Umbrellas and Polytopal Approximation of the Euclidean Ball Original Research Article

There are two positive, absolute constantsc1andc2so that the volume of the difference set of thed-dimensional Euclidean ballBd2and an inscribed polytope withnvertices is larger thanc1d vold(Bd2) n−2/(d−1)forn⩾(c2d)(d−1)/2.