Facets are flat faces on geometric shapes. The organization of naturally occurring facets was key to early developments in crystallography, since they reflect the underlying symmetry of the crystal structure. Gemstones commonly have facets cut into them in order to improve their appearance.

Of the many hundreds of facet arrangements that have been used, the most famous is probably the round brilliant cut, used for diamond and many colored gemstones. This arrangement of 57 facets was calculated by Marcel Tolkowsky in 1919. Slight improvements have been made since then, including the addition of a 58th facet (a culet) on the bottom of the stone. Since this is calculated to show maximum brilliance, round diamonds are rarely cut in any other arrangement, although recently the Princess cut is becoming popular. Other cuts, including "rose" cuts, are most typically found in antique jewelry. See diamond cuts for an in-depth discussion and diagrams of various shapes and ways of cutting faceted stones.

==Cutting Facets==

The art of cutting a gem with facets is a very precise activity done on a faceting machine. The aim with a faceted cut is to produce an article that sparkles with internally reflected light, and that shows off the "fire" of the stone. Accordingly, only transparent or translucent stones are usually faceted.

The angles between each facet are precisely calculated. As the aim is to maximise the effect of the internal reflections, these angles depend on the refractive index of the material. This means that although the name and general shape of a particular cut may be the same between different materials, the actual angles will be slightly different, for the maximum effect.

Thus, although cubic zirconia and rock crystal may look similar to diamond, and all can be cut in a round brilliant cut, the angles must be different to produce the same optical effects. Additionally, as diamond has a refractive index significantly higher than most other natural transparent stones, it can have a much greater sparkle than other materials.

While some facets can be cut by cleavage, specialised faceting machines are used for cutting arbitrary facets. These consist of two main features:

a flat abrasive, usually diamond dust of precise size bonded onto a metal disk (called 'laps') or carried by an oily fluid on a smooth metal or ceramic disk, and
a system (goniometer) for holding a stone onto the disk at a precise angle and position.
This usually requires the stone to be attached to a holder or dop, which is then placed in an indexed vice. This allows progressively finer abrasives to be used without disrupting the orientation of the stone. The final abrasive must be smaller than the wavelength of lig

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