A round brilliant cut diamond consists of 57 to 58 facets. The last optional 58th facet would be the culet- a small polished facet at the pavilion point area. This was originally done to prevent point chipping, however larger culets are a lot less commonly seen on most newly cut round brilliants today.
A facet is a small polished surface. Brilliant cut diamonds are created with triangular or kite-shaped facets that cover the entire gemstone's surface. Facets allow us to better view the scintillation and brilliant beauty of a diamond, while providing us with many windows to look into its transparent body as well.
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Emerald cut and Asscher cut diamonds are created with step-cut facets instead of brilliant facets. This means that their facets are usually four-sided shapes such as trapezoidal designs, rather than triangular. While some people prefer step-cuts for their diamonds, it all depends on the visual effect desired for the stone.
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Brilliant cut stones, as the same suggests- show more sharp and numerous brilliant reflections. They also heighten color dispersion or 'fire' as most people term it. The round brilliant style is very specific in its ideal proportions, which is why different laboratories also assign a cut-grade to these stones, as a way of judging how well their cutting accentuates the gem's optical beauty.
Step-cut stones are often done on diamonds with very high clarity, as a way of visually showcasing the top-notch grade through an absence of inclusions. For colored stones on the other hand, a mix of brilliant and step-cut facets is preferred by many. This style is what's referred to as a mixed-cut. More often than not, mixed cuts use a brilliant cut crown with a step-cut pavilion. The latter helps to save weight from the raw crystal.
The term mixed-cut though can also refer to other combinations of faceting styles. Combined with the current diversity of shape choices, the gemstone industry actually has a very wide array of gem cutting designs to suit anyone's personal taste and preference.
You would almost never see a standard-sized diamond cut in a mixed-cut style because it just doesn't bode as well with diamond's optical properties, as the traditional full-brilliant cuts do.
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Specific angles and facet placements are needed to direct light from the stone, back into your eyes in the form of brilliance and sparkle. Light leakage can occur if the diamond is either too shallow or too deep, resulting in either a watery-looking effect with grayish girdle reflections, or a darkened center area known as extinction.
The round brilliant style has been very popular for several decades now, despite newer more proprietary cuts coming into the market. Some diamonds are even cut with over 200 small facets to create a novel appeal.