We study the many facets of periodic entanglements found in various biological, molecular, and chemical structures like polymers, liquid crystals, and DNA origami. We use techniques from geometry, topology, combinatorics and graph theory to enumerate and characterise potential structures, in many cases using periodic graphs or triply-periodic minimal surfaces as scaffolds for the structures. In this case, tangling, graphs and surfaces are all related objects of study. On the other hand, we are also developing techniques for the characterisation of these structures, where we look at crossing diagrams and related invariants.
Diagrammatic representations of 3-periodic entanglements
Ideal geometry of periodic entanglements
Periodic entanglement III: tangled degree-3 finite and layer net intergrowths from rare forests
Periodic entanglement II: weavings from hyperbolic line patterns
