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X(3), X(4), X(5), X(5403), X(5404), X(8798) midpoints of BC, CA, AB and AH, BH, CH reflections of A, B, C in X(5) i.e. centers of the Johnson circles points on the circumcircle and on the Napoleon cubic. infinite points of the McCay cubic points Na, Nb, Nc mentioned in Central Cubics X3OAP points, see Table 53 

We meet this K60++ cubic in a paper by Musselman (see bibliography) and in a totally different context in Special isocubics ยง6.5.3. K026 is a central equilateral cubic with center X(5), the nine point center, with inflexional tangent X(5)X(51) i.e. the Euler line of the orthic triangle. Its three asymptotes are perpendicular to the sidelines of the Morley triangle and parallel to those of the McCay cubic. It is the homothetic of K080 = KO++ under h(H,1/2) and the isogonal transform of K361. K026 is also psK(X51, X2, X3) in PseudoPivotal Cubics and Poristic Triangles. See also Table 50. K026 is spK(X3, X140) as in CL055. Locus properties :

