Polyhedra of three quasilattices associated with the icosahedral group

A systematic approach is presented for the construction of families of polytopes associated with a given group G and subgroup H. This procedure is applied to the icosahedral group and its three dihedral subgroups yielding three families of polyhedra in ³. These families form the cells of three types of quasilattices associated with the icosahedral group, and hence are candidates for modelling quasicrystal structures. Some of the polyhedra are illustrated.