Platonic solids

The stuffed tori are kind of winding down now, so I'm on the look out for new mathsy projects.
Next up will be this one - to crochet all the Platonic solids.

The Platonic solids(or regular polyhedra) are the analogue of regular polygons in three dimensions. They're as symmetric is it's possible to be(well... with discrete symmetries, at least- spheres and things do better. And tori. But that's another story)- every face, edge and vertex can be mapped to any other face, edge or vertex by a rotation.
The neat thing is, unlike regular polygons, for which you can make one with any number of sides, there are only a finite number of Platonic solids. Five, in fact. The reason for this is a little obscure - it all comes from the Euler formula V-E+F=2, and then a certain amount of fiddling with combinatorics to see what choices that leaves.

I'm hoping crochet will be good for this, I understand there's something you can do to make crocheted objects rigid(something to do with sugar solution?). I'm also hoping that this'll make for nicer edges, since I think this would be a bit of an issue if you were to knit something with so many pieces. I'm *also* hoping that I still remember how to crochet, I haven't tried it for quite a while...

Hugh :o).