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
K318 has the same asymptotic directions as pK(X6, X72).
K318 is the isogonal transform of the Spieker central cubic K033 = pK(X37, X8).
K318 is a circumcevian pK. See CL072.