Paper by Erik D. Demaine
- 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.
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 Erik Demaine.
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