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Mat. Zametki, 2004, Volume 75, Issue 6, Pages 909–916 (Mi mz80)  

This article is cited in 12 scientific papers (total in 12 papers)

Hyperbolic Coxeter $N$-Polytopes with $n+2$ Facets

P. V. Tumarkin

Independent University of Moscow

Abstract: In this paper, we classify all the hyperbolic noncompact Coxeter polytopes of finite volume whose combinatorial type is either that of a pyramid over a product of two simplices or a product of two simplices of dimension greater than one. Combined with the results of Kaplinskaja (1974) and Esselmann (1996), this completes the classification of hyperbolic Coxeter $N$-polytopes of finite volume with $n+2$ facets.

DOI: https://doi.org/10.4213/mzm80

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English version:
Mathematical Notes, 2004, 75:6, 848–854

Bibliographic databases:

UDC: 512.817.72
Received: 15.01.2003

Citation: P. V. Tumarkin, “Hyperbolic Coxeter $N$-Polytopes with $n+2$ Facets”, Mat. Zametki, 75:6 (2004), 909–916; Math. Notes, 75:6 (2004), 848–854

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Allcock D., “Infinitely many hyperbolic Coxeter groups through dimension 19”, Geom. Topol., 10 (2006), 737–758  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    2. Zehrt T., “Schläfli numbers and reduction formula”, European J. Combin., 29:3 (2008), 601–616  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    3. Felikson A., Tumarkin P., “On hyperbolic Coxeter polytopes with mutually intersecting facets”, J. Combin. Theory Ser. A, 115:1 (2008), 121–146  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    4. Mcleod J., “Hyperbolic Reflection Groups Associated to the Quadratic Forms-3X(0)(2) + X(1)(2) +...... + X(N)(2)”, Geod. Dedic., 152:1 (2011), 1–16  crossref  mathscinet  zmath  isi  scopus
    5. Paupert J., “A Simple Method to Compute Volumes of Even-Dimensional Coxeter Polyhedra”, In the Tradition of Ahlfors-Bers, VI, Contemporary Mathematics, 590, eds. Hamenstadt U., Reid A., Rodriguez R., Rohde S., Wolf M., Amer Mathematical Soc, 2013, 167–175  crossref  mathscinet  zmath  isi
    6. Kellerhals R., “Hyperbolic Orbifolds of Minimal Volume”, Comput. Methods Funct. Theory, 14:2-3, SI (2014), 465–481  crossref  mathscinet  zmath  isi  scopus
    7. Jacquemet M., “The Inradius of a Hyperbolic Truncated -Simplex”, Discret. Comput. Geom., 51:4 (2014), 997–1016  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Guglielmetti R., “Coxlter - Computing Invariants of Hyperbolic Coxeter Groups”, LMS J. Comput. Math., 18:1 (2015), 754–773  crossref  mathscinet  zmath  isi  scopus  scopus
    9. Chen H., “Even More Infinite Ball Packings From Lorentzian Coxeter Systems”, Electron. J. Comb., 23:3 (2016), P3.16  mathscinet  isi  elib
    10. Guglielmetti R., Jacquemet M., Kellerhals R., “On commensurable hyperbolic Coxeter groups”, Geod. Dedic., 183:1 (2016), 143–167  crossref  mathscinet  zmath  isi  scopus
    11. Kellerhals R., “On Minimal Covolume Hyperbolic Lattices”, 5, no. 3, 2017, 43  crossref  zmath  isi  scopus  scopus
    12. Yukita T., “Growth Rates of 3-Dimensional Hyperbolic Coxeter Groups Are Perron Numbers”, Can. Math. Bul.-Bul. Can. Math., 61:2 (2018), 405–422  crossref  mathscinet  zmath  isi  scopus
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