The vertex graph of the Ammann–Beenker tiling is a well-known quasiperiodic graph with an eightfold rotational symmetry. The coordination sequence and coordination shells of this graph are studied. It is proved that there exists a limit growth form for the vertex graph of the Ammann–Beenker tiling. This growth form is an explicitly calculated regular octagon. Moreover, an asymptotic formula for the coordination numbers of the vertex graph of the Ammann–Beenker tiling is also proved.

中文翻译：

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Ammann-Beenker 平铺顶点图的配位壳和配位数

Ammann-Beenker 平铺的顶点图是著名的具有八重旋转对称性的准周期图。研究了该图的配位序列和配位壳。证明了Ammann-Beenker 平铺的顶点图存在极限增长形式。这种生长形式是明确计算的正八边形。此外，还证明了Ammann-Beenker平铺顶点图配位数的渐近公式。