I am currently writing about the ancient Greek and Roman gods, and I am looking to find the correct phrase for a chariot drawn by four horses made of gold. The closest I have come using google is khrūsoûs tethrippon (χρυσοῦς τέθριππον) /quadriga aureolus. Also, any help in a possessive adjective, such as Helios' golden chariot would be extremely helpful.
I think the Greek for Apollo's golden chariot would be ἅρμα χρύσεον Ἀπόλλωνος. I don't think Apollo's chariot would be τέθριππον, which means "four-horse," since it's actually pulled by swans.
I get the impression from WP that Helios was not really a big deal in classical Greek culture until the Romans exerted an influence back on the Greeks. But if you really want Helios with the iconography of the four horses, then I think it would be τέθριππον χρύσεον Ἠελίοιο. The word for the god is just the word for the sun, so this is "the four-horsed, golden chariot of the Sun."
Ἐκ δὲ τῆς ἀγορᾶς ἐξιόντων τὴν ἐπὶ Λεχαίου προπύλαιά ἐστι καὶ ἐπ᾿ αὐτῶν ἅρματα ἐπίχρυσα, τὸ μὲν Φαέθοντα Ἡλίου παῖδα, τὸ δὲ Ἥλιον αὐτὸν φέρον.
For anyone leaving the forum on the road to Lechaeum, there is a gateway, and on top of it are gilded chariots, one carrying Phaethon son of Helios, the other carrying Helios himself.
Which seems like good ancient evidence that Helios had a ἅρμα, not a τέθριππος. The real one, presumably, would be χρυσόν (gold) rather than ἐπίχρυσον (gilded).