Does Zeus live on mount Olympus?

Zeus was one of the Olympian gods, and all the Olympian gods lived on Mt. Olympus. There were twelve Olympians. They were: Zeus, Hera, Poseidon, Demeter, Athena, Apollo, Artemis, Ares, Aphrodite, Hephaestus, Hermes, and Dionysus.

Hades was not considered one of the twelve Olympians, even though he is one of the major gods because he was not allowed on Olympus except on the winter solstice, the darkest day of the year. (Hades has his own palace down in the Underworld where he rules.)