Nick wrote:
I say the surface of a hypersphere.

It'll work for this problem, as long as you bear in mind that it only
represents one of the three possibilities, the others being an infinite
flat universe and an infinite saddle-shaped universe. If you want to
get an idea of what each looks like, you can build a model. You can
approximate a sphere nicely with pentagons and hexagons in the pattern
of a soccer ball. Substitute hexagons for the pentagons, and you get
flat space. Substitute seven-sided heptagons, and you get the
saddle-shaped possibility.

The next step in what it seems you are trying to do is to introduce
time. Special relativity treats time as a dimension, just like length,
width, and height. The main difference between time and space is that
for a right triangle where the legs are distances, the hypotenuse has a
length of sqrt(x^2 + y^2), but if one of the legs is a time, the
hypotenuse's length is sqrt(x^2 - c^2 t^2).