The symmetry groups of periodic isonemal fabrics

An isonemal fabric is a weaving in which the symmetry group is transitive on the strands. Its symmetry groups is a layer group. In this paper we determine the 21 possible layer groups which occur as symmetry groups of (2-way, 2-fold) periodic isonemal fabrics. In addition, utilizing the induced strand subgroup, we classify the fabrics into 42 symmetry types.