  The closed 3-manifolds of constant positive curvature were classified long
ago by Seifert and Threlfall. Using well-known information about the orthogonal
group O(4), we calculate their full isometry groups Isom(M), determine which
elliptic 3-manifolds admit Seifert fiberings that are invariant under all
isometries, and verify that the inclusion of Isom(M) to Diff(M) is a bijection
on path components.
