  We determine the intrinsic axial ratio distribution of the 'gas' disks of
extremely faint M_B > -14.5 dwarf irregular galaxies. We start with the
measured (beam corrected) distribution of apparent axial ratios in the HI 21cm
images of dwarf irregular galaxies observed as part of the Faint Irregular
Galaxy GMRT Survey (FIGGS). Assuming that the disks can be approximated as
oblate spheroids, the intrinsic axial ratio distribution can be obtained from
the observed apparent axial ratio distribution. We use a couple of methods to
do this, and our final results are based on using Lucy's deconvolution
algorithm. This method is constrained to produce physically plausible
distributions, and also has the added advantage of allowing for observational
errors to be accounted for. While one might a priori expect that gas disks
would be thin (because collisions between gas clouds would cause them to
quickly settle down to a thin disk), we find that the HI disks of faint dwarf
irregulars are quite thick, with mean axial ratio <q> ~ 0.6. While this is
substantially larger than the typical value of ~ 0.2 for the 'stellar' disks of
large spiral galaxies, it is consistent with the much larger ratio of velocity
dispersion to rotational velocity (sigma/v_c) in dwarf galaxy HI disks as
compared to that in spiral galaxies. Our findings have implications for studies
of the mass distribution in and the Tully - Fisher relation for faint dwarf
irregular galaxies, where it is often assumed that the gas is in a thin disk.
