The first thing I'm inclined to say is: Have you EVER seen a professional installation which left an
exposed edge in a sheet of 1" marble mosaic?
NO, and there's a reason for that: The numerous and easy-to-damage lines of exposed grout are going to get beat up, and the tiles will probably get bumped loose over time.
The second thing I'll say is a restatement of a point Dave made: It's very likely that the "polish" on your mosaic sheets is
not a genuine "polish", created using abrasives and acid melting of the pure marble: rather, it's much more likely a due to a color/shine enhancing chemical treatment-- basically, a "varnish" on the stone surfaces.
- - - -
But for the case of
genuine polished marble, without chemical treatments on the surface of the tile, here's what you
would do: get a set of P-grit wet/dry sandpaper sheets (very cheap on EBay), ranging from about 400 grit to 2500 or so. Each sheet should slightly larger than half the size of the preceding sheet. (Go from #400 to #600, not all the way from #400 to #800.) 400/600/1000/1500/2000/2500 makes a pretty good series for polished marble. All sanding is done wet, of course. A wet grinder is faster than sandpaper for working through the larger grits, but too violent for achieving an actual "shine" in marble via the finer wheel sizes (e.g. 3000 grit, 6000 grit, 8000 grit): The wheels are made to grind granite, a much harder stone, and they simply "tear up" marble too much to leave the shiny surface you want.
If the edges aren't flat already, then you'll need to set the first few pieces of sandpaper, WET, onto a piece of glass or polished granite tile in order to keep the paper flat for grinding the marble target surface into an equally flat surface. Don't press too hard-- this sandpaper is silicone carbide, MOH value approx. 9, and it will rip the marble to shreds, if you let it. The first grinding step is the long one, flattening any really big bumps in the area. Later grits need only about 10-15 soft, circular strokes each (do change directions halfway through), followed by a few linear strokes (lengthwise, not across the shorter up/down direction).
When you're done, it's smooth, but not yet shiny. DuPont's "shining powder" does a pretty good job; although the grit is slightly larger (2000 grit), a lot of it is tin oxide rather than aluminim oxide. Tin oxide is much softer (it can barely scratch glass), so the pieces wear down their own sharp edges while you use it, ending up in more gentle "ball-like" shapes. It also contain shellac, you're actually varnishing your stone.
On your mosaic edges, that's plenty good enough already. But for big, exposed bevels and faces on large polished marble tiles, people like me want even more: we want it match the finest levels of factory polish. In order to do that, without using chemical varnish/shellac agents, you have to do as the factories do: Oxalic Acid.
If you didn't get A's in your high school and college chemistry lab coursework, don't go there-- I think Dave is right in labeling this a "professional" technique, the chemical mix is dangerous. (You HAVE TO wear high-quality gloves and complete eye protection, and you need to have emergency water-wash equipment, at least a high-volume "monster" squirt-gun, loaded and sitting at the ready, in case there's an accident. After the squirt gun, you need to sit under the shower, blinking your eyes open and shut, for about 15 minutes.
THEN you go to the ER. Got it?) Oxalic Acid is only a "weak acid", not anywhere hear as dangerous as sulfuric or hydrochloric-- but at PH around 1.6, it's many times more acidic than lemon juice. So: before you read the rest of this post, Google for "Oxalic Acid MSDS", select a data sheet from one of the companies which sells it, and
read read the entire thing. Do it now; then come back and finish here.
They say things like "Very hazardous in case of skin contact of eye contact of ingestion, of inhalation.... Eye contact can result in blindness....Severe
over-exposure can produce lung damage, choking, unconsciousness or death." Believe it, these are the facts. A respirator is recommended, although I wear only an N95 mask. (My supply is in large crystals, not dust-like small particles.) Wear thick rubber gloves, the best of the "household gloves" sold at grocery stores. You MUST have coverage reaching at least 4 inches uo your arms-- the solution will splash a bit, while you're working, and you don't want to "enjoy" another 15-minute cold shower for the sake of avoiding chemical burns on your arms, either. If you're still thinking of using a to-the-wrist glove, or a pair of those ultra-thin medical lab gloves-- stop reading, this is not for you.
Put on your gloves, chemistry lab goggles, and respirator first. Then, in a glass bowl, not TOO large, but with plenty of extra room to prevent spilling over the edge, you make a small amount of fully saturated solution (room temperature). Keep the container of crystals and the bowl, as well as your scooping tool, TOTALLY dry while moving the crystals into the bowl. (Use about a tablespoon, until you have enough experience to judge for yourself.) Then add purified water , slowly and carefully, until the crystals dissolve. The amount of water is about 5x the volume of crystals.
Now reduce the concentration further, by adding roughly two more portions of the same size as you used to dissolve the crystals. (The ration of water to solid crystals, by volume, is now around 15:1.) Water into acid solution, NEVER "stronger" acid solution into water! Then microwave it for just a few seconds, it works better warm. (All glass equipment, of course, including the microwave turntable).
Set your tiles on one side of your working sink, WELL AWAY from the sink. A double-bowl kitchen sink works well for the actual work. Put your bowl of solution down in one sink, and grab a small piece of lint-free, CLEAN chamois. (I use small cut-outs of sham-wows, just a couple inches square after folding them up. You need to use a SMALL working cloth, you can't let it slop all over in an "uncontrolled" way.) Dip your chamois and start rubbing GENTLY. Keep it wet, and DO NOT leave an area unrubbed for more than a couple of seconds- even though it's still liquid, the acid will burn an uneven pattern into the surface it's left standing for just a few moments.
You're achieving the factory-like "shiny as a mirror" finish by actually melting the surface of the marble. Light pressure from the chamois causes more melt to occur on ridges, and less in valleys, leaving everything much smoother. Determining the "feel" of being done is mostly a matter of practice, and of watching how wet versus "filmy" the previously clear acid solution has become. When you think that you're about finished, at some more water from the tap into the folded chamois to thin out the solution; keep rubbing and adding more water, in ever-increasing volumes, until you've diluted the solution so much that's nearly inactive on the tile (and in the chamois).
Finally, rinse the gloves on both hands under the tap (between the fingers, too), and wash the tile. THOROUGHLY with a generous water spray-- you can't leave any acid behind, because it will etch the surface later. Dry the tile with a clean lint-free dishcloth. (Change those dishcloths often, too.) Check your work under a bright light, and "re-work" any spots which stil show flaws. Move the dry tile (or mosaic sheet) to a "finished work" area well away from the sink, where it can't get splashed on. Grab the next mosaic sheet, squeeze dry and reload the small "working" piece of chamois with more acid, and start on the next one.
It's slow, but the shine comes out so bright that you'll need sunglasses when you turn on the lights in the room.