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∑ a (a^3 + a b c - b^3 - c^3) x (c^2 y^2 - b^2 z^2) = 0

X(1), X(9), X(57), X(846), X(1282), X(1757), X(1929), X(3509), X(3512), X(9499), X(13610), X(17738), X(17739), X(18206)

isogonal conjugates of X(17738), X(17739), X(18206)

excenters

vertices of the cevian triangle of X(3509)

other points below

Geometric properties :

An isogonal pK anharmonically equivalent to K131 must have its pivot on the rectangular diagonal hyperbola passing through the in/excenters and the centers X(3509), X(3510). These two latter points are the pivots of K1025, K1026 respectively. See also Table 67.

These two cubics meet at A, B, C, the four in/excenters and two other isogonal conjugate points P, P* on the line passing through the pivots and X(694).

These points are very simple with 1st barycentrics P = a (a^2 - b c) / (a^2 + b c) and P* = a (a^2 + b c) / (a^2 - b c) respectively.

K1025 is the barycentric product X(1) x K1002.