Reprint of: Refold rigidity of convex polyhedra |
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Institution: | 1. MIT, United States;2. Kumamoto Univ., Japan;3. Univ. Waterloo, Canada;4. Tokai Univ., Japan;5. Smith College, Northampton, MA 01063, United States |
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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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Keywords: | Polyhedra Unfolding Folding Rigidity |
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