  In the canonical picture of pulsars, radio emission arises from a narrow cone
centered on the star's magnetic axis but many basic details remain unclear. We
use high-quality polarization data taken with the Parkes radio telescope to
constrain the geometry and emission heights of pulsars showing interpulse
emission, and include the possibility that emission heights in the main and
interpulse may be different. We show that emission heights are low in the
centre of the beam, typically less than 3\% of the light cylinder radius. The
emission beams are under-filled in longitude, with an average profile width
only 60% of the maximal beam width and there is a strong preference for the
visible emission to be located on the trailing part of the beam. We show
substantial evidence that the emission heights are larger at the beam edges
than in the beam centre. There is some indication that a fan-like emission beam
explains the data better than conal structures. Finally, there is a strong
correlation between handedness of circular polarization in the main and
interpulse profiles which implies that the hand of circular polarization is
determined by the hemisphere of the visible emission.
