I searched a few days ago for ABCarter's gem cutting tutorial which used to be hosted here at Renderosity as:

http://market.renderosity.com/~rhino/abcarter/gemtut/facettutorial.htm

It looks like it is no longer around.  However, I was able to see a Google cached version in a text only version.  That was enough to get me going. I thought I would attempt to recreate it here.

The "Brilliant Cut" is what we will try to achieve.  Other cuts use different angles and facet counts.   The whole process is quite easy. 

Everything is done with Boolean operations between primitives.  Only two shapes are used; a cylinder which will be "cut" into a diamond, and a cube as the cutting tool.