Soft tilings
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917423248048128 |
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| author | Ambrus, Gergely Dancsó, Dorottya |
| author_facet | Ambrus, Gergely Dancsó, Dorottya |
| contents | By means of constructing a new edge-bending algorithm, we prove that every locally polyhedral tiling of $\mathbb{R}^3$ can be completely softened. A weaker form of this statement, for polyhedral space tilings, was conjectured by Domokos, Goriely, G. Horváth and Regős in 2024. We also provide a short proof for a result of Domokos, G. Horváth, and Regős, stating that in a balanced polygonic tiling of the plane, the average number of spikes is at least 2 per cell. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18545 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Soft tilings Ambrus, Gergely Dancsó, Dorottya Metric Geometry Combinatorics Geometric Topology By means of constructing a new edge-bending algorithm, we prove that every locally polyhedral tiling of $\mathbb{R}^3$ can be completely softened. A weaker form of this statement, for polyhedral space tilings, was conjectured by Domokos, Goriely, G. Horváth and Regős in 2024. We also provide a short proof for a result of Domokos, G. Horváth, and Regős, stating that in a balanced polygonic tiling of the plane, the average number of spikes is at least 2 per cell. |
| title | Soft tilings |
| topic | Metric Geometry Combinatorics Geometric Topology |
| url | https://arxiv.org/abs/2604.18545 |