Video demonstration of a variation of the Yoshimoto cube, invented in 1971. Link includes a video on how to make one yourself out of paper, as well as an introduction to the Banach-Tarski paradox ("a pea can be chopped up and reassembled into the Sun").
Made up of eight interconnected cubes, it's capable of unfolding itself in a cyclic fashion. That means you could keep folding, or unfolding it, indefinitely.
In the toy Brocoum's mom bought him, the cubes were also cut into two identical polyhedra, each capable of forming a Yoshimoto cube containing a hollow space inside with the exact shape of another Yoshimoto cube "open" as as dodecahedron (several other shapes are also possible).
If that sounded somewhat complicated, the animated GIF on the right may illustrate the miracle of the multiplication of Yoshimoto cubes better. It's simply that a solid Yoshimoto cube can unfold into two hollow Yoshimoto cubes.