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Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/3885

Title: On Universal Covers for Four-Dimensional Sets of a Given Diameter
Authors: Lángi, Zsolt
Keywords: Polytopal Approximation
Universal Cover
Constant-Width Body
Circumscribe
Diameter
Borsuk's Problem
Issue Date: 2010
Publisher: EUT Edizioni Università di Trieste
Citation: Zsolt Lángi, "On Universal Covers for Four-Dimensional Sets of a Given Diameter", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 42 (2010), pp. 59-64.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics;42 (2010)
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.
URI: http://hdl.handle.net/10077/3885
ISSN: 0049-4704
MS Classification 2000: 52A27
52C17
52B45
Appears in Collections:Rendiconti dell‘ Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.42 (2010)

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