Symmetry

Symmetry controls how many times your design repeats around the stone and whether it's mirrored. Every tier's index list is generated from a global symmetry setting, so changing symmetry updates all tiers at once.

Fold count

Fold count is how many times the design repeats going around the stone:

• 4-fold: The design repeats 4 times (90° apart). A facet at index 0 appears again at 24, 48, 72.
• 8-fold: The design repeats 8 times (45° apart). A facet at index 0 appears again at 12, 24, 36, 48, 60, 72, 84.
• 16-fold: The design repeats 16 times (22.5° apart). A facet at index 0 appears at 6, 12, 18, 24, …

You can set any divisor of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, or 96.

Mirror

Mirror means the design is symmetric across a plane:

• No mirror: Plain rotational symmetry — the design just repeats (4-fold, 8-fold, etc.).
• Mirror: The design repeats and flips across a plane passing through the stone. Most real cuts use mirror symmetry.

For example, 4-fold + mirror (the Round Brilliant's symmetry) means:

• The design repeats 4 times.
• Each repeat is mirrored.
• The result is 8-fold symmetry (4 repeats × 2 for mirror = 8 copy).

How the Symmetry panel works

In the Build panel, below the tier list, you'll see:

• Fold: A number (4, 8, 16, etc.).
• Mirror: A toggle (on/off).

When you change these, GemDiagram re-generates the index list for every tier. For example, if a tier is marked "Mains (8 positions)" and you switch from 8-fold to 4-fold, it updates to use 4 positions instead, evenly spaced.

The axis-locked gotcha

Under mirror symmetry, some positions sit exactly on the mirror plane — these are called axis-locked. For 4-fold + mirror symmetry, positions 0 and 48 are axis-locked.

If you click position 0 in the gear (or use the Symmetry panel to set "add position 0"), GemDiagram adds facets at indices [0, 24, 48, 72] — but position 0 mirrors to position 0 (it's on the axis), so the mirror doesn't add a new copy. Same with position 48. You get 4 facets, not 8.

To get the full 8-facet star pattern, click both 0 and 48 — this gives you [0, 24, 48, 72] from position 0, plus nothing new from 48 (since 48 is also axis-locked), yielding exactly 8 unique facets around the stone.

Alternatively, pick an off-axis position like 6: [6, 30, 54, 78] (4 repeats) mirrors to [18, 42, 66, 90] (4 more), totaling 8.

Non-mirrored (radial) symmetry

If you turn off Mirror, a position generates only a rotational copy, not a mirrored one. So position 0 under 4-fold + no mirror yields [0, 24, 48, 72] (4 facets), not 8. This is useful for patterns that aren't symmetric across a plane (though rare in real cuts).

Changing symmetry mid-design

You can change fold or mirror at any time. All tiers re-compute their indices. This can break a design (some tiers might lose facets), so it's usually done at the start.