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.
9 h& i5 k& {- W0 N# oThe Inversion Operation takes
$ ^5 K6 E- g& t& j(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.
" E3 G4 b+ I( }) W4 XThe Mirror Plane symmetry operation takes
(x,y,z)=>(x,y,-z)=>(x,-y,z)
8 i! L& G1 u' }/ e# @# B) Fetc., which is equivalent to 2.