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X(4), X(17), X(18) points Y and Y' on the Euler line reflections A', B', C' of A, B, C in the sidelines of ABC points at infinity of the Napoleon cubic 

This cubic belongs to the pencil of cubics containing the Neuberg cubic, the Soddy cubic and the union of the three altitudes. See "Two Remarkable Pencils..." in the Downloads page. It also belongs to the pencil of cubics generated by the Napoleon cubic K005 and the union of the line at infinity with the Kiepert hyperbola. This pencil also contains K948. Its asymptotes are parallel to those of the Napoleon cubic. 
