Let $(X_{\Sigma},D_{\Psi})$ be a toric variety with a $\mathbb{T}$-Cartier divisor. Every toric model $({\mathcal{X}},D,e)$ of $(X_{\Sigma},D_{\Psi})$ induces a model $({\mathcal{X}},\mathcal{O}(D),e)$ of $(X_{\Sigma},L_{\Psi})$, in the sense of Definition 2.16, where the identification of $\mathcal{O}(D)|_{X_{\Sigma}}$ with $L_{\Psi}^{\otimes e}$ matches the toric sections. Such models will be called toric models.