  We present a method to measure the the oblateness parameter q of the dark
matter halos of gas rich galaxies that have extended HI disks. We have applied
our model to a sample of 20 nearby galaxies that are gas rich and close to
face-on, of which 6 are large disk galaxies, 8 have moderate stellar masses and
6 are low surface brightness (LSB) dwarf galaxies. We have used the stacked HI
velocity dispersion and HI surface densities to derive q in the outer disk
regions. Our most important result is that gas dominated galaxies (such as LSB
dwarfs) that have M(gas)/M(baryons)>0.5 have oblate halos (q<0.55), whereas
stellar dominated galaxies have a range of q values from 0.2 to 1.3. We also
find a significant positive correlation between q and stellar mass, which
indicates that galaxies with massive stellar disks have a higher probability of
having halos that are spherical or slightly prolate, whereas low mass galaxies
preferably have oblate halos. We briefly also discuss how the halo shape
affects the disks of galaxies, especially the oblate halos.
