The Calypso, docked on the underside of the saucer section
The Calypso was a Federation captain's yacht that was in service to Starfleet in the latter half of the 24th century, attached to the USS Enterprise-D. (Star Trek: The Next Generation)
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Background
The Calypso was never seen in use or mentioned in dialog, but its designation comes from the Star Trek: The Next Generation Technical Manual. It was named for Jacques-Yves Cousteau's ship Calypso by Patrick Stewart. Production staff wanted to use the yacht in episodes such as TNG: "The Neutral Zone" and "Samaritan Snare", but budget restrictions prohibited building a miniature and sets. Captain's Yachts did not become part of Trek canon until the debut of the USS Enterprise-E's Cousteau in Star Trek: Insurrection.
The reference work Star Trek: Starship Spotter categorizes the Calypso as a Mark I Captain's Yacht.