Geometric analysis classifies symmetric rectilinear tangles and Hopf link configurations, highlighting structural principles for designing complex spatial networks.
Finite tangles are embeddings of graphs that include knots or links as subcomponents. We describe vertex-transitive tangles with 12 or fewer crossings, as well as tangles with just two crossings that feature the Hopf link. Additionally, we consider tangles formed by adding edges to a ravel. This article is part of the theme issue ‘Geometry, materials and the imagination’.
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O'Keeffe et al. (2026) studied this question.
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