After the time of Plato passed, the settlers moved on to another planet, a class M planet, they named Platonius. Here they continued to follow the teachings of Plato, but soon they discovered that they had developed psychokinetic powers, attributed to the planet's kironide-rich food.
They described their colony as a principality, but their government was set up on the most powerful psionic, in this case Parmen being supreme. Considering that each Platonian's ability appeared to attuned to a different frequency, which made combining their powers impossible, Parmen's authority was unchallenged. (TOS: "Plato's Stepchildren")