Torggler actually has more than one alternative to the classic door concept that’s been around for centuries. They all utilize rotating squares, but some use rods, wheels and a track system arranged in an epitrochoid curve.
According to io9:
The Evolution Door works by virtue of four strategically attached triangles that separate, fold and rotate with a gentle flick of the wrist. It’s a wonderful play on geometry that makes it possible to move the screen from side to side without the use of a track, a topological trick that Torggler says “opens up new applications for the door.”Look: