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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 | Source: | 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 |
| Appears in Collections: | Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.42 (2010) |
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| File | Description | Size | Format | |
|---|---|---|---|---|
| Langi RendMat42.pdf | 187.89 kB | Adobe PDF | View/Open |
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