Arrange the lettuce leaves so that they cover the platter.
Mix the rice and corn and place in the center.
Slice, dice, or grate all the vegetables and cheese.
Place half of the cucumber on one side of the platter and the other half directly opposite. Repeat with carrot, peppers, and cheese, so that you have colorful, alternating piles of food.
Serve with your favorite dressing on the side.