Butterfly
2019

Width 14", Length 6", Height 11"

Tinted Mi-Teintes Paper

Butterfly belongs to a new class of infinite bi-foldable polyhedral complexes that are the result of a collaboration between Jiangmei Wu and mathematician Matthias Weber. Currently, our initial result has been published at: https://arxiv.org/abs/1809.01698. These polyhedral complexes that can be flat-folded or collapsed into two perpendicular planes.

 

There are three vertex types in Butterfly: valency 4, 6, and 8. Butterfly is named after the vertex of valency 8 as it resembles a symmetrically balanced butterfly. This vertex is translated to create the triply periodic construction. Butterfly is made using a polyhedral weaving technique that employs a four-color complementary scheme. Each color represents a distinctive zone using the concept of zonohedron proposed by H.S.M. Coxeter. Each face is alternated and interwoven by two zones of two colors. A few deviations from the regularity are inserted to create the rhythmic changes.

To construct a triply periodic Butterfly pattern, start with a vertex type of valency 8 that resembles a symmetrically balanced butterfly. This vertex is translated in two directions, and then in a third direction, to create an infinite triply periodic polyhedral complex.

Weber’s blog on Butterfly