Face Centered Cubic Unit Cell (FCC)

In the face-centred cubic (fcc) unit cell, identical atoms sit at every one of the 8 corners AND at the centre of every one of the 6 faces. Corner atoms touch the face-centred atoms, but corner atoms do not touch each other directly. Each face-centred atom sits on the shared boundary between exactly 2 neighbouring unit cells, so it contributes only 1/2 of itself to any one cell (unlike the body-centre atom of the bcc cell, which belongs wholly to one cell).

Counting atoms per cell: the 8 corner atoms contribute Nc/8 = 8/8 = 1, and the 6 face-centred atoms contribute Nf/2 = 6/2 = 3:

$\text{Number of atoms per fcc unit cell} = \dfrac{N_c}{8} + \dfrac{N_f}{2} = 1 + 3 = 4$ …