Virtual facet patterns and diamond design

Diamonds used in jewellery represent the quintessential fusion of aesthetic appeal and technical expertise. Not only does it require extreme skill to cut a diamond, analyzing and predicting a diamond's Visual PerformanceTM is essentially a technical mathematical problem. In particular, diamonds and other faceted gems have the property that they fragment the visual field into a set of polygons called virtual facets, which represent equivalence classes of light paths according to their facet interactions with the gem polyhedron. In this paper we explain how this mathematically elegant conception forms a framework from which to analyze a diamond's appearance and beauty. We intend this framework to form the foundation for a fancy-shaped diamond cut grading system. Although virtual facet patterning has been studied before, mostly in the context of round brilliant diamonds, a significant new feature of our approach is to take into account the effect varying visual depths of virtual facets has on visual perception. We also showcase some novel designs created by our team at GIA using a mathematical enumeration algorithm for symmetric diamond-like polyhedra.