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The Allardice (second) cubic A2(P) is the anticomplement of the Allardice (first) cubic A1(P).

A2(P) is a nK with root G, with pole the barycentric square of the anticomplement of P. It contains the anticomplement aP of P (singular), the points at infinity of the sidelines of ABC. Thus A2(P) is cK(#aP, G).

When P lies on the Steiner inscribed ellipse, A2(P) is a nK0+.

With P = u : v : w, the general equation of A2(P) is :

∑[(-u + v + w)^2 (y + z) y z] + 2 (u^2 + v^2 + w^2 - 2(v w + w u + u v)) x y z = 0

A2(X2) is the Tucker nodal cubic K015. A2(X115) = K052 is the most remarkable.

See also A2(X3) = K406, A2(X5) = K1320.