Representing a 3D toroidal universe How would one represent a 3-D wrapping object as outlined in the linked article, Classic JRPG Worlds Are Actually Donuts? In short, it explained that to achieve the x-axis and y-axis wrap that is common in games, that world would have to be a torus.

One of the ideas I've heard about the edge of the universe is that is just kind wraps around so that you never realize you hit the edge until you are back where you started. This may have been disproven (I'm not sure) for the actual universe, but I was wondering how one would represent this?
Obviously, when you try to do this for a three dimensional object, you have to wrap the z-axis as well. Does this mean that any accurate model would have to be in the fourth dimension? Are we even able to comprehend this.
To be clear, I'm not asking if this is how the universe works, I was presenting that as an example. I'm curious how one could model such a universe. Or if that is even possible.
 A: You're right that you need more than three dimensions to embed a three-dimensional torus, but that's beside the point: you don't have to embed a shape in a higher-dimensional space. 
The code for the JRPG doesn't contain a donut-shaped embedding for the world map in three-dimensional space anywhere. It just keeps track of your position with two coordinates, and wraps you back around when you hit the edge. 
Similarly, if I wanted to mathematically define a three-dimensional torus I would just say it's the set of points $(x, y, z)$ where
$$(x, y, z) \sim (x+L, y, z) \sim (x, y+L, z) \sim (x, y, z+L)$$
and $\sim$ means 'is actually the same point'. Insisting that the torus had to be embedded in a higher-dimensional space would just make everything more complicated.
To get some intuition for what a toroidal universe would look like, imagine standing in the middle of a cubical room where all the walls are mirrors. (This isn't perfect because the mirrors also add an extra flip.) You can see the periodic structure, no extra dimensions needed. 
A: You can easily construct this object mathematically : consider $\mathbb{R}^3$, the usual three-dimensional space, and take the quotient by the translations by one unit in the three directions. This means that you consider a new space whose points are sets of the form $$\langle x,y,z \rangle := \{(x+n,y+m,z+p) | n,m,p \in \mathbb{Z}\} \, , $$for any $(x,y,z) \in \mathbb{R}^3$. As you can see, $$\langle x,y,z \rangle = \langle x+1,y,z \rangle = \langle x,y+1,z \rangle = \langle x,y,z+1 \rangle$$
What is difficult to visualize is how to embed this in a four-dimensional space, to have the equivalent of your donut. This is simply because we are not able to visualize four dimensions. 
