Your definition of "uniform" doesn't look quite right: It's not enough for the symmetry group to be vertex transitive, you also have to require that the faces be regular polygons (see the wikipedia page on isogonal solids for examples of vertex-transitive solids which don't have regular faces). Also, "vertex-transitive" means that for any pair of vertices, there is a rotation or reflection symmetry of the solid which sends the first vertex to the second -- this is not equivalent to the definition you give, for example, the pentagonal cupola is not vertex-transitive but it does seem to satisfy your definition. The standard definition of "uniform" for higher dimensions is recursive: A convex polytope is called uniform if its facets are uniform and its symmetry group (including reflections) is vertex-transitive; a 2-dimensional polytope is called uniform if it is regular (i.e., is a regular polygon). So, in three dimensions, a convex polyhedron is called uniform if it has regular faces and its symmetry group is vertex-transitive.