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X(6), X(13), X(14), X(111), X(543), X(671), X(6094)

O(X111) is the orthopivotal cubic with orthopivot the Parry point. See the FG paper "Orthocorrespondence and orthopivotal cubics" in the Downloads page and Orthopivotal cubics in the glossary.

The singular focus is the Lemoine point K whose polar conic is the circle passing through X(6), X(23), X(111), X(381), X(671), X(2080).

K063 is the locus of contacts of tangents drawn from K to the circles passing through X(111) and X(671).

The isogonal transform of K063 is K435, a central circular cubic.