Before I went off February 1st for ten wonderful days in Tucson, I was trying some variations to better understand how different facet placements would impact the resulting gem. While there are software programs that will attempt to do that for flat facets, concave facets and fantasy variations are not included. So I set up several stones and cut them with the same flat facet pattern but differences with the fantasy machine cuts. (Besides, faceting is more fun that sitting at the keyboard.)
The first one is a 12.61 carat lemon citrine which has all of the pavilion row of facets done with the regular mandrels for concave work. It is 14.6 mm. across, so I managed to work in more facets than I have been using in some of the smaller hexagons.
Using that same flat facet arrangement, I did two somewhat smaller amethysts. For one, a 6.60 carat, 12.8 mm. stone when done, I used a rounded fantasy wheel and made some small curved cuts. These added some "lights" which seem to be inside the stone.
On the other amethyst, which finished at 5.65 carats, 11.2 mm., I added a lot more of these compound concave "facets". It looks like the stone is full of glitter.
For a totally different variation, after returning from Tucson, I tried something along the lines of the demonstration done at the USFG seminar on Fantasy cutting. For this one, which is 5.40 carats and 11.0 mm. across, I used a slitter and cut grooves from the culet most of the length of the corner facets. These were left unpolished and they are reflected by the other facets to give the appearance of having many more grooves than were actually created.