I'm not sure that the Earth as-a-sphere/as-a-projection is the best practical example. It is not isomorphic, which is a pretty strong requirement for representa

I'm not sure that the Earth as-a-sphere/as-a-projection is the best practical example. It is not isomorphic, which is a pretty strong requirement for representations that are not local mappings. For this reason, useful representations of the Earth that are not spheres tend to be homeomorphisms, like projections onto a cube, or embeddings. The fact that projections are both popular and not isomorphic is a source of continuous pain when dealing with Earth-scale geospatial data models.