Symmetry Operation h- A# ?& @0 m( O; ` j% {- Z' 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. N0 K: o, B9 { d! D( X
The Inversion Operation takes / S+ I' V) o/ C1 b
(x,y,z)=>(-x,-y,-z)$ }: ^% Y9 I% H( g
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. s" y7 S9 K+ x7 k4 v: j; H
The Mirror Plane symmetry operation takes - j F3 g: v2 C# d( P3 o" C' B+ D
(x,y,z)=>(x,y,-z)=>(x,-y,z) ) ~4 o( c- f- \+ N. K* [etc., which is equivalent to 2.