Symmetry Operation

OLS

Symmetry Operation
* q' H& }: f2 {. ^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
; B  E/ J3 [4 _, x(x,y,z)=>(-x,-y,-z)
) G& Y, V6 I/ c1 P( N: G! r9 V 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.
) D# i3 F: I5 ?% U: P3 cThe Mirror Plane symmetry operation takes
(x,y,z)=>(x,y,-z)=>(x,-y,z)
etc., which is equivalent to 2.