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 |
---|---|

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

Additional Information: | © 2009 Springer |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Date Deposited: | 09 Oct 2009 09:41 |

Last Modified: | 20 Feb 2019 08:41 |

URI: | http://eprints.lse.ac.uk/id/eprint/25412 |

### Actions (login required)

View Item |