  For flexibility of an octahedron we find necessary metric conditions in terms
of edge lengths. These conditions yield a new description of Bricard's
octahedra, suitable for solving some problems in metric geometry of octahedra,
in particular, for searching the proof of I.\,Hh~Sabitov hypothesis that all
non-leading coefficients of the volume polynomial for an octahedron of third
type are zero.
