A problem in Euclidean Geometry

I describe below an elementary problem in Euclidean (or Hyperbolic) geometry which remains unsolved more than 10 years after it was first formulated. There is a proof for n = 3 and (when the ball is the whole of 3-space) when n = 4. There is strong numerical evidence for n 6 30. Let (x1, x2, ...xn) be n distinct points inside the ball of radius R in Euclidean 3-space. Let the oriented line xixj meet the boundary 2-sphere in a point tij (regarded as a point of the complex Riemann sphere (C ∪∞)). Form the complex polynomial pi, of degree n−1, whose roots are tij : this is determined up to a scalar factor. The open problem is