Create a single path and then use the follow me tool.
It looks like 5 equal segments, if you can get hold of the original logo in vector from the client, take out one segment and import it into SketchUp.
You will have to guesstimate the height yourself but I would say that each segment is not more than half as high as it’s width judging by the shadows.
Create the paths from that segment, duplicate and paste in place another 4 times and rotate from a centre point to make the shape. Some segments you will also flip along Blue axis.
There may be a plugin to help that somebody who knows more can advise on, but that’s how I would do it if I was given the same task.
I have just freehanded this, however I have not taken into account the height.
You would need to figure out how high you want it and then either pull all the surfaces in towards the centre for each segment so the whole unit sits flat like a donut but each segment flows ‘underneath’ the next, or stack it really small with a supporting structure internally.
Hope that makes sense, sorry for the crude drawings, in the middle of my own non-3D freelance deadline! I did not join up the paths in this example, ideally you need to measure it beforehand to make sure it all lines up otherwise it will be as wonky as mine.