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Enumerating Foldings and Unfoldings between Polygons and Polytopes

Erik D. Demaine·Martin L. Demaine·Anna Lubiw·Joseph O'Rourke
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Abstract

We pose and answer several questions concerning the number of ways to fold a polygon to a polytope, and how many polytopes can be obtained from one polygon; and the analogous questions for unfolding polytopes to polygons. Our answers are, roughly: exponentially many, or nondenumerably infinite.

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Erik D. Demaine, Martin L. Demaine, Anna Lubiw, Joseph O'Rourke. 2001-07-18. Enumerating Foldings and Unfoldings between Polygons and Polytopes. https://arxiv.org/abs/cs/0107024

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