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.
Demaine, E. D., Demaine, M. L., Itoh, J. I., Lubiw, A., Nara, C., & O’Rourke, J. (2014). Reprint of: Refold rigidity of convex polyhedra. Computational Geometry: Theory and Applications, 47(3 PART B), 507–517. https://doi.org/10.1016/j.comgeo.2013.11.001