Remark 2

Assume that $W$ is irreducible and essential. If $H$ and $H'$ are two walls of $C$, then $m_{HH'} = +\infty$ if and only if $e_H = -e_{H'}$ (Prop. 3). By Props. 7 and 8, this can happen only if $H$ and $H'$ are the only walls of $C$ and $E$ is of dimension 1. Thus, the only case in which one of the $m_{HH'}$ is infinite is that in which $E$ is of dimension 1 and the group $W$ is generated by the reflections associated to two distinct points (cf. § 2, no. 4).

In the general case, the entries of the Coxeter matrix associated to $W$ are finite unless at least one of $E_1, \ldots, E_s$ is of the preceding type.