Reprint of: Refold rigidity of convex polyhedra

  • Demaine E
  • Demaine M
  • Itoh J
 et al. 
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Abstract

We show that every convex polyhedron may be unfolded to one planar piece, and then refolded to a different convex polyhedron. If the unfolding is restricted to cut only edges of the polyhedron, we identify several polyhedra that are "edge-refold rigid" in the sense that each of their unfoldings may only fold back to the original. For example, each of the 43,380 edge unfoldings of a dodecahedron may only fold back to the dodecahedron, and we establish that 11 of the 13 Archimedean solids are also edge-refold rigid. We begin the exploration of which classes of polyhedra are and are not edge-refold rigid, demonstrating infinite rigid classes through perturbations, and identifying one infinite nonrigid class: tetrahedra. © 2013 Elsevier B.V.

Author-supplied keywords

  • Folding
  • Polyhedra
  • Rigidity
  • Unfolding

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Authors

  • Erik D. Demaine

  • Martin L. Demaine

  • Jin Ichi Itoh

  • Anna Lubiw

  • Chie Nara

  • Joseph O'Rourke

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