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X(2), X(4), X(6), X(262), X(264), X(458), X(1007) 

We meet this cubic in the paper McCay Stelloids. K677 has the same asymptotic directions as pK(X2, X1350) and meets the Steiner ellipse at the same points as pK(X2, X1351). Its isogonal transform is pK(X184, X182) and its isotomic transform is pK(X69, X183). K677 is the locus of M such that the cevian triangle of M and the Artzt triangle are perspective. The locus of the perspector is pK(X7735, X9756). (César Lozada, see the preamble of X(9742) in ETC). See the related K790 where "cevian" is replaced with "anticevian". 
