  The recent articles of Waldspurger and Meinrenken contained the results of
tilings formed by the sets of type $(1-w)C^\circ$, $w\in W$, where $W$ is a
linear or affine Weyl group, and $C^\circ$ is an open kernel of a fundamental
chamber $C$ of the group $W$. In this article we generalize these results to
cocompact hyperbolic reflection groups. We also give more clear and simple
proofs of the Waldspurger and Meinrenken theorems.
