Symmetry Operation

OLS

Symmetry Operation
3 y9 H' O9 v% O* O9 O9 b3 k) w; J4 |7 cSymmetry operations include the Improper Rotation, Inversion Operation, Mirror Plane, and Rotation. Together, these operations create 32 crystal classes corresponding to the 32 Point Groups.
3 z. _3 ]7 K. mThe Inversion Operation takes
(x,y,z)=>(-x,-y,-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.
6 o4 a! O4 B/ ?( v) E9 _# ZThe Mirror Plane symmetry operation takes
(x,y,z)=>(x,y,-z)=>(x,-y,z)
etc., which is equivalent to 2.