  We prove that the simplicial boundary of a CAT(0) cube complex admitting a
proper, cocompact action by a virtually $\integers^n$ group is isomorphic to
the hyperoctahedral triangulation of $S^{n-1}$, providing a class of groups $G$
for which the simplicial boundary of a $G$-cocompact cube complex depends only
on $G$. We also use this result to show that the cocompactly cubulated
crystallographic groups in dimension $n$ are precisely those that are
\emph{hyperoctahedral}. We apply this result to answer a question of Wise on
cocompactly cubulating virtually free abelian groups.
