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X(7), X(9), X(366), X(527), X(1156), X(5528)

vertices of the anticevian triangle of X(366)

vertices of the cevian triangle of X(527)

Geometric properties :

K1080 is the image of the Neuberg cubic K001 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.

K1080 meets the line at infinity at X(527) and two other imaginary points on the circum-conic (C) with perspector X(1). The real asymptote of K1080 meets the cubic at X(1156), also on (C).

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