Commentarii Mathematici Helvetici

, Volume 71, Issue 1, pp 229–242 | Cite as

The classification of compact hyperbolic Coxeterd-polytopes withd+2 facets

  • Frank Esselmann


This paper provides a list of all compact hyperbolic Coxeter polytopes the combinatorial type of which is the product of two simplices of dimension greater than 1. Combined with results of Kaplinskaja ([Ka]) this completes the classification of compact hyperbolic Coxeterd-polytopes withd+2 facets.


Finite Volume Open Vertex Hyperbolic Space Coxeter Group Single Edge 
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  1. [An]E. M. Andreev,On convex polyhedra in Lobacevskii spaces. Math. USSR Sbornik,10 (1970), 413–440.CrossRefGoogle Scholar
  2. [Bou]N. Bourbaki,Groupes et Algèbres de Lie, Chap. IV, V und VI, Hermann, Paris 1968.zbMATHGoogle Scholar
  3. [Bu]V. O. Bugaenko,Arithmetic crystallographic groups generated by reflections, and reflective hyperbolic lattices, Adv. Sov. Math.,8 (1992), 33–55.MathSciNetGoogle Scholar
  4. [Ch]M. Chein, Recherche des graphes des matrices de Coxeter hyperboliques d'ordre ≤10. Revue française d'informatique et de recherche operationelle 3, No. R-3, (1969), 3–16.Google Scholar
  5. [Es]F. Esselmann, Über kompakte hyperbolische Coxeter-Polytope mit wenigen Facetten. Universität Bielefeld, Sonderforschungsbereich 343, Preprint No. 94-087.Google Scholar
  6. [Gr]B. Grünbaum,Convex Polytopes. John Wiley & Sons, 1967.Google Scholar
  7. [ImH]H.-C. Im Hof,Napier cycles and hyperboic Coxeter groups. Bull Soc. Math. de Belg. Série A (1990), 523–545.Google Scholar
  8. [Ka]I. M. Kaplinskaya,Discrete groups generated by reflections in the faces of simplicial prisms in Lobachevskian spaces. Math. Notes,15 (1974), 88–91.Google Scholar
  9. [Ko]J. L. Koszul, Lectures on hyperbolic Coxeter groups. University of Notre Dame, 1967.Google Scholar
  10. [La]F. Lannér,On complexes with transitive groups of automorphisms, Comm. Sem. Math. Univ. Lund,11 (1950), 1–71.Google Scholar
  11. [Po]H. Poincaré,Theorie des groupes fuchsiennes, Acta Math.,1 (1882), 1–62.CrossRefGoogle Scholar
  12. [Vil]È. B. Vinberg,The absence of crystallographic groups of reflections in Lobachevsky spaces of large dimensions. Trans. Moscow Math. Soc.,47 (1985), 75–112.Google Scholar
  13. [Vi2]E. B. Vinberg,Hyperbolic reflection groups, Russian Math. Surveys,40 (1985), 31–75.CrossRefMathSciNetGoogle Scholar
  14. [vD]W. von Dyck,Gruppentheoretische Studien, Math. Ann.,20 (1882), 1–45.CrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Verlag, Basel 1996

Authors and Affiliations

  • Frank Esselmann
    • 1
  1. 1.Fachbereich MathematikUniversität DortmundDortmund

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