  For a compact right-angled polyhedron $R$ in $\mathbb H^3$ denote by
$\operatorname{vol} (R)$ the volume and by $\operatorname{vert} (R)$ the number
of vertices. Upper and lower bounds for $\operatorname{vol} (R)$ in terms of
$\operatorname{vert} (R)$ were obtained in \cite{A09}. Constructing a
2-parameter family of polyhedra, we show that the asymptotic upper bound $5 v_3
/ 8$, where $v_3$ is the volume of the ideal regular tetrahedron in $\mathbb
H^3$, is a double limit point for ratios $\operatorname{vol} (R) /
\operatorname{vert} (R)$. Moreover, we improve the lower bound in the case
$\operatorname{vert} (R) \leqslant 56$.

Geometric Topology;Metric Geometry