I'm trying to create a shape that I can map to both a plane and a sphere.
I don't care about distortions at all, so, for example, platonic solids work. However, I need a solution that works for a large amount of tiles, preferably arbitrarily large. Hosohedra satisfy this criteria, but they only tile in one direction, and ideally I would want to have different tiles for different latitudes as well.
I'm aware that this is likely impossible without making some sort of compromise somewhere, but I figured I might as well ask those who specialise in this sort of thing.