Kollos, the Medusan ambassador
The Medusans were a telepathic non-corporeal race. Their thoughts were the most sublime in the galaxy, however, their physical appearance was exactly the opposite. Their appearance was so utterly hideous that the sight of a Medusan renders any Human mad. Vulcans were capable of viewing Medusans, but only with the use of a specially filtered visor. For these reasons, Medusans usually used an opaque carrier pod when interacting with other species. The Medusans were renowned for their navigational abilities. (TOS: "Is There in Truth No Beauty?")
List of Medusans
Background
The Medusans were named for the Greek mythological character of Medusa whose sight was so hideous that anyone who laid eyes on her was turned to stone.
Due to the facts stated above, it is unknown how Medusans came to interact with other member species of the Federation. Due to their effect on humans, integration into Starfleet seems unlikely, as does the placing of ambassadors at the Federation Council.
According to the story outline and script of the episode, their name was spelled "Medeusan", while the the non-canon Star Trek: The Next Generation Officer's Manual spells it "Medusan". The Officer's Manual also states that Medusans were permitted to serve in Starfleet as emergency navigators onboard Template:ShipClass starships. Such Medusans were honorary Lieutenant Commanders and had special quarters off of an emergency navigation center which kept them isolated from the rest of the crew.