I suppose the simple answers are:
- yes, studies of facets and cuts have been done
- yes, to some degree, the cutting can help with attributions
The problems though, are numerous. Even just thinking about 19th century weights, we are faced with all sorts of variations in faceting / cutting. Many makers used simple round, flat cuts with 5, 6, 7 and 8 being often seen around the circumference. Some makers, St Louis in particular, seem to have enjoyed using all-over faceting, for which the only way to count to the number of cuts would be to mark each one as you count! There were many variations between the extremes.
In Identyfying Antique Paperweights Millefiori
, by George N. Kulles, published 1985, there is a section on "facets" which shows that is the overall style of cutting rather than a specific number of cuts that can help to make an attribution. But even then, the rest of the weight, its canes or lampwork, need to be checked to be sure.
As for cutting turntables being a factor in the number of cuts, as far as I know this did not apply to paperweights, where the cuts were "simply" marked out by hand and then actioned.
[Just for interest - A current Scottish cutter is apparently able to produce a complex, curved "Gingham" cut around the entire surface of a double-overlay domed paperweight without even marking it up!]
And just for more fun:
Leni mentioned "prunties". For the record, this should be "printies". But, as with many terms, there can be confusion through everyday usage. Paul Hollister Jr. wrote, in his Glossary to The Encyclopedia of Glass Paperweights
Facet. Decorative plane-cut surface having three or more sides.
Flute. Deep, narrow cut whose ends taper to a point.
Window. Any round or oval, flat, or concave cut through overlay that gives a view into the interior of the weight.
Printy. Any circular or oval concave cut on the outer surface of a weight. This nineteenth century term is here substituted for the American term, "punty," to avoid confusion with the term "pontil", for which punty is also a synonym.
Those of us who browse the main Glass forum know what fun we have when using terms such as "pontil" and "punty" to describe the unfinished mark on the base of pieces - it's just as much fun in paperweight-speak when talking about facets, flutes, windows and printies. Personally, I normally use "facet" to mean almost any cut on a paperweight, other than obvious "stars", cogs", "sprays" and the like. But according to my understanding of Hollister, I should not even use that word if the cut has less than three sides! And I am sure I have seen "flute" cuts on antique weights that do not have tapered ends (as per Hollister), but are just thin concave cuts - I wonder what I should "properly" call those?