {11530, 12625}, {15726, 37712}, {16670, 49772}, {17294, 32850}, {17297, 49451}, {17668, 34717}, {19883, 43179}, {20053, 30340}, {21151, 50818}, {21153, 50821}, {28581, 51057}, {31164, 33110}, {31165, 40659}, {31424, 34707}, {31435, 34719}, {31658, 38066}, {34627, 35514}, {34631, 38073}, {34747, 38024}, {34748, 38065}, {38053, 38201}, {38107, 50805}, {38111, 50831}, {38122, 50824}, {38185, 51000}, {38190, 50951}, {38314, 40333}, {49698, 49722}
X(51102) = midpoint of X(i) and X(j) for these {i,j}: {7, 31145}, {34627, 35514}
X(51102) = reflection of X(i) in X(j) for these {i,j}: {9, 3679}, {3241, 142}, {3243, 6173}, {6172, 24393}, {6173, 2550}, {30331, 3828}, {31165, 40659}, {34628, 11495}, {34747, 42871}, {38053, 38201}, {38316, 38200}, {43166, 381}, {47357, 10}
X(51102) = complement of X(50839)
X(51102) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 3679, 38097}, {3241, 38092, 142}, {3828, 30331, 38025}, {34747, 38024, 42871}
X(51103) lies on these lines: {1, 2}, {11, 11274}, {30, 13464}, {40, 15698}, {55, 19705}, {56, 19704}, {81, 16489}, {106, 3750}, {165, 50872}, {214, 3748}, {354, 3898}, {376, 4301}, {381, 5882}, {390, 38024}, {392, 3892}, {514, 9269}, {515, 3845}, {516, 3534}, {517, 12100}, {518, 4532}, {527, 42819}, {528, 43179}, {535, 25405}, {537, 15569}, {549, 10222}, {553, 1319}, {597, 49465}, {599, 49684}, {726, 50111}, {740, 51061}, {758, 5049}, {944, 12571}, {946, 3655}, {952, 10109}, {960, 4536}, {962, 15697}, {999, 4428}, {1255, 24858}, {1317, 33709}, {1385, 8703}, {1386, 8584}, {1387, 33812}, {1388, 4298}, {1482, 3653}, {1483, 38022}, {1621, 37602}, {1699, 50862}, {1992, 16491}, {2325, 39260}, {2784, 50882}, {2796, 4353}, {2802, 3742}, {3057, 33815}, {3081, 49585}, {3242, 38023}, {3243, 38025}, {3246, 49737}, {3295, 40726}, {3303, 16371}, {3304, 16370}, {3523, 16189}, {3524, 7982}, {3543, 11522}, {3545, 9624}, {3576, 19708}, {3579, 15711}, {3654, 10165}, {3663, 49614}, {3664, 17320}, {3723, 4908}, {3746, 13587}, {3754, 31792}, {3817, 7967}, {3822, 3829}, {3833, 3880}, {3848, 3968}, {3860, 9955}, {3874, 31165}, {3878, 17609}, {3884, 5045}, {3889, 4067}, {3890, 4084}, {3946, 49738}, {3982, 39782}, {3986, 37654}, {3993, 31178}, {4021, 4398}, {4125, 20942}, {4297, 10595}, {4315, 4654}, {4342, 10385}, {4421, 6767}, {4424, 42040}, {4430, 4525}, {4539, 10176}, {4653, 42028}, {4664, 49479}, {4667, 24441}, {4670, 28301}, {4688, 49471}, {4694, 42038}, {4700, 16590}, {4717, 4742}, {4757, 50192}, {4758, 10022}, {4793, 19804}, {4856, 17330}, {4870, 10106}, {4887, 39704}, {4909, 17249}, {4995, 5048}, {5054, 11362}, {5055, 37727}, {5066, 5901}, {5071, 5881}, {5248, 7373}, {5249, 9963}, {5257, 50131}, {5258, 16861}, {5289, 5325}, {5298, 11011}, {5493, 5734}, {5542, 47357}, {5563, 17549}, {5587, 50818}, {5603, 15682}, {5710, 16402}, {5731, 28158}, {5750, 46845}, {5844, 11540}, {5846, 50786}, {5847, 22165}, {5850, 38316}, {5883, 5919}, {5886, 19709}, {6173, 30331}, {6684, 11812}, {7987, 34632}, {7988, 50871}, {7991, 15692}, {8162, 25439}, {8227, 34627}, {8236, 38054}, {8610, 39974}, {8666, 16418}, {8715, 16417}, {9588, 15721}, {9884, 38220}, {10031, 16173}, {10164, 15719}, {10175, 50798}, {10436, 50108}, {10624, 24926}, {10707, 33337}, {11038, 50836}, {11114, 34637}, {11231, 50823}, {11263, 15679}, {11278, 19711}, {11705, 47865}, {11706, 47866}, {11725, 36523}, {12101, 18483}, {12258, 50887}, {12263, 14711}, {12436, 19706}, {12513, 16857}, {12563, 24928}, {12575, 34471}, {12699, 15685}, {12702, 15716}, {12735, 45310}, {13624, 15759}, {15533, 47356}, {15534, 34379}, {15640, 34628}, {15672, 16126}, {15675, 34195}, {15690, 28198}, {15695, 31730}, {15703, 31399}, {15713, 28234}, {15888, 17533}, {16475, 50999}, {16484, 46922}, {16490, 32911}, {16777, 50115}, {17078, 25723}, {17132, 49482}, {17133, 49472}, {17379, 50090}, {17392, 28562}, {17393, 50099}, {17398, 50123}, {17502, 50832}, {17525, 20323}, {17530, 37722}, {17579, 34649}, {18145, 25303}, {18613, 19251}, {19710, 22791}, {19722, 48866}, {19907, 44257}, {21358, 49681}, {22475, 44422}, {24167, 46190}, {24325, 49461}, {26446, 50805}, {27268, 49504}, {28212, 31662}, {28522, 51060}, {28534, 43180}, {28538, 50991}, {28580, 50293}, {28639, 50112}, {29350, 38238}, {30308, 50864}, {30392, 50816}, {31138, 49700}, {31150, 50761}, {31151, 49696}, {31666, 45759}, {32941, 50109}, {33699, 34773}, {34122, 50846}, {34123, 50841}, {34718, 38068}, {34748, 47745}, {34937, 48846}, {35752, 50849}, {36330, 50852}, {36767, 50847}, {37611, 43151}, {37734, 38027}, {37904, 47495}, {38042, 50831}, {38047, 50790}, {38049, 47359}, {38052, 50839}, {41193, 49549}, {43531, 48865}, {45314, 48296}, {45316, 48287}, {45320, 48285}, {45341, 48286}, {45667, 48294}, {47097, 47491}, {47311, 47472}, {47352, 49529}, {48284, 50760}, {49455, 50118}, {49478, 50094}, {49739, 50226}, {50053, 50072}, {50062, 50070}, {50064, 50069}, {50091, 50130}, {50096, 50778}, {50285, 50294}, {50777, 51055}, {50781, 50993}, {50788, 50950}, {50843, 50892}, {50992, 51004}
X(51103) = midpoint of X(i) and X(j) for these {i,j}: {1, 551}, {10, 3241}, {11, 11274}, {145, 34641}, {354, 3898}, {376, 4301}, {381, 5882}, {392, 3892}, {549, 10222}, {597, 49465}, {599, 49684}, {944, 34648}, {946, 3655}, {962, 34638}, {1992, 49505}, {3244, 3679}, {3625, 34747}, {3635, 3828}, {3817, 7967}, {3874, 31165}, {3878, 24473}, {3993, 31178}, {4297, 31162}, {4430, 4525}, {4664, 49479}, {4667, 24441}, {4688, 49471}, {5049, 10179}, {5542, 47357}, {5883, 5919}, {6173, 30331}, {8236, 38054}, {9884, 50884}, {10031, 50889}, {10164, 16200}, {10165, 10247}, {10707, 33337}, {11114, 34637}, {12735, 45310}, {17579, 34649}, {31138, 49700}, {31150, 50761}, {31151, 49696}, {32941, 50109}, {34748, 47745}, {41193, 49549}, {45314, 48296}, {45316, 48287}, {45320, 48285}, {45341, 48286}, {45667, 48294}, {47097, 47491}, {47356, 49511}, {47358, 51005}, {47495, 47593}, {48284, 50760}, {49455, 50118}, {49478, 50094}, {49579, 49583}, {49739, 50226}, {50053, 50072}, {50062, 50070}, {50064, 50069}, {50091, 50130}, {50096, 50778}, {50285, 50294}, {50777, 51055}, {50781, 51000}
X(51103) = reflection of X(i) in X(j) for these {i,j}: {551, 3636}, {1125, 551}, {3626, 3828}, {3654, 50829}, {3679, 3634}, {3828, 1125}, {3968, 3848}, {4701, 3679}, {4745, 2}, {10022, 4758}, {31145, 4746}, {34641, 4691}, {34648, 12571}, {43174, 549}, {50787, 51003}, {50887, 12258}, {50950, 50788}
X(51103) = complement of X(4669)
X(51103) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1125, 3635}, {1, 1698, 20057}, {1, 3616, 3244}, {1, 3622, 10}, {1, 3624, 3623}, {1, 3636, 1125}, {1, 25055, 3241}, {1, 38314, 551}, {1, 41150, 4745}, {2, 3241, 4677}, {2, 4677, 10}, {2, 4745, 3828}, {8, 15808, 19878}, {8, 19872, 10}, {10, 551, 25055}, {10, 3244, 3621}, {10, 34595, 3634}, {145, 19862, 4691}, {145, 19875, 34641}, {551, 3244, 19883}, {551, 19883, 3616}, {551, 38314, 3636}, {944, 38021, 34648}, {1125, 3626, 31253}, {1125, 3635, 3626}, {1125, 4701, 3634}, {1125, 4745, 2}, {1698, 31145, 38098}, {3241, 3622, 25055}, {3241, 25055, 10}, {3241, 38314, 3622}, {3244, 3616, 3634}, {3244, 3634, 4701}, {3244, 19883, 3679}, {3616, 3621, 34595}, {3616, 3634, 1125}, {3616, 3679, 19883}, {3621, 3622, 3616}, {3621, 34595, 10}, {3622, 25055, 551}, {3623, 3624, 3625}, {3633, 5550, 10}, {3633, 25055, 19876}, {3654, 10165, 50829}, {3679, 19883, 3634}, {3679, 25055, 34595}, {3890, 50190, 4084}, {4677, 25055, 2}, {4701, 19883, 3828}, {5734, 30389, 5493}, {5901, 13607, 19925}, {8227, 34627, 38076}, {9884, 38220, 50884}, {10031, 16173, 50889}, {15808, 19878, 1125}, {19862, 34641, 19875}, {19875, 34641, 4691}, {19876, 25055, 5550}, {25055, 34747, 46931}, {31145, 38098, 4746}, {34648, 38021, 12571}, {38315, 47358, 51005}, {49614, 49616, 3663}
X(51104) lies on these lines: {1, 2}, {515, 50806}, {516, 50819}, {517, 15711}, {946, 12101}, {1385, 15759}, {1482, 15716}, {1699, 50863}, {3303, 19705}, {3304, 19704}, {3534, 4301}, {3576, 50809}, {3653, 15722}, {3656, 15685}, {3817, 50799}, {3830, 13464}, {3845, 5882}, {3860, 28224}, {4297, 19710}, {5493, 8703}, {5603, 50862}, {5734, 15697}, {5847, 50791}, {5850, 50840}, {5886, 50797}, {5901, 38076}, {7967, 50802}, {7982, 15698}, {10164, 44580}, {10165, 50825}, {10172, 50804}, {10222, 12100}, {10246, 50808}, {10247, 50828}, {10283, 50796}, {11224, 50814}, {11362, 11812}, {11725, 41154}, {12258, 41147}, {13607, 34648}, {15534, 49505}, {15690, 28174}, {15692, 16189}, {15695, 28194}, {15719, 43174}, {17394, 50108}, {19711, 33179}, {22165, 49684}, {28160, 33699}, {28164, 50873}, {28484, 51060}, {28516, 51059}, {28582, 50111}, {30392, 50872}, {38022, 47745}, {38023, 49536}, {38028, 50822}, {38049, 50998}, {38316, 50834}, {41149, 51005}, {41152, 51003}, {41153, 51006}, {46845, 50115}, {50784, 51000}
X(51104) = midpoint of X(i) and X(j) for these {i,j}: {1698, 3241}, {15692, 16189}, {20052, 34747}, {50784, 51000}
X(51104) = reflection of X(i) in X(j) for these {i,j}: {3679, 31253}, {4668, 3828}, {19862, 551}, {34641, 3617}
X(51104) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 38314, 551}, {551, 3625, 19883}, {551, 38098, 1125}, {1125, 20050, 10}, {3241, 3636, 19883}, {3241, 19883, 3625}, {3241, 38314, 46934}, {3616, 3623, 4816}, {3625, 4745, 4669}, {3626, 46930, 10}, {3635, 25055, 34641}, {3636, 19883, 551}, {3636, 20054, 15808}, {4677, 38098, 4669}, {20054, 46931, 4678}
X(51105) lies on these lines: {1, 2}, {30, 11522}, {35, 19705}, {36, 4428}, {40, 3653}, {57, 24857}, {80, 38026}, {165, 15698}, {191, 15673}, {354, 3899}, {355, 10109}, {376, 9589}, {381, 9624}, {392, 3894}, {515, 30308}, {516, 15697}, {517, 15693}, {524, 16491}, {547, 37727}, {549, 7982}, {553, 13462}, {597, 16496}, {631, 16189}, {758, 15675}, {940, 16489}, {944, 41106}, {946, 15682}, {1001, 37602}, {1319, 4654}, {1385, 3534}, {1386, 15534}, {1388, 4870}, {1482, 15701}, {1621, 37587}, {1699, 3830}, {2163, 8616}, {3058, 13384}, {3303, 16417}, {3304, 16418}, {3340, 5298}, {3524, 7991}, {3545, 5882}, {3576, 3656}, {3579, 15716}, {3654, 11812}, {3655, 3845}, {3746, 16371}, {3751, 38023}, {3758, 31332}, {3817, 50864}, {3901, 5045}, {4040, 45667}, {4234, 28619}, {4301, 10304}, {4312, 38024}, {4338, 37299}, {4383, 16490}, {4653, 42025}, {4658, 17553}, {4664, 49532}, {4688, 49469}, {4692, 20942}, {4755, 49490}, {4798, 28309}, {4859, 49738}, {4862, 17320}, {4898, 17398}, {4908, 16777}, {4912, 16484}, {4975, 42034}, {4995, 7962}, {5032, 49505}, {5049, 5692}, {5054, 9588}, {5055, 5881}, {5066, 5886}, {5071, 37714}, {5223, 38025}, {5258, 16857}, {5259, 7373}, {5264, 16402}, {5426, 17525}, {5432, 8275}, {5437, 5541}, {5506, 6762}, {5563, 16370}, {5587, 50797}, {5603, 11001}, {5690, 11540}, {5731, 15640}, {5734, 15692}, {5847, 50990}, {5902, 10179}, {6173, 37525}, {6174, 12653}, {6684, 34631}, {7967, 7988}, {7972, 45310}, {7987, 10595}, {7989, 13607}, {8148, 15722}, {8162, 48696}, {8227, 19709}, {8584, 16475}, {8666, 16858}, {8715, 36006}, {9053, 50953}, {9614, 24926}, {9875, 36523}, {9897, 11274}, {9956, 34748}, {10031, 37718}, {10165, 11224}, {10247, 50821}, {10389, 15015}, {10716, 47115}, {11038, 50840}, {11230, 50798}, {11362, 15702}, {11531, 15719}, {11705, 35752}, {11706, 36330}, {11739, 36366}, {11740, 36368}, {12101, 34773}, {12156, 12264}, {12245, 38068}, {12268, 22484}, {12269, 22485}, {12513, 17542}, {12531, 38104}, {12635, 36946}, {12645, 38083}, {12699, 19710}, {13174, 36521}, {13888, 44636}, {13942, 44635}, {14093, 31666}, {15300, 50886}, {15485, 46922}, {15533, 38315}, {15569, 31178}, {15670, 16126}, {15678, 35016}, {15685, 41869}, {15690, 22791}, {15695, 28198}, {15707, 31425}, {15708, 43174}, {15711, 35242}, {16173, 50843}, {16191, 50829}, {16192, 34632}, {16236, 31231}, {16558, 23958}, {16672, 36911}, {16673, 50115}, {17079, 25723}, {17274, 17394}, {17304, 28562}, {17392, 35227}, {17530, 37720}, {17533, 37719}, {18146, 25303}, {18398, 44663}, {18481, 33699}, {18493, 28208}, {18613, 19254}, {19706, 24929}, {20582, 49681}, {21356, 49684}, {21630, 27186}, {22165, 47356}, {24473, 50190}, {24821, 36522}, {24858, 25430}, {25405, 31160}, {26446, 50817}, {28333, 41312}, {28484, 51037}, {28516, 50111}, {28538, 50993}, {28582, 51035}, {31423, 33179}, {32557, 50890}, {34122, 50893}, {37611, 44284}, {37710, 38027}, {37712, 50818}, {38042, 50804}, {38047, 50998}, {38057, 50838}, {38059, 50835}, {43997, 48805}, {44567, 50767}, {45316, 48282}, {46845, 50087}, {47313, 47495}, {47352, 49465}, {47865, 50849}, {47866, 50852}, {48310, 49688}, {48812, 48820}, {49472, 50089}, {49498, 50094}, {49511, 50992}, {50049, 50069}, {50064, 50066}, {50176, 50225}, {50782, 51000}, {50784, 50950}, {50787, 51001}, {50802, 50863}
X(51105) = midpoint of X(i) and X(j) for these {i,j}: {3241, 3617}, {5734, 15692}, {50782, 51000}
X(51105) = reflection of X(i) in X(j) for these {i,j}: {3616, 551}, {3654, 50825}, {3679, 1698}, {4816, 3679}, {14093, 31666}, {37714, 5071}, {50791, 51003}, {50950, 50784}
X(51105) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 551, 25055}, {1, 1125, 3632}, {1, 3616, 1698}, {1, 3624, 3633}, {1, 4668, 3623}, {1, 19875, 3241}, {1, 25055, 3679}, {1, 34595, 145}, {2, 3241, 4669}, {2, 4669, 19875}, {8, 19883, 19876}, {145, 15808, 34595}, {551, 3636, 38314}, {551, 38314, 1}, {1125, 3241, 19875}, {1125, 3632, 19872}, {1125, 4669, 2}, {1125, 19872, 3624}, {1698, 3632, 3617}, {3241, 19875, 3632}, {3241, 25055, 19872}, {3616, 3617, 1125}, {3616, 3623, 19862}, {3622, 3636, 1}, {3622, 38314, 551}, {3623, 19862, 4668}, {3624, 4816, 1698}, {3632, 19875, 3679}, {3655, 5901, 38021}, {3655, 38021, 5691}, {3656, 50832, 50812}, {3679, 19872, 19875}, {3679, 25055, 3624}, {4668, 19862, 1698}, {13464, 30389, 9589}, {16475, 47358, 50952}, {36440, 36458, 20049}, {36444, 36462, 19876}, {38024, 47357, 4312}, {47358, 51006, 16475}, {50806, 50811, 50866}
X(51106) lies on these lines: {1, 2}, {515, 50807}, {516, 50820}, {517, 19711}, {946, 33699}, {1385, 15690}, {1386, 41149}, {1699, 50867}, {3534, 13464}, {3576, 50813}, {3656, 15695}, {3817, 50824}, {3845, 15178}, {3860, 5901}, {4297, 15685}, {4301, 8703}, {4755, 49504}, {5066, 5882}, {5493, 19708}, {5847, 50792}, {5886, 50800}, {7982, 15719}, {8584, 49505}, {9624, 41106}, {9779, 50868}, {10164, 15722}, {10171, 50818}, {10222, 11812}, {10246, 28172}, {10283, 19710}, {11362, 15713}, {11522, 15640}, {11725, 41147}, {12101, 28186}, {13607, 38076}, {15570, 38101}, {15708, 16189}, {15711, 31663}, {15716, 50828}, {15759, 17502}, {16200, 50829}, {25723, 43186}, {28164, 50874}, {28555, 50111}, {30392, 50815}, {31666, 46332}, {33179, 38068}, {35381, 38066}, {38028, 50826}, {38094, 43179}, {38315, 51004}, {41154, 50884}, {47356, 50989}, {49684, 50991}
X(51106) = midpoint of X(19876) and X(20057)
X(51106) = reflection of X(i) in X(j) for these {i,j}: {551, 3622}, {4678, 3828}, {15808, 551}, {19876, 1125}
X(51106) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 551, 19883}, {1, 3616, 4691}, {1, 19878, 3244}, {1, 25055, 31145}, {1, 46933, 3635}, {2, 41150, 551}, {551, 3244, 25055}, {1125, 46932, 19862}, {3636, 38314, 551}, {4677, 4691, 4669}, {4745, 31145, 4669}, {19883, 34641, 22266}, {25055, 31145, 19878}
X(51107) lies on these lines: {1, 2}, {515, 12101}, {516, 19710}, {517, 15759}, {1385, 15711}, {1699, 50868}, {3303, 19704}, {3304, 19705}, {3576, 50814}, {3654, 15722}, {3655, 15685}, {3656, 28164}, {3817, 50818}, {3830, 5882}, {3845, 13464}, {3860, 12571}, {4301, 11001}, {4909, 7321}, {5557, 36005}, {5886, 50801}, {7967, 50870}, {7982, 19708}, {8584, 49465}, {8703, 10222}, {9041, 41153}, {9884, 50887}, {10031, 50892}, {10165, 50805}, {10171, 50798}, {10246, 15716}, {10247, 15695}, {10304, 16189}, {10595, 34648}, {11230, 50831}, {11362, 15701}, {12100, 15178}, {13607, 22793}, {15533, 49684}, {15690, 28194}, {15693, 43174}, {16200, 50808}, {19709, 37727}, {19711, 50828}, {28158, 50811}, {28234, 50829}, {28236, 50803}, {28538, 41152}, {32557, 50846}, {38028, 50827}, {38049, 50790}, {38054, 50839}, {47311, 47491}, {49511, 50989}, {49681, 50993}, {50787, 51000}, {50788, 51003}
X(51107) = midpoint of X(i) and X(j) for these {i,j}: {551, 3635}, {1125, 3241}, {3244, 3828}, {4701, 34747}, {9884, 50887}, {10031, 50892}, {50787, 51000}
X(51107) = reflection of X(i) in X(j) for these {i,j}: {2, 41150}, {3634, 551}, {3679, 19878}, {4746, 3828}, {50788, 51003}
X(51107) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {551, 19875, 1125}, {551, 20049, 3828}, {1125, 3626, 19877}, {3241, 38314, 3617}, {3244, 38314, 3828}, {3617, 4677, 4669}, {3624, 38314, 551}, {4669, 19875, 4745}, {20049, 38314, 3624}
X(51108) lies on these lines: {1, 2}, {40, 15719}, {142, 19706}, {214, 38026}, {376, 9624}, {390, 38094}, {515, 5066}, {516, 8703}, {517, 11812}, {545, 4758}, {547, 15178}, {549, 13464}, {553, 15950}, {726, 51061}, {944, 38076}, {946, 3534}, {1317, 38104}, {1385, 3845}, {1386, 22165}, {1482, 38068}, {1483, 38083}, {1699, 15640}, {2796, 11725}, {2802, 3848}, {3081, 11831}, {3242, 38089}, {3243, 38101}, {3304, 17542}, {3524, 4301}, {3543, 30389}, {3576, 11001}, {3579, 19711}, {3655, 19709}, {3656, 10165}, {3746, 36006}, {3817, 41099}, {3830, 5886}, {3833, 10179}, {3860, 28208}, {4127, 50191}, {4234, 28620}, {4297, 15682}, {4298, 4870}, {4694, 42039}, {4908, 5750}, {4909, 17271}, {4975, 4980}, {4989, 50309}, {5054, 43174}, {5055, 5882}, {5248, 40726}, {5258, 17547}, {5493, 15692}, {5542, 38025}, {5563, 16858}, {5603, 15698}, {5731, 30308}, {5734, 15721}, {5847, 50788}, {5901, 12100}, {6684, 15713}, {7982, 15702}, {7987, 34638}, {7988, 50864}, {7991, 15708}, {8227, 34648}, {8584, 34379}, {8666, 16857}, {9955, 12101}, {10109, 28204}, {10164, 50814}, {10171, 10246}, {10175, 50801}, {10222, 11539}, {10283, 50821}, {10304, 11522}, {11038, 50834}, {11230, 28236}, {11231, 50827}, {11263, 15678}, {11281, 15673}, {11362, 15694}, {11705, 36769}, {11706, 47867}, {12258, 15300}, {12512, 19708}, {12699, 15695}, {13624, 15690}, {15533, 50787}, {15534, 38023}, {15679, 26725}, {15685, 18493}, {15686, 31666}, {15697, 50865}, {15703, 37727}, {15711, 22791}, {15759, 28198}, {16173, 50892}, {16475, 51004}, {16490, 37687}, {16491, 21356}, {16674, 17355}, {16675, 50115}, {17079, 43186}, {17252, 31334}, {17553, 28619}, {18483, 33699}, {18613, 19252}, {21358, 49684}, {24857, 39962}, {25485, 38069}, {28172, 31662}, {28522, 50111}, {28562, 40344}, {30331, 38093}, {30392, 50868}, {30598, 50088}, {31423, 34631}, {32557, 50843}, {34123, 50844}, {37734, 38105}, {38034, 50832}, {38049, 47358}, {38054, 50836}, {38127, 50805}, {38155, 50818}, {38176, 50831}, {38191, 50790}, {38201, 50839}, {38213, 50846}, {38220, 50887}, {38315, 50781}, {45316, 48065}, {47311, 47495}, {47356, 50993}, {48310, 49465}, {50786, 51000}
X(51108) = midpoint of X(i) and X(j) for these {i,j}: {1, 3828}, {547, 15178}, {549, 13464}, {551, 1125}, {3241, 3626}, {3635, 3679}, {3655, 19925}, {3833, 10179}, {10171, 10246}, {12512, 31162}, {50786, 51000}, {50787, 51005}
X(51108) = reflection of X(i) in X(j) for these {i,j}: {3636, 551}, {3828, 19878}, {4691, 3828}
X(51108) = complement of X(4745)
X(51108) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2, 4669}, {1, 1125, 19878}, {1, 1698, 20053}, {1, 3624, 46933}, {1, 4678, 3244}, {1, 5550, 22266}, {1, 19878, 4691}, {1, 19883, 3828}, {2, 4669, 3828}, {10, 551, 38314}, {10, 3244, 4816}, {10, 46934, 1125}, {145, 19876, 38098}, {551, 15808, 25055}, {551, 19883, 1}, {551, 25055, 1125}, {1125, 3626, 3624}, {1125, 3635, 19862}, {1125, 3636, 3634}, {1125, 3828, 19883}, {1125, 31253, 5550}, {3244, 5550, 31253}, {3244, 22266, 4678}, {3616, 15808, 1125}, {3616, 25055, 551}, {3622, 19862, 3635}, {3622, 19877, 1}, {3636, 4691, 1}, {3828, 19883, 19878}, {4669, 19883, 2}, {4691, 19878, 3634}, {4816, 46930, 10}, {5731, 30308, 50862}, {19875, 22266, 3828}, {31145, 38314, 1}
X(51109) lies on these lines: {1, 2}, {30, 31666}, {354, 4525}, {392, 4744}, {515, 19709}, {516, 19708}, {517, 15713}, {547, 5882}, {549, 4301}, {597, 49505}, {946, 8703}, {1385, 5066}, {1386, 50991}, {1699, 50815}, {3304, 19536}, {3524, 5493}, {3534, 5886}, {3576, 15682}, {3579, 44580}, {3653, 3830}, {3655, 38076}, {3656, 10164}, {3671, 5298}, {3817, 3845}, {3839, 30389}, {3848, 3898}, {3860, 31673}, {3986, 15492}, {4098, 4908}, {4342, 4995}, {4432, 36525}, {4537, 25917}, {4663, 41153}, {4694, 42041}, {4698, 49504}, {4755, 49479}, {4758, 24441}, {4798, 28301}, {5054, 13464}, {5248, 19704}, {5267, 40726}, {5563, 16861}, {5603, 15719}, {5731, 50863}, {5847, 50784}, {5901, 11812}, {6667, 11274}, {7967, 50801}, {7982, 15709}, {7987, 15697}, {7988, 50803}, {7991, 15721}, {8227, 41099}, {8584, 49511}, {8666, 17542}, {9589, 15705}, {9955, 33699}, {10109, 11230}, {10124, 10222}, {10165, 12100}, {10172, 50798}, {10175, 50824}, {10246, 50797}, {10247, 50827}, {10283, 50822}, {11001, 38021}, {11263, 17525}, {11362, 11539}, {11522, 15692}, {11540, 50821}, {11599, 15300}, {11705, 36768}, {11711, 36523}, {12258, 36521}, {12571, 34628}, {13624, 19710}, {15015, 50892}, {15178, 15699}, {15533, 38023}, {15534, 50791}, {15673, 17768}, {15678, 26725}, {15693, 28194}, {15695, 18493}, {15698, 31162}, {15702, 43174}, {15711, 28198}, {15759, 31730}, {16173, 50844}, {16475, 50787}, {19711, 22791}, {20582, 49684}, {21630, 38026}, {22165, 51005}, {23789, 45316}, {28164, 30308}, {28484, 50111}, {28516, 51060}, {28582, 50777}, {30392, 50864}, {32557, 50889}, {33337, 45310}, {38049, 51003}, {38059, 50834}, {38083, 47745}, {38089, 49536}, {38094, 47357}, {38191, 50998}, {38315, 50782}, {41106, 50811}, {44567, 50761}, {48310, 49529}, {49535, 50094}, {50781, 51006}, {50788, 51001}
X(51109) = midpoint of X(i) and X(j) for these {i,j}: {551, 19862}, {3241, 4668}, {3623, 3679}, {11522, 15692}
X(51109) = reflection of X(i) in X(j) for these {i,j}: {551, 3616}, {3617, 3828}, {51004, 50791}
X(51109) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2, 4745}, {1, 1698, 20052}, {1, 4746, 3244}, {1, 20054, 3635}, {2, 4677, 3828}, {2, 38314, 4677}, {8, 22266, 10}, {551, 1125, 19883}, {551, 3244, 38314}, {551, 19883, 10}, {551, 25055, 15808}, {1125, 3616, 19862}, {1125, 3636, 5550}, {1125, 15808, 10}, {1125, 25055, 551}, {3241, 3634, 38098}, {3616, 5550, 3623}, {3617, 3623, 20053}, {3622, 19878, 3625}, {3624, 4677, 2}, {3624, 38314, 3828}, {3828, 38314, 3244}, {4745, 41150, 1}, {15808, 19883, 551}, {20049, 38314, 1}
X(51110) lies on these lines: {1, 2}, {30, 9624}, {40, 15693}, {57, 16558}, {86, 4902}, {140, 16189}, {165, 3656}, {191, 15675}, {376, 11522}, {515, 41106}, {517, 15701}, {547, 5881}, {549, 7991}, {599, 16491}, {946, 11001}, {1001, 37587}, {1385, 3830}, {1386, 15533}, {1420, 4870}, {1699, 15682}, {3247, 4908}, {3304, 16857}, {3339, 5298}, {3524, 13464}, {3534, 3576}, {3601, 19706}, {3653, 5901}, {3654, 10283}, {3655, 5066}, {3746, 16417}, {3845, 5886}, {3860, 34773}, {4297, 15640}, {4301, 15692}, {4423, 37602}, {4428, 5010}, {4654, 13462}, {4755, 49448}, {4975, 42029}, {4995, 9819}, {5054, 7982}, {5055, 15178}, {5071, 5882}, {5258, 17542}, {5259, 11194}, {5426, 15678}, {5493, 15705}, {5563, 16418}, {5587, 10109}, {5603, 19708}, {5657, 16191}, {5691, 41099}, {5731, 50802}, {5734, 15708}, {5847, 50994}, {7280, 19704}, {7373, 25542}, {7967, 50871}, {7988, 10246}, {7989, 28204}, {8056, 24857}, {8584, 38023}, {8666, 16861}, {9588, 15702}, {9589, 10304}, {9619, 39593}, {9779, 50862}, {9812, 50815}, {9897, 45310}, {10031, 32557}, {10164, 50872}, {10165, 15719}, {10175, 50818}, {10222, 15694}, {10247, 50817}, {11055, 12263}, {11230, 37712}, {11231, 50805}, {11238, 13384}, {11274, 31272}, {11281, 17525}, {11362, 15709}, {11531, 11812}, {11540, 26446}, {11705, 35751}, {11706, 36329}, {11725, 15300}, {11739, 36386}, {11740, 36388}, {11831, 34582}, {12101, 18481}, {12513, 19536}, {12690, 25525}, {12699, 15690}, {12702, 15722}, {13607, 38074}, {13624, 15695}, {15534, 16475}, {15570, 38097}, {15671, 16126}, {15679, 35016}, {15689, 31666}, {15698, 16192}, {15699, 30315}, {15716, 35242}, {15721, 43174}, {15759, 22791}, {16173, 50396}, {16200, 50821}, {16487, 17392}, {16489, 37674}, {16490, 37679}, {16496, 47352}, {16673, 17340}, {16801, 20155}, {17364, 31334}, {17502, 50812}, {18398, 31165}, {19710, 41869}, {22165, 50792}, {22475, 33706}, {28555, 51061}, {28640, 50112}, {31139, 36834}, {31178, 49523}, {32558, 50889}, {33179, 38066}, {33595, 38093}, {34123, 50891}, {34471, 50444}, {34631, 38068}, {34748, 38083}, {36521, 50886}, {37718, 50843}, {38032, 50908}, {38049, 50999}, {38053, 50836}, {38092, 43179}, {38133, 50910}, {38204, 50839}, {38315, 50785}, {45316, 47970}, {47314, 47495}, {47356, 50991}, {50790, 50953}, {50992, 51005}
X(51110) = midpoint of X(i) and X(j) for these {i,j}: {1, 19876}, {551, 15808}, {3241, 4678}
X(51110) = reflection of X(i) in X(j) for these {i,j}: {3622, 551}, {3654, 50826}, {3679, 9780}, {9588, 15702}, {19876, 3624}, {50950, 50785}
X(51110) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2, 4677}, {1, 19875, 34747}, {1, 34595, 4668}, {2, 3241, 4745}, {2, 4677, 19875}, {2, 4745, 1698}, {551, 1125, 38314}, {551, 3616, 25055}, {551, 19883, 3636}, {551, 25055, 1}, {1125, 3636, 3625}, {1125, 4746, 19862}, {1125, 9780, 3624}, {1125, 38314, 3679}, {1385, 38021, 34628}, {1698, 3636, 1}, {3241, 19883, 1698}, {3241, 46934, 19883}, {3616, 3622, 15808}, {3622, 3624, 1}, {3622, 15808, 3624}, {3622, 25055, 19876}, {3622, 46934, 4678}, {3636, 19883, 3241}, {3636, 46934, 1698}, {3653, 5901, 31162}, {3653, 31162, 7987}, {3655, 38022, 8227}, {3679, 25055, 1125}, {3679, 38314, 1}, {4745, 19883, 2}, {4746, 19862, 46930}, {5886, 50811, 30308}, {19875, 34747, 4668}, {19877, 20049, 38098}, {20049, 38098, 4816}, {30308, 30392, 50811}, {34595, 34747, 19875}
X(51111) lies on these lines: {1, 21}, {2, 21842}, {5, 38162}, {8, 37291}, {9, 17438}, {10, 140}, {12, 1125}, {35, 2802}, {36, 3754}, {55, 22837}, {56, 5883}, {65, 4973}, {79, 20067}, {100, 37616}, {142, 38208}, {145, 2320}, {149, 5441}, {355, 40260}, {392, 41554}, {404, 3918}, {405, 1388}, {484, 5303}, {515, 6842}, {516, 30264}, {517, 5267}, {519, 2646}, {529, 551}, {535, 12047}, {549, 8256}, {936, 30392}, {944, 6853}, {946, 5841}, {950, 10959}, {956, 22836}, {958, 10176}, {960, 1493}, {976, 16499}, {999, 30143}, {1320, 37563}, {1329, 38028}, {1389, 5535}, {1483, 15862}, {1706, 3576}, {2098, 16370}, {2329, 24036}, {2475, 36975}, {2801, 21740}, {2886, 5499}, {3057, 30538}, {3218, 4757}, {3244, 5855}, {3294, 17439}, {3476, 10198}, {3486, 45700}, {3589, 38198}, {3601, 25439}, {3612, 3872}, {3616, 20060}, {3626, 5440}, {3628, 38183}, {3634, 17614}, {3635, 37080}, {3636, 12572}, {3652, 48667}, {3655, 5794}, {3678, 4511}, {3689, 4701}, {3746, 38460}, {3753, 37605}, {3811, 13384}, {3812, 5126}, {3822, 24541}, {3825, 8068}, {3833, 5253}, {3913, 37606}, {3916, 11011}, {3919, 37582}, {3968, 4881}, {4051, 4262}, {4084, 50194}, {4127, 4867}, {4189, 5697}, {4297, 5842}, {4304, 49600}, {4311, 12609}, {4325, 20292}, {4640, 10222}, {4652, 25415}, {4868, 15955}, {5010, 14923}, {5046, 37735}, {5080, 5443}, {5087, 38045}, {5122, 10107}, {5123, 38114}, {5218, 49169}, {5251, 18254}, {5260, 41689}, {5288, 34772}, {5289, 37624}, {5444, 27529}, {5542, 5857}, {5690, 26287}, {5731, 37163}, {5745, 13607}, {5795, 24927}, {5836, 13624}, {5847, 51009}, {5849, 49511}, {5852, 42819}, {5884, 32153}, {5901, 11813}, {6224, 47033}, {6265, 20117}, {6647, 17758}, {6666, 38217}, {6667, 38219}, {6668, 19862}, {6681, 24982}, {6906, 11014}, {6910, 12647}, {7294, 34122}, {7483, 10944}, {7967, 30478}, {9623, 30389}, {9678, 44636}, {9780, 38411}, {10056, 36977}, {10572, 24387}, {10914, 37600}, {11010, 17549}, {11263, 18990}, {12248, 49178}, {12648, 31452}, {12737, 37621}, {12773, 33858}, {13145, 38602}, {13375, 14804}, {14988, 33281}, {15064, 45770}, {15171, 21630}, {16139, 35457}, {16611, 21008}, {17221, 18698}, {17440, 21061}, {17619, 20107}, {18253, 44254}, {18447, 47115}, {18481, 47032}, {19860, 37618}, {21888, 37512}, {22758, 31803}, {22765, 31870}, {24301, 34823}, {25485, 26087}, {26066, 37727}, {26364, 34918}, {28234, 33596}, {28236, 33597}, {30323, 35258}, {31453, 35762}, {31650, 50824}, {31806, 46920}, {32636, 33815}, {37562, 46684}, {37592, 49682}, {43174, 50371}
X(51111) = midpoint of X(i) and X(j) for these {i,j}: {1, 2975}, {35, 4861}, {3916, 11011}, {5288, 34772}, {6906, 11014}
X(51111) = reflection of X(i) in X(j) for these {i,j}: {10, 4999}, {12, 1125}
X(51111) = complement of X(37710)
X(51111) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 21, 3884}, {1, 993, 3878}, {1, 5248, 3898}, {1, 8666, 3874}, {10, 1385, 214}, {12, 1125, 38062}, {56, 30147, 5883}, {145, 2320, 37571}, {956, 34471, 22836}, {958, 10246, 30144}, {958, 30144, 10176}, {993, 3878, 3647}, {3612, 3872, 8715}, {3616, 20060, 37701}, {4511, 5258, 3678}, {5258, 24926, 4511}, {11260, 24929, 3244}, {22758, 40257, 31803}, {24541, 45287, 3822}, {31260, 38058, 3634}
X(51112) lies on these lines: {1, 529}, {2, 952}, {12, 551}, {55, 25416}, {442, 5882}, {498, 34717}, {519, 2646}, {758, 5919}, {944, 17532}, {1145, 37525}, {1483, 3897}, {1621, 12735}, {2975, 3241}, {3036, 5444}, {3623, 50742}, {3649, 34637}, {3653, 31659}, {3655, 11112}, {3656, 5841}, {3679, 4999}, {3828, 31260}, {3925, 33337}, {4018, 34646}, {4187, 15178}, {5326, 15863}, {5734, 50242}, {5842, 50811}, {5849, 47358}, {5852, 50836}, {5901, 37375}, {6690, 7972}, {7483, 37727}, {8068, 38026}, {10197, 10944}, {10609, 34612}, {11194, 11507}, {11235, 12690}, {11491, 16371}, {11849, 17549}, {12732, 34607}, {17530, 26470}, {17556, 37737}, {17579, 34773}, {19704, 50810}, {21155, 50828}, {22836, 34689}, {22837, 34699}, {24987, 32900}, {25055, 37710}, {28194, 30264}, {28538, 51009}, {34471, 45701}, {34697, 40257}, {38051, 51006}
X(51112) = midpoint of X(i) and X(j) for these {i,j}: {2975, 3241}, {31157, 37734}
X(51112) = reflection of X(i) in X(j) for these {i,j}: {12, 551}, {3679, 4999}
X(51112) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 50824, 50843}, {12, 551, 38027}, {31260, 38100, 3828}
X(51113) lies on these lines: {2, 758}, {10, 529}, {12, 553}, {191, 37375}, {519, 2646}, {551, 4999}, {952, 4669}, {993, 5727}, {2975, 3679}, {3219, 6702}, {3647, 11113}, {3874, 10197}, {3878, 11376}, {3962, 20104}, {3988, 27529}, {4015, 5445}, {4134, 11231}, {4745, 38214}, {5054, 37733}, {5258, 37293}, {5841, 50796}, {5842, 50808}, {5849, 50781}, {5852, 38204}, {6763, 19875}, {8068, 38104}, {15065, 20879}, {19883, 37737}, {21155, 50829}, {26363, 34744}, {26470, 28194}, {31260, 38027}, {31659, 38068}, {36004, 47033}
X(51113) = midpoint of X(2975) and X(3679)
X(51113) = reflection of X(i) in X(j) for these {i,j}: {12, 3828}, {551, 4999}
X(51113) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {12, 3828, 38105}, {4669, 50821, 50841}
X(51114) lies on these lines: {1, 616}, {2, 9901}, {10, 618}, {13, 1125}, {226, 18974}, {515, 5617}, {516, 5473}, {519, 5463}, {530, 551}, {532, 11707}, {542, 11709}, {950, 12952}, {993, 22773}, {2482, 50850}, {2796, 9116}, {3576, 6770}, {3634, 36770}, {3817, 5478}, {4297, 41022}, {4669, 36768}, {4745, 36767}, {5459, 19883}, {5460, 50884}, {5847, 51010}, {5886, 13103}, {6669, 19862}, {6771, 10165}, {8983, 49208}, {10062, 13411}, {10078, 44675}, {10106, 12942}, {11230, 20252}, {11599, 11706}, {12053, 13076}, {12337, 25440}, {12922, 17647}, {13624, 47610}, {13971, 49209}, {18481, 48655}, {19925, 36765}, {21636, 41023}, {22577, 50887}, {22796, 31673}, {28164, 36961}
X(51114) = midpoint of X(i) and X(j) for these {i,j}: {1, 616}, {5463, 50849}, {7975, 12781}, {18481, 48655}
X(51114) = reflection of X(i) in X(j) for these {i,j}: {10, 618}, {13, 1125}, {11599, 11706}, {22577, 50887}, {31673, 22796}, {47610, 13624}, {50847, 5463}, {50850, 2482}, {50884, 5460}
X(51114) = complement of X(9901)
X(51114) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5463, 7975, 12781}, {12781, 50849, 7975}
X(51115) lies on these lines: {1, 617}, {2, 9900}, {10, 619}, {14, 1125}, {226, 18975}, {515, 5613}, {516, 5474}, {519, 5464}, {531, 551}, {533, 11708}, {542, 11709}, {950, 12951}, {993, 22774}, {2482, 50847}, {2784, 36776}, {2796, 9114}, {3576, 6773}, {3817, 5479}, {4297, 41023}, {5459, 50884}, {5460, 19883}, {5847, 51013}, {5886, 13102}, {6670, 19862}, {6774, 10165}, {8983, 49210}, {10061, 13411}, {10077, 44675}, {10106, 12941}, {11230, 20253}, {11599, 11705}, {12053, 13075}, {12336, 25440}, {12921, 17647}, {13624, 47611}, {13971, 49211}, {18481, 48656}, {21636, 41022}, {22578, 50887}, {22797, 31673}, {28164, 36962}
X(51115) = midpoint of X(i) and X(j) for these {i,j}: {1, 617}, {5464, 50852}, {7974, 12780}, {18481, 48656}
X(51115) = reflection of X(i) in X(j) for these {i,j}: {10, 619}, {14, 1125}, {11599, 11705}, {22578, 50887}, {31673, 22797}, {47611, 13624}, {50847, 2482}, {50850, 5464}, {50884, 5459}
X(51115) = complement of X(9900)
X(51115) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5464, 7974, 12780}, {12780, 50852, 7974}
X(51116) lies on these lines: {1, 627}, {2, 22652}, {10, 629}, {17, 1125}, {226, 18973}, {515, 16626}, {516, 22890}, {519, 22896}, {532, 551}, {950, 22905}, {993, 22772}, {3576, 22532}, {3616, 22113}, {3636, 22844}, {3817, 22832}, {4297, 44666}, {5847, 51020}, {5886, 16629}, {5965, 12266}, {6673, 19862}, {8983, 49238}, {10106, 22904}, {10165, 49106}, {12053, 22910}, {13411, 22929}, {13971, 49239}, {15808, 33465}, {17647, 22902}, {18481, 48666}, {22558, 25440}, {22795, 31673}, {22930, 44675}, {33387, 49591}, {36782, 49603}
X(51116) = midpoint of X(i) and X(j) for these {i,j}: {1, 627}, {18481, 48666}, {22896, 22912}
X(51116) = reflection of X(i) in X(j) for these {i,j}: {10, 629}, {17, 1125}, {31673, 22795}
X(51116) = complement of X(22652)
X(51116) = {X(22912),X(50859)}-harmonic conjugate of X(22896)
X(51117) lies on these lines: {1, 628}, {2, 22651}, {10, 630}, {18, 1125}, {226, 18972}, {515, 16627}, {516, 22843}, {519, 22851}, {533, 551}, {950, 22860}, {993, 22771}, {3576, 22531}, {3616, 22114}, {3636, 22845}, {3817, 22831}, {4297, 44667}, {5847, 51021}, {5886, 16628}, {5965, 12266}, {6674, 19862}, {8983, 49236}, {10106, 22859}, {10165, 49105}, {12053, 22865}, {13411, 22884}, {13971, 49237}, {15808, 33464}, {17647, 22857}, {18481, 48665}, {22557, 25440}, {22794, 31673}, {22885, 44675}, {33386, 49590}, {36781, 49603}
X(51117) = midpoint of X(i) and X(j) for these {i,j}: {1, 628}, {18481, 48665}, {22851, 22867}
X(51117) = reflection of X(i) in X(j) for these {i,j}: {10, 630}, {18, 1125}, {31673, 22794}
X(51117) = complement of X(22651)
X(51117) = {X(22867),X(50860)}-harmonic conjugate of X(22851)
X(51118) lies on these lines: {1, 3146}, {2, 10248}, {3, 3817}, {4, 9}, {5, 10164}, {7, 6744}, {8, 9589}, {20, 1125}, {30, 551}, {33, 4347}, {35, 36002}, {55, 3947}, {57, 5225}, {65, 9844}, {72, 31871}, {140, 28182}, {145, 50690}, {165, 3091}, {185, 31757}, {226, 4314}, {329, 6743}, {355, 3830}, {376, 8227}, {377, 40998}, {381, 6684}, {382, 515}, {388, 9580}, {390, 5290}, {405, 12511}, {442, 7965}, {497, 4298}, {499, 4333}, {517, 3625}, {519, 962}, {527, 34706}, {529, 21627}, {535, 49600}, {546, 3579}, {548, 11230}, {550, 9955}, {631, 10171}, {726, 51063}, {758, 12688}, {938, 4312}, {942, 15726}, {944, 15682}, {950, 1836}, {952, 33697}, {971, 3874}, {1012, 5267}, {1058, 12577}, {1210, 1770}, {1478, 10624}, {1479, 3338}, {1483, 28208}, {1537, 33337}, {1593, 49553}, {1597, 9911}, {1657, 5886}, {1697, 5229}, {1698, 3832}, {1702, 23249}, {1703, 23259}, {1737, 18514}, {1750, 3811}, {1864, 12432}, {1898, 15556}, {2777, 13605}, {2784, 10722}, {2794, 3429}, {2802, 13227}, {2807, 13598}, {2816, 10747}, {2829, 21630}, {2901, 22035}, {3008, 7406}, {3070, 49548}, {3071, 49547}, {3090, 35242}, {3189, 28609}, {3361, 5274}, {3434, 12527}, {3474, 9581}, {3475, 41864}, {3488, 12563}, {3520, 9625}, {3522, 3624}, {3523, 7988}, {3529, 3576}, {3545, 31423}, {3585, 31397}, {3586, 4295}, {3616, 5059}, {3622, 50692}, {3626, 7991}, {3635, 50691}, {3636, 5731}, {3653, 15685}, {3654, 38335}, {3656, 13607}, {3663, 4911}, {3678, 5927}, {3679, 20070}, {3742, 31805}, {3743, 15852}, {3825, 37374}, {3828, 3839}, {3841, 8226}, {3843, 26446}, {3845, 9956}, {3850, 11231}, {3851, 10172}, {3853, 11362}, {3854, 19877}, {3856, 31447}, {3860, 38083}, {3861, 31399}, {3878, 9856}, {3881, 12680}, {3911, 10896}, {3919, 7686}, {3927, 16112}, {4018, 12690}, {4082, 5300}, {4084, 6001}, {4134, 5777}, {4293, 9614}, {4294, 9612}, {4299, 44675}, {4302, 13411}, {4304, 12047}, {4311, 10483}, {4315, 7354}, {4342, 10106}, {4355, 10580}, {4356, 5717}, {4425, 48890}, {4512, 5177}, {4691, 37714}, {4701, 37712}, {4745, 34632}, {4857, 16118}, {4872, 10481}, {4973, 34862}, {5046, 8582}, {5056, 31253}, {5066, 38068}, {5071, 50829}, {5073, 13464}, {5076, 12702}, {5080, 6736}, {5122, 10593}, {5129, 38052}, {5175, 12526}, {5178, 17781}, {5248, 7580}, {5259, 7411}, {5261, 30332}, {5265, 50444}, {5284, 35202}, {5342, 17860}, {5439, 5918}, {5446, 31728}, {5475, 31396}, {5506, 6894}, {5536, 10916}, {5542, 9668}, {5550, 50693}, {5603, 33703}, {5690, 15687}, {5721, 29223}, {5732, 38054}, {5735, 9799}, {5787, 31671}, {5805, 43182}, {5806, 5883}, {5840, 21635}, {5842, 6260}, {5847, 36990}, {5850, 36991}, {5882, 22791}, {5893, 40660}, {5902, 9961}, {5907, 31737}, {6000, 31732}, {6147, 31795}, {6173, 43181}, {6245, 37532}, {6253, 21077}, {6256, 49184}, {6564, 13912}, {6565, 13975}, {6700, 50700}, {6737, 11415}, {6836, 9843}, {6851, 26333}, {6871, 35258}, {6920, 7688}, {6960, 20104}, {6972, 20107}, {6986, 41853}, {6991, 41858}, {6996, 31191}, {6998, 48925}, {6999, 29571}, {7379, 39580}, {7380, 49631}, {7407, 9746}, {7968, 42272}, {7969, 42271}, {7982, 28236}, {8193, 11403}, {8583, 37435}, {8591, 50882}, {8720, 49554}, {8726, 43178}, {8727, 25639}, {8728, 38059}, {8983, 42258}, {9041, 51026}, {9583, 43408}, {9591, 14118}, {9613, 30305}, {9616, 31412}, {9619, 43619}, {9624, 49138}, {9626, 37925}, {9670, 10404}, {9671, 17728}, {9780, 50689}, {9800, 18391}, {9842, 31777}, {9899, 32064}, {10039, 18513}, {10176, 31793}, {10198, 37421}, {10222, 28186}, {10246, 49136}, {10265, 22938}, {10304, 30308}, {10441, 29353}, {10446, 35633}, {10588, 35445}, {10591, 15803}, {10595, 50811}, {10625, 31751}, {10724, 34789}, {10728, 14217}, {10884, 41860}, {10915, 41698}, {11001, 38021}, {11012, 21669}, {11108, 11495}, {11177, 50887}, {11220, 18398}, {11235, 34646}, {11236, 34639}, {11278, 28224}, {11496, 37411}, {11661, 11681}, {11813, 37468}, {12102, 18357}, {12103, 17502}, {12173, 49542}, {12245, 34641}, {12261, 34584}, {12435, 45829}, {12520, 30143}, {12545, 31964}, {12564, 14100}, {12579, 37443}, {12608, 33596}, {12610, 29050}, {12679, 36999}, {12723, 35650}, {12909, 16159}, {13624, 15704}, {13731, 41430}, {13883, 23251}, {13888, 43512}, {13902, 42413}, {13936, 23261}, {13942, 43511}, {13959, 42414}, {13971, 42259}, {14893, 50821}, {14927, 16475}, {15022, 19872}, {15030, 31752}, {15171, 21620}, {15177, 35502}, {15310, 15488}, {15338, 17605}, {15640, 34628}, {15680, 24541}, {15681, 50828}, {15683, 25055}, {15692, 50816}, {15694, 50807}, {15702, 50812}, {15717, 34595}, {15908, 37447}, {15931, 33557}, {16128, 48680}, {16143, 18444}, {16174, 38761}, {16616, 31788}, {17579, 41012}, {17690, 25881}, {17768, 24391}, {17800, 18493}, {18482, 38151}, {18525, 28234}, {18527, 24470}, {19130, 38118}, {19541, 25440}, {19861, 31295}, {19875, 50803}, {20117, 37585}, {20420, 21616}, {21062, 37398}, {21636, 23698}, {22615, 35774}, {22644, 35775}, {24309, 37415}, {26363, 37434}, {28168, 34773}, {28204, 33699}, {28538, 51022}, {28550, 49609}, {29012, 39870}, {29054, 49520}, {29181, 49511}, {30389, 49140}, {31398, 39590}, {31404, 31421}, {31415, 31422}, {31418, 31424}, {31806, 31937}, {31837, 44286}, {32049, 34739}, {32557, 38759}, {33709, 38693}, {35402, 50797}, {35434, 50798}, {37108, 38037}, {37423, 38150}, {37428, 38094}, {38035, 48905}, {38036, 43176}, {38049, 44882}, {38089, 50959}, {39586, 44431}, {42283, 49227}, {42284, 49226}, {42561, 49619}, {43223, 50694}, {43531, 48900}, {44980, 48357}, {48482, 49170}, {48899, 48921}, {48910, 49505}, {50736, 50836}
X(51118) = midpoint of X(i) and X(j) for these {i,j}: {1, 3146}, {4, 41869}, {8, 9589}, {355, 48661}, {382, 12699}, {962, 5691}, {3543, 50865}, {3656, 15684}, {5073, 18481}, {10724, 34789}, {10728, 14217}, {15640, 34628}, {15682, 31162}, {16128, 48680}, {44980, 48357}
X(51118) = reflection of X(i) in X(j) for these {i,j}: {3, 18483}, {10, 4}, {20, 1125}, {40, 19925}, {72, 31871}, {185, 31757}, {376, 50802}, {550, 9955}, {946, 22793}, {1385, 40273}, {3244, 4301}, {3543, 50869}, {3579, 546}, {3878, 9856}, {4067, 31803}, {4297, 946}, {4301, 12699}, {4669, 34648}, {5493, 10}, {5882, 22791}, {6361, 43174}, {7686, 31822}, {7957, 3678}, {7991, 3626}, {8591, 50882}, {9943, 5806}, {10265, 22938}, {10625, 31751}, {11177, 50887}, {11362, 18480}, {12512, 12571}, {12680, 3881}, {15681, 50828}, {15683, 50815}, {15704, 13624}, {18357, 12102}, {18480, 3853}, {18481, 13464}, {31673, 3627}, {31728, 5446}, {31730, 5}, {31737, 5907}, {31788, 16616}, {31806, 31937}, {33337, 1537}, {34632, 4745}, {34638, 2}, {34639, 11236}, {34646, 11235}, {34648, 3830}, {37585, 20117}, {38761, 16174}, {40660, 5893}, {43182, 5805}, {50796, 15687}, {50808, 381}, {50821, 14893}, {50862, 3543}
X(51118) = anticomplement of X(12512)
X(51118) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3817, 19862}, {3, 18483, 3817}, {4, 40, 19925}, {4, 5657, 18492}, {4, 6361, 5587}, {5, 31730, 10164}, {20, 1699, 1125}, {40, 19925, 10}, {165, 3091, 3634}, {226, 6284, 4314}, {376, 50802, 19883}, {388, 9580, 12575}, {442, 7965, 12558}, {497, 4298, 21625}, {497, 9579, 4298}, {546, 3579, 10175}, {550, 9955, 10165}, {946, 4297, 551}, {950, 1836, 3671}, {962, 3543, 5691}, {1385, 22793, 40273}, {1385, 40273, 946}, {1479, 4292, 11019}, {1750, 12651, 3811}, {1770, 3583, 1210}, {1836, 12953, 950}, {2550, 18250, 10}, {3146, 9812, 1}, {3522, 9779, 3624}, {3523, 7988, 19878}, {3586, 4295, 6738}, {3830, 48661, 355}, {3832, 9778, 1698}, {4294, 9612, 13405}, {5587, 6361, 43174}, {5587, 43174, 10}, {5691, 50865, 962}, {5731, 11522, 3636}, {5806, 9943, 5883}, {5927, 7957, 3678}, {7354, 12053, 4315}, {9616, 31412, 49618}, {10106, 12701, 4342}, {10483, 30384, 4311}, {11362, 18480, 38155}, {12512, 12571, 2}, {12701, 12943, 10106}, {15171, 21620, 30331}, {15683, 25055, 50815}, {15704, 38034, 13624}, {50864, 50870, 50862}, {50864, 50874, 50870}, {50865, 50866, 50872}, {50865, 50869, 50862}, {50865, 50873, 50869}, {50865, 50874, 50864}, {50866, 50868, 50862}, {50866, 50872, 50868}, {50869, 50870, 50874}
X(51119) lies on these lines: {3, 50802}, {4, 50814}, {30, 3636}, {355, 35402}, {516, 3845}, {519, 962}, {547, 12571}, {551, 5059}, {3533, 50813}, {3545, 3634}, {3576, 11001}, {3626, 50687}, {3627, 50830}, {3656, 28164}, {3817, 15719}, {3828, 3832}, {3830, 28228}, {3850, 28202}, {3853, 28194}, {4691, 12702}, {4746, 34648}, {5847, 51025}, {9955, 41982}, {11278, 50831}, {11539, 18483}, {11812, 28146}, {12101, 28232}, {12512, 15702}, {15682, 16200}, {15686, 22793}, {15687, 50827}, {15690, 28150}, {15708, 19878}, {17578, 34641}, {28182, 46332}, {28236, 33699}, {30392, 41150}, {31730, 50807}, {33703, 50811}, {34747, 50690}, {35400, 37624}, {35401, 48661}, {35434, 47745}, {38076, 50809}, {38155, 50810}, {38758, 50845}, {43174, 50799}
X(51119) = midpoint of X(50865) and X(50869)
X(51119) = reflection of X(i) in X(j) for these {i,j}: {4746, 34648}, {34638, 19878}, {50816, 50802}, {50870, 50869}
X(51119) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3543, 50871, 50862}, {50862, 50871, 50868}, {50862, 50873, 50869}, {50865, 50866, 962}, {50865, 50873, 50862}, {50865, 50874, 50872}, {50868, 50869, 3543}, {50872, 50873, 50874}, {50872, 50874, 50862}
X(51120) lies on these lines: {1, 34638}, {2, 28228}, {3, 551}, {4, 34641}, {10, 3545}, {30, 3244}, {40, 15702}, {381, 38098}, {515, 50805}, {516, 7967}, {517, 3845}, {519, 962}, {547, 946}, {553, 4342}, {1125, 15708}, {1699, 4745}, {3146, 34747}, {3241, 5059}, {3524, 15808}, {3534, 28232}, {3576, 50813}, {3579, 41983}, {3625, 12699}, {3626, 3839}, {3632, 50687}, {3635, 34628}, {3636, 10304}, {3654, 3817}, {3679, 3832}, {3828, 5056}, {3830, 28234}, {3850, 11362}, {3860, 38176}, {4297, 15686}, {4677, 9812}, {5066, 38127}, {5067, 38021}, {5603, 15719}, {5846, 51025}, {5847, 51027}, {5882, 28202}, {6361, 50812}, {6684, 15723}, {7982, 33703}, {8703, 31662}, {9956, 50822}, {10164, 11812}, {10165, 19711}, {11224, 28158}, {11539, 19862}, {12512, 38314}, {12645, 35402}, {13607, 15681}, {15682, 28236}, {15687, 47745}, {15690, 28174}, {16239, 38068}, {18483, 34718}, {20070, 25055}, {24644, 50837}, {28208, 50831}, {29054, 51059}, {30392, 50816}, {31663, 50833}, {34631, 41869}, {34639, 34647}, {34640, 34646}, {35400, 48661}, {37727, 49133}, {38191, 50959}, {38758, 50841}
X(51120) = midpoint of X(i) and X(j) for these {i,j}: {3146, 34747}, {3241, 9589}, {3543, 11531}, {34631, 41869}, {50865, 50872}
X(51120) = reflection of X(i) in X(j) for these {i,j}: {10, 31162}, {551, 4301}, {3625, 34648}, {5493, 551}, {7991, 3828}, {15681, 13607}, {15686, 33179}, {34628, 3635}, {34632, 1125}, {34638, 1}, {34639, 34647}, {34641, 4}, {34646, 34640}, {34648, 12699}, {34718, 18483}, {47745, 15687}, {50808, 3656}, {50810, 50802}, {50817, 50801}, {50862, 50865}, {50864, 50869}, {50871, 50868}
X(51120) = anticomplement of X(50814)
X(51120) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 50817, 50801}, {962, 50872, 50865}, {3543, 50868, 50862}, {3543, 50871, 50868}, {3656, 50808, 551}, {4301, 50808, 3656}, {5691, 50865, 50873}, {5691, 50870, 50862}, {5691, 50873, 50870}, {11531, 50865, 50871}, {31162, 50810, 50802}, {50801, 50817, 34641}, {50802, 50810, 10}, {50864, 50865, 50869}, {50864, 50869, 50862}, {50865, 50871, 3543}
See Angel Montesdeoca, euclid 5290 and HG140319.
X(51121) lies on these lines: {514,3158}, {519,42050}, {527,43161}, {812,20317}, {3160,21096}, {3576,46180}, {3756,25567}, {4859,4962}, {10563,17132}, {30813,43057}
See Angel Montesdeoca, euclid 5290 and HG140319.
X(51122) lies on these lines: {2,2418}, {3,538}, {69,8354}, {83,1975}, {99,1384}, {194,1003}, {381,9767}, {385,15655}, {524,3534}, {525,3167}, {543,3830}, {574,8556}, {698,5050}, {754,15681}, {1351,5969}, {1569,36784}, {1657,7758}, {2516,3633}, {2782,9764}, {3053,41748}, {3161,4009}, {3311,22623}, {3312,22594}, {3716,4962}, {3734,14535}, {3843,7764}, {3845,9770}, {3849,15685}, {3857,28915}, {3926,33184}, {3933,32986}, {4779,6553}, {5013,9466}, {5055,34505}, {5066,7620}, {5073,7759}, {5077,7788}, {5254,33240}, {5286,8368}, {5305,33191}, {5477,11173}, {5503,17503}, {5858,35696}, {5859,35692}, {5860,43257}, {5861,43256}, {6144,6781}, {6221,22716}, {6294,33381}, {6392,33216}, {6398,22718}, {6581,33380}, {7610,15701}, {7618,13468}, {7739,33237}, {7754,13586}, {7762,33193}, {7774,47287}, {7775,14269}, {7776,33017}, {7778,14148}, {7798,15301}, {7799,11318}, {7804,22246}, {7813,44526}, {7816,43136}, {7819,32824}, {7837,8591}, {7855,44519}, {7866,32820}, {8359,32836}, {9350,12625}, {9740,19708}, {9888,12188}, {9909,15652}, {11152,22498}, {11159,41624}, {11184,18546}, {11287,32833}, {11485,22687}, {11486,22689}, {11648,39785}, {14023,15696}, {14692,48662}, {14892,25683}, {15484,32815}, {15689,34504}, {15695,47101}, {15707,34506}, {16508,33894}, {17130,22332}, {20081,33273}, {22575,22665}, {22576,22666}, {23334,33699}, {36373,42115}, {36378,42116}
X(51122) = midpoint of X(i) and X(j) for these {i, j}: {194,32474}, {9741,11148}
X(51122) = reflection of X(i) in X(j) for these (i, j): {3,8716}, {381,34511}, {3830,9766}, {5485,12040}, {8716,7781}, {11165,9741}, {12188,9888}, {40727,11165}
See Angel Montesdeoca, euclid 5290 and HG140319.
X(51123) lies on these lines: {2,2418}, {5,7781}, {30,8716}, {99,12156}, {141,14148}, {194,35297}, {524,3098}, {525,10190}, {538,549}, {543,3845}, {547,34505}, {548,7758}, {550,754}, {591,42215}, {599,8358}, {698,38110}, {1353,14645}, {1657,34547}, {1975,31406}, {1991,42216}, {2482,5306}, {2896,3933}, {3036,10005}, {3627,7764}, {3629,32456}, {3830,9770}, {3849,19710}, {3926,11287}, {4962,45337}, {5026,8584}, {5066,11184}, {5305,6337}, {5395,14033}, {5452,14548}, {5503,35705}, {5569,19711}, {5860,9541}, {5874,32419}, {5875,32421}, {6179,33227}, {6309,32516}, {6661,32474}, {7610,11812}, {7615,10109}, {7618,8667}, {7620,19709}, {7622,15713}, {7739,8368}, {7751,15712}, {7757,8369}, {7759,15704}, {7762,33265}, {7765,33186}, {7767,33008}, {7775,15687}, {7776,33272}, {7777,47287}, {7780,44682}, {7788,8354}, {7798,32459}, {7799,33184}, {7813,14929}, {7837,8598}, {7840,8353}, {7863,9607}, {7902,33212}, {7906,33264}, {8182,15759}, {8357,32821}, {8359,32833}, {8362,10159}, {8588,15480}, {9605,14039}, {9740,15698}, {11055,11149}, {11168,14711}, {11318,32837}, {11648,22110}, {13571,33250}, {14023,33923}, {14537,15300}, {14614,27088}, {15686,34504}, {15690,47102}, {15699,38231}, {15711,46893}, {21356,32896}, {22165,40344}, {26288,26294}, {26289,26295}, {31470,32957}, {32538,36523}, {32818,33210}, {32831,33285}, {33459,36768}, {36775,43228}
X(51123) = midpoint of X(i) and X(j) for these {i, j}: {8716,34511}, {9741,11165}, {11148,40727}
X(51123) = reflection of X(i) in X(j) for these (i, j): {8667,12100}, {12040,11165}, {15686,34504}, {15687,7775}, {16509,12040}, {34505,547}, {47102,15690}
X(51124) lies on these lines: {1, 20583}, {2, 50791}, {6, 38314}, {141, 51004}, {145, 190}, {165, 50970}, {518, 3898}, {519, 3629}, {524, 3416}, {597, 1125}, {599, 9780}, {3242, 5032}, {3625, 28538}, {3631, 19875}, {3655, 12007}, {4715, 49630}, {4753, 34824}, {5587, 50958}, {5657, 50973}, {5790, 50961}, {5846, 15534}, {6329, 25055}, {7277, 49720}, {9053, 41149}, {11160, 38087}, {12035, 37684}, {17332, 48830}, {22165, 34379}, {26446, 50982}, {28333, 50282}, {28582, 49543}, {32455, 47356}, {38047, 50991}, {38112, 50985}, {38140, 47354}, {47358, 51110}, {48310, 49511}, {50112, 50283}, {50782, 51068}
X(51124) = midpoint of X(47359) and X(50952)
X(51124) = reflection of X(i) in X(j) for these {i,j}: {1, 20583}, {597, 4663}, {3655, 12007}, {47356, 32455}, {50112, 50283}, {50949, 47359}, {50950, 50951}, {50998, 51005}, {50999, 51006}
X(51124) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 50999, 51006}, {3416, 47359, 50953}, {3751, 50952, 47359}, {8584, 50998, 51005}, {47359, 50949, 49524}, {47359, 50950, 50951}, {50950, 50951, 50949}
X(51125) lies on these lines: {2, 50789}, {6, 38098}, {8, 48639}, {10, 38023}, {515, 50968}, {517, 50956}, {518, 50784}, {519, 3763}, {524, 3416}, {599, 3626}, {952, 50980}, {3617, 28538}, {3618, 47356}, {3620, 49688}, {3632, 20582}, {3654, 29012}, {3844, 31145}, {4141, 33074}, {4668, 9041}, {4669, 47358}, {4677, 50998}, {4691, 38087}, {4745, 38047}, {5657, 50975}, {5790, 50963}, {5846, 51066}, {5847, 51067}, {15534, 38191}, {19875, 49681}, {19883, 49679}, {20423, 38176}, {21358, 34641}, {28301, 49630}, {28313, 48829}, {34379, 50782}, {37712, 50965}, {38112, 50987}, {38127, 43273}, {38155, 51024}, {38210, 50997}, {38315, 51069}, {47353, 50827}, {50781, 50989}, {51001, 51068}
X(51125) = reflection of X(i) in X(j) for these {i,j}: {47356, 3618}, {47358, 50993}, {47359, 50953}, {50989, 50781}
X(51125) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3679, 50949, 47359}, {3679, 50950, 50951}, {4745, 50783, 38047}, {38191, 50786, 15534}, {47359, 50949, 3416}, {49524, 50952, 47359}, {50949, 50951, 50950}, {50950, 50951, 47359}
X(51126) lies on these lines: {2, 6}, {3, 43621}, {5, 5092}, {140, 3098}, {156, 182}, {187, 5103}, {206, 11548}, {239, 48636}, {344, 16674}, {373, 3313}, {427, 44091}, {441, 10979}, {468, 3867}, {511, 632}, {518, 19862}, {545, 17304}, {546, 17508}, {547, 3818}, {549, 19130}, {574, 7819}, {583, 29492}, {594, 4405}, {625, 38010}, {631, 29181}, {698, 7786}, {732, 31239}, {742, 31238}, {894, 48631}, {1030, 21540}, {1086, 7231}, {1100, 29596}, {1125, 49465}, {1350, 3525}, {1352, 5070}, {1386, 3634}, {1469, 7294}, {1495, 37439}, {1503, 1656}, {1691, 8363}, {1698, 5846}, {1843, 40670}, {2030, 5031}, {2177, 29663}, {2321, 50112}, {2345, 4395}, {2916, 13595}, {3008, 17385}, {3056, 5326}, {3090, 5085}, {3096, 43527}, {3230, 16818}, {3242, 5550}, {3247, 17045}, {3524, 48910}, {3526, 14561}, {3530, 48901}, {3533, 14853}, {3545, 48905}, {3564, 48154}, {3616, 9053}, {3624, 16496}, {3663, 28322}, {3703, 29684}, {3723, 17023}, {3731, 4422}, {3739, 31191}, {3758, 48632}, {3759, 29613}, {3821, 28546}, {3839, 50971}, {3844, 38049}, {3845, 48892}, {3850, 48898}, {3855, 33750}, {3858, 29323}, {3861, 48896}, {3932, 29646}, {3934, 32449}, {3943, 17358}, {3946, 17359}, {3973, 17306}, {4000, 7227}, {4026, 15485}, {4048, 43620}, {4085, 48810}, {4256, 17698}, {4265, 17531}, {4357, 15492}, {4364, 16814}, {4370, 17247}, {4399, 5222}, {4437, 29612}, {4472, 17278}, {4478, 29611}, {4665, 17117}, {4687, 9055}, {4698, 49481}, {4798, 5845}, {4852, 50097}, {4856, 50081}, {4859, 49733}, {4884, 26061}, {4969, 17228}, {4971, 17286}, {5008, 6292}, {5020, 31521}, {5024, 7789}, {5026, 6722}, {5033, 8361}, {5047, 5096}, {5054, 31670}, {5055, 46264}, {5056, 36990}, {5066, 48884}, {5067, 10516}, {5097, 41992}, {5124, 21516}, {5157, 22112}, {5159, 19126}, {5207, 14047}, {5210, 16043}, {5254, 7859}, {5257, 6687}, {5296, 25503}, {5318, 11290}, {5321, 11289}, {5439, 9021}, {5476, 10124}, {5585, 32990}, {5749, 7228}, {5750, 17356}, {5847, 31253}, {5888, 22336}, {5965, 40331}, {5969, 31274}, {5972, 25328}, {6247, 14786}, {6411, 11291}, {6412, 11292}, {6593, 6723}, {6666, 25498}, {6680, 41413}, {6683, 24256}, {6688, 9969}, {6694, 42124}, {6695, 42121}, {6697, 34774}, {6698, 25329}, {6748, 11331}, {7263, 16706}, {7277, 17227}, {7375, 23249}, {7376, 23259}, {7388, 42284}, {7389, 42283}, {7392, 41424}, {7405, 20300}, {7483, 33844}, {7486, 25406}, {7494, 31860}, {7495, 10545}, {7499, 34417}, {7716, 38282}, {7750, 16897}, {7782, 19702}, {7800, 21309}, {7808, 8364}, {7832, 9606}, {7834, 43291}, {7844, 8367}, {7854, 14075}, {7866, 31415}, {7913, 18424}, {7915, 31406}, {7943, 32992}, {8167, 12329}, {8289, 9478}, {8359, 8588}, {8368, 15482}, {8369, 8589}, {8550, 24206}, {8703, 25565}, {8705, 47452}, {9015, 31250}, {9024, 31235}, {9030, 31277}, {9607, 16896}, {9780, 38315}, {9822, 10219}, {10022, 24199}, {10160, 47609}, {10168, 15699}, {10192, 23300}, {10303, 31884}, {10304, 51029}, {10436, 40480}, {10541, 46936}, {10546, 13394}, {10645, 37341}, {10646, 37340}, {11178, 47599}, {11179, 50954}, {11284, 35707}, {11286, 43619}, {11287, 43618}, {11295, 42113}, {11296, 42112}, {11297, 42086}, {11298, 42085}, {11303, 42101}, {11304, 42102}, {11305, 42111}, {11306, 42114}, {11311, 18581}, {11312, 18582}, {11313, 42274}, {11314, 42277}, {11480, 37178}, {11481, 37177}, {11539, 21850}, {11574, 16776}, {11742, 32981}, {12100, 48880}, {13925, 42832}, {13993, 42833}, {14064, 18584}, {14067, 18906}, {14096, 35222}, {14767, 20204}, {14810, 14869}, {14861, 15105}, {14927, 15022}, {14928, 14971}, {15080, 37990}, {15585, 23327}, {15686, 48943}, {15687, 48891}, {15689, 50964}, {15702, 38072}, {15703, 18440}, {15705, 50972}, {15708, 51024}, {15709, 50966}, {15712, 29317}, {15713, 19924}, {15717, 48872}, {15720, 48873}, {15808, 38191}, {15826, 47279}, {16045, 43448}, {16239, 18583}, {16474, 19881}, {16475, 19872}, {16483, 19784}, {16484, 29633}, {16677, 17321}, {16808, 37351}, {16809, 37352}, {16842, 36741}, {16862, 36740}, {16884, 29579}, {17014, 17309}, {17229, 50114}, {17235, 50115}, {17246, 17354}, {17255, 26104}, {17263, 29614}, {17267, 26626}, {17268, 50113}, {17280, 17395}, {17284, 17390}, {17285, 17388}, {17291, 17365}, {17292, 17362}, {17302, 17340}, {17305, 17334}, {17324, 49742}, {17325, 26685}, {17338, 17400}, {17339, 17399}, {17341, 17397}, {17342, 17396}, {17348, 29604}, {17351, 49741}, {17355, 17382}, {17394, 29629}, {18538, 23312}, {18762, 23311}, {19127, 19137}, {19140, 40685}, {19875, 49681}, {19876, 38023}, {19883, 49529}, {20108, 50609}, {20190, 39884}, {21496, 36743}, {21519, 36744}, {21543, 37503}, {21747, 32781}, {23046, 50988}, {23324, 37347}, {23328, 37470}, {25055, 49688}, {25101, 41311}, {25326, 36950}, {25555, 48876}, {26235, 42554}, {28653, 29607}, {30745, 47453}, {31423, 38035}, {32459, 33237}, {33184, 43457}, {33923, 48904}, {34200, 48879}, {37338, 41328}, {37491, 37827}, {37911, 47449}, {38089, 49505}, {38314, 49690}, {39080, 40478}, {40425, 41884}, {42894, 50855}, {42895, 50858}, {43150, 50979}, {44456, 46219}, {44682, 48885}, {45339, 50780}, {47598, 50977}, {48815, 48866}, {48821, 49482}, {48845, 48863}, {48847, 48859}, {49684, 50949}
X(51126) = midpoint of X(i) and X(j) for these {i,j}: {6, 3620}, {1992, 50989}, {3618, 3763}, {7786, 40332}, {11179, 50954}, {30745, 47453}
X(51126) = reflection of X(i) in X(j) for these {i,j}: {141, 3763}, {3618, 3589}, {50987, 10168}, {50993, 20582}
X(51126) = complement of X(3763)
X(51126) = complement of the isogonal conjugate of X(39955)
X(51126) = complement of the isotomic conjugate of X(43527)
X(51126) = X(i)-complementary conjugate of X(j) for these (i,j): {7954, 4369}, {39955, 10}, {43527, 2887}
X(51126) = crosspoint of X(2) and X(43527)
X(51126) = crosssum of X(6) and X(7772)
X(51126) = barycentric product X(39676)*X(42554)
X(51126) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6, 34573}, {2, 3589, 141}, {2, 3618, 3763}, {2, 16987, 7792}, {2, 17352, 1213}, {2, 17381, 17245}, {2, 37650, 17327}, {2, 47352, 20582}, {2, 47355, 3589}, {2, 48310, 597}, {6, 141, 3630}, {6, 599, 11008}, {6, 3619, 3631}, {6, 3630, 3629}, {6, 3763, 3620}, {6, 11008, 32455}, {6, 34573, 141}, {69, 6329, 8584}, {69, 20582, 141}, {69, 47352, 6329}, {140, 5480, 21167}, {140, 38317, 5480}, {141, 597, 3629}, {141, 3589, 597}, {141, 3629, 22165}, {141, 8584, 69}, {141, 48310, 3589}, {182, 42786, 18358}, {549, 19130, 48881}, {590, 615, 9300}, {597, 3630, 6}, {3589, 6329, 47352}, {3589, 20582, 6329}, {3589, 34573, 6}, {3589, 47355, 48310}, {3618, 3620, 6}, {3619, 3631, 141}, {3628, 18358, 42786}, {3631, 34573, 3619}, {3759, 29613, 48635}, {5222, 17293, 4399}, {5749, 17290, 7228}, {5750, 17356, 34824}, {6329, 20582, 69}, {7889, 39784, 8362}, {8584, 47352, 597}, {10168, 15699, 47354}, {11488, 11489, 37665}, {14869, 38136, 14810}, {16706, 17369, 7263}, {17023, 17357, 17243}, {17279, 29598, 17045}, {17289, 17366, 4665}, {17289, 29630, 17366}, {17327, 37650, 49731}, {17353, 17384, 4364}, {17354, 17383, 17246}, {17358, 17380, 3943}, {17367, 17371, 594}, {17368, 17370, 1086}, {20582, 47352, 8584}, {23302, 23303, 3815}, {24206, 38110, 8550}, {32789, 32790, 3055}, {38049, 51073, 3844}, {39022, 39023, 50251}, {45871, 45872, 15491}
X(51127) lies on these lines: {2, 6}, {5, 17508}, {140, 14810}, {468, 46026}, {511, 16239}, {518, 4547}, {546, 48891}, {547, 5092}, {548, 48943}, {549, 48880}, {576, 41992}, {594, 29630}, {625, 6704}, {631, 48910}, {632, 21850}, {698, 6683}, {1125, 9053}, {1350, 3533}, {1386, 51073}, {1503, 3628}, {1656, 46264}, {1698, 49681}, {3008, 28633}, {3090, 44882}, {3098, 11539}, {3416, 19872}, {3524, 50972}, {3525, 21167}, {3526, 5480}, {3545, 50971}, {3616, 49690}, {3624, 49524}, {3634, 5846}, {3793, 6292}, {3818, 15699}, {3844, 31253}, {3857, 48896}, {3859, 48942}, {3861, 33751}, {3867, 37453}, {3946, 28309}, {4265, 17535}, {4370, 17324}, {4371, 17293}, {4395, 17289}, {4399, 17367}, {4402, 4665}, {4422, 17384}, {4472, 17356}, {4478, 17292}, {4657, 16676}, {4687, 49533}, {4698, 9055}, {4859, 10022}, {5054, 48881}, {5055, 50960}, {5066, 48892}, {5067, 5085}, {5070, 18440}, {5071, 48905}, {5096, 17536}, {5206, 8362}, {5222, 48636}, {5349, 11289}, {5350, 11290}, {5749, 48631}, {5750, 40480}, {6030, 37990}, {6666, 25358}, {7222, 17290}, {7227, 16706}, {7228, 17368}, {7229, 7263}, {7238, 17291}, {7375, 23253}, {7376, 23263}, {7486, 36990}, {7499, 44106}, {7745, 7937}, {7762, 43527}, {7819, 32459}, {7852, 12815}, {7859, 47286}, {7889, 35007}, {8705, 9822}, {9019, 10219}, {9024, 25144}, {10168, 18358}, {10304, 51026}, {11540, 19924}, {11574, 40670}, {11812, 25565}, {12017, 47354}, {12100, 48895}, {12108, 29317}, {12811, 29323}, {12812, 48889}, {14561, 46219}, {14712, 16897}, {14869, 48901}, {15693, 43621}, {15694, 31670}, {15706, 50964}, {15709, 50965}, {15723, 33878}, {16491, 50949}, {16673, 17279}, {16854, 36741}, {16864, 36740}, {17023, 46845}, {17045, 17357}, {17243, 29598}, {17286, 50112}, {17304, 49726}, {17340, 17383}, {17355, 28297}, {17358, 17395}, {17362, 29613}, {17365, 48637}, {17366, 17371}, {17369, 17370}, {17385, 31191}, {17390, 29596}, {17504, 48879}, {18230, 25503}, {19862, 49529}, {19877, 38315}, {19883, 49465}, {21520, 36743}, {21527, 36744}, {23332, 31267}, {24206, 48154}, {24295, 28530}, {25055, 50951}, {25406, 46935}, {25498, 31285}, {29012, 35018}, {31239, 41622}, {31268, 41749}, {32154, 41593}, {33186, 42534}, {34595, 38047}, {37439, 44082}, {37517, 38079}, {39899, 50958}, {41985, 50664}, {42786, 48906}, {44682, 48904}, {48843, 48865}
X(51127) = midpoint of X(i) and X(j) for these {i,j}: {141, 6329}, {3589, 34573}, {3861, 33751}, {11812, 25565}, {20583, 41152}
X(51127) = complement of X(34573)
X(51127) = complement of the isogonal conjugate of X(34572)
X(51127) = isotomic conjugate of the isogonal conjugate of X(34571)
X(51127) = X(34572)-complementary conjugate of X(10)
X(51127) = crosssum of X(6) and X(5041)
X(51127) = barycentric product X(76)*X(34571)
X(51127) = barycentric quotient X(34571)/X(6)
X(51127) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3589, 34573}, {2, 47355, 141}, {2, 48310, 20582}, {6, 3763, 21356}, {6, 11160, 3629}, {6, 48310, 3589}, {141, 193, 3631}, {141, 597, 193}, {141, 3589, 6329}, {141, 3618, 32455}, {141, 47355, 3589}, {193, 3763, 141}, {597, 3763, 3631}, {597, 21356, 41149}, {3589, 3631, 597}, {3589, 20582, 6}, {3589, 32455, 3618}, {3618, 32455, 6329}, {3619, 3629, 50991}, {3619, 47352, 3629}, {6329, 34573, 141}, {20582, 41149, 21356}, {20583, 21358, 41152}, {39022, 39023, 50248}
X(51128) lies on these lines: {2, 6}, {5, 14810}, {30, 42786}, {140, 3818}, {182, 16239}, {206, 16187}, {518, 51073}, {546, 48879}, {547, 3098}, {549, 48892}, {575, 41992}, {594, 17370}, {631, 48905}, {632, 20190}, {1086, 17371}, {1350, 5067}, {1352, 46219}, {1386, 19878}, {1503, 3526}, {1531, 7399}, {1656, 31670}, {1698, 49688}, {2916, 7496}, {3090, 29181}, {3242, 19877}, {3313, 40670}, {3416, 34595}, {3524, 50976}, {3525, 10516}, {3533, 5085}, {3545, 50969}, {3616, 49679}, {3624, 5846}, {3628, 5480}, {3634, 49524}, {3828, 49465}, {3844, 19862}, {3858, 48885}, {3912, 46845}, {3932, 25539}, {3933, 39784}, {3943, 17383}, {3946, 50097}, {4265, 17536}, {4364, 17357}, {4370, 17249}, {4395, 17293}, {4399, 29611}, {4405, 5564}, {4422, 17306}, {4472, 17282}, {4478, 5222}, {4657, 16673}, {4665, 16706}, {4751, 9055}, {4969, 48634}, {5031, 33185}, {5054, 50957}, {5055, 50964}, {5056, 31884}, {5066, 48880}, {5068, 48872}, {5071, 48910}, {5079, 48873}, {5092, 11539}, {5096, 17535}, {5103, 31275}, {5159, 47451}, {5206, 7819}, {5349, 11290}, {5350, 11289}, {5749, 7238}, {6030, 15321}, {6292, 35007}, {6390, 7822}, {6683, 32449}, {6697, 10192}, {6723, 25328}, {7227, 17290}, {7231, 7321}, {7263, 17289}, {7277, 48633}, {7375, 23263}, {7376, 23253}, {7499, 44082}, {7750, 16896}, {7786, 41747}, {7807, 31268}, {7815, 42421}, {7820, 8362}, {7821, 41623}, {7844, 8364}, {8550, 43150}, {9041, 19876}, {9053, 9780}, {9607, 46226}, {10007, 12815}, {10124, 18358}, {10303, 36990}, {10304, 50960}, {11178, 47598}, {12017, 15723}, {12100, 48884}, {12108, 48898}, {12272, 44323}, {12811, 48904}, {14869, 29012}, {14928, 31274}, {15082, 16776}, {15694, 46264}, {15699, 19130}, {15707, 50956}, {15708, 50971}, {15712, 48889}, {15713, 25561}, {15826, 47278}, {16676, 17279}, {16854, 36740}, {16864, 36741}, {17045, 17284}, {17229, 50112}, {17235, 49726}, {17239, 31191}, {17243, 17384}, {17246, 17358}, {17262, 26104}, {17285, 17395}, {17303, 40480}, {17305, 17340}, {17355, 49741}, {17356, 29604}, {17362, 29630}, {17367, 48635}, {17368, 48632}, {17385, 34824}, {17388, 29587}, {17390, 29598}, {17400, 29629}, {17504, 48891}, {18440, 50983}, {19121, 37283}, {19137, 32217}, {19709, 43621}, {19872, 38047}, {19875, 50998}, {19883, 50949}, {20987, 40916}, {21520, 36744}, {21527, 36743}, {21637, 32154}, {23046, 48943}, {23324, 35228}, {24256, 33186}, {25326, 40478}, {25498, 50013}, {29323, 44682}, {30745, 32218}, {31521, 40920}, {35018, 48901}, {37439, 44106}, {37517, 41985}, {38317, 48154}, {40802, 46223}, {47599, 50977}, {48815, 48836}, {48843, 48859}, {50687, 50972}
X(51128) = midpoint of X(3619) and X(47355)
X(51128) = reflection of X(141) in X(3619)
X(51128) = complement of X(47355)
X(51128) = isotomic conjugate of the isogonal conjugate of X(41940)
X(51128) = barycentric product X(76)*X(41940)
X(51128) = barycentric quotient X(41940)/X(6)
X(51128) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3619, 47355}, {2, 3763, 3589}, {2, 16988, 7792}, {2, 17265, 6707}, {2, 17283, 17398}, {2, 17307, 17337}, {2, 20582, 48310}, {2, 34573, 141}, {6, 141, 22165}, {6, 20582, 141}, {141, 597, 3630}, {141, 3589, 3629}, {141, 8584, 3631}, {141, 48310, 6}, {302, 303, 37671}, {3589, 3629, 597}, {3589, 3763, 141}, {3589, 34573, 3763}, {3618, 3619, 50994}, {3618, 3631, 8584}, {3618, 11160, 6}, {3618, 21358, 3631}, {3620, 47352, 32455}, {3631, 21358, 141}, {3763, 6144, 21358}, {6144, 8584, 3629}, {6329, 41149, 6}, {17291, 17369, 48631}, {17292, 17366, 48636}, {17366, 48636, 4405}, {17369, 48631, 7231}, {17370, 29613, 594}, {17384, 29596, 17243}, {20582, 48310, 22165}, {22165, 48310, 597}
X(51129) lies on these lines: {2, 50968}, {3, 51026}, {4, 50975}, {5, 50965}, {141, 38071}, {381, 524}, {518, 51074}, {542, 3858}, {546, 597}, {549, 48920}, {599, 3855}, {1503, 41099}, {1699, 50953}, {3098, 14892}, {3146, 50976}, {3545, 3763}, {3589, 14269}, {3618, 3839}, {3620, 50982}, {3627, 25565}, {3830, 50971}, {3832, 8550}, {3845, 29012}, {3851, 20582}, {3854, 50973}, {3857, 25561}, {3860, 5476}, {5054, 50972}, {5055, 48881}, {5066, 50977}, {5846, 50799}, {7394, 35266}, {8584, 38136}, {9053, 50806}, {10109, 21167}, {10124, 48904}, {10516, 50990}, {11179, 51025}, {11737, 48901}, {12101, 38317}, {14853, 51027}, {14893, 44882}, {15687, 48310}, {15699, 48895}, {19130, 23046}, {19709, 29181}, {31670, 50970}, {33699, 50988}, {38034, 50998}, {38140, 50949}, {41106, 50967}, {47599, 48880}
X(51129) = midpoint of X(i) and X(j) for these {i,j}: {20423, 50954}, {50956, 50963}, {50966, 51024}, {50968, 51029}
X(51129) = reflection of X(i) in X(j) for these {i,j}: {47354, 50956}, {50963, 50959}, {50965, 50980}, {50975, 50983}
X(51129) = complement of X(50968)
X(51129) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 51029, 50968}, {381, 20423, 50960}, {381, 50959, 47354}, {381, 50963, 50956}, {381, 50964, 50959}, {3763, 51024, 50966}, {20423, 50956, 50954}, {20423, 50957, 50958}, {20423, 50960, 47354}, {47354, 50959, 5480}, {50954, 50963, 20423}, {50957, 50958, 47354}, {50958, 50960, 50957}, {50959, 50960, 20423}
X(51130) lies on these lines: {2, 50970}, {4, 20583}, {5, 50982}, {6, 43507}, {20, 597}, {30, 6329}, {140, 50984}, {141, 51028}, {182, 44903}, {381, 524}, {511, 10109}, {518, 51075}, {542, 3861}, {599, 5068}, {1503, 12101}, {1992, 50689}, {3090, 20582}, {3524, 3589}, {3545, 3631}, {3627, 22234}, {3629, 3839}, {3818, 50986}, {3860, 5965}, {5073, 14848}, {5097, 14893}, {5102, 41099}, {5476, 8703}, {5846, 50801}, {7000, 13664}, {7374, 13784}, {7610, 14484}, {8584, 51023}, {9053, 51077}, {12007, 15687}, {14561, 15701}, {14853, 15682}, {14891, 19924}, {14892, 19130}, {15685, 41153}, {15689, 31670}, {15691, 18583}, {15699, 21850}, {15721, 48310}, {21167, 50966}, {21735, 50968}, {32455, 50974}, {33699, 39561}, {37517, 38071}, {38079, 44682}, {38136, 41152}, {38317, 50980}, {41149, 47353}, {45762, 48889}, {48910, 50975}
X(51130) = midpoint of X(i) and X(j) for these {i,j}: {4, 20583}, {5097, 14893}, {12007, 15687}, {20423, 50959}, {41149, 47353}, {43273, 51026}, {50971, 51024}
X(51130) = reflection of X(i) in X(j) for these {i,j}: {50960, 50959}, {50972, 50983}
X(51130) = complement of X(50970)
X(51130) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {381, 50961, 47354}, {597, 51024, 50971}, {5480, 20423, 50959}, {5480, 47354, 50963}, {20423, 50956, 1351}, {20423, 50963, 47354}, {20423, 50964, 50962}, {47354, 50961, 50958}, {47354, 50963, 50959}, {50958, 50959, 381}, {50962, 50963, 50964}, {50962, 50964, 47354}
X(51131) lies on these lines: {2, 50972}, {4, 50971}, {5, 50984}, {381, 524}, {518, 51076}, {542, 3856}, {547, 48885}, {597, 3832}, {599, 3854}, {1503, 3860}, {1699, 50951}, {3090, 50968}, {3091, 20582}, {3545, 34573}, {3589, 3839}, {3631, 51028}, {3845, 38317}, {3855, 50967}, {3857, 50982}, {3858, 50979}, {3859, 25561}, {3861, 25565}, {5066, 29181}, {5846, 50803}, {6329, 39874}, {9041, 12571}, {9053, 50802}, {9779, 50998}, {10168, 41987}, {10516, 41152}, {10519, 41106}, {14892, 48895}, {14893, 48942}, {23046, 48906}, {32455, 51027}, {38071, 50977}, {41099, 43273}
X(51131) = midpoint of X(i) and X(j) for these {i,j}: {3861, 25565}, {50959, 50960}, {50972, 51026}
X(51131) = complement of X(50972)
X(51131) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 51026, 50972}, {381, 50959, 50960}, {381, 50964, 47354}, {5480, 47354, 50962}, {5480, 50956, 50958}, {47354, 50962, 50958}, {47354, 50964, 50959}, {50956, 50962, 47354}, {50958, 50959, 5480}
X(51132) lies on these lines: {2, 5102}, {3, 20583}, {4, 51027}, {5, 50985}, {6, 3524}, {20, 1992}, {30, 3629}, {140, 576}, {141, 15699}, {182, 14891}, {193, 50687}, {323, 20192}, {376, 12007}, {381, 524}, {511, 8584}, {518, 51077}, {542, 3627}, {549, 5097}, {575, 44682}, {599, 3090}, {1350, 5032}, {1353, 19924}, {1503, 15534}, {1993, 35266}, {3545, 40341}, {3564, 12101}, {3630, 11178}, {3631, 5055}, {3818, 41987}, {3830, 51025}, {3839, 11008}, {3845, 5965}, {5050, 15716}, {5054, 6329}, {5068, 11160}, {5070, 14848}, {5093, 15701}, {5107, 5355}, {5111, 5306}, {5476, 10109}, {5648, 41585}, {5846, 50804}, {5847, 50801}, {6144, 11180}, {10168, 50980}, {10516, 50992}, {11173, 20194}, {11179, 15689}, {11482, 38064}, {11694, 34155}, {12100, 39561}, {12811, 34507}, {13340, 44323}, {13567, 13857}, {14561, 50991}, {14853, 15533}, {14912, 50975}, {15069, 50689}, {15520, 21167}, {15685, 29181}, {15691, 44882}, {17504, 50664}, {21735, 50966}, {21969, 34750}, {22330, 50988}, {25406, 50976}, {28538, 47745}, {31670, 51026}, {34379, 51075}, {38071, 43150}, {38079, 40107}, {38110, 50981}, {38136, 41990}, {38176, 50949}, {48310, 48876}, {50690, 51029}
X(51132) = midpoint of X(i) and X(j) for these {i,j}: {1992, 11477}, {6144, 11180}, {11179, 44456}, {20423, 50962}, {43273, 51028}, {50974, 51024}
X(51132) = reflection of X(i) in X(j) for these {i,j}: {3, 20583}, {376, 12007}, {549, 5097}, {597, 576}, {3630, 11178}, {8550, 1992}, {11179, 32455}, {13340, 44323}, {21167, 15520}, {22165, 5476}, {47354, 20423}, {48881, 11179}, {50955, 50959}, {50961, 50958}, {50965, 50979}, {50967, 50983}, {50973, 50982}
X(51132) = complement of X(50973)
X(51132) = anticomplement of X(50982)
X(51132) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 50973, 50982}, {6, 50967, 50983}, {381, 50958, 47354}, {381, 50961, 50958}, {1351, 50962, 20423}, {1352, 20423, 50963}, {1352, 50960, 47354}, {1352, 50963, 50960}, {1992, 51028, 43273}, {8584, 50965, 50979}, {11178, 42785, 14892}, {11477, 43273, 51028}, {15534, 51024, 50974}, {20423, 47354, 5480}, {20423, 50955, 50959}, {20423, 50961, 381}, {32455, 44456, 48881}, {50955, 50959, 47354}
X(51133) lies on these lines: {2, 50976}, {4, 50969}, {5, 50988}, {30, 42786}, {141, 23046}, {381, 524}, {382, 50972}, {518, 51078}, {542, 3857}, {546, 50977}, {549, 48942}, {597, 3850}, {1503, 41106}, {3091, 43273}, {3098, 41987}, {3545, 47355}, {3619, 3839}, {3830, 50984}, {3843, 20582}, {3845, 29317}, {3854, 38072}, {3855, 8550}, {3858, 25561}, {5055, 50971}, {5066, 38317}, {5846, 50807}, {9053, 50800}, {10516, 50982}, {10519, 41099}, {11737, 44882}, {12101, 21167}, {14269, 48881}, {15687, 48885}, {18553, 50986}, {25565, 50987}, {34573, 38335}, {38071, 48906}, {47478, 48884}, {48310, 48889}, {50687, 50968}, {50689, 51029}
X(51133) = midpoint of X(50957) and X(50964)
X(51133) = reflection of X(i) in X(j) for these {i,j}: {47354, 50957}, {50965, 50981}
X(51133) = complement of X(50976)
X(51133) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {381, 50956, 50959}, {381, 50957, 50964}, {381, 50960, 47354}, {11898, 50963, 20423}, {50956, 50959, 47354}, {50959, 50960, 50956}
X(51134) lies on these lines: {3, 50956}, {20, 50959}, {141, 15688}, {376, 524}, {518, 51079}, {548, 50977}, {550, 597}, {1503, 15695}, {3524, 50960}, {3528, 20582}, {3534, 14561}, {3618, 51024}, {3620, 50958}, {3763, 10304}, {3818, 41982}, {5480, 15691}, {5846, 50812}, {8703, 21167}, {9053, 50819}, {11001, 51026}, {11482, 15696}, {14891, 48896}, {15681, 48310}, {15685, 50964}, {15686, 33751}, {15689, 20423}, {15690, 39561}, {15697, 29181}, {15704, 50988}, {15710, 34573}, {15711, 29323}, {17504, 48891}, {31884, 50990}, {46264, 50982}, {48881, 50979}, {48905, 51025}, {50993, 51023}
X(51134) = midpoint of X(i) and X(j) for these {i,j}: {43273, 50966}, {50968, 50975}
X(51134) = reflection of X(i) in X(j) for these {i,j}: {47354, 50980}, {50963, 50983}, {50965, 50968}, {50975, 50971}, {51022, 50956}, {51029, 50959}
X(51134) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 43273, 50972}, {376, 50971, 50965}, {376, 50975, 50968}, {376, 50976, 50971}, {43273, 50968, 50966}, {43273, 50969, 50970}, {43273, 50972, 50965}, {50965, 50971, 44882}, {50966, 50975, 43273}, {50969, 50970, 50965}, {50970, 50972, 50969}, {50971, 50972, 43273}
X(51135) lies on these lines: {2, 51025}, {3, 50958}, {5, 50960}, {20, 20583}, {30, 6329}, {141, 15705}, {182, 35404}, {376, 524}, {518, 51080}, {542, 33923}, {597, 3146}, {599, 21734}, {1503, 10193}, {1657, 20423}, {3523, 20582}, {3589, 3839}, {3630, 35418}, {3631, 10304}, {3818, 50988}, {3830, 14561}, {3860, 29012}, {5054, 34573}, {5085, 41106}, {5092, 47599}, {5846, 50814}, {8703, 50982}, {9053, 51082}, {10124, 11645}, {12007, 15686}, {12017, 50964}, {14927, 48310}, {15520, 19710}, {15688, 50961}, {25406, 51024}, {32455, 51028}, {37712, 50951}, {41152, 50955}, {45759, 50977}, {48881, 50962}
X(51135) = midpoint of X(i) and X(j) for these {i,j}: {20, 20583}, {12007, 15686}, {43273, 50971}
X(51135) = reflection of X(i) in X(j) for these {i,j}: {50960, 50983}, {50972, 50971}
X(51135) = complement of X(51025)
X(51135) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 50973, 50965}, {43273, 44882, 50971}, {43273, 50968, 6776}, {43273, 50975, 50965}, {43273, 50976, 50974}, {44882, 50965, 50975}, {50965, 50973, 50970}, {50965, 50975, 50971}, {50970, 50971, 376}, {50974, 50975, 50976}, {50974, 50976, 50965}
X(51136) lies on these lines: {2, 50958}, {3, 50961}, {4, 20583}, {5, 542}, {6, 3839}, {30, 3629}, {69, 15705}, {98, 9771}, {141, 5054}, {182, 10124}, {376, 524}, {381, 12007}, {511, 19710}, {518, 51082}, {599, 3523}, {1352, 15703}, {1353, 11645}, {1503, 3830}, {1657, 50962}, {1992, 3146}, {3524, 3631}, {3525, 15069}, {3545, 6329}, {3564, 12100}, {3589, 11180}, {3630, 45759}, {3815, 11177}, {3860, 5476}, {5032, 36990}, {5050, 50954}, {5066, 39561}, {5085, 50991}, {5092, 50980}, {5097, 15687}, {5102, 15682}, {5480, 13687}, {5846, 50817}, {5847, 50814}, {5921, 47352}, {5965, 8703}, {6770, 33474}, {6773, 33475}, {6811, 13664}, {6813, 13784}, {8593, 35954}, {9143, 37648}, {9744, 15597}, {10304, 40341}, {10706, 41595}, {11160, 21734}, {11178, 47599}, {11459, 44323}, {11477, 49138}, {11539, 43150}, {12108, 34507}, {13567, 35266}, {14561, 50957}, {14848, 50964}, {14912, 41106}, {15360, 45968}, {15533, 25406}, {15534, 29181}, {15699, 50664}, {16226, 41579}, {18358, 45757}, {18440, 50956}, {20126, 23328}, {20192, 46818}, {31884, 50992}, {32234, 35492}, {32455, 39874}, {34379, 51080}, {34782, 37490}, {35409, 48910}, {37712, 47359}, {38064, 46219}, {38127, 50949}, {38323, 43612}, {39878, 47356}, {40107, 50981}
X(51136) = midpoint of X(i) and X(j) for these {i,j}: {11179, 39899}, {39878, 47356}, {43273, 50974}
X(51136) = reflection of X(i) in X(j) for these {i,j}: {4, 20583}, {141, 11179}, {381, 12007}, {597, 8550}, {10706, 41595}, {11180, 3589}, {11459, 44323}, {15069, 20582}, {15687, 5097}, {25561, 33749}, {47354, 50979}, {50955, 50983}, {50961, 50982}, {50965, 43273}, {50967, 50971}, {50973, 50970}, {51022, 20423}, {51023, 50959}, {51027, 50958}
X(51136) = complement of X(51027)
X(51136) = anticomplement of X(50958)
X(51136) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 51027, 50958}, {3, 50961, 50982}, {6, 51023, 50959}, {376, 50970, 50965}, {376, 50973, 50970}, {1350, 43273, 50975}, {1350, 50972, 50965}, {1350, 50975, 50972}, {6776, 50974, 43273}, {8550, 47354, 50979}, {8584, 51022, 20423}, {11179, 50955, 50983}, {43273, 50965, 44882}, {43273, 50967, 50971}, {43273, 50973, 376}, {47354, 50979, 597}, {50955, 50983, 141}, {50967, 50971, 50965}
X(51137) lies on these lines: {2, 6030}, {3, 38072}, {5, 50971}, {6, 15707}, {20, 25565}, {140, 47354}, {182, 524}, {376, 48904}, {381, 48896}, {511, 15693}, {518, 51084}, {542, 631}, {547, 48898}, {575, 50962}, {576, 3523}, {597, 3530}, {599, 15720}, {1350, 15718}, {1352, 15721}, {1503, 15713}, {3098, 3524}, {3526, 25561}, {3543, 33751}, {3545, 48892}, {3576, 50953}, {3589, 17504}, {3620, 11179}, {3763, 5054}, {3818, 11539}, {3830, 50976}, {5050, 15722}, {5055, 48884}, {5085, 15701}, {5476, 12100}, {5480, 14891}, {5846, 50825}, {6034, 15515}, {6036, 9877}, {7485, 13857}, {7775, 49112}, {8703, 38317}, {8724, 37479}, {9053, 50832}, {10124, 44882}, {10249, 46265}, {10304, 19130}, {11160, 33749}, {11645, 15694}, {12108, 34507}, {14269, 48891}, {14561, 15698}, {14810, 15700}, {14869, 20582}, {14890, 18358}, {15055, 25566}, {15360, 43650}, {15520, 21167}, {15686, 51026}, {15688, 47355}, {15689, 48895}, {15692, 19924}, {15699, 50960}, {15702, 24206}, {15703, 48889}, {15705, 31670}, {15709, 46264}, {15711, 29181}, {15715, 48873}, {15717, 25555}, {15719, 39561}, {15723, 36990}, {19708, 29317}, {19709, 29323}, {19711, 38110}, {21843, 42852}, {25563, 31166}, {34200, 48310}, {37517, 41983}, {38079, 44682}, {40107, 50961}, {42773, 44511}, {42774, 44512}, {42786, 47598}, {45759, 48880}, {48906, 50958}, {50974, 50990}
X(51137) = midpoint of X(i) and X(j) for these {i,j}: {3620, 11179}, {20423, 50966}, {43273, 50954}, {50956, 50975}, {50963, 50968}, {50980, 50987}
X(51137) = reflection of X(i) in X(j) for these {i,j}: {3618, 10168}, {11178, 3763}, {50977, 50980}, {50987, 50983}
X(51137) = complement of X(50956)
X(51137) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 50975, 50956}, {3, 50963, 50968}, {549, 50979, 50984}, {549, 50983, 50977}, {549, 50987, 50980}, {549, 50988, 50983}, {3524, 10168, 3098}, {3618, 50966, 20423}, {3763, 43273, 50954}, {5054, 5092, 11178}, {15700, 47352, 14810}, {34200, 48310, 48901}, {50977, 50983, 182}, {50979, 50981, 50982}, {50979, 50984, 50977}, {50981, 50982, 50977}, {50982, 50984, 50981}, {50983, 50984, 50979}
X(51138) lies on these lines: {2, 50958}, {3, 20583}, {4, 597}, {6, 10304}, {30, 6329}, {141, 15709}, {182, 524}, {381, 51025}, {511, 15759}, {518, 51085}, {542, 3628}, {548, 575}, {599, 10303}, {1503, 5066}, {1992, 10541}, {3524, 3629}, {3526, 8550}, {3534, 5050}, {3564, 11540}, {3589, 5055}, {3631, 5054}, {3856, 25555}, {3857, 38079}, {5012, 35266}, {5072, 50956}, {5085, 8584}, {5097, 34200}, {5102, 19708}, {5476, 33699}, {5480, 15684}, {5846, 50827}, {5965, 11812}, {6776, 48310}, {8703, 39561}, {9041, 13607}, {9053, 51087}, {9730, 44323}, {10168, 34573}, {11477, 50966}, {12017, 15706}, {13353, 20126}, {14848, 17800}, {14912, 22165}, {15534, 21167}, {15640, 25406}, {15683, 44882}, {15708, 40341}, {16226, 17710}, {18583, 48942}, {23046, 48906}, {25561, 44904}, {37517, 45759}, {46264, 50963}, {46333, 50975}, {47352, 51023}
X(51138) = midpoint of X(i) and X(j) for these {i,j}: {3, 20583}, {549, 12007}, {3589, 11179}, {5097, 34200}, {8550, 20582}, {9730, 44323}, {20423, 50971}, {43273, 50959}, {50979, 50983}
X(51138) = reflection of X(i) in X(j) for these {i,j}: {5476, 41153}, {34573, 10168}, {50984, 50983}
X(51138) = complement of X(50958)
X(51138) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {182, 50977, 50987}, {182, 50979, 50983}, {549, 50985, 50977}, {597, 43273, 50959}, {8550, 38064, 20582}, {10168, 43150, 47598}, {12007, 50983, 50982}, {50977, 50985, 50982}, {50977, 50987, 50983}, {50979, 50980, 1353}, {50979, 50987, 50977}, {50979, 50988, 50986}, {50982, 50983, 549}, {50986, 50987, 50988}, {50986, 50988, 50977}
X(51139) lies on these lines: {2, 50960}, {3, 50959}, {140, 25561}, {141, 15708}, {182, 524}, {376, 51026}, {511, 41153}, {518, 51086}, {542, 12108}, {597, 3523}, {631, 20582}, {1503, 11812}, {3524, 3589}, {3526, 50956}, {3530, 25555}, {3545, 50976}, {3576, 50951}, {3631, 50974}, {5054, 34573}, {5085, 50991}, {5102, 15719}, {5476, 19711}, {5480, 15700}, {5846, 50829}, {6329, 15707}, {9053, 50828}, {10164, 51006}, {10168, 41983}, {10299, 38072}, {10304, 51029}, {10519, 41149}, {11482, 38064}, {11539, 42786}, {11540, 29012}, {11737, 33751}, {12017, 50961}, {12100, 29181}, {14892, 48891}, {15688, 50964}, {15692, 48310}, {15693, 20423}, {15698, 50968}, {15701, 50958}, {15702, 44882}, {15705, 47355}, {15706, 48881}, {15709, 50975}, {15711, 38317}, {15713, 17508}, {15720, 50955}, {15721, 51023}, {25565, 33923}, {32455, 50973}, {34200, 48920}, {37455, 44401}, {41982, 48895}, {47599, 48892}
X(51139) = midpoint of X(i) and X(j) for these {i,j}: {11737, 33751}, {25565, 33923}, {50959, 50972}, {50960, 50971}, {50983, 50984}
X(51139) = complement of X(50960)
X(51139) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 50971, 50960}, {3, 50959, 50972}, {182, 50977, 50986}, {182, 50980, 50982}, {549, 50983, 50984}, {549, 50988, 50977}, {50977, 50986, 50982}, {50977, 50988, 50983}, {50980, 50986, 50977}, {50982, 50983, 182}
X(51140) lies on these lines: {2, 5965}, {3, 50973}, {4, 542}, {5, 20583}, {6, 5055}, {30, 3629}, {32, 8724}, {69, 10168}, {141, 47598}, {182, 524}, {184, 15360}, {193, 3098}, {194, 12117}, {195, 45622}, {381, 5097}, {511, 3534}, {518, 51087}, {548, 8550}, {575, 599}, {597, 3628}, {1147, 11694}, {1351, 11645}, {1352, 5032}, {1503, 33699}, {1993, 13857}, {3524, 11008}, {3564, 5066}, {3630, 14890}, {3631, 11539}, {3818, 23046}, {3830, 5102}, {3857, 50960}, {5050, 15533}, {5054, 40341}, {5072, 14848}, {5092, 6144}, {5093, 47353}, {5111, 11648}, {5642, 37644}, {5648, 44490}, {5846, 50830}, {5847, 50827}, {6036, 9770}, {6054, 7766}, {6055, 7774}, {6329, 15699}, {6776, 15683}, {7486, 25555}, {7775, 49102}, {7850, 39099}, {8703, 50970}, {9140, 11004}, {9143, 34417}, {9939, 32467}, {10303, 11160}, {11165, 47113}, {11180, 19130}, {11422, 44555}, {11477, 17800}, {11482, 18553}, {11485, 43275}, {11486, 43274}, {11540, 22165}, {11649, 15531}, {11898, 15516}, {12151, 39750}, {13352, 20126}, {14614, 35377}, {14853, 50964}, {14912, 15698}, {15022, 25565}, {15640, 29012}, {15687, 51025}, {15717, 33749}, {15759, 34380}, {21358, 46267}, {22491, 32907}, {22492, 32909}, {25406, 50966}, {33878, 50968}, {34379, 51085}, {34986, 37453}, {35266, 44077}, {35814, 44657}, {35815, 44656}, {37645, 45311}, {38071, 42785}, {38110, 50991}, {39899, 48884}, {44109, 47596}, {44456, 48879}, {46264, 46333}, {48901, 51022}, {48906, 50971}, {50693, 50975}
X(51140) = midpoint of X(i) and X(j) for these {i,j}: {193, 11179}, {20423, 50974}, {43273, 50962}, {50979, 50986}
X(51140) = reflection of X(i) in X(j) for these {i,j}: {5, 20583}, {69, 10168}, {381, 5097}, {549, 12007}, {576, 1992}, {599, 575}, {3098, 11179}, {5476, 8584}, {11160, 40107}, {11178, 6}, {11180, 19130}, {15069, 25561}, {17508, 14912}, {25561, 22330}, {34507, 597}, {50977, 50979}, {50978, 50983}, {50985, 50982}
X(51140) = complement of X(50961)
X(51140) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {549, 50982, 50977}, {549, 50985, 50982}, {1353, 50986, 50979}, {1992, 50974, 20423}, {5055, 43150, 11178}, {5476, 8584, 15520}, {11160, 38064, 40107}, {14848, 15069, 25561}, {15534, 43273, 50962}, {22330, 25561, 14848}, {48876, 50979, 50987}, {48876, 50984, 50977}, {48876, 50987, 50984}, {50977, 50979, 182}, {50978, 50979, 50983}, {50978, 50983, 50977}, {50979, 50985, 549}
X(51141) lies on these lines: {2, 29317}, {3, 25561}, {5, 51026}, {30, 42786}, {140, 50965}, {141, 41983}, {182, 524}, {381, 48920}, {511, 15701}, {518, 51088}, {542, 3523}, {547, 48904}, {550, 50960}, {575, 50973}, {576, 15720}, {597, 12108}, {631, 20423}, {1503, 19711}, {3098, 5054}, {3524, 3619}, {3525, 25565}, {3545, 48879}, {3763, 15706}, {3818, 17504}, {3845, 50972}, {5055, 50968}, {5071, 48885}, {5085, 15722}, {5092, 15707}, {5476, 11812}, {5846, 50833}, {9053, 50826}, {10124, 48901}, {10168, 15708}, {10304, 48884}, {10516, 15716}, {11539, 50959}, {11645, 15700}, {12100, 47354}, {14093, 48889}, {14561, 50966}, {14810, 15694}, {14891, 48898}, {15692, 24206}, {15693, 17508}, {15698, 29012}, {15699, 48880}, {15702, 19924}, {15705, 48892}, {15709, 19130}, {15712, 20582}, {15713, 38317}, {15715, 33751}, {15717, 50975}, {15718, 21358}, {15719, 50994}, {22234, 38064}, {31884, 50963}, {34200, 48896}, {34573, 45759}, {39561, 50962}, {40107, 50974}, {47598, 48881}
X(51141) = midpoint of X(i) and X(j) for these {i,j}: {50957, 50976}, {50964, 50969}, {50981, 50988}
X(51141) = reflection of X(i) in X(j) for these {i,j}: {11178, 3619}, {50977, 50981}
X(51141) = complement of X(50964)
X(51141) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 50969, 50964}, {3, 50957, 50976}, {549, 50980, 50983}, {549, 50981, 50988}, {549, 50984, 50977}, {11812, 21167, 5476}, {50980, 50983, 50977}, {50983, 50984, 50980}
X(51142) lies on these lines: {2, 6}, {518, 51067}, {542, 15711}, {1352, 15685}, {1503, 15695}, {3860, 11178}, {5846, 50784}, {7854, 27088}, {8550, 11812}, {8703, 40107}, {9053, 50791}, {10519, 50958}, {12100, 34507}, {12101, 47354}, {15069, 15698}, {15690, 48898}, {15716, 21167}, {15759, 50977}, {19662, 41154}, {19710, 29012}, {19711, 50980}, {28313, 50081}, {28322, 50097}, {28538, 51104}, {33699, 48876}, {47353, 50966}, {50781, 50998}, {50787, 50949}, {50788, 51003}, {50954, 51022}, {50956, 50982}
X(51142) = midpoint of X(i) and X(j) for these {i,j}: {2, 50989}, {599, 3620}, {47353, 50966}, {50990, 50993}
X(51142) = reflection of X(i) in X(j) for these {i,j}: {597, 3763}, {3618, 20582}, {22165, 50990}, {50993, 50991}
X(51142) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 599, 41152}, {2, 15533, 41149}, {2, 15534, 41153}, {2, 41149, 597}, {2, 41152, 22165}, {2, 50990, 50989}, {141, 22165, 8584}, {597, 21356, 141}, {597, 22165, 15533}, {599, 21356, 3631}, {599, 50991, 22165}, {599, 50993, 50990}, {599, 50994, 50991}, {3620, 50990, 50993}, {3620, 50993, 50991}, {3631, 15533, 22165}, {3631, 21356, 597}, {15533, 50993, 3763}, {20582, 41153, 2}, {22165, 50991, 141}, {41152, 50991, 2}, {50989, 50993, 2}, {50990, 50994, 3620}
X(51143) lies on these lines: {2, 6}, {511, 10109}, {518, 51069}, {542, 11812}, {547, 40107}, {575, 47598}, {1350, 41099}, {1352, 15693}, {1503, 10193}, {3098, 33699}, {3242, 51072}, {3416, 51105}, {3534, 47354}, {3564, 11540}, {3818, 19710}, {3819, 8705}, {3830, 48873}, {3844, 4745}, {3845, 29181}, {3860, 19924}, {3934, 8355}, {4395, 29615}, {4399, 48634}, {4478, 17291}, {4669, 9053}, {5066, 24206}, {5476, 50982}, {5846, 50786}, {6292, 39785}, {6488, 11292}, {6489, 11291}, {7228, 48633}, {7238, 17292}, {7849, 8367}, {7863, 8359}, {7911, 8352}, {7928, 40246}, {8358, 19662}, {8546, 16419}, {8550, 15694}, {8598, 31168}, {8703, 11178}, {8787, 31274}, {9306, 37283}, {9855, 46226}, {10302, 47286}, {10516, 15682}, {10519, 41106}, {11001, 40330}, {11539, 34507}, {11645, 15759}, {12101, 25561}, {15069, 15702}, {15520, 50985}, {15690, 18358}, {15697, 36990}, {15698, 44882}, {15701, 50958}, {15713, 50983}, {15716, 46264}, {15719, 43273}, {15810, 32459}, {16239, 46267}, {16475, 50784}, {17227, 49727}, {17228, 50098}, {17237, 49737}, {18553, 34200}, {18840, 34505}, {19708, 21167}, {19709, 50959}, {21849, 40670}, {28297, 50092}, {28309, 29594}, {28538, 51108}, {29617, 48639}, {31884, 51022}, {32218, 47313}, {35954, 47005}, {37756, 48635}, {38317, 50978}, {47311, 47556}, {47358, 50951}, {48638, 50128}, {49543, 50081}, {50781, 51006}, {50785, 51001}, {50789, 50949}, {50792, 50952}
X(51143) = midpoint of X(i) and X(j) for these {i,j}: {2, 50991}, {69, 20583}, {141, 20582}, {547, 40107}, {597, 3631}, {599, 3589}, {5476, 50982}, {15533, 41149}, {18553, 34200}, {47353, 50971}, {47358, 50951}, {50781, 51006}
X(51143) = reflection of X(i) in X(j) for these {i,j}: {8584, 41153}, {34573, 20582}, {41152, 50991}, {46267, 16239}
X(51143) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 141, 50991}, {2, 599, 8584}, {2, 8584, 3589}, {2, 15533, 597}, {2, 21356, 15533}, {2, 50990, 6}, {2, 50993, 22165}, {2, 50994, 15534}, {69, 48310, 20583}, {141, 597, 21356}, {141, 3619, 3589}, {141, 3763, 3631}, {141, 21358, 20582}, {141, 22165, 50993}, {193, 3619, 3763}, {193, 8584, 41149}, {193, 21356, 599}, {597, 15533, 41149}, {597, 21356, 3631}, {599, 21358, 3619}, {599, 50992, 22165}, {3589, 3631, 193}, {3589, 8584, 41153}, {3631, 41149, 15533}, {3763, 15533, 2}, {3763, 21356, 597}, {8584, 22165, 50992}, {15534, 50993, 50994}, {15534, 50994, 22165}, {20582, 50991, 2}, {21167, 47353, 50971}, {22165, 50993, 50991}, {39022, 39023, 41136}, {41149, 50991, 3631}
X(51144) lies on these lines: {6, 144}, {7, 3589}, {9, 141}, {182, 5843}, {390, 9053}, {516, 17351}, {518, 3244}, {524, 6172}, {527, 597}, {673, 7263}, {910, 25355}, {971, 44882}, {1350, 21168}, {1386, 5850}, {1503, 5779}, {2550, 7227}, {3618, 20059}, {4312, 38047}, {4361, 5838}, {4363, 5819}, {4437, 17336}, {4718, 50026}, {5085, 36996}, {5223, 5846}, {5480, 5762}, {5728, 9021}, {5735, 38145}, {5759, 29181}, {6068, 9024}, {6173, 48310}, {9041, 50836}, {9055, 51052}, {15492, 50011}, {17225, 51053}, {17340, 20533}, {17345, 49775}, {18230, 34573}, {21167, 31658}, {25555, 38164}, {27481, 49496}, {28538, 50834}, {30424, 38194}, {47357, 50998}
X(51144) = midpoint of X(i) and X(j) for these {i,j}: {6, 144}, {6172, 50997}
X(51144) = reflection of X(i) in X(j) for these {i,j}: {7, 3589}, {141, 9}, {50998, 47357}
X(51145) lies on these lines: {1, 20582}, {145, 597}, {515, 51026}, {517, 50971}, {518, 41149}, {519, 3589}, {524, 3241}, {599, 3623}, {952, 50959}, {3244, 4432}, {3631, 49681}, {3633, 38023}, {3635, 28538}, {5476, 50831}, {5480, 34748}, {5603, 50960}, {5731, 50972}, {5844, 50983}, {5846, 50781}, {5847, 51095}, {7967, 50965}, {8584, 50790}, {8705, 47493}, {9053, 16475}, {9055, 50778}, {10246, 50984}, {10247, 47354}, {12630, 38086}, {16200, 51025}, {17225, 49478}, {20049, 47352}, {20050, 38087}, {28309, 50130}, {31145, 48310}, {32218, 47472}, {32455, 47356}, {34573, 38314}, {34631, 44882}, {34747, 49524}, {47358, 51097}, {49465, 51004}, {50789, 51105}
X(51145) = midpoint of X(i) and X(j) for these {i,j}: {145, 597}, {5476, 50831}, {5480, 34748}, {8584, 50790}, {34631, 44882}, {34747, 49524}, {50998, 51000}
X(51145) = reflection of X(i) in X(j) for these {i,j}: {20582, 1}, {32218, 47472}, {32455, 47356}, {50951, 51006}
X(51145) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3241, 51000, 50998}, {3242, 51000, 51001}, {50951, 51006, 3589}
X(51146) lies on these lines: {2, 50789}, {8, 51006}, {145, 47359}, {515, 51029}, {517, 50975}, {518, 50840}, {519, 3618}, {524, 3241}, {597, 20050}, {599, 20057}, {952, 50963}, {1386, 20049}, {1992, 3244}, {3620, 49681}, {3621, 38023}, {3623, 28538}, {3635, 51004}, {3763, 38314}, {5603, 50956}, {5731, 50968}, {5844, 50987}, {5846, 50782}, {5847, 51097}, {7967, 50966}, {10246, 50980}, {10247, 50954}, {16200, 51023}, {16475, 51096}, {20053, 38087}, {38315, 50951}, {49684, 50952}, {50787, 50950}, {50992, 51095}, {51005, 51093}, {51089, 51094}
X(51146) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3241, 51000, 50999}, {3241, 51001, 50998}, {50998, 51000, 51001}, {50998, 51001, 50999}
X(51147) lies on these lines: {1, 141}, {6, 145}, {8, 3589}, {31, 4884}, {44, 49527}, {69, 3623}, {182, 5844}, {390, 17318}, {511, 1483}, {516, 49463}, {517, 44882}, {518, 3244}, {519, 597}, {524, 3241}, {528, 32921}, {545, 49446}, {551, 3844}, {698, 7976}, {742, 49478}, {752, 49464}, {940, 19993}, {944, 29181}, {952, 5480}, {1086, 50289}, {1100, 49466}, {1211, 29815}, {1279, 17243}, {1317, 1469}, {1350, 7967}, {1352, 10247}, {1385, 21167}, {1482, 1503}, {1616, 20009}, {1992, 50790}, {2550, 4395}, {3056, 37734}, {3058, 32928}, {3243, 5845}, {3246, 4078}, {3555, 9021}, {3616, 34573}, {3617, 47355}, {3618, 3621}, {3622, 3763}, {3625, 38049}, {3630, 3635}, {3631, 20057}, {3632, 16491}, {3633, 16475}, {3655, 50965}, {3663, 28566}, {3679, 48310}, {3696, 4405}, {3703, 17469}, {3751, 8584}, {3755, 50112}, {3826, 50023}, {3827, 34791}, {3867, 12135}, {3871, 5096}, {3879, 4864}, {3883, 4364}, {3886, 4971}, {3920, 5743}, {3923, 28503}, {4030, 17017}, {4307, 7228}, {4310, 7238}, {4344, 4363}, {4353, 49741}, {4360, 49704}, {4383, 20020}, {4422, 7290}, {4437, 17389}, {4645, 48631}, {4648, 39567}, {4665, 5263}, {4677, 38023}, {4852, 5853}, {4865, 17061}, {4899, 16669}, {4929, 16670}, {4969, 49450}, {5085, 12245}, {5227, 37556}, {5266, 50589}, {5695, 28472}, {5718, 20045}, {5855, 47373}, {5881, 38035}, {6329, 20050}, {6707, 39581}, {7174, 17332}, {7231, 49483}, {7263, 32922}, {7277, 49499}, {7984, 32298}, {8148, 46264}, {8236, 50995}, {9055, 49470}, {10168, 50823}, {10283, 24206}, {10516, 10595}, {10800, 42421}, {11179, 50805}, {12583, 16211}, {12645, 14561}, {13910, 49232}, {13972, 49233}, {14839, 32449}, {15534, 51092}, {15826, 47489}, {16468, 49534}, {16972, 49451}, {17121, 49698}, {17225, 51055}, {17259, 39587}, {17366, 32850}, {17599, 44419}, {17602, 32844}, {17724, 33070}, {17726, 26227}, {17765, 49477}, {17766, 49472}, {17768, 49455}, {17769, 49482}, {17777, 32926}, {18526, 31670}, {19130, 37705}, {19875, 50789}, {20041, 28369}, {20423, 34748}, {20582, 38314}, {22165, 28538}, {24280, 28297}, {25555, 38165}, {28212, 48898}, {28216, 48896}, {28224, 48901}, {28530, 49453}, {28581, 49481}, {29832, 35466}, {29840, 37646}, {31145, 47352}, {31162, 51022}, {32924, 34612}, {34319, 50923}, {34627, 50959}, {34631, 43273}, {34632, 50971}, {34718, 50983}, {34747, 47359}, {34773, 48881}, {36404, 50131}, {42871, 50284}, {48856, 49731}, {49531, 49678}, {49536, 51005}, {49726, 50294}, {50011, 50125}
X(51147) = midpoint of X(i) and X(j) for these {i,j}: {1, 49681}, {6, 145}, {8, 49679}, {1992, 50790}, {3241, 51000}, {3244, 49684}, {3633, 49688}, {7984, 32298}, {8148, 46264}, {11179, 50805}, {18526, 31670}, {20050, 49690}, {20423, 34748}, {34319, 50923}, {34631, 43273}, {34747, 47359}, {47356, 51093}, {49531, 49678}
X(51147) = reflection of X(i) in X(j) for these {i,j}: {8, 3589}, {141, 1}, {3679, 51006}, {8584, 47356}, {31145, 50951}, {34627, 50959}, {34632, 50971}, {34718, 50983}, {37705, 19130}, {48881, 34773}, {49465, 3635}, {49524, 1386}, {49726, 50294}, {50783, 20582}, {50823, 10168}, {50949, 551}, {50965, 3655}, {50998, 3241}, {51022, 31162}
X(51147) = crossdifference of every pair of points on line {2483, 6363}
X(51147) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 49506, 4026}, {8, 38315, 3589}, {1279, 49476, 17243}, {1386, 49524, 597}, {3244, 49696, 49471}, {3632, 16491, 38047}, {3633, 16475, 49688}, {3679, 51006, 48310}, {31145, 47352, 50951}, {38314, 50783, 20582}, {38315, 49679, 8}, {50023, 50288, 3826}
X(51148) lies on these lines: {2, 50782}, {6, 50951}, {8, 20583}, {10, 597}, {141, 16491}, {518, 51059}, {519, 3629}, {524, 3241}, {599, 3622}, {1992, 3621}, {3416, 19876}, {3630, 49684}, {3631, 38314}, {3633, 9041}, {4677, 5846}, {5550, 20582}, {5603, 50958}, {5731, 50970}, {5847, 22165}, {7967, 50973}, {9053, 15534}, {9812, 51025}, {10246, 50982}, {10247, 50961}, {12007, 34718}, {28566, 49543}, {34595, 38023}, {38034, 47354}, {38315, 50991}, {49630, 50112}, {50783, 51068}, {50784, 51110}
X(51148) = midpoint of X(51000) and X(51001)
X(51148) = reflection of X(i) in X(j) for these {i,j}: {8, 20583}, {141, 47356}, {34718, 12007}, {50949, 51005}, {50950, 51006}, {50998, 51000}
X(51148) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {47356, 50950, 51006}, {50949, 51005, 597}, {50950, 51006, 141}
X(51149) lies on these lines: {1, 38087}, {6, 36911}, {145, 50949}, {517, 50968}, {518, 51097}, {519, 3763}, {524, 3241}, {597, 20057}, {599, 3244}, {952, 50956}, {3618, 51006}, {3620, 49679}, {3623, 4473}, {3635, 51005}, {5844, 50980}, {5846, 50791}, {7967, 50975}, {10247, 50963}, {15533, 51094}, {15534, 51089}, {15570, 38086}, {16200, 51024}, {20050, 20582}, {21358, 34747}, {28301, 50130}, {33179, 38072}, {38047, 51107}, {38314, 49690}, {38315, 47359}, {47353, 51087}, {47358, 50989}, {49465, 50950}, {49681, 51004}, {50783, 50993}
X(51149) = reflection of X(i) in X(j) for these {i,j}: {50783, 50993}, {50989, 47358}
X(51149) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3241, 50998, 51000}, {50790, 51071, 38315}, {50998, 51000, 3242}
X(51150) lies on these lines: {1, 38046}, {2, 38086}, {3, 38115}, {4, 38143}, {5, 38164}, {6, 7}, {8, 38185}, {9, 3589}, {10, 141}, {11, 38188}, {12, 38189}, {41, 7198}, {144, 3618}, {182, 5762}, {390, 38315}, {496, 40690}, {511, 31657}, {516, 1386}, {524, 6173}, {527, 597}, {528, 50112}, {529, 24249}, {674, 8255}, {742, 7263}, {954, 36741}, {971, 5480}, {999, 17044}, {1001, 17045}, {1268, 3619}, {1329, 17048}, {1350, 21151}, {1352, 38107}, {1475, 3665}, {1503, 5805}, {2140, 6147}, {2160, 39273}, {2486, 42356}, {2550, 4361}, {3242, 4648}, {3243, 4851}, {3338, 20269}, {3416, 38052}, {3629, 50013}, {3672, 41325}, {3674, 40133}, {3751, 4859}, {3943, 49533}, {4312, 16475}, {4360, 20533}, {4395, 5880}, {4437, 17234}, {4663, 17067}, {4675, 16973}, {4852, 5853}, {4904, 5902}, {4966, 49531}, {5045, 34847}, {5085, 5759}, {5223, 17306}, {5224, 27484}, {5434, 9317}, {5572, 18589}, {5698, 38048}, {5732, 29181}, {5779, 14561}, {5843, 18583}, {6172, 47352}, {6666, 25498}, {9000, 21195}, {9024, 10427}, {9041, 17313}, {9055, 16593}, {10520, 40869}, {11372, 38035}, {13407, 24774}, {14377, 24470}, {14853, 36996}, {15299, 20270}, {15668, 19288}, {16972, 17301}, {17244, 49502}, {17245, 27475}, {17246, 51052}, {17276, 36404}, {17296, 49688}, {17300, 32029}, {17327, 38057}, {17351, 49775}, {17390, 42871}, {17728, 30742}, {17754, 25355}, {17761, 39542}, {18230, 47355}, {20195, 34573}, {20247, 40997}, {20330, 24220}, {20582, 38093}, {21239, 40646}, {21358, 50996}, {21746, 38989}, {24206, 38171}, {25555, 38166}, {28538, 51100}, {28634, 38200}, {31671, 46264}, {37676, 40688}, {38023, 50836}, {38024, 47358}, {38049, 51090}, {38073, 47353}, {38087, 50835}, {38089, 50834}, {38092, 50783}, {38094, 50781}, {38111, 48876}, {38137, 39884}, {38454, 47373}, {47357, 51006}, {48627, 49496}, {48854, 49738}
X(51150) = midpoint of X(i) and X(j) for these {i,j}: {6, 7}, {6173, 51002}, {31671, 46264}
X(51150) = reflection of X(i) in X(j) for these {i,j}: {9, 3589}, {141, 142}, {47357, 51006}
X(51150) = complement of X(50995)
X(51150) = crossdifference of every pair of points on line {926, 21007}
X(51150) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 5222, 5819}, {9, 38186, 3589}, {141, 49481, 49524}, {5222, 5244, 5834}, {16593, 51058, 17243}
X(51151) lies on these lines: {2, 5845}, {7, 594}, {9, 20582}, {141, 527}, {142, 597}, {516, 50965}, {518, 3919}, {524, 6173}, {528, 49741}, {542, 31657}, {742, 51057}, {971, 47354}, {1992, 38086}, {2550, 9041}, {3589, 38093}, {4437, 49722}, {5542, 28538}, {5762, 50977}, {5846, 51099}, {5847, 51098}, {5853, 50998}, {5880, 7238}, {6172, 21358}, {9053, 51102}, {11038, 51000}, {11179, 38065}, {17225, 51058}, {20195, 38088}, {20423, 38107}, {21151, 43273}, {21153, 50984}, {21356, 50995}, {25557, 50023}, {38024, 47356}, {38052, 47359}, {38053, 51006}, {38054, 51005}, {38087, 40333}, {38111, 50979}, {38122, 50983}, {38150, 50959}, {38200, 50951}, {49524, 49733}
X(51151) = midpoint of X(i) and X(j) for these {i,j}: {7, 599}, {6173, 47595}
X(51151) = reflection of X(i) in X(j) for these {i,j}: {9, 20582}, {597, 142}
X(51151) = complement of X(50997)
X(51152) lies on these lines: {6, 38093}, {7, 11160}, {9, 599}, {69, 527}, {142, 1992}, {516, 50967}, {518, 4677}, {524, 6173}, {542, 5732}, {597, 20195}, {971, 50955}, {3243, 28538}, {5762, 50978}, {5845, 22165}, {5847, 51099}, {5853, 50999}, {6172, 29577}, {8584, 38186}, {11038, 51001}, {11178, 38075}, {16496, 49747}, {20423, 38150}, {20582, 38088}, {21151, 50974}, {21153, 50977}, {34379, 51100}, {38052, 50952}, {38053, 51005}, {38107, 50962}, {38111, 50986}, {38122, 50979}, {38200, 47359}, {38316, 51003}, {47357, 49511}
X(51152) = midpoint of X(7) and X(11160)
X(51152) = reflection of X(i) in X(j) for these {i,j}: {9, 599}, {1992, 142}, {6173, 47595}, {47357, 49511}
X(51153) lies on these lines: {2, 50786}, {10, 38023}, {515, 50963}, {516, 50975}, {517, 50987}, {518, 51104}, {519, 3618}, {524, 551}, {597, 3244}, {599, 15808}, {1125, 50950}, {1992, 3636}, {3576, 50966}, {3589, 38098}, {3620, 25055}, {3625, 38089}, {3763, 19883}, {3817, 50956}, {4669, 38049}, {5476, 51082}, {5847, 50784}, {5886, 50954}, {10165, 50980}, {13607, 14848}, {16475, 50999}, {19862, 28538}, {28164, 51029}, {28301, 50300}, {30392, 51028}, {34379, 51105}, {34641, 47352}, {38029, 50808}, {38035, 50862}, {38040, 50796}, {38048, 50834}, {38050, 50889}, {38079, 47745}, {38314, 49505}, {38315, 47359}, {47358, 51106}, {49684, 50949}, {50787, 51110}, {50990, 51108}
X(51153) = midpoint of X(3763) and X(47356)
X(51153) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {551, 51005, 51004}, {1386, 51006, 51005}, {51005, 51006, 551}
X(51154) lies on these lines: {1, 20582}, {2, 9053}, {141, 38314}, {515, 50960}, {516, 50972}, {517, 50984}, {518, 51108}, {519, 34573}, {524, 551}, {597, 3616}, {599, 3622}, {1125, 9041}, {1699, 51026}, {3242, 48310}, {3576, 50971}, {3589, 16496}, {3624, 50953}, {3631, 47356}, {3636, 28538}, {5550, 38087}, {5603, 50965}, {5731, 51022}, {5846, 50786}, {5847, 41150}, {5886, 50959}, {9055, 51061}, {10246, 47354}, {10283, 50977}, {15569, 17225}, {16475, 41149}, {19883, 49465}, {20583, 38023}, {22165, 38315}, {28297, 48810}, {30392, 51025}, {38028, 50983}, {38049, 41153}, {47358, 51110}, {50781, 51106}, {50784, 50950}
X(51154) = midpoint of X(i) and X(j) for these {i,j}: {1, 20582}, {3631, 47356}, {50951, 50998}, {51003, 51006}
X(51154) = complement of X(50951)
X(51154) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 50998, 50951}, {551, 51003, 51006}, {1386, 51003, 51004}
X(51155) lies on these lines: {2, 50784}, {6, 19875}, {8, 1992}, {10, 20583}, {193, 17488}, {518, 3899}, {519, 3629}, {524, 551}, {542, 22793}, {597, 3634}, {599, 3624}, {1699, 51027}, {2836, 41720}, {3416, 5032}, {3576, 50973}, {3631, 19883}, {3635, 50998}, {3817, 50958}, {4141, 4641}, {4672, 50084}, {4745, 5847}, {4852, 28558}, {4906, 20086}, {5846, 41149}, {5886, 50961}, {10165, 50982}, {11008, 38314}, {11160, 38023}, {15254, 50125}, {15533, 16475}, {17768, 49543}, {25055, 40341}, {28208, 37517}, {28534, 50131}, {32455, 50951}, {34379, 51107}, {38028, 50985}, {38049, 50991}, {50783, 50953}, {50791, 51110}
X(51155) = midpoint of X(i) and X(j) for these {i,j}: {193, 47356}, {47359, 51001}, {50952, 51000}
X(51155) = reflection of X(i) in X(j) for these {i,j}: {10, 20583}, {4663, 1992}, {49465, 47356}, {50084, 4672}, {51003, 51005}, {51004, 51006}
X(51155) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1992, 51001, 47359}, {15534, 51000, 50952}, {51003, 51005, 1386}, {51004, 51005, 51006}, {51004, 51006, 51003}
X(51156) lies on these lines: {2, 38191}, {10, 50998}, {515, 50956}, {516, 50968}, {517, 50980}, {518, 51109}, {519, 3763}, {524, 551}, {597, 15808}, {599, 3636}, {1125, 38089}, {1699, 51029}, {3244, 20582}, {3576, 50975}, {3618, 25055}, {3620, 38314}, {3622, 51001}, {4141, 29686}, {5603, 50966}, {5846, 51104}, {5847, 50990}, {5886, 50963}, {9041, 19862}, {10246, 50954}, {19878, 38087}, {19883, 49529}, {28322, 48810}, {30392, 51023}, {34573, 38098}, {38028, 50987}, {38049, 47358}, {38315, 41150}, {47353, 51085}, {48310, 49536}, {49465, 50951}, {50781, 50993}, {50783, 51107}, {50789, 51095}, {50790, 51069}, {50949, 51071}, {50952, 51110}
X(51156) = reflection of X(i) in X(j) for these {i,j}: {50781, 50993}, {50989, 50787}
X(51156) = complement of X(50953)
X(51156) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 51089, 38191}, {551, 51003, 51005}, {551, 51004, 51006}, {41150, 50787, 38315}, {47358, 51108, 38049}, {51003, 51005, 49511}, {51003, 51006, 51004}, {51004, 51006, 51005}
X(51157) lies on these lines: {6, 100}, {11, 2330}, {80, 38047}, {104, 5085}, {119, 1503}, {141, 3035}, {149, 3618}, {153, 25406}, {182, 952}, {214, 518}, {511, 33814}, {524, 6174}, {528, 597}, {545, 5091}, {611, 10090}, {613, 10087}, {692, 1083}, {765, 27950}, {1026, 17455}, {1086, 4579}, {1145, 5846}, {1317, 1428}, {1320, 38315}, {1350, 10759}, {1352, 38752}, {1386, 2802}, {1484, 38110}, {1492, 17369}, {1691, 13194}, {1862, 1974}, {2163, 3751}, {2787, 5026}, {2805, 28662}, {2806, 28343}, {2829, 44882}, {2830, 14688}, {2932, 36740}, {3254, 38186}, {3573, 4370}, {3629, 35023}, {4265, 17100}, {4553, 20958}, {4585, 31073}, {4996, 5096}, {5050, 12331}, {5092, 38602}, {5135, 10609}, {5138, 9945}, {5480, 5840}, {5541, 16475}, {5845, 10427}, {6034, 10769}, {6154, 6329}, {6593, 8674}, {7972, 49688}, {8299, 23344}, {9021, 11570}, {9041, 50843}, {9055, 51062}, {10265, 38118}, {10541, 38669}, {10707, 47352}, {10711, 43273}, {10728, 48905}, {10738, 14561}, {10742, 46264}, {11698, 48906}, {12017, 12773}, {12138, 19124}, {12653, 16491}, {12737, 38029}, {13199, 14853}, {13331, 32454}, {14217, 38035}, {16799, 41701}, {19130, 22938}, {19914, 38116}, {20119, 38185}, {21630, 38049}, {22799, 29012}, {24264, 49726}, {24466, 29181}, {25555, 38168}, {26890, 44419}, {28538, 50841}, {31235, 34573}, {31272, 47355}, {33337, 49529}, {35423, 38657}, {37222, 38310}, {37726, 38119}, {38023, 50891}, {38087, 50890}, {38089, 50889}, {38521, 39560}, {38655, 50659}, {45310, 48310}
X(51157) = midpoint of X(i) and X(j) for these {i,j}: {6, 100}, {1350, 10759}, {6174, 51008}, {7972, 49688}, {10711, 43273}, {10728, 48905}, {10742, 46264}, {11698, 48906}, {16799, 41701}, {33337, 49529}
X(51157) = reflection of X(i) in X(j) for these {i,j}: {11, 3589}, {141, 3035}, {22938, 19130}, {38602, 5092}
X(51157) = crosssum of X(2) and X(31118)
X(51157) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 19112, 48703}, {100, 19113, 48704}, {10759, 34474, 1350}
X(51158) lies on these lines: {2, 9024}, {11, 20582}, {69, 27756}, {100, 599}, {141, 528}, {214, 28538}, {518, 50841}, {524, 6174}, {542, 33814}, {597, 3035}, {952, 50949}, {1145, 9041}, {1350, 10711}, {2802, 51003}, {2829, 50965}, {5840, 47354}, {5846, 50843}, {5847, 50844}, {5848, 22165}, {5854, 50998}, {9053, 50842}, {10031, 50783}, {10707, 21358}, {10755, 47352}, {15015, 50950}, {17225, 51062}, {20423, 38752}, {21154, 50984}, {22938, 25561}, {31235, 38090}, {34123, 51006}, {34379, 50845}, {34474, 43273}, {38064, 38762}, {38760, 50983}
X(51158) = midpoint of X(i) and X(j) for these {i,j}: {100, 599}, {1350, 10711}, {6174, 51007}, {10031, 50783}
X(51158) = reflection of X(i) in X(j) for these {i,j}: {11, 20582}, {597, 3035}, {22938, 25561}
X(51159) lies on these lines: {6, 616}, {13, 3589}, {14, 23019}, {15, 524}, {30, 22687}, {39, 9115}, {69, 30471}, {99, 42942}, {141, 542}, {182, 3643}, {298, 12215}, {395, 5980}, {396, 1691}, {518, 51114}, {530, 597}, {623, 11645}, {624, 10168}, {629, 18553}, {636, 20190}, {1503, 5617}, {3867, 12142}, {5085, 6770}, {5182, 14904}, {5459, 48310}, {5473, 29181}, {5846, 12781}, {6114, 9830}, {6582, 42913}, {6782, 33459}, {7975, 9053}, {8356, 42943}, {8584, 36769}, {9041, 50849}, {9116, 22579}, {9901, 38047}, {10645, 51013}, {11646, 23303}, {13103, 14561}, {13910, 49208}, {13972, 49209}, {16241, 51018}, {20252, 38317}, {22165, 36768}, {22580, 35751}, {28538, 50847}, {34573, 36770}, {35696, 36772}, {36767, 50991}, {41022, 44882}, {44382, 50983}, {46264, 48655}
X(51159) = midpoint of X(i) and X(j) for these {i,j}: {6, 616}, {5463, 51012}, {9116, 22579}, {22580, 35751}, {46264, 48655}
X(51159) = reflection of X(i) in X(j) for these {i,j}: {13, 3589}, {141, 618}, {47610, 5092}
X(51160) lies on these lines: {6, 617}, {13, 23025}, {14, 3589}, {16, 524}, {30, 22689}, {39, 9117}, {69, 30472}, {99, 42943}, {141, 542}, {182, 3642}, {299, 12215}, {395, 1691}, {396, 5981}, {518, 51115}, {531, 597}, {623, 10168}, {624, 11645}, {630, 18553}, {635, 20190}, {1503, 5613}, {3867, 12141}, {5085, 6773}, {5182, 14905}, {5460, 48310}, {5474, 29181}, {5846, 12780}, {6115, 9830}, {6295, 42912}, {6783, 33458}, {7974, 9053}, {8356, 42942}, {8584, 47867}, {9041, 50852}, {9114, 22580}, {9900, 38047}, {10646, 51010}, {11646, 23302}, {13102, 14561}, {13910, 49210}, {13972, 49211}, {16242, 51016}, {20253, 38317}, {22579, 36329}, {28538, 50850}, {41023, 44882}, {44383, 50983}, {46264, 48656}
X(51160) = midpoint of X(i) and X(j) for these {i,j}: {6, 617}, {5464, 51015}, {9114, 22580}, {22579, 36329}, {46264, 48656}
X(51160) = reflection of X(i) in X(j) for these {i,j}: {14, 3589}, {141, 619}, {47611, 5092}
X(51161) lies on these lines: {5, 141}, {6, 621}, {13, 524}, {15, 3589}, {30, 22687}, {69, 42142}, {83, 398}, {316, 5318}, {396, 5978}, {397, 7762}, {531, 597}, {618, 19924}, {732, 31713}, {1350, 37463}, {1503, 20428}, {2076, 10617}, {3564, 44488}, {3629, 44498}, {3642, 5476}, {5085, 36993}, {5104, 23303}, {5321, 8370}, {5611, 14561}, {5617, 44385}, {5846, 50853}, {5969, 6115}, {6329, 36757}, {9041, 50854}, {11308, 42490}, {14538, 29181}, {16808, 51018}, {18583, 22683}, {21359, 51010}, {22797, 47354}, {23025, 25200}, {31670, 37333}, {34573, 40334}, {35943, 42942}, {36755, 48881}, {37832, 51013}, {40706, 43104}, {44659, 49524}, {44666, 44882}, {45879, 48310}
X(51161) = midpoint of X(i) and X(j) for these {i,j}: {6, 621}, {22493, 22580}, {23025, 25200}, {50855, 51017}
X(51161) = reflection of X(i) in X(j) for these {i,j}: {15, 3589}, {141, 623}, {3629, 44498}, {48881, 36755}
X(51161) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {623, 7684, 625}, {623, 19130, 5103}
X(51162) lies on these lines: {5, 141}, {6, 622}, {14, 524}, {16, 3589}, {30, 22689}, {69, 42139}, {83, 397}, {316, 5321}, {395, 5979}, {398, 7762}, {530, 597}, {619, 19924}, {732, 31714}, {1350, 37464}, {1503, 20429}, {2076, 10616}, {3564, 44487}, {3629, 44497}, {3643, 5476}, {5085, 36995}, {5104, 23302}, {5318, 8370}, {5613, 44384}, {5615, 14561}, {5846, 50856}, {5969, 6114}, {6329, 36758}, {9041, 50857}, {11307, 42491}, {14539, 29181}, {16809, 51016}, {18583, 22685}, {21360, 51013}, {22796, 47354}, {23019, 25204}, {31670, 37332}, {34573, 40335}, {35942, 42943}, {36756, 48881}, {37835, 51010}, {40707, 43101}, {44219, 44382}, {44660, 49524}, {44667, 44882}, {45880, 48310}
X(51162) = midpoint of X(i) and X(j) for these {i,j}: {6, 622}, {22494, 22579}, {23019, 25204}, {50858, 51019}
X(51162) = reflection of X(i) in X(j) for these {i,j}: {16, 3589}, {141, 624}, {3629, 44497}, {48881, 36756}
X(51162) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {624, 7685, 625}, {624, 19130, 5103}
X(51163) lies on these lines: {2, 48872}, {3, 43621}, {4, 141}, {5, 14810}, {6, 3146}, {20, 3589}, {30, 182}, {69, 17578}, {110, 34603}, {140, 48880}, {159, 5893}, {193, 50690}, {376, 48310}, {381, 48873}, {382, 1351}, {428, 5651}, {511, 3627}, {516, 17351}, {518, 51118}, {524, 3543}, {542, 33699}, {546, 3098}, {548, 38317}, {549, 48885}, {550, 19130}, {599, 50687}, {962, 9053}, {1352, 3830}, {1353, 11645}, {1370, 3066}, {1386, 28164}, {1657, 14561}, {1843, 40929}, {1885, 3867}, {2777, 25328}, {2781, 12295}, {2854, 13202}, {2916, 12087}, {3091, 31884}, {3242, 9812}, {3522, 47355}, {3529, 5085}, {3564, 48884}, {3618, 5059}, {3619, 50689}, {3631, 50688}, {3763, 3832}, {3815, 40236}, {3818, 3853}, {3839, 20582}, {3845, 24206}, {4265, 36002}, {5050, 49136}, {5071, 50984}, {5073, 46264}, {5076, 33878}, {5092, 15704}, {5097, 8550}, {5102, 39874}, {5103, 18860}, {5189, 37648}, {5229, 10387}, {5254, 12212}, {5646, 7392}, {5691, 5846}, {5743, 37456}, {5894, 23300}, {5895, 36851}, {5969, 39838}, {6247, 18382}, {6329, 25406}, {6361, 38144}, {6703, 50698}, {6707, 7390}, {6756, 37480}, {6776, 8584}, {7391, 13567}, {7394, 21766}, {7408, 17811}, {7500, 23292}, {7517, 35228}, {7519, 11064}, {7540, 37477}, {7553, 13352}, {7576, 43576}, {7667, 22112}, {8703, 48920}, {8705, 44439}, {9019, 12294}, {9041, 50865}, {9055, 51063}, {9589, 49688}, {10007, 22682}, {10168, 19710}, {10192, 32237}, {10541, 49140}, {11001, 38072}, {11178, 12101}, {11403, 37485}, {11745, 34938}, {12007, 15684}, {12017, 49137}, {12102, 18358}, {12103, 17508}, {12811, 42786}, {13394, 37900}, {13473, 41585}, {13598, 34146}, {13910, 42258}, {13972, 42259}, {14389, 20063}, {14677, 20301}, {14790, 15873}, {14853, 33703}, {14893, 50977}, {15107, 45303}, {15491, 37182}, {15516, 29323}, {15577, 18534}, {15681, 50983}, {15683, 47352}, {15685, 38064}, {15686, 33751}, {15687, 19924}, {15692, 50972}, {15694, 50964}, {15702, 50968}, {16051, 31860}, {17225, 51065}, {17504, 25565}, {17810, 44442}, {19145, 42275}, {19146, 42276}, {20062, 37649}, {20192, 47314}, {20300, 23328}, {21356, 50970}, {21358, 50960}, {22676, 40332}, {23311, 36658}, {23312, 36657}, {23324, 31723}, {23327, 50709}, {25555, 48891}, {28538, 50862}, {31099, 47296}, {31133, 32269}, {31162, 50998}, {31802, 44762}, {32455, 50691}, {33851, 46686}, {34417, 46517}, {34628, 51006}, {34632, 50951}, {34648, 50949}, {35402, 50954}, {35434, 50955}, {36709, 45498}, {36714, 45499}, {38110, 48892}, {40825, 43618}, {44437, 50668}, {44883, 47527}
X(51163) = midpoint of X(i) and X(j) for these {i,j}: {3, 43621}, {4, 48910}, {6, 3146}, {382, 31670}, {3543, 51024}, {5073, 46264}, {5895, 36851}, {9589, 49688}, {15684, 20423}, {33703, 48905}, {48901, 48904}
X(51163) = reflection of X(i) in X(j) for these {i,j}: {5, 48895}, {20, 3589}, {141, 4}, {159, 5893}, {376, 50959}, {550, 19130}, {3098, 546}, {3543, 51026}, {3818, 3853}, {5480, 48901}, {5894, 23300}, {6247, 18382}, {8550, 21850}, {11178, 12101}, {14677, 20301}, {15681, 50983}, {15683, 50971}, {15704, 5092}, {18358, 12102}, {19710, 10168}, {33851, 46686}, {34628, 51006}, {34632, 50951}, {40929, 1843}, {44882, 5480}, {47354, 15687}, {48874, 24206}, {48876, 48889}, {48879, 548}, {48880, 140}, {48881, 5}, {48891, 25555}, {48898, 18583}, {50949, 34648}, {50965, 381}, {50977, 14893}, {50998, 31162}, {51022, 3543}
X(51163) = complement of X(48872)
X(51163) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 48881, 21167}, {376, 50959, 48310}, {3091, 31884, 34573}, {3845, 48874, 24206}, {5480, 44882, 597}, {14853, 33703, 48905}, {15683, 47352, 50971}, {15687, 48876, 48889}, {15704, 38136, 5092}, {38317, 48879, 548}, {48876, 48889, 47354}, {51024, 51026, 51022}, {51024, 51029, 51026}
X(51164) lies on these lines: {4, 50969}, {30, 47355}, {381, 48920}, {382, 575}, {518, 50874}, {524, 3543}, {597, 50691}, {599, 3627}, {3091, 50972}, {3146, 50959}, {3619, 50687}, {3763, 38335}, {3830, 10516}, {3845, 50968}, {3853, 50956}, {5846, 50867}, {15640, 50971}, {15684, 47352}, {15687, 48872}, {18583, 35404}, {20423, 33699}, {24206, 35401}, {25565, 49139}, {29181, 50994}, {31670, 50986}, {31884, 50960}, {35434, 48904}, {38072, 50987}, {43150, 48910}, {48884, 50962}, {48905, 50963}
X(51164) = reflection of X(50976) in X(50964)
X(51164) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3543, 51026, 51024}, {3543, 51029, 51022}, {50964, 50976, 47355}, {51022, 51024, 51027}, {51022, 51026, 51029}, {51022, 51027, 36990}, {51022, 51029, 51024}
X(51165) lies on these lines: {3, 50959}, {4, 50970}, {30, 6329}, {518, 51119}, {524, 3543}, {547, 14810}, {597, 5059}, {1352, 35402}, {3146, 20583}, {3533, 50969}, {3545, 34573}, {3627, 50985}, {3631, 50687}, {3830, 50958}, {3832, 20582}, {3845, 29181}, {3853, 18553}, {5085, 11001}, {5102, 15682}, {5846, 50868}, {9053, 51120}, {11812, 29317}, {15686, 48901}, {15687, 50982}, {15719, 50968}, {19130, 41982}, {33703, 43273}, {33878, 38335}, {37517, 50986}, {41152, 50967}, {43621, 50963}, {48881, 50964}, {48904, 50979}
X(51165) = midpoint of X(i) and X(j) for these {i,j}: {3146, 20583}, {51024, 51026}
X(51165) = reflection of X(50972) in X(50959)
X(51165) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3543, 51027, 51022}, {51022, 51027, 51025}, {51022, 51029, 51026}, {51024, 51029, 51022}, {51025, 51026, 3543}
X(51166) lies on these lines: {2, 50970}, {3, 597}, {4, 50958}, {6, 50971}, {20, 20583}, {30, 3629}, {141, 3545}, {381, 50982}, {511, 3845}, {518, 51120}, {524, 3543}, {547, 5480}, {599, 3832}, {1350, 15702}, {1503, 50962}, {1992, 5059}, {3098, 41983}, {3589, 15708}, {3630, 31670}, {3631, 3839}, {3830, 50961}, {5032, 48872}, {5056, 20582}, {5067, 38072}, {5085, 50969}, {5097, 15686}, {5102, 8584}, {5476, 11812}, {5846, 50871}, {5847, 50868}, {5965, 33699}, {6329, 10304}, {9041, 11531}, {11477, 33703}, {11539, 21850}, {11645, 50986}, {11898, 35402}, {12007, 15681}, {14810, 50988}, {14853, 15719}, {15687, 50985}, {15690, 39561}, {16200, 50998}, {25561, 41991}, {30392, 51006}, {34379, 51119}, {38155, 50949}, {40341, 50687}, {42785, 47599}, {48874, 50987}, {48881, 50664}
X(51166) = midpoint of X(51024) and X(51028)
X(51166) = reflection of X(i) in X(j) for these {i,j}: {20, 20583}, {15681, 12007}, {15686, 5097}, {50965, 20423}, {50967, 50959}, {50973, 50958}, {51022, 51024}, {51023, 51026}, {51027, 51025}
X(51166) = anticomplement of X(50970)
X(51166) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 50973, 50958}, {3543, 51025, 51022}, {3543, 51027, 51025}, {20423, 50965, 597}, {36990, 51024, 51029}, {50959, 50967, 141}, {51023, 51024, 51026}, {51023, 51026, 51022}, {51024, 51027, 3543}
X(51167) lies on these lines: {4, 50975}, {5, 50976}, {6, 42641}, {20, 50960}, {30, 3763}, {381, 48896}, {382, 599}, {518, 50866}, {524, 3543}, {597, 50688}, {1350, 35404}, {3146, 50965}, {3618, 50687}, {3627, 20423}, {3830, 5050}, {3839, 50971}, {3853, 38072}, {5073, 50957}, {5085, 12101}, {5846, 50873}, {9053, 50863}, {10519, 15682}, {11645, 35434}, {12102, 38064}, {14269, 47355}, {15640, 31884}, {15683, 50984}, {15684, 48872}, {15687, 47352}, {20582, 49135}, {24206, 35400}, {25561, 49136}, {29181, 50990}, {33699, 47353}, {38335, 48905}, {39899, 48884}, {48910, 50955}, {50690, 50958}
X(51167) = reflection of X(i) in X(j) for these {i,j}: {43273, 50963}, {50966, 47354}, {50968, 50956}, {50989, 47353}, {51024, 51029}
X(51167) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3543, 51022, 51024}, {3543, 51023, 51026}, {36990, 51024, 51027}, {47354, 50966, 50993}, {50956, 50968, 3763}, {51022, 51024, 36990}, {51022, 51026, 51023}, {51023, 51026, 51024}
X(51168) lies on these lines: {1, 51146}, {2, 50786}, {8, 51004}, {10, 51001}, {165, 50975}, {193, 38098}, {515, 50966}, {517, 50954}, {518, 50782}, {519, 3620}, {524, 3416}, {599, 3632}, {1698, 28538}, {1699, 50956}, {3576, 50980}, {3618, 19875}, {3624, 51006}, {3626, 11160}, {3633, 50998}, {3763, 25055}, {4677, 50781}, {4816, 9041}, {5587, 50963}, {5846, 51105}, {5847, 51066}, {9053, 50784}, {16475, 51148}, {19872, 38023}, {21356, 34747}, {26446, 50987}, {28313, 49630}, {34379, 51072}, {37712, 50967}, {38127, 50974}, {38155, 51028}, {38176, 50962}, {47356, 51126}, {47358, 51142}, {49681, 51154}, {50783, 50993}, {50789, 50991}, {50994, 51089}
X(51168) = midpoint of X(i) and X(j) for these {i,j}: {50783, 50993}, {50950, 50953}
X(51168) = reflection of X(i) in X(j) for these {i,j}: {47356, 51126}, {47358, 51142}, {50953, 51125}, {50990, 50781}, {51125, 50949}, {51146, 51156}, {51149, 51003}
X(51168) = anticomplement of X(51153)
X(51168) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3416, 50949, 50950}, {3679, 50950, 50952}, {50949, 50950, 3679}, {50953, 51125, 3679}, {50993, 51149, 51003}, {51146, 51156, 1}
X(51169) lies on these lines: {145, 51156}, {165, 50976}, {515, 50969}, {517, 50957}, {518, 50785}, {519, 3619}, {524, 3416}, {599, 4668}, {952, 50981}, {1125, 51146}, {1698, 51006}, {1699, 51133}, {1992, 4691}, {3576, 51141}, {3617, 51001}, {3626, 51004}, {3632, 50998}, {3633, 20582}, {3844, 34747}, {4669, 50787}, {4677, 50790}, {5587, 50964}, {5847, 51068}, {16475, 50783}, {16491, 19875}, {25055, 51128}, {26446, 50988}, {38047, 51148}, {38087, 51155}, {50781, 51072}, {50786, 51067}, {50789, 51105}, {51069, 51153}
X(51169) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3416, 50951, 50952}, {3416, 50952, 50950}, {3679, 50949, 50950}, {3679, 50950, 50953}, {3679, 50952, 50951}, {50783, 51066, 16475}, {50949, 50951, 3416}, {50949, 51125, 3679}, {50950, 50953, 3751}
X(51170) lies on these lines: {2, 6}, {3, 33748}, {4, 1353}, {7, 17121}, {8, 17120}, {9, 29585}, {20, 1351}, {23, 19459}, {32, 439}, {51, 12272}, {144, 4393}, {145, 3685}, {147, 9748}, {148, 5477}, {182, 15717}, {194, 5052}, {239, 31995}, {251, 6339}, {263, 38262}, {316, 1570}, {317, 40138}, {344, 16669}, {376, 44456}, {393, 32002}, {487, 6420}, {488, 6419}, {511, 3522}, {518, 3623}, {568, 37460}, {575, 10519}, {576, 3146}, {621, 42998}, {622, 42999}, {631, 34380}, {648, 3087}, {698, 19693}, {742, 4821}, {858, 47463}, {894, 32087}, {895, 14683}, {1092, 11431}, {1199, 7400}, {1249, 27377}, {1278, 49496}, {1285, 31859}, {1350, 21734}, {1352, 5068}, {1384, 35287}, {1444, 37503}, {1449, 17257}, {1503, 17578}, {1587, 12221}, {1588, 12222}, {1743, 17316}, {1843, 11002}, {1974, 9544}, {1995, 19588}, {2257, 26699}, {2452, 36181}, {2916, 8546}, {2996, 7745}, {3060, 6467}, {3088, 18917}, {3089, 12161}, {3090, 11898}, {3091, 3564}, {3124, 10553}, {3161, 17389}, {3241, 17261}, {3244, 25728}, {3284, 40680}, {3448, 5095}, {3523, 5050}, {3524, 50962}, {3543, 21850}, {3545, 50954}, {3567, 34382}, {3616, 17331}, {3617, 5847}, {3621, 4663}, {3622, 16475}, {3672, 20072}, {3729, 4856}, {3758, 5564}, {3759, 4644}, {3785, 7772}, {3793, 33215}, {3818, 3832}, {3839, 18440}, {3870, 20978}, {3875, 28301}, {3879, 16670}, {3926, 5007}, {3973, 29574}, {4189, 37492}, {4232, 19118}, {4254, 21508}, {4260, 37267}, {4360, 20073}, {4402, 50128}, {4416, 16667}, {4452, 31300}, {4461, 20016}, {4558, 13345}, {4643, 16668}, {4699, 4747}, {4700, 10436}, {4851, 16671}, {4852, 28322}, {4888, 41140}, {4916, 17264}, {4969, 42696}, {5008, 34511}, {5017, 33014}, {5028, 20065}, {5034, 7793}, {5039, 33201}, {5041, 14023}, {5055, 50986}, {5056, 18583}, {5059, 5102}, {5092, 15705}, {5107, 14712}, {5111, 32997}, {5120, 21537}, {5189, 32220}, {5207, 33290}, {5222, 17364}, {5261, 39897}, {5274, 39873}, {5305, 32972}, {5309, 32827}, {5319, 7838}, {5346, 31275}, {5395, 43681}, {5446, 12283}, {5480, 50689}, {5640, 14913}, {5702, 32001}, {5749, 17363}, {5846, 20052}, {5965, 40330}, {5984, 10753}, {6172, 17319}, {6179, 31400}, {6375, 46948}, {6390, 30435}, {6391, 7398}, {6392, 7760}, {6403, 21852}, {6417, 11292}, {6418, 11291}, {6423, 6463}, {6424, 6462}, {6542, 49783}, {6636, 37491}, {6646, 17014}, {6680, 32825}, {6995, 12167}, {7229, 29617}, {7277, 42697}, {7289, 23958}, {7378, 11405}, {7391, 18935}, {7396, 11245}, {7404, 14627}, {7408, 8541}, {7426, 47281}, {7487, 37493}, {7500, 10602}, {7519, 34777}, {7754, 32971}, {7758, 7820}, {7762, 32974}, {7785, 32980}, {7787, 32830}, {7798, 32815}, {7803, 7850}, {7804, 32836}, {7805, 32828}, {7812, 43448}, {7813, 14075}, {7855, 34571}, {7893, 33202}, {7900, 33200}, {7906, 33181}, {7920, 33180}, {7941, 33199}, {7947, 33183}, {8267, 46712}, {8356, 14482}, {8359, 22246}, {8573, 35296}, {8593, 8596}, {8705, 47466}, {8737, 16770}, {8738, 16771}, {9001, 26777}, {9308, 40065}, {9545, 19128}, {9605, 32990}, {9706, 23042}, {9742, 37071}, {9812, 39878}, {9974, 39875}, {9975, 39876}, {10008, 32835}, {10303, 48876}, {10304, 33878}, {10565, 11402}, {10754, 14928}, {10755, 20095}, {10756, 20096}, {10760, 20097}, {10761, 20098}, {10765, 20099}, {10989, 47541}, {11003, 19121}, {11173, 33208}, {11179, 37517}, {11180, 19130}, {11216, 36851}, {11225, 23291}, {11422, 21637}, {11426, 44683}, {11477, 12007}, {11606, 43951}, {11800, 32248}, {12017, 15692}, {12220, 40673}, {12317, 39562}, {13330, 33244}, {13571, 32831}, {14001, 43136}, {14031, 18906}, {14033, 22253}, {14037, 32840}, {14230, 49057}, {14233, 49056}, {14561, 15022}, {14826, 15004}, {14848, 18358}, {14927, 50692}, {15032, 34621}, {15048, 33272}, {15471, 35265}, {15683, 46264}, {15708, 50980}, {15709, 50978}, {15741, 19467}, {16496, 51005}, {16666, 17321}, {16981, 32366}, {17037, 40896}, {17117, 35578}, {17276, 50124}, {17351, 50131}, {17355, 50079}, {17367, 21296}, {17368, 32099}, {17391, 18230}, {17548, 36740}, {17813, 34774}, {18919, 26926}, {19122, 34986}, {19617, 40819}, {20014, 49679}, {20018, 50600}, {20049, 49681}, {20050, 49536}, {20063, 47465}, {20078, 45222}, {20079, 39125}, {20081, 32451}, {20423, 48895}, {20794, 37465}, {21309, 32985}, {22152, 37338}, {22486, 41622}, {23249, 39894}, {23259, 39893}, {23300, 31857}, {24280, 49488}, {24599, 26806}, {24695, 28546}, {25329, 32255}, {26039, 32025}, {26869, 30769}, {27549, 50284}, {30745, 47462}, {31145, 49529}, {32621, 37913}, {32841, 33225}, {32872, 33020}, {32873, 33262}, {32964, 40825}, {33022, 50659}, {33025, 44499}, {35284, 36277}, {35418, 50969}, {35439, 44434}, {35840, 43134}, {35841, 43133}, {36741, 37307}, {37188, 38292}, {37907, 47279}, {37909, 47545}, {38314, 49505}, {43653, 44111}, {46934, 49511}, {47356, 51146}, {48836, 48857}, {49497, 50303}, {50953, 51001}, {50968, 51132}, {51124, 51149}, {51125, 51155}, {51136, 51167}
X(51170) = midpoint of X(193) and X(3620)
X(51170) = reflection of X(i) in X(j) for these {i,j}: {69, 3763}, {3618, 6}, {3620, 3618}, {11160, 50990}, {11180, 50956}, {50975, 11179}, {50993, 597}, {51146, 47356}
X(51170) = isotomic conjugate of X(43681)
X(51170) = anticomplement of X(3620)
X(51170) = anticomplement of the isotomic conjugate of X(5395)
X(51170) = isotomic conjugate of the isogonal conjugate of X(22331)
X(51170) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1973, 8892}, {5395, 6327}, {31506, 21289}
X(51170) = X(5395)-Ceva conjugate of X(2)
X(51170) = X(31)-isoconjugate of X(43681)
X(51170) = X(2)-Dao conjugate of X(43681)
X(51170) = barycentric product X(76)*X(22331)
X(51170) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 43681}, {22331, 6}
X(51170) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 193, 20080}, {6, 193, 2}, {6, 599, 6329}, {6, 1992, 193}, {6, 3629, 69}, {6, 6144, 3589}, {6, 15534, 141}, {6, 32455, 1992}, {6, 40341, 597}, {69, 1992, 3629}, {69, 3618, 3763}, {69, 3629, 193}, {69, 3763, 3620}, {141, 11008, 11160}, {141, 15534, 11008}, {141, 20583, 6}, {141, 50990, 3620}, {193, 5032, 6}, {193, 11160, 11008}, {302, 303, 34803}, {385, 37665, 2}, {391, 17379, 2}, {597, 40341, 3619}, {648, 3087, 43981}, {895, 25321, 14683}, {1249, 27377, 37174}, {1270, 1271, 7788}, {1285, 31859, 35927}, {1351, 14912, 20}, {1353, 5093, 4}, {1992, 5032, 2}, {1992, 8584, 5032}, {1992, 20583, 11160}, {3068, 3069, 37637}, {3329, 15589, 2}, {3589, 3629, 6144}, {3589, 6144, 69}, {3618, 3620, 2}, {3618, 11008, 50990}, {3630, 47355, 21356}, {3729, 4856, 50129}, {3879, 16670, 26685}, {3879, 26685, 29583}, {3945, 17349, 2}, {4416, 16667, 26626}, {5304, 7774, 2}, {5319, 7838, 32816}, {5921, 14853, 3832}, {6189, 6190, 50774}, {7585, 7586, 7735}, {7736, 14614, 37667}, {7736, 37667, 2}, {7777, 37689, 2}, {7837, 16989, 37668}, {8584, 32455, 6}, {11008, 15534, 193}, {11477, 12007, 25406}, {16989, 37668, 2}, {17300, 37681, 2}, {19053, 26339, 491}, {19054, 26340, 492}, {21850, 39874, 3543}, {39365, 39366, 50251}
X(51171) lies on these lines: {1, 4899}, {2, 6}, {4, 5050}, {5, 5921}, {7, 17120}, {8, 16475}, {9, 26626}, {20, 182}, {23, 47457}, {32, 32990}, {39, 32973}, {44, 17321}, {51, 10565}, {58, 37339}, {83, 2996}, {110, 19137}, {115, 45018}, {125, 25321}, {140, 5093}, {144, 17302}, {145, 1386}, {146, 5622}, {148, 5182}, {159, 10169}, {184, 7398}, {192, 17014}, {194, 33198}, {206, 7693}, {216, 47740}, {239, 5749}, {264, 40138}, {297, 40065}, {316, 1692}, {344, 1100}, {346, 4393}, {373, 14913}, {376, 12017}, {381, 39874}, {390, 2330}, {393, 30535}, {404, 37492}, {405, 19783}, {439, 5013}, {441, 15851}, {458, 1249}, {487, 6419}, {488, 6420}, {511, 3523}, {518, 3622}, {549, 44456}, {569, 7487}, {574, 35287}, {575, 3091}, {576, 10303}, {611, 14986}, {621, 36757}, {622, 36758}, {631, 1351}, {698, 19692}, {742, 4772}, {858, 47459}, {894, 5222}, {1084, 25319}, {1176, 7500}, {1194, 18287}, {1199, 19139}, {1278, 49481}, {1285, 8356}, {1350, 15717}, {1352, 5056}, {1353, 1656}, {1384, 33215}, {1428, 3600}, {1449, 17316}, {1469, 5265}, {1475, 21371}, {1503, 3832}, {1570, 31401}, {1691, 32965}, {1724, 13736}, {1743, 17023}, {1843, 4232}, {1974, 5012}, {1995, 18919}, {2030, 14712}, {2071, 47571}, {2076, 33022}, {2082, 27059}, {2285, 26998}, {2321, 50129}, {2345, 3759}, {2456, 10359}, {2548, 7829}, {2896, 41623}, {2987, 46952}, {2998, 11175}, {3056, 5281}, {3060, 11574}, {3066, 9924}, {3087, 17907}, {3088, 36752}, {3089, 39588}, {3090, 3564}, {3094, 32964}, {3098, 15053}, {3146, 5480}, {3161, 17319}, {3241, 16491}, {3311, 11291}, {3312, 11292}, {3407, 14484}, {3416, 46933}, {3448, 15118}, {3522, 5085}, {3524, 33878}, {3525, 11482}, {3526, 34380}, {3543, 5476}, {3545, 18440}, {3548, 15047}, {3552, 50659}, {3553, 26639}, {3567, 9967}, {3616, 3751}, {3617, 38047}, {3621, 49524}, {3623, 38315}, {3624, 34379}, {3628, 11898}, {3672, 17350}, {3729, 50114}, {3758, 4000}, {3767, 32987}, {3785, 5007}, {3817, 39878}, {3839, 11179}, {3844, 46931}, {3850, 48662}, {3855, 39884}, {3867, 7408}, {3875, 50115}, {3879, 29579}, {3912, 16667}, {3926, 7772}, {3946, 50127}, {3972, 35927}, {3977, 5256}, {4021, 25728}, {4085, 50303}, {4188, 36740}, {4189, 36741}, {4190, 5135}, {4254, 21495}, {4265, 37307}, {4346, 31300}, {4357, 16670}, {4402, 17116}, {4416, 29598}, {4419, 17380}, {4422, 16884}, {4464, 4873}, {4473, 32029}, {4643, 16671}, {4644, 16706}, {4657, 16669}, {4663, 46934}, {4667, 17282}, {4672, 24280}, {4678, 5846}, {4689, 35284}, {4699, 24599}, {4700, 17270}, {4747, 26806}, {4748, 17400}, {4851, 16668}, {4852, 50107}, {4856, 17294}, {4916, 17240}, {4969, 17293}, {5017, 33004}, {5021, 22267}, {5024, 32985}, {5026, 20094}, {5028, 31400}, {5033, 12150}, {5038, 14035}, {5039, 7793}, {5041, 7795}, {5046, 5800}, {5052, 7786}, {5054, 50981}, {5055, 50974}, {5059, 44882}, {5068, 8550}, {5071, 18358}, {5092, 10304}, {5094, 46444}, {5095, 15059}, {5096, 17548}, {5111, 33206}, {5116, 33014}, {5120, 21511}, {5133, 19119}, {5138, 6904}, {5158, 40680}, {5159, 47461}, {5169, 15431}, {5189, 47458}, {5207, 33283}, {5227, 27065}, {5254, 32979}, {5262, 11851}, {5296, 17397}, {5305, 32968}, {5308, 17338}, {5319, 7808}, {5459, 42111}, {5460, 42114}, {5462, 6403}, {5477, 14061}, {5550, 49511}, {5596, 23327}, {5644, 6677}, {5645, 39125}, {5702, 32000}, {5818, 38167}, {5839, 17289}, {5847, 9780}, {5943, 6467}, {5946, 18438}, {6172, 17247}, {6194, 35439}, {6339, 39951}, {6353, 12167}, {6390, 9605}, {6392, 7770}, {6393, 32835}, {6462, 45512}, {6463, 45513}, {6542, 49775}, {6593, 14683}, {6622, 39871}, {6658, 42421}, {6661, 32817}, {6671, 42149}, {6672, 42152}, {6680, 32829}, {6723, 32244}, {6803, 11426}, {6997, 18935}, {7222, 37756}, {7229, 17117}, {7269, 28966}, {7277, 17290}, {7289, 27003}, {7378, 44102}, {7388, 7581}, {7389, 7582}, {7391, 41256}, {7392, 11402}, {7394, 19153}, {7404, 18917}, {7426, 47456}, {7485, 37491}, {7486, 15516}, {7494, 9777}, {7496, 31521}, {7664, 39024}, {7668, 25314}, {7737, 33272}, {7738, 32981}, {7739, 7804}, {7745, 32982}, {7753, 32827}, {7754, 16045}, {7755, 32838}, {7758, 7889}, {7762, 32956}, {7765, 32826}, {7769, 10008}, {7776, 33221}, {7783, 33201}, {7785, 33180}, {7791, 40825}, {7798, 32836}, {7807, 39142}, {7810, 14075}, {7817, 31415}, {7822, 41940}, {7823, 33025}, {7827, 43448}, {7828, 31404}, {7834, 32816}, {7839, 16898}, {7850, 7859}, {7851, 32980}, {7854, 34571}, {7892, 32831}, {7912, 33182}, {7920, 16924}, {7923, 33200}, {7932, 33199}, {8359, 21309}, {8362, 43136}, {8363, 32823}, {8541, 12834}, {8589, 37809}, {8796, 40393}, {8889, 45298}, {9001, 27115}, {9540, 35841}, {9541, 26618}, {9698, 32839}, {9748, 37182}, {9822, 11451}, {10168, 15708}, {10191, 31390}, {10272, 39562}, {10485, 33192}, {10516, 12007}, {10541, 29181}, {10553, 20976}, {10574, 12294}, {10583, 33181}, {10586, 45729}, {10587, 45728}, {10588, 39897}, {10589, 39873}, {10590, 39901}, {10591, 39900}, {10595, 38040}, {10759, 38119}, {11188, 32366}, {11206, 15583}, {11245, 46442}, {11284, 19588}, {11293, 19145}, {11294, 19146}, {11301, 42634}, {11302, 42633}, {11313, 19116}, {11314, 19117}, {11317, 18842}, {11331, 32001}, {11405, 38282}, {11416, 32223}, {11432, 44683}, {11465, 32284}, {11485, 37173}, {11486, 37172}, {11511, 15019}, {11539, 50962}, {11645, 42785}, {12055, 33266}, {12212, 33258}, {12317, 45016}, {12848, 17086}, {13196, 44000}, {13330, 33012}, {13331, 14037}, {13341, 36212}, {13353, 19154}, {13366, 14826}, {13562, 45968}, {13674, 45439}, {13794, 45438}, {13881, 33684}, {13935, 35840}, {14002, 20987}, {14033, 15048}, {14039, 14482}, {14360, 36696}, {14927, 17578}, {14965, 37186}, {15028, 44495}, {15045, 37511}, {15088, 32272}, {15246, 37485}, {15321, 43697}, {15484, 16041}, {15485, 48830}, {15492, 41312}, {15585, 17813}, {15655, 19661}, {15683, 48910}, {15688, 50987}, {15697, 48880}, {15705, 50983}, {15721, 46267}, {15751, 43831}, {15826, 47453}, {16043, 30435}, {16226, 21851}, {16477, 50295}, {16496, 38314}, {16666, 17279}, {16793, 29829}, {16798, 29832}, {16799, 29831}, {16826, 18230}, {16834, 17355}, {16885, 17045}, {16973, 29570}, {17037, 42287}, {17229, 50131}, {17266, 49783}, {17273, 26104}, {17286, 50079}, {17291, 21296}, {17292, 32099}, {17298, 31191}, {17299, 50124}, {17314, 17354}, {17331, 29614}, {17339, 29584}, {17351, 50101}, {17358, 29616}, {17363, 29611}, {17364, 29630}, {17366, 42697}, {17369, 42696}, {17383, 20072}, {17391, 29627}, {17484, 19823}, {17504, 50966}, {17784, 19133}, {18164, 29552}, {18228, 29841}, {18451, 18489}, {18800, 41135}, {18907, 32986}, {19127, 20062}, {19131, 43651}, {19155, 36153}, {19875, 51001}, {19883, 50952}, {20014, 51147}, {20018, 50595}, {20049, 49690}, {20059, 51150}, {20063, 32217}, {20065, 33202}, {20075, 47373}, {20081, 24256}, {20095, 51157}, {20099, 28662}, {20105, 32449}, {20190, 33750}, {20775, 37465}, {20794, 37338}, {21508, 36743}, {21537, 36744}, {21735, 48874}, {21736, 45410}, {21843, 44562}, {22234, 24206}, {22246, 33237}, {22829, 29959}, {23515, 32234}, {23583, 40867}, {24598, 39956}, {25055, 49505}, {25072, 29597}, {25099, 40133}, {25317, 36213}, {25318, 39080}, {25590, 41140}, {26223, 30699}, {26245, 46897}, {26881, 44091}, {29012, 50688}, {29590, 50013}, {29833, 31018}, {30712, 47595}, {30745, 32220}, {31145, 49681}, {31276, 32451}, {31406, 32970}, {31412, 49229}, {31467, 32977}, {31693, 42816}, {31694, 42815}, {31958, 44423}, {32064, 34774}, {32450, 32824}, {32488, 39875}, {32489, 39876}, {32818, 33217}, {33159, 50284}, {33203, 44499}, {33260, 39560}, {33269, 42534}, {33560, 41120}, {33561, 41119}, {33632, 42037}, {34507, 46935}, {34565, 43653}, {35578, 48627}, {36990, 50689}, {37126, 37488}, {37170, 42975}, {37171, 42974}, {37184, 40981}, {37335, 40947}, {37337, 41334}, {37460, 37506}, {37760, 47455}, {37874, 41899}, {37901, 47544}, {37907, 47454}, {37911, 47463}, {38023, 49465}, {39893, 42274}, {39894, 42277}, {39957, 39975}, {42561, 49228}, {42988, 47520}, {42989, 47518}, {43030, 50858}, {43031, 50855}, {43232, 50860}, {43233, 50859}, {43273, 50687}, {47478, 50954}, {47599, 50986}, {48810, 49680}, {48817, 48847}, {48837, 48867}, {48843, 48870}, {48857, 48866}, {48891, 50975}, {48898, 49140}, {48901, 49135}, {49482, 50282}, {49533, 50779}, {49685, 50316}, {50692, 51163}, {51023, 51133}, {51138, 51164}
X(51171) = midpoint of X(i) and X(j) for these {i,j}: {6, 47355}, {1992, 50994}, {11179, 50964}
X(51171) = reflection of X(i) in X(j) for these {i,j}: {3619, 47355}, {51128, 3589}, {51141, 10168}
X(51171) = anticomplement of X(3619)
X(51171) = anticomplement of the isotomic conjugate of X(18841)
X(51171) = complement of the isotomic conjugate of X(18845)
X(51171) = isogonal conjugate of the complement of X(41927)
X(51171) = isotomic conjugate of the polar conjugate of X(7714)
X(51171) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {18841, 6327}, {46289, 41928}
X(51171) = X(18845)-complementary conjugate of X(2887)
X(51171) = X(18841)-Ceva conjugate of X(2)
X(51171) = crosspoint of X(2) and X(18845)
X(51171) = crosssum of X(6) and X(15815)
X(51171) = barycentric product X(69)*X(7714)
X(51171) = barycentric quotient X(7714)/X(4)
X(51171) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6, 193}, {2, 193, 3620}, {2, 5032, 11160}, {2, 5304, 37667}, {2, 7766, 15589}, {2, 14930, 7774}, {2, 20080, 141}, {2, 20090, 4869}, {2, 37677, 3945}, {5, 14912, 5921}, {6, 141, 1992}, {6, 193, 5032}, {6, 597, 3618}, {6, 599, 32455}, {6, 3589, 69}, {6, 3618, 2}, {6, 3763, 3629}, {6, 20806, 1994}, {6, 40341, 8584}, {6, 47352, 141}, {6, 51126, 11008}, {69, 1992, 6144}, {69, 3589, 2}, {69, 3618, 3589}, {69, 6144, 20080}, {83, 5034, 39141}, {83, 5286, 32971}, {86, 37650, 2}, {141, 1992, 20080}, {141, 3630, 41152}, {141, 6144, 69}, {182, 14853, 20}, {193, 3620, 11160}, {302, 303, 1007}, {344, 1100, 29585}, {458, 1249, 43981}, {575, 6776, 33748}, {575, 14561, 6776}, {597, 6329, 6}, {599, 32455, 11008}, {966, 17381, 2}, {1351, 38110, 631}, {1449, 17353, 17316}, {1724, 19766, 13736}, {1743, 17023, 17257}, {1992, 20080, 193}, {1992, 47352, 2}, {3068, 3069, 3815}, {3087, 17907, 37174}, {3091, 33748, 6776}, {3329, 16989, 2}, {3589, 3629, 3763}, {3589, 51128, 47355}, {3619, 47355, 2}, {3619, 50994, 141}, {3620, 5032, 193}, {3629, 3763, 69}, {3630, 51127, 21358}, {3672, 17350, 20073}, {3751, 38049, 3616}, {4648, 17352, 2}, {5050, 18583, 4}, {5286, 32971, 2996}, {5319, 7808, 32828}, {5476, 50664, 46264}, {5480, 25406, 3146}, {6144, 51128, 50994}, {6189, 6190, 15480}, {6593, 25320, 14683}, {6776, 14561, 3091}, {7388, 7581, 12222}, {7389, 7582, 12221}, {7585, 7586, 37665}, {7735, 11174, 2}, {7736, 7792, 2}, {7739, 7804, 32815}, {7774, 7875, 2}, {7828, 31404, 32988}, {7839, 16898, 32830}, {8584, 34573, 40341}, {9822, 40673, 12272}, {10168, 50967, 15708}, {10601, 11427, 2}, {11433, 37649, 2}, {11451, 12272, 9822}, {11488, 11489, 3055}, {12017, 14848, 21850}, {12017, 21850, 376}, {13846, 45872, 32813}, {13847, 45871, 32812}, {14039, 14482, 31859}, {15583, 19132, 11206}, {16491, 49529, 3241}, {17120, 17367, 7}, {17121, 17368, 8}, {17352, 46922, 4648}, {17825, 37669, 2}, {18928, 23292, 2}, {20190, 48873, 33750}, {20583, 51127, 3630}, {23300, 41719, 20079}, {23327, 41593, 5596}, {25555, 39561, 1352}, {32455, 51126, 599}, {32812, 45871, 2}, {32813, 45872, 2}, {34573, 40341, 21356}, {37640, 37641, 9300}, {38317, 40330, 7486}
X(51172) lies on these lines: {3, 50966}, {4, 50986}, {6, 15688}, {193, 14269}, {381, 524}, {382, 1992}, {511, 15693}, {542, 5076}, {576, 1657}, {597, 15720}, {599, 5079}, {1353, 15684}, {3526, 11477}, {3534, 5093}, {3618, 5054}, {3620, 5055}, {3763, 37517}, {3830, 50974}, {3851, 11160}, {5032, 15681}, {5050, 50965}, {5072, 50985}, {5102, 29012}, {5476, 50973}, {5847, 50797}, {10246, 51153}, {11179, 51166}, {11482, 15696}, {14561, 50982}, {14853, 50990}, {14912, 15685}, {15690, 33748}, {15706, 33878}, {15723, 18583}, {19709, 34380}, {20080, 38071}, {21850, 38335}, {31670, 51136}, {34379, 50806}, {35402, 36990}, {38064, 50970}, {38136, 50992}, {39899, 48884}
X(51172) = midpoint of X(i) and X(j) for these {i,j}: {50954, 50962}, {50966, 51028}
X(51172) = reflection of X(i) in X(j) for these {i,j}: {50954, 50963}, {50955, 50956}, {50963, 20423}, {50966, 50987}, {50967, 50980}, {50975, 50979}, {50993, 5476}
X(51172) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1351, 20423, 50962}, {1351, 50955, 51132}, {1352, 20423, 51130}, {3618, 50967, 50980}, {5480, 50961, 50957}, {20423, 50961, 5480}, {20423, 50962, 381}, {20423, 51132, 50955}, {50954, 50963, 381}, {50955, 50956, 50954}, {50955, 50963, 50956}, {50955, 51132, 50962}, {50966, 50987, 3}
X(51173) lies on these lines: {2, 50981}, {3, 38079}, {5, 51028}, {6, 38335}, {20, 50987}, {140, 50966}, {193, 23046}, {381, 524}, {382, 575}, {546, 50986}, {576, 51027}, {597, 1657}, {599, 5072}, {1350, 15723}, {1656, 25565}, {1992, 3843}, {3098, 5054}, {3534, 5085}, {3545, 44456}, {3589, 15706}, {3618, 15689}, {3619, 5055}, {3620, 14892}, {3830, 14853}, {3845, 5093}, {3850, 11160}, {5032, 14893}, {5073, 51029}, {5076, 51022}, {5847, 50800}, {6776, 35403}, {10168, 50968}, {12017, 50971}, {12101, 14912}, {14093, 47352}, {14269, 39899}, {14561, 15693}, {15681, 18583}, {15685, 50975}, {15688, 31670}, {15695, 38110}, {15696, 38064}, {15700, 19924}, {15716, 51137}, {15718, 48874}, {18440, 51140}, {19709, 38136}, {33878, 51128}, {34379, 50807}, {34380, 41106}, {46264, 51026}, {46267, 48872}, {48895, 51167}, {49136, 51138}
X(51173) = midpoint of X(i) and X(j) for these {i,j}: {20423, 50964}, {43273, 51164}, {50976, 51024}
X(51173) = reflection of X(i) in X(j) for these {i,j}: {50957, 50964}, {50969, 50988}, {51133, 50959}
X(51173) = anticomplement of X(50981)
X(51173) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {381, 20423, 50962}, {381, 50962, 50954}, {5032, 14893, 48662}, {5480, 20423, 50963}, {5480, 51130, 20423}, {20423, 47354, 1351}, {20423, 50956, 51132}, {20423, 50959, 50955}, {20423, 50963, 381}, {50954, 50962, 11898}, {50955, 50959, 381}, {50955, 50963, 50959}, {50956, 51132, 50955}, {50957, 50964, 381}, {50959, 51132, 50956}, {50959, 51133, 50964}, {50969, 50988, 3}
X(51174) lies on these lines: {2, 50985}, {3, 50973}, {20, 50974}, {30, 11008}, {69, 15699}, {140, 1992}, {193, 3524}, {381, 524}, {382, 51166}, {511, 15685}, {542, 5073}, {599, 5070}, {1353, 14891}, {3090, 11160}, {3167, 15360}, {3526, 20583}, {3534, 51136}, {3564, 15682}, {3618, 41984}, {3627, 51023}, {3629, 5054}, {3830, 5965}, {5050, 15534}, {5055, 40341}, {5093, 15533}, {5097, 15703}, {5102, 19709}, {5847, 50804}, {6144, 15689}, {6776, 15691}, {8703, 25406}, {10109, 50992}, {10246, 51155}, {10519, 44580}, {12007, 15700}, {14269, 37517}, {15520, 50993}, {15688, 50970}, {15693, 51138}, {15696, 51135}, {15721, 48876}, {18440, 50687}, {34379, 51077}, {38079, 46935}, {38176, 50950}, {38317, 50989}, {44245, 50975}, {44456, 48884}, {48906, 50966}
X(51174) = reflection of X(i) in X(j) for these {i,j}: {50955, 50962}, {50961, 51132}, {50967, 50986}, {50973, 51140}
X(51174) = anticomplement of X(50985)
X(51174) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {381, 50961, 50955}, {381, 50962, 51132}, {1351, 50955, 50963}, {1351, 50957, 20423}, {1352, 20423, 51129}, {11898, 47354, 50955}, {20423, 50955, 50957}, {20423, 50957, 50963}, {20423, 50958, 381}, {20423, 50961, 50958}, {50955, 50962, 1351}, {50958, 51132, 20423}, {50961, 51132, 381}, {50973, 51140, 3}
X(51175) lies on these lines: {2, 50986}, {3, 11160}, {30, 20080}, {69, 5054}, {193, 5055}, {381, 524}, {382, 51023}, {511, 51027}, {542, 1657}, {575, 599}, {1353, 15694}, {1656, 1992}, {3098, 15688}, {3534, 3564}, {3630, 11179}, {3830, 34380}, {5032, 15703}, {5050, 22165}, {5076, 15069}, {5079, 14848}, {5085, 5965}, {5790, 50952}, {5847, 50805}, {5921, 15684}, {6144, 11178}, {6776, 14093}, {7776, 49102}, {10246, 51004}, {10247, 51001}, {10519, 15716}, {11180, 38335}, {12017, 50984}, {12355, 14645}, {14912, 15701}, {15360, 35264}, {15520, 15534}, {15689, 50966}, {15696, 50965}, {15700, 48876}, {15707, 50981}, {15713, 33748}, {15720, 50983}, {15723, 21356}, {18440, 51024}, {34379, 50798}, {35381, 41152}, {37071, 44367}, {37779, 47597}, {37958, 47552}, {38110, 50994}, {46264, 50970}
X(51175) = reflection of X(i) in X(j) for these {i,j}: {3, 11160}, {381, 11898}, {6144, 11178}, {11179, 3630}, {15684, 5921}, {44456, 11180}, {50955, 50961}, {50962, 50955}, {50967, 50985}, {50974, 50978}
X(51175) = anticomplement of X(50986)
X(51175) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1351, 50955, 47354}, {1352, 20423, 50960}, {1352, 51132, 50963}, {11160, 50974, 50978}, {11180, 44456, 38335}, {11898, 50962, 50955}, {20423, 50954, 381}, {20423, 50955, 50954}, {20423, 50958, 50957}, {20423, 50960, 50963}, {50954, 50962, 20423}, {50955, 50957, 50958}, {50955, 50961, 11898}, {50955, 50962, 381}, {50955, 50963, 1352}, {50957, 50958, 50954}, {50960, 51132, 20423}, {50967, 50992, 50985}, {50974, 50978, 3}
X(51176) lies on these lines: {2, 50954}, {4, 14848}, {6, 42641}, {20, 50962}, {69, 15710}, {376, 524}, {542, 631}, {575, 50964}, {597, 3855}, {599, 10299}, {1353, 15683}, {1503, 41099}, {1992, 3529}, {3090, 47354}, {3524, 3620}, {3528, 11160}, {3534, 50986}, {3545, 3618}, {3564, 19708}, {3763, 11180}, {3845, 33748}, {5050, 41106}, {5085, 50958}, {5093, 15640}, {5603, 51153}, {5847, 50809}, {5921, 15702}, {8550, 33703}, {10304, 39899}, {10519, 50989}, {11001, 51028}, {12156, 14912}, {14853, 51022}, {15069, 50984}, {15688, 20080}, {15697, 34380}, {15698, 25406}, {15717, 50981}, {15719, 50993}, {17508, 50994}, {19459, 37948}, {21735, 50961}, {22165, 33750}, {31670, 35409}, {34379, 50819}, {38072, 51025}, {46264, 46333}, {47353, 51138}, {48905, 51166}
X(51176) = midpoint of X(50966) and X(50974)
X(51176) = reflection of X(i) in X(j) for these {i,j}: {3618, 11179}, {11180, 3763}, {50954, 50987}, {50955, 50980}, {50963, 50979}, {50966, 50975}, {50967, 50968}, {50975, 43273}, {51023, 50956}, {51029, 20423}
X(51176) = anticomplement of X(50954)
X(51176) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1350, 43273, 51135}, {3618, 51023, 50956}, {6776, 43273, 50974}, {6776, 50967, 51136}, {11179, 39874, 3545}, {43273, 50973, 44882}, {43273, 50974, 376}, {43273, 51136, 50967}, {44882, 50973, 50969}, {50954, 50987, 2}, {50955, 50980, 3620}, {50966, 50975, 376}, {50967, 50968, 50966}, {50967, 50975, 50968}, {50967, 51136, 50974}
X(51177) lies on these lines: {2, 50957}, {3, 50981}, {4, 20190}, {6, 46333}, {20, 11482}, {193, 15689}, {376, 524}, {542, 3528}, {548, 11160}, {550, 50962}, {597, 33703}, {599, 21735}, {631, 47354}, {1352, 15715}, {1503, 15698}, {1992, 17538}, {3146, 50963}, {3524, 3619}, {3525, 51137}, {3529, 51024}, {3533, 51025}, {3534, 14912}, {3545, 47355}, {3620, 45759}, {3830, 50987}, {5032, 15686}, {5059, 14848}, {5071, 14927}, {5085, 41099}, {5092, 50956}, {5476, 51029}, {5847, 50813}, {5921, 34200}, {10299, 50984}, {10304, 39874}, {10516, 51139}, {10519, 51027}, {11001, 20423}, {11179, 48880}, {11180, 15710}, {11645, 15702}, {12017, 50687}, {12100, 50954}, {14853, 51138}, {14891, 48662}, {15080, 30775}, {15360, 18950}, {15682, 51164}, {15688, 50978}, {15690, 50986}, {15705, 18440}, {15709, 51128}, {15719, 33750}, {15721, 39884}, {17578, 38079}, {19708, 50977}, {29012, 41106}, {34379, 50820}, {48892, 51140}, {48905, 50959}
X(51177) = midpoint of X(43273) and X(50976)
X(51177) = reflection of X(i) in X(j) for these {i,j}: {50957, 50988}, {50969, 50976}, {51133, 50983}
X(51177) = anticomplement of X(50957)
X(51177) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 43273, 50974}, {376, 50974, 50966}, {33750, 47353, 15719}, {43273, 44882, 50975}, {43273, 50965, 6776}, {43273, 50968, 51136}, {43273, 50971, 50967}, {43273, 50975, 376}, {44882, 51135, 43273}, {50957, 50988, 2}, {50967, 50971, 376}, {50967, 50975, 50971}, {50968, 51136, 50967}, {50969, 50976, 376}, {50971, 51136, 50968}, {50983, 51133, 47355}
X(51178) lies on these lines: {2, 5965}, {3, 50985}, {4, 51027}, {5, 1992}, {30, 11008}, {69, 5054}, {193, 3818}, {376, 524}, {542, 3146}, {576, 3854}, {599, 3525}, {631, 51138}, {1351, 14893}, {1353, 10124}, {3090, 20583}, {3523, 11160}, {3524, 40341}, {3545, 3629}, {3564, 3830}, {3618, 47599}, {3630, 50984}, {3631, 15709}, {3860, 50963}, {5032, 40330}, {5050, 50990}, {5102, 41099}, {5603, 51155}, {5847, 50817}, {6144, 51024}, {6392, 9880}, {9974, 42570}, {9975, 42571}, {10516, 41149}, {10519, 12100}, {11179, 15705}, {11477, 51022}, {11898, 15703}, {12007, 15702}, {12017, 50981}, {12108, 50987}, {13857, 23291}, {14853, 15534}, {14912, 15533}, {15069, 50959}, {15682, 51166}, {15718, 48876}, {15722, 50980}, {19710, 34380}, {32816, 49102}, {34379, 51082}, {34507, 46936}, {37517, 50687}, {37712, 50952}, {38127, 50950}
X(51178) = reflection of X(i) in X(j) for these {i,j}: {11180, 193}, {20080, 11179}, {50955, 50986}, {50961, 51140}, {50967, 50974}, {50973, 51136}, {51023, 50962}, {51027, 51132}
X(51178) = anticomplement of X(50961)
X(51178) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {376, 50973, 50967}, {376, 50974, 51136}, {1350, 43273, 51134}, {6776, 50967, 50975}, {6776, 50969, 43273}, {43273, 50967, 50969}, {43273, 50969, 50975}, {43273, 50970, 376}, {43273, 50973, 50970}, {50955, 50986, 1992}, {50961, 51140, 2}, {50967, 50974, 6776}, {50970, 51136, 43273}, {50973, 51136, 376}, {51027, 51132, 4}
X(51179) lies on these lines: {2, 5093}, {3, 50986}, {4, 11160}, {6, 15709}, {30, 20080}, {69, 1568}, {193, 3524}, {376, 524}, {511, 11455}, {542, 3529}, {575, 631}, {597, 3533}, {599, 3090}, {1351, 5071}, {1353, 15692}, {3147, 41616}, {3523, 50987}, {3543, 11898}, {3564, 11001}, {3629, 50984}, {3630, 50958}, {3839, 44456}, {3855, 11477}, {5032, 15702}, {5050, 50980}, {5067, 14848}, {5102, 50991}, {5476, 50990}, {5603, 51004}, {5657, 50952}, {5847, 50818}, {6353, 15360}, {7967, 51001}, {9880, 32006}, {10516, 51130}, {10519, 15534}, {11008, 11179}, {11180, 40341}, {12243, 14645}, {14561, 50994}, {14853, 22165}, {14912, 15698}, {15069, 51022}, {15533, 41099}, {15693, 33748}, {15708, 50981}, {16051, 44555}, {21850, 50957}, {33703, 51027}, {34379, 50810}, {34507, 50956}, {37491, 37939}, {39874, 46333}, {41106, 50963}, {47353, 51166}, {48910, 51025}
X(51179) = reflection of X(i) in X(j) for these {i,j}: {4, 11160}, {3543, 11898}, {11008, 11179}, {11180, 40341}, {50955, 50985}, {50962, 50978}, {50967, 50973}, {50974, 50967}, {51023, 50961}, {51028, 50955}
X(51179) = anticomplement of X(50962)
X(51179) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1350, 43273, 50972}, {1350, 51136, 50975}, {5032, 48876, 15702}, {6776, 50967, 50965}, {11160, 51028, 50955}, {43273, 50966, 376}, {43273, 50967, 50966}, {43273, 50970, 50969}, {43273, 50972, 50975}, {50955, 50985, 11160}, {50955, 51028, 4}, {50962, 50978, 2}, {50966, 50974, 43273}, {50967, 50969, 50970}, {50967, 50974, 376}, {50967, 50975, 1350}, {50969, 50970, 50966}, {50972, 51136, 43273}, {50992, 51023, 50961}
X(51180) lies on these lines: {5, 50954}, {6, 38071}, {182, 524}, {193, 17504}, {511, 51134}, {542, 3858}, {550, 1992}, {1351, 44903}, {3618, 15699}, {3620, 11539}, {3627, 20423}, {3845, 14853}, {3857, 14848}, {5032, 15687}, {5050, 50990}, {5093, 33699}, {5097, 51022}, {5847, 50822}, {5965, 51142}, {6776, 35404}, {8550, 51166}, {8584, 29012}, {8703, 14912}, {10283, 51153}, {11160, 14869}, {11179, 50968}, {11812, 33748}, {15520, 51130}, {15686, 51028}, {15711, 34380}, {18583, 51027}, {19710, 43273}, {21850, 51026}, {23046, 39899}, {32455, 48879}, {34379, 50832}, {38079, 50958}, {45759, 50967}, {48906, 51132}, {50961, 50993}
X(51180) = midpoint of X(i) and X(j) for these {i,j}: {50954, 50974}, {50962, 50966}
X(51180) = reflection of X(i) in X(j) for these {i,j}: {50978, 50980}, {50987, 50979}
X(51180) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {182, 50985, 50981}, {1353, 50978, 51140}, {1353, 50979, 50986}, {12007, 50977, 50979}, {48876, 50979, 51138}, {50978, 50987, 50980}, {50978, 51140, 50986}, {50979, 50985, 182}, {50979, 50986, 549}, {50979, 51140, 50978}
X(51181) lies on these lines: {5, 50957}, {6, 45759}, {140, 50974}, {182, 524}, {193, 41983}, {550, 20423}, {575, 46853}, {597, 3627}, {632, 15069}, {1351, 15714}, {1992, 15712}, {3618, 23046}, {3619, 11539}, {3620, 14890}, {3628, 50954}, {3845, 14561}, {3858, 38079}, {5032, 14891}, {5050, 8703}, {5085, 15711}, {5092, 51132}, {5093, 15759}, {5476, 51026}, {5847, 50826}, {10168, 51128}, {10541, 44682}, {11160, 12108}, {11179, 15699}, {11812, 14912}, {12017, 17504}, {12100, 50962}, {14848, 15704}, {14927, 15687}, {15693, 33748}, {15713, 50994}, {17508, 50970}, {18583, 35404}, {19710, 29317}, {19711, 34380}, {21850, 50971}, {25406, 33699}, {25555, 51129}, {34200, 51028}, {34379, 50833}, {38071, 48906}, {38081, 39870}, {38110, 47354}, {39874, 47478}, {39884, 46267}, {39899, 47598}, {44903, 51024}, {46264, 51167}, {48881, 50664}, {48884, 50959}, {48896, 51165}
X(51181) = midpoint of X(i) and X(j) for these {i,j}: {11179, 47355}, {20423, 50976}, {43273, 50964}, {50979, 50988}
X(51181) = reflection of X(i) in X(j) for these {i,j}: {50981, 50988}, {51128, 10168}, {51141, 50983}
X(51181) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {182, 50979, 50987}, {182, 51138, 50979}, {549, 50979, 50986}, {50977, 50979, 1353}, {50978, 50983, 549}, {50978, 50987, 50983}, {50979, 50980, 51140}, {50979, 50983, 50978}, {50979, 50987, 549}, {50980, 51140, 50978}, {50981, 50988, 549}, {50983, 51140, 50980}, {50983, 51141, 50988}
X(51182) lies on these lines: {4, 50962}, {5, 50961}, {30, 11008}, {69, 47598}, {182, 524}, {193, 5055}, {548, 50967}, {550, 51136}, {1992, 3628}, {3526, 11160}, {3534, 34380}, {3564, 33699}, {3627, 51025}, {3629, 15699}, {3845, 5965}, {3856, 50963}, {3857, 47354}, {3858, 51130}, {5066, 14853}, {5847, 50830}, {6144, 20423}, {8703, 50973}, {10283, 51155}, {11539, 40341}, {11540, 50992}, {14848, 44904}, {15684, 51028}, {15687, 51027}, {15709, 20080}, {15759, 33750}, {34379, 51087}, {35404, 51166}, {38071, 50958}, {39899, 46333}
X(51182) = reflection of X(i) in X(j) for these {i,j}: {50978, 50986}, {50985, 51140}
X(51182) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {549, 50985, 50978}, {549, 50986, 51140}, {1353, 50978, 50987}, {1353, 50981, 50979}, {48876, 50979, 51137}, {50977, 51140, 12007}, {50978, 50979, 50981}, {50978, 50986, 1353}, {50979, 50981, 50987}, {50979, 50982, 549}, {50979, 50985, 50982}, {50982, 51140, 50979}, {50985, 51140, 549}
X(51183) lies on these lines: {5, 11160}, {30, 20080}, {69, 15699}, {182, 524}, {193, 11539}, {550, 50967}, {632, 1992}, {3564, 19710}, {3627, 15069}, {3845, 34380}, {3857, 50963}, {3858, 47354}, {5847, 50831}, {5965, 50965}, {8703, 50974}, {10283, 51004}, {11898, 15687}, {14561, 15533}, {14912, 19711}, {14927, 44903}, {15520, 41152}, {18358, 20423}, {21850, 50958}, {23046, 50954}, {34379, 50823}, {35404, 51023}, {37517, 50960}, {38112, 50952}, {39884, 51166}, {39899, 50966}, {43150, 51129}, {48884, 51025}
X(51183) = reflection of X(i) in X(j) for these {i,j}: {5, 11160}, {15687, 11898}, {50978, 50985}, {50986, 50978}
X(51183) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1353, 50978, 50977}, {48876, 50979, 50984}, {48876, 51140, 50987}, {50978, 50981, 50982}, {50978, 50986, 549}, {50978, 50987, 48876}, {50979, 50982, 50981}, {50979, 50984, 50987}, {50984, 51140, 50979}
X(51184) lies on these lines: {5, 50963}, {30, 3620}, {69, 17504}, {140, 50962}, {141, 38071}, {182, 524}, {518, 50822}, {542, 46853}, {547, 51028}, {550, 599}, {1350, 35404}, {1352, 44903}, {1992, 14869}, {3098, 50958}, {3530, 11160}, {3564, 15711}, {3618, 11539}, {3627, 40107}, {3763, 15699}, {3845, 10516}, {5093, 11540}, {5847, 50832}, {8703, 10519}, {10283, 51156}, {11178, 50970}, {11898, 14891}, {12100, 50974}, {14912, 44580}, {15686, 51023}, {15687, 21356}, {15707, 20080}, {15713, 34380}, {18440, 50969}, {19710, 29012}, {23046, 33878}, {24206, 51166}, {34379, 50825}, {34507, 50971}, {38028, 51153}, {38112, 50953}, {38136, 51143}, {39874, 41982}, {43273, 45759}, {44456, 47599}, {44682, 50961}, {48874, 51022}, {48892, 51134}
X(51184) = midpoint of X(i) and X(j) for these {i,j}: {50954, 50966}, {50955, 50975}, {50963, 50967}, {50978, 50987}
X(51184) = reflection of X(i) in X(j) for these {i,j}: {50979, 51137}, {50980, 50977}, {50987, 50980}
X(51184) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {549, 50978, 50986}, {1353, 50978, 50985}, {3620, 50966, 50954}, {48876, 50977, 50978}, {48876, 50979, 50982}, {50975, 50990, 50955}, {50977, 50978, 549}, {50977, 50979, 50981}, {50977, 50982, 50979}, {50978, 50981, 50979}, {50979, 50980, 51137}, {50979, 50981, 549}, {50979, 50982, 50978}, {50979, 51137, 50987}, {50980, 50987, 549}, {50983, 50985, 1353}
X(51185) lies on these lines: {2, 6}, {30, 47458}, {83, 34505}, {115, 10488}, {154, 10169}, {182, 3534}, {251, 47075}, {376, 10541}, {381, 575}, {511, 15693}, {518, 51105}, {542, 19709}, {549, 11477}, {576, 5054}, {598, 45103}, {1030, 21497}, {1180, 25334}, {1350, 12100}, {1351, 10168}, {1352, 10109}, {1386, 51093}, {1449, 41310}, {1503, 41099}, {1656, 22234}, {1743, 41311}, {2548, 8355}, {2854, 11451}, {2930, 5020}, {3098, 15716}, {3242, 38023}, {3416, 38089}, {3526, 22330}, {3545, 8550}, {3751, 51110}, {3796, 47313}, {3830, 5050}, {3845, 11179}, {3851, 33749}, {3972, 42536}, {4265, 19705}, {4663, 25055}, {4669, 38087}, {4677, 16475}, {4745, 38047}, {4908, 16972}, {5012, 32069}, {5013, 27088}, {5023, 47061}, {5034, 39593}, {5038, 11159}, {5055, 15069}, {5064, 44102}, {5066, 14561}, {5085, 8703}, {5093, 50977}, {5096, 19704}, {5102, 11812}, {5124, 21498}, {5138, 19706}, {5210, 19661}, {5215, 44496}, {5222, 49727}, {5319, 8367}, {5355, 40727}, {5459, 42095}, {5460, 42098}, {5461, 18584}, {5480, 15682}, {5644, 5648}, {5749, 50098}, {5846, 51072}, {5847, 50782}, {6034, 18800}, {6636, 37827}, {6669, 43333}, {6670, 43332}, {6776, 41106}, {7484, 38402}, {7770, 11054}, {7772, 33237}, {7787, 9855}, {7810, 43136}, {7827, 11317}, {7829, 11318}, {7841, 7878}, {7864, 40246}, {8546, 13595}, {8716, 35954}, {8787, 9166}, {8889, 15471}, {9053, 51092}, {9140, 25336}, {10510, 15004}, {10516, 39561}, {10519, 51132}, {11001, 14853}, {11178, 15516}, {11180, 12007}, {11425, 44273}, {11482, 15694}, {11540, 48876}, {12017, 15695}, {12101, 48906}, {12150, 35955}, {13330, 44562}, {14912, 47354}, {14971, 41672}, {15019, 47596}, {15118, 25335}, {15303, 25331}, {15484, 50280}, {15520, 50962}, {15531, 40670}, {15640, 25406}, {15685, 48910}, {15688, 20190}, {15690, 21850}, {15697, 29181}, {15698, 31884}, {15703, 34507}, {15722, 44456}, {15826, 37907}, {16226, 37473}, {16491, 51097}, {16666, 29573}, {16667, 17267}, {16668, 17311}, {16670, 17325}, {16671, 17253}, {16884, 41313}, {16885, 41312}, {17281, 49543}, {17293, 50077}, {17366, 35578}, {17810, 37904}, {18842, 32532}, {19710, 31670}, {20113, 23293}, {21539, 37503}, {22236, 35303}, {22238, 35304}, {22331, 33215}, {22332, 32985}, {22579, 47867}, {22580, 36769}, {25328, 37353}, {25561, 39899}, {26615, 41946}, {26616, 41945}, {26626, 49737}, {28301, 49721}, {28313, 50115}, {28322, 50127}, {28538, 51066}, {33699, 46264}, {33748, 51023}, {34379, 50791}, {34898, 39951}, {35750, 51159}, {36331, 51160}, {36767, 42521}, {37476, 44261}, {37506, 44265}, {38049, 47358}, {38088, 50995}, {38191, 50789}, {38315, 47359}, {38317, 50955}, {43428, 48314}, {43429, 48313}, {46332, 48874}, {47097, 47460}, {47311, 47459}, {47465, 47473}, {47865, 51012}, {47866, 51015}, {48842, 48867}, {48861, 48862}, {48905, 48943}, {49529, 51091}, {49688, 51096}, {49909, 49910}, {50087, 50124}
X(51185) = midpoint of X(i) and X(j) for these {i,j}: {1992, 3620}, {11482, 15694}, {15534, 50989}
X(51185) = reflection of X(i) in X(j) for these {i,j}: {599, 3763}, {3618, 597}, {15533, 50990}, {47353, 50956}, {47358, 51156}, {50783, 51125}, {50790, 51149}, {50963, 5476}, {50989, 50993}, {50993, 2}
X(51185) = complement of X(50990)
X(51185) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 6, 15534}, {2, 69, 51143}, {2, 193, 50994}, {2, 1992, 22165}, {2, 5032, 50992}, {2, 8584, 15533}, {2, 15534, 599}, {2, 22165, 21358}, {2, 50992, 141}, {2, 50993, 3763}, {2, 50994, 20582}, {6, 597, 47352}, {6, 3589, 40341}, {6, 3618, 3763}, {6, 15533, 8584}, {6, 21358, 1992}, {6, 47352, 599}, {6, 47355, 6144}, {141, 41149, 50992}, {576, 46267, 5054}, {599, 47352, 47355}, {1992, 3589, 21358}, {1992, 21358, 40341}, {3589, 22165, 2}, {3618, 3620, 3589}, {3763, 15534, 50989}, {3763, 40341, 3620}, {3763, 50989, 50993}, {5032, 50992, 41149}, {5050, 5476, 43273}, {8584, 15533, 15534}, {8974, 19054, 32787}, {11179, 18583, 38072}, {11179, 38072, 36990}, {13846, 13847, 31489}, {13950, 19053, 32788}, {14561, 50979, 47353}, {15533, 50990, 50989}, {15533, 50993, 50990}, {15534, 47352, 2}, {19053, 19054, 14930}, {20423, 50987, 50968}, {20583, 48310, 69}, {21358, 40341, 599}, {32787, 32788, 7736}, {38047, 51005, 50783}, {38315, 47359, 50790}, {43273, 50963, 51167}, {47359, 51153, 51149}, {48310, 51143, 2}, {50989, 50993, 599}
X(51186) lies on these lines: {2, 6}, {542, 15701}, {547, 11477}, {575, 15723}, {620, 10488}, {1350, 3845}, {1352, 12100}, {1503, 15698}, {2854, 44299}, {2930, 7484}, {3096, 34505}, {3242, 4669}, {3416, 51103}, {3534, 11178}, {3818, 15685}, {3830, 10516}, {3844, 51066}, {4677, 50790}, {4745, 47358}, {5054, 15069}, {5055, 40107}, {5066, 50964}, {5085, 11812}, {5102, 50978}, {5642, 25336}, {5648, 25330}, {5847, 50785}, {7784, 11317}, {7789, 47061}, {7800, 27088}, {7865, 11159}, {7937, 10302}, {8367, 31417}, {8550, 15709}, {8703, 47353}, {9041, 51068}, {10109, 38072}, {10147, 11292}, {10148, 11291}, {10519, 41099}, {10541, 15702}, {10989, 47448}, {11001, 31884}, {11164, 11742}, {11179, 15713}, {11180, 15719}, {11540, 38064}, {11646, 36521}, {13169, 25331}, {14561, 50973}, {14853, 50982}, {15300, 19662}, {15640, 50965}, {15682, 40330}, {15688, 18553}, {15693, 17508}, {15694, 34507}, {15695, 48905}, {15711, 46264}, {15716, 18440}, {16673, 17231}, {16676, 17237}, {17253, 41310}, {17290, 29615}, {17293, 48638}, {17304, 50084}, {17306, 46845}, {17311, 41311}, {17325, 29573}, {18358, 19710}, {18840, 32532}, {18906, 33288}, {19709, 24206}, {21167, 51023}, {25406, 50958}, {25561, 48910}, {25565, 44456}, {28538, 51110}, {29579, 49737}, {29587, 49748}, {29611, 49727}, {31168, 35955}, {33237, 35007}, {34379, 50792}, {37756, 48634}, {37904, 47451}, {38047, 50787}, {38049, 50788}, {38087, 49511}, {38110, 50961}, {38315, 50781}, {47097, 47446}, {47311, 47447}, {47313, 47450}, {47314, 47556}, {47356, 51109}, {47359, 50791}, {49679, 51097}, {49681, 51104}, {49688, 51067}, {50782, 51000}, {50783, 51071}, {50784, 51005}, {50786, 51156}, {50789, 51149}, {51089, 51125}
X(51186) = midpoint of X(i) and X(j) for these {i,j}: {2, 50994}, {599, 47355}, {47353, 50976}
X(51186) = reflection of X(i) in X(j) for these {i,j}: {10541, 15702}, {51128, 20582}
X(51186) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 141, 50993}, {2, 599, 15534}, {2, 3620, 50992}, {2, 15534, 47352}, {2, 21356, 22165}, {2, 22165, 6}, {2, 50990, 8584}, {2, 50991, 15533}, {2, 50992, 597}, {2, 50993, 599}, {2, 51143, 21358}, {6, 21356, 599}, {6, 21358, 20582}, {6, 51128, 47355}, {69, 51127, 6}, {141, 20582, 21356}, {141, 21358, 599}, {141, 51143, 2}, {597, 41152, 50992}, {599, 3763, 47352}, {599, 15534, 50989}, {599, 21358, 3763}, {599, 47352, 40341}, {3619, 47355, 3763}, {3619, 50994, 2}, {3620, 50992, 41152}, {3763, 15534, 2}, {3763, 50993, 50989}, {8584, 50990, 15533}, {8584, 50991, 50990}, {11160, 48310, 6}, {15533, 50991, 599}, {15533, 50993, 50991}, {15534, 50989, 40341}, {20582, 21356, 6}, {20582, 22165, 2}, {21358, 50993, 2}, {22165, 41149, 11160}, {22165, 48310, 41149}, {47352, 50989, 15534}
X(51187) lies on these lines: {2, 6}, {155, 44266}, {182, 15722}, {511, 15685}, {576, 19709}, {1350, 15695}, {1353, 19711}, {3053, 39785}, {3242, 51097}, {3416, 51067}, {3564, 33699}, {3830, 11477}, {3845, 15069}, {3860, 20423}, {4663, 51066}, {5085, 51140}, {5102, 50955}, {5585, 11165}, {5847, 50789}, {5965, 47353}, {7758, 27088}, {7863, 22331}, {7877, 11054}, {7890, 15815}, {8550, 19708}, {9027, 21969}, {10516, 50961}, {10541, 15693}, {10542, 39593}, {11057, 33683}, {11179, 15759}, {11898, 38072}, {12101, 39884}, {13330, 14711}, {15690, 34380}, {15700, 33749}, {15703, 22330}, {15711, 50986}, {16475, 50791}, {16675, 50125}, {17118, 50077}, {17814, 39487}, {19710, 48873}, {31884, 50973}, {33748, 50984}, {34379, 51000}, {34898, 36616}, {37904, 47276}, {38315, 51155}, {40727, 50280}, {41150, 51005}, {44456, 48943}, {44580, 50979}, {47097, 47466}, {47280, 47311}, {47356, 51107}, {47358, 51104}, {47359, 50786}, {47448, 47546}, {47450, 47541}, {47453, 47551}, {49543, 49747}, {50783, 50952}, {50790, 51001}
X(51187) = reflection of X(i) in X(j) for these {i,j}: {599, 193}, {11160, 3629}, {15533, 15534}, {20080, 597}, {40341, 1992}, {47353, 50962}, {50783, 50952}, {50790, 51001}, {50992, 8584}
X(51187) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 69, 51142}, {6, 15533, 50993}, {193, 3619, 3629}, {193, 8584, 15534}, {193, 50992, 8584}, {599, 3589, 21358}, {599, 15534, 8584}, {599, 47352, 3619}, {599, 50992, 15533}, {1992, 21358, 6}, {1992, 40341, 21358}, {3629, 11160, 47352}, {3630, 8584, 51143}, {5858, 5859, 11184}, {8584, 22165, 3589}, {8584, 50992, 599}, {15533, 15534, 6}, {15533, 21358, 22165}, {22165, 40341, 15533}, {41149, 41153, 8584}, {41153, 50992, 50989}, {49905, 49906, 37637}, {49947, 49948, 7735}
X(51188) lies on these lines: {2, 6}, {511, 51027}, {518, 51037}, {542, 15685}, {1350, 15690}, {1352, 3860}, {2930, 9909}, {3242, 51091}, {3416, 51070}, {3564, 19710}, {3830, 15069}, {3845, 11477}, {5085, 19711}, {5206, 39785}, {5648, 25331}, {5847, 50790}, {5965, 15695}, {8550, 15698}, {9872, 34481}, {9939, 44519}, {10488, 15300}, {10516, 50962}, {10541, 15719}, {11054, 44518}, {11055, 44453}, {11179, 15711}, {11646, 41147}, {11898, 48889}, {12101, 34380}, {13169, 25330}, {14023, 27088}, {14912, 50982}, {15693, 20190}, {15707, 33749}, {15716, 17508}, {15722, 50977}, {15723, 22234}, {15759, 50985}, {16673, 50125}, {17131, 50280}, {19709, 34507}, {31884, 50974}, {33699, 36990}, {34379, 50783}, {36386, 42504}, {36388, 42505}, {37904, 47446}, {38047, 50785}, {38049, 50792}, {38315, 51004}, {41150, 49511}, {44580, 48876}, {47276, 47313}, {47356, 51104}, {47358, 51107}, {47359, 50782}, {47451, 47551}, {49919, 49920}, {49959, 49960}, {50791, 51005}, {51000, 51097}
X(51188) = Xreflection of X(i) in X(j) for these {i,j}: {6, 11160}, {599, 40341}, {1992, 3630}, {6144, 599}, {11008, 597}, {15533, 50992}, {15534, 15533}, {47353, 50961}
X(51188) = X{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 69, 41152}, {2, 15533, 50989}, {2, 41149, 6}, {2, 41152, 50993}, {2, 50989, 599}, {6, 15533, 22165}, {6, 20582, 47352}, {69, 193, 51126}, {69, 8584, 50993}, {69, 47352, 599}, {141, 41153, 2}, {1992, 48310, 6}, {3630, 6329, 69}, {3763, 40341, 3630}, {5858, 5859, 7610}, {5862, 5863, 9740}, {6329, 20582, 48310}, {8584, 22165, 20582}, {8584, 41152, 2}, {8584, 50993, 47352}, {11160, 22165, 15533}, {15533, 15534, 599}, {15533, 50992, 40341}, {15533, 50993, 69}, {15534, 40341, 15533}, {15534, 47352, 8584}, {15534, 50989, 2}, {22165, 41149, 2}, {22165, 48310, 50991}, {50990, 51126, 50993}
X(51189) lies on these lines: {2, 6}, {511, 50957}, {518, 50785}, {1350, 15685}, {1352, 33699}, {1503, 50969}, {3534, 34507}, {3564, 19711}, {3830, 18553}, {5054, 33749}, {5085, 15722}, {5847, 50792}, {7860, 11317}, {7879, 11054}, {8703, 15069}, {10516, 50964}, {10519, 51027}, {10541, 15701}, {11179, 44580}, {11477, 19709}, {12101, 51024}, {14711, 44453}, {15690, 48876}, {15693, 40107}, {15695, 31884}, {15716, 50977}, {15759, 43273}, {15815, 39785}, {17814, 44266}, {29317, 47353}, {37904, 47448}, {41150, 47356}, {47276, 47311}, {47358, 51096}, {47359, 50788}, {49511, 51091}, {50076, 50108}, {50782, 50999}, {50784, 51004}, {50787, 51000}, {50791, 50950}, {50967, 51164}
X(51189) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1992, 41153}, {2, 22165, 50989}, {2, 41152, 599}, {2, 50989, 15533}, {2, 50990, 41152}, {2, 50992, 41149}, {69, 599, 21358}, {69, 3620, 32455}, {69, 15534, 15533}, {69, 34573, 40341}, {69, 50991, 15534}, {141, 41149, 2}, {599, 15533, 50993}, {599, 15534, 50991}, {599, 22165, 15533}, {599, 40341, 21356}, {599, 47352, 3620}, {599, 50989, 2}, {3631, 22165, 50990}, {13846, 13847, 37689}, {15533, 21358, 15534}, {15533, 50993, 6}, {15534, 50991, 21358}, {21358, 50991, 50993}, {22165, 41152, 2}, {22165, 50990, 599}, {22165, 50991, 69}, {32455, 50991, 51143}, {49905, 49906, 230}, {49947, 49948, 5304}
X(51190) lies on these lines: {2, 2348}, {6, 7}, {9, 69}, {41, 348}, {141, 18230}, {142, 3618}, {144, 145}, {182, 21151}, {218, 17170}, {497, 10025}, {511, 5759}, {513, 2402}, {516, 3751}, {524, 6172}, {527, 1992}, {575, 38115}, {631, 38117}, {674, 36976}, {742, 5839}, {894, 2550}, {950, 30625}, {954, 37492}, {971, 6776}, {1001, 17257}, {1156, 5848}, {1200, 6168}, {1351, 5762}, {1352, 5817}, {1353, 5843}, {1386, 11038}, {1445, 2183}, {1503, 36991}, {1654, 38057}, {1656, 38166}, {1698, 38194}, {1837, 30694}, {1843, 7717}, {2082, 6604}, {2647, 12560}, {3062, 39878}, {3091, 38145}, {3161, 4437}, {3189, 25242}, {3207, 17081}, {3242, 8236}, {3416, 5686}, {3476, 20096}, {3564, 5779}, {3616, 38048}, {3617, 38190}, {3619, 6666}, {3620, 30833}, {3729, 5853}, {3732, 18391}, {3827, 7672}, {3875, 49783}, {3945, 27475}, {4326, 24708}, {4419, 16973}, {4461, 49688}, {4648, 36404}, {5032, 51002}, {5050, 31657}, {5088, 7960}, {5223, 5847}, {5476, 38073}, {5542, 16475}, {5728, 34381}, {5732, 25406}, {5805, 14853}, {5850, 49455}, {5856, 10755}, {7222, 49481}, {7229, 49524}, {7671, 9004}, {7676, 12329}, {7677, 22769}, {8545, 9028}, {9041, 50839}, {9053, 12630}, {9317, 17079}, {10519, 31658}, {10889, 24705}, {11008, 29605}, {12718, 44670}, {12848, 34371}, {14548, 40131}, {14912, 36996}, {15507, 42884}, {16496, 30331}, {16503, 17321}, {16593, 26685}, {17139, 41610}, {17333, 47357}, {17350, 20533}, {17379, 38053}, {17756, 24499}, {18583, 38107}, {21356, 51152}, {21850, 31671}, {25050, 25304}, {28538, 50835}, {30340, 38046}, {31272, 38195}, {31300, 41845}, {34379, 51090}, {37650, 50011}, {38047, 40333}, {38108, 40330}, {47352, 51151}
X(51190) = midpoint of X(i) and X(j) for these {i,j}: {144, 193}, {3062, 39878}
X(51190) = reflection of X(i) in X(j) for these {i,j}: {7, 6}, {69, 9}, {6172, 50997}, {16496, 30331}, {31671, 21850}, {50995, 51144}, {50996, 6172}, {50999, 47357}
X(51190) = anticomplement of X(47595)
X(51190) = crossdifference of every pair of points on line {926, 20980}
X(51190) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 5838, 673}, {144, 390, 51052}, {4644, 5819, 7}, {50995, 50997, 51144}, {50995, 51144, 6172}
X(51191) lies on these lines: {7, 20582}, {9, 597}, {141, 527}, {144, 599}, {516, 50949}, {518, 3898}, {524, 6172}, {971, 50965}, {5220, 36479}, {5223, 9041}, {5686, 50951}, {5762, 47354}, {5817, 50959}, {5843, 50977}, {5845, 22165}, {5846, 50836}, {5847, 50837}, {5850, 51003}, {5851, 51158}, {8236, 51145}, {9053, 50835}, {9055, 51053}, {11038, 51154}, {17225, 51052}, {18230, 38086}, {21151, 50984}, {21168, 43273}, {28538, 51090}, {38093, 51128}, {38139, 51129}, {47357, 51147}, {48310, 51150}
X(51191) = midpoint of X(i) and X(j) for these {i,j}: {144, 599}, {6172, 50995}, {50996, 50997}
X(51191) = reflection of X(i) in X(j) for these {i,j}: {7, 20582}, {597, 9}, {51144, 6172}, {51147, 47357}
X(51191) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6172, 50996, 50997}, {50995, 50997, 50996}
X(51192) lies on these lines: {1, 69}, {2, 1386}, {6, 8}, {7, 32922}, {9, 49476}, {10, 3618}, {31, 345}, {40, 25406}, {44, 27549}, {75, 4307}, {86, 39581}, {100, 36741}, {141, 3616}, {144, 145}, {182, 5657}, {189, 1814}, {238, 344}, {239, 2550}, {320, 4310}, {329, 32926}, {346, 4676}, {355, 14853}, {387, 5015}, {391, 39587}, {497, 1999}, {511, 944}, {516, 3875}, {517, 6776}, {519, 1992}, {524, 3241}, {527, 49446}, {528, 32029}, {536, 24280}, {542, 7978}, {551, 21356}, {575, 38116}, {597, 50783}, {599, 38314}, {612, 14555}, {613, 18391}, {614, 18141}, {631, 38029}, {726, 24695}, {730, 18906}, {742, 4644}, {752, 24248}, {937, 6765}, {946, 39885}, {952, 1351}, {956, 37492}, {960, 20009}, {962, 1503}, {966, 16830}, {1001, 17316}, {1002, 39713}, {1036, 1791}, {1043, 4339}, {1125, 3619}, {1266, 4312}, {1279, 4851}, {1320, 5848}, {1350, 5731}, {1352, 5603}, {1353, 5844}, {1385, 10519}, {1428, 1788}, {1469, 3476}, {1482, 3564}, {1483, 34380}, {1656, 38040}, {1698, 38049}, {1743, 3717}, {1836, 30699}, {1843, 7718}, {1997, 11814}, {2098, 39873}, {2099, 39897}, {2263, 6604}, {2308, 32854}, {2551, 41261}, {2836, 4430}, {2854, 32298}, {2895, 29815}, {2975, 36740}, {3006, 24597}, {3011, 30828}, {3091, 38035}, {3187, 3434}, {3189, 3779}, {3210, 3474}, {3243, 49771}, {3244, 11008}, {3246, 29583}, {3262, 4008}, {3306, 49987}, {3475, 17778}, {3485, 12588}, {3488, 10477}, {3555, 34381}, {3589, 9780}, {3600, 24471}, {3617, 38047}, {3620, 3622}, {3621, 4663}, {3623, 20080}, {3629, 9053}, {3632, 49529}, {3635, 49505}, {3655, 50967}, {3656, 11180}, {3672, 24723}, {3679, 51005}, {3681, 20020}, {3685, 17314}, {3687, 5269}, {3703, 26065}, {3705, 37642}, {3712, 35261}, {3749, 4028}, {3755, 16834}, {3757, 5712}, {3759, 32850}, {3763, 5550}, {3773, 50300}, {3791, 4865}, {3827, 3868}, {3870, 14547}, {3871, 12329}, {3873, 19993}, {3891, 5905}, {3896, 20075}, {3912, 7290}, {3920, 5739}, {3932, 26685}, {3936, 26228}, {3974, 27064}, {3977, 36277}, {4000, 4645}, {4026, 26626}, {4259, 20040}, {4313, 10387}, {4349, 10436}, {4353, 17274}, {4362, 25385}, {4371, 49481}, {4402, 51150}, {4416, 7174}, {4427, 42058}, {4429, 5222}, {4460, 30332}, {4648, 16823}, {4649, 36479}, {4655, 28498}, {4660, 28512}, {4668, 38191}, {4700, 24393}, {4719, 37339}, {4725, 49467}, {4852, 28566}, {4901, 16670}, {4916, 49706}, {4991, 50287}, {5032, 31145}, {5039, 12195}, {5050, 5690}, {5093, 12645}, {5208, 41718}, {5211, 37684}, {5212, 46917}, {5223, 49527}, {5227, 5250}, {5476, 38074}, {5697, 39900}, {5734, 15069}, {5790, 18583}, {5818, 14561}, {5845, 24841}, {5853, 49495}, {5886, 40330}, {5903, 39901}, {5965, 7979}, {6224, 9024}, {6327, 17150}, {6361, 46264}, {7613, 37756}, {8148, 39899}, {8192, 37491}, {8240, 8424}, {8679, 36977}, {9001, 47729}, {9014, 48298}, {9015, 48304}, {9041, 15534}, {9312, 12573}, {9778, 44882}, {9812, 36990}, {9933, 34382}, {10246, 48876}, {10247, 11898}, {10327, 32911}, {10449, 50629}, {10453, 37676}, {11038, 39567}, {11160, 47358}, {11179, 50810}, {11269, 32844}, {11531, 39878}, {12135, 12167}, {12245, 14912}, {12410, 19459}, {12583, 16212}, {12648, 45729}, {12649, 45728}, {12652, 28849}, {12702, 48906}, {12898, 14984}, {13211, 25320}, {13605, 32261}, {14839, 32451}, {15569, 29585}, {15601, 25101}, {16020, 17234}, {16468, 32847}, {16469, 17353}, {16477, 33165}, {16704, 29832}, {17017, 26034}, {17024, 32863}, {17025, 33086}, {17061, 26132}, {17126, 17740}, {17127, 17776}, {17147, 20064}, {17162, 21283}, {17225, 51056}, {17270, 19868}, {17276, 28570}, {17294, 50294}, {17299, 49484}, {17300, 38053}, {17346, 48856}, {17349, 38057}, {17389, 47357}, {17469, 32852}, {17716, 32861}, {17718, 26245}, {17726, 37660}, {17763, 28808}, {17765, 49497}, {17766, 49488}, {17768, 49453}, {17769, 32935}, {17770, 49455}, {17772, 32941}, {17784, 20043}, {17792, 20036}, {18230, 38048}, {18358, 18493}, {18440, 22791}, {18525, 21850}, {18526, 44456}, {19789, 20292}, {19851, 28629}, {19877, 47355}, {20011, 25050}, {20016, 49531}, {20045, 31034}, {20049, 51155}, {20053, 32455}, {20057, 40341}, {20069, 41839}, {20076, 20082}, {20423, 34627}, {21358, 51006}, {21747, 33161}, {23340, 39902}, {24357, 49478}, {24474, 39903}, {24477, 29840}, {24599, 38186}, {25055, 50781}, {25321, 32278}, {29575, 38025}, {29819, 33080}, {29831, 31017}, {30340, 32093}, {30652, 33168}, {30653, 32849}, {30741, 35466}, {31091, 33114}, {31162, 51023}, {31232, 50752}, {31272, 38050}, {31663, 33750}, {32394, 44668}, {32930, 42032}, {32942, 34255}, {32946, 33144}, {33090, 37685}, {33100, 50071}, {33104, 50756}, {33121, 37666}, {33878, 34773}, {34631, 50974}, {34632, 43273}, {34718, 50979}, {34747, 50952}, {34748, 50962}, {35774, 39875}, {35775, 39876}, {36404, 37654}, {37625, 49164}, {37681, 39570}, {37714, 38146}, {38087, 51072}, {38089, 51066}, {42334, 48802}, {42696, 50314}, {42697, 50017}, {46922, 48849}, {47352, 50949}, {48798, 48857}, {48800, 48861}, {48805, 50079}, {49473, 50316}, {49489, 50282}, {49534, 49712}, {50110, 50836}, {50133, 51099}, {50990, 51103}, {50992, 51071}, {50994, 51105}
X(51192) = midpoint of X(i) and X(j) for these {i,j}: {145, 193}, {3241, 51001}, {8148, 39899}, {11531, 39878}, {18526, 44456}, {34631, 50974}, {34747, 50952}, {34748, 50962}
X(51192) = reflection of X(i) in X(j) for these {i,j}: {1, 49684}, {2, 47356}, {8, 6}, {40, 39870}, {69, 1}, {145, 49681}, {3241, 51000}, {3242, 51147}, {3416, 1386}, {3621, 49688}, {3632, 49529}, {3679, 51005}, {4655, 49472}, {4660, 49477}, {6361, 46264}, {10449, 50629}, {11160, 47358}, {11180, 3656}, {12702, 48906}, {16496, 3244}, {17276, 49463}, {17294, 50294}, {17299, 49484}, {18440, 22791}, {18525, 21850}, {20050, 49679}, {20053, 49690}, {24248, 32921}, {25304, 4259}, {31145, 47359}, {32261, 13605}, {33878, 34773}, {34627, 20423}, {34632, 43273}, {34718, 50979}, {39885, 946}, {39898, 1482}, {48798, 48857}, {48800, 48861}, {48806, 48870}, {49502, 49462}, {49505, 3635}, {49688, 4663}, {50079, 48805}, {50107, 50303}, {50636, 50635}, {50783, 597}, {50810, 11179}, {50950, 551}, {50967, 3655}, {50996, 47357}, {50999, 3241}, {51023, 31162}
X(51192) = anticomplement of X(3416)
X(51192) = anticomplement of the isogonal conjugate of X(3415)
X(51192) = X(3415)-anticomplementary conjugate of X(8)
X(51192) = crossdifference of every pair of points on line {2484, 6371}
X(51192) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 50295, 17321}, {8, 4344, 5263}, {10, 16475, 3618}, {31, 33088, 345}, {40, 39870, 25406}, {141, 38315, 3616}, {145, 390, 49470}, {239, 50289, 2550}, {551, 50950, 21356}, {1386, 3416, 2}, {2308, 32854, 33163}, {3210, 20101, 3474}, {3242, 51000, 51147}, {3242, 51147, 3241}, {3416, 47356, 1386}, {3745, 3966, 2}, {3769, 33071, 2}, {3791, 4865, 33137}, {4649, 49506, 36479}, {5032, 31145, 47359}, {6327, 17150, 19785}, {12627, 19065, 8}, {12628, 19066, 8}, {17126, 32842, 17740}, {17127, 33093, 17776}, {17147, 20064, 44447}, {17469, 32852, 33171}, {24248, 32921, 50101}, {29840, 37683, 24477}, {49232, 49329, 8}, {49233, 49330, 8}, {49470, 49709, 390}, {50999, 51000, 51146}, {51000, 51001, 50999}, {51000, 51148, 51001}
X(51193) lies on these lines: {1, 51153}, {2, 38191}, {8, 48639}, {145, 50950}, {517, 50966}, {519, 3620}, {524, 3241}, {599, 20050}, {952, 50954}, {1992, 20057}, {3244, 11160}, {3616, 9041}, {3618, 38314}, {5603, 50963}, {5657, 50980}, {5731, 50975}, {5846, 50989}, {5847, 51092}, {9053, 51072}, {9778, 50968}, {9779, 51129}, {9780, 50951}, {9812, 51029}, {10246, 50987}, {16200, 51028}, {16496, 51005}, {20049, 49511}, {30614, 31247}, {34379, 51097}, {47358, 50990}, {50783, 51142}, {50789, 50994}, {50790, 50949}, {50952, 51071}, {51004, 51093}, {51126, 51154}
X(51193) = midpoint of X(i) and X(j) for these {i,j}: {50790, 50993}, {50999, 51146}
X(51193) = reflection of X(i) in X(j) for these {i,j}: {50783, 51142}, {50953, 51156}, {50990, 47358}, {51125, 51003}, {51146, 51149}, {51149, 50998}
X(51193) = anticomplement of X(50953)
X(51193) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3241, 50999, 51001}, {3242, 50998, 50999}, {50953, 51156, 2}, {50998, 50999, 3241}, {51146, 51149, 3241}
X(51194) lies on these lines: {1, 6}, {7, 193}, {57, 3684}, {63, 2280}, {69, 142}, {78, 1475}, {141, 16832}, {144, 4393}, {169, 3874}, {182, 21153}, {200, 17754}, {269, 34253}, {282, 14943}, {284, 1444}, {354, 37658}, {391, 11038}, {480, 21010}, {511, 5732}, {516, 4780}, {519, 24247}, {524, 6173}, {527, 1992}, {528, 50131}, {575, 38117}, {599, 38093}, {604, 1445}, {614, 37657}, {672, 3870}, {673, 3759}, {742, 17151}, {966, 38053}, {971, 1351}, {988, 2271}, {1352, 38150}, {1353, 5762}, {1405, 30318}, {1469, 4321}, {1572, 50028}, {1707, 1914}, {2082, 3868}, {2171, 11526}, {2223, 5120}, {2238, 5272}, {2262, 5781}, {2269, 7675}, {2285, 7672}, {2321, 49451}, {2345, 49529}, {2346, 23407}, {2550, 5839}, {2801, 10756}, {2999, 37676}, {3056, 4326}, {3169, 3174}, {3254, 5848}, {3340, 4051}, {3416, 4034}, {3501, 6765}, {3564, 5805}, {3589, 28640}, {3618, 6666}, {3620, 16815}, {3629, 5845}, {3693, 41711}, {3811, 4253}, {3826, 17275}, {3873, 40131}, {3875, 32029}, {3894, 5540}, {3984, 39244}, {4007, 49688}, {4254, 37575}, {4263, 50612}, {4360, 51052}, {4851, 16593}, {4859, 50011}, {4969, 5880}, {5021, 37552}, {5032, 6172}, {5050, 31658}, {5093, 5779}, {5268, 24512}, {5476, 38075}, {5528, 9024}, {5542, 16825}, {5575, 24471}, {5686, 16830}, {5750, 24393}, {5759, 14912}, {5850, 49477}, {5853, 49495}, {7289, 20367}, {8584, 51144}, {9593, 50581}, {11520, 17451}, {11898, 38107}, {15069, 38143}, {15533, 38086}, {16816, 20080}, {16826, 18230}, {17277, 27475}, {17355, 49458}, {17379, 27484}, {17474, 19861}, {18068, 41250}, {18440, 18482}, {18583, 38108}, {20162, 49514}, {20229, 22163}, {20262, 41573}, {20335, 24600}, {21620, 26036}, {21850, 31672}, {24331, 49505}, {25426, 45705}, {25590, 49481}, {28538, 51102}, {29597, 50996}, {31429, 37573}, {31657, 34380}, {31671, 39899}, {37654, 51099}, {38057, 39586}, {38122, 48876}, {39870, 43161}, {41325, 49684}, {46922, 51053}, {47357, 51005}, {48818, 48848}, {50016, 50026}, {50082, 50950}
X(51194) = midpoint of X(i) and X(j) for these {i,j}: {7, 193}, {31671, 39899}
X(51194) = reflection of X(i) in X(j) for these {i,j}: {9, 6}, {69, 142}, {6173, 51002}, {16496, 42871}, {18440, 18482}, {31672, 21850}, {43161, 39870}, {47357, 51005}, {47595, 51150}, {51152, 6173}
X(51194) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1743, 16970}, {6, 1100, 16475}, {6, 16973, 1}, {6, 49509, 36404}, {9, 1449, 16503}, {9, 3243, 51058}, {141, 38186, 20195}, {32029, 49496, 3875}, {36404, 49509, 3731}, {47595, 51002, 51150}, {47595, 51150, 6173}
X(51195) lies on these lines: {7, 597}, {141, 5936}, {142, 20582}, {516, 50971}, {518, 3968}, {524, 6173}, {527, 3589}, {971, 50959}, {4312, 38023}, {5476, 38164}, {5542, 9041}, {5762, 50983}, {5846, 51100}, {5853, 51145}, {6172, 48310}, {9053, 51099}, {9055, 51057}, {11038, 50998}, {11178, 38080}, {21151, 50965}, {21153, 51139}, {25557, 36480}, {34573, 38093}, {36525, 50779}, {36996, 38072}, {38052, 50949}, {38053, 51154}, {38054, 51003}, {38107, 47354}, {38111, 50977}, {38122, 50984}, {38150, 50960}, {47352, 51144}
X(51195) = midpoint of X(i) and X(j) for these {i,j}: {7, 597}, {6173, 51150}, {51002, 51151}
X(51195) = reflection of X(20582) in X(142)
X(51195) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 38086, 597}, {6173, 51002, 51151}, {51150, 51151, 51002}
X(51196) lies on these lines: {1, 193}, {6, 10}, {8, 17120}, {9, 50284}, {31, 4028}, {40, 14912}, {44, 4078}, {58, 332}, {69, 1125}, {86, 39580}, {141, 19862}, {142, 4974}, {145, 25269}, {182, 10164}, {226, 3791}, {238, 3879}, {239, 50307}, {306, 2308}, {355, 5093}, {391, 39586}, {511, 4297}, {515, 1351}, {516, 4780}, {517, 1353}, {518, 3244}, {519, 1992}, {524, 551}, {527, 32921}, {542, 11599}, {575, 38118}, {597, 3844}, {599, 19883}, {613, 11019}, {726, 32451}, {730, 5052}, {742, 50117}, {752, 3755}, {946, 3564}, {962, 39878}, {993, 37492}, {1069, 45728}, {1100, 50290}, {1210, 27401}, {1352, 3817}, {1385, 34380}, {1449, 50295}, {1469, 4315}, {1503, 51118}, {1699, 5921}, {1738, 3759}, {1757, 49476}, {1829, 46444}, {1843, 31757}, {1999, 17777}, {2321, 4672}, {2550, 50022}, {2784, 10753}, {2796, 8593}, {2836, 25329}, {2948, 25321}, {3011, 31034}, {3056, 4314}, {3187, 41011}, {3241, 50952}, {3242, 15534}, {3589, 51073}, {3616, 17252}, {3618, 3634}, {3619, 19878}, {3620, 3624}, {3625, 4663}, {3635, 16496}, {3636, 11008}, {3655, 50962}, {3663, 17770}, {3664, 16825}, {3679, 5032}, {3696, 4969}, {3707, 3842}, {3745, 4104}, {3773, 50115}, {3779, 50590}, {3821, 4991}, {3827, 4084}, {3828, 50950}, {3840, 37676}, {3874, 34381}, {3875, 24695}, {3883, 4649}, {3912, 16468}, {3932, 16669}, {3946, 4655}, {3947, 12588}, {3986, 16972}, {4001, 17017}, {4026, 16666}, {4035, 6679}, {4054, 50756}, {4062, 21747}, {4085, 28498}, {4098, 50995}, {4138, 32946}, {4260, 9025}, {4292, 39901}, {4356, 16973}, {4368, 42057}, {4418, 50306}, {4464, 49452}, {4480, 49445}, {4644, 50020}, {4645, 17121}, {4667, 24325}, {4669, 8584}, {4676, 17377}, {4733, 50082}, {4743, 28494}, {4753, 24393}, {4852, 17768}, {5034, 31396}, {5039, 49545}, {5050, 6684}, {5097, 38155}, {5121, 37684}, {5257, 50293}, {5267, 36740}, {5294, 32852}, {5476, 38076}, {5493, 8550}, {5542, 50023}, {5839, 50314}, {5848, 21630}, {5850, 49455}, {5852, 49463}, {5853, 49497}, {5886, 11898}, {6144, 38315}, {7191, 20086}, {7277, 49483}, {7290, 49768}, {9001, 48284}, {9028, 49683}, {9031, 49288}, {9041, 41149}, {9791, 29584}, {10165, 48876}, {10171, 40330}, {10175, 18583}, {10624, 39900}, {10789, 39141}, {10916, 41610}, {11160, 25055}, {11179, 50808}, {11180, 50802}, {11365, 19588}, {11574, 31737}, {11711, 14645}, {12053, 39873}, {12167, 49542}, {12512, 25406}, {12699, 39899}, {13912, 48764}, {13975, 48765}, {14853, 19925}, {14927, 28158}, {15069, 38035}, {15254, 17390}, {15533, 38023}, {15808, 40341}, {16477, 17353}, {16670, 49766}, {16704, 29639}, {16823, 20090}, {16834, 24248}, {17023, 33082}, {17364, 24231}, {17766, 49685}, {17771, 49472}, {17781, 32928}, {18440, 18483}, {18481, 44456}, {19065, 49079}, {19066, 49078}, {19459, 49553}, {20423, 34648}, {20583, 38098}, {21850, 31673}, {24239, 37683}, {24280, 50129}, {24295, 29594}, {24342, 50095}, {24349, 50017}, {24597, 50752}, {24603, 43997}, {25320, 32261}, {26723, 32949}, {28558, 50109}, {28580, 49486}, {31162, 50974}, {31399, 38167}, {31730, 48906}, {32930, 50292}, {33071, 41629}, {33104, 50758}, {34628, 51028}, {34638, 43273}, {34641, 47359}, {37595, 41002}, {38054, 47595}, {38087, 51067}, {39874, 41869}, {41662, 48932}, {45729, 49626}, {46922, 48853}, {49473, 50294}, {49474, 49770}, {49498, 49771}, {49527, 49712}, {49531, 50026}, {49750, 49767}, {49772, 50289}, {50091, 50124}, {50992, 51108}
X(51196) = midpoint of X(i) and X(j) for these {i,j}: {1, 193}, {962, 39878}, {3241, 50952}, {3655, 50962}, {3679, 51001}, {3875, 24695}, {12699, 39899}, {15534, 47356}, {18481, 44456}, {31162, 50974}, {34628, 51028}, {39874, 41869}
X(51196) = reflection of X(i) in X(j) for these {i,j}: {10, 6}, {69, 1125}, {551, 51005}, {1843, 31757}, {2321, 4672}, {3244, 49684}, {3625, 49529}, {3663, 49477}, {3755, 49489}, {3821, 4991}, {4133, 3923}, {4297, 39870}, {4655, 3946}, {4663, 32455}, {4780, 49488}, {11160, 50787}, {11180, 50802}, {16496, 3635}, {18440, 18483}, {31673, 21850}, {31730, 48906}, {31737, 11574}, {34638, 43273}, {34641, 47359}, {34648, 20423}, {39885, 19925}, {49488, 4856}, {49505, 1}, {49511, 1386}, {49529, 4663}, {49536, 3751}, {49750, 49767}, {50091, 50124}, {50781, 597}, {50808, 11179}, {50950, 3828}, {51004, 551}, {51071, 47356}
X(51196) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 16475, 1125}, {141, 38049, 19862}, {1386, 49511, 551}, {3244, 49705, 30331}, {3244, 51090, 3993}, {3686, 50302, 10}, {3821, 4991, 50114}, {3993, 49710, 51090}, {4062, 21747, 35263}, {4753, 50288, 24393}, {5032, 51001, 3679}, {5750, 50308, 10}, {11160, 25055, 50787}, {13883, 49347, 10}, {13936, 49348, 10}, {14853, 39885, 19925}, {16477, 32846, 17353}, {32946, 40940, 4138}, {49511, 51005, 1386}, {49547, 49586, 10}, {49548, 49587, 10}, {51004, 51005, 51153}
X(51197) lies on these lines: {2, 50788}, {10, 1992}, {69, 19883}, {193, 519}, {515, 50962}, {516, 50974}, {517, 50986}, {518, 51059}, {524, 551}, {542, 51118}, {597, 51073}, {599, 19862}, {1125, 11160}, {1351, 34648}, {3244, 51000}, {3625, 28538}, {3629, 38098}, {3751, 34641}, {3817, 50955}, {3828, 5032}, {4663, 50951}, {4669, 5847}, {6144, 47356}, {6776, 34638}, {8584, 50781}, {10164, 50979}, {10165, 50978}, {15533, 50792}, {16475, 50787}, {16496, 51146}, {17770, 49543}, {20080, 25055}, {20583, 38089}, {22165, 38049}, {28164, 51028}, {34379, 50999}, {38054, 51152}, {47358, 51104}, {49684, 50998}, {50786, 51067}, {51089, 51145}
X(51197) = midpoint of X(i) and X(j) for these {i,j}: {6144, 47356}, {50952, 51001}
X(51197) = reflection of X(i) in X(j) for these {i,j}: {10, 1992}, {11160, 1125}, {34638, 6776}, {34641, 3751}, {34648, 1351}, {49505, 47356}, {50781, 8584}, {50992, 50787}, {51004, 51005}, {51005, 51155}
X(51197) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {193, 51001, 50952}, {16475, 50787, 51109}, {16475, 50992, 50787}, {49511, 51005, 51006}, {51003, 51005, 51153}, {51003, 51153, 551}, {51004, 51005, 551}, {51004, 51153, 51003}, {51005, 51156, 1386}
X(51198) lies on these lines: {6, 11}, {69, 3035}, {100, 193}, {104, 14912}, {119, 3564}, {120, 4585}, {141, 31235}, {182, 21154}, {214, 34379}, {511, 24466}, {518, 1317}, {524, 6174}, {528, 1992}, {575, 38119}, {651, 18343}, {952, 1353}, {1145, 5847}, {1351, 5840}, {1387, 16475}, {1862, 46444}, {2787, 5477}, {2829, 6776}, {3618, 6667}, {3629, 3779}, {3738, 20455}, {5032, 10707}, {5050, 6713}, {5093, 10738}, {5095, 8674}, {5476, 38077}, {5800, 13273}, {9028, 12831}, {9037, 15326}, {9041, 50846}, {10058, 37492}, {10711, 50974}, {10728, 39874}, {10742, 39899}, {10956, 39897}, {11008, 35023}, {11570, 34381}, {11898, 38752}, {12735, 16496}, {12775, 39877}, {18583, 23513}, {20958, 26932}, {25406, 38759}, {25416, 49684}, {28538, 50842}, {33814, 34380}, {34123, 49511}, {34789, 39878}, {38760, 48876}, {38761, 48906}
X(51198) = midpoint of X(i) and X(j) for these {i,j}: {100, 193}, {6776, 10759}, {10711, 50974}, {10728, 39874}, {10742, 39899}, {34789, 39878}
X(51198) = reflection of X(i) in X(j) for these {i,j}: {11, 6}, {69, 3035}, {6174, 51008}, {16496, 12735}, {25416, 49684}, {38761, 48906}, {51007, 51157}
X(51198) = crossdifference of every pair of points on line {928, 10756}
X(51198) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1317, 6068, 51062}, {51007, 51008, 51157}, {51007, 51157, 6174}
X(51199) lies on these lines: {100, 597}, {214, 9041}, {518, 50844}, {524, 6174}, {528, 3589}, {952, 50951}, {2802, 51006}, {2829, 50971}, {3035, 20582}, {5528, 38088}, {5541, 38023}, {5840, 50959}, {5846, 50841}, {5847, 50845}, {5848, 50991}, {5854, 51145}, {6154, 38090}, {6224, 38087}, {9053, 50843}, {10707, 48310}, {10711, 44882}, {12331, 38064}, {13199, 38072}, {15015, 47359}, {20583, 35023}, {21154, 51139}, {34123, 51154}, {34474, 50965}, {38752, 47354}, {38758, 51025}, {38760, 50984}
X(51199) = midpoint of X(i) and X(j) for these {i,j}: {100, 597}, {6174, 51157}, {10711, 44882}, {51008, 51158}
X(51199) = reflection of X(20582) in X(3035)
X(51199) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6174, 51008, 51158}, {51157, 51158, 51008}
X(51200) lies on these lines: {2, 6782}, {3, 9115}, {6, 13}, {15, 524}, {16, 11179}, {17, 15069}, {18, 575}, {30, 23006}, {62, 8550}, {69, 618}, {141, 36770}, {182, 16242}, {193, 616}, {395, 50979}, {396, 3564}, {511, 5473}, {518, 7975}, {530, 1992}, {531, 8593}, {533, 22687}, {543, 23013}, {576, 16964}, {597, 22489}, {599, 16241}, {619, 5182}, {1350, 42529}, {1351, 42154}, {1352, 36765}, {1353, 6772}, {1503, 36961}, {2482, 51014}, {2782, 41746}, {2854, 30439}, {3180, 5979}, {3181, 5980}, {3200, 15462}, {3411, 33749}, {3618, 6669}, {5026, 51013}, {5032, 5334}, {5039, 12205}, {5050, 6771}, {5093, 13103}, {5321, 25154}, {5339, 11482}, {5459, 18581}, {5460, 11161}, {5464, 18800}, {5478, 14853}, {5847, 12781}, {5921, 43403}, {5965, 36782}, {6054, 6783}, {6104, 14173}, {6108, 6770}, {6109, 9762}, {6115, 37640}, {6776, 10653}, {6780, 9114}, {8584, 22580}, {8724, 9117}, {8787, 51015}, {9019, 36979}, {9143, 37776}, {9830, 22579}, {9916, 19459}, {10168, 33416}, {10753, 41023}, {11178, 16966}, {11180, 18582}, {11477, 42157}, {11581, 22826}, {11645, 19106}, {11705, 16475}, {12007, 22511}, {12142, 12167}, {12177, 22997}, {12942, 39897}, {12952, 39873}, {13105, 45729}, {13107, 45728}, {13705, 22631}, {13825, 22602}, {15533, 36767}, {15534, 25235}, {16267, 36771}, {16268, 46054}, {16644, 50955}, {16941, 36320}, {16962, 36764}, {16967, 47352}, {18358, 43104}, {19924, 42099}, {20415, 42153}, {20423, 36970}, {20583, 43419}, {21356, 42092}, {21358, 33417}, {21359, 51016}, {21467, 40855}, {21850, 42940}, {22491, 40671}, {22496, 42035}, {22847, 42778}, {25166, 44488}, {25555, 42580}, {28538, 50848}, {33878, 42626}, {34379, 51114}, {34394, 38413}, {35749, 49827}, {35750, 49876}, {36251, 42999}, {36363, 43228}, {36383, 43229}, {36768, 50992}, {36769, 42511}, {36968, 43273}, {37517, 43245}, {38079, 43101}, {41039, 41060}, {41113, 47865}, {42429, 48905}, {42913, 47610}, {42943, 48906}, {42990, 44512}, {43150, 43544}, {43200, 50664}, {43399, 51022}, {43484, 51138}, {47861, 51023}
X(51200) = midpoint of X(i) and X(j) for these {i,j}: {193, 616}, {39899, 48655}
X(51200) = reflection of X(i) in X(j) for these {i,j}: {13, 6}, {69, 618}, {5463, 51012}, {5464, 18800}, {10653, 41620}, {10654, 47863}, {11161, 5460}, {18440, 22796}, {22580, 8584}, {23006, 41745}, {35752, 22580}, {36776, 12177}, {51010, 51159}, {51011, 5463}, {51013, 5026}, {51014, 2482}, {51015, 8787}
X(51200) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 6777, 41042}, {15, 22998, 5463}, {381, 5472, 13}, {6268, 19074, 13}, {6270, 19073, 13}, {6770, 37641, 6108}, {6779, 36967, 5473}, {9112, 41042, 13}, {16962, 36766, 36764}, {49208, 49305, 13}, {49209, 49306, 13}, {51010, 51012, 51159}, {51010, 51159, 5463}
X(51201) lies on these lines: {6, 22489}, {13, 1992}, {15, 524}, {193, 530}, {531, 23006}, {533, 12155}, {542, 1351}, {599, 36770}, {618, 11160}, {3180, 9762}, {3564, 22495}, {3629, 22580}, {5032, 5459}, {5182, 36388}, {5210, 9115}, {5464, 5477}, {5469, 11161}, {5847, 50848}, {6780, 36777}, {8584, 22846}, {8593, 9114}, {8787, 51013}, {9112, 50855}, {9116, 14645}, {10754, 22577}, {18800, 51014}, {21156, 50979}, {34379, 50849}, {36765, 50955}, {36767, 50992}, {41022, 50974}
X(51201) = reflection of X(i) in X(j) for these {i,j}: {13, 1992}, {5464, 5477}, {9114, 8593}, {11160, 618}, {22577, 10754}, {22580, 3629}, {51011, 51012}, {51013, 8787}, {51014, 18800}
X(51201) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {22998, 36775, 5463}, {51011, 51012, 5463}
X(51202) lies on these lines: {13, 20582}, {15, 524}, {141, 530}, {518, 50847}, {542, 8703}, {597, 618}, {599, 616}, {1351, 49961}, {2482, 51160}, {3589, 22580}, {5008, 9115}, {5846, 50849}, {5969, 33459}, {5979, 51161}, {8584, 36768}, {8595, 35943}, {9041, 12781}, {9053, 50848}, {9116, 35692}, {9762, 44383}, {11295, 22861}, {14145, 15533}, {21156, 50984}, {21356, 42120}, {22489, 34573}, {28538, 51114}, {29181, 41042}, {33474, 51162}, {35750, 50993}, {35751, 50991}, {35752, 51143}, {36765, 50959}, {41022, 50965}, {42121, 48310}, {48311, 51128}
X(51202) = midpoint of X(i) and X(j) for these {i,j}: {599, 616}, {5463, 51010}, {51011, 51012}
X(51202) = reflection of X(i) in X(j) for these {i,j}: {13, 20582}, {597, 618}, {22580, 3589}, {51159, 5463}, {51160, 2482}
X(51202) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5463, 51011, 51012}, {51010, 51012, 51011}
X(51203) lies on these lines: {2, 6783}, {3, 9117}, {6, 13}, {15, 11179}, {16, 524}, {17, 575}, {18, 15069}, {30, 23013}, {61, 8550}, {69, 619}, {141, 50859}, {182, 16241}, {193, 617}, {395, 3564}, {396, 50979}, {511, 5474}, {518, 7974}, {530, 8593}, {531, 1992}, {532, 22689}, {543, 23006}, {576, 16965}, {597, 22490}, {599, 16242}, {618, 5182}, {1152, 35748}, {1350, 42528}, {1351, 42155}, {1352, 37835}, {1353, 6775}, {1503, 36962}, {2482, 51011}, {2782, 41745}, {2854, 30440}, {3180, 5981}, {3181, 5978}, {3201, 15462}, {3412, 33749}, {3618, 6670}, {5026, 51010}, {5032, 5335}, {5039, 12204}, {5050, 6774}, {5093, 13102}, {5318, 25164}, {5340, 11482}, {5459, 11161}, {5460, 18582}, {5463, 18800}, {5479, 14853}, {5847, 12780}, {5921, 43404}, {6054, 6782}, {6105, 14179}, {6108, 9760}, {6109, 6773}, {6114, 37641}, {6776, 10654}, {6779, 9116}, {8584, 22579}, {8724, 9115}, {8787, 51012}, {9019, 36981}, {9143, 37775}, {9830, 22580}, {9915, 19459}, {10168, 33417}, {10753, 41022}, {11178, 16967}, {11180, 18581}, {11477, 42158}, {11582, 22827}, {11645, 19107}, {11706, 16475}, {12007, 22510}, {12141, 12167}, {12177, 22998}, {12941, 39897}, {12951, 39873}, {13104, 45729}, {13106, 45728}, {13703, 22633}, {13823, 22604}, {15534, 25236}, {16267, 46053}, {16645, 50955}, {16940, 36318}, {16966, 47352}, {18358, 43101}, {19924, 42100}, {20416, 42156}, {20423, 36969}, {20583, 43418}, {21356, 42089}, {21358, 33416}, {21360, 51018}, {21466, 40854}, {21850, 42941}, {22492, 40672}, {22495, 42036}, {22893, 42777}, {25156, 44487}, {25555, 42581}, {28538, 50851}, {33878, 42625}, {34379, 51115}, {34395, 38414}, {36252, 42998}, {36327, 49826}, {36331, 49875}, {36362, 43229}, {36382, 43228}, {36967, 43273}, {37517, 43244}, {38079, 43104}, {41038, 41061}, {41112, 47866}, {42430, 48905}, {42510, 47867}, {42912, 47611}, {42942, 48906}, {42991, 44511}, {43150, 43545}, {43199, 50664}, {43400, 51022}, {43483, 51138}, {47862, 51023}
X(51203) = midpoint of X(i) and X(j) for these {i,j}: {193, 617}, {39899, 48656}
X(51203) = reflection of X(i) in X(j) for these {i,j}: {14, 6}, {69, 619}, {5463, 18800}, {5464, 51015}, {10653, 47864}, {10654, 41621}, {11161, 5459}, {18440, 22797}, {22579, 8584}, {23013, 41746}, {36330, 22579}, {51010, 5026}, {51011, 2482}, {51012, 8787}, {51013, 51160}, {51014, 5464}
X(51203) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 6778, 41043}, {16, 22997, 5464}, {381, 5471, 14}, {6269, 19076, 14}, {6271, 19075, 14}, {6773, 37640, 6109}, {6780, 36968, 5474}, {9113, 41043, 14}, {49210, 49307, 14}, {49211, 49308, 14}, {51013, 51015, 51160}, {51013, 51160, 5464}
X(51204) lies on these lines: {6, 22490}, {14, 1992}, {16, 524}, {193, 531}, {530, 23013}, {532, 12154}, {542, 1351}, {619, 11160}, {3181, 9760}, {3564, 22496}, {3629, 22579}, {5032, 5460}, {5182, 36386}, {5210, 9117}, {5463, 5477}, {5470, 11161}, {5847, 50851}, {8584, 22891}, {8593, 9116}, {8787, 51010}, {9113, 50858}, {9114, 14645}, {10754, 22578}, {18800, 51011}, {21157, 50979}, {34379, 50852}, {41023, 50974}
X(51204) = reflection of X(i) in X(j) for these {i,j}: {14, 1992}, {5463, 5477}, {9116, 8593}, {11160, 619}, {22578, 10754}, {22579, 3629}, {51010, 8787}, {51011, 18800}, {51014, 51015}
X(51204) = {X(51014),X(51015)}-harmonic conjugate of X(5464)
X(51205) lies on these lines: {14, 20582}, {16, 524}, {141, 531}, {518, 50850}, {542, 8703}, {597, 619}, {599, 617}, {1351, 49962}, {2482, 51159}, {3589, 22579}, {5008, 9117}, {5846, 50852}, {5969, 33458}, {5978, 51162}, {8594, 35942}, {9041, 12780}, {9053, 50851}, {9114, 35696}, {9760, 44382}, {11296, 22907}, {14144, 15533}, {21157, 50984}, {21356, 42119}, {22490, 34573}, {28538, 51115}, {29181, 41043}, {33475, 51161}, {36329, 50991}, {36330, 51143}, {36331, 50993}, {41023, 50965}, {42124, 48310}, {48312, 51128}
X(51205) = midpoint of X(i) and X(j) for these {i,j}: {599, 617}, {5464, 51013}, {51014, 51015}
X(51205) = reflection of X(i) in X(j) for these {i,j}: {14, 20582}, {597, 619}, {22579, 3589}, {51159, 2482}, {51160, 5464}
X(51205) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5464, 51014, 51015}, {51013, 51015, 51014}
X(51206) lies on these lines: {3, 6}, {4, 33518}, {13, 524}, {14, 20423}, {30, 23006}, {69, 623}, {115, 20425}, {141, 16966}, {193, 621}, {202, 8540}, {298, 6115}, {316, 33517}, {323, 37776}, {531, 1992}, {542, 23004}, {597, 16242}, {599, 37832}, {1080, 6782}, {1352, 16808}, {1353, 42118}, {1503, 19106}, {2854, 10657}, {2987, 3457}, {3170, 44122}, {3180, 5978}, {3200, 18374}, {3564, 5318}, {3589, 33416}, {3618, 6671}, {3751, 44659}, {5321, 21850}, {5475, 20426}, {5476, 37835}, {5480, 16809}, {5847, 50853}, {5921, 42134}, {5965, 22900}, {6108, 37786}, {6109, 37641}, {6403, 10641}, {6776, 42086}, {6779, 51012}, {7006, 19369}, {7684, 14853}, {7737, 23013}, {8550, 42158}, {8584, 41100}, {9023, 9162}, {9970, 10658}, {10516, 42919}, {10519, 42092}, {10661, 34382}, {10676, 34779}, {10677, 44668}, {11002, 37775}, {11160, 43403}, {11178, 41098}, {11179, 36968}, {11476, 39588}, {11542, 34380}, {11707, 16475}, {11898, 42128}, {14561, 16967}, {14848, 16645}, {14912, 36993}, {14927, 42113}, {14984, 36978}, {15069, 42813}, {15533, 41121}, {15534, 41107}, {15993, 22511}, {16267, 46054}, {16627, 18358}, {16628, 39590}, {18440, 42094}, {18583, 23303}, {19107, 31670}, {19130, 42918}, {19140, 32302}, {20080, 22113}, {21356, 42911}, {21359, 36771}, {22165, 49907}, {23302, 48876}, {24206, 42915}, {25406, 42091}, {25555, 42937}, {29181, 42099}, {36208, 46342}, {36766, 51010}, {38136, 42107}, {39874, 42141}, {39884, 42102}, {39899, 42127}, {40107, 42488}, {40330, 42114}, {41119, 50992}, {42088, 48906}, {42100, 46264}, {42796, 51138}, {42943, 50979}, {42974, 50962}, {43245, 51166}, {43544, 50982}
X(51206) = midpoint of X(193) and X(621)
X(51206) = reflection of X(i) in X(j) for these {i,j}: {6, 44498}, {15, 6}, {69, 623}, {22495, 22580}, {33878, 36755}, {50855, 51017}, {51016, 51161}
X(51206) = 2nd-Lemoine-circle-inverse of X(36758)
X(51206) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 15, 36757}, {6, 11173, 41407}, {6, 11481, 5050}, {6, 11486, 36758}, {6, 19780, 1692}, {15, 62, 41406}, {15, 10646, 21158}, {15, 34755, 39554}, {187, 5611, 15}, {1666, 1667, 36758}, {5093, 11486, 6}, {5611, 11486, 187}, {8586, 44488, 15}, {23004, 47859, 36969}, {51016, 51017, 51161}, {51016, 51161, 50855}
X(51207) lies on these lines: {3, 6}, {4, 33517}, {13, 20423}, {14, 524}, {30, 23013}, {69, 624}, {115, 20426}, {141, 16967}, {193, 622}, {203, 8540}, {299, 6114}, {316, 33518}, {323, 37775}, {383, 6783}, {530, 1992}, {542, 23005}, {597, 16241}, {599, 37835}, {1352, 16809}, {1353, 42117}, {1503, 19107}, {2854, 10658}, {2987, 3458}, {3171, 44083}, {3181, 5979}, {3201, 18374}, {3564, 5321}, {3589, 33417}, {3618, 6672}, {3751, 44660}, {5318, 21850}, {5475, 20425}, {5476, 37832}, {5480, 16808}, {5847, 50856}, {5921, 42133}, {5965, 22856}, {6108, 37640}, {6109, 37785}, {6403, 10642}, {6776, 42085}, {6779, 36772}, {6780, 51015}, {7005, 19369}, {7685, 14853}, {7737, 23006}, {8550, 42157}, {8584, 41101}, {9023, 9163}, {9970, 10657}, {10516, 42918}, {10519, 42089}, {10662, 34382}, {10675, 34779}, {10678, 44668}, {11002, 37776}, {11160, 43404}, {11178, 41094}, {11179, 36967}, {11475, 39588}, {11543, 34380}, {11708, 16475}, {11898, 42125}, {14561, 16966}, {14848, 16644}, {14912, 36995}, {14927, 42112}, {14984, 36980}, {15069, 42814}, {15533, 41122}, {15534, 41108}, {15993, 22510}, {16268, 46053}, {16626, 18358}, {16629, 39590}, {18440, 42093}, {18583, 23302}, {19106, 31670}, {19130, 42919}, {19140, 32301}, {20080, 22114}, {21356, 42910}, {22165, 49908}, {23303, 48876}, {24206, 42914}, {25406, 42090}, {25555, 42936}, {29181, 42100}, {36209, 46343}, {38136, 42110}, {39874, 42140}, {39884, 42101}, {39899, 42126}, {40107, 42489}, {40330, 42111}, {41120, 50992}, {42087, 48906}, {42099, 46264}, {42795, 51138}, {42942, 50979}, {42975, 50962}, {43244, 51166}, {43545, 50982}
X(51207) = midpoint of X(193) and X(622)
X(51207) = reflection of X(i) in X(j) for these {i,j}: {6, 44497}, {16, 6}, {69, 624}, {22496, 22579}, {33878, 36756}, {50858, 51019}, {51018, 51162}
X(51207) = 2nd-Lemoine-circle-inverse of X(36757)
X(51207) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 16, 36758}, {6, 11173, 41406}, {6, 11480, 5050}, {6, 11485, 36757}, {6, 19781, 1692}, {16, 61, 41407}, {16, 10645, 21159}, {16, 34754, 39555}, {187, 5615, 16}, {1666, 1667, 36757}, {5093, 11485, 6}, {5615, 11485, 187}, {8586, 44487, 16}, {23005, 47860, 36970}, {51018, 51019, 51162}, {51018, 51162, 50858}
X(51208) lies on these lines: {6, 17}, {14, 5097}, {16, 12007}, {61, 3629}, {69, 629}, {193, 627}, {511, 22890}, {518, 22912}, {524, 41943}, {532, 1992}, {542, 11602}, {1351, 42154}, {1353, 6775}, {3564, 16626}, {3618, 6673}, {3631, 42936}, {5039, 22523}, {5050, 42491}, {5093, 16629}, {5102, 16964}, {5480, 22900}, {5847, 22896}, {6329, 42489}, {6776, 42086}, {8584, 22891}, {8593, 22488}, {11008, 42152}, {11179, 42631}, {11739, 16475}, {12167, 22482}, {14853, 22832}, {14912, 22532}, {15534, 36386}, {16268, 20583}, {18440, 22795}, {18583, 43101}, {19459, 22657}, {22895, 44497}, {22904, 39897}, {22905, 39873}, {22931, 45729}, {22932, 45728}, {31705, 42982}, {32455, 51162}, {33465, 40694}, {34379, 51116}, {37517, 42157}, {39899, 48666}, {42581, 43150}
X(51208) = midpoint of X(i) and X(j) for these {i,j}: {193, 627}, {39899, 48666}
X(51208) = reflection of X(i) in X(j) for these {i,j}: {17, 6}, {69, 629}, {18440, 22795}
X(51208) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {19070, 22899, 17}, {19071, 22898, 17}, {49238, 49335, 17}, {49239, 49336, 17}
X(51209) lies on these lines: {6, 17}, {13, 5097}, {15, 12007}, {62, 3629}, {69, 630}, {193, 628}, {511, 22843}, {518, 22867}, {524, 41944}, {533, 1992}, {542, 11603}, {1351, 42155}, {1353, 6772}, {3564, 16627}, {3618, 6674}, {3631, 42937}, {5039, 22522}, {5050, 42490}, {5093, 16628}, {5102, 16965}, {5480, 22856}, {5847, 22851}, {6329, 42488}, {6776, 42085}, {8584, 22846}, {8593, 22487}, {11008, 42149}, {11179, 42632}, {11740, 16475}, {12167, 22481}, {14853, 22831}, {14912, 22531}, {15534, 36388}, {16267, 20583}, {18440, 22794}, {18583, 43104}, {19459, 22656}, {22849, 44498}, {22859, 39897}, {22860, 39873}, {22886, 45729}, {22887, 45728}, {31706, 42983}, {32455, 51161}, {33464, 40693}, {34379, 51117}, {36763, 43228}, {37517, 42158}, {39899, 48665}, {42580, 43150}
X(51209) = midpoint of X(i) and X(j) for these {i,j}: {193, 628}, {39899, 48665}
X(51209) = reflection of X(i) in X(j) for these {i,j}: {18, 6}, {69, 630}, {18440, 22794}
X(51209) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {19069, 22853, 18}, {19072, 22854, 18}, {49236, 49333, 18}, {49237, 49334, 18}
X(51210) lies on these lines: {1, 23620}, {6, 19}, {48, 77}, {69, 18589}, {78, 20727}, {141, 31261}, {182, 21160}, {193, 4329}, {219, 34381}, {511, 30265}, {516, 4780}, {524, 31158}, {534, 1992}, {610, 5018}, {1100, 1486}, {1386, 44101}, {2191, 46149}, {2876, 3056}, {3618, 40530}, {3751, 44661}, {3811, 14963}, {3951, 3958}, {5839, 11677}, {5847, 50861}, {8680, 49496}, {10602, 44670}, {16972, 44093}, {17275, 23305}, {18161, 39273}, {18732, 22131}, {32451, 46181}
X(51210) = midpoint of X(193) and X(4329)
X(51210) = reflection of X(i) in X(j) for these {i,j}: {19, 6}, {69, 18589}
X(51211) lies on these lines: {2, 38136}, {4, 50954}, {20, 575}, {376, 50987}, {524, 3543}, {542, 50691}, {1992, 49135}, {3091, 51129}, {3146, 50974}, {3523, 50965}, {3618, 10304}, {3620, 3839}, {3763, 50959}, {5476, 50969}, {5480, 15721}, {5731, 51153}, {5847, 50863}, {10303, 51141}, {10519, 50964}, {11001, 33748}, {11160, 50688}, {14848, 50693}, {15640, 29012}, {15682, 50962}, {15683, 50979}, {15684, 50986}, {15692, 19924}, {15697, 29181}, {34379, 50873}, {47354, 50990}, {48872, 51138}, {48910, 51132}, {50687, 50955}, {50689, 50957}
X(51211) = reflection of X(i) in X(j) for these {i,j}: {50966, 50963}, {50967, 50956}, {50975, 20423}, {51023, 51167}, {51029, 51024}
X(51211) = anticomplement of X(50966)
X(51211) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {36990, 51024, 51165}, {50956, 50967, 3620}, {50963, 50966, 2}, {51023, 51029, 51167}, {51023, 51166, 51028}, {51024, 51027, 51163}, {51024, 51028, 3543}, {51024, 51166, 51023}
X(51212) lies on these lines: {2, 1350}, {3, 3618}, {4, 69}, {5, 3619}, {6, 20}, {8, 43216}, {22, 11427}, {23, 15577}, {24, 28708}, {25, 37669}, {30, 1351}, {51, 7386}, {52, 18909}, {64, 15583}, {66, 15077}, {67, 43699}, {74, 25320}, {81, 50698}, {86, 7390}, {141, 3091}, {146, 2854}, {147, 5969}, {152, 2810}, {153, 9024}, {182, 376}, {184, 34608}, {185, 18935}, {186, 47581}, {193, 1503}, {206, 34148}, {263, 37190}, {265, 32247}, {287, 9530}, {297, 10002}, {323, 7519}, {343, 7378}, {378, 37488}, {381, 21356}, {382, 3564}, {388, 3056}, {389, 41256}, {393, 37200}, {394, 6995}, {403, 47468}, {411, 36740}, {428, 14826}, {441, 34815}, {487, 1161}, {488, 1160}, {491, 7000}, {492, 7374}, {497, 1469}, {516, 3751}, {518, 962}, {524, 3543}, {542, 10721}, {547, 50963}, {548, 12017}, {550, 5050}, {573, 36706}, {575, 17538}, {576, 3529}, {578, 1176}, {597, 10304}, {599, 3839}, {611, 4294}, {613, 4293}, {631, 3098}, {858, 37643}, {895, 2777}, {938, 24471}, {966, 7379}, {991, 36698}, {1007, 1513}, {1032, 14944}, {1370, 3060}, {1386, 5731}, {1593, 37491}, {1656, 38136}, {1657, 5093}, {1698, 38146}, {1699, 49511}, {1738, 43173}, {1885, 12167}, {1899, 21969}, {1974, 13346}, {1993, 7500}, {1994, 20062}, {2393, 41735}, {2549, 5052}, {2551, 17792}, {2781, 3448}, {2794, 10754}, {2829, 10755}, {2883, 9924}, {2979, 6997}, {3088, 17834}, {3089, 28419}, {3090, 7944}, {3094, 7736}, {3313, 6815}, {3430, 37176}, {3436, 25304}, {3522, 5085}, {3523, 3589}, {3524, 5476}, {3525, 38317}, {3528, 5092}, {3537, 36987}, {3542, 28408}, {3545, 24206}, {3552, 47619}, {3580, 23049}, {3616, 38035}, {3617, 38144}, {3620, 3832}, {3627, 18440}, {3629, 49135}, {3763, 5056}, {3830, 11180}, {3843, 18358}, {3845, 50990}, {3855, 40107}, {3917, 7392}, {3933, 40268}, {4232, 11064}, {4259, 6836}, {4260, 9535}, {4297, 16475}, {4301, 16496}, {4329, 10394}, {4648, 7385}, {5017, 5999}, {5028, 7737}, {5032, 12007}, {5039, 12203}, {5059, 5102}, {5071, 50977}, {5073, 39899}, {5094, 47582}, {5097, 11001}, {5107, 43618}, {5157, 13434}, {5159, 21970}, {5177, 26543}, {5182, 38738}, {5188, 16043}, {5189, 16981}, {5224, 7407}, {5225, 12589}, {5229, 12588}, {5446, 6643}, {5622, 16111}, {5640, 46336}, {5656, 39879}, {5663, 32255}, {5691, 5847}, {5712, 37443}, {5728, 17170}, {5734, 49465}, {5739, 37456}, {5800, 6925}, {5813, 41228}, {5840, 10759}, {5848, 10724}, {5889, 12324}, {5965, 48884}, {5972, 6353}, {6090, 10301}, {6101, 11487}, {6144, 50691}, {6193, 7553}, {6194, 24256}, {6201, 7389}, {6202, 7388}, {6243, 11411}, {6329, 10541}, {6393, 32816}, {6560, 35841}, {6561, 35840}, {6781, 39764}, {6803, 15644}, {6804, 10110}, {6811, 32805}, {6813, 32806}, {6816, 9969}, {6872, 15988}, {6909, 36741}, {6966, 33844}, {7396, 13567}, {7398, 17811}, {7400, 45089}, {7401, 10625}, {7404, 37486}, {7484, 40918}, {7486, 34573}, {7487, 20806}, {7493, 15107}, {7503, 37485}, {7528, 37484}, {7580, 37492}, {7667, 9777}, {7706, 9967}, {7710, 7774}, {7714, 9306}, {7728, 14984}, {7792, 9748}, {7987, 38049}, {7991, 49529}, {8229, 30828}, {8549, 40318}, {8703, 14848}, {8722, 33215}, {9019, 44439}, {9041, 50872}, {9541, 19145}, {9733, 21736}, {9753, 35387}, {9756, 37667}, {9815, 13348}, {9833, 34779}, {9968, 15801}, {9970, 12383}, {9974, 43408}, {9975, 43407}, {10008, 32827}, {10168, 15698}, {10263, 14790}, {10295, 47571}, {10299, 25555}, {10303, 21167}, {10483, 39901}, {10565, 23292}, {10752, 11061}, {10753, 23698}, {10996, 11574}, {11002, 16063}, {11004, 20063}, {11147, 37461}, {11160, 47353}, {11173, 43448}, {11178, 41099}, {11257, 35439}, {11291, 11824}, {11292, 11825}, {11382, 22555}, {11424, 19126}, {11444, 15435}, {11479, 11821}, {11482, 15704}, {11541, 29323}, {11579, 12244}, {11645, 50974}, {12086, 44883}, {12110, 13355}, {12160, 34781}, {12177, 13172}, {12220, 37201}, {12221, 13748}, {12222, 13749}, {12256, 45488}, {12257, 45489}, {12289, 29012}, {12584, 20125}, {12699, 39898}, {12943, 39897}, {12953, 39873}, {13142, 18945}, {13202, 41737}, {13331, 32522}, {13391, 18420}, {13421, 32140}, {13725, 48883}, {13860, 34229}, {14001, 30270}, {14449, 18951}, {14532, 15048}, {14538, 37172}, {14539, 37173}, {14540, 37177}, {14541, 37178}, {14555, 26118}, {14645, 39838}, {14693, 35383}, {14893, 50978}, {15055, 15118}, {15069, 17578}, {15081, 49116}, {15516, 48920}, {15520, 48879}, {15534, 15640}, {15681, 50979}, {15684, 50962}, {15686, 50975}, {15687, 50955}, {15692, 47352}, {15693, 38079}, {15702, 50966}, {15721, 48310}, {15723, 50980}, {15749, 16774}, {16982, 18952}, {17040, 31371}, {17508, 21735}, {17845, 34774}, {18124, 38442}, {18230, 38145}, {18533, 22151}, {18860, 32985}, {18925, 31305}, {18931, 37489}, {19118, 27082}, {19119, 19467}, {19137, 43652}, {19146, 35946}, {19459, 31802}, {19583, 25332}, {19708, 38064}, {20300, 31074}, {21358, 50959}, {21851, 39571}, {22330, 48891}, {22486, 32986}, {22728, 37348}, {23291, 34609}, {24220, 36660}, {24553, 36007}, {24981, 31383}, {25321, 32233}, {25898, 50408}, {26668, 37254}, {26864, 37899}, {26869, 46517}, {26870, 30258}, {28228, 49536}, {28538, 50864}, {30769, 47296}, {30775, 32225}, {31162, 50999}, {31272, 38147}, {31304, 34117}, {31673, 39885}, {32114, 38791}, {32218, 46451}, {32423, 48679}, {32455, 49140}, {32911, 50699}, {33007, 39141}, {34153, 45016}, {34200, 50969}, {34379, 51118}, {34417, 40132}, {34473, 46453}, {34628, 51005}, {34632, 47359}, {34648, 50950}, {35242, 38118}, {35389, 36998}, {35456, 37466}, {35471, 44469}, {35474, 41371}, {35922, 46124}, {36474, 48875}, {36526, 48934}, {36662, 48888}, {36674, 48908}, {36757, 42150}, {36758, 42151}, {36989, 41719}, {37197, 41584}, {37444, 37473}, {37460, 37497}, {37952, 47455}, {38383, 50640}, {38749, 41400}, {39561, 48892}, {39588, 44492}, {39871, 44438}, {40341, 50688}, {41465, 49669}, {42263, 49228}, {42264, 49229}, {42287, 42352}, {42313, 44924}, {44280, 47457}, {46034, 47286}, {46935, 51128}, {48837, 50600}
X(51212) = midpoint of X(i) and X(j) for these {i,j}: {193, 3146}, {382, 44456}, {3543, 51028}, {5073, 39899}, {11477, 48910}, {15684, 50962}, {33703, 39874}
X(51212) = reflection of X(i) in X(j) for these {i,j}: {3, 21850}, {4, 31670}, {20, 6}, {64, 15583}, {69, 4}, {193, 11477}, {376, 20423}, {1350, 5480}, {1352, 48901}, {1657, 48906}, {1843, 13598}, {3146, 48910}, {3529, 46264}, {3543, 51024}, {5059, 48905}, {5921, 36990}, {6776, 1351}, {7991, 49529}, {9833, 34779}, {9924, 2883}, {10295, 47571}, {11001, 11179}, {11061, 10752}, {11160, 47353}, {11180, 3830}, {11257, 35439}, {11898, 39884}, {12220, 50649}, {12244, 11579}, {12324, 36851}, {12383, 9970}, {13172, 12177}, {14532, 15048}, {14927, 6776}, {15681, 50979}, {15683, 43273}, {16496, 4301}, {17845, 34774}, {18440, 3627}, {19459, 31802}, {20080, 15069}, {26926, 13142}, {32114, 38791}, {32247, 265}, {33703, 43621}, {33878, 5}, {34507, 48895}, {34628, 51005}, {34632, 47359}, {36990, 51163}, {36998, 35389}, {37511, 5446}, {39885, 31673}, {39898, 12699}, {41465, 49669}, {41716, 12294}, {41737, 13202}, {46264, 576}, {48872, 44882}, {48873, 182}, {48874, 18583}, {48880, 575}, {48891, 22330}, {48898, 5097}, {48905, 8550}, {48920, 15516}, {50640, 38383}, {50641, 39838}, {50950, 34648}, {50955, 15687}, {50967, 381}, {50978, 14893}, {50992, 11180}, {50999, 31162}, {51023, 3543}
X(51212) = anticomplement of X(1350)
X(51212) = polar conjugate of X(42373)
X(51212) = anticomplement of the isogonal conjugate of X(3424)
X(51212) = isotomic conjugate of the isogonal conjugate of X(41266)
X(51212) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {3424, 8}, {42287, 4329}
X(51212) = X(48)-isoconjugate of X(42373)
X(51212) = X(1249)-Dao conjugate of X(42373)
X(51212) = crossdifference of every pair of points on line {3049, 47133}
X(51212) = barycentric product X(76)*X(41266)
X(51212) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 42373}, {41266, 6}
X(51212) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 14853, 3618}, {3, 21850, 14853}, {4, 43999, 39530}, {5, 10519, 3619}, {5, 33878, 10519}, {6, 20, 25406}, {6, 48872, 44882}, {20, 15741, 13568}, {23, 37645, 35260}, {51, 7386, 18928}, {52, 34938, 18909}, {182, 48873, 376}, {381, 48876, 40330}, {381, 50967, 21356}, {548, 12017, 33750}, {576, 46264, 14912}, {962, 36991, 51063}, {1160, 36709, 488}, {1161, 36714, 487}, {1350, 5480, 2}, {1351, 6776, 1992}, {1352, 31670, 48901}, {1352, 48901, 4}, {1370, 3060, 11433}, {1657, 5093, 48906}, {1992, 14927, 6776}, {1993, 7500, 11206}, {3098, 14561, 631}, {3529, 14912, 46264}, {3543, 5921, 36990}, {3589, 31884, 3523}, {3620, 3832, 10516}, {3830, 11898, 39884}, {5032, 15683, 43273}, {5085, 48881, 3522}, {5097, 48898, 11179}, {5102, 48905, 8550}, {5189, 16981, 37644}, {5921, 36990, 51023}, {6515, 7391, 32064}, {6560, 35841, 39875}, {6561, 35840, 39876}, {7774, 40236, 7710}, {11160, 50687, 47353}, {11898, 39884, 11180}, {12296, 12297, 382}, {12322, 12323, 32006}, {18583, 48874, 3}, {20423, 48873, 182}, {21167, 47355, 10303}, {21850, 48874, 18583}, {31305, 36747, 18925}, {34609, 41588, 23291}, {36990, 51024, 51163}, {36990, 51163, 3543}, {37200, 44704, 393}, {37517, 43621, 39874}, {40236, 44434, 7774}, {40330, 48876, 21356}, {40330, 50967, 48876}, {44882, 48872, 20}, {47352, 50965, 15692}, {51023, 51024, 51029}, {51024, 51027, 51026}, {51024, 51028, 51023}, {51024, 51166, 51028}, {51024, 51167, 51165}
X(51213) lies on these lines: {2, 29317}, {4, 50957}, {20, 38072}, {376, 50988}, {381, 50981}, {382, 50974}, {524, 3543}, {542, 50690}, {597, 49140}, {1992, 50691}, {3091, 50965}, {3146, 20423}, {3545, 50980}, {3619, 3839}, {3620, 38335}, {3627, 11160}, {3818, 50687}, {3830, 50978}, {3845, 50966}, {3853, 50954}, {5032, 15684}, {5056, 51129}, {5059, 50975}, {5847, 50867}, {10304, 47355}, {11001, 38110}, {11541, 14848}, {15640, 33748}, {15683, 46267}, {15708, 50968}, {15721, 48872}, {25406, 51130}, {31670, 51140}, {31884, 51131}, {33699, 50962}, {34379, 50874}, {35409, 48906}, {47354, 50994}
X(51213) = midpoint of X(51024) and X(51164)
X(51213) = reflection of X(50969) in X(50964)
X(51213) = anticomplement of X(50969)
X(51213) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3543, 51024, 51028}, {50964, 50969, 2}, {51023, 51026, 3543}, {51023, 51029, 51026}, {51024, 51026, 51023}, {51024, 51029, 3543}, {51024, 51163, 51029}, {51024, 51167, 51166}, {51026, 51166, 51167}, {51163, 51165, 51024}, {51166, 51167, 51023}
X(51214) lies on these lines: {2, 5102}, {3, 1992}, {4, 50961}, {6, 15708}, {20, 51136}, {30, 11008}, {69, 1568}, {193, 43273}, {376, 51140}, {381, 50985}, {511, 11001}, {524, 3543}, {542, 33703}, {547, 1351}, {576, 3533}, {599, 5056}, {2080, 11147}, {3091, 51130}, {3523, 20583}, {3524, 50664}, {3618, 11539}, {3629, 10304}, {3630, 50960}, {3832, 11160}, {3839, 40341}, {3845, 34380}, {3850, 50963}, {5032, 50983}, {5050, 19711}, {5097, 15702}, {5476, 50994}, {5731, 51155}, {5847, 50871}, {5965, 15682}, {6776, 15686}, {8550, 50968}, {10519, 11812}, {11179, 50966}, {11180, 38335}, {14853, 50990}, {15533, 50959}, {15534, 25406}, {15690, 50975}, {15692, 51138}, {15697, 51135}, {15719, 39561}, {15723, 48876}, {16200, 50999}, {21850, 50954}, {30392, 51005}, {31884, 41149}, {33878, 50969}, {34379, 51120}, {34507, 50964}, {35401, 39884}, {38155, 50950}
X(51214) = reflection of X(i) in X(j) for these {i,j}: {11160, 11477}, {11180, 44456}, {50967, 50962}, {50973, 51132}, {51023, 51028}, {51027, 51166}
X(51214) = anticomplement of X(50973)
X(51214) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3543, 51027, 51023}, {3543, 51028, 51166}, {5921, 51022, 51023}, {50962, 50967, 1992}, {50973, 51132, 2}, {51024, 51025, 3543}, {51024, 51027, 51025}, {51025, 51166, 51024}, {51027, 51166, 3543}
X(51215) lies on these lines: {2, 3167}, {4, 50962}, {6, 50958}, {20, 542}, {30, 20080}, {69, 10304}, {147, 9740}, {193, 3818}, {376, 11898}, {381, 50986}, {511, 15640}, {524, 3543}, {576, 50964}, {597, 7486}, {599, 3523}, {1352, 5032}, {1353, 5071}, {1503, 50973}, {1992, 3091}, {2996, 9880}, {3524, 39899}, {3545, 50954}, {3620, 11179}, {3629, 50960}, {3630, 50970}, {3832, 50963}, {4232, 44555}, {5068, 14848}, {5085, 50994}, {5093, 41106}, {5731, 51004}, {5847, 50872}, {5965, 36324}, {6054, 37667}, {6776, 15692}, {8724, 35287}, {10303, 34507}, {11177, 37668}, {13449, 41895}, {14853, 50956}, {15533, 15697}, {15534, 50959}, {15682, 34380}, {15683, 50985}, {15702, 50987}, {15705, 48906}, {15721, 21356}, {18440, 50687}, {21358, 51138}, {22165, 25406}, {30769, 40112}, {31884, 51135}, {32972, 49102}, {34379, 50864}, {39874, 50966}, {46264, 50969}, {47353, 51132}
X(51215) = reflection of X(i) in X(j) for these {i,j}: {20, 11160}, {193, 11180}, {376, 11898}, {1992, 15069}, {3543, 5921}, {50967, 50961}, {50974, 50955}, {51023, 51027}, {51028, 51023}
X(51215) = anticomplement of X(50974)
X(51215) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {193, 11180, 3839}, {3620, 11179, 15708}, {5921, 51028, 51023}, {36990, 51166, 51029}, {50955, 50974, 2}, {50961, 50967, 11160}, {51023, 51027, 5921}, {51023, 51028, 3543}, {51023, 51029, 36990}
X(51216) lies on these lines: {2, 6030}, {4, 14848}, {20, 47354}, {30, 3620}, {376, 50980}, {381, 50987}, {382, 11160}, {518, 50863}, {524, 3543}, {542, 17578}, {599, 49135}, {1699, 51153}, {1992, 50688}, {3146, 34507}, {3523, 50971}, {3524, 50957}, {3534, 50981}, {3618, 3839}, {3627, 50962}, {3763, 10304}, {3830, 50974}, {3854, 38064}, {5032, 15687}, {5085, 51133}, {5731, 51156}, {5847, 50873}, {11178, 50969}, {11180, 48884}, {12101, 14912}, {14927, 50983}, {15640, 47353}, {15682, 50955}, {15683, 48920}, {15684, 50978}, {15708, 48905}, {15717, 25561}, {18358, 46333}, {20423, 48895}, {29181, 50989}, {34379, 50866}, {38335, 39874}, {48662, 50986}, {50689, 50964}, {50690, 50961}, {50960, 51126}, {50965, 50993}
X(51216) = midpoint of X(51023) and X(51029)
X(51216) = reflection of X(i) in X(j) for these {i,j}: {43273, 51129}, {50966, 50954}, {50968, 47354}, {50975, 50956}, {50990, 47353}, {51029, 51167}, {51167, 51022}
X(51216) = anticomplement of X(50975)
X(51216) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3543, 51023, 51028}, {36990, 51022, 51023}, {36990, 51024, 51025}, {43273, 51129, 3618}, {50954, 50966, 3620}, {50956, 50975, 2}, {51022, 51023, 3543}, {51022, 51025, 51024}, {51023, 51028, 5921}, {51024, 51025, 51023}, {51029, 51167, 3543}
X(51217) lies on these lines: {2, 50976}, {4, 20190}, {20, 50984}, {30, 3619}, {69, 48943}, {376, 51141}, {381, 50988}, {382, 50967}, {518, 50867}, {524, 3543}, {599, 50691}, {1992, 3627}, {3091, 50971}, {3098, 35409}, {3146, 47354}, {3545, 48892}, {3618, 38335}, {3818, 50966}, {3830, 14853}, {3839, 47355}, {3845, 50975}, {3853, 50963}, {3860, 33750}, {5059, 50968}, {5847, 50874}, {8550, 17578}, {10304, 50960}, {11001, 50956}, {14927, 15687}, {15640, 50965}, {15682, 29317}, {15684, 21356}, {15708, 51134}, {18583, 35401}, {20423, 39874}, {20582, 49140}, {25406, 50959}, {25561, 49138}, {29323, 41106}, {33699, 50955}, {43273, 50687}, {48905, 51129}, {48942, 50977}
X(51217) = reflection of X(i) in X(j) for these {i,j}: {50969, 50957}, {50976, 51133}
X(51217) = anticomplement of X(50976)
X(51217) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3543, 51022, 51023}, {3543, 51023, 51029}, {3543, 51028, 51026}, {36990, 51026, 51028}, {36990, 51028, 51023}, {50957, 50969, 3619}, {50976, 51133, 2}, {51022, 51026, 36990}, {51022, 51167, 3543}
See Antreas Hatzipolakis and César Lozada, euclid 5305.
X(51218) lies on these lines: {4, 7}, {25, 32625}, {1597, 35454}, {2202, 28044}, {3064, 3700}, {6001, 38388}, {7079, 15837}, {17112, 28120}, {25640, 35593}, {38966, 50940}
X(51218) = X(77)-isoconjugate-of-X(15731)
X(51218) = X(607)-reciprocal conjugate of-X(15731)
X(51218) = perspector of the circumconic {{A, B, C, X(281), X(13149)}}
X(51218) = inverse of X(7) in polar circle
X(51218) = orthoassociate of X(7)
X(51218) = Zosma transform of X(1323)
X(51218) = barycentric product X(281)*X(15726)
X(51218) = barycentric quotient X(607)/X(15731)
X(51218) = trilinear product X(33)*X(15726)
X(51218) = trilinear quotient X(33)/X(15731)
X(51218) = reflection of X(4) in the line X(3900)X(39532)
X(51218) = X(32625)-of-anti-Ara triangle
See Antreas Hatzipolakis and César Lozada, euclid 5305.
X(51219) lies on these lines: {4, 15}, {61, 33496}, {511, 20411}, {6110, 15609}
X(51219) = inverse of X(17) in polar circle
X(51219) = orthoassociate of X(17)
See Antreas Hatzipolakis and César Lozada, euclid 5305.
X(51220) lies on these lines: {4, 16}, {62, 33497}, {511, 20412}, {6111, 15610}, {32428, 44223}
X(51220) = inverse of X(18) in polar circle
X(51220) = orthoassociate of X(18)
See Antreas Hatzipolakis and César Lozada, euclid 5305.
X(51221) lies on the nine-point circle and these lines: {2, 41904}, {4, 102}, {5, 38977}, {11, 225}, {113, 21664}, {116, 18634}, {117, 14304}, {122, 3142}, {123, 6831}, {125, 407}, {235, 20620}, {1826, 5514}, {5587, 46663}, {16177, 36195}, {18641, 35968}
X(51221) = midpoint of X(4) and X(26704)
X(51221) = reflection of X(38977) in X(5)
X(51221) = complement of X(41904)
X(51221) = complementary conjugate of the isogonal conjugate of X(41904)
X(51221) = X(2)-Ceva conjugate of-X(8755)
X(51221) = X(31)-complementary conjugate of-X(8755)
X(51221) = center of the circumconic {{A, B, C, X(4), X(7452)}}
X(51221) = inverse of X(102) in polar circle
X(51221) = antipode of X(38977) in nine-point circle
X(51221) = orthoassociate of X(102)
X(51221) = orthojoin of X(8755)
X(51221) = Poncelet point of X(i) for these i: {7452, 23987, 26704, 36127}
X(51221) = Zosma transform of X(36055)
X(51221) = (medial)-isotomic conjugate-of-X(8755)
X(51221) = X(26704)-of-Euler triangle
X(51221) = X(38977)-of-Johnson triangle
See Antreas Hatzipolakis and César Lozada, euclid 5305.
X(51222) lies on the circumcircle and these lines: {4, 138}, {6, 933}, {51, 112}, {53, 107}, {99, 343}, {110, 216}, {111, 42651}, {935, 15340}, {1141, 14582}, {1300, 35361}, {1899, 13527}, {2351, 32692}, {9142, 26717}, {11077, 46966}, {12022, 30247}
X(51222) = X(1084)-Dao conjugate of X(42731)
X(51222) = X(662)-isoconjugate-of-X(42731)
X(51222) = X(512)-reciprocal conjugate of-X(42731)
X(51222) = inverse of X(138) in polar circle
X(51222) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(51)}} and circumcircle
X(51222) = trilinear pole of the line {6, 15451}
X(51222) = Collings transform of X(15450)
X(51222) = orthoassociate of X(138)
X(51222) = barycentric quotient X(512)/X(42731)
X(51222) = trilinear quotient X(661)/X(42731)
See Ivan Pavlov, euclid 5311.
X(51223) lies on the Jerabek circumhyperbola, the conic {{A,B,C X(1), X(2)}}, and these lines: {1, 71}, {2, 72}, {3, 81}, {4, 40952}, {6, 28}, {7, 28786}, {20, 5751}, {54, 7501}, {56, 2982}, {57, 73}, {64, 4219}, {65, 278}, {66, 5800}, {68, 6826}, {69, 274}, {74, 36077}, {88, 5708}, {89, 37582}, {105, 16466}, {145, 35058}, {184, 1175}, {265, 44229}, {277, 24476}, {279, 1439}, {330, 20018}, {389, 37028}, {895, 16428}, {940, 7523}, {999, 40399}, {1104, 5165}, {1119, 1425}, {1170, 16453}, {1176, 5138}, {1193, 2282}, {1219, 3555}, {1224, 5904}, {1255, 15934}, {1466, 34051}, {1714, 5902}, {1899, 43712}, {1903, 5746}, {2006, 5292}, {2095, 19543}, {2287, 19285}, {3216, 8056}, {3338, 39947}, {3527, 7497}, {3601, 39948}, {3927, 16848}, {4259, 4340}, {4295, 15320}, {4846, 6851}, {5208, 37176}, {5320, 17562}, {5707, 7549}, {5712, 10974}, {5738, 37179}, {5747, 18397}, {5757, 7513}, {6857, 34259}, {6869, 34800}, {6904, 39747}, {7520, 37685}, {7535, 32911}, {8728, 32782}, {8811, 46017}, {10449, 30710}, {10477, 37037}, {10479, 24391}, {10693, 15904}, {10914, 20019}, {11402, 37236}, {11518, 25430}, {14017, 37538}, {15232, 18391}, {15474, 28787}, {15803, 39980}, {16082, 38955}, {17749, 39963}, {18180, 37666}, {19366, 44696}, {19716, 47512}, {24929, 25417}, {34772, 36000}, {36025, 42461}, {36029, 36742}, {36754, 37275}, {37266, 41014}, {37280, 43698}, {39959, 41863}, {43724, 50701}
X(51223) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}} and {{A, B, C, X(3), X(4)}}
X(51223) = isogonal conjugate of the anticomplement of X(8728)
X(51223) = isogonal conjugate of the complement of X(377)
X(51223) = isotomic conjugate of the anticomplement of X(4261)
X(51223) = X(4261)-cross conjugate of X(2)
X(51223) = cevapoint of X(i) and X(j) for these (i,j): {6, 37538}, {56, 19349}, {838, 1015}
X(51223) = trilinear pole of line {513, 647}
X(51223) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 44140), (3, 405), (9, 5271), (10, 5295), (206, 5320), (478, 37543), (1015, 23882), (8054, 46385), (36103, 39585), (40620, 15417)
X(51223) = X(i)-isoconjugate of X(j) for these (i,j): {1, 405}, {3, 39585}, {6, 5271}, {8, 1451}, {9, 37543}, {31, 44140}, {58, 5295}, {75, 5320}, {100, 46385}, {101, 23882}, {283, 1882}, {648, 46382}, {1474, 42706}, {1621, 14549}
X(51223) = barycentric product X(i)*X(j) for these {i,j}: {7, 2335}, {75, 2215}, {525, 36077}, {693, 36080}
X(51223) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 5271}, {2, 44140}, {6, 405}, {19, 39585}, {32, 5320}, {37, 5295}, {56, 37543}, {72, 42706}, {513, 23882}, {604, 1451}, {649, 46385}, {810, 46382}, {1880, 1882}, {2215, 1}, {2335, 8}, {2350, 14549}, {7192, 15417}, {36077, 648}, {36080, 100}, {45128, 5278}
X(51223) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 579, 13726}, {57, 386, 37264}
X(51224) lies on the cubics K394 and K435 and these lines: {2, 187}, {3, 7812}, {4, 23055}, {6, 35955}, {15, 530}, {16, 531}, {20, 6179}, {30, 98}, {32, 7827}, {39, 34604}, {50, 45331}, {76, 33007}, {83, 8359}, {99, 524}, {112, 37765}, {115, 8597}, {141, 35954}, {148, 32479}, {183, 11159}, {194, 34504}, {230, 8352}, {249, 40112}, {315, 7870}, {325, 27088}, {340, 4235}, {376, 511}, {381, 8860}, {384, 7810}, {385, 543}, {512, 9147}, {519, 5184}, {538, 8591}, {542, 11676}, {547, 38230}, {549, 38225}, {550, 7760}, {551, 38221}, {597, 1691}, {599, 1003}, {648, 10295}, {754, 2482}, {842, 44265}, {1078, 8370}, {1285, 2030}, {1384, 5077}, {1509, 50235}, {1641, 17941}, {2021, 33008}, {2407, 46069}, {2459, 13757}, {2460, 13637}, {2959, 50089}, {3053, 7802}, {3096, 33237}, {3111, 33873}, {3363, 37688}, {3524, 47113}, {3534, 9301}, {3545, 13449}, {3552, 7768}, {3618, 38010}, {3767, 33192}, {4226, 15360}, {4234, 31144}, {4785, 41190}, {5007, 33260}, {5023, 7752}, {5032, 5107}, {5055, 14693}, {5099, 37907}, {5111, 20583}, {5140, 7714}, {5148, 10385}, {5182, 41146}, {5201, 11634}, {5206, 7769}, {5207, 14039}, {5210, 11184}, {5306, 8353}, {5309, 10631}, {5319, 33253}, {5461, 14041}, {5463, 35917}, {5464, 35918}, {5476, 10788}, {5978, 35303}, {5979, 35304}, {6054, 37461}, {6055, 21445}, {6337, 7949}, {6566, 13759}, {6567, 13639}, {6655, 7817}, {6658, 7780}, {6661, 20582}, {6787, 47638}, {7426, 35278}, {7610, 11317}, {7615, 17008}, {7617, 17004}, {7618, 7774}, {7619, 17005}, {7620, 37667}, {7622, 7777}, {7669, 37903}, {7736, 47061}, {7739, 33207}, {7745, 43459}, {7747, 33013}, {7750, 7832}, {7751, 33257}, {7753, 33273}, {7755, 33256}, {7758, 33254}, {7759, 33014}, {7763, 35287}, {7764, 33276}, {7765, 33267}, {7766, 32480}, {7772, 33275}, {7779, 32456}, {7781, 33268}, {7782, 7905}, {7784, 8366}, {7785, 15513}, {7786, 33215}, {7792, 19661}, {7796, 33235}, {7809, 22110}, {7813, 36521}, {7814, 32964}, {7818, 33246}, {7830, 7859}, {7843, 33259}, {7845, 41136}, {7856, 22331}, {7857, 11318}, {7860, 16925}, {7865, 14036}, {7873, 33225}, {7878, 32965}, {7884, 32986}, {7910, 33190}, {7911, 8360}, {7921, 15515}, {7922, 32973}, {7925, 9167}, {7926, 9770}, {7936, 14001}, {7940, 32006}, {7943, 33230}, {8584, 8586}, {8596, 19570}, {8627, 35295}, {8703, 35002}, {9127, 35279}, {9150, 38890}, {9218, 50706}, {9300, 11155}, {9420, 14275}, {9466, 19686}, {9740, 32815}, {9862, 11645}, {9891, 13677}, {9893, 13797}, {10159, 19697}, {10304, 18860}, {11001, 43453}, {11063, 35936}, {11104, 49723}, {11160, 32833}, {11161, 15993}, {11299, 39555}, {11300, 39554}, {11586, 21469}, {11707, 50857}, {11708, 50854}, {12110, 37345}, {13857, 35922}, {14023, 33244}, {14033, 39266}, {14061, 37350}, {15480, 47287}, {15534, 31859}, {15688, 47618}, {15743, 21468}, {16046, 31143}, {16508, 35705}, {16712, 50264}, {17006, 43457}, {17103, 50260}, {18800, 39099}, {19312, 50230}, {19924, 38749}, {20088, 37512}, {21163, 22503}, {23234, 37459}, {28562, 41193}, {31417, 33188}, {32817, 50992}, {33228, 44401}, {34507, 35951}, {34508, 35230}, {34509, 35229}, {35915, 50234}, {35916, 50226}, {35925, 50977}, {35933, 44555}, {35950, 40107}, {36196, 46998}, {37023, 50236}, {38704, 47333}, {40246, 41135}, {40334, 48314}, {40335, 48313}, {40884, 44569}, {41626, 50187}, {44969, 47584}, {50254, 50885}, {50775, 50886}
X(51224) = midpoint of X(i) and X(j) for these {i,j}: {2, 14712}, {385, 9855}, {3534, 9301}, {8591, 44367}, {11001, 43453}
X(51224) = reflection of X(i) in X(j) for these {i,j}: {2, 187}, {99, 8598}, {316, 2}, {325, 27088}, {671, 22329}, {842, 44265}, {5978, 35303}, {5979, 35304}, {6054, 37461}, {6787, 47638}, {7779, 39785}, {7799, 13586}, {7809, 35297}, {7813, 36521}, {7840, 2482}, {8352, 230}, {8586, 8584}, {8597, 115}, {9855, 6781}, {11054, 385}, {11161, 15993}, {22503, 21163}, {33873, 3111}, {35002, 8703}, {36196, 46998}, {39099, 18800}, {39785, 32456}, {50854, 11708}, {50855, 45880}, {50857, 11707}, {50858, 45879}, {50885, 50254}, {50886, 50775}
X(51224) = isotomic conjugate of X(36882)
X(51224) = anticomplement of X(31173)
X(51224) = reflection of X(11673) in the Brocard axis
X(51224) = orthoptic-circle-of-Steiner-inellipse-inverse of X(10162)
X(51224) = psi-transform of X(10166)
X(51224) = X(i)-isoconjugate of X(j) for these (i,j): {31, 36882}, {661, 9186}, {798, 9187}
X(51224) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 36882), (31998, 9187), (36830, 9186)
X(51224) = trilinear pole of line {9185, 9188}
X(51224) = crossdifference of every pair of points on line {9171, 17414}
X(51224) = barycentric product X(i)*X(j) for these {i,j}: {99, 9185}, {670, 9188}
X(51224) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 36882}, {99, 9187}, {110, 9186}, {9185, 523}, {9188, 512}
X(51224) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 187, 26613}, {2, 7737, 598}, {2, 8182, 7771}, {2, 44678, 48913}, {2, 47102, 11057}, {32, 7833, 7827}, {187, 14712, 316}, {230, 8352, 9166}, {315, 32985, 7870}, {316, 26613, 2}, {325, 27088, 41134}, {598, 7771, 2}, {625, 5215, 2}, {671, 22329, 14568}, {1153, 7603, 2}, {2482, 7840, 7799}, {3053, 7802, 7828}, {3552, 9939, 7801}, {3972, 14907, 7831}, {5206, 7775, 33274}, {5206, 7823, 7769}, {5475, 5569, 2}, {7737, 8182, 2}, {7747, 34506, 33013}, {7750, 8369, 7883}, {7775, 33274, 7769}, {7782, 20065, 7905}, {7801, 9939, 7768}, {7804, 15810, 2}, {7823, 33274, 7775}, {7827, 7833, 7847}, {7840, 13586, 2482}, {7883, 8369, 7832}, {8597, 8859, 115}, {14537, 46893, 2}, {20065, 33208, 34511}, {22331, 33234, 7856}, {33208, 34511, 7782}, {33265, 44367, 8591}, {39554, 50855, 45880}, {39555, 50858, 45879}
X(51225) lies on the cubic K185 and these lines: {2, 661}, {291, 4753}, {334, 17790}, {335, 740}, {524, 18827}, {660, 20683}, {876, 24516}, {2245, 4584}, {3661, 35025}, {3764, 36817}, {3943, 4562}, {3948, 4639}, {7233, 17950}, {16826, 36218}, {20142, 37128}, {20337, 36800}, {33079, 40217}
X(51225) = X(2238)-isoconjugate of X(12031)
X(51225) = barycentric product X(99)*X(18009)
X(51225) = barycentric quotient X(i)/X(j) for these {i,j}: {741, 12031}, {5147, 3747}, {18009, 523}
X(51226) lies on the cubics K185 and K394 and these lines: {2, 690}, {67, 11161}, {99, 524}, {297, 17952}, {542, 46069}, {671, 1648}, {1641, 9170}, {1992, 48654}, {2418, 50567}, {2482, 5468}, {4235, 5095}, {5026, 20380}, {8030, 31614}, {8591, 45291}, {10754, 34898}, {35279, 39446}, {37880, 38239}, {44915, 45018}
X(51226) = midpoint of X(8591) and X(45291)
X(51226) = reflection of X(i) in X(j) for these {i,j}: {671, 1648}, {1992, 48654}, {5468, 2482}, {9180, 34763}
X(51226) = isogonal conjugate of X(17964)
X(51226) = isotomic conjugate of X(17948)
X(51226) = antitomic image of X(5468)
X(51226) = isotomic conjugate of the isogonal conjugate of X(48450)
X(51226) = X(1641)-cross conjugate of X(524)
X(51226) = cevapoint of X(524) and X(1641)
X(51226) = trilinear pole of line {524, 1649}
X(51226) = crossdifference of every pair of points on line {2502, 9171}
X(51226) = X(i)-isoconjugate of X(j) for these (i,j): {1, 17964}, {6, 17955}, {31, 17948}, {163, 18007}, {543, 923}, {661, 23348}, {662, 17993}, {798, 34760}, {897, 2502}, {8371, 36142}, {9171, 36085}, {9181, 23894}
X(51226) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 17948), (3, 17964), (9, 17955), (115, 18007), (524, 1641), (1084, 17993), (1648, 33921), (2482, 543), (6593, 2502), (23992, 8371), (31998, 34760), (36830, 23348), (38988, 9171)
X(51226) = barycentric product X(i)*X(j) for these {i,j}: {76, 48450}, {99, 34763}, {524, 18823}, {690, 9170}, {843, 3266}, {5468, 9180}
X(51226) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 17955}, {2, 17948}, {6, 17964}, {99, 34760}, {110, 23348}, {187, 2502}, {351, 9171}, {512, 17993}, {523, 18007}, {524, 543}, {690, 8371}, {843, 111}, {1641, 35087}, {1649, 33921}, {2482, 1641}, {3266, 45809}, {5467, 9181}, {5468, 9182}, {9170, 892}, {9180, 5466}, {14443, 14423}, {14444, 41176}, {18823, 671}, {34763, 523}, {48450, 6}
X(51227) lies on the cubic K185 and these lines: {2, 525}, {30, 74}, {287, 524}, {297, 671}, {323, 44575}, {401, 44555}, {441, 14919}, {468, 22265}, {542, 7473}, {1304, 35266}, {3589, 46751}, {5641, 41254}, {7799, 11064}, {9214, 18808}, {9410, 44576}, {14999, 23967}, {16243, 44347}, {16280, 36166}, {20423, 35908}, {24975, 39290}, {34664, 38933}, {34761, 45662}, {36875, 50974}
X(51227) = midpoint of X(i) and X(j) for these {i,j}: {401, 44555}, {1494, 44769}
X(51227) = reflection of X(i) in X(j) for these {i,j}: {297, 44569}, {14999, 23967}, {40112, 441}
X(51227) = isogonal conjugate of X(48453)
X(51227) = antitomic image of X(14999)
X(51227) = isotomic conjugate of the isogonal conjugate of X(48451)
X(51227) = isotomic conjugate of the polar conjugate of X(17986)
X(51227) = X(48451)-cross conjugate of X(17986)
X(51227) = X(i)-isoconjugate of X(j) for these (i,j): {1, 48453}, {842, 2173}, {5641, 9406}
X(51227) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 48453), (9410, 5641), (23967, 30), (36896, 842), (42426, 1990)
X(51227) = barycentric product X(i)*X(j) for these {i,j}: {69, 17986}, {76, 48451}, {542, 1494}, {2247, 33805}, {2394, 14999}, {7473, 34767}, {16092, 36890}, {18312, 44769}, {35910, 46786}
X(51227) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 48453}, {74, 842}, {542, 30}, {1494, 5641}, {1640, 1637}, {2247, 2173}, {2394, 14223}, {2433, 14998}, {5191, 1495}, {6041, 14398}, {6103, 1990}, {7473, 4240}, {14380, 35909}, {14999, 2407}, {16092, 9214}, {17986, 4}, {18312, 41079}, {23968, 41392}, {32112, 23350}, {34369, 35906}, {35910, 46787}, {36875, 34174}, {43087, 14254}, {44769, 5649}, {45662, 5642}, {46147, 46157}, {48451, 6}
X(51227) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36890, 35910}, {16077, 16080, 297}, {36308, 36311, 12079}
X(51228) lies on the cubic K185 and these lines: {2, 1637}, {287, 671}, {297, 340}, {323, 9141}, {542, 34174}, {842, 1302}, {1494, 1989}, {2407, 3163}, {3978, 9211}, {4240, 5642}, {5649, 30528}, {6034, 41254}, {6035, 22254}, {9033, 9214}, {9530, 40080}, {11070, 24975}, {11078, 36839}, {11092, 36840}, {14995, 23350}, {36890, 44427}, {38340, 41804}, {41253, 47110}, {41887, 41996}, {41888, 41995}
X(51228) = reflection of X(2407) in X(3163)
X(51228) = isogonal conjugate of X(48451)
X(51228) = polar conjugate of X(17986)
X(51228) = antitomic image of X(2407)
X(51228) = isotomic conjugate of the isogonal conjugate of X(48453)
X(51228) = X(i)-isoconjugate of X(j) for these (i,j): {1, 48451}, {48, 17986}, {74, 2247}, {542, 2159}, {1640, 36034}, {2349, 5191}, {6103, 35200}
X(51228) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 48451), (133, 6103), (1249, 17986), (3163, 542), (3258, 1640)
X(51228) = trilinear pole of line {30, 5664}
X(51228) = barycentric product X(i)*X(j) for these {i,j}: {30, 5641}, {76, 48453}, {842, 3260}, {1637, 6035}, {2407, 14223}, {5649, 41079}, {34174, 36891}
X(51228) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 17986}, {6, 48451}, {30, 542}, {842, 74}, {1495, 5191}, {1637, 1640}, {1990, 6103}, {2173, 2247}, {2407, 14999}, {4240, 7473}, {5641, 1494}, {5642, 45662}, {5649, 44769}, {9214, 16092}, {14223, 2394}, {14254, 43087}, {14398, 6041}, {14998, 2433}, {23350, 32112}, {34174, 36875}, {35906, 34369}, {35909, 14380}, {41079, 18312}, {41392, 23968}, {46157, 46147}, {46787, 35910}, {48453, 6}
X(51228) = {X(9979),X(34765)}-harmonic conjugate of X(14223)
X(51229) lies on the cubic K185 and these lines: {2, 3569}, {110, 237}, {287, 694}, {297, 3978}, {524, 46142}, {526, 9513}, {1987, 31635}, {2396, 36790}, {2421, 11672}, {4230, 36213}, {25046, 46039}
X(51229) = reflection of X(2421) in X(11672)
X(51229) = isogonal conjugate of X(48452)
X(51229) = antitomic image of X(2421)
X(51229) = X(i)-isoconjugate of X(j) for these (i,j): {1, 48452}, {1910, 2782}
X(51229) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 48452), (11672, 2782)
X(51229) = barycentric product X(i)*X(j) for these {i,j}: {325, 2698}, {511, 46142}, {2421, 46040}, {16069, 40810}
X(51229) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 48452}, {511, 2782}, {2698, 98}, {14251, 16068}, {16069, 14382}, {23098, 6072}, {46039, 14265}, {46040, 43665}, {46142, 290}
X(51230) lies on the cubics K213 and these lines: {2, 11058}, {6, 3830}, {23, 14614}, {6322, 40344}, {11057, 35138}
X(51230) = reflection of X(i) in X(j) for these {i,j}: {2, 19601}, {11058, 2}
X(51231) lies on the curve Q125 and these lines: {30, 74}, {399, 15329}, {526, 1511}, {549, 46129}, {2088, 44468}, {3134, 40685}
X(51232) lies on these lines: {99, 476}, {115, 125}, {512, 6033}, {620, 44814}, {804, 12042}, {2782, 23105}, {3005, 42553}, {3014, 22260}, {8574, 44534}, {9479, 24978}, {10264, 14695}, {13162, 14443}, {13187, 23301}
X(51232) = reflection of X(42738) in X(1116)
X(51233) lies on the cubic K513 and these lines: {6, 74}, {186, 3016}, {3569, 13318}, {5663, 14591}, {7722, 32761}, {10986, 45723}, {11454, 39575}, {12270, 32661}
X(51234) lies on the cubic K13 and these lines: {30, 74}, {50, 110}, {1495, 11751}, {2088, 5640}, {15080, 15920}, {18578, 45237}
X(51235) lies on the cubic K312 and these lines: {6, 6187}, {31, 3122}, {36, 19619}, {55, 184}, {56, 106}, {103, 28170}, {654, 1960}, {902, 7113}, {942, 16110}, {1385, 1768}, {1623, 4588}, {2110, 5040}, {2183, 2361}, {2964, 20831}, {3207, 35326}, {7004, 34471}, {7355, 14529}, {8614, 23850}, {8648, 21786}, {23344, 23858}, {26884, 41341}
X(51235) = isogonal conjugate of X(36917)
X(51235) = isogonal conjugate of the isotomic conjugate of X(6224)
X(51235) = X(36)-Ceva conjugate of X(6)
X(51235) = X(i)-isoconjugate of X(j) for these (i,j): {1, 36917}, {75, 34431}, {18359, 19619}
X(51235) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 36917), (80, 20566), (206, 34431)
X(51235) = crosssum of X(i) and X(j) for these (i,j): {2, 20085}, {522, 46398}
X(51235) = crossdifference of every pair of points on line {1639, 10015}
X(51235) = barycentric product X(i)*X(j) for these {i,j}: {1, 16554}, {6, 6224}
X(51235) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 36917}, {32, 34431}, {6224, 76}, {16554, 75}
X(51235) = {X(692),X(34858)}-harmonic conjugate of X(215)
X(51236) lies on the cubics K312 and these lines: {1, 22775}, {3, 102}, {6, 909}, {34, 20832}, {36, 1455}, {56, 244}, {73, 37564}, {106, 1617}, {222, 14793}, {227, 11012}, {478, 5124}, {603, 8614}, {651, 4996}, {902, 1457}, {934, 38374}, {1035, 5204}, {1394, 7280}, {1413, 36052}, {1421, 37583}, {1616, 37579}, {2361, 34182}, {2932, 23703}, {3428, 24028}, {6914, 34029}, {6924, 34030}, {8071, 34046}, {10090, 43043}, {14792, 34043}, {15306, 33925}, {19524, 37558}, {21147, 26286}, {32612, 37697}
X(51236) = isogonal conjugate of the isotomic conjugate of X(36918)
X(51236) = X(i)-Ceva conjugate of X(j) for these (i,j): {36, 56}, {1455, 221}, {1465, 6}
X(51236) = X(8)-isoconjugate of X(47645)
X(51236) = X(2006)-Dao conjugate of X(20566)
X(51236) = crosssum of X(521) and X(10017)
X(51236) = barycentric product X(i)*X(j) for these {i,j}: {6, 36918}, {57, 6326}
X(51236) = barycentric quotient X(i)/X(j) for these {i,j}: {604, 47645}, {6326, 312}, {36918, 76}
X(51237) lies on these lines: {2, 5206}, {3, 9166}, {17, 530}, {18, 531}, {30, 38223}, {99, 17004}, {140, 26613}, {384, 1153}, {543, 50570}, {549, 7827}, {576, 631}, {598, 3526}, {599, 1078}, {671, 7749}, {1975, 11149}, {2896, 22247}, {3589, 5104}, {3849, 16923}, {5054, 12150}, {5215, 7824}, {5569, 7883}, {7617, 33014}, {7619, 34604}, {7622, 7760}, {7763, 50992}, {7782, 8860}, {7812, 21843}, {7832, 51143}, {7847, 44401}, {7863, 33259}, {7909, 9167}, {7919, 33215}, {8182, 33000}, {8598, 15031}, {14971, 33260}, {15810, 33245}, {33276, 47617}, {37334, 43148}, {39142, 50990}
X(51237) {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5569, 7907, 7883}, {33259, 34506, 41134}
X(51238) lies on the cubics K and K and these lines: {2, 7748}, {5, 41135}, {17, 531}, {18, 530}, {69, 8586}, {148, 37647}, {381, 9863}, {384, 20112}, {524, 50570}, {542, 38228}, {546, 8859}, {597, 7797}, {2896, 37350}, {3090, 32480}, {3091, 5032}, {3860, 18503}, {5025, 21358}, {5461, 15031}, {5569, 19691}, {6655, 7617}, {7610, 14062}, {7615, 32966}, {7620, 32963}, {7769, 8596}, {7775, 19570}, {7785, 15534}, {7827, 33024}, {7836, 32984}, {7860, 32993}, {8355, 17128}, {8370, 16984}, {9166, 16044}, {10303, 41895}, {14712, 18424}, {14971, 33225}, {15597, 33256}, {33011, 34511}
X(51239) lies on the cubic K108 and these lines: {3, 524}, {6, 38532}, {23, 13493}, {111, 2393}, {2930, 47063}, {6093, 30247}, {8428, 22259}, {9027, 15406}, {9872, 10354}, {10870, 31961}
X(51239) = isogonal conjugate of X(34166)
X(51239) = circumcircle-inverse of X(13608)
X(51239) = isogonal conjugate of the anticomplement of X(10354)
X(51239) = isogonal conjugate of the isotomic conjugate of X(39157)
X(51239) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34166}, {75, 13493}
X(51239) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 34166), (206, 13493)
X(51239) = crosspoint of X(15406) and X(35188)
X(51239) = barycentric product X(i)*X(j) for these {i,j}: {6, 39157}, {5486, 11580}, {13492, 13608}
X(51239) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 34166}, {32, 13493}, {11580, 11185}, {35188, 39296}, {39157, 76}
X(51240) lies on the cubics K108 and K904 and these lines: {3, 1177}, {6, 3455}, {23, 22258}, {25, 111}, {32, 7669}, {132, 18494}, {154, 1625}, {187, 18374}, {206, 18472}, {351, 9517}, {381, 2794}, {403, 13200}, {468, 34163}, {2070, 2080}, {2393, 5938}, {2482, 34319}, {2844, 23383}, {2936, 5467}, {5024, 10766}, {5094, 11605}, {9142, 21309}, {9512, 36156}, {9818, 11637}, {9829, 10718}, {10254, 48681}, {10735, 18386}, {12593, 13493}, {13115, 34217}, {13236, 21177}, {14357, 16176}, {14574, 22146}, {14983, 37196}, {20975, 30435}
X(51240) = midpoint of X(112) and X(9157)
X(51240) = reflection of X(i) in X(j) for these {i,j}: {3, 14649}, {9157, 40121}, {11641, 9157}
X(51240) = isogonal conjugate of X(14364)
X(51240) = circumcircle-inverse of X(6593)
X(51240) = Stammler-circle-inverse of X(48679)
X(51240) = isogonal conjugate of the anticomplement of X(15900)
X(51240) = isogonal conjugate of the isotomic conjugate of X(11061)
X(51240) = tangential-isogonal conjugate of X(5938)
X(51240) = X(23)-Ceva conjugate of X(6)
X(51240) = X(i)-isoconjugate of X(j) for these (i,j): {1, 14364}, {75, 22258}, {10417, 46277}
X(51240) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 14364), (67, 18019), (206, 22258)
X(51240) = crosssum of X(525) and X(38971)
X(51240) = crossdifference of every pair of points on line {14417, 18310}
X(51240) = barycentric product X(i)*X(j) for these {i,j}: {6, 11061}, {23, 15900}, {187, 10416}
X(51240) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 14364}, {32, 22258}, {10416, 18023}, {11061, 76}, {14567, 10417}, {15900, 18019}
X(51240) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 19153, 37808}, {112, 40121, 11641}, {187, 18374, 21419}, {1384, 5191, 34106}, {14676, 19165, 13310}
X(51241) lies on the cubic K410 and these lines: {1, 3224}, {1759, 21387}, {16552, 16569}, {16557, 25264}, {16574, 21384}
X(51241) = X(194)-Ceva conjugate of X(1)
X(51241) = X(3223)-Dao conjugate of X(2998)
X(51242) lies on the cubics K050 and K1132 and these lines: {4, 2992}, {16, 184}, {51, 6116}, {128, 130}, {185, 3480}, {418, 44712}, {3129, 8479}, {11600, 14372}, {16807, 21648}, {20411, 21661}, {21660, 38931}
X(51242) = reflection of X(21661) in X(20411)
X(51242) = X(i)-isoconjugate of X(j) for these (i,j): {621, 2190}, {3129, 40440}
X(51242) = X(5)-Dao conjugate of X(621)
X(51242) = barycentric product X(i)*X(j) for these {i,j}: {216, 2992}, {343, 3438}, {40156, 44713}
X(51242) = barycentric quotient X(i)/X(j) for these {i,j}: {216, 621}, {217, 3129}, {2992, 276}, {3438, 275}
X(51243) lies on the cubics K050 and K1132b and these lines: {4, 2993}, {15, 184}, {51, 6117}, {128, 130}, {185, 3479}, {418, 44711}, {3130, 8471}, {11601, 14373}, {16806, 21647}, {20412, 21661}, {21660, 38932}
X(51243) = reflection of X(21661) in X(20412)
X(51243) = X(i)-isoconjugate of X(j) for these (i,j): {622, 2190}, {3130, 40440}
X(51243) = X(5)-Dao conjugate of X(622)
X(51243) = barycentric product X(i)*X(j) for these {i,j}: {216, 2993}, {343, 3439}, {40157, 44714}
X(51243) = barycentric quotient X(i)/X(j) for these {i,j}: {216, 622}, {217, 3130}, {2993, 276}, {3439, 275}
X(51244) lies on the cubics K020 and K1065 and these lines: {1, 8867}, {3, 147}, {4, 34130}, {39, 8861}, {76, 3492}, {384, 3493}, {3224, 8743}, {3491, 8864}, {3494, 8862}, {8866, 8868}
X(51244) = isogonal conjugate of X(3493)
X(51244) = X(i)-isoconjugate of X(j) for these (i,j): {1, 3493}, {694, 19555}, {1581, 6660}, {1916, 19559}, {1934, 19558}, {1967, 5207}, {18896, 19560}, {19572, 41517}
X(51244) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 3493), (8290, 5207), (19576, 6660), (35078, 14316), (39031, 19559), (39043, 19555)
X(51244) = barycentric product X(i)*X(j) for these {i,j}: {385, 43696}, {3978, 41533}
X(51244) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 3493}, {385, 5207}, {804, 14316}, {1580, 19555}, {1691, 6660}, {1933, 19559}, {4027, 19571}, {14602, 19558}, {18902, 19556}, {41533, 694}, {43696, 1916}
X(51245) lies on the cubic K020 and these lines: {3, 8928}, {39, 8863}, {76, 3505}, {194, 39938}, {384, 3492}, {2896, 3491}, {3493, 8790}, {3496, 8866}, {3499, 8861}, {3933, 40035}, {6196, 8867}, {8862, 8865}
X(51245) = isogonal conjugate of X(3492)
X(51245) = X(695)-cross conjugate of X(76)
X(51245) = X(1)-isoconjugate of X(3492)
X(51245) = X(3)-Dao conjugate of X(3492)
X(51245) = barycentric quotient X(6)/X(3492)
X(5126) lies on the cubics K020 and these lines: {3, 6374}, {32, 3186}, {76, 3504}, {83, 8874}, {184, 194}, {228, 22028}, {384, 3491}, {2200, 21080}, {3493, 8873}, {3496, 8872}, {3501, 8866}, {6196, 8862}, {8783, 8858}, {8861, 8871}, {8867, 8876}, {9229, 39927}, {14199, 17797}
X(51246) = isogonal conjugate of X(3491)
X(51246) = isogonal conjugate of the isotomic conjugate of X(43715)
X(51246) = X(i)-cross conjugate of X(j) for these (i,j): {695, 83}, {17984, 98}
X(51246) = X(1)-isoconjugate of X(3491)
X(51246) = X(3)-Dao conjugate of X(3491)
X(51246) = trilinear pole of line {3049, 23301}
X(51246) = barycentric product X(6)*X(43715)
X(51246) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 3491}, {43715, 76}
X(51247) lies on the cubic K020 and these lines: {32, 8874}, {76, 22252}, {194, 38817}, {384, 8790}, {2896, 8873}, {3491, 3499}, {3492, 8871}, {6196, 8866}, {8863, 8870}, {8865, 8872}
X(51247) = isogonal conjugate of X(8790)
X(51247) = X(695)-cross conjugate of X(32)
X(51247) = X(1)-isoconjugate of X(8790)
X(51247) = X(3)-Dao conjugate of X(8790)
X(51247) = barycentric quotient X(6)/X(8790)
X(51248) lies on the cubic K020 and these lines: {3, 46286}, {39, 3493}, {76, 148}, {384, 8864}, {512, 5007}, {3224, 3492}, {3494, 3496}, {3500, 8867}, {8865, 8868}, {11229, 33260}, {30496, 43183}
X(51248) = isogonal conjugate of X(8864)
X(51248) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8864}, {3225, 17799}, {7779, 43761}
X(51248) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 8864), (39080, 7779)
X(51248) = crosssum of X(2076) and X(8290)
X(51248) = barycentric product X(i)*X(j) for these {i,j}: {698, 46286}, {3229, 11606}
X(51248) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 8864}, {3229, 7779}, {9429, 5113}, {32748, 2076}, {46286, 3225}
X(51249) lies on the cubics K020 and K547 and these lines: {4, 8790}, {32, 3499}, {39, 8871}, {76, 41520}, {194, 263}, {384, 8870}, {512, 3934}, {2896, 34214}, {3503, 6196}, {8865, 8875}
X(51249) = isogonal conjugate of X(8870)
X(51249) = X(5976)-cross conjugate of X(511)
X(51249) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8870}, {1910, 40858}
X(51249) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 8870), (8623, 38382), (11672, 40858)
X(51249) = crosssum of X(38382) and X(40858)
X(51249) = barycentric product X(511)*X(39939)
X(51249) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 8870}, {511, 40858}, {36213, 38382}, {39939, 290}
X(51250) lies on the cubic K020 and these lines: {3, 3492}, {76, 8863}, {185, 15407}, {384, 8861}, {525, 5305}, {2896, 42313}, {3172, 40802}, {3491, 3493}, {3496, 8862}, {3501, 8867}
X(51250) = isogonal conjugate of X(8861)
X(51250) = X(i)-isoconjugate of X(j) for these (i,j): {1, 8861}, {3404, 8928}
X(51250) = X(3)-Dao conjugate of X(8861)
X(51250) = barycentric product X(325)*X(43721)
X(51250) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 8861}, {43721, 98}
X(51251) lies on the cubic K020 and these lines: {39, 8866}, {384, 8865}, {2896, 4388}, {3492, 3503}, {3494, 8790}, {3496, 3499}, {3497, 39725}, {3498, 8862}, {3500, 8874}, {8867, 8870}
X(51251) = isogonal conjugate of X(8865)
X(51251) = X(695)-cross conjugate of X(3500)
X(51251) = X(1)-isoconjugate of X(8865)
X(51251) = X(3)-Dao conjugate of X(8865)
X(51251) = barycentric quotient X(6)/X(8865)
X(51252) lies on the cubic K106 and these lines: {3, 1176}, {22, 76}, {83, 7503}, {251, 26216}, {3785, 5596}, {7404, 17500}, {7488, 21458}, {7494, 28417}, {10548, 14118}, {23208, 46442}
X(51252) = barycentric product X(5133)*X(28724)
X(51252) = barycentric quotient X(9969)/X(27376)
X(51253) lies on the cubic K1065 and these lines: {3, 895}, {4, 5968}, {22, 10422}, {76, 30786}, {691, 11413}, {2353, 14366}, {3265, 3926}, {14357, 33927}, {14961, 34158}, {19330, 26283}
X(51253) = X(14273)-isoconjugate of X(36095)
X(51253) = X(i)-Dao conjugate of X(j) for these (i, j): (895, 10424), (5181, 468)
X(51253) = crosssum of X(468) and X(41616)
X(51253) = barycentric product X(i)*X(j) for these {i,j}: {305, 34158}, {14961, 30786}
X(51253) = barycentric quotient X(i)/X(j) for these {i,j}: {858, 37778}, {14961, 468}, {34158, 25}, {42665, 14273}
X(51254) lies on the cubic K1065 and these lines: {3, 125}, {4, 250}, {5, 3233}, {20, 476}, {30, 14254}, {76, 328}, {376, 5627}, {520, 5489}, {542, 14264}, {550, 21317}, {1495, 34104}, {1531, 3284}, {1989, 44518}, {2777, 41512}, {3258, 15454}, {3534, 14993}, {6344, 18848}, {7471, 18279}, {7802, 35139}, {8431, 18318}, {10316, 32662}, {11589, 12113}, {12022, 18114}, {12028, 18531}, {12383, 14385}, {12605, 16934}, {14559, 15063}, {14670, 32423}, {15329, 18400}, {16186, 44665}, {16868, 23956}, {18404, 42424}, {30714, 41390}, {34298, 39290}, {34664, 43084}, {39643, 50433}
X(51254) = X(328)-Ceva conjugate of X(11064)
X(51254) = X(i)-cross conjugate of X(j) for these (i,j): {1650, 43083}, {39008, 41077}
X(51254) = X(i)-isoconjugate of X(j) for these (i,j): {158, 14385}, {186, 36119}, {2159, 14165}, {2624, 15459}, {32679, 32695}, {36131, 44427}
X(51254) = X(i)-Dao conjugate of X(j) for these (i, j): (265, 10421), (1147, 14385), (1511, 186), (3163, 14165), (7687, 43911), (9033, 3258), (38999, 526), (39008, 44427), (39170, 4)
X(51254) = cevapoint of X(1568) and X(16163)
X(51254) = crosspoint of X(265) and X(12028)
X(51254) = crosssum of X(i) and X(j) for these (i,j): {186, 1986}, {34397, 36423}
X(51254) = trilinear pole of line {1636, 18558}
X(51254) = barycentric product X(i)*X(j) for these {i,j}: {99, 18558}, {110, 18557}, {265, 11064}, {328, 3284}, {394, 14254}, {476, 41077}, {1636, 35139}, {1650, 39295}, {2407, 43083}, {3260, 50433}, {3265, 41392}, {3926, 14583}, {18478, 46809}, {36789, 50464}
X(51254) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 14165}, {265, 16080}, {476, 15459}, {577, 14385}, {1568, 14918}, {1636, 526}, {3284, 186}, {9033, 44427}, {9409, 47230}, {11064, 340}, {14254, 2052}, {14560, 32695}, {14582, 18808}, {14583, 393}, {16163, 14920}, {18478, 46808}, {18557, 850}, {18558, 523}, {32662, 1304}, {39008, 3258}, {39295, 42308}, {41077, 3268}, {41392, 107}, {43083, 2394}, {47405, 1986}, {50433, 74}, {50464, 40384}, {50467, 40391}
X(51254) = {X(3),X(265)}-harmonic conjugate of X(39170)
X(51224) lies on the cubic K1065 and these lines: {3, 54}, {4, 160}, {24, 275}, {25, 4994}, {39, 41270}, {76, 95}, {140, 8901}, {378, 8884}, {578, 21638}, {1141, 20189}, {1151, 16034}, {1152, 16029}, {1209, 50947}, {1593, 19173}, {1594, 23195}, {1599, 16037}, {1600, 16032}, {3133, 14389}, {3520, 19172}, {3541, 19174}, {4993, 6642}, {5489, 23286}, {7488, 43768}, {7503, 19179}, {7512, 36842}, {7526, 19176}, {7547, 19177}, {7604, 18369}, {9707, 26887}, {11456, 19206}, {14366, 14587}, {14533, 39643}, {14652, 27423}, {15329, 44516}, {18859, 19651}, {18912, 26954}, {19169, 35502}, {19180, 19357}, {19192, 35477}, {19197, 39588}, {20775, 34224}, {23295, 37119}, {37126, 40631}, {38848, 44890}
X(51255) = isogonal conjugate of X(40449)
X(51255) = X(i)-Ceva conjugate of X(j) for these (i,j): {95, 37636}, {99, 15412}
X(51255) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40449}, {5, 2216}, {1087, 1166}, {1179, 44706}, {1953, 40393}, {2617, 50946}
X(51255) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 40449), (570, 45793), (1209, 5), (8901, 523)
X(51255) = cevapoint of X(570) and X(23195)
X(51255) = crosspoint of X(54) and X(252)
X(51255) = crosssum of X(i) and X(j) for these (i,j): {5, 143}, {51, 36412}
X(51255) = barycentric product X(i)*X(j) for these {i,j}: {54, 37636}, {95, 570}, {97, 1594}, {275, 1216}, {276, 23195}, {1238, 8882}, {15108, 30490}, {15412, 50947}, {23286, 41677}, {34386, 47328}
X(51255) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40449}, {54, 40393}, {570, 5}, {1209, 45793}, {1216, 343}, {1238, 28706}, {1594, 324}, {2148, 2216}, {2623, 50946}, {6152, 14129}, {8882, 1179}, {14533, 40441}, {23195, 216}, {30490, 11538}, {37636, 311}, {47328, 53}, {50947, 14570}
X(51255) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 16030, 54}, {54, 19168, 19170}, {275, 19185, 24}
X(51256) lies on the cubic K1065 and these lines: {2, 18127}, {3, 2888}, {4, 3447}, {140, 45737}, {477, 3520}, {5489, 23286}, {5562, 14366}, {6794, 14354}, {12028, 35921}, {22115, 47055}, {34178, 35473}
X(51256) = X(i)-isoconjugate of X(j) for these (i,j): {2070, 2166}, {24978, 32678}
X(51256) = X(i)-Dao conjugate of X(j) for these (i, j): (11597, 2070), (18334, 24978)
X(51256) = barycentric product X(i)*X(j) for these {i,j}: {323, 33565}, {7799, 34448}, {9381, 22115}
X(51256) = barycentric quotient X(i)/X(j) for these {i,j}: {50, 2070}, {186, 37766}, {526, 24978}, {9381, 18817}, {33565, 94}, {34418, 30529}, {34448, 1989}
X(51256) = {X(3),X(38542)}-harmonic conjugate of X(34418)
X(51257) lies on the cubic K056 and these lines: {3, 16083}, {4, 290}, {76, 525}, {182, 14382}, {327, 40804}, {2966, 10316}, {7745, 44549}, {7763, 14376}, {9476, 18022}, {14965, 44137}, {18024, 42287}, {31636, 44185}
X(51257) = X(15595)-cross conjugate of X(30737)
X(51257) = X(i)-isoconjugate of X(j) for these (i,j): {1297, 9417}, {9247, 39265}, {36046, 39469}
X(51257) = X(i)-Dao conjugate of X(j) for these (i, j): (441, 11672), (15595, 3289), (23976, 237), (33504, 39469), (39058, 1297), (39073, 9419), (50938, 2211)
X(51257) = cevapoint of X(15595) and X(30737)
X(51257) = barycentric product X(i)*X(j) for these {i,j}: {290, 30737}, {1503, 18024}, {18022, 34156}
X(51257) = barycentric quotient X(i)/X(j) for these {i,j}: {264, 39265}, {290, 1297}, {441, 3289}, {685, 32649}, {1503, 237}, {2312, 9417}, {9475, 9419}, {15595, 11672}, {16081, 43717}, {16318, 2211}, {17875, 23996}, {18024, 35140}, {22456, 44770}, {23977, 34859}, {30737, 511}, {34156, 184}, {34211, 14966}, {42671, 9418}, {43665, 34212}
X(51258) lies on the cubic K217 and these lines: {2, 47293}, {5, 5968}, {30, 98}, {111, 468}, {115, 523}, {125, 525}, {148, 7472}, {187, 47238}, {230, 36180}, {265, 895}, {339, 3267}, {381, 2452}, {543, 40544}, {546, 14246}, {858, 31125}, {868, 2394}, {879, 10097}, {1312, 50944}, {1313, 50945}, {1499, 16278}, {1550, 22265}, {1551, 12243}, {2782, 36170}, {2794, 46982}, {2970, 10555}, {3143, 9178}, {3150, 15421}, {3767, 36156}, {3906, 15359}, {4064, 21046}, {4580, 34978}, {5159, 6390}, {5254, 14609}, {5461, 46986}, {5512, 8754}, {6036, 46987}, {6530, 9139}, {6776, 36894}, {7615, 50149}, {8753, 10151}, {8901, 9213}, {9137, 41125}, {10416, 37897}, {10561, 47175}, {10735, 13473}, {11799, 43917}, {13869, 37049}, {14061, 47288}, {14651, 36166}, {14729, 44533}, {15899, 46517}, {16760, 20398}, {16934, 18531}, {17948, 37350}, {17964, 47242}, {18583, 21460}, {23698, 46981}, {32113, 46154}, {32740, 47188}, {34169, 47155}, {34320, 47311}, {36174, 47291}, {36194, 40727}, {36196, 41135}, {38224, 46634}, {38613, 49102}, {42008, 47097}, {43448, 45143}, {47239, 47326}
X(51258) = midpoint of X(i) and X(j) for these {i,j}: {148, 7472}, {671, 16092}, {858, 47286}, {1550, 22265}, {1551, 12243}, {6321, 46633}, {36174, 47291}
X(51258) = reflection of X(i) in X(j) for these {i,j}: {187, 47238}, {468, 43291}, {6390, 5159}, {14120, 115}, {16760, 20398}, {36180, 230}, {46986, 5461}, {46987, 6036}, {47326, 47239}
X(51258) = complement of X(47293)
X(51258) = X(i)-Ceva conjugate of X(j) for these (i,j): {671, 10097}, {10415, 523}, {17983, 5466}, {30786, 14977}
X(51258) = X(i)-isoconjugate of X(j) for these (i,j): {112, 23889}, {162, 5467}, {163, 4235}, {250, 896}, {468, 1101}, {922, 18020}, {2642, 47443}, {3292, 24000}, {5468, 32676}, {14567, 46254}, {23200, 23999}, {23995, 44146}, {24041, 44102}
X(51258) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 4235), (125, 5467), (523, 468), (525, 6390), (647, 524), (1649, 5095), (3005, 44102), (15526, 5468), (15899, 250), (18311, 7664), (18314, 44146), (23285, 3266), (34591, 23889), (39061, 18020), (41167, 9155)
X(51258) = crosspoint of X(i) and X(j) for these (i,j): {5466, 17983}, {14977, 30786}
X(51258) = crosssum of X(3292) and X(5467)
X(51258) = barycentric product X(i)*X(j) for these {i,j}: {111, 339}, {115, 30786}, {125, 671}, {338, 895}, {523, 14977}, {525, 5466}, {850, 10097}, {897, 20902}, {3267, 9178}, {3269, 46111}, {3708, 46277}, {8753, 36793}, {9213, 14592}, {10555, 34897}, {14208, 23894}, {14908, 23962}, {15526, 17983}, {17879, 36128}, {18023, 20975}, {23994, 36060}
X(51258) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 250}, {115, 468}, {125, 524}, {338, 44146}, {339, 3266}, {523, 4235}, {525, 5468}, {647, 5467}, {656, 23889}, {671, 18020}, {691, 47443}, {895, 249}, {1648, 5095}, {2970, 37778}, {3124, 44102}, {3269, 3292}, {3708, 896}, {4466, 6629}, {5466, 648}, {5489, 14417}, {6791, 15471}, {8029, 14273}, {8430, 4230}, {8753, 23964}, {9178, 112}, {9213, 14590}, {10097, 110}, {10555, 37765}, {14208, 24039}, {14582, 14559}, {14908, 23357}, {14977, 99}, {15526, 6390}, {17983, 23582}, {18210, 16702}, {20902, 14210}, {20975, 187}, {21046, 4062}, {21134, 4750}, {23894, 162}, {30786, 4590}, {34953, 45291}, {36060, 1101}, {36128, 24000}, {41172, 9155}, {46277, 46254}
X(51258) = {X(31125),X(46783)}-harmonic conjugate of X(858)
X(51259) lies on the cubic K527 and these lines: {3, 76}, {262, 523}, {879, 18304}, {5967, 11422}, {7757, 37858}, {7998, 20021}, {9744, 44155}, {14355, 36820}, {40820, 43754}, {40822, 43461}
X(51259) = barycentric product X(i)*X(j) for these {i,j}: {290, 15993}, {2021, 18024}
X(51259) = barycentric quotient X(i)/X(j) for these {i,j}: {2021, 237}, {15993, 511}
X(51260) lies on the cubic K527 and these lines: {2, 1235}, {4, 2393}, {76, 648}, {193, 41370}, {264, 5523}, {339, 45141}, {378, 11257}, {1236, 17907}, {7812, 37855}, {32708, 50437}
X(51260) = {X(1235),X(41361)}-harmonic conjugate of X(43678)
X(51261) lies on the cubic K032 and these lines: {6, 1131}, {631, 5907}, {1906, 1992}, {10938, 45959}, {11020, 17609}, {12279, 37669}, {15063, 49138}, {15644, 16935}, {15717, 43691}, {15748, 21734}
X(51261) = reflection of X(15749) in X(15751)
X(51262) lies on the cubic K147 and these lines: {3, 74}, {691, 1304}, {2394, 4226}, {2420, 2433}, {5467, 14380}, {5649, 34291}, {5664, 14611}, {7471, 18556}, {9139, 23348}, {14560, 46608}, {14685, 48871}, {14687, 35908}, {34761, 45662}
X(51262) = X(i)-isoconjugate of X(j) for these (i,j): {842, 36035}, {1577, 48453}, {1784, 35909}, {2173, 14223}, {3258, 36096}, {14206, 14998}
X(51262) = X(i)-Dao conjugate of X(j) for these (i, j): (23967, 41079), (36896, 14223)
X(51262) = crosssum of X(i) and X(j) for these (i,j): {526, 47214}, {542, 22104}
X(51262) = crossdifference of every pair of points on line {1637, 3258}
X(51262) = barycentric product X(i)*X(j) for these {i,j}: {74, 14999}, {99, 48451}, {542, 44769}, {4558, 17986}, {7473, 14919}, {9717, 50941}, {34761, 35910}
X(51262) = barycentric quotient X(i)/X(j) for these {i,j}: {74, 14223}, {542, 41079}, {1576, 48453}, {2247, 36035}, {5191, 1637}, {7473, 46106}, {9717, 50942}, {14999, 3260}, {17986, 14618}, {18877, 35909}, {23968, 14254}, {32640, 842}, {35910, 34765}, {40352, 14998}, {44769, 5641}, {48451, 523}
X(51262) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 9717, 35910}, {5467, 14380, 44769}
X(51263) lies on the cubic K147 and these lines: {23, 110}, {250, 4230}, {526, 14560}, {691, 9409}, {3284, 48453}, {4226, 50942}, {6035, 17941}, {7468, 14998}, {7471, 14223}, {7480, 35911}, {10420, 23969}, {33803, 42656}, {40866, 40885}
X(51263) = X(i)-isoconjugate of X(j) for these (i,j): {656, 17986}, {1577, 48451}, {1640, 2349}, {2159, 18312}, {2247, 2394}, {6041, 33805}
X(51263) = X(i)-Dao conjugate of X(j) for these (i, j): (3163, 18312), (40596, 17986)
X(51263) = trilinear pole of line {1511, 2420}
X(51263) = barycentric product X(i)*X(j) for these {i,j}: {30, 5649}, {99, 48453}, {842, 2407}, {1495, 6035}, {2420, 5641}, {6148, 23969}
X(51263) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 18312}, {112, 17986}, {842, 2394}, {1495, 1640}, {1576, 48451}, {2420, 542}, {5649, 1494}, {9407, 6041}, {14998, 12079}, {23347, 6103}, {23969, 5627}, {41392, 43087}, {48453, 523}
X(51263) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {23, 46787, 842}, {5467, 23350, 5649}
X(51264) lies on the cubic K420a and these lines: {2, 18}, {5, 195}, {14, 5616}, {302, 45799}, {323, 11543}, {395, 11063}, {398, 11146}, {636, 15108}, {1993, 42153}, {3181, 11087}, {3410, 5872}, {5615, 11671}, {7685, 14683}, {8836, 33530}, {10218, 16771}, {11004, 18581}, {11130, 16961}, {16628, 48794}, {16770, 19713}, {20416, 23061}, {20426, 34009}, {42993, 44718}
X(51264) = anticomplement of the isogonal conjugate of X(11088)
X(51264) = anticomplement of the isotomic conjugate of X(8836)
X(51264) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2154, 634}, {8836, 6327}, {11088, 8}, {35198, 1272}, {50469, 4329}
X(51264) = X(i)-Ceva conjugate of X(j) for these (i,j): {8836, 2}, {33530, 19773}
X(51264) = barycentric product X(299)*X(8930)
X(51264) = barycentric quotient X(i)/X(j) for these {i,j}: {8839, 8457}, {8930, 14}
X(51264) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 22114, 19778}, {18, 11127, 2}, {33464, 33529, 11143}
X(51265) lies on the cubic K420a and these lines: {2, 11121}, {5, 303}, {14, 299}, {15, 22866}, {18, 76}, {69, 22114}, {99, 6672}, {298, 11543}, {301, 10218}, {383, 5981}, {395, 19570}, {622, 6773}, {3589, 7797}, {3642, 16966}, {3818, 16627}, {5965, 44487}, {5983, 31712}, {6390, 42591}, {6670, 7799}, {6674, 44030}, {7752, 22871}, {8836, 41001}, {11128, 16268}, {11132, 22891}, {11303, 31703}, {11304, 22861}, {11308, 42675}, {22506, 33400}, {22848, 30472}, {22855, 34509}, {44362, 47856}
X(51265) = reflection of X(i) in X(j) for these {i,j}: {299, 40706}, {22850, 624}
X(51265) = X(i)-Ceva conjugate of X(j) for these (i,j): {8836, 302}, {41001, 299}
X(51265) = X(38404)-Dao conjugate of X(6151)
X(51265) = {X(18),X(11133)}-harmonic conjugate of X(302)
X(51266) lies on the cubic K420a and these lines: {2, 19774}, {4, 45257}, {5, 3462}, {14, 275}, {18, 471}, {53, 395}, {324, 8836}, {398, 470}, {1629, 7685}, {11143, 14918}, {11547, 18581}, {41100, 44701}
X(51266) = polar conjugate of the isotomic conjugate of X(46754)
X(51266) = polar conjugate of the isogonal conjugate of X(8839)
X(51266) = X(i)-Ceva conjugate of X(j) for these (i,j): {324, 473}, {8836, 471}
X(51266) = X(8839)-cross conjugate of X(46754)
X(51266) = barycentric product X(i)*X(j) for these {i,j}: {4, 46754}, {264, 8839}
X(51266) = barycentric quotient X(i)/X(j) for these {i,j}: {8839, 3}, {46754, 69}
X(51266) = {X(275),X(6117)}-harmonic conjugate of X(473)
X(51267) lies on the cubic K420a and these lines: {2, 13}, {5, 8929}, {14, 14993}, {62, 10217}, {265, 6104}, {302, 43085}, {395, 18285}, {476, 11582}, {547, 34325}, {3411, 8919}, {5321, 11586}, {5612, 37779}, {5616, 10272}, {6105, 32223}, {6116, 36306}, {8836, 46072}, {10218, 11087}, {10413, 11063}, {11080, 37835}, {11537, 11543}, {11555, 42581}, {15441, 16809}, {16268, 36299}, {16461, 47517}, {16961, 18777}, {16964, 45778}, {36296, 45972}, {37340, 41474}
X(51267) = X(5612)-cross conjugate of X(13)
X(51267) = X(i)-isoconjugate of X(j) for these (i,j): {1094, 46072}, {2151, 13582}, {6149, 46076}
X(51267) = X(i)-Dao conjugate of X(j) for these (i, j): (8562, 30465), (14993, 46076), (40578, 13582)
X(51267) = barycentric product X(i)*X(j) for these {i,j}: {13, 37779}, {94, 5612}, {300, 11063}, {10272, 36308}, {23895, 45147}, {36299, 46751}, {37943, 40709}
X(51267) = barycentric quotient X(i)/X(j) for these {i,j}: {13, 13582}, {1989, 46076}, {3457, 14579}, {5612, 323}, {5616, 11131}, {5995, 1291}, {6140, 6137}, {10272, 41887}, {10413, 30465}, {11063, 15}, {11080, 46072}, {36296, 43704}, {36299, 3471}, {37779, 298}, {37943, 470}, {45147, 23870}, {47053, 17402}, {50461, 44718}
X(51267) = {X(8014),X(37832)}-harmonic conjugate of X(13)
X(51268) lies on the cubics K420a and these lines: {5, 49}, {14, 275}, {95, 302}, {97, 466}, {301, 34385}, {395, 11077}, {3458, 42300}, {8613, 50469}, {8795, 36297}, {10218, 16771}, {11087, 19712}, {11543, 46064}, {23896, 46138}, {34390, 44718}
X(51268) = isotomic conjugate of X(33530)
X(51268) = polar conjugate of X(6116)
X(51268) = isotomic conjugate of the complement of X(11126)
X(51268) = X(i)-cross conjugate of X(j) for these (i,j): {18, 11120}, {470, 36311}, {11600, 11117}
X(51268) = X(i)-isoconjugate of X(j) for these (i,j): {5, 2152}, {13, 2290}, {16, 1953}, {19, 44712}, {31, 33530}, {48, 6116}, {299, 2179}, {1154, 2153}, {2181, 44719}, {2617, 6138}, {8740, 44706}, {14213, 34395}, {35199, 36300}
X(51268) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 33530), (6, 44712), (1249, 6116), (30471, 1273), (38993, 2081), (40579, 5), (40580, 1154), (43961, 41078)
X(51268) = cevapoint of X(i) and X(j) for these (i,j): {2, 11126}, {14, 36297}
X(51268) = trilinear pole of line {15, 15412}
X(51268) = barycentric product X(i)*X(j) for these {i,j}: {14, 95}, {15, 46138}, {54, 301}, {275, 40710}, {276, 36297}, {298, 1141}, {3458, 34384}, {8738, 34386}, {15412, 23896}, {36311, 43768}, {39378, 43752}
X(51268) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 33530}, {3, 44712}, {4, 6116}, {14, 5}, {15, 1154}, {54, 16}, {95, 299}, {97, 44719}, {265, 44713}, {275, 471}, {298, 1273}, {301, 311}, {470, 14918}, {1141, 13}, {1157, 5612}, {2148, 2152}, {2151, 2290}, {2154, 1953}, {2623, 6138}, {3458, 51}, {5994, 1625}, {6137, 2081}, {8738, 53}, {8739, 11062}, {8882, 8740}, {8901, 30468}, {10218, 44714}, {10632, 20411}, {11077, 36296}, {11087, 36300}, {11092, 33529}, {11138, 36301}, {14533, 46113}, {15412, 23871}, {18315, 17403}, {20579, 12077}, {23870, 41078}, {23896, 14570}, {30453, 41221}, {36297, 216}, {36309, 35360}, {38413, 23181}, {38808, 44701}, {39378, 44715}, {40710, 343}, {41998, 35442}, {43768, 41888}, {44687, 44689}, {46076, 1263}, {46077, 35194}, {46138, 300}, {50466, 44711}
X(51269) lies on the cubic K420a and these lines: {2, 2992}, {3, 14}, {5, 8839}, {16, 6106}, {95, 302}, {140, 50466}, {395, 11088}, {471, 8738}, {3458, 11489}, {5961, 38943}, {5994, 6672}, {8836, 19713}, {11086, 23303}, {23283, 43083}, {33416, 36209}, {40581, 47201}
X(51269) = X(8836)-Ceva conjugate of X(14)
X(51269) = X(15778)-cross conjugate of X(628)
X(51269) = X(2152)-isoconjugate of X(19713)
X(51269) = X(40579)-Dao conjugate of X(19713)
X(51269) = barycentric product X(i)*X(j) for these {i,j}: {14, 628}, {3458, 46756}, {11120, 15778}
X(51269) = barycentric quotient X(i)/X(j) for these {i,j}: {14, 19713}, {628, 299}, {3458, 3490}, {8015, 39135}, {11138, 40168}, {15778, 619}
X(51269) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 50469, 38944}, {18, 6105, 14}, {23715, 47482, 40579}
X(51270) lies on the cubic K420a and these lines: {2, 19776}, {3, 45778}, {5, 8919}, {6, 13}, {16, 15441}, {62, 11581}, {264, 300}, {303, 23895}, {395, 11080}, {3411, 8929}, {8014, 37641}, {8838, 36296}, {10218, 14254}, {10646, 11586}, {11082, 18814}, {11120, 39290}, {11537, 23303}, {14583, 40579}, {16242, 46078}, {16770, 19713}, {34325, 43229}, {36211, 37835}, {42099, 48354}, {44713, 46925}
X(51270) = isogonal conjugate of X(40156)
X(51270) = X(3129)-cross conjugate of X(13)
X(51270) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40156}, {2151, 2992}
X(51270) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 40156), (15, 11131), (40578, 2992), (46666, 6137)
X(51270) = barycentric product X(i)*X(j) for these {i,j}: {13, 621}, {265, 11093}, {300, 3129}, {8014, 46758}, {39262, 43085}
X(51270) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40156}, {13, 2992}, {621, 298}, {3129, 15}, {3457, 3438}, {8014, 38931}, {11093, 340}, {39262, 38403}, {40580, 11131}
X(51270) = {X(2),X(36299)}-harmonic conjugate of X(40578)
X(51271) lies on the cubic K420b and these lines: {2, 17}, {5, 195}, {13, 5612}, {303, 45799}, {323, 11542}, {396, 11063}, {397, 11145}, {635, 15108}, {1993, 42156}, {3180, 11082}, {3410, 5873}, {5611, 11671}, {6770, 10210}, {7684, 14683}, {8838, 33529}, {10217, 16770}, {11004, 18582}, {11131, 16960}, {16629, 48796}, {16771, 19712}, {20415, 23061}, {20425, 34008}, {42992, 44719}
X(51271) = anticomplement of the isogonal conjugate of X(11083)
X(51271) = anticomplement of the isotomic conjugate of X(8838)
X(51271) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2153, 633}, {8838, 6327}, {11083, 8}, {35199, 1272}, {50468, 4329}
X(51271) = X(i)-Ceva conjugate of X(j) for these (i,j): {8838, 2}, {33529, 19772}
X(51271) = barycentric product X(298)*X(8929)
X(51271) = barycentric quotient X(i)/X(j) for these {i,j}: {8837, 8447}, {8929, 13}
X(51271) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 22113, 19779}, {17, 11126, 2}, {33465, 33530, 11144}
X(51271) lies on the cubic K420b and these lines: {2, 11122}, {5, 302}, {13, 298}, {16, 22911}, {17, 76}, {69, 22113}, {99, 6671}, {299, 11542}, {300, 10217}, {396, 19570}, {621, 6770}, {1080, 5980}, {3589, 7797}, {3643, 16967}, {3818, 16626}, {5965, 44488}, {5982, 31711}, {6390, 42590}, {6669, 7799}, {6673, 44032}, {7752, 22916}, {8838, 41000}, {11129, 16267}, {11133, 22846}, {11303, 22907}, {11304, 31704}, {11307, 42674}, {22508, 33401}, {22892, 30471}, {22901, 34508}, {44361, 47855}
X(51272) = reflection of X(i) in X(j) for these {i,j}: {298, 40707}, {22894, 623}
X(51272) = X(i)-Ceva conjugate of X(j) for these (i,j): {8838, 303}, {41000, 298}
X(51272) = X(38403)-Dao conjugate of X(2981)
X(51272) = {X(17),X(11132)}-harmonic conjugate of X(303)
X(51273) lies on the cubic K420b and these lines: {2, 19775}, {4, 45256}, {5, 3462}, {13, 275}, {17, 470}, {53, 396}, {324, 8838}, {397, 471}, {1629, 7684}, {11144, 14918}, {11547, 18582}, {41101, 44700}
X(51273) = polar conjugate of the isotomic conjugate of X(46753)
X(51273) = polar conjugate of the isogonal conjugate of X(8837)
X(51273) = X(i)-Ceva conjugate of X(j) for these (i,j): {324, 472}, {8838, 470}
X(51273) = X(8837)-cross conjugate of X(46753)
X(51273) = barycentric product X(i)*X(j) for these {i,j}: {4, 46753}, {264, 8837}
X(51273) = barycentric quotient X(i)/X(j) for these {i,j}: {8837, 3}, {46753, 69}
X(51273) = {X(275),X(6116)}-harmonic conjugate of X(472)
X(51274) lies on the cubic K420b and these lines: {2, 14}, {5, 8930}, {13, 14993}, {61, 10218}, {265, 6105}, {303, 43086}, {396, 18285}, {476, 11581}, {547, 34326}, {3412, 8918}, {5318, 15743}, {5612, 10272}, {5616, 37779}, {6104, 32223}, {6117, 36309}, {8838, 46076}, {10217, 11082}, {10413, 11063}, {11085, 37832}, {11542, 11549}, {11556, 42580}, {15442, 16808}, {16267, 36298}, {16462, 47519}, {16960, 18776}, {16965, 45779}, {36297, 45972}, {37341, 41475}
X(51274) = X(5616)-cross conjugate of X(14)
X(51274) = X(i)-isoconjugate of X(j) for these (i,j): {1095, 46076}, {2152, 13582}, {6149, 46072}
X(51274) = X(i)-Dao conjugate of X(j) for these (i, j): (8562, 30468), (14993, 46072), (40579, 13582)
X(51274) = barycentric product X(i)*X(j) for these {i,j}: {14, 37779}, {94, 5616}, {301, 11063}, {10272, 36311}, {23896, 45147}, {36298, 46751}, {37943, 40710}
X(51274) = barycentric quotient X(i)/X(j) for these {i,j}: {14, 13582}, {1989, 46072}, {3458, 14579}, {5612, 11130}, {5616, 323}, {5994, 1291}, {6140, 6138}, {10272, 41888}, {10413, 30468}, {11063, 16}, {11085, 46076}, {36297, 43704}, {36298, 3471}, {37779, 299}, {37943, 471}, {45147, 23871}, {47053, 17403}, {50461, 44719}
X(51274) = {X(8015),X(37835)}-harmonic conjugate of X(14)
X(51275) lies on the cubic K420b and these lines: {5, 49}, {13, 275}, {95, 303}, {97, 465}, {300, 34385}, {396, 11077}, {3457, 42300}, {8613, 50468}, {8795, 36296}, {10217, 16770}, {11082, 19713}, {11542, 46064}, {23895, 46138}, {34389, 44719}
X(51275) = isotomic conjugate of X(33529)
X(51275) = polar conjugate of X(6117)
X(51275) = isotomic conjugate of the complement of X(11127)
X(51275) = X(i)-cross conjugate of X(j) for these (i,j): {17, 11119}, {471, 36308}, {11601, 11118}
X(51275) = X(i)-isoconjugate of X(j) for these (i,j): {5, 2151}, {14, 2290}, {15, 1953}, {19, 44711}, {31, 33529}, {48, 6117}, {298, 2179}, {1154, 2154}, {2181, 44718}, {2617, 6137}, {8739, 44706}, {14213, 34394}, {35198, 36301}
X(51275) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 33529), (6, 44711), (1249, 6117), (30472, 1273), (38994, 2081), (40578, 5), (40581, 1154), (43962, 41078)
X(51275) = cevapoint of X(i) and X(j) for these (i,j): {2, 11127}, {13, 36296}
X(51275) = trilinear pole of line {16, 15412}
X(51275) = barycentric product X(i)*X(j) for these {i,j}: {13, 95}, {16, 46138}, {54, 300}, {275, 40709}, {276, 36296}, {299, 1141}, {3457, 34384}, {8737, 34386}, {15412, 23895}, {36308, 43768}, {39377, 43752}
X(51275) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 33529}, {3, 44711}, {4, 6117}, {13, 5}, {16, 1154}, {54, 15}, {95, 298}, {97, 44718}, {265, 44714}, {275, 470}, {299, 1273}, {300, 311}, {471, 14918}, {1141, 14}, {1157, 5616}, {2148, 2151}, {2152, 2290}, {2153, 1953}, {2623, 6137}, {3457, 51}, {5995, 1625}, {6138, 2081}, {8737, 53}, {8740, 11062}, {8882, 8739}, {8901, 30465}, {10217, 44713}, {10633, 20412}, {11077, 36297}, {11078, 33530}, {11082, 36301}, {11139, 36300}, {14533, 46112}, {15412, 23870}, {18315, 17402}, {20578, 12077}, {23871, 41078}, {23895, 14570}, {30452, 41221}, {36296, 216}, {36306, 35360}, {38414, 23181}, {38808, 44700}, {39377, 44715}, {40709, 343}, {41997, 35442}, {43768, 41887}, {44687, 44688}, {46072, 1263}, {46073, 35194}, {46138, 301}, {50465, 44712}
X(51276) lies on the cubic K420b and these lines: {2, 2993}, {3, 13}, {5, 8837}, {15, 6107}, {95, 303}, {140, 50465}, {396, 11083}, {470, 8737}, {3457, 11488}, {5961, 38944}, {5995, 6671}, {8838, 19712}, {11081, 23302}, {23284, 43083}, {33417, 36208}, {40580, 47201}
X(51276) = X(8838)-Ceva conjugate of X(13)
X(51276) = X(15802)-cross conjugate of X(627)
X(51276) = X(2151)-isoconjugate of X(19712)
X(51276) = X(40578)-Dao conjugate of X(19712)
X(51276) = barycentric product X(i)*X(j) for these {i,j}: {13, 627}, {3457, 46755}, {11119, 15802}
X(51276) = barycentric quotient X(i)/X(j) for these {i,j}: {13, 19712}, {627, 298}, {3457, 3489}, {8014, 39134}, {11139, 40167}, {15802, 618}
X(51276) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 50468, 38943}, {17, 6104, 13}, {23714, 47481, 40578}
X(51277) lies on the cubic K420b and these lines: {2, 19777}, {3, 45779}, {5, 8918}, {6, 13}, {15, 15442}, {61, 11582}, {264, 301}, {302, 23896}, {396, 11085}, {3412, 8930}, {8015, 37640}, {8836, 36297}, {10217, 14254}, {10645, 15743}, {11087, 18813}, {11119, 39290}, {11549, 23302}, {14583, 40578}, {16241, 46074}, {16771, 19712}, {34326, 43228}, {36210, 37832}, {42100, 48356}, {44714, 46926}
X(51277) = isogonal conjugate of X(40157)
X(51277) = X(3130)-cross conjugate of X(14)
X(51277) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40157}, {2152, 2993}
X(51277) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 40157), (16, 11130), (40579, 2993), (46667, 6138)
X(51277) = barycentric product X(i)*X(j) for these {i,j}: {14, 622}, {265, 11094}, {301, 3130}, {8015, 46757}, {39261, 43086}
X(51277) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40157}, {14, 2993}, {622, 299}, {3130, 16}, {3458, 3439}, {8015, 38932}, {11094, 340}, {39261, 38404}, {40581, 11130}
X(51277) = {X(2),X(36298)}-harmonic conjugate of X(40579)
See Stanley Rabinowitz, Antreas Hatzipolakis, César Lozada and Peter Moses, euclid 5321 and euclid 5324.
X(51278) lies on these lines: {5, 13}, {396, 31703}, {533, 11542}, {547, 22848}, {549, 22862}, {618, 43102}, {620, 6669}, {5066, 31706}, {5470, 41943}, {6770, 41054}, {11121, 37170}, {11298, 30471}, {11603, 43548}, {16628, 37640}, {21843, 42086}, {22831, 43417}, {22850, 41121}, {22856, 43228}, {22892, 34602}, {33627, 49945}, {37352, 40706}, {42139, 48655}, {42154, 47610}
X(51278) = midpoint of X(i) and X(j) for these {i, j}: {13, 22847}, {396, 31703}, {6770, 41054}
X(51278) = {X(13), X(22846)}-harmonic conjugate of X(22847)
See Stanley Rabinowitz, Antreas Hatzipolakis, César Lozada and Peter Moses, euclid 5321 and euclid 5324.
X(51279) lies on these lines: {5, 14}, {395, 31704}, {532, 11543}, {547, 22892}, {549, 22906}, {619, 43103}, {620, 6670}, {5066, 31705}, {5469, 41944}, {6773, 41055}, {11122, 37171}, {11297, 30472}, {11602, 43549}, {16629, 37641}, {21843, 42085}, {22832, 43416}, {22894, 41122}, {22900, 43229}, {33626, 49946}, {37351, 40707}, {42142, 48656}, {42155, 47611}
X(51279) = midpoint of X(i) and X(j) for these {i, j}: {14, 22893}, {395, 31704}, {6773, 41055}
X(51279) = {X(14), X(22891)}-harmonic conjugate of X(22893)
X(51280) = lies on these lines: {6, 519}, {214, 4070}, {391, 16086}, {514, 661}, {742, 36230}, {1213, 49758}, {3061, 4153}, {4482, 17264}, {17234, 20444}, {17240, 49779}, {17310, 31034}, {20234, 20893}, {21070, 49763}, {21071, 49767}, {30169, 41771}, {30811, 41141}, {34542, 49769}
X(51280) = midpoint of X(6) and X(49778)
X(51280) = reflection of X(49782) in X(49781)
X(51280) = crossdifference of every pair of points on line {31, 9002}
See Ivan Pavlov, euclid 5333.
X(51281) lies on these lines: {1, 3}, {4, 22361}, {29, 5705}, {33, 21165}, {58, 35981}, {63, 3465}, {73, 6876}, {90, 2648}, {212, 6905}, {255, 411}, {283, 1816}, {603, 3651}, {902, 30305}, {1013, 31424}, {1069, 36600}, {1479, 30943}, {1935, 6985}, {2000, 4652}, {2654, 6875}, {3074, 3149}, {4257, 4304}, {4294, 11269}, {5715, 7567}, {6734, 7538}, {6942, 22072}, {7531, 40950}, {7741, 37370}, {8616, 30384}, {15485, 23708}, {26091, 26363}, {37428, 43043}
X(51281) = intersection, other than A, B, C, of circumconics {{A, B, C, X(46), X(2648)}} and {{A, B, C, X(65), X(3362)}}
X(51281) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 1936, 1), (255, 411, 1745), (3072, 26357, 1)
See Ivan Pavlov, euclid 5333.
X(51282) lies on these lines: {1, 4}, {3, 42385}, {29, 3612}, {35, 1013}, {36, 37258}, {46, 158}, {55, 39529}, {57, 1784}, {90, 1896}, {92, 5119}, {318, 41229}, {381, 42387}, {382, 42379}, {498, 39574}, {920, 1715}, {1118, 1770}, {1210, 43160}, {1723, 8748}, {1727, 1748}, {1737, 1857}, {1895, 3338}, {2646, 7524}, {2656, 3362}, {3560, 40946}, {4305, 7518}, {5125, 10826}, {5174, 37711}, {6985, 22341}, {7049, 36599}, {7741, 37371}, {7951, 39531}, {11375, 44225}, {12514, 17860}, {14803, 37253}, {17923, 23708}
X(51282) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(43764)}} and {{A, B, C, X(73), X(90)}}
X(51282) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (4, 243, 1), (158, 412, 46)
See See Ivan Pavlov, euclid 5333.
X(51283) lies on these lines: {1, 5}, {655, 1087}
X(51283) = {X(5), X(2596)}-harmonic conjugate of X(1)
See Ivan Pavlov, euclid 5333.
X(51284) lies on these lines: {1, 2}, {40, 190}, {57, 4737}, {63, 4723}, {346, 8074}, {1265, 11362}, {1697, 46937}, {1706, 4385}, {2093, 32937}, {2899, 10624}, {3421, 26929}, {3586, 36926}, {3596, 10444}, {3717, 5657}, {3869, 4767}, {3886, 33845}, {3895, 4358}, {3913, 4702}, {3992, 5119}, {4646, 17318}, {5100, 9581}, {5587, 32850}, {5775, 10005}, {5815, 6552}, {9369, 15803}, {17595, 50078}, {18743, 31393}, {30615, 40663}, {37704, 37758}
X(51284) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (8, 5205, 1), (3992, 5119, 30568)
See Ivan Pavlov, See Ivan Pavlov, euclid 5333.
X(51285) lies on these lines: {1, 2}, {35, 3714}, {46, 4659}, {190, 191}, {321, 484}, {333, 3992}, {1759, 16548}, {3219, 4125}, {3337, 4968}, {3376, 44691}, {3383, 44690}, {3416, 7951}, {3678, 4767}, {3702, 37563}, {3706, 48696}, {3746, 4702}, {3814, 33075}, {3822, 33078}, {4054, 11552}, {4385, 6763}, {4670, 37559}, {4692, 14829}, {5143, 5295}, {5315, 30818}, {5692, 5774}, {5694, 31778}, {17335, 46937}, {34790, 50362}, {37572, 50044}
X(51285) = {X(10), X(17763)}-harmonic conjugate of X(1)
See See Ivan Pavlov, euclid 5333.
X(51286) lies on these lines: {1, 5}, {150, 21635}, {655, 1090}, {658, 1111}, {1768, 24618}
See Ivan Pavlov, euclid 5333.
X(51287) lies on these lines: {1, 5}, {655, 1091}
See Ivan Pavlov, euclid 5333.
X(51288) lies on these lines: {1, 19}, {63, 2181}, {158, 1733}, {162, 1096}, {278, 18193}, {897, 36063}, {920, 33781}, {988, 1871}, {1784, 4008}, {1859, 17594}, {1861, 18395}, {1956, 2184}, {1957, 16570}, {3751, 14571}, {15430, 51292}
X(51288) = barycentric product X(i)*X(j) for these {i, j}: {1, 37174}, {19, 1007}, {92, 1351}, {1096, 10008}
X(51288) = barycentric quotient X(i)/X(j) for these (i, j): (19, 7612), (158, 42298), (1007, 304), (1096, 47735), (1351, 63)
X(51288) = trilinear product X(i)*X(j) for these {i, j}: {4, 1351}, {6, 37174}, {25, 1007}
X(51288) = trilinear quotient X(i)/X(j) for these (i, j): (4, 7612), (393, 47735), (1007, 69), (1351, 3)
X(51288) = Mimosa transform of X(40801)
X(51288) = intersection, other than A, B, C, of circumconics {{A, B, C, X(28), X(37174)}} and {{A, B, C, X(48), X(8769)}}
X(51288) = X(4)-gimel conjugate of-X(33781)
X(51288) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 7612}, {394, 47735}, {577, 42298}
X(51288) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (19, 7612), (158, 42298), (1007, 304), (1096, 47735), (1351, 63)
X(51288) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 18594, 1955), (19, 240, 1), (1096, 1748, 1707)
See Ivan Pavlov, euclid 5333.
X(51289) lies on these lines: {1, 20}, {658, 1097}
See Ivan Pavlov, euclid 5333.
X(51290) lies on these lines: {1, 21}, {3, 662}, {4, 25446}, {9, 5060}, {46, 409}, {60, 4189}, {261, 10446}, {270, 1013}, {333, 3419}, {411, 21363}, {643, 956}, {978, 34882}, {1092, 6875}, {1155, 11116}, {1175, 34259}, {1509, 50739}, {2185, 16370}, {2194, 37303}, {4302, 19642}, {4640, 17512}, {5267, 17104}, {5327, 11110}, {6061, 37106}, {11114, 24624}, {17549, 40214}, {19763, 20846}, {37284, 50619}
X(51290) = barycentric product X(63)*X(1982)
X(51290) = trilinear product X(3)*X(1982)
X(51290) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(37142)}} and {{A, B, C, X(4), X(2650)}}
X(51290) = {X(21), X(2651)}-harmonic conjugate of X(1)
See See Ivan Pavlov, euclid 5333.
X(51291) lies on these lines: {1, 21}, {6, 50613}, {32, 2319}, {43, 2210}, {87, 7122}, {182, 6210}, {560, 662}, {922, 36289}, {1423, 3506}, {1438, 36598}, {1486, 16800}, {1582, 16571}, {1973, 38275}, {3097, 37586}, {3113, 3403}, {3223, 46289}, {3492, 3500}, {4112, 9902}, {4251, 42043}, {4650, 18208}, {5042, 16779}, {5299, 23538}, {7350, 8922}, {8626, 24598}, {12194, 24264}, {17126, 40790}, {17754, 40746}, {33782, 33783}
X(51291) = barycentric product X(i)*X(j) for these {i, j}: {1, 7766}, {31, 41259}, {82, 32449}, {560, 10010}, {662, 25423}
X(51291) = barycentric quotient X(i)/X(j) for these (i, j): (1, 43688), (163, 25424)
X(51291) = trilinear product X(i)*X(j) for these {i, j}: {6, 7766}, {32, 41259}, {110, 25423}, {251, 32449}, {691, 45680}, {1501, 10010}
X(51291) = trilinear quotient X(i)/X(j) for these (i, j): (2, 43688), (110, 25424)
X(51291) = Mimosa transform of X(43722)
X(51291) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(43761)}} and {{A, B, C, X(19), X(17799)}}
X(51291) = X(9)-Dao conjugate of X(43688)
X(51291) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 43688}, {523, 25424}
X(51291) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 43688), (163, 25424)
X(51291) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 1707, 17799), (31, 1580, 1), (560, 33760, 1740)
See See Ivan Pavlov, euclid 5333.
X(51292) lies on these lines: {1, 4}, {653, 1721}, {15430, 51288}
See See Ivan Pavlov, euclid 5333.
X(51293) lies on these lines: {1, 4}, {653, 1722}
See Ivan Pavlov, euclid 5333.
X(51294) lies on these lines: {1, 6}, {2, 21093}, {10, 9791}, {100, 756}, {190, 3842}, {191, 13610}, {498, 27547}, {726, 17260}, {1255, 4722}, {1334, 41323}, {1621, 42041}, {1654, 6541}, {1698, 3729}, {1961, 3219}, {3550, 7322}, {3624, 17368}, {3634, 17116}, {3679, 3790}, {3715, 17592}, {3773, 17256}, {3775, 17264}, {3826, 49742}, {3836, 17258}, {3923, 36531}, {3929, 37604}, {3932, 24697}, {3943, 42334}, {3989, 27065}, {3993, 50016}, {3994, 5235}, {4026, 49737}, {4078, 33082}, {4364, 33159}, {4384, 27481}, {4389, 25590}, {4413, 17596}, {4414, 9330}, {4429, 19875}, {4473, 24295}, {4527, 4668}, {4535, 32025}, {4641, 9332}, {4656, 33138}, {4677, 49746}, {4681, 4716}, {4687, 32935}, {4704, 49488}, {4942, 19744}, {5018, 29007}, {5260, 11533}, {5263, 50094}, {5284, 42039}, {6211, 8245}, {6536, 33166}, {7226, 29820}, {7308, 17591}, {7609, 31395}, {9345, 32913}, {9505, 22116}, {9780, 25269}, {15430, 51300}, {16815, 50117}, {16823, 49520}, {17235, 31252}, {17257, 29674}, {17259, 49493}, {17277, 49456}, {17317, 17771}, {17332, 32846}, {17335, 32921}, {17336, 50302}, {17355, 19856}, {17738, 31323}, {19876, 24441}, {24231, 25072}, {24248, 40333}, {24325, 24821}, {24331, 31302}, {25101, 29637}, {25601, 26364}, {25728, 39586}, {26580, 29862}, {26685, 29646}, {26792, 29682}, {27549, 29659}, {29657, 31018}, {30363, 37619}, {30393, 36634}, {33087, 41313}, {35595, 46901}, {43997, 50127}, {48829, 51066}, {50291, 51090}
X(51294) = intersection, other than A, B, C, of circumconics {{A, B, C, X(6), X(28482)}} and {{A, B, C, X(37), X(36632)}}
X(51294) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (37, 1757, 1), (37, 15481, 4649), (37, 21879, 20685), (190, 3842, 24342), (3989, 27065, 29821), (4078, 50093, 33082), (4649, 15481, 1757), (7174, 15485, 1), (16676, 51297, 1)
See Ivan Pavlov, euclid 5333.
X(51295) lies on these lines: {1, 3}, {280, 6736}, {651, 1103}, {5121, 9614}, {6048, 9365}, {8056, 30384}
X(51295) = {X(40), X(9371)}-harmonic conjugate of X(1)
See See Ivan Pavlov, euclid 5333.
X(51296) lies on these lines: {1, 2}, {100, 40749}, {190, 872}, {2663, 4670}, {3736, 4753}, {4090, 25264}, {4096, 32026}, {16468, 40732}, {21805, 40773}, {21870, 37596}, {21904, 39252}
X(51296) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 36634, 16832), (42, 2664, 1), (16831, 42042, 1)
See See Ivan Pavlov, euclid 5333.
X(51297) lies on these lines: {1, 6}, {10, 4480}, {88, 36263}, {89, 9330}, {190, 3679}, {192, 50018}, {210, 17601}, {239, 51035}, {537, 17335}, {726, 16816}, {756, 37604}, {899, 3097}, {1698, 17250}, {3219, 3550}, {3240, 40774}, {3551, 32635}, {3617, 4660}, {3634, 3662}, {3678, 37574}, {3715, 16569}, {3758, 50094}, {3842, 41847}, {3912, 51004}, {3952, 30564}, {3989, 17013}, {4363, 19875}, {4384, 24821}, {4393, 50777}, {4407, 17354}, {4416, 49766}, {4432, 50075}, {4439, 17346}, {4473, 50311}, {4557, 5010}, {4664, 4753}, {4668, 5695}, {4677, 4693}, {4704, 49685}, {4709, 25269}, {4741, 49769}, {4759, 36534}, {6646, 9780}, {9324, 39335}, {9345, 40434}, {17021, 32912}, {17160, 49445}, {17256, 50313}, {17261, 49469}, {17277, 49532}, {17282, 19872}, {17332, 33165}, {17336, 49457}, {17338, 19862}, {17348, 49517}, {17349, 49520}, {19856, 26039}, {25352, 50128}, {27549, 33082}, {29571, 50834}, {29601, 34379}, {29602, 50952}, {29659, 50093}, {32857, 38057}, {33761, 42042}, {36531, 50127}, {49701, 49746}, {49710, 50286}, {49721, 51066}, {50022, 50090}
X(51297) = barycentric product X(190)*X(48213)
X(51297) = trilinear product X(100)*X(48213)
X(51297) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(35170)}} and {{A, B, C, X(88), X(16468)}}
X(51297) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 44, 16468), (1, 51294, 16676), (9, 49448, 15485), (44, 984, 1), (45, 5220, 49712), (45, 49712, 1), (3751, 16676, 1), (4649, 16672, 1), (15254, 49503, 1)
See Ivan Pavlov, euclid 5333.
X(51298) lies on these lines: {1, 3}, {225, 7040}, {651, 920}, {1937, 36599}
X(51298) = {X(46), X(8758)}-harmonic conjugate of X(1)
See Ivan Pavlov, euclid 5333.
X(51299) lies on these lines: {1, 19}, {922, 4008}
X(51299) = {X(48), X(1955)}-harmonic conjugate of X(1)
See Ivan Pavlov, euclid 5333.
X(51300) lies on these lines: {1, 3}, {170, 10482}, {220, 4421}, {294, 41423}, {651, 1253}, {673, 15485}, {902, 5222}, {3008, 8616}, {3939, 24708}, {4304, 49772}, {9440, 11495}, {10481, 50808}, {15430, 51294}, {17745, 42043}, {28043, 35258}
X(51300) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(36628)}} and {{A, B, C, X(57), X(36601)}}
X(51300) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (55, 9441, 1), (1253, 7676, 1742)
See Ivan Pavlov, euclid 5333.
X(51301) lies on these lines: {1, 3}, {651, 978}, {1413, 36602}, {6048, 9363}
X(51301) = {X(56), X(9364)}-harmonic conjugate of X(1)
See Ivan Pavlov, euclid 5333.
X(51302) lies on these lines: {1, 3}, {2, 10481}, {7, 3731}, {9, 1418}, {37, 7274}, {77, 16667}, {85, 16832}, {218, 1407}, {220, 3928}, {222, 17745}, {226, 24797}, {269, 651}, {277, 7365}, {279, 3008}, {348, 29598}, {948, 3911}, {1014, 18186}, {1170, 17074}, {1212, 5437}, {1323, 5222}, {1423, 5575}, {1427, 16572}, {1462, 16487}, {1742, 30330}, {2310, 30353}, {3062, 9442}, {3160, 50114}, {3218, 25930}, {3243, 42314}, {3306, 24635}, {3668, 4859}, {3973, 6180}, {4326, 21346}, {4328, 16673}, {4334, 5223}, {5018, 16469}, {5219, 20121}, {5308, 21454}, {5666, 8583}, {6604, 29573}, {6610, 16670}, {6743, 37655}, {9312, 16833}, {9436, 17284}, {11495, 18216}, {25242, 30567}, {25718, 50019}, {29621, 32098}, {31225, 40719}, {32003, 49765}, {34578, 43043}
X(51302) = barycentric product X(i)*X(j) for these {i, j}: {7, 3243}, {57, 29627}, {75, 42314}, {269, 10005}
X(51302) = barycentric quotient X(i)/X(j) for these (i, j): (57, 42318), (1407, 42315)
X(51302) = trilinear product X(i)*X(j) for these {i, j}: {2, 42314}, {56, 29627}, {57, 3243}, {1407, 10005}
X(51302) = trilinear quotient X(i)/X(j) for these (i, j): (7, 42318), (269, 42315)
X(51302) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(3243)}} and {{A, B, C, X(2), X(10389)}}
X(51302) = X(333)-beth conjugate of-X(30625)
X(51302) = X(223)-Dao conjugate of X(42318)
X(51302) = X(i)-isoconjugate-of-X(j) for these {i, j}: {55, 42318}, {200, 42315}
X(51302) = X(57)-reciprocal conjugate of-X(42318)
X(51302) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (9, 1418, 7271), (57, 241, 1), (269, 1445, 1743), (279, 5435, 3008), (948, 3911, 31183), (3668, 8732, 4859), (13388, 13389, 10389), (21314, 31183, 948), (37772, 37773, 35445)
See Ivan Pavlov, euclid 5333.
X(51303) lies on these lines: {1, 21}, {662, 849}, {4256, 30576}, {17271, 34016}
See Ivan Pavlov, euclid 5333.
X(51304) lies on these lines: {1, 21}, {2, 3674}, {9, 7146}, {40, 25083}, {57, 3061}, {69, 18725}, {75, 18713}, {77, 5279}, {78, 7291}, {92, 1930}, {144, 17261}, {192, 10889}, {200, 18788}, {239, 20535}, {304, 2184}, {306, 36850}, {326, 610}, {329, 3912}, {908, 17284}, {1429, 3928}, {1581, 8769}, {1958, 18594}, {2172, 6507}, {2329, 3929}, {2349, 37216}, {2951, 12530}, {3666, 9575}, {3729, 10446}, {5227, 18161}, {5272, 18208}, {5744, 17023}, {5748, 29596}, {8557, 34377}, {10436, 11683}, {10444, 25252}, {11679, 17760}, {17742, 18727}, {17781, 29573}, {18656, 20223}, {18691, 21406}, {18695, 21582}, {20245, 45738}, {21446, 42309}, {25590, 30035}, {26575, 31080}, {27834, 36101}, {36973, 41772}
X(51304) = isotomic conjugate of the polar conjugate of X(23052)
X(51304) = barycentric product X(i)*X(j) for these {i, j}: {1, 37668}, {75, 1350}, {304, 45141}, {326, 10002}
X(51304) = barycentric quotient X(i)/X(j) for these (i, j): (1, 3424), (63, 42287), (1350, 1)
X(51304) = trilinear product X(i)*X(j) for these {i, j}: {2, 1350}, {6, 37668}, {20, 40813}, {69, 45141}, {250, 12037}, {394, 10002}
X(51304) = trilinear quotient X(i)/X(j) for these (i, j): (69, 42287), (1350, 6), (1529, 16318)
X(51304) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(23052)}} and {{A, B, C, X(31), X(2184)}}
X(51304) = X(9)-Dao conjugate of X(3424)
X(51304) = X(69)-gimel conjugate of-X(1)
X(51304) = X(i)-isoconjugate-of-X(j) for these {i, j}: {6, 3424}, {25, 42287}
X(51304) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (1, 3424), (63, 42287)
X(51304) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 16570, 1580), (1, 17799, 1707), (63, 1959, 1), (326, 1760, 610)
See Ivan Pavlov, euclid 5333.
X(51305) lies on these lines: {1, 3}, {10, 17950}, {651, 1046}, {2647, 7098}, {3671, 29640}, {24987, 26840}
X(51305) = {X(65), X(1758)}-harmonic conjugate of X(1)
See Ivan Pavlov, euclid 5333.
X(51306) lies on these lines: {1, 6}, {100, 2939}
See Ivan Pavlov, euclid 5333.
X(51307) lies on these lines: {1, 73}, {653, 1047}
X(51307) = {X(73), X(2655)}-harmonic conjugate of X(1)
See Ivan Pavlov, euclid 5333.
X(51308) lies on these lines: {1, 7}, {223, 658}
See Ivan Pavlov, euclid 5333.
X(51309) lies on these lines: {1, 2}, {190, 1490}
X(51309) = {X(78), X(23691)}-harmonic conjugate of X(1)
See Ivan Pavlov, euclid 5333.
X(51310) lies on these lines: {1, 5}, {484, 655}, {5541, 18359}
X(51310) = {X(80), X(14204)}-harmonic conjugate of X(1)
See Ivan Pavlov, euclid 5333.
X(51311) lies on the cubic K285 and these lines: {1, 21}, {2, 1171}, {6, 662}, {9, 1963}, {32, 593}, {86, 4643}, {99, 4393}, {162, 28044}, {239, 17103}, {261, 17379}, {270, 37396}, {333, 29576}, {741, 869}, {1178, 23524}, {1412, 41526}, {1414, 5228}, {1449, 38814}, {1475, 17209}, {2134, 5256}, {2308, 16480}, {3219, 21816}, {3661, 17731}, {3758, 19623}, {3765, 5209}, {4251, 30581}, {4641, 21879}, {5222, 24617}, {5333, 17210}, {6626, 17397}, {6629, 17023}, {7304, 24621}, {8025, 29592}, {8033, 20913}, {14534, 37683}, {16369, 16826}, {16481, 21747}, {16666, 16702}, {16777, 40438}, {17018, 33774}, {17120, 27958}, {17277, 30593}, {17378, 25536}, {17389, 32004}, {19308, 20970}, {20142, 51314}, {29570, 33770}, {29588, 31059}, {29617, 41629}, {37666, 50735}
X(51311) = isogonal conjugate of the isotomic conjugate of X(51314)
X(51311) = barycentric product X(i)*X(j) for these {i, j}: {6, 51314}, {63, 31904}, {81, 16826}, {86, 4649}, {99, 4784}, {662, 28840}
X(51311) = barycentric quotient X(i)/X(j) for these (i, j): (58, 30571), (81, 27483), (163, 28841), (1333, 25426)
X(51311) = trilinear product X(i)*X(j) for these {i, j}: {3, 31904}, {31, 51314}, {58, 16826}, {81, 4649}, {110, 28840}, {593, 3842}
X(51311) = trilinear quotient X(i)/X(j) for these (i, j): (58, 25426), (81, 30571), (86, 27483), (110, 28841)
X(51311) = perspector of the circumconic {{A, B, C, X(662), X(36066)}}
X(51311) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4649)}} and {{A, B, C, X(2), X(1962)}}
X(51311) = crossdifference of every pair of points on line {X(4155), X(8663)}
X(51311) = X(i)-isoconjugate-of-X(j) for these {i, j}: {10, 25426}, {37, 30571}, {42, 27483}, {523, 28841}
X(51311) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (58, 30571), (81, 27483), (163, 28841)
X(51311) = {X(81), X(1931)}-harmonic conjugate of X(1)
See Ivan Pavlov, euclid 5333.
X(51312) lies on these lines: {1, 82}, {31, 4599}, {83, 4660}, {33760, 33793}
X(51312) = barycentric product X(i)*X(j) for these {i, j}: {75, 41295}, {82, 3329}
X(51312) = barycentric quotient X(82)/X(42006)
X(51312) = trilinear product X(i)*X(j) for these {i, j}: {2, 41295}, {83, 12212}, {251, 3329}
X(51312) = trilinear quotient X(i)/X(j) for these (i, j): (83, 42006), (827, 43357)
X(51312) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(43763)}} and {{A, B, C, X(19), X(16556)}}
X(51312) = X(i)-isoconjugate-of-X(j) for these {i, j}: {39, 42006}, {826, 43357}
X(51312) = X(82)-reciprocal conjugate of-X(42006)
X(51312) = {X(82), X(34054)}-harmonic conjugate of X(1)
See Ivan Pavlov, euclid 5333.
X(51313) lies on these lines: {1, 84}, {189, 3586}, {1256, 15803}, {30282, 41081}, {38271, 46355}
See Ivan Pavlov, euclid 5333.
X(51314) lies on the cubic K286 and these lines: {1, 75}, {2, 799}, {6, 1509}, {39, 20133}, {43, 2668}, {76, 15668}, {99, 1001}, {238, 17103}, {261, 19309}, {310, 5333}, {670, 10009}, {870, 40328}, {940, 7304}, {984, 18827}, {1423, 1434}, {2106, 40728}, {4568, 24092}, {4635, 10004}, {4649, 40734}, {14621, 40759}, {16705, 26976}, {16712, 41312}, {16741, 24589}, {16831, 40874}, {16917, 41333}, {17018, 40439}, {17063, 32010}, {17277, 29459}, {18021, 19701}, {18140, 18143}, {20134, 27318}, {20142, 51311}, {25507, 31008}, {26102, 39915}, {27705, 28010}, {28365, 40409}, {30092, 40827}, {32004, 49497}
X(51314) = isotomic conjugate of the isogonal conjugate of X(51311)
X(51314) = barycentric product X(i)*X(j) for these {i, j}: {76, 51311}, {274, 16826}, {304, 31904}, {310, 4649}, {670, 4784}, {799, 28840}
X(51314) = barycentric quotient X(i)/X(j) for these (i, j): (81, 25426), (86, 30571), (274, 27483), (662, 28841)
X(51314) = trilinear product X(i)*X(j) for these {i, j}: {69, 31904}, {75, 51311}, {86, 16826}, {99, 28840}, {274, 4649}, {799, 4784}
X(51314) = trilinear quotient X(i)/X(j) for these (i, j): (86, 25426), (99, 28841), (274, 30571), (310, 27483)
X(51314) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(4649)}} and {{A, B, C, X(2), X(740)}}
X(51314) = X(870)-Ceva conjugate of-X(8033)
X(51314) = X(i)-isoconjugate-of-X(j) for these {i, j}: {42, 25426}, {213, 30571}, {512, 28841}
X(51314) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (81, 25426), (86, 30571), (274, 27483), (662, 28841)
X(51314) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 873, 8033), (86, 274, 30940), (86, 2669, 1), (16709, 18157, 274), (17175, 18792, 86)
See Ivan Pavlov, euclid 5333.
X(51315) lies on these lines: {1, 29}, {19, 823}, {63, 1969}, {610, 9252}, {1748, 21374}
X(51315) = barycentric product X(i)*X(j) for these {i, j}: {19, 44144}, {92, 458}, {158, 183}, {393, 3403}, {823, 23878}, {1096, 20023}
X(51315) = barycentric quotient X(i)/X(j) for these (i, j): (19, 43718), (92, 42313), (158, 262), (182, 255), (183, 326), (393, 2186)
X(51315) = trilinear product X(i)*X(j) for these {i, j}: {4, 458}, {25, 44144}, {107, 23878}, {182, 2052}, {183, 393}, {264, 10311}
X(51315) = trilinear quotient X(i)/X(j) for these (i, j): (4, 43718), (107, 26714), (158, 2186), (182, 577), (183, 394), (264, 42313)
X(51315) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(1821)}} and {{A, B, C, X(29), X(458)}}
X(51315) = X(i)-isoconjugate-of-X(j) for these {i, j}: {3, 43718}, {184, 42313}, {255, 2186}, {262, 577}, {263, 394}
X(51315) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (19, 43718), (92, 42313), (158, 262), (182, 255), (183, 326)
See Angel Montesdeoca, euclid 5336.
X(51316) lies on these lines: {6,3091}, {25,37689}, {115,34570}, {230,36616}, {493,8972}, {494,13941}, {1968,8882}, {2987,20080}, {3620,40802}, {6622,33630}, {14572,47296}, {17907,42373}, {32830,42407}, {41890,43448}, {41891,43620}
X(51316) = isogonal conjugate of X(37672)
X(51316) = isotomic conjugate of X(32831)
X(51317) lies on these lines: {2, 47883}, {325, 523}, {514, 4120}, {522, 47755}, {661, 47674}, {812, 47791}, {824, 21115}, {918, 48423}, {3667, 5214}, {3676, 17161}, {3700, 47675}, {3776, 4838}, {3835, 47667}, {4024, 21116}, {4106, 28195}, {4122, 48127}, {4379, 27486}, {4382, 49282}, {4453, 4777}, {4467, 28205}, {4500, 4931}, {4608, 28191}, {4728, 47781}, {4762, 4789}, {4773, 47762}, {4778, 20295}, {4802, 48550}, {4885, 47661}, {4926, 43067}, {4928, 47878}, {4958, 28886}, {6548, 28169}, {6590, 26824}, {7662, 44433}, {14425, 31150}, {17494, 47766}, {21104, 47665}, {21183, 28161}, {21212, 50482}, {23813, 28199}, {26248, 48220}, {26277, 48240}, {26985, 44432}, {28151, 48558}, {28165, 47754}, {28183, 47891}, {28294, 47721}, {28468, 50457}, {28894, 47871}, {39386, 48107}, {44449, 48133}, {45320, 47782}, {46915, 47757}, {47650, 47660}, {47652, 48397}, {47658, 47960}, {47659, 48398}, {47670, 48404}, {47673, 48415}, {47699, 48090}, {47703, 48394}, {47719, 48393}, {47775, 47787}, {47776, 47789}, {47798, 47834}, {47930, 48430}, {47988, 48604}, {48126, 49275}, {48222, 48408}, {48266, 49291}, {48275, 49289}, {49287, 50522}
X(51317) = midpoint of X(i) and X(j) for these {i,j}: {4024, 21116}, {4931, 47672}, {26824, 47773}, {44435, 47656}, {47792, 47869}
X(51317) = reflection of X(i) in X(j) for these {i,j}: {4728, 48419}, {4931, 4500}, {17494, 47766}, {21116, 48399}, {25259, 4931}, {27486, 4379}, {31150, 47788}, {44433, 7662}, {44435, 693}, {45745, 44432}, {45746, 44435}, {46915, 47757}, {47663, 47773}, {47676, 21116}, {47755, 47780}, {47769, 47790}, {47771, 4789}, {47773, 6590}, {47774, 47786}, {47775, 47787}, {47776, 47789}, {47781, 4728}, {47782, 45320}, {47790, 48416}, {47798, 47834}, {47878, 4928}, {47892, 47881}, {47894, 21183}, {47975, 48182}, {48187, 48396}, {48408, 48222}, {48543, 21297}
X(51317) = anticomplement of X(47883)
X(51317) = crossdifference of every pair of points on line {32, 21747}
X(51317) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {693, 47655, 3004}, {693, 47656, 45746}, {693, 48274, 47656}, {3835, 47671, 47667}, {4024, 48399, 47676}, {4500, 47672, 25259}, {4789, 47892, 47881}, {6590, 26824, 47663}, {47660, 48125, 47650}, {47671, 48418, 3835}, {47675, 48424, 3700}, {47881, 47892, 47771}, {48275, 49289, 49298}
X(51318) lies on the cubic K788 and thesae lines: {6, 157}, {32, 694}, {110, 699}, {172, 19578}, {251, 3124}, {385, 18902}, {827, 9427}, {1184, 20998}, {1580, 39043}, {1691, 8623}, {1914, 1933}, {2076, 36790}, {3229, 16385}, {5012, 5116}, {12829, 40820}, {14660, 34482}, {17941, 39080}, {19120, 25332}, {38873, 44453}, {39087, 41331}
X(51318) = isogonal conjugate of the isotomic conjugate of X(4027)
X(51318) = X(i)-isoconjugate of X(j) for these (i,j): {75, 41517}, {694, 1934}, {1581, 1916}, {1927, 44160}, {1967, 18896}, {30663, 40099}
X(51318) = X(i)-Dao conjugate of X(j) for these (i, j): (206, 41517), (804, 338), (8290, 18896), (19576, 1916), (39031, 1581), (39043, 1934), (41178, 23285)
X(51318) = crosspoint of X(385) and X(51244)
X(51318) = crosssum of X(694) and X(3493)
X(51318) = crossdifference of every pair of points on line {2799, 23596}
X(51318) = barycentric product X(i)*X(j) for these {i,j}: {6, 4027}, {249, 35078}, {385, 1691}, {512, 46294}, {798, 46295}, {1580, 1580}, {1914, 27982}, {1933, 1966}, {3978, 14602}, {5027, 17941}, {12215, 44089}, {14603, 18902}, {19576, 51244}, {36213, 40820}
X(51318) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 41517}, {385, 18896}, {1580, 1934}, {1691, 1916}, {1933, 1581}, {3978, 44160}, {4027, 76}, {14602, 694}, {18902, 9468}, {19575, 3493}, {27982, 18895}, {35078, 338}, {46294, 670}, {46295, 4602}
X(51318) = {X(32),X(3506)}-harmonic conjugate of X(694)
X(512) lies on the cubic K788 and these lines: {6, 31}, {32, 2319}, {37, 11688}, {100, 699}, {171, 172}, {213, 893}, {292, 1402}, {345, 6542}, {385, 17787}, {579, 24525}, {1403, 2176}, {2240, 32948}, {2242, 37604}, {2275, 23853}, {2345, 4386}, {3744, 17448}, {5143, 16584}, {8624, 17596}, {9310, 21001}, {9454, 21792}, {14829, 31027}, {20359, 20719}, {33863, 41346}
X(51319) = isogonal conjugate of X(27447)
X(51319) = isogonal conjugate of the isotomic conjugate of X(17752)
X(51319) = X(7122)-Ceva conjugate of X(172)
X(51319) = X(i)-isoconjugate of X(j) for these (i,j): {1, 27447}, {87, 257}, {256, 330}, {893, 6384}, {904, 6383}, {1431, 27424}, {1432, 7155}, {1581, 39914}, {1916, 34252}, {2162, 7018}, {2319, 7249}, {4451, 7153}, {7121, 44187}, {16606, 32010}, {27805, 43931}, {40432, 42027}, {40738, 45782}
X(51319) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 27447), (19576, 39914), (21051, 16732), (39031, 34252), (40597, 6384), (40598, 44187)
X(51319) = crosspoint of X(1423) and X(3502)
X(51319) = crosssum of X(2319) and X(3494)
X(51319) = barycentric product X(i)*X(j) for these {i,j}: {6, 17752}, {31, 41318}, {43, 171}, {100, 24533}, {109, 30584}, {172, 192}, {894, 2176}, {1215, 38832}, {1403, 7081}, {1423, 2329}, {1580, 41531}, {1691, 40848}, {1909, 2209}, {1918, 27891}, {2295, 27644}, {2330, 3212}, {3208, 7175}, {4083, 4579}, {4595, 20981}, {6376, 7122}, {7009, 20760}, {7119, 22370}, {17787, 41526}, {18047, 20979}, {20964, 33296}
X(51319) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 27447}, {43, 7018}, {171, 6384}, {172, 330}, {192, 44187}, {894, 6383}, {1403, 7249}, {1691, 39914}, {1933, 34252}, {2176, 257}, {2209, 256}, {2329, 27424}, {2330, 7155}, {4579, 18830}, {7122, 87}, {7175, 7209}, {17752, 76}, {20760, 7019}, {20964, 42027}, {24533, 693}, {30584, 35519}, {38832, 32010}, {40848, 18896}, {41318, 561}, {41526, 1432}, {41531, 1934}
X(51319) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {213, 37619, 893}, {1403, 2176, 20284}
X(51320) lies on the cubic K788 and these lines: {6, 22}, {32, 695}, {172, 1933}, {248, 43721}, {385, 18902}, {694, 19558}, {699, 46970}, {1613, 14575}, {1691, 2679}, {1914, 19578}, {1915, 37893}, {3005, 3050}, {3224, 44162}, {3398, 14133}, {3499, 10547}, {8623, 19576}, {9418, 39087}, {18274, 18892}, {20968, 33786}, {33773, 44164}
X(51320) = isogonal conjugate of X(40847)
X(51320) = isogonal conjugate of the isotomic conjugate of X(16985)
X(51320) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40847}, {561, 14946}, {694, 9239}, {695, 1934}, {711, 20627}, {1581, 9229}, {1916, 9285}, {8061, 18828}, {9236, 44160}, {9288, 18896}
X(51320) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 40847), (19576, 9229), (37895, 18896), (39031, 9285), (39043, 9239), (40368, 14946)
X(51320) = crosssum of X(i) and X(j) for these (i,j): {695, 3505}, {3852, 8265}
X(51320) = crossdifference of every pair of points on line {626, 826}
X(51320) = barycentric product X(i)*X(j) for these {i,j}: {6, 16985}, {384, 1691}, {385, 1915}, {419, 37893}, {710, 38826}, {782, 827}, {1580, 1582}, {1932, 1966}, {1933, 1965}, {4630, 35558}, {9230, 14602}, {11380, 12215}, {16101, 19575}, {35530, 44167}, {37894, 44089}
X(51320) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40847}, {384, 18896}, {710, 44166}, {782, 23285}, {827, 18828}, {1501, 14946}, {1580, 9239}, {1582, 1934}, {1691, 9229}, {1915, 1916}, {1932, 1581}, {1933, 9285}, {4630, 783}, {9230, 44160}, {14602, 695}, {16985, 76}, {19575, 3505}, {35530, 8039}, {37893, 40708}, {44089, 37892}, {44167, 711}
X(51320) = {X(32),X(3492)}-harmonic conjugate of X(695)
X(51321) lies on the cubics K773 and K788 and these lines: {6, 20667}, {31, 172}, {32, 2319}, {58, 23525}, {87, 1716}, {251, 16606}, {292, 23566}, {593, 27455}, {932, 9111}, {1575, 34077}, {1580, 1914}, {1691, 2210}, {2275, 15373}, {4264, 21759}, {5053, 34071}
X(51321) = isogonal conjugate of X(40848)
X(51321) = isogonal conjugate of the isotomic conjugate of X(39914)
X(51321) = X(238)-cross conjugate of X(1914)
X(51321) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40848}, {2, 41531}, {43, 335}, {192, 291}, {292, 6376}, {334, 2176}, {660, 3835}, {694, 41318}, {813, 20906}, {876, 4595}, {1423, 4518}, {1575, 33680}, {1581, 17752}, {1911, 6382}, {2209, 18895}, {3208, 7233}, {3212, 4876}, {3572, 36863}, {3971, 37128}, {4083, 4562}, {4583, 20979}, {4584, 21051}, {4589, 21834}, {4639, 50491}, {5378, 21138}, {7077, 30545}, {14598, 40367}, {18827, 20691}, {27644, 43534}, {36801, 43051}, {40155, 40844}
X(51321) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 40848), (6651, 6382), (18277, 40367), (19557, 6376), (19576, 17752), (32664, 41531), (39029, 192), (39043, 41318), (40623, 20906)
X(51321) = cevapoint of X(238) and X(34252)
X(51321) = crosspoint of X(3500) and X(7166)
X(51321) = crosssum of X(i) and X(j) for these (i,j): {1575, 17792}, {3501, 3507}
X(51321) = crossdifference of every pair of points on line {3835, 3971}
X(51321) = barycentric product X(i)*X(j) for these {i,j}: {1, 34252}, {6, 39914}, {87, 238}, {239, 2162}, {242, 23086}, {330, 1914}, {350, 7121}, {659, 932}, {812, 34071}, {1428, 7155}, {1429, 2319}, {1447, 2053}, {1691, 27447}, {1929, 8843}, {2210, 6384}, {3573, 43931}, {3684, 7153}, {4598, 8632}, {5009, 42027}, {6383, 14599}, {8848, 43747}, {21759, 30940}, {23493, 33295}
X(51321) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40848}, {31, 41531}, {87, 334}, {238, 6376}, {239, 6382}, {330, 18895}, {659, 20906}, {727, 33680}, {932, 4583}, {1428, 3212}, {1429, 30545}, {1580, 41318}, {1691, 17752}, {1914, 192}, {1921, 40367}, {2053, 4518}, {2162, 335}, {2210, 43}, {3573, 36863}, {3684, 4110}, {3747, 3971}, {4455, 21051}, {5009, 33296}, {6383, 44170}, {6384, 44172}, {7121, 291}, {8632, 3835}, {8843, 20947}, {14599, 2176}, {18892, 2209}, {23086, 337}, {23493, 43534}, {27447, 18896}, {34071, 4562}, {34252, 75}, {39914, 76}, {40736, 3862}, {41333, 20691}
X(51322) lies on the cubic K788 and these lines: {6, 694}, {32, 99}, {39, 21444}, {76, 10342}, {248, 19222}, {385, 3978}, {1384, 33756}, {1580, 1914}, {3229, 32748}, {5007, 9427}, {5027, 30654}, {8023, 8267}, {9431, 30435}, {10685, 43765}, {20457, 23640}, {20463, 20464}, {20975, 23642}, {32540, 47648}, {39643, 43183}
X(51322) = isogonal conjugate of the isotomic conjugate of X(39080)
X(51322) = X(i)-Ceva conjugate of X(j) for these (i,j): {6, 32748}, {32, 8623}, {99, 5027}, {4027, 36213}, {32540, 3229}
X(51322) = X(i)-isoconjugate of X(j) for these (i,j): {699, 1934}, {1581, 3225}, {1916, 43761}
X(51322) = X(i)-Dao conjugate of X(j) for these (i, j): (2086, 523), (3229, 76), (19576, 3225), (35540, 1502), (39031, 43761), (39080, 1916)
X(51322) = crosspoint of X(i) and X(j) for these (i,j): {6, 385}, {3229, 51248}
X(51322) = crosssum of X(i) and X(j) for these (i,j): {2, 694}, {3225, 8864}
X(51322) = crossdifference of every pair of points on line {804, 881}
X(51322) = barycentric product X(i)*X(j) for these {i,j}: {6, 39080}, {385, 3229}, {698, 1691}, {804, 41337}, {880, 9429}, {1580, 2227}, {3978, 32748}, {4027, 47648}, {5026, 36821}, {5976, 32540}, {8290, 51248}, {14602, 35524}
X(51322) = barycentric quotient X(i)/X(j) for these {i,j}: {698, 18896}, {1691, 3225}, {1933, 43761}, {2227, 1934}, {3229, 1916}, {9429, 882}, {14602, 699}, {32540, 36897}, {32748, 694}, {35524, 44160}, {39080, 76}, {41337, 18829}, {51248, 9477}
X(51322) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 3511, 9468}, {3511, 9468, 5106}
X(51323) lies on the cubic K788 and these lines: {32, 983}, {37, 82}, {101, 7104}, {172, 1691}, {385, 17787}, {1613, 18900}, {1918, 18274}, {2209, 9310}, {2670, 16785}, {18047, 39928}
X(51323) = isogonal conjugate of the isotomic conjugate of X(39929)
X(51323) = X(983)-Ceva conjugate of X(2330)
X(51323) = X(i)-isoconjugate of X(j) for these (i,j): {256, 39746}, {1581, 39937}, {3495, 7249}, {40432, 43687}
X(51323) = X(19576)-Dao conjugate of X(39937)
X(51323) = barycentric product X(i)*X(j) for these {i,j}: {6, 39929}, {172, 26752}, {2329, 3503}
X(51323) = barycentric quotient X(i)/X(j) for these {i,j}: {172, 39746}, {1691, 39937}, {20964, 43687}, {26752, 44187}, {39929, 76}
X(51324) lies on the cubics K782 and K788 and these lines: {2, 36425}, {4, 32}, {6, 43702}, {22, 23584}, {25, 694}, {39, 35476}, {114, 14966}, {186, 5162}, {187, 33874}, {232, 511}, {297, 8840}, {385, 17984}, {419, 8623}, {468, 46302}, {577, 37182}, {648, 25054}, {695, 43721}, {736, 44146}, {754, 46511}, {804, 12829}, {1194, 38356}, {1235, 18806}, {1284, 1914}, {1691, 2679}, {1843, 35432}, {2458, 19128}, {3053, 11325}, {3199, 46321}, {3563, 26714}, {4027, 16069}, {5028, 15920}, {5976, 39931}, {6680, 37125}, {8743, 43183}, {9420, 17994}, {9474, 34214}, {10313, 40236}, {10985, 41413}, {11547, 36417}, {21444, 27369}, {32452, 39575}, {35388, 41363}, {37187, 37669}, {37930, 38663}, {38652, 41172}, {38970, 44953}, {44099, 46627}
X(51324) = isogonal conjugate of the isotomic conjugate of X(39931)
X(51324) = polar conjugate of the isotomic conjugate of X(36213)
X(51324) = X(i)-Ceva conjugate of X(j) for these (i,j): {25, 232}, {39931, 36213}, {42396, 16230}
X(51324) = X(i)-isoconjugate of X(j) for these (i,j): {63, 36897}, {75, 15391}, {248, 1934}, {287, 1581}, {293, 1916}, {304, 34238}, {336, 694}, {656, 39291}, {879, 37134}, {1821, 36214}, {1910, 40708}, {17970, 46273}
X(51324) = X(i)-Dao conjugate of X(j) for these (i, j): (132, 1916), (206, 15391), (325, 305), (2491, 125), (3162, 36897), (8623, 69), (11672, 40708), (19576, 287), (24284, 15526), (39031, 293), (39039, 1934), (39043, 336), (40596, 39291), (40601, 36214)
X(51324) = crosspoint of X(i) and X(j) for these (i,j): {25, 44089}, {511, 51250}, {1691, 32542}
X(51324) = crosssum of X(i) and X(j) for these (i,j): {69, 40708}, {98, 8861}
X(51324) = crossdifference of every pair of points on line {684, 879}
X(51324) = barycentric product X(i)*X(j) for these {i,j}: {4, 36213}, {6, 39931}, {25, 5976}, {232, 385}, {237, 17984}, {240, 1580}, {297, 1691}, {325, 44089}, {419, 511}, {804, 4230}, {877, 5027}, {1933, 40703}, {2211, 3978}, {2679, 18020}, {2967, 40820}, {6531, 46888}, {12215, 34854}, {14602, 44132}, {17941, 17994}
X(51324) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 36897}, {32, 15391}, {112, 39291}, {232, 1916}, {237, 36214}, {240, 1934}, {297, 18896}, {419, 290}, {511, 40708}, {1580, 336}, {1691, 287}, {1933, 293}, {1974, 34238}, {2211, 694}, {2679, 125}, {4230, 18829}, {5027, 879}, {5976, 305}, {9418, 17970}, {14602, 248}, {17984, 18024}, {18902, 14600}, {32696, 18858}, {36213, 69}, {39931, 76}, {44089, 98}, {44132, 44160}, {46888, 6393}, {47418, 3269}
X(51324) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {32, 8922, 248}, {5017, 46272, 17970}
X(51325) lies on the cubic K788 and these lines: {32, 3499}, {110, 251}, {248, 682}, {385, 732}, {699, 43357}, {880, 19590}, {1613, 23173}, {1914, 30634}, {1971, 3852}, {19597, 33786}
X(51325) = isogonal conjugate of the isotomic conjugate of X(38382)
X(51325) = X(32)-Ceva conjugate of X(1691)
X(51325) = X(1581)-isoconjugate of X(39939)
X(51325) = X(i)-Dao conjugate of X(j) for these (i, j): (3978, 1502), (19576, 39939)
X(51325) = barycentric product X(i)*X(j) for these {i,j}: {6, 38382}, {1691, 40858}, {8870, 36213}
X(51325) = barycentric quotient X(i)/X(j) for these {i,j}: {1691, 39939}, {38382, 76}, {40858, 18896}
X(51326) lies on the cubic K788 and these lines: {6, 19585}, {32, 3499}, {83, 9427}, {99, 42346}, {183, 3224}, {213, 19580}, {1613, 46319}, {1918, 18274}, {8623, 9468}, {39087, 46308}
X(51326) = isogonal conjugate of X(40858)
X(51326) = isogonal conjugate of the anticomplement of X(3978)
X(51326) = isogonal conjugate of the isotomic conjugate of X(39939)
X(51326) = X(i)-cross conjugate of X(j) for these (i,j): {385, 6}, {733, 46286}
X(51326) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40858}, {1581, 38382}, {1959, 8870}
X(51326) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 40858), (19576, 38382)
X(51326) = cevapoint of X(i) and X(j) for these (i,j): {5027, 9427}, {8623, 42548}
X(51326) = crosspoint of X(i) and X(j) for these (i,j): {733, 9497}, {39953, 41520}
X(51326) = crosssum of X(i) and X(j) for these (i,j): {732, 9496}, {3499, 3511}
X(51326) = trilinear pole of line {669, 20965}
X(51326) = barycentric product X(i)*X(j) for these {i,j}: {6, 39939}, {98, 51249}
X(51326) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40858}, {1691, 38382}, {1976, 8870}, {39939, 76}, {51249, 325}
X(51327) lies on the cubic K788 and these lines: {32, 8870}, {98, 8623}, {237, 694}, {248, 290}, {699, 6037}, {1613, 32540}, {1910, 1914}, {2715, 14602}, {25332, 39941}, {39291, 39935}
X(51327) = isogonal conjugate of the isotomic conjugate of X(39941)
X(51327) = X(i)-Ceva conjugate of X(j) for these (i,j): {32, 248}, {40820, 1976}
X(51327) = X(1959)-isoconjugate of X(41520)
X(51327) = barycentric product X(i)*X(j) for these {i,j}: {6, 39941}, {98, 3511}, {1976, 25332}, {39092, 40820}
X(51327) = barycentric quotient X(i)/X(j) for these {i,j}: {1976, 41520}, {3511, 325}, {39941, 76}
X(51328) lies on the cubic K773 and these lines: {6, 692}, {31, 292}, {32, 101}, {58, 1015}, {110, 1977}, {184, 23538}, {238, 1691}, {251, 7109}, {1146, 15628}, {1191, 9259}, {1500, 4251}, {1501, 17127}, {1621, 5371}, {1633, 24289}, {1914, 2210}, {2162, 9306}, {3094, 7295}, {3573, 17475}, {3743, 16519}, {3792, 5104}, {3802, 8300}, {4517, 10987}, {4586, 30667}, {6184, 17735}, {6652, 39044}, {8632, 22384}, {12212, 40728}, {20333, 27916}, {21769, 23075}
X(51328) = isogonal conjugate of X(40098)
X(51328) = isogonal conjugate of the isotomic conjugate of X(4366)
X(51328) = X(i)-Ceva conjugate of X(j) for these (i,j): {31, 1691}, {251, 41333}, {593, 5009}
X(51328) = crosspoint of X(593) and X(5009)
X(51328) = crosssum of X(i) and X(j) for these (i,j): {2, 6653}, {594, 43534}, {1086, 4444}
X(51328) = crossdifference of every pair of points on line {918, 3837}
X(51328) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40098}, {2, 30663}, {291, 335}, {292, 334}, {660, 4444}, {876, 4562}, {893, 30642}, {1502, 18267}, {1581, 30669}, {1911, 18895}, {1916, 18787}, {1922, 44172}, {3572, 4583}, {4584, 35352}, {4876, 7233}, {7018, 30657}, {14598, 44170}, {23596, 30664}, {30671, 41072}, {37128, 43534}
X(51328) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 40098), (740, 28654), (812, 23989), (1966, 561), (6651, 18895), (18277, 44170), (19557, 334), (19576, 30669), (32664, 30663), (39028, 44172), (39029, 335), (39031, 18787), (39786, 850), (40597, 30642)
X(51328) = barycentric product X(i)*X(j) for these {i,j}: {1, 8300}, {6, 4366}, {8, 12835}, {31, 39044}, {58, 4368}, {60, 3027}, {101, 4375}, {238, 238}, {239, 1914}, {242, 7193}, {292, 6652}, {350, 2210}, {593, 35068}, {659, 3573}, {692, 27855}, {740, 5009}, {757, 4094}, {985, 3802}, {1178, 4154}, {1252, 35119}, {1428, 3685}, {1429, 3684}, {1438, 27919}, {1580, 18786}, {1691, 17493}, {1921, 14599}, {2201, 20769}, {3253, 20663}, {3570, 8632}, {3747, 33295}, {8298, 40767}, {16360, 18754}, {17962, 27926}, {18891, 18892}, {18894, 44169}, {27982, 30658}, {30940, 41333}
X(51328) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40098}, {31, 30663}, {171, 30642}, {238, 334}, {239, 18895}, {350, 44172}, {1428, 7233}, {1691, 30669}, {1914, 335}, {1917, 18267}, {1921, 44170}, {1933, 18787}, {2210, 291}, {3027, 34388}, {3573, 4583}, {3747, 43534}, {3802, 33931}, {4094, 1089}, {4154, 1237}, {4366, 76}, {4368, 313}, {4375, 3261}, {4455, 35352}, {5009, 18827}, {6652, 1921}, {7193, 337}, {8300, 75}, {8632, 4444}, {12835, 7}, {14599, 292}, {17493, 18896}, {18786, 1934}, {18892, 1911}, {18894, 1922}, {27855, 40495}, {35068, 28654}, {35119, 23989}, {39044, 561}
X(51328) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {31, 2112, 292}, {238, 14599, 1691}
X(51329) lies on the cubic K773 and these lines: {31, 57}, {36, 23996}, {38, 5083}, {56, 292}, {238, 1447}, {651, 9359}, {659, 3808}, {672, 1362}, {1106, 4350}, {1193, 7117}, {1357, 28360}, {1403, 3052}, {1428, 1691}, {1429, 3747}, {1477, 8693}, {1755, 20470}, {1758, 16586}, {1967, 29055}, {2116, 42290}, {2239, 3911}, {2876, 20786}, {3212, 16476}, {7146, 20985}, {8299, 20778}, {9472, 20663}, {17596, 46684}, {20665, 20995}
X(51329) = isogonal conjugate of X(33676)
X(51329) = isogonal conjugate of the isotomic conjugate of X(39775)
X(51329) = X(i)-Ceva conjugate of X(j) for these (i,j): {56, 1458}, {7132, 9454}
X(51329) = X(i)-isoconjugate of X(j) for these (i,j): {1, 33676}, {105, 4518}, {291, 14942}, {292, 36796}, {294, 335}, {334, 2195}, {660, 885}, {673, 4876}, {876, 36802}, {884, 4583}, {1024, 4562}, {1027, 36801}, {2481, 7077}, {7233, 28071}, {18785, 36800}
X(51329) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 33676), (665, 4858), (2238, 312), (3716, 24026), (3912, 3596), (19557, 36796), (27918, 35519), (36905, 18895), (39029, 14942), (39046, 4518), (39063, 334)
X(51329) = crosspoint of X(56) and X(1428)
X(51329) = crosssum of X(i) and X(j) for these (i,j): {8, 4518}, {2310, 28132}
X(51329) = crossdifference of every pair of points on line {885, 3716}
X(51329) = barycentric product X(i)*X(j) for these {i,j}: {1, 34253}, {6, 39775}, {56, 17755}, {57, 8299}, {238, 241}, {239, 1458}, {278, 20778}, {518, 1429}, {659, 1025}, {672, 1447}, {812, 2283}, {883, 8632}, {1284, 18206}, {1362, 6654}, {1428, 3912}, {1876, 20769}, {1914, 9436}, {2210, 40704}, {2223, 10030}, {2284, 43041}, {3286, 16609}, {3684, 34855}, {4435, 41353}, {4564, 38989}, {5236, 7193}, {9454, 18033}, {12835, 40217}
X(51329) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 33676}, {238, 36796}, {241, 334}, {672, 4518}, {1025, 4583}, {1362, 40217}, {1428, 673}, {1429, 2481}, {1447, 18031}, {1458, 335}, {1914, 14942}, {2210, 294}, {2223, 4876}, {2283, 4562}, {2284, 36801}, {3286, 36800}, {8299, 312}, {8632, 885}, {9436, 18895}, {9454, 7077}, {12835, 6654}, {14599, 2195}, {17755, 3596}, {20778, 345}, {27919, 4087}, {34253, 75}, {38989, 4858}, {39775, 76}, {40704, 44172}
X(51330) lies on the cubic K773 and these lines: {6, 2670}, {9, 40731}, {31, 2106}, {58, 86}, {81, 9401}, {110, 7122}, {284, 893}, {501, 595}, {662, 1918}, {1045, 18756}, {1963, 20985}, {2375, 43076}, {3747, 38814}, {5019, 9306}, {7168, 20663}, {21779, 23079}, {34021, 40743}
X(51330) = isogonal conjugate of the isotomic conjugate of X(39915)
X(51330) = X(31)-Ceva conjugate of X(58)
X(51330) = X(i)-isoconjugate of X(j) for these (i,j): {10, 40737}, {42, 18298}, {213, 43684}, {291, 39926}, {321, 40770}
X(51330) = X(i)-Dao conjugate of X(j) for these (i, j): (274, 561), (6626, 43684), (39029, 39926), (40592, 18298)
X(51330) = cevapoint of X(18756) and X(21779)
X(51330) = crosspoint of X(31) and X(18756)
X(51330) = crosssum of X(i) and X(j) for these (i,j): {75, 18298}, {523, 21725}
X(51330) = crossdifference of every pair of points on line {2533, 4079}
X(51330) = barycentric product X(i)*X(j) for these {i,j}: {6, 39915}, {27, 23079}, {31, 34021}, {58, 1655}, {81, 1045}, {86, 21779}, {274, 18756}, {757, 21883}, {3736, 40752}, {4610, 9402}
X(51330) = barycentric quotient X(i)/X(j) for these {i,j}: {81, 18298}, {86, 43684}, {1045, 321}, {1333, 40737}, {1655, 313}, {1914, 39926}, {2206, 40770}, {9402, 4024}, {18756, 37}, {21779, 10}, {21883, 1089}, {23079, 306}, {34021, 561}, {39915, 76}
X(51331) lies on the cubic K773 and these lines: {31, 1979}, {58, 101}, {238, 1914}, {333, 31027}, {727, 28841}, {893, 2195}, {1206, 38346}, {1691, 30634}, {1792, 28631}, {2176, 18756}, {3570, 19579}, {3725, 5147}, {20677, 39029}
X(51331) = isogonal conjugate of the isotomic conjugate of X(39916)
X(51331) = X(31)-Ceva conjugate of X(1914)
X(51331) = X(i)-isoconjugate of X(j) for these (i,j): {291, 39925}, {335, 2665}, {741, 43685}, {2107, 40017}, {40098, 40769}
X(51331) = X(i)-Dao conjugate of X(j) for these (i, j): (350, 561), (8299, 43685), (39029, 39925), (39056, 334), (46390, 3120)
X(51331) = crosssum of X(3125) and X(4444)
X(51331) = crossdifference of every pair of points on line {876, 4010}
X(51331) = barycentric product X(i)*X(j) for these {i,j}: {6, 39916}, {31, 39028}, {101, 27854}, {238, 2664}, {239, 21788}, {242, 20796}, {1914, 17759}, {2106, 2238}, {2669, 3747}, {3802, 40772}, {4600, 38978}, {8300, 40796}, {40874, 41333}
X(51331) = barycentric quotient X(i)/X(j) for these {i,j}: {1914, 39925}, {2106, 40017}, {2210, 2665}, {2238, 43685}, {2664, 334}, {17759, 18895}, {20796, 337}, {21788, 335}, {27854, 3261}, {38978, 3120}, {39028, 561}, {39916, 76}
X(51332) lies on the cubic K773 and these lines: {6, 20668}, {31, 2054}, {58, 1015}, {238, 1929}, {893, 20663}, {1247, 3496}, {1914, 8852}, {2176, 18784}, {2702, 17735}, {3437, 21004}, {6626, 39921}
X(51332) = isogonal conjugate of the isotomic conjugate of X(39921)
X(51332) = X(2054)-Ceva conjugate of X(17962)
X(51332) = X(i)-isoconjugate of X(j) for these (i,j): {291, 39922}, {1757, 6625}, {2248, 20947}, {6542, 13610}, {20693, 40164}
X(51332) = X(39029)-Dao conjugate of X(39922)
X(51332) = crossdifference of every pair of points on line {18004, 20529}
X(51332) = barycentric product X(i)*X(j) for these {i,j}: {6, 39921}, {846, 1929}, {1654, 17962}, {2054, 6626}, {2702, 21196}, {4213, 17972}, {6650, 18755}, {9278, 38814}, {17982, 22139}
X(51332) = barycentric quotient X(i)/X(j) for these {i,j}: {846, 20947}, {1914, 39922}, {17962, 6625}, {18755, 6542}, {39921, 76}
X(51333) lies on the cubic K773 and these lines: {6, 1045}, {31, 1979}, {81, 1977}, {100, 21753}, {739, 3231}, {1001, 2162}, {1911, 3747}, {4164, 43929}, {4623, 18166}, {14621, 40743}, {20142, 20332}, {20172, 23538}
X(51333) = isogonal conjugate of X(17759)
X(51333) = isogonal conjugate of the anticomplement of X(350)
X(51333) = isogonal conjugate of the isotomic conjugate of X(39925)
X(51333) = X(i)-cross conjugate of X(j) for these (i,j): {238, 6}, {741, 17962}, {2107, 2665}
X(51333) = X(i)-isoconjugate of X(j) for these (i,j): {1, 17759}, {2, 2664}, {10, 2106}, {37, 2669}, {42, 40874}, {75, 21788}, {86, 21897}, {92, 20796}, {213, 41535}, {239, 40796}, {291, 39916}, {292, 39028}, {306, 15148}, {660, 27854}, {3783, 40742}, {3797, 40772}
X(51333) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 17759), (206, 21788), (6626, 41535), (19557, 39028), (22391, 20796), (32664, 2664), (39029, 39916), (40589, 2669), (40592, 40874), (40600, 21897)
X(51333) = cevapoint of X(i) and X(j) for these (i,j): {238, 40769}, {1977, 8632}, {3747, 21753}
X(51333) = crosspoint of X(2111) and X(40737)
X(51333) = crosssum of X(i) and X(j) for these (i,j): {1045, 24578}, {20796, 21788}
X(51333) = trilinear pole of line {667, 20963}
X(51333) = barycentric product X(i)*X(j) for these {i,j}: {1, 2665}, {6, 39925}, {86, 2107}, {291, 40769}, {1333, 43685}, {8934, 9499}, {8937, 13610}
X(51333) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 17759}, {31, 2664}, {32, 21788}, {58, 2669}, {81, 40874}, {86, 41535}, {184, 20796}, {213, 21897}, {238, 39028}, {1333, 2106}, {1911, 40796}, {1914, 39916}, {2107, 10}, {2203, 15148}, {2665, 75}, {8632, 27854}, {8937, 17762}, {39925, 76}, {40769, 350}, {43685, 27801}
X(51334) lies on the cubic K782 and these lines: {4, 1987}, {6, 32713}, {24, 112}, {25, 248}, {53, 338}, {107, 3124}, {232, 237}, {240, 39039}, {393, 694}, {2967, 11672}, {3094, 10002}, {3569, 16230}, {3981, 6525}, {4230, 47406}, {8743, 9707}, {8744, 9408}, {13450, 27376}, {17994, 43112}, {35474, 41368}, {36426, 36790}, {39931, 51329}
X(51334) = isogonal conjugate of the isotomic conjugate of X(36426)
X(51334) = polar conjugate of the isotomic conjugate of X(2967)
X(51334) = X(i)-Ceva conjugate of X(j) for these (i,j): {107, 17994}, {2052, 6530}, {36426, 2967}
X(51334) = X(i)-isoconjugate of X(j) for these (i,j): {63, 47388}, {248, 336}, {255, 34536}, {287, 293}, {326, 41932}, {1821, 17974}, {1910, 6394}, {24018, 41173}
X(51334) = X(i)-Dao conjugate of X(j) for these (i, j): (132, 287), (511, 394), (2799, 36793), (3162, 47388), (6523, 34536), (11672, 6394), (15259, 41932), (39039, 336), (40601, 17974), (41172, 3265)
X(51334) = crosspoint of X(i) and X(j) for these (i,j): {297, 39265}, {2052, 6530}
X(51334) = crosssum of X(i) and X(j) for these (i,j): {248, 34156}, {577, 17974}
X(51334) = crossdifference of every pair of points on line {17974, 39473}
X(51334) = barycentric product X(i)*X(j) for these {i,j}: {4, 2967}, {6, 36426}, {107, 41167}, {132, 39265}, {158, 23996}, {232, 297}, {240, 240}, {325, 34854}, {393, 36790}, {511, 6530}, {877, 17994}, {2052, 11672}, {2207, 32458}, {2211, 44132}, {4230, 16230}, {9419, 18027}, {19189, 39569}, {23964, 35088}
X(51334) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 47388}, {232, 287}, {237, 17974}, {240, 336}, {393, 34536}, {511, 6394}, {1355, 1804}, {2207, 41932}, {2211, 248}, {2967, 69}, {4230, 17932}, {6530, 290}, {7062, 1259}, {9419, 577}, {11672, 394}, {17994, 879}, {23996, 326}, {32713, 41173}, {34854, 98}, {34859, 2715}, {35088, 36793}, {36425, 14585}, {36426, 76}, {36790, 3926}, {41167, 3265}, {42075, 255}
X(51335) lies on the cubic K782 and these lines: {2, 38383}, {3, 38873}, {4, 40867}, {6, 157}, {25, 110}, {51, 1196}, {52, 27369}, {182, 37457}, {184, 5028}, {193, 3186}, {237, 511}, {246, 2781}, {263, 694}, {287, 1316}, {389, 11326}, {418, 9967}, {460, 3564}, {524, 50707}, {576, 3506}, {868, 15595}, {888, 9135}, {1154, 21177}, {1180, 9157}, {1350, 41275}, {1495, 5107}, {1570, 42671}, {1625, 2971}, {1986, 38551}, {2088, 47426}, {2300, 3271}, {2308, 20974}, {2393, 38368}, {2456, 37183}, {2502, 34417}, {2782, 25046}, {2790, 6776}, {2979, 20885}, {3053, 39907}, {3170, 44122}, {3171, 44083}, {3269, 39846}, {3569, 17994}, {4226, 46039}, {5017, 38880}, {5095, 9033}, {5118, 47412}, {5359, 9777}, {5360, 7062}, {5477, 42663}, {5889, 11325}, {6101, 11360}, {6243, 20960}, {7664, 47582}, {8540, 17455}, {9486, 11173}, {11002, 34098}, {11205, 13366}, {11477, 20897}, {12829, 47734}, {13354, 14096}, {13355, 46546}, {13754, 46522}, {14570, 25314}, {17810, 20998}, {18873, 40810}, {19571, 39099}, {20021, 46124}, {21748, 23659}, {31860, 46276}, {35236, 40948}, {35296, 35383}, {35926, 39141}, {39835, 47421}, {41266, 44456}, {44102, 47405}
X(51335) = reflection of X(i) in X(j) for these {i,j}: {246, 46130}, {20975, 6}, {36790, 36213}
X(51335) = isogonal conjugate of X(40428)
X(51335) = isogonal conjugate of the isotomic conjugate of X(114)
X(51335) = polar conjugate of the isotomic conjugate of X(47406)
X(51335) = X(i)-Ceva conjugate of X(j) for these (i,j): {6, 1692}, {25, 237}, {110, 3569}, {114, 47406}, {2967, 9475}, {14052, 868}, {14265, 230}
X(51335) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40428}, {75, 2065}, {98, 8773}, {290, 36051}, {293, 35142}, {336, 3563}, {879, 36105}, {1821, 2987}, {1910, 8781}, {32654, 46273}, {35364, 36036}, {36120, 43705}
X(51335) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 40428), (114, 290), (132, 35142), (206, 2065), (230, 76), (868, 850), (2679, 35364), (11672, 8781), (36212, 305), (39001, 879), (39069, 1821), (39072, 98), (40601, 2987), (46094, 43705)
X(51335) = crosspoint of X(i) and X(j) for these (i,j): {6, 511}, {25, 460}, {230, 14265}
X(51335) = crosssum of X(i) and X(j) for these (i,j): {2, 98}, {69, 43705}, {647, 15630}, {2987, 34157}
X(51335) = crossdifference of every pair of points on line {287, 2395}
X(51335) = X(i)-lineconjugate of X(j) for these (i,j): {25, 2987}, {1316, 287}
X(51335) = barycentric product X(i)*X(j) for these {i,j}: {1, 17462}, {4, 47406}, {6, 114}, {230, 511}, {232, 3564}, {250, 41181}, {325, 1692}, {460, 36212}, {1733, 1755}, {1959, 8772}, {2396, 42663}, {3289, 44145}, {3569, 4226}, {5477, 5968}, {6393, 44099}, {11672, 14265}, {12829, 40810}, {36213, 47734}
X(51335) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40428}, {32, 2065}, {114, 76}, {230, 290}, {232, 35142}, {237, 2987}, {460, 16081}, {511, 8781}, {1692, 98}, {1733, 46273}, {1755, 8773}, {2211, 3563}, {2491, 35364}, {3289, 43705}, {4226, 43187}, {8772, 1821}, {9417, 36051}, {9418, 32654}, {9419, 34157}, {12829, 14382}, {14966, 10425}, {17462, 75}, {41181, 339}, {42663, 2395}, {44099, 6531}, {47406, 69}
X(51335) = {X(36213),X(36790)}-harmonic conjugate of X(9155)
X(51336) lies on the cubics K782 and K1009 and these lines: {2, 43188}, {154, 237}, {232, 800}, {248, 9306}, {647, 1899}, {1968, 33581}, {2056, 14575}, {3167, 3289}, {3563, 34481}, {6337, 6509}, {9243, 18909}, {9255, 42702}, {9258, 30456}, {9544, 23357}, {15391, 34156}, {26887, 33629}, {42287, 46831}
X(51336) = isogonal conjugate of X(9308)
X(51336) = isogonal conjugate of the anticomplement of X(41005)
X(51336) = isogonal conjugate of the isotomic conjugate of X(9289)
X(51336) = isotomic conjugate of the polar conjugate of X(9292)
X(51336) = isogonal conjugate of the polar conjugate of X(9307)
X(51336) = X(9307)-Ceva conjugate of X(9292)
X(51336) = X(i)-cross conjugate of X(j) for these (i,j): {185, 6}, {511, 248}, {647, 43188}, {6467, 3}, {6776, 43718}, {21655, 6415}, {21656, 6416}, {48445, 36214}
X(51336) = X(i)-isoconjugate of X(j) for these (i,j): {1, 9308}, {2, 1957}, {4, 1958}, {19, 1975}, {75, 1968}, {92, 9306}, {112, 17893}, {162, 30476}, {293, 40887}, {648, 17478}, {662, 16229}, {811, 2451}, {823, 22089}, {1783, 17215}, {1821, 15143}, {5379, 21137}, {8769, 37199}
X(51336) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 9308), (6, 1975), (125, 30476), (132, 40887), (206, 1968), (1084, 16229), (17423, 2451), (22391, 9306), (32664, 1957), (34591, 17893), (36033, 1958), (39006, 17215), (40601, 15143)
X(51336) = crosspoint of X(i) and X(j) for these (i,j): {1073, 3504}, {1988, 8770}, {9289, 9307}
X(51336) = crosssum of X(i) and X(j) for these (i,j): {6, 30549}, {193, 3164}, {1249, 3186}, {1968, 9306}
X(51336) = trilinear pole of line {2524, 39469}
X(51336) = crossdifference of every pair of points on line {15143, 16229}
X(51336) = barycentric product X(i)*X(j) for these {i,j}: {1, 9255}, {3, 9307}, {6, 9289}, {63, 9258}, {69, 9292}, {647, 43188}, {6776, 43727}
X(51336) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 1975}, {6, 9308}, {31, 1957}, {32, 1968}, {48, 1958}, {184, 9306}, {232, 40887}, {237, 15143}, {512, 16229}, {647, 30476}, {656, 17893}, {810, 17478}, {1459, 17215}, {3049, 2451}, {3053, 37199}, {9255, 75}, {9258, 92}, {9289, 76}, {9292, 4}, {9307, 264}, {39201, 22089}, {43188, 6331}
X(51337) lies on the cubic K782 and these lines: {4, 99}, {6, 694}, {232, 15143}, {248, 9306}, {682, 3491}, {1974, 4558}, {3619, 14060}, {5027, 6132}, {14913, 20975}, {21531, 44377}, {47079, 47620}
X(51337) = X(25)-Ceva conjugate of X(511)
X(51337) = X(6393)-Dao conjugate of X(305)
X(51337) = crossdifference of every pair of points on line {804, 44534}
X(51337) = barycentric product X(232)*X(19599)
X(51338) lies on the cubic K782 and these lines: {3, 46317}, {6, 160}, {262, 14494}, {327, 3620}, {511, 40803}, {3186, 34208}, {3563, 26714}, {3619, 8797}, {5052, 14252}, {14489, 33878}, {39682, 39874}
X(51338) = barycentric product X(i)*X(j) for these {i,j}: {262, 1351}, {263, 1007}, {9752, 40803}, {37174, 43718}
X(51338) = barycentric quotient X(i)/X(j) for these {i,j}: {263, 7612}, {1007, 20023}, {1351, 183}, {37174, 44144}
See Kadir Altintas and César Lozada, euclid 5352.
X(51339) lies on these lines: {3, 6}, {30, 1029}, {35, 3065}, {55, 5899}, {3746, 44913}, {8143, 27787}
X(51339) = {X(36742), X(50948)}-harmonic conjugate of X(3)
See Kadir Altintas and César Lozada, euclid 5352.
X(51340) lies on these lines: {1, 399}, {3, 6}, {4, 14996}, {5, 26131}, {21, 323}, {30, 81}, {42, 35000}, {55, 6149}, {60, 1511}, {106, 39633}, {140, 37680}, {165, 39523}, {171, 18524}, {186, 44097}, {222, 15934}, {283, 37292}, {376, 37685}, {381, 940}, {382, 5707}, {394, 16418}, {404, 15018}, {405, 15066}, {517, 2941}, {549, 32911}, {601, 2177}, {631, 14997}, {651, 5719}, {902, 37621}, {999, 1464}, {1012, 11456}, {1064, 22765}, {1203, 13624}, {1385, 5315}, {1396, 15762}, {1437, 1495}, {1449, 7171}, {1456, 5045}, {1480, 1482}, {1597, 44105}, {1657, 5706}, {1834, 47032}, {1963, 38330}, {1993, 16370}, {1994, 17549}, {2003, 23071}, {2163, 26286}, {2194, 22115}, {2292, 13465}, {2915, 15107}, {3073, 16484}, {3247, 7330}, {3333, 33633}, {3560, 15068}, {3651, 48927}, {3652, 3743}, {4189, 11004}, {4340, 44229}, {4383, 5054}, {4653, 28453}, {4658, 48903}, {4868, 12515}, {5055, 37674}, {5204, 16472}, {5217, 16473}, {5422, 16371}, {5428, 16948}, {5499, 24883}, {5640, 16427}, {5710, 18526}, {5711, 18525}, {6841, 49743}, {6906, 15032}, {6912, 15052}, {7373, 15306}, {7489, 50317}, {10021, 24936}, {10222, 16490}, {10246, 11203}, {10391, 18455}, {10394, 37729}, {10601, 16417}, {10742, 37715}, {11539, 37687}, {12083, 37538}, {12112, 21669}, {13587, 34545}, {13632, 37676}, {13730, 26864}, {13745, 26637}, {14815, 37535}, {15047, 22392}, {15080, 20833}, {15178, 16489}, {15694, 37679}, {15696, 37537}, {15703, 37682}, {15952, 48909}, {16117, 48897}, {16485, 37615}, {16486, 37624}, {16857, 17811}, {18445, 28444}, {18480, 37559}, {18541, 37543}, {22936, 32167}, {25526, 48887}, {28458, 48847}, {34120, 37643}, {34435, 43704}, {35243, 44094}, {37230, 49745}, {37251, 37522}, {37402, 48924}, {37594, 40263}, {37732, 45976}, {46623, 48926}
X(51340) = reflection of X(45923) in X(81)
X(51340) = inverse of X(1030) in Schoute circle
X(51340) = intersection, other than A, B, C, of circumconics {{A, B, C, X(74), X(1030)}} and {{A, B, C, X(84), X(15792)}}
X(51340) = X(45923)-of-anti-orthocentroidal triangle
X(51340) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 7701, 8143), (3, 36742, 36750), (3, 36750, 37509), (15, 16, 1030), (58, 500, 3), (601, 37698, 11849), (991, 5398, 3), (5396, 37469, 3), (11485, 11486, 4254), (13323, 37482, 3), (36742, 36746, 3), (36754, 37501, 3)
See Angel Montesdeoca, euclid 5356.
X(51341) lies on these lines: {1,1696}, {6,7091}, {7,2999}, {44,7285}, {84,1743}, {90,3973}, {2324,3680}, {3731,7160}, {7070,33590}, {7655,35355}, {8809,14557}, {9372,18594}, {37269,43744}
See Angel Montesdeoca, euclid 5364 and HG040722.
X(51342) lies on these lines: {3,133}, {4,64}, {5,20203}, {53,42458}, {107,5925}, {381,14059}, {546,15312}, {1498,1559}, {2883,36876}, {3091,3346}, {3462,41372}, {6529,46829}, {6616,34782}, {6624,16252}
X(51342) = midpoint of X(4) and X(6523)
X(51342) = reflection of X(42457) in X(6523)
X(51343) lies on the cubic K1009 and these lines: {2, 9476}, {22, 110}, {25, 39265}, {184, 15407}, {251, 16040}, {427, 47105}, {6353, 32649}, {9306, 40810}, {19158, 46594}, {32687, 36417}, {33514, 33651}
X(51343) = X(51324)-cross conjugate of X(385)
X(51343) = X(i)-isoconjugate of X(j) for these (i,j): {1503, 1581}, {1916, 2312}, {1934, 42671}, {1967, 30737}, {17875, 34238}
X(51343) = X(i)-Dao conjugate of X(j) for these (i, j): (8290, 30737), (8623, 15595), (19576, 1503), (39031, 2312)
X(51343) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(16591)}, {{A, B, C, X(22), X(419)}}, {{A, B, C, X(110), X(251)}}, {{A, B, C, X(111), X(38873)}}, {{A, B, C, X(154), X(44089)}}, {{A, B, C, X(385), X(394)}}
X(51343) = barycentric product X(i)*X(j) for these {i,j}: {385, 1297}, {1691, 35140}, {9476, 36213}, {12215, 43717}, {15407, 39931}, {17941, 34212}, {24284, 44770}
X(51343) = barycentric quotient X(i)/X(j) for these {i,j}: {385, 30737}, {1297, 1916}, {1691, 1503}, {1933, 2312}, {14382, 51257}, {14602, 42671}, {35140, 18896}, {36213, 15595}, {44089, 16318}, {51324, 132}
X(51344) lies on the cubic K1009 and these lines: {2, 43188}, {25, 385}, {154, 3164}, {194, 3167}, {394, 401}, {8770, 40815}, {9306, 40807}, {9544, 40642}, {34405, 39359}
X(51344) = anticomplement of the isotomic conjugate of X(9306)
X(51344) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {31, 1899}, {1957, 11442}, {1958, 315}, {1968, 21270}, {1975, 21275}, {2451, 21294}, {9306, 6327}
X(51344) = X(9306)-Ceva conjugate of X(2)
X(51345) lies on the cubic K614 and these lines: {3, 14583}, {30, 74}, {110, 18285}, {186, 18384}, {231, 1989}, {376, 14254}, {457, 16240}, {1138, 1511}, {1319, 50148}, {3830, 39170}, {5054, 14356}, {5961, 37922}, {6344, 35489}, {11586, 36210}, {11749, 15051}, {12028, 44265}, {12121, 38580}, {14560, 22115}, {14731, 38794}, {14851, 38700}, {14980, 37943}, {15035, 33855}, {15681, 51254}, {15743, 36211}, {16168, 38723}, {18318, 18508}, {20124, 40685}, {26700, 38588}, {32417, 36193}, {38582, 41392}, {38609, 38728}
X(51345) = reflection of X(i) in X(j) for these {i,j}: {265, 14993}, {1138, 1511}, {14731, 45694}, {14851, 38700}, {14993, 476}
X(51345) = barycentric quotient X(15782)/X(40604)
X(51345) = {X(46074),X(46078)}-harmonic conjugate of X(1989)
X(51346) lies on the cubic K009 and these lines: {3, 113}, {4, 2693}, {20, 250}, {32, 39008}, {185, 520}, {1650, 11589}, {3163, 3172}, {8431, 18390}, {14249, 18848}, {14385, 15404}, {31945, 44247}, {34156, 39169}, {39170, 39174}, {40948, 51254}, {44240, 47084}
X(51346) = isogonal conjugate of X(38937)
X(51346) = X(22239)-Ceva conjugate of X(9033)
X(51346) = X(i)-isoconjugate of X(j) for these (i,j): {1, 38937}, {2071, 36119}, {2349, 15262}, {34170, 35200}
X(51346) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 38937), (133, 34170), (1511, 2071), (9033, 16177)
X(51346) = intersection, other than A, B, C, of circumconics {A, B, C, X(3), X(30)}, {A, B, C, X(4), X(2777)}, {A, B, C, X(5), X(18508)}, {A, B, C, X(6), X(2935)}, {A, B, C, X(20), X(122)}, {A, B, C, X(32), X(9409)}, {A, B, C, X(54), X(13293)}, {A, B, C, X(64), X(10117)}, {A, B, C, X(68), X(16111)}, {A, B, C, X(69), X(37853)}, {A, B, C, X(74), X(13289)}, {A, B, C, X(113), X(4846)}, {A, B, C, X(185), X(933)} and {A, B, C, X(265), X(20127)}
X(51346) = cevapoint of X(9409) and X(39008)
X(51346) = crosssum of X(2071) and X(12825)
X(51346) = crossdifference of every pair of points on line {15262, 46425}
X(51346) = barycentric product X(i)*X(j) for these {i,j}: {9033, 48373}, {11064, 11744}, {22239, 41077}, {40082, 46106}
X(51346) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 38937}, {1495, 15262}, {1990, 34170}, {3284, 2071}, {9409, 46425}, {11744, 16080}, {22239, 15459}, {39008, 16177}, {40082, 14919}, {47405, 12825}, {48373, 16077}
X(51347) lies on the cubic K009 and these lines: {3, 1661}, {4, 5897}, {32, 39020}, {1249, 41890}, {3348, 12241}, {15261, 34156}, {15394, 41005}, {17409, 40186}, {20207, 31829}, {27089, 35602}, {34233, 44247}, {34853, 39174}
X(51347) = isogonal conjugate of X(39268)
X(51347) = X(30249)-Ceva conjugate of X(8057)
X(51347) = X(184)-cross conjugate of X(1249)
X(51347) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39268}, {75, 17510}, {92, 14390}, {1895, 33583}, {2155, 46927}
X(51347) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 39268), (206, 17510), (8057, 35968), (22391, 14390), (45245, 46927), (45248, 11413)
X(51347) = cevapoint of X(39020) and X(42658)
X(51347) = crosssum of X(14390) and X(17510)
X(51347) = barycentric product X(i)*X(j) for these {i,j}: {18213, 40170}, {20580, 30249}, {37669, 43695}
X(51347) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39268}, {20, 46927}, {32, 17510}, {184, 14390}, {14642, 33583}, {15905, 11413}, {18213, 14572}, {35602, 2063}, {39020, 35968}, {43695, 459}
X(51348) lies on the cubic K032 and these lines: {4, 20329}, {20, 51261}, {1249, 3522}, {1657, 33702}, {3346, 15105}, {3523, 14249}, {5059, 33893}, {5068, 20203}, {5930, 9778}, {10152, 49135}, {33897, 34186}
X(51348) = isotomic conjugate of the anticomplement of X(33630)
X(51348) = X(33630)-cross conjugate of X(2)
X(51349) lies on the cubic K1280 and these lines: {4, 476}, {30, 15469}, {265, 523}, {477, 15396}, {1138, 34312}, {1990, 41392}, {3258, 15454}, {41512, 46045}
X(51349) = reflection of X(i) in X(j) for these {i,j}: {476, 39170}, {15454, 3258}
X(51349) = isogonal conjugate of X(15468)
X(51349) = antigonal image of X(15454)
X(51349) = symgonal image of X(39170)
X(51349) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(30)}}, {{A, B, C, X(113), X(115)}}, {{A, B, C, X(265), X(476)}}
X(51349) = X(i)-isoconjugate of X(j) for these (i,j): {1, 15468}, {6149, 34150}
X(51349) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 15468), (14993, 34150), (39170, 17702)
X(51349) = barycentric product X(i)*X(j) for these {i,j}: {94, 15469}, {35189, 41079}
X(51349) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 15468}, {1989, 34150}, {14583, 3018}, {15469, 323}, {32711, 1304}, {35189, 44769}, {41392, 7471}
See Ivan Pavlov, euclid 5367.
X(51350) lies on these lines: {2, 3}, {69, 40897}, {97, 46717}, {99, 40870}, {182, 47740}, {187, 40814}, {264, 22052}, {287, 3098}, {290, 35178}, {394, 36617}, {577, 648}, {1993, 7783}, {3284, 47383}, {5012, 32522}, {6194, 46806}, {7709, 34396}, {7782, 36212}, {7904, 37636}, {8588, 41254}, {10979, 36794}, {14810, 42313}, {15595, 48892}, {20477, 36748}, {40867, 46264}
X(51350) = barycentric product X(75)*X(51299)
X(51350) = trilinear product X(2)*X(51299)
X(51350) = intersection, other than A, B, C, of circumconics {{A, B, C, X(4), X(38256)}} and {{A, B, C, X(25), X(36617)}}
X(51350) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (3, 401, 2), (3, 35941, 401), (3, 37124, 3523), (7824, 41231, 2)
See Ivan Pavlov, euclid 5367.
X(51351) lies on these lines: {1, 32098}, {2, 7}, {8, 10481}, {10, 32086}, {65, 24797}, {77, 3957}, {85, 3617}, {145, 279}, {200, 7271}, {241, 29621}, {269, 3870}, {348, 3622}, {519, 21314}, {948, 24599}, {1088, 4373}, {1323, 3241}, {1418, 3693}, {1434, 11115}, {1536, 36996}, {1788, 24796}, {3160, 3623}, {3161, 30813}, {3485, 24798}, {3600, 30617}, {3621, 9312}, {3663, 9801}, {3664, 10578}, {3668, 4452}, {3672, 14548}, {3679, 20121}, {3744, 3945}, {3873, 34855}, {3999, 4346}, {4059, 5261}, {4188, 38859}, {4328, 4666}, {4350, 34772}, {4355, 19868}, {4678, 31994}, {4712, 39570}, {4847, 31995}, {4862, 11019}, {4888, 13405}, {4904, 7960}, {5708, 36682}, {6605, 25878}, {7190, 29817}, {7232, 25355}, {7274, 10582}, {10405, 20089}, {11036, 36706}, {14828, 37540}, {17079, 31145}, {17093, 32093}, {17170, 20070}, {20014, 25718}, {20052, 25719}, {21453, 30712}, {26531, 30695}, {26690, 45227}, {27086, 38900}, {27541, 40483}, {29583, 39775}, {29627, 51302}, {31130, 40704}, {33298, 46933}, {36606, 36620}, {41004, 50696}
X(51351) = isotomic conjugate of the isogonal conjugate of X(42314)
X(51351) = barycentric product X(i)*X(j) for these {i, j}: {7, 29627}, {75, 51302}, {76, 42314}, {85, 3243}, {279, 10005}
X(51351) = barycentric quotient X(i)/X(j) for these (i, j): (7, 42318), (269, 42315)
X(51351) = trilinear product X(i)*X(j) for these {i, j}: {2, 51302}, {7, 3243}, {57, 29627}, {75, 42314}, {269, 10005}
X(51351) = trilinear quotient X(i)/X(j) for these (i, j): (85, 42318), (279, 42315)
X(51351) = intersection, other than A, B, C, of circumconics {{A, B, C, X(2), X(29627)}} and {{A, B, C, X(9), X(1280)}}
X(51351) = X(i)-isoconjugate-of-X(j) for these {i, j}: {41, 42318}, {220, 42315}
X(51351) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (7, 42318), (269, 42315)
X(51351) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 20059, 10025), (2, 40868, 144), (7, 9436, 2), (8, 10481, 43983), (279, 6604, 145), (9312, 32003, 3621)
See Ivan Pavlov, euclid 5367.
X(51352) lies on these lines: {2, 7}, {45, 14828}, {85, 43984}, {190, 37658}, {200, 25728}, {220, 664}, {1212, 32100}, {2348, 51052}, {2481, 16816}, {3693, 17336}, {3870, 17261}, {3957, 4704}, {3973, 24600}, {4666, 17120}, {5220, 14942}, {6603, 31169}, {6706, 32088}, {10580, 32912}, {16885, 24352}, {17331, 25006}, {17343, 26593}, {20089, 30625}, {20173, 37652}, {25243, 43989}, {29817, 37677}, {33298, 40483}
X(51352) = barycentric product X(75)*X(51300)
X(51352) = trilinear product X(2)*X(51300)
X(51352) = intersection, other than A, B, C, of circumconics {{A, B, C, X(8), X(40868)}} and {{A, B, C, X(57), X(36601)}}
X(51352) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 144, 40868), (9, 10025, 2), (220, 32024, 3177)
See Ivan Pavlov, euclid 5367.
X(51353) lies on these lines: {1, 2}, {86, 4478}, {190, 594}, {192, 4748}, {319, 4670}, {321, 25280}, {335, 4732}, {671, 27797}, {1213, 32101}, {1268, 17390}, {1278, 5232}, {2895, 6539}, {3620, 4772}, {3696, 27495}, {3842, 31308}, {3871, 19237}, {3943, 31144}, {3969, 26044}, {4007, 17248}, {4034, 17368}, {4058, 17261}, {4060, 17319}, {4371, 17383}, {4399, 17307}, {4431, 17252}, {4440, 4665}, {4445, 17300}, {4470, 50133}, {4473, 17330}, {4645, 50312}, {4659, 6646}, {4690, 20072}, {4753, 42334}, {4781, 46918}, {4798, 50132}, {4967, 17287}, {5224, 17318}, {5564, 17239}, {5690, 6999}, {5790, 7384}, {6707, 32089}, {8025, 32004}, {12531, 24583}, {14433, 26798}, {17228, 28634}, {17236, 32087}, {17238, 42696}, {17275, 17280}, {17277, 48636}, {17278, 48640}, {17305, 50098}, {17317, 28633}, {17325, 50088}, {17343, 31300}, {17372, 28653}, {17391, 36834}, {20337, 31037}, {23905, 41809}, {24349, 31329}, {24628, 33079}, {31314, 49450}, {31319, 49678}, {33888, 49457}, {40480, 48635}, {41847, 50076}, {43990, 46707}, {50223, 50267}
X(51353) = reflection of X(29586) in X(29610)
X(51353) = anticomplement of X(29586)
X(51353) = barycentric product X(75)*X(51294)
X(51353) = trilinear product X(2)*X(51294)
X(51353) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(51294)}} and {{A, B, C, X(2), X(35162)}}
X(51353) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (2, 8, 20016), (2, 20055, 29588), (2, 29616, 29589), (8, 9780, 49488), (8, 29593, 2), (10, 6542, 2), (10, 29615, 6542), (239, 29591, 2), (319, 28604, 20090), (1698, 17389, 29592), (1698, 29592, 2), (2895, 6625, 31064), (3634, 49761, 29580), (3661, 4384, 29587), (4384, 29587, 2), (4665, 17271, 4440), (4668, 17308, 29617), (4967, 17287, 26806), (5564, 17239, 17302), (9780, 29570, 2), (9780, 50079, 29570), (16816, 29611, 2), (17292, 29590, 2), (17292, 50095, 29590), (17294, 29576, 29569), (19875, 29605, 29612), (26801, 27044, 2), (29569, 29576, 2), (29585, 46933, 2), (29586, 29610, 2)
See Ivan Pavlov, euclid 5367.
X(51354) lies on these lines: {2, 3}, {648, 3187}, {26223, 40395}
X(51354) = {X(27), X(447)}-harmonic conjugate of X(2)
See Ivan Pavlov, euclid 5367.
X(51355) lies on these lines: {2, 7}, {664, 1407}, {4398, 43036}, {6180, 24620}, {37684, 39126}
X(51355) = barycentric product X(75)*X(51301)
X(51355) = trilinear product X(2)*X(51301)
X(51355) = {X(57), X(40862)}-harmonic conjugate of X(2)
See Ivan Pavlov, euclid 5367.
X(51356) lies on the cubic K1018 and these lines: {1, 99}, {2, 6}, {7, 40164}, {8, 32004}, {31, 757}, {75, 873}, {115, 50262}, {187, 50264}, {274, 4658}, {316, 49744}, {319, 8013}, {350, 4038}, {551, 6629}, {662, 2280}, {799, 9345}, {892, 24345}, {894, 4037}, {1014, 1403}, {1125, 16480}, {1434, 35915}, {1621, 16679}, {1698, 32014}, {1931, 29570}, {2276, 37128}, {3616, 6626}, {3622, 16527}, {3730, 46194}, {3879, 21085}, {4216, 5937}, {4360, 17140}, {4573, 40719}, {4615, 27922}, {4649, 40734}, {4687, 33766}, {6625, 23903}, {7304, 10436}, {7771, 37522}, {7845, 50266}, {9782, 17169}, {10471, 35615}, {16369, 16826}, {16741, 26234}, {17014, 24378}, {17193, 45221}, {25526, 33297}, {28653, 32864}, {32772, 41851}, {33947, 35916}, {37159, 49743}, {47286, 50185}
X(51356) = isotomic conjugate of the polar conjugate of X(31904)
X(51356) = barycentric product X(i)*X(j) for these {i, j}: {1, 51314}, {69, 31904}, {75, 51311}, {86, 16826}, {99, 28840}, {274, 4649}
X(51356) = barycentric quotient X(i)/X(j) for these (i, j): (58, 25426), (81, 30571), (86, 27483), (110, 28841)
X(51356) = trilinear product X(i)*X(j) for these {i, j}: {2, 51311}, {6, 51314}, {63, 31904}, {81, 16826}, {86, 4649}, {99, 4784}
X(51356) = trilinear quotient X(i)/X(j) for these (i, j): (81, 25426), (86, 30571), (274, 27483), (662, 28841)
X(51356) = trilinear pole of the line {20142, 28840}
X(51356) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(16369)}} and {{A, B, C, X(2), X(16826)}}
X(51356) = X(i)-isoconjugate-of-X(j) for these {i, j}: {37, 25426}, {42, 30571}, {213, 27483}, {661, 28841}
X(51356) = X(i)-reciprocal conjugate of-X(j) for these (i, j): (58, 25426), (81, 30571), (86, 27483), (110, 28841)
X(51356) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i, j, k): (1, 1509, 17103), (2, 20090, 20536), (81, 86, 33295), (81, 2106, 6), (86, 2668, 37632), (86, 17731, 2), (1963, 17379, 27958), (8025, 30941, 86), (40721, 40750, 3570)
See Ivan Pavlov, euclid 5367.
X(51357) lies on these lines: {2, 11}, {101, 47776}, {190, 47772}, {664, 48571}, {666, 1252}, {693, 14589}, {901, 47763}, {4781, 35281}, {4998, 26985}, {5375, 26777}, {6162, 17693}, {7192, 41405}, {14513, 47759}, {43991, 46725}
X(51357) = {X(693), X(14589)}-harmonic conjugate of X(43986)
X(51358) lies on these lines: {2, 253}, {4, 3426}, {5, 1075}, {20, 41425}, {30, 5667}, {53, 2052}, {92, 16608}, {107, 1503}, {112, 40884}, {125, 6530}, {133, 1515}, {186, 47146}, {196, 445}, {264, 37648}, {287, 20031}, {297, 525}, {323, 15262}, {343, 15466}, {393, 37643}, {394, 46927}, {403, 12079}, {427, 3168}, {436, 11245}, {450, 3564}, {458, 41370}, {468, 41204}, {470, 11542}, {471, 11543}, {472, 43417}, {473, 43416}, {495, 1148}, {496, 7049}, {648, 11064}, {685, 41175}, {858, 35360}, {1304, 47152}, {1495, 47204}, {1513, 47202}, {1585, 13665}, {1586, 13785}, {1853, 42854}, {1941, 16196}, {1990, 14165}, {3087, 11433}, {3146, 3183}, {3176, 3617}, {3462, 3628}, {4240, 46818}, {5094, 41371}, {5554, 25988}, {6225, 6526}, {6247, 14249}, {6331, 6393}, {6523, 12324}, {6524, 23291}, {6525, 32064}, {6716, 34147}, {6776, 37070}, {8794, 26954}, {10152, 15311}, {11331, 41361}, {11547, 26958}, {13450, 26879}, {14363, 20299}, {14461, 32428}, {15005, 17578}, {15258, 35260}, {15312, 34186}, {16264, 34417}, {16813, 46064}, {17907, 37638}, {17923, 18644}, {19772, 44700}, {19773, 44701}, {27377, 37644}, {31510, 47147}, {34289, 43678}, {35474, 47582}, {37765, 44569}, {38294, 47155}, {44576, 46808}, {45200, 46717}
X(51358) = midpoint of X(6761) and X(40664)
X(51358) = reflection of X(i) in X(j) for these {i,j}: {1304, 47152}, {1515, 133}, {15459, 1990}, {31510, 47147}, {34147, X(51358) = 6716}
X(51358) = polar conjugate of X(1294)
X(51358) = polar conjugate of the isogonal conjugate of X(6000)
X(51358) = X(5897)-anticomplementary conjugate of X(4329)
X(51358) = X(1494)-Ceva conjugate of X(4)
X(51358) = X(i)-isoconjugate of X(j) for these (i,j): {48, 1294}, {162, 2430}, {163, 43701}, {2173, 15404}, {2416, 32676}, {32320, 36043}
X(51358) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 43701), (125, 2430), (1249, 1294), (1990, 30), (15526, 2416), (35579, 32320), (36896, 15404), (44436, 11064), (50937, 6)
X(51358) = cevapoint of X(i) and X(j) for these (i,j): {1249, 5667}, {1990, 15311}
X(51358) = crosspoint of X(2052) and X(16080)
X(51358) = crosssum of X(i) and X(j) for these (i,j): {577, 3284}, {1636, 47409}
X(51358) = trilinear pole of line {133, 50937}
X(51358) = crossdifference of every pair of points on line {184, 2430}
X(51358) = barycentric product X(i)*X(j) for these {i,j}: {133, 1494}, {253, 1559}, {264, 6000}, {525, 2404}, {850, 46587}, {1515, 36889}, {2052, 44436}, {2442, 3267}, {6530, 36893}
X(51358) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 1294}, {74, 15404}, {133, 30}, {523, 43701}, {525, 2416}, {647, 2430}, {1301, 46968}, {1515, 376}, {1559, 20}, {2404, 648}, {2442, 112}, {6000, 3}, {6529, 32646}, {36126, 36043}, {36893, 6394}, {39376, 50464}, {44436, 394}, {46587, 110}, {47433, 3284}, {50937, 15311}
X(51358) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {53, 13567, 43462}, {133, 1515, 1559}, {459, 14361, 2}, {858, 35360, 44704}, {1990, 47296, 14165}, {2052, 43462, 53}, {3580, 46106, 297}, {5523, 50188, 297}, {14165, 16080, 47296}
X(51359) lies on these lines: {1, 406}, {4, 57}, {10, 459}, {11, 1875}, {33, 18391}, {34, 3086}, {108, 515}, {158, 225}, {186, 17010}, {204, 461}, {235, 1426}, {240, 522}, {318, 24982}, {393, 24005}, {429, 40952}, {451, 13411}, {519, 15500}, {938, 4194}, {950, 7412}, {1119, 24213}, {1249, 20262}, {1319, 23711}, {1421, 1870}, {1498, 10361}, {1512, 45766}, {1528, 6001}, {1753, 1788}, {1767, 14647}, {1783, 40869}, {1845, 30384}, {1848, 1905}, {1877, 36110}, {1878, 6075}, {1890, 15299}, {1891, 11399}, {1895, 6734}, {1897, 6735}, {2883, 15498}, {3194, 17188}, {3911, 37305}, {4200, 5704}, {4304, 37441}, {5081, 26015}, {5657, 40971}, {5728, 37321}, {12616, 14257}, {15633, 36121}, {30686, 50195}, {33305, 46974}, {37410, 44695}
X(51359) = reflection of X(1528) in X(25640)
X(51359) = X(34234)-Ceva conjugate of X(19)
X(51359) = X(i)-isoconjugate of X(j) for these (i,j): {3, 1295}, {517, 15405}, {651, 2431}, {1415, 2417}, {36059, 43737}
X(51359) = X(i)-Dao conjugate of X(j) for these (i, j): (1146, 2417), (14571, 908), (20620, 43737), (36103, 1295), (38991, 2431)
X(51359) = crosspoint of X(158) and X(36123)
X(51359) = crosssum of X(255) and X(22350)
X(51359) = crossdifference of every pair of points on line {48, 2431}
X(51359) = barycentric product X(i)*X(j) for these {i,j}: {92, 6001}, {189, 1528}, {318, 43058}, {522, 2405}, {653, 14312}, {1577, 7435}, {2443, 35519}, {25640, 34234}
X(51359) = barycentric quotient X(i)/X(j) for these {i,j}: {19, 1295}, {522, 2417}, {663, 2431}, {909, 15405}, {1528, 329}, {2405, 664}, {2443, 109}, {3064, 43737}, {6001, 63}, {7435, 662}, {14312, 6332}, {25640, 908}, {43058, 77}, {47434, 22350}
X(51359) = {X(1737),X(1785)}-harmonic conjugate of X(1861)
X(51360) lies on these lines: {2, 3098}, {3, 3574}, {4, 5651}, {5, 5650}, {6, 31152}, {20, 35268}, {22, 48880}, {23, 5972}, {25, 48910}, {30, 113}, {38, 17055}, {51, 1368}, {110, 5189}, {115, 3231}, {122, 852}, {125, 511}, {126, 2679}, {141, 427}, {182, 16063}, {184, 1370}, {186, 15473}, {193, 1899}, {195, 18128}, {265, 37496}, {323, 542}, {373, 5480}, {376, 18388}, {382, 35259}, {394, 11550}, {468, 29181}, {524, 47155}, {546, 35283}, {550, 13394}, {576, 18911}, {578, 47528}, {623, 33500}, {624, 33498}, {625, 2450}, {826, 2474}, {1092, 14790}, {1154, 10264}, {1209, 10627}, {1350, 5094}, {1352, 31099}, {1503, 3292}, {1594, 15644}, {1657, 5448}, {1853, 34777}, {1995, 48901}, {2070, 14156}, {2071, 37853}, {2393, 32114}, {2777, 7464}, {2937, 43839}, {2979, 7703}, {3060, 31101}, {3153, 10733}, {3284, 6793}, {3448, 5965}, {3520, 35240}, {3529, 35260}, {3564, 47315}, {3581, 6699}, {3589, 43957}, {3618, 7386}, {3818, 15066}, {3819, 5133}, {4563, 5207}, {4576, 46157}, {5025, 35275}, {5064, 17811}, {5092, 14389}, {5159, 32269}, {5169, 7998}, {5181, 8705}, {5254, 40130}, {5446, 37452}, {5447, 5576}, {5449, 37484}, {5562, 23335}, {5999, 47200}, {6053, 12112}, {6090, 36990}, {6247, 45187}, {6388, 20977}, {6636, 32598}, {6643, 11424}, {6677, 44106}, {6723, 30745}, {6781, 8627}, {6791, 39602}, {6800, 48898}, {7391, 9306}, {7484, 47355}, {7492, 48885}, {7493, 48873}, {7495, 14810}, {7500, 44082}, {7519, 48904}, {7540, 43586}, {7556, 10182}, {7574, 15136}, {7575, 38793}, {7667, 22352}, {7728, 35001}, {7790, 37190}, {8889, 43653}, {9140, 37779}, {9218, 9514}, {9855, 35295}, {10263, 43817}, {10300, 18583}, {10301, 51163}, {10619, 34148}, {10625, 13371}, {10691, 37649}, {11178, 31105}, {11202, 44831}, {11245, 32455}, {11412, 20299}, {11477, 26869}, {11585, 45186}, {11591, 18488}, {11645, 40112}, {11649, 12827}, {11793, 15559}, {11799, 36518}, {12036, 31173}, {12295, 18572}, {12383, 18400}, {12901, 18859}, {13160, 13348}, {13346, 21659}, {13352, 14791}, {13391, 20304}, {13399, 13754}, {13414, 14808}, {13415, 14807}, {13434, 44862}, {13564, 44516}, {13567, 21969}, {14003, 30270}, {14157, 20125}, {14165, 35474}, {14467, 47286}, {14561, 22112}, {14643, 37924}, {14915, 15063}, {15072, 36852}, {15080, 48892}, {15122, 32110}, {15131, 32227}, {15311, 47091}, {15360, 45311}, {15448, 37899}, {15760, 36987}, {16051, 51212}, {16111, 37950}, {16275, 37894}, {17810, 31255}, {18281, 37478}, {18325, 46686}, {18390, 31180}, {18474, 31181}, {18860, 47526}, {19510, 32113}, {20021, 31125}, {20725, 47337}, {21531, 47638}, {21663, 47090}, {21970, 30771}, {22115, 44407}, {23217, 44886}, {23315, 41603}, {26864, 48905}, {26883, 34938}, {27553, 48897}, {27685, 48883}, {30436, 48887}, {31107, 46900}, {31383, 37669}, {31857, 33884}, {31860, 47597}, {32142, 33332}, {32225, 47097}, {32237, 37900}, {32257, 41721}, {32267, 37901}, {32966, 35288}, {33256, 35301}, {33260, 35277}, {33533, 44287}, {33878, 37638}, {34565, 45298}, {34603, 48943}, {34750, 41602}, {35254, 44218}, {35282, 37916}, {35452, 38790}, {35912, 43768}, {35933, 38736}, {36185, 40855}, {36186, 40854}, {37119, 46728}, {37517, 37644}, {37952, 48375}, {37967, 38795}, {38317, 40916}, {38749, 50706}, {41254, 43453}, {44109, 48906}, {44210, 48881}, {44231, 44436}, {44863, 50139}, {45303, 48876}, {46147, 46155}
X(51360) = midpoint of X(i) and X(j) for these {i,j}: {4, 43576}, {110, 5189}, {265, 37496}, {3448, 23061}, {7574, 37477}, {7728, 35001}, {40112, 47314}, {43574, 46450}
X(51360) = reflection of X(i) in X(j) for these {i,j}: {23, 5972}, {125, 858}, {1495, 11064}, {1533, 113}, {2070, 14156}, {3581, 6699}, {5642, 13857}, {12112, 6053}, {12295, 18572}, {13202, 1531}, {15107, 32223}, {15360, 45311}, {16111, 37950}, {16163, 10564}, {18325, 46686}, {20725, 47337}, {21663, 47090}, {24981, 3292}, {32110, 15122}, {32113, 19510}, {32225, 47097}, {32269, 5159}, {37899, 15448}, {37900, 32237}, {37901, 32267}, {41583, 141}, {41586, 125}, {41603, 23315}, {41721, 32257}, {47582, 47296}
X(51360) = complement of X(15107)
X(51360) = anticomplement of X(32223)
X(51360) = reflection of X(3258) in the De Longchamps axis
X(51360) = X(i)-Ceva conjugate of X(j) for these (i,j): {2420, 9033}, {46155, 826}
X(51360) = crosspoint of X(30) and X(3260)
X(51360) = crosssum of X(74) and X(40352)
X(51360) = crossdifference of every pair of points on line {251, 2433}
X(51360) = X(i)-isoconjugate of X(j) for these (i,j): {74, 82}, {83, 2159}, {251, 2349}, {1176, 36119}, {1494, 46289}, {2394, 34072}, {2433, 4599}, {3112, 40352}, {4580, 36131}, {8749, 34055}, {18070, 32640}, {32085, 35200}, {33805, 46288}
X(51360) = X(i)-Dao conjugate of X(j) for these (i, j): (39, 1494), (133, 32085), (141, 74), (1511, 1176), (3124, 2433), (3163, 83), (15449, 2394), (34452, 40352), (39008, 4580), (40585, 2349), (40938, 16080)
X(51360) = barycentric product X(i)*X(j) for these {i,j}: {30, 141}, {38, 14206}, {39, 3260}, {427, 11064}, {826, 2407}, {1235, 3284}, {1495, 8024}, {1634, 41079}, {1637, 4576}, {1930, 2173}, {1964, 46234}, {1990, 3933}, {2420, 23285}, {2525, 4240}, {2530, 42716}, {3665, 7359}, {3703, 6357}, {3917, 46106}, {4568, 11125}, {5642, 31125}, {5664, 46155}, {7813, 9214}, {9033, 41676}, {13857, 23297}, {15523, 18653}, {36789, 46147}, {41077, 46151}
X(51360) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 83}, {38, 2349}, {39, 74}, {141, 1494}, {427, 16080}, {826, 2394}, {1495, 251}, {1634, 44769}, {1843, 8749}, {1930, 33805}, {1964, 2159}, {1990, 32085}, {2173, 82}, {2407, 4577}, {2420, 827}, {2525, 34767}, {3005, 2433}, {3051, 40352}, {3260, 308}, {3284, 1176}, {3688, 15627}, {3917, 14919}, {4020, 35200}, {4240, 42396}, {6793, 21458}, {7813, 36890}, {8041, 46147}, {9033, 4580}, {9406, 46289}, {9407, 46288}, {11064, 1799}, {11125, 10566}, {13857, 10130}, {14206, 3112}, {14398, 18105}, {14399, 18108}, {17442, 36119}, {20775, 18877}, {27369, 40354}, {33299, 44693}, {35319, 36831}, {35325, 1304}, {36035, 18070}, {39691, 12079}, {41676, 16077}, {43768, 39287}, {46106, 46104}, {46147, 40384}, {46151, 15459}, {46154, 9139}, {46155, 39290}, {46234, 18833}
X(51360) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15107, 32223}, {2, 31670, 34417}, {394, 34609, 11550}, {1368, 21850, 37648}, {1370, 37645, 46264}, {1495, 11064, 5642}, {1495, 13857, 11064}, {1533, 1568, 113}, {2979, 31074, 21243}, {5169, 7998, 24206}, {5480, 30739, 373}, {7667, 23292, 22352}, {13346, 37444, 21659}, {14499, 14500, 5642}, {14561, 46336, 22112}, {15066, 31133, 3818}, {15122, 32110, 38727}, {21850, 37648, 51}, {34148, 44829, 10619}, {37645, 46264, 184}, {37669, 44442, 31383}, {46166, 46167, 3917}, {47097, 47582, 47296}, {47296, 47582, 32225}
X(51361) lies on these lines: {1, 227}, {8, 27379}, {10, 7515}, {11, 1279}, {12, 37368}, {19, 25}, {31, 1864}, {35, 9590}, {40, 1854}, {42, 21860}, {44, 2342}, {100, 3100}, {102, 517}, {109, 971}, {117, 515}, {171, 10391}, {200, 219}, {210, 212}, {221, 1490}, {225, 6253}, {241, 18461}, {255, 14872}, {497, 3744}, {516, 16870}, {518, 1936}, {603, 12680}, {650, 663}, {692, 10535}, {750, 17603}, {902, 2310}, {919, 28071}, {950, 5266}, {976, 3057}, {990, 37541}, {1001, 9817}, {1012, 36985}, {1040, 1376}, {1062, 11499}, {1071, 1771}, {1100, 21854}, {1104, 1837}, {1155, 7004}, {1319, 33646}, {1331, 17615}, {1364, 8679}, {1456, 2635}, {1754, 41539}, {1785, 5842}, {1861, 25968}, {2077, 10016}, {2177, 4336}, {2646, 27622}, {2654, 37080}, {2968, 50366}, {3052, 30223}, {3072, 44547}, {3075, 12675}, {3085, 37799}, {3465, 6001}, {3486, 37539}, {3683, 7069}, {3745, 14547}, {3752, 11502}, {3938, 17642}, {4318, 36002}, {4640, 24430}, {4849, 19354}, {4864, 18839}, {5048, 17460}, {5264, 12711}, {5269, 10382}, {5440, 22306}, {5711, 10393}, {5787, 34030}, {6198, 11491}, {6796, 17102}, {7078, 17857}, {7124, 46830}, {7580, 8270}, {8144, 32141}, {9628, 14882}, {10149, 47185}, {10267, 37696}, {10394, 17126}, {10571, 20324}, {10830, 26357}, {11429, 20986}, {13405, 40960}, {14827, 20310}, {15622, 22341}, {17613, 23703}, {18340, 28160}, {18455, 18524}, {18491, 37697}, {19541, 34036}, {20962, 40172}, {21334, 22282}, {22276, 44707}, {26014, 40861}, {27542, 32850}, {28052, 28053}, {30284, 37633}, {33129, 45043}, {40962, 40970}
X(51361) = reflection of X(i) in X(j) for these {i,j}: {1455, 46974}, {1535, 117}, {2968, 50366}, {38357, 16870}
X(51361) = X(i)-Ceva conjugate of X(j) for these (i,j): {515, 2182}, {517, 44}, {1807, 37}, {2222, 650}, {34242, 14737}
X(51361) = crosspoint of X(80) and X(281)
X(51361) = crosssum of X(i) and X(j) for these (i,j): {1, 1465}, {36, 222}, {57, 1455}, {10015, 38357}
X(51361) = crossdifference of every pair of points on line {57, 905}
X(51361) = X(i)-isoconjugate of X(j) for these (i,j): {7, 102}, {56, 34393}, {57, 36100}, {77, 36121}, {85, 32677}, {273, 36055}, {279, 15629}, {658, 2432}, {693, 36040}, {1461, 2399}, {3261, 32643}, {4025, 36067}, {7339, 15633}, {15413, 32667}
X(51361) = X(i)-Dao conjugate of X(j) for these (i, j): (1, 34393), (5452, 36100), (6608, 15633), (10017, 693), (23986, 85), (35508, 2399), (36944, 18816), (46974, 320), (51221, 273)
X(51361) = barycentric product X(i)*X(j) for these {i,j}: {8, 2182}, {9, 515}, {41, 35516}, {78, 8755}, {101, 14304}, {200, 34050}, {281, 46974}, {346, 1455}, {663, 42718}, {1783, 39471}, {1897, 46391}, {2406, 3900}, {2425, 4397}, {7452, 8611}, {11700, 36910}, {15629, 24034}
X(51361) = barycentric quotient X(i)/X(j) for these {i,j}: {9, 34393}, {41, 102}, {55, 36100}, {515, 85}, {607, 36121}, {1253, 15629}, {1455, 279}, {2175, 32677}, {2182, 7}, {2406, 4569}, {2425, 934}, {3119, 15633}, {3900, 2399}, {8641, 2432}, {8755, 273}, {11700, 17078}, {14304, 3261}, {23987, 13149}, {32739, 36040}, {34050, 1088}, {35516, 20567}, {39471, 15413}, {40972, 46359}, {42076, 34050}, {42718, 4572}, {46391, 4025}, {46974, 348}
X(51361) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 11500, 227}, {1, 44425, 1465}, {100, 3100, 9371}, {200, 7070, 7074}
X(51362) lies on these lines: {1, 31246}, {4, 5828}, {5, 6736}, {8, 3090}, {10, 141}, {12, 13601}, {40, 22792}, {63, 50821}, {72, 6937}, {78, 46920}, {80, 3689}, {100, 28160}, {119, 517}, {144, 5657}, {145, 17619}, {153, 17613}, {200, 5790}, {329, 3654}, {355, 6847}, {480, 5587}, {515, 9945}, {516, 38757}, {519, 1387}, {529, 5122}, {944, 27525}, {952, 6745}, {956, 11231}, {971, 37725}, {999, 31190}, {1000, 5328}, {1155, 12763}, {1329, 9957}, {1385, 5552}, {1466, 9578}, {1656, 4853}, {1698, 3304}, {1706, 9654}, {2099, 3679}, {2136, 9669}, {2771, 17615}, {2802, 5087}, {3035, 5126}, {3421, 5744}, {3434, 38140}, {3436, 3579}, {3555, 25005}, {3621, 7705}, {3632, 17606}, {3656, 5748}, {3660, 10956}, {3698, 3824}, {3753, 31019}, {3814, 3880}, {3816, 49626}, {3820, 5316}, {3871, 31795}, {3872, 11230}, {3893, 7741}, {3895, 17556}, {4187, 31792}, {4315, 17564}, {4511, 12531}, {4652, 31447}, {4770, 4777}, {4847, 38042}, {4864, 6788}, {4928, 14077}, {5044, 10039}, {5045, 24982}, {5048, 26726}, {5049, 17051}, {5080, 28146}, {5119, 31141}, {5176, 5440}, {5223, 44785}, {5436, 31480}, {5541, 31160}, {5687, 18480}, {5690, 21075}, {5722, 34619}, {5726, 17528}, {5853, 12019}, {5903, 37829}, {6174, 21578}, {7988, 11525}, {8256, 21077}, {9623, 31479}, {9708, 31434}, {9955, 10914}, {10106, 47742}, {10593, 21627}, {10713, 41310}, {10942, 31788}, {12751, 50371}, {13528, 33898}, {14526, 21677}, {15178, 27385}, {16610, 24222}, {18242, 31798}, {18391, 36867}, {20060, 31776}, {21060, 38127}, {21290, 32851}, {24474, 46677}, {24870, 31138}, {24928, 26364}, {24929, 45701}, {25006, 38058}, {25405, 38455}, {25681, 49169}, {26015, 34122}, {27383, 37727}, {27757, 36919}, {28534, 50841}, {30144, 32537}, {37582, 37828}
X(51362) = midpoint of X(i) and X(j) for these {i,j}: {80, 3689}, {153, 17613}, {908, 1145}, {4867, 36920}, {5176, 5440}, {5223, 44785}, {6735, 17757}, {12751, 50371}
X(51362) = reflection of X(i) in X(j) for these {i,j}: {1538, 119}, {5126, 3035}, {7743, 3814}
X(51362) = X(i)-complementary conjugate of X(j) for these (i,j): {106, 40587}, {1000, 121}, {34446, 4370}, {36596, 1329}
X(51362) = X(27757)-Ceva conjugate of X(4908)
X(51362) = X(i)-isoconjugate of X(j) for these (i,j): {89, 909}, {104, 2163}, {2364, 34051}, {2401, 34073}, {2423, 4604}, {28607, 34234}, {34858, 39704}
X(51362) = X(i)-Dao conjugate of X(j) for these (i, j): (1145, 2320), (16586, 39704), (23980, 89), (36911, 34234), (36912, 36944), (40587, 104), (40613, 2163)
X(51362) = crossdifference of every pair of points on line {2423, 21007}
X(51362) = barycentric product X(i)*X(j) for these {i,j}: {45, 3262}, {517, 4671}, {908, 3679}, {1145, 4945}, {2397, 4777}, {4752, 36038}, {4767, 10015}, {4873, 22464}, {5219, 6735}, {5235, 17757}, {26611, 36921}
X(51362) = barycentric quotient X(i)/X(j) for these {i,j}: {45, 104}, {517, 89}, {908, 39704}, {2099, 34051}, {2177, 909}, {2183, 2163}, {2397, 4597}, {2427, 4588}, {3262, 20569}, {3679, 34234}, {4671, 18816}, {4752, 36037}, {4767, 13136}, {4775, 2423}, {4777, 2401}, {4908, 36944}, {4944, 43728}, {6735, 30608}, {17757, 30588}, {36920, 40218}
X(51362) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 12607, 942}, {908, 6735, 1145}, {1145, 17757, 908}, {1329, 10915, 9957}, {3679, 4867, 36920}, {3679, 5219, 40587}, {3698, 37719, 3824}, {8256, 21077, 50193}, {10039, 21031, 5044}, {10914, 11681, 9955}, {26364, 32049, 24928}
X(51363) lies on these lines: {6, 5064}, {51, 53}, {112, 15340}, {115, 3331}, {125, 232}, {132, 1503}, {185, 27376}, {216, 40588}, {217, 3574}, {230, 1495}, {343, 13157}, {381, 41376}, {393, 1899}, {1249, 32064}, {1562, 5523}, {1568, 1625}, {1853, 45141}, {1968, 21659}, {1970, 10619}, {1971, 6103}, {2081, 2600}, {3269, 13399}, {3767, 26883}, {5254, 11381}, {5304, 9993}, {5305, 16655}, {6529, 6761}, {7735, 31383}, {7745, 11572}, {8743, 18381}, {8744, 25739}, {8778, 17845}, {10312, 13419}, {10313, 13236}, {10317, 44407}, {14216, 41361}, {14864, 41366}, {15262, 41738}, {15595, 30737}, {20299, 39575}, {21243, 22240}, {32445, 43831}
X(51363) = midpoint of X(112) and X(15340)
X(51363) = reflection of X(i) in X(j) for these {i,j}: {1562, 5523}, {8779, 16318}
X(51363) = crosssum of X(3) and X(10313)
X(51363) = crossdifference of every pair of points on line {54, 2435}
X(51363) = X(i)-isoconjugate of X(j) for these (i,j): {97, 8767}, {1297, 2167}, {2148, 35140}, {2169, 6330}, {36134, 43673}
X(51363) = X(i)-Dao conjugate of X(j) for these (i, j): (137, 43673), (216, 35140), (14363, 6330), (15450, 2435), (15595, 34386), (23976, 95), (39019, 2419), (39071, 97), (40588, 1297), (50938, 275)
X(51363) = barycentric product X(i)*X(j) for these {i,j}: {5, 1503}, {51, 30737}, {53, 441}, {311, 42671}, {324, 8779}, {343, 16318}, {1154, 43089}, {2312, 14213}, {2409, 6368}, {12077, 34211}, {34156, 39569}
X(51363) = barycentric quotient X(i)/X(j) for these {i,j}: {5, 35140}, {51, 1297}, {53, 6330}, {441, 34386}, {1503, 95}, {2181, 8767}, {2312, 2167}, {2409, 18831}, {2445, 933}, {3199, 43717}, {6368, 2419}, {6793, 43768}, {8779, 97}, {12077, 43673}, {15451, 2435}, {16318, 275}, {21458, 39287}, {23977, 16813}, {30737, 34384}, {39473, 15414}, {42671, 54}, {43089, 46138}
X(51363) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {217, 27371, 3574}, {8779, 16318, 6793}
X(51364) lies on these lines: {2, 77}, {4, 7177}, {7, 1699}, {8, 23244}, {10, 3160}, {11, 34855}, {273, 1088}, {279, 1210}, {307, 31627}, {347, 4847}, {348, 6734}, {515, 934}, {522, 693}, {651, 40869}, {658, 4872}, {664, 6735}, {738, 9581}, {971, 1543}, {1146, 43064}, {1323, 1737}, {1419, 24553}, {1439, 8727}, {1442, 13405}, {1804, 7580}, {1996, 14548}, {2124, 23058}, {3086, 4350}, {5543, 21625}, {5691, 17106}, {6245, 14256}, {6359, 18650}, {6736, 25718}, {7053, 19541}, {7179, 31526}, {7190, 10580}, {8582, 31994}, {9312, 24982}, {15634, 43672}, {24987, 27187}, {25006, 31600}, {26001, 43035}, {33864, 35312}, {34028, 40942}, {34029, 40719}, {38459, 44675}
X(51364) = reflection of X(1543) in X(44993)
X(51364) = X(18025)-Ceva conjugate of X(7)
X(51364) = X(i)-isoconjugate of X(j) for these (i,j): {55, 972}, {2175, 46137}
X(51364) = X(i)-Dao conjugate of X(j) for these (i, j): (223, 972), (35593, 4105), (40593, 46137), (43035, 516), (50930, 33)
X(51364) = cevapoint of X(971) and X(43044)
X(51364) = barycentric product X(i)*X(j) for these {i,j}: {75, 43044}, {85, 971}, {1121, 28344}, {2272, 6063}
X(51364) = barycentric quotient X(i)/X(j) for these {i,j}: {57, 972}, {85, 46137}, {971, 9}, {2272, 55}, {28344, 527}, {42772, 46393}, {43044, 1}
X(51364) = {X(1440),X(5932)}-harmonic conjugate of X(77)
X(51365) lies on these lines: {1, 10361}, {2, 34032}, {57, 5928}, {65, 39579}, {108, 1503}, {109, 33305}, {221, 406}, {223, 17073}, {225, 26955}, {226, 1439}, {278, 13567}, {429, 1425}, {525, 1577}, {651, 11064}, {860, 38955}, {946, 15498}, {1146, 37790}, {1210, 12664}, {1211, 1214}, {1465, 26005}, {1528, 6001}, {1848, 46017}, {1865, 6354}, {1881, 26957}, {2182, 3911}, {2321, 26942}, {3564, 41349}, {3580, 37798}, {4205, 37558}, {4554, 6393}, {5257, 30456}, {5706, 18915}, {6247, 7952}, {7046, 20307}, {10535, 23711}, {20623, 39063}, {23710, 26956}, {25964, 37695}, {26932, 34050}, {37648, 37800}, {37799, 47296}, {40669, 50705}
X(51365) = X(i)-isoconjugate of X(j) for these (i,j): {162, 2431}, {163, 43737}, {284, 1295}, {2417, 32676}, {23090, 36044}
X(51365) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 43737), (125, 2431), (15526, 2417), (35580, 23090), (40590, 1295)
X(51365) = crossdifference of every pair of points on line {2194, 2431}
X(51365) = barycentric product X(i)*X(j) for these {i,j}: {321, 43058}, {525, 2405}, {1441, 6001}, {2443, 3267}, {4566, 14312}
X(51365) = barycentric quotient X(i)/X(j) for these {i,j}: {65, 1295}, {523, 43737}, {525, 2417}, {647, 2431}, {2405, 648}, {2443, 112}, {6001, 21}, {14312, 7253}, {43058, 81}
X(51366) lies on these lines: {1, 25964}, {2, 954}, {3, 26939}, {4, 27508}, {8, 25000}, {10, 37}, {72, 307}, {100, 33305}, {101, 1503}, {118, 516}, {198, 49132}, {228, 440}, {406, 5687}, {461, 17784}, {525, 656}, {860, 17757}, {936, 17306}, {971, 40880}, {1145, 41215}, {1146, 29016}, {1331, 11064}, {1368, 20760}, {1565, 34381}, {1818, 26932}, {1944, 5762}, {2318, 21912}, {3089, 10306}, {3190, 13567}, {3198, 21062}, {3564, 17976}, {3682, 18643}, {4561, 6393}, {5728, 25019}, {5759, 27382}, {5783, 37148}, {5805, 27384}, {6745, 25882}, {6776, 20818}, {7085, 7536}, {7360, 15252}, {7515, 11517}, {7580, 27540}, {8728, 25521}, {13727, 27547}, {16252, 38857}, {16844, 19843}, {17484, 46488}, {19541, 27539}, {21913, 40967}, {22117, 37669}, {23089, 26929}, {23095, 48906}, {23693, 36949}, {24320, 49131}
X(51366) = midpoint of X(101) and X(41327)
X(51366) = reflection of X(i) in X(j) for these {i,j}: {1146, 31897}, {1547, 118}
X(51366) = isotomic conjugate of the polar conjugate of X(17747)
X(51366) = X(i)-isoconjugate of X(j) for these (i,j): {27, 911}, {28, 103}, {58, 36122}, {162, 2424}, {1019, 40116}, {1396, 2338}, {1474, 36101}, {1815, 5317}, {2203, 18025}, {2299, 43736}, {2400, 32676}, {8747, 36056}, {16751, 32701}, {17925, 36039}, {17926, 32668}
X(51366) = X(i)-Dao conjugate of X(j) for these (i, j): (10, 36122), (125, 2424), (226, 43736), (1566, 17925), (15526, 2400), (20622, 8747), (23972, 27), (40591, 103), (40869, 15149), (46095, 58), (50441, 29)
X(51366) = crossdifference of every pair of points on line {1474, 2424}
X(51366) = barycentric product X(i)*X(j) for these {i,j}: {10, 26006}, {69, 17747}, {71, 35517}, {72, 30807}, {306, 516}, {307, 40869}, {525, 2398}, {656, 42719}, {910, 20336}, {1231, 41339}, {2426, 3267}, {3265, 41321}, {3695, 14953}, {3710, 43035}, {3952, 39470}
X(51366) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 36122}, {71, 103}, {72, 36101}, {228, 911}, {306, 18025}, {516, 27}, {525, 2400}, {647, 2424}, {676, 17925}, {910, 28}, {1214, 43736}, {1456, 1396}, {1886, 8747}, {2318, 2338}, {2398, 648}, {2426, 112}, {3234, 4241}, {3682, 1815}, {3990, 36056}, {4055, 32657}, {4466, 15634}, {4557, 40116}, {4574, 677}, {17747, 4}, {26006, 86}, {28346, 423}, {30807, 286}, {35517, 44129}, {39470, 7192}, {40869, 29}, {41321, 107}, {41339, 1172}, {42719, 811}, {50441, 15149}
X(51366) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {198, 50861, 49132}, {228, 21015, 440}, {2318, 21912, 26942}, {4026, 5257, 4205}, {40869, 50441, 1536}
X(51367) lies on these lines: {2, 2256}, {8, 5721}, {69, 22129}, {100, 1503}, {119, 517}, {141, 17595}, {192, 26579}, {306, 307}, {313, 321}, {343, 345}, {344, 37648}, {442, 4158}, {525, 14208}, {914, 25083}, {1265, 3617}, {1332, 11064}, {3035, 5137}, {3564, 17977}, {3580, 32849}, {3713, 5739}, {3932, 21920}, {3935, 5846}, {3977, 26932}, {3995, 26609}, {4358, 26005}, {5552, 5706}, {5554, 37614}, {5710, 10528}, {5799, 11681}, {13567, 17776}, {17923, 40863}, {23600, 26872}, {26543, 32779}, {28297, 50043}, {28420, 37638}, {33168, 37636}
X(51368) lies on these lines: {2, 7011}, {3, 388}, {5, 20764}, {7, 6350}, {12, 18641}, {35, 44244}, {37, 226}, {56, 7515}, {57, 16608}, {108, 33305}, {109, 1503}, {117, 515}, {243, 15252}, {278, 19542}, {496, 38284}, {497, 38288}, {518, 2968}, {525, 8611}, {856, 17757}, {908, 16596}, {1375, 37799}, {1465, 5236}, {1813, 11064}, {3086, 38290}, {3564, 17975}, {3600, 27407}, {5219, 17073}, {5226, 6349}, {5261, 37180}, {5786, 34030}, {5800, 37541}, {8545, 30675}, {10319, 10401}, {12709, 41340}, {14206, 21452}, {15888, 40946}, {17102, 21620}, {22119, 34048}, {26942, 40152}, {37798, 46487}, {45206, 46017}
X(51368) = reflection of X(i) in X(j) for these {i,j}: {243, 15252}, {1549, 117}
X(51368) = X(22383)-complementary conjugate of X(38981)
X(51368) = X(i)-isoconjugate of X(j) for these (i,j): {28, 15629}, {29, 32677}, {102, 1172}, {162, 2432}, {284, 36121}, {1021, 36067}, {2204, 34393}, {2299, 36100}, {2399, 32676}, {7253, 32667}, {8748, 36055}, {17926, 36040}
X(51368) = X(i)-Dao conjugate of X(j) for these (i, j): (125, 2432), (226, 36100), (10017, 17926), (15526, 2399), (23986, 29), (40590, 36121), (40591, 15629), (51221, 8748)
X(51368) = crossdifference of every pair of points on line {2299, 2432}
X(51368) = barycentric product X(i)*X(j) for these {i,j}: {73, 35516}, {306, 34050}, {307, 515}, {525, 2406}, {1231, 2182}, {1441, 46974}, {1455, 20336}, {2425, 3267}, {3265, 23987}, {4566, 39471}, {24018, 24035}
X(51368) = barycentric quotient X(i)/X(j) for these {i,j}: {65, 36121}, {71, 15629}, {73, 102}, {307, 34393}, {515, 29}, {525, 2399}, {647, 2432}, {1214, 36100}, {1409, 32677}, {1455, 28}, {2182, 1172}, {2406, 648}, {2425, 112}, {8755, 8748}, {10017, 14010}, {11700, 17515}, {22341, 36055}, {23987, 107}, {24035, 823}, {34050, 27}, {35516, 44130}, {39471, 7253}, {46391, 1021}, {46974, 21}
X(51368) = {X(12),X(22341)}-harmonic conjugate of X(18641)
X(51369) lies on these lines: {6, 21485}, {65, 17103}, {69, 24523}, {72, 34016}, {76, 37536}, {81, 593}, {86, 1431}, {99, 517}, {110, 2856}, {114, 325}, {183, 37521}, {274, 18180}, {286, 6385}, {314, 35626}, {315, 37482}, {320, 350}, {354, 51356}, {518, 7061}, {620, 5164}, {662, 910}, {758, 6629}, {760, 3110}, {942, 1509}, {960, 6626}, {1078, 5482}, {1414, 1455}, {1755, 1959}, {1975, 10441}, {2106, 3290}, {3027, 17768}, {3125, 16756}, {3185, 44179}, {3263, 4576}, {3873, 17393}, {3917, 37664}, {5045, 33770}, {5208, 8822}, {5752, 7763}, {7381, 18144}, {7769, 34466}, {14131, 43459}, {15488, 32819}, {15635, 17929}, {16735, 18167}, {17172, 37796}, {18178, 33296}, {18191, 33295}, {18827, 20358}, {19623, 34377}, {27958, 43216}, {32004, 34791}, {34371, 40882}, {35297, 50361}
X(51369) = reflection of X(5164) in X(620)
X(51369) = X(7095)-anticomplementary conjugate of X(2895)
X(51369) = X(274)-Ceva conjugate of X(16725)
X(51369) = X(i)-cross conjugate of X(j) for these (i,j): {511, 17209}, {16725, 274}
X(51369) = X(i)-isoconjugate of X(j) for these (i,j): {10, 1976}, {37, 1910}, {42, 98}, {71, 6531}, {101, 2395}, {190, 2422}, {213, 1821}, {228, 36120}, {248, 1826}, {287, 2333}, {290, 1918}, {293, 1824}, {313, 14601}, {878, 1897}, {879, 8750}, {1400, 15628}, {2200, 16081}, {2205, 46273}, {2715, 4024}, {2966, 4079}, {3404, 18098}, {4039, 34238}, {4064, 32696}, {4600, 15630}, {4705, 36084}, {32739, 43665}, {36036, 50487}
X(51369) = X(i)-Dao conjugate of X(j) for these (i, j): (132, 1824), (511, 5360), (1015, 2395), (2679, 50487), (5976, 321), (6626, 1821), (11672, 37), (16609, 7235), (26932, 879), (34021, 290), (34467, 878), (35088, 4036), (38987, 4705), (39039, 1826), (39040, 10), (40582, 15628), (40589, 1910), (40592, 98), (40601, 213), (40619, 43665), (46094, 228), (50440, 210), (50497, 15630)
X(51369) = cevapoint of X(511) and X(1959)
X(51369) = crosssum of X(4455) and X(4516)
X(51369) = trilinear pole of line {16725, 39040}
X(51369) = crossdifference of every pair of points on line {213, 2422}
X(51369) = barycentric product X(i)*X(j) for these {i,j}: {28, 6393}, {58, 46238}, {75, 17209}, {81, 325}, {86, 1959}, {237, 6385}, {240, 17206}, {274, 511}, {286, 36212}, {290, 16725}, {297, 1444}, {310, 1755}, {314, 43034}, {513, 2396}, {593, 42703}, {693, 2421}, {877, 905}, {1434, 44694}, {1437, 44132}, {1790, 40703}, {3261, 23997}, {3405, 16887}, {3569, 4623}, {4230, 15413}, {5968, 16741}, {7192, 42717}, {14966, 40495}, {16696, 20022}, {16756, 36892}
X(51369) = barycentric quotient X(i)/X(j) for these {i,j}: {21, 15628}, {27, 36120}, {28, 6531}, {58, 1910}, {81, 98}, {86, 1821}, {232, 1824}, {237, 213}, {240, 1826}, {274, 290}, {286, 16081}, {297, 41013}, {310, 46273}, {325, 321}, {511, 37}, {513, 2395}, {667, 2422}, {693, 43665}, {877, 6335}, {905, 879}, {1333, 1976}, {1437, 248}, {1444, 287}, {1755, 42}, {1790, 293}, {1959, 10}, {2396, 668}, {2421, 100}, {2491, 50487}, {2799, 4036}, {3121, 15630}, {3289, 228}, {3405, 18082}, {3569, 4705}, {4230, 1783}, {4556, 36084}, {4610, 36036}, {4623, 43187}, {5360, 1500}, {6385, 18024}, {6393, 20336}, {9155, 21839}, {9417, 1918}, {9418, 2205}, {11672, 5360}, {14966, 692}, {15631, 42717}, {16591, 7235}, {16696, 20021}, {16702, 5967}, {16725, 511}, {16726, 43920}, {16756, 36874}, {17187, 3404}, {17206, 336}, {17209, 1}, {18604, 17974}, {22383, 878}, {23997, 101}, {32458, 42703}, {36212, 72}, {42702, 3690}, {42703, 28654}, {42717, 3952}, {43034, 65}, {44114, 21833}, {44694, 2321}, {46238, 313}, {50440, 4037}, {50567, 42713}
X(51370) lies on these lines: {58, 86}, {76, 24220}, {99, 516}, {114, 325}, {142, 51314}, {226, 8033}, {274, 1432}, {310, 17167}, {315, 991}, {514, 1921}, {573, 7763}, {620, 20666}, {799, 908}, {873, 5249}, {1738, 2669}, {1959, 46238}, {1975, 48902}, {3006, 4576}, {3120, 17204}, {3403, 30035}, {3912, 24479}, {3926, 10446}, {3933, 48934}, {3936, 16741}, {4416, 27691}, {4573, 34050}, {4610, 18653}, {6337, 48918}, {7304, 40940}, {7750, 48929}, {7752, 48888}, {7773, 48938}, {7776, 48908}, {15634, 17930}, {16591, 43034}, {16705, 17202}, {16748, 17173}, {16891, 17187}, {17103, 50307}, {17171, 44129}, {17182, 31008}, {17197, 30940}, {17203, 18169}, {17731, 34379}, {18827, 24231}, {20335, 40017}, {21246, 29968}, {23636, 29972}, {24210, 39915}, {24239, 32010}, {32816, 48878}, {32819, 48940}
X(51370) = reflection of X(20666) in X(620)
X(51370) = isotomic conjugate of the isogonal conjugate of X(17209)
X(51370) = X(39040)-cross conjugate of X(75)
X(51370) = X(i)-isoconjugate of X(j) for these (i,j): {37, 1976}, {42, 1910}, {98, 213}, {100, 2422}, {228, 6531}, {248, 1824}, {290, 2205}, {293, 2333}, {321, 14601}, {692, 2395}, {878, 1783}, {1402, 15628}, {1821, 1918}, {2200, 36120}, {2715, 4705}, {2966, 50487}, {4079, 36084}, {4567, 15630}, {5360, 41932}, {14600, 41013}
X(51370) = X(i)-Dao conjugate of X(j) for these (i, j): (132, 2333), (325, 4039), (1086, 2395), (5976, 10), (6626, 98), (8054, 2422), (11672, 42), (34021, 1821), (35088, 4024), (38987, 4079), (39006, 878), (39039, 1824), (39040, 37), (40589, 1976), (40592, 1910), (40601, 1918), (40605, 15628), (40618, 879), (40627, 15630), (46094, 2200), (50440, 1334)
X(51370) = cevapoint of X(325) and X(1959)
X(51370) = crosspoint of X(4620) and X(4639)
X(51370) = crossdifference of every pair of points on line {1918, 2422}
X(51370) = barycentric product X(i)*X(j) for these {i,j}: {27, 6393}, {76, 17209}, {81, 46238}, {86, 325}, {274, 1959}, {297, 17206}, {310, 511}, {514, 2396}, {757, 42703}, {877, 4025}, {1444, 40703}, {1755, 6385}, {1790, 44132}, {2421, 3261}, {2799, 4610}, {3405, 16703}, {7199, 42717}, {16725, 46273}, {16887, 20022}, {23997, 40495}, {28660, 43034}, {36212, 44129}
X(51370) = barycentric quotient X(i)/X(j) for these {i,j}: {27, 6531}, {58, 1976}, {81, 1910}, {86, 98}, {232, 2333}, {237, 1918}, {240, 1824}, {274, 1821}, {286, 36120}, {297, 1826}, {310, 290}, {325, 10}, {333, 15628}, {511, 42}, {514, 2395}, {649, 2422}, {868, 21043}, {877, 1897}, {1444, 293}, {1459, 878}, {1755, 213}, {1790, 248}, {1959, 37}, {2206, 14601}, {2396, 190}, {2421, 101}, {2799, 4024}, {3122, 15630}, {3261, 43665}, {3289, 2200}, {3405, 18098}, {3569, 4079}, {4025, 879}, {4230, 8750}, {4556, 2715}, {4610, 2966}, {4623, 36036}, {5360, 872}, {5976, 4039}, {6333, 4064}, {6385, 46273}, {6393, 306}, {6629, 5967}, {9417, 2205}, {14966, 32739}, {16696, 3404}, {16725, 1755}, {16887, 20021}, {17205, 43920}, {17206, 287}, {17209, 6}, {18653, 35906}, {20022, 18082}, {23996, 5360}, {23997, 692}, {36212, 71}, {40703, 41013}, {42703, 1089}, {42717, 1018}, {43034, 1400}, {44129, 16081}, {44694, 210}, {46238, 321}, {50567, 4062}
X(51371) lies on these lines: {2, 4121}, {6, 3788}, {39, 141}, {54, 69}, {76, 3399}, {99, 5207}, {114, 325}, {115, 698}, {125, 3266}, {193, 33203}, {305, 21243}, {315, 3098}, {316, 29317}, {524, 1692}, {542, 5152}, {599, 30532}, {620, 1691}, {626, 3094}, {754, 2076}, {826, 23285}, {1007, 14561}, {1350, 7776}, {1352, 3926}, {1503, 6390}, {1506, 24256}, {1570, 44380}, {1975, 3818}, {1992, 33231}, {2024, 15993}, {2482, 10291}, {3492, 8788}, {3564, 12042}, {3589, 7874}, {3618, 32952}, {3619, 7803}, {3763, 7834}, {3819, 45201}, {4048, 7863}, {4175, 8024}, {4576, 46157}, {5017, 7759}, {5028, 7888}, {5039, 7774}, {5103, 5969}, {5111, 14645}, {5477, 13196}, {5921, 32841}, {5972, 37804}, {6033, 35456}, {6337, 46264}, {6388, 48444}, {6723, 37803}, {6776, 32831}, {7749, 8177}, {7750, 14810}, {7752, 18906}, {7762, 41413}, {7768, 35422}, {7773, 48901}, {7779, 10352}, {7782, 48892}, {7788, 50977}, {7795, 13356}, {7802, 48885}, {7809, 19924}, {7820, 42534}, {7838, 12212}, {7852, 34573}, {7906, 32451}, {8041, 16893}, {9306, 34254}, {9744, 10519}, {9865, 45803}, {10008, 32825}, {11178, 32833}, {11179, 32837}, {11646, 14148}, {11898, 50684}, {13354, 48876}, {15595, 34138}, {16925, 41412}, {18553, 32820}, {23098, 44716}, {28419, 44141}, {31670, 32816}, {32006, 48873}, {32819, 48889}, {32821, 34507}, {32823, 51212}, {32830, 40330}, {35377, 39099}, {35389, 37466}, {39569, 44132}, {40123, 43653}, {40708, 40876}
X(51371) = midpoint of X(i) and X(j) for these {i,j}: {99, 5207}, {325, 6393}, {6033, 35456}, {9865, 45803}
X(51371) = reflection of X(i) in X(j) for these {i,j}: {115, 5031}, {1570, 44380}, {1691, 620}, {5477, 13196}, {50567, 6393}
X(51371) = X(2421)-Ceva conjugate of X(6333)
X(51371) = X(i)-isoconjugate of X(j) for these (i,j): {82, 1976}, {98, 46289}, {251, 1910}, {1821, 46288}, {2395, 34072}, {2422, 4599}, {3112, 14601}, {10547, 36120}, {18105, 36084}
X(51371) = X(i)-Dao conjugate of X(j) for these (i, j): (39, 98), (141, 1976), (339, 43665), (441, 21458), (3124, 2422), (5976, 83), (6665, 20021), (11672, 251), (15449, 2395), (34452, 14601), (38987, 18105), (39040, 82), (40585, 1910), (40601, 46288), (40938, 6531), (46094, 10547), (47648, 733)
X(51371) = crosssum of X(1976) and X(14601)
X(51371) = crossdifference of every pair of points on line {2422, 18105}
X(51371) = barycentric product X(i)*X(j) for these {i,j}: {38, 46238}, {141, 325}, {297, 3933}, {427, 6393}, {511, 8024}, {826, 2396}, {877, 2525}, {1235, 36212}, {1930, 1959}, {2421, 23285}, {2799, 4576}, {3917, 44132}, {6333, 41676}, {7794, 20022}, {14994, 46807}, {16696, 42703}, {20021, 32458}, {31125, 50567}, {35540, 40810}, {42717, 48084}
X(51371) = barycentric quotient X(i)/X(j) for these {i,j}: {38, 1910}, {39, 1976}, {141, 98}, {237, 46288}, {297, 32085}, {325, 83}, {427, 6531}, {511, 251}, {732, 40820}, {826, 2395}, {868, 34294}, {877, 42396}, {1235, 16081}, {1634, 2715}, {1755, 46289}, {1930, 1821}, {1959, 82}, {2396, 4577}, {2421, 827}, {2525, 879}, {3005, 2422}, {3051, 14601}, {3289, 10547}, {3313, 11610}, {3569, 18105}, {3703, 15628}, {3917, 248}, {3933, 287}, {4576, 2966}, {6333, 4580}, {6393, 1799}, {7794, 20021}, {7813, 5967}, {8024, 290}, {14966, 4630}, {14994, 46806}, {15595, 21458}, {20021, 41932}, {20775, 14600}, {20883, 36120}, {23285, 43665}, {23997, 34072}, {31125, 9154}, {32458, 20022}, {34138, 16277}, {35325, 32696}, {35540, 14382}, {36212, 1176}, {40810, 733}, {41676, 685}, {44132, 46104}, {46151, 20031}, {46238, 3112}, {46807, 42299}
X(51371) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 7763, 182}, {141, 3933, 14994}, {141, 10007, 6292}, {7752, 18906, 19130}, {7838, 12212, 41623}, {8041, 16893, 21248}, {14501, 14502, 32458}
X(51372) lies on these lines: {2, 187}, {30, 113}, {32, 41238}, {99, 401}, {114, 47526}, {127, 441}, {183, 458}, {232, 41253}, {287, 39099}, {323, 538}, {325, 40884}, {343, 14929}, {373, 10796}, {385, 41254}, {511, 1316}, {524, 48721}, {543, 40112}, {754, 3580}, {858, 2794}, {868, 13449}, {1007, 37188}, {1993, 7798}, {2407, 3260}, {2453, 10510}, {2549, 37645}, {2782, 3292}, {3199, 28704}, {3288, 23878}, {3734, 15066}, {4045, 14389}, {4226, 18860}, {5107, 35606}, {5112, 5972}, {5651, 35930}, {5915, 37350}, {5999, 35278}, {6593, 11594}, {7766, 40814}, {7809, 44575}, {12042, 21531}, {14165, 40889}, {14581, 46106}, {14957, 42671}, {15013, 44436}, {15980, 47200}, {16321, 41583}, {17941, 39266}, {18502, 21513}, {18907, 37648}, {32110, 36177}, {32225, 34094}, {32456, 35933}, {34217, 37183}, {34986, 39906}, {46981, 47097}
X(51372) = midpoint of X(2453) and X(10510)
X(51372) = reflection of X(i) in X(j) for these {i,j}: {1555, 113}, {5112, 5972}, {32110, 36177}, {32225, 34094}, {41583, 16321}
X(51372) = X(i)-isoconjugate of X(j) for these (i,j): {74, 2186}, {262, 2159}, {263, 2349}, {1494, 3402}, {32112, 36132}, {33805, 46319}, {36119, 43718}
X(51372) = X(i)-Dao conjugate of X(j) for these (i, j): (1511, 43718), (3163, 262), (38997, 2433), (39009, 32112)
X(51372) = crossdifference of every pair of points on line {263, 2433}
X(51372) = barycentric product X(i)*X(j) for these {i,j}: {30, 183}, {182, 3260}, {458, 11064}, {1495, 20023}, {2173, 3403}, {2407, 23878}, {3284, 44144}
X(51372) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 262}, {182, 74}, {183, 1494}, {458, 16080}, {1495, 263}, {2173, 2186}, {2420, 26714}, {3260, 327}, {3284, 43718}, {3288, 2433}, {3403, 33805}, {9406, 3402}, {9407, 46319}, {10311, 8749}, {11064, 42313}, {14096, 46147}, {23878, 2394}, {34396, 40352}, {43768, 42300}
X(51372) = {X(41887),X(41888)}-harmonic conjugate of X(13857)
X(51373) lies on these lines: {2, 39}, {69, 9744}, {98, 12215}, {99, 5999}, {114, 325}, {182, 183}, {187, 5149}, {216, 40073}, {230, 732}, {232, 44132}, {262, 1007}, {315, 5188}, {316, 40236}, {385, 1692}, {570, 44166}, {620, 736}, {641, 48769}, {642, 48768}, {698, 2023}, {1078, 37455}, {1502, 14767}, {1570, 36849}, {1916, 7925}, {1975, 6248}, {2782, 6390}, {3003, 35549}, {3094, 7778}, {3095, 37071}, {3815, 24256}, {3906, 6333}, {3933, 37451}, {4048, 42535}, {5052, 7774}, {5207, 43460}, {5305, 41651}, {5969, 22110}, {6194, 9742}, {6337, 11257}, {7735, 32451}, {7752, 13862}, {7755, 41756}, {7759, 46321}, {7764, 18806}, {7770, 13356}, {7776, 9821}, {7807, 13357}, {7821, 46283}, {7888, 32452}, {7901, 32476}, {7907, 9983}, {8667, 12151}, {9753, 35439}, {9766, 13330}, {9770, 22486}, {10011, 32515}, {10997, 32456}, {12251, 32818}, {12829, 13196}, {13334, 37450}, {14931, 15301}, {15271, 50659}, {17932, 47382}, {22564, 41136}, {35377, 39093}, {35436, 37466}, {37688, 50652}, {41624, 44500}, {44137, 46271}, {44534, 44771}
X(51373) = midpoint of X(i) and X(j) for these {i,j}: {99, 39266}, {325, 5976}, {9466, 39785}
X(51373) = reflection of X(i) in X(j) for these {i,j}: {2021, 620}, {2023, 44377}
X(51373) = X(40824)-Ceva conjugate of X(32458)
X(51373) = X(i)-isoconjugate of X(j) for these (i,j): {98, 3402}, {263, 1910}, {512, 36132}, {661, 32716}, {798, 6037}, {1821, 46319}, {1976, 2186}, {3404, 42288}
X(51373) = X(i)-Dao conjugate of X(j) for these (i, j): (5976, 262), (11672, 263), (31998, 6037), (33569, 6784), (36830, 32716), (38997, 2422), (39009, 512), (39040, 2186), (39054, 36132), (40601, 46319)
X(51373) = crosspoint of X(183) and X(8842)
X(51373) = crossdifference of every pair of points on line {669, 2422}
X(51373) = barycentric product X(i)*X(j) for these {i,j}: {183, 325}, {458, 6393}, {511, 20023}, {1959, 3403}, {2396, 23878}, {4609, 9420}, {5976, 8842}, {14994, 20022}, {32458, 46806}, {36212, 44144}
X(51373) = barycentric quotient X(i)/X(j) for these {i,j}: {99, 6037}, {110, 32716}, {182, 1976}, {183, 98}, {237, 46319}, {325, 262}, {458, 6531}, {511, 263}, {662, 36132}, {1755, 3402}, {1959, 2186}, {2421, 26714}, {3288, 2422}, {3403, 1821}, {6393, 42313}, {6784, 15630}, {8842, 36897}, {9420, 669}, {14994, 20021}, {20022, 42299}, {20023, 290}, {23878, 2395}, {32458, 46807}, {33569, 2491}, {34396, 14601}, {36212, 43718}, {44144, 16081}, {46806, 41932}
X(51373) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39, 7874, 6683}, {39, 31239, 7834}, {76, 7763, 39}, {325, 6393, 32458}, {385, 10352, 1692}, {1007, 18906, 262}, {3788, 8149, 39}, {7764, 18806, 46305}, {7769, 32832, 39784}, {7799, 32833, 39785}, {9744, 22712, 13354}, {14994, 15819, 183}, {31276, 32830, 76}, {36849, 39101, 1570}
X(51374) lies on these lines: {4, 10008}, {6, 16925}, {20, 64}, {76, 48876}, {99, 3564}, {114, 325}, {141, 5025}, {148, 44395}, {183, 10519}, {193, 439}, {230, 46236}, {315, 33878}, {468, 4563}, {524, 2076}, {599, 33017}, {620, 1570}, {670, 17984}, {698, 15993}, {877, 6530}, {1351, 7763}, {1352, 32819}, {1692, 14645}, {2080, 6390}, {2211, 2421}, {2979, 45201}, {3580, 4576}, {3589, 33245}, {3618, 10542}, {3619, 33199}, {3620, 7784}, {3630, 33268}, {3631, 33256}, {3763, 33248}, {3933, 9821}, {5028, 7807}, {5207, 29181}, {7752, 21850}, {7769, 18583}, {7773, 51212}, {7782, 48906}, {7788, 50967}, {7802, 48874}, {8781, 10011}, {9606, 51171}, {14561, 37647}, {15514, 44380}, {22329, 50639}, {30262, 41005}, {32113, 36792}, {33254, 40341}, {35265, 38940}
X(51374) = reflection of X(i) in X(j) for these {i,j}: {325, 6393}, {1570, 620}, {6393, 50567}, {15514, 44380}
X(51374) = X(297)-Ceva conjugate of X(325)
X(51374) = X(i)-isoconjugate of X(j) for these (i,j): {98, 38252}, {293, 14248}, {1910, 8770}, {1976, 8769}, {36120, 40319}
X(51374) = X(i)-Dao conjugate of X(j) for these (i, j): (69, 287), (132, 14248), (5976, 2996), (6388, 879), (11672, 8770), (15525, 2395), (39040, 8769), (46094, 40319)
X(51374) = crosssum of X(878) and X(15630)
X(51374) = barycentric product X(i)*X(j) for these {i,j}: {193, 325}, {297, 6337}, {1707, 46238}, {1959, 18156}, {2396, 3566}, {3167, 44132}, {6353, 6393}
X(51374) = barycentric quotient X(i)/X(j) for these {i,j}: {193, 98}, {232, 14248}, {297, 34208}, {325, 2996}, {511, 8770}, {1707, 1910}, {1755, 38252}, {1959, 8769}, {2396, 35136}, {2421, 3565}, {3053, 1976}, {3167, 248}, {3289, 40319}, {3566, 2395}, {6337, 287}, {6353, 6531}, {6393, 6340}, {8651, 2422}, {10607, 17974}, {18156, 1821}, {32459, 5967}, {36212, 6391}, {47430, 15630}
X(51374) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {69, 1350, 7750}, {1513, 32458, 325}
X(51375) lies on these lines: {1, 2}, {40, 196}, {117, 515}, {221, 6260}, {255, 12527}, {341, 1097}, {516, 1785}, {517, 15252}, {912, 12016}, {1394, 12667}, {1433, 9370}, {1512, 1870}, {1771, 4292}, {2800, 16869}, {2956, 6223}, {3074, 18250}, {3075, 4298}, {5089, 8074}, {5587, 34231}, {5930, 11500}, {6001, 16870}, {6129, 8058}, {6245, 34030}, {6684, 17102}, {7078, 20264}, {7680, 40960}, {7682, 34036}, {9812, 31516}, {15524, 37725}, {20263, 22124}, {21620, 41344}, {28194, 44901}
X(51375) = X(i)-isoconjugate of X(j) for these (i,j): {84, 102}, {189, 32677}, {513, 6081}, {1422, 15629}, {1433, 36121}, {1436, 36100}, {2208, 34393}, {2432, 37141}, {36055, 40836}
X(51375) = X(i)-Dao conjugate of X(j) for these (i, j): (6129, 15633), (23986, 189), (39026, 6081), (51221, 40836)
X(51375) = crossdifference of every pair of points on line {649, 1436}
X(51375) = barycentric product X(i)*X(j) for these {i,j}: {190, 6087}, {198, 35516}, {322, 2182}, {329, 515}, {2406, 8058}, {6129, 42718}, {7080, 34050}
X(51375) = barycentric quotient X(i)/X(j) for these {i,j}: {40, 36100}, {101, 6081}, {198, 102}, {329, 34393}, {515, 189}, {1455, 1422}, {2182, 84}, {2187, 32677}, {2331, 36121}, {2425, 8059}, {5514, 15633}, {6087, 514}, {7074, 15629}, {8058, 2399}, {8755, 40836}, {34050, 1440}, {35516, 44190}, {46974, 41081}
X(51376) lies on these lines: {9, 55}, {37, 16283}, {41, 12711}, {44, 8608}, {48, 10167}, {63, 77}, {71, 2253}, {72, 1802}, {101, 2739}, {118, 516}, {169, 11496}, {220, 12514}, {281, 17784}, {518, 8558}, {521, 652}, {610, 10860}, {758, 6603}, {906, 46974}, {1146, 31896}, {1212, 5248}, {1252, 5089}, {1621, 40937}, {1709, 5781}, {2266, 5728}, {2272, 17613}, {2323, 8758}, {2324, 8270}, {3207, 12520}, {3695, 18249}, {4251, 12710}, {4294, 6554}, {4314, 41006}, {4386, 20310}, {5179, 5842}, {5282, 6602}, {5440, 34591}, {5687, 7079}, {7368, 17742}, {7719, 10306}, {9310, 12709}, {9778, 27382}, {17102, 22131}, {25440, 46830}
X(51376) = reflection of X(1146) in X(31896)
X(51376) = isotomic conjugate of the polar conjugate of X(41339)
X(51376) = X(i)-isoconjugate of X(j) for these (i,j): {19, 43736}, {34, 36101}, {57, 36122}, {103, 278}, {273, 911}, {608, 18025}, {653, 2424}, {1118, 1815}, {1119, 2338}, {1876, 9503}, {2400, 32674}, {3064, 24016}, {3676, 40116}, {7115, 15634}, {32668, 44426}
X(51376) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 43736), (5452, 36122), (11517, 36101), (23972, 273), (35072, 2400), (39077, 5236), (40628, 15634), (46095, 57), (50441, 92)
X(51376) = crosssum of X(19) and X(1876)
X(51376) = crossdifference of every pair of points on line {34, 2424}
X(51376) = barycentric product X(i)*X(j) for these {i,j}: {9, 26006}, {63, 40869}, {69, 41339}, {78, 516}, {212, 35517}, {219, 30807}, {345, 910}, {521, 2398}, {644, 39470}, {652, 42719}, {676, 4571}, {1265, 1456}, {1812, 17747}, {1886, 3719}, {2426, 35518}, {3692, 43035}, {3694, 14953}
X(51376) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 43736}, {55, 36122}, {78, 18025}, {212, 103}, {219, 36101}, {516, 273}, {521, 2400}, {910, 278}, {1456, 1119}, {1802, 2338}, {1946, 2424}, {2289, 1815}, {2398, 18026}, {2426, 108}, {6056, 36056}, {7004, 15634}, {9502, 5236}, {17747, 40149}, {26006, 85}, {30807, 331}, {32660, 32668}, {36059, 24016}, {39470, 24002}, {40869, 92}, {41339, 4}, {42719, 46404}, {43035, 1847}, {46392, 3064}, {47422, 3675}
X(51377) lies on these lines: {1, 28238}, {2, 35645}, {3, 16980}, {8, 970}, {10, 3142}, {11, 38472}, {12, 22300}, {21, 23841}, {25, 7074}, {31, 23638}, {40, 42448}, {42, 181}, {46, 23154}, {51, 55}, {52, 32141}, {100, 511}, {119, 517}, {165, 26892}, {184, 197}, {185, 11500}, {200, 26893}, {209, 3198}, {210, 430}, {227, 1425}, {283, 38903}, {373, 1001}, {375, 3683}, {389, 11491}, {512, 661}, {516, 38389}, {519, 3032}, {674, 3689}, {692, 1495}, {756, 21804}, {851, 4551}, {869, 9561}, {899, 3030}, {902, 3271}, {957, 1000}, {1155, 3937}, {1201, 44845}, {1211, 22325}, {1376, 3917}, {1460, 44104}, {1468, 50580}, {1486, 34417}, {1621, 5943}, {1682, 10459}, {1828, 7957}, {1843, 11383}, {2177, 21746}, {2183, 41215}, {2225, 14936}, {2390, 5183}, {2807, 44425}, {2810, 3218}, {2818, 48363}, {2841, 3245}, {2975, 15489}, {3035, 50362}, {3214, 10822}, {3240, 4260}, {3291, 21788}, {3293, 10974}, {3697, 43213}, {3925, 22278}, {3935, 9052}, {3936, 22294}, {4046, 14973}, {4413, 5650}, {4421, 21969}, {4511, 45955}, {4819, 44671}, {4847, 10440}, {4890, 21806}, {5057, 29309}, {5264, 50594}, {5284, 6688}, {5291, 50361}, {5399, 16453}, {5446, 11849}, {5462, 37621}, {5552, 10441}, {5562, 11499}, {5687, 5752}, {5929, 40999}, {6745, 29311}, {7211, 17874}, {8192, 36745}, {8677, 45884}, {9352, 23155}, {9535, 36855}, {9564, 31330}, {11248, 45186}, {11681, 15488}, {13329, 20999}, {13366, 20986}, {13754, 18524}, {14839, 32927}, {15030, 18491}, {16589, 22191}, {17441, 41539}, {17763, 35104}, {20455, 35505}, {20988, 44106}, {21031, 22299}, {21870, 22277}, {22321, 44661}, {24390, 34466}, {27385, 35631}, {35238, 36987}, {37516, 37540}, {37568, 42450}, {37603, 50578}, {41797, 47513}
X(51377) = reflection of X(i) in X(j) for these {i,j}: {11, 38472}, {3937, 1155}, {50362, 3035}
X(51377) = reflection of X(3259) in the anti-Orthic axis
X(51377) = isogonal conjugate of the isotomic conjugate of X(17757)
X(51377) = X(i)-Ceva conjugate of X(j) for these (i,j): {517, 21801}, {38955, 37}
X(51377) = crosspoint of X(i) and X(j) for these (i,j): {37, 38955}, {42, 34857}, {517, 2183}
X(51377) = crosssum of X(i) and X(j) for these (i,j): {21, 16704}, {81, 859}, {104, 34234}, {1565, 4453}, {4560, 14010}
X(51377) = crossdifference of every pair of points on line {81, 2401}
X(51377) = X(i)-isoconjugate of X(j) for these (i,j): {58, 18816}, {81, 34234}, {86, 104}, {274, 909}, {286, 1795}, {310, 34858}, {333, 34051}, {662, 2401}, {757, 38955}, {799, 2423}, {1019, 13136}, {1412, 36795}, {1414, 43728}, {1444, 36123}, {1509, 2250}, {1790, 16082}, {2720, 18155}, {4560, 37136}, {4592, 43933}, {4600, 15635}, {7192, 36037}, {7199, 32641}, {10428, 30939}, {14578, 44129}
X(51377) = X(i)-Dao conjugate of X(j) for these (i, j): (10, 18816), (517, 17139), (1084, 2401), (1145, 314), (3259, 7192), (5139, 43933), (16586, 310), (23980, 274), (25640, 286), (38981, 18155), (38996, 2423), (40586, 34234), (40599, 36795), (40600, 104), (40607, 38955), (40608, 43728), (40613, 86), (50497, 15635)
X(51377) = barycentric product X(i)*X(j) for these {i,j}: {1, 21801}, {6, 17757}, {10, 2183}, {37, 517}, {42, 908}, {71, 1785}, {72, 14571}, {106, 21942}, {210, 1465}, {213, 3262}, {512, 2397}, {523, 2427}, {594, 859}, {813, 42767}, {1016, 42752}, {1018, 1769}, {1252, 42759}, {1334, 22464}, {1400, 6735}, {1457, 2321}, {1500, 17139}, {1826, 22350}, {1875, 3694}, {2250, 24028}, {2804, 4559}, {3310, 3952}, {3700, 23981}, {3943, 14260}, {4041, 24029}, {4551, 46393}, {4557, 10015}, {4574, 39534}, {8611, 23706}, {16586, 34857}, {23980, 38955}
X(51377) = barycentric quotient X(i)/X(j) for these {i,j}: {37, 18816}, {42, 34234}, {210, 36795}, {213, 104}, {512, 2401}, {517, 274}, {669, 2423}, {859, 1509}, {872, 2250}, {908, 310}, {1402, 34051}, {1457, 1434}, {1500, 38955}, {1769, 7199}, {1785, 44129}, {1824, 16082}, {1918, 909}, {2183, 86}, {2200, 1795}, {2205, 34858}, {2333, 36123}, {2397, 670}, {2427, 99}, {2489, 43933}, {3121, 15635}, {3262, 6385}, {3310, 7192}, {3709, 43728}, {4557, 13136}, {6735, 28660}, {8677, 15419}, {14571, 286}, {15507, 30940}, {17757, 76}, {21801, 75}, {21942, 3264}, {22350, 17206}, {23220, 7254}, {23980, 17139}, {23981, 4573}, {24029, 4625}, {39258, 36819}, {42752, 1086}, {42753, 16727}, {42759, 23989}, {46393, 18155}
X(51377) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {42, 181, 40952}, {209, 3198, 3611}, {210, 22276, 3690}, {692, 20989, 1495}, {902, 20962, 3271}
X(51378) lies on these lines: {2, 17642}, {8, 3427}, {63, 6244}, {65, 10528}, {72, 3426}, {78, 22770}, {100, 518}, {119, 517}, {144, 3059}, {200, 15104}, {210, 3434}, {392, 40587}, {516, 14740}, {912, 12331}, {960, 3617}, {971, 46685}, {1445, 1617}, {1621, 15837}, {1864, 20075}, {3035, 18839}, {3057, 5554}, {3158, 16465}, {3309, 4468}, {3436, 7957}, {3555, 4855}, {3740, 11680}, {3871, 44547}, {3880, 36920}, {3913, 41538}, {4662, 5086}, {5175, 45120}, {5440, 22765}, {5493, 12059}, {5836, 33108}, {6001, 12532}, {9779, 45776}, {9954, 17781}, {10707, 17636}, {10914, 31837}, {13374, 27529}, {15733, 50573}, {17626, 31224}, {28160, 34790}
X(51378) = reflection of X(i) in X(j) for these {i,j}: {17615, 14740}, {18839, 3035}
X(51378) = X(i)-isoconjugate of X(j) for these (i,j): {104, 2191}, {277, 909}, {2342, 40154}, {2423, 37206}
X(51378) = X(i)-Dao conjugate of X(j) for these (i, j): (1145, 6601), (4904, 43728), (23980, 277), (40613, 2191)
X(51378) = crossdifference of every pair of points on line {1643, 2423}
X(51378) = barycentric product X(i)*X(j) for these {i,j}: {218, 3262}, {344, 517}, {908, 3870}, {1445, 6735}, {2397, 3309}, {3991, 17139}, {17757, 41610}, {24029, 44448}
X(51378) = barycentric quotient X(i)/X(j) for these {i,j}: {218, 104}, {344, 18816}, {517, 277}, {1457, 17107}, {1465, 40154}, {1617, 34051}, {2183, 2191}, {2427, 1292}, {3309, 2401}, {3870, 34234}, {3991, 38955}, {4878, 2250}, {7719, 36123}, {8642, 2423}, {21059, 909}
X(51378) = {X(7957),X(46677)}-harmonic conjugate of X(3436)
X(51379) lies on these lines: {1, 10601}, {3, 63}, {8, 210}, {10, 10523}, {20, 18239}, {40, 2057}, {59, 518}, {65, 5552}, {100, 2745}, {119, 517}, {190, 10538}, {200, 5119}, {329, 6925}, {392, 3305}, {515, 17615}, {519, 14740}, {521, 6332}, {643, 15776}, {758, 6745}, {855, 44694}, {942, 13747}, {997, 20588}, {1331, 46974}, {1785, 26611}, {2476, 5836}, {3035, 18838}, {3091, 14923}, {3419, 6929}, {3436, 14110}, {3678, 6737}, {3681, 6992}, {3753, 31266}, {3811, 11508}, {3812, 27529}, {3868, 5435}, {3869, 6838}, {3878, 6736}, {3890, 5129}, {3939, 45272}, {3965, 4271}, {4158, 4187}, {4186, 41609}, {4297, 12059}, {4420, 37568}, {4847, 10176}, {4853, 41702}, {4861, 5047}, {5081, 16086}, {5176, 6840}, {5687, 5887}, {5790, 10914}, {5794, 10522}, {5904, 37618}, {6068, 15326}, {6172, 41228}, {6872, 20007}, {6959, 24474}, {7686, 11681}, {7957, 11415}, {9119, 27396}, {10527, 25917}, {11523, 34489}, {12635, 41538}, {15347, 17622}, {16465, 18397}, {17625, 35262}, {17781, 37429}, {18455, 22141}, {18524, 35460}, {18856, 38760}, {21075, 31806}, {23528, 25253}, {26003, 40863}, {31835, 37290}, {31895, 38389}, {34772, 44547}, {40255, 45770}, {43135, 44670}
X(51379) = midpoint of X(i) and X(j) for these {i,j}: {72, 5440}, {3057, 44784}
X(51379) = reflection of X(i) in X(j) for these {i,j}: {18838, 3035}, {38389, 31895}
X(51379) = crosspoint of X(8) and X(45393)
X(51379) = crosssum of X(56) and X(18838)
X(51379) = crossdifference of every pair of points on line {608, 2423}
X(51379) = X(i)-isoconjugate of X(j) for these (i,j): {19, 34051}, {34, 104}, {56, 36123}, {109, 43933}, {273, 34858}, {278, 909}, {513, 36110}, {514, 32702}, {604, 16082}, {608, 34234}, {653, 2423}, {1015, 39294}, {1118, 1795}, {1119, 2342}, {1309, 43924}, {1395, 18816}, {1396, 2250}, {1877, 10428}, {2401, 32674}, {2720, 7649}, {3676, 14776}, {6591, 37136}, {7012, 15635}, {8752, 40218}, {17924, 32669}, {36037, 43923}
X(51379) = X(i)-Dao conjugate of X(j) for these (i, j): (1, 36123), (6, 34051), (11, 43933), (517, 1875), (1145, 4), (3161, 16082), (3259, 43923), (7358, 43728), (11517, 104), (16586, 273), (23980, 278), (25640, 1118), (35014, 39534), (35072, 2401), (38981, 7649), (39004, 513), (39026, 36110), (40613, 34), (45247, 36125)
X(51379) = barycentric product X(i)*X(j) for these {i,j}: {63, 6735}, {78, 908}, {219, 3262}, {312, 22350}, {332, 21801}, {345, 517}, {521, 2397}, {646, 8677}, {1016, 35014}, {1264, 14571}, {1265, 1465}, {1332, 2804}, {1785, 3719}, {1809, 26611}, {1812, 17757}, {2183, 3718}, {2427, 35518}, {3692, 22464}, {3694, 17139}, {4561, 46393}, {4571, 10015}, {4587, 36038}, {15416, 23981}
X(51379) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 34051}, {8, 16082}, {9, 36123}, {78, 34234}, {101, 36110}, {212, 909}, {219, 104}, {345, 18816}, {517, 278}, {521, 2401}, {644, 1309}, {650, 43933}, {692, 32702}, {765, 39294}, {859, 1396}, {906, 2720}, {908, 273}, {1145, 37790}, {1265, 36795}, {1331, 37136}, {1457, 1435}, {1465, 1119}, {1802, 2342}, {1946, 2423}, {2183, 34}, {2289, 1795}, {2318, 2250}, {2397, 18026}, {2427, 108}, {2804, 17924}, {3262, 331}, {3310, 43923}, {3694, 38955}, {4571, 13136}, {4587, 36037}, {5440, 40218}, {6056, 14578}, {6735, 92}, {7117, 15635}, {8677, 3669}, {14571, 1118}, {17757, 40149}, {21801, 225}, {22350, 57}, {22464, 1847}, {23980, 1875}, {23981, 32714}, {24029, 36118}, {32656, 32669}, {35014, 1086}, {46393, 7649}, {47408, 18838}
X(51379) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {392, 17658, 3872}, {1260, 3940, 78}, {3057, 46677, 8}, {3868, 6921, 37566}, {3876, 3877, 18228}
X(51380) lies on these lines: {1, 46677}, {2, 12915}, {3, 2057}, {8, 392}, {9, 55}, {10, 26011}, {63, 9954}, {72, 5657}, {78, 956}, {100, 971}, {104, 5440}, {119, 517}, {329, 35514}, {354, 31190}, {497, 18236}, {518, 3035}, {942, 5552}, {960, 6736}, {1108, 3190}, {1259, 26285}, {1376, 20588}, {1391, 4511}, {1863, 5423}, {2340, 21805}, {2950, 13528}, {2968, 3717}, {3036, 3880}, {3239, 3900}, {3434, 10157}, {3436, 31793}, {3452, 15845}, {3555, 27383}, {3681, 5744}, {3699, 7360}, {3740, 3816}, {3753, 8164}, {3812, 44848}, {3868, 27525}, {3870, 42884}, {3967, 17860}, {4009, 24026}, {4015, 6743}, {4551, 43058}, {4662, 6737}, {4853, 25917}, {5045, 27385}, {5253, 11035}, {5574, 24771}, {5687, 5777}, {5748, 8166}, {5784, 46917}, {5806, 11681}, {5818, 10598}, {5853, 46694}, {5927, 17784}, {6065, 41391}, {8256, 13601}, {9778, 11678}, {9779, 14923}, {9943, 12059}, {10284, 38176}, {10707, 17652}, {10863, 45776}, {12641, 44784}, {17642, 30827}, {18227, 40998}, {18242, 21075}, {25568, 41539}, {26364, 50196}, {28582, 44311}, {45701, 50195}
X(51380) = midpoint of X(i) and X(j) for these {i,j}: {100, 17615}, {1145, 41389}, {6745, 14740}
X(51380) = reflection of X(3660) in X(3035)
X(51380) = crosspoint of X(9) and X(12641)
X(51380) = crosssum of X(i) and X(j) for these (i,j): {57, 5193}, {3669, 42753}
X(51380) = crossdifference of every pair of points on line {1407, 2423}
X(51380) = X(i)-isoconjugate of X(j) for these (i,j): {57, 34051}, {104, 269}, {279, 909}, {479, 2342}, {658, 2423}, {1088, 34858}, {1106, 18816}, {1119, 1795}, {1407, 34234}, {1461, 2401}, {1847, 14578}, {2720, 3676}, {3669, 37136}, {6614, 43728}, {7045, 15635}, {7053, 36123}, {7099, 16082}, {7366, 36795}, {24002, 32669}, {36037, 43932}
X(51380) = X(i)-Dao conjugate of X(j) for these (i, j): (1145, 7), (3259, 43932), (5452, 34051), (6552, 18816), (6600, 104), (16586, 1088), (17115, 15635), (23050, 36123), (23757, 1111), (23980, 279), (24771, 34234), (25640, 1119), (35508, 2401), (38966, 43933), (38981, 3676), (40613, 269)
X(51380) = barycentric product X(i)*X(j) for these {i,j}: {9, 6735}, {200, 908}, {220, 3262}, {341, 2183}, {346, 517}, {644, 2804}, {728, 22464}, {1043, 21801}, {1265, 14571}, {1457, 30693}, {1465, 5423}, {1769, 6558}, {1785, 3692}, {1875, 30681}, {2287, 17757}, {2397, 3900}, {2427, 4397}, {3699, 46393}, {4163, 24029}, {4515, 17139}, {4578, 10015}, {7101, 22350}
X(51380) = barycentric quotient X(i)/X(j) for these {i,j}: {55, 34051}, {200, 34234}, {220, 104}, {346, 18816}, {517, 279}, {908, 1088}, {1253, 909}, {1457, 738}, {1465, 479}, {1785, 1847}, {1802, 1795}, {2183, 269}, {2397, 4569}, {2427, 934}, {2804, 24002}, {3310, 43932}, {3689, 40218}, {3900, 2401}, {3939, 37136}, {4130, 43728}, {4515, 38955}, {4578, 13136}, {5423, 36795}, {6602, 2342}, {6735, 85}, {7046, 16082}, {7079, 36123}, {7368, 15501}, {8641, 2423}, {14010, 16727}, {14571, 1119}, {14827, 34858}, {14936, 15635}, {17757, 1446}, {21801, 3668}, {22350, 7177}, {22464, 23062}, {23981, 4617}, {24029, 4626}, {46393, 3676}
X(51380) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {210, 3711, 40659}, {480, 3711, 200}, {1145, 17757, 1512}
X(51381) lies on these lines: {2, 2170}, {6, 24324}, {8, 7385}, {63, 3732}, {100, 28850}, {119, 517}, {126, 5517}, {239, 385}, {312, 4595}, {322, 21371}, {544, 50095}, {812, 3766}, {1213, 25367}, {1654, 21233}, {2183, 3262}, {2262, 29967}, {2347, 26665}, {3169, 20171}, {3218, 35102}, {3310, 10015}, {3434, 28118}, {3666, 21138}, {3687, 34454}, {3882, 4858}, {3975, 35544}, {4019, 17788}, {4124, 8299}, {4165, 33077}, {4369, 24636}, {4384, 24591}, {4432, 36815}, {4904, 5249}, {5011, 24630}, {5440, 29331}, {5826, 28789}, {14557, 30076}, {16610, 49777}, {17060, 26001}, {17277, 21231}, {17793, 27838}, {20237, 21361}, {20881, 21362}, {21129, 47892}, {21271, 27108}, {24029, 46805}, {24980, 26231}, {26282, 49487}, {32851, 49755}, {35342, 45749}, {35466, 50014}, {46790, 50841}
X(51381) = crosspoint of X(10030) and X(27922)
X(51381) = crossdifference of every pair of points on line {1911, 2423}
X(51381) = X(i)-isoconjugate of X(j) for these (i,j): {104, 292}, {291, 909}, {335, 34858}, {660, 2423}, {741, 2250}, {875, 13136}, {876, 32641}, {1911, 34234}, {1922, 18816}, {2196, 36123}, {2401, 34067}, {3572, 36037}, {7077, 34051}, {18268, 38955}
X(51381) = X(i)-Dao conjugate of X(j) for these (i, j): (1145, 4876), (2238, 36819), (3259, 3572), (6651, 34234), (8299, 2250), (16586, 335), (19557, 104), (23980, 291), (35068, 38955), (35119, 2401), (39028, 18816), (39029, 909), (40613, 292), (46398, 4444)
X(51381) = barycentric product X(i)*X(j) for these {i,j}: {75, 15507}, {99, 42767}, {238, 3262}, {239, 908}, {350, 517}, {740, 17139}, {812, 2397}, {859, 35544}, {874, 1769}, {1145, 27922}, {1447, 6735}, {1457, 4087}, {1465, 3975}, {1921, 2183}, {3310, 27853}, {3570, 10015}, {3573, 36038}, {3685, 22464}, {17757, 33295}, {21801, 30940}, {22350, 40717}
X(51381) = barycentric quotient X(i)/X(j) for these {i,j}: {238, 104}, {239, 34234}, {242, 36123}, {350, 18816}, {517, 291}, {740, 38955}, {812, 2401}, {859, 741}, {908, 335}, {1429, 34051}, {1769, 876}, {1914, 909}, {2183, 292}, {2210, 34858}, {2238, 2250}, {2397, 4562}, {2427, 813}, {3262, 334}, {3310, 3572}, {3570, 13136}, {3573, 36037}, {3716, 43728}, {3975, 36795}, {4432, 36944}, {4693, 36921}, {6735, 4518}, {7193, 1795}, {8299, 36819}, {8632, 2423}, {10015, 4444}, {15507, 1}, {17139, 18827}, {17757, 43534}, {22350, 295}, {22464, 7233}, {27846, 15635}, {36815, 40437}, {42767, 523}
X(51382) lies on these lines: {2, 45924}, {10, 13746}, {21, 36}, {29, 270}, {30, 113}, {58, 17584}, {60, 950}, {86, 17078}, {110, 515}, {125, 44910}, {163, 5179}, {448, 26006}, {516, 1325}, {517, 3109}, {519, 6740}, {522, 663}, {643, 6735}, {759, 30384}, {908, 1793}, {946, 11101}, {1010, 24564}, {1099, 1784}, {1737, 5127}, {1792, 27412}, {2077, 3658}, {2328, 11103}, {2478, 25441}, {2617, 22350}, {4234, 24556}, {4304, 40214}, {4720, 6737}, {5196, 28150}, {5546, 40869}, {5972, 36195}, {6684, 37158}, {6738, 46441}, {7054, 40942}, {7478, 28194}, {10572, 17104}, {12512, 37294}, {15677, 17190}, {17167, 36011}, {17209, 37009}, {18483, 37369}, {31730, 37405}
X(51382) = midpoint of X(110) and X(7424)
X(51382) = reflection of X(i) in X(j) for these {i,j}: {125, 44910}, {1558, 113}, {36195, 5972}
X(51382) = crossdifference of every pair of points on line {1400, 2433}
X(51382) = X(i)-isoconjugate of X(j) for these (i,j): {65, 74}, {73, 36119}, {108, 14380}, {225, 35200}, {226, 2159}, {651, 2433}, {1042, 44693}, {1214, 8749}, {1231, 40354}, {1400, 2349}, {1402, 1494}, {1409, 16080}, {1415, 2394}, {1427, 15627}, {1441, 40352}, {1880, 14919}, {18808, 36059}, {18877, 40149}
X(51382) = X(i)-Dao conjugate of X(j) for these (i, j): (133, 225), (1146, 2394), (1511, 73), (3163, 226), (6739, 10), (20620, 18808), (38983, 14380), (38991, 2433), (40582, 2349), (40602, 74), (40605, 1494), (40626, 34767)
X(51382) = barycentric product X(i)*X(j) for these {i,j}: {8, 18653}, {21, 14206}, {29, 11064}, {30, 333}, {86, 7359}, {99, 14400}, {283, 46106}, {284, 3260}, {314, 2173}, {332, 1990}, {521, 24001}, {522, 2407}, {645, 11125}, {811, 14395}, {1043, 6357}, {1495, 28660}, {1784, 1812}, {2194, 46234}, {2420, 35519}, {3284, 44130}, {3737, 42716}, {4240, 6332}, {4612, 36035}, {4636, 41079}, {7257, 14399}, {9406, 40072}
X(51382) = barycentric quotient X(i)/X(j) for these {i,j}: {21, 2349}, {29, 16080}, {30, 226}, {283, 14919}, {284, 74}, {314, 33805}, {333, 1494}, {522, 2394}, {652, 14380}, {663, 2433}, {1172, 36119}, {1495, 1400}, {1784, 40149}, {1990, 225}, {2173, 65}, {2193, 35200}, {2194, 2159}, {2287, 44693}, {2299, 8749}, {2328, 15627}, {2407, 664}, {2420, 109}, {3064, 18808}, {3260, 349}, {3284, 73}, {4240, 653}, {4636, 44769}, {6332, 34767}, {6357, 3668}, {7359, 10}, {9406, 1402}, {11064, 307}, {11125, 7178}, {14206, 1441}, {14395, 656}, {14399, 4017}, {14400, 523}, {18653, 7}, {21044, 12079}, {23347, 32674}, {24001, 18026}
X(51382) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21, 3615, 1125}, {13746, 35193, 10}
X(51383) lies on these lines: {50, 323}, {67, 69}, {76, 15067}, {99, 5663}, {114, 325}, {183, 7998}, {298, 34375}, {299, 34373}, {302, 11626}, {303, 11624}, {315, 13340}, {373, 37647}, {526, 3268}, {568, 7763}, {620, 15544}, {1007, 11002}, {1154, 7799}, {1232, 36901}, {1511, 10411}, {1975, 11459}, {2421, 36790}, {2871, 2979}, {3098, 38641}, {3819, 6784}, {3917, 34383}, {5118, 38650}, {5562, 32820}, {5650, 37688}, {6101, 7796}, {7768, 10627}, {7769, 13363}, {7809, 13391}, {7814, 10263}, {9027, 44369}, {11412, 32821}, {15030, 32819}, {23039, 32833}
X(51383) = reflection of X(i) in X(j) for these {i,j}: {6784, 3819}, {15544, 620}
X(51383) = crossdifference of every pair of points on line {2422, 11060}
X(51383) = X(i)-isoconjugate of X(j) for these (i,j): {293, 18384}, {878, 36129}, {1821, 11060}, {1910, 1989}, {1976, 2166}, {2395, 32678}, {2422, 32680}, {14582, 36104}, {15475, 36084}
X(51383) = X(i)-Dao conjugate of X(j) for these (i, j): (132, 18384), (441, 43089), (3284, 35906), (5976, 94), (11597, 1976), (11672, 1989), (18334, 2395), (34544, 1910), (35088, 10412), (38987, 15475), (39000, 14582), (39040, 2166), (40601, 11060), (40604, 98)
X(51383) = barycentric product X(i)*X(j) for these {i,j}: {186, 6393}, {323, 325}, {340, 36212}, {511, 7799}, {526, 2396}, {877, 8552}, {2421, 3268}, {2799, 10411}, {4230, 45792}, {6148, 35910}, {6149, 46238}, {6333, 14590}, {14355, 32458}, {22115, 44132}
X(51383) = barycentric quotient X(i)/X(j) for these {i,j}: {50, 1976}, {186, 6531}, {232, 18384}, {237, 11060}, {297, 6344}, {323, 98}, {325, 94}, {340, 16081}, {511, 1989}, {526, 2395}, {684, 14582}, {877, 46456}, {1511, 35906}, {1959, 2166}, {2396, 35139}, {2421, 476}, {2799, 10412}, {3268, 43665}, {3569, 15475}, {6149, 1910}, {6333, 14592}, {6393, 328}, {7799, 290}, {8552, 879}, {10411, 2966}, {14270, 2422}, {14355, 41932}, {14590, 685}, {14591, 32696}, {14966, 14560}, {15595, 43089}, {19627, 14601}, {22115, 248}, {23997, 32678}, {35910, 5627}, {36212, 265}, {36790, 14356}, {42743, 23968}, {44132, 18817}, {50567, 43084}
X(51384) lies on these lines: {2, 6}, {8, 21258}, {9, 30813}, {11, 20335}, {12, 17046}, {72, 34847}, {85, 40997}, {116, 17757}, {120, 518}, {142, 354}, {190, 40868}, {200, 8271}, {220, 28740}, {241, 3693}, {320, 10025}, {346, 51351}, {442, 17758}, {519, 4904}, {594, 26593}, {672, 16593}, {958, 26101}, {1038, 18639}, {1086, 3726}, {1146, 30806}, {1229, 1233}, {1280, 9053}, {1358, 46180}, {1418, 45791}, {1818, 4966}, {1834, 26978}, {2140, 24390}, {2886, 30949}, {2887, 11019}, {3263, 4437}, {3290, 50011}, {3662, 26590}, {3684, 26007}, {3739, 25006}, {3782, 20173}, {3811, 20269}, {3834, 20541}, {3870, 4851}, {3873, 51150}, {3932, 4712}, {3957, 17390}, {4000, 17597}, {4369, 6003}, {4434, 13405}, {4511, 17044}, {4513, 6604}, {4645, 9453}, {4657, 4666}, {4859, 32865}, {5347, 35977}, {5526, 40534}, {6706, 6734}, {6745, 36956}, {7223, 24247}, {7232, 24352}, {7767, 29473}, {7819, 33953}, {8226, 24220}, {8580, 33084}, {8727, 37521}, {9317, 44669}, {10580, 32773}, {10582, 17306}, {10916, 24774}, {15325, 25532}, {15888, 17062}, {16284, 26531}, {17045, 29817}, {17169, 17672}, {17231, 44798}, {17282, 24600}, {17298, 40719}, {17347, 51352}, {17747, 20347}, {21049, 26563}, {21232, 40663}, {24953, 25500}, {25664, 37527}, {26932, 40869}, {27006, 34772}, {37270, 37538}, {40131, 47595}
X(51384) = reflection of X(5526) in X(40534)
X(51384) = X(649)-complementary conjugate of X(38980)
X(51384) = X(i)-Ceva conjugate of X(j) for these (i,j): {1026, 918}, {40017, 16708}
X(51384) = crosspoint of X(i) and X(j) for these (i,j): {3912, 40704}, {40017, 40217}
X(51384) = crossdifference of every pair of points on line {512, 884}
X(51384) = X(i)-isoconjugate of X(j) for these (i,j): {105, 1174}, {1170, 2195}, {1416, 6605}, {1438, 2346}, {1462, 10482}, {8751, 47487}
X(51384) = X(i)-Dao conjugate of X(j) for these (i, j): (142, 294), (1212, 673), (6184, 2346), (17755, 32008), (36905, 21453), (39046, 1174), (39063, 1170), (40606, 105), (40609, 6605)
X(51384) = barycentric product X(i)*X(j) for these {i,j}: {142, 3912}, {241, 1229}, {354, 3263}, {518, 20880}, {672, 1233}, {883, 6362}, {1212, 40704}, {3717, 10481}, {3925, 30941}, {3930, 16708}, {3932, 17169}, {4847, 9436}, {18157, 21808}, {21104, 42720}, {35312, 50333}
X(51384) = barycentric quotient X(i)/X(j) for these {i,j}: {142, 673}, {241, 1170}, {354, 105}, {518, 2346}, {672, 1174}, {883, 6606}, {1212, 294}, {1229, 36796}, {1233, 18031}, {1418, 1462}, {1475, 1438}, {1818, 47487}, {2293, 2195}, {2340, 10482}, {2488, 884}, {3059, 28071}, {3693, 6605}, {3912, 32008}, {3925, 13576}, {4847, 14942}, {6362, 885}, {9436, 21453}, {20880, 2481}, {21127, 1024}, {21808, 18785}, {22053, 36057}, {35312, 927}, {35326, 919}, {35335, 35333}, {35338, 36086}, {40704, 31618}, {48151, 1027}
X(51384) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 69, 37658}, {2, 17300, 14828}, {3912, 9436, 3693}
X(51385) lies on the cubic K741 and these lines: {2, 36876}, {3, 5879}, {4, 64}, {5, 14057}, {30, 107}, {133, 1515}, {186, 34178}, {230, 41368}, {235, 1093}, {325, 6528}, {403, 523}, {427, 47392}, {436, 16657}, {1075, 2883}, {1294, 39464}, {1503, 6761}, {1552, 10151}, {1568, 44704}, {1596, 2052}, {1896, 15763}, {2072, 34334}, {3089, 41365}, {3545, 10002}, {5656, 6624}, {6344, 48374}, {6524, 6623}, {6529, 16318}, {6616, 34781}, {6716, 12096}, {7680, 47372}, {13450, 17703}, {14157, 32713}, {14165, 37942}, {18554, 44576}, {21312, 46927}, {21396, 43615}, {21663, 47204}, {23239, 27089}, {33228, 36426}, {33703, 34286}, {37943, 47166}, {40887, 47286}, {44732, 44803}, {46106, 47096}
X(51385) = midpoint of X(i) and X(j) for these {i,j}: {4, 40664}, {107, 34170}
X(51385) = reflection of X(i) in X(j) for these {i,j}: {186, 47152}, {1515, 1559}, {1552, 10151}, {1559, 133}, {12096, 6716}
X(51385) = X(16080)-Ceva conjugate of X(393)
X(51385) = X(50937)-cross conjugate of X(4)
X(51385) = crosssum of X(3) and X(6760)
X(51385) = crossdifference of every pair of points on line {577, 2430}
X(51385) = X(i)-isoconjugate of X(j) for these (i,j): {163, 2416}, {255, 1294}, {662, 2430}, {4575, 43701}
X(51385) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 2416), (136, 43701), (1084, 2430), (1990, 11064), (6523, 1294), (50937, 3)
X(51385) = barycentric product X(i)*X(j) for these {i,j}: {133, 16080}, {459, 1559}, {523, 2404}, {850, 2442}, {1093, 44436}, {2052, 6000}, {14618, 46587}
X(51385) = barycentric quotient X(i)/X(j) for these {i,j}: {133, 11064}, {393, 1294}, {512, 2430}, {523, 2416}, {1559, 37669}, {2404, 99}, {2442, 110}, {2501, 43701}, {6000, 394}, {8749, 15404}, {44436, 3964}, {46587, 4558}
X(51385) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36876, 41372}, {4, 41425, 12250}, {64, 51342, 4}, {6523, 6526, 4}, {6624, 14361, 5656}
X(51386) lies on these lines: {51, 1007}, {69, 305}, {76, 11793}, {99, 2706}, {114, 325}, {183, 3819}, {184, 9723}, {185, 6337}, {232, 36790}, {315, 15644}, {373, 34803}, {389, 7763}, {394, 577}, {520, 3265}, {620, 50387}, {1216, 3933}, {1238, 4175}, {1975, 5907}, {2979, 37668}, {3098, 15574}, {3289, 36212}, {3292, 47390}, {3926, 5562}, {4558, 8779}, {4576, 30737}, {5447, 7767}, {5650, 34229}, {5866, 21663}, {5889, 32831}, {6390, 13754}, {6688, 37647}, {7750, 13348}, {7752, 10110}, {7769, 11695}, {7773, 13598}, {7776, 10625}, {7796, 15606}, {7998, 15589}, {8781, 39817}, {10513, 33884}, {11412, 32818}, {11444, 32830}, {11459, 32817}, {14831, 32837}, {15030, 32815}, {15043, 32835}, {15058, 32822}, {15630, 40428}, {22352, 44180}, {32816, 45186}, {32819, 44870}, {40077, 47389}
X(51386) = reflection of X(50387) in X(620)
X(51386) = isotomic conjugate of the polar conjugate of X(36212)
X(51386) = isogonal conjugate of the polar conjugate of X(6393)
X(51386) = X(6393)-Ceva conjugate of X(36212)
X(51386) = crosspoint of X(69) and X(43705)
X(51386) = crosssum of X(25) and X(460)
X(51386) = crossdifference of every pair of points on line {2207, 2422}
X(51386) = X(i)-isoconjugate of X(j) for these (i,j): {19, 6531}, {25, 36120}, {98, 1096}, {158, 1976}, {248, 6520}, {293, 6524}, {393, 1910}, {661, 20031}, {823, 2422}, {878, 36126}, {1821, 2207}, {1973, 16081}, {2395, 24019}, {2501, 36104}, {6521, 14600}, {15630, 23999}, {24006, 32696}, {36417, 46273}
X(51386) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 6531), (132, 6524), (511, 34854), (1147, 1976), (5976, 2052), (6337, 16081), (6338, 290), (6503, 98), (6505, 36120), (11672, 393), (35071, 2395), (36212, 44145), (36830, 20031), (37867, 248), (39000, 2501), (39039, 6520), (39040, 158), (40601, 2207), (41167, 8754), (46093, 878), (46094, 25), (50440, 1857)
X(51386) = barycentric product X(i)*X(j) for these {i,j}: {3, 6393}, {69, 36212}, {232, 4176}, {240, 1102}, {255, 46238}, {297, 3964}, {305, 3289}, {325, 394}, {326, 1959}, {511, 3926}, {520, 2396}, {684, 4563}, {1092, 44132}, {1264, 43034}, {2421, 3265}, {4131, 42717}, {4143, 4230}, {4558, 6333}, {6394, 36790}, {6507, 40703}, {7183, 44694}, {17974, 32458}, {18604, 42703}, {34386, 44716}, {41172, 47389}
X(51386) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 6531}, {63, 36120}, {69, 16081}, {110, 20031}, {232, 6524}, {237, 2207}, {240, 6520}, {255, 1910}, {297, 1093}, {325, 2052}, {326, 1821}, {394, 98}, {511, 393}, {520, 2395}, {577, 1976}, {684, 2501}, {877, 15352}, {1092, 248}, {1102, 336}, {1259, 15628}, {1755, 1096}, {1959, 158}, {2396, 6528}, {2421, 107}, {3265, 43665}, {3289, 25}, {3926, 290}, {3964, 287}, {4230, 6529}, {4558, 685}, {4563, 22456}, {4575, 36104}, {6333, 14618}, {6393, 264}, {6394, 34536}, {6507, 293}, {9418, 36417}, {11672, 34854}, {14585, 14601}, {14966, 32713}, {17209, 8747}, {17974, 41932}, {23098, 51334}, {23606, 14600}, {23997, 24019}, {32320, 878}, {32661, 32696}, {34854, 36434}, {36212, 4}, {36790, 6530}, {39201, 2422}, {39469, 2489}, {40703, 6521}, {41172, 8754}, {42702, 1824}, {42743, 35907}, {43034, 1118}, {44716, 53}, {47389, 41174}, {47406, 460}, {50567, 37778}
X(51387) lies on these lines: {2, 16940}, {13, 33460}, {14, 11297}, {15, 620}, {16, 754}, {61, 6680}, {62, 7838}, {69, 5613}, {99, 621}, {114, 325}, {115, 623}, {141, 6114}, {298, 542}, {302, 5981}, {315, 47066}, {383, 51018}, {395, 533}, {491, 48725}, {492, 48724}, {524, 6108}, {531, 618}, {543, 23004}, {599, 9760}, {617, 3524}, {622, 7809}, {626, 3104}, {627, 12252}, {633, 1078}, {634, 7917}, {635, 6292}, {1350, 9750}, {2794, 14538}, {3105, 7764}, {3106, 4045}, {3589, 14137}, {5026, 6782}, {5464, 5569}, {5471, 22689}, {5611, 15561}, {5858, 51203}, {5864, 7776}, {5965, 5982}, {5969, 6115}, {5979, 19924}, {6054, 51010}, {6109, 44383}, {6671, 31274}, {6722, 22510}, {7684, 36519}, {7763, 47068}, {7798, 43455}, {7844, 43454}, {9167, 45879}, {9302, 40707}, {9736, 14907}, {9763, 51014}, {10007, 22692}, {13350, 38748}, {14645, 51206}, {14921, 35315}, {18122, 34375}, {19130, 23024}, {20428, 23698}, {21166, 36993}, {22714, 40107}, {23019, 34540}, {31693, 31695}, {33459, 51160}, {33474, 51205}, {36755, 38749}, {37825, 41057}, {38738, 44666}
X(51387) = midpoint of X(i) and X(j) for these {i,j}: {99, 621}, {298, 5978}, {5464, 22493}
X(51387) = reflection of X(i) in X(j) for these {i,j}: {15, 620}, {115, 623}, {6109, 44383}, {6782, 44385}, {9117, 619}, {31695, 31693}, {38749, 36755}, {41070, 114}
X(51387) = X(1910)-isoconjugate of X(6151)
X(51387) = X(i)-Dao conjugate of X(j) for these (i, j): (619, 98), (5976, 40706), (11672, 6151), (33527, 14355)
X(51387) = barycentric product X(i)*X(j) for these {i,j}: {325, 395}, {462, 6393}, {511, 41001}, {2799, 35315}, {14356, 14921}
X(51387) = barycentric quotient X(i)/X(j) for these {i,j}: {297, 38427}, {325, 40706}, {395, 98}, {462, 6531}, {511, 6151}, {2421, 10410}, {9117, 5967}, {19295, 14355}, {35315, 2966}, {35330, 2715}, {41001, 290}
X(51387) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {302, 5981, 6774}, {22510, 40334, 6722}, {22689, 34508, 5471}
X(51388) lies on these lines: {2, 16941}, {13, 11298}, {14, 33461}, {15, 754}, {16, 620}, {61, 7838}, {62, 6680}, {69, 5617}, {99, 622}, {114, 325}, {115, 624}, {141, 6115}, {299, 542}, {303, 5980}, {315, 47068}, {396, 532}, {491, 48723}, {492, 48722}, {524, 6109}, {530, 619}, {543, 23005}, {599, 9762}, {616, 3524}, {621, 7809}, {626, 3105}, {628, 12252}, {633, 7917}, {634, 1078}, {636, 6292}, {1080, 51016}, {1350, 9749}, {2794, 14539}, {3104, 7764}, {3107, 4045}, {3589, 14136}, {5026, 6783}, {5463, 5569}, {5472, 22687}, {5615, 15561}, {5859, 51200}, {5865, 7776}, {5965, 5983}, {5969, 6114}, {5978, 19924}, {6054, 51013}, {6108, 44382}, {6672, 31274}, {6722, 22511}, {7685, 36519}, {7763, 47066}, {7798, 43454}, {7844, 43455}, {9167, 45880}, {9302, 40706}, {9735, 14907}, {9761, 51011}, {10007, 22691}, {11295, 36772}, {11301, 36764}, {11305, 36771}, {13349, 38748}, {14645, 51207}, {14922, 35314}, {16963, 36770}, {18122, 34373}, {19130, 23018}, {20429, 23698}, {21166, 36995}, {22715, 40107}, {23025, 34541}, {31694, 31696}, {33458, 51159}, {33475, 51202}, {36756, 38749}, {37824, 41056}, {38738, 44667}
X(51388) = midpoint of X(i) and X(j) for these {i,j}: {99, 622}, {299, 5979}, {5463, 22494}
X(51388) = reflection of X(i) in X(j) for these {i,j}: {16, 620}, {115, 624}, {6108, 44382}, {6783, 44384}, {9115, 618}, {31696, 31694}, {38749, 36756}, {41071, 114}
X(51388) = X(1910)-isoconjugate of X(2981)
X(51388) = X(i)-Dao conjugate of X(j) for these (i, j): (618, 98), (5976, 40707), (11672, 2981), (33526, 14355)
X(51388) = barycentric product X(i)*X(j) for these {i,j}: {325, 396}, {463, 6393}, {511, 41000}, {2799, 35314}, {14356, 14922}
X(51388) = barycentric quotient X(i)/X(j) for these {i,j}: {297, 38428}, {325, 40707}, {396, 98}, {463, 6531}, {511, 2981}, {2421, 10409}, {9115, 5967}, {19294, 14355}, {35314, 2966}, {35329, 2715}, {41000, 290}
X(51388) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {303, 5980, 6771}, {22511, 40335, 6722}, {22687, 34509, 5472}
X(51389) lies on these lines: {2, 99}, {3, 47200}, {20, 35278}, {22, 34217}, {30, 113}, {98, 35922}, {110, 2794}, {114, 868}, {125, 2782}, {132, 4230}, {232, 297}, {247, 1316}, {316, 40885}, {323, 754}, {394, 1625}, {468, 46987}, {511, 5112}, {523, 5181}, {524, 16303}, {538, 3580}, {542, 6795}, {736, 47181}, {1294, 35513}, {1634, 3014}, {1637, 5664}, {1975, 11331}, {2396, 32458}, {2407, 3163}, {2799, 3569}, {3016, 7761}, {3018, 40879}, {3849, 40112}, {4226, 35282}, {4558, 23583}, {5191, 38749}, {5463, 11658}, {5464, 11659}, {5651, 37242}, {6390, 44216}, {6394, 34229}, {6791, 15048}, {7737, 37645}, {7748, 41238}, {7798, 37644}, {7799, 44579}, {7804, 14389}, {7809, 44577}, {7853, 41237}, {9125, 19912}, {9818, 34840}, {10513, 35140}, {10992, 15000}, {14165, 15014}, {14570, 15526}, {14928, 41145}, {15550, 18883}, {16311, 32515}, {17235, 26543}, {18122, 34990}, {21731, 45687}, {24206, 48716}, {27371, 28417}, {32827, 37174}, {32836, 46808}, {32986, 35279}, {35906, 36891}, {36177, 38793}, {37765, 40888}, {40866, 45772}, {41676, 50188}, {46634, 47220}
X(51389) = midpoint of X(110) and X(36163)
X(51389) = reflection of X(i) in X(j) for these {i,j}: {125, 11007}, {1316, 5972}, {1561, 113}
X(51389) = X(36891)-Ceva conjugate of X(30)
X(51389) = crossdifference of every pair of points on line {351, 878}
X(51389) = X(i)-isoconjugate of X(j) for these (i,j): {74, 1910}, {98, 2159}, {248, 36119}, {293, 8749}, {336, 40354}, {879, 36131}, {1821, 40352}, {1976, 2349}, {2395, 36034}, {2433, 36084}, {6531, 35200}, {14380, 36104}, {14601, 33805}, {18877, 36120}
X(51389) = X(i)-Dao conjugate of X(j) for these (i, j): (30, 35906), (132, 8749), (133, 6531), (230, 36875), (1511, 248), (3163, 98), (3258, 2395), (3284, 14355), (5976, 1494), (6739, 15628), (11672, 74), (35088, 2394), (38970, 18808), (38987, 2433), (39000, 14380), (39008, 879), (39039, 36119), (39040, 2349), (40601, 40352), (41172, 32112), (46094, 18877), (50440, 15627)
X(51389) = barycentric product X(i)*X(j) for these {i,j}: {30, 325}, {114, 36891}, {297, 11064}, {511, 3260}, {877, 9033}, {1637, 2396}, {1755, 46234}, {1959, 14206}, {1990, 6393}, {2173, 46238}, {2407, 2799}, {2421, 41079}, {3284, 44132}, {4240, 6333}, {6148, 14356}, {9214, 50567}, {32458, 35906}, {35910, 36789}, {36212, 46106}, {43752, 44716}
X(51389) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 98}, {114, 36875}, {232, 8749}, {237, 40352}, {240, 36119}, {297, 16080}, {325, 1494}, {511, 74}, {684, 14380}, {868, 12079}, {877, 16077}, {1495, 1976}, {1511, 14355}, {1637, 2395}, {1755, 2159}, {1784, 36120}, {1959, 2349}, {1990, 6531}, {2173, 1910}, {2211, 40354}, {2407, 2966}, {2420, 2715}, {2421, 44769}, {2799, 2394}, {2967, 35908}, {3163, 35906}, {3260, 290}, {3284, 248}, {3289, 18877}, {3569, 2433}, {4230, 1304}, {4240, 685}, {5642, 5967}, {5968, 9139}, {6333, 34767}, {7359, 15628}, {9033, 879}, {9155, 9717}, {9214, 9154}, {9407, 14601}, {9409, 878}, {10564, 11653}, {11064, 287}, {14206, 1821}, {14356, 5627}, {14398, 2422}, {14966, 32640}, {16163, 35912}, {16230, 18808}, {23347, 32696}, {23997, 36034}, {35906, 41932}, {35910, 40384}, {35912, 47388}, {36212, 14919}, {36790, 35910}, {36891, 40428}, {41079, 43665}, {41167, 32112}, {42743, 51262}, {44694, 44693}, {44704, 10152}, {44716, 44715}, {44728, 44727}, {46106, 16081}, {46234, 46273}, {46238, 33805}, {50567, 36890}
X(51389) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 148, 41254}, {868, 9155, 114}, {35282, 38738, 4226}, {41887, 41888, 5642}
X(51390) lies on these lines: {2, 644}, {8, 36652}, {11, 14839}, {115, 1211}, {119, 517}, {141, 545}, {190, 26932}, {226, 21232}, {241, 3693}, {312, 1952}, {321, 34387}, {329, 3732}, {344, 16608}, {513, 51007}, {538, 15986}, {594, 4957}, {918, 4437}, {1026, 50441}, {1086, 20881}, {1332, 36949}, {3035, 5091}, {3140, 50440}, {3161, 26540}, {3573, 26231}, {4415, 21138}, {4417, 4595}, {4752, 30858}, {5241, 27747}, {5432, 24264}, {6745, 28849}, {9620, 17720}, {10015, 26611}, {13567, 30568}, {17230, 25242}, {17233, 25252}, {17264, 37796}, {17339, 26530}, {17355, 26543}, {18639, 30701}, {21252, 40521}, {21942, 42754}, {23151, 28795}, {23681, 24795}, {24265, 39897}, {25101, 25964}, {25593, 26672}, {46790, 50842}
X(51390) = reflection of X(i) in X(j) for these {i,j}: {11, 24250}, {5091, 3035}
X(51390) = crossdifference of every pair of points on line {884, 2423}
X(51390) = X(i)-isoconjugate of X(j) for these (i,j): {104, 1438}, {105, 909}, {673, 34858}, {884, 37136}, {885, 32669}, {1024, 2720}, {1027, 32641}, {1462, 2342}, {1795, 8751}, {2195, 34051}, {2401, 32666}, {2423, 36086}, {14578, 36124}, {23696, 32702}, {32658, 36123}, {36037, 43929}, {36819, 41934}
X(51390) = X(i)-Dao conjugate of X(j) for these (i, j): (1145, 294), (3259, 43929), (6184, 104), (16586, 673), (17755, 34234), (23980, 105), (25640, 8751), (35094, 2401), (38981, 1024), (38989, 2423), (39046, 909), (39063, 34051), (40613, 1438)
X(51390) = barycentric product X(i)*X(j) for these {i,j}: {517, 3263}, {518, 3262}, {668, 42758}, {883, 2804}, {908, 3912}, {918, 2397}, {1016, 42770}, {1026, 36038}, {3717, 22464}, {3932, 17139}, {6735, 9436}, {10015, 42720}, {17757, 30941}, {18157, 21801}
X(51390) = barycentric quotient X(i)/X(j) for these {i,j}: {241, 34051}, {517, 105}, {518, 104}, {665, 2423}, {672, 909}, {908, 673}, {918, 2401}, {1025, 37136}, {1026, 36037}, {1457, 1416}, {1465, 1462}, {1769, 1027}, {1785, 36124}, {1818, 1795}, {1861, 36123}, {2183, 1438}, {2223, 34858}, {2283, 2720}, {2284, 32641}, {2340, 2342}, {2397, 666}, {2427, 919}, {2804, 885}, {3262, 2481}, {3263, 18816}, {3310, 43929}, {3675, 15635}, {3912, 34234}, {3930, 2250}, {3932, 38955}, {4712, 36819}, {6735, 14942}, {14571, 8751}, {17757, 13576}, {20752, 14578}, {21801, 18785}, {22350, 36057}, {23981, 32735}, {24029, 36146}, {34230, 10428}, {42720, 13136}, {42753, 43921}, {42758, 513}, {42770, 1086}, {42771, 3271}, {46108, 16082}, {46393, 1024}, {50333, 43728}
X(51391) lies on these lines: {2, 3581}, {3, 34798}, {4, 37477}, {5, 141}, {23, 14643}, {30, 113}, {49, 13470}, {51, 50140}, {52, 49673}, {110, 7574}, {140, 32110}, {156, 37444}, {186, 38794}, {193, 18449}, {265, 323}, {381, 15066}, {403, 13391}, {427, 15060}, {547, 32225}, {548, 43831}, {549, 18388}, {550, 5448}, {599, 39484}, {858, 5663}, {1092, 18377}, {1154, 2072}, {1352, 10510}, {1503, 5609}, {1594, 11591}, {2071, 20127}, {2777, 37950}, {2979, 10254}, {3001, 14670}, {3098, 44262}, {3153, 12383}, {3260, 14254}, {3292, 32423}, {3574, 3628}, {3917, 46029}, {4549, 18580}, {4550, 44287}, {5055, 15360}, {5071, 15362}, {5159, 34128}, {5462, 20424}, {5562, 10224}, {5576, 14128}, {5654, 14791}, {5655, 10989}, {5876, 13371}, {5890, 36852}, {5891, 39504}, {5944, 9820}, {5946, 37648}, {5965, 36253}, {5972, 7575}, {6102, 11585}, {6644, 40909}, {7464, 7728}, {7530, 48910}, {7577, 15110}, {7699, 7998}, {7703, 11459}, {9306, 44288}, {10024, 10627}, {10095, 50143}, {10113, 10297}, {10255, 11412}, {10264, 13754}, {10296, 12121}, {10540, 20125}, {10610, 12362}, {10625, 13406}, {10733, 18403}, {12041, 15122}, {12105, 38795}, {12225, 32171}, {12605, 43394}, {12900, 32223}, {13160, 32142}, {13491, 22660}, {13561, 18436}, {13630, 37452}, {14156, 15646}, {14644, 23061}, {14845, 50142}, {14852, 40341}, {15061, 30745}, {15068, 18440}, {15081, 37779}, {15448, 47342}, {15454, 45821}, {15473, 44272}, {15559, 45958}, {15704, 32903}, {15800, 44802}, {16072, 39522}, {16534, 29012}, {16619, 29181}, {16868, 37484}, {17702, 18572}, {18325, 43576}, {18400, 40111}, {18435, 31074}, {18445, 31180}, {18451, 31181}, {18531, 37645}, {18571, 38793}, {18859, 38790}, {18874, 50139}, {19924, 44266}, {20957, 36188}, {23236, 40113}, {23515, 41586}, {25739, 50461}, {29317, 37967}, {31282, 37490}, {31670, 44275}, {32227, 37980}, {34152, 37853}, {35001, 38789}, {35228, 48880}, {36518, 44961}, {38322, 43586}, {38724, 41724}, {41597, 45731}, {44235, 45186}, {44267, 46686}, {46261, 48884}, {47334, 47569}
X(51391) = midpoint of X(i) and X(j) for these {i,j}: {4, 37477}, {110, 7574}, {265, 323}, {1352, 10510}, {1531, 10564}, {3153, 22115}, {5655, 10989}, {7464, 7728}, {10296, 12121}, {10540, 46450}, {18325, 43576}, {18403, 43574}, {20957, 36188}, {25739, 50461}
X(51391) = reflection of X(i) in X(j) for these {i,j}: {1495, 10272}, {1511, 11064}, {3580, 20304}, {7575, 5972}, {8262, 24206}, {10113, 10297}, {12041, 15122}, {15361, 2}, {15646, 14156}, {32110, 140}, {32223, 12900}, {32225, 547}, {44267, 46686}, {47342, 15448}, {48876, 19510}
X(51391) = complement of X(3581)
X(51391) = complement of the isogonal conjugate of X(18316)
X(51391) = X(18316)-complementary conjugate of X(10)
X(51391) = X(2159)-isoconjugate of X(7578)
X(51391) = X(i)-Dao conjugate of X(j) for these (i, j): (566, 46808), (3163, 7578)
X(51391) = crosspoint of X(3260) and X(46809)
X(51391) = crossdifference of every pair of points on line {2433, 3050}
X(51391) = barycentric product X(i)*X(j) for these {i,j}: {566, 3260}, {7577, 11064}, {23039, 46106}, {36829, 41079}
X(51391) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 7578}, {566, 74}, {7577, 16080}, {18117, 2433}, {23039, 14919}, {36829, 44769}
X(51391) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {623, 624, 34827}, {1531, 13857, 10564}, {2072, 3580, 20304}, {5562, 10224, 34826}, {12900, 32223, 44282}
X(51392) lies on these lines: {2, 37478}, {3, 18388}, {4, 43614}, {5, 3917}, {20, 5448}, {23, 38795}, {30, 113}, {49, 44829}, {52, 11585}, {74, 44450}, {110, 44407}, {115, 45935}, {125, 1154}, {140, 3574}, {184, 14791}, {186, 14156}, {323, 539}, {381, 17811}, {389, 37452}, {394, 18474}, {427, 5891}, {511, 2072}, {541, 13445}, {542, 50461}, {550, 43831}, {569, 6643}, {858, 13754}, {1092, 18569}, {1147, 11750}, {1209, 1216}, {1368, 9730}, {1370, 5654}, {1506, 41480}, {1656, 17810}, {1657, 17821}, {1993, 31180}, {1994, 43573}, {2070, 5972}, {2071, 16111}, {2777, 18859}, {2979, 7577}, {3153, 17702}, {3292, 47341}, {3524, 41465}, {3581, 44673}, {3763, 5055}, {3819, 37347}, {5097, 45967}, {5133, 10170}, {5181, 11649}, {5189, 14157}, {5447, 13160}, {5449, 11412}, {5480, 14845}, {5562, 13371}, {5576, 11793}, {5651, 11818}, {5890, 31101}, {5899, 14643}, {5907, 18488}, {6101, 10224}, {6143, 7691}, {6639, 46728}, {6640, 46730}, {6689, 37126}, {7391, 46261}, {7488, 43839}, {7512, 44516}, {7574, 15139}, {7576, 43586}, {7579, 40107}, {7687, 37496}, {7728, 35452}, {9306, 31723}, {9955, 13852}, {9971, 24206}, {10024, 15644}, {10110, 50143}, {10254, 13340}, {10255, 37484}, {10257, 32110}, {10263, 49673}, {10510, 19380}, {10539, 14790}, {10540, 29012}, {10575, 22660}, {10619, 13470}, {11457, 15083}, {11459, 31074}, {11550, 15068}, {11563, 36518}, {11565, 36966}, {11803, 34564}, {11898, 17813}, {12006, 20424}, {12038, 12225}, {12162, 23335}, {12242, 13353}, {12295, 18403}, {12900, 15107}, {13346, 18404}, {13352, 18531}, {13403, 37495}, {13413, 44324}, {13419, 18350}, {13431, 32358}, {13619, 38726}, {14128, 33332}, {14641, 44866}, {15051, 35489}, {15061, 32608}, {15067, 39504}, {15122, 21663}, {15473, 37917}, {15699, 20192}, {15800, 43809}, {15801, 43808}, {16072, 44413}, {18358, 46026}, {18436, 20299}, {18442, 35498}, {18451, 34609}, {18536, 37506}, {21243, 23039}, {22051, 36153}, {23061, 36253}, {23292, 37513}, {29181, 37971}, {30771, 37489}, {32263, 45780}, {32269, 44911}, {34224, 41597}, {35001, 38791}, {37922, 38794}, {37955, 48378}, {43576, 46686}
X(51392) = midpoint of X(i) and X(j) for these {i,j}: {110, 46450}, {323, 25739}, {3153, 43574}, {5189, 14157}, {7574, 22115}, {7728, 35452}, {18403, 37477}
X(51392) = reflection of X(i) in X(j) for these {i,j}: {113, 1568}, {125, 37938}, {186, 14156}, {1511, 46114}, {2070, 5972}, {3581, 44673}, {12295, 18403}, {13619, 38726}, {14157, 16534}, {16111, 2071}, {21663, 15122}, {30714, 22115}, {32110, 10257}, {32269, 44911}
X(51392) = X(i)-isoconjugate of X(j) for these (i,j): {74, 2216}, {1179, 35200}, {2159, 40393}, {36034, 50946}, {36119, 40441}
X(51392) = X(i)-Dao conjugate of X(j) for these (i, j): (133, 1179), (1209, 74), (1511, 40441), (3163, 40393), (3258, 50946)
X(51392) = crosspoint of X(3260) and X(43768)
X(51392) = barycentric product X(i)*X(j) for these {i,j}: {30, 37636}, {570, 3260}, {1209, 43768}, {1216, 46106}, {1238, 1990}, {1594, 11064}, {9033, 41677}, {41079, 50947}, {42445, 43752}
X(51392) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 40393}, {570, 74}, {1216, 14919}, {1594, 16080}, {1637, 50946}, {1990, 1179}, {2173, 2216}, {3284, 40441}, {23195, 18877}, {37636, 1494}, {41677, 16077}, {42445, 44715}, {47328, 8749}, {50947, 44769}
X(51392) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {52, 11585, 43817}, {186, 14156, 38793}, {1147, 37444, 11750}, {1216, 1594, 1209}, {12242, 44862, 13353}, {14499, 14500, 1511}, {15068, 31181, 11550}
X(51393) lies on these lines: {2, 11464}, {3, 64}, {4, 11449}, {5, 13367}, {20, 26882}, {23, 15034}, {24, 52}, {25, 13352}, {26, 1092}, {30, 113}, {49, 389}, {51, 12106}, {54, 5462}, {68, 3147}, {74, 37941}, {110, 186}, {125, 44452}, {140, 5944}, {155, 3515}, {156, 185}, {182, 29959}, {184, 6644}, {187, 1625}, {195, 16625}, {206, 37511}, {232, 32661}, {323, 37940}, {343, 34351}, {376, 26881}, {378, 16194}, {381, 11430}, {394, 14070}, {399, 37955}, {403, 17702}, {468, 30714}, {511, 2070}, {539, 3580}, {541, 44280}, {542, 44214}, {546, 43394}, {549, 22352}, {567, 5943}, {568, 9703}, {569, 6642}, {578, 7506}, {858, 14156}, {924, 12095}, {1154, 3292}, {1199, 9706}, {1204, 32139}, {1209, 7542}, {1216, 7488}, {1493, 16881}, {1503, 10257}, {1594, 43839}, {1614, 22467}, {1658, 5562}, {1899, 45730}, {1971, 14961}, {1995, 14845}, {2071, 14157}, {2072, 5972}, {2079, 50387}, {2393, 15462}, {2420, 14581}, {2777, 44246}, {2883, 44240}, {2931, 34397}, {2937, 15644}, {2979, 7556}, {3043, 11557}, {3047, 11806}, {3060, 47485}, {3146, 38942}, {3167, 37489}, {3431, 3545}, {3517, 36747}, {3518, 5446}, {3524, 15080}, {3542, 12118}, {3546, 41738}, {3548, 9833}, {3564, 37935}, {3567, 9545}, {3574, 31830}, {3575, 9820}, {3581, 37922}, {3628, 10610}, {3763, 5054}, {3917, 7502}, {4240, 15454}, {4653, 28445}, {5012, 5892}, {5020, 37506}, {5050, 9813}, {5055, 14805}, {5097, 11935}, {5447, 7512}, {5448, 6240}, {5449, 10018}, {5504, 37951}, {5609, 18571}, {5650, 34513}, {5651, 7514}, {5654, 18533}, {5663, 15646}, {5876, 15331}, {5889, 41597}, {5890, 9544}, {5899, 32237}, {5946, 13366}, {6030, 44832}, {6101, 12107}, {6102, 43844}, {6146, 16238}, {6241, 43604}, {6622, 25712}, {6640, 18381}, {6689, 14788}, {6699, 46818}, {7387, 35602}, {7464, 15020}, {7505, 9927}, {7517, 13346}, {7529, 11425}, {7530, 44082}, {7689, 11441}, {7712, 10304}, {8538, 34787}, {9603, 44523}, {9704, 37481}, {9707, 17928}, {9714, 37498}, {9729, 43809}, {9818, 35259}, {9909, 37483}, {9967, 15577}, {10110, 13621}, {10113, 46031}, {10116, 26879}, {10125, 34826}, {10127, 37649}, {10151, 12295}, {10170, 35921}, {10182, 21243}, {10192, 15760}, {10224, 11572}, {10245, 33878}, {10255, 18383}, {10295, 16534}, {10297, 38795}, {10298, 11459}, {11003, 15045}, {11250, 11381}, {11410, 11472}, {11424, 13861}, {11438, 18445}, {11439, 35475}, {11440, 17506}, {11456, 15078}, {11550, 18281}, {11563, 34153}, {11585, 11750}, {11695, 13353}, {11801, 15350}, {11845, 47050}, {12041, 17856}, {12083, 37480}, {12084, 26883}, {12111, 21844}, {12112, 13445}, {12121, 31726}, {12163, 15750}, {12278, 16868}, {12370, 44232}, {12383, 37943}, {13160, 44516}, {13348, 13564}, {13391, 37936}, {13399, 38727}, {13431, 16624}, {13491, 43615}, {13557, 14703}, {13567, 44211}, {13595, 15033}, {13598, 18378}, {14094, 37952}, {14118, 43598}, {14130, 44870}, {14165, 39118}, {14643, 18403}, {14709, 32550}, {14710, 32549}, {14852, 37453}, {14865, 46849}, {14913, 19129}, {14984, 44102}, {15012, 43845}, {15030, 18570}, {15032, 15053}, {15039, 32608}, {15040, 18859}, {15063, 47335}, {15066, 44837}, {15068, 18324}, {15083, 35479}, {15107, 37939}, {15115, 37981}, {15136, 21284}, {15305, 35473}, {15311, 15647}, {15448, 37971}, {16195, 37486}, {16222, 32411}, {16226, 44109}, {16336, 34827}, {16386, 32111}, {16531, 24981}, {16657, 44233}, {18388, 38321}, {18404, 34785}, {18534, 37497}, {19128, 34382}, {19131, 23041}, {20125, 35489}, {21850, 44091}, {22955, 32379}, {22966, 44866}, {23061, 37953}, {23323, 36518}, {23515, 44911}, {26864, 37470}, {26917, 34799}, {31383, 44441}, {32352, 47360}, {32423, 44234}, {34417, 39522}, {35231, 43395}, {35232, 43396}, {35452, 38638}, {35500, 43614}, {37440, 45186}, {37452, 44829}, {37496, 37956}, {37933, 41615}, {37945, 43576}, {41580, 44259}, {44788, 49136}
X(51393) = midpoint of X(i) and X(j) for these {i,j}: {3, 10540}, {23, 43574}, {110, 186}, {2070, 22115}, {2071, 14157}, {3581, 50461}, {5899, 37477}, {7575, 40111}, {11563, 34153}, {12112, 13445}, {12121, 31726}, {12383, 50435}, {15035, 35265}, {16386, 32111}, {37940, 43572}, {37945, 43576}
X(51393) = reflection of X(i) in X(j) for these {i,j}: {125, 44452}, {858, 14156}, {2072, 5972}, {3292, 40111}, {5899, 32237}, {10113, 46031}, {11801, 15350}, {12041, 37968}, {12295, 10151}, {13851, 5}, {16386, 38726}, {21663, 15646}, {32110, 186}, {37971, 15448}
X(51393) = complement of X(25739)
X(51393) = X(i)-Ceva conjugate of X(j) for these (i,j): {5961, 52}, {46106, 3284}
X(51393) = crosspoint of X(317) and X(18883)
X(51393) = crosssum of X(12079) and X(14380)
X(51393) = crossdifference of every pair of points on line {2165, 2433}
X(51393) = barycentric product X(i)*X(j) for these {i,j}: {24, 11064}, {30, 1993}, {47, 14206}, {52, 43768}, {99, 14397}, {317, 3284}, {571, 3260}, {924, 2407}, {1147, 46106}, {1495, 7763}, {1511, 18883}, {1990, 9723}, {2173, 44179}, {2420, 6563}, {5961, 14920}, {9033, 41679}, {34948, 42716}
X(51393) = barycentric quotient X(i)/X(j) for these {i,j}: {24, 16080}, {30, 5392}, {47, 2349}, {563, 35200}, {571, 74}, {924, 2394}, {1147, 14919}, {1495, 2165}, {1511, 37802}, {1990, 847}, {1993, 1494}, {2173, 91}, {2407, 46134}, {2420, 925}, {3284, 68}, {4240, 30450}, {6753, 18808}, {11064, 20563}, {14206, 20571}, {14397, 523}, {14581, 14593}, {30451, 14380}, {34952, 2433}, {39176, 5962}, {41679, 16077}, {43768, 34385}, {44077, 8749}, {44179, 33805}, {47421, 12079}
X(51393) = X(i)-isoconjugate of X(j) for these (i,j): {68, 36119}, {74, 91}, {847, 35200}, {1820, 16080}, {2159, 5392}, {2165, 2349}, {2394, 36145}, {20571, 40352}
X(51393) = X(i)-Dao conjugate of X(j) for these (i, j): (133, 847), (135, 18808), (577, 14919), (1511, 68), (3163, 5392), (3284, 37802), (34116, 74), (39013, 2394)
X(51393) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11464, 18475}, {2, 18475, 37513}, {3, 3357, 43907}, {3, 6759, 10575}, {3, 8780, 18451}, {3, 9306, 5891}, {3, 10539, 12162}, {3, 18350, 5907}, {4, 11449, 12038}, {5, 32171, 13367}, {24, 1147, 52}, {25, 47391, 13352}, {26, 1092, 10625}, {49, 45735, 389}, {54, 44802, 5462}, {156, 37814, 185}, {184, 6644, 9730}, {378, 35264, 46261}, {378, 46261, 16194}, {394, 14070, 37478}, {568, 9703, 34986}, {1495, 1511, 10564}, {1511, 20771, 113}, {1511, 20773, 16163}, {1614, 22467, 40647}, {2070, 32609, 22115}, {2071, 35265, 14157}, {3518, 34148, 5446}, {6146, 16238, 43817}, {6642, 19357, 569}, {8780, 18451, 10539}, {9306, 11202, 3}, {10018, 14516, 5449}, {10575, 43898, 3}, {11441, 32534, 7689}, {11464, 43586, 37513}, {11585, 34782, 11750}, {12112, 37948, 13445}, {12383, 37943, 50435}, {13445, 15051, 37948}, {13621, 37472, 10110}, {14157, 15035, 2071}, {16165, 35266, 1495}, {18378, 37495, 13598}, {18475, 43586, 2}, {20773, 46817, 1495}, {37922, 50461, 3581}, {43614, 51033, 35500}, {43839, 45286, 1594}
X(51394) lies on these lines: {2, 11430}, {3, 49}, {4, 18418}, {5, 15807}, {6, 16226}, {20, 10282}, {22, 11202}, {23, 15020}, {24, 13346}, {25, 37497}, {30, 113}, {51, 6644}, {52, 37814}, {54, 9729}, {69, 3431}, {74, 37948}, {86, 21162}, {110, 2071}, {125, 10257}, {140, 12370}, {154, 21312}, {156, 10575}, {182, 32127}, {186, 249}, {187, 3289}, {323, 12227}, {343, 549}, {376, 11464}, {378, 9306}, {381, 43586}, {389, 1994}, {403, 5972}, {520, 4091}, {539, 6699}, {548, 5944}, {550, 32171}, {567, 5892}, {575, 15045}, {578, 5422}, {631, 18912}, {648, 40664}, {858, 18400}, {1154, 14708}, {1192, 12160}, {1199, 15012}, {1350, 19153}, {1498, 41427}, {1503, 47090}, {1597, 35259}, {1614, 46850}, {1650, 51254}, {1658, 10625}, {1812, 21161}, {1993, 11438}, {2063, 11456}, {2070, 15040}, {2072, 13851}, {2407, 11845}, {2777, 16386}, {2904, 16879}, {2979, 10298}, {3047, 17855}, {3091, 44872}, {3098, 20806}, {3260, 43752}, {3269, 40349}, {3284, 47405}, {3313, 35228}, {3357, 11441}, {3484, 18315}, {3515, 37498}, {3516, 17814}, {3518, 13598}, {3519, 16665}, {3520, 5907}, {3523, 41724}, {3529, 26882}, {3530, 10610}, {3546, 19467}, {3548, 12118}, {3564, 16976}, {3574, 31833}, {3580, 44673}, {3581, 37955}, {3818, 28408}, {3819, 35921}, {3839, 10546}, {4240, 23097}, {5012, 16836}, {5054, 14805}, {5085, 9027}, {5446, 37495}, {5462, 15038}, {5498, 34826}, {5504, 21649}, {5622, 8681}, {5650, 7514}, {5651, 9818}, {5663, 34152}, {5876, 10226}, {5878, 30552}, {5890, 34986}, {5891, 18570}, {5899, 38638}, {5943, 15033}, {5946, 34565}, {5965, 48375}, {6053, 50434}, {6090, 11410}, {6101, 15331}, {6102, 43615}, {6146, 16196}, {6193, 26937}, {6337, 44141}, {6640, 9927}, {6642, 11424}, {6677, 16657}, {6759, 11413}, {6760, 8431}, {7464, 14157}, {7488, 15644}, {7512, 13348}, {7575, 13391}, {7691, 15606}, {7740, 15329}, {8115, 38708}, {8116, 38709}, {8779, 14961}, {9544, 15072}, {9545, 10574}, {9730, 13366}, {9820, 43831}, {10024, 43839}, {10110, 44802}, {10112, 26879}, {10151, 36518}, {10304, 15080}, {10419, 43755}, {10539, 11381}, {10540, 14915}, {11003, 20791}, {11250, 12162}, {11402, 37475}, {11412, 21844}, {11414, 17821}, {11425, 17825}, {11440, 35497}, {11442, 23329}, {11454, 35493}, {11459, 35473}, {11550, 44441}, {11572, 13371}, {11585, 21659}, {11589, 40948}, {11695, 13434}, {11793, 14118}, {12041, 17853}, {12085, 26883}, {12086, 13474}, {12100, 44683}, {12106, 44106}, {12113, 51346}, {12121, 18403}, {12241, 22966}, {12278, 18383}, {12295, 23323}, {12383, 25739}, {12825, 25564}, {12893, 45780}, {12901, 21650}, {13382, 43601}, {13399, 24981}, {13596, 46847}, {14070, 37483}, {14379, 16391}, {14516, 20299}, {14531, 16266}, {14585, 22401}, {14643, 31726}, {14810, 41716}, {14855, 44108}, {14865, 43598}, {14919, 34329}, {14984, 21639}, {15043, 37505}, {15058, 35475}, {15063, 15311}, {15107, 37940}, {15122, 30714}, {15448, 47093}, {15469, 39371}, {15472, 37951}, {15750, 17834}, {15774, 47304}, {18180, 44220}, {18281, 18474}, {18324, 37478}, {18369, 44863}, {18388, 38323}, {18396, 18466}, {18484, 36789}, {18534, 44082}, {18860, 47426}, {19374, 19510}, {21243, 37118}, {21268, 35235}, {21637, 37511}, {21651, 43587}, {21971, 34417}, {22133, 37508}, {22251, 43893}, {22416, 37512}, {22660, 44240}, {23061, 37952}, {23325, 30744}, {28419, 46264}, {28708, 31670}, {30522, 34153}, {32062, 46261}, {32138, 43907}, {32225, 44214}, {32237, 37925}, {32269, 37935}, {33851, 41612}, {34146, 34947}, {34382, 34982}, {34386, 43459}, {34545, 43584}, {34782, 41602}, {34785, 37444}, {35243, 35268}, {35260, 35513}, {35265, 37944}, {35478, 43613}, {37126, 51033}, {37470, 44109}, {37487, 37672}, {37496, 37922}, {37506, 43650}, {37917, 44084}, {38444, 46728}, {38726, 44246}, {38793, 44452}, {38795, 47336}, {40112, 44280}, {41670, 44272}, {42671, 47620}, {43815, 44495}
X(51394) = midpoint of X(i) and X(j) for these {i,j}: {3, 22115}, {110, 2071}, {186, 43574}, {1568, 16163}, {2070, 37477}, {3292, 21663}, {7464, 14157}, {10540, 18859}, {12121, 18403}, {12383, 25739}, {13399, 24981}, {15469, 39371}, {34152, 40111}, {34153, 37938}, {37925, 43576}, {37948, 43572}, {40112, 44280}
X(51394) = reflection of X(i) in X(j) for these {i,j}: {125, 10257}, {403, 5972}, {1531, 1568}, {1568, 11064}, {2072, 14156}, {3292, 22115}, {3580, 44673}, {12295, 23323}, {13851, 2072}, {21663, 3}, {32110, 15646}, {32225, 44214}, {32269, 37935}, {37925, 32237}, {44102, 15462}, {44246, 38726}, {44673, 48378}, {47093, 15448}
X(51394) = complement of X(50435)
X(51394) = isotomic conjugate of the polar conjugate of X(3284)
X(51394) = isogonal conjugate of the polar conjugate of X(11064)
X(51394) = X(i)-Ceva conjugate of X(j) for these (i,j): {11064, 3284}, {43755, 647}
X(51394) = crosspoint of X(3) and X(5504)
X(51394) = crosssum of X(i) and X(j) for these (i,j): {4, 403}, {12079, 18808}
X(51394) = crossdifference of every pair of points on line {393, 2433}
X(51394) = X(i)-isoconjugate of X(j) for these (i,j): {4, 36119}, {19, 16080}, {74, 158}, {92, 8749}, {162, 18808}, {393, 2349}, {661, 15459}, {823, 2433}, {1093, 35200}, {1096, 1494}, {1118, 44693}, {1304, 24006}, {1577, 32695}, {1969, 40354}, {2052, 2159}, {2207, 33805}, {2394, 24019}, {2643, 42308}, {6520, 14919}, {6521, 18877}, {12079, 24000}, {14380, 36126}, {14618, 36131}, {35908, 36120}
X(51394) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 16080), (125, 18808), (133, 1093), (1147, 74), (1511, 4), (3163, 2052), (3284, 14165), (6503, 1494), (11064, 44138), (14401, 338), (22391, 8749), (35071, 2394), (36033, 36119), (36830, 15459), (37867, 14919), (38999, 523), (39008, 14618), (39170, 6344), (45248, 10152), (46093, 14380), (46094, 35908)
X(51394) = barycentric product X(i)*X(j) for these {i,j}: {3, 11064}, {30, 394}, {69, 3284}, {97, 1568}, {99, 1636}, {110, 41077}, {249, 1650}, {255, 14206}, {323, 51254}, {326, 2173}, {520, 2407}, {577, 3260}, {1092, 46106}, {1259, 6357}, {1495, 3926}, {1784, 6507}, {1804, 7359}, {1990, 3964}, {2420, 3265}, {2631, 4592}, {3682, 18653}, {4143, 23347}, {4176, 14581}, {4558, 9033}, {4563, 9409}, {5562, 43768}, {6148, 50433}, {6516, 14395}, {6517, 14400}, {10411, 18558}, {11589, 37669}, {14919, 16163}, {16165, 34897}, {23224, 42716}, {35912, 36212}
X(51394) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 16080}, {30, 2052}, {48, 36119}, {110, 15459}, {184, 8749}, {249, 42308}, {255, 2349}, {326, 33805}, {394, 1494}, {520, 2394}, {577, 74}, {647, 18808}, {1092, 14919}, {1495, 393}, {1511, 14165}, {1568, 324}, {1576, 32695}, {1636, 523}, {1650, 338}, {1784, 6521}, {1990, 1093}, {2173, 158}, {2289, 44693}, {2407, 6528}, {2420, 107}, {2631, 24006}, {3260, 18027}, {3269, 12079}, {3284, 4}, {3289, 35908}, {4100, 35200}, {4240, 15352}, {4558, 16077}, {5642, 37778}, {6056, 15627}, {9033, 14618}, {9406, 1096}, {9407, 2207}, {9409, 2501}, {11064, 264}, {11589, 459}, {14391, 23290}, {14395, 44426}, {14575, 40354}, {14581, 6524}, {14585, 40352}, {15905, 10152}, {16163, 46106}, {16165, 37765}, {18558, 10412}, {23347, 6529}, {23606, 18877}, {32320, 14380}, {32661, 1304}, {35912, 16081}, {39201, 2433}, {40373, 40351}, {41077, 850}, {43768, 8795}, {47405, 403}, {47414, 35235}, {50433, 5627}, {51254, 94}
X(51394) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 49, 40647}, {3, 155, 1204}, {3, 1092, 5562}, {3, 1147, 185}, {3, 3167, 10605}, {3, 12038, 13367}, {3, 18475, 22352}, {3, 19357, 10984}, {3, 34783, 43604}, {3, 35602, 1092}, {3, 47391, 184}, {20, 11449, 10282}, {20, 38942, 11449}, {22, 37480, 36987}, {24, 13346, 45186}, {52, 43898, 37814}, {140, 12370, 43817}, {185, 1147, 43844}, {378, 9306, 15030}, {1199, 43597, 15012}, {1511, 10564, 1495}, {1511, 25487, 113}, {1993, 11438, 14831}, {1993, 15078, 11438}, {1994, 15053, 389}, {1994, 22467, 15053}, {6644, 13352, 51}, {6760, 15781, 44436}, {10539, 12084, 11381}, {11064, 16163, 1531}, {11202, 37480, 22}, {13367, 22352, 18475}, {14865, 43598, 44870}, {14961, 32661, 8779}, {15035, 43574, 186}, {15053, 34148, 1994}, {18859, 32609, 10540}, {22467, 34148, 389}, {37472, 43809, 5462}, {37495, 45735, 5446}, {41427, 45248, 1498}, {41597, 43604, 34783}
X(51395) lies on these lines: {39, 640}, {69, 45554}, {114, 325}, {115, 32432}, {182, 491}, {298, 48722}, {299, 48724}, {315, 9738}, {371, 7759}, {372, 3788}, {490, 7690}, {492, 576}, {590, 641}, {620, 2459}, {626, 3103}, {637, 45542}, {638, 7763}, {639, 7821}, {754, 2460}, {1271, 45510}, {1504, 35685}, {1570, 44392}, {1692, 44394}, {3102, 7764}, {3525, 32806}, {5207, 33340}, {5965, 44365}, {6230, 8294}, {6566, 32421}, {6567, 7845}, {6811, 42858}, {7750, 43144}, {7761, 45564}, {7776, 9732}, {8997, 50374}, {11314, 45512}, {18993, 31463}, {32490, 45577}, {32811, 50974}, {32831, 49038}, {35840, 45472}, {39387, 43124}, {45486, 45515}
X(51395) = midpoint of X(6567) and X(7845)
X(51395) = reflection of X(i) in X(j) for these {i,j}: {115, 32432}, {2459, 620}
X(51395) = X(i)-isoconjugate of X(j) for these (i,j): {588, 1910}, {8825, 36120}
X(51395) = X(i)-Dao conjugate of X(j) for these (i, j): (641, 98), (11672, 588), (46094, 8825)
X(51395) = barycentric product X(325)*X(590)
X(51395) = barycentric quotient X(i)/X(j) for these {i,j}: {511, 588}, {590, 98}, {3289, 8825}, {5062, 1976}
X(51395) = {X(638),X(7763)}-harmonic conjugate of X(9739)
X(51396) lies on these lines: {6, 754}, {30, 14928}, {69, 1568}, {76, 6249}, {99, 19924}, {114, 325}, {115, 524}, {141, 7603}, {182, 14907}, {183, 5476}, {187, 44380}, {298, 51017}, {299, 51019}, {315, 576}, {316, 542}, {575, 7750}, {597, 5008}, {599, 8176}, {620, 5104}, {625, 15993}, {626, 13330}, {637, 44472}, {638, 44471}, {1078, 25555}, {1352, 32827}, {1992, 7790}, {2882, 14962}, {3314, 22486}, {3849, 18800}, {5026, 6781}, {5038, 7830}, {5039, 16989}, {5052, 7853}, {5182, 14712}, {5207, 5965}, {5480, 14994}, {5642, 26276}, {5969, 7813}, {6656, 44500}, {7752, 31958}, {7762, 44499}, {7764, 44453}, {7771, 10168}, {7773, 34507}, {7776, 11477}, {7778, 11173}, {7779, 10754}, {8586, 14645}, {9866, 50248}, {9993, 37668}, {11416, 13219}, {12215, 29317}, {14561, 34229}, {14853, 15589}, {21849, 45201}, {23061, 38940}, {31670, 32815}, {32817, 51212}, {41136, 50639}, {41137, 51224}, {41586, 46124}
X(51396) = midpoint of X(i) and X(j) for these {i,j}: {316, 39099}, {5107, 7845}, {7779, 10754}
X(51396) = reflection of X(i) in X(j) for these {i,j}: {187, 44380}, {5104, 620}, {6781, 5026}, {15993, 625}, {18800, 41146}, {50567, 325}
X(51396) = X(1910)-isoconjugate of X(39389)
X(51396) = X(i)-Dao conjugate of X(j) for these (i, j): (5976, 10302), (11672, 39389), (15810, 98)
X(51396) = crossdifference of every pair of points on line {2422, 9012}
X(51396) = barycentric product X(i)*X(j) for these {i,j}: {325, 597}, {511, 26235}, {2396, 12073}, {2799, 35356}, {6393, 10301}
X(51396) = barycentric quotient X(i)/X(j) for these {i,j}: {325, 10302}, {511, 39389}, {597, 98}, {2396, 42367}, {2421, 12074}, {5008, 1976}, {10301, 6531}, {12073, 2395}, {26235, 290}, {35356, 2966}, {35357, 2715}
X(51397) lies on these lines: {69, 3431}, {76, 11261}, {99, 11645}, {114, 325}, {141, 538}, {524, 620}, {542, 6390}, {574, 599}, {575, 7763}, {625, 5969}, {698, 32457}, {1007, 5476}, {1352, 32817}, {1975, 18553}, {3094, 7853}, {3292, 38940}, {3619, 14568}, {3788, 44499}, {3818, 32815}, {3819, 4121}, {3906, 19510}, {3926, 34507}, {3933, 13334}, {4175, 37636}, {5033, 12151}, {5104, 7845}, {5207, 29323}, {5971, 32225}, {6034, 31275}, {7764, 44500}, {7813, 15993}, {7821, 44453}, {7913, 21358}, {7925, 10754}, {9146, 13857}, {10513, 10519}, {11185, 25561}, {14645, 44380}, {14810, 14907}, {32827, 48901}, {34349, 36212}, {34803, 38317}, {35297, 38010}, {39602, 45672}
X(51397) = midpoint of X(i) and X(j) for these {i,j}: {325, 50567}, {599, 39785}, {5104, 7845}, {7813, 15993}
X(51397) = reflection of X(i) in X(j) for these {i,j}: {2030, 620}, {44496, 44380}
{2422, 17413}, {8599, 35088}, {30491, 39000}, {38987, 46001}
X(51397) = crossdifference of every pair of points on line {2422, 46001}
X(51397) = X(i)-isoconjugate of X(j) for these (i,j): {1383, 1910}, {30491, 36104}, {36084, 46001}
X(51397) = X(i)-Dao conjugate of X(j) for these (i, j): (5976, 598), (8542, 1976), (11165, 98), (11672, 1383), (17416, 2395)
X(51397) = barycentric product X(i)*X(j) for these {i,j}: {325, 599}, {511, 9464}, {2396, 3906}, {2799, 9146}, {5094, 6393}, {36263, 46238}, {42008, 50567}
X(51397) = barycentric quotient X(i)/X(j) for these {i,j}: {325, 598}, {511, 1383}, {574, 1976}, {599, 98}, {684, 30491}, {2396, 35138}, {2421, 11636}, {2799, 8599}, {3569, 46001}, {3906, 2395}, {5094, 6531}, {9145, 2715}, {9146, 2966}, {9464, 290}, {13857, 35906}, {17414, 2422}, {36212, 43697}, {36263, 1910}, {39785, 5967}, {42008, 9154}
X(51397) = {X(325),X(6393)}-harmonic conjugate of X(50567)
As a point on the Euler line, X(51398) has Shinagawa coefficients {4 (E+F)^3 (E+4*F)-(E+4*F)^2 S^2,-4 (E+F)^3 (3*E+4*F)-3 (E+4*F)^2 S^2}.
See Tran Quang Hung and Ercole Suppa, euclid 5374.
X(51398) lies on this line: {2, 3}
X(51398) = inverse in Euler asymptotic hyperbola of X(30)
X(51399) lies on these lines: {4, 10309}, {33, 64}, {34, 1407}, {56, 1452}, {57, 1905}, {108, 517}, {196, 50195}, {221, 36103}, {393, 2358}, {406, 12709}, {513, 1835}, {910, 32674}, {942, 34231}, {1118, 1426}, {1319, 10016}, {1467, 7713}, {1528, 6001}, {1845, 5570}, {1870, 3660}, {2262, 3213}, {3827, 34187}, {6198, 13601}, {7952, 31788}, {11398, 34489}, {11406, 37550}, {14257, 34339}
X(51399) = polar conjugate of the isotomic conjugate of X(43058)
X(51399) = X(i)-Ceva conjugate of X(j) for these (i,j): {34051, 608}, {36121, 34}
X(51399) = crosssum of X(i) and X(j) for these (i,j): {3, 15524}, {1259, 51379}
X(51399) = crossdifference of every pair of points on line {219, 2431}
X(51399) = barycentric product X(i)*X(j) for these {i,j}: {4, 43058}, {28, 51365}, {57, 51359}, {278, 6001}, {513, 2405}, {693, 2443}, {1422, 1528}, {7178, 7435}, {14312, 32714}, {25640, 34051}
X(51399) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 2417}, {608, 1295}, {667, 2431}, {2405, 668}, {2443, 100}, {6001, 345}, {6591, 43737}, {7435, 645}, {14312, 15416}, {43058, 69}, {47434, 51379}, {51359, 312}, {51365, 20336}
X(51399) = X(i)-isoconjugate of X(j) for these (i,j): {78, 1295}, {101, 2417}, {190, 2431}, {1331, 43737}, {6735, 15405}
X(51399) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 2417), (5521, 43737)
X(51399) = {X(1875),X(18838)}-harmonic conjugate of X(1876)
X(51400) lies on these lines: {1, 26101}, {2, 7}, {3, 20269}, {4, 277}, {5, 24774}, {12, 6706}, {65, 21258}, {72, 14019}, {105, 516}, {116, 1737}, {120, 518}, {140, 24784}, {141, 210}, {220, 30617}, {238, 36057}, {239, 20552}, {241, 5089}, {294, 3008}, {305, 20923}, {354, 51150}, {427, 1827}, {495, 20328}, {497, 614}, {515, 9317}, {517, 4904}, {519, 10699}, {612, 3475}, {673, 4872}, {858, 20129}, {910, 26007}, {946, 16020}, {1086, 3290}, {1111, 5179}, {1146, 43037}, {1212, 3665}, {1319, 17044}, {1358, 44664}, {1429, 26006}, {1565, 43065}, {1699, 1721}, {1738, 13576}, {1754, 24220}, {1770, 14377}, {1848, 24789}, {1861, 20621}, {1936, 3011}, {2082, 17170}, {2140, 12047}, {2238, 50011}, {2254, 3667}, {2299, 17171}, {2321, 31130}, {2348, 5845}, {2975, 27006}, {3177, 7185}, {3212, 26531}, {3263, 3912}, {3663, 26242}, {3664, 5276}, {3673, 17671}, {3674, 17451}, {3693, 16593}, {3739, 3925}, {3946, 7191}, {4223, 4292}, {4361, 4863}, {4384, 45962}, {4423, 4657}, {4511, 26140}, {4675, 5275}, {4679, 17290}, {4851, 4952}, {4869, 6555}, {4911, 17682}, {4967, 31077}, {4986, 49773}, {5074, 17761}, {5853, 20344}, {6554, 7195}, {6714, 17768}, {6734, 17046}, {6735, 21232}, {6996, 24781}, {7146, 25935}, {7289, 15487}, {7292, 17067}, {10327, 17296}, {10382, 26052}, {13161, 26978}, {13407, 17758}, {14189, 14732}, {15271, 30754}, {15668, 16353}, {16580, 17278}, {16608, 41539}, {16609, 26001}, {16713, 17177}, {16823, 17050}, {17058, 20461}, {17062, 24987}, {17073, 25907}, {17232, 30791}, {17234, 30758}, {17356, 25345}, {18343, 28849}, {18635, 40952}, {18651, 26723}, {19314, 25500}, {20752, 34253}, {20880, 33839}, {21060, 21255}, {21062, 23681}, {21495, 25593}, {21627, 39567}, {22070, 28278}, {23537, 24790}, {24199, 26234}, {24471, 25964}, {25497, 50716}, {26274, 48627}, {27000, 33867}, {30296, 45704}, {30385, 31534}, {30386, 31535}, {30753, 44377}, {30810, 37597}, {34855, 39063}, {37658, 47595}, {40534, 41391}, {46399, 47806}
X(51400) = reflection of X(41391) in X(40534)
X(51400) = X(6)-complementary conjugate of X(39048)
X(51400) = X(i)-Ceva conjugate of X(j) for these (i,j): {673, 2082}, {36086, 514}
X(51400) = crosspoint of X(i) and X(j) for these (i,j): {85, 673}, {15149, 18157}
X(51400) = crosssum of X(41) and X(672)
X(51400) = crossdifference of every pair of points on line {663, 2440}
X(51400) = X(i)-isoconjugate of X(j) for these (i,j): {105, 7123}, {294, 1037}, {673, 7084}, {2195, 7131}, {32666, 48070}
X(51400) = X(i)-Dao conjugate of X(j) for these (i, j): (4000, 6559), (6554, 673), (15487, 105), (17060, 9), (17755, 30701), (18589, 18785), (35094, 48070), (36905, 8817), (39046, 7123), (39063, 7131)
X(51400) = barycentric product X(i)*X(j) for these {i,j}: {497, 9436}, {518, 3673}, {614, 3263}, {673, 17060}, {918, 3732}, {1861, 17170}, {2082, 40704}, {3717, 7195}, {3912, 4000}, {3914, 30941}, {3930, 16750}, {5236, 27509}, {7289, 46108}, {15149, 18589}, {16583, 18157}, {42720, 48398}
X(51400) = barycentric quotient X(i)/X(j) for these {i,j}: {241, 7131}, {497, 14942}, {614, 105}, {672, 7123}, {918, 48070}, {1458, 1037}, {1473, 36057}, {1633, 36086}, {1851, 36124}, {1876, 1041}, {2082, 294}, {2223, 7084}, {3673, 2481}, {3732, 666}, {3912, 30701}, {3914, 13576}, {4000, 673}, {4319, 28071}, {6554, 6559}, {7083, 2195}, {7289, 1814}, {9436, 8817}, {15149, 40411}, {16502, 1438}, {16583, 18785}, {17060, 3912}, {17170, 31637}, {18206, 40403}, {28017, 1462}, {41353, 8269}, {41785, 31638}
X(51400) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7, 40131}, {2, 3598, 40127}, {142, 226, 30949}, {2140, 40690, 12047}, {5074, 17761, 30384}, {17170, 41785, 2082}, {30380, 30381, 7}, {30382, 30383, 41857}
X(51401) lies on these lines: {39, 639}, {69, 45555}, {114, 325}, {115, 32435}, {182, 492}, {298, 48723}, {299, 48725}, {315, 9739}, {371, 3788}, {372, 7759}, {489, 7692}, {491, 576}, {615, 642}, {620, 2460}, {626, 3102}, {637, 7763}, {638, 45543}, {640, 7821}, {754, 2459}, {1270, 45511}, {1505, 35684}, {1570, 44394}, {1692, 44392}, {3103, 7764}, {3525, 32805}, {5207, 33341}, {5965, 44364}, {6231, 8293}, {6566, 7845}, {6567, 32419}, {6813, 42859}, {7750, 43141}, {7761, 45565}, {7776, 9733}, {11313, 45513}, {13989, 50375}, {32491, 45576}, {32810, 50974}, {32831, 49039}, {35841, 45473}, {39388, 43125}, {45487, 45514}
X(51401) = midpoint of X(6566) and X(7845)
X(51401) = reflection of X(i) in X(j) for these {i,j}: {115, 32435}, {2460, 620}, {51395, 325}
X(51401) = X(589)-isoconjugate of X(1910)
X(51401) = X(i)-Dao conjugate of X(j) for these (i, j): (642, 98), (11672, 589)
X(51401) = barycentric product X(325)*X(615)
X(51401) = barycentric quotient X(i)/X(j) for these {i,j}: {511, 589}, {615, 98}, {5058, 1976}
X(51401) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {114, 51371, 51395}, {637, 7763, 9738}
X(51402) lies on these lines: {11, 522}, {65, 31680}, {116, 47882}, {214, 519}, {244, 656}, {518, 15632}, {521, 14115}, {523, 6075}, {650, 1146}, {900, 3259}, {918, 40629}, {952, 38617}, {953, 18341}, {1086, 23809}, {1565, 47754}, {1638, 35094}, {1647, 23757}, {1737, 16610}, {2348, 39050}, {3025, 3738}, {3258, 46660}, {3684, 34544}, {3700, 46101}, {3756, 6129}, {3900, 33646}, {4152, 6745}, {4511, 32851}, {4706, 8758}, {4904, 7658}, {6370, 38982}, {6615, 7004}, {6741, 34589}, {9001, 15635}, {14584, 36944}, {18191, 38992}, {18210, 21121}, {38989, 50440}
X(51402) = midpoint of X(953) and X(18341)
X(51402) = reflection of X(38385) in X(3259)
X(51402) = complement of the isotomic conjugate of X(4453)
X(51402) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 1639}, {36, 513}, {56, 3738}, {57, 46397}, {320, 21260}, {513, 3814}, {514, 21237}, {604, 10015}, {649, 908}, {654, 3452}, {667, 44}, {758, 31946}, {849, 6370}, {1408, 21180}, {1443, 17072}, {1870, 20316}, {1919, 49758}, {1983, 4422}, {2245, 4129}, {2323, 20317}, {2361, 4521}, {3218, 3835}, {3724, 661}, {3733, 758}, {3738, 1329}, {3904, 21244}, {3960, 141}, {4089, 21252}, {4453, 2887}, {4585, 27076}, {4707, 21245}, {7113, 514}, {8648, 9}, {9456, 21198}, {16944, 900}, {20924, 21262}, {21758, 2}, {21828, 1211}, {22379, 3}, {23345, 6702}, {27950, 27854}, {28607, 23884}, {32669, 40536}, {40215, 4928}, {43924, 1737}
X(51402) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 1639}, {8, 3738}, {596, 6370}, {4858, 4530}, {36588, 23884}, {36917, 514}, {36944, 900}
X(51402) = X(i)-isoconjugate of X(j) for these (i,j): {59, 1168}, {655, 32665}, {901, 2222}, {1411, 9268}, {3257, 32675}, {16944, 46649}, {24027, 36590}, {32719, 35174}
X(51402) = X(i)-Dao conjugate of X(j) for these (i, j): (44, 4564), (522, 36590), (900, 14584), (1639, 2), (3936, 4998), (3960, 7), (6544, 2006), (6615, 1168), (21198, 41803), (35092, 655), (35128, 3257), (35204, 9268), (38979, 2222), (38984, 901)
X(51402) = crosspoint of X(i) and X(j) for these (i,j): {2, 4453}, {8, 4768}, {519, 522}
X(51402) = crosssum of X(106) and X(109)
X(51402) = crossdifference of every pair of points on line {23981, 32665}
X(51402) = barycentric product X(i)*X(j) for these {i,j}: {214, 4858}, {320, 4530}, {900, 3904}, {1146, 41801}, {1227, 2170}, {1639, 4453}, {1647, 32851}, {2325, 4089}, {3738, 3762}, {3960, 4768}, {17455, 34387}, {36944, 46398}
X(51402) = barycentric quotient X(i)/X(j) for these {i,j}: {214, 4564}, {654, 901}, {900, 655}, {1146, 36590}, {1635, 2222}, {1647, 2006}, {1960, 32675}, {2087, 1411}, {2170, 1168}, {2323, 9268}, {3025, 40215}, {3738, 3257}, {3762, 35174}, {3904, 4555}, {4511, 5376}, {4530, 80}, {4768, 36804}, {8648, 32665}, {14584, 23592}, {17455, 59}, {35092, 14584}, {41801, 1275}, {46384, 23838}
X(51403) lies on these lines: {2, 13445}, {4, 54}, {5, 10575}, {23, 38791}, {24, 22802}, {30, 113}, {49, 12897}, {51, 1596}, {74, 37943}, {115, 3331}, {125, 403}, {146, 32223}, {154, 44438}, {156, 44271}, {185, 235}, {186, 2777}, {232, 1562}, {381, 10601}, {382, 5448}, {399, 539}, {427, 32062}, {468, 10990}, {511, 47096}, {542, 37784}, {546, 6346}, {550, 43898}, {1147, 31725}, {1154, 13417}, {1199, 40240}, {1204, 3542}, {1209, 45959}, {1498, 37197}, {1503, 10151}, {1510, 16337}, {1516, 43919}, {1559, 6530}, {1594, 13474}, {1885, 13367}, {1899, 5656}, {1906, 12233}, {2070, 7728}, {2071, 5972}, {2072, 14915}, {3147, 20427}, {3153, 15462}, {3357, 7505}, {3426, 5055}, {3515, 5895}, {3518, 34563}, {3521, 13621}, {3575, 5893}, {3839, 11179}, {5133, 46847}, {5449, 18439}, {5480, 40673}, {5576, 46849}, {5655, 50461}, {5663, 11563}, {5899, 38789}, {5907, 37636}, {5925, 15750}, {6146, 44226}, {6225, 6622}, {6241, 44958}, {6524, 6624}, {6793, 14581}, {7488, 35240}, {7507, 15811}, {7577, 11455}, {7687, 10821}, {9306, 44440}, {9730, 46030}, {10110, 44803}, {10112, 43605}, {10117, 37954}, {10182, 35473}, {10282, 18560}, {10540, 17702}, {10606, 37453}, {10721, 13619}, {11202, 35481}, {11456, 18390}, {11558, 32423}, {11649, 32271}, {11744, 37917}, {11799, 13754}, {11800, 13446}, {12041, 44234}, {12162, 15761}, {12290, 16868}, {12295, 30522}, {13160, 44870}, {13289, 37970}, {13352, 44276}, {13366, 16657}, {13391, 16105}, {13473, 15152}, {13491, 43817}, {14130, 44516}, {14156, 14643}, {14641, 37452}, {14677, 16532}, {14807, 32615}, {14808, 32614}, {14940, 25563}, {15030, 15760}, {15105, 43903}, {15125, 37981}, {15305, 21243}, {15350, 34128}, {15448, 37931}, {15646, 16111}, {16003, 44961}, {16534, 18325}, {16621, 23047}, {16659, 18383}, {17824, 22972}, {18128, 43821}, {18374, 36201}, {18381, 35488}, {18386, 19153}, {18396, 32063}, {18403, 44407}, {18436, 44322}, {18533, 44082}, {18537, 43650}, {18555, 32358}, {20125, 43572}, {20127, 37955}, {20725, 47114}, {21451, 43601}, {22352, 34664}, {22467, 22800}, {22660, 45186}, {23515, 46031}, {24981, 44665}, {26879, 44959}, {29181, 47094}, {29317, 37945}, {30714, 44267}, {32743, 46431}, {32767, 35487}, {34152, 38793}, {34170, 41204}, {34785, 35490}, {35579, 50937}, {37201, 43652}, {37853, 37941}, {37922, 38790}, {37944, 38792}, {37948, 48378}, {37950, 38795}, {38727, 44452}, {40664, 47204}, {43577, 45735}, {44231, 44437}, {44668, 48914}, {46852, 50137}
X(51403) = midpoint of X(i) and X(j) for these {i,j}: {4, 14157}, {403, 32111}, {1533, 1568}, {2070, 7728}, {10540, 31726}, {10721, 13619}, {12112, 25739}, {18325, 22115}
X(51403) = reflection of X(i) in X(j) for these {i,j}: {74, 44673}, {125, 403}, {1568, 113}, {2071, 5972}, {10990, 21663}, {11800, 13446}, {12041, 44234}, {12295, 44283}, {13399, 125}, {13851, 10151}, {16111, 15646}, {16163, 51393}, {18403, 46686}, {18859, 14156}, {20725, 47114}, {21663, 468}, {22115, 16534}, {25739, 7687}, {37931, 15448}, {51360, 1568}, {51393, 46817}
X(51403) = complement of X(13445)
X(51403) = X(1141)-Ceva conjugate of X(16035)
X(51403) = X(i)-isoconjugate of X(j) for these (i,j): {74, 775}, {801, 2159}, {1105, 35200}, {2349, 41890}
X(51403) = X(i)-Dao conjugate of X(j) for these (i, j): (133, 1105), (2883, 74), (3163, 801), (6509, 1494), (14091, 16080)
X(51403) = crosspoint of X(i) and X(j) for these (i,j): {4, 43917}, {1141, 14254}, {22239, 32230}
X(51403) = crosssum of X(i) and X(j) for these (i,j): {3, 43574}, {1154, 14385}, {15291, 40352}
X(51403) = crossdifference of every pair of points on line {2433, 17434}
X(51403) = barycentric product X(i)*X(j) for these {i,j}: {30, 13567}, {185, 46106}, {235, 11064}, {774, 14206}, {800, 3260}, {1624, 41079}, {1784, 6508}, {1990, 41005}, {2173, 17858}, {3284, 44131}, {9033, 41678}
X(51403) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 801}, {185, 14919}, {235, 16080}, {774, 2349}, {800, 74}, {1495, 41890}, {1624, 44769}, {1990, 1105}, {2173, 775}, {3260, 40830}, {13567, 1494}, {17858, 33805}, {41678, 16077}, {44079, 8749}
X(51403) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 1614, 13403}, {4, 6759, 21659}, {4, 13419, 32340}, {4, 14862, 10619}, {4, 43831, 3574}, {4, 51031, 35717}, {5, 32137, 18488}, {74, 37943, 44673}, {113, 1533, 51360}, {115, 3331, 51363}, {235, 2883, 185}, {546, 16655, 11572}, {1495, 1514, 13202}, {1554, 2682, 13202}, {1614, 13403, 10619}, {1885, 16252, 13367}, {3542, 5878, 1204}, {5656, 6623, 1899}, {6225, 6622, 26937}, {11799, 15063, 41586}, {12290, 16868, 20299}, {13403, 14862, 1614}, {13491, 44235, 43817}, {14499, 14500, 13202}, {14643, 18859, 14156}, {32340, 32364, 3574}
X(51404) lies on these lines: {5, 45910}, {6, 36183}, {30, 48452}, {98, 230}, {115, 512}, {125, 647}, {248, 265}, {287, 11064}, {290, 47286}, {297, 22456}, {339, 525}, {524, 37858}, {879, 10097}, {1495, 47198}, {1648, 2395}, {1976, 8791}, {2211, 16318}, {2501, 2970}, {2549, 36822}, {2623, 8901}, {3049, 34978}, {3094, 51259}, {3231, 20021}, {3288, 36189}, {3289, 3564}, {3331, 43291}, {3580, 46786}, {5254, 14265}, {5967, 41939}, {6531, 20031}, {6656, 14382}, {7473, 46253}, {9154, 34169}, {16081, 51358}, {18907, 35906}, {35912, 48906}, {36874, 43448}, {36897, 46292}
X(51404) = X(i)-Ceva conjugate of X(j) for these (i,j): {98, 878}, {287, 879}, {6531, 2395}, {34536, 523}
X(51404) = crosspoint of X(i) and X(j) for these (i,j): {98, 43665}, {287, 879}, {2395, 6531}
X(51404) = crosssum of X(i) and X(j) for these (i,j): {232, 4230}, {511, 14966}, {2421, 36212}
X(51404) = crossdifference of every pair of points on line {2421, 4230}
X(51404) = X(i)-isoconjugate of X(j) for these (i,j): {162, 2421}, {163, 877}, {232, 24041}, {237, 46254}, {240, 249}, {250, 1959}, {297, 1101}, {648, 23997}, {662, 4230}, {811, 14966}, {1755, 18020}, {2211, 24037}, {2396, 32676}, {3289, 23999}, {5379, 17209}, {15631, 36104}, {23357, 40703}, {23995, 44132}, {24000, 36212}, {41174, 42075}
X(51404) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 877), (125, 2421), (512, 2211), (523, 297), (525, 6393), (647, 325), (1084, 4230), (3005, 232), (15526, 2396), (17423, 14966), (17434, 51386), (18314, 44132), (24284, 46888), (36899, 18020), (39000, 15631), (39085, 249), (41167, 36790)
X(51404) = barycentric product X(i)*X(j) for these {i,j}: {98, 125}, {115, 287}, {248, 338}, {290, 20975}, {293, 1109}, {305, 15630}, {336, 2643}, {339, 1976}, {523, 879}, {525, 2395}, {647, 43665}, {685, 5489}, {850, 878}, {868, 47388}, {1821, 3708}, {1910, 20902}, {2422, 3267}, {2632, 36120}, {2970, 17974}, {3269, 16081}, {3695, 43920}, {5967, 51258}, {6394, 8754}, {6531, 15526}, {8029, 17932}, {12079, 35912}, {14600, 23962}, {20031, 23616}, {23105, 43754}, {34536, 41172}
X(51404) = barycentric quotient X(i)/X(j) for these {i,j}: {98, 18020}, {115, 297}, {125, 325}, {248, 249}, {287, 4590}, {293, 24041}, {336, 24037}, {338, 44132}, {512, 4230}, {523, 877}, {525, 2396}, {647, 2421}, {684, 15631}, {810, 23997}, {878, 110}, {879, 99}, {1084, 2211}, {1109, 40703}, {1821, 46254}, {1976, 250}, {2086, 51324}, {2395, 648}, {2422, 112}, {2643, 240}, {2715, 47443}, {2971, 34854}, {2972, 51386}, {3049, 14966}, {3124, 232}, {3269, 36212}, {3708, 1959}, {4466, 51370}, {5489, 6333}, {6394, 47389}, {6531, 23582}, {8029, 16230}, {8754, 6530}, {14600, 23357}, {15526, 6393}, {15630, 25}, {16186, 51383}, {17932, 31614}, {18210, 51369}, {20902, 46238}, {20975, 511}, {22260, 17994}, {23216, 9418}, {34536, 41174}, {34982, 21525}, {36120, 23999}, {41172, 36790}, {41221, 39569}, {43665, 6331}, {44114, 2967}
X(51404) = {X(98),X(47388)}-harmonic conjugate of X(41175)
X(51405) lies on these lines: {5, 21460}, {30, 14833}, {69, 525}, {111, 3580}, {249, 45018}, {265, 895}, {287, 11064}, {316, 524}, {323, 31125}, {427, 10559}, {542, 1550}, {691, 1503}, {858, 32583}, {1352, 5968}, {2966, 45774}, {3448, 46783}, {5133, 10558}, {5169, 10560}, {5181, 47293}, {6390, 34897}, {8869, 26926}, {9214, 11180}, {18023, 44137}, {32729, 46818}, {40112, 42008}, {50941, 51227}
X(51405) = reflection of X(i) in X(j) for these {i,j}: {895, 51258}, {47293, 5181}
X(51405) = isotomic conjugate of the polar conjugate of X(16092)
X(51405) = X(32676)-isoconjugate of X(50942)
X(51405) = X(i)-Dao conjugate of X(j) for these (i, j): (15526, 50942), (23967, 468)
X(51405) = barycentric product X(i)*X(j) for these {i,j}: {69, 16092}, {525, 50941}, {542, 30786}, {14977, 14999}
X(51405) = barycentric quotient X(i)/X(j) for these {i,j}: {525, 50942}, {542, 468}, {895, 842}, {1640, 14273}, {5191, 44102}, {10097, 14998}, {14977, 14223}, {14999, 4235}, {16092, 4}, {30786, 5641}, {39474, 1649}, {45662, 5095}, {50941, 648}
X(51406) lies on these lines: {2, 5845}, {6, 3756}, {9, 1768}, {10, 28877}, {11, 2246}, {37, 14936}, {41, 21049}, {44, 3911}, {45, 5218}, {101, 952}, {118, 516}, {125, 1213}, {150, 40483}, {169, 5886}, {220, 5657}, {346, 43290}, {375, 6784}, {514, 35110}, {676, 9502}, {900, 1635}, {1023, 1145}, {1086, 9318}, {1212, 10165}, {1317, 4530}, {1565, 6710}, {2238, 39686}, {2264, 28019}, {3204, 21933}, {3207, 5731}, {3509, 5852}, {3570, 4437}, {3689, 3943}, {3732, 17044}, {3932, 4070}, {4413, 17369}, {4534, 17439}, {4969, 22356}, {5011, 28212}, {5134, 28182}, {5179, 28160}, {5276, 17726}, {5540, 16173}, {5587, 46835}, {5792, 28827}, {5819, 9779}, {5843, 8558}, {5848, 17330}, {6184, 35111}, {6603, 8074}, {7359, 44425}, {11219, 16554}, {15288, 38031}, {16593, 24685}, {17281, 46917}, {17455, 41556}, {17718, 40131}, {20096, 31640}, {20401, 31851}, {23058, 37712}, {23980, 23986}, {26258, 37658}
X(51406) = midpoint of X(3732) and X(38941)
X(51406) = reflection of X(38941) in X(17044)
X(51406) = tripolar centroid of X(2398)
X(51406) = X(i)-isoconjugate of X(j) for these (i,j): {88, 103}, {106, 36101}, {677, 1022}, {679, 45144}, {903, 911}, {1797, 36122}, {1815, 36125}, {2316, 43736}, {2400, 32665}, {2424, 3257}, {6336, 36056}, {6548, 36039}, {9456, 18025}, {9503, 34230}
X(51406) = X(i)-Dao conjugate of X(j) for these (i, j): (214, 36101), (1566, 6548), (4370, 18025), (6544, 15634), (20622, 6336), (23972, 903), (35092, 2400), (46095, 1797), (50441, 4997)
X(51406) = crosssum of X(i) and X(j) for these (i,j): {103, 45144}, {2316, 34230}
X(51406) = crossdifference of every pair of points on line {103, 106}
vbarycentric product X(i)*X(j) for these {i,j}: {44, 30807}, {516, 519}, {676, 17780}, {900, 2398}, {902, 35517}, {910, 4358}, {1456, 4723}, {1635, 42719}, {1886, 3977}, {2325, 43035}, {3911, 40869}, {3943, 14953}, {4241, 14429}, {4528, 23973}, {8756, 26006}, {14427, 24015}, {16704, 17747}, {37168, 51366}, {37790, 51376}
X(51406) = barycentric quotient X(i)/X(j) for these {i,j}: {44, 36101}, {516, 903}, {519, 18025}, {676, 6548}, {900, 2400}, {902, 103}, {910, 88}, {1017, 45144}, {1319, 43736}, {1647, 15634}, {1886, 6336}, {1960, 2424}, {2251, 911}, {2398, 4555}, {2426, 901}, {17747, 4080}, {22356, 1815}, {23202, 36056}, {23344, 677}, {30807, 20568}, {40869, 4997}, {41339, 1320}
X(51406) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {910, 40869, 17747}, {9318, 26007, 1086}
X(51407) lies on these lines: {8, 37715}, {11, 35104}, {12, 9565}, {78, 5396}, {100, 29207}, {119, 517}, {200, 33076}, {219, 28807}, {345, 41883}, {1211, 2092}, {1259, 5810}, {1329, 10480}, {2968, 44694}, {3035, 5061}, {3580, 27757}, {3912, 26005}, {4415, 20237}, {4417, 26942}, {4434, 5847}, {5552, 5711}, {5743, 11679}, {7358, 7360}, {14555, 23600}, {16608, 30828}, {20895, 26580}, {23691, 51366}, {26932, 32851}, {27385, 37594}, {28813, 37680}
X(51407) = reflection of X(5061) in X(3035)
X(51407) = X(i)-isoconjugate of X(j) for these (i,j): {909, 961}, {2423, 36098}, {4581, 32669}
X(51407) = X(i)-Dao conjugate of X(j) for these (i, j): (1145, 2298), (1211, 34051), (2092, 104), (23980, 961), (38992, 2423)
X(51407) = barycentric product X(i)*X(j) for these {i,j}: {908, 3687}, {960, 3262}, {2397, 3910}, {3704, 17139}, {4357, 6735}
X(51407) = barycentric quotient X(i)/X(j) for these {i,j}: {517, 961}, {960, 104}, {2269, 909}, {2397, 6648}, {2427, 8687}, {2804, 4581}, {3262, 31643}, {3666, 34051}, {3687, 34234}, {3704, 38955}, {3882, 37136}, {3910, 2401}, {6735, 1220}, {20967, 34858}, {21033, 2250}, {22074, 14578}, {46878, 36123}, {51379, 1791}
X(51407) = {X(908),X(51367)}-harmonic conjugate of X(51390)
X(51408) lies on these lines: {1, 11219}, {6, 43960}, {109, 15252}, {117, 515}, {125, 17056}, {354, 33883}, {614, 3756}, {650, 23972}, {940, 3475}, {1060, 26446}, {1086, 45946}, {1125, 20324}, {1149, 34590}, {1155, 23710}, {1214, 10164}, {1638, 6174}, {1936, 38454}, {2968, 6718}, {5348, 6354}, {5432, 20277}, {5658, 34032}, {5848, 17392}, {6357, 44425}, {6510, 6745}, {7100, 31659}, {21664, 38607}, {23711, 40560}, {23986, 46391}
X(51408) = tripolar centroid of X(2406)
X(51408) = crossdifference of every pair of points on line {102, 2291}
X(51408) = X(i)-isoconjugate of X(j) for these (i,j): {102, 1156}, {1121, 32677}, {2291, 36100}, {2399, 36141}, {2432, 37139}, {15629, 34056}, {34068, 34393}
X(51408) = X(i)-Dao conjugate of X(j) for these (i, j): (23986, 1121), (35091, 2399), (35110, 34393)
X(51408) = barycentric product X(i)*X(j) for these {i,j}: {515, 527}, {1055, 35516}, {2182, 30806}, {2406, 6366}, {6745, 34050}, {14304, 23890}, {14413, 42718}, {14414, 24035}, {37780, 51361}, {37805, 46974}
X(51408) = barycentric quotient X(i)/X(j) for these {i,j}: {515, 1121}, {527, 34393}, {1055, 102}, {1155, 36100}, {1455, 34056}, {2182, 1156}, {2406, 35157}, {2425, 14733}, {6139, 2432}, {6366, 2399}, {33573, 15633}, {51361, 41798}
X(51408) = {X(109),X(15252)}-harmonic conjugate of X(38357)
X(51409) lies on these lines: {1, 529}, {2, 36279}, {3, 11415}, {4, 5730}, {5, 3869}, {8, 381}, {10, 3614}, {11, 758}, {12, 3878}, {21, 12913}, {30, 4511}, {36, 17768}, {44, 50759}, {46, 13747}, {63, 5886}, {65, 4187}, {72, 946}, {78, 12699}, {80, 5855}, {100, 5180}, {119, 517}, {144, 20330}, {145, 4930}, {191, 4999}, {200, 31162}, {214, 15326}, {226, 392}, {329, 956}, {355, 11682}, {405, 3485}, {430, 1230}, {442, 960}, {474, 4295}, {484, 3035}, {495, 3877}, {496, 3868}, {515, 13257}, {516, 5440}, {518, 30384}, {527, 38026}, {535, 12831}, {546, 5086}, {553, 1125}, {856, 16596}, {859, 15507}, {942, 41012}, {952, 5080}, {962, 5687}, {993, 15950}, {995, 3782}, {997, 1836}, {999, 5905}, {1086, 49997}, {1149, 32856}, {1193, 33145}, {1210, 4018}, {1329, 5903}, {1387, 17484}, {1454, 7483}, {1478, 5289}, {1479, 12635}, {1482, 3436}, {1484, 12532}, {1565, 20347}, {1621, 5719}, {1699, 3419}, {1737, 5087}, {1749, 38063}, {1864, 3555}, {2093, 30827}, {2292, 29688}, {2886, 5692}, {2975, 5901}, {3057, 10955}, {3218, 15325}, {3336, 6691}, {3339, 25522}, {3421, 6957}, {3434, 3940}, {3452, 3753}, {3474, 16371}, {3487, 13615}, {3579, 27385}, {3582, 4880}, {3583, 4867}, {3616, 6147}, {3622, 31156}, {3632, 13463}, {3648, 5303}, {3656, 3872}, {3671, 5439}, {3686, 44730}, {3695, 25253}, {3742, 11551}, {3811, 12701}, {3812, 17575}, {3813, 5904}, {3814, 34122}, {3816, 5902}, {3820, 27131}, {3824, 24564}, {3825, 4084}, {3874, 37722}, {3876, 31419}, {3884, 15888}, {3899, 7951}, {3901, 37720}, {3918, 50038}, {3925, 10176}, {3927, 10527}, {3957, 15170}, {3962, 10916}, {4004, 8582}, {4028, 50122}, {4046, 4717}, {4067, 24387}, {4292, 17614}, {4301, 10914}, {4305, 50242}, {4338, 17583}, {4424, 37662}, {4539, 24393}, {4640, 37298}, {4848, 17619}, {4857, 41696}, {4966, 4975}, {4996, 48698}, {5046, 37730}, {5074, 51384}, {5176, 5844}, {5221, 10200}, {5231, 38021}, {5250, 11374}, {5253, 14450}, {5259, 11281}, {5315, 17061}, {5330, 20060}, {5529, 24715}, {5538, 34789}, {5552, 12702}, {5657, 5748}, {5690, 6980}, {5694, 26470}, {5697, 12607}, {5698, 16370}, {5841, 6265}, {5842, 6326}, {5852, 16173}, {5887, 6831}, {6001, 37374}, {6224, 28186}, {6284, 22836}, {6361, 27383}, {6690, 37701}, {6734, 9955}, {6737, 18483}, {6745, 28194}, {6763, 37735}, {6882, 14988}, {6894, 15911}, {6943, 33899}, {6968, 12245}, {6976, 10595}, {7082, 11376}, {7191, 39544}, {7354, 30144}, {7508, 38033}, {7681, 37625}, {7682, 17618}, {7743, 26015}, {8227, 12526}, {8255, 50836}, {8543, 37306}, {9352, 17564}, {9612, 15829}, {9614, 11523}, {9623, 31142}, {9669, 12649}, {9708, 31018}, {9945, 28178}, {10225, 38760}, {10427, 28534}, {10742, 35457}, {10896, 49168}, {11019, 24473}, {11236, 12647}, {11362, 40260}, {11680, 38034}, {11729, 22765}, {11827, 40257}, {12019, 37375}, {12433, 34195}, {12527, 13464}, {12608, 14110}, {12609, 17529}, {12653, 32426}, {12732, 48696}, {15015, 15228}, {15171, 34772}, {15908, 31806}, {16483, 33144}, {16594, 49993}, {16842, 28629}, {17556, 18391}, {17724, 40091}, {17734, 37691}, {18481, 41543}, {18541, 35272}, {19927, 43053}, {21630, 34503}, {21677, 25639}, {21740, 31789}, {24045, 40997}, {24541, 31445}, {24982, 50193}, {25055, 25557}, {25416, 38455}, {25568, 30305}, {26066, 37692}, {26364, 37567}, {26446, 30852}, {28234, 38156}, {28916, 36728}, {29824, 46521}, {30323, 32049}, {31160, 41684}, {31937, 37447}, {33099, 37617}, {33134, 48847}, {37356, 40266}, {37359, 39599}, {37468, 45770}, {37536, 42448}, {37646, 49500}, {40292, 42843}
X(51409) = midpoint of X(i) and X(j) for these {i,j}: {100, 5180}, {3583, 4867}, {4511, 5057}, {5538, 34789}, {10742, 35457}
X(51409) = reflection of X(i) in X(j) for these {i,j}: {11, 11813}, {484, 3035}, {1145, 17757}, {1737, 5087}, {3218, 15325}, {4973, 1125}, {10609, 4511}, {12690, 3583}, {12732, 48696}, {15326, 214}, {17757, 908}, {22765, 11729}, {26015, 7743}, {40663, 3814}
X(51409) = X(i)-isoconjugate of X(j) for these (i,j): {104, 1126}, {909, 1255}, {1171, 2250}, {1268, 34858}, {2423, 37212}, {28615, 34234}, {32641, 47947}, {33635, 34051}, {36037, 50344}
X(51409) = X(i)-Dao conjugate of X(j) for these (i, j): (1125, 38955), (1145, 32635), (1213, 34234), (3259, 50344), (3647, 104), (16586, 1268), (23980, 1255), (35076, 2401), (40613, 1126), (46398, 4608)
X(51409) = crosspoint of X(908) and X(17139)
X(51409) = crossdifference of every pair of points on line {2423, 28615}
X(51409) = barycentric product X(i)*X(j) for these {i,j}: {517, 4359}, {553, 6735}, {859, 1230}, {908, 1125}, {1100, 3262}, {1213, 17139}, {1269, 2183}, {1465, 3702}, {1785, 4001}, {2397, 4977}, {3686, 22464}, {4115, 23788}, {4427, 10015}, {4985, 24029}, {8025, 17757}, {16709, 21801}, {31900, 51367}, {35342, 36038}
X(51409) = barycentric quotient X(i)/X(j) for these {i,j}: {517, 1255}, {859, 1171}, {908, 1268}, {1100, 104}, {1125, 34234}, {1145, 31011}, {1213, 38955}, {1769, 47947}, {1839, 36123}, {1962, 2250}, {2183, 1126}, {2308, 909}, {2397, 6540}, {2427, 8701}, {3262, 32018}, {3310, 50344}, {3702, 36795}, {4359, 18816}, {4427, 13136}, {4969, 36944}, {4976, 43728}, {4977, 2401}, {5298, 40218}, {6735, 4102}, {10015, 4608}, {17139, 32014}, {17757, 6539}, {22054, 1795}, {22350, 1796}, {23201, 14578}, {32636, 34051}, {35327, 32641}, {35342, 36037}, {36075, 2720}, {50512, 2423}
X(51409) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 24703, 11113}, {10, 17605, 17530}, {46, 25681, 13747}, {65, 21616, 4187}, {72, 946, 24390}, {191, 5443, 4999}, {329, 5603, 956}, {960, 12047, 442}, {997, 1836, 11112}, {1125, 3683, 15670}, {1125, 4973, 5298}, {1737, 5087, 17533}, {3683, 4870, 1125}, {3814, 40663, 34122}, {3877, 31053, 495}, {3927, 18493, 10527}, {4301, 21075, 10914}, {5253, 14450, 24470}, {5692, 18393, 2886}, {11375, 12514, 7483}, {12609, 25917, 17529}, {17605, 31165, 10}, {24703, 34647, 1}
X(51410) lies on these lines: {2, 41007}, {11, 44661}, {19, 37695}, {30, 5146}, {92, 19542}, {119, 517}, {226, 2262}, {242, 33305}, {278, 7011}, {442, 1829}, {851, 2969}, {916, 13257}, {946, 43213}, {1068, 13737}, {1375, 17923}, {1465, 14571}, {1730, 6354}, {1731, 35466}, {1763, 3772}, {1824, 8226}, {1848, 6708}, {1851, 7580}, {1871, 6831}, {2264, 40940}, {2968, 8229}, {3100, 33302}, {4187, 41340}, {4271, 4415}, {7291, 33129}, {11349, 37798}, {15252, 33849}, {17056, 17443}, {20243, 37358}, {20989, 45946}, {21370, 24789}, {21452, 22464}, {35221, 41345}, {37790, 51368}
X(51410) = X(i)-isoconjugate of X(j) for these (i,j): {104, 2983}, {909, 1257}, {14578, 40445}
X(51410) = X(i)-Dao conjugate of X(j) for these (i, j): (440, 34234), (23980, 1257), (40613, 2983)
X(51410) = barycentric product X(i)*X(j) for these {i,j}: {517, 17863}, {908, 40940}, {950, 22464}, {1104, 3262}, {1785, 18650}, {1834, 17139}, {2397, 29162}, {10015, 14543}
X(51410) = barycentric quotient X(i)/X(j) for these {i,j}: {517, 1257}, {1104, 104}, {1457, 951}, {1785, 40445}, {1834, 38955}, {1842, 36123}, {2183, 2983}, {2427, 29163}, {14543, 13136}, {17863, 18816}, {29162, 2401}, {40940, 34234}, {40977, 2250}
X(51411) lies on these lines: {10, 50032}, {11, 740}, {12, 25385}, {43, 20545}, {119, 517}, {325, 4087}, {594, 2886}, {1329, 37598}, {2092, 24210}, {2887, 25140}, {3032, 11813}, {3035, 5143}, {3142, 3702}, {3685, 37370}, {3741, 30097}, {3816, 17592}, {3931, 4187}, {4271, 24703}, {5295, 24390}, {10453, 20256}, {20486, 21241}, {20487, 29673}, {20557, 20760}, {24248, 30960}, {32929, 37354}, {32932, 37365}
X(51411) = X(i)-Dao conjugate of X(j) for these (i, j): (16586, 40418), (21838, 34234), (23980, 1258)
X(51411) =barycentric product X(i)*X(j) for these {i,j}: {517, 20891}, {908, 3741}, {1107, 3262}, {6735, 30097}, {16738, 17757}, {17139, 21024}
X(51411) =barycentric quotient X(i)/X(j) for these {i,j}: {517, 1258}, {908, 40418}, {1107, 104}, {1197, 34858}, {2309, 909}, {3262, 1221}, {3728, 2250}, {3741, 34234}, {17139, 40409}, {20891, 18816}, {21024, 38955}, {22065, 1795}, {22389, 14578}, {42752, 40525}, {50510, 2423}
X(51411) ={X(20557),X(27518)}-harmonic conjugate of X(20760)
X(51412) lies on these lines: {2, 1843}, {5, 16983}, {20, 40325}, {25, 577}, {30, 5140}, {51, 7736}, {114, 325}, {183, 14913}, {185, 7710}, {187, 2386}, {216, 20885}, {230, 2393}, {232, 237}, {262, 10110}, {385, 8681}, {389, 9744}, {427, 14767}, {1184, 19459}, {1194, 20775}, {1370, 41762}, {1611, 9924}, {2387, 50387}, {2854, 50774}, {3284, 44089}, {3313, 7778}, {3815, 9969}, {3819, 7868}, {5139, 47096}, {5167, 6000}, {5171, 15574}, {5304, 40673}, {5306, 32366}, {5943, 11174}, {6054, 39846}, {6291, 7374}, {6406, 7000}, {6467, 7735}, {8705, 44381}, {9019, 44377}, {9027, 15480}, {9729, 40951}, {9752, 15073}, {9769, 32260}, {9770, 21969}, {9967, 37071}, {9971, 31489}, {9973, 37637}, {10313, 44099}, {11163, 21849}, {11188, 34229}, {11325, 22401}, {11513, 45401}, {11514, 45400}, {12272, 37667}, {13166, 37931}, {14961, 21177}, {15271, 29959}, {15491, 16776}
X(51412) = X(i)-Dao conjugate of X(j) for these (i, j): (5976, 40831), (40125, 98)
X(51412) = barycentric product X(i)*X(j) for these {i,j}: {232, 7386}, {297, 19459}, {325, 1184}, {511, 5286}
X(51412) = barycentric quotient X(i)/X(j) for these {i,j}: {325, 40831}, {1184, 98}, {5286, 290}, {19459, 287}
X(51413) lies on these lines: {2, 14557}, {51, 11018}, {119, 517}, {223, 7053}, {957, 39779}, {971, 34462}, {1465, 2183}, {1763, 4383}, {1824, 10157}, {1828, 31793}, {1829, 5044}, {2262, 5219}, {3091, 43213}, {3149, 5909}, {3660, 8679}, {3666, 21361}, {3827, 38472}, {3911, 34371}, {3937, 11575}, {5045, 16980}, {5122, 36058}, {5908, 6834}, {7013, 11347}, {7291, 37680}, {8712, 40137}, {9535, 20921}, {11227, 26892}, {21370, 37679}, {21871, 31142}, {31787, 42448}
X(51413) = reflection of X(3937) in X(11575)
X(51413) = X(i)-isoconjugate of X(j) for these (i,j): {104, 2297}, {909, 1219}, {7050, 34234}
X(51413) = X(i)-Dao conjugate of X(j) for these (i, j): (23980, 1219), (40613, 2297)
X(51413) = crossdifference of every pair of points on line {2423, 7050}
X(51413) = barycentric product X(i)*X(j) for these {i,j}: {517, 3672}, {908, 2999}, {1191, 3262}, {1465, 18228}, {1697, 22464}, {2397, 8712}, {4646, 17139}
X(51413) = barycentric quotient X(i)/X(j) for these {i,j}: {517, 1219}, {1191, 104}, {1457, 7091}, {1875, 11546}, {2183, 2297}, {2427, 6574}, {2999, 34234}, {3672, 18816}, {4646, 38955}, {8662, 2423}, {8712, 2401}, {18228, 36795}
X(51414) lies on these lines: {2, 198}, {4, 15844}, {11, 1284}, {55, 26118}, {57, 19542}, {63, 5928}, {109, 29207}, {117, 515}, {197, 25907}, {325, 4872}, {429, 22345}, {440, 5745}, {851, 26933}, {940, 2286}, {1150, 21270}, {1211, 19608}, {1214, 21621}, {1376, 7386}, {1503, 1936}, {1565, 18593}, {1764, 26942}, {1848, 3666}, {1951, 35466}, {2183, 26005}, {2968, 44661}, {3004, 3910}, {3185, 23304}, {3198, 34822}, {3218, 46487}, {3220, 33305}, {3704, 41600}, {3752, 16580}, {3782, 36503}, {3911, 26012}, {4329, 17740}, {4966, 50362}, {5233, 41828}, {5513, 16593}, {6284, 36496}, {11347, 20266}, {14829, 21276}, {18589, 25939}, {19645, 28774}, {25365, 47522}, {29057, 38357}, {30847, 37660}, {36504, 44416}, {37613, 39566}
X(51414) = X(i)-isoconjugate of X(j) for these (i,j): {102, 2298}, {961, 15629}, {1220, 32677}, {2359, 36121}, {2432, 36098}
X(51414) = X(i)-Dao conjugate of X(j) for these (i, j): (1211, 36100), (23986, 1220), (38992, 2432)
X(51414) = barycentric product X(i)*X(j) for these {i,j}: {515, 4357}, {1193, 35516}, {2182, 20911}, {2406, 3910}, {3687, 34050}, {42718, 48131}
X(51414) = barycentric quotient X(i)/X(j) for these {i,j}: {515, 1220}, {1193, 102}, {1455, 961}, {1829, 36121}, {2182, 2298}, {2269, 15629}, {2300, 32677}, {2406, 6648}, {2425, 8687}, {3666, 36100}, {3910, 2399}, {4357, 34393}, {22345, 36055}, {35516, 1240}, {46974, 1791}
X(51415) lies on these lines: {1, 9711}, {2, 6}, {5, 17749}, {11, 899}, {12, 1450}, {37, 5316}, {39, 38930}, {43, 3816}, {44, 3911}, {88, 17484}, {121, 519}, {140, 37469}, {142, 31197}, {226, 16602}, {238, 3035}, {239, 37758}, {312, 27130}, {386, 17527}, {518, 3756}, {594, 30818}, {595, 47742}, {740, 11814}, {748, 5432}, {902, 6174}, {908, 1086}, {952, 45763}, {978, 1329}, {995, 3820}, {1054, 17768}, {1104, 6700}, {1146, 50027}, {1201, 21031}, {1279, 6745}, {1532, 33810}, {1575, 17747}, {1616, 7080}, {1647, 21805}, {1722, 25681}, {1724, 13747}, {1738, 5087}, {1743, 31190}, {1834, 3216}, {1901, 46838}, {2324, 3772}, {2886, 16569}, {2999, 20196}, {3008, 6547}, {3214, 37722}, {3218, 43055}, {3264, 3943}, {3306, 17365}, {3452, 3663}, {3628, 24880}, {3662, 31233}, {3687, 17229}, {3699, 5211}, {3704, 25079}, {3740, 24239}, {3782, 27131}, {3813, 6048}, {3814, 49992}, {3817, 21949}, {3826, 17717}, {3829, 32865}, {3840, 50315}, {3846, 6686}, {3880, 38471}, {3912, 25125}, {3932, 24003}, {3977, 4370}, {4000, 5328}, {4023, 30942}, {4110, 17242}, {4129, 6002}, {4205, 20108}, {4252, 17567}, {4255, 5084}, {4257, 17564}, {4328, 5219}, {4361, 28808}, {4395, 4997}, {4422, 32851}, {4644, 31202}, {4849, 11019}, {4850, 17246}, {4871, 4966}, {4884, 27538}, {4888, 5437}, {4902, 8056}, {4967, 44417}, {5096, 33849}, {5205, 5846}, {5212, 28581}, {5230, 31246}, {5247, 6691}, {5297, 17726}, {5400, 37374}, {5513, 5519}, {5529, 44669}, {5692, 24223}, {5706, 6983}, {5721, 6963}, {5744, 16885}, {5847, 50535}, {5852, 18201}, {6557, 42047}, {6667, 33140}, {6688, 18165}, {6690, 17123}, {6736, 45219}, {6882, 45926}, {6944, 36745}, {6953, 37537}, {7263, 24620}, {7277, 37520}, {7292, 17724}, {8055, 42049}, {9041, 50533}, {9342, 33107}, {9350, 34612}, {9458, 32844}, {10459, 50038}, {11681, 27625}, {12053, 21896}, {12607, 21214}, {15621, 28364}, {15888, 28352}, {16486, 34619}, {16706, 30867}, {17051, 49490}, {17233, 30861}, {17243, 30829}, {17276, 31142}, {17332, 24627}, {17334, 17595}, {17340, 17740}, {17366, 17720}, {17495, 30566}, {17529, 37693}, {17531, 49745}, {17546, 24936}, {17757, 24222}, {17775, 27186}, {17777, 28530}, {20072, 31227}, {20470, 28239}, {21060, 21342}, {21120, 28006}, {23361, 28271}, {24789, 30852}, {25882, 26010}, {26748, 43036}, {26791, 32939}, {27002, 33066}, {27489, 49509}, {28248, 44411}, {31053, 40688}, {31242, 33084}, {31272, 33139}, {32918, 41002}, {33106, 49732}, {33129, 37691}, {33141, 36634}, {37787, 43056}, {38455, 47623}, {43290, 49704}
X(51415) = midpoint of X(3699) and X(5211)
X(51415) = reflection of X(3756) in X(5121)
X(51415) = complement of the isotomic conjugate of X(14554)
X(51415) = X(i)-complementary conjugate of X(j) for these (i,j): {14554, 2887}, {50039, 21260}
X(51415) = X(24624)-Ceva conjugate of X(18163)
X(51415) = X(i)-isoconjugate of X(j) for these (i,j): {106, 23617}, {1222, 9456}, {1320, 3451}, {1476, 2316}
X(51415) = X(i)-Dao conjugate of X(j) for these (i, j): (214, 23617), (2170, 23838), (3452, 88), (3752, 4997), (4370, 1222), (6544, 40451)
X(51415) = crosspoint of X(i) and X(j) for these (i,j): {2, 14554}, {3911, 4358}, {14628, 24624}
X(51415) = crosssum of X(i) and X(j) for these (i,j): {6, 5053}, {2316, 9456}
X(51415) = crossdifference of every pair of points on line {512, 2441}
X(51415) = barycentric product X(i)*X(j) for these {i,j}: {44, 26563}, {519, 3663}, {900, 21272}, {1122, 4723}, {1201, 3264}, {1319, 20895}, {1635, 21580}, {3452, 3911}, {3752, 4358}, {3762, 21362}, {3943, 18600}, {4415, 16704}, {4642, 30939}, {17183, 40663}, {24004, 48334}, {25268, 30725}
X(51415) = barycentric quotient X(i)/X(j) for these {i,j}: {44, 23617}, {519, 1222}, {1201, 106}, {1319, 1476}, {1404, 3451}, {1647, 40451}, {1828, 36125}, {1877, 40446}, {2347, 2316}, {3057, 1320}, {3452, 4997}, {3663, 903}, {3689, 1261}, {3752, 88}, {3911, 40420}, {4358, 32017}, {4415, 4080}, {4642, 4674}, {6363, 23345}, {6615, 23838}, {17780, 8706}, {20228, 9456}, {21272, 4555}, {21362, 3257}, {22344, 36058}, {23845, 901}, {25268, 4582}, {26563, 20568}, {45204, 31227}, {48334, 1022}
X(51415) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4383, 37646}, {2, 5233, 141}, {2, 5241, 1213}, {2, 5712, 37682}, {2, 5718, 17245}, {2, 30828, 17265}, {2, 30832, 34573}, {2, 32911, 37634}, {2, 37650, 31187}, {2, 37651, 5718}, {2, 37662, 17056}, {2, 37663, 37662}, {2, 37680, 35466}, {908, 16610, 1086}, {3216, 4187, 1834}, {3452, 3752, 4415}, {3452, 45204, 3752}, {4383, 25934, 6}, {5718, 17245, 17056}, {5718, 37651, 37662}, {5718, 37663, 37651}, {17245, 37662, 5718}, {17595, 31018, 17334}, {23511, 30827, 3772}, {31187, 37679, 37650}
X(51416) lies on these lines: {2, 42884}, {5, 5082}, {8, 442}, {10, 26005}, {11, 3689}, {12, 6736}, {78, 5886}, {100, 37374}, {119, 517}, {142, 354}, {145, 25962}, {200, 2886}, {226, 17658}, {390, 14022}, {480, 31140}, {496, 27383}, {497, 6600}, {1058, 50206}, {1259, 18517}, {1260, 3434}, {1329, 1697}, {1387, 4511}, {1706, 15844}, {1836, 20588}, {2078, 3035}, {2340, 33136}, {2550, 37363}, {2968, 3006}, {3295, 4187}, {3340, 12607}, {3421, 6907}, {3695, 23528}, {3703, 17860}, {3816, 10389}, {3826, 5231}, {3932, 24026}, {4193, 27525}, {4853, 25466}, {5687, 6831}, {5748, 7956}, {5837, 21031}, {6737, 11011}, {6881, 10247}, {6882, 12331}, {7046, 25985}, {7360, 32850}, {7373, 8728}, {8727, 17784}, {9779, 11681}, {10388, 15845}, {10527, 17529}, {10707, 17533}, {10742, 35461}, {11019, 25973}, {13257, 17615}, {15837, 40998}, {15908, 21075}, {17575, 27529}, {19542, 36855}, {20075, 37358}, {21077, 46677}, {23541, 51366}, {27542, 33305}
X(51416) = midpoint of X(10742) and X(35461)
X(51416) = reflection of X(2078) in X(3035)
X(51416) = X(i)-isoconjugate of X(j) for these (i,j): {909, 1170}, {1174, 34051}, {21453, 34858}
X(51416) = X(i)-Dao conjugate of X(j) for these (i, j): (142, 104), (1145, 2346), (16586, 21453), (23980, 1170), (40606, 34051)
X(51416) = crosspoint of X(3262) and X(6735)
X(51416) = barycentric product X(i)*X(j) for these {i,j}: {142, 6735}, {517, 1229}, {908, 4847}, {1212, 3262}, {2397, 6362}, {16713, 17757}, {35341, 36038}
X(51416) = barycentric quotient X(i)/X(j) for these {i,j}: {354, 34051}, {517, 1170}, {908, 21453}, {1212, 104}, {1229, 18816}, {1855, 36123}, {2293, 909}, {2397, 6606}, {2488, 2423}, {3262, 31618}, {4847, 34234}, {6362, 2401}, {6735, 32008}, {8012, 2342}, {20229, 34858}, {21039, 2250}, {22079, 14578}, {22350, 1803}, {22464, 10509}, {35326, 2720}, {35338, 37136}, {35341, 36037}, {51380, 6605}
X(51416) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {119, 51362, 17757}, {908, 6735, 51380}
X(51417) lies on these lines: {1, 27688}, {8, 27704}, {69, 7410}, {99, 20558}, {114, 325}, {115, 726}, {125, 3006}, {442, 24199}, {518, 44396}, {620, 1326}, {982, 46828}, {984, 46826}, {1100, 1125}, {1211, 24239}, {3663, 37159}, {3701, 30436}, {3710, 27555}, {3729, 37049}, {3751, 27556}, {3836, 17058}, {3932, 8287}, {3977, 33329}, {5051, 17324}, {5145, 7764}, {5846, 50773}, {5949, 49483}, {6033, 35462}, {6367, 30591}, {7380, 50632}, {10026, 34379}, {16830, 27707}, {20337, 24231}, {30171, 34829}, {34528, 49511}, {39040, 44694}
X(51417) = midpoint of X(i) and X(j) for these {i,j}: {99, 20558}, {6033, 35462}
X(51417) = reflection of X(i) in X(j) for these {i,j}: {115, 20546}, {1326, 620}
X(51417) = X(i)-isoconjugate of X(j) for these (i,j): {1171, 1910}, {1976, 40438}, {2715, 47947}, {36084, 50344}
X(51417) = X(i)-Dao conjugate of X(j) for these (i, j): (1125, 98), (5976, 32014), (11672, 1171), (35088, 4608), (38987, 50344), (39040, 40438)
X(51417) = crossdifference of every pair of points on line {2422, 50344}
X(51417) = barycentric product X(i)*X(j) for these {i,j}: {297, 41014}, {325, 1213}, {430, 6393}, {511, 1230}, {1100, 42703}, {1959, 4647}, {1962, 46238}, {2396, 6367}, {2799, 4427}, {3958, 40703}, {8013, 51370}, {22080, 44132}, {30591, 42717}, {36212, 44143}
X(51417) = barycentric quotient X(i)/X(j) for these {i,j}: {325, 32014}, {430, 6531}, {511, 1171}, {1213, 98}, {1230, 290}, {1959, 40438}, {1962, 1910}, {2421, 6578}, {2799, 4608}, {3569, 50344}, {3958, 293}, {4046, 15628}, {4427, 2966}, {4647, 1821}, {5360, 28615}, {6367, 2395}, {8663, 2422}, {20970, 1976}, {22080, 248}, {35327, 2715}, {35342, 36084}, {41014, 287}, {42703, 32018}, {42717, 4596}, {44143, 16081}
X(51418) lies on these lines: {1, 6}, {41, 14100}, {55, 28070}, {101, 971}, {118, 516}, {144, 348}, {210, 6602}, {390, 6554}, {480, 4515}, {527, 36956}, {657, 3900}, {673, 34852}, {919, 40567}, {1146, 5853}, {1260, 45791}, {1334, 15837}, {1456, 9502}, {1615, 10860}, {1802, 3059}, {2550, 46835}, {3119, 3689}, {3158, 5574}, {3207, 5732}, {3683, 8012}, {3685, 6559}, {3730, 31658}, {4258, 4326}, {4421, 41795}, {5819, 27508}, {5845, 40880}, {6605, 27065}, {6745, 13609}, {8581, 9310}, {10164, 45203}, {14189, 44664}, {15855, 35258}, {16283, 20310}, {18482, 24045}, {20533, 37774}, {21153, 42316}, {21856, 46839}, {26006, 39063}, {27382, 41325}, {30331, 41006}
X(51418) = X(2736)-complementary conjugate of X(17072)
X(51418) = X(40869)-Ceva conjugate of X(41339)
X(51418) = crosspoint of X(i) and X(j) for these (i,j): {9, 28071}, {1275, 36802}
X(51418) = crosssum of X(57) and X(34855)
X(51418) = crossdifference of every pair of points on line {269, 513}
X(51418) = X(i)-isoconjugate of X(j) for these (i,j): {57, 43736}, {103, 279}, {269, 36101}, {479, 2338}, {514, 24016}, {658, 2424}, {693, 32668}, {911, 1088}, {1119, 1815}, {1262, 15634}, {1407, 18025}, {1461, 2400}, {1847, 36056}, {7177, 36122}, {9503, 34855}
X(51418) = X(i)-Dao conjugate of X(j) for these (i, j): (5452, 43736), (6600, 36101), (20622, 1847), (23972, 1088), (24771, 18025), (35508, 2400), (46095, 7177), (50441, 85)
X(51418) = barycentric product X(i)*X(j) for these {i,j}: {8, 41339}, {9, 40869}, {190, 46392}, {200, 516}, {220, 30807}, {281, 51376}, {346, 910}, {657, 42719}, {676, 4578}, {728, 43035}, {1253, 35517}, {1456, 5423}, {1886, 3692}, {2287, 17747}, {2398, 3900}, {2426, 4397}, {4183, 51366}, {4515, 14953}, {6559, 9502}, {7079, 26006}, {28071, 50441}
X(51418) = barycentric quotient X(i)/X(j) for these {i,j}: {55, 43736}, {200, 18025}, {220, 36101}, {516, 1088}, {692, 24016}, {910, 279}, {1253, 103}, {1456, 479}, {1802, 1815}, {1886, 1847}, {2310, 15634}, {2398, 4569}, {2426, 934}, {3234, 24015}, {3900, 2400}, {6602, 2338}, {7071, 36122}, {8641, 2424}, {14827, 911}, {17747, 1446}, {28345, 37757}, {32739, 32668}, {40869, 85}, {41321, 13149}, {41339, 7}, {42719, 46406}, {43035, 23062}, {46392, 514}, {51376, 348}
X(51418) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 1001, 1212}, {9, 2324, 50995}, {7079, 7368, 4515}, {40869, 51376, 910}
X(51419) lies on these lines: {2, 1565}, {11, 2809}, {100, 28915}, {101, 5723}, {119, 517}, {142, 374}, {226, 4904}, {513, 10427}, {948, 37272}, {1086, 21362}, {1211, 21253}, {2348, 3008}, {2808, 13257}, {2810, 38055}, {3434, 10743}, {3452, 5514}, {4928, 16594}, {5219, 43960}, {5845, 24618}, {6084, 16593}, {7291, 19512}, {9004, 41555}, {10015, 42762}, {16551, 17337}, {17056, 20982}, {17060, 34852}, {18421, 26727}, {19542, 20921}, {21138, 37662}, {23511, 24795}, {28344, 39063}, {28827, 30808}, {30810, 30854}, {46790, 50843}
X(51419) = X(i)-isoconjugate of X(j) for these (i,j): {909, 1280}, {2342, 43760}, {32641, 35355}, {34858, 36807}
X(51419) = X(i)-Dao conjugate of X(j) for these (i, j): (16586, 36807), (16593, 34234), (23980, 1280), (39048, 104)
X(51419) = crossdifference of every pair of points on line {2342, 2423}
X(51419) = barycentric product X(i)*X(j) for these {i,j}: {908, 3008}, {1279, 3262}, {2397, 6084}, {5853, 22464}
X(51419) = barycentric quotient X(i)/X(j) for these {i,j}: {517, 1280}, {908, 36807}, {1279, 104}, {1457, 1477}, {1465, 43760}, {1769, 35355}, {2427, 6078}, {3008, 34234}, {6084, 2401}, {8647, 2342}, {8659, 2423}, {20780, 1795}, {22350, 1810}, {22464, 35160}
X(51419) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {908, 51381, 51390}, {51381, 51390, 1145}
X(51420) lies on these lines: {1, 47484}, {21, 4881}, {28, 60}, {30, 113}, {36, 238}, {58, 14158}, {65, 17104}, {110, 517}, {125, 44898}, {154, 37241}, {163, 910}, {354, 9275}, {392, 17512}, {501, 2360}, {515, 3109}, {662, 5440}, {759, 1319}, {849, 1104}, {971, 2074}, {1071, 13739}, {1098, 3916}, {1155, 5127}, {1175, 37544}, {1354, 6357}, {1385, 11101}, {1408, 5358}, {1790, 13151}, {2173, 9406}, {2182, 2341}, {3290, 5006}, {3579, 35193}, {3615, 9955}, {3753, 11116}, {3794, 17513}, {4383, 37034}, {5196, 28146}, {5972, 30447}, {6003, 47402}, {6740, 7478}, {7424, 28160}, {7452, 45766}, {9956, 37158}, {10282, 37468}, {10540, 37976}, {13367, 20420}, {13369, 44253}, {13746, 18480}, {14192, 15524}, {15035, 36001}, {15792, 37080}, {17209, 46548}, {17523, 36742}, {17579, 26881}, {18475, 28452}, {20840, 48897}, {23059, 34339}, {23692, 46974}, {24929, 40214}, {25507, 25516}, {27643, 27652}, {28459, 43586}, {31663, 37294}, {31794, 46441}, {40589, 40937}
X(51420) = midpoint of X(i) and X(j) for these {i,j}: {110, 1325}, {10540, 37976}, {18653, 51382}
X(51420) = reflection of X(i) in X(j) for these {i,j}: {125, 44898}, {30447, 5972}
X(51420) = X(2173)-cross conjugate of X(18653)
X(51420) = cevapoint of X(1495) and X(2173)
X(51420) = crosssum of X(210) and X(4053)
X(51420) = crossdifference of every pair of points on line {37, 2433}
X(51420) = X(i)-isoconjugate of X(j) for these (i,j): {10, 74}, {37, 2349}, {42, 1494}, {65, 44693}, {71, 16080}, {72, 36119}, {101, 2394}, {190, 2433}, {213, 33805}, {226, 15627}, {306, 8749}, {313, 40352}, {321, 2159}, {1304, 4064}, {1331, 18808}, {1826, 14919}, {1897, 14380}, {4024, 44769}, {4036, 36034}, {4062, 9139}, {4570, 12079}, {8750, 34767}, {18082, 46147}, {35200, 41013}, {40071, 40354}
X(51420) = X(i)-Dao conjugate of X(j) for these (i, j): (133, 41013), (1015, 2394), (1511, 72), (3163, 321), (3258, 4036), (3284, 42701), (5521, 18808), (6626, 33805), (6739, 3701), (26932, 34767), (34467, 14380), (40589, 2349), (40592, 1494), (40602, 44693), (50330, 12079)
X(51420) = barycentric product X(i)*X(j) for these {i,j}: {1, 18653}, {21, 6357}, {28, 11064}, {30, 81}, {57, 51382}, {58, 14206}, {86, 2173}, {99, 14399}, {274, 1495}, {286, 3284}, {310, 9406}, {513, 2407}, {662, 11125}, {693, 2420}, {905, 4240}, {1014, 7359}, {1333, 3260}, {1414, 14400}, {1437, 46106}, {1444, 1990}, {1459, 24001}, {1784, 1790}, {2206, 46234}, {3733, 42716}, {4556, 36035}, {4623, 14398}, {6385, 9407}, {9214, 16702}, {15413, 23347}, {15454, 18609}, {16164, 21907}, {18180, 43768}, {35906, 51369}
X(51420) = barycentric quotient X(i)/X(j) for these {i,j}: {28, 16080}, {30, 321}, {58, 2349}, {81, 1494}, {86, 33805}, {284, 44693}, {513, 2394}, {667, 2433}, {905, 34767}, {1333, 74}, {1437, 14919}, {1474, 36119}, {1495, 37}, {1511, 42701}, {1568, 42698}, {1637, 4036}, {1990, 41013}, {2173, 10}, {2194, 15627}, {2203, 8749}, {2206, 2159}, {2407, 668}, {2420, 100}, {2631, 4064}, {3125, 12079}, {3233, 42716}, {3260, 27801}, {3284, 72}, {4240, 6335}, {5642, 42713}, {6357, 1441}, {6591, 18808}, {7359, 3701}, {9406, 42}, {9407, 213}, {10564, 42704}, {11064, 20336}, {11125, 1577}, {14206, 313}, {14398, 4705}, {14399, 523}, {14400, 4086}, {14581, 1824}, {16164, 32849}, {16702, 36890}, {18653, 75}, {22383, 14380}, {23347, 1783}, {35266, 42724}, {42716, 27808}, {51372, 42711}, {51382, 312}, {51389, 42703}, {51393, 42700}, {51394, 3998}
X(51420) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {28, 1437, 18180}, {60, 229, 942}, {501, 37816, 2646}, {3615, 37369, 9955}, {35193, 37405, 3579}
X(51421) lies on the cubic K741 and these lines: {1, 6831}, {3, 34030}, {4, 221}, {5, 10571}, {10, 227}, {11, 1457}, {12, 73}, {30, 109}, {34, 1837}, {36, 43043}, {53, 21767}, {55, 13734}, {56, 5230}, {65, 225}, {80, 6357}, {117, 515}, {151, 37420}, {201, 21677}, {222, 1478}, {223, 5587}, {226, 37715}, {230, 17966}, {255, 11827}, {278, 5721}, {325, 664}, {355, 1060}, {381, 34029}, {388, 940}, {393, 3197}, {394, 3436}, {442, 37558}, {495, 50317}, {523, 656}, {603, 5348}, {612, 5252}, {651, 5080}, {860, 38955}, {976, 10944}, {1038, 5794}, {1042, 21935}, {1076, 14110}, {1086, 18838}, {1146, 5089}, {1213, 40590}, {1319, 3011}, {1329, 37694}, {1394, 5691}, {1406, 18961}, {1409, 1901}, {1413, 12667}, {1422, 5923}, {1456, 1877}, {1465, 1737}, {1479, 34040}, {1512, 43058}, {1745, 18242}, {1771, 37468}, {1783, 45929}, {1785, 6001}, {1826, 30456}, {1838, 7686}, {1846, 2390}, {1854, 7952}, {1875, 3827}, {1880, 21933}, {2182, 8755}, {2886, 24806}, {2968, 50368}, {3157, 10526}, {3419, 8270}, {3585, 34043}, {3649, 50705}, {4296, 5086}, {4551, 17757}, {4559, 17747}, {4694, 41556}, {5090, 8900}, {5722, 34036}, {5725, 45126}, {5881, 34039}, {6826, 34042}, {6839, 34035}, {6882, 34586}, {6905, 51236}, {7066, 22299}, {8283, 22654}, {8757, 37821}, {11237, 17392}, {11500, 41402}, {12616, 17102}, {14594, 16086}, {15252, 45272}, {15253, 30117}, {16318, 32674}, {17555, 20306}, {18419, 33146}, {20617, 39791}, {22072, 50031}, {23536, 37566}, {25466, 37523}, {26012, 43035}, {26332, 41344}, {28774, 49492}, {30725, 45884}, {35110, 46415}, {35580, 51221}, {36127, 51385}, {37541, 48837}
X(51421) = midpoint of X(i) and X(j) for these {i,j}: {109, 38945}, {151, 37420}
X(51421) = reflection of X(i) in X(j) for these {i,j}: {1455, 34050}, {2968, 50368}, {38357, 1785}, {45272, 15252}, {51361, 51375}
X(51421) = polar conjugate of the isotomic conjugate of X(51368)
X(51421) = X(38955)-Ceva conjugate of X(65)
X(51421) = crosssum of X(102) and X(36055)
X(51421) = crossdifference of every pair of points on line {284, 2432}
X(51421) = X(i)-isoconjugate of X(j) for these (i,j): {21, 102}, {29, 36055}, {81, 15629}, {163, 2399}, {283, 36121}, {284, 36100}, {333, 32677}, {662, 2432}, {2194, 34393}, {7253, 36040}, {15411, 32667}
X(51421) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 2399), (1084, 2432), (1214, 34393), (1465, 17139), (10017, 7253), (23986, 333), (40586, 15629), (40590, 36100), (40611, 102), (51221, 29)
X(51421) = barycentric product X(i)*X(j) for these {i,j}: {4, 51368}, {10, 34050}, {226, 515}, {307, 8755}, {321, 1455}, {523, 2406}, {525, 23987}, {656, 24035}, {850, 2425}, {1020, 14304}, {1400, 35516}, {1441, 2182}, {1446, 51361}, {4017, 42718}, {8808, 51375}, {40149, 46974}
X(51421) = barycentric quotient X(i)/X(j) for these {i,j}: {42, 15629}, {65, 36100}, {226, 34393}, {512, 2432}, {515, 333}, {523, 2399}, {1400, 102}, {1402, 32677}, {1409, 36055}, {1455, 81}, {1880, 36121}, {2182, 21}, {2406, 99}, {2425, 110}, {8755, 29}, {21044, 15633}, {23987, 648}, {24035, 811}, {34050, 86}, {35516, 28660}, {39471, 15411}, {42718, 7257}, {46974, 1812}, {51361, 2287}, {51368, 69}, {51375, 27398}
X(51421) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 5930, 227}, {1409, 8736, 1901}
X(51422) lies on these lines: {1, 1537}, {56, 3756}, {65, 3937}, {80, 43043}, {104, 51236}, {109, 952}, {117, 515}, {221, 944}, {223, 50811}, {227, 4297}, {388, 17724}, {513, 1361}, {519, 13539}, {603, 10950}, {651, 6224}, {900, 1317}, {1062, 18481}, {1086, 1411}, {1145, 23703}, {1146, 1415}, {1319, 1846}, {1359, 6087}, {1362, 34194}, {1465, 21578}, {2099, 17365}, {3315, 3600}, {3476, 6180}, {3486, 34046}, {4551, 10609}, {4565, 6740}, {10246, 34029}, {10571, 34773}, {12832, 14584}, {15252, 18340}, {18525, 34030}, {24028, 24466}, {28186, 38945}, {37706, 46819}
X(51422) = reflection of X(i) in X(j) for these {i,j}: {10017, 39762}, {18340, 15252}, {38357, 1}
X(51422) = X(36944)-Ceva conjugate of X(1319)
X(51422) = X(i)-isoconjugate of X(j) for these (i,j): {88, 15629}, {102, 1320}, {2316, 36100}, {2399, 32665}, {2432, 3257}, {4997, 32677}
X(51422) = X(i)-Dao conjugate of X(j) for these (i, j): (23986, 4997), (35092, 2399)
X(51422) = crossdifference of every pair of points on line {2316, 2432}
X(51422) = barycentric product X(i)*X(j) for these {i,j}: {515, 3911}, {519, 34050}, {900, 2406}, {1404, 35516}, {1455, 4358}, {11700, 14628}, {37168, 51368}, {37790, 46974}
X(51422) = barycentric quotient X(i)/X(j) for these {i,j}: {515, 4997}, {900, 2399}, {902, 15629}, {1319, 36100}, {1404, 102}, {1455, 88}, {1960, 2432}, {2182, 1320}, {2406, 4555}, {2425, 901}, {3911, 34393}, {4530, 15633}, {34050, 903}
X(51423) lies on these lines: {1, 5905}, {2, 2093}, {4, 11682}, {8, 1699}, {10, 3899}, {11, 44663}, {21, 41551}, {40, 6962}, {55, 34647}, {63, 5603}, {65, 3816}, {72, 22010}, {78, 962}, {100, 28194}, {119, 517}, {145, 3586}, {149, 519}, {226, 3877}, {329, 3872}, {377, 15829}, {390, 41570}, {392, 5249}, {452, 4323}, {496, 4018}, {515, 5057}, {516, 4511}, {529, 5048}, {535, 11274}, {551, 11551}, {758, 26015}, {946, 3869}, {956, 3656}, {960, 3925}, {1056, 31164}, {1058, 11520}, {1125, 3336}, {1149, 24231}, {1319, 17768}, {1457, 17139}, {1479, 41575}, {1737, 11813}, {1770, 30144}, {1836, 5289}, {2099, 24703}, {2390, 50362}, {2476, 5837}, {2478, 3340}, {2886, 31165}, {2975, 13464}, {3035, 5183}, {3218, 44675}, {3241, 4342}, {3361, 3616}, {3434, 18406}, {3436, 7982}, {3474, 35262}, {3485, 5250}, {3576, 44447}, {3577, 6957}, {3636, 3648}, {3754, 25011}, {3813, 3962}, {3822, 3878}, {3868, 12053}, {3870, 30305}, {3884, 13407}, {3890, 21620}, {3895, 25568}, {3901, 49627}, {3916, 5901}, {3984, 5082}, {4004, 17527}, {4101, 4673}, {4187, 50193}, {4193, 4848}, {4295, 19861}, {4298, 14450}, {4640, 15950}, {4684, 4742}, {4855, 6361}, {4861, 12527}, {4870, 6690}, {4880, 16173}, {4930, 9668}, {5086, 18483}, {5087, 40663}, {5122, 34123}, {5128, 6921}, {5176, 28234}, {5330, 10106}, {5440, 28174}, {5542, 38314}, {5552, 7991}, {5657, 30852}, {5692, 25006}, {5697, 21077}, {5730, 12699}, {5903, 21616}, {5904, 49600}, {6224, 28164}, {6745, 28228}, {6836, 7971}, {7962, 28609}, {9614, 12649}, {9623, 31018}, {9785, 10382}, {9819, 11239}, {9945, 28216}, {10527, 11522}, {10589, 34744}, {10609, 28146}, {10624, 34772}, {11113, 50194}, {11362, 11681}, {12514, 24541}, {12532, 21630}, {12609, 24564}, {12635, 12701}, {14923, 21075}, {15326, 28534}, {17484, 38460}, {20070, 27383}, {21578, 39778}, {24171, 28370}, {25681, 37567}, {26892, 39550}, {27529, 43174}, {31053, 31397}, {32857, 47623}, {35631, 42448}, {44840, 49736}
X(51423) = midpoint of X(i) and X(j) for these {i,j}: {4511, 5180}, {17484, 38460}
X(51423) = reflection of X(i) in X(j) for these {i,j}: {1737, 11813}, {3218, 44675}, {5183, 3035}, {6735, 908}, {26015, 30384}, {40663, 5087}
X(51423) = X(i)-isoconjugate of X(j) for these (i,j): {104, 2334}, {909, 25430}, {2401, 34074}, {2423, 4606}, {5936, 34858}, {32641, 47915}, {34051, 34820}
X(51423) = X(i)-Dao conjugate of X(j) for these (i, j): (1145, 4866), (16586, 5936), (23980, 25430), (40613, 2334)
X(51423) = barycentric product X(i)*X(j) for these {i,j}: {391, 22464}, {517, 19804}, {908, 3616}, {1449, 3262}, {1465, 4673}, {2397, 4778}, {4811, 24029}, {5257, 17139}, {6735, 21454}, {17757, 42028}, {31903, 51367}
X(51423) = barycentric quotient X(i)/X(j) for these {i,j}: {517, 25430}, {908, 5936}, {1449, 104}, {1769, 47915}, {2183, 2334}, {2427, 8694}, {3262, 40023}, {3361, 34051}, {3616, 34234}, {4258, 2342}, {4673, 36795}, {4700, 36944}, {4765, 43728}, {4778, 2401}, {5257, 38955}, {5342, 16082}, {19804, 18816}, {37593, 2250}
X(51423) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {392, 39542, 5249}, {946, 3869, 6734}, {3878, 12047, 24987}, {3899, 18393, 10}, {5903, 21616, 24982}, {11522, 12526, 10527}
X(51424) lies on these lines: {1, 6357}, {4, 34046}, {11, 1458}, {117, 515}, {225, 12680}, {227, 6245}, {354, 1827}, {408, 23361}, {497, 6180}, {603, 6253}, {971, 38357}, {1076, 14872}, {1468, 1834}, {1496, 6284}, {1836, 17365}, {1837, 4320}, {1838, 12675}, {1854, 9799}, {3000, 33136}, {3434, 22129}, {3925, 22053}, {4293, 5721}, {4551, 37374}, {4847, 13156}, {5723, 18461}, {5787, 21147}, {6362, 6608}, {6836, 9370}, {10431, 23144}, {17747, 20752}, {18450, 33129}, {43043, 44425}
X(51424) = reflection of X(51361) in X(34050)
X(51424) = X(i)-isoconjugate of X(j) for these (i,j): {102, 2346}, {1170, 15629}, {1174, 36100}, {32008, 32677}, {36121, 47487}
X(51424) = X(i)-Dao conjugate of X(j) for these (i, j): (1212, 34393), (23986, 32008), (40606, 36100)
X(51424) = crossdifference of every pair of points on line {1174, 2432}
X(51424) = barycentric product X(i)*X(j) for these {i,j}: {142, 515}, {1229, 1455}, {1475, 35516}, {2182, 20880}, {2406, 6362}, {4847, 34050}, {13156, 51375}, {42718, 48151}
X(51424) = barycentric quotient X(i)/X(j) for these {i,j}: {142, 34393}, {354, 36100}, {515, 32008}, {1455, 1170}, {1475, 102}, {2182, 2346}, {2293, 15629}, {2406, 6606}, {2488, 2432}, {6362, 2399}, {34050, 21453}, {51361, 6605}
X(51425) lies on these lines: {2, 11456}, {3, 1661}, {4, 9820}, {5, 156}, {24, 22660}, {25, 5654}, {30, 113}, {49, 12241}, {51, 44233}, {52, 21841}, {110, 403}, {125, 44911}, {140, 12162}, {146, 37941}, {154, 18531}, {155, 3542}, {185, 16238}, {230, 1625}, {235, 1147}, {323, 46451}, {343, 10201}, {381, 8780}, {399, 47296}, {427, 46261}, {468, 13148}, {511, 37971}, {524, 45016}, {525, 47221}, {858, 14157}, {1112, 45780}, {1154, 32269}, {1351, 41585}, {1352, 19153}, {1498, 3548}, {1503, 2072}, {1576, 13557}, {1596, 13352}, {1885, 12038}, {1990, 47405}, {2070, 15448}, {2071, 32111}, {2931, 37951}, {3089, 36747}, {3147, 12163}, {3153, 35265}, {3545, 14389}, {3549, 17814}, {3564, 37942}, {3575, 5448}, {3580, 20125}, {3589, 5055}, {3850, 15806}, {3917, 16618}, {5159, 38795}, {5562, 13383}, {5655, 44214}, {5663, 44452}, {5876, 10020}, {5891, 6676}, {5899, 29181}, {5907, 7542}, {5972, 6000}, {6053, 44673}, {6102, 44232}, {6193, 6622}, {6247, 6640}, {6353, 37489}, {6677, 9730}, {6696, 18439}, {6759, 11585}, {6841, 17188}, {7499, 10170}, {7505, 11441}, {7506, 12233}, {7514, 13394}, {7552, 37636}, {7568, 14128}, {7728, 44246}, {8254, 12811}, {9306, 15760}, {9544, 12022}, {10018, 12111}, {10024, 18350}, {10151, 17702}, {10154, 37478}, {10282, 12605}, {10297, 18400}, {10575, 16196}, {10706, 44280}, {11202, 44249}, {11251, 15454}, {11438, 44211}, {11449, 18560}, {11459, 44201}, {11562, 44234}, {11563, 40111}, {11745, 13621}, {11793, 34002}, {11799, 22115}, {11911, 34810}, {12007, 45967}, {12118, 37197}, {12168, 37917}, {12225, 26882}, {12278, 18504}, {12370, 44235}, {13160, 43598}, {13292, 43844}, {13353, 50139}, {13371, 16655}, {13391, 16619}, {13473, 46686}, {13567, 18445}, {13568, 45735}, {13851, 36518}, {13861, 45089}, {14156, 14915}, {14516, 16868}, {14561, 32621}, {14788, 43614}, {14845, 18583}, {14862, 46850}, {15035, 16386}, {15063, 21663}, {15067, 25337}, {15305, 37118}, {15585, 18438}, {15873, 36749}, {16003, 37911}, {16072, 26864}, {16111, 47114}, {16657, 46030}, {16658, 31074}, {16976, 38793}, {18282, 31834}, {18404, 34782}, {18420, 35259}, {18475, 34664}, {18537, 37506}, {18914, 43817}, {18917, 26958}, {18928, 36752}, {22802, 44240}, {23047, 45286}, {23323, 30522}, {23335, 26883}, {23515, 44912}, {25739, 46818}, {26451, 47050}, {26879, 43605}, {27087, 44816}, {30714, 37984}, {30771, 32063}, {31726, 32609}, {31833, 43831}, {32110, 37935}, {32348, 40247}, {32411, 41671}, {32423, 46031}, {34153, 44283}, {35254, 44837}, {37483, 37669}, {37645, 44413}, {37948, 50434}, {38791, 47308}, {39522, 44275}, {43574, 47096}, {43898, 44247}, {44282, 44569}, {44829, 50414}
X(51425) = midpoint of X(i) and X(j) for these {i,j}: {110, 403}, {113, 51393}, {858, 14157}, {1495, 1568}, {2071, 32111}, {2072, 10540}, {5655, 44214}, {6053, 44673}, {7728, 44246}, {10706, 44280}, {11563, 40111}, {11799, 22115}, {15063, 21663}, {25739, 46818}, {34153, 44283}, {43574, 47096}
X(51425) = reflection of X(i) in X(j) for these {i,j}: {125, 44911}, {2070, 15448}, {10257, 5972}, {13473, 46686}, {16111, 47114}, {32110, 37935}, {32411, 41671}, {44569, 44282}, {47090, 14156}
X(51425) = X(i)-isoconjugate of X(j) for these (i,j): {74, 921}, {254, 35200}, {2159, 6504}, {15316, 36119}
X(51425) = X(i)-Dao conjugate of X(j) for these (i, j): (133, 254), (1511, 15316), (3163, 6504)
X(51425) = barycentric product X(i)*X(j) for these {i,j}: {30, 6515}, {155, 46106}, {920, 14206}, {1609, 3260}, {1990, 40697}, {2173, 33808}, {3542, 11064}, {39116, 51393}, {41587, 43768}
X(51425) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 6504}, {155, 14919}, {920, 2349}, {1609, 74}, {1990, 254}, {2173, 921}, {2420, 13398}, {3284, 15316}, {3542, 16080}, {6515, 1494}, {14581, 39109}, {33808, 33805}, {46106, 46746}
X(51425) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 156, 6146}, {5, 10539, 12134}, {155, 3542, 41587}, {7505, 11441, 12359}, {10018, 12111, 44158}, {10201, 15068, 343}, {10272, 46817, 11064}, {10539, 34116, 156}, {10540, 14643, 2072}
X(51426) lies on these lines: {2, 6467}, {25, 10607}, {99, 5140}, {114, 325}, {230, 8681}, {232, 15143}, {620, 2386}, {1007, 1843}, {1196, 20794}, {1368, 31367}, {1611, 19588}, {2393, 44377}, {2854, 44381}, {3491, 9729}, {3815, 9822}, {4558, 44099}, {5020, 5065}, {5889, 9742}, {5943, 7736}, {6337, 40325}, {6688, 11174}, {7710, 46850}, {7778, 11574}, {9027, 50774}, {9770, 21849}, {10011, 34382}, {11188, 34803}, {29959, 31489}, {33755, 39095}
X(51426) = midpoint of X(99) and X(5140)
X(51426) = X(34854)-Ceva conjugate of X(511)
X(51426) = X(i)-isoconjugate of X(j) for these (i,j): {287, 2129}, {336, 15369}, {1821, 40322}, {1910, 6339}
X(51426) = X(i)-Dao conjugate of X(j) for these (i, j): (11672, 6339), (40601, 40322)
X(51426) = crossdifference of every pair of points on line {2422, 40322}
X(51426) = barycentric product X(i)*X(j) for these {i,j}: {232, 19583}, {240, 2128}, {297, 19588}, {325, 1611}, {511, 6392}, {877, 2519}, {1755, 33787}, {1959, 33781}, {6338, 34854}, {6461, 6530}
X(51426) = barycentric quotient X(i)/X(j) for these {i,j}: {237, 40322}, {511, 6339}, {1611, 98}, {2128, 336}, {2211, 15369}, {2519, 879}, {6392, 290}, {6461, 6394}, {19588, 287}, {33781, 1821}, {33787, 46273}
X(51427) lies on these lines: {3, 3491}, {51, 7777}, {99, 5167}, {114, 325}, {141, 1368}, {211, 7764}, {230, 34383}, {232, 40810}, {237, 51337}, {327, 6248}, {385, 33755}, {439, 9292}, {512, 32456}, {577, 1971}, {620, 2387}, {924, 6132}, {1613, 20794}, {1975, 6310}, {2421, 9418}, {2979, 7897}, {3186, 6374}, {3221, 21191}, {3229, 3511}, {3289, 36213}, {3314, 3917}, {3815, 5943}, {4173, 7807}, {4576, 35524}, {5650, 16986}, {7779, 11673}, {7888, 41262}, {8681, 15993}, {11174, 34236}, {11325, 40811}, {32547, 33014}
X(51427) = midpoint of X(99) and X(5167)
X(51427) = reflection of X(35060) in X(620)
X(51427) = X(237)-Ceva conjugate of X(511)
X(51427) = X(i)-isoconjugate of X(j) for these (i,j): {98, 3223}, {290, 34248}, {1821, 3224}, {1910, 2998}, {1976, 18832}, {3504, 36120}
X(51427) = X(i)-Dao conjugate of X(j) for these (i, j): (76, 18024), (5976, 40162), (8623, 39927), (11672, 2998), (23301, 15630), (32746, 290), (39040, 18832), (40601, 3224), (46094, 3504)
X(51427) = crosspoint of X(1613) and X(47642)
X(51427) = crosssum of X(2998) and X(39927)
X(51427) = crossdifference of every pair of points on line {2422, 3224}
X(51427) = barycentric product X(i)*X(j) for these {i,j}: {194, 511}, {237, 6374}, {297, 20794}, {325, 1613}, {877, 2524}, {1424, 44694}, {1513, 40811}, {1740, 1959}, {1755, 17149}, {2396, 3221}, {2421, 23301}, {3186, 36212}, {5976, 47642}, {6393, 11325}, {9417, 18837}, {17209, 21080}, {20910, 23997}, {21877, 51369}, {38834, 51371}, {42717, 50516}
X(51427) = barycentric quotient X(i)/X(j) for these {i,j}: {194, 290}, {237, 3224}, {325, 40162}, {511, 2998}, {1613, 98}, {1740, 1821}, {1755, 3223}, {1959, 18832}, {2421, 3222}, {2524, 879}, {3186, 16081}, {3221, 2395}, {3289, 3504}, {6374, 18024}, {9417, 34248}, {9491, 2422}, {11325, 6531}, {17149, 46273}, {20794, 287}, {23301, 43665}, {36212, 43714}, {36213, 39927}, {47642, 36897}
X(51428) lies on these lines: {4, 9154}, {115, 512}, {125, 523}, {230, 1495}, {524, 47155}, {542, 1550}, {826, 35605}, {1499, 16278}, {1503, 16315}, {1533, 46999}, {1648, 8029}, {2393, 15993}, {2501, 6791}, {2966, 9862}, {3005, 8288}, {3124, 30452}, {3800, 34953}, {3906, 15357}, {5099, 12073}, {5191, 23967}, {5254, 10568}, {5642, 46980}, {6103, 34369}, {6699, 46634}, {7735, 41932}, {9181, 50711}, {11074, 11080}, {11645, 22329}, {13202, 46982}, {15448, 47240}, {16163, 46981}, {16316, 47296}, {16318, 44102}, {16341, 36523}, {17702, 46633}, {23991, 39691}, {32225, 47146}, {38727, 46987}
X(51428) = reflection of X(i) in X(j) for these {i,j}: {1495, 230}, {1533, 46999}, {2682, 115}, {5099, 15359}, {5642, 46980}, {13202, 46982}, {16163, 46981}, {16278, 51258}, {16316, 47296}, {46634, 6699}
X(51428) = X(i)-Ceva conjugate of X(j) for these (i,j): {542, 1640}, {6103, 6041}
X(51428) = X(i)-isoconjugate of X(j) for these (i,j): {163, 6035}, {662, 5649}, {842, 24041}, {1101, 5641}, {10411, 36096}
X(51428) = X(i)-Dao conjugate of X(j) for these (i, j): (115, 6035), (523, 5641), (1084, 5649), (3005, 842), (23967, 4590), (35582, 5468), (42426, 18020)
X(51428) = crosspoint of X(542) and X(1640)
X(51428) = crosssum of X(i) and X(j) for these (i,j): {842, 5649}, {36790, 42743}
X(51428) = crossdifference of every pair of points on line {249, 2420}
X(51428) = barycentric product X(i)*X(j) for these {i,j}: {115, 542}, {125, 6103}, {338, 5191}, {512, 18312}, {523, 1640}, {850, 6041}, {868, 34369}, {1109, 2247}, {1648, 16092}, {2088, 43087}, {5489, 35907}, {8029, 14999}, {33919, 50941}, {44114, 46786}
X(51428) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 5641}, {512, 5649}, {523, 6035}, {542, 4590}, {1640, 99}, {2247, 24041}, {3124, 842}, {5191, 249}, {6041, 110}, {6103, 18020}, {8029, 14223}, {14398, 51263}, {14999, 31614}, {18312, 670}, {22260, 14998}, {33919, 50942}, {44114, 46787}
X(51429) lies on these lines: {4, 5641}, {114, 325}, {115, 3906}, {125, 523}, {230, 6793}, {373, 18122}, {468, 524}, {512, 15357}, {525, 14120}, {542, 36166}, {620, 9181}, {626, 45284}, {684, 38987}, {690, 2682}, {826, 15359}, {842, 11005}, {868, 35088}, {1495, 16320}, {1503, 16316}, {1533, 46993}, {1648, 1649}, {3124, 23991}, {3233, 32269}, {5972, 14999}, {6388, 45212}, {6699, 46633}, {6784, 8675}, {6791, 9209}, {7794, 35077}, {7840, 15360}, {7927, 35605}, {12036, 13857}, {13202, 46988}, {15000, 23967}, {16092, 45311}, {16163, 46987}, {16280, 36189}, {16315, 47296}, {17702, 46634}, {36207, 37638}, {38727, 46981}, {39099, 41721}
X(51429) = midpoint of X(i) and X(j) for these {i,j}: {842, 11005}, {7840, 15360}, {39099, 41721}
X(51429) = reflection of X(i) in X(j) for these {i,j}: {1495, 16320}, {1533, 46993}, {2682, 5099}, {5095, 47550}, {5181, 47557}, {5642, 46986}, {9181, 620}, {13202, 46988}, {13857, 22110}, {14999, 5972}, {16092, 45311}, {16163, 46987}, {16278, 14120}, {16315, 47296}, {46633, 6699}
X(51429) = tripolar centroid of X(50942)
X(51429) = X(i)-Ceva conjugate of X(j) for these (i,j): {5967, 690}, {36892, 6333}
X(51429) = X(i)-isoconjugate of X(j) for these (i,j): {691, 36084}, {1101, 9154}, {2715, 36085}, {2966, 36142}, {32729, 36036}
X(51429) = X(i)-Dao conjugate of X(j) for these (i, j): (523, 9154), (690, 5967), (1649, 98), (2679, 32729), (21905, 1976), (23992, 2966), (35088, 892), (35582, 34761), (38987, 691), (38988, 2715), (41167, 895), (48317, 685)
X(51429) = crosspoint of X(690) and X(5967)
X(51429) = crosssum of X(691) and X(5968)
X(51429) = crossdifference of every pair of points on line {691, 2420}
X(51429) = barycentric product X(i)*X(j) for these {i,j}: {115, 50567}, {325, 1648}, {338, 9155}, {524, 868}, {690, 2799}, {2396, 33919}, {3266, 44114}, {3569, 35522}, {5967, 35088}, {6333, 14273}, {14417, 16230}, {17994, 45807}, {41172, 44146}
X(51429) = barycentric quotient X(i)/X(j) for these {i,j}: {115, 9154}, {351, 2715}, {690, 2966}, {868, 671}, {1648, 98}, {2421, 45773}, {2491, 32729}, {2642, 36084}, {2682, 35906}, {2799, 892}, {3569, 691}, {5968, 34539}, {8430, 34574}, {9155, 249}, {14273, 685}, {14417, 17932}, {21906, 1976}, {23992, 5967}, {33919, 2395}, {35522, 43187}, {41172, 895}, {44114, 111}, {44146, 41174}, {50567, 4590}
X(51430) lies on these lines: {2, 5191}, {3, 35278}, {5, 47200}, {25, 41253}, {30, 113}, {83, 21513}, {110, 1316}, {114, 35282}, {127, 6676}, {187, 44215}, {385, 419}, {511, 37906}, {523, 6593}, {524, 16321}, {542, 34094}, {754, 32223}, {804, 4107}, {868, 22505}, {1576, 40879}, {1995, 10796}, {2409, 2967}, {2790, 6795}, {2794, 5972}, {3167, 22253}, {3260, 9407}, {3292, 32515}, {3734, 4074}, {3972, 11328}, {4226, 9155}, {5663, 36177}, {5976, 17941}, {6334, 45687}, {7473, 46634}, {9544, 39906}, {10418, 18907}, {11174, 31636}, {11176, 14270}, {11272, 37335}, {11286, 35279}, {11818, 39118}, {12188, 41254}, {14880, 41238}, {18374, 32224}, {21531, 42671}, {21973, 43291}, {34319, 50146}, {35259, 35930}, {35606, 39689}, {35922, 38741}, {39072, 44377}
X(51430) = midpoint of X(i) and X(j) for these {i,j}: {110, 1316}, {1495, 51372}, {1561, 16163}, {34319, 50146}
X(51430) = reflection of X(11007) in X(5972)
X(51430) = X(35906)-Ceva conjugate of X(30)
X(51430) = crossdifference of every pair of points on line {694, 2433}
X(51430) = X(i)-isoconjugate of X(j) for these (i,j): {74, 1581}, {694, 2349}, {1494, 1967}, {1916, 2159}, {1934, 40352}, {2433, 37134}, {9468, 33805}, {36119, 36214}, {43763, 46147}
X(51430) = X(i)-Dao conjugate of X(j) for these (i, j): (1511, 36214), (3163, 1916), (8290, 1494), (8623, 35910), (19576, 74), (35078, 2394), (36213, 46147), (39031, 2159), (39043, 2349), (39044, 33805)
X(51430) = barycentric product X(i)*X(j) for these {i,j}: {30, 385}, {419, 11064}, {804, 2407}, {880, 14398}, {1495, 3978}, {1580, 14206}, {1637, 17941}, {1691, 3260}, {1926, 9406}, {1933, 46234}, {1966, 2173}, {1990, 12215}, {2420, 14295}, {3284, 17984}, {4039, 18653}, {4164, 42716}, {4240, 24284}, {5026, 9214}, {5976, 35906}, {9407, 14603}, {12829, 36891}, {35912, 39931}, {40820, 51389}
X(51430) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 1916}, {385, 1494}, {419, 16080}, {804, 2394}, {1495, 694}, {1580, 2349}, {1691, 74}, {1933, 2159}, {1966, 33805}, {2173, 1581}, {2407, 18829}, {2420, 805}, {3260, 18896}, {3284, 36214}, {5026, 36890}, {5027, 2433}, {8623, 46147}, {9406, 1967}, {9407, 9468}, {11064, 40708}, {12829, 36875}, {14206, 1934}, {14398, 882}, {14581, 17980}, {14602, 40352}, {24284, 34767}, {35906, 36897}, {36213, 35910}, {44089, 8749}, {51324, 35908}, {51372, 8842}
X(51430) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5191, 12042}, {4226, 9155, 33813}
X(51431) lies on these lines: {2, 10722}, {4, 35278}, {25, 1560}, {30, 113}, {51, 15510}, {110, 23698}, {114, 4226}, {115, 5191}, {125, 1316}, {184, 1562}, {187, 50707}, {230, 460}, {237, 6781}, {401, 43460}, {468, 46988}, {523, 5095}, {524, 16312}, {804, 32121}, {868, 35282}, {1576, 3018}, {1637, 9409}, {2452, 2847}, {2782, 24981}, {3148, 5475}, {3150, 14689}, {5355, 34396}, {5477, 42663}, {5972, 36163}, {6128, 9142}, {6791, 7737}, {6793, 35906}, {7473, 47220}, {7835, 35926}, {9155, 38738}, {9862, 41254}, {10568, 10990}, {12828, 47146}, {14003, 36997}, {14583, 41392}, {14900, 47202}, {15048, 44109}, {16303, 44102}, {18374, 47275}, {26864, 44526}, {36177, 38727}
X(51431) = midpoint of X(110) and X(36181)
X(51431) = reflection of X(i) in X(j) for these {i,j}: {125, 1316}, {13202, 1561}, {36163, 5972}, {51360, 51372}
X(51431) = X(36875)-Ceva conjugate of X(230)
X(51431) = crosspoint of X(i) and X(j) for these (i,j): {30, 35906}, {230, 36875}
X(51431) = crosssum of X(74) and X(35910)
X(51431) = crossdifference of every pair of points on line {2433, 2987}
X(51431) = X(i)-isoconjugate of X(j) for these (i,j): {74, 8773}, {1494, 36051}, {2159, 8781}, {2349, 2987}, {14380, 36105}, {32654, 33805}, {35142, 35200}, {36119, 43705}
X(51431) = X(i)-Dao conjugate of X(j) for these (i, j): (30, 36891), (114, 1494), (133, 35142), (1511, 43705), (3163, 8781), (39001, 14380), (39069, 2349), (39072, 74)
X(51431) = barycentric product X(i)*X(j) for these {i,j}: {30, 230}, {114, 35906}, {460, 11064}, {1637, 4226}, {1692, 3260}, {1733, 2173}, {1990, 3564}, {3163, 36875}, {3284, 44145}, {5477, 9214}, {6782, 36299}, {6783, 36298}, {8772, 14206}
X(51431) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 8781}, {230, 1494}, {460, 16080}, {1495, 2987}, {1692, 74}, {1733, 33805}, {1990, 35142}, {2173, 8773}, {2420, 10425}, {3163, 36891}, {3284, 43705}, {5477, 36890}, {8772, 2349}, {9406, 36051}, {9407, 32654}, {14398, 35364}, {14581, 3563}, {23347, 32697}, {35906, 40428}, {36875, 31621}, {42663, 2433}, {44099, 8749}, {51335, 35910}
X(51431) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 35278, 47200}, {35282, 39838, 868}
X(51432) lies on these lines: {3, 3419}, {8, 6261}, {10, 1479}, {55, 24982}, {63, 6925}, {72, 37406}, {78, 6834}, {100, 1737}, {119, 517}, {224, 2900}, {1210, 4855}, {1319, 26015}, {1331, 1877}, {2476, 10039}, {2886, 3057}, {3436, 41338}, {3983, 37829}, {3984, 6736}, {4847, 28236}, {5175, 5273}, {5176, 36002}, {5552, 37569}, {5794, 10966}, {5842, 13528}, {5855, 44784}, {6690, 25011}, {6959, 27385}, {6992, 17784}, {7682, 30852}, {10609, 18857}, {10915, 25415}, {10916, 37618}, {13747, 24929}, {15094, 46685}, {16465, 37566}, {20075, 25005}, {24564, 31245}, {31266, 31397}, {37797, 38460}
X(51432) = X(i)-isoconjugate of X(j) for these (i,j): {104, 34430}, {909, 39947}, {1795, 41505}, {34858, 39695}
X(51432) = X(i)-Dao conjugate of X(j) for these (i, j): (78, 1809), (16586, 39695), (23980, 39947), (25640, 41505), (40613, 34430)
X(51432) = barycentric product X(i)*X(j) for these {i,j}: {908, 12649}, {1723, 3262}
X(51432) = barycentric quotient X(i)/X(j) for these {i,j}: {517, 39947}, {908, 39695}, {1723, 104}, {2183, 34430}, {3211, 1795}, {12649, 34234}, {14571, 41505}, {34489, 34051}
X(51432) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1145, 1532, 51379}, {1532, 51379, 908}
X(51433) lies on these lines: {1, 6921}, {2, 4345}, {8, 20}, {10, 3877}, {36, 100}, {46, 49169}, {57, 12648}, {78, 6927}, {119, 517}, {145, 1420}, {224, 6765}, {497, 34711}, {516, 5176}, {529, 5183}, {644, 8074}, {956, 3654}, {1155, 38455}, {1210, 3885}, {1319, 5854}, {1320, 44675}, {1329, 37829}, {1482, 27385}, {1697, 5554}, {1737, 2802}, {1788, 36846}, {1842, 5174}, {2098, 37828}, {2136, 12649}, {2183, 21942}, {2646, 32157}, {2975, 43174}, {3035, 5048}, {3057, 3816}, {3340, 10528}, {3421, 17781}, {3434, 3583}, {3436, 7991}, {3582, 12653}, {3617, 5837}, {3621, 24391}, {3625, 37572}, {3626, 5086}, {3667, 4404}, {3680, 10529}, {3689, 5855}, {3698, 24564}, {3812, 45081}, {3822, 10039}, {3869, 6736}, {3872, 5657}, {3880, 13996}, {3890, 8582}, {3895, 18391}, {3911, 38460}, {3913, 37579}, {3925, 5836}, {4190, 37709}, {4301, 11681}, {4315, 9352}, {4421, 37740}, {4511, 28234}, {4669, 49719}, {4678, 5175}, {4861, 6684}, {5057, 28228}, {5080, 28194}, {5128, 20076}, {5193, 12641}, {5249, 31397}, {5330, 6700}, {5433, 33895}, {5440, 5844}, {5541, 41684}, {5552, 7982}, {5687, 11249}, {5690, 6734}, {5727, 20075}, {5853, 37787}, {5902, 49626}, {5903, 10915}, {6001, 46685}, {6172, 24393}, {7080, 11682}, {7354, 32537}, {7672, 41570}, {7743, 34122}, {8666, 38901}, {9436, 21272}, {9780, 25522}, {10107, 15888}, {10273, 32213}, {10912, 24914}, {11239, 11529}, {12053, 25005}, {12531, 28236}, {13463, 17606}, {13464, 27529}, {15326, 50842}, {15637, 37743}, {15803, 36977}, {17636, 32198}, {18395, 49600}, {18524, 34718}, {25006, 37358}, {25304, 49529}, {25405, 25416}, {25415, 45701}, {25438, 32760}, {26364, 30323}, {28204, 38761}, {31145, 34716}, {32049, 37567}, {36920, 41542}, {44720, 44721}
X(51433) = midpoint of X(i) and X(j) for these {i,j}: {1155, 44784}, {5541, 41684}, {7991, 41698}, {13996, 40663}
X(51433) = reflection of X(i) in X(j) for these {i,j}: {908, 6735}, {1320, 44675}, {5048, 3035}, {6735, 1145}, {25416, 25405}, {26015, 40663}, {30384, 10}, {38460, 3911}
X(51433) = X(22464)-Ceva conjugate of X(908)
X(51433) = X(i)-isoconjugate of X(j) for these (i,j): {104, 3445}, {909, 8056}, {2342, 19604}, {2401, 34080}, {2423, 27834}, {4373, 34858}, {34234, 38266}
X(51433) = X(i)-Dao conjugate of X(j) for these (i, j): (1145, 3680), (3756, 43728), (16586, 4373), (23980, 8056), (40613, 3445), (40621, 2401), (45036, 104)
X(51433) = crosspoint of X(31227) and X(39126)
X(51433) = crossdifference of every pair of points on line {2423, 38266}
X(51433) = barycentric product X(i)*X(j) for these {i,j}: {145, 908}, {517, 18743}, {1145, 31227}, {1457, 44723}, {1465, 44720}, {1743, 3262}, {2397, 3667}, {3161, 22464}, {3950, 17139}, {4248, 51367}, {5435, 6735}, {10015, 43290}, {17757, 41629}, {42754, 44724}
X(51433) = barycentric quotient X(i)/X(j) for these {i,j}: {145, 34234}, {517, 8056}, {908, 4373}, {1420, 34051}, {1457, 40151}, {1465, 19604}, {1743, 104}, {2183, 3445}, {2427, 1293}, {3052, 909}, {3262, 40014}, {3667, 2401}, {3950, 38955}, {4521, 43728}, {4849, 2250}, {6735, 6557}, {8643, 2423}, {17757, 4052}, {18743, 18816}, {20818, 1795}, {22464, 27818}, {23981, 38828}, {43290, 13136}, {44720, 36795}, {51378, 27819}
X(51433) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 5697, 41012}, {1145, 18802, 39776}, {3057, 8256, 24982}, {3913, 41687, 41575}, {4848, 12640, 145}, {5690, 10914, 6734}
X(51434) lies on these lines: {4, 5039}, {6, 3574}, {112, 29012}, {115, 2211}, {125, 14580}, {132, 1503}, {184, 13854}, {511, 5523}, {542, 41363}, {648, 5207}, {826, 21108}, {1352, 39604}, {1562, 34146}, {1570, 5095}, {1691, 6103}, {1843, 19595}, {1974, 3767}, {3162, 11550}, {3172, 36990}, {3818, 8743}, {5254, 12294}, {5922, 41489}, {6240, 41413}, {8778, 48905}, {8879, 31383}, {10516, 45141}, {18553, 41366}, {24206, 39575}, {27366, 27371}, {32250, 41358}, {35325, 51360}, {41676, 51371}
X(51434) = X(20021)-Ceva conjugate of X(1843)
X(51434) = X(i)-isoconjugate of X(j) for these (i,j): {1297, 34055}, {2419, 34072}, {2435, 4599}, {3405, 15407}, {8767, 28724}
X(51434) = X(i)-Dao conjugate of X(j) for these (i, j): (232, 20022), (3124, 2435), (15449, 2419), (23976, 1799), (39071, 28724), (40938, 35140), (50938, 83)
X(51434) = crossdifference of every pair of points on line {1176, 2435}
X(51434) = barycentric product X(i)*X(j) for these {i,j}: {132, 20021}, {141, 16318}, {427, 1503}, {441, 27376}, {826, 2409}, {1235, 42671}, {1843, 30737}, {2312, 20883}, {2445, 23285}, {2525, 23977}
X(51434) = barycentric quotient X(i)/X(j) for these {i,j}: {132, 20022}, {427, 35140}, {826, 2419}, {1503, 1799}, {1843, 1297}, {2312, 34055}, {2409, 4577}, {2445, 827}, {3005, 2435}, {8779, 28724}, {16318, 83}, {23977, 42396}, {27376, 6330}, {42671, 1176}
X(51435) lies on these lines: {1, 3732}, {3, 43163}, {9, 9746}, {10, 30618}, {31, 26267}, {101, 28850}, {105, 9318}, {114, 124}, {118, 516}, {142, 6714}, {169, 48900}, {214, 2826}, {238, 1447}, {242, 740}, {514, 11712}, {537, 9451}, {659, 812}, {676, 39470}, {908, 26231}, {927, 36905}, {1083, 21232}, {1125, 1565}, {1146, 2784}, {1212, 48932}, {1281, 8932}, {1282, 14942}, {1360, 39063}, {1376, 3923}, {2246, 13576}, {2310, 14543}, {2607, 20677}, {3035, 3452}, {3573, 51381}, {3742, 33682}, {4366, 27947}, {4471, 24424}, {4650, 5435}, {4672, 17754}, {4724, 39046}, {4974, 7193}, {5179, 28845}, {6654, 8300}, {6682, 36540}, {8074, 28849}, {24315, 25375}, {24320, 24325}, {24329, 24336}, {25354, 25361}, {28877, 50896}, {29043, 31897}
X(51435) = midpoint of X(i) and X(j) for these {i,j}: {1, 3732}, {1282, 14942}
X(51435) = reflection of X(i) in X(j) for these {i,j}: {1565, 1125}, {50441, 28346}
X(51435) = X(i)-isoconjugate of X(j) for these (i,j): {103, 291}, {292, 36101}, {295, 36122}, {335, 911}, {660, 2424}, {677, 876}, {1911, 18025}, {2400, 34067}, {3252, 9503}, {4444, 36039}, {7077, 43736}
X(51435) = X(i)-Dao conjugate of X(j) for these (i, j): (1566, 4444), (6651, 18025), (19557, 36101), (23972, 335), (35119, 2400), (39029, 103), (39077, 22116), (40869, 40217), (46095, 295), (50441, 4518)
X(51435) = crosspoint of X(1447) and X(6654)
X(51435) = crosssum of X(3252) and X(7077)
X(51435) = crossdifference of every pair of points on line {292, 2424}
X(51435) = barycentric product X(i)*X(j) for these {i,j}: {238, 30807}, {239, 516}, {242, 26006}, {350, 910}, {659, 42719}, {676, 3570}, {740, 14953}, {812, 2398}, {1447, 40869}, {1456, 3975}, {1914, 35517}, {3685, 43035}, {4148, 23973}, {4241, 24459}, {6654, 50441}, {10030, 41339}, {17747, 33295}, {28346, 40725}, {31905, 51366}
X(51435) = barycentric quotient X(i)/X(j) for these {i,j}: {238, 36101}, {239, 18025}, {516, 335}, {676, 4444}, {812, 2400}, {910, 291}, {1429, 43736}, {1914, 103}, {2201, 36122}, {2210, 911}, {2398, 4562}, {2426, 813}, {7193, 1815}, {8632, 2424}, {9502, 22116}, {14953, 18827}, {17747, 43534}, {26006, 337}, {27918, 15634}, {30807, 334}, {35517, 18895}, {40869, 4518}, {41339, 4876}, {42719, 4583}, {43035, 7233}, {50441, 40217}
X(51436) lies on these lines: {25, 14827}, {32, 7083}, {37, 44661}, {41, 21746}, {101, 511}, {118, 516}, {169, 31394}, {197, 16283}, {213, 1042}, {220, 573}, {228, 21795}, {512, 798}, {991, 3207}, {1284, 18785}, {1495, 32739}, {1500, 2333}, {2200, 20970}, {2205, 21813}, {3185, 16588}, {3271, 9454}, {3730, 48886}, {4251, 39543}, {5011, 29309}, {5452, 15494}, {6603, 29311}, {13329, 20672}, {15507, 20605}, {19554, 20670}, {20459, 20662}, {20991, 30706}, {22080, 40586}, {24045, 48940}, {27624, 27634}
X(51436) = midpoint of X(101) and X(41323)
X(51436) = isogonal conjugate of the isotomic conjugate of X(17747)
X(51436) = X(i)-isoconjugate of X(j) for these (i,j): {81, 18025}, {86, 36101}, {103, 274}, {286, 1815}, {310, 911}, {333, 43736}, {662, 2400}, {677, 7199}, {799, 2424}, {4567, 15634}, {9503, 30941}, {17206, 36122}, {36056, 44129}
X(51436) = X(i)-Dao conjugate of X(j) for these (i, j): (1084, 2400), (20622, 44129), (23972, 310), (38996, 2424), (39077, 18157), (40586, 18025), (40600, 36101), (40627, 15634), (46095, 17206), (50441, 28660)
X(51436) = crosssum of X(i) and X(j) for these (i,j): {86, 14953}, {333, 30941}, {18025, 36101}
X(51436) = crossdifference of every pair of points on line {86, 2400}
X(51436) = barycentric product X(i)*X(j) for these {i,j}: {6, 17747}, {25, 51366}, {37, 910}, {42, 516}, {65, 41339}, {71, 1886}, {210, 1456}, {213, 30807}, {512, 2398}, {523, 2426}, {647, 41321}, {676, 4557}, {798, 42719}, {1020, 46392}, {1334, 43035}, {1400, 40869}, {1500, 14953}, {1880, 51376}, {1918, 35517}, {2054, 28346}, {2333, 26006}, {4524, 23973}, {9502, 18785}
X(51436) = barycentric quotient X(i)/X(j) for these {i,j}: {42, 18025}, {213, 36101}, {512, 2400}, {516, 310}, {669, 2424}, {910, 274}, {1402, 43736}, {1886, 44129}, {1918, 103}, {2200, 1815}, {2205, 911}, {2398, 670}, {2426, 99}, {3122, 15634}, {9502, 18157}, {17747, 76}, {30807, 6385}, {40869, 28660}, {41321, 6331}, {41339, 314}, {42719, 4602}, {51366, 305}
X(51436) = {X(2205),X(21813)}-harmonic conjugate of X(40984)
X(51437) lies on these lines: {6, 64}, {24, 41412}, {32, 1843}, {51, 17409}, {112, 511}, {132, 1503}, {182, 8743}, {184, 3162}, {232, 1691}, {459, 34407}, {512, 1692}, {648, 12215}, {1249, 25406}, {1350, 8778}, {1495, 14580}, {1899, 8879}, {1974, 2207}, {1976, 34854}, {2030, 8744}, {2032, 15630}, {2393, 34190}, {3199, 44091}, {3292, 35325}, {5039, 39588}, {5085, 45141}, {5092, 39575}, {5523, 29012}, {6000, 34137}, {6403, 41413}, {11550, 13854}, {14561, 41370}, {20031, 47388}, {20232, 33581}, {22352, 40938}, {36417, 42295}, {40130, 44080}, {41361, 46264}
X(51437) = midpoint of X(112) and X(41363)
X(51437) = isogonal conjugate of the isotomic conjugate of X(16318)
X(51437) = polar conjugate of the isotomic conjugate of X(42671)
X(51437) = X(i)-Ceva conjugate of X(j) for these (i,j): {1976, 1974}, {16318, 42671}, {34854, 44099}, {43717, 25}
X(51437) = crosspoint of X(i) and X(j) for these (i,j): {4, 34129}, {25, 43717}
X(51437) = crosssum of X(i) and X(j) for these (i,j): {3, 34137}, {69, 441}, {3926, 6393}
X(51437) = crossdifference of every pair of points on line {69, 2419}
X(51437) = X(i)-isoconjugate of X(j) for these (i,j): {63, 35140}, {304, 1297}, {326, 6330}, {662, 2419}, {799, 2435}, {3926, 8767}, {4143, 36092}, {4592, 43673}, {15407, 46238}
X(51437) = X(i)-Dao conjugate of X(j) for these (i, j): (1084, 2419), (3162, 35140), (5139, 43673), (15259, 6330), (23976, 305), (38996, 2435), (39071, 3926), (39073, 6393), (50938, 76)
X(51437) = barycentric product X(i)*X(j) for these {i,j}: {4, 42671}, {6, 16318}, {19, 2312}, {25, 1503}, {132, 1976}, {393, 8779}, {441, 2207}, {512, 2409}, {523, 2445}, {607, 43045}, {647, 23977}, {810, 24024}, {1096, 8766}, {1843, 21458}, {1974, 30737}, {2489, 34211}, {6531, 9475}, {6793, 8749}, {8753, 35282}, {8791, 28343}, {8882, 51363}, {15639, 34212}, {23976, 43717}, {34156, 34854}, {34397, 43089}
X(51437) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 35140}, {512, 2419}, {669, 2435}, {1503, 305}, {1974, 1297}, {2207, 6330}, {2312, 304}, {2409, 670}, {2445, 99}, {2489, 43673}, {8779, 3926}, {9475, 6393}, {14601, 15407}, {16318, 76}, {23977, 6331}, {27369, 46164}, {28343, 37804}, {30737, 40050}, {36417, 43717}, {42671, 69}, {51363, 28706}
X(51437) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 1968, 12294}, {1692, 2211, 44102}, {1692, 14581, 2211}, {2207, 40825, 1974}, {36417, 42295, 44079}
X(51438) lies on these lines: {6, 35297}, {23, 38940}, {30, 69}, {99, 524}, {114, 325}, {141, 7934}, {187, 14645}, {193, 13586}, {230, 10754}, {237, 36892}, {297, 877}, {542, 44369}, {599, 8352}, {620, 5107}, {1350, 14907}, {1351, 37459}, {1384, 1992}, {3564, 13188}, {3620, 14041}, {3793, 50249}, {3815, 22486}, {4563, 32269}, {5182, 32459}, {5468, 7426}, {5476, 37647}, {5477, 32456}, {5969, 15993}, {5999, 15589}, {6390, 9301}, {6656, 44453}, {7664, 40112}, {7763, 11477}, {7774, 11173}, {7782, 8550}, {8586, 44380}, {9146, 15360}, {9855, 11160}, {10008, 32827}, {10011, 14853}, {10411, 32217}, {10513, 40236}, {10519, 34229}, {10997, 50248}, {11676, 32817}, {12215, 34380}, {14360, 44555}, {15638, 37745}, {15980, 18906}, {20080, 33265}, {21356, 37350}, {30786, 44569}, {32220, 36180}, {32515, 50640}, {32819, 34507}, {36166, 47468}, {36196, 47473}, {37688, 50977}
X(51438) = midpoint of X(9855) and X(11160)
X(51438) = reflection of X(i) in X(j) for these {i,j}: {325, 50567}, {1351, 37459}, {1992, 27088}, {5107, 620}, {5477, 32456}, {6393, 51374}, {8352, 599}, {8586, 44380}, {10754, 230}, {15980, 48876}, {32220, 36180}, {36166, 47468}, {36196, 47473}, {39099, 6390}, {47286, 15993}, {50249, 3793}, {51396, 51397}
X(51438) = X(i)-isoconjugate of X(j) for these (i,j): {1821, 39238}, {1910, 21448}, {2422, 37216}
X(51438) = X(i)-Dao conjugate of X(j) for these (i, j): (5976, 5485), (11147, 98), (11672, 21448), (35133, 2395), (40601, 39238)
X(51438) = crossdifference of every pair of points on line {2422, 9171}
X(51438) = barycentric product X(i)*X(j) for these {i,j}: {325, 1992}, {511, 11059}, {1499, 2396}, {4232, 6393}, {36277, 46238}, {42724, 51369}
X(51438) = barycentric quotient X(i)/X(j) for these {i,j}: {237, 39238}, {325, 5485}, {511, 21448}, {1384, 1976}, {1499, 2395}, {1992, 98}, {2396, 35179}, {2421, 1296}, {4232, 6531}, {8644, 2422}, {11059, 290}, {12093, 13492}, {27088, 5967}, {35266, 35906}, {36277, 1910}
X(51438) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {325, 50567, 6393}, {325, 51374, 50567}, {50567, 51396, 51397}, {51396, 51397, 325}
X(51439) lies on these lines: {52, 7763}, {66, 69}, {76, 1216}, {99, 13754}, {114, 325}, {183, 3917}, {232, 2421}, {315, 10625}, {394, 1971}, {571, 1993}, {924, 6563}, {1007, 3060}, {1078, 5447}, {1154, 6390}, {1350, 15574}, {1975, 5562}, {3289, 36790}, {3567, 32829}, {3819, 37688}, {3926, 11412}, {3933, 6101}, {5012, 44180}, {5446, 7752}, {5462, 7769}, {5640, 34803}, {5889, 6337}, {5891, 11185}, {5907, 32819}, {5943, 37647}, {6403, 10008}, {7750, 15644}, {7767, 10627}, {7773, 45186}, {7776, 37484}, {7782, 40647}, {7998, 34229}, {7999, 32828}, {8681, 44369}, {11459, 32815}, {12058, 20477}, {13137, 40428}, {15024, 32839}, {15058, 32826}, {15575, 32964}, {15589, 33884}, {35296, 43705}, {35297, 50387}, {36212, 41270}, {39807, 46236}
X(51439) = reflection of X(325) in X(51386)
X(51439) = X(44132)-Ceva conjugate of X(36212)
X(51439) = X(i)-isoconjugate of X(j) for these (i,j): {91, 1976}, {293, 14593}, {1820, 6531}, {1910, 2165}, {2351, 36120}, {2395, 36145}, {14601, 20571}
X(51439) = X(i)-Dao conjugate of X(j) for these (i, j): (132, 14593), (577, 248), (5976, 5392), (11672, 2165), (34116, 1976), (39013, 2395), (39040, 91), (46094, 2351)
X(51439) = barycentric product X(i)*X(j) for these {i,j}: {24, 6393}, {47, 46238}, {297, 9723}, {317, 36212}, {325, 1993}, {511, 7763}, {924, 2396}, {1147, 44132}, {1959, 44179}, {2421, 6563}, {6333, 41679}, {11547, 51386}, {18605, 42703}, {18883, 51383}, {31635, 36790}, {42700, 51369}
X(51439) = barycentric quotient X(i)/X(j) for these {i,j}: {24, 6531}, {47, 1910}, {232, 14593}, {297, 847}, {317, 16081}, {325, 5392}, {511, 2165}, {571, 1976}, {877, 30450}, {924, 2395}, {1147, 248}, {1748, 36120}, {1959, 91}, {1993, 98}, {2396, 46134}, {2421, 925}, {3289, 2351}, {6393, 20563}, {6563, 43665}, {7763, 290}, {9723, 287}, {14966, 32734}, {23997, 36145}, {30451, 878}, {31635, 34536}, {34952, 2422}, {36212, 68}, {41270, 41271}, {41679, 685}, {44179, 1821}, {46238, 20571}, {51383, 37802}, {51393, 35906}
X(51439) = {X(325),X(51383)}-harmonic conjugate of X(51386)
X(51440) lies on these lines: {51, 37647}, {69, 1369}, {76, 6101}, {99, 1154}, {114, 325}, {143, 7769}, {183, 2979}, {302, 36980}, {303, 36978}, {315, 37484}, {316, 13391}, {1078, 10627}, {1510, 41298}, {1975, 11412}, {1994, 2965}, {2393, 44369}, {3917, 37688}, {5562, 32819}, {5989, 39807}, {6102, 7782}, {6243, 7763}, {7750, 10625}, {7752, 10263}, {9723, 39231}, {11002, 34803}, {11185, 23039}, {13340, 14907}, {14128, 15031}, {15574, 33878}, {33884, 34229}, {34373, 44361}, {34375, 44362}
X(51440) = reflection of X(16979) in the Lemoine axis
X(51440) = X(i)-isoconjugate of X(j) for these (i,j): {1910, 2963}, {1976, 2962}, {2395, 36148}
X(51440) = X(i)-Dao conjugate of X(j) for these (i, j): (5976, 11140), (11672, 2963), (39018, 2395), (39040, 2962)
X(51440) = crossdifference of every pair of points on line {2422, 37085}
X(51440) = barycentric product X(i)*X(j) for these {i,j}: {49, 44132}, {297, 44180}, {325, 1994}, {511, 7769}, {1510, 2396}, {2421, 41298}, {2964, 46238}, {3518, 6393}, {30529, 51383}, {32002, 36212}
X(51440) = barycentric quotient X(i)/X(j) for these {i,j}: {49, 248}, {297, 93}, {325, 11140}, {511, 2963}, {877, 38342}, {1510, 2395}, {1959, 2962}, {1994, 98}, {2396, 46139}, {2421, 930}, {2964, 1910}, {2965, 1976}, {3518, 6531}, {7769, 290}, {14966, 32737}, {23997, 36148}, {32002, 16081}, {36212, 3519}, {41298, 43665}, {44132, 20572}, {44180, 287}
X(51441) lies on the cubic K741 and these lines: {2, 36822}, {5, 14265}, {30, 98}, {115, 512}, {125, 31174}, {230, 237}, {290, 325}, {338, 523}, {385, 14957}, {460, 6531}, {524, 20021}, {597, 5967}, {685, 47158}, {868, 879}, {882, 44114}, {1084, 2489}, {1976, 1989}, {2086, 2422}, {2395, 9178}, {3143, 43665}, {4079, 21043}, {5191, 48721}, {5254, 32540}, {5306, 35906}, {6036, 47079}, {6394, 40428}, {6543, 17747}, {7697, 51259}, {9124, 41146}, {9140, 36826}, {10602, 36207}, {12188, 14999}, {13137, 15535}, {16081, 16098}, {18105, 31644}, {23291, 36893}, {39022, 41881}, {39023, 41880}, {39663, 44227}, {43920, 50344}
X(51441) = midpoint of X(i) and X(j) for these {i,j}: {98, 34175}, {385, 14957}
X(51441) = reflection of X(i) in X(j) for these {i,j}: {237, 230}, {325, 21531}, {47079, 6036}
X(51441) = isotomic conjugate of the isogonal conjugate of X(15630)
X(51441) = X(i)-Ceva conjugate of X(j) for these (i,j): {98, 2395}, {6531, 2422}, {18024, 43665}, {36897, 523}
X(51441) = X(2086)-cross conjugate of X(34294)
X(51441) = crosspoint of X(i) and X(j) for these (i,j): {98, 2395}, {18024, 43665}
X(51441) = crosssum of X(i) and X(j) for these (i,j): {511, 2421}, {9418, 14966}
X(51441) = trilinear pole of line {3124, 8029}
X(51441) = crossdifference of every pair of points on line {2421, 14966}
X(51441) = X(i)-isoconjugate of X(j) for these (i,j): {99, 23997}, {163, 2396}, {237, 24037}, {249, 1959}, {325, 1101}, {511, 24041}, {662, 2421}, {799, 14966}, {877, 4575}, {1755, 4590}, {3289, 46254}, {4230, 4592}, {4556, 42717}, {4567, 17209}, {4570, 51369}, {9417, 34537}, {15631, 36084}, {23357, 46238}, {24000, 51386}, {40703, 47390}
X(51441) = barycentric product X(i)*X(j) for these {i,j}: {76, 15630}, {98, 115}, {125, 6531}, {248, 2970}, {287, 8754}, {290, 3124}, {338, 1976}, {512, 43665}, {523, 2395}, {594, 43920}, {850, 2422}, {868, 41932}, {878, 14618}, {879, 2501}, {1084, 18024}, {1109, 1910}, {1365, 15628}, {1648, 9154}, {1821, 2643}, {2715, 23105}, {2966, 8029}, {3708, 36120}, {5489, 20031}, {12079, 35906}, {14601, 23962}, {16081, 20975}, {20021, 34294}, {22260, 43187}, {34536, 44114}
X(51441) = barycentric quotient X(i)/X(j) for these {i,j}: {98, 4590}, {115, 325}, {125, 6393}, {287, 47389}, {290, 34537}, {512, 2421}, {523, 2396}, {669, 14966}, {798, 23997}, {868, 32458}, {878, 4558}, {879, 4563}, {1084, 237}, {1109, 46238}, {1648, 50567}, {1821, 24037}, {1910, 24041}, {1976, 249}, {2086, 36213}, {2088, 51383}, {2395, 99}, {2422, 110}, {2489, 4230}, {2501, 877}, {2643, 1959}, {2679, 46888}, {2966, 31614}, {2970, 44132}, {2971, 232}, {3120, 51370}, {3122, 17209}, {3124, 511}, {3125, 51369}, {3269, 51386}, {3569, 15631}, {4117, 9417}, {4705, 42717}, {6041, 42743}, {6388, 51374}, {6531, 18020}, {8029, 2799}, {8288, 51397}, {8754, 297}, {9427, 9418}, {14600, 47390}, {14601, 23357}, {15628, 6064}, {15630, 6}, {18024, 44168}, {20975, 36212}, {21906, 9155}, {22260, 3569}, {23099, 2491}, {32696, 47443}, {34294, 20022}, {36120, 46254}, {36897, 39292}, {39691, 51371}, {42068, 2211}, {43665, 670}, {43920, 1509}, {44114, 36790}
X(51441) = {X(2),X(36874)}-harmonic conjugate of X(36822)
See Antreas Hatzipolakis and Francisco Javier García Capitán, euclid 5385.
X(51442) lies on these lines: {8,36590}, {11,522}, {513,38385}, {523,3259}, {765,17777}, {900,6075}, {1086,45320}, {1146,4944}, {1168,10774}, {2618,8286}, {2802,13756}, {2969,16228}, {3120,30591}, {4009,6735}, {4086,6741}, {4762,40629}, {4976,46101}, {9001,44013}, {21132,23615}, {34590,43909}, {44675,44901}
See Ivan Pavlov, euclid 5387.
X(51443) lies on these lines: {21, 1509}, {25, 1396}, {31, 1412}, {41, 58}, {55, 81}, {105, 1014}, {593, 2194}, {609, 2279}, {884, 3733}
See Ivan Pavlov, euclid 5387.
X(51444) lies on these lines: {25, 262}, {32, 54}, {95, 98}, {97, 184}
See Ivan Pavlov, euclid 5387.
X(51445) lies on this line: {197, 2985}
See Ivan Pavlov, euclid 5387.
X(51446) lies on these lines: {4, 616}, {25, 2981}, {112, 2380}, {378, 38403}, {403, 11119}, {463, 18384}, {1843, 2914}, {3563, 10409}, {7576, 11117}, {8739, 16459}, {8740, 34321}
X(51446) = polar conjugate of X(41000)
X(51446) = isogonal conjugate of the anticomplement of X(11542)
X(51446) = isogonal conjugate of the isotomic conjugate of X(38428)
X(51446) = polar conjugate of the isotomic conjugate of X(2981)
X(51446) = X(38428)-Ceva conjugate of X(2981)
X(51446) = X(186)-cross conjugate of X(51447)
X(51446) = cevapoint of X(25) and X(8739)
X(51446) = crosspoint of X(3440) and X(3489)
X(51446) = crosssum of X(616) and X(627)
X(51446) = trilinear pole of line {2489, 8740}
X(51446) = X(i)-isoconjugate of X(j) for these (i,j): {48, 41000}, {63, 396}, {293, 51388}, {326, 463}, {656, 35314}, {14208, 35329}
X(51446) = X(i)-Dao conjugate of X(j) for these (i, j): (132, 51388), (1249, 41000), (3162, 396), (15259, 463), (40596, 35314)
X(51446) = barycentric product X(i)*X(j) for these {i,j}: {4, 2981}, {6, 38428}, {25, 40707}, {340, 11084}, {470, 16459}, {471, 2380}, {473, 34321}, {2501, 10409}, {8737, 38403}, {8739, 11119}, {8740, 11117}
X(51446) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 41000}, {25, 396}, {112, 35314}, {186, 14922}, {232, 51388}, {2207, 463}, {2380, 40710}, {2981, 69}, {8737, 43085}, {8739, 618}, {8740, 532}, {10409, 4563}, {10642, 6671}, {11084, 265}, {16459, 40709}, {34321, 40712}, {34397, 19294}, {38428, 76}, {40707, 305}, {44102, 9115}
See Ivan Pavlov, euclid 5387.
X(51447) lies on these lines: {4, 617}, {25, 6151}, {112, 2381}, {378, 38404}, {403, 11120}, {462, 18384}, {1843, 2914}, {3563, 10410}, {7576, 11118}, {8739, 34322}, {8740, 16460}
X(51447) = polar conjugate of X(41001)
X(51447) = isogonal conjugate of the anticomplement of X(11543)
X(51447) = isogonal conjugate of the isotomic conjugate of X(38427)
X(51447) = polar conjugate of the isotomic conjugate of X(6151)
X(51447) = X(38427)-Ceva conjugate of X(6151)
X(51447) = X(186)-cross conjugate of X(51446)
X(51447) = cevapoint of X(25) and X(8740)
X(51447) = crosspoint of X(3441) and X(3490)
X(51447) = crosssum of X(617) and X(628)
X(51447) = trilinear pole of line {2489, 8739}
X(51447) = X(i)-isoconjugate of X(j) for these (i,j): {48, 41001}, {63, 395}, {293, 51387}, {326, 462}, {656, 35315}, {14208, 35330}
X(51447) = X(i)-Dao conjugate of X(j) for these (i, j): (132, 51387), (1249, 41001), (3162, 395), (15259, 462), (40596, 35315)
X(51447) = barycentric product X(i)*X(j) for these {i,j}: {4, 6151}, {6, 38427}, {25, 40706}, {340, 11089}, {470, 2381}, {471, 16460}, {472, 34322}, {2501, 10410}, {8738, 38404}, {8739, 11118}, {8740, 11120}
X(51447) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 41001}, {25, 395}, {112, 35315}, {186, 14921}, {232, 51387}, {2207, 462}, {2381, 40709}, {6151, 69}, {8738, 43086}, {8739, 533}, {8740, 619}, {10410, 4563}, {10641, 6672}, {11089, 265}, {16460, 40710}, {34322, 40711}, {34397, 19295}, {38427, 76}, {40706, 305}, {44102, 9117}
See Ivan Pavlov, euclid 5387.
X(51448) lies on this line: {801, 1661}
See Ivan Pavlov, euclid 5387.
X(51449) lies on these lines: {43, 81}, {58, 2176}
See Ivan Pavlov, euclid 5387.
X(51450) lies on these lines: {83, 194}, {251, 1613}
As a point on the Euler line, X(51451) has Shinagawa coefficients {E^2 + 8*E*F - 4 (5*F^2 + S^2), -3*E^2 - 16*E*F - 4*F^2 + 12*S^2}.
See Tran Quang Hung and Ercole Suppa, euclid 5403.
X(51451) lies on inverse in Euler asymptotic hyperbola of X(30) and these lines: {2,3}, {523,12359}, {2452,18951}, {3258,5562}, {10539,16319}, {15112,23293}
X(51451) = reflection of X(i) in X(j)X(k) for these (i,j,k): (3,523,44158), (5,523,5449)
X(51451) = trilinear quotient X(3)/X(35235)
See Antreas Hatzipolakis and Peter Moses, euclid 5409.
X(51452) lies on this line: {3024, 6741}
X(51452) = barycentric quotient X(44409)/X(38340)
As a point on the Euler line, X(51453) has Shinagawa coefficients {4*(E-2*F)*F*(E+F)^3-(E-2*F)^2(E+2*F)S^2,-4*F*(E+F)^3(E+2*F)+(E-2*F)^3*S^2}.
See Tran Quang Hung and Ercole Suppa, euclid 5403.
X(51453) lies on inverse in Euler asymptotic hyperbola of X(30) and this line: {2,3}
X(51454) lies on the cubic K1281 and these lines: {2, 38652}, {3, 114}, {112, 7807}, {132, 37071}, {232, 34129}, {325, 11610}, {339, 3767}, {394, 4121}, {538, 34897}, {1297, 1513}, {2799, 44534}, {2974, 6389}, {3564, 17974}, {3926, 28405}, {5481, 37450}, {6393, 10766}, {6720, 32954}, {10718, 35297}, {13219, 16925}, {14919, 44767}, {28697, 28724}
X(51454) = isogonal conjugate of X(41363)
X(51454) = circumcircle-inverse of X(39644)
X(51454) = X(i)-isoconjugate of X(j) for these (i,j): {1, 41363}, {19, 37183}
X(51454) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 41363), (6, 37183)
X(51454) = cevapoint of X(684) and X(38356)
X(51454) = trilinear pole of line {520, 6467}
X(51454) = barycentric product X(i)*X(j) for these {i,j}: {305, 39644}, {525, 44767}, {3926, 39645}, {40708, 50732}
X(51454) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 37183}, {6, 41363}, {39644, 25}, {39645, 393}, {44767, 648}, {50732, 419}
X(51455) lies on the cubic K1281 and these lines: {3, 512}, {98, 325}, {805, 3563}, {2080, 32654}, {2421, 13137}, {2987, 14510}, {3398, 45915}, {35002, 45938}
X(51455) = isogonal conjugate of X(46039)
X(51455) = X(i)-isoconjugate of X(j) for these (i,j): {1, 46039}, {1733, 2698}, {8772, 46142}
X(51455) = X(3)-Dao conjugate of X(46039)
X(51455) = barycentric product X(2782)*X(2987)
X(51455) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 46039}, {2987, 46142}, {16068, 47734}, {32654, 2698}, {34157, 51229}, {35364, 46040}, {48452, 14265}
X(51455) = {X(2065),X(10425)}-harmonic conjugate of X(42065)
X(51456) lies on the cubic K1281 and these lines: {3, 523}, {30, 50}, {67, 3564}, {98, 858}, {687, 691}, {1494, 7799}, {3580, 34310}, {5877, 18281}, {6103, 16188}, {7471, 47208}, {14611, 34834}, {14911, 44280}, {17986, 51262}, {24975, 43090}, {34150, 39295}, {37118, 38936}
X(51456) = X(842)-isoconjugate of X(1725)
X(51456) = X(i)-Dao conjugate of X(j) for these (i, j): (23967, 3580), (42426, 403)
X(51456) = barycentric product X(i)*X(j) for these {i,j}: {542, 2986}, {1640, 18878}, {5191, 40832}, {7473, 15421}, {10420, 18312}, {14999, 15328}, {15454, 51227}
X(51456) = barycentric quotient X(i)/X(j) for these {i,j}: {542, 3580}, {2247, 1725}, {2986, 5641}, {5191, 3003}, {6041, 21731}, {6103, 403}, {7473, 16237}, {10420, 5649}, {14910, 842}, {15328, 14223}, {15454, 51228}, {18878, 6035}, {23968, 41512}, {48451, 14264}
X(51457) lies on the cubic K1281 and these lines: {3, 690}, {98, 35191}, {110, 468}, {113, 2420}, {1637, 34810}, {1691, 14982}, {2986, 35235}, {3003, 14559}, {4240, 20772}, {5063, 46129}, {15454, 41079}
X(51457) = X(i)-isoconjugate of X(j) for these (i,j): {2349, 2493}, {14984, 36119}
X(51457) = X(1511)-Dao conjugate of X(14984)
X(51457) = barycentric product X(11064)*X(40118)
X(51457) = barycentric quotient X(i)/X(j) for these {i,j}: {1495, 2493}, {2407, 14221}, {2420, 7468}, {3284, 14984}, {35906, 34175}, {40083, 35910}, {40118, 16080}, {48453, 38939}
X(51458) lies on the cubic K1281 and these lines: {3, 49}, {50, 647}, {96, 275}, {97, 23195}, {98, 858}, {186, 8154}, {250, 11657}, {323, 14652}, {340, 47201}, {421, 44375}, {450, 47208}, {468, 1576}, {511, 13558}, {648, 47143}, {852, 23200}, {933, 14165}, {1495, 14673}, {1516, 17702}, {1613, 22391}, {1629, 6240}, {1899, 23606}, {1993, 2351}, {3291, 10311}, {6146, 19210}, {7507, 21268}, {7778, 10163}, {9512, 41202}, {16319, 38861}, {18374, 44890}, {19165, 21284}, {34834, 43969}, {34986, 50648}
X(51458) = reflection of X(13557) in X(14889)
X(51458) = reflection of X(13558) in the Lemoine axis
X(51458) = circumcircle-inverse of X(184)
X(51458) = Moses-radical-circle-inverse of X(1971)
X(51458) = isogonal conjugate of the polar conjugate of X(44375)
X(51458) = crosssum of X(4) and X(41203)
X(51458) = crossdifference of every pair of points on line {5, 2501}
X(51458) = barycentric product X(i)*X(j) for these {i,j}: {3, 44375}, {394, 421}
X(51458) = barycentric quotient X(i)/X(j) for these {i,j}: {421, 2052}, {44375, 264}
X(51458) = {X(50),X(15139)}-harmonic conjugate of X(44886)
X(51459) lies on the cubic K1281 and these lines: {2, 14885}, {3, 305}, {468, 4577}, {827, 37803}, {858, 16095}, {3266, 9076}, {3763, 10160}, {5157, 26190}, {7836, 10130}, {18105, 23285}
X(51459) = circumcircle-inverse of X(1799)
X(51459) = X(9076)-Ceva conjugate of X(1799)
X(51459) = barycentric product X(1799)*X(19577)
X(51459) = barycentric quotient X(i)/X(j) for these {i,j}: {8869, 46154}, {19577, 427}
X(51460) lies on these lines: {3, 115}, {24, 5139}, {182, 12893}, {186, 691}, {3565, 5966}, {5961, 15475}, {6644, 14655}, {7502, 14650}, {11616, 25644}, {13335, 22467}, {34217, 37814}, {37917, 41521}
X(51460) = midpoint of X(i) and X(j) for these {i,j}: {3, 2079}, {3565, 14669}
X(51460) = circumcircle-inverse of X(6321)
X(51460) = {X(3565),X(15565)}-harmonic conjugate of X(14669)
See Antreas Hatzipolakis and Peter Moses, euclid 5409.
X(51461) lies on this line: {3023, 3907}
X(51461) = barycentric quotient X(44410)/X(37137)
See Antreas Hatzipolakis and Peter Moses, euclid 5409.
X(51462) lies on these lines: {758, 3028}, {1155, 6718}, {1836, 17073}, {2361, 17923}, {4552, 21920}, {4854, 18635}, {11064, 17768}, {15668, 32776}
X(51462) = X(759)-isoconjugate of X(37741)
X(51462) = X(i)-Dao conjugate of X(j) for these (i, j): (17073, 6740), (34586, 37741)
X(51462) = crosspoint of X(860) and X(41804)
X(51462) = barycentric product X(i)*X(j) for these {i,j}: {860, 17073}, {1836, 3936}, {17860, 18593}, {17923, 21912}, {41804, 46835}
X(51462) = barycentric quotient X(i)/X(j) for these {i,j}: {1836, 24624}, {2245, 37741}, {3936, 34409}, {4336, 2341}, {46835, 6740}
See Antreas Hatzipolakis and Peter Moses, euclid 5409.
X(51463) lies on these lines: {1, 5791}, {2, 3711}, {7, 31140}, {8, 3304}, {9, 31146}, {10, 17609}, {11, 518}, {12, 3555}, {36, 9945}, {38, 4854}, {55, 5744}, {57, 4863}, {63, 3058}, {72, 37722}, {100, 41341}, {141, 33120}, {142, 354}, {144, 497}, {145, 5218}, {149, 17768}, {191, 15172}, {200, 17728}, {210, 5316}, {214, 519}, {239, 26007}, {329, 11238}, {385, 29840}, {442, 3881}, {495, 17057}, {496, 5904}, {523, 13277}, {524, 9318}, {528, 3218}, {535, 12690}, {594, 31136}, {758, 17638}, {899, 3756}, {952, 44425}, {1086, 17449}, {1155, 5853}, {1210, 21031}, {1211, 29655}, {1279, 49989}, {1387, 4867}, {1647, 21805}, {1737, 51362}, {1738, 3999}, {1788, 6764}, {1836, 24392}, {1837, 6762}, {2099, 34625}, {2550, 4860}, {2886, 3873}, {2975, 10543}, {3006, 4966}, {3011, 4864}, {3035, 3935}, {3057, 24391}, {3189, 5204}, {3219, 49736}, {3242, 11269}, {3243, 5231}, {3244, 45081}, {3315, 33139}, {3419, 5434}, {3434, 11246}, {3475, 31245}, {3621, 8256}, {3626, 46916}, {3632, 46917}, {3633, 5690}, {3649, 3874}, {3681, 3816}, {3699, 49707}, {3703, 10453}, {3706, 4431}, {3715, 26105}, {3742, 25006}, {3748, 5745}, {3751, 17721}, {3755, 4003}, {3782, 33141}, {3811, 5433}, {3813, 3868}, {3829, 31053}, {3870, 5432}, {3889, 25466}, {3893, 4848}, {3894, 39542}, {3901, 22791}, {3914, 21342}, {3932, 29824}, {3936, 17145}, {3938, 37646}, {3940, 10072}, {3943, 14439}, {3957, 6690}, {3961, 37634}, {3962, 12053}, {3977, 4702}, {3983, 9843}, {4009, 4899}, {4015, 17575}, {4018, 49600}, {4023, 49450}, {4026, 29835}, {4030, 14829}, {4046, 17135}, {4062, 21676}, {4126, 18743}, {4152, 49702}, {4369, 4807}, {4420, 6691}, {4423, 10580}, {4430, 11680}, {4442, 17154}, {4649, 17726}, {4662, 50038}, {4679, 5223}, {4865, 36538}, {4871, 49693}, {4880, 28174}, {4884, 32915}, {4906, 26723}, {4969, 22356}, {5057, 5852}, {5082, 5221}, {5119, 34699}, {5137, 5846}, {5175, 9657}, {5205, 49698}, {5241, 49457}, {5252, 34749}, {5258, 12433}, {5288, 37730}, {5289, 11240}, {5537, 13226}, {5718, 29676}, {5722, 34606}, {5771, 34486}, {5839, 40127}, {5843, 34789}, {5844, 11219}, {5855, 38460}, {5901, 41696}, {5905, 11235}, {6224, 22560}, {6253, 12704}, {6362, 6608}, {6702, 17757}, {6734, 15888}, {6737, 20323}, {6745, 31235}, {6763, 15171}, {6765, 24914}, {7171, 34630}, {7173, 21077}, {8728, 50190}, {9041, 32927}, {9052, 50362}, {9053, 17763}, {10529, 12635}, {10707, 17484}, {10944, 26437}, {10948, 41686}, {10950, 10966}, {10957, 14054}, {11260, 37734}, {11375, 41863}, {11376, 11523}, {11531, 33899}, {12437, 37605}, {12531, 38455}, {12611, 12665}, {12629, 41687}, {13476, 21926}, {14151, 37797}, {15104, 37364}, {15950, 45700}, {16496, 17720}, {16594, 49701}, {16610, 24216}, {16704, 20042}, {17056, 29690}, {17061, 33142}, {17070, 33148}, {17236, 32773}, {17241, 29641}, {17245, 17450}, {17248, 29843}, {17365, 33104}, {17597, 33137}, {17605, 24386}, {17717, 49498}, {17724, 33140}, {17740, 49460}, {18398, 31419}, {18481, 41709}, {21242, 49479}, {23958, 49719}, {24003, 49697}, {24217, 49448}, {24841, 37759}, {24929, 31157}, {25385, 49491}, {25557, 33108}, {26627, 49725}, {27003, 49732}, {29639, 49478}, {29844, 32853}, {30350, 41867}, {30567, 30615}, {30818, 49529}, {30942, 49524}, {31137, 33165}, {32848, 50001}, {32865, 40688}, {32943, 44416}, {36479, 37660}, {37758, 49714}, {49694, 49991}
X(51463) = reflection of X(i) in X(j) for these {i,j}: {11, 26015}, {3689, 3911}, {3935, 3035}, {4867, 1387}, {5537, 13226}, {6154, 1155}
X(51463) = X(1023)-Ceva conjugate of X(900)
X(51463) = X(i)-isoconjugate of X(j) for these (i,j): {88, 1174}, {106, 2346}, {1170, 2316}, {9456, 32008}, {36125, 47487}
X(51463) = X(i)-Dao conjugate of X(j) for these (i, j): (142, 1320), (214, 2346), (1212, 903), (4370, 32008), (40606, 88)
X(51463) = barycentric product X(i)*X(j) for these {i,j}: {44, 20880}, {142, 519}, {354, 4358}, {902, 1233}, {1229, 1319}, {1418, 4723}, {1475, 3264}, {1639, 35312}, {2325, 10481}, {3762, 35338}, {3911, 4847}, {3925, 16704}, {3943, 17169}, {3992, 18164}, {16708, 21805}, {16713, 40663}, {17780, 21104}, {21808, 30939}, {22053, 46109}, {24004, 48151}, {40218, 51416}
X(51463) = barycentric quotient X(i)/X(j) for these {i,j}: {44, 2346}, {142, 903}, {354, 88}, {519, 32008}, {902, 1174}, {1212, 1320}, {1319, 1170}, {1475, 106}, {2293, 2316}, {3689, 6605}, {3911, 21453}, {3925, 4080}, {4847, 4997}, {20880, 20568}, {21104, 6548}, {21127, 23838}, {21808, 4674}, {22053, 1797}, {22356, 47487}, {35326, 901}, {35338, 3257}, {40983, 8752}, {48151, 1022}
X(51463) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {{2, 42871, 37703}, {57, 4863, 34612}, {72, 49627, 37722}, {354, 4847, 3925}, {1647, 21805, 51415}, {3242, 11269, 17602}, {3243, 5231, 17718}, {3555, 10916, 12}, {3689, 3911, 6174}, {3874, 24390, 3649}, {6734, 34791, 15888}, {11260, 41575, 37734}, {12513, 12649, 10950}, {12832, 36920, 40663}, {17449, 33136, 1086}, {24216, 49772, 16610}, {24477, 36845, 55}, {29676, 49490, 5718}, {29835, 46909, 4026}, {33140, 49675, 17724}
See Antreas Hatzipolakis and Peter Moses, euclid 5409.
X(51464) lies on these lines: {115, 2388}, {325, 6007}, {594, 20723}, {740, 3027}, {2886, 18165}, {3056, 33141}, {4890, 17056}, {10026, 44671}, {17747, 20683}, {20863, 33136}
X(51464) = X(i)-isoconjugate of X(j) for these (i,j): {741, 40419}, {3449, 18827}
X(51464) = X(i)-Dao conjugate of X(j) for these (i, j): (8299, 40419), (16588, 40017)
X(51464) = barycentric product X(i)*X(j) for these {i,j}: {238, 21029}, {239, 21804}, {740, 17451}, {1284, 40997}, {2238, 2886}, {3747, 20236}, {3948, 21746}, {4037, 18165}, {7235, 16699}, {18033, 21819}
X(51464) = barycentric quotient X(i)/X(j) for these {i,j}: {2238, 40419}, {2886, 40017}, {17451, 18827}, {21029, 334}, {21746, 37128}, {21804, 335}, {21819, 7077}, {41333, 3449}, {46177, 4584}
See Antreas Hatzipolakis and Peter Moses, euclid 5409.
X(51465) lies on these lines: {758, 3028}, {1495, 17768}, {3782, 16700}
X(51465) = X(2341)-isoconjugate of X(3450)
X(51465) = X(i)-Dao conjugate of X(j) for these (i, j): (1329, 34079), (17053, 6740)
X(51465) = barycentric product X(i)*X(j) for these {i,j}: {1329, 41804}, {3782, 3936}, {17078, 21030}, {18593, 20237}, {21936, 40075}, {24443, 35550}
X(51465) = barycentric quotient X(i)/X(j) for these {i,j}: {1329, 6740}, {1464, 3450}, {3782, 24624}, {3936, 2985}, {17053, 34079}, {17452, 2341}, {21030, 36910}, {21936, 6187}, {24443, 759}
See Antreas Hatzipolakis and Peter Moses, euclid 5409.
X(51466) lies on these lines: { }
See Antreas Hatzipolakis and Peter Moses, euclid 5409.
X(51467) lies on these lines: { }
See Antreas Hatzipolakis and Peter Moses, euclid 5409.
X(51468) lies on these lines: {3325, 4160}, {4897, 17058}, {17213, 17476}
X(51468) = barycentric product X(4789)*X(4897)
X(51468) = barycentric quotient X(i)/X(j) for these {i,j}: {4897, 37210}, {17213, 34914}
See Antreas Hatzipolakis and Peter Moses, euclid 5409.
X(51469) lies on these lines: { }
X(51470) lies on the cubic K009 and these lines: {3, 191}, {4, 2687}, {32, 35090}, {56, 38982}, {14357, 34160}, {14385, 39175}, {34159, 39169}, {39170, 39173}
X(51470) = X(2766)-Ceva conjugate of X(8674)
X(51470) = X(i)-isoconjugate of X(j) for these (i,j): {1290, 21180}, {1325, 5620}, {16548, 21907}
X(51470) = X(8674)-Dao conjugate of X(5520)
X(51470) = cevapoint of X(35090) and X(42670)
X(51470) = barycentric product X(i)*X(j) for these {i,j}: {10693, 37783}, {32849, 34442}
X(51470) = barycentric quotient X(i)/X(j) for these {i,j}: {5172, 37798}, {17796, 5080}, {19622, 1325}, {34442, 21907}, {35090, 5520}, {42670, 47227}
X(51471) lies on the cubic K009 and these lines: {3, 4549}, {4, 1302}, {20, 39263}, {32, 3163}, {3146, 47103}, {13352, 32738}, {13608, 34157}, {14376, 39174}, {37645, 40387}
X(51471) = barycentric product X(i)*X(j) for these {i,j}: {4846, 37645}, {11064, 40387}, {34289, 47391}
X(51471) = barycentric quotient X(i)/X(j) for these {i,j}: {37645, 44134}, {40387, 16080}, {47391, 15066}
X(51472) lies on the cubic K009 and these lines: {3, 684}, {4, 842}, {32, 14385}, {6337, 51346}, {8743, 48453}, {14376, 39170}, {14378, 38542}, {14379, 39169}, {38987, 44895}
X(51472) = X(842)-Ceva conjugate of X(2781)
X(51472) = X(2781)-Dao conjugate of X(42426)
X(51472) = crosssum of X(542) and X(38552)
X(51472) = barycentric product X(i)*X(j) for these {i,j}: {35911, 37937}, {40079, 46787}
X(51472) = barycentric quotient X(i)/X(j) for these {i,j}: {40079, 46786}, {47427, 38552}
X(51473) lies on the cubic K009 and these lines: {3, 6511}, {4, 13397}, {14376, 34159}, {14379, 39173}, {34160, 39172}, {37275, 39267}, {39166, 39167}, {39175, 51347}
X(51474) lies on the cubic K009 and these lines: {3, 690}, {4, 691}, {32, 23967}, {1147, 14357}, {5967, 43754}, {6337, 14385}, {14566, 46981}, {15261, 51346}, {18312, 51456}
X(51474) = isogonal conjugate of X(38939)
X(51474) = X(40118)-Ceva conjugate of X(542)
X(51474) = X(1)-isoconjugate of X(38939)
X(51474) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 38939), (542, 16188)
X(51474) = cevapoint of X(5191) and X(23967)
X(51474) = barycentric product X(i)*X(j) for these {i,j}: {40083, 46786}, {51227, 51457}
X(51474) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 38939}, {5191, 2493}, {14999, 14221}, {23967, 16188}, {34369, 34175}, {40083, 46787}, {51457, 51228}
X(51475) lies on the cubic K009 and these lines: {3, 9033}, {4, 477}, {32, 32663}, {1147, 51346}, {1614, 34210}, {7740, 31510}, {14379, 39170}, {16186, 36164}, {22802, 39985}
X(51475) = X(477)-Ceva conjugate of X(2777)
X(51475) = X(2693)-isoconjugate of X(36063)
X(51475) = X(2777)-Dao conjugate of X(18809)
X(51475) = barycentric quotient X(32663)/X(2693)
See Ivan Pavlov, euclid 5422.
X(51476) lies on circumconics {A,B,C,X(1),X(33)}, {A,B,C,X(2),X(2291)}, {A,B,C,X(3),X(5269)}, {A,B,C,X(6),X(1743)}, {A,B,C,X(9),X(42467)}, {A,B,C,X(10),X(2357)}, {A,B,C,X(19),X(2983)}, {A,B,C,X(25),X(106)}, {A,B,C,X(31),X(32)}, {A,B,C,X(35),X(3745)}, {A,B,C,X(42),X(902)}, {A,B,C,X(57),X(7123)}, {A,B,C,X(79),X(8605)}, {A,B,C,X(81),X(1174)}, {A,B,C,X(101),X(31615)}, {A,B,C,X(109),X(40150)}, {A,B,C,X(171),X(2223)}, {A,B,C,X(210),X(5559)}, {A,B,C,X(212),X(1795)}, {A,B,C,X(251),X(739)}, {A,B,C,X(284),X(572)}
and on these lines: {1,1106}, {3,53089}, {6,52804}, {31,200}, {32,220}, {33,1395}, {55,572}, {58,519}, {109,3744}, {165,7218}, {171,1416}, {212,52429}, {238,20103}, {595,997}, {727,8706}, {750,31249}, {902,2206}, {985,29649}, {1864,40528}, {2801,7281}, {3304,14261}, {3550,7220}, {3664,21453}, {3745,7073}, {4339,5264}, {5053,15621}, {5266,6001}, {7191,35281}, {9310,9315}, {17126,36845}, {20015,30652}
X(51476) = trilinear pole of line {657,1919}
X(51476) = X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 3663}, {2, 3752}, {6, 26563}, {7, 3057}, {8, 1122}, {9, 52563}, {37, 18600}, {56, 20895}, {57, 3452}, {65, 17183}, {69, 1828}, {75, 1201}, {76, 20228}, {81, 4415}, {85, 2347}, {86, 4642}, {190, 48334}, {192, 27499}, {226, 18163}, {264, 22344}, {269, 6736}, {273, 22072}, {274, 21796}, {329, 42549}, {513, 21272}, {514, 21362}, {649, 21580}, {651, 21120}, {664, 6615}, {668, 6363}, {693, 23845}, {905, 17906}, {934, 42337}, {1014, 21031}, {1434, 21809}, {3161, 45205}, {3212, 52195}, {3669, 25268}, {4373, 45219}, {7182, 40982}, {8056, 45204}, {12640, 19604}, {17924, 23113}, {28006, 37137}, {44720, 46367}
X(51476) = X(i)-vertex conjugate of X(j) for these {i, j}: {2, 1412}, {9315, 51476}
X(51476) = X(i)-Dao conjugate of X(j) for these {i, j}: {1, 20895}, {3, 3663}, {9, 26563}, {206, 1201}, {478, 52563}, {5375, 21580}, {5452, 3452}, {6600, 6736}, {14714, 42337}, {32664, 3752}, {38991, 21120}, {39025, 6615}, {39026, 21272}, {40586, 4415}, {40589, 18600}, {40600, 4642}, {40602, 17183}
X(51476) = X(i)-cross conjugate of X(j) for these {i, j}: {55, 1261}, {3063, 101}, {4130, 36049}, {4162, 3939}
X(51476) = barycentric product X(i)*X(j) for these (i, j): {1, 23617}, {6, 1222}, {8, 3451}, {9, 1476}, {31, 32017}, {55, 40420}, {56, 52549}, {57, 1261}, {219, 40446}, {649, 8706}, {657, 6613}, {1252, 40451}, {4564, 40528}
X(51476) = barycentric quotient X(i)/X(j) for these (i, j): {1, 26563}, {6, 3663}, {9, 20895}, {31, 3752}, {32, 1201}, {41, 3057}, {42, 4415}, {55, 3452}, {56, 52563}, {58, 18600}, {100, 21580}, {213, 4642}, {220, 6736}, {284, 17183}, {560, 20228}, {604, 1122}, {657, 42337}, {663, 21120}, {667, 48334}, {692, 21362}, {902, 51415}, {1222, 76}, {1261, 312}, {1334, 21031}, {1476, 85}, {1918, 21796}, {1919, 6363}, {1973, 1828}, {2175, 2347}, {2194, 18163}, {2208, 42549}, {3052, 45204}, {3063, 6615}, {3451, 7}, {3939, 25268}, {5255, 24994}, {6613, 46406}, {7121, 27499}, {8706, 1978}, {8750, 17906}, {9247, 22344}, {16945, 45205}, {23617, 75}, {32017, 561}, {32656, 23113}, {32739, 23845}, {40420, 6063}, {40446, 331}, {40451, 23989}, {40528, 4858}, {52425, 22072}, {52549, 3596}
See Ivan Pavlov, euclid 5422.
lies on circumconics {A,B,C,X(2),X(37457)}, {A,B,C,X(3),X(25)}, {A,B,C,X(6),X(10979)}, {A,B,C,X(22),X(41275)}, {A,B,C,X(51),X(54)},{A,B,C,X(68),X(34154)}, {A,B,C,X(97),X(647)}, {A,B,C,X(186),X(418)}, {A,B,C,X(216),X(570)}, {A,B,C,X(237),X(6636)}, {A,B,C,X(248),X(3108)} and on these lines: {3,539}, {17,1607}, {18,1608}, {25,2934}, {32,8565}, {51,51546}, {54,47895}, {93,186}, {98,930}, {184,10979}, {237,3456}, {378,14111}, {418,52153}, {562,35473}, {570,8603}, {1487,3518}, {2353,41275}, {2937,18370}, {3425,7485}, {3438,37848}, {3439,37850}, {3917,42065}, {5899,31392}, {7502,25043}, {10547,52144}, {19778,22532}, {19779,22531}, {32637,34418}, {32737,40352}
= X(i)-isoconjugate-of-X(j) for these {i, j}: {1, 32002}, {19, 7769}, {75, 3518}, {92, 1994}, {143, 40440}, {158, 44180}, {162, 41298}, {264, 2964}, {811, 1510}, {1969, 2965}, {2167, 14129}, {30529, 52414}, {36120, 51440}
= X(i)-vertex conjugate of X(j) for these {i, j}: {39284, 39284}
= X(i)-Dao conjugate of X(j) for these {i, j}: {3, 32002}, {6, 7769}, {125, 41298}, {206, 3518}, {1147, 44180}, {15450, 20577}, {17423, 1510}, {21975, 264}, {22391, 1994}, {39171, 311}, {40588, 14129}, {46094, 51440}, {46604, 4}
= X(i)-cross conjugate of X(j) for these {i, j}: {23195, 184}
= barycentric product X(i)*X(j) for these (i, j): {3, 2963}, {6, 3519}, {17, 32586}, {18, 32585}, {48, 2962}, {93, 577}, {184, 11140}, {216, 252}, {525, 32737}, {562, 50433}, {647, 930}, {656, 36148}, {1487, 22052}, {3049, 46139}, {8603, 52204}, {8604, 52203}, {14533, 25043}, {14585, 20572}, {21461, 40711}, {21462, 40712}, {21975, 34433}, {38342, 39201}
= barycentric quotient X(i)/X(j) for these (i, j): {3, 7769}, {6, 32002}, {32, 3518}, {51, 14129}, {93, 18027}, {184, 1994}, {217, 143}, {252, 276}, {577, 44180}, {647, 41298}, {930, 6331}, {2962, 1969}, {2963, 264}, {3049, 1510}, {3289, 51440}, {3519, 76}, {9247, 2964}, {11140, 18022}, {14575, 2965}, {14585, 49}, {15451, 20577}, {19627, 52417}, {21461, 472}, {21462, 473}, {32585, 303}, {32586, 302}, {32737, 648}, {36148, 811}, {40981, 14577}, {52153, 30529}
= {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {51890, 51891, 2963}
X(51478) lies on the cubic K1282 and these lines: {54, 575}, {99, 35191}, {110, 249}, {111, 39448}, {526, 10411}, {1511, 14355}, {5182, 5648}, {5968, 32609}, {9160, 45773}, {10097, 35324}
X(51478) = X(i)-isoconjugate of X(j) for these (i,j): {94, 2642}, {661, 43084}, {690, 2166}, {896, 10412}, {1109, 14559}, {1648, 32680}, {4062, 43082}, {14210, 15475}
X(51478) = X(i)-Dao conjugate of X(j) for these (i, j): (11597, 690), (15477, 15475), (15899, 10412), (36830, 43084), (40604, 35522)
X(51478) = barycentric product X(i)*X(j) for these {i,j}: {50, 892}, {111, 10411}, {249, 9213}, {323, 691}, {895, 14590}, {2088, 45773}, {6149, 36085}, {7799, 32729}, {14591, 30786}, {34539, 44814}
X(51478) = barycentric quotient X(i)/X(j) for these {i,j}: {50, 690}, {110, 43084}, {111, 10412}, {323, 35522}, {691, 94}, {892, 20573}, {895, 14592}, {9213, 338}, {10411, 3266}, {14270, 1648}, {14590, 44146}, {14591, 468}, {14908, 14582}, {19627, 351}, {22115, 14417}, {23357, 14559}, {32729, 1989}, {32740, 15475}, {34397, 14273}, {36142, 2166}
X(51479) lies on the cubic K1282 and these lines: {5, 523}, {94, 9180}, {99, 476}, {115, 12077}, {128, 16188}, {265, 512}, {690, 41586}, {826, 18557}, {6344, 14618}
X(51479) = X(i)-isoconjugate of X(j) for these (i,j): {50, 36085}, {323, 36142}, {691, 6149}, {923, 10411}, {1101, 9213}, {14590, 36060}
X(51479) = X(i)-Dao conjugate of X(j) for these (i, j): (523, 9213), (690, 44814), (1560, 14590), (1649, 526), (2482, 10411), (14993, 691), (15295, 32729), (21905, 14270), (23992, 323), (38988, 50), (48317, 186)
X(51479) = barycentric product X(i)*X(j) for these {i,j}: {94, 690}, {328, 14273}, {338, 14559}, {351, 20573}, {468, 14592}, {523, 43084}, {524, 10412}, {1648, 35139}, {1989, 35522}, {3266, 15475}, {6344, 14417}, {14582, 44146}, {18384, 45807}, {37778, 43083}, {42713, 43082}, {43087, 50942}
X(51479) = barycentric quotient X(i)/X(j) for these {i,j}: {94, 892}, {115, 9213}, {351, 50}, {468, 14590}, {524, 10411}, {690, 323}, {1648, 526}, {1989, 691}, {2166, 36085}, {2642, 6149}, {10412, 671}, {11060, 32729}, {14273, 186}, {14559, 249}, {14582, 895}, {14592, 30786}, {15475, 111}, {21906, 14270}, {23992, 44814}, {33919, 2088}, {35522, 7799}, {39295, 45773}, {43084, 99}, {43087, 50941}, {44102, 14591}
X(51480) lies on the Jerabek circumhyperbola, the cubic K1282, and these lines: {3, 690}, {6, 14273}, {67, 924}, {68, 9517}, {69, 526}, {74, 3566}, {99, 35191}, {115, 10097}, {125, 35364}, {265, 512}, {338, 15328}, {523, 895}, {525, 5504}, {826, 43704}, {1176, 22105}, {1499, 34802}, {1510, 18125}, {1576, 14559}, {2775, 34800}, {2780, 4846}, {3265, 43705}, {6391, 9033}, {10293, 20186}, {11559, 32478}, {20184, 34437}, {23287, 43697}, {35909, 36189}
X(51480) = reflection of X(35364) in X(125)
X(51480) = isogonal conjugate of X(7468)
X(51480) = isotomic conjugate of X(14221)
X(51480) = circumcircle-inverse of X(40083)
X(51480) = antigonal image of X(35364)
X(51480) = isogonal conjugate of the anticomplement of X(36189)
X(51480) = X(i)-isoconjugate of X(j) for these (i,j): {1, 7468}, {31, 14221}, {162, 14984}, {662, 2493}, {23997, 34175}
X(51480) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 14221), (3, 7468), (125, 14984), (1084, 2493)
X(51480) = cevapoint of X(512) and X(1640)
X(51480) = trilinear pole of line {647, 1648}
X(51480) = crossdifference of every pair of points on line {2493, 14984}
X(51480) = barycentric product X(i)*X(j) for these {i,j}: {525, 40118}, {2394, 51457}, {14223, 51474}, {40083, 43665}
X(51480) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 14221}, {6, 7468}, {512, 2493}, {647, 14984}, {1640, 16188}, {2395, 34175}, {14998, 38939}, {40083, 2421}, {40118, 648}, {51457, 2407}, {51474, 14999}
X(51481) lies on these lines: {2, 39}, {3, 39906}, {4, 52}, {6, 311}, {22, 39646}, {23, 5986}, {50, 44376}, {51, 6248}, {69, 41760}, {83, 11140}, {94, 671}, {98, 37183}, {99, 35296}, {110, 419}, {112, 44328}, {125, 33314}, {141, 1232}, {148, 40853}, {193, 264}, {230, 47406}, {231, 46184}, {237, 2782}, {239, 34387}, {248, 290}, {287, 34137}, {297, 525}, {300, 37786}, {301, 37785}, {308, 30535}, {313, 25978}, {315, 45794}, {316, 37779}, {323, 1236}, {327, 7777}, {328, 41626}, {338, 524}, {339, 441}, {343, 5254}, {350, 26639}, {394, 41238}, {458, 1235}, {460, 3564}, {467, 27376}, {511, 14957}, {599, 44148}, {648, 37778}, {698, 36790}, {894, 34388}, {1234, 3770}, {1269, 26538}, {1273, 44388}, {1495, 46493}, {1916, 46807}, {1992, 44135}, {1994, 7760}, {2052, 2996}, {2393, 25051}, {2979, 12251}, {2986, 17708}, {2987, 16081}, {2990, 43189}, {2998, 40815}, {3001, 7668}, {3003, 14570}, {3068, 34391}, {3069, 34392}, {3095, 37988}, {3186, 12272}, {3292, 46512}, {3620, 44149}, {3701, 25984}, {3963, 25245}, {4226, 14265}, {4558, 44375}, {5117, 23293}, {5422, 7770}, {5485, 34289}, {5921, 43976}, {6381, 25007}, {6504, 43678}, {6636, 12203}, {6656, 37636}, {6660, 12188}, {7468, 47207}, {7745, 45793}, {7762, 41628}, {7793, 51350}, {8882, 34385}, {9308, 40318}, {9722, 39113}, {10104, 37457}, {10358, 15004}, {11008, 44136}, {11160, 44133}, {11185, 37644}, {11205, 37649}, {11257, 37184}, {11328, 13108}, {11338, 46900}, {12243, 15360}, {12362, 31388}, {14096, 49111}, {14615, 20080}, {14880, 46546}, {15066, 41235}, {15143, 47202}, {16985, 40870}, {17862, 25977}, {17984, 40867}, {18033, 23989}, {20022, 39266}, {20891, 26573}, {21531, 32515}, {23235, 35298}, {31859, 37067}, {33529, 36251}, {33530, 36252}, {34148, 37124}, {34854, 35360}, {36789, 44569}, {37188, 41009}, {37874, 43681}, {41194, 44780}, {41195, 44781}, {41617, 48540}, {41676, 44893}, {41757, 41762}, {43084, 45331}
X(51481) = reflection of X(i) in X(j) for these {i,j}: {3001, 7668}, {3260, 338}, {7468, 47207}, {14570, 3003}
X(51481) = isogonal conjugate of X(32654)
X(51481) = isotomic conjugate of X(2987)
X(51481) = anticomplement of X(36212)
X(51481) = polar conjugate of X(3563)
X(51481) = anticomplement of the isogonal conjugate of X(6531)
X(51481) = anticomplement of the isotomic conjugate of X(16081)
X(51481) = isotomic conjugate of the isogonal conjugate of X(230)
X(51481) = isotomic conjugate of the polar conjugate of X(44145)
X(51481) = polar conjugate of the isogonal conjugate of X(3564)
X(51481) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {19, 147}, {98, 4329}, {293, 6527}, {661, 14721}, {685, 7192}, {1096, 40867}, {1821, 1370}, {1910, 20}, {1973, 39355}, {1976, 6360}, {6531, 8}, {16081, 6327}, {20031, 7253}, {22456, 17217}, {32696, 4560}, {36084, 6563}, {36104, 523}, {36120, 69}
X(51481) = X(i)-Ceva conjugate of X(j) for these (i,j): {264, 2974}, {290, 14265}, {16081, 2}, {43187, 850}, {44132, 30737}
X(51481) = X(i)-cross conjugate of X(j) for these (i,j): {230, 44145}, {2974, 264}, {38359, 99}
X(51481) = X(i)-isoconjugate of X(j) for these (i,j): {1, 32654}, {6, 36051}, {19, 42065}, {31, 2987}, {32, 8773}, {48, 3563}, {163, 35364}, {560, 8781}, {798, 10425}, {810, 32697}, {1755, 2065}, {1910, 34157}, {1973, 43705}, {3049, 36105}, {9247, 35142}, {9417, 40428}
X(51481) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 2987), (3, 32654), (6, 42065), (9, 36051), (114, 6), (115, 35364), (230, 511), (1249, 3563), (6337, 43705), (6374, 8781), (6376, 8773), (11672, 34157), (31998, 10425), (34156, 248), (35067, 3), (36899, 2065), (39001, 3049), (39058, 40428), (39062, 32697), (39069, 31), (39072, 32), (41181, 520), (44377, 1570)
X(51481) = cevapoint of X(i) and X(j) for these (i,j): {6, 39828}, {230, 3564}
X(51481) = crosspoint of X(i) and X(j) for these (i,j): {76, 290}, {6528, 41174}
X(51481) = crosssum of X(i) and X(j) for these (i,j): {32, 237}, {3569, 47421}
X(51481) = trilinear pole of line {114, 2974}
X(51481) = crossdifference of every pair of points on line {184, 669}
X(51481) = barycentric product X(i)*X(j) for these {i,j}: {69, 44145}, {75, 1733}, {76, 230}, {114, 290}, {264, 3564}, {300, 6782}, {301, 6783}, {305, 460}, {325, 14265}, {561, 8772}, {850, 4226}, {1502, 1692}, {2974, 35142}, {3260, 36875}, {3978, 47734}, {4609, 42663}, {5477, 18023}, {12829, 18896}, {17462, 46273}, {18024, 51335}, {40050, 44099}, {41174, 41181}
X(51481) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 36051}, {2, 2987}, {3, 42065}, {4, 3563}, {6, 32654}, {69, 43705}, {75, 8773}, {76, 8781}, {98, 2065}, {99, 10425}, {114, 511}, {230, 6}, {264, 35142}, {290, 40428}, {460, 25}, {511, 34157}, {523, 35364}, {648, 32697}, {811, 36105}, {1692, 32}, {1733, 1}, {2782, 51455}, {2974, 3564}, {3260, 36891}, {3564, 3}, {4226, 110}, {5477, 187}, {6782, 15}, {6783, 16}, {8772, 31}, {10011, 1351}, {12829, 1691}, {12830, 2076}, {14265, 98}, {14356, 39374}, {17462, 1755}, {17984, 47736}, {31842, 34382}, {34174, 842}, {36875, 74}, {38359, 6132}, {41181, 41172}, {42663, 669}, {44099, 1974}, {44145, 4}, {46039, 2698}, {47406, 3289}, {47734, 694}, {51335, 237}, {51431, 1495}
X(51481) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {76, 5286, 26214}, {76, 20023, 8024}, {76, 40814, 2}, {343, 5254, 41237}, {458, 1235, 40684}, {458, 7754, 1993}, {648, 44138, 37778}, {5392, 6515, 324}, {12251, 37190, 2979}, {13428, 13439, 11442}, {26539, 26588, 2}, {26541, 26592, 2}, {41000, 41001, 3266}
X(51482) lies on these lines: {2, 13}, {4, 542}, {14, 41135}, {15, 25156}, {30, 5611}, {62, 5460}, {115, 37641}, {147, 41043}, {148, 531}, {193, 22576}, {265, 21468}, {298, 31683}, {299, 11296}, {302, 42128}, {303, 35303}, {316, 51017}, {376, 9735}, {381, 37785}, {383, 11163}, {396, 35931}, {397, 597}, {398, 20583}, {470, 44569}, {519, 9901}, {524, 621}, {532, 42973}, {543, 617}, {598, 51019}, {599, 634}, {619, 9116}, {628, 5464}, {631, 20415}, {633, 5344}, {1080, 22329}, {2043, 13637}, {2044, 13757}, {2482, 37173}, {2782, 44464}, {3146, 41020}, {3181, 22491}, {3448, 46856}, {3524, 6771}, {3534, 47610}, {3543, 41022}, {3545, 5617}, {3629, 42102}, {3642, 22494}, {3830, 33625}, {3839, 5478}, {3845, 36344}, {5032, 5334}, {5055, 20252}, {5321, 8584}, {5469, 40694}, {5472, 6772}, {5473, 10304}, {5476, 20429}, {5859, 33624}, {5863, 33626}, {5981, 42036}, {6670, 42800}, {6773, 11632}, {6782, 43404}, {6783, 8594}, {7714, 12142}, {7775, 33460}, {7818, 37170}, {8588, 11488}, {8596, 22113}, {8860, 37463}, {9114, 20094}, {9115, 11489}, {9763, 35932}, {9885, 42120}, {9900, 50884}, {10385, 13076}, {10654, 23005}, {10657, 11004}, {11001, 49858}, {11121, 12816}, {11177, 22573}, {11179, 44477}, {11239, 49144}, {11240, 49143}, {11289, 20582}, {11295, 42974}, {11542, 35304}, {11705, 38314}, {13083, 36968}, {13172, 25559}, {13174, 50850}, {13859, 14002}, {15534, 42094}, {15682, 33623}, {15692, 21156}, {16267, 30560}, {16963, 22846}, {18581, 22998}, {19053, 49209}, {19054, 49208}, {19776, 43091}, {19875, 50847}, {21356, 51010}, {21358, 51202}, {22490, 32553}, {22493, 40898}, {22570, 34511}, {22572, 42103}, {22575, 51203}, {22796, 36363}, {22847, 49906}, {25055, 51114}, {25226, 30440}, {25235, 37835}, {25561, 37825}, {30471, 33618}, {31144, 37144}, {31709, 51206}, {32455, 42101}, {33458, 35691}, {33465, 43633}, {33475, 42943}, {33477, 42142}, {33602, 33622}, {33609, 36388}, {33610, 49862}, {33611, 36366}, {34508, 42813}, {35020, 43233}, {35696, 42588}, {36251, 42998}, {36302, 37765}, {36386, 49951}, {36775, 43465}, {36961, 50687}, {37172, 37809}, {37332, 48657}, {40672, 47864}, {42035, 43540}, {42062, 43542}, {42133, 51170}, {45420, 49034}, {45421, 49035}, {47352, 51159}, {49814, 49950}, {49830, 49962}, {49901, 49903}
X(51482) = midpoint of X(i) and X(j) for these {i,j}: {13, 35752}, {616, 35749}, {22495, 36969}
X(51482) = reflection of X(i) in X(j) for these {i,j}: {2, 13}, {4, 25154}, {13, 47865}, {147, 41043}, {298, 31693}, {616, 2}, {671, 31695}, {1992, 22580}, {3180, 22495}, {3534, 47610}, {5463, 5459}, {5980, 40671}, {6773, 11632}, {8591, 5464}, {8594, 6783}, {8595, 6108}, {8596, 22577}, {9114, 32552}, {9116, 619}, {9900, 50884}, {13174, 50850}, {20094, 9114}, {25154, 16001}, {31693, 43416}, {33622, 40707}, {33627, 11121}, {35304, 11542}, {35750, 616}, {35751, 618}, {35931, 396}, {36344, 48655}, {36363, 22796}, {36768, 35019}, {36769, 6669}, {40671, 47861}, {40898, 22493}, {41042, 5478}, {48655, 3845}, {50849, 11705}
X(51482) = anticomplement of X(5463)
X(51482) = circumcircle-of-inner-Napoleon-triangle-inverse of X(5459)
X(51482) = circumcircle-of-outer-Napoleon-triangle-inverse of X(45880)
X(51482) = psi-transform of X(5460)
X(51482) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 35749, 35750}, {2, 35752, 35749}, {13, 5463, 5459}, {13, 6115, 43403}, {13, 6779, 46054}, {13, 23006, 6108}, {13, 35751, 22489}, {13, 36770, 35019}, {13, 47859, 10653}, {115, 41745, 37641}, {618, 22489, 2}, {5459, 5463, 2}, {5472, 6772, 37640}, {5478, 41042, 3839}, {6108, 9762, 2}, {6302, 6306, 36770}, {9762, 23006, 8595}, {9763, 42155, 35932}, {10653, 22492, 2}, {11705, 50849, 38314}, {13084, 37832, 2}, {22489, 35751, 618}, {22580, 25154, 671}, {31710, 51200, 5334}, {35019, 36768, 48311}, {35752, 47865, 2}, {36768, 48311, 36770}, {36770, 48311, 2}, {47363, 47364, 45880}
X(51483) lies on these lines: {2, 14}, {4, 542}, {13, 41135}, {16, 25166}, {30, 5615}, {61, 5459}, {115, 37640}, {147, 41042}, {148, 530}, {193, 22575}, {265, 21469}, {298, 11295}, {299, 31684}, {302, 35304}, {303, 42125}, {316, 51019}, {376, 9736}, {381, 37786}, {383, 22329}, {395, 35932}, {397, 20583}, {398, 597}, {471, 44569}, {519, 9900}, {524, 622}, {533, 42972}, {543, 616}, {598, 51017}, {599, 633}, {618, 9114}, {627, 5463}, {631, 20416}, {634, 5343}, {1080, 11163}, {2043, 13757}, {2044, 13637}, {2482, 37172}, {2782, 44460}, {3146, 41021}, {3180, 22492}, {3448, 46857}, {3524, 6774}, {3534, 47611}, {3543, 41023}, {3545, 5613}, {3629, 42101}, {3643, 22493}, {3830, 33623}, {3839, 5479}, {3845, 36319}, {5032, 5335}, {5055, 20253}, {5318, 8584}, {5470, 40693}, {5471, 6775}, {5474, 10304}, {5476, 20428}, {5858, 33622}, {5862, 33627}, {5980, 42035}, {6669, 42799}, {6770, 11632}, {6782, 8595}, {6783, 43403}, {7714, 12141}, {7775, 33461}, {7818, 37171}, {8588, 11489}, {8596, 22114}, {8860, 37464}, {9116, 20094}, {9117, 11488}, {9761, 35931}, {9886, 42119}, {9901, 50884}, {10385, 13075}, {10653, 23004}, {10658, 11004}, {11001, 49855}, {11122, 12817}, {11177, 22574}, {11179, 44478}, {11239, 49146}, {11240, 49145}, {11290, 20582}, {11296, 42975}, {11543, 35303}, {11706, 38314}, {13084, 36967}, {13172, 25560}, {13174, 50847}, {13858, 14002}, {15534, 42093}, {15682, 33625}, {15692, 21157}, {16268, 30559}, {16962, 22891}, {18582, 22997}, {19053, 49211}, {19054, 49210}, {19777, 43092}, {19875, 50850}, {21356, 51013}, {21358, 51205}, {22489, 32552}, {22494, 40899}, {22568, 34511}, {22571, 42106}, {22576, 51200}, {22797, 36362}, {22893, 49905}, {25055, 51115}, {25225, 30439}, {25236, 37832}, {25561, 37824}, {30472, 33619}, {31144, 37145}, {31710, 51207}, {32455, 42102}, {33459, 35695}, {33464, 43632}, {33474, 42942}, {33476, 42139}, {33603, 33624}, {33608, 36386}, {33610, 36368}, {33611, 49861}, {34509, 42814}, {35019, 43232}, {35692, 42589}, {36252, 42999}, {36303, 37765}, {36388, 49954}, {36962, 50687}, {37173, 37809}, {37333, 48657}, {40671, 47863}, {42036, 43541}, {42063, 43543}, {42134, 51170}, {45420, 49036}, {45421, 49037}, {47352, 51160}, {49815, 49949}, {49831, 49961}, {49902, 49904}
X(51483) = midpoint of X(i) and X(j) for these {i,j}: {14, 36330}, {617, 36327}, {22496, 36970}
X(51483) = reflection of X(i) in X(j) for these {i,j}: {2, 14}, {4, 25164}, {14, 47866}, {147, 41042}, {299, 31694}, {617, 2}, {671, 31696}, {1992, 22579}, {3181, 22496}, {3534, 47611}, {5464, 5460}, {5981, 40672}, {6770, 11632}, {8591, 5463}, {8594, 6109}, {8595, 6782}, {8596, 22578}, {9114, 618}, {9116, 32553}, {9901, 50884}, {13174, 50847}, {20094, 9116}, {25164, 16002}, {31694, 43417}, {33624, 40706}, {33626, 11122}, {35303, 11543}, {35932, 395}, {36319, 48656}, {36329, 619}, {36331, 617}, {36362, 22797}, {40672, 47862}, {40899, 22494}, {41043, 5479}, {47867, 6670}, {48656, 3845}, {50852, 11706}
X(51483) = anticomplement of X(5464)
X(51483) = circumcircle-of-inner-Napoleon-triangle-inverse of X(45879)
X(51483) = circumcircle-of-outer Napoleon-triangle-inverse of X(5460)
X(51483) = psi-transform of X(5459)
X(51483) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36327, 36331}, {2, 36330, 36327}, {14, 5464, 5460}, {14, 6114, 43404}, {14, 6780, 46053}, {14, 23013, 6109}, {14, 36329, 22490}, {14, 47860, 10654}, {115, 41746, 37640}, {619, 22490, 2}, {5460, 5464, 2}, {5471, 6775, 37641}, {5479, 41043, 3839}, {6109, 9760, 2}, {9760, 23013, 8594}, {9761, 42154, 35931}, {10654, 22491, 2}, {11706, 50852, 38314}, {13083, 37835, 2}, {22490, 36329, 619}, {22579, 25164, 671}, {31709, 51203, 5335}, {36330, 47866, 2}, {47361, 47362, 45879}
X(51484) lies on these lines: {2, 14}, {3, 37785}, {6, 35932}, {30, 5611}, {99, 51012}, {182, 22579}, {187, 37641}, {298, 6390}, {299, 11295}, {302, 42116}, {303, 31694}, {316, 43482}, {376, 511}, {524, 616}, {530, 3180}, {533, 5463}, {574, 41746}, {597, 11300}, {599, 11299}, {618, 22493}, {622, 3849}, {628, 11304}, {631, 21401}, {633, 7801}, {634, 9939}, {2549, 37640}, {2992, 43092}, {3105, 34604}, {3241, 44659}, {3524, 13350}, {3543, 44666}, {3545, 20428}, {3839, 7684}, {3845, 33625}, {5032, 51206}, {5189, 34314}, {5238, 34508}, {5321, 33475}, {5352, 22114}, {5459, 16962}, {5979, 36775}, {6582, 46708}, {6771, 31696}, {6772, 9117}, {6781, 41745}, {7812, 47068}, {8584, 42943}, {8595, 51200}, {9114, 22687}, {9761, 11480}, {9763, 42154}, {10304, 14538}, {10617, 49906}, {10645, 13084}, {10653, 32480}, {10667, 32787}, {10671, 32788}, {11296, 11485}, {11303, 22236}, {11488, 18424}, {11586, 16770}, {11707, 38314}, {11812, 49855}, {13637, 36455}, {13757, 36437}, {15534, 42626}, {15640, 33623}, {15692, 21158}, {16940, 19661}, {16963, 30560}, {17503, 43542}, {19106, 47865}, {19708, 36755}, {19780, 43229}, {19924, 22580}, {21356, 51016}, {22492, 42085}, {22494, 40901}, {23004, 41135}, {23005, 40246}, {25166, 46054}, {31173, 37171}, {31693, 42912}, {33459, 33627}, {33611, 43228}, {33624, 49897}, {33960, 50860}, {34315, 37909}, {34509, 42157}, {35229, 40694}, {35749, 42087}, {35750, 42122}, {35752, 42099}, {36992, 50687}, {37341, 42925}, {39555, 45880}, {41134, 51387}, {44250, 50979}, {47352, 51161}
X(51484) = midpoint of X(35752) and X(42099)
X(51484) = reflection of X(i) in X(j) for these {i,j}: {2, 15}, {298, 35304}, {616, 35931}, {617, 8594}, {621, 2}, {5189, 34314}, {19106, 47865}, {22493, 618}, {31693, 42912}, {35931, 42942}, {40246, 23005}, {50854, 11707}, {50855, 45879}
X(51484) = anticomplement of X(50855)
X(51484) = circumcircle-of-inner-Napoleon-triangle-inverse of X(5460)
X(51484) = psi-transform of X(45880)
X(51484) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 13083, 2}, {15, 50855, 45879}, {10645, 22496, 13084}, {11707, 50854, 38314}, {40334, 48313, 2}, {45879, 50855, 2}, {47361, 47362, 5460}
X(51485) lies on these lines: {2, 13}, {3, 37786}, {6, 35931}, {30, 5615}, {99, 51015}, {182, 22580}, {187, 37640}, {298, 11296}, {299, 6390}, {302, 31693}, {303, 42115}, {316, 43481}, {376, 511}, {524, 617}, {531, 3181}, {532, 5464}, {574, 41745}, {597, 11299}, {599, 11300}, {619, 22494}, {621, 3849}, {627, 11303}, {631, 21402}, {633, 9939}, {634, 7801}, {2549, 37641}, {2993, 43091}, {3104, 34604}, {3241, 44660}, {3365, 35741}, {3524, 13349}, {3543, 44667}, {3545, 20429}, {3839, 7685}, {3845, 33623}, {5032, 51207}, {5189, 34313}, {5237, 34509}, {5318, 33474}, {5351, 22113}, {5460, 16963}, {6295, 46709}, {6774, 31695}, {6775, 9115}, {6781, 41746}, {7812, 47066}, {8584, 42942}, {8594, 51203}, {9116, 22689}, {9761, 42155}, {9763, 11481}, {10304, 14539}, {10616, 49905}, {10646, 13083}, {10654, 32480}, {10668, 32787}, {10672, 32788}, {11295, 11486}, {11304, 22238}, {11489, 18424}, {11708, 38314}, {11812, 49858}, {13637, 36437}, {13757, 36455}, {15534, 42625}, {15640, 33625}, {15692, 21159}, {15743, 16771}, {16941, 19661}, {16962, 30559}, {17503, 43543}, {19107, 47866}, {19708, 36756}, {19781, 43228}, {19924, 22579}, {21356, 51018}, {22491, 42086}, {22493, 40900}, {23004, 40246}, {23005, 41135}, {25156, 46053}, {31173, 37170}, {31694, 42913}, {33458, 33626}, {33610, 43229}, {33622, 49898}, {33959, 50859}, {34316, 37909}, {34508, 42158}, {35230, 40693}, {36327, 42088}, {36330, 42100}, {36331, 42123}, {36994, 50687}, {37340, 42924}, {39554, 45879}, {41134, 51388}, {47352, 51162}
X(51485) = midpoint of X(36330) and X(42100)
X(51485) = reflection of X(i) in X(j) for these {i,j}: {2, 16}, {299, 35303}, {616, 8595}, {617, 35932}, {622, 2}, {5189, 34313}, {19107, 47866}, {22494, 619}, {31694, 42913}, {35932, 42943}, {40246, 23004}, {50857, 11708}, {50858, 45880}
X(51485) = anticomplement of X(50858)
X(51485) = circumcircle-of-outer-Napoleon-triangle-inverse of X(5459)
X(51485) = psi-transform of X(45879)
X(51485) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 13084, 2}, {16, 50858, 45880}, {10646, 22495, 13083}, {11708, 50857, 38314}, {40335, 48314, 2}, {45880, 50858, 2}, {47363, 47364, 5459}
X(51486) lies on these lines: {2, 17}, {3, 49858}, {4, 33625}, {5, 49914}, {6, 22893}, {13, 148}, {30, 16629}, {69, 40707}, {141, 42777}, {299, 11542}, {303, 11302}, {376, 9735}, {381, 37786}, {396, 622}, {519, 22652}, {530, 30559}, {533, 41121}, {547, 37785}, {597, 42898}, {616, 5472}, {621, 16634}, {623, 40899}, {633, 5859}, {1992, 5071}, {3180, 18582}, {3181, 22894}, {3524, 49106}, {3543, 44666}, {3545, 16626}, {3629, 43104}, {3643, 16960}, {3839, 22832}, {3845, 48666}, {5032, 51208}, {5487, 33607}, {5863, 7751}, {5979, 47857}, {6669, 34540}, {7714, 22482}, {7753, 37171}, {8259, 11304}, {8716, 9763}, {10304, 22890}, {10385, 22910}, {10611, 37170}, {10653, 22900}, {10654, 31704}, {11117, 19712}, {11132, 32833}, {11239, 49175}, {11240, 49174}, {11297, 42988}, {11303, 33458}, {11305, 44776}, {11602, 41135}, {11739, 38314}, {12815, 49812}, {16241, 22895}, {19053, 49239}, {19054, 49238}, {20583, 42899}, {21356, 51020}, {22795, 41099}, {22845, 49809}, {22901, 37835}, {25055, 51116}, {32455, 43101}, {33387, 49819}, {33405, 42990}, {33459, 42598}, {33604, 43676}, {33959, 45879}, {34508, 49907}, {35020, 43031}, {35689, 42992}, {37007, 41108}, {37172, 49862}, {41104, 41112}, {41107, 44029}, {41114, 41119}, {41117, 49874}, {41129, 49825}, {42975, 51279}, {45420, 49066}, {45421, 49067}
X(51486) = midpoint of X(i) and X(j) for these {i,j}: {2, 22113}, {17, 36366}, {627, 33626}
X(51486) = reflection of X(i) in X(j) for these {i,j}: {2, 17}, {627, 2}, {22113, 36366}, {33622, 627}, {33626, 22113}, {36352, 22844}, {36366, 33465}, {36386, 629}, {48666, 3845}
X(51486) = anticomplement of X(50859)
X(51486) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 33626, 33622}, {2, 36326, 36386}, {2, 36366, 33626}, {17, 22113, 627}, {17, 22844, 6673}, {17, 33465, 22113}, {633, 42156, 33413}, {16267, 34509, 2}
X(51487) lies on these lines: {2, 18}, {3, 49855}, {4, 33623}, {5, 49911}, {6, 22847}, {14, 148}, {30, 16628}, {69, 40706}, {141, 42778}, {298, 11543}, {302, 11301}, {376, 9736}, {381, 37785}, {395, 621}, {519, 22651}, {531, 30560}, {532, 41122}, {547, 37786}, {597, 42899}, {617, 5471}, {622, 16635}, {624, 40898}, {634, 5858}, {1992, 5071}, {3180, 22850}, {3181, 18581}, {3524, 49105}, {3543, 44667}, {3545, 16627}, {3629, 43101}, {3642, 16961}, {3839, 22831}, {3845, 48665}, {5032, 51209}, {5488, 33606}, {5862, 7751}, {5978, 47858}, {6670, 34541}, {7714, 22481}, {7753, 37170}, {8260, 11303}, {8716, 9761}, {10304, 22843}, {10385, 22865}, {10612, 37171}, {10653, 31703}, {10654, 22856}, {11118, 19713}, {11133, 32833}, {11239, 49173}, {11240, 49172}, {11298, 42989}, {11304, 33459}, {11306, 44777}, {11603, 41135}, {11740, 38314}, {12815, 49813}, {16242, 22849}, {19053, 49237}, {19054, 49236}, {20583, 42898}, {21356, 51021}, {22794, 41099}, {22844, 49806}, {22855, 37832}, {25055, 51117}, {32455, 43104}, {33386, 49816}, {33404, 42991}, {33458, 42599}, {33605, 43676}, {33960, 45880}, {34509, 49908}, {35019, 43030}, {35688, 42993}, {36344, 44289}, {37008, 41107}, {37173, 49861}, {41105, 41113}, {41108, 44031}, {41115, 41120}, {41118, 49873}, {41128, 49824}, {42974, 51278}, {45420, 49064}, {45421, 49065}
X(51487) = midpoint of X(i) and X(j) for these {i,j}: {2, 22114}, {18, 36368}, {628, 33627}
X(51487) = reflection of X(i) in X(j) for these {i,j}: {2, 18}, {628, 2}, {22114, 36368}, {33624, 628}, {33627, 22114}, {36346, 22845}, {36368, 33464}, {36388, 630}, {48665, 3845}
X(51487) = anticomplement of X(50860)
X(51487) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 33627, 33624}, {2, 36324, 36388}, {2, 36368, 33627}, {18, 22114, 628}, {18, 22845, 6674}, {18, 33464, 22114}, {634, 42153, 33412}, {16268, 34508, 2}
X(51488) lies on these lines: {1, 4753}, {2, 37}, {6, 29580}, {9, 17394}, {44, 29570}, {45, 3758}, {86, 3731}, {141, 29582}, {190, 16676}, {239, 16672}, {319, 5296}, {320, 5308}, {335, 4370}, {376, 51038}, {381, 30273}, {518, 38023}, {519, 41848}, {527, 27475}, {537, 25055}, {547, 51040}, {549, 20430}, {551, 984}, {597, 49509}, {599, 29575}, {650, 50763}, {726, 19883}, {740, 19875}, {742, 21358}, {872, 42042}, {894, 16675}, {966, 17315}, {1086, 29581}, {1125, 17354}, {1213, 17242}, {1654, 17386}, {1698, 50096}, {1992, 51050}, {2667, 42043}, {3241, 15569}, {3247, 16834}, {3543, 51042}, {3589, 49502}, {3616, 49499}, {3622, 49515}, {3624, 49456}, {3634, 49452}, {3636, 49503}, {3679, 3842}, {3696, 51054}, {3723, 17349}, {3759, 16777}, {3828, 3993}, {3834, 29599}, {3912, 17250}, {3943, 29576}, {3986, 5224}, {4029, 24603}, {4098, 4967}, {4357, 17241}, {4360, 16673}, {4363, 29578}, {4364, 17227}, {4389, 29571}, {4422, 17397}, {4428, 34247}, {4473, 29592}, {4643, 17387}, {4648, 17258}, {4670, 29595}, {4673, 27785}, {4677, 49471}, {4708, 17230}, {4709, 51069}, {4725, 16590}, {4745, 49459}, {4748, 29583}, {4851, 17328}, {4971, 31322}, {5055, 29010}, {5071, 51043}, {5257, 17233}, {5550, 49483}, {5750, 30598}, {6172, 51057}, {6173, 51052}, {6666, 17380}, {7611, 44430}, {9055, 48310}, {9466, 32453}, {9780, 49462}, {10124, 51048}, {10180, 42056}, {13635, 46475}, {14829, 25430}, {15492, 37677}, {15668, 16677}, {15692, 30271}, {15694, 51039}, {15702, 51049}, {16568, 40131}, {16674, 17259}, {16814, 17379}, {16815, 17318}, {16817, 50072}, {16830, 48805}, {16832, 17160}, {17045, 17338}, {17228, 17243}, {17234, 17249}, {17237, 29572}, {17245, 17247}, {17246, 27147}, {17251, 17310}, {17252, 17311}, {17253, 17312}, {17254, 17313}, {17256, 17316}, {17257, 17317}, {17265, 17324}, {17266, 17325}, {17267, 17326}, {17268, 17327}, {17269, 29610}, {17271, 29573}, {17290, 29626}, {17294, 31144}, {17300, 17329}, {17330, 17389}, {17331, 17390}, {17332, 17391}, {17333, 17392}, {17337, 17396}, {17339, 17398}, {17346, 29574}, {17350, 28639}, {17352, 25072}, {17369, 29612}, {17378, 50093}, {17381, 25101}, {17395, 29628}, {17448, 39738}, {18146, 21615}, {19853, 50122}, {19862, 49493}, {19876, 49474}, {20582, 51051}, {20943, 27255}, {20945, 27285}, {21330, 42039}, {24325, 51035}, {24349, 51061}, {25358, 29608}, {26255, 44670}, {27776, 31179}, {27811, 44671}, {29054, 38021}, {29617, 49731}, {31145, 50778}, {31319, 47352}, {31336, 36911}, {31997, 32009}, {32092, 32102}, {34641, 49678}, {36817, 36872}, {39586, 50126}, {40328, 51060}, {41875, 50179}, {45310, 51062}, {46933, 49468}, {49448, 51105}, {49457, 51093}, {49469, 51066}, {49479, 51108}, {49490, 51103}, {49501, 51110}, {49504, 51104}, {49507, 50109}, {49518, 50118}, {49520, 51109}, {49523, 51056}, {49533, 51126}, {49722, 50090}, {49738, 49742}, {49740, 50286}, {49746, 50291}, {49748, 50116}, {50074, 50125}, {50088, 50110}, {50095, 50121}, {51053, 51058}
X(51488) = barycentric product X(190)*X(48548)
X(51488) = barycentric quotient X(48548)/X(514)
X(51488) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 50094, 50075}, {2, 37, 4664}, {2, 192, 4688}, {2, 4664, 75}, {2, 4688, 4751}, {2, 4704, 4740}, {2, 4740, 3739}, {2, 4755, 4687}, {2, 27268, 4755}, {2, 41312, 17399}, {2, 41313, 17342}, {9, 29597, 46922}, {37, 3739, 4704}, {37, 4687, 75}, {37, 4698, 192}, {37, 4755, 2}, {37, 27268, 4687}, {45, 16826, 3758}, {86, 3731, 17336}, {190, 16831, 41847}, {192, 4698, 4751}, {192, 4751, 75}, {344, 17322, 17371}, {376, 51038, 51063}, {381, 30273, 51065}, {381, 51045, 30273}, {547, 51046, 51040}, {549, 20430, 51044}, {551, 984, 51055}, {599, 50779, 49496}, {1125, 50777, 31178}, {1213, 17242, 48630}, {3241, 51034, 49450}, {3247, 17277, 17393}, {3644, 3739, 75}, {3679, 50111, 49470}, {3739, 4704, 3644}, {3828, 3993, 50086}, {3842, 50111, 3679}, {3912, 17250, 48639}, {4357, 17241, 48638}, {4364, 17244, 17227}, {4643, 29569, 17387}, {4664, 4687, 2}, {4681, 4699, 4764}, {4687, 4751, 4698}, {4688, 4698, 2}, {4699, 4764, 75}, {5224, 17240, 48640}, {15569, 51034, 3241}, {15668, 16677, 17261}, {15692, 51064, 30271}, {16674, 17259, 17319}, {16676, 16831, 190}, {16777, 17260, 3759}, {17234, 17249, 48637}, {17243, 17248, 17228}, {17245, 17247, 48629}, {17254, 29620, 17313}, {17256, 17316, 17360}, {17257, 17317, 17361}, {17263, 17321, 17370}, {17330, 17389, 50077}, {17333, 29622, 17392}, {17346, 29574, 50132}, {17392, 49737, 17333}, {17395, 31285, 29628}, {29597, 46922, 17394}, {31178, 50777, 49447}, {49731, 50113, 29617}, {49738, 49742, 50128}
See Ivan Pavlov, euclid 5444.
X(51489) lies on these lines: {3, 9}, {144, 1071}, {165, 1864}, {390, 3488}
See Ivan Pavlov, euclid 5444.
X(51490) lies on the cubic K401 and these lines: {3, 77}, {4, 189}, {20, 145}, {40, 222}, {57, 1433}, {65, 1359}
See Ivan Pavlov, euclid 5444.
X(51491) lies on these lines: {4, 64}, {5, 1539}, {154, 3529}, {156, 1147}, {185, 1112}, {382, 1351}
X(51492) has Steiner coordinates (0, (-2*(-a^2 + b^2)*(b^2 - c^2)*(-a^2 + c^2)*(a^4 + b^4 + c^4 - (a^2 + b^2 + c^2)*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]))/(a^2*b^2 + a^2*c^2 + b^2*c^2)).
X(51492) lies on the Steiner minor axis, the cubics K248 and K553, and on these lines: {2, 1340}, {6, 99}, {148, 31863}, {187, 6189}, {194, 3413}, {384, 14630}, {385, 1379}, {538, 2029}, {1380, 13586}, {1916, 46024}, {2028, 32456}, {3552, 3558}, {6248, 47366}, {7783, 14631}, {35297, 39023}, {39022, 47286}
X(51492) = reflection of X(6190) in X(2029)
X(51492) = crossdifference of every pair of points on line {888, 5638}
X(51492) = {X(39204),X(39205)}-harmonic conjugate of X(5639)
X(51493) has Steiner coordinates ((-2*(-a^2 + b^2)*(b^2 - c^2)*(-a^2 + c^2)*(a^4 + b^4 + c^4 + (a^2 + b^2 + c^2)*Sqrt[a^4 - a^2*b^2 + b^4 - a^2*c^2 - b^2*c^2 + c^4]))/(a^2*b^2 + a^2*c^2 + b^2*c^2), 0).
X(51493) lies on the Steiner minor axis, the cubics K248 and K553, and on these lines: {2, 1341}, {6, 99}, {148, 31862}, {187, 6190}, {194, 3414}, {384, 14631}, {385, 1380}, {538, 2028}, {1379, 13586}, {1916, 46023}, {2029, 32456}, {3552, 3557}, {6248, 47365}, {7783, 14630}, {35297, 39022}, {39023, 47286}
X(51493) = reflection of X(6189) in X(2028)
X(51493) = crossdifference of every pair of points on line {888, 5639}
X(51493) = {X(39202),X(39203)}-harmonic conjugate of X(5638)
X(51494) lies on the cubics K248 and K353 and on these lines: {39, 512}, {187, 729}, {511, 694}, {538, 671}, {574, 45146}, {625, 18896}, {1570, 34238}, {1692, 9467}, {2021, 47642}, {2023, 35078}, {5969, 35077}, {36214, 46292}, {44422, 47734}
X(51494) = midpoint of X(1916) and X(18829)
X(51494) = reflection of X(35078) in X(2023)
X(51494) = isogonal conjugate of X(47646)
X(51494) = X(i)-isoconjugate of X(j) for these (i,j): {1, 47646}, {1580, 35146}, {1966, 5970}
X(51494) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 47646), (9467, 5970), (35077, 3978), (39092, 35146)
X(51494) = barycentric product X(i)*X(j) for these {i,j}: {694, 5969}, {805, 11182}, {882, 14607}, {1916, 5106}
X(51494) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 47646}, {694, 35146}, {881, 14606}, {5106, 385}, {5969, 3978}, {9468, 5970}, {11182, 14295}, {14607, 880}
X(51494) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {805, 9468, 187}, {14251, 47648, 39}
See Ivan Pavlov, euclid 5453.
X(51495) lies on this line: {28, 216}
X(51495) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}} and {{A, B, C, X(3), X(5)}}
See Ivan Pavlov, euclid 5453.
X(51496) lies on these lines: {3, 2982}, {57, 581}, {278, 942}
X(51496) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}} and {{A, B, C, X(3), X(7)}}
See Ivan Pavlov, euclid 5453.
X(51497) lies on this line: {999, 2982}
X(51497) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}} and {{A, B, C, X(3), X(8)}}
See Ivan Pavlov, euclid 5453.
X(51498) lies on these lines: {3, 1422}, {28, 2270}, {40, 278}, {81, 1819}
X(51498) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}} and {{A, B, C, X(3), X(9)}}
See Ivan Pavlov, euclid 5453.
X(51499) lies on this line: {28, 573}
X(51499) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}} and {{A, B, C, X(3), X(10)}}
See Ivan Pavlov, euclid 5453.
X(51500) lies on these lines: {5, 81}, {28, 53}, {274, 311}
X(51500) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}} and {{A, B, C, X(4), X(5)}}
See Ivan Pavlov, euclid 5453.
X(51501) lies on these lines: {12, 2982}, {28, 1865}, {81, 442}, {274, 1234}
X(51501) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}} and {{A, B, C, X(4), X(12)}}
See Ivan Pavlov, euclid 5453.
X(51502) lies on these lines: {20, 81}, {28, 1249}, {57, 387}
X(51502) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}} and {{A, B, C, X(4), X(20)}}
See Ivan Pavlov, euclid 5453.
X(51503) lies on this line: {52, 81}
X(51503) = intersection, other than A, B, C, of circumconics {{A, B, C, X(1), X(2)}} and {{A, B, C, X(5), X(6)}}
Perspectors involving the García-Moses triangle: X(51504)-X(51507)
This preamble is contributed by Clark Kimberling, based on notes from Emmanuel José García and Peter Moses.
In the plane of a triangle ABC, let
A'B'C' = cevian triangle of X(1); Ma = midpoint of AA', and define Mb and Mc cyclically; A'' = BMc∩CMb, and define B'' and C'' cyclicaly. The triangle A''B''C'' is here named the García-Moses triangle. Barycentrics for the vertices are given by
A'' = a : a+c : a+b, B'' = b+c : b + b+a, C'' = c+b : c+a : c.
The appearance of (T,i) in the following list means that T is perspective to A'B'C', and the perspector is X(i):
(ABC, 10), (medial, 9), (excentral, 9), (extouch, 1), (1st circumperp, 4220), (half-altitude, 1), (1st Sharygin, 4220), (outer García, 10), (2nd extouch, 9), (tangential of excentral, 9), (García reflection, 9), (2nd Zaniah, 9), (Gemini 4, 9), (Gemini 5, 9), (Gemini 7, 2), (Gemini 8, 9), Gemini 15, 2), (Gemini 17, 2), (Gemini 25, 2), (Gemini 26, 10), (Gemini 119, 9), (extangents, 51504), (1st Conway, 51505), (anti-inner-García, 51506), (Aquilla, 51507)
The appearance of (T,i) in the following list means that T is orthologic to A'B'C', and the orthology center is X(i):
(Jenkins [centers of Jenkins circles], 10), (Ehrmann cross triangle, 30), (centers of the Apollonius circles, 511), (8th Brocard, 511), (1st Savin [c.f. X(44301), 10)
The appearance of (T,i) in the following list means that T is paralogic to A'B'C', and the parallelogy center is X(i):
(Ehrmann cross triangle, 523), (centers of the Apollonius circles, 512), (8th Brocard, 512)
X(51504) lies on these lines: {1, 3688}, {5, 40}, {9, 20306}, {55, 3216}, {71, 3294}, {573, 19855}, {1018, 4647}, {1764, 19854}, {3730, 4295}, {4026, 31435}, {4972, 5250}, {5251, 48883}, {5584, 33536}, {6254, 30503}, {6684, 26031}, {8274, 11529}, {10624, 13576}, {10901, 41342}, {12514, 37330}, {17524, 35338}, {21362, 32277}
X(51505) lies on these line:s {7, 21471}, {21, 42}, {63, 3731}, {2345, 5273}, {4220, 31445}, {7411, 8580}, {28610, 49737}
X(51506) lies on these lines: {1, 1331}, {2, 4996}, {3, 119}, {8, 10087}, {9, 48}, {10, 21}, {11, 405}, {12, 37308}, {36, 908}, {40, 12775}, {55, 1145}, {56, 34123}, {63, 11570}, {72, 12739}, {149, 16865}, {153, 37106}, {191, 11571}, {210, 41541}, {392, 12740}, {404, 7951}, {442, 13273}, {474, 31235}, {528, 16418}, {529, 41345}, {631, 18861}, {936, 15015}, {943, 6596}, {952, 958}, {954, 6068}, {956, 1317}, {960, 6265}, {999, 42843}, {1001, 1387}, {1012, 24466}, {1259, 49168}, {1319, 41389}, {1320, 1621}, {1376, 6914}, {1377, 48715}, {1378, 48714}, {1478, 37300}, {1512, 2077}, {1537, 3428}, {1697, 2802}, {1718, 16586}, {1768, 31424}, {1807, 24433}, {1826, 4227}, {2478, 39692}, {2550, 13199}, {2551, 6875}, {2771, 31445}, {2800, 12514}, {2886, 7489}, {2932, 6174}, {2950, 30503}, {2975, 5692}, {3036, 9708}, {3219, 12532}, {3295, 5854}, {3303, 25416}, {3419, 12743}, {3436, 36152}, {3560, 5840}, {3585, 35979}, {3651, 10728}, {3683, 17638}, {3746, 13278}, {3811, 14740}, {3814, 6905}, {3820, 7508}, {3878, 10698}, {4127, 8666}, {4187, 37564}, {4189, 17100}, {4293, 37313}, {4299, 37301}, {4316, 36003}, {4640, 12515}, {5044, 22935}, {5047, 31272}, {5080, 27086}, {5119, 39776}, {5172, 17757}, {5234, 5531}, {5250, 12758}, {5253, 37701}, {5258, 7972}, {5259, 13279}, {5267, 5660}, {5273, 9803}, {5289, 19907}, {5302, 12738}, {5428, 11698}, {5432, 19525}, {5450, 5720}, {5533, 10527}, {5541, 9623}, {5587, 6906}, {5693, 18232}, {5705, 37718}, {5727, 8715}, {5745, 10265}, {5850, 7677}, {6154, 19526}, {6667, 11108}, {6675, 13272}, {6702, 37306}, {6713, 6883}, {6734, 10073}, {6735, 32760}, {6745, 17010}, {6874, 38163}, {6907, 12761}, {6909, 28164}, {6912, 10724}, {6920, 25639}, {8069, 45701}, {8071, 10200}, {8256, 11849}, {9678, 48700}, {9840, 34868}, {10057, 24987}, {10198, 37248}, {10483, 35976}, {10707, 16858}, {10711, 21161}, {10902, 12751}, {10956, 37579}, {11012, 21616}, {11113, 12764}, {11249, 11729}, {11508, 49169}, {11517, 22760}, {11700, 16578}, {12119, 17647}, {12513, 12735}, {12572, 21635}, {12611, 24703}, {12619, 26066}, {12749, 14798}, {12776, 15829}, {13243, 15096}, {13271, 15171}, {13274, 24390}, {13587, 31160}, {13732, 15654}, {15528, 18443}, {15863, 38665}, {16857, 45310}, {16872, 49128}, {17571, 35023}, {18397, 22836}, {18406, 21669}, {21077, 37583}, {25005, 45392}, {25531, 37017}, {25681, 26286}, {26031, 37043}, {26285, 37828}, {28376, 49553}, {28453, 49732}, {31458, 37726}, {32612, 37713}, {33337, 38669}, {34583, 36058}, {36740, 51007}, {37560, 46684}, {38109, 45976}, {41229, 46685}
X(51506) = crossdifference of every pair of points on line {1769, 21828}
X(51506) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4996, 10090}, {9, 6326, 18254}, {21, 100, 10058}, {55, 1145, 25438}, {80, 35204, 100}, {214, 993, 104}, {214, 18254, 6326}, {1001, 22560, 1387}, {1329, 3035, 38752}, {3219, 39778, 12532}, {5251, 35204, 80}, {8071, 25875, 10200}, {9708, 12331, 3036}
X(51507) lies on these lines: {1, 966}, {10, 329}, {72, 8274}, {1203, 37658}, {1211, 1698}, {1453, 17330}, {1745, 8580}, {3175, 3679}, {3624, 4038}, {3707, 37037}, {5739, 19859}, {9614, 31330}, {19872, 30811}, {31142, 39564}, {37554, 49724}
X(51507) = reflection of X(41921) in X(10)
X(51508) lies on these lines: {25, 251}, {64, 1176}, {83, 3091}, {827, 1297}, {1042, 46289}, {9292, 33632}, {10002, 10548}, {10313, 20968}, {14885, 21637}, {16277, 18841}, {18105, 46615}, {19153, 26216}, {20993, 22240}, {23047, 32581}
X(51508) = X(1176)-Ceva conjugate of X(251)
X(51508) = X(i)-isoconjugate of X(j) for these (i,j): {38, 253}, {64, 1930}, {141, 2184}, {427, 19611}, {1073, 20883}, {1235, 19614}, {1964, 41530}, {2155, 8024}, {3665, 44692}, {3703, 8809}, {8061, 44326}, {17442, 34403}
X(51508) = X(i)-Dao conjugate of X(j) for these (i, j): (4, 1235), (122, 23285), (41884, 41530), (45245, 8024), (45248, 3933)
X(51508) = barycentric product X(i)*X(j) for these {i,j}: {20, 251}, {82, 610}, {83, 154}, {204, 34055}, {827, 6587}, {1176, 1249}, {1799, 3172}, {4628, 21172}, {6525, 28724}, {10547, 15466}, {14615, 46288}, {15905, 32085}, {17500, 33629}, {17898, 34072}, {18105, 36841}, {18750, 46289}, {26224, 40174}, {42396, 42658}
X(51508) = barycentric quotient X(i)/X(j) for these {i,j}: {20, 8024}, {83, 41530}, {154, 141}, {204, 20883}, {251, 253}, {610, 1930}, {827, 44326}, {1176, 34403}, {1249, 1235}, {3172, 427}, {4630, 46639}, {6587, 23285}, {10547, 1073}, {15905, 3933}, {42658, 2525}, {46288, 64}, {46289, 2184}
X(51509) lies on these lines: {3, 3162}, {4, 251}, {6, 64}, {20, 112}, {24, 14580}, {32, 3575}, {235, 36417}, {1092, 35325}, {1498, 22135}, {1503, 19595}, {1560, 3548}, {2353, 27373}, {2937, 8428}, {5085, 44885}, {5889, 41363}, {6753, 34116}, {7503, 8743}, {8778, 37198}, {9818, 40144}, {11325, 44077}, {12225, 36414}, {37126, 39575}, {37196, 41358}
X(51509) = reflection of X(3) in X(44884)
X(51509) = X(1176)-Ceva conjugate of X(25)
X(51509) = X(27376)-Dao conjugate of X(1235)
X(51509) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {112, 41361, 10316}, {1033, 3172, 2138}
X(51510) = X(i)-isoconjugate of X(j) for these (i,j): {538, 1967}, {694, 2234}, {888, 37134}, {1581, 3231}, {1927, 30736}, {1934, 33875}
X(51510) = X(i)-Dao conjugate of X(j) for these (i, j): (8290, 538), (8623, 6786), (19576, 3231), (35078, 9148), (39043, 2234)
X(51510) = trilinear pole of line {385, 5027}
X(51510) = barycentric product X(i)*X(j) for these {i,j}: {385, 3228}, {729, 3978}, {804, 9150}, {886, 5027}, {1691, 34087}, {1966, 37132}, {14295, 32717}
X(51510) = barycentric quotient X(i)/X(j) for these {i,j}: {385, 538}, {729, 694}, {804, 9148}, {1580, 2234}, {1691, 3231}, {3228, 1916}, {3978, 30736}, {5026, 45672}, {5027, 888}, {9150, 18829}, {14602, 33875}, {17941, 23342}, {32717, 805}, {34087, 18896}, {36133, 37134}, {36213, 6786}, {37132, 1581}, {40820, 36822}, {41309, 18872}, {44089, 46522}
X(51510) = {X(2),X(41309)}-harmonic conjugate of X(9150)
X(51511) lies on these lines: {2, 46278}, {6, 1916}, {39, 512}, {694, 9465}, {805, 3094}, {20965, 47734}
X(51511) = X(737)-isoconjugate of X(1966)
X(51511) = X(9467)-Dao conjugate of X(737)
X(51511) = barycentric product X(i)*X(j) for these {i,j}: {694, 736}, {9468, 35542}
X(51511) = barycentric quotient X(i)/X(j) for these {i,j}: {736, 3978}, {9468, 737}, {35542, 14603}
X(51512) lies on the Feuerbach circumhyperbola and these lines: {8, 5173}, {9, 3485}, {21, 41549}, {84, 3671}, {388, 6598}, {942, 3427}, {943, 3428}, {3486, 5665}, {3889, 43740}, {4866, 6856}, {6988, 7160}, {10390, 12573}, {12047, 38271}, {12608, 38308}, {12867, 19843}, {17097, 50695}
See Angel Montesdeoca, euclid 5464.
X(51513) lies on these lines: {4,18335}, {24,39481}, {25,15475}, {51,35361}, {186,39606}, {378,1116}, {427,39512}, {460,512}, {523,37942}, {690,16229}, {826,14618}, {1499,42399}, {1637,39201}, {3566,39533}, {3850,44926}, {6368,18314}, {7577,39494}, {8754,43967}, {12077,15451}, {17994,39799}.
X(51513) = midpoint of X(i) and X(j) for these {i,j}: {12077, 15451}, {14618, 16230}
See Ivan Pavlov, euclid 5465.
X(51514) lies on these lines: {3, 7}, {144, 1656}
See Ivan Pavlov, euclid 5465.
X(51515) lies on these lines: {3, 8}, {5, 3621}, {140, 4678}, {145, 1656}, {355, 3625}
See Ivan Pavlov, euclid 5465.
X(51516) lies on these lines: {3, 9}, {5, 144}, {7, 1656}
See Ivan Pavlov, euclid 5465.
X(51517) lies on these lines: {3, 11}, {4, 1484}, {5, 149}, {80, 1482}, {100, 1656}, {104, 382}, {119, 3851}, {153, 546}, {381, 3241}
See Ivan Pavlov, euclid 5465.
X(51518) lies on these lines: {3, 12}, {381, 3241}
See Ivan Pavlov, euclid 5465.
X(51519) lies on these lines: {2, 3}, {49, 44078}, {143, 9707}, {154, 568}, {542, 20987}, {567, 17810}, {1147, 21969}, {1154, 35264}, {1351, 9703}, {1495, 14831}, {1609, 1989}, {2931, 5655}, {3167, 45780}, {3581, 18451}, {3654, 49553}, {3679, 9625}, {5050, 9971}, {5093, 19153}, {5309, 9699}, {5892, 35268}, {5898, 19588}, {5946, 6800}, {6243, 37672}, {6759, 37490}, {7716, 19129}, {7739, 9608}, {8185, 28204}, {8193, 38066}, {8584, 15582}, {8724, 39828}, {8780, 50461}, {9306, 37494}, {9590, 31162}, {9626, 25055}, {9682, 41945}, {9704, 37493}, {9880, 39854}, {10117, 20126}, {10282, 21849}, {10540, 37489}, {11402, 13321}, {11464, 39522}, {11632, 39857}, {12161, 26882}, {12824, 32609}, {13364, 34513}, {13754, 44082}, {14805, 31860}, {15080, 41448}, {15087, 26864}, {15577, 20423}, {15578, 51022}, {15580, 51136}, {16266, 43572}, {17821, 37472}, {17834, 18350}, {18474, 32223}, {18475, 34417}, {20771, 44456}, {22115, 33586}, {22655, 32447}, {23039, 35259}, {34225, 36609}, {37488, 50955}, {38794, 48910}
X(51519) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {{2, 13490, 381}, {2, 37939, 26}, {3, 5899, 44457}, {3, 20850, 5899}, {3, 37956, 9909}, {3, 44454, 35452}, {4, 37940, 18324}, {23, 6644, 12083}, {23, 47485, 6644}, {24, 7517, 3}, {24, 35471, 3515}, {24, 37440, 7517}, {25, 2070, 3}, {25, 3515, 403}, {25, 9715, 11818}, {25, 9818, 7545}, {25, 14070, 381}, {26, 3518, 7506}, {26, 7506, 3}, {26, 7516, 38435}, {26, 7568, 9715}, {26, 44213, 14070}, {381, 382, 18568}, {381, 2070, 14070}, {381, 14070, 3}, {382, 3515, 3}, {403, 18568, 381}, {1656, 9715, 3}, {2937, 6642, 3}, {3517, 9714, 3}, {3518, 37939, 2}, {3543, 47334, 381}, {3627, 32534, 47524}, {3830, 37922, 3}, {6644, 12083, 3}, {7387, 45735, 3}, {7426, 7576, 10201}, {7529, 16195, 3}, {7556, 13595, 7514}, {7576, 10201, 381}, {9714, 9909, 37956}, {10254, 18494, 3843}, {11414, 43809, 3}, {12106, 37936, 22}, {13490, 44213, 2}, {15682, 37941, 12084}, {15682, 44879, 37941}, {15694, 34006, 3}, {18378, 37922, 3830}, {32534, 47524, 3}, {37444, 44232, 1656}
See Ivan Pavlov, euclid 5467.
X(51520) lies on this line: {5, 141}
See Ivan Pavlov, euclid 5467.
X(51521) lies on this line: {3, 74}
See Ivan Pavlov, euclid 5467.
X(51522) lies on the circle ((X3), 3R/2) and these lines: {3, 74}, {113, 3628}, {125, 546}, {146, 3090}
See Ivan Pavlov, euclid 5467.
X(51523) lies on the circle ((X3), 3R/2) and these lines: {3, 76}, {5, 575}, {114, 3628}, {115, 546}, {147, 3090}, {148, 3529}, {382, 671}
See Ivan Pavlov, euclid 5467.
X(51524) lies on the circle ((X3), 3R/2) and these lines: {3, 76}, {26, 2936}, {114, 546}, {115, 3628}, {147, 3529}, {148, 3090}
See Ivan Pavlov, euclid 5467.
X(51525) lies on the circle ((X3), 3R/2) and these lines: {3, 8}, {11, 3628}, {119, 546}, {149, 3090}, {153, 3529}
See Ivan Pavlov, euclid 5467.
X(51526) lies on the circle ((X3), 3R/2) and these lines: {3, 101}, {116, 3628}, {150, 3090}, {152, 3529}
See Ivan Pavlov, euclid 5467.
X(51527) lies on the circle ((X3), 3R/2) and these lines: {3, 102}, {117, 3628}, {124, 546}, {151, 3090}
See Ivan Pavlov, euclid 5467.
X(51528) lies on the circle ((X3), 3R/2) and these lines: {3, 101}, {116, 546}, {118, 3628}, {150, 3529}, {152, 3090}
See Ivan Pavlov, euclid 5467.
X(51529) lies on the circle ((X3), 3R/2) and these lines: {3, 8}, {11, 546}, {119, 3628}, {149, 3529}, {153, 3090}
See Ivan Pavlov, euclid 5467.
X(515300) lies on the circle ((X3), 3R/2) and these lines: {3, 105}, {120, 3628}
See Ivan Pavlov, euclid 5467.
X(51531) lies on the circle ((X3), 3R/2) and these lines: {3, 106}, {121, 3628}
See Ivan Pavlov, euclid 5467.
X(51532) lies on the circle ((X3), 3R/2) and these lines: {3, 107}, {122, 3628}, {133, 546}
See Ivan Pavlov, euclid 5467.
X(51533) lies on the circle ((X3), 3R/2) and these lines: {3, 108}, {123, 3628}
See Ivan Pavlov, euclid 5467.
X(51534) lies on the circle ((X3), 3R/2) and these lines: {3, 102}, {117, 546}, {124, 3628}, {151, 3529}
See Ivan Pavlov, euclid 5467.
X(51535) lies on the circle ((X3), 3R/2) and these lines: {3, 111}, {126, 3628}
See Ivan Pavlov, euclid 5467.
X(51536) lies on the circle ((X3), 3R/2) and these lines: {3, 112}, {132, 546}
X(51537) lies on these lines: {2, 14927}, {4, 69}, {5, 12017}, {6, 1131}, {20, 3619}, {30, 40330}, {66, 6225}, {141, 3146}, {146, 32274}, {182, 3545}, {193, 50689}, {343, 7408}, {376, 24206}, {381, 6776}, {382, 10519}, {394, 7409}, {487, 36711}, {488, 36712}, {516, 17286}, {542, 41099}, {546, 1353}, {549, 50957}, {599, 50687}, {631, 29012}, {1176, 26883}, {1350, 3543}, {1351, 3845}, {1386, 9779}, {1503, 3091}, {1539, 32247}, {1699, 51192}, {1853, 7398}, {1992, 3839}, {2883, 20079}, {3088, 28408}, {3090, 46264}, {3098, 33703}, {3313, 15056}, {3416, 9812}, {3424, 7792}, {3448, 7394}, {3522, 3763}, {3523, 48905}, {3524, 25561}, {3526, 33750}, {3529, 48884}, {3533, 17508}, {3544, 38317}, {3564, 3843}, {3589, 5068}, {3620, 17578}, {3830, 48876}, {3844, 9778}, {3850, 5050}, {3851, 48906}, {3853, 33878}, {3854, 51171}, {3855, 14561}, {3860, 14848}, {4048, 37690}, {4232, 45303}, {5032, 50959}, {5056, 5085}, {5059, 31884}, {5064, 14826}, {5067, 5092}, {5071, 11645}, {5072, 38110}, {5097, 50974}, {5133, 11206}, {5225, 12588}, {5229, 12589}, {5972, 8889}, {6393, 32826}, {6515, 37349}, {6564, 39876}, {6565, 39875}, {6811, 32813}, {6813, 32812}, {6995, 32269}, {6997, 11451}, {7000, 32805}, {7374, 32806}, {7378, 37669}, {7392, 11550}, {7403, 18925}, {7527, 15577}, {7528, 18909}, {7544, 7729}, {7687, 25320}, {7714, 21243}, {9822, 11381}, {9969, 12111}, {10019, 19118}, {10151, 32220}, {10299, 48892}, {11001, 14810}, {11008, 15069}, {11178, 15682}, {11179, 41106}, {11439, 34146}, {11541, 48880}, {11898, 14269}, {12007, 38072}, {12571, 16475}, {13860, 34803}, {14118, 20987}, {14232, 48467}, {14237, 48466}, {14484, 41624}, {14893, 50955}, {14912, 19130}, {14982, 32255}, {15022, 47355}, {15059, 36201}, {15073, 46852}, {15305, 19161}, {15435, 37201}, {15683, 21358}, {15687, 50967}, {15692, 51216}, {15694, 50975}, {15698, 33751}, {15717, 34573}, {17040, 18296}, {17538, 29323}, {18141, 37456}, {18386, 39871}, {18480, 39898}, {18483, 39885}, {18537, 41257}, {19119, 43831}, {19924, 51029}, {21167, 50693}, {22682, 32451}, {32822, 51371}, {33006, 39141}, {33522, 34603}, {34648, 50999}, {35260, 36989}, {35403, 50954}, {36757, 42921}, {36758, 42920}, {37511, 46849}, {38136, 39899}, {38146, 39878}, {39902, 45631}, {39903, 45630}, {40107, 43621}, {44442, 44833}, {44802, 44883}, {47352, 50960}, {48310, 51025}, {48881, 49135}, {48910, 50688}, {48942, 50977}, {50982, 51213}
X(51537) = midpoint of X(i) and X(j) for these {i,j}: {3620, 17578}, {11482, 18440}, {15692, 51216}, {35403, 50954}
X(51537) = reflection of X(i) in X(j) for these {i,j}: {3522, 3763}, {3618, 3091}, {5071, 50956}, {12017, 5}, {22234, 19130}, {50975, 15694}
X(51537) = anticomplement of the isogonal conjugate of X(43951)
X(51537) = X(43951)-anticomplementary conjugate of X(8)
X(51537) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 36990, 14927}, {4, 1352, 51212}, {20, 10516, 3619}, {381, 39884, 6776}, {381, 48662, 18583}, {382, 18358, 10519}, {546, 18440, 14853}, {1352, 48889, 4}, {1352, 51212, 69}, {3543, 47354, 21356}, {3818, 48889, 1352}, {3839, 5921, 5480}, {3839, 47353, 1992}, {3855, 39874, 14561}, {5480, 5921, 1992}, {5480, 47353, 5921}, {6776, 39884, 51023}, {6997, 32064, 18928}, {7687, 41737, 25320}, {12322, 12323, 76}, {18583, 39884, 48662}, {18583, 48662, 6776}, {21358, 51022, 15683}
X(51538) lies on these lines: {2, 21167}, {3, 38136}, {4, 69}, {6, 3146}, {20, 3618}, {30, 5050}, {51, 44442}, {64, 15741}, {66, 15749}, {141, 3832}, {146, 32255}, {165, 38146}, {182, 3529}, {193, 17578}, {343, 7409}, {373, 7386}, {376, 10168}, {381, 10519}, {382, 5093}, {394, 7408}, {428, 6090}, {487, 36712}, {488, 36711}, {516, 50127}, {518, 9812}, {524, 50687}, {546, 33878}, {568, 18909}, {575, 11541}, {576, 39874}, {597, 15683}, {631, 19130}, {698, 44434}, {895, 13202}, {1176, 11424}, {1350, 3091}, {1351, 3627}, {1370, 5640}, {1469, 5225}, {1503, 1992}, {1513, 34803}, {1656, 48874}, {1657, 18583}, {1692, 43618}, {2777, 25320}, {3056, 5229}, {3060, 32064}, {3089, 28408}, {3090, 3098}, {3424, 14614}, {3522, 3589}, {3523, 48881}, {3524, 38317}, {3525, 14810}, {3528, 48880}, {3534, 33750}, {3545, 19924}, {3564, 3830}, {3620, 50689}, {3751, 51118}, {3763, 5068}, {3839, 10516}, {3843, 48876}, {3845, 50957}, {3853, 18440}, {3855, 24206}, {4872, 5809}, {5034, 43619}, {5059, 44882}, {5073, 48906}, {5076, 39884}, {5092, 17538}, {5103, 37690}, {5133, 33522}, {5175, 43216}, {5261, 10387}, {5476, 11001}, {5650, 7392}, {5691, 51192}, {5731, 38035}, {5893, 9924}, {5895, 15583}, {5921, 11008}, {6225, 36851}, {6293, 12324}, {6393, 32827}, {6515, 16981}, {6800, 7500}, {6811, 32812}, {6813, 32813}, {6995, 35259}, {6997, 7998}, {7000, 32806}, {7374, 32805}, {7378, 33586}, {7391, 11002}, {7394, 33884}, {7396, 17810}, {7487, 28708}, {7519, 35265}, {7528, 13340}, {7553, 18925}, {7736, 40236}, {7738, 13331}, {7757, 15428}, {8550, 50691}, {8584, 51026}, {8703, 50963}, {9589, 49529}, {9730, 34938}, {9778, 38047}, {10002, 37200}, {10113, 32247}, {10304, 38072}, {10733, 11061}, {10752, 12295}, {10753, 39809}, {10754, 39838}, {10762, 38956}, {11174, 14484}, {11179, 29323}, {11180, 15687}, {11206, 34603}, {11403, 37491}, {12017, 15704}, {12101, 50955}, {12156, 14912}, {12317, 32273}, {12383, 32271}, {13203, 45237}, {13910, 43512}, {13972, 43511}, {14555, 37456}, {15022, 34573}, {15312, 31886}, {15437, 20859}, {15531, 41735}, {15533, 51166}, {15534, 51022}, {15640, 33748}, {15685, 50975}, {15689, 38079}, {15693, 50969}, {15697, 50983}, {15705, 48310}, {15717, 47355}, {15740, 41256}, {16051, 34417}, {16475, 28164}, {16774, 18296}, {18918, 31723}, {18950, 21849}, {19119, 21659}, {19145, 43408}, {19146, 43407}, {20070, 49524}, {20079, 41362}, {21735, 48885}, {22491, 41024}, {22492, 41025}, {22615, 35840}, {22644, 35841}, {22682, 32983}, {22793, 39898}, {25555, 48879}, {31099, 37643}, {31305, 37506}, {31861, 41465}, {31952, 40981}, {33280, 39141}, {33703, 39561}, {34608, 35268}, {35502, 37488}, {35820, 39875}, {35821, 39876}, {36002, 36740}, {36757, 42085}, {36758, 42086}, {38147, 38693}, {38168, 38754}, {40132, 51360}, {41106, 50977}, {42104, 51206}, {42105, 51207}, {47353, 50992}, {47354, 50990}, {48898, 49138}, {48905, 49135}, {50690, 51170}, {50960, 50993}, {50964, 50966}, {50970, 51186}, {50974, 51217}, {51130, 51185}, {51132, 51216}, {51136, 51164}
X(51538) = midpoint of X(i) and X(j) for these {i,j}: {382, 5093}, {5085, 48910}, {14912, 15682}, {39561, 48904}
X(51538) = reflection of X(i) in X(j) for these {i,j}: {3, 38136}, {20, 5085}, {165, 38146}, {376, 14561}, {3534, 38110}, {5085, 5480}, {5093, 21850}, {5731, 38035}, {6776, 5093}, {9778, 38047}, {10304, 38072}, {10519, 381}, {14912, 20423}, {15689, 38079}, {21167, 50959}, {21356, 3839}, {25406, 14853}, {38693, 38147}, {38754, 38168}, {46264, 39561}
X(51538) = anticomplement of X(31884)
X(51538) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 31670, 51212}, {4, 51212, 69}, {6, 3146, 14927}, {6, 51163, 3146}, {20, 5480, 3618}, {182, 43621, 3529}, {193, 17578, 36990}, {382, 21850, 6776}, {546, 33878, 40330}, {1350, 3091, 3619}, {1352, 48895, 4}, {3534, 38110, 33750}, {3589, 48872, 3522}, {5059, 51171, 44882}, {5076, 44456, 39884}, {5480, 48910, 20}, {5921, 11477, 11008}, {12322, 12323, 315}, {18906, 32006, 69}, {19130, 48873, 631}, {31670, 48901, 4}, {46264, 48904, 33703}, {47353, 51028, 50992}
X(51539) lies on the conic {{A,B,C,X(4),X(5)}}, the cubic K1284, and these lines: {5, 39642}, {160, 184}, {32046, 39641}
X(51539) = barycentric product X(39642)*X(39642)
X(51539) = barycentric quotient X(51540)/X(32)
X(51540) lies on the conic {{A,B,C,X(4),X(5)}}, the cubic K1284, and these lines: {5, 39641}, {160, 184}, {32046, 39642}
X(51540) = barycentric product X(39641)*X (39641)
X(51540) = barycentric quotient X(51539)/X(32)
X(51541) lies on the cubic K1285 and these lines: {2, 187}, {6, 10166}, {23, 671}, {111, 8859}, {325, 9164}, {351, 523}, {385, 18823}, {524, 7664}, {597, 13410}, {599, 9516}, {1691, 9169}, {1992, 5486}, {1995, 8860}, {2482, 3266}, {2770, 11636}, {4590, 7840}, {5467, 11163}, {5967, 32225}, {5971, 41134}, {7495, 15464}, {7665, 46275}, {8591, 15390}, {8596, 19577}, {8787, 14567}, {9855, 42008}, {10717, 13586}, {11059, 11149}, {11183, 34763}, {13574, 37760}, {14568, 37909}, {14614, 18361}, {22110, 36953}, {23055, 26255}, {26235, 40826}, {30491, 45335}, {31125, 32479}, {35511, 44367}, {40511, 44401}, {46806, 46808}, {46807, 46809}
X(51541) = isogonal conjugate of X(42007)
X(51541) = isotomic conjugate of X(42008)
X(51541) = X(i)-Ceva conjugate of X(j) for these (i,j): {598, 20380}, {10511, 23297}, {18818, 598}
X(51541) = X(i)-cross conjugate of X(j) for these (i,j): {8262, 44146}, {9125, 5468}, {20380, 598}, {20382, 8599}
X(51541) = X(i)-isoconjugate of X(j) for these (i,j): {1, 42007}, {31, 42008}, {111, 36263}, {163, 23288}, {574, 897}, {599, 923}, {661, 32583}, {3906, 36142}, {5094, 36060}, {9145, 23894}, {17414, 36085}
X(51541) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 42008), (3, 42007), (115, 23288), (187, 10510), (524, 39785), (1560, 5094), (1649, 8288), (2482, 599), (6593, 574), (14961, 19510), (23992, 3906), (36830, 32583), (38988, 17414)
X(51541) = cevapoint of X(i) and X(j) for these (i,j): {23, 11580}, {524, 27088}
X(51541) = crosspoint of X(i) and X(j) for these (i,j): {598, 18818}, {10512, 40826}
X(51541) = trilinear pole of line {690, 15303}
X(51541) = crossdifference of every pair of points on line {574, 17414}
X(51541) = barycentric product X(i)*X(j) for these {i,j}: {99, 23287}, {187, 40826}, {524, 598}, {671, 20380}, {690, 35138}, {1383, 3266}, {2482, 18818}, {5468, 8599}, {6593, 10512}, {7664, 10511}, {11636, 35522}, {43697, 44146}
X(51541) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 42008}, {6, 42007}, {110, 32583}, {187, 574}, {351, 17414}, {468, 5094}, {523, 23288}, {524, 599}, {598, 671}, {690, 3906}, {896, 36263}, {1383, 111}, {1648, 8288}, {2482, 39785}, {3266, 9464}, {5181, 19510}, {5467, 9145}, {5468, 9146}, {5642, 13857}, {6593, 10510}, {8599, 5466}, {10511, 10415}, {11636, 691}, {20380, 524}, {20382, 1648}, {23287, 523}, {23297, 31125}, {27088, 11165}, {30489, 46154}, {30491, 10097}, {35138, 892}, {40826, 18023}, {43697, 895}, {44102, 8541}, {46001, 9178}, {50567, 51397}
X(51541) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 598, 23297}, {2, 1383, 598}
X(51542) lies on the cubic K1284 and these lines: {6, 157}, {53, 6531}, {95, 141}, {98, 230}, {183, 46806}, {290, 8177}, {577, 34383}, {694, 32654}, {2065, 5111}, {2076, 46237}, {2422, 2492}, {2966, 43664}, {3094, 37813}, {3506, 11672}, {3589, 31636}, {5085, 17974}, {6394, 34828}, {6784, 10311}, {10313, 46303}, {11610, 14495}, {12042, 32661}, {18898, 47737}, {20021, 45838}, {35906, 45819}
X(51542) = isogonal conjugate of X(46807)
X(51542) = isogonal conjugate of the isotomic conjugate of X(46806)
X(51542) = X(i)-isoconjugate of X(j) for these (i,j): {1, 46807}, {240, 42313}, {262, 1959}, {263, 46238}, {325, 2186}, {327, 1755}, {40703, 43718}
X(51542) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 46807), (36899, 327), (38997, 2799), (39085, 42313)
X(51542) = trilinear pole of line {3288, 34396}
X(51542) = crossdifference of every pair of points on line {2799, 41167}
X(51542) = barycentric product X(i)*X(j) for these {i,j}: {6, 46806}, {98, 182}, {183, 1976}, {248, 458}, {287, 10311}, {290, 34396}, {2715, 23878}, {2966, 3288}, {14600, 44144}, {14601, 20023}, {17974, 33971}, {32545, 39683}
X(51542) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 46807}, {98, 327}, {182, 325}, {248, 42313}, {458, 44132}, {1976, 262}, {3288, 2799}, {6784, 868}, {9420, 41167}, {10311, 297}, {14096, 51371}, {14600, 43718}, {14601, 263}, {34396, 511}, {46806, 76}
X(51542) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {248, 1976, 6}, {287, 31635, 141}
X(51543) lies on the cubic K1284 and these lines: {6, 160}, {30, 34359}, {39, 30499}, {53, 141}, {230, 694}, {250, 32217}, {262, 1513}, {325, 36790}, {446, 44453}, {511, 11672}, {523, 3569}, {524, 46142}, {842, 5104}, {868, 18575}, {1350, 40801}, {1503, 1987}, {1691, 2065}, {1971, 32716}, {2076, 34130}, {2186, 3863}, {2211, 19189}, {2450, 3613}, {3425, 5017}, {5116, 46317}, {6037, 34369}, {6530, 51334}, {7426, 36885}, {9139, 42007}, {13330, 14252}, {14533, 46288}
X(51543) = isogonal conjugate of X(46806)
X(51543) = isogonal conjugate of the isotomic conjugate of X(46807)
X(51543) = X(i)-isoconjugate of X(j) for these (i,j): {1, 46806}, {182, 1821}, {183, 1910}, {293, 458}, {336, 10311}, {1976, 3403}, {3288, 36036}, {17974, 51315}, {23878, 36084}, {34396, 46273}
X(51543) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 46806), (132, 458), (2679, 3288), (5976, 20023), (11672, 183), (38987, 23878), (39040, 3403), (40601, 182), (47648, 8842)
X(51543) = crossdifference of every pair of points on line {182, 23878}
X(51543) = barycentric product X(i)*X(j) for these {i,j}: {6, 46807}, {232, 42313}, {237, 327}, {262, 511}, {263, 325}, {297, 43718}, {1513, 40803}, {1959, 2186}, {2799, 26714}, {3402, 46238}, {6037, 41167}, {23350, 36885}, {39569, 51444}, {39682, 40804}, {42288, 51371}
X(51543) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 46806}, {232, 458}, {237, 182}, {262, 290}, {263, 98}, {297, 44144}, {325, 20023}, {327, 18024}, {511, 183}, {1959, 3403}, {2186, 1821}, {2211, 10311}, {2491, 3288}, {3402, 1910}, {3569, 23878}, {9418, 34396}, {26714, 2966}, {32716, 41173}, {34854, 33971}, {36790, 51373}, {40810, 8842}, {43718, 287}, {46319, 1976}, {46807, 76}
X(51543) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {263, 43718, 6}, {327, 42313, 141}, {43718, 51338, 263}
X(51544) lies on the cubic K1284 and these lines: {6, 74}, {141, 1494}, {399, 47405}, {1304, 16328}, {1495, 3003}, {1987, 41433}, {1990, 14165}, {2433, 2492}, {3163, 6699}, {3457, 39380}, {3458, 39381}, {3569, 14380}, {4550, 5158}, {6128, 13202}, {6748, 10152}, {9139, 42007}, {11060, 11074}, {12079, 16303}, {14385, 18573}, {14581, 34329}, {14989, 47275}, {34150, 47322}, {37638, 46808}
X(51544) = isogonal conjugate of X(46809)
X(51544) = isogonal conjugate of the isotomic conjugate of X(46808)
X(51544) = X(32681)-Ceva conjugate of X(2433)
X(51544) = X(i)-isoconjugate of X(j) for these (i,j): {1, 46809}, {3431, 14206}
X(51544) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 46809), (4550, 11064)
X(51544) = crosssum of X(3284) and X(10564)
X(51544) = crossdifference of every pair of points on line {5664, 9033}
X(51544) = barycentric product X(i)*X(j) for these {i,j}: {6, 46808}, {74, 381}, {1494, 34417}, {3581, 5627}, {5158, 16080}, {8749, 37638}, {9139, 32225}, {18477, 36119}, {18487, 40384}, {40352, 44135}
X(51544) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 46809}, {381, 3260}, {3581, 6148}, {5158, 11064}, {8749, 43530}, {18479, 51254}, {18487, 36789}, {34416, 1495}, {34417, 30}, {40352, 3431}, {40355, 18316}, {46808, 76}
X(51544) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 74, 18877}, {6, 9412, 39176}, {74, 8749, 6}
X(51545) lies on these lines: {6, 186}, {50, 74}, {53, 16263}, {141, 44578}, {526, 647}, {577, 33533}, {1495, 39176}, {1511, 3284}, {1990, 9408}, {6148, 11064}, {6749, 43462}, {8882, 46091}, {18877, 40384}, {32663, 34210}
X(51545) = isogonal conjugate of X(46808)
X(51545) = isogonal conjugate of the isotomic conjugate of X(46809)
X(51545) = X(i)-isoconjugate of X(j) for these (i,j): {1, 46808}, {381, 2349}, {2159, 44135}, {16080, 18477}, {18486, 40384}, {33805, 34417}, {36119, 37638}
X(51545) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 46808), (1511, 37638), (3163, 44135)
X(51545) = crosspoint of X(18316) and X(43530)
X(51545) = crosssum of X(i) and X(j) for these (i,j): {381, 18487}, {3581, 5158}
X(51545) = barycentric product X(i)*X(j) for these {i,j}: {6, 46809}, {30, 3431}, {1511, 18316}, {3284, 43530}, {16163, 22455}, {16263, 51394}
X(51545) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 46808}, {30, 44135}, {1495, 381}, {3284, 37638}, {3431, 1494}, {9407, 34417}, {9408, 18487}, {42074, 18486}, {46809, 76}
X(51546) lies on the cubic K1284 and these lines: {6, 3131}, {15, 18}, {16, 10263}, {51, 51477}, {53, 462}, {61, 1493}, {141, 40711}, {216, 11088}, {302, 11143}, {2005, 10639}, {2380, 16807}, {2913, 11267}, {2963, 3458}, {2965, 11083}, {3443, 30403}, {3489, 19781}, {10642, 11135}, {10645, 37850}, {11086, 14533}, {19778, 34540}
X(51546) = isogonal conjugate of X(11144)
X(51546) = isogonal conjugate of the isotomic conjugate of X(11143)
X(51546) = X(11138)-Ceva conjugate of X(8604)
X(51546) = X(11137)-cross conjugate of X(11083)
X(51546) = X(i)-isoconjugate of X(j) for these (i,j): {1, 11144}, {3375, 8836}
X(51546) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 11144), (10640, 303)
X(51546) = barycentric product X(i)*X(j) for these {i,j}: {6, 11143}, {14, 10678}, {18, 61}, {302, 21462}, {473, 32586}, {8604, 16771}, {10642, 40711}, {11082, 11146}, {11083, 19778}, {11126, 11138}, {16807, 23872}, {42678, 42681}
X(51546) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 11144}, {18, 34389}, {61, 303}, {8604, 19779}, {10642, 472}, {10678, 299}, {11083, 16770}, {11135, 11145}, {11137, 11127}, {11141, 8836}, {11143, 76}, {11146, 11133}, {16807, 32036}, {21462, 17}, {32586, 40712}, {34394, 10677}
X(51546) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 32586, 8604}, {2963, 11138, 36301}, {21462, 32586, 6}
X(51547) lies on the cubic K1284 and these lines: {6, 3132}, {15, 10263}, {16, 17}, {51, 51477}, {53, 463}, {62, 1493}, {141, 40712}, {216, 11083}, {303, 11144}, {2004, 10640}, {2381, 16806}, {2912, 11268}, {2963, 3457}, {2965, 11088}, {3442, 30402}, {3490, 19780}, {10641, 11136}, {10646, 37848}, {11081, 14533}, {19779, 34541}
X(51547) = isogonal conjugate of X(11143)
X(51547) = isogonal conjugate of the isotomic conjugate of X(11144)
X(51547) = X(11139)-Ceva conjugate of X(8603)
X(51547) = X(11134)-cross conjugate of X(11088)
X(51547) = X(i)-isoconjugate of X(j) for these (i,j): {1, 11143}, {3384, 8838}
X(51547) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 11143), (10639, 302)
X(51547) = barycentric product X(i)*X(j) for these {i,j}: {6, 11144}, {13, 10677}, {17, 62}, {303, 21461}, {472, 32585}, {8603, 16770}, {10641, 40712}, {11087, 11145}, {11088, 19779}, {11127, 11139}, {16806, 23873}, {42676, 42679}
X(51547) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 11143}, {17, 34390}, {62, 302}, {8603, 19778}, {10641, 473}, {10677, 298}, {11088, 16771}, {11134, 11126}, {11136, 11146}, {11142, 8838}, {11144, 76}, {11145, 11132}, {16806, 32037}, {21461, 18}, {32585, 40711}, {34395, 10678}
X(51547) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 32585, 8603}, {2963, 11139, 36300}, {21461, 32585, 6}
See Ivan Pavlov, euclid 5479.
X(51548) lies on these lines: {4, 567}, {113, 1495}, {146, 3581}, {597, 3845}
X(51548) = Orthopole of the trilinear polar of X(7578)
See Ivan Pavlov, euclid 5481.
X(51549) lies on this line: {20, 101}
X(51550) lies on these lines: {1, 50014}, {2, 3}, {3303, 36480}, {3304, 24331}, {3746, 36531}, {5563, 36529}, {25352, 36475}
{X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 16855, 19320}, {405, 19309, 19329}, {5047, 19318, 3}
X(51551) lies on these lines: {1, 20924}, {2, 3}, {315, 17103}, {1468, 5015}, {4389, 5263}
X(51551) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1010, 13727, 1008}
X(51552) lies on these lines: {1, 50025}, {2, 3}, {3826, 4265}, {3874, 36480}, {6763, 36531}
X(51552) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {16454, 37149, 474}
X(51553) lies on these lines: {1, 49756}, {2, 3}, {1453, 29660}
X(51554) lies on these lines: {1, 5319}, {2, 3}, {1453, 29676}, {7869, 50224}, {9607, 19758}, {15888, 36486}, {29659, 37721}, {36479, 37724}
X(51555) lies on these lines: {1, 9351}, {2, 3}, {1453, 29820}, {3246, 4290}, {8666, 24331}, {23855, 49725}
X(51555) = crossdifference of every pair of points on line {647, 50359}
X(51555) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {405, 4223, 13723}, {405, 19309, 1009}
X(51556) lies on these lines: {1, 7760}, {2, 3}, {595, 36480}, {1104, 25368}, {1724, 7878}, {3923, 27971}, {5007, 50225}, {7283, 24326}, {7768, 49723}, {7794, 50224}, {7873, 50220}
X(51556) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {405, 1008, 37027}, {4195, 13723, 11104}
X(51557) lies on these lines: {1, 50036}, {2, 3}, {1211, 21616}, {1453, 7741}, {1728, 1901}, {1834, 10826}, {2360, 32431}, {3714, 17757}, {3966, 24390}, {11375, 45126}, {17056, 37692}, {37696, 44113}
X(51557) = orthocentroidal-circle-inverse of X(37063)
X(51557) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 37063}, {5, 429, 442}, {5, 1985, 37359}, {3136, 21530, 442}, {3136, 27555, 21530}, {3142, 30444, 442}, {14008, 37983, 6841}
X(51558) lies on these lines: {1, 2051}, {2, 3}, {8, 970}, {10, 21363}, {12, 21321}, {355, 34466}, {386, 10454}, {388, 5718}, {497, 5710}, {515, 1193}, {516, 3831}, {517, 3702}, {519, 9569}, {573, 10479}, {602, 27631}, {944, 5396}, {952, 5754}, {959, 18391}, {962, 15488}, {978, 5400}, {1210, 1400}, {1478, 37693}, {1479, 5264}, {1724, 13478}, {1764, 50605}, {1826, 28266}, {2183, 34831}, {2551, 5743}, {2829, 27657}, {3436, 5741}, {3616, 6176}, {3670, 29069}, {3679, 9568}, {3840, 12545}, {4383, 5786}, {5225, 37540}, {5230, 48482}, {5278, 5788}, {5307, 19372}, {5587, 31339}, {5740, 21279}, {5767, 36754}, {5797, 12116}, {6245, 28274}, {6734, 39591}, {7080, 36855}, {9535, 10449}, {9548, 31330}, {9553, 10473}, {9554, 10480}, {10476, 30942}, {10886, 19858}, {18180, 20028}, {20923, 51063}, {23383, 26095}, {27627, 31673}, {29824, 35631}, {35206, 44425}, {37536, 48941}, {46827, 51118}
X(51558) = reflection of X(i) in X(j) for these {i,j}: {19648, 5}, {50702, 19513}
X(51558) = complement of X(50702)
X(51558) = anticomplement of X(19513)
X(51558) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 50702, 19513}, {3, 4, 15971}, {4, 6836, 36496}, {4, 6865, 26118}, {4, 36575, 37456}, {5, 13731, 2}, {3142, 28238, 2}, {5192, 19645, 37415}, {13740, 23512, 37399}, {14784, 14785, 19543}, {35732, 42282, 19647}
X(51559) lies on these lines: {1, 50038}, {2, 3}, {9, 34753}, {10, 10179}, {12, 13462}, {78, 15935}, {392, 25011}, {495, 3624}, {496, 1698}, {551, 9711}, {936, 12433}, {942, 5316}, {946, 31797}, {952, 8583}, {1001, 47742}, {1125, 3820}, {1329, 19862}, {1376, 10386}, {1483, 19861}, {2886, 51073}, {3452, 6147}, {3634, 3816}, {3646, 26446}, {3695, 30829}, {3813, 3828}, {3825, 3826}, {3841, 3847}, {3848, 21077}, {3925, 10593}, {3968, 13463}, {4358, 50042}, {4413, 15171}, {5044, 9843}, {5326, 26476}, {5432, 25542}, {5433, 13370}, {5437, 24470}, {5550, 17757}, {5690, 8582}, {5708, 18228}, {6260, 10156}, {6684, 7956}, {6688, 37536}, {6692, 31445}, {7173, 41859}, {7681, 38059}, {7741, 31508}, {7988, 50031}, {8167, 26364}, {9342, 26127}, {9669, 26040}, {9709, 15172}, {9842, 31805}, {10283, 19860}, {11374, 20196}, {16589, 31406}, {16610, 50067}, {17337, 45939}, {17619, 24564}, {17749, 48847}, {19117, 31473}, {19875, 37722}, {19876, 37720}, {19877, 24390}, {19878, 25466}, {21031, 25055}, {21060, 50192}, {23537, 31197}, {24954, 37737}, {24982, 38112}, {24987, 32214}, {37719, 44847}
X(51559) = midpoint of X(5084) and X(16408)
X(51559) = complement of X(16408)
X(51559) = orthocentroidal-circle-inverse of X(16863)
X(51559) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 16863}, {2, 377, 16864}, {2, 2478, 16862}, {2, 3090, 50726}, {2, 4187, 8728}, {2, 4193, 17529}, {2, 5047, 13747}, {2, 5055, 50395}, {2, 5084, 16408}, {2, 6675, 632}, {2, 6933, 50207}, {2, 11108, 140}, {2, 16842, 6675}, {2, 16845, 3526}, {2, 16853, 50205}, {2, 17527, 5}, {2, 17536, 7483}, {2, 17546, 17590}, {2, 17554, 3525}, {2, 17559, 3}, {2, 17570, 17566}, {2, 17575, 17527}, {2, 33034, 8362}, {2, 33042, 7866}, {2, 37162, 17535}, {2, 50202, 11539}, {3, 1656, 6964}, {3, 5129, 50243}, {5, 140, 37424}, {5, 11539, 44222}, {21, 17564, 15712}, {140, 3628, 6959}, {381, 17582, 50238}, {404, 50241, 8703}, {442, 4187, 5154}, {452, 16417, 548}, {547, 37356, 5}, {1656, 6922, 5}, {3090, 8727, 5}, {3526, 6961, 140}, {3634, 3816, 31419}, {3825, 31253, 3826}, {4187, 8728, 5}, {5046, 50240, 15687}, {6825, 6841, 37406}, {6919, 17528, 3850}, {7483, 17536, 50202}, {8728, 17527, 4187}, {9709, 26105, 15172}, {11111, 17573, 33923}, {11113, 17531, 17563}, {11113, 17563, 15704}, {16418, 17567, 3530}, {16842, 19520, 11108}, {17535, 37162, 11112}, {17566, 17570, 15670}
X(51560) lies on these lines: {100, 693}, {105, 8709}, {294, 30627}, {350, 14942}, {643, 799}, {644, 666}, {664, 4449}, {673, 4607}, {765, 20954}, {789, 919}, {812, 813}, {874, 4583}, {1280, 34018}, {1320, 2481}, {1577, 34906}, {1897, 46107}, {1909, 40724}, {1966, 33676}, {1978, 3699}, {3570, 42719}, {3685, 14197}, {3766, 36236}, {3903, 21272}, {4358, 36796}, {4569, 41075}, {4589, 4645}, {4593, 32666}, {4602, 7257}, {4625, 35338}, {6163, 23794}, {6654, 18064}, {9318, 35961}, {20920, 46277}, {33805, 44693}, {35167, 38980}, {36037, 39293}, {36146, 36147}
X(51560) = isotomic conjugate of X(2254)
X(51560) = isotomic conjugate of the anticomplement of X(3716)
X(51560) = isotomic conjugate of the isogonal conjugate of X(36086)
X(51560) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {813, 14732}, {32735, 39362}, {39293, 20345}
X(51560) = X(46135)-Ceva conjugate of X(34085)
X(51560) = X(i)-cross conjugate of X(j) for these (i,j): {350, 7035}, {666, 34085}, {1026, 190}, {1027, 673}, {3570, 799}, {3716, 2}, {3907, 33676}, {31637, 39293}, {35333, 36086}, {42719, 4554}
X(51560) = X(i)-isoconjugate of X(j) for these (i,j): {4, 23225}, {6, 665}, {7, 8638}, {31, 2254}, {32, 918}, {56, 926}, {57, 46388}, {241, 3063}, {512, 3286}, {513, 2223}, {514, 9454}, {518, 667}, {649, 672}, {659, 40730}, {663, 1458}, {669, 30941}, {692, 3675}, {693, 9455}, {798, 18206}, {875, 8299}, {884, 1362}, {919, 35505}, {927, 15615}, {1015, 2284}, {1019, 39258}, {1026, 3248}, {1027, 42079}, {1333, 24290}, {1397, 50333}, {1415, 17435}, {1459, 2356}, {1876, 1946}, {1918, 23829}, {1919, 3912}, {1924, 18157}, {1960, 34230}, {1977, 42720}, {1980, 3263}, {2175, 43042}, {2206, 4088}, {2283, 3271}, {2340, 43924}, {2720, 42771}, {3049, 15149}, {3252, 8632}, {3733, 20683}, {5089, 22383}, {6184, 43929}, {6591, 20752}, {8641, 34855}, {34067, 38989}, {34858, 42758}
X(51560) = X(i)-Dao conjugate of X(j) for these (i, j): (1, 926), (2, 2254), (9, 665), (37, 24290), (666, 39344), (1086, 3675), (1146, 17435), (5375, 672), (5452, 46388), (6376, 918), (6631, 518), (9296, 3912), (9428, 18157), (10001, 241), (16586, 42758), (17755, 3126), (31998, 18206), (33675, 514), (34021, 23829), (35119, 38989), (36033, 23225), (38980, 35505), (38981, 42771), (39026, 2223), (39053, 1876), (39054, 3286), (39060, 5236), (40593, 43042), (40603, 4088)
X(51560) = cevapoint of X(i) and X(j) for these (i,j): {1, 812}, {190, 1026}, {514, 1738}, {522, 3912}, {666, 36802}, {668, 874}, {673, 1027}, {740, 1577}, {1966, 3907}
X(51560) = crosspoint of X(36803) and X(46135)
X(51560) = trilinear pole of line {9, 75}
X(51560) = barycentric product X(i)*X(j) for these {i,j}: {1, 36803}, {8, 34085}, {9, 46135}, {75, 666}, {76, 36086}, {85, 36802}, {100, 18031}, {105, 1978}, {190, 2481}, {294, 4572}, {308, 35333}, {312, 927}, {561, 919}, {664, 36796}, {668, 673}, {670, 18785}, {799, 13576}, {889, 36816}, {1027, 31625}, {1438, 6386}, {1502, 32666}, {3261, 5377}, {3596, 36146}, {3699, 34018}, {3729, 14727}, {4391, 39293}, {4554, 14942}, {4569, 6559}, {4583, 6654}, {6335, 31637}, {18833, 46163}, {28071, 46406}, {28659, 32735}, {30854, 41075}
X(51560) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 665}, {2, 2254}, {9, 926}, {10, 24290}, {41, 8638}, {48, 23225}, {55, 46388}, {75, 918}, {85, 43042}, {99, 18206}, {100, 672}, {101, 2223}, {105, 649}, {190, 518}, {274, 23829}, {294, 663}, {312, 50333}, {321, 4088}, {514, 3675}, {522, 17435}, {644, 2340}, {646, 3717}, {651, 1458}, {653, 1876}, {658, 34855}, {660, 3252}, {662, 3286}, {664, 241}, {666, 1}, {668, 3912}, {670, 18157}, {673, 513}, {692, 9454}, {765, 2284}, {799, 30941}, {811, 15149}, {812, 38989}, {813, 40730}, {874, 17755}, {885, 2170}, {908, 42758}, {919, 31}, {927, 57}, {1016, 1026}, {1018, 20683}, {1024, 3271}, {1025, 1362}, {1026, 6184}, {1027, 1015}, {1275, 41353}, {1331, 20752}, {1332, 1818}, {1438, 667}, {1462, 43924}, {1783, 2356}, {1814, 1459}, {1897, 5089}, {1978, 3263}, {2195, 3063}, {2254, 35505}, {2284, 42079}, {2398, 9502}, {2481, 514}, {3257, 34230}, {3570, 8299}, {3699, 3693}, {3729, 42341}, {3912, 3126}, {3952, 3930}, {4033, 3932}, {4554, 9436}, {4557, 39258}, {4561, 25083}, {4562, 22116}, {4564, 2283}, {4572, 40704}, {4583, 40217}, {4606, 14626}, {4998, 1025}, {5377, 101}, {6185, 1027}, {6335, 1861}, {6559, 3900}, {6654, 659}, {7035, 42720}, {9503, 2424}, {13136, 36819}, {13576, 661}, {14625, 4822}, {14727, 9311}, {14942, 650}, {14947, 34905}, {17780, 14439}, {18026, 5236}, {18031, 693}, {18047, 4447}, {18743, 4925}, {18785, 512}, {19804, 50357}, {20906, 23773}, {23696, 7117}, {28071, 657}, {28132, 2310}, {31637, 905}, {31638, 3309}, {32666, 32}, {32735, 604}, {32739, 9455}, {34018, 3676}, {34085, 7}, {34906, 5091}, {35313, 17439}, {35333, 39}, {36038, 42770}, {36057, 22383}, {36086, 6}, {36124, 6591}, {36146, 56}, {36796, 522}, {36802, 9}, {36803, 75}, {36816, 891}, {39293, 651}, {41075, 21446}, {42719, 50441}, {42720, 4712}, {43921, 21143}, {43929, 3248}, {46135, 85}, {46149, 21123}, {46163, 1964}, {46388, 15615}, {46393, 42771}
X(51561) lies on these lines: {1, 24038}, {81, 644}, {86, 3699}, {100, 1014}, {111, 524}, {643, 757}, {664, 3896}, {873, 7257}, {1320, 23829}, {3873, 3903}, {3875, 6742}, {9041, 9146}
X(51561) = isogonal conjugate of X(39688)
X(51561) = isotomic conjugate of X(4442)
X(51561) = isotomic conjugate of the anticomplement of X(3712)
X(51561) = X(3712)-cross conjugate of X(2)
X(51561) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39688}, {4, 23230}, {6, 16611}, {31, 4442}, {37, 16784}, {42, 7292}, {56, 24394}, {213, 37756}, {923, 16597}, {2832, 4557}, {3952, 8650}, {6088, 8691}
X(51561) = X(i)-Dao conjugate of X(j) for these (i, j): (1, 24394), (2, 4442), (3, 39688), (9, 16611), (2482, 16597), (6626, 37756), (36033, 23230), (40589, 16784), (40592, 7292), (40620, 47871)
X(51561) = cevapoint of X(i) and X(j) for these (i,j): {1, 524}, {690, 17058}, {34892, 34893}
X(51561) = trilinear pole of line {9, 1019}
X(51561) = barycentric product X(i)*X(j) for these {i,j}: {86, 34892}, {274, 34893}, {2748, 7199}, {4789, 6082}, {5387, 17205}
X(51561) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 16611}, {2, 4442}, {6, 39688}, {9, 24394}, {48, 23230}, {58, 16784}, {81, 7292}, {86, 37756}, {524, 16597}, {1019, 2832}, {2748, 1018}, {5235, 4956}, {6082, 37210}, {7192, 47871}, {34892, 10}, {34893, 37}
X(51562) lies on these lines: {2, 51402}, {5, 7979}, {80, 519}, {100, 522}, {101, 47874}, {145, 14584}, {149, 51442}, {350, 20566}, {476, 8701}, {513, 15343}, {518, 14204}, {521, 34151}, {523, 14513}, {643, 765}, {644, 3239}, {660, 17763}, {664, 693}, {666, 30565}, {900, 901}, {918, 37143}, {952, 38954}, {1120, 1411}, {1252, 3700}, {1280, 2006}, {1737, 33129}, {1807, 4358}, {1897, 44426}, {2397, 17780}, {2804, 46649}, {3241, 34232}, {3699, 4397}, {3732, 48557}, {3870, 14628}, {3900, 15632}, {3932, 46785}, {3935, 14942}, {4467, 4998}, {4551, 6742}, {4583, 17935}, {4723, 15898}, {4820, 14589}, {6187, 8851}, {6735, 15633}, {6740, 15065}, {7035, 7257}, {8707, 36069}, {17989, 34067}, {18341, 31841}, {21093, 39136}, {32675, 36147}, {33136, 41684}, {33148, 46972}, {36037, 43728}, {36815, 40172}, {36910, 40869}, {40865, 47790}, {41405, 48266}
X(51562) = reflection of X(i) in X(j) for these {i,j}: {149, 51442}, {18341, 31841}, {36590, 36909}
X(51562) = isotomic conjugate of X(4453)
X(51562) = anticomplement of X(51402)
X(51562) = isotomic conjugate of the anticomplement of X(1639)
X(51562) = isotomic conjugate of the complement of X(47772)
X(51562) = X(35174)-Ceva conjugate of X(655)
X(51562) = X(i)-cross conjugate of X(j) for these (i,j): {522, 36590}, {1023, 190}, {1639, 2}, {2804, 8}, {3943, 1016}, {7359, 46102}, {17757, 15742}, {44669, 4076}
X(51562) = X(i)-isoconjugate of X(j) for these (i,j): {2, 21758}, {4, 22379}, {6, 3960}, {7, 8648}, {31, 4453}, {36, 513}, {56, 3738}, {57, 654}, {81, 21828}, {214, 23345}, {320, 667}, {514, 7113}, {593, 2610}, {603, 44428}, {604, 3904}, {649, 3218}, {663, 1443}, {692, 4089}, {757, 42666}, {758, 3733}, {849, 6370}, {900, 16944}, {1015, 4585}, {1019, 2245}, {1022, 17455}, {1086, 1983}, {1262, 46384}, {1333, 4707}, {1459, 1870}, {1464, 3737}, {1635, 40215}, {1835, 23189}, {1919, 20924}, {1980, 40075}, {2222, 3025}, {2323, 3669}, {2361, 3676}, {2423, 16586}, {3063, 17078}, {3572, 27950}, {3724, 7192}, {3937, 4242}, {4282, 7178}, {4511, 43924}, {4973, 50344}, {6591, 22128}, {7252, 18593}, {17923, 22383}, {23884, 28607}, {32669, 46398}
X(51562) = X(i)-Dao conjugate of X(j) for these (i, j): (1, 3738), (2, 4453), (9, 3960), (37, 4707), (1086, 4089), (3161, 3904), (4075, 6370), (5375, 3218), (5452, 654), (6631, 320), (7952, 44428), (9296, 20924), (10001, 17078), (15898, 513), (32664, 21758), (36033, 22379), (36909, 522), (36910, 21198), (36911, 23884), (38984, 3025), (39026, 36), (40586, 21828), (40607, 42666)
X(51562) = cevapoint of X(i) and X(j) for these (i,j): {1, 900}, {2, 47772}, {514, 17067}, {519, 522}, {2427, 4557}, {3952, 17780}
X(51562) = crosspoint of X(i) and X(j) for these (i,j): {4555, 13136}, {35174, 36804}
X(51562) = crosssum of X(i) and X(j) for these (i,j): {1960, 3310}, {8648, 21758}
X(51562) = trilinear pole of line {9, 80}
X(51562) = barycentric product X(i)*X(j) for these {i,j}: {1, 36804}, {8, 655}, {9, 35174}, {10, 47318}, {55, 46405}, {80, 190}, {100, 18359}, {101, 20566}, {312, 2222}, {476, 3969}, {644, 18815}, {646, 1411}, {662, 15065}, {664, 36910}, {668, 2161}, {759, 4033}, {799, 34857}, {1018, 14616}, {1089, 37140}, {1168, 24004}, {1807, 6335}, {1978, 6187}, {2006, 3699}, {2397, 40437}, {3596, 32675}, {3678, 32680}, {3904, 46649}, {3952, 24624}, {4552, 6740}, {4562, 36815}, {4582, 14584}, {6742, 41226}, {14147, 17791}, {27808, 34079}, {28654, 36069}
X(51562) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3960}, {2, 4453}, {8, 3904}, {9, 3738}, {10, 4707}, {31, 21758}, {41, 8648}, {42, 21828}, {48, 22379}, {55, 654}, {80, 514}, {100, 3218}, {101, 36}, {190, 320}, {281, 44428}, {514, 4089}, {594, 6370}, {644, 4511}, {651, 1443}, {654, 3025}, {655, 7}, {664, 17078}, {668, 20924}, {692, 7113}, {756, 2610}, {759, 1019}, {765, 4585}, {901, 40215}, {1018, 758}, {1023, 214}, {1110, 1983}, {1168, 1022}, {1331, 22128}, {1411, 3669}, {1500, 42666}, {1639, 51402}, {1783, 1870}, {1807, 905}, {1897, 17923}, {1978, 40075}, {2006, 3676}, {2161, 513}, {2222, 57}, {2310, 46384}, {2341, 3737}, {2427, 34586}, {2804, 46398}, {3204, 39478}, {3573, 27950}, {3678, 32679}, {3679, 23884}, {3699, 32851}, {3939, 2323}, {3952, 3936}, {3969, 3268}, {4033, 35550}, {4373, 27836}, {4551, 18593}, {4552, 41804}, {4557, 2245}, {4559, 1464}, {4752, 4867}, {4767, 27757}, {6187, 649}, {6740, 4560}, {7069, 2600}, {14147, 3065}, {14584, 30725}, {14616, 7199}, {15065, 1577}, {18359, 693}, {18815, 24002}, {20566, 3261}, {21801, 42768}, {23344, 17455}, {24004, 1227}, {24624, 7192}, {32665, 16944}, {32671, 849}, {32675, 56}, {34079, 3733}, {34857, 661}, {35174, 85}, {35342, 4973}, {36069, 593}, {36804, 75}, {36815, 812}, {36909, 21198}, {36910, 522}, {37140, 757}, {37630, 43048}, {38938, 47680}, {40172, 1635}, {40437, 2401}, {40521, 4053}, {41226, 4467}, {46405, 6063}, {46649, 655}, {47318, 86}
X(51563) lies on these lines: {86, 2293}, {99, 644}, {100, 4573}, {643, 4610}, {662, 36138}, {664, 4635}, {799, 3699}, {3903, 17136}, {4625, 35338}, {5235, 41798}, {8849, 8851}, {28840, 28841}, {37684, 42290}
X(51563) = isotomic conjugate of X(4804)
X(51563) = isotomic conjugate of the anticomplement of X(4913)
X(51563) = X(i)-cross conjugate of X(j) for these (i,j): {3907, 40739}, {4913, 2}, {16054, 4620}
X(51563) = X(i)-isoconjugate of X(j) for these (i,j): {31, 4804}, {42, 4724}, {213, 4762}, {512, 1001}, {661, 2280}, {663, 42289}, {667, 3696}, {669, 4441}, {798, 4384}, {1400, 45755}, {1471, 4041}, {1893, 1946}, {1919, 4044}, {1924, 21615}, {2489, 23151}, {3709, 5228}, {7180, 37658}
X(51563) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 4804), (6626, 4762), (6631, 3696), (9296, 4044), (9428, 21615), (31998, 4384), (36830, 2280), (39053, 1893), (39054, 1001), (40582, 45755), (40592, 4724)
X(51563) = cevapoint of X(i) and X(j) for these (i,j): {1, 28840}, {522, 24603}, {1019, 3736}, {32041, 37138}
X(51563) = trilinear pole of line {9, 86}
X(51563) = barycentric product X(i)*X(j) for these {i,j}: {86, 32041}, {99, 27475}, {274, 37138}, {310, 8693}, {668, 42302}, {670, 2279}, {799, 1002}, {1978, 51443}, {4625, 40779}, {7257, 42290}
X(51563) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 4804}, {21, 45755}, {81, 4724}, {86, 4762}, {99, 4384}, {110, 2280}, {190, 3696}, {643, 37658}, {645, 3886}, {651, 42289}, {653, 1893}, {662, 1001}, {668, 4044}, {670, 21615}, {799, 4441}, {1002, 661}, {1414, 5228}, {2279, 512}, {4565, 1471}, {4573, 40719}, {4592, 23151}, {4616, 42309}, {7257, 28809}, {8693, 42}, {18791, 9279}, {27475, 523}, {32041, 10}, {37138, 37}, {40779, 4041}, {42290, 4017}, {42302, 513}, {51443, 649}
X(51564) lies on these lines: {2, 1000}, {200, 4738}, {643, 43290}, {644, 17780}, {1120, 3870}, {2415, 3952}, {3699, 24004}, {3939, 36037}, {6006, 6014}, {6742, 14594}, {8851, 11345}, {36916, 41798}
X(51564) = isotomic conjugate of X(21183)
X(51564) = X(i)-cross conjugate of X(j) for these (i,j): {997, 765}, {4752, 190}
X(51564) = X(i)-isoconjugate of X(j) for these (i,j): {31, 21183}, {244, 35281}, {513, 999}, {649, 3306}, {667, 42697}, {1919, 20925}, {3063, 17079}, {3733, 3753}, {3872, 43924}, {6591, 22129}
X(51564) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 21183), (5375, 3306), (6631, 42697), (9296, 20925), (10001, 17079), (39026, 999)
X(51564) = cevapoint of X(i) and X(j) for these (i,j): {1, 6006}, {522, 3679}, {1512, 23757}
X(51564) = trilinear pole of line {9, 519}
X(51564) = barycentric product X(i)*X(j) for these {i,j}: {190, 1000}, {664, 36916}, {1897, 30680}, {1978, 34446}
X(51564) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 21183}, {100, 3306}, {101, 999}, {190, 42697}, {644, 3872}, {664, 17079}, {668, 20925}, {1000, 514}, {1018, 3753}, {1252, 35281}, {1331, 22129}, {3699, 28808}, {3952, 4054}, {4752, 40587}, {30680, 4025}, {34446, 649}, {36916, 522}
X(51565) lies on these the conic {{A,B,C,X(1),X(3)}} and these lines: {1, 318}, {3, 8}, {4, 945}, {75, 77}, {78, 341}, {102, 515}, {124, 18340}, {145, 280}, {200, 4738}, {219, 346}, {283, 643}, {284, 2322}, {296, 518}, {332, 7257}, {497, 3478}, {517, 10538}, {519, 1795}, {522, 10703}, {909, 2359}, {947, 5882}, {951, 10106}, {1036, 3486}, {1037, 3476}, {1057, 3488}, {1069, 36626}, {1219, 34051}, {1280, 2401}, {1317, 4081}, {1320, 2804}, {1794, 6737}, {1807, 4358}, {2370, 2720}, {2811, 10695}, {2829, 33650}, {3345, 12650}, {3422, 37295}, {3616, 15252}, {3903, 4451}, {4768, 37628}, {4861, 6742}, {5603, 21664}, {6556, 7080}, {6734, 40442}, {6735, 32851}, {6736, 50914}, {7046, 7967}, {7219, 36977}, {14942, 23696}, {24203, 34387}, {26027, 43533}, {38460, 48380}
X(51565) = reflection of X(i) in X(j) for these {i,j}: {8, 2968}, {1897, 1}, {18340, 124}
X(51565) = isogonal conjugate of X(1457)
X(51565) = isotomic conjugate of X(22464)
X(51565) = isotomic conjugate of the isogonal conjugate of X(2342)
X(51565) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {102, 153}, {104, 151}
X(51565) = X(18816)-Ceva conjugate of X(34234)
X(51565) = X(i)-cross conjugate of X(j) for these (i,j): {519, 8}, {2323, 333}, {4768, 3699}, {36910, 4997}, {37628, 36037}, {46391, 653}
X(51565) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1457}, {3, 1875}, {6, 1465}, {31, 22464}, {34, 22350}, {56, 517}, {57, 2183}, {59, 42753}, {65, 859}, {104, 1361}, {108, 8677}, {109, 1769}, {222, 14571}, {513, 23981}, {603, 1785}, {604, 908}, {649, 24029}, {651, 3310}, {1014, 51377}, {1106, 6735}, {1145, 1417}, {1319, 14260}, {1397, 3262}, {1398, 51379}, {1402, 17139}, {1408, 17757}, {1411, 34586}, {1412, 21801}, {1415, 10015}, {1459, 23706}, {1461, 46393}, {1846, 36058}, {2149, 42754}, {2427, 3669}, {2720, 42757}, {7023, 51380}, {16945, 51433}, {17101, 34346}, {18026, 23220}, {18838, 39173}, {23980, 34051}, {24027, 35015}, {32735, 42758}, {36040, 42755}, {36059, 39534}, {36141, 42762}
X(51565) = X(i)-Dao conjugate of X(j) for these (i, j): (1, 517), (2, 22464), (3, 1457), (8, 51433), (9, 1465), (11, 1769), (522, 35015), (650, 42754), (656, 35014), (1145, 24028), (1146, 10015), (2968, 2804), (3161, 908), (5375, 24029), (5452, 2183), (6552, 6735), (6615, 42753), (7952, 1785), (10017, 42755), (11517, 22350), (20619, 1846), (20620, 39534), (23757, 3326), (35091, 42762), (35111, 51419), (35204, 34586), (35508, 46393), (36103, 1875), (36944, 515), (38981, 42757), (38983, 8677), (38991, 3310), (39026, 23981), (40599, 21801), (40602, 859), (40605, 17139), (40613, 1361), (40624, 36038), (40625, 23788), (51402, 23757)
X(51565) = cevapoint of X(i) and X(j) for these (i,j): {1, 515}, {8, 4511}, {104, 15501}, {200, 2325}, {519, 36944}, {663, 4530}, {1639, 4081}, {2968, 39471}
X(51565) = crosspoint of X(i) and X(j) for these (i,j): {4997, 34393}, {18816, 36795}
X(51565) = trilinear pole of line {9, 652}
X(51565) = barycentric product X(i)*X(j) for these {i,j}: {1, 36795}, {8, 34234}, {9, 18816}, {76, 2342}, {78, 16082}, {92, 1809}, {104, 312}, {190, 43728}, {314, 2250}, {333, 38955}, {341, 34051}, {345, 36123}, {522, 13136}, {909, 3596}, {1309, 6332}, {1795, 7017}, {2401, 3699}, {2968, 39294}, {4391, 36037}, {4397, 37136}, {4997, 36944}, {6335, 37628}, {15416, 36110}, {15501, 34404}, {28659, 34858}, {30608, 36921}, {32641, 35519}, {32851, 40437}, {36796, 36819}
X(51565) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1465}, {2, 22464}, {6, 1457}, {8, 908}, {9, 517}, {11, 42754}, {19, 1875}, {33, 14571}, {55, 2183}, {100, 24029}, {101, 23981}, {104, 57}, {210, 21801}, {219, 22350}, {281, 1785}, {284, 859}, {312, 3262}, {333, 17139}, {346, 6735}, {391, 51423}, {522, 10015}, {650, 1769}, {652, 8677}, {663, 3310}, {728, 51380}, {909, 56}, {950, 51410}, {1146, 35015}, {1309, 653}, {1334, 51377}, {1639, 23757}, {1697, 51413}, {1731, 15906}, {1783, 23706}, {1795, 222}, {1809, 63}, {2170, 42753}, {2183, 1361}, {2250, 65}, {2316, 14260}, {2321, 17757}, {2323, 34586}, {2325, 1145}, {2342, 6}, {2401, 3676}, {2423, 43924}, {2720, 1461}, {3064, 39534}, {3161, 51433}, {3239, 2804}, {3684, 15507}, {3685, 51381}, {3686, 51409}, {3692, 51379}, {3699, 2397}, {3710, 51367}, {3717, 51390}, {3900, 46393}, {3939, 2427}, {4391, 36038}, {4511, 16586}, {4530, 3259}, {4560, 23788}, {4873, 51362}, {5853, 51419}, {6366, 42762}, {6735, 26611}, {8756, 1846}, {13136, 664}, {14400, 42750}, {14430, 42764}, {14432, 42760}, {14578, 603}, {14776, 32674}, {15501, 223}, {16082, 273}, {18816, 85}, {21044, 42759}, {32641, 109}, {34051, 269}, {34234, 7}, {34591, 35014}, {34858, 604}, {36037, 651}, {36110, 32714}, {36123, 278}, {36795, 75}, {36819, 241}, {36921, 5219}, {36944, 3911}, {37136, 934}, {37628, 905}, {38955, 226}, {40437, 2006}, {43728, 514}, {46393, 42757}
X(51565) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {104, 36921, 38955}, {104, 38955, 34234}, {36921, 36944, 34234}, {36944, 38955, 104}
X(51566) lies on these lines: {100, 1305}, {272, 40039}, {322, 1320}, {334, 7270}, {643, 668}, {644, 4033}, {2218, 8851}, {3699, 27808}, {6386, 7257}, {6740, 20566}, {14942, 40011}, {29013, 29014}
X(51566) = isotomic conjugate of X(23800)
X(51566) = X(i)-cross conjugate of X(j) for these (i,j): {27410, 46102}, {44426, 312}
X(51566) = X(i)-isoconjugate of X(j) for these (i,j): {6, 43060}, {31, 23800}, {56, 8676}, {209, 3733}, {513, 2352}, {579, 649}, {663, 4306}, {667, 3868}, {1019, 2198}, {1397, 20294}, {1919, 18134}, {3190, 43924}, {5190, 32660}
X(51566) = X(i)-Dao conjugate of X(j) for these (i, j): (1, 8676), (2, 23800), (9, 43060), (5375, 579), (6631, 3868), (9296, 18134), (39026, 2352)
X(51566) = cevapoint of X(i) and X(j) for these (i,j): {1, 29013}, {78, 4391}, {306, 522}
X(51566) = trilinear pole of line {9, 321}
X(51566) = barycentric product X(i)*X(j) for these {i,j}: {100, 40011}, {190, 2997}, {272, 4033}, {312, 1305}, {644, 15467}, {668, 1751}, {799, 41506}, {811, 40161}, {1978, 2218}
X(51566) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 43060}, {2, 23800}, {9, 8676}, {100, 579}, {101, 2352}, {190, 3868}, {272, 1019}, {312, 20294}, {644, 3190}, {651, 4306}, {668, 18134}, {1018, 209}, {1305, 57}, {1751, 513}, {2218, 649}, {2997, 514}, {3699, 27396}, {3952, 22021}, {4557, 2198}, {6335, 5125}, {15467, 24002}, {23289, 2170}, {35519, 17878}, {40011, 693}, {40161, 656}, {41506, 661}, {44426, 5190}
X(51567) lies on the conic {{A,B,C,X(2),X(7)}} and these lines: {2, 644}, {7, 100}, {75, 3699}, {86, 643}, {200, 1111}, {273, 1897}, {310, 7257}, {527, 2291}, {664, 1088}, {673, 908}, {675, 2742}, {1280, 4453}, {1320, 6548}, {1440, 13138}, {3306, 27475}, {3903, 7249}, {3935, 30806}, {4025, 24841}, {4373, 31343}, {5057, 10426}, {5328, 42318}, {9436, 36037}, {13588, 39734}, {14828, 39704}, {14942, 36038}, {17740, 39749}, {30565, 41798}, {32851, 36807}, {36620, 36845}, {37206, 38375}
X(51567) = isotomic conjugate of X(26015)
X(51567) = isotomic conjugate of the anticomplement of X(6745)
X(51567) = isotomic conjugate of the complement of X(3935)
X(51567) = X(10426)-anticomplementary conjugate of X(329)
X(51567) = X(i)-cross conjugate of X(j) for these (i,j): {3254, 1121}, {3887, 190}, {6745, 2}, {35348, 37143}
X(51567) = X(i)-isoconjugate of X(j) for these (i,j): {6, 43065}, {31, 26015}, {32, 37788}, {41, 30379}, {55, 3660}, {56, 15733}, {692, 2826}, {2175, 38468}, {5580, 15728}, {10427, 34068}
X(51567) = X(i)-Dao conjugate of X(j) for these (i, j): (1, 15733), (2, 26015), (9, 43065), (223, 3660), (1086, 2826), (1212, 41555), (3160, 30379), (6376, 37788), (35110, 10427), (40593, 38468)
X(51567) = cevapoint of X(i) and X(j) for these (i,j): {1, 527}, {2, 3935}, {1086, 6366}, {4105, 33573}
X(51567) = trilinear pole of line {9, 514}
X(51567) = barycentric product X(i)*X(j) for these {i,j}: {8, 43762}, {85, 34894}, {312, 15728}, {2742, 3261}
X(51567) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 43065}, {2, 26015}, {7, 30379}, {9, 15733}, {57, 3660}, {75, 37788}, {85, 38468}, {142, 41555}, {514, 2826}, {527, 10427}, {2742, 101}, {3911, 41556}, {10426, 2291}, {15728, 57}, {34894, 9}, {43762, 7}, {50573, 18801}
X(51568) lies on these lines: {100, 4025}, {643, 4576}, {644, 4568}, {693, 1897}, {918, 919}, {927, 47695}, {1280, 9436}, {1320, 49771}, {3100, 14942}, {3218, 32029}, {3699, 25724}, {4560, 41676}, {15420, 17136}, {31022, 31058}
X(51568) = isotomic conjugate of X(47695)
X(51568) = isotomic conjugate of the anticomplement of X(50333)
X(51568) = X(i)-cross conjugate of X(j) for these (i,j): {9053, 1016}, {23696, 36101}, {35333, 660}, {50333, 2}
X(51568) = X(i)-isoconjugate of X(j) for these (i,j): {31, 47695}, {513, 40910}, {663, 4318}, {667, 32850}, {36086, 38363}
X(51568) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 47695), (6631, 32850), (38989, 38363), (39026, 40910)
X(51568) = cevapoint of X(i) and X(j) for these (i,j): {1, 918}, {39, 926}, {518, 905}, {522, 3008}, {16502, 21003}
X(51568) = trilinear pole of line {9, 141}
X(51568) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 47695}, {101, 40910}, {190, 32850}, {651, 4318}, {665, 38363}
X(51569) lies on the Feuerbach circumhyperbola of the medial triangle and on these lines: {1, 149}, {2, 3065}, {3, 16128}, {10, 2771}, {11, 6701}, {30, 214}, {79, 100}, {80, 6175}, {140, 33856}, {226, 41541}, {442, 6702}, {484, 17484}, {758, 1145}, {908, 35204}, {946, 35597}, {952, 49107}, {1125, 46816}, {2476, 41862}, {2800, 37401}, {2802, 3649}, {3035, 3647}, {3651, 47034}, {3652, 38752}, {5134, 39041}, {5840, 16125}, {5856, 13159}, {6265, 47032}, {6326, 6951}, {6594, 17768}, {6972, 15017}, {8261, 12267}, {9945, 12444}, {10087, 16153}, {10090, 16152}, {10123, 11517}, {11530, 12247}, {12531, 47033}, {15015, 16118}, {15767, 19658}, {16113, 34474}, {17532, 50889}, {19079, 19113}, {19080, 19112}, {26726, 34195}, {33557, 34789}, {36004, 50844}, {40587, 50798}, {48714, 49243}, {48715, 49242}
X(51569) = midpoint of X(i) and X(j) for these {i,j}: {79, 100}, {2475, 34600}, {3651, 47034}, {6265, 47032}, {11604, 13146}, {33557, 34789}
X(51569) = reflection of X(i) in X(j) for these {i,j}: {11, 6701}, {3647, 3035}, {21630, 33593}, {33856, 140}, {46816, 1125}
X(51569) = complement of X(3065)
X(51569) = complement of the isogonal conjugate of X(484)
X(51569) = complement of the isotomic conjugate of X(17791)
X(51569) = medial-isogonal conjugate of X(11813)
X(51569) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 11813}, {6, 3218}, {56, 3582}, {106, 33709}, {484, 10}, {1411, 33593}, {4559, 32679}, {6126, 214}, {11076, 5249}, {17484, 141}, {17791, 2887}, {19297, 2}, {21864, 1211}, {23071, 3}, {35055, 34589}, {42657, 1146}, {47058, 3834}, {50148, 25639}
X(51569) = crosspoint of X(2) and X(17791)
X(51569) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {11263, 21630, 33593}, {11604, 31019, 33593}
X(51570) lies on the Feuerbach circumhyperbola of the medial triangle and on these lines: {1, 89}, {2, 5561}, {10, 550}, {119, 10164}, {142, 5122}, {214, 4640}, {442, 51073}, {551, 4031}, {993, 40587}, {1145, 4669}, {2092, 16669}, {3828, 17057}, {4134, 5010}, {4781, 4793}, {4867, 17549}, {4973, 42819}, {6594, 15481}, {7171, 49183}, {10129, 19878}, {10427, 51090}, {12514, 45036}, {16675, 34261}, {22266, 50240}, {41451, 49712}, {41886, 49992}
X(51570) = midpoint of X(2320) and X(16558)
X(51570) = complement of X(5561)
X(51570) = complement of the isogonal conjugate of X(5010)
X(51570) = complement of the isotomic conjugate of X(17360)
X(51570) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 31019}, {31, 16666}, {692, 4944}, {4134, 3454}, {5010, 10}, {17360, 2887}, {34073, 21199}
X(51570) = X(2)-Ceva conjugate of X(16666)
X(51570) = X(5561)-isoconjugate of X(41434)
X(51570) = X(16666)-Dao conjugate of X(2)
X(51570) = crosspoint of X(2) and X(17360)
X(51570) = barycentric product X(i)*X(j) for these {i,j}: {4134, 26860}, {5010, 24589}, {16666, 17360}
X(51570) = barycentric quotient X(i)/X(j) for these {i,j}: {4134, 27797}, {5010, 40434}, {16666, 5561}
X(51571) lies on the Feuerbach circumhyperbola of the medial triangle and on these lines: {1, 141}, {2, 2221}, {3, 16872}, {9, 5743}, {10, 8230}, {142, 2887}, {332, 38814}, {442, 3739}, {966, 27509}, {1145, 17239}, {1211, 2092}, {1460, 26034}, {2345, 7377}, {2886, 10472}, {3126, 50330}, {3220, 49728}, {3846, 21246}, {3883, 37539}, {4000, 16062}, {5132, 11517}, {5241, 17353}, {6703, 16470}, {15985, 19557}, {17257, 17740}, {17382, 50051}, {18635, 21240}, {20891, 26601}, {21250, 41886}, {27626, 37266}, {34824, 41862}, {35204, 45388}
X(51571) = complement of X(2298)
X(51571) = complement of the isogonal conjugate of X(3666)
X(51571) = complement of the isotomic conjugate of X(20911)
X(51571) = medial-isogonal conjugate of X(44417)
X(51571) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 44417}, {2, 3831}, {6, 5750}, {56, 39595}, {57, 3812}, {58, 6703}, {63, 37613}, {81, 49598}, {109, 3910}, {110, 8045}, {190, 6371}, {256, 15985}, {513, 17197}, {649, 3125}, {960, 3452}, {1193, 2}, {1211, 3454}, {1829, 226}, {1848, 5}, {2092, 1213}, {2269, 9}, {2292, 1211}, {2300, 37}, {2354, 6}, {3004, 116}, {3666, 10}, {3674, 2886}, {3687, 1329}, {3725, 16589}, {3733, 24195}, {3882, 513}, {3910, 124}, {4267, 5745}, {4357, 141}, {4509, 21252}, {6371, 1086}, {16705, 3741}, {16739, 21240}, {17185, 960}, {17420, 26932}, {18697, 21245}, {20911, 2887}, {20967, 1212}, {21124, 125}, {22076, 440}, {22097, 3}, {22345, 1214}, {24471, 142}, {27455, 3840}, {40153, 1125}, {40966, 38930}, {40976, 46835}, {41003, 17052}, {42467, 44545}, {42661, 6627}, {45218, 21024}, {46878, 41883}, {48131, 11}, {50330, 8287}, {51414, 117}
X(51571) = X(100)-Ceva conjugate of X(3910)
X(51571) = crosspoint of X(2) and X(20911)
X(51571) = barycentric quotient X(29142)/X(4581)
X(51572) lies on the Feuerbach circumhyperbola of the medial triangle and on these lines: {1, 210}, {2, 3296}, {3, 3740}, {5, 38057}, {8, 15170}, {9, 3579}, {10, 381}, {44, 34261}, {45, 2092}, {55, 41872}, {119, 9711}, {142, 3634}, {149, 1145}, {214, 958}, {329, 442}, {354, 16855}, {405, 4420}, {517, 11530}, {518, 16853}, {936, 13624}, {952, 45085}, {960, 8148}, {1001, 4015}, {1158, 51516}, {1376, 3647}, {1482, 10176}, {1698, 3715}, {2551, 18357}, {3126, 47949}, {3240, 4204}, {3295, 3305}, {3303, 5506}, {3452, 12864}, {3626, 12640}, {3678, 15934}, {3681, 16842}, {3711, 5259}, {3811, 16857}, {3873, 16854}, {3913, 3956}, {3921, 5250}, {4075, 4361}, {4413, 37524}, {4430, 17546}, {4539, 11520}, {4661, 17534}, {4662, 6767}, {4860, 19872}, {4930, 19860}, {5217, 35204}, {5258, 35272}, {5273, 47742}, {5297, 37060}, {5534, 38031}, {5550, 17590}, {5686, 17559}, {5687, 27065}, {5715, 9956}, {5779, 6684}, {5790, 48482}, {5886, 31494}, {6260, 26446}, {6537, 8818}, {6600, 8668}, {8580, 31445}, {9623, 11278}, {9669, 25006}, {10164, 12684}, {10427, 45084}, {10864, 33575}, {10941, 17757}, {11231, 31446}, {11517, 13615}, {12331, 18233}, {13089, 37572}, {16408, 32636}, {16860, 37080}, {17057, 37567}, {18228, 31419}, {18250, 31673}, {18253, 48668}, {22793, 38200}, {25568, 50205}, {26066, 41540}, {26202, 35238}, {31594, 40653}, {37271, 37582}, {48928, 49730}
X(51572) = midpoint of X(i) and X(j) for these {i,j}: {3646, 4866}, {5586, 41852}
X(51572) = reflection of X(1) in X(14150)
X(51572) = complement of X(3296)
X(51572) = complement of the isogonal conjugate of X(3295)
X(51572) = complement of the isotomic conjugate of X(42696)
X(51572) = medial-isogonal conjugate of X(31419)
X(51572) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 31419}, {31, 16777}, {48, 6349}, {692, 4765}, {3295, 10}, {3305, 141}, {3697, 3454}, {4917, 2885}, {7190, 2886}, {42032, 21244}, {42696, 2887}, {47965, 116}, {48268, 21252}, {48340, 11}
X(51572) = X(2)-Ceva conjugate of X(16777)
X(51572) = X(16777)-Dao conjugate of X(2)
X(51572) = crosspoint of X(2) and X(42696)
X(51572) = barycentric product X(i)*X(j) for these {i,j}: {1698, 3305}, {3295, 28605}, {3697, 5333}, {4007, 7190}, {4756, 47965}, {5221, 42032}, {16777, 42696}
X(51572) = barycentric quotient X(i)/X(j) for these {i,j}: {3295, 25417}, {3305, 30598}, {3927, 30679}, {16777, 3296}, {48340, 48074}
X(51572) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3646, 14150}, {1698, 3715, 3927}, {3305, 3697, 3295}, {3634, 5220, 5708}
X(51573) lies on the Feuerbach circumhyperbola of the medial triangle and on these lines: {1, 748}, {2, 5557}, {3, 15064}, {10, 546}, {142, 5852}, {214, 5044}, {442, 3828}, {993, 45036}, {1145, 4691}, {2092, 16814}, {3634, 3982}, {3647, 3740}, {3715, 3874}, {3746, 4015}, {3878, 40587}, {3881, 35595}, {3951, 5883}, {4547, 5259}, {4669, 12640}, {4701, 15862}, {4973, 17531}, {5220, 16855}, {5302, 17502}, {5905, 9782}, {7997, 25440}, {12864, 21616}, {13089, 35982}, {16885, 34261}, {17057, 46933}, {19883, 50205}, {24036, 39041}, {38130, 43182}
X(51573) = midpoint of X(5506) and X(32635)
X(51573) = complement of X(5557)
X(51573) = complement of the isogonal conjugate of X(3746)
X(51573) = complement of the isotomic conjugate of X(5564)
X(51573) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 3723}, {692, 4976}, {3746, 10}, {4015, 3454}, {5564, 2887}, {7269, 2886}, {27065, 141}, {48003, 116}, {48306, 11}
X(51573) = X(2)-Ceva conjugate of X(3723)
X(51573) = X(3723)-Dao conjugate of X(2)
X(51573) = crosspoint of X(2) and X(5564)
X(51573) = barycentric product X(i)*X(j) for these {i,j}: {3634, 27065}, {3723, 5564}, {3746, 4980}, {4060, 7269}
X(51573) = barycentric quotient X(3723)/X(5557)
X(51574) lies on the Feuerbach circumhyperbola of the medial triangle and on these lines: {1, 4261}, {2, 2335}, {3, 48}, {6, 11517}, {10, 5721}, {37, 442}, {42, 6600}, {72, 18591}, {100, 1172}, {119, 1826}, {142, 3666}, {198, 4456}, {209, 579}, {214, 50650}, {216, 5440}, {284, 2983}, {306, 307}, {313, 25252}, {346, 26027}, {906, 1333}, {1108, 1145}, {1400, 23067}, {2092, 16584}, {2257, 3293}, {2276, 11358}, {2360, 38868}, {3126, 50350}, {4055, 20741}, {4255, 15276}, {5125, 27396}, {6260, 8804}, {17077, 17740}, {17757, 21854}, {18734, 25083}, {22276, 40600}, {33149, 41862}
X(51574) = isogonal conjugate of X(40574)
X(51574) = complement of X(2997)
X(51574) = complement of the isogonal conjugate of X(2352)
X(51574) = complement of the isotomic conjugate of X(3868)
X(51574) = isotomic conjugate of the polar conjugate of X(209)
X(51574) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 72}, {109, 8676}, {184, 7515}, {209, 3454}, {579, 141}, {2198, 1211}, {2352, 10}, {3190, 1329}, {3868, 2887}, {4306, 2886}, {5125, 21243}, {8676, 124}, {18134, 626}, {22021, 21245}, {23800, 21252}, {27396, 21244}, {41320, 41883}, {43060, 116}
X(51574) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 72}, {100, 8676}, {2983, 219}, {27396, 22021}
X(51574) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40574}, {19, 272}, {27, 2218}, {28, 1751}, {1474, 2997}, {2203, 40011}, {2204, 15467}
X(51574) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 40574), (6, 272), (72, 2), (40591, 1751)
X(51574) = crosspoint of X(2) and X(3868)
X(51574) = crosssum of X(6) and X(2218)
X(51574) = barycentric product X(i)*X(j) for these {i,j}: {63, 22021}, {69, 209}, {71, 18134}, {72, 3868}, {304, 2198}, {306, 579}, {307, 3190}, {1214, 27396}, {2352, 20336}, {3682, 5125}, {3710, 4306}, {20294, 23067}
X(51574) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 272}, {6, 40574}, {71, 1751}, {72, 2997}, {209, 4}, {228, 2218}, {306, 40011}, {307, 15467}, {579, 27}, {2198, 19}, {2352, 28}, {3190, 29}, {3690, 41506}, {3868, 286}, {7066, 28786}, {18134, 44129}, {22021, 92}, {23067, 1305}, {27396, 31623}, {40572, 40395}, {41320, 8748}, {43060, 17925}
X(51574) = {X(71),X(3682)}-harmonic conjugate of X(219)
X(51575) lies on the Feuerbach circumhyperbola of the medial triangle and on these lines: {1, 75}, {2, 256}, {3, 3923}, {9, 1755}, {10, 511}, {37, 3229}, {141, 24327}, {142, 3840}, {171, 385}, {214, 2783}, {244, 27017}, {333, 25123}, {442, 3831}, {714, 16696}, {896, 17350}, {1125, 28358}, {1145, 40608}, {1221, 7168}, {1403, 3980}, {1431, 16609}, {1441, 41350}, {1575, 2092}, {1580, 27958}, {1581, 36800}, {1909, 7184}, {2309, 20891}, {2345, 19584}, {2887, 29967}, {3122, 26979}, {3123, 26971}, {3647, 29301}, {3662, 30982}, {3663, 12263}, {3724, 4418}, {3728, 16738}, {3739, 19563}, {3741, 30097}, {3794, 27798}, {3821, 37148}, {3846, 21246}, {3978, 27890}, {4039, 28369}, {4357, 5976}, {4363, 20990}, {4368, 45705}, {4459, 27697}, {4553, 28593}, {4672, 5156}, {5224, 25120}, {6184, 17355}, {6600, 29670}, {7104, 25842}, {7227, 25382}, {7379, 50295}, {8053, 24425}, {8845, 16917}, {10472, 37521}, {12640, 35104}, {17178, 25295}, {17260, 24003}, {17277, 25106}, {17787, 40790}, {17861, 24293}, {19270, 25079}, {19278, 25591}, {20236, 24255}, {20359, 31993}, {20892, 21352}, {21330, 27145}, {21688, 30055}, {24450, 27164}, {24456, 26107}, {24697, 25688}, {25570, 34284}, {25785, 44187}, {28604, 40848}, {29649, 34261}, {30035, 31330}, {31785, 35628}, {32935, 44421}, {35078, 35118}, {37596, 42027}, {37619, 40600}, {49488, 50598}, {50169, 50299}
X(51575) = midpoint of X(i) and X(j) for these {i,j}: {314, 1045}, {7168, 18830}
X(51575) = complement of X(256)
X(51575) = complement of the isogonal conjugate of X(171)
X(51575) = complement of the isotomic conjugate of X(1909)
X(51575) = medial isogonal conjugate of X(3846)
X(51575) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 3846}, {6, 4357}, {31, 1107}, {37, 46826}, {56, 24239}, {57, 17062}, {58, 6682}, {100, 21051}, {101, 25666}, {109, 3907}, {171, 10}, {172, 2}, {292, 325}, {335, 5031}, {385, 20333}, {604, 28358}, {692, 3709}, {893, 26558}, {894, 141}, {1215, 3454}, {1415, 24782}, {1492, 3805}, {1580, 17793}, {1691, 17755}, {1909, 2887}, {1911, 18904}, {1914, 39044}, {1920, 626}, {1922, 3229}, {1966, 20542}, {2162, 30038}, {2295, 1211}, {2298, 15985}, {2329, 3452}, {2330, 9}, {2533, 125}, {3287, 26932}, {3907, 124}, {3955, 3}, {3963, 21245}, {4032, 17052}, {4039, 45162}, {4164, 38989}, {4367, 11}, {4369, 116}, {4374, 21252}, {4434, 121}, {4447, 120}, {4459, 46100}, {4477, 5514}, {4504, 5510}, {4567, 40546}, {4579, 513}, {4588, 48289}, {4774, 15614}, {4922, 3259}, {6647, 31844}, {6649, 17072}, {7009, 5}, {7081, 1329}, {7119, 226}, {7122, 37}, {7175, 142}, {7176, 2886}, {7196, 17046}, {7205, 17047}, {7211, 34829}, {7234, 115}, {7267, 126}, {8033, 21240}, {14006, 34831}, {16720, 21248}, {17103, 3741}, {17752, 21250}, {17787, 21244}, {18047, 3835}, {18111, 44312}, {18200, 17761}, {18787, 3836}, {20964, 1213}, {20981, 1086}, {21725, 24040}, {21823, 23991}, {22061, 440}, {22093, 2968}, {24533, 5518}, {27958, 21246}, {27982, 39080}, {30657, 26582}, {30669, 20541}, {40519, 21099}, {40745, 21264}, {51319, 6376}
X(51575) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 1107}, {100, 3907}
X(51575) = X(i)-isoconjugate of X(j) for these (i,j): {893, 1258}, {904, 40418}, {1221, 7104}, {40409, 40729}
X(51575) = X(i)-Dao conjugate of X(j) for these (i, j): (1107, 2), (21838, 257), (40597, 1258)
X(51575) = crosspoint of X(2) and X(1909)
X(51575) = crosssum of X(6) and X(904)
X(51575) = barycentric product X(i)*X(j) for these {i,j}: {171, 20891}, {274, 27880}, {894, 3741}, {1107, 1909}, {1215, 16738}, {1920, 2309}, {3728, 8033}, {3963, 18169}, {7081, 30097}, {16720, 18091}, {17103, 21024}
X(51575) = barycentric quotient X(i)/X(j) for these {i,j}: {171, 1258}, {894, 40418}, {1107, 256}, {1197, 904}, {1909, 1221}, {2309, 893}, {3741, 257}, {4128, 40525}, {16738, 32010}, {17103, 40409}, {18169, 40432}, {20891, 7018}, {22065, 7015}, {22389, 7116}, {23473, 3863}, {27880, 37}, {30097, 7249}
X(51576) lies on the Feuerbach circumhyperbola of the medial triangle and on these lines: {1, 3052}, {2, 5556}, {3, 7992}, {9, 16192}, {10, 20}, {21, 3339}, {35, 5223}, {36, 22754}, {40, 40587}, {55, 9898}, {84, 49183}, {100, 4866}, {119, 10270}, {142, 3624}, {145, 8275}, {191, 30282}, {214, 1768}, {411, 3062}, {442, 16118}, {936, 3647}, {958, 11530}, {960, 45036}, {993, 7991}, {1145, 4668}, {1707, 45784}, {1743, 2092}, {2975, 9819}, {3086, 50836}, {3126, 3803}, {3189, 3632}, {3216, 24708}, {3220, 15592}, {3361, 3616}, {3522, 18249}, {3523, 51090}, {3601, 3962}, {3636, 11034}, {3646, 5122}, {3731, 34261}, {3820, 31425}, {3878, 30392}, {3922, 5128}, {3929, 4005}, {4189, 12526}, {4882, 35445}, {4915, 37568}, {5010, 11517}, {5087, 5131}, {5119, 15347}, {5248, 10980}, {5250, 13462}, {5267, 30389}, {5785, 37105}, {6361, 12864}, {6738, 50742}, {7990, 38669}, {7997, 25440}, {8580, 31445}, {8666, 30337}, {8727, 15908}, {9589, 30478}, {10058, 12653}, {10268, 18481}, {10304, 12447}, {10398, 37284}, {11529, 17571}, {12409, 12639}, {16209, 41540}, {16570, 37574}, {16673, 17736}, {17057, 50239}, {18229, 24850}, {19877, 37161}, {21153, 43182}, {24703, 34595}, {26363, 50865}, {46932, 50725}
X(51576) = complement of X(5556)
X(51576) = complement of the isogonal conjugate of X(5217)
X(51576) = complement of the isotomic conjugate of X(32099)
X(51576) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 1449}, {3929, 141}, {4005, 3454}, {5217, 10}, {32099, 2887}
X(51576) = X(2)-Ceva conjugate of X(1449)
X(51576) = X(2334)-isoconjugate of X(5556)
X(51576) = X(1449)-Dao conjugate of X(2)
X(51576) = crosspoint of X(2) and X(32099)
X(51576) = barycentric product X(i)*X(j) for these {i,j}: {1449, 32099}, {3616, 3929}, {4005, 42028}, {5217, 19804}
X(51576) = barycentric quotient X(i)/X(j) for these {i,j}: {1449, 5556}, {3929, 5936}, {5217, 25430}, {32099, 40023}
X(51576) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {165, 31424, 5234}, {4512, 4652, 3361}, {31445, 35242, 8580}
X(51577) lies on the Feuerbach circumhyperbola of the medial triangle and on these lines: {1, 3922}, {2, 43734}, {9, 1385}, {10, 3526}, {56, 16126}, {100, 1392}, {119, 6971}, {142, 3636}, {145, 1145}, {214, 1482}, {442, 496}, {517, 45036}, {999, 11517}, {1388, 3632}, {2092, 16884}, {3624, 5727}, {3635, 12640}, {3647, 13465}, {3723, 34261}, {3940, 21842}, {3962, 37618}, {4004, 35262}, {4018, 4930}, {4127, 11194}, {4757, 37545}, {5044, 30392}, {5552, 50843}, {6260, 18481}, {6594, 22836}, {6600, 7373}, {6767, 22754}, {9709, 11530}, {10427, 22791}, {11011, 17573}, {13089, 37525}, {20107, 34700}, {31424, 31662}, {34710, 50844}, {37624, 40587}
X(51577) = complement of X(43734)
X(51577) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 16885}, {4018, 3454}, {4930, 21251}
X(51577) = X(2)-Ceva conjugate of X(16885)
X(51577) = X(16885)-Dao conjugate of X(2)
X(51577) = barycentric product X(4018)*X(4921)
X(51577) = barycentric quotient X(16885)/X(43734)
X(51578) lies on the Kiepert circumhyperbola of the medial triangle and on these lines: {2, 846}, {3, 2784}, {10, 99}, {39, 8258}, {40, 21636}, {98, 10164}, {100, 8935}, {114, 516}, {115, 3634}, {147, 165}, {148, 1698}, {171, 643}, {244, 41820}, {376, 50879}, {515, 33813}, {519, 2482}, {543, 3828}, {551, 7983}, {620, 1125}, {726, 5976}, {740, 44379}, {946, 15561}, {950, 15452}, {986, 15903}, {1210, 10086}, {1326, 8298}, {1649, 45674}, {2782, 6684}, {2786, 9508}, {2792, 48886}, {2794, 12512}, {3027, 3911}, {3029, 6685}, {3097, 8782}, {3626, 35022}, {3666, 16598}, {4297, 9864}, {4745, 36521}, {5026, 5847}, {5182, 51196}, {5184, 7799}, {5248, 13173}, {5461, 50887}, {5463, 50850}, {5464, 50847}, {5587, 13172}, {6033, 31730}, {6054, 50808}, {6055, 50829}, {6321, 10175}, {6337, 49488}, {6541, 39922}, {6721, 10171}, {6722, 31253}, {8290, 17766}, {8591, 19875}, {9167, 12258}, {9780, 20094}, {9862, 35242}, {9884, 34641}, {10026, 17770}, {10089, 31397}, {10165, 38750}, {10353, 10789}, {11632, 38068}, {11710, 38748}, {12117, 34648}, {12571, 36519}, {12778, 14850}, {12780, 51114}, {12781, 51115}, {13188, 26446}, {13405, 24472}, {13883, 49267}, {13936, 49266}, {14061, 51073}, {14651, 31423}, {15300, 51069}, {17768, 44399}, {19108, 49548}, {19109, 49547}, {19862, 38220}, {19876, 41135}, {19878, 31274}, {19883, 50886}, {19925, 23698}, {20362, 20687}, {22505, 28150}, {28158, 39838}, {28164, 38738}, {31422, 43449}, {31673, 38730}, {31737, 39846}, {34379, 50567}, {35297, 50775}, {35369, 46932}, {38098, 50885}, {38481, 43223}, {39652, 49545}
X(51578) = midpoint of X(i) and X(j) for these {i,j}: {10, 99}, {40, 21636}, {376, 50879}, {551, 9881}, {4297, 9864}, {5463, 50850}, {5464, 50847}, {6033, 31730}, {6054, 50808}, {8591, 50884}, {9884, 34641}, {11599, 13174}, {12117, 34648}, {12780, 51114}, {12781, 51115}, {31673, 38730}, {31737, 39846}
X(51578) = reflection of X(i) in X(j) for these {i,j}: {115, 3634}, {1125, 620}, {6055, 50829}, {50887, 5461}
X(51578) = complement of X(11599)
X(51578) = complement of the isogonal conjugate of X(1326)
X(51578) = complement of the isotomic conjugate of X(17731)
X(51578) = polar conjugate of the isogonal conjugate of X(20784)
X(51578) = medial-isogonal conjugate of X(20546)
X(51578) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 20546}, {6, 20337}, {31, 10026}, {58, 49676}, {163, 2786}, {423, 20305}, {1326, 10}, {1333, 239}, {1757, 3454}, {1931, 141}, {2786, 21253}, {5029, 8287}, {6542, 21245}, {8298, 45162}, {9508, 125}, {17731, 2887}, {17735, 1211}, {17934, 21260}, {17943, 513}, {17976, 21530}, {18266, 1213}
X(51578) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 10026}, {99, 2786}
X(51578) = X(1929)-isoconjugate of X(28482)
X(51578) = X(i)-Dao conjugate of X(j) for these (i, j): (10026, 2), (35114, 6650), (41841, 35162)
X(51578) = crosspoint of X(2) and X(17731)
X(51578) = crosssum of X(6) and X(2054)
X(51578) = crossdifference of every pair of points on line {5029, 17962}
X(51578) = barycentric product X(i)*X(j) for these {i,j}: {264, 20784}, {4600, 41180}, {6542, 17770}, {10026, 17731}
X(51578) = barycentric quotient X(i)/X(j) for these {i,j}: {6542, 35162}, {10026, 11599}, {17735, 28482}, {17770, 6650}, {20666, 2054}, {20784, 3}, {41180, 3120}
X(51578) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13174, 11599}, {8591, 19875, 50884}, {9864, 21166, 4297}, {9881, 41134, 551}
X(51579) lies on the Kiepert circumhyperbola of the medial triangle and on these lines: {2, 15815}, {3, 3620}, {20, 114}, {39, 32973}, {99, 2996}, {193, 439}, {489, 33364}, {490, 33365}, {620, 32972}, {629, 18581}, {630, 18582}, {641, 6561}, {642, 6560}, {1003, 5395}, {1125, 17304}, {2482, 3926}, {3091, 14162}, {3291, 18287}, {3314, 21734}, {3522, 7710}, {3523, 11257}, {3788, 33272}, {5023, 20080}, {5032, 11165}, {5056, 38228}, {5059, 7925}, {5204, 8299}, {5304, 10335}, {5940, 40321}, {5976, 20081}, {6292, 15515}, {6392, 35297}, {6461, 37784}, {6462, 45515}, {6463, 45514}, {6503, 35296}, {6636, 40125}, {7487, 34835}, {7763, 35927}, {7782, 32974}, {7783, 33205}, {7795, 15810}, {7816, 32987}, {7836, 10304}, {7879, 19708}, {7881, 21735}, {8290, 33014}, {8598, 32823}, {10565, 30793}, {13586, 32831}, {14063, 45017}, {15814, 33192}, {20094, 33262}, {21843, 32824}, {32456, 32816}, {32834, 33274}, {32835, 33007}, {32868, 34506}, {32871, 33016}, {32898, 33013}, {33228, 39142}, {33620, 35303}, {33621, 35304}
X(51579) = reflection of X(38259) in X(39143)
X(51579) = complement of X(38259)
X(51579) = anticomplement of X(39143)
X(51579) = complement of the isogonal conjugate of X(5023)
X(51579) = complement of the isotomic conjugate of X(20080)
X(51579) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 193}, {5023, 10}, {16570, 141}, {20080, 2887}, {38252, 39143}, {38282, 20305}
X(51579) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 193}, {38282, 20080}
X(51579) = X(i)-isoconjugate of X(j) for these (i,j): {8769, 36616}, {38252, 38259}
X(51579) = X(193)-Dao conjugate of X(2)
X(51579) = crosspoint of X(2) and X(20080)
X(51579) = crosssum of X(6) and X(36616)
X(51579) = barycentric product X(i)*X(j) for these {i,j}: {193, 20080}, {6337, 38282}, {16570, 18156}
X(51579) = barycentric quotient X(i)/X(j) for these {i,j}: {193, 38259}, {3053, 36616}, {3167, 38263}, {5023, 8770}, {6353, 36611}, {16570, 8769}, {20080, 2996}, {38282, 34208}
X(51579) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 38259, 39143}, {99, 32989, 2996}, {439, 6337, 193}, {6337, 32459, 439}
X(51580) lies on the Kiepert circumhyperbola of the medial triangle and on these lines: {2, 12215}, {3, 315}, {6, 5976}, {22, 34452}, {39, 1975}, {69, 35423}, {76, 32467}, {98, 50684}, {99, 262}, {114, 3818}, {147, 39096}, {182, 183}, {194, 39095}, {384, 6337}, {458, 8842}, {1003, 2482}, {1007, 5999}, {1649, 30474}, {1692, 14614}, {1995, 38998}, {2076, 9766}, {3053, 35701}, {3329, 10335}, {3788, 6292}, {3815, 4048}, {5017, 7774}, {5024, 11356}, {5026, 42535}, {5116, 7778}, {5152, 6054}, {5939, 9756}, {6194, 39099}, {6811, 43155}, {6813, 43156}, {7470, 32816}, {7622, 7865}, {7752, 43460}, {7754, 8149}, {7769, 38907}, {7771, 9751}, {7777, 8290}, {7784, 34873}, {7788, 50977}, {7809, 9774}, {7832, 46307}, {7836, 46315}, {8304, 48785}, {8305, 48784}, {9723, 46094}, {9770, 11147}, {11165, 11286}, {15850, 43157}, {20885, 24729}, {22712, 35429}, {32458, 35424}, {32829, 37334}, {35925, 40824}, {41624, 51374}
X(51580) = complement of the isogonal conjugate of X(5017)
X(51580) = complement of the isotomic conjugate of X(7774)
X(51580) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 183}, {5017, 10}, {7774, 2887}, {50550, 8287}
X(51580) = X(2)-Ceva conjugate of X(183)
X(51580) = X(183)-Dao conjugate of X(2)
X(51580) = crosspoint of X(2) and X(7774)
X(51580) = barycentric product X(i)*X(j) for these {i,j}: {183, 7774}, {5017, 20023}
X(51580) = barycentric quotient X(i)/X(j) for these {i,j}: {5017, 263}, {7774, 262}
X(51580) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {182, 51373, 183}, {7763, 9744, 325}
X(51581) lies on the Kiepert circumhyperbola of the medial triangle and on these lines: {2, 7748}, {3, 43150}, {32, 11165}, {39, 6329}, {99, 43676}, {114, 550}, {187, 6337}, {546, 15850}, {574, 33242}, {620, 33229}, {629, 42163}, {630, 42166}, {641, 42258}, {642, 42259}, {1125, 28550}, {1649, 8651}, {2482, 3933}, {2548, 18843}, {3528, 7710}, {3530, 15819}, {3629, 35007}, {3631, 7863}, {3788, 33253}, {5023, 39785}, {5041, 32985}, {5206, 40341}, {5976, 35022}, {6292, 8589}, {7280, 8299}, {7752, 32456}, {7789, 15810}, {7801, 11147}, {7813, 33227}, {7819, 15602}, {7842, 41134}, {7855, 35287}, {7871, 33014}, {8290, 33276}, {10335, 32450}, {23217, 38998}, {30471, 41745}, {30472, 41746}, {33620, 42631}, {33621, 42632}, {34200, 34510}
X(51581) = complement of the isogonal conjugate of X(5206)
X(51581) = complement of the isotomic conjugate of X(40341)
X(51581) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 3629}, {5206, 10}, {37453, 20305}, {40341, 2887}
X(51581) = X(2)-Ceva conjugate of X(3629)
X(51581) = X(3629)-Dao conjugate of X(2)
X(51581) = crosspoint of X(2) and X(40341)
X(51581) = barycentric product X(3629)*X(40341)
X(51581) = barycentric quotient X(40341)/X(43676)
X(51582) lies on the Kiepert circumhyperbola of the medial triangle and on these lines: {2, 1501}, {3, 3096}, {39, 325}, {114, 5092}, {141, 5976}, {262, 7934}, {316, 11356}, {620, 10291}, {1506, 8363}, {1513, 15819}, {1649, 5996}, {2482, 7880}, {2896, 34870}, {3094, 3314}, {3619, 37182}, {3666, 26590}, {5116, 7778}, {5162, 7761}, {6292, 7807}, {6337, 7791}, {6626, 21993}, {7485, 14713}, {7736, 7912}, {7752, 7859}, {7799, 11165}, {7819, 10292}, {7846, 38905}, {7849, 15821}, {7901, 39095}, {7911, 37243}, {7931, 8290}, {8569, 33734}, {9744, 12054}, {10336, 50249}, {11147, 33008}, {15810, 35297}, {33190, 40824}, {35002, 37242}, {37455, 39096}
X(51582) = reflection of X(10291) in X(620)
X(51582) = complement of X(3407)
X(51582) = complement of the isogonal conjugate of X(3094)
X(51582) = complement of the isotomic conjugate of X(3314)
X(51582) = medial isogonal conjugate of X(24256)
X(51582) = X(i)-complementary conjugate of X(j) for these (i,j): {1, 24256}, {31, 7792}, {661, 6784}, {788, 21138}, {869, 17353}, {982, 21264}, {2186, 34236}, {2275, 24325}, {3094, 10}, {3116, 2}, {3117, 37}, {3250, 3271}, {3314, 2887}, {3408, 49111}, {4602, 9006}, {5117, 20305}, {7032, 17023}, {7146, 17792}, {17415, 16592}, {18899, 16584}, {19603, 19602}, {33946, 788}, {42061, 18904}, {43977, 16600}, {46507, 5}, {50549, 8287}
X(51582) = X(2)-Ceva conjugate of X(7792)
X(51582) = X(7792)-Dao conjugate of X(2)
X(51582) = crosspoint of X(2) and X(3314)
X(51582) = crosssum of X(6) and X(18898)
X(51582) = barycentric product X(3314)*X(7792)
X(51582) = barycentric quotient X(7792)/X(3407)
X(51583) lies on the Kiepert circumhyperbola of the medial triangle and on these lines: {2, 45}, {3, 8}, {7, 30834}, {11, 4427}, {39, 4850}, {57, 18139}, {63, 5741}, {75, 18359}, {81, 40605}, {89, 17378}, {99, 24624}, {114, 1281}, {121, 1054}, {165, 5014}, {214, 36923}, {239, 2482}, {244, 1125}, {320, 2245}, {321, 20879}, {329, 25737}, {333, 19302}, {345, 21488}, {519, 678}, {528, 4781}, {618, 39150}, {619, 39151}, {672, 4070}, {896, 49710}, {900, 39155}, {902, 49700}, {908, 4480}, {982, 29638}, {993, 6187}, {1016, 37222}, {1155, 3006}, {1227, 40988}, {1635, 3762}, {1647, 4432}, {2108, 29827}, {2246, 3707}, {2295, 29569}, {2325, 3911}, {3035, 3952}, {3244, 3722}, {3285, 4969}, {3306, 16549}, {3315, 3622}, {3578, 3687}, {3661, 15810}, {3666, 29833}, {3679, 9324}, {3689, 49702}, {3705, 4450}, {3712, 8299}, {3904, 3960}, {3909, 3937}, {3912, 24593}, {3928, 32859}, {3935, 49714}, {3969, 14829}, {3995, 37634}, {4000, 31229}, {4003, 26230}, {4009, 37762}, {4115, 24069}, {4141, 4439}, {4152, 6174}, {4274, 45048}, {4359, 4858}, {4395, 17495}, {4437, 31020}, {4442, 32845}, {4552, 43043}, {4553, 34583}, {4644, 31179}, {4650, 29849}, {4652, 5016}, {4689, 29835}, {4696, 6684}, {4697, 29688}, {4712, 6745}, {4738, 41529}, {4750, 4763}, {4860, 29830}, {4873, 50105}, {4933, 49764}, {4972, 17596}, {4999, 17164}, {5109, 17012}, {5161, 8300}, {5217, 36500}, {5222, 11165}, {5235, 6626}, {5432, 17165}, {5433, 25253}, {5435, 17776}, {5739, 37781}, {6184, 42723}, {6292, 17292}, {6337, 24597}, {6687, 16610}, {6690, 17140}, {6703, 41820}, {7238, 31029}, {8298, 14459}, {8720, 21935}, {9352, 29641}, {11288, 30884}, {13587, 16086}, {14193, 21290}, {17146, 37703}, {17147, 37646}, {17154, 17724}, {17191, 17455}, {17244, 27754}, {17330, 30564}, {17346, 24616}, {17350, 37651}, {17360, 33077}, {17593, 29631}, {17601, 33120}, {17729, 24638}, {17777, 31272}, {18134, 23958}, {18151, 19804}, {18201, 29632}, {18253, 27628}, {20880, 24589}, {21129, 47892}, {23757, 47695}, {24004, 36791}, {24344, 49720}, {24636, 45674}, {25248, 26686}, {25734, 30827}, {26073, 46933}, {26738, 50128}, {26840, 30831}, {26842, 41878}, {27003, 33116}, {29656, 42038}, {29662, 32934}, {29672, 42040}, {29689, 42053}, {29832, 37540}, {29872, 33068}, {30172, 37524}, {30568, 31224}, {30588, 50116}, {32918, 33167}, {33150, 41806}, {36913, 41801}, {38000, 41809}
X(51583) = midpoint of X(4080) and X(30579)
X(51583) = reflection of X(4080) in X(37691)
X(51583) = complement of X(4080)
X(51583) = anticomplement of X(37691)
X(51583) = complement of the isogonal conjugate of X(3285)
X(51583) = complement of the isotomic conjugate of X(16704)
X(51583) = isotomic conjugate of the isogonal conjugate of X(17455)
X(51583) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 3936}, {44, 3454}, {58, 3834}, {81, 21241}, {110, 4928}, {163, 900}, {284, 5123}, {519, 21245}, {849, 4395}, {900, 21253}, {902, 1211}, {1023, 31946}, {1319, 17052}, {1333, 519}, {1404, 442}, {1408, 17067}, {1576, 3960}, {1635, 125}, {1960, 8287}, {2206, 16610}, {2251, 1213}, {3285, 10}, {9459, 16589}, {16704, 2887}, {17455, 31845}, {18268, 25351}, {22086, 34846}, {22356, 21530}, {23202, 440}, {23344, 4129}, {30576, 3741}, {30939, 626}, {32739, 21894}, {34079, 6702}, {37168, 20305}
X(51583) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 3936}, {75, 519}, {99, 900}, {190, 3904}, {1016, 4585}, {2985, 323}, {4998, 17780}
X(51583) = X(i)-cross conjugate of X(j) for these (i,j): {214, 41801}, {40988, 214}
X(51583) = X(i)-isoconjugate of X(j) for these (i,j): {6, 1168}, {80, 9456}, {88, 6187}, {106, 2161}, {604, 36590}, {1411, 2316}, {1417, 36910}, {1807, 8752}, {2226, 40172}, {4674, 34079}, {23838, 32675}
X(51583) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 1168), (44, 1), (214, 2161), (1639, 11), (2245, 14260), (3161, 36590), (3218, 47058), (3936, 2), (3960, 1086), (4370, 80), (35069, 4674), (35128, 23838), (35204, 2316), (36914, 5219), (40584, 106), (40612, 88)
X(51583) = cevapoint of X(1145) and X(4370)
X(51583) = crosspoint of X(i) and X(j) for these (i,j): {2, 16704}, {75, 20924}, {1016, 24004}
X(51583) = crossdifference of every pair of points on line {1960, 3310}
X(51583) = X(993)-lineconjugate of X(6187)
X(51583) = barycentric product X(i)*X(j) for these {i,j}: {1, 1227}, {8, 41801}, {36, 3264}, {44, 20924}, {75, 214}, {76, 17455}, {274, 40988}, {320, 519}, {321, 17191}, {758, 30939}, {902, 40075}, {1443, 4723}, {2325, 17078}, {3218, 4358}, {3762, 4585}, {3911, 32851}, {3936, 16704}, {3960, 24004}, {3977, 17923}, {4453, 17780}, {4998, 51402}, {22128, 46109}, {30608, 36913}, {36791, 40215}, {36923, 39704}
X(51583) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1168}, {8, 36590}, {36, 106}, {44, 2161}, {214, 1}, {320, 903}, {519, 80}, {678, 40172}, {758, 4674}, {902, 6187}, {1227, 75}, {1317, 14584}, {1319, 1411}, {1870, 36125}, {1983, 32665}, {2323, 2316}, {2325, 36910}, {3218, 88}, {3264, 20566}, {3285, 34079}, {3738, 23838}, {3911, 2006}, {3936, 4080}, {3960, 1022}, {3992, 15065}, {4089, 6549}, {4358, 18359}, {4432, 36815}, {4453, 6548}, {4511, 1320}, {4585, 3257}, {4707, 4049}, {4867, 4792}, {5440, 1807}, {7113, 9456}, {14628, 34535}, {16704, 24624}, {17191, 81}, {17455, 6}, {17923, 6336}, {20924, 20568}, {21805, 34857}, {22128, 1797}, {23703, 2222}, {23884, 23598}, {24004, 36804}, {27757, 4945}, {30939, 14616}, {32851, 4997}, {34586, 14260}, {36913, 5219}, {36923, 3679}, {36944, 40437}, {40215, 2226}, {40612, 47058}, {40988, 37}, {41801, 7}, {50843, 34232}, {51402, 11}
X(51583) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 88, 24183}, {2, 190, 30566}, {2, 4080, 37691}, {2, 17487, 4945}, {2, 30577, 88}, {2, 30578, 4997}, {2, 30579, 4080}, {57, 33113, 18139}, {190, 4997, 30578}, {320, 27757, 3936}, {320, 32851, 27757}, {1054, 33115, 24988}, {3218, 27757, 320}, {3218, 32851, 3936}, {3911, 3977, 4358}, {4422, 43055, 2}, {4997, 30578, 30566}, {5744, 17740, 1150}, {14829, 33168, 3969}, {17596, 33119, 4972}, {26070, 30577, 2}, {32845, 33140, 4442}, {41138, 41802, 2}
X(51584) lies on the Kiepert circumhyperbola of the medial triangle and on these lines: {2, 8589}, {3, 50993}, {30, 15850}, {39, 27088}, {99, 8587}, {114, 8703}, {187, 11165}, {620, 15814}, {629, 35304}, {630, 35303}, {1649, 8644}, {2482, 22165}, {3787, 50729}, {5008, 7618}, {5475, 42011}, {5976, 14711}, {6337, 7855}, {6626, 22351}, {7710, 19708}, {8289, 46893}, {8584, 33550}, {8588, 15533}, {8594, 30472}, {8595, 30471}, {8598, 50280}, {8786, 41134}, {11147, 50994}, {12100, 15819}, {15655, 51187}, {15810, 32459}, {22848, 40672}, {22892, 40671}, {34835, 44261}, {35007, 35287}, {42625, 50858}, {42626, 50855}
X(51584) = midpoint of X(99) and X(8587)
X(51584) = reflection of X(15814) in X(620)
X(51584) = complement of X(17503)
X(51584) = complement of the isogonal conjugate of X(8588)
X(51584) = complement of the isotomic conjugate of X(15533)
X(51584) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 8584}, {8588, 10}, {15533, 2887}
X(51584) = X(2)-Ceva conjugate of X(8584)
X(51584) = X(8584)-Dao conjugate of X(2)
X(51584) = crosspoint of X(2) and X(15533)
X(51584) = barycentric product X(8584)*X(15533)
X(51584) = barycentric quotient X(8584)/X(17503)
X(51585) lies on the Kiepert circumhyperbola of the medial triangle and on these lines: {2, 7756}, {114, 548}, {620, 33267}, {629, 5321}, {630, 5318}, {1657, 10242}, {2482, 7767}, {3053, 11165}, {3627, 15850}, {3630, 15513}, {5206, 6337}, {6292, 32459}, {7710, 21735}, {7810, 11147}, {7890, 35287}, {15712, 15819}
X(51585) = complement of the isogonal conjugate of X(15513)
X(51585) = complement of the isotomic conjugate of X(3630)
X(51585) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 32455}, {3630, 2887}, {15513, 10}
X(51585) = X(2)-Ceva conjugate of X(32455)
X(51585) = X(32455)-Dao conjugate of X(2)
X(51585) = crosspoint of X(2) and X(3630)
X(51585) = barycentric product X(3630)*X(32455)
X(51586) lies on the Kiepert circumhyperbola of the medial triangle and on these lines: {2, 1171}, {3, 31872}, {115, 3634}, {239, 41820}, {1100, 1125}, {1649, 4988}, {1698, 23903}, {3337, 46196}, {3666, 16589}, {3828, 23905}, {5257, 15349}, {5259, 8299}, {5745, 38930}, {6626, 31248}, {7410, 7710}, {10026, 19878}, {25946, 40592}, {35068, 35076}, {36812, 46842}, {40605, 41817}
X(51586) = complement of X(32014)
X(51586) = complement of the isogonal conjugate of X(20970)
X(51586) = complement of the isotomic conjugate of X(1213)
X(51586) = X(i)-complementary conjugate of X(j) for these (i,j): {6, 27798}, {31, 6707}, {32, 3743}, {41, 18253}, {42, 17239}, {163, 6367}, {213, 3634}, {430, 20305}, {667, 24185}, {669, 16726}, {798, 3120}, {872, 41809}, {1100, 3741}, {1125, 21240}, {1213, 2887}, {1230, 21235}, {1918, 44307}, {1962, 141}, {2308, 3739}, {2355, 34830}, {3649, 17046}, {3683, 21246}, {3958, 1368}, {4046, 21244}, {4115, 21260}, {4427, 42327}, {4557, 48049}, {4647, 626}, {4983, 116}, {4988, 21252}, {6367, 21253}, {8013, 21245}, {8663, 8287}, {20970, 10}, {21816, 3454}, {22080, 18589}, {32636, 17050}, {32739, 8043}, {35327, 4369}, {35342, 512}, {50512, 17761}
X(51586) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 6707}, {99, 6367}
X(51586) = X(6707)-Dao conjugate of X(2)
X(51586) = crosspoint of X(2) and X(1213)
X(51586) = crosssum of X(6) and X(1171)
X(51586) = crossdifference of every pair of points on line {8663, 50344}
X(51586) = barycentric product X(i)*X(j) for these {i,j}: {1213, 6707}, {4988, 24074}
X(51586) = barycentric quotient X(i)/X(j) for these {i,j}: {6707, 32014}, {24074, 4632}
X(51587) lies on the Kiepert circumhyperbola of the medial triangle and on these lines: {2, 7765}, {3, 5965}, {99, 35005}, {114, 546}, {397, 619}, {398, 618}, {532, 42792}, {533, 42791}, {641, 43880}, {642, 43879}, {1125, 17246}, {1649, 2525}, {2482, 5007}, {3529, 7710}, {3544, 38228}, {3629, 35007}, {3631, 37512}, {5206, 11008}, {5563, 8299}, {5976, 32450}, {6292, 6390}, {6337, 7772}, {7764, 33257}, {7794, 15810}, {7820, 22332}, {7845, 44245}, {7858, 36521}, {7903, 17538}, {8290, 35022}, {8786, 14042}, {11147, 34511}, {11165, 33242}, {13701, 41945}, {13821, 41946}, {14869, 15819}, {33614, 51487}, {33615, 51486}, {33616, 37172}, {33617, 37173}, {33618, 41100}, {33619, 41101}, {33620, 50860}, {33621, 50859}, {36849, 39091}
X(51587) = midpoint of X(i) and X(j) for these {i,j}: {99, 35005}, {22844, 22845}
X(51587) = complement of X(43676)
X(51587) = complement of the isogonal conjugate of X(35007)
X(51587) = complement of the isotomic conjugate of X(3629)
X(51587) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 3631}, {163, 32478}, {3629, 2887}, {32478, 21253}, {35007, 10}
X(51587) = X(i)-Ceva conjugate of X(j) for these (i,j): {2, 3631}, {99, 32478}
X(51587) = X(3631)-Dao conjugate of X(2)
X(51587) = crosspoint of X(2) and X(3629)
X(51587) = barycentric product X(3629)*X(3631)
X(51587) = barycentric quotient X(3631)/X(43676)
X(51588) lies on the Kiepert circumhyperbola of the medial triangle and on these lines: {2, 14482}, {3, 597}, {6, 15810}, {30, 14484}, {114, 5055}, {381, 7710}, {524, 22246}, {543, 14535}, {599, 6292}, {641, 13783}, {642, 13663}, {671, 11174}, {1125, 41313}, {1384, 51185}, {1649, 45327}, {1992, 7767}, {2482, 5024}, {3329, 5077}, {3524, 46944}, {3589, 11165}, {3618, 11147}, {5050, 14830}, {5070, 7817}, {6329, 8182}, {6337, 33237}, {6767, 8299}, {7786, 8860}, {7923, 11318}, {8290, 8591}, {8359, 43136}, {8362, 11160}, {8981, 33365}, {10291, 50659}, {11057, 12156}, {13966, 33364}, {15603, 47061}, {15694, 15819}, {15707, 47618}, {21309, 44839}, {21509, 40592}, {33220, 39091}, {37344, 40604}
X(51588) = midpoint of X(2) and X(14482)
X(51588) = complement of the isogonal conjugate of X(21309)
X(51588) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 21358}, {1973, 31415}, {21309, 10}
X(51588) = X(2)-Ceva conjugate of X(21358)
X(51588) = X(21358)-Dao conjugate of X(2)
X(51589) lies on the Kiepert circumhyperbola of the medial triangle and on these lines: {2, 32532}, {3, 50991}, {39, 51185}, {99, 10153}, {114, 3534}, {381, 15850}, {2482, 5210}, {6337, 27088}, {7710, 8703}, {8584, 11165}, {8588, 50989}, {11147, 50990}, {15534, 33554}, {15655, 50992}, {15692, 47586}, {15693, 15819}, {15810, 51186}, {15814, 41134}, {21498, 40592}
X(51589) = midpoint of X(99) and X(10153)
X(51589) = complement of X(32532)
X(51589) = complement of the isogonal conjugate of X(15655)
X(51589) = complement of the isotomic conjugate of X(50992)
X(51589) = X(i)-complementary conjugate of X(j) for these (i,j): {31, 15534}, {15655, 10}, {50992, 2887}
X(51589) = X(2)-Ceva conjugate of X(15534)
X(51589) = X(15534)-Dao conjugate of X(2)
X(51589) = crosspoint of X(2) and X(50992)
X(51589) = barycentric product X(15534)*X(50992)
X(51589) = barycentric quotient X(i)/X(j) for these {i,j}: {15534, 32532}, {15655, 40103}
X(51590) lies on these lines: {1, 50041}, {2, 3}, {10, 50070}, {536, 25055}, {551, 50048}, {1125, 4387}, {1211, 48870}, {1698, 50051}, {3241, 50047}, {3616, 50043}, {3622, 50042}, {3624, 50054}, {3679, 50064}, {3828, 50046}, {3920, 48804}, {5550, 50045}, {6703, 48859}, {19784, 49732}, {19862, 50065}, {29667, 48800}, {32783, 48825}, {33171, 48823}, {50049, 50063}
X(51590) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 50052, 50041}, {2, 21, 50410}, {2, 376, 13728}, {2, 964, 381}, {2, 1010, 44217}, {2, 11115, 50321}, {2, 15670, 16343}, {2, 16394, 50056}, {2, 17526, 50202}, {2, 31156, 4205}, {2, 37037, 50323}, {2, 37176, 15670}, {2, 50059, 16394}, {2, 50061, 50058}, {2, 50407, 442}, {549, 50318, 2}, {551, 50048, 50072}, {1125, 50053, 50068}, {3616, 50043, 50069}, {11115, 50321, 3534}, {50053, 50068, 50044}
X(51591) lies on these lines: {1, 50043}, {2, 3}, {8, 50052}, {145, 50041}, {306, 48828}, {536, 38314}, {551, 50049}, {940, 48859}, {1125, 50066}, {3241, 50048}, {3616, 50045}, {3622, 50044}, {3623, 50042}, {3920, 48806}, {5550, 50065}, {5739, 48870}, {9780, 50051}, {10436, 15956}, {19877, 50050}, {20020, 48804}, {25055, 33147}, {29667, 48798}, {31145, 50047}, {33171, 48825}, {46934, 50067}
X(51591) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 50053, 50043}, {2, 20, 50321}, {2, 3543, 5051}, {2, 4195, 31156}, {2, 11115, 376}, {2, 15677, 13725}, {2, 16394, 50061}, {2, 31156, 37314}, {2, 50061, 50055}, {2, 50408, 6175}, {3, 50323, 2}, {376, 37037, 2}, {551, 50049, 50071}, {2049, 15670, 2}, {3616, 50045, 50068}, {16394, 50059, 2}, {16458, 50202, 2}, {17698, 44217, 2}, {37176, 50407, 2}, {50048, 50064, 3241}, {50052, 50070, 8}, {50054, 50068, 50045}
X(51592) lies on these lines: {1, 50045}, {2, 3}, {8, 50053}, {145, 50043}, {3241, 50049}, {3616, 50066}, {3617, 50052}, {3621, 50041}, {3622, 50068}, {3623, 50044}, {19993, 48824}, {20014, 50042}, {20020, 48806}, {31145, 50048}, {46932, 50050}, {46933, 50051}, {46934, 50065}, {50064, 50071}
X(51592) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15683, 17676}, {2, 50322, 3543}, {21, 50407, 2}, {376, 964, 2}, {1010, 31156, 2}, {4217, 19276, 2}, {6175, 37176, 2}, {11001, 37037, 50321}, {16394, 50061, 2}, {17526, 44217, 2}, {37037, 50321, 2}, {50043, 50070, 145}, {50054, 50070, 50043}, {50055, 50059, 2}
X(51593) lies on these lines: {1, 50051}, {2, 3}, {8, 50069}, {10, 50041}, {536, 19875}, {551, 50046}, {1125, 50070}, {1211, 48857}, {1698, 50044}, {1714, 49730}, {3624, 50050}, {3634, 50053}, {3679, 50063}, {3828, 50048}, {3920, 48800}, {4026, 10056}, {5739, 48861}, {9780, 50043}, {19876, 50049}, {19877, 50045}, {20083, 49729}, {29667, 48804}, {46933, 50042}, {50047, 50071}
X(51593) = orthocentroidal-circle-inverse of X(50323)
X(51593) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4, 50323}, {2, 3543, 37037}, {2, 5051, 381}, {2, 6175, 2049}, {2, 11359, 19290}, {2, 13725, 15670}, {2, 16062, 44217}, {2, 17679, 19332}, {2, 31156, 17698}, {2, 37314, 50202}, {2, 44217, 16458}, {2, 50055, 50059}, {2, 50056, 16394}, {2, 50058, 50056}, {2, 50321, 3}, {2, 50410, 16343}, {10, 50068, 50041}, {1698, 50066, 50052}, {3679, 50063, 50072}, {3828, 50062, 50048}, {50052, 50066, 50044}
X(51594) lies on these lines: {1, 50074}, {2, 3}, {17320, 19851}, {17330, 20018}, {17378, 49728}, {48838, 50224}, {48858, 49729}, {49723, 50133}
X(51594) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {33309, 50410, 2}
X(51595) lies on these lines: {1, 4753}, {2, 3}, {536, 16817}, {551, 5247}, {1104, 4755}, {1453, 29597}, {1724, 46922}, {4688, 7283}, {5263, 19871}, {16824, 50122}, {17297, 49723}, {19723, 48858}, {19851, 50072}, {19853, 48805}, {25507, 48866}, {41229, 51055}, {41813, 50111}
X(51595) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 405, 13735}, {2, 13735, 1010}, {2, 14020, 17677}, {2, 16858, 4234}, {2, 16861, 33309}, {2, 16865, 16393}, {2, 31156, 48816}, {2, 48814, 17678}, {2, 50430, 37038}, {405, 19241, 21}, {405, 37035, 1010}, {5047, 11110, 13741}, {11357, 16857, 2}, {13735, 37035, 2}, {13736, 17552, 33833}, {16351, 19536, 2}, {16844, 16860, 17697}, {16844, 17697, 19280}, {17547, 17553, 2}, {50056, 50714, 2}
X(51596) lies on these lines: {1, 50076}, {2, 3}, {4688, 19857}, {17303, 50049}, {17321, 50072}, {19871, 48821}, {25498, 50064}, {28606, 50047}, {31993, 50062}, {46922, 49716}, {50122, 50290}
X(51596) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13725, 16394}, {2, 48814, 50323}, {2, 50055, 2049}, {2, 50058, 442}, {13728, 17514, 17529}, {13728, 37039, 17514}, {50058, 50409, 2}
X(51597) lies on these lines: {1, 31144}, {2, 3}, {86, 49723}, {551, 41816}, {3616, 31143}, {4653, 41817}, {5333, 50234}, {16817, 41311}, {25507, 50226}, {42028, 49729}
X(51597) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 13745, 1010}, {2, 50165, 14005}, {2, 50171, 14007}, {405, 19318, 17513}, {13745, 17514, 2}
X(51598) lies on these lines: {1, 25503}, {2, 3}, {41311, 50072}
X(51598) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4217, 50318}, {2, 50321, 19277}
X(51599) lies on these lines: {1, 50082}, {2, 3}, {16828, 48829}, {17251, 50259}, {17281, 19857}
X(51599) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 14020, 2049}, {2, 37038, 16458}, {2, 37314, 37150}
X(51600) = X(51600) lies on these lines: {1, 50084}, {2, 3}, {17327, 49723}, {21358, 25526}, {41311, 50044}
X(51600) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 37037, 13745}
X(51601) lies on these lines: {1, 50085}, {2, 3}, {3241, 27790}, {17251, 25526}, {25055, 28617}
X(51601) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 2049, 17556}, {2, 11111, 17514}, {2, 14005, 17528}, {2, 50323, 19536}
X(51602) lies on these lines: {1, 4688}, {2, 3}, {37, 50049}, {75, 50072}, {958, 19871}, {1125, 47040}, {1698, 4252}, {3679, 37559}, {3739, 50064}, {3916, 19859}, {4664, 50044}, {4755, 50054}, {5247, 19875}, {6051, 50126}, {7283, 51488}, {9534, 46922}, {12635, 41812}, {17251, 50276}, {19797, 50041}, {19819, 50069}, {19822, 50047}, {19870, 48832}, {25526, 50259}, {42028, 48850}, {47037, 50163}, {50122, 50314}
X(51602) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 377, 50058}, {2, 1010, 16394}, {2, 11354, 17542}, {2, 16394, 405}, {2, 16397, 16342}, {2, 19276, 16370}, {2, 19290, 16371}, {2, 19336, 19279}, {2, 37150, 17556}, {2, 48816, 50056}, {2, 50055, 4205}, {2, 50169, 17532}, {1010, 16458, 405}, {2049, 16454, 474}, {4189, 17551, 16457}, {11115, 16844, 19526}, {16300, 16395, 37057}, {16394, 16458, 2}, {16395, 19283, 16300}, {16418, 19346, 16370}, {16454, 17589, 2049}, {16849, 37241, 405}, {17524, 19282, 405}, {19273, 19284, 19537}, {19277, 19332, 2}, {19279, 19336, 19705}, {48816, 50056, 50397}
X(51603) lies on these lines: {1, 4727}, {2, 3}, {1453, 19875}, {17251, 50272}, {17313, 25526}, {17320, 50044}, {19784, 49725}, {19865, 49746}, {24931, 27739}, {41311, 50049}
X(51603) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4217, 4205}, {2, 19277, 44217}, {2, 50059, 16370}, {1010, 37035, 16913}
X(51604) lies on these lines: {1, 50088}, {2, 3}, {17378, 25526}, {19865, 48829}
X(51604) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1010, 37038}, {2, 37038, 37039}
X(51605) lies on these lines: {1, 4527}, {2, 3}, {551, 42029}, {597, 9534}, {4340, 21356}, {5224, 49723}, {5247, 48809}, {7283, 41312}, {17320, 50049}, {18134, 50226}, {19883, 24178}, {32782, 50234}, {41311, 50054}, {41816, 48870}
X(51605) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4195, 13745}, {2, 13745, 37039}, {2, 16394, 37038}, {2, 50171, 16062}, {1010, 37036, 33833}, {1010, 37037, 37036}, {7833, 13745, 37038}
X(51606) lies on these lines: {1, 4480}, {2, 3}, {1043, 37654}, {1104, 50101}, {1265, 4370}, {3871, 34446}, {4304, 26685}, {4339, 50286}, {5248, 48833}, {5436, 50116}, {5657, 35284}
X(51606) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {21, 4217, 2}, {376, 33309, 2}, {4195, 11106, 13736}, {11111, 13735, 2}, {16394, 50430, 2}, {16418, 48817, 2}, {16858, 50061, 2}, {17576, 17697, 37339}
X(51607) lies on these lines: {3, 69}, {7, 58}, {99, 29242}, {239, 514}, {283, 17170}, {348, 1437}, {379, 24597}, {5744, 24632}, {6604, 37227}, {31016, 31017}
X(51607) = X(37)-isoconjugate of X(9085)
X(51607) = X(i)-Dao conjugate of X(j) for these (i, j): (5513, 1826), (40589, 9085)
X(51607) = crossdifference of every pair of points on line {42, 2489}
X(51607) = barycentric product X(i)*X(j) for these {i,j}: {86, 9028}, {99, 2504}, {3011, 17206}, {4025, 4237}, {4563, 29240}
X(51607) = barycentric quotient X(i)/X(j) for these {i,j}: {58, 9085}, {2504, 523}, {3011, 1826}, {4237, 1897}, {4558, 29241}, {7254, 35365}, {9028, 10}, {29240, 2501}
X(51608) lies on these lines: {2, 45930}, {3, 69}, {514, 661}, {664, 860}, {1150, 24581}, {1441, 12609}, {6505, 41809}, {20926, 20930}, {27249, 27267}, {29961, 29981}, {30033, 30034}, {30808, 30828}
X(51608) = anticomplement of X(45930)
X(51608) = crossdifference of every pair of points on line {31, 2489}
X(51608) = barycentric product X(1231)*X(1776)
X(51608) = barycentric quotient X(1776)/X(1172)
X(51609) lies on these lines: {3, 69}, {241, 514}, {30810, 30811}, {31184, 31232}
X(51609) = crossdifference of every pair of points on line {55, 2489}
X(51610) lies on the cubic K203 and these lines: {3, 69}, {115, 2971}
X(51610) = X(i)-complementary conjugate of X(j) for these (i,j): {35364, 4138}, {36051, 3566}
X(51610) = X(98)-Ceva conjugate of X(3566)
X(51610) = X(3565)-isoconjugate of X(36105)
X(51610) = X(39001)-Dao conjugate of X(3565)
X(51610) = crosssum of X(3563) and X(10425)
X(51610) = crossdifference of every pair of points on line {2489, 4558}
X(51610) = barycentric product X(3564)*X(6388)
X(51610) = barycentric quotient X(i)/X(j) for these {i,j}: {6388, 35142}, {8651, 32697}, {47430, 3563}
X(51611) lies on these lines: {3, 69}, {187, 47279}, {230, 231}, {235, 30549}, {441, 20975}, {460, 1632}, {1352, 10608}, {1609, 41584}, {3284, 47277}, {5181, 44395}, {5201, 47582}, {6467, 34828}, {7493, 37667}, {7778, 30739}, {8667, 44210}, {10602, 37188}, {11063, 32113}, {11799, 38580}, {14601, 41909}, {18365, 47280}, {32114, 32459}, {34569, 47462}, {35282, 40135}, {40809, 44556}, {43291, 47285}
X(51611) = crossdifference of every pair of points on line {3, 2489}
X(51611) = X(i)-line conjugate of X(j) for these (i,j): {69, 3}, {230, 2489}
X(51611) = {X(40947),X(41005)}-harmonic conjugate of X(26926)
X(51612) lies on these lines: {3, 69}, {10, 75}, {57, 3719}, {86, 7763}, {190, 18747}, {274, 51499}, {304, 307}, {325, 10446}, {345, 26942}, {573, 4417}, {1102, 7013}, {1264, 4561}, {1265, 51366}, {3729, 16603}, {3945, 32831}, {4201, 5232}, {4254, 22374}, {5207, 35462}, {7799, 17378}, {11359, 32836}, {17271, 32833}, {17272, 17596}, {17740, 32782}, {18135, 24986}, {24282, 41003}, {25000, 28809}, {48902, 51417}
X(51612) = isotomic conjugate of the polar conjugate of X(4417)
X(51612) = X(4998)-Ceva conjugate of X(4561)
X(51612) = X(i)-isoconjugate of X(j) for these (i,j): {25, 2217}, {667, 26704}, {1395, 10570}, {1973, 13478}, {1974, 2995}, {2203, 15232}, {2204, 40160}, {6591, 32653}
X(51612) = X(i)-Dao conjugate of X(j) for these (i, j): (4417, 16066), (6332, 11), (6337, 13478), (6505, 2217), (6589, 8735), (6631, 26704), (37646, 37226)
X(51612) = crossdifference of every pair of points on line {1919, 2489}
X(51612) = barycentric product X(i)*X(j) for these {i,j}: {69, 4417}, {304, 3869}, {305, 573}, {561, 22134}, {3185, 40364}, {3718, 17080}, {3926, 17555}, {4225, 40071}, {4998, 40626}
X(51612) = barycentric quotient X(i)/X(j) for these {i,j}: {63, 2217}, {69, 13478}, {124, 8735}, {190, 26704}, {304, 2995}, {306, 15232}, {307, 40160}, {332, 19607}, {345, 10570}, {573, 25}, {1331, 32653}, {1332, 36050}, {3185, 1973}, {3192, 2207}, {3869, 19}, {4225, 1474}, {4417, 4}, {4561, 44765}, {10571, 608}, {17080, 34}, {17555, 393}, {21078, 1824}, {21189, 6591}, {22134, 31}, {22276, 2333}, {34588, 2170}, {40626, 11}, {44717, 15386}, {47411, 3271}
X(51613) lies on these lines: {2, 6}, {3124, 8754}, {6388, 15525}
X(51613) = X(i)-Ceva conjugate of X(j) for these (i,j): {3564, 42663}, {40120, 669}
X(51613) = X(2489)-Dao conjugate of X(35142)
X(51613) = crossdifference of every pair of points on line {512, 3565}
X(51613) = barycentric product X(i)*X(j) for these {i,j}: {230, 6388}, {3564, 5139}, {8772, 17876}, {47430, 51481}
X(51613) = barycentric quotient X(i)/X(j) for these {i,j}: {5139, 35142}, {6388, 8781}, {8651, 10425}, {42663, 3565}, {47430, 2987}
X(51613) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1992, 44401, 1641}
X(51614) lies on these lines: {99, 29037}, {100, 4467}, {518, 7061}, {644, 3807}, {664, 3907}, {693, 6742}, {740, 7281}, {1320, 7261}, {2702, 2786}, {3699, 4505}, {3732, 9237}, {3900, 3903}, {4564, 36147}, {8844, 8851}, {32927, 40846}
X(51614) = isotomic conjugate of X(4458)
Incircle-inverses of points on the Euler line: X(51615) - X(51618)
X(51614) = isotomic conjugate of the complement of X(4088)
X(51614) = X(3573)-cross conjugate of X(190)
X(51614) = X(i)-isoconjugate of X(j) for these (i,j): {31, 4458}, {513, 17798}, {514, 19554}, {649, 3509}, {663, 5018}, {665, 40754}, {667, 4645}, {693, 18262}, {875, 1281}, {876, 19561}, {1919, 17789}, {1922, 27951}, {3572, 19557}, {3733, 20715}, {4367, 41532}, {4369, 41882}, {4444, 18038}, {6591, 20741}, {20981, 40873}
X(51614) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 4458), (5375, 3509), (6631, 4645), (9296, 17789), (39026, 17798), (39028, 27951)
X(51614) = cevapoint of X(i) and X(j) for these (i,j): {1, 2786}, {2, 4088}, {239, 522}, {3930, 23954}, {24129, 27846}
X(51614) = trilinear pole of line {9, 1654}
X(51614) = barycentric product X(i)*X(j) for these {i,j}: {100, 40845}, {101, 18036}, {190, 7261}, {668, 3512}, {874, 24479}, {1978, 8852}, {3903, 40846}, {4554, 7281}, {7061, 27805}, {27853, 30648}
X(51614) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 4458}, {100, 3509}, {101, 17798}, {190, 4645}, {350, 27951}, {651, 5018}, {666, 40724}, {668, 17789}, {692, 19554}, {874, 18037}, {1018, 20715}, {1331, 20741}, {3512, 513}, {3570, 1281}, {3573, 19557}, {3903, 40873}, {3952, 4071}, {4427, 4987}, {7061, 4369}, {7261, 514}, {7281, 650}, {8852, 649}, {18036, 3261}, {24479, 876}, {30648, 3572}, {32739, 18262}, {36086, 40754}, {40781, 2254}, {40845, 693}, {40846, 4374}, {41534, 4367}
This preamble is contributed by Clark Kimberling and Peter Moses, August 30, 2022.
The incenter-inverse of the Euler line is the circle with center X(39540) and pass-through points as indicated in the following list, in which the appearance of (i,j) means that X(i) is on the Euler line, and X(j) = incircle-inverse of X(i):
(2,51615), (3,5590), (4,51616), (5,5533), (20, 51617), (30, 1), (1012, 51618), (1314,1315), (1315, 1314), (3109, 55509)
See the preambles just before X(39486), X(39475), and X(51619).
X(51615) lies on these lines: {1, 2}, {88, 15637}, {516, 18201}, {518, 3038}, {908, 22942}, {1155, 3021}, {3664, 17721}, {3667, 3676}, {3756, 5853}, {4353, 24217}, {4392, 24802}, {4896, 10520}, {4899, 26139}, {4909, 17726}, {7963, 12536}, {11031, 50534}, {15601, 24477}, {21621, 46957}, {24175, 24392}, {33103, 50802}, {36263, 40998}
X(51615) = incircle-inverse of X(2)
X(51615) = orthoptic-circle-of-Steiner-inellipse-inverse of X(16020)
X(51615) = orthoptic-circle-of-Steiner-circumellipse-inverse of X(39567)
X(51615) = psi-transform of X(7613)
X(51615) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {17222, 8055}, {31316, 3436}
X(51615) = {X(1647),X(49989)}-harmonic conjugate of X(6745)
X(51616) lies on these lines: {1, 4}, {516, 46974}, {517, 15252}, {522, 905}, {1125, 6509}, {1210, 50368}, {1319, 1359}, {1324, 11365}, {1455, 38357}, {1456, 15524}, {1735, 3911}, {1736, 50759}, {1854, 6245}, {1875, 2817}, {1886, 34591}, {2331, 20263}, {2716, 5193}, {2723, 36079}, {3086, 5573}, {3616, 10538}, {3663, 14878}, {3671, 41344}, {4975, 24014}, {6001, 12016}, {6051, 13411}, {12915, 39544}, {15633, 36121}, {18237, 41402}, {18339, 50443}, {24034, 38462}, {39595, 50195}
X(51616) = midpoint of X(i) and X(j) for these {i,j}: {1, 1785}, {1319, 3326}, {1455, 38357}
X(51616) = reflection of X(i) in X(j) for these {i,j}: {1785, 44901}, {16870, 16869}, {51375, 15252}
X(51616) = incircle-inverse of X(4)
X(51616) = polar-circle-inverse of X(7952)
X(51616) = circumcircle-of-anticomplementary-triangle-inverse of X(34936)
X(51616) = X(i)-complementary conjugate of X(j) for these (i,j): {56, 25640}, {1295, 1329}, {36044, 20316}
X(51616) = crossdifference of every pair of points on line {198, 652}
X(51616) = {X(1),X(1699)}-harmonic conjugate of X(34231)
X(51617) lies on these lines: {1, 7}, {514, 44409}, {938, 5199}, {1210, 31897}, {3562, 31896}, {4649, 6738}, {4658, 6744}, {5853, 6510}, {11019, 16475}, {11028, 34381}
X(51617) = incircle-inverse of X(20)
X(51618) lies on these lines: {1, 84}, {72, 50379}, {521, 7649}, {912, 15500}, {1712, 14054}, {3193, 8885}, {7149, 43740}, {7952, 40263}, {24474, 44696}
X(51618) = reflection of X(72) in X(50379)
X(51618) = incircle-inverse of X(1012)
X(51618) = crossdifference of every pair of points on line {14298, 19350}
Circumcircle-inverses of points on the Nagel line: X(51619) - X(51631)
This preamble is contributed by Clark Kimberling and Peter Moses, August 30, 2022.
The circumcircle-inverse of the Nagel line is the circle with center X(39225) and pass-through points as indicated in the following list, in which the appearance of (i,j) means that X(i) is on the Nagel line, and X(j) = circumcircle-inverse of X(i):
(1,36), (2,23), (8,17100), (10,1324), (42, 32759), (78, 51629), (386, 51619), (519, 3), (997, 51620), (1125, 51621), (3811, 51622), (5121,51623), (5205, 51630), (5529, 51624), (6788, 51625), (6789, 39225), (22837, 51626), (23869, 51627), (30144, 51628)
See the preambles just before X(39486), X(39475), and X(51615).
X(51619) lies on these lines: {3, 6}, {23, 902}, {35, 20964}, {199, 38832}, {316, 13740}, {385, 726}, {512, 4057}, {595, 23868}, {612, 846}, {754, 51417}, {2244, 3647}, {2702, 28476}, {2711, 29187}, {2712, 8694}, {3743, 5184}, {3849, 11354}, {4195, 14712}, {4234, 31144}, {7295, 39582}, {12031, 15322}, {15485, 19318}, {17735, 21830}, {18792, 19308}, {19312, 25354}, {28369, 37023}, {37617, 38221}
X(51619) = midpoint of X(i) and X(j) for these {i,j}: {9301, 35462}, {14712, 20558}
X(51619) = reflection of X(i) in X(j) for these {i,j}: {316, 20546}, {1326, 187}
X(51619) = reflection of X(1326) in the Lemoine axis
X(51619) = circumcircle-inverse of X(386)
X(51619) = crossdifference of every pair of points on line {523, 17398}
X(51619) = barycentric product X(58)*X(27573)
X(51619) = barycentric quotient X(27573)/X(313)
X(51619) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {187, 20666, 1691}, {1379, 1380, 386}, {2076, 20675, 187}
X(51620) lies on these lines: {3, 960}, {8, 35988}, {23, 38460}, {40, 1603}, {56, 34049}, {101, 2745}, {104, 2728}, {521, 4057}, {603, 995}, {1737, 33849}, {8668, 39600}
X(51620) = circumcircle-inverse of X(997)
X(51620) = {X(3435),X(3556)}-harmonic conjugate of X(1158)
X(51621) lies on these lines: {1, 20836}, {3, 142}, {6, 41323}, {23, 20999}, {25, 92}, {55, 1961}, {56, 5018}, {101, 9052}, {149, 33325}, {198, 51058}, {199, 1621}, {238, 17798}, {284, 39543}, {405, 19865}, {511, 36942}, {514, 4057}, {595, 2305}, {674, 17976}, {692, 37510}, {740, 8301}, {831, 2725}, {859, 34179}, {902, 32759}, {927, 9108}, {947, 13598}, {962, 20838}, {999, 2097}, {1284, 6660}, {1617, 9909}, {1622, 39568}, {2076, 9259}, {2178, 37590}, {2702, 20472}, {2726, 8707}, {3286, 16686}, {3295, 5011}, {4245, 41327}, {5020, 49653}, {5078, 23404}, {5088, 13730}, {5263, 19329}, {5527, 8273}, {5687, 17233}, {5989, 5991}, {6186, 17469}, {6690, 19516}, {7083, 37507}, {8424, 24325}, {9708, 31897}, {9709, 17293}, {11349, 20533}, {11350, 31319}, {12410, 13737}, {15494, 20760}, {16059, 37577}, {16422, 37557}, {16678, 20834}, {16684, 20831}, {16689, 50293}, {20841, 37578}, {20918, 38863}, {20991, 37581}, {23095, 45728}, {23379, 23850}, {37502, 37580}
X(51621) = circumcircle-inverse of X(1125)
X(51621) = Stammler-circle-inverse of X(12699)
X(51621) = X(6650)-Ceva conjugate of X(6)
X(51621) = X(17735)-Dao conjugate of X(6542)
X(51621) = crosspoint of X(2702) and X(15378)
X(51621) = crosssum of X(116) and X(2786)
X(51621) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1001, 1631, 3}, {16678, 20988, 20834}, {20470, 20872, 3}, {20470, 23854, 20872}
X(51622) lies on these lines: {3, 518}, {23, 14664}, {36, 38695}, {165, 7298}, {2736, 15344}, {3309, 4057}, {5526, 37508}, {7390, 24309}
X(51622) = circumcircle-inverse of X(3811)
X(51623) lies on these lines: {2, 10058}, {3, 5121}, {22, 36}, {23, 11809}, {25, 1324}, {109, 7295}, {165, 7298}, {1283, 39475}, {1617, 9909}, {5119, 5310}, {5345, 13462}, {35988, 36152}
X(51623) = circumcircle-inverse of X(5121)
X(51623) = orthoptic-circle-of-Steiner-inellipse-inverse of X(39692)
X(51624) lies on these lines: {1, 20836}, {3, 5529}, {23, 3743}, {35, 228}, {36, 58}, {199, 1046}, {213, 2305}, {1030, 21879}, {1281, 4647}, {2092, 5280}, {3647, 17100}, {3778, 18757}, {4471, 16478}, {5009, 14815}, {5259, 25354}, {5526, 37508}, {17524, 24436}, {38882, 39633}
X(51624) = circumcircle-inverse of X(5529)
X(51624) = {X(58),X(501)}-harmonic conjugate of X(19655)
X(51625) lies on these lines: {3, 6788}, {23, 3011}, {36, 244}, {186, 7649}, {759, 859}, {1725, 5497}, {1737, 17010}, {20918, 38863}, {31841, 38612}, {36152, 38511}
X(51625) = midpoint of X(36) and X(1283)
X(51625) = circumcircle-inverse of X(6788)
X(51626) lies on these lines: {3, 2802}, {106, 32612}, {1293, 26286}, {2827, 4057}, {5450, 10744}, {10700, 26285}, {11012, 38620}, {11717, 37535}, {19649, 38693}, {32153, 50914}, {37561, 38604}
X(51626) = circumcircle-inverse of X(22837)
X(51627) lies on these lines: {3, 23869}, {23, 105}, {36, 1279}, {238, 3446}, {528, 5172}, {1324, 20470}, {5078, 32759}, {5540, 19297}
X(51627) = circumcircle-inverse of X(23869)
X(51627) = {X(36),X(38863)}-harmonic conjugate of X(20872)
X(51628) lies on these lines: {3, 214}, {36, 2841}, {80, 28077}, {109, 34880}, {1324, 2802}, {2217, 10738}, {3417, 10698}, {3705, 35996}, {3738, 4057}, {9798, 22560}, {11715, 23850}, {12737, 23843}
X(51628) = circumcircle-inverse of X(30144)
X(51629) lies on these lines: {3, 63}, {36, 1331}, {102, 6099}, {643, 2075}, {1725, 5497}, {4057, 15313}, {5119, 5310}, {6735, 49207}, {6921, 20266}
X(51629) = circumcircle-inverse of X(78)
X(51629) = crossdifference of every pair of points on line {6591, 20227}
X(51630) lies on these lines: {2, 36}, {3, 5205}, {5, 26259}, {8, 35988}, {22, 1324}, {23, 26227}, {25, 92}, {55, 4664}, {75, 20989}, {100, 3790}, {197, 32932}, {612, 846}, {1623, 26272}, {1995, 16823}, {2915, 4385}, {2975, 33849}, {3011, 17522}, {3705, 35996}, {3920, 37610}, {4057, 15621}, {4220, 29641}, {4672, 5363}, {4676, 5078}, {5211, 8666}, {5285, 32937}, {5297, 32759}, {5314, 27538}, {5329, 27064}, {6636, 17100}, {7283, 39582}, {7411, 38712}, {11194, 50533}, {14002, 26261}, {19649, 38693}, {23407, 47523}, {26231, 44210}, {26268, 39572}, {29634, 37325}
X(51630) = circumcircle-inverse of X(5205)
X(51630) = orthoptic-circle-of-Steiner-inellipse-inverse of X(3814)
X(51630) = orthoptic-circle-of-Steiner-circumellipse-inverse of X(5080)
X(51630) = psi-transform of X(5150)
X(51630) = {X(3),X(26264)}-harmonic conjugate of X(5205)
X(51631) lies on these lines: {1, 900}, {2, 3}, {5690, 38569}, {10944, 24864}, {14260, 36944}, {16944, 34590}, {24871, 37735}
X(51631) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 24875, 24877}, {2, 24877, 24865}, {2475, 17539, 404}, {7447, 7451, 859}, {13744, 37043, 3109}, {24865, 24866, 24867}, {24866, 24875, 24865}, {24866, 24877, 2}
Circumcircle-inverses of points on the line X(1)X(6): X(51632) - X(51639)
This preamble is contributed by Clark Kimberling and Peter Moses, August 31, 2022.
The circumcircle-inverse of the line X(1)X(6) is the circle with center X(39227) and pass-through points as indicated in the following list, in which the appearance of (i,j) means that X(i) is on X(1)X(6), and X(j) = circumcircle-inverse of X(i):
(1,36), (6,187), (9,32625), (37,32758), (72,51632), (220,51633), (238,51634), (405,51635), (518,3) (956,51636), (958, 51637), (960, 51638), (5220,51639), (1001,5144), (1083,667), (3230,11650)
See the preambles just before X(39486), X(39475), X(51615), and X(51619).
X(51632) lies on the cubic K039 and these lines: {3, 63}, {28, 47106}, {74, 6099}, {100, 186}, {187, 906}, {667, 15313}, {1030, 51574}, {2077, 50530}, {2915, 41507}, {5080, 36001}, {5172, 23067}, {32849, 43659}
X(51632) = circumcircle-inverse of X(72)
X(51632) = X(i)-Ceva conjugate of X(j) for these (i,j): {32849, 22123}, {43659, 72}
X(51632) = crossdifference of every pair of points on line {6591, 40941}
X(51633) lies on these lines: {3, 101}, {41, 1362}, {667, 926}, {910, 2809}, {1212, 11714}, {3022, 9310}, {17732, 38765}, {46835, 50903}
X(51633) = circumcircle-inverse of X(220)
X(51633) = crosssum of X(514) and X(44012)
X(51633) = crossdifference of every pair of points on line {676, 4000}
X(51633) = {X(101),X(103)}-harmonic conjugate of X(220)
X(51634) lies on these lines: {1, 667}, {3, 238}, {31, 46597}, {35, 1083}, {41, 813}, {727, 38986}, {898, 25439}, {932, 8851}, {1016, 8715}, {1283, 17664}, {2053, 46032}, {2382, 43362}, {3871, 9266}, {4057, 24338}, {5143, 8626}, {6376, 8709}, {11650, 16784}
X(51634) = midpoint of X(932) and X(8851)
X(51634) = circumcircle-inverse of X(238)
X(51634) = crossdifference of every pair of points on line {1575, 21348}
X(51635) lies on these lines: {2, 3}, {187, 3290}, {229, 49743}, {511, 51420}, {517, 1495}, {523, 667}, {1781, 3247}, {5842, 9625}, {7286, 32636}, {10149, 20129}, {17757, 20989}, {35193, 48924}
X(51635) = midpoint of X(i) and X(j) for these {i,j}: {23, 1325}, {5899, 37976}
X(51635) = reflection of X(i) in X(j) for these {i,j}: {858, 44898}, {17757, 47149}, {30447, 468}
X(51635) = reflection of X(30447) in the Orthic axis
X(51635) = circumcircle-inverse of X(405)
X(51635) = polar-circle-inverse of X(5142)
X(51635) = crossdifference of every pair of points on line {647, 4261}
X(51635) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 4228, 15670}, {3, 36009, 8226}, {28, 2915, 442}, {1113, 1114, 405}, {7520, 17562, 405}
X(51636) lies on these lines: {3, 8}, {9, 15015}, {11, 10199}, {36, 528}, {46, 12653}, {55, 50843}, {65, 15999}, {153, 6966}, {187, 43065}, {214, 392}, {404, 12019}, {442, 6667}, {667, 900}, {993, 6174}, {1001, 10058}, {1155, 2802}, {1317, 25439}, {1320, 36279}, {1470, 41556}, {2646, 15558}, {2771, 41389}, {2800, 17613}, {2801, 5440}, {2829, 37374}, {3035, 5251}, {3419, 11219}, {3911, 5427}, {4015, 5267}, {4299, 13272}, {4413, 34122}, {4855, 12738}, {5204, 48713}, {5450, 37725}, {5541, 11256}, {5880, 16173}, {6909, 51409}, {7483, 31235}, {8666, 13996}, {9024, 33844}, {10074, 13205}, {10090, 12690}, {10306, 12776}, {10310, 48694}, {10993, 26286}, {12732, 22560}, {13257, 48695}, {17010, 35271}, {17528, 31272}, {17647, 44848}, {20418, 24390}, {31190, 37718}, {32612, 37726}, {37428, 38761}, {37587, 50891}
X(51636) = circumcircle-inverse of X(956)
X(51636) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {100, 104, 956}, {100, 956, 1145}, {104, 2932, 1145}, {214, 41166, 392}, {956, 2932, 100}, {10074, 13205, 25416}
X(51637) lies on these lines: {3, 10}, {28, 1785}, {35, 1610}, {36, 1738}, {56, 24177}, {57, 49487}, {187, 910}, {198, 16370}, {226, 37397}, {522, 667}, {610, 3465}, {859, 17010}, {929, 29310}, {950, 37259}, {968, 3601}, {1210, 20842}, {1603, 8185}, {2182, 5440}, {2751, 6574}, {3220, 6909}, {3435, 49553}, {3452, 49128}, {4304, 11334}, {7501, 45766}, {7520, 10538}, {11700, 44662}, {12572, 15952}, {13411, 37227}, {16870, 37052}, {24892, 37262}, {27621, 38945}, {44661, 46974}
X(51637) = circumcircle-inverse of X(958)
X(51637) = crossdifference of every pair of points on line {2277, 6589}
X(51637) = {X(2217),X(2933)}-harmonic conjugate of X(10)
X(51638) lies on the cuibc K904 and these lines: {3, 960}, {521, 667}, {910, 32758}, {999, 10829}, {1324, 9912}, {1603, 5687}, {1610, 2915}, {2070, 12773}, {2217, 20831}, {2720, 38882}, {2750, 29163}, {4185, 38949}, {17638, 34442}, {19914, 35221}
X(51638) = circumcircle-inverse of X(960)
X(51638) = Stammler-circle-inverse of X(40266)
X(51638) = crosspoint of X(2766) and X(15385)
X(51638) = crosssum of X(123) and X(2850)
X(51639) lies on these lines: {3, 2801}, {36, 2809}, {55, 11712}, {100, 17294}, {101, 5010}, {528, 5144}, {667, 3887}, {4256, 44858}, {10695, 37587}, {26086, 51526}
X(51639) = circumcircle-inverse of X(5220)
Points on the Helman line: X(51640) - X(51664)
This preamble is based on notes from Dan Reznik and Peter Moses, August 31, 2022.
The radical axis of the incircle and circumcircle is here named the Helman line, after Mark Helman, who discovered special properties of this line under isgonal conjugation; see X(1319). The Helman line passes through X(1319) and is parallel to X(1)X(3); the Helman line is also L(9), the trilinear polar of X(57), and it passes through X(i) for these i:
513, 663, 855, 1149, 1279, 1284, 1319, 1455, 1456, 1457, 1458, 1459, 1463, 1464, 1769, 2605, 3669, 3777, 4017, 4367, 4822, 6129, 6610, 6615, 14292, 14413, 25569, 39688, 42336, 43924, 48116, 48121, 48122, 48123, 48128, 48129, 48131, 48136, 48137, 48144, 48149, 48150, 48151, 48306, 48329, 48330, 48336, 48340, 48350, 48367, 48597, 48616, 50332, 50353, 50354, 50458, 50459, 50508, 50517, 50523, 50526, and 51640-to-51664.
X(51640) lies on these lines: {73, 656}, {109, 2719}, {222, 23189}, {513, 663}, {603, 23226}, {810, 42658}, {822, 32320}, {1363, 38985}, {4077, 48281}, {4086, 37558}, {8062, 37523}
X(51640) = X(39201)-cross conjugate of X(822)
X(51640) = X(i)-isoconjugate of X(j) for these (i,j): {4, 36797}, {8, 107}, {9, 823}, {29, 1897}, {33, 811}, {55, 6528}, {78, 36126}, {99, 1857}, {100, 1896}, {112, 7017}, {158, 643}, {162, 318}, {190, 8748}, {219, 15352}, {281, 648}, {312, 24019}, {345, 6529}, {393, 645}, {607, 6331}, {646, 5317}, {653, 2322}, {670, 6059}, {1043, 36127}, {1096, 7257}, {1118, 7256}, {1172, 6335}, {1783, 31623}, {2052, 5546}, {2332, 46404}, {3596, 32713}, {3699, 8747}, {3700, 23582}, {4041, 23999}, {4086, 24000}, {4183, 18026}, {4552, 36421}, {5379, 44426}, {7359, 15459}, {8750, 44130}, {14308, 44181}, {17926, 46102}, {30730, 36419}, {34856, 36801}
X(51640) = X(i)-Dao conjugate of X(j) for these (i, j): (125, 318), (130, 7069), (223, 6528), (478, 823), (1147, 643), (6503, 7257), (8054, 1896), (17423, 33), (26932, 44130), (34467, 29), (34591, 7017), (35071, 312), (36033, 36797), (38985, 8), (38986, 1857), (39006, 31623), (46093, 78)
X(51640) = crosspoint of X(1459) and X(23224)
X(51640) = crosssum of X(i) and X(j) for these (i,j): {318, 4086}, {7069, 8611}
X(51640) = crossdifference of every pair of points on line {9, 318}
X(51640) = barycentric product X(i)*X(j) for these {i,j}: {7, 822}, {48, 17094}, {56, 24018}, {57, 520}, {65, 4091}, {73, 905}, {77, 647}, {85, 39201}, {163, 1367}, {201, 7254}, {222, 656}, {226, 23224}, {255, 7178}, {273, 32320}, {307, 22383}, {326, 7180}, {348, 810}, {394, 4017}, {512, 7183}, {513, 40152}, {514, 22341}, {523, 7125}, {525, 603}, {577, 4077}, {604, 3265}, {652, 1439}, {661, 1804}, {798, 7055}, {823, 1363}, {1019, 7066}, {1020, 1364}, {1214, 1459}, {1259, 7216}, {1395, 4143}, {1400, 4131}, {1402, 30805}, {1409, 4025}, {1410, 6332}, {1414, 3269}, {1415, 17216}, {1577, 7335}, {1813, 18210}, {2632, 4565}, {3049, 7182}, {3125, 6517}, {3668, 36054}, {3669, 3682}, {3676, 3990}, {3719, 7250}, {3942, 23067}, {3998, 43924}, {4055, 24002}, {4466, 36059}, {4560, 7138}, {7053, 8611}, {16730, 36127}, {23189, 37755}, {23286, 44708}
X(51640) = barycentric quotient X(i)/X(j) for these {i,j}: {34, 15352}, {48, 36797}, {56, 823}, {57, 6528}, {73, 6335}, {77, 6331}, {222, 811}, {255, 645}, {394, 7257}, {520, 312}, {577, 643}, {603, 648}, {604, 107}, {608, 36126}, {647, 318}, {649, 1896}, {656, 7017}, {667, 8748}, {798, 1857}, {810, 281}, {822, 8}, {905, 44130}, {1259, 7258}, {1363, 24018}, {1367, 20948}, {1395, 6529}, {1397, 24019}, {1409, 1897}, {1410, 653}, {1439, 46404}, {1459, 31623}, {1804, 799}, {1924, 6059}, {1946, 2322}, {2289, 7256}, {3049, 33}, {3265, 28659}, {3269, 4086}, {3682, 646}, {3990, 3699}, {4017, 2052}, {4055, 644}, {4077, 18027}, {4091, 314}, {4131, 28660}, {4565, 23999}, {6056, 7259}, {6517, 4601}, {7055, 4602}, {7066, 4033}, {7125, 99}, {7138, 4552}, {7180, 158}, {7183, 670}, {7335, 662}, {17094, 1969}, {18210, 46110}, {22341, 190}, {22383, 29}, {23224, 333}, {24018, 3596}, {30805, 40072}, {32320, 78}, {32660, 5379}, {34980, 8611}, {36054, 1043}, {39201, 9}, {40152, 668}, {42293, 7069}, {46088, 44687}
X(51641) lies on these lines: {1, 4170}, {42, 4729}, {56, 16695}, {109, 2703}, {181, 50493}, {512, 810}, {513, 663}, {667, 50514}, {798, 3049}, {1042, 7216}, {1356, 38986}, {1414, 29055}, {3900, 23655}, {4010, 17478}, {4077, 29051}, {4449, 4804}, {4815, 48281}, {7178, 47998}, {22090, 50336}
X(51641) = isogonal conjugate of X(7257)
X(51641) = isogonal conjugate of the anticomplement of X(16613)
X(51641) = isogonal conjugate of the isotomic conjugate of X(4017)
X(51641) = X(i)-Ceva conjugate of X(j) for these (i,j): {1397, 3248}, {4551, 1400}, {4625, 57}, {7180, 798}, {29055, 56}, {43924, 7180}
X(51641) = X(i)-cross conjugate of X(j) for these (i,j): {669, 798}, {8034, 3248}
X(51641) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 7257), (115, 28659), (125, 3718), (206, 643), (223, 670), (244, 3596), (478, 799), (512, 4041), (513, 18155), (798, 27527), (1015, 28660), (1084, 312), (1086, 40072), (1214, 6386), (2679, 44694), (3005, 4086), (3160, 4602), (4858, 40363), (5139, 318), (5452, 7258), (5521, 44130), (6609, 4625), (8054, 314), (17423, 78), (32664, 645), (34467, 332), (36908, 4572), (38985, 1264), (38986, 8), (38996, 9), (39025, 1043), (40586, 646), (40589, 4631), (40590, 1978), (40593, 4609), (40600, 3699), (40608, 341), (40611, 668), (40615, 6385), (40617, 310), (40622, 561), (40627, 4391), (50330, 35519), (50497, 522)
X(51641) = crosspoint of X(i) and X(j) for these (i,j): {1, 6010}, {56, 4559}, {57, 4625}, {1400, 4551}, {7180, 7250}
X(51641) = crosssum of X(i) and X(j) for these (i,j): {1, 6002}, {8, 4560}, {200, 4529}, {312, 4086}, {314, 18155}, {333, 3737}, {514, 24178}, {522, 3687}, {645, 7256}, {646, 3699}, {663, 3691}, {668, 4561}, {1193, 4498}, {3702, 4391}, {4041, 33299}, {4110, 30584}
X(51641) = trilinear pole of line {3121, 21755}
X(51641) = crossdifference of every pair of points on line {9, 312}
X(51641) = X(i)-isoconjugate of X(j) for these (i,j): {1, 7257}, {2, 645}, {7, 7256}, {8, 99}, {9, 799}, {21, 668}, {29, 4561}, {37, 4631}, {41, 4602}, {55, 670}, {57, 7258}, {60, 27808}, {69, 36797}, {75, 643}, {76, 5546}, {78, 811}, {81, 646}, {85, 7259}, {86, 3699}, {100, 314}, {101, 28660}, {107, 1264}, {110, 3596}, {162, 3718}, {163, 28659}, {190, 333}, {200, 4625}, {210, 4623}, {219, 6331}, {261, 3952}, {274, 644}, {281, 4563}, {284, 1978}, {286, 4571}, {310, 3939}, {312, 662}, {313, 4636}, {318, 4592}, {321, 4612}, {332, 1897}, {341, 1414}, {345, 648}, {346, 4573}, {391, 4633}, {522, 4600}, {523, 6064}, {650, 4601}, {664, 1043}, {689, 3688}, {692, 40072}, {728, 4635}, {765, 18155}, {789, 3786}, {823, 3719}, {873, 4069}, {892, 3712}, {1016, 4560}, {1259, 6528}, {1331, 44130}, {1332, 31623}, {1434, 6558}, {1509, 30730}, {1576, 40363}, {1792, 18026}, {1812, 6335}, {2175, 4609}, {2185, 4033}, {2194, 6386}, {2238, 36806}, {2287, 4554}, {2311, 27853}, {2319, 36860}, {2321, 4610}, {2325, 4615}, {2327, 46404}, {2328, 4572}, {2329, 7260}, {2396, 15628}, {3239, 4620}, {3570, 36800}, {3684, 4639}, {3685, 4589}, {3686, 4632}, {3689, 4634}, {3700, 4590}, {3702, 4596}, {3703, 4577}, {3709, 34537}, {3737, 7035}, {3886, 51563}, {3975, 4584}, {4030, 35137}, {4041, 24037}, {4076, 7192}, {4086, 24041}, {4092, 31614}, {4391, 4567}, {4552, 7058}, {4556, 30713}, {4557, 18021}, {4558, 7017}, {4570, 35519}, {4582, 16704}, {4587, 44129}, {4593, 33299}, {4594, 7081}, {4597, 4720}, {4603, 17787}, {4614, 4673}, {4616, 5423}, {4622, 4723}, {4637, 30693}, {4998, 7253}, {5379, 35518}, {5383, 27527}, {6632, 17197}, {7252, 31625}, {8611, 46254}, {8706, 17183}, {11609, 17935}, {14574, 44159}, {15411, 46102}, {27382, 44326}, {27398, 44327}, {27805, 27958}, {30729, 32014}, {30941, 36802}, {32851, 47318}, {33295, 36801}, {36036, 44694}, {37204, 40972}
X(51641) = barycentric product X(i)*X(j) for these {i,j}: {1, 7180}, {6, 4017}, {7, 798}, {9, 7250}, {31, 7178}, {32, 4077}, {34, 647}, {37, 43924}, {42, 3669}, {55, 7216}, {56, 661}, {57, 512}, {65, 649}, {71, 43923}, {73, 6591}, {77, 2489}, {85, 669}, {109, 3125}, {163, 1365}, {181, 1019}, {201, 43925}, {213, 3676}, {225, 22383}, {226, 667}, {244, 4559}, {269, 3709}, {273, 3049}, {278, 810}, {349, 1980}, {513, 1400}, {514, 1402}, {523, 604}, {525, 1395}, {603, 2501}, {608, 656}, {650, 1042}, {651, 3122}, {652, 1426}, {663, 1427}, {664, 3121}, {738, 4524}, {799, 1356}, {822, 1118}, {872, 17096}, {875, 16609}, {1014, 4079}, {1015, 4551}, {1018, 1357}, {1020, 3271}, {1021, 7143}, {1084, 4625}, {1106, 3700}, {1254, 7252}, {1284, 3572}, {1334, 43932}, {1393, 2623}, {1397, 1577}, {1398, 8611}, {1407, 4041}, {1408, 4024}, {1409, 7649}, {1410, 3064}, {1411, 21828}, {1412, 4705}, {1414, 3124}, {1415, 3120}, {1416, 24290}, {1417, 4120}, {1432, 7234}, {1434, 50487}, {1441, 1919}, {1459, 1880}, {1461, 4516}, {1500, 7203}, {1911, 7212}, {1918, 24002}, {1924, 6063}, {1973, 17094}, {2171, 3733}, {2642, 7316}, {2643, 4565}, {3063, 3668}, {3248, 4552}, {4036, 16947}, {4128, 37137}, {4171, 7023}, {4564, 8034}, {4635, 7063}, {4729, 40151}, {6614, 36197}, {7131, 50490}, {7147, 21789}, {7153, 50491}, {7337, 24018}, {8639, 44733}, {9426, 20567}, {9456, 30572}, {14321, 16945}, {16592, 29055}, {18097, 50521}, {18210, 32674}, {20948, 41280}, {20982, 26700}, {23493, 43051}, {32669, 42759}, {37136, 42752}, {39258, 43930}
X(51641) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 7257}, {7, 4602}, {31, 645}, {32, 643}, {34, 6331}, {41, 7256}, {42, 646}, {55, 7258}, {56, 799}, {57, 670}, {58, 4631}, {65, 1978}, {85, 4609}, {109, 4601}, {163, 6064}, {181, 4033}, {213, 3699}, {226, 6386}, {512, 312}, {513, 28660}, {514, 40072}, {523, 28659}, {560, 5546}, {603, 4563}, {604, 99}, {608, 811}, {647, 3718}, {649, 314}, {661, 3596}, {667, 333}, {669, 9}, {688, 33299}, {741, 36806}, {798, 8}, {810, 345}, {822, 1264}, {872, 30730}, {875, 36800}, {1015, 18155}, {1019, 18021}, {1042, 4554}, {1084, 4041}, {1106, 4573}, {1284, 27853}, {1356, 661}, {1357, 7199}, {1365, 20948}, {1395, 648}, {1397, 662}, {1400, 668}, {1402, 190}, {1403, 36860}, {1407, 4625}, {1408, 4610}, {1409, 4561}, {1412, 4623}, {1414, 34537}, {1415, 4600}, {1417, 4615}, {1426, 46404}, {1427, 4572}, {1431, 7260}, {1577, 40363}, {1918, 644}, {1919, 21}, {1924, 55}, {1973, 36797}, {1977, 3737}, {1980, 284}, {2084, 3703}, {2171, 27808}, {2175, 7259}, {2200, 4571}, {2205, 3939}, {2206, 4612}, {2489, 318}, {2491, 44694}, {3049, 78}, {3063, 1043}, {3121, 522}, {3122, 4391}, {3124, 4086}, {3125, 35519}, {3248, 4560}, {3249, 18191}, {3669, 310}, {3676, 6385}, {3709, 341}, {4017, 76}, {4077, 1502}, {4079, 3701}, {4117, 3709}, {4455, 3975}, {4524, 30693}, {4551, 31625}, {4559, 7035}, {4565, 24037}, {4625, 44168}, {4705, 30713}, {4729, 44723}, {4832, 4673}, {6591, 44130}, {7023, 4635}, {7063, 4171}, {7109, 4069}, {7178, 561}, {7180, 75}, {7212, 18891}, {7216, 6063}, {7234, 17787}, {7250, 85}, {7337, 823}, {7366, 4616}, {8027, 17197}, {8034, 4858}, {8639, 11679}, {9426, 41}, {9491, 7075}, {9494, 40972}, {14407, 4723}, {17094, 40364}, {20948, 44159}, {21751, 40499}, {21755, 3907}, {21832, 4087}, {21835, 4147}, {22383, 332}, {38986, 27527}, {39201, 3719}, {41280, 163}, {42336, 18600}, {43923, 44129}, {43924, 274}, {46386, 3786}, {50487, 2321}, {50491, 4110}
X(51642) lies on these lines: {57, 14419}, {65, 9508}, {85, 14296}, {110, 934}, {226, 2787}, {388, 4922}, {513, 663}, {891, 43050}, {905, 1938}, {928, 3960}, {1387, 2826}, {2775, 24929}, {2785, 17992}, {3340, 4730}, {3485, 4010}, {4077, 48288}, {4449, 9397}, {4870, 45342}, {5219, 14431}, {5226, 30709}, {7178, 47799}, {8674, 12739}, {9511, 14414}, {15253, 29240}, {17094, 48290}, {23770, 30725}, {37583, 42670}, {37761, 44435}, {43049, 48332}
X(51642) = X(i)-isoconjugate of X(j) for these (i,j): {8, 2701}, {42, 17931}, {55, 35154}, {100, 2648}, {101, 17947}, {190, 17963}, {643, 2652}, {1897, 17973}, {4570, 18013}, {4600, 18000}, {5546, 11608}
X(51642) = X(i)-Dao conjugate of X(j) for these (i, j): (223, 35154), (1015, 17947), (8054, 2648), (34467, 17973), (35086, 312), (39055, 190), (40592, 17931), (50330, 18013), (50497, 18000)
X(51642) = crossdifference of every pair of points on line {9, 2648}
X(51642) = barycentric product X(i)*X(j) for these {i,j}: {57, 2785}, {81, 18006}, {85, 5075}, {274, 17992}, {513, 17950}, {514, 1758}, {693, 17966}, {905, 17985}, {2651, 7178}, {3125, 17933}, {4017, 40882}, {4077, 5060}, {16732, 17942}, {17924, 17975}
X(51642) = barycentric quotient X(i)/X(j) for these {i,j}: {57, 35154}, {81, 17931}, {513, 17947}, {604, 2701}, {649, 2648}, {667, 17963}, {1758, 190}, {2651, 645}, {2785, 312}, {3121, 18000}, {3125, 18013}, {4017, 11608}, {5060, 643}, {5075, 9}, {7180, 2652}, {17933, 4601}, {17942, 4567}, {17950, 668}, {17966, 100}, {17975, 1332}, {17985, 6335}, {17992, 37}, {18006, 321}, {22383, 17973}, {40882, 7257}
X(51643) lies on these lines: {65, 8674}, {108, 110}, {513, 663}, {521, 43923}, {1462, 10099}, {1476, 46041}, {2285, 24290}, {3738, 4458}, {3801, 9001}, {6003, 44410}, {7178, 9013}, {30212, 44409}, {31603, 47755}
X(51643) = X(i)-isoconjugate of X(j) for these (i,j): {55, 35169}, {3939, 16099}, {36797, 43693}
X(51643) = X(i)-Dao conjugate of X(j) for these (i, j): (223, 35169), (35122, 312), (40617, 16099)
X(51643) = crosspoint of X(2006) and X(18026)
X(51643) = crosssum of X(1946) and X(2323)
X(51643) = barycentric product X(i)*X(j) for these {i,j}: {85, 42662}, {651, 867}, {3669, 16086}, {42709, 43924}
X(51643) = barycentric quotient X(i)/X(j) for these {i,j}: {57, 35169}, {867, 4391}, {3669, 16099}, {16086, 646}, {42662, 9}
X(51644) lies on these lines: {388, 2517}, {513, 663}, {514, 43923}, {521, 4025}, {522, 23732}, {656, 9051}, {905, 23187}, {1461, 46152}, {8760, 44409}, {9373, 47136}, {11934, 39540}, {14300, 40628}, {18344, 21172}, {21107, 49296}, {23727, 47960}
X(51644) = reflection of X(i) in X(j) for these {i,j}: {11934, 39540}, {18344, 21172}
X(51644) = crossdifference of every pair of points on line {9, 607}
X(51644) = X(i)-Ceva conjugate of X(j) for these (i,j): {388, 26933}, {7091, 7004}
X(51644) = X(i)-isoconjugate of X(j) for these (i,j): {8, 32691}, {9, 36099}, {33, 1310}, {100, 1039}, {607, 37215}, {1036, 1897}, {1245, 36797}, {1783, 2339}, {8750, 30479}
X(51644) = X(i)-Dao conjugate of X(j) for these (i, j): (478, 36099), (5515, 318), (8054, 1039), (17421, 8), (26932, 30479), (26933, 2478), (34467, 1036), (39006, 2339)
X(51644) = barycentric product X(i)*X(j) for these {i,j}: {7, 2522}, {57, 23874}, {77, 6590}, {222, 2517}, {348, 8678}, {388, 905}, {514, 1038}, {521, 7365}, {525, 5323}, {651, 26933}, {693, 2286}, {1214, 47844}, {1460, 15413}, {2285, 4025}, {2303, 17094}, {2484, 7182}, {3610, 7203}, {3676, 5227}, {3942, 14594}, {4320, 6332}, {7085, 24002}, {10376, 15411}, {19799, 43924}
X(51644) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 36099}, {77, 37215}, {222, 1310}, {388, 6335}, {604, 32691}, {649, 1039}, {905, 30479}, {1038, 190}, {1459, 2339}, {1460, 1783}, {2285, 1897}, {2286, 100}, {2303, 36797}, {2484, 33}, {2517, 7017}, {2522, 8}, {4320, 653}, {5227, 3699}, {5323, 648}, {6590, 318}, {7085, 644}, {7197, 13149}, {7365, 18026}, {8646, 607}, {8678, 281}, {22383, 1036}, {23874, 312}, {26933, 4391}, {47844, 31623}
X(51645) lies on these lines: {7, 27}, {34, 39791}, {221, 4331}, {241, 27637}, {513, 663}, {527, 20752}, {651, 17950}, {940, 50197}, {1400, 1427}, {1409, 3668}, {1423, 7106}, {1430, 26884}, {1439, 1880}, {1469, 2393}, {2286, 6180}, {3330, 4466}, {3649, 34046}, {4334, 5429}, {6349, 17257}, {18607, 28287}, {26109, 26119}, {28015, 28031}
X(51645) = X(42669)-cross conjugate of X(851)
X(51645) = X(i)-isoconjugate of X(j) for these (i,j): {8, 2249}, {9, 37142}, {55, 35145}, {296, 2322}, {1043, 1945}, {1937, 2287}, {1952, 2328}, {3900, 41206}, {4183, 40843}
X(51645) = X(i)-Dao conjugate of X(j) for these (i, j): (223, 35145), (478, 37142), (35075, 312), (36908, 1952), (39032, 1043), (39037, 2287)
X(51645) = barycentric product X(i)*X(j) for these {i,j}: {7, 851}, {56, 44150}, {57, 8680}, {65, 5088}, {85, 42669}, {243, 1439}, {307, 1430}, {1427, 1944}, {1441, 26884}, {1446, 1951}, {1936, 3668}, {6063, 44112}, {7180, 15418}, {17094, 23353}
X(51645) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 37142}, {57, 35145}, {604, 2249}, {851, 8}, {1042, 1937}, {1410, 296}, {1427, 1952}, {1430, 29}, {1461, 41206}, {1936, 1043}, {1951, 2287}, {2202, 2322}, {5088, 314}, {8680, 312}, {23353, 36797}, {26884, 21}, {32714, 41207}, {42669, 9}, {44112, 55}, {44150, 3596}
X(51646) lies on these lines: {1, 30572}, {35, 2776}, {109, 110}, {513, 663}, {1400, 5029}, {1405, 14407}, {3737, 21180}, {4145, 11011}, {4814, 7627}, {5040, 17992}, {5903, 44812}, {8648, 8677}, {8674, 41541}, {21112, 46385}, {21118, 48281}, {39771, 39778}
X(51646) = X(34921)-Ceva conjugate of X(56)
X(51646) = crosspoint of X(109) and X(1411)
X(51646) = crosssum of X(i) and X(j) for these (i,j): {522, 4511}, {663, 1731}
X(51646) = crossdifference of every pair of points on line {9, 11604}
X(51646) = X(i)-isoconjugate of X(j) for these (i,j): {8, 1290}, {55, 35156}, {100, 11604}, {643, 5620}, {644, 21907}
X(51646) = X(i)-Dao conjugate of X(j) for these (i, j): (223, 35156), (8054, 11604), (35090, 312)
X(51646) = barycentric product X(i)*X(j) for these {i,j}: {57, 8674}, {77, 47235}, {85, 42670}, {226, 42741}, {514, 5172}, {1022, 41541}, {1459, 37799}, {3676, 17796}, {4017, 37783}, {4077, 19622}, {5127, 7178}, {32849, 43924}, {41542, 47947}
X(51646) = barycentric quotient X(i)/X(j) for these {i,j}: {57, 35156}, {604, 1290}, {649, 11604}, {5127, 645}, {5172, 190}, {7180, 5620}, {8674, 312}, {17796, 3699}, {19622, 643}, {37783, 7257}, {41541, 24004}, {42670, 9}, {42741, 333}, {43924, 21907}, {47235, 318}
X(51647) lies on these lines: {1, 12725}, {21, 77}, {34, 604}, {56, 8615}, {109, 2747}, {221, 2256}, {222, 11031}, {223, 4220}, {513, 663}, {614, 2208}, {651, 44694}, {846, 34033}, {1035, 3145}, {1254, 7122}, {1503, 8766}, {1580, 5018}, {2199, 37237}, {2312, 8779}, {5930, 48890}, {8229, 34050}, {11203, 34027}, {18623, 37443}, {34044, 35623}
X(51647) = X(i)-Ceva conjugate of X(j) for these (i,j): {26702, 56}, {43045, 2312}
X(51647) = X(42671)-cross conjugate of X(2312)
X(51647) = crosssum of X(78) and X(44694)
X(51647) = X(i)-isoconjugate of X(j) for these (i,j): {8, 1297}, {55, 35140}, {78, 8767}, {219, 6330}, {345, 43717}, {645, 34212}, {2435, 36797}, {5546, 43673}
X(51647) = X(i)-Dao conjugate of X(j) for these (i, j): (223, 35140), (15595, 3718), (23976, 312), (39071, 78), (39073, 44694), (50938, 318)
X(51647) = barycentric product X(i)*X(j) for these {i,j}: {1, 43045}, {7, 2312}, {34, 441}, {57, 1503}, {77, 16318}, {85, 42671}, {273, 8779}, {278, 8766}, {604, 30737}, {3213, 16096}, {4017, 34211}, {7182, 51437}
X(51647) = barycentric quotient X(i)/X(j) for these {i,j}: {34, 6330}, {57, 35140}, {441, 3718}, {604, 1297}, {608, 8767}, {1395, 43717}, {1503, 312}, {2312, 8}, {3213, 14944}, {4017, 43673}, {8766, 345}, {8779, 78}, {9475, 44694}, {16318, 318}, {30737, 28659}, {34211, 7257}, {42671, 9}, {43045, 75}, {51437, 33}
X(51648) lies on these lines: {1, 15313}, {56, 34948}, {513, 663}, {521, 14353}, {522, 3960}, {523, 905}, {650, 4802}, {656, 4449}, {676, 43049}, {764, 22654}, {832, 48328}, {834, 48332}, {900, 39540}, {1734, 48293}, {1946, 48382}, {2254, 48303}, {2509, 21348}, {2517, 47796}, {3309, 48302}, {3762, 48186}, {3900, 48292}, {3907, 47843}, {4036, 4885}, {4086, 47795}, {4132, 50336}, {4378, 50330}, {4391, 48209}, {4397, 48246}, {4404, 48228}, {4458, 28984}, {4462, 48165}, {4815, 48321}, {4824, 27674}, {4905, 48307}, {6588, 7180}, {6591, 23770}, {7250, 8677}, {7650, 17496}, {7655, 8674}, {7661, 30719}, {8043, 28151}, {9001, 21189}, {12114, 24457}, {14838, 28147}, {16754, 47844}, {16757, 47691}, {17420, 48342}, {20317, 48181}, {21147, 42769}, {21222, 48173}, {22091, 48391}, {23880, 30591}, {28175, 47965}, {28191, 48003}, {28199, 47921}, {35057, 48287}, {38469, 48344}, {40134, 47799}, {44444, 47819}
X(51648) = midpoint of X(i) and X(j) for these {i,j}: {1, 23800}, {656, 4449}, {663, 50354}, {1459, 4017}, {1734, 48293}, {1769, 43924}, {2254, 48303}, {3669, 6129}, {3777, 50353}, {4378, 50330}, {4815, 48321}, {4905, 48307}, {7650, 17496}, {7661, 30719}, {17420, 48342}, {21189, 48281}, {48144, 50332}, {48151, 48340}, {48292, 50350}
X(51648) = reflection of X(i) in X(j) for these {i,j}: {650, 31947}, {4036, 4885}
X(51648) = X(i)-Ceva conjugate of X(j) for these (i,j): {7649, 513}, {21188, 46389}
X(51648) = crosspoint of X(i) and X(j) for these (i,j): {1, 13397}, {28, 13486}, {108, 1063}, {278, 934}
X(51648) = crosssum of X(i) and X(j) for these (i,j): {1, 15313}, {6, 50501}, {219, 3900}, {521, 1062}, {522, 10916}, {650, 7082}
X(51648) = crossdifference of every pair of points on line {9, 35}
X(51648) = X(i)-isoconjugate of X(j) for these (i,j): {8, 36082}, {90, 100}, {101, 2994}, {109, 36626}, {190, 2164}, {664, 7072}, {692, 20570}, {1069, 1897}, {1331, 7040}, {1783, 6513}, {3939, 7318}
X(51648) = X(i)-Dao conjugate of X(j) for these (i, j): (11, 36626), (63, 4561), (1015, 2994), (1086, 20570), (5521, 7040), (6506, 345), (8054, 90), (34467, 1069), (39006, 6513), (39025, 7072), (40617, 7318)
X(51648) = barycentric product X(i)*X(j) for these {i,j}: {1, 21188}, {7, 46389}, {46, 514}, {513, 5905}, {649, 20930}, {693, 2178}, {905, 1068}, {934, 6506}, {1019, 21077}, {1406, 4391}, {3157, 17924}, {3193, 7178}, {3669, 5552}, {4017, 31631}, {6505, 7649}, {7192, 21853}
X(51648) = barycentric quotient X(i)/X(j) for these {i,j}: {46, 190}, {513, 2994}, {514, 20570}, {604, 36082}, {649, 90}, {650, 36626}, {667, 2164}, {1068, 6335}, {1406, 651}, {1459, 6513}, {2178, 100}, {3063, 7072}, {3157, 1332}, {3193, 645}, {3669, 7318}, {5552, 646}, {5905, 668}, {6505, 4561}, {6506, 4397}, {6591, 7040}, {20930, 1978}, {21077, 4033}, {21188, 75}, {21853, 3952}, {22383, 1069}, {23224, 6512}, {31631, 7257}, {46389, 8}
X(51648) = {X(4017),X(14413)}-harmonic conjugate of X(1459)
X(51649) lies on these lines: {1, 5553}, {3, 73}, {34, 4306}, {36, 10692}, {56, 26892}, {109, 32760}, {201, 18607}, {221, 11510}, {513, 663}, {1064, 22767}, {1066, 11508}, {1193, 34880}, {1393, 1427}, {1410, 30493}, {1413, 34430}, {1415, 8776}, {1532, 2635}, {1737, 14266}, {1745, 6834}, {1818, 51379}, {2252, 47408}, {2478, 37523}, {3057, 4300}, {4337, 5119}, {6905, 34051}, {6921, 37694}, {10571, 37618}, {10966, 34046}, {14798, 34043}, {18857, 34586}, {22341, 23154}, {34052, 37395}
X(51649) = crosssum of X(i) and X(j) for these (i,j): {4, 15500}, {10692, 36052}
X(51649) = crossdifference of every pair of points on line {9, 3064}
X(51649) = X(i)-isoconjugate of X(j) for these (i,j): {4, 45393}, {8, 915}, {9, 37203}, {55, 46133}, {281, 2990}, {312, 913}, {318, 36052}, {522, 36106}, {3657, 36797}, {4391, 32698}, {6099, 44426}, {7017, 32655}
X(51649) = X(i)-Dao conjugate of X(j) for these (i, j): (119, 318), (223, 46133), (478, 37203), (36033, 45393), (39002, 522), (39175, 51565)
X(51649) = barycentric product X(i)*X(j) for these {i,j}: {7, 2252}, {56, 914}, {57, 912}, {63, 18838}, {77, 8609}, {222, 1737}, {603, 48380}, {1797, 12832}, {37136, 42769}
X(51649) = barycentric quotient X(i)/X(j) for these {i,j}: {48, 45393}, {56, 37203}, {57, 46133}, {603, 2990}, {604, 915}, {912, 312}, {914, 3596}, {1397, 913}, {1415, 36106}, {1737, 7017}, {2252, 8}, {8609, 318}, {12832, 46109}, {18838, 92}, {32660, 6099}, {47408, 6735}
X(51649) = {X(1455),X(1464)}-harmonic conjugate of X(1457)
X(51650) lies on these lines: {42, 4139}, {513, 663}, {1042, 7250}, {4170, 42312}, {4449, 4815}, {4804, 23655}, {7180, 42664}, {7265, 30572}, {8611, 21894}, {10571, 34496}, {20295, 48307}
X(51650) = X(4552)-Ceva conjugate of X(1400)
X(51650) = crosspoint of X(56) and X(4551)
X(51650) = crosssum of X(i) and X(j) for these (i,j): {8, 3737}, {663, 3686}
X(51650) = X(i)-isoconjugate of X(j) for these (i,j): {8, 34594}, {9, 37205}, {21, 8050}, {314, 40519}, {596, 643}, {644, 39747}, {645, 39798}, {3699, 39949}, {4612, 40085}, {5546, 40013}, {7256, 20615}, {7257, 40148}
X(51650) = X(i)-Dao conjugate of X(j) for these (i, j): (478, 37205), (649, 4560), (4129, 18155), (40611, 8050)
X(51650) = barycentric product X(i)*X(j) for these {i,j}: {56, 4129}, {57, 4132}, {65, 4063}, {73, 17922}, {225, 22154}, {226, 4057}, {595, 7178}, {1042, 47793}, {1400, 20295}, {1402, 20949}, {1427, 48307}, {2220, 4077}, {3293, 3669}, {3871, 7216}, {3995, 43924}, {4017, 32911}, {4360, 7180}, {4552, 8054}, {4559, 21208}
X(51650) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 37205}, {595, 645}, {604, 34594}, {1400, 8050}, {2220, 643}, {3293, 646}, {3871, 7258}, {4017, 40013}, {4057, 333}, {4063, 314}, {4129, 3596}, {4132, 312}, {7180, 596}, {8054, 4560}, {17922, 44130}, {20295, 28660}, {20949, 40072}, {22154, 332}, {32911, 7257}, {43924, 39747}
X(51651) lies on these lines: {1, 29057}, {29, 34}, {56, 904}, {65, 41350}, {73, 8766}, {109, 2699}, {307, 15991}, {511, 43034}, {513, 663}, {603, 604}, {664, 1966}, {741, 36065}, {872, 19369}, {971, 45932}, {1038, 25898}, {1350, 20753}, {1394, 1424}, {1395, 7125}, {1399, 7122}, {1415, 19554}, {1428, 3248}, {1469, 1964}, {1755, 3289}, {1911, 30648}, {2234, 7235}, {4296, 7187}, {4434, 4551}, {5145, 7146}, {16609, 18792}, {26110, 26121}
X(51651) = X(i)-Ceva conjugate of X(j) for these (i,j): {741, 56}, {43034, 1755}
X(51651) = X(237)-cross conjugate of X(1755)
X(51651) = crosspoint of X(1) and X(29056)
X(51651) = crosssum of X(i) and X(j) for these (i,j): {1, 29057}, {200, 3985}, {3716, 24026}
X(51651) = crossdifference of every pair of points on line {9, 4086}
X(51651) = X(i)-isoconjugate of X(j) for these (i,j): {2, 15628}, {8, 98}, {9, 1821}, {33, 336}, {41, 46273}, {55, 290}, {78, 36120}, {219, 16081}, {248, 7017}, {281, 287}, {293, 318}, {312, 1910}, {345, 6531}, {645, 2395}, {879, 36797}, {1857, 6394}, {1976, 3596}, {2175, 18024}, {2966, 3700}, {3709, 43187}, {3712, 9154}, {4041, 36036}, {4076, 43920}, {4086, 36084}, {5546, 43665}, {6064, 51441}, {14601, 40363}
X(51651) = X(i)-Dao conjugate of X(j) for these (i, j): (132, 318), (223, 290), (478, 1821), (511, 44694), (2679, 4041), (3160, 46273), (5976, 28659), (11672, 312), (16609, 35544), (32664, 15628), (38987, 4086), (39039, 7017), (39040, 3596), (40593, 18024), (40601, 9), (46094, 78), (50440, 341)
X(51651) = barycentric product X(i)*X(j) for these {i,j}: {1, 43034}, {7, 1755}, {34, 36212}, {56, 1959}, {57, 511}, {65, 17209}, {77, 232}, {85, 237}, {222, 240}, {273, 3289}, {297, 603}, {325, 604}, {741, 16591}, {1355, 1821}, {1395, 6393}, {1397, 46238}, {1400, 51369}, {1401, 3405}, {1402, 51370}, {1407, 44694}, {1414, 3569}, {1434, 5360}, {2211, 7182}, {2421, 4017}, {2491, 4625}, {4077, 14966}, {6063, 9417}, {6530, 7125}, {7178, 23997}, {7183, 34854}, {9418, 20567}, {16947, 42703}, {19189, 44708}, {37136, 42751}, {42717, 43924}
X(51651) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 46273}, {31, 15628}, {34, 16081}, {56, 1821}, {57, 290}, {85, 18024}, {222, 336}, {232, 318}, {237, 9}, {240, 7017}, {325, 28659}, {511, 312}, {603, 287}, {604, 98}, {608, 36120}, {1355, 1959}, {1395, 6531}, {1397, 1910}, {1414, 43187}, {1755, 8}, {1959, 3596}, {2211, 33}, {2421, 7257}, {2491, 4041}, {3289, 78}, {3569, 4086}, {4017, 43665}, {4565, 36036}, {5360, 2321}, {7125, 6394}, {9417, 55}, {9418, 41}, {11672, 44694}, {14966, 643}, {16591, 35544}, {17209, 314}, {23997, 645}, {36212, 3718}, {39469, 8611}, {41270, 44687}, {42702, 3710}, {43034, 75}, {46238, 40363}, {51369, 28660}, {51370, 40072}
X(51652) lies on these lines: {1, 30719}, {7, 30183}, {34, 1027}, {56, 8643}, {57, 4401}, {65, 4498}, {109, 1110}, {221, 8676}, {388, 28470}, {513, 663}, {652, 665}, {1413, 2424}, {1734, 43050}, {3309, 43049}, {3667, 34496}, {3676, 4040}, {4077, 29186}, {4449, 6362}, {4724, 7178}, {4794, 30723}, {7216, 48032}, {10397, 43060}, {10581, 20980}, {43052, 47929}
X(51652) = isogonal conjugate of the isotomic conjugate of X(31605)
X(51652) = X(i)-Ceva conjugate of X(j) for these (i,j): {101, 56}, {109, 21059}
X(51652) = crosspoint of X(i) and X(j) for these (i,j): {101, 218}, {109, 269}
X(51652) = crosssum of X(i) and X(j) for these (i,j): {200, 522}, {277, 514}, {650, 3059}, {3239, 4012}
X(51652) = crossdifference of every pair of points on line {9, 497}
X(51652) = X(i)-isoconjugate of X(j) for these (i,j): {8, 1292}, {9, 37206}, {100, 6601}, {277, 644}, {294, 2414}, {2191, 3699}, {2428, 36796}, {3717, 36041}, {4578, 40154}, {6558, 17107}
X(51652) = X(i)-Dao conjugate of X(j) for these (i, j): (220, 6558), (478, 37206), (3309, 44448), (3676, 3261), (4904, 341), (5519, 3717), (8054, 6601)
X(51652) = barycentric product X(i)*X(j) for these {i,j}: {1, 43049}, {6, 31605}, {34, 24562}, {56, 4468}, {57, 3309}, {59, 23760}, {85, 8642}, {101, 40615}, {109, 4904}, {218, 3676}, {344, 43924}, {513, 1445}, {514, 1617}, {649, 6604}, {650, 4350}, {663, 17093}, {667, 21609}, {934, 38375}, {1019, 41539}, {1407, 44448}, {1458, 2402}, {2440, 9436}, {3669, 3870}, {3991, 7203}, {4017, 41610}, {4565, 21945}, {4878, 17096}, {7649, 23144}, {21059, 24002}
X(51652) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 37206}, {218, 3699}, {604, 1292}, {649, 6601}, {1445, 668}, {1458, 2414}, {1617, 190}, {2440, 14942}, {3309, 312}, {3870, 646}, {4350, 4554}, {4468, 3596}, {4878, 30730}, {4904, 35519}, {6600, 6558}, {6604, 1978}, {8642, 9}, {17093, 4572}, {21059, 644}, {21609, 6386}, {23144, 4561}, {23760, 34387}, {24562, 3718}, {31605, 76}, {38375, 4397}, {40615, 3261}, {41539, 4033}, {41610, 7257}, {43049, 75}, {43924, 277}
X(51652) = {X(663),X(43924)}-harmonic conjugate of X(3669)
X(51653) lies on these lines: {6, 7614}, {7, 17482}, {56, 4471}, {57, 77}, {109, 2721}, {241, 1404}, {269, 7225}, {513, 663}, {524, 7181}, {527, 17439}, {664, 35155}, {672, 6510}, {896, 3292}, {1055, 34371}, {1429, 1443}, {1442, 2171}, {2173, 7202}, {3305, 25897}, {3664, 17440}, {3942, 7113}, {5226, 26109}, {5429, 13462}, {7122, 9340}, {17365, 17438}, {28368, 28387}
X(51653) = X(7181)-Ceva conjugate of X(896)
X(51653) = X(187)-cross conjugate of X(896)
X(51653) = crossdifference of every pair of points on line {9, 4041}
X(51653) = X(i)-isoconjugate of X(j) for these (i,j): {2, 5547}, {8, 111}, {9, 897}, {41, 46277}, {55, 671}, {78, 36128}, {219, 17983}, {281, 895}, {312, 923}, {318, 36060}, {345, 8753}, {346, 7316}, {607, 30786}, {643, 23894}, {645, 9178}, {650, 5380}, {691, 3700}, {892, 3709}, {2175, 18023}, {3596, 32740}, {3712, 10630}, {4041, 36085}, {4086, 36142}, {5466, 5546}, {5968, 15628}, {7017, 14908}, {7359, 9139}, {9214, 15627}, {10097, 36797}, {19626, 40363}, {30730, 43926}
X(51653) = X(i)-Dao conjugate of X(j) for these (i, j): (223, 671), (478, 897), (1560, 318), (2482, 312), (3160, 46277), (6593, 9), (23992, 4086), (32664, 5547), (38988, 4041), (40593, 18023)
X(51653) = barycentric product X(i)*X(j) for these {i,j}: {1, 7181}, {7, 896}, {34, 6390}, {56, 14210}, {57, 524}, {65, 6629}, {77, 468}, {85, 187}, {226, 16702}, {269, 3712}, {273, 3292}, {351, 4625}, {603, 44146}, {604, 3266}, {651, 4750}, {664, 14419}, {690, 1414}, {897, 1366}, {922, 6063}, {934, 14432}, {1014, 4062}, {1400, 16741}, {1412, 42713}, {1432, 7267}, {1434, 21839}, {2642, 4573}, {4017, 5468}, {4077, 5467}, {7125, 37778}, {7178, 23889}, {7180, 24039}, {7182, 44102}, {7316, 24038}, {14567, 20567}, {31013, 32636}, {37136, 42760}, {42721, 43924}
X(51653) = barycentric quotient X(i)/X(j) for these {i,j}: {7, 46277}, {31, 5547}, {34, 17983}, {56, 897}, {57, 671}, {77, 30786}, {85, 18023}, {109, 5380}, {187, 9}, {273, 46111}, {351, 4041}, {468, 318}, {524, 312}, {603, 895}, {604, 111}, {608, 36128}, {690, 4086}, {896, 8}, {922, 55}, {1106, 7316}, {1366, 14210}, {1395, 8753}, {1397, 923}, {1414, 892}, {2642, 3700}, {3266, 28659}, {3292, 78}, {3712, 341}, {4017, 5466}, {4062, 3701}, {4565, 36085}, {4750, 4391}, {4760, 3975}, {4831, 4673}, {5467, 643}, {5468, 7257}, {6390, 3718}, {6629, 314}, {7180, 23894}, {7181, 75}, {7267, 17787}, {9155, 44694}, {9717, 44693}, {14210, 3596}, {14419, 522}, {14432, 4397}, {14567, 41}, {16702, 333}, {16741, 28660}, {21839, 2321}, {23200, 212}, {23889, 645}, {42081, 3712}, {42713, 30713}, {44102, 33}
X(51653) = {X(1442),X(7175)}-harmonic conjugate of X(2171)
X(51654) lies on these lines: {1, 10308}, {28, 34}, {30, 6357}, {56, 6186}, {73, 500}, {109, 484}, {201, 1935}, {212, 3587}, {221, 2099}, {222, 15934}, {223, 30282}, {225, 46468}, {226, 49744}, {255, 37584}, {388, 17716}, {513, 663}, {601, 17699}, {759, 14158}, {896, 7286}, {1012, 20277}, {1038, 3305}, {1060, 7069}, {1254, 1399}, {1406, 3924}, {1465, 5122}, {1870, 7004}, {1877, 34050}, {2173, 3284}, {2292, 16140}, {2635, 46974}, {3468, 6906}, {4303, 13151}, {4642, 18360}, {4653, 47057}, {5119, 21147}, {5226, 26120}, {5425, 34043}, {5434, 17469}, {7100, 13743}, {7478, 9405}, {10571, 37525}, {18421, 34033}, {23071, 37496}, {24028, 35460}, {26892, 32065}, {28032, 28038}, {28380, 28387}, {32047, 44706}
X(51654) = isogonal conjugate of X(44693)
X(51654) = X(i)-Ceva conjugate of X(j) for these (i,j): {759, 56}, {6357, 2173}
X(51654) = X(1495)-cross conjugate of X(2173)
X(51654) = crosssum of X(44688) and X(44689)
X(51654) = crossdifference of every pair of points on line {9, 8611}
X(51654) = X(i)-isoconjugate of X(j) for these (i,j): {1, 44693}, {2, 15627}, {8, 74}, {9, 2349}, {41, 33805}, {55, 1494}, {78, 36119}, {219, 16080}, {281, 14919}, {312, 2159}, {318, 35200}, {345, 8749}, {645, 2433}, {2394, 5546}, {3445, 44727}, {3596, 40352}, {3700, 44769}, {3712, 9139}, {4086, 36034}, {5547, 36890}, {7017, 18877}, {7359, 40384}, {14380, 36797}, {15628, 35910}
X(51654) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 44693), (133, 318), (223, 1494), (478, 2349), (1511, 78), (3160, 33805), (3163, 312), (3258, 4086), (6739, 341), (18593, 35550), (32664, 15627), (45036, 44727)
X(51654) = barycentric product X(i)*X(j) for these {i,j}: {1, 6357}, {7, 2173}, {30, 57}, {34, 11064}, {56, 14206}, {65, 18653}, {77, 1990}, {85, 1495}, {222, 1784}, {226, 51420}, {269, 7359}, {273, 3284}, {603, 46106}, {604, 3260}, {651, 11125}, {664, 14399}, {934, 14400}, {1354, 2349}, {1393, 43768}, {1397, 46234}, {1414, 1637}, {1427, 51382}, {2407, 4017}, {2420, 4077}, {4565, 36035}, {4625, 14398}, {6063, 9406}, {7182, 14581}, {9407, 20567}, {11589, 44697}, {14395, 36118}, {37136, 42750}, {42716, 43924}
X(51654) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 44693}, {7, 33805}, {30, 312}, {31, 15627}, {34, 16080}, {56, 2349}, {57, 1494}, {603, 14919}, {604, 74}, {608, 36119}, {1354, 14206}, {1395, 8749}, {1397, 2159}, {1495, 9}, {1637, 4086}, {1743, 44727}, {1784, 7017}, {1990, 318}, {2173, 8}, {2407, 7257}, {2420, 643}, {3213, 10152}, {3260, 28659}, {3284, 78}, {4017, 2394}, {6357, 75}, {7359, 341}, {9406, 55}, {9407, 41}, {9409, 8611}, {11064, 3718}, {11125, 4391}, {14206, 3596}, {14398, 4041}, {14399, 522}, {14400, 4397}, {14581, 33}, {18653, 314}, {36298, 44691}, {36299, 44690}, {42074, 7359}, {46234, 40363}, {51394, 3719}, {51420, 333}
X(51654) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {34, 603, 1393}, {34, 1394, 603}, {1455, 1456, 1457}, {1935, 4296, 201}
X(51655) lies on these lines: {66, 73}, {77, 4357}, {513, 663}, {604, 608}, {1037, 34040}, {1201, 7083}, {1212, 30456}, {1818, 46153}, {4318, 49704}, {4551, 49991}, {25904, 37558}
X(51655) = crosspoint of X(34) and X(1416)
X(51655) = crosssum of X(i) and X(j) for these (i,j): {8, 3100}, {78, 3717}
X(51655) = X(i)-isoconjugate of X(j) for these (i,j): {8, 26703}, {15416, 32688}
X(51655) = X(39690)-Dao conjugate of X(37774)
X(51655) = barycentric product X(i)*X(j) for these {i,j}: {57, 3827}, {5236, 34160}
X(51655) = barycentric quotient X(i)/X(j) for these {i,j}: {604, 26703}, {3827, 312}, {47431, 3717}
X(51656) lies on these lines: {1, 30198}, {34, 23345}, {56, 37627}, {65, 23835}, {109, 2743}, {221, 15313}, {513, 663}, {522, 30725}, {650, 9364}, {651, 765}, {1394, 14812}, {3063, 17410}, {3309, 34496}, {3667, 4162}, {3676, 28225}, {3738, 7655}, {3945, 23819}, {4778, 7178}, {4790, 7180}, {4926, 30572}, {4977, 43052}, {6003, 42319}, {6006, 30726}, {6085, 7250}, {6363, 43051}, {7234, 7659}, {17418, 47921}, {39771, 39781}, {43932, 48032}
X(51656) = midpoint of X(14812) and X(23800)
X(51656) = reflection of X(i) in X(j) for these {i,j}: {650, 21173}, {3669, 43924}, {47921, 17418}
X(51656) = isogonal conjugate of X(31343)
X(51656) = X(i)-Ceva conjugate of X(j) for these (i,j): {100, 56}, {109, 45219}, {651, 1743}, {30719, 4394}, {43932, 3669}
X(51656) = X(i)-cross conjugate of X(j) for these (i,j): {4394, 3669}, {8643, 4394}, {23764, 18211}
X(51656) = crosspoint of X(i) and X(j) for these (i,j): {1, 30236}, {100, 145}, {269, 651}
X(51656) = crosssum of X(i) and X(j) for these (i,j): {1, 30198}, {9, 4162}, {200, 650}, {513, 3445}, {522, 6736}, {3900, 34524}
X(51656) = crossdifference of every pair of points on line {9, 3057}
X(51656) = X(i)-isoconjugate of X(j) for these (i,j): {1, 31343}, {8, 1293}, {9, 27834}, {100, 3680}, {101, 6557}, {109, 6556}, {312, 34080}, {346, 38828}, {644, 8056}, {646, 38266}, {650, 5382}, {2316, 2415}, {2429, 4997}, {3445, 3699}, {3939, 4373}, {4052, 5546}, {4578, 19604}, {4723, 36042}, {6558, 40151}, {33963, 43290}
X(51656) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 31343), (11, 6556), (478, 27834), (1015, 6557), (3669, 693), (3756, 341), (4394, 20317), (4521, 4391), (5516, 4723), (8054, 3680), (40615, 40014), (40617, 4373), (40621, 312), (45036, 3699)
X(51656) = barycentric product X(i)*X(j) for these {i,j}: {1, 30719}, {7, 4394}, {56, 4462}, {57, 3667}, {85, 8643}, {100, 40617}, {145, 3669}, {269, 4521}, {279, 4162}, {513, 5435}, {514, 1420}, {649, 39126}, {651, 3756}, {738, 4546}, {934, 4534}, {1014, 14321}, {1019, 4848}, {1319, 2403}, {1412, 4404}, {1414, 21950}, {1432, 4504}, {1434, 4729}, {1461, 4939}, {1462, 4925}, {1743, 3676}, {2976, 43760}, {3052, 24002}, {3161, 43932}, {3950, 7203}, {4017, 41629}, {4077, 33628}, {4552, 18211}, {4564, 23764}, {4617, 4953}, {4849, 17096}, {7178, 16948}, {18743, 43924}, {19604, 31182}
X(51656) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 31343}, {56, 27834}, {109, 5382}, {145, 646}, {513, 6557}, {604, 1293}, {649, 3680}, {650, 6556}, {1106, 38828}, {1319, 2415}, {1397, 34080}, {1420, 190}, {1743, 3699}, {2441, 1320}, {3052, 644}, {3158, 6558}, {3667, 312}, {3669, 4373}, {3676, 40014}, {3756, 4391}, {4017, 4052}, {4162, 346}, {4394, 8}, {4404, 30713}, {4462, 3596}, {4504, 17787}, {4521, 341}, {4534, 4397}, {4546, 30693}, {4729, 2321}, {4848, 4033}, {4849, 30730}, {5435, 668}, {8643, 9}, {14321, 3701}, {14425, 4723}, {16948, 645}, {18211, 4560}, {20818, 4571}, {21950, 4086}, {23764, 4858}, {30719, 75}, {31182, 44720}, {33628, 643}, {39126, 1978}, {40617, 693}, {41629, 7257}, {43924, 8056}, {43932, 27818}, {45219, 25268}
X(51657) lies on these lines: {1, 29069}, {31, 184}, {77, 4666}, {241, 46153}, {513, 663}, {674, 43039}, {869, 1405}, {1104, 40611}, {1400, 1964}, {1404, 3248}, {2171, 2309}, {2310, 45932}, {3745, 14547}, {6510, 39046}, {15733, 46177}
X(51657) = X(43039)-Ceva conjugate of X(2225)
X(51657) = X(8618)-cross conjugate of X(2225)
X(51657) = crosspoint of X(1) and X(29068)
X(51657) = crosssum of X(1) and X(29069)
X(51657) = X(i)-isoconjugate of X(j) for these (i,j): {8, 675}, {9, 37130}, {55, 43093}, {312, 2224}, {4391, 36087}, {32682, 35519}
X(51657) = X(i)-Dao conjugate of X(j) for these (i, j): (223, 43093), (478, 37130), (38990, 4391)
X(51657) = crossdifference of every pair of points on line {9, 4391}
X(51657) = barycentric product X(i)*X(j) for these {i,j}: {1, 43039}, {7, 2225}, {57, 674}, {65, 14964}, {85, 8618}, {604, 3006}, {1415, 23887}, {42723, 43924}
X(51657) = barycentric quotient X(i)/X(j) for these {i,j}: {56, 37130}, {57, 43093}, {604, 675}, {674, 312}, {1397, 2224}, {2225, 8}, {3006, 28659}, {8618, 9}, {14964, 314}, {43039, 75}
X(51658) lies on these lines: {226, 50329}, {513, 663}, {520, 7250}, {523, 4077}, {656, 7216}, {2485, 7180}, {3960, 23187}, {4815, 6362}, {7178, 47842}, {8676, 23800}, {35050, 37818}, {40933, 42768}, {43042, 48084}
X(51658) = crosspoint of X(i) and X(j) for these (i,j): {1, 44065}, {278, 4566}
X(51658) = crosssum of X(219) and X(21789)
X(51658) = X(i)-isoconjugate of X(j) for these (i,j): {272, 3939}, {643, 2218}, {1305, 2328}, {1751, 5546}, {2194, 51566}, {4570, 23289}, {4587, 40574}, {4636, 41506}
X(51658) = X(i)-Dao conjugate of X(j) for these (i, j): (72, 4571), (1214, 51566), (36908, 1305), (40617, 272), (40622, 2997), (50330, 23289)
X(51658) = barycentric product X(i)*X(j) for these {i,j}: {209, 24002}, {226, 23800}, {579, 4077}, {1427, 20294}, {1441, 43060}, {1446, 8676}, {1577, 4306}, {3676, 22021}, {3868, 7178}, {4017, 18134}
X(51658) = barycentric quotient X(i)/X(j) for these {i,j}: {209, 644}, {226, 51566}, {579, 643}, {1427, 1305}, {2198, 3939}, {2352, 5546}, {3125, 23289}, {3190, 7259}, {3669, 272}, {3868, 645}, {4017, 1751}, {4077, 40011}, {4306, 662}, {7178, 2997}, {7180, 2218}, {8676, 2287}, {18134, 7257}, {22021, 3699}, {23800, 333}, {27396, 7256}, {43060, 21}, {43923, 40574}, {51574, 4571}
X(51659) lies on these lines: {7, 4077}, {56, 4833}, {512, 30572}, {513, 663}, {661, 1400}, {1423, 27469}, {1469, 9013}, {2827, 4170}, {3738, 17496}, {4091, 17418}, {6003, 36975}, {8672, 23755}, {17077, 27114}, {28081, 28094}, {39771, 39780}
X(51659) = X(i)-isoconjugate of X(j) for these (i,j): {643, 994}, {645, 46018}, {4636, 45095}
X(51659) = barycentric product X(i)*X(j) for these {i,j}: {65, 48321}, {993, 7178}, {1150, 4017}, {2278, 4077}, {7216, 49492}
X(51659) = barycentric quotient X(i)/X(j) for these {i,j}: {993, 645}, {1150, 7257}, {2278, 643}, {7180, 994}, {48321, 314}, {49492, 7258}
X(51660) lies on these lines: {1, 10309}, {3, 2122}, {34, 207}, {55, 64}, {56, 1413}, {109, 2077}, {222, 1064}, {223, 30503}, {478, 2267}, {513, 663}, {581, 17831}, {603, 1193}, {608, 1033}, {909, 32667}, {1066, 34040}, {1394, 3576}, {1410, 42448}, {1433, 18237}, {2361, 34182}, {2635, 51421}, {3556, 7114}, {4337, 30282}, {6001, 43058}, {14547, 17832}, {23843, 47380}, {26105, 37523}, {34049, 46974}
X(51660) = X(102)-Ceva conjugate of X(56)
X(51660) = crosspoint of X(84) and X(36123)
X(51660) = crosssum of X(i) and X(j) for these (i,j): {8, 10538}, {40, 22350}, {78, 6735}
X(51660) = crossdifference of every pair of points on line {9, 14331}
X(51660) = X(i)-isoconjugate of X(j) for these (i,j): {8, 1295}, {100, 43737}, {1783, 2417}, {2431, 6335}, {15416, 32647}
X(51660) = X(i)-Dao conjugate of X(j) for these (i, j): (8054, 43737), (34050, 35516), (39006, 2417)
X(51660) = barycentric product X(i)*X(j) for these {i,j}: {1, 43058}, {57, 6001}, {58, 51365}, {63, 51399}, {222, 51359}, {1459, 2405}, {1461, 14312}, {2443, 4025}
X(51660) = barycentric quotient X(i)/X(j) for these {i,j}: {604, 1295}, {649, 43737}, {1459, 2417}, {2443, 1897}, {6001, 312}, {43058, 75}, {47434, 6735}, {51359, 7017}, {51365, 313}, {51399, 92}
X(51660) = {X(1456),X(1464)}-harmonic conjugate of X(1457)
X(51661) lies on these lines: {3, 77}, {25, 34052}, {223, 37366}, {513, 663}, {604, 2262}, {1037, 11508}, {1461, 1876}, {1813, 34381}, {1828, 34491}, {7099, 20277}, {7125, 17441}, {26884, 43058}, {34489, 34492}, {37516, 45963}
X(51662) lies on these lines: {7, 7199}, {56, 3737}, {57, 50346}, {65, 523}, {354, 34954}, {513, 663}, {1019, 34496}, {1363, 44044}, {1365, 3025}, {1409, 3050}, {2099, 48293}, {2616, 23286}, {3028, 3319}, {4077, 43067}, {4132, 30572}, {4170, 30198}, {4504, 6003}, {5214, 10473}, {6371, 30725}, {7178, 7250}, {11011, 48292}, {11375, 48209}, {17609, 39540}, {21173, 23187}, {24914, 48204}, {32636, 50349}, {38989, 40622}, {43923, 43927}
X(51662) = reflection of X(i) in X(j) for these {i,j}: {7178, 7250}, {44409, 34954}
X(51662) = X(i)-Ceva conjugate of X(j) for these (i,j): {7, 24237}, {7192, 7178}
X(51662) = crosspoint of X(i) and X(j) for these (i,j): {7, 1020}, {651, 31643}
X(51662) = crosssum of X(i) and X(j) for these (i,j): {55, 1021}, {521, 40946}, {650, 20967}
X(51662) = crossdifference of every pair of points on line {9, 16699}
X(51662) = X(i)-isoconjugate of X(j) for these (i,j): {101, 46880}, {643, 34434}, {2051, 5546}, {3939, 20028}
X(51662) = X(i)-Dao conjugate of X(j) for these (i, j): (12, 3952), (1015, 46880), (21796, 25268), (24237, 17183), (34589, 8), (40617, 20028)
X(51662) = barycentric product X(i)*X(j) for these {i,j}: {65, 17496}, {226, 21173}, {514, 37558}, {523, 17074}, {572, 4077}, {1020, 34589}, {2975, 7178}, {3669, 17751}, {3676, 21061}, {4017, 14829}, {4551, 24237}, {4560, 20617}, {4566, 11998}, {14973, 17096}, {23187, 40149}
X(51662) = barycentric quotient X(i)/X(j) for these {i,j}: {513, 46880}, {572, 643}, {2975, 645}, {3669, 20028}, {4017, 2051}, {7180, 34434}, {11998, 7253}, {14829, 7257}, {14973, 30730}, {17074, 99}, {17496, 314}, {17751, 646}, {20617, 4552}, {20986, 5546}, {21061, 3699}, {21173, 333}, {23187, 1812}, {24237, 18155}, {37558, 190}
X(51662) = {X(34954),X(44409)}-harmonic conjugate of X(354)
X(51663) lies on these lines: {12, 21714}, {56, 42741}, {110, 9811}, {513, 663}, {523, 36035}, {526, 3028}, {900, 3649}, {1365, 2611}, {2827, 46816}, {3738, 39778}, {4077, 45746}, {6050, 43923}, {9213, 18593}, {21828, 47230}, {23755, 50330}, {41003, 43042}
X(51663) = X(42666)-cross conjugate of X(2610)
X(51663) = crossdifference of every pair of points on line {9, 1793}
X(51663) = X(i)-isoconjugate of X(j) for these (i,j): {8, 36069}, {9, 37140}, {60, 51562}, {80, 4636}, {110, 6740}, {162, 1793}, {284, 47318}, {312, 32671}, {476, 35193}, {643, 759}, {645, 34079}, {655, 7054}, {662, 2341}, {1098, 2222}, {2150, 36804}, {2161, 4612}, {3700, 9273}, {4086, 9274}, {4556, 36910}, {5546, 24624}, {7058, 32675}, {9404, 39295}, {11107, 36061}, {32680, 35192}
X(51663) = X(i)-Dao conjugate of X(j) for these (i, j): (125, 1793), (244, 6740), (478, 37140), (1084, 2341), (15267, 2222), (16221, 11107), (34586, 643), (35069, 645), (35128, 7058), (38982, 8), (38984, 1098), (40584, 4612), (40590, 47318), (40622, 14616), (51583, 7257)
X(51663) = barycentric product X(i)*X(j) for these {i,j}: {7, 2610}, {12, 3960}, {57, 6370}, {65, 4707}, {85, 42666}, {523, 18593}, {525, 1835}, {526, 43682}, {661, 41804}, {758, 7178}, {1254, 3904}, {1365, 4585}, {1441, 21828}, {1443, 4024}, {1464, 1577}, {2171, 4453}, {2245, 4077}, {3676, 4053}, {3738, 6354}, {3936, 4017}, {4089, 21859}, {4705, 17078}, {7180, 35550}, {21758, 34388}, {37755, 44428}
X(51663) = barycentric quotient X(i)/X(j) for these {i,j}: {12, 36804}, {36, 4612}, {56, 37140}, {65, 47318}, {320, 4631}, {512, 2341}, {604, 36069}, {647, 1793}, {654, 1098}, {661, 6740}, {758, 645}, {1254, 655}, {1397, 32671}, {1443, 4610}, {1464, 662}, {1835, 648}, {2088, 35057}, {2171, 51562}, {2245, 643}, {2610, 8}, {2624, 35193}, {3028, 4585}, {3724, 5546}, {3738, 7058}, {3936, 7257}, {3960, 261}, {4017, 24624}, {4053, 3699}, {4585, 6064}, {4705, 36910}, {4707, 314}, {6354, 35174}, {6370, 312}, {7113, 4636}, {7178, 14616}, {7180, 759}, {8648, 7054}, {14270, 35192}, {17078, 4623}, {18593, 99}, {21758, 60}, {21828, 21}, {26700, 39295}, {41804, 799}, {42666, 9}, {43682, 35139}, {47230, 11107}
X(51664) lies on these lines: {7, 4560}, {12, 21052}, {56, 21789}, {57, 14838}, {65, 4041}, {73, 810}, {108, 2727}, {109, 2722}, {222, 7254}, {226, 1577}, {388, 3907}, {513, 663}, {514, 3064}, {520, 656}, {525, 8611}, {553, 45671}, {603, 22093}, {652, 905}, {661, 6587}, {942, 39212}, {1365, 3328}, {1367, 34591}, {1451, 21761}, {2254, 8676}, {3649, 4804}, {3671, 4151}, {3676, 14349}, {4063, 43050}, {4162, 38329}, {4391, 46396}, {4566, 35307}, {6332, 15413}, {7250, 50330}, {14414, 22091}, {14837, 46393}, {17496, 46400}, {20296, 24562}, {20318, 25925}, {28983, 47796}, {29162, 30725}, {30719, 48335}, {43052, 47918}, {43923, 46385}
X(51664) = midpoint of X(17496) and X(46400)
X(51664) = reflection of X(i) in X(j) for these {i,j}: {652, 905}, {4391, 46396}, {8611, 24018}
X(51664) = isotomic conjugate of the polar conjugate of X(4017)
X(51664) = isogonal conjugate of the polar conjugate of X(4077)
X(51664) = X(i)-Ceva conjugate of X(j) for these (i,j): {7, 7004}, {222, 3942}, {226, 4466}, {514, 7178}, {1414, 603}, {1439, 18210}, {4077, 4017}, {17094, 656}, {37136, 18593}
X(51664) = X(i)-cross conjugate of X(j) for these (i,j): {647, 656}, {18210, 1439}
X(51664) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 643), (9, 36797), (11, 2322), (115, 318), (125, 9), (223, 648), (226, 190), (244, 281), (478, 162), (647, 4086), (1015, 29), (1084, 33), (1086, 31623), (1214, 6335), (3125, 46878), (3160, 811), (4858, 7017), (4988, 44426), (5190, 1896), (5521, 8748), (6337, 7257), (6505, 645), (6615, 17926), (6741, 7101), (8054, 1172), (11517, 7259), (15450, 7069), (15526, 312), (17423, 41), (26932, 333), (34467, 284), (34591, 8), (35071, 78), (35072, 1043), (36033, 5546), (36908, 653), (38983, 2287), (38985, 219), (38986, 607), (38991, 4183), (38996, 2212), (39000, 44694), (39006, 21), (39025, 2332), (40590, 1897), (40591, 644), (40593, 6331), (40608, 7079), (40611, 1783), (40615, 286), (40617, 27), (40618, 314), (40619, 44130), (40622, 92), (40623, 14024), (40627, 18344), (40628, 7253), (40837, 823), (46093, 2289), (50330, 3064), (51574, 3699)
X(51664) = crosspoint of X(i) and X(j) for these (i,j): {85, 1414}, {226, 1020}, {514, 905}
X(51664) = crosssum of X(i) and X(j) for these (i,j): {9, 8611}, {41, 4041}, {101, 1783}, {281, 17926}, {284, 1021}, {650, 2264}, {3737, 5324}
X(51664) = trilinear pole of line {18210, 22094}
X(51664) = crossdifference of every pair of points on line {9, 33}
X(51664) = X(i)-isoconjugate of X(j) for these (i,j): {4, 5546}, {6, 36797}, {8, 112}, {9, 162}, {19, 643}, {21, 1783}, {25, 645}, {27, 3939}, {28, 644}, {29, 101}, {33, 662}, {34, 7259}, {41, 811}, {55, 648}, {59, 17926}, {78, 24019}, {99, 607}, {100, 1172}, {107, 219}, {108, 2287}, {109, 2322}, {110, 281}, {163, 318}, {190, 2299}, {212, 823}, {250, 3700}, {270, 1018}, {284, 1897}, {294, 4238}, {312, 32676}, {333, 8750}, {345, 32713}, {461, 4627}, {608, 7256}, {646, 2203}, {650, 5379}, {651, 4183}, {653, 2328}, {664, 2332}, {666, 37908}, {668, 2204}, {692, 31623}, {799, 2212}, {813, 14024}, {906, 1896}, {1021, 7012}, {1043, 32674}, {1259, 6529}, {1301, 27382}, {1304, 7359}, {1331, 8748}, {1395, 7258}, {1396, 4578}, {1414, 7079}, {1474, 3699}, {1576, 7017}, {1824, 4612}, {1826, 4636}, {1857, 4558}, {1973, 7257}, {2175, 6331}, {2189, 3952}, {2194, 6335}, {2289, 36126}, {2316, 46541}, {2326, 4551}, {2327, 36127}, {2338, 4241}, {2341, 4242}, {2489, 6064}, {3064, 4570}, {3688, 42396}, {3709, 18020}, {4076, 43925}, {4092, 47443}, {4230, 15628}, {4235, 5547}, {4240, 15627}, {4557, 46103}, {4563, 6059}, {4565, 7046}, {4567, 18344}, {4571, 5317}, {4573, 7071}, {4587, 8747}, {4633, 44100}, {5548, 37168}, {6056, 15352}, {6062, 34568}, {6065, 17925}, {6742, 41502}, {7115, 7253}, {7252, 15742}, {7452, 15629}, {8611, 24000}, {16813, 44707}, {21789, 46102}, {23067, 36421}, {32739, 44130}, {36104, 44694}, {44695, 46639}
X(51664) = barycentric product X(i)*X(j) for these {i,j}: {1, 17094}, {3, 4077}, {7, 656}, {34, 3265}, {56, 14208}, {57, 525}, {63, 7178}, {65, 4025}, {69, 4017}, {71, 24002}, {72, 3676}, {73, 693}, {77, 523}, {85, 647}, {108, 17216}, {125, 1414}, {162, 1367}, {201, 7192}, {222, 1577}, {225, 4131}, {226, 905}, {273, 520}, {278, 24018}, {279, 8611}, {304, 7180}, {306, 3669}, {307, 513}, {331, 822}, {345, 7216}, {348, 661}, {349, 22383}, {512, 7182}, {514, 1214}, {521, 3668}, {522, 1439}, {603, 850}, {604, 3267}, {649, 1231}, {651, 4466}, {652, 1446}, {664, 18210}, {810, 6063}, {1014, 4064}, {1019, 26942}, {1020, 26932}, {1021, 20618}, {1042, 35518}, {1111, 23067}, {1365, 4592}, {1400, 15413}, {1409, 3261}, {1410, 35519}, {1425, 18155}, {1427, 6332}, {1441, 1459}, {1565, 4551}, {1804, 24006}, {1813, 16732}, {1880, 30805}, {2171, 15419}, {2197, 7199}, {2501, 7183}, {3049, 20567}, {3120, 6516}, {3213, 14638}, {3695, 7203}, {3700, 7177}, {3708, 4573}, {3710, 43932}, {3718, 7250}, {3737, 6356}, {3942, 4552}, {3949, 17096}, {4041, 7056}, {4086, 7053}, {4091, 40149}, {4171, 30682}, {4560, 37755}, {4565, 20902}, {4566, 7004}, {4625, 20975}, {6358, 7254}, {7125, 14618}, {7131, 21107}, {7147, 15411}, {8057, 8809}, {9436, 10099}, {14321, 27832}, {15412, 44708}, {17924, 40152}, {20336, 43924}, {21174, 47344}, {21207, 36059}, {22341, 46107}, {23800, 28786}, {31603, 43708}, {37136, 42761}
X(51664) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 36797}, {3, 643}, {7, 811}, {34, 107}, {48, 5546}, {56, 162}, {57, 648}, {63, 645}, {65, 1897}, {69, 7257}, {71, 644}, {72, 3699}, {73, 100}, {77, 99}, {78, 7256}, {85, 6331}, {109, 5379}, {125, 4086}, {201, 3952}, {219, 7259}, {222, 662}, {226, 6335}, {228, 3939}, {273, 6528}, {278, 823}, {306, 646}, {307, 668}, {345, 7258}, {348, 799}, {512, 33}, {513, 29}, {514, 31623}, {520, 78}, {521, 1043}, {523, 318}, {525, 312}, {603, 110}, {604, 112}, {608, 24019}, {647, 9}, {649, 1172}, {650, 2322}, {652, 2287}, {656, 8}, {659, 14024}, {661, 281}, {663, 4183}, {667, 2299}, {669, 2212}, {684, 44694}, {693, 44130}, {798, 607}, {810, 55}, {822, 219}, {905, 333}, {1019, 46103}, {1020, 46102}, {1042, 108}, {1118, 36126}, {1214, 190}, {1231, 1978}, {1319, 46541}, {1365, 24006}, {1367, 14208}, {1393, 35360}, {1395, 32713}, {1397, 32676}, {1400, 1783}, {1402, 8750}, {1409, 101}, {1410, 109}, {1414, 18020}, {1425, 4551}, {1426, 36127}, {1427, 653}, {1437, 4636}, {1439, 664}, {1446, 46404}, {1455, 7452}, {1456, 4241}, {1457, 4246}, {1458, 4238}, {1459, 21}, {1464, 4242}, {1565, 18155}, {1577, 7017}, {1790, 4612}, {1804, 4592}, {1813, 4567}, {1919, 2204}, {1946, 2328}, {2170, 17926}, {2197, 1018}, {2318, 4578}, {2524, 7075}, {2605, 11107}, {2631, 7359}, {3049, 41}, {3063, 2332}, {3120, 44426}, {3122, 18344}, {3125, 3064}, {3265, 3718}, {3267, 28659}, {3269, 8611}, {3668, 18026}, {3669, 27}, {3676, 286}, {3682, 4571}, {3690, 4069}, {3694, 6558}, {3700, 7101}, {3708, 3700}, {3709, 7079}, {3733, 270}, {3937, 3737}, {3942, 4560}, {3949, 30730}, {3958, 30729}, {3990, 4587}, {4017, 4}, {4025, 314}, {4041, 7046}, {4047, 30728}, {4064, 3701}, {4077, 264}, {4091, 1812}, {4131, 332}, {4367, 14006}, {4404, 44721}, {4466, 4391}, {4551, 15742}, {4573, 46254}, {4592, 6064}, {4822, 461}, {6357, 24001}, {6516, 4600}, {6591, 8748}, {7004, 7253}, {7053, 1414}, {7056, 4625}, {7099, 4565}, {7117, 1021}, {7125, 4558}, {7138, 23067}, {7177, 4573}, {7178, 92}, {7180, 19}, {7182, 670}, {7183, 4563}, {7216, 278}, {7250, 34}, {7252, 2326}, {7254, 2185}, {7335, 4575}, {7649, 1896}, {8611, 346}, {8673, 4123}, {10099, 14942}, {14208, 3596}, {14380, 44693}, {14429, 4723}, {15413, 28660}, {15451, 7069}, {16732, 46110}, {17094, 75}, {17206, 4631}, {17216, 35518}, {18210, 522}, {20975, 4041}, {22094, 35057}, {22341, 1331}, {22383, 284}, {23067, 765}, {23189, 1098}, {23224, 283}, {23226, 35193}, {23286, 44687}, {24002, 44129}, {24018, 345}, {24459, 3975}, {26942, 4033}, {28786, 51566}, {30493, 2617}, {30572, 38462}, {30682, 4635}, {32320, 2289}, {36054, 2327}, {36059, 4570}, {37755, 4552}, {39201, 212}, {40152, 1332}, {42658, 7070}, {43923, 8747}, {43924, 28}, {44708, 14570}, {48144, 44734}, {50330, 46878}, {50332, 4194}, {50490, 40987}, {51368, 42718}
X(51664) = {X(661),X(7216)}-harmonic conjugate of X(7178)
X(51665) lies on these lines: {1, 50092}, {2, 3}, {388, 48799}, {958, 48821}, {2345, 50049}, {3666, 50046}, {3672, 50072}, {3679, 42049}, {4026, 4293}, {4294, 48805}, {4304, 17306}, {4657, 50064}, {5712, 48835}, {10385, 48803}, {14552, 48847}, {19766, 46922}, {37654, 49723}, {42047, 50066}
X(51665) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20, 16394}, {2, 13736, 51595}, {2, 16394, 37037}, {2, 17676, 50055}, {2, 37038, 11111}, {2, 50055, 4}, {2, 50165, 4217}, {2, 51595, 17552}, {3, 50058, 2}, {20, 13728, 37037}, {4201, 13725, 443}, {11112, 51596, 51602}, {13728, 16394, 2}, {13736, 33833, 17552}, {16052, 19279, 2}, {16418, 48815, 2}, {33833, 51595, 2}, {51596, 51602, 2}
X(51666) lies on these lines: {1, 50096}, {2, 3}, {3828, 5247}, {4755, 7283}, {16817, 50064}, {19865, 48821}, {25526, 46922}, {41813, 50086}, {41816, 48868}, {41817, 48835}, {42028, 48852}, {50049, 51488}
X(51666) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1010, 13735}, {2, 4201, 51596}, {2, 13735, 37035}, {2, 16393, 11110}, {2, 16394, 51595}, {2, 37038, 51597}, {2, 51602, 1010}, {1010, 51595, 16394}, {14007, 16454, 19270}, {16394, 51595, 13735}, {16458, 51602, 2}
X(51676) lies on these lines: {1, 50098}, {2, 3}, {524, 25526}, {1211, 50226}, {1213, 49723}, {3624, 17070}, {31143, 49743}, {31144, 49716}, {41809, 50234}
X(51667) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 1010, 13745}, {2, 11111, 51599}, {2, 11112, 51596}, {2, 13745, 17514}, {2, 17589, 50171}, {2, 19277, 11113}, {2, 50171, 4205}, {2, 50428, 51593}, {2, 51591, 11357}, {2, 51602, 11112}, {858, 8728, 442}, {51601, 51602, 2}
X(51668) lies on these lines: {1, 1266}, {2, 3}, {10, 48833}, {551, 24159}, {958, 49725}, {1043, 4340}, {1448, 17079}, {1453, 41140}, {3241, 50106}, {4252, 49734}, {4274, 9534}, {4292, 17274}, {4293, 5263}, {4294, 49746}, {4295, 41846}, {4304, 10436}, {16485, 24199}, {17281, 50054}, {17301, 50064}, {18141, 48863}, {20009, 50044}, {20077, 50074}, {42044, 50045}, {42051, 50070}, {47040, 50226}, {48832, 49732}, {50049, 50107}, {50586, 51223}
X(51668) = reflection of X(2) in X(19276)
X(51668) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 20, 37038}, {2, 6872, 14020}, {2, 11111, 50430}, {2, 17537, 2478}, {2, 17579, 48813}, {2, 37038, 13725}, {2, 48816, 50428}, {2, 50061, 48817}, {2, 50322, 17537}, {2, 50408, 37150}, {2, 50429, 17528}, {2, 51606, 405}, {3, 37150, 2}, {20, 1010, 13725}, {377, 11115, 37176}, {443, 4195, 13742}, {1010, 37038, 2}, {4195, 4201, 16898}, {4234, 48816, 2}, {11112, 16394, 2}, {11113, 19290, 2}, {11359, 50059, 2}, {13728, 51603, 2}, {13745, 51602, 2}, {14020, 16454, 2}, {16370, 50169, 2}, {16393, 50171, 2}, {16898, 37037, 13742}, {17537, 19284, 2}, {19284, 50322, 2478}
X(51669) lies on these lines: {1, 39711}, {2, 3}, {8, 41629}, {10, 16948}, {58, 3679}, {81, 519}, {86, 16711}, {99, 28539}, {333, 48832}, {540, 31143}, {551, 25526}, {612, 48812}, {940, 48862}, {1043, 3241}, {1778, 17330}, {1931, 48809}, {2287, 50115}, {2303, 17281}, {2363, 50052}, {2941, 5250}, {3175, 50054}, {3616, 4854}, {3786, 50127}, {4653, 5333}, {4658, 51093}, {5235, 19875}, {5260, 19870}, {5276, 48864}, {5303, 19863}, {5323, 5434}, {5429, 21020}, {17016, 50083}, {17180, 33953}, {17196, 28534}, {19722, 19767}, {19796, 19848}, {19883, 24617}, {24275, 37675}, {24557, 51382}, {24883, 49734}, {27644, 50300}, {28618, 51109}, {28619, 51103}, {28620, 51110}, {32782, 48834}, {32911, 48867}, {35016, 41812}, {37633, 48863}, {37680, 48866}, {39673, 48852}, {40773, 48854}, {41610, 47359}, {41816, 50215}, {42044, 50049}, {42051, 50064}
X(51669) = barycentric product X(99)*X(47881)
X(51669) = barycentric quotient X(47881)/X(523)
X(51669) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 21, 17553}, {2, 2475, 16052}, {2, 4189, 16351}, {2, 4195, 11346}, {2, 4234, 21}, {2, 11115, 4234}, {2, 11346, 5047}, {2, 13735, 16861}, {2, 15677, 13745}, {2, 16393, 17549}, {2, 16865, 11357}, {2, 17553, 17557}, {2, 19336, 404}, {2, 33309, 17547}, {2, 50061, 11114}, {2, 50171, 6175}, {2, 50172, 17677}, {2, 50428, 4197}, {2, 51592, 48817}, {21, 1010, 14005}, {21, 14005, 17557}, {21, 17551, 11110}, {58, 3679, 4921}, {405, 19332, 2}, {964, 19336, 2}, {1010, 4234, 2}, {1010, 11110, 17589}, {1010, 11115, 21}, {1010, 17539, 17551}, {1043, 42028, 3241}, {2049, 16351, 2}, {4184, 19259, 21}, {4195, 16454, 5047}, {4216, 11358, 404}, {4225, 19531, 21}, {11110, 17539, 21}, {11110, 17589, 17551}, {11112, 50059, 2}, {11115, 17589, 17539}, {11346, 16454, 2}, {11354, 19276, 19290}, {11354, 19290, 2}, {11357, 16458, 2}, {11359, 51590, 2}, {13740, 19284, 17531}, {14005, 17553, 2}, {16370, 19277, 2}, {16371, 19247, 4225}, {16371, 19531, 19247}, {16394, 19276, 2}, {16394, 19290, 11354}, {16418, 51602, 2}, {17539, 17589, 11110}, {17551, 17589, 14005}, {17677, 50172, 15679}, {37176, 50428, 2}
X(51670) lies on these lines: {1, 50107}, {2, 3}, {1220, 34619}, {1453, 50095}, {4340, 17297}, {5247, 48802}, {11240, 24552}, {14555, 48866}, {17281, 50064}, {17301, 50054}, {31030, 46934}, {38314, 42044}, {50049, 50101}
X(51670) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4195, 11111}, {2, 11111, 13725}, {2, 13735, 50430}, {2, 50061, 48813}, {2, 50408, 17528}, {2, 51592, 17579}, {2, 51606, 13745}, {4195, 37037, 13725}, {11111, 37037, 2}, {11113, 51590, 2}, {11354, 50059, 2}, {13735, 51605, 2}, {13745, 51603, 2}, {16370, 50323, 2}, {17528, 17698, 2}, {51595, 51604, 2}, {51596, 51600, 2}
X(51671) lies on these lines: {1, 4395}, {2, 3}, {10, 37520}, {72, 50116}, {392, 29309}, {529, 19870}, {752, 27637}, {3753, 3819}, {4273, 25526}, {4340, 37654}, {4472, 19867}, {5165, 17330}, {6051, 28580}, {9534, 17378}, {18990, 19874}, {41313, 50049}, {49723, 49731}
X(51671) = complement of X(14020)
X(51671) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4217, 11108}, {2, 11112, 13745}, {2, 13725, 51599}, {2, 17679, 50058}, {2, 19277, 50323}, {2, 36004, 17553}, {2, 48816, 11113}, {2, 48817, 17542}, {2, 50061, 16857}, {2, 50428, 17532}, {443, 16458, 13728}, {17563, 50432, 16342}, {17589, 17674, 50318}, {33833, 51604, 2}
X(51672) lies on these lines: {1, 3943}, {2, 3}, {72, 50115}, {551, 3175}, {1211, 48866}, {1453, 3679}, {1724, 4290}, {3058, 48811}, {7283, 17320}, {7354, 48808}, {17271, 49716}, {17301, 50049}, {17359, 50064}, {17382, 50054}, {19784, 48829}, {25526, 49738}, {34606, 48826}, {42044, 50069}, {42051, 50053}, {50044, 50101}, {50072, 50107}
X(51672) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 964, 37150}, {2, 4195, 37038}, {2, 11114, 50058}, {2, 11319, 14020}, {2, 11354, 11113}, {2, 13725, 51598}, {2, 13735, 13745}, {2, 13745, 51596}, {2, 14020, 4205}, {2, 16394, 11112}, {2, 17537, 5051}, {2, 17579, 48815}, {2, 37037, 51603}, {2, 37038, 13728}, {2, 37150, 442}, {2, 48817, 50056}, {2, 50061, 11359}, {2, 51591, 19276}, {2, 51594, 37039}, {2, 51606, 13725}, {405, 51603, 2}, {964, 17698, 442}, {1010, 37035, 16911}, {4195, 37036, 13728}, {13742, 16458, 17590}, {17698, 37150, 2}, {37036, 37038, 2}
X(51673) lies on these lines: {1, 2325}, {2, 3}, {388, 48833}, {519, 1453}, {958, 48810}, {1104, 17281}, {1724, 37654}, {3488, 5294}, {3974, 49480}, {4080, 46934}, {4294, 48829}, {4340, 17313}, {5247, 50316}, {5657, 35263}, {5698, 19869}, {5712, 48866}, {6361, 25904}, {7283, 50101}, {10385, 48831}, {16485, 17355}, {19855, 49725}, {41313, 50064}
X(51673) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4217, 4}, {2, 11319, 4217}, {2, 13735, 11111}, {2, 51606, 37038}, {405, 1009, 19256}, {4195, 13742, 443}, {4217, 17526, 2}, {11319, 17526, 4}, {13735, 37038, 51606}, {16857, 50059, 2}, {17697, 37176, 5084}, {19277, 50202, 2}, {37035, 51604, 2}, {37038, 51606, 11111}, {51595, 51605, 2}
X(51674) lies on these lines: {1, 1278}, {2, 3}, {192, 50054}, {894, 11523}, {1043, 17379}, {1104, 4699}, {1453, 16816}, {3616, 33147}, {3617, 5247}, {3945, 33954}, {4292, 17236}, {4302, 19865}, {4340, 17375}, {4704, 7283}, {4740, 50064}, {4772, 19851}, {4788, 50044}, {5263, 12513}, {16996, 19761}, {17343, 20077}, {19827, 50050}, {20018, 37677}, {24598, 50622}, {26111, 32942}, {27269, 50164}
X(51674) = anticomplement of X(37164)
X(51674) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1010, 4195, 2}, {1010, 13735, 16458}, {1010, 16394, 4195}, {1010, 37035, 51602}, {4201, 37037, 2}, {11115, 17589, 4184}, {16454, 17697, 2}, {16865, 17589, 2}, {16926, 17696, 2}, {26051, 37176, 2}, {51594, 51604, 2}
X(51675) lies on these lines: {1, 50118}, {2, 3}, {3679, 4339}, {5232, 49723}, {5304, 24275}, {5716, 50104}, {7229, 16485}, {11036, 35578}, {34610, 48810}, {34619, 48826}, {34625, 48811}, {37666, 48863}
X(51675) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4234, 10304}, {2, 11106, 13745}, {2, 15683, 11359}, {2, 48817, 3543}, {2, 50171, 4208}, {2, 50687, 16052}, {4190, 6872, 20063}, {11346, 51591, 2}, {13735, 51605, 50430}, {13745, 37037, 2}, {17526, 50171, 2}, {50430, 51605, 2}
X(51676) lies on these lines: {1, 4755}, {2, 3}, {37, 50072}, {3739, 50049}, {4428, 19870}, {4664, 16817}, {4688, 50044}, {4698, 50064}, {5247, 25055}, {5259, 19871}, {5302, 51061}, {17251, 50260}, {17313, 49723}, {17776, 50047}, {19723, 48855}, {24789, 50062}
X(51676) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 405, 16394}, {2, 11114, 50427}, {2, 11346, 19277}, {2, 13735, 51602}, {2, 14020, 17528}, {2, 16394, 16458}, {2, 16418, 19290}, {2, 16858, 19276}, {2, 16861, 11354}, {2, 17553, 19279}, {2, 37314, 50058}, {2, 48814, 44217}, {2, 50055, 8728}, {2, 50430, 11112}, {2, 51595, 405}, {2, 51605, 51601}, {405, 51602, 13735}, {5047, 19238, 405}, {5259, 19871, 48805}, {13735, 51602, 16394}, {16408, 17588, 19289}, {19238, 37035, 16844}, {37035, 51595, 2}, {50058, 50205, 2}
X(51677) lies on these lines: {1, 599}, {2, 3}, {6, 49723}, {45, 19867}, {540, 19722}, {597, 49728}, {956, 4026}, {1724, 47352}, {1992, 19766}, {3679, 4646}, {7761, 50230}, {7801, 19758}, {7810, 19761}, {7865, 50225}, {9534, 31144}, {11160, 19783}, {11178, 48894}, {15360, 19771}, {16466, 50296}, {17251, 50179}, {17313, 25499}, {17320, 50072}, {19684, 50234}, {19701, 48835}, {19723, 49729}, {19732, 48843}, {19738, 50215}, {19767, 31143}, {19782, 50977}, {37631, 48834}, {48840, 50305}, {48845, 49730}, {48857, 49724}, {48868, 50268}
X(51677) = crossdifference of every pair of points on line {647, 2515}
X(51677) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4234, 51590}, {2, 11112, 51602}, {2, 11357, 50714}, {2, 11359, 44217}, {2, 13725, 13745}, {2, 13745, 405}, {2, 16394, 51603}, {2, 17579, 19277}, {2, 17676, 50171}, {2, 17679, 50427}, {2, 37038, 16394}, {2, 48813, 50169}, {2, 48817, 50323}, {2, 49735, 11354}, {2, 50055, 37150}, {2, 50056, 17532}, {2, 50165, 964}, {2, 50171, 2049}, {2, 50321, 11359}, {2, 51594, 51595}, {2, 51602, 51601}, {2, 51605, 51600}, {2049, 17676, 50239}, {4201, 37039, 16458}, {4202, 16844, 50207}, {11112, 51596, 2}, {11359, 50410, 2}, {11359, 50427, 17679}, {13725, 13728, 405}, {13728, 13745, 2}, {16351, 51593, 2}, {16394, 51598, 2}, {16394, 51600, 51605}, {17679, 50427, 44217}, {19266, 37329, 37058}, {37038, 51598, 51603}, {48813, 50169, 50397}, {50321, 50410, 44217}, {51600, 51605, 51603}
X(51678) lies on these lines: {1, 2796}, {2, 3}, {8, 896}, {99, 50230}, {519, 1046}, {524, 1043}, {894, 4304}, {958, 49720}, {1104, 37756}, {1220, 15338}, {1654, 14712}, {1975, 17378}, {1992, 20018}, {2650, 3241}, {3616, 24851}, {4313, 35578}, {4653, 26109}, {5550, 25378}, {5731, 29057}, {6224, 24852}, {6781, 24275}, {7270, 50104}, {7750, 17271}, {7779, 50236}, {15326, 32942}, {16485, 48627}, {16712, 50225}, {17320, 50064}, {17778, 50234}, {20065, 50074}, {20101, 49492}, {31144, 49728}, {34620, 48805}, {34626, 48832}, {34701, 50127}, {37589, 37764}, {42028, 49739}, {44367, 50156}, {50164, 51224}
X(51678) = reflection of X(2) in X(4234)
X(51678) = anticomplement of X(17677)
X(51678) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 15680, 50165}, {2, 50165, 26117}, {2, 50171, 26051}, {20, 4195, 4201}, {21, 50171, 2}, {376, 48817, 2}, {1010, 13745, 2}, {11112, 13735, 2}, {11114, 16393, 2}, {11115, 15680, 26117}, {11115, 50165, 2}, {11319, 20063, 26117}, {15680, 37256, 20063}, {16046, 50170, 2}, {16394, 37038, 2}, {16397, 17537, 2}, {16418, 48816, 2}, {17561, 50428, 2}, {19276, 48814, 2}, {35935, 50168, 2}
X(51679) lies on these lines: {1, 4285}, {2, 3}, {392, 29311}, {528, 19871}, {1453, 25055}, {3679, 48846}, {5259, 48810}, {16817, 17320}, {16828, 49725}, {17251, 50235}, {17378, 49716}, {17392, 49723}, {19853, 49746}, {37631, 48839}, {48844, 50224}, {48848, 50316}, {48852, 49739}, {48855, 49724}, {49728, 49738}
X(51679) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4195, 51604}, {2, 4217, 2049}, {2, 11111, 51602}, {2, 13745, 11112}, {2, 14020, 37150}, {2, 16858, 50059}, {2, 31156, 19277}, {2, 33309, 50323}, {2, 48814, 50169}, {2, 50055, 50427}, {2, 50430, 16394}, {2, 51594, 37038}, {2, 51599, 17514}, {405, 51599, 2}, {13728, 37035, 17590}, {14020, 37150, 11113}, {16844, 37314, 442}, {37038, 51594, 13745}, {51595, 51597, 2}
X(51680) lies on these lines: {1, 17250}, {2, 3}, {16817, 17382}, {19766, 37654}, {19853, 48829}, {25507, 48835}, {25526, 41923}, {26044, 48847}, {46922, 49723}
X(51680) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 4195, 51603}, {2, 11111, 51605}, {2, 13725, 37038}, {2, 13745, 13735}, {2, 14020, 13740}, {2, 26117, 37150}, {2, 37038, 1010}, {2, 37150, 19280}, {2, 51594, 405}, {2, 51606, 37037}, {405, 51598, 2}, {13725, 37039, 1010}, {13745, 51596, 2}, {26117, 50409, 19280}, {37038, 37039, 2}, {37150, 50409, 2}
X(51681) lies on these lines: {1, 4741}, {2, 3}, {1043, 17251}, {1104, 17399}, {4304, 17248}, {10449, 48841}, {16485, 17324}, {16824, 50080}, {17301, 19851}, {17346, 20018}, {48850, 49729}, {48869, 50224}, {49723, 50074}
X(51681) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 11111, 4195}, {2, 13745, 51594}, {11110, 17528, 2}, {11111, 13725, 2}, {13745, 37038, 2}, {16342, 17577, 2}, {16858, 50321, 2}, {17556, 19270, 2}, {51596, 51605, 2}, {51597, 51602, 2}
X(51682) lies one these lines: {1, 3}, {6, 59}, {7, 3446}, {105, 5723}, {108, 17724}, {388, 37009}, {405, 19890}, {513, 1037}, {651, 16686}, {1086, 40576}, {1458, 20872}, {1471, 51627}, {1602, 1618}, {1995, 14513}, {2222, 2725}, {2720, 28838}, {3433, 43947}, {3476, 47043}, {5096, 7677}, {14733, 43079}, {14936, 51633}, {20468, 34253}, {37815, 42884}
X(51682) = circumcircle-inverse of X(241)
X(51682) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 40577, 38530}, {55, 56, 2283}, {1037, 1486, 6180}, {1381, 1382, 241}
X(51683) lies on these lines: {1, 21}, {2, 10950}, {3, 1389}, {5, 944}, {8, 7483}, {36, 33815}, {65, 5303}, {80, 1125}, {86, 17221}, {100, 2646}, {110, 40430}, {145, 18231}, {149, 10543}, {214, 17531}, {355, 38183}, {388, 1388}, {404, 30147}, {442, 6224}, {515, 7548}, {551, 5443}, {950, 10707}, {1001, 40269}, {1006, 46920}, {1320, 3746}, {1385, 5253}, {1482, 7508}, {2099, 4189}, {3295, 19525}, {3306, 30389}, {3486, 11680}, {3487, 11113}, {3601, 14923}, {3636, 11813}, {3649, 20067}, {3754, 13587}, {3812, 4881}, {3871, 37571}, {3918, 15015}, {3957, 11260}, {4004, 17502}, {4297, 20292}, {4313, 34611}, {4323, 44447}, {4511, 5044}, {4861, 24929}, {5047, 30144}, {5080, 37737}, {5086, 24541}, {5176, 13411}, {5289, 16865}, {5428, 35457}, {5438, 13384}, {5603, 7491}, {5691, 10129}, {5731, 37468}, {5777, 6265}, {5784, 30284}, {5901, 38039}, {5903, 17549}, {6049, 37358}, {6690, 37734}, {6852, 7967}, {6912, 40257}, {6940, 26287}, {6965, 10805}, {7419, 23846}, {7489, 37624}, {7987, 9352}, {8572, 9335}, {9964, 12675}, {10039, 12531}, {10197, 37707}, {10584, 46934}, {10698, 33281}, {10954, 11681}, {11035, 25405}, {11263, 36975}, {12671, 18444}, {17541, 30140}, {17548, 37567}, {18481, 49107}, {20323, 29817}, {20846, 26437}, {21740, 40263}, {21842, 30143}, {27003, 37605}, {31649, 48667}, {32633, 50193}, {33108, 47516}, {34339, 38693}, {34773, 37230}, {37080, 38460}, {37291, 40663}
X(51683) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2975, 34195}, {1, 3897, 2975}, {1, 5248, 5330}, {1, 5426, 3884}, {80, 1125, 7504}, {3622, 5046, 15950}, {3754, 37616, 13587}, {7483, 37728, 8}, {30147, 37525, 404}
See Angel Montesdeoca, euclid 5486.
X(51684) lies on this line: {1, 2}
See Angel Montesdeoca, euclid 5486.
X(51685) lies on these lines: {3624,4657}, {3966,4034}
See Angel Montesdeoca, euclid 5486.
X(51686) lies on these lines: {1,25}, {3,2339}, {4,1220}, {6,1245}, {19,34261}, {28,86}, {34,7337}, {56,1395}, {58,1473}, {72,12410}, {87,1044}, {106,32691}, {198,2336}, {269,1398}, {427,19784}, {468,19836}, {573,2983}, {870,37101}, {939,20991}, {977,1870}, {996,4186}, {998,1828}, {1203,19118}, {1222,4222}, {1310,15344}, {1474,16502}, {1593,2297}, {1707,39946}, {1851,8747}, {1974,16466}, {2215,2281}, {2334,2356}, {4185,12609}, {5331,34260}, {7085,8193}, {14017,40436}, {16483,44091}, {19881,37453}, {23383,34430}, {24320,30479}, {26927,42467}, {36099,37129}, {37034,37613}
X(51687) lies on these lines: {1, 19}, {2, 5285}, {3, 142}, {7, 3220}, {9, 4223}, {10, 7535}, {21, 10436}, {22, 5249}, {23, 31019}, {25, 226}, {30, 25365}, {31, 57}, {35, 37264}, {40, 21160}, {55, 11347}, {56, 2218}, {63, 4228}, {65, 2175}, {73, 40983}, {92, 107}, {154, 37543}, {197, 13405}, {198, 954}, {206, 942}, {212, 1730}, {238, 579}, {355, 7562}, {390, 24604}, {404, 17282}, {405, 5750}, {443, 11677}, {497, 7490}, {515, 7497}, {527, 24320}, {534, 551}, {553, 1473}, {758, 34176}, {894, 17522}, {908, 1995}, {929, 2725}, {950, 4185}, {993, 8680}, {1012, 44356}, {1104, 5019}, {1203, 51223}, {1279, 5301}, {1376, 20106}, {1436, 42884}, {1439, 1456}, {1479, 14018}, {1503, 16608}, {1598, 6260}, {1621, 1817}, {1633, 4312}, {1691, 20271}, {1699, 4219}, {1738, 37576}, {1763, 5338}, {1836, 14667}, {2182, 5728}, {2214, 38315}, {2328, 24310}, {2355, 17441}, {2550, 40910}, {2876, 4260}, {2886, 6678}, {2975, 45738}, {3008, 36741}, {3211, 45728}, {3246, 37582}, {3306, 37449}, {3452, 5020}, {3487, 17562}, {3556, 3671}, {3576, 30265}, {3601, 4319}, {3616, 4329}, {3622, 20061}, {3624, 7523}, {3664, 36740}, {3755, 37580}, {3836, 16415}, {3883, 26241}, {3924, 7122}, {4031, 26866}, {4220, 25525}, {4222, 9612}, {4265, 4675}, {4292, 13730}, {4298, 22654}, {4304, 37241}, {4331, 37583}, {4357, 19310}, {4423, 21483}, {4667, 37492}, {5096, 17278}, {5219, 33849}, {5250, 37277}, {5257, 19309}, {5259, 13726}, {5263, 16054}, {5316, 11284}, {5347, 24789}, {5436, 37399}, {5437, 19649}, {5450, 43160}, {5480, 36949}, {5542, 22769}, {5603, 7501}, {5715, 7412}, {5745, 25514}, {6636, 27186}, {6692, 16434}, {7295, 50307}, {7419, 30035}, {7453, 30961}, {7549, 8227}, {8021, 16678}, {8185, 13407}, {8299, 16056}, {8301, 29671}, {8727, 23304}, {8728, 23305}, {9250, 9254}, {9257, 16592}, {9318, 46586}, {9579, 28029}, {9798, 21620}, {9856, 12262}, {11712, 37533}, {11719, 15746}, {12047, 14017}, {12053, 37245}, {12263, 46181}, {13411, 37034}, {13595, 31053}, {15569, 24929}, {15951, 51118}, {16048, 17353}, {16428, 45765}, {16475, 51210}, {17248, 19318}, {17560, 31424}, {17581, 19859}, {17718, 20989}, {17810, 34048}, {18446, 36009}, {19322, 50092}, {20258, 28383}, {20266, 26118}, {21258, 44882}, {22791, 44220}, {25055, 31158}, {25439, 50288}, {27339, 37103}, {27626, 28288}, {27802, 34937}, {28348, 30097}, {30267, 41869}, {31266, 35996}, {32942, 37092}, {37261, 41867}, {37538, 40940}, {51616, 51637}
X(51687) = midpoint of X(1) and X(19)
X(51687) = reflection of X(i) in X(j) for these {i,j}: {10, 40530}, {18589, 1125}
X(51687) = complement of X(50861)
X(51687) = crossdifference of every pair of points on line {656, 6586}
X(51687) = barycentric product X(i)*X(j) for these {i,j}: {1, 379}, {75, 44081}
X(51687) = barycentric quotient X(i)/X(j) for these {i,j}: {379, 75}, {44081, 1}
X(51687) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {7, 37254, 3220}, {5880, 20872, 24309}, {7535, 37547, 10}, {8225, 31546, 946}, {25514, 37581, 5745}
X(51688) lies on these lines: {1, 15}, {10, 621}, {30, 9901}, {40, 511}, {165, 14538}, {515, 36993}, {517, 5611}, {519, 51484}, {531, 3679}, {533, 12781}, {623, 1698}, {1277, 1757}, {1699, 7684}, {3576, 13350}, {3624, 6671}, {5587, 20428}, {5690, 22651}, {5691, 22652}, {7968, 10671}, {7969, 10667}, {7987, 21158}, {10789, 36759}, {11705, 16962}, {11708, 39555}, {19875, 50855}, {22851, 33960}, {25055, 45879}, {35242, 36755}, {38047, 51161}
X(51688) = reflection of X(i) in X(j) for these {i,j}: {1, 15}, {621, 10}, {50854, 45879}
X(51688) = {X(45879),X(50854)}-harmonic conjugate of X(25055)
X(51689) lies on these lines: {1, 15}, {8, 623}, {10, 40334}, {30, 7975}, {145, 621}, {511, 1482}, {515, 36992}, {517, 14538}, {518, 51206}, {519, 50853}, {531, 3241}, {944, 22912}, {946, 41036}, {952, 20428}, {1385, 21158}, {1386, 36757}, {3616, 6671}, {5184, 11708}, {5603, 7684}, {5611, 10247}, {5846, 51016}, {7967, 36993}, {9041, 51017}, {9053, 51161}, {9901, 42973}, {10246, 13350}, {10800, 36759}, {11705, 16267}, {11725, 22510}, {12702, 36755}, {22511, 50254}, {38314, 45879}
(51689) = midpoint of X(145) and X(621)
(51689) = reflection of X(i) in X(j) for these {i,j}: {8, 623}, {15, 1}, {5184, 11708}, {12702, 36755}, {50855, 50854}
(51689) = {X(5184),X(11708)}-harmonic conjugate of X(39554)
X(51690) lies on these lines: {1, 16}, {10, 622}, {30, 9900}, {40, 511}, {165, 14539}, {515, 36995}, {517, 5615}, {519, 51485}, {530, 3679}, {532, 12780}, {624, 1698}, {1276, 1757}, {1699, 7685}, {3576, 13349}, {3624, 6672}, {5587, 20429}, {5690, 22652}, {5691, 22651}, {7968, 10672}, {7969, 10668}, {7987, 21159}, {10789, 36760}, {11706, 16963}, {11707, 39554}, {19875, 50858}, {22896, 33959}, {25055, 45880}, {35242, 36756}, {38047, 51162}
X(51690) = reflection of X(i) in X(j) for these {i,j}: {1, 16}, {622, 10}, {50857, 45880}
X(51690) = {X(45880),X(50857)}-harmonic conjugate of X(25055)
X(51691) lies on these lines: {1, 16}, {8, 624}, {10, 40335}, {30, 7974}, {145, 622}, {511, 1482}, {515, 36994}, {517, 14539}, {518, 51207}, {519, 50856}, {530, 3241}, {944, 22867}, {946, 41037}, {952, 20429}, {1385, 21159}, {1386, 36758}, {3616, 6672}, {5184, 11707}, {5603, 7685}, {5615, 10247}, {5846, 51018}, {7967, 36995}, {9041, 51019}, {9053, 51162}, {9900, 42972}, {10246, 13349}, {10800, 36760}, {11706, 16268}, {11725, 22511}, {12702, 36756}, {22510, 50254}, {38314, 45880}
X(51691) = midpoint of X(145) and X(622)
X(51691) = reflection of X(i) in X(j) for these {i,j}: {8, 624}, {16, 1}, {5184, 11707}, {12702, 36756}, {50858, 50857}
X(51691) = {X(5184),X(11707)}-harmonic conjugate of X(39555)
X(51692) lies on these lines: {1, 22}, {10, 6676}, {30, 551}, {40, 44837}, {378, 3576}, {427, 1125}, {515, 15760}, {516, 44239}, {517, 7502}, {518, 19127}, {519, 44210}, {952, 25337}, {1062, 39582}, {1319, 40961}, {1386, 9019}, {2781, 11720}, {2915, 9630}, {3616, 7391}, {3622, 20062}, {3624, 31236}, {3679, 47596}, {5603, 44831}, {5731, 44440}, {5847, 16789}, {5882, 16618}, {5886, 31723}, {7555, 10222}, {9626, 37932}, {9955, 44288}, {10246, 12083}, {11230, 39504}, {13624, 18570}, {18480, 46029}, {25055, 31133}, {28160, 44263}, {28194, 44261}, {28204, 44262}, {44218, 50828}, {44260, 44662}
X(51692) = midpoint of X(1) and X(22)
X(51692) = reflection of X(i) in X(j) for these {i,j}: {10, 6676}, {427, 1125}, {18480, 46029}, {18570, 13624}, {44218, 50828}, {44288, 9955}
X(51693) lies on these lines: {1, 23}, {8, 37760}, {10, 468}, {30, 551}, {40, 186}, {165, 37952}, {403, 19925}, {511, 11720}, {515, 11799}, {516, 10295}, {517, 7575}, {518, 32217}, {519, 7426}, {523, 1960}, {691, 38221}, {858, 1125}, {952, 25338}, {1319, 7286}, {1325, 37571}, {1386, 8705}, {1482, 2070}, {1503, 13605}, {1699, 10296}, {1902, 44281}, {2071, 7987}, {2646, 5160}, {2690, 29330}, {2948, 35265}, {3241, 37909}, {3244, 37897}, {3416, 47450}, {3576, 7464}, {3579, 18571}, {3616, 5189}, {3622, 20063}, {3624, 30745}, {3625, 47316}, {3636, 37900}, {3679, 37907}, {3817, 10297}, {4301, 47471}, {4669, 47496}, {5159, 19862}, {5446, 43822}, {5493, 37934}, {5818, 37943}, {5844, 44264}, {5846, 32218}, {5847, 32113}, {5882, 16619}, {5886, 7574}, {5899, 37624}, {6684, 44214}, {7469, 22836}, {7982, 37953}, {7991, 37957}, {8193, 37920}, {9798, 37973}, {9955, 18572}, {9956, 44282}, {10149, 20129}, {10165, 15122}, {10222, 12105}, {10246, 37924}, {10247, 37923}, {10989, 25055}, {11365, 37972}, {11531, 37940}, {11709, 14915}, {11735, 29012}, {12030, 29095}, {12112, 33535}, {12512, 44280}, {12702, 37958}, {13624, 37950}, {15178, 37967}, {15646, 31663}, {15808, 46517}, {16192, 37941}, {18323, 18483}, {18325, 18481}, {18374, 32278}, {18480, 44961}, {19883, 47097}, {21284, 49553}, {28160, 44267}, {28194, 44265}, {28204, 44266}, {30143, 37959}, {31673, 47336}, {31730, 47335}, {32220, 34379}, {33179, 37936}, {34638, 47031}, {34641, 47488}, {34648, 47332}, {37901, 38314}, {37904, 47472}, {37911, 51073}, {37981, 49542}, {38047, 47453}, {44569, 50919}, {47245, 50776}, {47246, 50772}, {47310, 50862}, {47311, 51109}, {47312, 47593}, {47313, 51103}, {47314, 51108}, {47333, 50808}, {47334, 50796}, {47477, 49505}, {47506, 49536}, {47540, 51096}, {47556, 50781}
X(51693) = midpoint of X(i) and X(j) for these {i,j}: {1, 23}, {10149, 51635}, {12112, 33535}, {16619, 47476}, {18325, 18481}, {37904, 47472}, {47245, 50776}, {47312, 47593}
X(51693) = reflection of X(i) in X(j) for these {i,j}: {10, 468}, {551, 47495}, {858, 1125}, {3244, 47491}, {3579, 18571}, {3625, 47492}, {4301, 47471}, {4669, 47496}, {5882, 47476}, {18323, 18483}, {18480, 44961}, {18572, 9955}, {31673, 47336}, {31730, 47335}, {34638, 47031}, {34641, 47488}, {34648, 47332}, {37950, 13624}, {49505, 47477}, {49536, 47506}, {50781, 47556}, {50796, 47334}, {50808, 47333}, {50862, 47310}, {50919, 44569}, {51071, 47472}, {51096, 47540}
X(51693) = crossdifference of every pair of points on line {4286, 46381}
X(51694) lies on these lines: {1, 24}, {10, 16238}, {30, 551}, {40, 15078}, {235, 515}, {516, 44240}, {517, 37814}, {519, 44211}, {952, 44232}, {1125, 11585}, {1386, 12266}, {1699, 35490}, {3576, 11413}, {3579, 43615}, {3616, 37444}, {3622, 31304}, {3624, 31282}, {5603, 35471}, {5882, 21841}, {5886, 18404}, {7517, 10246}, {8758, 37812}, {10165, 16196}, {11230, 49673}, {11709, 12262}, {11720, 31732}, {15178, 37440}, {18480, 44235}, {18481, 31725}, {21842, 34036}, {24299, 51687}, {25055, 31180}, {28160, 44271}, {28194, 44268}, {28204, 44270}, {31673, 44226}, {31730, 44247}, {37624, 51519}
X(51694) = midpoint of X(i) and X(j) for these {i,j}: {1, 24}, {18481, 31725}
X(51694) = reflection of X(i) in X(j) for these {i,j}: {10, 16238}, {3579, 43615}, {11585, 1125}, {18480, 44235}, {31673, 44226}, {31730, 44247}
X(51695) lies on these lines: {1, 25}, {10, 6677}, {30, 551}, {515, 1596}, {516, 44241}, {517, 6644}, {518, 19136}, {519, 44212}, {952, 44233}, {1060, 1486}, {1125, 1368}, {1319, 34036}, {1370, 3616}, {1386, 2393}, {1479, 40985}, {1699, 44438}, {2646, 37241}, {2790, 11710}, {2834, 11716}, {3241, 26255}, {3576, 21312}, {3622, 7500}, {3624, 31255}, {3679, 47597}, {3817, 44920}, {5603, 18533}, {5847, 8263}, {5886, 18531}, {7530, 15178}, {8227, 16072}, {8758, 11334}, {10222, 12106}, {10246, 18534}, {10602, 16475}, {11522, 37196}, {11720, 14984}, {11721, 11722}, {11735, 36201}, {13464, 37458}, {15569, 24929}, {18480, 46030}, {25055, 31152}, {28160, 44276}, {28194, 44273}, {28204, 44275}, {31811, 44547}, {37613, 49553}, {37729, 40635}, {37951, 41722}
X(51695) = midpoint of X(1) and X(25)
X(51695) = reflection of X(i) in X(j) for these {i,j}: {10, 6677}, {1368, 1125}, {18480, 46030}
X(51696) lies on these lines: {1, 26}, {5, 11363}, {10, 10020}, {30, 551}, {40, 18324}, {156, 912}, {355, 10201}, {515, 15761}, {516, 44242}, {517, 1658}, {518, 19154}, {519, 44213}, {952, 13383}, {1125, 13371}, {1319, 32047}, {1482, 14070}, {1483, 10154}, {1829, 37440}, {1902, 18570}, {2070, 41722}, {2646, 8144}, {3576, 12084}, {3579, 15331}, {3616, 14790}, {3622, 31305}, {3624, 31283}, {5663, 40658}, {5690, 34351}, {5844, 44277}, {5886, 18569}, {6684, 34477}, {7387, 10246}, {7525, 37613}, {7542, 12135}, {7968, 11265}, {7969, 11266}, {8141, 37080}, {9645, 34471}, {9714, 11396}, {9909, 37624}, {9955, 18377}, {10125, 11231}, {10165, 23336}, {10222, 12107}, {10224, 11230}, {10226, 17502}, {10247, 16195}, {11250, 13624}, {11720, 31738}, {13406, 18480}, {15178, 17714}, {15330, 50821}, {23335, 38028}, {25055, 31181}, {28160, 44279}, {28194, 48368}, {28204, 44278}, {28454, 33596}, {32046, 44547}
X(51696) = midpoint of X(1) and X(26)
X(51696) = reflection of X(i) in X(j) for these {i,j}: {10, 10020}, {3579, 15331}, {11250, 13624}, {13371, 1125}, {18377, 9955}, {18480, 13406}, {50821, 15330}
X(51696) = {X(11363),X(24301)}-harmonic conjugate of X(5)
X(51697) lies on these lines: {1, 27}, {10, 6678}, {30, 551}, {40, 21162}, {440, 1125}, {515, 15762}, {516, 44243}, {993, 8680}, {997, 36019}, {1012, 43160}, {1455, 4298}, {1762, 42055}, {2822, 11714}, {2939, 31903}, {3151, 3616}, {3576, 30266}, {3622, 31292}, {3624, 31256}, {3874, 49683}, {11365, 20834}, {12263, 46182}, {16418, 25363}, {18673, 31900}, {25055, 31153}, {26128, 37098}, {28194, 48369}
X(51697) = midpoint of X(1) and X(27)
X(51697) = reflection of X(i) in X(j) for these {i,j}: {10, 6678}, {440, 1125}
X(51698) lies on these lines: {1, 19}, {30, 551}, {110, 39772}, {226, 11363}, {515, 15763}, {517, 44220}, {692, 12432}, {758, 44253}, {950, 40985}, {999, 11365}, {1015, 1104}, {1125, 21530}, {1420, 4320}, {1437, 10122}, {1486, 4347}, {2646, 40960}, {2817, 45176}, {2828, 11715}, {2838, 11716}, {3145, 18593}, {3576, 30267}, {3622, 31293}, {3624, 31257}, {3874, 42463}, {5884, 6759}, {10158, 17581}, {12564, 20986}, {23171, 23383}, {25055, 31154}, {26702, 40431}, {28194, 48370}
X(51698) = midpoint of X(1) and X(28)
X(51698) = reflection of X(21530) in X(1125)
X(51699) lies on these lines: {1, 29}, {30, 551}, {515, 44225}, {516, 44244}, {1125, 18641}, {1621, 15777}, {2605, 42455}, {2654, 38983}, {2816, 11713}, {3152, 3616}, {3468, 14004}, {3576, 30268}, {3622, 31294}, {3624, 31258}, {5136, 45131}, {5625, 7100}, {6198, 35109}, {11365, 20836}, {15171, 17043}, {25055, 31155}, {44290, 44661}
X(51699) = midpoint of X(1) and X(29)
X(51699) = reflection of X(18641) in X(1125)
X(51700) lies on these lines: {1, 140}, {2, 1483}, {3, 3622}, {5, 944}, {8, 632}, {10, 16239}, {11, 24926}, {30, 551}, {40, 3653}, {56, 7508}, {104, 31649}, {145, 3526}, {355, 547}, {376, 50832}, {390, 38111}, {392, 24475}, {442, 1484}, {495, 1388}, {496, 34471}, {499, 37728}, {500, 32486}, {515, 3850}, {516, 44245}, {517, 3530}, {519, 10124}, {542, 51154}, {546, 5691}, {548, 3576}, {549, 1482}, {550, 5603}, {631, 10247}, {758, 44254}, {952, 1125}, {962, 8703}, {1001, 5843}, {1159, 5265}, {1201, 50418}, {1317, 34126}, {1319, 13407}, {1386, 34380}, {1387, 2646}, {1420, 6147}, {1621, 37535}, {1656, 7967}, {3090, 18526}, {3241, 11539}, {3242, 38110}, {3243, 38113}, {3244, 11231}, {3523, 8148}, {3525, 3623}, {3533, 3621}, {3617, 46219}, {3624, 37727}, {3627, 5731}, {3635, 45760}, {3655, 5066}, {3656, 7987}, {3679, 47598}, {3746, 33814}, {3817, 3856}, {3828, 41984}, {3853, 9624}, {3861, 9955}, {3884, 5885}, {3898, 35004}, {4301, 17502}, {4323, 37545}, {5045, 31838}, {5049, 31837}, {5054, 12245}, {5126, 24470}, {5253, 37621}, {5330, 37298}, {5426, 12409}, {5427, 5563}, {5428, 22765}, {5550, 5790}, {5587, 12812}, {5657, 14869}, {5719, 24928}, {5734, 44682}, {5818, 15699}, {5882, 11230}, {6265, 10021}, {6361, 46853}, {6684, 11812}, {6713, 33281}, {6863, 10586}, {6883, 7373}, {6914, 16203}, {6920, 12773}, {6924, 16202}, {6958, 10587}, {7294, 41684}, {7583, 35762}, {7584, 35763}, {7989, 47478}, {8728, 32214}, {8981, 44636}, {9626, 12105}, {9957, 12736}, {10039, 12735}, {10109, 28204}, {10164, 11278}, {10165, 10222}, {10179, 34339}, {10248, 35404}, {10386, 37606}, {10543, 16173}, {10950, 15079}, {11108, 24558}, {11365, 17714}, {11373, 13384}, {11531, 41983}, {11540, 51071}, {11545, 37734}, {11707, 11740}, {11708, 11739}, {11729, 24927}, {11735, 32423}, {11737, 19925}, {12101, 38021}, {12102, 28160}, {12103, 12699}, {12255, 13743}, {12266, 50708}, {12331, 17531}, {12433, 44675}, {12512, 13464}, {12515, 35010}, {12571, 28208}, {12702, 15712}, {12747, 32558}, {12811, 18480}, {13373, 14988}, {13411, 25405}, {13902, 19117}, {13959, 19116}, {13966, 44635}, {14891, 31663}, {14893, 50811}, {14986, 15935}, {15026, 16980}, {15170, 37571}, {15171, 37525}, {15174, 37722}, {15687, 50867}, {15690, 31162}, {15691, 50820}, {15694, 50823}, {15700, 50872}, {15701, 34631}, {15702, 50805}, {15703, 50818}, {15711, 34632}, {15713, 34718}, {15721, 50826}, {15759, 28194}, {15854, 26728}, {15950, 18990}, {16617, 21740}, {16826, 19512}, {17527, 32213}, {18483, 28190}, {19861, 50205}, {19883, 47745}, {19907, 38032}, {21214, 37698}, {23841, 32205}, {24299, 37281}, {25524, 32141}, {28178, 31662}, {28198, 50816}, {30308, 41987}, {31650, 34195}, {31657, 38316}, {31666, 31730}, {32789, 35842}, {32790, 35843}, {34753, 50194}, {35255, 35642}, {35256, 35641}, {37618, 39542}, {37935, 41722}, {38068, 51104}, {38165, 47355}, {38176, 51073}, {38315, 48876}, {41988, 50862}, {43822, 50476}, {44234, 47321}, {44580, 51106}, {46933, 51515}
X(51700) = midpoint of X(i) and X(j) for these {i,j}: {1, 140}, {546, 34773}, {547, 50824}, {548, 22791}, {1125, 15178}, {1385, 5901}, {3655, 5066}, {3656, 34200}, {3853, 18481}, {3884, 5885}, {4297, 40273}, {5045, 31838}, {5882, 18357}, {6684, 33179}, {9956, 13607}, {12103, 12699}, {12104, 16137}, {13464, 13624}, {14893, 50811}, {15690, 31162}
X(51700) = reflection of X(i) in X(j) for these {i,j}: {10, 16239}, {3628, 1125}, {3861, 9955}, {14891, 50828}, {18357, 35018}, {18480, 12811}, {23841, 32205}, {33923, 13624}, {50862, 41988}
X(51700) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 38028, 140}, {2, 34748, 38081}, {2, 37624, 1483}, {3, 3622, 10283}, {145, 3526, 38112}, {551, 1385, 5901}, {1125, 13607, 9956}, {1387, 2646, 15172}, {1656, 7967, 37705}, {3090, 18526, 38138}, {3576, 22791, 548}, {3616, 10246, 5}, {3624, 37727, 38042}, {3624, 38042, 48154}, {3655, 38022, 5066}, {3655, 51110, 38022}, {5731, 18493, 3627}, {5882, 11230, 18357}, {5882, 15808, 11230}, {5886, 34773, 546}, {6684, 51103, 33179}, {7967, 46934, 1656}, {9624, 18481, 38034}, {9624, 30392, 18481}, {9956, 15178, 13607}, {11230, 18357, 35018}, {15950, 21842, 18990}, {18481, 38034, 3853}, {25055, 50824, 547}
X(51701) lies on these lines: {1, 186}, {10, 44452}, {30, 551}, {40, 37941}, {389, 43822}, {403, 515}, {468, 5882}, {516, 44246}, {517, 15646}, {519, 44214}, {944, 37943}, {952, 44234}, {1125, 2072}, {1319, 47115}, {1482, 37955}, {1483, 16532}, {2070, 10246}, {2071, 3576}, {2646, 10149}, {3153, 3616}, {3244, 16531}, {3579, 37968}, {3817, 23323}, {4301, 47335}, {5603, 13619}, {5886, 18403}, {5899, 11365}, {6000, 11709}, {7464, 30389}, {7575, 15178}, {7982, 37952}, {7987, 37948}, {9624, 10296}, {10151, 11363}, {10165, 10257}, {10175, 44911}, {10222, 18571}, {10295, 13464}, {10595, 35489}, {11362, 47491}, {11563, 34773}, {11720, 13754}, {11735, 18400}, {12261, 30522}, {13607, 47321}, {13624, 34152}, {15350, 18357}, {18480, 46031}, {18481, 31726}, {18579, 51071}, {28160, 44283}, {28194, 44280}, {28204, 44282}, {30392, 37925}, {31399, 37911}, {31730, 47471}, {37624, 37922}, {37938, 38028}, {44265, 51103}, {44272, 44662}, {47569, 49684}
X(51701) = midpoint of X(i) and X(j) for these {i,j}: {1, 186}, {10151, 47469}, {11563, 34773}, {18481, 31726}, {44452, 47476}
X(51701) = reflection of X(i) in X(j) for these {i,j}: {10, 44452}, {2072, 1125}, {3579, 37968}, {18357, 15350}, {18480, 46031}, {31673, 10151}, {34152, 13624}
X(51702) lies on these lines: {1, 235}, {24, 5603}, {30, 551}, {515, 44226}, {516, 44247}, {517, 16238}, {952, 44235}, {962, 15078}, {1125, 16196}, {3616, 11413}, {3656, 44211}, {5886, 11585}, {10246, 31725}, {12699, 44240}, {13464, 21841}, {18404, 18493}, {22791, 37814}, {28174, 43615}, {31162, 44268}, {34773, 44271}
X(51702) = midpoint of X(i) and X(j) for these {i,j}: {1, 235}, {3656, 44211}, {12699, 44240}, {22791, 37814}, {31162, 44268}, {34773, 44271}
X(51702) = reflection of X(16196) in X(1125)
X(51703) lies on these lines: {1, 237}, {30, 551}, {460, 11363}, {512, 48064}, {515, 44227}, {517, 44221}, {519, 44215}, {1125, 21531}, {3576, 47620}, {3616, 14957}, {3622, 46518}
X(51703) = midpoint of X(1) and X(237)
X(51703) = reflection of X(21531) in X(1125)
X(51704) lies on these lines: {1, 297}, {10, 44334}, {30, 551}, {401, 3616}, {441, 1125}, {515, 44228}, {516, 44248}, {519, 44216}, {525, 676}, {3241, 44579}, {3576, 44252}, {3622, 40853}, {3679, 44576}, {5603, 35474}, {5886, 44231}, {6660, 11365}, {19862, 44335}, {19883, 44346}, {25055, 40884}, {38314, 40885}, {49768, 51616}
X(51704) = midpoint of X(1) and X(297)
X(51704) = reflection of X(i) in X(j) for these {i,j}: {10, 44334}, {441, 1125}
X(51705) lies on these lines: {1, 376}, {2, 515}, {3, 519}, {4, 25055}, {5, 19883}, {8, 15692}, {10, 549}, {20, 13464}, {30, 551}, {40, 3241}, {57, 14563}, {84, 50742}, {104, 15931}, {140, 31399}, {142, 13151}, {145, 35242}, {165, 7967}, {214, 3452}, {226, 21578}, {355, 3828}, {381, 1125}, {392, 17525}, {500, 50604}, {511, 51005}, {516, 3534}, {517, 3892}, {524, 39870}, {527, 37611}, {528, 11715}, {535, 28459}, {541, 11720}, {542, 11709}, {543, 11710}, {544, 11714}, {547, 18480}, {548, 5493}, {550, 4301}, {572, 50115}, {631, 19875}, {758, 44255}, {944, 3524}, {950, 10072}, {952, 4669}, {991, 50294}, {993, 5325}, {1000, 31508}, {1071, 31165}, {1201, 48897}, {1210, 5298}, {1319, 3058}, {1350, 47356}, {1388, 10624}, {1420, 4305}, {1482, 12512}, {1483, 31663}, {1503, 51003}, {1698, 15702}, {1699, 15682}, {1770, 24926}, {2320, 5249}, {2646, 4311}, {2784, 8724}, {2800, 10167}, {2816, 50901}, {3098, 49684}, {3146, 9624}, {3244, 3579}, {3304, 37426}, {3333, 15933}, {3361, 17706}, {3476, 30282}, {3488, 13462}, {3522, 7982}, {3523, 5881}, {3525, 37714}, {3528, 7991}, {3529, 11522}, {3530, 38098}, {3543, 3616}, {3545, 5691}, {3564, 51004}, {3582, 10572}, {3584, 37616}, {3612, 10056}, {3622, 15683}, {3624, 5071}, {3625, 14891}, {3626, 15700}, {3632, 15715}, {3634, 15694}, {3635, 12702}, {3636, 12699}, {3651, 5563}, {3746, 37403}, {3817, 3845}, {3829, 6907}, {3830, 5886}, {3839, 8227}, {3878, 13369}, {3881, 37585}, {4031, 5425}, {4292, 34471}, {4293, 4654}, {4313, 40270}, {4314, 15170}, {4315, 24929}, {4342, 25405}, {4511, 17781}, {4677, 5657}, {4691, 15718}, {4745, 15693}, {4847, 10609}, {4848, 7280}, {4870, 7354}, {4995, 31397}, {5055, 19925}, {5066, 11230}, {5085, 47359}, {5092, 49529}, {5122, 37728}, {5126, 11019}, {5248, 28444}, {5267, 5837}, {5270, 6903}, {5450, 9948}, {5476, 38049}, {5550, 18492}, {5603, 11001}, {5690, 17504}, {5732, 47357}, {5734, 50693}, {5790, 15701}, {5818, 15709}, {5844, 15759}, {5884, 31786}, {6173, 43161}, {6175, 24541}, {6246, 45310}, {6260, 11113}, {6261, 11111}, {6702, 38069}, {6796, 16371}, {6909, 34486}, {6987, 28609}, {7415, 42028}, {7968, 41945}, {7969, 41946}, {7988, 41106}, {8983, 35822}, {9143, 33535}, {9530, 11722}, {9583, 19054}, {9588, 10299}, {9589, 17538}, {9626, 37940}, {9778, 16200}, {9780, 15721}, {9864, 41134}, {9875, 14651}, {9881, 21166}, {9884, 34473}, {9955, 15687}, {9956, 11539}, {10031, 38693}, {10109, 38140}, {10124, 18357}, {10168, 38089}, {10171, 19709}, {10247, 15695}, {10268, 34744}, {10270, 34711}, {10283, 19710}, {10476, 48858}, {10519, 50950}, {10680, 12511}, {10707, 12119}, {10884, 40257}, {10902, 17549}, {11114, 12608}, {11224, 50813}, {11231, 11812}, {11237, 13411}, {11238, 44675}, {11274, 46684}, {11500, 16417}, {12005, 14110}, {12053, 21842}, {12101, 28190}, {12114, 16418}, {12117, 50886}, {12245, 15710}, {12258, 23698}, {12355, 50887}, {12515, 33812}, {12571, 14269}, {12616, 37298}, {12645, 15706}, {12675, 31806}, {12680, 20117}, {12773, 24393}, {13405, 37606}, {13490, 34633}, {13587, 37561}, {13634, 50305}, {13635, 50291}, {13971, 35823}, {14893, 33697}, {14912, 50952}, {15677, 16132}, {15678, 50908}, {15684, 18493}, {15685, 28158}, {15686, 22791}, {15689, 37624}, {15690, 28174}, {15697, 28232}, {15703, 19878}, {15705, 31145}, {15708, 31423}, {15711, 50823}, {15713, 38042}, {15714, 32900}, {15716, 50804}, {15719, 50871}, {15723, 31253}, {16174, 38026}, {16226, 31760}, {17614, 34697}, {17642, 46681}, {19711, 38112}, {19861, 31156}, {20323, 34630}, {20423, 38029}, {21077, 34698}, {21167, 50949}, {21356, 39885}, {24387, 37401}, {25406, 50999}, {25439, 35238}, {25485, 38759}, {26287, 34637}, {28168, 33699}, {28212, 51083}, {28460, 33858}, {28534, 43177}, {29010, 51060}, {29012, 51156}, {29054, 51042}, {29181, 51006}, {30273, 31178}, {30503, 34607}, {31787, 34639}, {31803, 31838}, {31805, 45776}, {31884, 51000}, {33337, 38602}, {33595, 50371}, {33597, 34606}, {34380, 51197}, {34617, 37571}, {34618, 37080}, {34619, 34716}, {34620, 34647}, {34625, 34701}, {34626, 34640}, {34745, 49600}, {34937, 48818}, {36444, 36463}, {36445, 36462}, {37474, 50300}, {37499, 50131}, {37602, 41853}, {37620, 42057}, {38035, 51024}, {38118, 50983}, {38123, 51100}, {38165, 50988}, {38176, 44580}, {43273, 47358}, {44273, 44662}, {44566, 44819}, {44661, 48370}, {47031, 47593}, {47097, 47469}, {48906, 49505}, {49102, 50884}, {50096, 51049}, {50130, 50677}, {50777, 51045}, {50781, 50977}, {50787, 50955}, {50791, 51027}, {50799, 50868}, {50805, 50814}, {50806, 50869}, {50809, 51097}
X(51705) = midpoint of X(i) and X(j) for these {i,j}: {1, 376}, {2, 50811}, {3, 3655}, {4, 34628}, {20, 31162}, {40, 3241}, {165, 7967}, {381, 18481}, {549, 34773}, {551, 4297}, {944, 3679}, {1071, 31165}, {1350, 47356}, {3058, 37429}, {3534, 3656}, {3576, 5731}, {4301, 34638}, {4669, 51082}, {4677, 50818}, {5434, 37428}, {5732, 47357}, {6173, 43161}, {7982, 34632}, {7991, 34631}, {8703, 50824}, {9143, 33535}, {9778, 16200}, {10707, 12119}, {11001, 50865}, {11274, 46684}, {12117, 50886}, {12245, 34747}, {12699, 15681}, {14110, 24473}, {15677, 16132}, {15683, 41869}, {15686, 22791}, {28460, 33858}, {30273, 31178}, {34619, 34716}, {34620, 34647}, {34625, 34701}, {34626, 34640}, {34718, 37727}, {43273, 47358}, {47031, 47593}, {47097, 47469}, {48897, 50422}, {50808, 51071}, {50809, 51097}, {50810, 51093}, {50814, 51091}, {50815, 51103}, {50816, 51107}, {50819, 51105}, {51079, 51104}, {51080, 51108}
X(51705) = reflection of X(i) in X(j) for these {i,j}: {2, 50828}, {10, 549}, {355, 3828}, {381, 1125}, {549, 13624}, {551, 1385}, {946, 551}, {3241, 13607}, {3534, 50815}, {3543, 18483}, {3579, 34200}, {3656, 51103}, {3679, 6684}, {3817, 38028}, {3830, 50802}, {4669, 50821}, {4677, 50827}, {4745, 50829}, {5325, 28466}, {5882, 3655}, {6246, 45310}, {10164, 17502}, {10165, 3576}, {10175, 10165}, {12355, 50887}, {15687, 9955}, {18357, 10124}, {18480, 547}, {24473, 12005}, {31162, 13464}, {31673, 381}, {31730, 376}, {33697, 14893}, {34633, 13490}, {34638, 550}, {34641, 5690}, {34648, 5}, {34718, 43174}, {38028, 31662}, {38127, 10164}, {38155, 11231}, {44566, 44819}, {47745, 3679}, {50096, 51049}, {50777, 51045}, {50781, 50977}, {50796, 2}, {50798, 4745}, {50801, 51069}, {50802, 51108}, {50805, 51091}, {50808, 8703}, {50821, 12100}, {50862, 3845}, {50884, 49102}, {50955, 50787}, {51067, 50825}, {51069, 51086}, {51071, 50824}, {51074, 51109}, {51075, 41150}, {51077, 51071}, {51096, 51087}, {51103, 51085}, {51109, 50832}
X(51705) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 3576, 50828}, {2, 5731, 50811}, {2, 50796, 10175}, {2, 50828, 10165}, {2, 50864, 5587}, {3, 5882, 11362}, {3, 37727, 43174}, {10, 549, 38068}, {20, 38314, 31162}, {165, 51093, 50810}, {355, 5054, 3828}, {381, 3653, 1125}, {547, 18480, 38076}, {548, 10222, 5493}, {550, 15178, 4301}, {631, 34627, 19875}, {944, 3524, 3679}, {944, 6684, 47745}, {944, 7987, 6684}, {1125, 18481, 31673}, {1385, 4297, 946}, {2646, 4311, 21620}, {3241, 10304, 40}, {3524, 3679, 6684}, {3534, 10246, 3656}, {3543, 3616, 38021}, {3543, 38021, 18483}, {3576, 50811, 2}, {3653, 18481, 381}, {3656, 10246, 51103}, {3679, 7987, 3524}, {3817, 3845, 51074}, {3817, 50862, 3845}, {3830, 5886, 50802}, {3845, 50832, 38028}, {4669, 10164, 50821}, {4669, 50821, 38127}, {4677, 5657, 50827}, {4745, 50829, 26446}, {5603, 11001, 50865}, {5603, 50819, 11001}, {5657, 50818, 4677}, {5818, 15709, 19876}, {5901, 51118, 946}, {7967, 19708, 50810}, {7967, 50810, 51093}, {10124, 18357, 38083}, {10124, 38083, 51073}, {10164, 51082, 4669}, {10165, 50796, 2}, {10171, 50803, 19709}, {11231, 51084, 11812}, {12100, 50821, 10164}, {12100, 51082, 38127}, {13624, 34773, 10}, {15687, 38022, 9955}, {15693, 26446, 50829}, {15693, 50798, 26446}, {15698, 50818, 5657}, {15700, 18526, 38066}, {15702, 38074, 1698}, {17502, 50821, 12100}, {19708, 50810, 165}, {19711, 38112, 50825}, {19862, 38076, 547}, {19883, 34648, 5}, {21578, 37525, 226}, {25055, 34628, 4}, {26446, 50798, 4745}, {30389, 34628, 25055}, {30392, 50865, 51105}, {31162, 38314, 13464}, {38042, 50833, 15713}, {50801, 51069, 5790}, {50802, 51108, 5886}, {50808, 50824, 51077}, {50811, 50828, 50796}, {50815, 51085, 3656}, {50862, 51109, 3817}, {50865, 51105, 5603}, {51085, 51103, 10246}, {51114, 51115, 49511}
X(51706) lies on these lines: {1, 224}, {2, 3338}, {4, 38053}, {5, 3742}, {7, 12514}, {8, 27186}, {10, 141}, {11, 9844}, {12, 5439}, {30, 551}, {35, 36003}, {40, 6173}, {56, 226}, {57, 10198}, {86, 4911}, {145, 50794}, {210, 17529}, {354, 442}, {386, 24178}, {388, 34489}, {392, 3649}, {443, 3475}, {474, 17718}, {496, 3838}, {498, 3306}, {499, 31266}, {515, 30143}, {516, 37426}, {517, 44222}, {519, 44217}, {527, 25363}, {595, 28026}, {758, 44256}, {908, 3624}, {960, 6147}, {975, 33144}, {997, 3487}, {999, 28628}, {1010, 33124}, {1056, 28629}, {1071, 12617}, {1086, 3931}, {1145, 3922}, {1210, 3822}, {1330, 16823}, {1386, 49743}, {1479, 4666}, {1519, 9624}, {1621, 1770}, {1698, 50393}, {1889, 39579}, {2886, 3824}, {3011, 37522}, {3085, 9776}, {3178, 24165}, {3244, 50238}, {3295, 5880}, {3296, 24477}, {3333, 25525}, {3339, 30379}, {3452, 4999}, {3555, 3925}, {3616, 4293}, {3622, 4305}, {3634, 4860}, {3635, 50713}, {3636, 12053}, {3646, 28609}, {3660, 3814}, {3663, 3743}, {3671, 3878}, {3679, 50793}, {3695, 49483}, {3753, 10915}, {3754, 31397}, {3782, 6051}, {3813, 5049}, {3817, 6260}, {3833, 8582}, {3841, 3881}, {3848, 17527}, {3869, 11551}, {3873, 4197}, {3889, 33108}, {3898, 4301}, {3918, 6736}, {3919, 11362}, {3921, 34501}, {3935, 26060}, {3953, 29639}, {3976, 33111}, {4078, 24068}, {4084, 5837}, {4208, 11038}, {4292, 5248}, {4315, 51111}, {4321, 5290}, {4325, 5426}, {4355, 31424}, {4385, 17234}, {4640, 24470}, {4654, 31435}, {4656, 27784}, {4675, 5711}, {4848, 33815}, {4966, 5295}, {4968, 18139}, {5119, 10587}, {5126, 11813}, {5219, 10200}, {5236, 39585}, {5264, 28027}, {5316, 19878}, {5437, 26364}, {5530, 24046}, {5550, 31053}, {5563, 24541}, {5692, 24564}, {5705, 10980}, {5708, 26066}, {5714, 26105}, {5725, 17054}, {5787, 38030}, {5794, 15934}, {5836, 49626}, {5886, 6259}, {5902, 24987}, {5927, 7958}, {6223, 38037}, {6245, 18260}, {6684, 10197}, {6685, 50199}, {6690, 37582}, {6700, 50203}, {6701, 24387}, {6734, 18398}, {6765, 38052}, {6837, 10085}, {6854, 17857}, {6889, 12704}, {6897, 37569}, {6907, 13374}, {7191, 26131}, {7483, 32636}, {7535, 22769}, {7680, 9940}, {8071, 13411}, {8226, 12680}, {8227, 10785}, {8255, 16201}, {8261, 24475}, {9612, 10582}, {9943, 31657}, {10056, 18223}, {10106, 30147}, {10164, 37623}, {10165, 26286}, {10176, 45120}, {10179, 22791}, {10202, 12616}, {10580, 31418}, {10586, 23708}, {11019, 16193}, {11024, 34619}, {11036, 12559}, {11037, 19843}, {11112, 37080}, {11374, 25524}, {11518, 49168}, {11523, 41870}, {12436, 13405}, {15171, 42819}, {15569, 50067}, {16454, 33122}, {16484, 24851}, {17023, 50200}, {17050, 49488}, {17056, 37592}, {17061, 37594}, {17167, 28619}, {17182, 28620}, {17582, 25568}, {17609, 24390}, {17674, 46897}, {17862, 23555}, {18249, 43180}, {18393, 50244}, {18443, 26332}, {19796, 41813}, {19883, 34646}, {20330, 37424}, {20418, 21635}, {21621, 29645}, {21627, 50396}, {21628, 43177}, {21677, 24473}, {23806, 48295}, {24199, 28612}, {24982, 37719}, {25006, 41859}, {25055, 31156}, {26015, 50190}, {27385, 37731}, {27475, 33838}, {27577, 46901}, {28160, 44286}, {28194, 44284}, {29675, 37603}, {31339, 33069}, {31419, 34791}, {31871, 41561}, {33073, 50589}, {33130, 37607}, {34046, 37695}, {37112, 41338}, {37329, 43223}, {37398, 40985}, {38316, 41869}, {39586, 51400}, {41814, 50095}, {47358, 50427}, {49477, 49564}, {50058, 51061}, {50394, 51073}, {50397, 51103}
X(51706) = midpoint of X(i) and X(j) for these {i,j}: {1, 377}, {405, 10404}
X(51706) = reflection of X(i) in X(j) for these {i,j}: {10, 8728}, {405, 1125}, {5302, 50205}
X(51706) = complement of X(41229)
X(51706) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5249, 12609}, {2, 13407, 21077}, {10, 5542, 3874}, {142, 21620, 10}, {226, 1125, 21616}, {354, 442, 10916}, {443, 3475, 3811}, {495, 3812, 10}, {551, 4297, 35016}, {551, 11263, 946}, {942, 25466, 10}, {1125, 4298, 993}, {1385, 11281, 551}, {2886, 5045, 49627}, {3333, 25525, 26363}, {3616, 31019, 12047}, {3753, 15888, 10915}, {3824, 5045, 2886}, {3826, 34790, 10}, {3841, 3881, 4847}, {3947, 9843, 3814}, {5563, 26725, 24541}, {12436, 13405, 25440}, {25466, 25557, 942}
X(51707) lies on these lines: {1, 378}, {22, 3576}, {30, 551}, {427, 515}, {516, 24301}, {517, 18570}, {519, 44218}, {952, 44236}, {1125, 15760}, {1386, 2781}, {1699, 35480}, {3616, 44440}, {5587, 31236}, {5603, 35481}, {5731, 7391}, {6676, 10165}, {7502, 13624}, {7555, 31666}, {7987, 44837}, {9955, 44263}, {11230, 46029}, {11363, 18483}, {11365, 12083}, {12082, 30389}, {12262, 12266}, {13151, 51687}, {13413, 38140}, {18480, 39504}, {18481, 31723}, {28160, 44288}, {28194, 44285}, {28204, 44287}, {31133, 50811}, {34036, 37525}, {37970, 41722}, {44210, 50828}, {44274, 44662}
X(51707) = midpoint of X(i) and X(j) for these {i,j}: {1, 378}, {18481, 31723}, {31133, 50811}
X(51707) = reflection of X(i) in X(j) for these {i,j}: {7502, 13624}, {15760, 1125}, {18480, 39504}, {44210, 50828}, {44263, 9955}
X(51708) lies on these lines: {1, 379}, {30, 551}, {993, 24331}, {1125, 30810}, {1386, 4667}, {3616, 31015}, {3874, 50023}, {5436, 43531}, {5792, 15934}, {9895, 34791}, {17647, 49768}, {17758, 24929}, {24315, 51687}, {30117, 41245}
X(51708) = midpoint of X(1) and X(379)
X(51708) = reflection of X(30810) in X(1125)
X(51709) lies on these lines: {1, 381}, {2, 392}, {3, 9589}, {4, 3655}, {5, 519}, {8, 5071}, {10, 547}, {11, 50194}, {30, 551}, {40, 5054}, {56, 28444}, {65, 3582}, {140, 4301}, {145, 38074}, {165, 15693}, {226, 1387}, {354, 2771}, {355, 3241}, {376, 3616}, {382, 34628}, {390, 38073}, {495, 15845}, {496, 15844}, {497, 18407}, {499, 50193}, {511, 51003}, {515, 3845}, {516, 8703}, {518, 5476}, {527, 20330}, {528, 11729}, {541, 11735}, {542, 1386}, {543, 11724}, {544, 11728}, {546, 5882}, {548, 34638}, {549, 1125}, {550, 31666}, {553, 39542}, {631, 34632}, {632, 43174}, {758, 44257}, {942, 10072}, {944, 3839}, {952, 3817}, {962, 3524}, {999, 4654}, {1001, 28466}, {1056, 18516}, {1058, 18517}, {1201, 48903}, {1317, 38077}, {1319, 18393}, {1352, 47356}, {1420, 31776}, {1478, 25405}, {1480, 37674}, {1482, 3679}, {1483, 19925}, {1503, 51006}, {1537, 38026}, {1656, 7982}, {1657, 30389}, {1698, 8148}, {1699, 3830}, {1836, 5126}, {2098, 37692}, {2099, 23708}, {2475, 35597}, {2782, 12258}, {2800, 38044}, {3057, 3584}, {3058, 15950}, {3086, 31794}, {3090, 5734}, {3091, 34627}, {3242, 38072}, {3243, 38075}, {3244, 11737}, {3304, 37234}, {3485, 5045}, {3487, 9844}, {3526, 7991}, {3530, 5493}, {3534, 3576}, {3543, 3622}, {3560, 11194}, {3564, 51005}, {3615, 7478}, {3624, 12702}, {3626, 38081}, {3628, 11362}, {3635, 37705}, {3636, 15687}, {3649, 26202}, {3746, 37251}, {3751, 14848}, {3828, 5690}, {3851, 5881}, {3860, 28224}, {3919, 32557}, {3953, 5492}, {3957, 12738}, {4323, 47743}, {4345, 8164}, {4413, 44455}, {4421, 6911}, {4428, 22753}, {4669, 5844}, {4677, 5790}, {4745, 10171}, {4857, 37230}, {5048, 7951}, {5072, 37714}, {5079, 16189}, {5093, 50952}, {5249, 37429}, {5298, 37582}, {5315, 45923}, {5425, 39782}, {5434, 12047}, {5439, 13145}, {5440, 49719}, {5550, 15702}, {5563, 13743}, {5587, 10247}, {5691, 14269}, {5694, 34647}, {5731, 15682}, {5777, 11240}, {5805, 47357}, {5816, 50131}, {5818, 31145}, {5885, 12672}, {5887, 6583}, {5919, 37701}, {5965, 51155}, {6173, 10269}, {6246, 11274}, {6265, 10707}, {6361, 15692}, {6684, 11539}, {6702, 38084}, {6767, 18491}, {6841, 37722}, {6913, 28609}, {6914, 28534}, {6918, 37622}, {7373, 18761}, {7576, 11363}, {7686, 10197}, {7741, 11011}, {7962, 31479}, {7967, 9779}, {7968, 35822}, {7969, 35823}, {7970, 9166}, {7983, 23234}, {7987, 15688}, {7989, 12645}, {8143, 37592}, {8226, 37726}, {8724, 50886}, {9580, 37606}, {9588, 46219}, {9591, 34006}, {9614, 31795}, {9626, 37956}, {9668, 13384}, {9778, 15698}, {9812, 11001}, {9856, 13373}, {9875, 38732}, {9881, 15561}, {9884, 14639}, {9957, 10056}, {10124, 19862}, {10164, 11812}, {10165, 12100}, {10172, 38112}, {10199, 35004}, {10297, 47472}, {10516, 51000}, {10591, 37739}, {10596, 37820}, {10597, 37821}, {10711, 12737}, {11009, 17606}, {11012, 28443}, {11178, 28538}, {11179, 38023}, {11218, 50891}, {11224, 50817}, {11248, 16417}, {11249, 16418}, {11365, 14070}, {11372, 38024}, {11374, 31792}, {11496, 32612}, {11531, 19876}, {11567, 17577}, {11632, 38220}, {11721, 32424}, {12053, 15170}, {12101, 28186}, {12268, 13667}, {12269, 13787}, {12512, 45759}, {12515, 27003}, {12571, 13607}, {12610, 49738}, {12619, 45310}, {12675, 31828}, {12688, 26201}, {12773, 37602}, {13374, 44663}, {13407, 34697}, {13462, 18541}, {13587, 26086}, {13846, 35775}, {13847, 35774}, {13911, 42602}, {13912, 43211}, {13973, 42603}, {13975, 43212}, {14561, 47359}, {14853, 50999}, {14892, 47745}, {14893, 31673}, {14986, 50192}, {15251, 50114}, {15670, 22937}, {15671, 16139}, {15677, 16159}, {15681, 41869}, {15690, 28178}, {15700, 35242}, {15706, 16192}, {15708, 20070}, {15711, 28232}, {15713, 28228}, {15723, 34595}, {15759, 28216}, {15764, 34556}, {15808, 31730}, {15829, 31493}, {15934, 37704}, {16137, 22798}, {16174, 19907}, {16370, 26286}, {16371, 26285}, {16491, 18440}, {16857, 22770}, {17382, 24220}, {17532, 46920}, {17579, 26287}, {17609, 40263}, {17614, 34629}, {17648, 34619}, {17781, 51409}, {18358, 49684}, {18398, 40266}, {18482, 42819}, {18515, 37587}, {19130, 49465}, {19706, 38107}, {19710, 28150}, {19711, 51086}, {19861, 44217}, {20126, 50878}, {20323, 34698}, {20423, 38035}, {20430, 31178}, {21949, 45763}, {22758, 31164}, {22765, 28453}, {24160, 45219}, {24474, 31165}, {25154, 50849}, {25164, 50852}, {26087, 37375}, {26200, 37562}, {28164, 33699}, {28172, 50869}, {28236, 50803}, {28454, 51687}, {28460, 49177}, {28461, 45977}, {29010, 50111}, {29054, 51045}, {29181, 51154}, {29597, 36731}, {30827, 40587}, {30852, 51362}, {31140, 37533}, {31394, 41311}, {31395, 41310}, {31399, 35018}, {31755, 31840}, {32486, 50103}, {33176, 37710}, {33595, 34611}, {34380, 51004}, {34640, 45701}, {34641, 47478}, {34745, 37080}, {34937, 48820}, {37712, 50797}, {37734, 38078}, {37943, 41722}, {38029, 43273}, {38036, 50836}, {38037, 51099}, {38038, 50843}, {38039, 51112}, {38040, 50979}, {38041, 51098}, {38093, 43166}, {38138, 50801}, {38144, 50790}, {38146, 51089}, {38149, 50839}, {38155, 51096}, {38156, 50846}, {38158, 51101}, {38172, 51100}, {38315, 47353}, {41106, 50799}, {44275, 44662}, {47097, 47471}, {47332, 47593}, {48887, 50608}, {50787, 50978}, {50791, 50973}, {50800, 50871}, {50814, 50825}
X(51709) = midpoint of X(i) and X(j) for these {i,j}: {1, 381}, {2, 3656}, {3, 31162}, {4, 3655}, {355, 3241}, {376, 12699}, {382, 34628}, {549, 22791}, {551, 946}, {1352, 47356}, {1482, 3679}, {1699, 10246}, {3058, 28452}, {3534, 50865}, {3543, 18481}, {3830, 50811}, {3845, 50824}, {4669, 51077}, {4677, 50805}, {5587, 10247}, {5603, 5886}, {5655, 50921}, {5790, 16200}, {5805, 47357}, {5881, 34748}, {5882, 34648}, {5887, 24473}, {6246, 11274}, {6265, 10707}, {7982, 34718}, {8724, 50886}, {10283, 38034}, {10297, 47472}, {10711, 12737}, {11632, 50881}, {12645, 34747}, {15677, 16159}, {15681, 41869}, {15687, 34773}, {20126, 50878}, {20423, 47358}, {20430, 31178}, {22758, 31164}, {24474, 31165}, {25154, 50849}, {25164, 50852}, {28460, 49177}, {31140, 37533}, {34627, 37727}, {34640, 45701}, {34647, 45700}, {47097, 47471}, {47332, 47593}, {48903, 50415}, {50796, 51071}, {50797, 51097}, {50798, 51093}, {50801, 51091}, {50802, 51103}, {50803, 51107}, {50806, 51105}, {51074, 51104}, {51075, 51108}
X(51709) = reflection of X(i) in X(j) for these {i,j}: {10, 547}, {376, 13624}, {381, 9955}, {549, 1125}, {551, 5901}, {1385, 551}, {3241, 33179}, {3579, 549}, {3655, 15178}, {3679, 9956}, {3845, 50802}, {5690, 3828}, {8703, 50828}, {11230, 5886}, {11231, 11230}, {12619, 45310}, {15687, 18483}, {17502, 38028}, {18357, 11737}, {18480, 381}, {19710, 50815}, {22937, 15670}, {24473, 6583}, {31673, 14893}, {31730, 34200}, {31840, 31755}, {33697, 15687}, {34638, 548}, {34648, 546}, {38042, 10171}, {38112, 10172}, {38140, 3817}, {38176, 10175}, {50796, 5066}, {50808, 12100}, {50821, 2}, {50823, 4745}, {50824, 51103}, {50827, 51069}, {50828, 51108}, {50831, 51091}, {50862, 12101}, {50978, 50787}, {51084, 51109}, {51085, 41150}, {51087, 51071}
X(51709) = complement of X(3654)
X(51709) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 7743, 18527}, {1, 9955, 18480}, {1, 18492, 18526}, {1, 18493, 9955}, {1, 18525, 32900}, {1, 38021, 381}, {2, 5603, 3656}, {2, 50810, 26446}, {2, 50821, 11231}, {2, 50872, 5657}, {4, 38314, 3655}, {5, 13464, 10222}, {10, 547, 38083}, {355, 10595, 33179}, {376, 3616, 3653}, {376, 3653, 13624}, {381, 18493, 38021}, {381, 38021, 9955}, {549, 38022, 1125}, {946, 1385, 22793}, {946, 4297, 40273}, {946, 5901, 1385}, {1125, 22791, 3579}, {1482, 5055, 3679}, {1482, 8227, 9956}, {1656, 34718, 19875}, {1699, 50811, 3830}, {1699, 51105, 50811}, {3241, 3545, 355}, {3485, 11373, 5045}, {3545, 10595, 3241}, {3576, 50865, 3534}, {3616, 12699, 13624}, {3636, 18483, 34773}, {3653, 12699, 376}, {3655, 38314, 15178}, {3656, 5886, 2}, {3679, 5055, 9956}, {3679, 8227, 5055}, {3817, 50796, 5066}, {3817, 51071, 50796}, {3830, 10246, 50811}, {3830, 50806, 1699}, {3845, 10283, 50824}, {3845, 38034, 50802}, {4677, 16200, 50805}, {5066, 50796, 38140}, {5587, 51093, 50798}, {5690, 15699, 3828}, {5790, 50805, 4677}, {7967, 41099, 50864}, {7982, 19875, 34718}, {7988, 16200, 5790}, {8148, 15703, 38066}, {8703, 38028, 50828}, {8703, 50828, 17502}, {9624, 11522, 3}, {9624, 31162, 25055}, {9779, 41099, 50807}, {9779, 50864, 41099}, {10109, 51077, 38176}, {10164, 11812, 51088}, {10165, 12100, 51084}, {10165, 50808, 12100}, {10172, 50827, 51069}, {10175, 51077, 4669}, {10246, 50806, 3830}, {10247, 19709, 50798}, {10247, 50798, 51093}, {10283, 50824, 51103}, {11224, 51066, 50817}, {11230, 50821, 2}, {11522, 25055, 31162}, {11705, 11706, 1386}, {11723, 12261, 11699}, {11737, 18357, 38076}, {15703, 38066, 1698}, {15950, 30384, 24929}, {18483, 34773, 33697}, {19709, 50798, 5587}, {19862, 38068, 10124}, {22791, 38022, 549}, {25055, 31162, 3}, {38034, 50824, 3845}, {38035, 47358, 20423}, {38042, 50823, 4745}, {38220, 50881, 11632}, {50808, 51109, 10165}, {50811, 51105, 10246}, {50827, 51069, 38112}, {50828, 51108, 38028}, {50865, 51110, 3576}
X(51710) lies on these lines: {1, 335}, {8, 19689}, {10, 7819}, {30, 551}, {76, 11368}, {141, 49561}, {145, 19692}, {515, 44230}, {516, 44251}, {517, 44224}, {518, 42421}, {519, 6661}, {612, 19670}, {614, 19669}, {698, 1386}, {736, 12263}, {952, 44237}, {1104, 50023}, {1125, 6656}, {1698, 19694}, {3244, 19697}, {3576, 7470}, {3616, 6655}, {3622, 6658}, {3624, 7948}, {3626, 19702}, {3636, 19687}, {3720, 19650}, {3920, 19700}, {3972, 9941}, {5886, 37243}, {7822, 9857}, {7924, 25055}, {8357, 15808}, {8364, 19862}, {10459, 19679}, {10582, 19666}, {11711, 12264}, {16826, 19667}, {17397, 19698}, {19664, 26102}, {19671, 30950}, {19674, 28082}, {19676, 30116}, {19680, 26230}, {19681, 29571}, {19682, 21352}, {19683, 29639}, {19686, 38314}, {19690, 46934}
X(51710) = midpoint of X(1) and X(384)
X(51710) = reflection of X(i) in X(j) for these {i,j}: {10, 7819}, {6656, 1125}
X(51711) lies on these lines: {1, 401}, {10, 441}, {30, 551}, {297, 1125}, {448, 30143}, {515, 44231}, {516, 44252}, {519, 40884}, {3576, 35474}, {3616, 40853}, {3679, 44575}, {3817, 44228}, {3828, 44578}, {19862, 44334}, {19883, 44216}, {25055, 40885}, {38314, 44651}, {44335, 51073}
X(51711) = midpoint of X(1) and X(401)
X(51711) = reflection of X(i) in X(j) for these {i,j}: {10, 441}, {297, 1125}
X(51712) lies on these lines: {1, 402}, {2, 12626}, {8, 15183}, {30, 551}, {145, 16210}, {944, 11897}, {962, 16190}, {1125, 11900}, {1388, 18958}, {1482, 26451}, {1650, 3616}, {1651, 38314}, {3303, 11848}, {3304, 22755}, {3576, 12696}, {3622, 4240}, {5603, 12113}, {7968, 19018}, {7969, 19017}, {10246, 11251}, {10283, 32162}, {10595, 11845}, {11049, 25055}, {11905, 15950}, {11909, 34471}, {11911, 37624}, {12583, 38315}, {12729, 16173}, {13894, 19066}, {13948, 19065}, {18493, 18507}, {34582, 51105}, {44610, 44636}, {44611, 44635}
X(51712) = midpoint of X(1) and X(402)
X(51712) = reflection of X(15184) in X(1125)
X(51712) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 11831, 402}, {3616, 16212, 1650}, {15183, 16211, 8}
X(51713) lies on these lines: {1, 403}, {5, 47491}, {10, 44911}, {30, 551}, {186, 5603}, {468, 13464}, {515, 10151}, {517, 44452}, {858, 9624}, {952, 46031}, {962, 37941}, {1125, 10257}, {1884, 45934}, {2070, 11365}, {2071, 3616}, {2072, 5886}, {3576, 16386}, {3656, 44214}, {5844, 15350}, {5882, 37984}, {6000, 11735}, {9955, 23323}, {10149, 15950}, {10165, 16976}, {10175, 44912}, {10222, 47492}, {10246, 31726}, {10283, 11563}, {10295, 11522}, {10595, 37943}, {11362, 37911}, {11709, 15311}, {11720, 44665}, {11723, 13754}, {12241, 43822}, {12266, 22476}, {12699, 44246}, {13473, 18483}, {15178, 47336}, {15646, 22791}, {18403, 18493}, {28174, 37968}, {31162, 44280}, {31730, 47114}, {34152, 38028}, {34773, 44283}, {40942, 47161}, {44282, 47496}, {47332, 51103}
X(51713) = midpoint of X(i) and X(j) for these {i,j}: {1, 403}, {3656, 44214}, {10257, 47471}, {12699, 44246}, {13473, 47469}, {15646, 22791}, {23323, 47476}, {31162, 44280}, {34773, 44283}
X(51713) = reflection of X(i) in X(j) for these {i,j}: {10, 44911}, {10257, 1125}, {13473, 18483}, {23323, 9955}, {31730, 47114}, {47496, 44282}
X(51714) lies on these lines: {1, 88}, {3, 3898}, {5, 11715}, {10, 6691}, {12, 1125}, {30, 551}, {36, 3884}, {56, 3878}, {58, 47623}, {104, 7701}, {355, 10199}, {392, 3647}, {474, 22837}, {515, 24927}, {519, 17614}, {535, 41012}, {758, 5563}, {993, 1420}, {997, 6762}, {999, 3874}, {1043, 47626}, {1388, 30147}, {1478, 3616}, {1482, 40726}, {1483, 11274}, {1960, 24099}, {2475, 16173}, {2646, 3636}, {2800, 37535}, {3304, 3892}, {3336, 5330}, {3337, 4757}, {3476, 10200}, {3576, 37403}, {3622, 4294}, {3626, 44848}, {3635, 5440}, {3742, 15178}, {3743, 37617}, {3746, 4881}, {3812, 25405}, {3822, 8070}, {3825, 45287}, {3869, 37587}, {3881, 4511}, {3890, 7280}, {3897, 25055}, {3918, 4861}, {3919, 10222}, {3968, 17531}, {4004, 33176}, {4015, 5288}, {4315, 21616}, {5126, 5267}, {5248, 37618}, {5255, 47622}, {5885, 19907}, {5886, 33898}, {6265, 12005}, {6584, 12030}, {6681, 10039}, {6702, 37710}, {6903, 10532}, {7173, 33709}, {7705, 38104}, {8666, 10176}, {9259, 16600}, {9782, 37571}, {10074, 47320}, {10179, 13624}, {10246, 11500}, {10283, 26287}, {10912, 16417}, {10944, 15863}, {11009, 27003}, {11011, 33815}, {11567, 34353}, {11813, 18990}, {12513, 35272}, {12514, 13462}, {12565, 30389}, {12737, 45976}, {12758, 14800}, {13463, 17563}, {13587, 37563}, {15854, 37592}, {15888, 34123}, {16116, 50908}, {16139, 22765}, {16203, 40257}, {17564, 50841}, {17567, 49169}, {19947, 48330}, {25005, 38213}, {25485, 35004}, {25639, 44675}, {32612, 46684}, {33337, 37730}, {33812, 37734}, {34772, 37602}, {37080, 51103}, {38054, 42819}, {38316, 43178}, {50604, 50627}, {50915, 51678}
X(51714) = midpoint of X(i) and X(j) for these {i,j}: {1, 404}, {3336, 5330}, {17614, 20323}
X(51714) = reflection of X(4187) in X(1125)
X(51714) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5253, 3754}, {1, 35262, 8715}, {56, 3878, 4973}, {551, 1385, 35016}, {551, 11263, 5901}, {999, 30144, 3874}, {1125, 1319, 51111}, {1125, 10106, 3814}, {3304, 22836, 3892}, {8666, 19861, 10176}
X(51715) lies on these lines: {1, 6}, {2, 3189}, {3, 3742}, {8, 3748}, {10, 12433}, {20, 38053}, {21, 354}, {30, 551}, {35, 5439}, {40, 4428}, {55, 3812}, {56, 4666}, {65, 1621}, {78, 4423}, {142, 4314}, {145, 50398}, {191, 24473}, {210, 5047}, {214, 15808}, {241, 4332}, {377, 497}, {390, 28629}, {452, 3475}, {474, 3848}, {496, 1125}, {517, 30143}, {519, 50202}, {536, 25363}, {612, 50715}, {614, 4719}, {936, 8167}, {938, 26066}, {942, 4640}, {950, 25466}, {962, 47357}, {968, 37549}, {976, 44307}, {993, 5045}, {1009, 28600}, {1043, 16823}, {1071, 7701}, {1210, 6690}, {1319, 3485}, {1329, 13405}, {1376, 50203}, {1468, 4883}, {1479, 3838}, {1698, 50795}, {1848, 11363}, {1889, 40985}, {2201, 37396}, {2320, 5556}, {2478, 17718}, {2551, 10578}, {2975, 17609}, {3035, 9843}, {3085, 5123}, {3295, 5836}, {3303, 3880}, {3306, 5217}, {3338, 16370}, {3487, 24703}, {3488, 5794}, {3560, 12675}, {3576, 37426}, {3579, 5883}, {3584, 17619}, {3601, 10582}, {3624, 5440}, {3636, 12577}, {3653, 44284}, {3666, 28082}, {3679, 50714}, {3681, 16859}, {3683, 3868}, {3689, 9780}, {3696, 16817}, {3698, 3871}, {3714, 3757}, {3720, 37329}, {3740, 3811}, {3744, 50717}, {3746, 3753}, {3750, 4646}, {3752, 37573}, {3816, 13411}, {3824, 31795}, {3869, 44840}, {3870, 4662}, {3873, 16865}, {3874, 31445}, {3884, 50194}, {3890, 11011}, {3897, 20323}, {3898, 10222}, {3913, 10389}, {3916, 18398}, {3924, 37548}, {3931, 30117}, {3935, 3983}, {3957, 5260}, {4002, 48696}, {4004, 11010}, {4005, 27065}, {4101, 41002}, {4189, 32636}, {4255, 5272}, {4292, 25557}, {4294, 5880}, {4339, 4648}, {4420, 17536}, {4512, 11518}, {4647, 49485}, {4652, 4860}, {4653, 4906}, {4661, 17544}, {4670, 24424}, {4682, 5266}, {4689, 24443}, {4711, 6765}, {4857, 20288}, {4891, 17733}, {4999, 11019}, {5016, 29830}, {5049, 8666}, {5087, 11374}, {5119, 10107}, {5129, 25568}, {5221, 35258}, {5249, 6284}, {5250, 44663}, {5252, 10587}, {5253, 36003}, {5262, 37593}, {5284, 25917}, {5426, 5563}, {5550, 50393}, {5698, 11036}, {5703, 25681}, {5719, 21616}, {5722, 10198}, {5745, 6744}, {5799, 6176}, {5853, 9710}, {5886, 24299}, {5919, 33895}, {6001, 37615}, {6261, 10246}, {6666, 6743}, {6675, 10916}, {6910, 17728}, {6912, 12680}, {6914, 13373}, {6920, 14872}, {6986, 7957}, {7283, 49483}, {7686, 10267}, {7987, 40726}, {8162, 36846}, {8227, 33597}, {8261, 16139}, {8720, 42053}, {8726, 10178}, {9614, 37525}, {9943, 11496}, {9956, 10197}, {9957, 30147}, {10180, 42443}, {10181, 40658}, {10572, 31936}, {10580, 30478}, {10884, 15726}, {10896, 31266}, {10912, 37556}, {11020, 15823}, {11024, 34607}, {11038, 11106}, {11113, 13407}, {11235, 17614}, {11495, 12651}, {12109, 22276}, {12128, 25405}, {12437, 24389}, {12514, 15934}, {12609, 15171}, {12688, 18444}, {12699, 13151}, {13742, 38047}, {13745, 51003}, {15170, 49600}, {16394, 51061}, {16826, 50200}, {17045, 18589}, {17054, 17594}, {17063, 37574}, {17201, 20880}, {17320, 41874}, {17441, 41591}, {17554, 38057}, {17558, 24477}, {17588, 46909}, {17688, 31306}, {17691, 27475}, {18221, 34744}, {18253, 24391}, {18527, 25639}, {18530, 31493}, {19267, 30116}, {19851, 49470}, {19862, 50394}, {19883, 50395}, {19919, 24475}, {21842, 50242}, {21935, 29689}, {22935, 32557}, {24316, 41312}, {24325, 50054}, {24541, 37722}, {24953, 26015}, {25364, 49740}, {26102, 50199}, {26117, 33124}, {26729, 33100}, {28639, 34830}, {31165, 34195}, {31272, 41541}, {37552, 37674}, {37594, 49480}, {38025, 45085}, {38028, 44222}, {38034, 44286}, {41245, 50400}, {46934, 50237}, {47358, 50430}, {49484, 49598}, {49511, 49728}, {50243, 51111}, {50396, 51108}, {50397, 51110}, {51034, 51595}
X(51715) = midpoint of X(i) and X(j) for these {i,j}: {1, 405}, {3303, 19860}, {6872, 10404}
X(51715) = reflection of X(i) in X(j) for these {i,j}: {10, 50205}, {5302, 405}, {8728, 1125}
X(51715) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 958, 34791}, {1, 1001, 960}, {1, 3555, 15570}, {1, 5234, 3243}, {1, 5247, 49478}, {1, 5251, 3555}, {1, 5259, 72}, {1, 5436, 958}, {1, 16478, 1100}, {1, 31435, 12635}, {37, 41239, 30618}, {72, 5259, 15254}, {497, 3616, 28628}, {551, 946, 11281}, {551, 35016, 1385}, {614, 19765, 4719}, {942, 5248, 4640}, {1001, 12635, 31435}, {2975, 29817, 17609}, {3601, 10582, 25524}, {3811, 11108, 3740}, {3897, 38314, 20323}, {5284, 34772, 25917}, {5703, 26105, 25681}, {5886, 24299, 37837}, {11281, 49736, 946}, {11496, 18443, 9943}, {12635, 31435, 960}, {25055, 37571, 17614}
X(51716) lies on these lines: {1, 407}, {30, 551}, {56, 24159}, {1437, 3649}, {1710, 3338}, {3145, 7742}, {3485, 14016}, {12047, 40985}, {14529, 39542}, {15253, 35650}, {16193, 51616}, {37737, 37836}
X(51716) = midpoint of X(1) and X(407)
X(51717) lies on these lines: {1, 411}, {3, 214}, {10, 37837}, {20, 37525}, {30, 551}, {80, 6960}, {104, 6597}, {165, 11682}, {515, 6842}, {516, 2646}, {519, 33597}, {550, 26287}, {758, 11012}, {944, 45700}, {950, 1319}, {958, 15064}, {962, 37571}, {993, 6261}, {1125, 6831}, {1479, 5731}, {1484, 11715}, {1768, 5303}, {2320, 3146}, {2801, 2975}, {2802, 11014}, {3149, 30147}, {3428, 22836}, {3576, 5248}, {3616, 6895}, {3622, 43161}, {3647, 5887}, {3678, 6326}, {3754, 6905}, {3874, 11249}, {3884, 10902}, {3892, 10680}, {3897, 5691}, {3898, 10267}, {4084, 37623}, {4301, 24929}, {4757, 5535}, {4973, 5884}, {5250, 7987}, {5267, 6001}, {5440, 43174}, {5443, 6840}, {5444, 6972}, {5536, 34195}, {5563, 10122}, {5690, 50841}, {5732, 24644}, {5836, 40262}, {5837, 10164}, {5882, 49627}, {6702, 6949}, {6909, 37616}, {6941, 38161}, {6962, 10573}, {7580, 34471}, {8666, 18446}, {9943, 13624}, {10167, 37605}, {10176, 45770}, {10884, 37618}, {11813, 31789}, {12005, 22765}, {12512, 50371}, {12758, 14795}, {13464, 24299}, {15680, 34789}, {17530, 19925}, {17614, 37298}, {21625, 24928}, {22753, 30143}, {28194, 33596}, {36002, 51683}
X(51717) = midpoint of X(i) and X(j) for these {i,j}: {1, 411}, {11012, 21740}, {11014, 11491}
X(51717) = reflection of X(6831) in X(1125)
X(51717) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 40257, 3878}, {946, 1385, 35016}, {993, 6261, 31803}, {5884, 26286, 4973}, {22765, 33858, 12005}
X(51718) lies on these lines: {1, 427}, {8, 31236}, {22, 3616}, {30, 551}, {378, 5603}, {952, 39504}, {1125, 6676}, {2781, 11735}, {3576, 44239}, {3622, 7391}, {3653, 44261}, {3656, 44218}, {5886, 15760}, {7502, 38028}, {10246, 31723}, {12699, 44249}, {13413, 18357}, {15950, 34036}, {17111, 37729}, {18570, 22791}, {25055, 44210}, {31133, 38314}, {31162, 44285}, {34773, 44288}, {38022, 44262}, {38034, 44263}
X(51718) = midpoint of X(i) and X(j) for these {i,j}: {1, 427}, {3656, 44218}, {12699, 44249}, {18570, 22791}, {31162, 44285}, {34773, 44288}
X(51718) = reflection of X(i) in X(j) for these {i,j}: {6676, 1125}, {18357, 13413}
X(51719) lies on these lines: {1, 428}, {2, 8193}, {10, 10128}, {30, 551}, {517, 10127}, {1125, 10691}, {3575, 11522}, {4301, 9825}, {5434, 34036}, {5603, 7576}, {6756, 13464}, {7667, 25055}, {7714, 9798}, {7734, 19883}, {11113, 48833}, {19875, 34656}, {34603, 34634}, {34664, 38021}, {37439, 37546}, {48810, 51687}
X(51719) = midpoint of X(i) and X(j) for these {i,j}: {1, 428}, {7667, 34657}, {34603, 34634}
X(51719) = reflection of X(i) in X(j) for these {i,j}: {10, 10128}, {10691, 1125}
X(51719) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {25055, 34657, 7667}, {34603, 38314, 34634}
X(51720) lies on these lines: {1, 429}, {30, 551}, {496, 23304}, {2778, 11735}, {2915, 11365}, {2960, 25055}, {3616, 16049}, {5603, 7414}, {5886, 37361}, {11376, 38336}, {15569, 37737}
X(51720) = midpoint of X(1) and X(429)
X(51721) lies on these lines: {1, 440}, {8, 31256}, {27, 3616}, {30, 551}, {497, 37098}, {1001, 36011}, {1125, 6678}, {1762, 31435}, {2822, 11728}, {3151, 3622}, {3576, 44243}, {3653, 48369}, {4234, 41874}, {4653, 41003}, {5603, 30266}, {5799, 30143}, {5886, 15762}, {8680, 15569}, {16418, 24316}, {18589, 24929}, {24424, 39544}, {25363, 50059}, {31153, 38314}
X(51721) = midpoint of X(1) and X(440)
X(51721) = reflection of X(6678) in X(1125)
X(51722) lies on these lines: {1, 441}, {10, 44335}, {30, 551}, {297, 3616}, {401, 3622}, {519, 44346}, {1125, 44334}, {3241, 44578}, {3576, 44248}, {5603, 44252}, {5886, 44228}, {10246, 44231}, {25055, 44216}, {30143, 44336}, {38314, 40884}
X(51722) = midpoint of X(1) and X(441)
X(51722) = reflection of X(i) in X(j) for these {i,j}: {10, 44335}, {44334, 1125}
X(51723) lies on these lines: {1, 142}, {2, 6762}, {8, 44841}, {9, 11037}, {10, 3742}, {20, 38316}, {30, 551}, {226, 452}, {354, 21677}, {388, 10582}, {442, 24386}, {495, 9843}, {515, 6849}, {527, 31435}, {553, 5250}, {908, 46934}, {942, 5837}, {950, 4666}, {958, 999}, {960, 5542}, {962, 6173}, {1001, 4298}, {1056, 5795}, {1191, 3664}, {1219, 29627}, {1616, 4675}, {1697, 9776}, {2136, 11024}, {2886, 21625}, {3085, 6692}, {3158, 17580}, {3295, 12436}, {3306, 10587}, {3333, 5745}, {3475, 8583}, {3555, 24393}, {3622, 4313}, {3624, 21075}, {3636, 12609}, {3671, 25557}, {3720, 23675}, {3753, 12640}, {3812, 12915}, {3816, 3947}, {3833, 10915}, {3848, 12607}, {3873, 24564}, {3931, 24171}, {3982, 11415}, {4208, 24392}, {4301, 10179}, {4308, 21617}, {4314, 42819}, {4323, 30379}, {4339, 35227}, {4355, 5698}, {4423, 12527}, {4428, 12512}, {4646, 24175}, {4667, 16466}, {4673, 24199}, {4847, 17609}, {5049, 8728}, {5257, 21384}, {5289, 12563}, {5290, 26105}, {5302, 38059}, {5316, 5550}, {5438, 10578}, {5439, 31397}, {5794, 6744}, {5836, 12855}, {5880, 12575}, {5882, 30143}, {5883, 11362}, {5886, 6260}, {6743, 42871}, {6764, 38200}, {6765, 17582}, {6904, 10389}, {8158, 38122}, {8227, 9842}, {8582, 15888}, {9710, 38204}, {9797, 40333}, {9856, 43177}, {10165, 11249}, {10175, 10942}, {10177, 12680}, {10404, 40998}, {10586, 31266}, {10588, 31249}, {10864, 38037}, {11019, 25466}, {11036, 15829}, {11038, 11523}, {11106, 41857}, {13405, 16411}, {13407, 25055}, {13464, 37611}, {14986, 25525}, {15808, 21616}, {15985, 49511}, {17244, 17480}, {20420, 43175}, {24177, 37548}, {25881, 46897}, {29639, 46190}, {34701, 38314}, {38049, 43149}, {41813, 50109}, {45085, 51099}, {49600, 51103}
X(51723) = midpoint of X(i) and X(j) for these {i,j}: {1, 443}, {37435, 41864}
X(51723) = reflection of X(11108) in X(1125)
X(51723) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 24178, 3755}, {1125, 12577, 958}, {1125, 18250, 8167}, {1125, 21620, 3452}, {3600, 3616, 5436}, {3622, 5249, 12053}
X(51724) lies on these lines: {1, 329}, {4, 38316}, {10, 1001}, {30, 551}, {40, 47357}, {55, 9843}, {142, 15171}, {390, 11024}, {392, 40661}, {443, 497}, {516, 8726}, {519, 31435}, {958, 40270}, {960, 3244}, {993, 21625}, {1058, 5436}, {1210, 1621}, {2886, 19862}, {3158, 17559}, {3189, 3646}, {3485, 3636}, {3616, 4304}, {3622, 4311}, {3663, 41874}, {3671, 34489}, {3742, 31730}, {3746, 8582}, {3748, 21075}, {3817, 6849}, {3874, 5572}, {3986, 40963}, {4292, 4666}, {4294, 10582}, {4301, 30143}, {4342, 30147}, {4428, 6684}, {4847, 5259}, {5049, 50241}, {5084, 10389}, {5129, 6765}, {5248, 11019}, {5493, 5883}, {5791, 18530}, {5795, 6767}, {5837, 12433}, {5882, 10179}, {6259, 10246}, {6675, 24386}, {6700, 26105}, {6744, 12514}, {7682, 10267}, {9623, 12541}, {10164, 11248}, {10580, 31424}, {11235, 19883}, {12635, 51071}, {15170, 21627}, {15808, 28628}, {16411, 25440}, {16845, 24392}, {16854, 46916}, {18250, 43179}, {21620, 42819}, {24171, 29820}, {33771, 45204}, {34649, 51100}, {37423, 43166}, {38053, 41869}, {47742, 51073}
X(51724) = midpoint of X(i) and X(j) for these {i,j}: {1, 452}, {443, 41864}
X(51724) = reflection of X(i) in X(j) for these {i,j}: {10, 11108}, {443, 1125}
X(51724) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1001, 24389, 38059}, {4294, 10582, 12436}, {5129, 8236, 6765}
X(51725) lies on these lines: {1, 468}, {2, 47472}, {3, 47471}, {4, 47469}, {5, 47476}, {6, 47477}, {7, 47470}, {8, 47489}, {9, 47507}, {10, 37911}, {23, 3622}, {30, 551}, {145, 47490}, {186, 10595}, {403, 944}, {515, 37984}, {518, 47457}, {858, 3616}, {962, 44280}, {1125, 5159}, {1482, 44214}, {1483, 44282}, {1503, 11735}, {3109, 16272}, {3241, 47488}, {3242, 47455}, {3243, 47508}, {3244, 47492}, {3564, 11720}, {3625, 47537}, {3632, 47536}, {3633, 47533}, {3636, 37897}, {3655, 47332}, {3656, 47333}, {3679, 47493}, {3751, 47459}, {4663, 47460}, {4669, 47540}, {4677, 47535}, {5603, 10295}, {5690, 44452}, {5691, 10151}, {5886, 10297}, {7286, 34036}, {7426, 38314}, {7575, 10283}, {9624, 47339}, {9798, 37777}, {9956, 44911}, {10246, 11799}, {12512, 47114}, {12699, 47308}, {13464, 37934}, {13607, 37942}, {13869, 16309}, {15122, 38028}, {15808, 47629}, {16304, 47274}, {16322, 47273}, {16475, 47277}, {16491, 47279}, {16496, 47456}, {18323, 18493}, {18481, 47309}, {20070, 37941}, {22791, 47335}, {25055, 47097}, {30745, 46934}, {31162, 47031}, {32113, 38315}, {34641, 47538}, {34747, 47531}, {34773, 47336}, {37904, 51105}, {44246, 48661}, {47240, 50254}, {47310, 50811}, {47311, 51110}, {47334, 50824}, {47356, 47473}, {47358, 47545}, {47454, 49465}, {47494, 51093}, {47496, 51071}
X(51725) = midpoint of X(i) and X(j) for these {i,j}: {1, 468}, {2, 47472}, {3, 47471}, {4, 47469}, {5, 47476}, {6, 47477}, {7, 47470}, {8, 47489}, {9, 47507}, {10, 47491}, {145, 47490}, {551, 47495}, {3109, 16272}, {3241, 47488}, {3242, 47506}, {3243, 47508}, {3244, 47492}, {3625, 47537}, {3632, 47536}, {3633, 47533}, {3655, 47332}, {3656, 47333}, {3679, 47493}, {4669, 47540}, {4677, 47535}, {7426, 47593}, {12699, 47308}, {13869, 16309}, {16304, 47274}, {16322, 47273}, {18481, 47309}, {22791, 47335}, {31162, 47031}, {34641, 47538}, {34747, 47531}, {34773, 47336}, {47310, 50811}, {47334, 50824}, {47356, 47473}, {47358, 47545}, {47494, 51093}, {47496, 51071}
X(51725) = reflection of X(i) in X(j) for these {i,j}: {10, 37911}, {4663, 47460}, {5159, 1125}
X(51725) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3242, 47455, 47506}, {7426, 38314, 47593}
X(51726) lies on these lines: {6, 6059}, {19, 2175}, {25, 31}, {154, 7337}, {184, 1096}, {204, 1397}, {240, 7193}, {243, 1944}, {281, 2330}, {692, 14571}, {1118, 26888}, {1172, 1859}, {1430, 26884}, {1456, 1875}, {1857, 11429}, {1957, 3955}, {1974, 40987}, {2223, 8750}, {7076, 26890}, {19133, 36010}, {30456, 44087}, {34068, 36140}
X(51726) = isogonal conjugate of the isotomic conjugate of X(243)
X(51726) = polar conjugate of the isotomic conjugate of X(1951)
X(51726) = X(243)-Ceva conjugate of X(1951)
X(51726) = X(i)-isoconjugate of X(j) for these (i,j): {2, 40843}, {63, 1952}, {69, 1937}, {75, 296}, {76, 1949}, {304, 1945}, {307, 37142}, {525, 41206}, {1214, 35145}, {1231, 2249}, {24018, 41207}
X(51726) = X(i)-Dao conjugate of X(j) for these (i, j): (206, 296), (3162, 1952), (32664, 40843), (39032, 304), (39033, 76), (39035, 305), (39036, 561), (39037, 69)
X(51726) = crosspoint of X(1430) and X(2202)
X(51726) = crossdifference of every pair of points on line {307, 6332}
X(51726) = barycentric product X(i)*X(j) for these {i,j}: {1, 2202}, {4, 1951}, {6, 243}, {9, 1430}, {19, 1936}, {25, 1944}, {29, 42669}, {31, 1948}, {281, 26884}, {450, 7106}, {607, 5088}, {608, 7360}, {650, 23353}, {663, 1981}, {851, 1172}, {1096, 6518}, {1400, 15146}, {1949, 41500}, {2204, 44150}, {2299, 8680}, {4183, 51647}, {7016, 41368}, {7107, 41497}, {7108, 44096}, {17963, 41499}, {31623, 44112}
X(51726) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 1952}, {31, 40843}, {32, 296}, {243, 76}, {560, 1949}, {851, 1231}, {1430, 85}, {1936, 304}, {1944, 305}, {1948, 561}, {1951, 69}, {1973, 1937}, {1974, 1945}, {1981, 4572}, {2202, 75}, {2204, 37142}, {2299, 35145}, {15146, 28660}, {23353, 4554}, {26884, 348}, {32676, 41206}, {32713, 41207}, {42669, 307}, {44096, 1943}, {44112, 1214}
X(51727) lies on these lines: {3, 6}, {4, 50246}, {13, 42280}, {17, 42228}, {18, 43880}, {398, 35738}, {485, 42236}, {590, 3367}, {632, 42564}, {1588, 3392}, {1656, 36453}, {2041, 3412}, {2042, 42991}, {2044, 41101}, {2045, 36467}, {3068, 3391}, {3071, 3366}, {3091, 42247}, {3146, 42249}, {3411, 32788}, {6459, 42257}, {6561, 42238}, {7583, 42237}, {7585, 42256}, {8252, 42593}, {8960, 16267}, {9112, 44647}, {10654, 35731}, {11542, 42240}, {13886, 42218}, {14814, 32787}, {16808, 42243}, {16960, 42200}, {16962, 18585}, {16964, 35730}, {18586, 41108}, {19107, 42245}, {22615, 42182}, {22927, 33350}, {31412, 42188}, {31414, 41112}, {31487, 49947}, {34552, 43228}, {35740, 42117}, {35813, 41944}, {35823, 42993}, {36709, 41020}, {40693, 42282}, {41973, 42279}, {42157, 42230}, {42173, 43014}, {42180, 42269}, {42185, 42895}, {42201, 42896}, {42210, 42630}, {42212, 42273}, {42214, 42271}, {42215, 42235}, {42231, 43776}, {42233, 42779}, {42234, 42432}, {42251, 43879}, {42278, 42992}, {43376, 49825}
X(51727) = isogonal conjugate of X(50245)
X(51727) = X(1)-isoconjugate of X(50245)
X(51727) = barycentric quotient X(6)/X(50245)
X(51727) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 6419, 62}, {6, 3389, 3365}, {15, 371, 3364}, {61, 62, 3364}, {61, 3389, 62}, {61, 5238, 372}, {62, 35739, 22238}, {1151, 11485, 3390}, {3068, 42255, 3391}, {6425, 22236, 3}, {16964, 35730, 42281}
X(51728) lies on these lines: {2, 42195}, {3, 6}, {4, 50245}, {13, 6561}, {14, 590}, {17, 3071}, {18, 5418}, {20, 42197}, {140, 42170}, {203, 2066}, {303, 35741}, {395, 35255}, {396, 42215}, {398, 8981}, {485, 16964}, {550, 42168}, {615, 16241}, {1328, 49907}, {1587, 42150}, {1588, 42152}, {2041, 19106}, {2042, 33416}, {2044, 16809}, {2046, 16966}, {2067, 7005}, {3068, 10654}, {3070, 42157}, {3200, 9676}, {3206, 9677}, {3366, 18581}, {3367, 18582}, {3391, 19107}, {3392, 32790}, {3411, 9680}, {5318, 42225}, {5321, 18538}, {5334, 8972}, {5335, 42255}, {5339, 8976}, {6306, 32552}, {6459, 40693}, {6560, 36967}, {6564, 36970}, {6565, 37832}, {7583, 42147}, {7584, 16772}, {8252, 36453}, {8253, 37835}, {8960, 41973}, {9540, 40694}, {9541, 10653}, {9681, 42990}, {10576, 42175}, {10577, 42936}, {10819, 36209}, {11488, 23273}, {13665, 42154}, {13785, 16644}, {13846, 41108}, {13951, 43238}, {13966, 42945}, {14241, 36446}, {14813, 16967}, {14814, 42100}, {16645, 35734}, {16808, 18585}, {16960, 42230}, {16961, 42199}, {16965, 42222}, {18586, 42914}, {18762, 23302}, {19054, 42511}, {22891, 35851}, {23249, 42085}, {23251, 42204}, {23261, 42206}, {23263, 42921}, {23267, 42119}, {23269, 43770}, {23303, 34551}, {31412, 42160}, {31454, 42991}, {32786, 42092}, {32787, 41101}, {35730, 43792}, {35732, 42111}, {35740, 42146}, {35815, 42934}, {35820, 43632}, {35821, 42813}, {35823, 41943}, {36208, 49216}, {36449, 41100}, {36468, 42532}, {36470, 42975}, {36969, 42263}, {37641, 43509}, {41112, 43257}, {42086, 42196}, {42087, 42226}, {42090, 42256}, {42099, 42172}, {42101, 42182}, {42102, 42180}, {42112, 42189}, {42113, 42282}, {42114, 42187}, {42121, 42167}, {42123, 42169}, {42124, 42562}, {42133, 42190}, {42134, 42188}, {42144, 42240}, {42151, 42638}, {42158, 42173}, {42161, 43408}, {42177, 42266}, {42178, 42919}, {42179, 42186}, {42181, 42184}, {42192, 42209}, {42194, 42207}, {42216, 42942}, {42243, 42630}, {42251, 42895}, {42259, 42434}, {42262, 42488}, {42265, 42814}, {42270, 42581}, {42279, 42918}, {42417, 42506}, {42930, 43315}, {42935, 43339}, {42998, 43512}
X(51728) = isogonal conjugate of X(50246)
X(51728) = Schoutte-circle-inverse of X(3389)}
X(51728) = X(1)-isoconjugate of X(50246)
X(51728) = barycentric quotient X(6)/X(50246)
X(51728) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 3364, 3390}, {3, 6200, 10645}, {3, 42115, 6412}, {6, 6200, 16}, {6, 11480, 6398}, {15, 16, 3389}, {15, 3364, 16}, {15, 10646, 6200}, {15, 35739, 11480}, {61, 371, 3389}, {372, 11481, 16}, {2046, 42174, 16966}, {3311, 22236, 3365}, {6199, 11485, 6}, {6200, 10645, 3389}, {6412, 42115, 3365}, {32785, 42198, 3366}, {32790, 42221, 3392}, {34755, 35739, 6398}, {36446, 42589, 14241}
X(51729) lies on these lines: {6, 21}, {30, 182}, {69, 15674}, {141, 5138}, {191, 16475}, {193, 15676}, {442, 3589}, {511, 5428}, {518, 35016}, {524, 15670}, {542, 44257}, {575, 31649}, {576, 12104}, {599, 15671}, {758, 1386}, {1350, 21161}, {1351, 28443}, {1428, 3649}, {1469, 5427}, {1503, 6841}, {1992, 15672}, {2194, 6703}, {2330, 10543}, {2475, 3618}, {2771, 6593}, {2795, 5026}, {2854, 16164}, {3564, 10021}, {3651, 5085}, {3751, 5426}, {3818, 46028}, {3827, 8261}, {4265, 27086}, {5050, 13743}, {5097, 28463}, {5320, 5743}, {5499, 38110}, {5846, 19133}, {6175, 47352}, {7193, 17045}, {8550, 16617}, {8584, 15673}, {9021, 39772}, {9024, 35204}, {10541, 33557}, {11263, 38049}, {12017, 16117}, {14561, 37230}, {15534, 15675}, {15678, 51185}, {15680, 51171}, {16126, 16491}, {16160, 48906}, {17768, 51150}, {20423, 28460}, {24471, 41547}, {25406, 37433}, {26543, 27083}, {29012, 44258}, {29181, 44238}, {31254, 47355}, {31650, 48876}, {33858, 38029}, {34195, 38315}, {34380, 44254}, {36740, 37308}, {36741, 37286}, {38035, 49177}, {38047, 47033}, {44669, 47373}
X(51729) = midpoint of X(i) and X(j) for these {i,j}: {6, 21}, {16160, 48906}, {20423, 28460}
X(51729) = reflection of X(i) in X(j) for these {i,j}: {141, 6675}, {442, 3589}, {3818, 46028}
X(51730) lies on these lines: {6, 24}, {25, 11746}, {26, 17710}, {30, 182}, {141, 16238}, {156, 32165}, {184, 12007}, {186, 44439}, {206, 8550}, {235, 1503}, {389, 41593}, {511, 37814}, {518, 51694}, {524, 44211}, {542, 44270}, {569, 6329}, {575, 9969}, {1147, 3629}, {1177, 3426}, {1192, 46374}, {1350, 15078}, {1351, 15040}, {1353, 44490}, {1495, 15580}, {2781, 44269}, {2854, 20771}, {3003, 37813}, {3060, 27866}, {3098, 43615}, {3200, 51208}, {3201, 51209}, {3517, 34777}, {3518, 9973}, {3532, 34778}, {3564, 33563}, {3589, 11585}, {3618, 37444}, {3818, 44235}, {5012, 17810}, {5026, 39811}, {5050, 7517}, {5085, 11413}, {5102, 34148}, {5622, 36990}, {6467, 15582}, {6593, 19138}, {6776, 18374}, {7506, 41579}, {8547, 51519}, {9019, 44259}, {10110, 50664}, {10282, 32366}, {11245, 44078}, {11579, 48662}, {12106, 41714}, {12283, 19596}, {12294, 15578}, {12893, 34155}, {13567, 41729}, {14491, 19151}, {14561, 18404}, {14853, 35471}, {15139, 37643}, {16196, 19126}, {19118, 34117}, {19142, 19149}, {19161, 44102}, {20300, 45179}, {23042, 44489}, {28343, 40825}, {29012, 44271}, {29181, 44240}, {31180, 47352}, {31282, 47355}, {31304, 51171}, {31725, 46264}, {32046, 39561}, {35228, 50649}, {36989, 41613}, {38110, 44491}, {38317, 49673}, {44247, 48881}
X(51730) = midpoint of X(i) and X(j) for these {i,j}: {6, 24}, {31725, 46264}
X(51730) = reflection of X(i) in X(j) for these {i,j}: {141, 16238}, {3098, 43615}, {3818, 44235}, {11585, 3589}, {48881, 44247}
X(51730) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {182, 19136, 5480}, {182, 19154, 19127}, {19121, 43815, 5085}
X(51731) lies on these lines: {6, 27}, {30, 182}, {141, 6678}, {440, 3589}, {518, 51697}, {1350, 21162}, {1503, 15762}, {3151, 3618}, {5085, 30266}, {7683, 23583}, {8680, 49481}, {24256, 46182}, {29181, 44243}, {31153, 47352}, {31256, 47355}, {31292, 51171}
X(51731) = midpoint of X(6) and X(27)
X(51731) = reflection of X(i) in X(j) for these {i,j}: {141, 6678}, {440, 3589}
X(51732) lies on these lines: {2, 1353}, {3, 51171}, {5, 3618}, {6, 140}, {30, 182}, {69, 632}, {125, 37649}, {141, 16239}, {143, 11574}, {156, 19137}, {184, 10128}, {193, 3526}, {206, 23411}, {376, 50987}, {468, 15018}, {511, 3530}, {518, 51700}, {524, 10124}, {542, 10109}, {546, 14561}, {547, 1352}, {548, 5085}, {549, 1351}, {550, 12017}, {569, 9825}, {575, 3564}, {576, 12108}, {599, 47598}, {631, 5093}, {1350, 12100}, {1386, 5844}, {1503, 3850}, {1570, 14138}, {1595, 19118}, {1656, 14912}, {1843, 15026}, {1992, 11539}, {2330, 15172}, {2854, 13392}, {3090, 33748}, {3313, 14449}, {3523, 44456}, {3525, 51170}, {3533, 20080}, {3545, 48662}, {3620, 46219}, {3627, 25406}, {3629, 22234}, {3751, 38028}, {3815, 39764}, {3818, 12811}, {3851, 39874}, {3853, 38136}, {3860, 48889}, {3861, 19130}, {5032, 15694}, {5034, 5305}, {5052, 40108}, {5055, 5921}, {5066, 11179}, {5092, 33923}, {5095, 34128}, {5097, 10168}, {5159, 14389}, {5422, 6676}, {5462, 44277}, {5477, 34127}, {5640, 37897}, {5644, 6353}, {5663, 32300}, {5690, 16475}, {5901, 38049}, {5943, 15448}, {5946, 9967}, {5965, 34573}, {6403, 37935}, {6642, 18919}, {6677, 10601}, {6756, 13353}, {7499, 34545}, {7508, 36741}, {7542, 15047}, {7605, 46818}, {7734, 43650}, {7792, 10011}, {8359, 11842}, {8550, 18358}, {8584, 11540}, {8703, 14848}, {8705, 44264}, {9306, 13361}, {9822, 32205}, {10096, 47453}, {10169, 15577}, {10257, 47461}, {10516, 12812}, {10519, 11482}, {10541, 12103}, {10592, 39901}, {10593, 39900}, {11231, 51196}, {11245, 11548}, {11451, 12283}, {11465, 12272}, {11645, 51138}, {11695, 34382}, {12101, 38072}, {12102, 29012}, {12362, 19129}, {13383, 44503}, {13394, 47316}, {13413, 20300}, {13434, 31829}, {13562, 43588}, {13910, 44657}, {13972, 44656}, {14683, 37990}, {14805, 37934}, {14810, 14891}, {14892, 47353}, {14893, 43273}, {14927, 15687}, {15019, 47582}, {15043, 18438}, {15045, 16976}, {15080, 37910}, {15118, 32423}, {15122, 47459}, {15583, 23042}, {15683, 51173}, {15691, 48872}, {15699, 40330}, {15700, 51028}, {15702, 50962}, {15703, 50974}, {15712, 33878}, {15718, 51172}, {15721, 50981}, {15759, 41153}, {16619, 47456}, {16989, 37451}, {18357, 38167}, {18538, 49229}, {18762, 49228}, {18914, 21637}, {19121, 37471}, {19697, 32448}, {19924, 50972}, {20190, 29181}, {20423, 34200}, {20582, 41984}, {21167, 37517}, {21356, 50986}, {21841, 39588}, {23300, 50138}, {23336, 44480}, {25338, 47455}, {26206, 36753}, {31831, 36153}, {31833, 43815}, {32113, 44234}, {32455, 40107}, {34126, 51198}, {34417, 47630}, {34507, 51126}, {35255, 35841}, {35256, 35840}, {35283, 44109}, {35404, 50963}, {37119, 46444}, {37648, 37911}, {37942, 39871}, {38071, 51537}, {38111, 51190}, {38112, 51192}, {38113, 51194}, {39893, 42583}, {39894, 42582}, {41257, 44288}, {41988, 51022}, {43102, 51208}, {43103, 51209}, {44452, 47277}, {44900, 47451}, {46031, 47474}, {47355, 48154}
X(51732) = midpoint of X(i) and X(j) for these {i,j}: {6, 140}, {143, 11574}, {182, 18583}, {546, 48906}, {547, 50979}, {548, 21850}, {575, 3589}, {3313, 14449}, {3853, 46264}, {5066, 11179}, {8550, 18358}, {12007, 24206}, {12103, 31670}, {13562, 43588}, {14893, 43273}, {18357, 39870}, {20423, 34200}, {25555, 50664}, {32455, 40107}
X(51732) = reflection of X(i) in X(j) for these {i,j}: {141, 16239}, {3628, 3589}, {3818, 12811}, {3861, 19130}, {9822, 32205}, {11812, 10168}, {14891, 50983}, {18358, 35018}, {33923, 5092}, {51022, 41988}
X(51732) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 38110, 140}, {182, 597, 18583}, {182, 5476, 44882}, {575, 24206, 12007}, {3090, 33748, 39899}, {3589, 12007, 24206}, {3618, 5050, 5}, {5032, 15694, 50978}, {5085, 21850, 548}, {5476, 48904, 5480}, {5480, 44882, 48904}, {8550, 38317, 18358}, {8981, 13966, 31401}, {11179, 38079, 5066}, {12017, 14853, 550}, {14561, 48906, 546}, {18358, 38317, 35018}, {38136, 46264, 3853}, {38167, 39870, 18357}, {47352, 50979, 547}
X(51733) lies on these lines: {6, 186}, {23, 3796}, {24, 12061}, {30, 182}, {51, 37969}, {54, 47280}, {110, 44569}, {141, 44452}, {154, 37962}, {184, 468}, {206, 37942}, {403, 1503}, {511, 15646}, {518, 51701}, {524, 15462}, {542, 44282}, {567, 44265}, {575, 5946}, {576, 18571}, {578, 37934}, {858, 37649}, {1092, 47546}, {1176, 47096}, {1177, 10293}, {1316, 30540}, {1350, 37941}, {1351, 37955}, {1353, 16532}, {1495, 12099}, {1974, 10151}, {2030, 28343}, {2070, 5050}, {2071, 5085}, {2072, 3589}, {2330, 10149}, {2393, 44272}, {2781, 21663}, {2854, 51393}, {3098, 37968}, {3153, 3618}, {3564, 44234}, {3629, 16531}, {3818, 46031}, {5012, 7426}, {5054, 37283}, {5092, 34152}, {5157, 47090}, {6593, 13754}, {6776, 37943}, {7464, 10541}, {8549, 37777}, {8584, 18579}, {9777, 21284}, {9969, 37936}, {10110, 37967}, {10169, 37458}, {10257, 19131}, {10295, 15033}, {10540, 11579}, {10601, 37980}, {10602, 15577}, {10605, 34117}, {11003, 37907}, {11477, 37952}, {11563, 48906}, {11645, 44872}, {11745, 13353}, {12007, 32113}, {12017, 18859}, {13198, 15448}, {13352, 47333}, {13473, 19124}, {13619, 14853}, {14561, 18403}, {14912, 47450}, {15118, 18400}, {15122, 44491}, {15350, 18358}, {15873, 16619}, {16308, 37930}, {16311, 36178}, {16386, 19121}, {16976, 19126}, {18572, 25555}, {19118, 44883}, {19137, 44912}, {19138, 44665}, {19142, 32344}, {20190, 37950}, {21639, 44668}, {23324, 37984}, {23332, 44077}, {29012, 44283}, {29181, 44246}, {31726, 46264}, {32233, 50435}, {32449, 47583}, {32599, 50461}, {34397, 47296}, {37814, 40929}, {37827, 39522}, {37931, 47459}, {37938, 38110}, {37991, 39560}, {43650, 47097}, {44470, 47549}, {44489, 47464}, {44503, 45171}, {47571, 48881}
X(51733) = midpoint of X(i) and X(j) for these {i,j}: {6, 186}, {5622, 18374}, {10540, 11579}, {11563, 48906}, {14912, 47450}, {31726, 46264}, {32233, 50435}, {32599, 50461}
X(51733) = reflection of X(i) in X(j) for these {i,j}: {141, 44452}, {2072, 3589}, {3098, 37968}, {3818, 46031}, {18358, 15350}, {34152, 5092}, {37942, 47454}, {47569, 16531}
X(51733) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {182, 19154, 44882}, {575, 7575, 15826}, {5622, 19128, 18374}, {19127, 47544, 32217}, {19154, 47581, 32217}
X(51734) lies on these lines: {6, 235}, {24, 14853}, {30, 182}, {428, 13198}, {468, 44439}, {511, 16238}, {518, 51702}, {1503, 44226}, {3089, 34777}, {3564, 44235}, {3589, 16196}, {3618, 11413}, {5050, 31725}, {5972, 21849}, {9969, 11808}, {11430, 11745}, {11585, 14561}, {12241, 41593}, {15078, 51212}, {16252, 32366}, {18390, 41729}, {19360, 23300}, {20423, 44211}, {21850, 37814}, {29181, 44247}, {31670, 44240}, {41714, 44233}, {44271, 48906}, {44493, 49673}
X(51734) = midpoint of X(i) and X(j) for these {i,j}: {6, 235}, {20423, 44211}, {21850, 37814}, {31670, 44240}, {44271, 48906}
X(51734) = reflection of X(16196) in X(3589)
X(51735) lies on these lines: {6, 160}, {30, 182}, {53, 460}, {98, 32716}, {110, 22329}, {184, 5306}, {230, 9418}, {511, 34990}, {512, 2030}, {518, 51703}, {524, 36213}, {1084, 1692}, {1495, 6784}, {1503, 7668}, {1513, 15920}, {1576, 1691}, {1976, 1989}, {2086, 14567}, {2871, 3003}, {3589, 3613}, {3618, 14957}, {5085, 47620}, {5118, 27088}, {5305, 40643}, {5651, 11168}, {6530, 19128}, {9306, 13468}, {11081, 44122}, {11086, 44083}, {13240, 34098}, {16308, 44114}, {19153, 21177}, {32738, 32741}, {36189, 47455}, {37809, 50672}, {39176, 44102}, {39560, 45900}, {46518, 51171}
X(51735) = midpoint of X(6) and X(237)
X(51735) = reflection of X(21531) in X(3589)
X(51735) = crossdifference of every pair of points on line {599, 23878}
X(51736) lies on these lines: {6, 297}, {30, 182}, {141, 44334}, {216, 441}, {287, 37765}, {401, 3618}, {468, 44114}, {511, 23583}, {518, 51704}, {524, 3163}, {525, 2492}, {599, 44576}, {1503, 39569}, {1992, 44579}, {2393, 46097}, {5085, 44252}, {7473, 47455}, {7829, 10110}, {14561, 44231}, {14853, 35474}, {15014, 30227}, {18487, 41145}, {24256, 44340}, {29181, 44248}, {34360, 44650}, {38049, 51711}, {40853, 51171}, {40884, 47352}, {44335, 51126}, {44342, 50609}, {44346, 48310}
X(51736) = midpoint of X(i) and X(j) for these {i,j}: {6, 297}, {18487, 41145}
X(51736) = reflection of X(i) in X(j) for these {i,j}: {141, 44334}, {441, 3589}
X(51737) lies on these lines: {2, 154}, {3, 524}, {4, 10541}, {5, 10168}, {6, 376}, {23, 20192}, {30, 182}, {40, 47356}, {69, 15692}, {74, 34319}, {98, 11168}, {140, 11178}, {141, 542}, {184, 43957}, {186, 41585}, {353, 5913}, {381, 3589}, {428, 19124}, {511, 8584}, {518, 51705}, {541, 6593}, {543, 14688}, {547, 3818}, {548, 576}, {550, 575}, {599, 3524}, {631, 11180}, {632, 18553}, {1003, 35423}, {1176, 11744}, {1350, 1992}, {1351, 15688}, {1352, 5054}, {1353, 14810}, {1386, 28194}, {1428, 3058}, {1513, 9774}, {1691, 5306}, {2030, 15048}, {2330, 5434}, {2393, 16836}, {2781, 15303}, {2883, 10984}, {3054, 11646}, {3098, 3629}, {3313, 14831}, {3522, 5032}, {3523, 15069}, {3530, 34507}, {3534, 5050}, {3543, 3618}, {3545, 36990}, {3549, 43592}, {3564, 12100}, {3576, 47358}, {3619, 15721}, {3627, 25555}, {3630, 14891}, {3631, 15700}, {3654, 5846}, {3655, 9041}, {3656, 38029}, {3763, 15702}, {3830, 14561}, {3839, 14927}, {3844, 38068}, {3845, 29012}, {3867, 7576}, {5033, 5309}, {5066, 38317}, {5071, 47355}, {5093, 15695}, {5097, 33751}, {5102, 33748}, {5135, 37428}, {5157, 15583}, {5158, 44248}, {5182, 8356}, {5254, 39560}, {5473, 22580}, {5474, 22579}, {5477, 8589}, {5621, 35921}, {5640, 47313}, {5642, 30739}, {5648, 15035}, {5655, 15462}, {5657, 50783}, {5892, 16776}, {5894, 34117}, {5921, 15708}, {5965, 15711}, {5969, 13354}, {6054, 37450}, {6055, 9830}, {6329, 14848}, {6644, 35707}, {6661, 34624}, {6749, 35474}, {7395, 44762}, {7426, 15080}, {7495, 9140}, {7496, 9143}, {7503, 15579}, {7540, 37471}, {7558, 16254}, {7606, 20112}, {7739, 40825}, {7967, 50790}, {8359, 37479}, {8370, 12203}, {8541, 37931}, {8593, 34473}, {8598, 22486}, {8705, 40280}, {8721, 33237}, {9019, 9730}, {9300, 50659}, {9530, 28343}, {9607, 44251}, {9744, 22110}, {9760, 33474}, {9762, 33475}, {9968, 15105}, {9971, 15045}, {10124, 18358}, {10164, 50781}, {10519, 15533}, {10606, 41719}, {10645, 51203}, {10646, 51200}, {10989, 14389}, {10991, 15810}, {11001, 14853}, {11003, 40112}, {11160, 15705}, {11177, 37455}, {11424, 34614}, {11539, 24206}, {11579, 37283}, {11623, 16509}, {11745, 34726}, {11812, 51137}, {11898, 15706}, {12041, 25329}, {12054, 37345}, {12177, 14830}, {12215, 37671}, {13567, 22352}, {13634, 17330}, {13635, 17392}, {13910, 35822}, {13972, 35823}, {14093, 32455}, {14677, 25556}, {14694, 32525}, {14893, 48884}, {14912, 15534}, {15018, 37901}, {15055, 41720}, {15074, 40929}, {15078, 35228}, {15311, 19153}, {15448, 47597}, {15471, 35485}, {15516, 48885}, {15578, 41729}, {15582, 17928}, {15682, 51164}, {15683, 48910}, {15685, 41153}, {15686, 21850}, {15687, 19130}, {15689, 48873}, {15690, 39561}, {15691, 48880}, {15693, 50955}, {15694, 18440}, {15697, 50976}, {15699, 25561}, {15701, 50958}, {15703, 51127}, {15709, 40330}, {15712, 40107}, {15713, 50988}, {15715, 40341}, {15716, 50961}, {15719, 50993}, {15759, 34380}, {15826, 47335}, {16226, 32191}, {17504, 48876}, {18382, 41256}, {18579, 34513}, {18800, 21163}, {18911, 44569}, {19133, 34618}, {19709, 50960}, {19710, 29317}, {19711, 50980}, {20791, 44280}, {22234, 44245}, {22489, 41019}, {23292, 31152}, {25565, 38071}, {26316, 37461}, {28204, 49524}, {28538, 39870}, {29323, 33699}, {31133, 37649}, {31162, 38023}, {32267, 44212}, {32274, 45311}, {33532, 37827}, {33749, 46853}, {34417, 47312}, {34613, 43651}, {34627, 38087}, {34648, 38089}, {34774, 44883}, {34782, 37515}, {35268, 37904}, {35303, 51012}, {35304, 51015}, {35404, 48895}, {36757, 41100}, {36758, 41101}, {37351, 41043}, {37352, 41042}, {37470, 47333}, {37513, 44218}, {38035, 50865}, {38115, 51195}, {38116, 50798}, {38118, 50796}, {38144, 50864}, {38146, 50862}, {40248, 44401}, {41149, 50962}, {41624, 47619}, {42528, 51206}, {42529, 51207}, {44268, 44668}, {44580, 51141}, {44820, 45336}, {44903, 48891}, {46475, 49737}, {47359, 50811}, {50805, 51145}, {50808, 51005}, {50810, 51000}, {50821, 50949}, {50824, 50998}, {50828, 51003}, {50871, 50953}, {50956, 51025}, {50963, 51026}, {50990, 51215}, {51120, 51153}, {51178, 51188}, {51179, 51187}
X(51737) = midpoint of X(i) and X(j) for these {i,j}: {2, 43273}, {3, 11179}, {6, 376}, {40, 47356}, {74, 34319}, {381, 46264}, {549, 48906}, {597, 44882}, {599, 6776}, {1350, 1992}, {3313, 14831}, {3534, 20423}, {3543, 48905}, {5085, 25406}, {5473, 22580}, {5474, 22579}, {8584, 50965}, {8703, 50979}, {9140, 32233}, {9143, 16010}, {10606, 41719}, {11001, 51024}, {12177, 14830}, {14912, 31884}, {15533, 50974}, {15534, 50967}, {15681, 31670}, {15683, 48910}, {15686, 21850}, {22165, 51136}, {41149, 50970}, {47359, 50811}, {50808, 51005}, {50810, 51000}, {50975, 51185}, {50993, 51176}, {51178, 51188}, {51179, 51187}
X(51737) = reflection of X(i) in X(j) for these {i,j}: {2, 50983}, {5, 10168}, {141, 549}, {381, 3589}, {549, 5092}, {597, 182}, {1351, 20583}, {1352, 20582}, {1992, 12007}, {3098, 34200}, {3534, 50971}, {3656, 51006}, {3818, 547}, {3830, 50959}, {5480, 597}, {8550, 11179}, {8584, 50979}, {10168, 20190}, {11178, 140}, {15533, 50982}, {15686, 48892}, {15687, 19130}, {16776, 5892}, {18358, 10124}, {19130, 46267}, {20112, 7606}, {21167, 17508}, {22165, 50977}, {32274, 45311}, {35404, 48895}, {39884, 25561}, {44903, 48891}, {45336, 44820}, {47354, 2}, {48880, 15691}, {48881, 376}, {48884, 14893}, {48889, 25565}, {50798, 50951}, {50805, 51145}, {50949, 50821}, {50955, 50991}, {50958, 51143}, {50962, 41149}, {50965, 8703}, {50977, 12100}, {50991, 50984}, {50998, 50824}, {51003, 50828}, {51022, 3845}, {51130, 41153}, {51132, 8584}, {51142, 50980}, {51143, 51139}
X(51737) = complement of X(47353)
X(51737) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 5085, 50983}, {2, 6800, 35266}, {2, 25406, 43273}, {2, 51023, 10516}, {5, 10168, 48310}, {182, 44882, 5480}, {182, 48898, 18583}, {381, 12017, 38064}, {381, 38064, 3589}, {631, 11180, 21358}, {1352, 5054, 20582}, {1992, 10304, 1350}, {3524, 6776, 599}, {3534, 5050, 20423}, {3543, 3618, 38072}, {3656, 38029, 51006}, {3830, 14561, 50959}, {3845, 50987, 38110}, {5085, 43273, 2}, {5092, 48906, 141}, {5097, 33751, 48874}, {6055, 37451, 15597}, {10519, 15533, 50982}, {10519, 50974, 15533}, {11001, 14853, 51024}, {12017, 46264, 3589}, {12100, 50977, 21167}, {14848, 15681, 31670}, {14853, 50975, 11001}, {14912, 19708, 50967}, {14912, 33750, 31884}, {14912, 50967, 15534}, {15534, 31884, 50967}, {15687, 38079, 19130}, {15690, 39561, 51166}, {15698, 50974, 10519}, {15699, 39884, 25561}, {17508, 50977, 12100}, {18583, 48898, 51163}, {18583, 51163, 5480}, {18911, 47596, 44569}, {19130, 46267, 38079}, {19708, 50967, 31884}, {21167, 22165, 50977}, {21167, 51136, 22165}, {25565, 48889, 38071}, {33750, 50967, 19708}, {38064, 46264, 381}, {38072, 48905, 3543}, {38116, 50798, 50951}, {43273, 50983, 47354}, {44882, 51163, 48898}, {48892, 50664, 21850}, {50965, 50979, 51132}, {50971, 51138, 20423}, {51024, 51185, 14853}, {51159, 51160, 141}
X(51738) lies on these lines: {6, 377}, {10, 141}, {30, 182}, {69, 50237}, {193, 50794}, {405, 3589}, {511, 44222}, {524, 44217}, {599, 50793}, {1386, 48847}, {1503, 44229}, {3618, 6872}, {3629, 50238}, {3763, 50393}, {3867, 37398}, {4265, 36003}, {5256, 50201}, {6329, 50239}, {6703, 16353}, {7469, 13394}, {8584, 50396}, {13728, 38047}, {14561, 37234}, {16056, 22769}, {29012, 44286}, {29181, 37426}, {30810, 38186}, {31156, 47352}, {31259, 47355}, {31295, 51171}, {32455, 50713}, {34573, 50207}, {48310, 50202}, {50205, 51126}, {50394, 51128}, {50795, 51127}
X(51738) = midpoint of X(6) and X(377)
X(51738) = reflection of X(i) in X(j) for these {i,j}: {141, 8728}, {405, 3589}
X(51739) lies on these lines: {3, 9019}, {4, 18374}, {6, 74}, {22, 5085}, {30, 182}, {110, 47353}, {184, 427}, {185, 15579}, {186, 9971}, {381, 15462}, {511, 18570}, {518, 51707}, {524, 13352}, {542, 44287}, {550, 44491}, {567, 11179}, {575, 40647}, {576, 7689}, {578, 6247}, {599, 43574}, {1176, 48905}, {1351, 32608}, {1352, 22115}, {1576, 32444}, {1593, 34117}, {1597, 19153}, {1691, 6785}, {1843, 35228}, {1995, 16165}, {2393, 11430}, {3431, 12367}, {3520, 37473}, {3541, 34118}, {3564, 44236}, {3589, 15760}, {3618, 44440}, {3818, 10272}, {3851, 43811}, {5012, 31133}, {5034, 19220}, {5092, 5892}, {5094, 32274}, {5157, 44239}, {5169, 32233}, {5943, 44260}, {6403, 37970}, {6593, 31861}, {6644, 16776}, {7391, 25406}, {7526, 44469}, {7527, 22151}, {7699, 14157}, {8262, 18580}, {8541, 44281}, {8549, 11425}, {8705, 39242}, {9306, 47354}, {9544, 51023}, {9703, 18440}, {9818, 44754}, {10110, 20190}, {10168, 44262}, {10516, 31236}, {10541, 12082}, {11003, 31105}, {11422, 16010}, {11424, 13568}, {11427, 34944}, {11464, 19596}, {11745, 13336}, {12017, 12083}, {12038, 43130}, {12084, 44480}, {13367, 15582}, {13482, 15534}, {13630, 44494}, {14156, 24206}, {14853, 35481}, {15069, 34148}, {15578, 19161}, {15581, 19357}, {15872, 44679}, {15873, 16618}, {16387, 37648}, {18388, 36201}, {18475, 35707}, {19121, 48910}, {19126, 48881}, {19128, 35480}, {19129, 31670}, {19130, 44263}, {19131, 29181}, {21639, 50649}, {29012, 44288}, {29959, 51394}, {31723, 46264}, {34417, 37969}, {38317, 46029}, {39588, 44269}, {43650, 44210}
X(51739) = midpoint of X(i) and X(j) for these {i,j}: {6, 378}, {31133, 43273}, {31723, 46264}
X(51739) = reflection of X(i) in X(j) for these {i,j}: {3818, 39504}, {7502, 5092}, {15760, 3589}, {19127, 182}, {35707, 18475}, {44210, 50983}, {44262, 10168}, {44263, 19130}
X(51739) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 5621, 5890}, {182, 48901, 19154}, {5622, 15033, 6}
X(51740) lies on these lines: {6, 401}, {30, 182}, {95, 34573}, {141, 441}, {287, 524}, {297, 3589}, {518, 51711}, {599, 44575}, {1503, 1576}, {3618, 40853}, {3763, 43980}, {4048, 15013}, {5031, 46184}, {5085, 35474}, {7473, 8705}, {13196, 25327}, {20021, 23200}, {20582, 44578}, {23583, 29012}, {26206, 44329}, {29181, 44252}, {40885, 47352}, {44216, 48310}, {44334, 51126}, {44335, 51128}
X(51740) = midpoint of X(6) and X(401)
X(51740) = reflection of X(i) in X(j) for these {i,j}: {141, 441}, {297, 3589}
X(51741) lies on these lines: {6, 402}, {30, 182}, {69, 15183}, {518, 51712}, {1351, 26451}, {1386, 11910}, {1650, 3618}, {3589, 15184}, {3751, 11831}, {4240, 51171}, {5050, 11251}, {5182, 13179}, {5622, 12369}, {6776, 11897}, {9033, 32300}, {11049, 47352}, {11832, 19118}, {12017, 35241}, {12113, 14853}, {12438, 16475}, {14912, 39886}, {16190, 51212}, {16210, 51192}, {34582, 51185}
X(51741) = midpoint of X(6) and X(402)
X(51741) = reflection of X(15184) in X(3589)
X(51742) lies on these lines: {4, 47458}, {5, 47549}, {6, 403}, {30, 182}, {51, 468}, {141, 44911}, {186, 14853}, {460, 18121}, {511, 14156}, {518, 51713}, {575, 47336}, {858, 10601}, {1503, 10151}, {1596, 10169}, {1899, 34117}, {2071, 3618}, {2072, 14561}, {2781, 16227}, {2854, 51425}, {3564, 34155}, {3589, 10257}, {5050, 31726}, {5085, 16386}, {5892, 15122}, {6000, 15118}, {6593, 44665}, {7426, 17810}, {8550, 18390}, {8705, 37971}, {9969, 11649}, {10110, 16619}, {11427, 37962}, {12007, 47461}, {12061, 21841}, {12828, 47296}, {14845, 25488}, {15350, 34380}, {15471, 32274}, {15577, 37951}, {15646, 21850}, {15826, 15873}, {16238, 40929}, {16306, 36183}, {16387, 37649}, {18382, 19118}, {19130, 23323}, {20423, 44214}, {31670, 44246}, {32113, 37943}, {34152, 38110}, {37931, 47456}, {37935, 47454}, {37941, 51212}, {44234, 47569}, {44282, 47556}, {44283, 48906}, {47114, 48881}
X(51742) = midpoint of X(i) and X(j) for these {i,j}: {6, 403}, {10257, 47571}, {14853, 47455}, {15646, 21850}, {20423, 44214}, {31670, 44246}, {44283, 48906}
X(51742) = reflection of X(i) in X(j) for these {i,j}: {141, 44911}, {10257, 3589}, {23323, 19130}, {37935, 47454}, {47556, 44282}, {47569, 44234}, {48881, 47114}
X(51742) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5476, 19136, 5480}, {19136, 47457, 47544}, {37984, 47460, 8550}, {47461, 47474, 12007}
X(51743) lies on these lines: {1, 6}, {30, 182}, {58, 16299}, {69, 17201}, {141, 50205}, {193, 50398}, {377, 3618}, {379, 38186}, {524, 50202}, {583, 13723}, {584, 1009}, {599, 50714}, {940, 50715}, {964, 19133}, {1428, 10404}, {1974, 37398}, {3416, 5278}, {3589, 5138}, {3740, 37060}, {3763, 50795}, {3844, 19732}, {4245, 22769}, {4383, 16353}, {4682, 19725}, {5047, 41610}, {5050, 37234}, {5085, 37426}, {5248, 22277}, {5640, 7469}, {6329, 50241}, {6872, 51171}, {11346, 47359}, {11357, 51003}, {14561, 44229}, {19723, 28538}, {19738, 38023}, {19742, 51192}, {20835, 36741}, {27632, 50717}, {36740, 37282}, {37492, 50204}, {38049, 51706}, {38064, 44284}, {38110, 44222}, {38136, 44286}, {44217, 47352}, {47355, 50207}, {47373, 48866}, {48310, 50395}, {48863, 49524}, {50394, 51126}
X(51743) = midpoint of X(6) and X(405)
X(51743) = reflection of X(i) in X(j) for these {i,j}: {141, 50205}, {8728, 3589}
X(51744) lies on these lines: {2, 16789}, {4, 19153}, {5, 44469}, {6, 66}, {22, 3618}, {30, 182}, {69, 31236}, {141, 9813}, {206, 3867}, {378, 14853}, {389, 2781}, {428, 18374}, {468, 9971}, {511, 44201}, {518, 51718}, {524, 21243}, {546, 6593}, {576, 12359}, {1177, 1885}, {1503, 18388}, {1594, 15141}, {1595, 34117}, {2393, 23292}, {3532, 38005}, {3564, 39504}, {3589, 5943}, {5050, 31723}, {5085, 44239}, {5133, 22151}, {5305, 7668}, {5486, 17813}, {5640, 16387}, {6677, 16776}, {7378, 41719}, {7391, 41256}, {7502, 38110}, {7699, 47474}, {7716, 31267}, {8550, 10250}, {9820, 43130}, {10024, 45034}, {10110, 16618}, {10300, 32154}, {10510, 37454}, {11064, 29959}, {11427, 32621}, {11536, 25328}, {13413, 18358}, {13567, 34177}, {14561, 15760}, {14865, 32262}, {16310, 37988}, {17810, 44210}, {18570, 21850}, {18907, 24270}, {20423, 37489}, {21637, 46026}, {23335, 44480}, {25488, 35370}, {31166, 36990}, {31670, 44249}, {34417, 47454}, {37969, 47455}, {38049, 51692}, {38064, 44261}, {38079, 44262}, {38136, 44263}, {39588, 45179}, {41585, 47449}, {42442, 47413}, {44288, 48906}
X(51744) = midpoint of X(i) and X(j) for these {i,j}: {6, 427}, {18570, 21850}, {20423, 44218}, {31670, 44249}, {44288, 48906}
X(51744) = reflection of X(i) in X(j) for these {i,j}: {6676, 3589}, {18358, 13413}
X(51744) = complement of X(16789)
X(51744) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {597, 5480, 19136}, {597, 19136, 47457}
X(51745) lies on these lines: {2, 37485}, {6, 428}, {30, 182}, {141, 10128}, {159, 7714}, {511, 10127}, {518, 51719}, {524, 9969}, {542, 10110}, {546, 37827}, {599, 17810}, {3564, 13451}, {3589, 10691}, {3861, 25328}, {5064, 23300}, {6593, 31830}, {6756, 37505}, {6995, 32621}, {7540, 14848}, {7576, 14853}, {7667, 47352}, {7734, 48310}, {8541, 47464}, {11745, 15644}, {13488, 15118}, {14449, 23410}, {15559, 32262}, {15873, 47354}, {20423, 36747}, {23411, 34507}, {34417, 47449}, {34634, 38023}, {34656, 38087}, {34664, 38072}, {41585, 47446}
X(51745) = midpoint of X(6) and X(428)
X(51745) = reflection of X(i) in X(j) for these {i,j}: {141, 10128}, {10691, 3589}
X(51746) lies on these lines: {6, 441}, {30, 182}, {141, 44335}, {297, 3087}, {401, 51171}, {518, 51722}, {524, 44346}, {1503, 23583}, {1992, 44578}, {3589, 44334}, {5050, 44231}, {5085, 44248}, {6723, 44401}, {14561, 44228}, {14853, 44252}, {26206, 44341}, {38049, 51704}, {42854, 46264}, {44216, 47352}
X(51746) = midpoint of X(6) and X(441)
X(51746) = reflection of X(i) in X(j) for these {i,j}: {141, 44335}, {44334, 3589}
X(51747) lies on these lines: {6, 442}, {21, 3618}, {30, 182}, {69, 31254}, {518, 11281}, {1386, 44669}, {2475, 51171}, {2771, 15118}, {3589, 4260}, {3651, 14853}, {3751, 26725}, {5050, 37230}, {5085, 44238}, {5428, 38110}, {6841, 14561}, {15670, 47352}, {16475, 47033}, {16617, 25555}, {21677, 38047}, {35016, 38049}, {35979, 36740}, {38064, 44255}, {38079, 44257}, {38136, 44258}
X(51747) = midpoint of X(6) and X(442)
X(51747) = reflection of X(6675) in X(3589)
See Ivan Pavlov and Peter Moses, euclid 5500.
X(51748) lies on these lines: {1, 14158}, {21, 36}, {58, 26202}, {81, 22461}, {1030, 8818}, {2160, 4877}, {3065, 13486}, {3649, 26700}, {4065, 6742}, {4658, 7073}, {16118, 37405}
X(51748) = {X(79),X(14844)}-harmonic conjugate of X(11263)
See Peter Moses, euclid 5501.
X(51749) lies on these lines: {1, 4}, {2, 37830}, {11, 559}, {17, 42677}, {57, 10652}, {142, 30357}, {354, 554}, {622, 4425}, {1082, 1836}, {1251, 30310}, {2783, 5613}, {2886, 5239}, {3638, 11019}, {5219, 30434}, {5226, 30339}, {5240, 24703}, {5249, 10650}, {6191, 40693}, {9812, 37833}, {10431, 10649}, {10580, 30344}, {10653, 11789}, {11246, 37772}, {11705, 36941}, {17728, 37773}, {18471, 31019}, {29821, 33396}
X(51749) = reflection of X(51750) in X(24210)
X(51749) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1082, 1836, 10651}
See Peter Moses, euclid 5501.
X(51750) lies on these lines: {1, 4}, {2, 37833}, {11, 1082}, {18, 42680}, {57, 10651}, {142, 30356}, {354, 1081}, {554, 16038}, {559, 1836}, {621, 4425}, {2783, 5617}, {2886, 5240}, {3639, 11019}, {5219, 30433}, {5226, 30338}, {5239, 24703}, {5249, 10649}, {6192, 40694}, {9812, 37830}, {10431, 10650}, {10580, 30345}, {10654, 11752}, {11246, 37773}, {11706, 36940}, {17728, 37772}, {18469, 31019}, {29821, 33397}, {30309, 33653}
X(51750) = reflection of X(51749) in X(24210)
X(51750) = {X(559),X(1836)}-harmonic conjugate of X(10652)
See Peter Moses, euclid 5501.
X(51751) lies on these lines: {1, 4}, {30, 11700}, {65, 43820}, {522, 4823}, {860, 24026}, {942, 36250}, {1074, 10165}, {1076, 31730}, {1324, 23383}, {1735, 10265}, {2222, 26707}, {2800, 51421}, {3028, 3326}, {4347, 10525}, {5172, 14667}, {5842, 15252}, {6882, 24025}, {11529, 33134}, {11813, 34586}, {15325, 17070}, {18407, 37729}, {22765, 38578}, {25639, 37565}, {34030, 40256}
X(51751) = midpoint of X(1) and X(38945)
X(51751) = reflection of X(16869) in X(44901)
X(51751) = incircle inverse of X(12047)
X(51751) = polar circle inverse of X(6198)
X(51751) = crossdifference of every pair of points on line {652, 2174}
See Ivan Pavlov, euclid 5496.
X(51752) lies on these lines: {4, 60}, {113, 946}
X(51752) = midpoint of X(4) and X(60)
See Ivan Pavlov, euclid 5496.
X(51753) lies on these lines {2, 14540}, {3, 6694}, {4, 13}, {5, 141}, {17, 383}, {62, 1080}, {132, 46652}, {381, 533}, {397, 5007}, {398, 7753}, {530, 37333}, {546, 5479}, {576, 5872}, {618, 47066}, {627, 5979}, {633, 3091}, {1350, 11311}, {3060, 33529}, {3104, 6115}, {3642, 5865}, {3818, 5873}, {5133, 33530}, {5318, 7747}, {5321, 39590}, {5869, 42974}, {8259, 10613}, {11289, 14541}, {11306, 38072}, {11307, 14538}, {12110, 16965}, {13111, 16629}, {14853, 40694}, {15609, 41059}, {16626, 20426}, {16630, 22693}, {16772, 41034}, {20423, 34508}, {20425, 37825}, {22512, 47861}, {22531, 41100}, {30439, 47026}, {37349, 51271}, {37464, 42488}, {41017, 42166}, {41035, 42148}, {41036, 42814}, {41040, 42153}, {42150, 44463}, {42161, 44459}, {45880, 49105}
X(51753) = midpoint of X(4) and X(61)
X(51753) = reflection of X(i) in X(j) for these {i,j}: {3, 6694}, {635, 5}
X(51753) = complement of X(14540)
X(51753) = X(51753)-Dao conjugate of X(14540)
X(51753) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 5480, 51754}, {5, 51754, 7685}, {5479, 22832, 546}, {5480, 7684, 7685}, {7684, 51754, 5}, {8259, 42147, 10613}
See Ivan Pavlov, euclid 5496.
X(51754) lies on these lines {2, 14541}, {3, 6695}, {4, 14}, {5, 141}, {18, 1080}, {61, 383}, {132, 46653}, {381, 532}, {397, 7753}, {398, 5007}, {531, 37332}, {546, 5478}, {576, 5873}, {619, 47068}, {628, 5978}, {634, 3091}, {1350, 11312}, {3060, 33530}, {3105, 6114}, {3643, 5864}, {3818, 5872}, {5133, 33529}, {5318, 39590}, {5321, 7747}, {5868, 42975}, {8260, 10614}, {11290, 14540}, {11305, 38072}, {11308, 14539}, {12110, 16964}, {13111, 16628}, {14853, 40693}, {15610, 41058}, {16627, 20425}, {16631, 22694}, {16773, 41035}, {20423, 34509}, {20426, 37824}, {22513, 47862}, {22532, 41101}, {30440, 47027}, {36765, 40707}, {37349, 51264}, {37463, 42489}, {41016, 42163}, {41034, 42147}, {41037, 42813}, {41041, 42156}, {42151, 44459}, {42160, 44463}, {45879, 49106}
X(51754) = midpoint of X(4) and X(62)
X(51754) = reflection of X(i) in X(j) for these {i,j}: {3, 6695}, {636, 5}
X(51754) = complement of X(14541)
X(51754) = X(51754)-Dao conjugate of X(14541)
X(51754) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 5480, 51753}, {5, 51753, 7684}, {5478, 22831, 546}, {5480, 7685, 7684}, {7685, 51753, 5}, {8260, 42148, 10614}
See Ivan Pavlov, euclid 5496.
X(51755) lies on these lines: {3, 10}, {4, 63}, {5, 226}, {38, 1072}, {57, 1478}, {116, 119}, {201, 1076}, {381, 2095}, {442, 1071}, {774, 1070}, {950, 3560}
X(51755) = midpoint of X(4) and X(63)
See Ivan Pavlov, euclid 5496.
X(51756) lies on these lines: {4, 66}, {5, 182}, {6, 3574}, {25, 125}, {265, 1351}
X(51756) = midpoint of X(4) and X(66)
See Ivan Pavlov, euclid 5496.
X(51757) lies on these lines: {4, 70}, {5, 156}, {24, 125}, {155, 265}
X(51757) = midpoint of X(4) and X(70)
See Ivan Pavlov, euclid 5496.
X(51758) lies on these lines: {2, 2947}, {4, 9}, {118, 125}
X(51758) = midpoint of X(4) and X(71)
See Ivan Pavlov, euclid 5496.
X(51759) lies on these lines: {1, 4}, {5, 34831}, {40, 26027}, {117, 125}, {942, 24030}, {1210, 19366}, {2183, 40942}, {2657, 9393}, {3074, 7567}, {3574, 14055}, {3791, 31812}, {5480, 7681}, {5777, 44916}, {5909, 6708}, {6001, 20617}, {6247, 7680}, {6684, 37154}, {10894, 15232}, {11496, 15622}, {21228, 26091}, {22753, 23361}, {43724, 45046}
X(51759) = midpoint of X(4) and X(73)
See Ivan Pavlov, euclid 5496.
X(51760) lies on these lines: {99, 1234}, {110, 442}, {112, 1865}
X(51760) = reflection of X(4) in the center of the rectangular circumhyperbola through X(12)
See Ivan Pavlov, euclid 5496.
X(51761) lies on these lines: {4, 1288}, {26, 110}, {476, 2072}
X(51761) = reflection of X(4) in the center of the rectangular circumhyperbola through X(26)
See Ivan Pavlov, euclid 5496.
X(51762) lies on these lines: {4, 934}, {33, 109}, {108, 1857}, {110, 4183}
X(51762) = reflection of X(4) in X(38966)
X(51763) lies on these lines: {1, 7}, {165, 13390}, {1697, 10911}, {1698, 14121}, {1699, 13388}, {3624, 31534}, {4014, 7353}, {7991, 31532}, {30556, 38052}
X(51763) = reflection of X(1) in X(175)
X(51763) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 30425, 4312}, {390, 31569, 1}, {390, 31602, 31569}, {481, 31568, 30342}, {5542, 30333, 1}, {30342, 31568, 1}
X(51764) lies on these lines: {1, 7}, {165, 1659}, {1697, 10910}, {1698, 7090}, {1699, 13389}, {3624, 31535}, {4014, 7362}, {7991, 31533}, {30557, 38052}
X(51764) = reflection of X(1) in X(176)
X(51764) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 30426, 4312}, {390, 31570, 1}, {390, 31601, 31570}, {482, 31567, 30341}, {5542, 30334, 1}, {21169, 30334, 5542}, {30341, 31567, 1}
X(51765) lies on these lines: {1, 9519}, {7, 2796}, {43, 57}, {56, 7312}, {106, 269}, {651, 3361}, {1293, 31508}, {1319, 5018}, {2099, 13541}, {2802, 4321}, {5223, 43760}, {5226, 11814}, {5726, 10713}, {24715, 40617}, {32920, 42304}
X(51765) = crossdifference of every pair of points on line {4435, 14427}
X(51766) lies on these lines {1, 651}, {7, 50282}, {43, 57}, {77, 49448}, {101, 604}, {103, 31508}, {109, 41553}, {150, 3664}, {202, 11752}, {203, 11789}, {222, 3961}, {238, 1319}, {241, 49712}, {518, 5018}, {519, 40862}, {537, 664}, {984, 2114}, {1046, 34925}, {1419, 16496}, {1456, 49675}, {1458, 1757}, {1742, 2807}, {2099, 6180}, {2263, 49498}, {2784, 4307}, {2786, 30572}, {2808, 31393}, {2809, 18421}, {2823, 12652}, {2943, 38502}, {3219, 25941}, {3476, 50303}, {3679, 41801}, {3973, 28345}, {4407, 17095}, {4552, 24821}, {4649, 8581}, {4674, 7271}, {5252, 50301}, {5290, 34929}, {5524, 9364}, {5726, 10708}, {7050, 7281}, {9440, 24929}, {11028, 30350}, {17625, 29821}, {24436, 51682}, {29820, 34048}, {39126, 49497}
X(51766) = reflection of X(1) in X(44858)
X(51767) lies on these lines {1, 6946}, {57, 1317}, {100, 13462}, {104, 31508}, {214, 4900}, {484, 28234}, {519, 37787}, {952, 10384}, {1000, 3065}, {1319, 15015}, {1768, 5119}, {2099, 12653}, {2801, 9819}, {2802, 4321}, {3305, 12531}, {3577, 24302}, {3895, 10031}, {5226, 21630}, {5425, 39779}, {5726, 10707}, {6264, 24929}, {7091, 10609}, {7962, 41701}, {8545, 12730}, {10087, 30282}, {11525, 20586}, {12736, 30350}, {40587, 41541}
X(51767) = reflection of X(18421) in X(14151)
X(51768) lies on these lines {1, 651}, {7, 3065}, {9, 80}, {11, 57}, {35, 5506}, {36, 15726}, {40, 12019}, {63, 10707}, {84, 20418}, {90, 3254}, {100, 3305}, {104, 3062}, {144, 21630}, {149, 3219}, {165, 41166}, {191, 1479}, {390, 9897}, {484, 516}, {496, 7701}, {517, 41700}, {527, 30384}, {673, 51286}, {952, 10384}, {956, 30294}, {971, 1319}, {1001, 5426}, {1158, 47744}, {1387, 50908}, {1708, 50865}, {1727, 28534}, {1728, 9589}, {1776, 5536}, {2099, 13253}, {2771, 15934}, {2800, 10398}, {2802, 4915}, {2932, 15587}, {2950, 10265}, {2951, 10090}, {3306, 38207}, {3336, 10591}, {3337, 30424}, {3582, 30379}, {3587, 5840}, {3624, 10427}, {3748, 37736}, {3895, 50890}, {3899, 5223}, {4309, 5766}, {5083, 30350}, {5131, 30295}, {5220, 5697}, {5226, 21635}, {5425, 5728}, {5437, 45310}, {5531, 10382}, {5692, 42014}, {5696, 36868}, {5726, 10711}, {5729, 5903}, {5779, 6264}, {5850, 51423}, {5851, 16173}, {5880, 7741}, {6068, 41229}, {6172, 30305}, {6173, 23708}, {6174, 7308}, {6326, 14100}, {6797, 41712}, {7082, 9580}, {7280, 43178}, {7290, 15430}, {7330, 37726}, {7675, 45764}, {7678, 16763}, {7704, 50444}, {7993, 15558}, {8068, 17699}, {8255, 37701}, {8581, 12773}, {10057, 15518}, {10058, 15015}, {10389, 33519}, {10392, 12247}, {10609, 31435}, {10738, 37584}, {10770, 34925}, {10826, 15297}, {11010, 30332}, {11570, 30330}, {11571, 12560}, {12331, 15837}, {12736, 12767}, {13205, 18236}, {13243, 18240}, {15932, 18483}, {16112, 42884}, {16133, 20116}, {17768, 41555}, {19875, 38216}, {25055, 38060}, {25557, 37735}, {29007, 30331}, {30275, 38037}, {30628, 47320}, {31424, 48713}, {32558, 38054}, {34894, 38271}, {36973, 50891}, {38052, 39692}
X(51768) = reflection of X(484) in X(37787)
X(51768) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {90, 9614, 6763}, {1709, 11219, 1768}, {11372, 15299, 4312}, {39144, 39145, 1768}
X(51769) lies on these lines {1, 9519}, {9, 80}, {57, 3021}, {105, 31508}, {1219, 4294}, {1292, 13462}, {2836, 5697}, {28915, 31393}
X(51770) lies on these lines {1, 38670}, {57, 1358}, {105, 13462}, {278, 7313}, {1292, 31508}, {2809, 18421}, {5726, 10712}, {9519, 9819}, {28915, 31393}
X(51771) lies on these lines {57, 1365}, {759, 13462}, {2099, 6180}, {5119, 34196}, {6011, 31508}
X(51772) lies on these lines {1, 3}, {1435, 1878}, {1476, 3812}, {3086, 12678}, {3880, 37789}, {5265, 25568}, {5815, 7288}, {5850, 34123}, {9850, 25524}
X(51772) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1319, 18838, 5048}, {3660, 5193, 1319}
X(51773) lies on these lines {1, 3}, {6, 4322}, {9, 9850}, {12, 17559}, {198, 40133}, {220, 604}, {388, 4423}, {405, 4315}, {480, 6762}, {948, 28037}, {954, 12577}, {956, 12447}, {958, 4308}, {1001, 3600}, {1014, 5543}, {1042, 1616}, {1106, 3052}, {1191, 1458}, {1212, 1696}, {1279, 4320}, {1376, 5265}, {1407, 3915}, {1427, 28011}, {1445, 34791}, {1476, 11194}, {1788, 6764}, {3555, 41712}, {3913, 5435}, {4297, 42884}, {4306, 16483}, {4350, 7023}, {4413, 7288}, {4512, 7091}, {5022, 7368}, {5261, 8167}, {5298, 11501}, {5433, 19855}, {5726, 16853}, {5732, 9848}, {6939, 7958}, {7191, 15832}, {7959, 10535}, {8059, 28193}, {8572, 11505}, {8581, 31435}, {9785, 11495}, {10866, 12565}, {11035, 15298}, {12128, 31658}, {12513, 20007}, {12573, 51723}, {15998, 34720}, {17745, 38296}, {33590, 43065}, {36846, 37309}, {37411, 37704}
X(51773) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 7957, 2098}, {1, 8273, 55}, {1, 15803, 6766}, {1, 37544, 2099}, {1, 37551, 3057}, {3, 3295, 31508}, {3, 13462, 56}, {56, 1319, 3304}, {56, 3303, 57}, {56, 11510, 1466}, {56, 37579, 5204}, {1420, 1617, 56}, {1420, 37583, 41426}, {1466, 11510, 55}, {1616, 42314, 1042}, {1617, 41426, 37583}, {3304, 5204, 10966}, {4308, 7677, 958}, {10966, 41341, 5204}, {37583, 41426, 56}
X(51774) lies on these lines {1, 3}, {499, 9947}, {513, 30723}, {631, 17624}, {971, 44675}, {3085, 12128}, {3555, 5265}, {3624, 9850}, {3742, 4315}, {3921, 31188}, {3956, 6681}, {4308, 5439}, {4311, 5806}, {4342, 10178}, {5731, 17626}, {6049, 10914}, {7288, 34790}, {8581, 25055}, {9780, 17644}, {10156, 31397}, {11035, 13411}, {12053, 31805}, {14027, 38471}, {24465, 28198}
X(51774) = midpoint of X(1319) and X(3660)
X(51774) = isogonal conjugate of X(12868)
X(51774) = incircle-inverse of X(3339)
X(51774) = X(1)-isoconjugate of X(12868)
X(51774) = barycentric quotient X(6)/X(12868)
X(51774) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {56, 5045, 37544}, {1319, 5193, 5126}, {2446, 2447, 3339}
See Francisco Javier García Capitán, euclid 5505.
X(51775) lies on these lines: {2, 5088}, {3, 142}, {12, 24784}, {25, 15497}, {56, 20269}, {101, 9436}, {116, 515}, {140, 6706}, {169, 348}, {214, 17060}, {241, 514}, {242, 7521}, {277, 7288}, {404, 27006}, {517, 17044}, {527, 28345}, {549, 20328}, {910, 1565}, {911, 15634}, {978, 5018}, {1308, 9061}, {1319, 4904}, {1385, 21258}, {1445, 4253}, {1478, 30742}, {1730, 18652}, {1737, 9317}, {3306, 5011}, {3323, 20662}, {3612, 26101}, {3732, 17078}, {4209, 17181}, {4278, 30733}, {4292, 40690}, {4881, 26140}, {5134, 14021}, {5195, 17397}, {5199, 31184}, {5249, 36016}, {5433, 24774}, {5745, 31896}, {6666, 27473}, {6710, 40869}, {6713, 40554}, {11347, 21621}, {11712, 28849}, {13411, 17758}, {17030, 27301}, {17046, 17647}, {17081, 41785}, {17095, 17682}, {17367, 38941}, {17683, 27187}, {17761, 44675}, {20244, 28969}, {20267, 23536}, {20367, 26006}, {21073, 28734}, {24582, 30806}, {25065, 25092}, {29069, 44356}, {32763, 32764}, {36907, 37034}
X(51776) is the perspector of ABC and the triangle A'B'C' constructed at X(41679).
X(51776) lies on these lines: {2, 11610}, {69, 248}, {97, 3917}, {98, 1370}, {112, 36426}, {290, 34385}, {317, 571}, {394, 14600}, {511, 1976}, {687, 2966}, {31636, 46184}.
X(51776) = reflection of X(4558) in X(577)
X(51776) = isogonal conjugate of the polar conjugate of X(31635)
X(51776) = X(290)-Ceva conjugate of X(17974)
X(51776) = X(i)-isoconjugate of X(j) for these (i,j): {91, 232}, {240, 2165}, {847, 1755}, {1820, 6530}, {1959, 14593}, {2168, 39569}, {2211, 20571}, {16230, 36145}
X(51776) = X(i)-Dao conjugate of X(j) for these (i, j): (577, 511), (34116, 232), (36899, 847), (39013, 16230), (39085, 2165)
X(51776) = barycentric product X(i)*X(j) for these {i,j}: {3, 31635}, {24, 6394}, {47, 336}, {98, 9723}, {248, 7763}, {287, 1993}, {290, 1147}, {293, 44179}, {317, 17974}, {563, 46273}, {924, 17932}, {6563, 43754}, {30451, 43187}, {47388, 51439}
X(51776) = barycentric quotient X(i)/X(j) for these {i,j}: {24, 6530}, {47, 240}, {52, 39569}, {98, 847}, {248, 2165}, {287, 5392}, {293, 91}, {336, 20571}, {563, 1755}, {571, 232}, {924, 16230}, {1147, 511}, {1976, 14593}, {1993, 297}, {2966, 30450}, {5961, 14356}, {6394, 20563}, {7763, 44132}, {9723, 325}, {14355, 5962}, {17932, 46134}, {17974, 68}, {30451, 3569}, {31635, 264}, {34952, 17994}, {43754, 925}, {44077, 34854}, {44179, 40703}
X(51777) is the perspector of the perspeconic of ABC and the triangle A'B'C' constructed at X(41679).
X(51777) lies on these lines: { }
X(51778) is the center of the perspeconic of ABC and the triangle A'B'C' constructed at X(41679).
X(51778) lies on these lines: { }
X(51779) lies on these lines: {1, 3}, {9, 3241}, {11, 51767}, {145, 3305}, {200, 10179}, {519, 7308}, {962, 3982}, {1056, 9580}, {1058, 9578}, {1317, 51768}, {1358, 51769}, {1706, 3622}, {2136, 3616}, {2170, 3247}, {2270, 3723}, {2999, 16486}, {3021, 51770}, {3022, 51766}, {3219, 3623}, {3243, 3877}, {3244, 31435}, {3475, 4342}, {3476, 30331}, {3488, 50818}, {3586, 15170}, {3632, 3646}, {3872, 38316}, {3880, 10582}, {3884, 41863}, {3890, 11523}, {3895, 5437}, {3929, 51071}, {4031, 34632}, {4114, 11037}, {4315, 10385}, {4423, 4915}, {4654, 30305}, {5226, 12053}, {5250, 20057}, {5436, 36846}, {5603, 7966}, {5726, 11238}, {5779, 18452}, {6018, 51765}, {6049, 7091}, {7171, 50824}, {8236, 8545}, {9579, 12575}, {9613, 15172}, {10056, 37704}, {10106, 41864}, {11239, 30827}, {12705, 13607}, {14151, 15558}, {15174, 16138}, {15600, 49454}, {20049, 35595}, {20196, 34619}, {31231, 38068}, {34194, 51771}, {35227, 49487}, {36973, 47357}, {37723, 40270}
X(51779) = reflection of X(44841) in X(1)
X(51779) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 2093, 5049}, {1, 3057, 11518}, {1, 3295, 1420}, {1, 3303, 3601}, {1, 5919, 7962}, {1, 6767, 10389}, {1, 7991, 17609}, {1, 9819, 354}, {1, 9957, 3340}, {1, 10389, 13384}, {1, 11224, 44840}, {1, 30337, 65}, {1, 31393, 57}, {1, 37556, 1697}, {57, 31393, 1697}, {57, 37556, 31393}, {484, 3333, 57}, {1466, 3303, 3295}, {3895, 38314, 5437}, {5919, 8162, 1}, {9957, 37544, 3057}
X(51780) lies on these lines: {1, 3697}, {2, 7}, {5, 3587}, {10, 1058}, {37, 23511}, {40, 3090}, {44, 37682}, {45, 16602}, {46, 5506}, {72, 16854}, {78, 17536}, {84, 140}, {165, 15254}, {171, 15601}, {200, 3748}, {210, 3243}, {405, 5438}, {484, 5087}, {496, 7160}, {497, 38200}, {518, 30350}, {549, 18540}, {612, 17125}, {614, 7322}, {631, 9841}, {632, 37534}, {738, 17095}, {748, 5269}, {756, 3677}, {899, 37553}, {936, 2900}, {940, 16670}, {942, 16855}, {958, 13462}, {960, 18421}, {984, 5573}, {1001, 3158}, {1125, 6762}, {1212, 5574}, {1255, 5256}, {1319, 8583}, {1376, 31508}, {1420, 5260}, {1449, 4383}, {1621, 46917}, {1656, 37584}, {1697, 5274}, {1698, 1706}, {1699, 3826}, {1743, 37674}, {2099, 15829}, {2257, 37662}, {2323, 17825}, {2999, 3247}, {3035, 51768}, {3036, 51767}, {3038, 51765}, {3039, 51770}, {3041, 51766}, {3057, 11530}, {3062, 10178}, {3091, 37551}, {3220, 16419}, {3333, 19862}, {3361, 5302}, {3525, 37526}, {3526, 7330}, {3601, 5047}, {3617, 37556}, {3624, 17590}, {3628, 5709}, {3666, 16676}, {3680, 45830}, {3681, 44841}, {3707, 37655}, {3731, 3752}, {3742, 5223}, {3751, 25502}, {3772, 31183}, {3781, 6688}, {3784, 15082}, {3789, 26102}, {3795, 16569}, {3848, 5220}, {3876, 11518}, {3886, 26038}, {3898, 11525}, {3916, 16864}, {3955, 16187}, {3961, 35227}, {4034, 34255}, {4035, 29627}, {4095, 4384}, {4326, 17604}, {4413, 4512}, {4415, 4859}, {4419, 24175}, {4652, 17535}, {4659, 19804}, {4682, 16469}, {4855, 16859}, {4866, 34791}, {4915, 10179}, {5044, 11523}, {5045, 51572}, {5054, 7171}, {5122, 16408}, {5227, 47355}, {5234, 25524}, {5250, 19877}, {5268, 7290}, {5272, 7174}, {5281, 10384}, {5284, 10389}, {5285, 11284}, {5287, 37680}, {5439, 16856}, {5440, 17542}, {5587, 6947}, {5705, 17527}, {5720, 13151}, {5732, 10157}, {5743, 17284}, {5779, 10156}, {5790, 7966}, {5791, 51559}, {5815, 51723}, {5927, 10857}, {6684, 6964}, {6700, 16845}, {6721, 24469}, {6738, 45085}, {6834, 12705}, {6896, 41869}, {6903, 18492}, {7079, 17917}, {7091, 7288}, {7289, 34573}, {7956, 26446}, {8056, 31197}, {9340, 17124}, {9342, 35258}, {9578, 24564}, {9579, 37462}, {9612, 17529}, {9842, 37108}, {10164, 11372}, {10167, 30326}, {10176, 11529}, {10580, 24393}, {11019, 38057}, {11679, 30829}, {12514, 51073}, {12572, 17582}, {12701, 34501}, {12717, 24295}, {13411, 17552}, {14151, 46694}, {14555, 17296}, {15803, 16862}, {16239, 24467}, {16572, 17056}, {16579, 26669}, {16832, 44417}, {16863, 31445}, {17021, 25417}, {17151, 35652}, {17259, 18229}, {17277, 30567}, {17784, 46916}, {18164, 25507}, {19541, 21153}, {19854, 25522}, {20103, 38059}, {21060, 38053}, {21520, 25083}, {21529, 25066}, {21547, 32555}, {21548, 32556}, {22112, 26885}, {24703, 38052}, {25072, 45204}, {26040, 40998}, {27385, 31259}, {31146, 38097}, {31273, 34925}, {34595, 41229}, {37364, 38108}, {37650, 39595}, {39962, 39963}
X(51780) = X(16673)-Dao conjugate of X(46933)
X(51780) = barycentric product X(8)*X(7274)
X(51780) = barycentric quotient X(7274)/X(7)
X(51780) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 9, 5437}, {2, 226, 20195}, {2, 908, 41867}, {2, 3305, 57}, {2, 3452, 25525}, {2, 5273, 6692}, {2, 5316, 30827}, {2, 5745, 31190}, {2, 7308, 9}, {2, 18228, 142}, {2, 18230, 5745}, {2, 27065, 3306}, {2, 31142, 38093}, {2, 35595, 63}, {9, 5437, 3928}, {10, 26105, 24392}, {57, 3305, 9}, {57, 7308, 3305}, {142, 18228, 28609}, {200, 4423, 38316}, {210, 10582, 3243}, {936, 11108, 5436}, {1001, 8580, 3158}, {1698, 31435, 1706}, {2999, 44307, 3247}, {3306, 27065, 3929}, {3740, 8167, 1}, {3848, 5220, 10980}, {3929, 27065, 9}, {4383, 17022, 1449}, {5268, 17123, 7290}, {5506, 19872, 46}, {9776, 20214, 4114}, {19804, 30568, 4659}
X(51781) lies on these lines: {1, 3848}, {8, 57}, {9, 80}, {10, 1058}, {40, 3529}, {200, 2099}, {484, 4668}, {519, 5437}, {738, 25719}, {936, 3680}, {958, 31508}, {997, 11525}, {1319, 4853}, {1376, 4915}, {1697, 3305}, {3035, 51767}, {3158, 9623}, {3219, 4678}, {3243, 3753}, {3306, 31145}, {3333, 3625}, {3338, 4816}, {3576, 38665}, {3587, 5690}, {3677, 4695}, {3740, 9819}, {3812, 30350}, {3872, 41553}, {3880, 8580}, {3893, 8583}, {3895, 7308}, {3913, 5436}, {3928, 4669}, {3929, 51072}, {4659, 4737}, {4662, 5927}, {4711, 5223}, {4731, 10582}, {4882, 5836}, {5687, 30282}, {5881, 9841}, {6666, 45116}, {6765, 15934}, {7171, 50798}, {7330, 35460}, {7966, 26446}, {9575, 21868}, {9709, 12629}, {9780, 37556}, {10860, 37712}, {10914, 15829}, {11239, 41867}, {11372, 38155}, {11519, 25524}, {17699, 41684}, {24393, 36991}, {25525, 34619}, {31190, 34625}, {31397, 38200}, {37560, 47745}
X(51781) = reflection of X(26105) in X(10)
X(51781) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 1706, 6762}, {4882, 5836, 11523}
X(51782) lies on these lines: {1, 3091}, {2, 4315}, {4, 12575}, {7, 3679}, {8, 3671}, {10, 57}, {12, 1125}, {20, 31508}, {34, 30145}, {55, 28164}, {56, 3634}, {65, 3626}, {80, 14151}, {85, 4737}, {149, 51767}, {150, 3664}, {153, 51768}, {226, 519}, {355, 6738}, {377, 6736}, {484, 4292}, {495, 515}, {498, 4311}, {516, 1478}, {518, 33558}, {529, 5745}, {546, 31792}, {551, 3476}, {553, 4745}, {938, 30350}, {942, 11545}, {946, 9654}, {950, 3748}, {999, 10175}, {1000, 31162}, {1056, 5587}, {1058, 18492}, {1210, 10827}, {1317, 4870}, {1323, 7179}, {1420, 10588}, {1441, 4692}, {1450, 49992}, {1697, 5229}, {1698, 3600}, {1699, 4342}, {1836, 28228}, {1837, 6744}, {2067, 49618}, {2093, 30424}, {2784, 15730}, {2801, 50195}, {2809, 34929}, {3085, 4297}, {3219, 12527}, {3244, 3485}, {3295, 31673}, {3305, 3436}, {3333, 5818}, {3339, 3617}, {3340, 3625}, {3361, 9780}, {3452, 11236}, {3475, 5727}, {3487, 5881}, {3545, 37704}, {3576, 8164}, {3584, 21578}, {3585, 10624}, {3586, 8232}, {3614, 20323}, {3624, 4308}, {3633, 4323}, {3635, 10944}, {3636, 11375}, {3649, 4701}, {3654, 18541}, {3660, 3833}, {3674, 32847}, {3753, 8581}, {3828, 3911}, {3838, 38455}, {3848, 51774}, {4114, 4691}, {4293, 10164}, {4301, 9612}, {4304, 10056}, {4314, 5691}, {4321, 38204}, {4654, 4669}, {4662, 37544}, {4709, 7201}, {4746, 41687}, {4853, 5177}, {4995, 50815}, {5045, 18357}, {5049, 12019}, {5068, 50444}, {5080, 40998}, {5122, 6684}, {5123, 6692}, {5176, 5249}, {5199, 40131}, {5225, 37556}, {5316, 31141}, {5425, 12563}, {5433, 31253}, {5435, 19875}, {5439, 9850}, {5493, 9579}, {5542, 18391}, {5714, 7982}, {5719, 28204}, {5722, 50796}, {5744, 34646}, {5794, 6743}, {5795, 25466}, {5828, 17580}, {5882, 11374}, {5883, 17625}, {5902, 43180}, {6223, 9949}, {6502, 49619}, {6700, 15844}, {6871, 36846}, {6943, 13411}, {7146, 49766}, {7176, 36531}, {7247, 10521}, {7288, 51073}, {7354, 12512}, {7951, 10171}, {7989, 14986}, {9581, 21625}, {9655, 31730}, {9656, 12701}, {9812, 9819}, {9957, 18483}, {10165, 31479}, {10172, 15325}, {10385, 50862}, {10386, 33697}, {10592, 24928}, {10865, 18412}, {10895, 12053}, {10956, 41553}, {11238, 50803}, {11551, 41684}, {12432, 34790}, {12447, 21075}, {12526, 20214}, {12573, 37787}, {12588, 34379}, {12629, 31418}, {12667, 21628}, {12943, 28158}, {13370, 17531}, {13464, 22835}, {13607, 37737}, {15950, 51103}, {16236, 31145}, {16842, 51773}, {17057, 34690}, {17077, 19870}, {17609, 17644}, {17757, 20103}, {19372, 30148}, {19876, 31188}, {20292, 51433}, {20344, 51770}, {21147, 30142}, {21290, 51765}, {25719, 33949}, {28234, 39542}, {29604, 41245}, {30384, 50802}, {31408, 49547}, {33709, 41554}, {34547, 51769}, {36279, 38127}, {36493, 43054}, {37694, 50604}, {37716, 39595}, {38207, 51098}, {49492, 50753}
X(51782) = midpoint of X(i) and X(j) for these {i,j}: {226, 5252}, {1478, 31397}
X(51782) = reflection of X(13405) in X(495)
X(51782) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 5261, 3947}, {1, 10590, 3817}, {8, 5290, 3671}, {10, 388, 4298}, {12, 10106, 1125}, {355, 21620, 6738}, {388, 9578, 10}, {1056, 5587, 11019}, {1420, 10588, 19862}, {1697, 5229, 51118}, {3085, 9613, 4297}, {3476, 5219, 551}, {3485, 37709, 3244}, {4292, 10039, 43174}, {4293, 31434, 10164}, {5252, 11237, 226}, {5270, 10039, 4292}, {5542, 38155, 18391}, {7951, 44675, 10171}, {10895, 12053, 12571}, {12527, 24987, 18249}, {20060, 24987, 12527}, {30331, 34648, 3586}, {37719, 45287, 13411}
X(51783) lies on these lines: {1, 3146}, {2, 31508}, {4, 12575}, {7, 30350}, {10, 1479}, {11, 10164}, {20, 13462}, {30, 4315}, {35, 5284}, {55, 3817}, {57, 497}, {80, 4669}, {142, 49736}, {149, 3219}, {152, 51766}, {153, 51767}, {165, 5274}, {226, 3058}, {329, 519}, {354, 4114}, {376, 37704}, {390, 1699}, {484, 1210}, {496, 5122}, {515, 4342}, {528, 3452}, {551, 4304}, {908, 34611}, {938, 9589}, {946, 4314}, {950, 2099}, {962, 6738}, {999, 28150}, {1001, 37271}, {1058, 4298}, {1125, 4294}, {1317, 51082}, {1319, 4297}, {1387, 51705}, {1697, 5225}, {1836, 3982}, {2801, 17642}, {2802, 17658}, {3057, 5927}, {3085, 12571}, {3086, 12512}, {3244, 5057}, {3295, 3947}, {3465, 49686}, {3475, 43179}, {3485, 41864}, {3488, 31162}, {3523, 50444}, {3583, 31397}, {3612, 15808}, {3625, 3681}, {3627, 31792}, {3634, 10591}, {3636, 4305}, {3663, 4872}, {3671, 12699}, {3715, 38210}, {3825, 25973}, {3839, 5726}, {3877, 30294}, {3880, 9954}, {3885, 11678}, {3911, 11238}, {3925, 38059}, {3950, 4865}, {4035, 4702}, {4052, 32920}, {4082, 5014}, {4292, 21625}, {4293, 28158}, {4295, 6744}, {4302, 44675}, {4309, 13411}, {4312, 10580}, {4313, 11522}, {4326, 30275}, {4349, 37595}, {4356, 20182}, {4423, 38204}, {4640, 24386}, {4666, 38054}, {5046, 6736}, {5082, 18250}, {5218, 10171}, {5219, 10385}, {5229, 37556}, {5252, 34648}, {5273, 50836}, {5281, 7988}, {5316, 34612}, {5691, 9785}, {5698, 24392}, {5722, 28194}, {5745, 11235}, {5787, 9949}, {5850, 20214}, {5853, 21060}, {5918, 17626}, {6684, 9669}, {6745, 20075}, {7673, 15104}, {7677, 41853}, {7741, 51073}, {7743, 10165}, {7962, 28236}, {9579, 12577}, {9581, 43174}, {9665, 31396}, {9955, 10386}, {9957, 31673}, {9965, 31146}, {10072, 34638}, {10106, 12953}, {10136, 31526}, {10167, 18240}, {10569, 31391}, {10589, 35445}, {11362, 11545}, {11813, 34649}, {12019, 38127}, {12609, 51724}, {12915, 15726}, {13912, 35802}, {13975, 35803}, {14151, 34789}, {15172, 21620}, {16236, 50872}, {17556, 34639}, {17716, 24210}, {17784, 20103}, {18193, 51615}, {18220, 30389}, {18391, 28228}, {18527, 28174}, {19883, 23708}, {20344, 51769}, {20347, 42057}, {21628, 48482}, {21633, 31770}, {21635, 41553}, {22791, 31795}, {24175, 24715}, {24177, 33094}, {25440, 25893}, {25525, 47357}, {28232, 36279}, {28526, 29844}, {29353, 35645}, {29571, 33109}, {30827, 34607}, {31164, 51071}, {33098, 49989}, {33110, 38201}, {33169, 50118}, {34547, 51770}, {34548, 51765}, {35242, 47743}, {43180, 44841}
X(51783) = midpoint of X(i) and X(j) for these {i,j}: {497, 9580}, {3586, 30305}
X(51783) = reflection of X(i) in X(j) for these {i,j}: {11019, 497}, {17784, 20103}, {21060, 24703}
X(51783) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {226, 3058, 30331}, {390, 1699, 13405}, {946, 15171, 4314}, {950, 12701, 4301}, {1058, 41869, 4298}, {1479, 10624, 10}, {1697, 5225, 19925}, {3295, 18483, 3947}, {3434, 40998, 10}, {4294, 9614, 1125}, {4304, 30384, 551}, {5274, 30332, 165}, {6284, 12053, 4297}, {9670, 12701, 950}, {15172, 22793, 21620}
X(51784) lies on these lines: {1, 2}, {4, 5726}, {5, 31393}, {7, 43174}, {9, 12607}, {11, 37556}, {12, 1697}, {20, 31508}, {35, 9613}, {37, 23058}, {40, 495}, {46, 4355}, {55, 5691}, {57, 9588}, {65, 15104}, {165, 388}, {226, 7991}, {390, 19925}, {497, 7989}, {516, 5261}, {631, 13462}, {946, 8164}, {950, 37714}, {954, 3913}, {962, 3947}, {999, 31423}, {1000, 13464}, {1015, 31428}, {1056, 3361}, {1058, 10175}, {1420, 5432}, {1482, 8275}, {1656, 31792}, {1695, 10408}, {1706, 25466}, {1768, 10956}, {1788, 10980}, {1837, 10389}, {1891, 38300}, {2093, 13407}, {2136, 2886}, {2476, 3895}, {2646, 37709}, {3057, 5219}, {3090, 50444}, {3091, 12575}, {3158, 5794}, {3247, 21049}, {3295, 5587}, {3297, 13947}, {3298, 13893}, {3303, 9581}, {3304, 31231}, {3333, 26446}, {3339, 5657}, {3340, 17718}, {3421, 5234}, {3436, 4512}, {3475, 4848}, {3476, 30389}, {3485, 11531}, {3486, 37712}, {3487, 11362}, {3523, 4315}, {3586, 3746}, {3600, 10164}, {3601, 5252}, {3646, 3820}, {3654, 6147}, {3673, 17885}, {3698, 41867}, {3731, 6554}, {3748, 37723}, {3817, 9785}, {3890, 30852}, {3893, 31245}, {3894, 13750}, {3986, 31325}, {4293, 16192}, {4297, 5281}, {4301, 5226}, {4326, 12617}, {4642, 23681}, {4654, 37567}, {4662, 5728}, {4859, 6706}, {4866, 10398}, {4917, 5178}, {5119, 9589}, {5122, 31425}, {5128, 10404}, {5129, 5828}, {5218, 7987}, {5435, 12577}, {5437, 37828}, {5531, 10393}, {5586, 36279}, {5690, 11529}, {5708, 50821}, {5714, 28194}, {5719, 16236}, {5727, 37080}, {5815, 18249}, {5836, 25525}, {5837, 25568}, {5880, 32157}, {5881, 24929}, {5904, 50195}, {5919, 50443}, {6690, 32049}, {6762, 26066}, {6767, 9956}, {7160, 15909}, {7308, 21031}, {7320, 18220}, {7354, 35445}, {7373, 11231}, {7951, 9614}, {7962, 11218}, {7982, 11374}, {7988, 10588}, {8227, 9957}, {8581, 31787}, {9579, 11237}, {9580, 10895}, {9590, 10831}, {9591, 10037}, {9646, 13888}, {9654, 41869}, {9848, 10157}, {9850, 11227}, {9947, 14100}, {10156, 12128}, {10172, 47743}, {10590, 10624}, {10944, 13384}, {10955, 30223}, {11108, 51362}, {11236, 50836}, {11246, 41348}, {11518, 40663}, {12588, 39878}, {12631, 17057}, {12710, 18908}, {14923, 31266}, {15017, 15558}, {15171, 18492}, {16200, 37737}, {16201, 41861}, {17757, 31435}, {18412, 34790}, {18990, 35242}, {20060, 35258}, {20789, 31246}, {25415, 37731}, {30282, 31452}, {30323, 37701}, {30330, 38057}, {31399, 40270}, {31432, 44622}, {31794, 41870}, {34639, 50736}, {37571, 37708}, {37725, 51768}, {37726, 51767}
X(51784) = reflection of X(1) in X(5703)
X(51784) = X(45830)-complementary conjugate of X(1329)
X(51784) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 498, 3624}, {1, 10039, 3679}, {1, 12647, 3633}, {1, 19875, 1210}, {1, 30286, 6738}, {1, 31434, 1698}, {1, 34595, 44675}, {8, 13405, 1}, {10, 4882, 3679}, {10, 34619, 4882}, {12, 1697, 1699}, {40, 495, 5290}, {40, 5290, 4312}, {55, 9578, 5691}, {1056, 6684, 3361}, {1656, 31792, 37704}, {1706, 25466, 38052}, {3057, 5219, 11522}, {3085, 31397, 1}, {3487, 11362, 18421}, {3617, 6738, 30286}, {3617, 10578, 6738}, {3746, 10827, 3586}, {3828, 21625, 5704}, {5119, 9612, 9589}, {5119, 37719, 9612}, {5218, 10106, 7987}, {5657, 21620, 3339}, {6738, 10578, 1}, {7988, 30337, 12053}, {9612, 31436, 5119}, {9957, 31479, 8227}, {10039, 10056, 1}, {10198, 10915, 9623}, {10528, 24987, 200}, {10587, 24982, 10582}, {10588, 12053, 7988}, {11237, 37568, 9579}, {11375, 45081, 7962}, {26363, 49626, 12629}, {31436, 37719, 9589}, {31452, 45287, 30282}
X(51785) lies on these lines: {1, 4}, {2, 12575}, {3, 37704}, {5, 31393}, {7, 21625}, {8, 4342}, {9, 3813}, {10, 5274}, {11, 1697}, {12, 37556}, {20, 13462}, {40, 496}, {55, 3624}, {56, 9580}, {57, 9589}, {149, 19861}, {165, 3086}, {200, 41012}, {381, 31792}, {390, 1125}, {516, 3361}, {517, 10866}, {528, 5438}, {551, 4313}, {613, 39878}, {631, 31508}, {938, 4301}, {942, 9848}, {960, 24392}, {962, 3339}, {999, 41869}, {1210, 7991}, {1319, 9670}, {1329, 2136}, {1387, 12119}, {1420, 6284}, {1482, 18527}, {1706, 3816}, {1836, 4355}, {1837, 3632}, {1858, 3894}, {2066, 13888}, {2098, 3633}, {2099, 37723}, {2478, 4853}, {2551, 4915}, {2646, 41864}, {3057, 3679}, {3058, 3601}, {3085, 7988}, {3091, 5726}, {3100, 30148}, {3146, 4315}, {3158, 25681}, {3244, 4345}, {3295, 7743}, {3296, 31507}, {3303, 5219}, {3304, 9579}, {3333, 4312}, {3421, 11519}, {3434, 8583}, {3452, 4882}, {3576, 11373}, {3600, 51118}, {3612, 16173}, {3616, 4314}, {3622, 50725}, {3649, 44841}, {3656, 12433}, {3671, 9800}, {3746, 23708}, {3868, 31146}, {3881, 10394}, {3890, 10707}, {3895, 4193}, {3913, 30827}, {3947, 9779}, {3976, 4862}, {4292, 50865}, {4294, 7987}, {4295, 5586}, {4298, 9812}, {4304, 30389}, {4305, 30392}, {4308, 28164}, {4309, 30282}, {4326, 12609}, {4333, 37587}, {4512, 10527}, {4654, 17609}, {4855, 34611}, {4859, 34847}, {4866, 18228}, {5045, 14100}, {5046, 36846}, {5082, 8580}, {5119, 5445}, {5128, 17728}, {5218, 34595}, {5231, 5250}, {5234, 40998}, {5248, 48713}, {5261, 12571}, {5265, 12512}, {5281, 19862}, {5289, 12625}, {5328, 12632}, {5414, 13942}, {5433, 35445}, {5435, 5493}, {5436, 49736}, {5587, 9669}, {5687, 25522}, {5703, 30331}, {5704, 43174}, {5705, 24387}, {5722, 5763}, {5758, 10398}, {5766, 19843}, {5833, 17558}, {5886, 15172}, {5904, 17642}, {5919, 9578}, {6223, 9851}, {6259, 9845}, {6684, 47743}, {6736, 6919}, {6745, 26129}, {6762, 24703}, {6763, 10959}, {6764, 21060}, {6765, 21616}, {6767, 9955}, {7288, 16192}, {7330, 37726}, {7373, 22793}, {7677, 12511}, {7741, 15845}, {7966, 18242}, {7989, 10591}, {8165, 12541}, {8951, 49772}, {9590, 10046}, {9591, 10832}, {9623, 49600}, {9624, 24929}, {9668, 24928}, {9844, 28609}, {9898, 21631}, {9943, 17626}, {10072, 15803}, {10246, 31795}, {10386, 10993}, {10389, 11375}, {10391, 50190}, {10826, 17622}, {10950, 51093}, {11023, 11407}, {11374, 15170}, {11529, 22791}, {11531, 18391}, {12245, 30286}, {12260, 37692}, {12526, 26015}, {12572, 34625}, {12672, 30294}, {12680, 16215}, {12688, 12915}, {12700, 37560}, {12711, 18398}, {12953, 20323}, {13370, 37022}, {13384, 50240}, {15006, 38053}, {15071, 50196}, {15325, 35242}, {15558, 37718}, {16200, 37730}, {16616, 39779}, {17272, 50608}, {17604, 34790}, {23681, 28011}, {24177, 28016}, {24390, 31435}, {24600, 27129}, {24644, 37434}, {24954, 46917}, {28198, 37545}, {28628, 38316}, {30323, 37702}, {31231, 37568}, {31424, 45700}, {31428, 31433}, {31432, 44623}, {34471, 51105}, {37429, 37618}, {37607, 48944}, {37707, 50871}, {37725, 51767}, {38314, 50737}, {41863, 51409}
X(51785) = reflection of X(3361) in X(14986)
X(51785) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1479, 5691}, {1, 1699, 5290}, {1, 3583, 9613}, {1, 4857, 3586}, {1, 9614, 1699}, {1, 30384, 11522}, {10, 9785, 9819}, {11, 1697, 1698}, {55, 50443, 3624}, {57, 12701, 9589}, {497, 12053, 1}, {938, 4301, 18421}, {946, 1058, 1}, {946, 40270, 3487}, {962, 11019, 3339}, {1058, 3487, 40270}, {1210, 30305, 7991}, {1837, 7962, 3632}, {2098, 5727, 3633}, {2551, 21627, 4915}, {3057, 9581, 3679}, {3057, 11238, 9581}, {3058, 11376, 3601}, {3086, 10624, 165}, {3295, 7743, 8227}, {3333, 12699, 4312}, {3487, 40270, 1}, {3488, 13464, 1}, {3601, 11376, 25055}, {3646, 31419, 1698}, {4294, 44675, 7987}, {4295, 10980, 5586}, {4313, 18220, 551}, {5265, 30332, 12512}, {5274, 9785, 10}, {5919, 10896, 9578}, {7989, 30337, 31397}, {9669, 9957, 5587}, {10591, 31397, 7989}, {11373, 15171, 3576}, {12701, 37722, 57}
X(51786) lies on these lines: {1, 3833}, {8, 3305}, {9, 31145}, {40, 20050}, {57, 145}, {63, 519}, {100, 13462}, {484, 3633}, {1319, 3913}, {1445, 41558}, {1621, 4915}, {1697, 3219}, {1706, 3623}, {2099, 3870}, {2975, 11519}, {3057, 3984}, {3158, 38460}, {3174, 14151}, {3218, 20049}, {3241, 3306}, {3587, 12245}, {3617, 37556}, {3632, 5250}, {3680, 34772}, {3681, 9819}, {3748, 3893}, {3871, 12629}, {3872, 24929}, {3875, 21272}, {3885, 6765}, {3890, 4882}, {3935, 7962}, {4487, 30568}, {4742, 51284}, {5226, 12541}, {5541, 10031}, {5844, 37584}, {5853, 8545}, {5919, 8168}, {6762, 20014}, {7171, 50818}, {7991, 11220}, {9802, 31162}, {10528, 21627}, {10914, 15934}, {11239, 31266}, {11240, 31224}, {11520, 14923}, {12531, 51768}, {12630, 37787}, {12640, 12649}, {13243, 18452}, {16140, 44669}, {24590, 29605}, {30852, 34619}, {32426, 37740}, {35262, 48696}, {36845, 51433}
X(51786) = reflection of X(63) in X(3895)
X(51786) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 31393, 3305}, {3885, 6765, 11682}, {3913, 36846, 4855}
X(51787) lies on these lines: {1, 3}, {6, 7086}, {10, 10386}, {140, 12575}, {226, 28198}, {390, 18527}, {495, 28146}, {497, 11231}, {528, 3828}, {950, 11545}, {1000, 3655}, {1478, 28154}, {2161, 16814}, {2771, 41553}, {2886, 51073}, {3085, 22793}, {3219, 3871}, {3305, 5687}, {3434, 17559}, {3488, 3654}, {3683, 48696}, {3830, 5726}, {3895, 16370}, {3911, 15170}, {3913, 31445}, {4294, 18480}, {4302, 28168}, {4304, 28204}, {4314, 5690}, {4315, 8703}, {4342, 38028}, {4640, 25439}, {4669, 5325}, {4678, 11106}, {4691, 50243}, {4701, 44669}, {4853, 17571}, {4995, 30384}, {5044, 8715}, {5054, 37704}, {5129, 20075}, {5218, 11230}, {5226, 12699}, {5252, 28208}, {5281, 5886}, {5432, 7743}, {5493, 6147}, {5719, 28194}, {5722, 10385}, {5766, 37822}, {6684, 15172}, {6690, 19878}, {6736, 50241}, {6939, 37820}, {8164, 30332}, {9578, 33697}, {9580, 31479}, {9612, 31480}, {9668, 31434}, {9856, 11491}, {9955, 10624}, {9956, 15171}, {10056, 28202}, {11113, 51362}, {12331, 15837}, {12433, 43174}, {12515, 14151}, {12701, 31452}, {12732, 15670}, {12773, 51767}, {13405, 28174}, {15481, 15733}, {16781, 31430}, {19535, 36846}, {28160, 31397}, {30305, 51709}, {31145, 50742}, {31439, 35809}, {31730, 31776}, {34744, 36867}, {34753, 40270}, {38574, 51766}, {38575, 51769}, {38589, 51770}, {38590, 51765}, {40262, 45776}, {46219, 50444}
X(51787) = midpoint of X(i) and X(j) for these {i,j}: {4640, 25439}, {5119, 24929}
X(51787) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {10, 10386, 31795}, {35, 9957, 13624}, {55, 5119, 24929}, {390, 26446, 18527}, {484, 3746, 3748}, {484, 3748, 942}, {3295, 3579, 5045}, {3746, 37568, 942}, {3748, 37568, 484}, {5010, 5919, 5126}, {9668, 31434, 38140}, {11010, 37080, 50193}, {13151, 35460, 31788}, {13528, 34486, 11227}, {25405, 37600, 31662}, {31393, 31508, 3}, {35460, 37621, 13151}
X(51788) lies on these lines: {1, 3}, {2, 51362}, {7, 3656}, {11, 38140}, {30, 4315}, {58, 45219}, {104, 10569}, {106, 3752}, {145, 17614}, {153, 17618}, {200, 35272}, {214, 14563}, {226, 1387}, {329, 38314}, {355, 6964}, {381, 37704}, {388, 9955}, {392, 3219}, {474, 36846}, {495, 11230}, {496, 10106}, {497, 28160}, {500, 4322}, {515, 7956}, {519, 6692}, {527, 42819}, {550, 12575}, {551, 3452}, {938, 37727}, {946, 22792}, {952, 11019}, {956, 3305}, {957, 25417}, {993, 10179}, {1000, 3654}, {1056, 5226}, {1058, 4308}, {1125, 3820}, {1210, 11545}, {1212, 9327}, {1317, 51087}, {1318, 47058}, {1320, 27003}, {1386, 2810}, {1407, 1480}, {1476, 15179}, {1478, 7743}, {1479, 33697}, {1483, 6738}, {1538, 12115}, {1737, 38176}, {2094, 2320}, {2096, 11036}, {2316, 16666}, {2771, 17625}, {2835, 47115}, {3035, 49626}, {3058, 21578}, {3086, 9956}, {3241, 5440}, {3244, 51714}, {3296, 4323}, {3419, 11240}, {3421, 3616}, {3476, 5722}, {3487, 37822}, {3488, 3655}, {3582, 38083}, {3586, 28208}, {3600, 12699}, {3622, 5129}, {3635, 17706}, {3689, 51093}, {3753, 38460}, {3754, 33895}, {3812, 22837}, {3817, 38757}, {3851, 50444}, {3890, 3916}, {3895, 16371}, {3897, 11106}, {3898, 4640}, {3911, 50821}, {3982, 39542}, {4018, 5330}, {4293, 28146}, {4297, 15172}, {4298, 22791}, {4301, 24470}, {4304, 15170}, {4311, 15171}, {4317, 12701}, {4342, 28174}, {4511, 17658}, {4849, 45763}, {4853, 16408}, {4861, 5439}, {4906, 49682}, {4995, 51084}, {5044, 12513}, {5055, 5726}, {5123, 10199}, {5252, 10072}, {5253, 10914}, {5288, 25917}, {5290, 18493}, {5315, 23071}, {5434, 30384}, {5437, 40587}, {5542, 11715}, {5714, 18220}, {5728, 6265}, {5777, 12128}, {5882, 7682}, {5901, 21620}, {5927, 38669}, {6147, 12577}, {6691, 10915}, {6744, 13607}, {6797, 20586}, {7967, 10580}, {8257, 42871}, {8545, 22758}, {8581, 12773}, {8666, 31445}, {9269, 48330}, {9580, 28154}, {9613, 9669}, {9614, 9655}, {9654, 50443}, {9668, 28168}, {9709, 12629}, {9840, 10108}, {9850, 40263}, {9965, 50742}, {10200, 32049}, {10241, 30283}, {10586, 36977}, {10595, 11037}, {11231, 15325}, {11237, 23708}, {11362, 34753}, {12053, 18990}, {12331, 51767}, {12647, 17728}, {12711, 26201}, {12735, 22935}, {12737, 17626}, {12763, 16173}, {13405, 38028}, {14663, 51771}, {15306, 34036}, {15570, 20116}, {15935, 50824}, {16140, 22936}, {16236, 50805}, {16486, 37817}, {16499, 44307}, {16610, 49494}, {17622, 26200}, {18541, 31162}, {19861, 34790}, {19907, 46681}, {20196, 25055}, {28198, 30305}, {29126, 48328}, {30144, 34791}, {30286, 51515}, {30331, 51705}, {31142, 51105}, {32900, 37739}, {34232, 40172}, {34862, 45776}, {37722, 45287}, {38295, 40985}, {38572, 51766}, {38575, 51770}, {38576, 51765}, {38589, 51769}, {50243, 51111}
X(51788) = midpoint of X(i) and X(j) for these {i,j}: {1, 999}, {1482, 3359}, {3476, 5722}, {5882, 7682}, {7962, 36279}, {8257, 42871}
X(51788) = reflection of X(i) in X(j) for these {i,j}: {3820, 1125}, {18516, 9955}, {35238, 13624}
X(51788) = crosspoint of X(1) and X(15180)
X(51788) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3, 31792}, {1, 36, 5919}, {1, 56, 9957}, {1, 354, 50194}, {1, 942, 10222}, {1, 1319, 24929}, {1, 1420, 3295}, {1, 3304, 942}, {1, 3333, 1482}, {1, 3338, 2098}, {1, 3576, 6767}, {1, 5563, 3057}, {1, 5902, 5048}, {1, 7373, 5045}, {1, 10980, 16200}, {1, 11529, 10247}, {1, 13462, 31393}, {1, 18398, 11011}, {1, 20323, 24928}, {1, 21842, 37080}, {1, 24928, 1385}, {1, 37525, 3748}, {1, 37602, 354}, {1, 37618, 3303}, {55, 5126, 17502}, {56, 5119, 5122}, {56, 9957, 3579}, {226, 1387, 51709}, {388, 11373, 9955}, {495, 44675, 11230}, {496, 10106, 18480}, {942, 9957, 13601}, {1000, 5435, 3654}, {1058, 4308, 18481}, {1058, 18481, 31795}, {1319, 3748, 37525}, {1319, 24929, 1385}, {1420, 3295, 13624}, {1482, 3333, 31794}, {2098, 3338, 50193}, {2099, 31393, 13600}, {3057, 5563, 37582}, {3600, 12699, 31776}, {3748, 37525, 24929}, {5049, 25405, 1}, {5119, 5122, 3579}, {5122, 9957, 5119}, {5882, 21625, 12433}, {10980, 16200, 1159}, {12053, 18990, 22793}, {12577, 13464, 6147}, {13462, 31393, 3}, {15325, 31397, 11231}, {24928, 24929, 1319}
X(51789) lies on these lines: {1, 546}, {8, 3982}, {10, 57}, {12, 13462}, {56, 19872}, {226, 3241}, {495, 30282}, {553, 51068}, {1319, 5219}, {1420, 5261}, {1478, 9580}, {1837, 30350}, {2099, 3633}, {3305, 20060}, {3340, 3621}, {3476, 51103}, {3622, 5226}, {3748, 5691}, {4654, 4677}, {5119, 5270}, {5122, 31434}, {5176, 6173}, {5229, 37556}, {5425, 5881}, {5434, 5726}, {5727, 15934}, {5837, 20214}, {7354, 31508}, {9613, 24929}, {9654, 50443}, {9963, 41553}, {11236, 20196}, {12763, 51768}, {13273, 51767}, {31266, 34716}, {37711, 41870}
X(51789) = {X(5434),X(5726)}-harmonic conjugate of X(31231)
X(51790) lies on these lines: {1, 3627}, {4, 57}, {7, 50687}, {12, 31508}, {30, 5219}, {226, 3543}, {381, 5122}, {382, 9612}, {484, 5587}, {546, 15803}, {938, 4114}, {942, 5076}, {950, 17578}, {1319, 1699}, {1420, 18483}, {1478, 9580}, {1697, 5229}, {1770, 18492}, {1836, 5727}, {1892, 13473}, {2093, 11545}, {2099, 5691}, {2475, 3305}, {3146, 3601}, {3340, 31673}, {3585, 5119}, {3586, 3830}, {3587, 6923}, {3614, 16192}, {3748, 5290}, {3839, 3911}, {3853, 37723}, {3982, 11518}, {4304, 15682}, {4313, 50690}, {4333, 31423}, {5128, 19925}, {5175, 20214}, {5218, 28158}, {5252, 50865}, {5438, 31295}, {5703, 50691}, {5719, 33699}, {5722, 15687}, {5818, 41348}, {7354, 13462}, {7962, 9812}, {7988, 15326}, {8227, 10483}, {9613, 22793}, {9614, 9655}, {10248, 12053}, {10385, 50869}, {10404, 30350}, {10590, 28150}, {10724, 41553}, {10725, 15730}, {10826, 16118}, {11112, 20196}, {11113, 41867}, {11114, 25525}, {12699, 37709}, {12763, 51767}, {13273, 51768}, {13384, 28164}, {13411, 33703}, {15950, 34628}, {17579, 30827}, {18228, 50737}, {18393, 50811}, {18541, 38335}, {21578, 38021}, {28146, 31434}, {28154, 31479}, {31053, 34701}, {31190, 37375}, {34595, 50243}
X(51790) = reflection of X(35445) in X(10590)
X(51790) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 9579, 9581}, {3585, 41869, 9578}, {5229, 51118, 1697}, {5290, 12953, 41864}
X(51791) lies on these lines: {1, 3627}, {11, 31508}, {57, 497}, {149, 3305}, {528, 20196}, {950, 5734}, {1319, 9670}, {1479, 9578}, {1697, 5818}, {1699, 3748}, {1836, 30350}, {3058, 5219}, {3219, 24392}, {3586, 28204}, {3982, 9812}, {4114, 10580}, {4857, 5119}, {5225, 37556}, {5226, 10389}, {5274, 35445}, {5425, 31162}, {5727, 5844}, {6284, 13462}, {9614, 18493}, {9668, 28168}, {11238, 31231}, {12701, 18421}, {12764, 51767}, {13274, 51768}, {15006, 30275}, {15171, 30282}, {30827, 34611}, {41867, 49736}
X(51792) lies on these lines: {1, 546}, {4, 57}, {5, 30282}, {11, 13462}, {12, 41858}, {30, 31231}, {80, 31162}, {226, 3839}, {381, 3586}, {382, 5122}, {484, 10826}, {938, 3982}, {950, 3832}, {1319, 5691}, {1420, 10591}, {1421, 36985}, {1479, 9578}, {1697, 5225}, {1698, 12953}, {1699, 2099}, {1718, 9611}, {1837, 15911}, {2093, 12019}, {3058, 5726}, {3091, 3601}, {3305, 5046}, {3340, 18483}, {3419, 31142}, {3476, 34648}, {3486, 12571}, {3488, 41099}, {3543, 3911}, {3545, 4304}, {3576, 6982}, {3583, 5119}, {3587, 6928}, {3627, 15803}, {3748, 10895}, {3817, 13384}, {3843, 9612}, {3845, 4654}, {3854, 4313}, {3855, 13411}, {3858, 11374}, {4333, 15079}, {5076, 37582}, {5080, 24392}, {5123, 34706}, {5128, 51118}, {5187, 5438}, {5435, 50687}, {5436, 6871}, {5560, 21398}, {5704, 50688}, {5719, 23046}, {6175, 20195}, {6284, 7989}, {7173, 7987}, {7741, 37406}, {8227, 37525}, {9613, 9669}, {9614, 18480}, {9668, 31434}, {10175, 35445}, {10385, 50803}, {10389, 10590}, {10589, 28164}, {11518, 50689}, {11545, 12699}, {12701, 37714}, {12764, 51768}, {13274, 51767}, {15683, 31188}, {15950, 30308}, {16860, 19872}, {17532, 41867}, {17556, 20196}, {17577, 25525}, {17579, 31190}, {18528, 37736}, {18782, 37584}, {20214, 24391}, {23708, 50811}, {30305, 50796}, {30827, 37375}, {30852, 34701}, {31410, 40270}, {40663, 50865}
X(51792) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 9581, 9579}, {381, 3586, 5219}, {1479, 18492, 9578}, {3583, 5587, 9580}, {5225, 19925, 1697}, {5691, 10896, 50443}, {9614, 18480, 37709}, {9668, 38140, 31434}, {10591, 31673, 1420}, {10826, 18514, 41869}
X(51793) lies on these lines: {1, 14094}, {57, 2948}, {74, 31508}, {110, 13462}, {222, 6126}, {2771, 15934}, {4315, 9143}, {5119, 9904}, {5226, 13605}, {5655, 37704}, {5663, 31393}, {5726, 9140}, {10088, 30282}, {24929, 33535}
X(51794) lies on these lines: {1, 15054}, {57, 3024}, {74, 13462}, {110, 31508}, {2836, 5697}, {2948, 5119}, {5663, 31393}, {5726, 10706}, {10065, 30282}, {20126, 37704}
X(51795) lies on these lines: {1, 23235}, {7, 2796}, {57, 3027}, {98, 31508}, {99, 13462}, {671, 5726}, {2782, 31393}, {2786, 30572}, {4315, 8591}, {5119, 9860}, {5219, 12350}, {5226, 11599}, {5252, 9875}, {8724, 37704}, {10086, 30282}, {24472, 30350}
X(51796) lies on these lines: {1, 38664}, {57, 3023}, {98, 13462}, {99, 31508}, {2782, 31393}, {2784, 4307}, {3586, 9875}, {4315, 11177}, {5119, 13174}, {5226, 21636}, {5726, 6054}, {10053, 30282}, {11632, 37704}, {12351, 31231}
X(51797) lies on the cubics K729 and K1286 and these lines: {3, 19140}, {6, 23}, {110, 599}, {182, 381}, {184, 15534}, {206, 3763}, {511, 11935}, {1176, 7703}, {1350, 7502}, {1351, 19150}, {1386, 5902}, {1495, 12039}, {2930, 26864}, {5012, 32069}, {5085, 11472}, {6144, 19121}, {6593, 15080}, {7728, 25566}, {7784, 14247}, {9306, 51186}, {9544, 15533}, {9970, 34513}, {9971, 32237}, {10117, 19153}, {10510, 35268}, {10546, 32154}, {10606, 15578}, {11179, 44266}, {11464, 33851}, {11579, 14852}, {12017, 18551}, {18550, 19151}, {18572, 46264}, {18911, 47453}, {21358, 37283}, {25335, 37638}, {32111, 51737}, {40341, 41615}, {43576, 48872}, {43977, 44557}, {44961, 47455}
X(51797) = midpoint of X(7712) and X(43697)
X(51797) = reflection of X(6) in X(43697)
X(51797) = isogonal conjugate of X(34213)
X(51797) = isogonal conjugate of the isotomic conjugate of X(6031)
X(51797) = X(i)-isoconjugate of X(j) for these (i,j): {1, 34213}, {75, 30488}
X(51797) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 34213), (206, 30488)
X(51797) = barycentric product X(6)*X(6031)
X(51797) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 34213}, {32, 30488}, {6031, 76}
X(51797) = {X(11003),X(32217)}-harmonic conjugate of X(6)
X(51798) lies on the cubic K1286 and these lines: {2, 353}, {3, 67}, {6, 543}, {30, 12151}, {83, 597}, {98, 11168}, {99, 524}, {110, 1641}, {114, 47353}, {115, 14535}, {126, 46276}, {141, 11161}, {147, 11150}, {182, 11632}, {187, 16508}, {194, 1992}, {230, 9877}, {530, 22689}, {531, 22687}, {549, 19905}, {590, 13642}, {615, 13761}, {620, 21358}, {690, 34319}, {732, 44367}, {804, 5652}, {1386, 50886}, {1503, 6054}, {1691, 22329}, {2782, 11179}, {2796, 49477}, {3589, 9166}, {3618, 41135}, {3763, 9167}, {5032, 20094}, {5085, 6055}, {5459, 33409}, {5460, 33408}, {5461, 7834}, {5471, 42035}, {5472, 42036}, {5476, 6321}, {5477, 11173}, {5978, 51159}, {5979, 51160}, {5989, 11163}, {6033, 11645}, {6593, 9144}, {6779, 9116}, {6780, 9114}, {7832, 20582}, {7840, 12215}, {8030, 9146}, {8352, 44380}, {8550, 23235}, {8584, 10754}, {8596, 14035}, {8597, 41137}, {9027, 32442}, {9041, 9884}, {9117, 36775}, {9127, 9225}, {9143, 14916}, {9172, 20998}, {9772, 11177}, {9773, 34803}, {9829, 15080}, {9855, 22561}, {9880, 38072}, {9881, 28538}, {9890, 37809}, {10168, 38224}, {10485, 11185}, {10541, 11623}, {10753, 12117}, {10808, 10809}, {10992, 11477}, {11160, 33208}, {11178, 15561}, {11711, 47358}, {12258, 38023}, {12355, 14848}, {14061, 48310}, {14360, 39689}, {14971, 47355}, {15533, 36521}, {15993, 19911}, {18440, 25562}, {19687, 20583}, {19924, 38730}, {22562, 22563}, {22579, 22685}, {22580, 22683}, {23234, 47354}, {33265, 50640}, {33432, 49214}, {33433, 49215}, {34369, 37858}, {34504, 44453}, {35749, 49804}, {35750, 49853}, {35751, 49900}, {35752, 49944}, {36327, 49805}, {36329, 49899}, {36330, 49943}, {36331, 49854}, {38064, 49102}, {40866, 45331}, {41939, 42008}, {42849, 50659}, {49524, 50885}, {50781, 51578}, {50888, 51147}
X(51798) = midpoint of X(i) and X(j) for these {i,j}: {99, 8593}, {599, 10488}, {1992, 8591}, {5477, 15300}, {9114, 51200}, {9116, 51203}, {9855, 39099}, {10753, 12117}, {11161, 45018}, {14928, 18800}
X(51798) = reflection of X(i) in X(j) for these {i,j}: {2, 5026}, {6, 18800}, {98, 51737}, {599, 2482}, {671, 597}, {1992, 8787}, {5104, 8598}, {5476, 32135}, {6034, 5182}, {6321, 5476}, {8352, 44380}, {9144, 6593}, {10754, 8584}, {11161, 141}, {11632, 182}, {11646, 2}, {15533, 50567}, {15534, 5477}, {15993, 27088}, {18440, 25562}, {19905, 549}, {47353, 114}, {47358, 11711}, {50567, 36521}, {50781, 51578}, {50885, 49524}, {50886, 1386}, {50888, 51147}
X(51798) = psi-transform of X(9829)
X(51798) = crossdifference of every pair of points on line {2492, 9023}
X(51798) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 8592, 35705}, {110, 10717, 1641}, {597, 671, 6034}, {671, 5182, 597}, {5463, 5464, 8724}, {8289, 8592, 2}, {9146, 10554, 8030}, {9167, 19662, 3763}, {9966, 34013, 2930}, {11161, 41134, 141}, {22562, 22563, 22566}, {41134, 45018, 11161}
X(51799) lies on the cubic K1286 and these lines: {3, 11178}, {23, 9829}, {32, 30489}, {110, 353}, {1995, 9699}, {3734, 7492}, {7617, 14002}, {11648, 13233}, {33981, 34013}
X(51800) lies on the cubic K1286 and these lines: {2, 5191}, {3, 19140}, {827, 14388}, {842, 2080}, {1384, 2079}, {1576, 35002}, {3398, 9142}, {13115, 34217}, {14270, 34291}, {14685, 32235}, {15922, 33980}
X(51800) = circumcircle-inverse of X(19140)
X(51800) = psi-transform of X(15080)
X(51800) = {X(5191),X(26316)}-harmonic conjugate of X(14830)
X(51801) lies on the cubic K1287 and these lines: {1, 1748}, {35, 186}, {36, 11587}, {158, 2962}, {162, 1749}, {204, 920}, {240, 522}, {1087, 2181}, {1870, 2914}, {6149, 35201}
X(51801) = polar conjugate of the isogonal conjugate of X(2290)
X(51801) = X(i)-Ceva conjugate of X(j) for these (i,j): {1, 35201}, {17515, 186}
X(51801) = X(i)-isoconjugate of X(j) for these (i,j): {2, 11077}, {3, 1141}, {4, 50463}, {54, 265}, {94, 14533}, {96, 5961}, {97, 1989}, {184, 46138}, {275, 50433}, {476, 23286}, {539, 15401}, {933, 43083}, {1157, 15392}, {2166, 2169}, {2616, 36061}, {3463, 34304}, {6344, 19210}, {6368, 46966}, {10412, 15958}, {11060, 34386}, {11079, 43768}, {14254, 46090}, {14582, 18315}, {14586, 14592}, {14859, 22115}, {15412, 32662}, {36296, 51268}, {36297, 51275}, {46088, 46456}
X(51801) = X(i)-Dao conjugate of X(j) for these (i, j): (11597, 2169), (14363, 2166), (14920, 75), (16221, 2616), (17433, 656), (18402, 1), (32664, 11077), (34544, 97), (36033, 50463), (36103, 1141)
X(51801) = barycentric product X(i)*X(j) for these {i,j}: {1, 14918}, {19, 1273}, {75, 11062}, {92, 1154}, {162, 41078}, {186, 14213}, {264, 2290}, {324, 6149}, {340, 1953}, {811, 2081}, {2181, 7799}, {2617, 44427}, {2618, 14590}, {14165, 44706}, {17923, 35194}, {32679, 35360}
X(51801) = barycentric quotient X(i)/X(j) for these {i,j}: {19, 1141}, {31, 11077}, {48, 50463}, {50, 2169}, {53, 2166}, {92, 46138}, {186, 2167}, {1154, 63}, {1273, 304}, {1625, 36061}, {1953, 265}, {2081, 656}, {2180, 5961}, {2181, 1989}, {2290, 3}, {2618, 14592}, {2624, 23286}, {6149, 97}, {11062, 1}, {14165, 40440}, {14213, 328}, {14591, 36134}, {14918, 75}, {34397, 2148}, {35201, 43768}, {35360, 32680}, {41078, 14208}, {47230, 2616}
X(51801) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {240, 1725, 1784}, {1725, 1784, 36063}
X(51802) lies on the cubic K1287 and these lines: {1, 35195}, {35, 1511}, {36, 1154}, {48, 16562}, {662, 2166}, {820, 2169}, {1100, 34544}, {2964, 4575}, {5353, 19294}, {5357, 19295}, {40214, 47054}
X(51802) = X(i)-Ceva conjugate of X(j) for these (i,j): {1, 6149}, {35195, 1154}
X(51802) = X(i)-isoconjugate of X(j) for these (i,j): {2, 11071}, {4, 15392}, {13, 46076}, {14, 46072}, {94, 14579}, {1117, 1138}, {1141, 1263}, {1291, 10412}, {1989, 13582}, {3459, 34302}, {3471, 5627}, {6344, 43704}
X(51802) = X(i)-Dao conjugate of X(j) for these (i, j): (323, 75), (10413, 1577), (32664, 11071), (34544, 13582), (36033, 15392)
X(51802) = crosspoint of X(1) and X(1749)
X(51802) = barycentric product X(i)*X(j) for these {i,j}: {1, 40604}, {63, 2914}, {163, 45790}, {323, 1749}, {662, 8562}, {1273, 19306}, {6149, 37779}, {32679, 47053}
X(51802) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 11071}, {48, 15392}, {1749, 94}, {2151, 46076}, {2152, 46072}, {2290, 1263}, {2914, 92}, {6149, 13582}, {8562, 1577}, {11063, 2166}, {19303, 1117}, {19306, 1141}, {40604, 75}, {45790, 20948}, {47053, 32680}
X(518031) lies on the cubic K1287 and these lines: {1, 195}, {11, 50708}, {12, 22051}, {35, 54}, {36, 1154}, {56, 12316}, {499, 12325}, {1493, 3746}, {1737, 5397}, {1870, 2914}, {2888, 7741}, {3299, 12965}, {3301, 12971}, {3583, 32423}, {3585, 20424}, {5270, 11803}, {5353, 10678}, {5357, 10677}, {5563, 7356}, {5697, 9905}, {6284, 36966}, {7127, 35199}, {7280, 12307}, {7343, 43704}, {9638, 12291}, {11271, 37720}, {11399, 12175}, {12266, 24926}, {12896, 14049}, {14101, 31674}, {14102, 27246}, {18514, 48675}, {19470, 43580}, {19658, 51751}, {22765, 32899}, {22781, 44759}, {38458, 50461}
X(51803) = X(6149)-cross conjugate of X(36)
X(51803) = X(i)-isoconjugate of X(j) for these (i,j): {2, 11069}, {80, 3336}, {484, 14452}, {1411, 27529}, {2161, 17483}, {2166, 35197}, {6187, 46749}, {7165, 34300}, {18359, 21773}, {21863, 24624}, {35174, 42649}
X(51803) = X(i)-Dao conjugate of X(j) for these (i, j): (11597, 35197), (32664, 11069), (35204, 27529), (40584, 17483), (40612, 46749)
X(51803) = barycentric product X(i)*X(j) for these {i,j}: {3218, 3467}, {7113, 46750}
X(51803) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 11069}, {36, 17483}, {50, 35197}, {2323, 27529}, {3218, 46749}, {3467, 18359}, {3724, 21863}, {7113, 3336}, {19302, 14452}
X(51803) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 195, 35197}, {54, 6286, 35}, {1493, 13079, 47378}, {7356, 10082, 5563}, {10082, 15801, 7356}, {13079, 47378, 3746}
X(51804) lies on the cubic K1287 and these lines: {1, 35195}, {10, 13582}, {19, 19303}, {35, 14367}, {37, 14579}, {65, 6126}, {484, 1263}, {759, 1291}, {1109, 2962}, {1749, 2166}, {1910, 16546}, {2153, 35198}, {2154, 35199}, {2190, 35201}, {3065, 5671}, {3336, 3471}, {3467, 38935}, {35055, 47054}
X(51804) = isogonal conjugate of X(1749)
X(51804) = X(6149)-cross conjugate of X(1)
X(51804) = X(i)-isoconjugate of X(j) for these (i,j): {1, 1749}, {2, 11063}, {3, 37943}, {4, 50461}, {5, 1157}, {6, 37779}, {13, 5616}, {14, 5612}, {15, 51267}, {16, 51274}, {30, 3470}, {74, 10272}, {99, 6140}, {110, 45147}, {195, 11584}, {249, 10413}, {265, 2914}, {399, 14451}, {476, 8562}, {523, 47053}, {1138, 15766}, {1495, 46751}, {1989, 40604}, {2070, 38542}, {3459, 15770}, {6592, 33643}, {8487, 18285}, {14213, 19306}, {14354, 14993}, {14560, 45790}
X(51804) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 1749), (9, 37779), (244, 45147), (32664, 11063), (34544, 40604), (36033, 50461), (36103, 37943), (38986, 6140)
X(51804) = cevapoint of X(2624) and X(2643)
X(51804) = trilinear pole of line {661, 17438}
X(51804) = barycentric product X(i)*X(j) for these {i,j}: {1, 13582}, {75, 14579}, {92, 43704}, {1263, 2167}, {1291, 1577}, {2349, 3471}, {20879, 43657}
X(51804) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 37779}, {6, 1749}, {19, 37943}, {31, 11063}, {48, 50461}, {163, 47053}, {661, 45147}, {798, 6140}, {1263, 14213}, {1291, 662}, {2148, 1157}, {2151, 5616}, {2152, 5612}, {2153, 51267}, {2154, 51274}, {2159, 3470}, {2173, 10272}, {2349, 46751}, {2624, 8562}, {2643, 10413}, {3471, 14206}, {6149, 40604}, {11071, 2166}, {13582, 75}, {14579, 1}, {19303, 15766}, {32679, 45790}, {43704, 63}
X(51805) lies on the cubics K221 and K1287 and these lines: {1, 1094}, {13, 79}, {35, 6104}, {80, 38943}, {1725, 2159}, {2154, 2166}, {5353, 6126}, {35199, 35201}, {39150, 46078}
X(51805) = X(i)-isoconjugate of X(j) for these (i,j): {2, 11086}, {4, 50466}, {6, 11092}, {13, 36209}, {14, 15}, {16, 36210}, {18, 6105}, {61, 11600}, {110, 23284}, {186, 10218}, {298, 3458}, {301, 34394}, {323, 11085}, {470, 36297}, {526, 36840}, {533, 16460}, {618, 2380}, {1094, 2166}, {1989, 11131}, {2307, 36932}, {5616, 46076}, {5994, 23870}, {6110, 39378}, {6137, 23896}, {8603, 16771}, {8738, 44718}, {8739, 40710}, {9204, 9207}, {11060, 11129}, {11087, 11146}, {11088, 19778}, {11127, 11138}, {14920, 39381}, {17402, 20579}, {18776, 47072}, {23715, 47482}, {39150, 42680}, {39152, 46077}
X(51805) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 11092), (244, 23284), (11597, 1094), (32664, 11086), (34544, 11131), (36033, 50466)
X(51805) = barycentric product X(i)*X(j) for these {i,j}: {1, 11078}, {75, 11081}, {92, 50465}, {94, 1095}, {299, 2153}, {300, 2152}, {559, 36933}, {662, 23283}, {2166, 11130}, {3375, 8838}, {32679, 36839}
X(51805) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 11092}, {31, 11086}, {48, 50466}, {50, 1094}, {661, 23284}, {1095, 323}, {1251, 36932}, {2151, 36209}, {2152, 15}, {2153, 14}, {2154, 36210}, {3383, 8836}, {3457, 2154}, {6149, 11131}, {8604, 3384}, {11078, 75}, {11080, 2166}, {11081, 1}, {11083, 3376}, {11134, 35198}, {23283, 1577}, {32678, 36840}, {34395, 2151}, {35199, 11146}, {36839, 32680}, {50465, 63}
X(51805) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3383, 2153}, {1, 19298, 1094}, {2306, 19551, 13}
X(51806) lies on the cubics K221 and K1287 and these lines: {1, 1095}, {14, 79}, {35, 6105}, {80, 38944}, {1725, 2159}, {2153, 2166}, {5357, 6126}, {35198, 35201}, {39151, 46074}
X(51806) = X(i)-isoconjugate of X(j) for these (i,j): {2, 11081}, {4, 50465}, {6, 11078}, {13, 16}, {14, 36208}, {15, 36211}, {17, 6104}, {62, 11601}, {110, 23283}, {186, 10217}, {299, 3457}, {300, 34395}, {323, 11080}, {471, 36296}, {526, 36839}, {532, 16459}, {619, 2381}, {1095, 2166}, {1989, 11130}, {5612, 46072}, {5995, 23871}, {6111, 39377}, {6138, 23895}, {8604, 16770}, {8737, 44719}, {8740, 40709}, {9205, 9206}, {11060, 11128}, {11082, 11145}, {11083, 19779}, {11126, 11139}, {14920, 39380}, {17403, 20578}, {18777, 47073}, {23714, 47481}, {39151, 42677}, {39153, 46073}
X(51806) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 11078), (244, 23283), (11597, 1095), (32664, 11081), (34544, 11130), (36033, 50465)
X(51806) = barycentric product X(i)*X(j) for these {i,j}: {1, 11092}, {75, 11086}, {92, 50466}, {94, 1094}, {298, 2154}, {301, 2151}, {662, 23284}, {1082, 36932}, {2166, 11131}, {3384, 8836}, {32679, 36840}
X(51806) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 11078}, {31, 11081}, {48, 50465}, {50, 1095}, {661, 23283}, {1094, 323}, {2151, 16}, {2152, 36208}, {2153, 36211}, {2154, 13}, {3376, 8838}, {3458, 2153}, {6149, 11130}, {8603, 3375}, {11085, 2166}, {11086, 1}, {11088, 3383}, {11092, 75}, {11137, 35199}, {23284, 1577}, {32678, 36839}, {33653, 36933}, {34394, 2152}, {35198, 11145}, {36840, 32680}, {50466, 63}
X(51806) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 3376, 2154}, {1, 19299, 1095}, {7126, 33654, 14}
X(51807) lies on these lines: {1, 6946}, {57, 1361}, {108, 13462}, {1054, 5119}, {1739, 47623}, {1769, 51768}, {4674, 8056}, {6014, 31508}, {29820, 37525}, {30282, 51769}
X(51808) lies on these lines: {1, 38667}, {57, 1364}, {102, 13462}, {109, 31508}, {151, 51782}, {1361, 51779}, {1742, 2807}, {2773, 51794}, {2779, 51793}, {2785, 51796}, {2792, 51795}, {2800, 51767}, {2814, 51770}, {2815, 51765}, {2817, 18421}, {2818, 31393}, {2835, 51769}, {3040, 51781}, {3042, 51780}, {3465, 34371}, {3738, 51768}, {5726, 10709}, {33650, 51783}, {38573, 51788}, {38579, 51787}
X(51809) lies on these lines: {1, 23056}, {57, 3022}, {101, 31508}, {103, 13462}, {150, 51783}, {152, 51782}, {165, 4845}, {1282, 5119}, {1362, 51779}, {2772, 51793}, {2774, 51794}, {2784, 51795}, {2786, 51796}, {2801, 9819}, {2808, 31393}, {2809, 51769}, {2820, 51770}, {2821, 51765}, {3041, 51781}, {3887, 51768}, {5726, 10710}, {11224, 34930}, {38572, 51787}, {38574, 51788}
X(51809) = reflection of X(51766) in X(31393)
X(51810) lies on these lines: {1, 38670}, {57, 5580}, {1282, 5119}, {2291, 31508}, {10058, 15015}, {13462, 28291}, {24333, 51796}, {24436, 40292}, {44764, 51794}, {47006, 51779}
X(51811) lies on these lines: {1, 38685}, {57, 6018}, {106, 31508}, {1054, 5119}, {1293, 13462}, {1357, 51779}, {2776, 51793}, {2789, 51795}, {2796, 51796}, {2802, 4915}, {2821, 51766}, {2827, 51767}, {2832, 51769}, {2842, 51794}, {3038, 51781}, {9519, 9819}, {21290, 51783}, {31393, 51765}, {34548, 51782}, {38576, 51787}, {38590, 51788}
X(51811) = reflection of X(51765) in X(31393)
X(51812) lies on these lines: {1, 15157}, {30, 31393}, {57, 2100}, {1113, 13462}, {1114, 31508}, {2101, 5119}, {2574, 51793}, {2575, 51794}, {4315, 15158}, {5726, 10719}, {14807, 51782}, {14808, 51783}, {15154, 51788}, {15155, 51787}, {20408, 51784}, {20409, 51785}
X(51813) lies on these lines: {1, 15156}, {30, 31393}, {57, 2101}, {1113, 31508}, {1114, 13462}, {2100, 5119}, {2574, 51794}, {2575, 51793}, {4315, 15159}, {5726, 10720}, {14807, 51783}, {14808, 51782}, {15154, 51787}, {15155, 51788}, {20408, 51785}, {20409, 51784}
X(51814) lies on these lines: {1, 38675}, {57, 3325}, {111, 13462}, {543, 51795}, {1296, 31508}, {2780, 51794}, {2793, 51796}, {2805, 51767}, {2813, 51766}, {2830, 51768}, {2837, 51770}, {2843, 51765}, {2854, 51793}, {5726, 10717}, {6019, 51779}, {9522, 51769}, {11258, 51788}, {14360, 51782}, {31393, 33962}, {38593, 51787}
X(51815) lies on these lines: {1, 38688}, {57, 6019}, {111, 31508}, {543, 51796}, {1296, 13462}, {2780, 51793}, {2793, 51795}, {2805, 51768}, {2824, 51766}, {2830, 51767}, {2837, 51769}, {2854, 51794}, {3325, 51779}, {4315, 37749}, {9522, 51770}, {9526, 51765}, {11258, 51787}, {14360, 51783}, {31393, 33962}, {38593, 51788}
X(51816) lies on these lines: {1, 3}, {7, 7284}, {9, 25055}, {58, 28011}, {63, 551}, {78, 3881}, {79, 4355}, {80, 41556}, {84, 5557}, {90, 3296}, {169, 17474}, {173, 30423}, {226, 10072}, {258, 30411}, {377, 49627}, {388, 6896}, {474, 34791}, {495, 17728}, {496, 10404}, {499, 21620}, {519, 3306}, {529, 17051}, {938, 37721}, {946, 3982}, {950, 4317}, {956, 3742}, {993, 4666}, {997, 3873}, {1056, 1737}, {1058, 1770}, {1125, 3305}, {1158, 10595}, {1210, 10827}, {1373, 34495}, {1374, 34494}, {1449, 2174}, {1468, 46190}, {1476, 17098}, {1478, 11019}, {1479, 4298}, {1698, 6762}, {1706, 3633}, {1709, 5603}, {1728, 3487}, {1743, 47299}, {1768, 11034}, {2163, 35227}, {2999, 16474}, {3086, 5226}, {3218, 38314}, {3219, 3616}, {3241, 27003}, {3244, 51786}, {3293, 11512}, {3476, 50818}, {3488, 21578}, {3524, 18490}, {3555, 25524}, {3577, 15180}, {3582, 5219}, {3583, 51790}, {3584, 31231}, {3585, 51792}, {3600, 10572}, {3622, 12514}, {3624, 17590}, {3632, 51781}, {3636, 5250}, {3649, 11373}, {3679, 5437}, {3689, 16417}, {3729, 4975}, {3751, 9039}, {3754, 36846}, {3811, 3889}, {3870, 3892}, {3872, 5883}, {3874, 19861}, {3895, 51071}, {3901, 15829}, {3911, 10056}, {3915, 9340}, {3928, 51105}, {3929, 51110}, {3983, 16863}, {4004, 10912}, {4031, 28194}, {4114, 12053}, {4292, 21625}, {4293, 10580}, {4304, 50815}, {4309, 40270}, {4311, 6744}, {4321, 41861}, {4324, 41864}, {4333, 15171}, {4338, 12701}, {4654, 18393}, {4662, 16862}, {4692, 30567}, {4857, 9579}, {4973, 35258}, {5234, 25542}, {5249, 45700}, {5251, 10582}, {5252, 11545}, {5270, 9581}, {5289, 24473}, {5290, 7741}, {5292, 23675}, {5298, 37703}, {5434, 5722}, {5439, 12513}, {5440, 40726}, {5443, 10396}, {5445, 51784}, {5529, 49498}, {5541, 50843}, {5542, 8545}, {5558, 5703}, {5587, 51789}, {5851, 16173}, {5904, 8583}, {6147, 11376}, {6261, 45977}, {6763, 31435}, {7171, 11552}, {7289, 16491}, {7313, 39958}, {7330, 9624}, {7956, 12678}, {8257, 51099}, {9331, 9574}, {9336, 9575}, {9589, 9841}, {9612, 37720}, {9613, 37702}, {9776, 34625}, {10074, 18240}, {10090, 41553}, {10106, 37711}, {10199, 30852}, {10385, 50813}, {10390, 15175}, {10461, 28619}, {10527, 51706}, {10529, 12609}, {10586, 21616}, {10597, 12616}, {10864, 22792}, {11038, 15298}, {11520, 30144}, {11712, 34925}, {11813, 31164}, {12047, 14986}, {12611, 18540}, {12763, 37718}, {12943, 18527}, {12953, 31776}, {15325, 17718}, {16137, 16140}, {16370, 42819}, {16666, 23073}, {17647, 41709}, {17722, 48825}, {17742, 29660}, {18391, 37708}, {18613, 23206}, {19875, 51362}, {21454, 30305}, {26725, 41571}, {28039, 49744}, {34036, 51656}, {38052, 41555}, {38476, 49474}, {41869, 51791}
X(51816) = X(18490)-Ceva conjugate of X(1)
X(51816) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 56, 3612}, {1, 57, 5119}, {1, 65, 30323}, {1, 484, 31393}, {1, 3333, 3338}, {1, 3336, 1697}, {1, 3337, 40}, {1, 3338, 46}, {1, 3339, 5697}, {1, 3361, 35}, {1, 5010, 10389}, {1, 5563, 37618}, {1, 5902, 25415}, {1, 10980, 5902}, {1, 11010, 37556}, {1, 13462, 37525}, {1, 15803, 3746}, {1, 18193, 4424}, {1, 37587, 3576}, {3, 17609, 1}, {55, 5049, 1}, {56, 5045, 1}, {56, 40292, 36}, {57, 5119, 46}, {57, 31393, 484}, {57, 51779, 40}, {65, 7373, 1}, {226, 10072, 23708}, {354, 999, 1}, {354, 1319, 15934}, {484, 31393, 5119}, {938, 45287, 37721}, {942, 3304, 1}, {942, 51788, 2099}, {999, 15934, 1319}, {999, 22767, 5563}, {1319, 15934, 1}, {2099, 3304, 51788}, {2099, 17699, 5119}, {2099, 51788, 1}, {3086, 11037, 13407}, {3086, 13407, 37692}, {3338, 5119, 57}, {3361, 30343, 1}, {3576, 44841, 1}, {3889, 5253, 3811}, {4355, 9614, 79}, {4654, 37704, 18393}, {5563, 37525, 13462}, {5563, 50190, 1}, {5902, 37602, 1}, {10222, 37612, 40}, {10246, 44840, 1}, {10980, 37602, 25415}, {11531, 35010, 37560}, {12701, 24470, 4338}, {13462, 30350, 1}, {13462, 37525, 37618}, {40726, 42871, 5440}
X(51817) lies on these lines: {1, 3}, {11, 11539}, {33, 47485}, {37, 20997}, {100, 16858}, {109, 28153}, {187, 9331}, {390, 3582}, {495, 15686}, {497, 15702}, {498, 3832}, {547, 5432}, {612, 37913}, {758, 16558}, {902, 5313}, {993, 4677}, {1015, 15602}, {1030, 16673}, {1124, 6430}, {1250, 34754}, {1253, 6149}, {1335, 6429}, {1376, 17542}, {1478, 11001}, {1479, 5067}, {1621, 36006}, {1698, 16859}, {2067, 6486}, {2276, 5008}, {2308, 5312}, {2330, 37517}, {3056, 50664}, {3058, 11812}, {3085, 4324}, {3244, 17548}, {3533, 4857}, {3543, 3584}, {3545, 3583}, {3585, 8164}, {3614, 41991}, {3632, 4189}, {3633, 5267}, {3636, 37307}, {3845, 4995}, {3850, 6284}, {4294, 5056}, {4304, 38155}, {4309, 5274}, {4316, 10056}, {4421, 5251}, {4668, 8715}, {4853, 45392}, {5041, 5332}, {5248, 17536}, {5258, 8168}, {5259, 16854}, {5268, 13595}, {5284, 17535}, {5288, 19535}, {5315, 21000}, {5326, 7741}, {5561, 28146}, {5687, 19539}, {5727, 28463}, {6484, 35809}, {6485, 35808}, {6487, 6502}, {6914, 37712}, {7031, 31451}, {8167, 16864}, {8540, 39561}, {9336, 37512}, {9778, 11552}, {10385, 15719}, {10386, 37720}, {10593, 41992}, {10638, 34755}, {11551, 50808}, {15079, 31795}, {15171, 16239}, {15228, 17718}, {15325, 41983}, {15338, 37719}, {16370, 48696}, {17549, 25439}, {18990, 41981}, {19704, 51094}, {21508, 29602}, {31245, 34707}, {31479, 38335}, {32141, 37714}, {40091, 41451}
X(51817) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {35, 55, 5010}, {35, 3746, 5217}, {55, 999, 3746}, {55, 5010, 1}, {55, 5217, 999}, {498, 4330, 18514}, {1697, 37616, 1}, {3584, 4302, 18513}, {3601, 11010, 1}, {3612, 37563, 1}, {3746, 5217, 7280}, {3746, 7280, 1}, {4302, 5281, 3584}, {5010, 37587, 3}, {8186, 8187, 4860}
X(51818) lies on the cubics K888 and K890 and these lines: {6, 3425}, {39, 15562}, {111, 47200}, {112, 186}, {184, 353}, {574, 2794}, {1297, 3098}, {5024, 11641}, {5171, 38676}, {5188, 38689}, {6200, 48789}, {6396, 48788}, {7761, 10718}, {10313, 11649}, {10979, 34841}, {13195, 41412}, {13509, 14917}, {15462, 22240}
X(51818) = {X(19165),X(38652)}-harmonic conjugate of X(11610)
X(51819) lies on the cubic K969 and these lines: {2, 99}, {25, 2489}, {32, 41936}, {184, 32740}, {1194, 5968}, {3291, 11634}, {3981, 46154}, {14948, 34574}, {15398, 36182}, {21001, 36821}, {40350, 46589}
X(51819) = isogonal conjugate of the isotomic conjugate of X(14263)
X(51819) = X(111)-Ceva conjugate of X(3291)
X(51819) = crosspoint of X(111) and X(41936)
X(51819) = crosssum of X(524) and X(36792)
X(51819) = crossdifference of every pair of points on line {351, 6390}
X(51819) = X(i)-isoconjugate of X(j) for these (i,j): {75, 34161}, {14210, 41909}, {24038, 44182}
X(51819) = X(i)-Dao conjugate of X(j) for these (i, j): (126, 3266), (206, 34161), (15477, 41909), (34158, 69)
X(51819) = barycentric product X(i)*X(j) for these {i,j}: {6, 14263}, {111, 3291}, {126, 41936}, {895, 5140}, {8681, 8753}, {9134, 32729}, {9178, 11634}, {21905, 34574}, {32740, 47286}
X(51819) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 34161}, {3291, 3266}, {5140, 44146}, {14263, 76}, {32740, 41909}, {41936, 44182}
X(51820) lies on the cubic K969 and these lines: {2, 98}, {4, 41173}, {22, 47635}, {25, 669}, {51, 15630}, {237, 32540}, {263, 34238}, {290, 35926}, {685, 6353}, {879, 38359}, {1007, 40428}, {1316, 34156}, {2396, 19599}, {2966, 36874}, {3060, 13137}, {4226, 14265}, {5191, 35606}, {5304, 47737}, {5306, 35906}, {6340, 31632}, {6524, 20031}, {6531, 47735}, {7735, 41932}, {7766, 18873}, {7793, 8870}, {8667, 36822}, {9755, 46124}, {12829, 47734}, {14163, 14583}, {14382, 20023}, {14593, 17409}, {34157, 46606}, {36899, 37689}
X(51820) = isogonal conjugate of the isotomic conjugate of X(14265)
X(51820) = X(i)-Ceva conjugate of X(j) for these (i,j): {98, 230}, {41173, 2395}
X(51820) = cevapoint of X(230) and X(12829)
X(51820) = crosspoint of X(98) and X(41932)
X(51820) = crosssum of X(511) and X(36790)
X(51820) = crossdifference of every pair of points on line {3569, 36212}
X(51820) = X(i)-isoconjugate of X(j) for these (i,j): {75, 34157}, {240, 43705}, {325, 36051}, {511, 8773}, {684, 36105}, {1755, 8781}, {1959, 2987}, {23996, 40428}, {32654, 46238}, {40703, 42065}
X(51820) = X(i)-Dao conjugate of X(j) for these (i, j): (114, 325), (206, 34157), (230, 32458), (15295, 39374), (34156, 69), (35067, 6393), (36899, 8781), (39001, 684), (39069, 1959), (39072, 511), (39085, 43705)
X(51820) = barycentric product X(i)*X(j) for these {i,j}: {6, 14265}, {98, 230}, {114, 41932}, {248, 44145}, {287, 460}, {290, 1692}, {1733, 1910}, {1821, 8772}, {1976, 51481}, {2395, 4226}, {3564, 6531}, {5477, 9154}, {12829, 36897}, {34174, 34369}, {34536, 51335}, {35906, 36875}, {40820, 47734}, {42663, 43187}, {46039, 48452}
X(51820) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 34157}, {98, 8781}, {114, 32458}, {230, 325}, {248, 43705}, {460, 297}, {1692, 511}, {1733, 46238}, {1910, 8773}, {1976, 2987}, {2422, 35364}, {2715, 10425}, {3564, 6393}, {4226, 2396}, {5477, 50567}, {6531, 35142}, {8772, 1959}, {11060, 39374}, {12829, 5976}, {14265, 76}, {14600, 42065}, {14601, 32654}, {32696, 32697}, {35906, 36891}, {36104, 36105}, {41932, 40428}, {42663, 3569}, {44099, 232}, {44145, 44132}, {51335, 36790}, {51431, 51389}
X(51820) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 40820, 5967}, {98, 40820, 2}, {98, 46806, 20021}
X(51821) lies on the cubic K969 and these lines: {2, 74}, {25, 512}, {184, 1576}, {394, 9717}, {3134, 15311}, {6515, 36831}, {6525, 14593}, {10419, 13352}, {10605, 34329}, {11074, 11080}, {11438, 32417}, {12079, 13567}, {13754, 14264}, {17409, 40354}, {32715, 44077}, {40630, 46868}
X(51821) = isogonal conjugate of the isotomic conjugate of X(14264)
X(51821) = X(74)-Ceva conjugate of X(3003)
X(51821) = crosspoint of X(i) and X(j) for these (i,j): {74, 40353}, {40352, 40355}
X(51821) = crosssum of X(i) and X(j) for these (i,j): {30, 36789}, {2986, 14911}, {3260, 6148}
X(51821) = crossdifference of every pair of points on line {11064, 41079}
X(51821) = X(i)-isoconjugate of X(j) for these (i,j): {75, 15454}, {1099, 40423}, {2173, 40832}, {2986, 14206}, {3260, 36053}, {14910, 46234}, {15421, 24001}, {18878, 36035}
X(51821) = X(i)-Dao conjugate of X(j) for these (i, j): (113, 3260), (206, 15454), (15295, 39375), (36896, 40832), (39174, 69)
X(51821) = barycentric product X(i)*X(j) for these {i,j}: {6, 14264}, {74, 3003}, {113, 40353}, {403, 18877}, {686, 1304}, {1725, 2159}, {1986, 11079}, {2315, 36119}, {2433, 15329}, {3580, 40352}, {6334, 32715}, {8749, 13754}, {14919, 44084}, {21731, 44769}, {34333, 40388}, {34834, 40355}
X(51821) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 15454}, {74, 40832}, {1725, 46234}, {3003, 3260}, {11060, 39375}, {14264, 76}, {19627, 39371}, {21731, 41079}, {32640, 18878}, {32715, 687}, {40352, 2986}, {40353, 40423}, {40354, 1300}, {40355, 40427}, {44084, 46106}
X(51822 lies on the cubic K979 and these lines: {2, 107}, {25, 647}, {184, 17409}, {237, 34859}, {1968, 15391}, {4230, 36212}, {14593, 17407}, {23357, 36414}, {43717, 43718}, {44770, 51343}, {51324, 51336}
X(51822) = polar conjugate of X(51257)
X(51822) = isogonal conjugate of the isotomic conjugate of X(39265)
X(51822) = X(1297)-Ceva conjugate of X(232)
X(51822) = cevapoint of X(17994) and X(38368)
X(51822) = trilinear pole of line {2211, 39469}
X(51822) = X(i)-isoconjugate of X(j) for these (i,j): {48, 51257}, {75, 34156}, {290, 8766}, {293, 30737}, {336, 1503}, {441, 1821}, {8779, 46273}, {17875, 47388}
X(51822) = X(i)-Dao conjugate of X(j) for these (i, j): (132, 30737), (206, 34156), (1249, 51257), (40601, 441)
X(51822) = barycentric product X(i)*X(j) for these {i,j}: {6, 39265}, {232, 1297}, {237, 6330}, {511, 43717}, {684, 32687}, {1755, 8767}, {2211, 35140}, {2419, 34859}, {2799, 32649}, {3569, 44770}, {4230, 34212}, {15407, 51334}
X(51822) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 51257}, {32, 34156}, {232, 30737}, {237, 441}, {2211, 1503}, {6330, 18024}, {8767, 46273}, {9417, 8766}, {9418, 8779}, {32649, 2966}, {32687, 22456}, {34859, 2409}, {36046, 36036}, {39265, 76}, {39469, 39473}, {43717, 290}, {44770, 43187}
X(51823) lies on the cubic K979 and these lines: {2, 112}, {4, 10415}, {25, 523}, {184, 1177}, {394, 36823}, {1992, 41511}, {2770, 6353}, {3266, 4235}, {4232, 10424}, {4590, 34254}, {5967, 12828}, {9516, 46165}
X(51823) = X(2373)-Ceva conjugate of X(468)
X(51823) = X(187)-cross conjugate of X(1177)
X(51823) = cevapoint of X(i) and X(j) for these (i,j): {187, 5095}, {5099, 14273}
X(51823) = crosssum of X(895) and X(14909)
X(51823) = trilinear pole of line {690, 44102}
X(51823) = crossdifference of every pair of points on line {14961, 42665}
X(51823) = X(i)-isoconjugate of X(j) for these (i,j): {19, 51253}, {75, 34158}, {858, 36060}, {895, 18669}, {897, 14961}, {14908, 20884}, {36085, 42665}
X(51823) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 51253), (206, 34158), (1560, 858), (2492, 38971), (6593, 14961), (38988, 42665), (48317, 47138)
X(51823) = barycentric product X(i)*X(j) for these {i,j}: {468, 2373}, {1177, 44146}, {10422, 34336}, {10423, 35522}, {18876, 37778}, {44102, 46140}
X(51823) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 51253}, {32, 34158}, {187, 14961}, {351, 42665}, {468, 858}, {1177, 895}, {2373, 30786}, {5095, 5181}, {5099, 38971}, {10422, 15398}, {10423, 691}, {12828, 12827}, {14273, 47138}, {36095, 36085}, {44102, 2393}, {44146, 1236}
X(51824) lies on the cubic K979 and these lines: {2, 104}, {25, 667}, {55, 184}, {56, 6075}, {57, 15635}, {3658, 14266}, {11248, 15381}, {14593, 17408}, {36944, 49492}
X(51824) = isogonal conjugate of the isotomic conjugate of X(14266)
X(51824) = X(104)-Ceva conjugate of X(8609)
X(51824) = crosspoint of X(104) and X(41933)
X(51824) = crosssum of X(517) and X(26611)
X(51824) = X(i)-isoconjugate of X(j) for these (i,j): {75, 39173}, {908, 2990}, {3262, 36052}, {6099, 36038}, {22350, 46133}, {22464, 45393}
X(51824) = X(i)-Dao conjugate of X(j) for these (i, j): (119, 3262), (206, 39173), (39175, 69)
X(51824) = barycentric product X(i)*X(j) for these {i,j}: {6, 14266}, {104, 8609}, {119, 41933}, {909, 1737}, {2252, 36123}, {34858, 48380}
X(51824) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 39173}, {8609, 3262}, {14266, 76}, {34858, 2990}
X(51825) lies on the cubic K1289 and these lines: {2, 1380}, {30, 1379}, {381, 511}, {524, 31862}, {543, 14501}, {671, 3414}, {1666, 35822}, {1667, 35823}, {2029, 11648}, {2038, 48852}, {2039, 3545}, {3413, 6040}, {3558, 7775}, {3830, 38596}, {5055, 38597}, {6189, 7809}, {7827, 14630}, {7841, 13325}, {13722, 34320}, {19570, 39365}
X(51825) = midpoint of X(3830) and X(38596)
X(51825) = reflection of X(i) in X(j) for these {i,j}: {2, 2040}, {1380, 2}
X(51825) = {X(47361),X(47363)}-harmonic conjugate of X(1379)
X(51826) lies on the cubic K1289 and these lines: {2, 1379}, {30, 1380}, {381, 511}, {524, 31863}, {543, 14502}, {671, 3413}, {1666, 35823}, {1667, 35822}, {2028, 11648}, {2037, 48852}, {2040, 3545}, {3414, 6039}, {3557, 7775}, {3830, 38597}, {5055, 38596}, {6190, 7809}, {7827, 14631}, {7841, 13326}, {13636, 34320}, {19570, 39366}
X(51826) = midpoint of X(3830) and X(38597)
X(51826) = reflection of X(i) in X(j) for these {i,j}: {2, 2039}, {1379, 2}
X(51826) = {X(47362),X(47364)}-harmonic conjugate of X(1380)
X(51827) lies on the cubic K459 and these lines: {2, 44772}, {6, 8150}, {39, 83}, {187, 12206}, {262, 12252}, {325, 6292}, {395, 25184}, {396, 25188}, {511, 49112}, {548, 13334}, {597, 18806}, {625, 2024}, {732, 3589}, {754, 8359}, {1506, 9478}, {2896, 7759}, {3618, 8149}, {3815, 32190}, {5041, 39089}, {5188, 9751}, {7736, 31982}, {7780, 41755}, {7808, 13331}, {7812, 9990}, {7838, 10007}, {7858, 9866}, {7878, 46283}, {7931, 31268}, {11171, 13111}, {11174, 32189}, {12122, 21163}, {12264, 14839}, {14881, 48892}, {14907, 20088}, {16987, 31239}, {29012, 50652}, {33468, 41632}, {33469, 41642}
X(51827) = midpoint of X(39) and X(83)
X(51827) = reflection of X(i) in X(j) for these {i,j}: {3934, 6704}, {6292, 6683}
X(51827) = isogonal conjugate of X(39397)
X(51827) = complement of X(44772)
X(51827) = X(1)-isoconjugate of X(39397)
X(51827) = X(3)-Dao conjugate of X(39397)
X(51827) = barycentric quotient X(6)/X(39397)
X(51828) lies on the cubic K459 and these lines: {2, 44771}, {5, 32449}, {6, 38907}, {39, 698}, {141, 32189}, {325, 732}, {511, 12042}, {736, 5103}, {1691, 1916}, {2024, 5026}, {3094, 7824}, {3329, 10334}, {5969, 35297}, {6393, 10007}, {8177, 32452}, {12055, 32476}, {16896, 40332}, {18906, 33225}, {32429, 40279}
X(51828) = midpoint of X(i) and X(j) for these {i,j}: {6, 45803}, {1691, 1916}
X(51828) = reflection of X(i) in X(j) for these {i,j}: {5026, 2024}, {5031, 2023}, {6393, 10007}
X(51828) = complement of X(44771)
X(51829) lies on the cubic K459 and these lines: {2, 44774}, {6, 11261}, {39, 25555}, {83, 43157}, {182, 262}, {395, 22691}, {396, 22692}, {511, 549}, {575, 11272}, {576, 7786}, {2023, 32135}, {3589, 32149}, {3618, 31958}, {3815, 24206}, {5085, 22728}, {5097, 10007}, {5309, 7697}, {5476, 11171}, {6683, 40107}, {7709, 14561}, {7792, 15819}, {7827, 43532}, {8704, 45690}, {10796, 39498}, {14881, 20190}, {14994, 37647}, {17005, 32451}, {17508, 22676}, {19063, 42833}, {19064, 42832}, {19130, 50652}, {19924, 21163}, {22650, 38029}, {22682, 29012}, {32429, 48663}, {32447, 47352}
X(51829) = midpoint of X(i) and X(j) for these {i,j}: {6, 11261}, {182, 262}, {576, 22677}, {5476, 11171}, {13331, 38317}, {32149, 44423}, {32429, 48663}
X(51829) = reflection of X(32149) in X(3589)
X(51829) = complement of X(44774)
X(51830) lies on the cubics K047 and K616 and these lines: {4, 141}, {20, 40187}, {376, 907}, {4298, 23051}, {7386, 40189}, {7392, 40182}, {10691, 45833}, {14930, 39951}
X(51830) = X(i)-Dao conjugate of X(j) for these (i, j): (15613, 3800), (22333, 3796), (40182, 22334)
X(51830) = barycentric product X(3522)*X(18840)
X(51830) = barycentric quotient X(i)/X(j) for these {i,j}: {3522, 3618}, {39951, 22334}
X(51830) = {X(4),X(14259)}-harmonic conjugate of X(18840)
X(51831) lies on the cubic K615 and these lines: {4, 2393}, {69, 46140}, {186, 3425}, {251, 6353}, {376, 1297}, {7386, 13575}, {11605, 41761}, {34208, 36877}
X(51831) = X(2156)-isoconjugate of X(41614)
X(51831) = X(i)-Dao conjugate of X(j) for these (i, j): (127, 30209), (427, 29959)
X(51831) = barycentric product X(i)*X(j) for these {i,j}: {5486, 17907}, {30247, 33294}
X(51831) = barycentric quotient X(i)/X(j) for these {i,j}: {22, 41614}, {2485, 30209}, {5486, 14376}, {8743, 1995}, {17409, 19136}, {17907, 11185}, {30247, 44766}, {40938, 29959}
X(51832) lies on the cubic K616 and these lines: {2, 45145}, {4, 513}, {69, 150}, {104, 376}, {1056, 34230}, {2250, 41325}, {2550, 36819}, {3434, 15635}, {5082, 21306}, {24247, 24484}, {30943, 34234}
X(51832) = X(i)-isoconjugate of X(j) for these (i,j): {2183, 2991}, {15344, 22350}
X(51832) = X(i)-Dao conjugate of X(j) for these (i, j): (120, 517), (3290, 51390), (3675, 42758)
X(51832) = barycentric product X(i)*X(j) for these {i,j}: {1738, 34234}, {3290, 18816}, {13136, 23770}, {16082, 34381}, {16752, 38955}
X(51832) = barycentric quotient X(i)/X(j) for these {i,j}: {104, 2991}, {120, 51390}, {1738, 908}, {3290, 517}, {13136, 35574}, {16752, 17139}, {21956, 17757}, {23770, 10015}
X(51833) lies on the cubic K616 and these lines: {4, 52}, {20, 46200}, {69, 46134}, {96, 459}, {186, 2351}, {376, 925}, {485, 13429}, {486, 13440}, {631, 34853}, {1249, 2165}, {3520, 16391}, {9308, 45179}, {20563, 32000}, {41371, 45178}
X(51833) = X(5891)-cross conjugate of X(378)
X(51833) = X(i)-isoconjugate of X(j) for these (i,j): {47, 4846}, {563, 34289}
X(51833) = X(34853)-Dao conjugate of X(4846)
X(51833) = barycentric product X(i)*X(j) for these {i,j}: {378, 5392}, {847, 15066}, {2165, 44134}, {8675, 30450}, {14593, 32833}
X(51833) = barycentric quotient X(i)/X(j) for these {i,j}: {378, 1993}, {847, 34289}, {2165, 4846}, {5063, 1147}, {11653, 51776}, {14593, 34288}, {15066, 9723}, {42660, 30451}, {44080, 571}, {44134, 7763}
X(51833) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {68, 847, 4}, {68, 14593, 5962}, {847, 5962, 14593}, {5962, 14593, 4}
X(51834) lies on the cubic K616 and these lines: {4, 6003}, {69, 14616}, {80, 3421}, {376, 759}, {2161, 41325}, {2550, 36815}, {6827, 37650}, {7735, 48449}, {36927, 37654}
X(51834) = barycentric product X(80)*X(24781)
X(51834) = barycentric quotient X(24781)/X(320)
X(51835) lies on the cubic K616 and these lines: {2, 34209}, {4, 94}, {69, 35139}, {376, 476}, {3090, 39170}, {3524, 14993}, {3529, 51254}, {3545, 5627}, {10412, 44834}, {12106, 31676}, {14583, 15682}
X(51835) = X(6149)-isoconjugate of X(10293)
X(51835) = X(i)-Dao conjugate of X(j) for these (i, j): (14993, 10293), (46436, 526)
X(51835) = barycentric product X(i)*X(j) for these {i,j}: {94, 7464}, {20573, 40114}
X(51835) = barycentric quotient X(i)/X(j) for these {i,j}: {1989, 10293}, {7464, 323}, {40114, 50}
X(51836) lies on the cubics K1015 and K1032 and these lines: {1, 21}, {2, 18208}, {48, 16556}, {69, 18207}, {75, 1581}, {141, 18168}, {192, 17470}, {304, 9239}, {561, 1928}, {982, 2275}, {984, 1469}, {1582, 1760}, {1740, 17446}, {2186, 17471}, {2223, 9941}, {2887, 33930}, {3507, 3681}, {3661, 3864}, {3662, 7237}, {3701, 29674}, {3705, 3865}, {3741, 17760}, {3905, 32853}, {3912, 3971}, {3961, 18788}, {3970, 21820}, {4137, 17155}, {4443, 35552}, {4446, 18179}, {4850, 17795}, {4876, 49509}, {4903, 29579}, {16571, 17872}, {16887, 18204}, {17244, 20703}, {17289, 20274}, {17445, 18041}, {17464, 21809}, {17789, 30953}, {17889, 20880}, {17890, 20889}, {17900, 21406}, {18055, 30982}, {18203, 20911}, {19603, 46507}, {20236, 24230}, {20895, 23669}, {20917, 43534}, {21808, 26102}, {22196, 27705}, {23486, 39731}, {24165, 30038}, {25591, 29637}, {27241, 31036}
X(51836) = isotomic conjugate of X(3113)
X(51836) = isotomic conjugate of the isogonal conjugate of X(3116)
X(51836) = isotomic conjugate of the polar conjugate of X(46507)
X(51836) = X(i)-Ceva conjugate of X(j) for these (i,j): {75, 19600}, {40773, 3117}
X(51836) = X(3116)-cross conjugate of X(46507)
X(51836) = X(i)-isoconjugate of X(j) for these (i,j): {2, 18898}, {4, 43722}, {6, 3407}, {31, 3113}, {32, 3114}, {251, 14617}, {512, 33514}, {560, 46281}, {983, 985}, {1976, 8840}, {2344, 7132}, {9063, 9426}, {17743, 40746}, {38813, 40718}
X(51836) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 3113), (9, 3407), (3094, 19591), (3789, 983), (6374, 46281), (6376, 3114), (10335, 75), (19584, 17743), (19602, 1), (27481, 7033), (32664, 18898), (36033, 43722), (39040, 8840), (39054, 33514), (40585, 14617), (41771, 870)
X(51836) = crosssum of X(1) and X(51291)
X(51836) = barycentric product X(i)*X(j) for these {i,j}: {1, 3314}, {63, 5117}, {69, 46507}, {75, 3094}, {76, 3116}, {561, 3117}, {799, 50549}, {824, 3888}, {982, 3661}, {984, 3662}, {1491, 33946}, {1581, 9865}, {1926, 42061}, {1928, 18899}, {2275, 33931}, {2276, 33930}, {2887, 40773}, {3061, 7179}, {3705, 7146}, {3721, 30966}, {3736, 20234}, {3776, 3799}, {3777, 3807}, {3786, 16888}, {3790, 41777}, {3794, 16603}, {3864, 33891}, {4602, 17415}, {19222, 19600}, {33890, 45782}
X(51836) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 3407}, {2, 3113}, {31, 18898}, {38, 14617}, {48, 43722}, {75, 3114}, {76, 46281}, {662, 33514}, {982, 14621}, {984, 17743}, {1469, 7132}, {1959, 8840}, {2275, 985}, {2276, 983}, {3056, 2344}, {3094, 1}, {3095, 3409}, {3116, 6}, {3117, 31}, {3314, 75}, {3408, 3406}, {3661, 7033}, {3662, 870}, {3721, 40718}, {3777, 4817}, {3778, 40747}, {3799, 4621}, {3808, 23597}, {3863, 40763}, {3865, 40738}, {3888, 4586}, {4481, 7255}, {4602, 9063}, {5117, 92}, {7032, 40746}, {7184, 40745}, {7239, 4613}, {9006, 1924}, {9865, 1966}, {17415, 798}, {18899, 560}, {19600, 18906}, {19602, 19591}, {19603, 11328}, {30966, 38810}, {33946, 789}, {40773, 40415}, {42061, 1967}, {43977, 46289}, {46507, 4}, {50549, 661}
X(51836) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 63, 1580}, {1, 17799, 31}, {38, 1959, 1}, {984, 7146, 40790}
X(51837) lies on the cubic K1032 and these lines: {1, 87}, {7, 20081}, {37, 27455}, {39, 6378}, {63, 2319}, {75, 257}, {76, 3662}, {239, 18906}, {312, 335}, {319, 44453}, {511, 17363}, {538, 50128}, {730, 50289}, {732, 17364}, {761, 932}, {984, 3116}, {1278, 20348}, {1916, 3705}, {2285, 7153}, {3094, 3661}, {3666, 16606}, {3739, 27432}, {3758, 32449}, {3790, 3864}, {3797, 7146}, {4359, 27438}, {4645, 9902}, {4699, 27430}, {4772, 27448}, {5969, 29617}, {7096, 30167}, {7148, 12782}, {7179, 9865}, {7275, 37598}, {10007, 29613}, {17248, 45197}, {17291, 31276}, {17367, 24256}, {19804, 27439}, {21080, 27880}, {22016, 22036}, {27466, 47677}, {27481, 40773}, {28606, 45218}, {32035, 44353}, {41838, 43225}, {43931, 48271}
X(51837) = reflection of X(i) in X(j) for these {i,j}: {192, 17760}, {33890, 75}
X(51837) = X(45782)-Ceva conjugate of X(3661)
X(51837) = X(33931)-cross conjugate of X(3661)
X(51837) = X(i)-isoconjugate of X(j) for these (i,j): {43, 40746}, {825, 4083}, {985, 2176}, {1403, 2344}, {1492, 20979}, {2209, 14621}, {3835, 34069}, {4586, 8640}, {5384, 6377}, {18898, 41886}, {21793, 40756}, {38832, 40747}, {40763, 51319}
X(51837) = X(i)-Dao conjugate of X(j) for these (i, j): (3789, 2176), (10335, 33890), (19584, 43), (19602, 20284), (27481, 192), (38995, 20979)
X(51837) = barycentric product X(i)*X(j) for these {i,j}: {75, 45782}, {87, 33931}, {330, 3661}, {824, 4598}, {984, 6384}, {1491, 18830}, {1502, 40736}, {2276, 6383}, {4505, 43931}, {7146, 27424}, {7155, 7179}, {30966, 42027}
X(51837) = barycentric quotient X(i)/X(j) for these {i,j}: {87, 985}, {330, 14621}, {788, 8640}, {824, 3835}, {869, 2209}, {932, 1492}, {984, 43}, {1469, 1403}, {1491, 4083}, {2162, 40746}, {2276, 2176}, {2319, 2344}, {3094, 20284}, {3250, 20979}, {3314, 33890}, {3661, 192}, {3736, 38832}, {3773, 3971}, {3775, 4970}, {3781, 20760}, {3790, 27538}, {3805, 24533}, {3807, 4595}, {3864, 41531}, {4122, 21051}, {4475, 3123}, {4481, 18197}, {4505, 36863}, {4522, 4147}, {4598, 4586}, {6384, 870}, {7146, 1423}, {7179, 3212}, {16606, 40747}, {18830, 789}, {27447, 40738}, {30966, 33296}, {33931, 6376}, {34071, 825}, {40736, 32}, {40773, 27644}, {40783, 16468}, {42027, 40718}, {45782, 1}
X(51837) = {X(330),X(7155)}-harmonic conjugate of X(39914)
X(51838) lies on the cubic K983 and these lines: {44, 9501}, {105, 910}, {238, 516}, {294, 518}, {666, 32922}, {765, 33676}, {1386, 40754}, {1428, 1456}, {1438, 9454}, {1458, 36146}, {9499, 9503}, {14942, 32850}, {16706, 40724}, {36041, 36057}, {36111, 36124}
X(51838) = midpoint of X(294) and X(9453)
X(51838) = isogonal conjugate of X(4712)
X(51838) = X(i)-cross conjugate of X(j) for these (i,j): {31, 1438}, {244, 1027}, {649, 36146}
X(51838) = X(i)-isoconjugate of X(j) for these (i,j): {1, 4712}, {2, 6184}, {3, 34337}, {6, 4437}, {8, 1362}, {37, 16728}, {69, 42071}, {75, 42079}, {76, 39686}, {100, 3126}, {105, 23102}, {120, 34159}, {241, 3693}, {264, 20776}, {665, 42720}, {672, 3912}, {883, 926}, {918, 2284}, {1016, 35505}, {1026, 2254}, {1252, 35094}, {1458, 3717}, {1818, 1861}, {2223, 3263}, {2283, 50333}, {2340, 9436}, {2481, 23612}, {3252, 17755}, {3286, 3932}, {3323, 6065}, {3930, 18206}, {4684, 14626}, {5089, 25083}, {7123, 17060}, {8299, 22116}, {14506, 28914}, {18157, 39258}, {20683, 30941}, {20752, 46108}, {32041, 33570}, {33700, 39350}
X(51838) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 4712), (9, 4437), (206, 42079), (661, 35094), (8054, 3126), (15487, 17060), (32664, 6184), (36103, 34337), (39046, 23102), (40589, 16728)
X(51838) = cevapoint of X(i) and X(j) for these (i,j): {31, 1438}, {244, 1027}
X(51838) = trilinear pole of line {1027, 1438}
X(51838) = barycentric product X(i)*X(j) for these {i,j}: {1, 6185}, {75, 41934}, {105, 673}, {666, 1027}, {884, 34085}, {885, 36146}, {927, 1024}, {1416, 36796}, {1438, 2481}, {1462, 14942}, {1814, 36124}, {2195, 34018}, {2402, 36041}, {8751, 31637}, {43929, 51560}
X(51838) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 4437}, {6, 4712}, {19, 34337}, {31, 6184}, {32, 42079}, {58, 16728}, {105, 3912}, {244, 35094}, {294, 3717}, {560, 39686}, {604, 1362}, {614, 17060}, {649, 3126}, {672, 23102}, {673, 3263}, {919, 1026}, {1024, 50333}, {1027, 918}, {1416, 241}, {1438, 518}, {1462, 9436}, {1973, 42071}, {2195, 3693}, {3248, 35505}, {6185, 75}, {8751, 1861}, {9247, 20776}, {9454, 23612}, {14267, 20431}, {18785, 3932}, {32658, 1818}, {32666, 2284}, {32735, 1025}, {36041, 2414}, {36057, 25083}, {36086, 42720}, {36124, 46108}, {36146, 883}, {41934, 1}, {43929, 2254}
X(51839) lies on the cubics K137 and K983 and these lines: {1, 474}, {6, 19604}, {9, 47636}, {37, 27819}, {44, 27834}, {239, 27830}, {1100, 27827}, {1429, 17967}, {3008, 35111}, {3669, 4394}, {3772, 6557}, {4000, 4373}, {4384, 27813}, {4513, 16602}, {5222, 27818}, {5382, 16610}, {6610, 38828}, {17023, 27820}, {17107, 40151}, {17348, 27835}, {17951, 37756}, {24151, 37679}, {24592, 27824}, {24599, 27828}, {24600, 27829}, {33963, 45219}
X(51839) = X(2348)-cross conjugate of X(1279)
X(51839) = X(i)-isoconjugate of X(j) for these (i,j): {1280, 1743}, {1477, 3161}, {3052, 36807}, {3158, 43760}, {3667, 6078}
X(51839) = X(i)-Dao conjugate of X(j) for these (i, j): (16593, 18743), (24151, 36807), (35111, 44720), (39048, 145)
X(51839) = crossdifference of every pair of points on line {3158, 4394}
X(51839) = X(i)-lineconjugate of X(j) for these (i,j): {1, 3158}, {3669, 4394}
X(51839) = barycentric product X(i)*X(j) for these {i,j}: {1279, 4373}, {2348, 27818}, {3008, 8056}, {5853, 19604}, {6084, 27834}
X(51839) = barycentric quotient X(i)/X(j) for these {i,j}: {1279, 145}, {2348, 3161}, {3008, 18743}, {3445, 1280}, {5853, 44720}, {6084, 4462}, {8056, 36807}, {8647, 3158}, {8659, 4394}, {16945, 1477}, {19604, 35160}, {20780, 4855}, {23704, 30720}, {34080, 6078}, {40151, 43760}, {48032, 3667}
X(51840) lies on the cubic K1032 and these lines: {1, 87}, {63, 17797}, {75, 337}, {305, 561}, {696, 4446}, {1194, 17053}, {2810, 6467}, {3056, 33946}, {3661, 9229}, {3662, 7237}, {3705, 20234}, {3778, 33890}, {9369, 21147}, {17181, 20629}, {17786, 23772}, {20294, 20504}, {21095, 29653}, {21142, 31337}, {21299, 46180}, {21804, 33933}, {23669, 29673}, {32937, 39930}
X(51840) = X(75)-Ceva conjugate of X(3662)
X(51840) = X(982)-Dao conjugate of X(1)
X(51840) = crosspoint of X(75) and X(17786)
X(51840) = barycentric product X(i)*X(j) for these {i,j}: {982, 17786}, {3501, 33930}, {3662, 32937}, {3888, 21438}, {13588, 20234}, {17072, 33946}
X(51840) = barycentric quotient X(i)/X(j) for these {i,j}: {982, 3500}, {3501, 983}, {17786, 7033}, {32937, 17743}
X(51841) lies on the cubic K351 and these lines: {1, 371}, {2, 31438}, {4, 19068}, {6, 57}, {7, 7585}, {9, 13388}, {12, 13893}, {35, 9582}, {40, 1335}, {46, 1703}, {55, 9616}, {56, 18992}, {65, 6415}, {109, 606}, {165, 5414}, {175, 30413}, {226, 3068}, {266, 7010}, {282, 15892}, {354, 19038}, {372, 15803}, {388, 13883}, {481, 30325}, {485, 9612}, {553, 19054}, {580, 3077}, {590, 5219}, {615, 31231}, {942, 3311}, {950, 6459}, {1124, 3333}, {1151, 3601}, {1155, 19037}, {1210, 1588}, {1420, 7968}, {1449, 13389}, {1500, 31437}, {1587, 4292}, {1617, 18999}, {1697, 3298}, {1698, 44622}, {1699, 44623}, {1743, 6203}, {1745, 32555}, {1781, 8938}, {1788, 13936}, {1836, 19030}, {1876, 5410}, {2078, 44591}, {2093, 35774}, {2276, 31427}, {2362, 3339}, {2646, 9615}, {2956, 6213}, {3008, 30276}, {3062, 7133}, {3069, 3911}, {3070, 9579}, {3071, 9581}, {3085, 13912}, {3256, 44590}, {3295, 31439}, {3299, 3338}, {3312, 37582}, {3340, 7969}, {3361, 6502}, {3485, 8983}, {3586, 6561}, {3592, 11518}, {3664, 30277}, {3947, 49618}, {4298, 31408}, {4304, 9541}, {4313, 43512}, {4654, 32787}, {4848, 19065}, {5045, 31474}, {5083, 19113}, {5122, 6398}, {5128, 49227}, {5226, 8972}, {5290, 31472}, {5393, 30324}, {5435, 7586}, {5437, 31473}, {5708, 6417}, {5714, 13886}, {5722, 42215}, {6199, 15934}, {6200, 30282}, {6221, 24929}, {6418, 37545}, {6424, 16780}, {6847, 8987}, {7288, 13971}, {8227, 9661}, {8583, 30556}, {8981, 11374}, {9540, 13411}, {9578, 13911}, {9613, 49601}, {10106, 19066}, {10253, 34495}, {10404, 19028}, {11036, 42522}, {11375, 18965}, {12047, 13904}, {12526, 30557}, {12736, 19082}, {12832, 19077}, {13407, 13905}, {13898, 17605}, {13901, 17718}, {13947, 19027}, {14121, 31532}, {15888, 31440}, {17728, 19029}, {18512, 18541}, {18995, 32636}, {19000, 37541}, {19056, 24472}, {19116, 34753}, {19117, 24470}, {26458, 37550}, {34033, 46378}, {36482, 36492}, {36538, 36553}, {36570, 36585}, {37709, 49232}, {37736, 48714}, {42283, 51792}, {42284, 51790}, {43826, 43855}
X(51841) = isogonal conjugate of X(15891)
X(51841) = X(i)-Ceva conjugate of X(j) for these (i,j): {13388, 1}, {13390, 45070}
X(51841) = X(i)-isoconjugate of X(j) for these (i,j): {1, 15891}, {2, 30336}, {6, 40699}, {57, 34911}, {7090, 46376}, {15889, 16214}
X(51841) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 15891), (9, 40699), (5452, 34911), (16663, 85), (32664, 30336)
X(51841) = cevapoint of X(2067) and X(8833)
X(51841) = crosspoint of X(175) and X(16662)
X(51841) = barycentric product X(i)*X(j) for these {i,j}: {1, 175}, {9, 16662}, {57, 30413}, {2362, 31547}, {32083, 34215}, {34033, 40700}
X(51841) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40699}, {6, 15891}, {31, 30336}, {55, 34911}, {175, 75}, {16662, 85}, {18992, 30417}, {30413, 312}, {34033, 176}, {46378, 7090}
X(51841) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 1702, 31432}, {46, 3301, 1703}, {65, 18996, 18991}, {2067, 16232, 1}, {3298, 49226, 1697}, {3339, 19004, 2362}, {3361, 19003, 6502}, {4298, 49548, 31408}, {19027, 24914, 13947}, {35768, 35775, 1}
X(51842) lies on the cubic K351 and these lines: {1, 372}, {4, 19067}, {6, 57}, {7, 7586}, {9, 13389}, {10, 31408}, {12, 13947}, {36, 9583}, {40, 1124}, {46, 1702}, {56, 18991}, {63, 31438}, {65, 6416}, {109, 605}, {165, 2066}, {176, 30412}, {226, 3069}, {266, 7001}, {282, 15891}, {354, 19037}, {371, 15803}, {388, 13936}, {482, 30324}, {486, 9612}, {553, 19053}, {580, 3076}, {590, 31231}, {615, 5219}, {942, 3312}, {950, 6460}, {1152, 3601}, {1155, 9616}, {1210, 1587}, {1335, 3333}, {1420, 7969}, {1449, 13388}, {1571, 31471}, {1588, 4292}, {1617, 19000}, {1697, 3297}, {1698, 31472}, {1699, 44624}, {1743, 6204}, {1745, 32556}, {1781, 8942}, {1788, 13883}, {1836, 19029}, {1876, 5411}, {2067, 3361}, {2078, 44590}, {2093, 35775}, {2956, 6212}, {3008, 30277}, {3062, 30289}, {3068, 3911}, {3070, 9581}, {3071, 9579}, {3085, 13975}, {3256, 44591}, {3301, 3338}, {3311, 37582}, {3339, 16232}, {3340, 7968}, {3485, 13971}, {3579, 31474}, {3586, 6560}, {3594, 11518}, {3664, 30276}, {3947, 49619}, {4298, 49547}, {4313, 43511}, {4654, 32788}, {4847, 31413}, {4848, 19066}, {5083, 19112}, {5122, 6221}, {5128, 49226}, {5204, 9615}, {5226, 13941}, {5231, 31484}, {5290, 44622}, {5405, 30325}, {5435, 7585}, {5708, 6418}, {5714, 13939}, {5722, 42216}, {6395, 15934}, {6396, 30282}, {6398, 24929}, {6417, 37545}, {6423, 16780}, {6847, 13974}, {7090, 31533}, {7288, 8983}, {7982, 38235}, {8583, 30557}, {9574, 31459}, {9578, 13973}, {9588, 31475}, {9613, 49602}, {9646, 31423}, {10106, 19065}, {10252, 34494}, {10404, 19027}, {11036, 42523}, {11374, 13966}, {11375, 18966}, {12047, 13962}, {12526, 30556}, {12736, 19081}, {12832, 19078}, {13407, 13963}, {13411, 13935}, {13893, 19028}, {13955, 17605}, {13958, 17718}, {17728, 19030}, {18510, 18541}, {18996, 32636}, {18999, 37541}, {19055, 24472}, {19116, 24470}, {19117, 34753}, {26464, 37550}, {34033, 46379}, {36482, 36491}, {36538, 36552}, {36570, 36584}, {37709, 49233}, {37736, 48715}, {42283, 51790}, {42284, 51792}, {43825, 43855}
X(51842) = isogonal conjugate of X(15892)
X(51842) = X(i)-Ceva conjugate of X(j) for these (i,j): {1659, 45069}, {13389, 1}
X(51842) = X(i)-isoconjugate of X(j) for these (i,j): {1, 15892}, {2, 30335}, {6, 40700}, {57, 34912}, {259, 5451}, {14121, 46377}, {15890, 16213}
X(51842) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 15892), (9, 40700), (5452, 34912), (16662, 85), (32664, 30335)
X(51842) = cevapoint of X(6502) and X(8831)
X(51842) = crosspoint of X(176) and X(16663)
X(51842) = barycentric product X(i)*X(j) for these {i,j}: {1, 176}, {9, 16663}, {57, 30412}, {16232, 31548}, {32082, 34216}, {34033, 40699}
X(51842) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40700}, {6, 15892}, {31, 30335}, {55, 34912}, {176, 75}, {266, 5451}, {16663, 85}, {18991, 30416}, {30412, 312}, {34033, 175}, {46379, 14121}
X(51842) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {9, 38004, 15892}, {40, 1124, 31432}, {46, 3299, 1702}, {65, 18995, 18992}, {1155, 19038, 9616}, {2362, 6502, 1}, {3297, 49227, 1697}, {3339, 19003, 16232}, {3361, 19004, 2067}, {19028, 24914, 13893}, {35769, 35774, 1}
X(51843) lies on the cubics K718 and K738 and these lines: {2, 17984}, {4, 3978}, {6, 43715}, {25, 5989}, {75, 24430}, {76, 5117}, {92, 17789}, {114, 43976}, {264, 305}, {287, 1988}, {290, 1853}, {297, 3981}, {317, 1899}, {419, 41259}, {850, 3060}, {1368, 40822}, {1843, 19573}, {1916, 2052}, {3186, 6374}, {5064, 46104}, {8889, 44144}, {8920, 37894}, {11550, 46247}, {19562, 25332}, {21536, 41009}, {22456, 40820}, {23962, 31074}, {37439, 46328}, {40877, 44146}
X(51843) = isogonal conjugate of X(15389)
X(51843) = isotomic conjugate of X(3504)
X(51843) = polar conjugate of X(3224)
X(51843) = isotomic conjugate of the isogonal conjugate of X(3186)
X(51843) = polar conjugate of the isotomic conjugate of X(6374)
X(51843) = polar conjugate of the isogonal conjugate of X(194)
X(51843) = orthic-isogonal conjugate of X(264)
X(51843) = X(4)-Ceva conjugate of X(264)
X(51843) = X(194)-cross conjugate of X(6374)
X(51843) = X(i)-isoconjugate of X(j) for these (i,j): {1, 15389}, {3, 34248}, {31, 3504}, {48, 3224}, {184, 3223}, {560, 43714}, {2998, 9247}, {14575, 18832}, {19606, 34055}
X(51843) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 3504), (3, 15389), (76, 69), (194, 22152), (1249, 3224), (6374, 43714), (21191, 22386), (23301, 23216), (32746, 3), (36103, 34248), (50516, 23227)
X(51843) = cevapoint of X(194) and X(3186)
X(51843) = crosspoint of X(4) and X(3186)
X(51843) = crosssum of X(3) and X(3504)
X(51843) = barycentric product X(i)*X(j) for these {i,j}: {4, 6374}, {19, 18837}, {76, 3186}, {92, 17149}, {194, 264}, {286, 22028}, {811, 20910}, {1502, 11325}, {1613, 18022}, {1740, 1969}, {6331, 23301}, {6335, 23807}, {7017, 17082}, {18027, 20794}, {21080, 44129}, {25128, 46404}, {40359, 41293}
X(51843) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 3504}, {4, 3224}, {6, 15389}, {19, 34248}, {76, 43714}, {92, 3223}, {194, 3}, {264, 2998}, {1235, 42551}, {1424, 603}, {1613, 184}, {1740, 48}, {1843, 19606}, {1969, 18832}, {2524, 39201}, {3186, 6}, {3221, 3049}, {6331, 3222}, {6374, 69}, {7075, 212}, {11325, 32}, {17082, 222}, {17149, 63}, {17984, 39927}, {18022, 40162}, {18837, 304}, {20794, 577}, {20910, 656}, {21080, 71}, {21191, 1459}, {21877, 228}, {22028, 72}, {23301, 647}, {23807, 905}, {25128, 652}, {27168, 22160}, {32746, 22152}, {38834, 10547}, {41293, 9233}, {43976, 40821}, {47642, 17970}, {50516, 22383}, {51427, 3289}
X(51843) = {X(427),X(18022)}-harmonic conjugate of X(264)
X(51844) lies on the cubic K1032 and these lines: {1, 2227}, {10, 33890}, {19, 16571}, {37, 19584}, {75, 18069}, {82, 1740}, {759, 25424}, {1423, 3507}, {1930, 18832}, {2319, 7166}, {3494, 3500}, {3501, 3502}, {3662, 42027}, {6210, 8926}, {7350, 23605}, {16569, 18785}, {17754, 17795}, {18833, 18837}, {19591, 51291}
X(51844) = isogonal conjugate of X(51291)
X(51844) = X(i)-isoconjugate of X(j) for these (i,j): {1, 51291}, {6, 7766}, {32, 41259}, {110, 25423}, {251, 32449}, {691, 45680}, {1501, 10010}, {10335, 18898}
X(51844) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 51291), (9, 7766), (244, 25423), (6376, 41259), (40585, 32449)
X(51844) = cevapoint of X(1491) and X(3123)
X(51844) = barycentric product X(i)*X(j) for these {i,j}: {1, 43688}, {1577, 25424}, {1930, 51450}
X(51844) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 7766}, {6, 51291}, {38, 32449}, {75, 41259}, {561, 10010}, {661, 25423}, {2642, 45680}, {25424, 662}, {43688, 75}, {51450, 82}
X(51845) lies on the conic {{A,B,C,I(1),X(6)}}, the cubic K983, and these lines: {1, 3732}, {6, 1633}, {87, 673}, {105, 3445}, {190, 4319}, {269, 3248}, {292, 910}, {294, 1376}, {659, 2424}, {1222, 14942}, {2279, 9315}, {2951, 9359}, {3000, 37129}, {3226, 14727}, {30610, 31638}, {31637, 32023}
X(51845) = X(i)-isoconjugate of X(j) for these (i,j): {6, 40883}, {9, 6168}, {100, 42341}, {200, 41355}, {241, 4513}, {518, 1376}, {672, 3729}, {1026, 4449}, {2284, 4885}, {2340, 9312}, {3286, 3967}, {3693, 6180}, {3717, 9316}, {3912, 9310}, {16283, 40704}, {20980, 42720}
X(51845) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 40883), (478, 6168), (6609, 41355), (8054, 42341), (45252, 3717)
X(51845) = trilinear pole of line {614, 649}
X(51845) = barycentric product X(i)*X(j) for these {i,j}: {7, 6169}, {105, 9311}, {649, 14727}, {673, 9309}, {1027, 30610}, {1438, 32023}, {2481, 9315}, {9439, 34018}
X(51845) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40883}, {56, 6168}, {105, 3729}, {649, 42341}, {1027, 4885}, {1407, 41355}, {1416, 6180}, {1438, 1376}, {1462, 9312}, {2195, 4513}, {6169, 8}, {9309, 3912}, {9311, 3263}, {9315, 518}, {9439, 3693}, {14727, 1978}, {18785, 3967}, {43921, 21139}, {43929, 4449}
X(51846) lies on the cubic K983 and these lines: {1, 3732}, {57, 658}, {294, 3212}, {518, 10025}, {910, 14189}, {1814, 6654}, {1966, 33675}, {2402, 9511}, {3061, 31637}, {6559, 16284}, {18031, 46792}, {20995, 31526}, {30567, 36796}
X(51846) = X(294)-Ceva conjugate of X(673)
X(51846) = X(85)-Dao conjugate of X(40704)
X(51846) = trilinear pole of line {1742, 21195}
X(51846) = barycentric product X(i)*X(j) for these {i,j}: {105, 20935}, {294, 40593}, {666, 21195}, {673, 3177}, {1742, 2481}, {14942, 31526}, {18031, 20995}, {34497, 36796}
X(51846) = barycentric quotient X(i)/X(j) for these {i,j}: {1742, 518}, {3177, 3912}, {20793, 1818}, {20935, 3263}, {20995, 672}, {21084, 3932}, {21195, 918}, {21856, 3930}, {31526, 9436}, {34497, 241}, {40593, 40704}
X(51847) lies on the cubic K164 and these lines: {5, 523}, {23, 30529}, {30, 50}, {94, 858}, {265, 895}, {328, 2072}, {468, 476}, {1141, 11635}, {2493, 16188}, {5961, 7575}, {6530, 46456}, {11064, 14595}, {14560, 47188}, {14583, 44212}, {17986, 39290}, {18572, 39818}
X(51847) = X(6149)-isoconjugate of X(40118)
X(51847) = X(i)-Dao conjugate of X(j) for these (i, j): (14993, 40118), (16188, 186), (39170, 51457)
X(51847) = X(30)-lineconjugate of X(50)
X(51847) = barycentric product X(i)*X(j) for these {i,j}: {94, 14984}, {328, 2493}, {7468, 14592}, {14221, 14582}
X(51847) = barycentric quotient X(i)/X(j) for these {i,j}: {1989, 40118}, {2493, 186}, {7468, 14590}, {14582, 51480}, {14984, 323}
X(51847) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {476, 18883, 468}, {14356, 43084, 5}, {14356, 43087, 43090}, {43087, 43090, 34209}
X(51848) lies on the cubic K458 and these lines: {2, 4048}, {5, 182}, {6, 5025}, {39, 5031}, {66, 24730}, {69, 7933}, {76, 141}, {115, 24256}, {316, 12212}, {325, 32449}, {384, 46285}, {511, 7861}, {524, 5028}, {574, 7789}, {597, 7884}, {599, 19570}, {626, 732}, {1194, 40379}, {1350, 43453}, {1352, 12188}, {1513, 44882}, {1691, 7828}, {1975, 3763}, {2076, 6655}, {2782, 4045}, {3098, 7872}, {3231, 31107}, {3407, 7792}, {3618, 32966}, {3628, 39498}, {3767, 8177}, {5017, 7841}, {5039, 7825}, {5085, 37446}, {5092, 7886}, {5480, 15980}, {6329, 39764}, {6680, 29012}, {7752, 13331}, {7765, 51371}, {7769, 12055}, {7796, 41747}, {7804, 48889}, {7821, 41622}, {7842, 41413}, {7853, 14994}, {7875, 44000}, {7887, 50659}, {7901, 12215}, {7919, 11646}, {7934, 32451}, {7943, 32992}, {8267, 16893}, {10516, 39646}, {11356, 43449}, {13862, 36990}, {15491, 43461}, {15821, 44772}, {16921, 47355}, {18440, 43456}, {26316, 44230}, {29181, 35387}, {31711, 36252}, {31712, 36251}, {37451, 44381}, {42286, 43084}
X(51848) = midpoint of X(i) and X(j) for these {i,j}: {66, 24730}, {141, 5254}, {3818, 14880}, {7842, 41413}, {11646, 19120}
X(51848) = reflection of X(7789) in X(34573)
X(51848) = complement of X(4048)
X(51848) = crosspoint of X(76) and X(3407)
X(51848) = crosssum of X(32) and X(3094)
X(51848) = crossdifference of every pair of points on line {5113, 9426}
X(51848) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 5025, 5103}, {76, 24733, 1502}, {1348, 1349, 7808}, {3818, 7834, 42534}, {4045, 24206, 10007}, {5207, 7797, 6}, {5989, 24273, 4048}, {7834, 42534, 3589}
X(51849) lies on the cubic K458 and these lines: {2, 6439}, {5, 3592}, {6, 43380}, {486, 15691}, {1132, 32788}, {1151, 41984}, {1328, 42226}, {3071, 15709}, {6434, 11001}, {6451, 8252}, {6454, 43439}, {6471, 43521}, {6484, 15723}, {9691, 42262}, {13951, 15688}, {15684, 23261}, {15687, 43435}, {15692, 41951}, {15759, 43569}, {22615, 35408}, {23251, 43341}, {32787, 42604}, {35409, 43209}, {41950, 43536}, {41968, 50693}, {42574, 42576}, {42642, 43571}, {43317, 43503}
X(51849) = crosssum of X(6398) and X(6434)
X(51849) = {X(13847),X(23259)}-harmonic conjugate of X(42577)
X(51850) lies on the cubic K458 and these lines: {2, 6440}, {5, 3594}, {6, 43380}, {485, 15691}, {1131, 32787}, {1152, 41984}, {1327, 42225}, {3070, 15709}, {6433, 11001}, {6452, 8253}, {6453, 43438}, {6470, 43522}, {6485, 15723}, {8976, 15688}, {15684, 23251}, {15687, 43434}, {15692, 41952}, {15759, 43568}, {22644, 35408}, {23261, 43340}, {32788, 42605}, {35409, 43210}, {41967, 50693}, {42575, 42577}, {42641, 43570}, {43316, 43504}
X(51850) = crosssum of X(6221) and X(6433)
X(51850) = {X(13846),X(23249)}-harmonic conjugate of X(42576)
X(51851) lies on the cubic K458 and these lines: {2, 2076}, {5, 32}, {6, 147}, {115, 22681}, {262, 1513}, {381, 43449}, {598, 33228}, {1506, 14881}, {2023, 19130}, {2896, 7773}, {3055, 3098}, {3070, 45434}, {3071, 45435}, {3096, 32992}, {3407, 7792}, {3972, 6656}, {5023, 7876}, {5025, 10583}, {5038, 43460}, {5116, 40236}, {5254, 44230}, {5306, 47354}, {5476, 9300}, {7603, 15819}, {7753, 22566}, {7777, 8782}, {7806, 9478}, {7811, 11168}, {7865, 8176}, {7875, 39560}, {8370, 10000}, {8570, 37988}, {9301, 31415}, {9756, 9862}, {15821, 31239}, {15980, 26316}, {22505, 43457}, {23055, 32994}, {33002, 34229}, {33013, 46318}
X(51851) = crosspoint of X(262) and X(3407)
X(51851) = crosssum of X(182) and X(3094)
X(51851) = {X(5475),X(10796)}-harmonic conjugate of X(7745)
X(51852) lies on the cubic K1198 and these lines: {2, 371}, {5, 13}, {6, 18586}, {14, 3071}, {15, 34551}, {16, 615}, {17, 43880}, {30, 3365}, {39, 48722}, {61, 14813}, {298, 640}, {372, 2044}, {383, 48466}, {396, 3364}, {398, 35738}, {485, 37641}, {590, 16967}, {619, 33392}, {629, 33424}, {641, 30472}, {1328, 36463}, {2042, 10654}, {2043, 6565}, {2045, 42247}, {2046, 40693}, {3070, 41107}, {3102, 6303}, {3367, 16242}, {3390, 32788}, {3391, 16963}, {5058, 48725}, {5335, 6564}, {5613, 49355}, {6114, 50719}, {6419, 40694}, {6420, 35732}, {6560, 42175}, {6561, 42119}, {6773, 48467}, {7583, 43229}, {10576, 42910}, {11304, 33440}, {11489, 42274}, {11543, 34559}, {13785, 42129}, {13951, 42563}, {13966, 41100}, {15764, 42258}, {16268, 32787}, {16645, 18587}, {16965, 42281}, {18762, 23303}, {19116, 43228}, {22604, 49220}, {23312, 33459}, {33361, 33472}, {33443, 35851}, {34508, 45463}, {34562, 42913}, {35733, 42633}, {35739, 42943}, {35813, 42229}, {35821, 42242}, {35822, 36467}, {36445, 36465}, {36449, 36469}, {36452, 42256}, {36454, 42245}, {36457, 42236}, {36468, 42257}, {37332, 49305}, {37640, 42230}, {37832, 42583}, {41944, 42241}, {42089, 42557}, {42149, 42233}, {42191, 42199}, {42232, 43404}, {42265, 49948}, {42270, 49908}, {42273, 43418}, {47864, 50720}
X(51852) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 3392, 15765}, {371, 486, 42564}, {3367, 16242, 34552}, {3389, 3392, 42565}, {16645, 42262, 18587}
X(51853) lies on the cubic K1198 and these lines: {2, 371}, {5, 14}, {6, 18587}, {13, 3071}, {15, 615}, {16, 34552}, {18, 43880}, {30, 3390}, {39, 48724}, {62, 14814}, {299, 640}, {372, 2043}, {395, 3389}, {485, 37640}, {590, 16966}, {618, 33395}, {630, 33427}, {641, 30471}, {1080, 48466}, {1328, 36445}, {2041, 10653}, {2044, 6565}, {2045, 40694}, {2046, 42246}, {3070, 41108}, {3102, 6302}, {3365, 32788}, {3366, 16962}, {3392, 16241}, {5058, 48723}, {5334, 6564}, {5617, 49355}, {6115, 50719}, {6419, 40693}, {6420, 42229}, {6560, 42177}, {6561, 42120}, {6770, 48467}, {7583, 43228}, {10576, 42911}, {11303, 33442}, {11488, 42274}, {11542, 34562}, {13785, 42132}, {13951, 42565}, {13966, 41101}, {16267, 32787}, {16644, 18586}, {16772, 35738}, {16964, 42280}, {18762, 23302}, {19116, 43229}, {22602, 49220}, {23312, 33458}, {33359, 33473}, {33441, 35754}, {34509, 45463}, {34559, 42912}, {35813, 42227}, {35821, 42244}, {35822, 36449}, {36436, 42243}, {36439, 42235}, {36447, 36463}, {36450, 42256}, {36452, 36467}, {36469, 42257}, {37333, 49307}, {37641, 42228}, {37835, 42583}, {41943, 42239}, {42092, 42557}, {42152, 42231}, {42192, 42201}, {42234, 43403}, {42258, 42631}, {42265, 49947}, {42270, 49907}, {42273, 43419}, {47863, 50720}
X(51853) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 3367, 18585}, {371, 486, 42562}, {3364, 3367, 42563}, {3392, 16241, 34551}, {16644, 42262, 18586}
X(51854) lies on the cubic K1198 and these lines: {2, 372}, {5, 13}, {6, 18587}, {14, 3070}, {15, 34552}, {16, 590}, {17, 43879}, {30, 3364}, {39, 48723}, {61, 14814}, {298, 639}, {371, 2043}, {383, 48467}, {396, 3365}, {486, 37641}, {549, 35739}, {615, 16967}, {619, 33394}, {629, 33426}, {642, 30472}, {1327, 36445}, {2041, 10654}, {2044, 6564}, {2045, 8960}, {2046, 42249}, {3071, 41107}, {3103, 6307}, {3366, 16242}, {3389, 32787}, {3392, 16963}, {5062, 48724}, {5335, 6565}, {5613, 49356}, {6114, 50720}, {6419, 42228}, {6420, 40694}, {6560, 42119}, {6561, 42176}, {6773, 48466}, {7584, 43229}, {8976, 42562}, {8981, 41100}, {10577, 42910}, {11304, 33441}, {11489, 42277}, {11543, 34562}, {13665, 42129}, {16268, 32788}, {16645, 18586}, {16773, 35738}, {16965, 42280}, {18538, 23303}, {19117, 43228}, {22633, 49221}, {23311, 33459}, {33358, 33470}, {33442, 35850}, {34508, 45462}, {34559, 42913}, {35740, 41944}, {35812, 42230}, {35820, 42243}, {35823, 36450}, {36436, 42244}, {36439, 42238}, {36446, 36463}, {36449, 42255}, {36453, 36468}, {36470, 42254}, {37332, 49306}, {37640, 42229}, {37832, 42582}, {42089, 42558}, {42149, 42234}, {42193, 42200}, {42223, 51728}, {42231, 43404}, {42259, 42632}, {42262, 49948}, {42270, 43418}, {42273, 49908}, {47864, 50719}
X(51854) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {14, 3391, 18585}, {372, 485, 42565}, {3366, 16242, 34551}, {3390, 3391, 42564}, {16645, 42265, 18586}
X(51855) lies on the cubic K1198 and these lines: {2, 372}, {5, 14}, {6, 18586}, {13, 3070}, {15, 590}, {16, 34551}, {18, 43879}, {30, 3389}, {39, 48725}, {62, 14813}, {299, 639}, {371, 2044}, {395, 3390}, {397, 35738}, {486, 37640}, {615, 16966}, {618, 33393}, {630, 33425}, {642, 30471}, {1080, 48467}, {1327, 36463}, {2042, 10653}, {2043, 6564}, {2045, 42248}, {2046, 8960}, {3071, 41108}, {3103, 6306}, {3364, 32787}, {3367, 16962}, {3391, 16241}, {3392, 50246}, {5062, 48722}, {5334, 6565}, {5617, 49356}, {6115, 50720}, {6419, 35732}, {6420, 40693}, {6560, 42120}, {6561, 42178}, {6770, 48466}, {7584, 43228}, {8976, 42564}, {8981, 41101}, {10577, 42911}, {11303, 33443}, {11488, 42277}, {11542, 34559}, {13665, 42132}, {15764, 42259}, {16267, 32788}, {16644, 18587}, {16964, 35730}, {18538, 23302}, {19117, 43229}, {22631, 49221}, {23311, 33458}, {33360, 33471}, {33440, 35753}, {34509, 45462}, {34562, 42912}, {35739, 41946}, {35812, 42228}, {35820, 42245}, {35823, 36468}, {36445, 36464}, {36450, 36470}, {36453, 42255}, {36454, 42242}, {36457, 42237}, {36467, 42254}, {37333, 49308}, {37641, 42227}, {37835, 42582}, {41943, 42240}, {42092, 42558}, {42152, 42232}, {42194, 42202}, {42233, 43403}, {42262, 49947}, {42270, 43419}, {42273, 49907}, {47863, 50719}
X(51855) = midpoint of X(35731) and X(42238)
X(51855) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {13, 3366, 15765}, {372, 485, 42563}, {3365, 3366, 42562}, {3391, 16241, 34552}, {16644, 42265, 18587}
X(51856) lies on the cubic K772 and these lines: {171, 40772}, {238, 292}, {660, 21830}, {741, 813}, {1015, 14665}, {1911, 2223}, {1918, 18263}, {1922, 9454}, {3508, 18787}, {9468, 19554}, {14598, 14599}, {19565, 41072}, {30642, 43262}, {30669, 40834}, {34067, 41333}, {37128, 40098}
X(51856) = X(i)-cross conjugate of X(j) for these (i,j): {31, 9468}, {669, 34067}, {3051, 18268}
X(51856) = X(i)-isoconjugate of X(j) for these (i,j): {2, 39044}, {75, 4366}, {76, 8300}, {190, 27855}, {238, 1921}, {239, 350}, {274, 4368}, {334, 6652}, {561, 51328}, {659, 27853}, {668, 4375}, {740, 30940}, {812, 874}, {873, 35068}, {1429, 4087}, {1447, 3975}, {1914, 18891}, {1966, 17493}, {2210, 44169}, {2481, 27919}, {3570, 3766}, {3684, 18033}, {3685, 10030}, {3948, 33295}, {3978, 18786}, {7035, 35119}, {12835, 28659}, {14599, 44171}, {18032, 27926}, {18035, 40767}, {19563, 40835}, {20769, 40717}, {27982, 30643}
X(51856) = X(i)-Dao conjugate of X(j) for these (i, j): (206, 4366), (9467, 17493), (9470, 1921), (32664, 39044), (36906, 18891), (40368, 51328)
X(51856) = crosssum of X(27855) and X(35119)
X(51856) = barycentric product X(i)*X(j) for these {i,j}: {31, 30663}, {32, 40098}, {75, 18267}, {291, 1911}, {292, 292}, {334, 14598}, {335, 1922}, {660, 875}, {813, 3572}, {876, 34067}, {893, 30657}, {1967, 18787}, {7233, 18265}, {9468, 30669}, {18893, 44172}, {18895, 18897}
X(51856) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 39044}, {32, 4366}, {291, 18891}, {292, 1921}, {334, 44171}, {335, 44169}, {560, 8300}, {667, 27855}, {813, 27853}, {875, 3766}, {1501, 51328}, {1911, 350}, {1918, 4368}, {1919, 4375}, {1922, 239}, {1927, 18786}, {1977, 35119}, {7077, 4087}, {7109, 35068}, {9454, 27919}, {9468, 17493}, {14598, 238}, {14599, 6652}, {18263, 40725}, {18265, 3685}, {18267, 1}, {18268, 30940}, {18787, 1926}, {18893, 2210}, {18897, 1914}, {18900, 3802}, {30657, 1920}, {30663, 561}, {30669, 14603}, {34067, 874}, {40098, 1502}, {41280, 12835}
X(51856) = {X(292),X(30657)}-harmonic conjugate of X(30663)
X(51857) lies on the cubic K1007 and these lines: {2, 39}, {75, 4425}, {99, 199}, {306, 21587}, {312, 18035}, {313, 1920}, {325, 34119}, {350, 29821}, {1909, 1961}, {1978, 28654}, {3596, 6382}, {3690, 33948}, {3701, 18760}, {3770, 8033}, {4505, 6057}, {17762, 21085}, {18137, 40035}, {18157, 27792}, {18835, 29671}, {22009, 41324}, {24169, 24731}, {29641, 33932}, {29643, 40365}, {29673, 33938}, {43534, 43684}
X(51857) = isotomic conjugate of X(2248)
X(51857) = isotomic conjugate of the isogonal conjugate of X(1654)
X(51857) = X(i)-Ceva conjugate of X(j) for these (i,j): {313, 76}, {1920, 6382}
X(51857) = X(27569)-cross conjugate of X(17762)
X(51857) = X(i)-isoconjugate of X(j) for these (i,j): {6, 18757}, {31, 2248}, {32, 13610}, {560, 6625}, {2203, 15377}, {2205, 40164}
X(51857) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 2248), (9, 18757), (86, 58), (6374, 6625), (6376, 13610), (6627, 649), (21196, 3124)
X(51857) = crosspoint of X(1978) and X(34537)
X(51857) = crosssum of X(1084) and X(1919)
X(51857) = barycentric product X(i)*X(j) for these {i,j}: {75, 17762}, {76, 1654}, {274, 27569}, {305, 4213}, {310, 21085}, {313, 6626}, {561, 846}, {668, 50451}, {1502, 18755}, {1978, 21196}, {2905, 40071}, {3596, 17084}, {6385, 21879}, {6627, 34537}, {18022, 22139}, {27691, 28660}, {27801, 38814}, {27954, 44187}
X(51857) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 18757}, {2, 2248}, {75, 13610}, {76, 6625}, {306, 15377}, {310, 40164}, {846, 31}, {1654, 6}, {2905, 1474}, {4213, 25}, {6626, 58}, {6627, 3124}, {14844, 6186}, {17084, 56}, {17762, 1}, {18035, 39922}, {18755, 32}, {21085, 42}, {21196, 649}, {21879, 213}, {22139, 184}, {24381, 7234}, {27569, 37}, {27691, 1400}, {27954, 172}, {33931, 40777}, {38814, 1333}, {39921, 17962}, {40722, 40746}, {45783, 18268}, {50451, 513}
X(51857) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {310, 1230, 76}, {1228, 28660, 76}, {1230, 3266, 310}, {8024, 18152, 76}
X(51858) lies on the cubics K532 and K772 and these lines: {6, 19587}, {9, 4518}, {21, 644}, {25, 5364}, {31, 1911}, {41, 18265}, {55, 7077}, {56, 292}, {63, 335}, {105, 238}, {171, 8932}, {213, 904}, {220, 2053}, {257, 3401}, {295, 3252}, {384, 3500}, {385, 3508}, {692, 18038}, {694, 51319}, {741, 8693}, {884, 46388}, {1707, 18787}, {1755, 2076}, {2198, 8615}, {2218, 4426}, {2225, 6187}, {3271, 36265}, {3550, 9315}, {3684, 8851}, {3730, 3864}, {4584, 43262}, {5282, 43534}, {8301, 14200}, {14974, 23392}, {18268, 34074}, {34067, 34068}, {34238, 41882}
X(51858) = isogonal conjugate of X(10030)
X(51858) = isogonal conjugate of the isotomic conjugate of X(4876)
X(51858) = X(i)-Ceva conjugate of X(j) for these (i,j): {292, 1911}, {2311, 7077}
X(51858) = X(18265)-cross conjugate of X(1911)
X(51858) = cevapoint of X(3501) and X(3508)
X(51858) = crosspoint of X(292) and X(7077)
X(51858) = crosssum of X(i) and X(j) for these (i,j): {239, 1447}, {9436, 43040}
X(51858) = trilinear pole of line {3063, 23522}
X(51858) = crossdifference of every pair of points on line {3716, 3766}
X(51858) = X(i)-isoconjugate of X(j) for these (i,j): {1, 10030}, {2, 1447}, {6, 18033}, {7, 239}, {56, 1921}, {57, 350}, {65, 30940}, {75, 1429}, {76, 1428}, {85, 238}, {86, 16609}, {99, 7212}, {190, 43041}, {222, 40717}, {226, 33295}, {242, 348}, {269, 3975}, {273, 20769}, {274, 1284}, {279, 3685}, {307, 31905}, {331, 7193}, {349, 5009}, {385, 7249}, {552, 4037}, {604, 18891}, {651, 3766}, {658, 3716}, {659, 4554}, {664, 812}, {673, 39775}, {740, 1434}, {874, 3669}, {1014, 3948}, {1088, 3684}, {1275, 4124}, {1397, 44169}, {1407, 4087}, {1412, 35544}, {1431, 3978}, {1432, 1966}, {1509, 7235}, {1874, 17206}, {1914, 6063}, {2201, 7182}, {2210, 20567}, {2481, 34253}, {3212, 39914}, {3253, 43040}, {3570, 3676}, {3573, 24002}, {3911, 27922}, {4010, 4573}, {4148, 4626}, {4366, 7233}, {4435, 4569}, {4572, 8632}, {4624, 4830}, {4625, 21832}, {4998, 27918}, {6654, 9436}, {7176, 17493}, {7196, 18786}, {8299, 34018}, {8850, 32020}, {12835, 18895}, {14296, 37137}, {14599, 41283}, {17078, 36815}, {18031, 51329}, {18815, 27950}, {18894, 41287}, {22384, 46404}, {27853, 43924}, {30545, 34252}
X(51858) = X(i)-Dao conjugate of X(j) for these (i, j): (1, 1921), (3, 10030), (9, 18033), (206, 1429), (3161, 18891), (5452, 350), (6600, 3975), (9467, 1432), (9470, 85), (24771, 4087), (32664, 1447), (36906, 6063), (38986, 7212), (38991, 3766), (39025, 812), (40599, 35544), (40600, 16609), (40602, 30940)
X(51858) = barycentric product X(i)*X(j) for these {i,j}: {1, 7077}, {6, 4876}, {8, 1911}, {9, 292}, {31, 4518}, {33, 295}, {37, 2311}, {41, 335}, {55, 291}, {75, 18265}, {210, 741}, {213, 36800}, {281, 2196}, {294, 3252}, {312, 1922}, {334, 2175}, {337, 2212}, {522, 34067}, {644, 3572}, {650, 813}, {660, 663}, {667, 36801}, {694, 2329}, {875, 3699}, {876, 3939}, {1253, 7233}, {1334, 37128}, {1581, 2330}, {1808, 1824}, {1967, 7081}, {2053, 41531}, {2194, 43534}, {2195, 22116}, {2223, 33676}, {2321, 18268}, {2344, 3862}, {3063, 4562}, {3271, 5378}, {3596, 14598}, {3709, 4584}, {4087, 18267}, {8851, 40155}, {9447, 18895}, {9448, 44172}, {9468, 17787}, {14942, 40730}, {18893, 40363}, {18897, 28659}, {34247, 43748}
X(51858) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 18033}, {6, 10030}, {8, 18891}, {9, 1921}, {31, 1447}, {32, 1429}, {33, 40717}, {41, 239}, {55, 350}, {200, 4087}, {210, 35544}, {213, 16609}, {220, 3975}, {284, 30940}, {291, 6063}, {292, 85}, {295, 7182}, {312, 44169}, {334, 41283}, {335, 20567}, {560, 1428}, {644, 27853}, {660, 4572}, {663, 3766}, {667, 43041}, {798, 7212}, {813, 4554}, {872, 7235}, {875, 3676}, {1253, 3685}, {1334, 3948}, {1911, 7}, {1918, 1284}, {1922, 57}, {1927, 1431}, {1967, 7249}, {2175, 238}, {2194, 33295}, {2196, 348}, {2204, 31905}, {2212, 242}, {2223, 39775}, {2311, 274}, {2329, 3978}, {2330, 1966}, {3063, 812}, {3252, 40704}, {3572, 24002}, {3596, 44171}, {3939, 874}, {4518, 561}, {4876, 76}, {7077, 75}, {7081, 1926}, {8641, 3716}, {9447, 1914}, {9448, 2210}, {9454, 34253}, {9455, 51329}, {9468, 1432}, {14598, 56}, {14827, 3684}, {17787, 14603}, {18265, 1}, {18268, 1434}, {18758, 39919}, {18787, 7205}, {18892, 12835}, {18893, 1397}, {18897, 604}, {20665, 33891}, {34067, 664}, {36800, 6385}, {36801, 6386}, {40730, 9436}, {44172, 41287}
X(51859) lies on the cubic K1007 and these lines: {2, 292}, {291, 29673}, {306, 4562}, {312, 18034}, {335, 3782}, {660, 33066}, {2887, 30663}, {3252, 18134}, {4388, 9470}, {6063, 6358}, {7018, 30642}, {22116, 29641}, {29653, 40794}, {30179, 40098}
X(51859) = X(4645)-cross conjugate of X(334)
X(51859) = X(i)-isoconjugate of X(j) for these (i,j): {1914, 8852}, {2210, 3512}, {7261, 14599}, {18036, 18894}, {18892, 40845}, {30648, 51328}
X(51859) = X(i)-Dao conjugate of X(j) for these (i, j): (238, 51328), (36906, 8852)
X(51859) = barycentric product X(i)*X(j) for these {i,j}: {334, 4645}, {335, 17789}, {3509, 18895}, {4071, 40017}, {4458, 4583}, {17798, 44172}, {18037, 40098}, {19554, 44170}
X(51859) = barycentric quotient X(i)/X(j) for these {i,j}: {291, 8852}, {334, 7261}, {335, 3512}, {1281, 8300}, {3509, 1914}, {4071, 2238}, {4458, 659}, {4518, 7281}, {4583, 51614}, {4645, 238}, {5018, 1428}, {17789, 239}, {17798, 2210}, {18037, 4366}, {18262, 18892}, {18895, 40845}, {19554, 14599}, {19557, 51328}, {20715, 3747}, {27951, 4375}, {30663, 30648}, {30669, 41534}, {40098, 24479}, {40217, 40781}, {44172, 18036}
X(51860) lies on the Kiepert circumhyperbola of the anticomplementary triangle, the cubic K1071, and these lines: {1, 3790}, {2, 3108}, {5, 147}, {6, 2896}, {20, 182}, {39, 8782}, {61, 617}, {62, 616}, {63, 17367}, {83, 148}, {194, 3618}, {382, 7864}, {384, 597}, {524, 16897}, {575, 37336}, {627, 3411}, {628, 3412}, {631, 3095}, {3526, 7616}, {3530, 47618}, {3589, 7839}, {3832, 7694}, {3933, 16987}, {4045, 20088}, {5007, 33021}, {5034, 10345}, {5041, 7779}, {5286, 10334}, {5309, 33020}, {6292, 50248}, {6329, 14712}, {6655, 7878}, {7486, 9742}, {7736, 7932}, {7757, 19689}, {7768, 41940}, {7774, 33221}, {7777, 33218}, {7781, 19692}, {7785, 7803}, {7791, 9731}, {7792, 9606}, {7793, 33258}, {7807, 12040}, {7812, 19690}, {7814, 7834}, {7827, 16044}, {7833, 51185}, {7836, 7875}, {7840, 8364}, {7881, 22246}, {7901, 9300}, {7902, 32993}, {7904, 43136}, {7907, 31492}, {7912, 37665}, {7920, 11174}, {7946, 32956}, {7948, 41624}, {8716, 14038}, {9855, 41153}, {9939, 33202}, {11003, 18796}, {11148, 33198}, {11163, 14065}, {11293, 13798}, {11294, 13678}, {12150, 33260}, {15717, 30270}, {16895, 47352}, {16984, 31406}, {17244, 41930}, {21378, 39724}, {22332, 33246}, {25555, 32467}, {29569, 30562}, {31400, 33262}, {31407, 33277}, {31417, 32966}, {31457, 33259}, {32480, 32981}, {33610, 41100}, {33611, 41101}
X(51860) = isotomic conjugate of X(40042)
X(51860) = anticomplement of X(10159)
X(51860) = anticomplement of the isogonal conjugate of X(5007)
X(51860) = anticomplement of the isotomic conjugate of X(3589)
X(51860) = isogonal conjugate of the isotomic conjugate of X(39999)
X(51860) = anticomplementary isogonal conjugate of X(7768)
X(51860) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 7768}, {6, 28599}, {31, 141}, {32, 28598}, {163, 7927}, {428, 21270}, {1973, 7762}, {3589, 6327}, {4030, 21286}, {5007, 8}, {7198, 21285}, {7927, 21294}, {8664, 21221}, {10330, 17217}, {11205, 21289}, {16707, 17138}, {17200, 17137}, {17457, 1369}, {17469, 69}, {18062, 44445}, {21802, 1330}, {22352, 4329}, {34072, 31065}, {39998, 21275}, {44091, 5905}, {46289, 83}, {48101, 21293}
X(51860) = X(i)-Ceva conjugate of X(j) for these (i,j): {3589, 2}, {7839, 194}, {46226, 2896}
X(51860) = X(31)-isoconjugate of X(40042)
X(51860) = X(2)-Dao conjugate of X(40042)
X(51860) = barycentric product X(6)*X(39999)
X(51860) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 40042}, {39999, 76}
X(51860) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 7772, 13571}, {3589, 7839, 46226}, {5041, 7859, 7779}, {5309, 33020, 50570}, {7792, 9606, 33245}, {7875, 9605, 7836}
X(51861) lies on the cubic K100 and these lines: {2, 330}, {38, 3778}, {75, 21949}, {76, 3705}, {305, 561}, {306, 1959}, {313, 325}, {321, 1916}, {350, 29840}, {354, 18052}, {668, 7081}, {982, 18067}, {1447, 44139}, {1920, 4518}, {3006, 8024}, {3314, 20891}, {3666, 18057}, {3701, 18760}, {4358, 31120}, {4710, 5988}, {5276, 39928}, {6381, 24239}, {7155, 20537}, {7172, 25278}, {11174, 18044}, {16703, 48647}, {17786, 20935}, {17787, 30660}, {18203, 20911}, {18906, 25306}, {20553, 37456}, {20892, 30631}, {20945, 30758}, {21241, 21416}, {24995, 29673}, {25303, 29838}
X(51861) = isotomic conjugate of the isogonal conjugate of X(17792)
X(51861) = X(i)-Ceva conjugate of X(j) for these (i,j): {1920, 321}, {4518, 3263}
X(51861) = X(i)-isoconjugate of X(j) for these (i,j): {560, 18299}, {1397, 39924}
X(51861) = X(i)-Dao conjugate of X(j) for these (i, j): (6374, 18299), (17760, 41886)
X(51861) = crosspoint of X(17760) and X(27436)
X(51861) = barycentric product X(i)*X(j) for these {i,j}: {75, 17760}, {76, 17792}, {1502, 18758}, {3596, 28391}, {6376, 27436}, {6386, 45902}, {8844, 18895}, {28659, 41350}
X(51861) = barycentric quotient X(i)/X(j) for these {i,j}: {76, 18299}, {312, 39924}, {8844, 1914}, {17760, 1}, {17792, 6}, {18758, 32}, {24349, 40758}, {27436, 87}, {28391, 56}, {39919, 1429}, {41350, 604}, {45240, 904}, {45902, 667}
X(51861) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {305, 29641, 3263}, {3596, 7179, 3263}
X(51862) lies on the cubics K1001 and 1057 and these lines: {2, 3613}, {3, 83}, {4, 51252}, {6, 22}, {21, 27067}, {23, 385}, {24, 28724}, {25, 183}, {26, 3425}, {82, 23868}, {160, 7774}, {182, 30499}, {230, 34294}, {237, 325}, {250, 21284}, {315, 20960}, {316, 21177}, {378, 32581}, {404, 27005}, {427, 10550}, {476, 9076}, {511, 9418}, {733, 805}, {827, 842}, {1634, 7779}, {1975, 9917}, {1995, 10130}, {2353, 42359}, {2421, 40810}, {2937, 14247}, {2966, 6660}, {2967, 19189}, {3053, 38834}, {3151, 18710}, {3289, 51543}, {3329, 6636}, {3511, 20854}, {4577, 39093}, {5017, 43977}, {5322, 18170}, {5345, 18194}, {5392, 16277}, {5899, 12188}, {5968, 21525}, {5989, 24729}, {6031, 13239}, {6781, 11634}, {7387, 39646}, {7418, 14356}, {7428, 29534}, {7467, 7792}, {7485, 39668}, {7488, 10548}, {7736, 37184}, {7737, 35924}, {7750, 27369}, {7752, 11360}, {7762, 23208}, {7766, 37913}, {7868, 11328}, {8667, 13481}, {8793, 41768}, {8852, 20872}, {9307, 9909}, {13595, 43458}, {14712, 37896}, {14885, 44525}, {15270, 20065}, {16276, 33769}, {16318, 21459}, {16453, 29568}, {17928, 26224}, {18091, 19312}, {19165, 34130}, {20775, 41624}, {20885, 45093}, {26184, 31268}, {30435, 39674}, {34098, 34229}, {37183, 39095}, {37898, 39857}, {37928, 46426}
X(51862) = isogonal conjugate of X(20021)
X(51862) = isogonal conjugate of the anticomplement of X(36213)
X(51862) = isogonal conjugate of the complement of X(25046)
X(51862) = isogonal conjugate of the isotomic conjugate of X(20022)
X(51862) = tangential isogonal conjugate of X(15588)
X(51862) = X(14970)-Ceva conjugate of X(6)
X(51862) = X(i)-cross conjugate of X(j) for these (i,j): {511, 20022}, {2491, 2421}, {2799, 4230}
X(51862) = cevapoint of X(237) and X(511)
X(51862) = crosspoint of X(i) and X(j) for these (i,j): {251, 733}, {805, 27867}
X(51862) = crosssum of X(i) and X(j) for these (i,j): {141, 732}, {688, 41178}, {804, 7668}, {1843, 51434}
X(51862) = trilinear pole of line {3569, 36213}
X(51862) = crossdifference of every pair of points on line {39, 826}
X(51862) = X(i)-isoconjugate of X(j) for these (i,j): {1, 20021}, {2, 3404}, {38, 98}, {39, 1821}, {141, 1910}, {248, 20883}, {287, 17442}, {290, 1964}, {293, 427}, {336, 1843}, {826, 36084}, {1923, 18024}, {1930, 1976}, {2084, 43187}, {2236, 36897}, {2525, 36104}, {2616, 35362}, {2966, 8061}, {3005, 36036}, {3051, 46273}, {3917, 36120}, {4020, 16081}
X(51862) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 20021), (132, 427), (325, 35540), (2679, 3005), (5976, 8024), (8623, 732), (11672, 141), (32664, 3404), (35088, 23285), (38987, 826), (39000, 2525), (39039, 20883), (39040, 1930), (40601, 39), (41884, 290), (46094, 3917), (50440, 3703)
X(51862) = barycentric product X(i)*X(j) for these {i,j}: {1, 3405}, {6, 20022}, {82, 1959}, {83, 511}, {232, 1799}, {237, 308}, {240, 34055}, {251, 325}, {297, 1176}, {684, 42396}, {689, 2491}, {733, 5976}, {827, 2799}, {1755, 3112}, {2396, 18105}, {3289, 46104}, {3569, 4577}, {4230, 4580}, {6530, 28724}, {8928, 51250}, {9417, 18833}, {9418, 40016}, {10547, 44132}, {14970, 36213}, {17209, 18082}, {18070, 23997}, {18098, 51369}, {18108, 42717}, {32085, 36212}, {39276, 50440}, {42288, 51373}, {46238, 46289}
X(51862) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 20021}, {31, 3404}, {82, 1821}, {83, 290}, {232, 427}, {237, 39}, {240, 20883}, {251, 98}, {297, 1235}, {308, 18024}, {325, 8024}, {511, 141}, {684, 2525}, {733, 36897}, {827, 2966}, {1176, 287}, {1625, 35362}, {1755, 38}, {1959, 1930}, {2211, 1843}, {2421, 4576}, {2491, 3005}, {2799, 23285}, {3112, 46273}, {3289, 3917}, {3405, 75}, {3569, 826}, {4230, 41676}, {4577, 43187}, {4599, 36036}, {4630, 2715}, {5360, 3954}, {5968, 31125}, {5976, 35540}, {9155, 7813}, {9417, 1964}, {9418, 3051}, {10547, 248}, {14966, 1634}, {17209, 16887}, {18105, 2395}, {20022, 76}, {28724, 6394}, {32085, 16081}, {34055, 336}, {34072, 36084}, {34854, 27376}, {36212, 3933}, {36213, 732}, {36790, 51371}, {36823, 46165}, {41270, 16030}, {42396, 22456}, {43034, 3665}, {44114, 39691}, {46288, 1976}, {46289, 1910}, {51369, 16703}
X(51862) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {23, 5201, 9149}, {308, 1799, 183}, {3329, 6636, 41328}, {7467, 40981, 7792}
X(51863) lies on the cubic K100 and these lines: {2, 3121}, {10, 1920}, {38, 75}, {141, 30631}, {210, 25280}, {257, 312}, {274, 27798}, {321, 27495}, {322, 325}, {333, 1966}, {334, 3925}, {350, 3706}, {668, 1215}, {670, 24450}, {740, 31008}, {756, 1978}, {799, 4418}, {846, 874}, {982, 10009}, {984, 6382}, {1045, 34021}, {1654, 30660}, {1655, 21883}, {1909, 31993}, {1921, 3741}, {1965, 5263}, {4087, 4357}, {4096, 36863}, {4425, 18035}, {4485, 5224}, {4981, 35543}, {5271, 18056}, {6384, 19804}, {8033, 24342}, {15523, 20932}, {16748, 27812}, {18064, 32914}, {18136, 24731}, {18138, 20955}, {18743, 22230}, {18832, 31359}, {20445, 20939}, {20532, 25134}, {20929, 31089}, {21779, 40743}, {25286, 46897}, {30632, 32782}, {30964, 32860}, {32942, 39044}, {41816, 43271}
X(51863) = isotomic conjugate of X(40737)
X(51863) = isotomic conjugate of the isogonal conjugate of X(1045)
X(51863) = X(i)-Ceva conjugate of X(j) for these (i,j): {10, 75}, {1920, 312}, {34021, 1655}
X(51863) = X(i)-isoconjugate of X(j) for these (i,j): {6, 40770}, {31, 40737}, {560, 18298}, {1501, 43684}, {40746, 40778}
X(51863) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 40737), (9, 40770), (274, 86), (6374, 18298), (19584, 40778)
X(51863) = barycentric product X(i)*X(j) for these {i,j}: {10, 34021}, {75, 1655}, {76, 1045}, {257, 27890}, {310, 21883}, {321, 39915}, {561, 21779}, {1502, 18756}, {1969, 23079}, {3661, 40743}, {4602, 9402}, {27801, 51330}, {33931, 40752}
X(51863) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40770}, {2, 40737}, {76, 18298}, {561, 43684}, {984, 40778}, {1045, 6}, {1655, 1}, {3948, 39926}, {9402, 798}, {18756, 32}, {21779, 31}, {21883, 42}, {23079, 48}, {27890, 894}, {34021, 86}, {39915, 81}, {40743, 14621}, {40752, 985}, {51330, 1333}
X(51863) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {38, 40087, 75}, {310, 21020, 75}, {561, 31330, 75}, {25280, 41318, 210}, {30966, 35544, 75}
X(51864) lies on the cubic K772 and these lines: {1, 41396}, {6, 43}, {213, 7121}, {292, 23566}, {330, 24282}, {932, 3230}, {1914, 34071}, {1919, 8640}, {2176, 17105}, {5383, 7035}, {7032, 23561}, {8709, 20669}, {20671, 21760}, {21001, 43114}, {23660, 40720}
X(51864) = isogonal conjugate of X(40844)
X(51864) = isogonal conjugate of the isotomic conjugate of X(40881)
X(51864) = X(20332)-Ceva conjugate of X(17105)
X(51864) = X(i)-cross conjugate of X(j) for these (i,j): {3009, 21760}, {38367, 34071}
X(51864) = X(i)-isoconjugate of X(j) for these (i,j): {1, 40844}, {43, 32020}, {192, 3226}, {239, 33680}, {727, 6382}, {3212, 36799}, {3253, 40848}, {3835, 8709}, {6376, 20332}, {8851, 30545}, {18793, 31008}, {27809, 33296}
X(51864) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 40844), (17793, 6382)
X(51864) = crosssum of X(1575) and X(24524)
X(51864) = crossdifference of every pair of points on line {4083, 6376}
X(51864) = barycentric product X(i)*X(j) for these {i,j}: {6, 40881}, {87, 3009}, {330, 21760}, {726, 7121}, {932, 6373}, {1463, 2053}, {1575, 2162}, {18792, 23493}, {34252, 40155}
X(51864) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 40844}, {1575, 6382}, {1911, 33680}, {2162, 32020}, {3009, 6376}, {6373, 20906}, {7121, 3226}, {21759, 27809}, {21760, 192}, {40881, 76}
X(51864) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 2162, 40753}, {2162, 40736, 21759}
X(51865) lies on the cubic K1007 and these lines: {2, 20939}, {75, 8033}, {92, 423}, {313, 1920}, {321, 1909}, {561, 33943}, {873, 1109}, {1441, 7196}, {1934, 40017}, {2886, 35960}, {3112, 18757}, {4418, 4600}, {4425, 18032}, {16708, 20511}, {16709, 44188}, {33779, 46277}
X(51865) = isotomic conjugate of X(846)
X(51865) = isotomic conjugate of the isogonal conjugate of X(13610)
X(51865) = X(i)-cross conjugate of X(j) for these (i,j): {274, 75}, {7018, 6384}, {23913, 10}
X(51865) = cevapoint of X(i) and X(j) for these (i,j): {75, 41875}, {693, 1109}
X(51865) = trilinear pole of line {1577, 2786}
X(51865) = X(i)-isoconjugate of X(j) for these (i,j): {6, 18755}, {25, 22139}, {31, 846}, {32, 1654}, {184, 4213}, {213, 38814}, {560, 17762}, {869, 40751}, {1333, 21879}, {1918, 6626}, {2175, 17084}, {2200, 2905}, {2206, 21085}, {2308, 38836}, {6627, 23357}, {7104, 27954}, {17735, 51332}, {21196, 32739}, {40722, 40728}, {41333, 45783}
X(51865) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 846), (9, 18755), (37, 21879), (6374, 17762), (6376, 1654), (6505, 22139), (6626, 38814), (34021, 6626), (40593, 17084), (40603, 21085), (40619, 21196)
X(51865) = barycentric product X(i)*X(j) for these {i,j}: {75, 6625}, {76, 13610}, {321, 40164}, {561, 2248}, {1502, 18757}
X(51865) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 18755}, {2, 846}, {10, 21879}, {63, 22139}, {75, 1654}, {76, 17762}, {85, 17084}, {86, 38814}, {92, 4213}, {274, 6626}, {286, 2905}, {313, 27569}, {321, 21085}, {693, 21196}, {870, 40722}, {1109, 6627}, {1255, 38836}, {1441, 27691}, {1909, 27954}, {1929, 51332}, {2248, 31}, {3261, 50451}, {6625, 1}, {13610, 6}, {14621, 40751}, {15377, 228}, {18032, 39921}, {18757, 32}, {18827, 45783}, {30690, 14844}, {31997, 17689}, {39922, 8298}, {39925, 8937}, {40164, 81}, {40777, 2276}
X(51866) lies on the cubic K772 and these lines: {6, 40730}, {9, 40217}, {31, 41934}, {105, 238}, {171, 40761}, {292, 1438}, {294, 34252}, {666, 2311}, {673, 37207}, {741, 919}, {875, 884}, {1416, 1428}, {2111, 6185}, {2280, 3252}, {3248, 18267}, {3253, 6654}, {3684, 36906}, {8300, 30663}, {24727, 33676}
X(51866) = isogonal conjugate of X(17755)
X(51866) = isogonal conjugate of the complement of X(335)
X(51866) = X(i)-cross conjugate of X(j) for these (i,j): {6, 1438}, {31, 741}, {649, 813}, {798, 32666}, {3248, 1027}, {16874, 36066}, {20981, 36146}
X(51866) = cevapoint of X(6) and X(292)
X(51866) = crosssum of X(239) and X(27945)
X(51866) = trilinear pole of line {1911, 3572}
X(51866) = X(i)-isoconjugate of X(j) for these (i,j): {1, 17755}, {2, 8299}, {8, 34253}, {9, 39775}, {92, 20778}, {238, 3912}, {239, 518}, {241, 3685}, {242, 25083}, {291, 27919}, {312, 51329}, {350, 672}, {659, 42720}, {665, 874}, {740, 18206}, {812, 1026}, {883, 4435}, {918, 3573}, {1016, 38989}, {1025, 3716}, {1281, 40781}, {1429, 3717}, {1447, 3693}, {1458, 3975}, {1861, 20769}, {1914, 3263}, {1921, 2223}, {2238, 30941}, {2254, 3570}, {2284, 3766}, {2340, 10030}, {3252, 39044}, {3286, 3948}, {3684, 9436}, {3747, 18157}, {3930, 33295}, {4148, 41353}, {4238, 24459}, {4366, 22116}, {4447, 17493}, {4712, 6654}, {7193, 46108}, {8300, 40217}, {9454, 18891}, {9455, 44169}, {14439, 27922}, {20683, 30940}, {20752, 40717}, {24578, 33701}, {36819, 51381}
X(51866) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 17755), (478, 39775), (9470, 3912), (22391, 20778), (32664, 8299), (33675, 18891), (36906, 3263), (39029, 27919)
X(51866) = barycentric product X(i)*X(j) for these {i,j}: {56, 33676}, {105, 291}, {292, 673}, {295, 36124}, {335, 1438}, {660, 1027}, {666, 3572}, {741, 13576}, {875, 51560}, {876, 36086}, {919, 4444}, {1416, 4518}, {1462, 4876}, {1911, 2481}, {1922, 18031}, {2195, 7233}, {3252, 6185}, {4562, 43929}, {5378, 43921}, {18785, 37128}, {24479, 40754}, {29956, 37207}, {30648, 40724}, {40217, 41934}
X(51866) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 17755}, {31, 8299}, {56, 39775}, {105, 350}, {184, 20778}, {291, 3263}, {292, 3912}, {294, 3975}, {604, 34253}, {666, 27853}, {673, 1921}, {741, 30941}, {813, 42720}, {875, 2254}, {884, 3716}, {919, 3570}, {1027, 3766}, {1397, 51329}, {1416, 1447}, {1438, 239}, {1462, 10030}, {1911, 518}, {1914, 27919}, {1922, 672}, {2195, 3685}, {2196, 25083}, {2481, 18891}, {3248, 38989}, {3252, 4437}, {3572, 918}, {7077, 3717}, {13576, 35544}, {14598, 2223}, {14942, 4087}, {18031, 44169}, {18265, 2340}, {18267, 40730}, {18268, 18206}, {18785, 3948}, {18893, 9455}, {18897, 9454}, {29956, 4486}, {32658, 20769}, {32666, 3573}, {33676, 3596}, {34067, 1026}, {36086, 874}, {36124, 40717}, {37128, 18157}, {40730, 4712}, {40754, 18037}, {41934, 6654}, {43929, 812}
X(51866) = {X(292),X(1914)}-harmonic conjugate of X(38874)
X(51867) lies on the cubic K772 and these lines: {6, 694}, {31, 110}, {58, 19561}, {99, 4154}, {171, 40759}, {238, 1931}, {261, 18827}, {292, 51330}, {1326, 2223}, {2300, 18268}, {4584, 18787}, {38814, 45783}
X(51867) = X(292)-Ceva conjugate of X(741)
X(51867) = X(i)-isoconjugate of X(j) for these (i,j): {740, 13610}, {2238, 6625}, {2248, 3948}, {9278, 39922}, {18757, 35544}
X(51867) = X(86)-Dao conjugate of X(1921)
X(51867) = barycentric product X(i)*X(j) for these {i,j}: {1, 45783}, {291, 38814}, {292, 6626}, {295, 2905}, {741, 1654}, {846, 37128}, {2311, 17084}, {17762, 18268}, {18755, 18827}
X(51867) = barycentric quotient X(i)/X(j) for these {i,j}: {741, 6625}, {846, 3948}, {1326, 39922}, {1654, 35544}, {2905, 40717}, {6626, 1921}, {18268, 13610}, {18755, 740}, {38814, 350}, {45783, 75}
X(51868) lies on the cubic K1007 and these lines: {38, 25757}, {171, 41072}, {312, 335}, {321, 40098}, {334, 561}, {1920, 30633}, {1965, 9470}, {3971, 4583}, {4639, 39915}, {7018, 30642}, {18895, 21416}, {30660, 30669}, {43534, 43684}
X(51868) = X(30663)-Ceva conjugate of X(334)
X(51868) = X(2210)-isoconjugate of X(7168)
X(51868) = X(1921)-Dao conjugate of X(39044)
X(51868) = barycentric product X(i)*X(j) for these {i,j}: {291, 18275}, {334, 19565}, {335, 19567}, {3510, 18895}, {18277, 30663}, {18278, 44172}, {19581, 40098}
X(51868) = barycentric quotient X(i)/X(j) for these {i,j}: {335, 7168}, {3510, 1914}, {18275, 350}, {18277, 39044}, {18278, 2210}, {19565, 238}, {19567, 239}, {19579, 8300}, {19580, 51328}, {19581, 4366}, {40098, 24576}, {40849, 18786}
X(51869) lies on the cubics K1001 and K1057 and these lines: {3, 76}, {6, 157}, {22, 42359}, {25, 6531}, {32, 27375}, {39, 3203}, {141, 1634}, {187, 15630}, {230, 237}, {287, 19459}, {385, 37183}, {574, 41440}, {755, 2715}, {878, 3455}, {882, 2422}, {1511, 11653}, {1593, 45031}, {1843, 41331}, {1910, 17798}, {2076, 34238}, {2080, 13137}, {2353, 14600}, {2421, 36214}, {2966, 6660}, {3329, 37335}, {3404, 3954}, {5013, 17042}, {5201, 25322}, {5967, 8546}, {6464, 26292}, {6664, 8177}, {9154, 37914}, {9418, 42671}, {11174, 31636}, {11610, 40121}, {17008, 36874}, {17423, 34156}, {17974, 19357}, {20897, 44533}, {24729, 39941}, {27369, 27376}, {32696, 44090}, {34218, 47082}, {40085, 40519}
X(51869) = isogonal conjugate of X(20022)
X(51869) = isogonal conjugate of the anticomplement of X(8623)
X(51869) = isogonal conjugate of the isotomic conjugate of X(20021)
X(51869) = X(i)-Ceva conjugate of X(j) for these (i,j): {98, 20021}, {2966, 2422}, {36897, 6}
X(51869) = cevapoint of X(39) and X(8623)
X(51869) = crosspoint of X(98) and X(1976)
X(51869) = crosssum of X(i) and X(j) for these (i,j): {2, 25046}, {325, 511}
X(51869) = trilinear pole of line {3005, 3051}
X(51869) = crossdifference of every pair of points on line {2491, 2799}
X(51869) = X(i)-line conjugate of X(j) for these (i,j): {3, 5976}, {882, 2491}
X(51869) = X(i)-isoconjugate of X(j) for these (i,j): {1, 20022}, {2, 3405}, {82, 325}, {83, 1959}, {237, 18833}, {240, 1799}, {251, 46238}, {297, 34055}, {308, 1755}, {511, 3112}, {1176, 40703}, {2421, 18070}, {2491, 37204}, {2799, 4599}, {3569, 4593}, {5976, 43763}, {9417, 40016}, {10566, 42717}, {18082, 51369}, {18098, 51370}
X(51869) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 20022), (141, 325), (3124, 2799), (32664, 3405), (34452, 511), (36213, 5976), (36899, 308), (39058, 40016), (39085, 1799), (40585, 46238), (40938, 44132)
X(51869) = barycentric product X(i)*X(j) for these {i,j}: {1, 3404}, {6, 20021}, {38, 1910}, {39, 98}, {141, 1976}, {248, 427}, {287, 1843}, {290, 3051}, {293, 17442}, {688, 43187}, {732, 34238}, {826, 2715}, {878, 41676}, {879, 35325}, {1235, 14600}, {1401, 15628}, {1634, 2395}, {1821, 1964}, {1923, 46273}, {2084, 36036}, {2422, 4576}, {2525, 32696}, {2623, 35362}, {2966, 3005}, {3917, 6531}, {4020, 36120}, {5967, 46154}, {8024, 14601}, {8061, 36084}, {8623, 36897}, {15407, 51434}, {16081, 20775}, {17974, 27376}, {18024, 41331}, {34369, 46157}, {35906, 46147}, {36822, 46156}
X(51869) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 20022}, {31, 3405}, {38, 46238}, {39, 325}, {98, 308}, {248, 1799}, {290, 40016}, {427, 44132}, {688, 3569}, {878, 4580}, {1634, 2396}, {1821, 18833}, {1843, 297}, {1910, 3112}, {1923, 1755}, {1964, 1959}, {1976, 83}, {2715, 4577}, {2966, 689}, {3005, 2799}, {3051, 511}, {3404, 75}, {3787, 51374}, {3917, 6393}, {3954, 42703}, {6531, 46104}, {8041, 51371}, {8623, 5976}, {9494, 2491}, {14096, 51373}, {14600, 1176}, {14601, 251}, {15630, 34294}, {17187, 51370}, {17442, 40703}, {20021, 76}, {20775, 36212}, {27369, 232}, {32696, 42396}, {34238, 14970}, {35325, 877}, {36036, 37204}, {36084, 4593}, {40972, 44694}, {41272, 5968}, {41331, 237}, {43187, 42371}
X(51869) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {98, 8870, 39685}, {248, 1976, 14601}, {290, 31635, 183}
X(51870) lies on the conic {{A,B,C,X(4),X(5)}}, the cubic K682, and these lines: {4, 23844}, {5, 10}, {12, 2292}, {21, 1220}, {42, 10950}, {53, 1826}, {71, 17369}, {80, 3293}, {311, 313}, {594, 21011}, {1089, 3704}, {1224, 47515}, {1263, 11698}, {1268, 20028}, {2486, 21935}, {3142, 40663}, {3159, 4013}, {3185, 50037}, {3214, 41506}, {4036, 42757}, {4651, 14008}, {4705, 42455}, {5046, 17500}, {7504, 19874}, {11681, 25253}, {15666, 39542}, {15971, 23845}, {23846, 51558}, {29822, 51683}, {34969, 42078}
X(51870) = X(46880)-Ceva conjugate of X(37)
X(51870) = cevapoint of X(i) and X(j) for these (i,j): {115, 42661}, {4705, 21044}
X(51870) = crosssum of X(572) and X(20986)
X(51870) = trilinear pole of line {4024, 12077}
X(51870) = X(i)-isoconjugate of X(j) for these (i,j): {27, 22118}, {58, 2975}, {60, 37558}, {81, 572}, {86, 20986}, {110, 21173}, {162, 23187}, {163, 17496}, {284, 17074}, {593, 21061}, {849, 17751}, {1333, 14829}, {1437, 11109}, {4636, 51664}
X(51870) = X(i)-Dao conjugate of X(j) for these (i, j): (10, 2975), (37, 14829), (115, 17496), (125, 23187), (244, 21173), (4075, 17751), (4988, 24237), (40586, 572), (40590, 17074), (40600, 20986)
X(51870) = barycentric product X(i)*X(j) for these {i,j}: {10, 2051}, {12, 46880}, {321, 34434}, {594, 20028}
X(51870) = barycentric quotient X(i)/X(j) for these {i,j}: {10, 14829}, {37, 2975}, {42, 572}, {65, 17074}, {213, 20986}, {228, 22118}, {523, 17496}, {594, 17751}, {647, 23187}, {661, 21173}, {756, 21061}, {762, 14973}, {1826, 11109}, {2051, 86}, {2171, 37558}, {2486, 26847}, {3120, 24237}, {4516, 11998}, {20028, 1509}, {21044, 34589}, {21051, 27346}, {34434, 81}, {40966, 46879}, {46880, 261}
X(51871) lies on the cubic K772 and these lines: {6, 41350}, {31, 56}, {109, 2700}, {171, 28391}, {213, 18784}, {222, 21010}, {238, 241}, {651, 4447}, {958, 4296}, {1403, 16502}, {1911, 30648}, {2275, 9316}, {6180, 7184}, {24806, 36476}, {34043, 37609}
X(51871) = isogonal conjugate of the isotomic conjugate of X(41352)
X(51871) = X(292)-Ceva conjugate of X(56)
X(51871) = X(8)-isoconjugate of X(43747)
X(51871) = X(1447)-Dao conjugate of X(1921)
X(51871) = crosssum of X(3716) and X(4081)
X(51871) = crossdifference of every pair of points on line {3239, 40998}
X(51871) = barycentric product X(i)*X(j) for these {i,j}: {6, 41352}, {57, 18788}
X(51871) = barycentric quotient X(i)/X(j) for these {i,j}: {604, 43747}, {8932, 3975}, {18788, 312}, {41352, 76}
X(51871) = {X(109),X(43034)}-harmonic conjugate of X(17798)
X(51872) lies on the cubic K440 and these lines: {2, 7711}, {3, 147}, {4, 13188}, {5, 39}, {15, 5617}, {16, 5613}, {20, 38744}, {26, 39803}, {30, 99}, {32, 12830}, {74, 14850}, {83, 44237}, {98, 140}, {141, 542}, {143, 39817}, {148, 381}, {160, 2934}, {376, 7897}, {382, 13172}, {384, 35464}, {399, 14972}, {495, 3023}, {496, 3027}, {517, 21636}, {523, 51232}, {543, 3845}, {546, 6321}, {547, 11632}, {548, 21166}, {550, 2794}, {568, 39808}, {574, 9996}, {590, 35824}, {615, 35825}, {616, 30472}, {617, 30471}, {631, 5984}, {632, 6036}, {671, 5066}, {804, 8552}, {952, 9864}, {1154, 39846}, {1263, 3613}, {1272, 47285}, {1352, 5116}, {1353, 41672}, {1385, 2784}, {1484, 2783}, {1513, 9772}, {1551, 47289}, {1595, 12131}, {1596, 5186}, {1656, 14651}, {1691, 3564}, {1916, 44230}, {1975, 40279}, {2079, 5877}, {2080, 40239}, {2482, 8703}, {2787, 11698}, {2795, 16160}, {2936, 18570}, {3070, 35879}, {3071, 35878}, {3091, 38732}, {3095, 9993}, {3098, 7908}, {3530, 34473}, {3579, 51578}, {3580, 44215}, {3627, 22505}, {3628, 7859}, {3788, 14880}, {3818, 6298}, {3830, 8591}, {3839, 12355}, {3850, 14639}, {3853, 10723}, {3857, 38734}, {3933, 5976}, {4027, 7807}, {5013, 43449}, {5054, 11177}, {5055, 12243}, {5149, 7789}, {5182, 8368}, {5305, 44534}, {5355, 33694}, {5477, 41675}, {5663, 6786}, {5844, 7970}, {5913, 32526}, {5969, 21850}, {5985, 7483}, {5986, 7499}, {5987, 7495}, {5988, 37592}, {5989, 7763}, {6055, 11539}, {6147, 24472}, {6243, 39807}, {6656, 32516}, {6721, 11623}, {6722, 15491}, {7470, 7947}, {7514, 39832}, {7530, 13175}, {7575, 39825}, {7697, 43461}, {7735, 37466}, {7737, 44532}, {7762, 39652}, {7764, 14881}, {7779, 9301}, {7783, 32528}, {7786, 9478}, {7796, 9821}, {7819, 10352}, {7835, 26316}, {7858, 18502}, {7892, 10353}, {7906, 8782}, {7921, 18501}, {7934, 11257}, {8550, 32135}, {8596, 41099}, {8981, 49212}, {9155, 11007}, {9166, 10109}, {9167, 15713}, {9744, 38654}, {9760, 44289}, {9766, 9890}, {9830, 12040}, {9860, 26446}, {9880, 23046}, {9955, 11599}, {10069, 15325}, {10086, 12185}, {10089, 12184}, {10272, 18332}, {10283, 11724}, {10753, 34380}, {10991, 15712}, {10992, 39838}, {11005, 32423}, {11152, 33228}, {11178, 15482}, {11288, 39899}, {11646, 12055}, {11710, 38028}, {11711, 34773}, {12100, 14830}, {12103, 38731}, {12161, 39820}, {12350, 15170}, {12699, 13174}, {13108, 37446}, {13178, 18357}, {13754, 51427}, {13862, 32447}, {13908, 42639}, {13966, 49213}, {13968, 42640}, {14643, 22265}, {14791, 39842}, {14849, 15059}, {14869, 38737}, {15068, 39849}, {15300, 33699}, {15484, 35930}, {15687, 39809}, {15696, 38635}, {15704, 38738}, {15928, 44287}, {18436, 39837}, {18572, 39847}, {19709, 41135}, {19710, 36521}, {20253, 36765}, {21525, 50947}, {21536, 36212}, {22247, 26614}, {23039, 39836}, {23318, 39816}, {24206, 40108}, {24469, 26921}, {28194, 50882}, {28204, 50879}, {30270, 40278}, {31401, 44531}, {31727, 31839}, {32469, 39663}, {33923, 38742}, {34013, 37950}, {34152, 39860}, {35071, 42353}, {36755, 41023}, {36756, 41022}, {37440, 39828}, {37938, 39845}, {38627, 38740}, {38642, 51582}, {38747, 46853}, {38953, 47288}, {40236, 47618}, {42215, 49266}, {42216, 49267}, {44386, 49006}, {45921, 47322}
X(51872) = midpoint of X(i) and X(j) for these {i,j}: {2, 48657}, {3, 147}, {4, 13188}, {20, 38744}, {99, 6033}, {114, 14981}, {382, 13172}, {399, 18331}, {616, 48656}, {617, 48655}, {3830, 8591}, {5617, 36776}, {6054, 8724}, {6243, 39807}, {6298, 6299}, {6321, 23235}, {7779, 9301}, {8782, 48673}, {9766, 9890}, {10722, 38730}, {10992, 39838}, {12699, 13174}, {14692, 38664}, {18436, 39837}, {20094, 38733}, {22505, 51524}, {35002, 43460}, {38953, 47288}, {40236, 47618}
X(51872) = reflection of X(i) in X(j) for these {i,j}: {5, 114}, {98, 140}, {550, 33813}, {671, 5066}, {1511, 33512}, {3579, 51578}, {3627, 22505}, {3845, 22566}, {6036, 20399}, {6321, 546}, {8550, 32135}, {8703, 2482}, {10723, 3853}, {11599, 9955}, {11623, 6721}, {11632, 547}, {11646, 18358}, {12042, 620}, {13178, 18357}, {14830, 12100}, {15704, 38738}, {18332, 10272}, {22505, 38745}, {31727, 31839}, {32521, 5976}, {34127, 38746}, {34773, 11711}, {38736, 35022}, {38741, 548}, {39817, 143}, {47610, 619}, {47611, 618}, {48906, 5026}, {49006, 44386}, {51523, 6036}
X(51872) = complement of X(12188)
X(51872) = orthoptic-circle-of-Steiner-inellipse-inverse of X(7711)
X(51872) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {4, 20094, 38733}, {98, 15561, 140}, {99, 6054, 6033}, {99, 10722, 38730}, {620, 12042, 549}, {6033, 8724, 99}, {6033, 38730, 10722}, {6721, 11623, 34127}, {7799, 43460, 35002}, {7832, 12054, 140}, {10086, 12185, 15171}, {10089, 12184, 18990}, {11623, 38746, 6721}, {11632, 23234, 547}, {13188, 38733, 20094}, {13188, 38743, 4}, {14692, 38224, 38664}, {14830, 41134, 12100}, {20399, 51523, 632}, {21166, 38741, 548}, {34473, 38750, 3530}, {35022, 38736, 33813}, {38745, 51524, 3627}, {49266, 50719, 42215}, {49267, 50720, 42216}
X(51873) lies on the incircle, the cubic K672, and these lines: {1, 30}, {2, 2463}, {4, 2464}, {11, 1312}, {12, 1313}, {35, 35232}, {36, 35231}, {55, 1114}, {56, 1113}, {57, 2100}, {388, 14807}, {497, 14808}, {612, 20406}, {614, 20405}, {999, 15154}, {1478, 10750}, {1479, 10751}, {1697, 2101}, {2098, 2103}, {2099, 2102}, {2554, 2565}, {2555, 2564}, {2574, 3028}, {2575, 3024}, {3295, 15155}, {3303, 15156}, {3304, 15157}, {3582, 13626}, {3584, 13627}, {3746, 30525}, {4293, 15160}, {4294, 15161}, {5204, 38708}, {5217, 38709}, {5563, 30524}, {10385, 15159}, {10387, 15163}, {10719, 11237}, {10720, 11238}, {10736, 12943}, {10737, 12953}, {10781, 13273}, {10782, 13274}, {14374, 43820}, {14375, 43819}, {15325, 31681}, {15326, 34592}, {15888, 20408}, {20409, 37722}, {51779, 51813}
X(51874) lies on the incircle, the cubic K672, and these lines: {1, 30}, {2, 2464}, {4, 2463}, {11, 1313}, {12, 1312}, {35, 35231}, {36, 35232}, {55, 1113}, {56, 1114}, {57, 2101}, {388, 14808}, {497, 14807}, {612, 20405}, {614, 20406}, {999, 15155}, {1478, 10751}, {1479, 10750}, {1697, 2100}, {2098, 2102}, {2099, 2103}, {2554, 2564}, {2555, 2565}, {2574, 3024}, {2575, 3028}, {3295, 15154}, {3303, 15157}, {3304, 15156}, {3582, 13627}, {3584, 13626}, {3746, 30524}, {4293, 15161}, {4294, 15160}, {5204, 38709}, {5217, 38708}, {5563, 30525}, {10385, 15158}, {10387, 15162}, {10719, 11238}, {10720, 11237}, {10736, 12953}, {10737, 12943}, {10781, 13274}, {10782, 13273}, {10944, 18871}, {14374, 43819}, {14375, 43820}, {15325, 31682}, {15326, 34593}, {15888, 20409}, {20408, 37722}, {51779, 51812}
X(51875) lies on the cubic K385 and these lines: {2, 72}, {4, 209}, {6, 943}, {1260, 40406}, {2215, 4253}, {2911, 30733}, {5752, 5759}, {11517, 40571}, {14054, 17776}, {15344, 36080}
X(51875) = X(i)-isoconjugate of X(j) for these (i,j): {1451, 43740}, {13397, 46385}, {37543, 39943}
X(51875) = barycentric product X(17776)*X(51223)
X(51875) = barycentric quotient X(i)/X(j) for these {i,j}: {2335, 43740}, {2911, 405}, {3811, 5271}, {15313, 23882}, {17776, 44140}, {36080, 13397}, {37579, 37543}, {51223, 15474}
X(51876) lies on the cubic K1159 and these lines: {3, 2542}, {83, 1380}, {99, 1379}, {141, 384}, {316, 2039}, {754, 6189}, {2029, 32450}, {6177, 7860}, {7809, 47088}, {13586, 39022}
X(51876) = cevapoint of X(2896) and X(3413)
X(51877) lies on the cubic K581 and these lines: {4, 51}, {107, 154}, {232, 37689}, {264, 11451}, {2979, 15466}, {3526, 15318}, {3628, 14059}, {5055, 10184}, {7486, 22257}, {8798, 15022}, {11204, 40664}, {14569, 43462}, {23332, 51358}, {35260, 42452}, {35450, 41372}, {37453, 47202}, {41204, 44082}
X(51877) = polar conjugate of the isogonal conjugate of X(41367)
X(51877) = Thomson-isogonal conjugate of X(3357)
X(51877) = barycentric product X(264)*X(41367)
X(51877) = barycentric quotient X(41367)/X(3)
X(51877) = {X(1075),X(14363)}-harmonic conjugate of X(14249)
X(51878) lies on the cubic K1159 and these lines: {3, 2543}, {83, 1379}, {99, 1380}, {141, 384}, {316, 2040}, {754, 6190}, {2028, 32450}, {6178, 7860}, {7809, 47089}, {13586, 39023}
X(51878) = cevapoint of X(2896) and X(3414)
X(51879) lies on the cubic K672 and these lines: {11, 2599}, {12, 1091}, {60, 655}, {140, 16577}, {201, 1834}, {389, 517}, {404, 4552}, {442, 6358}, {523, 2594}, {570, 8609}, {1825, 3575}, {1901, 2171}, {5396, 45238}
X(51879) = X(1)-Ceva conjugate of X(12)
X(51879) = X(6358)-Dao conjugate of X(75)
X(51879) = crosspoint of X(1) and X(37732)
X(51879) = barycentric product X(i)*X(j) for these {i,j}: {12, 18662}, {1441, 21860}, {4552, 8819}, {6358, 37732}, {21770, 34388}
X(51879) = barycentric quotient X(i)/X(j) for these {i,j}: {8819, 4560}, {18662, 261}, {21770, 60}, {21860, 21}, {37732, 2185}
X(51880) lies on the cubic K581 and these lines: {3, 41367}, {4, 39}, {237, 1384}, {376, 11672}, {647, 35260}, {1285, 3117}, {1625, 37184}, {5023, 17821}, {5167, 50370}, {11206, 40588}, {13531, 15340}, {26714, 47052}
X(51880) = Thomson-isogonal conjugate of X(9756)
X(51881) lies on the cubic K1052 and these lines: {6, 46408}, {36, 1464}, {74, 2720}, {110, 840}, {399, 41345}, {513, 1495}, {517, 10564}, {526, 3724}, {542, 15986}, {652, 1055}, {902, 1459}, {1155, 18593}, {2078, 3024}, {2771, 5126}, {3660, 15904}, {4257, 13868}, {5092, 34583}, {11430, 31849}, {31847, 43586}, {43610, 43820}
X(51881) = midpoint of X(36) and X(47379)
X(51881) = reflection of X(15904) in X(3660)
X(51882) lies on the cubic K440 and these lines: {2, 15106}, {4, 195}, {6, 3448}, {23, 110}, {67, 7570}, {74, 11562}, {113, 15052}, {125, 15018}, {146, 11456}, {265, 7565}, {542, 1994}, {567, 5663}, {1177, 41435}, {1511, 7488}, {1993, 9143}, {2781, 6636}, {3098, 13201}, {3581, 38898}, {4550, 12281}, {5092, 27866}, {5987, 38383}, {6243, 25714}, {6593, 7496}, {7492, 48679}, {7533, 15135}, {7552, 10272}, {7556, 32609}, {7712, 10117}, {7728, 10296}, {7731, 37478}, {9140, 34155}, {9730, 43578}, {10264, 15037}, {10545, 41671}, {10657, 33517}, {10658, 33518}, {10989, 19379}, {12308, 31861}, {12824, 13595}, {13403, 15063}, {15066, 17847}, {15131, 30745}, {15132, 44802}, {15140, 40342}, {15141, 16063}, {15246, 15462}, {16042, 41670}, {16223, 43584}, {18445, 37077}, {22467, 25711}, {24981, 32271}, {26284, 44456}, {34153, 37496}, {37784, 41720}, {38402, 43697}
X(51882) = reflection of X(i) in X(j) for these {i,j}: {74, 37513}, {41171, 113}
X(51882) = {X(9140),X(34155)}-harmonic conjugate of X(34545)
X(51883) lies on the cubic K685 and these lines: {1, 30}, {4, 6757}, {19, 403}, {40, 30447}, {102, 476}, {186, 5248}, {265, 517}, {484, 42422}, {515, 6742}, {516, 36001}, {946, 1325}, {1789, 11012}, {2006, 12028}, {2070, 20988}, {2166, 3583}, {2687, 11813}, {2694, 26700}, {3153, 14213}, {5180, 33650}, {5310, 37959}, {5627, 36910}, {8227, 44898}, {10738, 14980}, {10740, 34301}, {10902, 37979}, {18403, 18407}
X(51883) = reflection of X(i) in X(j) for these {i,j}: {40, 30447}, {484, 42422}, {1325, 946}, {2687, 11813}
X(51884) lies on the cubic K928 and these lines: {2, 2138}, {4, 339}, {20, 64}, {22, 7767}, {76, 44440}, {112, 14376}, {194, 39352}, {264, 7544}, {315, 28706}, {401, 7893}, {858, 7776}, {1369, 1370}, {1494, 38937}, {1593, 40995}, {1968, 15526}, {2071, 3926}, {2373, 41896}, {2896, 3164}, {3153, 32006}, {3172, 20208}, {3785, 7488}, {3933, 11413}, {6815, 32000}, {7219, 17170}, {7391, 18018}, {7394, 44142}, {7396, 40123}, {7503, 41005}, {7800, 22240}, {9308, 26154}, {10313, 14023}, {11348, 11433}, {12111, 44141}, {25053, 37644}, {26166, 44134}, {26170, 41361}, {30552, 32817}, {37126, 40680}
X(51884) = anticomplement of X(8743)
X(51884) = anticomplement of the isogonal conjugate of X(14376)
X(51884) = anticomplementary isogonal conjugate of X(41361)
X(51884) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 41361}, {3, 21215}, {63, 5596}, {66, 5905}, {69, 21288}, {293, 34137}, {2156, 193}, {2353, 21216}, {14376, 8}, {18018, 21270}, {40404, 17165}, {43678, 5906}, {44766, 7253}, {46244, 11442}, {46765, 17489}
{X(315),X(30737)}-harmonic conjugate of X(37444)
X(51885) lies on the cubic K125 and these lines: {3, 34564}, {5, 1173}, {6, 3411}, {20, 6102}, {49, 3629}, {52, 18476}, {143, 11271}, {382, 10112}, {631, 2889}, {1353, 41464}, {1493, 18368}, {1992, 47525}, {3530, 13353}, {3843, 9927}, {3853, 7728}, {5067, 45794}, {5900, 20379}, {6152, 23236}, {7506, 15534}, {10821, 15061}, {11536, 41586}, {13431, 18369}, {15800, 41362}, {16239, 44756}, {17823, 36747}, {33542, 37486}, {34224, 43599}, {37636, 48154}, {43601, 46853}
X(51885) = reflection of X(i) in X(j) for these {i,j}: {3, 34564}, {18368, 1493}, {34483, 15047}
X(51886) lies on the cubic K682 and these lines: {35, 2222}, {80, 517}, {484, 1263}, {901, 15228}, {953, 5443}, {5080, 15065}, {5444, 38617}, {5445, 31841}, {5697, 39270}, {7951, 34464}, {11280, 14584}, {18393, 38586}
X(51887) lies on the cubic K1057 and these lines: {3, 275}, {4, 19172}, {6, 24}, {25, 1093}, {97, 17928}, {107, 43918}, {183, 276}, {186, 51255}, {378, 4994}, {389, 19170}, {1181, 26887}, {1593, 19192}, {1598, 19169}, {3087, 26876}, {3515, 16030}, {3517, 19173}, {3575, 8901}, {4993, 7503}, {6642, 19179}, {6644, 19210}, {7395, 19188}, {7487, 19174}, {7506, 19176}, {9786, 19180}, {10605, 19206}, {11398, 19175}, {11399, 19182}, {12173, 19177}, {15203, 16032}, {15204, 16037}, {18533, 19205}, {19194, 37489}, {22467, 43768}
X(51887) = polar conjugate of the isotomic conjugate of X(19170)
X(51887) = X(40448)-isoconjugate of X(44706)
X(51887) = barycentric product X(i)*X(j) for these {i,j}: {4, 19170}, {275, 389}, {2167, 45225}, {2190, 45224}, {8882, 45198}, {8884, 46832}
X(51887) = barycentric quotient X(i)/X(j) for these {i,j}: {275, 42333}, {389, 343}, {6750, 45793}, {8882, 40448}, {19170, 69}, {45198, 28706}, {45224, 18695}, {45225, 14213}
X(51887) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {24, 54, 19189}, {25, 16035, 8884}, {3515, 16030, 19185}, {8794, 8884, 41365}
X(51888) lies on the cubic K714 and these lines: {3, 2052}, {5, 53}, {13, 46703}, {14, 46702}, {20, 1075}, {30, 143}, {51, 13322}, {52, 42453}, {54, 41202}, {68, 1987}, {381, 13599}, {418, 13450}, {1093, 42329}, {1154, 15912}, {1658, 5961}, {2055, 8613}, {2790, 6759}, {3070, 8954}, {3071, 32589}, {5562, 41481}, {6662, 32142}, {7387, 14880}, {14059, 46717}, {14152, 41204}, {14790, 14881}, {15780, 33664}, {26897, 44732}
X(51888) = midpoint of X(5562) and X(41481)
X(51888) = reflection of X(i) in X(j) for these {i,j}: {143, 6663}, {6662, 32142}
X(51888) = Taylor-circle-inverse of X(32411)
X(51888) = X(34538)-Ceva conjugate of X(1625)
X(51888) = X(2167)-isoconjugate of X(8612)
X(51888) = X(i)-Dao conjugate of X(j) for these (i, j): (38976, 15412), (40588, 8612)
X(51888) = cevapoint of X(15780) and X(41481)
X(51888) = crosssum of X(2623) and X(34980)
X(51888) = barycentric product X(i)*X(j) for these {i,j}: {5, 8613}, {324, 2055}
X(51888) = barycentric quotient X(i)/X(j) for these {i,j}: {51, 8612}, {2055, 97}, {8613, 95}, {38976, 2972}
X(51888) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {5, 35719, 42862}, {216, 8887, 5}, {10600, 39569, 5}
X(51889) lies on the cubic K682 and these lines: {1, 4}, {10, 522}, {11, 25437}, {30, 33649}, {35, 2222}, {40, 24029}, {119, 24025}, {496, 23869}, {1074, 10175}, {1324, 20831}, {1387, 11717}, {1647, 23536}, {1897, 13532}, {2716, 37561}, {2800, 38357}, {2817, 21664}, {2829, 11700}, {3057, 3326}, {5587, 18339}, {6788, 23537}, {7004, 10265}, {10017, 17102}, {10538, 27529}, {11373, 14028}, {18242, 34345}, {21635, 34586}, {23703, 31730}, {36250, 37730}, {47115, 51422}
X(51889) = midpoint of X(i) and X(j) for these {i,j}: {1, 18340}, {1897, 13532}, {3465, 38945}
X(51889) = reflection of X(i) in X(j) for these {i,j}: {11700, 15252}, {51422, 47115}, {51751, 1785}
X(51889) = incircle-inverse of X(30384)
X(51889) = polar circle inverse of X(1870)
X(51889) = crossdifference of every pair of points on line {652, 7113}
X(51889) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 35015, 946}, {24457, 42455, 21201}
X(51890) lies on the cubics K1054b and K1057 and these lines: {3, 13}, {6, 3132}, {16, 3201}, {25, 2934}, {50, 8740}, {183, 34389}, {299, 11145}, {395, 38432}, {599, 40712}, {930, 34376}, {2070, 15743}, {2379, 16806}, {3130, 11063}, {3131, 36300}, {8018, 15109}, {8604, 34395}, {9763, 11144}, {10677, 11486}, {11081, 46113}, {16460, 19781}, {19302, 19304}, {23283, 23286}, {34328, 38404}, {36304, 50660}
X(51890) = isogonal conjugate of X(16771)
X(51890) = isogonal conjugate of the anticomplement of X(11130)
X(51890) = isogonal conjugate of the isotomic conjugate of X(19779)
X(51890) = X(i)-Ceva conjugate of X(j) for these (i,j): {11087, 6}, {39432, 36304}
X(51890) = X(i)-isoconjugate of X(j) for these (i,j): {1, 16771}, {2, 3376}, {63, 46926}, {75, 11141}, {302, 2154}, {2166, 11146}, {3384, 30529}, {8838, 51806}, {24041, 43968}
X(51890) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 16771), (206, 11141), (3005, 43968), (3162, 46926), (11126, 11132), (11597, 11146), (15610, 41298), (32664, 3376), (38994, 23872), (40581, 302), (46604, 11138)
X(51890) = crossdifference of every pair of points on line {6671, 23872}
X(51890) = barycentric product X(i)*X(j) for these {i,j}: {1, 3375}, {6, 19779}, {16, 17}, {299, 21461}, {323, 11139}, {471, 32585}, {532, 34321}, {2963, 11145}, {2981, 40667}, {6138, 32036}, {8603, 11078}, {8604, 11144}, {8740, 40712}, {8741, 44719}, {10677, 11601}, {11087, 11130}, {11134, 11140}, {11600, 36208}, {16806, 23871}, {34389, 34395}, {36211, 37848}
X(51890) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 16771}, {16, 302}, {17, 301}, {25, 46926}, {31, 3376}, {32, 11141}, {50, 11146}, {3124, 43968}, {3375, 75}, {6138, 23872}, {8603, 11092}, {8604, 11143}, {8740, 473}, {11081, 8838}, {11130, 11132}, {11134, 1994}, {11139, 94}, {11142, 30529}, {11145, 7769}, {16806, 23896}, {19627, 11137}, {19779, 76}, {21461, 14}, {32585, 40710}, {34321, 11117}, {34395, 61}, {35331, 35316}, {40667, 41000}, {51547, 8836}
X(51890) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3130, 11063, 11141}, {8603, 21461, 6}, {8603, 51547, 21461}, {21461, 32585, 8603}, {32585, 51547, 6}
X(51891) lies on the cubics K1054a and K1057 and these lines: {3, 14}, {6, 3131}, {15, 3200}, {25, 2934}, {50, 8739}, {183, 34390}, {298, 11146}, {396, 38431}, {599, 40711}, {930, 34374}, {2070, 11586}, {2378, 16807}, {3129, 11063}, {3132, 36301}, {8019, 15109}, {8603, 34394}, {9761, 11143}, {10678, 11485}, {11086, 46112}, {16459, 19780}, {19302, 19305}, {21773, 42623}, {23284, 23286}, {34327, 38403}, {36305, 50660}
X(51891) = isogonal conjugate of X(16770)
X(51891) = isogonal conjugate of the anticomplement of X(11131)
X(51891) = isogonal conjugate of the isotomic conjugate of X(19778)
X(51891) = X(i)-Ceva conjugate of X(j) for these (i,j): {11082, 6}, {39433, 36305}
X(51891) = crossdifference of every pair of points on line {6672, 23873}
X(51891) = X(i)-isoconjugate of X(j) for these (i,j): {1, 16770}, {2, 3383}, {63, 46925}, {75, 11142}, {303, 2153}, {2166, 11145}, {3375, 30529}, {8836, 51805}, {24041, 43967}
X(51891) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 16770), (206, 11142), (3005, 43967), (3162, 46925), (11127, 11133), (11597, 11145), (15609, 41298), (32664, 3383), (38993, 23873), (40580, 303), (46604, 11139)
X(51891) = barycentric product X(i)*X(j) for these {i,j}: {1, 3384}, {6, 19778}, {15, 18}, {298, 21462}, {323, 11138}, {470, 32586}, {533, 34322}, {2963, 11146}, {6137, 32037}, {6151, 40668}, {8603, 11143}, {8604, 11092}, {8739, 40711}, {8742, 44718}, {10678, 11600}, {11082, 11131}, {11137, 11140}, {11601, 36209}, {16807, 23870}, {34390, 34394}, {36210, 37850}
X(51891) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 16770}, {15, 303}, {18, 300}, {25, 46925}, {31, 3383}, {32, 11142}, {50, 11145}, {3124, 43967}, {3384, 75}, {6137, 23873}, {8603, 11144}, {8604, 11078}, {8739, 472}, {11086, 8836}, {11131, 11133}, {11137, 1994}, {11138, 94}, {11141, 30529}, {11146, 7769}, {16807, 23895}, {19627, 11134}, {19778, 76}, {21462, 13}, {32586, 40709}, {34322, 11118}, {34394, 62}, {35332, 35317}, {40668, 41001}, {51546, 8838}
X(51891) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3129, 11063, 11142}, {8604, 21462, 6}, {8604, 51546, 21462}, {21462, 32586, 8604}, {32586, 51546, 6}
X(51892) lies on the cubic K449 and these lines: {2, 11589}, {4, 51}, {20, 12096}, {30, 1294}, {107, 1559}, {133, 40664}, {186, 18809}, {2072, 2693}, {3091, 34109}, {3146, 34147}, {3832, 35711}, {10304, 16253}, {11251, 38937}, {13473, 20774}, {13488, 51031}, {14165, 51403}, {15384, 47109}, {17037, 50687}, {18400, 48364}, {31725, 43995}, {37941, 40557}, {38719, 44246}, {44990, 44992}
X(51892) = reflection of X(i) in X(j) for these {i,j}: {20, 12096}, {107, 1559}, {186, 18809}, {2693, 2072}, {34170, 4}, {40664, 133}
X(51892) = anticomplement of X(11589)
X(51892) = polar-circle-inverse of X(11381)
X(51892) = circumcircle-of-anticomplementary-triangle-inverse of X(6225)
X(51892) = anticomplement of the isogonal conjugate of X(10152)
X(51892) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {204, 39358}, {1895, 146}, {2349, 253}, {8749, 18663}, {10152, 8}, {15291, 6360}, {36119, 3146}
X(51892) = crosssum of X(9409) and X(47409)
X(51892) = crossdifference of every pair of points on line {20233, 32320}
X(51892) = {X(4),X(5878)}-harmonic conjugate of X(14249)
X(51893) lies on the cubic K385 and these lines: {2, 6}, {7, 2997}, {20, 6604}, {75, 16465}, {85, 942}, {991, 9436}, {3190, 3879}, {3332, 14942}, {4352, 37549}, {4872, 10446}, {18650, 24310}
X(51893) = {X(69),X(30962)}-harmonic conjugate of X(18134)
X(51894) lies on the cubic K483 and these lines: {6, 23967}, {50, 67}, {111, 230}, {115, 38953}, {187, 11645}, {395, 43091}, {396, 43092}, {892, 45331}, {7669, 51428}, {11063, 37914}
X(51894) = crosssum of X(6) and X(38583)
X(51894) = crossdifference of every pair of points on line {20403, 33752}
X(51895) lies on the cubics K389 and K928 and these lines: {3, 523}, {22, 14911}, {24, 107}, {26, 16168}, {64, 155}, {378, 10419}, {382, 17703}, {2693, 10420}, {3053, 14910}, {6644, 12028}, {7503, 33927}, {7514, 47055}, {7526, 14670}, {18859, 39371}, {46587, 51385}
X(51895) = isogonal conjugate of the anticomplement of X(39174)
X(51895) = X(40948)-cross conjugate of X(6000)
X(51895) = X(1294)-isoconjugate of X(1725)
X(51895) = X(50937)-Dao conjugate of X(403)
X(51895) = crosspoint of X(1300) and X(10419)
X(51895) = crosssum of X(113) and X(13754)
X(51895) = barycentric product X(i)*X(j) for these {i,j}: {1300, 44436}, {2986, 6000}, {5504, 51358}, {15421, 46587}, {40423, 47433}
X(51895) = barycentric quotient X(i)/X(j) for these {i,j}: {6000, 3580}, {14910, 1294}, {46587, 16237}, {47433, 113}, {51358, 44138}
X(51895) = {X(15454),X(39986)}-harmonic conjugate of X(3)
X(51896) lies on the cubic K685 and these lines: {1, 2779}, {3, 102}, {4, 80}, {65, 34462}, {117, 6830}, {124, 2476}, {151, 6840}, {484, 6127}, {517, 38945}, {573, 4559}, {859, 5127}, {994, 1836}, {1361, 2099}, {1364, 34471}, {2475, 33650}, {2841, 3030}, {2849, 14299}, {3738, 6224}, {10693, 11670}, {10716, 17532}, {10895, 15050}, {11571, 18341}, {11700, 37525}, {12016, 30274}
X(51896) = reflection of X(i) in X(j) for these {i,j}: {10703, 1361}, {34242, 1845}, {38507, 109}
X(51897) lies on the cubic K913 and these lines: {1, 399}, {2, 1768}, {11, 41695}, {30, 12751}, {40, 38756}, {79, 24465}, {119, 3652}, {191, 2950}, {484, 10742}, {952, 16138}, {1709, 3158}, {1749, 47034}, {3255, 5851}, {3337, 12611}, {5536, 17768}, {7330, 12767}, {7993, 12705}, {10021, 35010}, {10269, 33856}, {10270, 45649}, {11684, 39776}, {11715, 28461}, {12515, 19919}, {13253, 22837}, {15910, 46435}, {16133, 18240}, {16143, 35204}, {22936, 37561}, {26364, 51569}, {33593, 45655}, {34600, 48695}
X(51897) = reflection of X(i) in X(j) for these {i,j}: {3065, 7701}, {12515, 19919}, {16143, 35204}, {49178, 119}
X(51898) lies on the major axis of the Steiner circumellipse, and X(51898) lies on minor axis.
X(51898) lies on the cubics K187 and K953 and these lines: {2, 1341}, {3, 47367}, {4, 14502}, {20, 3414}, {30, 6189}, {69, 74}, {193, 51492}, {325, 6040}, {631, 47369}, {1379, 39365}, {3524, 47366}, {3543, 31862}, {3545, 47370}, {6190, 6390}, {14712, 39366}, {15692, 47089}, {30508, 38940}, {36969, 47362}, {36970, 47364}
X(51898) = reflection of X(i) in X(j) for these {i,j}: {4, 47365}, {3543, 31862}, {31863, 47088}, {39365, 1379}, {47367, 3}
X(51898) = anticomplement of X(31863)
X(51898) = crossdifference of every pair of points on line {5639, 14398}
X(51898) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {31863, 47088, 2}, {39158, 39159, 30509}
X(51899) lies on the major axis of the Steiner circumellipse, and X(51898) lies on minor axis.
X(51899) lies on the cubics K187 and K953 and these lines: {2, 1340}, {3, 47368}, {4, 14501}, {20, 3413}, {30, 6190}, {69, 74}, {193, 51493}, {325, 6039}, {631, 47370}, {1380, 39366}, {3524, 47365}, {3543, 31863}, {3545, 47369}, {6189, 6390}, {14712, 39365}, {15692, 47088}, {30509, 38940}, {36969, 47361}, {36970, 47363}
X(51899) = reflection of X(i) in X(j) for these {i,j}: {4, 47366}, {3543, 31863}, {31862, 47089}, {39366, 1380}, {47368, 3}
X(51899) = anticomplement of X(31862)
X(51899) = crossdifference of every pair of points on line {5638, 14398}
X(51899) = {X(31862),X(47089)}-harmonic conjugate of X(2)
X(51900) lies on the cubics K1071 and K1256 and these lines: {3, 14818}, {13, 8837}, {15, 20}, {39, 46626}, {61, 185}, {62, 13434}, {2981, 43601}, {3106, 11424}, {3107, 7503}, {10613, 46850}, {14817, 15047}
X(51900) = X(397)-Ceva conjugate of X(62)
X(51901) lies on the cubics K1071 and K1256 and these lines: {3, 14819}, {14, 8839}, {16, 20}, {39, 46626}, {61, 13434}, {62, 185}, {3106, 7503}, {3107, 11424}, {6151, 43601}, {10614, 46850}, {14816, 15047}
X(51901) = X(3978)-Ceva conjugate of X(61)
X(51902) lies on the cubic K989 and these lines: {1, 6}, {31, 983}, {42, 256}, {43, 1403}, {58, 8669}, {86, 24659}, {87, 21010}, {171, 385}, {183, 10436}, {190, 1918}, {192, 2209}, {291, 1400}, {572, 11364}, {573, 12782}, {594, 50254}, {645, 51330}, {651, 41350}, {726, 4279}, {899, 28402}, {982, 21371}, {1045, 37619}, {1046, 6211}, {1376, 16571}, {1431, 1581}, {1580, 2330}, {1613, 40736}, {1740, 34247}, {1756, 3293}, {2183, 24478}, {2239, 6646}, {2650, 25024}, {3329, 17123}, {3507, 17792}, {3685, 37588}, {3718, 20947}, {3747, 17261}, {3831, 33159}, {3840, 17353}, {3846, 27296}, {3905, 18906}, {3923, 4385}, {3971, 38832}, {4039, 17787}, {4357, 6685}, {4447, 7184}, {4579, 7122}, {4641, 20359}, {4650, 20368}, {5156, 32935}, {6210, 50581}, {7175, 18787}, {7226, 27631}, {9441, 24728}, {14614, 50127}, {15624, 24696}, {17120, 20985}, {17717, 27254}, {17719, 29967}, {17795, 28358}, {18278, 21759}, {18754, 18758}, {20258, 20498}, {25108, 28362}, {27078, 32944}, {27644, 41531}, {27958, 40731}, {27963, 28008}, {28369, 40790}, {29507, 31337}, {51322, 51323}
X(51902) = isogonal conjugate of the isotomic conjugate of X(41318)
X(51902) = X(i)-Ceva conjugate of X(j) for these (i,j): {172, 171}, {4600, 4595}
X(51902) = X(17752)-cross conjugate of X(171)
X(51902) = crosspoint of X(172) and X(51319)
X(51902) = crosssum of X(i) and X(j) for these (i,j): {257, 27447}, {2053, 34249}, {6377, 50510}
X(51902) = X(i)-isoconjugate of X(j) for these (i,j): {6, 27447}, {87, 256}, {257, 2162}, {330, 893}, {694, 39914}, {904, 6384}, {1178, 42027}, {1431, 7155}, {1432, 2319}, {1581, 34252}, {1916, 51321}, {2053, 7249}, {3903, 43931}, {6383, 7104}, {7018, 7121}, {7148, 7303}, {16606, 40432}, {23493, 32010}, {40763, 45782}
X(51902) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 27447), (75, 44187), (19576, 34252), (21051, 3120), (39031, 51321), (39043, 39914), (40597, 330), (40598, 7018)
X(51902) = barycentric product X(i)*X(j) for these {i,j}: {1, 17752}, {6, 41318}, {43, 894}, {75, 51319}, {171, 192}, {172, 6376}, {190, 24533}, {213, 27891}, {385, 41531}, {651, 30584}, {1215, 27644}, {1403, 17787}, {1423, 7081}, {1580, 40848}, {1909, 2176}, {1920, 2209}, {2295, 33296}, {2329, 3212}, {2330, 30545}, {3208, 7176}, {3502, 17741}, {3835, 4579}, {3963, 38832}, {4083, 18047}, {4367, 4595}, {6382, 7122}, {7009, 22370}, {7175, 27538}, {7234, 36860}, {7304, 21803}, {17103, 20691}, {20964, 31008}, {20981, 36863}
X(51902) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 27447}, {43, 257}, {171, 330}, {172, 87}, {192, 7018}, {894, 6384}, {1403, 1432}, {1423, 7249}, {1580, 39914}, {1691, 34252}, {1909, 6383}, {1933, 51321}, {2176, 256}, {2209, 893}, {2295, 42027}, {2329, 7155}, {2330, 2319}, {3208, 4451}, {4579, 4598}, {6376, 44187}, {7081, 27424}, {7122, 2162}, {7176, 7209}, {17752, 75}, {18047, 18830}, {20284, 3865}, {20964, 16606}, {20981, 43931}, {22370, 7019}, {24533, 514}, {27644, 32010}, {27891, 6385}, {30584, 4391}, {38832, 40432}, {40848, 1934}, {41318, 76}, {41526, 1431}, {41531, 1916}, {51319, 1}
X(51902) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {31, 7766, 34252}, {43, 1423, 41886}, {894, 7081, 51575}, {894, 20964, 171}
X(51903) lies on the cubic K989 and these lines: {1, 163}, {31, 1581}, {82, 2643}, {171, 19576}, {238, 1691}, {560, 662}, {1580, 1933}, {1966, 19574}, {4117, 4599}, {17467, 18042}
X(51903) = X(i)-isoconjugate of X(j) for these (i,j): {2, 41517}, {694, 1916}, {882, 18829}, {1934, 1967}, {8789, 44160}, {9468, 18896}, {17980, 40708}, {36897, 40810}
X(51903) = X(i)-Dao conjugate of X(j) for these (i, j): (804, 1109), (8290, 1934), (19576, 1581), (32664, 41517), (39030, 44160), (39031, 694), (39043, 1916), (39044, 18896)
X(51903) = crosssum of X(1916) and X(40099)
X(51903) = barycentric product X(i)*X(j) for these {i,j}: {1, 4027}, {75, 51318}, {238, 27982}, {385, 1580}, {512, 46295}, {661, 46294}, {1691, 1966}, {1926, 14602}, {1933, 3978}, {6645, 8300}, {19572, 51244}, {24041, 35078}
X(51903) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 41517}, {385, 1934}, {1580, 1916}, {1691, 1581}, {1926, 44160}, {1933, 694}, {1966, 18896}, {4027, 75}, {6652, 30643}, {7369, 30642}, {8300, 40099}, {14602, 1967}, {18902, 1927}, {19578, 3493}, {27982, 334}, {35078, 1109}, {46294, 799}, {46295, 670}, {51318, 1}
X(51904) lies on the cubic K989 and these lines: {1, 82}, {31, 9285}, {171, 1691}, {238, 19576}, {1580, 19578}, {1581, 19559}, {1582, 1932}, {1740, 9247}, {1966, 19574}, {2236, 19572}, {8061, 8634}, {14599, 19580}, {17453, 33782}
X(51904) = X(i)-isoconjugate of X(j) for these (i,j): {6, 40847}, {76, 14946}, {626, 711}, {694, 9229}, {695, 1916}, {783, 826}, {1581, 9285}, {1934, 9288}, {1967, 9239}, {3005, 18828}, {36214, 37892}
X(51904) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 40847), (8290, 9239), (19576, 9285), (37895, 1934), (39031, 695), (39043, 9229)
X(51904) = crossdifference of every pair of points on line {4118, 8061}
X(51904) = X(i)-line conjugate of X(j) for these (i,j): {1, 4118}, {8634, 8061}
X(51904) = barycentric product X(i)*X(j) for these {i,j}: {1, 16985}, {75, 51320}, {384, 1580}, {385, 1582}, {782, 4599}, {1691, 1965}, {1915, 1966}, {1925, 14602}, {1932, 3978}, {1933, 9230}, {16101, 19578}, {34072, 35558}
X(51904) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40847}, {384, 1934}, {385, 9239}, {560, 14946}, {710, 20627}, {1580, 9229}, {1582, 1916}, {1691, 9285}, {1915, 1581}, {1925, 44160}, {1932, 694}, {1933, 695}, {1965, 18896}, {4599, 18828}, {14602, 9288}, {16985, 75}, {18902, 9236}, {19578, 3505}, {34072, 783}, {51320, 1}
X(51905) lies on the cubic K1047 and these lines: {2, 13960}, {3, 6414}, {6, 494}, {25, 26875}, {216, 5407}, {255, 606}, {371, 8277}, {372, 12160}, {394, 577}, {487, 3069}, {491, 27377}, {615, 11091}, {1351, 26894}, {1368, 26945}, {3167, 26920}, {3564, 26873}, {3796, 8908}, {5020, 26919}, {5050, 26891}, {5406, 22052}, {5408, 36748}, {5410, 10960}, {5413, 9732}, {6290, 44638}, {6391, 6413}, {6458, 12164}, {8576, 13943}, {8780, 26886}, {8946, 12960}, {9306, 26953}, {9937, 10897}, {10132, 11513}, {10133, 19447}, {12306, 17820}, {12978, 26293}, {15066, 26912}, {19355, 20794}, {19458, 44589}, {26454, 40322}, {26951, 30771}
X(51905) = isogonal conjugate of the isotomic conjugate of X(8223)
X(51905) = isotomic conjugate of the polar conjugate of X(10133)
X(51905) = isogonal conjugate of the polar conjugate of X(487)
X(51905) = X(i)-Ceva conjugate of X(j) for these (i,j): {487, 10133}, {5409, 3}
X(51905) = X(i)-isoconjugate of X(j) for these (i,j): {4, 19217}, {19, 24243}, {92, 8946}, {158, 494}, {1096, 5491}
X(51905) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 24243), (1147, 494), (6503, 5491), (8222, 76), (22391, 8946), (33365, 2052), (36033, 19217)
X(51905) = crosspoint of X(i) and X(j) for these (i,j): {6, 45596}, {487, 8223}
X(51905) = crosssum of X(2) and X(26503)
X(51905) = barycentric product X(i)*X(j) for these {i,j}: {3, 487}, {6, 8223}, {63, 19216}, {69, 10133}, {184, 46743}, {394, 3069}, {3926, 6424}, {4558, 17432}, {5409, 24245}, {8222, 45596}, {26922, 39388}
X(51905) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 24243}, {48, 19217}, {184, 8946}, {394, 5491}, {487, 264}, {577, 494}, {3069, 2052}, {6424, 393}, {8223, 76}, {10133, 4}, {14585, 26461}, {17432, 14618}, {19216, 92}, {19447, 3128}, {46743, 18022}
X(51905) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 8943, 494}, {6, 19409, 5409}, {6, 44630, 26455}, {6, 45595, 19034}, {19443, 45726, 8219}
X(51906) lies on the cubic K554 and these lines: {2, 38278}, {39, 83}, {111, 251}, {115, 804}, {308, 3228}, {512, 14990}, {1015, 4367}, {1176, 14498}, {1180, 41917}, {1500, 14992}, {3111, 9431}, {3124, 5027}, {3229, 7845}, {3291, 26276}, {5007, 9149}, {5052, 43977}, {5475, 17500}, {6375, 7853}, {7753, 8265}, {11060, 46288}, {15484, 34811}, {16589, 27067}, {18092, 45210}, {27375, 44164}, {32085, 33842}, {32581, 33843}, {35007, 38834}, {35971, 46654}
X(51906) = isogonal conjugate of the isotomic conjugate of X(34294)
X(51906) = X(i)-complementary conjugate of X(j) for these (i,j): {3108, 42327}, {4117, 15527}, {10159, 21263}, {31065, 21235}
X(51906) = X(i)-Ceva conjugate of X(j) for these (i,j): {83, 512}, {251, 18105}, {38278, 22105}
X(51906) = X(i)-cross conjugate of X(j) for these (i,j): {3124, 34294}, {8029, 2489}, {23099, 512}
X(51906) = cevapoint of X(i) and X(j) for these (i,j): {1084, 3124}, {21906, 38988}
X(51906) = crosspoint of X(251) and X(18105)
X(51906) = crosssum of X(i) and X(j) for these (i,j): {6, 10330}, {141, 4576}, {1634, 3051}, {35325, 41584}
X(51906) = trilinear pole of line {2086, 22260}
X(51906) = crossdifference of every pair of points on line {1634, 4576}
X(51906) = X(i)-isoconjugate of X(j) for these (i,j): {38, 4590}, {39, 24037}, {141, 24041}, {249, 1930}, {662, 4576}, {799, 1634}, {1101, 8024}, {1923, 44168}, {1964, 34537}, {2236, 39292}, {3917, 46254}, {4553, 4610}, {4567, 16887}, {4570, 16703}, {4592, 41676}, {4600, 16696}, {4601, 17187}, {4623, 46148}, {4631, 46153}, {7340, 33299}, {8061, 31614}, {17442, 47389}, {24039, 36827}
X(51906) = X(i)-Dao conjugate of X(j) for these (i, j): (512, 39), (523, 8024), (826, 14125), (1084, 4576), (3005, 141), (5139, 41676), (21905, 7813), (38996, 1634), (40627, 16887), (41884, 34537), (50330, 16703), (50497, 16696)
X(51906) = barycentric product X(i)*X(j) for these {i,j}: {6, 34294}, {82, 2643}, {83, 3124}, {115, 251}, {181, 18101}, {308, 1084}, {338, 46288}, {523, 18105}, {689, 23099}, {798, 18070}, {827, 8029}, {1109, 46289}, {1176, 8754}, {1799, 2971}, {2086, 14970}, {2489, 4580}, {2970, 10547}, {3122, 18082}, {3125, 18098}, {4079, 10566}, {4117, 18833}, {4577, 22260}, {4628, 21131}, {4630, 23105}, {4705, 18108}, {6784, 42299}, {9178, 22105}, {9427, 40016}, {15630, 20022}, {20975, 32085}, {23610, 42371}
X(51906) = barycentric quotient X(i)/X(j) for these {i,j}: {82, 24037}, {83, 34537}, {115, 8024}, {251, 4590}, {308, 44168}, {512, 4576}, {669, 1634}, {733, 39292}, {827, 31614}, {881, 46161}, {1084, 39}, {1176, 47389}, {1356, 1401}, {2086, 732}, {2489, 41676}, {2643, 1930}, {2971, 427}, {3121, 16696}, {3122, 16887}, {3124, 141}, {3125, 16703}, {4079, 4568}, {4117, 1964}, {6784, 14994}, {7063, 3688}, {8029, 23285}, {8754, 1235}, {9427, 3051}, {15449, 14125}, {15630, 20021}, {18070, 4602}, {18098, 4601}, {18101, 18021}, {18105, 99}, {18108, 4623}, {20975, 3933}, {21823, 16720}, {21906, 7813}, {22260, 826}, {23099, 3005}, {23216, 20775}, {23610, 688}, {33918, 14406}, {34294, 76}, {42068, 1843}, {44114, 51371}, {46288, 249}, {46289, 24041}, {50487, 4553}
X(51907) lies on the cubics K432 and K991 and these lines: {1, 75}, {6, 904}, {31, 19603}, {38, 45232}, {238, 38986}, {560, 1932}, {667, 788}, {704, 35539}, {896, 4117}, {1580, 1927}, {1755, 1967}, {1911, 2076}, {1918, 18758}, {2309, 4161}, {4116, 5145}, {8772, 42075}, {17149, 33782}, {18755, 20996}, {18904, 45905}, {20473, 37538}, {23489, 33764}
X(51907) = isogonal conjugate of the isotomic conjugate of X(2227)
X(51907) = X(i)-Ceva conjugate of X(j) for these (i,j): {1580, 1755}, {1927, 1964}, {37134, 798}
X(51907) = X(i)-isoconjugate of X(j) for these (i,j): {2, 3225}, {4, 8858}, {75, 43761}, {76, 699}, {1916, 32544}, {8864, 11606}
X(51907) = X(i)-Dao conjugate of X(j) for these (i, j): (206, 43761), (3229, 1926), (32664, 3225), (36033, 8858), (39031, 32544), (39080, 75), (40810, 1934)
X(51907) = crosspoint of X(i) and X(j) for these (i,j): {1, 1967}, {741, 7121}
X(51907) = crosssum of X(i) and X(j) for these (i,j): {1, 1966}, {740, 6376}, {812, 38986}
X(51907) = crossdifference of every pair of points on line {75, 798}
X(51907) = X(i)-lineconjugate of X(j) for these (i,j): {1, 75}, {667, 798}
X(51907) = barycentric product X(i)*X(j) for these {i,j}: {1, 3229}, {6, 2227}, {31, 698}, {75, 32748}, {560, 35524}, {661, 41337}, {799, 9429}, {896, 36821}, {1580, 47648}, {1581, 51322}, {1959, 32540}, {1967, 39080}, {17799, 51248}
X(51907) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 3225}, {32, 43761}, {48, 8858}, {560, 699}, {698, 561}, {1933, 32544}, {2227, 76}, {3229, 75}, {9429, 661}, {32540, 1821}, {32748, 1}, {35524, 1928}, {36821, 46277}, {39080, 1926}, {41337, 799}, {47648, 1934}, {51322, 1966}
X(51908) lies on the cubic K137 and these lines: {1, 513}, {44, 88}, {106, 3246}, {190, 46795}, {239, 903}, {320, 4080}, {518, 4792}, {527, 6549}, {536, 4555}, {545, 6633}, {1086, 46790}, {1155, 39154}, {3666, 47058}, {3834, 4997}, {4419, 36887}, {4440, 17953}, {4622, 16702}, {4634, 30938}, {4670, 27922}, {4674, 49712}, {4945, 31138}, {6548, 24407}, {6687, 31227}, {24416, 28220}, {27921, 34762}, {37520, 40215}
X(51908) = X(i)-isoconjugate of X(j) for these (i,j): {101, 34764}, {519, 2384}, {902, 35168}
X(51908) = X(i)-Dao conjugate of X(j) for these (i, j): (1015, 34764), (35121, 4358), (40594, 35168)
X(51908) = crossdifference of every pair of points on line {44, 3251}
X(51908) = X(i)-line conjugate of X(j) for these (i,j): {1, 3251}, {88, 44}
X(51908) = barycentric product X(i)*X(j) for these {i,j}: {88, 545}, {513, 34762}, {679, 1644}, {1022, 6633}, {1320, 43038}, {3257, 14475}, {4555, 14421}, {4618, 33920}, {8649, 20568}
X(51908) = barycentric quotient X(i)/X(j) for these {i,j}: {88, 35168}, {513, 34764}, {545, 4358}, {1644, 4738}, {6633, 24004}, {8649, 44}, {9456, 2384}, {14421, 900}, {14475, 3762}, {34762, 668}
X(51908) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {88, 3257, 44}, {88, 9326, 3257}, {679, 3257, 88}, {679, 9326, 44}, {2226, 40594, 16610}
X(51909) lies on the cubic K989 and these lines: {1, 3495}, {31, 19565}, {82, 34252}, {171, 1920}, {238, 9285}, {1580, 3955}, {1740, 23186}, {2236, 17797}, {6196, 23192}, {7083, 23853}, {8022, 19580}
X(51909) = X(31)-Ceva conjugate of X(171)
X(51909) = X(i)-isoconjugate of X(j) for these (i,j): {256, 7346}, {694, 39934}
X(51909) = X(i)-Dao conjugate of X(j) for these (i, j): (1920, 561), (39043, 39934)
X(51909) = barycentric product X(i)*X(j) for these {i,j}: {1, 39928}, {172, 24732}, {894, 6196}, {1909, 34251}
X(51909) = barycentric quotient X(i)/X(j) for these {i,j}: {172, 7346}, {1580, 39934}, {6196, 257}, {24732, 44187}, {34251, 256}, {39928, 75}
X(51910) lies on the cubic K1202 and these lines: {3, 3366}, {5, 43312}, {6, 15696}, {20, 486}, {30, 10577}, {371, 376}, {372, 550}, {382, 6412}, {485, 3528}, {548, 6200}, {549, 42272}, {590, 33923}, {615, 15704}, {631, 35786}, {1131, 5418}, {1152, 3534}, {1328, 46333}, {1350, 39894}, {1587, 9542}, {1657, 6410}, {2041, 42103}, {2042, 42106}, {3069, 6485}, {3070, 8703}, {3071, 12103}, {3311, 43339}, {3312, 15689}, {3316, 21735}, {3522, 6560}, {3523, 22644}, {3524, 42269}, {3529, 5420}, {3530, 42284}, {3850, 43785}, {3853, 32790}, {4297, 35611}, {5010, 35800}, {5059, 42268}, {5073, 6497}, {5412, 35503}, {5413, 35491}, {6361, 35811}, {6395, 43338}, {6409, 13903}, {6411, 35812}, {6419, 44245}, {6420, 42260}, {6422, 44541}, {6429, 42525}, {6430, 18510}, {6433, 31487}, {6434, 13961}, {6449, 15695}, {6450, 42263}, {6452, 17800}, {6453, 42216}, {6454, 6561}, {6456, 15681}, {6478, 42418}, {6481, 7584}, {6484, 32787}, {6487, 13966}, {6496, 13846}, {7280, 35802}, {8976, 14093}, {9541, 35771}, {9680, 23267}, {10295, 11474}, {10299, 12818}, {10898, 44246}, {11001, 22615}, {11514, 44240}, {12100, 42582}, {12124, 35944}, {12375, 38723}, {12376, 16111}, {14689, 35829}, {15022, 42601}, {15055, 35834}, {15326, 35809}, {15338, 35769}, {15690, 35770}, {15691, 32788}, {15692, 23253}, {15697, 43511}, {15698, 43558}, {15709, 43503}, {15710, 42602}, {15712, 42273}, {15715, 43515}, {15717, 42277}, {15722, 42576}, {16163, 35827}, {18481, 35843}, {19708, 31412}, {21734, 23249}, {24466, 35857}, {31663, 35788}, {31730, 35642}, {32785, 43336}, {32786, 49138}, {32789, 44682}, {33703, 42274}, {34091, 43255}, {34200, 43209}, {34782, 35865}, {35256, 42271}, {35824, 38742}, {35825, 38738}, {35826, 38788}, {35841, 48881}, {35856, 38754}, {35878, 38731}, {35879, 38749}, {35883, 38761}, {35947, 40275}, {42171, 43464}, {42173, 43463}, {42226, 46853}, {42232, 43770}, {42234, 43769}, {42413, 43510}, {42523, 43257}, {42569, 45385}, {43340, 43879}
X(51910) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 42264, 10576}, {3, 42267, 6564}, {20, 6396, 35821}, {20, 13935, 42275}, {376, 42261, 371}, {548, 42259, 6200}, {631, 42276, 35786}, {1152, 3534, 42266}, {1152, 42266, 35823}, {1657, 6410, 6565}, {3524, 42414, 42269}, {5073, 6497, 8252}, {6396, 35821, 35813}, {6452, 17800, 42262}, {6456, 15681, 23261}, {6561, 42637, 6454}, {10304, 43407, 5418}, {17538, 42637, 6561}
X(51911) lies on the cubic K1202 and these lines: {3, 3367}, {5, 43313}, {6, 15696}, {20, 485}, {30, 10576}, {371, 550}, {372, 376}, {382, 6411}, {486, 3528}, {548, 6396}, {549, 42271}, {590, 15704}, {615, 33923}, {631, 35787}, {1132, 5420}, {1151, 3534}, {1327, 46333}, {1350, 39893}, {1587, 9543}, {1588, 43884}, {1657, 6409}, {2041, 42106}, {2042, 42103}, {3068, 6484}, {3070, 12103}, {3071, 8703}, {3311, 15689}, {3312, 43338}, {3317, 21735}, {3522, 6561}, {3523, 22615}, {3524, 42268}, {3529, 5418}, {3530, 42283}, {3850, 43786}, {3853, 32789}, {4297, 35610}, {5010, 35801}, {5059, 42269}, {5073, 6496}, {5412, 35491}, {5413, 35503}, {6199, 43339}, {6361, 35810}, {6410, 13961}, {6412, 35813}, {6419, 9541}, {6420, 44245}, {6421, 44541}, {6429, 18512}, {6430, 42524}, {6433, 13903}, {6449, 8960}, {6450, 15695}, {6451, 17800}, {6453, 6560}, {6454, 42215}, {6455, 15681}, {6460, 9681}, {6468, 31487}, {6479, 42417}, {6480, 7583}, {6485, 32788}, {6486, 8981}, {6497, 13847}, {7280, 35803}, {9682, 33524}, {10295, 11473}, {10299, 12819}, {10897, 44246}, {11001, 22644}, {11513, 44240}, {12100, 42583}, {12123, 35945}, {12375, 16111}, {12376, 38723}, {13951, 14093}, {14689, 35828}, {15022, 42600}, {15055, 35835}, {15326, 35808}, {15338, 35768}, {15690, 35771}, {15691, 32787}, {15692, 23263}, {15697, 43512}, {15698, 43559}, {15709, 43504}, {15710, 42603}, {15712, 42270}, {15715, 43516}, {15717, 42274}, {15722, 42577}, {16163, 35826}, {18481, 35842}, {19708, 42561}, {21734, 23259}, {24466, 35856}, {31454, 42226}, {31663, 35789}, {31730, 35641}, {32785, 49138}, {32786, 43337}, {32790, 44682}, {33703, 42277}, {34089, 43254}, {34200, 43210}, {34782, 35864}, {35255, 42272}, {35733, 42430}, {35824, 38738}, {35825, 38742}, {35827, 38788}, {35840, 48881}, {35857, 38754}, {35878, 38749}, {35879, 38731}, {35882, 38761}, {35946, 40274}, {42172, 43464}, {42174, 43463}, {42225, 46853}, {42231, 43770}, {42233, 43769}, {42414, 43509}, {42522, 43256}, {42568, 45384}, {43341, 43880}
X(51911) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 42263, 10577}, {3, 42266, 6565}, {20, 6200, 35820}, {20, 9540, 42276}, {376, 42260, 372}, {548, 42258, 6396}, {631, 42275, 35787}, {1151, 3534, 42267}, {1151, 42267, 35822}, {1657, 6409, 6564}, {3524, 42413, 42268}, {5073, 6496, 8253}, {6200, 35820, 35812}, {6449, 42264, 8960}, {6451, 17800, 42265}, {6455, 15681, 23251}, {6560, 42638, 6453}, {9541, 42261, 6419}, {9541, 50693, 42261}, {10304, 43408, 5420}, {17538, 42638, 6560}
X(51912) lies on the cubic K989 and these lines: {1, 1581}, {31, 799}, {38, 23491}, {171, 8290}, {238, 385}, {1926, 1966}, {2309, 8299}, {3708, 21336}, {3720, 38346}, {4094, 39915}, {4117, 17469}, {17470, 20591}, {17752, 38382}, {18671, 23478}, {20356, 21334}, {20362, 20363}, {21001, 25853}
X(51912) = X(31)-Ceva conjugate of X(2236)
X(51912) = X(i)-isoconjugate of X(j) for these (i,j): {694, 3225}, {699, 1916}, {1581, 43761}, {8858, 17980}, {32544, 41517}
X(51912) = X(i)-Dao conjugate of X(j) for these (i, j): (2086, 661), (3229, 75), (19576, 43761), (35540, 561), (39031, 699), (39043, 3225), (39080, 1581)
X(51912) = crosspoint of X(1) and X(1966)
X(51912) = crosssum of X(1) and X(1967)
X(51912) = X(1)-line conjugate of X(1581)
X(51912) = X(51912) = barycentric product X(i)*X(j) for these {i,j}: {1, 39080}, {75, 51322}, {385, 2227}, {698, 1580}, {1926, 32748}, {1933, 35524}, {1966, 3229}
barycentric quotient X(i)/X(j) for these {i,j}: {698, 1934}, {1580, 3225}, {1691, 43761}, {1933, 699}, {2227, 1916}, {3229, 1581}, {32748, 1967}, {39080, 75}, {41337, 37134}, {51322, 1}
X(51913) lies on the cubic K432 and these lines: {1, 9285}, {6, 2201}, {19, 27}, {25, 2053}, {38, 46507}, {162, 43761}, {204, 9258}, {1096, 1967}, {1430, 3162}, {1580, 1957}, {3186, 7075}, {5247, 37101}, {8020, 37652}, {11325, 21877}, {15310, 23143}
X(51913) = polar conjugate of X(18832)
X(51913) = polar conjugate of the isotomic conjugate of X(1740)
X(51913) = X(i)-Ceva conjugate of X(j) for these (i,j): {1957, 204}, {1973, 19}
X(51913) = X(i)-isoconjugate of X(j) for these (i,j): {2, 3504}, {3, 2998}, {6, 43714}, {48, 18832}, {63, 3223}, {69, 3224}, {76, 15389}, {184, 40162}, {304, 34248}, {647, 3222}, {1176, 42551}, {6391, 47733}, {36214, 39927}
X(51913) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 43714), (76, 40364), (1249, 18832), (3162, 3223), (32664, 3504), (32746, 304), (36103, 2998), (39052, 3222)
X(51913) = crosssum of X(3) and X(23143)
X(51913) = crossdifference of every pair of points on line {810, 25098}
X(51913) = barycentric product X(i)*X(j) for these {i,j}: {1, 3186}, {4, 1740}, {19, 194}, {25, 17149}, {27, 21877}, {28, 21080}, {33, 17082}, {75, 11325}, {92, 1613}, {108, 25128}, {112, 20910}, {158, 20794}, {162, 23301}, {278, 7075}, {281, 1424}, {811, 3221}, {823, 2524}, {1474, 22028}, {1783, 21191}, {1897, 50516}, {1928, 41293}, {1973, 6374}, {1974, 18837}, {5379, 21144}, {6331, 23503}, {6335, 23572}, {8750, 23807}, {20883, 38834}, {36120, 51427}
X(51913) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 43714}, {4, 18832}, {19, 2998}, {25, 3223}, {31, 3504}, {92, 40162}, {162, 3222}, {194, 304}, {560, 15389}, {1424, 348}, {1613, 63}, {1740, 69}, {1973, 3224}, {1974, 34248}, {2524, 24018}, {3186, 75}, {3221, 656}, {6374, 40364}, {7075, 345}, {9491, 810}, {11325, 1}, {17082, 7182}, {17149, 305}, {17442, 42551}, {18837, 40050}, {20794, 326}, {20910, 3267}, {21080, 20336}, {21191, 15413}, {21877, 306}, {22028, 40071}, {23301, 14208}, {23503, 647}, {23572, 905}, {25128, 35518}, {38834, 34055}, {41293, 560}, {50516, 4025}
X(51914) lies on the cubic K432 and these lines: {1, 18270}, {6, 19579}, {31, 799}, {75, 1967}, {183, 2053}, {1580, 18271}, {1755, 1966}, {1910, 18832}, {1965, 39337}, {5989, 16364}
X(51914) = X(1580)-Ceva conjugate of X(75)
X(51914) = X(18896)-Dao conjugate of X(1934)
X(51914) = barycentric product X(1966)*X(39935)
X(51914) = barycentric quotient X(39935)/X(1581)
X(51914) = {X(19579),X(39933)}-harmonic conjugate of X(6)
X(51915) lies on the cubic K1202 and these lines: {3, 5349}, {6, 10304}, {13, 8703}, {16, 46332}, {140, 43400}, {376, 42098}, {395, 34200}, {396, 3528}, {548, 5350}, {3522, 42166}, {5237, 43233}, {5238, 33923}, {5321, 15759}, {10645, 41982}, {10653, 14093}, {11480, 43304}, {11543, 42505}, {12100, 42108}, {14891, 43402}, {15686, 43399}, {15688, 23302}, {15690, 42500}, {15692, 42107}, {15696, 43104}, {15697, 42110}, {15704, 42596}, {15706, 42101}, {15710, 23303}, {15711, 43101}, {16241, 42900}, {16242, 45759}, {19708, 33605}, {19711, 42430}, {21734, 42626}, {21735, 42147}, {22238, 42927}, {35418, 42693}, {36968, 42687}, {41944, 43335}, {41981, 42429}, {42087, 42956}, {42136, 43204}, {42434, 42778}, {42491, 43557}, {42509, 49812}, {42513, 42970}, {42520, 42791}, {42625, 49813}, {42794, 42974}, {42912, 43302}, {42913, 42934}, {43372, 43416}, {43428, 43481}
X(51916) lies on the cubic K1202 and these lines: {3, 5350}, {6, 10304}, {14, 8703}, {15, 46332}, {140, 43399}, {376, 42095}, {395, 3528}, {396, 34200}, {548, 5349}, {3522, 42163}, {5237, 33923}, {5238, 43232}, {5318, 15759}, {10646, 41982}, {10654, 14093}, {11481, 43305}, {11542, 42504}, {12100, 42109}, {14891, 43401}, {15686, 43400}, {15688, 23303}, {15690, 42501}, {15692, 42110}, {15696, 43101}, {15697, 42107}, {15704, 42597}, {15706, 42102}, {15710, 23302}, {15711, 43104}, {16241, 45759}, {16242, 42901}, {19708, 33604}, {19711, 42429}, {21734, 42625}, {21735, 42148}, {22236, 42926}, {35418, 42692}, {36967, 42686}, {41943, 43334}, {41981, 42430}, {42088, 42957}, {42137, 43203}, {42433, 42777}, {42490, 43556}, {42508, 49813}, {42512, 42971}, {42521, 42792}, {42626, 49812}, {42793, 42975}, {42912, 42935}, {42913, 43303}, {43373, 43417}, {43429, 43482}
X(51917) lies on the cubic K989 and these lines: {10, 82}, {31, 17743}, {43, 32468}, {100, 904}, {171, 172}, {213, 19580}, {1376, 2176}, {1740, 3499}, {2053, 37540}, {2236, 17741}, {2274, 12782}, {6647, 7188}, {8299, 37588}, {14133, 37570}, {17752, 38382}
X(51917) = X(17743)-Ceva conjugate of X(2329)
X(51917) = X(i)-isoconjugate of X(j) for these (i,j): {694, 39937}, {893, 39746}, {1178, 43687}, {1432, 3495}
X(51917) = X(i)-Dao conjugate of X(j) for these (i, j): (39043, 39937), (40597, 39746)
X(51917) = barycentric product X(i)*X(j) for these {i,j}: {1, 39929}, {75, 51323}, {171, 26752}, {3503, 7081}
X(51917) = barycentric quotient X(i)/X(j) for these {i,j}: {171, 39746}, {1580, 39937}, {2295, 43687}, {2330, 3495}, {3503, 7249}, {26752, 7018}, {39929, 75}, {51323, 1}
X(51918) lies on the cubic K297 and these lines: {3, 729}, {6, 37338}, {39, 33705}, {83, 1975}, {183, 3225}, {956, 27810}, {1974, 33875}, {2207, 46522}, {3114, 11174}, {3224, 5013}, {5023, 36615}, {5041, 10014}, {6531, 36822}, {32748, 46319}, {42346, 43136}
X(51918) = X(i)-isoconjugate of X(j) for these (i,j): {75, 14614}, {561, 41412}, {799, 32472}, {3112, 41622}
X(51918) = X(i)-Dao conjugate of X(j) for these (i, j): (206, 14614), (34452, 41622), (38996, 32472), (40368, 41412)
X(51918) = barycentric product X(512)*X(39639)
X(51918) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 14614}, {669, 32472}, {1501, 41412}, {3051, 41622}, {39639, 670}
X(51919) lies on the cubics K432 and K673 and these lines: {1, 40736}, {6, 19579}, {43, 7075}, {256, 16360}, {291, 16361}, {560, 30634}, {1403, 1613}, {1580, 1922}, {2053, 3224}, {2176, 18756}, {3499, 3502}, {4598, 40418}, {7104, 8300}, {17475, 33296}
X(51919) = isogonal conjugate of X(19565)
X(51919) = isotomic conjugate of X(18275)
X(51919) = isogonal conjugate of the anticomplement of X(1921)
X(51919) = X(i)-cross conjugate of X(j) for these (i,j): {239, 6}, {1967, 8852}
X(51919) = X(i)-isoconjugate of X(j) for these (i,j): {1, 19565}, {2, 3510}, {6, 19567}, {31, 18275}, {75, 18278}, {92, 23186}, {171, 40849}, {291, 19579}, {292, 19581}, {334, 18274}, {335, 19580}, {726, 40755}, {1911, 18277}, {4645, 8875}, {18895, 30634}
X(51919) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 18275), (3, 19565), (9, 19567), (206, 18278), (6651, 18277), (19557, 19581), (22391, 23186), (32664, 3510), (39029, 19579)
X(51919) = cevapoint of X(8632) and X(21762)
X(51919) = crosssum of X(i) and X(j) for these (i,j): {18278, 23186}, {30661, 30667}
X(51919) = trilinear pole of line {2309, 8630}
X(51919) = barycentric product X(i)*X(j) for these {i,j}: {1, 7168}, {238, 24576}, {893, 39933}, {2210, 30633}, {3512, 8868}, {20332, 40782}
X(51919) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 19567}, {2, 18275}, {6, 19565}, {31, 3510}, {32, 18278}, {184, 23186}, {238, 19581}, {239, 18277}, {893, 40849}, {1914, 19579}, {2210, 19580}, {7168, 75}, {8868, 17789}, {14599, 18274}, {18892, 30634}, {24576, 334}, {30633, 44172}, {34077, 40755}, {39933, 1920}
X(51928) lies on the cubics K155 and K989 and these lines: {1, 40736}, {31, 19580}, {171, 18270}, {238, 9468}, {1423, 1740}, {2106, 3009}, {2108, 8868}, {2144, 41534}, {3225, 34252}, {17752, 38382}, {51322, 51323}
X(51920) = X(i)-cross conjugate of X(j) for these (i,j): {292, 41534}, {1966, 171}
X(51920) = X(i)-isoconjugate of X(j) for these (i,j): {6, 40849}, {256, 3510}, {257, 18278}, {694, 19579}, {893, 19565}, {904, 19567}, {1581, 19580}, {1916, 18274}, {1934, 30634}, {1967, 19581}, {7104, 18275}, {8875, 40873}, {9468, 18277}
X(51920) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 40849), (8290, 19581), (19576, 19580), (39031, 18274), (39043, 19579), (39044, 18277), (40597, 19565)
X(51920) = barycentric product X(i)*X(j) for these {i,j}: {1, 39933}, {385, 24576}, {894, 7168}, {1691, 30633}, {7061, 8868}
X(51920) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40849}, {171, 19565}, {172, 3510}, {385, 19581}, {894, 19567}, {1580, 19579}, {1691, 19580}, {1909, 18275}, {1933, 18274}, {1966, 18277}, {7122, 18278}, {7168, 257}, {14602, 30634}, {24576, 1916}, {30633, 18896}, {39933, 75}
X(51921) lies on the cubic K432 and these lines: {1, 6}, {31, 19586}, {75, 17741}, {101, 1691}, {190, 698}, {560, 2053}, {595, 12212}, {660, 18278}, {726, 24294}, {732, 40859}, {872, 904}, {995, 13331}, {1580, 41531}, {1611, 38876}, {1755, 2076}, {2295, 4645}, {3094, 3730}, {3747, 7077}, {3774, 18755}, {3780, 49707}, {3943, 15990}, {3997, 17770}, {4136, 49693}, {4544, 17765}, {5017, 14974}, {5103, 41324}, {5116, 21008}, {12329, 23863}, {17750, 49676}, {17798, 46286}, {18047, 19565}, {20072, 28369}, {20995, 21780}, {21791, 37998}, {32449, 34063}
X(51921) = isogonal conjugate of the isotomic conjugate of X(33889)
X(51921) = X(41531)-Ceva conjugate of X(34247)
X(51921) = X(2)-isoconjugate of X(7166)
X(51921) = X(32664)-Dao conjugate of X(7166)
X(51921) = crosspoint of X(1016) and X(8684)
X(51921) = crosssum of X(i) and X(j) for these (i,j): {812, 21138}, {1015, 3808}
X(51921) = crossdifference of every pair of points on line {513, 17235}
X(51921) = barycentric product X(i)*X(j) for these {i,j}: {1, 3507}, {6, 33889}
X(51921) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 7166}, {3507, 75}, {33889, 76}
X(51922) lies on the cubic K1050 and these lines: {6, 513}, {44, 294}, {105, 910}, {528, 35113}, {536, 666}, {1100, 40754}, {1438, 7113}, {1462, 6610}, {2161, 2195}, {3834, 31637}, {4864, 9453}, {6687, 31638}, {7297, 18785}, {8751, 14571}, {14578, 32644}
X(51922) = X(i)-isoconjugate of X(j) for these (i,j): {518, 37131}, {672, 18821}, {840, 3912}, {34230, 46791}
X(51922) = X(35113)-Dao conjugate of X(3263)
X(51922) = crosssum of X(518) and X(1642)
X(51922) = crossdifference of every pair of points on line {518, 3126}
X(51922) = barycentric product X(i)*X(j) for these {i,j}: {105, 528}, {294, 5723}, {666, 1643}, {673, 2246}, {1642, 6185}, {42722, 43929}
X(51922) = barycentric quotient X(i)/X(j) for these {i,j}: {105, 18821}, {528, 3263}, {1438, 37131}, {1642, 4437}, {1643, 918}, {2246, 3912}, {5723, 40704}
X(51922) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {294, 36086, 44}, {1462, 36146, 6610}
X(51923) lies on the cubic K137 and these lines: {1, 659}, {44, 190}, {88, 292}, {2382, 29351}, {3768, 46782}, {4465, 13466}, {16507, 37129}, {23343, 42083}, {24407, 47070}, {27921, 46801}, {30579, 30667}, {39044, 41314}
X(51923) = X(i)-isoconjugate of X(j) for these (i,j): {537, 739}, {667, 46780}, {20331, 37129}, {34075, 36848}
X(51923) = X(i)-Dao conjugate of X(j) for these (i, j): (6631, 46780), (39011, 36848), (40614, 537)
X(51923) = trilinear pole of line {899, 14434}
X(51923) = barycentric product X(i)*X(j) for these {i,j}: {190, 46782}, {899, 18822}, {2382, 6381}
X(51923) = barycentric quotient X(i)/X(j) for these {i,j}: {190, 46780}, {891, 36848}, {899, 537}, {2382, 37129}, {3230, 20331}, {18822, 31002}, {46782, 514}
X(51924) lies on the cubic K1202 and these lines: {13, 382}, {14, 13951}, {15, 42206}, {30, 36449}, {61, 42278}, {371, 49947}, {372, 42154}, {381, 3366}, {396, 485}, {615, 42172}, {1152, 3534}, {1328, 42239}, {2041, 37640}, {2043, 3069}, {2044, 43408}, {3053, 49209}, {3070, 36466}, {3365, 13847}, {6301, 15294}, {6561, 42088}, {6564, 42817}, {6565, 42126}, {8976, 49905}, {10576, 43544}, {10577, 49908}, {10654, 42229}, {13665, 42176}, {13785, 42130}, {18585, 35255}, {18586, 42085}, {22615, 36448}, {23253, 49813}, {23261, 46335}, {35731, 36836}, {35820, 41101}, {35821, 36967}, {36453, 42265}, {42095, 42204}, {42232, 42975}, {42279, 43194}
X(51925) lies on the cubic K1202 and these lines: {13, 8976}, {14, 382}, {16, 42203}, {30, 36450}, {62, 42278}, {371, 42155}, {372, 49948}, {381, 3392}, {395, 486}, {590, 42173}, {1151, 3534}, {1327, 35740}, {2041, 37641}, {2043, 3068}, {2044, 43407}, {3053, 49210}, {3071, 36466}, {3389, 13846}, {6304, 15293}, {6560, 42087}, {6564, 42127}, {6565, 42818}, {8960, 16965}, {10576, 49907}, {10577, 43545}, {10653, 42228}, {13665, 42131}, {13785, 42177}, {13951, 49906}, {18585, 35256}, {18586, 42086}, {22644, 36448}, {23251, 46334}, {23263, 49812}, {31487, 42233}, {35739, 36470}, {35820, 36968}, {35821, 41100}, {36452, 42262}, {42098, 42205}, {42279, 43193}
X(51926) lies on the cubic K395 and these lines: {2, 523}, {25, 17983}, {381, 14246}, {671, 3830}, {691, 3534}, {892, 7788}, {895, 8877}, {3845, 51258}, {5309, 14263}, {7837, 31125}, {9154, 40820}, {9766, 11058}, {11648, 17964}, {14609, 39593}, {15398, 47597}, {21460, 51185}, {41404, 44526}
X(51926) = X(896)-isoconjugate of X(14388)
X(51926) = X(15899)-Dao conjugate of X(14388)
X(51926) = barycentric product X(i)*X(j) for these {i,j}: {671, 11645}, {30786, 41358}
X(51926) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 14388}, {11645, 524}, {41358, 468}
X(51926) = {X(9214),X(16092)}-harmonic conjugate of X(5968)
X(51927) lies on the cubic K297 and these lines: {3, 843}, {6, 9145}, {99, 598}, {183, 35146}, {249, 1384}, {512, 574}, {524, 47047}, {3815, 35606}, {5024, 5968}, {5210, 9217}, {33962, 34241}
X(51927) = X(i)-isoconjugate of X(j) for these (i,j): {897, 22329}, {2030, 46277}, {2793, 36085}, {23894, 34245}
X(51927) = X(i)-Dao conjugate of X(j) for these (i, j): (6593, 22329), (38988, 2793)
X(51927) = crosssum of X(18800) and X(22329)
X(51927) = crossdifference of every pair of points on line {2793, 22329}
X(51927) = barycentric product X(i)*X(j) for these {i,j}: {187, 5503}, {351, 46144}, {690, 2709}, {5467, 34246}
X(51927) = barycentric quotient X(i)/X(j) for these {i,j}: {187, 22329}, {351, 2793}, {2434, 17937}, {2709, 892}, {5467, 34245}, {5503, 18023}, {14567, 2030}, {39689, 18800}
X(51928) lies on the cubic K432 and these lines: {3, 11364}, {6, 31}, {75, 183}, {100, 385}, {187, 8671}, {190, 8844}, {220, 23863}, {692, 9418}, {872, 893}, {1001, 11174}, {1045, 37619}, {1575, 2110}, {1580, 18265}, {1621, 3329}, {1755, 7077}, {1910, 17798}, {1919, 23865}, {2053, 46319}, {2223, 19589}, {2329, 18758}, {3207, 20996}, {3507, 3511}, {3744, 18170}, {3749, 18194}, {4259, 12837}, {4413, 15271}, {4421, 14614}, {7754, 12338}, {8299, 37686}, {8852, 20872}, {9301, 35000}, {9318, 24326}, {9755, 22556}, {11490, 30435}, {11500, 39646}, {12188, 18524}, {16693, 20331}, {18278, 51326}
X(51928) = X(18265)-Ceva conjugate of X(34247)
X(51928) = X(i)-isoconjugate of X(j) for these (i,j): {2, 7167}, {81, 43686}
X(51928) = X(i)-Dao conjugate of X(j) for these (i, j): (32664, 7167), (40586, 43686)
X(51928) = crosspoint of X(i) and X(j) for these (i,j): {813, 4998}, {1252, 8684}
X(51928) = crosssum of X(i) and X(j) for these (i,j): {812, 3271}, {1086, 3808}
X(51928) = barycentric product X(i)*X(j) for these {i,j}: {1, 3508}, {7077, 39940}
X(51928) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 7167}, {42, 43686}, {3508, 75}, {39940, 18033}
X(520) lies on the cubic K137 and these lines: {1, 514}, {44, 673}, {190, 46798}, {239, 294}, {241, 292}, {672, 3008}, {3685, 33674}, {5088, 34906}, {6559, 34852}, {13576, 49772}, {16830, 40724}, {19624, 36086}, {34085, 40862}
X(51929) = X(2223)-isoconjugate of X(35167)
X(51929) = X(35120)-Dao conjugate of X(3912)
X(51929) = X(3008)-lineconjugate of X(672)
X(51929) = barycentric quotient X(673)/X(35167)
X(51929) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {666, 2481, 239}, {666, 6185, 294}
X(51930) lies on Feuerbach circumhyperbola of the tangential triangle, the cubic K432, and these lines: {1, 1581}, {3, 2053}, {6, 7166}, {75, 2640}, {560, 662}, {610, 16571}, {1575, 9509}, {1580, 2227}, {1755, 16559}, {2234, 39339}, {3216, 18754}, {3499, 3502}, {3507, 3511}, {8925, 23605}, {13174, 35916}, {17596, 24578}, {23080, 37580}, {23177, 37576}, {36292, 39337}
X(51930) = X(i)-Ceva conjugate of X(j) for these (i,j): {1580, 1}, {2227, 1740}
X(51930) = X(1916)-Dao conjugate of X(1934)
X(51930) = barycentric product X(1)*X(8782)
X(51930) = barycentric quotient X(8782)/X(75)
X(51931) lies on the cubic K432 and these lines: {1, 3511}, {6, 1967}, {31, 19561}, {55, 4094}, {75, 1281}, {238, 20677}, {560, 30634}, {1403, 37137}, {1755, 41532}, {1910, 2053}, {2110, 3185}, {2176, 23861}, {3556, 23863}, {4027, 30670}, {20994, 21004}
X(51931) = X(1580)-Ceva conjugate of X(6)
X(51931) = X(291)-isoconjugate of X(16364)
X(51931) = X(i)-Dao conjugate of X(j) for these (i, j): (1581, 1934), (39029, 16364)
X(51931) = barycentric quotient X(1914)/X(16364)
X(51931) = {X(8301),X(8424)}-harmonic conjugate of X(5989)
X(51932) lies on the cubic K728 and these lines: {2, 99}, {32, 5969}, {538, 5162}, {542, 30270}, {2936, 6660}, {3098, 14830}, {3407, 7757}, {3455, 46546}, {3506, 5118}, {5182, 7772}, {5206, 31981}, {5939, 17131}, {7781, 11152}, {7782, 8150}, {7798, 8289}, {7883, 9878}, {8177, 8588}, {8724, 9737}, {11645, 35002}, {12188, 14711}, {13188, 18860}, {33705, 34013}
X(51932) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {99, 9888, 2482}, {99, 14931, 3734}, {2482, 9888, 574}
X(51933) lies on the cubic K855 and these lines: {3, 33556}, {4, 9820}, {5, 14528}, {24, 15801}, {26, 9970}, {30, 44788}, {110, 12163}, {140, 1352}, {154, 550}, {155, 3515}, {156, 22955}, {382, 7666}, {399, 11999}, {575, 6642}, {1147, 1351}, {1181, 10937}, {1498, 1511}, {1656, 6288}, {1657, 7728}, {1993, 47486}, {3098, 10282}, {3516, 10539}, {3522, 35254}, {3523, 9707}, {3532, 5663}, {3576, 5887}, {3796, 15720}, {3850, 11425}, {3851, 35259}, {5056, 37506}, {5462, 38263}, {5944, 17811}, {6800, 10299}, {8780, 12038}, {9936, 37935}, {11413, 15034}, {11441, 17506}, {11449, 15062}, {12118, 44960}, {12174, 43898}, {14530, 35237}, {15805, 43586}, {17814, 32171}, {17821, 32379}, {17834, 40111}, {23041, 34507}, {26882, 37483}, {35265, 49135}, {38726, 48672}
X(51933) = reflection of X(i) in X(j) for these {i,j}: {3, 33556}, {32533, 5}
X(51934) lies on the cubic K989 and these lines: {1, 18270}, {31, 39337}, {42, 19579}, {213, 19580}, {1740, 3402}, {1967, 2236}, {3112, 4117}, {3223, 3403}, {3495, 7346}, {3503, 6196}, {3508, 3510}, {7167, 7168}, {8927, 43738}, {39933, 39937}
X(51934) = X(1966)-cross conjugate of X(1)
X(51934) = X(i)-isoconjugate of X(j) for these (i,j): {6, 40858}, {511, 8870}, {694, 38382}, {1916, 51325}
X(51934) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 40858), (39031, 51325), (39043, 38382)
X(51934) = trilinear pole of line {798, 17445}
X(51934) = barycentric product X(i)*X(j) for these {i,j}: {1, 39939}, {75, 51326}, {1821, 51249}
X(51934) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40858}, {1580, 38382}, {1910, 8870}, {1933, 51325}, {39939, 75}, {51249, 1959}, {51326, 1}
X(51935) lies on the cubic K989 and these lines: {1, 8925}, {98, 109}, {238, 1284}, {651, 1911}, {1403, 4383}, {1423, 1740}, {1431, 1581}, {1447, 2236}, {1966, 18033}, {6180, 21010}
X(51935) = X(i)-isoconjugate of X(j) for these (i,j): {2311, 43686}, {4876, 7167}, {8927, 43748}
X(51935) = barycentric product X(i)*X(j) for these {i,j}: {1, 39940}, {1447, 3508}
X(51935) = barycentric quotient X(i)/X(j) for these {i,j}: {1284, 43686}, {1428, 7167}, {3508, 4518}, {39940, 75}
X(51936) lies on the cubic K378 and these lines: {6, 64}, {25, 34818}, {32, 393}, {53, 428}, {112, 376}, {132, 41761}, {216, 7509}, {232, 1609}, {571, 1990}, {800, 8745}, {2165, 6103}, {2207, 8573}, {3003, 8746}, {3087, 13342}, {5065, 40138}, {5158, 35500}, {5301, 14571}, {5523, 34613}, {6748, 33872}, {7735, 36417}, {8778, 36748}, {8779, 17849}, {10316, 42459}, {10317, 34726}, {10979, 39575}, {14379, 18890}, {21767, 32674}, {34854, 40947}, {36751, 45141}, {42453, 43131}
X(51936) = polar conjugate of the isotomic conjugate of X(6759)
X(51936) = X(54)-Ceva conjugate of X(25)
X(51936) = X(i)-isoconjugate of X(j) for these (i,j): {63, 15318}, {75, 18890}, {304, 32319}, {656, 30441}, {14213, 14371}
X(51936) = X(i)-Dao conjugate of X(j) for these (i, j): (53, 311), (206, 18890), (3162, 15318), (40596, 30441)
X(51936) = crosspoint of X(112) and X(23590)
X(51936) = crossdifference of every pair of points on line {8057, 40494}
X(51936) = barycentric product X(i)*X(j) for these {i,j}: {4, 6759}, {25, 20477}, {54, 14363}, {648, 30442}
X(51936) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 15318}, {32, 18890}, {112, 30441}, {1974, 32319}, {6759, 69}, {14363, 311}, {20477, 305}, {30442, 525}
X(51936) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {53, 13345, 10311}, {112, 1249, 577}, {800, 14581, 8745}, {1033, 3172, 6}, {3172, 51509, 1968}, {16318, 17409, 10311}
X(51937) lies on the cubic K297 and these lines: {3, 112}, {6, 520}, {25, 32649}, {183, 35140}, {250, 15905}, {381, 47105}, {1597, 8431}, {2420, 51394}, {2693, 32687}, {3284, 23347}, {5020, 51343}, {5050, 15407}, {9818, 50464}, {11589, 14581}, {19153, 32738}, {40856, 43673}, {41392, 51254}
X(51937) = X(i)-isoconjugate of X(j) for these (i,j): {441, 36119}, {1494, 2312}, {1503, 2349}, {2159, 30737}, {8766, 16080}, {33805, 42671}, {43045, 44693}
X(51937) = X(i)-Dao conjugate of X(j) for these (i, j): (1511, 441), (3163, 30737), (38999, 39473)
X(51937) = crosssum of X(1503) and X(6793)
X(51937) = trilinear pole of line {1495, 1636}
X(51937) = barycentric product X(i)*X(j) for these {i,j}: {30, 1297}, {1495, 35140}, {2407, 34212}, {2419, 23347}, {2420, 43673}, {2435, 4240}, {3284, 6330}, {9033, 44770}, {11064, 43717}, {11589, 14944}, {32687, 41077}, {35912, 39265}
X(51937) = barycentric quotient X(i)/X(j) for these {i,j}: {30, 30737}, {1297, 1494}, {1495, 1503}, {1636, 39473}, {2420, 34211}, {2435, 34767}, {3284, 441}, {9406, 2312}, {9407, 42671}, {9408, 6793}, {11589, 16096}, {14581, 16318}, {14583, 43089}, {23347, 2409}, {32649, 1304}, {32687, 15459}, {34212, 2394}, {43717, 16080}, {44770, 16077}
X(51938) lies on the cubic K288 and these lines: {4, 1499}, {67, 524}, {98, 5913}, {111, 1503}, {468, 32729}, {691, 3580}, {1995, 9169}, {3448, 46783}, {3564, 32583}, {5968, 18911}, {5971, 31127}, {10558, 11245}, {10559, 45968}, {14908, 47526}, {14916, 16051}
X(51938) = barycentric product X(671)*X(41359)
X(51938) = barycentric quotient X(41359)/X(524)
X(51938) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3448, 46783, 51405}, {6792, 34169, 34806}
X(51939) lies on the cubic K288 and these lines: {2, 15258}, {4, 51}, {20, 34109}, {30, 23241}, {98, 468}, {107, 1503}, {125, 14165}, {133, 48364}, {138, 13509}, {140, 6760}, {186, 6070}, {264, 18911}, {275, 11245}, {297, 38664}, {340, 520}, {401, 14900}, {427, 42873}, {450, 542}, {459, 11206}, {648, 858}, {1629, 13567}, {1853, 15274}, {1897, 41327}, {2351, 5963}, {2719, 39429}, {3448, 46106}, {3462, 32767}, {3522, 11589}, {3523, 12096}, {5189, 12384}, {6032, 37665}, {8884, 26879}, {9140, 37765}, {11442, 15466}, {11547, 23291}, {14580, 34235}, {14920, 16177}, {18400, 40664}, {18914, 51031}, {25738, 43995}, {26869, 33971}, {26905, 46760}, {26944, 41365}, {35260, 41374}, {35474, 41586}, {41377, 50188}, {43460, 47202}, {44134, 46336}
X(51939) = reflection of X(i) in X(j) for these {i,j}: {20, 34109}, {107, 51358}, {34170, 6761}, {48364, 133}
X(51939) = anticomplement of X(34147)
X(51939) = polar-circle-inverse of X(51)
X(51939) = circumcircle-of-anticomplementary-triangle-inverse of X(32064)
X(51939) = polar conjugate of X(34579)
X(51939) = antigonal image of X(13509)
X(51939) = polar conjugate of the isogonal conjugate of X(13509)
X(51939) = X(48)-isoconjugate of X(34579)
X(51939) = X(1249)-Dao conjugate of X(34579)
X(51939) = crossdifference of every pair of points on line {217, 32320}
X(51939) = barycentric product X(264)*X(13509)
X(51939) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 34579}, {13509, 3}
X(51939) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {125, 41204, 14165}, {14363, 14864, 4}, {26869, 33971, 43462}
X(51940) lies on the cubic K537 and these lines: {4, 6}, {30, 935}, {112, 1529}, {1593, 5938}, {2697, 10297}, {2715, 45031}, {6000, 20410}, {10295, 42426}, {15311, 34163}, {18560, 36997}, {23047, 32581}, {44990, 45148}
X(51940) = reflection of X(i) in X(j) for these {i,j}: {112, 1529}, {2697, 10297}, {5523, 4}, {10295, 42426}
X(51940) = polar-circle-inverse of X(36990)
X(51940) = circumcircle-of-anticomplementary-triangle-inverse of X(41735)
X(51941) lies on the cubic K537 and these lines: {3, 19140}, {6, 5663}, {22, 110}, {25, 32235}, {67, 113}, {74, 5085}, {141, 32247}, {146, 1503}, {182, 5621}, {265, 25335}, {399, 511}, {524, 32111}, {541, 34319}, {542, 1351}, {599, 5655}, {611, 7727}, {613, 19470}, {895, 5102}, {1177, 17835}, {1386, 33535}, {1511, 31884}, {2777, 11820}, {2854, 10752}, {2935, 15138}, {3024, 32289}, {3028, 32290}, {3066, 12824}, {3098, 32609}, {3448, 5480}, {3564, 16176}, {3763, 14643}, {3818, 32306}, {5050, 25556}, {5055, 25566}, {5092, 15041}, {5093, 9976}, {5095, 12165}, {5097, 39562}, {5181, 6053}, {5544, 45311}, {5651, 15106}, {6776, 25329}, {7669, 14687}, {8547, 11456}, {8550, 25321}, {8705, 12112}, {9140, 38072}, {10088, 10387}, {10264, 14561}, {10510, 14915}, {10519, 20125}, {10541, 51522}, {10628, 34779}, {10706, 47353}, {12039, 15030}, {12041, 15462}, {12121, 48872}, {12163, 19138}, {12167, 32250}, {12168, 32262}, {12244, 44882}, {12294, 19504}, {12302, 19139}, {12317, 14853}, {12373, 32243}, {12374, 32297}, {12383, 29181}, {12584, 33878}, {13211, 38144}, {13605, 38035}, {14683, 51212}, {14810, 15040}, {14912, 41595}, {14982, 15063}, {15061, 47355}, {17702, 48910}, {18374, 32110}, {19125, 32607}, {19130, 38724}, {19145, 35826}, {19146, 35827}, {20126, 47352}, {21650, 32251}, {25711, 37475}, {29012, 38790}, {31670, 32423}, {32124, 35265}, {32237, 45082}, {32254, 44456}, {34153, 48873}, {34783, 44490}, {37473, 46261}, {38661, 47619}, {39899, 41731}, {41428, 44883}, {46817, 47450}
X(51941) = midpoint of X(i) and X(j) for these {i,j}: {146, 11061}, {399, 48679}, {1351, 12308}, {10752, 14094}, {14683, 51212}, {25336, 36990}, {32254, 44456}
X(51941) = reflection of X(i) in X(j) for these {i,j}: {3, 19140}, {6, 9970}, {67, 113}, {74, 6593}, {265, 32271}, {599, 5655}, {1350, 110}, {2930, 399}, {2935, 15141}, {3448, 5480}, {5181, 6053}, {5621, 45016}, {6776, 25329}, {10117, 19149}, {10620, 182}, {11477, 10752}, {12163, 19138}, {12244, 44882}, {12302, 19139}, {12317, 25328}, {12902, 48901}, {14982, 15063}, {15069, 14982}, {16010, 6}, {17835, 1177}, {25335, 265}, {32247, 141}, {32305, 25556}, {32306, 3818}, {33535, 1386}, {33878, 12584}, {36990, 7728}, {39899, 41731}, {43273, 34319}, {47353, 10706}, {48872, 12121}, {48873, 34153}, {48905, 32233}
X(51941) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {67, 113, 10516}, {74, 6593, 5085}, {182, 10620, 5621}, {10620, 45016, 182}, {12317, 14853, 25328}, {14643, 49116, 3763}, {25556, 32305, 5050}, {32306, 38789, 3818}
X(51942) lies on the cubic K728 and these lines: {3, 10706}, {22, 2930}, {23, 9140}, {74, 7575}, {110, 3098}, {895, 8705}, {1177, 5012}, {1995, 7703}, {3357, 15021}, {4550, 15055}, {6593, 15080}, {6800, 48679}, {7464, 12901}, {7496, 32600}, {7527, 32401}, {7530, 15044}, {7545, 15025}, {7550, 15029}, {7555, 7691}, {7556, 7689}, {9208, 11643}, {9938, 12082}, {10546, 12041}, {10721, 18550}, {10733, 37924}, {11999, 51522}, {12105, 20126}, {12106, 15057}, {13289, 37952}, {15041, 33887}, {23061, 41615}, {25328, 47313}, {32273, 37901}, {46602, 46608}
X(51942) = reflection of X(i) in X(j) for these {i,j}: {110, 7712}, {10721, 18550}
X(51943) lies on the cubic K288 and these lines: {4, 512}, {98, 230}, {287, 858}, {511, 16083}, {542, 37858}, {685, 14165}, {2794, 48452}, {3448, 46786}, {20021, 47638}, {35605, 40079}
X(51943) = reflection of X(98) in X(51404)
X(51943) = X(45158)-Dao conjugate of X(511)
X(51943) = crossdifference of every pair of points on line {3289, 41167}
X(51944) lies on the cubic K1202 and these lines: {2, 42514}, {3, 36969}, {6, 15688}, {14, 15696}, {16, 15695}, {20, 42776}, {30, 42111}, {62, 43420}, {376, 395}, {396, 3528}, {548, 22238}, {549, 42106}, {550, 16645}, {1656, 42429}, {1657, 10187}, {3146, 42501}, {3522, 22236}, {3523, 43401}, {3524, 42097}, {3534, 12817}, {3627, 42475}, {5054, 42498}, {5237, 43486}, {5321, 15697}, {5339, 44245}, {5340, 46853}, {8703, 10653}, {10304, 11488}, {10645, 43646}, {10646, 15689}, {11001, 42095}, {11485, 42631}, {11539, 42113}, {11812, 42105}, {12100, 42094}, {12103, 42491}, {14093, 16960}, {14891, 42586}, {15022, 42595}, {15684, 43468}, {15686, 42093}, {15691, 18581}, {15692, 42098}, {15693, 42100}, {15698, 42941}, {15700, 19106}, {15702, 42109}, {15704, 42774}, {15706, 16808}, {15708, 42102}, {15710, 23302}, {15711, 42584}, {15712, 42610}, {15714, 42092}, {15716, 16966}, {15717, 43104}, {15719, 42110}, {15759, 18582}, {16644, 34200}, {17504, 43029}, {17538, 42940}, {19708, 33602}, {19710, 42089}, {21734, 43238}, {21735, 42156}, {33923, 43193}, {36836, 42990}, {36843, 36967}, {40694, 41981}, {41982, 42118}, {41983, 42114}, {42086, 45759}, {42090, 49948}, {42115, 43301}, {42119, 42792}, {42124, 46332}, {42126, 43032}, {42141, 42500}, {42153, 43480}, {42157, 42796}, {42433, 42974}, {42490, 43416}, {42503, 43327}, {42504, 43004}, {42507, 42996}, {42587, 43417}, {42683, 43326}, {42686, 43543}, {42777, 43869}, {42793, 43494}, {42817, 43244}, {42913, 43194}, {42930, 49903}, {42945, 43332}, {42948, 49140}, {42989, 43245}, {42993, 43331}, {42999, 43305}, {43105, 49812}, {43231, 43373}, {43400, 49139}, {43402, 43474}, {43418, 49905}
X(51944) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3534, 42129, 42430}, {8703, 42625, 11480}, {11812, 42105, 42474}, {15688, 42528, 6}, {15711, 42584, 42911}, {34200, 42091, 16644}, {42625, 49947, 42123}
X(51945) lies on the cubic K1202 and these lines: {2, 42515}, {3, 36970}, {6, 15688}, {13, 15696}, {15, 15695}, {20, 42775}, {30, 42114}, {61, 43421}, {376, 396}, {395, 3528}, {548, 22236}, {549, 42103}, {550, 16644}, {1656, 42430}, {1657, 10188}, {3146, 42500}, {3522, 22238}, {3523, 43402}, {3524, 42096}, {3534, 12816}, {3627, 42474}, {5054, 42499}, {5238, 43485}, {5318, 15697}, {5339, 46853}, {5340, 44245}, {8703, 10654}, {10304, 11489}, {10645, 15689}, {10646, 43645}, {11001, 42098}, {11486, 42632}, {11539, 42112}, {11812, 42104}, {12100, 42093}, {12103, 42490}, {14093, 16961}, {14891, 42587}, {15022, 42594}, {15684, 43467}, {15686, 42094}, {15691, 18582}, {15692, 42095}, {15693, 42099}, {15698, 42940}, {15700, 19107}, {15702, 42108}, {15704, 42773}, {15706, 16809}, {15708, 42101}, {15710, 23303}, {15711, 42585}, {15712, 42611}, {15714, 42089}, {15716, 16967}, {15717, 43101}, {15719, 42107}, {15759, 18581}, {16645, 34200}, {17504, 43028}, {17538, 42941}, {19708, 33603}, {19710, 42092}, {21734, 43239}, {21735, 42153}, {33923, 43194}, {36836, 36968}, {36843, 42991}, {40693, 41981}, {41982, 42117}, {41983, 42111}, {42085, 45759}, {42091, 49947}, {42116, 43300}, {42120, 42791}, {42121, 46332}, {42127, 43033}, {42140, 42501}, {42156, 43479}, {42158, 42795}, {42434, 42975}, {42491, 43417}, {42502, 43326}, {42505, 43005}, {42506, 42997}, {42586, 43416}, {42682, 43327}, {42687, 43542}, {42778, 43870}, {42794, 43493}, {42818, 43245}, {42912, 43193}, {42931, 49904}, {42944, 43333}, {42949, 49140}, {42988, 43244}, {42992, 43330}, {42998, 43304}, {43106, 49813}, {43230, 43372}, {43399, 49139}, {43401, 43473}, {43419, 49906}
X(51945) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3534, 42132, 42429}, {8703, 42626, 11481}, {11812, 42104, 42475}, {15688, 42529, 6}, {15711, 42585, 42910}, {34200, 42090, 16645}, {42626, 49948, 42122}
X(51946) lies on the cubic K1047 and these lines: {2, 8966}, {3, 6413}, {6, 493}, {216, 5406}, {255, 605}, {371, 12160}, {372, 8276}, {394, 577}, {488, 3068}, {492, 27377}, {511, 26953}, {590, 11090}, {1152, 8963}, {1351, 26919}, {1368, 26873}, {1993, 26868}, {3167, 8911}, {3564, 26945}, {5020, 26894}, {5407, 22052}, {5409, 36748}, {5411, 10962}, {5412, 9733}, {6289, 44637}, {6391, 6414}, {6457, 12164}, {8577, 13889}, {8948, 12967}, {8969, 32421}, {9909, 26886}, {9937, 10898}, {10132, 19446}, {10133, 11514}, {12305, 17819}, {12979, 26292}, {19356, 20794}, {19458, 44588}, {26461, 40322}, {26950, 30771}
X(51946) = isogonal conjugate of the isotomic conjugate of X(8222)
X(51946) = isotomic conjugate of the polar conjugate of X(10132)
X(51946) = isogonal conjugate of the polar conjugate of X(488)
X(51946) = X(i)-Ceva conjugate of X(j) for these (i,j): {488, 10132}, {5408, 3}
X(51946) = X(i)-isoconjugate of X(j) for these (i,j): {4, 19218}, {19, 24244}, {92, 8948}, {158, 493}, {1096, 5490}
X(51946) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 24244), (1147, 493), (6503, 5490), (8223, 76), (22391, 8948), (33364, 2052), (36033, 19218)
X(51946) = crosspoint of X(i) and X(j) for these (i,j): {6, 45595}, {488, 8222}
X(51946) = crosssum of X(2) and X(26494)
X(51946) = barycentric product X(i)*X(j) for these {i,j}: {3, 488}, {6, 8222}, {63, 19215}, {69, 10132}, {184, 46742}, {394, 3068}, {487, 42022}, {3926, 6423}, {3964, 5200}, {4558, 17431}, {5408, 24246}, {8223, 45595}
X(51946) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 24244}, {48, 19218}, {184, 8948}, {394, 5490}, {488, 264}, {577, 493}, {3068, 2052}, {5200, 1093}, {6423, 393}, {8222, 76}, {10132, 4}, {14585, 26454}, {17431, 14618}, {19215, 92}, {19446, 3127}, {42022, 24243}, {46742, 18022}
X(51946) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 8939, 493}, {6, 19408, 5408}, {6, 44627, 26460}, {6, 45596, 19031}, {1993, 26912, 26868}, {19442, 45727, 8216}
X(51947) lies on the cubic K1008 and these lines: {2, 2112}, {25, 41}, {31, 1501}, {48, 1613}, {101, 3961}, {184, 18038}, {222, 604}, {284, 25058}, {692, 40972}, {893, 1915}, {1691, 30646}, {1965, 4586}, {2175, 5364}, {2210, 21750}, {2280, 17011}, {3051, 7104}, {3121, 5371}, {3185, 9447}, {3204, 20693}, {3220, 23636}, {3920, 9310}, {4228, 17451}, {4388, 40597}, {5310, 20684}, {20459, 26889}, {22230, 37325}
X(51947) = isogonal conjugate of the isotomic conjugate of X(3496)
X(51947) = X(893)-Ceva conjugate of X(31)
X(51947) = X(i)-isoconjugate of X(j) for these (i,j): {2, 7224}, {6, 18836}, {75, 3497}, {76, 34250}
X(51947) = X(i)-Dao conjugate of X(j) for these (i, j): (9, 18836), (171, 1920), (206, 3497), (32664, 7224)
X(51947) = crosssum of X(2) and X(33867)
X(51947) = crossdifference of every pair of points on line {4025, 17072}
X(51947) = barycentric product X(i)*X(j) for these {i,j}: {1, 23868}, {6, 3496}, {19, 23150}, {31, 4388}, {32, 17788}, {41, 17086}, {560, 18835}, {692, 4142}, {893, 40597}, {904, 17797}, {1333, 4109}
X(51947) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 18836}, {31, 7224}, {32, 3497}, {560, 34250}, {3496, 76}, {4109, 27801}, {4142, 40495}, {4388, 561}, {17086, 20567}, {17788, 1502}, {18835, 1928}, {23150, 304}, {23868, 75}, {40597, 1920}
X(51947) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {31, 32664, 19554}, {1501, 30647, 31}, {14599, 16584, 31}
X(51948) lies on the cubics K252 and X1008 and these lines: {3, 695}, {6, 3504}, {32, 46505}, {39, 37894}, {98, 1196}, {110, 711}, {184, 18899}, {228, 9288}, {238, 9285}, {385, 1194}, {419, 51246}, {1184, 47643}, {1915, 9468}, {2200, 9236}, {3051, 14946}, {3505, 8265}, {3866, 6308}, {8022, 14599}, {8290, 8858}, {10547, 14602}
X(51948) = isogonal conjugate of X(9230)
X(51948) = isogonal conjugate of the anticomplement of X(45210)
X(51948) = isogonal conjugate of the isotomic conjugate of X(695)
X(51948) = X(51245)-complementary conjugate of X(21235)
X(51948) = X(1691)-cross conjugate of X(9468)
X(51948) = X(i)-isoconjugate of X(j) for these (i,j): {1, 9230}, {2, 1965}, {6, 1925}, {75, 384}, {76, 1582}, {92, 37894}, {561, 1915}, {1502, 1932}, {1934, 16985}, {1969, 37893}, {3112, 4074}, {9239, 36432}, {11380, 40364}, {16101, 19555}, {18271, 22252}, {19564, 40835}
X(51948) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 9230), (9, 1925), (206, 384), (22391, 37894), (32664, 1965), (34452, 4074), (40368, 1915)
X(51948) = crosssum of X(i) and X(j) for these (i,j): {2, 37889}, {384, 37894}, {6374, 40035}, {17788, 24732}
X(51948) = trilinear pole of line {3049, 9006}
X(51948) = barycentric product X(i)*X(j) for these {i,j}: {1, 9288}, {6, 695}, {31, 9285}, {32, 9229}, {75, 9236}, {184, 37892}, {385, 14946}, {560, 9239}, {3505, 41533}, {14602, 40847}
X(51948) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 1925}, {6, 9230}, {31, 1965}, {32, 384}, {184, 37894}, {560, 1582}, {695, 76}, {1501, 1915}, {1917, 1932}, {3051, 4074}, {9229, 1502}, {9236, 1}, {9239, 1928}, {9285, 561}, {9288, 75}, {14575, 37893}, {14602, 16985}, {14946, 1916}, {18902, 51320}, {27369, 12143}, {37892, 18022}, {40847, 44160}, {41533, 16101}, {44162, 11380}
X(51948) = {X(1915),X(40377)}-harmonic conjugate of X(9468)
X(51949) lies on the cubic K1008 and these lines: {2, 1429}, {6, 18613}, {25, 41}, {31, 1911}, {43, 101}, {48, 2276}, {55, 9454}, {57, 23622}, {100, 7075}, {184, 19587}, {213, 23543}, {219, 604}, {644, 4203}, {692, 9447}, {1011, 1334}, {1055, 4191}, {1385, 25074}, {1397, 16283}, {1402, 5364}, {1500, 2304}, {1613, 51319}, {1958, 17759}, {2205, 2209}, {2280, 17018}, {2352, 39258}, {3185, 40972}, {3204, 21904}, {3217, 37657}, {3500, 40171}, {3501, 13588}, {3570, 25287}, {3684, 20012}, {4184, 41423}, {4209, 39741}, {4251, 42042}, {4390, 31330}, {4651, 26232}, {7122, 15370}, {7225, 30949}, {9620, 42669}, {14827, 23522}, {16788, 43223}, {17149, 18047}, {20460, 28348}, {20662, 23653}, {23638, 51436}, {24549, 27263}, {28751, 30956}
X(51949) = isogonal conjugate of the isotomic conjugate of X(3501)
X(51949) = X(i)-isoconjugate of X(j) for these (i,j): {75, 3500}, {7249, 39936}, {10030, 43748}, {17170, 30688}
X(51949) = X(i)-Dao conjugate of X(j) for these (i, j): (206, 3500), (810, 26932), (5518, 3261), (17072, 4858)
X(51949) = crosspoint of X(692) and X(4564)
X(51949) = crosssum of X(693) and X(2170)
X(51949) = crossdifference of every pair of points on line {3766, 4025}
X(51949) = barycentric product X(i)*X(j) for these {i,j}: {1, 34247}, {6, 3501}, {31, 32937}, {32, 17786}, {42, 13588}, {100, 23655}, {101, 21348}, {163, 21958}, {662, 22229}, {692, 17072}, {1110, 23772}, {1783, 22443}, {4551, 23864}, {4559, 21388}, {21438, 32739}
X(51949) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 3500}, {3501, 76}, {13588, 310}, {17072, 40495}, {17786, 1502}, {18265, 43748}, {21348, 3261}, {21958, 20948}, {22229, 1577}, {22443, 15413}, {23655, 693}, {23864, 18155}, {32937, 561}, {34247, 75}
X(51950) lies on the cubic K1008 and these lines: {2, 3}, {194, 23173}, {1194, 23209}, {1196, 21444}, {1501, 15389}, {1691, 23221}, {1915, 47642}, {3051, 14946}, {7783, 23174}, {10329, 20775}, {20859, 23635}
X(51950) = isogonal conjugate of X(43715)
X(51950) = isogonal conjugate of the isotomic conjugate of X(3491)
X(51950) = X(i)-Ceva conjugate of X(j) for these (i,j): {1915, 3051}, {47642, 32748}
X(51950) = X(i)-isoconjugate of X(j) for these (i,j): {1, 43715}, {75, 51246}
X(51950) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 43715), (206, 51246), (3491, 50666)
X(51950) = barycentric product X(6)*X(3491)
X(51950) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 43715}, {32, 51246}, {3491, 76}
X(51950) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 46505, 237}, {22, 33728, 237}
X(51951) lies on the cubics K693, K1008, and K1013, and these lines: {2, 699}, {32, 1613}, {39, 15371}, {184, 8789}, {251, 2998}, {1501, 15389}, {2205, 2209}, {3168, 40820}, {3407, 24733}, {9490, 32546}, {14602, 44162}, {36417, 44089}
X(51951) = isogonal conjugate of X(6374)
X(51951) = isogonal conjugate of the anticomplement of X(6375)
X(51951) = isogonal conjugate of the complement of X(2998)
X(51951) = isogonal conjugate of the isotomic conjugate of X(3224)
X(51951) = polar conjugate of the isotomic conjugate of X(15389)
X(51951) = X(i)-Ceva conjugate of X(j) for these (i,j): {6, 32546}, {3224, 15389}
X(51951) = X(i)-cross conjugate of X(j) for these (i,j): {6, 32}, {669, 3222}, {9490, 6}, {19606, 3224}
X(51951) = X(i)-isoconjugate of X(j) for these (i,j): {1, 6374}, {2, 17149}, {6, 18837}, {75, 194}, {76, 1740}, {86, 22028}, {99, 20910}, {190, 23807}, {274, 21080}, {304, 3186}, {310, 21877}, {312, 17082}, {561, 1613}, {668, 21191}, {799, 23301}, {1424, 3596}, {1926, 47642}, {1969, 20794}, {1978, 50516}, {3221, 4602}, {4554, 25128}, {4601, 21144}, {4609, 23503}, {4623, 21056}, {6063, 7075}, {6386, 23572}, {11325, 40364}, {46273, 51427}
X(51951) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 6374), (9, 18837), (206, 194), (32664, 17149), (38986, 20910), (38996, 23301), (40368, 1613), (40600, 22028)
X(51951) = cevapoint of X(6) and X(3224)
X(51951) = crosspoint of X(6) and X(32543)
X(51951) = crosssum of X(2) and X(32548)
X(51951) = trilinear pole of line {9426, 9429}
X(51951) = crossdifference of every pair of points on line {23301, 23807}
X(51951) = barycentric product X(i)*X(j) for these {i,j}: {1, 34248}, {4, 15389}, {6, 3224}, {25, 3504}, {31, 3223}, {32, 2998}, {83, 19606}, {560, 18832}, {669, 3222}, {1501, 40162}, {1974, 43714}, {9468, 39927}, {40799, 40821}, {42551, 46288}
X(51951) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 18837}, {6, 6374}, {31, 17149}, {32, 194}, {213, 22028}, {560, 1740}, {667, 23807}, {669, 23301}, {798, 20910}, {1397, 17082}, {1501, 1613}, {1918, 21080}, {1919, 21191}, {1974, 3186}, {1980, 50516}, {2205, 21877}, {2998, 1502}, {3222, 4609}, {3223, 561}, {3224, 76}, {3504, 305}, {8789, 47642}, {9418, 51427}, {9426, 3221}, {9447, 7075}, {14575, 20794}, {15389, 69}, {18832, 1928}, {19606, 141}, {32546, 32548}, {34248, 75}, {39927, 14603}, {40162, 40362}, {40821, 40822}, {40823, 40811}, {43714, 40050}, {44162, 11325}
X(51952) lies on on the Kiepert circumhyperbola of the anticomplementary triangle, the cubic K156, and these lines: {2, 489}, {20, 14242}, {69, 43691}, {148, 6569}, {487, 3146}, {488, 3522}, {491, 17578}, {637, 15717}, {638, 13798}, {1270, 21734}, {1271, 5059}, {3595, 50689}, {3854, 32806}, {5068, 45509}, {7000, 12509}, {9542, 11313}, {12221, 13933}, {12323, 50692}, {13835, 13935}, {15705, 45508}, {23312, 43508}, {32419, 45077}, {34573, 43383}, {43377, 45872}
X(51952) = reflection of X(i) in X(j) for these {i,j}: {148, 6569}, {1132, 33365}
X(51952) = anticomplement of X(1132)
X(51952) = anticomplement of the isogonal conjugate of X(1152)
X(51952) = anticomplement of the isotomic conjugate of X(1271)
X(51952) = anticomplementary isogonal conjugate of X(12323)
X(51952) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 12323}, {1152, 8}, {1271, 6327}, {3536, 21270}, {5410, 5905}
X(51952) = X(1271)-Ceva conjugate of X(2)
X(51952) = {X(1132),X(33365)}-harmonic conjugate of X(2)
X(51953) lies on the cubic K156 and these lines: {2, 490}, {20, 14227}, {69, 43691}, {148, 6568}, {487, 3522}, {488, 3146}, {492, 17578}, {637, 13678}, {638, 15717}, {1270, 5059}, {1271, 21734}, {3593, 50689}, {3854, 32805}, {5068, 45508}, {6462, 9543}, {7374, 12510}, {9540, 13712}, {12222, 13879}, {12322, 50692}, {15705, 45509}, {23311, 43507}, {32421, 45076}, {34573, 43382}, {43376, 45871}
X(51953) = reflection of X(i) in X(j) for these {i,j}: {148, 6568}, {1131, 33364}
X(51953) = anticomplement of X(1131)
X(51953) = anticomplement of the isogonal conjugate of X(1151)
X(51953) = anticomplement of the isotomic conjugate of X(1270)
X(51953) = anticomplementary isogonal conjugate of X(12322)
X(51953) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {1, 12322}, {1151, 8}, {1270, 6327}, {3535, 21270}, {5411, 5905}
X(51953) = X(1270)-Ceva conjugate of X(2)
X(51953) = {X(1131),X(33364)}-harmonic conjugate of X(2)
X(51954) lies on the cubic K1008 and these lines: {2, 9467}, {22, 40810}, {25, 694}, {51, 34238}, {184, 14251}, {805, 3917}, {1501, 9468}, {1915, 41517}, {3493, 6660}, {3796, 45146}
X(51954) = isogonal conjugate of the isotomic conjugate of X(3493)
X(51954) = X(41517)-Ceva conjugate of X(9468)
X(51954) = X(19556)-cross conjugate of X(9468)
X(51954) = X(i)-isoconjugate of X(j) for these (i,j): {75, 51244}, {1926, 41533}, {1966, 43696}
X(51954) = X(i)-Dao conjugate of X(j) for these (i, j): (206, 51244), (9467, 43696), (46669, 14295)
X(51954) = barycentric product X(i)*X(j) for these {i,j}: {6, 3493}, {694, 6660}, {1581, 19559}, {1916, 19558}, {1934, 19560}, {1967, 19555}, {5207, 9468}, {14316, 17938}, {18896, 19556}, {19576, 41517}
X(51954) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 51244}, {3493, 76}, {5207, 14603}, {6660, 3978}, {8789, 41533}, {9468, 43696}, {19555, 1926}, {19556, 1691}, {19558, 385}, {19559, 1966}, {19560, 1580}, {19575, 4027}
X(51955) lies on the cubic K156 and these lines: {1, 1151}, {4, 9}, {46, 51763}, {57, 175}, {165, 30556}, {517, 32556}, {1132, 41348}, {1449, 1702}, {1697, 6204}, {1703, 16670}, {1743, 49227}, {3579, 32555}, {5128, 6203}, {5437, 31534}, {6252, 21746}, {6404, 20683}, {7991, 30557}, {8957, 10624}, {13389, 31432}, {20070, 30413}
X(51955) = {X(40),X(6212)}-harmonic conjugate of X(9)
X(51956) lies on the cubic K788 and these lines: {6, 41}, {32, 1423}, {385, 10030}, {695, 51323}, {1284, 1914}, {1415, 1463}, {1429, 41333}, {5277, 30097}, {20769, 34253}, {51318, 51321}
X(51956) = isogonal conjugate of the isotomic conjugate of X(39930)
X(51956) = X(i)-isoconjugate of X(j) for these (i,j): {2, 43748}, {1581, 39936}, {3500, 4518}
X(51956) = X(i)-Dao conjugate of X(j) for these (i, j): (19576, 39936), (32664, 43748)
X(51956) = crossdifference of every pair of points on line {522, 20258}
X(51956) = barycentric product X(i)*X(j) for these {i,j}: {6, 39930}, {1284, 13588}, {1403, 14199}, {1428, 32937}, {1429, 3501}, {1447, 34247}
X(51956) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 43748}, {1691, 39936}, {34247, 4518}, {39930, 76}
X(51957) lies on the cubic K156 and these lines: {1, 1152}, {4, 9}, {46, 51764}, {57, 176}, {165, 30557}, {517, 32555}, {1131, 41348}, {1449, 1703}, {1697, 6203}, {1702, 16670}, {1743, 49226}, {3579, 32556}, {5128, 6204}, {5437, 31535}, {6252, 20683}, {6404, 21746}, {7991, 30556}, {8984, 9841}, {8986, 10860}, {20070, 30412}
X(51957) = {X(40),X(6213)}-harmonic conjugate of X(9)
X(51958) lies on the cubic K788 and these lines: {32, 39953}, {82, 172}, {251, 308}, {695, 1176}, {733, 40981}, {1627, 8265}, {4577, 9497}, {8623, 41884}, {24256, 46227}, {32085, 51324}, {46288, 51318}
X(51958) = isogonal conjugate of the isotomic conjugate of X(38817)
X(51958) = X(32)-Ceva conjugate of X(251)
X(51958) = X(3499)-cross conjugate of X(38817)
X(51958) = X(38)-isoconjugate of X(39953)
X(51958) = X(308)-Dao conjugate of X(1502)
X(51958) = barycentric product X(i)*X(j) for these {i,j}: {6, 38817}, {83, 3499}, {23174, 32085}
X(51958) = barycentric quotient X(i)/X(j) for these {i,j}: {251, 39953}, {3499, 141}, {23174, 3933}, {38817, 76}
X(51959) lies on on the Feuerbach circumhyperbola of the tangential triangle, the cubic K156, and these lines: {1, 43730}, {3, 15748}, {6, 1131}, {195, 38335}, {547, 15805}, {1498, 11001}, {6429, 8939}, {6430, 8943}, {11441, 16936}, {15047, 18451}, {35400, 37498}
X(51959) = reflection of X(43691) in X(15748)
X(51959) = X(5059)-Ceva conjugate of X(3)
X(51960) lies on the cubics K054 and K667 and these lines: {4, 1987}, {5, 525}, {6, 32542}, {143, 11437}, {458, 9476}, {1007, 34403}, {1972, 42287}, {3095, 14059}, {9475, 34156}, {13568, 44549}, {18338, 39575}
X(51960) = X(132)-cross conjugate of X(1503)
X(51960) = X(1297)-isoconjugate of X(1955)
X(51960) = X(i)-Dao conjugate of X(j) for these (i, j): (23976, 401), (50938, 41204)
X(51960) = barycentric product X(i)*X(j) for these {i,j}: {1503, 1972}, {1987, 30737}
X(51960) = barycentric quotient X(i)/X(j) for these {i,j}: {1503, 401}, {1972, 35140}, {1987, 1297}, {2312, 1955}, {16318, 41204}, {30737, 44137}, {32542, 51343}, {42671, 1971}, {51363, 32428}
X(51961) lies on the cubic K429 and these lines: {6, 513}, {66, 2911}, {193, 1814}, {219, 46163}, {393, 8751}, {478, 32735}, {571, 32658}, {608, 1974}, {666, 3596}, {4429, 40724}, {21769, 46149}
X(51961) = polar conjugate of the isotomic conjugate of X(34160)
X(51961) = X(3912)-isoconjugate of X(26703)
X(51961) = crosspoint of X(8751) and X(41934)
X(51961) = crosssum of X(i) and X(j) for these (i,j): {518, 47431}, {4437, 25083}
X(51961) = barycentric product X(i)*X(j) for these {i,j}: {4, 34160}, {105, 3827}, {4244, 10099}, {6185, 47431}, {14942, 51657}
X(51961) = barycentric quotient X(i)/X(j) for these {i,j}: {3827, 3263}, {34160, 69}, {47431, 4437}, {51657, 9436}
X(51962) lies on the cubic K429 and these lines: {6, 512}, {66, 193}, {69, 36827}, {206, 32729}, {393, 8753}, {571, 14908}, {892, 1502}, {1974, 32740}, {7790, 14246}, {8541, 51428}, {8542, 15899}, {8877, 48945}, {9973, 46154}, {10415, 45096}, {11188, 46783}, {11511, 38971}, {36851, 36894}
X(51962) = polar conjugate of the isotomic conjugate of X(34158)
X(51962) = X(i)-Ceva conjugate of X(j) for these (i,j): {892, 47138}, {8753, 14580}, {10415, 41272}
X(51962) = X(i)-isoconjugate of X(j) for these (i,j): {524, 37220}, {896, 46140}, {2373, 14210}, {36095, 45807}
X(51962) = X(i)-Dao conjugate of X(j) for these (i, j): (2393, 5181), (15477, 2373), (15899, 46140)
X(51962) = crosspoint of X(8753) and X(41936)
X(51962) = crosssum of X(i) and X(j) for these (i,j): {524, 47426}, {3266, 7664}, {6390, 36792}
X(51962) = crossdifference of every pair of points on line {524, 45807}
X(51962) = barycentric product X(i)*X(j) for these {i,j}: {4, 34158}, {111, 2393}, {858, 32740}, {895, 14580}, {923, 18669}, {1236, 19626}, {2207, 51253}, {5181, 41936}, {5523, 14908}, {8753, 14961}, {10097, 46592}, {10630, 47426}, {32729, 47138}
X(51962) = barycentric quotient X(i)/X(j) for these {i,j}: {111, 46140}, {923, 37220}, {2393, 3266}, {14580, 44146}, {19626, 1177}, {32740, 2373}, {34158, 69}, {41272, 46165}, {42665, 45807}, {47426, 36792}
X(51963) lies on the cubic K429 and these lines: {2, 9473}, {4, 47388}, {6, 523}, {20, 8861}, {66, 248}, {69, 2966}, {98, 3424}, {193, 253}, {393, 1974}, {685, 1249}, {1503, 34156}, {1609, 47635}, {2445, 16318}, {2697, 2715}, {2980, 51542}, {5304, 40820}, {6776, 32545}, {7735, 41932}, {8779, 30737}, {9292, 34238}, {9476, 42287}, {14853, 47741}, {21458, 51363}, {23977, 51437}, {28343, 43089}, {39141, 39941}, {40079, 44883}, {46767, 47731}
X(51963) = polar conjugate of the isotomic conjugate of X(34156)
X(51963) = X(i)-Ceva conjugate of X(j) for these (i,j): {6531, 16318}, {9476, 98}, {47388, 1976}
X(51963) = X(i)-cross conjugate of X(j) for these (i,j): {23976, 16318}, {51437, 1976}
X(51963) = X(i)-isoconjugate of X(j) for these (i,j): {63, 39265}, {1297, 1959}, {1755, 35140}, {3405, 46164}, {6333, 36046}, {8767, 36212}, {9476, 23996}, {23997, 43673}
X(51963) = X(i)-Dao conjugate of X(j) for these (i, j): (441, 32458), (1503, 15595), (3162, 39265), (15595, 6393), (23976, 325), (33504, 6333), (36899, 35140), (39071, 36212), (39073, 36790), (42671, 38652), (50938, 297)
X(51963) = crosspoint of X(i) and X(j) for these (i,j): {98, 9476}, {6531, 41932}
X(51963) = crosssum of X(i) and X(j) for these (i,j): {511, 9475}, {36212, 36790}
X(51963) = crossdifference of every pair of points on line {511, 39073}
X(51963) = barycentric product X(i)*X(j) for these {i,j}: {4, 34156}, {32, 51257}, {98, 1503}, {132, 47388}, {287, 16318}, {290, 42671}, {441, 6531}, {879, 2409}, {1821, 2312}, {1976, 30737}, {2395, 34211}, {8766, 36120}, {8779, 16081}, {9154, 35282}, {9475, 34536}, {9476, 23976}, {14355, 43089}, {15595, 41932}, {15628, 43045}, {20021, 21458}, {20031, 39473}
X(51963) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 39265}, {98, 35140}, {441, 6393}, {878, 2435}, {879, 2419}, {1503, 325}, {1976, 1297}, {2312, 1959}, {2395, 43673}, {2409, 877}, {2422, 34212}, {2445, 4230}, {6531, 6330}, {6793, 51389}, {8779, 36212}, {9475, 36790}, {15595, 32458}, {16318, 297}, {21458, 20022}, {23976, 15595}, {24023, 17875}, {32696, 44770}, {34156, 69}, {34211, 2396}, {35282, 50567}, {41932, 9476}, {42671, 511}, {51257, 1502}, {51437, 232}
X(51963) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {34369, 35906, 5967}, {36899, 47737, 2}
X(51964) lies on the cubic K429 and these lines: {6, 647}, {32, 40353}, {115, 393}, {193, 14919}, {571, 14642}, {577, 32640}, {1974, 40352}, {2132, 5158}, {14385, 33871}, {15291, 18890}, {39376, 47433}
X(51964) = polar conjugate of the isotomic conjugate of X(39174)
X(51964) = X(i)-isoconjugate of X(j) for these (i,j): {1294, 14206}, {24001, 43701}, {36043, 41077}
X(51964) = X(i)-Dao conjugate of X(j) for these (i, j): (35579, 41077), (50937, 46106)
X(51964) = crosspoint of X(8749) and X(40353)
X(51964) = crosssum of X(i) and X(j) for these (i,j): {30, 47433}, {11064, 36789}
X(51964) = barycentric product X(i)*X(j) for these {i,j}: {4, 39174}, {74, 6000}, {186, 39376}, {8749, 44436}, {14380, 46587}, {18877, 51358}, {40384, 47433}
X(51964) = barycentric quotient X(i)/X(j) for these {i,j}: {6000, 3260}, {39174, 69}, {39376, 328}, {40352, 1294}, {47433, 36789}
X(51965) lies on the cubic K429 and these lines: {4, 40388}, {6, 2501}, {112, 393}, {193, 2986}, {687, 5649}, {1249, 32708}, {1974, 16240}, {1990, 2420}, {2407, 46106}, {3258, 46262}, {12028, 43911}, {14642, 47731}, {34334, 39176}, {38936, 40138}
X(51965) = polar conjugate of the isotomic conjugate of X(15454)
X(51965) = X(i)-cross conjugate of X(j) for these (i,j): {3163, 1990}, {14583, 4}
X(51965) = X(i)-isoconjugate of X(j) for these (i,j): {63, 14264}, {1494, 2315}, {1725, 14919}, {2349, 13754}, {3580, 35200}, {6334, 36034}
X(51965) = X(i)-Dao conjugate of X(j) for these (i, j): (133, 3580), (3162, 14264), (3258, 6334)
X(51965) = cevapoint of X(i) and X(j) for these (i,j): {1990, 39176}, {14581, 16240}
X(51965) = crosssum of X(13754) and X(47405)
X(51965) = barycentric product X(i)*X(j) for these {i,j}: {4, 15454}, {30, 1300}, {186, 39375}, {687, 1637}, {1784, 36053}, {1990, 2986}, {4240, 15328}, {6344, 39371}, {10419, 34334}, {14254, 38936}, {14581, 40832}, {14910, 46106}, {16240, 40423}, {32708, 41079}, {36035, 36114}, {36789, 40388}, {39176, 40427}
X(51965) = barycentric quotient X(i)/X(j) for these {i,j}: {25, 14264}, {1300, 1494}, {1495, 13754}, {1637, 6334}, {1990, 3580}, {9406, 2315}, {9408, 47405}, {14398, 686}, {14581, 3003}, {14583, 39170}, {14910, 14919}, {15328, 34767}, {15454, 69}, {16240, 113}, {23347, 15329}, {32708, 44769}, {39176, 34834}, {39375, 328}, {40388, 40384}
X(51966) lies on the cubic K340 and these lines: {21, 2800}, {28, 1845}, {58, 65}, {81, 11700}, {102, 110}, {163, 284}, {215, 501}, {333, 13532}, {580, 27622}, {859, 5127}, {1325, 5535}, {2849, 35055}, {4221, 14690}, {4653, 10703}, {6718, 25526}, {8677, 42741}
X(51966) = X(1325)-Ceva conjugate of X(501)
X(51966) = X(10)-isoconjugate of X(47645)
X(51966) = barycentric product X(i)*X(j) for these {i,j}: {81, 6326}, {284, 36918}, {333, 51236}
X(51966) = barycentric quotient X(i)/X(j) for these {i,j}: {1333, 47645}, {6326, 321}, {36918, 349}, {51236, 226}
X(51967) lies on the cubic K279 and these lines: {2, 41678}, {69, 146}, {95, 40082}, {253, 339}, {287, 37784}, {328, 43090}, {1494, 44138}, {2071, 3260}, {2373, 22239}, {2419, 35522}, {6330, 37778}, {6527, 44402}, {20563, 35520}, {30737, 30786}
X(51967) = isotomic conjugate of X(2071)
X(51967) = polar conjugate of X(15262)
X(51967) = isotomic conjugate of the anticomplement of X(403)
X(51967) = isotomic conjugate of the isogonal conjugate of X(11744)
X(51967) = X(i)-cross conjugate of X(j) for these (i,j): {74, 94}, {403, 2}, {1514, 34289}, {15311, 2052}, {32125, 4}, {47296, 76}
X(51967) = X(i)-isoconjugate of X(j) for these (i,j): {31, 2071}, {48, 15262}, {163, 46425}
X(51967) = X(i)-Dao conjugate of X(j) for these (i, j): (2, 2071), (115, 46425), (1249, 15262), (34834, 12825)
X(51967) = cevapoint of X(6509) and X(13754)
X(51967) = trilinear pole of line {525, 13567}
X(51967) = barycentric product X(i)*X(j) for these {i,j}: {76, 11744}, {850, 48373}, {3267, 22239}, {7799, 48374}, {18027, 40082}
X(51967) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 2071}, {4, 15262}, {523, 46425}, {2052, 34170}, {3580, 12825}, {11744, 6}, {16080, 38937}, {22239, 112}, {40082, 577}, {47296, 11598}, {48373, 110}, {48374, 1989}, {51346, 3284}
X(51968) lies on the cubic K279 and these lines: {2, 41678}, {4, 74}, {92, 18625}, {323, 15262}, {459, 2986}, {648, 14361}, {858, 12384}, {1249, 14920}, {26212, 41253}, {36789, 41361}
X(51968) = polar conjugate of X(50480)
X(51968) = anticomplement of the isogonal conjugate of X(15262)
X(51968) = polar conjugate of the isogonal conjugate of X(2935)
X(51968) = X(i)-anticomplementary conjugate of X(j) for these (i,j): {2071, 4329}, {15262, 8}, {34170, 21270}
X(51968) = X(3260)-Ceva conjugate of X(4)
X(51968) = X(48)-isoconjugate of X(50480)
X(51968) = X(i)-Dao conjugate of X(j) for these (i, j): (1249, 50480), (8749, 74)
X(51968) = barycentric product X(264)*X(2935)
X(51968) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 50480}, {2935, 3}
X(51969) lies on the cubic K145 and these lines: {1, 6254}, {19, 57}, {73, 991}, {84, 3487}, {198, 34032}, {223, 18591}, {579, 43035}, {610, 1020}, {651, 2289}, {1423, 3220}, {1439, 18161}, {2114, 27626}, {2124, 3182}, {6282, 34488}, {6356, 15656}, {7013, 18631}, {18623, 40152}, {24220, 41010}, {34492, 34497}
X(51969) = X(3)-Ceva conjugate of X(57)
X(51969) = X(273)-Dao conjugate of X(264)
X(51969) = barycentric product X(7)*X(2947)
X(51969) = barycentric quotient X(2947)/X(8)
X(51970) lies on the cubic K340 and these lines: {28, 108}, {35, 2778}, {36, 1455}, {65, 34442}, {73, 501}, {1415, 2193}, {2817, 11012}, {2829, 3585}, {2849, 8648}, {37561, 38696}
X(51970) = X(1325)-Ceva conjugate of X(65)
X(51971) lies on the cubic K145 and these lines: {4, 57}, {19, 6524}, {33, 11435}, {71, 8802}, {108, 2947}, {204, 3192}, {207, 6254}, {243, 27659}, {1249, 40945}, {1400, 1857}, {36103, 37225}
X(51971) = X(3)-Ceva conjugate of X(19)
X(51971) = X(158)-Dao conjugate of X(264)
X(51972) lies on the cubic K1066 and these lines: {1, 21096}, {8, 9}, {10, 3693}, {41, 12437}, {69, 30625}, {72, 2809}, {76, 85}, {78, 40869}, {142, 1229}, {190, 34932}, {200, 6554}, {218, 519}, {220, 6737}, {306, 30807}, {321, 25002}, {329, 2391}, {345, 4384}, {515, 17742}, {672, 24391}, {946, 21073}, {1018, 11362}, {1043, 6559}, {1146, 4515}, {1210, 8568}, {1212, 4847}, {1759, 31730}, {1864, 6057}, {2170, 21627}, {2481, 29960}, {3061, 12053}, {3239, 42455}, {3419, 49782}, {3452, 27390}, {3501, 4848}, {3661, 27288}, {3687, 30854}, {3694, 20262}, {3729, 6604}, {3827, 8804}, {3893, 4534}, {3935, 26793}, {3970, 21620}, {3974, 10382}, {3985, 40661}, {3991, 31397}, {4136, 10395}, {4416, 32024}, {4454, 32098}, {4855, 26258}, {4869, 32086}, {4967, 27544}, {4987, 10123}, {5179, 21075}, {5257, 27396}, {5438, 40127}, {5525, 45287}, {5687, 8074}, {5927, 10324}, {6734, 25082}, {6738, 17355}, {6743, 37658}, {6745, 46835}, {7080, 23058}, {8232, 31994}, {8582, 21049}, {9436, 25242}, {9843, 25068}, {10106, 24247}, {10481, 51384}, {10572, 17744}, {10914, 23840}, {10916, 24036}, {12526, 41325}, {12527, 50995}, {12848, 32003}, {15490, 41789}, {16284, 17233}, {17294, 42032}, {17787, 30030}, {21090, 21616}, {22021, 42712}, {25019, 45744}, {25101, 32008}, {25525, 29627}, {25719, 40872}, {26015, 26690}, {27340, 31038}, {28739, 34059}, {30618, 44669}, {30806, 43971}, {41239, 49466}, {42033, 50095}
X(51972) = isotomic conjugate of X(10509)
X(51972) = isotomic conjugate of the isogonal conjugate of X(8012)
X(51972) = X(i)-Ceva conjugate of X(j) for these (i,j): {312, 1229}, {346, 45791}, {668, 4163}, {1229, 4847}, {4578, 3239}
X(51972) = X(3059)-cross conjugate of X(4847)
X(51972) = X(i)-isoconjugate of X(j) for these (i,j): {31, 10509}, {32, 42311}, {34, 1803}, {56, 1170}, {269, 1174}, {604, 21453}, {608, 40443}, {738, 10482}, {1106, 32008}, {1397, 31618}, {1407, 2346}, {1435, 47487}, {6605, 7023}
X(51972) = X(i)-Dao conjugate of X(j) for these (i, j): (1, 1170), (2, 10509), (142, 57), (1212, 279), (3119, 513), (3161, 21453), (4847, 1445), (5572, 1202), (6376, 42311), (6552, 32008), (6600, 1174), (11517, 1803), (24771, 2346), (40606, 269), (45791, 7674)
X(51972) = cevapoint of X(3059) and X(45791)
X(51972) = crosspoint of X(312) and X(346)
X(51972) = crosssum of X(604) and X(1407)
X(51972) = barycentric product X(i)*X(j) for these {i,j}: {8, 4847}, {9, 1229}, {75, 3059}, {76, 8012}, {85, 45791}, {142, 346}, {200, 20880}, {220, 1233}, {312, 1212}, {314, 21039}, {341, 354}, {345, 1855}, {646, 21127}, {668, 6608}, {1043, 3925}, {1418, 30693}, {1827, 3718}, {1978, 10581}, {2293, 3596}, {2321, 16713}, {3699, 6362}, {3701, 17194}, {4082, 17169}, {4163, 35312}, {4391, 35341}, {4397, 35338}, {4515, 16708}, {4572, 6607}, {5423, 10481}, {6558, 21104}, {6559, 51384}, {8551, 20567}, {20229, 28659}, {21795, 28660}, {51416, 51565}
X(51972) = barycentric quotient X(i)/X(j) for these {i,j}: {2, 10509}, {8, 21453}, {9, 1170}, {75, 42311}, {78, 40443}, {142, 279}, {200, 2346}, {219, 1803}, {220, 1174}, {312, 31618}, {346, 32008}, {354, 269}, {480, 10482}, {728, 6605}, {1212, 57}, {1229, 85}, {1260, 47487}, {1418, 738}, {1475, 1407}, {1827, 34}, {1855, 278}, {2293, 56}, {2488, 43924}, {3059, 1}, {3699, 6606}, {3925, 3668}, {4847, 7}, {6067, 10481}, {6362, 3676}, {6607, 663}, {6608, 513}, {8012, 6}, {8551, 41}, {10481, 479}, {10581, 649}, {15185, 4350}, {16713, 1434}, {17194, 1014}, {20229, 604}, {20880, 1088}, {21039, 65}, {21127, 3669}, {21795, 1400}, {21808, 1427}, {22053, 7053}, {22079, 603}, {35310, 1020}, {35312, 4626}, {35326, 1461}, {35338, 934}, {35341, 651}, {40983, 1398}, {42449, 45227}, {45791, 9}, {48151, 43932}, {51416, 22464}
X(51972) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {8, 346, 728}, {1146, 4515, 6736}, {1210, 25066, 8568}, {2321, 41006, 8}, {3693, 40997, 10}, {21049, 44798, 8582}
X(51973) lies on the cubics K775 and K787 and these lines: {1, 39}, {2, 7033}, {6, 19587}, {37, 4518}, {42, 694}, {43, 6377}, {55, 1911}, {172, 18265}, {190, 19579}, {334, 27295}, {335, 3666}, {727, 813}, {741, 43077}, {1458, 30657}, {1575, 32922}, {1966, 17759}, {2176, 38986}, {2238, 3508}, {2329, 9468}, {3224, 22061}, {3229, 3507}, {3510, 8844}, {3693, 20363}, {4562, 10027}, {4595, 16742}, {7245, 16712}, {9315, 40730}, {17594, 18787}, {18895, 24326}, {25058, 36800}, {27020, 40094}, {37128, 42028}, {38832, 51319}, {40093, 41240}, {41269, 43534}
X(51973) = isogonal conjugate of X(39914)
X(51973) = isogonal conjugate of the isotomic conjugate of X(40848)
X(51973) = X(1911)-Ceva conjugate of X(292)
X(51973) = X(41531)-cross conjugate of X(292)
X(51973) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39914}, {2, 34252}, {75, 51321}, {87, 239}, {238, 330}, {350, 2162}, {659, 4598}, {812, 932}, {1428, 27424}, {1429, 7155}, {1447, 2319}, {1580, 27447}, {1914, 6384}, {1921, 7121}, {2053, 10030}, {2210, 6383}, {3253, 40881}, {3500, 14199}, {3570, 43931}, {3685, 7153}, {3766, 34071}, {5383, 27846}, {6650, 8843}, {8632, 18830}, {15373, 40717}, {16606, 33295}, {23493, 30940}
X(51973) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 39914), (75, 18891), (206, 51321), (798, 27846), (3835, 27918), (9470, 330), (32664, 34252), (36906, 6384), (39092, 27447), (40598, 1921), (40610, 3766)
X(51973) = cevapoint of X(18758) and X(21760)
X(51973) = trilinear pole of line {20667, 20979}
X(51973) = crossdifference of every pair of points on line {659, 4107}
X(51973) = barycentric product X(i)*X(j) for these {i,j}: {1, 41531}, {6, 40848}, {43, 291}, {192, 292}, {334, 2209}, {335, 2176}, {660, 4083}, {694, 17752}, {741, 3971}, {813, 3835}, {875, 36863}, {1403, 4518}, {1423, 4876}, {1911, 6376}, {1916, 51319}, {1922, 6382}, {1967, 41318}, {3009, 33680}, {3123, 5378}, {3212, 7077}, {3572, 4595}, {4562, 20979}, {4583, 8640}, {4584, 21834}, {4589, 50491}, {16362, 40795}, {18897, 40367}, {20691, 37128}, {20906, 34067}, {38832, 43534}
X(51973) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39914}, {31, 34252}, {32, 51321}, {43, 350}, {192, 1921}, {291, 6384}, {292, 330}, {335, 6383}, {660, 18830}, {694, 27447}, {813, 4598}, {875, 43931}, {1403, 1447}, {1423, 10030}, {1911, 87}, {1922, 2162}, {2176, 239}, {2209, 238}, {3208, 3975}, {3212, 18033}, {3971, 35544}, {4083, 3766}, {4595, 27853}, {4876, 27424}, {6376, 18891}, {6377, 27918}, {6382, 44169}, {7077, 7155}, {8640, 659}, {14598, 7121}, {17752, 3978}, {18265, 2053}, {18266, 8843}, {20284, 33891}, {20691, 3948}, {20979, 812}, {21835, 39786}, {24533, 14296}, {27538, 4087}, {27644, 30940}, {34067, 932}, {34247, 14199}, {38832, 33295}, {38986, 27846}, {40848, 76}, {41318, 1926}, {41526, 1429}, {41531, 75}, {50491, 4010}, {51319, 385}
X(51974) lies on the conic {{A,B,C,X(1),X(6)}}, the cubic K787, and these lines: {1, 893}, {6, 904}, {39, 3494}, {56, 2162}, {58, 23525}, {86, 16744}, {87, 256}, {172, 7104}, {257, 3226}, {269, 7153}, {292, 1967}, {330, 870}, {694, 20460}, {733, 932}, {979, 23447}, {1015, 3865}, {1220, 16606}, {1431, 30658}, {1691, 41526}, {2329, 9468}, {4451, 20363}, {6378, 39977}, {7121, 40746}, {16720, 18830}, {18758, 51319}, {20471, 34445}, {21008, 34249}, {24528, 39969}, {34252, 40763}, {39972, 40729}
X(51974) = isogonal conjugate of X(17752)
X(51974) = isogonal conjugate of the anticomplement of X(30038)
X(51974) = isogonal conjugate of the isotomic conjugate of X(27447)
X(51974) = X(i)-cross conjugate of X(j) for these (i,j): {256, 893}, {50521, 18830}
X(51974) = X(i)-isoconjugate of X(j) for these (i,j): {1, 17752}, {6, 41318}, {43, 894}, {75, 51319}, {171, 192}, {172, 6376}, {190, 24533}, {213, 27891}, {385, 41531}, {651, 30584}, {1215, 27644}, {1403, 17787}, {1423, 7081}, {1580, 40848}, {1909, 2176}, {1920, 2209}, {2295, 33296}, {2329, 3212}, {2330, 30545}, {3208, 7176}, {3502, 17741}, {3835, 4579}, {3963, 38832}, {4083, 18047}, {4367, 4595}, {6382, 7122}, {7009, 22370}, {7175, 27538}, {7234, 36860}, {7304, 21803}, {17103, 20691}, {20964, 31008}, {20981, 36863}
X(51974) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 17752), (9, 41318), (206, 51319), (6626, 27891), (38991, 30584), (39092, 40848)
X(51974) = crossdifference of every pair of points on line {24533, 30584}
X(51974) = barycentric product X(i)*X(j) for these {i,j}: {6, 27447}, {87, 256}, {257, 2162}, {330, 893}, {694, 39914}, {904, 6384}, {1178, 42027}, {1431, 7155}, {1432, 2319}, {1581, 34252}, {1916, 51321}, {2053, 7249}, {3903, 43931}, {6383, 7104}, {7018, 7121}, {7148, 7303}, {16606, 40432}, {23493, 32010}, {40763, 45782}
X(51974) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 41318}, {6, 17752}, {32, 51319}, {86, 27891}, {87, 1909}, {256, 6376}, {257, 6382}, {330, 1920}, {663, 30584}, {667, 24533}, {694, 40848}, {893, 192}, {904, 43}, {1178, 33296}, {1431, 3212}, {1432, 30545}, {1967, 41531}, {2053, 7081}, {2162, 894}, {2319, 17787}, {3863, 33890}, {3903, 36863}, {4603, 36860}, {6378, 21021}, {7104, 2176}, {7116, 22370}, {7121, 171}, {7153, 7196}, {16606, 3963}, {21759, 2295}, {23493, 1215}, {27447, 76}, {34071, 18047}, {34249, 17741}, {34252, 1966}, {39914, 3978}, {40432, 31008}, {40729, 20691}, {42027, 1237}, {43931, 4374}, {44187, 40367}, {45209, 27880}, {45218, 27697}, {51321, 385}
X(51975) lies on the cubics K971 and K1066 and these lines: {1, 51562}, {2, 36909}, {8, 80}, {10, 522}, {12, 18120}, {76, 1227}, {85, 18821}, {214, 36944}, {341, 4076}, {355, 38954}, {519, 14584}, {759, 8706}, {956, 14204}, {997, 40437}, {1168, 4737}, {1411, 22837}, {1772, 18395}, {1807, 30144}, {2006, 45700}, {2161, 4095}, {2222, 2757}, {2325, 4169}, {2801, 14266}, {3244, 34232}, {3679, 36590}, {3701, 49998}, {3992, 17780}, {6554, 36910}, {18815, 36588}, {20900, 33937}, {24624, 51285}, {38955, 47320}
X(51975) = isogonal conjugate of X(16944)
X(51975) = isotomic conjugate of the isogonal conjugate of X(40172)
X(51975) = X(i)-Ceva conjugate of X(j) for these (i,j): {20566, 4358}, {35174, 3762}
X(51975) = X(i)-cross conjugate of X(j) for these (i,j): {900, 51562}, {1145, 519}, {3992, 15065}, {4370, 4358}
X(51975) = X(i)-isoconjugate of X(j) for these (i,j): {1, 16944}, {6, 40215}, {36, 106}, {88, 7113}, {1022, 1983}, {1417, 4511}, {1870, 36058}, {2226, 17455}, {3218, 9456}, {3257, 21758}, {3960, 32665}, {4453, 32719}, {4591, 21828}, {8752, 22128}, {10428, 34586}, {17923, 32659}, {36590, 41282}, {41935, 51583}
X(51975) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 16944), (9, 40215), (214, 36), (519, 214), (4370, 3218), (15898, 106), (20619, 1870), (35092, 3960), (36909, 1320), (36910, 40594), (36912, 4867), (51402, 3738)
X(51975) = cevapoint of X(i) and X(j) for these (i,j): {80, 36909}, {3992, 4738}
X(51975) = trilinear pole of line {1639, 3943}
X(51975) = crossdifference of every pair of points on line {7113, 21758}
X(51975) = barycentric product X(i)*X(j) for these {i,j}: {8, 14628}, {44, 20566}, {76, 40172}, {80, 4358}, {312, 14584}, {519, 18359}, {655, 4768}, {900, 36804}, {1168, 36791}, {1639, 35174}, {1807, 46109}, {2006, 4723}, {2161, 3264}, {2325, 18815}, {3762, 51562}, {3943, 14616}, {3992, 24624}, {4895, 46405}, {15065, 16704}
X(51975) = barycentric quotient X(i)/X(j) for these {i,j}: {1, 40215}, {6, 16944}, {44, 36}, {80, 88}, {519, 3218}, {678, 17455}, {900, 3960}, {902, 7113}, {1145, 16586}, {1168, 2226}, {1639, 3738}, {1807, 1797}, {1960, 21758}, {2161, 106}, {2325, 4511}, {3264, 20924}, {3689, 2323}, {3762, 4453}, {3911, 1443}, {3943, 758}, {3992, 3936}, {4358, 320}, {4370, 214}, {4432, 27950}, {4723, 32851}, {4727, 4880}, {4730, 21828}, {4738, 51583}, {4768, 3904}, {4895, 654}, {4908, 4867}, {4969, 4973}, {5440, 22128}, {6187, 9456}, {8756, 1870}, {14584, 57}, {14628, 7}, {15065, 4080}, {17780, 4585}, {18359, 903}, {20566, 20568}, {21805, 2245}, {22086, 22379}, {23344, 1983}, {36791, 1227}, {36804, 4555}, {36909, 40594}, {36910, 1320}, {38462, 17923}, {40172, 6}, {40663, 18593}, {47318, 4622}, {51562, 3257}
X(51976) lies on the cubic K1146 and these lines: {1, 15}, {6, 1653}, {9, 5362}, {37, 1082}, {57, 77}, {396, 1081}, {559, 16884}, {1046, 2307}, {1100, 37773}, {1277, 5353}, {3180, 17364}, {3945, 30281}, {5222, 30280}, {6127, 11789}
X(51976) = X(1082)-Ceva conjugate of X(1)
X(51976) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 37772, 1653}, {15, 39153, 1}
X(51977) lies on the cubic K1146 and these lines: {1, 16}, {6, 1652}, {9, 5367}, {37, 559}, {57, 77}, {395, 554}, {1082, 16884}, {1100, 37772}, {1276, 5357}, {3181, 17364}, {3945, 30280}, {5222, 30281}, {6127, 11752}
X(51977) = X(559)-Ceva conjugate of X(1)
X(51977) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {6, 37773, 1652}, {16, 39152, 1}
X(51978) lies on the cubic K1066 and these lines: {4, 69}, {8, 21}, {29, 1812}, {58, 49168}, {81, 5716}, {85, 30941}, {86, 938}, {274, 955}, {312, 41509}, {388, 5208}, {411, 14829}, {515, 10461}, {950, 17185}, {1010, 18391}, {1150, 20846}, {1444, 5768}, {1478, 35637}, {1479, 18417}, {1788, 13588}, {1834, 26543}, {1858, 3706}, {2287, 6554}, {2476, 18134}, {2551, 3786}, {3056, 18178}, {3086, 18465}, {3419, 18180}, {3434, 41723}, {3485, 10453}, {3869, 4673}, {3886, 12514}, {4305, 37303}, {4417, 6828}, {4966, 31936}, {5086, 7270}, {5730, 37357}, {5794, 18165}, {6734, 14547}, {6737, 46877}, {6841, 41014}, {6857, 9534}, {6872, 14552}, {7098, 32932}, {7253, 42455}, {7474, 10327}, {7491, 32128}, {8822, 9799}, {9581, 17182}, {10393, 11679}, {11114, 50215}, {12625, 18163}, {15984, 21024}, {16752, 17054}, {16992, 37149}, {18206, 24391}, {19259, 37730}, {22292, 22301}, {25015, 37796}, {27398, 28827}, {30943, 34259}, {37655, 50695}, {41610, 51192}, {48850, 50739}
X(51978) = isotomic conjugate of the isogonal conjugate of X(8021)
X(51978) = X(i)-isoconjugate of X(j) for these (i,j): {512, 36048}, {661, 32651}, {943, 1042}, {1175, 1254}, {1400, 2982}, {1409, 40573}, {1426, 1794}, {1427, 2259}, {4017, 15439}, {37755, 40570}
X(51978) = X(i)-Dao conjugate of X(j) for these (i, j): (442, 65), (942, 1425), (6734, 15556), (15607, 512), (16585, 3668), (18591, 1427), (34961, 15439), (36830, 32651), (39054, 36048), (40582, 2982), (40937, 6354)
X(51978) = crosspoint of X(314) and X(7058)
X(51978) = crossdifference of every pair of points on line {3049, 7180}
X(51978) = barycentric product X(i)*X(j) for these {i,j}: {76, 8021}, {314, 40937}, {333, 6734}, {442, 7058}, {670, 33525}, {1043, 5249}, {1234, 7054}, {3596, 46882}, {3718, 46884}, {7258, 50354}, {14547, 28660}
X(51978) = barycentric quotient X(i)/X(j) for these {i,j}: {21, 2982}, {29, 40573}, {110, 32651}, {442, 6354}, {662, 36048}, {942, 1427}, {1043, 40435}, {1841, 1426}, {1859, 1880}, {2260, 1042}, {2287, 943}, {2294, 1254}, {2327, 1794}, {2328, 2259}, {5249, 3668}, {5546, 15439}, {6734, 226}, {7054, 1175}, {7058, 40412}, {8021, 6}, {14547, 1400}, {14597, 1410}, {17926, 14775}, {18591, 1425}, {18607, 1439}, {23207, 1409}, {31938, 16577}, {33525, 512}, {40937, 65}, {40967, 2171}, {46882, 56}, {46883, 1435}, {46884, 34}, {46885, 4341}, {46890, 1398}, {50354, 7216}
X(51978) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {314, 44130, 44140}, {333, 1043, 1792}
X(51979) lies on the cubic K155 and K787 and these lines: {1, 2670}, {2, 893}, {6, 904}, {39, 256}, {238, 9468}, {292, 30658}, {672, 1967}, {1178, 23660}, {1931, 20332}, {2108, 16363}, {2111, 2114}, {2669, 40432}, {4279, 7104}, {18786, 24727}, {19579, 40849}
X(51979) = isogonal conjugate of X(39933)
X(51979) = isogonal conjugate of the isotomic conjugate of X(40849)
X(51979) = X(i)-Ceva conjugate of X(j) for these (i,j): {238, 41532}, {9468, 893}
X(51979) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39933}, {385, 24576}, {894, 7168}, {1691, 30633}, {7061, 8868}
X(51979) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 39933), (1921, 14603)
X(51979) = barycentric product X(i)*X(j) for these {i,j}: {6, 40849}, {256, 3510}, {257, 18278}, {694, 19579}, {893, 19565}, {904, 19567}, {1581, 19580}, {1916, 18274}, {1934, 30634}, {1967, 19581}, {7104, 18275}, {8875, 40873}, {9468, 18277}
X(51979) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39933}, {904, 7168}, {1581, 30633}, {1967, 24576}, {3510, 1909}, {8875, 40846}, {18274, 385}, {18277, 14603}, {18278, 894}, {19565, 1920}, {19579, 3978}, {19580, 1966}, {19581, 1926}, {30634, 1580}, {40849, 76}, {41882, 8868}
X(51979) = {X(292),X(30658)}-harmonic conjugate of X(41532)
X(51980) lies on the cubic K055 and these lines: {2, 36827}, {4, 542}, {6, 512}, {32, 1084}, {110, 10560}, {111, 263}, {182, 691}, {184, 10558}, {237, 14966}, {511, 2421}, {524, 3143}, {597, 36157}, {892, 44155}, {1316, 45329}, {3016, 42007}, {3818, 51405}, {5028, 37841}, {5039, 34238}, {5466, 46124}, {5476, 16092}, {5480, 51258}, {5640, 46783}, {5651, 32583}, {8542, 35087}, {8877, 15004}, {9306, 10559}, {9971, 13330}, {11511, 35923}, {14263, 44500}, {20022, 51396}, {22826, 22827}, {32648, 39238}, {33752, 36823}, {36892, 50567}, {44102, 46592}, {47572, 51736}
X(51980) = isogonal conjugate of the isotomic conjugate of X(5968)
X(51980) = X(9154)-Ceva conjugate of X(111)
X(51980) = X(i)-isoconjugate of X(j) for these (i,j): {75, 5967}, {98, 14210}, {187, 46273}, {290, 896}, {293, 44146}, {336, 468}, {524, 1821}, {690, 36036}, {922, 18024}, {1910, 3266}, {2395, 24039}, {2642, 43187}, {6390, 36120}, {9154, 24038}, {23889, 43665}, {35522, 36084}, {36104, 45807}
X(51980) = X(i)-Dao conjugate of X(j) for these (i, j): (132, 44146), (206, 5967), (511, 50567), (2679, 690), (11672, 3266), (15477, 98), (15899, 290), (38987, 35522), (39000, 45807), (39061, 18024), (40601, 524), (46094, 6390)
X(51980) = crosspoint of X(111) and X(9154)
X(51980) = crosssum of X(524) and X(9155)
X(51980) = trilinear pole of line {237, 2491}
X(51980) = crossdifference of every pair of points on line {524, 35522}
X(51980) = X(3143)-lineconjugate of X(524)
X(51980) = barycentric product X(i)*X(j) for these {i,j}: {6, 5968}, {110, 8430}, {111, 511}, {232, 895}, {237, 671}, {240, 36060}, {297, 14908}, {325, 32740}, {691, 3569}, {892, 2491}, {897, 1755}, {923, 1959}, {2211, 30786}, {2421, 9178}, {2799, 32729}, {3289, 17983}, {4230, 10097}, {5466, 14966}, {5547, 43034}, {8753, 36212}, {9154, 11672}, {9155, 10630}, {9417, 46277}, {9418, 18023}, {20022, 41272}, {23894, 23997}, {41936, 50567}
X(51980) = barycentric quotient X(i)/X(j) for these {i,j}: {32, 5967}, {111, 290}, {232, 44146}, {237, 524}, {511, 3266}, {671, 18024}, {684, 45807}, {691, 43187}, {897, 46273}, {923, 1821}, {1755, 14210}, {2211, 468}, {2491, 690}, {3289, 6390}, {3569, 35522}, {5360, 42713}, {5968, 76}, {8430, 850}, {8753, 16081}, {9155, 36792}, {9178, 43665}, {9417, 896}, {9418, 187}, {9419, 9155}, {11672, 50567}, {14908, 287}, {14966, 5468}, {19626, 1976}, {23997, 24039}, {32729, 2966}, {32740, 98}, {34854, 37778}, {36060, 336}, {36142, 36036}, {39469, 14417}, {41272, 20021}, {41936, 9154}
X(51980) = {X(691),X(21460)}-harmonic conjugate of X(182)
X(51981) lies on the cubic K787 and these lines: {2, 292}, {6, 2196}, {39, 8866}, {291, 23447}, {733, 932}, {1691, 14598}, {1911, 16372}, {3224, 22061}, {3229, 3510}, {9468, 40597}
X(51981) = isogonal conjugate of X(39934)
X(51981) = X(9468)-Ceva conjugate of X(292)
X(51981) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39934}, {239, 7346}
X(51981) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 39934), (1920, 14603)
X(51981) = barycentric product X(i)*X(j) for these {i,j}: {291, 6196}, {335, 34251}, {694, 39928}, {1911, 24732}
X(51981) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39934}, {1911, 7346}, {6196, 350}, {24732, 18891}, {34251, 239}, {39928, 3978}
X(51982) lies on the cubics K787 and K1023 and these lines: {39, 695}, {141, 9229}, {694, 1843}, {711, 827}, {733, 14370}, {755, 783}, {1915, 9468}, {1916, 42551}, {2353, 33786}, {3229, 3505}, {5207, 19566}, {9284, 9285}, {14970, 18828}, {18896, 40379}, {44163, 44166}
X(51982) = isogonal conjugate of X(16985)
X(51982) = isogonal conjugate of the anticomplement of X(40876)
X(51982) = isotomic conjugate of the isogonal conjugate of X(14946)
X(51982) = isogonal conjugate of the isotomic conjugate of X(40847)
X(51982) = X(i)-cross conjugate of X(j) for these (i,j): {2, 41517}, {882, 18828}, {23635, 36897}
X(51982) = X(i)-isoconjugate of X(j) for these (i,j): {1, 16985}, {75, 51320}, {384, 1580}, {385, 1582}, {782, 4599}, {1691, 1965}, {1915, 1966}, {1925, 14602}, {1932, 3978}, {1933, 9230}, {16101, 19578}, {34072, 35558}
X(51982) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 16985), (206, 51320), (3124, 782), (8265, 35530), (9467, 1915), (15449, 35558), (39092, 384)
X(51982) = trilinear pole of line {3005, 20859}
X(51982) = crossdifference of every pair of points on line {782, 39082}
X(51982) = barycentric product X(i)*X(j) for these {i,j}: {6, 40847}, {76, 14946}, {626, 711}, {694, 9229}, {695, 1916}, {783, 826}, {1581, 9285}, {1934, 9288}, {1967, 9239}, {3005, 18828}, {36214, 37892}
X(51982) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 16985}, {32, 51320}, {626, 35530}, {694, 384}, {695, 385}, {711, 40416}, {783, 4577}, {826, 35558}, {1581, 1965}, {1916, 9230}, {1927, 1932}, {1934, 1925}, {1967, 1582}, {3005, 782}, {3505, 19571}, {9229, 3978}, {9236, 1933}, {9239, 1926}, {9285, 1966}, {9288, 1580}, {9468, 1915}, {14946, 6}, {17970, 37893}, {18828, 689}, {20859, 710}, {36214, 37894}, {37892, 17984}, {40847, 76}
X(51983) lies on the cubic K787 and these lines: {2, 6}, {3, 33786}, {39, 3499}, {187, 9431}, {292, 1755}, {308, 4074}, {669, 2513}, {670, 19573}, {703, 9150}, {733, 805}, {893, 1964}, {1078, 44164}, {1186, 7786}, {1207, 6683}, {1576, 51320}, {1691, 9418}, {1915, 41331}, {1979, 16693}, {3053, 3224}, {3229, 3511}, {3819, 45210}, {8623, 9468}, {9225, 33875}, {10007, 43977}, {10191, 39968}, {10329, 41328}, {35325, 44090}, {38382, 40858}, {38854, 42548}, {39932, 47642}
X(51983) = isogonal conjugate of X(39939)
X(51983) = isogonal conjugate of the isotomic conjugate of X(40858)
X(51983) = X(i)-Ceva conjugate of X(j) for these (i,j): {8623, 2076}, {9468, 6}
X(51983) = X(38382)-cross conjugate of X(6)
X(51983) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39939}, {75, 51326}, {1821, 51249}
X(51983) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 39939), (206, 51326), (3978, 14603), (40601, 51249)
X(51983) = crosspoint of X(805) and X(34537)
X(51983) = crosssum of X(i) and X(j) for these (i,j): {6, 24729}, {523, 41178}, {804, 1084}
X(51983) = crossdifference of every pair of points on line {512, 3934}
X(51983) = barycentric product X(i)*X(j) for these {i,j}: {6, 40858}, {511, 8870}, {694, 38382}, {1916, 51325}
X(51983) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39939}, {32, 51326}, {237, 51249}, {8870, 290}, {38382, 3978}, {40858, 76}, {51325, 385}
X(51983) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 18899, 6}, {6, 21001, 183}, {385, 32748, 6}, {3051, 3329, 6}, {3231, 14607, 38303}, {3231, 32748, 385}, {3289, 39095, 6}
X(51984) lies on the cubic K1066 and these lines: {4, 6073}, {8, 11}, {106, 26364}, {341, 4397}, {901, 3436}, {3262, 51362}, {3421, 10428}, {5176, 17780}, {5687, 38950}, {6735, 35015}, {12607, 34230}, {14260, 17757}, {14923, 15632}, {21290, 36944}
X(51984) = X(i)-isoconjugate of X(j) for these (i,j): {604, 40218}, {1106, 36944}, {1404, 34051}, {30725, 32669}
X(51984) = X(i)-Dao conjugate of X(j) for these (i, j): (1145, 1319), (2804, 3259), (3161, 40218), (6552, 36944), (6735, 41554), (23757, 1647), (45247, 56)
X(51984) = barycentric product X(i)*X(j) for these {i,j}: {2804, 4582}, {4997, 6735}, {20568, 51380}
X(51984) = barycentric quotient X(i)/X(j) for these {i,j}: {8, 40218}, {346, 36944}, {1320, 34051}, {2804, 30725}, {5548, 2720}, {6735, 3911}, {14260, 1407}, {41215, 47420}, {51380, 44}
X(51985) lies on the cubic K787 and these lines: {2, 7033}, {6, 292}, {39, 8865}, {100, 733}, {213, 18274}, {239, 21897}, {1979, 20665}, {2092, 4876}, {2664, 3229}, {27633, 40093}
X(51985) = isogonal conjugate of X(39937)
X(51985) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39937}, {238, 39746}, {1447, 3495}
X(51985) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 39937), (9470, 39746)
X(51985) = barycentric product X(i)*X(j) for these {i,j}: {292, 26752}, {694, 39929}, {1916, 51323}, {3503, 4876}
X(51985) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39937}, {292, 39746}, {3503, 10030}, {26752, 1921}, {39929, 3978}, {51323, 385}
X(51986) lies on the cubic K787 and these lines: {19, 232}, {39, 3497}, {198, 7116}, {256, 1742}, {292, 694}, {573, 7015}, {664, 39928}, {1423, 3229}, {1432, 39970}, {1691, 41526}, {2305, 20676}, {7104, 29055}, {7131, 21371}, {27633, 37137}
X(51986) = isogonal conjugate of X(39936)
X(51986) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39936}, {385, 43748}, {3500, 7081}
X(51986) = X(3)-Dao conjugate of X(39936)
X(51986) = barycentric product X(i)*X(j) for these {i,j}: {694, 39930}, {1431, 32937}, {1432, 3501}, {7249, 34247}, {17072, 29055}, {21348, 37137}
X(51986) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39936}, {1967, 43748}, {3501, 17787}, {22229, 4140}, {23655, 3907}, {34247, 7081}, {39930, 3978}
X(51987) lies on the cubic K055 and these lines: {4, 218}, {6, 513}, {32, 56}, {105, 957}, {219, 44184}, {222, 36146}, {517, 2427}, {919, 953}, {1376, 35333}, {1814, 1992}, {2176, 18785}, {2238, 3140}, {5398, 36057}, {5452, 31140}, {24482, 36086}, {30962, 31637}
X(51987) = X(i)-isoconjugate of X(j) for these (i,j): {2, 36819}, {104, 3912}, {241, 51565}, {518, 34234}, {672, 18816}, {909, 3263}, {918, 36037}, {1025, 43728}, {1026, 2401}, {1458, 36795}, {1795, 46108}, {1809, 5236}, {1818, 16082}, {2250, 30941}, {2254, 13136}, {2342, 40704}, {3717, 34051}, {18206, 38955}, {25083, 36123}, {37136, 50333}
X(51987) = X(i)-Dao conjugate of X(j) for these (i, j): (517, 51390), (3259, 918), (23980, 3263), (25640, 46108), (32664, 36819), (40613, 3912)
X(51987) = crossdifference of every pair of points on line {518, 50333}
X(51987) = barycentric product X(i)*X(j) for these {i,j}: {105, 517}, {294, 1465}, {666, 3310}, {673, 2183}, {859, 13576}, {885, 23981}, {908, 1438}, {919, 10015}, {1024, 24029}, {1416, 6735}, {1457, 14942}, {1769, 36086}, {1785, 36057}, {1814, 14571}, {2195, 22464}, {2397, 43929}, {2804, 32735}, {4246, 10099}, {5377, 42753}, {22350, 36124}, {23696, 23706}, {32666, 36038}, {36146, 46393}, {41934, 51390}
X(51987) = barycentric quotient X(i)/X(j) for these {i,j}: {31, 36819}, {105, 18816}, {294, 36795}, {517, 3263}, {859, 30941}, {884, 43728}, {919, 13136}, {1438, 34234}, {1457, 9436}, {1465, 40704}, {2183, 3912}, {2195, 51565}, {2427, 42720}, {3310, 918}, {8751, 16082}, {14571, 46108}, {23980, 51390}, {23981, 883}, {32666, 36037}, {43929, 2401}, {51377, 3932}
X(51988) lies on the cubic K787 and these lines: {2, 216}, {19, 292}, {39, 8863}, {419, 6375}, {694, 1843}, {733, 32085}, {1691, 1968}, {3186, 3229}, {5117, 45210}, {40981, 51324}
X(51988) = polar conjugate of X(43715)
X(51988) = polar conjugate of the isotomic conjugate of X(3491)
X(51988) = X(9468)-Ceva conjugate of X(232)
X(51988) = X(i)-isoconjugate of X(j) for these (i,j): {48, 43715}, {63, 51246}
X(51988) = X(i)-Dao conjugate of X(j) for these (i, j): (1249, 43715), (3162, 51246)
X(51988) = crosssum of X(6) and X(24730)
X(51988) = barycentric product X(4)*X(3491)
X(51988) = barycentric quotient X(i)/X(j) for these {i,j}: {4, 43715}, {25, 51246}, {3491, 69}
X(51989) lies on the cubic K258 and these lines: {1, 39}, {2, 14267}, {3, 667}, {5, 120}, {518, 23102}, {1026, 2223}, {3293, 16479}, {3573, 21495}, {3675, 25083}, {5091, 21477}, {5880, 16593}, {17284, 24250}, {37828, 50441}
X(51989) = complement of X(14267)
X(51989) = complement of the isogonal conjugate of X(34159)
X(51989) = X(i)-complementary conjugate of X(j) for these (i,j): {2991, 20335}, {34159, 10}
X(51989) = X(105)-Ceva conjugate of X(518)
X(51989) = X(4437)-Dao conjugate of X(3263)
X(51989) = crossdifference of every pair of points on line {659, 3290}
X(51989) = barycentric product X(i)*X(j) for these {i,j}: {518, 32029}, {3263, 38865}
X(51989) = barycentric quotient X(i)/X(j) for these {i,j}: {32029, 2481}, {38865, 105}
X(51989) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 34159, 47080}, {8299, 22116, 1}, {34159, 47048, 3}
X(51990) lies on the cubic K055 and these lines: {6, 1597}, {32, 18877}, {184, 9407}, {287, 1992}, {394, 3284}, {520, 2430}, {577, 20233}, {5065, 14533}, {9064, 10311}, {36429, 41937}, {40065, 40402}
X(51990) = isogonal conjugate of the polar conjugate of X(3426)
X(51990) = X(i)-isoconjugate of X(j) for these (i,j): {19, 44133}, {63, 47392}, {75, 40138}, {92, 376}, {811, 9209}, {823, 9007}, {1969, 26864}
X(51990) = X(i)-Dao conjugate of X(j) for these (i, j): (6, 44133), (206, 40138), (3162, 47392), (17423, 9209), (22391, 376)
X(51990) = crosssum of X(376) and X(40138)
X(51990) = crossdifference of every pair of points on line {1515, 9007}
X(51990) = barycentric product X(i)*X(j) for these {i,j}: {3, 3426}, {184, 36889}, {520, 9064}
X(51990) = barycentric quotient X(i)/X(j) for these {i,j}: {3, 44133}, {25, 47392}, {32, 40138}, {184, 376}, {3049, 9209}, {3426, 264}, {9064, 6528}, {14575, 26864}, {36889, 18022}, {39201, 9007}
X(51991) lies on the cubic K258 and these lines: {1, 88}, {2, 38938}, {3, 3733}, {5, 25652}, {39, 35069}, {3878, 38568}, {6739, 13747}, {6906, 16528}, {25645, 36154}, {27690, 37710}
X(51991) = complement of X(38938)
X(51991) = complement of the isogonal conjugate of X(39166)
X(51991) = X(39166)-complementary conjugate of X(10)
X(51991) = X(759)-Ceva conjugate of X(758)
X(51992) lies on the cubic K787 and these lines: {39, 8864}, {385, 3225}, {699, 805}, {733, 19566}, {1916, 8858}, {3407, 32544}, {8871, 9490}, {14251, 47643}, {32531, 47648}, {36897, 45907}
X(51992) = isogonal conjugate of X(39080)
X(51992) = isogonal conjugate of the complement of X(694)
X(51992) = X(i)-cross conjugate of X(j) for these (i,j): {2, 733}, {6, 3225}, {669, 805}, {47648, 694}
X(51992) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39080}, {75, 51322}, {385, 2227}, {698, 1580}, {1926, 32748}, {1933, 35524}, {1966, 3229}
X(51992) = X(i)-Dao conjugate of X(j) for these (i, j): (3, 39080), (206, 51322), (9467, 3229), (39092, 698)
X(51992) = cevapoint of X(i) and X(j) for these (i,j): {6, 9468}, {694, 47648}, {882, 1084}
X(51992) = trilinear pole of line {694, 5027}
X(51992) = barycentric product X(i)*X(j) for these {i,j}: {694, 3225}, {699, 1916}, {1581, 43761}, {8858, 17980}, {32544, 41517}
X(51992) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39080}, {32, 51322}, {694, 698}, {699, 385}, {1916, 35524}, {1967, 2227}, {3225, 3978}, {8789, 32748}, {9468, 3229}, {17938, 41337}, {43761, 1966}
X(51993) lies on the cubic K934 and these lines: {4, 541}, {30, 182}, {51, 3830}, {381, 1531}, {547, 35254}, {1147, 20424}, {3426, 35403}, {3543, 4846}, {3545, 4549}, {5071, 41465}, {5462, 34725}, {5655, 46261}, {7576, 44080}, {7699, 37907}, {8262, 11178}, {8541, 18494}, {9971, 13754}, {10297, 20192}, {10989, 37470}, {11472, 14269}, {12101, 18376}, {13565, 46730}, {13851, 38335}, {15303, 17702}, {15684, 35237}, {15687, 18390}, {18388, 32267}, {18559, 44077}, {19709, 32620}, {19924, 50008}, {32423, 51140}, {45619, 45622}
X(51993) = midpoint of X(i) and X(j) for these {i,j}: {381, 40909}, {3543, 4846}, {15684, 35237}
X(51993) = reflection of X(i) in X(j) for these {i,j}: {4550, 381}, {35254, 547}
X(51993) = {X(5480),X(47544)}-harmonic conjugate of X(5476)
X(51994) lies on the cubic K934 and these lines: {4, 67}, {22, 7716}, {25, 16776}, {141, 427}, {143, 12585}, {378, 31884}, {394, 11188}, {468, 40670}, {524, 47328}, {599, 6403}, {2393, 23292}, {2854, 8541}, {6676, 9822}, {8263, 41714}, {9969, 15255}, {11746, 19136}, {12220, 31236}, {15577, 51739}, {15809, 34177}, {41618, 45237}, {44668, 45179}
X(51994) = midpoint of X(427) and X(1843)
X(51994) = reflection of X(6676) in X(9822)
X(51994) = barycentric product X(1843)*X(11056)
X(51994) = barycentric quotient X(35325)/X(44061)
X(51994) = {X(1843),X(29959)}-harmonic conjugate of X(41585)
X(51995) lies on the cubic K787 and these lines: {6, 2196}, {9, 22205}, {19, 292}, {39, 3500}, {57, 6377}, {284, 23522}, {333, 39936}, {893, 47642}, {2319, 14936}, {3229, 3512}
X(51995) = isogonal conjugate of X(39930)
X(51995) = X(i)-isoconjugate of X(j) for these (i,j): {1, 39930}, {1423, 14199}, {1428, 17786}, {1429, 32937}, {1447, 3501}, {8927, 39940}, {10030, 34247}, {13588, 16609}
X(51995) = X(3)-Dao conjugate of X(39930)
X(51995) = trilinear pole of line {663, 20460}
X(51995) = barycentric product X(i)*X(j) for these {i,j}: {1, 43748}, {694, 39936}, {3500, 4876}
X(51995) = barycentric quotient X(i)/X(j) for these {i,j}: {6, 39930}, {2053, 14199}, {3500, 10030}, {4876, 17786}, {7077, 32937}, {18265, 34247}, {39936, 3978}, {43748, 75}
X(51996) lies on the cubic K934 and these lines: {30, 3527}, {631, 9815}, {1656, 11821}, {3091, 15741}, {3522, 3618}, {5422, 16936}, {11433, 17578}, {11745, 37669}, {17538, 43651}, {18296, 22334}, {19136, 27082}
X(51996) = midpoint of X(3091) and X(15741)
X(51996) = reflection of X(i) in X(j) for these {i,j}: {631, 9815}, {11821, 1656}
X(51997) lies on the cubics K782 and K787 and these lines: {4, 39}, {6, 46317}, {32, 26714}, {263, 694}, {327, 31276}, {446, 44453}, {511, 40803}, {3053, 3224}, {3552, 39681}, {9781, 46305}
X(51997) = X(25)-Ceva conjugate of X(51338)
X(51997) = X(3403)-isoconjugate of X(47643)
X(51997) = barycentric product X(i)*X(j) for these {i,j}: {262, 11328}, {263, 18906}, {2186, 19591}
X(51997) = barycentric quotient X(i)/X(j) for these {i,j}: {263, 19222}, {6234, 8842}, {11328, 183}, {18906, 20023}, {19591, 3403}, {45907, 23878}, {46319, 47643}
X(51997) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {39, 14252, 43718}, {262, 14252, 39}
X(51998) lies on the cubic K934 and these lines: {4, 64}, {30, 5972}, {143, 12102}, {184, 5893}, {382, 51425}, {468, 50709}, {546, 43604}, {1147, 3627}, {1503, 13473}, {1514, 14157}, {1539, 44665}, {1992, 36990}, {2777, 44872}, {3146, 15748}, {3853, 16621}, {10151, 11598}, {15811, 50688}, {16252, 35490}, {18296, 22334}, {23292, 44438}, {37853, 44912}, {41362, 45010}
X(51998) = midpoint of X(i) and X(j) for these {i,j}: {382, 51425}, {10151, 13202}
X(51998) = reflection of X(i) in X(j) for these {i,j}: {37853, 44912}, {47296, 10151}
X(51998) = X(11598)-Dao conjugate of X(3532)
X(51998) = crosspoint of X(253) and X(46206)
X(51998) = crosssum of X(154) and X(34569)
X(51998) = barycentric product X(i)*X(j) for these {i,j}: {3146, 47296}, {18594, 18699}, {33630, 40996}
X(51998) = barycentric quotient X(i)/X(j) for these {i,j}: {3146, 44877}, {10151, 38253}, {21663, 36609}, {40135, 3532}, {47296, 35510}
X(51998) = {X(3146),X(15751)}-harmonic conjugate of X(27082)
X(51999) lies on the cubic K258 and these lines: {2, 14263}, {3, 669}, {5, 126}, {39, 597}, {384, 31128}, {524, 23106}, {631, 47046}, {3788, 46986}, {3933, 23992}, {6390, 21906}, {7664, 7807}, {7789, 14357}, {9177, 32459}, {27088, 38239}
X(51999) = complement of X(14263)
X(51999) = complement of the isogonal conjugate of X(34161)
X(51999) = X(i)-complementary conjugate of X(j) for these (i,j): {23889, 21905}, {34161, 10}, {41909, 4892}
X(51999) = X(111)-Ceva conjugate of X(524)
X(51999) = X(36792)-Dao conjugate of X(3266)
X(51999) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {3, 34161, 47077}, {2482, 40517, 39}, {34161, 47047, 3}
X(52000) lies on the cubic K934 and these lines: {3, 44405}, {4, 51}, {6, 18532}, {24, 52}, {25, 568}, {30, 1112}, {110, 37951}, {112, 50387}, {113, 403}, {143, 3575}, {186, 249}, {235, 6102}, {378, 5422}, {427, 5946}, {468, 1154}, {546, 43823}, {973, 11745}, {974, 15311}, {1199, 46363}, {1216, 10018}, {1495, 12227}, {1593, 37481}, {1594, 5462}, {1885, 13630}, {1992, 6403}, {1994, 45173}, {2070, 34397}, {2071, 15472}, {2072, 16222}, {2781, 16227}, {2979, 35486}, {3060, 18533}, {3147, 11412}, {3515, 6243}, {3518, 16625}, {3520, 9729}, {3541, 15043}, {3542, 5889}, {3581, 37954}, {3618, 15045}, {5446, 6240}, {5476, 12294}, {5562, 7505}, {5663, 10151}, {5892, 37118}, {5907, 16868}, {5943, 7577}, {6143, 11695}, {6146, 41589}, {6152, 10115}, {6242, 47486}, {6746, 6756}, {7576, 47328}, {7722, 10706}, {8745, 50647}, {9826, 10257}, {9967, 44837}, {10019, 45959}, {10095, 23047}, {10111, 12140}, {10575, 35490}, {10625, 32534}, {10982, 15138}, {11410, 40280}, {11438, 44269}, {11456, 41580}, {11793, 14940}, {11802, 12300}, {11806, 12292}, {12085, 45010}, {12162, 35488}, {12235, 14516}, {12358, 44911}, {13148, 37984}, {13289, 38534}, {13293, 13417}, {13321, 18494}, {13348, 17506}, {13391, 37931}, {13567, 45179}, {13598, 34797}, {14581, 15544}, {14831, 44079}, {14865, 15012}, {15010, 15030}, {15126, 26879}, {15473, 18400}, {15644, 21844}, {15646, 25487}, {15750, 37484}, {16836, 35473}, {18322, 44090}, {18559, 21849}, {18560, 40647}, {19136, 19161}, {19504, 22115}, {20791, 35485}, {21243, 45178}, {23039, 37453}, {25711, 44665}, {26206, 37511}, {26937, 43896}, {32110, 37970}, {32225, 37943}, {34146, 46430}, {34148, 45172}, {34783, 37197}, {35471, 45186}, {40111, 44272}
X(52000) = midpoint of X(i) and X(j) for these {i,j}: {52, 51393}, {403, 1986}, {13417, 21663}
X(52000) = reflection of X(i) in X(j) for these {i,j}: {403, 44084}, {10257, 9826}, {12358, 44911}
X(52000) = X(i)-isoconjugate of X(j) for these (i,j): {68, 36053}, {91, 5504}, {1820, 2986}, {15421, 36145}
X(52000) = X(i)-Dao conjugate of X(j) for these (i, j): (113, 68), (135, 15328), (34116, 5504), (34834, 20563), (35588, 520), (39013, 15421)
X(52000) = crosspoint of X(4) and X(38534)
X(52000) = crosssum of X(3) and X(2072)
X(52000) = barycentric product X(i)*X(j) for these {i,j}: {24, 3580}, {317, 3003}, {403, 1993}, {571, 44138}, {924, 16237}, {1725, 1748}, {1986, 18883}, {7763, 44084}, {11547, 13754}
X(52000) = barycentric quotient X(i)/X(j) for these {i,j}: {24, 2986}, {317, 40832}, {403, 5392}, {571, 5504}, {924, 15421}, {1986, 37802}, {3003, 68}, {3580, 20563}, {6753, 15328}, {8745, 1300}, {16237, 46134}, {41679, 18878}, {44077, 14910}, {44084, 2165}
X(52000) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {24, 2904, 1147}, {51, 185, 18390}, {186, 15463, 51394}, {3567, 5890, 11433}, {6756, 16881, 6746}, {19504, 37917, 22115}
| PART 1: | Introduction and Centers X(1) - X(1000) | PART 2: | Centers X(1001) - X(3000) | PART 3: | Centers X(3001) - X(5000) |
| PART 4: | Centers X(5001) - X(7000) | PART 5: | Centers X(7001) - X(10000) | PART 6: | Centers X(10001) - X(12000) |
| PART 7: | Centers X(12001) - X(14000) | PART 8: | Centers X(14001) - X(16000) | PART 9: | Centers X(16001) - X(18000) |
| PART 10: | Centers X(18001) - X(20000) | PART 11: | Centers X(20001) - X(22000) | PART 12: | Centers X(22001) - X(24000) |
| PART 13: | Centers X(24001) - X(26000) | PART 14: | Centers X(26001) - X(28000) | PART 15: | Centers X(28001) - X(30000) |
| PART 16: | Centers X(30001) - X(32000) | PART 17: | Centers X(32001) - X(34000) | PART 18: | Centers X(34001) - X(36000) |
| PART 19: | Centers X(36001) - X(38000) | PART 20: | Centers X(38001) - X(40000) | PART 21: | Centers X(40001) - X(42000) |
| PART 22: | Centers X(42001) - X(44000) | PART 23: | Centers X(44001) - X(46000) | PART 24: | Centers X(46001) - X(48000) |
| PART 25: | Centers X(48001) - X(50000) | PART 26: | Centers X(50001) - X(52000) | PART 27: | Centers X(52001) - X(54000) |
| PART 28: | Centers X(54001) - X(56000) | PART 29: | Centers X(56001) - X(58000) | PART 30: | Centers X(58001) - X(60000) |
| PART 31: | Centers X(60001) - X(62000) | PART 32: | Centers X(62001) - X(64000) | PART 33: | Centers X(64001) - X(66000) |
| PART 34: | Centers X(66001) - X(68000) | PART 35: | Centers X(68001) - X(70000) | PART 36: | Centers X(70001) - X(72000) |
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