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Mat. Zametki, 2004, Volume 75, Issue 2, Pages 277–286 (Mi mz14)  

This article is cited in 3 scientific papers (total in 3 papers)

Lambert Cubes Generating Discrete Reflection Groups

A. A. Felikson

Independent University of Moscow

Abstract: A Lambert cube $Q(\alpha,\beta, \gamma)$ is a combinatorial cube with dihedral angles $\alpha$, $\beta$, and $\gamma$ assigned to the three mutually noncomplanar edges and right angles at the remaining edges. In this paper, we classify the Lambert cubes in $S^3$, $\mathbb{E}^3$ and $\mathbb{H}^3$ such that the group $G_Q$ generated by the reflections with respect to the faces of a cube $Q$ is discrete.

DOI: https://doi.org/10.4213/mzm14

Full text: PDF file (287 kB)
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English version:
Mathematical Notes, 2004, 75:2, 250–258

Bibliographic databases:

UDC: 512.817.72+514.174.5
Received: 21.06.2002
Revised: 03.12.2002

Citation: A. A. Felikson, “Lambert Cubes Generating Discrete Reflection Groups”, Mat. Zametki, 75:2 (2004), 277–286; Math. Notes, 75:2 (2004), 250–258

Citation in format AMSBIB
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\transl
\jour Math. Notes
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\pages 250--258
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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, “Spherical simplices generating discrete reflection groups”, Sb. Math., 195:4 (2004), 585–598  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Felikson, A, “Euclidean simplices generating discrete reflection groups”, European Journal of Combinatorics, 28:4 (2007), 1056  crossref  mathscinet  zmath  isi  scopus  scopus
    3. D. A. Derevnin, A. D. Mednykh, “The Volume of the Lambert Cube in Spherical Space”, Math. Notes, 86:2 (2009), 176–186  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математические заметки Mathematical Notes
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