Minimum Number of Edges of Polytopes with $2d+2$ Vertices
| Autor: | Guillermo Pineda-Villavicencio, Julien Ugon, David Yost |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | The Electronic Journal of Combinatorics. 29 |
| ISSN: | 1077-8926 |
| DOI: | 10.37236/10374 |
| Popis: | We define two $d$-polytopes, both with $2d+2$ vertices and $(d+3)(d-1)$ edges, which reduce to the cube and the 5-wedge in dimension three. We show that they are the only minimisers of the number of edges, amongst all $d$-polytopes with $2d+2$ vertices, when $d=6$ or $d\ge8$. We also characterise the minimising polytopes for $d=4, 5$ or 7, where four sporadic examples arise. |
| Databáze: | OpenAIRE |
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