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HCA - Defining the Beauty and Desirability of Round Brilliant Diamonds

Inverse relationship between Crown and Pavilion Angles

After studying diamond cut as a student in 1984, and while buying and selling diamonds in my business, I observed that small variations in pavilion angles could be compensated for by a larger inverse variation in crown angle. Over time I formulated an approximation of 2C to 1P and I used this discovery secretly and commercially to buy a larger range of beautiful diamonds than the commonly applied tolerances based on Tolkowsky’s design criteria.
 
Diamonds in Figures 1 and 2 show a wide range of proportions that look and perform with similar characteristics. Knowledge of this inverse relationship between crown and pavilion angles makes it possible to cut diamonds more efficiently from the normal distribution of economically viable diamond rough. When buying diamonds with an Ideal-Scope I would find diamonds with proportions like these that had a beautiful appearance.

Figure 1. Even though the crown (top) of the blue profile is 6.5° steeper a compensating or inverse reduction in pavilion angle of just 1.2° results in similar ray paths. The red profile diamond weighs less and will be shown to have a higher light return, diamonds with shallow crowns and deeper pavilions are described here as a brilliant ideal cut (BIC). The steeper crown on the blue profile improves fire or dispersion, while the reduced pavilion angle optimizes light return. This steep / shallow combination is called a firey1 ideal cut (FIC). Figure 2 shows images of diamonds with these proportions that would be considered poor and extreme under existing cut grade standards.

It appears there is also a less critical relationship between crown and pavilion angles and table sizes. This would warrant further study.