Symmetry Operation

OLS

Symmetry Operation
; z+ n& g% p6 f' z+ |3 k6 J% _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.
" n0 }- ]6 j6 L4 q- l0 w  D4 K" n4 }The Inversion Operation takes
(x,y,z)=>(-x,-y,-z)
  p" _. n5 v& g 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
9 s. Z' i" z' h2 Y: C9 A, w& F(x,y,z)=>(x,y,-z)=>(x,-y,z)
etc., which is equivalent to 2.