Special sites with points located on rotation or inversion axes

3 Special sites with points located on rotation or inversion axes 

Both the rotation and inversion axes can also be the source of special positions. Consider, for example, the site 2a Table 1.18) where atoms are accommodated by the two-fold rotation axis that follows the line at which two mutually perpendicular mirror planes intersect. In this case two of the three coordinates in the triplet are fixed (x = 0 and y = 0), while the third coordinate (z) may assume any value. A similar special position is represented by the site 4c Table 1.18), where the two-fold rotation axis is parallel to Z and coincides with the line at which two mutually perpendicular 

Therefore, the number of positional degrees of freedom is further reduced to only one independent coordinate in special positions where atoms are located on rotation or inversion crystallographic axes. Similar to both the general position and special sites on mirror planes, any special equivalent position on a rotation or inversion axis can accommodate many independent atoms (geometrical constraints are always applicable). 

---