Weaving Bifoldable

Bifoldable is the result of a collaboration with mathematician Matthias Weber on a new class of infinite polyhedral complexes. Currently, the initial result has been published at: https://arxiv.org/abs/1809.01698.

The method used to make these bifoldable infinite polyhedral complexes is similar to the strips and rings discussed by artist Rinus Roelofs in which he gave a simple example of weaving a double-layered cube that is similar to a Borromean structure; the double-layered cube’s 12 faces can be divided into 3 strips of 4 faces that can then be folded and interwoven into three connected strips. Alternatively, the cube can be understood as a generalized zonohedron, or a convex polyhedron bounded by parallelograms. Since a cube has three distinct edge directions, and every edge direction determines a zone of faces, therefore three different zones. Since each face of the cube has one edge that is equal and parallel to one of the zone’s edges, and another edge that is equal and parallel to one of the other two edge directions, it can be understood that each face belongs to two zones which cross each other at the face. Using a method similar to this, weaving bifoldable aims to explore the various forms and expressions in woven infinite bi-foldable polyhedral complexes.

To learn more about the mathematics (explained in layman’s terms by Weber) behind these fun infinite bi-foldable polyhedral complexes, or the process of how they are found, please visit Weber’s blogs here:

Weber’s blog on Butterfly
Weber’s blog on Dos Equis