>>10166219Polishing wheel and polishing compound. I've polished many pieces, not just transparent ones with them using my bench grinder.
You just have to be careful, hold the piece in a way that the wheels won't catch it, and do it gently as too much pressure can built too much friction that can melt / damage the plastic.
I actually polished a fuck ton of my old childhood lego pieces last year, they had been in large tubs for decades and had quite a lot of scratches, and I stacked the bricks on each other making walls and then polished multiple pieces in one go. Was very time consuming but produced good results, the pieces were actually shinier than new pieces when done.
Also for tiles it's a great way to just stack a bunch of tiles on some flat 6x14 or larger plates, then just polish a bunch of them in one go.