Let $\Sigma$ be a complete fan on $N_{\mathbb{R}}$ and $\sigma\in\Sigma$ a cone of codimension $d$. To it, we have associated the dimension $d$ closed subvariety $V(\sigma)$ and the closed immersion $\iota_{\sigma}\colon X_{\Sigma(\sigma)}\to X_{\Sigma}$ whose image is $V(\sigma)$. Let $L$ be a toric line on $X_{\Sigma}$ generated by global sections, $s$ a toric section, $\Psi$ the corresponding support function, and $\|\cdot\|$ an approachable toric metric on $L^{{\text{\rm an}}}$. As usual write ${\overline{L}}=(L,\|\cdot\|)$. Then

$$\operatorname{h}^{\operatorname{tor}}_{{\overline{L}}}(V(\sigma))=\operatorname{h}^{\operatorname{tor}}_{\iota_{\sigma}^{\ast}{\overline{L}}}(X_{\Sigma(\sigma)})=(d+1)!\int_{F_{\sigma}}\vartheta_{{\overline{L}},s}\,\text{\rm d}\operatorname{vol}_{M(F_{\sigma})},$$

where $F_{\sigma}$ is the face of $\Delta_{\Psi}$ corresponding to $\sigma$, $M(F_{\sigma})$ is the lattice induced by $M$ on the linear space associated to $F_{\sigma}$ and $\iota_{\sigma}^{\ast}L$ has the structure of toric line bundle of Proposition 4.34.