Hi Rolf,
Still enjoying a remarkable IK-puzzle, aren’t you? 
Indeed rotation of the “opening” I think is the best way to drive the IK-chain. In the attached model I set the rotating opening free to move back and forth in accordance to its bindings.
Folding 001.3dm (73.9 KB)
As you can see the orthogonal ribs force the front to make a movement different from the diagonal connection.
Joining them into 1 object makes folding impossible.
In the images of the cube Ariadna shows above the “hinges” are made with snap locks. Probably such gives sufficient suppleness to deal with the dissimilarity. But then again Bongo does not offer “wobbly” hinges.
I did make a cardboard model and indeed … it does not fold.
Luc