The symmetry operation corresponding to a rotation followed by an inversion operation, also called a rotoinversion. This operation is denoted for an improper rotation by , so the crystallography restriction gives only , , , , for crystals. The mirror plane symmetry operation is , etc., which is equivalent to .
Improper Rotation
See also
Inversion Operation, Rotation, Symmetry OperationExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Improper Rotation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ImproperRotation.html