What is the name of the island of the sun god Helios?

The island of the sun god Helios is Thrinacia. In Homer's Odyssey, Odysseus and his exhausted crew reach the island near the end of their voyage home from Troy, after passing the dangers of the Sirens and Scylla and Charybdis.

Thrinacia is the grazing place of Helios's sacred cattle and sheep. The herds are tended by Helios's daughters, Phaethusa and Lampetia, and the crew is warned not to harm them. Odysseus receives this warning from both the prophet Tiresias and the sorceress Circe.

When unfavorable winds trap the crew on the island and their food runs out, Odysseus's men slaughter the cattle while he is asleep or away praying. Helios demands punishment, and Zeus destroys their ship with a thunderbolt. All the crew die except Odysseus. Thrinacia is sometimes associated with Sicily, whose ancient Greek name Trinacria referred to its three prominent capes, but the mythological name is Thrinacia.