The observed universe is flat.

The CMB of the universe is more concentrated across one plane of the universe, forming a straight line in the universe. As the amount of radiation in one area is limited, it’s indicative of the size of the area in that direction.

In theory, it can have a positive curvature, negative curvature, flat curvature, or possibly a combination of all two or three.

A positive curvature corresponds to a closed universe. In a closed universe, the expansion of the universe comes to a stop due to gravity, all matter collapses back into a singularity.

A negative curvature corresponds to an open universe. In an open universe the density is not large enough for gravity to take over, instead the universe will expand forever. It may slow down approximating to a limit, but never stop.

A flat curvature corresponds to a flat universe. In a flat universe space expands forever but will either accelerate or decelerate, according to the amount of dark energy.

With a torus, the geometry of the universe would be a combination of positive and negative curvature.

The three-torus model of the universe. Here, the shape of the universe is a three-dimensional torus, while a donut is a two-dimensional torus.