Journal of the Mathematical Society of Japan

A generalization of Andreev's Theorem

Raquel DÍAZ

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Abstract

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

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

Dates
First available in Project Euclid: 1 June 2006

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1149166778

Digital Object Identifier
doi:10.2969/jmsj/1149166778

Zentralblatt MATH identifier
1097.51009

Mathematical Reviews number (MathSciNet)
MR2228562

Subjects
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

Keywords
hyperbolic polyhedra dihedral angles Andreev's Theorem

Citation

DÍAZ, Raquel. A generalization of Andreev's Theorem. Journal of the Mathematical Society of Japan 58 (2006), no. 2, 333--349. doi:10.2969/jmsj/1149166778. http://projecteuclid.org/euclid.jmsj/1149166778.


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References

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