Reference
OpenAI's Answer
The conflict between the Dioscuri—Castor and Pollux—and their cousins, Idas and Lynceus, ultimately led to tragedy. According to the myths, the Dioscuri and their cousins both stole a herd of cattle. Conflict arose during the division of the livestock, leading to a violent encounter. In this confrontation, Castor was mortally wounded by Idas, while Pollux managed to kill Lynceus.
Pollux's great love for his brother Castor is particularly highlighted in this myth. As Pollux was immortal and Castor was not, the death of Castor left Pollux offering to share his immortality with him. The bond between the brothers was so powerful that Zeus allowed them to alternate between the heavens and the underworld, symbolizing both life and death. This led to their enduring depiction as the constellation Gemini.
For more detailed information, you can refer to the source here: Dioscuri - Greek Mythology.
Here are some images related to the Dioscuri and their myth: