Displaying similar documents to “Four series of hyperbolic space groups with simplicial domains, and their supergroups”

Andreev’s Theorem on hyperbolic polyhedra

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,  C , Andreev’s Theorem provides five classes of linear inequalities, depending on  C , for the dihedral angles, which are necessary and sufficient conditions for the existence of a hyperbolic polyhedron realizing C with the assigned dihedral angles. Andreev’s Theorem also shows that...

On three-dimensional space groups.

Conway, John H., Delgado Friedrichs, Olaf, Huson, Daniel H., Thurston, William P. (2001)

Beiträge zur Algebra und Geometrie

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Computing fundamental domains for Fuchsian groups

John Voight (2009)

Journal de Théorie des Nombres de Bordeaux

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We exhibit an algorithm to compute a Dirichlet domain for a Fuchsian group Γ with cofinite area. As a consequence, we compute the invariants of Γ , including an explicit finite presentation for Γ .