Cyclic twill-woven objects

Any arbitrary twist of the edges of an extended graph rotation system induces a cyclic weaving on the corresponding surface [Akleman et al. 2009]. This recent theoretical result allows us to study generalized versions of textile weaving structures as cyclic weaving structures on arbitrary surfaces. In this work, we extend the study to twill weaving, which is used in fabrics such as denim or gabardine. Biaxial twill is a textile weave in which the weft (filling) threads pass over and under two consecutive warp threads and each row is obtained from the row above it by a shift of 1 unit to the right or to the left. The shift operation creates the characteristic diagonal pattern that makes the twill fabric visually appealing.