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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

7 seven fixed points of a mapping mentioned at K1065

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.

The isogonal transform of K141 is K177. Its complement is K836. See also K002, property 10.

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.

K836 is the locus of poles and isopivots of all pKs having the same asymptotic directions as the Grebe cubic K102. The locus of the pivots is K141.