# 4.3 – Aut | Walls

A hyperplane $(v)^{\perp}$ of $\ppp_{S}$ such that $$v\in\{ x \in S\otimes \QQ \, \mid x\in \rl, (x)^\perp \cap \ps \neq \emptyset \}$$ is called a wall of a $\ps$-chamber $D$ whenever

$\text{Int}(D)\cap(v)^{\perp}=\emptyset$

and when there exists a non-empty open subset of $(v)^{\perp}$
contained in $D\cap(v)^{\perp}.$

Walls $(v)^\perp$ with $\langle v, v \rangle_{S}=-2$ are called

$\cu$-walls.