"not Eden" was how Spock described an otherwise unnamed, lifeless planet destroyed by nuclear war, which was located near Starbase 13 in or near the Federation Phalanx within the galaxy's Alpha or Beta Quadrant.
History and specifics
Starbase 13 was on the edge of the Federation Phalanx in the Marrat Nebula, which was near the border of the Klingon Empire. (TOS novel: Enterprise: The First Adventure; EV comic: "The Fires of Pharos")
In the 23rd century, nuclear war caused the extinction of all lifeforms on the class M world. Its surface appeared barren, with former capital cities littered with missile batteries and abandoned buildings. An automated weapons system remained active and was able to target spacecraft in orbit. Surviving records did not provide a name for the world.
In 2267, during a star charting mission, the starship USS Enterprise came upon the lifeless world and beamed up two stasis chambers for study, unaware that they would tap into the ship's power cells and regenerate their occupants. After regaining consciousness, mortal enemies Faron and Nadira resumed their war, manipulating the crew via telepathy into a deadly battle that culminated in a saucer separation near the planet.
The ship's saucer section and stardrive section departed the planet at impulse power to rendezvous with technicians sent from Starbase 13. (TOS - Star Trek: The Manga - Shinsei Shinsei comic: "'Til Death")
Points of interest