Hierarchical interlaced networks of disclination lines in non-periodic structures

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Abstract
We describe the defect set in non-crystalline structures derived from polytopes by an iterative flattening method. Defects appear as a hierarchy of interlaced disclination networks which form the locus of sites where the local order deviates from a perfect icosahedral environment. The iterative procedure is fully described in 2D and 3D. We also discuss the usefulness of introducing the concept of hierarchical defect structure for the microscopic description of icosahedral quasicrystals