Cover 6 baking sheets with aluminum foil, and lightly grease each. Arrange 6 lollipop sticks in parallel rows on each sheet. Set aside.
Combine sugar, corn syrup, and water in a 2-quart saucepan; stir well. Cook over medium heat, stirring frequently, until sugar dissolves. Cover and continue to cook over medium heat 2 to 3 minutes to wash down sugar crystals from sides of pan. Uncover and cook, without stirring, until mixture reaches soft crack stage (275°). Remove from heat, and stir in peppermint oil. Pour syrup evenly into 3 small saucepans. Add 3 drops food coloring to each portion of syrup, using a different color in each. Stir well, and place each saucepan over low heat.
Working rapidly, with 1 portion at a time, drop hot syrup from tip of a tablespoon over alternate ends of lollipop sticks to form circles, 2 inches in diameter. Cool completely. Gently remove lollipops from aluminum foil, and wrap each tightly in plastic wrap or cellophane. Store in a cool, dry place.