INSTRUCTION:Typically, new members are mentored by experienced members. Basic gemstone cutting does not require math skills. It does require following a cutting pattern, providing all necessary information to cut a brilliant gemstone. Most faceting machines operate in a similar manner.
The raw stone, or "rough" is affixed to a short rod called a dop or dop stick. Inserted into the faceting machine, the rough is cut by grinding it against a spinning disc called a lap.
Cutting laps are usually coated with diamond in various levels of coarseness, similar to sandpaper. Higher the number, the finer the diamond. An extremely coarse lap is in the 80 - 100 rating and will quickly grind the rough. A 260 is coarse, a 600 is medium and a 1200 is fine, and a 3000 is extremely fine. 1200 through 3000 are considered "pre-polish"
Polishing the stone can be done in a variety of ways. Laps are constructed of various metals or other material such as ceramic. A very common approach is to spraying a mist of diamond onto the lap. "Spray Diamond" is extremely fine and is rated by its coarseness or mesh.
Typical mesh values are 14,000, 50,000, 100,000 and 200,000. Polishing is also grinding the rough, but at extremely small amounts, resulting in a beautiful shine. Diamond is also found in paste form and other polishing methods are readily available....usually the cutter's own preference.
Faceting machines have index gears dividing a revolution into equal amounts. If a 96 gear is required, and the stone is 8 sided, the pattern might call for cuts at settings of 96(same as 0), 12, 24, 36, 48, 64, 72, 84. 96/8 is 12, the number of marks between cuts. However, the pattern may start at any index value, such as 3. Next rotation would be to (3+12) 15 (+12) 27, etc. No math is required as it's all on the pattern. Conceiveably, a stone could be cut on each of the 96 marks, giving you with a 96 sided stone!
Index gears can be found as 64, 80, 96 and 120. Other may exist, but would be quite rare. Most common is the 96 followed by the 64. The other requirement is the angle at which the stone is cut. Patterns usually state the angle out to two decimal places, such as 43.60 degrees.
Here is typical pattern data for a 96 index and two different angles.
44.00 3-15-27-39-51-63-75-87
41.50 96-12-24-36-48-60-72-84 (Note: 96 is the same as zero)
The material is rough cut, progressing to finer laps. Yes, you do end up working on the same spot a number of times...rough cut, medium, fine, pre-polish and final polish. Some cutters will even polish using different mesh, especially if for competition cutting.
Usually, the bottom (Pavillion) is cut first. The stone is then transferred to a second dop to allow cutting the top (crown). The outer edge, the girdle, is usually done during the pavillion cut.