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X(7), X(9), X(366), X(3174), X(24154), X(24155), X(24313), X(24314)

barycentric quotient X(1) ÷ X(3174)

vertices of the intouch triangle

vertices of the anticevian triangle of X(366)

Geometric properties :

K1082 is the image of the Orthocubic K006 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 K006. Some of them are now included in ETC namely Y(485), Y(486), Y(487), Y(488) as X(24154), X(24155), X(24313), X(24314).

X(1) ÷ X(3174) corresponds to X(254) on K006.

The polar conic of X(9) is the Feuerbach hyperbola meeting K1082 at A, B, C, X(7) and X(9) twice.

All the cubics in {K201, K365, K747, K748, K761, K1077, K1078, K1079, K1082} are anharmonically equivalent. They correspond to the cubics anharmonically equivalent to K006 in the family {K006, K070a, K070b, K168, K170, K171, K233, K424a, K424b, K678, K707, K857, K1039, K1045, K1046, K1047}, see Table 68.