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X(2), X(4), X(114), X(193), X(264), X(287), X(297), X(325), X(511), X(1916) infinite points of the Steiner ellipses S = isotomic conjugate of X(3564) vertices of the orthic triangle 

K718 is the only pK with pivot H passing through the infinite points of the Steiner ellipses. See the related CL019. It is the isogonal pK with pivot X(325) with respect to the orthic triangle or, equivalently, the locus of M such that X(325), M and H/M are collinear (H/M is the HCeva conjugate of M). See a generalization in CL041. K718 is the cornerstone of a group of 12 cubics all related between themselves under isogonal, isotomic, GHirst conjugations – denoted g, t, h in the following diagram – or a product of these such as e = gtg which is X(32)isoconjugation. All these cubics are strong cubics and contain a good number of ETC centers. A similar group of weak cubics is obtained when K718 is replaced with K323. 
