Suppose that $\Gamma$ is a lattice polytope and let $F$ be a facet of $\Gamma$. Recall that $M(F)$ is the lattice $L_{F}\cap M$ and let $M(F)^{\prime}$ be the sublattice of $M(F)$ generated by the differences of the lattice points in $F$. Then the vector $u_{F}$ can be alternatively defined as $[M(F):M(F)^{\prime}]$ times the primitive inner normal vector to the facet $F$.