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X(3), X(5), X(64), X(3146)

infinite points of the McCay cubic K003

vertices A', B', C' of the cevian triangle of X(253), the perspector of the inconic with center H.

K558 is an equilateral cubic with three real asymptotes parallel to those of the McCay cubic and forming a triangle with center the homothetic of X(64) under the homothety with center H and ratio 1/6.

See Pseudo-Pivotal Cubics and Poristic Triangles.