Through and Around Instead of Over and Under: Another Way of Weaving

Rinus Roelofs
Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture (2011)
Pages 319–328 Regular Papers


In Figure 1 you can see an iron window lattice that is constructed with bars: horizontal bars are threaded through holes in vertical bars and vice versa. You can call this a weaving, but here the `threads' are going through and around each other instead of over and under as in normal weaving. In this paper I will investigate the possibilities of this kind of weaving. There is a close relationship between the through and around weaving and the Borromean rings. In the three dimensional setting each ring goes through one of the other rings and is around the third ring.