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X(30), X(74), X(265), X(477)

K597 is a nodal stelloid with node the Tixier antipode X(477) which is a double pivot. The simple pivot is X(265). Hence, any circle passing through X(477) and X(265) meets the cubic again at three points which are the vertices of an equilateral triangle. See K028 for other stelloidal properties.

It has three real asymptotes concurring at X = X(14851). One is parallel to the Euler line and the remaining two are obtained under rotations about X with angles +/-60°.