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K426

too complicated to be written here. Click on the link to download a text file.

X(3), X(4), X(20), X(3532)

midpoints of ABC

antipodes of A, B, C in the circumcircle

infinite points of pK(X6, X3146)

K426 is a central cubic with center O.

It is the complement of K425. It is spK(X3146, X4) in CL055. Its isogonal transform is K841.

It is also psK(X154, X2, X3) in Pseudo-Pivotal Cubics and Poristic Triangles. See also Table 50.

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The Darboux cubic K004 and the decomposed cubic which is the union of the circumcircle and the Euler line generate a pencil of central cubics with center O passing through H, X(20) and the reflections A', B', C' of A, B, C about O. Each cubic has the same asymptotic directions as one of the isogonal pK of the Euler pencil. This pencil also contains (apart K004) the cubics K047, K080, K426, K443, K566 corresponding to K002, K003, pK(X6, X3146), K006, K005 respectively. These cubics are those in the column P = [X20] of Table 54.

This same table shows that K426 also belongs to the two pencils generated by K006 and K187, K002 and K009 respectively.