0 KB255 KB28 KB200820252012Hartley, Michael IanHubard, IsabelLeemans, Dimitrištevilka:2letnik:5str. 371-382COBISSID:16438873ISSN:1855-3966URN:URN:NBN:SI:doc-AC49Q498enDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneaabstract chiral polytopesalmost simple groupsenostavne grupegeometric group theorypolitopisimetrijateorija grupTwo atlases of abstract chiral polytopes for small groups|We construct chiral abstract polytopes in two different ways. Firstly we seek them as quotients of regular polytopes arising from the Atlas of Small Regular Polytopes (?http://www.abstract-polytopes.com/atlas/?); the resulting atlas of chiral polytopes atlas is available on the website ?http://www.abstract-polytopes.com/chiral/?. Secondly, for each almost simple group ?$\Gamma$? such that ?$S \le \Gamma \le \text{Aut}(S)$? where ?$S$? is a simple group and ?$\Gamma$? is a group of order less than 900,000 listed in the Atlas of Finite Groups, we give, up to isomorphism, the number of abstract chiral polytopes on which ?$\Gamma$? acts regularly. The results have been obtained using a series of ?\textsc{Magma}? programs. All these polytopes are made available on the third author's website, at ?http://math.auckland.ac.nz/~dleemans/CHIRAL/?TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije