I welcome JimLast's, Undidly's, and Vanamonde's comments. I'll respond to each:

Undidly: I am not aware of any basis for suspecting that the universe is spinning. There are no known phenomena that suggest that. Also, spin would not render an otherwise four-dimensional universe three-dimensional. Gravity is explained not by centripetal force but by the warping of spacetime in the manner described by the general theory of relativity. All masses accelerate at the same rate only within a volume of space in which the spacetime metric is uniform.

Vanamonde: I'm glad that you said that current evidence only indicates, not proves, that the universe is flat. WMAP has thus far been unable to detect any curvature. It is conceivable that it will detect a slight curvature after it has collected more data. Additional data has already refined the age of the universe from 13.7 to 13.73 billion years. It remains conceivable that lines that are parallel locally may converge at cosmological distances.

I am not aware of any valid argument for regarding the shape of the universe as like that of any kind of torus. As far as I am aware, only the three-dimensional "surface" of a four-dimensional hypersphere can model a finite homogeneous and isotropic universe in four dimensions. As for needing to eat very scary math for breakfast in order to understand how the universe can be as close to flat as it seems to be, it's sufficient only to recognize that a hypersphere expanding from a point in a four-dimensional space with a finite initial expansion rate and an always finite expansion rate may asymptotically approach flatness but cannot reach it within a finite time. I'm not so sure that we should not have expected the universe to have become very nearly flat over 13.7 billion years, especially after having started out with an inflation phase.