Dense-packed arrays on surfaces of constant negative curvature

Dense-packed assemblies of hard spheres are standard models of disorder in metallic glasses. Such packings are difficult to obtain with identical disks on flat two-dimensional surfaces because triangular packing units are easily incorporated into a hexagonal close-packed lattice. By packing disks on a two-dimensional manifold of constant negative curvature, however, one can study packing problems quite similar to those found in three-dimensional flat space.