Non-Orientable Shapes - I like that we can imagine shapes that are impossible in this universe. Two Mobius Loops create a Klein bottle: a shape with one side and no boundaries, inside of its outside, and contains nothing except itself. If you travel around its edge, you'll end up in the same place - only backwards. That's only with one more manifold than we're used to.
Add another manifold, and you've got a shape that seems to contain infinite space. If you walked through the right wall, you'd appear through the left wall.