Graphs and Combinatorics

, Volume 18, Issue 1, pp 93–104

Enumerating Foldings and Unfoldings Between Polygons and Polytopes

  • Erik D. Demaine
  • Martin L. Demaine
  • Anna Lubiw
  • Joseph O'Rourke

DOI: 10.1007/s003730200005

Cite this article as:
Demaine, E., Demaine, M., Lubiw, A. et al. Graphs Comb (2002) 18: 93. doi:10.1007/s003730200005


 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.

Copyright information

© Springer-Verlag Tokyo 2002

Authors and Affiliations

  • Erik D. Demaine
    • 1
  • Martin L. Demaine
    • 2
  • Anna Lubiw
    • 3
  • Joseph O'Rourke
    • 4
  1. 1.MIT Laboratory for Computer Science, Cambridge, MA 02139, USA e-mail: edemaine@mit.eduUS
  2. 2.MIT Laboratory for Computer Science, Cambridge, MA 02139, USA e-mail: mdemaine@mit.eduUS
  3. 3.Department of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada. e-mail: alubiw@uwaterloo.caCA
  4. 4.Department of Computer Science, Smith College, Northampton, MA 01063, USA e-mail: orourke@cs.smith.eduUS

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