Tolkowsky Revisited

Poor Marcel Tolkowsky. He’s the Belgian diamond cutter (1899-1991) who, in 1919, wrote a treatise entitled “Diamond Design,” which introduced what we now call the “ideal cut.” The concept became popular in the United States and later in the Far East, and even Gemological Institute of America courses called diamonds with Tolkowsky’s proportions (with a few modifications) the cream of the crop. With today’s emphasis on cut, “ideals” are more popular than ever. Yet Tolkowsky’s work is facing an unprecedented challenge. After embarking on an ambitious multi-year computer-simulation research project, GIA believes the term “ideal cut” should be abolished—mostly because it’s irrevocably linked to Tolkowsky’s measurements. “Furthermore, there is now even more evidence to support the conclusion that there is no one ‘best’ cut for a round brilliant diamond,” says GIA president Bill Boyajian.

GIA now believes that other diamonds with very different measurements and proportions can equal the brilliance, dispersion, and scintillation of a Tolkowsky ideal cut. GIA researchers also believe that someday it will be possible to predict how a cutter might, for example, take a diamond with a 60% table and 60% total depth—major deviations from Tolkowsky proportions—and without too much repolishing or changing proportions, manipulate the facets to yield a diamond that’s just as beautiful.

Tom Moses, vice president of the GIA Gem Trade Laboratory, anticipates the day when he can advise someone how to significantly improve a deficient stone by repolishing, with only a 1% or 2% weight loss. “We believe we will be able to provide information to the manufacturer who will then be able to decide whether or not to fix the stone,” Moses says.

But Richard von Sternberg of EightStar Diamond Co., Santa Rosa, Calif., doesn’t see how that’s possible. “It would be especially important for cutters if this were so, to take dark stones and turn them into French poodles,” he says. “But it doesn’t seem to be the way we do things. I haven’t found a way to do this yet.”

There are a number of cutters who agree with GIA that there is no one ideal cut, but who think the concept shouldn’t be thrown out. They say there may be several ideal cuts—and the way to prove it is to look past proportion percentages and angles and measure what diamonds are supposed to be about—beauty. They believe the term “ideal” should be redefined to mean “maximum brilliance and fire.”

Optical vs. physical. “We’ve changed the metric from measurements and proportions to performance, and this is an important place in the history of diamond cutting,” says von Sternberg, who believes the way to analyze performance is to view a diamond through a FireScope. This Japanese-developed device shows light leakage through a diamond’s pavilion. (Imitations of the FireScope are the small Hearts & Arrows readers.) Seeing white in a FireScope image indicates leakage. Von Sternberg notes that the absence of light leakage occurs when the diamond has “optical symmetry.”

This differs from “physical symmetry,” which is what the trade typically measures. Physical symmetry means the facets are well shaped and uniform. Optical symmetry means the facets are placed in relation to each other such that the light striking them is optimally bounced to another facet or out through the stone’s crown. Von Sternberg believes that a diamond’s crystallography dictates the angles of maximum performance, for both brilliance and dispersion. Thus, the way to determine the ideal cut for a diamond is not to measure angles, but to observe a diamond’s optical symmetry.

Failing grades. This contradicts not only GIA’s research but also the thinking behind most gem lab cut grades. Most measurements are determined by using electronic optical devices such as a Sarin or Megascope, made by OGI Systems, OGItech, New York. These machines also are programmed to note whether or not a diamond’s physical measurements reflect Tolkowsky’s angles and proportions.

The AGS laboratory, which follows this methodology, is the only major lab issuing a cut grade for round brilliants. It considers a diamond ideal if its measurements are equal to or close to Tolkowsky proportions. For stones with other proportions, the cut grade is an educated guess at loss-of-beauty based on how far a diamond’s measurements deviate from Tolkowsky’s.

Many find this inadequate, arguing that numbers and percentages can’t tell you if a diamond looks good. (Even some Tolkowsky ideal cuts look better than others.) Michael Cowing, a gemologist and appraiser who works for von Sternberg, says that angles and percentages don’t always correlate with each other—crown to pavilion, or even one side to the other side—to produce maximum brilliance and fire. Even if the vertical angle measurement is at Tolkowsky proportions, a facet may have to be twisted or rotated to line up optically with the other facets. The FireScope, according to von Sternberg, can determine if there’s interaction among facets.

Interestingly, although EightStar doesn’t cut specifically to Tolkowsky’s calculations, the angles and proportions of its diamonds approach Tolkowsky’s figures. “For the longest time, we were told by diamond dealers and retailers that we cut the best diamonds,” says von Sternberg. “The truth is, we had no capacity to measure angles. All we were concerned about was reflective technology. And until we got a Sarin, eight years later, we didn’t know just how close to Tolkowsky we were actually cutting.”

What would Marcel say? There is evidence that Tolkowsky himself believed a diamond’s look was more important than its measurements. “One thing Tolkowsky did to verify that his conclusions were correct was to ensure that his results agreed with what the best cutters had already known,” says Cowing. “Tolkowsky was involved in the manufacture of some million pounds worth of diamonds, cut to obtain ‘the liveliest fire and the greatest brilliancy.’ The most brilliant larger stones were measured and Tolkowsky notes ‘how remarkably close’ these measurements came to his mathematically calculated values.”

Moreover, Tolkowsky never said that one rigid set of numbers produced the best diamonds. His chart of the five best-cut diamonds, having maximum brilliance and fire, were averaged to his mathematically determined proportions for crown and pavilion angle. There was a two-degree variation in crown angle and a one-degree variation in pavilion angle among Tolkowsky’s top picks—meaning there is a range, albeit a small one, of acceptable proportions.

Another cutter who adheres to performance-based, rather than proportion-based, standards for cutting diamonds is Baruch “Barry” Gutwein of SuperbCert, New York. Gutwein doesn’t use EightStar’s FireScope, but he does use GemEx’s BrillianceScope to cut for brilliance and dispersion. “It helps me make a decision on where to place the facets in relation to each other,” he says. “I also have the analog version of the B-Scope that I use, and I’ve built a prototype FireScope I call the ImageScope, all used to see where the light is concentrating in the stone, and how it comes out to your eye. There’s an amazing relationship to the image of the ImageScope and [that of] the B-Scope.”

Although the angles of Gutwein’s stones are—like EightStar’s—close to Tolkowsky, there seems to be a difference in performance, at least according to the BrillianceScope. “EightStar is cut to slightly different angles than a SuperbCert,” notes Gutwein. “They look different on the B-Scope, but it’s not a detriment. When you get down to the nitty-gritty, it’s extremely subjective. One customer may love the look of an EightStar and another may love the look of a SuperbCert. One is not better than the other.”

Von Sternberg has noted that the actual angles of an EightStar are not as exact as one might expect. That’s why the FireScope is so important: It shows him how and where to cut. Gutwein concurs. “There’s a window of manipulation,” Gutwein says. “Based on my own cutting, I know that there are different ways to make a fine-looking stone without cutting exactly to Tolkowsky.”

“Just as in any of the existing cut systems, there is a range of proportions that will be judged ‘ideal,’ ” says Cowing. “The diamond’s optical performance, as seen by your eye and judged in more detail by devices like the FireScope, should be the criteria for deciding what range of proportions is ideal. Richard [von Sternberg] has shown that he obtains ideal performance over a range of proportions, which should make GIA happy that there is not just one exact set of ideal proportions. On the other hand, Richard also has shown that there is an ideal performance that can be obtained by cutting with the FireScope. So there is still an ‘ideal.’ That should make AGS and G.G.s and former GIA students who were taught ‘ideal’ happy. What G.G.s learned about ideal cutting wasn’t wrong in its conclusions, just inexact in the science of explaining it. The same can be said about Tolkowsky’s work: It wasn’t wrong in its conclusions of pavilion and crown angle, just inexact in the mathematics of explaining it.”

At present, there is no outside authority to affirm that EightStar’s or SuperbCert’s formula leads to the ideal of ideal cuts. Until performance-based standards are studied by researchers, recognized by major gem labs, and practiced by more cutters, the debate over ideal cut will remain a debate, and beauty will remain subjective—a matter of personal taste and preferences.

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