Paper by Erik D. Demaine

Reference:

Erik D. Demaine, Martin L. Demaine, Jin-ichi Itoh, Anna Lubiw, Chie Nara, and Joseph O'Rourke, “Refold Rigidity of Convex Polyhedra”, in Abstracts from the 28th European Workshop on Computational Geometry (EuroCG 2012), Assisi, Italy, March 19–21, 2012, pages 101–104.

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, then we show that many regular and semi-regular polyhedra are “edge-unfold rigid” in the sense that each of their unfoldings may only fold back to the original. For example, all of the 43,380 edge unfoldings of a dodecahedron may only fold back to the dodecahedron. We begin the exploration of which polyhedra are edge-unfold rigid, demonstrating infinite rigid classes through perturbations, and identifying one infinite nonrigid class: tetrahedra.

Comments:

The full 8-page paper is also available.

Length:

The abstract is 4 pages.

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The abstract is available in PDF (208k).

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Related papers:

RefoldRigidity_CGTA (Refold Rigidity of Convex Polyhedra)