Mobius Bands

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When you cut a Mobius band "in half", it ends up as one longer twice-twisted band -- what a surprise!
Cutting a Mobius band "in thirds" is also unusual: you end up with two pieces, one of which is a "mini-me" Mobius band, one third the width of the original; the other piece linking with the mini-me is a twice-twisted band. This figure shows the central band as a Mobius band.
The longer band we obtain by cutting a Mobius band "in thirds" is a twice-twisted band. This figure shows the two edges of the band.
Cutting a thrice-twisted Mobius band "in half", it ends up as one longer six-twisted band. The single edge is knotted into a trefoil knot, as this diagram shows.
PNC Bank Logo is a thrice-twisted Mobius band
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