Vertex-Minimal Paper Tori
Fuente:
arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | |
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| _version_ | 1866914255850176512 |
|---|---|
| author | Schwartz, Richard Evan |
| author_facet | Schwartz, Richard Evan |
| contents | A paper torus is an embedded polyhedral torus that is isometric to a flat torus in the intrinsic sense.
We prove that there does not exist a paper torus with $7$ vertices,
and that there does exist a paper torus with $8$ vertices.
This settles the question of the minimum number of
vertices needed for a paper torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14998 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Vertex-Minimal Paper Tori Schwartz, Richard Evan Metric Geometry A paper torus is an embedded polyhedral torus that is isometric to a flat torus in the intrinsic sense. We prove that there does not exist a paper torus with $7$ vertices, and that there does exist a paper torus with $8$ vertices. This settles the question of the minimum number of vertices needed for a paper torus. |
| title | Vertex-Minimal Paper Tori |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2507.14998 |