If anyone wants to take inspiration from this Rolite, here are two photos I saved that show a Rolite part way through being erected. The critical detail is that on all four corners there are L-shaped strips that hinge out to make the corner - that's how both the sides and the end can be narrow enough to fit under the top when it's lowered.
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And then how do they fold the ends and sides on top of each other, when the break is at the same height for both? They used offset hinges - see below:
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