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Enumerating Foldings and Unfoldings Between Polygons and Polytopes

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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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Authors and Affiliations

  1. MIT Laboratory for Computer Science, Cambridge, MA 02139, USA e-mail: edemaine@mit.edu, , , , , , US

    Erik D. Demaine

  2. MIT Laboratory for Computer Science, Cambridge, MA 02139, USA e-mail: mdemaine@mit.edu, , , , , , US

    Martin L. Demaine

  3. Department of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada. e-mail: alubiw@uwaterloo.ca, , , , , , CA

    Anna Lubiw

  4. Department of Computer Science, Smith College, Northampton, MA 01063, USA e-mail: orourke@cs.smith.edu, , , , , , US

    Joseph O'Rourke

Authors
  1. Erik D. Demaine
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  2. Martin L. Demaine
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  3. Anna Lubiw
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  4. Joseph O'Rourke
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Received: November 13, 2000 Final version received: August 21, 2001

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Demaine, E., Demaine, M., Lubiw, A. et al. Enumerating Foldings and Unfoldings Between Polygons and Polytopes. Graphs Comb 18, 93–104 (2002). https://doi.org/10.1007/s003730200005

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  • DOI: https://doi.org/10.1007/s003730200005

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