Möbius strip

A 2D object traversing once around the Möbius strip returns in mirrored form
A single off-center cut separates a Möbius strip (purple) from a two-sided strip
Subdivision into six mutually-adjacent regions, bounded by Tietze's graph

There are many different ways of defining geometric surfaces with the topology of the Möbius strip, yielding realizations with additional geometric properties.

Beyond the already-discussed applications of Möbius strips to the design of mechanical belts that wear evenly on their entire surface, and of the Plücker conoid to the design of gears, other applications of Möbius strips include: