On extreme constant width bodies in $\mathbb{R}^3$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866909468840689664 |
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| author | Hynd, Ryan |
| author_facet | Hynd, Ryan |
| contents | We consider the family of constant width bodies in $\mathbb{R}^3$ which is convex under Minkowski addition. Extreme shapes cannot be expressed as a nontrivial convex combination of other constant width bodies. We show that each Meissner polyhedra is extreme. We also explain that each constant width body obtained by rotating a symmetric Reuleaux polygon about its axis of symmetry is extreme. In addition, we conjecture a general characterization of all extreme constant width shapes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16940 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On extreme constant width bodies in $\mathbb{R}^3$ Hynd, Ryan Metric Geometry We consider the family of constant width bodies in $\mathbb{R}^3$ which is convex under Minkowski addition. Extreme shapes cannot be expressed as a nontrivial convex combination of other constant width bodies. We show that each Meissner polyhedra is extreme. We also explain that each constant width body obtained by rotating a symmetric Reuleaux polygon about its axis of symmetry is extreme. In addition, we conjecture a general characterization of all extreme constant width shapes. |
| title | On extreme constant width bodies in $\mathbb{R}^3$ |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2501.16940 |