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The Mobius Strip
The Mobius Strip is the simplest non-orientable surface. It is a two dimensional strip that has only one side. You can create one by taking a strip of tape, twist one end once, and then attach. Non-orientable surfaces are quite interesting in mathematics, and I invite you all to google the Klein Bottle, which is a three dimensional analog of the Mobius Strip.
The red stripe on the model is the proof that the strip has only one side - follow it and you will see that you go both on the inside and on the outside of the strip without lifting your finger. You will notice that I am not cheating - The red stripe really does follow the surface and at no point passes through it.
If you like my work, I also a have a Functional Road Sweeper here on Ideas, and I would appreciate your support. You can see even more of my MOCs on Rebrickable.com.