Alignment on leafworld: The four poles

Not so long ago, I talked about a strange flat world floating through infinite air.  The idea is still roaming around my head along with thoughts about alignment. Inevitably, that leads to thinking about how people align on leaf-world.

A world that floats like a leaf

It's a strange thing that fantasy world-builders will happily allow for biology that defies reason, but when it comes to the shape of the world they stay shackled to the globe.  Suppose that there is a world that isn't a sphere.  Suppose that it has a different shape, but that the logic of that shape still gave its creatures a day to day experience that is easily imagined.  Where would imagining such a world take us?