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X(2), X(3), X(154), X(3357), X(9756), X(47052)

infinite points of K004

vertices of the Thomson triangle Q1Q2Q3

vertices of the CircumTangential triangle T1T2T3

Geometric properties :

X1266 is the Thomson-isogonal transform of the stelloid K581.

It has three real (not concurring) asymptotes perpendicular to the sidelines of ABC i.e. parallel to those of the Darboux cubic K004. The two cubics meet again on the rectangular hyperbola passing through X3, X6, X2574, X2575, X3146.

K1266 and K581 meet at O, G, Q1, Q2, Q3 and four other points that lie on two perpendicular secant at X(5).

See Table 25 and Table 56.