On Hadwiger's covering functional for the simplex and the cross-polytope

Abstract

In 1957, Hadwiger made a conjecture that every $n$-dimensional convex body can be covered by $2^n$ translations of its interior. The Hadwiger's covering functional ${\gamma }_m(K)$ is the smallest positive number $r$ such that $K$ can be covered by $m$ translations of $rK$. Due to Zong's program, we study the Hadwiger's covering functional for the simplex and the cross-polytope. In this paper, we give upper bounds for the Hadwiger's covering functional of the simplex and the cross-polytope.

12 pages

References in corpus (2)

• On Lattice Coverings by Simplices
• Covering the crosspolytope with its smaller homothetic copies