Approximation of convex bodies by inscribed simplices of maximum volume

The Banach-Mazur distance between an arbitrary convex body and a simplex in Euclidean n-space E n is at most n + 2. We obtain this estimate as an immediate consequence of our theorem which says that for an arbitrary convex body C in E n and for any simplex S of maximum volume contained in C the homothetical copy of S with ratio n + 2 and center in the barycenter of S contains C. In general, this ratio cannot be improved, as it follows from the example of any double-cone.