Bipartite Q-Polynomial Quotients of Antipodal Distance-Regular Graphs

Let Γ denote a bipartite Q-polynomial distance-regular graph with diameter D⩾4. We show that Γ is the quotient of an antipodal distance-regular graph if and only if one of the following holds. (i) Γ is a cycle of even length. (ii) Γ is the quotient of the 2D-cube.