Symmetry Operation 6 h' c2 y3 E1 [
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. : o# U. y, d3 }) p( z/ t2 b
The Inversion Operation takes 2 h: L8 ]3 H) X7 Y
(x,y,z)=>(-x,-y,-z) . N' E7 E. \% L" Z 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. ( y# W/ H2 J9 y, P
The Mirror Plane symmetry operation takes 8 Y+ m8 ]/ f& W
(x,y,z)=>(x,y,-z)=>(x,-y,z) - H- H* ^5 U0 d. g8 Wetc., which is equivalent to 2.