Table of maximal density of a packing of equal spheres in n-dimensional Euclidean space. The values are proved for the cases n = 1, 2, 3, 8, 24, but only conjectural for n = 4, 5, 6, 7, 12, 16. Reference: J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer, 3rd. ed., 1998. See pp. xix and 15. The A-numbers refer to the decimal expansion of the corresponding constant in the OEIS. N. J. A. Sloane, Feb. 10 2013, and Andrey Zabolotskiy, Dec. 30 2023 dim. center-density A-number density A-number exact decimal exact decimal 1 1/2 0.5000000000 - 1 1 - 2 1/sqrt(12) 0.2886751347 A020769 (1/6)*3^(1/2)*Pi 0.9068996827 A093766 3 1/sqrt(32) 0.1767766952 A020789 (1/6)*2^(1/2)*Pi 0.7404804898 A093825 4 1/8 0.1250000000 - (1/16)*Pi^2 0.6168502752 A222068 5 1/(8*sqrt(2)) 0.08838834762 A222066 (1/30)*2^(1/2)*Pi^2 0.4652576133 A222069 6 1/(8*sqrt(3)) 0.07216878367 A222067 (1/144)*3^(1/2)*Pi^3 0.3729475457 A222070 7 1/16 0.06250000000 - (1/105)*Pi^3 0.2952978732 A222071 8 1/16 0.06250000000 - (1/384)*Pi^4 0.2536695081 A222072 12 1/27 0.03703703704 A021031 (1/19440)*Pi^6 0.0494541766 - 16 1/16 0.06250000000 - (1/645120)*Pi^8 0.0147081644 - 24 1 1 - (1/479001600)*Pi^12 0.0019295743 A260646