  Let X be a right-angled building. We show that the lattices in Aut(X) share
many properties with tree lattices. For example, we characterise the set of
covolumes of uniform and of nonuniform lattices in Aut(X), and show that the
group Aut(X) admits an infinite ascending tower of uniform and of nonuniform
lattices. These results are proved by constructing a functor from graphs of
groups to complexes of groups.
