The correspondence $\Pi\mapsto{\mathcal{X}}_{\operatorname{c}(\Pi)}$, where $\operatorname{c}(\Pi)$ is the fan introduced in Definition 3.7, is a bijection between the set of complete SCR polyhedral complexes in $N_{\mathbb{R}}$ and the set of isomorphism classes of proper toric schemes over $S$ of relative dimension $n$.