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Volterra's definition of dislocations in crystals distinguishes edge andscrew defects geometrically, according to whether the Burgers vector isperpendicular or parallel to the defect. Here, we demonstrate a distinctionbetween screw and edge dislocations that enables a unified, purely topologicalmeans of classification. Our construction relies on the construction of real orvirtual disclination-line pairs at the core of the dislocation in a smectic andcan be generalized to crystals with triply-periodic order. The connectionbetween topology and geometry is exploited.

Escape from the Second Dimension: A Topological Distinction Between Edge and Screw Dislocations