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Many temples, like the Parthenon at the Athenian Acropolis, were made of marble. Others, like the temple of Zeus at Olympia, were limestone. Greeks built using the materials they had access to.
The Classical temple that has survived was completed in 420 BCE. From several ancient accounts and by Pausanias we know the statue of Athena Nike in its cella was made of wood and held a pomegrade in the right hand and a helmet in the left.