Paper by Erik D. 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.

BibTeX

@Article{Aleks_GC2002,
  AUTHOR        = {Erik D. Demaine and Martin L. Demaine and Anna Lubiw and
                   Joseph O'Rourke},
  TITLE         = {Enumerating Foldings and Unfoldings between Polygons and
                   Polytopes},
  JOURNAL       = {Graphs and Combinatorics},
  JOURNALURL    = {http://link.springer.de/link/service/journals/00373/},
  VOLUME        = 18,
  NUMBER        = 1,
  YEAR          = 2002,
  PAGES         = {93--104},

  LENGTH        = {12 pages},
  WEBPAGES      = {aleksandrov},
  PAPERS        = {JCDCG2000c; AleksTR},
  replaces      = {JCDCG2000c},
  doi           = {https://dx.doi.org/10.1007/s003730200005},
  dblp          = {https://dblp.org/rec/journals/gc/DemaineDLO02},
  COMMENTS      = {This paper is also available from <A HREF="https://doi.org/10.1007/s003730200005">SpringerLink</A>.
                   <P>
                   A preliminary version of this paper is also available as
                   <A HREF="http://arXiv.org/abs/cs.CG/0107024">
                   arXiv:cs.CG/0107024</A> of the
                   <A HREF="http://arXiv.org/archive/cs/intro.html">
                   Computing Research Repository (CoRR)</A>.}
}

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 SpringerLink.

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).

See information on file formats.

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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