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math.MG2026
Vertex-Minimal Paper Tori
Richard Evan Schwartz
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 vertices, and that…
math.MG2025
Collapsibility and Near Universality for Vertex Minimal Paper Tori
Peter Doyle, Richard Evan Schwartz
A paper torus is a piecewise linear isometric embedding of a flat torus into . Following up on the -vertex paper tori discovered by the second author, we prove universalit…