  Hard-particle packings have served as useful starting points to study the
structure of diverse systems such as liquids, living cells, granular media,
glasses, and amorphous solids. Howard Reiss has played a major role in helping
to illuminate our understanding of hard-particle systems, which still offer
scientists many interesting conundrums. Jammed configurations of hard particles
are of great fundamental and practical interest. What one precisely means by a
"jammed" configuration is quite subtle and considerable ambiguity remains in
the literature on this question. We will show that there is a multiplicity of
generation, selection, and classification procedures for jammed configurations
of identical d-dimensional spheres. We categorize common ordered lattices
according to our definitions and discuss implications for random disk and
sphere packings. We also show how the concept of rigidity percolation (which
has been used to understand the mechanical properties of network glasses) can
be generalized to further characterize hard-sphere packings.
