Document Type
Article
Publication Date
6-2007
Publication Title
Graphs and Combinatorics
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 ɛ = 1/2Ω(n).
Keywords
General unfolding, Grid unfolding, Orthogonal polyhedra, Genus-zero
Volume
23
Issue
Supplement 1
First Page
179
Last Page
194
DOI
dx.doi.org/10.1007/s00373-007-0701-8
ISSN
1435-5914
Recommended Citation
Damian, Mirela; Flatland, Robin; and O'Rourke, Joseph, "Epsilon-Unfolding Orthogonal Polyhedra" (2007). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/50
Comments
Author’s submitted manuscript. Language included at the request of the publisher: The final publication is available at Springer via http://dx.doi.org/10.1007/s00373-007-0701-8.