300 KB42 KB200820252015Conder, Marston D. E.Cunningham, Gabeštevilka:1letnik:8str. 69-82COBISSID:17368665ISSN:1855-3966URN:URN:NBN:SI:doc-HFCV3M95enUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneaabstract regular polytopeabstrakten regularen politopekvivelaren politopequivelar polytopeflat polytopeploščat politoptesen politoptight polytopeTight orientably-regular polytopes|It is known that every equivelar abstract polytope of type ?$\{p_1, \dots, p_{n - 1}\}$? has at least ?$2p_1 \cdots p_{n - 1}$? flags. Polytopes that attain this lower bound are called tight. Here we investigate the conditions under which there is a tight orientably-regular polytope of type ?$\{p_1, \dots, p_{n - 1}\}$?. We show that it is necessary and sufficient that whenever ?$p_i$? is odd, both ?$p_{i - 1}$? and ?$p_{i + 1}$? (when defined) are even divisors of ?$2p_i$?Znano je, da ima vsak ekvivelaren abstrakten politop tipa ?$\{p_1, \dots, p_{n - 1}\}$? najmanj ?$2p_1 \cdots p_{n - 1}$? praporov. Politopi, ki dosežejo to spodnjo mejo, se imenujejo tesni. Tukaj raziskujemo pogoje, pri katerih obstaja tesen orientabilno-regularen politop tipa ?$\{p_1, \dots, p_{n - 1}\}$?. Pokažemo, da je potrebno in zadostno, da sta pri vsakem lihem številu ?$p_i$? tako ?$p_{i - 1}$? kot ?$p_{i + 1}$? (kadar sta definirana) soda delitelja števila ?$2p_i$?TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije