Shown above is what the science of sphere packing calls a closest-packed arrangement. Specifically, this eleven-sphere stack has a hexagonal close-packed (HCP) lattice. No other arrangement of spheres can exceed its packing density of 74%.^[1]

Mathematically, there is an infinite quantity of closest-packed arrangements (assuming an infinite-size volume in which to arrange spheres). In the field of crystal structure however, unit cells (a crystal’s repeating pattern) are composed of a limited number of atoms and this reduces the variety of closest-packed regular lattices found in nature to only two: hexagonal close packed (HCP), and face-centered cubic (FCC). As can be seen at this site at King’s College, archive copy at the Wayback Machine there is a distinct, real difference between different lattices; it’s not just a matter of how one slices 3D space. With all closest-packed lattices however, any given internal atom is in contact with 12 neighbors — the maximum possible.

Note that this stack does not constitute the HCP unit cell since it can not be tessellated in 3D space. Visit the Web site at King’s College to see FCC and HCP unit cells.

1. ↑ To 23 significant digits, the value is 74.048 048 969 306 104 116 931%

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