In Star Trek: The Original Series, the planet in “Return of the Archons” is Beta III.
“Return of the Archons” is the twenty-first episode of the first season of Star Trek: The Original Series. It was written by Boris Sobelman from a story by Gene Roddenberry and aired in 1967. The Enterprise visits Beta III, where the inhabitants live under the control of a computer system called Landru.
The episode is relevant to Pandora’s Box because the fictional Beta III appears again in the later episode “The Way to Eden,” which includes the title “The Apple” in some discussions of the series’ mythological and literary themes. The planet itself is not the Greek vessel, and it should not be confused with Talos IV, the setting of “The Cage” and “The Menagerie.”
Beta III is the crisp canonical planetary designation used in the episode’s story. Vulcan and Organia are other Star Trek planets, but neither is the setting of “Return of the Archons.”