This follows from Lemma 5.39 and the fact that the special fibre is

$${\mathcal{X}}_{\Lambda,o}=\coprod_{\Lambda^{\prime}\text{ face of }\Lambda}O(\Lambda^{\prime}),$$

and $\operatorname{ri}(\Lambda)=\Lambda\setminus\bigcup_{\Lambda^{\prime}\text{ proper face of }\Lambda}\Lambda^{\prime}$. ∎