I've been fascinated by the structure of Bathsheba Grossman's Quin Pendant Lamp since I first saw it. There are many tutorials around the web for making a similar structure in different 3D software packages. The method they all use seems to be based on a TopMod tutorial. TopMod (last updated about 2008?) works very differently from most other 3D modelling software with tools for making handles and bridges between polygons. Blender now has some similar tools for example Bridge Edge Loops Tools.
My method is different and works with the surface of a regular solid. The bridges between triangles and penatagons are created as a single layer. After these bridges are twisted up into the correct structure a Solidify modifier is used to make everything 3D.
Here is a screencast of the process.