It's actually fairly easy to describe the spatially flat, finite universe. It is a three dimensional version of a torus. The problem is that it is only locally isotropic and homogeneous, not globally so. A three dimensional torus has three 'special' directions which are periodic.
The easiest way to imagine this is to imagine all of flat, infinite, three dimensional Euclidean space to be filled with cubes stacked up and beside each other. If each cube is *identical* to every other cube, we can see this as a single cube with opposite faces identified.
In two dimensions, if you identify the opposite faces of a square, you get a torus (a bagel-shape). If you do the same for a cube, you get a three dimensional torus.
This is different than a spherical space in which you can 'go around' from any point and in any direction. For the torus, there are three 'special' directions where you can 'go around' once. Other directions can 'go around' more than once in different directions, or even in a path that goes around infinitely often, but gets close to every point.
Again, in such models, this torus would be the slice for a fixed time. In an expanding universe, the size of the cube increases over time.
For negatively curved space, similar tricks can give cases with finite space.
All of these tricks, though, have special directions, so are not globally isotropic, only locally so.