If G is a group 2-homogeneous but not k-homogeneous on the finite set S and B is any k-subset of S, where \(k<| S| -1,\) then the sets \(B^ g\) for g in G are the blocks of a design whose points are the elements of S. The author considers the case that G is already the automorphism group of a design, and applies the result to many configurations in PG(d,q) and AG(d,q). The recognition of these configurations as designs facilitates the calculation of various parameters.