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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