the Tale of Gemini
The father of Pollux was none other than Zeus, or Jupiter. Zeus visited Leda on her wedding night in the guise of a swan. Thus the twins would be born. (In fact two twins came from this double union, but let's not complicate the matter even more...)
It should be said, however, that Pollux had a sister as well by Leda and Zeus: the beautiful Helen, who would become Queen of Sparta, and whose abduction by Paris would lead to the Trojan War.
Castor was a great horseman and fighter. One of his pupils was Heracles. Like Heracles, both Castor and Pollux would become Argonauts, that is, join Jason in his quest for the golden fleece.
The twins spent their time raiding cattle and abducting young women, as Greek gods were wont to do. During one such cattle raid a cousin (Idas) became enraged at Castor and killed him. Zeus threw a thunderbolt at Idas, killing him instantly.
Since Pollux was the son of Zeus, he was immortal. But Pollux mourned over his brother's loss to such a point that he wanted to follow Castor into Hades. Zeus was so stricken by Pollux's love for his brother, he allowed them both to share Hades and Olympus, (on alternate days). Later Greek writers had Zeus place the two in the heavens side by side."
Source: the Constellations