Epsilon-Unfolding Orthogonal Polyhedra.

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 o...

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Main Authors: Damian, Mirela., Flatland, Robin., O'Rourke, Joesph.
Format: Villanova Faculty Authorship
Language:English
Published: 2007
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spelling Epsilon-Unfolding Orthogonal Polyhedra.
Damian, Mirela.
Flatland, Robin.
O'Rourke, Joesph.
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 e = 1/2 (n).
2007
Villanova Faculty Authorship
vudl:175671
Graphs and Combinatorics 23, June 2007, 179-194.
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dc.title_txt_mv Epsilon-Unfolding Orthogonal Polyhedra.
dc.creator_txt_mv Damian, Mirela.
Flatland, Robin.
O'Rourke, Joesph.
dc.description_txt_mv 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 e = 1/2 (n).
dc.date_txt_mv 2007
dc.format_txt_mv Villanova Faculty Authorship
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dc.source_txt_mv Graphs and Combinatorics 23, June 2007, 179-194.
dc.language_txt_mv en
author Damian, Mirela.
Flatland, Robin.
O'Rourke, Joesph.
spellingShingle Damian, Mirela.
Flatland, Robin.
O'Rourke, Joesph.
Epsilon-Unfolding Orthogonal Polyhedra.
author_facet Damian, Mirela.
Flatland, Robin.
O'Rourke, Joesph.
dc_source_str_mv Graphs and Combinatorics 23, June 2007, 179-194.
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dc_title_str Epsilon-Unfolding Orthogonal Polyhedra.
description 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 e = 1/2 (n).
title Epsilon-Unfolding Orthogonal Polyhedra.
title_full Epsilon-Unfolding Orthogonal Polyhedra.
title_fullStr Epsilon-Unfolding Orthogonal Polyhedra.
title_full_unstemmed Epsilon-Unfolding Orthogonal Polyhedra.
title_short Epsilon-Unfolding Orthogonal Polyhedra.
title_sort epsilon-unfolding orthogonal polyhedra.
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