Polish travertine floors every six to 12 months if they're in a high-traffic area. For travertine countertops that are used infrequently, polish every three years.
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Wipe the travertine with a damp cloth to remove any dirt or debris.
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Sand the tile using 400-grit sandpaper in a circular motion, with just enough pressure to remove only the imperfections on top of the tile. Wipe the travertine when you are finished sanding.
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Go over the travertine with 600-grit sandpaper to make the travertine shine a little. Take care to remove all the scuffs from the previous grit.
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Finish up the sanding with 800-grit sandpaper. This should leave the surface as smooth as possible.
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Use a buffing pad to buff the travertine to a glossy shine.