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X(30), X(381), X(31862), X(31863)

X(39162), X(39163), X(39164), X(39165) : foci of the Steiner inellipse

their reflections in X(381)

Geometric properties :

K800, K1092, K1288, K1289 are members of a same pencil of focal cubics that also contains the decomposed cubic which is the union of the line at infinity and the axes of the Steiner ellipses. All these cubics have their singular focus on the Fermat axis and share the same orthic line, namely the Euler line.

K1289 is the only undecomposed central cubic of the pencil, with center and singular focus X(381).

The centers of anallagmaty lie on the parallels at X(381) to the asymptotes of the Jerabek hyperbola and to the axes of the orthic inconic.