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Coxeter Decompositions of Hyperbolic Tetrahedra


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.

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  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.

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

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Felikson, A.A. Coxeter Decompositions of Hyperbolic Tetrahedra. J Math Sci 128, 3504–3512 (2005).

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  • Reflection
  • Hyperbolic Tetrahedron
  • Coxeter Subgroup