Swanepoel, Konrad
(2007)
*Upper bounds for edge-antipodal and subequilateral polytopes.*
Periodica Mathematica Hungarica, 54
(1).
pp. 99-106.
ISSN 0031-5303

## Abstract

A polytope in a finite-dimensional normed space is subequilateral if the length in the norm of each of its edges equals its diameter. Subequilateral polytopes occur in the study of two unrelated subjects: surface energy minimizing cones and edge-antipodal polytopes. We show that the number of vertices of a subequilateral polytope in any d-dimensional normed space is bounded above by (d / 2 + 1) d for any d ≥ 2. The same upper bound then follows for the number of vertices of the edge-antipodal polytopes introduced by I. Talata [19]. This is a constructive improvement to the result of A. Pór (to appear) that for each dimension d there exists an upper bound f(d) for the number of vertices of an edge-antipodal d-polytopes. We also show that in d-dimensional Euclidean space the only subequilateral polytopes are equilateral simplices.

Item Type: | Article |
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Official URL: | http://www.springer.com/math/journal/10998 |

Additional Information: | © 2009 Springer |

Library of Congress subject classification: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Rights: | http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx |

Date Deposited: | 09 Oct 2009 09:41 |

URL: | http://eprints.lse.ac.uk/25412/ |

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