2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59267The main result is that every complete finite area hyperbolic metric on a sphere with punctures can be uniquely realized as the induced metric on the surface of a convex ideal polyhedron in hyperbolic 3-space. A number of other observations are included.13 pages; appeared in proceedings of the 1992 nordic math congress; very difficult to findGeometric TopologyMathematical PhysicsCombinatoricsDifferential GeometryMetric Geometry52B70 ;51M10 ; 51M20; 52A55; 52B10; 57M50text