You may find the recent aticle from the International Gem Society site. The artical is the History of Lapidary and was written by Dr. Gerald Wykoff.
He shows a progression from
point cut
table cut
Old Single cut
Sancy Cut
Apex Cut
Rose Cut
Mazarin cut.
Old European cut
I don’t know what you expect, but the oldest designs seem very simple. and probably evolved from the crystal shape of a diamond. The crude methods available for cutting and shaping were so labor intensive that cutters wanted to remove a minimum material.
Also, there doesn’t seem to be much documentation until the 1400’s. When a Louis de Berquen developed technology and the “Sancy design”. This seems to have been a critical design where break facets and the design of the pavillion became important.
This history is really the story of diamond cutting. Not much attention is paid to colored stones. I don’t know if there is a separate evolution for colored gems or not.
I’m cutting replicas (from clear quartz) which has already lead to some unexpected results due to the large difference in diffraction.
There is a story here, and a lot to be learned, but, I am not sure of what you expect to see.