  We investigate discrete groups $G$ of isometries of a complete connected
Riemannian manifold $M$ which are generated by reflections, in particular those
generated by disecting reflections. We show that these are Coxeter groups, and
that the the orbit space $M/G$ is isometric to a Weyl chamber $C$ which is a
Riemannian manifold with corners and certain angle conditions along
intersections of faces. We can also reconstruct the manifold and its action
from the Riemannian chamber and its equipment of isotropy group data along the
faces. We also discuss these results from the point of view of Riemannian
orbifolds.
