Coordination sequences for lattices

Abstract

Abstract Coordination sequences for five 3-dimensional, ten 4-dimensional and eleven higher-dimensional lattices have been determined and all but one can be expressed as simple polynomials. Some regularities in these polynomials are observed. The correlation between topological and geometric density is demonstrated for 4-dimensional lattices. It is conjectured that hexagonal closest packing is topologically the densest packing in three dimensions.