Close-packing of
spheres is the arranging of an infinite lattice of spheres so that they take up the greatest possible fraction of an infinite 3-dimensional space.
Carl Friedrich Gauss proved that the highest average density that can be achieved by a regular lattice arrangement is . The
Kepler conjecture states that this is the highest density that can be achieved by any arrangement of spheres, either regular or irregular.
See more at Wikipedia.org...