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Improper Rotation

The symmetry operation corresponding to a rotation followed by an inversion operation, also called a rotoinversion. This operation is denoted n^_ for an improper rotation by 360 degrees/n, so the crystallography restriction gives only 1^_, 2^_, 3^_, 4^_, 6^_ for crystals. The mirror plane symmetry operation is (x,y,z)->(x,y,-z), etc., which is equivalent to 2^_.

See also

Inversion Operation, Rotation, Symmetry Operation

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Cite this as:

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

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