What is the diagram of the roto-inversion of $\bar 6$? Using the standard way of representation:



Here we have a rotation followed by an inversion (technically called 'rotational inversion'). So as to represent it, what I have done is:

1) Both rotation and inversion occur for the first time. The circle changes of plane:



2) Both rotation and inversion occur for the second time. The circle changes of plane again:



My issue is that I am not convinced of this, because in theory there is rotation followed by an inversion and they do not happen simultaneously. So if this is wrong, what is the correct representation and why?

Diagram for $\bar 3$



Diagram for $\bar 6$



METHOD:







NOTE: I have used comma to stress there was an inversion

Thank you
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.]