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Lumen: This is your everyday currency. You’ll need Lumen for things like purchasing different types of buildings or upgrading them. You can earn Lumen as you play by gathering and extracting resources from the ground using Supply Depots.
LOA$: Use LOA$ to speed up processes. You'll get a LOA$ bonus for every achievement target you hit! LOA$ can also be purchased within the store. You can also convert LOA$ directly to Lumen or vice-versa via the Bank.
Diamond: Diamonds get you access to premium buildings. These can’t be bought with either Lumen or LOA$; they must be earned by successfully mining a land and finding a loot box.