Obviously Transform / Rotate at 60° + ?? Would the 3 shapes at the top be created first or is it just the dark arts? Where is Panter off YT when you need him?
 Create one element and a circle outside it entered on the middle of the finished design
 Rotate the repeating element with the circle to the desired angle and repeat until the design is complete
 Delete the circles outside the design
This is not a 100% match, but I think if you played with the shapes you could get there, but it at least could give you a starting point hopefully.

I created a 6 pointed star and rounded it’s corners to get the shape on the right.
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I duplicated my rounded 6 pointed star and rotated the copy by 30 degrees

I then overlapped and centered the shapes

Then I realized to create the flattened edges I needed a 12 sided shape to fill the gaps. So using the polygon tool I created that 12 sided shape. Which I then rotated 15 degrees so that the flat edges would match how I needed them to match my earlier shapes.

I then overlaid all 3 shapes and resized the 12 sided shape until it barely overlapped the edges of my previous 2 shapes.

I then expanded all the shapes (really just the 2 rounded corner shapes so that they were truly rounded and not just having the rounded corner effect) I then used pathfinder to divide all the shapes and removed every other straight edge to have a “gap”. There also was a tiny triangle “point” on the end of each rounded point due to dividing the shapes that I had to remove from each curve. From there color as needed.
With all that being said, the original is much more pronounced in its curves. So, as I said it is not a 1 to 1 but at least you could potentially use it as a starting point. It may help to use a more pronounced 6 pointed star to start with. I’m not sure.
Well done Craig, I think you’ve cracked it. I just couldn’t get my head around it, I knew it was doable…
The only difference, give or take, is that the inside edge of the magenta parts are concave not convex, but that’s maybe a Shapebuilder and Path Smoothing action to follow.
Yup, I did notice that the inside had a little tweaking and nudging. I wasn’t sure how precise you were looking to get, or if you were just looking to get a similar look.
I will say, it also could potentially have been done in some sort of 3D tool especially with the slight shadowing effect.