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arXiv · 2507.14998

Vertex-Minimal Paper Tori

Richard Evan Schwartz
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Abstract

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.

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Richard Evan Schwartz. 2026-01-15. Vertex-Minimal Paper Tori. https://arxiv.org/abs/2507.14998

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