Symmetry Operation

OLS

Symmetry Operation
$ y/ F/ M, ^* b% E' D# m8 ^5 sSymmetry 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
) V8 ]( a) E: h# n(x,y,z)=>(-x,-y,-z)
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.
5 |& @+ W! t* K8 @  r: LThe Mirror Plane symmetry operation takes
2 D& C  s9 @. n! z, d7 U) {(x,y,z)=>(x,y,-z)=>(x,-y,z)
etc., which is equivalent to 2.