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X(1), X(2), X(8), X(40), X(57), X(144), X(189), X(366), X(3062)

vertices of the cevian triangle of X(8), the Nagel point

vertices of the anticevian triangle of X(366)

points at infinity of the Thomson cubic.

K308 is another example of pK with asymptotes parallel to those of the Thomson and Lucas cubics. See also K181 and "Asymptotic Directions of Pivotal Isocubics" in the downloads page.

K308 is the locus of point P such that the trilinear polar of P is perpendicular to the line PX(40). See CL040 for a generalization.

The isogonal transform of K308 is K760 = pK(X31, X9) and its isotomic transform is pK(X75, X312).