Let $\Sigma$ be a complete fan on $N_{\mathbb{R}}$. Let ${\overline{L}}_{i}=(L_{i},\|\cdot\|_{i})$, $i=0,\dots,n$, be toric line bundles on $X_{\Sigma}$ generated by its global sections and equipped with approachable adelic toric metrics. For each $i$, let $s_{i}$ be a toric section of $L_{i}$. Then the height of $X_{\Sigma}$ with respect to ${\overline{L}}_{0},\dots,{\overline{L}}_{n}$ is

(6.38)

$\displaystyle\operatorname{h}_{{\overline{L}}_{0},\dots,{\overline{L}}_{n}}(X_{\Sigma})=$

$\displaystyle\left[\sum_{v\in\mathfrak{M}_{\mathbb{K}}}n_{v}\operatorname{MI}_{M}(\vartheta_{{\overline{L}}_{0}^{v},s_{0}},\dots,\vartheta_{{\overline{L}}_{n}^{v},s_{n}})\right]\in\mathbb{R}/\operatorname{def}(\mathbb{K}^{\times}).$

In particular, if ${\overline{L}}_{0}=\dots={\overline{L}}_{n}={\overline{L}}$, let $s$ be a toric section and put $\Delta=\operatorname{stab}(\psi_{{\overline{L}}^{v},s})$. Then

$$\operatorname{h}_{{\overline{L}}}(X_{\Sigma})=\left[(n+1)!\sum_{v\in\mathfrak{M}_{\mathbb{K}}}n_{v}\int_{\Delta}\vartheta_{{\overline{L}}^{v},s}\,\text{\rm d}\operatorname{vol}_{M}\right].$$