Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-sided bounds for the volume of right-angled hyperbolic polyhedra   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
$\operatorname{vert} (R) \leqslant 56$.

11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th