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X(6), X(1249), X(1989), X(1990), X(3163), X(3284), X(36896)

midpoints of ABC

P1 = X(3) x X(1294)

P2 = X(1138) x X(1511)

Geometric properties :

K1348 is the locus of poles Ω of all (circular) pKs having the same infinite points as the Neuberg cubic K001, namely X(30) and the circular points at infinity.

The locus of the pivots P is K449 and the locus of the isopivots Q is K446 = psK(X1495, X2, X3). K449 is the anticomplement of K446.

Recall that Q = igP, hence Ω is the barycentic product P x igP.

Apart K001, K059 = pK(X1990, X4) and K060 = pK(X1989, X265) are the most remarkable examples of such cubics.

K1349 = pK(X3284, X20) is another example.