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NonCommercial-ShareAlike 4.0 International

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In the 2D lattice below is is possible to pick any
parallelogram to be the unit cell. In practice it is best to choose
the smallest unit cell or the unit cell which provides the most symmetry.

All the parallelograms represent valid unit cells

For some lattice patterns, the smallest unit cell doesn't
describe the present symmetry. It is then desirable to pick a larger
unit cell which does describe the symmetry. If the unit cell contains
another lattice point it is called **non-primitive**, otherwise it
is **primitive**.

The smallest unit cell doesn't reflect the symmetry within
the structure

In the special case where there is an angle of 120°
between the lattice directions, it is best to use a *hexagonal*
unit cell. This unit cell is **primitive** and, when repeated, leads
to 6-fold symmetry.

This idea holds for 3D lattices though it is more complicated
to demonstrate. Below is a simple example that shows two different units
cells for a **cubic close packed** lattice. (Crystal packing will
be discussed later in this TLP)

Shown is a rotating **cubic close packed** structure

This idea holds for 3D lattices though it is more complicated
to demonstrate. Below is a simple example that shows two different units
cells for a **cubic close packed** lattice. (Crystal packing will
be discussed later in this TLP)

The parallepiped shows one possible unit cell

This idea holds for 3D lattices though it is more complicated
to demonstrate. Below is a simple example that shows two different units
cells for a **cubic close packed** lattice. (Crystal packing will
be discussed later in this TLP)

The cube shows another possible unit cell. This is the
preferred unit cell for **cubic close packed structures** because
it contains the most symmetry