What the gem cutter or faceter does is cut many facets or faces on the rough stone. A faceter starts with a piece of rough stone. For good quality the rough should be transparent and free of inclusions or fractures. One of the easiest and most common types of minerals to facet is quartz. Quartz comes in many colors.
Amethyst is purple or lavender quartz.
Citrine is yellow quartz. There are also rose quartz, smoky quartz, and chocolate quartz. Quartz has a hardness of 7 on the Mohs scale of hardness. Other popular minerals are sapphire, ruby, topaz, opal, and tourmaline. Sapphire and ruby are much harder than quartz.