The 64 index — also referred to as the 64-tooth index or 64-division index gear — is one of the most widely used index gears in amateur and professional gem faceting. Mounted on the spindle of a faceting machine, it divides a full rotation of the gemstone into 64 equally spaced positions, each representing 5.625 degrees of arc (360° ÷ 64). This fine angular resolution makes the 64 index particularly well suited to cuts with high facet counts, including standard round brilliants, ovals, and many designer variations that demand precise, repeatable placement of facets around the girdle plane.

Function and Mechanics

An index gear — sometimes called a dividing head — is a toothed wheel that locks the gemstone's rotational position at defined intervals during cutting. The facetor engages a spring-loaded pawl or detent pin into successive teeth of the gear, advancing the stone by one index position at a time. Because the 64 index produces 64 discrete stops, each stop corresponds to a reproducible angular position; the facetor records these positions as part of a cutting diagram, allowing a facet sequence to be executed systematically and symmetrically.

The arithmetic of the 64 index is straightforward: 64 is a power of two (2⁶), meaning it divides evenly by 2, 4, 8, 16, and 32. This binary divisibility makes it compatible with any cut whose symmetry is based on those factors — four-fold symmetry (squares, cushions), eight-fold symmetry (standard rounds), sixteen-fold arrangements, and so on. A standard 57-facet round brilliant, for example, is typically executed on a 64-index gear, with main pavilion facets placed at positions 4, 12, 20, 28, 36, 44, 52, and 60 — eight equally spaced positions separated by eight index steps each.

Compatibility with Cutting Designs

Faceting diagrams published in books and databases always specify which index gear a design requires. The 64 index is among the most commonly specified, alongside the 96 index (which adds compatibility with three-fold and six-fold symmetry). Designs that require divisions by 3, 6, or 12 — such as triangular or hexagonal cuts — cannot be executed cleanly on a 64-tooth gear and instead call for a 96-tooth or other gear. Conversely, many classic American-style round brilliant diagrams were developed specifically around 64-index geometry, and the gear remains a standard inclusion in most entry-level and professional faceting machine kits.

Practical Considerations

Index gears are typically manufactured from aluminium alloy or engineering plastics and must be machined to close tolerances; any irregularity in tooth spacing introduces cumulative angular error that becomes visible as asymmetry in the finished stone. Quality gears are tested for concentricity and tooth-pitch accuracy before use. Most faceting machines accept interchangeable index gears on a common arbour, allowing the facetor to swap between a 64-tooth and a 96-tooth gear depending on the design being cut. Some machines are supplied with a single gear — often the 64 — while others include a set.

When reading a faceting diagram, index positions on a 64-gear are conventionally numbered 1 through 64, with position 1 (or 0 on some systems) serving as the reference point aligned to the transfer block or dop. The facetor works through the sequence of positions listed in the diagram for each tier of facets, maintaining a consistent cutting angle on the protractor head while rotating through the specified index stops.

In the Trade and Literature

The 64 index is referenced throughout the standard faceting literature, including diagrams published by the American Federation of Mineralogical Societies (AFMS) and resources such as the Faceter's Companion series. It is the default gear assumed in many introductory faceting courses and is the basis for the majority of round and oval designs taught to beginning facetors. Its prevalence means that a facetor equipped with only a 64-index gear can execute a broad and practical range of cuts, making it the logical starting point before expanding to additional gear sizes.