Paper by Martin L. 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
- The paper is available in PDF (245k).
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