The Basestar is the Cylon counterpart of the Colonial Battlestar. The Basestar has also been called a Baseship and a Cylon Battlestar in one episode but "Basestar" conforms to the Colonial ship naming system.
The Cylon Basestar is a superior warship to a Colonial Battlestar in a technological respect as it carries stronger weapons in greater quantity and carries a greater fighter complement as well. Because of this, the Galactica and her crew prefer to avoid combat with them as much as possible. They are propelled by a reactionless drive that appears to make the ship spin slowly on its axis while engaged. Basestars are considerably larger than Battlestars. More information of the Cylon Basestar at wikipedia.
You can download this papercraft model template here: Battlestar Galactica - Cylon Basestar Starship Free Paper Model Download