Now let $\sigma$ be a polyhedron of dimension $n$ in $N_{\mathbb{R}}$. By definition, $\sigma$ is the intersection of finitely many halfspaces $H_{i}:=\{\omega\in N_{\mathbb{R}}\mid\langle u_{i},\omega\rangle\leq c_{i}\}$ with $u_{i}\in M_{\mathbb{R}}$ and $c_{i}\in{\mathbb{R}}$. A polytope is a bounded polyhedron. We say that $\sigma$ is an integral $G$-affine polyhedron for a subgroup $G$ of ${\mathbb{R}}$ if we may choose all $u_{i}\in M$ and all $c_{i}\in G$. In this case, we have a canonical integral ${\mathbb{R}}$-affine structure on the affine space ${\mathbb{A}}_{\sigma}$ generated by $\sigma$. If ${\mathbb{L}}_{\sigma}$ is the underlying real vector space of ${\mathbb{A}}_{\sigma}$, then this integral structure is given by the lattice $N_{\sigma}:={\mathbb{L}}_{\sigma}\cap N$. Using 2.3 and the above, we get a well-defined integral $\int_{\sigma}\alpha$ for any $\alpha\in A_{c}^{n,n}(U)$, where $U$ is an open neighbourhood of $\sigma$.