title: On the subgroup structure of the hyperoctahedral group in six dimensions.
abstract: The subgroup structure of the hyperoctahedral group in six dimensions is investigated. In particular, the subgroups isomorphic to the icosahedral group are studied. The orthogonal crystallographic representations of the icosahedral group are classified and their intersections and subgroups analysed, using results from graph theory and their spectra.
authors.affiliation: Department of Mathematics, University of York, York, UK.
authors.forename: Emilio
authors.initials: E
authors.lastname: Zappa
authors.affiliation: Department of Mathematics, University of York, York, UK.
authors.forename: Eric C
authors.initials: EC
authors.lastname: Dykeman
authors.affiliation: Department of Mathematics, University of York, York, UK.
authors.forename: Reidun
authors.initials: R
authors.lastname: Twarock
mesh_terms: D000465:Algorithms; D003461:Crystallography / Q000379:methods*; D008956:Models, Chemical
keywords: crystallographic representation; hyperoctahedral group; icosahedral group; spectral graph theory; symmetry