A faceting diagram — also called a cut diagram — is a technical drawing that specifies, for every facet in a given gemstone design, the precise cutting angle (measured from the horizontal plane of the lap) and the index position (the rotational setting of the stone about its vertical axis). Together, these two parameters uniquely locate each facet on the stone's surface. By following a published diagram, a skilled lapidary can reproduce a designer's cut with sufficient fidelity that the finished gem will exhibit the same optical behaviour — light return, scintillation pattern, and windowing characteristics — as the original prototype.

Anatomy of a Diagram

A standard faceting diagram presents information in two complementary forms: a plan-view outline of the finished stone (typically showing the table-up silhouette and, separately, the pavilion outline) with each facet numbered, and an accompanying data table. The table lists, row by row:

• Facet number — a sequential identifier keyed to the outline drawing.
• Mast angle — the angle in degrees between the facet plane and the horizontal lap surface, set on the faceting machine's protractor or digital angle readout.
• Index positions — the gear-tooth or degree settings on the index wheel at which the handpiece is locked for each cut in that row. Multiple index positions sharing the same angle are typically grouped as a single step.
• Facet name or tier designation — e.g., main pavilion, break facet, girdle, star, table.

Many diagrams also include the recommended index-wheel size (commonly 96-tooth, though 64-, 80-, and 120-tooth wheels exist), the intended length-to-width ratio, and suggested critical-angle considerations for the target gem material.

Index Wheels and Angular Notation

The index wheel is the circular gear mounted on the faceting machine's handpiece spindle; its teeth or degree markings determine the rotational position of the stone for each cut. The 96-tooth wheel has become the de facto standard in most English-language diagram publishing, because 96 divides evenly into many symmetrical arrangements (2-, 3-, 4-, 6-, 8-, 12-, and 16-fold symmetry). Diagrams written for a 96-tooth wheel express index positions as integers from 1 to 96. Some European and older American diagrams use degree notation (0°–360°), which is wheel-independent and must be converted when a specific wheel is fitted.

Publication and Sources

Faceting diagrams are published through several channels. The United States Faceters Guild (USFG) maintains an extensive library of original designs contributed by its members, freely available to the cutting community. Individual designers — notably Lon Ramsey, Jeff Graham, and Glenn Klein, among many others — have self-published large catalogues, some in print and some as downloadable files. Specialist periodicals such as Facets (the USFG journal) and the now-archived Lapidary Journal published diagrams as regular features. Digital repositories and faceting-software packages (such as GemCad, the most widely used design application) allow diagrams to be stored in a standardised file format, rendered in three dimensions, and ray-traced to predict optical performance before a single facet is cut.

Reading and Executing a Diagram

The lapidary works through a diagram sequentially, completing all facets at a given angle-and-index combination before advancing to the next row. Meets — the precise junctions where adjacent facets intersect — are verified visually under magnification and by touch before the stone is advanced. A correctly executed diagram produces meets that are sharp, point-to-point, with no residual flat between them. Deviation from the specified angles, even by a degree or two, can shift meets, alter the girdle outline, or degrade light return, particularly in designs with tight optical tolerances such as Portuguese cuts or barion variants.

Relevance to Optical Performance

Because the critical angle varies with refractive index, a diagram optimised for quartz (RI approximately 1.54–1.55) will not perform identically when cut in corundum (RI approximately 1.76–1.77) or zircon (RI approximately 1.92–1.98). Responsible diagram publishers specify the intended material or refractive-index range, and note whether pavilion angles should be adjusted for higher- or lower-RI stones. Ray-tracing software has made it practical to model these differences before committing to a preform, a significant advance over the empirical trial-and-error of earlier decades.