In 1919, Marcel Tolkowsky empirically calculated the ideal proportions of a round diamond as part of his Ph.D. thesis in Mathematics. An "ideal cut," according to Tolkowsky, has the following characteristics:
It should be obvious that finding a Tolkowsky diamond is an expensive undertaking. To complicate matters even more, recent studies by the G.I.A. have demonstrated that a 59% table yields a more brilliant diamond (as opposed to Tolkowsky's 53% specification). Jewelers tend to confuse the issue even more, since their version of the "ideal cut" will likely vary from day to day, as their diamond inventory changes. So how do you, the consumer, go about making the right decision with regard to cut? What tradeoffs can you make that will yield an almost ideal-cut diamond? Also, what if you prefer a non-round shape?
The laws of physics relating to light, as applied by Tolkowsky, are the same for all shapes of diamonds. When you decide to purchase a diamond that is not round, you have an inherently asymmetrical diamond, and therefore you sacrifice brilliance and fire.
The picture above shows the top view of a princess-cut diamond and two side slices -- one represented by the blue diagonal line, the other by the red horizontal line. Because the diamond is not symmetrical about its center, it is not possible to create a Tolkowsky cut. If the diamond is cut such that its horizontal slice has the Tolkowsky depth percentage of 59%, its diagonal slice will have a depth percentage of 42%. A similar analysis can be done for ovals, marquises, hearts, and all the other fancy shapes. This is not to say that non-round cuts are inferior -- a fancy-cut stone can make a beautiful, distinctive engagement diamond. But the bottom line is that if you want the most sparkly, brilliant diamond possible, you should buy a round stone.
If you want the most "sparkly" diamond possible, you should buy a round shape. Because of their asymmetry, non-rounds will not sparkle as much. If you are set on buying a fancy (non-round) diamond and want the most sparkle, the tables on the next page will summarize the most important dimensions in each of the popular shapes, along with suggested guidelines.