  The aim of this paper is to determine the asymptotic growth rate of the
complexity function of cut-and-project sets in the non-abelian case. In the
case of model sets of polytopal type in homogeneous two-step nilpotent Lie
groups we can establish that the complexity function asymptotically behaves
like $r^{homdim(G) dim(H)}$. Further we generalize the concept of acceptance
domains to locally compact second countable groups.
