Isonemal prefabrics with no axes of symmetry

This paper refines Richard Roth’s taxonomy of isonemal weaving designs through the final types 33–39 in order to complete the solution of three problems for those designs: which designs exist in various sizes, which prefabrics can be doubled and remain isonemal, and which can be halved and remain isonemal. These types have no symmetry axes but have quarter-turn symmetries. Jean Pedersen’s problem of woven cubes is also discussed.