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X(1), X(3), X(21), X(28), X(56), X(58), X(84), X(1394), X(2360) A2, B2, C2 : vertices of CP2, the 2nd circumperp triangle (the tangents at these points are the perpendicular bisectors) 

K317 is the locus of point P whose cevian triangle is perspective to CP2, the 2nd circumperp triangle (see TCCT, §6.22). The locus of the perspector is K318. K318 is also the locus of point P whose
See also table 6. K318 has the same asymptotic directions as pK(X6, X72). K318 is the isogonal transform of the Spieker central cubic K033 = pK(X37, X8). It is anharmonically equivalent to the Thomson cubic. See Table 21. 
