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On simple ideal hyperbolic Coxeter polytopes

2008; IOP Publishing; Volume: 72; Issue: 1 Linguagem: Inglês

10.1070/im2008v072n01abeh002394

1468-4810

Pavel Tumarkin, Anna Felikson,

Algebraic structures and combinatorial models

A polytope in the hyperbolic space $\H^n$ is called an {\it ideal polytope} if all its vertices belong to the boundary of $\H^n$. We prove that no simple ideal Coxeter polytope exist in $\H^n$ for $n>8$.