From Halopedia, the Halo wiki
Undiminished Entelechy was a CCS-class battlecruiser that served in Thel 'Vadamee's Fleet of Particular Justice during the Battle of Installation 04 in September 2552. A recreation of the ship's command center saw use as a training scenario for UNSC Infinity's Spartan complement in 2558. Undiminished Entelechy was the sister-ship of Purity of Spirit.
Undiminished Entelechy was one of the first ships assigned to the Fleet of Particular Justice. During the Battle of Installation 04, Purity of Spirit and Undiminished Entelechy were secretly ordered to conduct a close-range survey of Installation 04 by the Minor Prophet of Stewardship after the arrival of Pillar of Autumn. During the ship's survey, she took aboard several Forerunner constructs and many records from the Halo's outlying installations, and several of its augurs attempted to learn the secrets of the installation from the control center. At some point in the battle, Undiminished Entelechy was boarded and infested by the Flood. Ultimately, the ship was destroyed by Supreme Commander Thel 'Vadamee to prevent the parasite from escaping the Soell system.
The ship crash-landed on Installation 04, her crew already dead. The wreckage became covered by the installation's vegetation; the growth of the local flora was accelerated by the ring's damaged control system and environmental remediation protocols. All data and research contained aboard the ship were lost when Installation 04 was destroyed by John-117, along with the ship, on September 22, 2552. Through unknown means the Office of Naval Intelligence gained details of the vessel for the Spartan-IVs' recreational War Games.
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