Let $\Lambda$ be a convex polyhedron in $N_{\mathbb{R}}$. Then both the indicator function $\iota_{\Lambda}$ and the support function $\Psi_{\Lambda}$ are concave and piecewise affine. We have $\Psi_{\Lambda}^{\vee}=\iota_{\Lambda}$. In particular, if we fix an isomorphism $N_{\mathbb{R}}\simeq\mathbb{R}^{n}$, the function

$$\Psi_{\Delta^{n}}\colon N_{\mathbb{R}}\longrightarrow\mathbb{R},\quad(u_{1},\dots,u_{n})\longmapsto\min\{0,u_{1},\dots,u_{n}\}$$

is the support function of the standard simplex $\Delta^{n}=\operatorname{conv}(\boldsymbol{0},e^{\vee}_{1},\dots,e^{\vee}_{n})\subset M_{\mathbb{R}}$, where $\{e_{1},\dots,e_{n}\}$ is the standard basis of $\mathbb{R}^{n}$ and $\{e_{1}^{\vee},\dots,e_{n}^{\vee}\}$ is the dual basis. Hence, $\operatorname{stab}(\Psi_{\Delta^{n}})=\Delta^{n}$ and $\Psi_{\Delta^{n}}^{\vee}=\iota_{\Delta^{n}}$.