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∑ a^3 (a^2 - b^2) (a^2 - c^2) x (c^4 y^2 - b^4 z^2) = 0

X(6), X(163), X(661), X(1953), X(2148), X(2576), X(2577), X(2578), X(2579), X(4559), X(7252)

vertices of the tangential triangle

vertices of the cevian triangle of X(163)

Geometric properties :

K1005 is the isogonal transform of K1004 , also the barycentric products X(1) x K316, X(6) x K1004.