Sphere Packing - Classification and Terminology

Classification and Terminology

A lattice arrangement (commonly called a regular arrangement) is one in which the centers of the spheres form a very symmetric pattern which only needs n vectors to be uniquely defined (in n-dimensional Euclidean space). Lattice arrangements are periodic. Arrangements in which the spheres do not form a lattice (often referred to as irregular) can still be periodic, but also aperiodic (properly speaking non-periodic) or random. Lattice arrangements are easier to handle than irregular ones—their high degree of symmetry makes it easier to classify them and to measure their densities.