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 Resource. https://mathworld.wolfram.com/ImproperRotation.html