The 120 index — also referred to as the 120-tooth index — is a circular index gear used on faceting machines to position a gemstone at precise, repeatable angles during the cutting and polishing of facets. The gear provides 120 evenly spaced detent positions around its circumference, each separated by exactly 3° (360° ÷ 120). It is one of the standard index gears supplied with or available for most modern faceting machines, alongside the 64- and 96-tooth gears.

Function and Principle

An index gear works in conjunction with a faceting machine's quill and index lever (or index pin): the lever engages a notch in the gear, locking the stone's rotational position before the lap descends. The faceter selects a sequence of index numbers from a cutting diagram — known as a faceting design or cutting diagram — and moves the gear to each specified position in turn to grind or polish the corresponding facet. The precision of the gear determines how accurately the facet placement can be reproduced, and a 120-tooth gear, with its 3° increment, offers finer angular resolution than the 96-tooth (3.75° increment) or 64-tooth (5.625° increment) alternatives.

Divisibility and Symmetry

The practical value of the 120 index lies largely in its arithmetic. Because 120 is divisible by a wide range of integers, it accommodates many symmetry classes encountered in faceted gem design:

• 2-fold symmetry — 60 positions apart
• 3-fold symmetry — 40 positions apart
• 4-fold symmetry — 30 positions apart
• 5-fold symmetry — 24 positions apart (72° divisions)
• 6-fold symmetry — 20 positions apart
• 8-fold symmetry — 15 positions apart (45° divisions)
• 10-fold symmetry — 12 positions apart
• 12-fold symmetry — 10 positions apart

This breadth makes the 120 index particularly attractive for cutting pentagons and five-pointed star designs (which require exact 72° divisions) and for octagonal cuts (45° divisions) — symmetries that neither the 64- nor the 96-tooth gear can satisfy cleanly. The 96-tooth gear, by contrast, excels at 4-, 6-, 8-, and 12-fold symmetry but cannot produce true 5-fold divisions. The 64-tooth gear is well suited to 4- and 8-fold designs but similarly cannot accommodate 5-fold or 3-fold work without compromise.

Selection in Practice

Faceters choose their index gear before beginning a cutting sequence, guided by the symmetry class specified in the design diagram. Published faceting designs — whether from sources such as the American Gem Society's faceting programmes, Faceter's Digest, or the extensive libraries maintained by organisations such as the United States Faceters Guild — specify which index gear is required. A design calling for a five-sided Portuguese-style cut or a pentagonal brilliant, for example, will specify the 120 index as the appropriate gear. Attempting to approximate such a design on a 96-tooth gear introduces angular errors that accumulate across the stone, resulting in misaligned meets and an asymmetric finished gem.

Many contemporary faceting machines — including those from Graves, Ultra Tec, and Facetron — accept interchangeable index gears, allowing the faceter to swap between 64, 96, and 120 configurations as the design demands. Some machines offer additional gears (such as 32, 48, or 144 teeth) for specialised work, but the 64/96/120 combination covers the vast majority of published designs.

Further Reading

• GIA Gems & Gemology — faceting reference material