Two interesting facet cutting articles in English from Hubert Heldner and International Gem Society:
What is the average gemstone faceting yield?
https://www.gemsociety.org/article/what-is-the-average-gemstone-faceting-yield/
Perfect faceting angles versus excess weight
https://www.free-form.ch/ceylonschliff.html
The work of the lapidary (facet cutting)
The purpose of faceting for coloured stones is to give the raw material an optimal performance in terms of brilliance.
It is therefore necessary to analyse and respect the characteristics of each stone, in particular the optical axis, the pleochroism and the possible colour zones.
The lapidary will always be confronted with the cornelian choice to maintain a higher carat weight, therefore more interesting from an economic point of view, even if it means letting more or less visible inclusions appear or reducing the stone as much as possible in order to opt for a high purity.
– First step:
Choose a rough stone for its colour, it must be neither too light nor too dark, its purity by scrupulously identifying the inclusions that are too disturbing as well as the cracks and also for its shape which must not be too flat.
– Second step:
Find a diagram of suitable size so as not to lose too much material. However, expect a loss of about 70% on average! Precision cutting techniques used today do not put weight first but optical performance. The sizing diagrams that have been used for a number of years have been developed with the help of software in order to obtain the best possible brilliance.
– Third step:
Begin to preform the stone to eliminate the areas that are too included, take into account the axis with the best colour and give it a shape close to the chosen size diagram. (pear, oval, rectangle, cushion,…).
– Fourth step:
Source: H. Heldner