  We introduce the notion of a "crystallographic sphere packing," defined to be
one whose limit set is that of a geometrically finite hyperbolic reflection
group in one higher dimension. We exhibit for the first time an infinite family
of conformally-inequivalent such with all radii being reciprocals of integers.
We then prove a result in the opposite direction: the "superintegral" ones
exist only in finitely many "commensurability classes," all in dimensions below
30.
