3-D ionization structure (in stereoscopic view) of planetary nebulae: the case of NGC 1501

Long-slit echellograms of the high excitation planetary nebula NGC 1501, re duced according to the methodology developed by Sabbadin et al. (2000a,b),a llowed us to obtain the "true" distribution of the ionized gas in the eight nebular slices covered by the spectroscopic slit. A 3-D rendering procedur e is described and applied, which assembles the tomographic maps and rebuil ds the spatial structure. The images of NGC 1501, as seen in 12 directions separated by 15 degrees, form a series of stereoscopic pairs giving surpris ing 3-D views in as many directions. The main nebula consists of an almost ablate ellipsoid of moderate ellipticity (a similar or equal to 44 arcsec, a/b similar or equal to 1.02, a/c similar or equal to 1.11), brighter in th e equatorial belt, deformed by several bumps, and embedded in a quite homog eneous, inwards extended cocoon. Some reliability tests are applied to the rebuilt nebula: the radial matter profile, the small scale density fluctuat ions and the 2-D (morphology) = 3-D (structure) correlation are presented a nd analysed. The wide applications of the 3-D reconstruction to the morphol ogy, physical conditions, ionization parameters and evolutionary status of expanding nebulae in general (planetary nebulae, nova and supernova remnant s, shells around Population I Wolf-Rayet stars, nebulae ejected by symbioti c stars, bubbles surrounding early spectral type main sequence stars etc.) are introduced.