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Dwarf galaxies and their dark matter (DM) haloes have velocity curves of a different character than those in large galaxies. These velocity curves are modelled by a simple pseudo-isothermal model containing only two parameters, which do not give us insight into the physics of the DM halo.Aims. We seek to obtain some insight into the physical conditions in DM haloes of dwarf galaxies by using a simple physically based model of DM haloes. To treat the diversity of the dwarf galaxy velocity profiles in a unifying framework, we applied polytropic spheres characterised by the polytropic index n and the relativistic parameter sigma as a model of dwarf-galaxy DM haloes and matched the velocity of circular geodesics of the polytropes to the velocity curves observed in the dwarf galaxies from the LITTLE THINGS ensemble. We introduce three classes of the LITTLE THINGS dwarf galaxies in relation to the polytrope models due to the different character of the velocity profile. The first class corresponds to polytropes that have n<1 with linearly increasing velocity along the whole profile, the second class has 1 < n < 2 and the velocity profile becomes flat in the external region, the third class has n > 2, and the velocity profile reaches a maximum and demonstrates a decline in the external region. The sigma parameter has to be strongly non-relativistic (sigma < 10^(-8)) for all dwarf galaxy models; this parameter varies for the models of each class, but these variations have negligible influence on the character of the velocity profile.Conclusions. Our results indicate a possibility that at least two different kinds of DM are behind the composition of DM haloes. The matches of the observational velocity curves are of the same quality as those obtained by the pseudo-isothermal, core-like models of dwarf galaxy DM haloes.