Lattices acting on polyhedral complexes

Let G be a locally compact topological group.  A discrete subgroup Γ
of G is called a lattice if the quotient of G by Γ has finite volume.
We study lattices in G the automorphism group of a locally finite
polyhedral complex.  Cases considered include right-angled buildings
and Fuchsian buildings, as well as certain non-buildings with links
such as the Petersen graph.