Symmetry Operation # ~' ^7 q+ s% R S- h( C. ~' }
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. 4 \- \ O4 @, |% y1 u; X$ k
The Inversion Operation takes 8 h2 Z, B- a. l. ~+ s. e. ^/ [4 w(x,y,z)=>(-x,-y,-z)& ]5 |; v8 D$ _# T
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. / W) N& ?2 q3 k% gThe Mirror Plane symmetry operation takes 9 n; ?5 {* W3 y& h- O
(x,y,z)=>(x,y,-z)=>(x,-y,z)' A* T# p/ R. H
etc., which is equivalent to 2.