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This style of cutting was specially devised to enhance both optical properties and yield between the weight of the rough and cut diamond. It may have 57 or 58 facets and a round, oval, pear shape of marquise contour.
Brilliant is the most popular cut shape for diamonds. The shape resembles that of a cone and is meant to maximize light return through the top of the diamond.
In Portugal the word brilhante, a brilliant, is popularly used to refer to diamonds in general, which is not very accurate.
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 brilliantwhich the particular crystal shape lends itself to.
The brilliant cut was introduced in the middle of the 17th century. The first brilliants were known as Mazarins. They had seventeen facets on the crown (upper half) and are called double-cut brilliants.
Vincent Peruzzi, a Venetian polisher, increased the number of crown facets from 17 to 33 (triple-cut brilliants), thereby dramatically increasing the fire and brilliance of the cut gem already much better in the double-cut brilliant than in the rose cut. When seen today, diamonds of that cut seem quite dull compared to modern-cut ones.
Around 1900, the development of diamond saws and good jewellery lathes enabled the development of modern diamond cuts, chief among them the round brilliant cut. In 1919, Marcel Tolkowsky analyzed this cut. His calculations took both brilliance (the amount of white light reflected) and fire (flashes of spectral colors) into consideration, creating a delicate balance between the two. His geometric calculations can be found in his book on Diamond Design.
In the 1970s, Bruce Harding developed another mathematical model for gem design. Since then, several groups have used computer models (e.g., MSU, OctoNus, GIA, and folds.net) and specialized scopes to optimize the round brilliant cut. (from: Wikipedia)