Gomez

Gomez is the person you are controlling (protagonist) throughout FEZ. After being bequeathed the titular hat from the Hexahedron, Gomez becomes aware of the 3rd dimension and is assigned the task of reclaiming all 32 Cubesand saving his universe with the help of his companion Dot.

Background
Gomez makes his home in his tiny house in the Village. Before his quest, he and the other Flat-heads appear to be living a quiet, peaceful existence.