Abstract: 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 istropy group data along the
faces.
We also discuss these results from the point of view of Riemannian
orbifolds.