Rigid origami is a branch of origami which is concerned with folding structures using flat rigid sheets joined by hinges. That is, unlike with paper origami, the sheets cannot bend during the folding process; they must remain flat at all times. However, there is no requirement that the structure start as a single flat sheet – for instance shopping bags with flat bottoms are studied as part of rigid origami.
The number of standard origami bases that can be folded using rigid origami is restricted by its rules. Rigid origami does not have to follow the Huzita–Hatori axioms, the fold lines can be calculated rather than having to be constructed from existing lines and points. When folding rigid origami flat, Kawasaki's theorem and Maekawa's theorem restrict the folding patterns that are possible, just as they do in conventional origami, but they no longer form an exact characterization: some patterns that can be folded flat in conventional origami cannot be folded flat rigidly.
The napkin folding problem asks whether it is possible to fold a square so the perimeter of the resulting flat figure is increased. That this can be solved within rigid origami was proved by A.S. Tarasov in 2004.
Kaleidocycles are toys, usually made of paper, which give an effect similar to a kaleidoscope when convoluted.
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