In 2268, the USS Enterprise conveyed the Medusans' ambassador to the Federation, Kollos, along with Miranda Jones, to a rendezvous with a Medusan vessel following an unspecified diplomatic mission, and a short diversion through the galactic barrier. Jones had originally intended to mind link with Kollos once the two had reached the Medusan vessel, which was bound for the Medusan homeworld; however, circumstances forced the link to be established aboard the Enterprise. (TOS: "Is There in Truth No Beauty?")
The Medusan vessel went unseen in the original airing of the episode, only being referenced in dialogue. Indeed, the original ending sequence had the Enterprise approaching the Medusan homeworld. This was altered in the 2008 remastered version of the episode, where a CGI model was created for the vessel.
Based on information obtained from Michael Okuda, no name or registry number was specifically assigned to the model. In terms of its design, Okuda added that "the basic idea was Dave Rossi's suggestion. He thought that because the Medusans were non-corporeal and might not have developed technology as we know it, they might use Federation hardware, so their ships could have a distinct Federation style."
According to Issue #92 of the Star Trek: The Official Starships Collection, the Medusan vessel was a type of transport and diplomatic vessel used by the Medusans. This class was approximately 90 meters in length, had a maximum speed of warp factor 6, and a crew complement of 30. It was equipped with phaser emitters.