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.
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.
K353 is spK(X385, X2) in CL055.