A Characterization of Inscribable Polyhedra; Resolution of a Question of J. Steiner Igor Rivin, NECI; W.D. Smith, NECI 06/20/91 ABSTRACT: Research announcement. This summarizes the most important results in some forthcoming large papers. We plan to submit a version of this announcement to \em {Bulletin of the AMS.} KEYWORDS: INSCRIBABLE, CIRCUMSCRIBABLE, POLYHEDRA, DELAUNAY TRIANGULATION