Refold rigidity of convex polyhedra
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Demaine_Refold rigidity.pdf
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Author(s)
Demaine, Erik D.
Demaine, Martin L.
Itoh, Jin-ichi
Lubiw, Anna
Nara, Chie
O'Rourke, Joseph
Date Issued
May 2013
Journal
Computational Geometry
Publisher
Elsevier
Citation
Demaine, Erik D., Martin L. Demaine, Jin-ichi Itoh, Anna Lubiw, Chie Nara, and Joseph OʼRourke. “Refold Rigidity of Convex Polyhedra.” Computational Geometry 46, no. 8 (October 2013): 979–989.
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Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1016/j.comgeo.2013.05.002
