X(2), X(4), X(6), X(22), X(69), X(76), X(1670), X(1671)
vertices of antimedial triangle
cevians of X(76)
points at infinity of the Grebe cubic
The parallels to the symmedians drawn through a point P meet the sidelines of ABC at Pa, Pb, Pc. ABC and PaPbPc are perspective if and only if P lies on pK(X39, X69) = K140. The locus of the perspector is pK(X2, X76) = K141. See Special isocubics §3.2.4.
The tangents at A, B, C are the symmedians. The asymptotes are parallel to those of the Grebe cubic i.e. pK(X6, X6) = K102.
K141 is a member of the class CL043 : it meets the circumcircle at A, B, C and three other points where the tangents are concurrent.