Approximation of the sphere by polytopes having few vertices
Imre Bárány, Zoltán Füredi · Proceedings of the American Mathematical Society · 1988
How well can a polytope with n n vertices approximate the unit ball B d {B^d} of the d d -dimensional Euclidean space? The answer is quite well known when d d is fixed and n n tends to infinity. In this paper the same question is answered when n n is a function of d d (a polynomial in d d , say) and d d tends to infinity. Some applications of the results are also indicated.