  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.
