The symmetry groups of periodic isonemal fabrics
The author considers the symmetry of periodic weavings having as symmetry a group transitive on the strands (warps and wefts) in at least two non- parallel directions. These weavings are the so-called periodic isonemal fabrics. Considered are realizations (designs of fabrics) consisting in an array of black and white squares, the rows corresponding to wefts and the columns corresponding to warps, the color depending whether the warp passes over the weft, or the other way around. Two kinds of groups can be used for classifying these fabrics: the layer groups of three-dimensional space and the two-color space groups of the plane. A more specific classification of fabric types is given in terms of pairs \(G\), \(Y\), with \(G\) the layer group of the fabric and \(Y\) its strands subgroup, the subgroup leaving a strand invariant (which is a double- sided frieze group). A list is given of the 42 symmetry types of periodic isonemal fabrics. In another table the 21 layer groups which appear as symmetry groups of those fabrics are given together with the corresponding color groups in the usual notation and according to the classification of E. A. Wood of the 80 diperiodic groups in three dimensions.
scientific article; zbMATH DE number 487620
scientific article