276 KB19 KB200820252021Bracho, JavierMontejano, LuisPérez, Eric PauliRamírez-Alfonsín, Jorge Luisštevilka:1letnik:20str. 143-149DOI:10.26493/1855-3974.2194.eabISSN:1855-3966COBISSID_HOST:91621379URN:URN:NBN:SI:doc-ASCWRHMQenUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneaantipodalantipodendualitydualnostgrafigraphspoliedripolyhedrasebi dualenself-dualStrongly involutive self-dual polyhedra|A polyhedron is a graph which is simple, planar and 3-connected. In this note, we classify the family of strongly involutive self-dual polyhedra. The latter is done by using a well-known result due to Tutte characterizing 3-connected graphs. We also show that in this special class of polyhedra self-duality behaves topologically as the antipodal mapping. These self-dual polyhedra are related with several problems in convex and discrete geometry including the Vázsonyi problemPolieder je graf, ki je enostaven, ravninski in 3-povezan. V tem prispevku klasificiramo družino krepko involutivnih sebi dualnih poliedrov. To storimo z uporabo znanega rezultata Tutteja o karakterizaciji 3-povezanih grafov. Pokažemo tudi, da se v tem posebnem razredu poliedrov lastnost sebi dualnost v topološkem smislu obnaša kot antipodna preslikava. Ti sebi dualni poliedri so povezani s številnimi problemi v konveksni in diskretni geometriji, med drugim tudi z Vázsonyijevim problemomTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije