the face-centered cubic structure

Stack cannonballs (or oranges) in the tightest possible pile: the bottom layer nestles together, the next layer drops into the hollows, and the third layer shifts again to a fresh set of hollows (an ABC stacking). That densest packing of equal spheres, boxed into a cube, is the face-centered cubic structure: an atom at every cube corner plus one centred on each of the six faces.

Counting atoms: 8 corners times 1/8 plus 6 faces times 1/2 equals 4 atoms per cell. The atoms touch along the face diagonal, so four radii span that diagonal: 4R = a times sqrt(2), giving a = 2R times sqrt(2). Each atom has 12 nearest neighbours (coordination number 12), and the packing factor is 0.74 — atoms fill 74 percent of space, the densest possible for equal spheres. Copper, aluminum, gold, nickel, gamma-iron (austenite), and austenitic stainless steel are all FCC.

This structure is why so many everyday metals are soft and formable. With 12 nearest neighbours and many densely packed planes to slide on, FCC metals deform by bending rather than snapping — which is exactly why aluminum and copper can be rolled, drawn, and pressed into shape, even cold.