  The band structure, density of states, and the Fermi surface of a recently
discovered superconductor, oxygen-deficient tungsten oxide WO$_{2.9}$ that is
equivalent to W$_{20}$O$_{58}$, studied within the density functional theory
(DFT) in the generalized gradient approximation (GGA). Here we show that
despite the extremely complicated structure containing 78 atoms in the unit
cell, the low-energy band structure is quite feasible. Fermi level is crossed
by no more than 10 bands per one spin projection (and even 9 bands per
pseudospin projection when the spin-orbit coupling is considered) originating
from the $d$-orbitals of tungsten atoms forming zigzag chains.
