Epsilon-Unfolding Orthogonal Polyhedra
Abstract
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 = 1/2^{Omega(n)}.
Keywords
Cite
@article{arxiv.cs/0602095,
title = {Epsilon-Unfolding Orthogonal Polyhedra},
author = {Mirela Damian and Robin Flatland and Joseph O'Rourke},
journal= {arXiv preprint arXiv:cs/0602095},
year = {2007}
}
Comments
23 pages, 20 figures, 7 references. Revised version improves language and figures, updates references, and sharpens the conclusion