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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.
MSC:
82D25 Statistical mechanical studies of crystals
52C22 Tilings in \(n\) dimensions (aspects of discrete geometry)
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