Knittable or unknittable?

Textiles are one of the most important inventions, and knitting is especially widely used. Knitting has long been the focus of attention from an engineering perspective and has recently attracted further interest in its mechanical properties and shape control. However, its topological aspect is still unclear. Even the fundamental question of "what is knitting" has no clear answer so far. This study reveals that knitting is a textile with marginal constraints. We discuss the boundary between knittable and non-knittable textiles, and state that the essence of knitting lies in the topological constraints in the making process. This research introduces small defects in textiles and examines the rules for their replication, which enables the determination of whether a textile is knittable or not. This approach provides us with a perspective on effectively screening complex textiles for knittable structures.