 Seifert fibrations of real projective 3-space

The Hopf circle action on $S^3$ descends through the antipodal quotient to a free circle action on ${\mathbb{RP}}^3$, giving a Seifert fibration over $S^2$ with no exceptional fibers. The weighted actionalso descends and, after dividing by its generic order-two kernel, gives a fibration over $S^2$ with one exceptional fiber of multiplicity three.