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Untap all artifacts you control during each other player's untap step.
Even if you control more than one Unwinding Clock, you'll only untap your artifacts once during each other player's untap step.
Some effects, such as the one generated by Rust Tick's ability, state that an artifact doesn't untap during its controller's untap step. These effects won't apply and stop the artifact from untapping during another player's untap step.
Those artifacts untap at the same time as the active player's permanents. You have no choice about what untaps and can't choose to not untap an artifact you control.
