Harmonic analysis and Radon transforms on pencils of geodesics.
The plane can be covered by n + 2 clouds iff .
A hyperideal polyhedron is a non-compact polyhedron in the hyperbolic -space which, in the projective model for , is just the intersection of with a projective polyhedron whose vertices are all outside and whose edges all meet . We classify hyperideal polyhedra, up to isometries of , in terms of their combinatorial type and of their dihedral angles.