You've got the idea
I start with 20 full circles then twist each circle back on itself to form a trefoil knot. If I design the model as a mathematical teaching set I will put in part about trefoil knots and knot theory. I probably need to make some design changes to that each loop of the knot twists the same way.
The result is that each of the twenty units which you show above is subdivided into four triangles and each lamination is two layers thick. It's only twenty parts.
I put on twelve stringer parts(pentagonal) as you describe for attaching the skin. The stingers all end up being 2 layers thick. My goal has been to make the model as simply as possible with the fewest number of steps and parts. The tiny version is more like what you describe but each part is a full circle and forms two units. The circle glues back to itself and then glues to adjacent units. It's kind of a pain to do since it's so small that it takes tweezers.
I'll have to get on my other computer to send photos.
I've been sizing the skin by trial and error I may have to do the math.
I'm considering getting adhesive backed paper. The parts would remaining on the backing(I hope so anyway) and it would require no glue to put together the model. Surprisingly most of the glue surfaces could be faced inwards. --I just had an idea which would cover more of the glue surfaces when assembled. This would work well as an educational kit because the kid could spend their time folding and assembling, not cutting or spreading glue. If I do go with sticky-backed paper, I'll have to adjust the skin size based what is available for paper thickness.
Good talking to you on this. I see that I probably can figure out the equation for the size of the skin.
Another thought from this. When the stringers go on the result is a low spot in the middle of each facet equivalent to two thicknesses of paper. I could cut the underlying parts in a way which compensates for this. It's easier than trying to piece in additional stringer material, which I've done with the 8 inch.
I love you guys. Thanks.