Knots and Coxeter Groups
Abstract
In this paper we study knots created by galleries in the affine Coxeter complex of type 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 935, 940, 941 and 947 in a way that has threefold rotational symmetry. We explain the construction of these galleries for 947 carefully. We conclude with three questions inspired by this work.
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