Sphere packings and local environments in Penrose tilings.
01 January 1986
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 3D 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.