the face-centered cubic structure

The face-centred cubic structure is one of the two ways to build a close-packed crystal, and it hides in a shape everyone knows: a cube. Put an atom at each of the eight corners of a cube and one at the centre of each of the six faces. That is FCC. It looks cubic and blocky, but if you tilt it and look down a body diagonal you see the very same ABCABC stacking of close-packed layers described under close packing.

Count the atoms carefully: each corner atom is shared by eight cubes so contributes 1/8, giving 8 times 1/8 = 1; each face atom is shared by two cubes so contributes 1/2, giving 6 times 1/2 = 3; total 4 atoms per unit cell. The atoms touch along the face diagonal, which fixes the lattice parameter as a = 2 times sqrt(2) times r for atomic radius r. The coordination number is 12 and the atomic packing factor is 0.74. The close-packed planes are the {111} family and the close-packed directions are the <110> family.

FCC metals include copper, aluminium, nickel, gold, silver, lead, and the high-temperature gamma form of iron. Their twelve slip systems, {111} planes gliding along <110> directions, make FCC metals famously ductile and easy to shape, which is why copper wire bends without snapping and aluminium can be rolled into foil.