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X(4), X(30), X(113), X(186), X(1511), X(2914), X(,3471), X(38936)

vertices of the orthic triangle

isogonal conjugates of the Ix-anticevian points. See Table 23.

infinite points of K668 = pK(X6, X265)

points of pK(X6, X113) on (O)

two (real or not) points on the Fermat line, on the circum-conic with perspector X(526), on the two pKs above

Geometric properties :

K1157 is the cubic with pivot X(4), isopivot X(1511) and pole their barycentric product X(39176).

K1157 is the Laplacian L of the quintic Q5 which is the isogonal transform of the quartic Q4, locus of P such that X(74), P, P*/P are collinear. Here, P* is the isogonal conjugate of P and P*/P is the P*-Ceva conjugate of P.

If X(74) is replaced by another point M, we obtain similar sets {M, Q4, Q5, L) such as {X3, Q002, Q003, K005}, {X6, Q043, Q042, K754}, {X4, Q083, Q084, K373}. Note that, for any point M, the cubic L is a circum-cubic passing through the isogonal conjugates of the Ix-anticevian points.

When M lies on the Neuberg cubic K001, L is a pK with pole on K1049, pivot on K005, isopivot on K073.