Gemstone Geometry

Most everyone has seen the “three bears” of stone geometry – Many American cutters have some version of this thing on their web site or brochure:

The first “bear” is “pappa bear” – he looks very big from the top, but is too shallow – light won’t reflect off the pavilion faces because it is striking those faces too square-on. Instead, light passes right through the stone, NOT returning to the eye of the beholder, and thus producing a stone that looks like a “fish-eye” – dead and lifeless – a window to the knuckle-hair of the wearer:
fish eye gem

The second is “mamma bear” – too deep, so light ricochets off the first pavilion face and slams into the second pavilion face square-on, “leaking” out the bottom of the stone. Although the viewer is not treated to “knuckle-hair window” created by the above example, the result is still a dark and lifeless stone:

extinction gemThe third, “baby bear” is just right – angles are carefully selected and placed so that light makes an elegant “double-bank-shot” off the pavilion faces, and returns to the eye of the dazzled beholder. This stone is beautiful:

well cut gem stoneMost people easily understand the point that “good cutting” means proper angles, properly placed about the stone. That’s what gives you the sparkle.

However, geometry is very important when selecting gem rough or planning a custom piece of jewelry – especially a ring.

Most colored gem materials should be cut so that the angle across the culet will be greater than 84 degrees – often closer to 90 degrees. This is necessary because light must reflect off the internal face of the gem rather than passing through it.
faceting angles for gemstones

To see this effect out in the “real world”, find a window or other flat piece of glass that is evenly lit from both sides. Look at the glass square-on and you can easily see whatever is on the other side. Then, begin to move so that you look through the glass at an increasingly narrow angle. As you sharpen the angle, you will begin to see more and more of the glare or reflection from objects on your own side of the glass. (Less and less light from the other side can leak through to you.) Eventually, you will not be able to see through to the other side at all, and you will be seeing only reflected light. Notice that this angle is usually close to 45 degrees under most conditions.

This is what we wish to impose on rays of light that enter the top of your gem – we want as little as possible leaking out the bottom of the stone by striking the pavilion faces at too great an angle. We work very hard to set up stone geometry so that most of the light that enters the crown will also exit back through the crown – hopefully to the dazzled eye of an appreciative viewer.


Stone Geometry and Planning a Custom Ring
or Custom Gems for an Existing Ring

I often receive requests to custom cut a stone for an existing setting – or to “liven-up” an existing stone in a ring. And, that’s where the geometry from above becomes a practical concern:

Remember that the angle across the pavilion is going to be between 84 and 90 degrees (if we want sparkle). So, depending on the design, for every millimeter of width across the stone, we are going to need from 0.6 to 0.75 millimeter or more of depth below the girdle to accommodate the pavilion. (Barions and other fancy designs will often require even more – as much as 1 millimeter of depth for each millimeter of width.)

You can’t stretch the width without adding a mathematically appropriate amount to the depth – or you’ll be back to the first of the “three bears” above – a stone that is too shallow for its width – a knuckle-hair aquarium like the one represented here:

ring with gemstoneThis large stone has been cut too shallow so that it neither sticks up too high from the hand, nor does it poke the finger of the wearer. The only trouble with such an arrangement is the stone does not sparkle – It is dead and lifeless, so what’s the point of wearing it?

To cut a stone of the same width (to fit the setting) we will produce a stone that is significantly deeper:

engagement ring customHowever, this stone is very tall – It seems to catch on everything – and it also pokes the finger of the wearer in a very uncomfortable way.

This is the conundrum we usually encounter with clients who have larger ring settings that they want a fine stone for – or from clients who have a large stone that doesn’t sparkle for them. Men’s rings, in particular, are often made very shallow so that they won’t appear too effeminate or become too bothersome.

As a rule, the culet portion of a stone will be 60%+ of that stone’s width. So, if you have a setting that is supposed to hold a 10 mm wide stone, you will need a MINIMUM of 6.5 mm below the seat to accommodate the culet without poking your finger uncomfortably:

faceting proportionsMany of the more fancy designs will need quite a bit more depth – I usually recommend a minimum of 75% of the width as a guideline.

If you have a ring with a stone that doesn’t sparkle well, it is probably cut like the first of the three “bears” – too shallow. We cannot add material to the stone, so recutting will probably make it smaller – too small to fit the setting. I usually recommend trading for a properly-cut stone that’s especially designed to fit the setting and to properly return light.

For those who have a large prong-type setting, where the setting itself is too shallow, I may recommend modifying the setting or possibly going to a cabochon-cut stone.

Those who have a bezel-type setting or who are willing to significantly modify their existing setting have a third option – something that I call a “catamaran” strategy – an idea taken from sailing. (See one of my “catamaran” designs for a man’s 12 x 10 Emerald-shaped setting here.)

For a “catamaran”, we divide the width of the setting in half, and cut two matching stones – one for each half of the setting width. When the bezel is rolled, the stones are locked together as if a single piece. (Picture channel-set princess-cut diamonds, only on a larger scale.) The stones will sit lower than any single stone could, so they are less prone to damage though they offer the same “size” sparkle:

fantasy cut gemstones


Stone Geometry and Recutting

I frequently receive requests from people who have a stone that is lifeless – the proverbial “knuckle-hair aquarium” – and they want me to “liven it up by adding some faces or something”. Of course, faces are added by cutting away gem material – weight, and often size as well.

The typical reason that a stone looks lifeless is that it has been cut to “poppa-bear” proportions – far too shallow for the existing width. Because of the physics of light, the only real solution to this problem is to reduce the angle across the point of the stone so that it comes close to 90 degrees (baby-bear proportions). Since we cannot add gemstone to increase the depth, the only alternative is to reduce the width – often by 50% or more.

Sometimes, aesthetics can be greatly improved without severely dropping the stone’s value. However, most often the stone is not cut too shallow because the cutter was incompetent, but because this was the original shape of the rough – and because cutting it to proper geometry would reduce the weight so greatly that the stone would actually be worth less money in that cutter’s particular market (overseas). In most cases of a bad fish-eye, recutting the stone will remove more weight and apparent size than the owener is prepared to suffer losing.

recutting gemstonesThis graphic shows proper angles superimposed on top of a shallow-cut stone. Notice that both images have the same depth – and that the proper geometry (which creates life, light, and sparkle) is perhaps less than half the width of the wide, lifeless fish-eyed stone. These proportions are unfortunately quite realistic in many cases.


Stone Geometry and Selecting Gem Rough

I often receive gem rough from someone who has looked at the front two dimensions of the stone – Let us say 12 x 12 mm – and they will expect a 10 x 10 mm stone (or larger) from this piece. That is not unreasonable, if the piece is very clean – and deep enough. However, people often neglect to study this necessary third dimension.

So, if we desire a 10 mm wide stone, we must anticipate a need for:

MINIMUM depth of 6.5 mm 6.5 mm
Crown depth between 30% and 60% of pavilion 1.95 mm
Reasonable girdle thickness 0.65 mm
Polishing will remove some material 1.0 mm
TOTAL 10 mm

You can see that proper geometry may sometimes require a stone to be nearly as deep as it is wide – in this example, fully as deep as it is wide. So, although this is not a hard-and-fast rule, it is wise when evaluating rough to err on the side of caution by estimating the finished stone’s width at no greater than 110% of the stone’s depth. This can save you grief when someone offers you a great deal on a “collector’s stone” that’s 40mm long, and 35mm wide, but only 10mm deep.

If you have any questions or comments, please contact me.

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