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X(6), X(66), X(69), X(141), X(159), X(1843), X(3313)

The parallels to the symmedians drawn through 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 ยง3.2.4.

This cubic is a central pK with center X(141). The inflexional tangent passes through X(39).

The three real concurring asymptotes are the parallels at X(141) to the symmedians of ABC.

The tangents at A, B, C, X(69) concur on the curve at E = X(1843) and the reflection of E in X(141) is F = X(3313).