The authors extend orbifold notation to three dimensions and provide a complete set of symbols for classifying all layer groups, demonstrated on knitted fabric motifs.
2025 arXiv: 2508.20055
2 Pith papers cite this work. Polarity classification is still indexing.
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Woven and knitted fabrics are doubly periodic soft materials whose topology is that of links in the thickened torus and whose mechanics follow from yarn contacts, crimp, and stitch geometry.
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An Orbifold Framework for Classifying Layer Groups with an Application to Knitted Fabrics
The authors extend orbifold notation to three dimensions and provide a complete set of symbols for classifying all layer groups, demonstrated on knitted fabric motifs.
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Textiles: from twisted yarn to topology and mechanics
Woven and knitted fabrics are doubly periodic soft materials whose topology is that of links in the thickened torus and whose mechanics follow from yarn contacts, crimp, and stitch geometry.