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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 |
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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 H-Ceva conjugate of M). See a generalization in CL041. K1406 is the transform of K718 under the symbolic substitution SS{a→ √a}. K718 is the cornerstone of a group of 12 cubics all related between themselves under isogonal, isotomic, G-Hirst 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. They are anharmonically equivalent. See also Table 68. A similar group of weak cubics is obtained when K718 is replaced with K323. See also Table 67. |
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