To respond to Ali Bahmani’s interesting question, if I am not mistaken the Concentric Winder should have greater resistance to weight than any of the candidates suggested thus far. See
http://origami-aesthetics.blogspot.co.il/2008/09/concentric-winder.html In particular it should be stronger than (another very good candidate) the Miura fold, if only because multiple layers of the same sheet end up being used. Of course the main reason is that as the folds are circular, there is no possibility of a hinge-action along the folds, as there is with Miuras. Wind it to a factor of at least 6; wind more if greater support strength is needed (winding hence layering and compressive strength can be added indefinitely). Each turn that aligns the slits is a full wind. The radius of the disk shrinks in direct proportion to the number of winds. For purists who want to avoid the radius cut, use the same crease pattern (concentric circles), fold the initial disk into a semicircle and wind that. Note also that you can make this also out of an A4—the interior crease pattern is what’s important, not the shape of the outer edge. The above answers I believe A.B’s question re the strongest possible fold resistant to weight from above. But there is also the interesting question of folds that are maximally resistant to TENSILE stresses. This is best thought of as a problem of two sheets rather than one: what sort of origami locks can be invented, that hold two sheets together strongly when being pulled in opposite directions? —At the limit, the paper would tear—and not along the folds—before the lock breaks. Saadya
