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The Möbius Band

The Möbius Band is the building block for non-orientable surfaces. It is formed by joining the ends of a rectangle with a twist (180 degrees). Any non-orientable surface contains a Möbius Band, and any surface which contains a Möbius Band is necessarily non-orientable. It is not closed--hence it is not a surface, and it contains one boundary curve. The Möbius Band cannot be embedded in the plane, R^2.

Description and pictures of the standard image of the Möbius band embedded in R^3.

Description and pictures of a Möbius band embedded in R^3 with three twists instead of one.

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Created: Aug 7 1995 ---- Last modified: Wed Oct 30 12:24:10 1996
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