Facet

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 by allowing them to reflect light.

Of the 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 first early version of what would become the modern Brilliant Cut is said to have been devised by an Italian named Peruzzi, sometime in the late 17th century.

Slight modifications have been made since then, but angles for "ideal" cut diamonds are still similar to Tolkowsky's formula.

Sometimes a 58th facet, called a culet is cut on the bottom of the stone to help prevent chipping of the pavilion point.

The ideal product of facet cutting is a gemstone that displays a pleasing balance of internal reflections of light known as brilliance, strong and colorful dispersion which is commonly referred to as "fire", and brightly colored flashes of reflected light known as scintillation.

This machine uses a motor-driven plate to hold a precisely flat disk (known as a "lap") for the purpose of cutting or polishing.

The dopped stone is ground at precise angles and indexes on cutting laps of progressively finer grit, and then the process is repeated a final time to polish each facet.

By placing the back end of the dop into one of the many holes, the stone could be introduced to the lap at precise angles.

If the surface energy as a function of the planes is known, the equilibrium shape of the crystal may be found via the Wulff construction.