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Use coarse sandpaper moistened slightly with water. Rub this over the geode to sand out any rough patches. Keep sanding the geode until it's as smooth as you want. Be gentle at first and increase pressure as you sand. Some geodes are softer than others, and you want to avoid damage as much as possible. Small bits of stone may fly off your geode while you polish it. Before you start polishing, put on a pair of protective goggles to keep yourself safe. Use a heavier fabric like denim to add a commercial finishing polish to your geode. Rub down the geode gently until it's as shiny as you want. You can buy commercial finishing polish for gems online or at some hardware stores.
Sand your geodes. Put on protective goggles. Polish your rocks.