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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 $\bar n$ for an improper rotation by $360^\circ/n$, so the Crystallography Restriction gives only $\bar 1$, $\bar 2$, $\bar 3$, $\bar 4$, $\bar 6$ for crystals. The Mirror Plane symmetry operation is $(x,y,z) \to (x,y,-z)$, etc., which is equivalent to $\bar 2$.

© 1996-9 Eric W. Weisstein