Two-sided bounds for the volume of right-angled hyperbolic polyhedra

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For a compact right-angled polyhedron R in H³ denote by vol (R) the volume and by vert (R) the number of vertices. Upper and lower bounds for vol (R) in terms of vert (R) were obtained in A09. Constructing a 2-parameter family of polyhedra, we show that the asymptotic upper bound 5 v₃ / 8, where v₃ is the volume of the ideal regular tetrahedron in H³, is a double limit point for ratios vol (R) / vert (R). Moreover, we improve the lower bound in the case vert (R) 56.