Symmetry Operation

OLS

Symmetry Operation
0 ?# `" L, l" I. ]' tSymmetry operations include the Improper Rotation, Inversion Operation, Mirror Plane, and Rotation. Together, these operations create 32 crystal classes corresponding to the 32 Point Groups.
) l8 d& [$ o0 _5 T8 FThe Inversion Operation takes
0 ~4 u4 l& y* s(x,y,z)=>(-x,-y,-z)
( N4 b2 ^! B& D: U 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.
. A$ w& Y0 f) i: V. D4 F/ eThe Mirror Plane symmetry operation takes
5 y" O# ^: o8 d% j& Y, G( K: V(x,y,z)=>(x,y,-z)=>(x,-y,z)
etc., which is equivalent to 2.