Abstract: A paper torus is a piece affine isometric embedding of a flat torus into R^3. These have been known to exist since 1960 but it has not been known how many vertices you need to make one. In this talk I will explain my proof that there exists an 8-vertex paper torus and that no 7-vertex paper torus exists. I'll also explain some of the remarkable properties of these 8-vertex paper tori.

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Last modified: Thu Oct 2 17:26:27 EDT 2025