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

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

2005-10-11

arxiv.org/abs/math/0510238v2

Mathematics

Metric Geometry

v2: the paper is rewritten. A new section added in which 7-dimensional polytopes are classified. 43 pages, a lot of figures

Scientific paper

We show that there is no compact hyperbolic Coxeter d-polytope with d+4
facets for d>7. This bound is sharp: examples of such polytopes up to dimension
7 were found by Bugaenko (1984). We also show that in dimension d=7 the
polytope with 11 facets is unique.

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