Symmetry Operation

OLS

Symmetry Operation
% Z- e$ W% p$ w* ~* `+ O4 \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)
7 K5 T' k$ }8 C* J 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.
9 \7 `' i2 ?/ x1 q* ]The Mirror Plane symmetry operation takes
1 N- L. A! `* [  m& p; J(x,y,z)=>(x,y,-z)=>(x,-y,z)
etc., which is equivalent to 2.