Project Gemini:

The second U.S. manned space program was announced in January 1962. Its two-man crew gave it its name, Gemini, for the third constellation of the Zodiac and its twin stars, Castor and Pollux. Gemini involved 12 flights, including two unmanned flight tests of the equipment.

Like Mercury's, its major objectives were clear-cut:

The National Aeronautics and Space Administration announced December 7, 1961, a plan to extend the existing manned space flight program by development of a two-man spacecraft. The program was officially designated Gemini on January 3, 1962. It was named after the third constellation of the zodiac, featuring the twin stars Castor and Pollux. The program was operationally completed with the Gemini XII flight.

Excerpt from the Encyclopedia Britannica without permission.