  In this paper we consider a class of right-angled polyhedra in
three-dimensional Lobachevsky space, all vertices of which lie on the absolute.
New upper bounds on volumes in terms the number of faces of the polyhedron are
obtained. Volumes of polyhedra with at most 23 faces are computed. It is shown
that the minimum volumes are realized on antiprisms and twisted antiprisms. The
first 248 values of volumes of ideal right-angled polyhedra are presented.
Moreover, the class of polyhedra with isolated triangles is introduces and
there are obtained combinatorial bounds on their existence as well as minimal
examples of such polyhedra are given.
