X(1), X(1083), X(14665), X(14839)
Brocard points = foci of the Brocard ellipse
K359 is an isogonal strophoid passing through the Brocard points. See also CL003.
It is the locus of foci of inconics centered on the line through the incenter I and the Brocard midpoint X(39).
Its point at infinity is that of the line X(1)X(39) i.e. Z = X(14839) and the isogonal conjugate of Z is the singular focus F = X(14665).
K359 is spK(Z, X1) in CL055.