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