Characterizing the Delaunay decompositions of compact hyperbolic surfaces.
Leibon, Gregory (2002)
Geometry & Topology
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Leibon, Gregory (2002)
Geometry & Topology
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Marica Šarac (1997)
Matematički Vesnik
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Dowty, James G. (2002)
Algebraic & Geometric Topology
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Francisco Perdomo, Ángel Plaza (2014)
Open Mathematics
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The Longest-Edge (LE) bisection of a triangle is obtained by joining the midpoint of its longest edge with the opposite vertex. Here two properties of the longest-edge bisection scheme for triangles are proved. For any triangle, the number of distinct triangles (up to similarity) generated by longest-edge bisection is finite. In addition, if LE-bisection is iteratively applied to an initial triangle, then minimum angle of the resulting triangles is greater or equal than a half of the...
Milica Stojanović (1997)
Matematički Vesnik
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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...
Broughton, S.Allen, Haney, Dawn M., McKeough, Lori T., Smith Mayfield, Brandy (2000)
The New York Journal of Mathematics [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...
von Gagern, Martin, Richter-Gebert, Jürgen (2009)
The Electronic Journal of Combinatorics [electronic only]
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