A polyhedral complex in $N_{\mathbb{R}}$ is a finite convex subdivision whose elements are convex polyhedra. A polyhedral complex is called strongly convex if all of its polyhedra are strongly convex. It is called conic if all of its elements are cones. A strongly convex conic polyhedral complex is called a fan. If $\Pi$ is a polyhedral complex, we will denote by $\Pi^{i}$ the subset of $i$-dimensional polyhedra of $\Psi$. In particular, if $\Sigma$ is a fan, $\Sigma^{i}$ is its subset of $i$-dimensional cones.