Remark 1

Assume that $W$ is essential, irreducible and infinite and retain the notation of Prop. 11. Since $U$ is an isomorphism from $W_a$ to $U(W)$, it follows that the Coxeter graph of the group of displacements $U(W)$ (which is generated by the reflections $U(s_H)$ for $H \in \mathfrak{H}$) can be obtained from the Coxeter graph of $W$ by omitting the vertex $i$ corresponding to the unique wall of $C$ that is not a wall of $C'$.