Knots and Coxeter Groups

Dylan Burke; Geoffrey Cuff-Chartrand; Malors Espinosa; Mateusz Kazimierczak; Mohammadamin Mobedi

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arXiv · 2503.10785

Knots and Coxeter Groups

Dylan Burke·Geoffrey Cuff-Chartrand·Malors Espinosa·Mateusz Kazimierczak·Mohammadamin Mobedi

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Abstract

In this paper we study knots created by galleries in the affine Coxeter complex of type \widewedge{B3}. We bound the stick number by 40 and prove that the smallest length of threefold rotationally symmetric trefoils is 42. We construct explicit galleries that knot as 9_35, 9_40, 9_41 and 9_47 in a way that has threefold rotational symmetry. We explain the construction of these galleries for 9_47 carefully. We conclude with three questions inspired by this work.

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BibTeX RIS

Dylan Burke, Geoffrey Cuff-Chartrand, Malors Espinosa, Mateusz Kazimierczak, Mohammadamin Mobedi. 2025-03-13. Knots and Coxeter Groups. https://arxiv.org/abs/2503.10785

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