[AntonioLao]

1848 was the year Auguste Bravais established that there are exactly 14 different kinds of 3D lattices. These are cubic P, cubic I, cubic F, tetragonal P, tetragonal I, orthorhombic P, orthorhombic C, orthorhombic I, orthorhombic F, monoclinic P, monoclinic C, Triclinic P, trigonal R, trigonal and hexagonal C (or P).

Applying these lattices to sphere packing, three different 3D structures can be obtained. In the order of highest density, these are face-centered cubic lattice (density is approximately 0.7404 or ), hexagonal lattice (density~0.6046 or ), and cubic lattice (density~0.5236 or ). All these research establishments still do not give a satisfactory answer to the general question: what is the most efficient of all packing arrangements, regular or otherwise? But it has been proven that no sphere packing can have density greater than 0.77736.

http://hyperphysics.phy-astr.gsu.edu...s/bravais.html