This article originally appeared in “Stonechat,” the journal of the UK Facet Cutter’s Guild, in December 1999. We’ve reproduced it here with the permission of the Guild. Although computers and faceting apps have changed tremendously since then, Dr. Washington’s nomogram has more than historical interest. This method for transposing faceting angles from published designs uses no computers (or calculations) at all.

Conversion Methods and Their Shortcomings

One of the first problems beginning faceters encounter is converting published faceting designs to forms suitable for materials besides quartz. Virtually all published designs use angles optimized for quartz. Since other materials have different refractive indices and critical angles, they require cutting their facets at different angles. These must differ from the original design in order to optimize optical performance or avoid a “fish eye” stone.

One of the simplest conversion methods requires adding or subtracting a fixed number of degrees from the design angles. You can follow published tables of recommended angles for crown and pavilion mains for different materials.

For example, to convert a design from quartz angles to topaz, check such a table. You find that quartz pavilion mains are cut at 43° and topaz at 39°