Bravais Lattices – The ‘Face-Centred’ Monoclinic Lattice
As mentioned, the face-centred and body-centred monoclinic lattices are actually identical to the base-centred monoclinic lattice. The face-centred monoclinic unit cell is shown on the left below. On the right is an image showing the lattice resulting from this unit cell and multiple base-centred monoclinic unit cells that can represent this lattice. The base-centred cells shown are by no means exhaustive. There are actually infinitely many base-centred unit cells giving this lattice point arrangement, though most will be distorted beyond easy use.
If you would like extra practice at different representations of unit cells, have a go at identifying the primitive unit cells in face-centred or body-centred monoclinic lattices. As we have shown these lattice types to be identical to the base-centred lattice, and the base-centred lattice has a primitive unit cell, body-centred and face-centred must also have primitive unit cells representing their lattices. You could also try identifying the body-centred unit cells in the lattice built from face-centred monoclinic unit cells (or vice versa).