Pollux IV was the inhabited fourth planet of the Beta Geminorum system of the Alpha Quadrant. It was the homeworld of the Greek gods and goddesses, an extinct interstellar humanoid species whose last member Apollo died in 2267. (TOS: "Who Mourns for Adonais?")
In 2293, the location of Pollux IV in the Milky Way Galaxy was labeled in a star chart that was in Captain James T. Kirk's quarters aboard the USS Enterprise-A. (Star Trek VI: The Undiscovered Country, okudagram)
In the distant past, this world was the home of a highly advanced civilization, who called their world Olympus. A group of Pollux IV inhabitants visited Earth in the 3rd millennium BC. They landed in the Mediterranean region and took residence on Mount Olympus. These aliens considered themselves to be gods and presented themselves as such to the primitive Humans. The worship of these aliens was the beginning of the Ancient Greek civilization and their deeds on Earth became the Greek classic myths. The aliens eventually left Earth to return to Pollux IV, when Humans lost interest in worshipping them. Absent worshippers, many of the Greek gods decided to end their own existence.
In 2267, USS Enterprise was surveying the Beta Geminorum system. Kirk and his crew made contact with Apollo, the last of his race, who had waited for his worshippers to develop space travel and seek out their beloved god. The encounter resulted in not only him forming a desire to take a Human woman as his queen and wife, but also the death of Apollo and the extinction of his species. (TOS: "Who Mourns for Adonais?")
By the late 24th century, Pollux IV had become a tourist destination. A view of the surface of Pollux IV was depicted on several viewscreens on Deep Space 9's Promenade and Replimat, advertising a visit to the "amazing ruins of Pollux IV". (DS9: "The Muse", "What You Leave Behind")