We report the analysis of near-infrared imaging, polarimetric and spectroscopic observations of the powerful radio galaxy 3C433, obtained with the HST and UKIRT telescopes. The high spatial resolution of HST allows us to study the near-nuclear regions of the galaxy (<1 kpc). In line with previous observations, we find that 3C433 has an unresolved core source that is detected in all near-IR bands, but dominates over the host galaxy emission at 2.05 um. Our analysis reveals: (1) the presence of a dust lane aligned close to perpendicular (PA$=70pm5degr$) to the inner radio jet axis (PA$=-12pm2degr$); (2) a steep slope to the near-IR SED ($alpha=5.8pm0.1$; F$_{ u}propto u^{-alpha}$); (3) an apparent lack of broad permitted emission lines at near-IR wavelengths, in particular the absence of a broad Pa$alpha$ emission line; and (4) high intrinsic polarization for the unresolved core nuclear source ($8.6pm1$ per cent), with an E-vector perpendicular (PA=$83.0pm 2.3degr$) to the inner radio jet. Using five independent techniques we determine an extinction to the compact core source in the range 3<A_V<67 mag. An analysis of the long wavelength SED rules out a synchrotron origin for the high near-IR polarization of the compact core source. Therefore, scattering and dichroic extinction are plausible polarizing mechanisms, although in both of these cases the broad permitted lines from the AGN are required to have a width >10^4 km/s (FWHM) to escape detection in our near-IR spectrum. Dichroic extinction is the most likely polarization mechanism because it is consistent with the various available extinction estimates. In this case, a highly ordered, coherent toroidal magnetic field must be present in the obscuring structure close to the nucleus.
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