Plato's Republic has been influential in literature and art.
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Aristophanes
Around the same time that the Republic was being composed, the playwright Aristophanes produced the play Assemblywomen. The state formed by the women in this play bears many similarities to the ideal government described by Plato. It is not discernible which was released first; most likely Aristophanes had heard an early form of the Republic before it was completed and used it as the basis for Assemblywomen. Certainly, the similarities have long been commented upon.
Utopias
Thomas More, when writing his Utopia, invented the technique of using the portrayal of a "utopia" as the carrier of his thoughts about the ideal society. In Thomas More's Utopia, the island Utopia is also similar to Plato's Republic in some aspects, among them common property and the lack of privacy.
Dystopias
The form of government described in the Republic has been adapted in several modern dystopic novels and stories. The separation of people by professional class, assignment of profession and purpose by the state, and the absence of traditional family units, replaced by state-organized breeding, was included by authors in descriptions of totalitarian dystopic governments. Government which bears resemblance to Plato's Republic is found in Aldous Huxley's Brave New World and Lois Lowry's The Giver.
The Orwellian dystopia depicted in the novel 1984 had many characteristics in common with Plato's description of the allegory of the Cave as Winston Smith strives to liberate himself from it.
Heinlein
Another satiric presentation of Platonic style government would be Robert A. Heinlein's Starship Troopers. His citizen can be compared to a Platonic Guardian, without the communal breeding and property, but still having a militaristic base. Although there are significant differences in the specifics of the system, Heinlein and Plato both describe systems of limited franchise, with a political class that has supposedly earned their power and wisely governs the whole. Republic is specifically attacked in Starship Troopers. Indeed, the arachnids can be seen as much closer to a Republic society than the humans.
Other
Although not directly referenced at any point the Mega City One of 2000AD's Judge Dredd storyline has broad similarities to the Platonic Republic – mainly in that it is governed by a Guardian Class (the Judges) raised from infancy to govern in the interests of the polity and bound by far stricter rules than apply to the common citizen.
The comic book Morning Glories takes place at a violent and secretive boarding school which is built on the grounds above Plato's Cave.
The experience of Jack in Emma Donoghue's 2010 novel "Room" contains many similarities to the experience of the people in Plato's Cave.