Tolkowsky Ideal Cut Diamond Proportions & Tolkowsky Diamonds Design

Marcel Tolkowsky created the framework for the modern round brilliant ideal cut diamond in 1919. The Tolkowsky family of diamond cutters moved from Byallstack, Poland to Antwerp, Belgium in the 1840’s. Marcel Tolkowsky is known to have been a mathematician, a physicist and an engineer. He was only 21 years old when he published Diamond Design, which was based on modern theories of light behavior. Tolkowsky’s Diamond Design became the formula for cutting diamonds that exhibit a virtual balance of brilliance and dispersion.

Diagram of Tolkowsky Diamond DesignMarcel Tolkowsky’s calculations indicate that for optimum brilliance and dispersion. According to Tolkowsky, a round brilliant cut diamond should be cut to the following measurements:

  • 34.5° Crown Angle.
  • 40.75° Pavilion Angle.
  • 59.3% Total Depth.
  • 53% Table Diameter.

According to Tolkowsky’s calculations, the total depth of a round brilliant cut diamond should be constructed as follows:

  • The crown (upper) section should comprise 16.2%
  • The Pavilion (lower) section should comprise 43.1%

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The Tolkowsky Cut Diamond Formula:

Now before you go running off thinking that you now possess the magic formula needed for you to be able to find the most brilliant and dispersive diamond on the planet, allow me to point out that for some reason, although Marcel Tolkowsky continually referred to the girdle edge of a diamond in his book Diamond Design, that none of his diagrams clearly define a measurable girdle edge.  Therefore, it has been historically accepted that Tolkowsky’s diamond design, called for a 0.00% thick “knife edge girdle”.  However it is technically impossible to produce a round brilliant cut diamond with a 0.00% thick, knife edge girdle, because there must be a measurable separation between the crown and pavilion sections in order for the facet sections to be properly shaped and constructed.

And we know that Marcel Tolkowsky recognized the existence of a girdle edge because in his works, he states: “Where the cut is somewhat less fine and the girdle is left somewhat thick (to save weight), that facet is sometimes made 3° steeper, or even more, than the pavilion.”  Don’t get all caught up in the technical aspects of the sentence, because I am taking it out of the middle of a paragraph without providing the rest of the context, I am merely using it as a reference to the fact that Tolkowsky recognized the existence of the girdle edge of a diamond in his diamond design.

Visual Properties of a Tolkowsky Cut Diamond:

Now I mentioned that the intent of Tolkowsky’s study of Diamond Design was to determine what the best proportions were to produce optimum brilliance and dispersion in a round brilliant cut diamond, however there was no mention of scintillation… none.  Hey at least the girdle edge of the diamond got an honorable mention, it seems like scintillation got tossed out with the bathwater, and it’s kind of an important factor of visual performance.  However none of these terms mean anything without explanation, so let’s take a moment to define each of them:

  • Brilliance is used to describe how bright our human eyes perceive a diamond to be. However it is not only the amount of light return, but also the perception of intensity created by the internal and external reflections of white light, as judged by looking at the diamond in a face-up position.
  • Dispersion, which is also known as “fire”, is the flashes of colored light that is created by the facets of a diamond. Technically these flashes of light are actually white, but our eyes break them up into colors like red, green and blue.
  • Scintillation is the contrast which is created within a diamond by the light and dark patterns created by the facet pattern; it is also the overall sparkle effect which is created when the diamond is in motion.

Clearly the ultimate in Diamond Design, would account for all three optical factors, brilliance, dispersion and scintillation, and a diamond optimized for brilliance and dispersion would deliver a virtual symphony of both, and not exhibit more brilliance than dispersion, or vice versa.

The American Round Brilliant Ideal Cut Diamond:

Marcel Tolkowsky’s early model of diamond design, which was designed to produce a round brilliant cut diamond, optimized for brilliance and dispersion, set the stage for what is commonly referred to as the “American Ideal Cut Diamond”.  It is referred to as the “American Ideal Cut Diamond” because it was first produced by Lazare Kaplan International (LKI) which was established in New York City in the early nineteen hundreds.  As a point of interest, Lazare Kaplan was Marcel Tolkowsky’s cousin… A majority share in Lazare Kaplan International was purchased by the Tempelsman Group in 1984; their primary diamond cutting factory is located in Puerto Rico. The company continues to produce “ideal cut diamonds” which are sold as “Lazare Kaplan Diamonds” and are available from a select group of authorized retail dealers.

World renowned diamond cutter, Gabi Tolkowsky, is another relative of Marcel Tolkowsky. Gabi Tolkowsky is best known for cutting the famous 545.65 carat, Golden Jubilee Diamond, which is a golden fancy brown colored diamond, shaped as a cushion cut diamond, which has 148 facets.  The original piece of diamond rough weighed 755.50 carats, the diamond was presented as a gift to the King of Thailand to celebrate his 50th year on the throne.  And reportedly, Jean Paul Tolkowsky, picked up the family torch in 2009, his lineage makes him a seventh generation diamond cutter.

Making Effective Use of Tolkowsky’s Diamond Design:

The selection criteria which I use for selecting round brilliant ideal cut diamonds, is based upon Tolkowsky’s Diamond Design, but is slightly expanded to account for the girdle edge of a diamond.  Using the modern influences of mathematical ray tracing and software which creates models of diamonds, and then analyzes them for light return, I determined that the following set of proportions produces round brilliant cut diamonds which are optimized for brilliance and dispersion:

  • Total depth between 59 – 61.8%
  • Table diameter between 53 – 58%
  • Crown angle between 34.3 – 34.9 degrees
  • Pavilion angle between 40.6 – 40.9 degrees
  • Girdle edge between 0.7% thin to medium
  • Culet: GIA “none” or AGS “pointed” (same thing)

Contrast image of Brian Gavin Signature Diamond, AGS#104047809010You might recall that earlier in this article I mentioned that Tolkowsky made no mention of scintillation, which is the contrast which is created within a diamond by the light and dark patterns created by the facet pattern; it is also the overall sparkle effect which is created when the diamond is in motion.  Perhaps Marcel Tolkowsky did not mention Scintillation, because it was not understood at the time, that extremely high levels of optical symmetry within the facet structure of a diamond is necessary to produce contrast… This is my assumption because I don’t recall contrast being discussed much prior to the mid-1990’s when Hearts & Arrows Diamonds were first introduced.

We were one of the original importers of Hearts and Arrows Diamonds to the U.S. Market, and I remember it causing quite a stir… The picture to the left is an example of a diamond which exhibits high levels of contrast because the optical symmetry is extremely precise, it is a 1.532 carat, D-color, VS-1 clarity, Signature Hearts & Arrows Diamond produced by Brian Gavin <==== Big Scary affiliate link ====>

Beyond the Realm of Tolkowsky Cut Diamonds:

Diamond cutters like Brian Gavin of Brian Gavin Diamonds, and Paul Slegers of Crafted by Infinity, have significantly improved upon the basics of Tolkowsky’s Diamond Design, by advancing diamond cutting beyond the focus of proportions, and extended it to include the importance of facet shape and alignment, for the purpose of creating diamonds which are optimized for all three factors of visual performance: brilliance, dispersion and scintillation.

Hearts pattern, Brian Gavin Signature Diamond, AGS#104047809010The easiest way to judge a diamond for optical symmetry is to examine the diamond, while unmounted, through a scope designed to demonstrate whether the diamond exhibits a crisp and complete pattern of hearts and arrows, like the 1.532 carat, D-color, VS-1 clarity, Signature Hearts & Arrows Diamond produced by Brian Gavin, which is pictured to the left. <==== same Big Scary affiliate link ====>

Diamonds which are cut to this level of precision, to the extent that they exhibit a crisp and complete pattern of Hearts & Arrows, and which are cut to the precise proportions outlined above, and which are graded with an overall cut rating of either GIA Excellent or AGS Ideal-0, represent about 0.001% of the world’s annual production of round brilliant cut diamonds!  Diamonds cut to the same proportions, without the presence of a crisp and complete pattern of hearts and arrows, with an overall cut rating of either GIA Excellent or AGS Ideal-0, represent about 1% of the world’s annual production of round brilliant cut diamonds.  The reason why more diamond cutters do not produce diamonds which are optimized for brilliance, dispersion and scintillation, is because it requires an extreme amount of skill, and more diamond rough is lost in the process of cutting the diamond.  Since diamond prices are structured by carat weight, to the extent where everything is discussed in terms of “Price Per Carat” (PPC), the heavier a diamond weighs, the more it is worth.

Arguably, the perception that a diamond is worth more because it is heavier, is a belief which is outdated; however since the majority of the diamond industry is either incapable, or unwilling, to produce diamonds which are optimized for light return and visual performance, it is a belief that is likely to continue to be used as the basis for diamond valuation. Interestingly enough, the industry does recognize the value of diamond cut quality and visual performance, but they do so in a manner which is virtually invisible to consumers… they use an undisclosed system of applying premiums for “diamonds of extremely fine make” over and above the “wholesale diamond prices” indicated as the base price on the Rapaport Diamond Report (RAP), and apply substantial discounts “off Rap” for diamonds with less desirable proportions and characteristics.  Additional discounts are taken for diamonds which are not graded by the AGS, GIA, or HRD laboratories.  For instance, as a general rule, diamonds which are graded by the IGI or EGL, tend to be sold “in back of Rap” at higher discounts than diamonds graded by the AGS, GIA, or HRD laboratories, which have diamond grading reports that indicate that they are the same carat weight, color and clarity.  My article, the Rap Trap, discloses the reasons why, but I’ll give you a hint…

When a “Tolkowsky Cut Diamond” is NOT:

Do not be confused or misled by the appearance of the words “Tolkowsky Cut” on some diamond grading reports. The words “Tolkowsky Cut” do not necessarily mean that a diamond has been cut to Tolkowsky’s exact specifications, nor does it necessarily imply that it was cut by a member of the Tolkowsky family. Some laboratories will say that a diamond is “Tolkowsky Cut” or within “Tolkowsky Range” if the diamond’s proportions are “within tolerance” of Tolkowsky’s original calculations. According to the specifications of one laboratory, “Tolkowsky Range” is as follows:

  • 33 – 36° Crown Angle.
  • 40 – 41.5° Pavilion Angles.
  • 56 – 63.7% Total Depth.
  • 53 – 57% Table Diameter.

Unlike Tolkowsky’s calculations, which call for the crown section to comprise 16.2% of the total depth and for the pavilion section to comprise 43.1% of the total depth, this laboratory has concluded that 14 – 16.5% of the crown and 42 – 44% of the pavilion section, should comprise the total depth of the diamond. That’s like saying that driving 45 – 85 miles per hour on a freeway with a posted speed limit of 65 mph, is “within tolerance” of the posted speed limit.

EGL graded, Tolkowsky Ideal Cut DiamondI ran across the image to the left, posted in this thread on the Pricescope Diamond Forum on May 02, 2011 (which references data sourced from my original page on Tolkowsky Cut Diamonds).  It is of a diamond grading report issued by the European Gemological Laboratory (EGL) as weighing 0.74 carats, measuring 5.71 – 5.66 x 3.63 mm with a total depth of 63.7% and a table diameter of 55% with a crown height of 16% and a pavilion height of 43% with a medium, faceted girdle and very good polish and symmetry.  The comments section of the lab report reads as follows: “TOLKOWSKY IDEAL CUT”  (highlighted in yellow) “the proportions of this diamond are within tolerance of those proposed by Marcel Tolkowsky as the ideal balance between brilliance and dispersion.”

Further down the comment section of the EGL diamond grading report, it mentions that this diamond has 81 facets, instead of the 57 facet structure of the round brilliant cut diamond that Marcel Tolkowsky’s Diamond Design is actually based upon.  Let me remind you that the specifications which Marcel Tolkowsky actually proposed for the “Tolkowsky Ideal Cut Diamond” are a crown angle of 34.5 degrees, offset by a pavilion angle of 40.75 degrees, with a total depth of 59.3% and a table diameter of 53% which is worlds apart, perhaps galaxies apart, from the measurements of this particular “Tolkowsky Ideal Cut” diamond which has “proportions that are within tolerance of those proposed by Marcel Tolkowsky”.

I’ve evaluated “Tolkowsky Cut” diamonds that scored overall proportions ratings as low as AGS-2 Very Good on our Sarin DiaPort computerized proportions analysis machine. Over the years, I’ve even seen the words “Tolkowsky Cut” used on some lab reports to describe the overall proportions rating of fancy shape diamonds such as Flanders Brilliant, marquise, and princess cut diamonds… What gives with that? How is it possible that the results from Tolkowsky’s analysis of round brilliant cut diamonds for brilliance and dispersion, can be applied to a diamond with a completely different shape and facet structure?  That would be kind of like the American Kennel Club (AKC) trying to judge my German shepherd, using the same basis which they would use to describe a Chihuahua, because they’re both dogs… And in case you’re wondering how the comparative “DOG” analogy ties into the use of terms like “Tolkowsky Ideal Cut Diamond” by some gemological laboratories to describe diamonds cut like this, I’ll leave that up to your imagination.