Vertex-Minimal Paper Tori

Fuente: arXiv
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Bibliographic Details
Main Author: Schwartz, Richard Evan
Format: Preprint
Published: 2025
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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