Using peeler, cut 8 twists from grapefruit skin; reserve for garnish. Slice off remaining peel and white pith; discard. Slice fruit into segments. In cocktail shaker, muddle 1 grapefruit segment. Add 1/4 cup gin, 1/4 cup grapefruit juice and 1 tsp. vermouth. Fill with ice; shake until very cold. Strain into chilled martini glass; garnish with grapefruit twist. Repeat with remaining ingredients.
