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Wet sand to 2K grit and then 0000 steel wool with polish. That usually gets them pretty shiny, unless of you have a buffer

This is another good source
White Mother of Pearl, Bone and Horn Flat Pieces items in Pietra Dura Etcetera store on eBay!

I find the horn very easy to work with. It machines easily with standard woodworking tools. Follow a sanding progression into 2K and then some polish and you will be golden. It also finishes up...