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We have made high time-resolution polarimetric observations of the 37.9\,ms relativistic binary pulsar B1534+12. Roughly 20\% of the main pulse emission is linearly polarized, and the position-angle swing within the pulse shows structure clearly inconsistent with purely dipolar emission. Our measurements were also sensitive to low-level off-pulse emission, allowing us to trace the variation in polarization angle, globally dipolar in nature, through a substantial fraction of the pulsar's rotation period. A preliminary rotating vector model fit to the position-angle swing results in an impact parameter (the angle between the magnetic axis of the pulsar and our line of sight) of $\beta = (3.5 \pm 1.5)^\circ$ and a magnetic alignment (the angle between the spin and magnetic axes of the pulsar) of $\alpha = (106 \pm 8)^\circ$. In addition to providing the geometry of the system and clues to the pulsar's emission mechanism, these measurements form a pulse polarization ``template'' against which future observations can be compared in order to constrain or detect the effects of relativistic precession of the pulsar's spin axis in its binary orbit.
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