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X(3), X(4) vertices of the circumtangential triangle infinite points of K024 feet U, V, W of the trilinear polar of X(1993) : U lies on the perpendicular at O to AO. Oa = OA /\ HU, Ob, Oc similarly Ha = HA /\ OU, Hb, Hc similarly 

K105 is an isogonal nK60 with root X(1993), the orthocorrespondent of O. See Special Isocubics ยง7.2.2. It is a member of the class CL004 of cubics. Its three real asymptotes are parallel to the sidelines of the Morley triangle and bound an equilateral triangle with center G, homothetic to the circumtangential triangle under h(H,2/3).See a generalization in the page K687. K105 is :
Other geometric properties :

