HST Planetary Camera narrow band emission-line and continuum images are used to study the nuclear region of NGC 4151 at the highest possible spatial resolution. The [O III] λ5007 image reveals a striking biconical structure with a projected opening angle of 75° ±10°, and whose apex coincides with the bright, unresolved central source. The projected axis is oriented along PA 60°/240° ± 5°, and is aligned with the extension of the nuclear VLBI radio source. Analysis of the geometry of the narrow-line region places our line of sight well outside the ionization cones, and yet we see nearly unobscured optical and near-UV continuum and broad lines. In addition, material with significantly different column densities is required to explain the numerous optical and UV absorption lines and the soft X-ray absorption. We conclude from these data that the simplest version of the obscuring torus unification model is inconsistent with the observations and some modifications are required. We discuss some alternative collimation mechanisms that are compatible with our observations.