An extremal property of the mean width of the simplex (Q1392406)

If \(K\) is a convex body in \(\mathbb{R}^n\) such that the Euclidean unit ball \(B^n_2\) is the maximal volume ellipsoid contained in \(K\), then the mean width of \(K\) is less than the mean width of any regular simplex circumscribed to \(B^n_2\).