Sea sponges are the only animals that do not have radial or bilateral symmetry.
All members of the animal kingdom display some type of body symmetry. The most common types are radial and bilateral symmetry. Radial symmetry exists in animals that can be cut evenly along multiple planes. Animals that can only be cut evenly along one plane display bilateral symmetry. If an animal cannot be cut evenly at all, it has asymmetry.
Radial Symmetry
Radial symmetry exists when an animal can be cut in half in multiple locations along many different planes. In radial symmetry, the center of mass is exactly in the middle of the organism. All parts of the organism at equal distances from the center are identical in both shape and size. Typically, radial symmetry exists in animals so they can reach objects in their environment. They need radial symmetry for this purpose because they are typically immobile.
Bilateral Symmetry
Animals with bilateral symmetry can only be evenly dissected along one plane. If they are cut in half in any other parts of their body, the resulting bodies would not be identical. In animals, bilateral symmetry usually occurs longitudinally, meaning it exists along the animal's back. Bilateral symmetry is the most common type of symmetry that occurs in animals. It is usually reserved for mobile animals.
Animals with Radial Symmetry
Jellyfish are a Cnidaria and have radial symmetry.
Radial symmetry is typically exclusive to Cnidaria. Certain types of Echinodermata, a classification that includes anything from star fish to sea cucumbers, display radial symmetry as well. Sand dollars are the best example of Echinodermata with radial symmetry. They can be dissected evenly along multiple planes. Sand dollars are considered pentameral, meaning they can be dissected along five different planes. All Cnidaria including jellyfish, corals, and anemones display radial symmetry.
Animals with Bilateral Symmetry
Animals as small as ants have bilateral symmetry.
Anything that is not classified as a Cnidaria or Echinodermata will most likely display bilateral symmetry. This includes animals in the Flatworm, Mollusk, Annelid, Roundworm, Arthropod and Chordate phyla. Humans display bilateral symmetry. If a human was cut from the top of his head to the middle of his pelvic bone, the two resulting bodies would mirror each other. Each body would have exactly one ear, one half of a nose and mouth, one eye, one arm and one leg. Another example of bilateral symmetry exists in small mammals such as possums. If a cut was made down the back of a possum, the resulting bodies would be identical.
Asymmetry
A third, less common type of symmetry is asymmetry. It is exclusive to Porifera, more commonly known as sponges. Animals with asymmetry cannot be evenly cut. When they are cut in half, the two resulting bodies will never be identical.
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