GemDiagram Docs

The Index Wheel

Every GemDiagram design sits on a wheel of equally spaced positions running around the stone. Each tier picks which of these positions its facets occupy.

Why are 96-index wheel designs most common?

96 is a highly composite number — divisible by 2, 3, 4, 6, 8, 12, 16, 24, 32, and 48. This means you can represent virtually any symmetry pattern (4-fold, 8-fold, mirrored, radial, stepped) as a clean list of indices without gaps or overlaps.

How tiers use the wheel

A tier specifies a list of index positions. Those positions repeat at whatever spacing produces the stone's symmetry. For example:

  • 8 positions: 0, 12, 24, 36, 48, 60, 72, 84 = one facet every 12 teeth (8-fold symmetry).
  • 16 positions: 3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 93 = one facet every 6 teeth, offset by 3 (16-fold, filling the gaps).
  • 4 positions: 0, 24, 48, 72 = one facet every 24 teeth (4-fold symmetry).

The Round Brilliant's pavilion mains use 8 positions (8 facets). Its pavilion breaks use 16 positions (16 facets), interleaved between the mains. The crown mains mirror the pavilion mains (8 positions each), but the star facets use only 8 positions at a different spacing.

Manually entering indices

You can type indices directly into a tier's index field. Separate them with commas: 0,12,24,36,48,60,72,84. GemDiagram validates them:

  • All indices must be in range [0, 95].
  • Duplicates are OK (ignored).
  • Order doesn't matter (GemDiagram sorts internally).

A tier with indices [0, 12, 24] has 3 facets, evenly spaced around the stone. A tier with [6, 18, 30, 42, 54, 66, 78, 90] has 8 facets, shifted 6 positions.

The Symmetry panel

Rather than typing index lists by hand, you can use the Symmetry controls in the Build panel: set a fold count (4, 8, 16, etc.) and optionally a mirror axis. GemDiagram auto-generates the indices for you. See Symmetry.

A gotcha: axis-locked positions

Under 4-fold symmetry with mirror, positions 0 and 48 sit exactly on the mirror axes — adding a facet at position 0 alone produces only 4 copies (the mirror lands back on a point already in the set), not 8. To get the full 8-facet star, you need both 0 and 48, or offset to a position off the axis. This is why the Guided wizard's second-step prompt asks you to click two gear positions for some tiers. See Symmetry for a deeper explanation.

Visualizing the wheel

In Guided Mode, the index gear (a circular SVG dial in the Design step) shows all 96 positions around the stone. Click a position to toggle whether that tier's facets occupy it. The number of facets updates as you click.

In Manual Mode, there's no visual gear — you type indices directly. The Diagrams (in the Inspect panel) show the final result of all tiers combined as a top-down view.

Beyond the wheel

While 96 is the standard, some cuts use non-96-based wheels (128, 144, custom). GemDiagram standardizes on 96 for simplicity — it's enough for virtually any real cutting pattern, and it makes the math cleaner.