Compact hyperbolic tetrahedra with non-obtuse dihedral angles

• Autores: Roland K. W. Roeder
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 50, Nº 1, 2006, págs. 211-227
• Idioma: inglés
• DOI: 10.5565/publmat_50106_12
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• Resumen

  • Given a combinatorial description O of a polyhedron having E edges, Ihe space of dihedral angles of ah compact hyperbohic polyhedra thaI realize O ja generally not a convex subset of 1E [9] If O has Ove or more faces, Andreev's Theorem states that the corresponding space of dihedral angles A0 obtained by restricting lo nea-sítase angles jo a convex polytope. Jo this paper we explain why Andreev Oid not consider tetrahedra, the only polyhedra hay-iog fewer thao fi~e faces, hy demoostratiog that the opace of dihedral angles of compact hyperbohic tetrahedra, after reotrictiog to non-ohtuse angles, is ooo-coosvex. Our proof provides a simple example of the "method of cootinuity", the technique used jo ciassification theorems 00 polyhedra by Alexandrow [4], Andreev [5], and Rivin-Hodgoon [18].