Paper by Martin L. Demaine

Erik D. Demaine, Martin L. Demaine, Anna Lubiw, and Joseph O'Rourke, “Enumerating Foldings and Unfoldings between Polygons and Polytopes”, Graphs and Combinatorics, volume 18, number 1, 2002, pages 93–104.

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.

This paper is also available from the publisher's website.

A preliminary version of this paper is also available as arXiv:cs.CG/0107024 of the Computing Research Repository (CoRR).

The paper is 12 pages.

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Related papers:
JCDCG2000c (Enumerating Foldings and Unfoldings between Polygons and Polytopes)
AleksTR (Examples, Counterexamples, and Enumeration Results for Foldings and Unfoldings between Polygons and Polytopes)

Related webpages:
Folding Polygons into Convex Polyhedra (Erik Demaine)

See also other papers by Martin Demaine.
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Last updated November 17, 2022 by Martin Demaine.