Here, for W the Coxeter group Dₙ where n > 4, it is proved that the maximal rank of an abstract regular polytope for W is n - 1 if n is even and n if n is odd. Further it is shown that W has abstract regular polytopes of rank r for all r such that 3 r n - 1, if n is even, and 3 r n, if n is odd. The possible ranks of abstract regular polytopes for the exceptional finite irreducible Coxeter groups are also determined.
Chen et al. (Fri,) studied this question.