Symmetry Operation ! u% Q3 L8 z; [1 k
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. ) {9 K- `% m+ j9 ~. HThe Inversion Operation takes 6 n' ]9 T4 } k' H9 L% p2 c8 K" f
(x,y,z)=>(-x,-y,-z)" U7 n4 B' F( G2 `
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. - c- ~( T* |0 I+ X! W
The Mirror Plane symmetry operation takes 8 z5 n: g; c& v# l& G
(x,y,z)=>(x,y,-z)=>(x,-y,z); j4 z5 N8 s1 e$ U: [' M
etc., which is equivalent to 2.