In the previous papers in this series, we have measured the stellar and hi content in a sample of edge-on galaxies. In the present paper, we perform a simultaneous rotation curve and vertical force field gradient decomposition for five of these edge-on galaxies. The rotation curve decomposition provides a measure of the radial dark matter potential, while the vertical force field gradient provide a measure of the vertical dark matter potential. We fit dark matter halo models to these potentials. Using our hi self-absorption results, we find that a typical dark matter halo has a less dense core ($0.094pm0.230$,M$_odot$/pc$^3$) compared to an optically thin hi model ($0.150pm0.124$,M$_odot$/pc$^3$). The HI self-absorption dark matter halo has a longer scale length $R_c$ of $1.42pm 3.48$,kpc, versus $1.10pm 1.81$,kpc for the optically thin HI model. The median halo shape is spherical, at $q=1.0pm0.6$ (self-absorbing hi), while it is prolate at $q=1.5pm0.6$ for the optically thin. Our best results were obtained for ESO,274-G001 and UGC,7321, for which we were able to measure the velocity dispersion in Paper III. These two galaxies have drastically different halo shapes, with one oblate and one strongly prolate. Overall, we find that the many assumptions required make this type of analysis susceptible to errors.
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