What is the diagram of the roto-inversion of $\bar 6$?
The image below gives some example of different rotation inversion operations. For the $\bar 6$ operation rotate by 60 degrees (black dot to open circle in the direction towards 3) then invert through the centre of coordinates to the opposite side. Inversion changes a point at (x, y, z) to (-x, -y, -z) thus, in the diagram point 1 becomes point 2 after the whole operation, then 2 becomes 3 and so on. Two $\bar 6$ operations moves 1 to 3 and 6 operations places it back where it started.



[The image is from 'Crystallography, An introduction ' by W. Borchardt-Ott, 3rd ed publ Springer.]