Collapsibility and Near Universality for Vertex Minimal Paper Tori
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | |
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| _version_ | 1866912679031996416 |
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| author | Doyle, Peter Schwartz, Richard Evan |
| author_facet | Doyle, Peter Schwartz, Richard Evan |
| contents | A paper torus is a piecewise linear isometric embedding of a flat
torus into $\R^3$.
Following up on the $8$-vertex paper tori discovered
by the second author, we prove universality and collapsibility results
about these objects. One corollary
is that any flat torus without reflection
symmetry is realized as an $8$-vertex paper torus. Another
corollary is that, for any $ε>0$, there is an $8$-vertex
paper torus within $ε$ of a unit equilateral triangle
in the Hausdorff metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12623 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Collapsibility and Near Universality for Vertex Minimal Paper Tori Doyle, Peter Schwartz, Richard Evan Metric Geometry A paper torus is a piecewise linear isometric embedding of a flat torus into $\R^3$. Following up on the $8$-vertex paper tori discovered by the second author, we prove universality and collapsibility results about these objects. One corollary is that any flat torus without reflection symmetry is realized as an $8$-vertex paper torus. Another corollary is that, for any $ε>0$, there is an $8$-vertex paper torus within $ε$ of a unit equilateral triangle in the Hausdorff metric. |
| title | Collapsibility and Near Universality for Vertex Minimal Paper Tori |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2510.12623 |