  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 eight
nebular slices covered by the spectroscopic slit. A 3-D rendering procedure is
described and applied, which assembles the tomographic maps and rebuilds the
spatial structure. The images of NGC 1501, as seen in 12 directions separated
by 15 deg, form a series of stereoscopic pairs giving surprising 3-D views in
as many directions. The main nebula consists of an almost oblate ellipsoid of
moderate ellipticity (a=44 arcsec, a/b=1.02, a/c=1.11), brighter in the
equatorial belt, deformed by several bumps, and embedded in a quite
homogeneous, inwards extended cocoon. Some reliability tests are applied to the
rebuilt nebula; the radial matter profile, the small scale density fluctuations
and the 2-D (morphology) - 3-D (structure) correlation are presented and
analysed. The wide applications of the 3-D reconstruction to the morphology,
physical conditions, ionization parameters and evolutionary status of expanding
nebulae in general (planetary nebulae, nova and supernova remnants, shells
around Population I Wolf-Rayet stars, nebulae ejected by symbiotic stars,
bubbles surrounding early spectral type main sequence stars etc.) are
introduced.
