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X(4), X(5), X(382) reflections A', B', C' of A, B, C in the sidelines of ABC Ixanticevian points : see table 23 

This cubic belongs to the pencil of cubics containing the Neuberg cubic, the Soddy cubic and the union of the three altitudes and also to the pencil of cubics containing the Napoleon cubic and the Kn cubic. See "Two Remarkable Pencils..." in the Downloads page. It follows from the definitions found in this paper that this cubic is the locus of point P such that :
See also Hyacinthos #27709. 
