What is a geometric model of the universe?

In simple terms it is the shape of the universe. Many theories have been put forward for the shape of the universe, but it is generally thought of as being flat, or very slightly curved, but not so curved that it would fold back on itself to form a sphere, cylinder or torus (doughnut shape). This concept of being "flat" requires some unusual thinking because the universe is clearly three dimensional (with a fourth dimension of time) and not a flat two dimensional surface.