

A161997


Number of distinct essential hyperbolic Coxeter polytopes of dimension n.


0




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), 413440.
Anna Felikson, Pavel Tumarkin, Essential hyperbolic Coxeter polytopes, arXiv:0906.4111 [math.CO], 20092014.
H. Poincaré, Théorie des groupes fuchsiens, Acta Math. 1 (1882), 162.


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 4polytopes 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 5polytopes 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



