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Transactions of the Moscow Mathematical Society
Transactions of the Moscow Mathematical Society
ISSN 1547-738X(online) ISSN 0077-1554(print)

 

On $ d$-dimensional compact hyperbolic Coxeter polytopes with $ d+4$ facets


Authors: Pavel Tumarkin and Anna Felikson
Translated by: Alex Martsinkovsky
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 69 (2008).
Journal: Trans. Moscow Math. Soc. 2008, 105-151
MSC (2000): Primary 52B11; Secondary 20F55
Published electronically: November 20, 2008
MathSciNet review: 2549446
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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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Additional 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

DOI: http://dx.doi.org/10.1090/S0077-1554-08-00172-6
PII: S 0077-1554(08)00172-6
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.
Article copyright: © Copyright 2008 American Mathematical Society