Unlike polishing metal using ceramic or porcelain media, water and soapy compounds, plastic often requires a different process. The pictures show a before and after of a molded acrylic part that required an absolute clear finish after processing. Polishing this type of plastic typically works best with dry, barrel tumbling. The heat from the tumbling process is trapped inside the barrel and enhances the polishing effect. A vibratory tumbler will typically allow that heat to dissipate.
The opaque original part (first picture) was tumbled in a barrel using Hardwood Pegs and Microlyte Polishing Cream for more than 12 hours (second picture). This long cycle time allowed the fine polishing agents to slowly create a polished and clear finish. Adding a pre-polishing step (also as much as 24 hours) with a slightly more abrasive cream will help to produce a very clean and clear surface.