Hyperbolic Realizations of Tilings by Zhuk Simplices
Milica Stojanović (1997)
Matematički Vesnik
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Milica Stojanović (1997)
Matematički Vesnik
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Marcel Hagelberg, Rubén A. Hidalgo (1997)
Revista Matemática Iberoamericana
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In this note we construct examples of geometric 3-orbifolds with (orbifold) fundamental group isomorphic to a (Z-extension of a) generalized Coxeter group. Some of these orbifolds have either euclidean, spherical or hyperbolic structure. As an application, we obtain an alternative proof of theorem 1 of Hagelberg, Maclaughlan and Rosenberg in [5]. We also obtain a similar result for generalized Coxeter groups.
Roland K.W. Roeder, John H. Hubbard, William D. Dunbar (2007)
Annales de l’institut Fourier
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In 1970, E.M.Andreev published a classification of all three-dimensional compact hyperbolic polyhedra (other than tetrahedra) having non-obtuse dihedral angles. Given a combinatorial description of a polyhedron, , Andreev’s Theorem provides five classes of linear inequalities, depending on , for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing with the assigned dihedral angles. Andreev’s Theorem also shows that...
Mohanty, Yana (2003)
Algebraic & Geometric Topology
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Baker, R.D., Ebert, G.L., Wantz, K.L. (2001)
Advances in Geometry
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Dowty, James G. (2002)
Algebraic & Geometric Topology
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Leibon, Gregory (2002)
Geometry & Topology
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von Gagern, Martin, Richter-Gebert, Jürgen (2009)
The Electronic Journal of Combinatorics [electronic only]
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Carlo Petronio (2000)
Bollettino dell'Unione Matematica Italiana
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Quello delle triangolazioni geodetiche ideali è un metodo molto potente per costruire strutture iperboliche complete di volume finito su 3-varietà non compatte, ma non è noto se il metodo sia applicabile in generale. È tuttavia noto che esistono triangolazioni ideali parzialmente piatte, ma l'analisi della situazione diviene più ardua sotto diversi aspetti, quando si ha a che fare con tetraedri piatti oltre che veri tetraedri. In particolare, la topologia dello spazio di identificazione...