1. Preheat the oven to 250°. Drop the potatoes into a large pot of lightly salted boiling water (enough to cover them) and boil them briskly until they are tender.
2. Meanwhile, make the sauce by combining the onions, lemon juice, fresh chili, salt, black pepper, Cayenne pepper and oil, and beat them together with a whisk or fork. Drain the potatoes and mash to a smooth puree with a fork, potato masher or electric mixer.
3. Beat in the sauce, a tablespoon at a time, and taste for seasoning. Mound the potatoes in the center of a large heatproof platter and cover the platter loosely with foil. Keep the potatoes warm in the preheated oven.
4. Into each of two 3. to 4-quart saucepans pour about 2 quarts of water. Bring to a boil and drop in the sweet potatoes and yuca. Boil briskly, uncovered, for 20 minutes, or until the vegetables are tender.
5. Then remove them from their pans with a slotted spoon and arrange them around the mashed potatoes. Cover the platter again and return it to the oven.
6. In a heavy 3-quart saucepan, bring 4 cups of water to a boil over high heat. Drop in the shrimp and cook them, uncovered, for 5 to 8 minutes, or until they are firm and pink.
7. Drain them and peel off their shells. If desired, devein them by making a shallow incision down their backs with a small knife and lifting out the black or white intestinal vein.
8. While the shrimp cook, bring 2 quarts of water to a boil over high heat in a 4-quart saucepan. Drop in the corn and boil, uncovered, for 5 to 10 minutes, until the corn is tender. Drain in a colander.
9. Remove the platter from the oven and place the corn on it. Alternate the shrimp and cheese triangles in a circular design on top of the potatoes. Add the olives and eggs to the arrangement, and serve at once.
