Insignia
Walter Schirra explained the patch in the book All We Did Was Fly to the Moon:
The Gemini 6 patch is hexagonal in shape, reflecting the mission number; and the spacecraft trajectory also traces out the number "6". The Gemini 6 spacecraft is shown superimposed on the "twin stars" Castor and Pollux, for "Gemini". I designed the patch to locate in the sixth hour of celestial right ascension. This was the predicted celestial area where the rendezvous should occur (in the constellation Orion). It finally did occur there.The original patch had called the flight GTA-6 (for Gemini-Titan-Agena) and showed the Gemini craft chasing an Agena. It was changed when the mission was altered to depict two Gemini spacecraft.
Read more about this topic: Gemini 6A