I’ve redone the Wikipedia page on convex uniform tilings of Euclidean 3-space.
It occurs to me that one could enumerate the convex uniform tilings of flat, spherical and hyperbolic 3-spaces by an approach similar to what I’ve used to find fullerenes. First make a list of the vertex figures of convex uniform polyhedra: these are polygons which share the property that their corners lie on a circle. Then use a spiral search to build irregular polyhedra from these polygons. Whenever such a polyhedron’s vertices all lie on a sphere, you have the vertex figure of a candidate solution (some of which will fail for other reasons). The size of the sphere tells you whether and which way the relevant space is curved.
Has this been done?