The other day, surfing through my blog roll, I found a link to a very interesting box, called impossible box.
The original box is a jpeg file for a square box (the black one with the read trim in the picture). When I first imported the file into the software, I tried to vectorize it. Eventually I gave up on that idea as I was getting a lot of round corners. Since the box is basically straight lines, I used it as a template and did all the lines again.
After I was done with the first one, I began wondering if other shapes would work as well. When J got home, we began talking about it and eventually came up with the pentagonal one.In theory, any polygon will work. The only problem is finding out the angles to make the lid collapse properly.
J changed the bottom, so they look like a flower (as seen on the blue one). I think, with a little manipulation, a similar effect can be used on the lid.