High symmetry embeddings of rectilinear tangles

Abstract 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’.