Can anyone help me out with a specific name for this? I have heard of a twisted setting, but this seems to pertain to the ring itself. Just a regular princess setting, but instead of the stone mounted square shape, turning the stone 45 degrees making it look like a diamond shape.
That would be called setting the stone "en pointe". Personally, I don't like stones set that way because it leaves it open to a greater risk of damaging the prongs or the stone itself. It does, however, make the stone look a little larger.