Grate 1 teaspoon of rind from an orange and then mix it with 2 tablespoons (1 ounce) orange juice, oil, cumin, salt and pepper. Whisk together and set aside.
Remove peels from oranges, grapefruit; split them into wedges and add to a large bowl with orange rind mixture; add beets shelled pistachios and edamame. Stir to coat evenly.