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X(1), X(10), X(65), X(145)

vertices of the intouch triangle

infinite points of the internal bisectors

common points of the circumcircle and pK(X6, X65)

K571 is an example of cubic psK passing through the vertices of two poristic equilateral triangles. See Pseudo-Pivotal Cubics and Poristic Triangles.

The sidelines of these triangles are parallel to those of the Morley triangle.

The equilateral triangle Q1Q2Q3 is inscribed in K571, in the circum-conic with center X(10) and perspector X(37), in the rectangular hyperbola passing through X(1), X(65), X(73), X(1469), X(2574), X(2575), X(3214).

K571 has three real asymptotes parallel to the (internal) bisectors of ABC.