How many types of body symmetry found in animals?

Body symmetry refers to the similarity with the arrangement of parts on the opposite sides of the body of a three dimensional animal.
(a) The body of some animals cannot be divided into two equal halves in any plane. Such animals are called asymmetric or asymetrical. e.g., some sponges.
(b) The body of other animals can be divided into two equal halves in one or more planes. Such animals are called symmetrical.
© The symmetrical animals may exhibit two types of symmetry-radial symmetry and bilateral symmetry.
(1) Radial Symmetry : If the body of an animal can be divided into two equal halves by cutting it in any plane passing through the central axis. Such a symmetry is called radial symmetry and the animals showing radial symmetry are called radiata.
(b) Radial symmetry permits an animal to detect food or danger approaching from any side, e.g., cnidarians, ctenophorans, echinodermates.
(2) Bilateral Symmetry : (a) In most mobile animals, the chief organs of the body are paired and are arranged on the sides of a central axis connecting head and tail.
(b) The body of such animals can be divided into similar left and right halves through one plane only. Such a symmetry is called bilateral symmetry and such animals are called bilateral.
(d) In bilaterally symmetrical animals, the sides, surfaces and ends of the body are clearly distinguishable. e.g., from phylum Platyhelminthes to Chordata.