The Mean Width of a Convex Polytope

In the case n=d = 2, because of Cauchy's surface-area formula [2; p. 208], relation (3) reduces to the trivial statement that the perimeter of a convex polygon is equal to the sum of the lengths of its edges. If K is any closed bounded convex set of dimension at most d, we may write KaEczE and use md(K) and mn(K) to denote the mean widths of K relative to the spaces E and E respectively. A simple calculation shows that for all such K, mn(K) is a constant multiple of md(K), to be precise, mn(K) md{K)