Let S^3 be the unit sphere in R^4 = C^2 given by {(z,w} : |z|^2 +|w|^2 = 1}, and let C and D be the great circles C = {(e^is, 0) : 0 <= s < 2pi}, D = {(0, e^it) : 0 <= t < 2pi}. Let R be a rotation of S^3 that interchanges C and D. PUZZLE: Identify the topology of the manifold X obtained as the quotient space of S^3 by the action of R, i.e. X = S^3 / p ~ R(p). --Dan