AGS has given us cut-grading standards for Princess cuts. Designs having pavilions with 2 chevrons came first and, just recently, those with 3 and 4 chevrons. I prefer designs with minimum facets because they give stronger 'bang-bang' on-off reflections/contrast that attract the eye; they also take less time to cut and offer less chance of cutting errors...

This article discusses the formation of scallops on an 8-pointed round brilliant where the break facets intersect a round girdle.

 

 

There are many theories about cutting ovals: many of them fail in the light of actual cutting. This article illustrates various concepts and discusses their faults or advantages. For those who care to know, it also lists depths, indexes (including special azimuths) and slopes for diamond.

This article shows an interesting effect of dispersion whereby color components are progressively diverted from the spectrum, as in 'fractional distillation' or 'fractional crystallization' of liquids.