Let $\Lambda$ be a rational polyhedron in $M_{\mathbb{R}}$ and $\operatorname{aff}(\Lambda)$ its affine hull. We denote by $L_{\Lambda}$ the linear subspace of $M_{\mathbb{R}}$ associated to $\operatorname{aff}(\Lambda)$ and by $M(\Lambda)$ the induced lattice $M\cap L_{\Lambda}$. By definition, $\operatorname{vol}_{M(\Lambda)}$ is a measure on $L_{\Lambda}$, and we will denote also by $\operatorname{vol}_{M(\Lambda)}$ the measure induced on $\operatorname{aff}(\Lambda)$. If $v\in N_{\mathbb{R}}$ is orthogonal to $L_{\Lambda}$, we define $\langle v,\Lambda\rangle=\langle v,x\rangle$ for any $x\in\Lambda$. Furthermore, when $\dim(\Lambda)=n$ and $F$ is a facet of $\Lambda$, we will denote by $v_{F}\in N$ the vector of minimal length that is orthogonal to $L_{F}$ and satisfies $\langle v_{F},F\rangle\leq\langle v_{F},x\rangle$ for each $x\in\Lambda$. In other words, $v_{F}$ is the minimal inner integral orthogonal vector of $F$ as a facet of $\Lambda$.