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Using the standard way of representation:

enter image description here

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:

enter image description here

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

enter image description here

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 $\bar 3$

enter image description here

Diagram for $\bar 6$

enter image description here

METHOD:

enter image description here

enter image description here

enter image description here

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

Thank you

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    – user7951
    Commented Dec 23, 2018 at 13:36

1 Answer 1

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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.

rotation inversion

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

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