X(4), X(6), X(32), X(218), X(1992)
vertices of the pedal triangle of K
projections of K on the altitudes
K055 is a generalized Lemoine cubic as seen in the FG paper.
It is a nodal cubic with node K and the nodal tangents are parallel to the asymptotes of the Jerabek hyperbola.
It has the same asymptotic directions as K169 = pK(X6, X69) and pK(X2, X315).
It meets the circumcircle at the same points as the isogonal pK whose pivot is the intersection of the lines X(3)X(194) and X(6)X(538).
The isogonal transform of K055 is K657.