Symmetry Operation ; s+ u/ x& l# O0 N9 C9 y+ gSymmetry operations include the Improper Rotation, Inversion Operation, Mirror Plane, and Rotation. Together, these operations create 32 crystal classes corresponding to the 32 Point Groups. & V- {7 I# i" b Q% x
The Inversion Operation takes 4 t: j% r0 R# z- m* i" W; f
(x,y,z)=>(-x,-y,-z)- ~. m- @2 `( }* ~7 j" q
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. ( k6 M. Z0 L, X' G; S5 _& f2 g0 {
The Mirror Plane symmetry operation takes ' a, {) I$ a4 Q/ m+ M/ `. g(x,y,z)=>(x,y,-z)=>(x,-y,z) ' s8 J! t3 x7 W9 Z3 I8 wetc., which is equivalent to 2.