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The Nine Types of Animal Phyla Essay Preview: The Nine Types of Animal Phyla Report this essay Porifera and Cnidaria are the phyla that lack organs. Porifera dont have symmetry in their body plan. Cnidaria have radial symmetry. Platyhelminthes, Nemadota, Annelida, Mollusca, Arthropoda and Chordata are all the phyla that show cephalization. Porifera and Cnidaria.