Symbolism of Ixion's Punishment
Ixion is punished for loving Hera by being tied to a wheel that travels through the sky:
Ixion fell in love with Hera and attempted to force her; and when Hera reported it, Zeus, wishing to know if the thing were so, made a cloud in the likeness of Hera and laid it beside him; and when Ixion boasted that he had enjoyed the favours of Hera, Zeus bound him to a wheel, on which he is whirled by winds through the air; such is the penalty he pays. And the cloud, impregnated by Ixion, gave birth to Centaurus.
They say that by the commands of the gods Ixion spins round and round on his feathered wheel, saying this to mortals: “Repay your benefactor frequently with gentle favors in return.”
My question is simple: what is the symbolism/meaning behind tying Ixion to a wheel? Why is that his punishment for rape?
Inspired by Arthur George's blog post that connects flaming wheels to the summer solstice. However, I am looking for an answer that specifically discusses the Ixion myth.
Since the questioner said that his inquiry was inspired by my blog post that featured a fiery wheel (see above) and since Anna quoted from my post and showed my photo of that wheel, I figure that I'd better address his question!
A wheel, especially a spoked one in the sky as in this case, is of course commonly a symbol of the sun. In this connection, Kerenyi in his The Gods of the Greeks (pp. 159-60) penned a conclusory statement, "One can easily recognise in the whole story the punishment of an older, savage sun-god who had to had to be tamed beneath the rule of Zeus." This might be the case since Zeus was in the business of absorbing other deities and their functions, but Kerenyi points to no sources or other grounds for this conclusion. The article that Anna quotes in her answer above, which relies on Cook's Zeus, takes the same view. There is indeed significant iconography showing the wheel to be flaming (just search on Google for Ixion images), so this image appears to have been popular. On the other hand, Robert Graves (Greek Myths, 63.1-2) goes off in another direction showing echoes of Frazer, claiming that Ixion was an oak-king who married a moon-goddess (Dia), and was then slain in a ritual involving him being spread-eagled on a tree, which image later became Ixion on the wheel. He also claims that old kings called themselves Zeus and their marriage to the moon-goddess displeased the later Olympian priests, hence the hubris theme leading to the punishment. Graves also links Ixion's name to vegetation, not anything solar. So no solar motif for Graves.
Turning to the actual sources, from what I see they don't seem to be stressing a solar theme. Although the Scholiast on Pindar's Pythians mentions that the wheel was fiery, Pindar himself (Pythian Ode 2.39-44), as well as Hyginus (Fabulae 62), Diodorus (Historical Library 4.69.5), Apollodorus (Library, Epit. 1.20), Virgil (Georgics 4.484; Aeneid 6.601), and Lucian (Dialogues of the Gods VI) never mention fire; they just mention the wheel spinning/whirling, not necessarily going across the sky (although that could be the case), and that the wheel turns due to the force of the winds (not its own power, as sun-gods do). To my mind, this, plus the fact that some later sources (Hyginus; Virgil, Aeneid; Lucian) felt comfortable placing the wheel in Hades rather than in the sky, suggests that a solar symbolism of the wheel is not the main point here, at least as the story appears in these later versions which differ from the presumed versions that Kerenyi and Cook were talking about. Thus, Kerenyi and Cook could be right in the sense that we may just be seeing later versions that mask the original, apples vs. oranges to some extent.
Based on what we do have for sources, for these authors the wheel and its spinning appear to symbolize primarily the passage of time into eternity, showing that Ixion's punishment is for eternity. Most of the sources (Pindar, Diodorus, Hyginus, and Lucian) stress that the wheel is supposed to turn for eternity. This has a rough parallel in the punishment of Prometheus for his act of hubris, which likewise was supposed to be eternal. Finally, Pindar mentions that the wheel has 4 spokes, which normally symbolizes dividing the passage of time into measures (seasons), which are endless cycles. That is, the hub, which appears not to move, represents eternity, while the outer part with the spokes moving represents time passing. See, e.g., The Book of Symbols, A. Ronnberg, ed., p. 504.
I don't think the wheel here has anything to do with the earthly punishment of being broken on the wheel. In that punishment, the victim dies within 1-3 days, whereas Ixion's punishment is eternal and none of the accounts has him dying. None of the accounts has him being broken or otherwise physically abused while on the wheel; except, of course, for the eternal flames in any versions of the story which have fire on the wheel, but that is very different from being broken on the wheel. Finally, based on my prior research, I don't recall this form of punishment being used in the ancient world. (I didn't research this point here since it was not mentioned in your original question, and was raised only in another answer above.)
I accepted this answer, not because you wrote the article, but because it made the most sense, included multiple interpretations, and had the best use of sources. That said, the other three answers were also very good. I'm glad my question (and your blog post) sparked this conversation.