Let $\Sigma_{\Delta}$ and $\Psi_{\Delta}$ be the fan and the support function on $N_{\mathbb{R}}$ induced by $\Delta$. Let $(X_{\Sigma_{\Delta}},D_{\Psi_{\Delta}})$ be the associated polarized toric variety over $\mathbb{Q}$ and write $L={\mathcal{O}}(D_{\Psi_{\Delta}})$. By Lemma 7.21(1), $\vartheta$ is a concave function on $\Delta$. By Theorem 5.73, it corresponds to some approachable toric metric on $L(\mathbb{C})$. We denote this metric by $\|\cdot\|_{\Delta,\ell,c}$. We write ${\overline{L}}$ for the line bundle $L$ equipped with the metric $\|\cdot\|_{\Delta,\ell,c}$ at the Archimedean place of $\mathbb{Q}$ and with the canonical metric at the non-Archimedean places. This is an example of an adelic toric metric.