Three Dimensional Brillouin Zones

While the construction of Brillouin zones is simple, the results are not.

Constructing Brillouin zones is a good example for the evolution of complex systems from the repeated application of simple rules to simple starting conditions - any 12-year old can do it in two dimensions.

Below the results for the first, second and third Brillouin zone (taken from the "Ashcroft/Mermin" and originating from the 1965 thesis of R. Lück (no computer graphics then!))

These pictures can be found in many text books, which shows that (in physics) you need not improve upon a good thing.

With frame

2.1.2 Diffraction of Electron Waves