2025/07/07 by Bredon, Naomi
#11R06 (secondary) #20F55 #51M20 (primary) #52B11 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2507.05153
In this paper, we establish that the non-zero dihedral angles of hyperbolic Coxeter polyhedra of large dimensions are not arbitrarily small. Namely, for dimensions n≥ 32, they are of the form \fracπm with m≤ 6. Moreover, this property holds in all dimensions n≥ 7 for Coxeter polyhedra with mutually intersecting facets. Then, we develop a constructive procedure tailored to Coxeter polyhedra with prescribed dihedral angles, from which we derive the complete classification of ADEG-polyhedra, characterized by having no pair of disjoint facets and dihedral angles \fracπ2, \fracπ3 and \fracπ6, only. Besides some well-known simplices and pyramids, there are three exceptional polyhedra, one of which is a new polyhedron P⋆⊂ \mathbb H9 with 14 facets.