The crystallographic point group or crystal class is the mathematical group comprising the symmetry operations that leave at least one point unmoved and that leave the appearance of the crystal structure unchanged. These symmetry operations include
*Reflection, which reflects the structure across a reflection plane
*Rotation, which rotates the structure a specified portion of a circle about a rotation axis
*Inversion, which changes the sign of the coordinate of each point with respect to a center of symmetry or inversion point
*Improper rotation, which consists of a rotation about an axis followed by an inversion.
Rotation axes (proper and improper), reflection planes, and centers of symmetry are collectively called symmetry elements. There are 32 possible crystal classes. Each one can be classified into one of the seven crystal systems.