Are there any aircraft that either fold or employ folding in their design (such as with origami)?
My favourite is probably the Nikitin-Shevchenko IS which could morph between biplane and monoplane by folding its lower wing up into the upper one. The lower wing had two hinges on each side, one at the root and the other at about one-third span, so its outer section was indeed double-hinged.

Does it count to do something similar but cruder and simply let the upper wing go once you have taken off? This slip-wing was trialled on the Hillson Bi-mono before being fitted to a Hurricane.
The Tu-144 airliner and Dassault Mirage &quot;Milan&quot; had retractable &quot;moustache&quot; canard foreplanes which they deployed to improve takeoff and landing performance. Being tailless deltas, they had limited scope for conventional flaps, so put moustaches at the front instead. The moustache of the TU-144 was quite complex, having full-span flaps which amounted to a variable-camber aerofoil, so their trailing sections provide another rare example of genuine double-movement. 
The XB-70 Valkyrie folded its wing tips down during Mach 3 cruise, to improve stability and waverider lift. The A-12 variant of the Blackbird was one of a small handful of types to have had a more prosaic ventral fin which folded up for landing and takeoff.
The Wild Goose and Swallow projects of Barnes Wallis at Vickers deserve mention, although they only flew as sub-scale test RPVs. They were examples of what he called the &quot;wing-controlled aerodyne&quot;, having swing-wings in place of conventional control and tail surfaces. Not so much a double-action as eliminating the double-action of control surfaces on a swing-wing by using the whole fuselage as one giant multi-functional control surface (a tip he picked up from his work on airships such as the R100).
Does sliding count? The Akaflieg Stuttgart fs29 sailplane has telescoping wings which can pull in to increase cross-country speed. A few other experimental types had them too, such as the Makhonine Mak-10. The Gérin Varivol had a more complex variation on the theme, with a full-span high-aspect-ratio fixed section, which supported leading- and trailing-edge sections that were stowed in the fuselage and scrolled out along the wing like lowering a Venetian blind.
Polyhedra are solids with flat surfaces. Folding them using origami techniques is quite an art form, so I make no apology for the next example. Most polyhedra assemble rigidly but some, known as &quot;breathing&quot; polyhedra, can flex to a limited extent. An example from aviation is the variable-thickness wing experimented with by Rocheville among others, which bulges its top surface upwards to provide high lift for takeoff and landing, then draws it back down to create a thin wing for high-speed flight.