  We consider averaged shelling and coordination numbers of aperiodic tilings.
Shelling numbers count the vertices on radial shells around a vertex.
Coordination numbers, in turn, count the vertices on coordination shells of a
vertex, defined via the graph distance given by the tiling. For the
Ammann-Beenker tiling, we find that coordination shells consist of complete
shelling orbits, which enables us to calculate averaged coordination numbers
for rather large distances explicitly. The relation to topological invariants
of tilings is briefly discussed.
