Brilliant (diamond cut)

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 results 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.
Facet proportions and names.
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. Some gem cutters refer to an American brilliant cut or a Scandinavian brilliant cut. Quoting Green et al. 2001:
Figures 1 and 2 show the facets of a round brilliant diamond.
Figure 1 assumes that the "thick part of the girdle" is the same thickness at all 16 "thick parts". It does not consider the effects of indexed upper girdle facets.
Figure 2 is adapted from Figure 37 of Marcel Tolkowsky's Diamond Design, which was originally published in 1919. Since 1919, the lower girdle facets have become longer. As a result, the pavilion main facets have become narrower.
Cut grading.
The relationship between the crown angle and the pavilion angle has the greatest effect on the look of the diamond. A slightly steep pavilion angle can sometimes be complemented by a shallower crown angle, and "vice versa".
Other proportions also affect the look of the diamond: 
Several groups have developed diamond cut grading standards. They all disagree somewhat on which proportions make the best cut. There are certain proportions that are considered best by two or more groups however.
The distance from the viewer's eye to the diamond is important.
The 2005 AGS cut standards are based on a distance of 25 centimeters (about 10 inches).
The 2004 HCA cut standards are based on a distance of 40 centimeters (about 16 inches).
Polish and symmetry are two important aspects of the cut. The polish grade describes the smoothness of the diamond's facets, and the symmetry grade refers to alignment of the facets. With poor polish, the surface of a facet can be dulled, and may create blurred or dulled sparkle. It may constantly look like it needs to be cleaned. With poor symmetry, light can be misdirected as it enters and exits the diamond.
Hearts and arrows phenomenon.
A diamond that has the top facet or "table facet" exactly perpendicular to the bottom of the diamond or "pavilion" and has its other facets precisely aligned with excellent symmetry, may show patterns that look like arrows from the top and hearts from the bottom. Generally it will need to be viewed loose under a gemscope to see the pattern very well. Although the hearts and arrows property is indicative of a top-tier cut, it does not always mean the diamond will be the most brilliant. Optimal facet placement is the key to brilliance and more important than facet patterning. Not all ideal round cuts will have the hearts and arrows effect either.