Cut the pineapple: Slice off the top and bottom, then stand the pineapple up. Slice away the skin, following the curve of the pineapple, cutting deep enough so most of the “eyes” are trimmed away too. With a paring knife or the tip of a vegetable peeler, pick out any “eyes” still poking out from the fruit.
Cut the pineapple into half lengthwise and then into quarters. Slice off and discard the tough core center from each quarter. Chop into chunks about 1/2" big. Put the pineapple in a bowl.
“Supreme” the oranges: Cut off the tops and bottoms and stand them top sides up. Slice away the peel following the orange's contour, completely removing the outside white pith as well as the orange peel. Remove the segments by cutting between the fruit and the membrane. Discard any seeds and set the juice aside in a separate bowl. Add the supremes to the pineapple.
Cut the mangoes into cubes: Slice the fattest sides down and around the mango’s large seed. Cut a crosshatch into the pulp of each these sides, being careful not to cut down into the peel. Turn the diced pulp inside out in the skin and slice out the diced pulp. Add the mango to the bowl.
Peel the jicama. Cut into ¼-inch slices, and then slice into ¼-inch strips. Cut into lengths about 1-inch long. Add to the bowl.
Grate the zest from the limes and stir into the fruit. Juice the limes. Whisk the lime juice, agave nectar and chopped cilantro into the orange juice. Toss with the fruit.
Peel and cut the whole pineapple. Save the second half for snacks, smoothies or tempeh kebobs.