Living in the surface-volume of a hypersphere
Context:
I'm designing a "demi-universe," accessible from Earth (via appropriately supernatural means), that has the following internal topological property: given any point in 3D space, and any 3D vector, the ray from that point along that vector will eventually reencounter itself from the opposite orientation. In less formal terms, if you go in any direction, in all three dimensions, you will eventually "loop" back to where you started:
* If you go east, you will eventually arrive at your starting point from the west.
* If you go west, you will eventually arrive at your starting point from the east.
* If you go north, you will eventually arrive at your starting point from the south.
* If you go south, you will eventually arrive at your starting point from the north.
* If you go up, you will eventually arrive at your starting point from below.
* If you go down, you will eventually arrive at your starting point from above.
Moreover, in any of these directions, or any other you could care to name, the distance required to make exactly one complete "loop" is the same (and is large by human terms but still significantly smaller than Earth's diameter). 229
These conditions force the world to be geometrically a hypersphere, or rather the "surface" of one.
In addition, the world has a form of gravity with a strength approximately that of Earth's, but always pointing in the same direction (which thus becomes "down" by virtue of there being no other way to distinguish directions).
Assume that this world contains air with approximately the right pressure and composition for humans to breathe comfortably, and further assume that there are mechanisms that will "refresh" the air's composition as humans convert the oxygen content to carbon dioxide. Also, assume that any food and material requirements that can't be produced on-location can always be imported from Earth without too much trouble, and that any unusable waste can be dealt with similarly. Finally, assume that the world is a completely closed system aside from any deliberate transport of matter and energy to and from Earth (and the above-mentioned air refreshment mechanisms).
Question 1:
What kinds of weather patterns can one expect from a world like this?
Question 2:
What sorts of societies would form from long-term human colonies within this world? 513