5531 KB56 KB200820252019Drach, KostiantynHaidamaka, YuriiMixer, MarkSkoryk, Maksymletnik:17številka:2str. 493-514ISSN:1855-3966COBISSID_HOST:18962521URN:URN:NBN:SI:doc-NU82PBVAenUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneacoversGaussian and Eisenstein integersGaussova in Eisensteinova cela številagroupsgrupekrovimapspolitopipolytopeszemljevidiArchimedean toroidal maps and their minimal almost regular covers|The automorphism group of a map acts naturally on its flags (triples of incident vertices, edges, and faces). An Archimedean map on the torus is called almost regular if it has as few flag orbits as possible for its type; for example, a map of type ?$(4.8^2)$? is called almost regular if it has exactly three flag orbits. Given a map of a certain type, we will consider other more symmetric maps that cover it. In this paper, we prove that each Archimedean toroidal map has a unique minimal almost regular cover. By using the Gaussian and Eisenstein integers, along with previous results regarding equivelar maps on the torus, we construct these minimal almost regular covers explicitlyGrupa avtomorfizmov zemljevida deluje naravno na njegovih praporih (trojicah incidentnih vozlišč, povezav in lic). Arhimedski zemljevid na torusu se imenuje skoraj regularen, če ima tako malo orbit praporov, kot je to le mogoče za njegov tip; na primer, zemljevid tipa ?$(4.8^2)$? se imenuje skoraj regularen, če ima natanko tri orbite praporov. Za dani zemljevid danega tipa bomo obravnavali druge, bolj simetrične zemljevide, ki so njegovi krovi. V članku dokažemo, da ima vsak arhimedski torusni zemljevid en sam minimalen skoraj regularen krov. Z uporabo Gaussovih in Eisensteinovih celih števil, skupaj s predhodnimi rezultati, ki se nanašajo na ekvivelarne zemljevide na torusu, eksplicitno konstruiramo te minimalne skoraj regularne kroveTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije