Symmetry Operation , Z4 n4 t" F& Y# ]$ U% F+ O" b- 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. 1 O0 K P; m! B. r4 X$ s0 W& aThe Inversion Operation takes , H! q+ I, Y6 X2 ~/ W(x,y,z)=>(-x,-y,-z) * e- w: A$ a2 I0 c8 N 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. 4 | K2 G8 x/ ? XThe Mirror Plane symmetry operation takes " f u: }0 d9 U& z, L# n L# {
(x,y,z)=>(x,y,-z)=>(x,-y,z): v5 X! f$ K) `, Z# c1 Z
etc., which is equivalent to 2.