 The Enterprise is fixed in orbit around the secret planet of the Platonians, who established their  Utopian  society after a stay in Ancient Greece i Plato s time, in order for McCoy to cure the strangely serious infection of a small wound on their philosopher-king Parmen, by far the champion in the amazing psycho-kinetic powers they developed on the planet while losing any natural resistance against infections. Alexander, the midget without powers the other Platonians treat as a serf, warns Kirk, Scott and McCoy, the party on the planet, only too late that the Platonians, who easily and cruelly toy with the mentally weaker humans, including Nurse Chapel and Lieutenant Uhura who are beamed down, will not let them leave, probably even kill them...