Take the shapes, use Rhino's Flatten command, see if you can reduce it to a 2D representation of the material before being twisted. May work.
Or try
Pepakura, which was specifically designed to handle the issue you're having- how to realize a model as a 2D object that can be unfolded. Be warned, however, that you need to have an object with the appropriate cuts already designed into the mesh, in this case, because you want it to lay out the objects on paper, ready to "fold". I've used it before, and it's pretty cool.
I really dunno how you're supposed to realize this, from a manufacturing standpoint, though, short of building it with stereolithography.
I'm trying to imagine doing it with paper, and I think that'll be a nightmare, due to the twisting- it'll almost certainly crinkle, probably as you work towards the "outside", and since paper doesn't have any stretch at all, the cuts of the geometry would be incredibly finicky, and would probably be an absolute bear to get correct without destroying it. Gluing it's no biggie- you could use some little bent strips somewhere in the middle where nobody could see to hold it together. I really don't think that's the problem, though.
Very thin-gauge metal would probably work better, I suspect, if you could get it cut on a laser and then formed the pieces mainly by hand, matching the corners to pins located at the appropriate points. You probably don't have the experience with that to do it without extensive help, though. Might want to talk online on the "real CAD" forums, where there are people who routinely have to deal with these issues.