Isonemal prefabrics with only parallel axes of symmetry

Isonemal weaving designs, introduced into mathematical literature by Grünbaum 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.