Paper by Erik D. Demaine

Zachary Abel, Erik D. Demaine, and Martin L. Demaine, “A Topologically Convex Vertex-Ununfoldable Polyhedron”, in Proceedings of the 23rd Canadian Conference on Computational Geometry (CCCG 2011), Toronto, Ontario, Canada, August 10–12, 2011, to appear.

We construct a polyhedron that is topologically convex (i.e., has the graph of a convex polyhedron) yet has no vertex unfolding: no matter how we cut along the edges and keep faces attached at vertices to form a connected (hinged) surface, the surface necessarily unfolds with overlap.

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Last updated March 21, 2017 by Erik Demaine.