So we learned how to fold a tetrahedron from A4 paper, and instead of studying for exams, we decided to make an stellated icosahedron by gluing 20 of them:

It also makes for a nice hat, if you remove some vertexes:

Cubes are possible as well, in fact all Platonic Solids with glue, and even without.

You can even “fold” in four dimensions.