The packing density of the $n$-dimensional cross-polytope
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2015
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| _version_ | 1866917390092075008 |
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| author | Tóth, G. Fejes Fodor, F. Vígh, V. |
| author_facet | Tóth, G. Fejes Fodor, F. Vígh, V. |
| contents | The packing density of the regular cross-polytope in Euclidean $n$-space is unknown except in dimensions $2$ and $4$ where it is 1. The only non-trivial upper bound is due to Gravel, Elser, and Kallus (2011) who proved that for $n=3$ the packing density of the regular octahedron is at most $1-1.4\ldots\times 10^{-12}$. In this paper, we prove upper bounds for the packing density of the $n$-dimensional regular cross-polytope in the case that $n\geq 7$. We use a modification of Blichfeldt's method due to G. Fejes Tóth and W. Kuperberg (1993). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1503_04571 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | The packing density of the $n$-dimensional cross-polytope Tóth, G. Fejes Fodor, F. Vígh, V. Metric Geometry The packing density of the regular cross-polytope in Euclidean $n$-space is unknown except in dimensions $2$ and $4$ where it is 1. The only non-trivial upper bound is due to Gravel, Elser, and Kallus (2011) who proved that for $n=3$ the packing density of the regular octahedron is at most $1-1.4\ldots\times 10^{-12}$. In this paper, we prove upper bounds for the packing density of the $n$-dimensional regular cross-polytope in the case that $n\geq 7$. We use a modification of Blichfeldt's method due to G. Fejes Tóth and W. Kuperberg (1993). |
| title | The packing density of the $n$-dimensional cross-polytope |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/1503.04571 |