Symmetry Operation

OLS

Symmetry Operation
8 n# V" _! Y8 E$ ESymmetry operations include the Improper Rotation, Inversion Operation, Mirror Plane, and Rotation. Together, these operations create 32 crystal classes corresponding to the 32 Point Groups.
0 c* X8 O1 P1 x* w8 j* R$ xThe Inversion Operation takes
(x,y,z)=>(-x,-y,-z)
$ P# F7 Z* x: e* O- c: @ 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.
The Mirror Plane symmetry operation takes
, u! a1 L  B) U& a( @  G( Q(x,y,z)=>(x,y,-z)=>(x,-y,z)
etc., which is equivalent to 2.