If you take a cube, and grow a new cube out from each of its six faces, you will get a "hyper plus sign":
This 3D solid has an interesting property. It can be sliced along its edges and unfolded into a single 2D shape that can then be re-folded to perfectly cover the surface of a cube. Your challenge is to show how this can be done.
- Show how to cut the surface of the above 3D solid along its edges so the entire surface can be unfolded into a single 2D shape.
- Then show how to re-fold this 2D shape onto the surface of a cube.
Some rules and clarifications:
- The original 3D solid may only be cut along its edges.
- You must unfold the entire surface of the original solid, in one continuous piece.
- The 2D shape must cover the entire surface of the cube, with no gaps and no overlaps.
- The edges of the 2D shape do not need to line up with the edges of the final cube. (If this was a requirement, the puzzle would be unsolvable.)
- I am aware of
onetwo basic solutions, but there are endless trivial variations of these solutions possible. Your solution does not need to look identical to mine. It just needs to meet all of the requirements above.