Isonemal Prefabrics with Perpendicular Axes of Symmetry

TL;DR

This paper refines Roth's taxonomy of isonemal weaving designs, focusing on types 11-32, and addresses questions about their existence in different sizes and their behavior under doubling and halving operations.

Contribution

It extends the classification of isonemal prefabrics by analyzing their size variations and how they transform when doubled or halved, enhancing understanding of their structural properties.

Findings

Identifies which designs exist in various sizes

Determines which prefabrics remain isonemal after doubling

Determines which prefabrics remain isonemal after halving

Abstract

This paper continues the refinement of Richard Roth's taxonomy of isonemal weaving designs through types 11--32 of the 39 in order to solve 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.