1964/01/01 by John Leech · 4 citations
Engineering · Computer Science · Mathematics · #Structural Analysis and Optimization #Advanced Materials and Mechanics #Computational Geometry and Mesh Generation #Sphere packing #SPHERES #Lattice (music) #Mathematics #Euclidean geometry #Euclidean space #Reciprocal lattice #Space (punctuation) #Combinatorics #Geometry #Physics #Optics
paper · pdf · doi:10.4153/cjm-1964-065-1
openalex publication_date 1964/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
This paper is concerned with the packing of equal spheres in Euclidean spaces [ n ] of n > 8 dimensions. To be precise, a packing is a distribution of spheres any two of which have at most a point of contact in common. If the centres of the spheres form a lattice, the packing is said to be a lattice packing . The densest lattice packings are known for spaces of up to eight dimensions (1, 2) , but not for any space of more than eight dimensions. Further, although non-lattice packings are known in [3] and [5] which have the same density as the densest lattice packings, none is known which has greater density than the densest lattice packings in any space of up to eight dimensions, neither, for any space of more than two dimensions, has it been shown that they do not exist.