Symmetry Operation

OLS

Symmetry Operation
' D: M6 p7 B4 k9 MSymmetry operations include the Improper Rotation, Inversion Operation, Mirror Plane, and Rotation. Together, these operations create 32 crystal classes corresponding to the 32 Point Groups.
5 _8 ]7 m' O  O/ mThe Inversion Operation takes
$ N2 I1 G6 }: ?" Y' N6 @* i(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.
The Mirror Plane symmetry operation takes
# B: j* M( B$ i9 l8 _(x,y,z)=>(x,y,-z)=>(x,-y,z)
etc., which is equivalent to 2.