Round brilliant

A brilliant is a diamond or other gemstone cut in a particular form with numerous facets so as to have exceptional brilliance. The shape resembles that of a cone and provides maximized light return through the top of the diamond.

Even with modern techniques, the cutting and polishing of a diamond crystal always result in a dramatic loss of weight; rarely is it less than 50%. The round brilliant cut is preferred when the crystal is an octahedron, as often two stones may be cut from one such crystal. Oddly shaped crystals such as macles are more likely to be cut in a fancy cut—that is, a cut other than the round brilliant—which the particular crystal shape lends itself to.

The original round brilliant-cut was developed by Marcel Tolkowsky in 1919. The modern round brilliant consists of 58 facets (or 57 if the culet is excluded), ordinarily today cut in two pyramids placed base to base: 33 on the crown (the top half above the middle or girdle of the stone), truncated comparatively near its base by the table, and 25 on the pavilion (the lower half below the girdle), which has only the apex cut off to form the culet, around which 8 extra facets are sometimes added. In recent decades, most girdles are faceted. Many girdles have 32, 64, 80, or 96 facets; these facets are not counted in the total. While the facet count is standard, the actual proportions (crown height and angle, pavilion depth, etc.) are not universally agreed upon. One may speak of the American cut or the Scandinavian standard (Scan. D.N.), to give but two examples.

Today, Tolkowsky's "ideal" model has been overused. The original model was a general guideline, as there were several aspects of diamond-cutting that were not explored or accounted for in that model.

Because every facet has the potential to change a light ray's plane of travel, every facet must be considered in any complete calculation of light paths. Just as a two-dimensional slice of a diamond provides incomplete information about the three-dimensional nature of light behavior inside a diamond, this two-dimensional slice also provides incomplete information about light behavior outside the diamond. A diamond's panorama is three-dimensional. Although diamonds are highly symmetrical, light can enter a diamond from many directions and many angles. This factor further highlights the need to reevaluate Tolkowsky's results, and to recalculate the effects of a diamond's proportions on its appearance aspects.

...
Wikipedia