As mentioned in previous sections, a unit cell is a parallelepiped that is the simplest repeating unit of a three-dimensional Bravais lattice, which is obtained by replicating one of the five two-dimensional lattices and stacking the replicated lattices above one another. The first two types of unit cells that form Bravais lattices are the ** triclinic** and

**unit cells.**

*monoclinic*There are three ways to stack the layers of the two-dimensional lattice depicted in figure I (where I** a**I ≠ I

**I and the angle between the basis vectors is not 90**

*b*^{o}) such that the space lattice maintains a 2-fold rotational symmetry.

The first way is to stack successive layers that are directly above one another (Ia), resulting in a *primitive*** monoclinic **unit cell(Ib), with I

**I ≠ I**

*a***I ≠ I**

*b***I and α = β = 90**

*c*^{o}, γ≠ 90

^{o}.

The second way is to stack a second layer such that its lattice points are in between the lattice points of the first layer (Ic). A third layer is then stacked directly above the first layer, giving a non-primitive unit cell known as a *base-centred*** monoclinic** unit cell (Id), with I

**I ≠ I**

*a***I ≠ I**

*b***I and α = β = 90**

*c*^{o}, γ≠ 90

^{o}.

The third way is the stack the second layer with its lattice points above the middle of parallelograms formed by the lattice points of the first layer (Ie). A third layer is then stacked directly above the first layer. With a different choice of basis vectors (If), we again obtain a based-centred monoclinic unit cell (Id).

If the second layer is stacked in a way that 2-fold rotational symmetry is no longer preserved in the space lattice (Ig), we have a ** triclinic** unit cell (Ih) with I

**I ≠ I**

*a***I ≠ I**

*b***I and α ≠ β ≠ γ.**

*c*All monoclinic units cells are described by the parameters of I** a**I ≠ I

**I ≠ I**

*b***I and α = β = 90**

*c*^{o}, γ≠ 90

^{o}. Furthermore, all monoclinic unit cells have just one 2-fold rotational axis of symmetry. Although it is possible to outline a primitive unit cell for the based-centred monoclinic lattice, the primitive unit cell has two angles that are not equal to 90

^{0}and is therefore less symmetrical and not monoclinic.

A triclinic unit cell, on the other hand, has no essential symmetry as it only has a 1-fold rotational axis of symmetry, which is trivial. We can therefore construct different three-dimensional Bravais lattices, each with 1-fold rotational symmetry, by replicating triclinic unit cells of different dimensions. This is the reason why a lattice with one-fold rotational symmetry is not included as one of the two-dimensional Bravais lattices (see earlier article).