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.
Keywords: coordination sequences; coordination shells; growth form; vertex graph of the Ammann–Beenker tiling.