They are probably something similar to Corian, although maybe not as tough. If they are a solid surface they can be polished. I would talk to someone who installs Corian or a similar type material, and ask them about polishing. Corian is not so widely used in residential applications (although I love it) but there is a lot of it in commercial applications, so you should be able to find an installer. Check around with some local cabinet shops if you have trouble finding a Corian installer.
Single empty-nester in Middle TN, sometimes with a friend or grandchild on board