the coordination number
In a packed crowd, count how many people are directly touching you — the ones pressed against your shoulders and back. For an atom in a crystal, the coordination number is the same idea: how many other atoms it directly touches, its nearest neighbours.
Different structures give different counts. FCC and HCP each have 12 (the maximum for equal spheres, because both are close-packed). BCC has 8. Simple cubic has 6. The diamond structure has only 4. As a rule, a higher coordination number goes with denser packing. In ionic crystals the coordination number is set by the ratio of the ion radii — a small cation can only touch so many big anions.
The coordination number is a quick fingerprint of a structure and tracks with packing and density. It even changes during a polymorphic transition: when iron heats from BCC to FCC, its coordination number jumps from 8 to 12 and the metal slightly densifies, which is one reason steel behaves so differently hot versus cold.
Walk down the coordination ladder: FCC and HCP have 12 touching neighbours, BCC has 8, simple cubic 6, diamond just 4. Fewer neighbours means more open space — diamond's coordination number of 4 gives it a very low packing factor of 0.34.
Coordination number falls as structures grow more open: 12 to 8 to 6 to 4.
Twelve is the maximum for equal-size spheres; higher values occur only when atoms differ in size (as in some intermetallics). Coordination number counts touching neighbours, not all atoms in the cell.