The broad-brimmed travel hat associated with the Greek god Hermes is called a petasos.
The petasos was a practical hat worn by travelers in ancient Greece. It usually had a broad brim that helped protect the wearer from sun and weather, making it a fitting attribute for Hermes, the god of travelers and roads.
In art, Hermes may appear with a petasos, winged sandals, and the caduceus. Artists sometimes add wings to the hat, especially in later representations, but the defining feature of the petasos is its broad brim.
The petasos is not the same object as the Talaria, Hermes’s winged sandals. Nor should it be confused with the Phrygian cap, a different type of headwear that became a later symbol of liberty and revolutionary politics.