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

Comments

Author's pre-print. 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.

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