  Let $(W,S)$ be a Coxeter system with Davis complex $\Sigma$. The polyhedral
automorphism group $G$ of $\Sigma$ is a locally compact group under the
compact-open topology. If $G$ is a discrete group (as characterised by
Haglund--Paulin), then the set $\mathcal V_u(G)$ of uniform lattices in $G$ is
discrete. Whether the converse is true remains an open problem. Under certain
assumptions on $(W,S)$, we show that $\mathcal V_u(G)$ is non-discrete and
contains rationals (in lowest form) with denominators divisible by arbitrarily
large powers of any prime less than a fixed integer. We explicitly construct
our lattices as fundamental groups of complexes of groups with universal cover
$\Sigma$. We conclude with a new proof of an already known analogous result for
regular right-angled buildings.
