Euclidean simplices generating discrete reflection groups

Let P be a convex polytope in the Euclidean space E-n. Consider the group G p generated by reflections in the facets of P. We say that P generates a reflection group) G p. 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) 173-2091. 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. (c) 2006 Elsevier Ltd. All rights reserved.