Sphere packings and packings of ellipsoids

Abstract

Homogeneous and heterogeneous sphere packings and packings of circles together with their densities are defined, and a classification into types of sphere packings and types of circle packings is introduced. Some properties of the 11 types of homogeneous circle packings are described in a table. As the derivation of all types of homogeneous sphere packings is not yet complete, a corresponding table presents only examples with high coordination numbers (10 to 12) and respective high densities and with low coordination numbers (3 and 4) and extremely low densities. The application of sphere packings to the description of inorganic crystal structures is demonstrated by examples. Interpenetrating sphere packings and their relations to other crystallographic problems are discussed. A short survey on the problem of packings of ellipses or ellipsoids is given. Keywords: basic structural features; ellipse and ellipsoid packing; interpenetrating packing; packing