The leader of a telekinetic people who modelled their society on ancient Greece and forced the Enterprise officers to perform for their amusement.
Parmen leads the Platonians, a small society of beings who fled their sun's destruction and settled on a remote world, modelling themselves on Plato's Greece. Their telekinetic powers come from a mineral in the local food, and they torment their dwarf servant Alexander, who lacks those powers.
After McCoy treats Parmen's injury, the Platonians demand that he stay, and they use their powers to humiliate Kirk, Spock, Uhura and Christine Chapel. Kirk and Spock gain the same ability, overcome Parmen, and leave with Alexander. He was played by Liam Sullivan.