Symmetry Operation

OLS

Symmetry Operation
8 ?7 b& w+ P. o/ y  g( ?- i6 T: C; D0 _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.
The Inversion Operation takes
(x,y,z)=>(-x,-y,-z)
" h: \) c  j- H  d( J. I 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
) f, L7 F; b0 m. w  W* N(x,y,z)=>(x,y,-z)=>(x,-y,z)
etc., which is equivalent to 2.