Density functional theory and quantum Monte Carlo simulations reveal that the structure of the Stone-Wales (SW) defect in graphene is more complex than hitherto appreciated. Rather than being a simple in-plane transformation of two carbon atoms, out-of-plane wavelike defect structures that extend over several nanometers are predicted. Equivalent wavelike SW reconstructions are predicted for hexagonal boron-nitride and polycyclic aromatic hydrocarbons above a critical size, demonstrating the relevance of these predictions to $s{p}^{2}$-bonded materials in general.
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