I put together this short tutorial, to explain the technique i used to model these diamonds.
The diamonds have the correct amount of sides, and shapes to provide good caustics and refractions/reflections.
Cylinder that we start with has 16 sides. I will add a link to the high res version of the movie when it's hosted. You can see the numbers then.
Dailymotion - streaming Link (http://www.dailymotion.com/video/x1it4n_diamond-tutorial)
hope you learn something