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X(2), X(13), X(14), X(30), X(1494), X(3163)

midpoints of ABC

infinite points of the Steiner ellipses

G-Ceva conjugates of the Fermat points

K472 is the locus of point M such that M, G/M, X(30) or M, M^2, X(30) are collinear where G/M is the G-Ceva conjugate of M and M^2 the barycentric square of M. Recall that G/M is the center of the circum-conic with perspector M and that M^2 is the pole of G in the pencil of conics passing through M and the vertices of the anticevian triangle of M.

K472 has one real asymptote parallel to the Euler line at X(3163), the barycentric square of X(30), and two imaginary asymptotes meeting at the reflection X of X(3163) about G.

The Brocard axis OK is the orthic line of K472 i.e. the polar conic of every point on OK is a rectangular hyperbola.

See the analogous cubic K357 = pK(X511, X2) and also K419a, K419b.

The anticomplement of K472 is K860 = pK(X2, X30).