Refold rigidity of convex polyhedra
Author(s)Demaine, Erik D.; Demaine, Martin L.; Itoh, Jin-ichi; Lubiw, Anna; Nara, Chie; O'Rourke, Joseph; ... Show more Show less
MetadataShow full item record
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.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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.
Author's final manuscript