a face-centered lattice
Now put a lattice point at each of the 8 corners AND one at the centre of each of the 6 faces of the box. That is a face-centered lattice (symbol F). Each face-centre point has the same environment as a corner, so all of them are equivalent lattice points.
Counting: 8 corners times 1/8 + 6 faces times 1/2 = 1 + 3 = 4 lattice points per cell — four times the primitive volume. The face-centre coordinates are (1/2,1/2,0), (1/2,0,1/2), (0,1/2,1/2), plus the corner. For example, aluminium, copper, gold, and gamma-iron are face-centered cubic; with one atom per point that is the FCC structure — atoms in ABCABC close-packed stacking, coordination number 12, packing factor 0.74.
Face-centered cubic is the archetype of close packing — the densest way to pack equal spheres — so most ductile metals adopt it. Diffraction signature: reflections appear only when h, k, l are all even or all odd (unmixed parity); mixed indices are systematically absent.
Face-centered cubic aluminium: a = 4.05 angstrom, 4 atoms per cell. Its diffraction pattern shows (111), (200), (220) but never (100), (110), or (210) — only all-even or all-odd indices survive. That unmixed-parity rule is the signature of F centering.
FCC allows only reflections with h, k, l all even or all odd.
FCC and cubic close-packed (CCP) name the same atomic arrangement — CCP describes the ABCABC stacking, FCC describes the lattice; they are two views of one structure.