It would be unimaginable to fold a bicycle, but there's a bike that can do just that. One reason it can do just that is because it is hubless. The Sada Bike uses 26 inch hubless wheels. Which means you can simply fold the frame away.

Gianluca Sada, it's designer, explains:
The wheels have no spokes, the system folds with a single movement, the packaging container can also be used as a backpack... It uses a system anchoring the wheels using smaller wheels held by a small frame and a specific quick clamping device. They allow you to fold the bike quickly and easily, using its special package like a trendy backpack.