The $n$-dimensional Manhattan network $M_n$---a special case of$n$-regular digraph---is formally defined and some of its structuralproperties are studied. In particular, it is shown that $M_n$ is aCayley digraph, which can be seen as a subgroup of the $n$-dimversion of the wallpaper group $pgg$. These results induce a usefulnew presentation of $M_n$, which can be applied to design a(shortest-path) local routing algorithm and to study some othermetric properties. Also it is shown that the $n$-dim Manhattannetworks are Hamiltonian and, in the standard case (that is,dimension two), they can be decomposed in two arc-disjointHamiltonian cycles. Finally, some results on the connectivity anddistance-related parameters of $M_n$, such as the distribution ofthe node  distances and the diameter are presented.