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, , 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...