The terrazzo floor is an old Italian method in which shards of glass, marble and other stones are pressed into concrete to form a decorative surface, then sealed and polished. Whether poured on-site or laid in tile form, terrazzo occasionally has to be re-polished and buffed to rertain its smooth, glossy surface. Rent a floor buffer and pads, and buy polishing powder made for stone or concrete floors (since terrazzo is basically both).
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Clean the floor with an neutral cleanser and rinse well. Starting in one corner, spray down a few square feet of the floor with a layer of warm water from a spray bottle. Sprinkle on your terrazzo polishing powder, coating the surface of the water. Spray a little more water to form a solution with the consistency of very thin oatmeal.
Use a 175-rpm electric floor buffer with a hogshair polishing pad. Mix up the solution on the floor and spread it around the area. Have more water handy to spray down and thin it as necessary; it should remain a "slurry'' while you buff, thin enough to spread around the floor but not so thin that it splashes. Buff systematically from left to right four or five times, slowly, covering the whole area. Then move on to the next section, putting down more water and polish. Continue until you've buffed the whole floor.
Rinsing & Polishing
Go over the floor with a wetvac, picking up the wet polishing slurry. Re-spray any areas that have started to dry, so you can get them up. Follow up by mopping the floor thoroughly with clean water with a little liquid stone floor cleaner added. Once it's dry, buff by hand with a soft, dry polishing pad.