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”, Graphs and Combinatorics, volume 18, number 1, 2002, pages 93–104.

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 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).

Length:

The paper is 12 pages.

Availability:

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

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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)