You searched for: “zooids
zooid (s) (noun), zooids (pl)
1. An animal cell capable of independent existence or movement: A zooid can be an ovum or a spermatozoon, or the segment of a tapeworm.
2. An individual invertebrate animal that reproduces nonsexually by budding or spliting: A good example of a zooid can be one that lives in a colony in which each member is joined to others by living material, e.g., a coral.

An individual zooid forms part of a colony and is characterized by a more or less fixed base, columnar body, and free end with mouth and tentacles.