So far, we’ve examined the roots of lapidary from the caves of ancient man to the steam powered factories of Victorian-era Boston. From table cuts to European cuts, we have watched the diamond shrink, grow taller, gain facets, shrink down again (while gaining even more facets), and both gain and lose a table around its middle. This next step in our diamond cutting story brings us to the discovery of a cut that is mathematically “perfect”: the round brilliant cut diamond.

Up to this point, we’ve been able to convey the work of diamond cutting using rough geometrical explanations. Unfortunately, the ability to get by with a mere “it was a round diamond” can no longer suffice, as the Transitional and Modern Brilliant cut are incredibly similar upon first glance. Their differences require an in-depth understanding of a diamond’s anatomy.

Diamond Anatomy

A diamond is comprised of two sections: the crown and the pavilion. The crown is anything above the girdle, a thin, usually polished edge which serves as the transition point of the top and bottom of the diamond. The girdle is primarily where certificate numbers are inscribed on a diamond if the stone is certified and inscribed.

The pavilion is anything below the girdle and serves as the base of the diamond which is usually hidden beneath the band of a ring. The table is the flat face of the diamond, and it is surrounded by facets which lead to the girdle’s edge. Dip down below the girdle and the facets continue, running in sharp lines until they reach a fine tip known as the culet. So if one were to examine it as a sliding line, it would look like this: Table, facet, girdle, facet, culet.

Still with us? Great! Let’s get way more complicated.

If you were to get down to an infinitesimal tiny scale, you’d find that diamonds are carbon atoms that are arranged in symmetrical repeating tetrahedral arrangements. This constant stacking results in diamonds having what are known as cleavage planes. It’s these planes that allowed early diamond cutters to smack a diamond and crack it into pieces to create cuts ranging from the hog back to the table cut. In modern diamonds, these planes run parallel to all their beautiful faces. That’s how those faces got there in the first place; a lapidarist had the skill and the tools to cut and polish the diamond just in the right place to make it sparkle. But each of those cleavage planes runs down the side of the diamond to its pointed tip. Without a culet any type of damage to the bottom of the diamond can result in a split going all the way up the pavilion.

Yes, diamonds are the hardest substance known to man, and yes, they can still break.

At the same time, large culets have their drawbacks. Some people don’t like looking into an old mine cut or old European cut and seeing the open culet staring back at them. The open culet sets a limitation on the amount of brilliance a stone is capable of producing. We want a stone that blinds someone with sparkle from across the room, and you can’t have that sort of blazing brilliance and keep the open culet.

Marcel Tolkowsky and the Math Behind Diamond Cutting

Marcel Tolkowsky was born in Belgium in 1899, the son of a Jewish diamond cutter from Poland. Before the age of ten, Marcel had already learned how to cut a diamond from the lap of his grandfather Abraham Tolkowsky. In his younger years, Abraham had been at the center of the diamond supply route for European nobility. The legacy of diamond crafting had already found its home in the next generation; his sons, Samuel and Maurice Tolkowsky, were making great strides in continuing the family legacy. Maurice is credited with inventing the first bruting machine in 1840. Innovation clearly ran in the family. But it was his son Isadore who fathered Marcel.

Overseen by his grandfather, Marcel soaked in the craft like water to a dry sponge, realizing that his family members weren’t artists so much as they were scientists. It was ironically this lack of romanticism which would allow him to push the diamond past its original confines of hand shaping. Determined to give himself the best foundation for success, Marcel settled on the idea of being a mathematician. He would leave the dusty confines of his family’s beloved polishing workshop to advance his studies abroad.

The year 1919 found Marcel in England, studying for his PhD in mathematics at the University of London. Like any PhD student, he would have to write a dissertation that could stand up to the scrutinization of a panel of grueling experts. If he pleased them, he would do his family the honor of being named Dr. Marcel Tolkowsky; if he failed, his efforts would all be in vain and he would return to Antwerp sans PhD. Marcel was prepared. He, unlike the majority of his peers, had known from the very beginning what he wanted to use as the topic for his dissertation. He would bring before the judges a study of light refraction in diamonds and would use the field of mathematics to create the most pristine diamond cut the world had ever seen.

You might be shocked to learn this, but despite the public’s long adoration for diamonds, Marcel was the first person in recorded history to make a mathematical study of it. Plenty of people had fawned and fretted over pretty diamonds; no one had dared to ask the question of “Is there actually an ‘ideal’ diamond cut? How do we make it repeatable?” Diamonds had long been romanticized for fear of the sterility of science. What would happen when they crossed the final barrier?

He found his recipe for success, and it contained the following requirements:

The diamond had to have 58 facets. 38 of those facets would be cut onto the crown of the diamond, and 20 would be below the girdle on the pavilion. The table of the stone should take up roughly 53% of the surface area, with a 16.2% rise above the girdle. The crown had to be at a 34.5° angle, and the pavilion had to be at 40.75°, with an ideal depth of 59.3%. Finally, the diamond would come to an obvious point on its pavilion. This formula culminated in a stone which mathematically produces the maximum amount of light reflection possible from the top of the diamond: “The Modern Brilliant Cut”.

How Diamonds are Cut Today

The diamond was once the most mysterious stone in existence, the only one unable to be altered by human interaction. Over many millennia, humans made small advancements in knowledge or technology that allowed for us to slowly, yet exponentially increase our ability to maximize life inside these beautiful miracles of nature. First, different types of skeifs allowed for stones to actually be polished, and primitive forms of diamond saws allowed for stones to be shaped with cleaving. Things kept moving forward and eventually there was a breaking point. The steam powered and then electric powered bruting machines were invented towards the end of the 19th century, in 1919 Marcel showed the world the math that proved how to maximize sparkle from a diamond, and in 1926, the electric diamond saw was invented, which allowed for more precise sawing of a diamond.

In a very short period of time (1870s to 1920s – about 50 years) the tools for how to fashion a diamond came into existence, as did the fundamental knowledge for how to unlock its beauty, as did new sources of natural diamonds that were finally able to satiate the world’s hunger for them. Fast forward to today, and diamond cutting is controlled more by AI, lasers, computers and other machines than it is by humans. Humans have finally conquered the unbreakable stone.


Decades ago, it took a seasoned diamond cutter to look into a rough diamond to find all inclusions and blemishes before planning out the shape of the final stone(s). Today, laser mapping documents every detail of the stone, and AI powered planning technology proposes to the user how to maximize profit from the diamond.


Marking is when a diamond cutter makes a mark on the stone to suggest where it needs to be cut to create the desired shape. Many decades ago, this was accomplished with ink from a pen. The 21st century diamond cutter will use a laser to etch a mark in the stone to guide the cut. Considering the slightest wrong angle or location could be catastrophic to the stone, things have come a long way.


Once upon a time, the only way known to break a diamond in two pieces was to hit the stone at its weakest plane with a hammer. Then, many years later, the diamond saw (a saw coated with diamond dust) allowed to diamonds to be sawed apart, but that took excessive human capital and oh so much time. Diamond cutters of today have access to lasers and other types of cutting machines that allow us to do the work much more precisely and much faster.


Bruting is when a rough diamond is shaped into the general end shape of the stone, and polishing is the practice of adding facets to maximize the light reflection through the top of the stone. These processes used to be painfully slow and take a toll on the humans working these machines. Once again, in the 21st century, technology has opened up new doors and possibilities. Machines are now capable of creating the ideal shape for the stone, without worrying about a human’s ability for errors, and automated faceting machines can place every facet exactly in the right spot to maximize brilliance or profit.

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