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

2023/10/16 by Brienne Elisabeth Brown, Richard Evan Schwartz, Brown, Brienne Elisabeth +1 · 3 citations
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2310.10000

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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• Ribbonlength bounds for pretzel links and knots with ≤ 9 crossings
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• Bounded ribbonlength for knot families and multi-twist Möbius bands

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