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X(2), X(3), X(4), X(262)

infinite points of the McCay cubic

points of the Thomson cubic on the circumcircle i.e. vertices of the Thomson triangle

foci of the inscribed conic with center X(549), midpoint of GO.

K581 is a K60+ (or a stelloid) with three real asymptotes parallel to those of the McCay cubic and concurring at X = X(5055), on the Euler line such that OX = 4/9 OH.

K581 is a member of the pencil generated by the Thomson cubic K002 and the union of the circumcircle and the Euler line. See also K615.

K581 is spK(X3, X549) in CL055. See also K759.