Let $\Sigma$ be a complete fan in $N_{\mathbb{R}}$. Then $\Sigma$ is also a complete SCR polyhedral complex. Clearly $\operatorname{rec}({\Sigma})=\Sigma$. The toric scheme ${\mathcal{X}}_{{\Sigma}}$ is a model over $S$ of $X_{\Sigma}$ which is called the canonical model. Its special fibre

$${\mathcal{X}}_{\Sigma,o}=X_{\Sigma,k}$$

is the toric variety over $k$ defined by the fan $\Sigma$.