Show that the maximum proportion of the available volume which can be filled by hard spheres arranged on various lattices is: simple cubic, 0.52; body-centered cubic, 0.68; face-centered cubic, 0.74; hexagonal close pack, 0.74, diamond 0.34.
If you pour hard spheres into a container so that they stack randomly, the filling is about 0.64. This is called random close pack.
Solution