Deneb IV was the fourth planet in the Deneb star system. This M-class planet was the homeworld of the Bandi.
History
Deneb IV was visited by Starfleet personnel as early as the 2260s, but in 2364, it was still at the edge of "the great unexplored mass of the galaxy".
During the first half of the 23rd century, a young James T. Kirk and Gary Mitchell came to this planet, where Mitchell got involved with a woman. Kirk later stated that he'd been worried about Mitchell ever since that night, and Mitchell referred to the girl as a Nova, a pun suggesting the danger he had been in.
Also during the 23rd century, inhabitants of Deneb IV communicated telepathically. In at least three cases during the 2260s, Gary Mitchell carried on long telepathic conversations with select Deneb IV natives and scored eighty percent or higher on comprehension. (TOS: "Where No Man Has Gone Before")
By 2364, the Bandi had seemingly constructed Farpoint Station, a base which they subsequently offered to Starfleet. Intrigued by the extremely short time in which it was built, Starfleet sent the USS Enterprise-D on its maiden voyage to the planet in order to investigate the base. It was subsequently discovered that the station was in fact a spaceborne entity, enslaved by the Bandi. Upon this discovery, the entity was released, and Starfleet and the Bandi began planning to reconstruct the station. (TNG: "Encounter at Farpoint")
Background information
Michael Okuda recalled how Deneb IV was originally depicted in "Encounter at Farpoint"; "The beautiful shot of Deneb IV was actually a matte painting done by Industrial Light & Magic, and that was done on film." Speaking shortly before the release of Star Trek: The Next Generation - The Next Level Blu-Ray sampler, Okuda also compared the remastered version of the planet with the original, saying, "The planet is pretty much dead on with what was done in the original shot." [1]
Location
According to the Star Trek: Star Charts, Deneb IV was a planet located in the Alpha Quadrant, and was the fourth planet in the Alpha Leonis system. (p. 34) However, Deneb IV was not in the Alpha Leonis system, and was rather in the Alpha Cygni (Deneb) system. This system was 3,230 light years from Sol, in the Alpha Quadrant. An error had crept into the production process, with Cygni being replaced with Leonis. (p. 41)
The planet visited in the mid-23rd century was the fourth planet of the Deneb (Deneb Kaitos, or Beta Ceti) system. (p. 41)
A star chart of the Alpha and Beta Quadrants, depicting the United Federation of Planets
However, according to canon, there is only one system named Deneb. In the episode "Conspiracy", there is a galactic map that shows the locations of several stars and planets from Star Trek: The Original Series and Star Trek: The Animated Series. In this map, Deneb is located in a block set between 345 and 346, and is one block from the galactic edge. Deneb shares this block with Gamma Trianguli and Makus III. (Sol is located in a block set between 348 and 349, and two blocks from the galactic edge.)
Historical notes
According to the book Star Trek: Star Charts, this planet, with a population of 450 million Bandi in 2378, signed a treaty with the United Federation of Planets in 2364. This treaty stipulated that Starfleet would operate Starbase Farpoint Station. Another attraction was the Old City, adjacent to the station. (p. 34) Both this Deneb IV and the other Deneb IV are listed, in the book, as Federation members. (United Federation of Planets I)