  We show that a point process of hard spheres exhibits long-range
orientational order. This process is designed to be a random perturbation of a
three-dimensional lattice that satisfies a specific rigidity property, examples
include the FCC and HCP lattices. We also define two-dimensional near-lattice
processes by local, geometry dependent hard disk conditions. Earlier results
about existence of long-range orientational order carry over and we obtain the
existence of infinite-volume measures on two-dimensional point configurations
that turn out to follow the orientation of a fixed triangular lattice arbitrary
closely.
