0 KB505 KB23 KB200820252013Gévay, GáborWills, Jörg M.številka:1letnik:6str. 1-11COBISSID:16467033ISSN:1855-3966URN:URN:NBN:SI:doc-7NEMPAQ5enDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneaequivelar polyhedrongenusLeonardo polyhedronregular polyhedronSchläfli symbolsymmetry groupOn regular and equivelar Leonardo polyhedra|A Leonardo polyhedron is a 2-manifold without boundary, embedded in Euclidean 3-space ?${\mathbb E}^3$?, built up of convex polygons and with the geometric symmetry (or rotation) group of a Platonic solid and of genus ?$g \ge 2$?. The polyhedra are named in honour of Leonardo's famous illustrations. Only six combinatorially regular Leonardo polyhedra are known: Coxeter's four regular skew polyhedra, and the polyhedral realizations of the regular maps by Klein of genus 3 and by Fricke and Klein of genus 5. In this paper we construct infinite series of equivelar (i.e. locally regular) Leonardo polyhedra, which share some properties with the regular ones, namely the same Schläfli symbols and related topological structure. So the weaker condition of local regularity allows a much greater variety of symmetric polyhedraTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije