108 citations · 399 across the 43 of their papers we have counts for
13 papers · 1 filter
Arithmetic Polyhedra
Daniel Allcock, Pat Devlin, Anna Felikson +2
The Koebe-Andreev-Thurston theorem assigns a 3-dimensional hyperbolic reflection group to each combinatorial polyhedron. A natural question is: which of them are arithmetic? In 201…
Coxeter polytopes with a unique pair of non-intersecting facets
Anna Felikson, Pavel Tumarkin
We consider compact hyperbolic Coxeter polytopes whose Coxeter diagram contains a unique dotted edge. We prove that such a polytope in d-dimensional hyperbolic space has at most d+…
On hyperbolic Coxeter polytopes with mutually intersecting facets
Anna Felikson, Pavel Tumarkin
We prove that, apart from some well-known low-dimensional examples, any compact hyperbolic Coxeter polytope has a pair of disjoint facets. This is one of very few known general res…
On compact hyperbolic Coxeter d-polytopes with d+4 facets
Anna Felikson, Pavel Tumarkin
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 (19…
On the volume of a six-dimensional polytope
Anna Felikson, Pavel Tumarkin
This note is a comment to the paper by D.R.Heath-Brown and B.Z.Moroz (Math Proc. Camb. Phil. Soc. 125 (1999)). That paper concerns with the projective surface in $\mathbb{P}^{3…
Euclidean simplices generating discrete reflection groups
Anna Felikson, Pavel Tumarkin
Let be a convex polytope in the Euclidean space $\E^n$. Consider the group generated by reflections in the facets of . We say that {\it generates a reflection grou…