{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-SB2VZORR/1f497766-d5a2-4c66-9ca8-9690e92b2c8b/PDF","dcterms:extent":"310 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-SB2VZORR/f8fec490-d448-4f3e-aaef-691cce7ac74a/TEXT","dcterms:extent":"15 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-SB2VZORR","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2017","dc:creator":"Kovič, Jurij","dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:13"},{"@xml:lang":"sl","#text":"str. 23-30"}],"dc:identifier":["COBISSID:17897561","ISSN:1855-3966","URN:URN:NBN:SI:doc-SB2VZORR"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"sl","#text":"Eulerjeva karakteristika"},{"@xml:lang":"sl","#text":"polieder"},{"@xml:lang":"sl","#text":"rotacijska orbita"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Classification of convex polyhedra by their rotational orbit Euler characteristic|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$\\mathcal P$? be a polyhedron whose boundary consists of flat polygonal faces on some compact surface ?$S(\\mathcal P)$? (not necessarily homeomorphic to the sphere ?$S^{2}$)?. Let ?$vo_{R}(\\mathcal P), eo_{R}(\\mathcal P)$?, ?$ fo_{R}(\\mathcal P)$? be the numbers of rotational orbits of vertices, edges and faces, respectively, determined by the group ?$G = G_{R}(P)$? of all the rotations of the Euclidean space ?$E^{3}$? preserving ?$\\mathcal P$?. We define the ''rotational orbit Euler characteristic'' of ?$\\mathcal P$? as the number ?$Eo_{R}(\\mathcal P) = vo_{R}(\\mathcal P) - eo_{R}(\\mathcal P) + fo_{R}(\\mathcal P)$?. Using the Burnside lemma we obtain the lower and the upper bound for ?$Eo_{R}(\\mathcal P)$? in terms of the genus of the surface ?$S(P)$?. We prove that ?$Eo_{R} \\in \\lbrace 2,1,0,-1\\rbrace $? for any convex polyhedron ?$\\mathcal P$?. In the non-convex case ?$Eo_{R}$? may be arbitrarily large or small"},{"@xml:lang":"sl","#text":"Naj bo ?$\\mathcal P$? polieder, katerega površje sestoji iz ploskih poligonskih lic na neki kompaktni ploskvi ?$S(\\mathcal P)$? (ne nujno homeomorfni sferi ?$S^{2}$)?. Naj bodo ?$vo_{R}(\\mathcal P), eo_{R}(\\mathcal P)$?, ?$ fo_{R}(\\mathcal P)$? ševila rotacijskih orbit vozlišč, povezav in lic, določena z grupo ?$G = G_{R}(P)$? vseh takšnih rotacij evklidskega prostora ?$E^{3}$?, ki ohranjajo polieder ?$\\mathcal P$?. Definiramo ''Eulerjevo karakteristiko rotacijskih orbit'' poliedra ?$\\mathcal P$? kot število ?$Eo_{R}(\\mathcal P) = vo_{R}(\\mathcal P) - eo_{R}(\\mathcal P) + fo_{R}(\\mathcal P)$?. S pomočjo Burnsidove leme dobimo spodnjo in zgornjo mejo za ?$Eo_{R}(\\mathcal P)$?, ki ju izrazimo kot funkcijo reda ploskve ?$S(P)$?. Dokažemo, da je ?$Eo_{R} \\in \\lbrace 2,1,0,-1\\rbrace $? za vsak konveksen polieder ?$\\mathcal P$?. V nekonveksnem primeru je ?$Eo_{R}$? lahko poljubno velik ali majhen"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-SB2VZORR","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-SB2VZORR"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-SB2VZORR/1f497766-d5a2-4c66-9ca8-9690e92b2c8b/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-SB2VZORR/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-SB2VZORR"}}}}