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

Tumarkin, Pavel; Felikson, Anna

doi:10.1090/S0077-1554-08-00172-6

On -dimensional compact hyperbolic Coxeter polytopes with 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
DOI: https://doi.org/10.1090/S0077-1554-08-00172-6
Published electronically: November 20, 2008
MathSciNet review: 2549446
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Abstract: We prove that there are no compact Coxeter polytopes with facets in a hyperbolic space of dimension . 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 there is a unique polytope with 11 facets.

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