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The Most Noob Question About "cut"


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I am just a newbie when it comes to the diamond world.

When it comes to diamonds the 4Cs are important. Everyone wants to buy the "perfect" diamond.

Just imagine you could chose a diamond and your resources are without any limits. What kind of a diamond would you chose?



This is obviously the most easy to answer, everyone would chose grade D (exclude personal preference)



This would not hard to answer either, all of us would chose F or IF



This is a little bit more difficult to answer, but in our situation where there is no limit to chose from, we would chose: the bigger the better.



The answer to this question would be tricky, since I was wondering: is there really a perfect cut?

Let's reduce our choice options and narrow it only to round brilliant cut diamonds.

Luckily for me I do not have to do the maths, someone else (Marcel Tolkowsky) decribed the perfect cut in his PhD thesis in 1919. According to him a diamond needs to be cut in a certain why to get the most "sparkling" effect:

* Round, Brilliant-Cut 57/58 facets

* Depth 59%

* Table: 53%

* Crown height: 16%

* Pavilion depth: 43%

* Girdle thickness: Medium

* Symmetry: perfect

* Cutlet: Tiny/Absent

* Facets: perfectly aligned


BUT Tolkowsky was not the only one who described the "perfect cut" and his cut may not even be the best. Have a look at the table for perfect cut benchmarks. It seems that the Eulitz Cut may be the most "perfect cut" of all this benchmark.


So let's come back to our choice of "perfect" diamond.

Our diamond would be: Grade D, F/IF, Big as possible, Eulitz cut?


Imagine that our financial resources are limitless too. Is it possible to go to a respectable jeweller (e.g. Cartier, HW, Graff or DeBeers) and ordered a customised perfect diamond?


Could anyone enlighten me on the choice of a "perfect diamond", especially regarding "perfect cut"?


And how about different cuts? Like Solasfera? Is Solasfera really a much better way of cutting a diamond?


BTW, IMHO the perfect diamond has 6Cs

Carat, Cut. Colour, Clarity, Cost, Certify


Edited by tqttong
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You postulate some impossible assumptions but unlimited money will buy you just about anything. I remember back when I was a jeweler that I had a client who required a D/IF/ideal that weighed exactly 3.333 carats. He was a professional baseball player and 3 was his lucky number. It was a big deal to him. We had to buy a bigger stone and have it recut in order to get that 3rd decimal place and then get it recerted in order to get the exact weight. We had to use AGS since GIA only uses 2 decimal places. It came back 3.334. We polished a tiny bit off and sent it in again. It took months and cost a fortune. Thank GOD it wasn't a 3.332. We charged a bundle of money to do this and earned every penny.


Back to your question. You want to exclude taste from the equation but it's absolutely critical. In fact it's the whole point. Tolkowski's taste may not be the same as yours. There's nothing about 8 fold symmetry that's 'best'. There's even nothing about round that's 'best'.

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Hearts and Arrows symmetry is very popular among cut fans.


The difference in cutting has to do with the total light return from the stone, the patterning of the sparkles and the light/dark contrast areas as the stone moves, and the price.


FWIW, I'm relatively recently engaged and I bought an AGS ideal cut that does NOT show perfect H&A symmetry (although it's pretty close). For ME, that was the 'best'. Unlike your scenario, for me money was definitely an important criteria in my shopping.

Edited by denverappraiser
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There isn't one.


And for example, going back to your list in the first post:


Colour: fancy red is significantly rarer (more desirable? I'd rather have a Fancy Vivid Yellow) than any colourless diamond.


Clarity: perhaps IF/FL, but it's not a factor in desirability for many people. What the majority of people want is "eye clean", and diamond is the only gem that is assessed under 10x; everything else is with the unaided eye, so it's quite easy to argue that the clarity grades above VS2 are pretty artificial.


Cut: Apart from issues of personal taste, Tolkowsky's calculations are hopelessly simplistic and based on non-real-world assumptions (e.g. knife edge girdle, perfect symmetry), to the point that in the same publication Tolkowsky himself gives a very broad list of parameters that according to him correspond to beautiful and brilliant stones. Same for all those you attached - average crown and pavilion only tell a part of the story. Important, but just a part.


Size: again, desirable in what sense? Over 10 carats, wearability is significantly limited. When you look at stones that can be found in large facetable sizes (aquamarine, tourmaline, topaz), they generally go down in price/carat over about 20 carats, and they are more difficult to sell. You may be trading off rarity (and perhaps price; at that level the market is so rarefied that price/carat is an after-the-sale calculation, not a guideline) for liquidity, so again, what is perfect?

Edited by davidelevi
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I get what you're asking, I really do, and I'm sure Davide does too. It's just not that easy a question.


Tolkowski's math was pretty good. 40.7 degree pavilion angles and 34.5 degree crown angles product good light return and internal reflection although this isn't the only combination that does. The knife edge girdle is a durability risk but it doesn't affect the math. He liked 54% tables but modern taste leads to more like 58-60. 8 fold symmetry, which is the 'typical' facet pattern seems to be popular but it's completely unrelated to the math of it. That's pure fashion and tradition. If you want to do it as a math problem, the classic Hearts and Arrows cut is a solid and safe bet although I won't call it 'best' for reasons described above.


By the way, I won't call D color's best either, and for the same reason. They cost the most, but color is not one of those things where one is better than another. Buy what you like and what suits your taste.

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To compound Neil's answer:


It was demonstrated using the same type of ray-tracing method that Tolkowsky used that a 58% table gives a brighter cut than the original T specification of 53%, so which "prescription" do you pick?


Secondly, all the "old" cut models (Eulitz, Parker, Eppler, etc.) all used a very simplified ray tracing that starts from a perfectly symmetrical diamond and within that considers only 16 facets that correspond to less than 50% of the gem surface (although they define its contour). The so-called minor facets have a considerable impact on the looks and the performance of the diamond, and they are taken into account in more sophisticated models.


Thirdly, and perhaps most importantly, there are different aspects to a diamond's optical performance, To lead things to extremes, a bathroom mirror is almost perfectly brilliant (it returns almost 100% of the light that it falls on it), but it is supremely uninteresting because it lacks any contrast, scintillation or fire. A prism that creates a rainbow out of an incident ray of white light has a lot of "fire", but it has no reflection and demands unusual observation angles (for a jewel) to see the effect. You can hardly call either one beautiful, yet from a mathematical point of view they are "optimal" (100% reflection or 100% diffraction).


Each declared "optimal" cut has a different balance of these four effects (brilliance, contrast, scintillation, fire), and ultimately the choice depends on personal preference. The recent (last 20 years) market preference - or marketing if you want - has been towards very symmetrical, extremely bright cuts to the expense of fire, contrast and a certain uniqueness in light patterns. But it's a market trend, not a mathematically necessary condition or even a demonstrated improvement over different preferences*. For example, I prefer "older style cuts, that have less brightness but greater contrast and fire, and they are probably what GIA calls "fair" cut. No matter how much maths you do you cannot call me wrong, nor can I say that those that prefer a modern superideal AGS 000 are in any way wrong. We are simply (in mathematical terms) pursuing different goal functions.


* There is a sense in which the introduction of the GIA and AGS cut grading systems has led to improvement: the average cut quality of the round diamonds for sale has improved considerably in the last 10 years, and nowadays finding a (GIA or AGS graded) poorly cut diamond is quite difficult. Most anything that is on the market has decent light return, and some contrast and fire. Whether the balance struck is "optimal" is again up to individual choice.

Edited by davidelevi
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