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X(1), X(2), X(7), X(21), X(29), X(77), X(81), X(86)

K317 is the locus of point P whose cevian triangle is perspective to CP2, the 2nd circumperp triangle (see TCCT, ยง6.22). The locus of the perspector (which is the cevian quotient of P^2 and K) is K318.

See also table 6.

K317 has the same asymptotic directions as K455 = pK(X2, X319).

K317 is the isogonal transform of K362 = pK(X213, X1) and the isotomic transform of K366 = pK(X321, X75).

It is anharmonically equivalent to the Thomson cubic. See Table 21.