Inscribing a regular crosspolytope

2009/05/16 by Роман Карасев, R. N. Karasev, Karasev, R. N. · 2 citations
Mathematics · #Advanced Operator Algebra Research #Geometric and Algebraic Topology #Point processes and geometric inequalities #math.AT #math.MG #msc:53A07 #msc:55M20 #msc:55M35

paper · pdf · doi:10.48550/arxiv.0905.2671

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

arxiv created 2009/07/21 · arxiv updated 2009/12/01

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.

Cited by

• Knaster’s Problem for (Z 2) k -Symmetric Subsets of the Sphere S^2^k-1
• A Survey on the Square Peg Problem

Related

• Covering the Crosspolytope with Crosspolytopes
• An extremum property characterizing the n-dimensional regular cross-polytope
• Covering the crosspolytope with its smaller homothetic copies
• Unfolding Restricted Convex Caps
• The Alon--Milman Theorem for non-symmetric bodies