A Finite Packing Problem

The maximum density of packings of a given type into the whole of a Euclidean space is defined to be the limit of the maximum density of such packings into a cube as the edge of the cube goes to infinity.For E2 in particular, a number of well known results such as those due to A. Thue [1], L. Fejes-Toth [2], and C. A. Rogers [3] yield precise information about packings into the whole space. They are however of limited applicability to problems of finite packing in so-far as each requires some restriction upon the boundary of the configuration.