The rings are to work up, so they have to get turned on snaps, cutouts receives the case band, and beds for the hinges und their stop faces are among as well as drillings and threads etc.
Milling and drilling is not easy with acryl glass because acryl warms up and unexpected cracks develop. From this follows: sharp cutters, slow revolutions and a thoughtful working.
The outer profil is to turn on not before the cutouts are finished because the rings are better to clamp in a lathe if their shape remains still cylindrical.
Also the three crystal glasses were to select and set in turned snaps.