We have the following canonical decomposition of the boundary $\partial\bar{\mathcal{P}_{n}}=\bigcup\limits_{j=0}^{n-1}\partial_{j}\bar{\mathcal{P}_{n}}$, where $\partial_{j}\bar{\mathcal{P}_{n}}$ is a $(2n-j)$-dimensional smooth manifold such that each its connected component is a trivial $T^{j}$-fibration over $\mathcal{P}_{n-j}$. Different parts do not intersect: $\partial_{j}\bar{\mathcal{P}_{n}}\cap\partial_{k}\bar{\mathcal{P}_{n}}=\emptyset$, if $j\neq k$, but the closure of $\partial_{j}\bar{\mathcal{P}_{n}}$ contains $\partial_{k}\bar{\mathcal{P}_{n}}$ for all $k\leq j$. The number of connected components is $\begin{pmatrix}n+2\\ j+2\end{pmatrix}$.