Symmetry Operation * v9 ]6 K, S& Q t
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. 8 z d9 p; o. `2 p' c7 V7 l/ g
The Inversion Operation takes ! S3 H" Z* ~$ A: d/ T( ?; U
(x,y,z)=>(-x,-y,-z)) t3 J" O' K3 V, c/ 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. 0 }+ p+ j! m/ S$ p0 J
The Mirror Plane symmetry operation takes 5 a. \/ r! {0 _! U
(x,y,z)=>(x,y,-z)=>(x,-y,z) 2 ?/ p8 f' d0 R2 Jetc., which is equivalent to 2.