Almost any type of lapidary rock can be polished.
Polishing a stone requires that the stone be ground down using progressively finer grades of sandpaper or grit. This grinding is usually done with a fixed wheel grinder with sanding belts attached to a rotating wheel. There is usually a water source added so that the cutter does not breath in the dust. Once the stone is very smooth there are several types of polish and buffs that are used on different materials to give it a glossy finish. The buffs are also mounted on a rotating wheel.
Stone slabs are usually sawed, then ground and polished on equipment known as a Flat Lap. Slabs are put in to a plaster cast and lay flat on the grinder, sometimes for many days. It is difficult to polish a stone slab by hand and keep it flat with no scratches!