It is the three-dimensional equivalent of the circle packing in a square problem in two dimensions.
The problem consists of determining the optimal packing of a given number of spheres inside the cube.
Gensane[1] traces the origin of the problem to work of J. Schaer in the mid-1960s.
[2] Reviewing Schaer's work, H. S. M. Coxeter writes that he "proves that the arrangements for
[1] In a 1971 paper, Goldberg found many non-optimal packings for other values of
, the optimal packing of spheres in a cube is a form of cubic close-packing.
However, omitting as few as two spheres from this number allows a different and tighter packing.