**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. **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.
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**Related papers**:- RefoldRigidity_EuroCG2012 (Refold Rigidity of Convex Polyhedra)

See also other papers by Martin Demaine.

Last updated July 7, 2019 by Martin Demaine.