Symmetry Operation % d; d; L7 y& d9 w# F3 F4 oSymmetry operations include the Improper Rotation, Inversion Operation, Mirror Plane, and Rotation. Together, these operations create 32 crystal classes corresponding to the 32 Point Groups. m- ?( \) x! q6 ~4 |The Inversion Operation takes 8 f1 Q9 I$ W: f7 j
(x,y,z)=>(-x,-y,-z)' w% d6 j: K! S8 h
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. ' }# b& O2 A2 e* |4 Q* W
The Mirror Plane symmetry operation takes 7 H* I4 z; f+ }( f% q
(x,y,z)=>(x,y,-z)=>(x,-y,z) ! ^# c+ g3 T) t* e7 cetc., which is equivalent to 2.