Quarter the grapefruits lengthwise and remove the pulp, reserving it for another use. Scrape as much of the pith from the rind as possible with a spoon, cut the pieces of zest in half crosswise, and cut them lengthwise into 1/4-inch-wide strips. In a kettle cover the zest with 4 cups of the water, bring the water to a boil, and simmer the zest for 10 minutes. Drain the zest, refresh it under cold water, and repeat the simmering, draining, and refreshing process 2 more times. Sprinkle each of 2 jelly-roll pans with 1 cup of the sugar. In the kettle combine the remaining 2 cups sugar, the remaining 1 cup water, and the corn syrup and boil the mixture, washing down any sugar crystals clinging to the side with a brush dipped in cold water, for 3 minutes. Stir in the zest and simmer it, stirring occasionally, for 15 minutes, or until the syrup is thickened. Continue to simmer the syrup, stirring constantly and being careful not to let it burn, until a candy thermometer registers 230F. Transfer the zest with a for k to the prepared pans, roll it in the sugar to coat it well, separating the strips, and let it cool. Transfer the zest to racks and let it dry for at least 4 hours or overnight. The candied zest keeps, separated by sheets of wax paper in an airtight container lined with wax paper, at room temperature for 2 weeks or chilled for 1 month.