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Diamond Cut Geometry

Updated on November 06, 2016
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TR Smith is a product designer and former teacher who uses math in her work every day.

Engagement ring with three Asscher cut diamonds.
Engagement ring with three Asscher cut diamonds.

Gem cuts are three-dimensional geometric designs developed to enhance the sparkle and fire of gemstones such as diamonds, emeralds, rubies, sapphires, cubic zirconia (ZC), moissanite, and other precious minerals made into jewelry. There are many varieties of gem cuts, and how a gem is cut depends on what features the jewelry make wants to highlight, the chemical and crystalline structure of the gem, and more practical matters such as waste. With diamonds, waste is not such a big deal because diamond is abundant on Earth, and small bits of diamond are valuable for making cutting tools, since diamond is the hardest substance known. However, waste is an important consideration in cutting emeralds.

When you look at a cut gem embedded in a ring, it can be difficult to tell what shape it is because some of it is hidden, and because light refraction makes it difficult to tell where one facet ends and another begins. Below are geometric diagrams to help you understand gem cut names such as round brilliant, princess cut, emerald cut, Asscher cut, and many others.

This is diamond cut guide for the lay person and avoids using too much technical jargon of gemology. For a tutorial on light refraction/reflection and ideal diamond cuts, see Refraction and Reflection of Light in Cut Diamonds.


The Round Brilliant Cut for Diamonds

Diamond cuts have evolved over the years to include more facets to bring out more of their sparkle and fire. The family of brilliant cuts is so named because the dazzling effect it produces when set in a ring. The round brilliant is the most popular diamond cut today. Before showing the geometry of the cut, we should first learn a few names of parts of a cut gem. These are shown in the diagram below.

The girdle is actually very thin (but drawn larger for emphasis) and may be faceted. But for purposes of classifying cuts and counting the facets, the faces on the crown and pavilion are what matter. The crown is the face-up part of the gem, and the pavilion is hidden in the well of the setting. The large flat facet on top of the crown is called the table.

In a round brilliant cut, the shape of the diamond from the top is that of a circle, and the table is an octagon. Surrounding the octagon are smaller quadrilateral and triangular facets. The total count of facets on the top is 33.

The pavilion is cone-like and divided into eight sectors, with each sector containing three triangular and quadrilateral facets. Additionally, there may be a tiny facet cut from off from the tip of the pavilion, called a culet. Without the culet there are 24 facets on the pavilion, and with the culet there are 25 . Thus, the total number of facets on a round brilliant cut diamond is either 57 or 58.

The top and bottom views of a round brilliant cut are shown in the diagram below, with the culet in the pavilion.

Princess Cut

The princess cut is renowned for its beautiful square symmetry and unique pattern of chevrons in the pavilion. It is the second most popular cut for diamond engagement rings. The crown of a princess cut has an irregular octagonal table whose sides are angled so that the table almost looks like a square. The table is surrounded by many elongated quadrilateral and triangular facets.

The pavilion is shaped like a square pyramid, with the sides faceted in a chevron pattern. There is usually no culet. The girdle is a often a bit thicker than in a round brilliant cut diamond

The larger the diamond, the more facets are needed on the crown and pavilion in order to produce the best sparkling effect. Smaller gems require fewer facets. Thus there are two variants of the princess cut, the three-chevron and four-chevron cuts.

Emerald Cut

As the name suggests, this cut is popular for emeralds. Used on a diamond, the emerald cut does not do full justice to a diamond's superior ability to refract light, but it is a beautiful cut in its simplicity nonetheless. The emerald cut is used for rectangular gems, and the facets are rectilinear, parallel to the girdle, enhancing the overall geometric effect. This cut is also known as the step cut or trap cut. Here is a diagram of the crown and pavilion.

Comparison of Round Brilliant, Princess, and Emerald

The picture below shows diamonds of the three cuts. The round brilliant and princess cuts can produce "crushed ice" effects with their many facets. The more facets, the more pronounced the effect. In comparison, the emerald cut has a chunkier look.

Diamonds in round brilliant, princess, and emerald cuts.
Diamonds in round brilliant, princess, and emerald cuts.

Cushion Cut

A cushion cut diamond has the shape of a rounded square or rectangle, in which the corners and sides are rounded. The overall pattern of facets on the crown and pavilion resemble that of the brilliant cut, except the shapes of the facets are adapted for arrangement on a non-circular gem. There are actually many facet patterns that can be called a cushion cut. Three particular styles are called cushion brilliant, modified cushion brilliant, and old mine brilliant.

A cushion cut is technically classified as an old mine cut if the table is small compared to the crown (53% or less), the angle of the crown with respect to the girdle is 40 degrees or greater, the culet is comparatively large, and the height of the pavilion is 60% or less that the total height. If at least three of the four conditions are met, it can be called an old mine cut. Old mine cuts are found in antique diamond pieces. A true old mine cut will have some asymmetry, whereas modern reproductions of old style cuts are more symmetric.


Radiant Cut

The crown of the radiant cut resembles that of the princess cut, while the pavilion of the radiant cut is an intricate arrangement of kites, rhombuses, and triangles. Several different styles of pavilion cuts can be called radiant; some strongly resemble the pavilions of modified cushion brilliants. The radiant cut is applied to octagonal-square and octagonal-rectangle diamonds.

Asscher cut variant with square pyramid tip.
Asscher cut variant with square pyramid tip.

Asscher Cut

The Asscher cut (pronounced "asher") is essentially the emerald cut applied to octagonal-square diamonds, but with more faceting in the pavilion. Although the Asscher cut was developed in 1902 by Joseph Asscher -- over a hundred years ago -- some novice diamond buyers perceive it as a modern cut. This may be due to the fact that it was never as popular as other cuts during most of its existence, but gained more recognition during the past decade when a number of celebrities started wearing Asscher cut engagement rings.

A variation on the Assher cut has a square pyramid at the tip of the pavilion, shown on the right. The standard Asscher cut is shown below.

Comparison of Cushion, Radiant, and Asscher Cuts

The three gems below display the cushion, radiant, and Asscher cuts. Note how each refracts light in different patterns. The Asscher has more square symmetry, while the radiant and cushion cuts have effects closer to crushed ice. The Asscher cut is a happy medium between the crushed ice and chunky look.

Trillion cuts / Trilliant cuts
Trillion cuts / Trilliant cuts

Other Gemstone Cuts

Other modern cuts for gems include the heart, marquise, pear (teardrop), and oval. All are highly faceted cuts with a geometric pattern of facets similar to that of the round brilliant and cushion brilliant cuts. The Trilliant or Trillion cut is another shape based on an equilateral triangle.

Older style cuts have fewer facets due to the lower state of cutting technology at the time when they were popular. It is rare to find them in modern jewelry; they are mainly found in antique and heirloom pieces. Their names include old single cut, old mine cut, Mazarin, and Peruzzi. Rose cuts are another antique style, unique because they have a crown but no pavilion.

Diagrams and photos for round, princess, Asscher, radiant, cushion, heart, oval, emerald, marquise, and pear cuts.
Diagrams and photos for round, princess, Asscher, radiant, cushion, heart, oval, emerald, marquise, and pear cuts.

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      Kelly 2 years ago

      I am ring shopping, thanks for the princess cut diagrams, I think that's my favorite cut.

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