Symmetry Operation

OLS

Symmetry Operation
2 J- o7 Z. y" u& a% tSymmetry operations include the Improper Rotation, Inversion Operation, Mirror Plane, and Rotation. Together, these operations create 32 crystal classes corresponding to the 32 Point Groups.
5 K9 K# T; T+ c$ }The Inversion Operation takes
! q- e7 N/ d7 l(x,y,z)=>(-x,-y,-z)
' V9 Y6 g$ z; [7 @3 R/ Y 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.
% |, F* _; `5 t; _: M6 ~The Mirror Plane symmetry operation takes
(x,y,z)=>(x,y,-z)=>(x,-y,z)
+ n7 C: C/ [) h0 oetc., which is equivalent to 2.