English

On universal covers for four-dimensional sets of a given diameter

Metric Geometry 2012-07-30 v2 Geometric Topology

Abstract

Makeev proved that among centrally symmetric four-dimensional polytopes, with more than twenty facets and circumscribed about the Euclidean ball of diameter one, there is no universal cover for the family of unit diameter sets. In this paper we examine the converse problem, and prove that each centrally symmetric polytope, with at most fourteen facets and circumscribed about the Euclidean ball of diameter one, is a universal cover for the family of unit diameter sets.

Keywords

Cite

@article{arxiv.1007.2520,
  title  = {On universal covers for four-dimensional sets of a given diameter},
  author = {Zsolt Langi},
  journal= {arXiv preprint arXiv:1007.2520},
  year   = {2012}
}

Comments

5 pages

R2 v1 2026-06-21T15:48:24.083Z