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Long-slit echellograms of the high excitation planetary nebula NGC1501,reduced according to the methodology developed by Sabbadin et al. (2000a, b),allowed us to obtain the ``true'' distribution of the ionized gas in the eightnebular slices covered by the spectroscopic slit. A 3-D rendering procedure isdescribed and applied, which assembles the tomographic maps and rebuilds thespatial structure. The images of NGC 1501, as seen in 12 directions separatedby 15 deg, form a series of stereoscopic pairs giving surprising 3-D views inas many directions. The main nebula consists of an almost oblate ellipsoid ofmoderate ellipticity (a=44 arcsec, a/b=1.02, a/c=1.11), brighter in theequatorial belt, deformed by several bumps, and embedded in a quitehomogeneous, inwards extended cocoon. Some reliability tests are applied to therebuilt nebula; the radial matter profile, the small scale density fluctuationsand the 2-D (morphology) - 3-D (structure) correlation are presented andanalysed. The wide applications of the 3-D reconstruction to the morphology,physical conditions, ionization parameters and evolutionary status of expandingnebulae in general (planetary nebulae, nova and supernova remnants, shellsaround Population I Wolf-Rayet stars, nebulae ejected by symbiotic stars,bubbles surrounding early spectral type main sequence stars etc.) areintroduced.

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