We present a method to measure the the oblateness parameter q of the dark matter halo 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 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.
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