Geodesic Folding of Tetrahedron

Seri Nishimoto; Takashi Horiyama; Tomohiro Tachi

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arXiv · 1912.01227

Geodesic Folding of Tetrahedron

Seri Nishimoto·Takashi Horiyama·Tomohiro Tachi

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Abstract

In this work, we show the geometric properties of a family of polyhedra obtained by folding a regular tetrahedron along regular triangular grids. Each polyhedron is identified by a pair of nonnegative integers. The polyhedron can be cut along a geodesic strip of triangles to be decomposed and unfolded into one or multiple bands (homeomorphic to a cylinder). The number of bands is the greatest common divisor of the two numbers. By a proper choice of pairs of numbers, we can create a common triangular band that folds into different multiple polyhedra that belongs to the family.

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Seri Nishimoto, Takashi Horiyama, Tomohiro Tachi. 2019-12-03. Geodesic Folding of Tetrahedron. https://arxiv.org/abs/1912.01227

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