Euclidean simplices generating discrete reflection groups

Abstract: Let be a convex polytope in the Euclidean space . Consider the group generated by reflections in the facets of . We say that generates a reflection group . The spherical simplices generating simply-laced reflection groups were described by P.J. Cameron, J.J. Seidel and S.V. Tsaranov [Signed graphs, root lattices and Coxeter groups, J. Algebra 164 (1994) 173–209]. The simplices generating the remaining spherical reflection groups were listed in [A. Felikson, Spherical simplices generating discrete reflection groups, Sb. Math. 195 (3–4) (2004) 585–598, arXiv:math.MG/0212244]. In the present paper, we find all Euclidean simplices generating discrete reflection groups. [Copyright &y& Elsevier]