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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
X3-OAP 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 §6.5.3.
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 Pseudo-Pivotal Cubics and Poristic Triangles. See also Table 50 and Table 76.
K026 is spK(X3, X140) as in CL055. See also Table 54 where K026 is mentioned in one line and three columns showing that it belongs to four pencils of cubics generated by :
• K006 and K187, line Q = X140,
• K002 and K009, column P = aaQ,
• K003 and the union of the line at infinity with the Jerabek hyperbola, column P = X3,
• K006 and K080, column P = S.
Locus properties :