Approximation of convex bodies by polytopes with uniformly bounded valences (Q1092412)

Given any convex body K in Euclidean n-space \(R^ n\) and any number \(\epsilon >0\), does there always exist a polytope \(P(K,\epsilon)\subset R^ n\) such that the number of vertices of a facet of P and the number of facets meeting in a common vertex are bounded by a constant depending on the dimension d only and such that the Hausdorff-distance \(\rho\) (K,P) of K and P is less than \(\epsilon\) ? This question of Ewald posed at the Durham Symposium in 1975 is answered in the affirmative.