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X(1), X(65), X(946), X(2089), X10481), X(10939)

A'B'C' = intouch triangle

infinite points of K414

K666 is the cubic L(X1) in the paper "Another kind of Lemoine cubics".

Let (Ka) be the decomposed cubic which is the union of the sidelines AB, AC and the line X(1)A'. Define (Kb), (Kc) likewise. The Jacobian of the net of cubics generated by (Ka), (Kb), (Kc) is K666. In other words, K666 is the locus of M whose polar lines in (Ka), (Kb), (Kc) concur.