You can get the topology of a sphere with holes at the poles by wrapping left/right but not up/down, like the Civilization games. Or you can do it with no holes by having left/right wrap, and top/bottom do a different wrap where you come back from the same direction but halfway around horizontally. (Imagine the path crossing over the poles projected onto a Mercator map.)

> You can get the topology of a sphere with holes at the poles by wrapping left/right but not up/down, like the Civilization games.

That is just a cylinder.