  The random polytope $K_n$, defined as the convex hull of $n$ points chosen
uniformly at random on the boundary of a smooth convex body, is considered.
Proofs for lower and upper variance bounds, strong laws of large numbers and
central limit theorems for the intrinsic volumes of $K_n$ are presented. A
normal approximation bound from Stein's method and estimates for surface bodies
are among the involved tools.

Probability;Metric Geometry