{"?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-HQ31X4IO/0a55783d-ff0a-4575-9316-5c688839f7af/PDF","dcterms:extent":"647 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-HQ31X4IO/7657f075-aeb9-416a-a323-97884251c839/TEXT","dcterms:extent":"66 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-HQ31X4IO/568d621b-c8f4-45d0-9913-1a81126364a9/PDF","dcterms:extent":"121 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-HQ31X4IO/91a936b1-ac64-4c13-978c-82c5018609b5/TEXT","dcterms:extent":"3 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-HQ31X4IO","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2023","dc:creator":["Göring, Frank","Winter, Martin"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:23"},{"@xml:lang":"sl","#text":"P2.01 (29 str.)"}],"dc:identifier":["DOI:10.26493/1855-3974.2712.6be","COBISSID_HOST:149468675","ISSN:1855-3966","URN:URN:NBN:SI:doc-HQ31X4IO"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"en","#text":"convex polytopes"},{"@xml:lang":"en","#text":"edge-transitive"},{"@xml:lang":"sl","#text":"konveksni politopi"},{"@xml:lang":"sl","#text":"povezavno tranzitiven"},{"@xml:lang":"sl","#text":"simetrija politopov"},{"@xml:lang":"en","#text":"symmetry of polytopes"},{"@xml:lang":"sl","#text":"točkovno tranzitiven"},{"@xml:lang":"en","#text":"vertex-transitive"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"The edge-transitive polytopes that are not vertex-transitive|"},"dc:description":[{"@xml:lang":"sl","#text":"In 3-dimensional Euclidean space there exist two exceptional polyhedra, the rhombic dodecahedron and the rhombic triacontahedron, the only known polytopes (besides polygons) that are edge-transitive without being vertex-transitive. We show that these polyhedra do not have higher-dimensional analogues, that is, that in dimension ?$d \\geq 4$?, edgetransitivity of convex polytopes implies vertex-transitivity. More generally, we give a classification of all convex polytopes which at the same time have all edges of the same length, an edge in-sphere and a bipartite edge-graph. We show that any such polytope in dimension ?$d \\geq 4$? is vertex-transitive"},{"@xml:lang":"sl","#text":"V 3-dimenzionalnem evklidskem prostoru obstajata dva izjemna poliedra, rombski dodekaeder in rombski triakontaeder, edina znana politopa (poleg poligonov), ki sta povezavno tranzitvna, ne pa tudi točkovno tranzitivna. Pokažemo, da za ta dva poliedra ne obstajajo nobene podobne strukture v višjih dimenzijah, to pomeni, da v dimenziji ?$d \\geq 4$? povezavna tranzitivnost konveksnega politopa implicira točkovno tranzitivnost. Splošneje, podamo klasifikacijo vseh konveksnih politopov, ki imajo hkrati vse povezave iste dolžine, včrtano sfero, ki se vsake povezave dotika v eni sami točki, ter dvodelen povezavni graf. Pokažemo, da je vsak tak politop v dimenziji ?$d \\geq 4$? točkovno tranzitiven"}],"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-HQ31X4IO","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-HQ31X4IO"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-HQ31X4IO/0a55783d-ff0a-4575-9316-5c688839f7af/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-HQ31X4IO/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-HQ31X4IO"}}}}