  We investigate ordering properties of two-dimensional granular materials
using several shapes created by welding ball bearings together. Ordered domains
form much more easily in two than in three dimensions, even when configurations
lack long-range order. The onset of ordered domains occurs near a packing
density of 0.8, a phenomenon observed previously for disks. One of our shapes,
the trapezoid, has packings that remain disordered and near the transition
density even after annealing by shaking. Since random packings are unstable for
disks and many other shapes in two dimensions, trapezoid packings provide a new
approach to studying two-dimensional randomness. We also find that the
rotational symmetry of a shape is an excellent predictor of how easily it
orders, and a potential guide to identifying two-dimensional shapes that remain
random after annealing.
