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)}.Comment: 23 pages, 20 figures, 7 references. Revised version improves language
and figures, updates references, and sharpens the conclusio
