  The band structure, density of states, and the Fermi surface of a tungsten
oxide WO$_{2.9}$ with idealized crystal structure (ideal octahedra WO$_6$
creating a "square lattice") is obtained within the density functional theory
in the generalized gradient approximation. Because of the oxygen vacancies
ordering this system is equivalent to the compound W$_{20}$O$_{58}$
(Magn\'{e}li phase), which has 78 atoms in unit cell. We show that
5$d$-orbitals of tungsten atoms located immediately around the voids in the
zigzag chains of edge-sharing octahedra give the dominant contribution near the
Fermi level. These particular tungsten atoms are responsible of a low-energy
properties of the system.
