On Origami Embeddings of Flat Tori

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J. Math. Sci. Univ. Tokyo
Vol. 31 (2024), No. 2, Page 105–126.

Tsuboi, Takashi
On Origami Embeddings of Flat Tori
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
We give explicit origami embeddings of a 2-dimensional flat torus of any modulus in the 3-dimensional Euclidean space. The existence of such embeddings was shown by Burago and Zalgaller in 1995 and our explicit construction gives an alternative proof.

Keywords: Origami embedding, flat tori, moduli, cycloid.

Mathematics Subject Classification (2020): 57Q35, 32G15, 32G10.

Received: 2020-07-08

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