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too complicated to be written here. Click on the link to download a text file. 

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 PseudoPivotal 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 circumconic 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. 
