One way to classify crystals is to look at their structure and to categorize them using seven different crystal families. In the following set of examples we will take a look at the basics of crystallography and we will introduce and explain each crystal system with the help of two examples.

To characterize the crystal’s structure we introduce a so called unit cell, which is basically a box containing one or more of the crystals’ atoms. There is one requirement though: We have to be able to rebuild the whole crystal stacking and aligning (identical) unit cells and the unit cell has to be as small as possible. The unit cell can be described by its side lengths a, b and c (also called lattice parameters) and the angles between them, alpha, beta and gamma. The atoms’ positions within the unit cell are often given using fractions of the side lengths as coordinates.