The shape of the universe

Did you know that our universe is (probably) flat?

Wait, I'm serious! Obviously it's not flat the way that the top of your desk is flat. But like the surface of that table is flat relative to the third dimension, our universe is likely to be flat relative to the fourth dimension. Or at the very least, any curvature is imperceptibly subtle. Beyond that the shape is unknown. It could be an infinite expanse or a bounded ball. It might even be a torus (think: doughnut), finite but without boundary.

Ultimately measuring the shape of the universe is quite a challenge given its size relative to us, but it's fun to think about. Does your universe have a particular shape? This might be important to consider if interstellar travel is possible. Is it infinite or is there an edge, and what might the edge of the universe look like?

My world is located in a 3-sphere. If we define a sphere as being the 2-dimensional boundary of a 3-dimensional ball (sphere and ball are commonly used interchangeably but the distinction matters here) then a 3-sphere is the 3-dimensional boundary of a 4-dimensional ball. This results in a universe that is finite but without an edge.

The most interesting property of this is that if you set off from any random point in the universe in any direction, as long as you maintain your heading you will eventually return to your starting point from the opposite side. Compare it to circumnavigating the world - if you walk out the front door of Santa's house at the North pole and keep going due South, you'll eventually pass by the South pole and then find yourself heading North again until you're standing at Santa's *back* door. So in my universe, if you instead launched a rocket from Santa's rooftop and flew through the universe in a straight line you'd eventually crash into Antarctica.

Don't ask me what people see when they look through a sufficiently strong telescope, though.

Anyway, what's the shape of your universe?