Topology in motion: Geometry-driven defect dynamics in social wasp nests.

Emergent geometric order characterizes social insect nests, exemplified by paper wasps, which collectively build arrays of hexagonal cells to optimize space and mechanical stability. These arrays contain topological defects in the form of nonhexagonal cells, which disrupt the order of the nest. A disclination like a single pentagon or heptagon modifies angular geometry and introduces curvature, whereas adjacent pentagon-heptagon pairs form dislocations that retain planarity by offsetting angular mismatch at the cost of translational order. Unlike the malleable wax of honeybee combs, the rigid materials like plant fibers used by wasps limit structural remodeling, making such defect management more challenging. Here, we show the migration of dislocations through a sequence of discrete steps involving splitting into different types of disclinations. Defects propagate via local rearrangements of walls and vertices, analogous to star-triangle transformations and node release events that conserve topological charge, as confirmed by Burgers circuits. The shift was likely intended to promote hexagonal cell formation, with a secondary aim of driving the defect to the boundary. This was not achieved because subsequent nest growth displaced the boundary farther away from the defect region. Our results suggest that wasps achieve global architectural coherence through local geometric transformations that preserve topology, enabling decentralized construction under material constraints.