Compact hyperbolic tetrahedra with non-obtuse dihedral angles.

Título inglés	Compact hyperbolic tetrahedra with non-obtuse dihedral angles.
Título español	Tetraedros hiperbólicos compactos con ángulos diedros no obtusos.
Autor/es	Roeder, Roland K.W.
Organización	Fields Inst., Toronto Ontario, Canadá
Revista	0214-1493
Publicación	2006, 50(1): 211-227, 27 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	Given a combinatorial description C of a polyhedron having E edges, the space of dihedral angles of all compact hyperbolic polyhedra that realize C is generally not a convex subset of RE. If C has five or more faces, Andreev's Theorem states that the corresponding space of dihedral angles AC obtained by restricting to non-obtuse angles is a convex polytope. In this paper we explain why Andreev did not consider tetrahedra, the only polyhedra having fewer than five faces, by demonstrating that the space of dihedral angles of compact hyperbolic tetrahedra, after restricting to non-obtuse angles, is non-convex. Our proof provides a simple example of the method of continuity, the technique used in classification theorems on polyhedra by Alexandrow, Andreev, and Rivin-Hodgson.
Clasificación UNESCO	120409
Palabras clave español	Convexidad ; Geometría hiperbólica ; Poliedro ; Tetraedros
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