  Let W be a polyconvex function defined on the 2 x 2 real matrices. The
Busemann representative f, say, of W is the largest possible convex
representative of W. Writing L for the set of affine functions on R^{5} such
that a(A, det A) is less than or equal to W(A) for all 2 x 2 real matrices A, f
can then be expressed as f(X) = sup {a(X): a lies in L}. This short note proves
the surprising result that f is in general strictly larger than the `natural'
convex representative g(X) = sup {a(X): a lies in L and a(A, det A)=W(A) for
some A}.
