When a stone has an overall polished dome shape we call it a cabochon cut.
A cabochon may be any of the shapes we have mentioned as well as a myriad of fancy or free form shapes. All cabochons have a smooth polished domed topside and either a flat or slightly domed underside. The underside is usually but not always polished.
A well cut cabochon has smooth all over even polish with no flat surfaces on the polished dome of the stone. The outer edge of a cabochon is called the girdle of the stone. It defines the outline of the stone's shape. An irregular girdle will give a stone an irregular and uneven shape. It is around or on the girdle that the setting will rest to secure the stone in the mount.
A cabochon cut is usually reserved for opaque or translucent gem material but transparent material can also be very beautiful when cut 'en cabochon'.
Freeform stones are often whimsical expressions of the cutters' art. They can be beautiful, precious small-scale sculptures, amazing works of art unto themselves and are often a hybrid combining elements of faceting and cabochon style polishing. Both transparent and opaque gem material are fashioned in this manner. Stones cut in the style are most often set in hand-made custom designed settings as they do not conform to traditional settings.