Cut off and discard peel from jicama; rinse jicama. Rinse cucumber; trim and discard ends. Rinse cantaloupe, watermelon, and honeydew; cut off peels and scoop out seeds. Cut jicama, cucumber, and melons into 1/2-inch cubes. Trim and discard tops and roots from radishes; rinse radishes and thinly slice. Attractively arrange trimmed produce on a large platter along with cabbage and grapes.
Just before serving, pit and peel avocado. Cut into 1/2-inch cubes and coat with lemon juice; add to platter. Sprinkle with peanuts or offer peanuts alongside. Serve with orange crema.