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P = X(7) and its isotomic conjugate P' = X(8), X(883), X(885).

ten points obtained from all the permutations of the coordinates of P and P'.

points at infinity of ABC sidelines (inflexion points)

It is the locus of point M such that the cevian triangles of X(7) and M have the same area. See "Tucker cubics" in the Downloads page.