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arXiv · 2310.10000

The Crisscross and the Cup: Two Short 3-Twist Paper Moebius Bands

Brienne Elisabeth Brown·Richard Evan Schwartz
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Abstract

We introduce the crisscross and the cup, both of which are immersed $3$-twist polygonal paper Moebius band of aspect ratio $3$. We explain why these two objects are limits of smooth embedded paper Moebius bands having knotted boundary. We conjecture that any smooth embedded paper Moebius band with knotted boundary has aspect ratio greater than $3$. The crisscross is planar but the cup is not.

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Brienne Elisabeth Brown, Richard Evan Schwartz. 2023-10-16. The Crisscross and the Cup: Two Short 3-Twist Paper Moebius Bands. https://arxiv.org/abs/2310.10000

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