  Isonemal weaving designs, introduced into mathematical literature by
Gr\"unbaum and Shephard, were classified into thirty-nine infinite sets and a
small number of exceptions by Richard Roth. This paper refines Roth's taxonomy
for the first ten of these families in order to solve three problems, which
designs exist in various sizes, which prefabrics can be doubled and remain
isonemal, and which can be halved and remain isonemal.
