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X(4), X(847)

A', B', C' : reflections of H in the sidelines of ABC

infinite points of the McCay cubic

K580 is a K60+ (or a stelloid) with three real asymptotes parallel to those of the McCay cubic and concurring at X(568).

Its hessian cubic is a focal cubic with focus X(568) passing through H and X(186). Hence H is a flex on K580 and the tangent is the Euler line.

K580 is spK(X3, X6102) as in CL055.