  Let C = C(l_1, ..., l_n) be the n-dimensional orthogonal cross-polytope whose
axes are of length l_1,..., l_n. Subject to the condition \sum l_i^2 = 1, the
mean width of C is minimised when l_i = 1/sqrt{n} for every i, and it is
maximised when C is at most two dimensional. As a corollary, a lower bound on
the mean width of a general convex body K is derived in terms of the successive
inner radii of K. A more general result is presented for Gaussian random
vectors.
