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

X(1), X(238), X(291), X(740), X(984), X(3736), X(3783), X(3795), X(3802), X(7220), X(7281), X(8298), X(17793)

vertices of the incentral triangle

Geometric properties :

K1040 is a weak cubic anharmonically equivalent to K131 as in Table 67.

More generally, a pK(X16514, P) is equivalent to K131 (hence a pK of Table 67) if and only if its pivot P lies on the rectangular diagonal hyperbola (H) with center X(110) passing through X(i) for i = 1, 9, 40, 188, 191, 366, 1045, 1050, 1490, 2136, 2949, 2950, 2951, 3174, 3307, 3308, 3646, 5506, 5528, 5541, 6326, 12658, 12660, 13144, 13146, 16009, 16550, 16558, 18598, etc.

(H) also passes through the vertices of the anticevian triangle of each of its points. (H) is also :

• the transform of the Stammler rectangular hyperbola under the symbolic substitution SS{ a -> √a},

• the antisupplement of this same hyperbola,

• the polar conic of P in pK(X16514, P) for any P on (H),

• the locus of the (real or not) square roots of the points on the line X(1)X(6).