If $\Delta$ is a lattice polytope, its indicator function is a V-lattice function, its support function $\Psi_{\Delta}$ is an H-lattice function and, when $\Delta$ has maximal dimension, the fan $\Sigma_{\Delta}$ is a rational fan. In particular, if the isomorphism $N\simeq\mathbb{R}^{n}$ of Example 3.65 is given by the choice of an integral basis $e_{1},\dots,e_{n}$ of $N$, then $\Delta^{n}$ is a lattice polytope, the function $\Psi_{\Delta^{n}}$ is an H-lattice concave function and $\Sigma_{\Delta^{n}}$ is a rational fan. If we write $e_{0}=-\sum_{i=1}^{n}e_{i}$, this is the fan generated by the vectors $e_{0},e_{1},\dots,e_{n}$ in the sense that each cone of $\Sigma_{\Delta^{n}}$ is the cone generated by a strict subset of the above set of vectors. Figure 3 illustrates the case $n=2$.