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K724

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X(74), X(265), X(5961), X(6344), X(11060)

X(1989)-isoconjugates of the infinite points of the McCay cubic K003, vertices of an equilateral (blue) triangle

vertices of the (yellow) cevian triangle of X(94)

infinite points of pK(X3003, X12383) and the stelloid pK(X11079, X74)

two imaginary points on (O) and on the perpendicular bisector of X(265), X(5961)

K724 is a nodal stelloid with node X(265) which is the double pivot, the simple pivot being X(5961). The nodal tangents are the parallels at X(265) to the asymptotes of the Jerabek hyperbola.

K724 is the X(1989)-isoconjugate of the third Musselman cubic K028. It follows that the circum-conic (C1989) with perspector X(1989) meets K724 again at the vertices of an equilateral triangle whose circumcircle passes through the pivots X(265) and X(5961).

More generally, any isoconjugation with pole on the circum-conic with perspector X(51) maps the infinite points of K003 to the vertices of an equilateral triangle. This latter circum-conic contains X(112), X(1625), X(1987), X(1989).

The asymptotes of K724 concur at X = X(14854).

See K028 for other stelloidal properties.