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X(3), X(39), X(76), X(596), X(7794), X(14357), X(14632), X(14633), X(22116)

midpoints of ABC

infinite points of (K∞) = pK(X6, X7760)

circumcircle points of (Ko) = pK(X6, X7794)

Geometric properties :

K1068 is the transform of the trilinear polar (L) of X(83) under the mapping 𝚹 : P -> aQ described in page K1065 where further informations and a generalization are given.

(L) is the anticomplement of the de Longchamps line and passes through X{23, 385, 523, 659, 669, 4057, 4580, 5201, 6562, 9147, 9149, 9485, 9870, 10566, 14272, 14275, 14420, 16158, 17494, 18010, 18105, 18108, 20045, 20475, 20875, 21005, 21006, 21225, 21458}.

K1068 is a nodal cubic with node X(39). The nodal tangents are parallel to the asymptotes of the circum-conic (C) with perspector X(3005), a conic passing through X(6), X(39), X(76), X(141), X(755), X(882), X(1843), X(2353), etc.

As seen in page K1065, the trilinear polar (L) of X(83) is associated with a quartic (Q) which is here Q144.