The 80 index — also referred to as the 80-tooth index or 80-tooth index gear — is a circular indexing wheel fitted to a faceting machine's quill assembly, providing exactly 80 equally spaced detent positions around its circumference. Each position represents 4.5 degrees of rotation (360° ÷ 80), giving the facetor fine angular control over the placement of each facet relative to the stone's central axis. Among the several standard index gears available to the gem cutter, the 80 index occupies a particularly useful niche for designs that demand divisions by 4, 5, 8, 10, 16, 20, or 40 — symmetry families that arise frequently in classical and high-facet-count cutting styles.

Function within the faceting machine

A faceting machine orients a rough gemstone on a rotating spindle (the quill or dop spindle) and presents each facet in turn to a flat, rotating lap charged with abrasive. The index gear, mounted concentrically with the spindle, is engaged by a spring-loaded pin that drops into each tooth notch, locking the stone at a precise rotational angle while the facetor grinds or polishes that facet. Releasing the pin and advancing to the next position rotates the stone by exactly one index increment — in the case of the 80 index, 4.5°. The facetor reads cutting diagrams (called cutting sequences or faceting diagrams) that specify which index numbers to use for each tier of facets, ensuring that the finished stone's facets meet cleanly at their junctions and produce the intended optical pattern.

Symmetry divisions supported

The practical value of any index gear lies in which whole-number symmetries it can produce cleanly — that is, which divisors of its tooth count yield an integer number of positions. The 80-tooth gear supports the following principal symmetries:

• 4-fold symmetry (square, cushion, and princess-style outlines) — 20 positions apart
• 5-fold symmetry (pentagonal outlines) — 16 positions apart
• 8-fold symmetry (standard round brilliant and octagonal cuts) — 10 positions apart
• 10-fold symmetry — 8 positions apart
• 16-fold symmetry (high-facet-count rounds) — 5 positions apart
• 20-fold symmetry — 4 positions apart
• 40-fold symmetry — 2 positions apart

This breadth of compatible symmetries makes the 80 index one of the more versatile gears in a facetor's collection, second in popularity among advanced cutters only to the 96-tooth gear, which better serves 6-fold and 12-fold symmetries but cannot produce clean 5-fold or 10-fold divisions.

Application to the Portuguese cut and related designs

The Portuguese cut — a high-facet-count round brilliant variant characterised by multiple additional rows of rhomboid and triangular facets on both crown and pavilion — is among the designs most closely associated with the 80 index. Its standard layout typically employs 8-fold symmetry with a large total facet count, and the 80-tooth gear provides the intermediate index positions needed to place the extra facet rows accurately. Other designs commonly diagrammed for the 80 index include various barion variations with 8-fold symmetry, certain fantasy cuts requiring 10-fold or 20-fold layouts, and a number of original designs published in the faceting literature that exploit the gear's 5-fold capability to produce pentagonal or star-shaped stones.

Comparison with other common index gears

Faceting machines are typically supplied with one or two index gears as standard equipment; additional gears are purchased separately. The most widely encountered sizes are 32, 64, 72, 80, and 96 teeth. The 64-tooth gear is well suited to 4-fold and 8-fold work at coarser angular increments (5.625° per step), while the 96-tooth gear — with 3.75° per step — excels at 6-fold, 8-fold, 12-fold, and 24-fold symmetries and is the standard choice for the classic round brilliant. The 72-tooth gear serves 6-fold and 9-fold designs. The 80-tooth gear's unique contribution is its clean 5-fold and 10-fold capability, which no other commonly stocked gear provides.

In the trade and among amateur facetors

Index gears are manufactured to close tolerances in aluminium or steel and must be matched to the specific faceting machine model, as spindle diameters and detent-pin geometry vary between manufacturers. Suppliers of faceting equipment — including Graves, Facetron, and Ultratec, among others — offer the 80-tooth gear as an optional accessory for their respective machines. Cutting diagrams specifying the 80 index are published in the Faceter's Gem Designs series, in the journal of the American Federation of Mineralogical Societies, and across numerous online facetor communities, making the gear accessible to both advanced hobbyists and professional cutters who wish to expand their repertoire beyond standard round-brilliant work.