Skip to main content

Coxeter Decompositions of Hyperbolic Tetrahedra

Abstract

In this paper we classify all Coxeter decompositions of hyperbolic tetrahedra. Using this classification one can find all Coxeter subgroups of the group generated by reflections with respect to the faces of the tetrahedra. The indices of such subgroups easily follow from the classification also.

This is a preview of subscription content, access via your institution.

REFERENCES

  1. 1.

    N. W. Johnson, R. Kellerhals, J. G. Ratcliffe, and S. T. Tschantz, “The size of a hyperbolic Coxeter simplex,” Transformation Groups, 4, No.4, 329–353 (1999).

    Article  Google Scholar 

  2. 2.

    A. Felikson, “Coxeter decompositions of hyperbolic polygons,” Eur. J. Combinatorics, 19, 801–817 (1998).

    Article  Google Scholar 

  3. 3.

    A. Felikson, Coxeter Decompositions of Spherical Tetrahedra, preprint, Bielefeld, No. 99-053.

  4. 4.

    A. Felikson, Coxeter Decompositions of Hyperbolic Pyramids and Triangular Prisms, preprint, Bielefeld, No. 00-006.

Download references

Author information

Affiliations

Authors

Additional information

__________

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 263–275, 2003.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Felikson, A.A. Coxeter Decompositions of Hyperbolic Tetrahedra. J Math Sci 128, 3504–3512 (2005). https://doi.org/10.1007/s10958-005-0286-9

Download citation

Keywords

  • Reflection
  • Hyperbolic Tetrahedron
  • Coxeter Subgroup