Parmen and the other natives of Sahndara called themselves Platonians and their new planet Platonius because they claimed to follow Plato's philosophy, but Spock noted that Plato wanted justice, which the Platonians did not seem to care too much about. (TOS: "Plato's Stepchildren")
Vulcan philosophers are known to study the works of Plato, as evidanced in the work: "A Cave Beyond Logic: Vulcan Perspectives on Platonic Thought". (VOY: "In the Flesh")
- In Diane Duane's novel Dark Mirror Plato's mirror universe counterpart is mentioned as writing that the perfect government is one that metes out fear in proper proportion to the people. In the mirror universe such a work would likely be titled "Kingdom and Empire" rather than "The Republic" as in the real universe.