Let $\Sigma$ be a complete fan in $N_{\mathbb{R}}$ and $\Psi$ a strictly concave function on $\Sigma$. The correspondence $F\mapsto O(\sigma_{F})$ is a bijection between the set of faces of $\Delta_{\Psi}$ and the set of the orbits under the action of $\mathbb{T}$ on $X_{\Sigma}$.