Did you know that the only way to embed a flat torus in 3D space preserving distance is to make the surface fractal?

i.e. infinitely crinkly. A flat torus is more or less... well you've encountered them in games before. If you imagine a rectangle, and if you go through the top you come out of the bottom, and vice versa, and if you go through the left you come out the right and vice versa. This is essentially a flat representation of a torus (doughnut shape). Can be topologically distorted in any way but here we actually want to preserve distances. But what ends up happening is that the line that goes around the long way ends up lengthening, and the line that goes around the center ends up shortening, with respect to the flat torus that it should be identical to with respect to its distance preservation. So what we do is we crinkle the surface, and keep crinkling the surface, and keep crinkling the surface, until the lengths are equal. It's not truly a fractal, but it uses the same iterative procedure as one, but it stops at a finite level (otherwise the lines would be infinitely long!