Insignia
The patch is simple in design but highly symbolic. The main feature is a large X with a Gemini and Agena orbiting around it. The two stars have a variety of meanings: the two rendezvous attempts, Castor and Pollux in Gemini or the two crew members. This is one of the few crew patches without the crew's name. It is able to be displayed "upside down" but is correctly shown with the spacecraft to the right. It was designed by Young's first wife, Barbara.
Read more about this topic: Gemini 10