Here's a fun tutorial I ran across, which shows you how to create a buckyball out of folded paper.
In essence, you download the buckyball model from the Google 3D Warehouse, and use a SketchUp plug-in to "unfold" it. Then you print, cut, fold, and tape.
I have a similar exercise in my Free Teacher Guide, which doesn't require you to download any models or use any plugins. You can start with any 3D shape you want, and take advantage of groups for doing the unfolding. (The exercise is in the Math category, Grades 6 - 9.)
For a printable version of my exercise from the Teacher Guide, click here.