The form of gemstone can be beautiful both in its natural state and as a cut-and-polished gem. As a general rule, only transparent gemstones are faceted, however some opaque substances such as hematite, are also faceted. The reason for faceting of gemstones is to allow light entering through the crown to internally reflect and travel around inside the gemstone, to pick up as much body color as the depth of stone will allow. In addition, rays of light entering and leaving the stone are broken into their component colors in the same way that sunlight passing through rain drops is broken in the colors of the rainbow. There are two main categories of faceted gemstones: round shapes and straight-sided shapes.
Faceted round cuts are divided in two categories: 1) Brilliant cut 2) Briolette cut
The brilliant cut has been developed as an ideal cut for mathematically calculated proportions. This cut maximizes a gemstone’s natural light dispersion, bending light rays toward the center of a stone and the reflecting them out again to produce fire and brilliance.
The briolette cut is actually a double rose cut with an elongated cone-shaped upper crown and rounded pavilion covered with triangular or rectangular facets.
Faceted square cuts are divided in three main categories: 1) step cut 2) cross cut 3) French cut
Step cut was originally developed for diamonds but as it does not produce the sparkle and life of brilliant cut it is just used for colored gemstones.
Cross cut and French cure are modifications of the step cut. In Cross cut, the steps are divided into triangular facets that introduce more light into gemstone. This cut is usually used for weak and dark gemstones. French cut is mainly used on small gemstones with rectangular, square and triangular shapes. Ruby and sapphire are the main gemstones that are cut this way to be used in line bracelets and necklace designs.
The Figure above was adopted from here