Journal of the Mathematical Society of Japan

A generalization of Andreev's Theorem

Raquel DÍAZ

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Andreev's Theorem studies the existence of compact hyperbolic polyhedra of a given combinatorial type and given dihedral angles, all of them acute. In this paper we consider the same problem but without any restriction on the dihedral angles. We solve it for the descendants of the tetrahedron, i.e. those polyhedra that can be obtained from the tetrahedron by successively truncating vertices; for instance, the first of them is the triangular prism.

Article information

J. Math. Soc. Japan, Volume 58, Number 2 (2006), 333-349.

First available in Project Euclid: 1 June 2006

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Zentralblatt MATH identifier

Primary: 51M10: Hyperbolic and elliptic geometries (general) and generalizations
Secondary: 51M20: Polyhedra and polytopes; regular figures, division of spaces [See also 51F15] 52B10: Three-dimensional polytopes

hyperbolic polyhedra dihedral angles Andreev's Theorem


DÍAZ, Raquel. A generalization of Andreev's Theorem. J. Math. Soc. Japan 58 (2006), no. 2, 333--349. doi:10.2969/jmsj/1149166778.

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