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A161997 Number of distinct essential hyperbolic Coxeter polytopes of dimension n. 0
20, 6, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

COMMENTS

From p.36, Table 8.1 of Felikson/Tumarkin reference.

Essential polytopes of dimension at least 4. In dimensions 2 and 3 compact hyperbolic Coxeter polytopes are completely classified by Poincaré and Andreev.

LINKS

Table of n, a(n) for n=4..8.

E. M. Andreev, On convex polyhedra in Lobachevskii spaces, Math. USSR Sb. 10 (1970), 413-440.

Anna Felikson, Pavel Tumarkin, Essential hyperbolic Coxeter polytopes, arXiv:0906.4111 [math.CO], 2009-2014.

H. Poincaré, Théorie des groupes fuchsiens, Acta Math. 1 (1882), 1-62.

EXAMPLE

a(4) = 20 because the essential hyperbolic Coxeter polytopes in 4 dimensions are proved to be 2 simplices, 2 Esselmann polytopes, 5 simplicial prisms, 8 4-polytopes with 7 facets, and 3 three times truncated simplices. a(5) = 6 because the essential hyperbolic Coxeter polytopes in 4 dimensions are proved to be 2 simplicial prisms, 3 5-polytopes with 8 facets, and 1 three times truncated simplex.

CROSSREFS

Sequence in context: A040387 A201137 A040385 * A274458 A327131 A076594

Adjacent sequences:  A161994 A161995 A161996 * A161998 A161999 A162000

KEYWORD

nonn,more

AUTHOR

Jonathan Vos Post, Jun 24 2009

EXTENSIONS

Edited by Ralf Stephan, Dec 23 2013

STATUS

approved

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Last modified January 29 00:42 EST 2022. Contains 350670 sequences. (Running on oeis4.)