Tuesday, August 7, 2012

Brillouin Zones with origami

(Click for a bigger version.  Guitar pick included for scale.)

As I said I would, I created the second Brillouin Zone of the fcc structure using modular origami.  It's a shape that's related to some crystal structures we study in condensed matter physics, though truth be told it is not a very useful shape.  It's pretty though.

It took 96 squares of paper, and four different kinds of modules.  It holds together, but I wouldn't want to toss it around like some of the more stable shapes.

It turns out that designing your own modular origami is nontrivial.  I started out by making the shapes exactly as they were in my origami book, and then I started making small modifications.  But the first few things I tried (with simpler shapes) were not very successful.  It's difficult to make them sufficiently stable.

Among the things I tried was the second Brillouin Zone of the bcc structure.  I have a small one pictured below, but it doesn't count because I cheated.  It completely fell apart and I had to cover it in tape.  I could probably just create 48 triangle modules, but I'm trying to think of a more elegant way.