Facets and Tiers

Facet commands translate the numbers you type into actual cuts. When you enter a line such as P1 0 @ 41.8 : 0.18 x8, you first describe one reference facet (P1 0 @ 41.8 : 0.18, with the legacy < token still accepted) and then immediately tell the studio to rotate it eight times (x8). Together, that single line defines the whole tier. This chapter spells out how the reference facet is evaluated and how symmetry turns it into a complete ring of facets.

Describe the reference facet

Every facet statement starts by naming the tier (P1, PF2, Break), optionally choosing a side (up for crown, down for pavilion), and giving an index. The index is the gear tooth where the reference facet begins, so it must be a whole number. If you omit up/down, the studio keeps the previous choice; crown tiers default to up, everything else keeps whatever you last typed.

Cut tiers before you reference them. Point helpers and edge lookups only work after the relevant facets exist, so keep the cut order and the reference order aligned.

Aim the reference facet

Once the tier, side, and base index are set, you provide one of three specifiers:

1. Angle + depth – supply both values and the studio cuts to that exact combination. Use the size keyword for 90° cuts (girdle and table facets) when you want the depth handled automatically.
2. Angle + point – pick an angle and let a point helper decide the depth. Add + girdle or - girdle to nudge toward or away from the girdle by the percentage you set earlier.
3. Point pair – specify two points and the studio slices a plane that touches both, which is ideal for matching opposing facets.

The key idea: the tier/side/index plus specifier only define a single, precise facet at the stated index. The tier becomes complete the moment you append symmetry (x8, xx6, etc.), because those modifiers rotate or mirror that one facet without re-aiming it.

Symmetry builds the tier

After the specifier, symmetry modifiers (xN, xxN) tell the studio how to copy the reference facet around the stone:

• xN rotates the reference facet every 360 / N degrees. The first rotation uses the index you typed; subsequent facets are pure rotations of that plane.
• xxN mirrors each rotated facet, creating alternating clockwise/counter-clockwise mates for designs that need paired faces.

Important: The studio never “hunts” for meet points when it replicates a tier. It evaluates the reference facet once—using your tier, side, index, and aiming instructions—and then performs exact rotations (and optional mirrors) to fill out the tier. No meetpoints are searched; the reference facet is simply rotated from the base index you specified. No extra math, no iterative refinement, no automatic adjustments.

The result is a full facet tier: the first facet establishes the geometry, symmetry copies it, and modifiers (below) tweak presentation.

Modifiers that follow the specifier

Modifiers can appear in any order after the main specifier.