a1 Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, 1364 Budapest, Hungary
a2 Mathematics Department, Athens University, Athens, 157-81, Greece.
A random polytope, Kn, is the convex hull of n points chosen randomly, independently, and uniformly from a convex body It is shown here that, with high probability, Kn can be obtained by taking the convex hull of m = o(n) points chosen independently and uniformly from a small neighbourhood of the boundary of K.
(Received May 01 1996)