336 KB42 KB200820252014Cunningham, Gabeštevilka:2letnik:7str. 299-315COBISSID:17046361ISSN:1855-3966URN:URN:NBN:SI:doc-EJ1Y63OOenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneaabstract regular polytopeequivelar polytopeflat polytopemixingMinimal equivelar polytopes|Every equivelar abstract polytope of type ?$\{p_1,\dots, p_{n-1}\}$? has at least ?$2p_1,\dots, 2p_{n-1}$? flags. In this paper, we study polytopes that attain this lower bound, called tight polytopes. Using properties of flat polytopes, we are able to give a complete local characterization of when a polytope is tight. We then show a way to construct tight polyhedra of type ?$\{p, q\}$? when ?$p$? and ?$q$? are not both odd, and a way to construct regular tight polytopes of type ?$\{2k_1,\dots, 2k_{n-1}\}$?TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije