Classification of (1,2) -reflective anisotropic hyperbolic lattices of rank 4

N. V. Bogachev

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1 Citation (Scopus)


A hyperbolic lattice is said to be (1,2)-reflective if its automorphism group is generated by 1- and 2-reflections up to finite index. We prove that the fundamental polyhedron of a Q-arithmetic cocompact reflection group in three-dimensional Lobachevsky space contains an edge with sufficiently small distance between its framing faces. Using this fact, we obtain a classification of (1, 2)-reflective anisotropic hyperbolic lattices of rank 4.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalIzvestiya Mathematics
Issue number1
Publication statusPublished - 2019
Externally publishedYes


  • Coxeter polyhedra
  • fundamental polyhedra
  • reflection groups
  • reflective hyperbolic lattices
  • roots


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