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X(9), X(57), X(517), X(1156), X(2161)

Foci of the Mandart ellipse (see Generalized Mandart Conics in the Downloads page and also K040)

infinite points of the Mandart circum-ellipse

K716 is the unique circum-cubic passing through the center, the foci and the infinite points of the Mandart circum-ellipse with perspector X(1).

K716 meets the line at infinity at the same points as pK(X6, X3218) = K717.

See K002, property 23 for a generalization and also the analogous cubic K715.