Approximation of convex bodies by polytopes with uniformly bounded valences

Given any convex bodyK in Euclideann-spaceR ⁿ and any number ?>0, does there always exist a polytopeP(K, ?)?R ⁿ such that the number of vertices of a facet ofP and the number of facets meeting in a common vertex are bounded by a constant depending on the dimensiond only and such that the Hausdorff-distance ? (K, P) ofK andP is less than ?? This question of Ewald posed at the Durham symposium in 1975 is answered in the affirmative.