Symmetry Operation , Q2 A& ~# N" g4 K) G3 h* @1 w
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. ' {% [; M/ P& l; m0 `; b- iThe Inversion Operation takes : q6 C" Y9 u& u- c- c
(x,y,z)=>(-x,-y,-z)2 h# F% P. G5 L; j/ P
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. & M/ I- w# |( K5 wThe Mirror Plane symmetry operation takes - D3 `5 l8 c: U" T& N2 }: b) L
(x,y,z)=>(x,y,-z)=>(x,-y,z) / W6 U" W7 E o* `" Vetc., which is equivalent to 2.