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Transactions of the Moscow Mathematical Society

This journal, a translation of Trudy Moskovskogo Matematicheskogo Obshchestva, contains the results of original research in pure mathematics.

ISSN 1547-738X (online) ISSN 0077-1554 (print)

The 2020 MCQ for Transactions of the Moscow Mathematical Society is 0.74.

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On $d$-dimensional compact hyperbolic Coxeter polytopes with $d+4$ facets
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by Pavel Tumarkin and Anna Felikson
Translated by: Alex Martsinkovsky
Trans. Moscow Math. Soc. 2008, 105-151
DOI: https://doi.org/10.1090/S0077-1554-08-00172-6
Published electronically: November 20, 2008

Abstract:

We prove that there are no compact Coxeter polytopes with $d+4$ facets in a hyperbolic space of dimension $d>7$. This estimate is sharp: examples of such polytopes in dimensions $d\le 7$ were found by V. O. Bugaenko in 1984. We also show that in dimension $7$ there is a unique polytope with 11 facets.
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Bibliographic Information
  • Pavel Tumarkin
  • Affiliation: Independent University of Moscow, Russia
  • Email: pasha@mccme.ru
  • Anna Felikson
  • Affiliation: Independent University of Moscow, Russia
  • Email: felikson@mccme.ru
  • Published electronically: November 20, 2008
  • Additional Notes: The first author was partially supported by the President of the Russian Federation grants MK-6290.2006.1 and NSh-5666.2006.1, the RFFI grant No. 07-01-00390-a, and the INTAS grant YSF-06-10000014-5766.
    The second author was partially supported by the President of the Russian Federation grant NSh-5666.2006.1, the RFFI grant No. 07-01-00390-a, and the INTAS grant YSF-06-10000014-5916.
  • © Copyright 2008 American Mathematical Society
  • Journal: Trans. Moscow Math. Soc. 2008, 105-151
  • MSC (2000): Primary 52B11; Secondary 20F55
  • DOI: https://doi.org/10.1090/S0077-1554-08-00172-6
  • MathSciNet review: 2549446