The Vault of Glass was a Vex experiment to try and write themselves into reality. They used Atheon, a mind connecting every timeline, every conflux that ever existed, to try and realize their goal. They also hoped to manifest the power of the Oracles, Templar, and Gorgons outside the Vault. The Hellmouth is the Hive base of operations. It's their HQ on the Moon; it branches out under the entire surface, connecting every single base or (possibly) other Hellmouths