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Coordination numbers of the vertex graph of a Penrose tiling. (English) Zbl 1444.82038
Summary: A new approach to study coordination shells and coordination sequences of quasiperiodic graphs is suggested. The structure of the coordination shells in the vertex graph of a Penrose tiling is described. An asymptotic formula for its coordination numbers is obtained. An essentially different behaviour of the coordination numbers for even and odd shells is revealed.
82D25 Statistical mechanical studies of crystals
52C22 Tilings in \(n\) dimensions (aspects of discrete geometry)
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