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Regulus (or Alpha Leonis) was the primary of the Regulus (or Alpha Leonis system). This system was located in the Alpha Quadrant. Its location in the Milky Way Galaxy was depicted on a Federation star chart in 2293. (Star Trek VI: The Undiscovered Country, production art)
In the 2150s, Regulus was located inside Vulcan territory, near the Andorian border. In 2154, for the preemptive strike against Andoria planned by Administrator V'Las, the Vulcan High Command amassed a fleet of twelve cruisers at Regulus. Regulus was chosen because it lay outside the range of Andorian listening stations. (ENT: "Kir'Shara")
The Explored Galaxy
"The Explored Galaxy" was a map of charted space in the Alpha Quadrant. Regulus was located between the Tholian Assembly and Romulus. Both locations were identified in DS9: "The Search, Part II", "Call to Arms" as being located in this quadrant. This chart was also seen in several Star Trek: The Next Generation and Star Trek: Deep Space Nine episodes set in the 24th century, from the year 2364 to 2370. These were: TNG: "Conspiracy", "The Measure Of A Man", "The Emissary", "The Mind's Eye", "The Game" and DS9: "In the Hands of the Prophets", "Cardassians".
Regulus was located in the Beta Quadrant. (page 61)