Solution
= Solution
The <Cayley graph> $\operatorname{Cay}_S(W)$ has vertex set $W$ and an unoriented edge $\{w,ws\}$ for every $w\in W$ and $s\in S$.
For a <reflection of a Coxeter group> $r\in R$, its wall is
$$
H_r=\bigl\{\{w,ws\}:wsw^{-1}=r\bigr\}.
$$
Equivalently, these are the edges fixed setwise and reversed by left multiplication by $r$. Removing their interiors separates the Cayley graph into two <half-space of a Coxeter group>[half-spaces].