Sculpture System No. 5

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, the idea of this 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. Sculpture system 5 is an attempt to do this. It can be constructed using reasonably (and increasingly) accessible 2D cutters.

Using the Fab Lab on the small island of Heimaey off the south coast of Iceland, we built twenty tiles from Sculpture System 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

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

• Getting excited and making stuff.
• Get people doing mathematics, and thinking mathematically without fear.
• Showing the power of Fab Labs and open access CAM to make interesting things.

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 build 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 5

Sculpture System 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.

Gallery

Designing the deltahedra

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CNC milling the tiles

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Painting

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Assembly

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Final result

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Credits

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

Links

• Edmund's blog post
• Sebastian's blog post
• Deltahedra on Wikipedia