Peel, section, and seed oranges, tangerines, and grapefruit. Cut the rind of 1 orange into thin strips. Set fruit aside.
Bring orange rind strips, sugar, and gin to a boil in a saucepan. Reduce heat; simmer, stirring constantly, 15 minutes or until thickened.
Twist lime rind strips into 6 individual compotes; layer fruit sections in compotes. Pour warm syrup over fruit.