Electron microscopy
  
Rotoinversion Axis in Crystallography
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The symmetry operation of roto-inversion (Rotoinversion axis (-4, S4) in crystallography) is composed of rotation by 360/n about the roto-inversion axis, followed by inversion through a point (roto-inversion center). Note that a mirror is equivalent to roto-inversion -2.

Figure 1615 shows the overall effect of the two steps is four-fold roto-inversion (-4, S4) around the axis.

Four-fold roto-inversion axis Four-fold roto-inversion axis
(a)
(b)
Figure 1615. Four-fold roto-inversion (-4, S4) axis: (a) The first step is fourfold rotation around the axis (from x, y, z to -y, x, z), and (b) The second step is inversion around the center of symmetry (from -y, x, z to y, -x, -z).

 

 

 

 

 
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