Finite sphere packing

In mathematics, the theory of finite sphere packing concerns the question of how a finite number of equally-sized spheres can be most efficiently packed. The question of packing finitely many spheres has only been investigated in detail in recent decades, with much of the groundwork being laid by László Fejes Tóth.

The similar problem for infinitely many spheres has a longer history of investigation, from which the Kepler conjecture is most well-known. Atoms in crystal structures can be simplistically viewed as closely-packed spheres and treated as infinite sphere packings thanks to their large number.

Sphere packing problems are distinguished between packings in given containers and free packings. This article primarily discusses free packings.