While cut proportion is the most important factor in a diamonds beauty unfortunately there is no uniformity in either terminology or method of grading between the major laboratories.

The first problem the consumer will encounter is the fact some labs have a top grading of "Ideal", others "Excellent" and another "Very good"

The diagram below is a simple comparison of the various grading labs terminology but not the actual grading.

You may from time to time notice that Cut grade assigned on this web site are not the same as that recorded on the grading reports

For direct comparison purposes this web site assigns a cut standard based on the interpretation of the Tolkowsky Ideal Cut theorem that predicts a range of Ideal Cut proportions from Brilliant Ideals to Fiery Ideals.

This standard that acknowledges that there is an inverse relationship between the crown and pavilion angles is used by manufacturers of Super Ideal Cut diamonds and also AGS  

In simple terms if you increase the crown angle of a diamond and decrease the pavilion angle in the predetermined ratio you obtain a very similar optical effect. Shallower crown angles with steeper pavilions produce more brilliant diamonds and steeper crown angles with shallower pavilions produce more fiery diamonds.

If a cut grading system uses maximum and minimum crown and pavilion angles it can penalize some magnificent Ideal Cuts and upgrade some really poor cuts into looking like good performers on paper.

In the images below you will notice that even though the angles vary considerably the light paths of the two diamonds are very similar.

The diamond above has a crown angle 10˚steeper and a pavilion angle 2˚shallower than the diamond below, yet the light paths are similar

Here is a link to the Tolkowsky work edited by the mathematician Jasper Paulsen

 Diamond Design

A Study of the Reflection and Refraction of Light in a Diamond
by    Marcel Tolkowsky,   B.Sc., A.C.G.I.

with formulas showing how the best crown angle
and table size depend on the pavilion angle

See also University of Moscow's Diamond Cut Study Research

GIA and AGS Cut grading Criteria >>>>