Paper by Martin L. Demaine

Reference:

Erik D. Demaine, Martin L. Demaine, Anna Lubiw, and Joseph O'Rourke, “Enumerating Foldings and Unfoldings between Polygons and Polytopes”, in Abstracts from the Japan Conference on Discrete and Computational Geometry (JCDCG 2000), Tokyo, Japan, November 22–25, 2000, pages 9–12.

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.

Comments:

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

Length:

The paper is 12 pages.

Availability:

The paper is available in PostScript (461k) and gzipped PostScript (129k).

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Related papers:

Aleks_GC2002 (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)