Trapdoor to Otherness!

To explore this amazing illusion you need a sheet of fairly stiff but not too-thick cardboard about the size of a sheet of printer or copier paper. I have seen these made from a playing card, or a dollar bill, but a slightly larger size is easiest to begin with. Take your sheet of cardboard and with a pencil mark a frame or margin all around the edge. For example, you could trace a line 2 inches from the edge, on top, bottom and sides. Now with a razor knife or box-cutter, cut out the sides and bottom of the inner edge of the frame. This produces a kind of trap-door hinged at the top. Now crease all the rest of the frame, so that it can easily be folded in either direction. In the sketch above, the dashed lines are the creases, the solid lines are the cuts.

Now here's the puzzle. Start with the trap door raised on one side, which we arbitrarily call the “front.” Your task is to fold the margins of the “frame” and then unfold them, leaving the trap door still raised, so that when the trap door is lowered, it is on the other side of the cardboard, which we arbitrarily call the “back.” This seems absolutely impossible, a violation of the well-known physics and math of three-dimensional space. But it can be done. You will see me do it in class. Is it magic? Mathematics? Or what? Try it yourself!