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 Operation## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Improper Rotation."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/ImproperRotation.html