improper rotation

In crystallography, "improper rotation" refers to a symmetry operation that combines rotation with reflection or inversion. This is distinct from a simple rotation, which only turns a crystal around an axis.1

Crystals possess symmetry elements, such as rotation axes, mirror planes, and centers of inversion. Improper rotations, also known as rotoreflections or rotoinversions, are combinations of these basic operations. For example, a rotoreflection involves rotating a crystal and then reflecting it across a plane.12

These symmetry operations are fundamental to understanding the orderly arrangement of atoms within crystalline solids. The specific elements of symmetry present in a crystal determine its overall shape and influence its physical properties. There are 32 distinct combinations of these symmetry operations, known as point groups or crystal classes, which classify crystals based on their atomic arrangements.132