Lattices in automorphism groups of hyperbolic buildings

Let $G$ be a locally compact group and $\Gamma$ a lattice in $G$. The
classical setting for studying lattices is that where $G$ is an
algebraic
group. More recently, the lattices in $G$ the automorphism group of a
tree have been studied. We consider the lattices in $G$ the
automorphism
group of a higher-dimensional polyhedral complex, such as a hyperbolic
building. In particular, when $G$ is the automorphism group of
Bourdon’s
building $I_{pq}$, we find the exact set of covolumes of cocompact
lattices, and show that $G$ admits an infinite ascending tower of
cocompact lattices.