On basic $r$-ball polyhedra
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910024526200832 |
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| author | Bezdek, Károly |
| author_facet | Bezdek, Károly |
| contents | This note introduces the class of basic $r$-ball polyhedra in the $d$-dimensional Euclidean space $\mathbb{E}^{d}$ for $d>1$ and $r>0$. We investigate their face structure and, for given integers $0\leq i\leq d-1$, $n\geq d+1\geq 3$ determine the maximal number of $i$-dimensional faces among all basic $r$-ball polyhedra in $\mathbb{E}^{d}$ with $n$ facets. In addition, we establish that for $d>2$, every basic $r$-ball polyhedron is globally rigid with respect to its inner dihedral angles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15347 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On basic $r$-ball polyhedra Bezdek, Károly Metric Geometry This note introduces the class of basic $r$-ball polyhedra in the $d$-dimensional Euclidean space $\mathbb{E}^{d}$ for $d>1$ and $r>0$. We investigate their face structure and, for given integers $0\leq i\leq d-1$, $n\geq d+1\geq 3$ determine the maximal number of $i$-dimensional faces among all basic $r$-ball polyhedra in $\mathbb{E}^{d}$ with $n$ facets. In addition, we establish that for $d>2$, every basic $r$-ball polyhedron is globally rigid with respect to its inner dihedral angles. |
| title | On basic $r$-ball polyhedra |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2602.15347 |