Díaz Sánchez, Raquel
(1997)
*Non-convexity of the space of dihedral angles of hyperbolic polyhedra.*
Comptes Rendus de l'Académie des Sciences. Série I. Mathématique , 325
(9).
pp. 993-998.
ISSN 0764-4442

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Restricted to Repository staff only until 31 December 2020. 443kB |

Official URL: http://www.sciencedirect.com/science/article/pii/S0764444297890921

## Abstract

We prove that the space of dihedralangles of hyperbolic three-dimensional polyhedra, or of compact hyperbolicpolyhedra, of a given combinatorial type is not convex.

Item Type: | Article |
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Uncontrolled Keywords: | Three-dimensional polytopes; Spherical and hyperbolic convexity |

Subjects: | Sciences > Mathematics > Geometry |

ID Code: | 15708 |

References: | E. Andreev. On convex polyhedra in Lobachevskii spaces. Math. USSR Sb., 10 (1970), pp. 413–440 E. Andreev. Convex polyhedra of finite volume in Lobachebskii space. Math. USSR Sb., 12 (1970), pp. 255–259 R. Diaz. Matrices de Gram y espacios de ángulos diédricos de poliedros. Ph. D. Thesis Universidad Complutense de Madrid (1996) R. Díaz. A characterization of Gram matrices of polytopes. preprint (1997) B. Grünbaum. Convex Polytopes. Pure and Applied Mathematics, Vol. XVI Interscience publishers (1967) C. Hodgson, I. Rivin. A characterization of compact convex polyhedra in hyperbolic 3-space. Invent. Math., 111 (1993), pp. 77–111 I. Rivin. On geometry of convex ideal polyhedra in hyperbolic 3-space. Topology, Vol. 32 (No. 1) (1993), pp. 87–92 I. Rivin. A characterization of ideal polyhedra in hyperbolic 3-space. Ann. Math., Vol. 143 (No. 1) (1996), pp. 51–70 |

Deposited On: | 21 Jun 2012 08:17 |

Last Modified: | 06 Feb 2014 10:30 |

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