For the interested, I use a facetron faceting machine. Not as refined as an ultratech but I don't make money cutting stones (because I am a hoarder) so the fact that it's a few thousand less made a difference for me...
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How to read a diagram. (I included the one for the stone I posted)
There's 3 dimentions to a facet, the angle or elevation, the index it is cut on, and the meet point where it *meets* another facet which is how you determine your depth of cut.
So for example P1 is set at 43 degrees elevation, so you crank the mast elevation to 43 degrees.
Then there is a series of index numbers in this case its 04-12-20-28-36-44-52-60-68-76-84-92. On the mast is a index gear, with x-number of teeth each tooth being numbered. The diagram calls for a 96 index gear so you load that into the machine and you can now cut symmetry to any number that 96 is divisible to, in this case 24.
The height of the mast is what determines where your facets are going to meet, for P1 this is the culet of the stone so you just need to cut them to a point in the middle, hopefully grinding off any imperfections on the outside of the stone in the process. (I try to only buy rough that will cut to an IF (internally flawless) or better)