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.
4 ]3 i8 Z7 Q# ?: C* g& fThe Inversion Operation takes
' N, \) }0 o- r* L" w  _! O(x,y,z)=>(-x,-y,-z)
; n. ^3 ^) I( ^& _/ X* L. S 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.
. d8 n+ I, r' `! e/ O1 }The Mirror Plane symmetry operation takes
# F9 j! ~1 l) c: }- p: X(x,y,z)=>(x,y,-z)=>(x,-y,z)
etc., which is equivalent to 2.