Toothpaste is used for brushing teeth, and it works for this because it has extremely fine abrasives in it that polish your teeth. I squirted a bit of toothpaste onto my plate and then used a cloth rag to rub it around. I scrubbed until the toothpaste became grey with aluminum and then washed it off. I repeated this process for about two hours.
Finally, at the end of the laborious process of sanding and polishing, I cleaned the plate off with a toothbrush and soap to remove the minty fresh smell. After drying the plate, I was stunned to see that it was really and truly shiny! I hadn't expected a lot from the toothpaste, but it did a dazzling job of shining up the cast plate. I was quite pleased with the end result of the casting, sanding, and polishing.