Let $H$ be an integral ${\mathbb{R}}$-affine halfspace in $N_{\mathbb{R}}$. This means that $H=\{\omega\in N_{\mathbb{R}}\mid\langle u,\omega\rangle\leq c\}$ for some $u\in M$ and $c\in{\mathbb{R}}$. Using a translation, we may assume that $c=0$ and hence the boundary $\partial H$ is a linear subspace of $N_{\mathbb{R}}$. Let $[\omega_{\partial H,H}]$ be the generator of $N/(N\cap\partial H)\cong{\mathbb{Z}}$ which points outwards, i.e. there is $u_{\partial H,H}\in M$ such that $u_{\partial H,H}(H)\leq 0$ and $u_{\partial H,H}(\omega_{\partial H,H})=1$. We choose a representative $\omega_{\partial H,H}\in N$ and we note also that $u_{\partial H,H}$ is uniquely determined by the above properties.