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X(2), X(4), X(3146) reflections A', B', C' of A, B, C in the sidelines of ABC images of A, B, C under h(G,4) vertices of pedal triangle of L1 image of K = X(6) under h(G,10) points at infinity of the Thomson cubic 

This cubic belongs to the pencil of cubics containing the Neuberg cubic, the Soddy cubic and the union of the three altitudes. See "Two Remarkable Pencils..." in the Downloads page. Its asymptotes are parallel to those of the Thomson cubic. See the related K127. 
