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X(13), X(14), X(530)

O(X13) is the orthopivotal cubic with orthopivot the first Fermat point. It is a strophoid. See the FG paper "Orthocorrespondence and orthopivotal cubics" in the Downloads page and Orthopivotal cubics in the glossary.

See also CL038, the class of non-isogonal circum-strophoids.