Approximation of smooth convex bodies by random circumscribed polytopes

Choose n independent random points on the boundary of a convex body K.\Rd. The intersection of the supporting halfspaces at these random points is a random convex polyhedron. The expectations of its volume, its surface area and its mean width are investigated. In the case that the boundary of K is sufficiently smooth, asymptotic expansions as n.. are derived even in the case when the curvature is allowed to be zero. We compare our results to the analogous results for best approximating polytopes.