Chapter 5: Decoding Classic Diagrams — The Symmetry Assistant

Open any classic gem-cutting book, guild newsletter, or magazine diagram and you will see cutting tables where each tier lists a long string of ascending index numbers:

• 96-12-24-36-48-60-72-84
• 02-10-14-22-26-34-38-46-50-58-62-70-74-82-86-94
• 04-08-16-20-28-32-40-44-52-56-64-68-76-80-88-92

When you are transcribing that printed sheet into ProFacet’s Interactive Slicer (or writing an FSL script), how do you convert 04-08-16-20... into the three drum dials (IDX, SYM, and MIR) without pausing to do mental math?

ProFacet’s Symmetry Assistant solves this for you instantaneously.

1. Using the Symmetry Assistant (? Button)

1. In the top-left corner of the Slicer's Precision Dial Deck, click the ? button directly beneath Dial.
2. The Symmetry Assistant (ADVANCED TOOLS · REVERSE SOLVER) dialog opens for your active gear:

3. Type just the first 2 or 3 ascending tooth numbers from your printed diagram into the Indices prefix input (for example, 4, 8, 16 or 02-10-14-22), or click one of the Quick Examples pills.
4. As you type, the Symmetry Assistant:
   • Completes the entire 360° tooth loop in ghost text and individual tooth chips (4, 8, 16, 20, 28, 32, 40, 44, 52, 56, 64, 68, 76, 80, 88, 92) so you can verify that it matches your printed diagram.
   • Displays the exact FSL rule (FSL 6 @ ... x 8 m 2) and dial settings (IDX (Middle) 6, SYM ×8, MIR ±2, Step 12).
   • Offers Next Tooth Candidates if only 1 or 2 teeth have been entered.
5. Click Send to slicer—ProFacet sets your IDX, SYM, and MIR drums to that exact symmetry rule immediately!

2. The Simple Logic Behind IDX, SYM, and MIR

Why did 4, 8, 16, 20, 28, 32... translate to IDX = 6, SYM = ×8, MIR = ±2?

1. Look at the first pair of teeth (4 and 8):
   • The symmetry axis sits right in the middle of the pair: IDX = (4 + 8) / 2 = 6.
   • The distance from the middle (6) out to 4 and 8 is MIR = ±2 (6 - 2 = 4 and 6 + 2 = 8).
2. Look at the next pair (16 and 20):
   • Its middle is (16 + 20) / 2 = 18.
   • The step from the first pair's middle (6) to the second pair's middle (18) is 18 - 6 = 12 teeth.
   • On a 96 gear, stepping by 12 teeth repeats 96 / 12 = 8 times around the circle: SYM = ×8.

[!TIP] Mirror Delta (xN m M) vs. Zero-Axis Mirror Shorthand (xxN) in FSL In IDX @ angle : ... xN m M, IDX is the mirror axis (center) and the number M after m is the ± delta index (IDX - M and IDX + M). By contrast, in the classic shorthand M @ angle : ... xxN, M is the actual cut tooth, mirrored across index 0 (0 ± M).

• That means 0 @ 43.0 : gp() x8 m 3 (mirror axis 0 with ±3 delta, cutting 03-09-15-21...) is 100% equivalent to 3 @ 43.0 : gp() xx8!
• Be careful: 3 @ 43.0 : gp() x8 m 3 places the mirror axis at 3 with a ±3 delta (3 - 3 = 0 and 3 + 3 = 6), which cuts 00-06-12-18... instead!

3. Quick Lookup Table: Common 96-Gear Printed Sequences

Next, let’s learn how to inspect your stone’s optical performance in real time using Chapter 6: Seeing Light — The 8 Viewport Shading Modes & Overlays.