  We use geometry of Davis complex of a Coxeter group to prove the following
result: if G is an infinite indecomposable Coxeter group and $H\subset G$ is a
finite index reflection subgroup then the rank of H is not less than the rank
of G. This generalizes results of math/0305093. We also describe some
properties of the nerves of the group and the subgroup in the case of equal
ranks.
