ETC

X(72409) = (name pending)

Barycentrics    a^2*(2*a^10 - 7*a^8*b^2 + 5*a^6*b^4 + 5*a^4*b^6 - 7*a^2*b^8 + 2*b^10 + 8*a^8*c^2 + 8*a^6*b^2*c^2 - 72*a^4*b^4*c^2 + 8*a^2*b^6*c^2 + 8*b^8*c^2 - 55*a^6*c^4 + 36*a^4*b^2*c^4 + 36*a^2*b^4*c^4 - 55*b^6*c^4 + 50*a^4*c^6 - 16*a^2*b^2*c^6 + 50*b^4*c^6 - a^2*c^8 - b^2*c^8 - 4*c^10)*(2*a^10 + 8*a^8*b^2 - 55*a^6*b^4 + 50*a^4*b^6 - a^2*b^8 - 4*b^10 - 7*a^8*c^2 + 8*a^6*b^2*c^2 + 36*a^4*b^4*c^2 - 16*a^2*b^6*c^2 - b^8*c^2 + 5*a^6*c^4 - 72*a^4*b^2*c^4 + 36*a^2*b^4*c^4 + 50*b^6*c^4 + 5*a^4*c^6 + 8*a^2*b^2*c^6 - 55*b^4*c^6 - 7*a^2*c^8 + 8*b^2*c^8 + 2*c^10) : :

Antreas Hatzipolakis and Ercole Suppa, euclid 9480.

X(72409) lies on the circumcircle and these lines: { }

X(72409) = intersection, other than A, B, C, of the circumconics : {{A, B, C, X (6), X (47588)}, {A, B, C, X (74), X (98)}, {A, B, C, X (13377), X (14490)}}

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X(72410) = X(2)X(47589)∩X(381)X(31748)

Barycentrics    -4*a^10-37*a^8*b^2+185*a^6*b^4-109*a^4*b^6-73*a^2*b^8+38*b^10-37*a^8*c^2-70*a^6*b^2*c^2+225*a^4*b^4*c^2+152*a^2*b^6*c^2-142*b^8*c^2+185*a^6*c^4+225*a^4*b^2*c^4-126*a^2*b^4*c^4+104*b^6*c^4-109*a^4*c^6+152*a^2*b^2*c^6+104*b^4*c^6-73*a^2*c^8-142*b^2*c^8+38*c^10 : :
X(72410) = X[2]+2*X[47589], 2*X[2]+X[50730], 4*X[47589]-X[50730], 2*X[381]+X[31748], 5*X[381]-2*X[46673], 5*X[31748]+4*X[46673], 5*X[1656]+4*X[47591], 7*X[3090]+2*X[47590], 2*X[3545]-X[13378], 2*X[14866]+X[50729], 2*X[46732]-5*X[61985]

Antreas Hatzipolakis and Ercole Suppa, euclid 9480.

X(72410) lies on these lines: {2, 47589}, {381, 31748}, {1656, 47591}, {3090, 47590}, {3545, 13378}, {3839, 11645}, {5056, 47592}, {14866, 50729}, {46732, 61985}

X(72410) = reflection of X(i) in X(j) for these {i,j}: {13378, 3545}
X(72410) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {2, 47589, 50730}

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