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Trinity Base is a Cylon base in operation during the last years of the Cylon War.
Lucky and his wingman, William Adama, perform a recon photo-op of this location in their Stealth Vipers when Lucky's engine flares out. When attempting to scrub the mission, the Cylons intercept and eventually capture Lucky and his stealth ship, since Adama is unwilling to target and destroy Lucky before bailing out of his own ship (Battlestar Galactica: Origins 5).
After the Armistice is signed, Galactica heads back to Trinity six weeks after the end of hostilities to take out a rogue force of Centurions known as the Annihilators, which results in Galactica being boarded and a large contingent of her crew killed, including Alexa Cain (Battlestar Galactica: Origins 6).