|Sobolev Institute of Mathematics, Novosibirsk, Russia
Volume is a useful invariant of hyperbolic 3-manifolds which can be computed from a polyhedral decomposition. Due to Andreev’s theorem an acute-angled polyhedron in a hyperbolic 3-space is uniquely determined by 1-dimensional skeleton and dihedral angles. We consider a class of hyperbolic polyhedra with finite or ideal vertices and with all dihedral angles equal pi/2. The upper bounds for volumes of polyhedra from this class are obtained. As applications, we will give upper bounds for volumes of generalized hyperbolic polyhedra via number of edges and for volumes of hyperbolic knot complements via number of twists.