EpsilonUnfolding 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...
Main Authors:  , , 

Format:  
Language:  English 
Published: 
2007

Online Access:  http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:175671 
id 
vudl:175671 

record_format 
vudl 
institution 
Villanova University 
collection 
Digital Library 
modeltype_str_mv 
vudlsystem:CollectionModel vudlsystem:CoreModel vudlsystem:ResourceCollection 
datastream_str_mv 
AUDIT STRUCTMAP RELSEXT PARENTQUERY MEMBERQUERY PARENTLIST PARENTLISTRAW THUMBNAIL MEMBERLISTRAW PROCESSMD LEGACYMETS LICENSE AGENTS DC 
hierarchytype 

hierarchy_all_parents_str_mv 
vudl:175631 vudl:172968 vudl:641262 vudl:3 vudl:1 
sequence_vudl_175631_str 
0000000013 
hierarchy_top_id 
vudl:641262 
hierarchy_top_title 
Villanova Faculty Publications 
fedora_parent_id_str_mv 
vudl:175631 
hierarchy_first_parent_id_str 
vudl:175671 
hierarchy_parent_id 
vudl:175631 
hierarchy_parent_title 
Damian Mirela 
hierarchy_sequence_sort_str 
0000000013 
hierarchy_sequence 
0000000013 
spelling 
EpsilonUnfolding 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, 179194. en 
dc.title_txt_mv 
EpsilonUnfolding 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 
dc.identifier_txt_mv 
vudl:175671 
dc.source_txt_mv 
Graphs and Combinatorics 23, June 2007, 179194. 
dc.language_txt_mv 
en 
author 
Damian, Mirela. Flatland, Robin. O'Rourke, Joesph. 
spellingShingle 
Damian, Mirela. Flatland, Robin. O'Rourke, Joesph. EpsilonUnfolding Orthogonal Polyhedra. 
author_facet 
Damian, Mirela. Flatland, Robin. O'Rourke, Joesph. 
dc_source_str_mv 
Graphs and Combinatorics 23, June 2007, 179194. 
format 
Villanova Faculty Authorship 
author_sort 
Damian, Mirela. 
dc_date_str 
2007 
dc_title_str 
EpsilonUnfolding 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 
EpsilonUnfolding Orthogonal Polyhedra. 
title_full 
EpsilonUnfolding Orthogonal Polyhedra. 
title_fullStr 
EpsilonUnfolding Orthogonal Polyhedra. 
title_full_unstemmed 
EpsilonUnfolding Orthogonal Polyhedra. 
title_short 
EpsilonUnfolding Orthogonal Polyhedra. 
title_sort 
epsilonunfolding orthogonal polyhedra. 
publishDate 
2007 
normalized_sort_date 
20070101T00:00:00Z 
language 
English 
collection_title_sort_str 
epsilonunfolding orthogonal polyhedra. 
relsext.sortOn_txt_mv 
title 
fgs.type_txt_mv 
http://www.w3.org/ns/ldp#BasicContainer http://fedora.info/definitions/v4/repository#Container http://www.w3.org/ns/ldp#Container http://www.w3.org/ns/ldp#Resource http://www.w3.org/ns/ldp#RDFSource http://fedora.info/definitions/v4/repository#Resource 
fgs.ownerId_txt_mv 
diglibEditor 
fgs.createdDate_txt_mv 
20130122T04:54:26.428Z 
relsext.hasLegacyURL_txt_mv 
http://digital.library.villanova.edu/Villanova%20Digital%20Collection/Faculty%20Fulltext/Damian%20Mirela/DamianMirela0850029fb39045c48553815d1f51268a.xml 
relsext.sequence_txt_mv 
vudl:175631#13 
fgs.createdBy_txt_mv 
fedoraAdmin 
fgs.lastModifiedDate_txt_mv 
20220819T17:51:38.194Z 
relsext.hasModel_txt_mv 
http://hades.library.villanova.edu:8080/rest/vudlsystem:CollectionModel http://hades.library.villanova.edu:8080/rest/vudlsystem:CoreModel http://hades.library.villanova.edu:8080/rest/vudlsystem:ResourceCollection 
fgs.label_txt_mv 
EpsilonUnfolding Orthogonal Polyhedra. 
fgs.state_txt_mv 
Active 
fgs.lastModifiedBy_txt_mv 
fedoraAdmin 
relsext.isMemberOf_txt_mv 
http://hades.library.villanova.edu:8080/rest/vudl:175631 
relsext.itemID_txt_mv 
oai:digital.library.villanova.edu:vudl:175671 
has_order_str 
no 
agent.name_txt_mv 
Falvey Memorial Library, Villanova University KHL 
license.mdRef_str 
http://digital.library.villanova.edu/copyright.html 
license_str 
protected 
has_thumbnail_str 
true 
THUMBNAIL_contentDigest_digest_str 
203c69e18f4f46c81e9892448d2c07cd 
first_indexed 
20140111T23:30:02Z 
last_indexed 
20220819T17:52:43Z 
_version_ 
1755567730873860096 
subpages 