Introduction to Crystallography
The definition of a lattice in three dimensions is the same as in two dimensions: a lattice is a set of points, regularly arranged in space, for which the environment of each point is identical.
A 3-D lattice is described by adding a third unit vector, c, to the unit vectors, a and b, which define the unit cell of the 2-D lattice. This is shown here for a small portion of a 3-D lattice. The unit cell of a 3-D lattice takes the general shape of a parallelepiped.
As in the 2-D case, the entire crystal lattice can be constructed by repeating these unit vectors indefinitely. A 3-D structure or crystal is created by adding a basis to each lattice point.
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