On the subgroup structure of the hyperoctahedral group in six dimensions
  We investigate the subgroup structure of the hyperoctahedral group in six dimensions. In particular, we study the subgroups isomorphic to the icosahedral group. We classify the orthogonal crystallographic representations of the icosahedral group and analyse their intersections and subgroups, using results from graph theory and their spectra. 
Emilio Zappa, Eric C. Dykeman, Reidun Twarock
math.GR