Sculpture System No. 5

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The assembled structure.

Can you get children and young people to build mathematical scultptures in their own time?

The goal of this project was to open the idea of mathematical art to the crowd and see where it is taken. Whilst traditional artwork is monolithic and static, our idea was to create a social piece of artwork that had the ability to evolve over time. In addition by playing a role in the design and construction the community is involved in the art from the beginning, not mearly as observers.

A natural way to do this is the use of modular sculptures that can be put together to make a wide variety of forms, Richard Grimes' Sculpture system No. 5, devloped for this project, is ideal. It can be constructed using reasonably (and increasingly) accessible 2D cutters, and put together easily with simple tools.

The project started at a Fab Lab on the small island of Heimaey off the south coast of Iceland, we built twenty tiles from Sculpture System No. 5 and assembled them on a cold Thursday evening in late April on a 36 year old lava field.

Many people participated in the action, which involved learning about deltahedra and three dimensional geometry, prototyping potential structures with Polydron, CNC milling, painting, and a fun few hours on the lava. Many of the people involved in the construction are already thinking about how the work can be developed and photographed.

Crowdsourced Art

A group taking a break during construction

It would be easy to write a long piece about the nature of crowdsourceing art, how it engages and empowers the community and initiates a dialogue could be buzzword compliant to geeks, the art world or the art for society world. If you were really good all three. We will do our best to avoid that. With this project our goals and ideas are simple:

  • Getting excited and making stuff.
  • Get people doing mathematics, and thinking mathematically without fear.
  • Getting people involved in the joy of making art, not just the consumption.
  • Showing the power of Fab Labs and open access CAM to make interesting things.
  • Open source our construction method so if they wish, others can take the project and run with it.

Deltahedra Assembly

A deltahedron is a polyhedron whose faces are equilateral triangles. There are infinitely many deltahedra, but only eight of them are convex. We decided to select a design that was non-convex and without rotational symmetry. Avoiding symmetry proved to be a good challenge, accessible, but not trivial to all. Four candidate shapes were constructed and voted on.

The winner was a highly irregular design. A helpful feature of the new design was that it could easily be built in stages. Deltahedra are rigid if they are missing a single face. In this case we could begin with four tetrahedra missing a base and add some tiles to these. This created modules that could then be connected together. The final connection is the only really technical part of the construction the rest can be accomplished by anyone with minimal supervision.

Sculpture System No. 5

Sculpture System No. 5 is the method used for construction. Deltahedra are built from equilateral triangles, but in order to construct arbitrary tetrahedra the tiles have to attach to each other on their edges and those edges need to have hinges. The system uses circles to approximate the triangles in such a way that there is almost no waste material and the pieces hinge naturally together.

Building the Blocks

Main article: Sculpture System No. 5 blocks
A Sculpture System No. 5 block

Building the blocks is quite simple. The basic unit is a triangle deformed so that it can be connected to others by a hinge. Its easier to look at the pictures than describe. These triangles can be built together to form a deltahedron, at which point the structure is rigid. (mathematicians out there, is there a proof of this?) The construction is very simple and probably foolproof, though the final stages of putting the model together can be a little technical.


Pictures of our construction process. A good time had by all!

Designing the deltahedra

CNC milling the tiles



Final result


  • Richard Grimes
  • Edmund Orme Harriss
  • Ásgerður Jóhannesdóttir
  • Valdimar Karl Sigurdsson
  • Smári McCarthy
  • Sebastian Stellingwerff
  • Arnar Smári Gústafsson
  • Gunnar Steingrímsson
  • Óskar Þór Jónasson
  • Þorgeir Elmar Ágústsson
  • Gísli Matthías Sigmarsson
  • Elvar Þór Eðvaldsson
  • Aníta Marý Kristmannsdóttir
  • Hjörleifur Guðnason
  • Sveinn Friðriksson
  • Elías Sifjarson
  • Friðrik Þór Jónasson
  • Frosti Gíslason