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.
! u0 f% U  b3 \3 F. ?1 J, `  `2 t% nThe Inversion Operation takes
( Z2 Q) o: ~' O( s2 X, N(x,y,z)=>(-x,-y,-z)
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
(x,y,z)=>(x,y,-z)=>(x,-y,z)
) |" \1 b! @1 G" @etc., which is equivalent to 2.