Symmetry Operation

OLS

Symmetry Operation
/ i) f  Y( f  jSymmetry 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
! J! o+ X% L" M5 b9 F; |(x,y,z)=>(-x,-y,-z)
# L3 P: H' d# G( r1 ~! J8 ` 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
4 q! Q" V4 Z0 Q: `* C) |8 |(x,y,z)=>(x,y,-z)=>(x,-y,z)
etc., which is equivalent to 2.