2006/02/27 by Mirela Damian, Damian, Mirela, Robin Flatland +4
Computer Science · Engineering · #Advanced Materials and Mechanics #Dynamics and Control of Mechanical Systems #Structural Analysis and Optimization #cs.CG
paper · pdf · doi:10.48550/arxiv.cs/0602095
23 pages, 20 figures, 7 references. Revised version improves language and figures, updates references, and sharpens the conclusion
arxiv created 2006/03/22 · arxiv updated 2009/12/01
An unfolding of a polyhedron is produced by cutting the surface and flattening to a single, connected, planar piece without overlap (except possibly at boundary points). It is a long unsolved problem to determine whether every polyhedron may be unfolded. Here we prove, via an algorithm, that every orthogonal polyhedron (one whose faces meet at right angles) of genus zero may be unfolded. Our cuts are not necessarily along edges of the polyhedron, but they are always parallel to polyhedron edges. For a polyhedron of n vertices, portions of the unfolding will be rectangular strips which, in the worst case, may need to be as thin as epsilon = 1/2Omega(n).