(5.1) Let $\mathscr{X}$ be a regular flat $R$-scheme such that $\mathscr{X}_{k}$ is a strict normal crossings divisor. We write $\mathscr{X}_{k}=\sum_{i\in I}N_{i}E_{i}$, where $E_{i},\,i\in I$ are the prime divisors in $\mathscr{X}_{k}$ and the numbers $N_{i}$ are their multiplicities. By the definition of a strict normal crossings divisor, every stratum of $\mathscr{X}_{k}$ is a regular $k$-scheme. Let $C$ be a stratum of $\mathscr{X}_{k}$. We say that $\mathscr{X}$ is toric along $C$ if there exist a regular toric $R$-scheme $\mathscr{Y}$ and a stratum $D$ of $\mathscr{Y}_{k}$ such that $\mathscr{Y}_{k}$ is a strict normal crossings divisor and the formal $R$-schemes $\widehat{\mathscr{X}_{/C}}$ and $\widehat{\mathscr{Y}_{/D}}$ are isomorphic.