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X(4), X(5), X(6), X(25), X(51), X(52), X(53) vertices of the orthic triangle midpoints of the orthic triangle all the related points of the Thomson cubic with respect to the orthic triangle 

K350 is the Thomson cubic of the orthic triangle. It is the pK with pole X(3199), pivot H, invariant in the isoconjugation which swaps H and X(51), the centroid of the orthic triangle. It has the same asymptotic directions as pK(X6, X2979). It is the isogonal transform of K646 = pK(X97, X95). K350 is the locus of the pseudopoles Ω of the stelloids psK60+ which have their asymptotes parallel to those of the McCay cubic K003. The corresponding pseudopivots P and pseudoisopivots P* lie on K045 and K350 respectively. More precisely, for any Ω on K350, the cubic psK(Ω, P, X4) where P is the anticomplement of the barycentric quotient X(51)÷Ω, is one of these stelloids. The radial center X lies on the image of K044 under the homothety h(X5, 1/3). For example, with Ω = X(4), X(5), X(6), X(25), X(51), X(53), X(14593) we find the cubics K028, K071, K003, K1140, K026, K049, K670 respectively. See the file McCay Stelloids for further explanations. 
