Torus Knots with Polygonal Faces

Chern Chuang and Bih-Yaw Jin
Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture (2014)
Pages 59–64

Abstract

We review several methods of constructing models of torus knots with non-planar polygonal faces, with the majority of hexagons and some non-hexagons. These methods were developed by the authors throughout recent years, albeit mostly in the context of chemical research on carbon nanostructures. The resulting hypothetical molecular structures are predicted to be chemically stable if care is taken in arranging non-hexagons in the midst of hexagons. Among them, a general scheme that is applicable to arbitrary torus knots (p, q) with p < q is presented. For the simplest nontrivial case, a trefoil knot, two additional routes can be drawn. Noteworthily, one of them is inspired by Escher's artwork Knots. These models are realized physically with the technique of mathematical beading.

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