Gauss’ braid

Design work @ HfG Offenbach | 2010


The project “Gauss’ braid” is an experiment on three-dimensional form generation. It introduces braiding as an analogue surface morphing method, demonstrates a gradual visual aesthetic of space composition. It discusses as well the role of material property plays during construction process.

More photos of working models to >download<


The braiding

“Gauss’ braid” started with manipulation of paper-stripes. As an economical and hands-on material, paper usually serves as a tool to experiment analogue surface morphing. Sophia Vyzoviti describes in her book <Supersurfaces> the basic paperfold algorithm as follow:

1. start with a flat paper surface

2. transform the paper surface (cut, score, crease, fold, twist, revolve, coil, turn, rotate, pleat, pull, push, wrap, pierce, hinge, knot, weave, compress, stretch, unfold…)

3. end with a three-dimensional paper surface.

Generating the paperfold algorithm is an improvisational method, that combines geometry, procedural instructions, “how to” and visual narratives. In “Gauss’ braid”, braiding stripes was adopted as a procedure to develop a complex space composition. The braiding phenomena is common in our daily life, yet attractive for mathematician as well. In topology, braid theory is an abstract geometric theory studying the everyday braid concept, and some generalizations. Gauss was the first mathematician who brought braid into topological research. Instead of abstracting their intrinsic morphology to a level of generalization, this project built explanatory models of braids to demonstrate the step-by-step procedure of transforming a flat plane into a three-dimensional surface. Rather than describing the formal characteristics of the end result, the focus of the project is on the process, on understanding the origin and evolution of the surface.


when braiding, each stripe was half-twist (as Mobius strip) to emphasize the curve of stripe. It also created a visually dynamic tension between stripes.


The composition

A group of braids were developed to generate a gradually evolved space composition. Each braid shared the similar braiding procedure. They were arranged next to each other. Starting from one, the number of stripes of each braid increased up to five then decreased to one.


The material

In the last step, paper was replaced by PP, which is more elastic and stable than paper.

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