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.

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.

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. This was fairly easy, and using Polydron four candidate shapes were constructed and voted on.

The winner was a highly irregular design. It had the nice interesting and helpful feature of consisting of four regular tetrahedra plus a couple of stray pieces, which made construction very simple. The four tetrahedra were assembled separately (with one side left out) and then attached to each other to form the final piece, consisting of 20 tiles in total.

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.

Credits

 * Edmund Orme Harriss
 * Ásgeður Jóhannesdóttir
 * Valdimar Karl Sigurdsson
 * Smári McCarthy
 * Sebastian Sterlingweriff
 * Arnar Smári Gústafsson
 * Óskar Þór Jónasson
 * Þorgeir Elmar Ágústsson
 * Gísli Matthías Sigmarsson
 * Elvar Þór Eðvaldsson
 * Frosti Gíslason

Links

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