If the universe is a $3$-torus, must it be longer in some direction? So in a finite universe, I've read one possible topology for a flat universe is a 3 torus. On a 2 torus, it's obviously longer in one direction than the other. Would the same hold true for the universe if it was a 3 torus? Can you not have a "cubic" space-time for the universe if it's a 3 torus, would it need to be a rectangular prism instead?
 A: No, the dimensions of the torus can have any size. Sometimes, we visualize the curvature of two-dimensional spaces by thinking of them as surfaces in a flat three-dimensional space. However, physical space does not have to be embedded in a larger space to make sense.
For example, one way of defining the $2$-torus is to consider the plane, with the identifications
$$(x, y) \sim (x + L_1, y), \quad (x, y) \sim (x, y + L_2)$$
where $\sim$ means that the two points are regarded as the same point. This yields a torus with side lengths $L_1$ and $L_2$. Similarly, the $3$-torus constructed from $\mathbb{R}^3$ can have any dimensions $L_i$, including having all the $L_i$ equal.
By the way, even if you insisted that physical space be embedded in a flat larger space, that still doesn't give you any constraints. The Nash embedding theorem states that any curved space can be embedded in a flat $\mathbb{R}^n$ for sufficiently large $n$. Unfortunately, $n$ is quite high, e.g. $n = 17$ for the $2$-torus, so the construction is not easy to picture. 
