Symmetry Operation

OLS

Symmetry Operation
Symmetry 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
- ^: O  b3 e( j2 a" L) W1 v# f4 b(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.
, r  T5 Z* r& a( LThe Mirror Plane symmetry operation takes
(x,y,z)=>(x,y,-z)=>(x,-y,z)
0 K$ b  f% y. wetc., which is equivalent to 2.