This project is a little late in the blogging but here it is:
Face folding is an idea that I came up with for Erik Demaine‘s folding class. Basically you start with a polyhedron and deform each face in plane while keeping the edge lengths fixed. Not too much is known about these mathematical objects but my concern was to build them:

Above is a dodecahedron. The next few are the slightly easier to see cube.

Everything is made of 1/16″ water-jet aluminum cut into a lot of very simple pieces.

Pieces are assembled into flat polygons.

Which are in turn assembled into polyhedra.