On small scales these different geometries are much alike. An ant on the surface of an apple might view its immediate surrounding as quite flat and might experience difficulty in figuring out that the apple is round. Likewise, if the curvature of the universe would become apparent only on scales beyond several billion light years we might be deceived into believing that its geometry is Euclidean. In all three cases, space is divided into identical cells, whose edges are indicated by the rods. The balls within the cells are of identical size, and increasing distance is indicated by reddening.
Hyperbolic space shown here is tiled with regular dodecahedra.
In Euclidean space such a regular tiling is impossible. The size of the cells is of the same order as the curvature scale. Although perspective for nearby objects in hyperbolic space is very nearly identical to Euclidean space, the apparent angular size of distant objects falls off much more rapidly, in fact exponentially, as can be seen in the figure. The spherical space space shown here is tiled with regular dodecahedra. Perspective in spherical space is peculiar.