Here is a fantastic little model similar to a Möbius strip. It is worth trying this one yourself. See if you can guess what will happen when you cut this.
- Cut a large "T" from a piece of paper with the upright and the crossbar each about an inch (2.5 cm) wide.
- Tape the crossbar's ends together in an untwisted loop.
- Snake the vertical part of the T through the hole (again no twist) and attach it to the opposite side and opposite edge of the loop.
- Cut the pieces along the midline of the bands as you would cut a Möbius strip.
- This model is topologically equivalent to a Klein bottle with a hole in it.