Above: A Grasshopper definition generating an entire building from Chris Ingram. This is for a growing TechHub around the Sillicon Roundabout.
Above: Floating Earth Island for the Twa tribe in Zambia by Kayleigh Dickson. The physical model is made from a steel mesh, a layer of waterproof cement and an earth and straw compound. PLants have started growing on the entire structure now.
TETRA is an installation that exploits the potential of mass participation to create a form that emerges from the interactions of hundreds of people with the construction system over a number of days.
Inspired by the work of R. Buckminster Fuller into space-packing polyhedra, it explores the unique three dimensional geometrical properties of the regular tetrahedron and related ‘tetrahelices’ [also known Boerdijk–Coxeter Helices]. Their geometries provide an invisible framework for the participants to work within. The modular tetrahedral construction system will be used by the participants to create forms that automatically diverge from one another.
These in turn provide spaces separated from other participants for individuals to pause and reflect on the location and nature of their surroundings. TETRA’s position out on the edge of Black Rock City means that once the structure starts to take shape, participants will be able to climb to positions that afford views across the city. Just as Burning Man asks participants to take a step back from the consumer capitalism, so TETRA allows participants to step back and view Black Rock City as a whole
TETRA is a modular kit of parts that are assembled by participants into a structure that changes form over the course of the festival. There are 160 modules, each one a tetrahedron made from four equilateral triangle shaped pieces of CNC cut exterior plywood. Each triangular face has a hole cut from its centre which, as well as decreasing the overall weight of the module, allows the modules to become rungs in a structure that can be climbed up, on, in and through.
The ply edges of the four plywood triangles are bound together with rope to ensure a joint that can transmit loads in tension from one sheet of ply to the adjacent two. There are pre-drilled re-enforced holes near each vertex to allow for adjacent modules to be bolted together with bolts and wing-nuts by participants.
Each module is designed for one person to carry while climbing sections of the structure already built. The participants are able to climb any of the structure that is already built, and bolt their new module onto the existing structure. Once built, participants are able to climb up, select a module to remove and move to another place. This means that the overall form is not set by the designer, but emerges from the collective desires of a large group of participants.
Because of the intrinsic geometry of tetrahedra and tetrahelices, the form will always contain diverging branches with inhabitable spaces within them.
This animation shows a model made from modular magnetic tetrahedra. Each tetrahedron has a side length of 50mm, and contains four spherical neodymium magnets.
The tetrahedra build up according to rules that stem from their dihedral angle [angle between two faces]. The dihedral angle of a tetrahedron given by θ=arccos(1/3) [approx 70.5288°]. This means that five tetrahedra placed face to face around a single axis fall approximately 7.2° short of a full 360°. Because of this, the tetrahedra do not fill space, and instead form sections of helical structures called Boerdijk–Coxeter Helices [Named ‘Tetrahelices’ by Buckminster Fuller].
The magnets in the tetrahedra ensure that when placed by hand, they lock together face to face to form structures that completely follow these rules. When pushed just within range of the magnets of other tetrahedra, they exhibit self organising properties, but due to the power of the magnets, occasionally stick edge to edge or vertex to vertex instead of face to face.