A parameterization of the Möbius strip in is:
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where is the radius of the center circle of the strip, is the width, is the number of half-twists, and is a parameter which runs from to . If , you obtain the classic Möbius strip, but for large you get a 'more twisted' shape. For even the surface is orientable and has a well-defined principal normal, while for odd it is non-orientable.