Magnetic field measurements from the Ulysses space mission over the south polar regions of the sun showed that the structure and properties of the three-dimensional heliosphere were determined by the fast solar wind flow and magnetic fields from the large coronal holes in the polar regions of the sun. This conclusion applies at the current, minimum phase of the 11-year solar activity cycle. Unexpectedly, the radial component of the magnetic field was independent of latitude. The high-latitude magnetic field deviated significantly from the expected Parker geometry, probably because of large amplitude transverse fluctuations. Low-frequency fluctuations had a high level of variance. The rate of occurrence of discontinuities also increased significantly at high latitudes.