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Mat. Sb. (N.S.), 1970, Volume 83(125), Number 2(10), Pages 256–260 (Mi msb3511)  

This article is cited in 32 scientific papers (total in 32 papers)

On convex polyhedra of finite volume in Lobachevskii space

E. M. Andreev


Abstract: The paper contains a complete description of the polyhedra of finite volume with dihedral angles not exceeding $90^\circ$ in three-dimensional Lobachevskii space.
Bibliography: 1 title.

Full text: PDF file (561 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1970, 12:2, 255–259

Bibliographic databases:

UDC: 513.34+513.812
MSC: 52B05, 52A15
Received: 08.01.1970

Citation: E. M. Andreev, “On convex polyhedra of finite volume in Lobachevskii space”, Mat. Sb. (N.S.), 83(125):2(10) (1970), 256–260; Math. USSR-Sb., 12:2 (1970), 255–259

Citation in format AMSBIB
\Bibitem{And70}
\by E.~M.~Andreev
\paper On~convex polyhedra of finite volume in Lobachevskii space
\jour Mat. Sb. (N.S.)
\yr 1970
\vol 83(125)
\issue 2(10)
\pages 256--260
\mathnet{http://mi.mathnet.ru/msb3511}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=273510}
\zmath{https://zbmath.org/?q=an:0203.54904}
\transl
\jour Math. USSR-Sb.
\yr 1970
\vol 12
\issue 2
\pages 255--259
\crossref{https://doi.org/10.1070/SM1970v012n02ABEH000920}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. È. B. Vinberg, “Discrete linear groups generated by reflections”, Math. USSR-Izv., 5:5 (1971), 1083–1119  mathnet  crossref  mathscinet  zmath
    2. V. V. Nikulin, “On arithmetic groups generated by reflections in Lobachevskii spaces”, Math. USSR-Izv., 16:3 (1981), 573–601  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. V. V. Nikulin, “On the classification of arithmetic groups generated by reflections in Lobachevsky spaces”, Math. USSR-Izv., 18:1 (1982), 99–123  mathnet  crossref  mathscinet  zmath  isi
    4. È. B. Vinberg, “Hyperbolic reflection groups”, Russian Math. Surveys, 40:1 (1985), 31–75  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. Andrew M. Brunner, Youn W. Lee, Norbert J. Wielenberg, “Polyhedral groups and graph amalgamation products”, Topology and its Applications, 20:3 (1985), 289  crossref  mathscinet  zmath
    6. Philip L. Bowers, Kenneth Stephenson, “The set of circle packing points in the Teichmüller space of a surface of finite conformal type is dense”, Math Proc Camb Phil Soc, 111:3 (1992), 487  crossref  mathscinet  zmath
    7. Horst Sachs, “Coin graphs, Polyhedra, and conformal mapping”, Discrete Mathematics, 134:1-3 (1994), 133  crossref  mathscinet  zmath
    8. He Z., Schramm O., “Hyperbolic and Parabolic Packings”, Discret. Comput. Geom., 14:2 (1995), 123–149  crossref  mathscinet  zmath  isi
    9. B Mohar, “Straight-line representations of maps on the torus and other flat surfaces”, Discrete Mathematics, 155:1-3 (1996), 173  crossref  mathscinet  zmath  elib
    10. Nikulin V., “Basis of the Diagram Method for Generalized Reflection Groups in Lobachevsky Spaces and Algebraic Surfaces with Nef Anticanonical Class”, Int. J. Math., 7:1 (1996), 71–108  crossref  mathscinet  zmath  isi
    11. R DIAZ, “Non-convexity of the space of dihedral angles of hyperbolic polyhedra”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 325:9 (1997), 993  crossref  mathscinet  zmath
    12. G. Brock Williams, “Earthquakes and circle packings”, J Anal Math, 85:1 (2001), 371  crossref  mathscinet  zmath  isi
    13. Shigeru MIZUSHIMA, “Computer Experiments for Circle Packings on Surfaces”, Iis, 9:1 (2003), 175  crossref  mathscinet  zmath
    14. P. V. Tumarkin, “Hyperbolic $n$-dimensional Coxeter polytopes with $n+3$ facets”, Russian Math. Surveys, 58:4 (2003), 805–806  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    15. Igor Rivin, “Combinatorial optimization in geometry”, Advances in Applied Mathematics, 31:1 (2003), 242  crossref  mathscinet  zmath
    16. P. V. Tumarkin, “Hyperbolic Coxeter $N$-Polytopes with $n+2$ Facets”, Math. Notes, 75:6 (2004), 848–854  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    17. Schlenker, JM, “The bellows conjecture”, Asterisque, 2004, no. 294, 77  zmath  isi
    18. E. Ya. Klimenko, N. V. Kopteva, “Discrete $\mathscr{RP}$-groups with a parabolic generator”, Siberian Math. J., 46:6 (2005), 1069–1076  mathnet  crossref  mathscinet  zmath  isi
    19. Daniel A. Spielman, Shang-Hua Teng, “Spectral partitioning works: Planar graphs and finite element meshes”, Linear Algebra and its Applications, 421:2-3 (2007), 284  crossref  mathscinet  zmath
    20. J. W. Cannon, W. J. Floyd, W. R. Parry, “Introduction to circle packing: the theory of discrete analytic functions”, The Mathematical Intelligencer, 29:3 (2007), 63  crossref
    21. Timothy A. Schroeder, “Geometrization of 3-dimensional Coxeter orbifolds and Singer’s conjecture”, Geom Dedicata, 2008  crossref  mathscinet  isi
    22. JEAN-FRANÇOIS LAFONT, BRUCE A. MAGURN, IVONNE J. ORTIZ, “Lower algebraic K-theory of certain reflection groups”, Math Proc Camb Phil Soc, 2009, 1  crossref  mathscinet
    23. Christopher K. Atkinson, “Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra”, Geom Dedicata, 2011  crossref  mathscinet
    24. G. Brock Williams, “Constructing conformal maps of triangulated surfaces”, Journal of Mathematical Analysis and Applications, 2012  crossref  mathscinet
    25. Shawn Rafalski, “Small hyperbolic polyhedra”, Pacific J. Math, 255:1 (2012), 191  crossref  mathscinet  zmath
    26. Alexander Kolpakov, “On the optimality of the ideal right-angled 24–cell”, Algebr. Geom. Topol, 12:4 (2012), 1941  crossref  mathscinet  zmath
    27. Chuanming Zong, “Packing, covering and tiling in two-dimensional spaces”, Expositiones Mathematicae, 2013  crossref  mathscinet
    28. Nikolay Dimitrov, “Hyper-ideal Circle Patterns with Cone Singularities”, Results. Math, 2015  crossref  mathscinet
    29. Jinsong Liu, Ze Zhou, “How many cages midscribe an egg”, Invent. math, 2015  crossref  mathscinet
    30. A. Yu. Vesnin, “Right-angled polyhedra and hyperbolic 3-manifolds”, Russian Math. Surveys, 72:2 (2017), 335–374  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    31. V. M. Buchstaber, N. Yu. Erokhovets, “Constructions of families of three-dimensional polytopes, characteristic patches of fullerenes, and Pogorelov polytopes”, Izv. Math., 81:5 (2017), 901–972  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    32. N. Yu. Erokhovets, “Three-Dimensional Right-Angled Polytopes of Finite Volume in the Lobachevsky Space: Combinatorics and Constructions”, Proc. Steklov Inst. Math., 305 (2019), 78–134  mathnet  crossref  crossref  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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