Symmetry Operation

OLS

Symmetry Operation
( w& K; \$ b# I2 NSymmetry 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
9 A8 j- D  C4 Y/ K0 _3 }(x,y,z)=>(-x,-y,-z)
9 d& [6 H, O0 e( G/ t 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
$ c  I; t  M6 q(x,y,z)=>(x,y,-z)=>(x,-y,z)
, Y$ @- ^; x3 Betc., which is equivalent to 2.