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X(2), X(6), X(262), X(511), X(574), X(671), X(694)

Foci of the Steiner in-ellipse, see also Table 48.

Infinite points of the Steiner ellipses

K353 is the unique circum-cubic passing through the foci, the center and the infinite points of the Steiner inscribed ellipse. See the similar cubic K715 related with the Steiner circum-ellipse.

K353 has one real asymptote parallel to the Brocard line OK.

K353 belongs to the pencil generated by the Thomson cubic K002 and the Brocard (second) cubic K018 that also contains K287.

Its equation shows that it also belongs to the pencil of cubics generated by K128 = pK(X6, X385) and K354 = pK(X694, X1916). This pencil contains a third pK which is K357 = pK(X511, X2). The nine common points of all these cubics are A, B, C, G, K, X(511), X(694) and the infinite points of the Steiner ellipses.

The isotomic transform of K353 is K356 and its isogonal transform is K705.

K353 is spK(X385, X2) in CL055.