On compact hyperbolic Coxeter d-polytopes with d+4 facets
arXiv:math/0510238 · doi:10.1090/s0077-1554-08-00172-6
Abstract
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.
v2: the paper is rewritten. A new section added in which 7-dimensional polytopes are classified. 43 pages, a lot of figures