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X(3), X(2041), X(2042), X(15318), X(16266)

infinite points of K003

points of pK(X6, X14216) on the circumcircle

A'B'C' : cevian triangle of X(15318)

Geometric properties :

K956 is the only pK60 with isopivot X(3).

It has three real asymptotes parallel to those of the McCay cubic K003 and bounding an equilateral triangle with center X(1853).

The polar conic of X(3) is the circum-conic (C1) with center X(2972).

K956 meets K003 at six finite points namely A, B, C, X(3) and two other isoconjugate points M, N (real when ABC is acutangle) which lie on the line X(216), X(631), X(1075), etc, and on the circum-conic (C2) with perspector X(520), the isoconjugate of the previous line.


More generally, there is one and only one pK60 with given isopivot Q.

Its asymptotes are parallel to those of K003 (resp. K024) when Q lies on K026 (resp. K607).

It is a stelloid (a pK60+) when Q lies on K060.