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Mat. Sb., 2002, Volume 193, Number 12, Pages 134–156 (Mi msb702)  

This article is cited in 9 scientific papers (total in 9 papers)

Coxeter decompositions of hyperbolic simplexes

A. A. Felikson

M. V. Lomonosov Moscow State University

Abstract: A Coxeter decomposition of a polyhedron in a hyperbolic space $\mathbb H^n$ is a decomposition of it into finitely many Coxeter polyhedra such that any two tiles having a common facet are symmetric with respect to it. The classification of Coxeter decompositions is closely related to the problem of the classification of finite-index subgroups generated by reflections in discrete hyperbolic groups generated by reflections. All Coxeter decompositions of simplexes in the hyperbolic spaces $\mathbb H^n$ with $n>3$ are described in this paper.

DOI: https://doi.org/10.4213/sm702

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English version:
Sbornik: Mathematics, 2002, 193:12, 1867–1888

Bibliographic databases:

UDC: 512.817.72+514.174.5
MSC: 20F55, 51F15, 51M20
Received: 23.11.2001

Citation: A. A. Felikson, “Coxeter decompositions of hyperbolic simplexes”, Mat. Sb., 193:12 (2002), 134–156; Sb. Math., 193:12 (2002), 1867–1888

Citation in format AMSBIB
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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. A. A. Felikson, “Coxeter Decompositions of Compact Hyperbolic Pyramids and Triangular Prisms”, Math. Notes, 75:4 (2004), 583–593  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. P. V. Tumarkin, “Maximum-rank root subsystems of hyperbolic root systems”, Sb. Math., 195:1 (2004), 121–134  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. A. A. Felikson, “Spherical simplices generating discrete reflection groups”, Sb. Math., 195:4 (2004), 585–598  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. A. A. Felikson, “Lambert Cubes Generating Discrete Reflection Groups”, Math. Notes, 75:2 (2004), 250–258  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. P. V. Tumarkin, A. A. Felikson, “Reflection subgroups of Euclidean reflection groups”, Sb. Math., 196:9 (2005), 1349–1369  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. Felikson A., Tumarkin P., Zehrt T., “On hyperbolic Coxeter $n$-polytopes with $n+2$ facets”, Adv. Geom., 7:2 (2007), 177–189  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    7. Felikson A., Tumarkin P., “Euclidean simplices generating discrete reflection groups”, European J. Combin., 28:4 (2007), 1056–1067  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    8. Anna Felikson, Pavel Tumarkin, “Essential hyperbolic Coxeter polytopes”, Isr. J. Math, 2013  crossref  mathscinet  scopus  scopus  scopus
    9. John Mcleod, “Hyperbolic Coxeter Pyramids”, APM, 03:01 (2013), 78  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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