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The fixed content of the wedge where two large triangles make contact severely constrains the way lattices can be filled up. The restriction manifests itself in many contexts, for example in trying to run triangles off in a given direction in a long strip.
Introducing defects into any lattice will almost certainly generate a wedge containing an alternate evolution. In time, although the time may be quite large, an equilibrium between the wedge and the undisturbed lattice will be reached. The boundary layers may define shift-periodic systems on their own account. None of these combinations have been indexed in the concordance.