Paper by Erik D. Demaine

Reference:

Erik D. Demaine, Martin L. Demaine, Jin-ichi Itoh, Anna Lubiw, Chie Nara, and Joseph O'Rourke, “Refold Rigidity of Convex Polyhedra”, Computational Geometry: Theory and Applications, volume 46, number 8, October 2013, pages 979–989.

BibTeX

@Article{RefoldRigidity_CGTA,
  AUTHOR        = {Erik D. Demaine and Martin L. Demaine and Jin-ichi Itoh and Anna Lubiw and Chie Nara and Joseph O'Rourke},
  TITLE         = {Refold Rigidity of Convex Polyhedra},
  JOURNAL       = {Computational Geometry: Theory and Applications},
  journalurl    = {https://www.sciencedirect.com/journal/computational-geometry},
  VOLUME        = 46,
  NUMBER        = 8,
  MONTH         = {October},
  YEAR          = 2013,
  PAGES         = {979--989},

  doi           = {https://dx.doi.org/10.1016/J.COMGEO.2013.05.002},
  dblp          = {https://dblp.org/rec/journals/comgeo/DemaineDILNO13},
  comments      = {This paper is also available from <A HREF="https://doi.org/10.1016/j.comgeo.2013.05.002">ScienceDirect</A>.},
  replaces      = {RefoldRigidity_EuroCG2012},
  papers        = {RefoldRigidity_EuroCG2012},
}

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.

Comments:

This paper is also available from ScienceDirect.

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Related papers:

RefoldRigidity_EuroCG2012 (Refold Rigidity of Convex Polyhedra)