Crystallographic Point Groups

The arrangements of atoms in unit cells can be classified into point groups in the same way as molecules. But the possibilities are limited by the symmetries of the seven crystal systems.

Space Group Solid

Decorated Solid” Representation

One means of illustrating the symmetries of the 32 crystallographic point groups is as solid objects decorated with patterns to give the appropriate symmetry. These representations were adapted from figures presented in Ashcroft and Mermin, Solid State Physics. Thanks to José Freire (Universidade Federal do Paraná, Brazil) for the suggestion.



Space Group Model

Unit Cell Representation

An alternate representation shows simplified unit cell models with atoms placed in all the positions generated by the symmetry operations of the crystallographic point group.