ETC

X(72980) = X(3)X(133)∩X(20)X(122)

Barycentrics    (3*a^4 - 2*a^2*b^2 - b^4 - 2*a^2*c^2 + 2*b^2*c^2 - c^4)*(2*a^12 - 2*a^10*b^2 - 11*a^8*b^4 + 24*a^6*b^6 - 16*a^4*b^8 + 2*a^2*b^10 + b^12 - 2*a^10*c^2 + 24*a^8*b^2*c^2 - 24*a^6*b^4*c^2 - 16*a^4*b^6*c^2 + 18*a^2*b^8*c^2 - 11*a^8*c^4 - 24*a^6*b^2*c^4 + 64*a^4*b^4*c^4 - 20*a^2*b^6*c^4 - 9*b^8*c^4 + 24*a^6*c^6 - 16*a^4*b^2*c^6 - 20*a^2*b^4*c^6 + 16*b^6*c^6 - 16*a^4*c^8 + 18*a^2*b^2*c^8 - 9*b^4*c^8 + 2*a^2*c^10 + c^12) : :
X(72980) = 3 X[3] - X[133], 5 X[3] - X[22337], 7 X[3] - 3 X[57301], 2 X[133] - 3 X[6716], 5 X[133] - 3 X[22337], 7 X[133] - 9 X[57301], X[133] + 3 X[63411], 5 X[6716] - 2 X[22337], 7 X[6716] - 6 X[57301], X[6716] + 2 X[63411], 7 X[22337] - 15 X[57301], X[22337] + 5 X[63411], 3 X[57301] + 7 X[63411], 3 X[20] + X[10152], X[20] + 3 X[38714], 3 X[122] - X[10152], X[122] - 3 X[38714], X[10152] - 9 X[38714], 3 X[34842] - 2 X[61583], X[107] - 5 X[3522], 3 X[376] + X[1294], 3 X[376] - X[3184], 9 X[376] - X[5667], 3 X[1294] + X[5667], 3 X[3184] - X[5667], X[382] - 3 X[36520], 3 X[549] - 2 X[58431], 5 X[631] - X[44985], X[1515] - 3 X[12096], X[1657] + 3 X[57329], 7 X[3528] - 3 X[23239], 3 X[3534] + X[10745], 3 X[5892] - 2 X[58530], 3 X[8703] - X[38605], 3 X[9778] + X[10701], 9 X[10304] - X[34549], X[10714] + 3 X[62120], 3 X[11589] - X[51358], 9 X[15688] - X[38577], 5 X[15696] - X[23240], X[23241] - 13 X[62117], X[34186] + 7 X[50693], 3 X[34200] - X[61569], X[38591] + 7 X[62100], X[52057] - 7 X[62100], X[38672] - 13 X[62092], X[38686] + 11 X[62097], X[51532] - 7 X[62091], 5 X[62104] + X[67836]

Antreas Hatzipolakis and Peter Moses, euclid 10248.

X(72980) lies on these lines: {2, 38956}, {3, 133}, {4, 58424}, {20, 122}, {22, 40082}, {30, 34842}, {107, 3522}, {112, 376}, {382, 36520}, {516, 11732}, {548, 52869}, {549, 58431}, {550, 1511}, {631, 44985}, {1515, 12096}, {1657, 57329}, {2790, 38736}, {2797, 38747}, {2803, 38759}, {2811, 38771}, {2816, 38783}, {2847, 34808}, {3528, 23239}, {3530, 61592}, {3534, 10745}, {5892, 58530}, {8703, 20207}, {9033, 37853}, {9528, 52829}, {9729, 68071}, {9778, 10701}, {10304, 34549}, {10714, 62120}, {11589, 51358}, {13598, 58524}, {14703, 35243}, {15688, 38577}, {15696, 23240}, {15704, 49117}, {17704, 58511}, {23241, 62117}, {33702, 33897}, {34186, 50693}, {34200, 61569}, {34841, 57626}, {35241, 47087}, {38591, 52057}, {38672, 62092}, {38686, 62097}, {44248, 68441}, {44280, 71391}, {51532, 62091}, {62104, 67836}

X(72980) = midpoint of X(i) and X(j) for these {i,j}: {3, 63411}, {20, 122}, {550, 38621}, {1294, 3184}, {15704, 49117}, {35241, 47087}, {38591, 52057}
X(72980) = reflection of X(i) in X(j) for these {i,j}: {4, 58424}, {6716, 3}, {13598, 58524}, {58511, 17704}, {61592, 3530}, {68071, 9729}
X(72980) = complement of X(38956)
X(72980) = X(i)-complementary conjugate of X(j) for these (i,j): {35200, 3184}, {40353, 1427}
X(72980) = X(4240)-Ceva conjugate of X(8057)
X(72980) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {20, 38714, 122}, {376, 1294, 3184}

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