The Perseus Arm planetoid was an otherwise unnamed planetoid located in the Perseus Arm of the galaxy's Alpha or Beta Quadrants. It was the site of a dimensional fissure to Mount Olympus and inhabited by a developing humanoid culture influenced by the Beings.
History and specifics
On the surface, James T. Kirk, Spock, and Leonard McCoy were led by the Beings through a recreation of Ulysses's travels in Homer's Odyssey. Mythological manifestations included cannibals, Aeolus, Cyclops, Charybdis, Scylla, and the Sirens.
Their journey culminated at a populated ancient Greek city maintained by the Beings. Under their alien influence, citizens were pleasure-seeking and immature. Perceiving their interference as a detriment to the culture's natural development, Kirk and Spock challenged Zeus. The Beings eventually abandoned the world, leaving its people to evolve on their own.