Inscribing a regular crosspolytope

Abstract

In this paper we prove that it is possible to inscribe a regular crosspolytope (multidimensional octahedron) into a smooth convex body in ${\mathbb{R}}^d$, where $d$ is an odd prime power. Some generalizations of this statement are also proved.

The reference to Schnirelmann is corrected. The previous results on inscribing are discussed in more detail