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The hexagonal cells built by honey bees and social wasps are an example of adaptive architecture; hexagons minimize material use, while maximizing storage space and structural stability. Hexagon building evolved independently in the bees and wasps, but in some species of both groups, the hexagonal cells are size dimorphic—small worker cells and large reproductive cells—which forces the builders to join differently sized hexagons together. This inherent tiling problem creates a unique opportunity to investigate how similar architectural challenges are solved across independent evolutionary origins. We investigated how 5 honey bee and 5 wasp species solved this problem by extracting per-cell metrics from 22,745 cells. Here, we show that all species used the same building techniques: intermediate-sized cells and pairs of non-hexagonal cells, which increase in frequency with increasing size dimorphism. We then derive a simple geometric model that explains and predicts the observed pairing of non-hexagonal cells and their rate of occurrence. Our results show that despite different building materials, comb configurations, and 179 million years of independent evolution, honey bees and social wasps have converged on the same solutions for the same architectural problems, thereby revealing fundamental building properties and evolutionary convergence in construction behavior.