# 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: , , Villanova Faculty Authorship English 2007 http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:175671
id vudl:175671 vudl Villanova University Digital Library vudl-system:CollectionModel vudl-system:CoreModel vudl-system:ResourceCollection AUDIT STRUCTMAP RELS-EXT PARENT-QUERY MEMBER-QUERY PARENT-LIST PARENT-LIST-RAW THUMBNAIL MEMBER-LIST-RAW PROCESS-MD LEGACY-METS LICENSE AGENTS DC vudl:175631 vudl:172968 vudl:641262 vudl:3 vudl:1 0000000013 vudl:641262 Villanova Faculty Publications vudl:175631 vudl:175671 vudl:175631 Damian Mirela 0000000013 0000000013 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. en 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. en Damian, Mirela. Flatland, Robin. O'Rourke, Joesph. Damian, Mirela. Flatland, Robin. O'Rourke, Joesph. Epsilon-Unfolding Orthogonal Polyhedra. Damian, Mirela. Flatland, Robin. O'Rourke, Joesph. Graphs and Combinatorics 23, June 2007, 179-194. Villanova Faculty Authorship Damian, Mirela. 2007 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 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). Epsilon-Unfolding Orthogonal Polyhedra. Epsilon-Unfolding Orthogonal Polyhedra. Epsilon-Unfolding Orthogonal Polyhedra. Epsilon-Unfolding Orthogonal Polyhedra. Epsilon-Unfolding Orthogonal Polyhedra. epsilon-unfolding orthogonal polyhedra. 2007 2007-01-01T00:00:00Z English epsilon-unfolding orthogonal polyhedra. title 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 diglibEditor 2013-01-22T04:54:26.428Z http://digital.library.villanova.edu/Villanova%20Digital%20Collection/Faculty%20Fulltext/Damian%20Mirela/DamianMirela-0850029f-b390-45c4-8553-815d1f51268a.xml vudl:175631#13 fedoraAdmin 2022-08-19T17:51:38.194Z http://hades.library.villanova.edu:8080/rest/vudl-system:CollectionModel http://hades.library.villanova.edu:8080/rest/vudl-system:CoreModel http://hades.library.villanova.edu:8080/rest/vudl-system:ResourceCollection Epsilon-Unfolding Orthogonal Polyhedra. Active fedoraAdmin http://hades.library.villanova.edu:8080/rest/vudl:175631 oai:digital.library.villanova.edu:vudl:175671 no Falvey Memorial Library, Villanova University KHL http://digital.library.villanova.edu/copyright.html protected true 203c69e18f4f46c81e9892448d2c07cd 2014-01-11T23:30:02Z 2022-08-19T17:52:43Z 1755567730873860096