Symmetry Operation : c: E+ N! }. U7 j |& ~0 n% NSymmetry operations include the Improper Rotation, Inversion Operation, Mirror Plane, and Rotation. Together, these operations create 32 crystal classes corresponding to the 32 Point Groups. . i; F& o8 p/ l
The Inversion Operation takes " L( e4 k ]8 e6 f
(x,y,z)=>(-x,-y,-z)9 g: Z, ~* D( M$ `
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. 9 n4 n& z* V9 \0 k
The Mirror Plane symmetry operation takes # d6 B+ ^8 B) e9 |: y% n
(x,y,z)=>(x,y,-z)=>(x,-y,z)5 H% S2 {0 k+ V) }7 j* P
etc., which is equivalent to 2.