Beta Geminorum (also called Pollux) was the primary of the Beta Geminorum 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. (TOS: "Who Mourns for Adonais?"; Star Trek VI: The Undiscovered Country, production art)
"The Explored Galaxy"
Michael Okuda, the creator of this chart, believed that Beta Geminorum and Pollux were two distinct stars. Working on this belief, he depicted the location of the two stars on the chart. These stars were within the same region of space.
"The Explored Galaxy" was a map of charted space in the Alpha Quadrant. Beta Geminorum and Pollux IV were 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. The chart, first seen chronologically in Star Trek VI: The Undiscovered Country, 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".
Star Trek: Star Charts
Geoffrey Mandel, the author of this book, believed that Beta Geminorum and Pollux were the same star. This star was located in the Beta Quadrant. The star was classified as a Class K star. It had a magnitude of -1, which was 100 times brighter than Sol. (page 60)