The star twins.
This was one a little challenging because the only reference I came across seemed to imply that Gemini should be represented with two long haired dudes hugging or holding hands. Twins indeed.
In the end I found a solution that I was pretty pleased with.
Individuals born when the Sun was in this sign are considered Gemini individuals. Under the tropical zodiac, the Sun is in the sign of Gemini roughly from May 21 to June 21. Under the sidereal zodiac, it is currently there roughly from June 15 to July 15.
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The constellation is associated with the story of Castor and Polydeuces. They were the brothers of Helen of Sparta and traveled with Jason on the Argo. In the myth the twins shared the same mother but had different fathers which meant that Polydeuces was immortal and Castor was mortal. When Castor died, Polydeuces asked Zeus to let him share his own immortality with his twin to keep them together and they were transformed into the Gemini constellation.