Metric characteristics of hyperbolic polygons and polyhedra

In this paper, we consider some properties of hyperbolic polyhedra, both common with Euclidean and specific. Asymptotic behavior of metric characteristics of polyhedra in the $n$-dimensional hyperbolic space is examined in the cases where parameters of the polyhedra change and the dimension of the space unboundedly increases; in particular, the radius of the inscribed sphere of a polyhedron is estimated and its asymptotic behavior is obtained. In connection with this, the problem of estimating the minimal number of faces of the described polyhedron in the $n$-dimensional hyperbolic space depending on the radius of the inscribed sphere is posed. We also consider some properties of hyperbolic polygons, both belonging to absolute geometry and only hyperbolic.