From the thread title, I thought it was the actual third edition of Gamma World and hoping that we might, eventually, see 1e and 2e. However, if it is the d20 version, that is the 6th edition of Gamma World.
3e (1985) Used the Action Table similar to the table used in other TSR games at the time (e.g., Conan, Marvel Super Heroes
4e (1992) Used a system based on AD&D 2e
5e (2000) Alternity system version
6e (2003) d20 system version licensed by Sword and Sorcery Studios/White Wolf
7e (2010) used a system based upon Dungeons and Dragons 4e