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.
Great video Dan, I thought I would post some links which you may already be aware of.
UPenn GRASP lab of robotics, quadrotors (helicopters) lifting parts into position. The idea at full scale would be helicopters replacing cranes lining up I-beams using the magnetic connections, then fixing via traditional connections. It’s great to see multiple quadrotors working together.
Advancing quadrotors tech.
Saul Griffith Phd at MIT 2004, Self Replicating Machines.
Voronoi stuff is maybe less relevant but uses a similar technique of an removing an offset on each surface of a set volume.
Andrew Kudless C. Wall
http://matsysdesign.com/2009/06/19/c_wall/
http://matsysdesign.com/category/projects/voronoi-morphologies/
Tom Tong AADip16_2007
http://voronoitom.blogspot.com/