Butter 10 assorted metal cookie cutters and place on a parchment paper-lined baking sheet; set aside. In a large heavy saucepan, combine the sugar, water, corn syrup and cream of tartar. Cook and stir over medium heat until sugar is dissolved. Bring to a boil. Cook, without stirring, until a candy thermometer reads 300° (hard-crack stage). Remove from the heat. Stir in oil, keeping face away from mixture as odor is very strong. For each color of candy swirls, pour 1/4 cup sugar mixture into a ramekin or custard cup; tint red or green. Immediately pour remaining sugar mixture into prepared cookie cutters. Drizzle with colored mixtures as desired; cut through with a toothpick to swirl. Remove cutters just before lollipops are set; firmly press a lollipop stick into each. Sprinkle peppermint candies over tops if desired. Yield: 10 lollipops.