## Close-packing of equal spheres |

in

,geometry **close-packing of equal**is a dense arrangement of congruent spheres in an infinite, regular arrangement (orspheres ).lattice proved that the highest average density – that is, the greatest fraction of space occupied by spheres – that can be achieved by acarl friedrich gauss packing islattice the same

can also be achieved by alternate stackings of the same close-packed planes of spheres, including structures that are aperiodic in the stacking direction. thepacking density states that this is the highest density that can be achieved by any arrangement of spheres, either regular or irregular. this conjecture was proven bykepler conjecture .t. c. hales ^{[1]}^{[2]}highest density is known only in case of 1, 2, 3, 8 and 24 dimensions.^{[3]}many

structures are based on a close-packing of a single kind of atom, or a close-packing of large ions with smaller ions filling the spaces between them. the cubic and hexagonal arrangements are very close to one another in energy, and it may be difficult to predict which form will be preferred from first principles.crystal - fcc and hcp lattices
- lattice generation
- miller indices
- filling the remaining space
- see also
- notes
- external links

In **close-packing of equal spheres** is a dense arrangement of congruent spheres in an infinite, regular arrangement (or

The same ^{[1]}^{[2]} Highest density is known only in case of 1, 2, 3, 8 and 24 dimensions.^{[3]}

Many