As Hades lives in the Underworld and not on Mount Olympus, he is not techincally classed as one of the twelve Olympian Gods.
When assigned parts of the world, Zeus claimed the sky, Poseidon claimed the sea and Hades became ruler of the Underworld. Spending most of his time there as the 'god of the dead,' he is often chatergorised as solemn and frightening and because of this, rarely is he depicted in ancient Greek art.
When he is,the three-headed dog, Cerberus, is usually by his side as the guard of the entrance to the Underworld.
Hades' symbols: Cerberus, the sceptre, the cornucopia.
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