Sphere packings and local environments in Penrose tilings

Abstract

Packings of spheres placed on vertices of two- or three-dimensional Penrose tilings arise in various models of glassy or ‘‘quasicrystal’’ metals. Such packings are described, with particular attention to the packing fractions and coordination numbers: In particular, one of the three-dimensional packings attains a packing fraction close to that of random close packing. The frequencies of various local environments are also enumerated. Relations between the tiling and density-wave pictures of icosahedral structures are clarified.