A volume formula for Reuleaux polyhedra
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866915736805441536 |
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| author | Hynd, Ryan |
| author_facet | Hynd, Ryan |
| contents | A ball polyhedron is a finite intersection of congruent balls in $\mathbb{R}^3$. These shapes arise in various contexts in discrete and convex geometry. We focus on Reuleaux polyhedra, the subclass of ball polyhedra whose centers and vertices coincide. Building on Bogosel's recent work on the volume of Meissner polyhedra, we derive a formula for the volume of Reuleaux polyhedra in terms of their edges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11756 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A volume formula for Reuleaux polyhedra Hynd, Ryan Metric Geometry A ball polyhedron is a finite intersection of congruent balls in $\mathbb{R}^3$. These shapes arise in various contexts in discrete and convex geometry. We focus on Reuleaux polyhedra, the subclass of ball polyhedra whose centers and vertices coincide. Building on Bogosel's recent work on the volume of Meissner polyhedra, we derive a formula for the volume of Reuleaux polyhedra in terms of their edges. |
| title | A volume formula for Reuleaux polyhedra |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2601.11756 |