Perfect Colourings of Isonemal Fabrics by Thick Striping

TL;DR

This paper explores perfect colourings of isonemal fabrics using thick striping, extending the catalogue of related prefabrics and their applications in cube weaving with colour symmetry.

Contribution

It extends the catalogue of isonemal prefabrics of genus V that fall apart to order 20 and explores their relation to cube weaving with colour symmetry.

Findings

Extended catalogue of isonemal prefabrics of genus V to order 20.

Identified designs suitable for cube weaving with colour symmetry.

Reconsidered the relation between perfect colouring and fabric fall-apart properties.

Abstract

Perfect colouring of isonemal fabrics by thick striping of warp and weft and the closely related topic of isonemal prefabrics that fall apart are reconsidered and their relation further explored. The catalogue of isonemal prefabrics of genus V that fall apart is extended to order 20 with designs that can be used to weave cubes with colour symmetry as well as weaving symmetry.