Symmetry Operation

OLS

Symmetry Operation
0 x% M# ~% f( `3 y' c9 P- C" o$ G/ vSymmetry operations include the Improper Rotation, Inversion Operation, Mirror Plane, and Rotation. Together, these operations create 32 crystal classes corresponding to the 32 Point Groups.
The Inversion Operation takes
(x,y,z)=>(-x,-y,-z)
( G% X. f6 j/ _. }; p" a' E and is denoted i. When used in conjunction with a Rotation, it becomes an Improper Rotation. An Improper Rotation by 360/n . For periodic crystals, the Crystallography Restriction allows only the Improper Rotations 1, 2, 3, 4, and 6.
/ n. p& L" W7 j( e( H9 L$ TThe Mirror Plane symmetry operation takes
+ I4 c0 E  e: t! z6 T(x,y,z)=>(x,y,-z)=>(x,-y,z)
etc., which is equivalent to 2.