Lower Bound on Translative Covering Density of Tetrahedra
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866911151595454464 |
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| author | Li, Yiming Fu, Miao Zhang, Yuqin |
| author_facet | Li, Yiming Fu, Miao Zhang, Yuqin |
| contents | In this paper, we present the first nontrivial lower bound on the translative covering density of tetrahedra. To this end, we show the lower bound, in any translative covering of tetrahedra, on the density relative to a given cube. The resulting lower bound on the translative covering density of tetrahedra is $1+1.227\times10^{-3}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_13252 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Lower Bound on Translative Covering Density of Tetrahedra Li, Yiming Fu, Miao Zhang, Yuqin Metric Geometry 52C17, 52B10, 52C07 In this paper, we present the first nontrivial lower bound on the translative covering density of tetrahedra. To this end, we show the lower bound, in any translative covering of tetrahedra, on the density relative to a given cube. The resulting lower bound on the translative covering density of tetrahedra is $1+1.227\times10^{-3}$. |
| title | Lower Bound on Translative Covering Density of Tetrahedra |
| topic | Metric Geometry 52C17, 52B10, 52C07 |
| url | https://arxiv.org/abs/2206.13252 |