X(2), X(6), X(599)
foci of the Steiner in-ellipse, see also Table 48.
points at infinity of the Grebe cubic K102
common points of the circumcircle and pK(X6, X599)
The Thomson cubic K002 and the Brocard (second) cubic K018 are both isogonal isocubics which pass through G, K and the (four) foci of the Steiner in-ellipse. Hence they generate a pencil of circum-cubics through the same points. This pencil contains K287, a central K++ with center G and also K353.
The three asymptotes are the parallels at G to those of the Grebe cubic K102. It meets the circumcircle at the same points as pK(X6, X599).