On the Distance of Polytopes with Few Vertices to the Euclidean Ball

Konstantin E. Tikhomirov

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Let n, N be natural numbers satisfying (Formula presented.) be the unit Euclidean ball in Rn, and let (Formula presented.) be a convex n-dimensional polytope with N vertices and the origin in its interior. We prove that (Formula presented.) where c>0 is a universal constant. As an immediate corollary, for any covering of Sn-1 by N spherical caps of geodesic radius ϕ, we get that (Formula presented.) for an absolute constant C>0. Both estimates are optimal up to the constant multiples c, C.

Original languageEnglish (US)
Pages (from-to)173-181
Number of pages9
JournalDiscrete and Computational Geometry
Volume53
Issue number1
DOIs
StatePublished - Jan 1 2015

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Keywords

  • Banach–Mazur distance
  • Convex polytope
  • Covering by spherical balls

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