Frustrated in trying to describe higher topology abstractly to students, Xian Wang invented a model train that can hug either side of a track:

It is therefore a primary object of the present invention to provide an electrically-operated ornament travelling on a rail which can be used to explain the Mobius Theorem. … In general textbooks, this advanced mathematic rule is usually explained by demonstrating a body circularly moving on a front and a reverse side of a twisted two-ends-connected belt. Most people can not understand and imagine the theorem from such explanation and demonstration.

Of course, once you’ve built one you can put it to other uses: