X(4), X(5), X(143), X(14374), X(14375), X(14254), X(14632), X(14633)
projections of X(5) on the altitudes
infinite points of the McCay cubic
This is a generalized Lemoine cubic as seen in the FG paper (See the Downloads page).
It is the only cubic of this type which is a K60+ i.e. a stelloid. One group of pivots consists in X(5) (counted twice) and X(143).
Its asymptotes are parallel to those of the McCay cubic and concur at X = X(13364), the homothetic of X(143) under h(X5, 1/3). It follows that any line passing through X meets K054 at three points whose isobarycenter is X.
K054 is spK(X3, X12006) as in CL055 where X(12006) is the midpoint of X140-X389.