An animal that has body parts that are arranged around a central point has

The answer is - radial symmetry.

The radial symmetry basically represents a central basic part and predominantly equally arranged other parts around it. In the animal kingdom this form is not the most often, it is usually found at animals that lack bone structure, and there's a very small (usually) body and much longer body parts arranged around it. The best examples for this are the starfish and the octopus. It's interesting that in the animals that do have this body shape it is pretty common that the parts around the body can function on their own and act independent from the central body, or in general are much more autonomous in their functioning.