Yahweh said:
I had always thought the universe was finite, but I'd never thought of a soccerball shaped universe, I'd always assume the universe would look a bit like a not-quite-spherical blob.
I obviously have no idea what a patched dodecohedron universe might be or look like. As for what might exist outside the universe... uh... antimatter? It might be other universes? Hey, it's worth a guess.
You can construct an Euclidean space-filling lattice of squares arranged around their angles as cubes.
Easy to picture.
One way of constructing a dodecahedron is by arranging regular pentagons around their angles, but not an Euclidean space-filling lattice that way.
But with some degree of space curvature pentagons of a certain size will have right angles.
Hard to picture, but by analogy think of equilateral triangles having right angles on a sphere, if the size of the triangle is the same as one with a vertex on the north pole, one on the equator at 0 longitude, and one on the equator at 90 (either direction) longitude.
So you could have a space-filling lattice of dodecahedrons, given the right parameters.
Maybe it's my American bias, but it seems to me that the stitching on a regulation baseball divides a finite unbounded two dimensional space (otherwise known as the surface of a sphere) into a higher dimensional version of the Euclidean yin-yang.
Maybe the universe is a baseball, not a soccer ball, after all. I like that. It proves God is on our side. But I hate to think of the possibility of the universe being shaped like an (American-style) football.
