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

X(2), X(4), X(66), X(69), X(315), X(1370), X(5596), X(13575), X(65598), X(65599), X(65600), X(65601), X(65602), X(65603)

vertices of the antimedial triangle

infinite points of K169 = pK(X6, X69)

points on (O) and pK(X6, X12220), pK(X69, X69), pK(X8879, X4)

Geometric properties :

For any point P on K1365, there is a point Ω on K177 such that pK(Ω, P) meets the line at infinity at the same points as K1365 itself.

This is the case of K177 = pK(X32, X2), K169 = pK(X6, X69), K233 = pK(X25, X4), and also pK(X3, X1370), pK(X66, X66), pK(X206, X5596).

K1365 is the isogonal transform of K174 and the complement of K177.

K1365 is anharmonically equivalent to K140, K141, K161, K174, K177, K644, K836, K959, K968. See Table 68.

More generally, every pK(Ω, P) with Ω on the circum-conic with perspector the barycentric product X(688) x P^2 is anharmonically equivalent to K1365. Equivalently, P^2 lies on the trilinear polar of the Ω-isoconjugate of X(688).