I'm using inkscape 0.92.3 and want to break a circular ring into 3 equal sections. I've created a ring from two circles and used Path > Difference, then Extensions > Modify Path > Add Nodes... with a selection of By number of segments, 3. The screenshot shows the result.
Now I need to create 3 divisions of the ring. Using a coordinate system where 0/360 degrees is to the centre right of the ring, I want to connect the nodes from the outer ring to the inner ring with straight segments as follows,
The dashed lines in the next screenshot show the segments.
I need the segments to break apart and be fitted back again with precision and no gaps. It is absolutely necessary that the radius remains the same when all three segments are rotated as a group.
For anyone who's interested, this is a trivial flower snark with the inner nodes rotated 60 degrees clockwise. In this case the nodes are infinitely small and the 3 sections will be coloured.