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X(4), X(20), X(140), X(15318), X(15644)

imaginary foci of the Brocard ellipse i.e. common points of the Brocard axis and the Kiepert hyperbola

CPCC or H-cevian (red) points, see Table 11

infinite points of the McCay cubic

points of pK(X6, X15644) on (O)

K268 is the Orion cubic K(X140), the only equilateral CPCC cubic. See Table 11 : CPCC points related curves.

It belongs to the pencil of cubics generated by the Darboux cubic and the Lucas cubic. See table 15.

It is also a member of the pencil of stelloids generated by the McCay cubic and the union of the line at infinity with the Kiepert hyperbola. See Table 51.

K268 is in fact a stelloid with three real asymptotes concurring at the point X = X(3819) and parallel to those of the McCay cubic. X lies on the lines X(2)X(511) and X(3)X(64). See also the pencil mentioned in page K071.

K268 meets the circumcircle at the same points as the isogonal pK with pivot X(15644), the reflection of X(389) about X(3), which also lies on K268.

K268 is also spK(X3, X13348) as in CL055.