We have a decomposition $B^{sing}=B^{sing}_{n-1}\cup B^{sing}_{\leq n-2}$, where $B^{sing}_{\leq n-2}$ consists of strata of dimension less or equal than $n-2$, $B^{sing}_{n-1}$ is the union of strata of dimension $n-1$, and locally near every point $x\in B^{sing}_{n-1}$ the ${\bf Z}$-affine structure is modeled by the “book” $\cup_{i\in I}{{\bf R}}^{n-1}\times{{\bf R}}_{\geq 0}$. Here $I$ is a finite set, all half-spaces have a common plane ${{\bf R}}^{n-1}\times\{0\}$ and $x$ belongs to this plane. ${\bf Z}$-affine structure on $B^{sm}=\sqcup_{i\in I}{{\bf R}}^{n-1}\times{{\bf R}}_{>0}$ is the natural one.