Cell geometry for cluster-based quasicrystal models

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Abstract
A new model of the geometrical structure of icosahedral quasicrystals is discussed that is based on icosahedral clusters connected by linkages (consistent with currently accepted motifs of the atomic structure), yet that is also a tiling by four kinds of ‘‘canonical cells.’’ Such a geometry is convenient for complete atomic structure models defined by decoration, especially if configurational disorder is to be included. The canonical-cell tiling is related and compared with previous models such as packings of Ammann rhombohedra, sphere packings on Penrose tilings, and two decoration models of Audier. The frequency of occurrence is estimated for each kind of cell or other geometrical object—the basis for stoichiometry calculations of decoration models. The 32 distinct local environments around a given cluster are described. Many useful periodic tilings of this class are described providing useful ‘‘rational approximants’’ of the true structure and hypothetical structure models for some recently discovered approximant crystal phases.