X(1), X(40), X(84), X(164), X(505), X(2956)
K414 = pK(X6, X40) is the Orthocubic for the excentral triangle IaIbIc. Hence, it is the locus of M such that :
– I (the incenter), M and the isogonal conjugate of M with respect to the excentral triangle are collinear,
– X(40) (the circumcenter of the excentral triangle), M and the isogonal conjugate of M are collinear.
K414 meets the Orthocubic at A, B, C, the in/excenters and two other isogonal points on the line HX(40) and on the circumconic through O and X(84).