  A Coxeter group acts properly and cocompactly by isometries on the Davis
complex for the group; we call the quotient of the Davis complex under this
action the Davis orbicomplex for the group. We prove the set of finite covers
of the Davis orbicomplexes for the set of one-ended Coxeter groups is not
topologically rigid. We exhibit a quotient of a Davis complex by a one-ended
right-angled Coxeter group which has two finite covers that are homotopy
equivalent but not homeomorphic. We discuss consequences for the abstract
commensurability classification of Coxeter groups.
