Crown and Pavilion Angles
In 1992 I discovered an inverse relationship between a diamond's top and bottom facet angles which gives diamond cutters new freedom to retain more weight out of the rough diamond, and cut a beautiful gem. The shallow stone on the left has more light return. The steeper stone on the right has more fire. I call them BIC - Brilliant Ideal Cut and FIC – Firey Ideal Cut.
The overlain profiles show how similar the light paths are, even though the angles vary considerably.
This is common sense; but common sense is not common. Many labs use grading systems with minimum & maximum crown and pavilion angles that penalizes cutters who produce BIC's and FIC's. The American Gem Society Lab was first to adopt this 'inverse proportion' approach. GIA is likely to follow soon.
If you know a diamonds proportions, you can use HCA to check if it can be ideal.
The crown (top) angle on the orange FIC profile is 10 degrees steeper but the pavilion (bottom) is 2 degree shallower than the blue BIC stone - the variations compensate for each other. The light rays travel on similar paths.