Symmetry Operation

OLS

Symmetry Operation
/ K  ], b4 x9 jSymmetry operations include the Improper Rotation, Inversion Operation, Mirror Plane, and Rotation. Together, these operations create 32 crystal classes corresponding to the 32 Point Groups.
( J. D$ i$ {& p9 _% w2 X6 FThe Inversion Operation takes
% i* n: j2 n8 F  r- p( I(x,y,z)=>(-x,-y,-z)
' b3 L! B$ h# o3 [& p5 q 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)
) N1 n3 |% g8 F  ~) j# D' i: A/ ietc., which is equivalent to 2.