Geodesic
Compact hyperbolic Coxeter \(n\)-polytopes with \(n+3\) facets
The electronic journal of combinatorics, Tome 14 (2007)
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We use methods of combinatorics of polytopes together with geometrical and computational ones to obtain the complete list of compact hyperbolic Coxeter $n$-polytopes with $n+3$ facets, $4\le n\le 7$. Combined with results of Esselmann this gives the classification of all compact hyperbolic Coxeter $n$-polytopes with $n+3$ facets, $n\ge 4$. Polytopes in dimensions $2$ and $3$ were classified by Poincaré and Andreev.
DOI : 10.37236/987
Classification : 51M20, 51F15, 20F55
Mots-clés : hyperbolic space, Coxeter polytope 
@article{10_37236_987,
     author = {Pavel Tumarkin},
     title = {Compact hyperbolic {Coxeter} \(n\)-polytopes with \(n+3\) facets},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/987},
     zbl = {1168.51311},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/987/}
}
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Pavel Tumarkin. Compact hyperbolic Coxeter \(n\)-polytopes with \(n+3\) facets. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/987

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