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X(2), X(25), X(278), X(1073), X(1993), X(2052), X(3190), X(17776), X(18018), X(34277), X(39116), X(40358), X(56549), X(57485), X(57486), X(57487), X(57488), X(57489), X(57490), X(57491), X(57492), X(57493), X(57494), X(57495), X(57496), X(57497), X(57498), X(57499), X(57500), X(57518), X(60000), X(60001), X(60002), X(69875), X(69876), X(69877)

The Shao-Cheng Liu cubic is defined in Trilinear polars and antiparallels, Forum Geometricorum, vol.9, pp.283--290, 2009.

It is the isogonal transform of K260 and the H-isoconjugate of K028.

K555 is the pseudo-pivotal cubic psK(X4, X264, X2). See Pseudo-Pivotal Cubics and Poristic Triangles.

The tangents at A, B, C are the symmedians. K555 meets (O) again at Q1, Q2, Q3 which lie on the rectangular hyperbola passing through X4, X858, X1007, X2696, X5913, with center X31655. The tangents at Q1, Q2, Q3 concur at X on the lines {X25, X187}, {X111, X378}, {X112, X1995}, etc, SEARCH = -5.98581395429210. X = a^2 (a^2+b^2-c^2) (a^2-b^2+c^2) (a^6-3 a^4 b^2-a^2 b^4+3 b^6-3 a^4 c^2+14 a^2 b^2 c^2-11 b^4 c^2-a^2 c^4-11 b^2 c^4+3 c^6) : : .

The MacBeath inconic with perspector X264, center X5, real foci O and H, is also inscribed in Q1Q2Q3 with contacts R1, R2, R3 also on K555.