Conceptual question about extended affine Weyl group $\hat{W}_a$

Question

Denote an affine Weyl group by $W_a$, and let $\mathcal{H}$ be the collection of hyperplanes $H_{\alpha, k}, \text{ } \alpha \in \Phi,k \in \mathbb{Z}$. I know for a fact that $W_a$ and the extended affine Weyl group $\hat{W}_a$ permute the hyperplanes in $\mathcal{H}$. Moreover, $W_a$ simply transitively permutes the alcoves $\mathcal{A}$, i.e. the collection of connected components of $V \setminus \bigcup_{H \in \mathcal{H}} H $, where $V$ is the underlying vector space. But is this also necessary true for $\hat{W}_a$, that is, does it also simply transitively permute the alcoves? If so, or if not, then why?