Origami Fibonacci torus and knotted torus: https://www.youtube.com/watch?v=LdnvxN4UUfs
I have the impression that the Fibonacci part just gives it a nice organic look (visible in much of Akio Hizume's other architecture at http://www.starcage.org/englishindex.html) but what interests me is the way it rotates smoothly. That's not something unfolded paper can do, because the inner parts of a torus have negative curvature, the outer parts are positive, and unfolded paper can't change curvature.
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