172 KB2 KB396 KB33 KB2021Ivić Weiss, AsiaMontero, Antonio12 str.DOI:10.26493/2590-9770.1354.b40ISSN:2590-9770COBISSID_HOST:70562563URN:URN:NBN:SI:doc-6NJFGQ90enFakulteta za matematiko, naravoslovje in informacijske tehnologijeThe art of discrete and applied mathematicsabstract polytopeshypermapshypertopesregularitythin geometriesLocally spherical hypertopes from generalised cubes|We show that every non-degenerate regular polytope can be used to construct a thin, residually-connected, chamber-transitive incidence geometry, i.e. a regular hypertope. These hypertopes are related to the semi-regular polyotopes with a tail-triangle Coxeter diagram constructed by Monson and Schulte. We discuss several interesting examples derived when this construction is applied to generalised cubes. In particular, we produce an example of a rank 5 finite locally spherical proper hypertope of hyperbolic type. No such examples were previously knownTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije