Walls in Coxeter complexes (Q1319975)

The author addresses the problem of which walls in a Coxeter complex are themselves Coxeter complexes. In the case of finite complexes, a complete answer is given. More generally, a sufficient condition is given; it depends on the entries in the Coxeter matrix of the complex (basically, for the \(i\)-th wall, all entries \(m_{ij}\) are even).