When Glaucon tells the story of the Ring of Gyges in Book II of the Republic, he includes an interesting detail:
According to the tradition, Gyges was a shepherd in the service of the king of Lydia; there was a great storm, and an earthquake made an opening in the earth at the place where he was feeding his flock. Amazed at the sight, he descended into the opening, where, among other marvels, he beheld a hollow brazen horse, having doors, at which he, stooping and looking in, saw a dead body of stature, as appeared to him, more than human, and having nothing on but a gold ring; this he took from the finger of the dead and reascended.
The hollow bronze horse (hippon khalkoun) with doors is an interesting detail, and I have often wondered about it. Why Glaucon includes it, I cannot say, but I think we can make sense of Plato including it if we keep in mind the (very obviously deliberate) contrast between Gyges' descent into the underworld and the Allegory of the Cave.
Gyges descends into the underworld; the man in the Allegory of the Cave ascends out of the underworld. Gyges brings back the ring from the underworld into our world; the man in the Allegory of the Cave brings back the message of the real world into the underworld. Gyges gets the ring from an image; the man in the Allegory breaks out of the world of images. It's a common feature of Plato's dialogues for Socrates to turn his interlocutor's story upside-down, so it's not surprising to find this here. But I think we can go farther.
The hollow horse in which the heroic more-than-human body is interred could be understood as implying that the corpse is the body of a hero of the Trojan War; a hollow bronze horse with someone inside could perhaps suggest a funerary commemoration of the hollow wooden horse of the Iliad. Depictions of the Trojan Horse in art as having doors in its side long precede Plato, and it would make sense for a hero of the Trojan War to be buried in something that made reference to the war, which is something found in almost all cultures.
Later in the same book of the dialogue, Socrates begins his attack on the poets (who Adeimantus had mentioned as only praising justice for its benefits), including Homer, arguing that their lies about the gods and heroes should not be admitted in the education of the just city. One of the lies that Socrates explicitly singles out, in early Book III, is a remark by Achilles from the Odyssey. Odysseus has gone to the underworld (NB!) and met Achilles, who tells him, "I would rather be the poor slave of a poor man than ruler of the realm of the dead." This lie, suggesting that dying and going to the underworld is a terrible thing, he argues is harmful, since it makes people fear death instead of slavery; the poets should commend the underworld rather than condemn it. This particular verse ends up being of some importance, because Socrates, having condemned it in Book III, brings it up again in Book VII in the Allegory of the Cave. In the Allegory, the cave represents our world -- the Allegory flips the story again by making our world the underworld, and of our world we can then truthfully say, "Better to be the poor slave of a poor master than to live as they do."
One way to understand the Ring of Gyges -- perhaps not Glaucon's intent, but surely part of Socrates' ironic use of its ideas in his response -- is that Gyges' descent into the underworld, with its suggestion of reaching back into a legendary time with the heroic-sized body and the hollow brazen horse and other marvels, is actually a descent into the kinds of lying poetry that Socrates soon goes on to attack. Gyges descends into the tales that, as Adeimantus says, seem to imply that might makes right; from the images there he brings back what he 'learns', and uses this to achieve success (apparently) in our world. But this is to learn about our world from what is only its deceitful imitation. The man in the Allegory of the Cave, however, recognizes that our world is an underworld imitating a higher world, goes to that higher world, and brings back what he learns. Because of this, he is not good at achieving success in our world, but our kind of success is not actually the kind of success worth having because it, too, is merely an imitation of something higher, according to which might does not make right.