Coordination numbers of the vertex graph of a Penrose tiling

Anton Shutov; Andrey Maleev

Index: 10.1107/S2053273318000062

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Abstract

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.