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X(4), X(550), X(1657) E = reflection of O in X(20) = X(1657) reflections A', B', C' of A, B, C in the sidelines of ABC 

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. 
