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X(7), X(9), X(142), X(366), X(2346)

vertices of the anticevian triangle of X(366)

Geometric properties :

K1081 is the image of the Napoleon cubic K005 under the symbolic substitution SS{a -> √a}. As such, it contains the counterparts – labelled Y(i) on the figure – of the points X(i) on K001.

The polar conic PC(X9) of X(9) is a rectangular hyperbola with center G, passing through X(1), X(9), X(3679), X(6173), homothetic to the Feuerbach hyperbola.

K1080 and K1081 are anharmonically equivalent since K001 and K005 are themselves anharmonically equivalent, see Table 68.