Symmetry Operation

OLS

Symmetry Operation
* u$ X' k8 ~3 f  v' 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.
( h! g* }# l: {' }# P8 Y# gThe Inversion Operation takes
; O7 L- q5 d' ]1 |9 Y6 t% L(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
(x,y,z)=>(x,y,-z)=>(x,-y,z)
etc., which is equivalent to 2.