Triangulated Screen: Tension rods?

This is not a worked out idea yet but we could explore this: what if the screen was made like a pop-up tent, in that it is made of a series of tension rods that stretch and lock into position with each other such that the tension of the material (think tent-like material) - and the triangulated faces and spiral shape - support the structure?

 

Here the dashed and undashed lines can be either tension rod or just tension, or either or both.

Done